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| |
| HYDROLIGHT Version 5.1.0 (MAIN CODE) |
| Copyright (c) 2013 by Curtis D. Mobley |
| |
| This copy of HE5 is licensed solely to |
| U Maine Optics Summer Class 2013 |
| |
| S/N Maine-500-31Aug2013 |
| |
| 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: Run1 (07/18/2013 15:08)
Run started on 07/18/2013 at 15:08:13.7
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 1 405.00
2 80.000 0.1730 2 15.00 2 0.010 2 415.00
3 70.000 0.3407 3 30.00 3 5.000 3 425.00
4 60.000 0.4981 4 45.00 4 5.010 4 435.00
5 50.000 0.6403 5 60.00 5 10.000 5 445.00
6 40.000 0.7631 6 75.00 6 10.010 6 455.00
7 30.000 0.8627 7 90.00 7 15.000 7 465.00
8 20.000 0.9361 8 105.00 8 15.010 8 475.00
9 10.000 0.9811 9 120.00 9 20.000 9 485.00
10 0.000 0.9981 10 135.00 10 20.010 10 495.00
11 150.00 11 25.000 11 505.00
12 165.00 12 25.010 12 515.00
13 180.00 13 525.00
14 195.00 14 535.00
15 210.00 15 545.00
16 225.00 16 555.00
17 240.00 17 565.00
18 255.00 18 575.00
19 270.00 19 585.00
20 285.00 20 595.00
21 300.00 21 605.00
22 315.00 22 615.00
23 330.00 23 625.00
24 345.00 24 635.00
25 645.00
26 655.00
27 665.00
28 675.00
29 685.00
30 695.00
***** BEGIN IOP MODEL SPECIFICATIONS *****
The IOP routine "abNewCase1" is being used:
Absorption and scattering coefficients for case 1 water (Morel et al. bio-optical models) are used.
component 1 is pure water
component 2 is small particles
component 3 is large particles
component 4 is CDOM
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
The Chlorophyll concentration is obtained from measured values read from the file:
C:\HE5\data\examples\Chlzdata.txt
(Linear interpolation is used to define Chl(z) at all depths)
The data file header records from C:\HE5\data\examples\Chlzdata.txt are:
Example "chlzdata" file showing the Hydrolight "Chlorophyll-data standard format"
These files are read by Hydrolight subroutine "chlzdata" on file ..\maincode\chlzdata.f
6 records read
The phase function for component 2 comes from a file titled
Morel Small Particle Case 1 phase function; (Jul 2004)
The chlorophyll values at the requested output depths are:
depth Chl
(m) (mg/m^3)
0.000 0.500
5.000 0.700
10.000 1.200
15.000 2.100
20.000 1.500
25.000 0.400
chlorophyll AE filename: ..\data\AE_midUVabs.txt
***** 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
The ozone concentration is computed from climatology using
Day of Year = 198
latitude = 60.0000 degrees (N is positive)
longitude = -68.0000 degrees (E is positive)
Binned Monthly Average TOMS v8 Ozone concentrations (in Dobson units) for use in HE5; Sept 2007
Data from 2000-2004 were averaged to give 5-year climatological averages for 5 x 10 deg latitude x longitude regions.
For missing data near the poles, the zonal average of the nearest valid latitude band is used.
Parameter values used in the RADTRANX model:
Solar zenith angle = 30.0 degrees
Pressure = 29.9 in. mercury
Day of year = 198
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 = 338.6 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 25.00 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 *****
***** WARNING MESSAGES FOR INPUT DATA FILES *****
NUMBER OF FILES WITH WARNINGS: 1
Data file: C:\HE5\data\examples\Chlzdata.txt
does not extend over the full range of depths and wavelengths selected for this run.
For depths greater than 25.0 m the value at 25.0 m will be used
HYDROLIGHT/ECOLIGHT OUTPUTS MAY BE UNPHYSICAL OR INACCURATE
FOR DEPTHS AND WAVELENGTHS OUTSIDE THE RANGE OF THE INPUT DATA.
***** END WARNING MESSAGES FOR INPUT DATA FILES *****
Initialization of Hydrolight Completed in 0.1 sec.
* * * * * Output for wavelength band 1 (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 103.6 m at 405.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 400.0 nm to 410.0 nm:
Ed(diffuse) = 4.148E-01 Ed(direct) = 6.766E-01 Ed(total) = 1.091E+00
Absorption Coefficients of Individual Components at 405.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0053 0.0276 0.0000 0.0109 0.0438
3 1.802 5.000 0.0053 0.0349 0.0000 0.0135 0.0537
5 4.257 10.000 0.0053 0.0507 0.0000 0.0191 0.0751
7 7.836 15.000 0.0053 0.0749 0.0000 0.0272 0.1074
9 11.641 20.000 0.0053 0.0593 0.0000 0.0220 0.0865
11 14.072 25.000 0.0053 0.0236 0.0000 0.0095 0.0384
Scattering Coefficients of Individual Components at 405.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0072 0.1319 0.1363 0.0000 0.2754
3 1.802 5.000 0.0072 0.1563 0.1831 0.0000 0.3465
5 4.257 10.000 0.0072 0.2031 0.2916 0.0000 0.5020
7 7.836 15.000 0.0072 0.2634 0.4710 0.0000 0.7416
9 11.641 20.000 0.0072 0.2255 0.3529 0.0000 0.5856
11 14.072 25.000 0.0072 0.1176 0.1118 0.0000 0.2366
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00359 0.00185 0.00024 0.00000 0.00568
3 1.802 5.000 0.00359 0.00219 0.00032 0.00000 0.00610
5 4.257 10.000 0.00359 0.00285 0.00051 0.00000 0.00695
7 7.836 15.000 0.00359 0.00369 0.00083 0.00000 0.00811
9 11.641 20.000 0.00359 0.00316 0.00062 0.00000 0.00737
11 14.072 25.000 0.00359 0.00165 0.00020 0.00000 0.00544
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 0.0438 0.2754 0.3192 0.8627 0.00568 0.02062
3 1.802 5.000 0.0537 0.3465 0.4003 0.8658 0.00610 0.01761
5 4.257 10.000 0.0751 0.5020 0.5771 0.8699 0.00695 0.01385
7 7.836 15.000 0.1074 0.7416 0.8489 0.8735 0.00811 0.01094
9 11.641 20.000 0.0865 0.5856 0.6721 0.8713 0.00737 0.01259
11 14.072 25.000 0.0384 0.2366 0.2750 0.8603 0.00544 0.02297
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4894E-01
8 20.00 8.2429E-01
7 30.00 6.5829E-01
6 40.00 4.8876E-01
5 50.00 3.4266E-01
4 60.00 2.3130E-01
3 70.00 1.5372E-01
2 80.00 1.0333E-01
1 87.50 7.7390E-02
1 92.50 6.3247E-02
2 100.00 4.9432E-02
3 110.00 3.7747E-02
4 120.00 3.0377E-02
5 130.00 2.5782E-02
6 140.00 2.2916E-02
7 150.00 2.1144E-02
8 160.00 2.0086E-02
9 170.00 1.9523E-02
10 180.00 1.9324E-02
Asymptotic AOP values are
MUu(inf) = 0.3952
MUd(inf) = 0.7031
MU(inf) = 0.5975
R(inf) = 0.0598
Lu(inf)/Ed(inf) = 0.013494 (1/sr)
k(inf) = 0.0643 (1/m)
absorp(check) = 0.0384 = 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 1.6813E-01 1.6183E+00 1.7864E+00 6.0056E-02 1.0914E+00 0.3572 0.6745 0.5774 5.5024E-02
1 0.00 0.00 1.0356E-01 1.2637E+00 1.3672E+00 4.4565E-02 1.0759E+00 0.4303 0.8514 0.7543 4.1419E-02
3 1.80 5.00 7.7300E-02 9.6471E-01 1.0420E+00 3.1134E-02 7.6853E-01 0.4028 0.7966 0.7077 4.0511E-02
5 4.26 10.00 4.8859E-02 6.3267E-01 6.8153E-01 1.8773E-02 4.8036E-01 0.3842 0.7593 0.6773 3.9080E-02
7 7.84 15.00 2.5762E-02 3.2877E-01 3.5453E-01 9.8070E-03 2.4127E-01 0.3807 0.7339 0.6529 4.0647E-02
9 11.64 20.00 1.4334E-02 1.5844E-01 1.7278E-01 5.6577E-03 1.1409E-01 0.3947 0.7201 0.6276 4.9591E-02
11 14.07 25.00 1.0155E-02 9.6176E-02 1.0633E-01 4.0478E-03 6.8532E-02 0.3986 0.7126 0.6064 5.9065E-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 0.05357 0.04669 0.04721 0.06105 0.05824 0.05812 0.07830
5.000 5.010 5.005 0.07517 0.06539 0.06612 0.08597 0.07635 0.07594 0.10059
10.000 10.010 10.005 0.11085 0.10308 0.10364 0.11784 0.11121 0.11094 0.12548
15.000 15.010 15.005 0.13581 0.15764 0.15605 0.13154 0.16311 0.16445 0.12084
20.000 20.010 20.005 0.09313 0.13257 0.12930 0.08473 0.13518 0.13781 0.07604
25.000 25.010 25.005 0.06061 0.06169 0.06159 0.06204 0.06328 0.06335 0.06319
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 1.11942E-01 5.90682E-03 6.29540E-03 1.22022E-02 5.41194E-03 0.056238
9 1 10.0 0.0 180.0 6.90728E-02 6.06432E-03 2.20955E-03 8.27387E-03 5.55624E-03 0.031989
9 4 10.0 45.0 135.0 7.58924E-02 6.01936E-03 2.52809E-03 8.54745E-03 5.51505E-03 0.033311
9 7 10.0 90.0 90.0 1.02537E-01 5.96104E-03 4.75333E-03 1.07144E-02 5.46161E-03 0.046357
8 1 20.0 0.0 180.0 5.42557E-02 6.17033E-03 1.31107E-03 7.48140E-03 5.65337E-03 0.024165
8 4 20.0 45.0 135.0 6.04013E-02 6.07619E-03 1.52530E-03 7.60149E-03 5.56712E-03 0.025253
8 7 20.0 90.0 90.0 8.88172E-02 5.99492E-03 3.05119E-03 9.04611E-03 5.49265E-03 0.034354
7 1 30.0 0.0 180.0 4.70427E-02 6.30935E-03 1.13243E-03 7.44179E-03 5.78075E-03 0.024073
7 4 30.0 45.0 135.0 5.21451E-02 6.25455E-03 1.27037E-03 7.52491E-03 5.73053E-03 0.024362
7 7 30.0 90.0 90.0 7.61190E-02 6.11592E-03 2.10404E-03 8.21997E-03 5.60352E-03 0.027642
6 1 40.0 0.0 180.0 4.46524E-02 6.43742E-03 1.25913E-03 7.69655E-03 5.89809E-03 0.028198
6 4 40.0 45.0 135.0 4.88250E-02 6.35996E-03 1.36559E-03 7.72555E-03 5.82711E-03 0.027969
6 7 40.0 90.0 90.0 6.85495E-02 6.20263E-03 1.97257E-03 8.17520E-03 5.68297E-03 0.028776
5 1 50.0 0.0 180.0 4.68165E-02 6.59086E-03 1.98898E-03 8.57985E-03 6.03867E-03 0.042485
5 4 50.0 45.0 135.0 4.98893E-02 6.46725E-03 2.07216E-03 8.53941E-03 5.92542E-03 0.041535
5 7 50.0 90.0 90.0 6.63153E-02 6.30419E-03 2.67889E-03 8.98308E-03 5.77602E-03 0.040396
4 1 60.0 0.0 180.0 5.55719E-02 6.56444E-03 4.63340E-03 1.11978E-02 6.01446E-03 0.083377
4 4 60.0 45.0 135.0 5.68296E-02 6.42356E-03 4.57540E-03 1.09990E-02 5.88539E-03 0.080511
4 7 60.0 90.0 90.0 7.01771E-02 6.32858E-03 5.34303E-03 1.16716E-02 5.79837E-03 0.076136
3 1 70.0 0.0 180.0 7.71065E-02 6.15600E-03 1.27987E-02 1.89547E-02 5.64025E-03 0.165987
3 4 70.0 45.0 135.0 7.49362E-02 6.08064E-03 1.23147E-02 1.83953E-02 5.57119E-03 0.164336
3 7 70.0 90.0 90.0 8.37769E-02 5.98457E-03 1.33917E-02 1.93762E-02 5.48318E-03 0.159849
2 1 80.0 0.0 180.0 1.31005E-01 5.32074E-03 3.18137E-02 3.71345E-02 4.87496E-03 0.242843
2 4 80.0 45.0 135.0 1.21308E-01 5.23635E-03 3.07705E-02 3.60068E-02 4.79764E-03 0.253655
2 7 80.0 90.0 90.0 1.20521E-01 5.14987E-03 3.22250E-02 3.73749E-02 4.71841E-03 0.267382
1 1 87.5 0.0 180.0 2.11811E-01 4.31827E-03 5.61079E-02 6.04262E-02 3.95648E-03 0.264896
1 4 87.5 45.0 135.0 1.90710E-01 4.04069E-03 5.57615E-02 5.98022E-02 3.70216E-03 0.292389
1 7 87.5 90.0 90.0 1.73504E-01 4.39309E-03 5.70682E-02 6.14613E-02 4.02503E-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 1.220E-02 1.119E-01 1.361E-01 1.175E-01 1.756E-01 1.118E-02 4.922E+00 5.907E-03 5.412E-03
1 0.00 0.00 1.096E-02 2.084E-01 2.231E-02 2.378E-02 3.047E-02 1.018E-02 4.067E+00
3 1.80 5.00 7.028E-03 3.403E-01 1.706E-02 2.056E-02 3.262E-02 9.145E-03 4.430E+00
5 4.26 10.00 3.988E-03 3.101E-01 1.134E-02 1.477E-02 2.483E-02 8.302E-03 4.707E+00
7 7.84 15.00 2.095E-03 1.780E-01 6.147E-03 8.327E-03 1.353E-02 8.685E-03 4.680E+00
9 11.64 20.00 1.283E-03 8.458E-02 3.477E-03 4.501E-03 6.505E-03 1.124E-02 4.411E+00
11 14.07 25.00 9.236E-04 5.014E-02 2.579E-03 3.105E-03 4.031E-03 1.348E-02 4.383E+00
Waveband 1 of 30 completed in 5.0 sec.
* * * * * Output for wavelength band 2 (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 103.6 m at 415.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 410.0 nm to 420.0 nm:
Ed(diffuse) = 4.252E-01 Ed(direct) = 7.344E-01 Ed(total) = 1.160E+00
Absorption Coefficients of Individual Components at 415.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0044 0.0301 0.0000 0.0095 0.0441
3 1.791 5.000 0.0044 0.0379 0.0000 0.0118 0.0541
5 4.237 10.000 0.0044 0.0547 0.0000 0.0166 0.0757
7 7.812 15.000 0.0044 0.0800 0.0000 0.0236 0.1081
9 11.614 20.000 0.0044 0.0636 0.0000 0.0191 0.0872
11 14.036 25.000 0.0044 0.0259 0.0000 0.0082 0.0386
Scattering Coefficients of Individual Components at 415.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0065 0.1309 0.1353 0.0000 0.2727
3 1.791 5.000 0.0065 0.1555 0.1820 0.0000 0.3440
5 4.237 10.000 0.0065 0.2026 0.2909 0.0000 0.4999
7 7.812 15.000 0.0065 0.2634 0.4710 0.0000 0.7408
9 11.614 20.000 0.0065 0.2251 0.3524 0.0000 0.5840
11 14.036 25.000 0.0065 0.1166 0.1109 0.0000 0.2340
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00323 0.00184 0.00024 0.00000 0.00530
3 1.791 5.000 0.00323 0.00218 0.00032 0.00000 0.00573
5 4.237 10.000 0.00323 0.00284 0.00051 0.00000 0.00658
7 7.812 15.000 0.00323 0.00369 0.00083 0.00000 0.00775
9 11.614 20.000 0.00323 0.00316 0.00062 0.00000 0.00701
11 14.036 25.000 0.00323 0.00163 0.00020 0.00000 0.00506
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 0.0441 0.2727 0.3168 0.8608 0.00530 0.01945
3 1.791 5.000 0.0541 0.3440 0.3981 0.8641 0.00573 0.01666
5 4.237 10.000 0.0757 0.4999 0.5756 0.8685 0.00658 0.01317
7 7.812 15.000 0.1081 0.7408 0.8489 0.8727 0.00775 0.01046
9 11.614 20.000 0.0872 0.5840 0.6711 0.8701 0.00701 0.01200
11 14.036 25.000 0.0386 0.2340 0.2725 0.8584 0.00506 0.02163
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4850E-01
8 20.00 8.2286E-01
7 30.00 6.5573E-01
6 40.00 4.8536E-01
5 50.00 3.3888E-01
4 60.00 2.2757E-01
3 70.00 1.5028E-01
2 80.00 1.0029E-01
1 87.50 7.4652E-02
1 92.50 6.0718E-02
2 100.00 4.7152E-02
3 110.00 3.5727E-02
4 120.00 2.8556E-02
5 130.00 2.4104E-02
6 140.00 2.1339E-02
7 150.00 1.9636E-02
8 160.00 1.8621E-02
9 170.00 1.8082E-02
10 180.00 1.7891E-02
Asymptotic AOP values are
MUu(inf) = 0.3920
MUd(inf) = 0.7053
MU(inf) = 0.6042
R(inf) = 0.0564
Lu(inf)/Ed(inf) = 0.012575 (1/sr)
k(inf) = 0.0639 (1/m)
absorp(check) = 0.0386 = 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 415.0 nm
iz zeta z(m) Eou Eod Eo Eu Ed MUBARu MUBARd MUBAR R = Eu/Ed
in air 1.7249E-01 1.7062E+00 1.8787E+00 6.1928E-02 1.1597E+00 0.3590 0.6797 0.5843 5.3402E-02
1 0.00 0.00 1.0384E-01 1.3368E+00 1.4406E+00 4.4544E-02 1.1423E+00 0.4290 0.8545 0.7620 3.8996E-02
3 1.79 5.00 7.8229E-02 1.0216E+00 1.0998E+00 3.1373E-02 8.1701E-01 0.4010 0.7997 0.7143 3.8400E-02
5 4.24 10.00 4.9939E-02 6.7090E-01 7.2084E-01 1.9085E-02 5.1108E-01 0.3822 0.7618 0.6825 3.7342E-02
7 7.81 15.00 2.6476E-02 3.4896E-01 3.7544E-01 1.0000E-02 2.5668E-01 0.3777 0.7356 0.6571 3.8960E-02
9 11.61 20.00 1.4616E-02 1.6808E-01 1.8270E-01 5.7149E-03 1.2128E-01 0.3910 0.7215 0.6325 4.7121E-02
11 14.04 25.00 1.0275E-02 1.0198E-01 1.1226E-01 4.0622E-03 7.2856E-02 0.3953 0.7144 0.6128 5.5756E-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 0.05151 0.04623 0.04661 0.05951 0.05794 0.05788 0.07721
5.000 5.010 5.005 0.07312 0.06512 0.06569 0.08412 0.07610 0.07578 0.09923
10.000 10.010 10.005 0.10886 0.10284 0.10325 0.11615 0.11113 0.11094 0.12455
15.000 15.010 15.005 0.13651 0.15755 0.15607 0.13279 0.16321 0.16444 0.12256
20.000 20.010 20.005 0.09550 0.13277 0.12979 0.08711 0.13535 0.13774 0.07777
25.000 25.010 25.005 0.06036 0.06145 0.06135 0.06171 0.06290 0.06297 0.06281
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 1.14741E-01 5.86445E-03 6.66125E-03 1.25257E-02 5.05704E-03 0.058054
9 1 10.0 0.0 180.0 7.08001E-02 6.01705E-03 2.29278E-03 8.30983E-03 5.18863E-03 0.032384
9 4 10.0 45.0 135.0 7.77902E-02 5.97371E-03 2.62731E-03 8.60102E-03 5.15125E-03 0.033774
9 7 10.0 90.0 90.0 1.05101E-01 5.91920E-03 5.00114E-03 1.09203E-02 5.10425E-03 0.047584
8 1 20.0 0.0 180.0 5.56125E-02 6.12122E-03 1.34527E-03 7.46649E-03 5.27845E-03 0.024190
8 4 20.0 45.0 135.0 6.19117E-02 6.02987E-03 1.56711E-03 7.59697E-03 5.19968E-03 0.025312
8 7 20.0 90.0 90.0 9.10382E-02 5.95488E-03 3.17654E-03 9.13142E-03 5.13502E-03 0.034892
7 1 30.0 0.0 180.0 4.82191E-02 6.25884E-03 1.16075E-03 7.41960E-03 5.39713E-03 0.024072
7 4 30.0 45.0 135.0 5.34502E-02 6.20733E-03 1.30231E-03 7.50964E-03 5.35270E-03 0.024365
7 7 30.0 90.0 90.0 7.80159E-02 6.07787E-03 2.16631E-03 8.24417E-03 5.24107E-03 0.027767
6 1 40.0 0.0 180.0 4.57690E-02 6.38661E-03 1.29061E-03 7.67723E-03 5.50730E-03 0.028198
6 4 40.0 45.0 135.0 5.00460E-02 6.31369E-03 1.39974E-03 7.71343E-03 5.44442E-03 0.027969
6 7 40.0 90.0 90.0 7.02637E-02 6.16904E-03 2.02253E-03 8.19157E-03 5.31969E-03 0.028785
5 1 50.0 0.0 180.0 4.79873E-02 6.54027E-03 2.03872E-03 8.57899E-03 5.63981E-03 0.042485
5 4 50.0 45.0 135.0 5.11369E-02 6.42251E-03 2.12397E-03 8.54649E-03 5.53826E-03 0.041535
5 7 50.0 90.0 90.0 6.79736E-02 6.27537E-03 2.74588E-03 9.02125E-03 5.41138E-03 0.040396
4 1 60.0 0.0 180.0 5.69616E-02 6.51573E-03 4.74926E-03 1.12650E-02 5.61865E-03 0.083377
4 4 60.0 45.0 135.0 5.82508E-02 6.38166E-03 4.68982E-03 1.10715E-02 5.50303E-03 0.080511
4 7 60.0 90.0 90.0 7.19321E-02 6.30518E-03 5.47664E-03 1.17818E-02 5.43709E-03 0.076136
3 1 70.0 0.0 180.0 7.90347E-02 6.11243E-03 1.31187E-02 1.92312E-02 5.27087E-03 0.165987
3 4 70.0 45.0 135.0 7.68102E-02 6.04394E-03 1.26227E-02 1.86666E-02 5.21181E-03 0.164336
3 7 70.0 90.0 90.0 8.58720E-02 5.96852E-03 1.37265E-02 1.96951E-02 5.14678E-03 0.159849
2 1 80.0 0.0 180.0 1.34281E-01 5.28484E-03 3.26093E-02 3.78941E-02 4.55723E-03 0.242843
2 4 80.0 45.0 135.0 1.24342E-01 5.20720E-03 3.15399E-02 3.67471E-02 4.49028E-03 0.253655
2 7 80.0 90.0 90.0 1.23535E-01 5.14078E-03 3.30309E-02 3.81717E-02 4.43300E-03 0.267382
1 1 87.5 0.0 180.0 2.17108E-01 4.29062E-03 5.75110E-02 6.18016E-02 3.69989E-03 0.264896
1 4 87.5 45.0 135.0 1.95479E-01 4.02006E-03 5.71559E-02 6.11760E-02 3.46658E-03 0.292389
1 7 87.5 90.0 90.0 1.77843E-01 4.38929E-03 5.84953E-02 6.28846E-02 3.78497E-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 1.253E-02 1.147E-01 1.395E-01 1.204E-01 1.799E-01 1.080E-02 4.944E+00 5.864E-03 5.057E-03
1 0.00 0.00 1.088E-02 2.136E-01 2.222E-02 2.388E-02 3.105E-02 9.524E-03 4.095E+00
3 1.79 5.00 7.019E-03 3.584E-01 1.715E-02 2.090E-02 3.375E-02 8.592E-03 4.469E+00
5 4.24 10.00 4.007E-03 3.299E-01 1.150E-02 1.518E-02 2.596E-02 7.840E-03 4.763E+00
7 7.81 15.00 2.103E-03 1.900E-01 6.304E-03 8.647E-03 1.425E-02 8.194E-03 4.755E+00
9 11.61 20.00 1.276E-03 9.029E-02 3.567E-03 4.669E-03 6.832E-03 1.052E-02 4.480E+00
11 14.04 25.00 9.151E-04 5.356E-02 2.628E-03 3.197E-03 4.201E-03 1.256E-02 4.439E+00
Waveband 2 of 30 completed in 4.9 sec.
* * * * * Output for wavelength band 3 (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 103.6 m at 425.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 420.0 nm to 430.0 nm:
Ed(diffuse) = 3.949E-01 Ed(direct) = 7.172E-01 Ed(total) = 1.112E+00
Absorption Coefficients of Individual Components at 425.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0048 0.0316 0.0000 0.0083 0.0447
3 1.780 5.000 0.0048 0.0395 0.0000 0.0102 0.0545
5 4.216 10.000 0.0048 0.0563 0.0000 0.0144 0.0754
7 7.780 15.000 0.0048 0.0813 0.0000 0.0206 0.1066
9 11.573 20.000 0.0048 0.0651 0.0000 0.0166 0.0865
11 13.984 25.000 0.0048 0.0273 0.0000 0.0072 0.0393
Scattering Coefficients of Individual Components at 425.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0058 0.1300 0.1343 0.0000 0.2702
3 1.780 5.000 0.0058 0.1546 0.1811 0.0000 0.3415
5 4.216 10.000 0.0058 0.2021 0.2901 0.0000 0.4980
7 7.780 15.000 0.0058 0.2634 0.4710 0.0000 0.7402
9 11.573 20.000 0.0058 0.2248 0.3518 0.0000 0.5825
11 13.984 25.000 0.0058 0.1156 0.1100 0.0000 0.2314
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00291 0.00182 0.00024 0.00000 0.00497
3 1.780 5.000 0.00291 0.00217 0.00032 0.00000 0.00540
5 4.216 10.000 0.00291 0.00283 0.00051 0.00000 0.00626
7 7.780 15.000 0.00291 0.00369 0.00083 0.00000 0.00744
9 11.573 20.000 0.00291 0.00315 0.00062 0.00000 0.00669
11 13.984 25.000 0.00291 0.00162 0.00019 0.00000 0.00473
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 0.0447 0.2702 0.3148 0.8581 0.00497 0.01841
3 1.780 5.000 0.0545 0.3415 0.3960 0.8624 0.00540 0.01582
5 4.216 10.000 0.0754 0.4980 0.5734 0.8684 0.00626 0.01257
7 7.780 15.000 0.1066 0.7402 0.8468 0.8741 0.00744 0.01005
9 11.573 20.000 0.0865 0.5825 0.6690 0.8707 0.00669 0.01148
11 13.984 25.000 0.0393 0.2314 0.2707 0.8549 0.00473 0.02044
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4771E-01
8 20.00 8.2030E-01
7 30.00 6.5128E-01
6 40.00 4.7963E-01
5 50.00 3.3278E-01
4 60.00 2.2180E-01
3 70.00 1.4525E-01
2 80.00 9.6057E-02
1 87.50 7.0996E-02
1 92.50 5.7440E-02
2 100.00 4.4300E-02
3 110.00 3.3295E-02
4 120.00 2.6431E-02
5 130.00 2.2195E-02
6 140.00 1.9577E-02
7 150.00 1.7970E-02
8 160.00 1.7017E-02
9 170.00 1.6511E-02
10 180.00 1.6333E-02
Asymptotic AOP values are
MUu(inf) = 0.3889
MUd(inf) = 0.7084
MU(inf) = 0.6124
R(inf) = 0.0527
Lu(inf)/Ed(inf) = 0.011601 (1/sr)
k(inf) = 0.0641 (1/m)
absorp(check) = 0.0393 = 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 1.6036E-01 1.6254E+00 1.7857E+00 5.7857E-02 1.1122E+00 0.3608 0.6843 0.5904 5.2021E-02
1 0.00 0.00 9.4295E-02 1.2771E+00 1.3713E+00 4.0384E-02 1.0947E+00 0.4283 0.8572 0.7688 3.6891E-02
3 1.78 5.00 7.2037E-02 9.7578E-01 1.0478E+00 2.8829E-02 7.8308E-01 0.4002 0.8025 0.7198 3.6815E-02
5 4.22 10.00 4.6896E-02 6.4338E-01 6.9028E-01 1.7864E-02 4.9138E-01 0.3809 0.7637 0.6860 3.6354E-02
7 7.78 15.00 2.5327E-02 3.3826E-01 3.6359E-01 9.4929E-03 2.4903E-01 0.3748 0.7362 0.6588 3.8120E-02
9 11.57 20.00 1.3868E-02 1.6456E-01 1.7843E-01 5.3539E-03 1.1879E-01 0.3861 0.7218 0.6357 4.5071E-02
11 13.98 25.00 9.5273E-03 9.9896E-02 1.0942E-01 3.7300E-03 7.1490E-02 0.3915 0.7156 0.6192 5.2175E-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 0.04894 0.04632 0.04650 0.05725 0.05810 0.05813 0.07536
5.000 5.010 5.005 0.06953 0.06487 0.06519 0.08070 0.07590 0.07571 0.09646
10.000 10.010 10.005 0.10433 0.10153 0.10172 0.11204 0.11009 0.11002 0.12168
15.000 15.010 15.005 0.13561 0.15468 0.15335 0.13307 0.16067 0.16176 0.12420
20.000 20.010 20.005 0.10002 0.13153 0.12908 0.09213 0.13404 0.13602 0.08175
25.000 25.010 25.005 0.06149 0.06233 0.06225 0.06247 0.06337 0.06342 0.06329
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 1.06573E-01 5.29310E-03 6.36568E-03 1.16588E-02 4.75919E-03 0.059731
9 1 10.0 0.0 180.0 6.57597E-02 5.42645E-03 2.15354E-03 7.57999E-03 4.87908E-03 0.032749
9 4 10.0 45.0 135.0 7.22522E-02 5.38877E-03 2.47112E-03 7.85989E-03 4.84520E-03 0.034201
9 7 10.0 90.0 90.0 9.76187E-02 5.34326E-03 4.75564E-03 1.00989E-02 4.80429E-03 0.048717
8 1 20.0 0.0 180.0 5.16534E-02 5.51866E-03 1.25071E-03 6.76938E-03 4.96200E-03 0.024214
8 4 20.0 45.0 135.0 5.75041E-02 5.43858E-03 1.45868E-03 6.89726E-03 4.88999E-03 0.025367
8 7 20.0 90.0 90.0 8.45570E-02 5.37705E-03 2.99243E-03 8.36948E-03 4.83467E-03 0.035390
7 1 30.0 0.0 180.0 4.47862E-02 5.64159E-03 1.07812E-03 6.71970E-03 5.07252E-03 0.024072
7 4 30.0 45.0 135.0 4.96459E-02 5.59831E-03 1.20975E-03 6.80806E-03 5.03361E-03 0.024368
7 7 30.0 90.0 90.0 7.24562E-02 5.49022E-03 2.02035E-03 7.51057E-03 4.93642E-03 0.027884
6 1 40.0 0.0 180.0 4.25106E-02 5.75601E-03 1.19873E-03 6.95474E-03 5.17540E-03 0.028198
6 4 40.0 45.0 135.0 4.64831E-02 5.69458E-03 1.30009E-03 6.99467E-03 5.12017E-03 0.027969
6 7 40.0 90.0 90.0 6.52615E-02 5.57618E-03 1.87908E-03 7.45526E-03 5.01372E-03 0.028793
5 1 50.0 0.0 180.0 4.45710E-02 5.89423E-03 1.89358E-03 7.78781E-03 5.29968E-03 0.042485
5 4 50.0 45.0 135.0 4.74964E-02 5.79334E-03 1.97276E-03 7.76611E-03 5.20897E-03 0.041535
5 7 50.0 90.0 90.0 6.31345E-02 5.67575E-03 2.55040E-03 8.22615E-03 5.10324E-03 0.040396
4 1 60.0 0.0 180.0 5.29064E-02 5.87191E-03 4.41116E-03 1.02831E-02 5.27961E-03 0.083377
4 4 60.0 45.0 135.0 5.41038E-02 5.75714E-03 4.35594E-03 1.01131E-02 5.17642E-03 0.080511
4 7 60.0 90.0 90.0 6.68111E-02 5.70612E-03 5.08675E-03 1.07929E-02 5.13054E-03 0.076136
3 1 70.0 0.0 180.0 7.34081E-02 5.50824E-03 1.21848E-02 1.76930E-02 4.95263E-03 0.165987
3 4 70.0 45.0 135.0 7.13419E-02 5.45305E-03 1.17240E-02 1.71771E-02 4.90300E-03 0.164336
3 7 70.0 90.0 90.0 7.97586E-02 5.40468E-03 1.27493E-02 1.81540E-02 4.85951E-03 0.159849
2 1 80.0 0.0 180.0 1.24721E-01 4.76223E-03 3.02878E-02 3.50500E-02 4.28186E-03 0.242843
2 4 80.0 45.0 135.0 1.15490E-01 4.69848E-03 2.92945E-02 3.39930E-02 4.22454E-03 0.253655
2 7 80.0 90.0 90.0 1.14740E-01 4.65745E-03 3.06794E-02 3.53368E-02 4.18765E-03 0.267382
1 1 87.5 0.0 180.0 2.01652E-01 3.86603E-03 5.34167E-02 5.72827E-02 3.47607E-03 0.264896
1 4 87.5 45.0 135.0 1.81562E-01 3.62745E-03 5.30869E-02 5.67143E-02 3.26155E-03 0.292389
1 7 87.5 90.0 90.0 1.65182E-01 3.97827E-03 5.43309E-02 5.83092E-02 3.57698E-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 1.166E-02 1.066E-01 1.295E-01 1.117E-01 1.671E-01 1.048E-02 4.963E+00 5.293E-03 4.759E-03
1 0.00 0.00 9.819E-03 1.984E-01 2.002E-02 2.168E-02 2.859E-02 8.969E-03 4.113E+00
3 1.78 5.00 6.407E-03 3.406E-01 1.561E-02 1.924E-02 3.157E-02 8.182E-03 4.500E+00
5 4.22 10.00 3.710E-03 3.170E-01 1.067E-02 1.426E-02 2.473E-02 7.550E-03 4.815E+00
7 7.78 15.00 1.959E-03 1.845E-01 6.009E-03 8.334E-03 1.391E-02 7.866E-03 4.846E+00
9 11.57 20.00 1.170E-03 8.848E-02 3.422E-03 4.527E-03 6.700E-03 9.851E-03 4.575E+00
11 13.98 25.00 8.288E-04 5.264E-02 2.468E-03 3.035E-03 4.036E-03 1.159E-02 4.501E+00
Waveband 3 of 30 completed in 4.9 sec.
* * * * * Output for wavelength band 4 (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 103.6 m at 435.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 430.0 nm to 440.0 nm:
Ed(diffuse) = 3.941E-01 Ed(direct) = 7.511E-01 Ed(total) = 1.145E+00
Absorption Coefficients of Individual Components at 435.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0053 0.0332 0.0000 0.0072 0.0457
3 1.773 5.000 0.0053 0.0412 0.0000 0.0089 0.0554
5 4.202 10.000 0.0053 0.0583 0.0000 0.0125 0.0761
7 7.763 15.000 0.0053 0.0835 0.0000 0.0179 0.1067
9 11.553 20.000 0.0053 0.0673 0.0000 0.0144 0.0870
11 13.958 25.000 0.0053 0.0288 0.0000 0.0062 0.0403
Scattering Coefficients of Individual Components at 435.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0053 0.1291 0.1334 0.0000 0.2678
3 1.773 5.000 0.0053 0.1538 0.1801 0.0000 0.3392
5 4.202 10.000 0.0053 0.2016 0.2893 0.0000 0.4962
7 7.763 15.000 0.0053 0.2634 0.4710 0.0000 0.7396
9 11.553 20.000 0.0053 0.2245 0.3513 0.0000 0.5811
11 13.958 25.000 0.0053 0.1147 0.1091 0.0000 0.2291
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00264 0.00181 0.00023 0.00000 0.00468
3 1.773 5.000 0.00264 0.00216 0.00032 0.00000 0.00511
5 4.202 10.000 0.00264 0.00283 0.00051 0.00000 0.00597
7 7.763 15.000 0.00264 0.00369 0.00083 0.00000 0.00716
9 11.553 20.000 0.00264 0.00315 0.00062 0.00000 0.00640
11 13.958 25.000 0.00264 0.00161 0.00019 0.00000 0.00444
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 0.0457 0.2678 0.3135 0.8542 0.00468 0.01748
3 1.773 5.000 0.0554 0.3392 0.3946 0.8595 0.00511 0.01506
5 4.202 10.000 0.0761 0.4962 0.5723 0.8670 0.00597 0.01203
7 7.763 15.000 0.1067 0.7396 0.8463 0.8739 0.00716 0.00968
9 11.553 20.000 0.0870 0.5811 0.6681 0.8698 0.00640 0.01102
11 13.958 25.000 0.0403 0.2291 0.2694 0.8504 0.00444 0.01937
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4668E-01
8 20.00 8.1699E-01
7 30.00 6.4557E-01
6 40.00 4.7240E-01
5 50.00 3.2521E-01
4 60.00 2.1483E-01
3 70.00 1.3931E-01
2 80.00 9.1200E-02
1 87.50 6.6886E-02
1 92.50 5.3815E-02
2 100.00 4.1209E-02
3 110.00 3.0719E-02
4 120.00 2.4224E-02
5 130.00 2.0240E-02
6 140.00 1.7792E-02
7 150.00 1.6297E-02
8 160.00 1.5412E-02
9 170.00 1.4945E-02
10 180.00 1.4780E-02
Asymptotic AOP values are
MUu(inf) = 0.3858
MUd(inf) = 0.7122
MU(inf) = 0.6214
R(inf) = 0.0489
Lu(inf)/Ed(inf) = 0.010637 (1/sr)
k(inf) = 0.0649 (1/m)
absorp(check) = 0.0403 = 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 1.5995E-01 1.6630E+00 1.8230E+00 5.7957E-02 1.1452E+00 0.3623 0.6887 0.5964 5.0606E-02
1 0.00 0.00 9.1288E-02 1.3096E+00 1.4009E+00 3.9019E-02 1.1263E+00 0.4274 0.8600 0.7761 3.4644E-02
3 1.77 5.00 7.0404E-02 9.9724E-01 1.0676E+00 2.8097E-02 8.0322E-01 0.3991 0.8054 0.7260 3.4980E-02
5 4.20 10.00 4.6393E-02 6.5676E-01 7.0316E-01 1.7603E-02 5.0314E-01 0.3794 0.7661 0.6905 3.4986E-02
7 7.76 15.00 2.5267E-02 3.4606E-01 3.7132E-01 9.3958E-03 2.5524E-01 0.3719 0.7376 0.6621 3.6812E-02
9 11.55 20.00 1.3640E-02 1.6854E-01 1.8218E-01 5.2021E-03 1.2186E-01 0.3814 0.7230 0.6403 4.2690E-02
11 13.96 25.00 9.1445E-03 1.0190E-01 1.1104E-01 3.5460E-03 7.3123E-02 0.3878 0.7176 0.6266 4.8495E-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 0.04696 0.04688 0.04689 0.05571 0.05877 0.05888 0.07430
5.000 5.010 5.005 0.06714 0.06540 0.06552 0.07851 0.07644 0.07636 0.09490
10.000 10.010 10.005 0.10162 0.10151 0.10152 0.10974 0.11025 0.11027 0.12057
15.000 15.010 15.005 0.13649 0.15390 0.15272 0.13497 0.16013 0.16109 0.12730
20.000 20.010 20.005 0.10510 0.13174 0.12974 0.09764 0.13418 0.13581 0.08627
25.000 25.010 25.005 0.06305 0.06361 0.06357 0.06367 0.06429 0.06432 0.06423
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 1.06352E-01 5.09249E-03 6.53260E-03 1.16251E-02 4.44662E-03 0.061424
9 1 10.0 0.0 180.0 6.56236E-02 5.21730E-03 2.17326E-03 7.39056E-03 4.55560E-03 0.033117
9 4 10.0 45.0 135.0 7.21027E-02 5.18216E-03 2.49712E-03 7.67928E-03 4.52492E-03 0.034633
9 7 10.0 90.0 90.0 9.74167E-02 5.14129E-03 4.85723E-03 9.99851E-03 4.48923E-03 0.049860
8 1 20.0 0.0 180.0 5.15465E-02 5.30455E-03 1.24935E-03 6.55390E-03 4.63179E-03 0.024237
8 4 20.0 45.0 135.0 5.73851E-02 5.22932E-03 1.45883E-03 6.68815E-03 4.56610E-03 0.025422
8 7 20.0 90.0 90.0 8.43821E-02 5.17500E-03 3.02862E-03 8.20361E-03 4.51867E-03 0.035892
7 1 30.0 0.0 180.0 4.46936E-02 5.42172E-03 1.07588E-03 6.49760E-03 4.73410E-03 0.024072
7 4 30.0 45.0 135.0 4.95441E-02 5.38256E-03 1.20740E-03 6.58996E-03 4.69991E-03 0.024370
7 7 30.0 90.0 90.0 7.23006E-02 5.28552E-03 2.02450E-03 7.31002E-03 4.61517E-03 0.028001
6 1 40.0 0.0 180.0 4.24226E-02 5.53093E-03 1.19625E-03 6.72718E-03 4.82946E-03 0.028198
6 4 40.0 45.0 135.0 4.63869E-02 5.47524E-03 1.29740E-03 6.77264E-03 4.78083E-03 0.027969
6 7 40.0 90.0 90.0 6.51265E-02 5.37109E-03 1.87573E-03 7.24682E-03 4.68989E-03 0.028801
5 1 50.0 0.0 180.0 4.44787E-02 5.66337E-03 1.88966E-03 7.55304E-03 4.94510E-03 0.042485
5 4 50.0 45.0 135.0 4.73981E-02 5.57057E-03 1.96868E-03 7.53925E-03 4.86407E-03 0.041535
5 7 50.0 90.0 90.0 6.30038E-02 5.46978E-03 2.54512E-03 8.01490E-03 4.77606E-03 0.040396
4 1 60.0 0.0 180.0 5.27970E-02 5.64164E-03 4.40203E-03 1.00437E-02 4.92612E-03 0.083377
4 4 60.0 45.0 135.0 5.39918E-02 5.53618E-03 4.34692E-03 9.88310E-03 4.83404E-03 0.080511
4 7 60.0 90.0 90.0 6.66728E-02 5.50185E-03 5.07622E-03 1.05781E-02 4.80407E-03 0.076136
3 1 70.0 0.0 180.0 7.32562E-02 5.29197E-03 1.21596E-02 1.74515E-02 4.62081E-03 0.165987
3 4 70.0 45.0 135.0 7.11943E-02 5.24420E-03 1.16998E-02 1.69440E-02 4.57909E-03 0.164336
3 7 70.0 90.0 90.0 7.95935E-02 5.21406E-03 1.27229E-02 1.79370E-02 4.55278E-03 0.159849
2 1 80.0 0.0 180.0 1.24463E-01 4.57503E-03 3.02251E-02 3.48001E-02 3.99479E-03 0.242843
2 4 80.0 45.0 135.0 1.15251E-01 4.51885E-03 2.92339E-02 3.37528E-02 3.94574E-03 0.253655
2 7 80.0 90.0 90.0 1.14502E-01 4.49532E-03 3.06159E-02 3.51112E-02 3.92519E-03 0.267382
1 1 87.5 0.0 180.0 2.01234E-01 3.71387E-03 5.33061E-02 5.70200E-02 3.24285E-03 0.264896
1 4 87.5 45.0 135.0 1.81187E-01 3.48898E-03 5.29770E-02 5.64660E-02 3.04648E-03 0.292389
1 7 87.5 90.0 90.0 1.64840E-01 3.84147E-03 5.42185E-02 5.80600E-02 3.35427E-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 1.163E-02 1.064E-01 1.291E-01 1.114E-01 1.667E-01 1.015E-02 4.985E+00 5.092E-03 4.447E-03
1 0.00 0.00 9.446E-03 1.980E-01 1.924E-02 2.100E-02 2.808E-02 8.387E-03 4.131E+00
3 1.77 5.00 6.203E-03 3.466E-01 1.512E-02 1.883E-02 3.141E-02 7.723E-03 4.529E+00
5 4.20 10.00 3.617E-03 3.247E-01 1.046E-02 1.414E-02 2.489E-02 7.188E-03 4.867E+00
7 7.76 15.00 1.904E-03 1.897E-01 5.985E-03 8.392E-03 1.417E-02 7.461E-03 4.934E+00
9 11.55 20.00 1.115E-03 9.106E-02 3.403E-03 4.549E-03 6.806E-03 9.149E-03 4.666E+00
11 13.96 25.00 7.777E-04 5.409E-02 2.400E-03 2.981E-03 4.009E-03 1.064E-02 4.559E+00
Waveband 4 of 30 completed in 5.0 sec.
