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| |
| HYDROLIGHT Version 5.1.0 (MAIN CODE) |
| Copyright (c) 2008 by Curtis D. Mobley |
| |
| This copy of HE5 is licensed solely to |
| Student Version for Maine 2011 Summer Class |
| |
| S/N Maine_500_31July2011 |
| |
| THIS PROGRAM IS EXPERIMENTAL AND IS LICENSED "AS IS" |
| WITHOUT REPRESENTATION OF WARRANTY OF ANY KIND, |
| EITHER EXPRESS OR IMPLIED. THE ENTIRE RISK AS TO |
| THE QUALITY AND PERFORMANCE OF HYDROLIGHT IS WITH |
| THE USER. HYDROLIGHT IS NOT FAULT TOLERANT. |
| |
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RUN TITLE: run5 (07/19/2011 13:43)
Run started on 07/19/2011 at 13:43:51.2
The radiance distribution is computed on the following (Theta,Phi,Depth,Wavelength) grid:
I Theta Mu J Phi K zeta z L Lambda
(deg) (deg) (m) (nm)
1 87.500 0.0436 1 0.00 1 0.000 1 355.00
2 80.000 0.1730 2 15.00 2 0.010 2 365.00
3 70.000 0.3407 3 30.00 3 5.000 3 375.00
4 60.000 0.4981 4 45.00 4 5.010 4 385.00
5 50.000 0.6403 5 60.00 5 10.000 5 395.00
6 40.000 0.7631 6 75.00 6 10.010 6 405.00
7 30.000 0.8627 7 90.00 7 415.00
8 20.000 0.9361 8 105.00 8 425.00
9 10.000 0.9811 9 120.00 9 435.00
10 0.000 0.9981 10 135.00 10 445.00
11 150.00 11 455.00
12 165.00 12 465.00
13 180.00 13 475.00
14 195.00 14 485.00
15 210.00 15 495.00
16 225.00 16 505.00
17 240.00 17 515.00
18 255.00 18 525.00
19 270.00 19 535.00
20 285.00 20 545.00
21 300.00 21 555.00
22 315.00 22 565.00
23 330.00 23 575.00
24 345.00 24 585.00
25 595.00
26 605.00
27 615.00
28 625.00
29 635.00
30 645.00
31 655.00
32 665.00
33 675.00
34 685.00
35 695.00
36 705.00
37 715.00
38 725.00
39 735.00
40 745.00
***** BEGIN IOP MODEL SPECIFICATIONS *****
The IOP routine "abcase1" is being used:
Absorption and scattering coefficients for case 1 water (Gordon and Morel bio-optical models) are used.
component 1 is pure water
component 2 is pigmented particles
component 3 is CDOM that covaries with chlorophyll
Pure water a and b values are obtained from the file:
..\data\H2OabDefaults.txt
(Linear interpolation is used to define values at all wavelengths)
The data file header records from ..\data\H2OabDefaults.txt are:
Default "pure water" absorption (a) and scattering (b) coefficients. Based on:
200-300 nm: R.C. Smith and K. Baker, 1981. Appl. Optics 20(2), 177-184.
191 records read
The phase function for component 1 comes from a file titled
pure sea water (Rayleigh-like phase function); standard quad partition; 7 Sept 98
Absorption for component 2 calculated from the Prieur-Sathyenranath-Morel model
141 records read
The chlorophyll concentration is constant with depth with a value of 2.30 (mg/m^3)
Scattering for component 2 calculated using a Power Law model
b = 0.3000 X^(0.6200) * (550./wavenm)^(1.0000)
The phase function for component 2 will be chosen to have a bb/b ratio of 0.0200
Chlorophyll concentrations at the requested output depths
depth Chl
(m) (mg/m^3)
0.000 2.300
5.000 2.300
10.000 2.300
***** END IOP MODEL SPECIFICATIONS *****
***** BEGIN INELASTIC SCATTER AND INTERNAL SOURCE SPECIFICATIONS *****
Chlorophyll fluorescence is included in this run
Chl fluorescent quantum efficiency set to 0.020
CDOM fluorescence is included in this run
Raman scattering is included in this run
Raman scattering cross-section set to 2.40E-04 m-1
at reference wavelength 488.0 nm
***** END INELASTIC SCATTER AND INTERNAL SOURCE SPECIFICATIONS *****
***** BEGIN ATMOSPHERIC MODEL SPECIFICATIONS *****
Normalized sky radiances are computed using sky model "HCNRAD" (Harrison and Coombes Normalized RADiances)
The cloud fraction is cloud = 0.0 (0 for a clear sky to 1 for a heavy overcast)
The sun is placed in quad Q(r,s) = Q( 7, 1) centered at (theta, phi) = (30.000, 0.000)
Diffuse and Direct Sky irradiances are computed using the "RADTRANX" (RADTRAN eXtended for 300-1000 nm) model
The RADTRAN clear-sky irradiances are adjusted for cloudiness by the model of Kasten and Czeplak
Parameter values used in the RADTRANX model:
Solar zenith angle = 30.0 degrees
Pressure = 29.9 in. mercury
Day of year = not set (mean earth-sun distance used)
Air mass type = 1.0
Relative Humidity = 80.0 %
Precipitable water = 2.5 cm
24-hr wind speed = 5.0 m/sec
Current wind speed = 5.0 m/sec
Visibility = 15.0 km
Total ozone = 300.0 Dobson units
Irradiances are computed just above the sea surface
Aerosol optical thickness at 550 nm = 0.261
***** END ATMOSPHERIC MODEL SPECIFICATIONS *****
***** BEGIN AIR-WATER SURFACE SPECIFICATIONS *****
The air-water surface is for a wind speed of 5.0 m/s
Index of refraction is constant for all wavelengths with the value: 1.340
***** END AIR-WATER SURFACE SPECIFICATIONS *****
***** BEGIN BOTTOM BOUNDARY SPECIFICATIONS *****
The bottom boundary is an infinitely deep, homogeneous water body below depth 10.00 m
The actual depth at which the infinitely deep bottom boundary condition will be applied
will be determined dynamically from the IOPs to insure a good solution at the
requested output depths
***** END BOTTOM BOUNDARY SPECIFICATIONS *****
Initialization of Hydrolight Completed in 0.2 sec.
* * * * * Output for wavelength band 1 (350.0 to 360.0 nm; nominal wavelength = 355.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 355.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 350.0 nm to 360.0 nm:
Ed(diffuse) = 2.986E-01 Ed(direct) = 3.214E-01 Ed(total) = 6.200E-01
Absorption Coefficients of Individual Components at 355.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0176 0.0582 0.0678 0.1435
3 4.676 5.000 0.0176 0.0582 0.0678 0.1435
5 9.352 10.000 0.0176 0.0582 0.0678 0.1435
Scattering Coefficients of Individual Components at 355.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0127 0.7790 0.0000 0.7917
3 4.676 5.000 0.0127 0.7790 0.0000 0.7917
5 9.352 10.000 0.0127 0.7790 0.0000 0.7917
Backscattering Coefficients of Individual Components at 355.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00634 0.01558 0.00000 0.02192
3 4.676 5.000 0.00634 0.01558 0.00000 0.02192
5 9.352 10.000 0.00634 0.01558 0.00000 0.02192
Summary of Inherent Optical Properties at 355.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1435 0.7917 0.9352 0.8465 0.02192 0.02769
3 4.676 5.000 0.1435 0.7917 0.9352 0.8465 0.02192 0.02769
5 9.352 10.000 0.1435 0.7917 0.9352 0.8465 0.02192 0.02769
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4671E-01
8 20.00 8.1837E-01
7 30.00 6.5010E-01
6 40.00 4.8197E-01
5 50.00 3.3984E-01
4 60.00 2.3272E-01
3 70.00 1.5806E-01
2 80.00 1.0883E-01
1 87.50 8.3197E-02
1 92.50 6.9211E-02
2 100.00 5.4892E-02
3 110.00 4.2069E-02
4 120.00 3.3660E-02
5 130.00 2.8202E-02
6 140.00 2.4666E-02
7 150.00 2.2404E-02
8 160.00 2.1015E-02
9 170.00 2.0264E-02
10 180.00 1.9997E-02
Asymptotic AOP values are
MUu(inf) = 0.3917
MUd(inf) = 0.6989
MU(inf) = 0.5849
R(inf) = 0.0654
Lu(inf)/Ed(inf) = 0.014045 (1/sr)
k(inf) = 0.2454 (1/m)
absorp(check) = 0.1435 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 355.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.1777E-01 9.7286E-01 1.0906E+00 4.0257E-02 6.2002E-01 0.3418 0.6373 0.5316 6.4929E-02
1 0.00 0.00 7.9158E-02 7.3813E-01 8.1729E-01 3.4018E-02 6.1377E-01 0.4297 0.8315 0.7094 5.5424E-02
3 4.68 5.00 3.1921E-02 2.7900E-01 3.1092E-01 1.2777E-02 2.0422E-01 0.4003 0.7320 0.6157 6.2566E-02
5 9.35 10.00 1.0175E-02 8.7733E-02 9.7909E-02 4.0138E-03 6.2263E-02 0.3945 0.7097 0.5949 6.4465E-02
K-functions (units of 1/meter) at 355.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.12115 0.15186 0.14889 0.14737 0.19936 0.20241 0.18902
5.000 5.010 5.005 0.21696 0.22177 0.22128 0.22214 0.23246 0.23314 0.23017
10.000 10.010 10.005 0.23639 0.23780 0.23765 0.23790 0.24107 0.24128 0.24035
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 355.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 8.05686E-02 4.48706E-03 3.68807E-03 8.17513E-03 7.23692E-03 0.045776
9 1 10.0 0.0 180.0 4.97141E-02 4.57687E-03 1.47713E-03 6.05400E-03 7.38176E-03 0.029712
9 4 10.0 45.0 135.0 5.46224E-02 4.55241E-03 1.67395E-03 6.22636E-03 7.34233E-03 0.030646
9 7 10.0 90.0 90.0 7.37994E-02 4.53097E-03 2.89959E-03 7.43056E-03 7.30775E-03 0.039290
8 1 20.0 0.0 180.0 3.90498E-02 4.64026E-03 9.37902E-04 5.57816E-03 7.48401E-03 0.024018
8 4 20.0 45.0 135.0 4.34729E-02 4.58548E-03 1.08299E-03 5.66848E-03 7.39567E-03 0.024912
8 7 20.0 90.0 90.0 6.39248E-02 4.56159E-03 1.99770E-03 6.55929E-03 7.35714E-03 0.031251
7 1 30.0 0.0 180.0 3.38583E-02 4.73053E-03 8.15058E-04 5.54559E-03 7.62960E-03 0.024073
7 4 30.0 45.0 135.0 3.75263E-02 4.71196E-03 9.13617E-04 5.62558E-03 7.59966E-03 0.024346
7 7 30.0 90.0 90.0 5.48121E-02 4.65974E-03 1.47534E-03 6.13508E-03 7.51542E-03 0.026916
6 1 40.0 0.0 180.0 3.21379E-02 4.81168E-03 9.06244E-04 5.71792E-03 7.76048E-03 0.028199
6 4 40.0 45.0 135.0 3.51411E-02 4.78351E-03 9.82865E-04 5.76637E-03 7.71504E-03 0.027969
6 7 40.0 90.0 90.0 4.93375E-02 4.73513E-03 1.41719E-03 6.15232E-03 7.63702E-03 0.028724
5 1 50.0 0.0 180.0 3.36955E-02 4.91467E-03 1.43154E-03 6.34622E-03 7.92660E-03 0.042485
5 4 50.0 45.0 135.0 3.59071E-02 4.85825E-03 1.49141E-03 6.34965E-03 7.83559E-03 0.041535
5 7 50.0 90.0 90.0 4.77295E-02 4.81954E-03 1.92809E-03 6.74762E-03 7.77316E-03 0.040396
4 1 60.0 0.0 180.0 3.99971E-02 4.88375E-03 3.33482E-03 8.21857E-03 7.87673E-03 0.083377
4 4 60.0 45.0 135.0 4.09023E-02 4.81974E-03 3.29308E-03 8.11281E-03 7.77348E-03 0.080511
4 7 60.0 90.0 90.0 5.05090E-02 4.84412E-03 3.84556E-03 8.68968E-03 7.81280E-03 0.076136
3 1 70.0 0.0 180.0 5.54963E-02 4.56872E-03 9.21166E-03 1.37804E-02 7.36863E-03 0.165987
3 4 70.0 45.0 135.0 5.39342E-02 4.55628E-03 8.86333E-03 1.34196E-02 7.34857E-03 0.164336
3 7 70.0 90.0 90.0 6.02972E-02 4.58462E-03 9.63845E-03 1.42231E-02 7.39427E-03 0.159849
2 1 80.0 0.0 180.0 9.42890E-02 3.94004E-03 2.28974E-02 2.68375E-02 6.35466E-03 0.242843
2 4 80.0 45.0 135.0 8.73097E-02 3.91868E-03 2.21466E-02 2.60653E-02 6.32021E-03 0.253655
2 7 80.0 90.0 90.0 8.67430E-02 3.94756E-03 2.31935E-02 2.71411E-02 6.36679E-03 0.267382
1 1 87.5 0.0 180.0 1.52448E-01 3.19076E-03 4.03828E-02 4.35736E-02 5.14619E-03 0.264896
1 4 87.5 45.0 135.0 1.37261E-01 3.02031E-03 4.01335E-02 4.31538E-02 4.87129E-03 0.292389
1 7 87.5 90.0 90.0 1.24877E-01 3.36877E-03 4.10740E-02 4.44428E-02 5.43329E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 355.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 8.175E-03 8.057E-02 9.801E-02 8.466E-02 1.265E-01 1.319E-02 4.924E+00 4.487E-03 7.237E-03
1 0.00 0.00 8.323E-03 1.500E-01 1.636E-02 1.841E-02 2.371E-02 1.356E-02 4.087E+00
3 4.68 5.00 2.839E-03 1.229E-01 7.536E-03 9.157E-03 1.283E-02 1.390E-02 4.500E+00
5 9.35 10.00 8.715E-04 4.337E-02 2.663E-03 3.110E-03 3.933E-03 1.400E-02 4.606E+00
Waveband 1 of 40 completed in 5.3 sec.
* * * * * Output for wavelength band 2 (360.0 to 370.0 nm; nominal wavelength = 365.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 365.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 360.0 nm to 370.0 nm:
Ed(diffuse) = 3.273E-01 Ed(direct) = 3.929E-01 Ed(total) = 7.202E-01
Absorption Coefficients of Individual Components at 365.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0132 0.0598 0.0589 0.1319
3 4.504 5.000 0.0132 0.0598 0.0589 0.1319
5 9.008 10.000 0.0132 0.0598 0.0589 0.1319
Scattering Coefficients of Individual Components at 365.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0113 0.7576 0.0000 0.7689
3 4.504 5.000 0.0113 0.7576 0.0000 0.7689
5 9.008 10.000 0.0113 0.7576 0.0000 0.7689
Backscattering Coefficients of Individual Components at 365.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00563 0.01515 0.00000 0.02078
3 4.504 5.000 0.00563 0.01515 0.00000 0.02078
5 9.008 10.000 0.00563 0.01515 0.00000 0.02078
Summary of Inherent Optical Properties at 365.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1319 0.7689 0.9008 0.8536 0.02078 0.02702
3 4.504 5.000 0.1319 0.7689 0.9008 0.8536 0.02078 0.02702
5 9.008 10.000 0.1319 0.7689 0.9008 0.8536 0.02078 0.02702
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4844E-01
8 20.00 8.2379E-01
7 30.00 6.5915E-01
6 40.00 4.9303E-01
5 50.00 3.5095E-01
4 60.00 2.4253E-01
3 70.00 1.6604E-01
2 80.00 1.1505E-01
1 87.50 8.8251E-02
1 92.50 7.3526E-02
2 100.00 5.8395E-02
3 110.00 4.4776E-02
4 120.00 3.5794E-02
5 130.00 2.9937E-02
6 140.00 2.6127E-02
7 150.00 2.3682E-02
8 160.00 2.2177E-02
9 170.00 2.1360E-02
10 180.00 2.1071E-02
Asymptotic AOP values are
MUu(inf) = 0.3912
MUd(inf) = 0.6947
MU(inf) = 0.5775
R(inf) = 0.0681
Lu(inf)/Ed(inf) = 0.014522 (1/sr)
k(inf) = 0.2284 (1/m)
absorp(check) = 0.1319 = k(inf)*MU(inf)
The CDOM absorption at each wavelength is constant with depth with a value of 0.00 (1/m)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 365.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.3334E-01 1.1135E+00 1.2468E+00 4.6640E-02 7.2024E-01 0.3498 0.6468 0.5403 6.4755E-02
1 0.00 0.00 9.5160E-02 8.5882E-01 9.5398E-01 4.0941E-02 7.1453E-01 0.4302 0.8320 0.7061 5.7298E-02
3 4.50 5.00 4.1883E-02 3.5408E-01 3.9596E-01 1.6782E-02 2.5896E-01 0.4007 0.7314 0.6116 6.4806E-02
5 9.01 10.00 1.4631E-02 1.2187E-01 1.3650E-01 5.7703E-03 8.6190E-02 0.3944 0.7072 0.5891 6.6949E-02
K-functions (units of 1/meter) at 365.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.10916 0.13886 0.13590 0.13348 0.18377 0.18682 0.17346
5.000 5.010 5.005 0.19839 0.20352 0.20297 0.20389 0.21488 0.21564 0.21239
10.000 10.010 10.005 0.21839 0.21996 0.21979 0.22007 0.22361 0.22386 0.22278
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 365.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 8.83253E-02 5.38890E-03 4.24954E-03 9.63844E-03 7.48204E-03 0.048112
9 1 10.0 0.0 180.0 5.45003E-02 5.49257E-03 1.64705E-03 7.13962E-03 7.62598E-03 0.030221
9 4 10.0 45.0 135.0 5.98811E-02 5.46468E-03 1.87076E-03 7.33544E-03 7.58726E-03 0.031241
9 7 10.0 90.0 90.0 8.09044E-02 5.44260E-03 3.30645E-03 8.74905E-03 7.55660E-03 0.040869
8 1 20.0 0.0 180.0 4.28092E-02 5.56726E-03 1.02960E-03 6.59685E-03 7.72967E-03 0.024051
8 4 20.0 45.0 135.0 4.76582E-02 5.50393E-03 1.19088E-03 6.69481E-03 7.64175E-03 0.024988
8 7 20.0 90.0 90.0 7.00791E-02 5.48133E-03 2.23859E-03 7.71992E-03 7.61037E-03 0.031944
7 1 30.0 0.0 180.0 3.71179E-02 5.67485E-03 8.93525E-04 6.56837E-03 7.87905E-03 0.024073
7 4 30.0 45.0 135.0 4.11402E-02 5.65592E-03 1.00175E-03 6.65767E-03 7.85277E-03 0.024350
7 7 30.0 90.0 90.0 6.00826E-02 5.60176E-03 1.62693E-03 7.22869E-03 7.77757E-03 0.027078
6 1 40.0 0.0 180.0 3.52319E-02 5.77227E-03 9.93490E-04 6.76576E-03 8.01432E-03 0.028199
6 4 40.0 45.0 135.0 3.85242E-02 5.74291E-03 1.07749E-03 6.82040E-03 7.97356E-03 0.027969
6 7 40.0 90.0 90.0 5.40874E-02 5.69637E-03 1.55425E-03 7.25062E-03 7.90894E-03 0.028736
5 1 50.0 0.0 180.0 3.69395E-02 5.89616E-03 1.56936E-03 7.46552E-03 8.18632E-03 0.042485
5 4 50.0 45.0 135.0 3.93640E-02 5.83374E-03 1.63499E-03 7.46873E-03 8.09966E-03 0.041535
5 7 50.0 90.0 90.0 5.23245E-02 5.80118E-03 2.11371E-03 7.91489E-03 8.05446E-03 0.040396
4 1 60.0 0.0 180.0 4.38478E-02 5.85930E-03 3.65587E-03 9.51517E-03 8.13515E-03 0.083377
4 4 60.0 45.0 135.0 4.48401E-02 5.78845E-03 3.61011E-03 9.39856E-03 8.03678E-03 0.080511
4 7 60.0 90.0 90.0 5.53716E-02 5.83367E-03 4.21579E-03 1.00495E-02 8.09957E-03 0.076136
3 1 70.0 0.0 180.0 6.08391E-02 5.48111E-03 1.00985E-02 1.55796E-02 7.61006E-03 0.165987
3 4 70.0 45.0 135.0 5.91267E-02 5.47238E-03 9.71663E-03 1.51890E-02 7.59794E-03 0.164336
3 7 70.0 90.0 90.0 6.61022E-02 5.52310E-03 1.05664E-02 1.60895E-02 7.66837E-03 0.159849
2 1 80.0 0.0 180.0 1.03367E-01 4.72634E-03 2.51019E-02 2.98282E-02 6.56213E-03 0.242843
2 4 80.0 45.0 135.0 9.57154E-02 4.70644E-03 2.42787E-02 2.89852E-02 6.53451E-03 0.253655
2 7 80.0 90.0 90.0 9.50940E-02 4.75658E-03 2.54264E-02 3.01830E-02 6.60412E-03 0.267382
1 1 87.5 0.0 180.0 1.67125E-01 3.82660E-03 4.42706E-02 4.80972E-02 5.31292E-03 0.264896
1 4 87.5 45.0 135.0 1.50475E-01 3.62685E-03 4.39973E-02 4.76242E-02 5.03558E-03 0.292389
1 7 87.5 90.0 90.0 1.36899E-01 4.05912E-03 4.50284E-02 4.90875E-02 5.63575E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 365.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 9.638E-03 8.833E-02 1.076E-01 9.299E-02 1.389E-01 1.338E-02 4.839E+00 5.389E-03 7.482E-03
1 0.00 0.00 9.996E-03 1.645E-01 1.950E-02 2.204E-02 2.853E-02 1.399E-02 4.096E+00
3 4.50 5.00 3.718E-03 1.527E-01 9.740E-03 1.191E-02 1.685E-02 1.436E-02 4.514E+00
5 9.01 10.00 1.247E-03 5.916E-02 3.779E-03 4.447E-03 5.689E-03 1.446E-02 4.628E+00
Waveband 2 of 40 completed in 4.8 sec.
* * * * * Output for wavelength band 3 (370.0 to 380.0 nm; nominal wavelength = 375.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 375.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 370.0 nm to 380.0 nm:
Ed(diffuse) = 3.130E-01 Ed(direct) = 4.113E-01 Ed(total) = 7.243E-01
Absorption Coefficients of Individual Components at 375.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0115 0.0619 0.0512 0.1246
3 4.360 5.000 0.0115 0.0619 0.0512 0.1246
5 8.720 10.000 0.0115 0.0619 0.0512 0.1246
Scattering Coefficients of Individual Components at 375.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0100 0.7374 0.0000 0.7475
3 4.360 5.000 0.0100 0.7374 0.0000 0.7475
5 8.720 10.000 0.0100 0.7374 0.0000 0.7475
Backscattering Coefficients of Individual Components at 375.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00501 0.01475 0.00000 0.01975
3 4.360 5.000 0.00501 0.01475 0.00000 0.01975
5 8.720 10.000 0.00501 0.01475 0.00000 0.01975
Summary of Inherent Optical Properties at 375.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1246 0.7475 0.8720 0.8571 0.01975 0.02643
3 4.360 5.000 0.1246 0.7475 0.8720 0.8571 0.01975 0.02643
5 8.720 10.000 0.1246 0.7475 0.8720 0.8571 0.01975 0.02643
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4931E-01
8 20.00 8.2651E-01
7 30.00 6.6372E-01
6 40.00 4.9862E-01
5 50.00 3.5656E-01
4 60.00 2.4748E-01
3 70.00 1.7004E-01
2 80.00 1.1813E-01
1 87.50 9.0718E-02
1 92.50 7.5604E-02
2 100.00 6.0046E-02
3 110.00 4.6010E-02
4 120.00 3.6729E-02
5 130.00 3.0663E-02
6 140.00 2.6709E-02
7 150.00 2.4168E-02
8 160.00 2.2602E-02
9 170.00 2.1752E-02
10 180.00 2.1450E-02
Asymptotic AOP values are
MUu(inf) = 0.3905
MUd(inf) = 0.6926
MU(inf) = 0.5744
R(inf) = 0.0691
Lu(inf)/Ed(inf) = 0.014646 (1/sr)
k(inf) = 0.2169 (1/m)
absorp(check) = 0.1246 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 375.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.3057E-01 1.1060E+00 1.2366E+00 4.6461E-02 7.2429E-01 0.3558 0.6549 0.5482 6.4146E-02
1 0.00 0.00 9.6677E-02 8.6344E-01 9.6012E-01 4.1600E-02 7.1942E-01 0.4303 0.8332 0.7060 5.7825E-02
3 4.36 5.00 4.5115E-02 3.7700E-01 4.2212E-01 1.8078E-02 2.7605E-01 0.4007 0.7322 0.6111 6.5489E-02
5 8.72 10.00 1.6770E-02 1.3794E-01 1.5471E-01 6.6085E-03 9.7477E-02 0.3941 0.7067 0.5873 6.7795E-02
K-functions (units of 1/meter) at 375.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.10164 0.13033 0.12744 0.12437 0.17348 0.17650 0.16318
5.000 5.010 5.005 0.18580 0.19122 0.19064 0.19154 0.20305 0.20385 0.20040
10.000 10.010 10.005 0.20616 0.20787 0.20769 0.20798 0.21182 0.21210 0.21091
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 375.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 8.44577E-02 5.46244E-03 4.24468E-03 9.70712E-03 7.54177E-03 0.050258
9 1 10.0 0.0 180.0 5.21139E-02 5.56437E-03 1.59925E-03 7.16362E-03 7.68250E-03 0.030688
9 4 10.0 45.0 135.0 5.72591E-02 5.53719E-03 1.82014E-03 7.35733E-03 7.64497E-03 0.031788
9 7 10.0 90.0 90.0 7.73618E-02 5.51758E-03 3.27379E-03 8.79137E-03 7.61789E-03 0.042318
8 1 20.0 0.0 180.0 4.09347E-02 5.63897E-03 9.85746E-04 6.62471E-03 7.78549E-03 0.024081
8 4 20.0 45.0 135.0 4.55714E-02 5.57659E-03 1.14192E-03 6.71852E-03 7.69937E-03 0.025058
8 7 20.0 90.0 90.0 6.70105E-02 5.55830E-03 2.18321E-03 7.74151E-03 7.67412E-03 0.032580
7 1 30.0 0.0 180.0 3.54926E-02 5.74740E-03 8.54399E-04 6.60180E-03 7.93520E-03 0.024073
7 4 30.0 45.0 135.0 3.93397E-02 5.73069E-03 9.58037E-04 6.68873E-03 7.91213E-03 0.024353
7 7 30.0 90.0 90.0 5.74460E-02 5.68233E-03 1.56408E-03 7.24641E-03 7.84536E-03 0.027227
6 1 40.0 0.0 180.0 3.36892E-02 5.84609E-03 9.49987E-04 6.79608E-03 8.07146E-03 0.028199
6 4 40.0 45.0 135.0 3.68373E-02 5.81965E-03 1.03031E-03 6.84996E-03 8.03496E-03 0.027969
6 7 40.0 90.0 90.0 5.17190E-02 5.78145E-03 1.48674E-03 7.26818E-03 7.98221E-03 0.028746
5 1 50.0 0.0 180.0 3.53220E-02 5.97181E-03 1.50064E-03 7.47246E-03 8.24504E-03 0.042485
5 4 50.0 45.0 135.0 3.76404E-02 5.91257E-03 1.56340E-03 7.47597E-03 8.16325E-03 0.041535
5 7 50.0 90.0 90.0 5.00334E-02 5.89059E-03 2.02116E-03 7.91175E-03 8.13290E-03 0.040396
4 1 60.0 0.0 180.0 4.19278E-02 5.93472E-03 3.49579E-03 9.43051E-03 8.19382E-03 0.083377
4 4 60.0 45.0 135.0 4.28767E-02 5.86749E-03 3.45203E-03 9.31952E-03 8.10100E-03 0.080511
4 7 60.0 90.0 90.0 5.29471E-02 5.92619E-03 4.03119E-03 9.95738E-03 8.18204E-03 0.076136
3 1 70.0 0.0 180.0 5.81751E-02 5.55164E-03 9.65632E-03 1.52080E-02 7.66492E-03 0.165987
3 4 70.0 45.0 135.0 5.65377E-02 5.54761E-03 9.29117E-03 1.48388E-02 7.65936E-03 0.164336
3 7 70.0 90.0 90.0 6.32078E-02 5.61282E-03 1.01037E-02 1.57165E-02 7.74940E-03 0.159849
2 1 80.0 0.0 180.0 9.88404E-02 4.78695E-03 2.40027E-02 2.87897E-02 6.60915E-03 0.242843
2 4 80.0 45.0 135.0 9.15242E-02 4.77133E-03 2.32156E-02 2.79869E-02 6.58759E-03 0.253655
2 7 80.0 90.0 90.0 9.09301E-02 4.83518E-03 2.43131E-02 2.91482E-02 6.67573E-03 0.267382
1 1 87.5 0.0 180.0 1.59807E-01 3.87521E-03 4.23321E-02 4.62073E-02 5.35035E-03 0.264896
1 4 87.5 45.0 135.0 1.43886E-01 3.67668E-03 4.20708E-02 4.57475E-02 5.07625E-03 0.292389
1 7 87.5 90.0 90.0 1.30905E-01 4.12682E-03 4.30567E-02 4.71835E-02 5.69773E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 375.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 9.707E-03 8.446E-02 1.030E-01 8.904E-02 1.329E-01 1.340E-02 4.786E+00 5.462E-03 7.542E-03
1 0.00 0.00 1.013E-02 1.573E-01 1.968E-02 2.234E-02 2.908E-02 1.408E-02 4.106E+00
3 4.36 5.00 3.993E-03 1.603E-01 1.037E-02 1.276E-02 1.823E-02 1.447E-02 4.527E+00
5 8.72 10.00 1.421E-03 6.634E-02 4.289E-03 5.084E-03 6.579E-03 1.458E-02 4.649E+00
Waveband 3 of 40 completed in 4.6 sec.
* * * * * Output for wavelength band 4 (380.0 to 390.0 nm; nominal wavelength = 385.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 385.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 380.0 nm to 390.0 nm:
Ed(diffuse) = 2.649E-01 Ed(direct) = 3.776E-01 Ed(total) = 6.425E-01
Absorption Coefficients of Individual Components at 385.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0094 0.0650 0.0445 0.1189
3 4.231 5.000 0.0094 0.0650 0.0445 0.1189
5 8.461 10.000 0.0094 0.0650 0.0445 0.1189
Scattering Coefficients of Individual Components at 385.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0089 0.7183 0.0000 0.7272
3 4.231 5.000 0.0089 0.7183 0.0000 0.7272
5 8.461 10.000 0.0089 0.7183 0.0000 0.7272
Backscattering Coefficients of Individual Components at 385.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00447 0.01437 0.00000 0.01883
3 4.231 5.000 0.00447 0.01437 0.00000 0.01883
5 8.461 10.000 0.00447 0.01437 0.00000 0.01883
Summary of Inherent Optical Properties at 385.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1189 0.7272 0.8461 0.8595 0.01883 0.02590
3 4.231 5.000 0.1189 0.7272 0.8461 0.8595 0.01883 0.02590
5 8.461 10.000 0.1189 0.7272 0.8461 0.8595 0.01883 0.02590
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4988E-01
8 20.00 8.2831E-01
7 30.00 6.6674E-01
6 40.00 5.0231E-01
5 50.00 3.6027E-01
4 60.00 2.5073E-01
3 70.00 1.7265E-01
2 80.00 1.2011E-01
1 87.50 9.2284E-02
1 92.50 7.6903E-02
2 100.00 6.1056E-02
3 110.00 4.6737E-02
4 120.00 3.7253E-02
5 130.00 3.1046E-02
6 140.00 2.6997E-02
7 150.00 2.4391E-02
8 160.00 2.2784E-02
9 170.00 2.1911E-02
10 180.00 2.1601E-02
Asymptotic AOP values are
MUu(inf) = 0.3898
MUd(inf) = 0.6914
MU(inf) = 0.5726
R(inf) = 0.0696
Lu(inf)/Ed(inf) = 0.014659 (1/sr)
k(inf) = 0.2077 (1/m)
absorp(check) = 0.1189 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 385.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.1286E-01 9.7025E-01 1.0831E+00 4.0762E-02 6.4248E-01 0.3612 0.6622 0.5555 6.3445E-02
1 0.00 0.00 8.6017E-02 7.6535E-01 8.5136E-01 3.7006E-02 6.3872E-01 0.4302 0.8345 0.7068 5.7939E-02
3 4.23 5.00 4.2065E-02 3.4982E-01 3.9188E-01 1.6853E-02 2.5659E-01 0.4006 0.7335 0.6118 6.5680E-02
5 8.46 10.00 1.6447E-02 1.3449E-01 1.5094E-01 6.4748E-03 9.5057E-02 0.3937 0.7068 0.5869 6.8115E-02
K-functions (units of 1/meter) at 385.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.09507 0.12353 0.12066 0.11712 0.16526 0.16823 0.15499
5.000 5.010 5.005 0.17561 0.18130 0.18069 0.18154 0.19348 0.19432 0.19071
10.000 10.010 10.005 0.19621 0.19806 0.19786 0.19814 0.20226 0.20257 0.20129
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 385.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 7.14888E-02 4.84772E-03 3.74265E-03 8.59037E-03 7.54530E-03 0.052353
9 1 10.0 0.0 180.0 4.41115E-02 4.93574E-03 1.37379E-03 6.30952E-03 7.68230E-03 0.031143
9 4 10.0 45.0 135.0 4.84666E-02 4.91245E-03 1.56652E-03 6.47897E-03 7.64605E-03 0.032322
9 7 10.0 90.0 90.0 6.54825E-02 4.89717E-03 2.86374E-03 7.76092E-03 7.62228E-03 0.043733
8 1 20.0 0.0 180.0 3.46490E-02 5.00107E-03 8.35396E-04 5.83647E-03 7.78399E-03 0.024110
8 4 20.0 45.0 135.0 3.85737E-02 4.94710E-03 9.69209E-04 5.91631E-03 7.69999E-03 0.025126
8 7 20.0 90.0 90.0 5.67207E-02 4.93443E-03 1.88321E-03 6.81764E-03 7.68026E-03 0.033201
7 1 30.0 0.0 180.0 3.00425E-02 5.09679E-03 7.23201E-04 5.81999E-03 7.93297E-03 0.024073
7 4 30.0 45.0 135.0 3.32996E-02 5.08385E-03 8.11052E-04 5.89491E-03 7.91284E-03 0.024356
7 7 30.0 90.0 90.0 4.86201E-02 5.04599E-03 1.33084E-03 6.37683E-03 7.85390E-03 0.027372
6 1 40.0 0.0 180.0 2.85161E-02 5.18428E-03 8.04110E-04 5.98839E-03 8.06915E-03 0.028199
6 4 40.0 45.0 135.0 3.11808E-02 5.16336E-03 8.72100E-04 6.03546E-03 8.03658E-03 0.027969
6 7 40.0 90.0 90.0 4.37773E-02 5.13643E-03 1.25889E-03 6.39532E-03 7.99467E-03 0.028757
5 1 50.0 0.0 180.0 2.98981E-02 5.29594E-03 1.27021E-03 6.56616E-03 8.24295E-03 0.042485
5 4 50.0 45.0 135.0 3.18605E-02 5.24647E-03 1.32333E-03 6.56980E-03 8.16594E-03 0.041535
5 7 50.0 90.0 90.0 4.23505E-02 5.23560E-03 1.71080E-03 6.94640E-03 8.14903E-03 0.040396
4 1 60.0 0.0 180.0 3.54895E-02 5.26321E-03 2.95900E-03 8.22221E-03 8.19200E-03 0.083377
4 4 60.0 45.0 135.0 3.62927E-02 5.20710E-03 2.92196E-03 8.12906E-03 8.10467E-03 0.080511
4 7 60.0 90.0 90.0 4.48168E-02 5.26934E-03 3.41218E-03 8.68152E-03 8.20153E-03 0.076136
3 1 70.0 0.0 180.0 4.92420E-02 4.92350E-03 8.17354E-03 1.30970E-02 7.66325E-03 0.165987
3 4 70.0 45.0 135.0 4.78560E-02 4.92368E-03 7.86446E-03 1.27881E-02 7.66354E-03 0.164336
3 7 70.0 90.0 90.0 5.35019E-02 4.99254E-03 8.55223E-03 1.35448E-02 7.77070E-03 0.159849
2 1 80.0 0.0 180.0 8.36629E-02 4.24522E-03 2.03170E-02 2.45622E-02 6.60754E-03 0.242843
2 4 80.0 45.0 135.0 7.74702E-02 4.23493E-03 1.96507E-02 2.38857E-02 6.59152E-03 0.253655
2 7 80.0 90.0 90.0 7.69673E-02 4.30203E-03 2.05797E-02 2.48817E-02 6.69596E-03 0.267382
1 1 87.5 0.0 180.0 1.35268E-01 3.43638E-03 3.58318E-02 3.92682E-02 5.34861E-03 0.264896
1 4 87.5 45.0 135.0 1.21792E-01 3.26330E-03 3.56106E-02 3.88739E-02 5.07922E-03 0.292389
1 7 87.5 90.0 90.0 1.10804E-01 3.67246E-03 3.64451E-02 4.01176E-02 5.71606E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 385.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 8.590E-03 7.149E-02 8.727E-02 7.546E-02 1.126E-01 1.337E-02 4.745E+00 4.848E-03 7.545E-03
1 0.00 0.00 8.992E-03 1.332E-01 1.741E-02 1.985E-02 2.598E-02 1.408E-02 4.116E+00
3 4.23 5.00 3.712E-03 1.469E-01 9.578E-03 1.185E-02 1.709E-02 1.447E-02 4.540E+00
5 8.46 10.00 1.387E-03 6.428E-02 4.170E-03 4.977E-03 6.512E-03 1.459E-02 4.668E+00
Waveband 4 of 40 completed in 4.5 sec.
