Low flow discharge analysis in Slovenia

Transcription

1 FRIEND: Flow Regimes from International Experimental and Network Data (Proceedings of the Braunschweig: Conference, October 1993). IAHS Publ. no. 221, Low flow discharge analysis in Slovenia M. KOBOLD & M. BRILLY University of Ljubljana, FAGG Hydraulics Division, Ljubljana, Slovenia Abstract A regional low flow analysis for Slovenia is outlined using the methodology developed by the FRIEND project. Catchment characteristics are determined by a geographical information system. The low flow statistics, the relationships between low flow statistics and catchment characteristics and the regional equations for evaluating low flows at ungauged catchments are presented. The relationships between different durations are analysed using the mean annual ten day minimum as a key variable. The accuracy of analysis is checked for 11 catchments. INTRODUCTION The region of Slovenia is very varied with influences from the Mediterranean, Pannonian lowland and Alps. Forty percent of its area is composed of limestone as karst land. Slovenia is km 2 in area and has a lot of water sources and a varied flow regime. The average annual rainfall is 1500 mm and the average annual runoff is 1000 mm. The same environmental concerns exist in protecting the flow regime and water quality. The increasing demand on water resources inevitably leads to a better understanding of low flows and processes. The regional low flow analysis in Slovenia used the methodology described in Regional Low Flow Studies (Gustard et al., 1989). In these studies relationships between flow statistics and catchment characteristics are developed in order to evaluate the main controlling influences on low flows. It also aims to provide methods of estimating low flows at ungauged sites, and regression relationships are presented between single flow statistics, such as the mean annual minimum and the 95 percentile discharge for the flow duration curve, and basin characteristics, such as area, mean annual rainfall and soil type. The relationship between low flows of different durations and different frequencies is also discussed. This method of analysis of low flows was followed in this paper to enable comparison of results. A regression analysis, varying the number of parameters is summarized by Radie (Radie, 1992) with some new accesses (Brilly & Kobold, 1993). The main emphasis was on the catchment geology because the minimum flows are a result of the outflow of groundwater and are hence dependent on catchment geology. CATCHMENT SELECTION AND DETERMINATION OF PARAMETERS The 11 catchments shown in Fig. 1 were selected with areas from 100 to 500 km 2. This number is small for statistical analysis, but no more stations with adequate data were available for the preliminary study. The representative stations each have at least 30 years of daily discharge data. Catchment characteristics such as catchment area (AREA),

2 120 M. Kobold & M. Brilly Fig. 1 Experimental catchments of Slovenia. annual average rainfall for catchment (AAR) and index of geology (GEO) are determined by SPANS geographical information system. Data with suitable attributes was digitized and included into a geographical information system (GIS). The determination of average attribute values for catchments was done by computer program. Catchment geology was indexed using values of the baseflow index. The following values for the different types of geology were assumed: alluvium, limestone sandstone, conglomerate, dolomite sandstone and marl marl and clay Using these classes the index of geology for each catchment was determined. Other characteristics such as the length of the main river (MSL), the average slope of the main river (SL), the altitude of the representative gauging station of the catchment (HSTN), median altitude of the catchment (HMEAN) (Radie, 1992) and the average elevation difference (HU), the difference between the median altitude of the catchment and altitude of the gauging station (Brilly & Kobold, 1993) were also determined. The selected catchments with their characteristics are presented in Table 1. CALCULATION AND PRESENTATION OF LOW FLOW STATISTICS Low flow statistics were derived using procedures described in the Low Flow Studies Report (Institute of Hydrology, 1980). Computer programs were written to derive and present flow duration curves (Fig. 2) flow frequency curves (Fig. 3) and baseflow index. Other low flow statistics such as the average flow (ADF), 95 percentile flow (<295) for different durations, mean annual minima (MAM) for different durations, baseflow index

