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POTENTIAL APPLICATION OF END-USE DEMAND

MODELLING IN SOUTH AFRICA

JE van Zyl, MSAICE, J Haarhoff, FSAICE, and ML Husselmann,

MSAICE

ABSTRACT

End-use water demand modelling is used to generate water demand projections by modelling

various end uses, for example showers, toilets and washing machines. End-use models can be

used to estimate water demand changes due to various scenarios, such as price increases,

housing densification and conservation programmes. This study reports on the potential

application of end-use modelling in South Africa, based on a pilot study that was done for

Rand Water. The model includes elasticities of water demand with respect to variations in

water price, household income, stand size and pressure. The study highlights many of the

difficulties and limitations, as well as the potential applications of end-use modelling as a

water demand predictor. A special effort is made to explain the meaning and application of

elasticity in end-use modelling. Various data sources were used to determine elasticities for

the variables used, and to identify minimum and maximum elasticity values. The implications

of the elasticities are illustrated using a sensitivity analysis and case study.

INTRODUCTION

Water demand modelling is used by engineers to analyse and predict water consumption in

cities and towns under varying conditions. In end-use modelling, the points of water

consumption, for example showers, toilets and washing machines, are modelled individually

or in groups. The characteristics of various water-using fixtures, the behaviour of users and

the sensitivity of water demand to different parameters can be incorporated in a very detailed

end-use model of water demand. Once an end-use model of a supply area is available, water

demand can be predicted under hypothetical scenarios.

Rand Water commissioned a pilot study to demonstrate the strengths and weaknesses of end-

use modelling as a water demand predictor for their supply area. The study included the

entire residential sectors of Alberton, Boksburg, Centurion and Midrand, consisting of more

than 110 000 stands. For the purpose of this pilot study, end-uses were grouped into outdoor

consumption, indoor consumption and leakage. The variables and elasticities in the model

were limited to water price, household income, stand size and pressure. Data for the end-use

model were obtained from numerous Rand Water consumer surveys, as well as published

international and local research.

The study was not aimed at developing a comprehensive model of water demand in the study

area, but limited to a pilot study to illustrate the difficulties, as well as the potential

application of end-use modelling as a water demand predictor. Various causative factors of

water demand, such as temperature, rainfall, level of service and age of infrastructure were

not considered. Although the study focussed on a restricted number of variables in a specific

geographical area, its results provide general pointers to the potential application of end-use

modelling in South Africa.

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The body of the paper starts with some background on end-use modelling, followed by a

discussion on the construction of the end-use model including the choice of modelling

parameters and data collection. The results of a sensitivity analysis in which each of the

elasticity parameters were varied between minimum, normal and maximum expected values

are then discussed. Finally, a case study comprising of the four areas included in the study

(Alberton, Boksburg, Centurion and Midrand) is used to show some of the possible

applications of end-use modelling in the Rand Water supply area.

DEFINITIONS OF ELASTICITY

A commonly used definition of elasticity is the relative change in demand if the given

causative factor doubles. For example, if the water price increases by 100 % and the demand

drops by 20 %, the elasticity would be –0,20. In mathematical terms:

∆

=

∆

F

F

E

D

D

... (1)

With ∆ = a change

F = a causative factor

D = water demand

E = a measure of elasticity

To determine the elasticity E, demand is plotted on a linear scale against the causative factor,

with a smoothing or regression line to achieve continuity. By determining the slope of the

line at a specific point, the elasticity E at that point can be determined:

∆

∆

=D

F

F

D

E

... (2)

By repeating this calculation for all the points on the curve, a second curve can be

constructed, showing elasticity as a function of the causative factor. In a previous Rand Water

study (Business Enterprises at University of Pretoria, 2000), the elasticity of water demand

with respect to water price was determined in this way. The demand versus price (as obtained

by consumer survey) was first obtained and the elasticity versus price was calculated next.

An example from this study is shown in Figure 1.

Ideal position for Figure 1

Although the above definition of elasticity is the one commonly used by economists, it is not

convenient for modelling. The elasticity E as defined above is not constant and is only

meaningful at a specific value of the causative factor. An alternative expression of elasticity β

can be formulated as:

β

=

1

2

1

2

F

F

D

D

... (3)

With β = a measure of elasticity

3

Subscript 1 = before a change

Subscript 2 = after a change

To obtain β, the demand is plotted against the causative factor F on a log-log scale. The slope

of the linear regression line will then be β. The same data shown in Figure 1 are re-analysed

in this way in Figure 2, yielding a β-value of -0,295.

Ideal position for Figure 2

The advantage of the constancy of this measure of elasticity β is obvious, and β has therefore

been adopted for use in this study.

