On the calibration and verification of two-dimensional,

Transcription

1 WATER RESOURCES RESEARCH, VOL. 36, NO. 6, PAGES , JUNE 2000 On the calibratin and verificatin f tw-dimensinal, distributed, Hrtnian, cntinuus watershed mdels Sharika U.S. Senarath, Fred L. Ogden, 2 Charles W. Dwner,,3 and Hatim O. Sharif Abstract. Physically based, tw-dimensinal, distributed parameter Hrtnian hydrlgic mdels are sensitive t a number f spatially varied parameters and inputs and are particularly sensitive t the initial sil misture field. Hwever, sil misture data are generally unavailable fr mst catchments. Given an errneus initial sil misture field, single-event calibratins are easily achieved using different cmbinatins f mdel parameters, including physically unrealistic values. Verificatin f single-event calibratins is very difficult fr mdels f this type because f parameter estimatin errrs that arise frm initial sil misture field uncertainty. The purpse f this study is t determine if the likelihd f btaining a verifiable calibratin increases when a cntinuus flw recrd, cnsisting f multiple runff prducing events is used fr mdel calibratin. The physically based, tw-dimensinal, distributed, Hrtnian hydrlgic mdel CASC2D [Julien et al., 1995] is cnverted t a cntinuus frmulatin that simulates the tempral evlutin f sil misture between rainfall events. Calibratin is perfrmed using 6 weeks f recrd frm the 21.3 km 2 Gdwin Creek Experimental Watershed, lcated in nrthern Mississippi. Mdel parameters are assigned based n sil textures, land use/land cver maps, and a cmbinatin f bth. The sensitivity f the new mdel frmulatin t parameter variatin is evaluated. Calibratin is perfrmed using the shuffled cmplex evlutin methd [Duan et al., 1991]. Three different tests are cnducted t evaluate mdel perfrmance based n cntinuus calibratin. Results shw that calibratin n a cntinuus basis significantly imprves mdel perfrmance fr perids, r subcatchments, nt used in calibratin and the likelihd f btaining realistic simulatins f spatially varied catchment dynamics. The autmated calibratin reveals that the parameter assignment methdlgy used in this study results in verparameterizatin. Additinal research is needed in spatially distributed hydrlgic mdel parameter assignment methdlgies fr hydrlgic frecasting. 1. Intrductin hydrlgic impact f land use change [Refsgaard, 1997]. Hwever, the apprpriate use f physically based mdels requires Physically based, distributed parameter hydrlgic mdels several steps. The first step requires the selectin f the apare increasingly used tday in bth engineering practice and prpriate mdel fr simulating the watershed under cnsiderscientific research. As pinted ut by Wlhiser [1996, p. 126], atin. The uncertainty regarding the apprpriateness f a par- "there seems t be little disagreement regarding the usefulness ticular mdeling apprach fr a specific watershed must be f physically-based mdels fr understanding hydrlgic sysreslved thrugh validatin tests. In this sense, mdel validatems." Distributed hydrlgic mdels have immense ptential tin is the perfrmance f tests t demnstrate the apprpriand utility in [Beven, 1985, p. 407] "frecasting the effects f ateness f the use f the particular mdel in a specific waterland-use change; frecasting the mvement f pllutants and shed. There are examples in the literature where a gd sediment; and frecasting the hydrlgical respnse f uncalibratin has been btained using the wrng representatin gaged catchments." Distributed hydrlgic mdels als have a f watershed physics [Graysn et al., 1992]. Mdel validatin is distinct advantage ver cnceptual mdels fr simulating exdefined here as the prcess f demnstrating that the mdel is treme events [Beven, 1985]. apprpriately simulating the dminant physical prcesses. In The calibratin f physically based distributed hydrlgic mst cases, validating a mdel by cnfirming that the dminant mdels is an active area f research. Mdels f this type are physical prcesses in the watershed are cmmensurate with widely held t ffer the greatest pprtunity t examine the thse simulated by the mdel is a very difficult task. Hwever, watershed characteristics may be relied upn t assist in selec- Department f Civil and Envirnmental Engineering, University f Cnnecticut, Strrs. tin f valid mdeling appraches, particularly in remving 2Department f Civil and Envirnmental Engineering, Envirnmen- mdels frm cnsideratin. tal Research Institute, University f Cnnecticut, Strrs. Mdel calibratins play an integral rle in distributed hy- 3U.S. Army Crps f Engineers, Engineer Research and Develp- drlgic mdeling. Mdel calibratin is the prcess f identiment Center, Vicksburg, Mississippi. fying mdel parameter values that allw the mdel t match Cpyright 2000 by the American Gephysical Unin. Paper number 2000WR /00/2000WR bserved hydrlgic variables as clsely as pssible using input data frm a selected perid f time. The selectin f apprpriate parameter values is greatly aided by use f a parameter 1495

2 1496 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS assignment prcedure that uses the maximum amunt f infrmatin t minimize the number f free parameters. Once calibrated, the mdel calibratin must be verified by testing using data frm ne r mre time perids different frm that used in mdel calibratin. In this paper, the term "verificatin" is used in the cntext f cnfirming the apprpriateness f a mdel parameter set btained thrugh calibratin by testing the calibrated mdel n perids f recrd different frm that used in mdel calibratin. achieve a greater degree f accuracy than that bserved in repeated, cntrlled experiments [Hillel, 1986]. The tw-dimensinal, physically based, Hrtnian hydrlgic mdel CASC2D [Julien et al., 1995] was used by Ogden and Julien [1993] t examine the influence f spatial variability in bth land surface characteristics and precipitatin n runff frm catchments up t 120 km 2 in size in single-event simulatins. Results f this study shw that the influence f spatial variability n Hrtnian runff is scaled by trite, where t r is the rainfall duratin and t e is the catchmentime t equilibrium. The calibratin and verificatin f physically based mdels has been presented as prblematic in certain applicatins [e.g., Graysn et al., 1992]. It is highly unlikely that [Gupta et al., 1998, p. 751] "the mdel calibratin prblem will simply disappear with the availability f mre and better field measure- Runff sensitivity t spatial variability diminishes as the scale f interest reaches equilibrium. Since smaller areas reach equilibrium befre larger nes, this finding indicates that the effect f input uncertainty n simulatins f Hrtnian runff is ments." Cmpared with lumped cnceptual mdels, distribsmallest at small scales. This result is valid fr Hrtnian uted mdels have a larger number f parameters and inputs runff prductin in cases f extreme rainfall, small, cnstant and are therefre susceptible t nnunique calibratins. As infiltratin rates, r n impervius surfaces. pinted ut by Beven [1989], calibrating t match a single event Cntinuus hydrlgic mdels simulate the tempral evluis nt difficult at all: a lss functin and a ruting functin are tin f sil misture ver an extended perid f interest. In this all that is needed. Hwever, as Bathurst [1986b, p. 103] pinted study the hydrlgic mdel CASC2D [Julien et al., 1995] is cnverted int a cntinuus frmulatin t determine if the ut, "the scpe fr achieving equally satisfactry calibratins based n different cmbinatins f parameter values is limited cntinuus mdel frmulatin imprves mdel perfrmance in calibratin/verificatin tests. The new frmulatin is calibrated as lng as several different hydrgraphs are cnsidered." Bathurst [1986b] emplyed this criterin t increase the likeliagainst an extended discharge time series cntaining a number hd f btaining a unique calibratin using the mdel f runff events and perids f strm hiatus. Spatially varied Syst me Hydrlgique Eurp6en (SHE) [Abbtt et al., 1986] mdel parameters are initially assigned based n published values and spatially distributed using land use and land class n multiple hydrgraphs withut emplying cntinuu simulatins. (LULC) r cmpsite sil/lulc maps. The sensitivity f the new cntinuus frmulatin t changes in parameter magni- Distributed hydrlgic simulatins require spatially distribtude is systematically examined. The shuffled cmplex evluuted rainfall input that adequately captures rainfall rate gratin (SCE) methd [Duan et al., 1991] is used t estimate dients [Ogden and Julien, 1994]. Recrding rain gauges f difvalues fr mdel parameters that require calibratin using data ferent designs each have their wn unique limitatins [Nystuen, frm a Hrtnian catchment where the mdel applicatin is 1999]. Rain gauge netwrks ften have ne r mre gauges at valid. Three different verificatin tests are cnducted by apany given time that are inperative r prviding errneus plying the mdel t simulate space/time recrds different frm rainfall measurements [Steiner et al., 1999]. Errneus rain that used in mdel calibratin. gauge bservatins are very difficult t detect withut redundant measurements at each gauge lcatin. Furthermre, rain gauges measure rainfall at a pint, while watershed scale run- 2. Statement f the Prblem ff is the result f really distributed rainfall. This pint-area The calibratin f physically based, distributed Hrtnian difference can result in significant errrs when estimating spahydrlgic mdels n single events is a tremendusly verdetially distributed rainfall frm pint measurements [Ciach and termined prblem withut initial sil misture data. Prvided Krajewski, 1999]. Rainfall input errrs are very difficult t dethere are reasnably accurate rainfall and spatially varied sil tect and quantify and can be a significant surce f hydrlgic hydraulic characteristics data, the mst significant surce f mdel errr. uncertainty is sil misture. Physically based mdels require an The traditinal calibratin/verificatin cycle fr hydrlgic initial estimate f the spatially varied sil misture field. Hwmdels requires cmparing simulatin results with bserved ever, given that sil misture data are presently unbtainable runff data. Hwever, since the bserved data are nt ttally fr all but a few select sites, this imprtant input variable is free frm defect, evaluatin f mdel perfrmance must als ften derived by crude estimatin depending n the mdelers' cnsider errrs assciated with the bserved data. Nticeable expectatin f the sil misture state. Such expectatins are changes in discharge measurements have been reprted in typically carse (e.g., dry, average, and wet). These values are cntrlled experiments repeated fr nearly identical initial either distributed unifrmly r in an ad hc fashin. Errrs in cnditins. Accrding t Smith et al. [1994], Wu et al. [1982] the estimate f the initial sil misture field ultimately lead t fund 4% differences in measured peak discharge during re- errneus mdel parameter assignment upn calibratin. petitive runff experiments cnducted n an impervius sur- Fr thse unfamiliar with the prblem, Figure 1 illustrates face. The situatin becmes even mre uncertain fr pervius the situatin. Figure l a shws the results f three independent surfaces. In a sprinkling plt experiment cnducted at the single-event calibratins f CASC2D n the Gdwin Creek Bernardin Plt 164 at Walnut Gulch in Arizna, Smith et al. Watershed (which is described later in sectin 4). Parameters [1994] fund that despite practically identical initial cnditins, used in these calibratins were distributed in space using the measured peak discharges in runff frm the study plt varied same methdlgy, which is based n maps f sil texture, by as much as 35%. This illustrates the cnsiderable natural LULC, channel lcatins, and channel crss sectins. Each f variability f the prcesses hydrlgic mdels are suppsed t the three parameter sets was btained thrugh independent simulate. Mathematical mdels shuld nt be expected t manual calibratins by different authrs f this paper. There

