Estimation of fl ow rate calculation errors on the example of five rapid response catchments in the Mecsek Hills 331 Hungarian Geographical Bulletin 62 (4) (2013) 331–350. Estimation of fl ow rate calculation errors on the example of fi ve rapid response catchments in the Mecsek Hills Péter HEGEDŰS1, Szabolcs CZIGÁNY2, Ervin PIRKHOFFER2 László BALATONYI1 and Levente RONCZYK3 Abstract Today fl ash fl oods are one of the most signifi cant extreme weather-related natural hazards. Due to the global climate change and altered land use, intense runoff and fl ash fl oods may exert catastrophic hydrologic impacts on developed areas. To measure and observe runoff - aff ecting environmental factors we have calculated characteristic fl ow values (CFV) with fi ve empirical equations for fi ve selected watersheds in the Mecsek Hills, SW Hungary. CFV’s were then compared with measured characteristic Qmax values of 5, 10, 20, 33 and 100-year return period. From the empirical equations the Rational method was the most accurate while the largest diff erences between the calculated and measured values was ob- served for the Csermák-method. Nonetheless, determination of the input parameters for the Rational and Virág methods is rather challenging, thus, for practical applications, the Koris- method was found to be the most applicable equation to determine CFVs. Additionally, the median Koris errors showed a strong exponential correlation with the 5% specifi c runoff . If specifi c runoff could be estimated for any given outfl ow point, then error-specifi c runoff functions could be used to increase the accuracy of the Koris calculation method. To fur- ther increase the accuracy of CFVs for selected outfl ow points and cross sections, area and watershed-specifi c variables need to be included in the equation to account for topography, land use and soil properties. Keywords: fl ash fl ood, runoff calculation, CFV, calculation error 1 Doctoral School of Earth Sciences, University of Pécs, H-7624 Pécs, Ifj úság u. 6. E-mail: hp88@gamma.tt k.pte.hu (corresponding author), balatonyi.laszlo@gmail.com 2 Department of Physical and Environmental Geography, Institute of Geography, University of Pécs, H-7624 Pécs, Ifj úság u.6. E-mail: sczigany@gamma.tt k.pte.hu and pirkhoff @ gamma.tt k.pte.hu 3 Institute of Geography, University of Pécs, H-7624 Pécs, Ifj úság u.6. E-mail: hidrogen@ gamma.tt k.pte.hu 332 Introduction Today fl ash fl oods are one of the most signifi cant extreme weather-related natu- ral hazards. Due to the global climate change and altered land use, intense runoff and fl ash fl oods may exert catastrophic hydrologic impacts on developed areas (Montenegro, S and Ragab, R. 2012). In Hungary, weather phenomena oft en cause disasters (hail storms, fl oods and mudfl ows) that subsequently generate considerable economic loss and may jeopardize human life. The most severe natural hazards in the country are associated with atmospheric convections and storms (Horváth, A. 2005). Intense upward con- vection triggers various atmospheric phenomena ranging from small cumulus clouds to devastating super cells. Their devastation is further exacerbated by prediction challenges, as their magnitude and exact location varies consider- ably in space (Bartholy, J. and Pongrácz, R. 2010, 2013). Convective processes develop rapidly and, with their associated fea- tures and consequences, may generate catastrophic damage. Typical observed hydrologic consequences and phenomena related to convective storms in hilly and mountainous regions are fl ash fl oods that are primarily characterized with short (less than 6 hours) response time and high fl ux (Horváth, E. 1999). According to the report of the Environmental Protection Agency of the European Union, fl oods generate the largest economic loss in Europe (Lóczy, D. and Juhász, Á. 1996; Gaume, E. et al. 2009). Over the period of 1998 to 2002, about 100 devastating fl oods caused 700 fatalities, evacuation of 25,000 people and an economic loss of 25 billion Euros (Gaume, E. et al. 2009). Although the majority of the losses are caused by „conventional” large-river fl oods, over the past decades, fl oods more frequently occur on small streams located in small (10 to 100 km2) mountainous watersheds (Marchi, L. et al. 2010; Mueller, E.N. and Pfister, A. 2011). Flash fl oods are usually last for a few hours (in extreme cases up to a day) and due to their short time of concentration, prevention and evacuation eff ort are oft en challenging. In certain cases, however, snowmelt may also con- tribute to the generation of fl ash fl oods, hence low-intensity rainfall, amid ideal environmental sett ings may also trigger fl ash fl oods (Pirkhoffer, E. et al. 2008). A third, recently more frequent type of fl ash fl ood occurs in heavily urbanized areas, where paved surfaces are impervious and, in general, runoff is aff ected by various human factors (Gyenizse, P. 2009). This latt er type of fl oods is called urban fl oods; however, some authors clearly diff erentiate them from typical fl ash fl oods (e. g. Georgakakos, K.P. 1986, 2006; Cobby, D. et al. 2008). The majority of fl ash fl oods, at least in