Exploitation of error correlation in a large analysis validation: GlobCurrent case study

• Published in: Remote sensing of environment 2018-11, Vol.217, p.476-490
• Main Authors: Danielson, Richard E., Johannessen, Johnny A., Quartly, Graham D., Rio, Marie-Hélène, Chapron, Bertrand, Collard, Fabrice, Donlon, Craig
• Format: Article
• Language: English
• Subjects: Autocorrelation; Autoregressive models; Calibration; Case studies; Collocation; Correlation; Correlation analysis; Data processing; Drift; Error analysis; Exploitation; Measurement errors; Measurement model; Ocean current; Ocean currents; Oceans; Parameter identification; Regression analysis; Sciences of the Universe; Signal to noise ratio; Surface water; Topography; Validation
• ISSN: 0034-4257; 1879-0704
• DOI: 10.1016/j.rse.2018.07.016

An assessment of variance in ocean current signal and noise shared by in situ observations (drifters) and a large gridded analysis (GlobCurrent) is sought as a function of day of the year for 1993–2015 and across a broad spectrum of current speed. Regardless of the division of collocations, it is difficult to claim that any synoptic assessment can be based on independent observations. Instead, a measurement model that departs from ordinary linear regression by accommodating error correlation is proposed. The interpretation of independence is explored by applying Fuller's (1987) concept of equation and measurement error to a division of error into shared (correlated) and unshared (uncorrelated) components, respectively. The resulting division of variance in the new model favours noise. Ocean current shared (equation) error is of comparable magnitude to unshared (measurement) error and the latter is, for GlobCurrent and drifters respectively, comparable to ordinary and reverse linear regression. Although signal variance appears to be small, its utility as a measure of agreement between two variates is highlighted. Sparse collocations that sample a dense (high resolution) grid permit a first order autoregressive form of measurement model to be considered, including parameterizations of analysis-in situ error cross-correlation and analysis temporal error autocorrelation. The former (cross-correlation) is an equation error term that accommodates error shared by both GlobCurrent and drifters. The latter (autocorrelation) facilitates an identification and retrieval of all model parameters. Solutions are sought using a prescribed calibration between GlobCurrent and drifters (by variance matching). Because the true current variance of GlobCurrent and drifters is small, signal to noise ratio is near zero at best. This is particularly evident for moderate current speed and for the meridional current component. •Signal/noise of two ocean current datasets are compared by day of the year and speed.•A first order autoregressive form of regression model and its solution are derived.•Fuller's (1987) equation/measurement errors are applied to shared/unshared errors.•Shared true variance is smaller, and equation error larger, than expected.•Measurement error is saturated at ordinary and reverse least squares bounds.