3 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS 1497 Calibratin Event 30 I ' I- & Observed! "! :j... Cal. 1 O,=0.4 [_.' Xt\ Cal. 2,=0 $ 10 '., Julian Day 1982 Validatin Event 2,,= ,,, C Itt -- Observed '( 150 I- t I /. x... Call g [.}1 \ --- Ca,.2 50._ Julian Day 1983 '( g 0.5 Validatin Event 1,,= Julian Day 1982 Validatin Event 3,,=0.8 30, D) -- Observed' (/)... Cal. 1 'E 20 / Cal. 2 = lo Julian Day 1986 Figure 1. Results f the single-event calibratin and three calibratin-verificatin tests. are n sil misture data fr the Gdwin Creek Watershed during the calibratin perid. Therefre the basin-averaged initial relative water cntents were assumed t be spatially unifrm and equal t 0.4, 0.5, and 0.6 fr calibratins 1, 2, and 3, respectively. Initial sil hydraulic parameters were assigned cnsidering sil textural classificatin and land use data frm published surces [e.g., Rawls and Brakensiek, 1983]. Sil hy- draulic parameters were nt allwed t vary by mre than _+50% f the published expected values. As Figure la shws, CASC2D, with three independently calibrated parameter sets, is able t perfrm quite well cmpared with the bserved hydrgraph fr this mderate event. Figure 1 als shws the results f three separate verificatin tests n three events f significantly different magnitude using the mdel parameters identified thrugh the three independent manual calibratins. Each verificatin simulatin uses the same exact basin average initial sil water cntent, with each calibrated parameter set t illustrate the effect f calibratin errrs. The basin average effective relative saturatin is defined as fllws: :-1 n 1 n Oi_ Or i=1 T}e- O r where 0i is the initial sil misture cntent in the ith grid cell, Or is the residual saturatin, and */e is the effective prsity at each grid cell with n being the ttal number f grid cells in the watershed numerical dmain. Initial water cntent values are arbitrarily selected simply t demnstrate differences in mdel perfrmance in verificatin tests under different calibrated parameter sets. Figure lb shws simulatin results fr a very small runff event with an assumed value f Simulatin results n a large event assuming is 0.8 are shwn in Figure lc. Figure ld shws simulatin results frm the three independent calibratin data sets n an event that is similar in magnitude t the calibratin event shwn in Figure l a with assumed t be 0.8. Figures lb-ld clearly illustrate significant errrs in the mdel parameter sets identified in the three independent single-event calibratins due t differences in assumed initial misture cntent. Having illustrated the prblem with this simple demnstratin, we d nt dwell n the partic- ulars f it. Rather, we devte the remainder f this paper t the remedy. This paper is rganized as fllws: Sectin 3 details sme f the key features f the new cntinuus frmulatin f CASC2D; sectin 4 prvides a brief descriptin f the study watershed and data set; sectin 5 presents the parameter assignment methdlgy, sensitivity analysis, and mdel calibratin prcedure; sectin 6 scrutinizes the results f the three calibratin-verificatin tests; sectin 7 discusses the results; and sectin 8 summarizes the key cnclusins f this study. 3. CASC2D Cntinuus Frmulatin 3.1. Hydrlgic Mdel CASC2D CASC2D (CASCade f planes, tw-dimensinal) uses a square grid representatin f the watershed at a user-selected grid size. Typical grid sizes that are used in CASC2D range frm 30 t 200 m. The riginal CASC2D frmulatin [Julien et al., 1995] includes fully spatially varied rainfall input, Green and Ampt [1911] infiltratin, tw-dimensinal diffusive wave verland flw ruting, and ne-dimensinal diffusive wave channel ruting in rectangular channels. Since the riginal publicatin n CASC2D [Julien et al., 1995], the mdel has been significantly enhanced. These enhancements include Preissmann full dynamic channel ruting [Ogden, 1994], rainfall interceptin and retentin [Ogden, 1998], infiltratin with redistributin [Ogden and Sagharlan, 1997], and cnsideratin f a variety f channel crss sectins [Ogden, 1998]. CASC2D is supprted by the Watershed Mdeling System (WMS) hydrlgic mdel interface develped at the Engineering Cmputer Graphics Labratry at Brigham Yung University thrugh funding by the U.S. Army Crps f Engineers, Waterways Experiment Statin. The WMS interface signifi- cantly simplifies creatin f CASC2D input and parameter sets and prvides a link between CASC2D and the Arc/Inf and GRASS Gegraphical Infrmatin Systems. CASC2D has been used as a hypthesis testing and a predictive tl [e.g., Sagharlan et al., 1995; De et al., 1996] in watersheds where infiltratin excess is the predminant runff-prducing mechanism [Ogden and Julien, 1994; Ogden and Senarath, 1997]. Ogden [1998] gives cmplete descriptin f the current mdel Evaptranspiratin Frmulatin Tw different ptins are available fr cntinuus sil misture mdeling in CASC2D. The first ptin is a bare grund evapratin frmulatin fr watersheds with sparse data r vegetatin. This methd is essentially a simple Fickian flux frmula that is dependent n the gradient f specific humidity and is similar t the apprach taken by Deardrff [1977]. The secnd ptin mdels evaptranspiratin frm a vegetated land surface using the mre advanced Penman-Mnteith frmula [Mnteith, 1965, 1981]. Variants f these tw ptins are widely used in land surface schemes f climate mdels and distributed hydrlgic mdels [e.g., Dickinsn et al., 1986; Beven, 1979]. Measured hurly values f diffuse radiatin, ttal sky cver, dry bulb temperature, relative humidity statin pressure, and wind speed are required inputs fr bth methds. The use f the Penman-Mnteith frmulatin additinally requires input f spatially varied values fr vegetatin height, canpy resistance at nn, shrtwave albed, and vegetatin transmissin cefficient. Fr simplicity, seasnality effects n these parameters are nt included in the frmulatin, which restricts use f the methd t similar perids during the grw-

