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Please cite this article in press as:Okoye, C.O., et al., Optimal sizingof storage tanks in domestic rainwater harvesting systems: A linear

programming approach. Resour Conserv Recy (2015), http://dx.doi.org/10.1016/j.resconrec.2015.08.015

ARTICLE IN PRESSG Model

RECYCL-3096; No.of Pages10

Resources, Conservation and Recycling xxx (2015)xxxxxx

Contents lists available at ScienceDirect

Resources, Conservation and Recycling

j ournal homepage: www.elsevier .com/ locate / resconrec

Optimal sizing ofstorage tanks in domestic rainwater harvestingsystems: A linear programming approach

Chiemeka Onyeka Okoyea, Oguz Solyalb,, Bertug Akntug c

a Sustainable Environmentand EnergySystems,Middle East TechnicalUniversity, Northern Cyprus Campus, Kalkanl,Mersin 10, Turkeyb Business Administration Program, Middle East TechnicalUniversity, Northern Cyprus Campus, Kalkanl,Mersin 10, Turkeyc Civil EngineeringProgram, Middle East TechnicalUniversity, Northern Cyprus Campus, Kalkanl, Mersin 10, Turkey

a r t i c l e i n f o

Article history:Received 6 July 2015

Received in revised form 25 August 2015

Accepted 27 August 2015

Available online xxx

Keywords:

Domestic rainwater harvesting

Sustainablewateruse

Tank storage

Linear programming

Cost optimization

a b s t r a c t

This paper proposes an optimization model to determine the optimal tank size of a single residentialhousing unit for rainwater harvesting and storage. Taking into account the site specific data such as

the rainfall profile, the roofarea of the building, the water consumption per capita and the number of

residents, an integrated optimization model based on linear programming is proposed to decide on the

size ofrainwater storage tank to build such that the net present value of the total tank construction

costs and freshwater purchase costs is minimized. The proposed model was tested ona case study from

Northern Cyprus, the results ofwhich emphasized the feasibility ofrainwater harvesting as a sustainable

supplement to thedepletingaquifers in the region. Thestudyalsooffersmanagerial insights on the impact

ofvarious parameters such as the number ofresidents, roofarea, discount rate, water consumption per

capita, unit cost ofbuilding the rainwater tank, and rainfall characteristics on the optimal tank size and

on the net financial benefit gained from rainwater harvesting through detailed sensitivity analysis.

2015 Elsevier B.V. All rights reserved.

1. Introduction

The quest to curb the menace of water scarcity has motivated

considerableresearchinterestin awiderangeof applicationsaimed

at providing a sustainable solution to ensure water security in

both rural and urban areas. Desalination, greywater harvesting,

rainwater harvesting (RWH), and virtual water are some of these

notable applications with proven documented research results

(Bani-Melhemet al., 2015; Jiang et al., 2015;Morales-Pinzn et al.,

2015; Scarborough et al., 2015). Among these alternatives, RWH

systems have stood out and their application has gained wider

acceptance (Aladenola and Adeboye, 2010; Morales-Pinzn et al.,

2015; Silva et al., 2015; Unami et al., 2015) because these systems

are not only sustainable means of supplementing available water

resources to overcome the chronic water scarcity but also proac-

tivewaysofmitigating themenaceof urban flood (Sampleand Liu,

2014).

Thedomestic useof freshwater accounts forapproximately 10%

of the total global freshwater consumption (Bocanegra-Martnez

et al., 2014). RWH has been widely applied for the domestic use

Corresponding author.

E-mail addresses: [email protected] (C.O.Okoye), [email protected]

(O. Solyal), [email protected] (B. Akntug).

under different climatic conditions (Domnech and Saur, 2011;

Hadadin et al., 2010; Silva et al., 2015; Ward et al., 2012). The

low-quality domestic use of rainwater includes but not limited

to toilet flushing, laundry, car washing, and irrigation (Villarreal

and Dixon, 2005), whereas the high-quality domestic use of har-

vested rainwater includes potable uses after some treatment.

Although the technology of RWH has been recommended for

areaswithannual rainfallabove1000mm(Aladenola andAdeboye,

2010), considerable research studies have been performed for the

areascharacterizedwithlowprecipitation(AbdullaandAl-Shareef,

2009;Domnech and Saur, 2011; Hadadin et al., 2012).

