Computer application of regional low flow study in Baden-Wurttemberg, Germany

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FRIEND: Flw Regimes frm Internatinal Experimental and Netwrk Data (Prceedings f the Braunschweig, Cnference, Octber 1993). IAHS Publ. n. 221, 1994.

1 FRIEND: Flw Regimes frm Internatinal Experimental and Netwrk Data (Prceedings f the Braunschweig, Cnference, Octber 1993). IAHS Publ. n. 221, Cmputer applicatin f reginal lw flw study in BadenWurttemberg, Germany A. WESSELINK 1 Institute f Hydrlgy, Wallingfrd, Oxfrdshire 0X10 8BB, UK I. HAGEMANN & S. DEMUTH Department f Hydrlgy, University f Freiburg, Werderring 4, D79085 Freiburg, Germany A. GUSTARD Institute f Hydrlgy, Wallingfrd, Oxfrdshire OX10 8BB, UK Abstract Within the framewrk f the UNESCO IHPIV prject FRIEND (Flw Regimes frm Internatinal Experimental and Netwrk Data), a reginal lw flw study was perfrmed fr the state f Baden Wùrttemberg, suthwest Germany, using data frm 67 gauged catchments. The study examined the internal relatinship between derived flw statistics. Subsequently, the relatin between the flw statistics and catchment characteristics was examined. Factrs taken int accunt were area, slpe, land use (frest, urban area, lake), drainage density, sil and precipitatin characteristics. Regressin equatins fr estimatin f the flw statistics resulted with cefficients f determinatin f 88 % t 92 %. The catchment characteristics that were significant in the regressin equatins were available in digitized frm, as 2.5 x 2.5 km r 1.25 X 1.25 km grid cells. In additin, the river netwrk fr 17 f the 67 catchments has been digitized. The digital data have been transferred t the Micr Lw Flws system, a micr cmputer package fr autmated estimatin f lw flw characteristics develped at the Institute f Hydrlgy. At any site in these 17 catchments, flw statistics may be estimated by simply mving the cursr t the desired lcatin, prviding a ptentially time saving tl fr water resurce engineers and planners. INTRODUCTION During the first phase f the UNESCO IHP prject FRIEND ( ) a reginal analysis f the variability f lw flw parameters was perfrmed (Gustard et al., 1989, vl.1). The variability f annual and seasnal runff in the prject area, cmprising nrthern and western Eurpe, was described using maps and regressin analysis t determine the relatinship between lw flw indices and catchment characteristics (Gustard, 1989; Gustard & Grss, 1989). The internatinal basis f the prject, with daily data available fr 1350 statins enabled regressin relatinships t be derived fr the whle regin, as well as fr physically distinguishable subsets, e.g. the Rhine basin, r the lwlands f The Netherlands, Belgium and Denmark. Althugh catchment characteristics were successful in explaining between 70 and Nw at PNUD, Bangui, Central African Republic

2 142 A. Wesselink et al. 80% f the variance, it was clear that the understanding f lw flw behaviur wuld benefit frm mre detailed analysis f smaller regins. In particular, the relatinship between sil and gelgy and lw flw variables was nt satisfactrily reslved. The state BadenWurttemberg (suthwest Germany) was chsen fr the first f these studies because clse cllabratin between the University f Freiburg, in BadenWurttemberg, and the Institute f Hydrlgy had develped as a result f the FRIEND prject (Fig. 1). It was envisaged that the result f the reginal regressin analysis wuld be input int the cmputerized lw flw estimatin package, Micr Lw Flw system, develped at the Institute f Hydrlgy, in rder t test its viability in ther cuntries. This limited the chice f data and methds t thse that had been, r culd easily be digitized and applied t the cmputer package. Five steps can be identified in rder t set up a test versin f the lw flw estimatin package; they will be discussed belw. METHODS Daily flw data were available n the FRIEND data base fr 58 gauging statins in BadenWurttemberg (Gustard et al., 1989, vl. II), and these data were cllected fr anther 25 statins. 16 statins had t be mitted because f shrt r incmplete recrds r excessive human influences n the lw flw regime. Frm the remaining data series, 8 fistl. L 9 10 Fig. 1 Gauged catchments in BadenWurttemberg that were used in this study.

