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Adaptive bias corrections for satellite radiances need to separate the observation bias from the systematic errors in the background in order to prevent the analysis from drifting towards its own climate. The variational bias correction scheme (VarBC) is a particular adaptive scheme that is embedded inside the assimilation system.VarBC is compared with an offline adaptive and a static bias correction scheme. In simulation, the three schemes are exposed to artificial shifts in the observations and the background. The VarBC scheme can be considered as a good compromise between the static and the offline adaptive schemes. It shows some skill in distinguishing between the background-error and the observation biases when other unbiased observations are available to anchor the system. Tests of VarBC in a real numerical weather prediction (NWP) environment show a significant reduction in the misfit with radiosonde observations (especially in the stratosphere) due to NWP model error. The scheme adapts to an instrument error with only minimal disruption to the analysis.In VarBC, the bias is constrained by the fit to observations -such as radiosondes -that are not bias-corrected to the NWP model. In parts of the atmosphere where no radiosonde observations are available, the radiosonde network still imposes an indirect constraint on the system, which can be enhanced by applying a mask to VarBC.

The status of current efforts to assimilate cloud-and precipitation-affected satellite data is summarised with special focus on infrared and microwave radiance data obtained from operational Earth observation satellites. All global centres pursue efforts to enhance infrared radiance data usage due to the limited availability of temperature observations in cloudy regions where forecast skill is estimated to strongly depend on the initial conditions. Most systems focus on the sharpening of weighting functions at cloud top providing high vertical resolution temperature increments to the analysis, mainly in areas of persistent high and low cloud cover. Microwave radiance assimilation produces impact on the deeper atmospheric moisture structures as well as cloud microphysics and, through control variable and background-error formulation, also on temperature but to lesser extent than infrared data. Examples of how the impacts of these two observation types are combined are shown for subtropical low-level cloud regimes. The overall impact of assimilating such data on forecast skill is measurably positive despite the fact that the employed assimilation systems have been constructed and optimized for clear-sky data. This leads to the conclusion that a better understanding and modelling of model processes in cloud-affected areas and data assimilation system enhancements through inclusion of moist processes and their error characterization will contribute substantially to future forecast improvement.

The major goal of this two-part study is to assimilate radar data into the high-resolution Advanced Research Weather Research and Forecasting Model (ARW-WRF) for the improvement of short-term quantitative precipitation forecasting (QPF) using a four-dimensional variational data assimilation (4D-Var) technique. In Part I the development of a radar data assimilation scheme within the WRF 4D-Var system (WRF 4D-Var) and the preliminary testing of the scheme are described. In Part II the performance of the enhanced WRF 4D-Var system is examined by comparing it with the three-dimensional variational data assimilation system (WRF 3D-Var) for a convective system over the U.S. Great Plains. The WRF 4D-Var radar data assimilation system has been developed with the existing framework of an incremental formulation. The new development for radar data assimilation includes the tangent-linear and adjoint models of a Kessler warm-rain microphysics scheme and the new control variables of cloud water, rainwater, and vertical velocity and their error statistics. An ensemble forecast with 80 members is used to produce background error covariance. The preliminary testing presented in this paper includes single-observation experiments as well as real data assimilation experiments on a squall line with assimilation windows of 5, 15, and 30 min. The results indicate that the system is able to obtain anisotropic multivariate analyses at the convective scale and improve precipitation forecasts. The results also suggest that the incremental approach with successive basic-state updates works well at the convection-permitting scale for radar data assimilation with the selected assimilation windows.

Convective-scale models used in NWP nowadays include detailed realistic parameterization for the representation of cloud and precipitation processes. Yet they still lack advanced data assimilation schemes able to efficiently use observations to initialize hydrometeor fields. This challenging task may benefit from a better understanding of the statistical structure of background errors in precipitating areas for both traditional and hydrometeor variables, which is the goal of this study. A special binning has been devised to compute separate background error covariance matrices for precipitating and nonprecipitating areas. This binning is based on bidimensional geographical masks defined by the vertical averaged rain content of the background error perturbations. The sample for computing the covariances is taken from an ensemble of short range forecasts run at 3-km resolution for the prediction of two specific cases of convective storms over the United States. The covariance matrices and associated diagnostics are built on the control variable transform formulation typical of variational data assimilation. The comparison especially highlights the strong coupling of specific humidity, cloud, and rain content with divergence. Shorter horizontal correlations have been obtained in precipitating areas. Vertical correlations mostly reflect the cloud vertical extension due to the convective processes. The statistics for hydrometeor variables show physically meaningful autocovariances and statistical couplings with other variables. Issues for data assimilation of radar reflectivity or more generally of observations linked to cloud and rain content with this kind of background error matrix formulation are thereon briefly discussed.

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Abstract. The specification of state background error statistics is a key component of data assimilation since it affects the impact observations will have on the analysis. In the variational data assimilation approach, applied in geophysical sciences, the dimensions of the background error covariance matrix (B) are usually too large to be explicitly determined and B needs to be modeled. Recent efforts to include new variables in the analysis such as cloud parameters and chemical species have required the development of the code to GENerate the Background Errors (GEN_BE) version 2.0 for the Weather Research and Forecasting (WRF) community model. GEN_BE allows for a simpler, flexible, robust, and community-oriented framework that gathers methods used by some meteorological operational centers and researchers. We present the advantages of this new design for the data assimilation community by performing benchmarks of different modeling of B and showing some of the new features in data assimilation test cases. As data assimilation for clouds remains a challenge, we present a multivariate approach that includes hydrometeors in the control variables and new correlated errors. In addition, the GEN_BE v2.0 code is employed to diagnose error parameter statistics for chemical species, which shows that it is a tool flexible enough to implement new control variables. While the generation of the background errors statistics code was first developed for atmospheric research, the new version (GEN_BE v2.0) can be easily applied to other domains of science and chosen to diagnose and model B. Initially developed for variational data assimilation, the model of the B matrix may be useful for variational ensemble hybrid methods as well.

An increasing number of observations have contributed to the performance of numerical weather prediction systems. Accordingly, it is important to evaluate the impact of these observations on forecast accuracy. While the observing system experiment (OSE) requires considerable computational resources, the adjoint-derived method can evaluate the impact of all observational components at a lower cost. In this study, the effect of observations on forecasts is evaluated by the adjoint-derived method using the Weather Research and Forecasting Model, its adjoint model, and a corresponding three-dimensional variational data assimilation system in East Asia and the western North Pacific for the 2008 typhoon season. Radiance observations had the greatest total impact on forecasts, but conventional wind observations had the greatest impact per observation. For each observation type, the total impact was greatest for radiosonde and each Advanced Microwave Sounding Unit (AMSU)-A satellite, followed by surface synoptic observation from a land station (SYNOP), Quick Scatterometer (QuikSCAT), atmospheric motion vector (AMV) wind from a geostationary satellite (GEOAMV), and aviation routine weather reports (METARs). The fraction of beneficial observations was approximately 60%–70%, which is higher than that reported in previous studies. For several analyses of Typhoons Sinlaku (200813) and Jangmi (200815), dropsonde soundings taken near the typhoon had similar or greater observation impacts than routine radiosonde soundings. The sensitivity to the error covariance parameter indicates that reducing (increasing) observation (background) error covariance helps to reduce forecast error in the current analysis framework. The observation impact from OSEs is qualitatively similar to that from the adjoint method for major observation types. This study confirms that radiosonde observations provide primary information on the atmospheric state as in situ observations and that satellite radiances are an essential component of atmospheric observation systems.