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Urban Water Balance 1. A Model for Daily Totals. Steyn, Douw G.; Oke, Timothy R.; Grimmond, C. S. B. 1986

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WATER RESOURCES RESEARCH, VOL. 22, NO. 10, PAGES 1397-1403,SEPTEMBER 1986  Urban le  Water  Balance  A Model for Daily Totals  C. S. B. GRIMMOND, T. R. OKE, AND D. G. STEYN Departmentof Geography,The Universityof British Columbia,Fancouver,British Columbia,Canada The water balanceprovidesa frameworkthroughwhichto studythe interactionsbetweenthe elements of the hydrologiccycle.This paperpresentsa simplemodelfor evaluatingthe components of the urban water balancebasedon standardclimatedata and easilyobtainedparametersto describethe site.The timescalecanbe variedfrom 1 day to at least1 yeardepending on the availabilityof appropriateinput data and the form of the evapotranspiration submodelchosen.The evapotranspiration modelproposed is of the combinationtype with modificationsto allow for applicationto the suburbanenvironment.An importantmethodologicalconceptthroughoutthe model is the recognitionthat a suburbanarea can be subdivided into threediscretesurfacetypesfor hydroclimate purposes (impervious, perviousunirrigated, and perviousirrigated).Presentedin this paper is an outline of the model, sensitivityanalyses,and information for its implementation.  INTRODUCTION  Water supply and flood runoff have been dominant research  energy budget and thereforein urban climate [Grimmondand Oke, this issue].  loci of urban hydrology,largelybecauseof their directimporURBAN HYDROLOGIC SYSTEM tance in water resourceand storm water managementconThe water balance of an urban volume, which can be considerations[Hen•leveldand De Vocht, 1982]. In much of this sidered to be a box with unit surface horizontal area that work it is eitherstated,or implicit,that other hydrologicprocessesare of negligibleimportance.The presentstudytakesa extendsfrom roof level to a depth in the ground below which broaderviewof the urbanwatersystemby explicitlyinvoking no net exchange of water occurs over the period of interest the concept of a water balance. The use of the water balance JOke, 1978, Figure 8.7b], may be expressedon an areal basis (which is the principle of mass conservationapplied to ex- as a depth of water: changesof water) ensuresthat the magnitudesof the various p + I = r + E + AS (1) water exchangeprocessesare viewed in context. In addition, this approachallows investigationof the interactionbetween wherep is precipitation,I is the piped-inwater supply,r is net runoff, E is evapotranspiration,and AS is the net water storthe elementsof the hydrologiccycle. This paper,the first of two, presentsa model for evaluating age change. The urban system(Figure 1) differs from that of undevelthe componentsof the urban water balance basedon standard climate data and easily obtained parametersto describethe oped areas in that in addition to the standard hydrologic site.The secondpaper [Grimmondand Oke, this issue]reports cycle, there is the provision of piped water supply and orgathe result of a study using this model in a suburbanarea of nized water disposal(gutters,sewers,floodways,and snow removal). This givesrise to two urban water subsystems.First, Vancouver,British Columbia, for I year. Such a model could be used in conjunctionwith existing the "internal" system,which consistsof water piped into, and urban runoff modelsto provide a "continuous"simulation,i.e., out of, the buildings for drinking, sanitary, industrial, and a running water balancefor a catchmentbetweenstorms.This cooling purposes(i.e., it does not interact with the outdoor would be of great value in determiningthe water statusof the environment within the catchment). Second, the "external" surfaceprior to the next precipitation event. The present systemconsistsof all the remaining water exchangesin the model permits a more rigorousdeterminationof the evapo- catchmentincludingpiped water applied for irrigation, swimtranspiration than is usually employedin continuoussimula- ming pools etc. tion models. More traditional continuous simulation models In someurban areaswhere water use is restrictedto genuhave utilized evaporation pan data: see, for example, the inely internal domestic or industrial purposes the external Wenzel and Voorhees[1980] adaptation of the Illinois Urban cycle