The process of developing an integrated water demand model integrating end uses of water has been presented. The model estimates and forecasts average daily water demand based on the end-use pattern and trend of residential water consumption, daily rainfall and temperature, water restrictions and water conservation programmes. The end-use model uses the latest end-use data set collected from Yarra Valley Water, Australia. A computer interface has also been developed using hypertext markup language and hypertext pre-processor. The developed model can be used by water authorities and water resource planners in forecasting water demand and by household owners in determining household water consumption.

## INTRODUCTION

Water demand management is not only an important issue warranting careful attention, but also a well-recognised tool within water supply industries in Australia and overseas. However, there is a great challenge in quantifying the impact of water conservation programmes on reducing water demand. In addition, considerable efforts are essential to evaluate the effectiveness of these options since these options have distinguishable and discernible sets of economic, social and environmental consequences. Recently, residential water demand modelling has been undertaken by various researchers (e.g. Jacobs & Haarhoff 2002; Gato *et al*. 2005, 2007a, 2007b; Blokker *et al*. 2010). However, there is a lack of integration of end uses of water, climatic factors (e.g. rainfall and temperature), water restrictions and water conservation programmes in total water demand modelling in the context of current climate and for sustainable water management.

End-use modelling is an approach or strategy for quantifying and forecasting water demand of individual end uses such as shower, toilet, tap, bath, dishwashing, laundry, garden watering, etc. (Rathnayaka *et al*. 2011). However, integrating output of these end-use models in forecasting water demand is currently not undertaken. There is also the issue of drought, possible effect of climate change and growing population which led to water authorities and government worldwide to enforce water restrictions and to implement water conservation programmes. Again these parameters are not included in the current water demand forecasting models; therefore, it is necessary to develop a new integrated water demand model which will incorporate end uses of water, climatic factors (e.g. rainfall and temperature), water restrictions and water conservation programmes. The integration of these parameters is a complex process and the question is how these parameters can be integrated in total water demand modelling.

The objective of this paper is to illustrate the process of integration of a proposed integrated water demand model integrating end uses of water (DMEUW) to overcome the limitations in current water demand models. Garden watering is not included in end-use components in this study because garden watering is considered as seasonal use not base use.

## BRIEF LITERATURE REVIEW

Historical demand forecasting methods have considered relationships obtained from regression analysis, but have not considered the demand at the end-use level, or at different sectors, which may change over time. Gato *et al*. (2005) used simple time series analysis and multiple regression analysis to forecast short-term residential water use for East Doncaster, Victoria, Australia considering climatic variables such as temperature and rainfall and also rainfall threshold and temperature threshold (Gato *et al*. 2007b), but did not consider water restrictions. Sarker *et al*. (2013) also analysed temperature and rainfall thresholds of water uses from mixed areas (i.e. residential, industrial, and commercial) for Greater Melbourne, Australia. Since regression analysis cannot be used to determine how and which factors have affected the historical demand analysis, the end-use method could be extremely useful as it enables a far more refined analysis (Turner *et al*. 2008). Gato-Trinidad *et al*. (2011) also noted that understanding the end use of water will assist water planners, water authorities and household owners in discovering where, how much, and how often water is used/wasted.

The integration of a custom-built regression model for forecasting total customer water demand and end-use based water projections using the integrated supply demand planning model will result in a better forecast. This is because the regression model component allows future changes in climate or periods of restrictions to be modelled although it does not show where water demand increases post-drought (e.g. longer showers and greater garden irrigation). Conversely, the end-use model offers the ability to construct future scenarios (Giurco *et al*. 2013). For this reason, integration of end uses of water into total demand forecasting is necessary for long-term sustainable water management. There are already some end-use studies such as the domestic water end-use study of Gold Coast, Australia (Willis *et al*. 2009) and simulating residential water demand with a Stochastic End-Use Model (Blokker *et al*. 2010), but these only cover the end-use modelling and do not include estimates or forecasts of total water demand.

In addition, there is a need for climate variables to be considered since climate change poses a significant or moderate risk to the sustainable management of water (AWA/Deloitte State of the Water Sector Survey 2012). Water conservation should also be included in an integrated end-use model to analyse the cost effectiveness of the programmes (Maddaus & Maddaus 2004). So far, no known model has considered all these factors and this could be attributed to the complexities in smaller known models let alone integrating these complex models.

