Spatial and temporal Hurst exponent variability of rainfall series based on the climatological distribution in a semiarid region in Mexico

A fractal analysis from rainfall events registered in a semiarid region was carried out. The analysis was executed for Baja California, Mexico, a region that presents a high climatological variability. Rainfall data from 92 climate stations distributed along the region of study with at least 30 years of records were used. By studying the rainfall series patterns, the Hurst exponent values were obtained (both spatial and temporal) as well as their relation with the variables for annual average temperature, annual average rainfall, altitude and climatological distribution. The rescaled range method, box counting method, and multifractal detrended fluctuation analysis were successfully applied, having as a result the average value of the Hurst exponent for different time scales. Data showed that the daily rainfall series tend to present a persistent pattern; besides, the Hurst exponent values (Hu) were related to the type of climate, altitude, rainfall regime, and temperature of the studied area. The analysis of the Hurst exponent for different time scales showed that, at a smaller time scale, the Hurst value tends to increase; thus, the series present a stronger persistent behavior. Moreover, it can be confirmed that the fractal theory methodology allows analyzing the behaivor of a climate variable, in this case rainfall.