The influence of the choice of method on the results of frequency analysis of peaks, volumes and durations of flood waves of the Sava River in Litija
- Authors: Mojca Šraj, Nejc Bezak, Mitja Brilly
- Citation: Acta hydrotechnica, vol. 25, no. 42, pp. 41-58, 2012.
- Abstract: Complex hydrological events such as floods always appear as a consequence of several correlated random variables (peak, volume, duration). Therefore single-variable frequency analysis can only provide limited assessment of these events. To fully understand all three variables and their relationship, a multivariate statistical approach is necessary. A precondition for such an approach is a complete analysis of all individual variables. 58 years of data from gauging station Litija on the Sava River were analyzed. Peaks, volumes and durations of flood waves were considered in the flood frequency analysis. Statistical and graphical tests were used to assess performance of the most commonly used distribution functions and parameter estimation techniques. Log-Pearson III distribution gave the best results in case of peaks and durations of flood waves and Pearson III distribution in case of volumes. Method of L-moments, which has not yet been used in Slovenian hydrological practice, gave the best estimation of parameters for most distributions.
- Keywords: flood frequency analysis, method of moments, method of L-moments, maximum likelihood method, marginal distributions, statistical tests
- Full text: a42ms.pdf
- References:
- Bezak, N. (2012). Verjetnostna analiza visokovodnih konic z metodo vrednosti nad izbranim pragom in z metodo letnih maksimumov (Flood frequency analysis with peaks over threshold method and annual maximum series method). Unpublished Thesis, Univerza v Ljubljani, FGG, 106 p. (in Slovenian).
- Brilly, M., Polič, M. (2005). Public perception of flood risks, flood forecasting and mitigation, Natural Hazards and Earth System Sciences, 5(3), 345–355.
- Brilly, M., Šraj, M. (2005). Osnove hidrologije. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo, 309 p. (in Slovenian).
- Đurović, B., Mikoš, M. (2004). Preventive management of risks due to natural hazards – Procedures in the alpime countries and in Slovenia, Acta hydrotechnica, 22(36), 17–35.
- Frantar, P., Hrvatin, M. (2008). ”Pretočni režimi” v P. Frantar (ur.), Vodna bilanca Slovenije 1971–2000. MOP ARSO, Ljubljana, 43–50.
- Favre, A. C., El Adlouni, S., Perreault, L., Thiemonge, N., Bobee, B. (2004). Multivariate hydrological frequency analysis using copulas, Water Resources Research, 40, W01101, doi:10.1029/2003WR002456.
- Genest, C., Favre, A. C. (2007). Everything you always wanted to know about copula modeling but were afraid to ask, Journal of Hydrologic Engineering, 12(4), 347–368.
- Grimaldi, S., Serinaldi, F. (2006). Asymmetric copula in multivariate flood frequency analysis, Advances in Water Resources, 29, 1155–1167.
- Haan, C. T. (2002). Statistical methods in hydrology. Iowa State Press, 496 p.
- Haddad, K., Rahman, A. (2010). Selection of the best fit flood frequency distribution and parameter estimation procedure: a case study for Tasmania in Australia. Stochastic Environmental Research and Risk Assessment, 25(3), 415–428.
- Hosking, J. R. M. (1990). L-moments: analysis and estimation of distributions using linear combinations of order statistic,Journal of the Royal Statistical Society: Series B (Statistical Methodology), 52(1), 105–124.
- Hosking, J. R. M., Wallis, J. R. (1997). Regional frequency analysis: an approach based on L-moments. Cambridge University Press, Cambridge, 224 p.
- Karmakar, S., Simonovic, S. P. (2008). Bivariate flood frequency analysis: Part 1. Determination of marginals by parametric and nonparametric techniques, Journal Flood Risk Management, 1(4), 190–200.
- Kobold, M., Zgonc, A., Sušnik, M. (2005). Uncertainty of precipitation measurements and predictions in flash flood modelling, Acta hydrotechnica, 23(39), 79–98.
- Kottegoda, N. T., Rosso, R. (2008). Applied statistics for civil and environmental engineers. Qxford, Blackwell Publishing, 718 p.
- Kučić, K. 2007. Metoda momentov L pri analizi visokih vod (Method of L-moments for flood frequency analysis). Unpublished Thesis, Univerza v Ljubljani, FGG, 85 p. (in Slovenian).
- Maidment, D. (1993). Handbook of hydrology. McGrow-Hill, New York, 1424 p.
- Mikoš, M., Brilly, M., Ribičič, M. (2004). Floods and landslides in Slovenia, Acta hydrotechnica, 22(37), 113–133.
- Pugelj, A. 2012. Analiza visokovodnih valov Save v Šentjakobu (Water wave analysis of Sava in Šentjakob). Unpublished Thesis, Univerza v Ljubljani, FGG, 98 p. (in Slovenian).
- Renard, B., Lang, M. (2007). Use of a Gaussian copula for multivariate extreme value analysis: Some case studies in hydrology, Advances in Water Resources, 30, 897–912.
- Ricci, V. (2005). Fitting distributions with R. http://cran.r-project.org/doc/contrib/Ricci-distributions-en.pdf (Pridobljeno 1. 3. 2012.).
- Salvadori, G., De Michele, C., (2004). Frequency analysis via copulas: Theory aspects and applications to hydrological events, Water Resources Researsch, 40, W12511, doi:10.1029/2004WR003133.
- Salvadori, G., De Michele, C. (2007). On the use of Copulas in hydrology: Theory and practice, Journal of Hydrologic Engineering, ASCE, 12(4), 369–380.
- Swanson, D. A., Tayman, J., Bryan, T. M. (2011). MAPE-R: a rescaled measure of accuracy for cross-sectional subnational population forecasts. Journal of Population Research, 28(2-3), 225–243.
- Šraj, M., Dirnbek, L., Brilly, M. (2010). The influence of effective rainfall on modeled runoff hydrograph, Journal of Hydrology and Hydromechanics, 58(1), 3–14.
- Turk, G. (2012). Verjetnostni račun in statistika. Ljubljana, Univerza v Ljubljani, Fakulteta za gradbeništvo in geodezijo, 264 p. (in Slovenian).
- Ulaga, F. (2011). Hidrološka postaja Litija na Savi, Naše okolje, 18(8), 81–85 (in Slovenian).
- Zhang, L., Singh, V. P. (2006). Bivariate Flood Frequency Analysis Using the Copula Method, Journal of Hydrologic Engineering, 11(2), 150–164.
- Zhang, L., Singh, V. P. (2007). Trivariate Flood Frequency Analysis Using the Gumbel-Hougaard Copula, Journal of Hydrologic Engineering, 12(4), 431–439.