* * * * * Output for wavelength band 5 (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 103.6 m at 445.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 440.0 nm to 450.0 nm:
Ed(diffuse) = 4.530E-01 Ed(direct) = 8.990E-01 Ed(total) = 1.352E+00
Absorption Coefficients of Individual Components at 445.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0075 0.0325 0.0000 0.0062 0.0463
3 1.763 5.000 0.0075 0.0401 0.0000 0.0077 0.0553
5 4.178 10.000 0.0075 0.0560 0.0000 0.0109 0.0744
7 7.718 15.000 0.0075 0.0793 0.0000 0.0155 0.1023
9 11.485 20.000 0.0075 0.0643 0.0000 0.0125 0.0844
11 13.876 25.000 0.0075 0.0283 0.0000 0.0054 0.0412
Scattering Coefficients of Individual Components at 445.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0048 0.1282 0.1325 0.0000 0.2655
3 1.763 5.000 0.0048 0.1530 0.1792 0.0000 0.3370
5 4.178 10.000 0.0048 0.2010 0.2886 0.0000 0.4945
7 7.718 15.000 0.0048 0.2634 0.4710 0.0000 0.7391
9 11.485 20.000 0.0048 0.2242 0.3508 0.0000 0.5798
11 13.876 25.000 0.0048 0.1138 0.1082 0.0000 0.2268
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00239 0.00180 0.00023 0.00000 0.00442
3 1.763 5.000 0.00239 0.00215 0.00032 0.00000 0.00485
5 4.178 10.000 0.00239 0.00282 0.00051 0.00000 0.00572
7 7.718 15.000 0.00239 0.00369 0.00083 0.00000 0.00691
9 11.485 20.000 0.00239 0.00314 0.00062 0.00000 0.00615
11 13.876 25.000 0.00239 0.00160 0.00019 0.00000 0.00418
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 0.0463 0.2655 0.3118 0.8516 0.00442 0.01665
3 1.763 5.000 0.0553 0.3370 0.3923 0.8590 0.00485 0.01439
5 4.178 10.000 0.0744 0.4945 0.5688 0.8692 0.00572 0.01156
7 7.718 15.000 0.1023 0.7391 0.8414 0.8784 0.00691 0.00935
9 11.485 20.000 0.0844 0.5798 0.6642 0.8730 0.00615 0.01061
11 13.876 25.000 0.0412 0.2268 0.2680 0.8462 0.00418 0.01841
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4574E-01
8 20.00 8.1397E-01
7 30.00 6.4041E-01
6 40.00 4.6590E-01
5 50.00 3.1846E-01
4 60.00 2.0866E-01
3 70.00 1.3411E-01
2 80.00 8.6983E-02
1 87.50 6.3340E-02
1 92.50 5.0701E-02
2 100.00 3.8566E-02
3 110.00 2.8528E-02
4 120.00 2.2352E-02
5 130.00 1.8586E-02
6 140.00 1.6283E-02
7 150.00 1.4883E-02
8 160.00 1.4058E-02
9 170.00 1.3622E-02
10 180.00 1.3469E-02
Asymptotic AOP values are
MUu(inf) = 0.3829
MUd(inf) = 0.7155
MU(inf) = 0.6294
R(inf) = 0.0456
Lu(inf)/Ed(inf) = 0.009809 (1/sr)
k(inf) = 0.0655 (1/m)
absorp(check) = 0.0412 = 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 1.8442E-01 1.9528E+00 2.1372E+00 6.7180E-02 1.3520E+00 0.3643 0.6924 0.6012 4.9689E-02
1 0.00 0.00 1.0353E-01 1.5419E+00 1.6454E+00 4.4269E-02 1.3291E+00 0.4276 0.8620 0.7809 3.3308E-02
3 1.76 5.00 8.1549E-02 1.1750E+00 1.2566E+00 3.2573E-02 9.4883E-01 0.3994 0.8075 0.7292 3.4330E-02
5 4.18 10.00 5.5506E-02 7.8161E-01 8.3712E-01 2.1056E-02 5.9950E-01 0.3794 0.7670 0.6910 3.5123E-02
7 7.72 15.00 3.1314E-02 4.2215E-01 4.5346E-01 1.1568E-02 3.1096E-01 0.3694 0.7366 0.6602 3.7202E-02
9 11.49 20.00 1.6853E-02 2.1079E-01 2.2764E-01 6.3300E-03 1.5209E-01 0.3756 0.7215 0.6403 4.1621E-02
11 13.88 25.00 1.0888E-02 1.2805E-01 1.3894E-01 4.1752E-03 9.1889E-02 0.3835 0.7176 0.6313 4.5437E-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 0.04367 0.04726 0.04703 0.05225 0.05902 0.05925 0.07113
5.000 5.010 5.005 0.06140 0.06465 0.06444 0.07291 0.07577 0.07587 0.09010
10.000 10.010 10.005 0.09391 0.09838 0.09809 0.10257 0.10750 0.10768 0.11512
15.000 15.010 15.005 0.13290 0.14735 0.14636 0.13319 0.15408 0.15489 0.12784
20.000 20.010 20.005 0.11081 0.12818 0.12690 0.10459 0.13055 0.13168 0.09203
25.000 25.010 25.005 0.06544 0.06533 0.06534 0.06530 0.06530 0.06530 0.06529
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 1.22238E-01 5.76616E-03 7.69016E-03 1.34563E-02 4.26488E-03 0.062911
9 1 10.0 0.0 180.0 7.54258E-02 5.90081E-03 2.52228E-03 8.42309E-03 4.36447E-03 0.033441
9 4 10.0 45.0 135.0 8.28726E-02 5.86317E-03 2.90151E-03 8.76468E-03 4.33663E-03 0.035012
9 7 10.0 90.0 90.0 1.11968E-01 5.82227E-03 5.69522E-03 1.15175E-02 4.30638E-03 0.050865
8 1 20.0 0.0 180.0 5.92460E-02 5.99643E-03 1.43720E-03 7.43363E-03 4.43520E-03 0.024258
8 4 20.0 45.0 135.0 6.59567E-02 5.91481E-03 1.67993E-03 7.59474E-03 4.37483E-03 0.025470
8 7 20.0 90.0 90.0 9.69862E-02 5.86222E-03 3.52378E-03 9.38600E-03 4.33593E-03 0.036333
7 1 30.0 0.0 180.0 5.13694E-02 6.12649E-03 1.23659E-03 7.36308E-03 4.53140E-03 0.024072
7 4 30.0 45.0 135.0 5.69454E-02 6.08699E-03 1.38790E-03 7.47488E-03 4.50218E-03 0.024372
7 7 30.0 90.0 90.0 8.30944E-02 5.98968E-03 2.33532E-03 8.32499E-03 4.43020E-03 0.028104
6 1 40.0 0.0 180.0 4.87593E-02 6.24755E-03 1.37493E-03 7.62248E-03 4.62093E-03 0.028198
6 4 40.0 45.0 135.0 5.33157E-02 6.19097E-03 1.49119E-03 7.68216E-03 4.57909E-03 0.027969
6 7 40.0 90.0 90.0 7.48544E-02 6.09015E-03 2.15646E-03 8.24661E-03 4.50451E-03 0.028809
5 1 50.0 0.0 180.0 5.11225E-02 6.39516E-03 2.17192E-03 8.56708E-03 4.73011E-03 0.042485
5 4 50.0 45.0 135.0 5.44779E-02 6.29793E-03 2.26274E-03 8.56068E-03 4.65820E-03 0.041535
5 7 50.0 90.0 90.0 7.24147E-02 6.20466E-03 2.92529E-03 9.12995E-03 4.58921E-03 0.040396
4 1 60.0 0.0 180.0 6.06832E-02 6.36851E-03 5.05956E-03 1.14281E-02 4.71040E-03 0.083377
4 4 60.0 45.0 135.0 6.20566E-02 6.25805E-03 4.99622E-03 1.12543E-02 4.62870E-03 0.080511
4 7 60.0 90.0 90.0 7.66317E-02 6.24318E-03 5.83446E-03 1.20776E-02 4.61770E-03 0.076136
3 1 70.0 0.0 180.0 8.41984E-02 5.97111E-03 1.39759E-02 1.99470E-02 4.41647E-03 0.165987
3 4 70.0 45.0 135.0 8.18286E-02 5.92619E-03 1.34474E-02 1.93735E-02 4.38324E-03 0.164336
3 7 70.0 90.0 90.0 9.14824E-02 5.91750E-03 1.46234E-02 2.05409E-02 4.37681E-03 0.159849
2 1 80.0 0.0 180.0 1.43054E-01 5.15973E-03 3.47398E-02 3.98995E-02 3.81634E-03 0.242843
2 4 80.0 45.0 135.0 1.32466E-01 5.10470E-03 3.36006E-02 3.87053E-02 3.77564E-03 0.253655
2 7 80.0 90.0 90.0 1.31606E-01 5.10188E-03 3.51890E-02 4.02908E-02 3.77355E-03 0.267382
1 1 87.5 0.0 180.0 2.31293E-01 4.18616E-03 6.12685E-02 6.54546E-02 3.09625E-03 0.264896
1 4 87.5 45.0 135.0 2.08251E-01 3.93949E-03 6.08902E-02 6.48297E-02 2.91381E-03 0.292389
1 7 87.5 90.0 90.0 1.89462E-01 4.35902E-03 6.23171E-02 6.66761E-02 3.22410E-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 1.346E-02 1.222E-01 1.484E-01 1.281E-01 1.916E-01 9.953E-03 4.992E+00 5.766E-03 4.265E-03
1 0.00 0.00 1.070E-02 2.276E-01 2.159E-02 2.375E-02 3.215E-02 8.047E-03 4.139E+00
3 1.76 5.00 7.162E-03 4.063E-01 1.720E-02 2.165E-02 3.657E-02 7.548E-03 4.548E+00
5 4.18 10.00 4.285E-03 3.861E-01 1.230E-02 1.678E-02 2.986E-02 7.148E-03 4.914E+00
7 7.72 15.00 2.295E-03 2.305E-01 7.369E-03 1.042E-02 1.776E-02 7.379E-03 5.041E+00
9 11.49 20.00 1.321E-03 1.131E-01 4.264E-03 5.753E-03 8.691E-03 8.684E-03 4.793E+00
11 13.88 25.00 9.020E-04 6.773E-02 2.909E-03 3.650E-03 4.964E-03 9.816E-03 4.629E+00
Waveband 5 of 30 completed in 4.9 sec.
* * * * * Output for wavelength band 6 (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 103.6 m at 455.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 450.0 nm to 460.0 nm:
Ed(diffuse) = 4.729E-01 Ed(direct) = 9.738E-01 Ed(total) = 1.447E+00
Absorption Coefficients of Individual Components at 455.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0096 0.0301 0.0000 0.0054 0.0451
3 1.745 5.000 0.0096 0.0369 0.0000 0.0067 0.0533
5 4.134 10.000 0.0096 0.0513 0.0000 0.0095 0.0704
7 7.641 15.000 0.0096 0.0722 0.0000 0.0135 0.0953
9 11.375 20.000 0.0096 0.0588 0.0000 0.0109 0.0793
11 13.742 25.000 0.0096 0.0262 0.0000 0.0047 0.0406
Scattering Coefficients of Individual Components at 455.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0043 0.1274 0.1316 0.0000 0.2633
3 1.745 5.000 0.0043 0.1522 0.1783 0.0000 0.3348
5 4.134 10.000 0.0043 0.2006 0.2879 0.0000 0.4928
7 7.641 15.000 0.0043 0.2634 0.4710 0.0000 0.7387
9 11.375 20.000 0.0043 0.2239 0.3504 0.0000 0.5786
11 13.742 25.000 0.0043 0.1129 0.1074 0.0000 0.2246
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00217 0.00179 0.00023 0.00000 0.00419
3 1.745 5.000 0.00217 0.00213 0.00031 0.00000 0.00462
5 4.134 10.000 0.00217 0.00281 0.00051 0.00000 0.00549
7 7.641 15.000 0.00217 0.00369 0.00083 0.00000 0.00669
9 11.375 20.000 0.00217 0.00314 0.00062 0.00000 0.00593
11 13.742 25.000 0.00217 0.00158 0.00019 0.00000 0.00394
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 0.0451 0.2633 0.3084 0.8537 0.00419 0.01591
3 1.745 5.000 0.0533 0.3348 0.3881 0.8627 0.00462 0.01379
5 4.134 10.000 0.0704 0.4928 0.5632 0.8750 0.00549 0.01114
7 7.641 15.000 0.0953 0.7387 0.8340 0.8857 0.00669 0.00906
9 11.375 20.000 0.0793 0.5786 0.6579 0.8795 0.00593 0.01024
11 13.742 25.000 0.0406 0.2246 0.2652 0.8470 0.00394 0.01755
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4594E-01
8 20.00 8.1459E-01
7 30.00 6.4137E-01
6 40.00 4.6695E-01
5 50.00 3.1933E-01
4 60.00 2.0920E-01
3 70.00 1.3431E-01
2 80.00 8.6912E-02
1 87.50 6.3116E-02
1 92.50 5.0389E-02
2 100.00 3.8176E-02
3 110.00 2.8082E-02
4 120.00 2.1877E-02
5 130.00 1.8099E-02
6 140.00 1.5791E-02
7 150.00 1.4388E-02
8 160.00 1.3562E-02
9 170.00 1.3126E-02
10 180.00 1.2973E-02
Asymptotic AOP values are
MUu(inf) = 0.3803
MUd(inf) = 0.7156
MU(inf) = 0.6311
R(inf) = 0.0444
Lu(inf)/Ed(inf) = 0.009434 (1/sr)
k(inf) = 0.0643 (1/m)
absorp(check) = 0.0406 = 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 1.9464E-01 2.0796E+00 2.2742E+00 7.1482E-02 1.4468E+00 0.3673 0.6957 0.6047 4.9409E-02
1 0.00 0.00 1.1087E-01 1.6493E+00 1.7601E+00 4.7472E-02 1.4227E+00 0.4282 0.8626 0.7813 3.3367E-02
3 1.74 5.00 8.9912E-02 1.2713E+00 1.3612E+00 3.6015E-02 1.0274E+00 0.4006 0.8081 0.7283 3.5056E-02
5 4.13 10.00 6.3873E-02 8.6518E-01 9.2905E-01 2.4282E-02 6.6295E-01 0.3802 0.7663 0.6874 3.6627E-02
7 7.64 15.00 3.7833E-02 4.8630E-01 5.2414E-01 1.3930E-02 3.5685E-01 0.3682 0.7338 0.6543 3.9035E-02
9 11.37 20.00 2.0705E-02 2.5293E-01 2.7363E-01 7.6844E-03 1.8158E-01 0.3711 0.7179 0.6355 4.2319E-02
11 13.74 25.00 1.3110E-02 1.5648E-01 1.6959E-01 4.9799E-03 1.1189E-01 0.3799 0.7150 0.6304 4.4508E-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 0.03928 0.04597 0.04555 0.04729 0.05738 0.05773 0.06613
5.000 5.010 5.005 0.05384 0.06156 0.06105 0.06538 0.07286 0.07313 0.08316
10.000 10.010 10.005 0.08400 0.09246 0.09188 0.09310 0.10204 0.10238 0.10702
15.000 15.010 15.005 0.12563 0.13757 0.13671 0.12759 0.14485 0.14556 0.12447
20.000 20.010 20.005 0.11234 0.12157 0.12087 0.10755 0.12395 0.12468 0.09445
25.000 25.010 25.005 0.06571 0.06497 0.06503 0.06490 0.06437 0.06434 0.06439
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 1.27614E-01 6.16376E-03 8.20805E-03 1.43718E-02 4.26040E-03 0.064320
9 1 10.0 0.0 180.0 7.87429E-02 6.29740E-03 2.65733E-03 8.95473E-03 4.35278E-03 0.033747
9 4 10.0 45.0 135.0 8.65172E-02 6.26063E-03 3.06015E-03 9.32079E-03 4.32737E-03 0.035370
9 7 10.0 90.0 90.0 1.16892E-01 6.22552E-03 6.05687E-03 1.22824E-02 4.30310E-03 0.051816
8 1 20.0 0.0 180.0 6.18514E-02 6.39531E-03 1.50162E-03 7.89693E-03 4.42045E-03 0.024278
8 4 20.0 45.0 135.0 6.88573E-02 6.31385E-03 1.75697E-03 8.07082E-03 4.36415E-03 0.025516
8 7 20.0 90.0 90.0 1.01251E-01 6.27182E-03 3.72103E-03 9.99285E-03 4.33510E-03 0.036750
7 1 30.0 0.0 180.0 5.36285E-02 6.53125E-03 1.29097E-03 7.82222E-03 4.51442E-03 0.024072
7 4 30.0 45.0 135.0 5.94506E-02 6.49691E-03 1.44909E-03 7.94600E-03 4.49068E-03 0.024375
7 7 30.0 90.0 90.0 8.67430E-02 6.41276E-03 2.44633E-03 8.85909E-03 4.43251E-03 0.028202
6 1 40.0 0.0 180.0 5.09036E-02 6.65862E-03 1.43540E-03 8.09402E-03 4.60246E-03 0.028198
6 4 40.0 45.0 135.0 5.56604E-02 6.60864E-03 1.55677E-03 8.16541E-03 4.56791E-03 0.027969
6 7 40.0 90.0 90.0 7.81463E-02 6.52754E-03 2.25184E-03 8.77938E-03 4.51185E-03 0.028816
5 1 50.0 0.0 180.0 5.33708E-02 6.81509E-03 2.26743E-03 9.08253E-03 4.71061E-03 0.042485
5 4 50.0 45.0 135.0 5.68737E-02 6.72371E-03 2.36225E-03 9.08596E-03 4.64745E-03 0.041535
5 7 50.0 90.0 90.0 7.55993E-02 6.65593E-03 3.05393E-03 9.70986E-03 4.60060E-03 0.040396
4 1 60.0 0.0 180.0 6.33519E-02 6.78578E-03 5.28206E-03 1.20678E-02 4.69035E-03 0.083377
4 4 60.0 45.0 135.0 6.47857E-02 6.68178E-03 5.21594E-03 1.18977E-02 4.61846E-03 0.080511
4 7 60.0 90.0 90.0 8.00018E-02 6.70208E-03 6.09104E-03 1.27931E-02 4.63250E-03 0.076136
3 1 70.0 0.0 180.0 8.79013E-02 6.36072E-03 1.45905E-02 2.09512E-02 4.39655E-03 0.165987
3 4 70.0 45.0 135.0 8.54272E-02 6.32698E-03 1.40387E-02 2.03657E-02 4.37322E-03 0.164336
3 7 70.0 90.0 90.0 9.55055E-02 6.35512E-03 1.52665E-02 2.16216E-02 4.39267E-03 0.159849
2 1 80.0 0.0 180.0 1.49346E-01 5.49461E-03 3.62676E-02 4.17622E-02 3.79789E-03 0.242843
2 4 80.0 45.0 135.0 1.38291E-01 5.44889E-03 3.50783E-02 4.05271E-02 3.76628E-03 0.253655
2 7 80.0 90.0 90.0 1.37393E-01 5.48013E-03 3.67365E-02 4.22166E-02 3.78788E-03 0.267382
1 1 87.5 0.0 180.0 2.41464E-01 4.45568E-03 6.39629E-02 6.84186E-02 3.07978E-03 0.264896
1 4 87.5 45.0 135.0 2.17409E-01 4.20349E-03 6.35680E-02 6.77715E-02 2.90546E-03 0.292389
1 7 87.5 90.0 90.0 1.97794E-01 4.68136E-03 6.50577E-02 6.97390E-02 3.23577E-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 1.437E-02 1.276E-01 1.549E-01 1.338E-01 2.001E-01 9.934E-03 4.974E+00 6.164E-03 4.260E-03
1 0.00 0.00 1.143E-02 2.376E-01 2.283E-02 2.533E-02 3.460E-02 8.036E-03 4.152E+00
3 1.74 5.00 7.884E-03 4.360E-01 1.856E-02 2.354E-02 4.010E-02 7.674E-03 4.568E+00
5 4.13 10.00 4.899E-03 4.246E-01 1.385E-02 1.904E-02 3.412E-02 7.390E-03 4.956E+00
7 7.64 15.00 2.711E-03 2.624E-01 8.797E-03 1.253E-02 2.148E-02 7.598E-03 5.137E+00
9 11.37 20.00 1.563E-03 1.335E-01 5.270E-03 7.168E-03 1.091E-02 8.609E-03 4.916E+00
11 13.74 25.00 1.059E-03 8.152E-02 3.543E-03 4.487E-03 6.164E-03 9.461E-03 4.704E+00
Waveband 6 of 30 completed in 4.9 sec.
* * * * * Output for wavelength band 7 (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 103.6 m at 465.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 460.0 nm to 470.0 nm:
Ed(diffuse) = 4.602E-01 Ed(direct) = 9.804E-01 Ed(total) = 1.441E+00
Absorption Coefficients of Individual Components at 465.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0101 0.0281 0.0000 0.0047 0.0430
3 1.722 5.000 0.0101 0.0346 0.0000 0.0058 0.0505
5 4.085 10.000 0.0101 0.0481 0.0000 0.0082 0.0664
7 7.564 15.000 0.0101 0.0677 0.0000 0.0117 0.0896
9 11.268 20.000 0.0101 0.0551 0.0000 0.0095 0.0747
11 13.609 25.000 0.0101 0.0245 0.0000 0.0041 0.0387
Scattering Coefficients of Individual Components at 465.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0040 0.1265 0.1307 0.0000 0.2612
3 1.722 5.000 0.0040 0.1515 0.1774 0.0000 0.3328
5 4.085 10.000 0.0040 0.2001 0.2872 0.0000 0.4913
7 7.564 15.000 0.0040 0.2634 0.4710 0.0000 0.7383
9 11.268 20.000 0.0040 0.2236 0.3499 0.0000 0.5774
11 13.609 25.000 0.0040 0.1121 0.1066 0.0000 0.2226
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00198 0.00177 0.00023 0.00000 0.00398
3 1.722 5.000 0.00198 0.00212 0.00031 0.00000 0.00441
5 4.085 10.000 0.00198 0.00281 0.00051 0.00000 0.00529
7 7.564 15.000 0.00198 0.00369 0.00083 0.00000 0.00650
9 11.268 20.000 0.00198 0.00313 0.00062 0.00000 0.00573
11 13.609 25.000 0.00198 0.00157 0.00019 0.00000 0.00374
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 0.0430 0.2612 0.3042 0.8588 0.00398 0.01524
3 1.722 5.000 0.0505 0.3328 0.3833 0.8682 0.00441 0.01326
5 4.085 10.000 0.0664 0.4913 0.5577 0.8809 0.00529 0.01076
7 7.564 15.000 0.0896 0.7383 0.8279 0.8918 0.00650 0.00880
9 11.268 20.000 0.0747 0.5774 0.6521 0.8854 0.00573 0.00992
11 13.609 25.000 0.0387 0.2226 0.2613 0.8517 0.00374 0.01678
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4702E-01
8 20.00 8.1800E-01
7 30.00 6.4708E-01
6 40.00 4.7387E-01
5 50.00 3.2613E-01
4 60.00 2.1497E-01
3 70.00 1.3872E-01
2 80.00 9.0064E-02
1 87.50 6.5463E-02
1 92.50 5.2235E-02
2 100.00 3.9507E-02
3 110.00 2.8955E-02
4 120.00 2.2447E-02
5 130.00 1.8473E-02
6 140.00 1.6040E-02
7 150.00 1.4560E-02
8 160.00 1.3686E-02
9 170.00 1.3225E-02
10 180.00 1.3064E-02
Asymptotic AOP values are
MUu(inf) = 0.3780
MUd(inf) = 0.7130
MU(inf) = 0.6279
R(inf) = 0.0448
Lu(inf)/Ed(inf) = 0.009388 (1/sr)
k(inf) = 0.0617 (1/m)
absorp(check) = 0.0388 = 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 1.9288E-01 2.0615E+00 2.2544E+00 7.1605E-02 1.4405E+00 0.3712 0.6988 0.6072 4.9707E-02
1 0.00 0.00 1.1483E-01 1.6451E+00 1.7600E+00 4.9234E-02 1.4181E+00 0.4288 0.8620 0.7778 3.4717E-02
3 1.72 5.00 9.5142E-02 1.2893E+00 1.3845E+00 3.8227E-02 1.0412E+00 0.4018 0.8075 0.7244 3.6715E-02
5 4.09 10.00 6.9714E-02 8.9914E-01 9.6885E-01 2.6582E-02 6.8753E-01 0.3813 0.7647 0.6822 3.8664E-02
7 7.56 15.00 4.2858E-02 5.2321E-01 5.6607E-01 1.5792E-02 3.8240E-01 0.3685 0.7309 0.6476 4.1299E-02
9 11.27 20.00 2.4067E-02 2.8195E-01 3.0601E-01 8.9014E-03 2.0139E-01 0.3699 0.7143 0.6290 4.4200E-02
11 13.61 25.00 1.5350E-02 1.7839E-01 1.9374E-01 5.8082E-03 1.2693E-01 0.3784 0.7115 0.6252 4.5760E-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 0.03644 0.04357 0.04310 0.04356 0.05455 0.05494 0.06197
5.000 5.010 5.005 0.04850 0.05763 0.05700 0.05994 0.06909 0.06944 0.07778
10.000 10.010 10.005 0.07700 0.08672 0.08603 0.08624 0.09664 0.09706 0.10061
15.000 15.010 15.005 0.11866 0.12961 0.12878 0.12140 0.13725 0.13794 0.11945
20.000 20.010 20.005 0.10930 0.11535 0.11488 0.10533 0.11784 0.11841 0.09253
25.000 25.010 25.005 0.06345 0.06252 0.06259 0.06244 0.06175 0.06171 0.06182
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 1.24169E-01 6.36912E-03 8.15369E-03 1.45228E-02 4.42136E-03 0.065666
9 1 10.0 0.0 180.0 7.66173E-02 6.49473E-03 2.60804E-03 9.10277E-03 4.50856E-03 0.034040
9 4 10.0 45.0 135.0 8.41817E-02 6.46100E-03 3.00643E-03 9.46743E-03 4.48514E-03 0.035714
9 7 10.0 90.0 90.0 1.13736E-01 6.43502E-03 5.99682E-03 1.24318E-02 4.46711E-03 0.052726
8 1 20.0 0.0 180.0 6.01818E-02 6.59059E-03 1.46222E-03 8.05281E-03 4.57510E-03 0.024297
8 4 20.0 45.0 135.0 6.69986E-02 6.51358E-03 1.71248E-03 8.22606E-03 4.52164E-03 0.025560
8 7 20.0 90.0 90.0 9.85182E-02 6.48703E-03 3.65993E-03 1.01470E-02 4.50321E-03 0.037150
7 1 30.0 0.0 180.0 5.21809E-02 6.72738E-03 1.25612E-03 7.98350E-03 4.67006E-03 0.024072
7 4 30.0 45.0 135.0 5.78467E-02 6.70166E-03 1.41011E-03 8.11177E-03 4.65220E-03 0.024377
7 7 30.0 90.0 90.0 8.43961E-02 6.63812E-03 2.38804E-03 9.02616E-03 4.60810E-03 0.028296
6 1 40.0 0.0 180.0 4.95295E-02 6.85719E-03 1.39665E-03 8.25384E-03 4.76017E-03 0.028198
6 4 40.0 45.0 135.0 5.41579E-02 6.81841E-03 1.51475E-03 8.33316E-03 4.73325E-03 0.027969
6 7 40.0 90.0 90.0 7.60368E-02 6.76547E-03 2.19156E-03 8.95703E-03 4.69650E-03 0.028822
5 1 50.0 0.0 180.0 5.19301E-02 7.01879E-03 2.20623E-03 9.22501E-03 4.87235E-03 0.042485
5 4 50.0 45.0 135.0 5.53385E-02 6.93955E-03 2.29848E-03 9.23804E-03 4.81735E-03 0.041535
5 7 50.0 90.0 90.0 7.35586E-02 6.90558E-03 2.97150E-03 9.87708E-03 4.79377E-03 0.040396
4 1 60.0 0.0 180.0 6.16418E-02 6.98939E-03 5.13948E-03 1.21289E-02 4.85194E-03 0.083377
4 4 60.0 45.0 135.0 6.30369E-02 6.89874E-03 5.07515E-03 1.19739E-02 4.78901E-03 0.080511
4 7 60.0 90.0 90.0 7.78422E-02 6.95975E-03 5.92662E-03 1.28864E-02 4.83137E-03 0.076136
3 1 70.0 0.0 180.0 8.55285E-02 6.55247E-03 1.41966E-02 2.07491E-02 4.54864E-03 0.165987
3 4 70.0 45.0 135.0 8.31211E-02 6.53441E-03 1.36598E-02 2.01942E-02 4.53610E-03 0.164336
3 7 70.0 90.0 90.0 9.29275E-02 6.60374E-03 1.48544E-02 2.14581E-02 4.58423E-03 0.159849
2 1 80.0 0.0 180.0 1.45314E-01 5.66066E-03 3.52886E-02 4.09492E-02 3.92955E-03 0.242843
2 4 80.0 45.0 135.0 1.34558E-01 5.62861E-03 3.41314E-02 3.97600E-02 3.90731E-03 0.253655
2 7 80.0 90.0 90.0 1.33685E-01 5.69675E-03 3.57448E-02 4.14416E-02 3.95461E-03 0.267382
1 1 87.5 0.0 180.0 2.34946E-01 4.59015E-03 6.22363E-02 6.68264E-02 3.18642E-03 0.264896
1 4 87.5 45.0 135.0 2.11540E-01 4.34222E-03 6.18520E-02 6.61942E-02 3.01431E-03 0.292389
1 7 87.5 90.0 90.0 1.92455E-01 4.86661E-03 6.33015E-02 6.81681E-02 3.37834E-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 1.452E-02 1.242E-01 1.509E-01 1.303E-01 1.949E-01 1.008E-02 4.931E+00 6.369E-03 4.421E-03
1 0.00 0.00 1.181E-02 2.312E-01 2.343E-02 2.616E-02 3.581E-02 8.330E-03 4.168E+00
3 1.72 5.00 8.342E-03 4.375E-01 1.934E-02 2.459E-02 4.190E-02 8.012E-03 4.582E+00
5 4.09 10.00 5.341E-03 4.373E-01 1.488E-02 2.052E-02 3.681E-02 7.769E-03 4.977E+00
7 7.56 15.00 3.049E-03 2.789E-01 9.842E-03 1.406E-02 2.416E-02 7.973E-03 5.180E+00
9 11.27 20.00 1.788E-03 1.463E-01 6.097E-03 8.327E-03 1.272E-02 8.879E-03 4.978E+00
11 13.61 25.00 1.221E-03 9.132E-02 4.143E-03 5.277E-03 7.289E-03 9.623E-03 4.755E+00
Waveband 7 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 8 (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 103.6 m at 475.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 470.0 nm to 480.0 nm:
Ed(diffuse) = 4.572E-01 Ed(direct) = 1.005E+00 Ed(total) = 1.462E+00
Absorption Coefficients of Individual Components at 475.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0114 0.0259 0.0000 0.0041 0.0414
3 1.703 5.000 0.0114 0.0318 0.0000 0.0051 0.0483
5 4.042 10.000 0.0114 0.0441 0.0000 0.0072 0.0627
7 7.492 15.000 0.0114 0.0620 0.0000 0.0102 0.0836
9 11.166 20.000 0.0114 0.0505 0.0000 0.0082 0.0702
11 13.485 25.000 0.0114 0.0226 0.0000 0.0036 0.0376
Scattering Coefficients of Individual Components at 475.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0036 0.1257 0.1299 0.0000 0.2593
3 1.703 5.000 0.0036 0.1507 0.1765 0.0000 0.3309
5 4.042 10.000 0.0036 0.1996 0.2866 0.0000 0.4898
7 7.492 15.000 0.0036 0.2634 0.4710 0.0000 0.7380
9 11.166 20.000 0.0036 0.2233 0.3494 0.0000 0.5763
11 13.485 25.000 0.0036 0.1112 0.1058 0.0000 0.2206
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00180 0.00176 0.00023 0.00000 0.00379
3 1.703 5.000 0.00180 0.00211 0.00031 0.00000 0.00423
5 4.042 10.000 0.00180 0.00280 0.00050 0.00000 0.00511
7 7.492 15.000 0.00180 0.00369 0.00083 0.00000 0.00632
9 11.166 20.000 0.00180 0.00313 0.00061 0.00000 0.00555
11 13.485 25.000 0.00180 0.00156 0.00019 0.00000 0.00355
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 0.0414 0.2593 0.3007 0.8622 0.00379 0.01464
3 1.703 5.000 0.0483 0.3309 0.3792 0.8727 0.00423 0.01277
5 4.042 10.000 0.0627 0.4898 0.5524 0.8865 0.00511 0.01042
7 7.492 15.000 0.0836 0.7380 0.8216 0.8982 0.00632 0.00857
9 11.166 20.000 0.0702 0.5763 0.6465 0.8915 0.00555 0.00963
11 13.485 25.000 0.0376 0.2206 0.2582 0.8544 0.00355 0.01608
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4764E-01
8 20.00 8.1994E-01
7 30.00 6.5030E-01
6 40.00 4.7775E-01
5 50.00 3.2992E-01
4 60.00 2.1813E-01
3 70.00 1.4107E-01
2 80.00 9.1674E-02
1 87.50 6.6600E-02
1 92.50 5.3077E-02
2 100.00 4.0050E-02
3 110.00 2.9235E-02
4 120.00 2.2555E-02
5 130.00 1.8472E-02
6 140.00 1.5972E-02
7 150.00 1.4449E-02
8 160.00 1.3550E-02
9 170.00 1.3076E-02
10 180.00 1.2909E-02
Asymptotic AOP values are
MUu(inf) = 0.3758
MUd(inf) = 0.7117
MU(inf) = 0.6270
R(inf) = 0.0446
Lu(inf)/Ed(inf) = 0.009217 (1/sr)
k(inf) = 0.0600 (1/m)
absorp(check) = 0.0376 = 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 1.9447E-01 2.0839E+00 2.2784E+00 7.2836E-02 1.4620E+00 0.3745 0.7016 0.6097 4.9818E-02
1 0.00 0.00 1.1916E-01 1.6713E+00 1.7904E+00 5.1191E-02 1.4404E+00 0.4296 0.8619 0.7759 3.5540E-02
3 1.70 5.00 1.0113E-01 1.3265E+00 1.4277E+00 4.0776E-02 1.0711E+00 0.4032 0.8075 0.7217 3.8068E-02
5 4.04 10.00 7.6702E-02 9.4559E-01 1.0223E+00 2.9334E-02 7.2189E-01 0.3824 0.7634 0.6775 4.0635E-02
7 7.49 15.00 4.9030E-02 5.6982E-01 6.1885E-01 1.8041E-02 4.1482E-01 0.3680 0.7280 0.6412 4.3492E-02
9 11.17 20.00 2.8022E-02 3.1823E-01 3.4626E-01 1.0280E-02 2.2616E-01 0.3668 0.7107 0.6235 4.5453E-02
11 13.48 25.00 1.7724E-02 2.0515E-01 2.2287E-01 6.6588E-03 1.4536E-01 0.3757 0.7086 0.6223 4.5808E-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 0.03310 0.04196 0.04137 0.03939 0.05252 0.05301 0.05758
5.000 5.010 5.005 0.04240 0.05441 0.05356 0.05381 0.06603 0.06651 0.07205
10.000 10.010 10.005 0.06915 0.08128 0.08037 0.07877 0.09159 0.09214 0.09421
15.000 15.010 15.005 0.11237 0.12126 0.12056 0.11645 0.12937 0.12996 0.11634
20.000 20.010 20.005 0.10913 0.10936 0.10934 0.10632 0.11189 0.11216 0.09333
25.000 25.010 25.005 0.06272 0.06131 0.06143 0.06126 0.06016 0.06011 0.06031
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 1.23372E-01 6.60398E-03 8.25799E-03 1.48620E-02 4.51695E-03 0.066935
9 1 10.0 0.0 180.0 7.61258E-02 6.72240E-03 2.61234E-03 9.33474E-03 4.59795E-03 0.034316
9 4 10.0 45.0 135.0 8.36417E-02 6.69147E-03 3.01420E-03 9.70567E-03 4.57679E-03 0.036037
9 7 10.0 90.0 90.0 1.13007E-01 6.67444E-03 6.05524E-03 1.27297E-02 4.56514E-03 0.053583
8 1 20.0 0.0 180.0 5.97958E-02 6.81695E-03 1.45391E-03 8.27086E-03 4.66261E-03 0.024315
8 4 20.0 45.0 135.0 6.65688E-02 6.74385E-03 1.70425E-03 8.44810E-03 4.61261E-03 0.025601
8 7 20.0 90.0 90.0 9.78863E-02 6.73259E-03 3.67330E-03 1.04059E-02 4.60491E-03 0.037526
7 1 30.0 0.0 180.0 5.18462E-02 6.95543E-03 1.24806E-03 8.20349E-03 4.75733E-03 0.024072
7 4 30.0 45.0 135.0 5.74764E-02 6.93796E-03 1.40120E-03 8.33916E-03 4.74538E-03 0.024379
7 7 30.0 90.0 90.0 8.38498E-02 6.89472E-03 2.37996E-03 9.27468E-03 4.71580E-03 0.028384
6 1 40.0 0.0 180.0 4.92118E-02 7.08814E-03 1.38769E-03 8.47583E-03 4.84810E-03 0.028198
6 4 40.0 45.0 135.0 5.38105E-02 7.06009E-03 1.50503E-03 8.56512E-03 4.82891E-03 0.027969
6 7 40.0 90.0 90.0 7.55491E-02 7.03529E-03 2.17797E-03 9.21326E-03 4.81195E-03 0.028829
5 1 50.0 0.0 180.0 5.15970E-02 7.25472E-03 2.19207E-03 9.44680E-03 4.96204E-03 0.042485
5 4 50.0 45.0 135.0 5.49835E-02 7.18698E-03 2.28374E-03 9.47072E-03 4.91570E-03 0.041535
5 7 50.0 90.0 90.0 7.30867E-02 7.18730E-03 2.95244E-03 1.01397E-02 4.91592E-03 0.040396
4 1 60.0 0.0 180.0 6.12464E-02 7.22386E-03 5.10651E-03 1.23304E-02 4.94093E-03 0.083377
4 4 60.0 45.0 135.0 6.26325E-02 7.14589E-03 5.04259E-03 1.21885E-02 4.88760E-03 0.080511
4 7 60.0 90.0 90.0 7.73429E-02 7.24895E-03 5.88860E-03 1.31376E-02 4.95809E-03 0.076136
3 1 70.0 0.0 180.0 8.49798E-02 6.77106E-03 1.41056E-02 2.08766E-02 4.63122E-03 0.165987
3 4 70.0 45.0 135.0 8.25879E-02 6.76842E-03 1.35722E-02 2.03406E-02 4.62942E-03 0.164336
3 7 70.0 90.0 90.0 9.23314E-02 6.88074E-03 1.47591E-02 2.16398E-02 4.70624E-03 0.159849
2 1 80.0 0.0 180.0 1.44382E-01 5.84796E-03 3.50622E-02 4.09102E-02 3.99985E-03 0.242843
2 4 80.0 45.0 135.0 1.33695E-01 5.82934E-03 3.39124E-02 3.97418E-02 3.98711E-03 0.253655
2 7 80.0 90.0 90.0 1.32827E-01 5.93640E-03 3.55155E-02 4.14519E-02 4.06034E-03 0.267382
1 1 87.5 0.0 180.0 2.33439E-01 4.73999E-03 6.18371E-02 6.65770E-02 3.24203E-03 0.264896
1 4 87.5 45.0 135.0 2.10183E-01 4.49546E-03 6.14553E-02 6.59507E-02 3.07478E-03 0.292389
1 7 87.5 90.0 90.0 1.91220E-01 5.06999E-03 6.28954E-02 6.79654E-02 3.46774E-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 1.486E-02 1.234E-01 1.500E-01 1.296E-01 1.938E-01 1.017E-02 4.901E+00 6.604E-03 4.517E-03
1 0.00 0.00 1.225E-02 2.297E-01 2.405E-02 2.703E-02 3.720E-02 8.503E-03 4.180E+00
3 1.70 5.00 8.870E-03 4.461E-01 2.016E-02 2.577E-02 4.405E-02 8.281E-03 4.597E+00
5 4.04 10.00 5.856E-03 4.564E-01 1.606E-02 2.225E-02 4.004E-02 8.111E-03 5.010E+00
7 7.49 15.00 3.433E-03 3.001E-01 1.113E-02 1.598E-02 2.754E-02 8.275E-03 5.256E+00
9 11.17 20.00 2.024E-03 1.625E-01 7.110E-03 9.767E-03 1.500E-02 8.949E-03 5.079E+00
11 13.48 25.00 1.380E-03 1.034E-01 4.813E-03 6.175E-03 8.595E-03 9.495E-03 4.825E+00
