A study of the relationship between rainfall variability and the improvement of using a distributed model

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188 GIS and Remte Sensing in Hydrlgy, Water Resurces and Envirnment (Prceedings f 1CGRHWE held at the Three Grges Dam, China, September 2003). IAHS Publ.

1 188 GIS and Remte Sensing in Hydrlgy, Water Resurces and Envirnment (Prceedings f 1CGRHWE held at the Three Grges Dam, China, September 2003). IAHS Publ. 289, 2004 A study f the relatinship between rainfall variability and the imprvement f using a distributed mdel ZIYA ZHANG, MICHAEL SMITH, VICTOR KOREN, SEANN REED, FEKADU MOREDA, VADIM KUZMIN & RICHARD ANDERSON Hydrlgy Labratry, Office f Hydrlgie Develpment, Natinal Weather Service, NOAA, 1325 East West Highway, SSMC-2, Silver Spring, Maryland 20910, USA ziva.zhang(a>,naa,gv Abstract NEXRAD precipitatin estimates have high spatial and tempral reslutin. Hydrlgical researchers have an pprtunity t study hw these gridded precipitatin data can be effectively used in an peratinal envirnment t enhance river-frecasting capabilities. A methd is suggested that will allw an analysis f bserved precipitatin frcing and streamflw data fr a basin t determine the ptential usefulness f applying a distributed mdel in that basin withut actually having t set up and run a disfributed mdel. The methd analyses the relatinship between a precipitatin lcatin index (cmputed using relatinships between basin centrid and rainfall mass centre) and basin respnse time (difference between rainfall and hydrgraph mass centre). The Sacrament Sil Misture Accunting mdel (SAC-SMA) is used t generate runff in all simulatins. Limited cmparisns f flw simulatin results frm lumped and distributed mdels suggest the methd is valid. Three test basins are selected within the Arkansas-Red River basin in the US. The results shw that ne basin cntains cmplexities that may warrant the use f a distributed mdelling apprach fr imprved basin utlet simulatins. Key wrds Arkansas-Red River basin; basin respnse; distributed mdelling; lumped mdelling; rainfall lcatinal index; SAC-SMA mdel INTRODUCTION Currently, lumped hydrlgie mdels are used fr peratinal river frecasting acrss the United States and its territries by River Frecast Centers (RFCs) f the Natinal Weather Service (NWS). Traditinally, lumped mdels have been used because the data available frm peratinal raingauge netwrks will usually nt supprt finer reslutin mdelling, bth in spatial and tempral scales. With the establishment f the Next Generatin Weather Radar (NEXRAD) prgram, Weather Surveillance Radar 1988 Dppler (WSR-88D) radars have been deplyed acrss the United States, beginning in 1991 (Heiss et al, 1990). The high spatial and tempral reslutins f these precipitatin inputs are attractive fr use in distributed mdelling. Other emerging spatial data sets such as sil, vegetatin, and ther meterlgical data tgether with DEM data have als added t the impetus fr develpment and applying distributed hydrlgie mdels. Althugh a distributed mdel can prvide spatially-varied infrmatin n the states f hydrlgical prcesses, it may nt always prvide imprved utlet simulatins cmpared t lumped cnceptual mdels fr all basins as suggested by

A study f the relatinship between rainfall variability and the imprvement f using a distributed mdel 189 recent studies (Carpenter et al, 2001; Smith et al, 1999) and by the results frm the

