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TANK SIZING FROM RAINFALL RECORDS FOR
RAINWATER HARVESTING UNDER CONSTANT DEMAND
BY

JACQUELINE ELSA ALLEN
920407518

A dissertation submitted to the Faculty of Engineering and the Built
Environment in partial fulfilment of the requirements for the degree

MAGISTER INGENERIAE
IN
CIVIL ENGINEERING SCIENCE
in the
Faculty of Engineering and the Built Environment
AT

UNIVERSITY OF JOHANNESBURG
(AUCKLAND PARK KINGSWAY CAMPUS)

STUDY LEADER: PROF J. HAARHOFF
AUGUST
2012

Abstract

In recent years, there has been an international trend towards installing rainwater tanks in
an attempt to save water. However, there are no clear guidelines for determining the
optimal size of such a tank in South Africa. This study investigates the possibility of
simplifying the process of sizing a rainwater tank for optimal results. It utilises daily data
from four rainfall stations, namely Kimberley, Mossel Bay, Punda Maria and Rustenburg,
obtained from the South African Weather Services. The water use is considered to be for
indoor purposes only, therefore assuming a constant daily demand to be extracted from the
tank. The required size of a rainwater tank is influenced by the MAP, the area of the roof
draining into the tank, the water demand (both the average demand and seasonal
variations), the desired reliability of supply, and the rainfall patterns. The first step in
simplifying the process is to consolidate the above variables. The tank volume is expressed
as the number of days it could supply the average daily water demand. Another variable is
created which provides the ratio of the total water volume which could theoretically be
harvested from the roof in an average year, to the total water demand, from the tank, for a
year. This has the effect of consolidating the MAP, the roof area, the water demand and the
tank volume into two variables only and eliminates the need to consider numerous demand
values. Using simulations over 16 years for each location, the relationships between these
variables were determined to ensure 90%, 95% and 98% assurance of supply. These
relationships were generalised with the equation DD=a(DAU-1)b+c, which was found to
produce a good fit, taking DD as the number of days of storage and DAU as the ratio of total
amount of water available to the total amount of water demand. This model allows the
rapid determination of the required tank size for a given roof area, once the location and
assurance of supply is provided. The procedure presented, provides a reasonable correlation
with the simulated results, but, at times, does over-estimate the required size. The study
suggests that the proposed method is feasible, however further research is required in
order to refine the method.

Table of Contents
List of Figures ............................................................................................................................ iv
List of Tables .............................................................................................................................. v
List of Abbreviations and Acronyms .......................................................................................... v
1

Problem Statement ............................................................................................................ 1

2

Introduction ....................................................................................................................... 2
2.1

3

Literature Review ............................................................................................................... 5
3.1

Worldwide Use of Rainwater Tanks in the Urban Environment ................................. 5

3.2

Use of Rainwater Tanks in South Africa ...................................................................... 9

3.2.1

Legal provisions concerning rainwater harvesting in South Africa ..................... 9

3.2.2

Domestic use of rainwater tanks in South Africa ................................................ 9

3.2.3

Agricultural use of rainwater tanks in South Africa ........................................... 11

3.2.4

Suitability of rainwater tanks in South Africa .................................................... 12

3.3

4

Scope and Limitations ................................................................................................. 3

Sizing of Rainwater Tanks .......................................................................................... 13

3.3.1

Sizing methods ................................................................................................... 13

3.3.2

Simulation of a rainwater tank .......................................................................... 15

3.3.3

Expressing the reliability of a rainwater tank .................................................... 17

3.3.4

Selecting the operating rule............................................................................... 18

3.3.5

The time-step ..................................................................................................... 19

3.3.6

Selecting the length of the simulation period ................................................... 21

3.3.7

Selecting the initial condition ............................................................................ 22

3.3.8

Ratio between rainwater demand and rainwater availability ........................... 22

Method ............................................................................................................................ 23
4.1

Rainwater Tank Simulation ....................................................................................... 23

i

4.1.1

Operating rule .................................................................................................... 23

4.1.2

Conservation of volume ..................................................................................... 23

4.1.3

Time-step ........................................................................................................... 26

4.1.4

Rainfall stations selected ................................................................................... 26

4.1.5

Length of simulation period ............................................................................... 27

4.1.6

Initial tank condition .......................................................................................... 27

4.1.7

Effect of demand................................................................................................ 28

4.1.8

Describing the reliability of the tank ................................................................. 29

4.2

4.2.1

Reducing the variables ....................................................................................... 31

4.2.2

Calibrating the model ........................................................................................ 32

4.2.3

Directly predicting the modelling constants ...................................................... 32

4.3
5

Simplifying the Process ............................................................................................. 31

Verification of the Time-Step .................................................................................... 33

Results .............................................................................................................................. 36
5.1

Rainwater Tank Simulation ....................................................................................... 36

5.1.1

Graphs obtained ................................................................................................ 36

5.1.2

Range of possible tank sizes .............................................................................. 39

5.1.3

Local design curves ............................................................................................ 40

5.2

Generalising the Modelling Constants ...................................................................... 45

5.2.1

Parameters considered ...................................................................................... 45

5.2.2

Effect of MAP on tank size ................................................................................. 46

5.2.3

Best correlation for a ......................................................................................... 48

5.2.4

Best correlation for b ......................................................................................... 49

5.2.5

Best correlation for c ......................................................................................... 50

5.3

Proposed Sizing Method ........................................................................................... 51

5.4

Testing the Validity of the Time-step ........................................................................ 53
ii

5.5

Testing the Accuracy of the Design Curves ............................................................... 55

5.5.1

Local design curves (i.e curves for Kimberley, Mossel Bay, Punda Maria and

Rustenburg)...................................................................................................................... 55
5.5.2

Generalised design curves (i.e. curves obtained using the DSM)...................... 56

6

Conclusion ........................................................................................................................ 61

7

Recommendations for Future Research .......................................................................... 64

8

References ....................................................................................................................... 66

iii

List of Figures

Figure 3-1: Distribution of rainwater tanks in South Africa, in absolute numbers (Mwenge
Kahinda, et al., 2010) ............................................................................................................... 10
Figure 3-2: Percentages of rural household use of water sources (DWAF, 2007) .................. 11
Figure 3-3: In-field RWH suitability map .................................................................................. 12
Figure 3-4: The Yield-Before-Spillage operating rule for a single time-step (Mitchell, 2007) . 18
Figure 3-5: The Yield-After-Spillage operating rule for a single time-step (Mitchell, 2007) ... 19
Figure 4-1: Locations of the four rainfall stations.................................................................... 27
Figure 4-2: Comparison of constant and variable demand ..................................................... 29
Figure 4-3: Plot showing the valid interval for a daily time-step............................................. 35
Figure 5-1: Simulation curves for Kimberley............................................................................ 36
Figure 5-2: Simulation curves for Mossel Bay.......................................................................... 37
Figure 5-3: Simulation curves for Punda Maria ....................................................................... 37
Figure 5-4: Simulation curves for Rustenburg ......................................................................... 38
Figure 5-5: Graph showing DD=a(DAU-1)b+c, DD=c and DAU =1............................................ 42
Figure 5-6: Local design curves for Kimberley ......................................................................... 43
Figure 5-7: Local design curves for Mossel Bay ....................................................................... 43
Figure 5-8: Local design curves for Punda Maria ..................................................................... 44
Figure 5-9: Local design curves for Rustenburg ....................................................................... 44
Figure 5-10: Graph of a vs. MAP .............................................................................................. 46
Figure 5-11: Graph of b vs. MAP .............................................................................................. 47
Figure 5-12: Graph of c vs. MAP .............................................................................................. 47
Figure 5-13: Best correlation for a ........................................................................................... 49
Figure 5-14: Best correlation for b (note that there is no constant progression from (90% to
98%) ......................................................................................................................................... 50
Figure 5-15: Best correlation for c ........................................................................................... 51
Figure 5-16: Validity of time-step for 90% volumetric reliability ............................................ 54
Figure 5-17: Validity of time-step for 95% volumetric reliability ............................................ 54
Figure 5-18: Validity of time-step for 98% volumetric reliability ............................................ 55
iv

Figure 5-19: Comparison of simulation to DSM for Kimberley................................................ 58
Figure 5-20: Comparison of simulation to DSM for Mossel Bay.............................................. 58
Figure 5-21: Comparison of simulation to DSM for Punda Maria ........................................... 59
Figure 5-22: Comparison of simulation to DSM for Rustenburg ............................................. 59

List of Tables

Table 4-1 Effect of a changing a constant demand from 100 l/day to 150 l/day .................... 28
Table 5-1: Range of tank sizes obtained .................................................................................. 40
Table 5-2: Table of coefficients of determination for trend lines ........................................... 41
Table 5-3: Constants of local design curves ............................................................................. 45
Table 5-4: Difference in required tank size determined by simulation and local design curves
or generalised design curves ................................................................................................... 56
Table 5-5: Coefficient of determination for the DSM when compared to the simulated
results....................................................................................................................................... 60

List of Abbreviations and Acronyms

DAU: Dimensionless area units
DD:

Days of demand

DSM: Dimensionless sizing method
MAP: Mean annual precipitation
RH:

Rainwater harvesting

RHS:

Rainwater harvesting system

v

1 Problem Statement

Internationally there has been a trend towards implementing rainwater harvesting as a form
of water conservation as well as a flood control strategy. However in South Africa,
implementation, especially in urban areas has been limited. In urban areas, rainwater
harvesting systems are generally installed from necessity caused by drought or an
inadequate water supply from a piped water distribution system. Implementation of
rainwater harvesting for stormwater management is unusual. Possible reasons for the lack
of implementation include a lack of financial incentive to install rainwater harvesting
systems and the fact that no design guidelines for rainwater harvesting systems exist for
South Africa. In order to address an aspect of the current lack of design guidelines, this
study investigates the feasibility of a simplified sizing method for rainwater tanks in South
Africa. The study uses rainfall data, supplied by the South African Weather Services, to first
simulate the behaviour of a rainwater tank and then attempts to develop a simplified sizing
method from the simulation results.

1

2 Introduction

Rainwater harvesting (RH) is a general term used to refer to the collection, storage and use
of rainwater for both domestic and agricultural purposes. In recent years there has been an
international trend towards the utilisation of rainwater harvesting systems (RHS) both as a
water conservation technique and a form of stormwater management. In a number of
countries, this has been encouraged by government, either through subsidies or by the
introduction of laws which make the implementation of such systems mandatory
(Herrmann, et al., 1999; GDRC, 2007; Gold Coast City Council, 2005; Texas Water
Development Board, 2005).

Current implementation of RHSs in South Africa is generally due to necessity with
implementation for water conservation or stormwater management being unusual (Jacobs,
et al., 2011; Mwenge Kahinda, et al., 2010). Most RHSs in South Africa are found in rural
areas and are used as an alternative source of water to augment poor service supply. In
urban areas, implementation is generally related to drought conditions, with households
using rainwater to supplement the municipal water supply when water restrictions are in
place.

