A triple collocation-based 2D soil moisture merging methodology considering spatial and temporal non-stationary errors

Abstract Random error in remotely sensed (RS) and modeled soil moisture (SM) products is typically assumed to be statistically stationary for the purpose of SM merging applications. In reality, such error is often non-stationary, which may undermine applications based on a stationary assumption. Here, we introduce a dual time-space (2D) SM merging approach that considers a class of inferred error that is non-stationary and undetectable in time (or space) but stationary and detectable in space (or time). Such 2D merging is realized in a least-squares framework where spatial and temporal error variances for each product are estimated via a triple collocation (TC) analysis. As a test case, a 2D-merged SM product is obtained by combining three independent SM products – including two RS SM products and one modeled SM product. Results show that the 2D merging method can effectively handle non-stationary errors and, as a result, produces a superior merged SM product than classical 1D merging methods. The spatial and temporal correlations with in-situ observations are 0.62 and 0.63 [−] on average for 2D merging methods, and 0.58 and 0.59 [−] on average for classical 1D merging methods. By providing a more effective way to detect and remove non-stationary errors during the process of merging multi-source SM products, this approach will improve future global multi-source merged SM products.