Extended Triple Collocation: Estimating Errors And Correlation Coefficients With Respect To An Unknown Target

Kaighin A Mccoll, Harvard University, Earth and Planetary Sciences and School of Engineering and Applied Sciences, Cambridge, MA, United States, Jur Vogelzang, Royal Netherlands Meteorological Institute, De Bilt, Netherlands, Alexandra G Konings, Stanford University, Earth System Science, Stanford, CA, United States, Dara Entekhabi, Massachusetts Institute of Technology, Civil and Environmental Engineering, Cambridge, MA, United States, Maria Piles, SMOS Barcelona Expert Center, Barcelona, Spain and Ad Stoffelen, Royal Netherlands Meteorological Institute, De Bilt, 3730, Netherlands
Abstract:
Calibration, validation and error-characterization of geophysical measurement systems typically requires knowledge of the “true” value of the target variable. However, the data considered to represent the “true” values often include their own measurement errors, biasing calibration 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, R2. We demonstrate that R2 is the scaled, unbiased signal-to-noise ratio, and provides a complementary perspective compared to the RMSE. We apply it to three collocated wind datasets: the ECMWF numerical weather prediction forecast, ASCAT scatterometer retrievals and in-situ buoy measurements. Since ETC is as easy to implement as TC, requires no additional assumptions, and provides an extra performance metric, it may be of interest in a wide range of geophysical disciplines.
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