Using Markov Chains, Regression and Time Series Models to Predict Supply and Demand for Water and Their Behavior: Case Study Tulkarm City

Abstract

This study aimed to predict the amount of water supply and demand in Tulkarm municipality, based on monthly data within the period from January 2010 to December 2019. The matrix of transitional possibilities was formed and then predicted values based on the probability transition matrix were obtained by using the MatLabstatistical program, the results showed that the supply chain stabilizes after (24 months) where we have reached a rise in the amount of water demand at the rate (55.8%). While the rate of decrease was (36.71%) and the rate of stability was (7.54%). Referring to water demand chain, the probability transition matrix stabilizes after (16) months, in which a rise in the amount of water demand has been reached also at the rate (55.46%) while the rate of decrease was (34.45%) and the rate of stability was (10.08%) xiv The study also tried to compare statistical models (Markov model, time series model, and simple linear regression model) to predict the future values of both series. This has been done through using the forecast accuracy scale to find the most suitable model for analyzing the data in the study. The study found that the Markov model with the lowest criterion value (RMSE) is the most appropriate model to analyze the data of the water demand chain in Tulkarm municipality, but for the data of the water supply chain, it was found that the model of time series ARIMA (2, 1, 2) (0, 1, 1) is the most appropriate because it has the lowest forecast criterion value. Based on previous models, the amount of water supply and demand in Tulkarmmunicipality were forecasted for 2030. The amount of Water supply in Tukaram is expected to increase to 1081098.91 MCM, while the total amount of demand in 2030 is expected to increase up to 680779.2 MCM. The forecasted results emphasize the necessity for implementing an integrated water resources management plan in the district, thus utilize the excess supply and demand to ensure sustainable water for the local community on the future. The models shows good potential for expecting such critical water situation that needs an urgent action by the stakeholders through a comprehensive water management plan to ensure water security for the next generations.