Data assimilation (DA) methods for convective‐scale numerical weather prediction at operational centres are surveyed. The operational methods include variational methods (3D‐Var and 4D‐Var), ensemble methods (LETKF) and hybrids between variational and ensemble methods (3DEnVar and 4DEnVar). At several operational centres, other assimilation algorithms, like latent heat nudging, are additionally applied to improve the model initial state, with emphasis on convective scales. It is demonstrated that the quality of forecasts based on initial data from convective‐scale DA is significantly better than the quality of forecasts from simple downscaling of larger‐scale initial data. However, the duration of positive impact depends on the weather situation, the size of the computational domain and the data that are assimilated. Furthermore it is shown that more advanced methods applied at convective scales provide improvements over simpler methods. This motivates continued research and development in convective‐scale DA. Challenges in research and development for improvements of convective‐scale DA are also reviewed and discussed. The difficulty of handling the wide range of spatial and temporal scales makes development of multi‐scale assimilation methods and space–time covariance localization techniques important. Improved utilization of observations is also important. In order to extract more information from existing observing systems of convective‐scale phenomena (e.g. weather radar data and satellite image data), it is necessary to provide improved statistical descriptions of the observation errors associated with these observations.

SUMMARYWe present an overview of the 3D-Var data assimilation in the framework of the ALADIN/France model. The purpose of this system is to provide improved precipitation forecasts at mesoscale and in the short range, up to 18 hours. The goal of the paper is threefold. Firstly, we present initial considerations for the design of the 3D-Var system. Secondly, we discuss in more detail the specification of the background-error covariance matrix, by comparing three different error simulation techniques, namely two variants of the NMC method and an ensemble-based approach. The formal, diagnostic and impact studies have led to the selection of the ensemblebased covariances for the ALADIN/France assimilation. Thirdly, scores of quantitative precipitation forecasts are shown in order to illustrate the robustness and the preliminary meteorological performance of the ALADIN/France assimilation suite. The results indicate that the tested configuration improves some aspects of the precipitation forecast, while being neutral for others, when compared with the spin-up model.We conclude the paper by providing a more explicit insight into the future evolution of limited-area variational analysis towards convective-scale data assimilation.

In data assimilation (DA) schemes for numerical weather prediction (NWP) systems, the estimation of forecast error covariances is a key point to get some flow dependency. As shown in previous studies, ensemble data assimilation methods are the most accurate for this task. However, their huge computational cost raises a strong limitation to the ensemble size. Consequently, covariances estimated with small ensembles are affected by random sampling errors. The aim of this study is to develop a theory of covariance filtering in order to remove most of the sampling noise while keeping the signal of interest and then to use it in the DA scheme of a real NWP system. This first part of a two-part study presents the theoretical aspects of such criteria for optimal filtering based on the merging of the theories of optimal linear filtering and of sample centered moments estimation. Its strength relies on the use of sample estimated quantities and filter output only. These criteria pave the way for new algorithms and interesting applications for NWP. Two of them are detailed here: spatial filtering of variances and covariance localization. Results obtained in an idealized 1D analytical framework are shown for illustration. Applications on real forecast error covariances deduced from ensembles at convective scale are discussed in a companion paper.