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

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 de-correlation length scales are estimated from rawinsonde height observed-minus-forecast residuals. Sea-level pressure error standard deviations and de-correlation length scales are obtained from ship reports, and wind observation error standard deviations and forecast error stream function and velocity potential de-correlation 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 o...