## 4 Nowcasting of Rainfall Field
### Result of Rainfall Field Nowcasting  
In this section, we try to achieve the nowcasting of rainfall field by using our designed learning network. We select 386 rainfall events from CMORPH measurements between 2016 and 2019 to generate a dataset, which comprises 2649 sequential rainfall fields. In this article, the selection of rainfall events follows two principles:  
1. Long duration. Because the time interval of CMORPH measurements is only 30 min, a shorter duration may not reflect the detailed spatiotemporal change of rain intensity in a rainfall event. The duration of selected rainfall event exceeds 4 h which means that an event includes at least eight continuous rainfall fields. 2. Heavy rainfall intensity. The aim of this work is to achieve the nowcasting of heavy rainfall that closely relates to instantaneous natural disaster, whose intensity is higher than 10 mm/h according to the WMO Guide to Meteorological Instruments and Methods of Observation (WMO-No.8, the CIMO Guide). Therefore, the maximum rain intensity in each rainfall event is higher than 10 mm/h. In addition, the optimizer employed in the training process is an adaptive moment algorithm (Adam) and the initial learning rate is 0.02. To prevent gradient explosion and overfitting, the gradient threshold is set as 1 and the learning rate drop factor is set as 0.5 after 300 iterations. The maximum number of iterations is 500. Figure 6 shows the comparisons between predictions and measurements from the OELs network for two precipitation events (from top to bottom), where the first two lines are results of 31 May 2016 and the last two lines are results of 2 August 2016. Here, we only display five continuous predictions of each rainfall event (from left to right) because the duration (2.5 h) is enough for us to observe the change of rainfall field in time sequence. For the event of May 31, two rain cells move from south to north. According to the variation of rain intensity, we can clearly observe the development and weakening of the second rain cell after the first leaves the monitoring region. For the event of 2 August the centers of heavy rainfall grew from one to two and then gradually weakeneds. As can be seen from the comparisons, the motion of rain cell and the change of peak rain intensity are predicted successfully, which is of great significance for nature disaster alerts. The corresponding evaluation metrics are given in Table 3. As for the given two rainfall events, it can be found that the learning network has a good performance on the nowcasting of rainfall field with _RMSE_ lower than 3.5 mm/h and _CC_ higher than 0.77. Table 4 is a contingency table, showing the skill score of our prediction method on heavy rainfall alarm for each grid cell in a monitored region [52]. In the table, _TH_ denotes the number of grid cells with heavy rainfall that are predicted correctly, _FH_ denotes the number of grid cells with \(R<10\) mm/h that are wrongly predicted as heavy rainfall, _FN_ denotes the number of grid cells with \(R>10\) mm/h that are not alarmed successfully, and _TN_ denotes the number of non-heavy rainfall grid cells that are predicted correctly. Proportion correct (PC) indicates the accuracy that the learning network predicts rainfall categories: heavy rainfall or not. Probability of detection (POD) reflects the probability of predicting heavy rainfall accurately. False alarm ratio (FAR) denotes the ratio that the non-heavy rainfall is mis-predicted. Frequency bias index (FBI) indicates the learning network is better at predicting heavy rainfall (\(>\)1) or not (\(<\)1), and FBI = 1 indicating similar ability to predict the two situations. As can be seen from Table 4, the heavy rainfall of each grid cell can be predicted with high accuracy (PC = 0.94, POD = 0.96, FAR = 0.051), and FBI = 1.01 indicates a slightly better ability to predict heavy rainfall. In total, our work provides a general framework for the nowcasting of rainfall field by the OELs network.