* * * * * Output for wavelength band 5 (390.0 to 400.0 nm; nominal wavelength = 395.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 395.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 390.0 nm to 400.0 nm:
Ed(diffuse) = 3.149E-01 Ed(direct) = 4.830E-01 Ed(total) = 7.979E-01
Absorption Coefficients of Individual Components at 395.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0081 0.0691 0.0387 0.1159
3 4.120 5.000 0.0081 0.0691 0.0387 0.1159
5 8.240 10.000 0.0081 0.0691 0.0387 0.1159
Scattering Coefficients of Individual Components at 395.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0080 0.7001 0.0000 0.7081
3 4.120 5.000 0.0080 0.7001 0.0000 0.7081
5 8.240 10.000 0.0080 0.7001 0.0000 0.7081
Backscattering Coefficients of Individual Components at 395.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00400 0.01400 0.00000 0.01800
3 4.120 5.000 0.00400 0.01400 0.00000 0.01800
5 8.240 10.000 0.00400 0.01400 0.00000 0.01800
Summary of Inherent Optical Properties at 395.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1159 0.7081 0.8240 0.8593 0.01800 0.02542
3 4.120 5.000 0.1159 0.7081 0.8240 0.8593 0.01800 0.02542
5 8.240 10.000 0.1159 0.7081 0.8240 0.8593 0.01800 0.02542
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4984E-01
8 20.00 8.2818E-01
7 30.00 6.6648E-01
6 40.00 5.0192E-01
5 50.00 3.5978E-01
4 60.00 2.5017E-01
3 70.00 1.7207E-01
2 80.00 1.1954E-01
1 87.50 9.1724E-02
1 92.50 7.6357E-02
2 100.00 6.0531E-02
3 110.00 4.6241E-02
4 120.00 3.6782E-02
5 130.00 3.0595E-02
6 140.00 2.6560E-02
7 150.00 2.3965E-02
8 160.00 2.2365E-02
9 170.00 2.1496E-02
10 180.00 2.1188E-02
Asymptotic AOP values are
MUu(inf) = 0.3888
MUd(inf) = 0.6917
MU(inf) = 0.5741
R(inf) = 0.0687
Lu(inf)/Ed(inf) = 0.014390 (1/sr)
k(inf) = 0.2019 (1/m)
absorp(check) = 0.1159 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 395.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.3631E-01 1.1930E+00 1.3293E+00 4.9828E-02 7.9790E-01 0.3655 0.6688 0.5628 6.2449E-02
1 0.00 0.00 1.0560E-01 9.4864E-01 1.0542E+00 4.5403E-02 7.9347E-01 0.4299 0.8364 0.7096 5.7221E-02
3 4.12 5.00 5.3131E-02 4.4584E-01 4.9897E-01 2.1272E-02 3.2801E-01 0.4004 0.7357 0.6147 6.4851E-02
5 8.24 10.00 2.1441E-02 1.7685E-01 1.9829E-01 8.4288E-03 1.2524E-01 0.3931 0.7081 0.5891 6.7303E-02
K-functions (units of 1/meter) at 395.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.09136 0.11937 0.11657 0.11300 0.16024 0.16311 0.15024
5.000 5.010 5.005 0.16927 0.17505 0.17444 0.17536 0.18746 0.18830 0.18478
10.000 10.010 10.005 0.18998 0.19186 0.19166 0.19203 0.19626 0.19656 0.19537
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 395.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 8.49787E-02 5.93576E-03 4.62298E-03 1.05587E-02 7.43919E-03 0.054402
9 1 10.0 0.0 180.0 5.24353E-02 6.04138E-03 1.65639E-03 7.69777E-03 7.57156E-03 0.031589
9 4 10.0 45.0 135.0 5.76123E-02 6.01355E-03 1.89219E-03 7.90575E-03 7.53669E-03 0.032844
9 7 10.0 90.0 90.0 7.78390E-02 5.99664E-03 3.51185E-03 9.50849E-03 7.51549E-03 0.045117
8 1 20.0 0.0 180.0 4.11872E-02 6.12043E-03 9.94217E-04 7.11465E-03 7.67063E-03 0.024139
8 4 20.0 45.0 135.0 4.58525E-02 6.05549E-03 1.15516E-03 7.21064E-03 7.58924E-03 0.025193
8 7 20.0 90.0 90.0 6.74239E-02 6.04298E-03 2.27954E-03 8.32251E-03 7.57356E-03 0.033809
7 1 30.0 0.0 180.0 3.57115E-02 6.23693E-03 8.59667E-04 7.09659E-03 7.81664E-03 0.024073
7 4 30.0 45.0 135.0 3.95842E-02 6.22263E-03 9.64244E-04 7.18688E-03 7.79872E-03 0.024359
7 7 30.0 90.0 90.0 5.77892E-02 6.18058E-03 1.59002E-03 7.77060E-03 7.74601E-03 0.027514
6 1 40.0 0.0 180.0 3.38970E-02 6.34353E-03 9.55845E-04 7.29937E-03 7.95024E-03 0.028198
6 4 40.0 45.0 135.0 3.70646E-02 6.32000E-03 1.03666E-03 7.35666E-03 7.92075E-03 0.027969
6 7 40.0 90.0 90.0 5.20381E-02 6.29308E-03 1.49697E-03 7.79005E-03 7.88701E-03 0.028767
5 1 50.0 0.0 180.0 3.55399E-02 6.47996E-03 1.50990E-03 7.98986E-03 8.12122E-03 0.042485
5 4 50.0 45.0 135.0 3.78725E-02 6.42197E-03 1.57304E-03 7.99501E-03 8.04855E-03 0.041535
5 7 50.0 90.0 90.0 5.03420E-02 6.41631E-03 2.03363E-03 8.44994E-03 8.04146E-03 0.040396
4 1 60.0 0.0 180.0 4.21864E-02 6.43976E-03 3.51736E-03 9.95711E-03 8.07084E-03 0.083377
4 4 60.0 45.0 135.0 4.31411E-02 6.37407E-03 3.47333E-03 9.84740E-03 7.98852E-03 0.080511
4 7 60.0 90.0 90.0 5.32736E-02 6.45941E-03 4.05606E-03 1.05155E-02 8.09547E-03 0.076136
3 1 70.0 0.0 180.0 5.85340E-02 6.02398E-03 9.71588E-03 1.57399E-02 7.54975E-03 0.165987
3 4 70.0 45.0 135.0 5.68864E-02 6.02745E-03 9.34848E-03 1.53759E-02 7.55411E-03 0.164336
3 7 70.0 90.0 90.0 6.35977E-02 6.12189E-03 1.01660E-02 1.62879E-02 7.67246E-03 0.159849
2 1 80.0 0.0 180.0 9.94501E-02 5.19397E-03 2.41508E-02 2.93447E-02 6.50951E-03 0.242843
2 4 80.0 45.0 135.0 9.20888E-02 5.18452E-03 2.33588E-02 2.85433E-02 6.49767E-03 0.253655
2 7 80.0 90.0 90.0 9.14910E-02 5.27652E-03 2.44630E-02 2.97396E-02 6.61297E-03 0.267382
1 1 87.5 0.0 180.0 1.60792E-01 4.20421E-03 4.25933E-02 4.67975E-02 5.26907E-03 0.264896
1 4 87.5 45.0 135.0 1.44774E-01 3.99514E-03 4.23303E-02 4.63254E-02 5.00704E-03 0.292389
1 7 87.5 90.0 90.0 1.31712E-01 4.50536E-03 4.33223E-02 4.78276E-02 5.64649E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 395.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.056E-02 8.498E-02 1.038E-01 8.977E-02 1.340E-01 1.323E-02 4.719E+00 5.936E-03 7.439E-03
1 0.00 0.00 1.101E-02 1.583E-01 2.128E-02 2.436E-02 3.206E-02 1.388E-02 4.124E+00
3 4.12 5.00 4.675E-03 1.855E-01 1.201E-02 1.494E-02 2.174E-02 1.425E-02 4.550E+00
5 8.24 10.00 1.800E-03 8.445E-02 5.401E-03 6.489E-03 8.580E-03 1.437E-02 4.684E+00
Waveband 5 of 40 completed in 4.3 sec.
* * * * * Output for wavelength band 6 (400.0 to 410.0 nm; nominal wavelength = 405.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 405.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 400.0 nm to 410.0 nm:
Ed(diffuse) = 4.287E-01 Ed(direct) = 6.992E-01 Ed(total) = 1.128E+00
Absorption Coefficients of Individual Components at 405.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0053 0.0804 0.0337 0.1194
3 4.047 5.000 0.0053 0.0804 0.0337 0.1194
5 8.094 10.000 0.0053 0.0804 0.0337 0.1194
Scattering Coefficients of Individual Components at 405.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0072 0.6828 0.0000 0.6900
3 4.047 5.000 0.0072 0.6828 0.0000 0.6900
5 8.094 10.000 0.0072 0.6828 0.0000 0.6900
Backscattering Coefficients of Individual Components at 405.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00359 0.01366 0.00000 0.01725
3 4.047 5.000 0.00359 0.01366 0.00000 0.01725
5 8.094 10.000 0.00359 0.01366 0.00000 0.01725
Summary of Inherent Optical Properties at 405.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1194 0.6900 0.8094 0.8525 0.01725 0.02499
3 4.047 5.000 0.1194 0.6900 0.8094 0.8525 0.01725 0.02499
5 8.094 10.000 0.1194 0.6900 0.8094 0.8525 0.01725 0.02499
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4819E-01
8 20.00 8.2293E-01
7 30.00 6.5755E-01
6 40.00 4.9077E-01
5 50.00 3.4825E-01
4 60.00 2.3965E-01
3 70.00 1.6318E-01
2 80.00 1.1233E-01
1 87.50 8.5662E-02
1 92.50 7.1036E-02
2 100.00 5.6046E-02
3 110.00 4.2593E-02
4 120.00 3.3749E-02
5 130.00 2.7997E-02
6 140.00 2.4265E-02
7 150.00 2.1874E-02
8 160.00 2.0405E-02
9 170.00 1.9608E-02
10 180.00 1.9327E-02
Asymptotic AOP values are
MUu(inf) = 0.3870
MUd(inf) = 0.6965
MU(inf) = 0.5843
R(inf) = 0.0642
Lu(inf)/Ed(inf) = 0.013382 (1/sr)
k(inf) = 0.2043 (1/m)
absorp(check) = 0.1194 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 405.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.8527E-01 1.6724E+00 1.8577E+00 6.7989E-02 1.1279E+00 0.3670 0.6745 0.5706 6.0277E-02
1 0.00 0.00 1.4022E-01 1.3327E+00 1.4729E+00 6.0108E-02 1.1200E+00 0.4287 0.8404 0.7196 5.3666E-02
3 4.05 5.00 6.9765E-02 6.1796E-01 6.8773E-01 2.7837E-02 4.5776E-01 0.3990 0.7408 0.6251 6.0813E-02
5 8.09 10.00 2.7854E-02 2.4241E-01 2.7027E-01 1.0910E-02 1.7287E-01 0.3917 0.7131 0.5993 6.3109E-02
K-functions (units of 1/meter) at 405.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.09217 0.12120 0.11844 0.11517 0.16267 0.16536 0.15282
5.000 5.010 5.005 0.17143 0.17737 0.17677 0.17759 0.18965 0.19043 0.18712
10.000 10.010 10.005 0.19216 0.19406 0.19386 0.19427 0.19847 0.19875 0.19770
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 405.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.15686E-01 7.83546E-03 6.50596E-03 1.43414E-02 6.94665E-03 0.056238
9 1 10.0 0.0 180.0 7.13830E-02 7.97575E-03 2.28345E-03 1.02592E-02 7.07103E-03 0.031989
9 4 10.0 45.0 135.0 7.84307E-02 7.93855E-03 2.61264E-03 1.05512E-02 7.03806E-03 0.033311
9 7 10.0 90.0 90.0 1.05966E-01 7.91537E-03 4.91231E-03 1.28277E-02 7.01751E-03 0.046357
8 1 20.0 0.0 180.0 5.60704E-02 8.08022E-03 1.35492E-03 9.43515E-03 7.16366E-03 0.024165
8 4 20.0 45.0 135.0 6.24214E-02 7.99367E-03 1.57631E-03 9.56998E-03 7.08692E-03 0.025253
8 7 20.0 90.0 90.0 9.17877E-02 7.97591E-03 3.15324E-03 1.11292E-02 7.07118E-03 0.034354
7 1 30.0 0.0 180.0 4.86160E-02 8.23386E-03 1.17031E-03 9.40417E-03 7.29986E-03 0.024073
7 4 30.0 45.0 135.0 5.38891E-02 8.21384E-03 1.31286E-03 9.52670E-03 7.28212E-03 0.024362
7 7 30.0 90.0 90.0 7.86649E-02 8.15692E-03 2.17442E-03 1.03313E-02 7.23165E-03 0.027642
6 1 40.0 0.0 180.0 4.61458E-02 8.37393E-03 1.30124E-03 9.67517E-03 7.42404E-03 0.028198
6 4 40.0 45.0 135.0 5.04580E-02 8.34147E-03 1.41127E-03 9.75274E-03 7.39527E-03 0.027969
6 7 40.0 90.0 90.0 7.08422E-02 8.30497E-03 2.03855E-03 1.03435E-02 7.36291E-03 0.028776
5 1 50.0 0.0 180.0 4.83824E-02 8.55349E-03 2.05551E-03 1.06090E-02 7.58324E-03 0.042485
5 4 50.0 45.0 135.0 5.15579E-02 8.47562E-03 2.14146E-03 1.06171E-02 7.51421E-03 0.041535
5 7 50.0 90.0 90.0 6.85333E-02 8.46844E-03 2.76849E-03 1.12369E-02 7.50783E-03 0.040396
4 1 60.0 0.0 180.0 5.74306E-02 8.50009E-03 4.78837E-03 1.32885E-02 7.53590E-03 0.083377
4 4 60.0 45.0 135.0 5.87304E-02 8.41230E-03 4.72843E-03 1.31407E-02 7.45806E-03 0.080511
4 7 60.0 90.0 90.0 7.25243E-02 8.52681E-03 5.52173E-03 1.40485E-02 7.55958E-03 0.076136
3 1 70.0 0.0 180.0 7.96854E-02 7.95161E-03 1.32267E-02 2.11784E-02 7.04963E-03 0.165987
3 4 70.0 45.0 135.0 7.74426E-02 7.95566E-03 1.27266E-02 2.06822E-02 7.05322E-03 0.164336
3 7 70.0 90.0 90.0 8.65789E-02 8.08447E-03 1.38396E-02 2.19240E-02 7.16742E-03 0.159849
2 1 80.0 0.0 180.0 1.35387E-01 6.85663E-03 3.28778E-02 3.97344E-02 6.07886E-03 0.242843
2 4 80.0 45.0 135.0 1.25365E-01 6.84420E-03 3.17996E-02 3.86438E-02 6.06784E-03 0.253655
2 7 80.0 90.0 90.0 1.24552E-01 6.97123E-03 3.33028E-02 4.02741E-02 6.18046E-03 0.267382
1 1 87.5 0.0 180.0 2.18895E-01 5.55108E-03 5.79845E-02 6.35356E-02 4.92140E-03 0.264896
1 4 87.5 45.0 135.0 1.97088E-01 5.27551E-03 5.76265E-02 6.29020E-02 4.67709E-03 0.292389
1 7 87.5 90.0 90.0 1.79307E-01 5.95602E-03 5.89769E-02 6.49329E-02 5.28041E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 405.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.434E-02 1.157E-01 1.412E-01 1.221E-01 1.823E-01 1.271E-02 4.741E+00 7.835E-03 6.947E-03
1 0.00 0.00 1.453E-02 2.155E-01 2.820E-02 3.244E-02 4.307E-02 1.298E-02 4.136E+00
3 4.05 5.00 6.098E-03 2.575E-01 1.578E-02 1.976E-02 2.907E-02 1.332E-02 4.565E+00
5 8.09 10.00 2.320E-03 1.175E-01 7.020E-03 8.497E-03 1.137E-02 1.342E-02 4.702E+00
Waveband 6 of 40 completed in 4.3 sec.
* * * * * Output for wavelength band 7 (410.0 to 420.0 nm; nominal wavelength = 415.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 415.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 410.0 nm to 420.0 nm:
Ed(diffuse) = 4.394E-01 Ed(direct) = 7.590E-01 Ed(total) = 1.198E+00
Absorption Coefficients of Individual Components at 415.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0044 0.0907 0.0293 0.1244
3 3.986 5.000 0.0044 0.0907 0.0293 0.1244
5 7.973 10.000 0.0044 0.0907 0.0293 0.1244
Scattering Coefficients of Individual Components at 415.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0065 0.6664 0.0000 0.6728
3 3.986 5.000 0.0065 0.6664 0.0000 0.6728
5 7.973 10.000 0.0065 0.6664 0.0000 0.6728
Backscattering Coefficients of Individual Components at 415.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00323 0.01333 0.00000 0.01656
3 3.986 5.000 0.00323 0.01333 0.00000 0.01656
5 7.973 10.000 0.00323 0.01333 0.00000 0.01656
Summary of Inherent Optical Properties at 415.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1244 0.6728 0.7973 0.8439 0.01656 0.02461
3 3.986 5.000 0.1244 0.6728 0.7973 0.8439 0.01656 0.02461
5 7.973 10.000 0.1244 0.6728 0.7973 0.8439 0.01656 0.02461
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4611E-01
8 20.00 8.1639E-01
7 30.00 6.4654E-01
6 40.00 4.7720E-01
5 50.00 3.3445E-01
4 60.00 2.2726E-01
3 70.00 1.5289E-01
2 80.00 1.0410E-01
1 87.50 7.8825E-02
1 92.50 6.5082E-02
2 100.00 5.1075E-02
3 110.00 3.8597E-02
4 120.00 3.0459E-02
5 130.00 2.5203E-02
6 140.00 2.1811E-02
7 150.00 1.9649E-02
8 160.00 1.8325E-02
9 170.00 1.7610E-02
10 180.00 1.7357E-02
Asymptotic AOP values are
MUu(inf) = 0.3852
MUd(inf) = 0.7022
MU(inf) = 0.5961
R(inf) = 0.0593
Lu(inf)/Ed(inf) = 0.012305 (1/sr)
k(inf) = 0.2088 (1/m)
absorp(check) = 0.1244 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 415.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.8874E-01 1.7632E+00 1.9520E+00 6.9402E-02 1.1984E+00 0.3677 0.6797 0.5784 5.7910E-02
1 0.00 0.00 1.3785E-01 1.4061E+00 1.5439E+00 5.8876E-02 1.1879E+00 0.4271 0.8448 0.7313 4.9563E-02
3 3.99 5.00 6.7215E-02 6.3629E-01 7.0350E-01 2.6710E-02 4.7495E-01 0.3974 0.7464 0.6372 5.6239E-02
5 7.97 10.00 2.6287E-02 2.4417E-01 2.7045E-01 1.0254E-02 1.7554E-01 0.3901 0.7189 0.6111 5.8413E-02
K-functions (units of 1/meter) at 415.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.09358 0.12481 0.12203 0.11860 0.16709 0.16962 0.15694
5.000 5.010 5.005 0.17556 0.18189 0.18129 0.18172 0.19397 0.19470 0.19127
10.000 10.010 10.005 0.19630 0.19839 0.19819 0.19843 0.20278 0.20305 0.20190
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 415.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.18579E-01 7.64861E-03 6.88404E-03 1.45327E-02 6.38210E-03 0.058054
9 1 10.0 0.0 180.0 7.31681E-02 7.78774E-03 2.36947E-03 1.01572E-02 6.49819E-03 0.032384
9 4 10.0 45.0 135.0 8.03920E-02 7.75052E-03 2.71518E-03 1.04657E-02 6.46713E-03 0.033774
9 7 10.0 90.0 90.0 1.08616E-01 7.72601E-03 5.16841E-03 1.28944E-02 6.44668E-03 0.047584
8 1 20.0 0.0 180.0 5.74725E-02 7.89049E-03 1.39027E-03 9.28076E-03 6.58392E-03 0.024190
8 4 20.0 45.0 135.0 6.39824E-02 7.80440E-03 1.61952E-03 9.42392E-03 6.51209E-03 0.025312
8 7 20.0 90.0 90.0 9.40831E-02 7.78418E-03 3.28278E-03 1.10670E-02 6.49522E-03 0.034892
7 1 30.0 0.0 180.0 4.98318E-02 8.04081E-03 1.19958E-03 9.24038E-03 6.70935E-03 0.024072
7 4 30.0 45.0 135.0 5.52379E-02 8.01908E-03 1.34587E-03 9.36495E-03 6.69122E-03 0.024365
7 7 30.0 90.0 90.0 8.06253E-02 7.95987E-03 2.23876E-03 1.01986E-02 6.64181E-03 0.027767
6 1 40.0 0.0 180.0 4.72998E-02 8.17722E-03 1.33378E-03 9.51100E-03 6.82317E-03 0.028198
6 4 40.0 45.0 135.0 5.17198E-02 8.14280E-03 1.44656E-03 9.58936E-03 6.79446E-03 0.027969
6 7 40.0 90.0 90.0 7.26138E-02 8.10346E-03 2.09017E-03 1.01936E-02 6.76163E-03 0.028785
5 1 50.0 0.0 180.0 4.95923E-02 8.35211E-03 2.10691E-03 1.04590E-02 6.96911E-03 0.042485
5 4 50.0 45.0 135.0 5.28472E-02 8.27325E-03 2.19501E-03 1.04683E-02 6.90330E-03 0.041535
5 7 50.0 90.0 90.0 7.02471E-02 8.26360E-03 2.83772E-03 1.11013E-02 6.89525E-03 0.040396
4 1 60.0 0.0 180.0 5.88668E-02 8.29968E-03 4.90811E-03 1.32078E-02 6.92535E-03 0.083377
4 4 60.0 45.0 135.0 6.01990E-02 8.21127E-03 4.84667E-03 1.30579E-02 6.85159E-03 0.080511
4 7 60.0 90.0 90.0 7.43379E-02 8.32201E-03 5.65981E-03 1.39818E-02 6.94399E-03 0.076136
3 1 70.0 0.0 180.0 8.16781E-02 7.76450E-03 1.35575E-02 2.13220E-02 6.47880E-03 0.165987
3 4 70.0 45.0 135.0 7.93792E-02 7.76643E-03 1.30448E-02 2.08113E-02 6.48041E-03 0.164336
3 7 70.0 90.0 90.0 8.87440E-02 7.89386E-03 1.41856E-02 2.20795E-02 6.58673E-03 0.159849
2 1 80.0 0.0 180.0 1.38772E-01 6.69604E-03 3.36999E-02 4.03960E-02 5.58726E-03 0.242843
2 4 80.0 45.0 135.0 1.28500E-01 6.68270E-03 3.25948E-02 3.92775E-02 5.57613E-03 0.253655
2 7 80.0 90.0 90.0 1.27666E-01 6.81048E-03 3.41356E-02 4.09461E-02 5.68275E-03 0.267382
1 1 87.5 0.0 180.0 2.24369E-01 5.42229E-03 5.94345E-02 6.48568E-02 4.52443E-03 0.264896
1 4 87.5 45.0 135.0 2.02017E-01 5.15271E-03 5.90676E-02 6.42203E-02 4.29948E-03 0.292389
1 7 87.5 90.0 90.0 1.83791E-01 5.82295E-03 6.04518E-02 6.62747E-02 4.85874E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 415.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.453E-02 1.186E-01 1.446E-01 1.250E-01 1.867E-01 1.213E-02 4.776E+00 7.649E-03 6.382E-03
1 0.00 0.00 1.419E-02 2.209E-01 2.769E-02 3.202E-02 4.295E-02 1.194E-02 4.150E+00
3 3.99 5.00 5.830E-03 2.661E-01 1.523E-02 1.922E-02 2.860E-02 1.227E-02 4.582E+00
5 7.97 10.00 2.172E-03 1.205E-01 6.636E-03 8.094E-03 1.096E-02 1.238E-02 4.720E+00
Waveband 7 of 40 completed in 4.3 sec.
* * * * * Output for wavelength band 8 (420.0 to 430.0 nm; nominal wavelength = 425.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 425.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 420.0 nm to 430.0 nm:
Ed(diffuse) = 4.082E-01 Ed(direct) = 7.412E-01 Ed(total) = 1.149E+00
Absorption Coefficients of Individual Components at 425.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0048 0.0959 0.0254 0.1261
3 3.913 5.000 0.0048 0.0959 0.0254 0.1261
5 7.826 10.000 0.0048 0.0959 0.0254 0.1261
Scattering Coefficients of Individual Components at 425.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0058 0.6507 0.0000 0.6565
3 3.913 5.000 0.0058 0.6507 0.0000 0.6565
5 7.826 10.000 0.0058 0.6507 0.0000 0.6565
Backscattering Coefficients of Individual Components at 425.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00291 0.01301 0.00000 0.01593
3 3.913 5.000 0.00291 0.01301 0.00000 0.01593
5 7.826 10.000 0.00291 0.01301 0.00000 0.01593
Summary of Inherent Optical Properties at 425.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1261 0.6565 0.7826 0.8389 0.01593 0.02426
3 3.913 5.000 0.1261 0.6565 0.7826 0.8389 0.01593 0.02426
5 7.826 10.000 0.1261 0.6565 0.7826 0.8389 0.01593 0.02426
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4489E-01
8 20.00 8.1257E-01
7 30.00 6.4015E-01
6 40.00 4.6939E-01
5 50.00 3.2658E-01
4 60.00 2.2025E-01
3 70.00 1.4710E-01
2 80.00 9.9511E-02
1 87.50 7.5014E-02
1 92.50 6.1765E-02
2 100.00 4.8307E-02
3 110.00 3.6368E-02
4 120.00 2.8618E-02
5 130.00 2.3631E-02
6 140.00 2.0425E-02
7 150.00 1.8386E-02
8 160.00 1.7141E-02
9 170.00 1.6469E-02
10 180.00 1.6232E-02
Asymptotic AOP values are
MUu(inf) = 0.3839
MUd(inf) = 0.7056
MU(inf) = 0.6031
R(inf) = 0.0565
Lu(inf)/Ed(inf) = 0.011667 (1/sr)
k(inf) = 0.2091 (1/m)
absorp(check) = 0.1261 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 425.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.7545E-01 1.6797E+00 1.8552E+00 6.4809E-02 1.1494E+00 0.3694 0.6843 0.5846 5.6386E-02
1 0.00 0.00 1.2598E-01 1.3427E+00 1.4687E+00 5.3679E-02 1.1382E+00 0.4261 0.8477 0.7385 4.7159E-02
3 3.91 5.00 6.1350E-02 6.0523E-01 6.6658E-01 2.4319E-02 4.5414E-01 0.3964 0.7504 0.6448 5.3549E-02
5 7.83 10.00 2.4000E-02 2.3200E-01 2.5599E-01 9.3352E-03 1.6766E-01 0.3890 0.7227 0.6185 5.5679E-02
K-functions (units of 1/meter) at 425.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.09334 0.12551 0.12275 0.11908 0.16780 0.17021 0.15750
5.000 5.010 5.005 0.17559 0.18222 0.18161 0.18177 0.19422 0.19493 0.19137
10.000 10.010 10.005 0.19521 0.19855 0.19824 0.19833 0.20299 0.20326 0.20199
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 425.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.10138E-01 6.95396E-03 6.57864E-03 1.35326E-02 6.05012E-03 0.059731
9 1 10.0 0.0 180.0 6.79596E-02 7.08081E-03 2.22558E-03 9.30640E-03 6.16048E-03 0.032749
9 4 10.0 45.0 135.0 7.46693E-02 7.04675E-03 2.55379E-03 9.60055E-03 6.13085E-03 0.034201
9 7 10.0 90.0 90.0 1.00884E-01 7.02417E-03 4.91474E-03 1.19389E-02 6.11120E-03 0.048717
8 1 20.0 0.0 180.0 5.33813E-02 7.17434E-03 1.29256E-03 8.46690E-03 6.24185E-03 0.024214
8 4 20.0 45.0 135.0 5.94278E-02 7.09567E-03 1.50748E-03 8.60315E-03 6.17341E-03 0.025367
8 7 20.0 90.0 90.0 8.73858E-02 7.07692E-03 3.09254E-03 1.01695E-02 6.15710E-03 0.035390
7 1 30.0 0.0 180.0 4.62845E-02 7.31102E-03 1.11418E-03 8.42520E-03 6.36077E-03 0.024072
7 4 30.0 45.0 135.0 5.13067E-02 7.29071E-03 1.25022E-03 8.54093E-03 6.34310E-03 0.024368
7 7 30.0 90.0 90.0 7.48801E-02 7.23662E-03 2.08794E-03 9.32456E-03 6.29604E-03 0.027884
6 1 40.0 0.0 180.0 4.39327E-02 7.43483E-03 1.23883E-03 8.67367E-03 6.46849E-03 0.028198
6 4 40.0 45.0 135.0 4.80381E-02 7.40292E-03 1.34358E-03 8.74650E-03 6.44072E-03 0.027969
6 7 40.0 90.0 90.0 6.74447E-02 7.36753E-03 1.94194E-03 9.30947E-03 6.40993E-03 0.028793
5 1 50.0 0.0 180.0 4.60620E-02 7.59370E-03 1.95693E-03 9.55062E-03 6.60670E-03 0.042485
5 4 50.0 45.0 135.0 4.90853E-02 7.52151E-03 2.03876E-03 9.56027E-03 6.54390E-03 0.041535
5 7 50.0 90.0 90.0 6.52465E-02 7.51430E-03 2.63572E-03 1.01500E-02 6.53763E-03 0.040396
4 1 60.0 0.0 180.0 5.46763E-02 7.54598E-03 4.55872E-03 1.21047E-02 6.56519E-03 0.083377
4 4 60.0 45.0 135.0 5.59137E-02 7.46536E-03 4.50166E-03 1.19670E-02 6.49505E-03 0.080511
4 7 60.0 90.0 90.0 6.90461E-02 7.56903E-03 5.25692E-03 1.28259E-02 6.58524E-03 0.076136
3 1 70.0 0.0 180.0 7.58638E-02 7.05974E-03 1.25924E-02 1.96521E-02 6.14215E-03 0.165987
3 4 70.0 45.0 135.0 7.37285E-02 7.06170E-03 1.21162E-02 1.91779E-02 6.14385E-03 0.164336
3 7 70.0 90.0 90.0 8.24268E-02 7.18237E-03 1.31758E-02 2.03582E-02 6.24884E-03 0.159849
2 1 80.0 0.0 180.0 1.28894E-01 6.08875E-03 3.13010E-02 3.73897E-02 5.29736E-03 0.242843
2 4 80.0 45.0 135.0 1.19353E-01 6.07722E-03 3.02746E-02 3.63518E-02 5.28733E-03 0.253655
2 7 80.0 90.0 90.0 1.18578E-01 6.19920E-03 3.17057E-02 3.79049E-02 5.39346E-03 0.267382
1 1 87.5 0.0 180.0 2.08398E-01 4.93123E-03 5.52036E-02 6.01349E-02 4.29029E-03 0.264896
1 4 87.5 45.0 135.0 1.87636E-01 4.68690E-03 5.48628E-02 5.95497E-02 4.07772E-03 0.292389
1 7 87.5 90.0 90.0 1.70708E-01 5.30309E-03 5.61485E-02 6.14516E-02 4.61382E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 425.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.353E-02 1.101E-01 1.343E-01 1.161E-01 1.734E-01 1.177E-02 4.789E+00 6.954E-03 6.050E-03
1 0.00 0.00 1.290E-02 2.051E-01 2.525E-02 2.933E-02 3.964E-02 1.133E-02 4.162E+00
3 3.91 5.00 5.293E-03 2.525E-01 1.389E-02 1.762E-02 2.648E-02 1.166E-02 4.594E+00
5 7.83 10.00 1.972E-03 1.155E-01 6.051E-03 7.427E-03 1.016E-02 1.176E-02 4.734E+00
Waveband 8 of 40 completed in 4.3 sec.
* * * * * Output for wavelength band 9 (430.0 to 440.0 nm; nominal wavelength = 435.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 435.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 430.0 nm to 440.0 nm:
Ed(diffuse) = 4.073E-01 Ed(direct) = 7.763E-01 Ed(total) = 1.184E+00
Absorption Coefficients of Individual Components at 435.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0053 0.1031 0.0221 0.1305
3 3.858 5.000 0.0053 0.1031 0.0221 0.1305
5 7.715 10.000 0.0053 0.1031 0.0221 0.1305
Scattering Coefficients of Individual Components at 435.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0053 0.6357 0.0000 0.6410
3 3.858 5.000 0.0053 0.6357 0.0000 0.6410
5 7.715 10.000 0.0053 0.6357 0.0000 0.6410
Backscattering Coefficients of Individual Components at 435.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00264 0.01271 0.00000 0.01535
3 3.858 5.000 0.00264 0.01271 0.00000 0.01535
5 7.715 10.000 0.00264 0.01271 0.00000 0.01535
Summary of Inherent Optical Properties at 435.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1305 0.6410 0.7715 0.8308 0.01535 0.02395
3 3.858 5.000 0.1305 0.6410 0.7715 0.8308 0.01535 0.02395
5 7.715 10.000 0.1305 0.6410 0.7715 0.8308 0.01535 0.02395
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4295E-01
8 20.00 8.0654E-01
7 30.00 6.3016E-01
6 40.00 4.5733E-01
5 50.00 3.1460E-01
4 60.00 2.0976E-01
3 70.00 1.3859E-01
2 80.00 9.2859E-02
1 87.50 6.9565E-02
1 92.50 5.7066E-02
2 100.00 4.4431E-02
3 110.00 3.3291E-02
4 120.00 2.6109E-02
5 130.00 2.1516E-02
6 140.00 1.8576E-02
7 150.00 1.6715E-02
8 160.00 1.5582E-02
9 170.00 1.4971E-02
10 180.00 1.4756E-02
Asymptotic AOP values are
MUu(inf) = 0.3824
MUd(inf) = 0.7107
MU(inf) = 0.6132
R(inf) = 0.0527
Lu(inf)/Ed(inf) = 0.010836 (1/sr)
k(inf) = 0.2128 (1/m)
absorp(check) = 0.1305 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 435.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.7428E-01 1.7187E+00 1.8930E+00 6.4527E-02 1.1836E+00 0.3702 0.6887 0.5912 5.4517E-02
1 0.00 0.00 1.2106E-01 1.3749E+00 1.4960E+00 5.1406E-02 1.1705E+00 0.4246 0.8513 0.7481 4.3918E-02
3 3.86 5.00 5.7893E-02 6.0661E-01 6.6451E-01 2.2867E-02 4.5819E-01 0.3950 0.7553 0.6551 4.9907E-02
5 7.72 10.00 2.2244E-02 2.2815E-01 2.5039E-01 8.6229E-03 1.6606E-01 0.3876 0.7278 0.6288 5.1927E-02
K-functions (units of 1/meter) at 435.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.09485 0.12898 0.12621 0.12225 0.17169 0.17396 0.16117
5.000 5.010 5.005 0.17918 0.18615 0.18554 0.18535 0.19795 0.19861 0.19494
10.000 10.010 10.005 0.19985 0.20229 0.20208 0.20201 0.20668 0.20693 0.20554
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 435.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.09916E-01 6.63891E-03 6.75154E-03 1.33904E-02 5.60894E-03 0.061424
9 1 10.0 0.0 180.0 6.78230E-02 6.76187E-03 2.24609E-03 9.00796E-03 5.71282E-03 0.033117
9 4 10.0 45.0 135.0 7.45191E-02 6.72859E-03 2.58081E-03 9.30940E-03 5.68470E-03 0.034633
9 7 10.0 90.0 90.0 1.00682E-01 6.70545E-03 5.02001E-03 1.17255E-02 5.66516E-03 0.049860
8 1 20.0 0.0 180.0 5.32740E-02 6.85184E-03 1.29122E-03 8.14306E-03 5.78883E-03 0.024237
8 4 20.0 45.0 135.0 5.93083E-02 6.77542E-03 1.50772E-03 8.28314E-03 5.72427E-03 0.025422
8 7 20.0 90.0 90.0 8.72100E-02 6.75508E-03 3.13012E-03 9.88520E-03 5.70709E-03 0.035892
7 1 30.0 0.0 180.0 4.61914E-02 6.98267E-03 1.11194E-03 8.09462E-03 5.89937E-03 0.024072
7 4 30.0 45.0 135.0 5.12045E-02 6.96148E-03 1.24786E-03 8.20934E-03 5.88146E-03 0.024370
7 7 30.0 90.0 90.0 7.47236E-02 6.90675E-03 2.09235E-03 8.99910E-03 5.83522E-03 0.028001
6 1 40.0 0.0 180.0 4.38444E-02 7.10070E-03 1.23634E-03 8.33704E-03 5.99908E-03 0.028198
6 4 40.0 45.0 135.0 4.79415E-02 7.06796E-03 1.34088E-03 8.40884E-03 5.97142E-03 0.027969
6 7 40.0 90.0 90.0 6.73091E-02 7.03096E-03 1.93860E-03 8.96956E-03 5.94017E-03 0.028801
5 1 50.0 0.0 180.0 4.59694E-02 7.25207E-03 1.95299E-03 9.20506E-03 6.12697E-03 0.042485
5 4 50.0 45.0 135.0 4.89866E-02 7.18077E-03 2.03466E-03 9.21543E-03 6.06674E-03 0.041535
5 7 50.0 90.0 90.0 6.51153E-02 7.17148E-03 2.63042E-03 9.80189E-03 6.05888E-03 0.040396
4 1 60.0 0.0 180.0 5.45664E-02 7.20626E-03 4.54956E-03 1.17558E-02 6.08827E-03 0.083377
4 4 60.0 45.0 135.0 5.58013E-02 7.12701E-03 4.49261E-03 1.16196E-02 6.02131E-03 0.080511
4 7 60.0 90.0 90.0 6.89073E-02 7.22479E-03 5.24635E-03 1.24711E-02 6.10393E-03 0.076136
3 1 70.0 0.0 180.0 7.57113E-02 6.74216E-03 1.25671E-02 1.93093E-02 5.69617E-03 0.165987
3 4 70.0 45.0 135.0 7.35803E-02 6.74230E-03 1.20919E-02 1.88342E-02 5.69628E-03 0.164336
3 7 70.0 90.0 90.0 8.22610E-02 6.85847E-03 1.31493E-02 2.00078E-02 5.79443E-03 0.159849
2 1 80.0 0.0 180.0 1.28635E-01 5.81540E-03 3.12380E-02 3.70534E-02 4.91319E-03 0.242843
2 4 80.0 45.0 135.0 1.19113E-01 5.80331E-03 3.02137E-02 3.60170E-02 4.90298E-03 0.253655
2 7 80.0 90.0 90.0 1.18340E-01 5.92243E-03 3.16419E-02 3.75644E-02 5.00361E-03 0.267382
1 1 87.5 0.0 180.0 2.07978E-01 4.71078E-03 5.50926E-02 5.98034E-02 3.97994E-03 0.264896
1 4 87.5 45.0 135.0 1.87259E-01 4.47695E-03 5.47525E-02 5.92294E-02 3.78239E-03 0.292389
1 7 87.5 90.0 90.0 1.70364E-01 5.06967E-03 5.60356E-02 6.11052E-02 4.28315E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 435.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.339E-02 1.099E-01 1.339E-01 1.157E-01 1.729E-01 1.131E-02 4.819E+00 6.639E-03 5.609E-03
1 0.00 0.00 1.231E-02 2.047E-01 2.424E-02 2.828E-02 3.858E-02 1.052E-02 4.175E+00
3 3.86 5.00 4.962E-03 2.534E-01 1.312E-02 1.676E-02 2.545E-02 1.083E-02 4.608E+00
5 7.72 10.00 1.816E-03 1.152E-01 5.612E-03 6.937E-03 9.598E-03 1.094E-02 4.748E+00
Waveband 9 of 40 completed in 4.2 sec.
* * * * * Output for wavelength band 10 (440.0 to 450.0 nm; nominal wavelength = 445.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 445.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 440.0 nm to 450.0 nm:
Ed(diffuse) = 4.682E-01 Ed(direct) = 9.292E-01 Ed(total) = 1.397E+00
Absorption Coefficients of Individual Components at 445.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0075 0.1000 0.0192 0.1267
3 3.765 5.000 0.0075 0.1000 0.0192 0.1267
5 7.530 10.000 0.0075 0.1000 0.0192 0.1267
Scattering Coefficients of Individual Components at 445.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0048 0.6214 0.0000 0.6262
3 3.765 5.000 0.0048 0.6214 0.0000 0.6262
5 7.530 10.000 0.0048 0.6214 0.0000 0.6262
Backscattering Coefficients of Individual Components at 445.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00239 0.01243 0.00000 0.01482
3 3.765 5.000 0.00239 0.01243 0.00000 0.01482
5 7.530 10.000 0.00239 0.01243 0.00000 0.01482
Summary of Inherent Optical Properties at 445.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1267 0.6262 0.7530 0.8317 0.01482 0.02366
3 3.765 5.000 0.1267 0.6262 0.7530 0.8317 0.01482 0.02366
5 7.530 10.000 0.1267 0.6262 0.7530 0.8317 0.01482 0.02366
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4316E-01
8 20.00 8.0717E-01
7 30.00 6.3118E-01
6 40.00 4.5852E-01
5 50.00 3.1571E-01
4 60.00 2.1065E-01
3 70.00 1.3924E-01
2 80.00 9.3304E-02
1 87.50 6.9883E-02
1 92.50 5.7307E-02
2 100.00 4.4590E-02
3 110.00 3.3376E-02
4 120.00 2.6144E-02
5 130.00 2.1517E-02
6 140.00 1.8555E-02
7 150.00 1.6679E-02
8 160.00 1.5537E-02
9 170.00 1.4922E-02
10 180.00 1.4705E-02
Asymptotic AOP values are
MUu(inf) = 0.3818
MUd(inf) = 0.7103
MU(inf) = 0.6130
R(inf) = 0.0526
Lu(inf)/Ed(inf) = 0.010777 (1/sr)
k(inf) = 0.2068 (1/m)
absorp(check) = 0.1268 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 445.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 2.0237E-01 2.0183E+00 2.2207E+00 7.5506E-02 1.3974E+00 0.3731 0.6924 0.5953 5.4033E-02
1 0.00 0.00 1.4214E-01 1.6219E+00 1.7640E+00 6.0313E-02 1.3822E+00 0.4243 0.8522 0.7494 4.3635E-02
3 3.76 5.00 6.9986E-02 7.3619E-01 8.0617E-01 2.7627E-02 5.5711E-01 0.3947 0.7567 0.6568 4.9590E-02
5 7.53 10.00 2.7782E-02 2.8584E-01 3.1362E-01 1.0758E-02 2.0827E-01 0.3872 0.7286 0.6298 5.1654E-02
K-functions (units of 1/meter) at 445.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.09078 0.12472 0.12198 0.11773 0.16649 0.16871 0.15601
5.000 5.010 5.005 0.17269 0.17987 0.17924 0.17896 0.19180 0.19247 0.18871
10.000 10.010 10.005 0.19336 0.19592 0.19569 0.19560 0.20046 0.20072 0.19927
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 445.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.26342E-01 7.76988E-03 7.94837E-03 1.57182E-02 5.56021E-03 0.062911
9 1 10.0 0.0 180.0 7.79584E-02 7.91157E-03 2.60697E-03 1.05185E-02 5.66161E-03 0.033441
9 4 10.0 45.0 135.0 8.56552E-02 7.87341E-03 2.99894E-03 1.08723E-02 5.63430E-03 0.035012
9 7 10.0 90.0 90.0 1.15727E-01 7.84837E-03 5.88645E-03 1.37348E-02 5.61638E-03 0.050865
8 1 20.0 0.0 180.0 6.12352E-02 8.01627E-03 1.48545E-03 9.50172E-03 5.73654E-03 0.024258
8 4 20.0 45.0 135.0 6.81713E-02 7.92812E-03 1.73634E-03 9.66446E-03 5.67345E-03 0.025470
8 7 20.0 90.0 90.0 1.00243E-01 7.90776E-03 3.64209E-03 1.15499E-02 5.65888E-03 0.036333
7 1 30.0 0.0 180.0 5.30942E-02 8.16920E-03 1.27811E-03 9.44731E-03 5.84598E-03 0.024072
7 4 30.0 45.0 135.0 5.88574E-02 8.14616E-03 1.43450E-03 9.58066E-03 5.82949E-03 0.024372
7 7 30.0 90.0 90.0 8.58844E-02 8.08706E-03 2.41373E-03 1.05008E-02 5.78719E-03 0.028104
6 1 40.0 0.0 180.0 5.03965E-02 8.30777E-03 1.42110E-03 9.72887E-03 5.94514E-03 0.028198
6 4 40.0 45.0 135.0 5.51058E-02 8.27185E-03 1.54126E-03 9.81312E-03 5.91943E-03 0.027969
6 7 40.0 90.0 90.0 7.73677E-02 8.23555E-03 2.22887E-03 1.04644E-02 5.89346E-03 0.028809
5 1 50.0 0.0 180.0 5.28390E-02 8.48562E-03 2.24484E-03 1.07305E-02 6.07241E-03 0.042485
5 4 50.0 45.0 135.0 5.63071E-02 8.40517E-03 2.33872E-03 1.07439E-02 6.01484E-03 0.041535
5 7 50.0 90.0 90.0 7.48461E-02 8.40319E-03 3.02351E-03 1.14267E-02 6.01342E-03 0.040396
4 1 60.0 0.0 180.0 6.27208E-02 8.43284E-03 5.22944E-03 1.36623E-02 6.03464E-03 0.083377
4 4 60.0 45.0 135.0 6.41402E-02 8.34358E-03 5.16398E-03 1.35076E-02 5.97076E-03 0.080511
4 7 60.0 90.0 90.0 7.92047E-02 8.46875E-03 6.03036E-03 1.44991E-02 6.06033E-03 0.076136
3 1 70.0 0.0 180.0 8.70255E-02 7.89058E-03 1.44451E-02 2.23357E-02 5.64659E-03 0.165987
3 4 70.0 45.0 135.0 8.45761E-02 7.89456E-03 1.38989E-02 2.17934E-02 5.64944E-03 0.164336
3 7 70.0 90.0 90.0 9.45540E-02 8.04248E-03 1.51144E-02 2.31569E-02 5.75530E-03 0.159849
2 1 80.0 0.0 180.0 1.47858E-01 6.80657E-03 3.59062E-02 4.27128E-02 4.87086E-03 0.242843
2 4 80.0 45.0 135.0 1.36913E-01 6.79615E-03 3.47288E-02 4.15249E-02 4.86340E-03 0.253655
2 7 80.0 90.0 90.0 1.36024E-01 6.94717E-03 3.63705E-02 4.33177E-02 4.97148E-03 0.267382
1 1 87.5 0.0 180.0 2.39059E-01 5.51407E-03 6.33256E-02 6.88397E-02 3.94593E-03 0.264896
1 4 87.5 45.0 135.0 2.15243E-01 5.24353E-03 6.29347E-02 6.81782E-02 3.75233E-03 0.292389
1 7 87.5 90.0 90.0 1.95824E-01 5.94862E-03 6.44095E-02 7.03581E-02 4.25690E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 445.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.572E-02 1.263E-01 1.539E-01 1.331E-01 1.989E-01 1.125E-02 4.804E+00 7.770E-03 5.560E-03
1 0.00 0.00 1.441E-02 2.353E-01 2.836E-02 3.321E-02 4.549E-02 1.043E-02 4.185E+00
3 3.76 5.00 5.981E-03 3.043E-01 1.577E-02 2.023E-02 3.092E-02 1.074E-02 4.619E+00
5 7.53 10.00 2.259E-03 1.436E-01 6.969E-03 8.660E-03 1.208E-02 1.084E-02 4.763E+00
Waveband 10 of 40 completed in 4.0 sec.
