Agricultural drought periods analysis by using nonhomogeneous poisson models and regionalization of appropriate model parameters

Abstract

Precipitation has a dominant role in agriculture, and a regular rain pattern is usually vital to agriculture; excessive or inadequate rainfall can be harmful. In this paper, an agricultural drought index is utilized to study the agricultural drought periods and analyze them with their intensities at various locations. Some nonhomogeneous Poisson models are also used to calculate the probability of agricultural droughts (number of times occurred) in a time interval of interest. It is to be assumed that the number of agricultural drought event occurrences is a Nonhomogeneous Poisson Process (NHPP) has a rate function, which depends on some parameters that must be estimated. Two cases of these functions are considered: the Weibull and linear intensity function. The Bayesian approach with Gibbs sampling under the Markov Chain Monte Carlo (MCMC) algorithm is used to estimate the parameters of these functions. The most appropriate fitted model is selected by using Deviance Information Criteria (DIC) and use that appropriately fitted model to calculate the accumulated events of agricultural drought in a time interval of interest at each location. Ordinary Kriging (OK) is used to regionalize the parameters and present its spatial behavior. The results based on the DIC indicate that the Power Law Process (PLP) performs better than the linear intensity function, NHPP model. The interpolated parameter values for the appropriate model, their patterns, and fluctuations for the study area are efficiently presented using contour maps. It is a novel and straightforward approach to assess the selected model parameter values used to predict the accumulated drought events at un-sampled locations. The proposed framework might also help to analyze other spatial variables of interest and can be used for climate-change study, ecosystem modeling, etc. The findings can also help to make decisions for sustainable environmental management in Pakistan.

Keywords

• standard precipitation index
• agricultural drought
• nonhomogeneous poisson process
• power law process
• linear intensity function
• regionalization
• variogram
• ordinary kriging