Data fusion is a process for combining two, or more, sources of information to improve the representation of a given system. In a recent paper, data fusion has been used to remove noise from SMOS sea surface salinity (SSS) products, by fusing SMOS data with sea surface temperature (SST) fields.
Our approach is justified by the correspondence between the singularity exponents of SSS and SST. The singularity exponent is a non-dimensional measure of the regularity or irregularity of a field in a given point. The value of the singularity exponent increases with the smoothness of a field. The correspondence between the singularity exponents of SST and SSS implies the existence of a local functional dependence between these two variables. This correspondence can be illustrated using data of a numerical simulation (OFES, Ocean General Circulation Model for the Earth Simulator).
Figure 1 shows two conditioned histograms. The one in the top illustrates the histogram of SSS conditioned by each given value of SST. The conditioned histogram looks like a superposition of narrow lines. It indicates that, while strong local SSS-SST correlations exist, these relations do change from one region to the other. On the contrary, the conditioned histogram of SSS singularity exponents conditioned by the value of the singularity exponents of SST indicates that a unique correlation exists all over the world ocean. In fact, the slope of the maximum probability line is close to one, indicating an almost perfect identity between the singularity exponents of SST and SSS.