Natural Hazards and Earth System Science www.nat-hazards-earth-syst-sci.net 1561-8633 1684-9981 8 4 2008 10.5194/nhess-8-685-2008 http://www.nat-hazards-earth-syst-sci.net/8/685/2008/ http://www.nat-hazards-earth-syst-sci.net/8/685/2008/nhess-8-685-2008.html http://www.nat-hazards-earth-syst-sci.net/8/685/2008/nhess-8-685-2008.pdf 685 705 2008-07-16 Regional evaluation of three day snow depth for avalanche hazard mapping in Switzerland D. Bocchiola daniele.bocchiola@polimi.it E. Bianchi Janetti E. Gorni C. Marty B. Sovilla Dept. of Hydraulic, Environmental, Surveying and Road Structures Engineering, Politecnico di Milano, L. Da Vinci Square 32, 20133 Milano, Italy WSL, Swiss Federal Institute for Snow and Avalanche Research SLF, Flüelastr. 11, 7260 Davos Dorf, Switzerland The distribution of the maximum annual three day snow fall depth <i>H₇₂</i>, used for avalanche hazard mapping according to the Swiss procedure (<i>Sp</i>), is investigated for a network of 124 stations in the Alpine part of Switzerland, using a data set dating back to 1931. Stationarity in time is investigated, showing in practice no significant trend for the considered period. Building on previous studies about climatology of Switzerland and using an iterative approach based on statistical tests for regional homogeneity and scaling of <i>H₇₂</i> with altitude, seven homogenous regions are identified. A regional approach based on the index value is then developed to estimate the <i>T</i>-years return period quantiles of <i>H₇₂</i> at each single site <i>i</i>, <i>H_72i(T)</i>. The index value is the single site sample average &mu;_{<i>H_72i</i>}. The dimensionless values of <i>H^*_72i=H_72i / &mu;_{H_72i}</i> are grouped in one sample for each region and their frequency of occurrence is accommodated by a General Extreme Value, GEV, probability distribution, including Gumbel. The proposed distributions, valid in each site of the homogeneous regions, can be used to assess the <i>T</i>-years return period quantiles of <i>H^*_72i</i>. It is shown that the value of <i>H_72i(T)</i> estimated with the regional approach is more accurate than that calculated by single site distribution fitting, particularly for high return periods. A sampling strategy based on accuracy is also suggested to estimate the single site index value, i.e. the sample average &mu;_{<i>H_72i</i>}, critical for the evaluation of the distribution of <i>H_72i</i>. The proposed regional approach is valuable because it gives more accurate snow depth input to dynamics models than the present procedure based on single site analysis, so decreasing uncertainty in hazard mapping procedure. Ancey, C. and Meunier, M.: Utilizzo di tecniche statistiche per la determinazione di scenari di valanghe di riferimento e aiuto alla decisione (Use of statistical techniques for the definition of avalanche scenarios and as a support for decisions), Proc. of TRACE 99 (Table Ronde Avalanche Control in Europe), Breuil Cervinia, Italy, 19–20 April 1999, 47–58, 1999 (in Italian). Ancey, C., Meunier, M., and Richard, D.: Inverse problem in avalanche dynamics models, Water Resour. Res., 39(4), 1099, doi:10.1029/2002WR001749, 2003. Ancey, C., Gervasoni, C. and Meunier, M.: Computing extreme avalanches, Cold Reg. Sci. Technol., 39, 161–180, 2004. Baeriswyl, P. A. and Rebetez, M.: Regionalization of precipitation in Switzerland by means of principal components analysis, Theor. App. Climatol., 58, 31–41, 1997. Barbolini, M., Natale, L., Cordola, M., and Tecilla, G.: Guidelines for mapping of avalanche hazard prone areas (Linee Guida metodologiche per la perimetrazione delle aree esposte al pericolo di valanghe), Neve e Valanghe, 53, 6–13, 2004 (in Italian with abstract in English). Barbolini, M., Cappabianca F., and Savi, F.: A new method for estimation of avalanche distance exceeded probability, Surv. Geophys., 24, 587–601, 