household water use and conservation models using monte carlo techniques

Hydrol Earth Syst Sci 17 3957ndash3967 2013wwwhydrol-earth-syst-scinet1739572013doi105194hess-17-3957-2013copy Author(s) 2013 CC Attribution 30 License

Hydrology and Earth System

SciencesO

pen Access

Household water use and conservation models using Monte Carlotechniques

R Cahill1 J R Lund2 B DeOreo3 and J Medelliacuten-Azuara2

1United States Army Corps of Engineers Portland Oregon USA2Center for Watershed Sciences University of California Davis Davis California USA3Aquacraft Inc Boulder Colorado USA

Correspondence toR Cahill (ryancahillusacearmymil)

Received 17 March 2013 ndash Published in Hydrol Earth Syst Sci Discuss 17 April 2013Revised 19 August 2013 ndash Accepted 4 September 2013 ndash Published 15 October 2013

Abstract The increased availability of end use measurementstudies allows for mechanistic and detailed approaches to es-timating household water demand and conservation poten-tial This study simulates water use in a single-family res-idential neighborhood using end-water-use parameter prob-ability distributions generated from Monte Carlo samplingThis model represents existing water use conditions in 2010and is calibrated to 2006ndash2011 metered data A two-stagemixed integer optimization model is then developed to esti-mate the least-cost combination of long- and short-term con-servation actions for each household This least-cost conser-vation model provides an estimate of the upper bound of rea-sonable conservation potential for varying pricing and rebateconditions The models were adapted from previous work inJordan and are applied to a neighborhood in San Ramon Cal-ifornia in the eastern San Francisco Bay Area The existingconditions model produces seasonal use results very closeto the metered data The least-cost conservation model sug-gests clothes washer rebates are among most cost-effectiverebate programs for indoor uses Retrofit of faucets and toi-lets is also cost-effective and holds the highest potential forwater savings from indoor uses This mechanistic modelingapproach can improve understanding of water demand andestimate cost-effectiveness of water conservation programs

1 Introduction

Models predicting residential water use and conservation po-tential based on empirically estimated parameters water-consuming device turnover rates and regression analysis are

fairly common The uses and drawbacks of various types ofthese models are detailed and then contrasted with the modeldeveloped here

Some water utilities develop regression relations for totalsingle-family residential water use based on historical trendsfor planning purposes (Sacramento Department of Utilities2011 San Jose Environmental Services Department 2011)Such models assume increasing levels of conservation in thefuture but often give little indication of where this conser-vation will come from Estimating realistic conservation po-tential for each end use under various drought pricing anddemographic conditions requires an understanding of wherewater is currently being used in homes Measurement-basedstudies now provide reliable data on water consumption foreach end use (eg toilets showers irrigation) (Mayer andDeOreo 1999) yet these studies can be costly

Using end use data some models estimate conservationpotential by assuming natural replacement rates of appli-ances with more efficient appliances and calculating the ex-pected amount of water saved (CALFED Bay Delta Program2006 Blokker et al 2010 Gleick et al 2003) These modelsoften assume average savings values for retrofitting devicesand apply them uniformly to the proportion of the populationexpected to adopt the devices Such a modeling approach isuseful for long-term large-scale predictions of conservationpotential but does not allow for much heterogeneity of be-havior or population characteristics

Case studies for Europe Africa America and Australia(Blokker et al 2010 Gumbo et al 2003 Kampragou etal 2011 Sauri 2003) highlight the use of modeling toassess the effectiveness of water conservation programs

Published by Copernicus Publications on behalf of the European Geosciences Union

3958 R Cahill et al Household water use and conservation models

Kampragou et al (2011) summarize guiding principles ofwater demand management strategies and programs present-ing case studies for Canada the US Europe and Asia thatemploy both market and non-market incentives The effec-tiveness of economically driven strategies seems to be linkedto the prevailing socioeconomic conditions (Kampragou etal 2011) Sauri (2003) presents a qualitative approach towater demand with historical information on water use andurban development patterns that discusses the role of pric-ing water sources augmentation technology and consumeroutreach for the Metropolitan Region of Barcelona in SpainJacobs and Haarhoff (2004) present a model that predicts enduses by household using detailed physical and behavioralparameters affecting demand

Some models rely heavily on large amounts of datato model end use and conservation potential Blokker etal (2010) present a simulation model for water demandpatterns in a region of the Netherlands using a very smalltimescale at the residential level This method is presentedas an alternative to metering using data management pro-grams that have proved to be useful in other areas (Gumboet al 2003) The end-use model developed by Blokker esti-mates water demand based on parameters affecting water use(eg frequency of hand washing) Compared to householdmetered data the model had good fit overall The end-usemodel includes pulse intensity time of use and duration foreach end-use type user and busy time per end use Howeverthis model does not include outdoor uses (which are small inthe Netherlands) and whereas aggregate demand is close tothe measured data the approach relies on high quality appli-ance information and behavioral data which is more suitablefor regions with homogeneous demographics (Sauri 2003)

Still other household use models attempt to calculate thewater used for each end use of individual homes using re-gression analysis (DeOreo et al 2011) These models buildheavily on end use measurement data paired with survey re-sponses and find statistically significant parameters affect-ing each end use of water Empirical equations are then de-veloped to predict each end use as a function of these sig-nificant parameters The strength of the regression analysisresults for estimating water demand of individual homes isoften low with coefficients of determination (R2) typicallyaround 04 (DeOreo 2011) Such models perform reason-ably for estimating current average water use for groups ofhouseholds and are useful in estimating the effectiveness ofand potential for water conservation measures under differ-ent scenarios Water pricing or more complex rationing con-ditions are usually absent from these models However liter-ature on household water demand often concludes that priceis an important factor affecting total water use (Dalhuisen etal 2003 Rosenberg 2010)