Hungary, occur between March and mid-October. Torrential, high-intensity precipitation caused signifi cant economic loss in the hilly and low-mountain parts of Hungary. For example, a stream in North-West Hungary, the Által-ér inundated its valley following a 333 253 mm torrential rainfall on June 4, 1953 (Szilágyi, J. 1954). On June 27, 1987, several houses and part of the railroad were washed away in the Bükkösd Valley (Mecsek Hills, South-West Hungary) when 71 to 88 mm rain fell dur- ing a 6-hour period (Eszéky, O. 1987, 1992; Vass, P. 1997; Gyenizse, P. and Vass, P. 1998). Perhaps the largest economic loss was associated with fl ash fl oods in Mátrakeresztes, when a fl ash fl ood inundated the valley of the Csörgő and Kövicses Streams on April 18, 2005 (Horváth, A. 2005). Economic loss was estimated to reach 1 billion HUF (approx. 5 million USD) there (Koris, K. and Winter, J. 2000). The city of Kaposvár was fl ooded by the Kapos Stream on August 21, 2008 (Hizsák, I. 2005) when 105 mm rain fell in 3 hours. According to insurance claim records, many of these torrential rainfall-associated fl oods in South-West Hungary occurred at and around the foothills of the Mecsek Hills on the catch- ments of the Kapos, Völgységi and Bükkösd Stream (Figure 1). Fig. 1. Location of reported fl ood events in South-West Hungary between 1985 and 2005 334 Literature overview on the prediction methods usually applied in Hungary Flash fl ood prediction is rather challenging, due to the large spatial and temporal variability of the convective rainfall events and the heterogene- ous patt ern of topography, land use and soil types (Yates, D.N. et al. 1999; Szlávik, L. and Kling, Z. 2007). In addition, prediction uncertainty is very high due to the available rainfall forecasting methods, and the localized characteristics of the precipitation (Szlávik, L. et al. 2002; Szlávik, L., Sziebert, J. and Zellei, L. 2002; Szlávik, L. 2003). One way to estimate runoff and fl ow at the outfl ow point of the studied watershed is to use empirically derived equations. Equations of these types have been developed for small rapid-response watersheds located in Hungary. The most widely used equations employed by Hungarian researchers in the fi eld of fl uvial hydrology as well as the Hungarian Water Directorates include the Koris, Csermák, Kollár, Rational and Virág equations (estimation methods). Neither in the Introduction, nor in the Materials and Methods chapters of this paper it was not intended to describe these methods in full detail, instead a selection of literature was presented from which the reader could obtain fur- ther information about the calculation methodologies (e.g. Csermák, B. 1985; Zsuffa, I. 1996; Koris, K. 2001, 2002; Kontur, I. et al. 2003; Kaszab, F. 2009). The basis of the calculations, with the exception of the Csermák rely on area-specifi c runoff (runoff calculated for a unit area, usually with a unit of m3 km-2 s-1) correlations (functions). Primarily based on topographic att ributes, for the Koris equation Hungary is subdivided into broad runoff regions of about 15,000 to 25,000 km2, each region having its own area-specifi c runoff correlation function (e.g. South-West Hungary, South Transdanubia Region). The other equations, however, do not diff erentiate unique runoff regions in Hungary. The specifi c runoff value is then multiplied with the area of the water- shed to obtain total runoff for a given recurrence time. Recurrence probability fl ow values calculated by the multiplication of the area and the specifi c runoff are discharge values of 5% and 10% probabilities for the Koris and the Kollár equations, respectively. The rational and Virág equations calculate a given probability runoff of Qp% as a function of the fl ood-generating rainfall inten- sity with the same recurrence period (ip%). The Virág equation was primarily elaborated for large watersheds covering at least several 100s km2 making it hard to accurately estimate runoff from minute watersheds. The Csermák method considers an empirically generated map of run- off regions with a higher resolution than the aforementioned Kollár map. The individual runoff regions (classifi ed from 1 to 5, 5 having the highest specifi c runoff ) here are bordered by isohyets are the basis for determining the relative runoff att ributes of the given watershed. 335 The rational method includes parameters that account for land use, soil and hydraulic properties (time of concentration). Nevertheless, when compared with measured fl ow data, the output results of these equations are oft en burdened with signifi cant errors when used for watersheds that were not included in the elaboration and calibration processes used during the generation of the given equations. To increase the accuracy of the equation, and to minimize the diff erences between the meas- ured and calculated fl ow values, the equations need to be further improved by introducing modifying variables to account for the diff erences in topography, land use and soil properties among the individual watersheds. Although these equations were developed in the 1970s and 1980s, there have not yet been fully adapted to