Maximum-Likelihood Estimation of Forecast and Observation Error Covariance Parameters. Part II: Applications

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Abstract
Three different applications of maximum-likelihood estimation of error covariance parameters for atmospheric data assimilation are described. Height error standard deviations, vertical correlation coefficients, and isotropic decorrelation length scales are estimated from rawinsonde height observed-minus-forecast residuals. Sea level pressure error standard deviations and decorrelation length scales are obtained from ship reports, and wind observation error standard deviations and forecast error stream function and velocity potential decorrelation length scales are estimated from aircraft data. These applications serve to demonstrate the ability of the method to estimate covariance parameters using multivariate data from moving observers. Estimates of the parameter uncertainty due to sampling error can be obtained as a by-product of the maximum-likelihood estimation. By bounding this source of error, it is found that many statistical parameters that are usually presumed constant in operational data assimilation systems in fact vary significantly with time. This may well reflect the use of overly simplistic covariance models that cannot adequately describe state-dependent error components such as representativeness error. The sensitivity of the parameter estimates to the treatment of bias, and to the choice of the model representing spatial correlations, is examined in detail. Several experiments emulate an online covariance parameter estimation procedure using a sliding window of data, and it is shown that such a procedure is both desirable and computationally feasible.

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