The lack of large scale implementation of RHSs in South African urban areas may be related
to the fact that to have a significant impact, even for individual households, large tanks are
required. These large tanks are aesthetically unappealing and require a large initial capital
expenditure, making them uneconomical. In conjunction with this problem is the fact that
there are currently no guidelines or subsidies provided for sizing or implementation of such
systems in South Africa. Research is being done on the feasibility of RH, especially for small
scale agricultural use, but there is no significant research into the sizing of RHSs based on
domestic demand in South Africa.

2

The sizing of the tank of a RHS is complicated due to the large number of variables that play
a role in determining the optimum tank size, which means that every tank must be
individually sized. The most common approach used for sizing the tank of a RHS is a water
balance approach in which the behaviour of the tank is simulated over time. In order to
obtain an accurate result the simulation must be run over a period of at least 10 years with
a relatively small time step (generally a daily time-step) and thus requires a relatively
detailed and complete rainfall record, often difficult to obtain.

This study investigates the development of a simplified method for sizing the tank of a RHS
in South Africa. The water balance approach is used to simulate the behaviour of tanks at
four locations in South Africa. The results of the simulations are then used to identify
correlations between parameters obtained from the rainfall records and the required tank
size. These correlations provide a simplified method for sizing a rainwater tank, the results
of which are compared to the simulated results in order to determine the accuracy of the
method.

2.1 Scope and Limitations

The current study is a preliminary study on the feasibility of a simplified rainwater tank
sizing method which can be applied at any location within South Africa and is suitable for all
roof sizes. As such data from all climatic regions were used in order to develop a possible
sizing method and simulations for large roof areas or large tank sizes were included in the
study.

The study considers a constant demand intended for indoor use. The harvested water would
thus be used for toilet flushing and laundry purposes, but not for garden irrigation. This
assumed usage requires a high reliability of supply, as such the study is conducted for 90%,
95% and 98% reliability.
3

As the study is a preliminary study, the quality of the harvested rainwater was not
considered. This means that no first flush system was included in the study. The efficiency of
the harvesting system was also neglected for the purpose of the study. If the results of the
study show that the developed sizing method shows promise, future studies would need to
incorporate such considerations.

4

3 Literature Review

3.1 Worldwide Use of Rainwater Tanks in the Urban Environment

In recent years, the trends towards sustainable development and Integrated Urban Water
Management have led to worldwide encouragement of water re-use and RH. A number of
countries have introduced subsidies for installing rainwater tanks and, in some cities, the
installation of rainwater tanks has become a mandatory requirement for any new building.
A number of these cities have found that the rainwater tanks provide significant reductions
in the amount of water supplied through the city’s water supply system and some have also
found that rainwater tanks decrease the stormwater runoff and thus assist in stormwater
management (Hamdan, 2009). In this section, selected cases from both developed and
developing countries are reviewed.

In Berlin, Germany, a basement rainwater tank was installed in a large scale urban
development (Daimler Chrysler Potsdamer Platz) in 1998. This tank collected water from the
roofs of 19 buildings. The purpose of the system was to decrease the stormwater in order to
prevent flooding, save water and also to improve the micro-climate of the area. Another
system in Berlin collected rainwater from streets and parking areas as well as roofs and
diverted it to a 160 m3 tank. This water was then treated and used for flushing toilets and
watering gardens. An estimated 58% of the stormwater runoff from the area was retained
by this system (GDRC, 2007). During the 1990’s more than 100 000 rainwater storage tanks,
providing water for non-potable use, were installed in Germany. A number of city councils in
Germany provided financial incentives to promote the use of rainwater tanks as an
alternative water supply. For instance, if a RHS was installed and used, the storm water
taxes did not need to be paid (Herrmann, et al., 1999).

Another example from the developed world is Tokoyo (Japan). In Tokyo, both the Ryogoku
Kokugikan Sumo-wrestling Arena and the Sumida City Hall installed systems which diverted
5

rainwater into underground storage tanks. The rainwater was then used for flushing toilets
and also in the air conditioning system of the buildings. After the successful implementation
of these systems, a number of other public facilities introduced similar systems. By 2007,
approximately 750 buildings in Tokyo, both public and private, had introduced RHSs (GDRC,
2007).

Bangladesh is an example of a developing country. Contamination of the groundwater
supply with arsenic in parts of Bangladesh has led to the use of RHSs to provide drinking
water. Studies have shown that this water is safe for drinking and can be stored for up to 5
months without fear of bacterial contamination. Starting in 1997, approximately 1000 RHSs
were installed in the country and the Forum for Drinking Water Supply & Sanitation has
been promoting rainwater as a safe water supply in urban areas (GDRC, 2007).

Since 2000, more than 2 million rainwater tanks have been installed in Gansu Province in
China. These tanks have a combined storage volume of more than 73 million m 3, supply
drinking water to 1.97 million people and help to irrigate 236 400 ha of land in the province.
Seventeen provinces in China have adopted RH as an alternative water source and a total of
5.6 million rainwater tanks have been installed in the country (GDRC, 2007).

RHS also offers great, but as yet unrealised, potential for households in Barcelona, Spain. It
has been found that a small tank could supply a family in Barcelona with enough water to
flush their toilets and do their washing without using the municipal supply. It has also been
found that increasing the tank size would allow for a substantial portion of the family’s
irrigation requirements to be met by the tank. The study found that large scale
implementation of such systems would be extremely beneficial in Barcelona (Domenech, et
al., 2011).

6

In Bermuda, limestone “glides” have been added to roofs to divert rainwater into storage
tanks, which are generally underground. These systems are regulated by a Public Health Act
requiring the roof area to be painted with a non-toxic paint, free from metals. The Act also
required owners to keep their roofs, gutters and pipes clean and to clean the tank at least
once every six years (GDRC, 2007).

After the tsunami of 2004, the general population was left without a water supply system in
Banda Aceh (Indonesia). Initially the people relied on shallow wells that had been dug by
individual households. It was later discovered that a number of these wells were
contaminated and the water was not safe for drinking. A project was initiated in 2007, in
which a number of RHSs were installed and monitored. The study determined that RH is the
most suitable method of supplying the community with water. Indonesia is an ideal place
for RH due to the high annual rainfall combined with the fact that the rain is evenly
distributed throughout the year, thus eliminating the need for large tanks to provide enough
water throughout a dry season (Teh, et al., 2009).

RHS was a prerequisite for obtaining a residential building permit in St. Thomas, US Virgin
Islands. A single-family house was required to have a system which drained an area of at
least 112 m2 into a tank which had to provide at least 45 m3 in storage volume. Although no
limits have been put in place on the materials used for the system, the usage of the water
has been limited to non-potable uses unless treatment is provided (GDRC, 2007).

In Seoul, South Korea, a major real-estate development known as Star City implemented a
RHS as a flood control measure in 2007. The development consisted of 4 high-rise buildings
located on a 5ha site. This RHS was found to adequately control a 50-year flood. The system
included a network which monitors the level of water in the tanks at the Central Disaster
Prevention Agency in the City Office. Depending on the level in the tanks and the amount of
rain expected, it was possible for the agency to issue an order for the building owners to

7

empty their tanks, so as to ensure that the system provided adequate protection against the
predicted flood (Mun, 2011).

A number of RH guidelines have been developed for particular cities or areas around the
world. Examples of these guidelines are the Texas Manual on Rainwater Harvesting,
released by the Texas Water Development Board (2005) in the USA and the Interim
Rainwater Tank Guidelines released by the Gold Coast City Council (2005) in Australia. Both
of these documents contain information on the functional requirements of RHSs, the basic
design requirements and the method which should be used to design such a system.
Unfortunately, very few authorities have compiled such guidelines and there are none
available for most of the world’s cities. Furthermore, the water laws in most countries do
not encourage the use of such systems (Hamdan, 2009).

In both Australia and Poland, life cycle costing determined that RHSs are not a financially
viable option for individual home owners. A 2010 study by Rahman et al, conducted in
Australia, found that it would take a typical homeowner approximately 30 years to recoup
the cost of a tank without government subsidies. In a number of countries where rainwater
tanks are utilised on a large scale, it is done because of necessity, due to lack of adequate
water supply, or due to government intervention - either by introducing regulations making
RH mandatory or by providing individual homeowners with substantial financial incentives
to install such systems (Slys, 2009; Rahman, et al., 2010).

A number of cases where successful implementation of RH by utilising rainwater tanks can
be found internationally. This suggests that large scale deployment of rainwater tanks could
have a significant effect on the water volume supplied to urban areas by municipal supply
systems in South Africa. However further investigation is required to determine the effect of
such an implementation in South Africa.

8

3.2 Use of Rainwater Tanks in South Africa

3.2.1 Legal provisions concerning rainwater harvesting in South Africa

The legal provisions pertaining to RH in South Africa are contained in the National Water Act
(NWA) (Act No 36 of 1998), with the Water Services Act (WSA) (Act No 108 of 1997) playing
a limited role in determining the legal requirements for utilising such a system. Under the
NWA any “taking of water from a resource” requires a licence, unless stipulated in section
22 of the act. Section 22 of the act allows a user to take water directly from any water
resource to which the user has lawful access for reasonable domestic use and specifically
allows the storage and use of runoff water from a roof. However it does state that the use
of water for commercial purposes (such as farming) is not covered by this section. This
means that the use of a domestic RHS without a licence can be deemed legal in South Africa,
unless the local municipality has by-laws enforcing the registration of such a system
(Mwenge Kahinda, et al., 2007; Jacobs, et al., 2011).

3.2.2 Domestic use of rainwater tanks in South Africa

The use of rainwater tanks in South African urban areas is relatively uncommon. This is
mainly due to the high cost of installing a rainwater tank, the fact that they are aesthetically
unappealing and the limited saving (in monetary terms) that they can offer. The potential
yield of a typical RHS in Johannesburg would only be able to supply approximately 36% of
the water required for garden irrigation (Jacobs, 2010). In addition to this, the seasonal
rainfall which prevails over most of South Africa means that a very large tank is required to
capture enough water during the rainy season to provide any significant supply during the
dry season. This entails a large initial capital cost with relatively small financial savings,
making the installation of such a tank uneconomical for the individual home owner (Jacobs,
et al., 2011; Mwenge Kahinda, et al., 2008).

9

The use of rainwater tanks in rural areas is more common and, in some cases, rainwater
tanks are relied upon as the primary source of drinking water. This is especially true of areas
in the Eastern Cape and KwaZulu-Natal. Figure 3-1 shows the number of rainwater tanks
found in each of the provinces of South Africa in 2010. However, according to the 2006
water services coverage as shown in Figure 3-2, released by the Department of Water
Affairs and Forestry, domestic rainwater harvesting (DRWH) is one of two least used water
sources in rural communities, with only 0.3% of rural households using domestic RH as a
source of water (Mwenge Kahinda, et al., 2010).

Figure 3-1: Distribution of rainwater tanks in South Africa, in absolute numbers (Mwenge Kahinda,
et al., 2010)

10

Figure 3-2: Percentages of rural household use of water sources (DWAF, 2007)

3.2.3 Agricultural use of rainwater tanks in South Africa

The use of rainwater tanks as a water supply for irrigation supply is well established and
rainwater tanks can be found on commercial farms. However, the use of RH by small-scale
farmers is negligible and should be encouraged as it has the potential to cater for the
irrigation needs of the population in areas of the country where there is no readily available
water source (Mwenge Kahinda, et al., 2011).