Waveband 8 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 9 (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 103.6 m at 485.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 480.0 nm to 490.0 nm:
Ed(diffuse) = 4.342E-01 Ed(direct) = 9.814E-01 Ed(total) = 1.416E+00
Absorption Coefficients of Individual Components at 485.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0136 0.0236 0.0000 0.0036 0.0407
3 1.688 5.000 0.0136 0.0289 0.0000 0.0044 0.0470
5 4.009 10.000 0.0136 0.0402 0.0000 0.0062 0.0600
7 7.436 15.000 0.0136 0.0565 0.0000 0.0089 0.0789
9 11.087 20.000 0.0136 0.0460 0.0000 0.0072 0.0668
11 13.387 25.000 0.0136 0.0206 0.0000 0.0031 0.0373
Scattering Coefficients of Individual Components at 485.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0033 0.1250 0.1291 0.0000 0.2573
3 1.688 5.000 0.0033 0.1500 0.1757 0.0000 0.3290
5 4.009 10.000 0.0033 0.1991 0.2859 0.0000 0.4883
7 7.436 15.000 0.0033 0.2634 0.4710 0.0000 0.7377
9 11.087 20.000 0.0033 0.2230 0.3490 0.0000 0.5753
11 13.387 25.000 0.0033 0.1104 0.1050 0.0000 0.2187
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00165 0.00175 0.00023 0.00000 0.00363
3 1.688 5.000 0.00165 0.00210 0.00031 0.00000 0.00406
5 4.009 10.000 0.00165 0.00279 0.00050 0.00000 0.00494
7 7.436 15.000 0.00165 0.00369 0.00083 0.00000 0.00617
9 11.087 20.000 0.00165 0.00313 0.00061 0.00000 0.00539
11 13.387 25.000 0.00165 0.00155 0.00018 0.00000 0.00338
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 0.0407 0.2573 0.2981 0.8633 0.00363 0.01409
3 1.688 5.000 0.0470 0.3290 0.3760 0.8751 0.00406 0.01234
5 4.009 10.000 0.0600 0.4883 0.5483 0.8906 0.00494 0.01012
7 7.436 15.000 0.0789 0.7377 0.8166 0.9033 0.00617 0.00836
9 11.087 20.000 0.0668 0.5753 0.6420 0.8960 0.00539 0.00937
11 13.387 25.000 0.0373 0.2187 0.2560 0.8544 0.00338 0.01545
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4765E-01
8 20.00 8.1994E-01
7 30.00 6.5026E-01
6 40.00 4.7760E-01
5 50.00 3.2962E-01
4 60.00 2.1770E-01
3 70.00 1.4054E-01
2 80.00 9.1099E-02
1 87.50 6.6009E-02
1 92.50 5.2482E-02
2 100.00 3.9462E-02
3 110.00 2.8667E-02
4 120.00 2.2008E-02
5 130.00 1.7944E-02
6 140.00 1.5458E-02
7 150.00 1.3946E-02
8 160.00 1.3054E-02
9 170.00 1.2583E-02
10 180.00 1.2418E-02
Asymptotic AOP values are
MUu(inf) = 0.3735
MUd(inf) = 0.7121
MU(inf) = 0.6291
R(inf) = 0.0435
Lu(inf)/Ed(inf) = 0.008871 (1/sr)
k(inf) = 0.0593 (1/m)
absorp(check) = 0.0373 = 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 1.8645E-01 2.0105E+00 2.1969E+00 7.0280E-02 1.4156E+00 0.3769 0.7041 0.6124 4.9647E-02
1 0.00 0.00 1.1550E-01 1.6177E+00 1.7332E+00 4.9711E-02 1.3950E+00 0.4304 0.8623 0.7762 3.5635E-02
3 1.69 5.00 1.0017E-01 1.2933E+00 1.3935E+00 4.0513E-02 1.0451E+00 0.4044 0.8080 0.7209 3.8766E-02
5 4.01 10.00 7.8315E-02 9.3639E-01 1.0147E+00 3.0010E-02 7.1445E-01 0.3832 0.7630 0.6745 4.2004E-02
7 7.44 15.00 5.1662E-02 5.7997E-01 6.3163E-01 1.8950E-02 4.2103E-01 0.3668 0.7259 0.6366 4.5009E-02
9 11.09 20.00 2.9743E-02 3.3305E-01 3.6280E-01 1.0796E-02 2.3581E-01 0.3630 0.7080 0.6202 4.5780E-02
11 13.39 25.00 1.8448E-02 2.1730E-01 2.3574E-01 6.8704E-03 1.5358E-01 0.3724 0.7068 0.6223 4.4734E-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 0.02985 0.04128 0.04051 0.03558 0.05152 0.05211 0.05377
5.000 5.010 5.005 0.03686 0.05237 0.05125 0.04835 0.06410 0.06474 0.06720
10.000 10.010 10.005 0.06237 0.07720 0.07606 0.07249 0.08787 0.08854 0.08932
15.000 15.010 15.005 0.10807 0.11458 0.11405 0.11362 0.12313 0.12358 0.11555
20.000 20.010 20.005 0.11122 0.10485 0.10537 0.10967 0.10739 0.10728 0.09622
25.000 25.010 25.005 0.06336 0.06135 0.06150 0.06130 0.05970 0.05962 0.05990
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 1.17169E-01 6.40079E-03 7.98054E-03 1.43813E-02 4.52166E-03 0.068111
9 1 10.0 0.0 180.0 7.22983E-02 6.50582E-03 2.49948E-03 9.00531E-03 4.59586E-03 0.034572
9 4 10.0 45.0 135.0 7.94364E-02 6.47916E-03 2.88644E-03 9.36560E-03 4.57702E-03 0.036337
9 7 10.0 90.0 90.0 1.07325E-01 6.47086E-03 5.83602E-03 1.23069E-02 4.57115E-03 0.054377
8 1 20.0 0.0 180.0 5.67894E-02 6.59347E-03 1.38174E-03 7.97521E-03 4.65777E-03 0.024331
8 4 20.0 45.0 135.0 6.32218E-02 6.52814E-03 1.62099E-03 8.14912E-03 4.61162E-03 0.025640
8 7 20.0 90.0 90.0 9.29647E-02 6.53071E-03 3.52103E-03 1.00517E-02 4.61344E-03 0.037875
7 1 30.0 0.0 180.0 4.92394E-02 6.72486E-03 1.18531E-03 7.91017E-03 4.75059E-03 0.024072
7 4 30.0 45.0 135.0 5.45873E-02 6.71542E-03 1.33087E-03 8.04629E-03 4.74392E-03 0.024380
7 7 30.0 90.0 90.0 7.96297E-02 6.69234E-03 2.26668E-03 8.95902E-03 4.72762E-03 0.028465
6 1 40.0 0.0 180.0 4.67375E-02 6.85156E-03 1.31792E-03 8.16947E-03 4.84009E-03 0.028198
6 4 40.0 45.0 135.0 5.11050E-02 6.83429E-03 1.42936E-03 8.26365E-03 4.82789E-03 0.027969
6 7 40.0 90.0 90.0 7.17506E-02 6.83545E-03 2.06888E-03 8.90433E-03 4.82871E-03 0.028834
5 1 50.0 0.0 180.0 4.90028E-02 7.01140E-03 2.08186E-03 9.09326E-03 4.95300E-03 0.042485
5 4 50.0 45.0 135.0 5.22190E-02 6.95756E-03 2.16892E-03 9.12647E-03 4.91497E-03 0.041535
5 7 50.0 90.0 90.0 6.94121E-02 6.98783E-03 2.80399E-03 9.79183E-03 4.93636E-03 0.040396
4 1 60.0 0.0 180.0 5.81670E-02 6.98016E-03 4.84977E-03 1.18299E-02 4.93094E-03 0.083377
4 4 60.0 45.0 135.0 5.94834E-02 6.91779E-03 4.78906E-03 1.17068E-02 4.88688E-03 0.080511
4 7 60.0 90.0 90.0 7.34542E-02 7.05146E-03 5.59253E-03 1.26440E-02 4.98130E-03 0.076136
3 1 70.0 0.0 180.0 8.07072E-02 6.54013E-03 1.33963E-02 1.99365E-02 4.62009E-03 0.165987
3 4 70.0 45.0 135.0 7.84356E-02 6.55086E-03 1.28898E-02 1.94406E-02 4.62767E-03 0.164336
3 7 70.0 90.0 90.0 8.76891E-02 6.69432E-03 1.40170E-02 2.07113E-02 4.72901E-03 0.159849
2 1 80.0 0.0 180.0 1.37123E-01 5.64593E-03 3.32993E-02 3.89453E-02 3.98841E-03 0.242843
2 4 80.0 45.0 135.0 1.26973E-01 5.63999E-03 3.22074E-02 3.78473E-02 3.98421E-03 0.253655
2 7 80.0 90.0 90.0 1.26149E-01 5.77517E-03 3.37299E-02 3.95050E-02 4.07971E-03 0.267382
1 1 87.5 0.0 180.0 2.21702E-01 4.57332E-03 5.87280E-02 6.33013E-02 3.23069E-03 0.264896
1 4 87.5 45.0 135.0 1.99616E-01 4.34702E-03 5.83654E-02 6.27124E-02 3.07083E-03 0.292389
1 7 87.5 90.0 90.0 1.81606E-01 4.93022E-03 5.97332E-02 6.46634E-02 3.48281E-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 1.438E-02 1.172E-01 1.425E-01 1.231E-01 1.842E-01 1.016E-02 4.887E+00 6.401E-03 4.522E-03
1 0.00 0.00 1.187E-02 2.182E-01 2.305E-02 2.609E-02 3.616E-02 8.509E-03 4.188E+00
3 1.69 5.00 8.783E-03 4.321E-01 1.958E-02 2.520E-02 4.334E-02 8.405E-03 4.612E+00
5 4.01 10.00 5.944E-03 4.499E-01 1.611E-02 2.244E-02 4.059E-02 8.319E-03 5.049E+00
7 7.44 15.00 3.543E-03 3.030E-01 1.162E-02 1.677E-02 2.904E-02 8.416E-03 5.348E+00
9 11.09 20.00 2.077E-03 1.680E-01 7.594E-03 1.050E-02 1.621E-02 8.808E-03 5.198E+00
11 13.39 25.00 1.403E-03 1.083E-01 5.063E-03 6.549E-03 9.190E-03 9.133E-03 4.898E+00
Waveband 9 of 30 completed in 4.7 sec.
* * * * * Output for wavelength band 10 (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 103.6 m at 495.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 490.0 nm to 500.0 nm:
Ed(diffuse) = 4.329E-01 Ed(direct) = 1.004E+00 Ed(total) = 1.437E+00
Absorption Coefficients of Individual Components at 495.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0173 0.0204 0.0000 0.0031 0.0408
3 1.678 5.000 0.0173 0.0252 0.0000 0.0038 0.0464
5 3.985 10.000 0.0173 0.0355 0.0000 0.0054 0.0582
7 7.395 15.000 0.0173 0.0507 0.0000 0.0077 0.0757
9 11.029 20.000 0.0173 0.0409 0.0000 0.0062 0.0645
11 13.316 25.000 0.0173 0.0177 0.0000 0.0027 0.0377
Scattering Coefficients of Individual Components at 495.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0030 0.1242 0.1283 0.0000 0.2555
3 1.678 5.000 0.0030 0.1493 0.1749 0.0000 0.3272
5 3.985 10.000 0.0030 0.1987 0.2853 0.0000 0.4870
7 7.395 15.000 0.0030 0.2634 0.4710 0.0000 0.7374
9 11.029 20.000 0.0030 0.2227 0.3485 0.0000 0.5743
11 13.316 25.000 0.0030 0.1096 0.1043 0.0000 0.2169
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00151 0.00174 0.00023 0.00000 0.00348
3 1.678 5.000 0.00151 0.00209 0.00031 0.00000 0.00391
5 3.985 10.000 0.00151 0.00279 0.00050 0.00000 0.00480
7 7.395 15.000 0.00151 0.00369 0.00083 0.00000 0.00603
9 11.029 20.000 0.00151 0.00312 0.00061 0.00000 0.00524
11 13.316 25.000 0.00151 0.00154 0.00018 0.00000 0.00323
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 0.0408 0.2555 0.2963 0.8623 0.00348 0.01360
3 1.678 5.000 0.0464 0.3272 0.3736 0.8759 0.00391 0.01195
5 3.985 10.000 0.0582 0.4870 0.5452 0.8932 0.00480 0.00985
7 7.395 15.000 0.0757 0.7374 0.8131 0.9069 0.00603 0.00818
9 11.029 20.000 0.0645 0.5743 0.6387 0.8991 0.00524 0.00913
11 13.316 25.000 0.0377 0.2169 0.2546 0.8520 0.00323 0.01489
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4711E-01
8 20.00 8.1822E-01
7 30.00 6.4728E-01
6 40.00 4.7383E-01
5 50.00 3.2567E-01
4 60.00 2.1407E-01
3 70.00 1.3746E-01
2 80.00 8.8593E-02
1 87.50 6.3901E-02
1 92.50 5.0633E-02
2 100.00 3.7897E-02
3 110.00 2.7374E-02
4 120.00 2.0909E-02
5 130.00 1.6977E-02
6 140.00 1.4579E-02
7 150.00 1.3124E-02
8 160.00 1.2268E-02
9 170.00 1.1816E-02
10 180.00 1.1659E-02
Asymptotic AOP values are
MUu(inf) = 0.3712
MUd(inf) = 0.7141
MU(inf) = 0.6339
R(inf) = 0.0415
Lu(inf)/Ed(inf) = 0.008386 (1/sr)
k(inf) = 0.0595 (1/m)
absorp(check) = 0.0377 = 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 1.8685E-01 2.0342E+00 2.2211E+00 7.0759E-02 1.4371E+00 0.3787 0.7064 0.6152 4.9239E-02
1 0.00 0.00 1.1540E-01 1.6403E+00 1.7557E+00 4.9751E-02 1.4160E+00 0.4311 0.8633 0.7782 3.5134E-02
3 1.68 5.00 1.0200E-01 1.3148E+00 1.4168E+00 4.1345E-02 1.0639E+00 0.4053 0.8091 0.7217 3.8862E-02
5 3.98 10.00 8.1756E-02 9.6160E-01 1.0434E+00 3.1353E-02 7.3389E-01 0.3835 0.7632 0.6733 4.2722E-02
7 7.39 15.00 5.5189E-02 6.0741E-01 6.6260E-01 2.0157E-02 4.4023E-01 0.3652 0.7248 0.6340 4.5787E-02
9 11.03 20.00 3.1765E-02 3.5576E-01 3.8752E-01 1.1392E-02 2.5130E-01 0.3587 0.7064 0.6191 4.5334E-02
11 13.32 25.00 1.9158E-02 2.3358E-01 2.5274E-01 7.0660E-03 1.6493E-01 0.3688 0.7061 0.6246 4.2841E-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 0.02683 0.04134 0.04039 0.03223 0.05137 0.05206 0.05063
5.000 5.010 5.005 0.03206 0.05131 0.04992 0.04373 0.06312 0.06390 0.06336
10.000 10.010 10.005 0.05698 0.07437 0.07301 0.06766 0.08534 0.08613 0.08597
15.000 15.010 15.005 0.10547 0.10977 0.10941 0.11245 0.11868 0.11898 0.11645
20.000 20.010 20.005 0.11476 0.10175 0.10281 0.11457 0.10427 0.10378 0.10059
25.000 25.010 25.005 0.06520 0.06242 0.06263 0.06241 0.06019 0.06009 0.06044
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 1.16812E-01 6.39776E-03 8.08759E-03 1.44854E-02 4.45195E-03 0.069236
9 1 10.0 0.0 180.0 7.20776E-02 6.49458E-03 2.50949E-03 9.00408E-03 4.51933E-03 0.034817
9 4 10.0 45.0 135.0 7.91939E-02 6.47068E-03 2.90033E-03 9.37101E-03 4.50269E-03 0.036623
9 7 10.0 90.0 90.0 1.06997E-01 6.46924E-03 5.89952E-03 1.23688E-02 4.50169E-03 0.055137
8 1 20.0 0.0 180.0 5.66160E-02 6.57881E-03 1.37842E-03 7.95723E-03 4.57794E-03 0.024347
8 4 20.0 45.0 135.0 6.30288E-02 6.51806E-03 1.61835E-03 8.13641E-03 4.53566E-03 0.025676
8 7 20.0 90.0 90.0 9.26809E-02 6.53193E-03 3.54120E-03 1.00731E-02 4.54531E-03 0.038209
7 1 30.0 0.0 180.0 4.90891E-02 6.70766E-03 1.18169E-03 7.88935E-03 4.66760E-03 0.024072
7 4 30.0 45.0 135.0 5.44213E-02 6.70440E-03 1.32691E-03 8.03131E-03 4.66533E-03 0.024382
7 7 30.0 90.0 90.0 7.93824E-02 6.69713E-03 2.26584E-03 8.96297E-03 4.66027E-03 0.028543
6 1 40.0 0.0 180.0 4.65948E-02 6.83229E-03 1.31389E-03 8.14619E-03 4.75433E-03 0.028198
6 4 40.0 45.0 135.0 5.09490E-02 6.82324E-03 1.42500E-03 8.24824E-03 4.74803E-03 0.027969
6 7 40.0 90.0 90.0 7.15315E-02 6.84564E-03 2.06296E-03 8.90860E-03 4.76362E-03 0.028840
5 1 50.0 0.0 180.0 4.88532E-02 6.99006E-03 2.07551E-03 9.06556E-03 4.86411E-03 0.042485
5 4 50.0 45.0 135.0 5.20596E-02 6.94605E-03 2.16230E-03 9.10834E-03 4.83348E-03 0.041535
5 7 50.0 90.0 90.0 6.92001E-02 7.00175E-03 2.79543E-03 9.79719E-03 4.87225E-03 0.040396
4 1 60.0 0.0 180.0 5.79894E-02 6.95696E-03 4.83496E-03 1.17919E-02 4.84108E-03 0.083377
4 4 60.0 45.0 135.0 5.93018E-02 6.90562E-03 4.77444E-03 1.16801E-02 4.80535E-03 0.080511
4 7 60.0 90.0 90.0 7.32300E-02 7.06806E-03 5.57546E-03 1.26435E-02 4.91839E-03 0.076136
3 1 70.0 0.0 180.0 8.04608E-02 6.51521E-03 1.33555E-02 1.98707E-02 4.53368E-03 0.165987
3 4 70.0 45.0 135.0 7.81961E-02 6.53704E-03 1.28504E-02 1.93875E-02 4.54887E-03 0.164336
3 7 70.0 90.0 90.0 8.74214E-02 6.71018E-03 1.39742E-02 2.06844E-02 4.66935E-03 0.159849
2 1 80.0 0.0 180.0 1.36704E-01 5.62130E-03 3.31977E-02 3.88190E-02 3.91164E-03 0.242843
2 4 80.0 45.0 135.0 1.26585E-01 5.62552E-03 3.21090E-02 3.77346E-02 3.91458E-03 0.253655
2 7 80.0 90.0 90.0 1.25764E-01 5.78787E-03 3.36269E-02 3.94148E-02 4.02755E-03 0.267382
1 1 87.5 0.0 180.0 2.21025E-01 4.55006E-03 5.85487E-02 6.30988E-02 3.16621E-03 0.264896
1 4 87.5 45.0 135.0 1.99006E-01 4.33309E-03 5.81872E-02 6.25203E-02 3.01523E-03 0.292389
1 7 87.5 90.0 90.0 1.81052E-01 4.93869E-03 5.95508E-02 6.44895E-02 3.43664E-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 1.449E-02 1.168E-01 1.421E-01 1.228E-01 1.836E-01 1.008E-02 4.885E+00 6.398E-03 4.452E-03
1 0.00 0.00 1.186E-02 2.175E-01 2.278E-02 2.597E-02 3.629E-02 8.379E-03 4.193E+00
3 1.68 5.00 8.932E-03 4.372E-01 1.959E-02 2.538E-02 4.400E-02 8.396E-03 4.629E+00
5 3.98 10.00 6.156E-03 4.609E-01 1.656E-02 2.322E-02 4.224E-02 8.388E-03 5.093E+00
7 7.39 15.00 3.700E-03 3.158E-01 1.234E-02 1.791E-02 3.116E-02 8.406E-03 5.447E+00
9 11.03 20.00 2.139E-03 1.782E-01 8.182E-03 1.139E-02 1.769E-02 8.514E-03 5.325E+00
11 13.32 25.00 1.422E-03 1.158E-01 5.334E-03 6.955E-03 9.839E-03 8.619E-03 4.971E+00
Waveband 10 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 11 (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 102.8 m at 505.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 500.0 nm to 510.0 nm:
Ed(diffuse) = 4.179E-01 Ed(direct) = 9.930E-01 Ed(total) = 1.411E+00
Absorption Coefficients of Individual Components at 505.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0256 0.0161 0.0000 0.0027 0.0444
3 1.685 5.000 0.0256 0.0203 0.0000 0.0033 0.0492
5 3.995 10.000 0.0256 0.0293 0.0000 0.0047 0.0596
7 7.403 15.000 0.0256 0.0428 0.0000 0.0067 0.0751
9 11.034 20.000 0.0256 0.0340 0.0000 0.0054 0.0651
11 13.324 25.000 0.0256 0.0139 0.0000 0.0023 0.0418
Scattering Coefficients of Individual Components at 505.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0028 0.1234 0.1275 0.0000 0.2538
3 1.685 5.000 0.0028 0.1487 0.1741 0.0000 0.3255
5 3.995 10.000 0.0028 0.1983 0.2846 0.0000 0.4856
7 7.403 15.000 0.0028 0.2634 0.4710 0.0000 0.7371
9 11.034 20.000 0.0028 0.2224 0.3481 0.0000 0.5733
11 13.324 25.000 0.0028 0.1089 0.1035 0.0000 0.2152
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00138 0.00173 0.00022 0.00000 0.00334
3 1.685 5.000 0.00138 0.00208 0.00031 0.00000 0.00377
5 3.995 10.000 0.00138 0.00278 0.00050 0.00000 0.00466
7 7.403 15.000 0.00138 0.00369 0.00083 0.00000 0.00591
9 11.034 20.000 0.00138 0.00312 0.00061 0.00000 0.00511
11 13.324 25.000 0.00138 0.00153 0.00018 0.00000 0.00309
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 0.0444 0.2538 0.2982 0.8510 0.00334 0.01316
3 1.685 5.000 0.0492 0.3255 0.3747 0.8686 0.00377 0.01159
5 3.995 10.000 0.0596 0.4856 0.5452 0.8908 0.00466 0.00960
7 7.403 15.000 0.0751 0.7371 0.8122 0.9075 0.00591 0.00801
9 11.034 20.000 0.0651 0.5733 0.6384 0.8981 0.00511 0.00892
11 13.324 25.000 0.0418 0.2152 0.2570 0.8373 0.00309 0.01437
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.4383E-01
8 20.00 8.0782E-01
7 30.00 6.2975E-01
6 40.00 4.5230E-01
5 50.00 3.0406E-01
4 60.00 1.9517E-01
3 70.00 1.2238E-01
2 80.00 7.7142E-02
1 87.50 5.4821E-02
1 92.50 4.3044E-02
2 100.00 3.1874E-02
3 110.00 2.2784E-02
4 120.00 1.7292E-02
5 130.00 1.3998E-02
6 140.00 1.2014E-02
7 150.00 1.0821E-02
8 160.00 1.0124E-02
9 170.00 9.7585E-03
10 180.00 9.6311E-03
Asymptotic AOP values are
MUu(inf) = 0.3684
MUd(inf) = 0.7237
MU(inf) = 0.6521
R(inf) = 0.0358
Lu(inf)/Ed(inf) = 0.007198 (1/sr)
k(inf) = 0.0641 (1/m)
absorp(check) = 0.0418 = 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 1.7855E-01 1.9912E+00 2.1698E+00 6.7561E-02 1.4110E+00 0.3784 0.7086 0.6191 4.7883E-02
1 0.00 0.00 1.0380E-01 1.6023E+00 1.7061E+00 4.4859E-02 1.3882E+00 0.4322 0.8664 0.7874 3.2313E-02
3 1.69 5.00 9.2867E-02 1.2616E+00 1.3545E+00 3.7719E-02 1.0250E+00 0.4062 0.8125 0.7289 3.6799E-02
5 3.99 10.00 7.5764E-02 9.1365E-01 9.8941E-01 2.9033E-02 6.9972E-01 0.3832 0.7659 0.6779 4.1493E-02
7 7.40 15.00 5.1664E-02 5.7845E-01 6.3011E-01 1.8691E-02 4.1988E-01 0.3618 0.7259 0.6367 4.4515E-02
9 11.03 20.00 2.8763E-02 3.3934E-01 3.6810E-01 1.0099E-02 2.4004E-01 0.3511 0.7074 0.6247 4.2072E-02
11 13.32 25.00 1.5991E-02 2.1909E-01 2.3508E-01 5.8122E-03 1.5543E-01 0.3635 0.7095 0.6365 3.7393E-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 0.02461 0.04507 0.04383 0.03026 0.05525 0.05609 0.04950
5.000 5.010 5.005 0.02839 0.05444 0.05265 0.04048 0.06618 0.06717 0.06168
10.000 10.010 10.005 0.05305 0.07533 0.07362 0.06477 0.08655 0.08749 0.08585
15.000 15.010 15.005 0.10779 0.10821 0.10818 0.11700 0.11752 0.11754 0.12406
20.000 20.010 20.005 0.12738 0.10257 0.10451 0.12925 0.10487 0.10380 0.11358
25.000 25.010 25.005 0.07352 0.06899 0.06930 0.06911 0.06557 0.06544 0.06584
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 1.12773E-01 5.79975E-03 7.92802E-03 1.37278E-02 4.11051E-03 0.070301
9 1 10.0 0.0 180.0 6.95856E-02 5.88455E-03 2.43885E-03 8.32339E-03 4.17061E-03 0.035048
9 4 10.0 45.0 135.0 7.64558E-02 5.86353E-03 2.82079E-03 8.68432E-03 4.15571E-03 0.036894
9 7 10.0 90.0 90.0 1.03298E-01 5.86398E-03 5.76982E-03 1.16338E-02 4.15603E-03 0.055856
8 1 20.0 0.0 180.0 5.46586E-02 5.95815E-03 1.33157E-03 7.28973E-03 4.22278E-03 0.024362
8 4 20.0 45.0 135.0 6.08497E-02 5.90414E-03 1.56451E-03 7.46864E-03 4.18449E-03 0.025711
8 7 20.0 90.0 90.0 8.94766E-02 5.91958E-03 3.44702E-03 9.36660E-03 4.19544E-03 0.038524
7 1 30.0 0.0 180.0 4.73919E-02 6.07161E-03 1.14083E-03 7.21244E-03 4.30319E-03 0.024072
7 4 30.0 45.0 135.0 5.25404E-02 6.07002E-03 1.28114E-03 7.35115E-03 4.30206E-03 0.024384
7 7 30.0 90.0 90.0 7.66341E-02 6.06748E-03 2.19306E-03 8.26054E-03 4.30026E-03 0.028617
6 1 40.0 0.0 180.0 4.49839E-02 6.17884E-03 1.26847E-03 7.44730E-03 4.37918E-03 0.028198
6 4 40.0 45.0 135.0 4.91875E-02 6.17246E-03 1.37573E-03 7.54819E-03 4.37466E-03 0.027969
6 7 40.0 90.0 90.0 6.90584E-02 6.19826E-03 1.99200E-03 8.19026E-03 4.39295E-03 0.028845
5 1 50.0 0.0 180.0 4.71641E-02 6.31496E-03 2.00375E-03 8.31871E-03 4.47566E-03 0.042485
5 4 50.0 45.0 135.0 5.02597E-02 6.27734E-03 2.08754E-03 8.36487E-03 4.44899E-03 0.041535
5 7 50.0 90.0 90.0 6.68076E-02 6.33452E-03 2.69879E-03 9.03330E-03 4.48952E-03 0.040396
4 1 60.0 0.0 180.0 5.59845E-02 6.27787E-03 4.66780E-03 1.09457E-02 4.44937E-03 0.083377
4 4 60.0 45.0 135.0 5.72516E-02 6.23398E-03 4.60937E-03 1.08433E-02 4.41826E-03 0.080511
4 7 60.0 90.0 90.0 7.06981E-02 6.38868E-03 5.38269E-03 1.17714E-02 4.52790E-03 0.076136
3 1 70.0 0.0 180.0 7.76790E-02 5.87046E-03 1.28937E-02 1.87642E-02 4.16062E-03 0.165987
3 4 70.0 45.0 135.0 7.54926E-02 5.89270E-03 1.24061E-02 1.82988E-02 4.17639E-03 0.164336
3 7 70.0 90.0 90.0 8.43989E-02 6.05745E-03 1.34911E-02 1.95485E-02 4.29315E-03 0.159849
2 1 80.0 0.0 180.0 1.31978E-01 5.05761E-03 3.20499E-02 3.71075E-02 3.58453E-03 0.242843
2 4 80.0 45.0 135.0 1.22209E-01 5.06376E-03 3.09989E-02 3.60627E-02 3.58888E-03 0.253655
2 7 80.0 90.0 90.0 1.21415E-01 5.21842E-03 3.24643E-02 3.76827E-02 3.69850E-03 0.267382
1 1 87.5 0.0 180.0 2.13384E-01 4.08744E-03 5.65245E-02 6.06119E-02 2.89693E-03 0.264896
1 4 87.5 45.0 135.0 1.92126E-01 3.89459E-03 5.61755E-02 6.00701E-02 2.76025E-03 0.292389
1 7 87.5 90.0 90.0 1.74792E-01 4.44683E-03 5.74919E-02 6.19387E-02 3.15165E-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 1.373E-02 1.128E-01 1.370E-01 1.184E-01 1.771E-01 9.729E-03 4.921E+00 5.800E-03 4.111E-03
1 0.00 0.00 1.076E-02 2.100E-01 2.029E-02 2.325E-02 3.287E-02 7.748E-03 4.171E+00
3 1.69 5.00 8.153E-03 4.201E-01 1.756E-02 2.295E-02 4.032E-02 7.954E-03 4.626E+00
5 3.99 10.00 5.647E-03 4.406E-01 1.515E-02 2.142E-02 3.933E-02 8.071E-03 5.141E+00
7 7.40 15.00 3.343E-03 3.022E-01 1.158E-02 1.693E-02 2.966E-02 7.962E-03 5.591E+00
9 11.03 20.00 1.834E-03 1.707E-01 7.611E-03 1.067E-02 1.671E-02 7.642E-03 5.505E+00
11 13.32 25.00 1.156E-03 1.099E-01 4.609E-03 6.061E-03 8.654E-03 7.434E-03 5.030E+00
Waveband 11 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 12 (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 100.8 m at 515.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 510.0 nm to 520.0 nm:
Ed(diffuse) = 3.962E-01 Ed(direct) = 9.620E-01 Ed(total) = 1.358E+00
Absorption Coefficients of Individual Components at 515.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0396 0.0125 0.0000 0.0023 0.0545
3 1.725 5.000 0.0396 0.0160 0.0000 0.0029 0.0585
5 4.070 10.000 0.0396 0.0238 0.0000 0.0041 0.0674
7 7.509 15.000 0.0396 0.0357 0.0000 0.0058 0.0812
9 11.171 20.000 0.0396 0.0280 0.0000 0.0047 0.0723
11 13.497 25.000 0.0396 0.0107 0.0000 0.0020 0.0523
Scattering Coefficients of Individual Components at 515.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0025 0.1227 0.1268 0.0000 0.2521
3 1.725 5.000 0.0025 0.1480 0.1733 0.0000 0.3239
5 4.070 10.000 0.0025 0.1978 0.2840 0.0000 0.4844
7 7.509 15.000 0.0025 0.2634 0.4710 0.0000 0.7369
9 11.171 20.000 0.0025 0.2222 0.3477 0.0000 0.5724
11 13.497 25.000 0.0025 0.1081 0.1028 0.0000 0.2135
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00127 0.00172 0.00022 0.00000 0.00322
3 1.725 5.000 0.00127 0.00207 0.00031 0.00000 0.00365
5 4.070 10.000 0.00127 0.00277 0.00050 0.00000 0.00454
7 7.509 15.000 0.00127 0.00369 0.00083 0.00000 0.00579
9 11.171 20.000 0.00127 0.00311 0.00061 0.00000 0.00500
11 13.497 25.000 0.00127 0.00152 0.00018 0.00000 0.00297
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 0.0545 0.2521 0.3065 0.8223 0.00322 0.01276
3 1.725 5.000 0.0585 0.3239 0.3824 0.8469 0.00365 0.01127
5 4.070 10.000 0.0674 0.4844 0.5518 0.8778 0.00454 0.00938
7 7.509 15.000 0.0812 0.7369 0.8181 0.9008 0.00579 0.00786
9 11.171 20.000 0.0723 0.5724 0.6446 0.8879 0.00500 0.00873
11 13.497 25.000 0.0523 0.2135 0.2658 0.8033 0.00297 0.01390
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.3629E-01
8 20.00 7.8438E-01
7 30.00 5.9134E-01
6 40.00 4.0685E-01
5 50.00 2.6040E-01
4 60.00 1.5876E-01
3 70.00 9.4708E-02
2 80.00 5.7114E-02
1 87.50 3.9472E-02
1 92.50 3.0516E-02
2 100.00 2.2219E-02
3 110.00 1.5658E-02
4 120.00 1.1818E-02
5 130.00 9.5747E-03
6 140.00 8.2519E-03
7 150.00 7.4708E-03
8 160.00 7.0208E-03
9 170.00 6.7873E-03
10 180.00 6.7059E-03
Asymptotic AOP values are
MUu(inf) = 0.3660
MUd(inf) = 0.7436
MU(inf) = 0.6864
R(inf) = 0.0268
Lu(inf)/Ed(inf) = 0.005446 (1/sr)
k(inf) = 0.0762 (1/m)
absorp(check) = 0.0523 = 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 1.6361E-01 1.9117E+00 2.0753E+00 6.1312E-02 1.3582E+00 0.3748 0.7105 0.6249 4.5141E-02
1 0.00 0.00 8.0815E-02 1.5265E+00 1.6073E+00 3.4918E-02 1.3318E+00 0.4321 0.8725 0.8069 2.6218E-02
3 1.72 5.00 7.1474E-02 1.1369E+00 1.2084E+00 2.8981E-02 9.3131E-01 0.4055 0.8191 0.7467 3.1119E-02
5 4.07 10.00 5.7892E-02 7.8285E-01 8.4075E-01 2.2087E-02 6.0508E-01 0.3815 0.7729 0.6934 3.6502E-02
7 7.51 15.00 3.8696E-02 4.7651E-01 5.1521E-01 1.3791E-02 3.4878E-01 0.3564 0.7319 0.6502 3.9542E-02
9 11.17 20.00 1.9821E-02 2.6828E-01 2.8810E-01 6.7706E-03 1.9157E-01 0.3416 0.7141 0.6414 3.5343E-02
11 13.50 25.00 9.4671E-03 1.6319E-01 1.7266E-01 3.3881E-03 1.1748E-01 0.3579 0.7199 0.6608 2.8839E-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 0.02528 0.05522 0.05371 0.03277 0.06626 0.06716 0.05351
5.000 5.010 5.005 0.02930 0.06550 0.06336 0.04188 0.07686 0.07798 0.06505
10.000 10.010 10.005 0.05393 0.08457 0.08246 0.06687 0.09572 0.09681 0.09152
15.000 15.010 15.005 0.11902 0.11504 0.11534 0.13062 0.12458 0.12434 0.14081
20.000 20.010 20.005 0.15204 0.11195 0.11471 0.15622 0.11377 0.11222 0.13804
25.000 25.010 25.005 0.09146 0.08403 0.08444 0.08435 0.07895 0.07878 0.07885
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 1.06920E-01 4.57294E-03 7.62097E-03 1.21939E-02 3.36683E-03 0.071277
9 1 10.0 0.0 180.0 6.59743E-02 4.64465E-03 2.32629E-03 6.97095E-03 3.41963E-03 0.035261
9 4 10.0 45.0 135.0 7.24880E-02 4.62570E-03 2.69243E-03 7.31814E-03 3.40568E-03 0.037143
9 7 10.0 90.0 90.0 9.79372E-02 4.62036E-03 5.53497E-03 1.01553E-02 3.40175E-03 0.056516
8 1 20.0 0.0 180.0 5.18219E-02 4.70150E-03 1.26318E-03 5.96468E-03 3.46149E-03 0.024375
8 4 20.0 45.0 135.0 5.76917E-02 4.65490E-03 1.48515E-03 6.14005E-03 3.42718E-03 0.025743
8 7 20.0 90.0 90.0 8.48330E-02 4.65770E-03 3.29269E-03 7.95039E-03 3.42924E-03 0.038814
7 1 30.0 0.0 180.0 4.49324E-02 4.78739E-03 1.08163E-03 5.86902E-03 3.52473E-03 0.024072
7 4 30.0 45.0 135.0 4.98142E-02 4.78055E-03 1.21474E-03 5.99529E-03 3.51969E-03 0.024385
7 7 30.0 90.0 90.0 7.26537E-02 4.76555E-03 2.08408E-03 6.84963E-03 3.50864E-03 0.028685
6 1 40.0 0.0 180.0 4.26493E-02 4.86299E-03 1.20264E-03 6.06563E-03 3.58039E-03 0.028198
6 4 40.0 45.0 135.0 4.66348E-02 4.85065E-03 1.30433E-03 6.15498E-03 3.57130E-03 0.027969
6 7 40.0 90.0 90.0 6.54745E-02 4.85378E-03 1.88893E-03 6.74271E-03 3.57360E-03 0.028850
5 1 50.0 0.0 180.0 4.47164E-02 4.95976E-03 1.89976E-03 6.85951E-03 3.65163E-03 0.042485
5 4 50.0 45.0 135.0 4.76514E-02 4.92164E-03 1.97920E-03 6.90084E-03 3.62357E-03 0.041535
5 7 50.0 90.0 90.0 6.33405E-02 4.94660E-03 2.55873E-03 7.50532E-03 3.64194E-03 0.040396
4 1 60.0 0.0 180.0 5.30791E-02 4.91978E-03 4.42555E-03 9.34533E-03 3.62220E-03 0.083377
4 4 60.0 45.0 135.0 5.42803E-02 4.87599E-03 4.37015E-03 9.24614E-03 3.58995E-03 0.080511
4 7 60.0 90.0 90.0 6.70291E-02 4.97529E-03 5.10335E-03 1.00786E-02 3.66307E-03 0.076136
3 1 70.0 0.0 180.0 7.36476E-02 4.58906E-03 1.22246E-02 1.68136E-02 3.37870E-03 0.165987
3 4 70.0 45.0 135.0 7.15747E-02 4.59711E-03 1.17623E-02 1.63594E-02 3.38463E-03 0.164336
3 7 70.0 90.0 90.0 8.00188E-02 4.70445E-03 1.27909E-02 1.74954E-02 3.46366E-03 0.159849
2 1 80.0 0.0 180.0 1.25128E-01 3.94490E-03 3.03866E-02 3.43315E-02 2.90444E-03 0.242843
2 4 80.0 45.0 135.0 1.15866E-01 3.94136E-03 2.93901E-02 3.33315E-02 2.90183E-03 0.253655
2 7 80.0 90.0 90.0 1.15114E-01 4.04386E-03 3.07795E-02 3.48233E-02 2.97730E-03 0.267382
1 1 87.5 0.0 180.0 2.02310E-01 3.18184E-03 5.35910E-02 5.67728E-02 2.34264E-03 0.264896
1 4 87.5 45.0 135.0 1.82155E-01 3.02548E-03 5.32601E-02 5.62856E-02 2.22752E-03 0.292389
1 7 87.5 90.0 90.0 1.65721E-01 3.44005E-03 5.45082E-02 5.79483E-02 2.53274E-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 1.219E-02 1.069E-01 1.295E-01 1.118E-01 1.675E-01 8.978E-03 5.028E+00 4.573E-03 3.367E-03
1 0.00 0.00 8.481E-03 1.990E-01 1.577E-02 1.811E-02 2.607E-02 6.368E-03 4.117E+00
3 1.72 5.00 6.308E-03 3.829E-01 1.349E-02 1.784E-02 3.207E-02 6.773E-03 4.594E+00
5 4.07 10.00 4.274E-03 3.858E-01 1.156E-02 1.652E-02 3.083E-02 7.064E-03 5.167E+00
7 7.51 15.00 2.405E-03 2.554E-01 8.815E-03 1.300E-02 2.304E-02 6.894E-03 5.735E+00
9 11.17 20.00 1.190E-03 1.391E-01 5.477E-03 7.744E-03 1.224E-02 6.212E-03 5.689E+00
11 13.50 25.00 6.741E-04 8.551E-02 2.873E-03 3.805E-03 5.478E-03 5.738E-03 5.026E+00
Waveband 12 of 30 completed in 4.9 sec.
