Acta geographica Slovenica, 46-1, 2006, 93-123 ESTIMATION OF MAGNITUDES OF DEBRIS FLOWS IN SELECTED TORRENTIAL WATERSHEDS IN SLOVENIA OCENA MAGNITUD DROBIRSK [ H TOKOV V IZBRANIH HUDOURNI I KIH OBMO^JIH V SLOVENIJI Jo{t Sodnik, Matja` Miko{ Debris flow in the village of Log pod Mangartom in November 2000 (photograph: authors, November 22,2000). Drobirski tok v Logu pod Mangartom novembra 2000 (fotografija: avtorja, 22. november 2000). Jo{t Sodnik, Matja` Miko{, Estimation of magnitudes of debris flows in selected torrential watersheds in Slovenia Estimation of magnitudes of debris flows in selected torrential watersheds in Slovenia UDC: 551.435.6(497.4) COBISS: 1.01 ABSTRACT: In this paper the application of different methods for estimation of magnitudes of rainfall-in-duced debris flows in 18 torrents in the Upper Sava River valley, NW Slovenia, and in 2 torrents in Pohorje, N Slovenia is described. Additional verification of the methods was performed in the torrential waters-heds with active debris flows in the recent past (Predelica and Brusnik in the So~a River basin, W Slovenia). For some of the methods, the knowledge of morphometric characteristics of a torrential watershed, torrential channel and torrential fan is enough. For other methods, a mathematical tool (HEC-HMS) had to be applied in order to develop ahydrologic run-off model of precipitation that can trigger debris flows. Computed debris-flow magnitudes were of the order between 6,500 m3 and 340,000 m3. Their values are a function of torrential watershed parameters, such as: watershed area, Melton number, fan gradient, and torrential channel gradient. The investigated fans were classified into 3 groups with regard to the debris-flow hazard: debris-flow fans (hazard exists), torrential fans (no hazard), and transitional fans (debris flows are possible, but with low possibility). A limit between debris-flow fans and torrential fans is proposed: Melton number 0.3 and torrential fan gradient 4°, that is, 7%. Out of 24 investigated torrential fans, 13 fans were classified into the group of debris-flow fans, 5 fans were classified into the group of torrential fans, and the rest 6 fans were classified into the group of transitional fans. KEY WORDS: erosion, mass movements, debris flows, empirical models, hazard estimation, fans, Upper Sava River valley, Pohorje, Slovenia. The article was submitted for publication on April 24, 2006. ADDRESSES: Jo{t Sodnik, B. Civ. Eng. VGP d. d. Ulica Mirka Vadnova 5, SI - 4000 Kranj E-mail: jost.sodnik@vgp-kranj.si Matja` Miko{, Ph. D., Professor University of Ljubljana Faculty of Civil and Geodetic Engineering Jamova cesta 2, SI - 1000 Ljubljana E-mail: matjaz.mikos@fgg.uni-lj.si Contents 1 Introduction 2 Hydrological calculations 3 Analysis of hydrological parameters 4 Calculation of magnitudes of debris flows 5 Analysis of magnitudes of debris flows 6 Classification of torrential fans 7 Conclusion 8 References 95 96 99 102 102 107 109 109 94 Acta geographica Slovenica, 46-1, 2006 1 Introduction Debris flows as a form of mass movements of sediments on slopes or in torrential channels have trans-formed the relief in Slovenia in the geological past and are becoming more and more frequent recently. Due to the dispersed settlement pattern and dense traffic network in Slovenia, it has become necessary to investigate debris flow hazards into more detail. Debris flows as a form of mass movement of sediments (Skaberne 2001) can develop on slopes or in torrential channels. Knowing their dynamics (Miko{ 2001) makes it possible to plan adequate preventive countermeasures. One of the most frequent questions rela-ted to debris flows is related to the location of their initiation. Also, for planning of countermeasures it is necessary to know the process magnitude that can be expected. Using estimated magnitudes one can also estimate the debris flow run-out by modelling debris flow routing as well as their flowing velocities and depths that are usually used with hazard assessment (Miko{ 1997). Any large-scale planning of preventive countermeasures against different landslide and rockfall pro-cesses must tackle each case separately. Each case has its specific characteristics that may greatly effect the course of events. One of the basic data is the catchment area of a torrential watershed under investiga-tion. The ratio between the amount of available debris material and the amount of released debris material varies from one case to another. Nevertheless one tried to develop methods that would be generally appli-cable for the estimation of debris flow magnitudes in the past. Geomorphic processes on torrential fans have been so far investigated in many field studies. In one of the earliest studies, Melton (1965) sugge-sted a relation between the gradient of a torrential fan (S) and some other topographic parameters: S=a[(H - H .)A–0,5]n, (1) L v max min' J ' v ' where a and n are independent coefficients, H (km) and H . (km) are elevations of the highest point r max v ' min v ' o r and the lowest point of the torrential watershed (i. e. highest point of the torrential fan), respectively, and A (km2) is the catchment area of the torrential watershed. The term Mel = (H - H . )A–0,5 is simply called the Mel- 1 max min' r ' ton number after its author. This approach is the ground for investigation of alluvial processes on fans, oriented into a classification of fans on the basis of morphological parameters of torrential watersheds and fans. There are many methods for estimation of debris flow magnitudes, being one of the bases for debris flow risk estimation, and one can divide them into: • empirical methods (e. g. Takei 1984, Kronfellner-Kraus 1984, Marchi & D'Agostino 2002) that they pro-vide the estimation of debris-flow magnitudes; • morphological methods (e. g. Jackson et al. 1987, Marchi et al. 1993, Marchi &D'Agostino 2002, Jakob 2005) that can be divided into those that estimate the magnitude and those that aim at the determination of debris-flow hazard on torrential fans; • combined methods (e. g. Ceriani et al. 2000) that are a combination of different other methods, which based on statistical analysis determine the relevant torrential watershed parameters in the form of an empirical equation for the estimation of the debris-flow magnitude; • computer methods (e. g. Schöberl et al. 2004) are computer programs that take into account sediment production in the watershed under investigation and sediment transport capacity of the torrent inclu-ding sediment deposition in the torrential channel. A detailed description of these methods is given elsewhere (Sodnik 2005; Sodnik & Miko{ 2005). For computation of debris flow magnitudes m in selected torrential watersheds in Slovenia the follo-wing empirical and morphological methods have been used: Takei (1984): Vd= 13600A0.61 …..[m3] (2) Kronfellner-Kraus (1984): M = K·A·Sc…..[m3] (3) K = 1150/e0.014A…..[-] (4) Marchi & DAgostino (2002): Method 1:M = 65000A1.35S1.7…..[m3] (5) Method 2:M / V = 2,9 S2………] (6) r > L J V > Ceriani et al. (2000): M = k · (A)a · (Mb)b · (Scl_c)c·(I_F)–d …..[103m3], (7) 95 Jo{t Sodnik, Matja` Miko{, Estimation of magnitudes of debris flows in selected torrential watersheds in Slovenia Figure 1: Torrential watersheds in Slovenia treated in this paper. where the parameters in the equations are follows: K- coefficient of the torrential watershed, given for separate parts of the Alps in Austria [-]; A- catchment area of the torrential watershed [km2]; S - average gradient of the torrential channel [%]; c G G L J' S- average gradient of the torrential channel [m/m]; V - the total run-off volume [m3]; I_F- landslide index [-]; Mb - Melton number [-]; Scl_c- gradient of the torrential channel on the fan [%]. In this paper, the results of application of the empirical and morphological methods to selected Slove-nian torrents are discussed. The purpose of the analysis was to check the possibility of estimating the magnitude of potential debris flows and their distribution in relation to hazard. The estimated values obtained with the chosen methods should be compared to historical records on the volume of past events. Unfor-tunately, no systematic analysis of past events was ever performed and the comparison of results acquired with the chosen methods with events that occurred in the past is rather the exception, not the rule. The estimates of magnitudes of debris flows were performed in selected torrential tributaries of the Sava Dolinka (the Upper Sava valley) and two torrents in Pohorje (Figure 1). For additional verification, the methods were tested in the torrents of Predelica and Brusnik, where debris flows have occurred in the recent past (Miko{ et al. 2004; 2006). 