The influence of implementing field RH for small scale irrigation purposes on catchment
runoff was investigated in two catchments and found to be negligible (Mwenge Kahinda, et
al., 2009). Another study stated that the implementation of RH in the Modder River basin
has decreased the annual runoff by approximately 26%, but that further research must be
done to determine what the impact of this decrease will be on downstream areas
(Tetsoane, et al., 2008).

11

3.2.4 Suitability of rainwater tanks in South Africa

In South Africa, the use of rainwater tanks could be used as an alternative water source for
people in areas where bulk supply lines are not available. This would not provide savings in
terms of monetary gains to the households, but would provide savings by obviating the
need for a reticulation system. It would also have a social impact. Amongst other things, it
would decrease the time individuals take to carry water from the source to their homes.
This suggests that the feasibility of installing a rainwater tank for the individual should be
determined by considering the social impact as well as the installation costs. A set of
suitability maps for field RH in South Africa, which include the social impact have been
developed. The maps were based on aridity zones, rainfall, land cover, soil cover, ecological
sensitivity and socio-economic aspects. An example of such a map can be seen in Figure 3-3
below. As can be seen in the figure, most of the country falls into either the moderate or
high suitability zones (Mwenge Kahinda, et al., 2008).

Figure 3-3: In-field RWH suitability map

12

3.3 Sizing of Rainwater Tanks

3.3.1 Sizing methods

Methods used to size rainwater tanks can be categorised as simplified methods (including
graphical methods), matrix methods, statistical methods and simulation methods. The
simplified methods should only be used as preliminary design methods: they require little
calculation, but are not very accurate. The most commonly used method is a simulation
method based on the conservation of volume, as this method provides accurate results and
also provides continuous results for the inflow, outflow and volume of water available in the
tank at a given time (Palla, et al., 2011; Liaw, et al., 2004).

3.3.1.1 Simplified sizing methods
Demand Side Approach
When using the demand side approach, the storage requirement is assumed to be equal to
the largest demand which must be supplied by the tank. This is simply calculated by
determining the daily water demand and multiplying by the number of days in the average
longest dry period. This method assumes that the roof is large enough to capture the
required amount of rain. It does not account for the possibility that the rainfall patterns may
not provide enough rain to fill the tank immediately before the dry period. This approach is
best suited to areas with year-round rainfall. Due to the assumptions this approach entails,
the result can lead to a less reliable water supply than expected (Centre for Science and
Environment). Due to the fact that the method ignores important parameters in the sizing of
rainwater tanks it is not comparable to data driven methods.

A variation on this method for sizing rainwater tanks has been developed in the United
Kingdom (Fewkes, et al., 2000). The method requires the calculation of an input ratio, which
is defined as A*(MAP)/D, where A is the catchment area, MAP is the MAP and D is the
average annual demand. This ratio is then used along with a desired performance level to
determine the number of day’s storage that ought to be provided by means of a set of
13

design curves. The design curves are curves showing the storage period versus the
volumetric reliability for different values of the input ratio. The method uses a single curve
for a given input ratio, as it was found that in the United Kingdom, very little difference
exists from one location to another (Fewkes, et al., 2000).

Supply Side Approach
The supply side approach is generally used for areas which have a long dry period. The
required tank size is assumed to be large enough to capture the maximum amount of rain in
the wet season. This assumption makes it easy to over-size the tank and so this method can
lead to an unnecessarily expensive design (Rees, et al., 2002). The supply side approach
provides a maximum limit for the tank size and would provide a required tank size which is
larger for a large roof area than that obtained when using a smaller roof size, which
contradicts the resulted obtained when simulating the behaviour of a rainwater tank. The
supply side approach does not consider the effect of demand on the required tank size and
is thus, not comparable to a data driven process, such as simulating the behaviour of a tank.

The United Kingdom’s Environment Agency recommends a method, which combines the
Supply and Demand Side Approaches. The method determines the required size of the tank
as being either a user-defined percentage of the MAP (5% is suggested for the UK), or of the
average annual demand, whichever is smaller (Ward, et al., 2010). Ward, Memon and Butler
(2010) state that the size is then calculated as:
𝑆 = 𝑃𝐴𝐶𝐹 𝐹𝑅
Where:

P= user defined percentage
A= area of the roof
Cf= runoff coefficient
F = system filter efficiency
R= annual rainfall

R would be replaced by the annual demand (D), if D<R.

14

3.3.1.2 Computer simulation methods
The most accurate method for determining the optimal tank size is to simulate the
behaviour of the tank by using a computer model. A number of computer models which are
capable of performing such a simulation are available. These include the Model for Urban
Stormwater Improvement Conceptualisation (MUSIC), Aquacycle and Raincycle (Ward, et
al., 2010).

Studies conducted by Ghisi (2010) and Ward (2010) compared results from various methods
as well as considering the possibility of using a simplified sizing method. Both studies
determined that each rainwater tank must be individually sized based, on the specific
location, catchment size and water demand. The study by Ward (2010) also found that the
use of a single average rainfall value was not adequate, and recommended using a
simulation process to obtain an accurate size.

3.3.2 Simulation of a rainwater tank

Sizing a rainwater tank can become rather complicated as the required size is dependent on
a number of factors. The optimal tank size depends on the collection system, the area of the
roof from which water will be collected, the volume of water that the tank will be required
to supply, whether the demand will be constant or variable, the required reliability of the
water supply from the tank, the depth of precipitation which can be expected and the
rainfall pattern of the area where the tank will be situated (Ghisi, 2010). The most common
method for determining the correct size for a rainwater tank is thus to do a continuous
simulation of the tank behaviour for a given rainfall record. The continuous simulation of a
rainwater tank is popular, because the mathematics required is very easily understood, it is
relatively easy to develop a model or spreadsheet which will do such a simulation, the
behaviour of the system is accurately mimicked and it is easy to incorporate seasonal
changes in rainfall or water demand (Fewkes, et al., 2000).

15

3.3.2.1 Conservation of volume approach
The conservation of volume approach simply ensures the volume of water in the tank at the
end of a given time-step must be equal to the volume of water in the tank at the beginning
of the time-step (end of the previous time-step) plus the amount of water that has entered
the tank during the given time-step minus the water which has left the tank during the timestep and is given by the following equation (Male, et al., 2006; Su, et al., 2009).
𝑉𝑡 = 𝑉𝑡−1 + 𝑄𝑡 − 𝐷𝑡

3-1

This is subject to the constraint that the maximum volume of water in the tank is limited to
the size of the tank i.e. 0 ≤ 𝑉𝑡 ≤ 𝑆.
Where:

Vt = volume of rainwater in the tank at the end of time interval t
Qt = volume of rainwater that enters the tank during time interval t
Dt = demand (volume of water that is removed from the tank) during
time interval t
S = maximum storage capacity.

3.3.2.2 Yield-after-spill and yield-before-spill operating rules
Inflow and outflow from a tank is a continuous process in time. By approximating this
process with discrete time intervals, the inflow and outflow over the time interval has to be
reduced to a point inflow and point outflow.

The literature suggests two different approaches that can be used to overcome the
problem. The first option is the yield-after-spill (YAS) approach. For this approach, the
rainwater is added to the tank and the spillage is immediately removed by limiting the tank
volume. At the end of the time-step, the water demanded from the tank is subtracted from
a volume which can never exceed the maximum storage volume. In reality the water could
be removed and rainwater added to the tank simultaneously. This could mean that the
maximum limit would not be reached in reality even though it is reached computationally.
When spillage does occur, this option effectively decreases the tank capacity and thus
underestimates the amount of water which can be supplied by the tank. For this approach
the following equations can be used to determine the yield from the tank and the volume of
water in the tank (Fewkes, et al., 2000; Liaw, et al., 2004; Palla, et al., 2011).
16

𝑌𝑡 = 𝑚𝑖𝑛 𝐷𝑡 ; 𝑉𝑡−1

3-2

𝑉𝑡 = 𝑚𝑖𝑛 𝑉𝑡−1 + 𝑄𝑡 − 𝑌𝑡 ; 𝑆 − 𝑌𝑡

3-3

Where

Yt= yield from the tank during the time interval t
Vt = volume of rainwater in the tank at the end of time interval t
Qt = volume of rainwater that enters the tank during time interval t
Dt = demand (volume of water that is removed from the tank) during
time interval t
S = maximum storage capacity.

The second approach, the yield-before-spill (YBS) approach, effectively does not allow the
tank to spill during the time step. It collects all the inflow, and satisfies the full demand. If
any surplus remains at the end of the time step, this surplus is spilled. This has the opposite
effect on the tank capacity and thus overestimates the water which can be supplied by the
tank. This approach is described by the following equations (Fewkes, et al., 2000; Liaw, et
al., 2004; Palla, et al., 2011).

𝑌𝑡 = 𝑚𝑖𝑛 𝐷𝑡 ; 𝑉𝑡−1 + 𝑄𝑡

3-4

𝑉𝑡 = 𝑚𝑖𝑛 𝑉𝑡−1 + 𝑄𝑡 − 𝑌𝑡 ; 𝑆

3-5

Where the symbols are as described above.

3.3.3 Expressing the reliability of a rainwater tank

The performance of a rainwater tank could be assessed by either the volumetric reliability
(water-saving efficiency) or a time-based reliability. The volumetric reliability is calculated by
dividing the total volume of rainwater supplied by the tank by the total volume of water
which is required during the simulation period (total demand). The time based reliability is a
measure of the amount of time for which the tank provides the total amount of water

17

demanded. It can be calculated by dividing the number of time-steps when the full demand
is met by the total number of time-steps (Liaw, et al., 2004; Palla, et al., 2011).

The volumetric reliability method is not as greatly influenced by the choice of time-step. It
also has the advantage of taking into account all of the water that the tank provides. The
time-based reliability disregards any water supplied by the tank when the demand is only
partially met and, consequently, the time-based reliability will be zero for all tank volumes
below a certain size, whereas the volumetric reliability will reflect values which continue to
decrease with tank size (Liaw, et al., 2004; Mitchell, 2007; Palla, et al., 2011).

3.3.4 Selecting the operating rule

Figures 3-4 and 3-5 show graphical representations of the computational process for a single
time-step for the yield-before-spillage and yield-after-spillage operating rules respectively.
The figures show the temporary storage which is created by using the yield-before-storage
operating rule, as well as the reduced effective capacity that results from using the yieldafter-spillage operating rule. By comparing the position of the final storage level in the two
figures it can be seen that the yield-after-spillage operating rule will provide storage
volumes which are lower than those obtained by using the yield-before-spillage operating
rule. The yield-after-spillage operating rule thus provides larger values for the required tank
size and is a more conservative operating rule than the yield-before-spillage operating rule.

