runoff using radar-based rainfall estimates: Effects of algorithm uncertainty and pixel aggregation

Transcription

1 WATER RESOURCES RESEARCH, VOL. 34, NO. 10, PAGES , OCTOBER 1998 On the simulatin f infiltratin- and saturatin-excess runff using radar-based rainfall estimates: Effects f algrithm uncertainty and pixel aggregatin Michael Winchell, 1 Hshin Vijai Gupta, and Srsh Srshian Department f Hydrlgy and Water Resurces, University f Arizna, Tucsn Abstract. The effects f uncertainty in radar-estimated precipitatin input n simulated runff generatin frm a medium-sized (100-km 2) basin in nrthern Texas are investigated. The radar-estimated rainfall was derived frm Next Generatin Weather Radar (NEXRAD) Level II base reflectivity data and was supplemented by grund-based rain-gauge data. Tw types f uncertainty in the precipitatin estimates are cnsidered: (1) thse arising frm the transfrmatin f reflectivity t rainfall rate and (2) thse due t the spatial and tempral representatin f the "true" rainfall field. The study explicitly differentiates between the respnse f simulated saturatin-excess runff and infiltratinexcess runff t these uncertainties. The results indicate that infiltratin-excess runff generatin is much mre sensitive than saturatin-excess runff generatin t bth types f precipitatin uncertainty. Furthermre, significant reductins in infiltratin-excess runff vlume ccur when the tempral and spatial reslutin f the precipitatin input is decreased. A methd is develped t relate this strm-dependent reductin in runff vlume t the spatial hetergeneity f the highest-intensity rainfall perids during a strm. 1. Intrductin 1993; Becchi et al., 1994; Mimiku and Baltas, 1996]. Unfrtunately, meaningful hydrlgic predictins are nt pssible un- The past decade has marked a new era in the field f hy- less the uncertainty assciated with the radar-derived precipidrlgy, resulting frm the installatin f the U.S. Natinal tatin can be quantified and crrected fr. The uncertainty in Weather Service Next Generatin Weather Radar rainfall estimatin frm radar reflectivity may be separated (NEXRAD) netwrk [Klazurand Imy, 1993]. This netwrk f int tw brad categries: (1) errrs resulting frm the trans- WSR-88D Dppler radars has nt nly revlutinized mdern frmatin f reflectivity t rainfall and (2) errrs due t the meterlgical frecasting but als prmises t imprve hy- spatial and tempral representatin f the true rainfall field. drlgical frecasting. The primary cntributin f the radar There has nt been a cnsensus as t the effects f uncert hydrlgy is the high spatial and tempral reslutin and tainty in the transfrmatin f reflectivity t rainfall n runff large areal cverage f the precipitatin prducts which are mdeling, nr has the tpic received substantial attentin. generated. These prducts prvide detailed infrmatin n Wyss et al. [1990] suggested that errrs in runff predictins precipitatin events, previusly unattainable with simple net- due t errrs in the radar-estimated rainfall input are f less wrks f grund-based rain gauges. The benefits f having significance than the errrs intrduced in the cnversin frm quantitative rainfall infrmatin ver large areas with a high rainfall t runff. This is cntradictry t the cnclusins f tempral and spatial reslutin have applicatins in all aspects Numec [1985] and Hudlw et al. [1983], wh argued that errrs f hydrlgy and water resurces management [see Cluckie, in precipitatin input t a rainfall-runff mdel will result in 1991]. Cluckie [1991] emphasized that in rder fr weather substantial errrs in simulated runff. Cllier and Knwles radar t reach its ptential in hydrlgy, high-quality radars [1986] indicated that specifi circumstances exist where errrs capable f prducing prducts at a small spatial and tempral in precipitatin input t a rainfall-runff mdel will be dampscale will be necessary. This task is far frm trivial as expressed ened in the cnversin t runff and ther circumstances by the wrk f numerus authrs wh have spent many years where the precipitatin errrs will be magnified in the cnveraddressing the prblem [Cllier, 1986a, b; Tees and Austin, sin t runff. While the abve cited studies address the effects 1991; Kitchen and Blackall, 1992; Se et al., 1995; Smith et al., f rainfall errrs n runff simulatins, the authrs f this 1996a]. While cntinuing t imprve techniques fr estimating paper are aware f nly ne publicatin which has investigated rainfall frm radar, these authrs acknwledge that a great hw hydrlgic predictins are affected by changes in the padeal f uncertainty in the quality f the estimate still exists. In rameters f the reflectivity t rainfall transfrmatin. In that the meantime, many studies have fcused n the applicatin f paper, Pessa et al. [1993] fund that different widely accepted radar-estimated precipitatin in fld-frecasting applicatins reflectivity-rainfall (Z-R) relatinships resulted in significantly [Kuwen and Garland, 1989; Schell et al., 1992; James et al., different simulated hydrgraphs. The paper suggests that identificatin f apprpriate Z-R relatinship parameters in real 1Nw at Nrtheast River Frecast Center, Natinal Weather Sertime is necessary in rder t prduce reliable hydrlgic vice, Tauntn, Massachusetts. Cpyright 1998 by the American Gephysical Unin. Paper number 98WR /98/98 WR $ frecasts with radar-estimated precipitatin. In the use f histrical radar data fr hydrlgic simulatins, there are many ptins available fr the identificatin f prper Z-R parameters and subsequent precipitatin bias crrectin.

2 2656 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL An investigatin int the effects f emplying different strategies fr Z-R parameter identificatin n hydrlgic simulatins is still needed. Cnsiderably mre attentin has been given t studying the effects f uncertainty in precipitatin input, due t its spatial and tempral representatin, n runff simulatins. The cnclusins have been that runff generatin is highly sensitive t the spatial and tempral scale f the input [Milly and Eaglesn, 1988; Lague, 1988; Kuwen and Garland, 1989; Krajewski et al., 1991; Ogden and Julien, 1993, 1994; Michaud and Srshian, 1994; Faures et al., 1995; Shah et al., 1996]. Several f these studies fund that runff vlumes increase as the hetergeneity f the rainfall field becmes better represented [Milly and Eaglesn, 1988; Kuwen and Garland, 1989; Michaud and Srshian, 1994], while ne study [Faures et al., 1995] fund a general reductin in runff vlumes as the hetergeneity in the rainfall becmes better represented. In additin, Obled et al. [1994] fund that while runff simulatins were quite sensitive t the spatial scale f the precipitatin input, they were nt sensitive t the tempral representatin f the precipitatin. This finding cntradicts a primary cnclusin f Krajewski et al. [1991] that representatin f the tempral variability f the rainfall is mre imprtant than prperly representing the spatial variability. One pssible explanatin t the apparent discrepancy in these cnclusins is the difference in the rainfall-runff mdels emplyed. In the study by Obled et al. [1994], saturatin-excess runff was mdeled by the TOPMODEL apprach, while Krajewski et al. [1991] mdeled the infiltratin-excess runff mechanism with a mdi- fied Sil Cnservatin Service curve number methd. Lague [1988] actually simulated bth types f runff generatin, shwing significant differences in their respnse t precipitatin variability. Lking mre clsely at the ther past studies which examined runff sensitivity t precipitatin scale, all f thse cited happened t use the infiltratinexcess mechanism t mdel the runff generatin. A review f these past studies suggests that there has been a bias tward the use f infiltratin-excess type runff as ppsed t the saturatin-excess type in the investigatins int precipitatin scale effects n runff simulatins. The few studies which have investigated the saturatin-excess mechanism prvided evidence that generalizatins cncerning the effects f rainfall variability n runff generatin cannt be made. Shah et al. [1996] recgnized this when they suggested that t understand why averaging f rainfall prduces larger errrs in runff fr sme strms than thers requires that an investigatin int the active runff-generatin mechanisms be perfrmed. shed in nrthern Texas. Table 1. Strm Events Studied and Lcatin f Radar Data Strm Date Oct. 28, 1991 Oct. 31, 1991 Sept. 10, 1992 Feb. 24, 1993 May 9, 1993 May 12, 1994 April 10, Backgrund Infrmatin 2.1. Study Site Origin f Radar Data Twin Lakes (KTLX) Twin Lakes (KTLX) Frederick (KFDR) Twin Lakes (KTLX) Frederick (KFDR) Twin Lakes (KTLX) Twin Lakes (KTLX) The regin chsen fr this study was the suthern plains f the United States. The climate f this regin in nrth central Texas near Gainesville is dminated by frntal precipitatin assciated with large synptic scale lw-pressure systems during the fall and winter, with intense cnvective activity during the spring and early summer. Accrdingly, rainfall is unifrmly distributed thrughut the year, with a slight maximum during the spring. Snw is infrequent. The physical highlights f this regin are the Red River and Lake Texma t the nrth and the brad-slping plains and gently rlling hills which cver the regin. The Timber Creek watershed was chsen fr this study because f minimal flw regulatin, its size (102 km :) and susceptibility t flash flds, and the ccurrence f several large flds during the perid f radar data availability. The watershed is riented primarily nrth t suth and varies in elevatin frm 282 m at the hilltps f the headwaters t 198 m at the watershed utlet. Timber Creek cnsists primarily f pasture, with small areas f wdlands and numerus agricultural stck pnds. Watershed sils are primarily sandy lam and lamy sand, with small areas f lam and lamy clay. The main channel length f Timber Creek is 22.9 km, with an average slpe f In mst years, Timber Creek is a perennial stream with very lw flws during August and September; hwever, in sme years it dries up fr a few weeks during thse mnths. The peak flw f recrd (since 1985) fr Timber Creek is m3/s Descriptin f Data One reasn fr chsing nrth central Texas fr this study was the relatively lng perid f radar data cvering the regin. Twin Lakes, Oklahma, is the site f the first radar t begin peratin and, accrdingly, has the lngest recrd f data. Alng with data frm the Twin Lakes, Oklahma, radar (KTLX), data frm Frederick, Oklahma (KFDR), were als used in this study. An effrt was made t btain the largest Several questins related t the use f radar data fr rainstrms with a cmplete radar recrd which als resulted in fall-runff mdeling remain unreslved, including (1) hw sig- significant flding n Timber Creek. In additin, the strms nificantly will errrs in the precipitatin data, due t the trans- analyzed fr this study all had an areal extent large enugh t frmatin f reflectivity t rainfall, affect runff simulatins, cver the entire basin fr the majrity f the strm's duratin. (2) hw significantly will the aggregatin f the radar prduct As such, this study examines the effects f within-strm rainfall in time and space affect runff simulatins, and (3) d differ- variability n runff generatin. A summary f the strms used ently mdeled surface-runff mechanisms (infiltratin-excess in this study and the radar lcatins where the data riginated and saturatin-excess) respnd differently t these surces f is prvided in Table 1. A significant aspect f this study is the precipitatin uncertainty? This paper addresses these questins thrugh applicatin f radar-estimated precipitatin t a distributed rainfall-runff mdel fr a medium-sized water- lcatin f the radar with respect t the watershed being studied. It has ften been nted that the perfrmance f a weather radar tends t deterirate at ranges far frm the radar site [Smith et al., 1996a]. Bth f the radars used in this study are