In the context of the current situation in Australia and worldwide and for more precise and accurate demand forecasting, this paper tries to develop a framework and structure of an integrated water demand model capable of incorporating: (i) end-use analysis, (ii) water conservation programmes, (iii) climate factors, (iv) population, and (v) water restrictions.

## PROPOSED METHODOLOGY FOR DEVELOPING THE MODEL

This section illustrates the process of integrating end uses of water, climate factors (rainfall and temperature), water restrictions and water conservation programme in developing the structure of the integrated water demand model DMEUW.

### Data set

The required data for this model include:

(i) daily residential water consumption data (water end-use data, e.g. toilet flushing, clothes washing, dish washing, bath, shower, tap, and garden irrigation);

(ii) climatic data (daily rainfall and temperature);

(iii) water storage level.

Residential water consumption data can be collected from Yarra Valley Water, Australia, and the climatic data are from Bureau of Meteorology, Australia.

### Algorithm/mathematical structure of the model

Water demand models are based on the premise that total water use can be divided into base use and seasonal use, where base use is characterised by the water use during winter months, and seasonal use is dependent upon climatic conditions (e.g. rainfall) (Maidment & Miaou 1985). Most of the previous end-use models were developed based on monthly billing data (Mayer & DeOreo 1999; Jacobs & Haarhoff 2002; Worthington *et al*. 2009). The DMEUW model is based on a daily total water demand (*W*_{TD}) and consists of two components: (i) base use, *W*_{BU} (daily), and (ii) seasonal use, *W*_{SU} (daily).

#### Base use, *W*_{BU}

The estimation of daily base use of total water demand depends on end-use modelling. Base use equations were developed for both a household and a region as follows:

where *W*_{BU} = base use of the daily water demand (litre/day), *B* = absence (0) or presence (1) of an end use, *Q* = volume (litre/event), *F* = frequency of the event (events/person/day), *N* = household size, e = end-use components.

*h*= household size (may vary from 1 to 6, or more),

*n*= number of households with household size

*h*. If ‘

*n*’ is unavailable, the total base use of daily water demand of a region containing population

*p*is estimated as

#### Water conservation programme in base use

The model estimates the water consumption of a household at every end-use level. The water savings of a water conservation programme, such as retrofitting an efficient showerhead, can be estimated through changing the volume parameter of this model.

#### Seasonal use, *W*_{SU}

Seasonal use (*W*_{SU}) is calculated by deducting the estimated base use from observed total water consumption, i.e. *W*_{SU} = *W*_{TD} – *W*_{BU} (modelled). The variations in seasonal water consumption depend on several factors such as air temperature, rainfall, evapotranspiration, wind speed, etc. Among these factors, rainfall and temperature play a key role in determining the variations of seasonal water use (Gato *et al*. 2005). Therefore, in this model *W*_{SU} is dependent on climatic variables such as rainfall and temperature. *W*_{SU} has two components: (i) potential seasonal water use (*W*_{PU}), which varies depending on the variation in surface air temperature; and (ii) the short memory use (*W*_{SM}) which has the effect of rainfall, air temperature and random errors which represents the quick response of people to weather changes (Maidment & Miaou 1985).

#### Modelling potential seasonal water use

*W*

_{PU}), the regression of

*W*

_{PU}against a seasonal variable such as maximum temperature has been adopted (Maidment & Miaou 1985). While, it is recognised that there are other methods of modelling potential seasonal water use variations ‘the regression of

*W*

_{PU}, against a seasonal variable’ considers the change in water use if temperature and rainfall changes. A change in air temperature can increase or decrease water usage, but occurrence of rainfall only leads to reduction in water usage. This type of effect cannot be incorporated properly into a conventional method such as Fourier series model of historical seasonal water use (Maidment & Miaou 1985) because this model considers the effect of both rainfall and temperature, which is inconsistent with basic assumptions – when there is no rainfall there should be an increase in water usage. Potential seasonal water use is modelled using this heat function. Heat function is expressed as (Maidment & Miaou 1985)

*C*

_{0}and

*C*

_{1}are coefficients to be estimated by applying iterative trial and error techniques of linear regression,

*H*(

*T*) is the heat function of air temperature

*T*. The daily

*W*

_{PU}is calculated by substituting the normal daily air temperature,

*T*estimated from long-term records, into the heat function for each rainless day of the year.

_{N}#### Modelling short-memory water use

*W*_{SM} is calculated using the method transfer function noise model (Box & Jenkins 1976) as rainfall has dynamic effects on the variation of water consumption, and can be incorporated through the transfer function.

