Demand Forecasting for Irrigation Water Distribution Systems I. Pulido-Calvo 1 ; J. Rolda ´ n 2 ; R. Lo ´ pez-Luque 3 ; and J. C. Gutie ´ rrez-Estrada 4 Abstract: One of the main problems in the management of large water supply and distribution systems is the forecasting of daily demand in order to schedule pumping effort and minimize costs. This paper examines methodologies for consumer demand modeling and prediction in a real-time environment for an on-demand irrigation water distribution system. Approaches based on linear multiple regression, univariate time series models exponential smoothing and ARIMA models, and computational neural networks CNNs are developed to predict the total daily volume demand. A set of templates is then applied to the daily demand to produce the diurnal demand profile. The models are established using actual data from an irrigation water distribution system in southern Spain. The input variables used in various CNN and multiple regression models are 1 water demands from previous days; 2 climatic data from previous days maximum temperature, minimum temperature, average temperature, precipitation, relative humidity, wind speed, and sunshine duration; 3 crop data surfaces and crop coefficients; and 4 water demands and climatic and crop data. In CNN models, the training method used is a standard back-propagation variation known as extended-delta-bar-delta. Different neural architectures are compared whose learning is carried out by controlling several threshold determination coefficients. The nonlinear CNN model approach is shown to provide a better prediction of daily water demand than linear multiple regression and univariate time series analysis. The best results were obtained when water demand and maximum temperature variables from the two previous days were used as input data. DOI: 10.1061/ASCE0733-94372003129:6422 CE Database subject headings: Neural networks; Irrigation system; Forecasting; Water distribution; Water demanded. Introduction Fundamental to the real-time operational control of an on-demand water distribution system is the ability to forecast consumer de- mand. Typically, an operating plan is prepared for a period of 24 h in advance since demands display a pronounced daily cycle and energy tariffs are based on time of day. Most water distribution systems include storage facilities op- erated on a daily cycle to reduce energy charges by shifting pumping away from times of high energy tariffs. This storage operation smooths instantaneous peak demands and reduces the importance of short-duration peaks Shvartser et al. 1993. There- fore this study focuses on the development of total daily volume demand models, which are subsequently applied to a daily de- mand pattern normalized by the mean daily value to achieve tem- poral distribution. Daily water requirements for crop irrigation can be estimated by the rates of percolation and evapotranspiration that have been predicted at the stage of irrigation planning. However, this water requirement does not always meet the actual use that is, con- sumer demand due to changes in the field environment such as weather conditions, farm management practices, and so on, which influence the actual amounts of water needed. Actual water man- agement in some irrigation districts is carried out depending only on the experience and knowledge of the administrator, and his or her attention is always drawn to how to forecast daily water de- mand. Procedures for short-term demand forecasting in urban water systems have been reported in the literature; essentially two basic techniques are developed. The first technique consists of estab- lishing mathematical models based on the correlation between the demand data and demographic and environmental factors Maid- ment et al. 1985; Ru ¨ fenatch and Guibentif 1997. The second technique calculates the relationship between present and past demand data stochastic analysis of time seriesHartley and Powell 1991; Jowitt and Xu 1992; Shvartser et al. 1993; Molino et al. 1996. The Box-Jenkins form of time series models and linear regression have been most commonly used in such situa- tions because they are relatively easy to develop and implement. Significant progress in the fields of nonlinear pattern recogni- tion and system control theory has recently been made possible through advances in a branch of nonlinear system theoretic mod- eling called computational neural networks CNNs. A CNN is a nonlinear mathematical structure capable of representing complex nonlinear processes that relate the inputs to the outputs of any system. CNN models are increasingly being applied in many 1 Associate Professor, Dept. Ciencias Agroforestales, Univ. Huelva, EPS, Campus Universitario de La Ra ´bida, 21819 Palos de la Frontera Huelva, Spain. E-mail: ipulido@uhu.es 2 Professor, Dept. Agronomı ´a, Univ. Co ´rdoba, ETSIAM, Apdo. 3048, 14080 Co ´rdoba, Spain. E-mail: jroldan@uco.es 3 Professor, Dept. Fı ´sica Aplicada, Univ. Co ´rdoba, ETSIAM, Apdo. 3048, 14080 Co ´rdoba, Spain. E-mail: fa1lolur@uco.es 4 Assistant Professor, Dept. Ciencias Agroforestales, Univ. Huelva, EPS, Campus Universitario de La Ra ´bida, 21819 Palos de la Frontera Huelva, Spain. E-mail: juanc@uhu.es Note. Discussion open until May 1, 2004. Separate discussions must be submitted for individual papers. To extend the closing date by one month, a written request must be filed with the ASCE Managing Editor. The manuscript for this paper was submitted for review and possible publication on February 5, 2002; approved on January 2, 2003. This paper is part of the Journal of Irrigation and Drainage Engineering, Vol. 129, No. 6, December 1, 2003. ©ASCE, ISSN 0733-9437/2003/6- 422– 431/$18.00. 422 / JOURNAL OF IRRIGATION AND DRAINAGE ENGINEERING © ASCE / NOVEMBER/DECEMBER 2003