Figure 3-4: The Yield-Before-Spillage operating rule for a single time-step (Mitchell, 2007)

18

Figure 3-5: The Yield-After-Spillage operating rule for a single time-step (Mitchell, 2007)

Liaw and Tsai (2004) investigated the effect of the operating rule on both the volumetric
and time based reliability of a rainwater tank. They found that the reliabilities determined
using the yield-before-spillage operating rule exceeded those calculated using the yieldafter-spillage operating rule. They also found that when using the yield-after-spillage
operating rule for tanks where the ratio of demand for a given time-step to storage capacity
was greater than 0.5, the time based reliability fell rapidly to zero. They also found that
there was a minimum storage capacity required for the time based reliability to exceed zero
and for these reasons they recommended using the yield-before-spillage operating rule.

Similarly, a study by Mitchell (2007) found that the yield-before-spillage operating rule
provided an overestimate of the volume of water which could be supplied by a tank. The
study also determined that the effect of the temporary storage or reduced effective
capacity was increased for a larger time-step. The author suggested using both of the
operating rules and taking the average of the two sets of results as the final result.

3.3.5 The time-step

The simplified sizing methods for rainwater tanks generally use a single average rainfall
value to estimate the required size of a rainwater tank. However, the use of an average
value disregards the variability of the rainfall and thus does not provide an accurate result.
19

As such, it is suggested that continuous simulations using smaller time-steps should be used
in order to obtain a realistic and appropriate tank size (Male, et al., 2006; Ward, et al.,
2010).

Fewkes and Butler (2000) determined that the selection of an appropriate time-step for
simulating a given rainwater tank should be based on the storage fraction of the given tank.
The study found that larger time-steps could be used for larger storage tanks, without
compromising the accuracy of the results obtained. The appropriate intervals for given timesteps are given below.

𝑆𝑓 = 𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝑓𝑟𝑎𝑐𝑡𝑖𝑜𝑛 =

𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝑉𝑜𝑙𝑢𝑚𝑒
𝐴𝑛𝑛𝑢𝑎𝑙 𝐴𝑣𝑒𝑟𝑎𝑔𝑒 𝐼𝑛𝑓𝑙𝑜𝑤 𝑉𝑜𝑙𝑢𝑚𝑒

=

𝑆 1000
𝑀𝐴𝑃 𝐴

3-6

Where S and A are as previously defined

Hourly models:

Sf ≤0.01

(small storage volumes)

Daily models:

0.01<Sf<0.125 (medium storage volumes)

Monthly models:

0.125≤Sf

(large storage volumes)

In Taiwan, simulations of rainwater tank behaviour are usually done using either a daily or a
10-day time-interval. The study conducted by Liaw and Tsai (2004) found that the use of a
10-day time-step greatly underestimated the amount of water that could be supplied by a
system. Similar to the study by Fewkes and Butler (2000), they found that the difference
between the results obtained using different time-steps was less pronounced when the
storage capacity was increased, thus suggesting that a larger time-step could be used for
larger storage tanks.

Mitchell (2007) suggested selecting an appropriate time-step depending on the ratio
between the average demand volume for the selected time-step and the storage volume of
the tank. The study found that results within 5% of the reference values (a simulation using
the yield-after-spillage operating rule with a 50 year data set using a 6 minute time-step)
could be obtained by adhering to the following:

20

For yield-after-spillage operating rule:

For yield-before-spillage operating rule:

Constant demand

𝐷𝑡 𝑆 < 0.7

3-7

Seasonal demand

𝐷𝐴𝑣𝑒 𝑆 < 0.35

3-8

Constant demand

𝐷𝑡 𝑆 < 0.18

3-9

Seasonal demand

𝐷𝐴𝑣𝑒 𝑆 < 0.09

3-10

If the ratio between the demand in a given time-step and the storage volume of the tank is
larger than the appropriate value given in Equations 3-7, 3-8, 3-9 and 3-10, selecting a
smaller time-step, will decrease the demand within a given time-step and thus decrease the
value of the ratio, if the maximum storage volume of the tank (S) remains constant.

3.3.6 Selecting the length of the simulation period

The length of the simulation period is determined by two considerations, namely the effect
on tank size relating to the volumetric reliability and possibly an effect on the required timestep.

The first consideration was investigated by Liaw and Tsai (2004). The study found that the
accuracy of the calculated volumetric reliability improved as the length of the simulation
period increased. As such they suggested using a record length of 50 years.

Mitchell (2007) further investigated the effect of an increased simulation period and found
that a 10-year simulation period provided results within 3% of those obtained by using a 50year simulation period. Consequently, the author suggested using a 10-year simulation
period, which was representative of the long-term rainfall trends at the site in question, as
this required less computational effort and was also easier to obtain than 50-year records,
but did not significantly compromise the accuracy of the results.

Mitchell (2007) also showed that the 10-year simulation period had the same level of
sensitivity to the selected time-step as the 50-year simulation period. Thus, the length of the
simulation period did not affect the selection of an appropriate time-step in any way. This
means that the length of the simulation can be selected independently of the time-step.
21

3.3.7 Selecting the initial condition

Mitchell (2007) determined that starting the simulation with an empty tank provided more
accurate long term estimates regardless of the period over which the simulation was run.
The author also commented that it was likely that a tank would be used as soon as it was
installed, rather than waiting for it to be filled first. Consequently, he suggested that the
simulation be started with an empty tank.

3.3.8 Ratio between rainwater demand and rainwater availability

Ghisi (2010) attempted to find a correlation between the ratio of rainwater demand to
availability on the one hand and the tank capacity on the other. Ghisi referred to the ratio as
factor F which is the inverse of the input ratio described by Fewkes and Warm (discussed in
section 3.3.1.1, above). No correlation between the ratio of rainwater demand to availability
on the one hand and the tank capacity on the other could be found. However, it was found
that the range of possible tank sizes is smaller for a higher value for factor F.

𝐹=

(𝐷𝑎𝑖𝑙𝑦 𝐷𝑒𝑚𝑎𝑛𝑑 ) (1000 )(365)

3-11

𝑅𝑜𝑜𝑓 𝐴𝑟𝑒𝑎 (𝑀𝐴𝑃 )

22

4 Method

4.1 Rainwater Tank Simulation

4.1.1 Operating rule

As discussed in section 3.3.4 above, two possible operating rules can be used to simulate
the behaviour of a rainwater tank, namely the yield-before-spill and the yield-after-spill
operating rules. This study uses the suggestion made by Mitchell (2007) that a simulation
should be run using both operating rules and then the average of the two sets of results
should be taken as the final result. This should provide more accurate results as the yieldbefore-spillage operating rule has been found to underestimate the required tank size and
the yield-after-spillage has been found to overestimate the required size. It is assumed that
taking the average of the two will balance the errors of the two rules and thus provide a
tank size which is closer to the actual size required.

4.1.2 Conservation of volume

The first step in simulating the behaviour of a rainwater tank was to set up the equations so
as to ensure conservation of volume throughout the simulation. Microsoft Excel was used to
perform the following sequence of calculations for each time-step.

4.1.2.1 Yield-after-spill

First the volume of rain water which can be collected from the tank is calculated

𝑉𝑃 =

𝐴∗𝑃𝑡

4-1

1000

23

The volume of rainwater which is added to the tank during the time-step is then the
minimum of the water that can be collected or the volume of empty space remaining in the
tank, as shown in Equation 4-2.
𝑄𝑡 = 𝑚𝑖𝑛 𝑉𝑃 ; 𝑆 − 𝑉𝑡−1

4-2

The volume of spillage, or overflow from the tank is then calculated as the difference
between the amount of rainwater which could be collected during the time-step and the
volume of water which was added to the tank, or zero, if this is less than zero.
𝑉𝑆 = 𝑚𝑎𝑥 𝑉𝑃 + 𝑉𝑡−1 − 𝑆 ; 0

4-3

The yield from the tank during the time-step is then equal to the demand during the timestep, or the amount of water in the tank at the beginning of the tank plus the amount of
water which has been added to the tank, whichever is smaller
𝑌𝑡 = 𝑚𝑖𝑛 𝐷𝑡 ; 𝑉𝑡−1 + 𝑄𝑡

4-4

Finally the volume of water in the tank at the end of the time-step can be calculated as the
volume of water in the tank at the beginning of the tank plus the volume of water which is
added to the tank during the time-step minus the yield from the tank during the time-step
𝑉𝑡 = 𝑉𝑡−1 + 𝑄𝑡 − 𝑌𝑡

4-5

Where:
Vp

=

Volume of precipitation on catchment

(m3)

A

=

Area of catchment

(m2)

Pt

=

Precipitation during time-step t

(mm)

Qt

=

Volume of water added to tank during time-step

(m3)

S

=

Maximum storage volume of tank

(m3)

Vt-1

=

Volume of water in tank at the beginning of time-step

(m3)

24

Vs

=

Volume of spillage

(m3)

Yt

=

Yield during time-step

(m3)

Dt

=

Water demand during time-step

(m3)

Vt

=

Volume of water in the tank at the end of the time-step

(m3)

4.1.2.2 Yield-before-spill

As for the yield-after-spill operating rule, the volume of rain water which can be collected
from the tank is calculated

𝑉𝑃 =

𝐴∗𝑃𝑡

4-6

1000

In the case of the yield-before-spill the yield during the time-step is calculated next. This is
the minimum of the demand during the time-step or the volume of water in the tank plus
the volume of water which is added to the tank during the time-step
𝑌𝑡 = 𝑚𝑖𝑛 𝐷𝑡 ; 𝑉𝑡−1 + 𝑉𝑃

4-7

Next the volume of spillage or overflow from the tank is calculated as the maximum of the
volume of rainfall which can be collected plus the volume of water that was in the tank at
the beginning of the time-step minus the maximum storage volume of the tank and minus
the yield from the tank during the time-step
𝑉𝑆 = 𝑚𝑎𝑥 𝑉𝑃 + 𝑉𝑡−1 − 𝑆 − 𝑌𝑡 ; 0

4-8

25

Finally the volume of water in the tank at the end of the time-step is then calculated as the
volume of water in the tank at the beginning of the time-step plus the volume of water
added to the tank during the time-step minus the yield from the tank and minus the volume
of spillage
𝑉𝑡 = 𝑉𝑡−1 + 𝑉𝑃 − 𝑌𝑡 − 𝑉𝑆

4-9

Where the symbols are as listed above.

4.1.3 Time-step

Studies by Fewkes and Butler (2000) and Mitchell (2007) provided methods for determining
the appropriate time-step. Both methods required using the tank volume to determine the
time-step. This created a problem, as the current study required a selected time-step to
determine an appropriate tank volume. A daily time-step was used as starting point and its
validity was subsequently checked once the tank volume had been determined.

4.1.4 Rainfall stations selected

Rainfall data for four rainfall stations (Kimberley, Mossel Bay, Punda Maria and Rustenburg)
obtained from the South African Weather Services was used for simulating a rainfall tank at
each location. The locations of the four stations can be seen in Figure 4-1, shown below. The
rainfall stations selected included three locations which have a long dry season, namely
Kimberley, Punda Maria and Rustenburg. These locations would thus require large tanks in
order to provide water throughout the dry period. Mossel Bay, however, receives rainfall
throughout the year, with no significant dry season, thus providing an indication of the
effect of abundant rainfall on the storage capacity of a rainwater tank.