#### Transfer function noise model for DMEUW

where = short-memory water use; = transformed daily temperature; = rainfall; = error or noise term; = delay (*b* time units of delay between the response and the input); = transfer function for temperature and rainfall; = transfer function weights for temperature and rainfall; = transfer function coefficients; = backshift operator or time lag; = no of day – time index (daily basis)

The general steps for developing the transfer function model involves (i) plotting the data, (ii) prewhitening, (iii) rational polynomial representation of the transfer function, (iv) fitting a model for the noise, (v) fitting the transfer function-noise model, and (vi) diagnostic checks (Bisgaard & Kulahci 2011).

*T*

_{i}) as

#### Water restrictions in seasonal use

Water restrictions depend on water storage level. Figure 1 shows the relationship between water restriction stages in Greater Melbourne and their corresponding water storage levels on different seasons of the year.

*R*). Mathematically One component of DMEUW investigates the effect of rainfall on storage level and on water restrictions which eventually determines the prospective WRL. Then, the model will incorporate the corresponding percentage reduction in seasonal use and total water demand based on determined WRL.

#### Parameters for consideration

Population growth, climatic variables (rainfall and temperature), water restrictions, water conservation, and residential water end use are incorporated in this model. End-use parameter values considered by Roberts (2005), Roberts *et al*. (2011), and Athuraliya *et al*. (2012) have been adopted as default values (see Table 1) in the initial development of DMEUW. The model is parameters can be changed depending on the region's water end-use trends and patterns.

Appliances | Parameter | Value | |||||||
---|---|---|---|---|---|---|---|---|---|

End use | Type | Measurement | Notation | Description | Unit | 2004 | Winter 2010 | Summer 2012 | Combined 2010 & 2012 |

Shower | Standard | Flow rate | q | Volume | L/m | 9.8 | 8.7 | 8.3 | 8.4 |

3 Star | Flow rate | q | Volume | L/m | 6.7 | 6.3 | 6.4 | 6.4 | |

All shower | Flow rate | q | Volume | L/m | 9.5 | 7.3 | 7.2 | 7.2 | |

All shower | Average time of uses | t | Duration | Minutes/event | 7.1 | 7.1 | 6.5 | 6.8 | |

Standard | Volume | Q | Volume | L/event | 69.58 | 61.77 | 58.93 | 59.64 | |

3 Star | Volume | Q | Volume | L/event | 47.57 | 44.73 | 45.44 | 45.44 | |

All shower | Volume | Q | Volume | L/event | 67.45 | 51.83 | 51.12 | 51.12 | |

All shower | Frequency of use | F | Frequency | Events/person/day | 0.76 | 0.73 | 0.73 | 0.73 | |

Toilet | All type | Average flush volume | Q | Volume | L/flush | 7.6 | 5.6 | 5.5 | 5.6 |

All type | Flush frequency | F | Frequency | Events/person/day | 4.2 | 3.9 | 3.9 | 3.9 | |

Clothes washing | All type | Average load volume | Q | Volume | L/load | 143 | 110 | 93 | 101 |

Front loader | Average load volume | Q | Volume | L/load | 75 | 64 | 58 | 61 | |

Top loader | Average load volume | Q | Volume | L/load | 152 | 147 | 131 | 139 | |

All type –measured | Frequency of average load per week | F | Frequency | Events/house/week | 6.4 | 4.5 | 5.2 | 4.8 | |

All type –modelled | Frequency of average load per week | F | Frequency | Events/house/week | 5.7 | 4.4 | 4.9 | 4.6 | |

Household size = 2.6 persons. No. loads/week_{CW} = 2.62 * ln(household size) + 1.87 [winter 2010]. No. loads/week_{CW} = 2.28 * ln(household size) + 2.09 [combined 2010 & 2012] | |||||||||

Dish washer | All type | Average load volume | Q | Volume | L/load | 23.9 | 16 | 14 | 15 |

All type –measured | Frequency of average load per week | F | Frequency | Events/house/week | 3.4 | 3.5 | 3.5 | 3.5 | |

All type –modelled | Frequency of average load per week | F | Frequency | Events/house/week | 3 | 3.2 | 3.3 | 3.2 | |

Household size = 2.6 persons. No. loads/week_{DW} = 2.77 * ln(household size) + 0.64 [winter 2010]. No. loads/week_{DW} = 1.896 × ln(household size) + 1.28 [combined 2010 & 2012] | |||||||||