Various models ranging from behavioral (Liaw and Tsai, 2005;

Palla et al., 2011) to probabilistic (Basinger et al., 2010; Kim et al.,

2012; Su et al., 2009) have been used in the literature for the rain-

water harvesting practice. The assessment of suitability of some

models for domestic application was performed by Ward et al.

(2010). Campisano and Modica (2012) mentioned that the feasi-

bility of RWH systems depends entirely on the characteristic of

the rainwater storage tank, water demand pattern of households,

rooftop effective area of thebuilding, andrainfallprofileof thesite.

Similarly, Santos and Taveira-Pinto (2013) concluded that varia-

tion in rainfall profilehas themost significant effecton theoptimal

tank sizewhen they applied different criteria in the sizing of rain-

water storage tanks. Thementioned characteristics not only affect

the water saving efficiency but also the economy of the designed

http://dx.doi.org/10.1016/j.resconrec.2015.08.015

0921-3449/ 2015 Elsevier B.V. All rightsreserved.

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2 C.O. Okoye et al./ Resources, ConservationandRecycling xxx(2015) xxxxxx

Nomenclature

Acronyms

CV coefficient o f variation

IBR increasing block rate

LP linear programming

NFB net financial benefit

RWH rainwater harvesting

TDC total discounted costTL Turkish lira

Indices

j price levels

t periods of the year

Parameters

a costincurredperunitvolumeof rainwater tankbuilt

Acol area of the rooftop collector

btj cost pervolumeofpurchasingwaterfromtheutility

network in period tat the price levelj

cf dimensionless runoff coefficient

CostPFN total discounted cost of satisfying demand com-

pletely by purchasing water from the utilitynetwork

CPt costof purchasingwater from the utility network in

period t

dt domestic household water demand in period t

fini fixed cost of installing the rainwater tank

i discount rate

J number of price levelsk price levelwiththegreatestunitpriceto beincurred

for a purchased volumeof freshwater

n number of residents

Nt number of days in period t

rdt measured rainfall depth in period t

rt amount of rainwater that can be harvested and

stored in period t

smax maximumsize forthevolumeof rainwater tank that

can be built

lengthof the planninghorizonV purchased volume of freshwater

Vj maximum cumulative volume of freshwater that

can be purchased at thejth price level

Wd volume of water usage per day per capita

Variables

It inventory level of the rainwater tank at the end of

period t

Ptj amountofwaterpurchasedfromtheutilitynetwork

at thejth price level in period t

Rt amount of rainfall stored by the rainwater tank in

period tTcap volumeof the rainwater tank to buildUt amount of water used from the rainwater tank to

satisfy demand in period t

Z objective function value

storagetank.Often times, theeconomicpotentialof RWHexistsdue

to avoiding freshwater purchase but the overall feasibility of inte-

grating a rainwater storage unitmaystill be infeasible dueto initial

capital cost of installation (Kim et al., 2014). For this reason, most

governments are providing rebates in the form of exemption from

stormwater taxes or offset in the initial capital cost of installation

to encourage thedeployment of theRWHsystems (Domnechand

Saur, 2011; Imteaz et al., 2012; Rahman et al., 2012). Domnech

andSaur (2011)mentioned thatsubsidiesupto1200D aregranted

to a household installing a RWH system in Barcelona, Spain. Simi-

larly, theVictoriaGovernmentandSydneyWaterCorporationoffer

up to Aus $500 and Aus $1400, respectively, as rebates to proper-

ties that have rainwater tanks installed in Australia (Imteaz et al.,

2012; Rahman et al., 2012).

Coombes andBarry (2008)compared the relative efficiencies of

runoff into dams with rooftop RWH using duration curves devel-

oped for supplying water to the cities of Brisbane, Melbourne,

Perth, and Sydney. They concluded that RWH is more resilient

to the impacts of climate change. Ghisi (2010) considered the

parameters affectingthe sizingof rainwater tanks fordomestic use

andrecommended that regional assessment of rainwater tank siz-

ing be carried out by taking into account local rainfall data, roof

areas, number of residents, potable water demand, and rainwa-

ter demand. Tam et al. (2010) compared the cost of procurement,

installation and operation of rainwater tanks to the benefits of

the use of a rainwater tank in an empirical study to aid residen-

tial decision-making. Domnech and Saur (2011) assessed the

social experience, freshwater savings, and economic costs associ-

ated with the use of RWH in single and multi-family buildings in

Spain. Imteaz et al. (2011) presented a daily water balance model

for domestic rainwater usage so as to provide decision support forthe performance analysis of rainwater tanks in commercial build-