2 Hydrological calculations Before applying some of the methods in the chosen torrential watersheds, the total run-off volume of the precipitation relevant for debris-flow initiation was to be calculated. The modelling was performed with the HEC-HMS program (Hydrologic Modeling System2000; 2001). The purpose of modelling was to deter- 96 Table 1. Results of run-off modelling in the torrential watersheds of the Upper Sava River. Torrential area [km2] slope [%] channel channel discharge Qm Curve number SCS method Clarck-Kirpich Snyder - Riverside Total run-off watershed length [km] length [%] [m3/s] CN [-] T [hour] method Tc [hour] County method T [hour] [m3] UPPER SAVA RIVER Trebi`a 5.3 38 3.8 8.6 40 67 0.560 0.376 0.432 407,150 Krotnjek 3.7 48 3.2 9.6 36 67 0.435 0.301 0.363 326,000 Suhelj 1.9 57 3.2 16.9 23 71 0.359 0.282 0.351 182,050 Velika Pi{nica 37.9 67 9.2 3.3 128 57 1.107 0.598 0.760 2,092,700 Jure`ev graben 2 47 2.7 28.6 19 66 0.394 0.267 0.320 158,380 Martuljek 11.4 72 4.1 11.4 82 64 0.468 0.312 0.406 803,620 Hladnik 15 60 6.6 12.1 99 66 0.713 0.483 0.603 1,174,600 Beli potok 5.3 72 3.8 21 39 63 0.452 0.294 0.383 355,690 Belca 17.6 65 7 8.5 107 64 0.756 0.490 0.621 1,307,100 Bistrica 43.7 64 12.6 4 197 61 1.317 0.775 0.974 3,303,100 Mlinca 7.9 59 4.9 17.1 56 60 0.661 0.386 0.482 593,910 Presu{nik 4.7 49 4.1 21.2 38 61 0.613 0.362 0.436 387,770 Dobr{nik 1.8 45 3.3 24.8 18 63 0.511 0.316 0.376 165,300 Jesenica 20.5 41 7.9 8.7 122 64 1.049 0.642 0.743 1,676,900 Ukova 4.3 37 4.5 14.2 38 68 0.634 0.433 0.494 384,740 Javornik 16.6 42 6.8 7.8 94 61 0.992 0.567 0.660 1,304,400 Bela 6.2 52 3.9 11.9 52 62 0.557 0.340 0.415 479,390 Sevnik 1.9 39 2.9 24.6 16 59 0.548 0.303 0.350 144,660 POHORJE Lobnica 44.3 29.6 16.5 6.51 116 54 2.866 0.414 1.383 3,547,000 Lobni~ica 3 46.2 3.6 19.78 19.5 53 0.696 0.305 0.399 241,200 PREDELICA Predelica 9.3 60 6.2 15.7 77 36 1.481 0.316 0.575 1,345,000 KOSE^ Brusnik upstream of Kose~ 0.56 70 1.5 37.2 8.4 43 0.363 0.297 0.190 82,360 Brusnik upstream of Ro~ica 0.9 56 2.3 32.5 12.0 43 0.572 0.324 0.274 136,500 Ro~ica 10.6 60 6.7 14.1 79.0 38 1.488 0.277 0.610 1,313,000 Jo{t Sodnik, Matja` Miko{, Estimation of magnitudes of debris flows in selected torrential watersheds in Slovenia 120 -100 - "s 80 - 2 60 - -S 40 - 20 - 0 - 0 500 1000 1500 2000 time/~as (min) ----------- Lobnica ----------- Predelica Suhelj Figure 2: Modelled run-off hydrographs using HEC-HMS model for selected torrential watersheds (Suhelj in the Upper Sava River valley, Lobnica in Pohorje and Predelica in the So~a River basin). mine the total volume of run-off based on given precipitation and calculated discharge values, since in the method for estimation of magnitude of debris flow the estimate of run-off volume is required. The morphometric data on torrential areas were taken from hydrological studies (VGI1993, 1995a, 1995b, 1999, 2002), Table 1. The data on surface characterists were taken from the Naravovarstveni atlas (NVA 2005), where the airborne imagery can be acquired. The precipitation data for hydrological modelling were taken from hydrological studies (VGI 1993, 1995b, 1999, 2002) and they are shown in Table 2. Based on the posi-tion, an associated precipitation station was attributed to each torrential area, and precipitation data were considered in the analysis. For torrential watersheds in the upstream part of the Upper Sava River, inc-luding the Belca Torrent, the data for rainfall station Rate~e - Planica were used, and for other areas with the inclusion of the Bistrica Torrent the data from the precipitation station Javorni{ki Rovt were used. For the Lobnica River and the Lobni~ica Torrent on Pohorje, the data of the precipitation station Ko~a nad [umikom were used, for the Predelica Torrent and the Brusnik Stream the data from Bovec. In the vicinity of torrential areas there are other stations, which, however, are not equipped with raingauges (om-brographs) that would record short heavy rain showers and enable their statistical analysis. Thus in the Upper Sava River valley there are 8 precipitation stations, but only three are equipped with ombrographs. Only stations Rate~e - Planica and Javorni{ki Rovt could therefore be included in the analysis. Hydrological Table 2. Rainfall data from raingauge stations, used for hydrologic modelling - shown are precipitation totals in mm of showers of short duration between 5 minutes and 1440 minutes with the recurrence interval of 100 years. Raingauge station/Duration of precipitation [minutes] 5 15 60 120 180 360 720 1440 Javorni{ki Rovt (1966-1993) Rate~e - PJanica (1966-1993) Ko~a nad [umikom (1975-1997) Bovec (1959-1987) 22.5 15.1 21.2 20.2 34.0 25.2 33.6 41.9 57.5 48.1 59.9 104.9 74.5 66.5 80.1 165.9 86.8 80.4 94.9 217.0 112.7 110.5 126.8 293.3 146.3 138.9 169.5 358.0 190.0 174.6 226.5 437.0 98 Acta geographica Slovenica, 46-1, 2006 studies provide statistically calculated precipitation of different return periods/recurrence intervals and duration, calculated with the help of measurements for particular periods (see Table 2). For the preparation of data in the HEC-HMS model there are several methods to choose from, howe-ver, the methods are limited by several factors, such as relief gradient, channel gradient, characteristics of terrain, and thus some of them were not applicable. The following methods have proven as suitable: SCS method (Soil Conservation Service), SRC method (Snyder - Riverside County) and Clark-Kirpich method (Brilly & [raj 2005). The calculated values of the time of concentration Tc or the time delay T between precipitation and run-off peak are shown in Table 1. Based on the results we have decided to use the SCS method, which is widely used in practice. The CN (curve number) as a parameter indicating the soil characteristics (infiltration etc.) was based on surface characteristics, such as ratio of forest, meadows, shrubs and rocks. The initial CN value was based on the data provided by remote sensing. The final value of CN parameter was based by calibrating the hydro-logical model, so that the peak of the calculated runoff and data on high water with 100-year recurrence period were correlated. The calculated runoffs in the hydrological studies were determined in a similar way, by way of a synthetic hydrograph, computed from assumed precipitation, however, they only give peak values, and not the total volume of the flood wave. The calculated volumes of runoff volume with the SCS method are shown in Table 1, and the synthetic run-off hydrographs for the selected torrential areas in Figure 2. 3 Analysis of hydrological parameters This was followed by the analysis of the calculated hydrological parameters as a function of the size of the torrential watershed. The basis for determination of empirical equations were the results for 18 torrential areas of the Upper Sava River: Figure 3 shows the relation between the 100-year discharge Q100 (m3/s) and the torrential watershed area A (km2) and Figure 4 the relation between the run-off volume V (m3) and the torrential watershed area A (km2). 100-year discharge analysis Q100 and run-off analysis V give statistically reliable equations (in both cases the regression coefficient is R2 > 0.97 for n = 18). These two Figure 3: Relation between the 100-year discharge Q100and the catchment area of the torrential watersheds in the Upper Sava River valley (n = 18) and in Pohorje (n= 11). 99 Jo{t Sodnik, Matja` Miko{, Estimation of magnitudes of debris flows in selected torrential watersheds in Slovenia Figure 4: Relation between the volume of the flood hydrograph with a peak discharge of Q100and the catchment area of the torrential watersheds in the Upper Sava River valley (n=18) and in Pohorje (n=11). equations can be used also in other torrential areas of the Upper Sava River valley without previous hydro-logical modelling. The relation between runoff volume and torrential watershed area accelerates the estimate of magnitude of debris flow using the methods that require the knowledge of runoff volume. Figure 3 also shows the relation between 100-year discharges Q100 and the area of watershed A of sin-gle torrents in the Pohorje area. In Pohorje only two torrents (the Lobnica and Lobni~ica) were used for the analysis of applicability of methods for estimation of magnitude of debris flows, however, for discharge analysis other torrents from SW part of Pohorje were used, which are covered in the hydrological study for this particular area (VGI1999). Thus, a total of 11 torrential areas (n= 11) of asize of between 0.17 km2 and 44,3 km2 were at our disposal. Based on discharge analysis and run-off volumes the following empirical equations were obtained (Fi-gures 3 and 4): Q100 for torrents on the Upper Sava River: Q100 for torrents in the Pohorje area: Volume of flood wave in the Upper Sava River: Q100= 12.5 A0,72 [m3/s] Q1= 7 A0,76 [m3/s] Vr= 90,000 A0,93 [m3] (8) (9) (10) Table 3. Computed run-off volumes for the torrential watersheds in Pohorje. Torrential area A (km2) Upper Sava River (Eq. 10) watershed Volume Vr = 90,000A 0,93 (m3) Pohorje (Eq. 11) Volume Vr = 90,000 A 0,96 (m3) HEC-HMS method Volume Vr(m3) Lobnica 44.3 3,057,722 Lobni~ica 3.0 250,015 3,426,022 258,392 3,547,000 241,200 The empirical equations for calculation of flood wave volume in Pohorje could not be obtained in the same way as for the torrents on the Upper Sava River, since in the Pohorje area only two torrents (Lobnica 100 Table 4. Parameters of the torrential watersheds, used for the estimation of debris-flow magnitudes. Torrential watershed Area [km2] Slope [%] Channel length [km] Channel slop [%] dH – height difference [km] Melton number [-] Fan gradient [%] Vr – water run-off [m3] Annual sediment yield [m3/year] UPPER SAVA RIVER Trebi`a Krotnjek Suhelj Velika Pi{nica Jure`ev graben Martuljek Hladnik Beli potok Belca Bistrica Mlinca Presu{nik Dobr{nik Jesenica Ukova Javornik Bela Sevnik 5.3 3.7 1.9 37.9 2.0 11.4 15.0 