* * * * * Output for wavelength band 13 (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 100.8 m at 525.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 520.0 nm to 530.0 nm:
Ed(diffuse) = 3.989E-01 Ed(direct) = 9.886E-01 Ed(total) = 1.387E+00
Absorption Coefficients of Individual Components at 525.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0417 0.0101 0.0000 0.0020 0.0539
3 1.712 5.000 0.0417 0.0132 0.0000 0.0025 0.0574
5 4.042 10.000 0.0417 0.0200 0.0000 0.0036 0.0652
7 7.463 15.000 0.0417 0.0308 0.0000 0.0051 0.0776
9 11.106 20.000 0.0417 0.0238 0.0000 0.0041 0.0695
11 13.417 25.000 0.0417 0.0085 0.0000 0.0018 0.0520
Scattering Coefficients of Individual Components at 525.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0023 0.1220 0.1261 0.0000 0.2504
3 1.712 5.000 0.0023 0.1474 0.1726 0.0000 0.3223
5 4.042 10.000 0.0023 0.1974 0.2834 0.0000 0.4832
7 7.463 15.000 0.0023 0.2634 0.4710 0.0000 0.7367
9 11.106 20.000 0.0023 0.2219 0.3473 0.0000 0.5715
11 13.417 25.000 0.0023 0.1074 0.1022 0.0000 0.2119
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00117 0.00171 0.00022 0.00000 0.00310
3 1.712 5.000 0.00117 0.00207 0.00030 0.00000 0.00354
5 4.042 10.000 0.00117 0.00277 0.00050 0.00000 0.00444
7 7.463 15.000 0.00117 0.00369 0.00083 0.00000 0.00569
9 11.106 20.000 0.00117 0.00311 0.00061 0.00000 0.00489
11 13.417 25.000 0.00117 0.00151 0.00018 0.00000 0.00286
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 0.0539 0.2504 0.3043 0.8229 0.00310 0.01239
3 1.712 5.000 0.0574 0.3223 0.3796 0.8489 0.00354 0.01098
5 4.042 10.000 0.0652 0.4832 0.5484 0.8810 0.00444 0.00918
7 7.463 15.000 0.0776 0.7367 0.8143 0.9047 0.00569 0.00773
9 11.106 20.000 0.0695 0.5715 0.6410 0.8915 0.00489 0.00856
11 13.417 25.000 0.0520 0.2119 0.2639 0.8030 0.00286 0.01348
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.3624E-01
8 20.00 7.8421E-01
7 30.00 5.9102E-01
6 40.00 4.0641E-01
5 50.00 2.5991E-01
4 60.00 1.5826E-01
3 70.00 9.4241E-02
2 80.00 5.6693E-02
1 87.50 3.9088E-02
1 92.50 3.0156E-02
2 100.00 2.1889E-02
3 110.00 1.5360E-02
4 120.00 1.1543E-02
5 130.00 9.3164E-03
6 140.00 8.0048E-03
7 150.00 7.2308E-03
8 160.00 6.7851E-03
9 170.00 6.5539E-03
10 180.00 6.4733E-03
Asymptotic AOP values are
MUu(inf) = 0.3641
MUd(inf) = 0.7441
MU(inf) = 0.6879
R(inf) = 0.0261
Lu(inf)/Ed(inf) = 0.005262 (1/sr)
k(inf) = 0.0756 (1/m)
absorp(check) = 0.0520 = 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 1.6583E-01 1.9478E+00 2.1137E+00 6.2459E-02 1.3875E+00 0.3766 0.7123 0.6269 4.5015E-02
1 0.00 0.00 8.2573E-02 1.5590E+00 1.6416E+00 3.5744E-02 1.3608E+00 0.4329 0.8728 0.8072 2.6268E-02
3 1.71 5.00 7.4419E-02 1.1682E+00 1.2426E+00 3.0259E-02 9.5747E-01 0.4066 0.8196 0.7462 3.1603E-02
5 4.04 10.00 6.1771E-02 8.1461E-01 8.7639E-01 2.3604E-02 6.2937E-01 0.3821 0.7726 0.6912 3.7505E-02
7 7.46 15.00 4.2277E-02 5.0655E-01 5.4883E-01 1.5031E-02 3.6997E-01 0.3555 0.7304 0.6467 4.0629E-02
9 11.11 20.00 2.1807E-02 2.9142E-01 3.1323E-01 7.3863E-03 2.0749E-01 0.3387 0.7120 0.6389 3.5597E-02
11 13.42 25.00 1.0241E-02 1.7902E-01 1.8926E-01 3.6371E-03 1.2863E-01 0.3552 0.7185 0.6604 2.8276E-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 0.02238 0.05460 0.05298 0.02937 0.06541 0.06638 0.05016
5.000 5.010 5.005 0.02465 0.06381 0.06147 0.03734 0.07525 0.07649 0.06112
10.000 10.010 10.005 0.04868 0.08130 0.07900 0.06209 0.09273 0.09392 0.08792
15.000 15.010 15.005 0.11563 0.10996 0.11040 0.12834 0.11984 0.11948 0.14017
20.000 20.010 20.005 0.15331 0.10838 0.11150 0.15870 0.11020 0.10841 0.14044
25.000 25.010 25.005 0.09228 0.08405 0.08449 0.08456 0.07856 0.07839 0.07855
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 1.07640E-01 4.67589E-03 7.77472E-03 1.24506E-02 3.37003E-03 0.072229
9 1 10.0 0.0 180.0 6.64186E-02 4.74319E-03 2.35571E-03 7.09889E-03 3.41853E-03 0.035468
9 4 10.0 45.0 135.0 7.29761E-02 4.72585E-03 2.72825E-03 7.45411E-03 3.40604E-03 0.037386
9 7 10.0 90.0 90.0 9.85967E-02 4.72545E-03 5.63562E-03 1.03611E-02 3.40576E-03 0.057158
8 1 20.0 0.0 180.0 5.21709E-02 4.79882E-03 1.27238E-03 6.07120E-03 3.45863E-03 0.024389
8 4 20.0 45.0 135.0 5.80802E-02 4.75457E-03 1.49695E-03 6.25152E-03 3.42674E-03 0.025774
8 7 20.0 90.0 90.0 8.54042E-02 4.76575E-03 3.33897E-03 8.10471E-03 3.43480E-03 0.039096
7 1 30.0 0.0 180.0 4.52350E-02 4.88486E-03 1.08891E-03 5.97377E-03 3.52064E-03 0.024072
7 4 30.0 45.0 135.0 5.01502E-02 4.88247E-03 1.22300E-03 6.10548E-03 3.51892E-03 0.024387
7 7 30.0 90.0 90.0 7.31397E-02 4.87871E-03 2.10285E-03 6.98156E-03 3.51621E-03 0.028751
6 1 40.0 0.0 180.0 4.29365E-02 4.96086E-03 1.21073E-03 6.17160E-03 3.57542E-03 0.028198
6 4 40.0 45.0 135.0 4.69488E-02 4.95433E-03 1.31312E-03 6.26744E-03 3.57071E-03 0.027969
6 7 40.0 90.0 90.0 6.59154E-02 4.97295E-03 1.90196E-03 6.87491E-03 3.58413E-03 0.028855
5 1 50.0 0.0 180.0 4.50175E-02 5.05864E-03 1.91255E-03 6.97119E-03 3.64589E-03 0.042485
5 4 50.0 45.0 135.0 4.79722E-02 5.02687E-03 1.99253E-03 7.01940E-03 3.62299E-03 0.041535
5 7 50.0 90.0 90.0 6.37670E-02 5.07063E-03 2.57596E-03 7.64659E-03 3.65453E-03 0.040396
4 1 60.0 0.0 180.0 5.34365E-02 5.01674E-03 4.45535E-03 9.47210E-03 3.61569E-03 0.083377
4 4 60.0 45.0 135.0 5.46459E-02 4.97998E-03 4.39958E-03 9.37956E-03 3.58920E-03 0.080511
4 7 60.0 90.0 90.0 6.74805E-02 5.10194E-03 5.13771E-03 1.02397E-02 3.67710E-03 0.076136
3 1 70.0 0.0 180.0 7.41436E-02 4.67761E-03 1.23069E-02 1.69845E-02 3.37127E-03 0.165987
3 4 70.0 45.0 135.0 7.20567E-02 4.69384E-03 1.18415E-02 1.65353E-02 3.38297E-03 0.164336
3 7 70.0 90.0 90.0 8.05577E-02 4.82432E-03 1.28771E-02 1.77014E-02 3.47701E-03 0.159849
2 1 80.0 0.0 180.0 1.25971E-01 4.01911E-03 3.05912E-02 3.46103E-02 2.89668E-03 0.242843
2 4 80.0 45.0 135.0 1.16647E-01 4.02273E-03 2.95881E-02 3.36108E-02 2.89928E-03 0.253655
2 7 80.0 90.0 90.0 1.15889E-01 4.14623E-03 3.09867E-02 3.51330E-02 2.98830E-03 0.267382
1 1 87.5 0.0 180.0 2.03672E-01 3.23965E-03 5.39519E-02 5.71915E-02 2.33490E-03 0.264896
1 4 87.5 45.0 135.0 1.83382E-01 3.08619E-03 5.36188E-02 5.67050E-02 2.22430E-03 0.292389
1 7 87.5 90.0 90.0 1.66837E-01 3.52546E-03 5.48753E-02 5.84007E-02 2.54089E-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 1.245E-02 1.076E-01 1.304E-01 1.126E-01 1.687E-01 8.973E-03 5.017E+00 4.676E-03 3.370E-03
1 0.00 0.00 8.672E-03 2.004E-01 1.596E-02 1.843E-02 2.669E-02 6.373E-03 4.122E+00
3 1.71 5.00 6.568E-03 3.912E-01 1.382E-02 1.837E-02 3.317E-02 6.860E-03 4.607E+00
5 4.04 10.00 4.536E-03 3.999E-01 1.216E-02 1.745E-02 3.267E-02 7.208E-03 5.203E+00
7 7.46 15.00 2.583E-03 2.698E-01 9.565E-03 1.416E-02 2.518E-02 6.983E-03 5.819E+00
9 11.11 20.00 1.273E-03 1.497E-01 6.049E-03 8.594E-03 1.365E-02 6.135E-03 5.802E+00
11 13.42 25.00 7.145E-04 9.304E-02 3.137E-03 4.180E-03 6.056E-03 5.555E-03 5.091E+00
Waveband 13 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 14 (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 100.8 m at 535.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 530.0 nm to 540.0 nm:
Ed(diffuse) = 3.977E-01 Ed(direct) = 1.004E+00 Ed(total) = 1.402E+00
Absorption Coefficients of Individual Components at 535.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0452 0.0084 0.0000 0.0018 0.0554
3 1.711 5.000 0.0452 0.0111 0.0000 0.0022 0.0585
5 4.036 10.000 0.0452 0.0171 0.0000 0.0031 0.0654
7 7.451 15.000 0.0452 0.0269 0.0000 0.0044 0.0765
9 11.089 20.000 0.0452 0.0205 0.0000 0.0036 0.0692
11 13.396 25.000 0.0452 0.0070 0.0000 0.0015 0.0538
Scattering Coefficients of Individual Components at 535.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0022 0.1213 0.1253 0.0000 0.2488
3 1.711 5.000 0.0022 0.1467 0.1718 0.0000 0.3207
5 4.036 10.000 0.0022 0.1970 0.2828 0.0000 0.4820
7 7.451 15.000 0.0022 0.2634 0.4710 0.0000 0.7365
9 11.089 20.000 0.0022 0.2216 0.3469 0.0000 0.5706
11 13.396 25.000 0.0022 0.1067 0.1015 0.0000 0.2103
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00108 0.00170 0.00022 0.00000 0.00300
3 1.711 5.000 0.00108 0.00206 0.00030 0.00000 0.00344
5 4.036 10.000 0.00108 0.00276 0.00050 0.00000 0.00434
7 7.451 15.000 0.00108 0.00369 0.00083 0.00000 0.00560
9 11.089 20.000 0.00108 0.00311 0.00061 0.00000 0.00480
11 13.396 25.000 0.00108 0.00150 0.00018 0.00000 0.00275
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 0.0554 0.2488 0.3042 0.8179 0.00300 0.01206
3 1.711 5.000 0.0585 0.3207 0.3792 0.8458 0.00344 0.01072
5 4.036 10.000 0.0654 0.4820 0.5474 0.8806 0.00434 0.00900
7 7.451 15.000 0.0765 0.7365 0.8130 0.9059 0.00560 0.00760
9 11.089 20.000 0.0692 0.5706 0.6399 0.8918 0.00480 0.00840
11 13.396 25.000 0.0538 0.2103 0.2641 0.7964 0.00275 0.01309
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.3481E-01
8 20.00 7.7980E-01
7 30.00 5.8394E-01
6 40.00 3.9824E-01
5 50.00 2.5226E-01
4 60.00 1.5206E-01
3 70.00 8.9633E-02
2 80.00 5.3412E-02
1 87.50 3.6587E-02
1 92.50 2.8113E-02
2 100.00 2.0305E-02
3 110.00 1.4172E-02
4 120.00 1.0609E-02
5 130.00 8.5410E-03
6 140.00 7.3279E-03
7 150.00 6.6144E-03
8 160.00 6.2045E-03
9 170.00 5.9923E-03
10 180.00 5.9185E-03
Asymptotic AOP values are
MUu(inf) = 0.3623
MUd(inf) = 0.7478
MU(inf) = 0.6946
R(inf) = 0.0244
Lu(inf)/Ed(inf) = 0.004886 (1/sr)
k(inf) = 0.0774 (1/m)
absorp(check) = 0.0538 = 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 1.6508E-01 1.9636E+00 2.1287E+00 6.2286E-02 1.4020E+00 0.3773 0.7140 0.6293 4.4427E-02
1 0.00 0.00 7.9973E-02 1.5721E+00 1.6521E+00 3.4645E-02 1.3743E+00 0.4332 0.8742 0.8109 2.5209E-02
3 1.71 5.00 7.2806E-02 1.1701E+00 1.2429E+00 2.9641E-02 9.6085E-01 0.4071 0.8212 0.7492 3.0848E-02
5 4.04 10.00 6.1337E-02 8.1445E-01 8.7579E-01 2.3444E-02 6.3022E-01 0.3822 0.7738 0.6928 3.7200E-02
7 7.45 15.00 4.2505E-02 5.0955E-01 5.5205E-01 1.5049E-02 3.7226E-01 0.3540 0.7306 0.6471 4.0425E-02
9 11.09 20.00 2.1696E-02 2.9491E-01 3.1660E-01 7.2747E-03 2.0997E-01 0.3353 0.7120 0.6402 3.4646E-02
11 13.40 25.00 9.8061E-03 1.8025E-01 1.9006E-01 3.4566E-03 1.2971E-01 0.3525 0.7196 0.6643 2.6649E-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 0.02054 0.05612 0.05440 0.02761 0.06694 0.06795 0.04865
5.000 5.010 5.005 0.02176 0.06488 0.06235 0.03457 0.07627 0.07760 0.05904
10.000 10.010 10.005 0.04530 0.08103 0.07853 0.05921 0.09261 0.09390 0.08642
15.000 15.010 15.005 0.11547 0.10796 0.10854 0.12930 0.11812 0.11765 0.14268
20.000 20.010 20.005 0.15855 0.10790 0.11137 0.16510 0.10965 0.10766 0.14641
25.000 25.010 25.005 0.09604 0.08676 0.08724 0.08742 0.08077 0.08059 0.08063
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 1.07317E-01 4.53690E-03 7.84642E-03 1.23833E-02 3.23605E-03 0.073114
9 1 10.0 0.0 180.0 6.62190E-02 4.59896E-03 2.36139E-03 6.96035E-03 3.28032E-03 0.035660
9 4 10.0 45.0 135.0 7.27568E-02 4.58311E-03 2.73648E-03 7.31958E-03 3.26901E-03 0.037611
9 7 10.0 90.0 90.0 9.83004E-02 4.58514E-03 5.67750E-03 1.02626E-02 3.27045E-03 0.057757
8 1 20.0 0.0 180.0 5.20141E-02 4.65104E-03 1.26920E-03 5.92024E-03 3.31746E-03 0.024401
8 4 20.0 45.0 135.0 5.79057E-02 4.60967E-03 1.49412E-03 6.10379E-03 3.28795E-03 0.025803
8 7 20.0 90.0 90.0 8.51476E-02 4.62449E-03 3.35130E-03 7.97579E-03 3.29852E-03 0.039359
7 1 30.0 0.0 180.0 4.50990E-02 4.73265E-03 1.08564E-03 5.81828E-03 3.37567E-03 0.024072
7 4 30.0 45.0 135.0 5.00000E-02 4.73244E-03 1.21941E-03 5.95185E-03 3.37552E-03 0.024388
7 7 30.0 90.0 90.0 7.29169E-02 4.73435E-03 2.10093E-03 6.83527E-03 3.37688E-03 0.028813
6 1 40.0 0.0 180.0 4.28075E-02 4.80390E-03 1.20709E-03 6.01100E-03 3.42649E-03 0.028198
6 4 40.0 45.0 135.0 4.68077E-02 4.80037E-03 1.30917E-03 6.10954E-03 3.42397E-03 0.027969
6 7 40.0 90.0 90.0 6.57173E-02 4.82587E-03 1.89653E-03 6.72240E-03 3.44216E-03 0.028859
5 1 50.0 0.0 180.0 4.48822E-02 4.89614E-03 1.90680E-03 6.80294E-03 3.49228E-03 0.042485
5 4 50.0 45.0 135.0 4.78281E-02 4.86869E-03 1.98654E-03 6.85523E-03 3.47271E-03 0.041535
5 7 50.0 90.0 90.0 6.35754E-02 4.92003E-03 2.56822E-03 7.48825E-03 3.50933E-03 0.040396
4 1 60.0 0.0 180.0 5.32759E-02 4.85297E-03 4.44196E-03 9.29494E-03 3.46149E-03 0.083377
4 4 60.0 45.0 135.0 5.44816E-02 4.82110E-03 4.38636E-03 9.20746E-03 3.43876E-03 0.080511
4 7 60.0 90.0 90.0 6.72777E-02 4.94942E-03 5.12227E-03 1.00717E-02 3.53029E-03 0.076136
3 1 70.0 0.0 180.0 7.39207E-02 4.52176E-03 1.22699E-02 1.67916E-02 3.22525E-03 0.165987
3 4 70.0 45.0 135.0 7.18401E-02 4.54126E-03 1.18059E-02 1.63472E-02 3.23916E-03 0.164336
3 7 70.0 90.0 90.0 8.03156E-02 4.67816E-03 1.28384E-02 1.75165E-02 3.33681E-03 0.159849
2 1 80.0 0.0 180.0 1.25592E-01 3.88254E-03 3.04993E-02 3.43818E-02 2.76931E-03 0.242843
2 4 80.0 45.0 135.0 1.16296E-01 3.88951E-03 2.94991E-02 3.33886E-02 2.77428E-03 0.253655
2 7 80.0 90.0 90.0 1.15541E-01 4.01885E-03 3.08936E-02 3.49125E-02 2.86653E-03 0.267382
1 1 87.5 0.0 180.0 2.03060E-01 3.12725E-03 5.37897E-02 5.69170E-02 2.23058E-03 0.264896
1 4 87.5 45.0 135.0 1.82830E-01 2.98197E-03 5.34576E-02 5.64396E-02 2.12696E-03 0.292389
1 7 87.5 90.0 90.0 1.66335E-01 3.41530E-03 5.47104E-02 5.81257E-02 2.43604E-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 1.238E-02 1.073E-01 1.300E-01 1.122E-01 1.681E-01 8.833E-03 5.030E+00 4.537E-03 3.236E-03
1 0.00 0.00 8.414E-03 1.998E-01 1.535E-02 1.781E-02 2.600E-02 6.122E-03 4.117E+00
3 1.71 5.00 6.430E-03 3.911E-01 1.337E-02 1.788E-02 3.255E-02 6.692E-03 4.610E+00
5 4.04 10.00 4.482E-03 4.003E-01 1.195E-02 1.724E-02 3.247E-02 7.111E-03 5.231E+00
7 7.45 15.00 2.551E-03 2.716E-01 9.595E-03 1.428E-02 2.549E-02 6.852E-03 5.900E+00
9 11.09 20.00 1.231E-03 1.515E-01 6.074E-03 8.672E-03 1.384E-02 5.862E-03 5.910E+00
11 13.40 25.00 6.735E-04 9.397E-02 3.046E-03 4.081E-03 5.946E-03 5.193E-03 5.132E+00
Waveband 14 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 15 (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 99.8 m at 545.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 540.0 nm to 550.0 nm:
Ed(diffuse) = 3.873E-01 Ed(direct) = 9.954E-01 Ed(total) = 1.383E+00
Absorption Coefficients of Individual Components at 545.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0511 0.0072 0.0000 0.0015 0.0598
3 1.725 5.000 0.0511 0.0095 0.0000 0.0019 0.0625
5 4.061 10.000 0.0511 0.0149 0.0000 0.0027 0.0687
7 7.487 15.000 0.0511 0.0237 0.0000 0.0038 0.0787
9 11.135 20.000 0.0511 0.0179 0.0000 0.0031 0.0721
11 13.454 25.000 0.0511 0.0060 0.0000 0.0013 0.0584
Scattering Coefficients of Individual Components at 545.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0020 0.1206 0.1247 0.0000 0.2473
3 1.725 5.000 0.0020 0.1461 0.1711 0.0000 0.3192
5 4.061 10.000 0.0020 0.1966 0.2822 0.0000 0.4808
7 7.487 15.000 0.0020 0.2634 0.4710 0.0000 0.7364
9 11.135 20.000 0.0020 0.2214 0.3465 0.0000 0.5698
11 13.454 25.000 0.0020 0.1060 0.1008 0.0000 0.2088
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00100 0.00169 0.00022 0.00000 0.00291
3 1.725 5.000 0.00100 0.00205 0.00030 0.00000 0.00335
5 4.061 10.000 0.00100 0.00276 0.00050 0.00000 0.00425
7 7.487 15.000 0.00100 0.00369 0.00083 0.00000 0.00552
9 11.135 20.000 0.00100 0.00310 0.00061 0.00000 0.00471
11 13.454 25.000 0.00100 0.00149 0.00018 0.00000 0.00266
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 0.0598 0.2473 0.3071 0.8052 0.00291 0.01175
3 1.725 5.000 0.0625 0.3192 0.3817 0.8362 0.00335 0.01048
5 4.061 10.000 0.0687 0.4808 0.5495 0.8750 0.00425 0.00884
7 7.487 15.000 0.0787 0.7364 0.8150 0.9035 0.00552 0.00749
9 11.135 20.000 0.0721 0.5698 0.6420 0.8876 0.00471 0.00826
11 13.454 25.000 0.0584 0.2088 0.2672 0.7815 0.00266 0.01273
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.3152E-01
8 20.00 7.6980E-01
7 30.00 5.6810E-01
6 40.00 3.8029E-01
5 50.00 2.3587E-01
4 60.00 1.3911E-01
3 70.00 8.0309E-02
2 80.00 4.6982E-02
1 87.50 3.1813E-02
1 92.50 2.4290E-02
2 100.00 1.7420E-02
3 110.00 1.2081E-02
4 120.00 9.0154E-03
5 130.00 7.2535E-03
6 140.00 6.2279E-03
7 150.00 5.6285E-03
8 160.00 5.2860E-03
9 170.00 5.1093E-03
10 180.00 5.0478E-03
Asymptotic AOP values are
MUu(inf) = 0.3609
MUd(inf) = 0.7557
MU(inf) = 0.7076
R(inf) = 0.0215
Lu(inf)/Ed(inf) = 0.004313 (1/sr)
k(inf) = 0.0825 (1/m)
absorp(check) = 0.0584 = 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 1.5893E-01 1.9325E+00 2.0915E+00 5.9848E-02 1.3828E+00 0.3766 0.7155 0.6325 4.3281E-02
1 0.00 0.00 7.1482E-02 1.5443E+00 1.6158E+00 3.0928E-02 1.3538E+00 0.4327 0.8767 0.8188 2.2845E-02
3 1.72 5.00 6.4899E-02 1.1219E+00 1.1868E+00 2.6392E-02 9.2463E-01 0.4067 0.8241 0.7568 2.8543E-02
5 4.06 10.00 5.4756E-02 7.6462E-01 8.1938E-01 2.0892E-02 5.9408E-01 0.3816 0.7770 0.6995 3.5168E-02
7 7.49 15.00 3.7846E-02 4.7142E-01 5.0927E-01 1.3315E-02 3.4561E-01 0.3518 0.7331 0.6525 3.8527E-02
9 11.13 20.00 1.8701E-02 2.6873E-01 2.8743E-01 6.1996E-03 1.9207E-01 0.3315 0.7147 0.6467 3.2278E-02
11 13.45 25.00 7.9127E-03 1.6024E-01 1.6815E-01 2.7711E-03 1.1599E-01 0.3502 0.7239 0.6733 2.3891E-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 0.02030 0.06059 0.05880 0.02822 0.07171 0.07273 0.04975
5.000 5.010 5.005 0.02142 0.06962 0.06698 0.03429 0.08083 0.08219 0.05945
10.000 10.010 10.005 0.04449 0.08477 0.08208 0.05886 0.09633 0.09770 0.08758
15.000 15.010 15.005 0.11944 0.11022 0.11090 0.13429 0.12055 0.12000 0.14897
20.000 20.010 20.005 0.16871 0.11159 0.11531 0.17631 0.11314 0.11103 0.15689
25.000 25.010 25.005 0.10372 0.09313 0.09363 0.09377 0.08651 0.08633 0.08583
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 1.04522E-01 4.06380E-03 7.73012E-03 1.17939E-02 2.93889E-03 0.073957
9 1 10.0 0.0 180.0 6.44944E-02 4.11971E-03 2.31171E-03 6.43142E-03 2.97933E-03 0.035844
9 4 10.0 45.0 135.0 7.08620E-02 4.10511E-03 2.68042E-03 6.78552E-03 2.96877E-03 0.037826
9 7 10.0 90.0 90.0 9.57404E-02 4.10602E-03 5.58412E-03 9.69014E-03 2.96943E-03 0.058326
8 1 20.0 0.0 180.0 5.06595E-02 4.16526E-03 1.23675E-03 5.40201E-03 3.01227E-03 0.024413
8 4 20.0 45.0 135.0 5.63977E-02 4.12752E-03 1.45676E-03 5.58428E-03 2.98498E-03 0.025830
8 7 20.0 90.0 90.0 8.29301E-02 4.13931E-03 3.28474E-03 7.42405E-03 2.99350E-03 0.039609
7 1 30.0 0.0 180.0 4.39245E-02 4.23657E-03 1.05736E-03 5.29393E-03 3.06384E-03 0.024072
7 4 30.0 45.0 135.0 4.86983E-02 4.23540E-03 1.18773E-03 5.42312E-03 3.06299E-03 0.024390
7 7 30.0 90.0 90.0 7.10151E-02 4.23508E-03 2.05029E-03 6.28537E-03 3.06276E-03 0.028871
6 1 40.0 0.0 180.0 4.16927E-02 4.29679E-03 1.17566E-03 5.47245E-03 3.10739E-03 0.028198
6 4 40.0 45.0 135.0 4.55887E-02 4.29237E-03 1.27508E-03 5.56745E-03 3.10419E-03 0.027969
6 7 40.0 90.0 90.0 6.40058E-02 4.31261E-03 1.84741E-03 6.16002E-03 3.11883E-03 0.028863
5 1 50.0 0.0 180.0 4.37134E-02 4.37550E-03 1.85714E-03 6.23265E-03 3.16431E-03 0.042485
5 4 50.0 45.0 135.0 4.65825E-02 4.34954E-03 1.93480E-03 6.28435E-03 3.14554E-03 0.041535
5 7 50.0 90.0 90.0 6.19197E-02 4.39265E-03 2.50133E-03 6.89398E-03 3.17672E-03 0.040396
4 1 60.0 0.0 180.0 5.18885E-02 4.33307E-03 4.32628E-03 8.65935E-03 3.13362E-03 0.083377
4 4 60.0 45.0 135.0 5.30628E-02 4.30310E-03 4.27212E-03 8.57522E-03 3.11195E-03 0.080511
4 7 60.0 90.0 90.0 6.55255E-02 4.41491E-03 4.98887E-03 9.40378E-03 3.19281E-03 0.076136
3 1 70.0 0.0 180.0 7.19956E-02 4.03345E-03 1.19503E-02 1.59838E-02 2.91695E-03 0.165987
3 4 70.0 45.0 135.0 6.99692E-02 4.04946E-03 1.14984E-02 1.55479E-02 2.92852E-03 0.164336
3 7 70.0 90.0 90.0 7.82239E-02 4.16931E-03 1.25040E-02 1.66733E-02 3.01520E-03 0.159849
2 1 80.0 0.0 180.0 1.22322E-01 3.46037E-03 2.97050E-02 3.31654E-02 2.50250E-03 0.242843
2 4 80.0 45.0 135.0 1.13267E-01 3.46543E-03 2.87309E-02 3.21963E-02 2.50616E-03 0.253655
2 7 80.0 90.0 90.0 1.12532E-01 3.57930E-03 3.00891E-02 3.36683E-02 2.58851E-03 0.267382
1 1 87.5 0.0 180.0 1.97772E-01 2.78523E-03 5.23889E-02 5.51741E-02 2.01425E-03 0.264896
1 4 87.5 45.0 135.0 1.78069E-01 2.65511E-03 5.20654E-02 5.47205E-02 1.92015E-03 0.292389
1 7 87.5 90.0 90.0 1.62004E-01 3.04038E-03 5.32855E-02 5.63259E-02 2.19876E-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 1.179E-02 1.045E-01 1.265E-01 1.092E-01 1.636E-01 8.529E-03 5.074E+00 4.064E-03 2.939E-03
1 0.00 0.00 7.537E-03 1.946E-01 1.369E-02 1.594E-02 2.354E-02 5.567E-03 4.103E+00
3 1.72 5.00 5.736E-03 3.758E-01 1.188E-02 1.602E-02 2.952E-02 6.203E-03 4.601E+00
5 4.06 10.00 3.983E-03 3.790E-01 1.063E-02 1.543E-02 2.933E-02 6.704E-03 5.246E+00
7 7.49 15.00 2.231E-03 2.539E-01 8.577E-03 1.283E-02 2.306E-02 6.455E-03 5.969E+00
9 11.13 20.00 1.033E-03 1.397E-01 5.315E-03 7.627E-03 1.224E-02 5.378E-03 6.002E+00
11 13.45 25.00 5.395E-04 8.506E-02 2.504E-03 3.370E-03 4.935E-03 4.651E-03 5.136E+00
Waveband 15 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 16 (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 98.2 m at 555.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 550.0 nm to 560.0 nm:
Ed(diffuse) = 3.803E-01 Ed(direct) = 9.931E-01 Ed(total) = 1.373E+00
Absorption Coefficients of Individual Components at 555.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0596 0.0060 0.0000 0.0013 0.0670
3 1.752 5.000 0.0596 0.0080 0.0000 0.0017 0.0693
5 4.114 10.000 0.0596 0.0127 0.0000 0.0023 0.0746
7 7.562 15.000 0.0596 0.0203 0.0000 0.0033 0.0832
9 11.233 20.000 0.0596 0.0153 0.0000 0.0027 0.0776
11 13.578 25.000 0.0596 0.0050 0.0000 0.0012 0.0658
Scattering Coefficients of Individual Components at 555.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0018 0.1200 0.1240 0.0000 0.2458
3 1.752 5.000 0.0018 0.1455 0.1704 0.0000 0.3177
5 4.114 10.000 0.0018 0.1962 0.2817 0.0000 0.4797
7 7.562 15.000 0.0018 0.2634 0.4710 0.0000 0.7362
9 11.233 20.000 0.0018 0.2211 0.3461 0.0000 0.5690
11 13.578 25.000 0.0018 0.1054 0.1002 0.0000 0.2074
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00092 0.00168 0.00022 0.00000 0.00282
3 1.752 5.000 0.00092 0.00204 0.00030 0.00000 0.00326
5 4.114 10.000 0.00092 0.00275 0.00050 0.00000 0.00417
7 7.562 15.000 0.00092 0.00369 0.00083 0.00000 0.00544
9 11.233 20.000 0.00092 0.00310 0.00061 0.00000 0.00463
11 13.578 25.000 0.00092 0.00148 0.00018 0.00000 0.00257
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 0.0670 0.2458 0.3128 0.7858 0.00282 0.01148
3 1.752 5.000 0.0693 0.3177 0.3870 0.8210 0.00326 0.01026
5 4.114 10.000 0.0746 0.4797 0.5543 0.8654 0.00417 0.00869
7 7.562 15.000 0.0832 0.7362 0.8194 0.8985 0.00544 0.00739
9 11.233 20.000 0.0776 0.5690 0.6466 0.8801 0.00463 0.00814
11 13.578 25.000 0.0658 0.2074 0.2732 0.7592 0.00257 0.01241
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.2661E-01
8 20.00 7.5504E-01
7 30.00 5.4522E-01
6 40.00 3.5509E-01
5 50.00 2.1359E-01
4 60.00 1.2210E-01
3 70.00 6.8459E-02
2 80.00 3.9068E-02
1 87.50 2.6065E-02
1 92.50 1.9753E-02
2 100.00 1.4055E-02
3 110.00 9.6868E-03
4 120.00 7.2169E-03
5 130.00 5.8145E-03
6 140.00 5.0061E-03
7 150.00 4.5375E-03
8 160.00 4.2715E-03
9 170.00 4.1349E-03
10 180.00 4.0874E-03
Asymptotic AOP values are
MUu(inf) = 0.3601
MUd(inf) = 0.7667
MU(inf) = 0.7247
R(inf) = 0.0182
Lu(inf)/Ed(inf) = 0.003668 (1/sr)
k(inf) = 0.0908 (1/m)
absorp(check) = 0.0658 = 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 1.5333E-01 1.9156E+00 2.0689E+00 5.7486E-02 1.3734E+00 0.3749 0.7169 0.6360 4.1858E-02
1 0.00 0.00 6.1653E-02 1.5259E+00 1.5876E+00 2.6597E-02 1.3425E+00 0.4314 0.8798 0.8289 1.9812E-02
3 1.75 5.00 5.5163E-02 1.0651E+00 1.1202E+00 2.2375E-02 8.8185E-01 0.4056 0.8280 0.7672 2.5373E-02
5 4.11 10.00 4.6146E-02 6.9914E-01 7.4528E-01 1.7564E-02 5.4638E-01 0.3806 0.7815 0.7095 3.2147E-02
7 7.56 15.00 3.1518E-02 4.1827E-01 4.4979E-01 1.1010E-02 3.0838E-01 0.3493 0.7373 0.6611 3.5701E-02
9 11.23 20.00 1.4823E-02 2.3122E-01 2.4604E-01 4.8577E-03 1.6633E-01 0.3277 0.7193 0.6563 2.9206E-02
11 13.58 25.00 5.7278E-03 1.3224E-01 1.3797E-01 1.9976E-03 9.6599E-02 0.3488 0.7305 0.6857 2.0679E-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 0.02179 0.06792 0.06613 0.03111 0.07951 0.08049 0.05316
5.000 5.010 5.005 0.02314 0.07765 0.07497 0.03596 0.08853 0.08990 0.06171
10.000 10.010 10.005 0.04530 0.09176 0.08888 0.06007 0.10318 0.10461 0.09039
