uk; modelling the hydrological performance of rainwater harvesting systems - bradford university

A Whole Life Costing Approach for Rainwater Harvesting Systems Richard Roebuck PhD, Bradford University

Rainwater harvesting software from: www.SUDSolutions.com

67

3.0 Methods of Modelling the Hydrological Performance of

Rainwater Harvesting Systems

3.1 Introduction

The purpose of this chapter is to review the literature and identify existing

methods for assessing the performance of RWH systems at the single building

scale in terms of their water saving reliability. That is, methods that are used to

determine the volume of potable mains water that can be substituted by

harvested rainwater. Techniques for investigating other potential hydrological

benefits, such as a reduction in peak sewer flows, do exist (e.g. Vaes &

Berlamont, 2001; Shaaban & Appan, 2003; Hardy et al, 2004) but these are not

considered here. The concepts presented in this chapter, coupled with financial

information presented in chapter four, were used as the basis for a new

modelling tool with which to investigate the hydrological and financial

performance of contemporary RWH systems in the UK.

There are numerous methods available for predicting the performance of RWH

systems and these range from the relatively simple, such as „rule-of-thumb‟

approaches to the more complex, such as statistical methods and sophisticated

computer programs. Existing techniques vary in comprehensiveness. Some

explicitly consider only one or a small number of RWH system components,

such as the catchment area (rainfall/runoff characteristics) or the primary

storage tank, whilst others include the explicit assessment of a wider range of

components. Evaluation at different spatial scales is also possible. Some

methodologies are concerned only with RWH system performance at the level



68

of a single building whilst others seek to investigate the impacts of wider

implementation, such as at the development or catchment scale (e.g. Liu et al,

2005; Sakellari et al, 2005; Sekar & Randhir, 2006), often with the aid of

Geographical Information Systems (GIS), for instance Prakash & Abrol (2005);

Kahinda et al (2006). Some methodologies focus solely on hydrological

performance whilst others include additional elements such as

economic/financial measures (e.g. Coombes et al, 2002, 2003b; Liaw & Tsai,

2004; Ghisi & Oliveira, 2007) and in some instances an assessment of system

„sustainability‟, for example see Parkinson et al (2001); Vleuten-Balkema

(2003); Anderson (2005); Sakellari et al (2005).

The use of computer software for modelling the hydraulic behaviour of both

traditional (piped) urban drainage systems and SUDS is now common practice

amongst drainage engineers and researchers (e.g. Swan et al, 2001; Kellagher

et al, 2003; Millerick, 2005a). Computer based methods offer a number of

advantages over manual calculations, such as much greater speed and

flexibility, sophisticated data handling capabilities, simulation of specific designs

under a wide range of circumstances, optimisation, assessment of associated

risk and identification of potential failure routes. Many RWH system models are

also computer based and the majority of the existing research reviewed made

reference to the use of software-based techniques. Given the advantages of

this approach, coupled with the ready availability of computing power and

suitable applications (e.g. spreadsheets), it would have made little sense to

employ manual calculation methods and therefore the model developed as part

of the thesis was also computer (spreadsheet) based. Given the wide-spread



69

use of computer orientated approaches, any future reference in this thesis to

RWH „models‟ should be assumed to refer to those that are either wholly or

largely software based. For any that use a different approach, for example

manual calculations, this fact will be stated explicitly in order to clarify the format

that was used.

3.2 Modelling concepts

Wainwright & Mulligan (2004) state that models can be classified hierarchically,

with mathematical and physical (or hardware) models located at the top.

Physical models are scaled down versions of real-world situations and are used

where mathematical variants would be too complex, too uncertain or not

possible due to a lack of knowledge. Examples are given as including laboratory

channel flumes, wind tunnels and the Eden project in the UK. Mathematical

models are abstractions of actual systems and are created by using the formal

language of mathematics to describe their behaviour. They are much more

common than the physical variants and can be further sub-divided into three

broad categories:

1. Empirical models describe the behaviour of a system on the basis of

observation alone and provide no information regarding the physical laws

that dictate the processes occurring within a system. They have high

predictive power but do not provide a great deal of information regarding

how a system works. Therefore they are usually specific to the conditions

under which data were collected and the results cannot easily be

generalised to other circumstances. Examples of empirical models

include those that use coefficients in order to adjust values so that they



70

better represent those observed in nature and regression analysis which

fits a mathematical function to the observed relationship between

variables.

2. Conceptual models are similar to empirical ones in that they describe the

observed relationship between variables and not the underlying

processes. They also include preconceived notions of how a system

functions, for example a hydrological model may be divided into separate

components such as rainfall, runoff, river flow and subsurface flow. Each

of the individual components would still be empirically based but the

technique provides a greater depth of understanding. As with the purely

empirical approach the results obtained from one location cannot easily

be transferred to others.

3. Physically based models are derived deductively from established

physical principles and results should be consistent with observations.

However, predicted system behaviour often diverges from that seen in

practice. Because of this these models tend to require calibration against

observations, for example by using empirical coefficients. This is often

the case when there are gaps in knowledge regarding the fundamental

processes that drive a system. They have good explanatory depth (i.e.

why does this particular result occur?) but low predictive power. It is often

the case that a model does not fall exclusively into one particular

category. There is a continuum of models which include elements of all

three of the sub-categories defined here. Providing that a high degree of

calibration is not required then physically based models can offer a



71

higher degree of generalisation than the empirical and conceptual

varieties.

Further subdivision is possible according to the mathematic techniques

employed. For example there are deterministic models which have a fixed

output for a specific input. That is, for a given input x the corresponding output y

will always be the same (Skidmore, 2002). The alternative to this is a stochastic

approach in which a given set of inputs can produce different outputs according

to some random process (Wainwright & Mulligan, 2004). Another important

distinction is how a model manages the passage of time. Static models exclude

time altogether whereas dynamic models include it explicitly. Time can be

considered as either passing continuously, and therefore represented using

differential equations, or in discrete packets such as one hour or one day. In the

latter case the system can be represented by using difference equations. There

are also hybrid systems which contain both continuous and discrete

components (Dabney & Harman, 2001).

A flow diagram is presented in figure 3.1 that shows the steps involved in the

creation of a simulation model (after James, 1984). Concerning model

accuracy, an important point to remember is that it is unrealistic to expect that

they will ever represent reality with complete fidelity. Thomas (2002a) states

that it is only possible to roughly predict the performance of a RWH system

because many of the factors upon which predictions are based, such as future

water demand and climate, are uncertain and hard to forecast accurately.

However, it has been noted that “all models are wrong, but some are useful”



72

(Box, 1984) and so the fact that a given model cannot mimic the real world with

complete accuracy does not mean that it cannot be useful as a predictive tool.

Further, although field studies have the advantages of realism and tangibility,

the investment in terms of time and money can be significant (Wainwright &

Mulligan, 2004). Models offer an alternative that is flexible and that do not

involve an excessive investment of resources (Dixon, 1999).

If the steps described in figure 3.1 are followed then the resulting simulation

model should tend towards the useful (Dixon, 1999). This chapter covers the

first two stages in detail: „problem definition‟ and „review of theoretical

background‟. Step three, „formulation of equations‟, is covered in somewhat less

detail by presenting key equations that are commonly used with existing and

accepted modelling approaches.

Figure 3.1 Diagrammatic representation of model development

After James (1984).

Problem definition

Review of theoretical

background

Formulation of equations

Creation of model

structure

Formulation of methods for solving

Formulation of

computational methods

Validation of model

Analysis of sensitivity

Iterative improvement



73

3.2.1 Problem definition

It was proposed, as part of this research project, to investigate existing

modelling methods applicable to contemporary RWH systems in the UK.

Particular attention was given to methods for modelling both the hydrological

and financial performance of these systems. Techniques suitable for use in this

thesis required identification. Key questions that required answers included:

What are the existing methods for assessing the hydrological aspects of

contemporary RWH systems at the single building scale?

What are the existing methods for assessing the financial aspects of

contemporary RWH systems at the single building scale?

Which of these methodologies is the most suitable for meeting the

objectives of this research project?

If the existing methods cannot satisfactorily meet these objectives, how is

this problem to be overcome? Can new methods be created or

transposed from another research area or discipline?

This chapter is primarily concerned with addressing the first question. That is,

the identification of existing methodologies for assessing the hydrological

performance of contemporary RWH systems in the UK. This consisted mainly of

reviewing the theoretical background and so the formulation of equations (stage

three in figure 3.1) was kept to a minimum at this juncture. See chapter four for

a review of the financial modelling aspects. Chapter five provides details of the

underlying equations and algorithms used in the thesis model.



74

3.3 General modelling considerations

Numerous methods exist for predicting the hydrological performance of RWH

systems. But what is meant by „performance‟ and what is it that we are trying to

measure and why? The literature refers to the use of various performance

indicators. Those that are applicable here include predictions of system

reliability and efficiency. The reliability of a rainwater store can be expressed

using either a time or volumetric basis (Fewkes & Butler, 1999). Reliability is

defined by Liaw & Tsai (2004) as either the total volume of harvested water

supplied divided by the total water demand (volumetric reliability, essentially the

portion of demand that is met) or the fraction of time that demand is fully met.

Thomas (2002a) also defines the volumetric reliability but labels it as the

satisfaction and adds the indicator of efficiency, defined as the fraction of runoff

from the contributing catchment that is utilised. Fewkes and Warm (2000)

describe the performance of a RWH system by its water saving efficiency as

shown in equation 3.1. This is the same as the volumetric reliability, as

previously discussed. However it is defined, a reliability of 100% indicates

complete security of supply provision (Fewkes & Butler, 1999).

100

1

1

T

tt

T

t

t

T

D

Y

E (3.1)

where:

ET = water saving efficiency (%)

Yt = yield from system in time t (m3)

Dt = demand from system in time t (m3)

T = total time under consideration



75

One limitation of the time reliability indicator is that it can give seemingly poor

results even for systems that meet a high percentage of demand. For example,

a system that is able to consistently supply 99% of the required water would

nevertheless have a time reliability of zero since it would always fail to meet all

of the demand. It also makes it difficult to distinguish between systems that

perform badly and those that perform well. Liaw & Tsai (2004) advise against

the use of time reliability as a performance indicator for domestic systems

precisely for this reason. Instead they recommend the use of the volumetric

reliability indicator.

Measuring performance using time reliability may be the rational choice for

critical systems that provide the only source of drinking water, such as those in

developing countries and rural areas of the developed world. However, for

urban systems supplying water for non-potable uses, and that almost always

have a mains top-up function, the volumetric reliability provides a more useful

measure of system performance. Therefore, unless otherwise stated,

hydrological performance relates to the volumetric reliability of a RWH system.

3.3.1 Why model RWH systems?

Mathematical models can be useful because they may be the only realistic

means of representing our understanding of the complex behaviour of a given

system (Jakeman et al, 1993). Wainwright & Mulligan (2004) provide a general

overview of the purpose of modelling from an environmental systems

perspective. They outline a total of seven purposes to which models are usually

put: research aids, tools for understanding, tools for simulation and prediction,



76

as virtual laboratories, as integrators within and between disciplines, as a

research product and as a means of communicating science and the results of

science. The primary aims of this thesis were to create a computer model of a

contemporary RWH system, and to simulate the behaviour under a range of

conditions so that system performance (both hydrological and financial) could

be predicted. The purpose of the model can therefore be considered to fall

within the „tools for simulation and prediction‟ category.

When assessing a RWH system there is a number of issues that require

consideration. For instance the associated costs and benefits, and whether the

objectives of the system could not be better met by investing in an alternative

option. Depending on the purpose of the system, questions regarding

performance could include:

What percentage of existing water demand is likely to be met by

harvested rainwater?

What is the unit cost of water supplied from the system and how does

this compare with the cost of other water conservation measures?

How long will the system take to pay for itself?

What will the ultimate return on investment be?

What are the associated risks? For example, what if the level of rainfall is

less than expected?