3 Low flow discharge analysis in Slovenia 121 Table 1 List of selected experimental catchments of Slovenia with characteristics. Catchment Gauging station Area (km 2 ) Period MSL (km) HSTN HMEAN (m) (m) SL HU (m) AAR (mm) GEO Pesnica ZamuSani Paka SoStanj Radovna Podhom Soca Krsovec Sora Suha Idrijca Hotescek Vipava Vipava Precna Precna Not.Reka Cerk.mlin Kolpa Petrina Lahinja Gradac (BFI) and the 50 percentile recession coefficient (REC50) were also calculated. All low flow statistics are presented in Table 2. The average flow is expressed in m 3 s" 1, the one day 95 percentile flow, 095(1), and mean annual 1 and 10 day minima, MAM(l) and MAM(10), are expressed in percentages of the average flow to give an easier comparison between catchments. The 10 day duration mean annual minimum (MAMSP) is given in m 3 s 1 km" 2. MAMCV is the coefficient of variation of MAMSP and ARCV the coefficient of variation of annual runoff. REGIONAL ANALYSIS OF LOW FLOW INDICES WITH CATCHMENT CHARACTERISTICS The main parameters affecting low flows were determined from the relationships between low flow indices and catchment characteristics. The results of the regression analysis were similar to those in the FRIEND study of low flows (Gustard et al., 1989). Preliminary regression analysis of the low flow indices with catchment characteristics showed that a logarithmic transformation was appropriate. The relationship between transforming variables is shown in the correlation matrix (Table 3). The correlation coefficients of two key statistics of low flow, <295(1) and MAM(10), with catchment characteristics are almost identical and therefore the regional equations derived from them will be similar. In terms of scale parameters, the catchment area (AREA) is poorly correlated with low flow indices, but the main stream length (MSL) does not show any correlation with low flow indices. The annual rainfall (AAR) and average elevation difference (HTJ) show considerably higher correlation coefficients with <295(1) and MAM(10). In the multivariate regression, the number of parameters was varied and the

4 122 M. Kobold & M. Brilly 1000: Soca Krsovec Idrijca Hotescek Vfpava Vipava Kolpa Petrina Uhinja Gradac NDLRekaCerk.mlin RadovnaPodhom Sora Suha Paka SostanJ Pesnica Zamusani Percentage of time flow exceeded Fig. 2 One day flow duration curves for selected catchments of Slovenia. following nonlinear model obtained: (295(1) = a*area* AAR C GEO d MSI/ Sl/fflF (1) By this method, a statistically optimal model with the greatest regression coefficient R and the minimal standard error of estimation was obtained. The regression models for 295(1) and MAM(10) with catchment characteristics are presented in Table 4 and Table 5 with R 2 and SE for each model. The comparison of regression coefficients R and standard errors SE shows that the model with all parameters gives the highest R 2, while the standard error is minimal for the model excluding main stream length and average slope of river. The regression equation for Slovenia is in the form:

5 Low flow discharge analysis in Slovenia 123 (295(1) = 1.75*10^ AREA 148 AAR" 139 GEO 348 MSL" 008 SL" 004 HU 119 (2) We get the similar equation for the variable MAM(IO): MAM(IO) = 1.10*10 1 AREA 140 AAR" 134 GEO 326 MSL" 004 SL" 010 HU 118 (3) o (!) c» > ;ent age Pert 60 sn 4( m * A * a D * * " ' 13 'Jmfm H Soca Krsovec Idrljca Hotescek ca Vipava Vipava w Kolpa Petrina A Lahinja Gradac X Not.Reka Cerk.mlin I 1! Weibull reduced variate XX Return period (years) % > s ** *w «X X Precna Precna w RadovnaPodhom * Paka Sostanj A Sora Suha " PesnlcaZamusanl 30 A A., ***w.*t***, *x x x x 20 ^IÏ A I Weibull reduced variate i Return period (years) Fig. 3 Ten day annual minimum series for selected catchments of Slovenia.

6 124 M. Kobold & M. Brilly Table 2 Calculated statistics of low flows. Gauging station ADF (m 3 s" 1 ) ARCV BFI 295(1) (%ADF) MAM(l) (%ADF) MAM(10) (%ADF) MAMCV MAMSP REC50 (m 3 s" 1 ) (km" 2 ) Zamusani Sostanj Podhom Krsovec Suha Hotescek Vipava Precna Cerk.mlin Petrina Gradac Table 3 Correlation matrix for logarithmic transformation of low flow indices and catchment characteristics. 95(1) MAM(10) BFI ADF AREA AAR GEO MSL SL HU 295(1) MAM(10) BFI ADF AREA AAR GEO MSL SL HU Equations (2) and (3) are the regional equations for the region of Slovenia for evaluating low flows, Q95(l) and MAM(10), at ungauged catchments. The equations show the great dependence on the index of geology (GEO). Low flows also increase with the area and average elevation difference (HU), but decrease with average annual rainfall. The negative value of the coefficient for variable AAR was an unexpected result and is caused by high orographic impact on the mean annual rainfall (Fig. 4). In future