While regression-based (inductive) models are useful fordifferent purposes a more mechanistic or deductive model-ing approach can now be undertaken with the large amountsof data available from end use measurement studies In

contrast to more inductive or empirical techniques for house-hold water demand analyses this paper presents a more de-ductive (ldquocausalrdquo) household end-use model based on phys-ical parameters affecting water use that vary by householdWe employ a Monte Carlo approach to include variability inhousehold physical characteristics and behavior when esti-mating distributions of household water use and conservationpotential This modeling approach is applied to a neighbor-hood in the East Bay Municipal Utility District (EBMUD)service area California The model extends a previously de-veloped model that estimated household water use in Am-man Jordan (Rosenberg et al 2007) Rosenbergrsquos modelaccurately reflected actual water use patterns in Jordan butsuch an approach has not been attempted in the US whereurban water utilities often offer water conservation rebates totheir customers

After an overview of the modeling approach a short sum-mary of the case study area (San Ramon California) is pre-sented Then (1) existing conditions use and (2) least-costconservation models are described in detail Third calibra-tion and modeling results are presented and discussed witha cost-effective assessment of different short- and long-termconservation actions Finally the inherent limitations and de-sirable extensions of this modeling approach are discussed

2 Modeling overview

The framework developed for this study can be thought ofas two interrelated models (1) ldquoexisting conditionsrdquo and (2)ldquoleast-cost conservationrdquo (Fig 1) The ldquoexisting conditionsrdquocomponent simulates water demand by end use for a neigh-borhood and can be calibrated to metered data The param-eterized demand equations from the ldquoexisting conditionsrdquocomponent are later employed by the ldquoleast-cost conserva-tionrdquo model to estimate the cost minimizing short- and long-term water saving actions for each household To make thedistinction between each model clearer Table 1 presents a listof possible outputs desired by utilities along with the modelthat can provide the output The list in Table 1 is not compre-hensive but it shows capabilities of each model

21 ldquoExisting conditionsrdquo water use model

The existing conditions model estimates household wateruse by end use using uncertain physical parameters cal-ibrated to metered data This model is analogous to themodels developed by Blokker et al (2010) and Jacobs andHaarhoff (2004) In this model conservation devices suchas low flow showerheads are present in their assumed mar-ket penetration rates and the households make no behavioralchanges This simulation approach allows evaluation of spe-cific alternativesrsquo effect on total water use (eg What wouldthe water use be if all households installed warm-seasonturf) The basic process is as follows

Hydrol Earth Syst Sci 17 3957ndash3967 2013 wwwhydrol-earth-syst-scinet1739572013

R Cahill et al Household water use and conservation models 3959

Table 1 Example capabilities of existing conditions and least-costconservation models

Existing Least-CostResult desired by utility Conditions Conservation

Water use by end use in 2010 x

Expected water use after price xincrease of 10

Savings after penetration of xHET increases to 40

Cost-effectiveness of payment xfor less-grass area (Cash for grass)

Budget for showerhead xreplacement rebate program

Water consumption of proposed xnew subdivision

Outdoor water consumption xwith climate change

Water use with water rationing xpolicy

1 Develop parameter probability distributions

2 Sample distributions to create a ldquohouserdquo

3 Calculate water use from sampled parameters

4 Repeat steps 2 and 3 for 500 households (Monte Carloiterations)

5 Calibrate results to metered data

22 ldquoLeast-cost conservationrdquo model

The least-cost conservation component incorporates house-hold behavior into the existing conditions component Thehousehold use and sampled parameters for each Monte Carloldquohouserdquo from the existing conditions model are used asstarting points (or initial conditions) for the least-cost con-servation model In the least-cost model each householdhas several available long-term and short-term conservationactions Long-term actions apply for all future conditionswhile short-term actions apply to individual water shortageevents Each conservation action has an associated cost andeffectiveness in reducing water use dependent on the sam-pled parameters of the house (eg a house with a larger num-ber of occupants that chooses to replace toilets will savemore water) For each household a combination of theselong-term and short-term conservation decisions exists thatwill minimize cost the least-cost conservation model findsthis mix of actions This two-stage (long-term and short-term) optimization approach has been used by Lund (1995)and Garcia-Alcubilla and Lund (2006) As a stochastic opti-mization model with recourse decisions the model may not

Fig 1Modeling framework for economic analysis of water conser-vation

actually predict what real homeowners will do The modelassumes cost-minimizing rational behavior of all homeown-ers assuming they have perfect knowledge of the probabil-ities of future shortages and corresponding price increasesHowever the model results do provide a likely upper bound(from an economic perspective) of the conservation potentialfor the neighborhood The changes in household water useresulting from policy changes (eg differing rebate strate-gies or pricing schemes) can be evaluated in the least-costconservation component The least-cost component is a help-ful complement to the existing conditions model while theexisting conditions model calculates end uses the least-costconservation model shows which end uses households findmost cost-effective to reduce The basic process is as follows

1 Define conservation actions and effectivenesses (howmuch water is saved)

2 Define event probabilities and corresponding water billincreases

3 Define costs of actions

4 Define and solve the optimization equations usingmixed integer linear programming

Steps 1ndash4 are performed separately for each of the house-holds previously generated in the existing conditions model

3 Metered data

EBMUD provided metered data for 151 households from2006ndash2011 in a neighborhood in San Ramon CA which

wwwhydrol-earth-syst-scinet1739572013 Hydrol Earth Syst Sci 17 3957ndash3967 2013


were employed to calibrate the model San Ramon is east ofthe Oakland Hills where there is less precipitation warmertemperatures and more sunny days than areas west of thehills Therefore the metered homes should have more out-door water use than the average EBMUD household Fur-thermore the houses are in an affluent neighborhood near agolf course where the median selling price of homes was ap-proximately $900 000 as of 2011 (Zillow 2011) The ldquostan-dard new homesrdquo end use study (DeOreo 2011) is particu-larly applicable to this neighborhood for obtaining parame-ter distributions on appliances and water use because boththe homes in the neighborhood and in the study were builtaround 2000

4 Existing conditions water use model

The basic modeling process for the existing conditions modelis described in Sect 21 now the details of the model arepresented

41 Parameter probability distributions

Many parameters affect household water use (eg type of toi-lets household size lot size etc) Instead of assuming av-erage numbers for each parameter probability distributionsare used to capture variability in water use parameters In themodel 69 parameters are used to define the water use of eachhouse The distributions of these parameters were taken fromend use studies mentioned earlier or other literature whenavailable otherwise engineering estimates were used A fulllist of the parameters and their distributions is presented inCahill (2011)

