For variational data assimilation, the background error covariance matrix plays a crucial role because it is strongly linked with the local meteorological features, and is especially dominated by error correlations between different analysis variables. Multivariate background error (MBE) statistics have been generated for two regions, namely the Tropics (covering Indonesia and its neighborhood) and the Arctic (covering high latitudes). Detailed investigation has been carried out for these MBE statistics to understand the physical processes leading to the balance (defined by the forecasts error correlations) characteristics between mass and wind fields for the low and high latitudes represented by these two regions. It is found that in tropical regions, the unbalanced (full balanced) part of the velocity potential (divergent part of wind) contributes more to the balanced part of the temperature, relative humidity, and surface pressure fields as compared with the stream function (rotational part of wind). However, the exact opposite happens in the Arctic. For both regions, the unbalanced part of the temperature field is the main contributor to the balanced part of the relative humidity field. Results of single observation tests and six-hourly data assimilation cycling experiments are consistent with the respective balance part contributions of different fields in the two regions. This study provides an understanding of the contrasting dynamical balance relationship that exists between the mass and wind fields in high- and low-latitude regions. The study also examines the impact of MBE on Weather Research and Forecasting model forecasts for the two regions.

In this paper, the theoretical model of Rossby waves in two-layer fluids is studied. A single quasi-geostrophic vortex equation is used to derive various models of Rossby waves in a one-layer fluid in previous research. In order to explore the propagation and interaction of Rossby waves in two-layer fluids, from the classical quasi-geodesic vortex equations, by employing the multi-scale analysis and turbulence method, we derived a new (2+1)-dimensional coupled equations set, namely the generalized Zakharov-Kuznetsov(gZK) equations set. The gZK equations set is an extension of a single ZK equation; they can describe two kinds of weakly nonlinear waves interaction by multiple coupling terms. Then, for the first time, based on the semi-inverse method and the variational method, a new fractional-order model which is the time-space fractional coupled gZK equations set is derived successfully, which is greatly different from the single fractional equation. Finally, group solutions of the time-space fractional coupled gZK equations set are obtained with the help of the improved $(G^{\prime }/G)$ -expansion method.

Assimilating radar reflectivity into NWP models is one of the keys to improve the accuracy of convective‐scale numerical weather prediction (NWP). There are generally two major branches of research in radar reflectivity assimilation: directly assimilating radar reflectivity, and indirectly assimilating reflectivity, i.e. assimilating hydrometeors retrieved from radar reflectivity. In this study, the indirect assimilation method based on background‐dependent hydrometeor retrievals is compared with the direct assimilation method using frequent data assimilation cycles for five real data cases. The retrieved hydrometeors in the indirect assimilation method are first verified against the hydrometeor types obtained from a polarimetric hydrometeor classification method. It is illustrated that the background‐dependent hydrometeor retrieval method can obtain reasonable model‐equivalent hydrometeors from radar reflectivity. The analysis increments for hydrometeors with both radar data assimilation methods show similar patterns but their magnitudes are different. Both quantitative and qualitative evaluations of forecasted composite reflectivities and accumulated precipitation indicate that the indirect assimilation method predicts the location and intensity of the simulated convection more accurately than the direct method. Furthermore, the indirect assimilation method is more efficient, which is valuable in real‐time applications by helping deliver forecasts quickly and thus helping forecasters make more timely warning decisions.

Accurate and long leading time flood forecasting is very important for flood disaster mitigation. It is an effective method to couple the Quantitative Precipitation Forecast (QPF) products provided by Numerical Weather Prediction (NWP) models to a distributed hydrological model with the goal of extending the leading time for flood forecasting. However, the QPF products contain a certain degree of uncertainty and would affect the accuracy of flood forecasting, especially in the mountainous regions. Radar data assimilation plays an important role in improving the quality of QPF and further improves flood forecasting. In this paper, radar data assimilation was applied in order to construct a high-resolution atmospheric-hydrological coupling model based on the WRF and WRF-Hydro models. Four experiments with conventional observational and radar data assimilation were conducted to evaluate the flood forecasting capability of this coupled model in a small-medium sized basin based on eight typical flood events. The results show that the flood forecast skills are highly QPF-dependent. The QPF from the WRF model is improved by assimilating radar data and further increasing the accuracy of flood forecasting, although both precipitation and flood are slightly over-forecasted. However, the improvements by assimilating conventional observational data are not obvious. In general, radar data assimilation can improve flood forecasting effectively in a small-medium sized basin based on the atmospheric-hydrological coupling model.

As the first Geostationary Satellite with the LMI (Lightning Mapping Imager) instrument aboard running over the eastern hemisphere, FY-4A (Feng-Yun-4A) can better indicate severe convection and compensate for the limitations of radar observation in temporal and spatial resolution. In order to realize the application of FY-4A lightning data in numerical weather prediction (NWP) models, a logarithmic relationship between FY-4A lightning density and maximum radar reflectivity is presented to convert FY-4A lightning data into maximum FY-4A proxy reflectivity. Then, according to the profiles of radar reflectivity, the maximum FY-4A proxy reflectivity is extended to 3D FY-4A proxy reflectivity. Finally, the 3D FY-4A proxy reflectivity is assimilated in RMAPS-ST (Rapid-refresh Multi-scale Analysis and Prediction System—Short Term) to compare with radar assimilation. Four groups of continuous cycling data assimilation and forecasting experiments are carried out for a severe rainfall case. The results demonstrate that cycling assimilation of 3D FY-4A proxy reflectivity can adjust the moisture condition effectively, and indirectly affects the temperature and wind fields, then makes the thermal and dynamic analysis more reasonable. The Fractions Skill Scores (FSSs) show that the rainfall forecasts are improved significantly within 6 h by assimilating 3D FY-4A proxy reflectivity, which is similar to the parallel experiments in assimilating radar reflectivity. In addition, other cycling data assimilation experiments are carried out in mountainous areas without radar data. The improvement of precipitation forecasts in mountainous areas further proves that the application of assimilating 3D FY-4A proxy reflectivity can be considered a useful substitute where observed radar data are missing. Through the two severe rainfall cases, this method could be framed as an example of how to use lightning for data assimilation.