Cmputer applicatin f reginal lw flw study in BadenWurttemberg 143 a cmmn perid f recrd was selected (19651985) fr which 52 statins qualified.

3 Cmputer applicatin f reginal lw flw study in BadenWurttemberg 143 a cmmn perid f recrd was selected ( ) fr which 52 statins qualified. During the FRIEND prject, a data base f gridded climate and land use data had been develped. It cnsisted f regular 1.25 x 1.25 km r 2.5 x 2.5 km grids with values fr e.g.: Average Annual Rainfall (AAR) 2day rainfall with 10 year return perid (M102D) Winter Rainfall Acceptance Ptential (WRAP): 5 classes Frest Cver (FOREST): yes r n Urban Area Cver (URBAN): yes r n Lake Cver (LAKE): yes r n The WRAP classificatin has been develped during the UK Fld Studies Reprt (NERC, 1975) in rder t index the sil respnse t rainfall. This apprach was chsen, rather than ne based n "true" hydrgelgical data, because f the lack f a cnsistent data set f hydrgelgical data. The WRAP classificatin scheme has been adpted fr the Eurpean Fld Study (Gustard, 1983). It recgnizes 5 types f sil respnse t rainfall, and the result is an index f catchment respnse t rainfall. It has been recgnized that the scheme lacks discriminatin (the respnse between tw classes can change by a factr f 2 r 3) and cnsistency acrss natinal frntiers, where different sil scientists have interpreted the guidelines differently. Hwever, the WRAP classes were the nly sil r hydrgelgical characteristic available in digital frmat. Catchment bundaries had been digitized fr mst f the daily flw statins n the FRIEND data base. They were drawn and digitized fr the 25 new statins. Algrithms had been develped t autmatically verlay the catchment bundaries nt the gridded data, giving the catchment average value r percentages f the different classes. In additin t these catchment characteristics derived frm gridded data, the slpe (SL1085), altitude f the gauging statin (HTSTN) and stream density (FOLIS: the number f streams intersecting a circle f 30 cm diameter n a 1:50000 map) were determined manually frm maps. Fur statistical analyses were applied t the daily flw data (Institute f Hydrlgy, 1980; Gustard et al., 1989), all cded in FORTRAN, ver the perids specified abve (Table 1): (a) Flw duratin curve: a plt f the cumulative frequency distributin f daily flws, Table 1 Summary f lw flw measures. Variable Number f statins Mean Standard deviatin Range: MIN MAX MFCnr's 1 ) Q95(%MF) MAM7(%MF) BFI K Nte: Abbreviatins used: MF mean flw, Q95 flw exceeded r equalled 95 % f the time, MAM7 mean annual minimum7 day flw, BFI Basefiw index, K50 median recessin rati.

4 144 A. Wesselink et al. shwing the percentage f time a certain flw is exceeded r equalled. The 95 percentile derived frm this curve (Q95) was used in this study as a lw flw parameter (Fig. 2). (b) Flw frequency plt: a plt f the ranked annual minimum «day flws, pltted against a Weibull distributin. Frm this curve the return perids f extreme lw flws can be estimated. The 7day annual minimum flw (MAM7) was used in this study as a single lw flw index (Fig. 3). (c) Baseflw index (BFI): an autmated prcedure fr separatin f baseflw frm the ttal hydrgraph, giving as a result the prprtin f the ttal hydrgraph which is derived frm stred surces. Althugh derived frm daily flw data, this parameter is ften used as a catchment characteristic, indexing the hydrgelgical respnse f the catchment (Fig. 4). (d) Recessin rati frequency plt: a plt f the distributin f the value f the rati f the current flw divided by the flw tw days befre. This rati is the recessin "cnstant" ver the tw days under cnsideratin. The median value f the calculated values (K50) was used in this study as a single catchment flw index (Fig. 5). Analysis f the data cnsisted f crrelatin analysis f catchment characteristics and flw indices, and subsequently stepwise regressin analysis in rder t determine the ptimal regressin equatin. These prcedures were perfrmed using the statistical package SAS. RESULTS Preliminary crrelatin analysis f the flw indices with catchment characteristics Flw Duratin Curves Years \ \ Neckar at Rttweil S ê 200. \ \ \ \ \ \ Jagst at Lippach \ \ \ \ \ «\ \ % f time discharge exceeded Fig. 2 Example flw duratin curve.

