Forecasting water use in selected water supply system

The study analyzed data on water consumption in selected municipal water supply system. The forecast was made based on daily water consumption from the period of five years (2012 ÷ 2016). The results are a valuable information source for municipal water supply system operator. Water consumption forecast allows to schedule the amount of water that should be produced e.g., taking into account day of the week, month, and the least onerous terms for water consumers to make repair or modernization of water supply system elements.


Introduction
By definition, forecasting, other word: prediction, is the rational prediction of events in a scientific manner. Otherwise, it is a possibility to conclude about so far unknown events based on known events that occurred in the recent past [1]. The primary function of the forecast is to provide the most objective solutions, which relate to the anticipated event occurring in the future [2][3][4]. Basic functions of the forecasts are [6,7]: x dissecting, which creates prerequisites to take rational decisions, x activating -stimulating to take action that favours the execution of forecast, x information.
The forecast can be presented in view of the so-called forecast horizon, i.e. the period for which it was made. In this classification we distinguish: x immediate, direct forecast which does not exceed 1 month, x short-range forecast, covering 1 -3 months, x medium-range forecast which does not exceed 2 years, x long-range forecast, made for more than 2 years.
Classification of forecasts can also be shown in view of the nature (e.g. simple or complex, single or repeatable, quantitative or qualitative), in view of the degree of details (general or detailed) or in view of the purpose of conducting (research, normative or active or passive) [7].

The method of exponential smoothing with seasonal additive
The equation describing the exponential smoothing model with additive seasonality: where: y t -the forecast variable at a moment or period of time t, F t -smoothed evaluation of the level (mean value) at a moment or period of time t, C t -evaluation of seasonality index at a moment or period of time t, α -smoothing parameter of forecast variable level with values from the range (0, 1], γ -evaluation parameter of seasonal index with values from the range (0, 1], r -the length of a seasonal cycle (number of phases of each cycle). The purpose of equation (1) is to determine a smoothed value of the entire time series and to determine the index of seasonality.
The parameters α and γ can not be equal to 0 and the sum of the weights should be equal to one.
The use of this model on the basis of the time series consisting of n-elements relies on calculating the following equation: wherein the coefficients F n and C T-r are calculated from the following formula: To perform the forecast, the necessary are values F n and C n , which are dependent on the F n-1 and C n-r . When calculating the forecast y t * the expired forecasts must be determined: where: Before the calculation, the initial values C 1 , …, C r and F r should be taken. The values should be adopted for the first cycle in accordance with the equation: The total sum of values of C 1 , C 2 , …, C r should be equal to 0: Value F r is calculated according to the expression: Table 1. shows the mechanism of calculations using EXCEL.

Forecasting water consumption in selected municipality
Data on water consumption for the period 2012 ÷ 2016 and the forecast for 2017 are characterized by fluctuations in water consumption with clearly shaping seasonality in the summer months. Table 2 shows the average value of the data (on the basis of which the forecast for 2012 ÷ 2016 was carried out) for each day of the week. On the basis of Table 2, it can be observed that the increase in water consumption took place at the weekend and the highest value for the week was reached on Sunday. This is due to lifestyle of the recipients -the longer time spent at home, compared to weekdays, and house chores. Then, on Monday, water consumption was reduced from 1557 m 3 to 1044 m 3 , and successively during a week it was about 1,200 m 3 .
Four years data was used for building the model and forecast for 2016 was made to compare it the forecasted data with historical data from 2016 (Fig. 1). Prepared model correctly predicts future water consumption. Figure 2 presents water consumption forecast for 2017. For comparison, the same data as Table 2. was created for the forecast of water consumption for 2017 on Fig. 3.

Conclusions
Data on water consumption for the period 2012-2016 and the forecast for 2017 are characterized. After analysing the results and comparing them to the previous water consumption, it was stated that the forecasting model was correct. The results of the method of exponential smoothing with seasonal additive as well as water consumption in the past, oscillate around the trend line and the apparent increase in water consumption also takes place during the summer (May-August).
The method meets the principle of the easy availability of output data that is convenient from a practical point of view. These data do not include external factors (for example environmental) -variables, but they are based on chronological data of the past.
In summary, this paper presents a model of the time series, which is a simple and flexible tool for forecasting. The basic argument, which supports the use of the above models is mainly good quality of water consumption forecast and hence a better quality of water distribution services. With the appropriate series of past data forecasting demand for water is possible. Choice of the correct methods and properly conducted forecast allow to draw the appropriate conclusions, thanks to which it is possible to improve the operation of water supply systems.
The paper presents the simple forecasting model that is a universal and fast tool to predict the demand for water in water supply system on the basis of the collected data. Additionally described model can be used during the operation of the water companies to plan, among others: -the purchase of reagents for treatment -repairs related to the shutdown of water supply -costs of pumping water.