5.3 17.6 43.7 7.9 4.7 1.8 20.5 4.3 16.6 6.2 1.9 38 48 57 67 47 72 60 72 65 64 59 49 45 41 37 42 52 39 3.8 3.2 3.2 9.2 2.7 4.1 6.6 3.8 7 12.6 4.9 4.1 3.3 7.9 4.5 6.8 3.9 2.9 8.6 9.6 16.9 3.3 28.6 11.4 12.1 21.0 8.5 4.0 17.1 21.2 24.8 8.7 14.2 7.8 11.9 24.6 0.687 0.592 0.727 1.500 0.867 1.066 1.134 1.367 1.067 1.650 1.231 1.150 0.970 1.093 0.739 1.230 0.570 0.480 0.298 0.308 0.527 0.244 0.613 0.316 0.293 0.594 0.254 0.250 0.438 0.530 0.723 0.241 0.356 0.302 0.229 0.348 4.157 5.024 11.828 2.218 11.842 4.211 6.496 10.010 5.182 1.448 8.100 12.261 10.000 3.382 9.348 5.900 9.058 14.500 407,150 326,000 182,050 2,092,700 158,380 803,620 1,174,600 355,690 1,307,100 3,303,100 593,910 387,770 165,300 1,676,900 384,740 1,304,400 479,390 144,660 No data available No data available No data available 69,325 265 19,848 9,654 7,053 18,297 No data available 11,481 9,521 2,396 10,402 885 7,280 4,968 No data available POHORJE Lobnica Lobni~ica 44.3 3.0 29.6 46.2 16.5 3.6 6.5 19.8 0.997 0.900 0.150 0.520 5.607 20.000 3,547,000 241,200 5,248 386 PREDELICA Predelica 9.3 60 6.2 15.7 2.049 0.672 9.200 1,345,000 No data available KOSE^ Brusnik upstream of Kose~ Brusnik upstream of Ro~ica Ro~ica 0.56 0.9 10.6 70 56 60 1.5 2.3 6.7 37.2 32.5 14.1 0.725 0.985 1.007 0.969 1.038 0.309 23.333 30.769 7.700 82,360 136,500 1,313,000 No data available No data available No data available Table 5. Estimated debris-flow magnitudes determined for all torrential watersheds. Takei (1984) Kronfellner-Kraus (1984) Marchi & D'Agostino (2002) Ceriani et al. (2000) Method 1 Method 2 Magnitude [m3] Magnitude Magnitude [m3] [m3] Torrential watershed Magnitude [m3] K[-] Magnitude [m3] Magnitude M/Vr Magnitude [m3] [m3] I_F=1 I_F=2 I_F=3 M/Vr M/Vr M/Vr UPPER SAVA RIVER Trebi`a Krotnjek Suhelj Velika Pi{nica Jure`ev graben Martuljek Hladnik Beli potok Belca Bistrica Mlinca Presu{nik Dobr{nik Jesenica Ukova Javornik Bela Sevnik 37,614 30,209 20,118 124,885 20,757 60,014 70,950 37,614 78,217 136,217 47,983 34,956 19,465 85,844 33,110 75,475 41,390 20,118 1067.76 1091.95 1119.81 676.49 1118.25 980.36 932.17 1067.76 898.85 623.73 1029.59 1076.77 1121.38 863.09 1082.81 911.52 1054.39 1119.81 48,668 38,786 35,957 84,609 63,964 127,407 169,189 118,842 134,468 109,028 139,087 107,289 50,058 153,932 66,117 118,024 77,793 52,340 9,535 7,077 7,527 26,641 19,730 43,299 69,402 43,497 47,246 44,778 52,578 37,585 13,431 60,390 16,865 37,724 20,468 14,250 0.021 0.027 0.083 0.003 0.237 0.038 0.042 0.128 0.021 0.005 0.085 0.130 0.178 0.022 0.058 0.018 0.041 0.175 8,733 8,713 15,079 6,609 37,569 30,287 49,872 45,489 27,387 15,326 50,363 50,541 29,483 36,808 22,498 23,014 19,687 25,387 45,221 39,102 72,742 146,677 86,468 103,057 196,955 188,803 164,708 112,596 178,510 187,379 74,985 120,105 95,085 202,874 93,231 63,975 11,305 9,775 18,185 36,669 21,617 25,764 49,239 47,201 41,177 28,147 44,627 46,845 18,746 30,026 23,771 50,718 23,308 15,994 5,025 4,345 8,082 16,297 9,608 11,451 21,884 20,978 18,301 12,511 19,834 20,820 8,332 13,345 10,565 22,542 10,359 7,108 0.111 0.120 0.400 0.070 0.546 0.128 0.168 0.531 0.126 0.034 0.301 0.483 0.454 0.072 0.247 0.156 0.194 0.442 0.028 0.030 0.100 0.018 0.136 0.032 0.042 0.133 0.032 0.009 0.075 0.121 0.113 0.018 0.062 0.039 0.049 0.111 0.012 0.013 0.044 0.008 0.061 0.014 0.019 0.059 0.014 0.004 0.033 0.054 0.050 0.008 0.027 0.017 0.022 0.049 POHORJE Lobnica Lobni~ica -- -- -- -- 0.012 0.113 43,593 27,367 293,738 191,907 73,434 47,977 32,638 21,323 0.083 0.796 0.021 0.199 0.009 0.088 PREDELICA Predelica - - - - 0.071 96,143 336,128 84,032 37,348 0.250 0.062 0.028 KOSE^ Brusnik upstream of Kose~ Brusnik upstream of Ro~ica Ro~ica --- --- --- --- 0.401 0.306 0.058 33,052 41,812 75,701 68,794 154,101 172,382 17,198 38,525 43,095 7,644 17,122 19,154 0.835 1.129 0.131 0.209 0.282 0.033 0.093 0.125 0.015 Acta geographica Slovenica, 46-1, 2006 and Lobni~ica) were modelled with HEC-HMS. So we could only test the applicability of equation (10), which applies for the torrents on the Upper Sava River. Table 3 shows the calculation of flood wave volu-me for both torrents in Pohorje in 3 different ways. Correlation with results of hydrological modeling with HEC-HMS model are bfollowing term is obtained (Figure 4): Flood wave volume in Pohorje: Vr= 90,000 A0,96 [m3] (11) Torrents Lobnica and Lobni~ica are fit for comparison, the former having large catchment area (A = 44.3 km2), and the latter having small catchment area (A = 3.0 km2). The proposed equation for wider use should be additionally verified with hydrological modelling. The values of coefficients in equations 8 and 9 are consistent with the values employed in engineering practice. The value of exponent 0.76 for torrents in Pohorje may come as a surprise, since this is contrary to the assumed maximum coefficient of 0.75, which should be used/valid in the alpine part of Slovenia. 4 Calculation of magnitudes of debris flows When estimating the magnitudes with different methods, we first determined the parameters of the met-hods for each torrential area; the parameters were either taken from hydrological studies, calculated or taken from topographic maps and airborne imagery. In Table 4 total precipitation run-offs are given, obtained by HEC-HMS. At the end of the table, the values of average release of erosion material for specific torrential areas are given, however, this data are not available for all torrents. In Table 5 the results of the methods used are given. In the 18 torrential areas of the Upper Sava River all the methods were used, while on other torrential areas only the 2nd method Marchi & D'Agostino (2002) and method of Ceriani et al. (2000) were used. The Takei method (1984) and Kronfellner-Krauss method (1984) gave very high values of magnitudes of debris flows for the torrential areas of the Upper Sava River and were therefore not used for other torrential areas. For the method of Ceriani et al. (2000) the results are given for different landslide indices (I_F): active landslides or landslides that may re-activate are present (I_F= 1); J2 16.000 -C « 12.000 -"G 'C 8.000 -&* 4.000 - « /¦ > / y = 17.689 x2.0984 R2 = 0.9924 0 /¦ ¦ +, ¡ y ( 0 5 10 15 20 25 3 channel gradient/strmec struge (%) Figure 5: Relation between the specific sediment yield, computed using the method 2 of Marchi & D'Agostino (2002), and the torrential channel gradient in the Upper Sava valley (n= 18). 103 Table 6. Specific sediment yields for torrential watersheds. Takei (1984) Kronfellner-Kraus (1984) Marchi & D'Agostino (2002) Ceriani et al. (2000) Method 1 Method 2 a) I_F= 1 b) I_F= 2 c) I_F=3 Torrential watershed [m3/km2] [m3/km2] [m3/km2] [m3/km2] [m3/km2] [m3/km2] [m3/km2] UPPER SAVA RIVER Trebi`a Krotnjek Suhelj Velika Pi{nica Jure`ev graben Martuljek Hladnik Beli potok Belca Bistrica Mlinca Presu{nik Dobr{nik Jesenica Ukova Javornik Bela Sevnik 7096.9 8164.7 10588.3 3295.1 10378.6 5264.4 4730.0 7096.9 4444.2 3117.1 6073.9 7437.4 10813.9 4187.5 7699.9 4546.7 6675.8 10588.3 9182.7 10482.7 18924.8 2232.4 31981.9 11176.1 11279.3 22422.9 7640.2 2494.9 17606.0 22827.4 27810.3 7508.9 15375.9 7109.9 12547.2 27547.4 1799.1 1912.7 3961.7 702.9 9865.0 3798.1 4626.8 8207.0 2684.4 1024.7 6655.4 7996.8 7461.5 2945.8 3922.1 2272.5 3301.3 7500.1 1647.7 2354.8 7936.1 174.4 18784.5 2656.8 3324.8 8582.9 1556.1 350.7 6375.1 10753.4 16379.5 1795.5 5232.1 1386.4 3175.3 13361.7 8532.2 10568.0 38285.1 3870.1 43234.1 9040.1 13130.3 35623.1 9358.4 2576.6 22596.1 39867.8 41658.4 5858.8 22112.9 12221.3 15037.2 33670.8 2133.0 2642.0 9571.3 967.5 10808.5 2260.0 3282.6 8905.8 2339.6 644.1 5649.0 9967.0 10414.6 1464.7 5528.2 3055.3 3759.3 8417.7 948.0 1174.2 4253.9 430.0 4803.8 1004.5 1458.9 3958.1 1039.8 286.3 2510.7 4429.8 4628.7 651.0 2457.0 1357.9 1670.8 3741.2 POHORJE Lobni~ica Lobnica 984.1 9122.3 6630.6 63969.0 1657.7 15992.2 736.7 7107.7 PREDELICA Predelica 10338.0 36142.8 9035.7 4015.9 KOSE^ Brusnik upstream of Kose~ Brusnik upstream of Ro~ica Ro~ica 59021.8 46457.4 7141.6 122845.6 1712231 16262.4 30711.4 42805.8 4065.6 13649.5 19024.8 1806.9 - - - Acta geographica Slovenica, 46-1, 2006 Figure 6: Relation between the specific sediment yield, computed using the method of Ceriani et al. (2000), and the torrential fan gradient in the Upper Sava valley (n = 18). landslides are present though not close to the torrent channel (I_F = 2); no larger or important landslides are present (I_F = 3). For representation purposes, with method 2 of Marchi & D'Agostino (2002) and the method of Ceriani et al. (2000) the ratio between the volume of debris flow (magnitude) and volume of waterM/V is given. Table 6 also gives specific sediment yield of debris material in single torrential areas. r G G r / G 5 Analysis of magnitudes of debris flows The next step was the analysis of calculated magnitudes of debris flows as a function of morphological parameters of the torrential area. The analysis was performed for 18 torrents of the Upper Sava River val-ley for the calculated magnitudes of debris flows, using the method 2 of Marchi & D Agostino (2002) and the method of Ceriani et al. (2000), with landslide index of I_F = 2. As the most useful relationship was taken the relation/connection between morphological parameters of the torrential area and specific sediment yield of debris material in an area (m3/km2). In this way, the effect of size of catchment