digital, specifi cally to GIS-environment (see more details is VMS 1977a; 1977b, 1977c, 1977d, 1977e). Thus, a two-fold long term goal of the recently initiated research study of the fl ash fl ood research group of University of Pécs, Pécs, Hungary would be the improvement and adaptation of the runoff -calculating equations for a visual, watershed-based digital interface. The short-term goal of the current paper is (a) to identify the most suit- able runoff -calculation method to reproduce runoff from minute (1.7 to 12.13 km2) watersheds of rugged topography that is characteristic for low-mountain conditions in Hungary and (b) to quantify the runoff calculation errors associ- ated with individual runoff calculating equations when compared with the corresponding characteristic fl ow values of 5 selected watersheds from the Mecsek Hills. Material and methods Location and properties of the studied pilot catchments To compare calculated and measured VFCs, fi ve pilot watersheds were se- lected in Baranya County, SW Hungary. All watersheds are characterized by, at least under conditions typical in Hungary, with relatively high relief. Four selected watersheds, namely the Sás, Gorica, Sormás and Kán are tributary watersheds of the Bükkösd Stream Watershed that ultimately belongs to the drainage area of the Drava River. For discharge value calculation and analysis, four pilot watersheds were selected – which are the tributary catchments of the Bükkösd Watershed – namely the Sás, Gorica, Sormás and Kán Watersheds. Each of the monitoring watersheds covers a relatively small land area (1.70 to 12.13 km2) and topog- raphy of high relief. The four larger watersheds are dominantly undeveloped and are covered by deciduous forests, mainly beech and hornbeam. 336 For modeling purposes 5 rapid response-type catchments were selected in the Mecsek Hills, South-West Hungary, namely the catchment area of Kán, Gorica, Sormás, Sás and Bálics streams. The latt er catchment is located on the Southern slopes of the Mecsek Hill within the administrative Borders of Pécs, with signifi cant fraction of built-up areas (27%). The other four catchments are located in the North-Western part of the Mecsek Hills in predominantly for- ested areas (Figure 2). Catchment areas range between 4.0 and 12.1 km2 while average slope values vary between 9.16 and 14.43 degrees (Table 1). Analysis of the selected runoff calculation methods and their comparison with measured characteristic fl ow values Discharge measurements at the outfl ow point of the four undeveloped water- sheds (Kán, Sormás, Gorica and Sás) were taken between January 1, 2005 and December 31, 2010 by the South Transdanubian Water Directorate (DDVIZIG) and the Mecsek Ore Company (Mecsekérc Zrt.). From the obtained data se- Fig. 2. Location of the studied watersheds (encircled by red lines) with the location of stream and precipitation gauges 337 ries, characteristic fl ow values (CFV) for 5 probabilities (1, 3, 5, 10 and 20%) were calculated for each watershed. Probability distributions were calculated with the Gumbel-probability function, widely used in hydrology. Hereaft er these characteristic fl ow values are called the measured CFVs. For the Bálics Stream stage values were available for 2012 and until March 31, 2013, using an automated logger and the att ached hydraulic head meter Dataqua (Dataqua Company, Balatonalmádi, Hungary). Stage values were then converted to discharge based on the Q-H function, which was generated with regular fl ow measurements. Due to the short measurement interval of this latt er watershed, the reliability of the peak fl ows of long recurrence time is relatively low. The CFVs (i.e. recurrence times of 5, 10, 20, 33 and 100 years) were calculated with 5 estimation methods being widely used by the Hungarian hydrological professionals. The employed runoff estimation methods are the following ones: Koris-, Csermák-, Kollár-, Rational, and the Virág-type dis- charge estimation. The calculated runoff (fl ow) values were then compared with the corresponding measured CFVs. The selected CFVs of 1, 3, 5, 10, 20% peak fl ow values (Qmax) values, are equivalent with recurrence periods of 100, 33, 20, 10, 5 years, respectively. For comparison, specifi c discharge values were also calculated by dividing the measured discharge values with the land area of the given watershed. Table 1. Land use and physical soil type characteristics of the studied watersheds Indicator Min Max Range Mean Std Sormás Stream, 12.13 km2 Elevation, m Slope, ° Aspect, azim ° 153.00 0.00 fl at 343.00 36.71 359.96 190.00 36.71 360.96 241.85 9.26 170.88 36.53 4.57 91.11 Gorica Stream, 5.84 km2 Elevation, m Slope, ° Aspect, azim ° 151.00 0.00 fl at 355.00 35.41 358.60 204.00 35.41 359.60 255.56 11.02 174.74 43.03 5.32 90.91 Kán Stream, 9.58 km2 Elevation, m Slope, ° Aspect, azim ° 154.00 0.00 fl at 356.00 35.16 359.78 202.00 35.16 360.78 248.88 10.00 160.82 43.63 4.86 88.04 Hetvehelyi/Sás Stream, 7.73 km2 Elevation, m Slope, ° Aspect, azim ° 181.00 0.00 fl at 437.00 38.67 359.99 256.00 38.67 360.99 303.45 14.43 184.67 53.97 6.60 111.98 Bálics Stream, 1.70 km2 Elevation, m Slope, ° Aspect, azim ° 166.00 0.00 fl at 390.00 36.15 354.80 493.00 36.15 355.80 262.11 10.72 183.20 28.47 7.15 99.24 338 These Qmax estimation methods are standardized hydrologic meth- ods in Hungary and have been developed for watersheds representative for Hungarian topographical conditions (lowlands and low-mountains). For these equations Qmax values are calculated as a function of watershed area and runoff characteristics (specifi c runoff , m3 s-1 km-2), while exclusively the rational- method considers precipitation as input parameter. Calculation methods of the fi ve selected runoff -estimating techniques are briefl y described below. a) Koris estimation method: Qp% = ai q5% A, (1) where ai is the probability multiplier which are 1.7, 1.2, 0.8 and 0.6 for the 1, 3, 10, 20% probabilities of discharge, q5% is the specifi c fl ow rate estimated form the appendix (VITUKI, 1977) and A is the area of the pilot watershed (km2). b) Csermák estimation method (based on the Myer equation): Qp% = rB3% Fn, (2) where r is a probability coeffi cient, B3% is the 3% probability of peak fl ow occurrence estimated for the area, F is the area of the watershed, and n is a constant equals to 0.75, if the area is under 10 km2; or 0.5, if the area is over than 10 km2. c) Kollár estimation method: Q10% = q10% A, (3) where q10% is a 10% probability of a specifi c peak fl ow occurrence (m3/s km2), and A is the extent of the watershed. Other than 10% probability estimation can be calculated with a multiplier factor based on the ratio of Qp%/Q10%. For the Kollár and Koris methods, we used the median of the func- tion range that accounts for the rainfall intensities (as well as topography and watershed shape) in the area-specifi c runoff correlation function. Here, when specifi c runoff is calculated using the lowest part of the range, low rainfall intensities and relatively fl at topography (long time of concentration and stor- age coeffi cient) is assumed. When the upper boundary of the range is used for calculating specifi c runoff for the Koris and Kollár methods, ‘torrential’ condi- tions are assumed, referring to high-intensity rainfall events and topography, land use and soil types favorable for intense runoff . 339 d) Rational method (fi rst applied by Mulvaney, T.J. in 1847): Qp% = ip% ᾳA, (4) where ip% is a p% probability (T = t) rainfall intensity, α is the runoff coeffi cient, A is the area of the watershed. e) Virág estimation method: Qp% = Aqp% Cp% (5) where A is the area of the watershed, qp% is an estimated specifi c runoff , and Cp% is a specifi c correlation factor. Results Regarding their land use types and physical soil properties, the studied wa- tersheds were divided into two main groups, an urban one and an undevel- oped category. The Bálics Stream watershed is exclusively located within the administrative borders of Pécs, predominantly in the North-West part of the city (150.286 residents according to the 2010 census). This catchment is a highly developed urban area with a high proportion of impermeable surfaces favo- rable for intense runoff . The other four catchments are primarily covered by deciduous forest (beech and hornbeam) in 81.53 to 95.05%. In the undeveloped watersheds natural conditions dominate the land use, paved surfaces cover only insignifi cant proportion of these watersheds (Table 2). The proportion of the paved surfaces is highest in the Bálics Watershed covering 26.78% of the entire land area of the watershed. Similarly, the area of agricultural and horticultural areas was highest in the Bálics Watershed, with the dominance Table 2. Land use and physical soil type characteristics of the pilot watersheds, in % Land use, physical soil type Sormás Gorica Kán Sás Bálics Watershed Agri/Horticultural areas Artifi cial surfaces Forests Shrubs Loam Clayey loam Clay Coarse fragments 8.98 – 81.53 9.48 100.00 – – – 10.08 – 89.91 – – 92.30 5.81 – 21.18 – 76.93 1.87 0.83 68.47 30.68 – – – 95.05 4.95 1.27 98.73 – – 65.47 26.78 7.73 – – – – 100.00 340 of grape, fruit trees, lawn and vegetable gardens. Forested areas within the Bálics Stream are only found in the northernmost tip of the watershed. The predominant physical soil types of the undeveloped watersheds are loam and clayey loam according to measurements of Zalavári, P. (2008). Loamy soils are the sole soil physical soil types in the Sormás Watershed, while clayey loam cover the surface almost exclusively in the Gorica and Sás Watersheds (Table 2). The prevailing physical soil types of the Bálics Watershed are characterized by rocky and stony topsoils, primarily at higher elevations at the Northern tip of the watershed by fi eld experiments, while, according to the AGROTOPO database, this soil type is the prevailing one within this watershed. Based on our fi eld experiences and the former studies of Zalavári (2008), genetic soil types in the Bálics Watershed include rendzinas, carbon- ate-rich forest soils formed on carbonaceous parent material and forest soils with signifi cant clay illuviation (FAO: Luvisols, USDA: Alfi sols, dominantly Xeralfs). CFV calculations and comparison of measured and calculated CFVs For the fi ve aforementioned watersheds we have