## 4 Discussion  
Satellite and radar observations represent the main remote sensing data which can be assimilated into NWP. Many studies analyzed the impacts of assimilating these data, and improvements of forecasts were found [15; 16; 19; 20; 33; 34; 35; 36]. A previous study has concentrated on the assimilation with traditional methods, such as 3/4 DVAR and EnKF [27; 28; 29]. This study first simultaneously assimilates satellite and radar data with the POD-4 DenVar method, which combines the advantages of variational and ensemble Kalman filter assimilation methods [5; 7]. For example, 4 DVAR can assimilate observations at multiple  
Figure 15: The vertical structure of rainwater mixing ratio (**a,b**) and cloud water mixing ratio (**c,d**) as the forecast time leads for CON (**a,c**) and POD (**b,d**). times, but with the static background error variance and lots of computational resources. EnKF can provide flow-dependent background error variance and require less work on coding, maintenance and development of an adjoint model [26], but limited by the quality of the ensemble forecast [2]. Thus, this study utilizes the POD-4 DEnVar method to assimilate both satellite and radar data. The final optimal solution of POD-4 DEnVar assimilation method Equation (10) shows that the analysis can be represented by model perturbation \(\mathbf{P}_{x}\), observation perturbation matrix \(\mathbf{P}_{y}\), the error covariances of observations \(\mathbf{R}\) and the observation innovation (\(\mathbf{y}^{obs}\)). Thus, the adjoint model of traditional 4 DVAR is no longer needed [5]. The ensemble of historical samples is used to construct the perturbation matrix, which is much more economical. The avoid of the adjoint model and choice of historical samples make POD-4 DEnVar assimilation much cheaper to run, which is better to be applied in higher-resolution NWP [37]. Furthermore, the \(\mathbf{B}\) matrix in POD-4 DEnVar method is constructed by ensemble forecasts, which is flow-dependent in comparison with the traditional static background error variance [38; 39]. The increments in Section 3.2.3 well display the flow-dependent pattern in POD-4 DEnVar method. Apparent local increments of wind, temperature and moisture are found in the precipitation area, indicating that POD-4 DEnVar assimilation can spread observation information spatially according to the current circulation pattern. The flow-dependent error structure is important for rapidly evolving synoptic systems [40]. In order to make an accurate forecast on precipitation, the accuracy of initial hydrometeor is important [27]. Increment results show that assimilating satellite and radar data with POD-4 DEnVar method can improve the initial analysis of hydrometeors for better heavy rainfall forecast (Figures 14 and 15). As is known, the WRF model needs a spin-up time to produce hydrometeor for rainfall forecast, which downgrades the short-term rainfall forecast. Even if the traditional variational assimilation method is applied (e.g., 3 DVAR or 4 DVAR), the initial field of hydrometeor cannot be changed. Cloud and precipitation processes have a flow-dependent and nonlinear characteristic, but variational assimilation method requires a tangent linear model and its adjoint for nonlinear moist physics parameterization [41], which is not required in POD-4 DEnVar method. In addition, POD-4 DEnVar can construct flow-dependent background error variance, which can better represent cloud and precipitation process than static background error in the traditional variational analysis [42]. Therefore, hydrometeor can be directly included in the control variables of POD-4 DEnVar method. The change in the initial field of hydrometeor can decrease the spin-up time. From the results of hydrometeor simulation, both the experiments can simulate the concentration of hydrometeor. However, CON produces hydrometeor after about 6 h, and POD produces hydrometeor as soon as the forecast begins (Figure 15).