26

Figure 4-1: Locations of the four rainfall stations

4.1.5 Length of simulation period

Mitchell (2007) suggested that a 10-year simulation period provided a good balance
between computational effort and accuracy. Liaw and Tsai (2004), however, showed that
the accuracy of a simulation would continue to improve, by as much as 3% as the length of
the simulation period increased. As each rainfall station had data for a 16 year period (19942009) readily available and the simulations were run using Microsoft Excel, the
computational effort demanded by a 16-year simulation period was not significantly greater
than that required for a 10 year period. Consequently the period from January 1994 to
December 2009 was used to simulate rainwater tanks at the four stations.

4.1.6 Initial tank condition

The simulations used a tank which was initially empty, as Mitchell (2007) had suggested that
doing so provided the best results and it was also considered to be the most likely scenario,
as the tank would be empty after installation.

27

4.1.7 Effect of demand

Both the DAU and the tank volume in terms of DD are ratios which are dependent on the
daily demand which will be extracted from the tank. The magnitude of the daily demand will
thus have no effect on the simulation results as long as the demand remains constant for
the duration of the simulation period. This can be confirmed by comparing the results of the
simulation for 90% volumetric reliability at Kimberley for 100 l/day to the results obtained
when the demand is changed to 150 l/day, these can be seen in Table 4-1, below. As
expected, there was no difference in the required DD obtained for a given value of DAU.
This clearly showed the advantage of using the dimensionless approach, as it allows the
same design curves to be used for any value of demand.

Table 4-1 Effect of a changing a constant demand from 100 l/day to 150 l/day

Dimensionless area units
1.5
2
2.5
3
3.5
4
4.5
5
5.5
6
6.5
7
7.5
8
8.5
9
9.5
10

100l/d
Days of Demand
109.7106
98.5475
89.2081
83.5493
80.1511
77.0900
74.0566
71.8348
69.6333
67.4506
65.5462
63.7439
61.9984
60.6486
59.3995
58.2509
57.2067
56.1673

28

150l/d
Days of Demand
109.7106
98.5475
89.2081
83.5493
80.1511
77.0900
74.0566
71.8348
69.6333
67.4506
65.5462
63.7439
61.9984
60.6486
59.3995
58.2509
57.2067
56.1673

Figure 4-2 shows the results of a simulation done using a constant demand and one done
after adjusting the demand to account for the fact that less water will be used when there is
less water available in the tank. In the latter case, the demand was assumed to decrease by
50% when the tank was less than 50% full. From the figure it was clear that the effect of a
variable demand on the simulation results is significant and thus results based upon a
constant demand could not be assumed to hold true for a variable demand. Using a
constant demand is thus a conservative approach, for tanks with DAU >2.

Kimberley (90%)
160
140

DD (days)

120
100
80
Constant
60

Variable

40
20
0

0

2

4

6

8

10

DAU

Figure 4-2: Comparison of constant and variable demand

4.1.8 Describing the reliability of the tank

A decision had to be made as to how the tank reliability would be calculated. Based on the
literature review, two possible approaches could be followed:

29



The volumetric reliability of a rainwater tank is the ratio of the total volume of water
supplied by the tank to the total water demand over the simulation period.



The time based reliability is a measure of the amount of time for which the tank
provides the total amount of water demanded.

The volumetric reliability is less affected by the time-step which is used for simulation as
the time based reliability ignores any time step where the demand is greater than the
supply. The volumetric reliability also considers all of the water supplied by the tank,
whereas the time based reliability does not take the water supplied during a time-step
where the entire demand cannot be met into account. It is for these reasons, that the
volumetric reliability was used rather than time based reliability.

The volumetric reliability is determined by:

𝑅𝑉 =

𝑌𝑡

4-10

𝐷𝑡

Where RV is the volumetric reliability
Yt is the yield from the tank in a given time-step
Dt is the demand for the time-step.
The simulations calculated the volumetric reliability by using the average result of the yieldbefore-spill and the yield-after-spill operating rules.

30

4.2 Simplifying the Process

4.2.1 Reducing the variables

In order to simplify the sizing process, the number of variables was decreased. This was
done by combining the tank volume and the daily demand from the tank to obtain a number
of DD, as can be seen in the equations below. The roof area and MAP can also be combined,
as shown below, to obtain a “dimensionless area” for the roof size, the dimensionless area
unit (DAU) is the inverse of the factor F, used by Ghisi (2010) and is equal to the input ratio
described by Fewkes and Warm (2000).

The tank volume is described as DD defined in Equation 4-11 below
𝑡𝑎𝑛𝑘 𝑣𝑜𝑙𝑢𝑚𝑒
𝑑𝑎𝑖𝑙𝑦 𝑑𝑒𝑚𝑎𝑛𝑑

𝑚3

= 𝑚3

= 𝐷𝐷

4-11

𝑑𝑎𝑦

The DAU could then be described as:
𝑅𝑜𝑜𝑓 𝐴𝑟𝑒𝑎 × 𝑀𝐴𝑃
𝐷𝑎𝑖𝑙𝑦 𝐷𝑒𝑚𝑎𝑛𝑑

Where

=

𝑚 2 ×𝑚𝑚 𝑦𝑒𝑎𝑟
𝑚3
𝑑𝑎𝑦

=

𝑚 2 ×𝑚 𝑑𝑎𝑦
3
1000 ×365×𝑚

= 𝐷𝐴𝑈
𝑑𝑎𝑦

DD

Days of Demand

DAU

Dimensionless Area Units

4-12

The DD is an indication of the tank size and the DAU provides an indication of the theoretical
maximum amount of rain water that will be able to enter the tank. By using Equations 4-11
and 4-12 a number of data points can be obtained for the DD versus DAU for a particular
weather station. The effect of tank size, daily demand, roof size and MAP are all
incorporated into these graphs.
31

The spreadsheet, which was created to simulate the rainwater tank, provided the
volumetric reliability as a percentage of the total water demand which was supplied by the
tank. This was used to plot graphs of DD versus DAU for various percentages of demand
supplied. As mentioned previously, the current study assumed that the tank would be used
for household water supply, such as flushing of toilets and not for garden irrigation, as this is
not a necessity. Thus, a high reliability was required for the supply. Consequently the graphs
were plotted for 90, 95 and 98 percent of the required demand being supplied by the tank.

4.2.2 Calibrating the model

A series of data points was extracted from the time simulations and plotted on a DAU versus
DD plot, thus defining relationships for different supply reliabilities at each location. This
data was further compacted to a few modelling constants by fitting least-square curves
through the data points in order to obtain the local design graphs.

4.2.3 Directly predicting the modelling constants

The modelling constants, described above were compared with numerous simplified
parameters obtained from the daily rainfall records in an effort to find a meaningful
relationships. If reliable relationships could be found, the proposed design procedure could
be applied based on summary statistics. The parameters obtained from the daily rainfall
records included, but were not limited to:


the MAP



the average percentage of the MAP that falls in the driest month



the average percentage of the MAP that falls in the driest 6 months per month
(calculated as the total volume of rainfall in the driest 6 months divided by 6 and
averaged over all of the years)

32



the average longest number of consecutive dry days (calculated as the average of
the longest number of consecutive dry days found each year)



the longest number of consecutive dry days during the simulated period.

4.3 Verification of the Time-Step

After the tank sizes had been calculated, it was possible to check the validity of using a daily
time-step for the simulations. This was done using both guidelines, described in section
3.3.5.

The first guideline, as suggested by Fewkes and Butler (2000) is defined by Equation 3-6 and
the relevant limits as discussed in section 3.3.5.

Introducing the DAU, given by Equation 4-12 in section 4.2.1 the guidelines can be adapted
for use with the graphs of DAU versus DD.

By rewriting Equation 4-12:
1000
𝑀𝐴𝑃 𝐴

=

1

4-13

𝐷𝐴𝑈 (365) 𝐷𝑡

Then substituting 4-14 into Equation 3-6:

𝑆𝑓 =

𝑆

4-14

𝐷𝐴𝑈 (365)(𝐷𝑡 )

33

Equation 4-11, defining the DD can then be applied to 4-15 to obtain:

𝑆𝑓 =

𝐷𝐷

4-15

𝐷𝐴𝑈 (365)

Then applying the limits as stated in section 3.3.5:

𝑆𝑓 =

𝐷𝐷
𝐷𝐴𝑈 365

≤ 0.01

4-16

Rearranging 4-16:
𝐷𝐷 ≤ 3.65(𝐷𝐴𝑈)

4-17

Using the same technique for the other limits, the following equations are obtained:
Hourly models :

𝐷𝐷 ≤ 3.65(𝐷𝐴𝑈)

4-18

Daily models :

3.65 (DAU) < 𝐷𝐷 < 45.625 (𝐷𝐴𝑈)

4-19

Monthly models :

𝐷𝐷 ≥ 45.625 (DAU)

4-20

Mitchell (2007) suggested that in order to use a daily time-step for simulations where a
constant demand is assumed a second set of intervals should be used. The intervals are
defined by Equation 3-7 and Equation 3-9, given in section 3.3.5.

Using Equation 4-11, for the DD:
For yield-after-spillage operating rule:

DD > 1/0.7 > 1.429 days

4-21

For yield-before-spillage operating rule:

DD > 1/0.18 > 5.556 days.

4-22

The first set of intervals as defined by Equation 4-18, Equation 4-19 and Equation 4-20,
provides an indication of the time-step which should be used depending on both the DAU
34

and the DD. The second set of intervals, defined by Equation 4-21 and 4-22, is only
dependent on the DD. However the second set of intervals also provides a way of checking
the reliability of the two different operating rules. The two sets of intervals provided vastly
different intervals, due to this, both sets of intervals are considered.

To investigate the validity of the daily time-step, the two sets of intervals were plotted on
the same set of axes used for the simulated graphs. The plot obtained can be seen in
Figure 4-3 below. In order for a daily time-step to be the best choice, all of the data points
should fall within the shaded area of the graph.

Figure 4-3: Plot showing the valid interval for a daily time-step

35

5 Results

5.1 Rainwater Tank Simulation

5.1.1 Graphs obtained

The simulation process provided a set of data points (DAU and DD) for each of the
volumetric reliabilities at each of the stations selected. These data points were plotted in
order to obtain a set of simulation curves at each of the four stations. These curves can be
seen in Figures 5-1, 5-2, 5-3 and 5-4 below.

Kimberley
250

DD (days)

200

150
98%
100

95%
90%

50

0
0

2

4

6
DAU

Figure 5-1: Simulation curves for Kimberley

36

8

10

Mossel Bay
250

DD (days)

200

150

98%
100

95%
90%

50

0
0

2

4

6

8

10

DAU

Figure 5-2: Simulation curves for Mossel Bay

Punda Maria
250

DD (days)

200

150
98%
100

95%
90%

50

0
0

2

4

6

8

DAU

Figure 5-3: Simulation curves for Punda Maria

37

10

Rustenburg
250

DD (days)

200

150

98%
100

95%
90%

50

0
0

2

4

6

8

10

DAU

Figure 5-4: Simulation curves for Rustenburg

The graphs showed that tank sizes must be significantly larger for smaller DAU. This was an
expected result as the DAU provides an indication of how much more water can be captured
than would be required to meet the demand. Thus, at smaller values of DAU, a larger
portion of the water which is available for capturing must be captured. To do this, a larger
tank is required to capture larger volumes. The graph for 98% reliability at Punda Maria was
not included, as the required tank size was considered to be unreasonably large.

