An empirical model of rainfall intensity as a function of rainfall duration and probability of occurrence

Rainfall is one of the main components of the hydrologic cycle; thus, the availability of accurate rainfall data is fundamental for designing and operating water resources systems and infrastructure. This study aims to develop an empirical model of rainfall intensity (I_t,p) as a function of its probability (p) and duration (t). In 1999–2020, data on the hourly duration of rainfall were collected from automatic rainfall recorder (ARR) gauges. The empirical model has been developed using a statistical approach based on duration (t) and probability (p), and subsequently they have been validated with those obtained from ARR data. The resulting model demonstrates good performance compared with other empirical formulas (Sherman and Ishiguro) as indicated by the percent bias (PBIAS) values (2.35–3.17), ratio of the RMSE (root mean square error) between simulated and observed values to the standard deviation of the observations (RSR, 0.028–0.031), Nash–Sutcliffe efficiency (NSE, 0.905–0.996), and index of agreement (d, 0.96–0.98) which classified in the rating of “very good” in model performance. The reliability of the estimated intensity based on the empirical model shows a tendency to decrease as duration (t) increases, and a good accuracy mainly for the rainfall intensity for shorter periods (1-, 2-, and 3-hours), whereas low accuracy for long rainfall periods. The study found that the empirical model exhibits a reliable estimate for rainfall intensity with small recurrence intervals (Tr) 2-, 5-, 10-, and a 20-year interval and for a shorter duration (t). Validation results confirm that the rainfall intensity model shows good performance; thus, it could be used as a reliable instrument to estimate rainfall intensity in the study area.