3 _ WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL 2657 lcated at a significant distance frm the watershed (200 km fr KTLX and 208 km fr KFDR), leading t l rther difficulties in btaining accurate estimatin f precipitatin. This issue highlights the imprtance f supplemental infrmatin frm rain gauges t calibrate and adjust the radar. Ten daily and hurly reprting rain gauges are lcated within 65 km f the utlet f the Timber Creek watershed; nwever, nne f... is... catcu ---'"-' w tmn the watc ncu. w nly these rain gauges a mdeling study n Timber Creek wuld be very difficult. The precipitatin measurements ver the entire 100-km 2 basin wuld be dminated by the data cllected frm the clsest gauge, prly representing the rainfall hetergeneity which ccurs ver the basin. Nevertheless, the scattered rain-gauge measurements are very useful fr calibratin and adjustment f the radar-estimated precipitatin. Of the ten gauges, fur were "hurly reprting" and the ther six were "daily reprting." The data frm the fur hurly reprting statins were btained frm the Western Reginal Climate Center in Ren, Nevada. The gauges are believed t be f the Fisher-Prter type and reprt accumulated rainfall in tenths f an inch. The data fr the daily reprting rain gauges were prvided by the Suthern Reginal Climate Center in New Orleans, Luisiana. Streamflw recrds fr Timber Creek were btained frm the U.S. Gelgical Survey (USGS). These 15-min flw data were termed "prvisinal" by the USGS, indicating that the data had nt been thrugh all f the quality cntrl prcedures. Nevertheless, they were the best data available fr the study. The streamflw data were used in calibrating several f the rainfall-runff mdel parameters. In additin, a 50-m reslutin digital evlutin mdel (DEM) was created fr the Timber Creek watershed frm USGS 1:100,000 scale digital line maps. The tpgrid functin within the arc/inf 7.0 Gegraphical Infrmatin System sftware was emplyed t cnvert these vectr line maps t a raster DEM. With tpgrid the user may specify the spatial reslutin and varius interplatin techniques t be used, as well as the filling f "sinks" t create a "hydrlgically crrected" DEM (in a hydrlgically crrected DEM, all f the water flws dwnhill tward the basin utlet by smthing ut lcal lw regins). Finally, dis- tributed sils data were btained frm the Natural Resurce study. An evaptranspiratin cmpnent was nt required, because the TCW mdel was t be run fr shrt duratin strm perids. A runff ruting cmpnent was als nt required, because the primary emphasis was in assessing the effects f radar-estimated precipitatin uncertainties n runff vlume generatin. Bth the infiltratin-excess [Hrtn, 1933] and saturatin-excess [Dunne and Black, 1970] runff generatin mccnamsmb were included in the... nlde, because f the suspicin that each respnds differently t changes in precipitatin input. The TCW rainfall-runff mdel develped fr this study incrprated a... A.+... [1 ] infiltratin mdel t cntrl the generatin f infiltratin-excess runff and used the TOPMODEL [Beven and Kirkby, 1979] apprach t cntrl the generatin f saturatin-excess runff. The Green- pt infiltratin mdel is an apprximate the -based mdel which utilizes Darcy's law. It was riginally develped t simulate infiltratin under pnded cnditins and was later mdified by Mein and Larsn [1973] t simulate infiltratin during a rainfall event. Water is assumed t enter the sil as pistn flw, prducing a sharp wetting frnt be een the wet and d znes. Parameters needed fr the Green- pt mdel include the effective hydraulic cnductivi, the effective suctin at the wetting frnt, the effective sil prsi, and the initial water cntent f the sil. Cmprehensive tables and figures fr estimating these parameters based n USDA sil texture data appear in the Handbk f Hydrl [Rawls et al., 1993]. The Green- pt mdel des nt explicitly accunt fr accelerated infiltratin rates due t macrpres; hwever, such effects can be mdeled by prperly adjusting hydraulic cnductivi [Rawls et al., 1993]. The Green-Ampt mdel als des nt accunt fr lateral mvement f sil water. This was nt cnsidered a great limitatin fr applicatin t Timber Creek, because the gentle slpes f the watershed are nt cnducive t significant lateral fluxes f sil water, assuming small hrizntal sil-misture gradients. One f the prima reasns fr chsing the Green- pt mdel t cntrl infiltratin-excess calculatins was that parameters culd be estimated frm sil-texture data. This was especially suitable fr parameterizing a spatially distributed infiltratin mdel, fr which calibratin wuld be practically infeasible. The mdel parameters estimated frm sil-texture data are likely a rugh estimate f parameter values suitable Cnservatin Service (previusly the Sil Cnservatin Service). These data have a 250-m spatial reslutin and cntain, amng ther things, infrmatin n the USDA sil series classificatin. USDA sil surveys fr Cke Cunty, Texas [Putfr the 250 x 250 m areas which they were meant t represent. Nevertheless, the spatial hetergenei f the infiltratin prcess in Timber Creek is fully represented by the applicatin f nam et al., 1979], and Graysn Cunty, Texas [Cchran, 1980], the Green- pt infiltratin scheme within the TCW mdel, were used t determine the varius physical prperties f interest fr each sil type. Withut a dubt, a great deal f uncertain exists in bth the sil pes and especially the sil prperties defined by the sils data set. The published sil which was the bjective f the infiltratin-excess runff cmpnent f the mdel. TOPMODEl. predicts the surface and subsurface hydrlgic respnse f watersheds which experience surface runff types and prperties were assumed t be true fr the purpses frm variable saturated areas [see Beven et al., 1995]. The f this study. TOPMODEL cnceptualizatin is premised upn three basic 2.3. Rainfall-Runff Mdel assumptins: (1) The dynamics f the saturated zne can be apprximated by successive steady state representatins, (2) The rainfall-runff mdel fr this study, hereafter called the Timber Creek Watershed (TCW) mdel, was required t be spatially distributed, event based, and able t simulate bth infiltratin-excess and saturatin-excess runff generatin. A the hydraulic gradient f the saturated zne can be apprximated by the lcal surface tpgraphic slpe, and (3) the distributin f dwnslpe transmissivity with depth is an expnential functin f strage deficit r depth t water table. mdel structure which lends itself t use f radar-estimated These assumptins lead t relatinships be een the catchprecipitatin is a spatially distributed grid-based discretizatin, ment sil strage deficit and the lcal water table level, where such as that emplyed by the SIMPLE mdel [Kuwen and Garland, 1989; Kuwen et al., 1993] and the Eurpean SHE mdel [Abbtt et al., 1986]. Such a structure was chsen fr this the main quanti used in the relatinship is the tpgraphic index ln(a/tan b) intrduced by Beven and Kirkby [1979], where a represents the upslpe cntributing area per unit