* * * * * Output for wavelength band 11 (450.0 to 460.0 nm; nominal wavelength = 455.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 455.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 450.0 nm to 460.0 nm:
Ed(diffuse) = 4.888E-01 Ed(direct) = 1.007E+00 Ed(total) = 1.495E+00
Absorption Coefficients of Individual Components at 455.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0096 0.0949 0.0167 0.1212
3 3.667 5.000 0.0096 0.0949 0.0167 0.1212
5 7.333 10.000 0.0096 0.0949 0.0167 0.1212
Scattering Coefficients of Individual Components at 455.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0043 0.6078 0.0000 0.6121
3 3.667 5.000 0.0043 0.6078 0.0000 0.6121
5 7.333 10.000 0.0043 0.6078 0.0000 0.6121
Backscattering Coefficients of Individual Components at 455.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00217 0.01216 0.00000 0.01433
3 3.667 5.000 0.00217 0.01216 0.00000 0.01433
5 7.333 10.000 0.00217 0.01216 0.00000 0.01433
Summary of Inherent Optical Properties at 455.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1212 0.6121 0.7333 0.8347 0.01433 0.02340
3 3.667 5.000 0.1212 0.6121 0.7333 0.8347 0.01433 0.02340
5 7.333 10.000 0.1212 0.6121 0.7333 0.8347 0.01433 0.02340
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4391E-01
8 20.00 8.0947E-01
7 30.00 6.3496E-01
6 40.00 4.6301E-01
5 50.00 3.2009E-01
4 60.00 2.1439E-01
3 70.00 1.4219E-01
2 80.00 9.5519E-02
1 87.50 7.1637E-02
1 92.50 5.8776E-02
2 100.00 4.5754E-02
3 110.00 3.4247E-02
4 120.00 2.6810E-02
5 130.00 2.2043E-02
6 140.00 1.8987E-02
7 150.00 1.7049E-02
8 160.00 1.5868E-02
9 170.00 1.5231E-02
10 180.00 1.5007E-02
Asymptotic AOP values are
MUu(inf) = 0.3815
MUd(inf) = 0.7086
MU(inf) = 0.6102
R(inf) = 0.0534
Lu(inf)/Ed(inf) = 0.010912 (1/sr)
k(inf) = 0.1986 (1/m)
absorp(check) = 0.1212 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 455.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 2.1442E-01 2.1495E+00 2.3640E+00 8.0728E-02 1.4954E+00 0.3765 0.6957 0.5985 5.3983E-02
1 0.00 0.00 1.5428E-01 1.7366E+00 1.8909E+00 6.5481E-02 1.4802E+00 0.4244 0.8523 0.7481 4.4238E-02
3 3.67 5.00 7.8959E-02 8.1971E-01 8.9867E-01 3.1190E-02 6.2065E-01 0.3950 0.7572 0.6559 5.0253E-02
5 7.33 10.00 3.2728E-02 3.3216E-01 3.6489E-01 1.2674E-02 2.4189E-01 0.3873 0.7282 0.6282 5.2395E-02
K-functions (units of 1/meter) at 455.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.08586 0.11883 0.11614 0.11176 0.15933 0.16153 0.14903
5.000 5.010 5.005 0.16412 0.17140 0.17076 0.17051 0.18354 0.18423 0.18044
10.000 10.010 10.005 0.18475 0.18738 0.18714 0.18709 0.19211 0.19238 0.19092
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 455.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.31908E-01 8.42219E-03 8.48427E-03 1.69065E-02 5.63191E-03 0.064320
9 1 10.0 0.0 180.0 8.13927E-02 8.57194E-03 2.74675E-03 1.13187E-02 5.73205E-03 0.033747
9 4 10.0 45.0 135.0 8.94286E-02 8.53193E-03 3.16313E-03 1.16951E-02 5.70529E-03 0.035370
9 7 10.0 90.0 90.0 1.20826E-01 8.50815E-03 6.26069E-03 1.47688E-02 5.68939E-03 0.051816
8 1 20.0 0.0 180.0 6.39329E-02 8.68407E-03 1.55216E-03 1.02362E-02 5.80703E-03 0.024278
8 4 20.0 45.0 135.0 7.11745E-02 8.59080E-03 1.81610E-03 1.04069E-02 5.74466E-03 0.025516
8 7 20.0 90.0 90.0 1.04659E-01 8.57429E-03 3.84625E-03 1.24205E-02 5.73362E-03 0.036750
7 1 30.0 0.0 180.0 5.54332E-02 8.84910E-03 1.33441E-03 1.01835E-02 5.91739E-03 0.024072
7 4 30.0 45.0 135.0 6.14512E-02 8.82725E-03 1.49785E-03 1.03251E-02 5.90277E-03 0.024375
7 7 30.0 90.0 90.0 8.96620E-02 8.77097E-03 2.52866E-03 1.12996E-02 5.86514E-03 0.028202
6 1 40.0 0.0 180.0 5.26166E-02 8.99940E-03 1.48370E-03 1.04831E-02 6.01789E-03 0.028198
6 4 40.0 45.0 135.0 5.75335E-02 8.96462E-03 1.60916E-03 1.05738E-02 5.99463E-03 0.027969
6 7 40.0 90.0 90.0 8.07761E-02 8.93574E-03 2.32762E-03 1.12634E-02 5.97532E-03 0.028816
5 1 50.0 0.0 180.0 5.51668E-02 9.19273E-03 2.34374E-03 1.15365E-02 6.14717E-03 0.042485
5 4 50.0 45.0 135.0 5.87877E-02 9.11048E-03 2.44175E-03 1.15522E-02 6.09217E-03 0.041535
5 7 50.0 90.0 90.0 7.81434E-02 9.12087E-03 3.15670E-03 1.22776E-02 6.09912E-03 0.040396
4 1 60.0 0.0 180.0 6.54838E-02 9.13626E-03 5.45982E-03 1.45961E-02 6.10941E-03 0.083377
4 4 60.0 45.0 135.0 6.69658E-02 9.04507E-03 5.39147E-03 1.44365E-02 6.04843E-03 0.080511
4 7 60.0 90.0 90.0 8.26940E-02 9.19503E-03 6.29602E-03 1.54910E-02 6.14871E-03 0.076136
3 1 70.0 0.0 180.0 9.08593E-02 8.54938E-03 1.50815E-02 2.36309E-02 5.71697E-03 0.165987
3 4 70.0 45.0 135.0 8.83020E-02 8.55941E-03 1.45112E-02 2.30706E-02 5.72367E-03 0.164336
3 7 70.0 90.0 90.0 9.87195E-02 8.73461E-03 1.57802E-02 2.45148E-02 5.84083E-03 0.159849
2 1 80.0 0.0 180.0 1.54371E-01 7.37516E-03 3.74880E-02 4.48632E-02 4.93176E-03 0.242843
2 4 80.0 45.0 135.0 1.42945E-01 7.36914E-03 3.62587E-02 4.36279E-02 4.92774E-03 0.253655
2 7 80.0 90.0 90.0 1.42017E-01 7.54650E-03 3.79727E-02 4.55192E-02 5.04634E-03 0.267382
1 1 87.5 0.0 180.0 2.49590E-01 5.97463E-03 6.61154E-02 7.20900E-02 3.99523E-03 0.264896
1 4 87.5 45.0 135.0 2.24725E-01 5.68577E-03 6.57072E-02 7.13929E-02 3.80207E-03 0.292389
1 7 87.5 90.0 90.0 2.04450E-01 6.46243E-03 6.72470E-02 7.37094E-02 4.32142E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 455.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.691E-02 1.319E-01 1.608E-01 1.391E-01 2.078E-01 1.131E-02 4.775E+00 8.422E-03 5.632E-03
1 0.00 0.00 1.562E-02 2.457E-01 3.067E-02 3.600E-02 4.940E-02 1.055E-02 4.192E+00
3 3.67 5.00 6.744E-03 3.343E-01 1.766E-02 2.272E-02 3.487E-02 1.087E-02 4.625E+00
5 7.33 10.00 2.655E-03 1.652E-01 8.146E-03 1.017E-02 1.428E-02 1.098E-02 4.774E+00
Waveband 11 of 40 completed in 3.9 sec.
* * * * * Output for wavelength band 12 (460.0 to 470.0 nm; nominal wavelength = 465.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 465.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 460.0 nm to 470.0 nm:
Ed(diffuse) = 4.757E-01 Ed(direct) = 1.013E+00 Ed(total) = 1.489E+00
Absorption Coefficients of Individual Components at 465.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0101 0.0928 0.0145 0.1174
3 3.580 5.000 0.0101 0.0928 0.0145 0.1174
5 7.161 10.000 0.0101 0.0928 0.0145 0.1174
Scattering Coefficients of Individual Components at 465.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0040 0.5947 0.0000 0.5987
3 3.580 5.000 0.0040 0.5947 0.0000 0.5987
5 7.161 10.000 0.0040 0.5947 0.0000 0.5987
Backscattering Coefficients of Individual Components at 465.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00198 0.01189 0.00000 0.01387
3 3.580 5.000 0.00198 0.01189 0.00000 0.01387
5 7.161 10.000 0.00198 0.01189 0.00000 0.01387
Summary of Inherent Optical Properties at 465.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1174 0.5987 0.7161 0.8360 0.01387 0.02317
3 3.580 5.000 0.1174 0.5987 0.7161 0.8360 0.01387 0.02317
5 7.161 10.000 0.1174 0.5987 0.7161 0.8360 0.01387 0.02317
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4422E-01
8 20.00 8.1043E-01
7 30.00 6.3652E-01
6 40.00 4.6486E-01
5 50.00 3.2187E-01
4 60.00 2.1590E-01
3 70.00 1.4334E-01
2 80.00 9.6364E-02
1 87.50 7.2285E-02
1 92.50 5.9305E-02
2 100.00 4.6153E-02
3 110.00 3.4525E-02
4 120.00 2.7004E-02
5 130.00 2.2180E-02
6 140.00 1.9085E-02
7 150.00 1.7122E-02
8 160.00 1.5925E-02
9 170.00 1.5279E-02
10 180.00 1.5052E-02
Asymptotic AOP values are
MUu(inf) = 0.3811
MUd(inf) = 0.7079
MU(inf) = 0.6093
R(inf) = 0.0536
Lu(inf)/Ed(inf) = 0.010910 (1/sr)
k(inf) = 0.1927 (1/m)
absorp(check) = 0.1174 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 465.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 2.1105E-01 2.1311E+00 2.3422E+00 8.0053E-02 1.4892E+00 0.3793 0.6988 0.6016 5.3756E-02
1 0.00 0.00 1.5419E-01 1.7292E+00 1.8834E+00 6.5435E-02 1.4746E+00 0.4244 0.8528 0.7482 4.4376E-02
3 3.58 5.00 8.1084E-02 8.3902E-01 9.2010E-01 3.2038E-02 6.3610E-01 0.3951 0.7581 0.6565 5.0366E-02
5 7.16 10.00 3.4673E-02 3.5066E-01 3.8534E-01 1.3424E-02 2.5551E-01 0.3872 0.7287 0.6283 5.2538E-02
K-functions (units of 1/meter) at 465.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.08263 0.11474 0.11211 0.10773 0.15425 0.15641 0.14418
5.000 5.010 5.005 0.15797 0.16530 0.16465 0.16446 0.17757 0.17827 0.17452
10.000 10.010 10.005 0.17850 0.18116 0.18092 0.18093 0.18604 0.18633 0.18491
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 465.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.28363E-01 8.40481E-03 8.42910E-03 1.68339E-02 5.64387E-03 0.065666
9 1 10.0 0.0 180.0 7.92052E-02 8.55139E-03 2.69613E-03 1.12475E-02 5.74231E-03 0.034040
9 4 10.0 45.0 135.0 8.70251E-02 8.51244E-03 3.10798E-03 1.16204E-02 5.71615E-03 0.035714
9 7 10.0 90.0 90.0 1.17578E-01 8.49114E-03 6.19937E-03 1.46905E-02 5.70185E-03 0.052726
8 1 20.0 0.0 180.0 6.22146E-02 8.66218E-03 1.51161E-03 1.01738E-02 5.81670E-03 0.024297
8 4 20.0 45.0 135.0 6.92616E-02 8.57074E-03 1.77032E-03 1.03411E-02 5.75530E-03 0.025560
8 7 20.0 90.0 90.0 1.01846E-01 8.55830E-03 3.78355E-03 1.23419E-02 5.74695E-03 0.037150
7 1 30.0 0.0 180.0 5.39434E-02 8.82618E-03 1.29855E-03 1.01247E-02 5.92683E-03 0.024072
7 4 30.0 45.0 135.0 5.98005E-02 8.80661E-03 1.45774E-03 1.02643E-02 5.91369E-03 0.024377
7 7 30.0 90.0 90.0 8.72468E-02 8.75613E-03 2.46870E-03 1.12248E-02 5.87979E-03 0.028296
6 1 40.0 0.0 180.0 5.12025E-02 8.97598E-03 1.44382E-03 1.04198E-02 6.02742E-03 0.028198
6 4 40.0 45.0 135.0 5.59872E-02 8.94426E-03 1.56591E-03 1.05102E-02 6.00612E-03 0.027969
6 7 40.0 90.0 90.0 7.86051E-02 8.92314E-03 2.26558E-03 1.11887E-02 5.99194E-03 0.028822
5 1 50.0 0.0 180.0 5.36841E-02 9.16911E-03 2.28075E-03 1.14499E-02 6.15711E-03 0.042485
5 4 50.0 45.0 135.0 5.72076E-02 9.09062E-03 2.37612E-03 1.14667E-02 6.10440E-03 0.041535
5 7 50.0 90.0 90.0 7.60432E-02 9.11032E-03 3.07186E-03 1.21822E-02 6.11763E-03 0.040396
4 1 60.0 0.0 180.0 6.37239E-02 9.11316E-03 5.31308E-03 1.44262E-02 6.11954E-03 0.083377
4 4 60.0 45.0 135.0 6.51660E-02 9.02622E-03 5.24657E-03 1.42728E-02 6.06116E-03 0.080511
4 7 60.0 90.0 90.0 8.04715E-02 9.18661E-03 6.12680E-03 1.53134E-02 6.16886E-03 0.076136
3 1 70.0 0.0 180.0 8.84173E-02 8.52815E-03 1.46761E-02 2.32043E-02 5.72670E-03 0.165987
3 4 70.0 45.0 135.0 8.59287E-02 8.54238E-03 1.41212E-02 2.26635E-02 5.73625E-03 0.164336
3 7 70.0 90.0 90.0 9.60663E-02 8.72857E-03 1.53561E-02 2.40847E-02 5.86129E-03 0.159849
2 1 80.0 0.0 180.0 1.50222E-01 7.35708E-03 3.64805E-02 4.38376E-02 4.94032E-03 0.242843
2 4 80.0 45.0 135.0 1.39103E-01 7.35501E-03 3.52842E-02 4.26392E-02 4.93893E-03 0.253655
2 7 80.0 90.0 90.0 1.38200E-01 7.54260E-03 3.69522E-02 4.44948E-02 5.06489E-03 0.267382
1 1 87.5 0.0 180.0 2.42882E-01 5.96003E-03 6.43384E-02 7.02985E-02 4.00219E-03 0.264896
1 4 87.5 45.0 135.0 2.18685E-01 5.67510E-03 6.39412E-02 6.96163E-02 3.81086E-03 0.292389
1 7 87.5 90.0 90.0 1.98955E-01 6.45988E-03 6.54396E-02 7.18995E-02 4.33784E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 465.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.683E-02 1.284E-01 1.566E-01 1.354E-01 2.023E-01 1.130E-02 4.755E+00 8.405E-03 5.644E-03
1 0.00 0.00 1.559E-02 2.391E-01 3.056E-02 3.595E-02 4.946E-02 1.057E-02 4.198E+00
3 3.58 5.00 6.921E-03 3.383E-01 1.803E-02 2.326E-02 3.585E-02 1.088E-02 4.629E+00
5 7.16 10.00 2.807E-03 1.733E-01 8.577E-03 1.075E-02 1.520E-02 1.099E-02 4.782E+00
Waveband 12 of 40 completed in 3.8 sec.
* * * * * Output for wavelength band 13 (470.0 to 480.0 nm; nominal wavelength = 475.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 475.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 470.0 nm to 480.0 nm:
Ed(diffuse) = 4.727E-01 Ed(direct) = 1.039E+00 Ed(total) = 1.512E+00
Absorption Coefficients of Individual Components at 475.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0114 0.0856 0.0126 0.1096
3 3.477 5.000 0.0114 0.0856 0.0126 0.1096
5 6.954 10.000 0.0114 0.0856 0.0126 0.1096
Scattering Coefficients of Individual Components at 475.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0036 0.5822 0.0000 0.5858
3 3.477 5.000 0.0036 0.5822 0.0000 0.5858
5 6.954 10.000 0.0036 0.5822 0.0000 0.5858
Backscattering Coefficients of Individual Components at 475.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00180 0.01164 0.00000 0.01345
3 3.477 5.000 0.00180 0.01164 0.00000 0.01345
5 6.954 10.000 0.00180 0.01164 0.00000 0.01345
Summary of Inherent Optical Properties at 475.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1096 0.5858 0.6954 0.8424 0.01345 0.02295
3 3.477 5.000 0.1096 0.5858 0.6954 0.8424 0.01345 0.02295
5 6.954 10.000 0.1096 0.5858 0.6954 0.8424 0.01345 0.02295
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4576E-01
8 20.00 8.1523E-01
7 30.00 6.4448E-01
6 40.00 4.7446E-01
5 50.00 3.3139E-01
4 60.00 2.2419E-01
3 70.00 1.5001E-01
2 80.00 1.0150E-01
1 87.50 7.6427E-02
1 92.50 6.2827E-02
2 100.00 4.9001E-02
3 110.00 3.6720E-02
4 120.00 2.8735E-02
5 130.00 2.3592E-02
6 140.00 2.0281E-02
7 150.00 1.8174E-02
8 160.00 1.6886E-02
9 170.00 1.6190E-02
10 180.00 1.5945E-02
Asymptotic AOP values are
MUu(inf) = 0.3812
MUd(inf) = 0.7041
MU(inf) = 0.6024
R(inf) = 0.0560
Lu(inf)/Ed(inf) = 0.011365 (1/sr)
k(inf) = 0.1820 (1/m)
absorp(check) = 0.1096 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 475.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 2.1421E-01 2.1546E+00 2.3689E+00 8.2114E-02 1.5117E+00 0.3833 0.7016 0.6035 5.4320E-02
1 0.00 0.00 1.6305E-01 1.7599E+00 1.9230E+00 6.9295E-02 1.4988E+00 0.4250 0.8517 0.7434 4.6232E-02
3 3.48 5.00 9.0144E-02 8.9962E-01 9.8976E-01 3.5694E-02 6.8117E-01 0.3960 0.7572 0.6522 5.2400E-02
5 6.95 10.00 4.0774E-02 3.9771E-01 4.3849E-01 1.5809E-02 2.8900E-01 0.3877 0.7266 0.6230 5.4702E-02
K-functions (units of 1/meter) at 475.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.07670 0.10688 0.10432 0.09995 0.14469 0.14686 0.13501
5.000 5.010 5.005 0.14685 0.15415 0.15348 0.15349 0.16673 0.16747 0.16377
10.000 10.010 10.005 0.16725 0.16993 0.16968 0.16982 0.17507 0.17538 0.17401
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 475.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.27561E-01 8.89241E-03 8.53835E-03 1.74308E-02 5.88246E-03 0.066936
9 1 10.0 0.0 180.0 7.87103E-02 9.04157E-03 2.70103E-03 1.17426E-02 5.98113E-03 0.034316
9 4 10.0 45.0 135.0 8.64814E-02 9.00251E-03 3.11653E-03 1.21190E-02 5.95529E-03 0.036037
9 7 10.0 90.0 90.0 1.16844E-01 8.98515E-03 6.26082E-03 1.52460E-02 5.94381E-03 0.053583
8 1 20.0 0.0 180.0 6.18259E-02 9.15670E-03 1.50327E-03 1.06600E-02 6.05729E-03 0.024315
8 4 20.0 45.0 135.0 6.88288E-02 9.06358E-03 1.76211E-03 1.08257E-02 5.99569E-03 0.025601
8 7 20.0 90.0 90.0 1.01210E-01 9.05890E-03 3.79801E-03 1.28569E-02 5.99259E-03 0.037526
7 1 30.0 0.0 180.0 5.36063E-02 9.32910E-03 1.29043E-03 1.06195E-02 6.17134E-03 0.024072
7 4 30.0 45.0 135.0 5.94277E-02 9.31336E-03 1.44877E-03 1.07621E-02 6.16092E-03 0.024379
7 7 30.0 90.0 90.0 8.66965E-02 9.27169E-03 2.46077E-03 1.17325E-02 6.13336E-03 0.028384
6 1 40.0 0.0 180.0 5.08826E-02 9.48785E-03 1.43480E-03 1.09227E-02 6.27635E-03 0.028198
6 4 40.0 45.0 135.0 5.56374E-02 9.46082E-03 1.55613E-03 1.10170E-02 6.25847E-03 0.027969
6 7 40.0 90.0 90.0 7.81140E-02 9.45381E-03 2.25191E-03 1.17057E-02 6.25383E-03 0.028829
5 1 50.0 0.0 180.0 5.33487E-02 9.69306E-03 2.26650E-03 1.19596E-02 6.41210E-03 0.042485
5 4 50.0 45.0 135.0 5.68502E-02 9.61765E-03 2.36127E-03 1.19789E-02 6.36222E-03 0.041535
5 7 50.0 90.0 90.0 7.55680E-02 9.65619E-03 3.05267E-03 1.27089E-02 6.38771E-03 0.040396
4 1 60.0 0.0 180.0 6.33257E-02 9.63498E-03 5.27988E-03 1.49149E-02 6.37368E-03 0.083377
4 4 60.0 45.0 135.0 6.47589E-02 9.55138E-03 5.21379E-03 1.47652E-02 6.31838E-03 0.080511
4 7 60.0 90.0 90.0 7.99687E-02 9.74050E-03 6.08852E-03 1.58290E-02 6.44348E-03 0.076136
3 1 70.0 0.0 180.0 8.78649E-02 9.01713E-03 1.45844E-02 2.36016E-02 5.96496E-03 0.165987
3 4 70.0 45.0 135.0 8.53918E-02 9.04053E-03 1.40329E-02 2.30735E-02 5.98044E-03 0.164336
3 7 70.0 90.0 90.0 9.54660E-02 9.25670E-03 1.52602E-02 2.45169E-02 6.12344E-03 0.159849
2 1 80.0 0.0 180.0 1.49284E-01 7.77902E-03 3.62526E-02 4.40316E-02 5.14593E-03 0.242843
2 4 80.0 45.0 135.0 1.38234E-01 7.78429E-03 3.50637E-02 4.28480E-02 5.14942E-03 0.253655
2 7 80.0 90.0 90.0 1.37336E-01 7.99955E-03 3.67213E-02 4.47208E-02 5.29182E-03 0.267382
1 1 87.5 0.0 180.0 2.41364E-01 6.30132E-03 6.39364E-02 7.02377E-02 4.16841E-03 0.264896
1 4 87.5 45.0 135.0 2.17319E-01 6.00590E-03 6.35417E-02 6.95476E-02 3.97299E-03 0.292389
1 7 87.5 90.0 90.0 1.97712E-01 6.85046E-03 6.50307E-02 7.18812E-02 4.53168E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 475.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.743E-02 1.276E-01 1.558E-01 1.348E-01 2.013E-01 1.153E-02 4.711E+00 8.892E-03 5.882E-03
1 0.00 0.00 1.649E-02 2.376E-01 3.218E-02 3.791E-02 5.211E-02 1.100E-02 4.202E+00
3 3.48 5.00 7.707E-03 3.565E-01 1.984E-02 2.562E-02 3.957E-02 1.131E-02 4.631E+00
5 6.95 10.00 3.301E-03 1.934E-01 9.982E-03 1.255E-02 1.783E-02 1.142E-02 4.789E+00
Waveband 13 of 40 completed in 3.7 sec.
* * * * * Output for wavelength band 14 (480.0 to 490.0 nm; nominal wavelength = 485.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 485.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 480.0 nm to 490.0 nm:
Ed(diffuse) = 4.491E-01 Ed(direct) = 1.015E+00 Ed(total) = 1.464E+00
Absorption Coefficients of Individual Components at 485.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0136 0.0794 0.0110 0.1040
3 3.387 5.000 0.0136 0.0794 0.0110 0.1040
5 6.775 10.000 0.0136 0.0794 0.0110 0.1040
Scattering Coefficients of Individual Components at 485.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0033 0.5702 0.0000 0.5735
3 3.387 5.000 0.0033 0.5702 0.0000 0.5735
5 6.775 10.000 0.0033 0.5702 0.0000 0.5735
Backscattering Coefficients of Individual Components at 485.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00165 0.01140 0.00000 0.01305
3 3.387 5.000 0.00165 0.01140 0.00000 0.01305
5 6.775 10.000 0.00165 0.01140 0.00000 0.01305
Summary of Inherent Optical Properties at 485.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1040 0.5735 0.6775 0.8465 0.01305 0.02276
3 3.387 5.000 0.1040 0.5735 0.6775 0.8465 0.01305 0.02276
5 6.775 10.000 0.1040 0.5735 0.6775 0.8465 0.01305 0.02276
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4676E-01
8 20.00 8.1837E-01
7 30.00 6.4971E-01
6 40.00 4.8081E-01
5 50.00 3.3773E-01
4 60.00 2.2976E-01
3 70.00 1.5450E-01
2 80.00 1.0497E-01
1 87.50 7.9239E-02
1 92.50 6.5220E-02
2 100.00 5.0934E-02
3 110.00 3.8206E-02
4 120.00 2.9902E-02
5 130.00 2.4538E-02
6 140.00 2.1077E-02
7 150.00 1.8870E-02
8 160.00 1.7519E-02
9 170.00 1.6788E-02
10 180.00 1.6531E-02
Asymptotic AOP values are
MUu(inf) = 0.3812
MUd(inf) = 0.7016
MU(inf) = 0.5978
R(inf) = 0.0576
Lu(inf)/Ed(inf) = 0.011654 (1/sr)
k(inf) = 0.1739 (1/m)
absorp(check) = 0.1040 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 485.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 2.0688E-01 2.0794E+00 2.2863E+00 7.9967E-02 1.4641E+00 0.3865 0.7041 0.6054 5.4619E-02
1 0.00 0.00 1.6201E-01 1.7073E+00 1.8693E+00 6.8912E-02 1.4530E+00 0.4254 0.8511 0.7404 4.7427E-02
3 3.39 5.00 9.2919E-02 9.0669E-01 9.9961E-01 3.6847E-02 6.8638E-01 0.3965 0.7570 0.6498 5.3683E-02
5 6.77 10.00 4.3836E-02 4.1802E-01 4.6186E-01 1.7011E-02 3.0335E-01 0.3881 0.7257 0.6200 5.6076E-02
K-functions (units of 1/meter) at 485.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.07227 0.10119 0.09868 0.09433 0.13766 0.13981 0.12829
5.000 5.010 5.005 0.13856 0.14585 0.14518 0.14531 0.15865 0.15941 0.15575
10.000 10.010 10.005 0.15881 0.16152 0.16126 0.16147 0.16686 0.16718 0.16583
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 485.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.21185E-01 8.83404E-03 8.25403E-03 1.70881E-02 6.03378E-03 0.068111
9 1 10.0 0.0 180.0 7.47760E-02 8.97775E-03 2.58514E-03 1.15629E-02 6.13193E-03 0.034572
9 4 10.0 45.0 135.0 8.21586E-02 8.94056E-03 2.98536E-03 1.19259E-02 6.10654E-03 0.036337
9 7 10.0 90.0 90.0 1.11003E-01 8.92722E-03 6.03602E-03 1.49632E-02 6.09742E-03 0.054377
8 1 20.0 0.0 180.0 5.87355E-02 9.09056E-03 1.42909E-03 1.05197E-02 6.20899E-03 0.024331
8 4 20.0 45.0 135.0 6.53884E-02 9.00076E-03 1.67654E-03 1.06773E-02 6.14765E-03 0.025640
8 7 20.0 90.0 90.0 9.61506E-02 9.00253E-03 3.64169E-03 1.26442E-02 6.14886E-03 0.037875
7 1 30.0 0.0 180.0 5.09268E-02 9.26100E-03 1.22593E-03 1.04869E-02 6.32540E-03 0.024072
7 4 30.0 45.0 135.0 5.64580E-02 9.24908E-03 1.37647E-03 1.06255E-02 6.31726E-03 0.024380
7 7 30.0 90.0 90.0 8.23585E-02 9.21659E-03 2.34436E-03 1.15609E-02 6.29507E-03 0.028465
6 1 40.0 0.0 180.0 4.83392E-02 9.41892E-03 1.36308E-03 1.07820E-02 6.43326E-03 0.028198
6 4 40.0 45.0 135.0 5.28563E-02 9.39696E-03 1.47835E-03 1.08753E-02 6.41827E-03 0.027969
6 7 40.0 90.0 90.0 7.42095E-02 9.40173E-03 2.13978E-03 1.15415E-02 6.42152E-03 0.028834
5 1 50.0 0.0 180.0 5.06821E-02 9.62345E-03 2.15321E-03 1.17767E-02 6.57296E-03 0.042485
5 4 50.0 45.0 135.0 5.40086E-02 9.55431E-03 2.24325E-03 1.17976E-02 6.52574E-03 0.041535
5 7 50.0 90.0 90.0 7.17908E-02 9.60628E-03 2.90008E-03 1.25064E-02 6.56123E-03 0.040396
4 1 60.0 0.0 180.0 6.01604E-02 9.56664E-03 5.01597E-03 1.45826E-02 6.53416E-03 0.083377
4 4 60.0 45.0 135.0 6.15219E-02 9.48996E-03 4.95318E-03 1.44431E-02 6.48178E-03 0.080511
4 7 60.0 90.0 90.0 7.59715E-02 9.69302E-03 5.78419E-03 1.54772E-02 6.62048E-03 0.076136
3 1 70.0 0.0 180.0 8.34730E-02 8.95377E-03 1.38554E-02 2.28092E-02 6.11556E-03 0.165987
3 4 70.0 45.0 135.0 8.11235E-02 8.98341E-03 1.33315E-02 2.23149E-02 6.13580E-03 0.164336
3 7 70.0 90.0 90.0 9.06942E-02 9.21341E-03 1.44974E-02 2.37108E-02 6.29290E-03 0.159849
2 1 80.0 0.0 180.0 1.41822E-01 7.72456E-03 3.44405E-02 4.21650E-02 5.27599E-03 0.242843
2 4 80.0 45.0 135.0 1.31324E-01 7.73557E-03 3.33111E-02 4.10467E-02 5.28351E-03 0.253655
2 7 80.0 90.0 90.0 1.30472E-01 7.96297E-03 3.48858E-02 4.28487E-02 5.43883E-03 0.267382
1 1 87.5 0.0 180.0 2.29300E-01 6.25695E-03 6.07406E-02 6.69975E-02 4.27359E-03 0.264896
1 4 87.5 45.0 135.0 2.06456E-01 5.96816E-03 6.03656E-02 6.63337E-02 4.07634E-03 0.292389
1 7 87.5 90.0 90.0 1.87830E-01 6.81896E-03 6.17802E-02 6.85992E-02 4.65745E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 485.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.709E-02 1.212E-01 1.481E-01 1.282E-01 1.914E-01 1.167E-02 4.680E+00 8.834E-03 6.034E-03
1 0.00 0.00 1.638E-02 2.257E-01 3.187E-02 3.760E-02 5.170E-02 1.128E-02 4.206E+00
3 3.39 5.00 7.953E-03 3.542E-01 2.029E-02 2.624E-02 4.061E-02 1.159E-02 4.633E+00
5 6.77 10.00 3.547E-03 2.008E-01 1.064E-02 1.342E-02 1.917E-02 1.169E-02 4.795E+00
Waveband 14 of 40 completed in 3.6 sec.
* * * * * Output for wavelength band 15 (490.0 to 500.0 nm; nominal wavelength = 495.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 495.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 490.0 nm to 500.0 nm:
Ed(diffuse) = 4.478E-01 Ed(direct) = 1.039E+00 Ed(total) = 1.487E+00
Absorption Coefficients of Individual Components at 495.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0173 0.0732 0.0095 0.1001
3 3.309 5.000 0.0173 0.0732 0.0095 0.1001
5 6.617 10.000 0.0173 0.0732 0.0095 0.1001
Scattering Coefficients of Individual Components at 495.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0030 0.5587 0.0000 0.5617
3 3.309 5.000 0.0030 0.5587 0.0000 0.5617
5 6.617 10.000 0.0030 0.5587 0.0000 0.5617
Backscattering Coefficients of Individual Components at 495.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00151 0.01117 0.00000 0.01268
3 3.309 5.000 0.00151 0.01117 0.00000 0.01268
5 6.617 10.000 0.00151 0.01117 0.00000 0.01268
Summary of Inherent Optical Properties at 495.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1001 0.5617 0.6617 0.8488 0.01268 0.02258
3 3.309 5.000 0.1001 0.5617 0.6617 0.8488 0.01268 0.02258
5 6.617 10.000 0.1001 0.5617 0.6617 0.8488 0.01268 0.02258
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4731E-01
8 20.00 8.2010E-01
7 30.00 6.5260E-01
6 40.00 4.8433E-01
5 50.00 3.4125E-01
4 60.00 2.3285E-01
3 70.00 1.5700E-01
2 80.00 1.0690E-01
1 87.50 8.0786E-02
1 92.50 6.6529E-02
2 100.00 5.1983E-02
3 110.00 3.9002E-02
4 120.00 3.0517E-02
5 130.00 2.5028E-02
6 140.00 2.1482E-02
7 150.00 1.9218E-02
8 160.00 1.7831E-02
9 170.00 1.7080E-02
10 180.00 1.6816E-02
Asymptotic AOP values are
MUu(inf) = 0.3811
MUd(inf) = 0.7002
MU(inf) = 0.5955
R(inf) = 0.0584
Lu(inf)/Ed(inf) = 0.011784 (1/sr)
k(inf) = 0.1680 (1/m)
absorp(check) = 0.1001 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 495.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 2.0875E-01 2.1044E+00 2.3131E+00 8.1212E-02 1.4866E+00 0.3890 0.7064 0.6076 5.4629E-02
1 0.00 0.00 1.6633E-01 1.7346E+00 1.9009E+00 7.0760E-02 1.4761E+00 0.4254 0.8510 0.7393 4.7936E-02
3 3.31 5.00 9.7964E-02 9.4658E-01 1.0445E+00 3.8876E-02 7.1710E-01 0.3968 0.7576 0.6493 5.4212E-02
5 6.62 10.00 4.7674E-02 4.5000E-01 4.9767E-01 1.8506E-02 3.2655E-01 0.3882 0.7257 0.6190 5.6672E-02
K-functions (units of 1/meter) at 495.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.06897 0.09716 0.09469 0.09028 0.13261 0.13474 0.12343
5.000 5.010 5.005 0.13247 0.13983 0.13914 0.13930 0.15276 0.15353 0.14983
10.000 10.010 10.005 0.15255 0.15534 0.15507 0.15529 0.16083 0.16117 0.15977
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 495.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.20839E-01 9.05905E-03 8.36643E-03 1.74255E-02 6.09374E-03 0.069236
9 1 10.0 0.0 180.0 7.45626E-02 9.20319E-03 2.59601E-03 1.17992E-02 6.19070E-03 0.034817
9 4 10.0 45.0 135.0 8.19242E-02 9.16622E-03 3.00032E-03 1.21665E-02 6.16583E-03 0.036623
9 7 10.0 90.0 90.0 1.10686E-01 9.15539E-03 6.10292E-03 1.52583E-02 6.15855E-03 0.055137
8 1 20.0 0.0 180.0 5.85679E-02 9.31781E-03 1.42594E-03 1.07438E-02 6.26780E-03 0.024347
8 4 20.0 45.0 135.0 6.52019E-02 9.22766E-03 1.67414E-03 1.09018E-02 6.20716E-03 0.025676
8 7 20.0 90.0 90.0 9.58762E-02 9.23420E-03 3.66329E-03 1.28975E-02 6.21156E-03 0.038209
7 1 30.0 0.0 180.0 5.07815E-02 9.49206E-03 1.22243E-03 1.07145E-02 6.38502E-03 0.024072
7 4 30.0 45.0 135.0 5.62976E-02 9.48248E-03 1.37266E-03 1.08551E-02 6.37857E-03 0.024382
7 7 30.0 90.0 90.0 8.21193E-02 9.45578E-03 2.34396E-03 1.17997E-02 6.36061E-03 0.028543
6 1 40.0 0.0 180.0 4.82013E-02 9.65424E-03 1.35919E-03 1.10134E-02 6.49411E-03 0.028198
6 4 40.0 45.0 135.0 5.27055E-02 9.63525E-03 1.47413E-03 1.11094E-02 6.48133E-03 0.027969
6 7 40.0 90.0 90.0 7.39977E-02 9.64902E-03 2.13408E-03 1.17831E-02 6.49060E-03 0.028840
5 1 50.0 0.0 180.0 5.05375E-02 9.86458E-03 2.14706E-03 1.20116E-02 6.63560E-03 0.042485
5 4 50.0 45.0 135.0 5.38545E-02 9.79788E-03 2.23684E-03 1.20347E-02 6.59073E-03 0.041535
5 7 50.0 90.0 90.0 7.15860E-02 9.86181E-03 2.89181E-03 1.27536E-02 6.63374E-03 0.040396
4 1 60.0 0.0 180.0 5.99887E-02 9.80707E-03 5.00165E-03 1.48087E-02 6.59691E-03 0.083377
4 4 60.0 45.0 135.0 6.13464E-02 9.73316E-03 4.93904E-03 1.46722E-02 6.54719E-03 0.080511
4 7 60.0 90.0 90.0 7.57547E-02 9.95351E-03 5.76768E-03 1.57212E-02 6.69542E-03 0.076136
3 1 70.0 0.0 180.0 8.32348E-02 9.17942E-03 1.38159E-02 2.29953E-02 6.17471E-03 0.165987
3 4 70.0 45.0 135.0 8.08921E-02 9.21466E-03 1.32935E-02 2.25081E-02 6.19842E-03 0.164336
3 7 70.0 90.0 90.0 9.04354E-02 9.46312E-03 1.44560E-02 2.39191E-02 6.36555E-03 0.159849
2 1 80.0 0.0 180.0 1.41417E-01 7.91956E-03 3.43422E-02 4.22618E-02 5.32724E-03 0.242843
2 4 80.0 45.0 135.0 1.30950E-01 7.93532E-03 3.32161E-02 4.11514E-02 5.33784E-03 0.253655
2 7 80.0 90.0 90.0 1.30099E-01 8.18007E-03 3.47862E-02 4.29663E-02 5.50248E-03 0.267382
1 1 87.5 0.0 180.0 2.28646E-01 6.41490E-03 6.05673E-02 6.69822E-02 4.31510E-03 0.264896
1 4 87.5 45.0 135.0 2.05867E-01 6.12243E-03 6.01933E-02 6.63158E-02 4.11837E-03 0.292389
1 7 87.5 90.0 90.0 1.87294E-01 7.00542E-03 6.16039E-02 6.86093E-02 4.71233E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 495.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.743E-02 1.208E-01 1.478E-01 1.280E-01 1.910E-01 1.172E-02 4.661E+00 9.059E-03 6.094E-03
1 0.00 0.00 1.680E-02 2.251E-01 3.263E-02 3.857E-02 5.311E-02 1.138E-02 4.212E+00
3 3.31 5.00 8.385E-03 3.654E-01 2.126E-02 2.755E-02 4.277E-02 1.169E-02 4.636E+00
5 6.62 10.00 3.854E-03 2.145E-01 1.149E-02 1.454E-02 2.089E-02 1.180E-02 4.801E+00
Waveband 15 of 40 completed in 3.6 sec.