is almost unaffected; thus the two cycles are isolated, Drainage Area Simulator (ILLUDAS) model and the Alley et and two distinct balances exist. These lend themselves to al. [1980] parametric-deterministic model. The model could simple accounting methods, especiallyif sanitary and storm also be used to study water conservationstrategies.Knowl- sewersare separate,and supply pipe leakage is small. More edge of water use patterns together with evapotranspiration commonly, very significantamounts of water are releasedto and the other componentsof the water balancegive insight the external environmentfor examplevia irrigation, vaporizainto where water is lost from the systemand where control tion in industrial cooling, pipe leakage, outfall into streams, measuresmay be most effective.The model has already been and the internaland externalsystemsare therebycoupled. In the suburbancase,to be consideredhere,the systemscan usefulin identifyingthe role of urban irrigation in the urban  be effectively recoupled 'in thefollowing ways:(1) on theinput side of equation (1) the portion of piped water supply (I) attributableto internal water use throughoutthe year can be approximatelyequatedto the mean daily water use in winter [American Water Works Association, Committee on Water Use (AWWA-CWU), 1973]; similarly, (2) on the output side,  Copyright 1986 by the AmericanGeophysicalUnion. Paper number 5W4317. 0043-1397/86/005W-4317505.00 1397  1398  GRIMMONDET AL.' URBAN WATER BALANCE,1 PRECIPITATION  (p)  ,  II II  PIPEDWATER  II II  EVAPOTRANSPIRA TION(E) II  SUPPLY(I) ...... ........  Domes tic  • r ..... Outdoor  ,• ,• II irrigation (Ie)  •1 '.. II  II  • I I  I  .  ,  I  •.•7•r.•o. • •  ]--•----•----  ' ........  --  •o•e  •  s•/•r• •r •r•  I I I(r'4•  I  / •  I  •  Po,r• •r,• •r•/o••r• j RUNOFF  I  [  I  (r)  Fig. 1. The urban hydrologicsystem(internal and externalcomponents).  the internal portion of r (which can be consideredto be the baseload of sewerage),is equivalentto [A WWA-CWU, 1973] the first of the above decouplingmethods. The modification of the hydrologic cycle which forms the external water system is usually viewed in a comparative (urban versusrural) framework. Urban precipitationmodification is a controversialsubject,but most climatologistsagree that somedegreeof enhancementis to be expected,especially in the downwind suburban or rural area [Changnon, 1981]. In temperate regions,evapotranspirationand water storage are generally thought to be reduced by urbanization due to the partial waterproofing of the surface JOke, 1982]; however, there is little work on the subject, and contradictionshave been noted JOke and McCaughey, 1983].  Water storagecomprisestwo components:surfaceretention and soil storage. Surface retention includesboth depression storage (surfacepuddles) and interception storage (held by surfacecover such as vegetationand buildings)[Aron, 1982], while soil storageresultsfrom infiltration. When the ability of the soil to transport the infiltrated water is greater than the precipitationrate it can be assumedthat all water falling on perviousareasenterssoil storageafter the surfaceretention is full.  A difficult problem in urban hydrology is the definition of appropriate catchment areas. Such definition can be based upon topography,the water supply pipe network, or the water removal pipe network. The latter can be complicateddepending on the presenceof combinedsewersor separatesanitary  Daily Weather/ Water Input  Daily Weather/ Water Input  I  EVAPO- I  WEATHER  UPDA  WEA 771ER  STORES AND J UPDATE I  TED  BUDGET  STORES  ,t  PRECIPI-  TA TION  PRECIPITA TION  PIPED WATER  DAY(t- 1) , ;q  UPDA TED STORES  PIPED WATER  DAY (t)  J-  DAY (t + 1) ,:,  ,  Fig.2. Schemat icdepicti ønofthe cømpUtatiOnal fordmat øfthe Water balan• model for aday, ß  GRIMMONDET AL.: URBAN WATER BALANCE,1  and stormwater pipes. Very rarely do the three criteria coincide.It is important to investigatethe extent to which net gain or lossof water occurs.Ideally, for water balancecalculations an area with no net accumulation/depletionis required. The nature of the surface cover is of fundamental importance in hydrologic study. A schemeto classifyland cover of urban areas for climatologicpurposeshas been suggestedby Auer [1978], but in the presentmodel it is sufficientto recognize three simplesurfacetypes:impervious,irrigated pervious, and unirrigated pervious.  