The relationship between E and β

Although the elasticity definitions used for E and β (Equations 1 and 3) are different, it is

useful to explore the relationship between them mathematically in the region of the base

point.

First, write Equation 3 in terms of D and ∆D:

β

∆

+=

∆

+F

F

D

D11

... (4)

Then replace Equation 1 into this equation:

β

∆

+=

∆

+F

F

F

F

E11

... (5)

The variable β can now be written in terms of E by taking the natural logarithm on both sides

of the equation and simplifying.

∆

+

∆

+

=

F

F

F

F

E

1

1

ln

ln

β

... (6)

Our interest is to find the relationship at the base point; in other words, where ∆F approaches

zero. Expanding each natural logarithm as a Maclaurin series,

()

...

!!!

ln +−+−=+ 432

1

432 xxx

xx ,

and then neglecting higher order terms (assuming small absolute elasticity values) further

simplifies the equation to:

E=

β

... (7)

4

The result shows that β and E has the same value at the base point and that these values can

be interchanged in calculations. However, care should be taken not to extrapolate calculations

too far beyond the base point, unless the elasticity value is based on a range of data points to

justify the greater range of application.

Working with unit consumptions

In some instances it is convenient to express demand as a consumption per unit of the

causative factor, rather than per stand. For example, water demand is sometimes expressed in

m3 consumption per square metre of stand area instead of m3 per stand. It is thus necessary to

derive an expression for the relationship between the elasticity values based on per unit

consumption and per stand consumption. Consider a unit consumption d, defined by

F

D

d= ... (8)

With D = water demand per stand

F = the value of the causative factor per stand

The variation of unit consumption with causative factor F can be expressed as (from Equation

3):

α

=

1

2

1

2

F

F

d

d ... (9)

With α = the elasticity based on unit consumption

Now, to convert elasticity based on unit consumption (α) to elasticity based on per-stand

consumption (β), the fraction (D2/D1) is first written in terms of d and F:

11

22

1

2

Fd

Fd

D

D= ... (10)

Equation 9 is replaced into Equation 10 and simplified to obtain:

1

1

2

1

2

+

=

α

F

F

D

D ... (11)

In other words, the relationship between elasticities based on D and d is given by:

1+=

α

β

... (12)

STRUCTURE OF THE WATER DEMAND MODEL

5

A water demand model incorporating water price, household income, stand size and pressure

was used in this study. The model is expressed mathematically as:

PAIT

P

P

A

A

I

I

T

T

AADDAADD average

ββββ

=

1

2

1

2

1

2

1

2

...(13)

With AADD = annual average daily demand

T = water price

I = household income

A = area or stand size

P = water pressure

The most basic classification of domestic consumption is between indoor and outdoor

consumption. The above model was thus applied separately to indoor and outdoor water

demand. System leakage was included as a third demand type in the model.

To differentiate between different classes of consumers, Rand Water adopted a three-tier

classification in its consumer surveys – informal settlements, townships and suburbs. Since it

is very difficult to obtain reliable data for informal settlements, only suburbs and townships

were included in this study.

Modelling was done using the software package IWR-Main (Planning and Management

Consultants, 1999). This package allows various different user types, elasticities and demand

scenarios to be modelled simultaneously, making it a powerful modelling tool.

ELASTICITIES

In order to model the response of the water demand to various scenarios, the elasticity of

water demand with respect to its causative factors must be known. In this study, four

causative factors were analysed, namely water price, household income, stand size and water

pressure. Elasticity values were estimated based on stand meter readings, thus excluding the

effect of leakage in the municipal pipe networks.

Price Elasticity

The price of water is arguably the most important determinant of water demand. It is also one

of the easiest and cheapest for a water supply authority to implement. Metcalf published the

first price elasticity values for water demand in 1926 (Wong, 1972). How and Linaweaver

(1967) presented the first detailed account of price elasticity for water demand.

Water consumption response to changes in price is reasonably simple to calculate when a

single water tariff is used. However, the problem becomes more complex for more

complicated tariff structures such as block rates. In such cases, the use of an average price

would result in a loss of modelling accuracy (Billings and Agthe, 1980). Block rates are

normally handled using the marginal price and a difference value. The difference value

typically represents the difference between a user’s actual water bill and what would have

been paid if the user’s full consumption were charged at the marginal rate (Billings and

Agthe, 1980).

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Numbering

6

There are both upper and lower limits to the applicability of price as a water demand

management tool. Water is necessary for life, and a certain minimum quantity of water will

thus always be consumed, no matter what the price is. On the other hand, there is a physical

limitation to the quantity of water that a user can obtain from the distribution system and thus

will never exceed, even if water is free.

