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.

Precipitation is a component of the hydrological cycle, knowing its spatial distribution is vital for the management of hydrographic basins, the territory and the development of fundamental activities for society. That is why the present study shows the spatial variability of rainfall in Cartagena de Indias city with a network of rain gauges, made up of nine pieces of equipment, separated from each other by 0.9–27 km. After a year of recording (2019), using historical series of data, it was found that the maximum rainfall occurs in the trimester between September and November, with interpolated maps made by the Ordinary Kriging (OK) method it was found that the maximum rainfall is focused on the north, centre and west of the territory, instead, the maximum intensities are presented in the centre and west, the minimums for both variables are presented to the east and south. The 70 and 90% of the rain events have a duration of less than 30 min and 1 h, respectively. Three-parameter exponential function was fitted to the paired correlation distances, and presented correlations lower than 0.8, 0.5 and 0.2 from distances of 1, 3 and 7 km, respectively, in 30 min rain integration. It was also found that with a pluviometric network conformed by at least six pieces of equipment and separated by a 5 km distance from each other in the urban area, a correlation of 0.5 and compliance with the WMO recommendations would be obtained.