5 Cmputer applicatin f reginal lw flw study in BadenWurttemberg Minimum Flw Analysis Neckar at Rttweil Windw: 1/1 fr 365 days I 70 a 60 Duratin (days) A 1 V 7 < v v A A A AYYV * AA AVVV V ; * * , 1.25 h treturn perid (years) Fig. 3 Example lw flw frequency curve tw Neckar at Rttweil Hydrgraph with separated flw, BFI=0, Fig. 4 Example hydrgraph with baseflw separatin. (Table 2) and inspectin f the distributin f the residuals shwed that a lgarithmic transfrmatin was apprpriate fr the derivatin f reginal regressin equatins. URBAN and SOIL fractins in a catchment are frequently zer and thus lgarithmic transfrmatins were based n (URBAN+1) and (SOIL+1). The scale parameter AREA has a significant crrelatin with all flw indices with the exceptin f Q95. Of the land use parameters URBAN and FOREST, nly URBAN is significantly crrelated with a flw parameter, Q95. All flw parameters are significantly crrelated with the

6 146 A. Wesselink et al < 0.6 g. ra frequency distributin (number f ccurences), 1, 1 _, 1, 1, cumulative distributin (%) Fig. 5 Example recessin rati frequency curve. drainage density FOLIS. Althugh the BFI is thught t index the hydrgelgical respnse f the catchment, there is n significant crrelatin f BFI with the three WRAP classes ccurring in BadenWiirttemberg (SOIL1, SOIL2 and SOIL4), the nly significant crrelatin which was fund being between SOIL2 and Q95. The crrelatin matrix was used as a basis fr deriving regressin equatins relating the lw flw indices Q95, MAM7 and K50 t catchment characteristics. All variables were lgarithmically transfrmed and input int a stepwise multiple regressin prcedure. The analysis was perfrmed with and withut BFI as an explaining variable. The preferred resulting regressin equatins are shwn in Table 3. All variables included in the equatins are significant at the 95 % level. Analysis f residuals shwed even distributin f the values, which indicates that the mdel chsen was apprpriate. The explaining variables in the equatins fr Q95, MAM7 and K50 are the mrphmetry variables AREA and drainage density (FOLIS), the climatic variable annual average rainfall (AAR), the land use parameter FOREST, and, where included, the "hydrgelgical" variable baseflw index (BFI). With the flw variables in m 3 s" 1, this result wuld be expected, because in general a larger catchment wuld result in a larger runff at all times. The same hlds fr the annual average rainfall. The effect f frest cver n lw flws is mre ambiguus but generally results in lwer minimum flws (Gustard & Wesselink, 1993; Tallaksen, 1994). The percentage f the variance explained by these variables is shwn in Table 4. The mst dminant variable is AREA, explaining 67% f the variance in Q95 and 50% f the variance in MAM7. The inclusin f the BFI as explaining variable leads t imprved mdels, with an increase in the cefficient f determinatin (K 2 ) f 7% fr Q95, 20% fr MAM7 and 21% fr K50.

