Coordinate-Transformed Dynamic Mode Decomposition for Short-Term Rainfall Forecasting

Lagrangian persistence method in nowcasting is a highly effective method for short-term weather forecasting. However, its performance is not as robust in long-term forecasting or situations of rapid weather changes due to the difficulty in analyzing the intensity variation of meteorological physical quantities. To address this shortcoming, in this study, we incorporated dynamic mode decomposition (DMD) into the Lagrangian persistence method. Specifically, we proposed a coordinate-transformed DMD (CT-DMD) model by integrating an optical flow model with a DMD model, providing an effective method for analyzing the intensity variation of meteorological physical quantities in the Lagrangian persistence method. The integration of the optical flow model and the DMD model involves the transformation of data between Eulerian and Lagrangian coordinate systems. The CT-DMD model was evaluated using radar-observed rainfall data from the Kanto region of Japan, with the Rainymotion model used as a benchmark. When the lead time was 5 min, 22.22% of the subsets in the experimental dataset showed that the CT-DMD model had a higher forecast accuracy compared to the Rainymotion model. When the lead time was 25 min, 88.89% of the subsets in the experimental dataset showed that the CT-DMD model had a higher forecast accuracy compared to the Rainymotion model. The accuracy advantage of the CT-DMD model became apparent after a lead time of 15 min and became increasingly significant as the lead time increased. The results demonstrated the validity of the CT-DMD model.