Estimating error cross‐correlations in soil moisture data sets using extended collocation analysis

Global soil moisture records are essential for studying the role of hydrologic processes within the larger earth system. Various studies have shown the benefit of assimilating satellite‐based soil moisture data into water balance models or merging multisource soil moisture retrievals into a unified data set. However, this requires an appropriate parameterization of the error structures of the underlying data sets. While triple collocation (TC) analysis has been widely recognized as a powerful tool for estimating random error variances of coarse‐resolution soil moisture data sets, the estimation of error cross covariances remains an unresolved challenge. Here we propose a method—referred to as extended collocation (EC) analysis—for estimating error cross‐correlations by generalizing the TC method to an arbitrary number of data sets and relaxing the therein made assumption of zero error cross‐correlation for certain data set combinations. A synthetic experiment shows that EC analysis is able to reliably recover true error cross‐correlation levels. Applied to real soil moisture retrievals from Advanced Microwave Scanning Radiometer‐EOS (AMSR‐E) C‐band and X‐band observations together with advanced scatterometer (ASCAT) retrievals, modeled data from Global Land Data Assimilation System (GLDAS)‐Noah and in situ measurements drawn from the International Soil Moisture Network, EC yields reasonable and strong nonzero error cross‐correlations between the two AMSR‐E products. Against expectation, nonzero error cross‐correlations are also found between ASCAT and AMSR‐E. We conclude that the proposed EC method represents an important step toward a fully parameterized error covariance matrix for coarse‐resolution soil moisture data sets, which is vital for any rigorous data assimilation framework or data merging scheme. Key Points Triple collocation analysis is extended to an arbitrary number of data sets Extended collocation analysis allows for the estimation of error cross‐correlations The method is evaluated using synthetic and real data