42 Distribution sampling

After the distributions have been developed each MonteCarlo iteration randomly samples these distributions in-dependently to create a modeled ldquohouserdquo Each sampledldquohouserdquo does not line up with a physical house but the wholesample of houses should approximate the neighborhoodrsquoswater use Covariance between parameters was not includedin the sampling process although such relations do exist(DeOreo et al 2011) Water use estimates could be unre-alistic for some households due to this assumption of param-eter independence For example shower length and showerfrequency may be inversely related but the model does notaccount for this so there may be some households that takelong showers very often This assumption of parameter inde-pendence could be removed as a future improvement to thismodel

43 Calculation of water use from parameters

After the parameters have been randomly sampled for ahousehold relations between the parameters are used to

estimate the water demand by end use For example waterused for laundry can be estimated using Eq (1)

Q =

(liters

cycle

)(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (1)

Each factor in the equation is randomly sampled for eachhousehold (except physical constants) Equations have beendeveloped for each end use and the full list of relations canbe found in Cahill (2011) For each end use and householdwater use is calculated within the Monte Carlo loop Themodel used two seasons (wet winter and dry summer) to fur-ther disaggregate the water use as precipitation and evap-otranspiration values are quite different in the dry and wetseasons and affect outdoor use (CIMIS 2011)

44 Calibration to metered data

The results from the existing conditions model are comparedto metered data to ensure that reasonable ranges of resultsare being produced Only one parameter was set to match themetered data ndash the percent of landscaped area that is lawnIt was set to a value of 65 which is close to the averagelawn proportion of landscape in the study area (EBMUD2002) This calibration was done manually by trial and er-ror although a more sophisticated approach could have beentaken to match the data more closely This paper focuses onnew modeling methods rather than rigorous calibration soa simple calibration scheme is sufficient for the purposes ofthis paper

Goodness of fit of the existing conditions model to themetered data was formally tested using the KolmogorovndashSmirnov 2 variable test (Smirnov 1948) resulting in ap

value of 036 which fails to reject the null hypothesis thatmodeled results and metered data have the same underlyingdistribution This is also illustrated in Fig 2

A summary of the modeled results for each end use is com-pared to the findings from other end use studies in Fig 3The existing conditions simulated water use fits well withthe standard new homes data set with the exception of out-door water use in winter This is not surprising since thesemetered houses are located near a golf course with a drierclimate than the standard new homes data set


The basic modeling process for the least-cost conservationcomponent described in Sect 21 and its relation to the ex-isting conditions component is given in Fig 1 The details ofthe model inputs and the optimization formulation are pre-sented below



Fig 2 Calibration of existing conditions modeled use to meteredseasonal use

51 Model inputs

511 Conservation actions and effectiveness

A list of the short-term and long-term conservation actionsand the end use available to households appears in Table 2Short-term actions may or may not be activated during eachevent while long-term actions apply to all events Both short-term and long-term actions are expected to decrease wateruse

Each conservation action saves a given amount of water(effectiveness) depending on the initial state of the house-hold For example the relationship estimating the amount ofwater saved on a daily basis by installing a water-conservinglaundry machine is shown in Eq (2) below

Qs =

((liters

cycleStd

)minus

(liters

cycleEfficient

))middot

(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (2)

From Eq (2) households that already have a water ef-ficient laundry machine will have an effectiveness value ofzero forQs Since each house in the Monte Carlo iterationshas a different value for each randomly sampled parameter inthe Eq (2) the amount of water saved by replacing a laundrymachine will vary by household The full set of equations canbe found in Cahill (2011)

512 Water shortage event descriptions

Six different water shortage events are considered in theleast-cost model ndash three events in the winter and the samethree corresponding events in the summer to account for sea-sonality in water supply These events were based on theEBMUD water shortage contingency plan and are presentedin Table 3 (EBMUD 2011)

In this study water shortage events are characterized bythe price paid for water by the homeowners In other words

0

100

200

300

400

500

0

20

40

60

80

100

120

140

Toilets ShowerBath Laundry Faucets Leaks Outdoor

Wate

r U

se (

lite

rs p

er

cap

ita p

er

day)

Wate

r U

se (

gall

on

s p

er

cap

ita p

er

day)

REUWS (Mayer amp DeOreo 1999)

CA Single Family Residential (DeOreo et al 2011)

Standard New Homes (DeOreo 2011)

Modeled Results

Fig 3Average annual modeled end uses of water compared to enduse studies

a household may use as much water as desired during a short-age event but the price paid for water use will be higher

513 Costs

In any optimization model the costs (penalties) of actions arethe main driver of the results Three components comprisethe total cost to a household the water bill the cost of long-term actions and the cost of short-term actions Costs aresummarized in Cahill (2011)

The water rates used in this model (typicallyUSD 0002 Lminus1 hereafter USD indicated as $) werebased on the 2010 increasing block rate schedule andinclude both water and wastewater charges more accuratelyreflecting the total cost to the homeowner (EBMUD 2010)Various surcharges can be incurred by households duringdrought events and are included in the model (EBMUD2011)

514 Long-term actions

All long-term conservation actions include installing somesort of new water-saving fixture (as opposed to behavioralchange) Since the devices have a limited lifespan designlives were used to annualize the costs assuming a discountrate of 6 Since each device in the house is modeled thenumber of devices needing replacement is considered in thecost For example a house may have 3 toilets one of which ishigh efficiency toilet (HET) one of which is ultra low flushtoilet (ULFT) and one of which is ldquostandardrdquo The modelrecognizes that 2 toilets must be replaced if all toilets are tobecome HET and adjusts the cost accordingly Alternativelyeach toilet could be considered as a separate decision vari-able

The costs in the model reflect both capital and installationcosts Not all homeowners are assumed to be equally capa-ble of installing devices so only a proportion of householdswere assumed able to independently install each type of de-vice Each house was assigned a random ldquohandiness factorrdquo



