Error characterization of soil moisture satellite products: retrieving error cross-correlation through extended quadruple collocation

The triple collocation (TC) technique is being increasingly used to validate soil moisture retrievals derived from different systems, like satellites, hydrological models, or in situ probes. In recent years, several extensions of this method were proposed in order to evaluate the error standard deviations of more than three systems and to soften the TC hypothesis. In this paper, a novel extended quadruple collocation (E-QC) method is proposed, in order to consider the possibility of a cross correlation between product errors, identifying automatically the couple of error cross-correlated systems. The method is applicable even to a larger number of collocated datasets, although it may be unfeasible to collect them in practice. A synthetic experiment showed promising results, concluding that the E-QC is able to individuate (if any) the pair of systems with cross-correlated errors. It correctly compensates for the latter contribution and accurately retrieves error standard deviations of each system, otherwise biased if cross correlation is not taken into account. The E-QC was applied to soil moisture retrievals provided by satellite (SMOS, ASCAT, and SMAP), model (ERA Interim), and in situ probes (ISMN). The E-QC method identified the presence of error cross-correlation between the satellite products. This was also confirmed by analyzing the five datasets all together. E-QC showed fair performances of satellite products, especially of SMAP, although not as good as in case the presence of error correlation is not correctly taken into account