The price elasticity of water is normally higher for outdoor use than for indoor use because

the outdoor consumption is typically less critical to the user. An important factor here is the

fraction of the total water consumption that is used outdoors. Areas with small stands and no

garden irrigation would typically have a smaller fraction of outdoor use, thus increasing the

significance of the indoor price elasticity values.

Price elasticity changes with time and it is possible to differentiate between short-term and

long-term elasticities. Price increases will have an immediate (short-term) effect by changing

consumers’ water use patterns, but will have little immediate effect on house fixtures.

However, in the longer term, the increased cost of water stimulates the installation of water

saving fixtures, resulting in higher elasticity values. Veck and Bill (2000) found from

literature that the average short-term price elasticity is –0,21, while the average long-term

price elasticity is –0,6. This gives some indication of how much more price increases can

affect water consumption in the long-term than in the short-term.

A number of international and local studies on short-term price elasticity have been identified

in the literature. A summary of the results of these studies is given in Table 1. Three South

African studies are included: Veck and Bill (2000) conducted a study on price elasticity by

means of a contingent valuation approach. In this approach, a survey of water users is done in

which they are asked to indicate how they would adjust their water consumption if the price

of water is increased or decreased by certain quantities. The results of this type of study are

not as reliable as actual measured responses, but unfortunately there is very little good data

available. Veck and Bill studied different income groups in Alberton and Thokoza and

determined indoor and outdoor price elasticity values of –0,13 and –0,47 respectively for

Alberton, and –0,14 and –0,19 respectively for Thokoza.

Ideal position for Table 1

In the second South African study, Döckel (1973) also used a contingent valuation approach

to study price elasticity in Gauteng. He found a price elasticity value of –0,69.

A third South African price elasticity study was done by a commercial company for Rand

Water (Business Enterprises at University of Pretoria, 2000) . The study was done in the

Alberton and Thokoza areas, also using a contingent valuation approach. This study provided

much more detailed data values for price elasticity and could be used to fit a β elasticity value

over a range of data points, instead of basing it on a single data point. The study only

determined overall elasticity values. To differentiate between indoor and outdoor

consumption, average outdoor consumptions of 40 % and 15 % were assumed respectively

for suburbs and townships.

Income Elasticity

7

Quality data on income elasticity of water use are scarcer than data on price elasticity.

Fortunately, Rand Water did a detailed survey (MSSA, 2001) on water consumption

behaviour in its supply area, providing a good basis for estimating elasticity values. No

logical differentiation could be made in this case between indoor and outdoor elasticities.

The survey data had to be sieved to obtain relevant elasticity values: the data were first

categorized according to town type (e.g. suburbs and townships). All non-residential users

and estates (townhouses, clusters, etc.) were removed from the data set to ensure that the

elasticities reflect only normal housing units. Data points in which the demand was estimated

by the user (rather than obtained from actual meter readings) were also eliminated from the

data set. The remaining data were then analysed to obtain income elasticity values.

The data used to calculate income elasticities are shown in Figures 3 and 4 for suburbs and

townships respectively. The resulting elasticity values (β) are 0,28 for suburbs and 0,21 for

townships.

Ideal position for Figures 3 and 4

Area Elasticity

Data for the investigation of area or stand size elasticity were extracted from treasury

databases using the SWIFT (Sewer & Water Interface to Treasury) software package. Data

for more than 110 000 domestic users in Alberton, Boksburg, Centurion and Midrand were

included in the analysis.

To ensure that the data used in the analysis were of good quality, a number of filters were

used to exclude suspect data points. The first filter excluded users with a stand AADD below

0,1 kl/d and above 30 kl/d. The second filter excluded users with a stand size smaller than

200 m² and larger than 2 000 m². A final filter excluded stands with a value (using municipal

valuations) below 10 R/m² and above 150 R/m².

The data were grouped according to their municipal valuations. Four stand value categories

were used as shown in Table 2. The number of stands and average AADD for each category

are also given in the table.

Ideal position for Table 2

A strong link exists between stand size and outdoor consumption. Larger stands would

typically have larger gardens and thus require more water for outdoor use. Within the same

stand value category, it may reasonably be assumed that the effect of stand size on indoor

consumption is negligible, i.e. have elasticities of zero. To separate indoor and outdoor

consumption figures it was subsequently assumed that the smallest stands in suburbs and

townships have outdoor consumptions of 10 % and 0 % of their total consumption

respectively. Increases in consumption with increasing stand size were then assigned to

outdoor consumption. The 10-30 R/m2 value category was taken as representative of

townships and the 50-70 R/m2 value category as representative of suburbs.

A summary of the outdoor unit consumption elasticities calculated for the different stand

value categories is shown in Figure 5. To obtain the elasticities for total consumption, the unit

consumption elasticities should be increased by 1 (see Equation 12).