Table 2Actions available to households in the least-cost conservation model

End Use Affected Long-term Actions Short-term Actions

Shower Retrofit showerheads Reduce shower lengthReduce shower-taking frequency

Toilet Retrofit all standard toilets with HETs Flush only when necessaryRetrofit all standard toilets with ULFTsRetrofit all ULFTs with HETs

Faucet Retrofit bathroom faucets Turn off faucets while washing

Laundry Install conserving laundry machine Reduce laundry-washing frequency

Leaks Find and fix leaks

Lawn Install xeriscape Stress irrigateInstall warm-season turfInstall smart irrigation controller

GardenLandscape Install xeriscape Stress irrigateInstall drip irrigation systemInstall smart irrigation controller

Car Wash Wash car with bucketsWash car at gas station

Pool Stop filling swimming pool

between 0 and 1 if the householdrsquos handiness factor exceedsthe cutoff proportion for a given action the household mustuse professional installation Households with handiness fac-tors below the cutoff have the option of installing the devicethemselves or having it professionally installed whicheverhas the lower cost Some tasks such as changing out shower-heads can be done by most people while more difficult taskslike installing xeriscapes have more restrictive handiness cut-offs

515 Short-term actions

The financial costs of nearly all short-term actions are zeroas they are behavioral changes rather than retrofits There isno concept of a ldquohandinessrdquo factor for the short-term actionsas it is assumed that everyone can carry out these actionsIf hassle costs are omitted nearly all short-term actions areimplemented in every event because they save water and costnothing to the household

Hassle costs are additions to financial costs that reflectinconvenience costs to households beyond purely financialcosts of conservation actions Often households do not re-duce consumption due to the hassle costs of conservation(Dolinicar and Hurlimann 2010) Unfortunately little hasbeen written on estimating hassle costs of conservation activ-ities Contingent valuation studies are the preferred methodof estimating hassle costs but such studies do not exist forthe water conservation activities considered in the model Inthe absence of contingent valuation studies economic liter-ature relating to opportunity costs is the most appropriate

When hassle costs are included the conservation actions areassumed to take a given amount of time which can then betranslated into a dollar amount based on the value of time toa particular household (Narasimhan 1984) To introduce un-certainty the annual household income was converted to anhourly amount and used as the value of time for a householdSuch an approach reflects a higher opportunity cost of timefor higher-income earners a common assumption in eco-nomics literature (Anderson and Song 2004 Narasimhan1984) These assumed hassle costs produce more realistic be-havior than assuming no hassle costs

52 Least-cost conservation model formulation

A two-stage mixed-integer linear program was used to for-mulate the optimization problem The first stage consists oflong-term actions and costs and the second stage includesactions and costs for each short-term shortage event For acomplete description of all inputs to the optimization modelsee Cahill (2011)

521 Decision variables

The decision variables are listed below

ndash Sse short-term actions a binary variable defined overthe sets of short-term actions (third column in Ta-ble 2) and for the sete of all six water shortage events



Table 3Description of water shortage events

Penalty forVolumetric Freeport Ration exceedinguse price source amount ( rationedincrease surcharge reduction in amount

Event Description Probability () (14 increase) original use) ($283 m3)

Summer

1 Regular delivery 035 0 no 0 $02 Shortage 01 10 no 20 $23 Severe Shortage 005 10 yes 30 $2

Winter


ndash Ll long-term actions a binary variable defined overthe setl of long-term actions (second column in in Ta-ble 2)

ndash Be water bill ($billing period) for each water shortageevente

ndash Ue water use (litersday) for each water shortage evente

ndash Eue end use saved (litersday) for each end useu andeach water shortage evente

ndash We water saved (litersday) for each water shortageevente

Decision variables for the water bill water use etc are notreally ldquodecisionsrdquo that the household has direct control overbut they are defined as decision variables to incorporate com-plexities such as piecewise-linear representation of waterbills and interactions between conservation actions

522 Objective function

The objective function (Eq 3) is to minimize the total ex-pected economic cost of all water conservation decisions in-cluding permanent conservationLl short-term conservationdecisions for each shortage eventSse and the household wa-ter bill for each shortage eventBe

MinimizeZ =

suml

clLl + jsum

e

[pe

(isum

s

(csSse

)+ Be

)] (3)

wherecl represents the annualized long-term action costs($year)cs represents the short-term action costs ($day)pe

is probability of evente i is the number of events per billingperiod (60 daysbilling period) andj is the number billingperiods per year (6 billing periodsyear)

523 Constraints

A summary of the constraints to the model is given below(non-negativity applies for all decision variables)

1 Maximum effectiveness the water saved cannot exceedthe initial water use (inequality 4) or the sum of thewater conserved in each end use category (inequality5)

We le Oe foralle (4)

We le

sumu

Eue foralle (5)

whereOe is the original water use of the householdin a water shortage evente (this input comes from theresults of the existing conditions component)

2 Conserved water usethe final water use is the origi-nal water use minus the amount of water saved fromconservation actions (inequality 6)

Ue ge Oe minus We foralle (6)

3 Discrete choices no conservation action can be par-tially implemented (Eqs 7 8)

Sse = 0 or 1 forallse (7)

Ll = 0 or 1 foralll (8)

4 Mutually exclusive actions some actions cannot beimplemented simultaneously (inequalities 9 and 10)

suml2

Ll2LX ll2 le 1 foralll (9)



sums2

Ss2eSXs2s le 1 forallse (10)

where LXll2 equals 0 or 1 for each possible combi-nation of long-term actions and setl2 is same as setlA value of 1 corresponds to mutually exclusive actions(eg washing car with buckets or washing car at carwash) Likewise SXs2s contains all possible combi-nations of short-term actions with 1 for mutually ex-clusive long-term actions and sets2 is an alias for sets

5 Mutually dependent actions some actions (inequali-ties 11 and 12) depend on implementation of other ac-tionssuml2

Ll2LRll2 = 0 foralll (11)

sums2


where LRll2 equals 0 or 1 for each possible combi-nation of long-term actions (same as inequality 9) Avalue of 0 corresponds to mutually dependent actions(eg ldquoinstall smart irrigation controllerrdquo applies to boththe lawn and garden end uses) Likewise SXs2s con-tains all possible combinations of short-term actions(same as inequality 10) with 0 for mutually requiringshort-term actions

