Improving the Combination of Satellite Soil Moisture Data Sets by Considering Error Cross Correlation: A Comparison Between Triple Collocation (TC) and Extended Double Instrumental Variable (EIVD) Alternatives

Satellite-derived geophysical variables provide valuable information about the earth's functioning, but there are errors that limit their direct uses. Linearly combining two or more data sources is a simple and efficient method to reduce the uncertainty between the truth and observations. However, calculating the optimal weight for such a linear combination generally needs a reference "truth" that is rarely available in practical applications. To address this limitation, a triple collocation (TC) technique is often used to estimate data error by using a data triplet without the truth. The TC-based error variances are then applied to calculate the optimal weight calculation with an assumption of independence between errors. However, ignoring the error cross-correlations (ECCs) can lead to inaccurate optimal weight for a linear combination and hence may degrade the performance of calculations using merged products. Recently, an extended double instrumental variable (EIVD) method has been proposed to estimate ECC using only three products like TC. In this study, we examined the performance of an EIVD-based linear combination approach through two applications using synthetic data and actual satellite-derived soil moisture (SM) products. For direct comparison, the TC-based linear combination was also implemented using the same data sets. The verification showed that the EIVD-based products are generally better than the TC-based products and result in statistically significant differences in correlation coefficients. While the results here are based on SM, the proposed method is potentially applicable for reconstruction of other data sets that seldom have suitable references in large-scale regional settings.