area was eliminated from the analysis. Relations with the magnitude of debris flow, calculated to the specific sediment yield, were checked for the following morphological parameters: channel gradient (%), fan gradient (%) and the Melton num-ber. The magnitude of debris flow following the method 2 of Marchi & DAgostino (2002) was most significantly related to the channel gradient (R2 = 0.9924, n = 18; Figure 5): M= 17.7·Is 2 [m3/km2], (12) where I is channel gradient [%], while the method Ceriani et al. (2000) showed most significant rela- s G l j> v : G tions to the fan gradient (R2 = 0.9377, n = 18; Figure 6): M= 330·Iv1,3[m3/km2], (13) where I fan gradient [%]. These two relations enable a quick assessment of magnitudes of debris flow in the Upper Sava River area. The reliability of both relations is a sound one, especially in using method 2 105 Jo{t Sodnik, Matja` Miko{, Estimation of magnitudes of debris flows in selected torrential watersheds in Slovenia Figure 7: Relation between the specific sediment yield, computed using the method 2 of Marchi & D'Agostino (2002), and the torrential channel gradient for all investigated torrential watersheds (the regression line is Eq. (12)). Figure 8: Relation between the specific sediment yield, computed using the Ceriani et al. (2000) method, and the torrential fan gradient for all investigated torrential watersheds (the regression line is Eq. (13)). 106 Acta geographica Slovenica, 46-1, 2006 of Marchi & D'Agostino (2002) (R2 = 0.9924, n = 18). For more exact results a more detailed analysis and calculations are required, taking into consideration all required parameters of the method in the torren-tial area investigated. The advantage of the empirical connection is that the either the channel gradient or the fan gradient are the basic parameters found in any hydrological study, or they can be easily deter-mined from topographic maps. Figures 7 in 8 show the results of all investigated torrents, and empirical equations (12) and (13). Clearly evident are the deviations between the estimated values of the specific sediment yield in different torren-tial areas from the proposed empirical relation. The Brusnik torrent situated in the area up to Kose~ shows most significant deviations. 6 Classification of torrential fans Further, we classified the investigated torrents in terms of the level of danger of occurrence of debris flows. In this respect, two limit values are given in the literature: the Melton number = 0.3 and torrential fan gradient = 4° (7%). Both are based on analysis of past events. These limit values should provide a crite-rion good enough for classification of torrential fans into three kinds: • fans that fullfilled both criteria were termed as debris-flow fans, since the hazard of occurrence of debris flows exists; • fans whose parameters did not exceed any of the limits were termed as torrential fans, with no hazard of occurrence of debris flows; • fans that fullfil only one criterion were termed as transitional fans, where there is the danger of occurrence of debris flows, but the probability of occurrence is relatively small. The parameters for this classification are relatively easy to obtain, that is, either from topographic maps or, to achieve higher accuracy, with field investigation. It should be noted that contrary to debris-flow fans, the torrential fans may not be subject to debris flows, however there may still be the danger of torrents or hyperconcetrated flow. Table 7 shows the classification of the investigated debris-flows based on the value of both limit parameters. The Predelica and Brusnik torrents are included among the torrents investigated, where debris flows occurred in the past. A debris flow triggered in the Predelica torrent strongly affected the village of Log pod Mangartom. In the Brusnik torrent in 2002 debris flows were triggered that posed a threat to the village of Kose~. If the classification of debris flows into classes from 1 to 10 is adopted, as proposed by Jakob (2005) that defines the possible consequences of debris flows of different classes using several debris flow parameters (magnitude, peak discharge, area of deposited sediment), the classification of these debris flows is the following one: Log pod Mangartom: Magnitude: M= 700,000-1,000,000 m3 (class 5-6) Peak debris flow discharge: Qb = 8000 m3/s (class 5) Area of deposited debris flow sediment: Bb = 250,000 m2 (class 5) The debris flow of 17 November 2000 in Log pod Mangartom is classified as class 5. Kose~: Magnitude: M= 100-1000 m3 (class 2) Peak debris flow discharge: Qb = 15-20 m3/s (class 2) Area of deposited debris flow sediment: Bb = several 100 m2 (class 2) Debris flows in 2002 in Kose~ are classified as class 2. Table 8 shows the results of the calculated magnitudes of debris flows with the method 2 of Marchi & DAgostino (2002) and the Ceriani et al. method (2000). The estimate of magnitude by these two methods gives an estimate of maximum possible events and differs from the actual volumes of investigated debris flows. In the case of Log pod Mangartom, the reason for the difference is the extremeness of event, when the debris flow with recurrence period of over 100 years was initiated in the area in spilled into the Koritnica valley in two phases. To reach the value of debris flow volume of approx. 900,000 m3 by the Ceriani et al. method (2000) one would have to use the landslide index I_F = 0.6. However, debris 107 Jo{t Sodnik, Matja` Miko{, Estimation of magnitudes of debris flows in selected torrential watersheds in Slovenia Table 7. Values of parameters and classification of torrential fans in terms of debris flow hazard. Torrential watershed Melton number [-] Fan gradient [%] Fan classification UPPER SAVA RIVER Trebi`a 0.298 4.157 transitional fan Krotnjek 0.308 5.024 transitional fan Suhelj 0.527 11.828 debris-flow fan Velika Pi{nica 0.244 2.218 torrential fan Jure`ev graben 0.613 11.842 debris-flow fan Martuljek 0.316 4.211 transitional fan Hladnik 0.293 6.496 transitional fan Beli potok 0.594 10.010 debris-flow fan Belca 0.254 5.182 torrential fan Bistrica 0.250 1.448 torrential fan Mlinca 0.438 8.100 debris-flow fan Presu{nik 0.530 12.261 debris-flow fan Dobr{nik 0.723 10.000 debris-flow fan Jesenica 0.241 3.382 torrential fan Ukova 0.356 9.348 debris-flow fan Javornik 0.302 5.900 transitional fan Bela 0.229 9.058 transitional fan Sevnik 0.348 14.500 debris-flow fan POHORJE Lobnica 0.150 5.607 torrential fan Lobni~ica 0.520 20.000 debris-flow fan PREDELICA Predelica 0.672 9.200 debris-flow fan KOSE^ Brusnik upstream of Kose~ 0.969 23.333 debris-flow fan Brusnik upstream of Ro~ica 1.038 30.769 debris-flow fan Ro~ica 0.309 7.700 debris-flow fan Table 8. The estimated debris-flow magnitudes for the Predelica Torrent and the Brusnik Stream upstream of Kose~. Marchi & D'Agostino (2002) Ceriani et al. (2000) Magnitude [m3] Magnitude [m3] Magnitude [m3] Magnitude [m3] Torrential watershed b) I_F= 1 a) I_F= 2 c) I_F=3 PREDELICA Predelica 96,143 336,128 84,032 37,348 KOSE^ Brusnik upstream of Kose~ 33,052 68,794 17,198 7,644 flows in Kose~ were of smaller volume since they were limited by the available quantity of debris material (Miko{ et al. 2005). If the Strug rockfall grew in its intensity, we could expect re-activation of debris flows. For delination of hazard area in Kose~ due to occurrence of debris flows under Strug, as the extre-me scenario the event with a volume (magnitude) of 25,000m3 was taken (Miko{ et al. 2006). 7 Conclusion The performed analysis showed the applicability of the chosen methods for estimation of magnitudes of debris flows based on the known morphological parameters of the torrential area. For Slovenian condi-tions two methods have proven adequate: the method 2 of Marchi & D'Agostino (2002) and the method 108 Acta geographica Slovenica, 46-1, 2006 of Ceriani et al. (2000). By way of hydrological modelling of the chosen torrential areas we developed our own empirical equations from the two methods. The decision on the applicability of the methods was based also on comparison of results of both methods with data on debris flows in Kose~ in 2002 and on debris flow that devastated the village of Log pod Mangartom on November 17, 2000. The critical limits for classification of fans into classes are only partly confirmed and require further validation, especially detailed field investigation of fans, which would confirm or adapt the values to Slo-venian conditions. The Ceriani et al. method (2000), which uses the landslide index I_F, requires field investigation and determination of the index based on frequency of erosion-related events in the torrential area. The index strongly influences the estimation of debris flow magnitude. 