ings with large roof area. The authors claimed that optimal tank

size was obtained by studying the effect of varying parameters of

tank size and roof areas on cumulative overflow loss and cumula-

tivewater saved. Khastagir andJayasuriya (2010)usedmultivariate

regression between domestic rainwater tank capacities and roof

catchment area to develop a dimensionless curve for assessing

water supply effectiveness.Theyconsidered thedevelopeddimen-

sionless curveas a step towarddevelopingaweb-basedinteractive

tool for optimum tank selection. Similarly, Campisano andModica

(2012) developeda regressionmodelwhich enables theevaluation

of water saving and overflow discharge from domestic RWH sys-

tems. They evaluatedthe optimal tank size byapplyingaminimum

cost approach on the developed regression model and concludedthat the economic attractiveness of large tanks decreases as rain-

water availabilitydecreases.Morales-Pinznet al. (2015)proposed

a predictive model for estimating thefinancial andenvironmental

feasibility of RWH for different housing configurations in Spain.

Imteazet al. (2012) assessed therainwater harvesting potential for

southwest Nigeria using a daily water balance model. They found

that the analysis using monthly rainfall data tends to overesti-

mate the required rainwater tank size and recommended the use

of daily data. L et al. (2013) presented a multi-criteria optimiza-

tionapproachfor rainwater utilization,which wasevaluatedusing

a case study in Shanghai, China. They concluded that the rainwa-

ter utilization could enhance the sustainability of cities with the

involvement of stakeholders preferences. Al-Ansari et al. (2013)

proposed a combination of linear programming model togetherwitha watershedmodelingsystemtomaximize theirrigation area,

which could be supplied from a selected reservoir. Huang et al.

(2013) proposed a stochastic optimization approach for the inte-

grated urban water resource planning with the aim of optimizing

water flows in cities facing significant water shortage. Sample and

Liu(2014)proposeda nonlinearmetaheuristicsearchalgorithmfor

the identification of near-optimal least cost solutions for the dual

purpose ofwater supply and runoff capture across a wide range of

land uses and locations in Virginia, USA. They concluded that the

net benefits are very sensitive to water and wastewater charges.

Gurung and Sharma (2014) presented the economies of scale on

communalrainwatertanksystemdesign.Bocanegra-Martnezet al.

(2014) proposed a nonlinear mixed integer programming model

to harvest, store, and distribute rainwater formultiple residential

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C.O. Okoye et al. / Resources, ConservationandRecycling xxx(2015) xxxxxx 3

housingunits. Theiroptimizationmodelminimizes thetotal annual

cost and freshwater consumption. Their model was developed for

communal harvesting involving multiple housing units to decide

on the size of the storage tanks, the housing units to be used for

harvesting, the connections between housing units and the stor-

age tanks, and the size of the elevated reservoir which stores both

freshwater and rainwater after treatment. The sizes of both the

storage tanks and the elevated reservoir are calculated using the

largest volume of rainwater storedover the planninghorizon of 12

months.

In this study,we consider a single residential housing unit con-

nected to the utility network and a decision is made on either

building a rainwater storage tank to satisfy some portion of the

water demand or meeting whole demand from the utility net-

work. Buildinga rainwater tankincurs an initial capital installation

cost while purchasingwater from theutility network incurs a cost

dependent on the amount purchased. The aim is to assess the eco-

nomic feasibility of building a rainwater tank compared to the

alternative of meeting whole demand from the utility network by

taking intoaccount sitespecificdataincluding theassociatedcosts.

Although existing studies in the literature offered some solu-

tions to their respective case applications, there is still a need to

have an integrated approachto thedomestic RWHproblemconsid-

ering tank costs and freshwater purchase costs. Therefore, wepropose for the first time an integrated optimizationmodel based

on linear programming (LP) to determine the optimal rainwater

tank size forthedomesticrainwaterharvestingandstorage ata sin-

gleresidentialhousingunit by takingintoaccount site specific data

such as the rainfall profile, the roof area of the building, the water

consumptionpercapita, the number of residents, the initial capital

cost of building a rainwater tank, and the cost of purchasingwater

from theutility network.Ourpaper is closely related toBocanegra-

Martnez et al. (2014), but unlikeBocanegra-Martnez et al. (2014),

ourmodelis fora singleresidentialhousingunit, involvesdecisions

on the amount of rainfall to store (or equivalently the overflow

decisions), allows separate storage of rainwater and freshwater,

considers volume-dependent increasing unit prices for freshwater

purchased from theutility network, and is able todirectly take intoaccountrainfallanddemanddataalongtheusefullife ofa rainwater

tank (i.e. over 20 years).

