A double instrumental variable method for geophysical product error estimation

The global validation of remotely sensed and/or modeled geophysical products is often complicated by a lack of suitable ground observations for comparison. By cross-comparing three independent collocated observations, triple collocation (TC) can solve for geophysical product errors in error-prone systems. However, acquiring three independent products for a geophysical variable of interest can be challenging. Here, a double instrumental variable based algorithm (IVd) is proposed as an extension of the existing single instrumental variable (IVs) approach to estimate product error standard deviation (sigma) and product-truth correlation (R) using only two independent products - an easier requirement to meet in practice. An analytical examination of the IVd method suggests that it is less prone to bias and has reduced sampling errors relative to IVs. Results from an example application of the IVd method to precipitation product error estimation show that IVd-based a and R are good approximations of reference values obtained from TC at the global extent. In addition to their spatial consistency, IVd estimated error metrics also have only marginal (less than 5%) relative biases versus a TC baseline. Consistent with our earlier analytical analysis, these empirical results are shown to be superior to those obtained by IVs. However, several caveats for the IVd approach should be acknowledged. As with TC and IVs, IVd estimates are less robust when the signal-to-noise ratio of geophysical products is very low. Additionally, IVd may be significantly biased when geophysical products have strongly contrasting error auto-correlations.