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8 148 A. Wesselink et al. Table 3 Regressin equatins relating lw flw indices t catchment characteristics (52 catchments, perid ). with BFI (1) Q95 = (2) MAM7 = (3) K50 withut BFI " 5 BFI 1 ' " 8 BFI " 1 BFI AREA AAR FOREST 0271 R 2 = 87.3% AREA AAR FOLIS 0705 R 2 = 84.1% AREA R 2 = 42.5% (4) Q95 = (5) MAM7 = (6) K AREA AAR FOREST FOLIS" R 2 = 80.3% AREA 1240 AAR FOLIS" 0991 R 2 = 65.2% 1.06 AREA 0013 FOLIS" 0053 R 2 = 21.9% Ntes: Abbreviatins used (flw parameters): Q95 flw exceeded r equalled 95 % f the time (m 3 /s), MAM7 mean annual minimum 7day flw (m 3 s" 1 ), K50 median recessin rati (n units). Abbreviatins used (catchment characteristics): BFI Baseflw Index (n units), AREA catchment area (km 2 ), AAR annual average rainfall (mm), FOREST prprtin under frest cver (n units), FOLIS drainage density index (n units). Table 4 Partial cefficients f determinatin (in %) f the significant variables in Table 3. Variables BFI AREA AAR FOREST FOLIS Equatins: (1) (2) (3) (4) (5) (6) _ The equatins which were derived fr K50 have a much lwer cefficient f determinatin than the equatins fr Q95 and MAM7. This may be explained by the fact that K50 des nt immediately depend n scale (the size f the catchment, the average rainfall) and will therefre be mre difficult t explain. APPLICATION The results that were btained have been input int the Micr Lw Flws cmputer package, a PCbased lw flw estimatin package fr autmated estimatin f lw flw characteristics at any pint n a river in the area. The methd which is applied t set up the package can be summarized as fllws: (a) Assembly f raster data sets fr the relevant area. In the case f Baden Wurttemberg, the grid cell values fr annual average rainfall (AAR), ptential

Cmputer applicatin f reginal lw flw study in BadenWUrttemberg 149 evapratin (PE) and stream density (FOREST) were entered int the system. (b) Establishment f digitized river netwrk.

9 Cmputer applicatin f reginal lw flw study in BadenWUrttemberg 149 evapratin (PE) and stream density (FOREST) were entered int the system. (b) Establishment f digitized river netwrk. In BadenWiirttemberg, 17 f the 67 catchments under study were digitized in the time available. (c) Autmated estimatin f catchment area fr each river stretch, with guidance frm previusly digitized catchment bundaries. (d) Autmated verlay f catchment bundaries fr each river stretch nt the raster data sets and determinatin f catchment values f AAR, PE and FOLIS. (e) Autmated determinatin, fr each river stretch, f mean flw and lw flw characteristics using the multiple regressin results described abve. The estimatin results are then stred fr each river stretch and can be displayed when required, as well as derived flw duratin curves. The present applicatin f the Micr Lw Flws package t a nnuk regin has shwn the viability f its use in ther regins. DISCUSSION The presented analysis shwed that the Winter Rain Acceptance Ptential classes (SOIL1, SOIL2 t SOIL4) were nt significant in explaining the variance f the lw flw indices. It was anticipated that this hydrgelgical variable wuld explain a significant part f the variance because lw flws depend t a large extend n the hydrgelgy f the catchments. The BFI des appear in the regressin equatins as an imprtant explaining variable. Althugh this index may be cnsidered an hydrgelgical catchment characteristic, fr estimatin purpses at ungauged sites the inclusin f this variable is nt satisfactry, because it has t be derived frm streamflw data. In rder t investigate the relevance f the SOIL parameters in explaining the lw flw statistics, a separate regressin mdel was tested, relating SOIL1, SOIL2 and SOIL4 (nt lgarithmic) t the flw parameters (Table 5). The highest cefficient f determinatin that was achieved was 41.9% fr MAM7, and the relatins between BFI r K and the WRAP classes were insignificant. This, and the abve bservatin indicate that there is a need fr imprvements in the classificatin f hydrgelgy in this regin. During the FRIEND study similar results had been arrived at, and, instead f the WRAP classes, the percentage cver f the riginal sil classes (CEC, 1985) were derived manually and subsequently used in regressin equatins. This imprved the cefficient f determinatin markedly. As a part f the FRIEND research prgramme, a Eurpewide revisin f the WRAP map, based n the digitized EC sil map (CEC, 1989), is being undertaken. The perfrmance f the new hydrlgical respnse classes, develped n a Eurpean scale, will be tested in smaller regins, e.g. Baden Table 5 Regressin equatins relating WRAP classes t lw flw indices. Q95 * = *SOILl *SOIL *SOIL4 R 2 = 18.5% MAM7* = *SOILl *SOIL *SOIL4 R z = 19.3% K n significant variables at 95% significance level (R 2 = 6.0%) BFI n significant variables at 95% significance level (R 2 = 8.3%)