6 Increasing block water bills unit water price increaseswith increasing use (inequality 13)

Be ge F + iV1Ue foralle (13)

whereF is the flat water fee for billing period andVn

the variable water fee for usage blockn

7 Rationing penalties surcharges apply if a householdexceeds their rationed water use (inequality 14)

Be ge F + i(V1Re + (Pe + V1)(Ue minus Re)) foralle (14)

whereRe is the rationed water amount for water short-age evente andPe the penalty for exceeding the ra-tioned amount in water shortage evente

8 Interactions between actions inequality 15 shows acap on effectiveness by end use is used to account forinteractions between conservation actions (eg savingsfrom reducing shower length and reducing shower fre-quency are not independent of each other) This con-straint ensures that water savings still make physicalsense when multiple actions are implemented

Eue le EMAXue foralluforalle (15)

where EMAXue is the maximum limit of water sav-ing for end useu in evente

6 Results

Results from ldquobase conditionrdquo runs are presented for thestudy neighborhood in San Ramon followed by the resultsof changing indoor device rebates

61 Base condition runs

The results from base condition runs are a benchmark for allalternative runs showing the reasonable conservation poten-tial beyond the existing conditions model These runs do nothave rebates for any conservation actions and water pricesare at 2010 levels Two separate base condition runs werecomputed ndash one with financial costs only and one includ-ing hassle costs The average household use after adoptingleast-cost conservation actions is 1820 L per household perday (Lphd) (480 gallons per household per day gphd) withfinancial costs only and 1930 Lphd (510 gphd) with hasslecosts while the average household use under the existingconditions model was 2040 Lphd (540 gphd) This reductionof 12 with financial costs only (6 with hassle costs)means it would be unrealistic to achieve conservation beyondthis amount under current water price rate structures and norebates as more conservation would not be cost-effectivefor the neighborhood and each home individually Figure 4shows water use after least-cost conservation compared toexisting conditions Many high water users reduce consump-tion by large amounts while the low water users can saveless

All future results are extracted from runs with hassle costsas these runs are expected to be more realistic The modeledadoption rates and ranges of effectiveness of conservation ac-tions for the base conditions are shown in Fig 5

For permanent conservation actions installing smart irri-gation controllers has a 45 adoption rate The relativelylow implementation rates of most other outdoor conserva-tion activities indicate that these conservation actions are notcost-effective for most households but the households thatimplement them save large amounts of water With currentwater price structures no household finds it worthwhile toinstall a xeriscape or warm-season turf (not shown in Fig 5)The indoor actions are implemented more often but theirsavings are usually less than outdoor conservation

The relative frequency of adoption of short-term conser-vation actions by season and drought event appear in Fig 6The short-term actions are adopted with highest frequencyduring severe shortages in the summer which is when adopt-ing these actions saves the most water and money Howeverit is financially worthwhile for some homes to adopt short-term actions even when there is no shortage Stress irrigationshows the greatest seasonal variation as the water saved bystress irrigation in the winter is much lower than in the sum-mer These preliminary model results also indicate where ad-ditional calibration and study seems desirable such as for the



Fig 4 CDF of water use under existing conditions and least-costconservation

Fig 5 Modeled market penetration and average water savings forlong-term conservation actions base conditions run with hasslecosts (error bars are 10th and 90th percentiles)

seemingly high percentage of households flushing only whennecessary

62 Indoor device rebates

While the least-cost conservation model can be used in manyways the effectiveness of indoor rebates will be focused onhere as an example application for utilities The ratio of watersaved to total rebates disbursed indicates cost-effectivenessRebate strategies with high ratios provide the highest watersavings per unit cost of conservation Figure 7 shows this re-lation for varying rebate levels These results were generatedby re-running the least-cost conservation model for each dis-tinct rebate scenario ndash the scenario with a rebate of $0 is theldquobase conditionrdquo run As nominal rebate levels increase thecost-effectiveness decreases due to free riders (who wouldhave conserved even with a lower rebate) The plot suggeststhat rebates for efficient clothes washers are the most cost-effective saving the most water per rebate dollar invested

0

5

10

15

20

25

30

35

40

45

50

Only flushwhen

necessary

Find andfix leaks

Turn offfaucetswhile

washing

Reduceshowerlength

Reduceshower-taking

frequency

Reducelaundry-washing

frequency

StressIrrigate

Wash carwith

buckets

Stop fillingswimming

pool

Perc

en

t a

do

pti

on

Summer Regular

Summer Shortage

Summer Severe Shortage

Winter Regular

Winter Shortage

Winter Severe Shortage

Fig 6 Modeled average market penetration for short-term conser-vation actions by season and drought event base conditions withhassle costs

Fig 7Cost-effectiveness of rebate programs average use reductionper rebate dollar invested by the utility per household

63 Limitations of the model

While the least-cost conservation model has many capabili-ties its limitations also are important

1 Rebate aspects of the model do not account for ldquofreeridersrdquo people who intend to replace their devices any-way and reap the benefit of a rebate without beingenticed by it (Sovocool 2005) However such house-holds can be identified by comparing results with andwithout rebates ndash the proportion of households thatconserve when there is a rebate of $0 are the free rid-ers

2 The model assumes that all households behave ratio-nally to minimize the cost to themselves which is notalways the case Many decisions on conservation arenot affected strongly by the actual savings gained orthe reduction in cost to the household (Komor andWiggins 1988) Calibration of hassle costs can helpin this regard Furthermore a payback period measurewould be a good addition to the model as the life spanof some appliances may exceed the planned occupancyperiod of some homeowners



3 The optimization model is built from a homeownerrsquosperspective so it cannot calculate the best suite of re-bates from the utilityrsquos perspective directly Howevera similar model from a utilityrsquos perspective might beformulated and used (Wilchfort and Lund 1997) andcalibrated based on household model results