2003. Barbolini, M., Gruber, U., Keylock, C. J., Naaim, M., and Savi, F.: Application of statistical and hydraulic-continuum dense-snow avalanche models to five real European sites, Cold Reg. Sci. Technol., 31, 133–149, 2000. Barbolini, M., Natale, L., and Savi, F.: Effect of release conditions uncertainty on avalanche hazard mapping, Nat. Hazards, 25, 225–244, 2002. Bartelt, P., Salm, B., and Gruber, U.: Calculating dense-snow avalanche runout using a Voellmy-fluid model with active/passive longitudinal straining, J. Glaciol., 45, 242–254, 1999. Bayazit, M. and Önöz, B.: Sampling variances of regional flood quantiles affected by inter site correlation, J. Hydrol., 291, 1–2, 42–51, 2004. Bianchi Janetti, E. and Gorni, E.: Avalanche dynamics calculations: a study on snow cover height in Switzerland with regional approach, Master Thesis, Politecnico di Milano, available at: http://www.diiar.polimi.it/cimi/persona.asp?id=35, 2007. Bianchi Janetti, E., Gorni, E., Sovilla, B., and Bocchiola, D.: Regional snow depth estimates for avalanche calculations using a 2d model with snow entrainment, Ann. Glaciol., 49, 8 pp., 2008. Bocchiola, D., De Michele, C., and Rosso, R.: Review of recent advances in index flood estimation, Hydrol. Earth Syst. Sci., 7(3), 283–296, 2003. Bocchiola, D., Medagliani, M., and Rosso, R.: Regional snow depth frequency curves for avalanche hazard mapping in central Italian Alps, Cold Reg. Sci. Technol., 46, 3, 204–221, 2006. Bocchiola, D. and Rosso, R.: The distribution of daily Snow Water Equivalent in the Central Italian Alps, Adv. Water Resour., 30, 135–147, 2007. Bohr, G. S. and Aguado, E.: Use of April 1 SWE measurements as estimates of peak seasonal snowpack and total cold-season precipitation, Water Resour. Res., 37, 1, 51–60, 2001. Bründl, M., Etter, H. J., Steiniger, M., Klingler, C., Rhyner, J., and Ammann, W. J.: IFKIS: a basis for managing avalanche risk in settlements and on roads in Switzerland., Nat. Hazards Earth Syst. Sci., 4, 257–262, 2004. Büchele, B., Kreibich, H. , Kron, A., Thieken, A., Ihringer, J., Oberle, P., Merz, B., and Nestmann, F.: Flood-risk mapping: contributions towards an enhanced assessment of extreme events and associated risks, Nat. Hazards Earth Syst. Sci., 6, 485–503, 2006. Buishand, T. A.: Extreme rainfall estimation by combining data from several sites, Hydrol. Sci. J., 36, 345–365, 1991. Burkard, A. and Salm, B.: Die Bestimmung der mittleren Anrissmächtigkeit $d_0$ zur Berechnung von Fliesslawinen (Estimate of the average release depth $d_0$ for the calculation of flowing avalanches), Internal Report of the Swiss Federal Institute for Snow and Avalanche Research, No 668, Davos, Switzerland, 1992 (in German, also available in French under the title: Estimation de l'epaisseur moyenne de declenchement $d_0$ pour le calcul des avalanches coulantes, translated in French by C Ancey, Cemagref, 1994). Burlando, P. and Rosso, R.: Scaling and multifractal Depth-Duration-Frequency curves of storm precipitation, J. Hydrol., 187/1–2, 45–64, 1996. Burn, D. H.: Hydrologic effects of climatic change in westcentral Canada, J. Hydrol., 160, 53–70, 1994. Burn, D. H.: Catchment similarity for regional flood frequency analysis using seasonality measures, J. Hydrol., 202, 212–230, 1997. Burn, D. H.: Catchment similarity for regional flood frequency analysis using seasonality measures, J. Hydrol., 202, 212–230, 1997. Carroll, S. S.: Modeling measurement errors when estimating snow water equivalent, J. Hydrol., 127, 247–260, 1995. Castellarin, A., Burn, D. H., and Brath, A.: Assessing the effectiveness of hydrological similarity measures for flood frequency analysis, J. Hydrol., 241, 270–285, 2001. Cislaghi, M., De Michele, C., Ghezzi, A., and Rosso, R.: Statistical assessment of trends and oscillations in rainfall dynamics: Analysis of long daily Italian series, Atmos. Res., 77, 