15.000 15.010 15.005 0.12641 0.11539 0.11616 0.14221 0.12585 0.12524 0.15792
20.000 20.010 20.005 0.18298 0.11850 0.12238 0.19146 0.11976 0.11760 0.17104
25.000 25.010 25.005 0.11488 0.10293 0.10343 0.10319 0.09558 0.09542 0.09365
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 1.02609E-01 3.51311E-03 7.66958E-03 1.11827E-02 2.55805E-03 0.074746
9 1 10.0 0.0 180.0 6.33137E-02 3.56380E-03 2.28026E-03 5.84406E-03 2.59496E-03 0.036015
9 4 10.0 45.0 135.0 6.95647E-02 3.55001E-03 2.64533E-03 6.19535E-03 2.58493E-03 0.038027
9 7 10.0 90.0 90.0 9.39876E-02 3.54802E-03 5.53199E-03 9.08000E-03 2.58347E-03 0.058859
8 1 20.0 0.0 180.0 4.97320E-02 3.60260E-03 1.21465E-03 4.81725E-03 2.62322E-03 0.024424
8 4 20.0 45.0 135.0 5.53652E-02 3.56801E-03 1.43151E-03 4.99952E-03 2.59803E-03 0.025856
8 7 20.0 90.0 90.0 8.14118E-02 3.57363E-03 3.24366E-03 6.81729E-03 2.60212E-03 0.039843
7 1 30.0 0.0 180.0 4.31204E-02 3.66256E-03 1.03801E-03 4.70056E-03 2.66687E-03 0.024072
7 4 30.0 45.0 135.0 4.78071E-02 3.65881E-03 1.16605E-03 4.82486E-03 2.66415E-03 0.024391
7 7 30.0 90.0 90.0 6.97125E-02 3.65221E-03 2.01650E-03 5.66871E-03 2.65934E-03 0.028926
6 1 40.0 0.0 180.0 4.09294E-02 3.71050E-03 1.15413E-03 4.86463E-03 2.70178E-03 0.028198
6 4 40.0 45.0 135.0 4.47541E-02 3.70314E-03 1.25173E-03 4.95487E-03 2.69642E-03 0.027969
6 7 40.0 90.0 90.0 6.28340E-02 3.71229E-03 1.81383E-03 5.52612E-03 2.70309E-03 0.028867
5 1 50.0 0.0 180.0 4.29131E-02 3.77407E-03 1.82314E-03 5.59722E-03 2.74807E-03 0.042485
5 4 50.0 45.0 135.0 4.57297E-02 3.74758E-03 1.89938E-03 5.64696E-03 2.72879E-03 0.041535
5 7 50.0 90.0 90.0 6.07861E-02 3.77519E-03 2.45554E-03 6.23073E-03 2.74889E-03 0.040396
4 1 60.0 0.0 180.0 5.09385E-02 3.73307E-03 4.24708E-03 7.98015E-03 2.71822E-03 0.083377
4 4 60.0 45.0 135.0 5.20913E-02 3.70280E-03 4.19391E-03 7.89671E-03 2.69618E-03 0.080511
4 7 60.0 90.0 90.0 6.43259E-02 3.78873E-03 4.89754E-03 8.68627E-03 2.75874E-03 0.076136
3 1 70.0 0.0 180.0 7.06776E-02 3.47085E-03 1.17316E-02 1.52024E-02 2.52728E-03 0.165987
3 4 70.0 45.0 135.0 6.86883E-02 3.48028E-03 1.12879E-02 1.47682E-02 2.53415E-03 0.164336
3 7 70.0 90.0 90.0 7.67918E-02 3.57347E-03 1.22751E-02 1.58486E-02 2.60201E-03 0.159849
2 1 80.0 0.0 180.0 1.20082E-01 2.97486E-03 2.91612E-02 3.21360E-02 2.16613E-03 0.242843
2 4 80.0 45.0 135.0 1.11194E-01 2.97542E-03 2.82049E-02 3.11803E-02 2.16654E-03 0.253655
2 7 80.0 90.0 90.0 1.10472E-01 3.06508E-03 2.95382E-02 3.26033E-02 2.23182E-03 0.267382
1 1 87.5 0.0 180.0 1.94151E-01 2.39280E-03 5.14298E-02 5.38226E-02 1.74230E-03 0.264896
1 4 87.5 45.0 135.0 1.74809E-01 2.27823E-03 5.11122E-02 5.33905E-02 1.65888E-03 0.292389
1 7 87.5 90.0 90.0 1.59038E-01 2.60253E-03 5.23100E-02 5.49126E-02 1.89502E-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 1.118E-02 1.026E-01 1.240E-01 1.070E-01 1.604E-01 8.143E-03 5.141E+00 3.513E-03 2.558E-03
1 0.00 0.00 6.516E-03 1.910E-01 1.182E-02 1.382E-02 2.067E-02 4.854E-03 4.082E+00
3 1.75 5.00 4.886E-03 3.586E-01 1.013E-02 1.377E-02 2.577E-02 5.540E-03 4.579E+00
5 4.11 10.00 3.350E-03 3.512E-01 8.956E-03 1.310E-02 2.516E-02 6.132E-03 5.243E+00
7 7.56 15.00 1.829E-03 2.292E-01 7.199E-03 1.083E-02 1.961E-02 5.930E-03 6.021E+00
9 11.23 20.00 8.002E-04 1.227E-01 4.293E-03 6.188E-03 9.982E-03 4.811E-03 6.071E+00
11 13.58 25.00 3.916E-04 7.227E-02 1.850E-03 2.496E-03 3.668E-03 4.054E-03 5.101E+00
Waveband 16 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 17 (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 97.6 m at 565.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 560.0 nm to 570.0 nm:
Ed(diffuse) = 3.727E-01 Ed(direct) = 9.883E-01 Ed(total) = 1.361E+00
Absorption Coefficients of Individual Components at 565.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0642 0.0053 0.0000 0.0012 0.0706
3 1.762 5.000 0.0642 0.0070 0.0000 0.0014 0.0726
5 4.132 10.000 0.0642 0.0110 0.0000 0.0020 0.0772
7 7.588 15.000 0.0642 0.0175 0.0000 0.0029 0.0846
9 11.266 20.000 0.0642 0.0132 0.0000 0.0023 0.0797
11 13.619 25.000 0.0642 0.0044 0.0000 0.0010 0.0696
Scattering Coefficients of Individual Components at 565.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0017 0.1193 0.1233 0.0000 0.2444
3 1.762 5.000 0.0017 0.1449 0.1697 0.0000 0.3163
5 4.132 10.000 0.0017 0.1958 0.2811 0.0000 0.4786
7 7.588 15.000 0.0017 0.2634 0.4710 0.0000 0.7361
9 11.266 20.000 0.0017 0.2209 0.3457 0.0000 0.5683
11 13.619 25.000 0.0017 0.1047 0.0996 0.0000 0.2060
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00085 0.00167 0.00022 0.00000 0.00274
3 1.762 5.000 0.00085 0.00203 0.00030 0.00000 0.00318
5 4.132 10.000 0.00085 0.00275 0.00049 0.00000 0.00409
7 7.588 15.000 0.00085 0.00369 0.00083 0.00000 0.00537
9 11.266 20.000 0.00085 0.00310 0.00061 0.00000 0.00456
11 13.619 25.000 0.00085 0.00147 0.00018 0.00000 0.00250
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 0.0706 0.2444 0.3150 0.7758 0.00274 0.01122
3 1.762 5.000 0.0726 0.3163 0.3889 0.8133 0.00318 0.01006
5 4.132 10.000 0.0772 0.4786 0.5558 0.8611 0.00409 0.00855
7 7.588 15.000 0.0846 0.7361 0.8207 0.8969 0.00537 0.00730
9 11.266 20.000 0.0797 0.5683 0.6480 0.8769 0.00456 0.00802
11 13.619 25.000 0.0696 0.2060 0.2755 0.7475 0.00250 0.01211
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.2402E-01
8 20.00 7.4735E-01
7 30.00 5.3351E-01
6 40.00 3.4248E-01
5 50.00 2.0271E-01
4 60.00 1.1400E-01
3 70.00 6.2953E-02
2 80.00 3.5459E-02
1 87.50 2.3468E-02
1 92.50 1.7711E-02
2 100.00 1.2543E-02
3 110.00 8.6073E-03
4 120.00 6.3991E-03
5 130.00 5.1526E-03
6 140.00 4.4376E-03
7 150.00 4.0248E-03
8 160.00 3.7911E-03
9 170.00 3.6714E-03
10 180.00 3.6298E-03
Asymptotic AOP values are
MUu(inf) = 0.3591
MUd(inf) = 0.7722
MU(inf) = 0.7334
R(inf) = 0.0165
Lu(inf)/Ed(inf) = 0.003341 (1/sr)
k(inf) = 0.0949 (1/m)
absorp(check) = 0.0696 = 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 1.4930E-01 1.8948E+00 2.0441E+00 5.5957E-02 1.3609E+00 0.3748 0.7183 0.6384 4.1116E-02
1 0.00 0.00 5.6646E-02 1.5083E+00 1.5649E+00 2.4397E-02 1.3294E+00 0.4307 0.8814 0.8339 1.8352E-02
3 1.76 5.00 5.0524E-02 1.0322E+00 1.0827E+00 2.0475E-02 8.5682E-01 0.4052 0.8301 0.7725 2.3896E-02
5 4.13 10.00 4.2361E-02 6.6625E-01 7.0861E-01 1.6110E-02 5.2223E-01 0.3803 0.7838 0.7142 3.0849E-02
7 7.59 15.00 2.8968E-02 3.9452E-01 4.2348E-01 1.0075E-02 2.9158E-01 0.3478 0.7391 0.6647 3.4554E-02
9 11.27 20.00 1.3307E-02 2.1583E-01 2.2913E-01 4.3273E-03 1.5566E-01 0.3252 0.7212 0.6605 2.7800E-02
11 13.62 25.00 4.8886E-03 1.2106E-01 1.2595E-01 1.6988E-03 8.8804E-02 0.3475 0.7335 0.6916 1.9130E-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 0.02180 0.07166 0.06985 0.03178 0.08341 0.08437 0.05404
5.000 5.010 5.005 0.02283 0.08150 0.07876 0.03560 0.09221 0.09360 0.06171
10.000 10.010 10.005 0.04414 0.09466 0.09163 0.05920 0.10606 0.10756 0.09063
15.000 15.010 15.005 0.12906 0.11669 0.11754 0.14563 0.12732 0.12667 0.16220
20.000 20.010 20.005 0.19064 0.12124 0.12527 0.19977 0.12235 0.12013 0.17881
25.000 25.010 25.005 0.12074 0.10797 0.10847 0.10792 0.10018 0.10003 0.09733
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 1.00566E-01 3.22750E-03 7.59293E-03 1.08204E-02 2.37151E-03 0.075502
9 1 10.0 0.0 180.0 6.20534E-02 3.27387E-03 2.24508E-03 5.51895E-03 2.40559E-03 0.036180
9 4 10.0 45.0 135.0 6.81800E-02 3.26110E-03 2.60581E-03 5.86691E-03 2.39621E-03 0.038220
9 7 10.0 90.0 90.0 9.21168E-02 3.25905E-03 5.46891E-03 8.72796E-03 2.39470E-03 0.059369
8 1 20.0 0.0 180.0 4.87421E-02 3.30873E-03 1.19099E-03 4.49972E-03 2.43120E-03 0.024435
8 4 20.0 45.0 135.0 5.42631E-02 3.27676E-03 1.40435E-03 4.68111E-03 2.40771E-03 0.025880
8 7 20.0 90.0 90.0 7.97913E-02 3.28158E-03 3.19698E-03 6.47856E-03 2.41125E-03 0.040067
7 1 30.0 0.0 180.0 4.22620E-02 3.36267E-03 1.01734E-03 4.38001E-03 2.47084E-03 0.024072
7 4 30.0 45.0 135.0 4.68559E-02 3.35893E-03 1.14290E-03 4.50184E-03 2.46809E-03 0.024392
7 7 30.0 90.0 90.0 6.83224E-02 3.35242E-03 1.97988E-03 5.33230E-03 2.46331E-03 0.028978
6 1 40.0 0.0 180.0 4.01147E-02 3.40458E-03 1.13116E-03 4.53575E-03 2.50164E-03 0.028198
6 4 40.0 45.0 135.0 4.38632E-02 3.39748E-03 1.22682E-03 4.62430E-03 2.49642E-03 0.027969
6 7 40.0 90.0 90.0 6.15833E-02 3.40536E-03 1.77795E-03 5.18331E-03 2.50220E-03 0.028871
5 1 50.0 0.0 180.0 4.20589E-02 3.46080E-03 1.78685E-03 5.24765E-03 2.54294E-03 0.042485
5 4 50.0 45.0 135.0 4.48194E-02 3.43613E-03 1.86157E-03 5.29770E-03 2.52482E-03 0.041535
5 7 50.0 90.0 90.0 5.95761E-02 3.46100E-03 2.40666E-03 5.86766E-03 2.54309E-03 0.040396
4 1 60.0 0.0 180.0 4.99246E-02 3.42107E-03 4.16254E-03 7.58361E-03 2.51375E-03 0.083377
4 4 60.0 45.0 135.0 5.10544E-02 3.39297E-03 4.11043E-03 7.50340E-03 2.49310E-03 0.080511
4 7 60.0 90.0 90.0 6.30455E-02 3.47145E-03 4.80005E-03 8.27150E-03 2.55077E-03 0.076136
3 1 70.0 0.0 180.0 6.92707E-02 3.17873E-03 1.14980E-02 1.46768E-02 2.33568E-03 0.165987
3 4 70.0 45.0 135.0 6.73210E-02 3.18710E-03 1.10633E-02 1.42504E-02 2.34183E-03 0.164336
3 7 70.0 90.0 90.0 7.52633E-02 3.27254E-03 1.20308E-02 1.53033E-02 2.40461E-03 0.159849
2 1 80.0 0.0 180.0 1.17692E-01 2.72302E-03 2.85807E-02 3.13037E-02 2.00083E-03 0.242843
2 4 80.0 45.0 135.0 1.08980E-01 2.72336E-03 2.76435E-02 3.03668E-02 2.00109E-03 0.253655
2 7 80.0 90.0 90.0 1.08273E-01 2.80591E-03 2.89502E-02 3.17562E-02 2.06174E-03 0.267382
1 1 87.5 0.0 180.0 1.90286E-01 2.18930E-03 5.04061E-02 5.25954E-02 1.60866E-03 0.264896
1 4 87.5 45.0 135.0 1.71329E-01 2.08446E-03 5.00948E-02 5.21793E-02 1.53163E-03 0.292389
1 7 87.5 90.0 90.0 1.55872E-01 2.38202E-03 5.12688E-02 5.36508E-02 1.75027E-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 1.082E-02 1.006E-01 1.214E-01 1.048E-01 1.571E-01 7.951E-03 5.171E+00 3.227E-03 2.372E-03
1 0.00 0.00 5.987E-03 1.872E-01 1.084E-02 1.272E-02 1.922E-02 4.503E-03 4.075E+00
3 1.76 5.00 4.477E-03 3.477E-01 9.254E-03 1.266E-02 2.392E-02 5.225E-03 4.573E+00
5 4.13 10.00 3.068E-03 3.366E-01 8.185E-03 1.204E-02 2.328E-02 5.875E-03 5.251E+00
7 7.59 15.00 1.660E-03 2.178E-01 6.628E-03 1.002E-02 1.822E-02 5.692E-03 6.070E+00
9 11.27 20.00 7.054E-04 1.155E-01 3.891E-03 5.631E-03 9.120E-03 4.532E-03 6.135E+00
11 13.62 25.00 3.333E-04 6.703E-02 1.597E-03 2.161E-03 3.188E-03 3.753E-03 5.097E+00
Waveband 17 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 18 (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 94.8 m at 575.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 570.0 nm to 580.0 nm:
Ed(diffuse) = 3.691E-01 Ed(direct) = 9.928E-01 Ed(total) = 1.362E+00
Absorption Coefficients of Individual Components at 575.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0772 0.0049 0.0000 0.0010 0.0831
3 1.817 5.000 0.0772 0.0065 0.0000 0.0013 0.0850
5 4.243 10.000 0.0772 0.0102 0.0000 0.0018 0.0892
7 7.754 15.000 0.0772 0.0163 0.0000 0.0025 0.0961
9 11.488 20.000 0.0772 0.0123 0.0000 0.0020 0.0916
11 13.897 25.000 0.0772 0.0041 0.0000 0.0009 0.0822
Scattering Coefficients of Individual Components at 575.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0016 0.1187 0.1227 0.0000 0.2430
3 1.817 5.000 0.0016 0.1443 0.1690 0.0000 0.3149
5 4.243 10.000 0.0016 0.1954 0.2806 0.0000 0.4776
7 7.754 15.000 0.0016 0.2634 0.4710 0.0000 0.7359
9 11.488 20.000 0.0016 0.2206 0.3453 0.0000 0.5675
11 13.897 25.000 0.0016 0.1041 0.0990 0.0000 0.2046
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00079 0.00166 0.00022 0.00000 0.00267
3 1.817 5.000 0.00079 0.00202 0.00030 0.00000 0.00311
5 4.243 10.000 0.00079 0.00274 0.00049 0.00000 0.00402
7 7.754 15.000 0.00079 0.00369 0.00083 0.00000 0.00531
9 11.488 20.000 0.00079 0.00309 0.00061 0.00000 0.00449
11 13.897 25.000 0.00079 0.00146 0.00017 0.00000 0.00242
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 0.0831 0.2430 0.3261 0.7450 0.00267 0.01099
3 1.817 5.000 0.0850 0.3149 0.3999 0.7875 0.00311 0.00988
5 4.243 10.000 0.0892 0.4776 0.5668 0.8426 0.00402 0.00842
7 7.754 15.000 0.0961 0.7359 0.8320 0.8845 0.00531 0.00722
9 11.488 20.000 0.0916 0.5675 0.6591 0.8611 0.00449 0.00791
11 13.897 25.000 0.0822 0.2046 0.2868 0.7134 0.00242 0.01184
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 9.1634E-01
8 20.00 7.2491E-01
7 30.00 5.0025E-01
6 40.00 3.0791E-01
5 50.00 1.7406E-01
4 60.00 9.3563E-02
3 70.00 4.9628E-02
2 80.00 2.7068E-02
1 87.50 1.7601E-02
1 92.50 1.3185E-02
2 100.00 9.2722E-03
3 110.00 6.3384E-03
4 120.00 4.7210E-03
5 130.00 3.8206E-03
6 140.00 3.3099E-03
7 150.00 3.0178E-03
8 160.00 2.8539E-03
9 170.00 2.7705E-03
10 180.00 2.7414E-03
Asymptotic AOP values are
MUu(inf) = 0.3598
MUd(inf) = 0.7870
MU(inf) = 0.7549
R(inf) = 0.0132
Lu(inf)/Ed(inf) = 0.002710 (1/sr)
k(inf) = 0.1089 (1/m)
absorp(check) = 0.0822 = 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 1.4445E-01 1.8929E+00 2.0373E+00 5.3759E-02 1.3619E+00 0.3722 0.7195 0.6421 3.9472E-02
1 0.00 0.00 4.6020E-02 1.5005E+00 1.5465E+00 1.9657E-02 1.3278E+00 0.4271 0.8849 0.8459 1.4804E-02
3 1.82 5.00 3.9055E-02 9.5535E-01 9.9440E-01 1.5704E-02 7.9783E-01 0.4021 0.8351 0.7865 1.9684E-02
5 4.24 10.00 3.1352E-02 5.7291E-01 6.0426E-01 1.1859E-02 4.5303E-01 0.3783 0.7907 0.7301 2.6178E-02
7 7.75 15.00 2.0504E-02 3.1589E-01 3.3640E-01 7.0828E-03 2.3592E-01 0.3454 0.7468 0.6803 3.0022E-02
9 11.49 20.00 8.6862E-03 1.6077E-01 1.6946E-01 2.8098E-03 1.1738E-01 0.3235 0.7301 0.6761 2.3938E-02
11 13.90 25.00 2.8391E-03 8.3559E-02 8.6398E-02 9.9289E-04 6.2203E-02 0.3497 0.7444 0.7085 1.5962E-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 0.02833 0.08480 0.08312 0.04113 0.09717 0.09801 0.06391
5.000 5.010 5.005 0.03140 0.09628 0.09373 0.04385 0.10640 0.10766 0.06974
10.000 10.010 10.005 0.05153 0.10929 0.10629 0.06644 0.12020 0.12164 0.09845
15.000 15.010 15.005 0.14317 0.13062 0.13139 0.15974 0.14106 0.14048 0.17579
20.000 20.010 20.005 0.21033 0.13596 0.13977 0.21912 0.13669 0.13467 0.19689
25.000 25.010 25.005 0.13626 0.12370 0.12411 0.12122 0.11531 0.11521 0.10841
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 9.96014E-02 2.61143E-03 7.59163E-03 1.02031E-02 1.91744E-03 0.076220
9 1 10.0 0.0 180.0 6.14581E-02 2.65379E-03 2.23314E-03 4.88694E-03 1.94855E-03 0.036336
9 4 10.0 45.0 135.0 6.75259E-02 2.64149E-03 2.59317E-03 5.23466E-03 1.93951E-03 0.038403
9 7 10.0 90.0 90.0 9.12331E-02 2.63505E-03 5.46070E-03 8.09575E-03 1.93478E-03 0.059854
8 1 20.0 0.0 180.0 4.82745E-02 2.68264E-03 1.18005E-03 3.86269E-03 1.96973E-03 0.024445
8 4 20.0 45.0 135.0 5.37425E-02 2.65346E-03 1.39214E-03 4.04560E-03 1.94830E-03 0.025904
8 7 20.0 90.0 90.0 7.90258E-02 2.64951E-03 3.18315E-03 5.83266E-03 1.94541E-03 0.040280
7 1 30.0 0.0 180.0 4.18566E-02 2.72565E-03 1.00758E-03 3.73323E-03 2.00131E-03 0.024072
7 4 30.0 45.0 135.0 4.64068E-02 2.71808E-03 1.13200E-03 3.85008E-03 1.99575E-03 0.024393
7 7 30.0 90.0 90.0 6.76647E-02 2.70194E-03 1.96420E-03 4.66614E-03 1.98390E-03 0.029028
6 1 40.0 0.0 180.0 3.97298E-02 2.75661E-03 1.12031E-03 3.87692E-03 2.02404E-03 0.028198
6 4 40.0 45.0 135.0 4.34424E-02 2.74500E-03 1.21505E-03 3.96005E-03 2.01551E-03 0.027969
6 7 40.0 90.0 90.0 6.09925E-02 2.73706E-03 1.76111E-03 4.49817E-03 2.00969E-03 0.028874
5 1 50.0 0.0 180.0 4.16554E-02 2.79900E-03 1.76971E-03 4.56871E-03 2.05517E-03 0.042485
5 4 50.0 45.0 135.0 4.43895E-02 2.77228E-03 1.84371E-03 4.61599E-03 2.03555E-03 0.041535
5 7 50.0 90.0 90.0 5.90046E-02 2.77583E-03 2.38357E-03 5.15941E-03 2.03816E-03 0.040396
4 1 60.0 0.0 180.0 4.94456E-02 2.76395E-03 4.12261E-03 6.88656E-03 2.02943E-03 0.083377
4 4 60.0 45.0 135.0 5.05646E-02 2.73388E-03 4.07100E-03 6.80488E-03 2.00735E-03 0.080511
4 7 60.0 90.0 90.0 6.24407E-02 2.77909E-03 4.75400E-03 7.53310E-03 2.04055E-03 0.076136
3 1 70.0 0.0 180.0 6.86062E-02 2.56617E-03 1.13877E-02 1.39539E-02 1.88421E-03 0.165987
3 4 70.0 45.0 135.0 6.66752E-02 2.56569E-03 1.09571E-02 1.35228E-02 1.88385E-03 0.164336
3 7 70.0 90.0 90.0 7.45412E-02 2.61698E-03 1.19153E-02 1.45323E-02 1.92152E-03 0.159849
2 1 80.0 0.0 180.0 1.16563E-01 2.19735E-03 2.83065E-02 3.05039E-02 1.61340E-03 0.242843
2 4 80.0 45.0 135.0 1.07935E-01 2.19132E-03 2.73783E-02 2.95696E-02 1.60897E-03 0.253655
2 7 80.0 90.0 90.0 1.07234E-01 2.24282E-03 2.86725E-02 3.09153E-02 1.64679E-03 0.267382
1 1 87.5 0.0 180.0 1.88461E-01 1.76688E-03 4.99225E-02 5.16894E-02 1.29733E-03 0.264896
1 4 87.5 45.0 135.0 1.69686E-01 1.67753E-03 4.96143E-02 5.12918E-02 1.23173E-03 0.292389
1 7 87.5 90.0 90.0 1.54377E-01 1.90498E-03 5.07769E-02 5.26819E-02 1.39873E-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 1.020E-02 9.960E-02 1.201E-01 1.035E-01 1.553E-01 7.492E-03 5.269E+00 2.611E-03 1.917E-03
1 0.00 0.00 4.844E-03 1.854E-01 8.915E-03 1.048E-02 1.610E-02 3.648E-03 4.058E+00
3 1.82 5.00 3.460E-03 3.250E-01 7.300E-03 1.008E-02 1.941E-02 4.336E-03 4.539E+00
5 4.24 10.00 2.277E-03 2.961E-01 6.140E-03 9.099E-03 1.783E-02 5.027E-03 5.207E+00
7 7.75 15.00 1.172E-03 1.801E-01 4.765E-03 7.241E-03 1.328E-02 4.969E-03 6.042E+00
9 11.49 20.00 4.614E-04 8.963E-02 2.588E-03 3.752E-03 6.101E-03 3.931E-03 6.090E+00
11 13.90 25.00 2.002E-04 4.870E-02 9.383E-04 1.266E-03 1.864E-03 3.218E-03 4.961E+00
Waveband 18 of 30 completed in 4.8 sec.
* * * * * Output for wavelength band 19 (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 87.9 m at 585.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 580.0 nm to 590.0 nm:
Ed(diffuse) = 3.569E-01 Ed(direct) = 9.725E-01 Ed(total) = 1.329E+00
Absorption Coefficients of Individual Components at 585.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1100 0.0050 0.0000 0.0009 0.1159
3 1.974 5.000 0.1100 0.0066 0.0000 0.0011 0.1177
5 4.557 10.000 0.1100 0.0103 0.0000 0.0015 0.1219
7 8.229 15.000 0.1100 0.0164 0.0000 0.0022 0.1285
9 12.124 20.000 0.1100 0.0124 0.0000 0.0018 0.1242
11 14.690 25.000 0.1100 0.0042 0.0000 0.0008 0.1150
Scattering Coefficients of Individual Components at 585.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0015 0.1181 0.1220 0.0000 0.2416
3 1.974 5.000 0.0015 0.1438 0.1684 0.0000 0.3136
5 4.557 10.000 0.0015 0.1951 0.2800 0.0000 0.4766
7 8.229 15.000 0.0015 0.2634 0.4710 0.0000 0.7358
9 12.124 20.000 0.0015 0.2204 0.3449 0.0000 0.5668
11 14.690 25.000 0.0015 0.1034 0.0984 0.0000 0.2033
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00073 0.00166 0.00021 0.00000 0.00260
3 1.974 5.000 0.00073 0.00202 0.00030 0.00000 0.00305
5 4.557 10.000 0.00073 0.00273 0.00049 0.00000 0.00396
7 8.229 15.000 0.00073 0.00369 0.00083 0.00000 0.00525
9 12.124 20.000 0.00073 0.00309 0.00061 0.00000 0.00443
11 14.690 25.000 0.00073 0.00145 0.00017 0.00000 0.00236
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 0.1159 0.2416 0.3575 0.6758 0.00260 0.01078
3 1.974 5.000 0.1177 0.3136 0.4313 0.7271 0.00305 0.00971
5 4.557 10.000 0.1219 0.4766 0.5984 0.7964 0.00396 0.00831
7 8.229 15.000 0.1285 0.7358 0.8644 0.8513 0.00525 0.00714
9 12.124 20.000 0.1242 0.5668 0.6910 0.8203 0.00443 0.00782
11 14.690 25.000 0.1150 0.2033 0.3182 0.6387 0.00236 0.01159
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.9857E-01
8 20.00 6.7511E-01
7 30.00 4.3108E-01
6 40.00 2.4150E-01
5 50.00 1.2362E-01
4 60.00 6.0544E-02
3 70.00 2.9731E-02
2 80.00 1.5339E-02
1 87.50 9.7167E-03
1 92.50 7.2257E-03
2 100.00 5.0580E-03
3 110.00 3.4667E-03
4 120.00 2.6127E-03
5 130.00 2.1471E-03
6 140.00 1.8878E-03
7 150.00 1.7420E-03
8 160.00 1.6615E-03
9 170.00 1.6210E-03
10 180.00 1.6068E-03
Asymptotic AOP values are
MUu(inf) = 0.3647
MUd(inf) = 0.8153
MU(inf) = 0.7931
R(inf) = 0.0086
Lu(inf)/Ed(inf) = 0.001846 (1/sr)
k(inf) = 0.1450 (1/m)
absorp(check) = 0.1150 = 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 1.3462E-01 1.8447E+00 1.9793E+00 4.9461E-02 1.3294E+00 0.3674 0.7207 0.6466 3.7206E-02
1 0.00 0.00 3.0064E-02 1.4525E+00 1.4825E+00 1.2617E-02 1.2925E+00 0.4197 0.8899 0.8633 9.7613E-03
3 1.97 5.00 2.1604E-02 7.6457E-01 7.8617E-01 8.5561E-03 6.4539E-01 0.3960 0.8441 0.8100 1.3257E-02
5 4.56 10.00 1.4890E-02 3.7687E-01 3.9176E-01 5.5913E-03 3.0324E-01 0.3755 0.8046 0.7598 1.8439E-02
7 8.23 15.00 8.4369E-03 1.7056E-01 1.7900E-01 2.9087E-03 1.3030E-01 0.3448 0.7639 0.7117 2.2324E-02
9 12.12 20.00 2.9662E-03 7.1175E-02 7.4141E-02 9.7684E-04 5.3371E-02 0.3293 0.7499 0.7067 1.8303E-02
11 14.69 25.00 8.0145E-04 3.0392E-02 3.1193E-02 2.9628E-04 2.3315E-02 0.3697 0.7672 0.7379 1.2708E-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 0.05344 0.12023 0.11888 0.07214 0.13340 0.13400 0.09539
5.000 5.010 5.005 0.06182 0.13517 0.13315 0.07318 0.14394 0.14489 0.09678
10.000 10.010 10.005 0.07883 0.14877 0.14611 0.09240 0.15840 0.15964 0.12259
15.000 15.010 15.005 0.17998 0.17006 0.17053 0.19430 0.17973 0.17939 0.20514
20.000 20.010 20.005 0.24889 0.17549 0.17843 0.25218 0.17554 0.17412 0.22392
25.000 25.010 25.005 0.16074 0.16259 0.16254 0.14068 0.15361 0.15378 0.12243
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 9.62947E-02 1.68791E-03 7.40416E-03 9.09207E-03 1.26968E-03 0.076891
9 1 10.0 0.0 180.0 5.94178E-02 1.72245E-03 2.16767E-03 3.89012E-03 1.29566E-03 0.036482
9 4 10.0 45.0 135.0 6.52841E-02 1.71177E-03 2.51823E-03 4.23000E-03 1.28763E-03 0.038573
9 7 10.0 90.0 90.0 8.82042E-02 1.70091E-03 5.31936E-03 7.02027E-03 1.27946E-03 0.060307
8 1 20.0 0.0 180.0 4.66718E-02 1.74279E-03 1.14131E-03 2.88411E-03 1.31097E-03 0.024454
8 4 20.0 45.0 135.0 5.19583E-02 1.71934E-03 1.34706E-03 3.06639E-03 1.29332E-03 0.025926
8 7 20.0 90.0 90.0 7.64022E-02 1.70579E-03 3.09266E-03 4.79845E-03 1.28313E-03 0.040479
7 1 30.0 0.0 180.0 4.04670E-02 1.77077E-03 9.74132E-04 2.74491E-03 1.33201E-03 0.024072
7 4 30.0 45.0 135.0 4.48664E-02 1.75959E-03 1.09447E-03 2.85407E-03 1.32360E-03 0.024394
7 7 30.0 90.0 90.0 6.54163E-02 1.73388E-03 1.90198E-03 3.63585E-03 1.30426E-03 0.029075
6 1 40.0 0.0 180.0 3.84108E-02 1.78849E-03 1.08311E-03 2.87160E-03 1.34534E-03 0.028198
6 4 40.0 45.0 135.0 4.20002E-02 1.77287E-03 1.17471E-03 2.94758E-03 1.33359E-03 0.027969
6 7 40.0 90.0 90.0 5.89676E-02 1.74750E-03 1.70284E-03 3.45034E-03 1.31451E-03 0.028878
5 1 50.0 0.0 180.0 4.02725E-02 1.81336E-03 1.71096E-03 3.52432E-03 1.36405E-03 0.042485
5 4 50.0 45.0 135.0 4.29158E-02 1.78669E-03 1.78250E-03 3.56919E-03 1.34398E-03 0.041535
5 7 50.0 90.0 90.0 5.70457E-02 1.76535E-03 2.30444E-03 4.06979E-03 1.32793E-03 0.040396
4 1 60.0 0.0 180.0 4.78041E-02 1.78827E-03 3.98574E-03 5.77401E-03 1.34518E-03 0.083377
4 4 60.0 45.0 135.0 4.88859E-02 1.75858E-03 3.93584E-03 5.69442E-03 1.32284E-03 0.080511
4 7 60.0 90.0 90.0 6.03677E-02 1.76155E-03 4.59617E-03 6.35772E-03 1.32507E-03 0.076136
3 1 70.0 0.0 180.0 6.63285E-02 1.65908E-03 1.10097E-02 1.26687E-02 1.24799E-03 0.165987
3 4 70.0 45.0 135.0 6.44616E-02 1.64860E-03 1.05933E-02 1.22419E-02 1.24011E-03 0.164336
3 7 70.0 90.0 90.0 7.20665E-02 1.65572E-03 1.15198E-02 1.31755E-02 1.24547E-03 0.159849
2 1 80.0 0.0 180.0 1.12693E-01 1.42044E-03 2.73668E-02 2.87872E-02 1.06848E-03 0.242843
2 4 80.0 45.0 135.0 1.04352E-01 1.40759E-03 2.64693E-02 2.78769E-02 1.05882E-03 0.253655
2 7 80.0 90.0 90.0 1.03674E-01 1.41811E-03 2.77206E-02 2.91387E-02 1.06673E-03 0.267382
1 1 87.5 0.0 180.0 1.82204E-01 1.14316E-03 4.82651E-02 4.94082E-02 8.59907E-04 0.264896
1 4 87.5 45.0 135.0 1.64052E-01 1.07851E-03 4.79671E-02 4.90456E-02 8.11275E-04 0.292389
1 7 87.5 90.0 90.0 1.49251E-01 1.20602E-03 4.90912E-02 5.02972E-02 9.07190E-04 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 9.092E-03 9.629E-02 1.158E-01 9.977E-02 1.498E-01 6.839E-03 5.440E+00 1.688E-03 1.270E-03
1 0.00 0.00 3.132E-03 1.792E-01 6.026E-03 7.086E-03 1.116E-02 2.423E-03 4.029E+00
3 1.97 5.00 1.923E-03 2.669E-01 4.255E-03 5.942E-03 1.173E-02 2.980E-03 4.448E+00
5 4.56 10.00 1.111E-03 2.053E-01 3.033E-03 4.520E-03 8.992E-03 3.665E-03 5.031E+00
7 8.23 15.00 5.034E-04 1.049E-01 2.028E-03 3.080E-03 5.678E-03 3.864E-03 5.778E+00
9 12.12 20.00 1.724E-04 4.362E-02 8.992E-04 1.290E-03 2.084E-03 3.229E-03 5.668E+00
11 14.69 25.00 6.666E-05 1.988E-02 2.549E-04 3.341E-04 4.786E-04 2.859E-03 4.445E+00
Waveband 19 of 30 completed in 5.2 sec.