The design curves for Mossel Bay (Figure 5-2) showed that the tank volumes required to
meet the demand there were significantly lower than those required for the other stations.
This could be attributed to the fact that Mossel Bay is situated in a year-round rainfall
region, whereas all three of the other stations are located in the summer rainfall region. This
leads to relatively smaller tank sizes being required in Mossel Bay, as there is no significant
dry period. The other stations received relatively lower rainfall during the winter months
and thus, tanks must be large enough to capture enough of the rainfall during the summer
38

months to ensure enough water is available during the winter months. A similar result for
tank sizes would be expected for winter rainfall regions as were obtained for summer
rainfall regions. This shows clearly that rainwater tanks are more effective in year-round
rainfall regions, as would be expected.

5.1.2 Range of possible tank sizes

Table 5-1 shows the range of tank sizes obtained when considering all of the rainfall stations
for 2.5, 5, 7.5 and 10 DAU as well as the difference between the largest and smallest sizes
obtained in all regions. For a given volumetric reliability (90%, 95% and 98%) the difference
between the largest and smallest tank sizes across the four stations decreases as the DAU
increases. This suggests that the rainfall region has somewhat less of an effect on the
required tank size when the area of the roof used as a catchment is large (roof size will
increase the volume of rain which can be captured in a year and will thus increase the DAU).
Conversely, when comparing the difference between the largest and smallest tank sizes for
a given dimensionless area unit, it can be seen that the range increases as the volumetric
reliability increases. From this it can be seen that the effect of rainfall region becomes more
pronounced when a higher volumetric reliability is required.

39

Table 5-1: Range of tank sizes obtained
Dimensionless Area units

Largest Tank size (days)

Smallest Tank size (days)

Difference (days)

2.5

127.5

25.4

102.1

5.0

104.0

19.3

84.6

7.5

95.7

17.6

78.1

10.0

89.0

17.0

78.1

2.5

161.4

35.3

126.1

5.0-

132.8

26.9

105.8

7.5

121.5

24.8

96.7

10.0

114.5

23.8

90.7

2.5

227.3

53.5

173.8

5.0

157.0

36.9

120.1

7.5

149.3

34.8

114.4

10.0

144.7

33.4

111.3

90% Volumetric Reliability

95% Volumetric Reliability

98% Volumetric Reliability

5.1.3 Local design curves

From the data points obtained from the simulations (Figures 5-1, 5-2, 5-3 and 5-4) it can be
seen that all the simulations produce curved results, with the highest tank volumes obtained
at the lowest DAU. In addition to this, all the results tend toward being parallel to the y-axis
for small DAU and parallel to the x-axis for large values of DAU, but they are not asymptotic
to the x and y axes. This suggests that curves with the same general shape could be fitted to
the simulated data.

The general shape of the simulations appear to be similar to that of a power function with a
negative exponent which would have the general equation y = axb, this was confirmed by
fiting trend lines to the data and comparing the coefficients of determination obtained.
Table 5-2 shows the various coefficients of determination, with the largest value for each
40

data set highlighted in yellow. The table shows that the power function provided the best
correlation in all but one case. However due to the fact that the data points are not
asymptotic to the x and y axes the general equation was adapted to DD=a(DAU-1)b+c. Using
the equation DD=a(DAU-1)b+c (where b is always a negative value) a local design curve can
be fitted to the data for each of the reliabilities at each location. These curves are
asymptotic to DD=c (the red line in Figure 5-5), which corresponds to the minimum tank
volume as determined by each simulation. The curves are also asymptotic to DAU=1 (the
green line in Figure 5-5), which corresponds to the minimum dimensionless area unit which
can be used to obtain 100% volumetric reliability (this is where the maximum amount of
water which can be captured per year is equal to the water demand for a year).

Table 5-2: Table of coefficients of determination for trend lines

Linear

R2 values
Logarithmic

90%
95%
98%

0.9343 0.8772
0.9551 0.9185
0.9246 0.8835

0.9853
0.9933
0.9717

0.9738 0.9983
0.9766 0.9942
0.9461 0.9823

90%
95%
98%
Punda Maria
90%
95%
Rustenburg
90%
95%
98%

0.7276 0.625
0.6945 0.5823
0.6531 0.5649

0.8177
0.7785
0.7746

0.8627 0.9014
0.8272 0.8757
0.8492 0.8502

0.9323 0.8816
0.8878 0.838

0.9872
0.9607

0.9858 0.9982
0.9509 0.9833

0.8798 0.8291
0.8282 0.7636
0.7935 0.7569

0.9631
0.9235
0.8978

0.9598 0.9852
0.9336 0.9622
0.9616 0.9232

Exponential

Polynomial

Power

Kimberley

Mossel Bay

41

DD=c and DAU=1

250

200

DD=14.63(DAU1)^-1.08+15.78

DD (days)

150

DD=c=15.78

100

DAU=1
50

0
0

2

4

6

DAU

8

10

Figure 5-5: Graph showing DD=a(DAU-1)b+c, DD=c and DAU =1

Figures 5-6, 5-7, 5-8 and 5-9 show the fitted curves obtained for each of the stations, with
Table 5-3 showing the values of a, b and c as well as the coefficient of determination for
each of the curves. The values obtained for the coefficients of determination are all close to
1 (0.9447 to 0.9996), consequently the curves can be considered to be reasonably close to
the data obtained from the simulations.

42

Kimberley
250

DD (days)

200

150

98%
100

95%
90%

50

0
0

2

4

6

8

10

DAU

Figure 5-6: Local design curves for Kimberley

Mossel Bay
250

DD (days)

200

150
98%
100

95%
90%

50

0
0

2

4

6

8

DAU

Figure 5-7: Local design curves for Mossel Bay

43

10

Punda Maria
250.00

DD (days)

200.00

150.00
95%

100.00

90%
50.00

0.00
0

2

4

6

8

10

DAU

Figure 5-8: Local design curves for Punda Maria

Rustenburg
250

DD (days)

200

150
98%
100

95%
90%

50

0
0

2

4

6

8

DAU

Figure 5-9: Local design curves for Rustenburg

44

10

Table 5-3: Constants of local design curves
c

R2

a

b

90%

62.3

-0.475 36.738 0.9597

95%

72.606 -0.369 52.84

0.9447

98%

76.241 -0.334 71.70

0.9558

90%

14.633 -1.08

0.9912

95%

21.845 -0.931 20.998 0.9996

98%

33.302 -0.942 28.858 0.982

Kimberley

Mossel Bay
15.78

Punda Maria
90%

104.27 -0.365 31.06

0.9762

95%

112.96 -0.274 54.08

0.9936

90%

85.627 -0.351 50.94

0.9933

95%

102.39 -0.431 74.709 0.9984

98%

141.73 -0.594 102.53 0.9501

Rustenburg

5.2 Generalising the Modelling Constants

5.2.1 Parameters considered

A number of parameters were determined from the rainfall data provided by the South
African Weather Services and compared to the constants in Table 5-2 above in order to find
a correlation. These parameters included: the MAP, the number of months per year in
which less than a given percentage of the MAP was recorded, the average monthly
percentage of MAP recorded in the driest six months and the average of the longest number
of consecutive days without rain per year, to name but a few. In most cases the results were
not useful, as no correlation could be found. The following sections discuss the most
significant results only.

45

5.2.2 Effect of MAP on tank size

Figures 5-10, 5-11 and 5-12 show the plots of a, b and c versus the MAP, respectively. The
plots clearly show that there was no correlation between the MAP and any of the constants.
The coefficient of determination obtained when fitting trend lines to the data ranges from
0.0061 to 0.3753, confirming that there is no correlation between the MAP and any of the
constants. This confirmed that the MAP should not be considered to be the determining
factor when sizing a rainwater tank. Even if a large amount of rain is expected at a given
location, if the rain is seasonal, a large tank will still be required.

Graph of a vs. MAP
700
600

MAP (mm/year)

500
400
90%
300

95%
98%

200
100

0
0

20

40

60

80

100

a

Figure 5-10: Graph of a vs. MAP

46

120

140

160

Graph of b vs. MAP
700
600

MAP (mm/year)

500
400

90%
300

95%
98%

200
100
0
-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

b

Figure 5-11: Graph of b vs. MAP

Graph of c vs. MAP
700
600

MAP (mm/year)

500
400
90%
300

95%
98%

200
100
0
0

20

40

60

80

c

Figure 5-12: Graph of c vs. MAP

47

100

120

5.2.3 Best correlation for a

Figure 5-13 shows the plot of a versus the average percentage of the MAP that fell in the
driest 6 months per month. This provided the best correlation to a. This was calculated as
the total rainfall in the driest 6 months divided by 6 and averaged over all of the years, and
taken as a percentage of MAP. The percentage of rain which fell in the driest 6 months
provides a good indication of the seasonality of the rainfall as 8.3% of MAP would normally
be expected in every month for a location where the rain was evenly distributed. As the
value of the percentage of MAP decreased the driest 6 months would be drier and the other
6 months would be wetter, thus the seasonality of the rainfall must be increased. The figure
shows the general trend that a will be higher when the seasonal variation of rainfall at the
location was greater, which would in turn increase the tank sizes obtained from the
equation. It would also have an effect on how quickly the tank sizes decreased: an increased
value for DAU (a larger a value would cause the graph to curve more, causing the tank size
to drop faster initially, but then stabilise more quickly for larger dimensionless area unit
values). This result clearly shows the impact of rainfall region on the required tank size.

48

Average % monthly rainfall in driest 6 month period

Graph of a vs average % rainfall per month in
driest 6 months
7
6
5
4
90%

3

95%

2

98%

1
0
0

20

40

60

80

100

120

140

160

a

Figure 5-13: Best correlation for a

5.2.4 Best correlation for b

The best correlation for b to all of the parameters tested was found when comparing b to
the average longest number of consecutive dry days (calculated as the average of the
longest number of consecutive dry days found each year). However, the parameter did not
correlate closely with b, as can be seen in Figure 5-14 below. The correlation with the
average number of consecutive dry days, once again confirmed the significance of the
rainfall region in determining the required tank size. Parameter b had an effect on the
magnitude of the tank volume. It also had an overwhelming effect on the curved shape of
the graph. When b decreased (all values of b are be negative) the graph would have a
steeper curve and the required tank volume would decrease more quickly and then, once
again, stabilise more quickly.