4 1498 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS ing seasn. Canpy resistance values are varied diurnally by multiplying the nn canpy resistance values by a nrmalized empirical time-based functin derived frm diurnal variability bservatins [Sziecz and Lng, 1969; Stewart and Thm, 1973]. The bare grund evapratin frmulatin requires nly the input f spatially varied values fr shrtwave albed. The fllwing sectins describe the key cmpnents f evaptranspiratin mdeling frmulatin emplyed in CASC2D Bare grund evapratin mdeling ptin. The bare grund evapratin rate f the grund is represented mathematically as fllws: E = pacml aot*[qsat(ta) -- qa], (2) where ioa is the air density and u a is the wind speed 2 m abve the grund surface. The dimensinless misture transfer cefficient applicable t bare sil is dented by c. The saturatin specific humidity is dented by qsat(tg) and is given by e S qsat(rg) = 8 p_ (1-8)es' (3) where A+',/ (r ) ' (6) A slpe f the specific humidity/temperature curve between the air temperature and the surface temperature f the vegetatin (kpa/øc); X latent heat f vaprizatin f water ( MJ/kg); a* sil wetness factr, as defined in (4); Cp specific heat f air at cnstant pressure, equal t kj/(kg øc); / the psychrmetricnstant (kpa/øc); r a aerdynamic resistance t the transprt f water vapr frm the surface t the reference level z (s/m); rc Mnteith canpy resistance (s/m) t the transprt f water frm sme regin within r belw the evaprating surface t the surface itself, expected t be a functin f the stmatal resistance f individual leaves (Under wet canpy cnditins, rc = 0.); A* available energy given by A* = (R l + Rs) - G (W/ R s net incming shrtwave radiatin measured at the reference level z (W/m2); where e is the rati f mlecular weight f water vapr t dry R l net lngwave radiatin measured at the reference level air (0.622); the specific humidity q a is btained by using e = z (W/m2); res, where r is the relative humidity; and T a is the grund G the sum f energy fluxes int the grund t adsrptin temperature. The wetness factr a* is a functin f sil misby phtsynthesis and respiratin and t strage ture. Fllwing Budyk [1948] and Manabe [1969], the wetness between grund level and z (W/m2). factr is estimated by using the fllwing tw relatinships: The height f the standard reference level z is taken as 2 m. The present frmulatin des nt calculate the vegetatin can- O/v -- W' (4) py leaf temperature. Therefre the grund temperature is Wee 1.0 W>_Wc W<Wc, substituted fr leaf temperature when calculating A. The psychrmetric cnstant, /is defined using the fllwing relatinship: where W is the misture available in the upper sil layer at the beginning f the time step and Wc represents the fractin f sil field capacity at which ptential evapratin ceases. The latter is represented mathematically as fllws: -3, (7) Wc = 0.75Wfc = 0.75r/e dsil, (s) where P is the atmspheric pressure (in kpa). The saturatin vapr pressure gradient A is apprximated using where Wfc is the sil field capacity and dsil is the depth f the upper sil layer. The cnstant 0.75 is taken frm Williamsn et A = 4098es/( Tg) 2. (8) al. [1987] and dentes the fractin f the field capacity at which The rate f water diffusin frm the grund surface due t ptential evapratin ceases. It is als assumed that evapturbulence is cntrlled by the aerdynamic resistance term r a transpiratin ceases when sil water cntent reaches the wiltin (6). This quantity is a functin f wind speed and height f ing pint. the vegetatin cver and is mathematically represented as fl Evaptranspiratin mdeling ptin. The Penlws: man-mnteith equatin is ne f the mst advanced resistance-based mdels available fr the predictin f evaptrans- In In piratin frm a vegetated land surface [Shuttlewrth, 1993]. Zrn Z v Evaptranspiratin estimates are btained by cnsidering the r a = (0.41)2U z canpy resistance and aerdynamic features f a vegetated, (9) surface under meterlgical frcing. As pinted ut by Mnteith [1965], several simplifying assumptins were used t derive the Penman-Mnteith evapratin frmula. Despite thse simplifying assumptins, Lemeur and Zhang [1990] fund that the Penman-Mnteith apprach is better than bth the cmplimentary relatinship areal evaptranspiratin (CRAE) [Mrtn, 1983] and the advectin-aridity [Brutsaert and Stricker, 1979] mdels fr arid watersheds. In ur applicatin f the Penman-Mnteith mdel, actual evaptranspiratin estimates are btained using the fllwing equatin: Ol * z4 * q- p ac p (es- e) where Zu and Z e are the heights f the wind speed and humidity measurements (in m), respectively, and Uz is the wind speed (in m/s). Fllwing Brutsaert [1975], it is assumed that Zm= 0.123hc and Z, = hc. In additin, fllwing Mnteith [1981], it is assumed that d = 0.67h c, where h c is the mean height f the crp Sil misture strage accunting. Actual evaptranspiratin estimates frm ne f the tw ptinal methds ((2) r (6)) are deducted frm the sil misture strage within each cmputatinal grid cell using an hurly time step. The maximum sil misture strage allwed in each grid cell is given by r edsil, and the wilting pint water cntent cntrls the minimum pssible sil misture strage. The use f the wetness factr a* in (2) and (6) prvides cupling between actual evaptranspiratin and sil misture state. In the

5 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS 1499 present frmulatin the thickness f the upper sil layer d sil is slutin f Richards' equatin fr the fine-textured sils typiassumed cnstant ver the entire watershed. This assumptin cally fund in Hrtnian watersheds. The full develpment f is mst apprpriate in watersheds where the thickness f the (11) is presented by Ogden and Sagharlan [1997]. rt zne is unifrm Cntinuus Infiltratin Frmulatin 3.4. Cntinuus Mdel Frmulatin The end f a runff event is defined in CASC2D when after Sil misture redistributin between pulses f rainfall is an the cessatin f rain, either f the tw fllwing cnditins is imprtant cnsideratin fr Hrtnian runff prductin. The true: (1) a discharge peak has been recrded and the discharge riginal frmulatin f CASC2D includes Green and Ampt at the catchment utlet has fallen t a value smaller than a [1911] infiltratin. The riginal Green and Ampt [1911] frmu- user-specified threshld r (2) n peak discharge has been latin is incapable f simulating sil misture redistributin bserved and the vlume f water in the channel netwrk is and is valid nly fr a single pulse f rainfall. In situatins smaller than a threshld. The latter case is indicative f strms where there are multiple pulses f rainfall separated by perids that prduce n significant runff. f rainfall hiatus, the Green and Ampt methd underestimates The sil misture-accunting schememplyed in CASC2D the infiltratin during the secnd and subsequent rainfall assumes that during an event, sil misture redistributin dmpulses because it des nt cnsider the redistributin f the inates the evlutin f the sil misture prfile and that evapsil misture prfile that ccurs during rainfall hiatus. transpiratin has a negligible effect. It als assumes that sil The Green and Ampt-based redistributin (GAR) tech- water redistributin has ended by the end f runff, and that nique derived by Ogden and Sagharlan [1997] is nw included evaptranspiratin dminates the tempral evlutin f sil in CASC2D. The GAR methd, which is similar t the methd misture between rainfall events as discussed in sectin intrduced by Smith et al. [1993], clsely apprximates the The quantity f sil water strage at the beginning f the next slutin f Richards' equatin fr a deep, well-drained sil rainfall event is used t initialize the Green and Ampt infiltrasubject multiple pulses f rainfall [Ogden and Sagharlan, tin parameter ]. The essence f the technique is described belw. Darcy's law fr unsaturated flw can be written in the fllwing frm, assuming a rectangular sil misture prfile 4. Study Data Set [Smith et al., 1993]: Hydrlgic data cllected by the U.S. Department f Agriculture Agricultural Research Service (USDA-ARS) Natinal Sedimentatin Labratry (NSL) at the 21.2 km 2 Gdwin d -= rh -- gi -- K + Z., (10) Creek Experimental Watershed lcated near Batesville, Miswhere 0 is the misture cntent at the sil surface, Z is the sissippi, are used in this study fr mdel calibratin and veridepth t the wetting frnt, K s is the saturated hydraulicn- ficatin. The Gdwin Creek Experimental Watershed has ductivity f the sil, r h is the rainfall rate during the hiatus been cntinuusly mnitred since 1981 by the NSL. A deperid (r h < Ks), g i is the unsaturated hydraulicnductivity tailed descriptin f the study watershed is prvided byalns f the sil at the initial water cntent 0i, K is the unsaturated [1996]. There are fur main land uses in the catchment: active hydraulic cnductivity f the sil at water cntent 0, and cultivatin (14%), pasture (44%), frest (27%), and gullied G(Oi, 0) is the unsaturated capillary drive between water land (15%) [Blackmarr, 1995]. Sil textures in the watershed cntents 0i and 0. The terms Ki and K are calculated using cnsist f silt lam (80%), clay lam (19%), and sand (1%) the Brks and Crey [1964] unsaturated hydraulicnductivity types. The bserved mean annual rainfall and runff at Gdrelatin, leaving the evaluatin f the term G(Op 0) fr the win Creek frm 1982 t 1992 are 1450 and 660 mm, respecapplicatin f (10) fr 0 < 0 < r e. The unsaturated capil- tively. The elevatin f the watershed ranges frm 127 t 68 m. lary drive term G( 0, 0) is evaluated by scaling the Green and The Gdwin Creek channel netwrk is highly incised because Ampt [1911] wetting frnt suctin head parameter H c using f general degradatin due t channel straightening. The main (11) [Ogden and Sagharlan, 1997]. channel f Gdwin Creek has an average channel slpe f [Bingrief, 1996]. Data cllected by NSL include precipitatin, runff, and meterlgical variables. Precipitatin G(O,, 0) = Hc /3+1/X ß (11) measurements at Gdwin Creek are made by a netwrk f ver 30 recrding tipping bucket-type rain gauges, which are In (11), X is the Brks and Crey [1964] pre distributin quite unifrmly distributed in and arund the watershed. With index and!9 dentes the abve water cntents expressed as this dense netwrk f rain gauges, quality cntrl is required t relative water cntents: identify malfunctining gauges [Steiner et al., 1999]. Discharge 19-' (0- Or)/(T}e- Or). (12) is mnitred in 14 subbasins ranging in size frm 0.06 t 21.2 km 2. Channel discharge measurements are made at engineered As applied in CASC2D, the riginal Green and Ampt [1911] structures at the utlet f each subcatchment. The lcatins f infiltratin equatin is used t estimate the infiltratin rate all rain gauges and flw measuring statins with respect t the befre the first rainfall hiatus. During the first hiatus perid, watershed bundary and drainage netwrk are shwn in Figure (10) is used t estimate the redistributin f the rectangular 2. sil water prfile with unsaturated capillary drive calculated Tpgraphic data fr Gdwin Creek were btained frm using (11). After the secnd pnding perid, the Green and U.S. Gelgical Survey (USGS) 30 m digital elevatin maps Ampt equatin is used t estimate the infiltratin int the sil (DEMs). These data were spatially aggregated t 125 m ressurface in the prtin f the prfile between 0 and 0e. An lutin, resulting in a finite difference verland flw grid with evaluatin f this apprach [Ogden and Sagharlan, 1997] re cells. The 125 m grid reslutin was used t reduce the vealed that the methd agrees quite well with the numerical number f grid cells in the finite difference mesh and decrease

