Se realiza un análisis fractal de los eventos de lluvia registrados en Baja California, México, una región semiárida que presenta amplia variabilidad climatológica. Se utilizan series de precipitación de 92 estaciones climatológicas con longitudes de registro mayores a 30 años. Se determinan patrones y características en las series de precipitaciones a partir de valores espaciales y temporales del exponente de Hurst, así como su relación con la temperatura y precipitación media anual, altitud y distribución climatológica. Se emplean con éxito los métodos de rango reescalado, conteo de cajas y análisis multifractal de fluctuación sin tendencia, lo cual permite obtener el valor promedio del exponente de Hurst para diferentes escalas de tiempo. Los datos muestran que la series de precipitación diaria tienden a presentar un patrón persistente; además, los valores del exponente de Hurst se relacionan con el tipo de clima, la altitud, el régimen de lluvias y la temperatura en la zona de estudio. El análisis del exponente de Hurst para diferentes escalas de tiempo evidencia que dicho exponente aumenta a medida que la escala de tiempo en consideración es menor; por lo tanto, la persistencia de la serie se hace más fuerte. Por otra parte, se puede confirmar que la teoría fractal permite analizar el comportamiento de una variable climática, en este caso, la precipitación.

Seasonal Auto Regressive Integrative Moving Average models (SARIMA) were developed for monthly rainfall time series. Normality of the rainfall time series was achieved by using the Box Cox transformation. The best SARIMA models were selected based on their autocorrelation function (ACF), partial autocorrelation function (PACF), and the minimum values of the Akaike Information Criterion (AIC). The result of the Ljung–Box statistical test shows the randomness and homogeneity of each model residuals. The performance and validation of the SARIMA models were evaluated based on various statistical measures, among these, the Student’s t-test. It is possible to obtain synthetic records that preserve the statistical characteristics of the historical record through the SARIMA models. Finally, the results obtained can be applied to various hydrological and water resources management studies. This will certainly assist policy and decision-makers to establish strategies, priorities, and the proper use of water resources in the Sinú river watershed.

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Intensity–Duration–Frequency (IDF) curves describe the relationship between rainfall intensity, rainfall duration, and return period. They are commonly used in the design, planning and operation of hydrologic, hydraulic, and water resource systems. Considering the intense rainfall presence with flooding occurrences, limited data used to develop IDF curves, and importance to improve the IDF design for the Ensenada City in Baja California, this research study aims to investigate the use and combinations of pluviograph and daily records, to assess rain behavior around the city, and select a suitable method that provides the best results of IDF relationship, consequently updating the IDF relationship for the city for return periods of 10, 25, 50, and 100 years. The IDF relationship is determined through frequency analysis of rainfall observations. Also, annual maximum rainfall intensity for several duration and return periods has been analyzed according to the statistical distribution of Gumbel Extreme Value (GEV). Thus, Chen’s method was evaluated based on the depth-duration ratio (R) from the zone, and the development of the IDF relationship for the rain gauges stations was focused on estimating the most suitable (R) ratio; chosen from testing several methods and analyzing the rain in the region from California and Baja California. The determined values of the rain for one hour and return period of 2 years obtained were compared to the values of some cities in California and Baja California, with a range between 10 and 16.61 mm, and the values of the (R) ratio are in a range between 0.35 and 0.44; this range is close to the (R) ratio of 0.44 for one station in Tijuana, a city 100 km far from Ensenada. The values found here correspond to the rainfall characteristics of the zone; therefore, the method used in this study can be replicated to other semi-arid zones with the same rain characteristics. Finally, it is suggested that these results of the IDF relationship should be incorporated on the Norm of the State of Baja California as the recurrence update requires it upon recommendation. This study is the starting point to other studies that imply the calculation of a peak flow and evaluation of hydraulic structures as an input to help improve flood resilience in the city of Ensenada.