2 A study f the relatinship between rainfall variability and the imprvement f using a distributed mdel 189 recent studies (Carpenter et al, 2001; Smith et al, 1999) and by the results frm the Distributed Mdelling Intercmparisn Prject (DMIP) (Reed et al, 2004). The develpment f distributed mdels has prgressed t the pint that their cnceptual scientific basis and utility are in large part n lnger questined. In additin, the predictin by Beven (1985) that cmputatinal capacities will mature t the degree that distributed mdels will nt be limited by prcessing speeds and strage requirements has largely cme true. Hwever, issues related t parameter estimatin/calibratin, sub-grid variability, and thers remain active areas f research. Mrever, there remains the questin psed by Beven (1985), which is ne f mdel applicability: under what cnditins and fr what type f frecasting prblem it is advantageus t use a distributed mdel? The NWS is particularly interested in this questin frm the standpint f imprving its frecasts f US rivers and streams. Seyfried & Wilcx (1995) restated this questin by nting that the applicatin f distributed mdels may nt be wrth the ften cnsiderable effrt utside f strictly research applicatins. Later, Krajewski et al. (1991) nted that the questin still remains as t hw much can be gained frm a distributed mdel and under what cnditins. Bell & Mre (1998) cntinued by nting that the selectin f a distributed mdel frm amngst a number f variants cnstitutes an imprtant scientific and peratinal issue. Finally, Schaake (2003) highlighted the need t develp diagnstic tls that uncver infrmatin in input frcing and utput streamflw bservatins that may yield clues as t the apprpriate mdel fr a particular applicatin. In light f this persistent questin, the purpse f this paper is t investigate the cnditins under which a distributed mdel can be expected t utperfrm a lumped mdel fr basin utlet simulatins. We attempt t discver this thrugh analysis f nly a priri infrmatin and nt thrugh the traditinal pathway f mdel applicatin. Of curse, we must use a lumped-distributed mdel pair t validate ur results, and in this regard ur cnclusins are smewhat mdel dependent. Our analyses are aimed at the particular practical issue f imprving simulatins at basin utlets. Recalling the cmments f Schaake (2003) stated earlier, we hypthesize that the bserved time series f precipitatin and streamflw cntain infrmatin that can be used t develp diagnstic indicatrs pinting t the apprpriate mdel structure. We prpse tw indices fr evaluating a basin's precipitatin spatial variability and ne index t quantify basin respnse. We use bserved data t avid mdel specific cnclusins as much as pssible. METHODOLOGY We fllw the analyses f Smith et al. (2004a) and cmpute specific indices fr general rainfall lcatin and rainfall variability. We als prpse a new index f runff variability. Rainfall lcatin index This analysis determines the effect f varying lcatins f strms, independent f intrastrm spatial variability f precipitatin. As described in Smith et al. (2004b), the

3 190 Ziya Zhang et al. rainfall centrid rati prpsed by Wei & Larsn (1971) is mdified s that distance is measured alng flw paths t the utlet instead f alng a straight line. Flw paths fr a 4-km gridded mdelling netwrk basin were cmputed using a higher reslutin DEM (Reed, 2003). Based n gridded precipitatin data, the centre f precipitatin mass fr each time step can be calculated as: (1) where P\ is precipitatin amunt at grid i, d\ is the distance f grid / t the basin utlet, A\ is the area f grid i, and jy is the ttal number f grids within the basin. Distance d\ is measured alng flw paths defined by DEM analysis. A basin's centre f mass C/ K can be calculated using the previus equatin by setting P,= 1. The rainfall centrid rati fr each time step can then be expressed as a dimensinless index I pcp = C pcp ICb s - Fr a specific time, if l pcp < 1, then the precipitatin fr this time step is generally lcated at the regin clser t the utlet. Values greater than 1.0 indicate that the centre f rainfall mass is away frm the utlet. I pcp values near 1.0 imply that the precipitatin is cncentrated near the basin centrid. Fr a specific event, we cmpute a lcatin index (weighted rainfall centrid rati) f precipitatin. This is determined by weighting the rainfall amunt during the perid as: where I pcp is the precipitatin lcatin index fr ne time step, and P t is the precipitatin amunt fr the same time, and ^ is the summatin ver all time steps in the event. (2) Rainfall variability index T understand hw intrastrm rainfall variability affects an utput hydrgraph, a rainfall variability index similar t the index C is prpsed. Fr each time interval f a rainfall-runff event, this index is expressed as: where all ntatins are the same as in the discussin f the lcatinal index C. The quantity G is basically the spatial standard deviatin f the hurly gridded NEXRAD precipitatin estimates cvering a basin. The rainfall variability index, l v, fr a fld event can then be estimated as a weighted value as: (3) (4) Runff variability index Smith et al. (2004a) prpsed an index fr runff variability based n wavelet analysis f cncurrent time series f precipitatin and streamflw. Their index measures the

