"Salting" South Atlantic XBTs
The regression models computed within overlapping shingles provide estimates of salinity to accompany XBT profiles within non-overlapping 4x1 regions at regularly spaced depths. A choice of 16 different models for each target region and each level is available. When compared against independent verification data the models using temperature, temperature squared, longitude, and latitude were among the best for all regions and for all depths.
The regression models can be represented as a table of coefficients and indicators of the region and level at which the coefficients apply. For the model employing all four regressors, salinity can be computed as:
S = a + b × T + c × T2 + d × longitude + e × latitude
Where longitude and latitude are the coordinates of the XBT station, T is the temperature at one of the standard pressure levels at 25 dbar intervals, a through e are the regression coefficients appropriate for that level for the shingle with center closest to the XBT station, and where S is the estimate for salinity at that station and level. The model coefficients can be tabulated along with information about the pressure level and the longitude and latitude of the center of the shingle to which they apply.
XBT temperatures are usually reported for depths determined from the fall time of the probe, which can be converted to pressure using the hydrostatic equation with the climatological density profile in the vicinity of the station. Once salinity values have been estimated from the measured temperatures, an improved density profile can be computed from the equation of state of sea-water to get an improved estimate of pressure to be used for a corrected estimate of salinity.
To get estimates at other levels, the regression coefficients can be interpolated from the standard levels to the desired levels, e.g. the levels where the XBT temperatures were recorded. Because surface processes make surface salinity very difficult to estimate, no regression coefficients were given for 0 dbar. Near-surface estimates might be made using the models for 25 dbar.