System behaviour depends upon a number of interrelated processes, some of

which are largely anthropogenic in origin (e.g. catchment characteristics, water

demand, system costs) and some of which are largely due to natural processes,



77

such as precipitation patterns. How well or how badly a RWH system performs

depends upon the interaction of these processes and the way that this will

proceed is not always obvious if one simply considers the constituent parts in

isolation. Modelling provides a way to enhance our understanding of how a set

of interrelated components behave as a unit (Chapra, 1997), thus facilitating a

higher level of learning about that unit than may have occurred from a simpler

reductionist-based investigation (Dixon, 1999).

3.3.2 Data requirements

Thomas (2002a) lists the minimum data requirements for RWH performance

models. These are given as:

Roof area and runoff coefficient.

Average daily water demand.

A historic rainfall record long enough to act as a reliable guide to future

precipitation patterns.

Proposed tank size.

Some assessment methods utilise more data than listed above. Fewkes (1997)

accounts for rainfall losses due to depression storage (water retained in small

depressions in the catchment surface) as well as using a catchment runoff

coefficient, Leggett et al (2001b) present a method which includes filter losses,

and Liaw & Tsai (2004) consider a number of financial performance indicators.

Conversely, some methods utilise less data such as many of the commonly

used „rule-of-thumb‟ approaches. Despite some differences, all of the

assessment methods investigated included at least three basic elements:



78

rainfall, catchment area and water demand. It is assumed that these parameters

represent the minimum data required to perform an objective, albeit basic,

assessment.

3.4 RWH system components: modelling considerations

Modern RWH systems consist of a variety of components which are integrated

in such a way as to provide a functional system, as discussed in chapter two. In

order to predict how a given system will perform it is necessary to consider at

least some of these components and to determine a suitable method for

simulating their behaviour. Clearly it is not feasible to construct a model that

includes every minor detail, nor is it realistic to expect that those elements that

are included will be modelled with complete accuracy. A more rational approach

is to limit the range of elements to those that represent the key components in

terms of their effect on the hydrological and financial performance. Then select

ways of modelling the behaviour of these in a way that gives reasonably

accurate and reliable results.

Wainwright & Mulligan (2004) state that the optimal model is one that contains

sufficient complexity to explain the observed behaviour, but no more. A set of

selection criteria were therefore required in order to determine which

components to include and which to exclude. Further, for those components

which were included it was necessary to determine which characteristics to

reproduce and to select a suitable method for modelling them.



79

For the hydrological model, the following selection criteria were used in order to

determine which elements required explicit consideration. For a component to

be included within the hydrological model, it was required to:

1. Directly affect the volume of harvested water or potable mains water

within, or to and from, the system, and/or:

2. Have a cost component dependent on a variable or variables other than

time alone1, and also:

3. Have a large enough effect on the hydrological and/or financial

performance to be worthwhile taking into account.

Following on from the information presented in chapter two and using the

selection rules outlined above, figure 3.2 presents those components selected

for explicit inclusion within the thesis model. The components consist of rainfall,

catchment surface, first-flush diverter, coarse filter, pump, potable (mains) water

supply and sewerage system (volumes to and from), storage tank and non-

potable supply and demand.

1The criteria „other than time alone‟ was added in relation to costs because

some components have associated expenditures that depend only on time and

do not affect the hydrological performance. For example, a system with a UV

unit will require replacement of the UV bulb at regular intervals. Clearly this will

have a cost but will not affect the water saving reliability in any noticeable way

and hence does not require inclusion in the hydrological model. Rather, it would

be taken into account by the financial model, which is discussed in the next

chapter.



80

Figure 3.2 RWH system components explicitly included within the

thesis model

3.5 Modelling system components: review of theoretical background

Sections 3.6-3.12 consider each of the RWH components shown above and

describe how they can be represented within a conceptual RWH system

hydrological model.

3.6 Rainfall

Rainfall varies with location, season and year. Its spatial variability is strongly

influenced by local topology and factors such as distance from coast (Thomas,

2002a). Annual rainfall depths in the UK vary from between 550mm and

3,000mm, with the bulk of the population living in areas that receive just 600-

Coarse filter

Storage tank

Pump

Non-potable supply & demand

Overflow

First flush diverter

Catchment surface

Potable (mains) water supply

Water meter

Key

Usable water

Discarded water

Volume of grey/black

water to foul sewer system

Mains top-up

Rainfall



81

800mm (Hassell, 2005). The south and south-east receive comparatively lower

rainfall than most other areas of the country whilst the north receives

comparatively more (Millerick, 2005b). Given that rainfall is a key factor in the

performance of RWH systems, in order for the thesis model to be functional, a

suitable method had to be found with which to represent the actual rainfall

profile in the region of interest (West Yorkshire). Existing methods for

incorporating rainfall data into the analysis can be placed into two broad

categories: historic and stochastic. The historic category consists of empirical

rainfall data series obtained from weather monitoring stations whilst the

stochastic category consists of rainfall data generated using some technique

that has a random/probabilistic element.

3.6.1 Historic rainfall data

One commonly applied technique is the use of historic time series rainfall. That

is, a continuous data set that has been gathered by recording the depth of rain

falling at a given location within a specified time frame. The data is presented in

the form of depth per unit time, for example mm/hour or mm/day. This would

then be collated, edited so as to be in a suitable format and then used directly in

a RWH model without the generation of any new information. This approach

has been used by a number of researchers such as Dixon (1999), Fewkes

(1999a), Rahman & Yusaf (2000), Dominguez et al (2001), Liaw & Tsia (2004),

Ghisi et al (2006, 2007), amongst others.

In the UK, rainfall data of this type is often available from a variety of sources

such as the Met. Office, British Atmospheric Data Centre (BADC), universities



82

and research institutions. The collection of short-duration rainfall data (in the

region of 1-5 minutes) is rare compared to the collection of data at an hourly or

daily timescale (Kellagher, 2005).

3.6.2 Stochastic rainfall data

Synthetic rainfall data series can be generated from a statistical analysis of

historic rainfall records. Various researchers have generated synthetic rainfall

data sets for use with RWH models. Fewkes & Ferris (1982) used a Monte

Carlo simulation technique to generate daily rainfall profiles for the Nottingham

area of the UK. The resulting rainfall data was used in conjunction with a mass-

balance model in order to investigate the performance of a RWH system

supplying water to a WC. In Australia, Coombes (2002) used the stochastically-

based Disaggregated Rectangular Intensity Pulse (DRIP) rainfall event model of

Heneker et al (2001) as part of a computer based allotment water balance

model to predict the performance of domestic systems.

Stochastic methods are useful for generating synthetic rainfall time series for

areas that have no historic data or where such data is limited, for example to a

few years or less, when a longer time series is required (Kellagher, 2005).

Calibration and validation against observed data is required in order to have

confidence in the accuracy of synthetic rainfall profiles generated for a given

location (Lanza et al, 2001). However, this will not be possible if directly

measured historic rainfall data is not available in the first place. There are a

number of stochastic rainfall generation programs available for the UK, for



83

example RainSim from the University of Newcastle Upon Tyne and both

TSRsim and StormPAC from HR Wallingford Ltd (Kellagher, 2005).

3.6.3 Criteria for assessing suitability of historic rainfall data

If a historic rainfall time series is to be used then three questions need to be

asked:

1. what is a suitable timestep?

2. what is a suitable length of rainfall record?

3. how close does the RWH system need to be to the location of rain depth

measurement?

The first of these questions has implications beyond the selection of an

appropriate rainfall data set and is discussed in more detail in section 3.14. With

regards to the second and third questions, there are a number of sources of

advice and these are summarised in table 3.1. The length of rainfall record is

important since the data set needs to reflect local climatic variations if it is to

more accurately predict system performance. If a short data set were to be used

then there would be a greater risk that the information collected would not

reflect typical conditions. For example, if data were collected during a period of

abnormally low rainfall then this could potentially lead to an underestimation of

average system performance (e.g. see MJA, 2007). The distance of the RWH

system from the location that the rainfall depth was measured is also important

since precipitation conditions often vary geographically and rainfall patterns can

differ even over short distances (Gould & Nissen-Peterson, 1999).



84

Table 3.1 Summary of advice for selecting historic rainfall data

Reference

Recommended/min. record length

Max. distance from RWH system

Environment Agency, 2003b

- Within 10 miles

Heggen, 2000 “A rainwater catchment system can often be reasonably assessed from five years of data”

-

Konig, 2001 10 years of daily rainfall data Obtain data from nearest location

Mitchell, 2007 10 years gives satisfactory results Schiller & Latham, 1982

At least 10 years of data preferable -

Gould & Nissen-Peterson, 1999

At least 10 years of accurate local data. 20-30 years preferable (especially for drought-prone areas)

Closest location that has similar climate and topography

Liaw & Tsai, 2004

Minimum of 50 years data -

Thomas, 2004 For large RWH systems in arid areas that constitute critical water supplies, use long data sequences (say 25 years). Low-security systems can be usefully modelled with 5-10 years worth off rainfall data

-

Table 3.1 demonstrates that there is no definitive guidance concerning suitable

spatial and temporal scales for historic rainfall data when assessing RWH

systems. However, the information presented would suggest that a minimum of

ten years worth of rainfall records ought to be used. These should be obtained

from a weather station subject to a similar climate, and that is located close to,

the site under investigation.

It needs to be noted that historic rainfall data cannot in itself account for the

potential effects of climate change. Whenever possible it would be prudent to

adjust the data in line with expected changes in order to provide a more realistic

representation of future precipitation patterns.



85

3.7 Catchment surface (rainfall/runoff characteristics)

Runoff can be harvested from a number of different surface types including

pavements, roads and car parks but in urban areas the majority of rainwater

catchment surfaces tend to be restricted to roofs (see chapter two). Therefore,

the discussion here is limited to the rainfall/runoff characteristics of roofs only.

Unless otherwise stated the use of the word „catchment‟ should be taken to

mean „roof‟.

Not all of the rain falling on a roof will flow from the surface. Surface wetting,

ponding in depressions, absorption, evaporation and the type of surface

material all influence the level of actual runoff (Wilson, 1990; Gould & Nissen-

Peterson, 1999; Leggett et al, 2001b; Butler & Davies, 2004). Water that flows

from the roof and can be collected is termed the „effective runoff‟ whilst water

that cannot be collected is termed the „runoff losses‟. Various methods exist for

estimating the volume of water which is translated into effective runoff. In

practice the most commonly applied are the dimensionless runoff coefficient

and the initial losses (the latter is also sometimes referred to as the depression

storage). Empirical modelling work conducted by Fewkes (1999a) found that the

consideration of rainfall losses was necessary in order for system behaviour to

be accurately reproduced. Models that used runoff coefficients or runoff

coefficients and initial losses were both found to give acceptable results.

Other techniques have been used to estimate the volume of runoff, such as the

Kinematic Wave Equation (Heggen, 1995; Giakoumakis & Tsakiris, 2001) and

the Dynamic Equations (Boers & Ben-Asher, 1982). However, the use of these



86

appears to be limited to a small number of academic studies with no empirical

verification of their accuracy with regards to modelling RWH systems. For this

reason they were not considered for the thesis model and are not discussed

further.

3.7.1 Runoff coefficients

The runoff coefficient is the ratio of the volume of water that runs off a surface

compared to the total volume of rain falling on it (Gould & Nissen-Peterson,

1999). Fewkes (2006) defines it as representing the proportion of rainwater

collected from an actual roof compared with an idealised roof from which no

losses occur. In order to calculate the coefficient, data is gathered for several

months or years and can include a large number of storm events. The runoff

coefficient value for each storm event are then combined to give an average

value. For example, see Zhu & Liu (1998) and Fewkes (1999a). The

dimensionless runoff coefficient, CR, can be expressed as shown in equation 3.2

(Gould & Nissen-Peterson, 1999).

t

tCR

in rainfall of Volume

in runoff of Volume (3.2)

where t is the time period over which the measurements are made. The volume

of rain falling on a catchment surface in time period t is given by multiplying the

depth of rainfall in time t by the effective catchment area, which is commonly

calculated by multiplying the horizontal length of the catchment by the horizontal

width (Environment Agency, 2003b) as shown in figure 3.3. This yields the plan



87

area, not the actual surface area, and this method assumes that the rainfall falls

vertically onto the roof surface.

