Decision Support Models In Water SupplySystems Planning

Abstract

In this work, the theory of time series in the analysis of water consumption was applied. The study was developed using forecasting (short term) SARIMA models. Then was applied to characterise the consumption of the distribution network served by the reservoir of Urgeses in the city of Guimaraes. The characterisation is basically done through the study of the peak factor and the definition of the chronological diagrams of flow. To project (long term) the consumption, a computer program was developed and applied for the cascade models which decomposes the consumption into different components to be analysed. These are the annual trend, seasonality, autocorrelation and climatic correlation. INTRODUCTION In today's world one billion (1 000 000 000) people do not have access to clean water according to Serageldin [1]! Indeed usable water is (becoming) one of the major limiting factors in planning and development. In this respect, it is fundamental to adequately assess the basic elements of design in order to assure resource conservation. In particular in the existing water infrastructures which are (not) functioning efficiently, there is a great need to develop formal methodologies to reduce the risk of losses and promote proper planning for the future. Short term forecasting is again important in the management of the systems in order to reduce the costs in a number of areas like the operation of a pumping plant. FORECASTING OF CONSUMPTION SARIMA METHODOLOGY SARIMA model represents a Seasonal AutoRegressive Integrated Moving Average which is given by Box [2] as: B*)s, (1) Transactions on Ecology and the Environment vol 7, © 1994 WIT Press, www.witpress.com, ISSN 1743-3541 66 Hydraulic Engineering Software This model is abbreviated as SARIMA(p,d,q).(P,D,Q)g, where p is the order of autoregression, d is the order of differencing, q is the order of moving average, the uppercase letters have the same definitions as the lowercases but are the seasonal values, S is the seasonally period. The ARIMA modelling of the water consumption time series follows the usual steps of: identification, estimation, evaluation of the diagnosis, and model selection, Box [2]. In this work the identification phase was done through the analysis of the Autocorrelation Function, ACF, and the Partial Autocorrelation Function, PACF. The estimation phase is done using the software package SPSS [3]. Evaluation of the diagnosis was analysed using the statistical qualities like T-Ratio and the correlation matrix, the quality of adjustment through the residual ACF and PACF, and other divers tests like Portmanteau. The final part of model selection can be done using the criterion of Akaike (AIC) or Bayesian (BIC) PROJECTION OF CONSUMPTION CASCADE METHODOLOGY Investigating the nature of the relationships between water consumption and the parameters that have quantitative influence on it, is an important part of any social and economic development. Among the factors that condition the use of water are number of people using the distribution network, their income, the price of water, and the climatic elements like temperature and precipitation. The Cascade model of long term projection starts with the elimination of the annual tendencies, and seasonal movements with regular periods. To characterise the structure of dependency inside the water consumption time series, an autoregressive model which explains the movement of the time series as a linear function of the previous values, was utilised. Finally the correlation between the consumptions and the climatic factors is studied. Schematically the cascade process is as follows, according to Mays et al [4]: CASCADE MODELOS 0 Historical Data Consumption, Number of Users, Income, Price of Water, Precipitation, Temperature