1399  TABLE 1. Catchment Parameters and Daily Data Requirements Catchment  Parameters  Units  PhysicalLandcover  Impervious,A x  fractionof total area  Pervious  unirrigated,A 2 irrigated,A 3 Displacementlength, d  fractionof total area fractionof total area m  Roughnesslength vapor, Zo•  m  momentum, Zo• Measurementheight of wind, zu  MODEL  The model presentedhere is designedto calculatethe water balance componentsfor an urbanized catchmerit.The time scalecan be varied from 1 day to at least 1 year dependingon the availability of appropriate input data. In the caseoutlined here it is suitable for daily calculationsin a suburban area. This is determinedby the form of the evapotranspirationsubmodel chosen.  The followingdescriptionof the model is organizedaccording to the order of calculationshown in the flow chart in Figure 2.  vapor,  m  m  zv  m  HydrologicPropertiesof the Surfaceand Subsurface  Imperviousretentioncapacity,Sx  mm  Pervious  unirrigatedretentioncapacity,S2 irrigated retentioncapacity,S3 Soil storagecapacity, S,•  mm mm mm  Fieldcapacity, 0j,  kg of water/kgof soil Water  Use  Mean daily winter water use,lw Impervious area receiving external piped water, fi  Model Input  mm  fraction  of total area  Initial StorageConditions  The input necessaryto specifythe characteristicsof the catchmentis listedin Table 1 (top). It consistsof information regardingthe nature of the physicalland cover, hydrologic propertiesof the surfaceand subsurfacematerials, data on water use, and the statusof the various water storagesat the time the model is to be initiated.  This information  Soil  mm  Retention, impervious Retention, pervious,unirrigated Retention, pervious,irrigated  mm mm mm  Daily Data, Julian day  is utilized in  the partitioning by surfacetype, evapotranspiration,storage and runoff stepsof the calculations(Figure 2). Table 1 (bottom) givesthe climatologicaland piped water inputs to the model. A new set of thesedata are requiredfor everyday of the modelrun. The precipitationand piped water specifythe daily incrementto the water balance;the remaining data ate required by the evapotranspirationsubmodel. Guidancein estimatingsomeof the lesseasilyavailableinputs in Table 1 is offered in the final sectionof this paper.  Daily Averages  Net radiation,Q* Storage heatflux,AQs  W m-2 W m-2  Temperature, T Vapor pressure,ea Wind speed,u Soil moisture,0  øC Pa -1 ms kg of water/kg of soil Daily Totals  Precipitation, p Water piped in, I  mm mm  Areal Partitioning of Water Input  An important conceptin the model is the recognitionthat a suburban  area can be subdivided  into the three discrete  face types of hydroclimaticpurposes,namely, (1) impervious (roads, parking lots, buildings),in terms of water availability' this is considered  to be a dichotomous  surface: it is either wet  (saturated) or dry; (2) pervious, unirrigated (lawns, other greenspace,and open land not artificially watered),capableof having a moisture statusanywherefrom totally wet to totally dry on a continuous scale; and (3) pervious, irrigated (lawns, parks, golf courses watered by sprinkling), assumed to be alwayswet. The water input to the systemis divided according to the fraction of the total catchmentarea occupiedby the ith surface area A i. Therefore the precipitation volume received by the ith surfacetype pi is Pi-- AiP  le = I-  sur-  (2)  where p is the averagedepth of precipitation acrossthe catchment. On the other hand, the piped water supply I is not  lw  where lw is the mean daily winter water use. Furthermore, only pervious irrigated, or possiblyimpervious,surfacesare open to irrigation. The fraction of the impervious area being sprinkled/• is specifiedTable 1 (top). Stores and Runoff  The retention characteristicsof each surface type and the existingwater content of each store (the three surfacestores imperviousSx, irrigated perviousS2, and unirrigatedpervious S3 and the soil storeS4)are taken into accountin the calculation of runoff (Figure 2). When the retention capacity of a particular surfaceis exceededa "cascade"is initiated leading to runoff  as follows.  