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.

The AROME-EPS convection-permitting ensemble prediction system has been evaluated over the HyMeX-SOP1 period. Objective verification scores are computed using dense observing networks prepared for the HyMeX experiment. In probabilistic terms, the AROME-EPS ensemble performs better than the AROME-France deterministic prediction system, and a state-of-the-art ensemble at a lower resolution. The strengths and weaknesses of AROME-EPS are discussed. Here, impact experiments are used to study perturbation schemes for the initial conditions and the model surface. Both have a significant effect on the ensemble performance. The interactions between the perturbations of lateral boundaries, initial conditions and surface perturbations are studied. The consistency between initial and lateral perturbations is found to be unimportant from a meteorological point of view. Ensemble data assimilation is not as effective as a simpler surface perturbation scheme, and it is noted that both approaches could be usefully combined.

Abstract. This paper investigates the potential benefit of ground-based microwave radiometers (MWRs) to improve the initial state (analysis) of current numerical weather prediction (NWP) systems during fog conditions. To this end, temperature, humidity and liquid water path (LWP) retrievals have been performed by directly assimilating brightness temperatures using a one-dimensional variational technique (1D-Var). This study focuses on a fog-dedicated field-experiment performed over winter 2016–2017 in France. In situ measurements from a 120 m tower and radiosoundings are used to assess the improvement brought by the 1D-Var analysis to the background. A sensitivity study demonstrates the importance of the cross-correlations between temperature and specific humidity in the background-error-covariance matrix as well as the bias correction applied on MWR raw measurements. With the optimal 1D-Var configuration, root-mean-square errors smaller than 1.5 K (respectively 0.8 K) for temperature and 1 g kg−1 (respectively 0.5 g kg−1) for humidity are obtained up to 6 km altitude (respectively within the fog layer up to 250 m). A thin radiative fog case study has shown that the assimilation of MWR observations was able to correct large temperature errors of the AROME (Application of Research to Operations at MEsoscale) model as well as vertical and temporal errors observed in the fog life cycle. A statistical evaluation through the whole period has demonstrated that the largest impact when assimilating MWR observations is obtained on the temperature and LWP fields, while it is neutral to slightly positive for the specific humidity. Most of the temperature improvement is observed during false alarms when the AROME forecasts tend to significantly overestimate the temperature cooling. During missed fog profiles, 1D-Var analyses were found to increase the atmospheric stability within the first 100 m above the surface compared to the initial background profile. Concerning the LWP, the RMSE with respect to MWR statistical regressions is decreased from 101 g m−2 in the background to 27 g m−2 in the 1D-Var analysis. These encouraging results led to the deployment of eight MWRs during the international SOFOG3D (SOuth FOGs 3D experiment for fog processes study) experiment conducted by Météo-France.