A multi-state Markov chain model to assess drought risks in rainfed agriculture: a case study in the Nineveh Plains of Northern Iraq

The occurrence of prolonged dry spells and the shortage of precipitation are two different hazardous factors affecting rainfed agriculture. This study investigates a multi-state Markov chain model with the states of dry spell length coupled with a probability distribution of positive rainfall depths. The Nineveh Plains of Northern Iraq is chosen as the study site, where the rainfed farmers are inevitably exposed to drought risks, for demonstration of applicability to real-time drought risk assessment. The model is operated on historical data of daily rainfall depths observed at the city Mosul bordering the Nineveh Plains during the period 1975-2018. The methodology is developed in the context of contemporary probability theory. Firstly, the Kolmogorov-Smirnov tests are applied to extracting two sub-periods where the positive rainfall depths obey to respective distinct gamma distributions. Then, empirical estimation of transition probabilities determining a multi-state Markov chain results in spurious oscillations, which are regularized in the minimizing total variation flow solving a singular diffusion equation with a degenerating coefficient that controls extreme values of 0 and 1. Finally, the model yields the statistical moments of the dry spell length in the future and the total rainfall depth until a specified terminal day. Those statistical moments, termed hazard futures, can quantify drought risks based on the information of the dry spell length up to the current day. The newly defined hazard futures are utilized to explore measures to avert drought risks intensifying these decades, aiming to establish sustainable rainfed agriculture in the Nineveh Plains.

Automated summary

The study utilizes a multi-state Markov chain model to assess drought risks in the Nineveh Plains of Iraq in real-time, combining dry spell length with probability distribution of positive rainfall depths. By analyzing historical rainfall data with probability theory, the model extracts distinct gamma distributions and provides statistical moments of future dry spell length and total rainfall depth to quantify drought risks. The newly defined hazard futures are aimed at exploring measures to prevent escalating drought risks and establish sustainable rainfed agriculture in the region.