7 Low flow discharge analysis in Slovenia 125 research mean annual evaporation should be included. Regression analysis without the variable HU gave similar results to those presented in Regional Low Flow Studies (Gustard, et al., 1989). The equations are: and: <295(1) = 4.41*10" 3 AREA 148 AAR 033 GEO 312 MSL" 025 SL 046 (4) MAM(IO) = 2.87*10 3 AREA 140 AAR 0 36 GEO 290 MSL/ 022 SL 40 (5) The values of coefficients R 2 and SE are and for (295(1) and Table 4 Regression models for Q95(l) with catchment characteristics. AREA AAR GEO MSL SL HU R 2 SE _ variable is included in model variable is not included in model Table 5 Regression models for MAM(10) with catchment characteristics. AREA AAR GEO MSL SL HU R 2 SE _ variable is included in model variable is not included in model

8 126 M. Kobold & M. Brilly 2800 CC 800 Fig. 4 The interdependence between mean annual rainfall and average elevation difference. and for MAM(IO). These values are similar to the values of coefficients obtained in Regional Low Flow Studies (Gustard et al., 1989) shown in Table 6. The regional equation for estimating the baseflow index, BFI, was derived by regression analysis of index BFI with catchment characteristics: catchment area (AREA), main stream length (MSL), average slope of river (SL), index of geology (GEO) and average elevation difference (HU). The linear model was used because the transformed variable gave no improvement in the regression. The results of linear regression model: BFI const a*area 6*AAR c*geo d*msl e*sl /*HU (6) are given in Table 7. The analyses of models show that BFI is the best correlated with the index GEO and average slope of river, while it is almost independent of other catchment characteristics. In the last model the regression coefficient is the smallest, but the standard error is minimal and the equation for this model is: BFI = *GEO 6.05*SL (7) DURATION RELATIONSHIPS The analysis of duration using the mean annual ten day minimum, MAM(IO), as a key variable, showed that it is possible to translate the results from one key duration to the duration of interest. The coefficients of linear model: MAM(D) = constant &*MAM(10) (8) were derived by regression analysis and are shown in Table 8. The results are similar

9 Low flow discharge analysis in Slovenia 127 Table 6 Exponents of significant variables in regression models relating 095(1) and MAM(IO) to catchment characteristics (Gustard et al., 1989). Constant AREA AAR SOIL URBAN1 FOREST1 FOLIS WSEA R 2 % f.s.e. G9S(1) m 3 s" 1 UK and Republic of Ireland 1.72*10" France 1.42*10" ns ns F.R. Germany 5.86*10 u Belgium, Netherlands, Denmark 9.74*10" ns 2.88 ns Austria and Switzerland 5.60*10" s na Norway, Sweden, Finland 6.32*10" na MAM(IO) m 3 s" 1 UK and Republic of Ireland 3.05*10"* France " ns ns F.R. Germany 2.29*10 u Belgium, Netherlands, Denmark 6.67*10" ns 2.27 Austria and Switzerland 1.84*10" na ns 0.29 ns Norway, Sweden, Finland 4.31*10"* na ns ns = variable not significant at 95 % level na = variable not available Table 7 Coefficients of regression model for BFI with catchment characteristics. const / R 2 SE _ variable is not included in model

10 128 M. Kobold & M. Brilly Table 8 Coefficients of regression model for estimating MAM(D) from MAM(IO). Duration Constant k R 2 SE D (days) to the results of the FRIEND study (Gustard et al., 1989) which showed that there is a consistent relationship between minimum flows of different durations across the entire study area. ACCURACY OF ANALYSIS First analyses using the derived interdependencies show unexpected accuracy. The obtained accuracy of interdependencies for the region of Slovenia exceeded the accuracy achieved by previous analyses in the FRIEND project. This is because analyses were based on homogeneous data from a relatively small area and improvements in the FRIEND methodology were used in low flow analysis. The best results are achieved by considering the index of geology and average elevation difference. The regional equations (2), (3), (4), (5) were tested for those catchments listed in Table 9. Calculated values of 295(1) and MAM(10) (using equations (2) and (3)) are compared to measured values in Table 10. In Table 11 these comparisons are repeated, but with (295(1) and MAM(10) calculated from equations (4) and (5) respectively. The average errors between calculated and measured flows for prediction of g95(l) and MAM(10) are about 20%. In Table 12 the FRIEND regional equations for Austria and Switzerland are used. The average errors and standard deviations are much greater. It can be concluded that low flows can be evaluated by the derived regional equations and the analysis therefore gives satisfactory results. APPLICATION POSSIBILITIES OF REGIONAL EQUATIONS IN SLOVENIA The derived interdependencies have practical applications for evaluating minimal flows on either ungauged catchments or where measured data are insufficient for statistical analysis. This would require derivation of characteristics from 1: topographic maps and 1: geology maps, which cover the whole of Slovenia. The methodology and derived interdependencies are also an ideal example of the use of the

