Estimating calibration coefficients for SBE 21 and SBE 3 and SBE 38

Sea Bird Temperature and conductivity sensors have originally a non-linear response. It means that the calibration in temperature or conductivity of raw data coming from these sensors will not give a straight line. In order to linearize the response curve, Sea Bird proposes formulas. These formulas appear in their calibration sheets:

For the conductivity sensor: 

For the temperature sensor: 

g, h, i, j represent the linearization coefficients of the conductivity sensor.

a , a1, a2, a3 represent the linearization coefficients of the temperature sensor.

Since 1990, all the temperature sensors are calibrated in the ITS-90 temperature scale. Before 1990 and after 1968 they were calibrated in the IPTS-68.

As the salinity scale has been created in 1978, at this time temperatures sensors were calibrated in the IPTS-68 and the temperatures used to retrieve practical salinity values must be expressed in IPTS-68.

In this way, Sea Bird propose in some calibration sheets, a set of coefficients a, b, c, d, to obtain directly temperatures in the IPTS-68. In these sheets, ITS-90 coefficients are also called g, h, i, j for temperature sensors.

The using of a, b, c, d coefficients is generally abandoned actually because software like Seasave proposes formulas to convert automatically temperatures ITS-90 in IPTS-68. 

Thereafter, only the sets g, h, i, j must be used and programmed in acquisition software for temperature and conductivity sensors.

When a sensor is linearized with these coefficients and formulas, it must keep its linearity and it is no more necessary to calculate new coefficients g, h, i, j at each calibration.

The calibration consists then in calculating the Offset and Slope coefficients of a straight line. The formulas:

  • Tcorrected = Offset  + Slope x Tinstrument


  • Ccorrected = Offset  + Slope x Cinstrument

given in the SHOM’s calibrations reports allow to correct the physical data of temperature and conductivity sensors contained in the SBE 21 messages.

These corrections may be  taken into account by data acquisition software before transmission.

The advantages of such way of practice are:

  • It offers lower risks of human errors than when programming  coefficients g, h, i, j;
  • It is possible to follow more easily the drift of sensors from years to years. For that reason, the calibration reports should contain graphs of drift established for each sensor, when they have been calibrated at least two times in this laboratory. These graphs can be used by users to assess the calibration periodicity for each sensor.

Sometimes, it appears during calibrations that sensors have lost their linearity. The laboratory must then calculate new g, h, i, j coefficients which must be programmed in software like Sea Bird coefficients.

A verification of their validity is made with new measurements in the calibration bath to validate them, before writing the report.

When the tests made with this new set of coefficients show that the errors generated by the conductivity sensor cannot be corrected to be less than 0.01 mS/cm, or 0.002 °C for a temperature sensor, the calibration report indicates that the sensor must be send back to Sea Bird for repairing. This case appends when the sensor has an electronic failure or when it is strongly fouled and cannot be cleaned.