Figure 3.3 Calculating the plan area of a catchment

Adapted from Environment Agency (2003b), p7.

Once the effective area of the catchment has been calculated and a suitable

runoff coefficient determined, the volume of runoff occurring in time period t can

be calculated using equation 3.3.

Rtt CARER (3.3)

where:

ERt = effective runoff in time t (m3)

Rt = rainfall depth in time t (m)

A = effective catchment area (m2)

CR = catchment runoff coefficient

Catchment area, A = L x W

Building

L

W



88

Other factors which may occasionally reduce the collection efficiency of roof

catchments are when precipitation occurs as snow or hail or is affected by very

strong winds (Gould & Nissen-Peterson, 1999), although studies by both

Fewkes (1999a) and Schemenauer & Cereceda (1993) found only a weak

correlation between the level of runoff and wind speed and direction.

Runoff coefficients have the advantage that they are easy to apply, simply

requiring that the volume of rain falling on a catchment in a specified time period

be multiplied by the runoff coefficient to yield the effective runoff volume.

Numerous researchers have used coefficients when estimating the volume of

effective runoff, such as Fewkes (1995, 1999a), Zhu & Liu (1998), Liaw & Tsai

(2004), Lau et al (2005) and Ghisi et al (2006), amongst others. The type of

material that a surface is constructed from, as well as the pitch, has been found

to strongly influence the resulting runoff coefficient (see table 3.2). Building

roofs are generally designed to shed rainwater as quickly as possible, for

instance by constructing sloped surfaces made from smooth materials such as

tiles or slate, and so most have a relatively high runoff coefficient.



89

Table 3.2 Examples of runoff coefficients for various roof types

Range of coefficients

Reference Surface Type High Average Low

BS EN 752-4 (1998) Steeply sloping roofs 1.00 0.90 Large flat roofs (>10,000m2) 0.50 Small flat roofs (<100m2) 1.00

DEHAA (1999) Pitched roof, domestic dwelling 0.90 Dharmabalan (1989) Roof tiles 0.90 0.80

Corrugated sheets 0.90 0.70 Plastic sheets 0.80 0.70 Thatched roof 0.60 0.50

Environment Agency (2003)

Pitched roof tiles 0.90 0.75 Flat roof, smooth tiles 0.50 Flat roof with gravel layer 0.50 0.40

Fewkes & Warm (2000)

Pitched roof, tiles or slates 0.75 1.00 Flat roof, impervious membrane 0.00 0.50 Green roof, flat 0.00 0.50

Herrmann & Hasse (1997)

Domestic roof 0.84

Leggett et al (2001b) Pitched roof tiles 0.90 0.75 Flat roof, smooth surface 0.50 Flat roof with gravel layer or thin turf (<150mm)

0.50 - 0.40

Liaw & Tsai (2004) Iron and cement roofs 0.82 Martin (1980) Pitched roof, domestic dwelling 0.85 0.80 Rahman & Yusaf (2000)

Corrugated sheets 0.80

Woods-Ballard et al (2007)

Pitched roof tiles 0.80 Flat roof 0.50 Flat roof, gravel 0.40 Extensive green roof 0.30 Intensive green roof 0.20

Yusuf (1999) Corrugated sheets 0.85 0.75

Note: coefficient of 0 = 0% runoff, coefficient of 1 = 100% runoff

3.7.2 Initial losses

Rainfall losses occurring due to depression storage, absorption and wind effects

can be accounted for by defining a minimum depth of rainfall below which no

runoff is assumed to occur (Fewkes, 1999a). For depths greater than this

threshold runoff is produced, but the threshold value is subtracted from the total

rainfall depth occurring during the time period in question. The type of material

that a roof surface is constructed from has been found to influence the

corresponding initial loss value, as shown in table 3.3.



90

Table 3.3 Examples of initial loss values for various roof types

Reference

Surface type

Initial losses (mm)

Fewkes, 1999a Pitched roof, concrete tiles 0.25 Pratt & Parker, 1987

Bungalow roofs, combination of pitched and flat surfaces

0.32

Li et al, 2004 Asphalt-fibreglass 0.10 Plastic film 0.20 Gravel covered plastic film 0.90

Mitchell, 2007 Typical urban roof catchment, Australia (assumed value)

1.00

MJA, 2007 Typical domestic roof (Australia) 0.50 NSWG, 2006 Domestic roof (Australia) 0.50-1.00

3.7.3 Roof areas for new-build residential houses

In order to conduct simulations of domestic RWH systems installed in new-build

houses it was necessary to obtain a range of realistic roof (plan) areas as a

function of household occupancy. This was because the level of occupancy has

been found to strongly influence the total water demand within a dwelling

(Butler, 1991; Butler & Memon, 2007; Jeffrey & Gearey, 2007). Other

researchers have used roof areas based on a limited number of empirical

modelling studies (e.g. Fewkes, 1997; Coombes et al, 2000a) or have used

figures derived from existing residential buildings, e.g. Liaw & Tsai (2004); Ghisi

et al (2006); Mitchell (2007); MJA (2007). There appears to have been no

studies that have included an attempt to derive probable roof areas for new

housing in the UK and it cannot be assumed that values for established housing

stock will be applicable to more recent dwellings. A methodology was devised

which produced a set of feasible roof areas as a function of household

occupancy for dwellings with 1-5 people. The methodology is described in detail

in appendix one. The main results are shown below in table 3.4. The average

figures presented here were used in the simulations of domestic RWH systems

conducted as part of the thesis research.



91

Table 3.4 Generated data for occupancy rate versus roof area

Occupancy

Average roof area (m2)

1 57 2 76 3 69 4 76 5 72

3.8 First flush diverters

Mitchell et al (1997) and also Cunliffe (1998) describe the first flush as a fixed

amount of roof runoff requiring separation. The recommended volume is often

given as a set figure for a given building type or a variable figure based on the

catchment area. For example, for domestic dwellings remove the first 20-25

litres of effective runoff, for commercial/industrial buildings remove the first 2mm

of rain falling on the roof surface. However, there is no universally agreed

volume of that should be captured. For small roofs Yaziz et al (1989)

recommend diverting the first 5 litres of runoff. For an „average‟ Australian

domestic roof Cunliffe (1998) states that 20-25 litres should be captured from

the initial flow. Coombes (2002) describes the development of 27 residential

units in Australia that were fitted with first flush devices designed to divert the

first 2mm of roof runoff away from the storage tank. However, it was also stated

that this was a conservative figure and was chosen due to concerns over the

possibility of industrial atmospheric fallout being washed from roofs, and to gain

planning permission for the development from the local authority. The modelling

and design of first-flush devices has been dominated by these types of

approaches (Coombes, 2002).



92

Only one relevant academic paper was located that discussed the use of a first-

flush device in a UK setting (Fewkes, 1989). This was in conjunction with a

proprietary system now almost two decades old and it does not appear to be a

feature which has been retained in this particular country. For this reason the

simple methodology described in Mitchell et al (1997) and Cunliffe (1998) was

used in the thesis model.

3.9 Coarse filters

Some types of filter are rarely if ever included in models of RWH systems.

Filters belonging to this category include screen, floating, cartridge, sand,

gravity, carbon and membrane (see chapter two). These require occasional

maintenance (i.e. cleaning or replacement) but this would be taken into account

as a financial item and therefore they are not considered further in terms of

hydrological modelling.

Crossflow filters are a common component in modern systems and these do

affect the volume of water entering the storage tank. They contain mesh

screens which water flows across and separates the flow into two fractions. The

portion that passes through the mesh is cleaned of all debris larger than the

mesh size (typically 0.2-1.0mm) and enters the storage tank. The residual

debris is washed from the mesh by the remaining fraction of water and diverted

away from the tank, typically to the sewer system or an infiltration device. The

filters are considered to be self-cleansing since debris is automatically washed

from the mesh screen but occasional manual cleaning is often recommended

(Shaffer et al, 2004).



93

The efficiency of crossflow filters is defined as the percentage of water filtered

and sent to the tank compared to the total amount of water entering the device.

A single average figure is usually given, with modern units achieving an

average efficiency of about 90% (Konig, 2001; Leggett et al, 2001b). Literature

provided by manufacturers would indicate that most modern varieties operate in

the 80-90% efficiency range, e.g. WISY vortex models. This is an approximation

however and the actual performance efficiency varies with the flow rate of the

incoming water, with higher flow rates leading to lower efficiencies. Figure 3.4

shows a graph of flow rate versus efficiency for a range of crossflow filters,

based on data supplied by the manufacturers (Herrmann & Schmida, 1999).



94

Figure 3.4 Crossflow filter efficiency versus incoming flow rate

Adapted from Herrmann & Schmida (1999).

0

20

40

60

80

100

0.0 0.5 1.0 1.5 2.0

Flow rate (litres/sec)

Fil

ter

eff

icie

ncy (

%).

A common method of modelling the performance of crossflow filters is to

multiply the volume of water entering the filter in a given time period by the

average filter efficiency, often called the filter coefficient, as shown by equation

3.4. This splits the flow into two components, the filtered component (routed into

the storage tank) and the unfiltered component (diverted away from the tank).

Ftt CEFF (3.4)

where:

Ft = course filter pass forward flow to the storage tank in time t (m3)

EFt = effective flow entering the coarse filter in time t (either directly from the catchment surface or via a first flush device, if present) (m3)

CF = coarse filter coefficient

Table 3.5 shows a range of typical crossflow filter coefficients and demonstrates

that a figure of 0.9 (i.e. 90% efficiency) is a commonly assumed value.

Key = filter 1 = filter 2 = filter 3 = filter 4



95

Table 3.5 Typical crossflow filter coefficients

Reference Comments Coefficient

Leggett et al (2001b) CIRIA best practice guidance. Figure refers to self-cleansing mesh filters

0.90

Environment Agency (2003b) Recommended value from "most" manufacturers

0.90

Various UK RWH system suppliers (via email & telephone contact)

All suppliers contacted quoted the same value

0.90

Konig (2001) Modern German-made filters 0.90 Gould & Nissen-Peterson (1999) Refers to downpipe and vortex type

crossflow filters 0.90

3.10 Pumps

Hydraulically a pump can be modelled in a simple fashion by considering the

amount of water that requires pumping per unit time and the rate at which it is

able to pump that water. Pump performance data is typically given by

manufacturers in the form a head versus discharge relationship for a pump of a

given type and power rating (see table 3.6 and figure 3.5). This can be used to

calculate the required operating period and from this the energy usage of the

pump can be determined, as demonstrated in equation 3.5.

PuEnt = PuPOW x PuTIME (3.5)

where

PuEnt = pump energy usage in time t (kWhrs)

PuPOW = pump power rating (kW)

PuTIME = pump operating period in time t (hrs)

From this the operating cost per unit time can be calculated by simply

multiplying PuEnt by the unit cost of electricity, which will depend on the amount

charged by the relevant energy utility.



96

Table 3.6 Typical domestic RWH pump performance data

(Adapted from information courtesy of Rainharvesting Ltd).

Pump

ID

Power Rating (kW)

Pumping output in:

l/min 20 30 40 60 80

cu.m/hr 1.4 1.8 2.4 3.6 4.8

40/06 0.80 With

pumping height of

(m)

32.5 30.0 27.0 19.5 10.0 40/08 1.00 43.3 40.2 36.3 26.1 13.4 80/12 1.33 47.0 45.6 44.0 38.8 32.0 40/10 1.25 54.1 50.2 45.4 32.6 16.8 40/12 1.42 64.9 60.2 54.5 39.2 20.2

The pump algorithm used in the thesis model assumes that the power

consumption and flow rate are constant for a given head. In practice variable

speed pumps are available in which the power consumption versus flow rate

can vary but this level of detail was not considered necessary for the model.

Figure 3.5 Typical head versus discharge relationship for RWH pump

(Courtesy of Rainharvesting Ltd)

The behaviour of pump units are not generally included in RWH system models.

