# Reconstruction of Missing Data in Weather Radar Image Sequences Using Deep Neuron Networks
###### Abstract  
Missing data in weather radar image sequences may cause bias in quantitative precipitation estimation (QPE) and quantitative precipitation forecast (QPF) studies, and also the obtainment of corresponding high-quality QPE and QPF products. The traditional approaches that are used to reconstruct missing weather radar images replace missing frames with the nearest image or with interpolated images. However, the performance of these approaches is defective, and their accuracy is quite limited due to neglecting the intensification and disappearance of radar echoes. In this study, we propose a deep neuron network (DNN), which combines convolutional neural networks (CNNs) and bi-directional convolutional long short-term memory networks (CNN-BiConvLSTMs), to address this problem and establish a deep-learning benchmark. The model is trained to be capable of dealing with arbitrary missing patterns by using the proposed training schedule. Then the performances of the model are evaluated and compared with baseline models for different missing patterns. These baseline models include the nearest neighbor approach, linear interpolation, optical flow methods, and two DNN models three-dimensional CNN (3 DCNN) and CNN-ConvLSTM. Experimental results show that the CNN-BiConvLSTM model outperforms all other baseline models. The influence of data quality on interpolation methods is further investigated, and the CNN-BiConvLSTM model is found to be basically uninfluenced by less qualified input weather radar images, which reflects the robustness of the model. Our results suggest good prospects for applying the CNN-BiConvLSTM model to improve the quality of weather radar datasets. w +
Footnote †: journal: Medical Imaging  
0000-0001-6600-00001-6600][PERSON]  
0000-0001-6600-0001-6600-0001-6600-0001-6600-0001-6600  
QPF products since the movements and intensities of radar echoes are non-negligible, especially in the circumstance in which multiple successive frames are missing. Efforts have also been made by using interpolation methods to reconstruct missing frames. For instance, interpolation techniques are widely used in meteorological data processing [6; 7; 8; 9; 10]. Methods based on optical flow (i.e., motion) [11; 12], complex empirical orthogonal functions [13], and fractals [14] have been developed and have been found to be more accurate than persistence or linear interpolation. Optical flow is one of the most popular techniques that is used for weather radar data interpolation as well as for weather radar echo extrapolation [15; 16]. The motion of radar echo features is first estimated from a sequence of radar images [17; 18; 19]. Then, the intermediate or future radar echoes are obtained according to their motion [20]. There are several schemes to calculate optical flow, such as gradient-based algorithms [21; 22], correlation-based algorithms [23], and spectral-based algorithms [9; 24], and all of them are used in meteorological studies. For instance, a local Lucas-Kanade optical flow method (gradient-based) is used in precipitation nowcasting [18]; both gradient-based and correlation-based optical flow algorithms are used for operational nowcasting in Hong Kong [15]; and studies show that correlation-based interpolation can improve the accuracy of hourly and daily accumulated rainfall [25; 26]. Fast Fourier transform is also used to estimate optical flow for nowcasting and interpolation [9; 24]. Despite the successful application of the optical flow method in the interpolation of radar and precipitation data, it cannot overcome the basic assumption that the intensity of the features remains constant [12]. This assumption is not appropriate because of the intensification and disappearance of radar echoes. Similar empirical assumptions have also been used in the nearest neighbor approach and the linear interpolation method. The former is based on persistence assumption, and the latter only takes account of the temporal evolution of radar echoes at each grid point but without considering spatial movements.