188–202, 2005. Cong, S., Li, Y., Vogel, J., and Shaake, J. C.: Identification of the underlying distribution form of precipitation by using regional data, Water Resources Res., 29, 1103–1111, 1993. Darlymple, T.: Flood frequency analysis, U.S. Geological Sur. Water Supply Pap., 1543-A, 1960. De Michele, C. and Rosso, R.: Uncertainty assessment of regionalized flood frequency estimates, J. Hydrol. Eng. ASCE, 6(6), 453–459, 2001. De Michele, C. and Rosso, R.: A multi-level approach to flood frequency regionalization, Hydrol. Earth Syst. Sci., 6, 185–194, 2002. Eglit, M. E. and Demidov, K. S.: Mathematical modeling of snow entrainment in avalanche motion, Cold Reg. Sci. Technol., 43, 10–23, 2005. Fuchs, S., Bründl, M., and Stötter, J.: Development of avalanche risk between 1950 and 2000 in the Municipality of Davos, Switzerland, Nat. Hazards Earth Syst. Sci., 4, 263–275, 2004. Fuchs, S. and McAlpin, M. C.: The net benefit of public expenditures on avalanche defence structures in the municipality of Davos, Switzerland, Nat. Hazards Earth Syst. Sci., 5, 319–330, 2005. Greenwood, J. A., Landwehr, J. M., Matalas, N. C., and Wallis, J. R.: Probability weighted moments: definition and relation to parameters of several distributions expressable in inverse form, Water Resour. Res., 15, 1049–1054, 1979. GREHYS: Presentation and review of some methods for regional frequency analysis, 186, J. Hydrol., 63–84, 1996. Haegeli, P. and McClung, D. M.: Expanding the snow climate classification with avalanche-relevant information: initial description of avalanche winter regimes for southwestern Canada, J. Glaciol., 53, 181, 266–276, 2007. Harbitz, C. B.: A survey of computational models for snow avalanche motion, NGI Report, 581220-1, Norwegian Geotechnical Institute, Oslo, 1998. Hopf, J.: An overview of natural hazard zoning with special reference to avalanches, in: Proceedings of the Anniversary Conference for the 25 Years of Snow Avalanche Research at NGI, Voss, Norway, 12–16 May 1998, NGI Publications No 203, 28–35, 1998. Hosking, J. R., Wallis, J. R., and Wood, E. F.: An appraisal of the regional flood frequency procedure in the UK flood studies report, Hydrol. Sci. J., 30, 85–109, 1985. Hosking, J. R. M.: The theory of probability weighted moments, Res. Rep. RC12210, IBM Res., Yorktown Heights, N.Y., 1986 Hosking, J. R. M. and Wallis, J. R.: The effect of inter site dependence on regional flood frequency analysis, Water Resour. Res., 24(4), 588–600, 1988. Hosking, J .R. M.: L-moments: analysis and estimation of distributions using linear combination of order statistics, J. R. Stat. Soc. Ser. B, 52, 105–124, 1990. Hosking, J .R. M. and Wallis, J. R.: Some statistics useful in regional frequency analysis, Water Resour. Res., 29(2), 271–281, 1993. Jiang, T., Su, B., and Hartmann, H.: Temporal and spatial trends of precipitation and river flow in the Yangtze River Basin, 1961–2000, Geomorphology, 85, 143–154, 2007. Katz, R. W., Parlange, M. B., and Naveau, P.: Statistics of extremes in hydrology, Adv. Water Resour., 25, 1287–1304, 2002. Keiler, M., Sailer, R, Jörg, P., Weber, C., Fuchs , S., Zischg, A., and Sauermoser, S.: Avalanche risk assessment: a multi-temporal approach, results from Galtür, Austria, Nat. Hazards Earth Syst. Sci, 6, 637–651, 2006. Keylock, C. J.: An alternative form for the statistical distribution of extreme avalanche runout distances, Cold Reg. Sci. Technol., 42, 185–193, 2005. Kottegoda, N. and Rosso, R.: Statistics, Probability and Reliability for Civil and Environmental Engineers, Mc. Graw-Hill, 1997. Laternser M.: Snow and avalanche climatology of Switzerland, Diss. ETH Zurich No 14493, available at: http://e-collection.ethbib.ethz.ch/show?type=diss&nr=14493, 2002. Laternser, M. and Schneebeli, M.: Temporal trend and spatial distribution of avalanche activity during the last 50 years in Switzerland, Nat. Hazards, 