### Climatological Mean Fields

Climatological fields provide simple estimates for salinity.

The mean salinity field at each pressure level provides a simplest temperature-independent estimate of salinity. Mean fields at pressure levels, like those for the salinity minimum, can be computed using inverse-square-distance weighted averages. The standard-deviation field gives an idea of the accuracy of such estimates.

A popular way to account for salinity's co-variability with temperature when the mean temperature field at each pressure level is known is to plot the TS curve for the means at a particular location and look up the salinity corresponding to the observed temperature. This works best when variability is dominated by vertical displacements that preserve water-mass properties. The mean temperature and its standard deviation can be easily computed.

An improvement to using the climatological mean salinity on a pressure surface would be to use the climatological mean on a temperature surface to estimate the salinity to accompany the measuered temperatures at the location of the XBT station. In fact, this is likely to be better than the estimate based on the climatological TS curve. The mean salinity on a temperature surface could be computed in a manner similar to that used for the means at the salinity minimum, or it might be computed using smoothing splines.

Because the equation of state relating salinity, temperature, density and pressure is not linear, mean salinity and mean temperature at a specified pressure might not characterize the water at that pressure level. For this reason some people prefer a climatology on density surfaces, which might be computed like the climatology at the salinity minimum. Such a climatology can be particularly useful for initializing a numerical ocean circulation model formulated in terms of density layers. Again, the TS curves for the means on density surfaces can be used as a basis for simple estimates of salinity. More conventional circulation models can be initialized using the mean density field at pressure levels, and for consistency with the equation of state either mean salinity or mean temperature at the pressure level can be prescribed and the other diagnosed.

While estimates of salinity based on climatological mean fields of salinity and temperature have proven useful over the years, it is possible to do better. Regression models at fixed depths (pressure levels) offer the possibility to capture the co-variability of salinity with temperature and to include systematic influences of longitude and latitude. In fact they can exploit any data that might provide information about salinity