Abstract: Forecast of urban water demand is a basic content of optimal allocation and planning for regional water resources. On the basis of gray GM(1,1) model of trend prediction, the weighted Markov chain prediction method is introduced to establish a weighted grey Markov GM(1,1) model for predicting urban water demand. This model combines the feature of dealing with numbers of strong monotonous series with the feature of random wave response in extracting relative residuals through state transfer probability matrix. The model is applied to the prediction of urban water demand in Chengdu city and the result indicates that the weighted grey Markov GM(1,1) model makes full use of the information given by urban water demand sequence and forecasts the transfer regularity of relative residuals sequence among system states, by which it enhances the precision correcting value of grey model prediction. Furthermore we compared this model with other two grey models and the prediction result suggests that the weighted gray Markov GM (1,1) model has higher accuracy. The urban water demand forecast in 2012 and 2013 is 742.5091 million m³ and 798.1834 million m³ in Chengdu city respectively, presenting a significant increasing trend. Therefore this model improves the accuracy when dealing with stochastic fluctuating data, and broadens the application scope of grey model prediction and makes it more scientific.

Key words: urban water demand prediction, GM(1,1) model, weighted Markov chain, transfer probability, prediction accuracy