8

Ideal position for Figure 5

Pressure Elasticity

Pressure affects the flow rate through an opening in a pipe, and thus the leakage rate in a

water distribution system. The theoretical relationship between pressure and flow rate dictates

that the flow rate should be proportional to the square root of the pressure (hence a β

elasticity value of 0,5). However, experience in actual systems indicates much higher values

for β, possibly due to the fact that the cross-sectional areas of some types of leaks are not

fixed, but expand with increasing pressure. A default β value of 1 is often used for water loss

estimation where measured data are not available (McKenzie, 2001).

Pressure can be expected to have an effect on non-leakage consumption as well, especially

when the consumption is not measured in terms of volume (for example a bath or toilet

cistern), but in terms of time. Wasteful water consumption (such as taps being left open for

unnecessary long periods) was assumed to have the theoretical β value of 0,5. Since irrigation

consumption can be controlled by time or volume, the elasticity value will typically vary

between 0,5 and 0. Taking all these factors into account, the elasticity of household

consumption was assumed to vary between 0,15 and 0,25.

SENSITIVITY ANALYSIS

Typical elasticity values for the causative parameters water price, household income, stand

size and pressure were estimated based on the literature review and data analyses. Probable

minimum and maximum elasticity values were also estimated. These values are given in

Table 3.

Ideal position for Table 3

The numerical values of the elasticities in Table 3 indicate which variables will have the

greatest effect on water demand. Increasing the price of water will, for instance, have the

greatest long-term effect on outside use in townships. However, this does not necessarily

translate into the largest total saving of water, since townships typically only use a small

fraction of their consumption outdoors.

To get the full picture, it is necessary to consider how the consumption is distributed between

indoor and outdoor use and what fraction of the total use falls in the category under

consideration. For the purpose of the study, suburbs were assumed to use 50 % of their

consumption outdoors, and townships 20 %.

A sensitivity analysis was performed by plotting the consumption response to normal,

minimum and maximum values for each parameter as given in Table 3. Only one parameter

was changed at a time.

Price Elasticity

Formatted: Bullets and

Numbering

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Numbering

9

Both long and short-term price elasticity values were considered in the sensitivity analysis.

Short-term price elasticity reflects the immediate change in consumption behaviour of

consumers due to a change in the water price, while long-term price elasticity also includes

longer-term effects such as the introduction of water-saving fixtures in homes. Veck and Bill

(2000) noted that long-term price elasticities can be three times higher than short-term price

elasticities. In this study, long-term price elasticities were conservatively estimated to be

twice that of the corresponding short-term elasticities.

The projected short-term changes in consumption due to changes in the water price are shown

in Figures 6 and 7 for suburbs and townships respectively. The graphs show that a 50 %

increase in water price will result in consumption reducing by between 7 % and 15 % for

suburbs, and between 2 % and 25 % for townships in the short term. The larger variation in

the response of townships to price increases can be explained by considering two factors.

Firstly, people in townships are generally poorer and will thus be influenced more by water

price increases. On the other hand, many people in townships already use little water and will

not be able to reduce their consumption by much, even if the water price increases.

Ideal position for Figures 6 and 7

The results for townships are complicated by a further two factors, namely the problem of

non-payment and the new free basic water policy of government. It can be expected that users

not paying for water will also not adjust their consumption to changes in the price of water.

Price increases may, in some cases, have the opposite effect by increasing the rate of non-

payment as a form of protest against the price increase.

The projected long-term changes in consumption due to changes in the water price follow the

same pattern as that for short-term changes, but with larger effects on the final water

consumption. The long-term price elasticity curves are shown in Figures 8 and 9 for suburbs

and townships respectively. The graphs show that a 50 % increase in water price will result in

consumption reducing by between 13 % and 27 % for suburbs, and between 3 % and 44 %

for townships in the long-term.

Ideal position for Figures 8 and 9

An interesting result is that local authorities will not only reduce consumption by increasing

the price of water, but will also increase their income from water sales. In the suburbs

example above, for instance, the local authority will increase their income from water sales

by between 28 % and 40 % in the short term, and between 10 % and 30 % in the long term.

Income Elasticity

The estimated changes in consumption due to changes in household income are shown in

Figures 10 and 11 for suburbs and townships respectively. The graphs show that a 20 %

increase in real income will result in consumption increasing by between 4 % and 7 % for

suburbs, and between 2 % and 8 % for townships. The effect of income on water

consumption is clearly much smaller than that of price. A factor that should be taken into

consideration when interpreting the income elasticity graphs is that large changes in income

would probably result in people moving out of a given area to poorer or more affluent areas.

Changes in income to specific areas should thus be limited to what can realistically be

expected to occur within a given area.