An important advantage of our LP model is that it can easily

be constructed and optimally solved withinmilliseconds because

of the availability of efficient commercial and non-commercial LP

solvers. In particular, our model has been coded in MS Excel and

solvedusing the open source solver, OpenSolver 2.6.1 (see Mason,

2012).

The proposed model was tested and validated on a case study

from Northern Cyprus. Finally, the study offersmanagerial insight

on the impact of various parameters such as the number of resi-

dents, roof area, discount rate, water consumption per capita, unit

cost of building the rainwater tank, and rainfall characteristics on

the optimal tank size and on the net financial benefit gained fromRWH through detailed sensitivity analysis.

Therestof thepaper isas follows.Thedetaileddescriptionof the

problem addressed is provided in Section 2. Section 3 presents the

proposed LPmodel fordomestic RWHand storage. The implemen-

tation of the proposedmodel to a case study is provided in Section

4. Finally, Section 5 concludes the paper.

2. Problem formulation

In this section, the problemaddressed inthis study ispresented.

A single residential housing unit is considered in a given location

with specified meteorological climatic variables, number of resi-

dents, dailywater consumption per capita, available roof area, and

Fig. 1. Increasingblock rate tariff scheme.

available space for rainwater tank. The aim is to determine the

optimal size of rainwater tank to build at the minimum total cost

which is composed of the capital cost of installing the tankand thefreshwater purchase cost.

Theproblemconsideredcanbe describedin differenttimescales

such as hourly, daily and monthly time periods depending on the

available input data (e.g., water demand and rainfall) resolution.

Although Imteaz et al. (2012) recommended the use of daily data

for more realistic results, due to the scarcity of daily rainfall data,

weconsidermonthly timeperiodsandusemonthandperiodwords

interchangeably.We define as thelengthof theplanninghorizonin terms of the number ofmonths.

The capital cost of installing the tank is composed of a fixed

cost and a variable cost. The fixed cost of installing the tank finiincludes the costs of tank, pump, pipe, pressure control, filter, and

installation while the variable cost of installing the tank, a, is the

cost incurred per unit volume of tank built. The cost of rainwaterpumping is neglectedas this cost is also incurredwhen purchasing

water from theutility network.

An increasing block rate (IBR) tariff scheme is used to calculate

the freshwater purchase cost. According to the IBR tariff scheme,

unit prices forwater purchased from the utility network increases

as the purchased volume increases. The IBR tariff schemeiswidely

applied inmanycountriessuchasSpain(Surez-Varelaetal.,2015),

Portugal (Silvaet al., 2015)andUSA(Boyer et al., 2012), asaneffec-

tive tool to prevent the wastage of the scarce water resources. In

IBR tariff scheme, btj is the cost per volume of purchasing water

from the utility network inperiod tat theprice leveljwithJdenot-

ing the number of price levels, and Vj is themaximum cumulative

volume of freshwater that can be purchased at the jth price level.

Note that VjVj1 denotes the maximum volume of freshwaterthat can be purchased at thejth price level. As unit prices increase

with the increasingpurchasevolumein IBRtariff scheme, wehavebt1

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Fig. 2. Schematic of a typical domestic rainwater harvestingsystem.

volume ofV in period t. Assuming that V2

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amount allowed at that price level. Note that because of the con-

vexity of the btj values (i.e., bt1 50 8.0

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2 3 4 5 6 7 8 910

11

12

13

0

400

800

1200

1600

2000

2400

2800

3200

NFB

TDC

Number of Residents

Ne

tFinanc

ialBene

fit(TL)

3000

6000

9000

12000

15000

18000

21000

24000

27000

30000

To

talDiscoun

tedCos

t(TL)

2 3 4 5 6 7 8 910

11

12

13

0

1

2

3

4

5

6

7

8

9

10

11

Tan

kSiz

e(m3)

