Triple collocation for binary and categorical variables: Application to validating landscape freeze/thaw retrievals

Triple collocation (TC) can be used to validate observations of a continuous geophysical target variable when the error-free true value is not known. However, as we show in this study, naive application of TC to categorical target variables results in biased error estimates. The bias occurs because the categorical variable is usually bounded, introducing correlations between the errors and the truth, violating TC's assumptions. We introduce Categorical Triple Collocation (CTC), a variant of TC that relaxes these assumptions and may be applied to categorical target variables. The method estimates the rankings of the three measurement systems for each category with respect to their balanced accuracies (a binary-variable performance metric). As an example application, we estimate performance rankings of landscape freeze/thaw (FT) observations derived from model soil temperatures, in situ station air temperatures and satellite-observed microwave brightness temperatures in Alberta and Saskatchewan, Canada. While rankings vary spatially, in most locations the model-based FT product is ranked the highest, followed by the satellite product and the in-situ air temperature product. These rankings are likely due to a combination of differences in measurement errors between FT products, and differences in scale. They illustrate the value in using a suite of different measurements as part of satellite FT validation, rather than simply treating in-situ measurements as an error-free 'truth'. (C) 2016 Elsevier Inc. All rights reserved.