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Numbering

10

Ideal position for Figures 10 and 11

Area Elasticity

The estimated changes in consumption due to changes in the stand size are shown in Figures

12 and 13 for suburbs and townships respectively. The graphs show that a 50 % reduction in

stand size (for example when stands are sub-divided) will result in per-stand consumption

decreasing by between 28 % and 40 % for suburbs, and about 12 % for townships. The sub-

division will have the effect of doubling the number of stands, thus resulting in a nett increase

in consumption by between 20 % and 44 % for suburbs, and by 76 % for townships.

Since it has been assumed that indoor consumption is not affected by stand size, the nett

effect of a change in stand size is a function of the outdoor elasticities (which are high for

both suburbs and townships) and the fraction of consumption that is used outdoors. In

townships this figure is generally low (20 % was assumed in the sensitivity analysis)

resulting in a relatively small reduction as a result of subdivision of stands. Densification in

townships, even if it is not by formal subdivision, will thus have a much greater effect on the

total water consumption than the same factor of densification in suburbs.

Ideal position for Figures 12 and 13

Pressure Elasticity

Pressure affects certain aspects of water demand in which time is generally used as a measure

instead of volume (for example irrigation). The pressure elasticities in this study were based

on the estimated effect on actual consumption and specifically exclude losses in the system.

As a result, the estimated pressure elasticity values are much lower than those normally used

in pressure management studies.

The estimated changes in consumption due to changes in pressure are shown in Figures 14

and 15 for suburbs and townships respectively. The graphs show that a 50 % reduction in

pressure will result in consumption decreasing by between 10 % and 16 % for suburbs, and

between 7 % and 13 % for townships. The effect of pressure reduction on demand is thus

expected to be small, although the main benefit of pressure control will be in the area of

leakage reduction.

Ideal position for Figures 14 and 15

CASE STUDY

The sensitivity analysis gives an indication of how much water demand would be affected by

changing a single parameter at a time. However, it does not provide information on the

cumulative effect of different parameters changing simultaneously. Modelling real life

scenarios requires the use of a software package, such as IWR-Main (Planning and

Management Consultants, 1999), to handle the complexities of the model.

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11

End-use software packages allow the user to model very detailed end-use behaviour. Typical

behaviour of individual components, such as toilets, baths and dishwashers, can be included

in the model, each with their own elasticity values. In this pilot study, demand was grouped

according to user category (suburbs and townships), type of demand (indoor and outdoor),

and losses. Losses were modelled as a separate user with a pressure elasticity value of 1,0.

This grouping is adequate to illustrate the mechanisms and capabilities of end-use modelling

without getting caught up in unnecessary detail.

The IWR-Main end-use model covers the residential areas of Alberton, Boksburg, Centurion

and Midrand. A general layout map of the areas is shown in Figure 16. The area considered

includes two township areas, namely Thokoza in Alberton and Vosloorus in Boksburg. The

GIS maps for the areas showed that the 10 – 30 R/m2 stand value category in Alberton falls

mainly in Thokoza. Similarly the 10 – 30 and 30 – 50 R/m2 categories in Boksburg falls

mainly in Vosloorus. These categories were subsequently modelled as township areas in the

IWR-Main model. The basic data used for suburbs and townships in the IWR-Main model is

given in Table 4.

Ideal position for Figure 16

Ideal position for Table 4

It was assumed that suburbs have 50 % of their consumption outdoors, and townships 20 %.

Losses were assumed to be 20 % of consumption for suburbs and 40 % for townships.

To show how end-use modelling can be employed to model future water demand, a

hypothetical scenario was compiled. The scenario consisted of the following:

• A projected real increase in household income of 1,5 % p.a. for both suburbs and

townships.

• A rate of densification of 0,5 % p.a. for suburbs and 2,0 % p.a. for townships.

• An immediate program to reduce the pressure in both suburbs and townships by 10 %

p.a. for three years.

• A planned increase in the water price of 10 % p.a. for suburbs and 5 % p.a. for

townships. The price increases will start in 2007 and will be implemented over a

period of five years.

The projected consumption of the study area was calculated for a design horizon of 10 years.

To obtain an envelope of minimum and maximum values, combinations of elasticities were

selected from Table 3 for the various parameters to either maximize or minimize the total

demand. For maximum demand, the minimum price, stand size and pressures elasticities, and

the maximum income elasticity value were used. Conversely, for minimum demand, the

maximum price, stand size and pressure elasticities, and the minimum income elasticity value

were used. The results of the simulation are shown in Figure 17.

Ideal position for Figure 17

The figure shows the cumulative effect of the various factors included in the scenario. A

number of these factors will increase demand, namely the increases in income and housing

density. Factors that will decrease the demand are decreases in system pressure, stand size

and increases in the water price. The reduction in system pressure takes place in the first three

12

years and is responsible for the initial reduction in demand. Most of this reduction is due to a

reduction in leakage.