Number of Residents

Fig. 4. Effect of varying thenumberof residentson thetank size andeconomic benefit.

with an optimal rainwater tank size of 2.2m3 is found. The net

financial benefit (NFB) is equal to 675 TL depicting a marginaleconomic return over the planning horizon for building the RWH

system. Considering the occasional flooding situation occurring in

the country in recent times, there can be an important environ-

mental benefit associated with RWH implementation besides its

financial benefit. Considering this environmental benefit, even if

there is no NFB (i.e., NFB= 0) of building of a RWH in a region, it

can be appropriate for the governments to offset some portion of

the cost of the system aswidely observed in other regions such as

Barcelonain SpainandVictoria and Sydneyin Australia(Domnech

and Saur, 2011; Imteaz et al., 2012; Rahman et al., 2012).

In order to observe the impact of varying the parameters, we

identified and evaluated different scenarios which are marked as

CaseA, B,C, D,E andF inthefollowing. Inallcases, the effectof vary-

ing one parameter at a time on the NFB, the total discounted cost(TDC) of satisfying waterdemand(i.e.,TDC=min{CostPFN,fini +Z*})

and the rainwater tank size is evaluated while all other parame-

ters remains the same as previously defined. The effect of varying

the number of residents from2 to 13 in Case A, the roof area from

80 to 300m2 in Case B, the discount rate from 3% to 12% in Case

C, the average daily water consumption per capita from 80 to 195Liters in Case D, the unit cost of building rainwater tank from 156

to336TL/m3 inCase E andfinally,several rainfall profilecharacter-

istics in Case F were examined andcritically analyzed.

4.1. Case A

The impact of varying the number of residents from 2 to 13 is

examined and the results are presented in Fig. 4, which indicates

the optimal tank size, the resulting NFB and TDC. The results show

thatwhen the numberof residents is less than5 orgreater than12,

buildinga rainwater tank is notfinancially feasible. Inotherwords,

the RWH systemwould not be able to recover the capital invest-

ment over its useful lifetime. Thus, in the presenceof less than5 or

greater than 12 residents, it is cheaper to use water from the util-ity network in catering for the demand. The NFB is positive for five

persons, increases steadily to its maximum at nine residents, and

then decreases gradually as the number of residents increases as

shown in Fig. 4. The corresponding optimal tank size is 4.9m3 for

80

100

120

140

160

180

200

220

240

260

280

300

580

600

620

640

660

680

700

720

740

760

780

NFB

TDC

Roof Area (m2)

Ne

tFinanc

ialBenef

it(TL)

8880

8900

8920

8940

8960

8980

9000

9020

9040

9060

9080

To

talDiscoun

tedCost

(TL)

80

100

120

140

160

180

200

220

240

260

280

300

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

Tan

kSize

(m3)

Roof Area (m2)

Fig. 5. Effect of varying the roof area on thetank size andeconomic benefit.

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0.0

8

0.0

9

0.1

0

0.1

1

0.1

2

0.1

3

0.1

4

0.1

5

0.1

6

0.1

7

0.1

8

0.1

9

0.2

0

0

400

800

1200

1600

2000

2400

2800

NFB

TDC

Consumption per cubic meter per capita

Ne

tFinanc

ial

Bene

fit(TL)

5000

6000

7000

8000

9000

10000

11000

12000

13000

To

talDiscoun

ted

Cos

t(TL)

0.0

8

0.0

9

0.1

0

0.1

1

0.1

2

0.1

3

0.1

4

0.1

5

0.1

6

0.1

7

0.1

8

0.1

9

0.2

0

0.0

0.5

1.0

1.5

2.0

2.5

Tan

kSi

ze

(m3)

Consumption per cubic meter per capita

Fig. 6. Effect of varying daily water consumption on thetank size andeconomic benefit.

the predicted maximum NFB of 2983TL. Note that more rainwa-

terand/or freshwater is neededto satisfy increasingwaterdemanddueto a largernumberofresidents andthewayto increasethe sup-

ply of rainwater is to build a larger tank size. We indeed observe

a larger rainwater tank size in Fig. 4 as the number of residents

increases (i.e. 2.2m3 for 58 residents, 4.9m3 for 9 residents and

10.7m3 for1012residents) until thelatterbecomes 13.However,

therainfallmay notfillup the largertank sizes sufficientlyand one

may still need to purchase freshwater to satisfy thewater demand.

