Error Characterization of Similar Products: Triple Collocation with Correlated Errors

Abstract:

Data assimilation applications require characterization of the errors in the products being assimilated. When true data are not available to explicitly compute these errors, triple collocation (TC) provides a methodology to estimate the root-mean-square errors (RMSEs) and correlations by combining three simultaneous co-located estimates. Triple collocation assumes that for each of the three products, the errors are independent of each other. In many cases, however, one may expect correlations between errors to be significant. Among others, they are likely to occur when there is a representativeness error between some of the products (e.g. if one of the products is based on in situ measurements) or if two out of the three products have a similar source – for example both coming from microwave remote sensing estimates or both originating in land surface models. Indeed, previous studies have shown that this assumption can induce significant inaccuracies in the error estimates. For classical TC, the assumption is needed for the system to be fully determined - only six independent equations are available for estimating 6 unknowns: 3 scale parameters and 3 error variances (i.e. RMSEs). In this presentation, we propose obtaining additional information from the triplet of observations by using errors-in-variables-based regressions between pairs of noisy observations to estimate the scale parameters. The introduction of additional equations allows for the derivation of additional unknowns, such that non-zero correlations between the errors of the different products can be derived. This significantly increases the accuracy of the estimated errors compared to classical triple collocation, as will be shown using both simulation studies with known errors and an application to soil moisture data.