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.

In this study, the single-moment 6-class bulk cloud microphysics scheme used in the operational numerical weather prediction system at the Japan Meteorological Agency was improved using the observations of the Global Precipitation Measurement (GPM) core satellite as reference values. The original cloud microphysics scheme has the following biases: underestimation of cloud ice compared to the brightness temperature of the GPM Microwave Imager (GMI) and underestimation of the lower troposphere rain compared to the reflectivity of GPM Dual-frequency Precipitation Radar (DPR). Furthermore, validation of the dual-frequency rate of reflectivity revealed that the dominant particles in the solid phase of simulation were graupel and deviated from DPR observation. The causes of these issues were investigated using a single-column kinematic model. The underestimation of cloud ice was caused by a high ice-to-snow conversion rate, and the underestimation of precipitation in the lower layers was caused by an excessive number of small-diameter rain particles. The parameterization of microphysics scheme is improved to eliminate the biases in the single-column model. In the forecast obtained using the improved scheme, the underestimation of cloud ice and rain is reduced. Consequently, the prediction errors of hydrometeors were reduced against the GPM satellite observations, and the atmospheric profiles and precipitation forecasts were improved.

Spaceborne precipitation radar such as Global Precipitation Measurement (GPM)/dual‐frequency precipitation radar (DPR) provides valuable observations of precipitation systems in three dimensions. Assimilation of GPM/DPR data is becoming an important technique for improving the accuracy of forecasting to complement scarce ground‐based observations. This study presents a new, one‐dimensional maximum‐likelihood estimation (1D‐MLE) method developed by the authors that enables the estimation of relative humidity profiles according to a non‐Gaussian probability density function. By assimilating the estimated relative humidity profiles using a four‐dimensional variational (4D‐Var) method, mesoscale precipitation forecasts by the Japan Meteorological Agency (JMA) have been considerably improved. The displacement of forecast precipitation during a severe weather event, in particular, is improved significantly. It was found that forecasting accuracy was maintained for a narrow GPM/DPR swath and low revisit frequency by repeating the assimilation–forecast cycle. Since the effectiveness was confirmed, the JMA began assimilating GPM/DPR data using the 1D‐MLE approach from March 2016.

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