8 References Brilly, M., [raj, M. 2005: Modeliranje povr{inskega odtoka in navodila za program HEC-HMS, university textbook. University of Ljubljana, Faculty of Civil and Geodetic Engineering. Ljubljana. Ceriani, M., Crosta, G., Frattini, P., Quattrini, S. 2000: Evaluation of hydrological hazard on alluvial fans. Interpreavent 2000 - Villach, Vol. 2. Villach. D'Agostino, V., Cerato, M., Coali, R. 1996: Extreme events of sediments transport in the eastern Trenti- no torrents. Interpreavent 1996 - Garmisch Partenkirchen, Vol. 1. Villach. Hydrologic Modeling System 2000: HEC-HMS, Tehnical Reference Manual. US Army Corps of Engineers, Hydrologic Engineering Center. Davis. Hydrologic Modeling System 2001: HEC-HMS, User's Manual. US Army Corps of Engineers, Hydrologic Engineering Center. Davis. Jackson, Lionel E. Jr., Kostaschuk, R. A., MacDonald, G. M., 1987: Identification of debris flow hazard on alluvial fans in the Canadian Rocky Mountain. Reviews in Engineering Geology 4. Boulder. Jakob, M. 2005: A size classification for debris flows. Engineering geology 79. Amsterdam. Kronfellner-Krauss, G. 1984: Extreme sedimentation and gullying of torrents. Interpreavent 1984- Villach, Vol. 2. Villach. Kronfellner-Krauss G. 1988: New results and experiences in the quantitative estimation of torrents. Mit- teilungen der Forstlichen Bundesversuchsanstalt. Beiträge zur Wildbacherosions- und Lawinenforschung, Heft 159. Wien. Marchi, L., Pasuto, A., Tecca, P. R., 1993: Flow processes on alluvial fans in the Eastern Italian Alps. Zeitschrift für Geomorphologie 37. Stuttgart, Berlin. Marchi, L., DAgostino, V. 2002: Estimation of debris-flow magnitude in the eastern Italian Alps. Earth Surface Processes and Landforms 29. Chichester. Melton, M. A, 1965: The geomorphic and paleoclimatic significance of alluvial deposits in Southern Arizona. Journal of Geology 73. Chicago. Miko{, M. 1997: Ocena ogro`enosti alpskega prostora. Gradbeni vestnik 46. Ljubljana. Miko{, M. 2001: Zna~ilnosti drobirskih tokov. Ujma 14-15. Ljubljana. Miko{, M., Majes, B., Fazarinc, R., Rajar, R., @agar, D, Krzyk, M., Hojnik, T, and ^etina, M. 2006: Numeri- cal simulation of debris flows triggered from the Strug rock fall source area, W Slovenia. Natural Hazards and Earth System Sciences 6. Katlenburg-Lindau. NVA 2005: Naravovarstveni atlas. Medmre`je: http://kremen.arso.gov.si/NVAtlas. Schöberl, F, Stötter, J., Schönlaub, H., Ploner, A., Sönser, T, Jenewein, S., Rinderer, M. 2004: PROMABGIS: A GIS-based tool for estimating runoff and sediment discharge in alpine catchment areas. Interprae- vent 2004 - Riva/Trient, Vol. 3. Klagenfurt. Skaberne, D. 2001: Predlog slovenskega izrazoslovja pobo~nih premikanj - pobo~nega transporta = Pro- posal of the Slovene terminology on slope movements - slope transport. Geologija 44. Ljubljana. Sodnik, J. 2005: Metode za ocenjevanje ogro`enosti z drobirskimi tokovi. Diplomska naloga. Fakulteta za gradbeni{tvo in geodezijo, Univerza v Ljubljani. Ljubljana. Sodnik, J., Miko{, M. 2005: Ocenjevanje magnitude drobirskih tokov. Slovensko zdru`enje za geodezijo in geofiziko. Ljubljana. Takei, A. 1984: Interdependence of sediment budget between individual torrents and river-system. Interpreavent 1984 - Villach, Vol. 2. Villach. 109 Jo{t Sodnik, Matja` Miko{, Estimation of magnitudes of debris flows in selected torrential watersheds in Slovenia VGI, 1993: Koritnica: hidrolo{ka {tudija. Ljubljana: {tevilka C-160. Vodnogospodarski in{titut. Ljubljana. VGI, 1995a: Vodnogospodarski na~rt povodja Save Dolinke - pritoki na obmo~ju od Jesenic do Rate~: {tudija. C-468. Vodnogospodarski in{titut. Ljubljana. VGI, 1995b: Hidrolo{ka {tudija Save Dolinke, C-159. Vodnogospodarski in{titut. Ljubljana. VGI, 1999: Hidrologija: Analiza poplavne varnosti JZ dela Maribora pred hudourni{kimi vodami s Pohorja na odsekih: Razvanjski potok - Bla`ovnica in Bla`ovnica - Lobnica. Vodnogospodarski in{titut. Ljubljana. VGI, 2002: Dolo~itev visokih vod z visokovodnimi valovi za potoka Brusnik in Ro~ica, 53-BA/02. Vodnogospodarski in{titut. Ljubljana. 110 Jo{t Sodnik, Matja` Miko{, Ocena magnitud drobirskih tokov v izbranih hudourni{kih obmo~jih v Sloveniji Ocena magnitud drobirskih tokov v izbranih hudourni{kih obmo~jih v Sloveniji UDC: 551.435.6(497.4) COBISS: 1.01 IZVLE^EK: V prispevku je opisana uporaba razli~nih metod za oceno magnitud drobirskih tokov, spro`enih ob padavinah, na 18 hudournikih v Zgornjesavski dolini in na dveh na Pohorju (Lobnica, Lobni~ica). Dodatno preverjanje metod je bilo opravljeno na hudourni{kih obmo~jih z aktivnimi drobirskimi tokovi v bli`nji preteklosti (Predelica, Brusnik). Za nekatere metode zado{~a poznavanje morfometri~nih lastnosti hudourni{kega obmo~ja, hudourni{ke struge in hudourni{kega vr{aja. Za druge metode je bilo treba uporabiti matemati~no orodje (HEC-HMS) in izdelati hidrolo{ki model odtoka izbranih padavin, ki lahko spro`ijo drobirske tokove. Izra~unane magnitude drobirskih tokov se gibljejo v obmo~ju od 6500 m3 do 340.000 m3. Vrednosti so odvisne od parametrov hudourni{kega obmo~ja; najpomembnej{i parametri so: povr{ina prispevnega obmo~ja, Meltonovo {tevilo, naklon vr{aja in strmec hudourni{ke struge. Obravnavane vr{aje smo razdelili v tri skupine glede na nevarnost delovanja drobirskih tokov: drobirski vr{aji (nevarnost obstaja), hudourni{ki vr{aji (ni nevarnosti) in prehodni vr{aji (drobirski tokovi so mo`ni, a malo verjetni). Predlagali smo mejni vrednosti Meltonovega {tevila (0,3) in naklona hudourni{kega vr{aja (4° oziroma 7 %) za razdelitev med drobirskimi in hudourni{kimi vr{aji. Od obravnavanih 24 hudourni{kih vr{ajev smo med drobirske vr{ajev razvrstili 13 vr{ajev, v hudourni{ke vr{aje pet, ostalih {est vr{ajev pa smo uvrstili med prehodne vr{aje. KLJU^NE BESEDE: erozija, masna gibanja, drobirski tokovi, empiri~ni modeli, ocena nevarnosti, vr{aji, Zgornjesavska dolina, Pohorje, Slovenija. Uredni{tvo je prejelo prispevek 24. aprila 2006. NASLOVA: Jo{t Sodnik, univ. dipl. in`. grad. VGP d. d. Ulica Mirka Vadnova 5, SI - 4000 Kranj E-po{ta: jost.sodnik@vgp-kranj.si Matja` Miko{, dr., red. prof. Univerza v Ljubljani Fakulteta za gradbeni{tvo in geodezijo Jamova cesta 2, SI - 1000 Ljubljana E-po{ta: matjaz.mikos@fgg.uni-lj.si Vsebina 1 Uvod 2 Hidrolo{ki ra~uni 3 Analiza hidrolo{kih parametrov 4 Izra~un magnitude drobirskih tokov 5 Analiza magnitud drobirskih tokov 6 Klasifikacija hudourni{kih vr{ajev 7 Sklep 8 Viri in literatura 113 115 116 117 117 121 123 123 112 Acta geographica Slovenica, 46-1, 2006 1 Uvod Drobirski tokovi kot oblika masnega gibanja sedimentov po pobo~jih ali hudourni{kih strugah so v preteklosti preoblikovali slovensko povr{je in so v zadnjem ~asu vse pogostej{i. Zaradi razpr{ene poselitve in goste mre`e prometnic je nujna podrobnej{a preu~itev ogro`enosti prostora zaradi njihovega delovanja. Gre za obliko masnega gibanja sedimentov (Skaberne 2001), ki se lahko razvije na pobo~jih ali v strugah hudournikov. Poznavanje njihove dinamike (Miko{ 2001) omogo~a na~rtovanje primernih preventivnih ukrepov. Eno najbolj pogostih vpra{anj v zvezi z drobirskimi tokovi je vpra{anje, kje lahko nastanejo. Ob tem je za na~rtovanje ukrepov nujno poznati obseg (magnitudo) pojava, ki jo lahko pri~akujemo. S pomo~-jo ocenjenih magnitud lahko z modeliranjem gibanja drobirskih tokov ocenimo njihov doseg in preto~ne hitrosti ter globine, ki jih obi~ajno uporabimo pri ocenah nevarnosti (Miko{ 1997). Ob{irnej{e na~rtovanje ukrepov za varstvo pred razli~nimi erozijskimi pojavi mora obravnavati vsak primer posebej, saj ima vsak primer svoje specifi~ne lastnosti, ki lahko bistveno vplivajo na potek dogodkov. Eden od bistvenih podatkov je velikost obravnavanega erozijskega obmo~ja. Razmerje med koli~ino erozijskega gradiva, ki je na dolo~enem obmo~ju na razpolago, in koli~ino materiala, ki se dejansko spro`i ob posameznem dogodku, je od primera do primera lahko zelo razli~no. Kljub temu so v preteklosti sku{ali razviti metode, ki bi bile splo{no uporabne za ocenjevanje magnitude drobirskih tokov. Geomorfne procese na hudourni{kih vr{ajih so obravnavale {tevilne terenske {tudije. V eni prvih je Melton (1965) predlagal zvezo med naklonom hudourni{kega vr{aja (S) in nekaterimi drugimi topografskimi parametri: S=a[(H - H .)A–0,5]n, (1) L v max min' J ' v ' pri ~emer sta a in n neodvisna koeficienta, H in H . sta vi{ina najvi{je to~ke in najni`je to~ke hudour- r max min ' ' ' ' ni{kega obmo~ja (t. j. najvi{ja to~ka vr{aja) [km], A pa je povr{ina hudourni{kega obmo~ja [km2]. ^len ena~be Mel = (H - H )A–0,5 po avtorju imenujemo Meltonovo {tevilo. Ta pristop je osnova za razi- * max min' r J J r r J skovanje naplavinskih procesov na vr{ajih, ki je usmerjeno v klasifikacijo vr{ajev na podlagi morfolo{kih parametrov hudourni{kih obmo~ij in hudourni{kih vr{ajev. Metode za ocenjevanje magnitude drobirskih tokov, ki so osnova za ocenjevanje ogro`enosti zaradi tega pojava, delimo na: • empiri~ne metode (npr. Takei 1984, Kronfellner-Kraus 1984, Marchi in D'Agostino 2002), ki so namenjene oceni magnitude drobirskega toka; • morfolo{ke metode (npr. Jackson s sod. 1987, Marchi s sod. 1993, Marchi in D'Agostino 2002, Jakob 2005), ki jih delimo na tiste, ki ocenjuje magnitudo, in na tiste, ki so namenjene dolo~evanju nevarnosti delovanja drobirskega toka na hudourni{kem vr{aju; • kombinirane metode (npr. Ceriani s sod. 2000), ki so kombinacija razli~nih drugih metod, ki na podlagi statisti~ne obdelave dolo~ijo odlo~ilne parametre hudourni{kega obmo~ja v obliki empiri~ne ena~be za izra~un magnitude drobirskega toka; • ra~unalni{ke metode (npr. Schöberl s sod. 2004), ki so ra~unalni{ki programi, ki upo{tevajo zalogo erozijskega drobirja v obravnavanem prispevnem obmo~ju in premestitveno zmogljivost hudournika z upo{tevanjem odlaganja materiala v strugi hudournika. Podroben opis metod je `e bil podan drugje (Sodnik 2005; Sodnik in Miko{ 2005). Za izra~un magnitud drobirskih tokov na izbranih hudournikih v Sloveniji smo uporabili naslednje empiri~ne in morfolo{ke metode: Takei (1984): Vd= 13600A0.61 ….. (2) Kronfellner-Kraus (1984): M = K·A·Sc…..