# Reconstruction of Missing Data in Weather Radar Image Sequences Using Deep Neuron Networks
## 4 Results
### Evaluation Results for the Case of Interpolation
\begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \begin{tabular}{c} **Missing** \\ **Patterns** \\ \end{tabular} & \begin{tabular}{c} **Metrics** \\ \end{tabular} & \begin{tabular}{c} **Nearest** \\ **Frame** \\ \end{tabular} & \begin{tabular}{c} **Linear** \\ \end{tabular} & \begin{tabular}{c} **Optical** \\ **Flow** \\ \end{tabular} & \
\begin{tabular}{c} **CNN-** \\ **ConvLSTM** \\ \end{tabular} &
\begin{tabular}{c} **3 DCNN** \\ **BiConvLSTM** \\ \end{tabular} \\ \hline \multirow{4}{*}{1111001111} & MAE & 2.5205 & 2.0783 & 1.8766 & 1.7332 & 1.5993 & **1.4650** \\  & CSI & 0.3431 & 0.4044 & 0.4223 & 0.4194 & 0.4763 & **0.5085** \\  & HSS & 0.6088 & 0.6790 & 0.6947 & 0.7023 & 0.7264 & **0.7465** \\ \hline \multirow{4}{*}{111100111} & MAE & 3.0002 & 2.3783 & 2.1617 & 1.9517 & 1.7244 & **1.5675** \\  & CSI & 0.2835 & 0.3412 & 0.376 & 0.3640 & 0.4424 & **0.4282** \\  & HSS & 0.5532 & 0.6404 & 0.6546 & 0.6697 & 0.7071 & **0.7305** \\ \hline \multirow{4}{*}{1110000111} & MAE & 3.7057 & 2.8644 & 2.6966 & 2.3433 & 1.9619 & **1.7777** \\  & CSI & 0.2121 & 0.2549 & 0.3029 & 0.2744 & 0.3781 & **0.4296** \\  & HSS & 0.4773 & 0.5804 & 0.5871 & 0.6129 & 0.6721 & **0.6976** \\ \hline \multirow{4}{*}{1100000011} & MAE & 4.2260 & 3.2542 & 3.2146 & 2.7135 & 2.2522 & **1.9966** \\  & CSI & 0.1708 & 0.2039 & 0.2446 & 0.1996 & 0.3049 & **0.3784** \\  & HSS & 0.4250 & 0.5338 & 0.5287 & 0.5606 & 0.6298 & **0.6651** \\ \hline \multirow{4}{*}{1000000001} & MAE & 4.6448 & 3.5841 & 3.6964 & 3.5725 & 2.8397 & **2.3731** \\  & CSI & 0.1431 & 0.1666 & 0.2007 & 0.0999 & 0.1883 & **0.3067** \\ \cline{1-1}  & HSS & 0.3849 & 0.4967 & 0.4781 & 0.4460 & 0.5442 & **0.6131** \\ \hline \multirow{4}{*}{1010101011} & MAE & 2.5156 & 2.0735 & 1.8717 & 1.8304 & 1.6085 & **1.4670** \\ \cline{1-1}  & CSI & 0.3446 & 0.4052 & 0.4236 & 0.4026 & 0.4454 & **0.5067** \\ \cline{1-1}  & HSS & 0.6092 & 0.6796 & 0.6950 & 0.6892 & 0.7244 & 0.7457 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Evaluation results of mean absolute error (MAE), Critical success index (CSI)-40 scores, and Heidke skill score (HSS) scores for the bi-directional convolutional long short-term memory networks (CNN-BiConvLSTM) model and baseline models and for 6 missing patterns with respect to interpolation. As the number of successive missing frames increased, the performance of all the models got worse. This was reasonable since the models received less information but generated many more outputs. Nonetheless, the CNN-BiConvLSTM model performed well enough when missing 4 successive frames, and even better than traditional interpolation models when only 1 frame was missing. For the case of 4 discrete intermediate frames missing (i.e., 1010101011), the performances of the linear model, the optical flow model, and CNN-BiConvLSTM were found to be nearly equivalent to those of 1 intermediate frame missing. This implied that the CNN-BiConvLSTM model did well in reconstructing discrete intermediate missing frames without losing accuracy, as the linear model and the optical flow model did. While the latter models used only 2 adjacent frames before and after missing frames to generate an interpolation, the CNN-BiConvLSTM model learned regularities from the whole radar sequence and may obtain higher accuracy. By contrast, the performances of the CNN-ConvLSTM model and the 3 DCNN model in the case of 4 discrete intermediate frames missing were slightly unstable. To provide more detail, Figure 6 shows an example of reconstructing missing radar images with the CNN-BiConvLSTM model for all 6 missing patterns. It was found that  
Figure 5: Histograms for the differences of mean absolute error (MAE) (**a**), Critical success index (CSI)-40 scores (**b**), and Heidke skill score (HSS) scores (**c**) between the CNN-BiConvLSTM model and baseline models for the missing pattern of ’110000111’. the reconstructed radar images were quite similar to the ground truth with respect to the shapes and values of the radar echoes.