4 2658 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL cntur length and tan b is the lcal grund slpe. In later mdificatins f the mdel the riginal tpgraphic index was replaced by a cmbined tpgraphic-sils index f the frm ln(a/t tan b), where T O represents the transmissivity when the sil prfile is fully saturated. This new frmulatin explic- Cllier, 1989]. The parameters a and b depend theretically n the hydrmeter drp-size distributin within a given sample vlume f the atmsphere, and it is intuitive that this distributin may vary cnsiderably frm strm t strm and even acrss different sectins f the same strm. Althugh certainly itly accunts fr variability in lcal transmissivity in the index nt the nly factr which cntributes uncertainty t the transf hydrlgic similarity. Furthermre, bth the secnd and frmatin f reflectivity t rainfall rate (thers include radar third assumptins listed abve have recently been bradened hardware calibratin, reflectivity field cntaminatin by hail t encmpass a greater variety f hydrlgic cnditins band bright band effects, and anmalus prpagatin [Smith et served in the field. Evidence frm several studies has suggested al., 1996a]), it is a significant ne. that the hydraulic gradient in a watershed may be significantly T cnsider the effects f this surce f uncertainty in radarinfluenced by the rientatin f subsurface features, such as a estimated precipitatin n runff predictins, three scenaris shallw bedrck layer, requiring the use f a reference level t fr determining the values f a and b were cnsidered. In the better apprximate the water table surface [Quinn et al., 1991]. In additin, the assumptin f an expnential transmissivity first scenari the values f the parameters were set at the functin has been bradened t include parablic and linear "default" parameters suggested by the NEXRAD algrithm transmissivity functins, thught t better represent sme wa- develpers. In the secnd scenari the parameters were calitershed behavir [Ambris et al., 1996]. Because sils in the brated fr a small regin f the radar umbrella crrespnding Timber Creek watershed are quite deep, surface tpgraphy t the area immediately surrunding the study site. In this was thught t be mre significantly related t the lcal hydraulic gradient than the subsurface gelgic structure. As such, the riginal TOPMODEL assumptin was adpted. Regarding selectin f the lcal transmissivity functin, the riginal expnential functin was chsen, as there was nt any evidence that either the linear r parablic functins wuld be mre apprpriate fr Timber Creek. scenari, all f the strms being studied were used tgether t find ne ptimal set f parameter values fr all the strms. In the third scenari the parameters a and b were calibrated fr each strm event separately, cnsistent with the ntin that these parameters vary frm strm t strm. The calibratin f the parameters in the radar equatin was perfrmed using the Shuffled Cmplex Evlutin (SCE-UA) The TCW mdel frmulatin allws fr the infiltratin- glbal search algrithm [Duan et al., 1992]. This methd has excess and saturatin-excess runff generatin mechanisms t ccur simultaneusly r separately. The mdel was designed s prven t be very efficient in lcating the ptimal set f parameter values and was mre than sufficient fr calibrathat each runff mechanism culd be "turned n" r "turned tin f the simple tw-parameter radar equatin. The bff" s that the respnse f each mechanism t precipitatin jective functin emplyed in the calibratin prcedures is uncertainty culd be evaluated independently. Althugh subdescribed by (2): surface runff cntributin t streamflw was cmputed thrugh the TOPMODEL prtin f the TCW mdel, it was nt included in the runff vlume analysis. The cntributin f subsurface runff t the ttal runff vlume was small cm- pared t the cntributins f surface runff fr the large events analyzed in this study. Thus the cnclusins derived frm this study will be mst applicable fr lcatins r strm events where surface runff is the dminant cntributr t stream- flw. 3. Methds 3.1. Develpment f Radar-Estimated Precipitatin Data One f the bjectives f this study was t examine the effects f the uncertainty in the transfrmatin f radar reflectivity t rainfall n predicted runff generatin frm a watershed. A prtin f this uncertainty was assumed t be due t the variability in the parameter values f the pwer law mdel used t transfrm reflectivity int rainfall rate, shwn by (1) as where Z radar reflectivity [dbz]; R rainfall rate [L/T]; a radar cefficient; b radar expnent. Z = ar b (1) It is well dcumented that values f the parameters a and b in the radar equatin are nt cnstant in time r in space [Martner, 1977; Smith et al., 1996b], and several authrs have suggested different values fr specific situatins [Battan, 1973; where in n MinF= IGi-R! (2) j=l i=1 G gauge strm ttal precipitatin (L); R radar strm ttal precipitatin (L); m number f strms; j strm number; n number f gauges fr strm j; i gauge number fr strm j. This bjective functin, which minimizes the abslute value f the radar-gauge difference, was chsen s that rughly equal emphasis wuld be placed n the small strms as n the large strms and, similarly, n the gauges with high precipitatin and lw precipitatin. A prcedure which is smetimes used t imprve the estimatin f rainfall frm radar is t perfrm additinal bias adjustments with rain-gauge data. In the NEXRAD precipitatin-prcessing algrithm a Kalman filter is emplyed, incrprating hurly gauge precipitatin in real time t determine a mean field bias in the radar estimates f precipitatin [Se et al., 1995]. Other simpler methds have been suggested by Cllinge [1991] which cmpute a bias crrectin factr simply n the basis f the rati f the precipitatin measured by the rain gauges t the precipitatin estimated by the radar. This type f bias crrectin was used in this study and is given by (3) as