6 1500 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS Legend / x Streamflw gage with rain gage 1- Rain gage clay Gullied land, silt lam Cttn/sy, clay lam vy [- ':':,... _... [ Pasture, silt lam $ i... '"'-" ' [ Cttn/sy, silt lam ' -" ' :'.... ' ' ' [ Pasture, clay l am r...' Frest, clay lam 4 [ Frest, silt 1a Water._,!4 ii! /--- 1 [ Scale(m) : Figure 2. Gdwin Creek Experimental Watershed.,000_._.020,000 -,000_._2 Scale(m) 0,00 Figure 4. Reclassified sil and land use cmpsite map f the Gdwin Creek. mdel run time. Nnetheless, the selected grid reslutin prvides an adequate descriptin f the spatial variability f sil textures and land use/land cver. Sil textural classificatins fr the watershed are btained frm the USDA-NRCS (frmerly SCS) cunty sil surveys. LULC data derived frm satellite imagery and grund survey recrds [Blackmarr, 1995] are btained frm NSL. The LULC map f Gdwin Creek is illustrated in Figure 3. The sil textures and LULC maps are merged tgether t identify regins with similar LULC and sil type. The resultant cmpsite is shwn in Figure 4. The infrmatin prvided in Figure 4 was used fr the assignment f sil hydraulic parameters. Hurly slar and meterlgical data are btained frm the NOAA surface weather statin in Mem- phis, Tennessee, which is situated -130 km nrth f the watershed. Grundwater des nt cntribute significantly t runff in the Gdwin Creek Watershed. The base flw at the utlet f the catchment is typically <0.05 m3/s. The channels in the watershed are incised 2-3 m as a result f the channel straightening wrk carried ut in the early 1900s and the subsequent degradatin f sme f these channels. Measurements f grundwater levels taken adjacent t the main channel shw that the grundwater table is several meters belw the grund surface. Grundwater fluctuatins during runff events bserved in wells adjacent the channel indicate a 5-10 cm rise in the grundwater table during significant runff events. This rise quickly subsides, indicating a mderate bank strage ef- [-]Frest..... Figure 3. Land use classificatin map f the Gdwin Creek Watershed. fect. Simn et al. [1999] bserved negative pre pressures during runff events in a study f bank failure mechanisms alng Gdwin Creek. These watershed characteristics, taken tgether with the predminance f fine sil textures, indicate that the infiltratin excess runff prductin mechanism is dminant in Gdwin Creek and that CASC2D has a valid frmulatin fr use in this watershed. 5. Mdel Parameter Assignment and Calibratin CASC2D parameters cnsist f spatially distributed tpgraphy, sil hydraulic characteristics, evaptranspiratin parameters, channel lcatin, and crss-sectin prperties. Given the large number f mdel grid cells within the watershed, a systematic apprach was develped t assign spatially varied parameters. The sil textural classificatin and LULC data were cnsidered in cmbinatin t identify areas within the watershed that have cmmn sils and land use classes (see Figure 4). This apprach acknwledges the influence f land use n sil hydraulic behavir. Each cmmn sil/lulc class was assumed t have identical sil hydraulic prperties. The use f classes greatly reduces the cmplexity f assigning spatially varied parameters. All spatially varied sil hydraulic characteristics parameter maps were derived frm the cmpsite sil/ LULC map. All vegetatin-based maps are derived frm the LULC map. Initial estimates f sil hydraulic prperty values, namely, saturated hydraulic cnductivity, Green and Ampt wetting frnt capillary head, effective prsity, residual water cntent, wilting pint water cntent, and pre-size distributin index, were btained frm surrgate published values [Rawls and Brakensiek, 1983, 1985]. Hwever, wing t the lack f spatially distributed sil misture data, initial sil misture input values were derived slely by calibratin n the first runff-prducing event in the cntinuus calibratin recrd. Sil misture was assumed spatially unifrm ver the entire watershed. Mdel parameter values with unknwn spatial distributins, such as the depth f the upper sil layer and channel rughness cefficients, were assumed spatially unifrm ver the entire watershed. Values f shrtwave albed, vegetatin height, vegetatin transmissin cefficient, and canpy resistance were assigned based n land use classificatin shwn in Figure 3, and initial values were btained frm published literature [e.g., Bras, 1990; Pielke, 1984].

