Extended triple collocation: estimating errors and correlation coefficients with respect to an unknown target

Calibration and validation of geophysical measurement systems typically requires knowledge of the “true” value of the target variable. However, the “true” values often include their own measurement errors, calibration biases, and validation results. Triple collocation (TC) can be used to estimate the root-mean-square-error (RMSE), using observations from three mutually-independent, error-prone measurement systems. Here, we introduce Extended Triple Collocation (ETC): using exactly the same assumptions as TC, we derive an additional performance metric, the correlation coefficient of the measurement system with respect to the unknown target, . We demonstrate that is the scaled, unbiased signal-to-noise ratio, providing a complementary (and sometimes, very different) perspective compared to the RMSE. We apply it to three collocated wind datasets. Since ETC is as easy to implement as TC, requires no additional assumptions, and provides an additional performance metric, we suggest it may be of interest in a wide range of geophysical disciplines.