4 A study f the relatinship between rainfall variability and the imprvement f using a distributed mdel 191 filtering effects f the basin by quantifying the transfrmatin f the input rainfall signal t the utput discharge signal. We prpse a new index, the basin respnse time, At, t quantify the variability f bserved runff as it relates t precipitatin. We define the At as the time difference between rainfall and discharge centrids. This index represents hw fast a basin respnds t a specific rainfall event. In cntrast t ther time measures, we measure the centrid frm the beginning f bserved rainfall, nt frm the beginning f effective rainfall. In this way, we accunt fr all hydrlgie prcesses that transfrm the variability f the rainfall time series int the variability f the utlet discharge time series: interceptin, depressin strage, initial sil misture states, sub-surface and surface ruting, and channel ruting. By analysing a number f events, we hpe t develp a cmpsite picture f the behaviur f a basin ver a wide range f initial sil misture cnditins. We use several ther statistics in ur analyses. Cvariance is used t evaluate the dependence between rainfall lcatin and a basin's respnse. It is defined as: I ( M _ "N Cv(I L,At) = izvu-*l)(at e -At) (5) ver M events. Larger abslute Cv values indicate a strnger dependence between the tw. A value f zer Cv means they are independent. We als cmpute the cefficient f variatin CV fr selected variables. CV f a variable is defined as the rati f the standard deviatin t its mean value fr selected events. Data In this study, we select rainfall-runff events frm the perid beginning in June, 1993 and ending in the spring f 2001 fr three basins: (BLU02 Blue River at Blue, Oklahma; TAL02 Illinis River at Tahlequah, Oklahma; and WTT02 Illinis River at Watts, Oklahma). These basins are within the Arkansas-Red River Basin in Oklahma (Table 1 and Figure 1). Here we extend the wrk f Smith et al. (2004a) by including a nested basin TAL02, cntaining WTT02. Smith et al. (2004b) prvided a discussin f these basins. Prvisinal (withut quality cntrl) hurly bserved discharge data frm the USGS were used. The NEXRAD 4 km radar rainfall estimates were used in this analysis and in the distributed mdelling. Hurly time series f mean areal rainfall ver each f the study basins were als prcessed as the input fr generating the lumped mdel simulatins. Table 1 Areas, number f selected events, and ther statistics fr three selected basins. Basin Area Number f Cvariance CVfr CV fr (km 2 ) events between rainfall basin respnse At selected /;. and At based n I Y BLU WTT TAL

5 192 Ziya Zhang et al. Kansas Missuri A- (Kilmeters) \ Basin Bundary Streams WTTOZ. Illinis River at Watts, OK, ; ELD02: Barn Frk at Eldn, OK. TAL02. Illinis River at Tahlequah, OK. KNS02: Flint Creek at Kansas, OK. TIFM7: Elk River at Tiff City, MO. BLUOZ Blue River at Blue, OK. Arkansas Oklahma Texas X Fig. 1 Map f selected basins within ABRFC. RESULTS AND ANALYSES Analysis f relatinship between precipitatin distributin and streamflw In this sectin, we cmpute the indices described in the previus sectin in rder t understand the nature f the rainfall variability and its effect n the utlet discharge variability. These indices are cmputed fr a selected number f rainfall-runff events fr WTT02, TAL02, and BLU02 (Table 1). Within each year, several events were selected, spanning a range f discharges. In rder t better shw the relatinship between rainfall and its respnse f a basin, mst events were selected as clse t single-peaked as pssible. Figure 2 presents the relatinship between the rainfall lcatinal variability, I L, and basin respnse time, At, fr the three basins based n the selected events. It clearly shws that different patterns between I L and At exist between BLU02 and the ther tw basins. Fr BLU02, when rainfall is generally lcated near the basin utlet (smaller I L ) the basin's respnse is generally faster (smaller At). Fr the ther tw basins, this relatinship is very weak. Values f cvariance listed in Table 1 shw that a much strnger dependence between I L and At exists fr BLU02 than fr the ther tw basins. In ther wrds, the general lcatin f rainfall ver the basin has a greater impact n BLU02's respnse than fr the ther tw catchments. Results in Fig. 2 als shw that the Blue River has a wide range f I L whereas fr the ther tw basins the range is a lt

6 A study f the relatinship between rainfall variability and the imprvement f using a distributed mdel 193 narrwer. In ther wrds, rainfall patterns in TAL02 and WTT02 have a relatively unifrm distributin. When the index I L is arund 1.0 (0.9 and abve), the relatin between I L and At is similar fr all three basins. The spread in At when h is arund 1.0 is prbably due t the difference in initial sil misture cnditins and rainfall intensities fr different events. Their effects are nt explicitly islated in this paper. Figure 3 shws the relatinship between general rainfall variability, I v, and basin respnse time, At. Fr nested basins TAL02 and WTT02, the basin respnse times lie in a relatively narrw time band fr different values f rainfall variability. The rainfall variability range fr bth basins is practically the same. There is a small tendency fr the basin respnse time t decrease as the variability increases. The tendency is very similar fr these tw nested basins. Overall, the general rainfall variability has a small effect n the flw respnse f WTT02 and TAL02. Hwever, the data pints exhibit a lt mre spread in basin respnse time fr BLU02 than fr the ther tw. Since the range f CV fr rainfall amng the three basins is clse (0.59, 0.55 and 0.46, see Table 1), the larger value f the CV f basin respnse time At, fr BLU02 (0.31, Table 1) suggests that BLU02 is mre sensitive t Iy. c 6iÊ i "cjl A BLU02 OWTT02 TAL Basin Respnse Time (Hurs}, A t Fig. 2 Rainfall lcatinal index vs basin flw respnse time. A BLU02 OWTT02 B TAL02 a a Basin Respnse Time (Hurs), At Fig. 3 Relatinship between rainfall variability and basin flw respnse time fr three basins.