[m3] (3) K = 1150/e0.014A…..[-] (4) Marchi & D'Agostino (2002): 1. metoda: M = 65000A135S1.7…..[m3] (5) 2. metoda: M / V = 2,9 S2…..[-] (6) 113 Preglednica 1. Rezultati modeliranja odtoka padavin na hudournikih Save Dolinke. hudourni{ko povr{ina naklon dol`ina vodotok stoletni {tevilo SCS metoda Clarck-Kirpichova SRC metoda skupni obmo~je [km2] povr{ja [%] vodotoka [km] [%] pretok Q100[m3/s] CN [-] Tp [ure] metoda Tc [ure] Tp [ure] odtok [m3] SAVA DOLINKA Trebi`a 5,3 38 3,8 8,6 40 67 0,560 0,376 0,432 407.150 Krotnjek 3,7 48 3,2 9,6 36 67 0,435 0,301 0,363 326.000 Suhelj 1,9 57 3,2 16,9 23 71 0,359 0,282 0,351 182.050 Velika Pi{nica 37,9 67 9,2 3,3 128 57 1,107 0,598 0,760 2.092.700 Jure`ev graben 2 47 2,7 28,6 19 66 0,394 0,267 0,320 158.380 Martuljek 11,4 72 4,1 11,4 82 64 0,468 0,312 0,406 803.620 Hladnik 15 60 6,6 12,1 99 66 0,713 0,483 0,603 1.174.600 Beli potok 5,3 72 3,8 21 39 63 0,452 0,294 0,383 355.690 Belca 17,6 65 7 8,5 107 64 0,756 0,490 0,621 1.307.100 Bistrica 43,7 64 12,6 4 197 61 1,317 0,775 0,974 3.303.100 Mlinca 7,9 59 4,9 17,1 56 60 0,661 0,386 0,482 593.910 Presu{nik 4,7 49 4,1 21,2 38 61 0,613 0,362 0,436 387.770 Dobr{nik 1,8 45 3,3 24,8 18 63 0,511 0,316 0,376 165.300 Jesenica 20,5 41 7,9 8,7 122 64 1,049 0,642 0,743 1.676.900 Ukova 4,3 37 4,5 14,2 38 68 0,634 0,433 0,494 384.740 Javornik 16,6 42 6,8 7,8 94 61 0,992 0,567 0,660 1.304.400 Bela 6,2 52 3,9 11,9 52 62 0,557 0,340 0,415 479.390 Sevnik 1,9 39 2,9 24,6 16 59 0,548 0,303 0,350 144.660 POHORJE Lobnica Lobni~ica 44,3 3 29,6 46,2 16,5 3,6 6,51 19,78 116 19,5 54 53 2,866 0,696 0,414 0,305 1,383 0,399 3.547.000 241.200 PREDELICA Predelica 9,3 60 6,2 15,7 77 36 1,481 0,316 0,575 1.345.000 KOSE^ Brusnik do Kose~a Brusnik do Ro~ice Ro~ica 0,56 0,9 10,6 70 56 60 1,5 2,3 6,7 37,2 32,5 14,1 8,4 12,0 79,0 43 43 38 0,363 0,572 1,488 0,297 0,324 0,277 0,190 0,274 0,610 82.360 136.500 1.313.000 Acta geographica Slovenica, 46-1, 2006 Ceriani s sod. (2000): M = k · (A)a · (Mb )b · (S l_)c ·(IF)–d…..[103m3], (7) kjer so parametri v ena~bah naslednji: K- koeficient lastnosti hudourni{kega obmo~ja, podan za posamezna obmo~ja Alp v Avstriji [-]; A - povr{ina prispevnega obmo~ja hudournika [km2]; S - povpre~en strmec hudourni{ke struge [%]; S- povpre~en strmec hudourni{ke struge [m/m]; V - celoten odtok vode [m3]; I_F- indeks plazljivosti [-]; Mb - Meltonovo {tevilo [-]; S l - strmec hudourni{ke struge na vr{aju [%]. a_c c / l j V tem prispevku prikazujemo rezultate uporabe omenjenih empiri~nih in morfolo{kih metod na slovenskih hudournikih. Namen analize je bil preveriti mo`nosti podajanja ocene magnitude morebitnih drobirskih tokov in njihovega razvr{~anja glede na nevarnost delovanja drobirskih tokov. Ocenjene koli~ine po izbranih metodah je treba primerjati z zgodovinskimi zapisi o koli~inah preteklih dogodkov. @al sistemati~ne analize zgodovinskih dogodkov ni in je primerjanje rezultatov po izbranih metodah z dogajanjem v preteklosti prej izjema kakor pravilo. Ocene magnitud drobirskih tokov smo opravili na hudourni{kih pritokih Save Dolinke in na dveh hudournikih na Pohorju (slika 1). Za dodatno preverjanje smo metode preizkusili tudi na hudournikih Predelica in Brusnik, kjer so se drobirski tokovi pojavljali v bli`nji preteklosti (Miko{ in sod. 2004; 2006). Slika 1: V tem prispevku obravnavana hudourni{ka obmo~ja v Sloveniji Glej angle{ki del prispevka. 2 Hidrolo{ki ra~uni Na izbranih hudourni{kih obmo~jih je bilo treba za uporabo nekaterih metod najprej izra~unati celotno prostornino odtoka za nastanek drobirskih tokov relevantnih padavin. Modelirali smo s programom HEC-HMS (Hydrologic Modeling System 2000; 2001). Namen modeliranja je bil dolo~iti celotno prostornino odtoka vode na podlagi podanih padavin in izra~unanih pretokov, saj metoda za oceno magnitude drobirskega toka kot parameter zahteva oceno prostornine odtekle vode. Morfometri~ne podatke o hudourni{kih obmo~jih smo privzeli po hidrolo{kih {tudijah (VGI 1993; 1995a; 1995b; 1999; 2002) in so prikazani v preglednici 1. Podatke o zna~ilnostih povr{ja smo privzeli po Naravovarstvenem atlasu (NVA 2005), kjer so dostopni aerofoto posnetki. Padavinske podatke za hidrolo{ko modeliranje smo povzeli iz hidrolo{kih {tudij (VGI 1993; 1995b; 1999; 2002) in so prikazani v preglednici 2. Preglednica 2. Podatki z de`emernih postaj, uporabljeni pri hidrolo{kem modeliranju - prikazane so vi{ine kratkotrajnih nalivov v mm s povratno dobo 100 let in trajanja od 5 minut do 1440 minut. De`emerna postaja 5 15 60 120 180 360 720 1440 Javorni{ki Rovt (1966–1993) Rate~e - PJanica (1966-1993) Ko~a nad [umikom (1975-1997) Bovec (1959-1987) 22,5 15,1 21,2 20,2 34,0 25,2 33,6 41,9 57,5 48,1 59,9 104,9 74,5 66,5 80,1 165,9 86,8 80,4 94,9 217,0 112,7 110,5 126,8 293,3 146,3 138,9 169,5 358,0 190,0 174,6 226,5 437,0 Vsakemu hudourni{kemu obmo~ju smo glede na lego dolo~ili pripadajo~o padavinsko postajo, katere padavine smo upo{tevali v analizi. Za hudourni{ka obmo~ja Save Dolinke vklju~no z Belco smo uporabili podatke za de`emerno postajo Rate~e - Planica, za ostala obmo~ja od vklju~no Bistrice pa podatki de`e-merne postaje Javorni{ki Rovt. Za Lobnico in Lobni~ico smo uporabili podatke de`emerne postaje Ko~a nad [umikom, za Predelico in Brusnik pa podatke iz Bovca. Sicer so v bli`ini nekaterih hudourni{kih obmo-~ij tudi druge postaje, vendar niso opremljene z ombrografi, ki bi merili kratkotrajne nalive in omogo~ili 115 Jo{t Sodnik, Matja` Miko{, Ocena magnitud drobirskih tokov v izbranih hudourni{kih obmo~jih v Sloveniji njihovo statisti~no analizo. Tako je v pore~ju Save Dolinke osem padavinskih postaj, a so le tri opremljene z ombrografi. Za analizo smo tako lahko uporabili le postaji Rate~e - Planica in Javorni{ki Rovt. Vhidrolo{kih {tudijah so podane statisti~no izra~unane padavine razli~nih povratnih dob in trajanja, izra~unane s pomo~jo meritev za dolo~eno obdobje (glej preglednico 2). Za pripravo podatkov v modelu HEC-HMS je na voljo veliko {tevilo metod, a ker so posamezne metode omejene z razli~nimi faktorji, kot so naklon terena, strmec struge, lastnosti obravnavanega povr{ja, so nekatere neuporabne. Kot primerne so se izkazale metode: metoda SCS (Soil Conservation Service), metoda SRC (metoda Snyder- Riverside County) in Clark-Kirpichova metoda (Brilly &[raj 2005). Izra~unane vrednosti kriti~nega ~asa stekanja Tc oziroma ~asa zamika T med te`i{~em padavin in konico odtoka so prikazane v preglednici 1. Na podlagi rezultatov smo se odlo~ili za uporabo metode SCS, ki se v praksi tudi sicer {iroko uporablja. [tevilo CN (angl.: curve number) je parameter, ki dolo~a lastnosti tal (infiltracija ipd.). Dolo~ili smo ga na podlagi zna~ilnosti povr{ja, kot so dele` gozdov, travnikov, grmovja in skal. Za~etno vrednost za CN smo dolo~ili na osnovi podatkov daljinskega zaznavanja. Kon~no vrednost CN smo dolo~ili s pomo~-jo umerjanja hidrolo{kega modela, tako da sta se ujemala konica izra~unanega odtoka in podatek o visoki vodi s 100-letno povratno dobo. Izra~unane pretoke vhidrolo{kih {tudijah smo dolo~ili na podoben na~in, s pomo~jo sinteti~nega hidrograma, izra~unanega iz predpostavljenih padavin. Vendar izra~uni podajajo le konico, ne pa tudi celotne prostornine visokovodnega vala. Izra~unane prostornine odtoka vode po metodi SCS so prikazane v preglednici 1, sinteti~ni hidrogrami odtoka za izbrana hudourni{ka obmo~ja pa na sliki 2. Slika 2: Z uporabo programa HEC-HMS modelirani hidrogrami odtoka za izbrana hudourni{ka obmo~ja (Suhelj v Zgornjesavski dolini, Lobnica na Pohorju in Predelica). Glej angle{ki del prispevka. 3 Analiza hidrolo{kih parametrov Sledila je analiza izra~unanih hidrolo{kih parametrov v odvisnosti od velikosti hudourni{kega obmo~ja. Kot osnovo za dolo~itev empiri~nih ena~b smo vzeli rezultate za 18 hudourni{kih obmo~ij Save Dolinke: na sliki 3 je prikazana zveza med stoletnim pretokom Q100 (m3/s) in povr{ino hudourni{kega obmo~ja A (km2) ter na sliki 4 zveza med prostornino odtoka V (m3) in povr{ino hudourni{kega obmo~ja A (km2). Analiza stoletnih pretokov Q100 in odtokov vode V daje statisti~no zanesljivi ena~bi (v obeh primerih je regresijski koeficient R2 > 0,97 za n= 18). Ti dve ena~bi lahko torej uporabimo tudi na drugih hudourni{kih obmo~jih Zgornjesavske doline brez predhodnega hidrolo{kega modeliranja. Predvsem zveza med prostornino odtoka in povr{ino hudourni{kega obmo~ja je pomembna za oceno magnitude drobirske-ga toka po metodah, ki zahtevajo poznavanje prostornine odtoka vode. Na sliki 3 je prikazana tudi zveza med pretoki Q100 in povr{ino prispevnega obmo~ja A posameznega hudournika na Pohorju. Za analizo uporabnosti metod za oceno magnitude drobirskih tokov sta bila na Pohorju obravnavana samo dva hudournika (Lobnica in Lobni~ica), za analizo pretokov pa smo uporabili {e druge hudournike iz JZ dela Pohorja, obravnavane v hidrolo{ki {tudiji tega obmo~ja (VGI1999). Tako smo imeli na razpolago skupaj 11 hudourni{kih obmo~ij (n= 11) velikosti od 0,17km2 do 44,3 km2. Na podlagi analize pretokov Q100 in prostornin odtokov V smo torej pri{li do naslednjih empiri~nih ena~b (sliki 3 in 4): Q100 za hudournike na Savi Dolinki [m3/s]: Q100= 12,5A0,72 (8) Q100 za hudournike na Pohorju [m3/s]: Q100 =7 A0,76 (9) Prostornina poplavnega vala na Savi Dolinki [m3]: V = 90.000 A0,93 (10) Slika 3: Zveza med stoletnimi pretoki Q100 in povr{ino prispevnega obmo~ja posameznega hudournika v Zgornjesavski dolini (n = 18) in na Pohorju (n= 11). Glej angle{ki del prispevka. 