5 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL 2659 CFi = (3) features imprtant in the hydrlgic respnse f smaller basins susceptible t flash flding. A tempral reslutin f the rder f 6 min is able t depict transient rainfall characteristics which define small-scale runff prductin in mst situatins, as suggested by Krajewski et al. [1991] and Michaud and Sj:l rshian [1994]. Truble arises when variable intensity rainfall where events are assumed t have a cnstant intensity fr lnger perids f time. While assuming that a cnstant rainfall inten- CF bias crrectin factr; sity duratin f i hur may be suitable fr large basin hydr- G gauge strm ttal precipitatin (L); lgic predictin, mdeling basins f the rder f 200 km 2 r R radar strm ttal precipitatin (L); smaller may require mre accurate capturing f the shrtn number f gauge/radar pairs; duratin rainfall dynamics, especially fr cnvective type i strm number; events. The questin f hw IT "- - uc aggregatin f this " : ' " ngu - j gauge number. reslutin rainfall data can ccur befre significant effects n runff predictin ccur is a primary issue explred in this The bia cm,ectin paper. basis using all r sme f the ten gauges surrunding Timber The bulk f this study cnsists f a sensitivity analysis per- Creek. The cmputed bias is specific nly t the lcatin surfrmed t investigate the effects f spatial and tempral agrunding Timber Creek and wuld nt apply t ther regins gregatin f the radar-estimated precipitatin data n runff f the radar umbrella. Once the crrectin factr is calculated, generatin. Spatial reslutins f 2 km, 4 km, 8 km, and 16 km a new value is btained fr each radar p el accrding t (4) as were generated frm the riginal 1-km data. Fr each spatial RA = R x CF (4) reslutin, 24-min, 42-min, and 60-min tempral reslutin where precipitatin estimates were generated frm the riginal 6-min reslutin data. This resulted in 20 different precipitatin data adjusted radar precipitatin [L/T]; sets fr each f the seven strms studied. These different R riginal radar precipitatin [L/T]; CF bias crrectin factr fr strm i. The bias crrectin factr was either applied r nt applied, precipitatin data sets were used as input t the TCW rainfallrunff mdel t assessensitivity f bth the saturatin-excess respnse and the infiltratin-excess respnse. resulting in alternatives in the precipitatin prcessing 3.3. Rainfall-Runff Mdel Calibratin prcedure emplyed. Calibratin f a limited number f rainfall-runff mdel Permutatins f the three scenaris fr determining the parameters was necessary fr prper implementatin f the values f the radar equatin parameters a and b and the scenaris fr incrprating a bias crrectin factr result in s TCW mdel. Althugh this study is nt specifically cncerned with assessing the perfrmance f a rainfall-runff mdel r different methds fr develping radar-estimated precipitatin testing a calibratin prcedure, it is imprtant that the hydrdata fr each strm. These sk methds represent the range in precipitatin data btainable by different precipitatin prlgic mdel prduce realistic simulatins if prper value is t cessing techniques which may be emplyed by independent be given t the results f later experiments. Because the emusers f NEX Level II base reflectiviw data. Fr each phasis f this study was n examining the sensitivity f surfacemethd the same preprcessed reflectiviw images were used. runff generatin t precipitatin uncertainty, the calibratin prcedure was designed t minimize the difference between Preprcessing f the reflectiviw data was perfrmed using a simplified versin f that emplyed by the NE algbserved and simulated surface-runff vlume. This required separating surface runff and base flw frm the bserved rithm [see Winchell et al., 1997]. The perfrmances f each f the s methds emplyed were streamflw recrds. The base flw separatin technique used evaluated statistically by cmparing the resulting rain gaugefr this study was centered n the develpment f a master base flw recessin curve fr the watershed, used t determine radar p el pairs. While sme f the techniques prduced better matches be een the gauges and radar, the results f these the time at which surface runff ends. Fr a descriptin f this technique, refer t Chw et al. [1988]. cmparisns will nt be discussed at this time. Instead, we are cncerned here with the fact that the techniques represent a The Shuffled Cmplex Evlutin autmatic ptimizatin range f pssible methds fr cnstructing precipitatin infrrutine [Duan et al., 1992] was used t identify the parameters 11 matin frm =v= A Level data and may result in a range fr the TCW mdel. The nly parameters which required calf ranff predictins. Fr a cmplete discussin f the perfribratin were the TOPMODEL transmissivity scaling parameter m and the initial sil-misture cnditins 0i fr each f mance f the different precipitatin prcessing techniques, refer t Winchell et al. [1997]. the seven strms studied. The remaining parameters were estimated frm published sil data. Althugh the initial silmisture cnditins technically are nt mdel parameters, they 3.2. Aggregatin f Precipitatin Data were calibrated in cnjunctin with the TOPMDEL m pa- The base-level precipitatin data sets generated accrding t rameter. The calibratin was arranged such that data frm five each f the six techniques were cnstructed using the 1 x 1 km, f the seven strms were used t identify m and the five Oi 6-min reflectivity data. A mre cmmn spatial reslutin fr values. Afterward, the Oi values fr the remaining tw strm quantitative radar-estimated precipitatin, such as the 4 x 4 events were determined using the m value btained frm the km, 1-hur NEXRAD prduct, is cnsidered t be sufficient five-strm calibratin. fr mdeling larger main stem river basins, yet it may nt The bjective functin used in the ptimizatin prgram was cntain enugh detail t prperly reflect small-scale rainfall the abslute difference between bserved and simulated sur-

6 2660 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL Table 2. Calibratin Results Observed Surface Simulated Surface 10-Day Antecedent Strm Date Runff, mm Runff, mm m, cm 0i, cm/cm Precipitatin Oct. 28, Oct. 31, Sept. 10, Feb. 24, May 9, May 12, April 10, Initial sil misture 0 i is expressed as a fractin f lcal field capacity. face runff vlume. This bjective functin frmulatin is expressed in (5) as where Min F = I Qs/bs- QSisiml (5) F bjective functin value [L]; QSb s bserved surface-runff vlume [L]; QSsim simulated surface-runff vlume [L]; i strm number; n number f strms in calibratin. i=1 The simulated surface runff fr the calibratin was generated with the 1 x 1 km, 6-min reslutin precipitatin input. The results f the TCW mdel calibratin are shwn in Table 2. The bserved and simulated runff vlume, the TOP- MODEL rn parameter value, and the 0i values are shwn fr each strm. The bserved and simulated surface-runff vl- umes are nearly identical. This was achievable thrugh the calibratin f the initial sil-misture cnditins. The 0i values representhe initial sil misture as a fractin f the lcal field capacity. The lcal field capacity is dependent n sil type and varies thrugh the watershed. This allws fr the vlumetric sil-misture cntent t vary as a functin f lcal field capacity. While the 0i values are all relatively high, they are nt unreasnable cnsidering the time f year and the 10-day antecedent precipitatin, als shwn in Table 2 (recall that because these were sme f the largest runff events during the perid f study, wet cnditinshuld be expected). While the calibratin f the TCW mdel parameters was relatively simple, it verified that the mdel was capable f prducing surface-runff amunts cmparable t thse bserved. 4. Results 4.1. Sensitivity f Runff Generatin t Reflectivity-Rainfall Transfrmatin Uncertainty The range in pssible precipitatin infrmatin btained frm the riginal reflectivity data was represented by the six Table 3. Radar Calibratin Methds Calibratin Radar Equatin Bias Crrectin Methd Parameters Factr 1 default nt applied 2 strm independent nt applied 3 strm dependent nt applied 4 default applied 5 strm independent applied 6 strm dependent applied different techniques fr calibrating and adjusting the radar data with rain gauges. The calibratin and bias adjustment cmbinatin defining methds 1-6 are given in Table 3. Each f these sets f data were used as input t the TCW rainfallrunff mdel t see hw runff generatin is affected by the uncertainty inherent in the transfrmatin f reflectivity t rainfall. The quantity being cmpared fr each f the cases studied is the cumulative surface runff generated during the strm perid. Where indicated, the cumulative runff shwn may nly be the saturatin-excess prtin r the infiltratin- excess prtin. The fractins f "true" runff prduced frm each f the six different precipitatin data sets fr the seven strms studied are shwn in Figure 1. The fractin f true runff is pltted n the y axis, and the calibratin/adjustment methd is pltted n the x axis. Each f the lines n the graph represents a different strm event. The true runff is assumed t be that which ccurred frm using the precipitatin generated using methd 6, because methd 6 was fund t prduce the best fit between the rain gauges and the radar [Winchell et al., 1997]. Several imprtant cnclusins are made frm Figure 1. First, the vlume f simulated surface runff is strngly dependent upn the methd used t cnstruc the precipitatin input. This is shwn by hw much the fractin f true runff varies frm methd 1 t methd 6 fr an individual strm. Secnd, Figure 1 shws that simulated runff frm sme strms is mre sensitive t the precipitatin calibratin/adjustment methd than ther strms. Fr example, the fractin f true runff generated fr ne strm varied frm 0 t 1.0, while anther O Radar Calibratin/Adjustment Methd Figure 1. Runff sensitivity t radar calibratin/adjustment methd; "true" runff represents runff generated frm methd 6 precipitatin input. Each line represents a different strm.