* * * * * Output for wavelength band 16 (500.0 to 510.0 nm; nominal wavelength = 505.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 505.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 500.0 nm to 510.0 nm:
Ed(diffuse) = 4.326E-01 Ed(direct) = 1.028E+00 Ed(total) = 1.460E+00
Absorption Coefficients of Individual Components at 505.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0256 0.0660 0.0083 0.0999
3 3.251 5.000 0.0256 0.0660 0.0083 0.0999
5 6.503 10.000 0.0256 0.0660 0.0083 0.0999
Scattering Coefficients of Individual Components at 505.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0028 0.5476 0.0000 0.5504
3 3.251 5.000 0.0028 0.5476 0.0000 0.5504
5 6.503 10.000 0.0028 0.5476 0.0000 0.5504
Backscattering Coefficients of Individual Components at 505.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00138 0.01095 0.00000 0.01234
3 3.251 5.000 0.00138 0.01095 0.00000 0.01234
5 6.503 10.000 0.00138 0.01095 0.00000 0.01234
Summary of Inherent Optical Properties at 505.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0999 0.5504 0.6503 0.8464 0.01234 0.02241
3 3.251 5.000 0.0999 0.5504 0.6503 0.8464 0.01234 0.02241
5 6.503 10.000 0.0999 0.5504 0.6503 0.8464 0.01234 0.02241
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4673E-01
8 20.00 8.1827E-01
7 30.00 6.4951E-01
6 40.00 4.8052E-01
5 50.00 3.3737E-01
4 60.00 2.2936E-01
3 70.00 1.5410E-01
2 80.00 1.0458E-01
1 87.50 7.8862E-02
1 92.50 6.4854E-02
2 100.00 5.0585E-02
3 110.00 3.7878E-02
4 120.00 2.9592E-02
5 130.00 2.4242E-02
6 140.00 2.0792E-02
7 150.00 1.8592E-02
8 160.00 1.7245E-02
9 170.00 1.6517E-02
10 180.00 1.6260E-02
Asymptotic AOP values are
MUu(inf) = 0.3804
MUd(inf) = 0.7019
MU(inf) = 0.5990
R(inf) = 0.0570
Lu(inf)/Ed(inf) = 0.011471 (1/sr)
k(inf) = 0.1668 (1/m)
absorp(check) = 0.0999 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 505.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 2.0182E-01 2.0611E+00 2.2630E+00 7.8720E-02 1.4605E+00 0.3900 0.7086 0.6106 5.3900E-02
1 0.00 0.00 1.5951E-01 1.7005E+00 1.8600E+00 6.7767E-02 1.4495E+00 0.4248 0.8524 0.7429 4.6752E-02
3 3.25 5.00 9.4377E-02 9.3159E-01 1.0260E+00 3.7407E-02 7.0791E-01 0.3964 0.7599 0.6535 5.2841E-02
5 6.50 10.00 4.6243E-02 4.4572E-01 4.9196E-01 1.7926E-02 3.2444E-01 0.3877 0.7279 0.6231 5.5253E-02
K-functions (units of 1/meter) at 505.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.06829 0.09662 0.09419 0.08978 0.13181 0.13387 0.12272
5.000 5.010 5.005 0.13121 0.13868 0.13799 0.13806 0.15153 0.15228 0.14862
10.000 10.010 10.005 0.15113 0.15399 0.15372 0.15391 0.15952 0.15985 0.15845
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 505.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.16731E-01 8.65975E-03 8.20628E-03 1.68660E-02 5.92939E-03 0.070301
9 1 10.0 0.0 180.0 7.20279E-02 8.79747E-03 2.52445E-03 1.13219E-02 6.02369E-03 0.035048
9 4 10.0 45.0 135.0 7.91393E-02 8.76211E-03 2.91979E-03 1.16819E-02 5.99948E-03 0.036894
9 7 10.0 90.0 90.0 1.06924E-01 8.75187E-03 5.97233E-03 1.47242E-02 5.99246E-03 0.055856
8 1 20.0 0.0 180.0 5.65770E-02 8.90708E-03 1.37831E-03 1.02854E-02 6.09874E-03 0.024362
8 4 20.0 45.0 135.0 6.29854E-02 8.82084E-03 1.61942E-03 1.04403E-02 6.03969E-03 0.025711
8 7 20.0 90.0 90.0 9.26170E-02 8.82737E-03 3.56800E-03 1.23954E-02 6.04416E-03 0.038524
7 1 30.0 0.0 180.0 4.90553E-02 9.07371E-03 1.18088E-03 1.02546E-02 6.21283E-03 0.024072
7 4 30.0 45.0 135.0 5.43844E-02 9.06448E-03 1.32610E-03 1.03906E-02 6.20651E-03 0.024384
7 7 30.0 90.0 90.0 7.93238E-02 9.03951E-03 2.27003E-03 1.13095E-02 6.18942E-03 0.028617
6 1 40.0 0.0 180.0 4.65627E-02 9.22885E-03 1.31299E-03 1.05418E-02 6.31906E-03 0.028198
6 4 40.0 45.0 135.0 5.09138E-02 9.21068E-03 1.42402E-03 1.06347E-02 6.30662E-03 0.027969
6 7 40.0 90.0 90.0 7.14822E-02 9.22508E-03 2.06191E-03 1.12870E-02 6.31647E-03 0.028845
5 1 50.0 0.0 180.0 4.88195E-02 9.43017E-03 2.07407E-03 1.15042E-02 6.45690E-03 0.042485
5 4 50.0 45.0 135.0 5.20237E-02 9.36656E-03 2.16080E-03 1.15274E-02 6.41335E-03 0.041535
5 7 50.0 90.0 90.0 6.91524E-02 9.42988E-03 2.79351E-03 1.22234E-02 6.45671E-03 0.040396
4 1 60.0 0.0 180.0 5.79495E-02 9.37555E-03 4.83163E-03 1.42072E-02 6.41950E-03 0.083377
4 4 60.0 45.0 135.0 5.92610E-02 9.30526E-03 4.77115E-03 1.40764E-02 6.37137E-03 0.080511
4 7 60.0 90.0 90.0 7.31795E-02 9.51924E-03 5.57162E-03 1.50909E-02 6.51789E-03 0.076136
3 1 70.0 0.0 180.0 8.04053E-02 8.77617E-03 1.33462E-02 2.21224E-02 6.00911E-03 0.165987
3 4 70.0 45.0 135.0 7.81422E-02 8.81057E-03 1.28416E-02 2.16521E-02 6.03265E-03 0.164336
3 7 70.0 90.0 90.0 8.73611E-02 9.05269E-03 1.39646E-02 2.30173E-02 6.19844E-03 0.159849
2 1 80.0 0.0 180.0 1.36610E-01 7.57234E-03 3.31748E-02 4.07471E-02 5.18483E-03 0.242843
2 4 80.0 45.0 135.0 1.26498E-01 7.58833E-03 3.20869E-02 3.96752E-02 5.19578E-03 0.253655
2 7 80.0 90.0 90.0 1.25677E-01 7.82745E-03 3.36037E-02 4.14312E-02 5.35951E-03 0.267382
1 1 87.5 0.0 180.0 2.20873E-01 6.13440E-03 5.85083E-02 6.46427E-02 4.20027E-03 0.264896
1 4 87.5 45.0 135.0 1.98869E-01 5.85570E-03 5.81471E-02 6.40028E-02 4.00944E-03 0.292389
1 7 87.5 90.0 90.0 1.80927E-01 6.70564E-03 5.95098E-02 6.62154E-02 4.59140E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 505.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.687E-02 1.167E-01 1.428E-01 1.236E-01 1.845E-01 1.155E-02 4.667E+00 8.660E-03 5.929E-03
1 0.00 0.00 1.606E-02 2.175E-01 3.125E-02 3.703E-02 5.120E-02 1.108E-02 4.219E+00
3 3.25 5.00 8.057E-03 3.575E-01 2.045E-02 2.658E-02 4.148E-02 1.138E-02 4.643E+00
5 6.50 10.00 3.727E-03 2.127E-01 1.112E-02 1.413E-02 2.043E-02 1.149E-02 4.810E+00
Waveband 16 of 40 completed in 3.6 sec.
* * * * * Output for wavelength band 17 (510.0 to 520.0 nm; nominal wavelength = 515.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 515.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 510.0 nm to 520.0 nm:
Ed(diffuse) = 4.102E-01 Ed(direct) = 9.960E-01 Ed(total) = 1.406E+00
Absorption Coefficients of Individual Components at 515.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0396 0.0598 0.0072 0.1066
3 3.231 5.000 0.0396 0.0598 0.0072 0.1066
5 6.461 10.000 0.0396 0.0598 0.0072 0.1066
Scattering Coefficients of Individual Components at 515.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0025 0.5370 0.0000 0.5395
3 3.231 5.000 0.0025 0.5370 0.0000 0.5395
5 6.461 10.000 0.0025 0.5370 0.0000 0.5395
Backscattering Coefficients of Individual Components at 515.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00127 0.01074 0.00000 0.01201
3 3.231 5.000 0.00127 0.01074 0.00000 0.01201
5 6.461 10.000 0.00127 0.01074 0.00000 0.01201
Summary of Inherent Optical Properties at 515.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1066 0.5395 0.6461 0.8350 0.01201 0.02226
3 3.231 5.000 0.1066 0.5395 0.6461 0.8350 0.01201 0.02226
5 6.461 10.000 0.1066 0.5395 0.6461 0.8350 0.01201 0.02226
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4399E-01
8 20.00 8.0969E-01
7 30.00 6.3522E-01
6 40.00 4.6316E-01
5 50.00 3.2002E-01
4 60.00 2.1409E-01
3 70.00 1.4168E-01
2 80.00 9.4893E-02
1 87.50 7.0954E-02
1 92.50 5.8064E-02
2 100.00 4.5024E-02
3 110.00 3.3515E-02
4 120.00 2.6083E-02
5 130.00 2.1325E-02
6 140.00 1.8277E-02
7 150.00 1.6345E-02
8 160.00 1.5167E-02
9 170.00 1.4533E-02
10 180.00 1.4310E-02
Asymptotic AOP values are
MUu(inf) = 0.3787
MUd(inf) = 0.7091
MU(inf) = 0.6129
R(inf) = 0.0518
Lu(inf)/Ed(inf) = 0.010407 (1/sr)
k(inf) = 0.1740 (1/m)
absorp(check) = 0.1066 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 515.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.8787E-01 1.9792E+00 2.1671E+00 7.2988E-02 1.4062E+00 0.3885 0.7105 0.6152 5.1903E-02
1 0.00 0.00 1.4043E-01 1.6263E+00 1.7668E+00 5.9404E-02 1.3926E+00 0.4230 0.8563 0.7546 4.2656E-02
3 3.23 5.00 8.0201E-02 8.5731E-01 9.3751E-01 3.1640E-02 6.5621E-01 0.3945 0.7654 0.6662 4.8216E-02
5 6.46 10.00 3.7875E-02 3.9507E-01 4.3294E-01 1.4619E-02 2.9009E-01 0.3860 0.7343 0.6363 5.0394E-02
K-functions (units of 1/meter) at 515.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.07212 0.10261 0.10019 0.09571 0.13875 0.14067 0.12953
5.000 5.010 5.005 0.13864 0.14632 0.14566 0.14540 0.15875 0.15943 0.15585
10.000 10.010 10.005 0.15846 0.16140 0.16114 0.16119 0.16673 0.16702 0.16567
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 515.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.10700E-01 7.56984E-03 7.89040E-03 1.54602E-02 5.38300E-03 0.071277
9 1 10.0 0.0 180.0 6.83067E-02 7.69502E-03 2.40853E-03 1.01035E-02 5.47201E-03 0.035261
9 4 10.0 45.0 135.0 7.50506E-02 7.66227E-03 2.78762E-03 1.04499E-02 5.44873E-03 0.037143
9 7 10.0 90.0 90.0 1.01400E-01 7.64918E-03 5.73065E-03 1.33798E-02 5.43942E-03 0.056516
8 1 20.0 0.0 180.0 5.36540E-02 7.79254E-03 1.30784E-03 9.10037E-03 5.54136E-03 0.024375
8 4 20.0 45.0 135.0 5.97313E-02 7.71404E-03 1.53765E-03 9.25169E-03 5.48554E-03 0.025743
8 7 20.0 90.0 90.0 8.78321E-02 7.71311E-03 3.40910E-03 1.11222E-02 5.48488E-03 0.038814
7 1 30.0 0.0 180.0 4.65209E-02 7.93911E-03 1.11987E-03 9.05898E-03 5.64559E-03 0.024072
7 4 30.0 45.0 135.0 5.15753E-02 7.92677E-03 1.25768E-03 9.18445E-03 5.63682E-03 0.024385
7 7 30.0 90.0 90.0 7.52222E-02 7.89609E-03 2.15775E-03 1.00538E-02 5.61500E-03 0.028685
6 1 40.0 0.0 180.0 4.41571E-02 8.07451E-03 1.24515E-03 9.31966E-03 5.74188E-03 0.028198
6 4 40.0 45.0 135.0 4.82834E-02 8.05313E-03 1.35045E-03 9.40357E-03 5.72667E-03 0.027969
6 7 40.0 90.0 90.0 6.77892E-02 8.05503E-03 1.95571E-03 1.00107E-02 5.72803E-03 0.028850
5 1 50.0 0.0 180.0 4.62973E-02 8.25001E-03 1.96692E-03 1.02169E-02 5.86667E-03 0.042485
5 4 50.0 45.0 135.0 4.93360E-02 8.18827E-03 2.04917E-03 1.02374E-02 5.82278E-03 0.041535
5 7 50.0 90.0 90.0 6.55798E-02 8.23271E-03 2.64918E-03 1.08819E-02 5.85437E-03 0.040396
4 1 60.0 0.0 180.0 5.49556E-02 8.20178E-03 4.58201E-03 1.27838E-02 5.83238E-03 0.083377
4 4 60.0 45.0 135.0 5.61993E-02 8.13396E-03 4.52465E-03 1.26586E-02 5.78415E-03 0.080511
4 7 60.0 90.0 90.0 6.93988E-02 8.31063E-03 5.28376E-03 1.35944E-02 5.90978E-03 0.076136
3 1 70.0 0.0 180.0 7.62513E-02 7.67790E-03 1.26567E-02 2.03346E-02 5.45984E-03 0.165987
3 4 70.0 45.0 135.0 7.41051E-02 7.70222E-03 1.21781E-02 1.98803E-02 5.47714E-03 0.164336
3 7 70.0 90.0 90.0 8.28477E-02 7.90598E-03 1.32431E-02 2.11491E-02 5.62203E-03 0.159849
2 1 80.0 0.0 180.0 1.29552E-01 6.62571E-03 3.14609E-02 3.80866E-02 4.71162E-03 0.242843
2 4 80.0 45.0 135.0 1.19963E-01 6.63510E-03 3.04292E-02 3.70643E-02 4.71829E-03 0.253655
2 7 80.0 90.0 90.0 1.19184E-01 6.83921E-03 3.18676E-02 3.87068E-02 4.86344E-03 0.267382
1 1 87.5 0.0 180.0 2.09462E-01 5.36925E-03 5.54856E-02 6.08548E-02 3.81813E-03 0.264896
1 4 87.5 45.0 135.0 1.88595E-01 5.12216E-03 5.51430E-02 6.02652E-02 3.64242E-03 0.292389
1 7 87.5 90.0 90.0 1.71580E-01 5.86357E-03 5.64353E-02 6.22988E-02 4.16965E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 515.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.546E-02 1.107E-01 1.352E-01 1.169E-01 1.747E-01 1.099E-02 4.721E+00 7.570E-03 5.383E-03
1 0.00 0.00 1.404E-02 2.062E-01 2.756E-02 3.278E-02 4.572E-02 1.008E-02 4.231E+00
3 3.23 5.00 6.796E-03 3.305E-01 1.750E-02 2.288E-02 3.602E-02 1.036E-02 4.656E+00
5 6.46 10.00 3.032E-03 1.918E-01 9.165E-03 1.170E-02 1.708E-02 1.045E-02 4.821E+00
Waveband 17 of 40 completed in 3.7 sec.
* * * * * Output for wavelength band 18 (520.0 to 530.0 nm; nominal wavelength = 525.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 525.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 520.0 nm to 530.0 nm:
Ed(diffuse) = 4.132E-01 Ed(direct) = 1.024E+00 Ed(total) = 1.437E+00
Absorption Coefficients of Individual Components at 525.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0417 0.0516 0.0063 0.0995
3 3.143 5.000 0.0417 0.0516 0.0063 0.0995
5 6.286 10.000 0.0417 0.0516 0.0063 0.0995
Scattering Coefficients of Individual Components at 525.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0023 0.5267 0.0000 0.5291
3 3.143 5.000 0.0023 0.5267 0.0000 0.5291
5 6.286 10.000 0.0023 0.5267 0.0000 0.5291
Backscattering Coefficients of Individual Components at 525.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00117 0.01053 0.00000 0.01170
3 3.143 5.000 0.00117 0.01053 0.00000 0.01170
5 6.286 10.000 0.00117 0.01053 0.00000 0.01170
Summary of Inherent Optical Properties at 525.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0995 0.5291 0.6286 0.8417 0.01170 0.02212
3 3.143 5.000 0.0995 0.5291 0.6286 0.8417 0.01170 0.02212
5 6.286 10.000 0.0995 0.5291 0.6286 0.8417 0.01170 0.02212
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4560E-01
8 20.00 8.1471E-01
7 30.00 6.4354E-01
6 40.00 4.7320E-01
5 50.00 3.2997E-01
4 60.00 2.2276E-01
3 70.00 1.4865E-01
2 80.00 1.0026E-01
1 87.50 7.5286E-02
1 92.50 6.1751E-02
2 100.00 4.8007E-02
3 110.00 3.5816E-02
4 120.00 2.7901E-02
5 130.00 2.2811E-02
6 140.00 1.9538E-02
7 150.00 1.7456E-02
8 160.00 1.6184E-02
9 170.00 1.5498E-02
10 180.00 1.5256E-02
Asymptotic AOP values are
MUu(inf) = 0.3791
MUd(inf) = 0.7050
MU(inf) = 0.6054
R(inf) = 0.0544
Lu(inf)/Ed(inf) = 0.010902 (1/sr)
k(inf) = 0.1644 (1/m)
absorp(check) = 0.0995 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 525.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.9301E-01 2.0178E+00 2.2108E+00 7.5625E-02 1.4373E+00 0.3918 0.7123 0.6159 5.2614E-02
1 0.00 0.00 1.5012E-01 1.6673E+00 1.8174E+00 6.3618E-02 1.4253E+00 0.4238 0.8549 0.7493 4.4634E-02
3 3.14 5.00 8.9572E-02 9.2014E-01 1.0097E+00 3.5431E-02 7.0321E-01 0.3956 0.7642 0.6614 5.0384E-02
5 6.29 10.00 4.4464E-02 4.4565E-01 4.9011E-01 1.7197E-02 3.2629E-01 0.3868 0.7322 0.6307 5.2706E-02
K-functions (units of 1/meter) at 525.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.06703 0.09566 0.09330 0.08887 0.13028 0.13221 0.12136
5.000 5.010 5.005 0.12882 0.13648 0.13580 0.13569 0.14918 0.14989 0.14628
10.000 10.010 10.005 0.14842 0.15141 0.15114 0.15127 0.15699 0.15731 0.15592
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 525.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.11508E-01 8.10407E-03 8.05409E-03 1.61582E-02 5.63821E-03 0.072229
9 1 10.0 0.0 180.0 6.88052E-02 8.23290E-03 2.44035E-03 1.06733E-02 5.72784E-03 0.035468
9 4 10.0 45.0 135.0 7.55983E-02 8.19973E-03 2.82629E-03 1.10260E-02 5.70476E-03 0.037386
9 7 10.0 90.0 90.0 1.02140E-01 8.19020E-03 5.83812E-03 1.40283E-02 5.69813E-03 0.057158
8 1 20.0 0.0 180.0 5.40455E-02 8.33545E-03 1.31810E-03 9.65355E-03 5.79919E-03 0.024389
8 4 20.0 45.0 135.0 6.01672E-02 8.25459E-03 1.55074E-03 9.80533E-03 5.74293E-03 0.025774
8 7 20.0 90.0 90.0 8.84730E-02 8.26094E-03 3.45894E-03 1.17199E-02 5.74735E-03 0.039096
7 1 30.0 0.0 180.0 4.68604E-02 8.49136E-03 1.12804E-03 9.61939E-03 5.90765E-03 0.024072
7 4 30.0 45.0 135.0 5.19522E-02 8.48249E-03 1.26695E-03 9.74944E-03 5.90149E-03 0.024387
7 7 30.0 90.0 90.0 7.57678E-02 8.45975E-03 2.17841E-03 1.06382E-02 5.88567E-03 0.028751
6 1 40.0 0.0 180.0 4.44793E-02 8.63646E-03 1.25424E-03 9.89069E-03 6.00861E-03 0.028198
6 4 40.0 45.0 135.0 4.86358E-02 8.61928E-03 1.36030E-03 9.97958E-03 5.99665E-03 0.027969
6 7 40.0 90.0 90.0 6.82839E-02 8.63439E-03 1.97030E-03 1.06047E-02 6.00717E-03 0.028855
5 1 50.0 0.0 180.0 4.66351E-02 8.82500E-03 1.98127E-03 1.08063E-02 6.13978E-03 0.042485
5 4 50.0 45.0 135.0 4.96960E-02 8.76555E-03 2.06412E-03 1.08297E-02 6.09842E-03 0.041535
5 7 50.0 90.0 90.0 6.60583E-02 8.82801E-03 2.66852E-03 1.14965E-02 6.14187E-03 0.040396
4 1 60.0 0.0 180.0 5.53566E-02 8.77423E-03 4.61544E-03 1.33897E-02 6.10446E-03 0.083377
4 4 60.0 45.0 135.0 5.66094E-02 8.70886E-03 4.55767E-03 1.32665E-02 6.05898E-03 0.080511
4 7 60.0 90.0 90.0 6.99052E-02 8.91410E-03 5.32232E-03 1.42364E-02 6.20177E-03 0.076136
3 1 70.0 0.0 180.0 7.68077E-02 8.21418E-03 1.27491E-02 2.09633E-02 5.71482E-03 0.165987
3 4 70.0 45.0 135.0 7.46458E-02 8.24733E-03 1.22670E-02 2.05143E-02 5.73788E-03 0.164336
3 7 70.0 90.0 90.0 8.34523E-02 8.48102E-03 1.33398E-02 2.18208E-02 5.90046E-03 0.159849
2 1 80.0 0.0 180.0 1.30497E-01 7.08843E-03 3.16904E-02 3.87789E-02 4.93160E-03 0.242843
2 4 80.0 45.0 135.0 1.20838E-01 7.10475E-03 3.06512E-02 3.77560E-02 4.94296E-03 0.253655
2 7 80.0 90.0 90.0 1.20054E-01 7.33659E-03 3.21002E-02 3.94368E-02 5.10426E-03 0.267382
1 1 87.5 0.0 180.0 2.10990E-01 5.74357E-03 5.58905E-02 6.16340E-02 3.99595E-03 0.264896
1 4 87.5 45.0 135.0 1.89971E-01 5.48410E-03 5.55454E-02 6.10295E-02 3.81543E-03 0.292389
1 7 87.5 90.0 90.0 1.72832E-01 6.28874E-03 5.68471E-02 6.31358E-02 4.37524E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 525.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.616E-02 1.115E-01 1.363E-01 1.180E-01 1.762E-01 1.124E-02 4.680E+00 8.104E-03 5.638E-03
1 0.00 0.00 1.503E-02 2.077E-01 2.936E-02 3.494E-02 4.864E-02 1.055E-02 4.233E+00
3 3.14 5.00 7.614E-03 3.489E-01 1.936E-02 2.530E-02 3.985E-02 1.083E-02 4.653E+00
5 6.29 10.00 3.566E-03 2.128E-01 1.065E-02 1.363E-02 1.995E-02 1.093E-02 4.822E+00
Waveband 18 of 40 completed in 3.5 sec.
* * * * * Output for wavelength band 19 (530.0 to 540.0 nm; nominal wavelength = 535.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 535.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 530.0 nm to 540.0 nm:
Ed(diffuse) = 4.123E-01 Ed(direct) = 1.041E+00 Ed(total) = 1.453E+00
Absorption Coefficients of Individual Components at 535.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0452 0.0454 0.0055 0.0960
3 3.075 5.000 0.0452 0.0454 0.0055 0.0960
5 6.151 10.000 0.0452 0.0454 0.0055 0.0960
Scattering Coefficients of Individual Components at 535.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0022 0.5169 0.0000 0.5191
3 3.075 5.000 0.0022 0.5169 0.0000 0.5191
5 6.151 10.000 0.0022 0.5169 0.0000 0.5191
Backscattering Coefficients of Individual Components at 535.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00108 0.01034 0.00000 0.01142
3 3.075 5.000 0.00108 0.01034 0.00000 0.01142
5 6.151 10.000 0.00108 0.01034 0.00000 0.01142
Summary of Inherent Optical Properties at 535.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0960 0.5191 0.6151 0.8439 0.01142 0.02199
3 3.075 5.000 0.0960 0.5191 0.6151 0.8439 0.01142 0.02199
5 6.151 10.000 0.0960 0.5191 0.6151 0.8439 0.01142 0.02199
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4613E-01
8 20.00 8.1638E-01
7 30.00 6.4632E-01
6 40.00 4.7657E-01
5 50.00 3.3332E-01
4 60.00 2.2568E-01
3 70.00 1.5100E-01
2 80.00 1.0206E-01
1 87.50 7.6732E-02
1 92.50 6.2974E-02
2 100.00 4.8988E-02
3 110.00 3.6562E-02
4 120.00 2.8481E-02
5 130.00 2.3275E-02
6 140.00 1.9924E-02
7 150.00 1.7791E-02
8 160.00 1.6486E-02
9 170.00 1.5781E-02
10 180.00 1.5534E-02
Asymptotic AOP values are
MUu(inf) = 0.3790
MUd(inf) = 0.7037
MU(inf) = 0.6031
R(inf) = 0.0552
Lu(inf)/Ed(inf) = 0.011035 (1/sr)
k(inf) = 0.1592 (1/m)
absorp(check) = 0.0960 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 535.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.9448E-01 2.0355E+00 2.2300E+00 7.6590E-02 1.4533E+00 0.3938 0.7140 0.6174 5.2702E-02
1 0.00 0.00 1.5363E-01 1.6869E+00 1.8405E+00 6.5127E-02 1.4418E+00 0.4239 0.8547 0.7480 4.5170E-02
3 3.08 5.00 9.3796E-02 9.5328E-01 1.0471E+00 3.7137E-02 7.2895E-01 0.3959 0.7647 0.6607 5.0946E-02
5 6.15 10.00 4.7843E-02 4.7424E-01 5.2208E-01 1.8516E-02 3.4720E-01 0.3870 0.7321 0.6296 5.3329E-02
K-functions (units of 1/meter) at 535.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.06423 0.09214 0.08981 0.08535 0.12586 0.12777 0.11708
5.000 5.010 5.005 0.12353 0.13124 0.13055 0.13045 0.14403 0.14476 0.14110
10.000 10.010 10.005 0.14292 0.14599 0.14571 0.14584 0.15170 0.15203 0.15059
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 535.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.11243E-01 8.28919E-03 8.13347E-03 1.64227E-02 5.70379E-03 0.073114
9 1 10.0 0.0 180.0 6.86415E-02 8.41836E-03 2.44778E-03 1.08661E-02 5.79267E-03 0.035660
9 4 10.0 45.0 135.0 7.54184E-02 8.38536E-03 2.83658E-03 1.12219E-02 5.76996E-03 0.037611
9 7 10.0 90.0 90.0 1.01897E-01 8.37788E-03 5.88520E-03 1.42631E-02 5.76482E-03 0.057757
8 1 20.0 0.0 180.0 5.39169E-02 8.52232E-03 1.31563E-03 9.83795E-03 5.86421E-03 0.024401
8 4 20.0 45.0 135.0 6.00240E-02 8.44117E-03 1.54878E-03 9.98995E-03 5.80836E-03 0.025803
8 7 20.0 90.0 90.0 8.82625E-02 8.45140E-03 3.47390E-03 1.19253E-02 5.81541E-03 0.039359
7 1 30.0 0.0 180.0 4.67489E-02 8.68127E-03 1.12535E-03 9.80662E-03 5.97358E-03 0.024072
7 4 30.0 45.0 135.0 5.18291E-02 8.67433E-03 1.26402E-03 9.93835E-03 5.96881E-03 0.024388
7 7 30.0 90.0 90.0 7.55844E-02 8.65629E-03 2.17779E-03 1.08341E-02 5.95639E-03 0.028813
6 1 40.0 0.0 180.0 4.43735E-02 8.82973E-03 1.25125E-03 1.00810E-02 6.07573E-03 0.028198
6 4 40.0 45.0 135.0 4.85201E-02 8.81498E-03 1.35706E-03 1.01720E-02 6.06558E-03 0.027969
6 7 40.0 90.0 90.0 6.81214E-02 8.83738E-03 1.96591E-03 1.08033E-02 6.08100E-03 0.028859
5 1 50.0 0.0 180.0 4.65242E-02 9.02291E-03 1.97656E-03 1.09995E-02 6.20866E-03 0.042485
5 4 50.0 45.0 135.0 4.95778E-02 8.96545E-03 2.05921E-03 1.10247E-02 6.16912E-03 0.041535
5 7 50.0 90.0 90.0 6.59011E-02 9.03755E-03 2.66217E-03 1.16997E-02 6.21874E-03 0.040396
4 1 60.0 0.0 180.0 5.52249E-02 8.97144E-03 4.60446E-03 1.35759E-02 6.17325E-03 0.083377
4 4 60.0 45.0 135.0 5.64747E-02 8.90832E-03 4.54682E-03 1.34551E-02 6.12981E-03 0.080511
4 7 60.0 90.0 90.0 6.97389E-02 9.12750E-03 5.30966E-03 1.44372E-02 6.28063E-03 0.076136
3 1 70.0 0.0 180.0 7.66250E-02 8.39915E-03 1.27188E-02 2.11179E-02 5.77946E-03 0.165987
3 4 70.0 45.0 135.0 7.44683E-02 8.43685E-03 1.22378E-02 2.06746E-02 5.80539E-03 0.164336
3 7 70.0 90.0 90.0 8.32537E-02 8.68536E-03 1.33080E-02 2.19934E-02 5.97639E-03 0.159849
2 1 80.0 0.0 180.0 1.30187E-01 7.24819E-03 3.16150E-02 3.88632E-02 4.98748E-03 0.242843
2 4 80.0 45.0 135.0 1.20551E-01 7.26835E-03 3.05783E-02 3.78466E-02 5.00135E-03 0.253655
2 7 80.0 90.0 90.0 1.19768E-01 7.51407E-03 3.20238E-02 3.95379E-02 5.17043E-03 0.267382
1 1 87.5 0.0 180.0 2.10488E-01 5.87292E-03 5.57575E-02 6.16304E-02 4.04115E-03 0.264896
1 4 87.5 45.0 135.0 1.89519E-01 5.61037E-03 5.54132E-02 6.10236E-02 3.86050E-03 0.292389
1 7 87.5 90.0 90.0 1.72420E-01 6.44101E-03 5.67118E-02 6.31528E-02 4.43206E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 535.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.642E-02 1.112E-01 1.361E-01 1.178E-01 1.759E-01 1.130E-02 4.664E+00 8.289E-03 5.704E-03
1 0.00 0.00 1.537E-02 2.072E-01 2.997E-02 3.572E-02 4.977E-02 1.066E-02 4.236E+00
3 3.08 5.00 7.980E-03 3.574E-01 2.016E-02 2.638E-02 4.163E-02 1.095E-02 4.654E+00
5 6.15 10.00 3.837E-03 2.246E-01 1.139E-02 1.461E-02 2.148E-02 1.105E-02 4.825E+00
Waveband 19 of 40 completed in 3.4 sec.
* * * * * Output for wavelength band 20 (540.0 to 550.0 nm; nominal wavelength = 545.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 545.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 540.0 nm to 550.0 nm:
Ed(diffuse) = 4.017E-01 Ed(direct) = 1.032E+00 Ed(total) = 1.434E+00
Absorption Coefficients of Individual Components at 545.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0511 0.0392 0.0047 0.0950
3 3.022 5.000 0.0511 0.0392 0.0047 0.0950
5 6.044 10.000 0.0511 0.0392 0.0047 0.0950
Scattering Coefficients of Individual Components at 545.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0020 0.5074 0.0000 0.5094
3 3.022 5.000 0.0020 0.5074 0.0000 0.5094
5 6.044 10.000 0.0020 0.5074 0.0000 0.5094
Backscattering Coefficients of Individual Components at 545.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00100 0.01015 0.00000 0.01114
3 3.022 5.000 0.00100 0.01015 0.00000 0.01114
5 6.044 10.000 0.00100 0.01015 0.00000 0.01114
Summary of Inherent Optical Properties at 545.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0950 0.5094 0.6044 0.8428 0.01114 0.02188
3 3.022 5.000 0.0950 0.5094 0.6044 0.8428 0.01114 0.02188
5 6.044 10.000 0.0950 0.5094 0.6044 0.8428 0.01114 0.02188
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4587E-01
8 20.00 8.1556E-01
7 30.00 6.4493E-01
6 40.00 4.7486E-01
5 50.00 3.3158E-01
4 60.00 2.2412E-01
3 70.00 1.4970E-01
2 80.00 1.0102E-01
1 87.50 7.5867E-02
1 92.50 6.2219E-02
2 100.00 4.8354E-02
3 110.00 3.6049E-02
4 120.00 2.8055E-02
5 130.00 2.2910E-02
6 140.00 1.9600E-02
7 150.00 1.7495E-02
8 160.00 1.6208E-02
9 170.00 1.5513E-02
10 180.00 1.5269E-02
Asymptotic AOP values are
MUu(inf) = 0.3786
MUd(inf) = 0.7045
MU(inf) = 0.6048
R(inf) = 0.0545
Lu(inf)/Ed(inf) = 0.010880 (1/sr)
k(inf) = 0.1571 (1/m)
absorp(check) = 0.0950 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 545.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.8993E-01 2.0041E+00 2.1940E+00 7.4986E-02 1.4340E+00 0.3948 0.7155 0.6194 5.2292E-02
1 0.00 0.00 1.4965E-01 1.6626E+00 1.8123E+00 6.3389E-02 1.4224E+00 0.4236 0.8555 0.7499 4.4566E-02
3 3.02 5.00 9.2142E-02 9.4724E-01 1.0394E+00 3.6465E-02 7.2587E-01 0.3957 0.7663 0.6633 5.0236E-02
5 6.04 10.00 4.7523E-02 4.7626E-01 5.2379E-01 1.8381E-02 3.4939E-01 0.3868 0.7336 0.6320 5.2608E-02
K-functions (units of 1/meter) at 545.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.06314 0.09098 0.08868 0.08416 0.12427 0.12614 0.11555
5.000 5.010 5.005 0.12142 0.12924 0.12855 0.12836 0.14199 0.14271 0.13902
10.000 10.010 10.005 0.14065 0.14380 0.14351 0.14359 0.14956 0.14989 0.14840
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 545.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.08392E-01 8.05745E-03 8.01634E-03 1.60738E-02 5.61900E-03 0.073957
9 1 10.0 0.0 180.0 6.68824E-02 8.18250E-03 2.39731E-03 1.05798E-02 5.70620E-03 0.035844
9 4 10.0 45.0 135.0 7.34857E-02 8.15057E-03 2.77967E-03 1.09302E-02 5.68394E-03 0.037826
9 7 10.0 90.0 90.0 9.92853E-02 8.14377E-03 5.79088E-03 1.39346E-02 5.67919E-03 0.058326
8 1 20.0 0.0 180.0 5.25352E-02 8.28339E-03 1.28254E-03 9.56592E-03 5.77656E-03 0.024413
8 4 20.0 45.0 135.0 5.84859E-02 8.20475E-03 1.51070E-03 9.71544E-03 5.72172E-03 0.025830
8 7 20.0 90.0 90.0 8.60007E-02 8.21552E-03 3.40636E-03 1.16219E-02 5.72923E-03 0.039609
7 1 30.0 0.0 180.0 4.55509E-02 8.43781E-03 1.09651E-03 9.53432E-03 5.88425E-03 0.024072
7 4 30.0 45.0 135.0 5.05014E-02 8.43140E-03 1.23170E-03 9.66310E-03 5.87978E-03 0.024390
7 7 30.0 90.0 90.0 7.36446E-02 8.41512E-03 2.12621E-03 1.05413E-02 5.86843E-03 0.028871
6 1 40.0 0.0 180.0 4.32364E-02 8.58213E-03 1.21919E-03 9.80132E-03 5.98490E-03 0.028198
6 4 40.0 45.0 135.0 4.72767E-02 8.56829E-03 1.32229E-03 9.89058E-03 5.97524E-03 0.027969
6 7 40.0 90.0 90.0 6.63757E-02 8.59203E-03 1.91581E-03 1.05078E-02 5.99180E-03 0.028863
5 1 50.0 0.0 180.0 4.53319E-02 8.77007E-03 1.92591E-03 1.06960E-02 6.11595E-03 0.042485
5 4 50.0 45.0 135.0 4.83073E-02 8.71490E-03 2.00644E-03 1.07213E-02 6.07748E-03 0.041535
5 7 50.0 90.0 90.0 6.42124E-02 8.78777E-03 2.59395E-03 1.13817E-02 6.12830E-03 0.040396
4 1 60.0 0.0 180.0 5.38097E-02 8.72027E-03 4.48647E-03 1.32067E-02 6.08123E-03 0.083377
4 4 60.0 45.0 135.0 5.50275E-02 8.65979E-03 4.43031E-03 1.30901E-02 6.03905E-03 0.080511
4 7 60.0 90.0 90.0 6.79517E-02 8.87649E-03 5.17359E-03 1.40501E-02 6.19017E-03 0.076136
3 1 70.0 0.0 180.0 7.46614E-02 8.16439E-03 1.23928E-02 2.05572E-02 5.69357E-03 0.165987
3 4 70.0 45.0 135.0 7.25599E-02 8.20212E-03 1.19242E-02 2.01263E-02 5.71989E-03 0.164336
3 7 70.0 90.0 90.0 8.11203E-02 8.44814E-03 1.29670E-02 2.14151E-02 5.89146E-03 0.159849
2 1 80.0 0.0 180.0 1.26851E-01 7.04597E-03 3.08049E-02 3.78508E-02 4.91362E-03 0.242843
2 4 80.0 45.0 135.0 1.17461E-01 7.06673E-03 2.97947E-02 3.68614E-02 4.92811E-03 0.253655
2 7 80.0 90.0 90.0 1.16699E-01 7.31022E-03 3.12031E-02 3.85134E-02 5.09790E-03 0.267382
1 1 87.5 0.0 180.0 2.05094E-01 5.70945E-03 5.43287E-02 6.00381E-02 3.98158E-03 0.264896
1 4 87.5 45.0 135.0 1.84662E-01 5.45529E-03 5.39932E-02 5.94485E-02 3.80434E-03 0.292389
1 7 87.5 90.0 90.0 1.68002E-01 6.26758E-03 5.52585E-02 6.15261E-02 4.37080E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 545.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.607E-02 1.084E-01 1.326E-01 1.148E-01 1.714E-01 1.121E-02 4.665E+00 8.057E-03 5.619E-03
1 0.00 0.00 1.494E-02 2.019E-01 2.916E-02 3.482E-02 4.864E-02 1.051E-02 4.242E+00
3 3.02 5.00 7.830E-03 3.525E-01 1.976E-02 2.592E-02 4.104E-02 1.079E-02 4.657E+00
5 6.04 10.00 3.806E-03 2.251E-01 1.128E-02 1.451E-02 2.145E-02 1.089E-02 4.830E+00
Waveband 20 of 40 completed in 3.4 sec.