calculated discharge values (a) at diff erent recurrence periods (5, 10, 20, 33 and 100 years), and (b) with diff erent estimation methods (Csermák, Koris, Kollár, Virág and Rational-type calculation). A total of 25 cases (fi ve watersheds, fi ve calculation methods) were analysed, i.e. for this many cases were the calculated and measured CFVs compared. In the majority of the analyzed cases, calculated CFVs were larger than the measured values. Out of the 25 analyzed cases, calculated values exceeded the measured values in 21 cases. In general, the highest error was found for the Csermák-type calculations with a mean error of 695% between the calculated and measured values. Best correspondence was observed for the Virág estimation method with a mean value of 102% (standard deviation, σ = 80.3). Error percentages ranged between 1.42 and 1641% for all cases (Table 3, Figure 3). Among all the 25 cases, the lowest error was found for the Sás Stream at a recurrence period of 5 years using the Virág equation. The highest error was found for the Sormás Stream at a recurrence period of 100 years. When the fi ve employed calculation methods were compared, the low- est error was found at the Virág-type estimation for the Sás and Kán Watershed (10.00 and 4.96%, respectively). The Sás Watershed has the highest mean slope (14.42%) among the fi ve studied watersheds and also has the highest pro- portion of clayey loam soils. These two factors likely contribute to increased runoff . However, the Sás Stream has the highest proportion of forest cover within its watershed; this property, through the process of interception will 341 Table 3. Calculated errors between the measured and calculated characteristic fl ow values of fi ve recurrence time intervals * Stream Return period, years Relative error of measured and specifi c Q Error of calculated – measured Q, % Koris Csermák Kollár Rational Virág Sás 5 10 20 33 100 1.243 1.410 1.550 1.640 1.798 84.41 115.27 145.33 179.10 261.14 612.13 693.54 809.49 879.84 1,152.82 157.42 192.70 246.90 317.44 373.70 21.40 14.14 4.87 3.56 26.00 10.00 35.63 94.11 118.10 169.00 Gorica 5 10 20 33 100 0.843 0.907 0.955 0.984 1.035 123.21 176.60 228.34 282.37 415.18 720.53 870.67 1,058.73 1,177.80 1,601.41 184.30 262.00 346.86 450.41 550.37 15.00 1.42 13.77 26.76 60.63 18.58 55.22 131.38 166.17 241.78 Sormás 5 10 20 33 100 1.025 1.228 1.416 1.546 1.812 208.27 242.84 271.85 308.60 393.80 927.43 990.68 1,089.75 1,137.98 1,378.55 330.93 392.37 455.40 533.76 584.16 59.34 65.81 74.86 83.81 108.90 123.00 161.96 256.82 287.30 346.10 Kán 5 10 20 33 100 2.830 3.726 4.586 5.200 6.532 8.83 7.67 6.23 0.91 11.91 327.30 313.07 321.90 322.20 371.25 39.54 29.26 26.02 29.47 34.93 50.17 52.77 53.37 52.86 49.92 38.00 33.68 15.42 11.71 4.96 Bálics 5 10 20 33 100 2.770 2.920 3.030 3.490 3.720 39.22 38.44 37.48 33.94 25.38 121.60 114.22 118.80 118.95 144.40 11.74 18.24 20.29 18.11 14.66 91.62 90.10 88.40 88.43 85.54 74.17 72.36 64.76 63.21 60.40 * 5, 10, 20, 33 and 100 years. The maximum errors are marked with bold italics, the minimum values with italics. delay and diminish throughfall and runoff as a direct consequence. The Kán watershed is slightly more developed than the Sás Stream Watershed, still, we found bett er correspondence between the calculated and the measured CFVs for this watershed using the Virág-type estimation method. Relatively low errors were found for the Rational method, however, in this case time of concentration, as an input value was set in a rather arbitrarily fashion (and unrealistic values were found) to obtain the best correspondence between the calculated and measured values. Nonetheless, the time of concentration values did not always represent the actual (fi eld-observed) values adequately. Calculated times of concentration are shown in Table 4, using the so-called Wisnovszky equa- tion (Koris, K. 2003).These values, in many cases, are rather diff erent from the observed data that was based on fi eld monitoring between 2005 and 2010. This 342 way, through its arduous parameterization protocol (in respect of the calculation of concentration times), the Rational method is considered rather inadequate for direct runoff estimation for the fi ve studied watersheds. In general, the third lowest errors were obtained for the Koris method when the centerline (median) of the 5% probability range was use to estimate specifi c runoff (Figure 3). This way, in respect of parameterization accuracy, the Koris equation seems to be the most adequate method for estimating runoff among the presented fi ve calculation methods. If the mean values analyzed with respect to the individual watersheds, lowest errors were detected for the Bálics Stream (65%). Due to its environ- mental sett ings (topographical, land use and soil properties), the Bálics Stream has the highest runoff coeffi cient value. The Sás, Gorica and Sormás Streams are characterized by relatively high mean errors ranging between 306.4% and 498.9%, with standard deviations of 299.2 to 394.4 (Table 5). Fig. 3. Error percentages for the fi ve selected CFV calculation methods for the fi ve studied watershed Table 4. Time of concentration values