Modeling monthly rainfall data using zero-adjusted models in the semi-arid, arid and extra-arid regions

Modeling rainfall data and analyzing precipitation variability are accurately critical for managing water resources. Generally, rainfall is one of the most important inputs in model fitting based on probability distribution functions. The probability functions provide the possibility of estimation rainfall variability within a specific range. But in many situations, especially in the low rainfall regions, there will be many zero rainfall values. In these cases, the common distributions applied in the literatures cannot be used for modeling those data since statistically they are defined on positive range values. To overcome this problem an edition on the common probability functions should be implemented. The aim of this study is to introduce the zero-adjusted models (ZAM) and then applying these models on monthly rainfall using 46 years of data from 25 stations in semi-arid, arid and extra-arid regions of Iran. The models that will be used through this study, are the zero-adjusted gamma (ZAGA), zero-adjusted Weibull (ZAWEI), zero-adjusted inverse Gaussian (ZAIG), zero-adjusted log-logistic (ZALL) and zero-adjusted log-normal (ZALN). For selecting the best fitted model some numerical validation methods such as the AIC, the BIC and the K-S test are used. Bedsides the numerical methods, some graphical aspects such as PDF, CDF, and Q-Q plots have been served. The results show that the ZAWEI model is suitable for the extra-arid regions, while the ZAGA model has a better performance in the semi-arid and arid regions. This study attempts to provide the technique of using ZA models for the rainfall data in the low-rainfall region and can be considered as a foundation of using these statistical models. The ZAMs can be applied to the rainfall data, and to classify (or cluster) the rainfall regimes, especially for the semi-arid, arid and extra-arid regions of Iran. Also, these probability models can be considered as decision-support tools for decision-makers to manage the water and agricultural resources as well as food reserves with assessing different scenarios in these regions.