27, 201–230, 2002. Laternser, M. and Schneebeli, M.: Long-term snow climate trends of the Swiss Alps (1931–99), Int. J. Climatol., 23, 733–750, 2003. Lu, L. H. and Stedinger, J. R.: Sampling variance of normalized GEV/PWM quantile estimators and a regional homogeneity test, J. Hydrol., 138, 223–245, 1992a. Lu, L. H. and Stedinger, J. R.: Variance of two and three parameter GEV/PWM quantile estimators: formulae, confidence intervals, and a comparison, J. Hydrol., 138, 247–267, 1992b. Madsen, H., Pearson, C. P., and Rosbjerg, D.: Comparison of annual maximum series and partial duration series methods for modeling extreme hydrologic events 2. Regional modelling, Water Resour. Res., 33(4), 759–769, 1997. McClung, D. M. and Mears, A. I.: Extreme value prediction of snow avalanche runout, Cold Reg. Sci. Technol., 19, 163–175, 1991. Menabde, M. and Sivapalan, M.: Modelling of rainfall time series and extremes using bounded random cascades and Levy-stable distributions, Water Resour. Res., 36(11), 3293–3300, 2000. Naaim, M., Faug, T., and Naaim-Bouvet, F.: Dry granular flow modelling including erosion and deposition, Surv. Geophys., 24(5), 569–585, 2003. Naaim, M., Naaim-Bouvet, F., Faug, T., and Bouchet, A.: Dense snow avalanche modeling: flow, erosion, deposition and obstacle effects, Cold Reg. Sci. Technol., 39, 193–204, 2004. Natale, L., Barbolini, M., and Savi, F.: Perimetrazione delle aree esposte al pericolo di valanghe con metodologia di tipo Monte Carlo (Mapping of avalanche prone areas using a Monte Carlo approach), Neve e valanghe, 43, 32–41, 2001 (in Italian). Rao, C. R. and Hamed, K. H.: Flood Frequency Analysis, CRC Press, Boca Raton, FL, 1999. Robson, A. and Reed, D.: Flood estimation handbook (FEH), Institute of Hydrology, Wallingford, U.K., Vol 3, 1999. Rohrer, M. B., Braun, L. N., and Lang, H.: Long Term Records of Snow Cover Water Equivalent in The Swiss Alps: 1. Analysis, Nord. Hydrol., 25, 53–64, 1994. Salm, B., Burkard, A., and Gubler, H.: Berechnung von Fliesslawinen: eine Anleitung für Praktiker mit Beispielen (Avalanche calculations: a practical method with examples), Eidg. Inst. Schnee- und Lawinenforsch. Mitt., 47, 41 pp., 1990 (in German). Salvadori, G., De Michele, C., Kottegoda, N., and Rosso, R.: Extremes in Nature: An Approach Using Copulas, Springer: Complexity, Dordrecht, 2007. Skaugen, T.: Estimating the mean areal snow water equivalent by integration in time and space, Hydrol. Process., 13, 2051–2066, 1999. Skaugen, T. and Vǽringstad, T.: A methodology for regional flood frequency estimation based on scaling properties, Hydrol. Process., 19, 1481–1495, 2005. SLF: Der Lawinenwinter 1999, Ereignisanalyse (The avalanches in winter 1999. Analysis of the events), Davos, Eidg. Institut für Schnee- und Lawinenforschung, 588 pp., ISBN 3-905620-80-4, 2000. Sovilla, B. and Bartelt, P.: Observations and modelling of snow avalanche entrainment, Nat. Hazards, 2, 169–179, 2002. Sovilla, B., Burlando, P., and Bartelt, P.: Field experiments and numerical modelling of mass entrainment in snow avalanches, J. Geophys. Res., 111, F03007, doi:10:1029/2005JF000391, 2006. Sovilla, B., Margreth, S., and Bartelt, P.: On snow entrainment in avalanche dynamics calculations, Cold Reg. Sci. Technol., 47, 69–79, 2007. Stedinger, J .R., Vogel, R .M., and Foufoula Georgiou, E.: Frequency analysis of extreme events, in: Handbook of Hydrology, Chap 18, edited by: Maidment D. R., McGraw Hill, 1992. Sveinsson, O., Boes, G. B., Duane C., and Salas, J. D.: Population index flood method for regional frequency analysis, Water Resour. Res., 37(11), 2733–2748, 2001. Valeo, C., Beaty, K., and Hesslein, R.: Influence of forest fires on climate change studies in the central boreal forest of Canada, J. Hydrol., 280, 91–104, 2003. Wiltshire, S. E.: Regional floods frequency analysis I: Homogeneity statistics, Hydrol. Sci. J., 31, 3–9, 1986.