* * * * * Output for wavelength band 21 (550.0 to 560.0 nm; nominal wavelength = 555.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 555.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 550.0 nm to 560.0 nm:
Ed(diffuse) = 3.946E-01 Ed(direct) = 1.031E+00 Ed(total) = 1.425E+00
Absorption Coefficients of Individual Components at 555.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0596 0.0330 0.0041 0.0967
3 2.984 5.000 0.0596 0.0330 0.0041 0.0967
5 5.968 10.000 0.0596 0.0330 0.0041 0.0967
Scattering Coefficients of Individual Components at 555.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0018 0.4983 0.0000 0.5001
3 2.984 5.000 0.0018 0.4983 0.0000 0.5001
5 5.968 10.000 0.0018 0.4983 0.0000 0.5001
Backscattering Coefficients of Individual Components at 555.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00092 0.00997 0.00000 0.01089
3 2.984 5.000 0.00092 0.00997 0.00000 0.01089
5 5.968 10.000 0.00092 0.00997 0.00000 0.01089
Summary of Inherent Optical Properties at 555.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0967 0.5001 0.5968 0.8380 0.01089 0.02177
3 2.984 5.000 0.0967 0.5001 0.5968 0.8380 0.01089 0.02177
5 5.968 10.000 0.0967 0.5001 0.5968 0.8380 0.01089 0.02177
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4471E-01
8 20.00 8.1192E-01
7 30.00 6.3887E-01
6 40.00 4.6749E-01
5 50.00 3.2421E-01
4 60.00 2.1763E-01
3 70.00 1.4442E-01
2 80.00 9.6902E-02
1 87.50 7.2502E-02
1 92.50 5.9328E-02
2 100.00 4.5985E-02
3 110.00 3.4187E-02
4 120.00 2.6556E-02
5 130.00 2.1661E-02
6 140.00 1.8522E-02
7 150.00 1.6530E-02
8 160.00 1.5315E-02
9 170.00 1.4660E-02
10 180.00 1.4429E-02
Asymptotic AOP values are
MUu(inf) = 0.3778
MUd(inf) = 0.7075
MU(inf) = 0.6108
R(inf) = 0.0523
Lu(inf)/Ed(inf) = 0.010416 (1/sr)
k(inf) = 0.1583 (1/m)
absorp(check) = 0.0967 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 555.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.8540E-01 1.9877E+00 2.1731E+00 7.3177E-02 1.4251E+00 0.3947 0.7169 0.6221 5.1350E-02
1 0.00 0.00 1.4277E-01 1.6472E+00 1.7900E+00 6.0347E-02 1.4122E+00 0.4227 0.8573 0.7552 4.2732E-02
3 2.98 5.00 8.7295E-02 9.3058E-01 1.0179E+00 3.4477E-02 7.1582E-01 0.3949 0.7692 0.6694 4.8164E-02
5 5.97 10.00 4.4752E-02 4.6476E-01 5.0952E-01 1.7276E-02 3.4244E-01 0.3860 0.7368 0.6382 5.0449E-02
K-functions (units of 1/meter) at 555.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.06372 0.09237 0.09008 0.08543 0.12572 0.12752 0.11693
5.000 5.010 5.005 0.12272 0.13070 0.13001 0.12962 0.14326 0.14395 0.14023
10.000 10.010 10.005 0.14180 0.14505 0.14477 0.14475 0.15076 0.15108 0.14955
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 555.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.06473E-01 7.65691E-03 7.95844E-03 1.56154E-02 5.37298E-03 0.074746
9 1 10.0 0.0 180.0 6.56983E-02 7.77739E-03 2.36614E-03 1.01435E-02 5.45752E-03 0.036015
9 4 10.0 45.0 135.0 7.21847E-02 7.74641E-03 2.74497E-03 1.04914E-02 5.43578E-03 0.038027
9 7 10.0 90.0 90.0 9.75275E-02 7.73853E-03 5.74034E-03 1.34789E-02 5.43025E-03 0.058859
8 1 20.0 0.0 180.0 5.16051E-02 7.87389E-03 1.26040E-03 9.13429E-03 5.52523E-03 0.024424
8 4 20.0 45.0 135.0 5.74504E-02 7.79804E-03 1.48543E-03 9.28346E-03 5.47201E-03 0.025856
8 7 20.0 90.0 90.0 8.44780E-02 7.80607E-03 3.36583E-03 1.11719E-02 5.47764E-03 0.039843
7 1 30.0 0.0 180.0 4.47444E-02 8.02097E-03 1.07710E-03 9.09807E-03 5.62845E-03 0.024072
7 4 30.0 45.0 135.0 4.96077E-02 8.01336E-03 1.20997E-03 9.22332E-03 5.62310E-03 0.024391
7 7 30.0 90.0 90.0 7.23380E-02 7.99502E-03 2.09245E-03 1.00875E-02 5.61023E-03 0.028926
6 1 40.0 0.0 180.0 4.24709E-02 8.15809E-03 1.19760E-03 9.35569E-03 5.72466E-03 0.028198
6 4 40.0 45.0 135.0 4.64396E-02 8.14299E-03 1.29888E-03 9.44187E-03 5.71407E-03 0.027969
6 7 40.0 90.0 90.0 6.52005E-02 8.16234E-03 1.88214E-03 1.00445E-02 5.72765E-03 0.028867
5 1 50.0 0.0 180.0 4.45293E-02 8.33657E-03 1.89181E-03 1.02284E-02 5.84991E-03 0.042485
5 4 50.0 45.0 135.0 4.74520E-02 8.28206E-03 1.97092E-03 1.02530E-02 5.81166E-03 0.041535
5 7 50.0 90.0 90.0 6.30755E-02 8.34844E-03 2.54802E-03 1.08965E-02 5.85824E-03 0.040396
4 1 60.0 0.0 180.0 5.28570E-02 8.28918E-03 4.40703E-03 1.26962E-02 5.81665E-03 0.083377
4 4 60.0 45.0 135.0 5.40532E-02 8.22964E-03 4.35187E-03 1.25815E-02 5.77487E-03 0.080511
4 7 60.0 90.0 90.0 6.67486E-02 8.43337E-03 5.08199E-03 1.35154E-02 5.91783E-03 0.076136
3 1 70.0 0.0 180.0 7.33395E-02 7.76115E-03 1.21734E-02 1.99346E-02 5.44612E-03 0.165987
3 4 70.0 45.0 135.0 7.12752E-02 7.79530E-03 1.17131E-02 1.95084E-02 5.47009E-03 0.164336
3 7 70.0 90.0 90.0 7.96840E-02 8.02832E-03 1.27374E-02 2.07657E-02 5.63360E-03 0.159849
2 1 80.0 0.0 180.0 1.24605E-01 6.69853E-03 3.02595E-02 3.69580E-02 4.70047E-03 0.242843
2 4 80.0 45.0 135.0 1.15382E-01 6.71706E-03 2.92672E-02 3.59842E-02 4.71347E-03 0.253655
2 7 80.0 90.0 90.0 1.14633E-01 6.94895E-03 3.06507E-02 3.75996E-02 4.87619E-03 0.267382
1 1 87.5 0.0 180.0 2.01463E-01 5.42876E-03 5.33668E-02 5.87955E-02 3.80945E-03 0.264896
1 4 87.5 45.0 135.0 1.81393E-01 5.18642E-03 5.30373E-02 5.82237E-02 3.63940E-03 0.292389
1 7 87.5 90.0 90.0 1.65027E-01 5.96030E-03 5.42802E-02 6.02405E-02 4.18244E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 555.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.562E-02 1.065E-01 1.301E-01 1.126E-01 1.682E-01 1.096E-02 4.686E+00 7.657E-03 5.373E-03
1 0.00 0.00 1.420E-02 1.983E-01 2.782E-02 3.330E-02 4.674E-02 1.006E-02 4.250E+00
3 2.98 5.00 7.393E-03 3.453E-01 1.874E-02 2.467E-02 3.928E-02 1.033E-02 4.664E+00
5 5.97 10.00 3.572E-03 2.206E-01 1.062E-02 1.372E-02 2.041E-02 1.043E-02 4.836E+00
Waveband 21 of 40 completed in 3.3 sec.
* * * * * Output for wavelength band 22 (560.0 to 570.0 nm; nominal wavelength = 565.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 44.1 m at 565.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 560.0 nm to 570.0 nm:
Ed(diffuse) = 3.870E-01 Ed(direct) = 1.026E+00 Ed(total) = 1.413E+00
Absorption Coefficients of Individual Components at 565.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0642 0.0278 0.0036 0.0956
3 2.934 5.000 0.0642 0.0278 0.0036 0.0956
5 5.868 10.000 0.0642 0.0278 0.0036 0.0956
Scattering Coefficients of Individual Components at 565.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0017 0.4894 0.0000 0.4912
3 2.934 5.000 0.0017 0.4894 0.0000 0.4912
5 5.868 10.000 0.0017 0.4894 0.0000 0.4912
Backscattering Coefficients of Individual Components at 565.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00085 0.00979 0.00000 0.01064
3 2.934 5.000 0.00085 0.00979 0.00000 0.01064
5 5.868 10.000 0.00085 0.00979 0.00000 0.01064
Summary of Inherent Optical Properties at 565.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0956 0.4912 0.5868 0.8370 0.01064 0.02167
3 2.934 5.000 0.0956 0.4912 0.5868 0.8370 0.01064 0.02167
5 5.868 10.000 0.0956 0.4912 0.5868 0.8370 0.01064 0.02167
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4449E-01
8 20.00 8.1124E-01
7 30.00 6.3773E-01
6 40.00 4.6610E-01
5 50.00 3.2282E-01
4 60.00 2.1639E-01
3 70.00 1.4340E-01
2 80.00 9.6090E-02
1 87.50 7.1828E-02
1 92.50 5.8741E-02
2 100.00 4.5494E-02
3 110.00 3.3791E-02
4 120.00 2.6227E-02
5 130.00 2.1380E-02
6 140.00 1.8272E-02
7 150.00 1.6302E-02
8 160.00 1.5100E-02
9 170.00 1.4452E-02
10 180.00 1.4224E-02
Asymptotic AOP values are
MUu(inf) = 0.3774
MUd(inf) = 0.7081
MU(inf) = 0.6121
R(inf) = 0.0517
Lu(inf)/Ed(inf) = 0.010293 (1/sr)
k(inf) = 0.1562 (1/m)
absorp(check) = 0.0956 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 565.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.8223E-01 1.9675E+00 2.1498E+00 7.2090E-02 1.4132E+00 0.3956 0.7183 0.6238 5.1011E-02
1 0.00 0.00 1.4003E-01 1.6320E+00 1.7720E+00 5.9145E-02 1.4003E+00 0.4224 0.8580 0.7568 4.2238E-02
3 2.93 5.00 8.6367E-02 9.2978E-01 1.0161E+00 3.4100E-02 7.1657E-01 0.3948 0.7707 0.6716 4.7587E-02
5 5.87 10.00 4.4781E-02 4.6941E-01 5.1419E-01 1.7279E-02 3.4649E-01 0.3859 0.7382 0.6403 4.9869E-02
K-functions (units of 1/meter) at 565.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.06256 0.09117 0.08891 0.08417 0.12408 0.12584 0.11530
5.000 5.010 5.005 0.12056 0.12866 0.12797 0.12747 0.14118 0.14187 0.13808
10.000 10.010 10.005 0.13949 0.14283 0.14254 0.14245 0.14858 0.14890 0.14730
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 565.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.04429E-01 7.49570E-03 7.88459E-03 1.53803E-02 5.30399E-03 0.075502
9 1 10.0 0.0 180.0 6.44370E-02 7.61320E-03 2.33131E-03 9.94451E-03 5.38713E-03 0.036180
9 4 10.0 45.0 135.0 7.07988E-02 7.58300E-03 2.70590E-03 1.02889E-02 5.36576E-03 0.038220
9 7 10.0 90.0 90.0 9.56551E-02 7.57570E-03 5.67898E-03 1.32547E-02 5.36060E-03 0.059369
8 1 20.0 0.0 180.0 5.06144E-02 7.70750E-03 1.23674E-03 8.94424E-03 5.45387E-03 0.024435
8 4 20.0 45.0 135.0 5.63474E-02 7.63347E-03 1.45830E-03 9.09176E-03 5.40148E-03 0.025880
8 7 20.0 90.0 90.0 8.28562E-02 7.64204E-03 3.31978E-03 1.09618E-02 5.40754E-03 0.040067
7 1 30.0 0.0 180.0 4.38854E-02 7.85140E-03 1.05642E-03 8.90782E-03 5.55569E-03 0.024072
7 4 30.0 45.0 135.0 4.86557E-02 7.84424E-03 1.18680E-03 9.03104E-03 5.55062E-03 0.024392
7 7 30.0 90.0 90.0 7.09468E-02 7.82737E-03 2.05593E-03 9.88330E-03 5.53868E-03 0.028978
6 1 40.0 0.0 180.0 4.16555E-02 7.98561E-03 1.17461E-03 9.16021E-03 5.65065E-03 0.028198
6 4 40.0 45.0 135.0 4.55481E-02 7.97126E-03 1.27394E-03 9.24520E-03 5.64050E-03 0.027969
6 7 40.0 90.0 90.0 6.39488E-02 7.99189E-03 1.84625E-03 9.83814E-03 5.65510E-03 0.028871
5 1 50.0 0.0 180.0 4.36744E-02 8.16041E-03 1.85549E-03 1.00159E-02 5.77434E-03 0.042485
5 4 50.0 45.0 135.0 4.65410E-02 8.10764E-03 1.93308E-03 1.00407E-02 5.73700E-03 0.041535
5 7 50.0 90.0 90.0 6.18645E-02 8.17502E-03 2.49910E-03 1.06741E-02 5.78468E-03 0.040396
4 1 60.0 0.0 180.0 5.18422E-02 8.11416E-03 4.32243E-03 1.24366E-02 5.74162E-03 0.083377
4 4 60.0 45.0 135.0 5.30155E-02 8.05665E-03 4.26832E-03 1.23250E-02 5.70092E-03 0.080511
4 7 60.0 90.0 90.0 6.54672E-02 8.25921E-03 4.98443E-03 1.32436E-02 5.84425E-03 0.076136
3 1 70.0 0.0 180.0 7.19315E-02 7.59754E-03 1.19397E-02 1.95372E-02 5.37605E-03 0.165987
3 4 70.0 45.0 135.0 6.99069E-02 7.63192E-03 1.14882E-02 1.91201E-02 5.40038E-03 0.164336
3 7 70.0 90.0 90.0 7.81542E-02 7.86385E-03 1.24929E-02 2.03567E-02 5.56450E-03 0.159849
2 1 80.0 0.0 180.0 1.22213E-01 6.55758E-03 2.96785E-02 3.62361E-02 4.64017E-03 0.242843
2 4 80.0 45.0 135.0 1.13166E-01 6.57673E-03 2.87053E-02 3.52820E-02 4.65372E-03 0.253655
2 7 80.0 90.0 90.0 1.12432E-01 6.80770E-03 3.00622E-02 3.68699E-02 4.81716E-03 0.267382
1 1 87.5 0.0 180.0 1.97595E-01 5.31481E-03 5.23422E-02 5.76570E-02 3.76078E-03 0.264896
1 4 87.5 45.0 135.0 1.77910E-01 5.07848E-03 5.20190E-02 5.70975E-02 3.59356E-03 0.292389
1 7 87.5 90.0 90.0 1.61859E-01 5.84020E-03 5.32381E-02 5.90783E-02 4.13255E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 565.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.538E-02 1.044E-01 1.276E-01 1.105E-01 1.650E-01 1.088E-02 4.687E+00 7.496E-03 5.304E-03
1 0.00 0.00 1.390E-02 1.945E-01 2.725E-02 3.267E-02 4.598E-02 9.928E-03 4.254E+00
3 2.93 5.00 7.308E-03 3.424E-01 1.850E-02 2.440E-02 3.897E-02 1.020E-02 4.666E+00
5 5.87 10.00 3.571E-03 2.222E-01 1.060E-02 1.373E-02 2.051E-02 1.031E-02 4.839E+00
Waveband 22 of 40 completed in 3.3 sec.
* * * * * Output for wavelength band 23 (570.0 to 580.0 nm; nominal wavelength = 575.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 43.9 m at 575.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 570.0 nm to 580.0 nm:
Ed(diffuse) = 3.835E-01 Ed(direct) = 1.031E+00 Ed(total) = 1.415E+00
Absorption Coefficients of Individual Components at 575.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0772 0.0268 0.0031 0.1071
3 2.948 5.000 0.0772 0.0268 0.0031 0.1071
5 5.896 10.000 0.0772 0.0268 0.0031 0.1071
Scattering Coefficients of Individual Components at 575.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0016 0.4809 0.0000 0.4825
3 2.948 5.000 0.0016 0.4809 0.0000 0.4825
5 5.896 10.000 0.0016 0.4809 0.0000 0.4825
Backscattering Coefficients of Individual Components at 575.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00079 0.00962 0.00000 0.01041
3 2.948 5.000 0.00079 0.00962 0.00000 0.01041
5 5.896 10.000 0.00079 0.00962 0.00000 0.01041
Summary of Inherent Optical Properties at 575.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1071 0.4825 0.5896 0.8183 0.01041 0.02157
3 2.948 5.000 0.1071 0.4825 0.5896 0.8183 0.01041 0.02157
5 5.896 10.000 0.1071 0.4825 0.5896 0.8183 0.01041 0.02157
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.3999E-01
8 20.00 7.9732E-01
7 30.00 6.1492E-01
6 40.00 4.3896E-01
5 50.00 2.9631E-01
4 60.00 1.9362E-01
3 70.00 1.2534E-01
2 80.00 8.2308E-02
1 87.50 6.0755E-02
1 92.50 4.9336E-02
2 100.00 3.7893E-02
3 110.00 2.7918E-02
4 120.00 2.1566E-02
5 130.00 1.7545E-02
6 140.00 1.4994E-02
7 150.00 1.3389E-02
8 160.00 1.2417E-02
9 170.00 1.1896E-02
10 180.00 1.1714E-02
Asymptotic AOP values are
MUu(inf) = 0.3754
MUd(inf) = 0.7193
MU(inf) = 0.6329
R(inf) = 0.0447
Lu(inf)/Ed(inf) = 0.008897 (1/sr)
k(inf) = 0.1693 (1/m)
absorp(check) = 0.1071 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 575.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.7482E-01 1.9664E+00 2.1412E+00 6.8569E-02 1.4148E+00 0.3922 0.7195 0.6287 4.8464E-02
1 0.00 0.00 1.2220E-01 1.6191E+00 1.7413E+00 5.1281E-02 1.3975E+00 0.4196 0.8632 0.7731 3.6694E-02
3 2.95 5.00 7.0747E-02 8.6158E-01 9.3233E-01 2.7736E-02 6.7031E-01 0.3920 0.7780 0.6892 4.1378E-02
5 5.90 10.00 3.4288E-02 4.0616E-01 4.4045E-01 1.3149E-02 3.0343E-01 0.3835 0.7471 0.6591 4.3335E-02
K-functions (units of 1/meter) at 575.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.06986 0.10214 0.09987 0.09466 0.13650 0.13810 0.12731
5.000 5.010 5.005 0.13408 0.14249 0.14186 0.14078 0.15434 0.15493 0.15111
10.000 10.010 10.005 0.15292 0.15641 0.15614 0.15575 0.16178 0.16206 0.16039
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 575.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.03470E-01 6.47900E-03 7.88652E-03 1.43655E-02 4.57932E-03 0.076220
9 1 10.0 0.0 180.0 6.38454E-02 6.58822E-03 2.31989E-03 8.90811E-03 4.65652E-03 0.036336
9 4 10.0 45.0 135.0 7.01489E-02 6.55922E-03 2.69390E-03 9.25312E-03 4.63602E-03 0.038403
9 7 10.0 90.0 90.0 9.47770E-02 6.54625E-03 5.67282E-03 1.22191E-02 4.62685E-03 0.059854
8 1 20.0 0.0 180.0 5.01497E-02 6.67242E-03 1.22589E-03 7.89831E-03 4.71603E-03 0.024445
8 4 20.0 45.0 135.0 5.58301E-02 6.60351E-03 1.44622E-03 8.04972E-03 4.66732E-03 0.025904
8 7 20.0 90.0 90.0 8.20955E-02 6.60019E-03 3.30679E-03 9.90698E-03 4.66498E-03 0.040280
7 1 30.0 0.0 180.0 4.34825E-02 6.79818E-03 1.04672E-03 7.84490E-03 4.80492E-03 0.024072
7 4 30.0 45.0 135.0 4.82094E-02 6.78524E-03 1.17597E-03 7.96122E-03 4.79577E-03 0.024393
7 7 30.0 90.0 90.0 7.02931E-02 6.75618E-03 2.04050E-03 8.79668E-03 4.77523E-03 0.029028
6 1 40.0 0.0 180.0 4.12731E-02 6.91364E-03 1.16383E-03 8.07747E-03 4.88652E-03 0.028198
6 4 40.0 45.0 135.0 4.51299E-02 6.89250E-03 1.26225E-03 8.15475E-03 4.87159E-03 0.027969
6 7 40.0 90.0 90.0 6.33617E-02 6.89245E-03 1.82952E-03 8.72197E-03 4.87155E-03 0.028874
5 1 50.0 0.0 180.0 4.32735E-02 7.06355E-03 1.83845E-03 8.90201E-03 4.99248E-03 0.042485
5 4 50.0 45.0 135.0 4.61137E-02 7.00808E-03 1.91533E-03 8.92341E-03 4.95327E-03 0.041535
5 7 50.0 90.0 90.0 6.12966E-02 7.04730E-03 2.47616E-03 9.52346E-03 4.98100E-03 0.040396
4 1 60.0 0.0 180.0 5.13663E-02 7.02226E-03 4.28275E-03 1.13050E-02 4.96330E-03 0.083377
4 4 60.0 45.0 135.0 5.25288E-02 6.96214E-03 4.22913E-03 1.11913E-02 4.92080E-03 0.080511
4 7 60.0 90.0 90.0 6.48662E-02 7.11820E-03 4.93867E-03 1.20569E-02 5.03111E-03 0.076136
3 1 70.0 0.0 180.0 7.12711E-02 6.57495E-03 1.18301E-02 1.84050E-02 4.64714E-03 0.165987
3 4 70.0 45.0 135.0 6.92651E-02 6.59500E-03 1.13827E-02 1.79777E-02 4.66131E-03 0.164336
3 7 70.0 90.0 90.0 7.74367E-02 6.77945E-03 1.23782E-02 1.91576E-02 4.79168E-03 0.159849
2 1 80.0 0.0 180.0 1.21091E-01 5.67565E-03 2.94061E-02 3.50817E-02 4.01152E-03 0.242843
2 4 80.0 45.0 135.0 1.12128E-01 5.68419E-03 2.84418E-02 3.41260E-02 4.01755E-03 0.253655
2 7 80.0 90.0 90.0 1.11400E-01 5.87216E-03 2.97863E-02 3.56584E-02 4.15042E-03 0.267382
1 1 87.5 0.0 180.0 1.95781E-01 4.60180E-03 5.18617E-02 5.64635E-02 3.25253E-03 0.264896
1 4 87.5 45.0 135.0 1.76277E-01 4.39146E-03 5.15415E-02 5.59329E-02 3.10386E-03 0.292389
1 7 87.5 90.0 90.0 1.60373E-01 5.04285E-03 5.27493E-02 5.77922E-02 3.56426E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 575.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.437E-02 1.035E-01 1.261E-01 1.091E-01 1.631E-01 1.015E-02 4.773E+00 6.479E-03 4.579E-03
1 0.00 0.00 1.202E-02 1.927E-01 2.387E-02 2.875E-02 4.096E-02 8.598E-03 4.268E+00
3 2.95 5.00 5.927E-03 3.207E-01 1.536E-02 2.039E-02 3.296E-02 8.842E-03 4.680E+00
5 5.90 10.00 2.713E-03 1.975E-01 8.212E-03 1.070E-02 1.615E-02 8.940E-03 4.847E+00
Waveband 23 of 40 completed in 3.5 sec.
* * * * * Output for wavelength band 24 (580.0 to 590.0 nm; nominal wavelength = 585.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 42.5 m at 585.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 580.0 nm to 590.0 nm:
Ed(diffuse) = 3.707E-01 Ed(direct) = 1.010E+00 Ed(total) = 1.381E+00
Absorption Coefficients of Individual Components at 585.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1100 0.0278 0.0027 0.1405
3 3.074 5.000 0.1100 0.0278 0.0027 0.1405
5 6.147 10.000 0.1100 0.0278 0.0027 0.1405
Scattering Coefficients of Individual Components at 585.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0015 0.4727 0.0000 0.4742
3 3.074 5.000 0.0015 0.4727 0.0000 0.4742
5 6.147 10.000 0.0015 0.4727 0.0000 0.4742
Backscattering Coefficients of Individual Components at 585.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00073 0.00945 0.00000 0.01019
3 3.074 5.000 0.00073 0.00945 0.00000 0.01019
5 6.147 10.000 0.00073 0.00945 0.00000 0.01019
Summary of Inherent Optical Properties at 585.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1405 0.4742 0.6147 0.7714 0.01019 0.02148
3 3.074 5.000 0.1405 0.4742 0.6147 0.7714 0.01019 0.02148
5 6.147 10.000 0.1405 0.4742 0.6147 0.7714 0.01019 0.02148
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.2861E-01
8 20.00 7.6298E-01
7 30.00 5.6088E-01
6 40.00 3.7777E-01
5 50.00 2.3972E-01
4 60.00 1.4758E-01
3 70.00 9.0601E-02
2 80.00 5.6955E-02
1 87.50 4.0956E-02
1 92.50 3.2807E-02
2 100.00 2.4806E-02
3 110.00 1.8017E-02
4 120.00 1.3823E-02
5 130.00 1.1233E-02
6 140.00 9.6237E-03
7 150.00 8.6303E-03
8 160.00 8.0378E-03
9 170.00 7.7238E-03
10 180.00 7.6141E-03
Asymptotic AOP values are
MUu(inf) = 0.3725
MUd(inf) = 0.7445
MU(inf) = 0.6767
R(inf) = 0.0324
Lu(inf)/Ed(inf) = 0.006483 (1/sr)
k(inf) = 0.2077 (1/m)
absorp(check) = 0.1406 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 585.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.5864E-01 1.9161E+00 2.0747E+00 6.1044E-02 1.3808E+00 0.3848 0.7207 0.6361 4.4209E-02
1 0.00 0.00 8.8548E-02 1.5550E+00 1.6436E+00 3.6680E-02 1.3564E+00 0.4142 0.8723 0.8030 2.7042E-02
3 3.07 5.00 4.2325E-02 6.7753E-01 7.1986E-01 1.6383E-02 5.3687E-01 0.3871 0.7924 0.7230 3.0517E-02
5 6.15 10.00 1.6792E-02 2.6098E-01 2.7777E-01 6.3774E-03 1.9982E-01 0.3798 0.7656 0.6964 3.1916E-02
K-functions (units of 1/meter) at 585.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.09499 0.13606 0.13385 0.12699 0.17333 0.17462 0.16312
5.000 5.010 5.005 0.17434 0.18315 0.18263 0.18033 0.19340 0.19382 0.18963
10.000 10.010 10.005 0.19265 0.19651 0.19627 0.19497 0.20094 0.20114 0.19877
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 585.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 1.00019E-01 4.62273E-03 7.69050E-03 1.23132E-02 3.34784E-03 0.076891
9 1 10.0 0.0 180.0 6.17156E-02 4.71331E-03 2.25150E-03 6.96481E-03 3.41344E-03 0.036482
9 4 10.0 45.0 135.0 6.78088E-02 4.68781E-03 2.61562E-03 7.30343E-03 3.39498E-03 0.038573
9 7 10.0 90.0 90.0 9.16153E-02 4.66733E-03 5.52507E-03 1.01924E-02 3.38014E-03 0.060307
8 1 20.0 0.0 180.0 4.84768E-02 4.77746E-03 1.18545E-03 5.96291E-03 3.45990E-03 0.024454
8 4 20.0 45.0 135.0 5.39677E-02 4.72012E-03 1.39915E-03 6.11927E-03 3.41838E-03 0.025926
8 7 20.0 90.0 90.0 7.93569E-02 4.69953E-03 3.21226E-03 7.91179E-03 3.40346E-03 0.040479
7 1 30.0 0.0 180.0 4.20320E-02 4.86889E-03 1.01180E-03 5.88070E-03 3.52612E-03 0.024072
7 4 30.0 45.0 135.0 4.66016E-02 4.84844E-03 1.13680E-03 5.98524E-03 3.51130E-03 0.024394
7 7 30.0 90.0 90.0 6.79461E-02 4.80285E-03 1.97553E-03 6.77839E-03 3.47829E-03 0.029075
6 1 40.0 0.0 180.0 3.98963E-02 4.94922E-03 1.12500E-03 6.07422E-03 3.58429E-03 0.028198
6 4 40.0 45.0 135.0 4.36245E-02 4.91950E-03 1.22014E-03 6.13964E-03 3.56276E-03 0.027969
6 7 40.0 90.0 90.0 6.12481E-02 4.88812E-03 1.76869E-03 6.65681E-03 3.54004E-03 0.028878
5 1 50.0 0.0 180.0 4.18299E-02 5.05268E-03 1.77713E-03 6.82981E-03 3.65922E-03 0.042485
5 4 50.0 45.0 135.0 4.45754E-02 4.99638E-03 1.85144E-03 6.84782E-03 3.61845E-03 0.041535
5 7 50.0 90.0 90.0 5.92518E-02 4.99002E-03 2.39356E-03 7.38358E-03 3.61384E-03 0.040396
4 1 60.0 0.0 180.0 4.96528E-02 5.01936E-03 4.13988E-03 9.15924E-03 3.63508E-03 0.083377
4 4 60.0 45.0 135.0 5.07765E-02 4.95859E-03 4.08806E-03 9.04664E-03 3.59107E-03 0.080511
4 7 60.0 90.0 90.0 6.27023E-02 5.03427E-03 4.77392E-03 9.80820E-03 3.64589E-03 0.076136
3 1 70.0 0.0 180.0 6.88936E-02 4.69708E-03 1.14355E-02 1.61325E-02 3.40169E-03 0.165987
3 4 70.0 45.0 135.0 6.69545E-02 4.69433E-03 1.10030E-02 1.56974E-02 3.39970E-03 0.164336
3 7 70.0 90.0 90.0 7.48536E-02 4.79387E-03 1.19653E-02 1.67591E-02 3.47178E-03 0.159849
2 1 80.0 0.0 180.0 1.17051E-01 4.05386E-03 2.84251E-02 3.24790E-02 2.93586E-03 0.242843
2 4 80.0 45.0 135.0 1.08387E-01 4.04543E-03 2.74930E-02 3.15384E-02 2.92975E-03 0.253655
2 7 80.0 90.0 90.0 1.07684E-01 4.15426E-03 2.87926E-02 3.29469E-02 3.00857E-03 0.267382
1 1 87.5 0.0 180.0 1.89250E-01 3.28810E-03 5.01317E-02 5.34198E-02 2.38129E-03 0.264896
1 4 87.5 45.0 135.0 1.70397E-01 3.12715E-03 4.98221E-02 5.29493E-02 2.26472E-03 0.292389
1 7 87.5 90.0 90.0 1.55023E-01 3.57309E-03 5.09897E-02 5.45628E-02 2.58768E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 585.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.231E-02 1.000E-01 1.213E-01 1.048E-01 1.569E-01 8.917E-03 4.958E+00 4.623E-03 3.348E-03
1 0.00 0.00 8.575E-03 1.862E-01 1.749E-02 2.123E-02 3.092E-02 6.321E-03 4.278E+00
3 3.07 5.00 3.500E-03 2.612E-01 9.475E-03 1.271E-02 2.093E-02 6.519E-03 4.681E+00
5 6.15 10.00 1.322E-03 1.357E-01 4.130E-03 5.420E-03 8.293E-03 6.614E-03 4.826E+00
Waveband 24 of 40 completed in 3.6 sec.
* * * * * Output for wavelength band 25 (590.0 to 600.0 nm; nominal wavelength = 595.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 40.3 m at 595.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 590.0 nm to 600.0 nm:
Ed(diffuse) = 3.536E-01 Ed(direct) = 9.762E-01 Ed(total) = 1.330E+00
Absorption Coefficients of Individual Components at 595.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1672 0.0247 0.0024 0.1943
3 3.302 5.000 0.1672 0.0247 0.0024 0.1943
5 6.604 10.000 0.1672 0.0247 0.0024 0.1943
Scattering Coefficients of Individual Components at 595.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0014 0.4648 0.0000 0.4661
3 3.302 5.000 0.0014 0.4648 0.0000 0.4661
5 6.604 10.000 0.0014 0.4648 0.0000 0.4661
Backscattering Coefficients of Individual Components at 595.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00068 0.00930 0.00000 0.00998
3 3.302 5.000 0.00068 0.00930 0.00000 0.00998
5 6.604 10.000 0.00068 0.00930 0.00000 0.00998
Summary of Inherent Optical Properties at 595.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1943 0.4661 0.6604 0.7058 0.00998 0.02140
3 3.302 5.000 0.1943 0.4661 0.6604 0.7058 0.00998 0.02140
5 6.604 10.000 0.1943 0.4661 0.6604 0.7058 0.00998 0.02140
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.1203E-01
8 20.00 7.1521E-01
7 30.00 4.9082E-01
6 40.00 3.0494E-01
5 50.00 1.7820E-01
4 60.00 1.0174E-01
3 70.00 5.8654E-02
2 80.00 3.5128E-02
1 87.50 2.4590E-02
1 92.50 1.9456E-02
2 100.00 1.4511E-02
3 110.00 1.0424E-02
4 120.00 7.9759E-03
5 130.00 6.5019E-03
6 140.00 5.6068E-03
7 150.00 5.0655E-03
8 160.00 4.7487E-03
9 170.00 4.5833E-03
10 180.00 4.5258E-03
Asymptotic AOP values are
MUu(inf) = 0.3716
MUd(inf) = 0.7747
MU(inf) = 0.7247
R(inf) = 0.0219
Lu(inf)/Ed(inf) = 0.004472 (1/sr)
k(inf) = 0.2681 (1/m)
absorp(check) = 0.1943 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 595.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.4313E-01 1.8424E+00 1.9856E+00 5.4094E-02 1.3298E+00 0.3779 0.7218 0.6425 4.0679E-02
1 0.00 0.00 6.0011E-02 1.4769E+00 1.5369E+00 2.4527E-02 1.3002E+00 0.4087 0.8804 0.8301 1.8864E-02
3 3.30 5.00 2.1008E-02 4.6805E-01 4.8906E-01 8.0584E-03 3.7852E-01 0.3836 0.8087 0.7575 2.1290E-02
5 6.60 10.00 6.1117E-03 1.3123E-01 1.3734E-01 2.3151E-03 1.0332E-01 0.3788 0.7873 0.7354 2.2406E-02
K-functions (units of 1/meter) at 595.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.14162 0.19343 0.19140 0.18163 0.23272 0.23371 0.22095
5.000 5.010 5.005 0.23766 0.24721 0.24680 0.24226 0.25548 0.25577 0.24941
10.000 10.010 10.005 0.25338 0.25945 0.25918 0.25445 0.26278 0.26297 0.25611
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 595.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 9.54262E-02 3.09554E-03 7.40045E-03 1.04960E-02 2.32783E-03 0.077552
9 1 10.0 0.0 180.0 5.88819E-02 3.16554E-03 2.15659E-03 5.32213E-03 2.38048E-03 0.036626
9 4 10.0 45.0 135.0 6.46953E-02 3.14487E-03 2.50641E-03 5.65128E-03 2.36493E-03 0.038742
9 7 10.0 90.0 90.0 8.74087E-02 3.12268E-03 5.31041E-03 8.43308E-03 2.34824E-03 0.060754
8 1 20.0 0.0 180.0 4.62509E-02 3.21122E-03 1.13145E-03 4.34267E-03 2.41483E-03 0.024463
8 4 20.0 45.0 135.0 5.14897E-02 3.16671E-03 1.33602E-03 4.50272E-03 2.38136E-03 0.025947
8 7 20.0 90.0 90.0 7.57132E-02 3.13906E-03 3.07961E-03 6.21867E-03 2.36057E-03 0.040675
7 1 30.0 0.0 180.0 4.01020E-02 3.27324E-03 9.65346E-04 4.23859E-03 2.46147E-03 0.024072
7 4 30.0 45.0 135.0 4.44621E-02 3.25111E-03 1.08466E-03 4.33576E-03 2.44482E-03 0.024395
7 7 30.0 90.0 90.0 6.48243E-02 3.20158E-03 1.88774E-03 5.08932E-03 2.40758E-03 0.029121
6 1 40.0 0.0 180.0 3.80644E-02 3.32451E-03 1.07335E-03 4.39786E-03 2.50003E-03 0.028198
6 4 40.0 45.0 135.0 4.16214E-02 3.29355E-03 1.16411E-03 4.45766E-03 2.47674E-03 0.027969
6 7 40.0 90.0 90.0 5.84358E-02 3.24824E-03 1.68767E-03 4.93591E-03 2.44267E-03 0.028881
5 1 50.0 0.0 180.0 3.99093E-02 3.38989E-03 1.69553E-03 5.08542E-03 2.54919E-03 0.042485
5 4 50.0 45.0 135.0 4.25287E-02 3.33946E-03 1.76643E-03 5.10589E-03 2.51127E-03 0.041535
5 7 50.0 90.0 90.0 5.65312E-02 3.30810E-03 2.28366E-03 5.59176E-03 2.48768E-03 0.040396
4 1 60.0 0.0 180.0 4.73729E-02 3.36329E-03 3.94979E-03 7.31308E-03 2.52918E-03 0.083377
4 4 60.0 45.0 135.0 4.84450E-02 3.30888E-03 3.90035E-03 7.20922E-03 2.48827E-03 0.080511
4 7 60.0 90.0 90.0 5.98232E-02 3.33081E-03 4.55472E-03 7.88553E-03 2.50476E-03 0.076136
3 1 70.0 0.0 180.0 6.57303E-02 3.14362E-03 1.09104E-02 1.40540E-02 2.36399E-03 0.165987
3 4 70.0 45.0 135.0 6.38802E-02 3.12844E-03 1.04978E-02 1.36262E-02 2.35258E-03 0.164336
3 7 70.0 90.0 90.0 7.14166E-02 3.16835E-03 1.14159E-02 1.45842E-02 2.38259E-03 0.159849
2 1 80.0 0.0 180.0 1.11677E-01 2.71098E-03 2.71199E-02 2.98309E-02 2.03865E-03 0.242843
2 4 80.0 45.0 135.0 1.03410E-01 2.69380E-03 2.62306E-02 2.89244E-02 2.02573E-03 0.253655
2 7 80.0 90.0 90.0 1.02739E-01 2.74482E-03 2.74706E-02 3.02154E-02 2.06409E-03 0.267382
1 1 87.5 0.0 180.0 1.80561E-01 2.19844E-03 4.78298E-02 5.00282E-02 1.65322E-03 0.264896
1 4 87.5 45.0 135.0 1.62573E-01 2.08223E-03 4.75345E-02 4.96167E-02 1.56583E-03 0.292389
1 7 87.5 90.0 90.0 1.47905E-01 2.36292E-03 4.86484E-02 5.10113E-02 1.77691E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 595.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 1.050E-02 9.543E-02 1.153E-01 9.946E-02 1.491E-01 7.893E-03 5.154E+00 3.096E-03 2.328E-03
1 0.00 0.00 5.743E-03 1.776E-01 1.203E-02 1.471E-02 2.192E-02 4.417E-03 4.271E+00
3 3.30 5.00 1.738E-03 1.889E-01 4.841E-03 6.550E-03 1.095E-02 4.592E-03 4.636E+00
5 6.60 10.00 4.896E-04 7.448E-02 1.536E-03 2.020E-03 3.112E-03 4.738E-03 4.729E+00
Waveband 25 of 40 completed in 3.8 sec.
* * * * * Output for wavelength band 26 (600.0 to 610.0 nm; nominal wavelength = 605.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 36.8 m at 605.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 600.0 nm to 610.0 nm:
Ed(diffuse) = 3.601E-01 Ed(direct) = 1.006E+00 Ed(total) = 1.366E+00
Absorption Coefficients of Individual Components at 605.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.2577 0.0278 0.0020 0.2876
3 3.730 5.000 0.2577 0.0278 0.0020 0.2876
5 7.459 10.000 0.2577 0.0278 0.0020 0.2876
Scattering Coefficients of Individual Components at 605.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0013 0.4571 0.0000 0.4584
3 3.730 5.000 0.0013 0.4571 0.0000 0.4584
5 7.459 10.000 0.0013 0.4571 0.0000 0.4584
Backscattering Coefficients of Individual Components at 605.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00063 0.00914 0.00000 0.00978
3 3.730 5.000 0.00063 0.00914 0.00000 0.00978
5 7.459 10.000 0.00063 0.00914 0.00000 0.00978
Summary of Inherent Optical Properties at 605.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.2876 0.4584 0.7459 0.6145 0.00978 0.02133
3 3.730 5.000 0.2876 0.4584 0.7459 0.6145 0.00978 0.02133
5 7.459 10.000 0.2876 0.4584 0.7459 0.6145 0.00978 0.02133
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.8645E-01
8 20.00 6.4648E-01
7 30.00 4.0009E-01
6 40.00 2.2146E-01
5 50.00 1.1589E-01
4 60.00 6.0288E-02
3 70.00 3.2396E-02
2 80.00 1.8482E-02
1 87.50 1.2630E-02
1 92.50 9.9093E-03
2 100.00 7.3232E-03
3 110.00 5.2343E-03
4 120.00 4.0187E-03
5 130.00 3.3045E-03
6 140.00 2.8812E-03
7 150.00 2.6317E-03
8 160.00 2.4893E-03
9 170.00 2.4165E-03
10 180.00 2.3914E-03
Asymptotic AOP values are
MUu(inf) = 0.3735
MUd(inf) = 0.8102
MU(inf) = 0.7763
R(inf) = 0.0136
Lu(inf)/Ed(inf) = 0.002882 (1/sr)
k(inf) = 0.3705 (1/m)
absorp(check) = 0.2876 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 605.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.3905E-01 1.8895E+00 2.0285E+00 5.1722E-02 1.3657E+00 0.3720 0.7228 0.6477 3.7873E-02
1 0.00 0.00 4.0435E-02 1.4994E+00 1.5398E+00 1.6305E-02 1.3302E+00 0.4032 0.8872 0.8533 1.2257E-02
3 3.73 5.00 8.2892E-03 2.7575E-01 2.8404E-01 3.1756E-03 2.2821E-01 0.3831 0.8276 0.7923 1.3915E-02
5 7.46 10.00 1.4772E-03 4.5209E-02 4.6686E-02 5.6925E-04 3.6733E-02 0.3854 0.8125 0.7746 1.5497E-02
K-functions (units of 1/meter) at 605.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.23244 0.29602 0.29435 0.28028 0.33603 0.33673 0.32176
5.000 5.010 5.005 0.34215 0.35575 0.35535 0.34382 0.36164 0.36189 0.34619
10.000 10.010 10.005 0.34347 0.36546 0.36476 0.33976 0.36771 0.36815 0.33348
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 605.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 9.71580E-02 2.06762E-03 7.59453E-03 9.66215E-03 1.51401E-03 0.078167
9 1 10.0 0.0 180.0 5.99505E-02 2.12077E-03 2.20375E-03 4.32452E-03 1.55292E-03 0.036759
9 4 10.0 45.0 135.0 6.58694E-02 2.10448E-03 2.56222E-03 4.66670E-03 1.54100E-03 0.038899
9 7 10.0 90.0 90.0 8.89950E-02 2.08379E-03 5.44376E-03 7.52756E-03 1.52585E-03 0.061169
8 1 20.0 0.0 180.0 4.70903E-02 2.15304E-03 1.15239E-03 3.30542E-03 1.57655E-03 0.024472
8 4 20.0 45.0 135.0 5.24241E-02 2.11909E-03 1.36131E-03 3.48040E-03 1.55169E-03 0.025967
8 7 20.0 90.0 90.0 7.70872E-02 2.09098E-03 3.14956E-03 5.24055E-03 1.53111E-03 0.040857
7 1 30.0 0.0 180.0 4.08298E-02 2.19483E-03 9.82865E-04 3.17770E-03 1.60715E-03 0.024072
7 4 30.0 45.0 135.0 4.52693E-02 2.17421E-03 1.10439E-03 3.27860E-03 1.59206E-03 0.024396
7 7 30.0 90.0 90.0 6.59988E-02 2.12783E-03 1.92477E-03 4.05259E-03 1.55809E-03 0.029164
6 1 40.0 0.0 180.0 3.87552E-02 2.22694E-03 1.09282E-03 3.31977E-03 1.63067E-03 0.028198
6 4 40.0 45.0 135.0 4.23767E-02 2.19857E-03 1.18524E-03 3.38381E-03 1.60989E-03 0.027969
6 7 40.0 90.0 90.0 5.94963E-02 2.15115E-03 1.71848E-03 3.86963E-03 1.57517E-03 0.028884
5 1 50.0 0.0 180.0 4.06335E-02 2.26731E-03 1.72630E-03 3.99361E-03 1.66023E-03 0.042485
5 4 50.0 45.0 135.0 4.33005E-02 2.22473E-03 1.79848E-03 4.02322E-03 1.62905E-03 0.041535
5 7 50.0 90.0 90.0 5.75571E-02 2.18442E-03 2.32510E-03 4.50952E-03 1.59953E-03 0.040396
4 1 60.0 0.0 180.0 4.82326E-02 2.24589E-03 4.02147E-03 6.26737E-03 1.64455E-03 0.083377
4 4 60.0 45.0 135.0 4.93242E-02 2.19991E-03 3.97113E-03 6.17104E-03 1.61088E-03 0.080511
4 7 60.0 90.0 90.0 6.09089E-02 2.19373E-03 4.63738E-03 6.83111E-03 1.60635E-03 0.076136
3 1 70.0 0.0 180.0 6.69231E-02 2.09566E-03 1.11084E-02 1.32040E-02 1.53454E-03 0.165987
3 4 70.0 45.0 135.0 6.50395E-02 2.07604E-03 1.06883E-02 1.27644E-02 1.52017E-03 0.164336
3 7 70.0 90.0 90.0 7.27126E-02 2.08289E-03 1.16230E-02 1.37059E-02 1.52519E-03 0.159849
2 1 80.0 0.0 180.0 1.13703E-01 1.80490E-03 2.76121E-02 2.94170E-02 1.32163E-03 0.242843
2 4 80.0 45.0 135.0 1.05287E-01 1.78512E-03 2.67066E-02 2.84918E-02 1.30715E-03 0.253655
2 7 80.0 90.0 90.0 1.04604E-01 1.80264E-03 2.79691E-02 2.97718E-02 1.31998E-03 0.267382
1 1 87.5 0.0 180.0 1.83838E-01 1.46255E-03 4.86978E-02 5.01603E-02 1.07094E-03 0.264896
1 4 87.5 45.0 135.0 1.65523E-01 1.37895E-03 4.83971E-02 4.97761E-02 1.00973E-03 0.292389
1 7 87.5 90.0 90.0 1.50590E-01 1.55210E-03 4.95313E-02 5.10834E-02 1.13652E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 605.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 9.662E-03 9.716E-02 1.170E-01 1.008E-01 1.513E-01 7.075E-03 5.353E+00 2.068E-03 1.514E-03
1 0.00 0.00 3.836E-03 1.808E-01 8.269E-03 1.018E-02 1.552E-02 2.884E-03 4.250E+00
3 3.73 5.00 7.018E-04 1.188E-01 1.949E-03 2.648E-03 4.468E-03 3.075E-03 4.525E+00
5 7.46 10.00 1.272E-04 2.889E-02 3.715E-04 4.830E-04 7.365E-04 3.462E-03 4.476E+00
Waveband 26 of 40 completed in 4.2 sec.