Only a small number of examples could be found that explicitly included



97

consideration of a pump (Dixon, 1999; Ghisi & Oliveira, 2007). Both of these

used a similar method to that outlined above.

3.11 Potable (mains) water supply and sewerage systems

The extent to which the public water supply system is incorporated into RWH

models is usually restricted to measuring the amount of mains top-up water

required when there is insufficient harvested rainwater available to meet

demand. For models that incorporate a financial assessment this would also

include the associated volumetric mains supply and sewerage charges. Most of

the RWH system case studies reviewed as part of the literature survey included

a mains top-up function (e.g. Fewkes, 1999a; Coombes et al, 2003b; Villarreal

& Dixon, 2005) as did the majority of models created for research into

contemporary systems (e.g. Fewkes, 1999b; Dominguez et al, 2001; Ghisi &

Ferreira, 2007; Mitchell, 2007).

Models that included a financial element typically used the value of the mains

supply substituted by harvested water as the primary indicator of financial

performance (known as avoided costs) as this is the primary way in which RWH

systems are potentially able to save money. For example see Appan (1991);

Dominguez et al (2001); Coombes et al (2003); Shaaban & Appan (2003); Ghisi

& Ferreira (2007); Ghisi & Oliveira (2007) and MJA (2007), amongst others.

Financial aspects relevant to this thesis are discussed in greater detail in

chapter four.



98

3.11.1 Disposal of used rainwater to the foul sewer system

Presently the UK water utilities do not impose charges for harvested water that

has undergone some use (e.g. WC flushing) and is then disposed of to the foul

sewer. There is no device in place with which to measure or estimate the

volume of used harvested water entering the sewer system, although this is

possible (e.g. see Konig, 2001). Essentially this means that the owner/operator

of a RWH system will not incur any associated sewerage charges even though

the water utility will incur some cost because they are still required to treat the

effluent.

Some people have argued that the tariff structures in the water industry may

have to change if demand for RWH systems grows in the UK (Utility Week,

2006). However, no evidence could be found that any water utility is considering

introducing such a charging scheme at present or in the foreseeable future.

Therefore, although the ability to include such charges was included within the

thesis model, a disposal cost of zero was assumed for all simulations.

3.12 Storage tanks

The hydrological performance of a rainwater tank is related to the size and

characteristics of the contributing catchment, level of rainfall and demand on the

system (Fewkes, 2006). Fewkes & Butler (2000) state that the capacity of the

RWH tank is important both economically and operationally since it influences

the following variables:

Volume of water conserved.

Installation costs.



99

Length of time rainwater is retained, which affects the final quality of the

water supplied.

Frequency of system overflow, which affects the removal rate of surface

pollutants.

Volume of water overflowing into the surface drain or soakaway.

A rainwater tank can be considered as a storage reservoir that receives

stochastic inflows (effective runoff) over time and is sized to satisfy the demand

on the system (Fewkes, 2006). Tank size is the one parameter controlled by the

designer (Fewkes, 1997) who therefore requires some technique with which to

determine the size that will provide the optimum level of service. The sizing of

storage reservoirs has been reviewed by McMahon & Mein (1978) who identify

two general categories of sizing techniques: Moran related methods and critical

period methods.

3.12.1 Moran related methods

Moran related methods are a development of Moran‟s theory of storage (Moran,

1959) in which a system of simultaneous equations are used to relate reservoir

capacity, water demand and water supply. The analysis is based upon queuing

theory (Fewkes & Butler, 2000) and Moran initially derived an integral equation

relating inflow to reservoir capacity and outflow such that the probable state of

the reservoir could be defined at any given time. However, when using this

approach solutions were only possible for idealised conditions. Practical

applications were developed by Moran by considering both time and flows as

discrete variables. The reservoir capacity, inflows and outflows could then be



100

related to each other by a series of simultaneous equations (Fewkes, 2006).

This method was subsequently modified by Gould (1961) to allow for

simultaneous inflows and outflows, seasonality of flows and serial correlation of

inflows (Ragab et al, 2001). This method, known as the „Gould matrix‟ or „Gould

probability matrix‟, is of more direct practical use to engineers although it has

not been widely applied to rainwater tanks (Fewkes, 2006).

3.12.2 Critical period methods

In reservoir terminology a „critical period‟ is one during which a reservoir goes

from full to empty (Ragab et al, 2001). Critical period methods use sequences of

flows, which are usually derived from historic data, where demand exceeds

supply to determine the required storage capacity (Fewkes & Butler, 2000).

These methods can be subdivided into two categories: mass curve and

behavioural analysis (Fewkes, 2006).

3.12.3 Mass curve analysis

The mass curve method was originally described by Rippl (1883) and has

subsequently formed the basis of many adaptations (Gould & Nissen-Peterson,

1999) such as in sizing fresh water supply reservoirs (McGhee, 1991). The

method involves the identification of critical periods in the data where the

difference between cumulative inflows (rainfall) and cumulative outflows

(demand) are at a maximum. This difference represents the maximum volume

available for future use and hence the necessary storage capacity required to

maximise supply (Gould & Nissen-Peterson, 1999). With regards to RWH, a



101

storage system will perform adequately provided that the relationship shown in

equation 3.6 is satisfied (Fewkes, 2006):

2

1

t

t

tt dtQDMaxS (3.6)

where t1 < t2 and:

S = storage capacity (m3)

Dt = demand during time interval t (m3)

Qt = inflow during time interval t (m3)

A more obvious graphical demonstration is provided in Gould & Nissen-

Peterson (1999), as shown in figure 3.6. This particular example uses monthly

data but daily and weekly data can be used if a more accurate assessment is

required.

Figure 3.6 Application of mass curve analysis for sizing RWH tanks

Adapted from Gould & Nissen-Peterson (1999), p57.



102

where in figure 3.6:

A = the minimum volume required for maximum efficiency, i.e. to store

and utilise 100% of the incoming water, which in this example equates to

27m3.

B = The residual storage in the tank at the start of the analysis period

(5m3 assumed in this instance).

C = residual storage in the tank at the end of the analysis period (5m3

assumed in this instance).

The main limitation of the mass curve method as demonstrated in the previous

example is that it is not possible to compute a storage size for a given reliability

of supply or, in other words, probability of failure (Gould & Nissen-Peterson,

1999; Fewkes, 2006). Ree et al (1971) describe a statistical approach that is

able to facilitate this based on an analysis of the frequency of occurrence of

minimum rainfall amounts for periods between 2 to 84 months in a 75-year

rainfall record. By applying standard statistical techniques, the minimum rainfall

for a given probability can be determined for various time periods. If the

cumulative minimum rainfall values are plotted against time, a mass curve can

be derived and mass curve analysis conducted (Gould & Nissen-Peterson,

1999; Fewkes, 2006).

3.12.4 Behavioural analysis

Within the general category of critical period methods McMahon & Mein (1978)

also include behavioural (or simulation) analysis. Here the changes in storage

content of a finite reservoir (one that can overflow and empty) are computed



103

using the water balance equation as shown in equation 3.7 (McMahon et al,

2007).

Vt = Vt-1 + Qt – Dt – ΔEt – Lt (3.7)

Subject to 0 ≤ Vt ≤ S

where:

Vt = storage content at time t (m3)

Vt-1 = storage content at time t-1 (m3)

Qt = flow into the reservoir during time interval t (m3)

Dt = controlled release during time interval t (m3)

ΔEt = net evaporation loss from the reservoir during time interval t (m3)

Lt = other losses during time interval t, e.g. seepage (m3)

S = active reservoir capacity (m3)

With regards to contemporary RWH systems, the most commonly used storage

device is the underground tank (Hassell, 2005). These are watertight and also

essentially airtight so the net evaporation loss term, ΔEt, and the other losses

term, Lt, can both be ignored (Chu et al, 1997). Equation 3.7 then becomes:

Vt = Vt-1 + Qt – Dt (3.8)

Subject to 0 ≤ Vt ≤ S

where the terms are as previously defined. The water in storage at the end of a

prescribed time interval is therefore equal to the volume of water remaining in

the storage from the previous interval plus any inflow and less any demand



104

during the time period. Provided, that is, the computed volume in the store does

not exceed the capacity of the store. Behavioural models therefore simulate the

operation of a reservoir with respect to time by routing simulated mass flows

through an algorithm which describes the operation of the reservoir (Fewkes,

2006). The advantages of behavioural models are that they are relatively simple

to develop, easily understood and mimic the behaviour of the physical system.

They are also flexible, able to use data based on any timestep and can simulate

variable demand patterns, for example seasonal variations in water use

(Fewkes & Butler, 2000). Figure 3.7 shows a diagrammatic sketch of the

storage tank water fluxes typically modelled as part of a behavioural analysis.

Figure 3.7 Typical RWH storage tank configuration used in behavioural

models (Adapted from Mitchell, 2007).

where:

Yt = yield (withdrawal) from the tank in time t (m3)

Ot = overflow from the tank in time t (m3)

Mt = volume of mains top-up required in time t (m3)

and Vt, Qt, Dt and S are as previously defined. It can be seen from figure 3.7

that, in relation to the operation of the storage device, the fundamental water

Runoff into tank, Qt

Mains top-up, Mt

Overflow, Ot

Water demand, Dt

Water in tank, Vt

Capacity of tank, S Yield from

tank, Yt

Tank



105

flux elements consist of the runoff into tank (inflow), overflow from the tank and

the yield extracted from the tank. At any specific moment in time it is possible

that none, all, or any combination of these elements may be operating

simultaneously, giving a total of 8 possible states as demonstrated in figure 3.8.

Figure 3.8 Possible states of fundamental water fluxes occurring

simultaneously within a RWH storage tank

Note that in figure 3.8, the horizontal bars indicate that an event is occurring

and do not represent any associated volumes.

Behavioural analysis models use a mass-balance-transfer principle and are

based upon a discrete time interval of either a minute, hour, day or month

(Fewkes & Butler, 2000). Behavioural models based on discrete timesteps have

a number of fundamental limitations which go beyond the accuracy of the data

input into them. For instance they cannot „know‟ what is happening on a

timescale smaller than the selected timestep and also cannot conduct



106

simultaneous computations on the water fluxes. By way of illustration, suppose

that the inflow, overflow and extract yield events are all occurring at the same

time, an eventuality which is possible in reality. The events are interrelated

because the rate of overflow at any specific moment in time is affected by both

the rate of inflow and yield occurring at that same moment. However, a mass-

balance model based on discrete timesteps is not able to compute the outcome

of these simultaneous events as this would require the application and solution

of differential equations, i.e. the simulation of continuous and not discrete time.

Therefore the model aggregates the occurrences of each water flux (inflow,

overflow and yield extracted) that occur during the selected time period and

assumes that they occur instantaneously at the end of that time period and also

in a predefined sequence, i.e. the assumption is that events do not overlap

chronologically. The order in which events are assumed to occur has been

shown to be an important factor in determining how a behavioural model of a

rainwater tank performs and influences the predicted reliability of supply (Chu et

al, 1997; Fewkes & Butler, 2000; Liaw & Tsai, 2004; Mitchell, 2007). However,

despite these limitations the methodology is still capable of modelling actual

tank behaviour with an acceptable degree of accuracy, as will be discussed

later in this chapter.

Three fundamental water fluxes have been identified thus far, namely runoff into

tank (inflow), overflow and extract yield. The yield cannot be extracted until its

magnitude has been calculated, therefore another term needs to be added to

the list and that is determine yield. This is the volume of harvested water

available to meet the demand in a given timestep and also has to be calculated



107

in sequence. This gives a total of four variables that need to be accounted for

and in terms of possible combinations there are now 4! = 24 unique ways to

arrange the sequence of events. Therefore a pertinent question to ask is: how

should the four water fluxes be arranged in order to produce a model that

reflects the actual behaviour of a rainwater tank?

The possible sequence of events were investigated by Jenkins et al (1978) who

identified two fundamental algorithms with which to describe the operation of a

rainwater tank:

1. yield after spillage (YAS) algorithm, and

2. yield before spillage (YBS) algorithm.