The second reduction in demand is caused by the increases in water price from 2007 to 2011.

In years where none of the reducing factors were active (2006 and 2012), the demand shows

a steady increase. Both factors decreasing demand can only be implemented up to a certain

level, after which they will not be viable. Under the assumed conditions, demand would thus

continue to increase in the long term unless more permanent water demand measures can be

enforced.

The minimum and maximum water demand curves in Figure 17 are the theoretical envelope

based on the elasticities used in the sensitivity analysis. It is highly unlikely that all the

elasticities would vary from their normal values in such a way that one of these extreme

curves will occur in practice. The actual demand curve can realistically be expected to be

much closer to the expected value curve.

A potential source of modelling errors in the case study is possible interdependence between

modelling variables. A relationship may, for instance, exist between stand size and household

income. To apply the water demand model to a real life system with increased accuracy, it is

thus necessary to calibrate the model using measured data. Consequently, developing a water

demand model should not be seen as a once-off exercise, but as a continuous project

requiring frequent updating and refinement.

The case study shows how powerful end-use modelling can be in making predictions of water

demand. Various possible scenarios can be identified and modelled to identify the most

critical ones. Other factors can also be included in the model, such as:

• The implementation over time of plumbing codes to install water saving fittings in

houses.

• Including seasonal variations in demand to estimate minimum and maximum

demands during each modelling year.

• Various active and passive conservation scenarios.

• Emergency conservation.

• Cost-Benefit analyses of various programmes.

Finally, it is important to stress that modelling results are dependent on the quality of the

input data. It is thus imperative to understand the area being modelled and collect accurate

and representative data for modelling purposes.

CONCLUSIONS AND RECOMMENDATIONS

The aim of this study was to demonstrate the strengths and weaknesses of end-use modelling

as a water demand predictor for the Rand Water supply area. The study focussed on four

areas, namely Alberton, Boksburg, Centurion and Midrand. Data were collected from various

Rand Water consumer surveys and studies, local and international literature and from

treasury data basis via the SWIFT interface to treasury databases of the study area. A special

effort was also made to understand and explain the meaning and application of elasticity in

end-use modelling.

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The data were used to identify ranges of elasticity values for the modelling parameters

selected, which were water price, household income, stand size and pressure. The effect of

these elasticity values on water demand was illustrated in a sensitivity analysis, which

highlighted the following factors:

• Elasticities for indoor and outdoor use differ for various parameters. The nett effect of

changes in these parameters do not only depend on the elasticity values, but also on

the quantities of indoor and outdoor consumption.

• When designing water demand management measures, the total demand of a given

user group should be taken into consideration, and not only the effect that changes in

parameters will have on the demand. A large reduction in the use of a group with a

relatively small consumption will not reduce the total consumption by much.

• On a purely technical level, an increase in the price of water can be a good method for

reducing water consumption. Not only does it have a large effect on demand, with the

effect increasing in the long term, but the nett income of the local authority also

increases. However, price may not be a good water demand measure in townships

where price increases may increase the number of non-paying customers and where

the effect of non-payment and the new free basic water will impact on the actual

water savings made in a way that is difficult to estimate. There may also be significant

political pressures against increasing the price of water.

• Income has a significant effect on consumption, but may not affect the overall

consumption of a given area by much due to movement of people with increasing or

decreasing income out of the area.

• Increase in consumption due to densification of suburban areas is tempered by the

reduced consumption due to smaller stand sizes. However, since township areas

generally have only a small fraction of their consumption outdoors, densification in

townships can substantially increase the water demand of these areas.

• Pressure management has a small, but significant effect on consumption. However,

the main benefit of pressure management will remain as a measure to decrease water

losses due to leakage in the system.

• It is necessary to view a water demand model as a continuous project, with increased

accuracy gained over time through frequent updating and refining the model, and

using measured data to calibrate the model variables.

Although the sensitivity analysis was useful in highlighting certain important aspects of

individual model parameters, it cannot be used to estimate the combined effects of different

areas, user types and parameters. Software packages are typically employed for this purpose.

A case study with arbitrarily selected parameters was used to illustrate the way end-use

modelling can be used to predict future water demand. This technique can also be applied to

estimate the effect of different water conservation measures on demand and prepare plans for

use in very dry periods or other emergencies affecting the availability of water.

End-use modelling can be expanded to include various factors such as plumbing codes,

conservation measures, emergency conservation and cost-benefit analyses. As with all types

14

of modelling, the quality of the input data are of the highest importance to obtain accurate

results from the analyses.

The study showed that end-use modelling is a powerful tool for estimating future water

demand that can be of great benefit to a bulk water supplier like Rand Water for planning and

emergency preparedness purposes.