Impervious. At time t if the combination of precipitation, irrigation and the water storedfrom the previousday (t- 1) exceedsthe retention capacity of the store S• c, then the excess runs off, i.e.,  received byallsurfaces. Onlytheexternal partofthesupply Ie can be used for irrigation. This can be found following the A WWA-CWU [1973] relation,notedearlier,to be  (3)  ½1 q- Iel + SI t- 1)> SI c  1400  GRIMMONDET AL.' URBAN WATERBALANCE,1  then  rainfall value is not critical to the operationof the model.The suggestedfigure is based on field experience.)On these occasionsall three surface types are assumedto be wet and to lose water to the air at the potential rate given by Priestley  re1= (Pl -•-lel + S1t- 1)_ S1c S1t = S1c Pervious unirrigated. No irrigation input is received on these surfaces.If the infiltration rate f2 exceedsthe precipitation rate all water in excessof the retention capacity S2½ goesto the soil store, i.e.,  (P2-•-S2t- 1)> S2C P2  and Taylor [1972]:  E = (•/Lo)[S/(S+ 7)](Q* -- AQs)  (4)  where E is evapotranspiration,L o is the latent heat of vaporization, s is the slope of the saturation vapor pressureversus temperaturerelationship,y is the psychrometricconstant,Q* is the net all-wave radiation flux density,and AQs the subsurfaceheat flux density.This equationhas beenshownto apply over suburban terrain in wet conditions with the value of 0•,an  empiricalcoefficient, between1.2 and 1.3 [Kalandaet al.,  then  1980;OkeandMcCaughey, 1983].Here the valueusedis • = 1.28,which is in agreementwith Brutsaert[1982]. 2. Moist or "dry": when the impervioussurfacesare dry; irrigated are wet; and the unirrigatedare either moist or dry. Evapotranspirationis then calculatedby the following modified version of Brutsaert and $tricker's [1979] advectionaridity equation:  So, t --(P2 q- S2t- 1)_ S2c On the other hand, if  P2 >f2 then  S4t-- (f2 q- S2t- 1)_ S2c re2 -- P2 --f2 -- S2c  -[AA(y/(s +y))Ea]} (5)  and for both casesS2t = S2c. The infiltration can be computed using an equation such as the Horton infiltration equation [see Aron, 1982]. Pervious irrigated. In this case the equations are the same  where Ai is the proportion of the catchment coveredwith the  as above exceptfor the inclusionof the irrigation term le3. Soil. If the infiltration fills the soil storage capacity, soil runoff is generated,i.e.,  type, AA is the status of the soil moisture related to area, and Eois the so-calleddrying power of the air'  if  Ea= (C/YX•-*-- •a){(ff/k2)/[(ln (Zv-- d + Zoo/Zoo))  ithsurface type,0q'istheempirical coefficient oftheithsurface  ß(In (z, - d + ZOm)/ZOm)] } (6)  S4t > S4c  where C is the heat capacityof dry air, • and gaare the mean saturation and ambient vapor pressuresat height Zo,respec-  then  re½= S½t -- S½c  tively,u is the meanhorizontalwindspeedat heightzu,k is  The model considersfive sourcesof runoff (Figure 1). The first is from impervious surfaces,rex, the secondis from pervious  the yon Karman constant (0.40), d is the zero-plane displace-  unirrigated surfaces whenthe preciptatiori rate exceeds the  mentlength,and Zooand Zo•are the watervaporand momentum roughness lengthsrespectively.  infiltration rate, re2, the third is the equivalent from pervious irrigated areas,re3,the fourth is from saturatedperviousareas,  First,thejuxtaposition of wetanddry suburban surfaces is  The suburbanmodificationsincorporatedin (5) are twofold.  Sincethere were no existingmodelsto calculateevapotranspiration from urban areas, it was necessaryto develop one.  known to increaseE due to oasis-typeadvection JOke, 1979; Oke and McCaughey, 1983]. The inclusion of 0q'weightedby the proportion of the total area coveredby that surfacetype in the first term of (5) allows for this augmentation.Estimation of %' for the unirrigated surfacearea is based on the observed amount of soil moisture presentin suchsurfacesand the equation of Davies and Allen [1973] (see the appendix). The irrigated areas are expectedto exhibit the largest advective ef-  That  fects.The methodusedto estimatevaluesof %' (appendix)  re•, and the fifth is the sanitarysewerflow from the internal piped water supply, r•,. So r = r e q- r w, where r e = re1 q- re2 + re3 + re4, and r,•= Ire (following AWWA-CWU [1973] and equation (3)). E vapotr anspir ati on  forwarded  here is a version  of the well-known  combi-  accounts for the relative dryness of surrounding surfaces energyavailabilityand aerodynamicinfluences on evapotran- (using0•2') and the magnitudeof availableenergy(Q* - AQs). nation model (incorporating terms to account for the roles of  spiration) with modifications to allow for special suburban characteristics.These special features include recognition of the wide diversity of surfacetypes encountered(i.e., the three already noted) and the possibility of "oasis"-typeadvection. No special provision is made for vaporization due to fuel combustionor the physiologicalcontrol exertedby plants. Evapotranspirationcalculationsin the submodeldependon the generalstate of surfacewetnessas follows. 