APPLICATION NOTE NO. 87

Calculating Calibration Coefficients for the Wet Labs ECO-BB Scattering/Turbidity Meter
May 2007

Application note in pdf format

This Application Note applies to the use of the Wet Labs ECO-BB series of scattering/turbidity meters with Sea-Bird CTDs. The ECO-BB has a response that is linear over the measurement range provided. The ECO-BB is not currently directly supported in Sea-Bird software. However, you can set up the ECO-BB channel as a User Polynomial in the configuration (.con) file, allowing you to define an equation relating sensor output voltage to calculated engineering units:

Value = a0 + (a1 * V) + (a2 * V²) + (a3 * V³)

Select the User Polynomial for the ECO-BB channel when setting up the configuration (.con) file in Sea-Bird software (SBE Data Processing or SEASAVE). The software prompts for a0, a1, a2, and a3. These values can be calculated from the calibration sheet provided by Wet Labs:

• ECO-BB with 0 - 25 NTU range: Wet Labs provides two calibration sheets, allowing calculation of output in NTU or in m ^-1 sr ^-1, as desired by the user.
• ECO-BB with 0 - 100 NTU range: Wet Labs provides a calibration sheet for output in NTU only. A calibration to m ^-1 sr ^-1 is available at additional cost.

Each calibration sheets provides a Dark Counts and Scale Factor value consistent with the output units. Derivation of a0, a1, a2, and a3 for the user polynomial follows for both NTU and m ^-1 sr ^-1.

Note: The Wet Labs calibration sheet actually lists Dark Counts, and then provides the value for Dark Counts in both counts and in volts. For clarity, we refer to it below as Dark Output, since we are dealing with voltage output.

One of Wet Labs’ calibration sheets defines ECO-BB output as:

        turbidity = (Output – Dark Output) * Scale Factor                     (turbidity in units of NTU)

where:
Output (volts) = in situ output of the ECO-BB
Dark Output (volts) = measured output obtained by covering detector with black tape and submersing in water.
Scale factor (NTU/volts) = multiplier

Setting the Wet Labs equation equal to the user polynomial equation and calculating a0, a1, a2, and a3:
(Output – Dark Output) * Scale Factor = a0 + (a1 * V) + (a2 * V²) + (a3 * V³)

Expanding the left side of the equation and using consistent notation (Output = V):
scale factor * V – scale factor * Dark Output = a0 + (a1 * V) + (a2 * V²) + (a3 * V³)

Rearranging:
(– scale factor * Dark Output) + (scale factor * V) = a0 + (a1 * V) + (a2 * V²) + (a3 * V³)

Solving for a0, a1, a2, and a3:
a0 = - scale factor * Dark Output          a1 = scale factor          a2 = a3 = 0

The other Wet Labs calibration sheet defines ECO-BB output as:

        β(Θc) = (Output – Dark Output) * Scale Factor                     (β(Θc) in units of m ^-1 sr ^-1)

where:
Output (volts) = in situ output of the ECO-BB
Dark Output (volts) = measured output obtained by covering detector with black tape and submersing in water.
Scale factor (β(Θc)/volts) = multiplier

Setting the Wet Labs equation equal to the user polynomial equation and calculating a0, a1, a2, and a3:
(Output – Dark Output) * Scale Factor = a0 + (a1 * V) + (a2 * V²) + (a3 * V³)

Expanding the left side of the equation and using consistent notation (Output = V):
scale factor * V – scale factor * Dark Output = a0 + (a1 * V) + (a2 * V²) + (a3 * V³)

Rearranging:
(– scale factor * Dark Output) + (scale factor * V) = a0 + (a1 * V) + (a2 * V²) + (a3 * V³)

Solving for a0, a1, a2, and a3:
a0 = - scale factor * Dark Output          a1 = scale factor          a2 = a3 = 0

While the factory-supplied Scale Factor can be used to obtain approximate values, field calibration is highly recommended. The relationship between ECO-BB output and turbidity or β(Θc) is somewhat variable, and is not easy to determine in the laboratory. Particle shape and size are some of the factors that affect the relationship. To accurately measure with the ECO-BB, perform calibrations on seawater samples with distributions of particles that are similar to what is expected in situ. Determine turbidity or β(Θc) independently, and use those values, as well as readings from the ECO-BB, to determine the correct Scale Factor. The Scale Factor is correct as long as the distribution of particle sizes and shapes does not change; the condition does change with season and geographic location.

Last modified: 05 Dec 2007

Sea-Bird Home     Phone: (+1) 425-643-9866     Fax: (+1) 425-643-9954     E-mail: seabird@seabird.com