Assimilation of salinity into ocean and climate general circulation models is a very important problem. ARGO data now provide far more salinity observations than ever before. In addition a good analysis of salinity over time in ocean reanalyses can give important results for understanding climate change. Here we show from the historical ocean database that over large regions of the globe (mainly mid and lower latitudes) variance of salinity on an isotherm S(T) is often less than variance measured at a particular depth S(z). We also show that the dominant temporal variability of S(T) is slower than S(z) based on power spectra from the Bermuda timeseries, and from ocean models we show that the horizontal spatial covariance of S(T) often
has larger scales than S(z).
These observations suggest an assimilation method based on analysing S(T). We present an algorithm for applying S(T) assimilation and show how it can be made orthogonal to the multivariate assimilation of temperature data which produces its own salinity correction. We argue that the larger space and timescales should allow larger gain matrices to be used for the S(T) assimilation leading to better use of scarce salinity observations.
Finally we show results of applying the salinity assimilation algorithm to a single analysis time within the
ECMWF seasonal forecasting ocean model. The separate salinity increments coming from temperature and salinity data are identified and the independence of these increments is demonstrated. Results of an ocean reanalysis with this method will appear in a companion paper
