A Bayesian technique for estimating continuously varying statistical parameters of a variational assimilation

¶Nonhydrostatic models with horizontal grid resolutions of around 10 km are becoming operational at several forecasting centers. At these scales it is particularly desirable that the covariances employed in variational or statistical analysis schemes be defined in a more general way than the spatially homogeneous and isotropic covariance models that have been typical in the analysis schemes adopted at larger scales. But allowing covariances to be defined in a more adaptive way leads to a much larger parameter space required to specify them. This note addresses the challenging problem of inferring, from observed meteorological data, a set of continuous parameters defining the error covariances used to analyze data in a variational assimilation scheme. The method we propose is a Bayesian extension of the “maximum-likelihood” technique, which means that prior information about the parameters is brought into play. The method uses a stochastic approximation in the computation of some of the required terms, which are difficult and costly to evaluate by other, more standard methods. One important advantage of the proposed Bayesian approach is that it makes it possible to estimate objectively a spatially dependent but smoothly varying set of parameters in a consistent manner, provided the scale over which the variations occur is sufficiently large. This ability is illustrated in the idealized tests presented here.