4 Although the model provides a more mechanisticframework for water conservation studies it requiresestimation of many parameters Much of this informa-tion is now available from recent end use studies Out-door water use data remains the greatest uncertainty

5 While household water conservation reduces watercosts at the household level this also reduces revenuesfor the utility that depend on the proportion of house-holds employing conservation measures Some pricingmechanisms are needed to cover operation costs of theutility however quantification of these are beyond thescope of this paper

7 Conclusions

The approach taken here produces reasonable existing con-ditions water use estimates and provides insights on house-hold conservation potential for the metered homes in a SanRamon California neighborhood The modeled results werecomparable to measurements from other end use studies andwere calibrated with little difficulty to the metered data

The least-cost conservation model can provide useful in-sights Indoor conservation is more widespread but thesavings are lower than outdoor conservation The mostcost-effective widely adopted indoor conservation actionsare retrofitting bathroom faucets and showerheads butretrofitting toilets with HETs holds the greater potential ofwater savings The rebates for high-efficiency laundry ma-chines give EBMUD the highest water saving per unit costof conservation Other insights such as the effectiveness ofreduced landscape water requirement rebates (cash for grass)or price increase effects can also be produced by the modeland are presented in Cahill (2011)

The least-cost modeling approach after further testing hasthe potential to be applied to other neighborhoods or citiesafter adjusting the parameter distributions The existing con-ditions model can be easily adapted to other communities orservice areas using reasonable market penetration assump-tions and adjusting for geographical factors Both modelingcomponents provide a more detailed and mechanistic un-derstanding of household water use and conservation deci-sions based on physical parameters rather than on empiri-cal relationships like many traditional regression analysis ap-proaches

AcknowledgementsSpecial thanks belong to David Rosenbergfor sharing his previously developed model for adaptation tothe EBMUD neighborhood Clifford Chan Richard Harris andDavid Wallenstein of EBMUD were willing to experiment andprovided useful data and insights Lisa Maddaus also providedhelpful information about studies on residential use throughoutCalifornia

Edited by S Thompson

References

Anderson E T and Song I Coordinating price reductions andcoupon events J Marketing Res 41 411ndash422 2004

Blokker E J M Vreeburg J H G and van Dijk J C SimulatingResidential Water Demand with a Stochastic End-Use Model JWater Res Pl-ASCE 136 19ndash26 doi101061(Asce)Wr1943-54520000002 2010

Cahill R Household Water Use and Conservation ModelsUsing Monte Carlo Techniques for the East Bay Munici-pal Utility District Masters Tesis Civil and Environmen-tal Engineering University of California Davis California92 pp available athttpceeengrucdavisedufacultylundstudentsCahillMSThesispdf(last access June 2013) 2011

CALFED Bay Delta Program Water Use Efficiency Comprehen-sive Evaluation CALFED Bay Delta Program SacramentoCalifornia available at httpwwwcalwatercagovcontentDocumentslibraryWUE2006_WUE_Public_Finalpdf(last ac-cess October 2011) 2006

CIMIS Monthly Report Evapotransipration Sacramento Califor-nia available athttpwwwcimiswatercagov(last access Oc-tober 2011) 2011

Dalhuisen J M Florax R J G M de Groot H L F and Ni-jkamp P Price and income elasticities of residential water de-mand A meta-analysis Land Econ 79 292ndash308 2003

DeOreo W Analysis of Water Use in New Single-Family Homes155 pp available athttpwwwaquacraftcomnode64(last ac-cess October 2011) 2011

DeOreo W Mayer P W Martien L Hayden M DavisD Davis R Henderson J Raucher R Gleick P andHeberger M Calfornia Single Family Water Use EfficiencyStudy 387 pp available athttpwwwaquacraftcom(last ac-cess October 2011) 2011

Dolinicar S and Hurlimann A Australianrsquos Water Conserva-tion Behaviours and Attitudes Australian Journal of Water Re-sources 14 43ndash53 2010

East Bay Municipal Utility District (EBMUD) Water Conserva-tion Market Prenetration Study Water Conservation DivisionWater Resources Engineering Inc San Francisco CA avail-able at httpwwwebmudcomsitesdefaultfilespdfsmarket_penetration_study_0pdf(last access October 2011) 2002

East Bay Municipal Utility District (EBMUD) Water Ratesand Service Charges East Bay Municipal Utility District(EBMUD) available athttpwwwebmudcomfor-customersaccount-informationwater-rates-service-charges(last accessMarch 2011) 2010

East Bay Municipal Utility District (EBMUD) Urban Wa-ter management Plan 2010 East Bay Municipal UtilityDistrict (EBMUD) Water Resources Planning Division



available at httpwwwebmudcomsitesdefaultfilespdfsUWMP-2010-2011-07-21-web-smallpdf(last access March2011) 2011

Garcia-Alcubilla R and Lund J R Derived willingness-to-payfor household water use with price and probabilistic supply JWater Res Pl-ASCE 132 424ndash433 doi101061(Asce)0733-9496(2006)1326(424) 2006

Gleick P Haasz D Henges-Jeck C Srinivasan V Wolff GCushing K K and Mann A Waste Not Want Not The Po-tential for Urban Water Conservation in California Pacific In-stitute available athttpwwwpacinstorgwp-contentuploads201302waste_not_want_not_full_report3pdf(last access Oc-tober 2013) 2003

Gumbo B Juizo D and van der Zaag P Information is aprerequisite for water demand management experiences fromfour cities in Southern Africa Phys Chem Earth 28 827ndash837doi101016jpce200308010 2003

Jacobs H E and Haarhoff J Structure and data requirements ofan end-use model for residential water demand and return flowWater Sa 30 293ndash304 2004

Kampragou E Lekkas D F and Assimacopoulos D Waterdemand management implementation principles and indicativecase studies Water Environ J 25 466ndash476 doi101111j1747-6593201000240x 2011

Komor P S and Wiggins L L Predicting Conservation Choicendash Beyond the Cost-Minimization Assumption Energy 13 633ndash645 1988

Lund J R Derived Estimation of Willingness-to-Pay to AvoidProbabilistic Shortage Water Resour Res 31 1367ndash13721995