7 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL 2661 varied nly frm 0.94 t Finally, the value in calibrating parameters in the Z-R relatinship, as well as incrprating a lcal bias adjustment t the precipitatin estimatin prcedure, is well supprted. It is fair t say that radar calibratin/ adjustment methds 4-6, which incrprated a bias crrectin factr, resulted in better runff simulatins than methds 1-3, which did nt incrprate a bias crrectin factr. Furthermre, the methds which incrprated strm-dependent Z-R parameter calibratin, methds 3 and 6, prduced better runff simulatins than methds 1-2 and 4-5, respectively. This analysis emphasizes the significant errrs that can result in runff predictins as a result f uncertainty in the precipitatin input. It als advises using methds fr btaining precipitatin data frm radar reflectivity which attempt t reduce the uncertainty in the reflectivity t rainfall transfrmatin. Using the same six sets f precipitatin input, the cumulative runff vlume was calculated separately fr the infiltratinexcess respnse and the saturatin-excess respnse. Alng with investigating whether these tw types f runff respnded differently t varying precipitatin input, it was desired t determine hw the resulting errrs in runff cmpared with the errrs in rainfall. The assumptin will be made that the "true" rainfall is that prduced accrding t methd 6 and that the true runff is that resulting frm the true rainfall. A plt f the rainfall errr versus the saturatin-excess and infiltratin- The difference in the behavir between the saturatin- excess and infiltratin-excess runff generatin is expected. Because saturatin-excess runff ccurs nly when the lcal sil prfile is saturated, the infiltratin rate f that sil regin is essentially zer. Fr a unit increase in rain falling n that a) g:2.s?, ,t 0.5 -, Fractin f "True" Rainfall b) , 1.5 õ Fractin f "True" Rainfall Figure 2. Rainfall errr versus runff errr resulting frm the six different sets f precipitatin input: (a) saturatinexcess and (b) infiltratin-excess runff; all strms are in- cluded. a) b) c õ ,,r 0.4 [ Fractin f "True" Rainfall Fractin f "True" Rainfall Figure 3. Rainfall errrs versus saturated-excess runff errr fr (a) "wet"(octber 31, 1991) antecedent cnditins and (b) "dry"(september 10, 1992) antecedent cnditins. saturated area a unit increase in runff generatin will result. Thus a 20% increase in rainfall will result in a 20% increase in runff frm a saturated area. Of curse, the dynamics f the expanding saturated areas add sme cmplicatin t this; hwever, this serves primarily t change the slpe f the linear relatinship between rainfall errrs and runff errrs. This can be seen by examining Figure 3, which plts the rainfall errr versus runff errr fr tw individual strms. One strm, frm September 10, 1992, ccurred under very dry antecedent cnditins, while the ther strm, frm Octber 31, 1991, ccurred under very wet antecedent cnditins. Bth plts indicate a nearly linear relatinship; hwever, the slpe fr the "wet" watershed case is -1, while the slpe fr the "dry" watershed excess runff errr fr all six precipitatin data sets and all seven strms studied are presented in Figure 2. The 1:1 line represents equally sized errrs fr rainfall and runff. Fr saturatin-excess runff (Figure 2a) the magnitude f the runff errrs is the same r slightly larger than the size f the crrespnding rainfall errrs. While this rainfall errr is quite case is significantly greater than 1. In the wet case a unit change in runff results frm a unit change in rainfall because a large percentage f the basin is saturated. In the dry case, small changes in rainfall result in larger changes in runff because significant at times (up t -80%), we d nt see dramatically sme f the areas f the watershed d nt becme saturated larger errrs in runff. Furthermre, the relatinship between rainfall errrs and runff errrs is generally linear. In the when the rainfall changes. The behavir seen here agrees with Numec [1985] that errrs in precipitatin input have a mre infiltratin-excess case (Figure 2b), much different behavir is serius effect n runff mdeling when the catchment is dry. bserved. Here very small rainfall errrs (10%) can result in The dramatic respnse f the infiltratin-excess runff t rainrunff errrs up t 170%, illustrating the extreme sensitivity f infiltratin-excess runff generatin t the rainfall input. Furthermre, the relatinship appears t be highly nnlinear as fall variatins is a direct result f the highly nnlinear nature f the infiltratin prcess. Althugh the ttal rainfall vlume may experience nly slight changes, the rainfall intensity structure ppsed t the relatively linear behavir f the saturatin- may have been sufficiently altered t cause radically different excess runff. interactins with the lcal infiltratin rate f the sil. This analysis suggests that when mdeling the infiltratinexcess type f runff, cautin shuld be exercised when the quality f the precipitatin data is in questin. If saturatinexcess is the runff-generatin mechanism being mdeled, then the size f the simulated runff errrs may nly be as large as the errrs in the rainfall. Of curse, this might change depending n the basin cnditins, with a drier basin being mre susceptible t larger runff errrs. Sectin 4.2 will exam- ;,, hw errrs in the rainfall a,,,,,,,h,,,i,,, th r. nh,tlnn n½ the data affect runff predictins Sensitivity f Runff Generatin t Precipitatin Aggregatin This sectin fcuses n the sensitivity f surface-runff generatin t the spatial and tempral reslutin f radarestimated precipitatin. This sectin als cnsiders hw aggregatin in time and space f high-reslutin radar-estimated precipitatin data affects bth the infiltratin-excess and the saturatin-excess mdes f surface-runff generatin. This is an imprtant issue, because many current hydrlgic mdels utilize precipitatin input that has undergne sme degree f spatial and/r tempral aggregatin. The spatial reslutins f

8 2662 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL ,.-, 3.5, O O ,0.6 EO , 0.2 ry. 1 Time (hr) Time (hr) Time (hr) , : ry , _ 0.6 O Time (hr) $ :2 0' Time (hr) Time (hr) 0.0 O Time (hr) Figure 4. Mean basin-average hyetgraphs fr the strm events studied. the precipitatin data that will be cnsidered here include (1) bserved. Fr the strm f Octber 31, 1991, the trend is fr 1 x lkm,(2) 2x2km,(3)4x4km,(4)8 x 8km, and(5) carsereslutins t prduce less runff. The May 9, 1993, 16 x 16 km. The tempral reslutins cnsidered include (1) strm shws peculiar behavir in that the 16-km reslutin 6 min, (2) 24 min, (3) 42 min, and (4) 60 min. Basin-average prduces the mst runff and the 8-km reslutin prduces hyetgraphs fr each f the seven strms studied are shwn in Figure 4. These hyetgraphs are based n the riginal 6-min data, befre any tempral aggregatin. The first set f sensithe least. The April 10, 1995, strm shw sme incnsistencies as well. A feature f interest frm Figure 5 is that amng the strms studied, there is n cnsistent trend fr mre r less tivity analyses cnsidered will nt frce basin precipitatin runff t be prduced as the level f precipitatin aggregatin vlume t be cnserved acrss aggregatin levels. A secnd set is increased. Furthermre, the magnitudes f the changes genf sensitivity analyses will keep basin precipitatin vlumes erally are nt very large, being f the rder f 10-15% fr mst preserved in an effrt t remve the effects f mapping errrs fr cmparisn purpses. cases. The effect f precipitatin aggregatin n infiltratin-excess The effect f precipitatin aggregatin n saturatin-excess runff is shwn in Figure 6. Once again, each f the subplts runff generatin fr fur different strms is shwn in Figure 5. Each f the subplts represents a different strm. The x axis represents the tempral reslutin f the precipitatin input, the y axis represents the fractin f true runff (runff frm 1-km 6-min precipitatin input) generated frm a given precipitatin reslutin, and each line n the plt refers t the spatial reslutin f the input. As seen in Figure 5, there is essentially n sensitivity f the runff generatin t the tempral reslutin f the input. This indicates that saturatinexcess runff is nt dependent n the intensity structure f the rainfall. Hwever, when the spatial aggregatin f the input is changed, the runff vlumes d change. Fr the case f September 10, 1992, there is a 50% increase in the runff vlume given the 16-km reslutin input. Fr this particular strm a trend fr the carser reslutins t prduce mre runff is represents a different strm. Much different behavir is bserved than fr the saturatin-excess runff case. First, there is cnsiderable sensitivity t the tempral reslutin n the rainfall input. The 1-hur, 1-km precipitatin input results in 58% less runff than the 6-min 1-km precipitatin input fr the Octber 31, 1991, strm. The general trend fr all f the strms is fr increasing tempral aggregatin f the precipitatin t result in decreasing amunts f runff. As fr the effects f spatial aggregatin f the precipitatin n runff generatin, there is smewhat f a trend fr the carser reslutins t prduce less runff; hwever, this is nt entirely cnsistent. The Octber 31, 1991, and the May 9, 1993, strms are mstly cnsistent with this behavir; hwever, the April 10, 1995, strm shws numerus ccasins where this trend is vilated. Fr example, the 8-km and 16-km reslutin inputs

