Cumulative distribution function of daily rainfall in the Tocantins–Araguaia hydrographic region, Amazon, Brazil

Abstract

Knowing the temporal and spatial variability of the probability of rainfall occurrence is indispensable for the planning and management of agricultural and agroindustrial activities. This study aims to evaluate the applicability of four cumulative distribution functions (CDFs; exponential, two-parameter exponential, mixed exponential, and gamma) to estimate the probability of daily rainfall in the Tocantins-Araguaia hydrographic region (TAHR). The CDFs were applied to 196 rainfall gauge stations distributed in three homogeneous regions (HRs) of rainfall in the TAHR. In relation to the CDFs, the Kolmogorov-Smirnov test and the probability-probability plot showed that the mixed exponential best adhered to the observed data for most of the months of the year in the three HRs that were analyzed. In the few months that this function did not have a good statistical performance, the gamma function was the one with the best fit quality. This study can be used as a guide for studies in other river basins in Brazil and around the world to estimate CDFs of daily rainfall. Recommendations for Resource Managers• Stochastic models using cumulative distribution functions (CDFs) allow the simulation of rainfall data by means of their frequency of occurrence. Some CDFs have been used to verify the behavior and variability of precipitation over the years. For example, the mixed exponential, the Weibull with two parameters, the generalized Pareto, the lognormal, and the gamma with two parameters.• Daily rainfall modeling is important to recognize the occurrence patterns for the prediction of the climatic behavior of a region. Sectors such as agriculture, flood control, and human supply projects need knowledge of precipitation for planning, management, and operation.• The knowledge of the rainfall behavior is very important in Tocantins-Araguaia hydrographic region because it is located in the arc of deforestation in the Amazon. In this case, the dry season and temperatures have been increasing due to global climate change and deforestation itself. K E Y W O R D S adherence test, agroindustrial activities, ecotone, homogeneous regions, water resources

Conversion of 15-Minutes to 1-Minute Rainfall Distribution Derived from Tropical Rainfall Distribution Measurement

“…The Cumulative Distribution Function (CDF) is a function that consists of a random variable that is nearly equivalent to the independent function variable. The optimization approach of CDFs enables the simulation of hydrological data with their probability of rainfall events [5]. Several CDFs were employed to validate rainfall distribution and variability throughout the years.…”

Optimization of Probability Density Functions Applicable for Hourly Rainfall

“…Problem 2: There are multiple mathematical expressions for the probability distribution, such as the cumulative probability distribution function (CDF) or PDF, the survival distribution function (SDF), or the return period. As for the rainfall probability distribution, a lot of investigations have been conducted on the selection of the applicable function, sampling method, fitting method, optimal parameters, and time scale [33][34][35][36][37][38]. Regarding rainfall probability distribution, the current prevailing method is annual maximum sampling (AMS) and extreme value sampling (EVS), with a focus on the daily precipitation and its CDF.…”