* * * * * Output for wavelength band 27 (610.0 to 620.0 nm; nominal wavelength = 615.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 36.8 m at 615.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 610.0 nm to 620.0 nm:
Ed(diffuse) = 3.486E-01 Ed(direct) = 9.845E-01 Ed(total) = 1.333E+00
Absorption Coefficients of Individual Components at 615.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.2678 0.0268 0.0018 0.2964
3 3.736 5.000 0.2678 0.0268 0.0018 0.2964
5 7.472 10.000 0.2678 0.0268 0.0018 0.2964
Scattering Coefficients of Individual Components at 615.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0012 0.4497 0.0000 0.4508
3 3.736 5.000 0.0012 0.4497 0.0000 0.4508
5 7.472 10.000 0.0012 0.4497 0.0000 0.4508
Backscattering Coefficients of Individual Components at 615.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00059 0.00899 0.00000 0.00958
3 3.736 5.000 0.00059 0.00899 0.00000 0.00958
5 7.472 10.000 0.00059 0.00899 0.00000 0.00958
Summary of Inherent Optical Properties at 615.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.2964 0.4508 0.7472 0.6034 0.00958 0.02126
3 3.736 5.000 0.2964 0.4508 0.7472 0.6034 0.00958 0.02126
5 7.472 10.000 0.2964 0.4508 0.7472 0.6034 0.00958 0.02126
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.8307E-01
8 20.00 6.3782E-01
7 30.00 3.8947E-01
6 40.00 2.1248E-01
5 50.00 1.0972E-01
4 60.00 5.6478E-02
3 70.00 3.0120E-02
2 80.00 1.7099E-02
1 87.50 1.1658E-02
1 92.50 9.1399E-03
2 100.00 6.7487E-03
3 110.00 4.8212E-03
4 120.00 3.7026E-03
5 130.00 3.0470E-03
6 140.00 2.6595E-03
7 150.00 2.4317E-03
8 160.00 2.3022E-03
9 170.00 2.2361E-03
10 180.00 2.2134E-03
Asymptotic AOP values are
MUu(inf) = 0.3736
MUd(inf) = 0.8141
MU(inf) = 0.7818
R(inf) = 0.0129
Lu(inf)/Ed(inf) = 0.002732 (1/sr)
k(inf) = 0.3791 (1/m)
absorp(check) = 0.2964 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 615.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.3438E-01 1.8420E+00 1.9764E+00 5.0030E-02 1.3331E+00 0.3723 0.7237 0.6492 3.7529E-02
1 0.00 0.00 3.7481E-02 1.4619E+00 1.4993E+00 1.5084E-02 1.2982E+00 0.4024 0.8880 0.8558 1.1619E-02
3 3.74 5.00 7.3073E-03 2.5606E-01 2.6337E-01 2.7975E-03 2.1258E-01 0.3828 0.8302 0.7965 1.3160E-02
5 7.47 10.00 1.2458E-03 4.0084E-02 4.1330E-02 4.8028E-04 3.2699E-02 0.3855 0.8157 0.7795 1.4688E-02
K-functions (units of 1/meter) at 615.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.24177 0.30600 0.30439 0.29014 0.34543 0.34608 0.33140
5.000 5.010 5.005 0.35161 0.36517 0.36479 0.35311 0.37082 0.37105 0.35519
10.000 10.010 10.005 0.35161 0.37457 0.37388 0.34755 0.37672 0.37715 0.34075
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 615.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 9.40678E-02 1.91186E-03 7.40839E-03 9.32025E-03 1.43414E-03 0.078756
9 1 10.0 0.0 180.0 5.80437E-02 1.96154E-03 2.14110E-03 4.10264E-03 1.47141E-03 0.036888
9 4 10.0 45.0 135.0 6.37743E-02 1.94628E-03 2.49030E-03 4.43658E-03 1.45995E-03 0.039049
9 7 10.0 90.0 90.0 8.61644E-02 1.92667E-03 5.30490E-03 7.23157E-03 1.44525E-03 0.061567
8 1 20.0 0.0 180.0 4.55925E-02 1.99156E-03 1.11611E-03 3.10767E-03 1.49392E-03 0.024480
8 4 20.0 45.0 135.0 5.07567E-02 1.95981E-03 1.31899E-03 3.27880E-03 1.47011E-03 0.025986
8 7 20.0 90.0 90.0 7.46354E-02 1.93304E-03 3.06243E-03 4.99547E-03 1.45003E-03 0.041032
7 1 30.0 0.0 180.0 3.95312E-02 2.03028E-03 9.51604E-04 2.98188E-03 1.52297E-03 0.024072
7 4 30.0 45.0 135.0 4.38298E-02 2.01072E-03 1.06931E-03 3.08003E-03 1.50829E-03 0.024397
7 7 30.0 90.0 90.0 6.38979E-02 1.96677E-03 1.86611E-03 3.83288E-03 1.47532E-03 0.029205
6 1 40.0 0.0 180.0 3.75225E-02 2.05985E-03 1.05807E-03 3.11791E-03 1.54515E-03 0.028198
6 4 40.0 45.0 135.0 4.10289E-02 2.03296E-03 1.14754E-03 3.18051E-03 1.52498E-03 0.027969
6 7 40.0 90.0 90.0 5.76039E-02 1.98780E-03 1.66399E-03 3.65179E-03 1.49110E-03 0.028887
5 1 50.0 0.0 180.0 3.93411E-02 2.09695E-03 1.67139E-03 3.76834E-03 1.57298E-03 0.042485
5 4 50.0 45.0 135.0 4.19233E-02 2.05684E-03 1.74128E-03 3.79812E-03 1.54289E-03 0.041535
5 7 50.0 90.0 90.0 5.57265E-02 2.01817E-03 2.25115E-03 4.26932E-03 1.51388E-03 0.040396
4 1 60.0 0.0 180.0 4.66985E-02 2.07689E-03 3.89357E-03 5.97045E-03 1.55793E-03 0.083377
4 4 60.0 45.0 135.0 4.77554E-02 2.03359E-03 3.84482E-03 5.87842E-03 1.52545E-03 0.080511
4 7 60.0 90.0 90.0 5.89717E-02 2.02647E-03 4.48988E-03 6.51636E-03 1.52011E-03 0.076136
3 1 70.0 0.0 180.0 6.47946E-02 1.93772E-03 1.07551E-02 1.26928E-02 1.45353E-03 0.165987
3 4 70.0 45.0 135.0 6.29709E-02 1.91884E-03 1.03484E-02 1.22672E-02 1.43937E-03 0.164336
3 7 70.0 90.0 90.0 7.03999E-02 1.92400E-03 1.12534E-02 1.31774E-02 1.44324E-03 0.159849
2 1 80.0 0.0 180.0 1.10087E-01 1.66871E-03 2.67339E-02 2.84026E-02 1.25175E-03 0.242843
2 4 80.0 45.0 135.0 1.01938E-01 1.64983E-03 2.58572E-02 2.75070E-02 1.23758E-03 0.253655
2 7 80.0 90.0 90.0 1.01277E-01 1.66518E-03 2.70795E-02 2.87447E-02 1.24909E-03 0.267382
1 1 87.5 0.0 180.0 1.77990E-01 1.35215E-03 4.71489E-02 4.85011E-02 1.01428E-03 0.264896
1 4 87.5 45.0 135.0 1.60258E-01 1.27443E-03 4.68578E-02 4.81323E-02 9.55985E-04 0.292389
1 7 87.5 90.0 90.0 1.45800E-01 1.43395E-03 4.79559E-02 4.93899E-02 1.07565E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 615.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 9.320E-03 9.407E-02 1.132E-01 9.759E-02 1.465E-01 6.991E-03 5.368E+00 1.912E-03 1.434E-03
1 0.00 0.00 3.547E-03 1.750E-01 7.680E-03 9.470E-03 1.449E-02 2.733E-03 4.252E+00
3 3.74 5.00 6.190E-04 1.102E-01 1.719E-03 2.340E-03 3.962E-03 2.912E-03 4.519E+00
5 7.47 10.00 1.076E-04 2.579E-02 3.129E-04 4.074E-04 6.233E-04 3.292E-03 4.462E+00
Waveband 27 of 40 completed in 4.3 sec.
* * * * * Output for wavelength band 28 (620.0 to 630.0 nm; nominal wavelength = 625.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 36.4 m at 625.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 620.0 nm to 630.0 nm:
Ed(diffuse) = 3.421E-01 Ed(direct) = 9.764E-01 Ed(total) = 1.319E+00
Absorption Coefficients of Individual Components at 625.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.2834 0.0299 0.0015 0.3148
3 3.792 5.000 0.2834 0.0299 0.0015 0.3148
5 7.584 10.000 0.2834 0.0299 0.0015 0.3148
Scattering Coefficients of Individual Components at 625.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0011 0.4425 0.0000 0.4436
3 3.792 5.000 0.0011 0.4425 0.0000 0.4436
5 7.584 10.000 0.0011 0.4425 0.0000 0.4436
Backscattering Coefficients of Individual Components at 625.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00055 0.00885 0.00000 0.00940
3 3.792 5.000 0.00055 0.00885 0.00000 0.00940
5 7.584 10.000 0.00055 0.00885 0.00000 0.00940
Summary of Inherent Optical Properties at 625.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3148 0.4436 0.7584 0.5849 0.00940 0.02119
3 3.792 5.000 0.3148 0.4436 0.7584 0.5849 0.00940 0.02119
5 7.584 10.000 0.3148 0.4436 0.7584 0.5849 0.00940 0.02119
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.7727E-01
8 20.00 6.2323E-01
7 30.00 3.7196E-01
6 40.00 1.9804E-01
5 50.00 1.0005E-01
4 60.00 5.0625E-02
3 70.00 2.6681E-02
2 80.00 1.5034E-02
1 87.50 1.0216E-02
1 92.50 8.0023E-03
2 100.00 5.9029E-03
3 110.00 4.2156E-03
4 120.00 3.2406E-03
5 130.00 2.6714E-03
6 140.00 2.3364E-03
7 150.00 2.1405E-03
8 160.00 2.0296E-03
9 170.00 1.9733E-03
10 180.00 1.9540E-03
Asymptotic AOP values are
MUu(inf) = 0.3741
MUd(inf) = 0.8206
MU(inf) = 0.7906
R(inf) = 0.0117
Lu(inf)/Ed(inf) = 0.002510 (1/sr)
k(inf) = 0.3983 (1/m)
absorp(check) = 0.3149 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 625.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.3129E-01 1.8196E+00 1.9509E+00 4.8875E-02 1.3185E+00 0.3723 0.7246 0.6508 3.7068E-02
1 0.00 0.00 3.4149E-02 1.4433E+00 1.4775E+00 1.3706E-02 1.2833E+00 0.4014 0.8892 0.8593 1.0680E-02
3 3.79 5.00 5.9953E-03 2.2774E-01 2.3373E-01 2.2953E-03 1.8994E-01 0.3828 0.8340 0.8028 1.2084E-02
5 7.58 10.00 9.3490E-04 3.2225E-02 3.3160E-02 3.6193E-04 2.6444E-02 0.3871 0.8206 0.7866 1.3687E-02
K-functions (units of 1/meter) at 625.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.26174 0.32672 0.32522 0.31052 0.36557 0.36616 0.35155
5.000 5.010 5.005 0.37142 0.38569 0.38532 0.37237 0.39092 0.39115 0.37356
10.000 10.010 10.005 0.36676 0.39446 0.39368 0.36147 0.39646 0.39695 0.35272
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 625.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 9.23208E-02 1.73737E-03 7.32262E-03 9.05999E-03 1.31766E-03 0.079317
9 1 10.0 0.0 180.0 5.69657E-02 1.78333E-03 2.10829E-03 3.89162E-03 1.35252E-03 0.037010
9 4 10.0 45.0 135.0 6.25899E-02 1.76914E-03 2.45300E-03 4.22215E-03 1.34176E-03 0.039192
9 7 10.0 90.0 90.0 8.45642E-02 1.75059E-03 5.23844E-03 6.98903E-03 1.32769E-03 0.061946
8 1 20.0 0.0 180.0 4.47458E-02 1.81086E-03 1.09573E-03 2.90659E-03 1.37340E-03 0.024488
8 4 20.0 45.0 135.0 4.98141E-02 1.78146E-03 1.29540E-03 3.07687E-03 1.35110E-03 0.026005
8 7 20.0 90.0 90.0 7.32493E-02 1.75593E-03 3.01775E-03 4.77367E-03 1.33174E-03 0.041198
7 1 30.0 0.0 180.0 3.87970E-02 1.84612E-03 9.33930E-04 2.78005E-03 1.40014E-03 0.024072
7 4 30.0 45.0 135.0 4.30160E-02 1.82759E-03 1.04950E-03 2.87708E-03 1.38609E-03 0.024398
7 7 30.0 90.0 90.0 6.27096E-02 1.78599E-03 1.83385E-03 3.61984E-03 1.35454E-03 0.029244
6 1 40.0 0.0 180.0 3.68257E-02 1.87275E-03 1.03842E-03 2.91117E-03 1.42034E-03 0.028198
6 4 40.0 45.0 135.0 4.02669E-02 1.84733E-03 1.12623E-03 2.97357E-03 1.40106E-03 0.027969
6 7 40.0 90.0 90.0 5.65341E-02 1.80419E-03 1.63324E-03 3.43743E-03 1.36834E-03 0.028890
5 1 50.0 0.0 180.0 3.86105E-02 1.90607E-03 1.64035E-03 3.54642E-03 1.44561E-03 0.042485
5 4 50.0 45.0 135.0 4.11447E-02 1.86849E-03 1.70894E-03 3.57743E-03 1.41711E-03 0.041535
5 7 50.0 90.0 90.0 5.46915E-02 1.83103E-03 2.20934E-03 4.04037E-03 1.38870E-03 0.040396
4 1 60.0 0.0 180.0 4.58313E-02 1.88738E-03 3.82126E-03 5.70864E-03 1.43144E-03 0.083377
4 4 60.0 45.0 135.0 4.68685E-02 1.84683E-03 3.77342E-03 5.62025E-03 1.40068E-03 0.080511
4 7 60.0 90.0 90.0 5.78765E-02 1.83794E-03 4.40650E-03 6.24444E-03 1.39394E-03 0.076136
3 1 70.0 0.0 180.0 6.35912E-02 1.76047E-03 1.05553E-02 1.23158E-02 1.33518E-03 0.165987
3 4 70.0 45.0 135.0 6.18014E-02 1.74215E-03 1.01562E-02 1.18983E-02 1.32128E-03 0.164336
3 7 70.0 90.0 90.0 6.90925E-02 1.74463E-03 1.10444E-02 1.27890E-02 1.32317E-03 0.159849
2 1 80.0 0.0 180.0 1.08042E-01 1.51577E-03 2.62374E-02 2.77532E-02 1.14960E-03 0.242843
2 4 80.0 45.0 135.0 1.00045E-01 1.49761E-03 2.53770E-02 2.68746E-02 1.13582E-03 0.253655
2 7 80.0 90.0 90.0 9.93957E-02 1.50981E-03 2.65766E-02 2.80864E-02 1.14508E-03 0.267382
1 1 87.5 0.0 180.0 1.74685E-01 1.22808E-03 4.62733E-02 4.75014E-02 9.31403E-04 0.264896
1 4 87.5 45.0 135.0 1.57282E-01 1.15675E-03 4.59876E-02 4.71443E-02 8.77309E-04 0.292389
1 7 87.5 90.0 90.0 1.43092E-01 1.30030E-03 4.70653E-02 4.83656E-02 9.86175E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 625.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 9.060E-03 9.232E-02 1.111E-01 9.573E-02 1.437E-01 6.871E-03 5.395E+00 1.737E-03 1.318E-03
1 0.00 0.00 3.224E-03 1.718E-01 7.021E-03 8.674E-03 1.334E-02 2.512E-03 4.252E+00
3 3.79 5.00 5.100E-04 9.845E-02 1.412E-03 1.925E-03 3.270E-03 2.685E-03 4.501E+00
5 7.58 10.00 8.199E-05 2.109E-02 2.338E-04 3.041E-04 4.653E-04 3.100E-03 4.414E+00
Waveband 28 of 40 completed in 4.4 sec.
* * * * * Output for wavelength band 29 (630.0 to 640.0 nm; nominal wavelength = 635.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 35.9 m at 635.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 630.0 nm to 640.0 nm:
Ed(diffuse) = 3.354E-01 Ed(direct) = 9.668E-01 Ed(total) = 1.302E+00
Absorption Coefficients of Individual Components at 635.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3012 0.0340 0.0013 0.3366
3 3.865 5.000 0.3012 0.0340 0.0013 0.3366
5 7.731 10.000 0.3012 0.0340 0.0013 0.3366
Scattering Coefficients of Individual Components at 635.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0010 0.4355 0.0000 0.4365
3 3.865 5.000 0.0010 0.4355 0.0000 0.4365
5 7.731 10.000 0.0010 0.4355 0.0000 0.4365
Backscattering Coefficients of Individual Components at 635.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00051 0.00871 0.00000 0.00922
3 3.865 5.000 0.00051 0.00871 0.00000 0.00922
5 7.731 10.000 0.00051 0.00871 0.00000 0.00922
Summary of Inherent Optical Properties at 635.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3366 0.4365 0.7731 0.5646 0.00922 0.02113
3 3.865 5.000 0.3366 0.4365 0.7731 0.5646 0.00922 0.02113
5 7.731 10.000 0.3366 0.4365 0.7731 0.5646 0.00922 0.02113
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.7067E-01
8 20.00 6.0697E-01
7 30.00 3.5306E-01
6 40.00 1.8296E-01
5 50.00 9.0256E-02
4 60.00 4.4847E-02
3 70.00 2.3351E-02
2 80.00 1.3061E-02
1 87.50 8.8474E-03
1 92.50 6.9256E-03
2 100.00 5.1046E-03
3 110.00 3.6453E-03
4 120.00 2.8057E-03
5 130.00 2.3175E-03
6 140.00 2.0315E-03
7 150.00 1.8651E-03
8 160.00 1.7715E-03
9 170.00 1.7243E-03
10 180.00 1.7081E-03
Asymptotic AOP values are
MUu(inf) = 0.3748
MUd(inf) = 0.8274
MU(inf) = 0.7998
R(inf) = 0.0107
Lu(inf)/Ed(inf) = 0.002293 (1/sr)
k(inf) = 0.4209 (1/m)
absorp(check) = 0.3366 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 635.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.2813E-01 1.7950E+00 1.9231E+00 4.7691E-02 1.3022E+00 0.3722 0.7255 0.6524 3.6622E-02
1 0.00 0.00 3.0899E-02 1.4231E+00 1.4540E+00 1.2370E-02 1.2669E+00 0.4003 0.8903 0.8628 9.7637E-03
3 3.87 5.00 4.8064E-03 1.9858E-01 2.0339E-01 1.8421E-03 1.6641E-01 0.3833 0.8380 0.8092 1.1070E-02
5 7.73 10.00 6.8290E-04 2.4955E-02 2.5638E-02 2.6670E-04 2.0602E-02 0.3905 0.8256 0.7932 1.2945E-02
K-functions (units of 1/meter) at 635.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.28508 0.35112 0.34972 0.33437 0.38934 0.38988 0.37504
5.000 5.010 5.005 0.39376 0.40982 0.40944 0.39383 0.41464 0.41487 0.39352
10.000 10.010 10.005 0.38011 0.41775 0.41675 0.37242 0.41966 0.42028 0.35998
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 635.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 9.05048E-02 1.56868E-03 7.22775E-03 8.79643E-03 1.20460E-03 0.079860
9 1 10.0 0.0 180.0 5.58452E-02 1.61092E-03 2.07342E-03 3.68434E-03 1.23704E-03 0.037128
9 4 10.0 45.0 135.0 6.13587E-02 1.59782E-03 2.41324E-03 4.01106E-03 1.22698E-03 0.039330
9 7 10.0 90.0 90.0 8.29008E-02 1.58039E-03 5.16582E-03 6.74620E-03 1.21359E-03 0.062313
8 1 20.0 0.0 180.0 4.38656E-02 1.63598E-03 1.07451E-03 2.71049E-03 1.25628E-03 0.024496
8 4 20.0 45.0 135.0 4.88342E-02 1.60894E-03 1.27079E-03 2.87973E-03 1.23551E-03 0.026022
8 7 20.0 90.0 90.0 7.18084E-02 1.58477E-03 2.96995E-03 4.55472E-03 1.21695E-03 0.041359
7 1 30.0 0.0 180.0 3.80338E-02 1.66785E-03 9.15559E-04 2.58341E-03 1.28075E-03 0.024072
7 4 30.0 45.0 135.0 4.21701E-02 1.65043E-03 1.02889E-03 2.67932E-03 1.26738E-03 0.024399
7 7 30.0 90.0 90.0 6.14745E-02 1.61134E-03 1.80005E-03 3.41139E-03 1.23736E-03 0.029281
6 1 40.0 0.0 180.0 3.61013E-02 1.69163E-03 1.01799E-03 2.70962E-03 1.29901E-03 0.028198
6 4 40.0 45.0 135.0 3.94748E-02 1.66777E-03 1.10408E-03 2.77185E-03 1.28069E-03 0.027969
6 7 40.0 90.0 90.0 5.54220E-02 1.62686E-03 1.60126E-03 3.22812E-03 1.24927E-03 0.028892
5 1 50.0 0.0 180.0 3.78510E-02 1.72128E-03 1.60808E-03 3.32937E-03 1.32178E-03 0.042485
5 4 50.0 45.0 135.0 4.03354E-02 1.68632E-03 1.67533E-03 3.36164E-03 1.29493E-03 0.041535
5 7 50.0 90.0 90.0 5.36157E-02 1.65032E-03 2.16588E-03 3.81620E-03 1.26729E-03 0.040396
4 1 60.0 0.0 180.0 4.49297E-02 1.70394E-03 3.74609E-03 5.45003E-03 1.30847E-03 0.083377
4 4 60.0 45.0 135.0 4.59466E-02 1.66621E-03 3.69919E-03 5.36540E-03 1.27949E-03 0.080511
4 7 60.0 90.0 90.0 5.67380E-02 1.65588E-03 4.31982E-03 5.97570E-03 1.27156E-03 0.076136
3 1 70.0 0.0 180.0 6.23404E-02 1.58888E-03 1.03477E-02 1.19366E-02 1.22011E-03 0.165987
3 4 70.0 45.0 135.0 6.05857E-02 1.57125E-03 9.95640E-03 1.15277E-02 1.20657E-03 0.164336
3 7 70.0 90.0 90.0 6.77334E-02 1.57138E-03 1.08271E-02 1.23985E-02 1.20667E-03 0.159849
2 1 80.0 0.0 180.0 1.05917E-01 1.36771E-03 2.57213E-02 2.70890E-02 1.05027E-03 0.242843
2 4 80.0 45.0 135.0 9.80772E-02 1.35037E-03 2.48778E-02 2.62282E-02 1.03696E-03 0.253655
2 7 80.0 90.0 90.0 9.74406E-02 1.35968E-03 2.60538E-02 2.74135E-02 1.04410E-03 0.267382
1 1 87.5 0.0 180.0 1.71249E-01 1.10794E-03 4.53631E-02 4.64710E-02 8.50794E-04 0.264896
1 4 87.5 45.0 135.0 1.54188E-01 1.04289E-03 4.50830E-02 4.61259E-02 8.00842E-04 0.292389
1 7 87.5 90.0 90.0 1.40277E-01 1.17104E-03 4.61395E-02 4.73105E-02 8.99251E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 635.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 8.796E-03 9.050E-02 1.089E-01 9.379E-02 1.408E-01 6.755E-03 5.422E+00 1.569E-03 1.205E-03
1 0.00 0.00 2.911E-03 1.684E-01 6.375E-03 7.895E-03 1.220E-02 2.297E-03 4.250E+00
3 3.87 5.00 4.118E-04 8.638E-02 1.132E-03 1.544E-03 2.630E-03 2.475E-03 4.473E+00
5 7.73 10.00 6.155E-05 1.664E-02 1.692E-04 2.192E-04 3.341E-04 2.988E-03 4.333E+00
Waveband 29 of 40 completed in 4.4 sec.
* * * * * Output for wavelength band 30 (640.0 to 650.0 nm; nominal wavelength = 645.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 35.4 m at 645.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 640.0 nm to 650.0 nm:
Ed(diffuse) = 3.226E-01 Ed(direct) = 9.388E-01 Ed(total) = 1.261E+00
Absorption Coefficients of Individual Components at 645.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3250 0.0330 0.0012 0.3592
3 3.944 5.000 0.3250 0.0330 0.0012 0.3592
5 7.889 10.000 0.3250 0.0330 0.0012 0.3592
Scattering Coefficients of Individual Components at 645.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0010 0.4287 0.0000 0.4297
3 3.944 5.000 0.0010 0.4287 0.0000 0.4297
5 7.889 10.000 0.0010 0.4287 0.0000 0.4297
Backscattering Coefficients of Individual Components at 645.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00048 0.00857 0.00000 0.00906
3 3.944 5.000 0.00048 0.00857 0.00000 0.00906
5 7.889 10.000 0.00048 0.00857 0.00000 0.00906
Summary of Inherent Optical Properties at 645.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3592 0.4297 0.7889 0.5447 0.00906 0.02107
3 3.944 5.000 0.3592 0.4297 0.7889 0.5447 0.00906 0.02107
5 7.889 10.000 0.3592 0.4297 0.7889 0.5447 0.00906 0.02107
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.6388E-01
8 20.00 5.9062E-01
7 30.00 3.3465E-01
6 40.00 1.6878E-01
5 50.00 8.1337E-02
4 60.00 3.9723E-02
3 70.00 2.0453E-02
2 80.00 1.1366E-02
1 87.50 7.6783E-03
1 92.50 6.0078E-03
2 100.00 4.4258E-03
3 110.00 3.1611E-03
4 120.00 2.4363E-03
5 130.00 2.0165E-03
6 140.00 1.7716E-03
7 150.00 1.6299E-03
8 160.00 1.5507E-03
9 170.00 1.5109E-03
10 180.00 1.4973E-03
Asymptotic AOP values are
MUu(inf) = 0.3755
MUd(inf) = 0.8339
MU(inf) = 0.8084
R(inf) = 0.0097
Lu(inf)/Ed(inf) = 0.002100 (1/sr)
k(inf) = 0.4443 (1/m)
absorp(check) = 0.3592 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 645.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.2279E-01 1.7368E+00 1.8596E+00 4.5700E-02 1.2614E+00 0.3722 0.7263 0.6538 3.6228E-02
1 0.00 0.00 2.7513E-02 1.3764E+00 1.4039E+00 1.0990E-02 1.2267E+00 0.3994 0.8912 0.8660 8.9585E-03
3 3.94 5.00 3.7858E-03 1.6910E-01 1.7289E-01 1.4543E-03 1.4235E-01 0.3842 0.8418 0.8149 1.0217E-02
5 7.89 10.00 4.9607E-04 1.8799E-02 1.9295E-02 1.9630E-04 1.5606E-02 0.3957 0.8301 0.7986 1.2579E-02
K-functions (units of 1/meter) at 645.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.30948 0.37654 0.37523 0.35904 0.41407 0.41457 0.39915
5.000 5.010 5.005 0.41567 0.43481 0.43439 0.41453 0.43924 0.43949 0.41220
10.000 10.010 10.005 0.38820 0.44170 0.44032 0.37720 0.44360 0.44445 0.36006
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 645.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 8.70599E-02 1.39469E-03 6.99727E-03 8.39196E-03 1.10563E-03 0.080373
9 1 10.0 0.0 180.0 5.37195E-02 1.43281E-03 2.00049E-03 3.43330E-03 1.13585E-03 0.037239
9 4 10.0 45.0 135.0 5.90232E-02 1.42094E-03 2.32910E-03 3.75003E-03 1.12644E-03 0.039461
9 7 10.0 90.0 90.0 7.97453E-02 1.40490E-03 4.99681E-03 6.40171E-03 1.11373E-03 0.062660
8 1 20.0 0.0 180.0 4.21959E-02 1.45522E-03 1.03392E-03 2.48914E-03 1.15362E-03 0.024503
8 4 20.0 45.0 135.0 4.69754E-02 1.43080E-03 1.22320E-03 2.65400E-03 1.13426E-03 0.026039
8 7 20.0 90.0 90.0 6.90751E-02 1.40843E-03 2.86741E-03 4.27584E-03 1.11653E-03 0.041511
7 1 30.0 0.0 180.0 3.65861E-02 1.48356E-03 8.80710E-04 2.36427E-03 1.17608E-03 0.024072
7 4 30.0 45.0 135.0 4.05652E-02 1.46754E-03 9.89768E-04 2.45730E-03 1.16338E-03 0.024399
7 7 30.0 90.0 90.0 5.91332E-02 1.43157E-03 1.73360E-03 3.16517E-03 1.13487E-03 0.029317
6 1 40.0 0.0 180.0 3.47272E-02 1.50444E-03 9.79240E-04 2.48368E-03 1.19263E-03 0.028198
6 4 40.0 45.0 135.0 3.79723E-02 1.48252E-03 1.06205E-03 2.54457E-03 1.17526E-03 0.027969
6 7 40.0 90.0 90.0 5.33125E-02 1.44459E-03 1.54045E-03 2.98504E-03 1.14519E-03 0.028895
5 1 50.0 0.0 180.0 3.64103E-02 1.53042E-03 1.54687E-03 3.07729E-03 1.21323E-03 0.042485
5 4 50.0 45.0 135.0 3.88001E-02 1.49851E-03 1.61156E-03 3.11007E-03 1.18794E-03 0.041535
5 7 50.0 90.0 90.0 5.15749E-02 1.46476E-03 2.08344E-03 3.54820E-03 1.16118E-03 0.040396
4 1 60.0 0.0 180.0 4.32196E-02 1.51458E-03 3.60350E-03 5.11808E-03 1.20067E-03 0.083377
4 4 60.0 45.0 135.0 4.41977E-02 1.48015E-03 3.55839E-03 5.03854E-03 1.17338E-03 0.080511
4 7 60.0 90.0 90.0 5.45784E-02 1.46910E-03 4.15539E-03 5.62449E-03 1.16462E-03 0.076136
3 1 70.0 0.0 180.0 5.99675E-02 1.41187E-03 9.95383E-03 1.13657E-02 1.11925E-03 0.165987
3 4 70.0 45.0 135.0 5.82796E-02 1.39533E-03 9.57743E-03 1.09728E-02 1.10614E-03 0.164336
3 7 70.0 90.0 90.0 6.51552E-02 1.39369E-03 1.04150E-02 1.18087E-02 1.10484E-03 0.159849
2 1 80.0 0.0 180.0 1.01886E-01 1.21503E-03 2.47423E-02 2.59573E-02 9.63212E-04 0.242843
2 4 80.0 45.0 135.0 9.43441E-02 1.19886E-03 2.39309E-02 2.51298E-02 9.50393E-04 0.253655
2 7 80.0 90.0 90.0 9.37317E-02 1.20570E-03 2.50621E-02 2.62678E-02 9.55808E-04 0.267382
1 1 87.5 0.0 180.0 1.64730E-01 9.84081E-04 4.36364E-02 4.46205E-02 7.80125E-04 0.264896
1 4 87.5 45.0 135.0 1.48319E-01 9.25732E-04 4.33670E-02 4.42927E-02 7.33869E-04 0.292389
1 7 87.5 90.0 90.0 1.34938E-01 1.03840E-03 4.43833E-02 4.54217E-02 8.23185E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 645.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 8.392E-03 8.706E-02 1.047E-01 9.018E-02 1.354E-01 6.653E-03 5.446E+00 1.395E-03 1.106E-03
1 0.00 0.00 2.588E-03 1.620E-01 5.698E-03 7.068E-03 1.097E-02 2.110E-03 4.247E+00
3 3.94 5.00 3.277E-04 7.401E-02 8.904E-04 1.215E-03 2.070E-03 2.302E-03 4.438E+00
5 7.89 10.00 4.644E-05 1.277E-02 1.211E-04 1.556E-04 2.353E-04 2.976E-03 4.227E+00
Waveband 30 of 40 completed in 4.5 sec.
* * * * * Output for wavelength band 31 (650.0 to 660.0 nm; nominal wavelength = 655.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 34.0 m at 655.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 650.0 nm to 660.0 nm:
Ed(diffuse) = 3.062E-01 Ed(direct) = 8.991E-01 Ed(total) = 1.205E+00
Absorption Coefficients of Individual Components at 655.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3710 0.0392 0.0010 0.4112
3 4.171 5.000 0.3710 0.0392 0.0010 0.4112
5 8.343 10.000 0.3710 0.0392 0.0010 0.4112
Scattering Coefficients of Individual Components at 655.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0009 0.4222 0.0000 0.4231
3 4.171 5.000 0.0009 0.4222 0.0000 0.4231
5 8.343 10.000 0.0009 0.4222 0.0000 0.4231
Backscattering Coefficients of Individual Components at 655.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00045 0.00844 0.00000 0.00889
3 4.171 5.000 0.00045 0.00844 0.00000 0.00889
5 8.343 10.000 0.00045 0.00844 0.00000 0.00889
Summary of Inherent Optical Properties at 655.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.4112 0.4231 0.8343 0.5071 0.00889 0.02102
3 4.171 5.000 0.4112 0.4231 0.8343 0.5071 0.00889 0.02102
5 8.343 10.000 0.4112 0.4231 0.8343 0.5071 0.00889 0.02102
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.5016E-01
8 20.00 5.5877E-01
7 30.00 3.0054E-01
6 40.00 1.4384E-01
5 50.00 6.6357E-02
4 60.00 3.1422E-02
3 70.00 1.5877E-02
2 80.00 8.7336E-03
1 87.50 5.8779E-03
1 92.50 4.5986E-03
2 100.00 3.3870E-03
3 110.00 2.4221E-03
4 120.00 1.8727E-03
5 130.00 1.5566E-03
6 140.00 1.3737E-03
7 150.00 1.2691E-03
8 160.00 1.2112E-03
9 170.00 1.1825E-03
10 180.00 1.1727E-03
Asymptotic AOP values are
MUu(inf) = 0.3771
MUd(inf) = 0.8457
MU(inf) = 0.8238
R(inf) = 0.0081
Lu(inf)/Ed(inf) = 0.001789 (1/sr)
k(inf) = 0.4992 (1/m)
absorp(check) = 0.4112 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 655.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.1574E-01 1.6578E+00 1.7735E+00 4.3026E-02 1.2053E+00 0.3717 0.7271 0.6554 3.5696E-02
1 0.00 0.00 2.2833E-02 1.3123E+00 1.3351E+00 9.1124E-03 1.1714E+00 0.3991 0.8927 0.8706 7.7789E-03
3 4.17 5.00 2.4884E-03 1.2023E-01 1.2272E-01 9.7506E-04 1.0193E-01 0.3918 0.8478 0.8226 9.5660E-03
5 8.34 10.00 3.2592E-04 1.0131E-02 1.0457E-02 1.3754E-04 8.4591E-03 0.4220 0.8349 0.7958 1.6259E-02
K-functions (units of 1/meter) at 655.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.36283 0.43485 0.43362 0.41156 0.47142 0.47189 0.44902
5.000 5.010 5.005 0.44716 0.49229 0.49138 0.43961 0.49625 0.49679 0.42813
10.000 10.010 10.005 0.35113 0.49394 0.48949 0.33130 0.49720 0.49994 0.30635
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 655.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 8.26289E-02 1.16310E-03 6.68238E-03 7.84548E-03 9.64957E-04 0.080872
9 1 10.0 0.0 180.0 5.09854E-02 1.19529E-03 1.90421E-03 3.09949E-03 9.91660E-04 0.037348
9 4 10.0 45.0 135.0 5.60192E-02 1.18519E-03 2.21768E-03 3.40287E-03 9.83286E-04 0.039588
9 7 10.0 90.0 90.0 7.56866E-02 1.17133E-03 4.76801E-03 5.93934E-03 9.71783E-04 0.062997
8 1 20.0 0.0 180.0 4.00483E-02 1.21387E-03 9.81576E-04 2.19545E-03 1.00708E-03 0.024510
8 4 20.0 45.0 135.0 4.45846E-02 1.19318E-03 1.16167E-03 2.35485E-03 9.89912E-04 0.026055
8 7 20.0 90.0 90.0 6.55595E-02 1.17368E-03 2.73118E-03 3.90485E-03 9.73733E-04 0.041660
7 1 30.0 0.0 180.0 3.47241E-02 1.23720E-03 8.35885E-04 2.07309E-03 1.02643E-03 0.024072
7 4 30.0 45.0 135.0 3.85009E-02 1.22338E-03 9.39428E-04 2.16281E-03 1.01497E-03 0.024400
7 7 30.0 90.0 90.0 5.61222E-02 1.19216E-03 1.64728E-03 2.83945E-03 9.89071E-04 0.029352
6 1 40.0 0.0 180.0 3.29597E-02 1.25387E-03 9.29401E-04 2.18327E-03 1.04026E-03 0.028198
6 4 40.0 45.0 135.0 3.60397E-02 1.23496E-03 1.00800E-03 2.24296E-03 1.02457E-03 0.027969
6 7 40.0 90.0 90.0 5.05991E-02 1.20162E-03 1.46217E-03 2.66379E-03 9.96913E-04 0.028897
5 1 50.0 0.0 180.0 3.45572E-02 1.27465E-03 1.46814E-03 2.74280E-03 1.05751E-03 0.042485
5 4 50.0 45.0 135.0 3.68253E-02 1.24728E-03 1.52954E-03 2.77681E-03 1.03480E-03 0.041535
5 7 50.0 90.0 90.0 4.89500E-02 1.21700E-03 1.97741E-03 3.19441E-03 1.00968E-03 0.040396
4 1 60.0 0.0 180.0 4.10199E-02 1.26054E-03 3.42010E-03 4.68064E-03 1.04580E-03 0.083377
4 4 60.0 45.0 135.0 4.19482E-02 1.23095E-03 3.37728E-03 4.60824E-03 1.02125E-03 0.080511
4 7 60.0 90.0 90.0 5.18006E-02 1.21920E-03 3.94390E-03 5.16310E-03 1.01150E-03 0.076136
3 1 70.0 0.0 180.0 5.69154E-02 1.17408E-03 9.44722E-03 1.06213E-02 9.74066E-04 0.165987
3 4 70.0 45.0 135.0 5.53134E-02 1.15932E-03 9.08998E-03 1.02493E-02 9.61822E-04 0.164336
3 7 70.0 90.0 90.0 6.18391E-02 1.15520E-03 9.88492E-03 1.10401E-02 9.58402E-04 0.159849
2 1 80.0 0.0 180.0 9.67001E-02 1.00963E-03 2.34830E-02 2.44926E-02 8.37633E-04 0.242843
2 4 80.0 45.0 135.0 8.95424E-02 9.95237E-04 2.27129E-02 2.37081E-02 8.25691E-04 0.253655
2 7 80.0 90.0 90.0 8.89611E-02 9.98354E-04 2.37866E-02 2.47849E-02 8.28278E-04 0.267382
1 1 87.5 0.0 180.0 1.56346E-01 8.17161E-04 4.14155E-02 4.22326E-02 6.77952E-04 0.264896
1 4 87.5 45.0 135.0 1.40771E-01 7.67933E-04 4.11598E-02 4.19277E-02 6.37110E-04 0.292389
1 7 87.5 90.0 90.0 1.28070E-01 8.59103E-04 4.21243E-02 4.29834E-02 7.12749E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 655.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 7.845E-03 8.263E-02 9.929E-02 8.553E-02 1.284E-01 6.509E-03 5.484E+00 1.163E-03 9.650E-04
1 0.00 0.00 2.158E-03 1.537E-01 4.766E-03 5.910E-03 9.189E-03 1.842E-03 4.222E+00
3 4.17 5.00 2.276E-04 5.375E-02 5.762E-04 7.739E-04 1.297E-03 2.233E-03 4.283E+00
5 8.34 10.00 3.555E-05 7.132E-03 7.349E-05 8.908E-05 1.251E-04 4.202E-03 3.869E+00
Waveband 31 of 40 completed in 4.8 sec.