116 Acta geographica Slovenica, 46-1, 2006 Slika 4: Zveza med prostornino poplavnega hidrograma s konico Q100 in povr{ino prispevnega obmo~ja posameznega hudournika v Zgornjesavski dolini (n = 18) in na Pohorju (n= 11). Glej angle{ki del prispevka. Preglednica 3. Izra~un prostornin odtoka vode za hudourni{ka obmo~ja Pohorja. hudourni{ko obmo~je povr{ina A (km2) Sava Dolinka (en. 10) prostornina Vr = 90.000 A 0,93 (m3) Pohorje (en. 11) prostornina Vr = 90.000 A 0,96 (m3) HEC-HMS metoda prostornina Vr(m3) Lobnica Lobni~ica 44,3 3,0 3.057.722 250.015 3.426.022 258.392 3.547.000 241.200 Empiri~ne ena~be za izra~un prostornine poplavnega vala za Pohorju na na~in kot smo to storili za hudournike na Savi Dolinki, ni bilo mogo~e dobiti, saj smo s pomo~jo HEC-HMS modelirali na Pohorju le dva hudournika (Lobnico in Lobni~ico). Zato smo lahko le preizkusili uporabnost ena~be (10), ki velja za hudournike na Savi Dolinki. V preglednici 3 je prikazan izra~un prostornine poplavnega vala V za oba hudournika na Pohorju na 3 razli~ne na~ine. Ujemanje z rezultati hidrolo{kega modeliranja s programom HEC-HMS dobimo tako, da eksponent v empiri~ni ena~bi (10) spremenimo z 0,93 na 0,96 in tako dobimo ena~bo (slika 4): Prostornina poplavnega vala na Pohorju: V = 90.000 A0,96 [m3] (11) Hudournika Lobnica in Lobni~ica sta primerna za primerjavo, saj ima prvi veliko (A = 44,3 km2), slednji pa majhno prispevno povr{ino (A = 3,0km2). Predlagano ena~bo je za {ir{o uporabo treba dodatno preveriti s pomo~jo hidrolo{kega modeliranja. Vrednosti koeficientov v ena~bah 8 in 9 so konsistentne z vrednostmi, ki so se uveljavile v in`enirski praksi, morda presene~a vrednost eksponenta 0,76 za hudournike na Pohorju, saj velja domneva, da je maksimalni koeficient 0,75, ki naj bi veljal v alpskem delu Slovenije. 4 Izra~un magnitude drobirskih tokov Pri oceni magnitud po posameznih metodah smo najprej dolo~ili parametre metode za vsako hudourni{ko obmo~je, ki smo jih povzeli po hidrolo{kih {tudijah, izra~unali ali povzeli iz topografskih kart in aerofoto posnetkov. V preglednici 4 so podani tudi celotni odtoki padavin, dobljeni s programom HEC-HMS. Na koncu preglednice so podane {e koli~ine povpre~nega spro{~anja erozijskega materiala za posamezno hudourni{ko obmo~je, vendar ta podatek ni na voljo za vse hudournike. V preglednici 5 so rezultati uporabljenih metod. Na 18 hudourni{kih obmo~jih Save Dolinke smo uporabili vse navedene metode, medtem ko smo na ostalih hudourni{kih obmo~jih uporabili le 2. metodo Marchi & D'Agostino (2002) in metodo Ceriani s sod. (2000). Metoda Takei (1984) in metoda Kronfell-ner-Krauss (1984) sta za hudourni{ka obmo~ja Save Dolinke dali primerjalno zelo visoke vrednosti magnitud drobirskih tokov in ju zato nismo uporabili tudi na drugih hudourni{kih obmo~jih. Za metodo Ceriani s sod. (2000) so rezultati podani za razli~ne indekse plazljivosti (I_F): prisotnost aktivnih plazov ali plazov z mo`nostjo ponovnega aktiviranja (I_F = 1); prisotnost plazov, ampak ne neposredno ob strugi (I_F = 2); ni ve~jih oziroma pomembnih plazov (I_F = 3). Pri 2. metodi Marchi & D'Agostino (2002) in metodi Ceriani s sod. (2000) je za bolj{o predstavljivost podano tudi razmerje med prostornino drobirske-ga toka (magnitudo) in prostornino vode M/ V. V preglednici 6 sledijo {e specifi~ni prispevki drobirskega materiala za posamezno hudourni{ko obmo~je. 5 Analiza magnitud drobirskih tokov Sledila je analiza izra~unanih magnitud drobirskih tokov v odvisnosti od morfolo{kih parametrov hudourni{kega obmo~ja. Opravili smo jo za 18 hudournikov v Zgornjesavski dolini za izra~unane magnitude drobirskih tokov po 2. metodi Marchi & D'Agostino (2002) in metodi Ceriani s sod. (2000) ob upo{tevanju faktorja plazljivosti I_F = 2. Kot najbolj uporabno zvezo smo privzeli povezavo med morfolo{kimi 117 Preglednica 4. Parametri hudourni{kih obmo~ij, uporabljeni pri oceni magnitud drobirskih tokov. povr{ina naklon povr{ja dol`ina in naklon vodotoka dH Meltonovo {tevilo naklon vr{aja prostornina Vr (odtok vode) letno spro{~anje gradiva Hudourni{ko obmo~je [km2; [%] [km] [%] [km] [–] [%] [m3; [m3/leto] SAVA Trebi`a 5,3 38 3,8 8,6 0,687 0,298 4,157 407.150 ni podatka Krotnjek 3,7 48 3,2 9,6 0,592 0,308 5,024 326.000 ni podatka Suhelj 1,9 57 3,2 16,9 0,727 0,527 11,828 182.050 ni podatka Velika Pi{nica 37,9 67 9,2 3,3 1,500 0,244 2,218 2.092.700 69.325 Jure`ev graben 2,0 47 2,7 28,6 0,867 0,613 11,842 158.380 265 Martuljek 11,4 72 4,1 11,4 1,066 0,316 4,211 803.620 19.848 Hladnik 15,0 60 6,6 12,1 1,134 0,293 6,496 1.174.600 9.654 Beli potok 5,3 72 3,8 21,0 1,367 0,594 10,010 355.690 7.053 Belca 17,6 65 7 8,5 1,067 0,254 5,182 1.307.100 18.297 Bistrica 43,7 64 12,6 4,0 1,650 0,250 1,448 3.303.100 ni podatka Mlinca 7,9 59 4,9 17,1 1,231 0,438 8,100 593.910 11.481 Presu{nik 4,7 49 4,1 21,2 1,150 0,530 12,261 387.770 9.521 Dobr{nik 1,8 45 3,3 24,8 0,970 0,723 10,000 165.300 2.396 Jesenica 20,5 41 7,9 8,7 1,093 0,241 3,382 1.676.900 10.402 Ukova 4,3 37 4,5 14,2 0,739 0,356 9,348 384.740 885 Javornik 16,6 42 6,8 7,8 1,230 0,302 5,900 1.304.400 7.280 Bela 6,2 52 3,9 11,9 0,570 0,229 9,058 479.390 4.968 Sevnik 1,9 39 2,9 24,6 0,480 0,348 14,500 144.660 ni podatka POHORJE Lobnica Lobni~ica 44,3 3,0 29,6 46,2 16,5 3,6 6,5 19,8 0,997 0,900 0,150 0,520 5,607 20,000 3.547.000 241.200 5.248 386 PREDELICA Predelica 9,3 60 6,2 15,7 2,049 0,672 9,200 1.345.000 ni podatka KOSE^ Brusnik do Kose~a Brusnik do Ro~ice Ro~ica 0,56 0,9 10,6 70 56 60 1,5 2,3 6,7 37,2 32,5 14,1 0,725 0,985 1,007 0,969 1,038 0,309 23,333 30,769 7,700 82.360 136.500 1.313.000 ni podatka ni podatka ni podatka Preglednica 5. Rezultati izra~una magnitud drobirskih tokov na vseh hudournikih. Takei (1984) Kronfellner-Kraus (1984) Marchi in D'Agostino (2002) Ceriani s sod. (2000) 1. metoda 2. metoda magnituda magnituda magnituda [m3] [m3] [m3] Hudourni{ko obmo~je magnituda [m3] K[-] magnituda magnituda [m3] [m3] M/V, magnituda [m3] I_F=1 I_F=2 I_F=3 M/V M/V M/V SAVA Trebi`a Krotnjek Suhelj Velika Pi{nica Jure`ev graben Martuljek Hladnik Beli potok Belca Bistrica Mlinca Presu{nik Dobr{nik Jesenica Ukova Javornik Bela Sevnik 37.614 30.209 20.118 124.885 20.757 60.014 70.950 37.614 78.217 136.217 47.983 34.956 19.465 85.844 33.110 75.475 41.390 20.118 1.067,76 1.091,95 1.119,81 676,49 1.118,25 980,36 932,17 1.067,76 898,85 623,73 1.029,59 1.076,77 1.121,38 863,09 1.082,81 911,52 1.054,39 1.119,81 48.668 38.786 35.957 84.609 63.964 127.407 169.189 118.842 134.468 109.028 139.087 107.289 50.058 153.932 66.117 118.024 77.793 52.340 9.535 7.077 7.527 26.641 19.730 43.299 69.402 43.497 47.246 44.778 52.578 37.585 13.431 60.390 16.865 37.724 20.468 14.250 0,021 0,027 0,083 0,003 0,237 0,038 0,042 0,128 0,021 0,005 0,085 0,130 0,178 0,022 0,058 0,018 0,041 0,175 8.733 8.713 15.079 6.609 37.569 30.287 49.872 45.489 27.387 15.326 50.363 50.541 29.483 36.808 22.498 23.014 19.687 25.387 45.221 39.102 72.742 146.677 86.468 103.057 196.955 188.803 164.708 112.596 178.510 187.379 74.985 120.105 95.085 202.874 93.231 63.975 11.305 9.775 18.185 36.669 21.617 25.764 49.239 47.201 41.177 28.147 44.627 46.845 18.746 30.026 23.771 50.718 23.308 15.994 5.025 4.345 8.082 16.297 9.608 11.451 21.884 20.978 18.301 12.511 19.834 20.820 8.332 13.345 10.565 22.542 10.359 7.108 0,111 0,120 0,400 0,070 0,546 0,128 0,168 0,531 0,126 0,034 0,301 0,483 0,454 0,072 0,247 0,156 0,194 0,442 0,028 0,030 0,100 0,018 0,136 0,032 0,042 0,133 0,032 0,009 0,075 0,121 0,113 0,018 0,062 0,039 0,049 0,111 0,012 0,013 0,044 0,008 0,061 0,014 0,019 0,059 0,014 0,004 0,033 0,054 0,050 0,008 0,027 0,017 0,022 0,049 POHORJE Lobnica Lobni~ica -- -- -- -- 0,012 0,113 43.593 27.367 293.738 191.907 73.434 47.977 32.638 21.323 0,083 0,796 0,021 0,199 0,009 0,088 PREDELICA Predelica - - - - 0,071 96.143 336.128 84.032 37.348 0,250 0,062 0,028 KOSE^ Brusnik do Kose~a Brusnik do Ro~ice Ro~ica --- --- --- --- 0,401 0,306 0,058 33.052 41.812 75.701 68.794 154.101 172.382 17.198 38.525 43.095 7.644 17.122 19.154 0,835 1,129 0,131 0,209 0,282 0,033 0,093 0,125 0,015 Preglednica 6. Podatki o specifi~nih prispevkih drobirskega materiala za posamezna hudourni{ka obmo~ja. Takei (1984) Kronfellner-Kraus (1984) Marchi in D'Agostino (2002) Ceriani s sod. (2000) 1. metoda 2. metoda a) I_F=1 b) I_F=2 c) I_F=3 Hudourni{ko obmo~je (m3/km2) (m3/km2) (m3/km2) (m3/km2) (m3/km2) (m3/km2) (m3/km2) SAVA Trebi`a 7.096,9 9.182,7 1.799,1 1.647,7 8.532,2 2.133,0 948,0 Krotnjek 8.164,7 10.482,7 1.912,7 2.354,8 10.568,0 2.642,0 1.174,2 Suhelj 10.588,3 18.924,8 3.961,7 7.936,1 38.285,1 9.571,3 4.253,9 Velika Pi{nica 3.295,1 2.232,4 702,9 174,4 3.870,1 967,5 430,0 Jure`ev graben 10.378,6 31.981,9 9.865,0 18.784,5 43.234,1 10.808,5 4.803,8 Martuljek 5.264,4 11176,1 3.798,1 2.656,8 9.040,1 2.260,0 1.004,5 Hladnik 4.730,0 11.279,3 4.626,8 3.324,8 13130,3 3.282,6 1.458,9 Beli potok 7.096,9 22.422,9 8.207,0 8.582,9 35.623,1 8.905,8 3.958,1 Belca 4.444,2 7.640,2 2.684,4 1.556,1 9.358,4 2.339,6 1.039,8 Bistrica 3.117,1 2.494,9 1.024,7 350,7 2.576,6 644,1 286,3 Mlinca 6.073,9 17.606,0 6.655,4 6.375,1 22.596,1 5.649,0 2.510,7 Presu{nik 7.437,4 22.827,4 7.996,8 10.753,4 39.867,8 9.967,0 4.429,8 Dobr{nik 10.813,9 27.810,3 7.461,5 