9 WINCHELL ET AL.' SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL 2663 Saturatin Excess Runff; 10/31/91,,,, '1 Saturatin Excess Runff; 9/10/92,,,,, mmmmmmmmmm, mmmmm mmmmmmm! lo Cnstant 20 Intensity 3O Re,0(min.) lo Cnstant 20 Intensity 3O Res. 40 (min.) 50 1 km. Res. 2 km. Res. 4 km. Res. --,-m 8 km. Res km. Res. Saturatin Excess Runff; 5/9/93 Saturatin Excess Runff; 4/10/95, ' ' ' ', i,,,.8,,*--06 (3O4 )5 O0 I I ,50 60 Cnstant Intensity Res, (min.) Cnstant Intensity Res. (min.) Figure 5. Saturatin-excess runff sensitivity t tempral and spatial reslutin f precipitatin input. fr the lnger tempral reslutins prduce significantly mre shed is calculated, then the resulting value will be larger than runff than the higher spatial reslutins. Fr the September the riginal mean watershed precipitatin depth because f the 10, 1992, strm the trend is strictly fr the carse reslutins influence f the cnvective cell utside the true watershed t prduce mre runff. Intuitively, is expected that carser bundary. A hypthetical example f this is shwn in Figure 7. spatial reslutin precipitatin shuld result in less infiltratin- In this example the riginal rainfall data are aggregated frm excess runff, because the lcalized high-intensity rainfall re- a 1 x 1 cell grid t a 3 x 3 cell grid. In ding s, the apparent gins are being smthed ut. It is these high-intensity rainfall ttal vlume f precipitatin falling within the watershed regins that are mst imprtant in generating infiltratin- bundary is reduced because f the areas f lighter precipitaexcess runff. tin falling utside f the watershed bundary. Thus spatial The incnsistencies in the behavir f the infiltratin-excess aggregatin f precipitatin can serve t either increase r runff respnse t spatial aggregatin f the precipitatin, and decrease the vlume f rain falling within a watershed. It is this all f the sensitivity f the saturatin-excess respnse, are due prcess f "smthing precipitatin vlume" which has caused t changes in ttal rainfall vlume falling within the watershed. the irregular sensitivity f the saturatin-excess runff t spa- This change in rainfall vlume falling within the watershed can tial reslutin f the rainfall and the incnsistent sensitivity f be cnsidered a mapping errr and ccurs as fllws. Typical the infiltratin-excess respnse. This is essentially the same spatially varying rainfall patterns cnsist f regins f heavier prcess bserved and described by Ogden and Julien [1994]. r lighter precipitatin utside the immediate bundaries f a The infrmatin in Table 4 supprts the direct relatinship watershed. Fr example, an individual cnvective cell may have fund between rainfall vlume and saturatin-excess runff mved just t the utside f the watershed bundary, drpping vlume fr the different spatial reslutins f precipitatin a swath f heavy precipitatin. Inside the watershed bundary tested. Fr each strm event a "rank" is given t the spatial the mean precipitatin depth may be much less than what was reslutin which prduced the greatesthrugh least amunt drpped by the cnvective cell. If an aggregatin f pixel-based f rainfall vlume and runff vlume. Examining the table precipitatin is perfrmed ver the regin surrunding this reveals that the rainfall rank and the runff rank match fr watershed and a new mean precipitatin depth fr the water- every ccasin. T determine if this "smthing f precipita-

10 2664 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL Infiltratin Excess Runff; 10/31/91 Infiltratin Excess Runff; 9/10/ fr- 7 \ \ \ = 0 C2 O4.9 (.) 3, 4'0 ;, ; 4'ø Cnstant Intensity Res. (min.) Cnstant Intensity Res. (min.) 1 km. Res km. Res. 4 km. Res km. Res km. Res. Infiltratin Excess Runff; 5/9/93 Infiltratin Excess Runff; 4/10/95 "!,.,, - XX [2-5 _ c) i::: 4._ (.103 LL 2 Ol Ol Figure SO Cnstant Intensity Res. (min.) Cnstant Intensity Res. (min.) Infiltratin-excess runff sensitivity t tempral and spatial reslutin f precipitatin input. tin vlume" was exclusively respnsible fr the sensitivity f the saturatin-excess runff vlume t spatial aggregatin f the rainfall, the ttal rainfall prduced by each spatial reslutin was nrmalized t be that which was prduced by the 1-km reslutin data. In this case, the spatial aggregatin is serving nly t smth the variability in rainfall intensity patterns thrughut the basin, while the ttal rainfall vlume remains cnstant. The sensitivity f saturatin-excess runff t aggregatin f the precipitatin input with "nrmalized" precipitatin vlume is displayed in Figure 8. Fr each f the strms shwn, there is essentially n sensitivity t precipitatin aggregatin f any kind. Fr the September 10, 1992, strm the effect f precipitatin aggregatin n the runff is much smaller than befre. This slight sensitivity may be due t the methd by which the precipitatin was nrmalized, which simply applied the same adjustment at each time step and did nt take int accunt the time-variant nature f the rainfall vlume errrs. These results indicate that if the change in precipitatin vlume falling in a basin due t spatial aggregatin is prperly accunted fr, the tempral and spatial reslutin f a radarderived precipitatin input will be incnsequential the generatin f saturatin-excess runff. The effect f spatial and tempral aggregatin n infiltratin-excess runff generatin with nrmalized precipitatin vlume fr the same strms previusly shwn are given in Figure 9. Cmparing Figure 9 with Figure 6, significant differences are bserved in the respnse f the runff generatin t changes in the spatial reslutin. Fr the May 9, 1993, strm the trend fr carser spatial reslutin t prduce less runff is nt vilated. The Octber 31, 1991, strm behavir becmes mre cnsistent fr the 1-km and 2-km reslutins at lnger tempral reslutins, and the April 10, 1995, strm becmes much better behaved as well. The September 10, 1992, strm changes the mst dramatically, with the expected behavir ccurring fr the nrmalized precipitatin vlume case. Obviusly, the smthing f precipitatin vlume plays a significant rle in infiltratin-excess runff generatin. When these effects are remved, a clear trend fr runff vlumes t decrease with increasing tempral and spatial aggregatin is bserved. The results f the discussin abve supprt the findings f bth Obled et al. [1994] and Krajewski et al. [1991]. Recall that Obled et al. fund that runff generatin was sensitive t spatial infrmatin in the precipitatin but insensitive t tempral infrmatin by using TOPMDEL t simulate saturatin-excess runff. Krajewski et al. fund runff generatin t be sensitive t bth the spatial and tempral infrmatin in the precipitatin by simulating infiltratin-excess runff. This study has verified that the differences in the cnclusins frm

11 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL 2665 \ ,,, Cell x 1 Cell Rainfall Reslutin / X ( 3.? 3, / Cell x 3 Cell Rainfall Reslutin Ttal Precipitatin Vlume = 54 Ttal Precipitatin Vlume = 42.7 Figure 7. Reductin in watershed precipitatin due t smthing f precipitatin vlumes frm spatial aggregatin; hypthetical case. these tw earlier studies are a result f the different runff mdels emplyed. An issue which was nt significantly addressed in previus wrk is the variatin in the sensitivity f runff generatin t precipitatin reslutin frm strm t strm. The magnitude f the sensitivity f the runff generatin t varius levels f rainfall aggregatin differs amng the fur strms shwn (Figure 9). The simulated runff frm the September 10, 1992, strm is much less sensitive t the precipitatin reslutin than the ther strms. A strm-dependent parameter may exist which dictates hw significantly predicted runff frm a given strm will be affected by aggregatin f the precipitatin input. These issues warrant additinal investigatin and are explred in sectin Estimatin f Infiltratin-Excess Runff Reductin Due t Precipitatin Aggregatin The strm characteristics thught t be mst related t the effects f precipitatin aggregatin n runff generatin are thse related t the spatial variability f the rainfall ver the watershed area. The rainfall characteristics f a strm can be represented in many pssible ways, such as the ttal rainfall depth, the average rainfall intensity, r the maximum rainfall intensity. The rainfall characteristic thught t be mst relevant in prducing infiltratin-excess runff is the maximum precipitatin intensity, because it is the high-intensity perids that determine when and where runff ccurs. The spatial variability f these characteristics als can be represented in many ways, ranging frm simple methds, such as determining the variance r standard deviatin, t mre cmplex methds, such as varigram analysis. Because the intent f this exercise was t develp a simple means fr accmmdating fr errrs in runff simulatin due t precipitatin aggregatin, the use f simple spatial variance f rainfall characteristics was chsen. Therefre the expectatin was that the spatial variability f the highest rainfall intensity perids wuld be related t hw sensitive the runff generatin wuld be t smthing the rainfall input in time and space. The specific statistic used t represent this was the spatial standard deviatin f the maximum precipitatin intensity (hereafter referred t as O'Maxlnt ). Mathematically, it is calculated accrding t (6) as where I i=1 n ] E (imax i 2 O'Maxlnt = ] -- Ft -- /max) (6) O'Maxlnt spatial standard deviatin f maximum intensity [L/T]; n number f 1 )< 1 km radar pixels ver watershed area; imax mean f maximum precipitatin intensity fr all pixels [L/T]; Table 4. Cmparisn Between Ranking f Precipitatin Vlume in Watershed and Saturatin-Excess Runff Generatin Event 1-km Rank 2-km Rank 4-km Rank 8-km Rank 16-km Rank Oct. 28, 1991 Precipitatin Oct. 28, 1991 Runff Oct. 31, 1991 Precipitatin Oct. 31, 1991 Runff Sept. 10, 1992 Precipitatin Sept. 10, 1992 Runff Feb. 24, 1993 Precipitatin Feb. 24, 1993 Runff May 9, 1993 Precipitatin May 9, 1993 Runff May 12, 1994 Precipitatin May 12, 1994 Runff April 10, 1995 Precipitatin April 10, 1995 Runff Here 1 represents "greatest" and 5 represents "least."

