Premium
Extended triple collocation: Estimating errors and correlation coefficients with respect to an unknown target
Author(s) -
McColl Kaighin A.,
Vogelzang Jur,
Konings Alexandra G.,
Entekhabi Dara,
Piles María,
Stoffelen Ad
Publication year - 2014
Publication title -
geophysical research letters
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 2.007
H-Index - 273
eISSN - 1944-8007
pISSN - 0094-8276
DOI - 10.1002/2014gl061322
Subject(s) - metric (unit) , collocation (remote sensing) , mean squared error , calibration , observational error , range (aeronautics) , noise (video) , square root , mathematics , statistics , computer science , algorithm , artificial intelligence , geometry , operations management , materials science , image (mathematics) , machine learning , economics , composite material
Calibration and validation of geophysical measurement systems typically require 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, ρ t , X i. We demonstrate that ρ t , X i 2 is the scaled, unbiased signal‐to‐noise ratio and provides a complementary perspective compared to the RMSE. We apply it to three collocated wind data sets. 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.