* * * * * Output for wavelength band 32 (660.0 to 670.0 nm; nominal wavelength = 665.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 32.2 m at 665.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 660.0 nm to 670.0 nm:
Ed(diffuse) = 3.168E-01 Ed(direct) = 9.381E-01 Ed(total) = 1.255E+00
Absorption Coefficients of Individual Components at 665.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.4290 0.0546 0.0009 0.4845
3 4.506 5.000 0.4290 0.0546 0.0009 0.4845
5 9.012 10.000 0.4290 0.0546 0.0009 0.4845
Scattering Coefficients of Individual Components at 665.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0008 0.4158 0.0000 0.4167
3 4.506 5.000 0.0008 0.4158 0.0000 0.4167
5 9.012 10.000 0.0008 0.4158 0.0000 0.4167
Backscattering Coefficients of Individual Components at 665.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00042 0.00832 0.00000 0.00874
3 4.506 5.000 0.00042 0.00832 0.00000 0.00874
5 9.012 10.000 0.00042 0.00832 0.00000 0.00874
Summary of Inherent Optical Properties at 665.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.4845 0.4167 0.9012 0.4624 0.00874 0.02097
3 4.506 5.000 0.4845 0.4167 0.9012 0.4624 0.00874 0.02097
5 9.012 10.000 0.4845 0.4167 0.9012 0.4624 0.00874 0.02097
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.3198E-01
8 20.00 5.1888E-01
7 30.00 2.6094E-01
6 40.00 1.1703E-01
5 50.00 5.1293E-02
4 60.00 2.3483E-02
3 70.00 1.1644E-02
2 80.00 6.3461E-03
1 87.50 4.2590E-03
1 92.50 3.3342E-03
2 100.00 2.4572E-03
3 110.00 1.7610E-03
4 120.00 1.3673E-03
5 130.00 1.1425E-03
6 140.00 1.0137E-03
7 150.00 9.4099E-04
8 160.00 9.0142E-04
9 170.00 8.8206E-04
10 180.00 8.7553E-04
Asymptotic AOP values are
MUu(inf) = 0.3793
MUd(inf) = 0.8591
MU(inf) = 0.8408
R(inf) = 0.0066
Lu(inf)/Ed(inf) = 0.001481 (1/sr)
k(inf) = 0.5763 (1/m)
absorp(check) = 0.4846 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 665.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.1963E-01 1.7242E+00 1.8438E+00 4.4536E-02 1.2549E+00 0.3723 0.7278 0.6564 3.5491E-02
1 0.00 0.00 2.1894E-02 1.3645E+00 1.3864E+00 8.8754E-03 1.2192E+00 0.4054 0.8935 0.8730 7.2797E-03
3 4.51 5.00 2.4677E-03 8.3878E-02 8.6346E-02 1.0578E-03 7.1293E-02 0.4287 0.8500 0.8134 1.4838E-02
5 9.01 10.00 5.9970E-04 5.2852E-03 5.8849E-03 2.7950E-04 4.2627E-03 0.4661 0.8065 0.6768 6.5568E-02
K-functions (units of 1/meter) at 665.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.41727 0.51683 0.51525 0.45385 0.55192 0.55264 0.47685
5.000 5.010 5.005 0.37110 0.56672 0.56113 0.34890 0.57254 0.57591 0.32352
10.000 10.010 10.005 0.21928 0.52279 0.49182 0.21050 0.54293 0.56630 0.20216
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 665.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 8.54737E-02 1.16512E-03 6.95328E-03 8.11841E-03 9.28493E-04 0.081350
9 1 10.0 0.0 180.0 5.27408E-02 1.19507E-03 1.97525E-03 3.17032E-03 9.52356E-04 0.037452
9 4 10.0 45.0 135.0 5.79479E-02 1.18562E-03 2.30109E-03 3.48671E-03 9.44827E-04 0.039710
9 7 10.0 90.0 90.0 7.82924E-02 1.17306E-03 4.95743E-03 6.13049E-03 9.34822E-04 0.063319
8 1 20.0 0.0 180.0 4.14272E-02 1.21169E-03 1.01565E-03 2.22734E-03 9.65602E-04 0.024516
8 4 20.0 45.0 135.0 4.61196E-02 1.19213E-03 1.20238E-03 2.39451E-03 9.50013E-04 0.026071
8 7 20.0 90.0 90.0 6.78167E-02 1.17461E-03 2.83482E-03 4.00943E-03 9.36056E-04 0.041801
7 1 30.0 0.0 180.0 3.59196E-02 1.23292E-03 8.64664E-04 2.09758E-03 9.82518E-04 0.024072
7 4 30.0 45.0 135.0 3.98266E-02 1.22064E-03 9.71806E-04 2.19244E-03 9.72733E-04 0.024401
7 7 30.0 90.0 90.0 5.80532E-02 1.19187E-03 1.70588E-03 2.89776E-03 9.49812E-04 0.029385
6 1 40.0 0.0 180.0 3.40945E-02 1.24671E-03 9.61399E-04 2.20811E-03 9.93509E-04 0.028198
6 4 40.0 45.0 135.0 3.72805E-02 1.22969E-03 1.04270E-03 2.27240E-03 9.79948E-04 0.027969
6 7 40.0 90.0 90.0 5.23412E-02 1.19870E-03 1.51264E-03 2.71133E-03 9.55248E-04 0.028900
5 1 50.0 0.0 180.0 3.57469E-02 1.26478E-03 1.51869E-03 2.78347E-03 1.00791E-03 0.042485
5 4 50.0 45.0 135.0 3.80932E-02 1.23937E-03 1.58220E-03 2.82157E-03 9.87661E-04 0.041535
5 7 50.0 90.0 90.0 5.06353E-02 1.21052E-03 2.04549E-03 3.25601E-03 9.64671E-04 0.040396
4 1 60.0 0.0 180.0 4.24322E-02 1.24811E-03 3.53785E-03 4.78596E-03 9.94625E-04 0.083377
4 4 60.0 45.0 135.0 4.33925E-02 1.22039E-03 3.49356E-03 4.71395E-03 9.72534E-04 0.080511
4 7 60.0 90.0 90.0 5.35840E-02 1.20868E-03 4.07969E-03 5.28837E-03 9.63203E-04 0.076136
3 1 70.0 0.0 180.0 5.88749E-02 1.15955E-03 9.77248E-03 1.09320E-02 9.24053E-04 0.165987
3 4 70.0 45.0 135.0 5.72178E-02 1.14605E-03 9.40294E-03 1.05490E-02 9.13292E-04 0.164336
3 7 70.0 90.0 90.0 6.39682E-02 1.13996E-03 1.02252E-02 1.13652E-02 9.08443E-04 0.159849
2 1 80.0 0.0 180.0 1.00029E-01 9.94657E-04 2.42915E-02 2.52861E-02 7.92647E-04 0.242843
2 4 80.0 45.0 135.0 9.26253E-02 9.80964E-04 2.34949E-02 2.44759E-02 7.81736E-04 0.253655
2 7 80.0 90.0 90.0 9.20240E-02 9.80767E-04 2.46055E-02 2.55863E-02 7.81579E-04 0.267382
1 1 87.5 0.0 180.0 1.61729E-01 8.02888E-04 4.28414E-02 4.36443E-02 6.39826E-04 0.264896
1 4 87.5 45.0 135.0 1.45617E-01 7.54565E-04 4.25769E-02 4.33314E-02 6.01317E-04 0.292389
1 7 87.5 90.0 90.0 1.32480E-01 8.39804E-04 4.35746E-02 4.44144E-02 6.69245E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 665.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 8.118E-03 8.547E-02 1.027E-01 8.845E-02 1.328E-01 6.470E-03 5.486E+00 1.165E-03 9.285E-04
1 0.00 0.00 2.162E-03 1.590E-01 4.599E-03 5.615E-03 8.542E-03 1.773E-03 4.105E+00
3 4.51 5.00 2.772E-04 3.830E-02 5.212E-04 6.339E-04 9.323E-04 3.888E-03 3.816E+00
5 9.01 10.00 7.985E-05 3.589E-03 1.154E-04 1.213E-04 1.347E-04 1.873E-02 3.500E+00
Waveband 32 of 40 completed in 5.0 sec.
* * * * * Output for wavelength band 33 (670.0 to 680.0 nm; nominal wavelength = 675.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 31.9 m at 675.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 670.0 nm to 680.0 nm:
Ed(diffuse) = 3.090E-01 Ed(direct) = 9.226E-01 Ed(total) = 1.232E+00
Absorption Coefficients of Individual Components at 675.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.4480 0.0557 0.0008 0.5044
3 4.575 5.000 0.4480 0.0557 0.0008 0.5044
5 9.149 10.000 0.4480 0.0557 0.0008 0.5044
Scattering Coefficients of Individual Components at 675.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0008 0.4097 0.0000 0.4105
3 4.575 5.000 0.0008 0.4097 0.0000 0.4105
5 9.149 10.000 0.0008 0.4097 0.0000 0.4105
Backscattering Coefficients of Individual Components at 675.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00040 0.00819 0.00000 0.00859
3 4.575 5.000 0.00040 0.00819 0.00000 0.00859
5 9.149 10.000 0.00040 0.00819 0.00000 0.00859
Summary of Inherent Optical Properties at 675.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.5044 0.4105 0.9149 0.4486 0.00859 0.02092
3 4.575 5.000 0.5044 0.4105 0.9149 0.4486 0.00859 0.02092
5 9.149 10.000 0.5044 0.4105 0.9149 0.4486 0.00859 0.02092
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.2593E-01
8 20.00 5.0618E-01
7 30.00 2.4905E-01
6 40.00 1.0943E-01
5 50.00 4.7222E-02
4 60.00 2.1409E-02
3 70.00 1.0561E-02
2 80.00 5.7423E-03
1 87.50 3.8510E-03
1 92.50 3.0156E-03
2 100.00 2.2227E-03
3 110.00 1.5938E-03
4 120.00 1.2389E-03
5 130.00 1.0366E-03
6 140.00 9.2111E-04
7 150.00 8.5613E-04
8 160.00 8.2096E-04
9 170.00 8.0384E-04
10 180.00 7.9807E-04
Asymptotic AOP values are
MUu(inf) = 0.3798
MUd(inf) = 0.8631
MU(inf) = 0.8458
R(inf) = 0.0062
Lu(inf)/Ed(inf) = 0.001394 (1/sr)
k(inf) = 0.5964 (1/m)
absorp(check) = 0.5045 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 675.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.1916E-01 1.6906E+00 1.8097E+00 4.4824E-02 1.2316E+00 0.3762 0.7285 0.6558 3.6396E-02
1 0.00 0.00 2.6314E-02 1.3428E+00 1.3691E+00 1.1093E-02 1.1978E+00 0.4216 0.8920 0.8668 9.2605E-03
3 4.57 5.00 4.8086E-03 7.7247E-02 8.2056E-02 2.1956E-03 6.4651E-02 0.4566 0.8369 0.7611 3.3960E-02
5 9.15 10.00 1.6578E-03 5.8105E-03 7.4683E-03 7.8595E-04 4.2434E-03 0.4741 0.7303 0.4630 1.8521E-01
K-functions (units of 1/meter) at 675.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.38207 0.53823 0.53522 0.39709 0.57199 0.57363 0.40022
5.000 5.010 5.005 0.26349 0.56710 0.54928 0.24874 0.58037 0.59204 0.23390
10.000 10.010 10.005 0.18773 0.43573 0.38063 0.18518 0.48139 0.54884 0.18287
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 675.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 8.33768E-02 1.53099E-03 6.82092E-03 8.35191E-03 1.24312E-03 0.081808
9 1 10.0 0.0 180.0 5.14469E-02 1.56267E-03 1.93192E-03 3.49459E-03 1.26884E-03 0.037552
9 4 10.0 45.0 135.0 5.65262E-02 1.55268E-03 2.25124E-03 3.80392E-03 1.26073E-03 0.039826
9 7 10.0 90.0 90.0 7.63717E-02 1.54137E-03 4.85946E-03 6.40082E-03 1.25154E-03 0.063629
8 1 20.0 0.0 180.0 4.04108E-02 1.57910E-03 9.90991E-04 2.57009E-03 1.28218E-03 0.024523
8 4 20.0 45.0 135.0 4.49881E-02 1.55763E-03 1.17356E-03 2.73119E-03 1.26475E-03 0.026086
8 7 20.0 90.0 90.0 6.61529E-02 1.54274E-03 2.77426E-03 4.31701E-03 1.25266E-03 0.041937
7 1 30.0 0.0 180.0 3.50384E-02 1.60171E-03 8.43451E-04 2.44516E-03 1.30054E-03 0.024072
7 4 30.0 45.0 135.0 3.88497E-02 1.59133E-03 9.47996E-04 2.53933E-03 1.29211E-03 0.024402
7 7 30.0 90.0 90.0 5.66278E-02 1.56408E-03 1.66580E-03 3.22989E-03 1.26999E-03 0.029417
6 1 40.0 0.0 180.0 3.32580E-02 1.61362E-03 9.37813E-04 2.55144E-03 1.31021E-03 0.028198
6 4 40.0 45.0 135.0 3.63659E-02 1.59852E-03 1.01712E-03 2.61564E-03 1.29795E-03 0.027969
6 7 40.0 90.0 90.0 5.10571E-02 1.56942E-03 1.47564E-03 3.04506E-03 1.27432E-03 0.028902
5 1 50.0 0.0 180.0 3.48699E-02 1.63201E-03 1.48143E-03 3.11344E-03 1.32514E-03 0.042485
5 4 50.0 45.0 135.0 3.71586E-02 1.60651E-03 1.54338E-03 3.14990E-03 1.30444E-03 0.041535
5 7 50.0 90.0 90.0 4.93930E-02 1.57877E-03 1.99530E-03 3.57408E-03 1.28191E-03 0.040396
4 1 60.0 0.0 180.0 4.13912E-02 1.60545E-03 3.45105E-03 5.05650E-03 1.30357E-03 0.083377
4 4 60.0 45.0 135.0 4.23279E-02 1.57693E-03 3.40785E-03 4.98479E-03 1.28042E-03 0.080511
4 7 60.0 90.0 90.0 5.22694E-02 1.56884E-03 3.97960E-03 5.54844E-03 1.27385E-03 0.076136
3 1 70.0 0.0 180.0 5.74306E-02 1.48589E-03 9.53273E-03 1.10186E-02 1.20650E-03 0.165987
3 4 70.0 45.0 135.0 5.58141E-02 1.47450E-03 9.17225E-03 1.06467E-02 1.19725E-03 0.164336
3 7 70.0 90.0 90.0 6.23988E-02 1.46861E-03 9.97439E-03 1.14430E-02 1.19246E-03 0.159849
2 1 80.0 0.0 180.0 9.75754E-02 1.26966E-03 2.36955E-02 2.49652E-02 1.03093E-03 0.242843
2 4 80.0 45.0 135.0 9.03529E-02 1.25629E-03 2.29185E-02 2.41748E-02 1.02006E-03 0.253655
2 7 80.0 90.0 90.0 8.97663E-02 1.25376E-03 2.40019E-02 2.52556E-02 1.01801E-03 0.267382
1 1 87.5 0.0 180.0 1.57761E-01 1.02032E-03 4.17903E-02 4.28107E-02 8.28472E-04 0.264896
1 4 87.5 45.0 135.0 1.42045E-01 9.61228E-04 4.15323E-02 4.24936E-02 7.80488E-04 0.292389
1 7 87.5 90.0 90.0 1.29229E-01 1.06370E-03 4.25056E-02 4.35693E-02 8.63688E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 675.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 8.352E-03 8.338E-02 1.003E-01 8.640E-02 1.297E-01 6.781E-03 5.367E+00 1.531E-03 1.243E-03
1 0.00 0.00 2.841E-03 1.551E-01 5.493E-03 6.454E-03 9.185E-03 2.372E-03 3.904E+00
3 4.57 5.00 6.138E-04 3.432E-02 9.389E-04 1.032E-03 1.280E-03 9.494E-03 3.577E+00
5 9.15 10.00 2.275E-04 3.176E-03 3.086E-04 3.129E-04 3.230E-04 5.362E-02 3.454E+00
Waveband 33 of 40 completed in 4.9 sec.
* * * * * Output for wavelength band 34 (680.0 to 690.0 nm; nominal wavelength = 685.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 31.4 m at 685.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 680.0 nm to 690.0 nm:
Ed(diffuse) = 2.816E-01 Ed(direct) = 8.472E-01 Ed(total) = 1.129E+00
Absorption Coefficients of Individual Components at 685.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.4860 0.0433 0.0007 0.5300
3 4.672 5.000 0.4860 0.0433 0.0007 0.5300
5 9.344 10.000 0.4860 0.0433 0.0007 0.5300
Scattering Coefficients of Individual Components at 685.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0007 0.4037 0.0000 0.4044
3 4.672 5.000 0.0007 0.4037 0.0000 0.4044
5 9.344 10.000 0.0007 0.4037 0.0000 0.4044
Backscattering Coefficients of Individual Components at 685.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00037 0.00807 0.00000 0.00844
3 4.672 5.000 0.00037 0.00807 0.00000 0.00844
5 9.344 10.000 0.00037 0.00807 0.00000 0.00844
Summary of Inherent Optical Properties at 685.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.5300 0.4044 0.9344 0.4328 0.00844 0.02088
3 4.672 5.000 0.5300 0.4044 0.9344 0.4328 0.00844 0.02088
5 9.344 10.000 0.5300 0.4044 0.9344 0.4328 0.00844 0.02088
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.1864E-01
8 20.00 4.9124E-01
7 30.00 2.3548E-01
6 40.00 1.0102E-01
5 50.00 4.2822E-02
4 60.00 1.9205E-02
3 70.00 9.4220E-03
2 80.00 5.1109E-03
1 87.50 3.4255E-03
1 92.50 2.6834E-03
2 100.00 1.9785E-03
3 110.00 1.4198E-03
4 120.00 1.1051E-03
5 130.00 9.2618E-04
6 140.00 8.2444E-04
7 150.00 7.6746E-04
8 160.00 7.3679E-04
9 170.00 7.2195E-04
10 180.00 7.1697E-04
Asymptotic AOP values are
MUu(inf) = 0.3805
MUd(inf) = 0.8676
MU(inf) = 0.8515
R(inf) = 0.0058
Lu(inf)/Ed(inf) = 0.001302 (1/sr)
k(inf) = 0.6225 (1/m)
absorp(check) = 0.5300 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 685.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.1048E-01 1.5481E+00 1.6586E+00 4.1912E-02 1.1288E+00 0.3794 0.7291 0.6553 3.7130E-02
1 0.00 0.00 2.7664E-02 1.2334E+00 1.2610E+00 1.1938E-02 1.0988E+00 0.4315 0.8909 0.8619 1.0864E-02
3 4.67 5.00 6.1285E-03 6.4486E-02 7.0615E-02 2.8547E-03 5.3149E-02 0.4658 0.8242 0.7122 5.3711E-02
5 9.34 10.00 2.2997E-03 5.5819E-03 7.8817E-03 1.0957E-03 3.7699E-03 0.4765 0.6754 0.3393 2.9065E-01
K-functions (units of 1/meter) at 685.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.36789 0.56587 0.56152 0.37166 0.59838 0.60087 0.36621
5.000 5.010 5.005 0.23141 0.57175 0.54217 0.22128 0.59279 0.61392 0.21128
10.000 10.010 10.005 0.18164 0.37369 0.31761 0.18034 0.42908 0.53118 0.17922
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 685.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 7.59819E-02 1.69483E-03 6.24883E-03 7.94366E-03 1.50145E-03 0.082241
9 1 10.0 0.0 180.0 4.68840E-02 1.72532E-03 1.76499E-03 3.49031E-03 1.52846E-03 0.037646
9 4 10.0 45.0 135.0 5.15128E-02 1.71571E-03 2.05725E-03 3.77295E-03 1.51994E-03 0.039937
9 7 10.0 90.0 90.0 6.95981E-02 1.70625E-03 4.44880E-03 6.15505E-03 1.51156E-03 0.063921
8 1 20.0 0.0 180.0 3.68267E-02 1.74025E-03 9.03321E-04 2.64357E-03 1.54169E-03 0.024529
8 4 20.0 45.0 135.0 4.09980E-02 1.71900E-03 1.07005E-03 2.78905E-03 1.52286E-03 0.026100
8 7 20.0 90.0 90.0 6.02856E-02 1.70732E-03 2.53594E-03 4.24327E-03 1.51251E-03 0.042065
7 1 30.0 0.0 180.0 3.19307E-02 1.76208E-03 7.68643E-04 2.53072E-03 1.56102E-03 0.024072
7 4 30.0 45.0 135.0 3.54042E-02 1.75400E-03 8.63944E-04 2.61794E-03 1.55387E-03 0.024402
7 7 30.0 90.0 90.0 5.16043E-02 1.73007E-03 1.51958E-03 3.24965E-03 1.53266E-03 0.029447
6 1 40.0 0.0 180.0 3.03083E-02 1.77147E-03 8.54636E-04 2.62610E-03 1.56934E-03 0.028198
6 4 40.0 45.0 135.0 3.31405E-02 1.75904E-03 9.26912E-04 2.68595E-03 1.55833E-03 0.027969
6 7 40.0 90.0 90.0 4.65287E-02 1.73369E-03 1.34486E-03 3.07856E-03 1.53587E-03 0.028904
5 1 50.0 0.0 180.0 3.17773E-02 1.78854E-03 1.35004E-03 3.13858E-03 1.58446E-03 0.042485
5 4 50.0 45.0 135.0 3.38629E-02 1.76499E-03 1.40649E-03 3.17148E-03 1.56360E-03 0.041535
5 7 50.0 90.0 90.0 4.50123E-02 1.74026E-03 1.81834E-03 3.55860E-03 1.54170E-03 0.040396
4 1 60.0 0.0 180.0 3.77201E-02 1.75629E-03 3.14497E-03 4.90126E-03 1.55589E-03 0.083377
4 4 60.0 45.0 135.0 3.85738E-02 1.72941E-03 3.10560E-03 4.83501E-03 1.53208E-03 0.080511
4 7 60.0 90.0 90.0 4.76335E-02 1.72471E-03 3.62664E-03 5.35134E-03 1.52791E-03 0.076136
3 1 70.0 0.0 180.0 5.23369E-02 1.62202E-03 8.68725E-03 1.03093E-02 1.43694E-03 0.165987
3 4 70.0 45.0 135.0 5.08638E-02 1.61314E-03 8.35874E-03 9.97189E-03 1.42908E-03 0.164336
3 7 70.0 90.0 90.0 5.68645E-02 1.60779E-03 9.08974E-03 1.06975E-02 1.42434E-03 0.159849
2 1 80.0 0.0 180.0 8.89212E-02 1.38294E-03 2.15939E-02 2.29769E-02 1.22514E-03 0.242843
2 4 80.0 45.0 135.0 8.23393E-02 1.37084E-03 2.08858E-02 2.22566E-02 1.21443E-03 0.253655
2 7 80.0 90.0 90.0 8.18047E-02 1.36662E-03 2.18731E-02 2.32397E-02 1.21068E-03 0.267382
1 1 87.5 0.0 180.0 1.43769E-01 1.10856E-03 3.80839E-02 3.91924E-02 9.82068E-04 0.264896
1 4 87.5 45.0 135.0 1.29447E-01 1.04575E-03 3.78487E-02 3.88945E-02 9.26425E-04 0.292389
1 7 87.5 90.0 90.0 1.17768E-01 1.15340E-03 3.87357E-02 3.98891E-02 1.02179E-03 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 685.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 7.944E-03 7.598E-02 9.148E-02 7.883E-02 1.182E-01 7.037E-03 5.276E+00 1.695E-03 1.501E-03
1 0.00 0.00 3.145E-03 1.414E-01 5.757E-03 6.597E-03 8.957E-03 2.863E-03 3.795E+00
3 4.67 5.00 8.144E-04 2.794E-02 1.162E-03 1.232E-03 1.417E-03 1.532E-02 3.505E+00
5 9.34 10.00 3.190E-04 2.523E-03 4.231E-04 4.259E-04 4.324E-04 8.462E-02 3.435E+00
Waveband 34 of 40 completed in 5.1 sec.
* * * * * Output for wavelength band 35 (690.0 to 700.0 nm; nominal wavelength = 695.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 30.3 m at 695.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 690.0 nm to 700.0 nm:
Ed(diffuse) = 2.700E-01 Ed(direct) = 8.188E-01 Ed(total) = 1.089E+00
Absorption Coefficients of Individual Components at 695.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.5590 0.0268 0.0006 0.5864
3 4.925 5.000 0.5590 0.0268 0.0006 0.5864
5 9.850 10.000 0.5590 0.0268 0.0006 0.5864
Scattering Coefficients of Individual Components at 695.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0007 0.3979 0.0000 0.3986
3 4.925 5.000 0.0007 0.3979 0.0000 0.3986
5 9.850 10.000 0.0007 0.3979 0.0000 0.3986
Backscattering Coefficients of Individual Components at 695.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00035 0.00796 0.00000 0.00831
3 4.925 5.000 0.00035 0.00796 0.00000 0.00831
5 9.850 10.000 0.00035 0.00796 0.00000 0.00831
Summary of Inherent Optical Properties at 695.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.5864 0.3986 0.9850 0.4047 0.00831 0.02084
3 4.925 5.000 0.5864 0.3986 0.9850 0.4047 0.00831 0.02084
5 9.850 10.000 0.5864 0.3986 0.9850 0.4047 0.00831 0.02084
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.0471E-01
8 20.00 4.6377E-01
7 30.00 2.1171E-01
6 40.00 8.6933E-02
5 50.00 3.5720E-02
4 60.00 1.5735E-02
3 70.00 7.6543E-03
2 80.00 4.1387E-03
1 87.50 2.7724E-03
1 92.50 2.1739E-03
2 100.00 1.6042E-03
3 110.00 1.1533E-03
4 120.00 9.0012E-04
5 130.00 7.5686E-04
6 140.00 6.7592E-04
7 150.00 6.3100E-04
8 160.00 6.0711E-04
9 170.00 5.9567E-04
10 180.00 5.9186E-04
Asymptotic AOP values are
MUu(inf) = 0.3820
MUd(inf) = 0.8755
MU(inf) = 0.8612
R(inf) = 0.0051
Lu(inf)/Ed(inf) = 0.001152 (1/sr)
k(inf) = 0.6810 (1/m)
absorp(check) = 0.5864 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 695.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.0379E-01 1.4919E+00 1.5957E+00 3.9093E-02 1.0888E+00 0.3766 0.7298 0.6578 3.5905E-02
1 0.00 0.00 2.0671E-02 1.1848E+00 1.2055E+00 8.7775E-03 1.0585E+00 0.4246 0.8933 0.8707 8.2927E-03
3 4.92 5.00 3.7064E-03 4.4571E-02 4.8278E-02 1.7314E-03 3.7164E-02 0.4671 0.8338 0.7339 4.6588E-02
5 9.85 10.00 1.3789E-03 3.0978E-03 4.4767E-03 6.6014E-04 2.0650E-03 0.4787 0.6666 0.3138 3.1968E-01
K-functions (units of 1/meter) at 695.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.43568 0.63015 0.62681 0.44209 0.66187 0.66371 0.43631
5.000 5.010 5.005 0.24159 0.63591 0.60558 0.22954 0.65624 0.67713 0.21779
10.000 10.010 10.005 0.18064 0.38541 0.32230 0.17951 0.44945 0.57655 0.17851
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 695.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 7.28671E-02 1.22751E-03 6.02455E-03 7.25205E-03 1.12741E-03 0.082679
9 1 10.0 0.0 180.0 4.49620E-02 1.25191E-03 1.69691E-03 2.94883E-03 1.14983E-03 0.037741
9 4 10.0 45.0 135.0 4.94011E-02 1.24416E-03 1.97842E-03 3.22258E-03 1.14270E-03 0.040048
9 7 10.0 90.0 90.0 6.67449E-02 1.23559E-03 4.28615E-03 5.52174E-03 1.13483E-03 0.064217
8 1 20.0 0.0 180.0 3.53170E-02 1.26410E-03 8.66506E-04 2.13060E-03 1.16102E-03 0.024535
8 4 20.0 45.0 135.0 3.93173E-02 1.24733E-03 1.02674E-03 2.27407E-03 1.14562E-03 0.026114
8 7 20.0 90.0 90.0 5.78143E-02 1.23614E-03 2.43949E-03 3.67563E-03 1.13534E-03 0.042195
7 1 30.0 0.0 180.0 3.06217E-02 1.28110E-03 7.37133E-04 2.01823E-03 1.17663E-03 0.024072
7 4 30.0 45.0 135.0 3.39530E-02 1.27337E-03 8.28554E-04 2.10193E-03 1.16954E-03 0.024403
7 7 30.0 90.0 90.0 4.94878E-02 1.25245E-03 1.45876E-03 2.71121E-03 1.15032E-03 0.029477
6 1 40.0 0.0 180.0 2.90658E-02 1.28903E-03 8.19600E-04 2.10863E-03 1.18392E-03 0.028198
6 4 40.0 45.0 135.0 3.17819E-02 1.27764E-03 8.88913E-04 2.16656E-03 1.17346E-03 0.027969
6 7 40.0 90.0 90.0 4.46213E-02 1.25518E-03 1.28983E-03 2.54501E-03 1.15283E-03 0.028906
5 1 50.0 0.0 180.0 3.04746E-02 1.30222E-03 1.29470E-03 2.59692E-03 1.19603E-03 0.042485
5 4 50.0 45.0 135.0 3.24747E-02 1.28254E-03 1.34884E-03 2.63137E-03 1.17795E-03 0.041535
5 7 50.0 90.0 90.0 4.31670E-02 1.26079E-03 1.74379E-03 3.00458E-03 1.15798E-03 0.040396
4 1 60.0 0.0 180.0 3.61738E-02 1.27949E-03 3.01605E-03 4.29554E-03 1.17516E-03 0.083377
4 4 60.0 45.0 135.0 3.69924E-02 1.25735E-03 2.97829E-03 4.23564E-03 1.15482E-03 0.080511
4 7 60.0 90.0 90.0 4.56808E-02 1.25078E-03 3.47797E-03 4.72875E-03 1.14879E-03 0.076136
3 1 70.0 0.0 180.0 5.01914E-02 1.18257E-03 8.33112E-03 9.51369E-03 1.08614E-03 0.165987
3 4 70.0 45.0 135.0 4.87787E-02 1.17389E-03 8.01608E-03 9.18997E-03 1.07816E-03 0.164336
3 7 70.0 90.0 90.0 5.45334E-02 1.16830E-03 8.71711E-03 9.88541E-03 1.07303E-03 0.159849
2 1 80.0 0.0 180.0 8.52759E-02 1.00913E-03 2.07087E-02 2.17178E-02 9.26845E-04 0.242843
2 4 80.0 45.0 135.0 7.89638E-02 9.98656E-04 2.00296E-02 2.10282E-02 9.17221E-04 0.253655
2 7 80.0 90.0 90.0 7.84512E-02 9.95267E-04 2.09764E-02 2.19717E-02 9.14108E-04 0.267382
1 1 87.5 0.0 180.0 1.37875E-01 8.09834E-04 3.65226E-02 3.73325E-02 7.43796E-04 0.264896
1 4 87.5 45.0 135.0 1.24140E-01 7.62922E-04 3.62971E-02 3.70601E-02 7.00710E-04 0.292389
1 7 87.5 90.0 90.0 1.12940E-01 8.42443E-04 3.71477E-02 3.79902E-02 7.73746E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 695.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 7.252E-03 7.287E-02 8.760E-02 7.547E-02 1.133E-01 6.661E-03 5.391E+00 1.228E-03 1.127E-03
1 0.00 0.00 2.278E-03 1.356E-01 4.333E-03 5.058E-03 7.126E-03 2.152E-03 3.853E+00
3 4.92 5.00 4.972E-04 1.988E-02 6.970E-04 7.403E-04 8.552E-04 1.338E-02 3.482E+00
5 9.85 10.00 1.938E-04 1.380E-03 2.503E-04 2.516E-04 2.545E-04 9.386E-02 3.406E+00
Waveband 35 of 40 completed in 4.8 sec.
* * * * * Output for wavelength band 36 (700.0 to 710.0 nm; nominal wavelength = 705.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 28.0 m at 705.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 700.0 nm to 710.0 nm:
Ed(diffuse) = 2.706E-01 Ed(direct) = 8.263E-01 Ed(total) = 1.097E+00
Absorption Coefficients of Individual Components at 705.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.7040 0.0165 0.0005 0.7210
3 5.570 5.000 0.7040 0.0165 0.0005 0.7210
5 11.139 10.000 0.7040 0.0165 0.0005 0.7210
Scattering Coefficients of Individual Components at 705.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0007 0.3923 0.0000 0.3929
3 5.570 5.000 0.0007 0.3923 0.0000 0.3929
5 11.139 10.000 0.0007 0.3923 0.0000 0.3929
Backscattering Coefficients of Individual Components at 705.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00033 0.00785 0.00000 0.00817
3 5.570 5.000 0.00033 0.00785 0.00000 0.00817
5 11.139 10.000 0.00033 0.00785 0.00000 0.00817
Summary of Inherent Optical Properties at 705.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.7210 0.3929 1.1139 0.3527 0.00817 0.02080
3 5.570 5.000 0.7210 0.3929 1.1139 0.3527 0.00817 0.02080
5 11.139 10.000 0.7210 0.3929 1.1139 0.3527 0.00817 0.02080
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 7.7506E-01
8 20.00 4.0988E-01
7 30.00 1.6938E-01
6 40.00 6.3938E-02
5 50.00 2.4852E-02
4 60.00 1.0636E-02
3 70.00 5.1141E-03
2 80.00 2.7563E-03
1 87.50 1.8472E-03
1 92.50 1.4518E-03
2 100.00 1.0738E-03
3 110.00 7.7502E-04
4 120.00 6.0829E-04
5 130.00 5.1470E-04
6 140.00 4.6250E-04
7 150.00 4.3406E-04
8 160.00 4.1930E-04
9 170.00 4.1240E-04
10 180.00 4.1013E-04
Asymptotic AOP values are
MUu(inf) = 0.3848
MUd(inf) = 0.8897
MU(inf) = 0.8782
R(inf) = 0.0040
Lu(inf)/Ed(inf) = 0.000917 (1/sr)
k(inf) = 0.8210 (1/m)
absorp(check) = 0.7211 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 705.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.0088E-01 1.5018E+00 1.6027E+00 3.7556E-02 1.0969E+00 0.3723 0.7304 0.6610 3.4238E-02
1 0.00 0.00 1.2390E-02 1.1870E+00 1.1994E+00 5.0243E-03 1.0644E+00 0.4055 0.8967 0.8832 4.7204E-03
3 5.57 5.00 9.8242E-04 2.0192E-02 2.1174E-02 4.5728E-04 1.7309E-02 0.4655 0.8572 0.7959 2.6419E-02
5 11.14 10.00 3.4417E-04 7.2448E-04 1.0687E-03 1.6630E-04 4.8214E-04 0.4832 0.6655 0.2955 3.4493E-01
K-functions (units of 1/meter) at 705.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 0.64280 0.78286 0.78141 0.66542 0.81285 0.81355 0.67095
5.000 5.010 5.005 0.29433 0.80041 0.77688 0.27295 0.81445 0.82918 0.25213
10.000 10.010 10.005 0.17920 0.43884 0.35515 0.17812 0.52408 0.70672 0.17713
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 705.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 7.30170E-02 6.69139E-04 6.06697E-03 6.73611E-03 6.10016E-04 0.083090
9 1 10.0 0.0 180.0 4.50545E-02 6.86467E-04 1.70444E-03 2.39090E-03 6.25812E-04 0.037831
9 4 10.0 45.0 135.0 4.95027E-02 6.80912E-04 1.98768E-03 2.66859E-03 6.20748E-04 0.040153
9 7 10.0 90.0 90.0 6.68822E-02 6.73352E-04 4.31355E-03 4.98690E-03 6.13856E-04 0.064495
8 1 20.0 0.0 180.0 3.53897E-02 6.95651E-04 8.68492E-04 1.56414E-03 6.34185E-04 0.024541
8 4 20.0 45.0 135.0 3.93982E-02 6.84201E-04 1.02938E-03 1.71359E-03 6.23747E-04 0.026128
8 7 20.0 90.0 90.0 5.79332E-02 6.73525E-04 2.45157E-03 3.12510E-03 6.14014E-04 0.042317
7 1 30.0 0.0 180.0 3.06847E-02 7.07252E-04 7.38649E-04 1.44590E-03 6.44761E-04 0.024072
7 4 30.0 45.0 135.0 3.40230E-02 6.99885E-04 8.30284E-04 1.53017E-03 6.38045E-04 0.024404
7 7 30.0 90.0 90.0 4.95886E-02 6.82456E-04 1.46315E-03 2.14561E-03 6.22156E-04 0.029506
6 1 40.0 0.0 180.0 2.91256E-02 7.14009E-04 8.21286E-04 1.53529E-03 6.50921E-04 0.028198
6 4 40.0 45.0 135.0 3.18473E-02 7.03789E-04 8.90742E-04 1.59453E-03 6.41604E-04 0.027969
6 7 40.0 90.0 90.0 4.47131E-02 6.84654E-04 1.29257E-03 1.97722E-03 6.24160E-04 0.028908
5 1 50.0 0.0 180.0 3.05372E-02 7.23098E-04 1.29736E-03 2.02046E-03 6.59207E-04 0.042485
5 4 50.0 45.0 135.0 3.25416E-02 7.07955E-04 1.35161E-03 2.05957E-03 6.45402E-04 0.041535
5 7 50.0 90.0 90.0 4.32558E-02 6.89649E-04 1.74738E-03 2.43703E-03 6.28713E-04 0.040396
4 1 60.0 0.0 180.0 3.62482E-02 7.12252E-04 3.02225E-03 3.73450E-03 6.49319E-04 0.083377
4 4 60.0 45.0 135.0 3.70685E-02 6.95688E-04 2.98442E-03 3.68010E-03 6.34219E-04 0.080511
4 7 60.0 90.0 90.0 4.57748E-02 6.86795E-04 3.48512E-03 4.17192E-03 6.26111E-04 0.076136
3 1 70.0 0.0 180.0 5.02946E-02 6.60310E-04 8.34826E-03 9.00857E-03 6.01967E-04 0.165987
3 4 70.0 45.0 135.0 4.88790E-02 6.51790E-04 8.03257E-03 8.68436E-03 5.94200E-04 0.164336
3 7 70.0 90.0 90.0 5.46456E-02 6.45856E-04 8.73504E-03 9.38090E-03 5.88790E-04 0.159849
2 1 80.0 0.0 180.0 8.54513E-02 5.65303E-04 2.07513E-02 2.13166E-02 5.15354E-04 0.242843
2 4 80.0 45.0 135.0 7.91262E-02 5.56698E-04 2.00708E-02 2.06275E-02 5.07509E-04 0.253655
2 7 80.0 90.0 90.0 7.86126E-02 5.54244E-04 2.10196E-02 2.15738E-02 5.05272E-04 0.267382
1 1 87.5 0.0 180.0 1.38159E-01 4.55465E-04 3.65978E-02 3.70532E-02 4.15221E-04 0.264896
1 4 87.5 45.0 135.0 1.24395E-01 4.27374E-04 3.63718E-02 3.67992E-02 3.89612E-04 0.292389
1 7 87.5 90.0 90.0 1.13172E-01 4.73490E-04 3.72242E-02 3.76977E-02 4.31654E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 705.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 6.736E-03 7.302E-02 8.761E-02 7.543E-02 1.133E-01 6.141E-03 5.575E+00 6.691E-04 6.100E-04
1 0.00 0.00 1.242E-03 1.358E-01 2.664E-03 3.255E-03 4.983E-03 1.167E-03 4.046E+00
3 5.57 5.00 1.322E-04 9.757E-03 1.842E-04 2.004E-04 2.433E-04 7.635E-03 3.460E+00
5 11.14 10.00 4.973E-05 3.388E-04 6.089E-05 6.112E-05 6.163E-05 1.032E-01 3.344E+00
Waveband 36 of 40 completed in 5.2 sec.