1. Wet: when surfaceretention storageis nonzero, and/or on days receivingmore than 5 mm of rainfall. (The threshold  Using a 1980 Vancouver data set values of %' were assigned as shown in the appendix.Their resultingmagnitudeseemsto be in correspondencewith the results of Shuttleworthand Calder[1979] for forestedsurfaces. The  second modification  is the addition  of AA  into  the  second termof (5).Thiscoefficient, calculated asin theappendix, is related to the areal moisture status of the suburb and  recognizes thefactthattheimpactof theaerodynamic aridity term will be directly correlated with the proportion of the total area possessing availablemoisture.  GRIMMONDET AL.: URBANWATERBALANCE,1  1401  TABLE 2. Comparisonof Measuredand Modeled Evapotranspiration  The evapotranspiration model was testedusingdata from the Sunset suburban site in Vancouver, British Columbia.  Energy balance and climatologicalobservationshave been  Mean  conducted from a 30-m tower at this location during the summer and fall periods of 1977, 1978, and 1980. The area  Bias Error,  consists ofS•ngle family housing (64%greenspace, 36%impervious, i.e.,built).Theevapotranspiration ratesweredeterminedusingthe Bowenratio-energy balanceand/oreddy  Year  n  r2  1980  29  1977, 1978  27  Root Mean  Square Error,  mm  mm  0.81  0.54  0.77  0.47  0.43  0.56  correlation-energybalanceapproaches.The former used reField data are daily averagevaluesfor the Sunsetsuburbansitein versing psychrometersthe latter a yaw sphere-thermometer British Columbia; n, number of days for which data are system.Both requirednet radiationfrom a pyrradiometerand Vancouver, available. subsurfaceheat storagefrom a parameterization.Full details of the site and instrumentation are available in the works by Kalanda et al. [1980], Steyn [1980], and Oke and McCaughey [1983].  A plot of the evapotranspiration estimates(usingthe model  plication. Evaporativelossesfrom the imperviousand pervious areas are  out]inedhereand climatological input from the Sunsetsite) versusthe measuredvalues(usingthe Sunsettower energy balancedata) is givenin Figure 3. The data includeboth the 1980 resultsused to assignthe model coefficientsand completelyindependentdata from 1977and 1978.The individual year and aggregatestatisticsare shownin Table 2. For most hydrologicpurposes,mean bias and root mean squareerrors  E• = E.A•  E2+3 = E-  E•  respectively. Thereforethe updatedimperviousretentionstorage for the next day (t q- 1) is  S•t+• =S• t-E• To avoid computingnegativestoragevalues when E > S, a  of about 0.5 mm are probably satisfactoryfor daily evapotranspiration estimates.It may also be noticed that the scatter becomeslargestat intermediatevalues.This may indicatethat the thresholdfor advectiveeffectsis improperly parameterized, or is not amenableto simpleanalysis.  surplusloss adjuster M-IS•+•l is introducedso that S•t+• = 0. ThenE2+3 is supplemented by M.  Stores and Budget Update  used,the calculationscontinue as follows:  If the "moist-dry"equation(5) is usedto calculateE, only pervioussurfacesare involvedin the update,none of the precedingadjustmentis necessary, and E z+ 3 = E. Followingthis partitioningof E, irrespectiveof the equation  After accounting for waterlossdue to runoffand evapotranspiration,the statusof the retentionand soil storesis updated(Figure 2). The partitioningof evaporativelossesis  S2t+ • = S2t - (E2+3[A2/(A2 + A3)]) and if  based on the areal fractions occupiedby each surface and  whichof tile twoevapotranspiration equations wasused.If  S2'+• <0  the "wet" equation (4) was used, all three surfacesare in-  S3t+l = S3t-(E2+3[A3/(A2 q- A3)] q- M)  volved. Thecaseof theimpervious surface addsa slightcom-  M=IS2 t+•l  S2t+• =0  and if  S3t+1 .