12 2666 WINCHELL ET AL.' SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL c- Saturatin Excess Runff; 10/31/91!,,! Saturatin Excess Runff; 9/10/92,._ 12[ ' ' ' -_ 0O6 O O 04 O2 ' I - I I I I Cnstant Intensity Res. (min.) lo Cnstant Intensity Res. (min.) 1 kin. Res. - 2 kin. Res. 4 km. Res. 8 kin. Res kin. Res. Saturatin Excess Runff; 5/12/94 Saturatin Excess Runff; 4/10/95,,,,, O 1 c:: :3 = O 0.6 O LL 0.2 O I ; 20 i 30 i 40 & ;0 60 O & 30 i 4 i 0 50 ' 60 Cnstant Intensity Res. (min.) Cnstant Intensity Res. (min.) Figure 8. Saturatin-excess runff sensitivity t tempral and spatial reslutin f nrmalized precipitatin input. I/max maximum precipitatin intensity fr pixel i [L/T]. The maximum precipitatin intensity at each pixel was determined by checking the rainfall intensity at each 6-min time step t see if it was greater than the previus maximum intensity. The O'Maxlnt is pltted against the fractin f true runff generated frm different tempral (Figure 10) and spatial (Figure 11) reslutins. The O'Maxlnt exhibits a strng crrelatin with the reductin f runff. Fr the cases f tempral aggregatin, there is an apprximate linear relatinship between the O'Maxlnt and the fractin f true runff prduced at each f the different levels f aggregatin. Recall that the true runff refers t that which was prduced by using the highest reslutin precipitatin data as input. In additin, the increase in runff reductins with increased tempral aggregatin is als apparent, shwn by the negative slpe f the least squares line increasing as the level f tempral aggregatin mves frm 24 t 60 min. Similarly, an apprximate linear relatinship between the O'Maxlnt and the reductin f runff exists fr the different cases f spatial aggregatin (Figure 11). Again, the increasing negative slpe f the least squares line as the spatial aggregatin ges frm 2 t 16 km indicates hw the increasing spatial aggregatin results in increasing runff reductins. The lack f scatter f the data arund the least squares line is remarkable. This suggests the pssibility f determining runff crrectins n the basis f the linear relatinships fund in these plts. Regressin equatins were develped t relate the fractin f true runff generated by a given level f precipitatin aggregatin t the O'Maxlnt determined frm the finest 1-km x 6-min precipitatin reslutin. A different equatin was develped fr each level f spatial and tempral aggregatin. Each equatin estimates the crrectin in simulated infiltratinexcess runff generatin required, given the reslutin f precipitatin input and a knwledge f the variability in the strms' maximum precipitatin intensity. These equatins and their assciated r 2 and crrelatin statistics are prvided in Tables 5 and 6. The infrmatin shwn in Table 5 indicates gd fits between simulated and actual runff reductins due t tempral aggregatin. The perfrmance f the regressin equatins is better fr the carser 42- and 60-min reslutins, suggesting that this relatinship may be mst effective at predicting runff crrectins due t significant aggregatin. Fr the cases f the different spatial reslutins (Table 6) the

13 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL 2667 Infiltratin Excess Runff; 10/31/91 Infiltratin Excess Runff; 9/10/ ::307 s L;-s r-. 04 O i 30 i 40 i Cnstant Intensity Res. (min.) 0 1 km. Res kin. Res. 4 kin. Res i 30 ; Cnstant Intensity Res. (min.) '-"-' 8 kin. Res kin. Res. Infiltratin Excess Runff; 5/9/93 Infiltratin Excess Runff; 4/10/ :'--'_-_ t O, 1; i 20 & 30 i 40 i Cnstant Intensity Res. (min.) I I 20 i 30 i 41 Cnstant Intensity Res. (min.) Figure 9. Infiltratin-excess runff sensitivity t tempral and spatial aggregatin f nrmalized precipitatin input. regressin statistics als are quite gd. Hwever, the r 2 values d drp belw 0.75 fr the 4-km and 2-km aggregatins. Again, this may suggesthat these regressin equatins are mre apprpriate fr predicting runff reductins due t significant precipitatin aggregatins. Nevertheless, predictive ability f all the equatins presented is high enugh t indicate the ptential in this methd fr crrecting errrs in runff simu- latins. 60 mm Reslutin 42 mm Reslutin 0.8 g. 0.8 C Standard Dev. f Max Int. (cm) Standard Dev f Max Int. (cm) It shuld be understd that these equatins, in their 24 mm Reslutin present frm, are nt suitable fr applicatin in a real-time mdeling envirnment. They require the knwledge f the precipitatin intensity distributin after the entire strm, frm the finest available reslutin data. In additin, these relatinships are likely site-specific, suggesting that additinal wrk be 0.4 perfrmed t verify this and investigate the cause. The main purpse fr the develpment f these equatins was as fllws. 0.2[ First, they shw that runff respnse t precipitatin reslu Standard Dev. f Max Int (cm) tin is nt randm, but that it is related t the O'Maxlnt. Secnd, they prvide the basis fr future research which might fcus n Figure 10. Spatial standar deviatin f m imum precipitaa technique which can, in real time, make adjustments t run- tin intensi versus fractin f true runff prduced; case f ff predictins n the basis f the reslutin f the precipita- tempral aggregatin. Each pint represents ne strm, and tin being used and the O'Maxlnt. the line represents the least squares line.