This pilot study was aimed at demonstrating the principles and potential application of end-

use modelling. A number of assumptions and simplifications were therefore made. To obtain

meaningful results from an end-use demand model, the following points should be

considered:

• Additional water use categories should be defined beyond “townships” and “suburbs”,

such as business districts, industries, parks, schools, flats, townhouses, etc. The water

use for each category needs to conceptualised to obtain an appropriate modelling

approach.

• The simple “indoor/outdoor” split may have to be extended to include pools, washing

machines, dishwashers, etc.

• With the extension of the model, there also comes the need for calibration of the

increasing number of model parameters. However daunting this may seem, this study

showed how a systematic analysis of the scant data available can render a fairly robust

set of model parameters, even for such notoriously whimsical parameters such as

income elasticity.

• The water demand of informal settlements is particularly troublesome from a

modelling perspective. A special effort will be required to reach consensus of how

non-payment and free water can be incorporated in a realistic model.

• It seems inevitable that even the best parameter estimates will be bounded by a

defined band of uncertainty. It was already pointed out that the upper and lower

estimates in the hypothetical case study presented are unrealistic – one would not

expect all four model parameters to be simultaneously low or high. As more

parameters are introduced, it will become necessary to apply a probabilistic technique

such as Monte Carlo Simulation to make more realistic estimates of area-wide water

consumption.

ACKNOWLEDGMENTS

The authors wish to record its appreciation towards Mr Hannes Buckle of Rand Water for his

management and encouragement of this project, and for Mr Alheit du Toit of Rand Water for

unconditionally sharing the unpublished results of previous consumer surveys. The

municipalities of Alberton, Boksburg, Centurion and Midrand are also thanked for allowing

their data to be used in this study.

REFERENCES

Formatted: Bullets and

Numbering

15

Billings RB and Agthe DE (1980) Price Elasticities for Water: a Case of Increasing Block

Rates, Land Economics 56(1).

Business Enterprises at University of Pretoria (2000) Rand Water: Elasticity Survey, Excel

Spreadsheets (unpublished).

Döckel JA (1973) The Influence of the Price of Water on Certain Water Demand Categories,

Agrikom 12(3)

How CW and Linaweaver FP (1967) The Impact of Price on Residential Water Demand and

its Relation to System Design and Price Structure, Water Resources Research 3(1)

McKenzie (2001) Presmac Pressure Management Program, WRC Report No TT 152/01,

Water Research Commission, Pretoria

MSSA (2001) Rand Water Household Survey: July 2001, Marketing Surveys & Statistical

Analysis (unpublished)

Planning and Management Consultants (1999) IWRMain Water Demand Suite – User’s

Manual and System Description, Planning and Management Consultants, Carbondale,

Illinois, USA

Veck GA and Bill MR (2000) Estimation of the Residential Price Elasticity of Demand for

Water by Means of a Contingent Valuation Approach, WRC Report No. 790/1/00, Water

Research Commission, Pretoria

Wong ST (1972) A Model on Municipal Water Demand: a Case Study from Northeastern

Illinois, Land Economics 48(1)

16

TABLES

Table 1 Summary of published of short-term price elasticities (adapted from Veck and Bill,

2000)

Price Elasticity Authors Year Location

Indoor Outdo or Total

Carver and Boland 1969 Washington, DC - - -0,1

Hanke and de Mare 1971 Malmo, Sweden - - -0,15

Döckel 1973 Gauteng, South Africa - - -0,69

Billings and Agthe 1974 Tucson, Arizona - - -0,18

Martin et al 1976 Tucson, Arizona - - -0,26

Gallagher et al 1972/3 &

1976/7

Toowoonba, Queensland - - -0,26

Thomas and Syme 1979 Perth, Australia -0,04 -0,31 -0,18

Boistard 1985 France - - -0,17

Alberton, South Africa -0,13 -0,47 -0,18

Thokoza, South Africa -0,14 -0,19 -0,14

Veck and Bill

2000

Alberton and Thokoza, South

Africa

-0,13 -0,38 -0,17

Alberton, South Africa -0,24 -0,39 -0,29 Rand Water study 2000

Thokoza, South Africa -0,67 -0,79 -0,69

17

Table 2 Distribution of stands used in the stand size elasticity analysis

Alberton Boksburg Centurion Midrand

Stand Value

Category

R/m² No of

stands

Ave AADD

l/m²

No of

stands

Ave

AADD

l/m²

No of

stands

Ave AADD

l/m²

No of

stands

Ave

AADD

l/m²

10-30 16168 1,76 8956 1,81 1706 0,95 2890 1,55

30-50 13219 1,33 20351 2,10 13090 1,23 7537 1,48

50-70 1245 1,23 10040 1,82 5964 1,67 2646 1,14

70-150 538 1,40 4584 1,36 1258 1,67 2967 1,69

Total 31170 43931 22018 16040

18

Table 3 Final elasticity parameters used in the sensitivity analysis

Note: Minimum and maximum values relate to the absolute of the elasticity values

Suburbs Townships Description

Inside Outside Inside Outside

Fraction of consumption 50 % 50 % 80 % 20 %

Min abs. -0,05 -0,30 -0,00 -0,20

Norm -0,20 -0,40 -0,30 -0,50

β price (short-term)