• 0  M - IS3t+•1  S3t+1 = 0  S•t+• = S•t-- M Following this update the new daily water balance can be calculated(Figure 2). The resultscan be aggregatedto give monthly,seasonaland annualbalancesand derivedparameters suchas the runoff and evapotranspirationratios.The balancescan refer to the whole hydrologic system(internal plus external)or to the externalsystemalone. SENSITIVITY ANALYSES  MODELLED  EVAPoTRANSPIRATION  (mm)  Fig. 3. Relationshipbetweenmodeledand measureddaily evapotranspiration. Measured values are from the Vancouver Sunsetsite. Solid circle• are the data usedto developthe model coefficients, open circlesare independenttestdata.  The modelpresentedin the precedingsectionsconsistsof a schemefor partitioning water within an urban hydrologic systemand a submodelfor estimatingevapotranspiration from sucha system.While the partitioning schemeis a relativelysimpleone,andthe evapotranspiration modelis a modification of existingones,an examinationof the sensitivityof computedresultsto input parametersremainsa usefulexercise.An examination of the partitioning schemeand evapotranspirationequationsrevealsthat with two minor exceptions,the model is a strictlylinear one.The two exceptionsare  ,thenonlinear dependence of evaPotran•piration on Zovand  ZOrn. Thelinearity permits themodel sensitivity tobeexpressed as a (constant)slope.  1402  GRIMMOND ET AL.' URBAN WATER BALANCE,1  Evapotranspiration  While the Priestley-Taylorequation(equation(4)) has wellknown dependenceon net radiation, storageheat flux, and temperature,the behavior of (5) is somewhatmore compli-  TABLE 3. SensitivityAnalysisof the Evapotranspiration Model (Equation (5))  Input  ClimatologicalParameters  cated, as is shown in Table 3. In addition to these depen-  dencies,the evapotranspiration is weaklydependenton O/O s (the relative soil moisture)via AA. Step changesin AA (and  henceevapotranspiration) occuras O/O s variesaboutthe two  Average Slope  Q AQs  0.04 mm W -x m -2 -0.04 mm W -x m -2  T  0.08 mm/øC 0.002 mm/Pa -1.47 mm m -x s-x  ea  critical values of 0.6 and 0.3 (see Table 2). Within the water  balance model the evapotranspirationsubmodelinfluences both soil storageand runoff.The linkagescannotbe expressed without reference (case specific) to antecedent conditions. However, they will be more evident in transition periods (springand fall). Water Inputs and CatchmentParameters  Catchment Parameters  A3 d  0.02 mm/% - 0.25 mm/m*  z0v  -7.14 mm/m*  Zorn  -0.91 mm/m*  Q and T affect L v,s, •, and •*. *Slightly nonlinear.  The formal notion of model sensitivityis not clearly appli-  cable to theseparameters.The nature of the modelis such  urban and suburban areas are given in' the work by Oke [1986]. Alternatively,net radiation can be calculatedas the statedepends on Criticalvaluesof the variables and often sum of the net solar and net longwave radiation. The latter antecedentconditions.A good example of this is the depen- can be found using one of an array of empirical relations denceof runoff on soil storage.When soil storageis below requiring only standard air temperature,or temperatureand capacity,runoff occursonly from imperviousareas,whereas humidity, observations (see, for example, Davies and Idso under conditionsof full storagecapacity,runoff occursfrom [1979] and Brutsaert [1982]). Once the•net radiation is known the entire area. A change in water input or size of storage the storage heat flux can be parameterized using a scheme capacity will thus alter the day on which runoff generation such as that of Oke et al. [1981], The only additional inforswitchesstate (i.e., from impervioussurfacesonly to all sur- mation neededfor this relation are the fractions of the surface faces,or vice versa). coveredby imperviousand perviousland useS• Estimation of surfaceaerodynamiccharacteristicsfor cities is not straightforward. Values of the zero-plane displacement IMPLEMENTATION OF THE MODEL that some of the internal variables act like switches Whose  •tnd roughness lengthsmay be obtainedfrom wind profile  Most of the input data necessary to run the model(Table 1) are easily obtained. They include the simple catchmentdescriptorssuchas the proportionsof perviousand impervious coverand valuesof surfaceretentionstorage,soil storage,and field capacitywhichcan be assessed from tables(see,for example, Brater [1968]). The standarddaily climatologicalinput is usually readily available, although urban station networks may be sparse.If only nonurban stationsare available some allowancemust be made for urban effectson climate [Parle,  measurements, algorithms based on measures of surface roughnessgeometry,or