A number of researchers have investigated the YAS/YBS operating algorithms

for the sizing of rainwater tanks, including Jenkins et al (1978); Chu et al (1997);

Fewkes & Butler (2000); Fewkes & Warm (2000); Liaw & Tsai (2004) and

Mitchell (2007), amongst others.

3.12.4.1 Yield after spillage (YAS) algorithm

In the YAS algorithm the order of operations occurring in time interval t is given

as: determine yield, runoff into tank (inflow), overflow, extract yield. The YAS

operating rules are given in equations 3.9 and 3.10.

1

mint

t

t

V

DY (3.9)



108

t

ttt

t

YS

YQVV

1

min (3.10)

where the terms are as previously defined. In the YAS algorithm, the yield is

determined by comparing the demand in time interval t with the volume in the

tank at time interval t-1 (the end of the previous time interval). The yield is

assigned to the smaller of the two values. The runoff into the tank (inflow) in the

current time interval t is then added to the volume of rainwater in the tank from

time interval t-1. If the capacity of the tank is exceeded then any surplus exits

via the overflow, and then finally the yield is extracted. The process is

demonstrated graphically in figure 3.9. Note that in this example it is assumed

that all demand can be met for this particular time interval.

Figure 3.9 Graphical representation of YAS algorithm

Adapted from Mitchell (2007).

Minimum storage level

1: Volume at t-1, determine yield Yt

Maximum storage level

2: Inflow in t 3: Overflow in t

4: Extract yield, Yt

Volume, Vt, at end of time t

Tank



109

3.12.4.2 Yield before spillage (YBS) algorithm

In the YBS algorithm the order of operations is given as: runoff into tank

(inflow), determine yield, extract yield, overflow. The YBS operating rules are

given in equations 3.11 and 3.12.

tt

t

t

QV

DY

1

min (3.11)

S

YQVV

ttt

t

1

min (3.12)

where the terms are as previously defined. In the YBS algorithm, the yield is

determined by comparing the demand in time interval t with the volume of water

in the tank at time interval t-1 plus the runoff into the tank in time interval t. The

yield is assigned to the smaller of the two values. The runoff into the tank

(inflow) in the current time interval t is then added to the volume of rainwater in

the tank from time interval t-1 and the yield is extracted. If the capacity of the

tank is exceeded after the yield has been extracted then any surplus exits via

the overflow. The process is demonstrated graphically in figure 3.10. Note that

in this example it is assumed that all demand can be met for this particular time

interval.



110

Figure 3.10 Graphical representation of YBS algorithm

Adapted from Mitchell (2007).

The YAS and YBS algorithms represent opposite ends of the behavioural model

spectrum (YAS, overflow first then withdrawal; YBS, withdrawal first then

overflow). In reality it is unlikely that any RWH tank will operate at either end of

these two extremes and a combination of YAS/YBS-style behaviour is more

likely. From the information presented thus far it would be reasonable to

conclude that the YAS algorithm has a tendency to underestimate the available

supply whilst the YBS algorithm tends to produce an overestimate. A number of

researchers have found this to be true when comparing the performance of the

two operating rules, for example Chu et al (1997, 1999); Liaw & Tsai (2004);

Mitchell (2007).

Minimum storage level

Volume at t-1

Maximum storage level

1: Inflow in t 2:determine yield Yt

4:Overflow in t

3: Extract yield, Yt

Volume, Vt, at end of time t

Tank



111

3.12.4.3 Adapting the YAS and YBS algorithms: the ‘storage operating

parameter’ θ

The use of a large rainfall timestep such as one month will result in a compact

and economical data set (Fewkes, 2006). However, the use of rainfall data on

such a large temporal scale has been shown to result in an inaccurate

prediction of system performance (Fewkes & Frampton, 1993). Latham (1983)

developed a model based on the YAS operating rule that used a monthly time

interval. He then used the model to predict the performance of RWH systems in

North America but discovered that it tended to significantly overestimate the

tank size required to provide a given volumetric reliability. Latham managed to

increase the accuracy of the monthly model to a level comparable with a daily

time step model by adapting the YAS and YBS algorithms to represent the more

general form shown in equations 3.13 and 3.14.

tt

t

t

QV

DY min (3.13)

t

tttt

t

YS

YYQVV

)1(

)1()( min

1

(3.14)

where θ represents a coefficient known as the „storage operating parameter‟

which can be assigned any value between 0 and 1 inclusive. The remaining

terms are as previously defined. If θ = 0 then the equations are the same as the

YAS operating rule and if θ = 1 then the equations are the same as the YBS

operating rule. Latham (1983) found a location-specific value for θ such that a

model based on monthly data gave similar results to that of a daily model, which



112

have been shown to be more accurate (Heggen, 1993; Thomas, 2002a). The

shorter timesteps of the daily model were in effect replicated in the monthly

model by the storage operating parameter (Fewkes, 1999b). This approach

provides a simple and versatile method of modelling the performance of RWH

systems using monthly rainfall data (Fewkes, 2006). However, it still requires

the use of a model with a smaller timestep (e.g. daily) with which to determine a

suitable value of θ for a given location. In the UK these were investigated for

five different locations by Fewkes (1999b) using a behavioural model with daily

and monthly timesteps.

3.12.5 Other design methods

Fewkes (2006) identifies a range of other critical period methods that have been

developed for the sizing of storage reservoirs. These are the semi-infinite

reservoir method (Hazen, 1914); Hurst‟s procedure (Hurst et al, 1965); sequent

peak algorithms (Thomas & Burden, 1963) and Alexander‟s method (Alexander,

1962). A comprehensive review of these methods is given in McMahon & Mein

(1978). Fewkes (2006) states that none of these methods have been widely

adopted for the sizing of rainwater stores and so they are not considered

further.

3.13 Selection of storage tank modelling approach

Of the techniques discussed in section 3.12 that could be used to model a RWH

storage tank (Moran related methods, mass curve analysis and behavioural

analysis) it was decided that a behavioural approach was the logical choice.

Moran methods and their derivatives (e.g. Gould matrix) were rejected because



113

they are primarily used for predicting the probability of failure associated with a

reservoir of a given capacity, or for sizing reservoirs to meet a given security of

supply, again using a probabilistic approach (e.g. see Ragab et al, 2001).

However, this approach is not particularly relevant for contemporary urban

RWH systems intended for non-potable uses. It is highly unlikely that such

systems would need to be designed to meet a given security of supply since the

uses are non-critical, and in any case it can be assumed that there will be a

mains top-up function available during times of short supply. It is not the

intention of this thesis to assess failure rates per se. Hydrological performance

is only of concern insofar as it effects the financial performance, the primary

focus of this research project. Sizing tanks to meet pre-defined water saving

reliability targets is not a valid approach in this context.

Further, the original approach as described in Moran (1959) is not capable of

taking into account within-year seasonality. A constant demand pattern is also

assumed throughout the analysis period (McMahon & Mein, 1978). These

limitations would mean that seasonal variations in rainfall patterns as well as

water demand (e.g. increased usage in summer for garden irrigation) could not

be simulated, which would limit the usefulness of the model. Gould (1961)

modified the basic method so that within-year variations in season and demand

could accounted for (Ragab et al, 2001). However, he did this by incorporating

elements of behavioural analysis. Since the probabilistic elements of the Moran

related methods are not required, it would make little sense to use the Gould-

modified approach in order to account for variations in season and demand



114

when a purely behavioural analysis approach could be used from the outset in

order to achieve this.

Application of Moran related methods to the sizing of rainwater stores appears

to have been limited and there are few examples of their use in this area (e.g.

Piggott et al, 1982). Even if these methods were compatible with the aims of

this thesis there is a lack of sufficient research with which to judge their ability to

accurately model RWH systems in a UK context.

With regards to mass curve analysis, in the original form one limitation is that

the approach is used to determine the storage capacity required to meet 100%

of the demand (Gould & Nissan-Peterson, 1999). Techniques exist for adapting

the method so that a statistical probability can be attached to meeting a given

percentage of demand which is less than 100%, for example see Ree et al

(1971). However, as previously stated, neither of these approaches is relevant

to this thesis. Further, McMahon & Mein (1978) state that seasonal variations in

demand are difficult to incorporate. This limits the usefulness of the approach

with regards to simulating RWH systems with a garden irrigation component.

Finally, it does not appear to be a popular approach amongst researchers for

sizing rainwater tanks and there are limited examples of its application. For

example see Ngigi (1999), but this paper relates to Kenya. Therefore it cannot

be validated as an accurate technique for simulating the performance of

rainwater tanks in the UK.



115

Behavioural analysis has a number of advantages compared to the Moran

related and mass curve methods and is a technique more suited to the thesis

research area. Importantly, it is an approach that does not assume that any

given level of water saving reliability is in itself preferable to any other. In other

words, behavioural analysis is not driven by a requirement to size the storage

reservoir based on the probability of meeting a predetermined level of demand.

As such it is a more flexible approach and allows the analysis to be guided by

criteria other than hydrological performance, which in this instance would be the

financial aspects.

It is also an established technique that has been used by a relatively large

number of researchers investigating RWH system performance, e.g. Jenkins et

al (1978); Latham (1983); Chu (1997); Fewkes (1999b); Fewkes & Butler (1999,

2000); Fewkes & Warm (2000); Coombes et al (2001); Liaw & Tsai (2004);

Ghisi et al (2007); Mitchell (2007) and MJA (2007), amongst others. The validity

of behavioural models has also been confirmed in a number of monitoring

studies, for example see Fewkes (1999a) and Coombes et al (2000a). Fewkes

(1999a) concerns the modelling of a domestic RWH system installed in a UK

property which was used for WC flushing. A behavioural model of the system

was created and simulation outputs were compared to data collected from the

RWH system over a twelve month monitoring period. The predicted behaviour

was found to be in good agreement with actual system performance and this

study provides empirical validation of a behavioural approach in a domestic UK

context.



116

Seasonal variations and changing demand patterns can also be accounted for.

If data is available, or can be generated, that reflects these variations then it is a

relatively simple matter to input this into the model, e.g. historic time series

rainfall data, results from domestic water consumption studies and so forth.

Behavioural models can also be programmed to take into account different

future conditions, for example rainfall time series data can be modified to take

into account the effects of climate change and then input into the model. Future

demand patterns that reflect changing consumer behaviour can be modelled. A

behavioural approach provides the researcher with a greater degree of flexibility

than the Moran related or mass curve analysis methods.

Having decided on a behavioural analysis approach a choice had to be made

between either the YAS or YBS operating rule. Fewkes & Butler (2000)

recommend the use of YAS for design purposes because it gives a

conservative estimate of system performance. Liaw & Tsai (2004) used the YBS

rule in preference to YAS because when investigating time reliability they found

that it resulted in less predictions of failure (<100% demand met), however this

appeared to be a case of the researchers choosing the modelling approach

based on a predefined notion of what results would be acceptable. In an

Australian study, Mitchell (2007) recommend the use of YAS because the

results of the investigation showed that it provided more accurate predictions of

yield than did YBS.

The generalised YAS/YBS algorithm was incorporated into the thesis model

with the storage operating parameter θ set to zero (YAS) as the default mode of



117

operation. It is acknowledged that the use of the YAS setting will have led to a

more conservative prediction of system performance than use of YBS.

However, work conducted by Fewkes & Butler (2000) suggests that as long as

certain constraints regarding the selected timestep are employed then YAS

models are capable of modelling system performance within ±10% of that

predicted by a more accurate hourly timestep model and this was considered to

be an acceptable margin of error. The YAS model constraints are discussed in

the following section.

3.14 Implications of the behavioural model timestep

The selected timestep of a behavioural model is often dictated by the temporal

resolution of the available rainfall data and a range of different timesteps has

been utilised by researchers in the field, such as six minutes (Coombes, 2002;

Mitchell, 2007), one hour (Fewkes & Butler, 1999), one day (Fewkes, 2001),

three, five, seven, ten days (Liaw & Tsai, 2004) and one month (Jenkins et al,

1978).