for the studied watersheds Stream Stream gauge loc. Area, km2 Calc. Tc, h Number of events studied Tc. used for best fi t, h Measured Tc., h Min. Max. Mean Bálics Gorica Kán Sormás Sás Pécs Bükkösd – Bükkösd Hetvehely 1.7 5.9 9.6 12.2 7.7 0.28 0.67 0.98 3.40 1.83 17 17 20 18 22 40.0 1.5 5.7 0.8 2.0 0.25 0.83 1.08 1.75 1.25 5.33 29.92 23.75 14.50 32.25 2.15 10.99 7.83 7.75 12.12 343 The Kán Stream has the second lowest mean error when the corre- sponding calculated and measured CFVs are compared (91%). This behavior is unexpected, as the Kán Watershed, regarding its general environmental sett ings and its catchment area (see Table 2 and 3) is rather similar to the Sás, Gorica and Sormás Watersheds. Slight diff erences, nevertheless, are observed at the higher proportion of clay-rich soils and the deforested areas, both pa- rameters being signifi cant contributors to increased runoff . Impact of runoff coeffi cient and specifi c runoff on the Koris median-derived CFV errors As it was concluded above, the Koris median calculation method was proven to be the most adequate to directly estimate runoff for the fi ve studied watersheds. Thus, in the current chapter we compared the impact of runoff coeffi cient (ratio of precipitation and outfl ow) and the specifi c area (runoff from a unit watershed area) on mean CFV errors that were obtained from the Koris median values. By looking at Table 4 two distinct groups of watershed types is identi- fi ed. The fi rst group consists of the Sás, Sormás and Gorica Watersheds, while the other group includes the Kán and Bálics Streams, two watersheds with rather diff erent environmental sett ings and medium runoff coeffi cients, at least among the fi ve studied watersheds. Highest runoff coeffi cient for the four undeveloped watersheds, based on the 2005 to 2010 fl ow and precipitation data, was found for the Sás Stream (0.4005). The Bálics Stream, which has the lowest mean error value among the fi ve studied watershed, has a runoff coef- fi cient value of 0.275 (second highest value) for the 5% probability discharge (Table 6) based over the period of October 1, 2012 to May 1, 2013 when 562 mm rain fell over the measurement period. Consequently, runoff coeffi cient, as a combined parameter that describes the general hydrologic behavior of a given watershed, does not readily infl uences the errors that appear between the calculated and measured CFVs (Figure 4). Table 5. Mean error (diff erences between the calculated and measured CFVs) percentages relative to the corresponding measured CFVs Stream Koris Csermák Kollár Rational Virág Mean St. dev. Sás Gorica Sormás Kán Bálics Mean St. dev. 157.0502 245.1400 285.0720 7.1100 34.8920 145.8528 123.4172 829.5640 1,085.8280 1,104.8780 331.1440 123.5940 695.0016 446.5843 257.6320 358.7880 459.3240 31.8440 16.6080 224.8392 196.6012 14.00 23.52 78.55 51.82 88.82 51.34 29.37 85.3680 102.3035 235.0360 20.7540 66.9800 102.0883 80.3159 268.72 363.11 432.58 108.90 66.18 – – 291.77 379.36 357.44 128.80 38.07 – – 344 Table 6. Specifi c runoff and runoff coeffi cient values comparing to mean error values Stream Mean Max Q5% measured Area, km2 Specifi c runoff 5%, m3/s/km2 Runoff coeffi cient mean Mean Koris errorm3/s Sás Gorica Sormás Kán Bálics 0.0657 0.0250 0.0316 0.0352 0.0025 1.580 1.000 1.530 1.960 0.548 1.789 1.150 1.542 5.119 0.964 7.73 5.84 12.13 9.58 1.70 0.231 0.195 0.126 0.533 0.567 0.401 0.202 0.123 0.174 0.275 157.0502 245.1400 285.0720 7.1100 45.8700 Fig. 4. Correlation between runoff coeffi cients and mean Koris estimation errors: two distinct groups are diff erentiated Bett er results were obtained when correlation between specifi c runoff (another combined parameter that illustrates the overall hydrologic behavior of a given watershed) and measured CFV errors was analyzed (r2 = 0.7643) (Figure 5). We need to emphasize that calculation errors are rather high for the Bálics Stream, fi rstly by the Q-H function calculation and secondly by the error arising from the short monitoring period used for the probability cal- culations of the CFVs, thirdly by the signifi cant communal waste water input and (d) karstic environment and the fl ow and basefl ow-buff ering due to the underground water storage of the limestone aquifer. The Kán Watershed seems to be a good example to demonstrate the correlation between measured and calculated discharges for diff erent estimation methods (Figure 6). Generally, with increasing return period, the errors have also increased. When error percentages were analyzed as a function of the fi ve studied recur- rence periods (recurrence probabilities) we found increasing error percentages 345 Fig. 5. Second degree polynomial correlations between the specifi c runoff and mean Koris estimation error Fig. 6. Correlation between measured and calculated discharges for diff erent estimation methods, at various return periods (5, 10, 20, 33, 100 years) for the Kán Watershed with increasing recurrence times for the Sás, Gorica and Sormás Streams. Error percentages as a function of recurrence time remained relatively constant for the Kán and Bálics Streams. This way one could again diff erentiate two types of watersheds regarding their hydrological and hydraulic behaviors. When the Koris-, and the Virág-type estimation were used to calculate peak runoff s for the Kán Watershed, decreasing error percentages were found with increasing return period (Figure 7). 