APPLICATION NOTE NO.
7
Calculation of Calibration Coefficients for
Sea Tech, Chelsea (Alphatracka), and WET Labs Cstar Transmissometers
Revised February 2010
Sea-Bird SEASOFT V2 software (Seasave V7 and SBE Data Processing) can output the following transmissometer results:
whereLight transmission [%] = ( M * voltage output ) + B
Beam attenuation coefficient c = - ( 1 / z ) * ln ( light transmission [decimal] )
Note: Edit the CTD configuration (.con or .xmlcon) file using the Configure Inputs menu in Seasave V7 (real-time data acquisition software) or the Configure menu in SBE Data Processing (data processing software).
M and B are listed on the Sea-Bird Calibration Sheet, and are calculated by Sea-Bird as follows:
M = ( Tw / [ W0 - Y0 ] ) * ( A0 - Y0 ) / ( A1 - Y1 )
B = - M * Y1
where the parameters are listed on the Sea-Bird Calibration Sheet:
Because obtaining a good pure water calibration can be difficult in the field, the voltage output in air is used as the reference to track the instrument drift over time. By comparing the original voltage output in air to subsequent voltage outputs in air in the field, the initial instrument slope (derived from the pure water calibration) can be adjusted to correct for instrument drift.
Sea-Bird does an initial calculation of M and B, based on A1 and Y1 measured at Sea-Bird, and using Tw = 100% (providing transmission measurements relative to water). These values are tabulated on the Calibration Sheet, and are input to the CTD configuration (.con or .xmlcon) file by Sea-Bird.
Example:
The Sea-Bird Calibration Sheet shows the following values:
z = 25 cm = 0.25 m
A0 = 4.743 volts
Y0 = 0.002 volts
W0 = 4.565 volts
Tw = 100% (for transmission relative to water)The current calibration provides the following voltages:
A1 = 4.719 volts
Y1 = 0.006 voltsCalculating the calibration coefficients:
M = (100 / [ 4.565 - 0.002 ] ) * (4.743 - 0.002) / (4.719 - 0.006) = 22.046
B = - 22.046 * 0.006 = -0.132The transmissometer is deployed and outputs 3.56 volts. Seasave V7 (or SBE Data Processing) calculates:
Light transmission [%] = ( M * voltage output ) + B = ( 22.046 * 3.56 ) - 0.132 = 78.351%
Beam attenuation coefficient c = - ( 1 / z ) * ln ( light transmission [decimal] ) = - ( 1 / 0.25 ) * ln ( 0.78351 ) = 0.976
For field recalibration, connect the transmissometer to the CTD, run Seasave V7, and view the transmissometer voltage with the light path in air (A1), and then with the light path blocked (Y1). Recalculate M and B, using the new values for A1 and Y1 and the original factory values for A0, Y0, and W0, and enter M and B in the .con or .xmlcon file. Refer to the Configuration Sheet in your CTD manual to determine the appropriate output channel for the transmissometer voltage.
Many optical oceanographers prefer reporting transmissometer measurements relative to water, because they are not based on (the currently accepted) values of Tw relative to air, which are subject to interpretation and may change in the future (see Table 1 below). Consequently, as of April 2004, Sea-Bird is calculating M and B relative to water, and indicating those values on the Calibration Sheet and in the configuration (.con or .xmlcon) file. However, if desired, you can calculate M and B relative to air, and input those values in the configuration file.
The relationship between measurements relative to air and relative to water is:
Light transmission (relative to air) =
Light transmission (relative to water) * Light transmission of pure water (relative to air)
But,
c = - ( 1 / z ) * ln ( light transmission [decimal] )
Therefore, rewriting the light transmission equation in terms of the beam attenuation coefficient c:
c (relative to air) = c (relative to water) + c of pure water (relative to air)
Note that if M and B are calculated and entered in the configuration (.con or .xmlcon) file relative to water, light transmission and beam attenuation are calculated by SEASOFT relative to water. Conversely, if M and B are calculated and entered in the configuration file relative to air, light transmission and beam attenuation are calculated by SEASOFT relative to air.
Light transmission of pure water relative to air is dependent on the path length and wavelength of the transmissometer. Table 1 lists the pure water percent transmission values (Tw), relative to air, for transmissometers with various wavelengths and path lengths. The values have been derived with help from transmissometer manufacturers and references in the literature, and seem to be generally accepted. However, variations of several percent in reported coefficients exist in the literature. Therefore, these values may be subject to change or debate; you may wish to consult the literature, and calculate M and B using your desired value of Tw.
Table 1. Nominal values of % transmission in pure water, relative to air, for transmissometers of listed wavelength and path length. Values derived with help from Wet Labs using the listed references. Historical Sea Tech values are also included.
| Wavelength | 10cm | 25cm | Reference |
| 488 nm (blue) | 99.8% | 99.6% | 1, 2 |
| 532 nm (green) | 99.5% | 98.8% | 1, 2 |
| 660 nm (red) | 96.0% | 90.2% | 1, 3 |
| 660 nm (red) | 96.4% | 91.3% |
4 (historical Sea Tech value) |
References:
1. Pope and Fry, Applied Optics, Vol. 36
2. Morrel, 1994 as communicated by Wet Labs
3. Smith and Baker, 1998, Applied Optics, Vol. 20, No. 2
4. Original Sea Tech Transmissometer manual
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