11 Low flow discharge analysis in Slovenia 129 Geographic Information System (GIS), because all necessary elements are simply determined using GIS base operation. The model has been inserted in Water Management Information System WMIS (Vidmar et al., 1992) and enables the calculation of Table 9 A list of catchments for testing the regional equations with their characteristics. Catchment Gauging station Area (km 2 ) AAR (mm) GEO MSL (km) SL HU (m) Mislinja Otiski vrh Radoljna Ruta Dravinja Draza vas Tr.Bistrica Preska Kokra Kokra Mirna Gaberje Dreta Krase Voglajna Celje Koritnica Kal Idrijca Podroteja Baca Baca Table 10 Calculated and measured values of Q95(l) and MAM(10) by equations (2) and (3). Gauging station 295(1) calculated (m 3 s" 1 ) measured error MAM(10) calculated (m 3 s 1 ) measured error Otiski vrh Ruta Dra2a vas Preska Kokra Gaberje Krase Celje Kal Podroteja Bafia Average 22.2% 21.8% Standard deviation 16.0% 18.5%

12 130 M. Kobold & M. Brilly Table 11 Calculated and measured values of 095(1) and MAM(IO) by equations (4) and (5). Gauging station 295(1) calculated (m 3 s" 1 ) measured error MAM(10) calculated (m 3 s" 1 ) measured error Otiski vrh Ruta Draza vas Preska Kokra Gaberje Krase Celje Kal Podroteja Baca Average 18.4% 20.5% Standard deviation 11.9% 14.0% Table 12 Calculated and measured values of Q95(l) and MAM(10) by FRIEND equations for Austria and Switzerland. Gauging station 095(1) calculated (m 3 s" 1 ) measured error MAM(10) calculated (m 3 s" 1 ) measured error Otiski vrh Ruta Draza vas Preska Kokra Gaberje KraSe Celje Kal Podroteja Baca Average 54.5% 49.8% Standard deviation 25.5% 40.4%

13 Low flow discharge analysis in Slovenia 131 low flow values for all catchments in Slovenia greater than 100 km 2. In further work it will be necessary to test and improve the accuracy of presented methodology and the possibilities of application, by evaluating low flows on catchments of about 10 km 2 in area. REFERENCES Brilly, M. &Kobold, M. (1993) Dolocanje nizkihpretokov (Low flow determination). FAGG LMTe, Ljubljana, Slovenia. Gustard, A., Marshall, D. C. W. & Sutcliffe, M. F. (1987) Low flow estimation in Scotland. Report no. 101, Institute of Hydrology, Wallingford, Oxfordshire, UK. Gustard, A., Roald.L., Demuth, S., Lumadjeng, H. & Gross, R. (1989) Flow Regimes from Experimental and Network Data (FREND), vol.2. Institute of Hydrology, Wallingford, Oxfordshire, UK. Gustard, A., Bullock, A. &. Dixon, J. M. (1992) Low flow estimation in the United Kingdom. Report no. 108, Institute of Hydrology, Wallingford, Oxfordshire, UK. Institute of Hydrology (1980) Low Flow Studies Report. Institute of Hydrology, Wallingford, Oxfordshire, UK. Radie, Z. M. (1992) Regional low flow frequency analysis. Perugia. Radie, Z. M., Stisovic, B. & Petrovic, J. (1992) Baseflow index regional analysis and low flow analysis and corrections. Perugia. Roald, L., Nordseth, K. & Hassel, K. A. (eds) (19S9) FRIENDS in Hydrology. (Proc. Bolkesjo Symp., April 1989). IAHS Publ. no INTERA TYDAC Technologies Inc. (1991) SPANS (Spatial Analysis System), Reference Manual. Canada. Vidmar, A., Globevnik, L., Smith, M. & Brilly, M. (1992) Uporaba in vkljucitev programskih paketov GIS v vodno gospodarstvo (The usage and incorporation of GIS program packages in water management). FAGG LMTe, Ljubljana, Slovenia.

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