Behavioural models tend to increase in accuracy the smaller the timestep of the

input data (Fewkes & Butler, 2000), for example a model which uses hourly

rainfall data is more accurate than a model using daily rainfall data. Whatever

data is employed it must be sufficiently precise for the purpose of the design

(Heggen,1993). However, as Thomas (2002a) highlights, meteorological data is

rarely detailed, reliable and free and as acquisition may be costly there is an

inefficiency in gathering more data than is needed (Heggen, 1993). Ideally a



118

researcher wants rainfall data that has low acquisition costs but that is accurate

enough and uses a timestep small enough to produce useful results.

A number of international researchers have investigated the implications of

using rainfall data with different temporal scales and this work is summarised in

table 3.7. It should be noted that most of this work relates to countries other

than the UK and its transferability to this country is unknown.

With regards to work relating specifically to the UK, key research has been

conducted by one researcher in particular (Fewkes), often in conjunction with

various others. The relevant research outputs (with regards to selection of an

appropriate behavioural mode timestep) produced by Fewkes and Fewkes et al

are discussed in more detail in section 3.14.1.



119

Table 3.7 Range of timesteps used in existing international RWH system models

Reference Description of work/comments

Heggen (1993)

Compared the performance of RWH systems (time reliability) in New Mexico using YAS/YBS algorithms with timesteps between one day and one month. Using a daily timestep and 7 years of daily rainfall data, found little difference between YAS/YBS. Used a daily YAS model as the benchmark against which to compare timesteps of 2, 3, 7, 14 and 31 days. As temporal scale increased, model accuracy decreased. Simulations with weekly data found to give results differing by up to 50% from the benchmark daily YAS model. Results for monthly timesteps differed by up to 90% from the daily YAS model. Heggen concluded that if daily rainfall data is available then there is no justification for using weekly or monthly time intervals.

Thomas (2002a)

Compared the performance (time reliability) of daily models to monthly models for four different regions (Kenya, Bangkok, Panama and Brazil). For large tanks the differences between the daily and monthly models was small. For small tanks the use of monthly data was found to introduce large errors.

Chu et al (1997)

Investigated the performance of domestic systems for WC flushing in Taiwan. Used YAS and YBS models with 84 years worth of rainfall data. Timesteps of 1, 3, 5, 7 and 10 days were used. Daily timesteps found to give results close to that of actual systems. YAS approach found underestimate actual supply to authors recommended the YBS approach. However, other researchers have shown that YBS tends to overestimate the water saving reliability (e.g. Liaw & Tsai, 2004; Mitchell, 2007)

Liaw & Tsai, 2004

Modelled RWH systems in Taiwan using timesteps of 1,3 5, 7 and 10 days using both YAS and YBS algorithms. Found that longer time intervals gave less accurate results, especially when modelling small tank sizes. Consequently the authors recommended the use of short timesteps and for the remainder of the study the authors used a timestep of 1 day.

Mitchell, 2007

Investigated the impact of computations timestep, tank operating rule, initial tank storage volume and length of simulation period on the accuracy of the storage-yield-reliability relationship for a wide range of RWH system configuration in three Australian cities (Melbourne, Sydney and Brisbane). Four timesteps were used: 6mins, 30mins, 3hrs and 24hrs in conjunction with both YAS and YBS models. A 50-year 6min YAS configuration was used as the benchmark model. For all combinations of timestep, demand level, demand pattern and location is was found that for tank sizes greater than 6,300 litres the difference in results was with ±1% of the benchmark model, indicating that large tank sizes are insensitive to the characteristics of the input data used to model them. YAS was found to underestimate performance, YBS to overestimate. Guidance was presented on selecting an appropriate timestep for a given set of system characteristics, notably the average demand per timestep and the proposed storage tank capacity. This approach was similar to that in Fewkes and Butler (2000) (see section 3.14.1)



120

3.14.1 Review of relevant work by Fewkes et al

A significant body of original work relating to RWH systems has been produced

by Fewkes and Fewkes et al over approximately the last 25 years (Fewkes &

Ferris, 1982; Fewkes, 1989; Fewkes & Tarran, 1992; Fewkes, 1993; Fewkes &

Frampton, 1993; Fewkes, 1995; Fewkes, 1997; Fewkes, 1999a; Fewkes,

1999b; Fewkes & Butler, 1999; Fewkes & Butler, 2000; Fewkes & Warm, 2000,

Fewkes & Warm, 2001). Much of this research was concerned with using

behavioural analysis to predict the performance of domestic rainwater tanks and

is noteworthy because it represents a significant portion of the limited number of

academically rigorous studies that relate specifically to the UK. The behavioural

models created by Fewkes are also worthy of mention because they were

validated using data collected from the monitoring of an actual domestic RWH

system (Fewkes, 1993, 1995, 1997, 1999a). The work by Fewkes and Fewkes

et al consists of at least twelve peer-reviewed papers but for the sake of brevity

only one key paper of direct relevance to the thesis is discussed in this chapter

(Fewkes & Butler, 2000) as this summarises findings and conclusions from the

earlier work that are relevant to this section of the thesis.

Earlier empirical work (Fewkes, 1999a) indicated that a YAS model using either

hourly or daily timesteps could be used to predict system performance. The

analysis undertaken in Fewkes & Butler (2000) extended this work and

proposed constraints for the application of hourly, daily and monthly models.

Different combinations of roof areas, tank storage capacities and water demand

were expressed in terms of two dimensionless ratios, namely the „demand

fraction‟ and the „storage fraction‟, as shown in equations 3.15 and 3.16.



121

yr

yr

RA

DDF (3.15)

yrRA

SSF (3.16)

where:

DF = demand fraction

Dyr = annual demand (m3/yr)

A = roof plan area (m2)

Ryr = annual rainfall (m/yr)

SF = storage fraction

S = storage capacity (m3)

Demand fractions of 0.27, 1.25 and 2.5 were investigated along with storage

fractions ranging from 0.0015 to 1.08. The analysis suggested that both YAS

and YBS behavioural models would be capable of modelling system

performance within ±10% of that predicted by a more accurate hourly model

providing that the following storage fraction constraints were applied:

1. Hourly models: S/A.Ryr ≤ 0.01

2. Daily models: 0.125 ≥ S/A.Ryr > 0.01

3. Monthly models: S/A.Ryr > 0.125

The constraints apply to all demand fractions. It was recommended that hourly

models are required for the sizing of small tanks whilst monthly models should

only be used to predict the performance of large capacity storage devices.

One limitation of the study was that only twelve months of historic rainfall data

were used in the model. From table 3.1 it can be seen that an historic rainfall



122

record length of at least 10 years is generally recommended. A further limitation

was that water demand was limited to WC flushing which has been shown to

relatively constant over time (Butler, 1991; Fewkes, 1999a). It did not

investigate the implications of seasonal variations such as the summer peak

which occurs due to garden watering (Herrington, 2006; Alegre et al, 2004) and

use of external taps (Environment Agency, 2003a). Therefore the applicability of

the above constraints for other than relatively constant uses such as WC

flushing have yet to be established. However, they were still nevertheless

applied to the thesis model as they currently represent the state of the art.

3.14.2 Selection of an appropriate model timestep

Prior to implementation of the selected YAS behavioural model a decision had

to be made regarding a suitable timestep. Theoretically any timestep can be

used but intervals based on a minute, hour, day or month are typically

employed (Fewkes & Butler, 2000). Wainwright & Mulligan (2004) state that the

optimal model is one that contains sufficient complexity to explain the observed

behaviour, but no more. The data requirements (and therefore complexity) of

RWH models tends to increase as the timestep decreases, therefore the

optimum approach is to use the largest timestep possible that is still capable of

producing acceptably accurate results.

With a daily model it is only necessary to obtain rainfall and water demand data

at daily intervals. The availability of information at this temporal scale is

relatively high. The Met. Office has extensive daily rainfall data sets for many

locations throughout the UK, and it is common for per capita water consumption



123

to be reported on a daily basis (e.g. Herrington, 1996; POST, 2000;

Environment Agency, 2001a; Downing et al, 2003; DCLG, 2006c; Ofwat,

2006a). With sub-daily timesteps such as hours or minutes it is necessary to

either know or estimate at what times during the day events occur and this adds

another level of complexity to the modelling process (e.g. see Dixon et al, 1999;

Wong & Mui, 2005). Water consumption data at the sub-daily scale is also more

limited than at the daily scale, although some research does exist (Butler, 1991;

Chambers et al, 2005).

At the opposite end of the scale are monthly models which use temporally

coarse data that is generally more readily available than either daily or sub-daily

information. Fewkes (2006) states that monthly models are also likely to be

compact and economical. However, models that use such long timesteps have

been found to produce inaccurate results (Latham, 1983; see also table 3.7)

and are only recommended for use when sizing large stores (Fewkes & Butler,

2000). This essentially precludes their use for modelling domestic RWH

systems as these generally utilize relatively small storage tanks.

Given the increased data requirements (and therefore complexity) of sub-daily

models, and the noted inaccuracies of the monthly variants, the rational choice

was judged to be a daily timestep. The availability of good quality daily rainfall

time series as well as per capita water consumption data was also a

determining factor in this decision. It was necessary to validate this choice with

the constraints proposed by Fewkes & Butler (2000) for selecting a suitable

timestep. In order for a daily model to produce results within ±10% of a more



124

accurate benchmark hourly model, the storage fraction S/A.Ryr needs to be

greater than 0.01. A smaller value than this indicates that an hourly timestep

should be used. The smallest possible storage fraction value that could occur

with the thesis simulations of domestic systems was calculated using the

following information:

Smallest domestic tank size for which cost data was available = 1.2m3.

Largest predicted roof area for new-building houses = 106m2.

Greatest annual rainfall depth (after accounting for climate change, see

section 3.16) = 0.950m/yr.

Inputting these values into the storage fraction equation gave a figure of 0.0108

which is close to but still greater than the threshold value. Therefore the use of

a daily YAS behavioural model was a valid approach.

3.15 Climate change

The Earth's climate has been relatively stable since the end of the last ice age

about 10,000 years ago but is currently undergoing a period of rapid warming

(UKCIP, 2007). The majority of current scientific opinion supports the view that

human activities are contributing to this change and that likely future changes

present a serious threat to human society and the natural environment (HMSO,

2006). Recent publications from the Intergovernmental Panel on Climate

Change (IPCC) are predicting that climatic changes are set to continue. The

trend is towards generally warmer temperatures and an increased risk of

extreme weather events such as floods, droughts, greater cyclone activity and

higher sea levels (IPCC, 2007). Variations in the global rate and distribution of



125

precipitation are also expected and it is believed that changes in rainfall

patterns could have more profound impacts on humans and ecosystems than

changes in temperature (Treydte et al, 2006). McEvoy et al (2006) state that

“climate change is now widely recognised as the biggest global challenge facing

humanity”.

The United Kingdom Climate Impacts Programme (UKCIP) is a research

organisation funded by the British Government that helps organisations assess

how they might be affected by climate change so that they can prepare for its

impact. It has undertaken a number of studies investigating likely regional and

sectoral effects. The latest UKCIP (2002a,b) results are based on outputs from

the Hadley Centre climate models which were used to create a high-resolution

(50x50km grid) atmospheric regional model of Europe. Four climate change

scenarios were investigated, each one using different assumptions regarding

future global emissions of greenhouse gases and associated impacts on the UK

climate over the next hundred years. The four scenarios relate to low, medium-

low, medium-high and high emission levels. Changes in climate for three 30

year periods were investigated with the first period centred on the 2020s and

running from 2011 to 2040, the second centred on the 2050s (2041 to 2070)

and the third centred on the 2080s (2071 to 2100).

The main results from the study are presented in UKCIP (2002b) as a series of

colour coded maps showing the UK divided into a grid array of 50x50km parcels

of land. Maps are available for each emission scenario and for each 30 year

time period and show, amongst various other results, predicted changes in the



126

mean temperature and precipitation. As an example, the predicted range of

impacts on England‟s northwest region were obtained from the maps and are

presented in table 3.8.

Table 3.8 Predicted range of climate change impacts on the northwest

region of England (from UKCIP dataset).