7 ,,,, SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS 1501 Spatially varied rainfall and runff data measured at the utlet f Gdwin Creek (gauging statin 1 n Figure 2) frm May 22 t June 30, 1982, were used fr mdel calibratin. Althugh available, n data frm interir stream flw gauges were used t calibrate the mdel. The mdel was calibrated against hydrgraphs recrded at gauging statin 1 nly. Ten strms with measurable precipitatin ccurred at Gdwin Creek during the calibratin perid. Fur f these strms prduced runff at the basin utlet. Unless therwise specified, a strm is classified as a runff-prducing event nly if its bserved peak discharge >0.5 m3/s. Hydrgraphs with peak discharges belw this threshld are inadequate fr any cmparative errr analysis because they cntain very few rdinates Manual Calibratin The manual calibratin prcess was tightly cnstrained in that maintaining physically realistic values f all mdel parameters is cnsidered paramunt in the cntext f physically based mdeling. The mst sensitive parameters were varied in a systematic fashin within each cmmn land use/sil type classificatin in an attempt t match the simulated hydrgraph. During manual calibratin the retentin depth, verland rughness, and channel hydraulic rughness were assumed spatially unifrm. Apprximately 70 manual calibratin simulatins were perfrmed. It became clear that manually btaining an ptimal calibratin with such a large number f parameters wuld take an inrdinate amunt f time Sensitivity Analysis A detailed sensitivity analysis was perfrmed t identify the mst sensitive parameters f the enhanced CASC2D frmulatin based n the results f the manual calibratin. The sen- sitivity f the mdel t 14 physically based mdel parameters was evaluated by systematically and unifrmly varying the calibrated mdel parameters by + 10% and -10%. The effect f each change n the fur runff-prducing events during the calibratin perid was evaluated separately t examine the evlutin f the sensitivity during the cntinuus simulatin. This sensitivity analysis cnsidered the percentage change in peak discharge (PCPD), the percentage change in runff vlume (PCRV), and the rt-mean-squarerrr (RMSE) f each runff hydrgraph. The PCPD is calculated as fllws: PCPD = Qm 100%, (13) where Qs and Qm refer t peak flws f the hydrgraphs with perturbed parameter values and the manually calibrated parameter values, respectively. The PCRV is calculated using PCRV -- Vm 100%, (14) where V s and Vm refer t the hydrgraph vlumes f the perturbed and the manually calibrated hydrgraphs, respectively. The rt-mean square-errr (RMSE) is anther useful indicatr f mdel perfrmance. The rt-mean-square difference between the bserved and simulated hydrgraph rdinates at all cmparable pints alng the time axis is very sensitive t hydrgraph timing differences. Nte that identical hydrgraphshifted in time can have large RMSE values. The mathematical definitin f RMSE is as fllws: = Q) t/ ' i=1 > H c --- Runf[ Event 1 Runff Event 3 [] z E i i n n []( X C,< )x h Percent change RMSE w th +10% change Peak d scharge w th +10% change Runff vlume w th +10% change Runff Event 2 Runff Event Percent change A RMSE w th -10% change + Peak discharge with -10% change x Runff vlume w th -10% change Figure 5. CASC2D sensitivity t parameter variatin f the manually calibrated flw recrd. where Qs and Q refer t the rdinates f the simulated and bserved hydrgraphs, respectively. Here n refers t the ttal number f hydrgraph rdinates used in the analysis, while the i is the index denting individual hydrgraph rdinates. The fllwing equatin is used t calculate the percent change in RMSE (PCRMS) due t parameter variatin: RMS- RMSm PCRMS = RMSm 100%. (16) The RMS m values used in (16) is btained by substituting Qm fr Qs in (15). The sensitivity f the mdel t parameter variatin during each f the fur runff-prducing events in the calibratin perid is illustrated in Figure 5. The mdel sensitivity t changes in pre distributin index k, capillary head H c, Manning's channel rughness n c, Manning's verland rughness n, initial sil misture cntent 0i, height f vegetatin h c, canpy resistance rc, saturated hydraulic cnductivity Ks, sil water retentin depth dr, and depth f upper sil layer du are illustrated in Figure 5. The mdel was fund t be mst sensitive t the fllwing parameters: channel hydraulic rughness cefficient, sil saturated hydraulic cnductivity, sil capillary head, verland flw rughness cefficient, and canpy resistance. Ntice that the mdel frmulatin is sensitive t a larger number f parameters fr the smallest event simulated during the calibratin perid. Als ntice that the sensitivity f the mdel t the estimates f initial sil misture is high during the first event but is greatly reduced during successivevents. Althugh CASC2D runff estimates are sensitive t the misture cntent at the beginning f the event, the cntinuus capability greatly reduces the imprtance f user estimates f initial misture Autmated Calibratin We decided t use an autmated calibratin prcedure t mre fully explre the parameter space. After a review f the available methds, we selected the SCE ptimizatin methd [Duan et al., 1992]. The SCE methd is rbust and develped specifically fr and is ideally suited t the autmated calibratin f lumped parameter hydrlgic mdels. In rder t use

8 1502 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS Table 1. Summary f Optimizatin Cst Functins fr Calibratin and Verificatin Perids Verificatin Verificatin Verificatin Optimizatin Calibratin Cst Cst Cst Set Number Cst Functin Functin Functin (OSN) Functin the SCE methd with the grid-based CASC2D mdel, mdel parameters were varied accrding t the sil texture/lulc classes. This reduced the number f pssible calibratin parameters t a mre manageable number. The SCE ptimizatin rutine requires cmputatin f a cst functin. The selectin f cst functin weights can have an impact n the perfrmance f ptimizatin methds [Gupta et al., 1998]. We subjectively used a cst functin that places 60% weight n the relative errr in peak discharge and 40% weight n the relative errr in runff vlume. The use f relative errrs rather than abslute errrs eliminates the influ- laxed, and anther series f 5000 simulatins started. At the end f the fifth series f 5000 simulatins, the SCE methd was prducing very small changes in the minimum cst functin, and all parameters were well within the range f cnstraints. The SCE ptimizatin prcedure resulted in a large number f ptential parameter sets as determined by the cst functin. The smallest cst functin btained ver the entire 25,000 calibratin attempts was The distributin f cst functins fr this last set f 5000 trials is quite flat. Of the 5000 trials in the last series, 30 f the parameter sets resulted in cst functins <0.045, 859 resulted in cst functins <0.050, and 2193 had cst functins < Selectin f the ptimal parameter set frm this flat distributin is very difficult. We decided t use additinal infrmatin t make the final selectin f the ptimal parameter set. The 500 parameter sets with the smallest calibratin cst functins were tested in CASC2D simulatins against three verificatin data sets frm 1983, 1985, and The tp 10 parameter sets, their resulting verificatin cst functins, and assciated parameter values are listed in Tables 1 and 2. The parameter set selected as ptimal had a calibratin cst functin f This parameter set cnsistently perfrms well ver the verificatin perids, as the results in Tables 1 and 2 shw. The hydrgraph btained using this parameter set is pltted tgether with the bserved hydrgraph fr the calibratin perid shwn in Figure 6. The related errr analysis is summarized in Table 3. The specific results f the verificatin tests n the ptimal parameter set are discussed in sectin 6. ence f event magnitude n the cst functin. The sensitivity f the SCE methd t cst functin weights was investigated. This 6. Verificatin f Calibrated Parameter Set analysis revealed that the ptimizatin methd is quite insensitive t the weights selected, prvided that the weight n relative errr in peak discharge is <70%. The cst functin was cmputed nly fr the last three runff-prducing events f the calibratin perid. The first event f the calibratin perid was nt used in calculating the cst functin because it is very sensitive t the initial estimate f the sil misture field, which we subjectively assumed was spatially unifrm. The ptimal selectin f cst functin weights is an imprtant issue [Gupta et al., 1999] but is beynd the scpe f this paper. The parameter values identified thrugh the manual calibratin were used as a starting pint fr the autmated calibratin prcedure. The manual calibratin ended with a cst functin f calculated as defined abve. In all, the SCE methd was used t ptimize the values f 16 parameters, 15 f which 6.1. Test 1: Split Sample Test This test was cnducted by extending the simulatin time by an additinal 2 mnths frm the end f the calibratin perid. This verificatin test is similar t the split sample test defined by Klemeg [1986]. Hwever, in this analysis the calibratin/ verificatin perids were nt reversed, as suggested by Klemeg [1986]. The cmparisn f simulated and bserved hydrgraphs is illustrated in Figure 7 fr the extended verificatin perid. A quantitative analysis f the results is given in Table 4 fr cmparisn. As Table 4 highlights, CASC2D verpredicts peak discharges fr the first tw runff events, mst significantly fr the smallest f the tw. The percentage difference in peak discharge values f the verificatin discharge time series vary between -44 and 57%. Out f the events illustrated in Figure 7 nly thse that have a peak discharge in excess f 0.5 m3/s are used in hydrgraph errr analysis. The largest event f are spatially varied and assigned using sil/lulc classes. the extended recrd is simulated mst accurately, within 9% f These parameters include seven saturated hydraulic cnductivities in different cmpsite sil/lulc classes that make up 98% f the watershed, fur verland flw rughness ceffithe bserved peak discharge and 25% f the bserved runff vlume. Overall, the abslute mean percentage difference in peak discharge, the abslute mean difference in time t peak, cients and fur verland flw retentin depths in different and the abslute mean difference in runff vlume f the LULC classes, and the channel hydraulic rughness ceffi- extended recrd are 34%, 41.2 min, and 54%, respectively. cient, which was assumed spatially unifrm. The ptimizatin was tightly cnstrained t insure that the parameter values 6.2. Test 2: Multiyear Test remained physically realistic. In all, 25,000 simulatins were perfrmed using the SCE ptimizatin technique n the same perid f recrd used in the manual calibratin. SCE ptimi- The bservedischarge time series frm mid-may t the end f June f the 1983, 1985, and 1986 water years were cmpared with mdel simulatin results. The same perid f each year is zatin was perfrmed in a series f 5000 simulatins per cn- simulated t minimize the effect f seasnal variatin f straint set. At the end f each set f 5000 ptimizatin simulatins, the parameter cnstraints were reevaluated n the basis f the new ptimal parameter estimates. When ptimized parameters apprached cnstraints, thse cnstraints were reevaptranspiratin parameters, particularly the canpy resistance. Withut detailed understanding f the interannual variability f evaptranspiratin parameters it is best t wrk with similar perids within the grwing seasn. N runff-