Max abs. -0,30 -0,50 -0,70 -0,80

Min abs. -0,10 -0,60 -0,00 -0,40

Norm -0,40 -0,80 -0,60 -1,00

β price (long-term)

Max abs. -0,60 -1,0 -1,40 -1,60

Min abs. 0,20 0,10

Norm 0,28 0,21

β income

Max abs. 0,35 0,40

Min abs. 0 1,2 0 1,2

Norm 0 1,6 0 1,28

β stand size

Max abs. 0 2,3 0 1,4

Min abs. 0,15 0,10

Norm 0,20 0,15

β pressure

Max abs. 0,25 0,20

19

Table 4 Basic data used in the IWR-Main model

Item Suburbs Townships Total

Number of stands 67 684 45 475 113 159

Total daily consumption (kl) 74 882 36 047 110 929

Daily consumption per stand (l) 1 106 793 -

Fraction of outdoor consumption assumed 50 % 20 % -

Fraction losses assumed 20 % 40 % -

Total daily losses (kl) 14 976 14 419 29 395

20

FIGURES

Figure 1 Elasticity values using the traditional approach (Equation 2). The elasticity value

(E) varies with water price. Data from Business Enterprises at University of Pretoria (2000)

0

20

40

60

80

100

120

50 100 150 200

Price (-)

Consumption (-)

-0.8

-0.7

-0.6

-0.5

-0.4

-0.3

-0.2

-0.1

0

50 100 150 200

Price (-)

Elast ici t

y

Deleted:

21

Figure 2 Elasticity value using the β approach (Equation 3). The slope of the curve (-0.295)

gives the value of β.

10

100

1000

10 100 1000

Price (-)

Consumption (-)

22

Figure 3 Income elasticities for suburbs

y = 1 .7 89 9x

0.2785

R

2

= 0.974

10.00

100.00

1000 10000 100000

Household I ncom e (R/mo nth)

Cons umption ( kl/m onth)

23

Figure 4 Income elasticities for townships

y = 3.7789x0.2099

R2 = 0.7412

10.00

100.00

100 1000 10000

Household I ncome (R/month)

Cons umption ( kl/month)

24

Figure 5 Summary of average outdoor elasticities based on unit consumption for different

stand value categories

y = 0.0265x

0.7671

R

2

= 0.7865

0.1

1

10 100 1000

Stand va lue (R/m

2

)

Elasticity

25

Figure 6 The short-term effect of changes in water price on consumption in suburbs

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Price

Consumption

Normal Min Max

26

Figure 7 The short-term effect of changes in water price on consumption in townships

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Price

Consumption

Normal Min Max

27

Figure 8 The long-term effect of changes in water price on consumption in suburbs

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Price

Consumption

Normal Min Max

28

Figure 9 The long-term effect of changes in water price on consumption in townships

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Price

Consumption

Normal Min Max

29

Figure 10 The effect of changes in income on consumption in suburbs

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Income

Consumption

Norma l Min Max

30

Figure 11 The effect of changes in income on consumption in townships

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Income

Consumption

Norma l Min Max

31

Figure 12 The effect of changes in stand size on per-stand consumption in suburbs

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Stand size

Consumption

Norma l Min Max

32

Figure 13 The effect of changes in stand size on per-stand consumption in townships

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Stand size

Consumption

Normal Mi n Max

33

Figure 14 The effect of changes in pressure on consumption in suburbs (excludes the effect

of pressure on losses)

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

P re ssu re

Consumption

Normal Mi n Max

34

Figure 15 The effect of changes in pressure on consumption in townships (excludes the effect

of pressure on losses)

50%

75%

100%

125%

150%

50% 75% 100% 125% 150% 175% 200%

Pressure

Consumption

Normal Min Max

35

Figure 16 Layout of the study area

36

Figure 17 The projected future water demand for the study area

100

105

110

115

120

125

130

135

140

145

150

2002 2004 2006 2008 2010 2012

Year

Demand (Ml/day)

Expected Minimum demand Maximum demand

37

Published as: Van Zyl, J.E., Haarhoff, J., Husselmann, M.L. (2003) Potential Application of

End-use Demand Modelling in South Africa, Journal of the South African Institute of Civil

Engineering, 45 (2).