## 1 Introduction  
Accurate initial field, boundary conditions and forecast model play important roles in numerical weather prediction (NWP). With the development of the forecast model, the high quality of the initial field is required. Data assimilation has been proved to be an effective way to provide much more accurate initial field. Currently, variational data assimilation and ensemble Kalman filter (EnKF) are the two widely used methods in data assimilation. For example, a four-dimensional variational (4 DVar) method can assimilate observations at multiple times with the constraint of the forecast model [1, 2]. However, 4 DVar cannot provide evolved, flow-dependent covariance model. Furthermore, the development and maintenance of the tangent linear and adjoint model in 4 DVar require a lot of computational resources. In comparison, the background-error covariances in EnKF are estimated from an ensemble forecast, which is flow-dependent [3]. EnKF successfully avoids the development of tangent linear and adjoint model. However, it is limited by the quality of the ensemble forecast. Thus, both methods have advantages and disadvantages. In recent decades, the hybrid data assimilation method combined variational and EnKF is proposed to overcome the shortcomings of their own [4; 5; 6]. [PERSON] [5; 7] proposed a POD-4 DEnVar method based on proper orthogonal decomposition (POD) and ensemble forecasting, in which the POD technique is adopted to 4 DVar, combining the advantages of variational and EnKF method. The POD-4 DEnVar method is evaluated by the Lorenz96 model, observing system simulation experiments (OSSEs), and the shallow water wave equation, outperforming 4 DVar and EnKF methods with lower computational costs [7]. Besides, this method has been successfully applied to land data assimilation, showing great potential [8; 9]. As two kinds of remote sensing observations, satellite and radar data have been the main resource of data assimilation in NWP. During the last few decades, satellite radiances represent the most numerous and widely available observations in numerical weather prediction system. Satellite observations have better spatiotemporal coverage, especially over ocean area where conventional and radar observations are extremely rare. Thus, the assimilation of satellite data in NWP has been widely used to provide synoptic and mesoscale atmospheric conditions, improving the quality of forecast significantly [10; 11; 12; 13; 14; 15; 16]. Compared with satellite data, radar data has higher a temporal and spatial resolution, which can be used to provide a more accurate analysis of three-dimensional wind field and cloud property. Radar data has been applied to the development of convection and improvement of the short-term forecast. Many studies carried out assimilation experiments on radar radial velocity and reflectivity observations, indicating improving forecasts of severe weather events, such as high winds, heavy rainfall, and tornadoes [17; 18; 19; 20; 21; 22]. Recently, there are some researches of satellite data or radar data assimilation using POD-3/4 DEnVar method. [PERSON] first assimilated satellite observations from Microwave Humidity Sounder (MWHS) and Microwave Temperature Sounder (MWTS) onboard Fengyun-3A with POD-3/4 DEnVar method, showing a positive impact on a heavy rainfall forecast [23; 24]. Radar data was first assimilated by [PERSON] with the POD-3 DEnVar [25]. It was then developed for POD-4 DenVar method to assimilate radar radial velocity and reflectivity with the OSSEs by [PERSON] et al. [26], showing that POD-4 DenVar outperformed the local ensemble transform Kalman filter (LETKF) method. Furthermore, POD-4 DenVar assimilation of radar data was demonstrated to improve the precipitation forecast through a case study. Since assimilating satellite and radar observations separately has led to the improvement of model forecasts, simultaneous assimilation of them has recently received a high degree of attention. [PERSON] et al.