Maximum-likelihood estimation of forecast and observation error covarianceparameters. Part I: Methodology

The maximum-likelihood method for estimating observation and forecast error covariance parameters is described. The method is presented in general ter ms but with particular emphasis on practical aspects of implementation. Iss ues such as bias estimation and correction, parameter identifiability, esti mation accuracy, and robustness of the method, are discussed in detail. The relationship between the maximum-likelihood method and generalized cross-v alidation is briefly addressed. The method can be regarded as a generalization of the traditional procedure For estimating covariance parameters from station data. It does not involv e any restrictions on the covariance models and can be used with data from moving observers, provided the parameters to be estimated are identifiable. Any available a priori information about the observation and forecast erro r distributions can be incorporated into the estimation procedure. Estimate s of parameter accuracy due to sampling error are obtained as a by-product.