16.379,5 41.658,4 10.414,6 4.628,7 Jesenica 4.187,5 7.508,9 2.945,8 1.795,5 5.858,8 1.464,7 651,0 Ukova 7.699,9 15.375,9 3.922,1 5.232,1 22112,9 5.528,2 2.457,0 Javornik 4.546,7 7.109,9 2.272,5 1.386,4 12.221,3 3.055,3 1.357,9 Bela 6.675,8 12.547,2 3.301,3 3.175,3 15.037,2 3.759,3 1.670,8 Sevnik 10.588,3 27.547,4 7.500,1 13.361,7 33.670,8 8.417,7 3.741,2 POHORJE Lobni~ica Lobnica -- -- -- 984,1 9.122,3 6.630,6 63.969,0 1.657,7 15.992,2 736,7 7.107,7 PREDELICA Predelica - - - 10.338,0 36142,8 9.035,7 4.015,9 KOSE^ Brusnik do Kose~a Brusnik do Ro~ice Ro~ica --- --- --- 59.021,8 46.457,4 7.141,6 122.845,6 171.223,1 16.262,4 30.711,4 42.805,8 4.065,6 13.649,5 19.024,8 1.806,9 Acta geographica Slovenica, 46-1, 2006 parametri hudourni{kega obmo~ja in specifi~nim prispevkom drobirskega materiala za posamezno obmo~-je (m3/km2). Na ta na~in smo iz analize izklju~ili vpliv velikosti prispevnega obmo~ja. Slika 5: Zveza med specifi~nim prispevkom drobirskega materiala, izra~unanim po 2. metodi Marchi & D'Agostino (2002), in padcem struge hudournika v Zgornjesavski dolini (n=18). Glej angle{ki del prispevka. Povezave z magnitudo drobirskega toka oziroma specifi~nim prispevkom drobirskega materiala smo iskali za naslednje morfolo{ke parametre: strmec vodotoka [%], naklon vr{aja [%] in Meltonovo {tevilo [-]. Magnituda drobirskega toka po 2. metodi Marchi in D'Agostino (2002) je imela najbolj{o povezavo s padcem struge hudournika (R2 = 0,9924, n = 18; slika 5): M= 17,7·Is 2 [m3/km2], (12) pri ~emer je I strmec struge [%], medtem ko je metoda Ceriani s sod. (2000) najbolj{o zvezo pokazala z naklonom vr{aja (R2 = 0,9377, n = 18; slika 6): M= 330·Iv1,3[m3/km2], (13) pri ~emer je I naklon vr{aja [%]. Ti dve zvezi omogo~ata hitro oceno magnitud drobirskih tokov na obmo~ju Save Dolinke. Zanesljivost teh dveh zvez je dobra, predvsem po 2. metodi Marchi & D'Agostino (2002) (R2 = 0,9924, n = 18). Za to~nej{e rezultate bi bila nujna podrobnej{a analiza in izra~un z upo{tevanjem vseh zahtevanih parametrov metode na obravnavanem hudourni{kem obmo~ju. Prednost te empiri~ne zveze je, da je strmec struge oziroma naklon vr{aja mogo~e preprosto dolo~iti s pomo~jo topografskih kart. Na slikah 7 in 8 so prikazani rezultati za vse obravnavane hudournike in empiri~ni ena~bi (12) in (13). Vidna so odstopanja med ocenjenimi koli~inami specifi~nega prispevka drobirskega materiala na razli~-nih hudourni{kih obmo~jih od predlagane empiri~ne zveze. Najbolj izrazito odstopa hudournik Brusnik na obmo~ju do Kose~a. Slika 6: Zveza med specifi~nim prispevkom drobirskega materiala, izra~unanim po metodi Ceriani s sod. (2000), in naklonom hudourni{-kega vr{aja v Zgornjesavski dolini (n=18). Glej angle{ki del prispevka. Slika 7: Zveza med specifi~nim prispevkom drobirskega materiala, izra~unanim po 2. metodi Marchi & D'Agostino (2002), in strmcem struge hudournika za vsa obravnavana hudourni{ka obmo~ja (regresijska ~rta je ena~ba (12)). Glej angle{ki del prispevka. Slika 8: Zveza med specifi~nim prispevkom drobirskega materiala, izra~unanim po metodi Ceriani s sod. (2000), in naklonom hudourni{-kega vr{aja za vsa obravnavana hudourni{ka obmo~ja (regresijska ~rta je ena~ba (13)). Glej angle{ki del prispevka. 6 Klasifikacija hudourni{kih vr{ajev Obravnavane hudournike smo nato razvrstili glede na nevarnost nastanka drobirskih tokov. V literaturi sta pogosti dve mejni vrednosti, dolo~eni iz analize preteklih dogodkov, ki sta dovolj dober kriterij za razvrstitev hudourni{kih vr{ajev v tri razrede: Meltonovo {tevilo = 0,3 in naklon hudourni{kega vr{aja = 4° (7 %). Vr{aje, ki so ustrezali obema kriterijema, smo ozna~ili kot drobirske vr{aje, saj na njih obstaja nevarnost delovanja drobirskih tokov. Vr{aje, katerih parametri niso presegli nobene od obeh mej, smo ozna~ili kot hudourni{ke vr{aje. Na hudourni{kih vr{ajih ni nevarnosti delovanja drobirskih tokov. Vr{aje, ki ustrezajo samo enemu kriteriju od obeh, smo ozna~ili kot prehodne vr{aje. Na njih sicer obstaja nevarnost delovanja drobirskih tokov, vendar je verjetnost tega dogodka relativno majhna. Parametri za tak{no klasifikacijo lahko enostavno dolo~imo bodisi na podlagi topografskih kart bodisi z natan~nej{imi terenskimi meritvami. Opozoriti moramo, da hudourni{ki vr{aj za razliko od drobirskega vr{aja morda res ni podvr`en delovanju drobirskih tokov, {e vedno pa na njem obstaja nevarnost delovanja hudournika in toka, prenasi~enega s sedimenti (hiperkoncentriranega toka). 121 Jo{t Sodnik, Matja` Miko{, Ocena magnitud drobirskih tokov v izbranih hudourni{kih obmo~jih v Sloveniji Preglednica 7. Vrednosti parametrov in dolo~ena ogro`enost vr{aja posameznega hudournika z drobirskimi tokovi. hudourni{ko obmo~je Meltonovo {tevilo [-] naklon vr{aja [%] uvrstitev vr{ajev v razrede SAVA Trebi`a 0,298 Krotnjek 0,308 Suhelj 0,527 Velika Pi{nica 0,244 Jure`ev graben 0,613 Martuljek 0,316 Hladnik 0,293 Beli potok 0,594 Belca 0,254 Bistrica 0,250 Mlinca 0,438 Presu{nik 0,530 Dobr{nik 0,723 Jesenica 0,241 Ukova 0,356 Javornik 0,302 Bela 0,229 Sevnik 0,348 POHORJE Lobnica Lobni~ica 0,150 0,520 5,607 20,000 ni ogro`enosti ogro`en vr{aj PREDELICA Predelica 0,672 9,200 ogro`en vr{aj KOSE^ Brusnik do Kose~a Brusnik do Ro~ice Ro~ica 0,969 1,038 0,309 23,333 30,769 7,700 ogro`en vr{aj ogro`en vr{aj ogro`en vr{aj Med obravnavanimi hudourniki sta tudi Predelica in Brusnik, kjer so se drobirski tokovi v preteklosti `e zgodili. Na hudourniku Predelica se je spro`il drobirski tok, ki je mo~no prizadel vas Log pod Mangartom. Na hudourniku Brusnik pa so se leta 2002 pro`ili drobirski tokovi, ki so ogro`ali Kose~. ^e privzamemo delitev drobirskih tokov v razrede od 1 do 10, kot jo je predlagal Jakob (2005), ki dolo~a mo`ne posledice drobirskih tokov razli~nih razredov z uporabo ve~ parametrov drobirskega toka (magnituda, maksimalni pretok, povr{ina odlo`enega toka), so poglavitne zna~ilnosti teh dveh drobirskih tokov naslednje: Log pod Mangartom: Magnituda: M = 700.000-1.000.000 m3 (razred 5-6) Maksimalni pretok drobirskega toka: Qb = 8.000 m3/s (razred 5) Povr{ina odlo`enega drobirskega toka: Bb = 250.000 m2 (razred 5) Drobirski tok 17.11.2000 v Logu pod Mangartom lahko uvrstimo v razred 5. Kose~: Magnituda: M = 100-1000 m3 (razred 2) Maksimalni pretok drobirskega toka: Qb = 15-20 m3/s (razred 2) Povr{ina odlo`enega drobirskega toka: Bb = nekaj 100 m2 (razred 2) Drobirske tokove leta 2002 v Kose~u lahko uvrstimo v razred 2. Rezultati izra~unanih magnitud drobirskih tokov z 2. metodo Marchi & D'Agostino (2002) in metodo Ceriani s sod. (2000) so prikazani v preglednici 8. Ocenjena magnituda je obenem tudi ocena maksimalnih mo`nih dogodkov, ki pa se razlikuje od dejanskih prostornin opazovanih drobirskih tokov. V primeru Loga po Mangartom je vzrok razlike ekstremnost dogodka, ko je drobirski tok s povratno dobo prek sto 4,157 prehodni primer 5,024 prehodni primer 11,828 ogro`en vr{aj 2,218 ni ogro`enosti 11,842 ogro`en vr{aj 4,211 prehodni primer 6,496 prehodni primer 10,010 ogro`en vr{aj 5,182 ni ogro`enosti 1,448 ni ogro`enosti 8,100 ogro`en vr{aj 12,261 ogro`en vr{aj 10,000 ogro`en vr{aj 3,382 ni ogro`enosti 9,348 ogro`en vr{aj 5,900 prehodni primer 9,058 prehodni primer 14,500 ogro`en vr{aj 122 Acta geographica Slovenica, 46-1, 2006 Preglednica 8. Magnitude drobirskih tokov za Predelico in Brusnik do Kose~a. Marchi in D'Agostino (2002) Ceriani s sod. (2000) magnituda [m3] magnituda [m3] magnituda [m3] magnituda [m3] Hudourni{ko obmo~je a) I_F= 2 b) I_F= 1 c) I_F= 3 PREDELICA Predelica 96.143 84.032 336.128 37.348 KOSE^ Brusnik do Kose~a 33.052 17.198 68.794 7.644 let nastal na pobo~ju in se razlil v dolini Koritnice v dveh fazah. Da bi dosegli prostornino dejanskega dro-birskega toka iz leta 2000 (npr. 900.000 m3) z metodo Ceriani s sod. (2000), bi morali uporabiti indeks plazljivosti I_F = 0,6. Drobirski tokovi v Kose~u so bili manj{ih dimenzij, ker so bili omejeni z razpolo`ljivo koli~ino drobir-skega materiala (Miko{ s sod. 2005). ^e bi se plaz Strug znova intenziviral, lahko pri~akujemo vnovi~no aktiviranje drobirskih tokov. Kot ekstremni scenarij za dolo~itev nevarnega obmo~ja v Kose~u zaradi delovanja drobirskih tokov izpod Struga smo privzeli dogodek s prostornino (magnitudo) 25.000 m3 (Miko{ s sod. 2006). 7 Sklep Analiza je pokazala uporabnost izbranih metod za oceno magnitud drobirskih tokov na osnovi znanih morfolo{kih parametrov hudourni{kega obmo~ja. Za slovenske razmere sta se kot primerni pokazali: 2. metoda Marchi in D'Agostino (2002) ter metoda Ceriani s sod. (2000). S pomo~jo hidrolo{kega modeliranja izbranih hudourni{kih obmo~ij smo s pomo~jo dveh metod razvili lastne empiri~ne ena~be. Odlo~itev o primernosti metod je slonela tudi na primerjavi rezultatov teh dveh metod s podatki o drobirskih tokovih v Kose~u v letu 2002 in o drobirskem toku, ki je 17. novembra 2000 prizadel Log pod Mangartom. Rezultati le deloma potrjujejo kriti~ni meji za razvr{~anje vr{ajev v posamezne tipe, zato je njuno nadaljnje preverjanje, predvsem podrobne terenske raziskave vr{ajev. Tkao bi ju lahko potrdili in prilagodili slovenskim razmeram. Metoda Ceriani s sod. (2000), ki vsebuje indeks plazljivosti, zahteva terenski ogled in dolo~anje tega indeksa na osnovi raz{irjenosti erozijskih pojavov v hudourni{kem obmo~ju. Omenjeni indeks mo~no vpliva na oceno magnitude drobirskega toka. 8 Viri in literatura Glej angle{ki del prispevka. 123