This is what happens when the number of residents exceeds 12

and it becomes financially better to satisfy all water demand by

purchasing freshwater than by building a large tank size incurring

a high capital installationcost besides thecost of purchasing fresh-

water.We also observe that theTDCincreasesexponentially as the

number of residents increases as depicted in Fig. 4.

4.2. Case B

For the considered roof areas from80 to 300m2, the results are

presented in Fig. 5, which shows that RWH roof area has a linear

relationship with the optimal tank size, the NFB, and the TDC. In

other words, increasing the roof area leads to increase in both the

tank size and the NFB, and decrease in the TDC.

4.3. Case C

The effect of changing the daily water consumption level

between 80 and 195l per capita is presented in Fig. 6, which indi-

catestheoptimaltanksize,theNFB,andtheTDC.Ascanbeobserved

from Fig. 6, the optimal tank size predicted by the model is not

sensitiveto thedaily consumptionlevel.Whenthedailywater con-

sumption per capita is greater than 0.10m3, the optimal tank size

to build stays constant at the size of 2.2m3 whereas no rainwater

tank is recommended to build when the daily water consumption

per capitais less than0.10m3. Ontheother hand, theNFB ofimple-

menting a RWH system enhances with an increase in the daily

water consumption per capita as expected.

4.4. Case D

Theresultsdueto varying the discountratebetween 3%and13%

arepresented in Fig. 7. The results in Fig. 7 reveal that the optimal

2 3 4 5 6 7 8 910

11

12

13

0

400

800

1200

1600

2000

2400

2800

NFB

TDC

Discount Rate (%)

Ne

tFinanc

ialBene

fit(TL

)

5500

6000

6500

7000

7500

8000

8500

9000

9500

10000

10500

11000

11500

To

talDiscoun

tedCos

t(TL)

2 3 4 5 6 7 8 910

11

12

13

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Tan

kSize

(m3)

Discount Rate (%)

Fig. 7. Effect of varying daily water consumption on thetank size andeconomic benefit.

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160

180

200

220

240

260

280

300

320

340

550

600

650

700

750

800

850

900

NFB

TDC

Unit Cost of Tank (TL/m3)

Ne

tFinanc

ialBene

fit

(TL)

8750

8800

8850

8900

8950

9000

9050

9100

9150

To

talDiscoun

tedCost

(TL)

160

180

200

220

240

260

280

300

320

340

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Tan

kSize(

m3)

Unit Cost of Tank (TL/m3)

Fig. 8. Effect of varying theunit cost of building thetank on thetank size andeconomic benefit.

tank size to build, the NFB, and the TDC decrease as the discount

rate increases. In particular, when thediscount rate is greater than

8%, the proposed model does not recommend building the RWH

system (i.e. tank size is equal to zero). This result is due to the fact

that the net present value of the cost of purchasingwater from the

utility network gets smaller as thediscount rate increaseswhereas

the capital cost of building the RWH system stays constant. Thus,

high discount rates make the option of purchasing freshwater to

satisfy all water demand financially more attractive than building

a RWHsystem.

4.5. Case E

Changing the unit cost of building a rainwater tank has a

significant impact not only on the economic benefit associated

with implementing the RWH system but also on the optimal

tank size as presented in Fig. 8. As expected, the NFB and the

tank size decrease with the corresponding increase in the unit

cost of building the tank. In Fig. 8, it is observed that there is a

threshold value of this cost after which it is not recommended to

build a rainwater tank. Specifically, when the unit cost of build-

ing the tank exceeds 336TL/m3, the model recommended not

building a tank. On the other hand, the TDC increases with a

gradually decreasing rate as the unit cost of building the tank

increases.

4.6. Case F

In this case, rainfall data of seven rainfall stations in Northern

Cyprus are utilized in the sensitivity analysis. The stations were

selected in a way not only to represent all the regions in the coun-

try but also to reflect the differences in the statistical coefficient

of variation (CV) values. The rainfall station location and regions

are as follows: Karpaz for the Karpaz Peninsula with a CV of 1.01,

Kyrenia for the North Coast with a CV of 1.00, Iskele for the East

coastwitha CVof0.90, Guzelyurt for theWestMesaoria Plainwith

a CV of 0.89, Kantara for the Besparmak Mountain with a CV of

0.86, Dortyol for the East Mesaoria Plain with a CV of 0.82, and

NicosiafortheMiddleMesaoriaPlainwitha CVof0.74, respectively.