2020’s (2011-2040)

2050’s (2041-2070)

2080’s (2071-2100)

Change in average annual temperature

0-1OC 1-2OC 1-4OC

Change in maximum summer temperature

0-1OC 1-3OC 2-6OC

Change in summer rainfall 5-15% decrease

10-30% decrease

15-50% decrease

Change in winter rainfall 5-10% increase

0-20% increase

15-30% increase

Change in winter snowfall 20-25% decrease

30-60% decrease

40-100% decrease

Change in summer and autumn soil moisture

0-10% decrease

10-25% decrease

20-40% decrease

Change in sea level Not available 7-36cm 7-67cm

Seasonal changes in precipitation and temperature will have implications for

RWH systems. The amount of rainfall and its temporal distribution directly

affects how effective a system will be at supplying water to the end user. The

level of demand can itself be influenced by the temperature. Herrington (1996)

suggests that “variations in peak [demand] factors over time…are largely

associated with climate”. The UKCIP reports predict a general trend towards

drier summers (UKCIP, 2002a). This implies that in the future there will be

comparatively less rainfall for RWH systems to collect during the summer

months and that this will occur during a time of year when demand is

traditionally higher than average, for example due to greater occurrences of



127

garden watering (CC:DW, 2001). Conversely, winters are predicted to become

wetter but demand at this time will be lower than in the summer.

The effects of climate change should be considered when predicting the

medium and long-term performance of RWH systems. However, there appears

to be no UK studies that have investigated or included the effects of climate

change on RWH systems. A number have incorporated intra-year climatic

effects, for example modelling the peak summer demand that occurs largely

due to increased garden watering (Alegre et al, 2004), but long-term climate

change has not been accounted for. This research project will, where possible,

take climate change effects into account in an explicit manner, particularly with

regards to the expected changes in temperature and precipitation.

3.16 Rainfall data used in the thesis model

The thesis model operates on a daily timestep and so historic rainfall data with

the same temporal scale was required. The information presented previously in

table 3.1 suggested that a minimum record length of ten years was advisable.

The distance of weather monitoring station from the site of interest was not a

criteria that could easily be assessed since the thesis is primarily concerned

with analysing domestic RWH systems in the West Yorkshire region, hence

there was no specific location (site) to investigate. For this reason the primary

selection criteria with regards to the selected weather station was that the

location should be representative of typical weather patterns in the West

Yorkshire area, i.e. the average annual rainfall depth should not be significantly

higher or lower than would be expected for the region as a whole.



128

Rainfall data was available from the Met. Office via the BADC. A continuous 37

year daily rainfall record covering the years 1964-2000 was obtained for the

Emley Moor weather station located in Huddersfield, West Yorkshire. Details of

the raw data set are given in table 3.9.

Table 3.9 Emley Moor historic rainfall data details

Parameter Value

Station name Emley Moor Location Huddersfield, West Yorkshire OS grid reference SE222130 Elevation 272m AOD Data type Daily rainfall data (mm/day) Record length 37 years, 1964-2000 inclusive % missing data 13% Average annual rainfall depth 794mm/yr Typical SAAR1 range for Yorkshire region 460-800mm/yr 1Standard annual average rainfall 1971-2000. Figures in table are Met. Office data obtained from Thornton (2005)

The available records were longer than the recommended minimum of ten

years and had an average annual depth of 794mm. Standard annual average

rainfall (SAAR) values for the Yorkshire region are in the range of 460-800mm

(Thornton, 2005). The Emley Moor average was towards the upper end of this

range but was still deemed to be within acceptable limits.

Some rainfall depth entries were missing and overall these accounted for

approximately 13% of the data set. Gaps were filled by interpolating between

the data points on either side of the missing entries. For example if the 1st

January 1990 data point was missing then a new value was generated by taking

the average of the 1st January 1989 and 1st January 1991 entries.



129

Figure 3.11 shows a graph of the annual rainfall depths contained within the

data set (post editing). Note the two extremes marked on the graph. These

correspond to the 1975 drought and 1998 floods which affected large parts of

the Yorkshire region.

Figure 3.11 Emley Moor historic annual rainfall depths 1964-2000

400

500

600

700

800

900

1000

1964 1969 1974 1979 1984 1989 1994 1999

Year

Rain

fall (

mm

/yr)

1998 flood

1975 drought

In order to take climate change effects into account the edited rainfall data set

was adjusted in accordance with the methodology presented in the UKCIP

(2002b) report. The work to date has not yet attached probabilities of

occurrence to each of the climate change scenarios (low, medium-low, medium-

high and high emissions) so there is currently no way to know which is more

likely to occur. An arbitrary decision was taken to use the medium-high

emissions scenario.

In UKCIP (2002b) the predicted regional changes in precipitation are given as

seasonal percentage variations from the historic rainfall record. Predicted



130

changes for the Yorkshire region corresponding to the medium-high emissions

scenario were extracted from the report and are presented in table 3.10.

Table 3.10 Predicted precipitation changes for the Yorkshire region

based on the UKCIP02 medium-high emissions scenario

Period and predicted % change in precipitation

Month 2020s 2050s 2080s

Jan 5.00 12.50 22.50 Feb 5.00 12.50 22.50 Mar 0.00 0.00 -5.00 Apr 0.00 0.00 -5.00 May 0.00 0.00 -5.00 Jun -15.00 -25.00 -45.00 Jul -15.00 -25.00 -45.00 Aug -15.00 -25.00 -45.00 Sep 0.00 -5.00 -5.00 Oct 0.00 -5.00 -5.00 Nov 0.00 -5.00 -5.00 Dec 5.00 12.50 22.50

The above percentage changes in rainfall were then applied to the historic

rainfall record for Emley Moor. This gave a climate change adjusted data set of

daily rainfall covering the period 2007-2100 as shown in figure 3.12. This rainfall

data set was used in all RWH system simulations performed as part of this

research project.



131

Figure 3.12 Climate change adjusted annual rainfall depths for Emley

Moor (UKCIP02 medium-high emissions scenario)

400

500

600

700

800

900

1000

1 8 15 22 29 36 43 50 57 64 71 78 85 92 99

Year

Rain

fall (

mm

/yr)

Historic 1964-2000 UKCIP02 Med-High scenario

The graph shows an overall decrease in the annual rainfall depth. On average,

for the 2020s period (2011-2040) this was equal to 33mm/yr (4.3%), for the

2050s period (2041-2070) 20mm/yr (2.5%) and for the 2080s (2071-2100)

47mm/yr (5.9%).

3.17 Predicting non-potable domestic demand

Average per capita water use in the UK domestic sector has risen from about

100 litres/day in 1970 (Thornton, 2005) to approximately 150 litres/day (Ofwat,

2006a). Per capita consumption varies with household size, type of property,

ages of household residents and time of year (Butler & Memon, 2006).

Research has shown that increases in household demand are primarily driven

by population growth, household occupancy and levels of affluence

(Environment Agency, 2001a; Sim et al, 2005). Average consumption levels



132

continue to rise with the EA predicting a demand of over 160 litres per capita

per day by 2030 (Thornton, 2005).

A pattern of rising demand in new-build houses is by no means certain. The

recently introduced Code For Sustainable Homes standard (DCLG, 2007) may

act as a significant driver for a reduction in domestic water use in modern

developments. For internal water use, a maximum per-capita consumption of

120 litres per day is required in order to achieve the lowest level of compliance

so this may come to represent the minimum standard for new housing stock.

Research conducted by Mactavish & Hill (2007) suggests that meeting this

target might in fact incur no additional cost to the developer since it may be

achieved simply by installing water efficient fixtures, fittings and appliances of

comparable cost to less efficient types. Compliance with the intermediate level

of no more than 105 litres per person per day was estimated to cost only an

additional £125 per dwelling, a very small fraction of the value of most new

houses. Therefore, from the developer‟s perspective, there would seem to be

no real disincentive in complying with at least the lowest level of the Code.

Further, the Government is currently consulting on new water performance

standards either within a new Building Regulation or by amendment to the

Water Supply Regulations (DCLG, 2006e). New mandatory regulations would

act to reduce water usage in new buildings. For these reasons a value of 120

litres was used throughout this thesis whenever the internal daily per capita

consumption required consideration.



133

Domestic RWH systems could potentially meet about 55% of total household

demand if used for non-potable applications such WC flushing, laundry washing

and garden irrigation (see chapter two). In order to model these uses some

methodology was required that was able to predict how often they occur and

how much water is consumed per use. Herrington (1987) states that demand

forecasting based on rules of thumb or naïve extrapolation is now recognised as

being inappropriate, since estimates obtained this way have been shown to

deviate significantly from what happens in reality. A micro-component approach

to water demand forecasting is often recommended (Environment Agency,

2001a). That is, the study of individual uses of water within a household such as

for WC flushing, personal washing etc (Butler & Memon, 2006). This approach

has been used in numerous studies for predicting future demand, e.g.

Environment Agency (2001a); Williamson et al (2002); Chambers et al (2005).

However, it is important to acknowledge that there can be no definitive

conclusions drawn regarding future water demand (Downing et al, 2003), only

more or less reasoned and transparent investigations (Alegre et al, 2004).

An understanding of the nature of domestic demand for water can be obtained

by examining information on household ownership of appliances, frequencies of

use and the volumes of water required per use (Downing et al, 2003). The

range of non-potable applications considered in this thesis consists of WC

flushing, laundry cleaning (washing machines) and garden irrigation. Feasible

values for future usage frequencies and associated volumes are presented in

the following subsections.



134

With regards to climate change it can be assumed that WC and washing

machine usage are not sensitive to long-term variations in climate (Downing et

al, 2003; Alegre et al, 2004). For garden irrigation climate sensitivity has been

assumed as this is in line with current research recommendations, e.g. Downing

et al (2003).

3.17.1 Water closet demand

Table 3.11 shows a range of WC usage frequencies. This data was based on

past monitoring studies. There is no reason to believe that WC usage frequency

will increase or decrease significantly and so the existing data was used as an

acceptable indicator of future behaviour. The average of the values in table 3.11

is equal to 4.59 flushes per person per day. Clearly it is not possible to flush a

toilet 4.59 times so it was assumed that weekday (Monday-Friday) per capita

usage was 4 times/day and weekend (Saturday and Sunday) usage was 6

times/day. This assumes higher weekend usage, which is not unreasonable,

and gives an average rate of 4.57/person/day which is close to the actual

average of 4.59. Butler (1991) found an essentially linear relationship between

household occupancy and frequency of WC flush. Therefore an acceptable

approach for calculating the household usage is to multiply the per capita usage

frequency by the household occupancy rate.



135

Table 3.11 Range of domestic WC usage frequencies

Uses/person/day References

3.3 Thackray et al (1978) 3.7 Butler (1991) 5.25 SODCON (1994) 6-8* Fewkes (1999a) 4.3 Environment Agency (2001a) 4.8 Chambers et al (2005) 4.8 DCLG (2007)

4.59 Average from above

*Fewkes notes that the one of the WCs monitored often required two flushes to clear the pan which may explain the higher than average values. The higher value was ignored when calculating the average figure

Current regulations permit a maximum flush volume of 6 litres for single-flush

WCs (HMSO, 1999). A range of dual-flush toilets are available, e.g. 6/4, 6/3, as

well as lower volume single flush such as 4.5 litres. Table 3.12 summarises the

range of existing and possible future flush volumes for modern domestic WCs.

Table 3.12 Range of modern domestic WC flush volumes

Volume/use (litres) References

6 single flush. Max. allowable flush volume (HMSO, 1999)

HMSO (1999); Grant (2003, 2006); Environment Agency (2001a); DCLG (2007)

6/4 dual flush Grant (2003) 6/3 dual flush Grant (2003, 2006) 4.5 single flush Grant (2006) 4 single flush1 Grant (2003, 2006);

Environment Agency (2001a)

4/2 dual flush Grant (2003); Environment Agency (2001a)

2-3 single flush2 Grant (2006) 1.5-2 litre single flush3 Millan (2007); Millan et al

(2007) 1.2 (vacuum toilet)4 Grant (2006) 0 (composting toilet) Environment Agency

(2001a) 1Considered to be probable lower limit for gravity drainage without flush boosters 2May be feasible with designs that collect a number of flushes and discharge them as a single larger flush to ensure good drain carry 3Prototype ultra-low flush design utilising air pressure to aid flushing 4Normally only recommended for use in extreme situations, e.g. aircraft and trains



136

The last three items in the table were included in order to demonstrate the

technical lower limit for flush volumes but there is no suggestion that these

methods are likely to see widespread implementation in the short to medium

term. The choice was therefore between flush volumes ranging from 6-litre

single to 4/2-litre dual. It was decided that installation of the 6/3 dual flush

variety would be assumed for all new houses.