9 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS _ 600 : l ;""L... Simulated ;,,,,,.,, Julian day, 1982 Figure 6. Observed and simulated hydrgraphs frm the calibratin perid. '"el.,_ prducing strms were recrded between May 22 and June 30, Therefre this perid is excluded frm the verificatin analysis. The same mdel parameter values established in the SCE calibratin were applied with the exceptin f the initial basin average sil misture cntent. Initial sil misture estimates were btained by varying the assumed unifrm initial sil misture value until the peak f the first runff-prducing event is matched. The initial basin average sil misture values identified using this apprach were 80, 80, and 75% fr 1983, 1985, and 1986, respectively. The bserved and simulated discharge time series fr the 1983, 1985, and 1986 test perids are illustrated in Figures 8, 9, and 10, respectively. Peak discharge, time t peak, runff vlume, and their assciated errrs fr the individual runff hydrgraphs during the 1983, 1985, and 1986 simulatins are listed in Table 5. The abslute mean percentage differences in peak discharge are 52, 26, and 33% fr 1983, 1985, and 1986, respectively. The abslute mean differences in time t peak fr 1983, 1985, and 1986 are 124, 63, and 26 min, respectively. Finally, the abslute mean differences in runff vlume are 49, 4, and 41% fr 1983, 1985, and 1986, respectively.,.....,_ 6.3. Test 3: Nested Subbasin Test As the third test, bserved hydrgraphs frm several internal stream gauging statins are cmpared with mdel-simulated hydrgraphs fr all test perids. Simulatin results are cmpared at gauging statins 2, 3, 5, and 8 alng the main stem f Gdwin Creek (see Figure 2). These gauges are selected fr cmparisn because Jhnsn et al. [1993] determined that these gauging statins are unlikely t be significantly influenced by backwater and because they cver a range f scales. Stream gauges 2, 3, 5, and 8 have cntributing areas f 17.9, 8.7, 4.2, and 1.5 km 2, respectively. Since the data frm these gauging statins were nt used in any way fr mdel calibratin, this cmparisn prvides a true test f mdel validity at internal lcatins. Peak discharges and runff vlumes fr each runff event during the split sample and multiyear tests were analyzed. The quantitative analysis f these cmparisns is given in Table 6. The abslute mean difference in peak discharges fr all tests at gauging statins 2, 3, 5, and 8 are 39, 44, 32, and 66%, respectively. Abslute errrs in runffvlume are 42, 39, 28, and 43% fr the same gauges, respectively.

10 1504 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS Table 3. Cmparisn f Hydrgraph Prperties fr the Calibratin Perid Event Simulated Number Simulated Peak Errr in Peak Time t Peak, Errr in Time Simulated Runff (1982) Discharge, m3/s Discharge, a % Julian Days t Peak, b min Vlume, m , , ,550 Errr in Runff Vlume, c % aerrr in peak discharge is [(simulated peak discharge - bserved peak discharge)/bserved peak discharge] 100%. berrr in time t peak is (simulated time t peak - bserved time t peak). CErrr in runff vlume is [(simulated runff vlume - bserved runff vlume)/bserved runff vlume] 100%. 7. Discussin 7.1. Sensitivity Analysis and Calibratin The calibratin perid f recrd is unremarkable. Althugh 10 strms ccur during the calibratin time perid, nly fur f these prduce runff at the basin utlet. The largest f these hydrgraphs has a peak discharge f 24 m3/s. CASC2D accurately discriminates between runff- and nnrunff-prducing rainstrms. The fur runff-prducing strms are mdeled with acceptable accuracy. It is als ntewrthy that the third runff-prducing event in Figure 6, althugh quite small in terms f peak discharge, is simulated with reasnable accuracy. The calibratin sensitivity results illustrated in Figure 5 shw that the peak discharge is mst affected by (in descending sets that resulted in a significantly smaller cst functin than the manual calibratin. Selectin f the calibratin parameter set that results in the smallest cst functin as the ptimal is nt a guarantee f the best perfrmance upn verificatin. The cst functin is rather flat in parameter space, which des nt indicate the existence f a unique calibratin. In fact, the large number f different parameter sets with cst functins near the minimum indicates that the particular parameter assignment scheme used in this study is nnptimal. In essence, the prblem is verdeter- indicate that the use f sils texture and LULC maps is imrder) saturated hydraulic cnductivity, verland rughness, perfect in parameter assignment. While this is n surprise, this channel rughness, and capillary head. The peak discharge is result indicates that there is cnsiderable need fr ptimal mderately affected by the depth f the upper sil layer, initial parameter assignment methdlgies. Ntice that the paramsil misture cntent, canpy resistance, and retentin depth. eter sets listed in Table 2 are quite similar. The autmated Runff vlume is mst affected by the saturated hydraulic calibratin results are in sme ways cunterintuitive. Fr incnductivity, capillary head, Manning's verland rughness, stance, there is a tendency fr clay-lam sils t have higher and fr the first strm nly, the initial sil misture cntent. saturated hydraulic cnductivity values than silt-lam sils. All The RMSE is mst affected by channel rughness, saturated f the resulting values are, hwever, physically realistic. The hydraulic cnductivity, capillary head, verland rughness, re- relative magnitudes f different sil types can be affected by tentin depth, and canpy resistance. The predicted hydrsil structure (e.g., layering, crusting, and cracking) and by graphs are nt affected by changes in transmissin cefficient systematic errrs in the riginal sil survey. values and are nly slightly affected by changes in shrtwave albed, vegetatin height, wilting sil misture cntent, initial 7.2. Split Sample Test sil misture (with the exceptin f the first strm), and resid- The results in Table 4 reveal that the simulated peak disual saturatin values. mined. The similarity in sme f the calibrated parameter values between different parameter sets shwn in Tables 1 and 2 charge, time t peak, and runff vlume deviate mre frm the The predicted hydrgraphs at the end f the calibratin bserved values during this verificatin perid than during the perid are practically insensitive t changes in the assumed calibratin perid. Overall, the perfrmance f the mdel is initial sil misture value cmpared t the first runff event. Figure 5 shws that the influence f errrs in the initial sil misture value Oi diminish ver time in the new CASC2D -- Observed frmulatin and are essentially gne by the third runff- Stmulated prducing event. Figure 5 als shws that the sensitivity f the mdel t changes in parameter values is highest fr events that prduce little runff. The third event in the calibratin perid 30 is the smallest. Cmpared t the larger events in the calibratin perid, the mdel is significantly mre sensitive t changes in sil hydraulic cnductivity, rughness cefficient, upper layer 20 sil depth, and retentin depth parameters during the third event. The peak discharge is mre affected by parameter variatin than the time t peak and runff vlume. 10 The SCE ptimizatin methd [Duan et al., 1992] is a capable methd fr estimating distributed Hrtnian hydrlgic 0 mdel parameters that require calibratin, prvided that a methdlgy is develped t assign spatially distributed parameters that limit the number f ptimizatin parameters. The SCE methd successfully fund a number f parameter Julian day, 1982 Figure 7. Observed and simulated hydrgraphs, 1982 split sample test.