7 194 Ziya Zhang et al. Verificatin frm simulatin results Frm the analyses f bserved rainfall and crrespnding discharge data, it is clear that the effect f rainfall distributin n the basin respnse fr BLU02 is much greater than fr WTT02 and TAL02. It is anticipated that the use f distributed mdelling wuld imprve the simulatin results mre fr BLU02 than fr the ther tw basins. In rder t verify this assumptin, simulatins were cnducted using bth lumped and distributed mdels. The Sacrament Sil Misture Accunt Mdel (SAC-SMA) (Burnash et al., 1973) is used in the rainfall runff prcess fr bth mdels. The lumped simulatin uses the hurly mean areal precipitatin time series based n gridded radar data as input frcing. Manual calibratins were cnducted based n histrical data. Distributed simulatins were generated by HL-RMS (Kren et al, 2003), a distributed mdel that uses gridded radar rainfall data and gridded parameters. An explicit verland and channel flw ruting algrithm is used in the mdel. Fr each event, we cmpare lumped and distributed simulatins t bserved flws using a mdified crrelatin cefficient R m d prpsed by McCuen & Snyder (1975). Figure 4 shws hw rainfall lcatin affects the lumped and distributed simulatins. Since the x-axis is the difference between the mdified crrelatin cefficient between distributed and lumped (JR m d_dsi - Rmdjmp), this plt represents the imprvement (r lss) realized by using distributed mdelling. Fr BLU02, distributed simulatins are cnsistently better than the lumped results when the rainfall lcatinal index, I L, is less than abut 0.8. In ther wrds, fr BLU02, distributed mdelling can imprve simulatin results when the rainfall is centred clser t the utlet. When I L is arund the 1.0 (apprximately between 0.9 and 1.1), the pints lie n at bth sides f the zer line (i.e. when R m d_dst - Rmdjmp = 0) fr all three basins. This means when the rainfall is relatively unifrm acrss a basin, the differences f simulatin results between distributed and lumped mdelling are randm. Fr selected events, mst pints are within the I L range f 0.9 and 1.1 fr WTT02 and TAL02 and the results shw that distributed mdelling fr these tw basins des nt imprve the hydrgraph simulatins ver lumped mdelling. The results shwn in Fig. 4 suggest that distributed 1.2 ^ 1.1 x" a 1 TS _c CO I 0.8 c ^ c 'c A BLU02 O WTT02 B TAL02 Aa 41 A A O A A. OL R md_dst " ^ mdjmp 0.4 Fig. 4 Imprvement f distributed mdelling ver lumped mdelling fr different rainfall lcatinal index.