49

Graph of b vs average of longest number of
consecutive dry days
120

Number of days

100
80
60

90%

40

95%
98%

20
0
-1.4

-1.2

-1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

b

Figure 5-14: Best correlation for b (note that there is no constant progression from (90% to 98%)

5.2.5 Best correlation for c

In the case of parameter c the correlation was logically determined by recognising that the
value of c for a 100% volumetric reliability would be equal to the longest number of
consecutive days with no rainfall which occurred during the simulation period. This would
provide the smallest tank size which would contain enough water to meet the demand for
those consecutive dry days. Thus the correlation between c and the longest number of
consecutive dry days would be the line y = x and would pass through the origin.
Consequently, it should not be surprising that the best correlation for c was obtained when
comparing c to the longest number of consecutive dry days and ensuring that the trend lines
passed through the origin, as shown in Figure 5-15. Unlike parameters a and b, parameter c
only had an effect on the magnitude of the required tank size. As c was equal to the
minimum tank size which was required to obtain a given volumetric reliability, it did not
have any effect on the curvature of the graphs. Once again the best correlation was

50

obtained by comparing the constant to a parameter related to the seasonality of the rainfall,
which once again confirmed the importance of rainfall region in determining required tank
size.

Graph of c vs Longest number of consecutive
days with no rainfall
Consecutive days with no rainfall

200
180
160
140
120
90%

100

95%

80

98%

60

100%

40
20
0
0

50

100

150

200

c

Figure 5-15: Best correlation for c

5.3 Proposed Sizing Method

By using the graphs of the best correlations for a, b and c (Figure 5-13, 5-14 and 5-15), it was
possible to size a tank by reading the values of the constants from the graphs and then using
the equation DD=a(DAU-1)b+c to obtain a generalised design curve relating the tank volume
in DD to the DAU. Once the generalised design curve has been obtained, the roof area can
be used to determine the DAU which correspond to the roof size at the given location and,
from there, the required tank size can be directly calculated.

51

The proposed method for sizing a rainwater tank could be illustrated the following
hypothetical design example for a house with a roof area of 75 m 2 in an area where the
MAP is 950 mm/year, the average number of consecutive dry days is 70 days/year and the
driest six months contribute on average, 5% to the MAP. If water were to be withdrawn at a
constant daily rate of 100 l/day (typical for four people in rural South Africa using
25 litre/capita/day), what tank size would be required to assure the supply at 90%, 95% and
98%?

Figures 5-13, 5-14 and 5-15are not verified sufficiently for such general application. Should
future work succeed in fairly robust correlations, then they could be used as demonstrated
below.

DAU

=

(75*950)/(1000*365*0.1)

=

1.952

Reading from Figures 5-14, 5-15 and 5-16:
a

=

36 (90%) or 46 (95%) or 54 (98%)

b

=

-0.42 (90%) or -0.34 (95%) or -0.46 (98%)

c

=

18 (90%) or 28 (95%) or 42 (98%)

DD

=

a(DAU-1)b+c =

54.75days(90%) or 74.77days(95%) or 97.23days(98%)

Tank volume =

DD * Daily Demand

Tank volume =

5.475 m3 (90%) or 7.477 m3 (95%) or 9.723 m3 (98%) m3.

The method described above will be referred to as the dimensionless sizing method (DSM)

52

5.4 Testing the Validity of the Time-step

Using the method described in section 4.3, the following equations provided limitations for
using a daily time-step:
From the suggestion by Fewkes and Butler (2000):
3.65 (DAU) < DD < 45.625 (DAU)
From the suggestion by Mitchell (2007):
For yield-after-spillage operating rule for constant demand

DD>1/0.7 > 1.429 days

For yield-before-spillage operating rule for constant demand

DD>1/0.18 > 5.556 days

Figures 5-16, 5-17 and 5-18 show the graphs obtained by plotting these equations, along
with the simulation results for each of the volumetric reliabilities, on the same set of axes.
The shaded area shows the region where the selection of a daily time-step would be a valid
choice. The points which lie above the shaded area are points which could rather be
obtained by using a monthly time-step in the simulation. Thus, these points have been
found by a simulation which is computationally more taxing due to using the smaller timestep. However, the accuracy of these values has not been compromised by selecting a
smaller time-step. Unfortunately the accuracy of the points which fall below the shaded
area (for Mossel Bay) were compromised by the selection of the daily time-step. In order for
the results obtained for Mossel Bay to be as accurate as possible, an hourly time-step
should have been selected.

53

Figure 5-16: Validity of time-step for 90% volumetric reliability

Figure 5-17: Validity of time-step for 95% volumetric reliability

54

Figure 5-18: Validity of time-step for 98% volumetric reliability

5.5 Testing the Accuracy of the Design Curves

5.5.1 Local design curves (i.e curves for Kimberley, Mossel Bay, Punda Maria and
Rustenburg)

Figures 5-6, 5-7, 5-8 and 5-9 showed the localised design curves that were obtained by
fitting curves with the general equation DD=a(DAU-1)b+c to the data obtained by simulating
the tank behaviour. As discussed before, the curves showed a close correlation to the
simulated data. However the curves for low values of DAU (especially DAU<2) were less
accurate. The third column of Table 5-4 below, shows the maximum difference, in terms of
DD, between the tank size obtained by simulating the tank behaviour and that found by
using the local design curves (positive values are overestimates, negative values are underestimates). The maximum difference between the simulated data and the local design
curves was always found at 1.5 or 2 DAU, with a maximum value of 13.62 days reflected for
55

90% volumetric reliability at Kimberley. For dimensionless area values of 5 or above the
difference was less than 7.7 for all of the local design curves.

Table 5-4: Difference in required tank size determined by simulation and local design curves or
generalised design curves
Location

Volumetric
Reliability
(%)

Max
difference Max
difference Max
difference
between simulation between
simulation between local and
and local (days)
and generalised (days) Generalised (days)

90
95
98

13.62
11.74
5.85

17.25
16.90
49.77

-7.18
-11.60
43.92

90
95
98

4.51
-1.26
-8.17

-5.14
-4.28
-22.00

-9.65
-3.02
-19.93

90
95

13.49
4.92

31.09
24.79

17.60
24.26

90
95
98

5.77
2.21
-13.38

24.51
43.07
49.57

22.97
42.51
50.52

Kimberly

Mossel Bay

Punda Maria

Rustenburg

5.5.2 Generalised design curves (i.e. curves obtained using the DSM)

The straight line graphs shown in Figure 5-13, 5-14 and 5-15, along with the data obtained
for each of the rainfall stations were used to determine the equation for the size of the
rainwater tank with respect to the DAU for each of the volumetric reliabilities at each of the
stations. These generalised design curves were then used to obtain a set of data points
which could be compared to the data obtained from the simulations.

Figures 5-19, 5-20, 5-21 and 5-22 show the comparisons between the simulated data points
(markers) and the generalised design curves (solid lines). Table 5-5 provided the values of
the coefficient of determination for each of the graphs obtained using the DSM when
compared to the results obtained from the simulations. The coefficient of determination
56

ranged from 0.9307 for Kimberley at 95% volumetric reliability to 0.9997 for Mossel Bay,
also at 95% volumetric reliability. As these values were all reasonably close to 1, the graphs
did provide results which related to the simulated results. Generally, the curved shape of
the graphs was reasonably close to the simulated data. However in some instances the
magnitude of the required tank volume was not accurate. This was especially evident in the
graphs obtained for Rustenburg (Figure 5-22), where the DSM provided a significant
overestimate of the required tank size. None of the generalised design curves had a
coefficient of determination as close to 1 as the corresponding local design curve, clearly
showing a decrease in accuracy caused by generalising the modelling constants.

The fourth column of Table 5-4 shows the difference in tank size determined by simulation
compared to that found using the generalised design curves.

When the differences

between the simulated data and the local design curves were compared to the differences
between the simulated data and the generalised design curves, it was clear that the local
design curves were significantly more accurate than the generalised design curves. Unlike
the local design curves, the difference between the simulated data and the generalised
design curves did not always decrease significantly for larger DAU. In fact the largest
differences found for Rustenburg were found at DAU of 10.

The final column of Table 5-4 shows the maximum difference in tank volume when the local
design curves were compared to the generalised design curves. The differences found
between the local and generalised design curves were significantly larger than the
differences found when comparing the simulated values to the local design curves. This
suggested that the error created by generalising the modelling constants was more
significant than the error introduced by fitting curves to the data to obtain the local design
curves.

57

Kimberley

250

200

98% Simulated
data
95% Simulated
data
90% Simulated
data
98% Generalised
design curves
95% Generalised
design curves
90% Generalised
design curves

DD (days)

150

100

50

0
0

2

4

DAU

6

8

10

Figure 5-19: Comparison of simulation to DSM for Kimberley

Mossel Bay
250

98% Simulated
data

Tank Volume (days)

200

95% Simulated
data
90% Simulated
data

150

98%
Generalised
design curves
95%
Generalised
design curves
90%
Generalised
design curves

100

50

0
0

2

4

6

8

10

Dimensionless Area Units

Figure 5-20: Comparison of simulation to DSM for Mossel Bay

58

Punda Maria
250

Tank Volume (days)

200

95% Simulated
data

90% Simulated
data

150

95%
Generalised
design curves
90%
Generalised
design curves

100

50

0
0

2

4

6

8

10

Dimensionless Area Units

Figure 5-21: Comparison of simulation to DSM for Punda Maria

Rustenburg
250

98% Simulated
data

Tank Volume (days)

200

95% Simulated
data

150

90% Simulated
data
100

98% Generalised
design curves
95% Generalised
design curves

50

90% Generalised
design curves

0
0

2

4

6

8

10

12

Dimensionless Area Units

Figure 5-22: Comparison of simulation to DSM for Rustenburg

59

Table 5-5: Coefficient of determination for the DSM when compared to the simulated results

R2
Kimberley
90%
95%
98%

0.9453
0.9307
0.9331

90%
95%
98%
Punda Maria
90%
95%
Rustenburg
90%
95%
98%

0.9924
0.9997
0.9789

Mossel Bay

60

0.9388
0.9813
0.9977
0.9794
0.9347

6 Conclusion

The aim of this study was to investigate the feasibility of a simplified sizing method for
rainwater tanks in South Africa, making use of rainfall data supplied by the South African
Weather Services, It began by simulating the behaviour of a rainwater tank and, on the
bases of the simulation results, attempted to develop a simplified sizing for rainwater tanks.

Initially, four rainfall stations from different rainfall regions in South Africa were identified
and the behaviour of a rainwater tank at each of the four was simulated. Sets of data with
similar characteristics were obtained for the different volumetric reliabilities at each
weather station. In each case, the data produced a curve which was parallel to the y-axis for
small values of DAU and parallel to the x-axis for large values of DAU. Thus, the behaviour of
a rainwater tank could be approximated by using the general equation DD = a(DAU)b+c,
where a, b and c are constants which differ depending on the rainfall at the given location
and the required volumetric reliability of the tank.

The simulations were reflected graphically and it was noted that a change in the demand
would not affect the graphs obtained for DAU versus tank volume expressed as DD, as long
as the demand was constant for the duration of the simulation period. This was due to the
use of ratios that were dependent on the demand (i.e. water that would be extracted from
the tank) for describing both the tank volume and the size of the catchment area. However,
the proposed method could only be applied for a constant demand. Changing demand has a
significant effect on the shape of the graphs obtained. Assuming a constant demand leads to
a conservative result, as people who are reliant on their own rainwater supply tend to use
less water when the tank starts to run dry.