* * * * * Output for wavelength band 20 (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 78.5 m at 595.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 590.0 nm to 600.0 nm:
Ed(diffuse) = 3.405E-01 Ed(direct) = 9.398E-01 Ed(total) = 1.280E+00
Absorption Coefficients of Individual Components at 595.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.1672 0.0050 0.0000 0.0008 0.1730
3 2.253 5.000 0.1672 0.0066 0.0000 0.0009 0.1747
5 5.114 10.000 0.1672 0.0101 0.0000 0.0013 0.1787
7 9.066 15.000 0.1672 0.0159 0.0000 0.0019 0.1850
9 13.242 20.000 0.1672 0.0121 0.0000 0.0015 0.1809
11 16.087 25.000 0.1672 0.0042 0.0000 0.0007 0.1720
Scattering Coefficients of Individual Components at 595.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0014 0.1175 0.1214 0.0000 0.2403
3 2.253 5.000 0.0014 0.1432 0.1677 0.0000 0.3123
5 5.114 10.000 0.0014 0.1947 0.2795 0.0000 0.4756
7 9.066 15.000 0.0014 0.2634 0.4710 0.0000 0.7357
9 13.242 20.000 0.0014 0.2202 0.3446 0.0000 0.5661
11 16.087 25.000 0.0014 0.1028 0.0978 0.0000 0.2020
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00068 0.00165 0.00021 0.00000 0.00254
3 2.253 5.000 0.00068 0.00201 0.00030 0.00000 0.00298
5 5.114 10.000 0.00068 0.00273 0.00049 0.00000 0.00390
7 9.066 15.000 0.00068 0.00369 0.00083 0.00000 0.00520
9 13.242 20.000 0.00068 0.00309 0.00061 0.00000 0.00437
11 16.087 25.000 0.00068 0.00144 0.00017 0.00000 0.00230
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 0.1730 0.2403 0.4132 0.5814 0.00254 0.01058
3 2.253 5.000 0.1747 0.3123 0.4870 0.6413 0.00298 0.00956
5 5.114 10.000 0.1787 0.4756 0.6542 0.7269 0.00390 0.00821
7 9.066 15.000 0.1850 0.7357 0.9207 0.7991 0.00520 0.00707
9 13.242 20.000 0.1809 0.5661 0.7470 0.7579 0.00437 0.00773
11 16.087 25.000 0.1720 0.2020 0.3740 0.5400 0.00230 0.01136
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.7189E-01
8 20.00 6.0563E-01
7 30.00 3.4482E-01
6 40.00 1.6910E-01
5 50.00 7.5842E-02
4 60.00 3.3174E-02
3 70.00 1.5010E-02
2 80.00 7.3797E-03
1 87.50 4.5995E-03
1 92.50 3.4255E-03
2 100.00 2.4101E-03
3 110.00 1.6729E-03
4 120.00 1.2853E-03
5 130.00 1.0777E-03
6 140.00 9.6400E-04
7 150.00 9.0132E-04
8 160.00 8.6741E-04
9 170.00 8.5066E-04
10 180.00 8.4465E-04
Asymptotic AOP values are
MUu(inf) = 0.3731
MUd(inf) = 0.8467
MU(inf) = 0.8325
R(inf) = 0.0052
Lu(inf)/Ed(inf) = 0.001180 (1/sr)
k(inf) = 0.2067 (1/m)
absorp(check) = 0.1721 = 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 1.2501E-01 1.7737E+00 1.8988E+00 4.5492E-02 1.2802E+00 0.3639 0.7218 0.6503 3.5535E-02
1 0.00 0.00 1.8211E-02 1.3899E+00 1.4081E+00 7.5055E-03 1.2422E+00 0.4121 0.8937 0.8768 6.0420E-03
3 2.25 5.00 9.5807E-03 5.2662E-01 5.3620E-01 3.7585E-03 4.4997E-01 0.3923 0.8544 0.8322 8.3529E-03
5 5.11 10.00 4.9791E-03 1.8595E-01 1.9093E-01 1.8821E-03 1.5275E-01 0.3780 0.8215 0.7902 1.2322E-02
7 9.07 15.00 2.2109E-03 6.0278E-02 6.2489E-02 7.8604E-04 4.7331E-02 0.3555 0.7852 0.7449 1.6607E-02
9 13.24 20.00 6.3255E-04 1.8069E-02 1.8701E-02 2.2970E-04 1.3981E-02 0.3631 0.7738 0.7353 1.6429E-02
11 16.09 25.00 1.8096E-04 5.6033E-03 5.7843E-03 7.8338E-05 4.4325E-03 0.4329 0.7910 0.7528 1.7674E-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 0.10643 0.18338 0.18238 0.13056 0.19661 0.19701 0.15335
5.000 5.010 5.005 0.11922 0.20165 0.20018 0.12825 0.20866 0.20934 0.14640
10.000 10.010 10.005 0.13008 0.21565 0.21342 0.13999 0.22366 0.22470 0.16239
15.000 15.010 15.005 0.23227 0.23646 0.23631 0.23828 0.24514 0.24525 0.23346
20.000 20.010 20.005 0.27130 0.24081 0.24184 0.25541 0.24050 0.24025 0.21168
25.000 25.010 25.005 0.13791 0.22483 0.22211 0.11709 0.21665 0.21844 0.09955
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 9.18686E-02 1.00961E-03 7.12455E-03 8.13417E-03 7.88627E-04 0.077552
9 1 10.0 0.0 180.0 5.66867E-02 1.03406E-03 2.07619E-03 3.11024E-03 8.07721E-04 0.036626
9 4 10.0 45.0 135.0 6.22834E-02 1.02627E-03 2.41297E-03 3.43924E-03 8.01638E-04 0.038742
9 7 10.0 90.0 90.0 8.41500E-02 1.01633E-03 5.11243E-03 6.12876E-03 7.93876E-04 0.060754
8 1 20.0 0.0 180.0 4.45266E-02 1.04736E-03 1.08927E-03 2.13663E-03 8.18116E-04 0.024463
8 4 20.0 45.0 135.0 4.95701E-02 1.03094E-03 1.28621E-03 2.31715E-03 8.05289E-04 0.025947
8 7 20.0 90.0 90.0 7.28905E-02 1.01715E-03 2.96480E-03 3.98194E-03 7.94512E-04 0.040675
7 1 30.0 0.0 180.0 3.86070E-02 1.06451E-03 9.29357E-04 1.99387E-03 8.31512E-04 0.024072
7 4 30.0 45.0 135.0 4.28045E-02 1.05455E-03 1.04422E-03 2.09876E-03 8.23725E-04 0.024395
7 7 30.0 90.0 90.0 6.24076E-02 1.03121E-03 1.81736E-03 2.84857E-03 8.05496E-04 0.029121
6 1 40.0 0.0 180.0 3.66453E-02 1.07436E-03 1.03333E-03 2.10769E-03 8.39206E-04 0.028198
6 4 40.0 45.0 135.0 4.00697E-02 1.06082E-03 1.12072E-03 2.18154E-03 8.28628E-04 0.027969
6 7 40.0 90.0 90.0 5.62572E-02 1.03504E-03 1.62475E-03 2.65980E-03 8.08491E-04 0.028881
5 1 50.0 0.0 180.0 3.84214E-02 1.08830E-03 1.63232E-03 2.72062E-03 8.50094E-04 0.042485
5 4 50.0 45.0 135.0 4.09432E-02 1.06745E-03 1.70057E-03 2.76803E-03 8.33809E-04 0.041535
5 7 50.0 90.0 90.0 5.44237E-02 1.04221E-03 2.19852E-03 3.24073E-03 8.14091E-04 0.040396
4 1 60.0 0.0 180.0 4.56068E-02 1.07232E-03 3.80254E-03 4.87486E-03 8.37607E-04 0.083377
4 4 60.0 45.0 135.0 4.66390E-02 1.04919E-03 3.75494E-03 4.80413E-03 8.19540E-04 0.080511
4 7 60.0 90.0 90.0 5.75930E-02 1.03700E-03 4.38492E-03 5.42192E-03 8.10023E-04 0.076136
3 1 70.0 0.0 180.0 6.32798E-02 9.94368E-04 1.05036E-02 1.14980E-02 7.76719E-04 0.165987
3 4 70.0 45.0 135.0 6.14987E-02 9.82760E-04 1.01064E-02 1.10892E-02 7.67652E-04 0.164336
3 7 70.0 90.0 90.0 6.87541E-02 9.72947E-04 1.09903E-02 1.19632E-02 7.59987E-04 0.159849
2 1 80.0 0.0 180.0 1.07513E-01 8.51309E-04 2.61089E-02 2.69602E-02 6.64973E-04 0.242843
2 4 80.0 45.0 135.0 9.95552E-02 8.38871E-04 2.52527E-02 2.60916E-02 6.55258E-04 0.253655
2 7 80.0 90.0 90.0 9.89089E-02 8.32646E-04 2.64465E-02 2.72791E-02 6.50395E-04 0.267382
1 1 87.5 0.0 180.0 1.73829E-01 6.85620E-04 4.60466E-02 4.67323E-02 5.35550E-04 0.264896
1 4 87.5 45.0 135.0 1.56512E-01 6.43176E-04 4.57624E-02 4.64055E-02 5.02397E-04 0.292389
1 7 87.5 90.0 90.0 1.42391E-01 7.08612E-04 4.68348E-02 4.75434E-02 5.53509E-04 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 8.134E-03 9.187E-02 1.103E-01 9.497E-02 1.426E-01 6.354E-03 5.593E+00 1.010E-03 7.886E-04
1 0.00 0.00 1.874E-03 1.709E-01 3.808E-03 4.487E-03 7.234E-03 1.508E-03 4.006E+00
3 2.25 5.00 8.715E-04 1.909E-01 1.984E-03 2.786E-03 5.595E-03 1.937E-03 4.313E+00
5 5.11 10.00 4.003E-04 1.092E-01 1.054E-03 1.558E-03 3.094E-03 2.620E-03 4.702E+00
7 9.07 15.00 1.530E-04 4.114E-02 5.427E-04 8.037E-04 1.453E-03 3.232E-03 5.138E+00
9 13.24 20.00 4.971E-05 1.257E-02 1.812E-04 2.467E-04 3.794E-04 3.556E-03 4.621E+00
11 16.09 25.00 2.176E-05 4.240E-03 4.475E-05 5.283E-05 6.739E-05 4.909E-03 3.600E+00
Waveband 20 of 30 completed in 5.7 sec.
* * * * * Output for wavelength band 21 (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 68.2 m at 605.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 600.0 nm to 610.0 nm:
Ed(diffuse) = 3.465E-01 Ed(direct) = 9.677E-01 Ed(total) = 1.314E+00
Absorption Coefficients of Individual Components at 605.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.2577 0.0048 0.0000 0.0007 0.2631
3 2.697 5.000 0.2577 0.0063 0.0000 0.0008 0.2648
5 6.003 10.000 0.2577 0.0097 0.0000 0.0012 0.2686
7 10.402 15.000 0.2577 0.0154 0.0000 0.0017 0.2747
9 15.025 20.000 0.2577 0.0117 0.0000 0.0013 0.2707
11 18.314 25.000 0.2577 0.0040 0.0000 0.0006 0.2623
Scattering Coefficients of Individual Components at 605.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0013 0.1169 0.1208 0.0000 0.2390
3 2.697 5.000 0.0013 0.1427 0.1671 0.0000 0.3110
5 6.003 10.000 0.0013 0.1943 0.2790 0.0000 0.4746
7 10.402 15.000 0.0013 0.2634 0.4710 0.0000 0.7356
9 15.025 20.000 0.0013 0.2200 0.3442 0.0000 0.5654
11 18.314 25.000 0.0013 0.1022 0.0972 0.0000 0.2007
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00063 0.00164 0.00021 0.00000 0.00249
3 2.697 5.000 0.00063 0.00200 0.00029 0.00000 0.00293
5 6.003 10.000 0.00063 0.00272 0.00049 0.00000 0.00385
7 10.402 15.000 0.00063 0.00369 0.00083 0.00000 0.00516
9 15.025 20.000 0.00063 0.00308 0.00061 0.00000 0.00432
11 18.314 25.000 0.00063 0.00143 0.00017 0.00000 0.00224
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 0.2631 0.2390 0.5021 0.4759 0.00249 0.01040
3 2.697 5.000 0.2648 0.3110 0.5758 0.5401 0.00293 0.00942
5 6.003 10.000 0.2686 0.4746 0.7432 0.6386 0.00385 0.00811
7 10.402 15.000 0.2747 0.7356 1.0103 0.7281 0.00516 0.00701
9 15.025 20.000 0.2707 0.5654 0.8362 0.6762 0.00432 0.00765
11 18.314 25.000 0.2623 0.2007 0.4630 0.4335 0.00224 0.01115
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.3606E-01
8 20.00 5.2180E-01
7 30.00 2.5588E-01
6 40.00 1.0668E-01
5 50.00 4.1324E-02
4 60.00 1.6218E-02
3 70.00 6.8986E-03
2 80.00 3.3132E-03
1 87.50 2.0641E-03
1 92.50 1.5520E-03
2 100.00 1.1052E-03
3 110.00 7.8088E-04
4 120.00 6.1270E-04
5 130.00 5.2376E-04
6 140.00 4.7585E-04
7 150.00 4.4996E-04
8 160.00 4.3628E-04
9 170.00 4.2967E-04
10 180.00 4.2723E-04
Asymptotic AOP values are
MUu(inf) = 0.3826
MUd(inf) = 0.8758
MU(inf) = 0.8668
R(inf) = 0.0032
Lu(inf)/Ed(inf) = 0.000744 (1/sr)
k(inf) = 0.3026 (1/m)
absorp(check) = 0.2623 = 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 1.2517E-01 1.8183E+00 1.9435E+00 4.5308E-02 1.3142E+00 0.3620 0.7228 0.6529 3.4475E-02
1 0.00 0.00 1.1660E-02 1.4211E+00 1.4327E+00 4.7352E-03 1.2736E+00 0.4061 0.8963 0.8857 3.7179E-03
3 2.70 5.00 3.7675E-03 3.2192E-01 3.2569E-01 1.4860E-03 2.7854E-01 0.3944 0.8652 0.8507 5.3351E-03
5 6.00 10.00 1.3204E-03 6.7942E-02 6.9262E-02 5.2173E-04 5.7004E-02 0.3951 0.8390 0.8155 9.1525E-03
7 10.40 15.00 4.6329E-04 1.3257E-02 1.3721E-02 1.8542E-04 1.0684E-02 0.4002 0.8059 0.7652 1.7354E-02
9 15.02 20.00 1.4900E-04 2.4642E-03 2.6132E-03 6.6240E-05 1.9434E-03 0.4446 0.7887 0.7184 3.4084E-02
11 18.31 25.00 7.0669E-05 5.1824E-04 5.8891E-04 3.4442E-05 4.0289E-04 0.4874 0.7774 0.6257 8.5487E-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 0.19971 0.28428 0.28359 0.22554 0.29664 0.29690 0.24619
5.000 5.010 5.005 0.20649 0.30473 0.30359 0.21009 0.30988 0.31041 0.21803
10.000 10.010 10.005 0.19650 0.31825 0.31593 0.19620 0.32478 0.32597 0.19945
15.000 15.010 15.005 0.25361 0.33607 0.33329 0.23919 0.34465 0.34652 0.21170
20.000 20.010 20.005 0.19176 0.33021 0.32231 0.16928 0.33337 0.33916 0.14110
25.000 25.010 25.005 0.07974 0.28831 0.26326 0.07482 0.29188 0.31220 0.07098
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 9.34977E-02 6.38689E-04 7.30842E-03 7.94711E-03 4.85986E-04 0.078167
9 1 10.0 0.0 180.0 5.76919E-02 6.55616E-04 2.12073E-03 2.77634E-03 4.98866E-04 0.036759
9 4 10.0 45.0 135.0 6.33879E-02 6.50159E-04 2.46570E-03 3.11585E-03 4.94713E-04 0.038899
9 7 10.0 90.0 90.0 8.56423E-02 6.42576E-04 5.23868E-03 5.88125E-03 4.88943E-04 0.061169
8 1 20.0 0.0 180.0 4.53162E-02 6.64581E-04 1.10897E-03 1.77355E-03 5.05687E-04 0.024472
8 4 20.0 45.0 135.0 5.04491E-02 6.53255E-04 1.31003E-03 1.96328E-03 4.97069E-04 0.025967
8 7 20.0 90.0 90.0 7.41831E-02 6.42358E-04 3.03091E-03 3.67327E-03 4.88777E-04 0.040857
7 1 30.0 0.0 180.0 3.92916E-02 6.75720E-04 9.45837E-04 1.62156E-03 5.14163E-04 0.024072
7 4 30.0 45.0 135.0 4.35639E-02 6.68113E-04 1.06278E-03 1.73090E-03 5.08374E-04 0.024396
7 7 30.0 90.0 90.0 6.35124E-02 6.50291E-04 1.85225E-03 2.50254E-03 4.94814E-04 0.029164
6 1 40.0 0.0 180.0 3.72952E-02 6.81806E-04 1.05165E-03 1.73346E-03 5.18794E-04 0.028198
6 4 40.0 45.0 135.0 4.07803E-02 6.71595E-04 1.14059E-03 1.81218E-03 5.11024E-04 0.027969
6 7 40.0 90.0 90.0 5.72548E-02 6.51176E-04 1.65374E-03 2.30492E-03 4.95487E-04 0.028884
5 1 50.0 0.0 180.0 3.91027E-02 6.90356E-04 1.66126E-03 2.35162E-03 5.25300E-04 0.042485
5 4 50.0 45.0 135.0 4.16692E-02 6.75242E-04 1.73073E-03 2.40597E-03 5.13799E-04 0.041535
5 7 50.0 90.0 90.0 5.53888E-02 6.54402E-04 2.23751E-03 2.89191E-03 4.97942E-04 0.040396
4 1 60.0 0.0 180.0 4.64156E-02 6.79921E-04 3.86997E-03 4.54989E-03 5.17359E-04 0.083377
4 4 60.0 45.0 135.0 4.74660E-02 6.63162E-04 3.82152E-03 4.48469E-03 5.04607E-04 0.080511
4 7 60.0 90.0 90.0 5.86143E-02 6.49965E-04 4.46267E-03 5.11264E-03 4.94566E-04 0.076136
3 1 70.0 0.0 180.0 6.44019E-02 6.30297E-04 1.06899E-02 1.13202E-02 4.79600E-04 0.165987
3 4 70.0 45.0 135.0 6.25893E-02 6.20819E-04 1.02857E-02 1.09065E-02 4.72388E-04 0.164336
3 7 70.0 90.0 90.0 6.99733E-02 6.08986E-04 1.11852E-02 1.17941E-02 4.63384E-04 0.159849
2 1 80.0 0.0 180.0 1.09420E-01 5.39569E-04 2.65719E-02 2.71114E-02 4.10564E-04 0.242843
2 4 80.0 45.0 135.0 1.01321E-01 5.29779E-04 2.57005E-02 2.62303E-02 4.03115E-04 0.253655
2 7 80.0 90.0 90.0 1.00663E-01 5.20751E-04 2.69154E-02 2.74362E-02 3.96245E-04 0.267382
1 1 87.5 0.0 180.0 1.76912E-01 4.34686E-04 4.68632E-02 4.72979E-02 3.30758E-04 0.264896
1 4 87.5 45.0 135.0 1.59287E-01 4.06282E-04 4.65739E-02 4.69801E-02 3.09145E-04 0.292389
1 7 87.5 90.0 90.0 1.44916E-01 4.43185E-04 4.76653E-02 4.81085E-02 3.37225E-04 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 7.947E-03 9.350E-02 1.121E-01 9.651E-02 1.450E-01 6.047E-03 5.701E+00 6.387E-04 4.860E-04
1 0.00 0.00 1.185E-03 1.739E-01 2.554E-03 3.023E-03 4.976E-03 9.307E-04 3.995E+00
3 2.70 5.00 3.592E-04 1.227E-01 7.990E-04 1.119E-03 2.252E-03 1.289E-03 4.138E+00
5 6.00 10.00 1.246E-04 4.388E-02 2.805E-04 3.978E-04 7.553E-04 2.185E-03 4.188E+00
7 10.40 15.00 4.539E-05 1.024E-02 1.063E-04 1.427E-04 2.324E-04 4.248E-03 4.085E+00
9 15.02 20.00 1.879E-05 1.941E-03 3.259E-05 3.764E-05 4.772E-05 9.668E-03 3.526E+00
11 18.31 25.00 1.084E-05 4.174E-04 1.269E-05 1.301E-05 1.356E-05 2.691E-02 3.177E+00
Waveband 21 of 30 completed in 6.6 sec.
* * * * * Output for wavelength band 22 (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 67.4 m at 615.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 610.0 nm to 620.0 nm:
Ed(diffuse) = 3.356E-01 Ed(direct) = 9.479E-01 Ed(total) = 1.284E+00
Absorption Coefficients of Individual Components at 615.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.2678 0.0049 0.0000 0.0006 0.2733
3 2.742 5.000 0.2678 0.0065 0.0000 0.0007 0.2750
5 6.093 10.000 0.2678 0.0102 0.0000 0.0010 0.2790
7 10.543 15.000 0.2678 0.0163 0.0000 0.0014 0.2855
9 15.217 20.000 0.2678 0.0123 0.0000 0.0012 0.2812
11 18.553 25.000 0.2678 0.0041 0.0000 0.0005 0.2724
Scattering Coefficients of Individual Components at 615.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0012 0.1163 0.1202 0.0000 0.2377
3 2.742 5.000 0.0012 0.1421 0.1665 0.0000 0.3098
5 6.093 10.000 0.0012 0.1940 0.2785 0.0000 0.4737
7 10.543 15.000 0.0012 0.2634 0.4710 0.0000 0.7355
9 15.217 20.000 0.0012 0.2197 0.3439 0.0000 0.5648
11 18.553 25.000 0.0012 0.1016 0.0967 0.0000 0.1995
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00059 0.00163 0.00021 0.00000 0.00243
3 2.742 5.000 0.00059 0.00199 0.00029 0.00000 0.00288
5 6.093 10.000 0.00059 0.00272 0.00049 0.00000 0.00380
7 10.543 15.000 0.00059 0.00369 0.00083 0.00000 0.00511
9 15.217 20.000 0.00059 0.00308 0.00061 0.00000 0.00428
11 18.553 25.000 0.00059 0.00143 0.00017 0.00000 0.00219
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 0.2733 0.2377 0.5110 0.4652 0.00243 0.01024
3 2.742 5.000 0.2750 0.3098 0.5848 0.5297 0.00288 0.00929
5 6.093 10.000 0.2790 0.4737 0.7527 0.6293 0.00380 0.00802
7 10.543 15.000 0.2855 0.7355 1.0211 0.7204 0.00511 0.00695
9 15.217 20.000 0.2812 0.5648 0.8460 0.6676 0.00428 0.00757
11 18.553 25.000 0.2724 0.1995 0.4719 0.4228 0.00219 0.01096
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.3187E-01
8 20.00 5.1266E-01
7 30.00 2.4713E-01
6 40.00 1.0120E-01
5 50.00 3.8602E-02
4 60.00 1.4988E-02
3 70.00 6.3389E-03
2 80.00 3.0364E-03
1 87.50 1.8898E-03
1 92.50 1.4208E-03
2 100.00 1.0112E-03
3 110.00 7.1393E-04
4 120.00 5.5997E-04
5 130.00 4.7862E-04
6 140.00 4.3481E-04
7 150.00 4.1112E-04
8 160.00 3.9861E-04
9 170.00 3.9256E-04
10 180.00 3.9033E-04
Asymptotic AOP values are
MUu(inf) = 0.3824
MUd(inf) = 0.8786
MU(inf) = 0.8701
R(inf) = 0.0030
Lu(inf)/Ed(inf) = 0.000696 (1/sr)
k(inf) = 0.3131 (1/m)
absorp(check) = 0.2724 = 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 1.2134E-01 1.7735E+00 1.8948E+00 4.4016E-02 1.2835E+00 0.3628 0.7237 0.6542 3.4293E-02
1 0.00 0.00 1.0713E-02 1.3872E+00 1.3979E+00 4.3342E-03 1.2439E+00 0.4046 0.8967 0.8867 3.4845E-03
3 2.74 5.00 3.2721E-03 2.9682E-01 3.0010E-01 1.2871E-03 2.5722E-01 0.3934 0.8666 0.8528 5.0038E-03
5 6.09 10.00 1.0918E-03 5.9133E-02 6.0225E-02 4.3131E-04 4.9732E-02 0.3951 0.8410 0.8186 8.6726E-03
7 10.54 15.00 3.7031E-04 1.0873E-02 1.1243E-02 1.4896E-04 8.7887E-03 0.4022 0.8083 0.7685 1.6948E-02
9 15.22 20.00 1.1796E-04 1.9095E-03 2.0275E-03 5.2774E-05 1.5095E-03 0.4474 0.7905 0.7185 3.4962E-02
11 18.55 25.00 5.5334E-05 3.8443E-04 4.3976E-04 2.6992E-05 2.9842E-04 0.4878 0.7763 0.6172 9.0449E-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 0.21011 0.29557 0.29492 0.23625 0.30775 0.30800 0.25699
5.000 5.010 5.005 0.21670 0.31615 0.31506 0.22004 0.32112 0.32162 0.22746
10.000 10.010 10.005 0.20492 0.32992 0.32765 0.20384 0.33629 0.33745 0.20585
15.000 15.010 15.005 0.25839 0.34808 0.34512 0.24278 0.35660 0.35857 0.21445
20.000 20.010 20.005 0.19229 0.34059 0.33196 0.17068 0.34415 0.35044 0.14405
25.000 25.010 25.005 0.08403 0.29519 0.26859 0.07951 0.29990 0.32185 0.07591
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 9.05701E-02 5.82122E-04 7.13293E-03 7.71505E-03 4.53528E-04 0.078756
9 1 10.0 0.0 180.0 5.58855E-02 5.97512E-04 2.06148E-03 2.65900E-03 4.65519E-04 0.036888
9 4 10.0 45.0 135.0 6.14030E-02 5.92557E-04 2.39771E-03 2.99026E-03 4.61658E-04 0.039049
9 7 10.0 90.0 90.0 8.29606E-02 5.85700E-04 5.10766E-03 5.69336E-03 4.56316E-04 0.061567
8 1 20.0 0.0 180.0 4.38973E-02 6.05719E-04 1.07461E-03 1.68033E-03 4.71913E-04 0.024480
8 4 20.0 45.0 135.0 4.88695E-02 5.95418E-04 1.26995E-03 1.86536E-03 4.63887E-04 0.025986
8 7 20.0 90.0 90.0 7.18602E-02 5.85578E-04 2.94856E-03 3.53414E-03 4.56221E-04 0.041032
7 1 30.0 0.0 180.0 3.80613E-02 6.15932E-04 9.16221E-04 1.53215E-03 4.79870E-04 0.024072
7 4 30.0 45.0 135.0 4.22001E-02 6.09027E-04 1.02955E-03 1.63858E-03 4.74490E-04 0.024397
7 7 30.0 90.0 90.0 6.15220E-02 5.92917E-04 1.79672E-03 2.38964E-03 4.61938E-04 0.029205
6 1 40.0 0.0 180.0 3.61274E-02 6.21588E-04 1.01872E-03 1.64031E-03 4.84276E-04 0.028198
6 4 40.0 45.0 135.0 3.95033E-02 6.12340E-04 1.10487E-03 1.71721E-03 4.77071E-04 0.027969
6 7 40.0 90.0 90.0 5.54621E-02 5.93925E-04 1.60212E-03 2.19604E-03 4.62724E-04 0.028887
5 1 50.0 0.0 180.0 3.78783E-02 6.29525E-04 1.60924E-03 2.23877E-03 4.90459E-04 0.042485
5 4 50.0 45.0 135.0 4.03645E-02 6.15829E-04 1.67654E-03 2.29236E-03 4.79789E-04 0.041535
5 7 50.0 90.0 90.0 5.36544E-02 5.97103E-04 2.16745E-03 2.76455E-03 4.65200E-04 0.040396
4 1 60.0 0.0 180.0 4.49622E-02 6.20170E-04 3.74879E-03 4.36896E-03 4.83171E-04 0.083377
4 4 60.0 45.0 135.0 4.59797E-02 6.04994E-04 3.70186E-03 4.30686E-03 4.71348E-04 0.080511
4 7 60.0 90.0 90.0 5.67789E-02 5.93313E-04 4.32294E-03 4.91625E-03 4.62247E-04 0.076136
3 1 70.0 0.0 180.0 6.23854E-02 5.75107E-04 1.03552E-02 1.09303E-02 4.48063E-04 0.165987
3 4 70.0 45.0 135.0 6.06294E-02 5.66593E-04 9.96359E-03 1.05302E-02 4.41430E-04 0.164336
3 7 70.0 90.0 90.0 6.77823E-02 5.56222E-04 1.08349E-02 1.13912E-02 4.33350E-04 0.159849
2 1 80.0 0.0 180.0 1.05994E-01 4.92501E-04 2.57399E-02 2.62324E-02 3.83705E-04 0.242843
2 4 80.0 45.0 135.0 9.81480E-02 4.83708E-04 2.48958E-02 2.53795E-02 3.76855E-04 0.253655
2 7 80.0 90.0 90.0 9.75109E-02 4.75901E-04 2.60726E-02 2.65485E-02 3.70772E-04 0.267382
1 1 87.5 0.0 180.0 1.71372E-01 3.96931E-04 4.53958E-02 4.57927E-02 3.09247E-04 0.264896
1 4 87.5 45.0 135.0 1.54300E-01 3.71122E-04 4.51155E-02 4.54866E-02 2.89140E-04 0.292389
1 7 87.5 90.0 90.0 1.40379E-01 4.05271E-04 4.61728E-02 4.65780E-02 3.15745E-04 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 7.715E-03 9.057E-02 1.086E-01 9.348E-02 1.404E-01 6.011E-03 5.705E+00 5.821E-04 4.535E-04
1 0.00 0.00 1.080E-03 1.685E-01 2.356E-03 2.800E-03 4.641E-03 8.686E-04 4.012E+00
3 2.74 5.00 3.104E-04 1.133E-01 6.952E-04 9.780E-04 1.979E-03 1.207E-03 4.147E+00
5 6.09 10.00 1.032E-04 3.852E-02 2.321E-04 3.298E-04 6.273E-04 2.076E-03 4.178E+00
7 10.54 15.00 3.678E-05 8.512E-03 8.468E-05 1.132E-04 1.835E-04 4.185E-03 4.050E+00
9 15.22 20.00 1.506E-05 1.526E-03 2.550E-05 2.921E-05 3.659E-05 9.980E-03 3.503E+00
11 18.55 25.00 8.503E-06 3.119E-04 9.907E-06 1.013E-05 1.051E-05 2.849E-02 3.174E+00
Waveband 22 of 30 completed in 6.8 sec.
* * * * * Output for wavelength band 23 (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 66.1 m at 625.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 620.0 nm to 630.0 nm:
Ed(diffuse) = 3.296E-01 Ed(direct) = 9.406E-01 Ed(total) = 1.270E+00
Absorption Coefficients of Individual Components at 625.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.2834 0.0050 0.0000 0.0005 0.2889
3 2.814 5.000 0.2834 0.0067 0.0000 0.0006 0.2907
5 6.239 10.000 0.2834 0.0106 0.0000 0.0009 0.2948
7 10.766 15.000 0.2834 0.0169 0.0000 0.0012 0.3016
9 15.519 20.000 0.2834 0.0128 0.0000 0.0010 0.2972
11 18.928 25.000 0.2834 0.0042 0.0000 0.0004 0.2880
Scattering Coefficients of Individual Components at 625.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0011 0.1158 0.1196 0.0000 0.2365
3 2.814 5.000 0.0011 0.1416 0.1658 0.0000 0.3086
5 6.239 10.000 0.0011 0.1936 0.2780 0.0000 0.4727
7 10.766 15.000 0.0011 0.2634 0.4710 0.0000 0.7355
9 15.519 20.000 0.0011 0.2195 0.3435 0.0000 0.5641
11 18.928 25.000 0.0011 0.1011 0.0961 0.0000 0.1983
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00055 0.00162 0.00021 0.00000 0.00238
3 2.814 5.000 0.00055 0.00199 0.00029 0.00000 0.00283
5 6.239 10.000 0.00055 0.00271 0.00049 0.00000 0.00376
7 10.766 15.000 0.00055 0.00369 0.00083 0.00000 0.00507
9 15.519 20.000 0.00055 0.00308 0.00060 0.00000 0.00423
11 18.928 25.000 0.00055 0.00142 0.00017 0.00000 0.00214
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 0.2889 0.2365 0.5254 0.4501 0.00238 0.01008
3 2.814 5.000 0.2907 0.3086 0.5993 0.5149 0.00283 0.00917
5 6.239 10.000 0.2948 0.4727 0.7676 0.6159 0.00376 0.00794
7 10.766 15.000 0.3016 0.7355 1.0371 0.7092 0.00507 0.00690
9 15.519 20.000 0.2972 0.5641 0.8613 0.6550 0.00423 0.00750
11 18.928 25.000 0.2880 0.1983 0.4863 0.4078 0.00214 0.01078
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.2577E-01
8 20.00 4.9961E-01
7 30.00 2.3495E-01
6 40.00 9.3793E-02
5 50.00 3.5017E-02
4 60.00 1.3404E-02
3 70.00 5.6298E-03
2 80.00 2.6905E-03
1 87.50 1.6739E-03
1 92.50 1.2592E-03
2 100.00 8.9640E-04
3 110.00 6.3307E-04
4 120.00 4.9691E-04
5 130.00 4.2505E-04
6 140.00 3.8637E-04
7 150.00 3.6548E-04
8 160.00 3.5445E-04
9 170.00 3.4912E-04
10 180.00 3.4716E-04
Asymptotic AOP values are
MUu(inf) = 0.3827
MUd(inf) = 0.8824
MU(inf) = 0.8746
R(inf) = 0.0027
Lu(inf)/Ed(inf) = 0.000640 (1/sr)
k(inf) = 0.3293 (1/m)
absorp(check) = 0.2880 = 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 1.1918E-01 1.7529E+00 1.8721E+00 4.3310E-02 1.2702E+00 0.3634 0.7246 0.6554 3.4098E-02
1 0.00 0.00 9.7966E-03 1.3720E+00 1.3818E+00 3.9472E-03 1.2308E+00 0.4029 0.8971 0.8879 3.2070E-03
3 2.81 5.00 2.7459E-03 2.6877E-01 2.7151E-01 1.0783E-03 2.3337E-01 0.3927 0.8683 0.8556 4.6203E-03
5 6.24 10.00 8.5490E-04 4.9012E-02 4.9867E-02 3.3902E-04 4.1352E-02 0.3966 0.8437 0.8224 8.1983E-03
7 10.77 15.00 2.7973E-04 8.2499E-03 8.5296E-03 1.1406E-04 6.6935E-03 0.4078 0.8113 0.7714 1.7040E-02
9 15.52 20.00 9.0256E-05 1.3362E-03 1.4265E-03 4.0931E-05 1.0577E-03 0.4535 0.7916 0.7128 3.8697E-02
11 18.93 25.00 4.2575E-05 2.5506E-04 2.9764E-04 2.0822E-05 1.9633E-04 0.4891 0.7697 0.5897 1.0605E-01
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 0.22670 0.31307 0.31246 0.25297 0.32500 0.32524 0.27360
5.000 5.010 5.005 0.23207 0.33378 0.33275 0.23473 0.33849 0.33897 0.24098
10.000 10.010 10.005 0.21602 0.34764 0.34538 0.21339 0.35381 0.35497 0.21294
15.000 15.010 15.005 0.26058 0.36554 0.36210 0.24302 0.37413 0.37641 0.21372
20.000 20.010 20.005 0.18749 0.35484 0.34425 0.16791 0.35945 0.36717 0.14441
25.000 25.010 25.005 0.08787 0.30167 0.27106 0.08414 0.30926 0.33600 0.08105
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 8.89363E-02 5.28083E-04 7.05417E-03 7.58226E-03 4.15752E-04 0.079317
9 1 10.0 0.0 180.0 5.48773E-02 5.42053E-04 2.03100E-03 2.57305E-03 4.26750E-04 0.037010
9 4 10.0 45.0 135.0 6.02954E-02 5.37559E-04 2.36307E-03 2.90063E-03 4.23212E-04 0.039192
9 7 10.0 90.0 90.0 8.14640E-02 5.31351E-04 5.04640E-03 5.57775E-03 4.18325E-04 0.061946
8 1 20.0 0.0 180.0 4.31054E-02 5.49546E-04 1.05556E-03 1.60511E-03 4.32650E-04 0.024488
8 4 20.0 45.0 135.0 4.79879E-02 5.40194E-04 1.24791E-03 1.78811E-03 4.25287E-04 0.026005
8 7 20.0 90.0 90.0 7.05639E-02 5.31288E-04 2.90711E-03 3.43840E-03 4.18275E-04 0.041198
7 1 30.0 0.0 180.0 3.73747E-02 5.58874E-04 8.99692E-04 1.45857E-03 4.39994E-04 0.024072
7 4 30.0 45.0 135.0 4.14391E-02 5.52599E-04 1.01102E-03 1.56362E-03 4.35053E-04 0.024398
7 7 30.0 90.0 90.0 6.04106E-02 5.38015E-04 1.76662E-03 2.30464E-03 4.23572E-04 0.029244
6 1 40.0 0.0 180.0 3.54756E-02 5.64098E-04 1.00035E-03 1.56444E-03 4.44106E-04 0.028198
6 4 40.0 45.0 135.0 3.87907E-02 5.55713E-04 1.08494E-03 1.64066E-03 4.37505E-04 0.027969
6 7 40.0 90.0 90.0 5.44616E-02 5.39064E-04 1.57337E-03 2.11243E-03 4.24397E-04 0.028890
5 1 50.0 0.0 180.0 3.71950E-02 5.71416E-04 1.58021E-03 2.15163E-03 4.49867E-04 0.042485
5 4 50.0 45.0 135.0 3.96363E-02 5.59007E-04 1.64629E-03 2.20530E-03 4.40098E-04 0.041535
5 7 50.0 90.0 90.0 5.26865E-02 5.42114E-04 2.12835E-03 2.67046E-03 4.26799E-04 0.040396
4 1 60.0 0.0 180.0 4.41511E-02 5.63055E-04 3.68117E-03 4.24422E-03 4.43285E-04 0.083377
4 4 60.0 45.0 135.0 4.51503E-02 5.49314E-04 3.63508E-03 4.18440E-03 4.32467E-04 0.080511
4 7 60.0 90.0 90.0 5.57547E-02 5.38862E-04 4.24495E-03 4.78382E-03 4.24238E-04 0.076136
3 1 70.0 0.0 180.0 6.12600E-02 5.22307E-04 1.01684E-02 1.06907E-02 4.11204E-04 0.165987
3 4 70.0 45.0 135.0 5.95357E-02 5.14630E-04 9.78385E-03 1.02985E-02 4.05160E-04 0.164336
3 7 70.0 90.0 90.0 6.65595E-02 5.05417E-04 1.06395E-02 1.11449E-02 3.97907E-04 0.159849
2 1 80.0 0.0 180.0 1.04082E-01 4.47432E-04 2.52755E-02 2.57229E-02 3.52257E-04 0.242843
2 4 80.0 45.0 135.0 9.63775E-02 4.39512E-04 2.44467E-02 2.48862E-02 3.46021E-04 0.253655
2 7 80.0 90.0 90.0 9.57518E-02 4.32642E-04 2.56023E-02 2.60350E-02 3.40613E-04 0.267382
1 1 87.5 0.0 180.0 1.68281E-01 3.60748E-04 4.45769E-02 4.49376E-02 2.84011E-04 0.264896
1 4 87.5 45.0 135.0 1.51516E-01 3.37358E-04 4.43017E-02 4.46390E-02 2.65597E-04 0.292389
1 7 87.5 90.0 90.0 1.37846E-01 3.68644E-04 4.53398E-02 4.57085E-02 2.90228E-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 7.582E-03 8.894E-02 1.066E-01 9.178E-02 1.379E-01 5.969E-03 5.712E+00 5.281E-04 4.158E-04
1 0.00 0.00 9.801E-04 1.654E-01 2.168E-03 2.587E-03 4.317E-03 7.963E-04 4.027E+00
3 2.81 5.00 2.601E-04 1.031E-01 5.845E-04 8.252E-04 1.677E-03 1.114E-03 4.146E+00
5 6.24 10.00 8.194E-05 3.236E-02 1.816E-04 2.574E-04 4.882E-04 1.982E-03 4.137E+00
7 10.77 15.00 2.877E-05 6.581E-03 6.321E-05 8.343E-05 1.332E-04 4.298E-03 3.965E+00
9 15.52 20.00 1.185E-05 1.085E-03 1.901E-05 2.138E-05 2.610E-05 1.120E-02 3.454E+00
11 18.93 25.00 6.580E-06 2.059E-04 7.558E-06 7.683E-06 7.901E-06 3.351E-02 3.165E+00
Waveband 23 of 30 completed in 6.9 sec.