Sep

t.

Oc

t.

Nov.

Dec.

Jan.

Fe

b.

Mar.

Apr.

May

Jun.

Ju

l.

Aug.

0

20

40

60

80

100

120

140

Average

Mon

thlyRa

infall(mm

)

Kantara

Karpaz

Kyrenia

Gzelyurt

Dortyol

Nicosia

Iskele

Fig. 9. Average monthly rainfall distribution of the selected stations.

Themonthlydistributionof theselectedrainfallstationsis depicted

in Fig. 9, which indicates that the maximum rainfall occurs in

Decemberwhile theminimumoccurs in July and August. In Fig. 10,

the optimal tank size and the NFB associatedwith seven locations

are presented. It is observed that contrary to the assumption thatincrease in rainfall will lead to an increase in the optimal tank size

and the NFB, the observed result shows that optimal tank size and

the NFB is actually more sensitive to the distribution of rainfall

over themonths than the annualaverage rainfall. Forexample, the

optimal tank size for Dortyol, which has an annual average rain-

fall depth of 268mm, is 2.8m3 relative to the sizes of 2.2m3 and

1.5m3 predicted for Kyrenia and Guzelyurt with average annual

rainfall of464mmand281mm, respectively.AlthoughDortyolhas

the lowestannualaveragerainfall,itsNFBismorethanthatofGuze-

lyurt and Karpaz which have better rainfall amounts on average.

The results in Fig. 10 reveal that it is wrong to make assumptions

on the financial benefit of RWH systems based on average rain-

fall data of an area without considering variability in the rainfall

amounts.

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Kan

tara

Karpaz

Kyren

ia

Iske

le

Nicos

ia

Guze

lyurt

Dortyo

l620

640

660

680

700

720

740

760

NFB

TDC

Ne

tFinanc

ial

Bene

fit(TL)

8880

8900

8920

8940

8960

8980

9000

9020

9040

To

talDiscoun

tedCos

t(TL)

Kan

tara

Karpaz

Kyren

ia

Iske

le

Nicos

ia

Guze

lyurt

Dortyo

l0.5

0.6

0.7

0.8

0.9

1.0

1.1

1.2

CV

Tank Size

Coe

fficiento

fVaria

tion

1.0

1.5

2.0

2.5

3.0

3.5

4.0

4.5

Tan

kS

ize

(m3)

Fig. 10. Effectof varying rainfall profiles on theoptimal tank size andeconomic benefit.

5. Conclusion

In this paper, a mathematical model based on linear program-

minghasbeenproposedandused inthe optimal sizingof rainwater

storage tank for domestic rainwater harvesting and storage. The

proposed optimization model determines the optimal size of the

rainwater tank to build at minimum total discounted cost. The

model was applied to a case study from Northern Cyprus, which

showed through sensitivity analysis how some parameters affect

both the net financial benefit and the optimal rainwater tank size.

Thesensitivity analysis reveals that the optimal tank size increases

with the roof area, but decreaseswith an increase in the discount

rate and the unit cost of building the tank. On the other hand, the

net financial benefit associatedwith implementing rainwater har-vesting increases with an increase in the roof area and the daily

water consumption per capita but decreases with an increase in

thediscount rate and the unit cost of building thetank. Until (resp.

after) a threshold value, an increase in the number of residents

leads to an increase (resp. decrease) in the optimal tank size and

the net financial benefit. We have also found that the daily con-

sumption level per capita has no effect on the optimal tank size

whereas the monthly distribution of rainfall significantly affects

both the optimal tank size and the net financial benefit.

As discussed in Section 2, we considered monthly time periods

in our LPmodel due to the scarcity of daily rainfall data. However,

the use of daily rainfall data leads tomore realistic results than the

useofmonthlydata because consecutiveheavyrainfallsin amonth

maycauseoverflowingof the rainwater tank several timesandthiscan only be captured by a daily analysis. Therefore, if daily rainfall

data is present, it is better to perform an analysis with daily data

which can be done by adapting the proposed LPmodel to the use

of daily rainfall anddemanddata.

Last but not least, as shown by the case study application, the

proposed LP model is an effective tool that can be used by pub-

lic authorities or individuals to make feasibility analysis of RWH

systems at residential housing units.

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