8 A study f the relatinship between rainfall variability and the imprvement f using a distributed mdel 195 mdelling prvides varying degrees f imprvement fr different basins and different rainfall distributins in the same basin. CONCLUSIONS Tw indices f bserved spatial rainfall variability were cmputed fr three basins. Of these basins, basin BLU02 exhibited prnunced rainfall lcatin variability, whereas basins WTT02 and TAL02 exhibit far less rainfall lcatinal variability. An attempt t relate the input rainfall spatial variability t bserved discharge and ultimately t the gains realized by distributed mdelling was made. Analysis f the bserved rainfall distributin and streamflw fr three basins shws that the BLU02 basin cntains cmplexities that suggest gains can be attained by using distributed mdels. While the simulatin results are mixed fr lumped and distributed mdelling when the rainfall is relatively unifrm, large imprvements were realized by distributed mdelling when the strm centre lcatins were clse t the basin utlet. Althugh the range f rainfall general variability fr three selected basins is similar, it has greater crrelatin with basin respnse time fr BLU02 than fr WTT02 and TAL02. Zhang et al. (2004) cmpared simulatins frm a lumped and a sub-basin mdelling appraches fr the BLU02 basin. The cnclusin was that BLU02 can benefit by using distributed rainfall and ther spatial infrmatin. Results frm this study supprt their cnclusins. We suggest that the indices presented here can be used t determine whether a basin can benefit frm distributed mdelling. Further testing n a wide variety f basins is needed. REFERENCES Bell, V. A. & Mre, R. J. (1998) A grid-based distributed fld frecasting mdel fr use with weather radar data: Part 2. Case studies. Hydrl. Earth System Sci. 2(3), Beven, K. (1985) Distributed mdels. In: Hydrlgical Frecasting (ed. by in M. G. Andersn & T. P. Burt), Jhn Wiley and Sns, Chichester, UK. Burnash, R. J. C, Ferrai, R. L. & McGuirc, R. A. (1973) A Generalized Streamflw Simulatin System - Cnceptual Mdelling fr Digital Cmputers. US Department f Cmmerce, Natinal Weather Service and State f Califrnia, Department f Water Resurces, Califrnia, USA. Carpenter, T. M., Gergakaks, K. P. & Spersflage, J. A. (2001) On the parametric and NEXRAD-radar sensitivities f a distributed hydrlgie mdel suitable fr peratinal use. J. Hydrl. 253, lieiss, W McGrew, D. & Sirmans, D. (1990) NEXRAD: Next Generatin Weather Radar (WSR-88D). Micrwave J. 33, Kren, V., Reed, S., Smith, M. & Zhang, Z. (2003) Cmbining physically-based and cnceptual appraches in the develpment and parameterizatin f a distributed system. In: Weather Radar Infrmatin and Distributed Hydrlgical Mdelling (ed. by Y. Tachikawa, B. E. Vieux, K. P. Gergakaks & E. Nakakita) (Prc. Symp. HS03, July 2003, Sappr, Japan). IAHS Publ IAHS Press, Wallingfrd, UK. Krajewski, W. F., Lakshmi, V., Gergakaks, K. P. & Jain, S.C. (1991) A Mnte Carl study f rainfall sampling effect n a distributed mdel. Water Resur. Res. 27(1), McCuen, R. H. & Snyder, W. M. (1975) A prpsed index fr cmparing hydrgraphs. Water Resur. Res. 11(6), Reed, S. (2003) Deriving flw directins fr carse reslutin (1-4 km) gridded hydrlgie mdelling. Water Resur. 39(19), Reed, S. M., Kren, K., Smith, M., Zhang, Z., Mreda, F., Se, D. -J. & DMIP Participants (2004) Overall distributed mdel inter-cmparisn prject results. J. Hydrl. (submitted). Schaake, J. S. (2003) Intrductin. Calibratin f Watershed Mdels, Water Science and Applicatin 6, American Gephysical Unin, 2003, 1-8. Res.

196 Ziya Zhang et al. Seyfried, M. S. & Wilcx, B. P. (1995) Scale and the nature f spatial variability: Field examples having implicatins fr hydrlgie mdelling. Water Resur. Res. 31(1), 173-184.

9 196 Ziya Zhang et al. Seyfried, M. S. & Wilcx, B. P. (1995) Scale and the nature f spatial variability: Field examples having implicatins fr hydrlgie mdelling. Water Resur. Res. 31(1), Smith, M. B., Kren, V., Finnerty, B. & Jhnsn, D. (1999) Distributed Mdelling: Phase 1 Results. NOAA Reprt NWS 44, February, 250 pp. Cpies available upn request. Technical Smith, M. B., Kren, V., Zhang, Z., Reed, S., Pan, J. -J. & Mreda, F. (2004a) Runff respnse t spatial variability in precipitatin: An analysis f bserved data. J. Hydrl. (submitted). Smith, M. B., Se, D. J., Kren, V. I., Reed, S., Zhang, Z., Duan, Q Cng, S., Mreda, F., Andersn, R. (2004b) The distributed mdel intercmparisn prject (DMIP): Mtivatin and Experiment Design.,/. Hydrl. (submitted). Wei, T. C. & Larsn, C. L (1971) Effects f areal and time distributin f rainfall n small watershed runff hydrgraphs. Bulletin 30, Water Resurces Research Center, University f Minnesta Graduate Schl, 118 pp. Zhang, Z., Kren, V., Smith, M. B., Reed, S. & Wang, D. (2004) Use f next generatin weather radar data and basin disaggregatin t imprve cntinuus hydrgraph simulatin. J. Hydrl. Engng 9(2) (In press).

APPLICATION OF THE BRATSETH SCHEME FOR HIGH LATITUDE INTERMITTENT DATA ASSIMILATION USING THE PSU/NCAR MM5 MESOSCALE MODEL

JP2.11 APPLICATION OF THE BRATSETH SCHEME FOR HIGH LATITUDE INTERMITTENT DATA ASSIMILATION USING THE PSU/NCAR MM5 MESOSCALE MODEL Xingang Fan * and Jeffrey S. Tilley University f Alaska Fairbanks, Fairbanks,