inspectionof tables,in reverseorder of ease. For most hydrologic studies the first approach is too detailed and expensive,the secondis time consumingbut possible and site sensitive,and the third is a practical last resort. Equations for calculatingtheseparametersfrom geometricinformation can be found in the work Kutzbach [1961], Lettau [1969], Oke [1974], and Brutsaert [1982]. Tables of urban and suburban values are given by EngineeringScienceData 1972]. Unit [1972], Oke [1974], and Counihan [1975]. The water Some terms presentgreater difficulty. Water pipe data are vapor roughnesslength can be approximated using the reavailablein citieswhere use is metered,but the information lationship between transfer coefficientsand the momentum may be in a highly aggregatedform. If meter data are not roughnesslength given by Brutsaert [1982]. available,recoursemust be made to statisticalrelationships Grimmondand Oke [1986] show the full model to perform  relatingwater useto daily climatologicaldata (see,for example, Grimmond[1983], Maidment et al. [1985], and S. M. Loudon and T. R. Oke, unpublishedmanuscript,1986).Such algorithmsare site specificand shouldbe transferredto other  in a realistic manner in the case of a suburb of Vancouver,  sites with caution. The value of the mean winter water use  mild droughtin summer.Many other mid-l•titudescitieshave broadlysimilarconditionswherethe modelmay be appropriate. Vancouver may be atypical becauseof its large amounts of greenspace areasand irrigation,but the modelincorporates  (usedto estimateinternal domesticuse and sanitarysewage) shouldbe availablefrom the city water engineer,and the areal coverageof sprinklingon perviouscover can be gaugedfrom simplefieldsurveys, sincethe modeloutputis not overlysensitive to this parameter.Note that if sprinklingoccursin winter  British Columbia, although a full set of independentdata were not available to validate the model. Vancouver experiencesa temperateclimate with frequentfrontal rainfall in winter and  these as variables. On the other hand, cities experiencingextended periods with snow cover, or frozen ground, t/resent the mean summer water use should be used. special hydrologic characteristicsthat are not built into the Net radiation and the subsurface heat flux data are not model. In terms of applicability, the most restrictivepart of routinelygathered. Net radiationcanbe obtainedby linear the schemeis likely to be the evapotranspirationsubmodel.It regressionanalysisusing solar, or net solar, radiation as the incorporates empirical coefficientsderived from Vancouver predictor [Davies and ldso, 1979]. Sunshinehours or cloud observationswhich limit its transferability.Other urban eva-  coverhavea!sobeenused[Revfeim, 1981].Net solarradiation potranspirationobservationsof sufficientquality to test the requiresknowledgeof the suburbansurfacealbedo; valuesfor  submodelare unfortunatelyalmostnonexistentat present.  GRIMMOND ET AL..' URBAN WATER BALANCE,1  APPENDIX: DETERMINATION OF COEFFICIENTS AND AA IN EQUATION(5)  1. Calculation of •2' [Daviesand Allen, 1973]:  0•2' = 0•[1 - exp(- bO/O where • = 1.28, b = 10.563,0 is soil moisture in the upper 0.2  m layer,and0s is soilmoistureat fieldcapacity. 2. Calculation of •3' (from 1980data):  o•2' < 1.0 then  1.28  1403  analysis of data from the period 1880-1972, Atmos. Environ., 9, 871-905, 1975.  Davies, J. A., and C. D. Allen, Equilibrium, potential, and actual evaporation from cropped surfacesin southern Ontario, J. Appl. Meteorol., 12, 649-657, 1973. Davies, J. A., and S. B. Idso, Estimating the surfaceradiation balance and its components,in Modification of the Aerial Environmentof Plants, edited by B. J. Barfield, and J. F. Gerber, pp. 183-210, American Society of Agricultural Engineers, St. Joseph, Mich., 1979.  Engineering ScienceData Unit, Characteristicsof wind speedin the lower layers of the atmosphere near the ground: Strong winds (neutral atmosphere), Eng. Sci. Data Item 72026, Eng. Sci. Data Unit, London, 1972.  Grimmond, C. S. B., The suburbanwater balance:daily, monthly and annual results from Vancouver, M.Sc. thesis, 172 pp., Dep. of Geogr., Univ. of B.C., Vancouver, 1983. Grimmond, C. S. B., and T. R. Oke, Urban water balance, 2, Results from a suburb of Vancouver, British Columbia, Water Resour. Res., this issue.  0•2' > 1.0  (Q* - AQs) = 8.64 to  10.37MJ m-2 d-1 0•3'= 1.70  (Q* - AQs)> 10.37MJ m-2 d- 1 o•3'= 2.60 3.  