Tap | All type | Average flow rate | q | Volume | L/m | 3.3 | 3 | 2.2 | 2.6 |

All type | Time of uses | t | Duration | Min/event | 0.39 | 0.33 | 0.45 | 0.38 | |

All type | Average volume per event | Q | Volume | L/event | 1.3 | 1 | 1 | 1 | |

All type | Frequency per day | F | Frequency | Events/person/day | 21 | 21 | 22 | 21 | |

All type | Average water use per capita per day | Q | Volume | L/person/day | 27 | 21 | 22 | 21 | |

All type | Modelled – average water use per capita per day | Q | Volume | L/person/day | 29 | 24 | 25 | 24 | |

Modelled – tap use/person = 33.8 – 10.2 × ln(household size) [combined 2010 & 2012] |

Appliances | Parameter | Value | |||||||
---|---|---|---|---|---|---|---|---|---|

End use | Type | Measurement | Notation | Description | Unit | 2004 | Winter 2010 | Summer 2012 | Combined 2010 & 2012 |

Shower | Standard | Flow rate | q | Volume | L/m | 9.8 | 8.7 | 8.3 | 8.4 |

3 Star | Flow rate | q | Volume | L/m | 6.7 | 6.3 | 6.4 | 6.4 | |

All shower | Flow rate | q | Volume | L/m | 9.5 | 7.3 | 7.2 | 7.2 | |

All shower | Average time of uses | t | Duration | Minutes/event | 7.1 | 7.1 | 6.5 | 6.8 | |

Standard | Volume | Q | Volume | L/event | 69.58 | 61.77 | 58.93 | 59.64 | |

3 Star | Volume | Q | Volume | L/event | 47.57 | 44.73 | 45.44 | 45.44 | |

All shower | Volume | Q | Volume | L/event | 67.45 | 51.83 | 51.12 | 51.12 | |

All shower | Frequency of use | F | Frequency | Events/person/day | 0.76 | 0.73 | 0.73 | 0.73 | |

Toilet | All type | Average flush volume | Q | Volume | L/flush | 7.6 | 5.6 | 5.5 | 5.6 |

All type | Flush frequency | F | Frequency | Events/person/day | 4.2 | 3.9 | 3.9 | 3.9 | |

Clothes washing | All type | Average load volume | Q | Volume | L/load | 143 | 110 | 93 | 101 |

Front loader | Average load volume | Q | Volume | L/load | 75 | 64 | 58 | 61 | |

Top loader | Average load volume | Q | Volume | L/load | 152 | 147 | 131 | 139 | |

All type –measured | Frequency of average load per week | F | Frequency | Events/house/week | 6.4 | 4.5 | 5.2 | 4.8 | |

All type –modelled | Frequency of average load per week | F | Frequency | Events/house/week | 5.7 | 4.4 | 4.9 | 4.6 | |

Household size = 2.6 persons. No. loads/week_{CW} = 2.62 * ln(household size) + 1.87 [winter 2010]. No. loads/week_{CW} = 2.28 * ln(household size) + 2.09 [combined 2010 & 2012] | |||||||||

Dish washer | All type | Average load volume | Q | Volume | L/load | 23.9 | 16 | 14 | 15 |

All type –measured | Frequency of average load per week | F | Frequency | Events/house/week | 3.4 | 3.5 | 3.5 | 3.5 | |

All type –modelled | Frequency of average load per week | F | Frequency | Events/house/week | 3 | 3.2 | 3.3 | 3.2 | |

Household size = 2.6 persons. No. loads/week_{DW} = 2.77 * ln(household size) + 0.64 [winter 2010]. No. loads/week_{DW} = 1.896 × ln(household size) + 1.28 [combined 2010 & 2012] | |||||||||

Tap | All type | Average flow rate | q | Volume | L/m | 3.3 | 3 | 2.2 | 2.6 |

All type | Time of uses | t | Duration | Min/event | 0.39 | 0.33 | 0.45 | 0.38 | |

All type | Average volume per event | Q | Volume | L/event | 1.3 | 1 | 1 | 1 | |

All type | Frequency per day | F | Frequency | Events/person/day | 21 | 21 | 22 | 21 | |

All type | Average water use per capita per day | Q | Volume | L/person/day | 27 | 21 | 22 | 21 | |

All type | Modelled – average water use per capita per day | Q | Volume | L/person/day | 29 | 24 | 25 | 24 | |

Modelled – tap use/person = 33.8 – 10.2 × ln(household size) [combined 2010 & 2012] |

#### Process of integration

The model's basic working steps and process of integration for estimating and forecasting total water demand is shown in Figure 2**.**

## COMPUTER INTERFACE OF THE DMEUW MODEL

### Operational feature of the model

#### Parameters required

The data required to run the model are: (i) household size (*h*), (ii) end-use data information about the old and new efficient water fixtures and appliances (*e*), (iii) rainfall and temperature data (daily) of a region or city (*R*, T), (iv) current population (*p*), (v) rate of population increase (*Rp*), (vi) number of households with different household-size (*N*−*h*), and (vii) dataset of record of population (*p*−*R*).

