On the Accuracy and Consistency of Quintuple Collocation Analysis of In Situ, Scatterometer, and NWP Winds

The accuracy and consistency of a quintuple collocation analysis of ocean surface vector winds from buoys, scatterometers, and NWP forecasts is established. A new solution method is introduced for the general multiple collocation problem formulated in terms of covariance equations. By a logarithmic transformation, the covariance equations reduce to ordinary linear equations that can be handled using standard methods. The method can be applied to each determined or overdetermined subset of the covariance equations. Representativeness errors are estimated from differences in spatial variances. The results are in good agreement with those from quadruple collocation analyses reported elsewhere. The geometric mean of all solutions from determined subsets of the covariance equations equals the least-squares solution of all equations. The accuracy of the solutions is estimated from synthetic data sets with random Gaussian errors that are constructed from the buoy data using the values of the calibration coefficients and error variances from the quintuple collocation analysis. For the calibration coefficients, the spread in the models is smaller than the accuracy, but for the observation error variances, the spread and the accuracy are about equal only for representativeness errors evaluated at a scale of 200 km for u and 100 km for v. Some average error covariances differ significantly from zero, indicating weak inconsistencies in the underlying error model. Possible causes for this are discussed. With a data set of 2454 collocations, the accuracy in the observation error standard deviation is 0.02 to 0.03 m/s at the one-sigma level for all observing systems.