Mayer P W and DeOreo W Residential End Uses of Wa-ter Denver Colorado available athttpwwwwaterrforgPublicReportLibraryRFR90781_1999_241Apdf(last accessOctober 2011) 1999

Narasimhan C A Price Discrimination Theory of Coupons Jour-nal of Marketing Science 3 128ndash147 1984

Rosenberg D E Residential Water Demand under Alterna-tive Rate Structures Simulation Approach J Water Re-sour Pl-ASCE 136 395ndash402 doi101061(Asce)Wr1943-54520000046 2010

Rosenberg D E Tarawneh T Abdel-Khaleq R and LundJ R Modeling integrated water user decisions in inter-mittent supply systems Water Resour Res 43 W07425doi1010292006wr005340 2007

Sacramento Department of Utilities Urban Water ManagementPlan 2010 City of Sacramento Sacramento California avail-able at httpwwwcityofsacramentoorg(last access Octo-ber 2011) 2011

San Jose Environmental Services Department 2010 Urban watermanagement Plan City of San Jose San Jose California avail-able athttpwww3sanjosecagov(last access October 2011)2011

Sauri D Lights and shadows of urban water demand managementThe case of the metropolitan region of Barcelona Eur PlanStud 11 229ndash243 doi10108009654310303639 2003

Smirnov N Tables for estimating the goodness of fit of empiricaldistributions Ann Math Stat 19 279ndash281 1948

Sovocool K Xeriscape Conversion Study Southern Nevada WaterAuthority available athttpwwwsnwacomassetspdfabout_reports_xeriscapepdf(last access October 2011) 2005

Wilchfort G and Lund J R Shortage management modeling forurban water supply systems J Water Resour Pl-ASCE 123250ndash258 1997

Zillow San Ramon Real Estate available athttpwwwzillowcom(last access October 2011) 2011



Kampragou et al (2011) summarize guiding principles ofwater demand management strategies and programs present-ing case studies for Canada the US Europe and Asia thatemploy both market and non-market incentives The effec-tiveness of economically driven strategies seems to be linkedto the prevailing socioeconomic conditions (Kampragou etal 2011) Sauri (2003) presents a qualitative approach towater demand with historical information on water use andurban development patterns that discusses the role of pric-ing water sources augmentation technology and consumeroutreach for the Metropolitan Region of Barcelona in SpainJacobs and Haarhoff (2004) present a model that predicts enduses by household using detailed physical and behavioralparameters affecting demand

Some models rely heavily on large amounts of datato model end use and conservation potential Blokker etal (2010) present a simulation model for water demandpatterns in a region of the Netherlands using a very smalltimescale at the residential level This method is presentedas an alternative to metering using data management pro-grams that have proved to be useful in other areas (Gumboet al 2003) The end-use model developed by Blokker esti-mates water demand based on parameters affecting water use(eg frequency of hand washing) Compared to householdmetered data the model had good fit overall The end-usemodel includes pulse intensity time of use and duration foreach end-use type user and busy time per end use Howeverthis model does not include outdoor uses (which are small inthe Netherlands) and whereas aggregate demand is close tothe measured data the approach relies on high quality appli-ance information and behavioral data which is more suitablefor regions with homogeneous demographics (Sauri 2003)

Still other household use models attempt to calculate thewater used for each end use of individual homes using re-gression analysis (DeOreo et al 2011) These models buildheavily on end use measurement data paired with survey re-sponses and find statistically significant parameters affect-ing each end use of water Empirical equations are then de-veloped to predict each end use as a function of these sig-nificant parameters The strength of the regression analysisresults for estimating water demand of individual homes isoften low with coefficients of determination (R2) typicallyaround 04 (DeOreo 2011) Such models perform reason-ably for estimating current average water use for groups ofhouseholds and are useful in estimating the effectiveness ofand potential for water conservation measures under differ-ent scenarios Water pricing or more complex rationing con-ditions are usually absent from these models However liter-ature on household water demand often concludes that priceis an important factor affecting total water use (Dalhuisen etal 2003 Rosenberg 2010)

While regression-based (inductive) models are useful fordifferent purposes a more mechanistic or deductive model-ing approach can now be undertaken with the large amountsof data available from end use measurement studies In

contrast to more inductive or empirical techniques for house-hold water demand analyses this paper presents a more de-ductive (ldquocausalrdquo) household end-use model based on phys-ical parameters affecting water use that vary by householdWe employ a Monte Carlo approach to include variability inhousehold physical characteristics and behavior when esti-mating distributions of household water use and conservationpotential This modeling approach is applied to a neighbor-hood in the East Bay Municipal Utility District (EBMUD)service area California The model extends a previously de-veloped model that estimated household water use in Am-man Jordan (Rosenberg et al 2007) Rosenbergrsquos modelaccurately reflected actual water use patterns in Jordan butsuch an approach has not been attempted in the US whereurban water utilities often offer water conservation rebates totheir customers

After an overview of the modeling approach a short sum-mary of the case study area (San Ramon California) is pre-sented Then (1) existing conditions use and (2) least-costconservation models are described in detail Third calibra-tion and modeling results are presented and discussed witha cost-effective assessment of different short- and long-termconservation actions Finally the inherent limitations and de-sirable extensions of this modeling approach are discussed

2 Modeling overview

The framework developed for this study can be thought ofas two interrelated models (1) ldquoexisting conditionsrdquo and (2)ldquoleast-cost conservationrdquo (Fig 1) The ldquoexisting conditionsrdquocomponent simulates water demand by end use for a neigh-borhood and can be calibrated to metered data The param-eterized demand equations from the ldquoexisting conditionsrdquocomponent are later employed by the ldquoleast-cost conserva-tionrdquo model to estimate the cost minimizing short- and long-term water saving actions for each household To make thedistinction between each model clearer Table 1 presents a listof possible outputs desired by utilities along with the modelthat can provide the output The list in Table 1 is not compre-hensive but it shows capabilities of each model