11 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS 1505 Table 4. Cmparisn f Hydrgraph Prperties During the Split Sample Test Event Simulated Number Simulated Peak Errr in Peak Time t Peak, Errr in Time Simulated Runff Errr in Runff (1982) Discharge, m3/s Discharge, % Julian Days t Peak, min Vlume, m 3 Vlume, % , , , , , pr during runff event number 8, the smallest runff event f the extended recrd. This is cnsistent with the results f the sensitivity analysis. The largest event f this perid (with a peak discharge f 38 m3/s) is simulated with a high degree f accuracy. Simulatin errrs in peak discharge, runff vlume, and time t peak fr this strm are 9%, 25%, and -45 min, respectively. In additin, CASC2D simulates the three cnsecutive strms that ccur beginning n Julian day 223 with mean abslute errrs in peak discharge, runff vlume, and time t peak f 34%, 29%, and 54 min, respectively. Figure 9 shws that during the 1985 verificatin perid all bserved runff events are cmparatively small, having peak discharges <9 m3/s. Bth significant runff hydrgraphs are underpredicted in terms f peak discharge (in errr by 27 and 24%, respectively), with relatively small errrs in runff vlume (28 and 6.9%, respectively). In 1986, all five events have peak discharges in excess f 10 m3/s, with the largest being 48 m3/s, as shwn in Figure 10. Adjusting the initial sil misture t match the peak discharge f the first event leads t significant underestimatin f the 7.3. Multiyear Test peak discharge fr the subsequenthree events by 42, 42, and 67%, respectively. The fifth and largest event f this series is The runff recrds at the utlet f Gdwin Creek fr simulated quite well, with CASC2D verestimating the peak mid-may thrugh late June f 1983, 1985, and 1986 are quite diverse (see Table 5). Tw significant events with peak discharges f 147 and 71 m3/s ccur in 1983 tgether with a discharge and runff vlume by 15 and 46%, respectively. This event is preceded by a 16 day lng rainfall hiatus. Lng perids f rainfall hiatus amplify the effect f evaptranspiratin panumber f relatively tiny (peak discharge <2 m3/s) events. rameter uncertainty. The errrs in the fifth simulated hydr- CASC2D underpredicts the peak discharge f the first event f the 1983 simulatins by 21%. The secnd event, which is the largest f the entire study in terms f peak discharge and runff vlume, is well simulated. It is ntewrthy that even graph are likely related t errrs and uncertainty in the calibrated evaptranspiratin parameters. Hwever, it is clear that parameter values derived thrugh calibratins in 1982 are nt perfrming as well in simulatins during thugh this event has a peak discharge 6 times larger than the largest event f the calibratin perid, it is simulated by 7.4. Nested Subbasin Test CASC2D with a 12% errr in peak discharge and a -21% errr in runff vlume. The tw significantly smaller events immediately fllwing the largest event are nt simulated well. Several recent publicatins have stated that unless validated, physically based hydrlgic mdels cannt be trusted t accurately predict flw variables (e.g., depth and discharge) at in- This culd pssibly be due t the influence f small-scale ternal pints when calibrated using data frm the catchment effects such as errrs in mdeling f sil layering/crusting, utlet nly [Graysn et al., 1992]. The purpse f the nested micrtpgraphy, partially filled retentin strage, and infil- subbasin test is t determine the skill f the new mdel fr- tratin area reductin. The last five runff events f 1983 are quite small, with bserved peak discharges <4.1 m3/s. CASC2D simulates nly the third event with a high degree f accuracy and the remainder with mderate degree f accuracy. mulatin in predicting flws at internal pints in the channel netwrk. The data frm internal gauging statins were nt used in any way during mdel calibratin. In general, the results shwn in Table 6 indicate that al E S mulated Observed Observed... S mulated 75._ 5O ,, Julian day, 1983 Figure 8. Observed and simulated hydrgraphs, 1983 test perid.,, Julian day, 1985 Figure 9. Observed and simulated hydrgraphs, 1985 test perid.

12 1506 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS Julian day, 1986 Figure 10. Observed and simulated hydrgraphs, 1986 test perid. ificatin simulatins are cnsidered in cmbinatin t evaluate the cnsistency f peak discharge and runff vlume predictins. The results f the peak discharge cmparisns are illus- trated in Figure 11. The values vary ver 3 rders f magnitude and are therefre pltted using a lgarithmic scale. The slpe f the linearly regressed best fit line is 0.89, with standard errr f The regressin intercept is -0.3 m3/s, and r 2 value is The standard deviatin f the bserved and simulated peak discharges are 31.5 and 28.4 m3/s, respectively, while the standard errr f simulatedischarges is 1.46 m3/s. The simulated runff vlumes are similarly pltted against bserved runff vlumes fr all verificatin tests in Figure 12. Similar t Figure 11, a lg-lg plt is used because the values vary ver 4 rders f magnitude. The slpe f the linearly regressed best fit line is 0.79 with a standard errr f The intercept ccurs at 21,230 m 3, and the r 2 value is The standard errr f the predicted runff vlume is 25,800 m 3. This regressin indicates a slight tendency f the mdel t verpredict runff vlumes fr smaller events and underpredict runff vlume fr larger events. The standard deviatin f the bserved runff vlumes is 277,600 m3; standar deviatin is 240,500 m 3 fr the simulated vlumes. This cmparisn f the mdel-predicted peak discharges and runff vlumes with bserved values indicates that in a thugh calibrated at the utlet nly, CASC2D is capable f simulating peak discharges at internal catchment lcatins with a reasnable degree f accuracy. This is particularly true fr the three internal gauging statins with the largest cntribstatistical sense, CASC2D simulatin results are relatively unbiased and similar t runff bservatins; this is particularly uting areas. The errrs are mst prnunced n the smallest true fr the split sample verificatin test. This is an imprtant subbasin (gauging statin 8), where the peak discharges and runff vlumes are simulated with average abslute errrs f bservatin, as it indicates that the CASC2D mdel simulatins are behaving similar t the runff measurements at 66 and 43%, respectively. The average errrs at gauge 8 in Gdwin Creek. This cnclusin is mre valid fr simulatins terms f peak discharge and runff vlume are -12 and -43%, respectively. The cntributing area t this gauging statin is smewhat atypical f the watershed because there is a clayey sil layer that creates a perched water table in places. This likely accunts fr the tendency f CASC2D t cnsistently underpredict runff vlumes in this regin. The distributin f time-t-peak values shws n clear trend. Overall, nearer t the calibratin perid. Peak discharges and runff vlumes fr all verificatin events at internal gauging statins 2, 3, 5, and 8 are pltted n Figure 13. Simulatins frm different years are dented with different symbls. It is quite interesting t nte the year-tyear changes in mdel perfrmance. Mdel predictins at internal pints are quite gd during the split sample perid the results f the nested basin verificatin test shw significant which immediately fllwed the calibratin perid. Relative t ptential fr mdeling f catchment dynamics f ungauged the line f perfect agreement, the mdel underpredicts disnested subbasins with the new CASC2D frmulatin. charge and runff vlume t varying degrees frm ne year t the next during 1983, 1985, and Mdel perfrmance 7.5. Overall Mdel Perfrmance deterirates during simulatin perids that are farther frm Simulated hydrgraphs at the catchment utlet frm all ver- the calibratin perid, particularly n the smaller subcatch- ments. Variability in watershed characteristics n the annual r climatic scale is neglected in ur study. These results indicate that the assumptin f parameter statinarity fr Hrtnian, Table 5. Cmparisn f Hydrgraph Prperties fr the Multiyear Test Event Simulated Peak Errr in Peak Simulated Time t Errr in Time Year Number Discharge, m3/s Discharge, % Peak, Julian Days t Peak, min Simulated Runff Vlume, m 3 620,410 1,897,900 2,000 45,840 1,730 20,532 25,230 20,240 17,670 38,470 89, , , ,650 59, ,570 Errr in Runff Vlume, %