#### Output

The expected output of the model for a household family or for a region includes: (i) daily base use (*B*_{SU}), (ii) daily water consumption of each major end use (*W*_{EU}), (iii) estimation of water savings in daily base use (*W*_{SV-BU}), (iv) seasonal water use (daily) (*W*_{SU}), and (v) total daily water demand (*W*_{TD}). The model users will be able to select the desired combination of output from this model and subsequently the model will automatically generate a display ‘what combination or what set of data are required for input’ as illustrated in Figure 3.

#### Compiling considerations and assumptions of the model

The compiling considerations and assumptions of the model are as follows:

Population is the same throughout the year.

If the rate of population increase data are unavailable, the model estimates the growth rate based on available population data, i.e. population is forecasted by extrapolating recorded information on the population.

Number of households with different household-size (

*N*−*h*) is preferred instead of population. The model does not convert population into corresponding*N*−*h*.No household size is forecasted. But, if the

*N*−*h*data set for a number of years from a region is available, then the model considers the percentage of*N*−*h*and extrapolates it to make the forecast.If the

*N*−*h*data set is unavailable, the model estimates water demand considering per capita water consumption for the given population.To calculate water consumption at major end-use level, the model considers the default end-use parameter values published by Yarra Valley Water; however, the model users can input their own end-use data and information about water fixtures and appliances for their customised assessment.

To assess the water savings from conservation programmes, such as retrofitting water efficient appliances, the end-use data and information about the old and new efficient fixtures and appliances must be inputted.

The model considers WRLs based on the relationship among storage level, restriction level, and rainfall.

No climate factor is forecasted by this model. The model uses climatic data (rainfall and temperature) inputted by the model users. The model considers the present inputted climatic data as a future one unless other users input the forecasted rainfall and temperature data.

#### Computer interface of DMEUW

The computer interface (web-based application) of the model DMEUW (Figure 4) was designed using hypertext markup language (HTML). An HTML-embedded web scripting language hypertext preprocessor (PHP) works for the calculation of the mathematical algorithm of the model, since PHP is applicable for database applications. Only the required data input options appear while running the model. The ‘Help’ menu, in the right-top corner of the window, contains detailed information about the model (e.g. default values of end uses, instructions for running the model, algorithm of the model, etc.) to provide the users with guidelines to run the model.

## LIMITATIONS

The model includes the following limitations:

The model is complex and a large amount of data is needed to run the model.

The model does not incorporate effect of rainwater tank on calculating water demand. This integrated model does also not consider water supply network issues, such as water supply pressure, water supply system – intermittent or continuous, etc.

The model does not consider a single event. The model is not capable of separating the demand for tourism, industrial, and commercial activities. Any demand during religious, national events and vacations are taken during those days and these may increase the average demand since the model considers historical demand, rainfall and temperature and uses time-series analysis.

## CONCLUSIONS

An integrated water demand model can be developed to contribute to sustainable water management, specifically, in water demand modelling, where there is a lack of integration of end uses of water, climatic factors, and water conservation programmes including water restrictions. This integrated model addresses the limitations of currently used models and will assist water authorities and water resource planners in their future planning of sustainable water management.

Specifically, the following can be concluded:

One component of DMEUW determines the prospective WRL through the direct relationship between rainfall and the WRL, which eventually estimates the seasonal and total water demand based on determined WRLs.

The model determines the amount of water savings of a household resident, a suburb or a region.

The model is able to estimate the water consumption at each major end-use level such as shower, toilet, clothes washing, dish washing, tap, etc. which can assist with determining areas, or regions, that are consuming more water and at which end-use level.

Eventually, this model could assist water resource managers and planners in developing, implementing and evaluating water management strategies and programmes including, but not limited to, retrofitting houses with efficient water appliances and fixtures to reduce the water demand.

Likewise, from a planning point of view, this model could help planners and demographers in their understanding of new urban planning and community development.