The use of dual-flush WCs also raises the issue of how many uses will involve a

full flush and how many only a part flush. Grant (2003) reports that it is often

assumed that the ratio of full to part flush will be 1:3 or 1:4. However, he goes

on to state that monitoring trials have shown the actual flush ratio to be in the

range of 1:0 (i.e. only full flush used) and 1:2 (1 full to 2 part flushes). In this

thesis a flush ratio of 1:2 has been adopted.

3.17.2 Washing machine demand

Table 3.13 shows a range of washing machine (WM) use frequencies. It is not

anticipated that future per capita use frequencies will differ significantly from

those occurring at present. The average of the figures presented in table 3.13 is

0.21 uses per person per day. This is close to a rate of once every 5 days and

so this latter figure was used as the standard value for domestic simulations.

Butler (1991) found a reasonably linear relationship between household

occupancy and frequency of washing machine usage. Therefore in order to

determine household usage the per capita frequency can simply be multiplied

by the household occupancy rate.



137

Table 3.13 Range of domestic washing machine usage frequencies

Uses/person/day References

0.16 Butler (1991) 0.18 SODCON (1994) 0.157 Environment Agency (2001a) 0.34 DCLG (2007)

0.21 Average from above

Table 3.14 presents data regarding the volume of water used by modern

washing machines for a typical wash cycle.

Table 3.14 Range of modern domestic washing machine water usage

volumes

Volume/use (litres) References

100 SODCON (1994) 27/kg of wash load* HMSO (1999) 45 Lallana et al (2001) 80 Butler & Memon (2006) 49 DCLG (2007) 40-80 Environment Agency (2001a) 35-40** Grant (2006)

*Maximum allowable under current regulations **30-40 litres per 5kg load probably technical limit due to rinse performance requirements

Grant (2006) reports that the energy and water efficiency of washing machines

has improved considerably over the past decade. It is also stated that research

has shown that wash performance is not correlated with water consumption, i.e.

high water use does not necessarily mean cleaner clothes. The most efficient

machines were generally as good as, if not better, than their less efficient

counterparts. Therefore there would appear to be little justification for the future

installation of the less efficient variants. Washing machines are already

available that use on average about 50 litres per cycle. In the Code for

Sustainable Homes documentation the standard volume for new machines is



138

taken as 49 litres/use (DCLG, 2007). Grant (2006) states that the technical limit

is probably in the range of 30-40 litres due to rinse performance requirements.

In this thesis a value of 50 litres per use was assumed as this is in line with

current practice and reasonably close to the lowest technically achievable level.

3.17.3 Garden irrigation

Water use in the garden has been reported to be sensitive to seasonal

variations in climate (Butler & Memon, 2006; Herrington, 2006) and usage

peaks in the summer relative to other times of the year (Environment Agency,

2001a; Sim et al, 2005). Herrington (1996) suggested that additional water

demand for lawn sprinkling and other garden uses would be predominantly

driven by temperature. A study in the Hastings area of England found a strong

correlation between the maximum daily temperature, rainfall and hours of

sunshine. Significant increases in outdoor water use were found to occur during

the peak demand period of July and August (Environment Agency, 2003a).

Garden irrigation only accounts for a small percentage of the total annual

domestic water use, typically between 4-6% (POST, 2000; CC:DW. 2001;

Environment Agency, 2001a; Herrington, 2006). However, it peaks at a time of

highest water stress (Grant, 2006). On hot, dry summer evenings up to 50% of

the public water supply may be used for garden watering (Environment Agency,

1999b).

Climate sensitive micro-components such as garden irrigation may vary over a

number of years due to the effects of climate change (Alegre et al, 2004). Whilst

total domestic demand has been projected to be fairly constant over the next



139

decade (Environment Agency, 2001a), garden watering is expected to increase

and be particularly sensitive to climate change. Downing et al (2003) state that

an increasing number of households are using hose pipes and sprinklers. It is

also noted that there is a trend towards garden designs and plant varieties that

require more water during warm, dry weather.

The approach used for predicting future garden irrigation requirements was

based on a methodology described in Downing et al (2003) (“Climate Change

and the Demand for Water”). This project began in 2000 with a review of the

benchmark study conducted by Herrington (1996). One of the key aims was to

update the methodologies and findings in Herrington (1996) taking into account

new data, updated UKCIP climate change scenarios (UKCIP, 2002b) and

demand scenarios developed by the Environment Agency (Environment

Agency, 2001a).

The method for estimating garden irrigation requirements was based on soil

moisture deficits, which in turn depend on the level of rainfall and air

temperature. This approach was therefore able to take into account the

changes in precipitation and temperature predicted in the UKCIP (2002b)

climate change scenarios report. A more detailed explanation of how the

methodology was implemented in the thesis model is provided in appendix one.

Briefly, the approach taken allows the volume of water required to irrigate a

given garden area to be calculated based on the predicted soil moisture deficit.

This is location-specific and depends upon the potential evapotranspiration,

average monthly temperature and average monthly rainfall for a given area. The



140

method employed allows the user to specify how many irrigation sessions occur

per week and so is able to take into account different user behaviour.

Figure 3.13 shows the predicted requirements for a garden of plan area 60m2

when one irrigation session per week is specified. The data corresponds to the

year 2007 and shows the predicted demand before climate change effects have

been factored in (UKCIP scenarios start in 2011). The chart shows that peak

usage occurs in July when 1,041 litres per weekly session are required. For the

months just before and after the peak period (June and August) usage is slightly

under 1,000 litres/week (921 and 973 litres respectively). Herrington (1996)

reports that garden watering in the south and east of England, using sprinklers,

took place once every six days during May to August in an average year in the

early 1990s. The estimated average volume for each irrigation session was in

the range of 1,000-1,200 litres. The results presented here are in reasonable

agreement with these findings for the months of June to August. The figures for

May are somewhat lower at 482 litres. However, it is argued that this is more

realistic than simply assuming the same rate for all months May to August

inclusive. A gradual increase in watering requirements as summer approaches

is more likely than an instant change from zero at the end of April to peak usage

at the beginning of May. Likewise, the reduction in garden watering that occurs

after July is more realistic than a sudden cessation of all irrigation activities. A

similar approach for the phasing in and out of garden irrigation activities was

used by Alegre et al (2004).



141

Figure 3.13 Predicted weekly garden irrigation requirements for 2007

(one irrigation session per week)

0

200

400

600

800

1000

1200

1 23 45 67 89 111 133 155 177 199 221 243 265 287 309 331 353

Day

Wate

r u

sag

e (

litr

es/s

essio

n)

May

Jun

Jul Aug

Sep

Oct

Notes: temperature and rainfall data refer to West Yorkshire region, irrigation area = 60m2

A report by Three Valleys Water Services (Three Valleys, 1991) found that

about 40% of households use hosepipes an average of three times per week in

hot, dry weather. It was reported that approximately 315 litres were used during

each session. Figure 3.14 shows the results from the thesis garden irrigation

model when three watering sessions per week are specified for an irrigation

area of 60m2. The predicted peak demand in July is in reasonable agreement

with the Three Valley‟s study at 347 litres. June and August show the strongest

agreement at 307 and 324 litres respectively. Again there is a phasing in and

out of water usage which is more realistic than assuming an „all or nothing‟

approach.



142

Figure 3.14 Predicted annual garden irrigation requirements for 2007

(three irrigation sessions per week)

0

50

100

150

200

250

300

350

400

1 23 45 67 89 111 133 155 177 199 221 243 265 287 309 331 353

Day

Wate

r u

sag

e (

litr

es/s

essio

n)

May

Jun

Jul Aug

Sep

Oct

Notes: temperature and rainfall data refer to West Yorkshire region, irrigation area = 60m2

A garden/irrigation area of 60m2 was found to produce results in good

agreement with those reported by Herrington (1996) and Three Valleys (1991).

Assuming a garden area of this size was found to be a realistic approach for

new-build residential dwellings (see appendix one). This value was used for all

subsequent simulations in the thesis in which garden irrigation was a

component. Figure 3.15 shows the predicted irrigation demand data used in the

thesis model (in m3/yr aggregated from m3/day) for those simulations in which

garden watering was a component. The chart shows that, although volumes

vary from year to year, there is a clear trend towards increasing irrigation

requirements (note the upward slope of the trend line).



143

Figure 3.15 Predicted annual water demand for a typical West Yorkshire

garden (new-build) for the period 2007-2100

0

5

10

15

20

25

30

35

40

1 5 9 13 17 21 25 29 33 37 41 45 49 53 57 61 65 69 73 77 81 85 89 93

Year

Irri

gati

on

vo

lum

e (

cu

.m/y

ear)

The approaches to water demand estimation discussed in sections 3.17.1-

3.17.3 were incorporated into the thesis model in a „Demand Generator‟

module. The user is required to enter the necessary data in terms of appliance

usage frequencies and volumes. The application then generates a 100 year

long daily demand profile for the selected uses. Whenever a simulation is run

the computer then automatically extracts the generated demand profile for each

year over the selected analysis horizon.

3.18 Methods of modelling the hydrological performance of RWH

systems: summary

This chapter began with a broad overview of modelling and associated

concepts. A range of different model types were identified including physical

and mathematical, with the latter broadly consisting of empirical, conceptual and

physically based. General advice on the process of model development and

implementation was presented. Reasons for modelling RWH systems were



144

identified along with a range of commonly employed performance indicators

with which to judge the predicted hydrological performance.

The range of RWH system components requiring explicit consideration within

the thesis model were identified and their selection justified. This list of

components consisted of rainfall, catchment surface (roof), first flush diverter,

coarse filter, pump, potable (mains) water supply and sewerage system

(volumes to and from), storage tank and non-potable supply and demand. A

range of existing methodologies for simulating the physical behaviour of these

components were discussed and suitable approaches selected.

With regards to the storage tank three important modelling techniques were

identified, namely Moran related methods, mass curve analysis and behavioural

analysis. The latter of these approaches was considered to offer a number of

advantages over the others and was selected as the basis for the thesis model.

Two fundamental behavioural algorithms with which to describe the operation of

a storage tank were identified, namely the Yield After Spillage (YAS) and Yield

Before Spillage (YBS) algorithms. The YAS variant was selected for

implementation and this choice was justified, as was the decision to use a daily

timestep.

The possible future effects of climate change on the UK weather system were

discussed, primarily with reference to the latest UKCIP climate change scenario

reports. A suitable source of rainfall data for use within the thesis model was

identified. Thirty seven years of historic daily rainfall statistics were obtained



145

from the Met. Office for the Emley Moor weather station in Huddersfield, West

Yorkshire. The historic rainfall time series was then adjusted for climate change

in line with the latest UKCIP recommendations. This gave a continuous rainfall

record ranging from 2007-2100 for use within the thesis simulations.

Methods for predicting non-potable domestic water demand were discussed.

Appliance usage data were presented for modern WCs and washing machines

and reasoned assumptions were made regarding probable future use volumes

and frequencies. For garden irrigation an existing methodology relating watering

requirements to temperature and precipitation (via soil moisture deficits) was

implemented. This allowed for possible climate change impacts to be accounted

for in the outdoor use component.

In the next chapter the financial aspects of RWH systems and the methods

available for performing a financial assessment are discussed.

uk; modelling the hydrological performance of rainwater harvesting systems - bradford university

Documents

performance of rwh systems

rwh models

rwh system models

rwh system performance

sakellari et

physical models

coombes et

parkinson et