Regional Frequency Analysis Using L-Moments for Determining Daily Rainfall Probability Distribution Function and Estimating the Annual Wastewater Discharges

The spatial distribution of precipitation is one of the major unknowns in hydrological modeling since meteorological stations do not adequately cover the territory, and their records are often short. In addition, regulations are increasingly restricting the amount of wastewater that can be discharged each year. Therefore, understanding the annual behavior of rainfall events is becoming increasingly important. This paper presents Rainfall Frequency Analysis (RainFA), a software package that applies a methodology for data curation and frequency analysis of precipitation series based on the evaluation of the L-moments for regionalization and cluster classification. This methodology is tested in the city of Palma (Spain), identifying a single homogeneous cluster integrated by 7 (out of 11) stations, with homogeneity values less than 0.6 for precipitation values greater than or equal to 0.4 mm. In the evaluation of the prediction capacity, the selected cluster of 7 stations performed in the first quartile of the 120 possible combinations of 7 stations, both for the detection of the occurrence of rainfall—in terms of Probability of Detection (POD), False Alarm Ratio (FAR), Critical Success Index (CSI) and Bias Score (BS) statistics—and for the accuracy of rainfall—according to Root Mean Square Error (RMSE), Nash–Sutcliffe Efficiency coefficient (NSE) and Percent Bias (PBIAS). The cluster was also excellent for predicting different rainfall ranges, resulting in the best combination for both light—i.e., [1, 5) mm—and moderate—i.e., [5, 20) mm—rainfall prediction. The Generalized Pareto gave the best probability distribution function for the selected region, and it was used to simulate daily rainfall and system discharges over annual periods using Monte Carlo techniques. The derived discharge values were consistent with observations for 2023, with an average discharge of about 700,000 m3 of wastewater. RainFA is an easy-to-use and open-source software programmed using Python that can be applied anywhere in the world.