61

It was also found that when the constants a, b and c were compared to the MAP, there was
no correlation between any of the constants and MAP. This suggested that as long as the
total rainfall was sufficient to provide the demand required from the tank, the MAP did not
greatly affect the required tank volume.

In fact, the best correlation that could be identified for a was with the average percentage
of the MAP per month for the driest 6 months of the year. This provided an indication of the
seasonality of the rainfall, as the MAP was smaller in areas where 6 months of the year did
not receive rainfall and higher where all 12 months received rain. The best correlation found
for b was with the average number of consecutive dry days per year. The best correlation
for c was found to be with the longest number of consecutive dry days over the simulation
period. The best correlations with a, b and c were all found with terms which relate to the
seasonality of the rainfall. This suggested that the seasonality of the rainfall actually played
the most important role in determining the required tank size.

The seasonality of the rainfall and thus the geographic location of the rainwater tank played
the largest role in determining the required size of the rainwater tank. However, certain
other factors did play a role in determining the extent of the effect of the rainfall region on
the tank size. When comparing the possible range of tank sizes for a given volumetric
reliability, the range of tank sizes decreased as the DAU increased. This suggested that the
effect of location and thus, rainfall region, was less when the roof area was large. When the
ranges were compared, the range of possible tank sizes for a given dimensionless area unit
increased as the volumetric reliability increased. This suggested that the rainfall region
exercised a greater influence on the required tanks size when a higher volumetric reliability
was required.

When the limitations on using a daily time-step were considered, it was found that some of
the data points determined for the Mossel Bay weather station did not fall within the
acceptable region on the graph. This suggested that the accuracy of these points was
62

compromised and an hourly time-step should have been used for these points. Any future
research in this field will have to pay special attention to the required time-step.

The local design curves had coefficients of determination close to 1, which suggested that
the general equation: DD = a(DAU-1)b+c accurately represented the data obtained by
simulation. The coefficients of determination obtained when comparing the generalised
design curves to results obtained from the simulations were more distant from 1 than those
obtained for the local design curves. The difference between the local design curves and the
simulated data was also smaller than the difference between the generalised design curves
and the simulated data. This showed that there was a significant decrease in accuracy
between the local and generalised design curves. When considering the difference between
the local and generalised design curves, it was found that the error introduced by
generalising the design curves was larger than the error obtained when using the local
design curves. This suggested that the most significant improvement in the method of
rainwater tank sizing could be achieved by improving the generalisation of the modelling
constants.

Could the local curves be generalised in a better way? This depends on the nature of the
variability of a, b and c. If they show sharp and random variations in different parts of the
country it may only be possible to map it, producing maps similar to those for MAP and
mean annual evaporation (MAE) etc. It may also be possible that a, b and c relate well to
some other rainfall statistic, which may allow the correlation approach attempted in the
previous pages. This matter is pursued in the final chapter.

63

7 Recommendations for Future Research

Although the DSM shows promise, further research to improve the method would be
advisable. The results of this research clearly showed that the selection of a daily time-step
for Mossel Bay does not provide results that satisfy the time-step verification. Future
research should use hourly simulations for areas where the required tank sizes do not fit
within the region, shown in figure 4-3, for daily simulations.

It would be advisable to increase the number of rainfall stations selected for the study as
this would improve the likelihood of an accurate result. The results of the study also suggest
that the generalisation of the modelling constants should be improved. The possibility of
using parabolic functions rather than straight lines should be considered. It would also be
useful to expand the number of parameters investigated in order to obtain a better
correlation for b, as this study was unable to identify a significant correlation between b and
any of the variables considered.

Currently, the method proposes using equations of the form DD=a(DAU-1)b+c. However the
volumetric reliability is the ratio between the amount of water which has been captured by
the tank and the amount of water which is demanded, and the DAU are a ratio of the
maximum amount of water which could theoretically be captured by a tank and the amount
of water which is demanded from the tank. Thus, for the volumetric reliability to be met,
the DAU must be of the same or greater value as the volumetric reliability. If this were the
case, the graph would be asymptotic to the line DAU=Rv and not the line DAU=1 as
suggested by the current method. This would suggest that the method might be improved
by using the general equation DD=a(DAU-Rv)b+c. An additional improvement would be
obtained by better generalisation of the modelling constants.

64

An alternative to the graphs obtained for a, b and c should also be considered. It may be
that the constants show sharp and random variations across South Africa, which may make
it impossible to find mathematical relationships to describe these constants. This would
become evident with a large increase in the number of rainfall stations selected. In such a
case it may be necessary to use a mapping technique to map the constants across South
Africa. This would then produce maps similar to those for MAP and MAE.

It is also possible that the constants, may show better correlation to given parameters if the
stations are grouped into different climatic regions. In this case it would be beneficial to
separate the stations into groups depending on identified climatic regions and develop a
separate set of graphs for each of the regions.

65

8 References
Centre for Science and Environment Design of storage tanks [Online] // Rainwater
harvesting. -

Centre

for

Science

and

Environment. -

10

08

2011. -

http://www.rainwaterharvesting.org/urban/design_storage.htm.
Domenech L. and Sauri D. A comparative appraisal of the use of rainwater harvesting in
single and multi-family buildings of the Metropolitan Area of Barcelona (Spain): social
experience, drinking water savings and economic costs [Journal] // Journal of Cleaner
Production. - 2011. - pp. 598-608.
DWAF Water Services Community Dataset [Report]. - Pretoria : Department of Water Affairs
and Forestry, 2007.
Fewkes A. and Butler D. Simulating the performance of rainwater collection and reuse
systems using behavioural models [Journal] // Building Services Engineering Research and
Technlogy. - 2000. - 2 : Vol. 21. - pp. 99-106.
Fewkes A.C. and Warm P. A method of modelling the performance of rainwater collection
systems in the UK [Journal] // Building Services Engineering Research and Technology. 2000. - pp. 257-265.
GDRC Global Development Research Centre [Online] // Rainwater guide. - 2007. - 4
November 2010. - http://www.gdrc.org/uem/water/rainwater/rainwaterguide.pdf.
Ghisi E. Parameters Influencing the Sizing of Rainwater Tanks for Use in Houses [Article] //
Water Resources Management. - 2010. - Vol. 24. - pp. 2381–2403.
Gold Coast City Council Interim Rainwater Tank Guidelines [Report] : Guidelines. - [s.l.] :
Gold Coast City Council, 2005.
Hamdan S.M. A literature based study of stormwater harvesting as a new water resource
[Journal] // Water Science & Technology. - 2009. - pp. 1327-1339.
Herrmann T. and Schmida U. Rainwater Utilisation in Germany: efficiency, dimensioning,
hydraulic and environmental aspects [Journal] // Urban Water. - 1999. - pp. 307-316.

66

Jacobs H.E. [et al.] Strategic assessment of Household On-Site Water as Supplementary
Resource to Potable Municipal Supply - Current Trends and Future Needs [Report]. - [s.l.] :
Water Research Commission, 2011. - ISBN 978-1-4312-0077-1.
Jacobs H.E. Assessing the impact of personal on-site water resources in serviced residential
areas on water demand and wastewater flow [Conference] // WISA Biennial Conference
2010. - Durban : Water Institute of Southern Africa, 2010.
Liaw C. and Tsai Y. Optimum Storage volume of rooftop rain water harvesting systems for
domestic use [Article] // Journal of the American Water Resources Association. - August
2004. - 4 : Vol. 40. - pp. 901-912.
Male J.W. and Kennedy M.S. Reliability of rainwater harvesting [Article] // Eco-Architecture:
Harmonisation between Architecture and Nature. - 2006. - Vol. 86. - pp. 391-400.
Mitchell V.G. How important is the selection of computational analysis method to the
accuracy of rainwater tank behaviour modelling? [Article] // Hydrological Processes. 2007. - Vol. 21. - pp. 2850–2861.
Mun M.Y. and Han J.S. Operational data of the Star City rainwater harvesting system and its
role as a climate change adaptation and a social influence. [Journal] // Water Science and
Technology. - 2011. - 12 : Vol. 63.
Mwenge Kahinda J. [et al.] A GIS-based decision support system for rainwater harvesting
[Journal] // Physics and Chemistry of the Earth. - 2009. - Vol. 34. - pp. 767-775.
Mwenge Kahinda J. [et al.] Develping suitability maps for rainwater harvesting in South
Africa [Journal] // Physics and Chemestry of the Earth. - 2008. - Vol. 33. - pp. 788-799.
Mwenge Kahinda J. and Taigbenu A.E. Rainwater harvesting in South Africa: challenges and
opportunities [Journal] // Physics and Chemistry of the Earth. - 2011.
Mwenge Kahinda J., Taigbenu A.E. and Boroto J.R. Domestic rainwater harvesting to
improve water supply in rural South Africa [Journal] // Physics and Chemistry of the Earth. 2007. - Vol. 32. - pp. 1050-1057.

67

Mwenge Kahinda J., Taigbenu A.E. and Boroto R.J. Domestic rainwater harvesting as an
adaption measure to climate change in South Africa [Journal] // Physics and Chemistry of
the Earth. - 2010. - Vol. 35. - pp. 742-751.
Palla A., Gnecco I. and Lanza L.G. Non-dimensional design parameters and performance
assessment of rainwater harvesting systems [Article] // Journal of Hydrology. - 2011. - 1 :
Vol. 40. - pp. 65–76.
Rahman A, Dbais J and Imteaz M Sustainability of Rainwater Harvesting Systems in
Multistorey Residential Buildings [Journal] // American Journal of Engineering and Applied
Sciences. - 2010. - 1 : Vol. 3. - pp. 73-82.
Rees D. and Ahmed S. Rainwater Harvesting [Online] // Practical action. - The Schumacher
Centre

for

Technlogy

and

Development,

Feb

2002. -

10

08

2011. -

http://practicalaction.org/docs/technical_information_service/rainwater_harvesting.pdf.
Slys Daniel Potential of rainwater utilization in residential housing in Poland [Journal] //
Water and Environment Journal. - 2009. - Vol. 23. - pp. 318-325.
Su M. [et al.] A probabilistic approach to rainwater harvesting systems design and
evaluation [Article] // Resources, Conservation and Recycling. - 2009. - Vol. 53. - pp. 393–
399.
Teh Tai Ring [et al.] Rainwater Harvesting as a Sustainable Water Supply Option in Banda
Aceh [Journal] // Desalination. - Nov 2009. - 1-3 : Vol. 248. - pp. 233-240.
Tetsoane S.T., Woyessa Y.E. and Pretorius E. Impact of rainwater harvesting on the
hydrology of Modder river basin [Conference] // WISA Conference 2008. - Sun City : WISA,
2008.
Texas Water Development Board The Texas Manual on Rainwater Harvesting [Report] :
Manual. - Austin, Texas : Taxas Water Development Board, 2005.
Ward S., Memon F.A. and Butler D. Rainwater harvesting: model-based design evaluation
[Article] // Water Science and Technology. - 2010. - 1 : Vol. 61. - pp. 85-96.

68

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