346 Conclusion During the course of the currently proposed research we investigated the ap- propriateness of 5 runoff estimation methods that are widely used in Hungar- ian hydrology were investigated for 5 selected watersheds in the Mecsek Hills, Baranya County. In general we claim that signifi cant deviations were found between the measured and calculated CFVs for the fi ve selected watersheds and all methods. Best results were obtained for the Virág and Rational meth- ods, however, both methods are diffi cult to use due to the diffi culties involved with input parameter estimation. Third lowest errors were associated when the Koris equation was used for the median of the area-specifi c runoff correla- tion range. Due to its easy parameterization and calculation methodology, this method was proven to be the most applicable with a reasonably accuracy to estimate runoff for the fi ve selected watersheds. Usually, for the Kollár and Koris-estimation methods, the lower bound- ary runoff character range within the area-specifi c runoff function gave the best results. This is likely explained in the light of climate change and the altered climatic conditions of today compared with the time when these es- timation methods were developed, dominantly over the period of 1970s and 1980s. Secondly, the dominance of the lower boundary runoff character is explained by the fact, that, with a very few exceptions, both methods were predominantly developed by calibrating the model for large watersheds (sev- eral 100s km2), rather than those used in the current study (around 10 km2). Furthermore, each watershed behaves according to an individual rainfall- Fig. 7. Error values for the diff erent estimation methods at diff erent recurrence periods (for the fi ve studied watersheds, in percentages) 347 runoff patt ern refl ecting its unique topographic, land use and soil properties, in addition to the topography-induced meso-scale climatic diff erences and spatial rainfall patt erns primarily due to the local orographic eff ects. To overcome this watershed-specifi c problem, i.e. the uniqueness of each watersheds from the viewpoint of hydrography, hydrology and hydraulics, wa- tersheds need to be categorized into selected classes according to their size, soil type, land use and topography. This way, based on the calculated fl ow correla- tions between the measured and calculated fl ow values, constants (being equal to the mean errors between calculated and measured CFVs) need to be developed to calibrate the various fl ow estimation methods in order to modify the currently available equations to obtain bett er correspondence with the measured values. Specifi c correlation functions need also be generated to account for the aforementioned att ributes of the watersheds. Such att empt is included in the rational method, however, this method needs to be automated and used in GIS- environment with subsequent calculations based on the available digital spatial databases (e. g. topography, land use and soil types). By the automatization of the runoff calculations for selected cross-sec- tions (outfl ow points) of the watershed of interest the CFVs could be calcu- lated over a relatively short period of time (if suffi cient calculation capacity is available). If pre-calculated inundation scenarios are available for the selected CFVs, the area of fl ooded terrain within the fl oodplains could be promptly determined, and warnings could be issued in advance with suffi ciently long time lead. This way, residents of the aff ected areas could be evacuated in a short period of time, primarily in fl ash fl ood aff ected watersheds and in areas of rapid-response catchments. With increasing fl ood resilience, socio-economic consequences of torrential weather phenomena and disastrous hydrologic events could be diminished. To develop an automated GIS-based method, correlations need to be found between the calculation errors and complex environmental param- eters that expresses the topographic, land use and soil properties of a given watershed and readily expresses the hydrologic behavior of the individual watershed. In the present study the impact of two types of complex proper- ties were analyzed: (i) runoff coeffi cient and (b) specifi c runoff . For the fi ve studied watersheds no correlation was found between runoff coeffi cients and the Koris median- derived errors. However, specifi c runoff exerts a strong impact on the Koris median- derived specifi c errors. In this case a relatively strong exponential correlation was found between the two parameters. This way, for any given cross-section along the watercourse relative error could be estimated for the Koris calculation method, and a correction constant could be introduced that accounts for the topo- graphic, land use and pedologic properties of the watersheds located upstream from the selected cross section (or outfl ow point). In an ideal