* * * * * Output for wavelength band 37 (710.0 to 720.0 nm; nominal wavelength = 715.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 24.3 m at 715.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 710.0 nm to 720.0 nm:
Ed(diffuse) = 2.466E-01 Ed(direct) = 7.579E-01 Ed(total) = 1.004E+00
Absorption Coefficients of Individual Components at 715.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 1.0070 0.0072 0.0004 1.0147
3 7.010 5.000 1.0070 0.0072 0.0004 1.0147
5 14.020 10.000 1.0070 0.0072 0.0004 1.0147
Scattering Coefficients of Individual Components at 715.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0006 0.3868 0.0000 0.3874
3 7.010 5.000 0.0006 0.3868 0.0000 0.3874
5 14.020 10.000 0.0006 0.3868 0.0000 0.3874
Backscattering Coefficients of Individual Components at 715.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00031 0.00774 0.00000 0.00804
3 7.010 5.000 0.00031 0.00774 0.00000 0.00804
5 14.020 10.000 0.00031 0.00774 0.00000 0.00804
Summary of Inherent Optical Properties at 715.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 1.0147 0.3874 1.4020 0.2763 0.00804 0.02076
3 7.010 5.000 1.0147 0.3874 1.4020 0.2763 0.00804 0.02076
5 14.020 10.000 1.0147 0.3874 1.4020 0.2763 0.00804 0.02076
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 7.1793E-01
8 20.00 3.2187E-01
7 30.00 1.1167E-01
6 40.00 3.6937E-02
5 50.00 1.3325E-02
4 60.00 5.5289E-03
3 70.00 2.6372E-03
2 80.00 1.4224E-03
1 87.50 9.5617E-04
1 92.50 7.5479E-04
2 100.00 5.6072E-04
3 110.00 4.0741E-04
4 120.00 3.2255E-04
5 130.00 2.7553E-04
6 140.00 2.4986E-04
7 150.00 2.3632E-04
8 160.00 2.2959E-04
9 170.00 2.2661E-04
10 180.00 2.2565E-04
Asymptotic AOP values are
MUu(inf) = 0.3893
MUd(inf) = 0.9100
MU(inf) = 0.9020
R(inf) = 0.0027
Lu(inf)/Ed(inf) = 0.000637 (1/sr)
k(inf) = 1.1251 (1/m)
absorp(check) = 1.0148 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 715.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 9.0530E-02 1.3742E+00 1.4647E+00 3.3523E-02 1.0045E+00 0.3703 0.7310 0.6629 3.3374E-02
1 0.00 0.00 6.9470E-03 1.0834E+00 1.0904E+00 2.7330E-03 9.7368E-01 0.3934 0.8987 0.8905 2.8069E-03
3 7.01 5.00 1.2614E-04 3.5824E-03 3.7085E-03 5.9801E-05 3.1354E-03 0.4741 0.8752 0.8293 1.9073E-02
5 14.02 10.00 4.4992E-05 6.3840E-05 1.0883E-04 2.2163E-05 3.7232E-05 0.4926 0.5832 0.1385 5.9527E-01
K-functions (units of 1/meter) at 715.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 1.02771 1.11335 1.11280 1.06182 1.13887 1.13909 1.07997
5.000 5.010 5.005 0.34202 1.11952 1.09297 0.30967 1.13299 1.14906 0.27788
10.000 10.010 10.005 0.17307 0.33295 0.26683 0.17291 0.42168 0.78869 0.17278
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 715.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 6.65321E-02 3.53025E-04 5.55348E-03 5.90651E-03 3.51452E-04 0.083471
9 1 10.0 0.0 180.0 4.10531E-02 3.63792E-04 1.55646E-03 1.92025E-03 3.62171E-04 0.037913
9 4 10.0 45.0 135.0 4.51062E-02 3.60323E-04 1.81552E-03 2.17584E-03 3.58717E-04 0.040250
9 7 10.0 90.0 90.0 6.09422E-02 3.55144E-04 3.94612E-03 4.30127E-03 3.53562E-04 0.064752
8 1 20.0 0.0 180.0 3.22466E-02 3.69632E-04 7.91531E-04 1.16116E-03 3.67985E-04 0.024546
8 4 20.0 45.0 135.0 3.58992E-02 3.62654E-04 9.38408E-04 1.30106E-03 3.61038E-04 0.026140
8 7 20.0 90.0 90.0 5.27880E-02 3.55118E-04 2.23980E-03 2.59492E-03 3.53536E-04 0.042430
7 1 30.0 0.0 180.0 2.79595E-02 3.76645E-04 6.73047E-04 1.04969E-03 3.74967E-04 0.024072
7 4 30.0 45.0 135.0 3.10015E-02 3.71476E-04 7.56566E-04 1.12804E-03 3.69821E-04 0.024404
7 7 30.0 90.0 90.0 4.51837E-02 3.59750E-04 1.33438E-03 1.69413E-03 3.58147E-04 0.029532
6 1 40.0 0.0 180.0 2.65389E-02 3.81102E-04 7.48345E-04 1.12945E-03 3.79404E-04 0.028198
6 4 40.0 45.0 135.0 2.90189E-02 3.74068E-04 8.11633E-04 1.18570E-03 3.72402E-04 0.027969
6 7 40.0 90.0 90.0 4.07420E-02 3.61000E-04 1.17785E-03 1.53885E-03 3.59392E-04 0.028910
5 1 50.0 0.0 180.0 2.78252E-02 3.86558E-04 1.18214E-03 1.56870E-03 3.84836E-04 0.042485
5 4 50.0 45.0 135.0 2.96514E-02 3.76742E-04 1.23157E-03 1.60831E-03 3.75063E-04 0.041535
5 7 50.0 90.0 90.0 3.94141E-02 3.64170E-04 1.59219E-03 1.95636E-03 3.62547E-04 0.040396
4 1 60.0 0.0 180.0 3.30289E-02 3.81347E-04 2.75384E-03 3.13518E-03 3.79648E-04 0.083377
4 4 60.0 45.0 135.0 3.37764E-02 3.70722E-04 2.71936E-03 3.09008E-03 3.69070E-04 0.080511
4 7 60.0 90.0 90.0 4.17094E-02 3.63442E-04 3.17560E-03 3.53904E-03 3.61823E-04 0.076136
3 1 70.0 0.0 180.0 4.58278E-02 3.54188E-04 7.60683E-03 7.96101E-03 3.52610E-04 0.165987
3 4 70.0 45.0 135.0 4.45379E-02 3.48053E-04 7.31918E-03 7.66723E-03 3.46502E-04 0.164336
3 7 70.0 90.0 90.0 4.97924E-02 3.43177E-04 7.95926E-03 8.30244E-03 3.41648E-04 0.159849
2 1 80.0 0.0 180.0 7.78622E-02 3.03826E-04 1.89083E-02 1.92121E-02 3.02472E-04 0.242843
2 4 80.0 45.0 135.0 7.20988E-02 2.97988E-04 1.82883E-02 1.85862E-02 2.96660E-04 0.253655
2 7 80.0 90.0 90.0 7.16308E-02 2.95827E-04 1.91528E-02 1.94486E-02 2.94509E-04 0.267382
1 1 87.5 0.0 180.0 1.25889E-01 2.45394E-04 3.33474E-02 3.35928E-02 2.44301E-04 0.264896
1 4 87.5 45.0 135.0 1.13347E-01 2.29457E-04 3.31415E-02 3.33710E-02 2.28435E-04 0.292389
1 7 87.5 90.0 90.0 1.03121E-01 2.54189E-04 3.39182E-02 3.41724E-02 2.53056E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 715.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 5.907E-03 6.653E-02 7.974E-02 6.865E-02 1.032E-01 5.880E-03 5.676E+00 3.530E-04 3.515E-04
1 0.00 0.00 6.552E-04 1.238E-01 1.556E-03 1.949E-03 3.116E-03 6.729E-04 4.171E+00
3 7.01 5.00 1.805E-05 1.942E-03 2.275E-05 2.472E-05 2.991E-05 5.757E-03 3.313E+00
5 14.02 10.00 6.928E-06 2.102E-05 7.584E-06 7.589E-06 7.601E-06 1.861E-01 3.199E+00
Waveband 37 of 40 completed in 6.2 sec.
* * * * * Output for wavelength band 38 (720.0 to 730.0 nm; nominal wavelength = 725.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 20.7 m at 725.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 720.0 nm to 730.0 nm:
Ed(diffuse) = 2.217E-01 Ed(direct) = 6.861E-01 Ed(total) = 9.077E-01
Absorption Coefficients of Individual Components at 725.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 1.4890 0.0031 0.0004 1.4925
3 9.372 5.000 1.4890 0.0031 0.0004 1.4925
5 18.745 10.000 1.4890 0.0031 0.0004 1.4925
Scattering Coefficients of Individual Components at 725.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0006 0.3814 0.0000 0.3820
3 9.372 5.000 0.0006 0.3814 0.0000 0.3820
5 18.745 10.000 0.0006 0.3814 0.0000 0.3820
Backscattering Coefficients of Individual Components at 725.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00029 0.00763 0.00000 0.00792
3 9.372 5.000 0.00029 0.00763 0.00000 0.00792
5 18.745 10.000 0.00029 0.00763 0.00000 0.00792
Summary of Inherent Optical Properties at 725.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 1.4925 0.3820 1.8745 0.2038 0.00792 0.02073
3 9.372 5.000 1.4925 0.3820 1.8745 0.2038 0.00792 0.02073
5 18.745 10.000 1.4925 0.3820 1.8745 0.2038 0.00792 0.02073
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 6.3765E-01
8 20.00 2.2768E-01
7 30.00 6.4051E-02
6 40.00 1.8573E-02
5 50.00 6.3311E-03
4 60.00 2.5899E-03
3 70.00 1.2379E-03
2 80.00 6.7153E-04
1 87.50 4.5362E-04
1 92.50 3.5980E-04
2 100.00 2.6859E-04
3 110.00 1.9654E-04
4 120.00 1.5696E-04
5 130.00 1.3532E-04
6 140.00 1.2379E-04
7 150.00 1.1795E-04
8 160.00 1.1521E-04
9 170.00 1.1408E-04
10 180.00 1.1373E-04
Asymptotic AOP values are
MUu(inf) = 0.3939
MUd(inf) = 0.9291
MU(inf) = 0.9237
R(inf) = 0.0018
Lu(inf)/Ed(inf) = 0.000424 (1/sr)
k(inf) = 1.6160 (1/m)
absorp(check) = 1.4927 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 725.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 8.0842E-02 1.2409E+00 1.3217E+00 2.9888E-02 9.0772E-01 0.3697 0.7315 0.6642 3.2927E-02
1 0.00 0.00 4.1040E-03 9.7730E-01 9.8140E-01 1.6009E-03 8.7943E-01 0.3901 0.8999 0.8945 1.8204E-03
3 9.37 5.00 2.4226E-05 2.5494E-04 2.7917E-04 1.2137E-05 2.1993E-04 0.5010 0.8627 0.7443 5.5184E-02
5 18.74 10.00 9.6024E-06 1.0895E-05 2.0497E-05 4.8414E-06 5.7280E-06 0.5042 0.5257 0.0433 8.4522E-01
K-functions (units of 1/meter) at 725.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 1.58895 1.65028 1.65002 1.61536 1.66844 1.66854 1.62845
5.000 5.010 5.005 0.23660 1.51192 1.40060 0.22398 1.57148 1.65075 0.21253
10.000 10.010 10.005 0.18193 0.18318 0.18259 0.18227 0.18921 0.22714 0.18314
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 725.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 5.98140E-02 2.05941E-04 5.01651E-03 5.22245E-03 2.26877E-04 0.083868
9 1 10.0 0.0 180.0 3.69077E-02 2.12523E-04 1.40249E-03 1.61501E-03 2.34128E-04 0.038000
9 4 10.0 45.0 135.0 4.05516E-02 2.10393E-04 1.63631E-03 1.84670E-03 2.31782E-04 0.040351
9 7 10.0 90.0 90.0 5.47885E-02 2.07130E-04 3.56238E-03 3.76951E-03 2.28187E-04 0.065021
8 1 20.0 0.0 180.0 2.89905E-02 2.16078E-04 7.11767E-04 9.27845E-04 2.38045E-04 0.024552
8 4 20.0 45.0 135.0 3.22742E-02 2.11824E-04 8.44069E-04 1.05589E-03 2.33358E-04 0.026153
8 7 20.0 90.0 90.0 4.74577E-02 2.07032E-04 2.01923E-03 2.22627E-03 2.28080E-04 0.042548
7 1 30.0 0.0 180.0 2.51363E-02 2.20282E-04 6.05085E-04 8.25367E-04 2.42676E-04 0.024072
7 4 30.0 45.0 135.0 2.78712E-02 2.17012E-04 6.80191E-04 8.97203E-04 2.39074E-04 0.024405
7 7 30.0 90.0 90.0 4.06205E-02 2.09633E-04 1.20074E-03 1.41037E-03 2.30945E-04 0.029560
6 1 40.0 0.0 180.0 2.38591E-02 2.22946E-04 6.72780E-04 8.95726E-04 2.45611E-04 0.028198
6 4 40.0 45.0 135.0 2.60886E-02 2.18512E-04 7.29677E-04 9.48189E-04 2.40726E-04 0.027969
6 7 40.0 90.0 90.0 3.66280E-02 2.10223E-04 1.05899E-03 1.26921E-03 2.31595E-04 0.028912
5 1 50.0 0.0 180.0 2.50155E-02 2.26138E-04 1.06277E-03 1.28891E-03 2.49128E-04 0.042485
5 4 50.0 45.0 135.0 2.66574E-02 2.20036E-04 1.10721E-03 1.32725E-03 2.42405E-04 0.041535
5 7 50.0 90.0 90.0 3.54342E-02 2.11994E-04 1.43142E-03 1.64341E-03 2.33546E-04 0.040396
4 1 60.0 0.0 180.0 2.96938E-02 2.23081E-04 2.47576E-03 2.69884E-03 2.45759E-04 0.083377
4 4 60.0 45.0 135.0 3.03658E-02 2.16483E-04 2.44477E-03 2.66125E-03 2.38491E-04 0.080511
4 7 60.0 90.0 90.0 3.74977E-02 2.11530E-04 2.85494E-03 3.06647E-03 2.33035E-04 0.076136
3 1 70.0 0.0 180.0 4.12003E-02 2.07181E-04 6.83872E-03 7.04590E-03 2.28243E-04 0.165987
3 4 70.0 45.0 135.0 4.00407E-02 2.03231E-04 6.58011E-03 6.78335E-03 2.23892E-04 0.164336
3 7 70.0 90.0 90.0 4.47645E-02 1.99783E-04 7.15556E-03 7.35535E-03 2.20094E-04 0.159849
2 1 80.0 0.0 180.0 6.99999E-02 1.77724E-04 1.69990E-02 1.71767E-02 1.95792E-04 0.242843
2 4 80.0 45.0 135.0 6.48186E-02 1.74006E-04 1.64416E-02 1.66156E-02 1.91696E-04 0.253655
2 7 80.0 90.0 90.0 6.43978E-02 1.72297E-04 1.72188E-02 1.73911E-02 1.89813E-04 0.267382
1 1 87.5 0.0 180.0 1.13177E-01 1.43567E-04 2.99801E-02 3.01237E-02 1.58162E-04 0.264896
1 4 87.5 45.0 135.0 1.01902E-01 1.34024E-04 2.97950E-02 2.99291E-02 1.47649E-04 0.292389
1 7 87.5 90.0 90.0 9.27084E-02 1.48175E-04 3.04933E-02 3.06414E-02 1.63239E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 725.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 5.222E-03 5.981E-02 7.165E-02 6.167E-02 9.269E-02 5.753E-03 5.723E+00 2.059E-04 2.269E-04
1 0.00 0.00 3.822E-04 1.113E-01 9.668E-04 1.217E-03 1.969E-03 4.346E-04 4.188E+00
3 9.37 5.00 4.019E-06 1.526E-04 3.916E-06 3.999E-06 4.215E-06 1.827E-02 3.020E+00
5 18.74 10.00 1.605E-06 2.109E-06 1.532E-06 1.532E-06 1.532E-06 2.803E-01 3.016E+00
Waveband 38 of 40 completed in 7.5 sec.
* * * * * Output for wavelength band 39 (730.0 to 740.0 nm; nominal wavelength = 735.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 18.0 m at 735.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 730.0 nm to 740.0 nm:
Ed(diffuse) = 2.418E-01 Ed(direct) = 7.532E-01 Ed(total) = 9.950E-01
Absorption Coefficients of Individual Components at 735.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 2.1289 0.0010 0.0003 2.1303
3 12.535 5.000 2.1289 0.0010 0.0003 2.1303
5 25.071 10.000 2.1289 0.0010 0.0003 2.1303
Scattering Coefficients of Individual Components at 735.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0005 0.3762 0.0000 0.3768
3 12.535 5.000 0.0005 0.3762 0.0000 0.3768
5 25.071 10.000 0.0005 0.3762 0.0000 0.3768
Backscattering Coefficients of Individual Components at 735.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00027 0.00752 0.00000 0.00780
3 12.535 5.000 0.00027 0.00752 0.00000 0.00780
5 25.071 10.000 0.00027 0.00752 0.00000 0.00780
Summary of Inherent Optical Properties at 735.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 2.1303 0.3768 2.5071 0.1503 0.00780 0.02070
3 12.535 5.000 2.1303 0.3768 2.5071 0.1503 0.00780 0.02070
5 25.071 10.000 2.1303 0.3768 2.5071 0.1503 0.00780 0.02070
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 5.4616E-01
8 20.00 1.5212E-01
7 30.00 3.5291E-02
6 40.00 9.3068E-03
5 50.00 3.0894E-03
4 60.00 1.2650E-03
3 70.00 6.0907E-04
2 80.00 3.3273E-04
1 87.50 2.2579E-04
1 92.50 1.7979E-04
2 100.00 1.3474E-04
3 110.00 9.9155E-05
4 120.00 7.9723E-05
5 130.00 6.9226E-05
6 140.00 6.3751E-05
7 150.00 6.1077E-05
8 160.00 5.9901E-05
9 170.00 5.9456E-05
10 180.00 5.9328E-05
Asymptotic AOP values are
MUu(inf) = 0.3974
MUd(inf) = 0.9435
MU(inf) = 0.9398
R(inf) = 0.0012
Lu(inf)/Ed(inf) = 0.000292 (1/sr)
k(inf) = 2.2671 (1/m)
absorp(check) = 2.1307 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 735.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 8.7895E-02 1.3591E+00 1.4470E+00 3.2489E-02 9.9497E-01 0.3696 0.7321 0.6651 3.2653E-02
1 0.00 0.00 3.0900E-03 1.0701E+00 1.0731E+00 1.2015E-03 9.6368E-01 0.3888 0.9006 0.8969 1.2468E-03
3 12.54 5.00 1.1452E-05 2.0467E-05 3.1920E-05 5.8372E-06 1.3815E-05 0.5097 0.6750 0.2499 4.2253E-01
5 25.07 10.00 4.1168E-06 4.5419E-06 8.6587E-06 2.0928E-06 2.3808E-06 0.5084 0.5242 0.0333 8.7905E-01
K-functions (units of 1/meter) at 735.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 2.32144 2.36647 2.36634 2.33176 2.37512 2.37517 2.33197
5.000 5.010 5.005 0.21054 1.01414 0.72508 0.21039 1.30771 2.11832 0.21108
10.000 10.010 10.005 0.20797 0.20197 0.20482 0.20833 0.20252 0.16033 0.20930
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 735.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 6.52449E-02 1.54595E-04 5.49659E-03 5.65118E-03 1.55377E-04 0.084245
9 1 10.0 0.0 180.0 4.02588E-02 1.59626E-04 1.53313E-03 1.69276E-03 1.60434E-04 0.038082
9 4 10.0 45.0 135.0 4.42335E-02 1.57995E-04 1.78913E-03 1.94712E-03 1.58794E-04 0.040447
9 7 10.0 90.0 90.0 5.97632E-02 1.55467E-04 3.90105E-03 4.05652E-03 1.56254E-04 0.065275
8 1 20.0 0.0 180.0 3.16227E-02 1.62333E-04 7.76560E-04 9.38893E-04 1.63154E-04 0.024557
8 4 20.0 45.0 135.0 3.52046E-02 1.59082E-04 9.21141E-04 1.08022E-03 1.59887E-04 0.026165
8 7 20.0 90.0 90.0 5.17667E-02 1.55357E-04 2.20836E-03 2.36372E-03 1.56142E-04 0.042660
7 1 30.0 0.0 180.0 2.74186E-02 1.65511E-04 6.60025E-04 8.25536E-04 1.66348E-04 0.024072
7 4 30.0 45.0 135.0 3.04019E-02 1.62977E-04 7.41971E-04 9.04948E-04 1.63801E-04 0.024405
7 7 30.0 90.0 90.0 4.43079E-02 1.57260E-04 1.31090E-03 1.46816E-03 1.58056E-04 0.029586
6 1 40.0 0.0 180.0 2.60254E-02 1.67508E-04 7.33866E-04 9.01375E-04 1.68355E-04 0.028198
6 4 40.0 45.0 135.0 2.84574E-02 1.64075E-04 7.95930E-04 9.60005E-04 1.64905E-04 0.027969
6 7 40.0 90.0 90.0 3.99538E-02 1.57625E-04 1.15521E-03 1.31284E-03 1.58422E-04 0.028914
5 1 50.0 0.0 180.0 2.72868E-02 1.69881E-04 1.15927E-03 1.32915E-03 1.70740E-04 0.042485
5 4 50.0 45.0 135.0 2.90778E-02 1.65179E-04 1.20774E-03 1.37292E-03 1.66014E-04 0.041535
5 7 50.0 90.0 90.0 3.86516E-02 1.58888E-04 1.56139E-03 1.72028E-03 1.59692E-04 0.040396
4 1 60.0 0.0 180.0 3.23899E-02 1.67553E-04 2.70056E-03 2.86811E-03 1.68400E-04 0.083377
4 4 60.0 45.0 135.0 3.31229E-02 1.62469E-04 2.66675E-03 2.82922E-03 1.63291E-04 0.080511
4 7 60.0 90.0 90.0 4.09024E-02 1.58482E-04 3.11416E-03 3.27264E-03 1.59284E-04 0.076136
3 1 70.0 0.0 180.0 4.49412E-02 1.55573E-04 7.45965E-03 7.61523E-03 1.56360E-04 0.165987
3 4 70.0 45.0 135.0 4.36762E-02 1.52480E-04 7.17757E-03 7.33005E-03 1.53251E-04 0.164336
3 7 70.0 90.0 90.0 4.88290E-02 1.49640E-04 7.80527E-03 7.95491E-03 1.50397E-04 0.159849
2 1 80.0 0.0 180.0 7.63557E-02 1.33426E-04 1.85425E-02 1.86759E-02 1.34101E-04 0.242843
2 4 80.0 45.0 135.0 7.07039E-02 1.30523E-04 1.79344E-02 1.80649E-02 1.31183E-04 0.253655
2 7 80.0 90.0 90.0 7.02449E-02 1.29032E-04 1.87822E-02 1.89112E-02 1.29685E-04 0.267382
1 1 87.5 0.0 180.0 1.23453E-01 1.07764E-04 3.27022E-02 3.28100E-02 1.08309E-04 0.264896
1 4 87.5 45.0 135.0 1.11154E-01 1.00517E-04 3.25003E-02 3.26008E-02 1.01025E-04 0.292389
1 7 87.5 90.0 90.0 1.01126E-01 1.10968E-04 3.32619E-02 3.33729E-02 1.11529E-04 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 735.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 5.651E-03 6.524E-02 7.813E-02 6.725E-02 1.011E-01 5.680E-03 5.749E+00 1.546E-04 1.554E-04
1 0.00 0.00 2.869E-04 1.214E-01 7.728E-04 9.732E-04 1.584E-03 2.977E-04 4.188E+00
3 12.54 5.00 1.989E-06 8.476E-06 1.779E-06 1.781E-06 1.785E-06 1.440E-01 2.934E+00
5 25.07 10.00 7.078E-07 8.569E-07 6.432E-07 6.432E-07 6.432E-07 2.973E-01 2.957E+00
Waveband 39 of 40 completed in 9.2 sec.
* * * * * Output for wavelength band 40 (740.0 to 750.0 nm; nominal wavelength = 745.0 nm) * * * * *
Index of refraction at this wavelength is 1.340
The infinitely deep bottom boundary condition is applied at 17.1 m at 745.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 740.0 nm to 750.0 nm:
Ed(diffuse) = 2.544E-01 Ed(direct) = 7.973E-01 Ed(total) = 1.052E+00
Absorption Coefficients of Individual Components at 745.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 2.4590 0.0000 0.0003 2.4593
3 14.155 5.000 2.4590 0.0000 0.0003 2.4593
5 28.310 10.000 2.4590 0.0000 0.0003 2.4593
Scattering Coefficients of Individual Components at 745.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0005 0.3712 0.0000 0.3717
3 14.155 5.000 0.0005 0.3712 0.0000 0.3717
5 28.310 10.000 0.0005 0.3712 0.0000 0.3717
Backscattering Coefficients of Individual Components at 745.0 nm
(computed from the scattering coefficients and the phase functions)
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Total
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00026 0.00742 0.00000 0.00768
3 14.155 5.000 0.00026 0.00742 0.00000 0.00768
5 28.310 10.000 0.00026 0.00742 0.00000 0.00768
Summary of Inherent Optical Properties at 745.0 nm
iz Opt Depth Geo Depth total a total b total c albedo total bb total bb/b
(m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 2.4593 0.3717 2.8310 0.1313 0.00768 0.02067
3 14.155 5.000 2.4593 0.3717 2.8310 0.1313 0.00768 0.02067
5 28.310 10.000 2.4593 0.3717 2.8310 0.1313 0.00768 0.02067
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 5.0203E-01
8 20.00 1.2464E-01
7 30.00 2.6745E-02
6 40.00 6.8387E-03
5 50.00 2.2592E-03
4 60.00 9.2773E-04
3 70.00 4.4836E-04
2 80.00 2.4565E-04
1 87.50 1.6699E-04
1 92.50 1.3315E-04
2 100.00 9.9930E-05
3 110.00 7.3683E-05
4 120.00 5.9383E-05
5 130.00 5.1694E-05
6 140.00 4.7717E-05
7 150.00 4.5806E-05
8 160.00 4.4988E-05
9 170.00 4.4692E-05
10 180.00 4.4611E-05
Asymptotic AOP values are
MUu(inf) = 0.3987
MUd(inf) = 0.9488
MU(inf) = 0.9457
R(inf) = 0.0011
Lu(inf)/Ed(inf) = 0.000249 (1/sr)
k(inf) = 2.6011 (1/m)
absorp(check) = 2.4599 = k(inf)*MU(inf)
Irradiances (units of W/m^2 nm), Mean Cosines (Mubars), and Irradiance Reflectance at 745.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 9.2474E-02 1.4356E+00 1.5280E+00 3.4218E-02 1.0517E+00 0.3700 0.7326 0.6658 3.2537E-02
1 0.00 0.00 2.7825E-03 1.1306E+00 1.1334E+00 1.0805E-03 1.0185E+00 0.3883 0.9009 0.8977 1.0609E-03
3 14.15 5.00 7.2951E-06 9.4582E-06 1.6753E-05 3.7246E-06 5.5342E-06 0.5106 0.5851 0.1080 6.7302E-01
5 28.31 10.00 2.2194E-06 2.4485E-06 4.6679E-06 1.1296E-06 1.2849E-06 0.5090 0.5248 0.0333 8.7912E-01
K-functions (units of 1/meter) at 745.0 nm (these are accurate local values only when zupper and zlower are closely spaced)
zupper zlower z Kou(z) Kod(z) Ko(z) Ku(z) Kd(z) Knet(z) KLu(z)
0.000 0.010 0.005 2.70027 2.73568 2.73559 2.70253 2.73936 2.73940 2.69674
5.000 5.010 5.005 0.24453 0.58920 0.43897 0.24511 0.79923 1.94953 0.24659
10.000 10.010 10.005 0.23828 0.23311 0.23557 0.23875 0.23379 0.19771 0.24000
Radiances Just Above the Water Surface (at z = a) (units of W/m^2 sr nm) at 745.0 nm
[(Theta,Phi) are the directions of photon travel.
Theta is measured from 0 at the zenith.
Solar photons travel in the Phi = 180 direction (the sun is located at Phi = 0).
(Thus Phi = 45 represents the 135 degree viewing angle for minimizing sun glitter.)]
I J Theta Phi Phi-view L(sky) L(water-lv) L(refl-sky) L(total up) Rrs rho
(zenith) (Lrefl/Lsky)
10 1 0.0 0.0 0.0 6.86470E-02 1.38968E-04 5.80772E-03 5.94668E-03 1.32141E-04 0.084603
9 1 10.0 0.0 180.0 4.23580E-02 1.43518E-04 1.61637E-03 1.75989E-03 1.36468E-04 0.038160
9 4 10.0 45.0 135.0 4.65400E-02 1.42042E-04 1.88665E-03 2.02870E-03 1.35064E-04 0.040538
9 7 10.0 90.0 90.0 6.28794E-02 1.39747E-04 4.11964E-03 4.25939E-03 1.32882E-04 0.065516
8 1 20.0 0.0 180.0 3.32716E-02 1.45966E-04 8.17220E-04 9.63185E-04 1.38795E-04 0.024562
8 4 20.0 45.0 135.0 3.70403E-02 1.43026E-04 9.69603E-04 1.11263E-03 1.36000E-04 0.026177
8 7 20.0 90.0 90.0 5.44660E-02 1.39640E-04 2.32928E-03 2.46892E-03 1.32780E-04 0.042766
7 1 30.0 0.0 180.0 2.88483E-02 1.48833E-04 6.94441E-04 8.43275E-04 1.41522E-04 0.024072
7 4 30.0 45.0 135.0 3.19873E-02 1.46532E-04 7.80681E-04 9.27212E-04 1.39333E-04 0.024406
7 7 30.0 90.0 90.0 4.66176E-02 1.41342E-04 1.38039E-03 1.52173E-03 1.34398E-04 0.029611
6 1 40.0 0.0 180.0 2.73825E-02 1.50634E-04 7.72133E-04 9.22767E-04 1.43234E-04 0.028198
6 4 40.0 45.0 135.0 2.99413E-02 1.47517E-04 8.37433E-04 9.84949E-04 1.40270E-04 0.027969
6 7 40.0 90.0 90.0 4.20371E-02 1.41655E-04 1.21553E-03 1.35718E-03 1.34696E-04 0.028916
5 1 50.0 0.0 180.0 2.87096E-02 1.52766E-04 1.21972E-03 1.37248E-03 1.45261E-04 0.042485
5 4 50.0 45.0 135.0 3.05940E-02 1.48503E-04 1.27072E-03 1.41922E-03 1.41208E-04 0.041535
5 7 50.0 90.0 90.0 4.06670E-02 1.42780E-04 1.64280E-03 1.78558E-03 1.35766E-04 0.040396
4 1 60.0 0.0 180.0 3.40788E-02 1.50668E-04 2.84137E-03 2.99204E-03 1.43267E-04 0.083377
4 4 60.0 45.0 135.0 3.48501E-02 1.46061E-04 2.80580E-03 2.95186E-03 1.38885E-04 0.080511
4 7 60.0 90.0 90.0 4.30352E-02 1.42407E-04 3.27654E-03 3.41895E-03 1.35411E-04 0.076136
3 1 70.0 0.0 180.0 4.72846E-02 1.39890E-04 7.84863E-03 7.98852E-03 1.33018E-04 0.165987
3 4 70.0 45.0 135.0 4.59537E-02 1.37074E-04 7.55184E-03 7.68891E-03 1.30340E-04 0.164336
3 7 70.0 90.0 90.0 5.13751E-02 1.34460E-04 8.21226E-03 8.34672E-03 1.27855E-04 0.159849
2 1 80.0 0.0 180.0 8.03372E-02 1.19971E-04 1.95094E-02 1.96293E-02 1.14078E-04 0.242843
2 4 80.0 45.0 135.0 7.43907E-02 1.17332E-04 1.88696E-02 1.89869E-02 1.11568E-04 0.253655
2 7 80.0 90.0 90.0 7.39078E-02 1.15945E-04 1.97616E-02 1.98775E-02 1.10249E-04 0.267382
1 1 87.5 0.0 180.0 1.29891E-01 9.68952E-05 3.44075E-02 3.45043E-02 9.21352E-05 0.264896
1 4 87.5 45.0 135.0 1.16950E-01 9.03572E-05 3.41950E-02 3.42854E-02 8.59183E-05 0.292389
1 7 87.5 90.0 90.0 1.06399E-01 9.97194E-05 3.49964E-02 3.50961E-02 9.48206E-05 0.328916
Selected Radiances (units of W/m^2 sr nm) and Radiance-Irradiance Ratios at 745.0 nm
[Here (theta,phi) are directions of photon travel relative to nadir (solar photons travel along phi=180).]
iz zeta z Lu(z) Ld(z) Lh(z,phi=0) Lh(z,phi=90) Lh(z,phi=180) Lu/Ed Q = Eu/Lu Lw(z) Rrs = Lw/Ed
(m) (theta=180) (theta=0) (theta=90) (theta=90) (theta=90) (1/sr) (sr) (theta=180) (1/sr)
in air 5.947E-03 6.865E-02 8.220E-02 7.075E-02 1.063E-01 5.655E-03 5.754E+00 1.390E-04 1.321E-04
1 0.00 0.00 2.579E-04 1.277E-01 7.173E-04 9.039E-04 1.475E-03 2.532E-04 4.189E+00
3 14.15 5.00 1.275E-06 2.725E-06 1.129E-06 1.129E-06 1.130E-06 2.303E-01 2.922E+00
5 28.31 10.00 3.832E-07 4.639E-07 3.458E-07 3.458E-07 3.458E-07 2.983E-01 2.948E+00
Waveband 40 of 40 completed in 9.8 sec.
Energy Eo as a function of depth and wavelength
Units are W/m^2 [values are integrated over the wavelength bands]
depth 355.0 365.0 375.0 385.0 395.0 405.0 415.0 425.0 435.0 445.0 455.0 465.0 475.0 485.0 495.0 505.0 515.0 525.0 535.0 545.0 555.0 565.0 575.0 585.0 595.0 605.0 615.0 625.0 635.0 645.0 655.0 665.0 675.0 685.0 695.0 705.0 715.0 725.0 735.0 745.0
in air 1.091E+01 1.247E+01 1.237E+01 1.083E+01 1.329E+01 1.858E+01 1.952E+01 1.855E+01 1.893E+01 2.221E+01 2.364E+01 2.342E+01 2.369E+01 2.286E+01 2.313E+01 2.263E+01 2.167E+01 2.211E+01 2.230E+01 2.194E+01 2.173E+01 2.150E+01 2.141E+01 2.075E+01 1.986E+01 2.029E+01 1.976E+01 1.951E+01 1.923E+01 1.860E+01 1.774E+01 1.844E+01 1.810E+01 1.659E+01 1.596E+01 1.603E+01 1.465E+01 1.322E+01 1.447E+01 1.528E+01
0.0 8.173E+00 9.540E+00 9.601E+00 8.514E+00 1.054E+01 1.473E+01 1.544E+01 1.469E+01 1.496E+01 1.764E+01 1.891E+01 1.883E+01 1.923E+01 1.869E+01 1.901E+01 1.860E+01 1.767E+01 1.817E+01 1.841E+01 1.812E+01 1.790E+01 1.772E+01 1.741E+01 1.644E+01 1.537E+01 1.540E+01 1.499E+01 1.477E+01 1.454E+01 1.404E+01 1.335E+01 1.386E+01 1.369E+01 1.261E+01 1.206E+01 1.199E+01 1.090E+01 9.814E+00 1.073E+01 1.133E+01
5.0 3.109E+00 3.960E+00 4.221E+00 3.919E+00 4.990E+00 6.877E+00 7.035E+00 6.666E+00 6.645E+00 8.062E+00 8.987E+00 9.201E+00 9.898E+00 9.996E+00 1.045E+01 1.026E+01 9.375E+00 1.010E+01 1.047E+01 1.039E+01 1.018E+01 1.016E+01 9.323E+00 7.199E+00 4.891E+00 2.840E+00 2.634E+00 2.337E+00 2.034E+00 1.729E+00 1.227E+00 8.635E-01 8.206E-01 7.061E-01 4.828E-01 2.117E-01 3.709E-02 2.792E-03 3.192E-04 1.675E-04
10.0 9.791E-01 1.365E+00 1.547E+00 1.509E+00 1.983E+00 2.703E+00 2.705E+00 2.560E+00 2.504E+00 3.136E+00 3.649E+00 3.853E+00 4.385E+00 4.619E+00 4.977E+00 4.920E+00 4.329E+00 4.901E+00 5.221E+00 5.238E+00 5.095E+00 5.142E+00 4.404E+00 2.778E+00 1.373E+00 4.669E-01 4.133E-01 3.316E-01 2.564E-01 1.930E-01 1.046E-01 5.885E-02 7.468E-02 7.882E-02 4.477E-02 1.069E-02 1.088E-03 2.050E-04 8.659E-05 4.668E-05
Quantum Eo as a function of depth and wavelength
Units are (micromol photons)/(m^2 s) [values are integrated over the wavelength bands]
depth 355.0 365.0 375.0 385.0 395.0 405.0 415.0 425.0 435.0 445.0 455.0 465.0 475.0 485.0 495.0 505.0 515.0 525.0 535.0 545.0 555.0 565.0 575.0 585.0 595.0 605.0 615.0 625.0 635.0 645.0 655.0 665.0 675.0 685.0 695.0 705.0 715.0 725.0 735.0 745.0
in air 3.236E+01 3.804E+01 3.876E+01 3.485E+01 4.388E+01 6.288E+01 6.771E+01 6.590E+01 6.883E+01 8.260E+01 8.990E+01 9.103E+01 9.405E+01 9.268E+01 9.570E+01 9.551E+01 9.328E+01 9.701E+01 9.971E+01 9.994E+01 1.008E+02 1.015E+02 1.029E+02 1.014E+02 9.874E+01 1.026E+02 1.016E+02 1.019E+02 1.021E+02 1.002E+02 9.709E+01 1.025E+02 1.021E+02 9.496E+01 9.269E+01 9.444E+01 8.753E+01 8.009E+01 8.889E+01 9.515E+01
0.0 2.425E+01 2.910E+01 3.009E+01 2.740E+01 3.481E+01 4.986E+01 5.355E+01 5.217E+01 5.439E+01 6.561E+01 7.191E+01 7.320E+01 7.634E+01 7.578E+01 7.864E+01 7.851E+01 7.605E+01 7.975E+01 8.230E+01 8.255E+01 8.303E+01 8.368E+01 8.368E+01 8.036E+01 7.643E+01 7.786E+01 7.707E+01 7.718E+01 7.717E+01 7.568E+01 7.309E+01 7.706E+01 7.724E+01 7.220E+01 7.003E+01 7.067E+01 6.516E+01 5.947E+01 6.592E+01 7.057E+01
5.0 9.225E+00 1.208E+01 1.323E+01 1.261E+01 1.647E+01 2.328E+01 2.440E+01 2.368E+01 2.416E+01 2.998E+01 3.418E+01 3.576E+01 3.929E+01 4.052E+01 4.321E+01 4.330E+01 4.035E+01 4.431E+01 4.682E+01 4.735E+01 4.722E+01 4.799E+01 4.481E+01 3.520E+01 2.432E+01 1.436E+01 1.354E+01 1.221E+01 1.079E+01 9.320E+00 6.718E+00 4.799E+00 4.629E+00 4.043E+00 2.804E+00 1.248E+00 2.216E-01 1.692E-02 1.961E-03 1.043E-03
10.0 2.905E+00 4.164E+00 4.849E+00 4.857E+00 6.546E+00 9.149E+00 9.381E+00 9.093E+00 9.104E+00 1.166E+01 1.388E+01 1.498E+01 1.741E+01 1.872E+01 2.059E+01 2.076E+01 1.864E+01 2.151E+01 2.335E+01 2.386E+01 2.363E+01 2.428E+01 2.117E+01 1.358E+01 6.830E+00 2.361E+00 2.124E+00 1.732E+00 1.361E+00 1.040E+00 5.725E-01 3.271E-01 4.213E-01 4.512E-01 2.600E-01 6.297E-02 6.504E-03 1.242E-03 5.319E-04 2.907E-04
PAR as a function of depth
The wavelengths used for this PAR calculation were 400.0 to 700.0 nm
depth PAR(from Eo) PAR(from Ed)
(m) (mumol phot/m^2/s) (mumol phot/m^2/s)
in air 2.7998E+03 1.8379E+03
0.00 2.2124E+03 1.8076E+03
5.00 8.2334E+02 5.8460E+02
10.00 3.4222E+02 2.2990E+02
K-function for PAR (units of 1/meter) (valid only when zupper and zlower are closely spaced)
zupper zlower z KPAR(from Eo)
0.000 0.010 0.005 0.21819
5.000 5.010 5.005 0.18108
10.000 10.010 10.005 0.17273
CIE 1931 chromaticity coordinates (x,y) and (il)luminance Y for selected quantities. Output is (x,y,Y).
Y is illuminance in lm/m^2 for Ed and Eu; Y is luminance in lm/(m^2 sr) for Lu and Lw
depth Ed Eu Lu Lw
in air (0.328, 0.339, 1.024E+05) (0.299, 0.333, 4.935E+03) (0.290, 0.335, 1.026E+03) (0.246, 0.331, 4.537E+02)
0.00 (0.327, 0.339, 1.010E+05) (0.247, 0.333, 3.570E+03) (0.246, 0.331, 8.415E+02)
5.00 (0.272, 0.364, 4.224E+04) (0.229, 0.357, 1.874E+03) (0.229, 0.356, 4.026E+02)
10.00 (0.251, 0.391, 1.829E+04) (0.225, 0.385, 8.879E+02) (0.225, 0.383, 1.841E+02)
WARNING: the current estimate for z_SD is greater than the maximum output depth for the run: z_SD cannot be further revised
max output depth = 10.00
For a better estimate, rerun HydroLight to a deeper depth
Run completed on 07/19/2011 at 13:46:54.2
Total (wall clock) run time = 182.9 sec