Exploring the most suitable probability distribution for analyzing annual rainfall data: a case study of Makkah and Jeddah cities

Abstract This study aims to determine the most suitable probability distribution that can effectively capture the statistical characteristics of rainfall in Makkah and Jeddah cities. The analysis focused on fitting probability distributions to the annual rainfall data between 1971 and 2013, which were provided by the Presidency of Meteorology and Environment. Three probability distributions, namely Normal, Gamma, and Weibull, were tested using a statistical goodness-of-fit test based on p-value and Anderson–Darling (AD) test with significance level of 0.05. For Makkah station, there is no significant evidence to conclude that the observed annual rainfall data significantly deviates from any of the tested distributions. Based on the AD test results, the observed annual rainfall data appears to be consistent with the three distributions. For Jeddah station, the rainfall data does not significantly deviate from a normal distribution while, it significantly deviates from both the Gamma and Weibull distributions at the same significance level. The ability to accurately model annual rainfall patterns using probability distributions has important practical applications, such as in water resource planning, drought forecasting, and climate change impact assessments. The insights from this case study can help inform such applications for the Makkah and Jeddah regions of Saudi Arabia.