Statistical methods such as multiple linear regression (MLR) and autoregressive moving average (ARIMA) models have traditionally been used for short-term urban water demand forecasting.
However, disadvantages of traditional urban water demand forecasting models include the requirement of a large number of input parameters, and the fact that most traditional modeling methods assume the data is linear and stationary. Traditionally, urban water demand has been forecasted by either analyzing historical water consumption or using statistical models with a range of inputs such as population, price of water, income, and various meteorological variables. For example, water managers find accurate short-term water demand forecasts important because it allows them to: (i) develop a better understanding of the dynamics and underlying factors that affect water use (ii) manage and optimize maintenance and operating schedules for pumps, wells, reservoirs, and mains (iii) balance the needs of water supply, residential/industrial demands, and stream flows for ecosystem health (iv) analyze the benefits and costs of water conservation, as well as the water saved by imposition of emergency water restrictions and (v) provide information on when peak day events are likely to occur. Since some Canadian water supply distribution networks such as in Montreal are deteriorating, accurate short-term water demand forecasts are becoming increasingly important in helping to find solutions to Canada's urban water supply management problems. An important component of optimizing water supply systems and implementing effective water demand management programs is the accurate forecasting of short-term water demands. Rather than finding additional resources, demand management strategies look at ways to decrease water requirements and to conserve water. The poor infrastructure, overuse, and lack of new water sources in urban areas in Canada and around the world has increased the need for demand management as a way to ensure sufficient and sustainable water for urban use. Although Canada has 7% of the world's fresh water and only 0.5% of the world's population, most of the fresh water flows north in the opposite direction of the main areas of population. Moreover, in Canada the use of water per capita is one of the highest in the world (it ranks 15th out of 16 peer countries and earns a “D” grade), and a false illusion of fresh water abundance exists among Canadians. Many water supply distribution networks currently being used in Canada were built prior to or just after World War II, and many have not been properly upgraded or maintained. Water loss in urban water supply distribution networks is also becoming a problem in certain cities in Canada. Many urban water supply systems in Canada are becoming stressed due to increasing peak and total water demand, a lack of new water sources, climate change, and other environmental and socioeconomic factors.
Even though it may not appear that Canada lacks fresh water, experts are seeing a growing problem involving municipal water and sewer infrastructure in Canada. The city of Montreal, along with other large urban cities in Canada and elsewhere, needs to find more effective methods to optimize the operation and management of its existing water supply system in addition to exploring the implementation of water demand management programs to decrease both peak and average urban water demand. The results of this study indicate that coupled wavelet-neural network models are a potentially promising new method of urban water demand forecasting that merit further study. The WA-ANN models were found to provide more accurate urban water demand forecasts than the MLR, MNLR, ARIMA, and ANN models. The key variables used to develop and validate the models were daily total precipitation, daily maximum temperature, and daily water demand data from 2001 to 2009 in the city of Montreal, Canada. Multiple linear regression (MLR), multiple nonlinear regression (MNLR), autoregressive integrated moving average (ARIMA), ANN and WA-ANN models for urban water demand forecasting at lead times of one day for the summer months (May to August) were developed, and their relative performance was compared using the coefficient of determination, root mean square error, relative root mean square error, and efficiency index. In this study, a method based on coupling discrete wavelet transforms (WA) and artificial neural networks (ANNs) for urban water demand forecasting applications is proposed and tested. Daily water demand forecasts are an important component of cost-effective and sustainable management and optimization of urban water supply systems.
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