10 150 A. Wesselink et al. Wûrttemberg. Appraching the prblem frm anther angle, the percentages f 14 hydrgelgical classes in the regin have been derived manually, and stepwise regressin has been applied reasnably successfully (Demuth & Hagemann, 1994) t these parameters in rder t explain lw flw parameters. Hwever, the apprach has t be limited t a relatively small regin because f the timecnsuming manual derivatin. Furthermre, the transfer t anther regin with anther hydrgelgical classificatin requires lcal calibratin. REFERENCES Cmmissin f the Eurpean Cmmunities (CEC) (1985) Sil Map f the Eurpean Cmmunities 1: Office fr Official Publicatins f the CEC, Luxemburg. Cmmissin f the Eurpean Cmmunities (CEC) (1989) CORINE Data Base Manual. CEC, Brussels. Demuth, S. & Hagemann, I. ( 1994) Estimatin f flw parameters apply inghydrgelgicaiarea infrmatin. In: FRIEND: Flw Regimesfrm Internatinal Experimental and NetwrkData. (Prc. Braunschweig Cnf., Octber 1993). IAHS Publ.n Grss, R., Eeles, C W. O. & Gustard, A. (1989) Applicatin f a lumped cnceptual mdel t FREND catchments. In: FRIENDS in Hydrlgy (Prc. Blkesj Symp., April 1989), IAHS Publ. n Gustard, A. (1983) Reginal variability f sil characteristics fr fld and lw flw estimatin. Agric. Wat. Man. 6, Gustard, A. (1989) FREND (Flw Regimes frm Experimental and Netwrk Data): The first ne hundred days. In: FRIENDS in Hydrlgy (Prc. Blkesj Symp., April 1989), xiiixvi. IAHS Publ. n Gustard, A. & Grss, R. (1989) Lw flw regimes f nrthern and western Eurpe. In: FRIENDS in Hydrlgy (Prc. Blkesj Symp., April 1989), IAHS Publ. n Gustard, A., Rald, L. A., Demuth, S., Lumadjeng, H., Grss, R. & Arnell, N. W. (1989) Flw Regimes frm Experimental and Netwrk Data (FREND), vl. I: Hydrlgical Studies; vl. II: Hydrlgical Data. Institute f Hydrlgy, Wallingfrd, Oxfrdshire, UK. Gustard, A., Bullck, A. & Dixn, J. M. (1992) Lw flw estimatin in the United Kingdm. Reprt n. 108, Institute f Hydrlgy, Wallingfrd, Oxfrdshire, UK. Gustard, A. & Wesselink, A. (1993) Impact f land use change n water resurces: Balquhidder catchments. J. Hydr!. 145(34), 389. Institute f Hydrlgy (1980) Lw Flw Studies Reprt. Institute f Hydrlgy, Wallingfrd, Oxfrdshire, UK. Natural Envirnment Research Cuncil (NERC) (1975) Fld Studies Reprt. NERC, Lndn, UK. Tallaksen, L. & Erichsen, B. (1994) Mdelling lw flw respnse t évaptranspiratin. In: FRIEND: Flw Regimes frm Internatinal Experimental and Netwrk Data (Prc Braunschweig Cnf., Octber 1993). IAHS Publ. n. 221.

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) >

Bootstrap Method > # Purpose: understand how bootstrap method works > obs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(obs) > Btstrap Methd > # Purpse: understand hw btstrap methd wrks > bs=c(11.96, 5.03, 67.40, 16.07, 31.50, 7.73, 11.10, 22.38) > n=length(bs) > mean(bs) [1] 21.64625 > # estimate f lambda > lambda = 1/mean(bs);