21 ldquoExisting conditionsrdquo water use model

The existing conditions model estimates household wateruse by end use using uncertain physical parameters cal-ibrated to metered data This model is analogous to themodels developed by Blokker et al (2010) and Jacobs andHaarhoff (2004) In this model conservation devices suchas low flow showerheads are present in their assumed mar-ket penetration rates and the households make no behavioralchanges This simulation approach allows evaluation of spe-cific alternativesrsquo effect on total water use (eg What wouldthe water use be if all households installed warm-seasonturf) The basic process is as follows



























3 Metered data














Q =

(liters

cycle

)(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (1)












51 Model inputs




Qs =

((liters

cycleStd

)minus

(liters

cycleEfficient

))middot

(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (2)





0

100

200

300

400

500

0

20

40

60

80

100

120

140


Wate

r U

se (

lite

rs p

er

cap

ita p

er

day)

Wate

r U

se (

gall

on

s p

er

cap

ita p

er

day)




Modeled Results



513 Costs


































Summer


Winter










MinimizeZ =

suml

clLl + jsum

e

[pe

(isum

s

(csSse

)+ Be

)] (3)



523 Constraints




We le

sumu

Eue foralle (5)








suml2




sums2





sums2













6 Results














0

5

10

15

20

25

30

35

40

45

50

Only flushwhen

necessary

Find andfix leaks


washing

Reduceshowerlength

Reduceshower-taking

frequency


frequency

StressIrrigate

Wash carwith

buckets


pool

Perc

en

t a

do

pti

on

Summer Regular

Summer Shortage


Winter Regular

Winter Shortage













7 Conclusions






References




























































3 Metered data














Q =

(liters

cycle

)(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (1)












51 Model inputs




Qs =

((liters

cycleStd

)minus

(liters

cycleEfficient

))middot

(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (2)





0

100

200

300

400

500

0

20

40

60

80

100

120

140


Wate

r U

se (

lite

rs p

er

cap

ita p

er

day)

Wate

r U

se (

gall

on

s p

er

cap

ita p

er

day)




Modeled Results



513 Costs


































Summer


Winter










MinimizeZ =

suml

clLl + jsum

e

[pe

(isum

s

(csSse

)+ Be

)] (3)



523 Constraints




We le

sumu

Eue foralle (5)








suml2




sums2





sums2













6 Results














0

5

10

15

20

25

30

35

40

45

50

Only flushwhen

necessary

Find andfix leaks


washing

Reduceshowerlength

Reduceshower-taking

frequency


frequency

StressIrrigate

Wash carwith

buckets


pool

Perc

en

t a

do

pti

on

Summer Regular

Summer Shortage


Winter Regular

Winter Shortage













7 Conclusions






References














































Q =

(liters

cycle

)(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (1)












51 Model inputs




Qs =

((liters

cycleStd

)minus

(liters

cycleEfficient

))middot

(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (2)





0

100

200

300

400

500

0

20

40

60

80

100

120

140


Wate

r U

se (

lite

rs p

er

cap

ita p

er

day)

Wate

r U

se (

gall

on

s p

er

cap

ita p

er

day)




Modeled Results



513 Costs


































Summer


Winter










MinimizeZ =

suml

clLl + jsum

e

[pe

(isum

s

(csSse

)+ Be

)] (3)



523 Constraints




We le

sumu

Eue foralle (5)








suml2




sums2





sums2













6 Results














0

5

10

15

20

25

30

35

40

45

50

Only flushwhen

necessary

Find andfix leaks


washing

Reduceshowerlength

Reduceshower-taking

frequency


frequency

StressIrrigate

Wash carwith

buckets


pool

Perc

en

t a

do

pti

on

Summer Regular

Summer Shortage


Winter Regular

Winter Shortage













7 Conclusions






References





































51 Model inputs




Qs =

((liters

cycleStd

)minus

(liters

cycleEfficient

))middot

(cycles

weekmiddot person

)(persons

house

)[1week

7days

] (2)





0

100

200

300

400

500

0

20

40

60

80

100

120

140


Wate

r U

se (

lite

rs p

er

cap

ita p

er

day)

Wate

r U

se (

gall

on

s p

er

cap

ita p

er

day)




Modeled Results



513 Costs


































Summer


Winter










MinimizeZ =

suml

clLl + jsum

e

[pe

(isum

s

(csSse

)+ Be

)] (3)



523 Constraints




We le

sumu

Eue foralle (5)








suml2




sums2





sums2













6 Results














0

5

10

15

20

25

30

35

40

45

50

Only flushwhen

necessary

Find andfix leaks


washing

Reduceshowerlength

Reduceshower-taking

frequency


frequency

StressIrrigate

Wash carwith

buckets


pool

Perc

en

t a

do

pti

on

Summer Regular

Summer Shortage


Winter Regular

Winter Shortage













7 Conclusions






References






























































Summer


Winter










MinimizeZ =

suml

clLl + jsum

e

[pe

(isum

s

(csSse

)+ Be

)] (3)



523 Constraints




We le

sumu

Eue foralle (5)








suml2




sums2





sums2













6 Results














0

5

10

15

20

25

30

35

40

45

50

Only flushwhen

necessary

Find andfix leaks


washing

Reduceshowerlength

Reduceshower-taking

frequency


frequency

StressIrrigate

Wash carwith

buckets


pool

Perc

en

t a

do

pti

on

Summer Regular

Summer Shortage


Winter Regular

Winter Shortage













7 Conclusions






References




































sums2





sums2













6 Results














0

5

10

15

20

25

30

35

40

45

50

Only flushwhen

necessary

Find andfix leaks


washing

Reduceshowerlength

Reduceshower-taking

frequency


frequency

StressIrrigate

Wash carwith

buckets


pool

Perc

en

t a

do

pti

on

Summer Regular

Summer Shortage


Winter Regular

Winter Shortage













7 Conclusions






References









































0

5

10

15

20

25

30

35

40

45

50

Only flushwhen

necessary

Find andfix leaks


washing

Reduceshowerlength

Reduceshower-taking

frequency


frequency

StressIrrigate

Wash carwith

buckets


pool

Perc

en

t a

do

pti

on

Summer Regular

Summer Shortage


Winter Regular

Winter Shortage













7 Conclusions






References







































7 Conclusions






References

































