Functional relations between probable and average rainfall in Brazilian regions and climates

Abstract

The objective of this work was to determine the statistical parameters of the probability density function (PDF) with the best fit to the values of decennial rainfall observed in several Brazilian localities, and also to determine the relationship between probable rainfall (75% probability, P75%) and average rainfall (_P) in these localities. Five PDFs were evaluated (normal, triangular, gamma, exponential, and uniform), adjusted to data from 43 municipalities, from eight states, in four Brazilian regions. The localities were evaluated singly or grouped into states or climate types. The Kolmogorov‑Smirnov adherence test was used to assess the statistical adjustment of the PDFs to the data series. Gamma and exponential distributions were the ones which more often had the best fit to the series of decennial rainfall (41.2 and 30.8%, respectively). The most promising functional relationships between _P and P75% were obtained at the climates Cwa (R² = 0.82), Aw (R² = 0.70), As (R² = 0.68), and Cwb (R² = 0.62), and at the states of Goiás (R² = 0.80), São Paulo (R² = 0.76), and Minas Gerais (R² = 0.70). The normal (19.3%), triangular (2.2%), and uniform (3.5%) distributions have the lowest participation in the best fits, but are important in the dry season analyzes.