* * * * * Output for wavelength band 24 (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 64.8 m at 635.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 630.0 nm to 640.0 nm:
Ed(diffuse) = 3.233E-01 Ed(direct) = 9.320E-01 Ed(total) = 1.255E+00
Absorption Coefficients of Individual Components at 635.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3012 0.0053 0.0000 0.0004 0.3070
3 2.898 5.000 0.3012 0.0071 0.0000 0.0005 0.3088
5 6.409 10.000 0.3012 0.0111 0.0000 0.0008 0.3131
7 11.025 15.000 0.3012 0.0179 0.0000 0.0011 0.3201
9 15.869 20.000 0.3012 0.0134 0.0000 0.0009 0.3155
11 19.364 25.000 0.3012 0.0044 0.0000 0.0004 0.3060
Scattering Coefficients of Individual Components at 635.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0010 0.1152 0.1191 0.0000 0.2353
3 2.898 5.000 0.0010 0.1411 0.1653 0.0000 0.3074
5 6.409 10.000 0.0010 0.1933 0.2775 0.0000 0.4718
7 11.025 15.000 0.0010 0.2634 0.4710 0.0000 0.7354
9 15.869 20.000 0.0010 0.2193 0.3432 0.0000 0.5635
11 19.364 25.000 0.0010 0.1005 0.0956 0.0000 0.1971
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00051 0.00162 0.00021 0.00000 0.00234
3 2.898 5.000 0.00051 0.00198 0.00029 0.00000 0.00278
5 6.409 10.000 0.00051 0.00271 0.00049 0.00000 0.00371
7 11.025 15.000 0.00051 0.00369 0.00083 0.00000 0.00504
9 15.869 20.000 0.00051 0.00307 0.00060 0.00000 0.00419
11 19.364 25.000 0.00051 0.00141 0.00017 0.00000 0.00209
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 0.3070 0.2353 0.5423 0.4339 0.00234 0.00994
3 2.898 5.000 0.3088 0.3074 0.6162 0.4989 0.00278 0.00906
5 6.409 10.000 0.3131 0.4718 0.7850 0.6011 0.00371 0.00787
7 11.025 15.000 0.3201 0.7354 1.0555 0.6967 0.00504 0.00685
9 15.869 20.000 0.3155 0.5635 0.8790 0.6411 0.00419 0.00744
11 19.364 25.000 0.3060 0.1971 0.5031 0.3918 0.00209 0.01061
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.1896E-01
8 20.00 4.8538E-01
7 30.00 2.2210E-01
6 40.00 8.6229E-02
5 50.00 3.1467E-02
4 60.00 1.1872E-02
3 70.00 4.9539E-03
2 80.00 2.3633E-03
1 87.50 1.4704E-03
1 92.50 1.1071E-03
2 100.00 7.8849E-04
3 110.00 5.5722E-04
4 120.00 4.3783E-04
5 130.00 3.7489E-04
6 140.00 3.4105E-04
7 150.00 3.2278E-04
8 160.00 3.1315E-04
9 170.00 3.0850E-04
10 180.00 3.0678E-04
Asymptotic AOP values are
MUu(inf) = 0.3832
MUd(inf) = 0.8864
MU(inf) = 0.8792
R(inf) = 0.0025
Lu(inf)/Ed(inf) = 0.000587 (1/sr)
k(inf) = 0.3481 (1/m)
absorp(check) = 0.3060 = 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 1.1694E-01 1.7302E+00 1.8471E+00 4.2571E-02 1.2552E+00 0.3640 0.7255 0.6565 3.3914E-02
1 0.00 0.00 8.9236E-03 1.3551E+00 1.3640E+00 3.5823E-03 1.2162E+00 0.4014 0.8976 0.8891 2.9454E-03
3 2.90 5.00 2.2769E-03 2.3984E-01 2.4212E-01 8.9471E-04 2.0869E-01 0.3929 0.8701 0.8583 4.2872E-03
5 6.41 10.00 6.6492E-04 3.9519E-02 4.0184E-02 2.6650E-04 3.3450E-02 0.4008 0.8464 0.8258 7.9673E-03
7 11.03 15.00 2.1615E-04 6.0204E-03 6.2366E-03 9.0460E-05 4.8996E-03 0.4185 0.8138 0.7711 1.8463E-02
9 15.87 20.00 7.5229E-05 8.9793E-04 9.7315E-04 3.4876E-05 7.0855E-04 0.4636 0.7891 0.6923 4.9222E-02
11 19.36 25.00 3.7683E-05 1.6793E-04 2.0561E-04 1.8527E-05 1.2597E-04 0.4917 0.7501 0.5225 1.4708E-01
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 0.24570 0.33323 0.33266 0.27178 0.34488 0.34509 0.29191
5.000 5.010 5.005 0.24814 0.35404 0.35305 0.24953 0.35849 0.35896 0.25356
10.000 10.010 10.005 0.22442 0.36789 0.36551 0.21915 0.37390 0.37514 0.21464
15.000 15.010 15.005 0.25164 0.38475 0.38013 0.23167 0.39373 0.39678 0.20179
20.000 20.010 20.005 0.16972 0.36712 0.35184 0.15356 0.37423 0.38566 0.13472
25.000 25.010 25.005 0.08599 0.29626 0.25769 0.08333 0.31024 0.34942 0.08098
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 8.72379E-02 4.77871E-04 6.96686E-03 7.44473E-03 3.80701E-04 0.079860
9 1 10.0 0.0 180.0 5.38294E-02 4.90493E-04 1.99857E-03 2.48907E-03 3.90757E-04 0.037128
9 4 10.0 45.0 135.0 5.91439E-02 4.86433E-04 2.32614E-03 2.81257E-03 3.87522E-04 0.039330
9 7 10.0 90.0 90.0 7.99084E-02 4.80837E-04 4.97936E-03 5.46019E-03 3.83065E-04 0.062313
8 1 20.0 0.0 180.0 4.22822E-02 4.97286E-04 1.03573E-03 1.53301E-03 3.96168E-04 0.024496
8 4 20.0 45.0 135.0 4.70715E-02 4.88826E-04 1.22492E-03 1.71374E-03 3.89429E-04 0.026022
8 7 20.0 90.0 90.0 6.92164E-02 4.80802E-04 2.86275E-03 3.34355E-03 3.83036E-04 0.041359
7 1 30.0 0.0 180.0 3.66610E-02 5.05746E-04 8.82511E-04 1.38826E-03 4.02908E-04 0.024072
7 4 30.0 45.0 135.0 4.06480E-02 5.00069E-04 9.91754E-04 1.49182E-03 3.98386E-04 0.024399
7 7 30.0 90.0 90.0 5.92555E-02 4.86922E-04 1.73508E-03 2.22200E-03 3.87912E-04 0.029281
6 1 40.0 0.0 180.0 3.47982E-02 5.10500E-04 9.81243E-04 1.49174E-03 4.06696E-04 0.028198
6 4 40.0 45.0 135.0 3.80500E-02 5.02932E-04 1.06422E-03 1.56716E-03 4.00667E-04 0.027969
6 7 40.0 90.0 90.0 5.34215E-02 4.87937E-04 1.54346E-03 2.03140E-03 3.88721E-04 0.028892
5 1 50.0 0.0 180.0 3.64847E-02 5.17175E-04 1.55004E-03 2.06721E-03 4.12013E-04 0.042485
5 4 50.0 45.0 135.0 3.88794E-02 5.05976E-04 1.61485E-03 2.12083E-03 4.03091E-04 0.041535
5 7 50.0 90.0 90.0 5.16804E-02 4.90790E-04 2.08770E-03 2.57849E-03 3.90994E-04 0.040396
4 1 60.0 0.0 180.0 4.33080E-02 5.09673E-04 3.61087E-03 4.12054E-03 4.06037E-04 0.083377
4 4 60.0 45.0 135.0 4.42881E-02 4.97278E-04 3.56567E-03 4.06294E-03 3.96162E-04 0.080511
4 7 60.0 90.0 90.0 5.46900E-02 4.87953E-04 4.16389E-03 4.65184E-03 3.88733E-04 0.076136
3 1 70.0 0.0 180.0 6.00901E-02 4.72883E-04 9.97418E-03 1.04471E-02 3.76727E-04 0.165987
3 4 70.0 45.0 135.0 5.83988E-02 4.65988E-04 9.59701E-03 1.00630E-02 3.71235E-04 0.164336
3 7 70.0 90.0 90.0 6.52885E-02 4.57815E-04 1.04363E-02 1.08941E-02 3.64723E-04 0.159849
2 1 80.0 0.0 180.0 1.02094E-01 4.05184E-04 2.47928E-02 2.51980E-02 3.22794E-04 0.242843
2 4 80.0 45.0 135.0 9.45370E-02 3.98074E-04 2.39798E-02 2.43779E-02 3.17130E-04 0.253655
2 7 80.0 90.0 90.0 9.39233E-02 3.92027E-04 2.51134E-02 2.55054E-02 3.12313E-04 0.267382
1 1 87.5 0.0 180.0 1.65067E-01 3.26776E-04 4.37256E-02 4.40524E-02 2.60330E-04 0.264896
1 4 87.5 45.0 135.0 1.48623E-01 3.05648E-04 4.34557E-02 4.37613E-02 2.43498E-04 0.292389
1 7 87.5 90.0 90.0 1.35214E-01 3.34176E-04 4.44740E-02 4.48082E-02 2.66225E-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 7.445E-03 8.724E-02 1.046E-01 9.001E-02 1.352E-01 5.931E-03 5.718E+00 4.779E-04 3.807E-04
1 0.00 0.00 8.869E-04 1.623E-01 1.989E-03 2.381E-03 3.998E-03 7.292E-04 4.039E+00
3 2.90 5.00 2.168E-04 9.255E-02 4.846E-04 6.852E-04 1.396E-03 1.039E-03 4.127E+00
5 6.41 10.00 6.576E-05 2.648E-02 1.403E-04 1.971E-04 3.700E-04 1.966E-03 4.053E+00
7 11.03 15.00 2.370E-05 4.894E-03 4.748E-05 6.115E-05 9.471E-05 4.837E-03 3.817E+00
9 15.87 20.00 1.035E-05 7.346E-04 1.510E-05 1.653E-05 1.936E-05 1.460E-02 3.370E+00
11 19.36 25.00 5.896E-06 1.292E-04 6.567E-06 6.634E-06 6.750E-06 4.680E-02 3.142E+00
Waveband 24 of 30 completed in 7.0 sec.
* * * * * Output for wavelength band 25 (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 63.0 m at 645.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 640.0 nm to 650.0 nm:
Ed(diffuse) = 3.112E-01 Ed(direct) = 9.056E-01 Ed(total) = 1.217E+00
Absorption Coefficients of Individual Components at 645.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3250 0.0056 0.0000 0.0004 0.3310
3 3.013 5.000 0.3250 0.0074 0.0000 0.0005 0.3329
5 6.639 10.000 0.3250 0.0116 0.0000 0.0007 0.3372
7 11.373 15.000 0.3250 0.0183 0.0000 0.0009 0.3443
9 16.336 20.000 0.3250 0.0139 0.0000 0.0008 0.3397
11 19.947 25.000 0.3250 0.0047 0.0000 0.0003 0.3300
Scattering Coefficients of Individual Components at 645.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0010 0.1147 0.1185 0.0000 0.2342
3 3.013 5.000 0.0010 0.1406 0.1647 0.0000 0.3062
5 6.639 10.000 0.0010 0.1930 0.2770 0.0000 0.4710
7 11.373 15.000 0.0010 0.2634 0.4710 0.0000 0.7353
9 16.336 20.000 0.0010 0.2191 0.3429 0.0000 0.5629
11 19.947 25.000 0.0010 0.1000 0.0951 0.0000 0.1960
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00048 0.00161 0.00021 0.00000 0.00230
3 3.013 5.000 0.00048 0.00197 0.00029 0.00000 0.00274
5 6.639 10.000 0.00048 0.00271 0.00049 0.00000 0.00367
7 11.373 15.000 0.00048 0.00369 0.00083 0.00000 0.00500
9 16.336 20.000 0.00048 0.00307 0.00060 0.00000 0.00416
11 19.947 25.000 0.00048 0.00140 0.00017 0.00000 0.00205
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 0.3310 0.2342 0.5652 0.4143 0.00230 0.00981
3 3.013 5.000 0.3329 0.3062 0.6391 0.4792 0.00274 0.00895
5 6.639 10.000 0.3372 0.4710 0.8082 0.5827 0.00367 0.00780
7 11.373 15.000 0.3443 0.7353 1.0796 0.6811 0.00500 0.00680
9 16.336 20.000 0.3397 0.5629 0.9026 0.6237 0.00416 0.00738
11 19.947 25.000 0.3300 0.1960 0.5260 0.3726 0.00205 0.01046
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 8.1023E-01
8 20.00 4.6767E-01
7 30.00 2.0671E-01
6 40.00 7.7531E-02
5 50.00 2.7526E-02
4 60.00 1.0214E-02
3 70.00 4.2344E-03
2 80.00 2.0182E-03
1 87.50 1.2566E-03
1 92.50 9.4744E-04
2 100.00 6.7557E-04
3 110.00 4.7812E-04
4 120.00 3.7639E-04
5 130.00 3.2283E-04
6 140.00 2.9407E-04
7 150.00 2.7855E-04
8 160.00 2.7039E-04
9 170.00 2.6646E-04
10 180.00 2.6501E-04
Asymptotic AOP values are
MUu(inf) = 0.3840
MUd(inf) = 0.8911
MU(inf) = 0.8846
R(inf) = 0.0022
Lu(inf)/Ed(inf) = 0.000530 (1/sr)
k(inf) = 0.3731 (1/m)
absorp(check) = 0.3300 = 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 1.1257E-01 1.6753E+00 1.7879E+00 4.1043E-02 1.2168E+00 0.3646 0.7263 0.6576 3.3731E-02
1 0.00 0.00 7.8661E-03 1.3128E+00 1.3206E+00 3.1467E-03 1.1789E+00 0.4000 0.8980 0.8903 2.6693E-03
3 3.01 5.00 1.7777E-03 2.0298E-01 2.0476E-01 7.0098E-04 1.7705E-01 0.3943 0.8723 0.8613 3.9592E-03
5 6.64 10.00 4.8549E-04 2.9253E-02 2.9739E-02 1.9838E-04 2.4852E-02 0.4086 0.8495 0.8290 7.9825E-03
7 11.37 15.00 1.6195E-04 3.9234E-03 4.0853E-03 7.0292E-05 3.2003E-03 0.4340 0.8157 0.7662 2.1964E-02
9 16.34 20.00 6.2727E-05 5.3438E-04 5.9711E-04 2.9730E-05 4.1706E-04 0.4740 0.7805 0.6487 7.1285E-02
11 19.95 25.00 3.3203E-05 1.0236E-04 1.3557E-04 1.6407E-05 7.3048E-05 0.4941 0.7136 0.4178 2.2461E-01
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 0.27132 0.36017 0.35964 0.29679 0.37144 0.37164 0.31601
5.000 5.010 5.005 0.26797 0.38096 0.37998 0.26724 0.38510 0.38557 0.26775
10.000 10.010 10.005 0.23016 0.39439 0.39171 0.22100 0.40029 0.40173 0.21119
15.000 15.010 15.005 0.23303 0.40826 0.40131 0.21213 0.41822 0.42285 0.18445
20.000 20.010 20.005 0.15066 0.37685 0.35307 0.13915 0.38902 0.40823 0.12568
25.000 25.010 25.005 0.08427 0.27659 0.22945 0.08250 0.29955 0.36252 0.08078
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 8.39766E-02 4.18855E-04 6.74946E-03 7.16832E-03 3.44236E-04 0.080373
9 1 10.0 0.0 180.0 5.18170E-02 4.29901E-04 1.92964E-03 2.35954E-03 3.53314E-04 0.037240
9 4 10.0 45.0 135.0 5.69329E-02 4.26346E-04 2.24661E-03 2.67296E-03 3.50393E-04 0.039461
9 7 10.0 90.0 90.0 7.69211E-02 4.21455E-04 4.81985E-03 5.24130E-03 3.46373E-04 0.062660
8 1 20.0 0.0 180.0 4.07016E-02 4.35855E-04 9.97302E-04 1.43316E-03 3.58208E-04 0.024503
8 4 20.0 45.0 135.0 4.53118E-02 4.28439E-04 1.17988E-03 1.60832E-03 3.52112E-04 0.026039
8 7 20.0 90.0 90.0 6.66288E-02 4.21424E-04 2.76586E-03 3.18729E-03 3.46347E-04 0.041511
7 1 30.0 0.0 180.0 3.52904E-02 4.43272E-04 8.49519E-04 1.29279E-03 3.64303E-04 0.024072
7 4 30.0 45.0 135.0 3.91286E-02 4.38292E-04 9.54715E-04 1.39301E-03 3.60210E-04 0.024399
7 7 30.0 90.0 90.0 5.70390E-02 4.26792E-04 1.67221E-03 2.09900E-03 3.50759E-04 0.029317
6 1 40.0 0.0 180.0 3.34973E-02 4.47433E-04 9.44560E-04 1.39199E-03 3.67723E-04 0.028198
6 4 40.0 45.0 135.0 3.66275E-02 4.40808E-04 1.02444E-03 1.46525E-03 3.62278E-04 0.027969
6 7 40.0 90.0 90.0 5.14244E-02 4.27696E-04 1.48589E-03 1.91359E-03 3.51502E-04 0.028895
5 1 50.0 0.0 180.0 3.51208E-02 4.53298E-04 1.49209E-03 1.94539E-03 3.72543E-04 0.042485
5 4 50.0 45.0 135.0 3.74260E-02 4.43497E-04 1.55448E-03 1.99798E-03 3.64488E-04 0.041535
5 7 50.0 90.0 90.0 4.97484E-02 4.30230E-04 2.00966E-03 2.43989E-03 3.53584E-04 0.040396
4 1 60.0 0.0 180.0 4.16889E-02 4.46748E-04 3.47588E-03 3.92263E-03 3.67160E-04 0.083377
4 4 60.0 45.0 135.0 4.26324E-02 4.35904E-04 3.43237E-03 3.86827E-03 3.58248E-04 0.080511
4 7 60.0 90.0 90.0 5.26455E-02 4.27787E-04 4.00823E-03 4.43602E-03 3.51577E-04 0.076136
3 1 70.0 0.0 180.0 5.78437E-02 4.14550E-04 9.60131E-03 1.00159E-02 3.40698E-04 0.165987
3 4 70.0 45.0 135.0 5.62156E-02 4.08534E-04 9.23824E-03 9.64678E-03 3.35753E-04 0.164336
3 7 70.0 90.0 90.0 6.28478E-02 4.01438E-04 1.00462E-02 1.04476E-02 3.29922E-04 0.159849
2 1 80.0 0.0 180.0 9.82774E-02 3.55254E-04 2.38660E-02 2.42213E-02 2.91966E-04 0.242843
2 4 80.0 45.0 135.0 9.10029E-02 3.49054E-04 2.30834E-02 2.34324E-02 2.86870E-04 0.253655
2 7 80.0 90.0 90.0 9.04121E-02 3.43825E-04 2.41746E-02 2.45184E-02 2.82573E-04 0.267382
1 1 87.5 0.0 180.0 1.58896E-01 2.86568E-04 4.20910E-02 4.23776E-02 2.35516E-04 0.264896
1 4 87.5 45.0 135.0 1.43067E-01 2.68072E-04 4.18311E-02 4.20992E-02 2.20315E-04 0.292389
1 7 87.5 90.0 90.0 1.30159E-01 2.93173E-04 4.28114E-02 4.31046E-02 2.40944E-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 7.168E-03 8.398E-02 1.006E-01 8.663E-02 1.302E-01 5.891E-03 5.726E+00 4.189E-04 3.442E-04
1 0.00 0.00 7.774E-04 1.562E-01 1.770E-03 2.126E-03 3.590E-03 6.594E-04 4.048E+00
3 3.01 5.00 1.714E-04 7.901E-02 3.775E-04 5.336E-04 1.086E-03 9.682E-04 4.089E+00
5 6.64 10.00 5.059E-05 1.998E-02 1.009E-04 1.394E-04 2.560E-04 2.036E-03 3.921E+00
7 11.37 15.00 1.932E-05 3.257E-03 3.405E-05 4.211E-05 6.182E-05 6.036E-03 3.639E+00
9 16.34 20.00 9.032E-06 4.340E-04 1.195E-05 1.268E-05 1.410E-05 2.166E-02 3.291E+00
11 19.95 25.00 5.258E-06 7.024E-05 5.685E-06 5.714E-06 5.764E-06 7.198E-02 3.120E+00
Waveband 25 of 30 completed in 7.1 sec.
* * * * * Output for wavelength band 26 (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 60.0 m at 655.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 650.0 nm to 660.0 nm:
Ed(diffuse) = 2.955E-01 Ed(direct) = 8.677E-01 Ed(total) = 1.163E+00
Absorption Coefficients of Individual Components at 655.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.3710 0.0064 0.0000 0.0003 0.3778
3 3.241 5.000 0.3710 0.0085 0.0000 0.0004 0.3799
5 7.098 10.000 0.3710 0.0131 0.0000 0.0006 0.3847
7 12.070 15.000 0.3710 0.0207 0.0000 0.0008 0.3925
9 17.272 20.000 0.3710 0.0157 0.0000 0.0007 0.3874
11 21.114 25.000 0.3710 0.0054 0.0000 0.0003 0.3766
Scattering Coefficients of Individual Components at 655.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0009 0.1142 0.1179 0.0000 0.2330
3 3.241 5.000 0.0009 0.1401 0.1641 0.0000 0.3051
5 7.098 10.000 0.0009 0.1926 0.2766 0.0000 0.4701
7 12.070 15.000 0.0009 0.2634 0.4710 0.0000 0.7353
9 17.272 20.000 0.0009 0.2189 0.3425 0.0000 0.5623
11 21.114 25.000 0.0009 0.0994 0.0946 0.0000 0.1949
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00045 0.00160 0.00021 0.00000 0.00226
3 3.241 5.000 0.00045 0.00196 0.00029 0.00000 0.00270
5 7.098 10.000 0.00045 0.00270 0.00049 0.00000 0.00364
7 12.070 15.000 0.00045 0.00369 0.00083 0.00000 0.00497
9 17.272 20.000 0.00045 0.00307 0.00060 0.00000 0.00412
11 21.114 25.000 0.00045 0.00139 0.00017 0.00000 0.00201
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 0.3778 0.2330 0.6108 0.3815 0.00226 0.00969
3 3.241 5.000 0.3799 0.3051 0.6850 0.4454 0.00270 0.00886
5 7.098 10.000 0.3847 0.4701 0.8548 0.5500 0.00364 0.00774
7 12.070 15.000 0.3925 0.7353 1.1278 0.6520 0.00497 0.00676
9 17.272 20.000 0.3874 0.5623 0.9497 0.5921 0.00412 0.00733
11 21.114 25.000 0.3766 0.1949 0.5715 0.3410 0.00201 0.01032
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 7.9446E-01
8 20.00 4.3707E-01
7 30.00 1.8167E-01
6 40.00 6.4205E-02
5 50.00 2.1789E-02
4 60.00 7.8876E-03
3 70.00 3.2458E-03
2 80.00 1.5489E-03
1 87.50 9.6707E-04
1 92.50 7.3155E-04
2 100.00 5.2330E-04
3 110.00 3.7191E-04
4 120.00 2.9414E-04
5 130.00 2.5330E-04
6 140.00 2.3142E-04
7 150.00 2.1967E-04
8 160.00 2.1352E-04
9 170.00 2.1057E-04
10 180.00 2.0948E-04
Asymptotic AOP values are
MUu(inf) = 0.3861
MUd(inf) = 0.8988
MU(inf) = 0.8932
R(inf) = 0.0019
Lu(inf)/Ed(inf) = 0.000453 (1/sr)
k(inf) = 0.4217 (1/m)
absorp(check) = 0.3767 = 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 1.0680E-01 1.5999E+00 1.7067E+00 3.8985E-02 1.1632E+00 0.3650 0.7271 0.6587 3.3514E-02
1 0.00 0.00 6.4935E-03 1.2541E+00 1.2606E+00 2.5901E-03 1.1268E+00 0.3989 0.8985 0.8919 2.2985E-03
3 3.24 5.00 1.1905E-03 1.4910E-01 1.5029E-01 4.7769E-04 1.3056E-01 0.4013 0.8757 0.8656 3.6587E-03
5 7.10 10.00 3.2003E-04 1.6581E-02 1.6901E-02 1.3866E-04 1.4155E-02 0.4333 0.8537 0.8293 9.7955E-03
7 12.07 15.00 1.3034E-04 1.7728E-03 1.9031E-03 6.0218E-05 1.4356E-03 0.4620 0.8098 0.7227 4.1947E-02
9 17.27 20.00 5.7644E-05 2.2809E-04 2.8574E-04 2.7740E-05 1.6674E-04 0.4812 0.7310 0.4865 1.6636E-01
11 21.11 25.00 2.9039E-05 5.4505E-05 8.3544E-05 1.4402E-05 3.4265E-05 0.4959 0.6287 0.2378 4.2030E-01
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 0.32134 0.41262 0.41215 0.34407 0.42320 0.42338 0.36050
5.000 5.010 5.005 0.29534 0.43327 0.43218 0.28793 0.43692 0.43747 0.27878
10.000 10.010 10.005 0.20843 0.44507 0.44058 0.19198 0.45132 0.45389 0.17587
15.000 15.010 15.005 0.18941 0.44287 0.42549 0.17639 0.45903 0.47143 0.16171
20.000 20.010 20.005 0.14737 0.35649 0.31427 0.14321 0.38594 0.43445 0.13622
25.000 25.010 25.005 0.08390 0.22604 0.17661 0.08263 0.25014 0.37177 0.08140
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 7.97432E-02 3.44973E-04 6.44902E-03 6.79399E-03 2.96561E-04 0.080872
9 1 10.0 0.0 180.0 4.92048E-02 3.54038E-04 1.83771E-03 2.19175E-03 3.04354E-04 0.037348
9 4 10.0 45.0 135.0 5.40628E-02 3.51114E-04 2.14023E-03 2.49135E-03 3.01841E-04 0.039588
9 7 10.0 90.0 90.0 7.30434E-02 3.47093E-04 4.60150E-03 4.94859E-03 2.98384E-04 0.062997
8 1 20.0 0.0 180.0 3.86497E-02 3.58904E-04 9.47296E-04 1.30620E-03 3.08537E-04 0.024510
8 4 20.0 45.0 135.0 4.30276E-02 3.52796E-04 1.12110E-03 1.47390E-03 3.03287E-04 0.026055
8 7 20.0 90.0 90.0 6.32700E-02 3.47024E-04 2.63580E-03 2.98282E-03 2.98325E-04 0.041660
7 1 30.0 0.0 180.0 3.35114E-02 3.64965E-04 8.06694E-04 1.17166E-03 3.13747E-04 0.024072
7 4 30.0 45.0 135.0 3.71563E-02 3.60859E-04 9.06620E-04 1.26748E-03 3.10218E-04 0.024400
7 7 30.0 90.0 90.0 5.41623E-02 3.51385E-04 1.58975E-03 1.94114E-03 3.02074E-04 0.029352
6 1 40.0 0.0 180.0 3.18087E-02 3.68300E-04 8.96943E-04 1.26524E-03 3.16615E-04 0.028198
6 4 40.0 45.0 135.0 3.47811E-02 3.62850E-04 9.72797E-04 1.33565E-03 3.11930E-04 0.027969
6 7 40.0 90.0 90.0 4.88321E-02 3.52027E-04 1.41111E-03 1.76313E-03 3.02625E-04 0.028897
5 1 50.0 0.0 180.0 3.33503E-02 3.73056E-04 1.41687E-03 1.78993E-03 3.20704E-04 0.042485
5 4 50.0 45.0 135.0 3.55393E-02 3.64991E-04 1.47612E-03 1.84111E-03 3.13770E-04 0.041535
5 7 50.0 90.0 90.0 4.72405E-02 3.54012E-04 1.90835E-03 2.26236E-03 3.04331E-04 0.040396
4 1 60.0 0.0 180.0 3.95873E-02 3.67599E-04 3.30066E-03 3.66826E-03 3.16012E-04 0.083377
4 4 60.0 45.0 135.0 4.04833E-02 3.58672E-04 3.25934E-03 3.61801E-03 3.08337E-04 0.080511
4 7 60.0 90.0 90.0 4.99915E-02 3.51900E-04 3.80617E-03 4.15807E-03 3.02516E-04 0.076136
3 1 70.0 0.0 180.0 5.49277E-02 3.41052E-04 9.11729E-03 9.45835E-03 2.93190E-04 0.165987
3 4 70.0 45.0 135.0 5.33817E-02 3.36091E-04 8.77253E-03 9.10862E-03 2.88926E-04 0.164336
3 7 70.0 90.0 90.0 5.96795E-02 3.30125E-04 9.53971E-03 9.86983E-03 2.83797E-04 0.159849
2 1 80.0 0.0 180.0 9.33230E-02 2.92236E-04 2.26629E-02 2.29551E-02 2.51225E-04 0.242843
2 4 80.0 45.0 135.0 8.64153E-02 2.87121E-04 2.19197E-02 2.22068E-02 2.46828E-04 0.253655
2 7 80.0 90.0 90.0 8.58543E-02 2.82677E-04 2.29559E-02 2.32386E-02 2.43007E-04 0.267382
1 1 87.5 0.0 180.0 1.50886E-01 2.35722E-04 3.99691E-02 4.02049E-02 2.02642E-04 0.264896
1 4 87.5 45.0 135.0 1.35854E-01 2.20494E-04 3.97224E-02 3.99429E-02 1.89551E-04 0.292389
1 7 87.5 90.0 90.0 1.23598E-01 2.40991E-04 4.06532E-02 4.08942E-02 2.07171E-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 6.794E-03 7.974E-02 9.555E-02 8.225E-02 1.236E-01 5.841E-03 5.738E+00 3.450E-04 2.966E-04
1 0.00 0.00 6.403E-04 1.483E-01 1.486E-03 1.789E-03 3.037E-03 5.682E-04 4.045E+00
3 3.24 5.00 1.205E-04 5.917E-02 2.493E-04 3.482E-04 6.981E-04 9.229E-04 3.964E+00
5 7.10 10.00 3.829E-05 1.172E-02 6.293E-05 8.141E-05 1.371E-04 2.705E-03 3.622E+00
7 12.07 15.00 1.760E-05 1.495E-03 2.509E-05 2.803E-05 3.515E-05 1.226E-02 3.422E+00
9 17.27 20.00 8.474E-06 1.624E-04 1.054E-05 1.074E-05 1.112E-05 5.082E-02 3.274E+00
11 21.11 25.00 4.630E-06 2.506E-05 4.909E-06 4.915E-06 4.924E-06 1.351E-01 3.110E+00
Waveband 26 of 30 completed in 7.6 sec.
* * * * * Output for wavelength band 27 (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 56.7 m at 665.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 660.0 nm to 670.0 nm:
Ed(diffuse) = 3.058E-01 Ed(direct) = 9.058E-01 Ed(total) = 1.212E+00
Absorption Coefficients of Individual Components at 665.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.4290 0.0094 0.0000 0.0003 0.4387
3 3.543 5.000 0.4290 0.0124 0.0000 0.0004 0.4418
5 7.710 10.000 0.4290 0.0193 0.0000 0.0005 0.4488
7 13.010 15.000 0.4290 0.0306 0.0000 0.0007 0.4604
9 18.544 20.000 0.4290 0.0232 0.0000 0.0006 0.4528
11 22.696 25.000 0.4290 0.0078 0.0000 0.0002 0.4371
Scattering Coefficients of Individual Components at 665.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0008 0.1136 0.1174 0.0000 0.2319
3 3.543 5.000 0.0008 0.1396 0.1635 0.0000 0.3040
5 7.710 10.000 0.0008 0.1923 0.2761 0.0000 0.4693
7 13.010 15.000 0.0008 0.2634 0.4710 0.0000 0.7352
9 18.544 20.000 0.0008 0.2187 0.3422 0.0000 0.5617
11 22.696 25.000 0.0008 0.0989 0.0941 0.0000 0.1938
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00042 0.00159 0.00021 0.00000 0.00222
3 3.543 5.000 0.00042 0.00196 0.00029 0.00000 0.00267
5 7.710 10.000 0.00042 0.00270 0.00049 0.00000 0.00360
7 13.010 15.000 0.00042 0.00369 0.00083 0.00000 0.00494
9 18.544 20.000 0.00042 0.00307 0.00060 0.00000 0.00409
11 22.696 25.000 0.00042 0.00139 0.00017 0.00000 0.00197
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 0.4387 0.2319 0.6706 0.3458 0.00222 0.00958
3 3.543 5.000 0.4418 0.3040 0.7458 0.4076 0.00267 0.00877
5 7.710 10.000 0.4488 0.4693 0.9181 0.5111 0.00360 0.00768
7 13.010 15.000 0.4604 0.7352 1.1956 0.6149 0.00494 0.00672
9 18.544 20.000 0.4528 0.5617 1.0145 0.5537 0.00409 0.00728
11 22.696 25.000 0.4371 0.1938 0.6309 0.3072 0.00197 0.01018
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 7.7522E-01
8 20.00 4.0215E-01
7 30.00 1.5541E-01
6 40.00 5.1332E-02
5 50.00 1.6605E-02
4 60.00 5.8737E-03
3 70.00 2.4070E-03
2 80.00 1.1527E-03
1 87.50 7.2242E-04
1 92.50 5.4850E-04
2 100.00 3.9380E-04
3 110.00 2.8123E-04
4 120.00 2.2359E-04
5 130.00 1.9339E-04
6 140.00 1.7725E-04
7 150.00 1.6862E-04
8 160.00 1.6413E-04
9 170.00 1.6199E-04
10 180.00 1.6119E-04
Asymptotic AOP values are
MUu(inf) = 0.3885
MUd(inf) = 0.9068
MU(inf) = 0.9021
R(inf) = 0.0016
Lu(inf)/Ed(inf) = 0.000381 (1/sr)
k(inf) = 0.4846 (1/m)
absorp(check) = 0.4371 = 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 1.1059E-01 1.6647E+00 1.7753E+00 4.0441E-02 1.2116E+00 0.3657 0.7278 0.6597 3.3379E-02
1 0.00 0.00 6.0915E-03 1.3055E+00 1.3116E+00 2.4547E-03 1.1736E+00 0.4030 0.8989 0.8929 2.0916E-03
3 3.54 5.00 1.1077E-03 1.1039E-01 1.1150E-01 4.8153E-04 9.6977E-02 0.4347 0.8785 0.8654 4.9654E-03
5 7.71 10.00 5.1617E-04 8.9991E-03 9.5153E-03 2.4774E-04 7.6075E-03 0.4800 0.8454 0.7735 3.2566E-02
7 13.01 15.00 3.3824E-04 9.9233E-04 1.3306E-03 1.6111E-04 7.0236E-04 0.4763 0.7078 0.4068 2.2938E-01
9 18.54 20.00 1.4116E-04 2.4325E-04 3.8441E-04 6.6625E-05 1.4111E-04 0.4720 0.5801 0.1938 4.7216E-01
11 22.70 25.00 4.5673E-05 7.5393E-05 1.2107E-04 2.2473E-05 4.2996E-05 0.4920 0.5703 0.1695 5.2267E-01
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 0.36971 0.48100 0.48048 0.38213 0.49062 0.49085 0.38768
5.000 5.010 5.005 0.23422 0.50052 0.49787 0.21034 0.50423 0.50570 0.18528
10.000 10.010 10.005 0.07968 0.49458 0.47203 0.07166 0.50881 0.52356 0.06975
15.000 15.010 15.005 0.16575 0.34633 0.30039 0.16677 0.40540 0.47654 0.16752
20.000 20.010 20.005 0.20466 0.22044 0.21465 0.20774 0.24334 0.27520 0.20955
25.000 25.010 25.005 0.08341 0.27751 0.20424 0.08102 0.26542 0.46772 0.07981
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 8.25261E-02 3.32596E-04 6.71350E-03 7.04609E-03 2.74515E-04 0.081350
9 1 10.0 0.0 180.0 5.09220E-02 3.40748E-04 1.90713E-03 2.24788E-03 2.81243E-04 0.037452
9 4 10.0 45.0 135.0 5.59495E-02 3.38100E-04 2.22173E-03 2.55983E-03 2.79057E-04 0.039710
9 7 10.0 90.0 90.0 7.55925E-02 3.34591E-04 4.78647E-03 5.12106E-03 2.76161E-04 0.063319
8 1 20.0 0.0 180.0 3.99985E-02 3.44971E-04 9.80623E-04 1.32559E-03 2.84728E-04 0.024516
8 4 20.0 45.0 135.0 4.45291E-02 3.39383E-04 1.16092E-03 1.50030E-03 2.80116E-04 0.026071
8 7 20.0 90.0 90.0 6.54780E-02 3.34398E-04 2.73706E-03 3.07146E-03 2.76001E-04 0.041801
7 1 30.0 0.0 180.0 3.46809E-02 3.50329E-04 8.34846E-04 1.18517E-03 2.89150E-04 0.024072
7 4 30.0 45.0 135.0 3.84532E-02 3.46777E-04 9.38293E-04 1.28507E-03 2.86219E-04 0.024401
7 7 30.0 90.0 90.0 5.60512E-02 3.38406E-04 1.64706E-03 1.98546E-03 2.79310E-04 0.029385
6 1 40.0 0.0 180.0 3.29187E-02 3.52923E-04 9.28245E-04 1.28117E-03 2.91292E-04 0.028198
6 4 40.0 45.0 135.0 3.59949E-02 3.48176E-04 1.00675E-03 1.35492E-03 2.87373E-04 0.027969
6 7 40.0 90.0 90.0 5.05362E-02 3.38615E-04 1.46047E-03 1.79909E-03 2.79482E-04 0.028900
5 1 50.0 0.0 180.0 3.45142E-02 3.56946E-04 1.46632E-03 1.82327E-03 2.94612E-04 0.042485
5 4 50.0 45.0 135.0 3.67795E-02 3.49733E-04 1.52763E-03 1.87737E-03 2.88658E-04 0.041535
5 7 50.0 90.0 90.0 4.88891E-02 3.39976E-04 1.97495E-03 2.31492E-03 2.80605E-04 0.040396
4 1 60.0 0.0 180.0 4.09689E-02 3.51187E-04 3.41585E-03 3.76703E-03 2.89859E-04 0.083377
4 4 60.0 45.0 135.0 4.18961E-02 3.43161E-04 3.37308E-03 3.71624E-03 2.83234E-04 0.080511
4 7 60.0 90.0 90.0 5.17361E-02 3.37316E-04 3.93900E-03 4.27631E-03 2.78410E-04 0.076136
3 1 70.0 0.0 180.0 5.68446E-02 3.25259E-04 9.43547E-03 9.76073E-03 2.68458E-04 0.165987
3 4 70.0 45.0 135.0 5.52447E-02 3.20962E-04 9.07867E-03 9.39964E-03 2.64912E-04 0.164336
3 7 70.0 90.0 90.0 6.17622E-02 3.15608E-04 9.87263E-03 1.01882E-02 2.60493E-04 0.159849
2 1 80.0 0.0 180.0 9.65799E-02 2.78235E-04 2.34538E-02 2.37320E-02 2.29646E-04 0.242843
2 4 80.0 45.0 135.0 8.94310E-02 2.73686E-04 2.26847E-02 2.29584E-02 2.25891E-04 0.253655
2 7 80.0 90.0 90.0 8.88505E-02 2.69534E-04 2.37570E-02 2.40265E-02 2.22465E-04 0.267382
1 1 87.5 0.0 180.0 1.56152E-01 2.24031E-04 4.13640E-02 4.15880E-02 1.84908E-04 0.264896
1 4 87.5 45.0 135.0 1.40596E-01 2.09766E-04 4.11086E-02 4.13184E-02 1.73134E-04 0.292389
1 7 87.5 90.0 90.0 1.27911E-01 2.29100E-04 4.20720E-02 4.23011E-02 1.89091E-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 7.046E-03 8.253E-02 9.887E-02 8.511E-02 1.279E-01 5.816E-03 5.739E+00 3.326E-04 2.745E-04
1 0.00 0.00 6.173E-04 1.535E-01 1.410E-03 1.689E-03 2.829E-03 5.260E-04 3.976E+00
3 3.54 5.00 1.342E-04 4.484E-02 2.136E-04 2.751E-04 4.925E-04 1.384E-03 3.588E+00
5 7.71 10.00 7.535E-05 6.455E-03 8.846E-05 9.640E-05 1.201E-04 9.905E-03 3.288E+00
7 13.01 15.00 4.707E-05 6.330E-04 6.182E-05 6.268E-05 6.473E-05 6.702E-02 3.423E+00
9 18.54 20.00 1.915E-05 7.908E-05 2.685E-05 2.689E-05 2.696E-05 1.357E-01 3.479E+00
11 22.70 25.00 7.033E-06 1.944E-05 7.886E-06 7.887E-06 7.888E-06 1.636E-01 3.195E+00
Waveband 27 of 30 completed in 7.9 sec.
