Extended triple collocation: Estimating errors and correlation coefficients with respect to an unknown target. Issue 17 (10th September 2014)

• Record Type: Journal Article
• Authors: McColl, Kaighin A.; Vogelzang, Jur; Konings, Alexandra G.; Entekhabi, Dara; Piles, María; Stoffelen, Ad
• Is Part Of: Geophysical research letters. Volume 41:Issue 17(2014:Sep.)
• Page Start: 6229
• Page End: 6236
• Publication Date: 2014-09-10
• Subjects: Geophysics -- Periodicals; Planets -- Periodicals; Lunar geology -- Periodicals; 550
• DOI: 10.1002/2014GL061322
• Languages: English
• ISSNs: 0094-8276

Abstract

<abstract abstract-type="main"> <title>Abstract</title> <p>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, <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1f9cps1b" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" overflow="scroll" altimg="urn:x-wiley:00948276:media:grl52030:grl52030-math-0001" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msub><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>, </mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow></mml:msub></mml:math></alternatives></inline-formula>. We demonstrate that <inline-formula><alternatives><inline-graphic mimetype="image" xlink:href="ark:/27927/pgh1f9cprzq" xlink:type="simple" xmlns:xlink="http://www.w3.org/1999/xlink" /><mml:math display="inline" overflow="scroll" altimg="urn:x-wiley:00948276:media:grl52030:grl52030-math-0002" xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:msubsup><mml:mi>ρ</mml:mi><mml:mrow><mml:mi>t</mml:mi><mml:mo>, </mml:mo><mml:msub><mml:mi>X</mml:mi><mml:mi>i</mml:mi></mml:msub></mml:mrow><mml:mn>2</mml:mn></mml:msubsup></mml:math></alternatives></inline-formula> 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.</p> </abstract>