case, the correction 348 factor would decrease moving upstream from the outfl ow points along the wa- tercourse, as the headwater portion of any watershed would express increased runoff characters, i.e. increased specifi c runoff , where CFV errors are expected to be lower than in the vicinity of the outfl ow point of the watershed. However, prior to generation of the correlation function between the upstream distance of the outfl ow point and the CFV errors, watersheds need to be classifi ed into individual groups according to their runoff characteristics. In the present study, the fi ve selected watersheds had very similar proper- ties; nevertheless, two distinct watersheds were identifi ed. This classifi cation scheme is rater arbitrary, thus it provides signifi cant challenges for reliable runoff prediction in watersheds of high relief. Hence, further studies are in- dispensable in order to increase the output accuracy of runoff calculations. Acknowledgement: This research was funded by the “TÁMOP 4.2.1.B-10/2/KONV-2010- 0002” Scholarship (Developing Competitiveness of Universities in the South Transdanubian Region), the grant of “SROP-4.2.2.C-11/1/KONV-2012-0005” Scholarship (Well-being in the Information Society) and the Baross Gábor Grant (Grant No. REG DD KFI 09/PTE TM09). The authors are also grateful to Gábor Horváth at the South Transdanubian Environmental and Water Directorate for providing fl ow data for the current research and Dénes Lóczy for proofreading the manuscript. 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Budapest, Műegyetemi Kiadó, 392 p. << /ASCII85EncodePages false /AllowTransparency false /AutoPositionEPSFiles true /AutoRotatePages /None /Binding /Left /CalGrayProfile (Dot Gain 20%) /CalRGBProfile (sRGB IEC61966-2.1) /CalCMYKProfile (U.S. Web Coated \050SWOP\051 v2) /sRGBProfile (sRGB IEC61966-2.1) /CannotEmbedFontPolicy /Error /CompatibilityLevel 1.3 /CompressObjects /Tags /CompressPages true /ConvertImagesToIndexed true /PassThroughJPEGImages true /CreateJobTicket false /DefaultRenderingIntent /Default /DetectBlends true /DetectCurves 0.0000 /ColorConversionStrategy /LeaveColorUnchanged /DoThumbnails false /EmbedAllFonts true /EmbedOpenType false /ParseICCProfilesInComments true /EmbedJobOptions true /DSCReportingLevel 0 /EmitDSCWarnings false /EndPage -1 /ImageMemory 1048576 /LockDistillerParams false /MaxSubsetPct 100 /Optimize false /OPM 1 /ParseDSCComments true /ParseDSCCommentsForDocInfo true /PreserveCopyPage true /PreserveDICMYKValues true /PreserveEPSInfo true /PreserveFlatness true /PreserveHalftoneInfo false /PreserveOPIComments true /PreserveOverprintSettings true /StartPage 1 /SubsetFonts true /TransferFunctionInfo /Apply /UCRandBGInfo /Preserve /UsePrologue false /ColorSettingsFile () /AlwaysEmbed [ true ] /NeverEmbed [ true ] /AntiAliasColorImages false /CropColorImages true /ColorImageMinResolution 300 /ColorImageMinResolutionPolicy /OK /DownsampleColorImages true /ColorImageDownsampleType /Bicubic /ColorImageResolution 300 /ColorImageDepth -1 /ColorImageMinDownsampleDepth 1 /ColorImageDownsampleThreshold 1.50000 /EncodeColorImages true /ColorImageFilter /DCTEncode /AutoFilterColorImages true /ColorImageAutoFilterStrategy /JPEG /ColorACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /ColorImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000ColorACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000ColorImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasGrayImages false /CropGrayImages true /GrayImageMinResolution 300 /GrayImageMinResolutionPolicy /OK /DownsampleGrayImages true /GrayImageDownsampleType /Bicubic /GrayImageResolution 300 /GrayImageDepth -1 /GrayImageMinDownsampleDepth 2 /GrayImageDownsampleThreshold 1.50000 /EncodeGrayImages true /GrayImageFilter /DCTEncode /AutoFilterGrayImages true /GrayImageAutoFilterStrategy /JPEG /GrayACSImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /GrayImageDict << /QFactor 0.15 /HSamples [1 1 1 1] /VSamples [1 1 1 1] >> /JPEG2000GrayACSImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /JPEG2000GrayImageDict << /TileWidth 256 /TileHeight 256 /Quality 30 >> /AntiAliasMonoImages false /CropMonoImages true /MonoImageMinResolution 1200 /MonoImageMinResolutionPolicy /OK /DownsampleMonoImages true /MonoImageDownsampleType /Bicubic /MonoImageResolution 1200 /MonoImageDepth -1 /MonoImageDownsampleThreshold 1.50000 /EncodeMonoImages true /MonoImageFilter /CCITTFaxEncode /MonoImageDict << /K -1 >> /AllowPSXObjects false /CheckCompliance [ /None ] /PDFX1aCheck false /PDFX3Check false /PDFXCompliantPDFOnly false /PDFXNoTrimBoxError true /PDFXTrimBoxToMediaBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXSetBleedBoxToMediaBox true /PDFXBleedBoxToTrimBoxOffset [ 0.00000 0.00000 0.00000 0.00000 ] /PDFXOutputIntentProfile (None) /PDFXOutputConditionIdentifier () /PDFXOutputCondition () /PDFXRegistryName () /PDFXTrapped /False /CreateJDFFile false /Description << /ARA /BGR /CHS /CHT /CZE /DAN /DEU /ESP /ETI /FRA /GRE /HEB /HRV (Za stvaranje Adobe PDF dokumenata najpogodnijih za visokokvalitetni ispis prije tiskanja koristite ove postavke. 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