* * * * * Output for wavelength band 28 (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 55.7 m at 675.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 670.0 nm to 680.0 nm:
Ed(diffuse) = 2.985E-01 Ed(direct) = 8.912E-01 Ed(total) = 1.190E+00
Absorption Coefficients of Individual Components at 675.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.4480 0.0116 0.0000 0.0002 0.4599
3 3.645 5.000 0.4480 0.0153 0.0000 0.0003 0.4636
5 7.920 10.000 0.4480 0.0238 0.0000 0.0004 0.4722
7 13.342 15.000 0.4480 0.0377 0.0000 0.0006 0.4863
9 18.999 20.000 0.4480 0.0286 0.0000 0.0005 0.4771
11 23.260 25.000 0.4480 0.0097 0.0000 0.0002 0.4579
Scattering Coefficients of Individual Components at 675.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0008 0.1131 0.1169 0.0000 0.2308
3 3.645 5.000 0.0008 0.1392 0.1630 0.0000 0.3029
5 7.920 10.000 0.0008 0.1920 0.2756 0.0000 0.4684
7 13.342 15.000 0.0008 0.2634 0.4710 0.0000 0.7352
9 18.999 20.000 0.0008 0.2185 0.3419 0.0000 0.5612
11 23.260 25.000 0.0008 0.0984 0.0936 0.0000 0.1928
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00040 0.00159 0.00021 0.00000 0.00219
3 3.645 5.000 0.00040 0.00195 0.00029 0.00000 0.00263
5 7.920 10.000 0.00040 0.00269 0.00049 0.00000 0.00357
7 13.342 15.000 0.00040 0.00369 0.00083 0.00000 0.00492
9 18.999 20.000 0.00040 0.00306 0.00060 0.00000 0.00406
11 23.260 25.000 0.00040 0.00138 0.00016 0.00000 0.00194
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 0.4599 0.2308 0.6907 0.3342 0.00219 0.00947
3 3.645 5.000 0.4636 0.3029 0.7665 0.3952 0.00263 0.00869
5 7.920 10.000 0.4722 0.4684 0.9407 0.4980 0.00357 0.00763
7 13.342 15.000 0.4863 0.7352 1.2215 0.6019 0.00492 0.00669
9 18.999 20.000 0.4771 0.5612 1.0382 0.5405 0.00406 0.00723
11 23.260 25.000 0.4579 0.1928 0.6506 0.2963 0.00194 0.01006
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 7.6837E-01
8 20.00 3.9034E-01
7 30.00 1.4705E-01
6 40.00 4.7473E-02
5 50.00 1.5119E-02
4 60.00 5.3103E-03
3 70.00 2.1735E-03
2 80.00 1.0415E-03
1 87.50 6.5307E-04
1 92.50 4.9612E-04
2 100.00 3.5626E-04
3 110.00 2.5448E-04
4 120.00 2.0241E-04
5 130.00 1.7514E-04
6 140.00 1.6056E-04
7 150.00 1.5275E-04
8 160.00 1.4869E-04
9 170.00 1.4676E-04
10 180.00 1.4604E-04
Asymptotic AOP values are
MUu(inf) = 0.3886
MUd(inf) = 0.9094
MU(inf) = 0.9050
R(inf) = 0.0015
Lu(inf)/Ed(inf) = 0.000356 (1/sr)
k(inf) = 0.5060 (1/m)
absorp(check) = 0.4579 = 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 1.0867E-01 1.6330E+00 1.7417E+00 3.9919E-02 1.1896E+00 0.3673 0.7285 0.6601 3.3555E-02
1 0.00 0.00 7.0378E-03 1.2826E+00 1.2896E+00 2.9527E-03 1.1527E+00 0.4196 0.8987 0.8915 2.5616E-03
3 3.65 5.00 2.0819E-03 9.7339E-02 9.9421E-02 9.8079E-04 8.5199E-02 0.4711 0.8753 0.8471 1.1512E-02
5 7.92 10.00 1.5269E-03 8.0871E-03 9.6140E-03 7.5187E-04 6.4504E-03 0.4924 0.7976 0.5927 1.1656E-01
7 13.34 15.00 1.1338E-03 1.7525E-03 2.8863E-03 5.4077E-04 1.0222E-03 0.4770 0.5832 0.1668 5.2905E-01
9 19.00 20.00 4.5560E-04 6.9373E-04 1.1493E-03 2.1345E-04 3.7510E-04 0.4685 0.5407 0.1406 5.6904E-01
11 23.26 25.00 1.1945E-04 2.0745E-04 3.2689E-04 5.8377E-05 1.1785E-04 0.4887 0.5681 0.1819 4.9534E-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 0.33110 0.50451 0.50357 0.32547 0.51364 0.51412 0.31331
5.000 5.010 5.005 0.10742 0.51851 0.50988 0.08970 0.52457 0.52965 0.07510
10.000 10.010 10.005 0.02931 0.44615 0.37983 0.02973 0.48633 0.54673 0.03559
15.000 15.010 15.005 0.16627 0.16445 0.16516 0.16939 0.21714 0.27081 0.17258
20.000 20.010 20.005 0.22473 0.18362 0.19991 0.23031 0.18612 0.12780 0.23735
25.000 25.010 25.005 0.08192 0.33351 0.24150 0.07877 0.30901 0.53552 0.07738
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 8.05378E-02 4.20128E-04 6.58867E-03 7.00880E-03 3.53156E-04 0.081808
9 1 10.0 0.0 180.0 4.96951E-02 4.28304E-04 1.86614E-03 2.29444E-03 3.60028E-04 0.037552
9 4 10.0 45.0 135.0 5.46015E-02 4.25591E-04 2.17458E-03 2.60017E-03 3.57748E-04 0.039826
9 7 10.0 90.0 90.0 7.37712E-02 4.22526E-04 4.69399E-03 5.11652E-03 3.55171E-04 0.063629
8 1 20.0 0.0 180.0 3.90348E-02 4.31984E-04 9.57247E-04 1.38923E-03 3.63122E-04 0.024523
8 4 20.0 45.0 135.0 4.34563E-02 4.26059E-04 1.13360E-03 1.55966E-03 3.58141E-04 0.026086
8 7 20.0 90.0 90.0 6.39004E-02 4.21946E-04 2.67980E-03 3.10175E-03 3.54684E-04 0.041937
7 1 30.0 0.0 180.0 3.38453E-02 4.37074E-04 8.14731E-04 1.25181E-03 3.67401E-04 0.024072
7 4 30.0 45.0 135.0 3.75269E-02 4.34133E-04 9.15717E-04 1.34985E-03 3.64928E-04 0.024402
7 7 30.0 90.0 90.0 5.46996E-02 4.26472E-04 1.60908E-03 2.03555E-03 3.58488E-04 0.029417
6 1 40.0 0.0 180.0 3.21256E-02 4.38307E-04 9.05880E-04 1.34419E-03 3.68437E-04 0.028198
6 4 40.0 45.0 135.0 3.51276E-02 4.34209E-04 9.82490E-04 1.41670E-03 3.64992E-04 0.027969
6 7 40.0 90.0 90.0 4.93186E-02 4.25564E-04 1.42540E-03 1.85096E-03 3.57725E-04 0.028902
5 1 50.0 0.0 180.0 3.36826E-02 4.41538E-04 1.43099E-03 1.87253E-03 3.71153E-04 0.042485
5 4 50.0 45.0 135.0 3.58934E-02 4.34544E-04 1.49083E-03 1.92537E-03 3.65274E-04 0.041535
5 7 50.0 90.0 90.0 4.77112E-02 4.25603E-04 1.92736E-03 2.35297E-03 3.57758E-04 0.040396
4 1 60.0 0.0 180.0 3.99818E-02 4.32631E-04 3.33355E-03 3.76618E-03 3.63666E-04 0.083377
4 4 60.0 45.0 135.0 4.08866E-02 4.24696E-04 3.29181E-03 3.71651E-03 3.56995E-04 0.080511
4 7 60.0 90.0 90.0 5.04896E-02 4.20308E-04 3.84409E-03 4.26440E-03 3.53307E-04 0.076136
3 1 70.0 0.0 180.0 5.54750E-02 3.98783E-04 9.20814E-03 9.60692E-03 3.35213E-04 0.165987
3 4 70.0 45.0 135.0 5.39136E-02 3.95244E-04 8.85994E-03 9.25518E-03 3.32238E-04 0.164336
3 7 70.0 90.0 90.0 6.02742E-02 3.90565E-04 9.63476E-03 1.00253E-02 3.28305E-04 0.159849
2 1 80.0 0.0 180.0 9.42529E-02 3.39520E-04 2.28887E-02 2.32282E-02 2.85397E-04 0.242843
2 4 80.0 45.0 135.0 8.72763E-02 3.35292E-04 2.21381E-02 2.24734E-02 2.81843E-04 0.253655
2 7 80.0 90.0 90.0 8.67098E-02 3.31196E-04 2.31846E-02 2.35158E-02 2.78400E-04 0.267382
1 1 87.5 0.0 180.0 1.52390E-01 2.71969E-04 4.03674E-02 4.06394E-02 2.28615E-04 0.264896
1 4 87.5 45.0 135.0 1.37208E-01 2.55541E-04 4.01182E-02 4.03737E-02 2.14805E-04 0.292389
1 7 87.5 90.0 90.0 1.24829E-01 2.79173E-04 4.10583E-02 4.13375E-02 2.34670E-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 7.009E-03 8.054E-02 9.651E-02 8.308E-02 1.248E-01 5.892E-03 5.696E+00 4.201E-04 3.532E-04
1 0.00 0.00 7.798E-04 1.498E-01 1.586E-03 1.851E-03 2.922E-03 6.766E-04 3.786E+00
3 3.65 5.00 2.956E-04 3.948E-02 3.626E-04 4.132E-04 5.920E-04 3.469E-03 3.318E+00
5 7.92 10.00 2.328E-04 5.225E-03 2.505E-04 2.562E-04 2.733E-04 3.609E-02 3.230E+00
7 13.34 15.00 1.570E-04 6.116E-04 2.064E-04 2.070E-04 2.082E-04 1.536E-01 3.445E+00
9 19.00 20.00 6.000E-05 1.512E-04 8.790E-05 8.792E-05 8.796E-05 1.600E-01 3.557E+00
11 23.26 25.00 1.788E-05 4.875E-05 2.099E-05 2.099E-05 2.099E-05 1.517E-01 3.265E+00
Waveband 28 of 30 completed in 7.9 sec.
* * * * * Output for wavelength band 29 (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 54.3 m at 685.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 680.0 nm to 690.0 nm:
Ed(diffuse) = 2.721E-01 Ed(direct) = 8.187E-01 Ed(total) = 1.091E+00
Absorption Coefficients of Individual Components at 685.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.4860 0.0073 0.0000 0.0002 0.4935
3 3.805 5.000 0.4860 0.0098 0.0000 0.0003 0.4961
5 8.232 10.000 0.4860 0.0158 0.0000 0.0004 0.5022
7 13.791 15.000 0.4860 0.0258 0.0000 0.0005 0.5123
9 19.583 20.000 0.4860 0.0192 0.0000 0.0004 0.5056
11 23.996 25.000 0.4860 0.0060 0.0000 0.0002 0.4922
Scattering Coefficients of Individual Components at 685.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0007 0.1126 0.1164 0.0000 0.2298
3 3.805 5.000 0.0007 0.1387 0.1624 0.0000 0.3019
5 8.232 10.000 0.0007 0.1917 0.2752 0.0000 0.4676
7 13.791 15.000 0.0007 0.2634 0.4710 0.0000 0.7351
9 19.583 20.000 0.0007 0.2183 0.3416 0.0000 0.5606
11 23.996 25.000 0.0007 0.0979 0.0931 0.0000 0.1917
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00037 0.00158 0.00020 0.00000 0.00215
3 3.805 5.000 0.00037 0.00194 0.00029 0.00000 0.00260
5 8.232 10.000 0.00037 0.00269 0.00048 0.00000 0.00354
7 13.791 15.000 0.00037 0.00369 0.00083 0.00000 0.00489
9 19.583 20.000 0.00037 0.00306 0.00060 0.00000 0.00403
11 23.996 25.000 0.00037 0.00137 0.00016 0.00000 0.00191
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 0.4935 0.2298 0.7233 0.3177 0.00215 0.00938
3 3.805 5.000 0.4961 0.3019 0.7980 0.3783 0.00260 0.00862
5 8.232 10.000 0.5022 0.4676 0.9698 0.4822 0.00354 0.00758
7 13.791 15.000 0.5123 0.7351 1.2474 0.5893 0.00489 0.00665
9 19.583 20.000 0.5056 0.5606 1.0662 0.5258 0.00403 0.00719
11 23.996 25.000 0.4922 0.1917 0.6839 0.2803 0.00191 0.00995
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 7.5773E-01
8 20.00 3.7259E-01
7 30.00 1.3502E-01
6 40.00 4.2121E-02
5 50.00 1.3118E-02
4 60.00 4.5657E-03
3 70.00 1.8679E-03
2 80.00 8.9687E-04
1 87.50 5.6315E-04
1 92.50 4.2837E-04
2 100.00 3.0793E-04
3 110.00 2.2027E-04
4 120.00 1.7548E-04
5 130.00 1.5204E-04
6 140.00 1.3951E-04
7 150.00 1.3280E-04
8 160.00 1.2932E-04
9 170.00 1.2767E-04
10 180.00 1.2705E-04
Asymptotic AOP values are
MUu(inf) = 0.3893
MUd(inf) = 0.9132
MU(inf) = 0.9091
R(inf) = 0.0014
Lu(inf)/Ed(inf) = 0.000324 (1/sr)
k(inf) = 0.5415 (1/m)
absorp(check) = 0.4923 = 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 9.9130E-02 1.4960E+00 1.5951E+00 3.6472E-02 1.0908E+00 0.3679 0.7291 0.6610 3.3437E-02
1 0.00 0.00 6.0526E-03 1.1756E+00 1.1816E+00 2.5440E-03 1.0568E+00 0.4203 0.8990 0.8922 2.4072E-03
3 3.81 5.00 1.7809E-03 7.4454E-02 7.6235E-02 8.4989E-04 6.5226E-02 0.4772 0.8761 0.8444 1.3030E-02
5 8.23 10.00 1.4101E-03 5.6228E-03 7.0329E-03 6.9858E-04 4.3706E-03 0.4954 0.7773 0.5221 1.5984E-01
7 13.79 15.00 1.0935E-03 1.5147E-03 2.6082E-03 5.2230E-04 8.4041E-04 0.4776 0.5548 0.1220 6.2148E-01
9 19.58 20.00 4.2757E-04 6.3815E-04 1.0657E-03 2.0039E-04 3.4172E-04 0.4687 0.5355 0.1326 5.8641E-01
11 24.00 25.00 1.0238E-04 1.7807E-04 2.8045E-04 5.0102E-05 1.0126E-04 0.4894 0.5686 0.1824 4.9480E-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 0.35466 0.54225 0.54129 0.34481 0.55084 0.55134 0.32862
5.000 5.010 5.005 0.08960 0.55219 0.54136 0.07284 0.55891 0.56534 0.05949
10.000 10.010 10.005 0.01545 0.43690 0.35226 0.01699 0.49006 0.58032 0.02410
15.000 15.010 15.005 0.17001 0.11968 0.14078 0.17341 0.16035 0.13891 0.17671
20.000 20.010 20.005 0.23599 0.18461 0.20522 0.24174 0.18402 0.10224 0.24942
25.000 25.010 25.005 0.08255 0.36111 0.25933 0.07929 0.33465 0.58538 0.07793
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 7.34216E-02 3.63148E-04 6.03827E-03 6.40142E-03 3.32931E-04 0.082241
9 1 10.0 0.0 180.0 4.53041E-02 3.70036E-04 1.70551E-03 2.07555E-03 3.39246E-04 0.037646
9 4 10.0 45.0 135.0 4.97770E-02 3.67743E-04 1.98793E-03 2.35567E-03 3.37143E-04 0.039937
9 7 10.0 90.0 90.0 6.72529E-02 3.65208E-04 4.29889E-03 4.66410E-03 3.34819E-04 0.063921
8 1 20.0 0.0 180.0 3.55858E-02 3.73082E-04 8.72882E-04 1.24596E-03 3.42038E-04 0.024529
8 4 20.0 45.0 135.0 3.96165E-02 3.68049E-04 1.03399E-03 1.40204E-03 3.37424E-04 0.026100
8 7 20.0 90.0 90.0 5.82542E-02 3.64677E-04 2.45049E-03 2.81517E-03 3.34332E-04 0.042065
7 1 30.0 0.0 180.0 3.08548E-02 3.77344E-04 7.42743E-04 1.12009E-03 3.45945E-04 0.024072
7 4 30.0 45.0 135.0 3.42112E-02 3.74921E-04 8.34833E-04 1.20975E-03 3.43724E-04 0.024402
7 7 30.0 90.0 90.0 4.98654E-02 3.68544E-04 1.46838E-03 1.83692E-03 3.37877E-04 0.029447
6 1 40.0 0.0 180.0 2.92870E-02 3.78237E-04 8.25838E-04 1.20408E-03 3.46764E-04 0.028198
6 4 40.0 45.0 135.0 3.20238E-02 3.74848E-04 8.95678E-04 1.27053E-03 3.43657E-04 0.027969
6 7 40.0 90.0 90.0 4.49609E-02 3.67671E-04 1.29955E-03 1.66722E-03 3.37077E-04 0.028904
5 1 50.0 0.0 180.0 3.07065E-02 3.80886E-04 1.30455E-03 1.68544E-03 3.49193E-04 0.042485
5 4 50.0 45.0 135.0 3.27219E-02 3.75016E-04 1.35910E-03 1.73412E-03 3.43811E-04 0.041535
5 7 50.0 90.0 90.0 4.34955E-02 3.67591E-04 1.75706E-03 2.12466E-03 3.37004E-04 0.040396
4 1 60.0 0.0 180.0 3.64491E-02 3.73068E-04 3.03900E-03 3.41207E-03 3.42025E-04 0.083377
4 4 60.0 45.0 135.0 3.72740E-02 3.66395E-04 3.00095E-03 3.36735E-03 3.35907E-04 0.080511
4 7 60.0 90.0 90.0 4.60284E-02 3.62887E-04 3.50444E-03 3.86732E-03 3.32691E-04 0.076136
3 1 70.0 0.0 180.0 5.05733E-02 3.43750E-04 8.39452E-03 8.73827E-03 3.15146E-04 0.165987
3 4 70.0 45.0 135.0 4.91499E-02 3.40856E-04 8.07709E-03 8.41794E-03 3.12493E-04 0.164336
3 7 70.0 90.0 90.0 5.49484E-02 3.37038E-04 8.78345E-03 9.12049E-03 3.08993E-04 0.159849
2 1 80.0 0.0 180.0 8.59249E-02 2.92560E-04 2.08663E-02 2.11588E-02 2.68216E-04 0.242843
2 4 80.0 45.0 135.0 7.95647E-02 2.89045E-04 2.01820E-02 2.04711E-02 2.64993E-04 0.253655
2 7 80.0 90.0 90.0 7.90482E-02 2.85660E-04 2.11361E-02 2.14217E-02 2.61890E-04 0.267382
1 1 87.5 0.0 180.0 1.38925E-01 2.34268E-04 3.68006E-02 3.70349E-02 2.14774E-04 0.264896
1 4 87.5 45.0 135.0 1.25085E-01 2.20209E-04 3.65734E-02 3.67936E-02 2.01885E-04 0.292389
1 7 87.5 90.0 90.0 1.13799E-01 2.40649E-04 3.74304E-02 3.76711E-02 2.20625E-04 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 6.401E-03 7.342E-02 8.798E-02 7.574E-02 1.138E-01 5.869E-03 5.697E+00 3.631E-04 3.329E-04
1 0.00 0.00 6.741E-04 1.366E-01 1.372E-03 1.602E-03 2.524E-03 6.378E-04 3.774E+00
3 3.81 5.00 2.600E-04 3.048E-02 3.039E-04 3.395E-04 4.653E-04 3.986E-03 3.269E+00
5 8.23 10.00 2.182E-04 3.495E-03 2.281E-04 2.315E-04 2.416E-04 4.992E-02 3.202E+00
7 13.79 15.00 1.519E-04 4.317E-04 1.983E-04 1.986E-04 1.993E-04 1.808E-01 3.438E+00
9 19.58 20.00 5.634E-05 1.305E-04 8.238E-05 8.239E-05 8.241E-05 1.649E-01 3.557E+00
11 24.00 25.00 1.538E-05 4.159E-05 1.791E-05 1.791E-05 1.791E-05 1.519E-01 3.258E+00
Waveband 29 of 30 completed in 8.0 sec.
* * * * * Output for wavelength band 30 (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 51.6 m at 695.0 nm
RADTRANX clear-sky spectral irradiances averaged over the band from 690.0 nm to 700.0 nm:
Ed(diffuse) = 2.610E-01 Ed(direct) = 7.914E-01 Ed(total) = 1.052E+00
Absorption Coefficients of Individual Components at 695.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.5590 0.0028 0.0000 0.0002 0.5620
3 4.139 5.000 0.5590 0.0040 0.0000 0.0002 0.5632
5 8.888 10.000 0.5590 0.0067 0.0000 0.0003 0.5660
7 14.751 15.000 0.5590 0.0115 0.0000 0.0005 0.5710
9 20.844 20.000 0.5590 0.0083 0.0000 0.0004 0.5677
11 25.579 25.000 0.5590 0.0023 0.0000 0.0002 0.5615
Scattering Coefficients of Individual Components at 695.0 nm
iz Opt Depth Geo Depth Comp 1 Comp 2 Comp 3 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.0007 0.1121 0.1159 0.0000 0.2287
3 4.139 5.000 0.0007 0.1382 0.1619 0.0000 0.3008
5 8.888 10.000 0.0007 0.1914 0.2748 0.0000 0.4668
7 14.751 15.000 0.0007 0.2634 0.4710 0.0000 0.7351
9 20.844 20.000 0.0007 0.2181 0.3413 0.0000 0.5600
11 25.579 25.000 0.0007 0.0974 0.0926 0.0000 0.1907
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 Comp 4 Total
(m) (1/m) (1/m) (1/m) (1/m) (1/m)
1 0.000 0.000 0.00035 0.00157 0.00020 0.00000 0.00212
3 4.139 5.000 0.00035 0.00194 0.00028 0.00000 0.00257
5 8.888 10.000 0.00035 0.00268 0.00048 0.00000 0.00352
7 14.751 15.000 0.00035 0.00369 0.00083 0.00000 0.00487
9 20.844 20.000 0.00035 0.00306 0.00060 0.00000 0.00401
11 25.579 25.000 0.00035 0.00137 0.00016 0.00000 0.00188
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 0.5620 0.2287 0.7908 0.2892 0.00212 0.00929
3 4.139 5.000 0.5632 0.3008 0.8640 0.3482 0.00257 0.00855
5 8.888 10.000 0.5660 0.4668 1.0329 0.4520 0.00352 0.00753
7 14.751 15.000 0.5710 0.7351 1.3061 0.5628 0.00487 0.00662
9 20.844 20.000 0.5677 0.5600 1.1277 0.4966 0.00401 0.00715
11 25.579 25.000 0.5615 0.1907 0.7522 0.2536 0.00188 0.00984
The shape of the asymptotic radiance distribution is given by
u theta Linf(theta)
10 0.00 1.0000E+00
9 10.00 7.3776E-01
8 20.00 3.4124E-01
7 30.00 1.1520E-01
6 40.00 3.3846E-02
5 50.00 1.0163E-02
4 60.00 3.4938E-03
3 70.00 1.4321E-03
2 80.00 6.9124E-04
1 87.50 4.3552E-04
1 92.50 3.3224E-04
2 100.00 2.3951E-04
3 110.00 1.7198E-04
4 120.00 1.3757E-04
5 130.00 1.1959E-04
6 140.00 1.0999E-04
7 150.00 1.0486E-04
8 160.00 1.0221E-04
9 170.00 1.0096E-04
10 180.00 1.0049E-04
Asymptotic AOP values are
MUu(inf) = 0.3911
MUd(inf) = 0.9195
MU(inf) = 0.9160
R(inf) = 0.0012
Lu(inf)/Ed(inf) = 0.000278 (1/sr)
k(inf) = 0.6130 (1/m)
absorp(check) = 0.5615 = 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 9.4545E-02 1.4421E+00 1.5366E+00 3.4736E-02 1.0524E+00 0.3674 0.7298 0.6623 3.3006E-02
1 0.00 0.00 4.0397E-03 1.1327E+00 1.1368E+00 1.6241E-03 1.0193E+00 0.4020 0.8998 0.8952 1.5934E-03
3 4.14 5.00 5.9332E-04 4.8704E-02 4.9298E-02 2.7426E-04 4.3044E-02 0.4622 0.8838 0.8676 6.3717E-03
5 8.89 10.00 3.9456E-04 2.3355E-03 2.7301E-03 1.9605E-04 1.8986E-03 0.4969 0.8129 0.6236 1.0326E-01
7 14.75 15.00 3.1168E-04 4.3562E-04 7.4730E-04 1.4969E-04 2.4545E-04 0.4803 0.5635 0.1281 6.0984E-01
9 20.84 20.00 1.2062E-04 1.7396E-04 2.9459E-04 5.7022E-05 9.2866E-05 0.4727 0.5338 0.1217 6.1403E-01
11 25.58 25.00 2.9366E-05 4.7171E-05 7.6538E-05 1.4489E-05 2.6548E-05 0.4934 0.5628 0.1576 5.4575E-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 0.48977 0.61932 0.61886 0.49047 0.62703 0.62725 0.48504
5.000 5.010 5.005 0.18011 0.63154 0.62610 0.15018 0.63552 0.63864 0.12240
10.000 10.010 10.005 0.01704 0.54289 0.46672 0.01688 0.58599 0.65173 0.02269
15.000 15.010 15.005 0.17313 0.13925 0.15338 0.17605 0.19169 0.21613 0.17846
20.000 20.010 20.005 0.23914 0.18960 0.20988 0.24347 0.18975 0.10435 0.24862
25.000 25.010 25.005 0.08712 0.35640 0.25299 0.08461 0.33536 0.63746 0.08361
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 7.04325E-02 2.20469E-04 5.82326E-03 6.04373E-03 2.09491E-04 0.082679
9 1 10.0 0.0 180.0 4.34597E-02 2.25668E-04 1.64022E-03 1.86589E-03 2.14431E-04 0.037741
9 4 10.0 45.0 135.0 4.77505E-02 2.23974E-04 1.91232E-03 2.13629E-03 2.12821E-04 0.040048
9 7 10.0 90.0 90.0 6.45149E-02 2.21789E-04 4.14295E-03 4.36473E-03 2.10744E-04 0.064217
8 1 20.0 0.0 180.0 3.41370E-02 2.28337E-04 8.37555E-04 1.06589E-03 2.16966E-04 0.024535
8 4 20.0 45.0 135.0 3.80037E-02 2.24730E-04 9.92440E-04 1.21717E-03 2.13539E-04 0.026114
8 7 20.0 90.0 90.0 5.58826E-02 2.21649E-04 2.35798E-03 2.57963E-03 2.10612E-04 0.042195
7 1 30.0 0.0 180.0 2.95986E-02 2.31761E-04 7.12504E-04 9.44265E-04 2.20220E-04 0.024072
7 4 30.0 45.0 135.0 3.28186E-02 2.29537E-04 8.00871E-04 1.03041E-03 2.18107E-04 0.024403
7 7 30.0 90.0 90.0 4.78343E-02 2.24287E-04 1.41002E-03 1.63431E-03 2.13118E-04 0.029477
6 1 40.0 0.0 180.0 2.80947E-02 2.33324E-04 7.92216E-04 1.02554E-03 2.21705E-04 0.028198
6 4 40.0 45.0 135.0 3.07201E-02 2.30357E-04 8.59214E-04 1.08957E-03 2.18886E-04 0.027969
6 7 40.0 90.0 90.0 4.31305E-02 2.24383E-04 1.24673E-03 1.47112E-03 2.13210E-04 0.028906
5 1 50.0 0.0 180.0 2.94564E-02 2.35876E-04 1.25144E-03 1.48732E-03 2.24130E-04 0.042485
5 4 50.0 45.0 135.0 3.13897E-02 2.31303E-04 1.30377E-03 1.53507E-03 2.19785E-04 0.041535
5 7 50.0 90.0 90.0 4.17247E-02 2.25223E-04 1.68553E-03 1.91075E-03 2.14007E-04 0.040396
4 1 60.0 0.0 180.0 3.49652E-02 2.31974E-04 2.91528E-03 3.14725E-03 2.20423E-04 0.083377
4 4 60.0 45.0 135.0 3.57565E-02 2.26878E-04 2.87878E-03 3.10566E-03 2.15580E-04 0.080511
4 7 60.0 90.0 90.0 4.41545E-02 2.23387E-04 3.36176E-03 3.58515E-03 2.12263E-04 0.076136
3 1 70.0 0.0 180.0 4.85144E-02 2.14768E-04 8.05277E-03 8.26754E-03 2.04073E-04 0.165987
3 4 70.0 45.0 135.0 4.71489E-02 2.12129E-04 7.74825E-03 7.96038E-03 2.01565E-04 0.164336
3 7 70.0 90.0 90.0 5.27114E-02 2.08909E-04 8.42586E-03 8.63477E-03 1.98506E-04 0.159849
2 1 80.0 0.0 180.0 8.24267E-02 1.83661E-04 2.00168E-02 2.02004E-02 1.74515E-04 0.242843
2 4 80.0 45.0 135.0 7.63255E-02 1.80827E-04 1.93604E-02 1.95412E-02 1.71822E-04 0.253655
2 7 80.0 90.0 90.0 7.58300E-02 1.78325E-04 2.02756E-02 2.04539E-02 1.69445E-04 0.267382
1 1 87.5 0.0 180.0 1.33269E-01 1.47844E-04 3.53024E-02 3.54502E-02 1.40482E-04 0.264896
1 4 87.5 45.0 135.0 1.19992E-01 1.38558E-04 3.50844E-02 3.52230E-02 1.31658E-04 0.292389
1 7 87.5 90.0 90.0 1.09166E-01 1.51494E-04 3.59066E-02 3.60581E-02 1.43950E-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 6.044E-03 7.043E-02 8.436E-02 7.261E-02 1.091E-01 5.743E-03 5.747E+00 2.205E-04 2.095E-04
1 0.00 0.00 4.092E-04 1.310E-01 9.692E-04 1.166E-03 1.965E-03 4.015E-04 3.969E+00
3 4.14 5.00 8.214E-05 2.060E-02 1.057E-04 1.260E-04 1.978E-04 1.908E-03 3.339E+00
5 8.89 10.00 6.202E-05 1.641E-03 6.336E-05 6.471E-05 6.868E-05 3.267E-02 3.161E+00
7 14.75 15.00 4.413E-05 1.363E-04 5.579E-05 5.586E-05 5.604E-05 1.798E-01 3.392E+00
9 20.84 20.00 1.636E-05 3.533E-05 2.276E-05 2.276E-05 2.276E-05 1.761E-01 3.486E+00
11 25.58 25.00 4.545E-06 1.075E-05 5.018E-06 5.018E-06 5.018E-06 1.712E-01 3.188E+00
Waveband 30 of 30 completed in 8.0 sec.
Energy Eo as a function of depth and wavelength
Units are W/m^2 [values are integrated over the wavelength bands]
depth 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
in air 1.786E+01 1.879E+01 1.786E+01 1.823E+01 2.137E+01 2.274E+01 2.254E+01 2.278E+01 2.197E+01 2.221E+01 2.170E+01 2.075E+01 2.114E+01 2.129E+01 2.091E+01 2.069E+01 2.044E+01 2.037E+01 1.979E+01 1.899E+01 1.943E+01 1.895E+01 1.872E+01 1.847E+01 1.788E+01 1.707E+01 1.775E+01 1.742E+01 1.595E+01 1.537E+01
0.0 1.367E+01 1.441E+01 1.371E+01 1.401E+01 1.645E+01 1.760E+01 1.760E+01 1.790E+01 1.733E+01 1.756E+01 1.706E+01 1.607E+01 1.642E+01 1.652E+01 1.616E+01 1.588E+01 1.565E+01 1.547E+01 1.483E+01 1.408E+01 1.433E+01 1.398E+01 1.382E+01 1.364E+01 1.321E+01 1.261E+01 1.312E+01 1.290E+01 1.182E+01 1.137E+01
5.0 1.042E+01 1.100E+01 1.048E+01 1.068E+01 1.257E+01 1.361E+01 1.384E+01 1.428E+01 1.393E+01 1.417E+01 1.354E+01 1.208E+01 1.243E+01 1.243E+01 1.187E+01 1.120E+01 1.083E+01 9.944E+00 7.862E+00 5.362E+00 3.257E+00 3.001E+00 2.715E+00 2.421E+00 2.048E+00 1.503E+00 1.115E+00 9.942E-01 7.623E-01 4.930E-01
10.0 6.815E+00 7.208E+00 6.903E+00 7.032E+00 8.371E+00 9.291E+00 9.689E+00 1.022E+01 1.015E+01 1.043E+01 9.894E+00 8.407E+00 8.764E+00 8.758E+00 8.194E+00 7.453E+00 7.086E+00 6.043E+00 3.918E+00 1.909E+00 6.926E-01 6.022E-01 4.987E-01 4.018E-01 2.974E-01 1.690E-01 9.515E-02 9.614E-02 7.033E-02 2.730E-02
15.0 3.545E+00 3.754E+00 3.636E+00 3.713E+00 4.535E+00 5.241E+00 5.661E+00 6.188E+00 6.316E+00 6.626E+00 6.301E+00 5.152E+00 5.488E+00 5.521E+00 5.093E+00 4.498E+00 4.235E+00 3.364E+00 1.790E+00 6.249E-01 1.372E-01 1.124E-01 8.530E-02 6.237E-02 4.085E-02 1.903E-02 1.331E-02 2.886E-02 2.608E-02 7.473E-03
20.0 1.728E+00 1.827E+00 1.784E+00 1.822E+00 2.276E+00 2.736E+00 3.060E+00 3.463E+00 3.628E+00 3.875E+00 3.681E+00 2.881E+00 3.132E+00 3.166E+00 2.874E+00 2.460E+00 2.291E+00 1.695E+00 7.414E-01 1.870E-01 2.613E-02 2.027E-02 1.426E-02 9.732E-03 5.971E-03 2.857E-03 3.844E-03 1.149E-02 1.066E-02 2.946E-03
25.0 1.063E+00 1.123E+00 1.094E+00 1.110E+00 1.389E+00 1.696E+00 1.937E+00 2.229E+00 2.357E+00 2.527E+00 2.351E+00 1.727E+00 1.893E+00 1.901E+00 1.681E+00 1.380E+00 1.260E+00 8.640E-01 3.119E-01 5.784E-02 5.889E-03 4.398E-03 2.976E-03 2.056E-03 1.356E-03 8.354E-04 1.211E-03 3.269E-03 2.805E-03 7.654E-04
Quantum Eo as a function of depth and wavelength
Units are (micromol photons)/(m^2 s) [values are integrated over the wavelength bands]
depth 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
in air 6.047E+01 6.516E+01 6.343E+01 6.628E+01 7.949E+01 8.649E+01 8.762E+01 9.045E+01 8.906E+01 9.189E+01 9.158E+01 8.933E+01 9.275E+01 9.519E+01 9.527E+01 9.597E+01 9.653E+01 9.791E+01 9.678E+01 9.443E+01 9.827E+01 9.740E+01 9.779E+01 9.803E+01 9.638E+01 9.343E+01 9.867E+01 9.826E+01 9.132E+01 8.926E+01
0.0 4.628E+01 4.997E+01 4.871E+01 5.093E+01 6.120E+01 6.694E+01 6.840E+01 7.108E+01 7.026E+01 7.264E+01 7.201E+01 6.918E+01 7.203E+01 7.387E+01 7.360E+01 7.364E+01 7.390E+01 7.432E+01 7.249E+01 7.003E+01 7.245E+01 7.185E+01 7.218E+01 7.239E+01 7.119E+01 6.901E+01 7.290E+01 7.276E+01 6.765E+01 6.603E+01
5.0 3.527E+01 3.815E+01 3.722E+01 3.882E+01 4.674E+01 5.177E+01 5.381E+01 5.668E+01 5.649E+01 5.862E+01 5.717E+01 5.201E+01 5.453E+01 5.558E+01 5.406E+01 5.196E+01 5.113E+01 4.779E+01 3.844E+01 2.667E+01 1.647E+01 1.543E+01 1.418E+01 1.285E+01 1.104E+01 8.227E+00 6.197E+00 5.609E+00 4.365E+00 2.864E+00
10.0 2.307E+01 2.500E+01 2.452E+01 2.556E+01 3.114E+01 3.533E+01 3.765E+01 4.059E+01 4.113E+01 4.317E+01 4.176E+01 3.619E+01 3.846E+01 3.916E+01 3.732E+01 3.457E+01 3.346E+01 2.904E+01 1.915E+01 9.495E+00 3.502E+00 3.096E+00 2.605E+00 2.133E+00 1.603E+00 9.252E-01 5.289E-01 5.424E-01 4.027E-01 1.586E-01
15.0 1.200E+01 1.302E+01 1.292E+01 1.350E+01 1.687E+01 1.993E+01 2.200E+01 2.457E+01 2.560E+01 2.741E+01 2.660E+01 2.218E+01 2.408E+01 2.469E+01 2.320E+01 2.086E+01 2.000E+01 1.617E+01 8.752E+00 3.108E+00 6.938E-01 5.779E-01 4.456E-01 3.310E-01 2.202E-01 1.042E-01 7.395E-02 1.628E-01 1.493E-01 4.341E-02
20.0 5.848E+00 6.337E+00 6.338E+00 6.624E+00 8.467E+00 1.041E+01 1.189E+01 1.375E+01 1.471E+01 1.603E+01 1.554E+01 1.240E+01 1.374E+01 1.416E+01 1.309E+01 1.141E+01 1.082E+01 8.144E+00 3.625E+00 9.300E-01 1.321E-01 1.042E-01 7.451E-02 5.165E-02 3.219E-02 1.564E-02 2.137E-02 6.484E-02 6.102E-02 1.711E-02
25.0 3.599E+00 3.894E+00 3.887E+00 4.037E+00 5.168E+00 6.449E+00 7.530E+00 8.848E+00 9.556E+00 1.046E+01 9.922E+00 7.432E+00 8.305E+00 8.499E+00 7.659E+00 6.400E+00 5.948E+00 4.152E+00 1.525E+00 2.877E-01 2.978E-02 2.260E-02 1.555E-02 1.091E-02 7.308E-03 4.574E-03 6.729E-03 1.844E-02 1.606E-02 4.446E-03
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 2.6849E+03 1.7739E+03
0.00 2.0399E+03 1.7318E+03
5.00 1.0601E+03 8.2289E+02
10.00 6.6127E+02 4.7722E+02
15.00 3.8025E+02 2.5845E+02
20.00 2.0484E+02 1.3603E+02
25.00 1.2369E+02 8.2915E+01
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 0.18365
5.000 5.010 5.005 0.09850
10.000 10.010 10.005 0.09668
15.000 15.010 15.005 0.12689
20.000 20.010 20.005 0.11840
25.000 25.010 25.005 0.07775
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. Y is not defined for Rrs
depth Ed Eu Lu Lw Rrs
in air (0.328, 0.339, 9.864E+04) (0.296, 0.321, 4.061E+03) (0.285, 0.318, 7.812E+02) (0.204, 0.279, 2.302E+02) (0.206, 0.272, 0.000E+00)
0.00 (0.326, 0.339, 9.633E+04) (0.202, 0.278, 1.754E+03) (0.204, 0.279, 4.270E+02)
5.00 (0.252, 0.330, 5.460E+04) (0.192, 0.292, 1.413E+03) (0.193, 0.291, 3.086E+02)
10.00 (0.219, 0.327, 3.223E+04) (0.190, 0.315, 1.075E+03) (0.190, 0.307, 2.077E+02)
15.00 (0.205, 0.336, 1.782E+04) (0.188, 0.330, 6.704E+02) (0.183, 0.308, 1.156E+02)
20.00 (0.198, 0.347, 9.572E+03) (0.175, 0.305, 3.201E+02) (0.170, 0.278, 5.571E+01)
25.00 (0.189, 0.343, 5.711E+03) (0.159, 0.256, 1.557E+02) (0.159, 0.245, 3.101E+01)
The Forel-Ule number of the nadir-viewing Rrs is FU = 4
The Forel-Ule number of the nadir-viewing, in-air Lu is FU = 4
The Forel-Ule number of the nadir-viewing Lw is FU = 4
The final depth-averaged photopic alpha and K are alpha = 0.4767 1/m and K = 0.1092 1/m
The final estimate for the Secchi depth is z_SD = 13.66 m
Run completed on 07/18/2013 at 15:11:05.7
Total (wall clock) run time = 172.0 sec