Calculation  of AA  Hengeveld, H., and C. De Vocht, Role of water in urban ecology, Urban Ecol., 6, 362 pp., 1982. Kalanda, B. D., T. R. Oke, and D. L. Spittlehouse,Suburban energy balance estimates for Vancouver, B.C., using the Bowen ratioenergybalanceapproach,J. Appl. Meteorol., 19, 791-802, 1980. Kutzbach, J. E., Investigationsof the modification of wind profiles from artifically controlledsurfaceroughness,Annual Report, Dep. of Meteorol., Univ. of Wisc., Madison, 1961. Lettau, H. H., Note on aerodynamicroughness-parameter estimation on the basisof roughness-element description,J. Appl. Meteorol.,8, 828-832, 1969.  O/O s > 0.6  AA = A2 + A3  Maidment, D. R., S. P. Miaou, D. N. Nvule, and S. G. Buchberger, Analysisof daily water usein nine cities,CRWR 201, 67 pp., Cent. for Res. in Water Resour., The Univ. of Tex. at Austin, 1985. Oke, T. R., Boundary Layer Climates, 372 pp., Methuen, London,  0.3 < O/O s < 0.6  0/0s < 0.3  AA = (A2 + 2A3/2)  AA = A3  where A2 and A3 are the fractionsof the suburbanarea with pervious surfacesthat are unirrigated and irrigated, respectively. Acknowledgments.This work was supported by funds from the Natural Sciencesand EngineeringResearchCouncil of Canada. The constructivecommentsof M. Church were much appreciatedas was the help providedby B. Kalanda and S. Loudon in gatheringdata for Figure 3. The diagramsweredrawn by P. Jance. REFERENCES  Alley, W. M., D. R. Dawdy, and J. C. Schaake, Jr., Parametricdeterministic urban watershed model, d. Hydraulics Div. Am. Soc. Civ. Eng., 106(HY5), 679-690, 1980. American Water Works Association, Committee on Water Use, Trends in water use, d. Am. Water Works Assoc.,6.5, 285-300, 1973. Aron, G., Rainfall abstractions, in Urban Stormwater Hydrology, edited by D. F. Kibler, Water Resour.Monogr. 7, pp. 69-86, AGU, Washington,D.C., 1982. Auer, A. H., Jr., Correlation of land use with meteorologicalanomalies,d. Appl. Meteorol., 17, 636-643, 1978. Brater, E. F., Steps toward a better understandingof urban runoff processes,Water Resour.Res.,4, 335-347, 1968. Brutsaert, W., Evaporationin to the Atmosphere:Theory, History and  Applications, 299 pp:,D. Reidel,Hingham,Mass.,1982. Brutsaert,W., and H. Stricker,An advection-aridityapproachto estimate actual regional evapotranspiration,Water Resour. Res., 15,  1978.  Oke, T. R., Review of urban climatology 1973-1976, WMO Tech. Note 169, World Meteorol. Org., Geneva, 1979. Oke, T. R., The energetic basis of the urban heat island, Q. J. R. Meteorol. Soc., 108, 1-24, 1982.  Oke, T. R., The surface energy budgets of urban areas, Meteorol. Monogr., in press,1986. Oke, T. R., and J. H. McCaughey, Suburban-rural energy balance comparisons for Vancouver B.C.: An extreme case? Boundary Layer Meteorol., 26, 337-354, 1983. Oke, T. R., B. D. Kalanda, and D. G. Steyn, Parameterisationof heat storagein urban ar.eas, Urban Ecol., 5, 45-54, 1981. Page, J. K., The problem of forecastingthe propertiesof the built environment from the climatological properties of the green-field site, in Weather Forecastingfor Agricultureand Industry,edited by J. A. Taylor, pp. 195-208, David and Charles,Newton Abbot, 1972. Priestley,C. H. B., and R. J. Taylor, On the assessment of surfaceheat flux and evaporation using large-scaleparameters,Month. Weather Rev., 100, 81-92, 1972.  Revfeim, K. J. A., Estimating solar radiation income from "bright" sunshinerecords,Q. J. R. Meteorol. Soc.,107, 427-435, 1981. Shuttleworth, W. J., and I. R. Calder, Has the Priestley-Taylor equation any relevance to forest evaporation? J. Appl. Meteorol., 18, 639-646, 1979.  Steyn, D. G., Turbulent diffusion and the daytime mixed layer depth over a coastal city, Ph.D. Thesis, 161 pp., Dep. of Geogr., Univ. of B C., Vancouver, 1980.  Wenzel, H. G., Jr., and M. L. Voorhees,Adaptation of ILLUDAS for continuous simulation, J. Hydraul. Div. Am. Soc. Civ. Eng., 106(HYll), 1795-18!2, 1980.  C. S.B. Grimmond, T. R. Oke,andD. G. Steyn, Department of Geography, The University of British Columbia, Vancouver, British Columbia, V6T 1W5, Canada.  443-450, 1979.  Changnon, S. A., Jr., METROMEX: A review and summary, Meteorol. Monogr., 18(40),181 pp., 1981. Counihan,J., Adiabatic atmosphericboundarylayers:A reviewand  (Received October 3,1985; revisedApril 11, 1986; acceptedMay 5, 1986.)  


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