Extreme Rainfall Time Series Prediction: A Comparative Analysis of SARIMA, Random Forest, LSTM and Prophet Models

In recent decades, the city of Chetumal in the state of Quintana Roo, Mexico has suffered from flooding due to extreme rainfall events (<tex xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">$&gt;50 \text{mm}$</tex> daily). Floods have a high destructive potential, causing socioeconomic damage and even human losses. Due to the high risk that floods represent, it is necessary to have information generated by the analysis and predictions of these rainfall events so that governments can prepare and elaborate well-adapted plans to face a high risk of floods. The prediction over short periods of time (ten-days of month) of rainfall can serve as a reference to determine the possibility of considerable loss and damage from these events. However, it is difficult to find a suitable prediction model for this context. This paper compares the performance of four different time series models: Seasonal Autoregressive Integrated Moving Average (SARIMA), Long Short-Term Memory (LSTM), Random Forest and Prophet to forecast rainfall in ten-days of month (3 periods of 10 days per month), using daily rainfall record data from January 2003 to September 2023. The results obtained indicate that SARIMA, with the lowest root mean square error (MSE) and root mean square error (RMSE), is the most suitable model for predicting rainfall in this context. While the Prophet model with the second-best value of MSE and RMSE represents another alternative for predictions. In the analysis of predictions against actual values, both models agree in predicting extreme events in ten-days of month corresponding mainly to the months of June to September of each year. SARIMA shows promising results in the analysis of data and predictions of extreme rainfall events for flood mitigation, and could be the basis for defining flood mitigation strategies.