A fast surrogate model to simulate flooding due to heavy rainfall events

Recent disasters stress the demand of fast and reliable tools for flooding forecasting, where the real-time prediction of extreme events becomes essential to avoid potential hazards for the population. In this work, we focus on the flash flooding phenomenon, given by the combination of temporally concentrated rainfall and steep slopes. Such configuration is typical in the St. Lucia island, in the eastern Caribbean Sea, that we exploit as a case study. It is possible to simulate the full evolution of rainfall by numerically solving the Shallow Waters equations (SW) on a computational domain. A preliminary comparison with historical events proved that an accurate solution is achieved only when the Digital Elevation Model (DEM) presents a resolution equal or inferior to 5 meters. With this grid resolution the whole island is discretized in over 60M cells at best, forbidding a real-time application of the SW solvers in flash flooding events.

 In this work we present a machine-learning surrogate model for a SW solver to estimate the level of the flooding danger. It is evaluated through a synthetic parameter, hereafter referred as flag, that takes in account both the water depth and its velocity. Therefore, flooding patterns in the island are represented through high-resolution maps with discrete values of flags, varying from 0 – safe to 4 – extremely dangerous.

The final aim is to solve a supervised regression, training a Multi-Layer Perceptron Neural Network (MLPNN) to map sequences of time- and spatial-varying rainfall (input features) to the corresponding previsions of flags (output features) shifted ahead of time. To do so, we first generate a rough database by simulating more than 30 flash flooding events, using an in-house validated code, whose input is the temporal and spatial rainfall distribution obtained by radar measurements of events occurred in the past. DEM resolution is set to 5 meters and SW solver solutions is sampled every 6 mins. Given the high dimensionality of the problem, both the inputs and the outputs of the simulations are preprocessed using an Incremental Principal Component Analysis (IPCA) to extract the scores and loadings. The elbow charts indicate the correct number of principal components, set to 8, that explains the 95% of the cumulative explained variance. The scores given by IPCA processing of rainfall are built into sequences of five elements, endowing the algorithm a memory. The min/max regularization are applied to the database. The MLPNN training phase is fastened through batch feeding and monitored to prevent overfitting, relying on Tensorflow library. To test the generalization capability of the synthetic model was verified by forwarding events that were not included in the original database.