deri_dyncorrT and deri_dyncorrS - derivation of practical salinity with dynamic correction

There are two types of dynamic errors affecting salinity measurements: response time and sensor misalignments, and thermal mass errors.

"Response time and sensor misalignments", or "C-T lag", refers to the time lag between temperature and conductivity measurements, which would result in "salinity spiking". It is generated by two separate mechanisms: the physical separation between the thermistor and the conductivity cell, and the inherent response time of the thermistor.

"Thermal mass errors" refers to the thermal mass of the conductivity cell impacting the temperature of the water column where the seawater conductivity is measured. It occurs when the CTD travels through a temperature gradient. Thermal mass errors present two main separate timescales: a long-term thermal mass error (timescales of minutes) and a short-term thermal mass error (timescales of seconds).

In order to correct all those dynamic errors, the logger provides two channels that implement the dynamic correction equations. They rely on two types of equations: deri_dyncorrT (temperature in °C) and deri_dyncorrS (salinity in PSU).

The C-T lag correction and the short-term thermal mass correction are only applied when the sample is acquired while the instrument is actively logging at a sampling rate of at least 1Hz.

The long-term thermal mass correction is only applied when the sample is acquired while the instrument is actively logging at a sampling rate of at least 0.1Hz.

deri_dyncorrT equation

If the sample is acquired or polled while actively logging at a sampling rate greater or equal to 1Hz,

Otherwise

where

• T_cor is the C-T lag corrected temperature (°C).

• T_meas is the marine temperature (°C).

• F_s is the sampling frequency (Hz).

• Δt is the C-T lag correction (s).

• n0 is the label of the supporting marine temperature channel  (n0=temperature_00 in the examples below). 
  value(n0) is the final output value of this channel in degree Celsius, i.e T_meas.

deri_dyncorrS equation

with

and

where

and

If the sample is polled or not acquired while actively sampling at a rate faster or equal to 1Hz,

If the sample is polled or not acquired while actively sampling at a rate faster or equal to 0.1Hz,

where:

• f_N is the Nyquist frequency, defined as half the sampling rate F_s.

• α(n) is the magnitude of short-term thermal mass correction and depends on the instantaneous ascent rate.

• τ(n) is the time constant of short-term thermal mass correction (s) and depends on the instantaneous ascent rate.

• ctcoeff(n) is the magnitude of the long-term thermal mass correction and depends on the instantaneous ascent rate.

• n0 is the label of the conductivity channel. (n0=conductivity_00 in examples below).
  value(n0) is the final output value of this channel in mS/cm, i.e. C.

• n1 is the label of the sea pressure channel. (n1=seapressure_00 in examples below).
  value(n1) is the final output value of this channel in dbar i.e. P.

• n2 is the label of the C-T lag corrected temperature channel. (n2=temperature_01 in examples below).
  value(n2) is the final output value of this channel in °C, i.e. T_cor .

• n3 is the label of the internal temperature of the conductivity cell channel. (n3=conductivitytemperature_00 in examples below).
  value(n3) is the final output value of this channel in °C, i.e. T_cond.
  Examples

>> calibration temperature_00 datetime= 20251001000000 x0=0.3500
<< calibration temperature_00 datetime= 20251001000000 x0=0.3500

Set the temperature coefficients.

>> calibration salinity_00 datetime=20251001000000 x0=0.1300 x1=5.9000 x2=1.0200e-00
<< calibration salinity_00 datetime=20251001000000 x0=0.1300 x1=5.9000 x2=1.0200e-00

Set the salinity coefficients provided.

>> calibration temperature_01
<< calibration temperature_01 datetime=20251001000000 equation=deri_dyncorrT offset=0.0000000e+000 slope=1.0000000e+000 x0=0.3500 n0=temperature_00

>> calibration salinity_01
<< calibration salinity_01 datetime=20251001000000 equation=deri_dyncorrS offset=0.0000000e+000 slope=1.0000000e+000 x0=0.3700 x1=-1.0300 x2=16.0200 x3=-0.2600 x4=0.1400 x5=-1.0000 x6=0.0400 x7=0.0500 x8=0.1500 n0=conductivity_00 n1=seapressure_00 n2=temperature_01 n3=conductivitytemperature_00