13 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS 1507 Table 6. Mdel Predictin Accuracy in Nested Subbasin Test Average Number f bserved hydrgraphs peak discharge, analyzed (mq s > 0.5 m3/s) Average simulated peak discharge, m3/s Standardeviatin f bserved peak discharges, m3/s Standard deviatin f simulated peak discharges, m3/s Simulated versus bserved peak discharge regressin slpe Standard errr f regressin slpe Simulated versus bserved peak discharge regressin intercept, m3/s Simulated versus bserved peak discharge regressin /,2 Average relative peak discharge predictin errr, % Average abslute peak discharge predictin errr, % Average bserved runff vlume, m 3 Average simulated runff vlume, m 3 Standard deviatin f bserved runff vlumes, m 3 Standard deviatin f simulated runff vlumes, m 3 Simulated versus bserved runff vlume regressin slpe Standard errr f regressin slpe Simulated versus bserved runff vlume regressin intercept, m3/s Simulated versus bserved runff vlume regressin /,2 Average relative runff vlume predictin errr, % Average abslute relative runff vlume predictin errr, % Stream Stream Stream Stream Gauge 2 Gauge 3 Gauge 5 Gauge ,000 85,190 50,890 19, ,940 62,920 43,690 12, ,320 91,110 40,210 14, ,330 73,180 44,370 11, , ,910-1, physically based hydrlgic mdels may need a clser lk. Agricultural land uses change frm year t year. In agricultural watersheds, flra and fauna vary at the annual timescale and clearly play a rle in Hrtnian runff prductin thrugh their impact n sil hydraulic prperties (e.g., livestck cmpactin f sils and wrm/mle sil aeratin) and transpiratin (e.g., grazing livestck). 8. Cnclusins New evaptranspiratin and infiltratin-redistributin cmpnents are added t CASC2D. This is dne t test whether cntinuus sil misture accunting imprves mdel perfrmance upn verificatin testing. The new frmulatin accunts fr sil misture redistributin during rainfall and changes in sil misture strage during perids f rainfall hiatus due t evaptranspiratin. The new frmulatin is physically based, unique, and parsimnius. A sensitivity analysis was perfrmed by systematically perturbing the calibrated mdel parameter values by _+ 10%. The new cntinuus CASC2D frmulatin is mst sensitive t the fllwing parameters: sil saturated hydraulic cnductivity, verland flw rughness, verland flw retentin depth, and channel hydraulic rughness, respectively. The tw mst sensitive evaptranspiratin parameters are the depth f the upper sil layer and the canpy resistance. The frmulatin is cnsiderably mre sensitive t parameter perturbatin n smaller runff events than n larger events h Calibratin (1982) I [] VSplit-sample (1982) H ß Multi-year (1983) I1 ß M' m,ear /1985 II I I I III II... - ' ' II IIIIII I I 1 I I III L,,/I IIIIII I.Multi-year(1986) II 1/ IIIII I ",',',:,,.,: iii" I I I IIIllll' 1./ I I Calibratin (1982) ß Split-sample (1982) H ß Multi-year (1983)!Jl [ [] ß Multi-year (1985) i,,,,,,,,,,,,,.,,,,,,,, = 10 s 104.Multi-year (1986) " Observed peak discharge (m 3 s -1) Figure 11. Mdeled versus bserved peak discharges fr all verificatin tests at catchment utlet. 1½ Obsemed runff vlume (m 3) Figure 12. Mdeled versus bserved runff vlumes fr all verificatin tests at catchment utlet.

14 1508 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS Peak Discharge (m a S -1) Runff Vlume (m a) Gage N. 2 Gage N i [ ' '1 ' [] ] [ ''O'1' ' [] 1983 [ A1986 I 105[ % ] E 10 ø ø Gage N, 3 Gage N [ % e3... O ' e I ø ' s 'O ß [] ' A 1986.E_ 10 ø, Gage N ø Gage N I 'O; 9'8 I2... I... ; I 'O 01 [ []1983 /.=' E ø Observed Gage N [] / 04 / Gage N C Obse ed Figure 13. Mdeled versus bserved runff peak discharges and runff vlumes at internal gauging statins 2, 3, 5, and 8, fr all verificatin tests. The calibratin discussed in this paper is based n bth manual and autmated techniques and is carried ut using 16 sil and land use-based parameter values, 15 f which are spatially varied using a sil/lulc-based scheme. It is interesting t nte that this number f calibratin parameters is equivalent t the number f parameters emplyed by the lumped parameter Sacrament Sil Misture Accunting Mdel [Burnash et al., 1973], as mdified by Peck [1976] fr inclusin in the Natinal Weather Service River Frecast System. CASC2D is calibrated at the watershed utlet using rainfall and runff data cllected frm the Gdwin Creek Watershed. The 40 day calibratin perid spans frm May 22 t June 30, A significant amunt f effrt and a high-quality rainfallrunff data set are necessary t achieve the calibratin results shwn in Figure 6. Three tests t verify the calibrated parameter set, namely, a split sample test, a multiyear test, and a nested subbasin test are cnducted. The results f these tests shw that the cntinuus CASC2D frmulatin is capable f simulating HrtnJan catchment dynamics with acceptable accuracy at bth the watershed utlet and internal lcatins. Cntinuus simulatin f sil misture greatly imprves the likelihd f btaining a verifiable calibratin. Calibrated mdel utput in terms f peak discharge and runff vlume are nearly unbiased, as shwn in Figures 11 and 12. The results f the verificatin tests shw that the cntinu- us CASC2D frmulatin has significant ptential fr a wide range f scientific and engineering applicatins in HrtnJan watersheds. The perfrmance f CASC2D in these verificatin tests, cupled with bservatins f verland flw, depth t water table, and sil textures, prvides a strict validatin f the HrtnJan runff-based CASC2D mdel fr the Gdwin Creek Watershed. Fr extreme rainfall n HrtnJan catchments, rainfall rates far exceed sil infiltratin rates. The finding that the cntinuus CASC2D frmulatin simulates larger strms mre accurately than small events indicates that the influence f uncertainty in watershed parameters n physically based, distributed, HrtnJan watershed mdels like CASC2D diminishes as strms becme mre extreme. This finding is cnsis- tent with the cnclusins by Ogden and Julien [1993], wh demnstrated that rainfall rate is a scaling variable fr Hrtnjan runff. The mst extreme event simulated in this study has a return perid f years. This strm has a peak discharge f 147 m3/s and is significantly larger than the largest runff prducing event used fr mdel calibratin (24 m3/s). The ability f CASC2D t simulate this strm with nly 12% errr in peak discharge highlights the diminishing influence f parameter uncertainty with increasing strm intensity. Larger predictin errrs assciated with smaller runff events are clearly crrelated with enhanced mdel sensitivity t smaller strms. Nevertheless, the influence f small r n runffprducing events n sil misture is significant and is cnsidered in the current frmulatin. Results frm the nested basin test shw n clear tendency tward increasing abslute relative errrs n smaller subcatchments. The mdel predictins have smaller average abslute errrs in bth peak discharge and runff vlume at gauging statin 5 than at gauging statin 2 and the calibratin pint (gauging statin 1). Mdel perfrmance n subbasin 8 is generally pr cmpared with the ther sites, with the exceptin f the split sample test. This may indicate enhanced sensitivity t seasnal/annual-scale watershed changes at smaller subcatchment scales. Hwever, the bjective f this paper is t explre the imprvement f mdel verificatin results thrugh a frmulatin that perfrms cntinuus sil misture accunting. Further study f all nested subbasins at Gdwin Creek is planned t explre this issue. It is clear, hwever, that mdel perfrmance at interir pints is significantly better fr larger events, with the exceptin f the 1986 test perid. The use f cntinuus sil misture accunting and an autmated calibratin methd makes it pssible t define an ptimal set f parameters fr CASC2D that cver a wider range f cnditins than is typical fr mdels f this type. The value f this apprach has been demnstrated with an unusually rigrus testing prcedure invlving split sample, multiyear, and nested basin tests t verify the ptimality f the calibrated parameter set. Despite the rigr f bth the calibratin and testing the ptimal parameter space is quite flat, indicating that many cmbinatins f parameters may give equally gd fits. This may pint t the need t use data ther than runff (e.g., sil misture) t further cnstrain the pa- rameter set. Acknwledgments. Carls Alns and the technical staff members at the USDA-ARS Natinal Sedimentatin Labratry at Oxfrd, Mississippi, and Billy E. Jhnsn f the U.S. Army Engineer Research and Develpment Center, Waterways Experiment Statin (ERDC- WES) prvided data used in this study. Jeff Jrgesn f ERDC-WES assisted with cntinuu simulatin frmulatin evaluatin. This study was supprted by the U.S. Army ERDC-WES thrugh cntract DACA39-96-K-0012 and the U.S. Army Research Office thrugh Yung Investigatr grant DAAH The authrs appreciate cnstructive reviews f this paper by Rdger Graysn, Hshin V. Gupta, and Jens C. Refsgaard.

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16 1510 SENARATH ET AL.: CALIBRATION AND VERIFICATION OF WATERSHED MODELS Williamsn D. L., J. T. Kiehl, V. Ramanathan, R. E. Dickinsn, and J. J. Hack, Descriptin f NCAR Cmmunity Climate Mdel (CCM1), NCAR/TN-285+STR, Natl. Cent. fr Atms. Res., Bulder, Cl., Wlhiser, D. A., Search fr physically based runff mdel--a hydrlgic E1 Drad?, J. Hydrl. Eng., 122, , Wu, Y.-H., D. A. Wlhiser, and V. Yevjevich, Effects f spatial variability f hydraulic resistance n runff hydrgraphs, J. Hydrl., 59, , F. L. Ogden, Department f Civil and Envirnmental Engineering, U-37, Envirnmental Research Institute, University f Cnnecticut, Strrs, CT (gden@engr.ucnn.edu) S. U.S. Senarath and H. O. Sharif, Department f Civil and Envirnmental Engineering, University f Cnnecticut, Strrs, CT C. W. Dwner, Engineer Research and Develpment Center, U.S. (Received August 23, 1999; revised February 8, 2000; Army Crps f Engineers, Vicksburg, MS accepted February 16, 2000.)