An instrument variable based algorithm for estimating cross-correlated hydrological remote sensing errors

Abstract

Optimally using multi-source remote-sensing (RS) and/or reanalyzed hydrological products requires knowledge of each product’s accuracy and inter-product error cross-correlations. Quadruple collocation (QC) analysis can potentially solve for this error information without the reliance of high-quality ground references. However, QC requires at least three independent products for a variable of interest. At the global scale, obtaining three independent products is often a challenge. To address this issue, this study proposes an extended double instrumental variable algorithm (denoted as EIVD), which can accurately estimate product error and inter-product error cross-correlations using only two independent products – a requirement easier to meet in practice. Synthetic numerical experiments demonstrate that EIVD is robust and unbiased – provided product error auto-correlations are not strongly contrasting. The performance of EIVD is further tested via a (real-data) global precipitation error analysis using traditional QC results as a validation reference. The global consistency (i.e., spatial correlation) of QC- and EIVD-estimated product-truth correlation is above 0.86 [–] for all precipitation products being considered, and the relative mean difference of QC- and EIVD-based correlations is, on average, less than 5%. The spatial consistency of QC- and EIVD-based inter-product error cross-correlation is 0.47 [–] with a relative bias of 8%. A quantitative analysis demonstrates that regions with inconsistent EIVD and QC results are likely attributable to the violation of the QC error independency assumptions. Given the robustness of EIVD in fully parameterizing hydrological product error information, it is expected to improve the accuracy and efficiency of multi-source hydrological data merging and data assimilation.