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  Calculated Parameters - Salinity

There is no easy way to directly measure the salinity of seawater.  However, there are a number of methods to calculate this parameter using accepted equations of state.  Essentially, if any three of the parameters listed below are known, it is possible to mathematically calculate the values for the other three parameters.  The parameters include: 

  • temperature
  • pressure
  • conductivity
  • salinity
  • sound speed (sound velocity)
  • density

The equations used to calculate salinity, density and sound velocity - or to reverse calculate conductivity, temperature, or pressure - include:

  Response Time and Calculated Parameters

Mismatches in sensor response times (primarily between C & T) cause anomalous errors in the salinity data.  These errors are typically referred to as salinity spikes.  Since salinity, temperature and pressure are used to calculate density and sound speed these data spikes also occur in those data sets.  The greater the mismatch in sensor response times between sensors, the larger the salinity spikes will be.  The salinity spike magnitude is also proportional to the thermal and conductivity gradients and the profiling speed.

The three following charts demonstrate salinity spiking. The ‘actual’ and ‘measured’ data were mathematically derived to demonstrate the principle.  The profiles were conducted at a 0.5 m/s descent speed and sampled at 10 Hz.  The solid lines are the ‘actual’ water conditions and the dotted lines are the ‘measured’ and calculated data. 

The two ‘measured’ data sets were derived using typical AML Oceanographic CTD sensor response times.  Our Micro CTD uses a 100ms response temperature sensor and the CTD Plus v2 uses a 350ms response temperature sensor. Both CTD’s use a 25ms response conductivity sensor and a 10ms response pressure sensor. 

The first chart - see below - shows the ‘actual’ and ‘measured’ temperature and conductivity of a ten meter column of water.  Note the depression of the thermocline caused by the slow response time of the temperature sensor.  Also note the smoothing of the small scale structure of the temperature profile.  This is where the majority of the errors originate.

The second chart shows the salinity and density profiles calculated from the ‘measured’ data as well as the ‘actual’ data set.  Note the false indications of less saline water intrusions in the salinity profile.  Also note the depression in depth and stronger picnoclines in the density profile.


In the field the actual data is never present so it is very difficult to assess the magnitude of the errors due to salinity spiking.  In this case, since there is not a large change in salinity the salinity spiking is readily apparent even without looking at the ‘actual’ profile.  However in profiles with strong haloclines the salinity spiking can be difficult to see in a profile, though the errors are still there.

The final chart shows the calculated sound speed profiles.  The salinity profiles are also included for reference.  The depth depression and smoothing effects can be seen in the sound speed profiles.

  What is the Difference Between Precision and Accuracy?
Many vendors of oceanographic instrumentation refer to accuracy and precision interchangeably.  They are not interchangeable.  In effect, accuracy refers to how well a sensor performs against a known third party standard.  For example, a temperature sensor may be +/- 0.001 C, as compared to a Black Stack themistor module.  Precision refers to the repeatability of the readings of a given sensor.   A sensor is precise when it repeatedly provides the same reading, regardless of how accurate that reading is.

A good analogy is a dart board.  The thrower of darts is accurate when he or she is able to reach the target, the bulls-eye.  He or she is precise if, having thrown three darts, all three land in the same location, irrespective of whether or not that location is the bulls-eye.