14 2668 WINCHELL ET AL.' SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL 1 16 km Reslutin 1 8 km Reslutin Table 5. Regressin Equatins fr Tempral Aggregatin f Precipitatin Min 42-Min 24-Min Statistic Reslutin Reslutin Reslutin Standard Dev, f Max Int. (cm) Standard Dev. f Max Int. (cm) 4 km Reslutin 2 km Reslutin 1 ß 0.8 g: _ Standard Dev. f Max Int. (cm) Standard Dev. f Max Int. (cm) Figure 11. Spatial standard deviatin f maximum precipitatin intensity versus fractin f true runff prduced; case f spatial aggregatin. Each pint represents ne strm, and the line represents the least squares line. 5. Summary and Cnclusins Several issues related t the use f radar-estimated precipitatin in rainfall-runff mdeling have been the fcus f this paper. The wrk was mtivated by the rapidly expanding bdy f NEXRAD Level II data available fr use in bth research and cmmercial applicatins. The increasing availability f NEXRAD Level II data requires that ptential users be prperly infrmed regarding effective methds fr wrking with and applying the data t hydrlgic applicatins. The areas emphasized in this reprt were (1) the effects f errrs intrduced int the precipitatin data by uncertainty in the transfrmatin f reflectivity t rainfall n runff simulatins, (2) hw the tempral and spatial reslutin f the radar-estimated precipitatin data affects runff simulatins, and (3) hw the reductin f infiltratin-excess runff resulting frm precipitatin aggregatin can be estimated n the basis f a strm's ttmaxint. The principal cnclusins f the paper are summa- rized belw. 1. Errrs in precipitatin data resulting frm the transfrmatin f reflectivity t rainfall were fund t result in equal r larger-sized errrs in simulated runff generatin. Errrs in simulated infiltratin-excess runff were much larger in magnitude than their respective rainfall errrs, while simulated saturatin-excess runff errrs were much clser t the size f their respective rainfall errrs. Errrs in simulated saturatinexcess runff were larger with respect t the rainfall errrs when antecedent basin cnditins were dry as ppsed t wet. 2. Saturatin-excess runff generatin was insensitive t Regressin y= x y= x y= x Equatin r Crrelatin Here y represents the fractin f "true" runff, andx represents the spatial standard deviatin f maximum precipitatin intensity. the tempral aggregatin f precipitatin input. Its apparent sensitivity t the spatial aggregatin f the precipitatin was shwn t be an artifact caused by incrrectly "smthing rain- fall vlume" either int r ut f the watershed. When this change in precipitatin vlume within the watershed was crrected fr, saturatin-excess runff was als insensitive t the spatial aggregatin f the precipitatin input. 3. Infiltratin-excess runff was very sensitive t the spatial and tempral aggregatin f the precipitatin input. After crrecting fr the change in precipitatin vlume falling within the watershed because f spatial aggregatin, results shwed the simulated runff vlume decreased as bth the spatial and tempral reslutin f the precipitatin decreased (frm 1 t 16 km and 6 t 60 min, respectively). The results als suggest that the reductins in infiltratin-excess runff as a result f tempral aggregatin are mre significant than thse due t spatial aggregatin. 4. The sensitivity f infiltratin-excess runff generatin t the spatial and tempral reslutin f the precipitatin input was fund t be strm-dependent. Strms having a high degree f spatial variatin in the maximum rainfall intensity ccurring ver the watershed were fund t be much mre susceptible t grss underestimatin f infiltratin-excess runff when the reslutin f the precipitatin was carsened. The linear relatinships between the reductin f infiltratin-excess runff vlume and the O'Maxlnt, resulting frm different levels f precipitatin aggregatin, were estimated using simple regressin techniques. These relatinships may be used t crrect the runff predictins made with aggregated precipitatin input, given knwledge f the rainfall characteristics f the strm. In additin t lending supprt t current pinin n several imprtant issues, the research presented in this paper has ffered several new cntributins t the current scientific wrk n the subject. These new cntributins include (1) addressing the issue f radar-estimated precipitatin uncertainty in the cntext f hydrlgic applicatins, (2) explicitly differentiating between the respnse f infiltratin-excess and saturatinexcess runff t uncertainties in precipitatin inputs, and (3) shwing that the sensitivity f runff generatin t precipitatin aggregatin may be directly related t a tangible strm Table 6. Regressin Equatins fr Spatial Aggregatin f Precipitatin Statistic 16-km Reslutin 8-km Reslutin 4-km Reslutin 2-km Reslutin Regressin Equatin /,2 Crrelatin y = x y = x y = x y = x Here y represents the fractin f true runff and x represents the spatial standard deviatin f maximum precipitatin intensity.

15 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL 2669 characteristic. These cntributins have the ptential t imprve the predictin f shrt-term hydrlgic phenmena, such as flash flds. When mdeling in regins where saturatin-excess is the dminant runff mechanism, the reslutin f the precipitatin input may nt be very imprtant. If infiltratin-excess is the dminant prcess, then using highreslutin precipitatin data will be essential in making an accurate predictin. If high-reslutin data (such as 1-km x 6-min) are nt available, then prper crrectins t the flashfld predictins culd ptentially be made n the basis f the reslutin f the available data and the ITMaxint. radar, III, Applicatin fr shrt-term fld frecasting, J. Hydrl., 83, , Cumnge, ":- V. K., '""+'""",, al, radar, aar, d,,n in real time: Prspects fr imprvement, in Hydrlgic Applicatins f Weather Radar, edited by I. D. Cluckie and C. G. Cllier, pp , Ellis Hrwd, Chichester, England, Duan, Q., S. Srshian, and V. K. Gupta, Effective and efficient glbal ptimizatin fr cnceptual rainfall-runff mdels, Water Resur. Res., 28(4), , Dunne, T., and R. D. Black, Partial area cntributins t strm runff in a small New England watershed, Water Resur. Res., 6(5), , Faures, J. M., D.C. Gdrich, D. A. Wlhiser, and S. Srshian, It wuld certainly be f interest t see if the cnclusins Impact f small-scale spatial rainfall variability n runff mdeling, J. Hydrl., 173, , drawn in this study can be applied t watersheds f different Green, W. H., and G. A. Ampt, Studies n sil physics, 1, The flw f sizes and in ther climatic regins. New regins t study might air and water thrugh sils, J. Agric. Sci., 4(1), 1-24, be the midwest and eastern United States. Larger basins, f the rder f ,000 km 2, shuld be studied as well, because Hrtn, R. E., The rle f infiltratin in the hydrlgic cycle, Es Trans. AGU, 14, , that is the basin size f interest t the Natinal Weather Ser- Hudlw, M.D., D. R. Greene, P. R. Ahnert, W. F. Krajewski, T. R. 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16 2670 WINCHELL ET AL.: SIMULATION OF RUNOFF USING RADAR-BASED RAINFALL hillslpe flw paths fr distributed hydrlgic mdeling using digital terrain mdels, Hydrlgic Prcesses, 5, 59-79, Rawls, W. J., L. R. Ahuja, D. L. Brakensiek, and A. Shirmhammadi, Infiltratin and sil water mvement, in Handbk f Hydrlgy, edited by D. R. Maidment, pp , McGraw-Hill, New Yrk, Schell, G. S., C. A. Madramt, G. L. Austin, and R. S. Brughtn, Use f radar measured rainfall fr hydrlgic mdeling, Can. Agric. Eng., 34(1), 41-48, Se, D. J., R. Fultn, J. Breidenbach, D. Miller, and E. Friend, Final reprt fr Octber 1, 1993 t Octber 31, 1994, interagency memrandum f understanding amng the NEXRAD Prgram, WSR- 88D Operatinal Supprt Facility, and the Natinal Weather Service Office f Hydrlgy Hydrlgic Research Labratry, Hydrl. Res. Lab., Off. f Hydrl., N1. Weather Serv., Silver Spring, Md., Shah, S. M. S., P. E. O'Cnnell, and J. R. M. Hsking, Mdeling the effects f spatial variability in rainfall n catchment respnse, 2, Experiments with distributed and lumped mdels, J. Hydrl., 175, , Smith, J. A., D. J. Se, M. L. Baeck, and M.D. Hudlw, An intercmparisn study f NEXRAD precipitatin estimates, Water Resur. Res., 32(7), , 1996a. Smith, J. A., M. L. Baeck, M. Steiner, B. Bauer-Messmer, W. Zha, and A. Tapia, Hydrmeterlgical assessments f the NEXRAD rainfall algrithms, final reprt, Dep. f Civ. Eng. and Oper. Res., Princetn Univ., Princetn, N.J., 1996b. Tees, D., and G. L. Austin, The effects f range n the radar measurement f rainfall, in Hydrlgic Applicatins f Weather Radar, edited by I. D. Cluckie and C. G. Cllier, pp , Ellis Hrwd, Chichester, England, Winchell, M., H. V. Gupta, and S. Srshian, Effects f radarestimated precipitatin uncertainty f different runff-generatin mechanisms, Tech. Rep. HWR , 285 pp., Dep. f Hydrl. and Water Resur., Univ. f Ariz., Tucsn, Wyss, J., E. R. Williams, and R. L. Bras, Hydrlgic mdeling f New England river basins using radar rainfall data, J. Gephys. Res., 95(D3), , H. V. Gupta and S. Srshian, Department f Hydrlgy and Water Resurces, University f Arizna, Bx , Tucsn, AZ ( hshin@hwr.arizna.edu) M. Winchell, Nrtheast River Frecast Center, Natinal Weather Service, Tauntn, MA ( Michael.Winchell@naa.gv) (Received June 30, 1997; revised June 8, 1998; accepted June 8, 1998.)