Quantile estimation of probability distributions for maximum daily precipitation and short time series of observational data for engineering design

• Autorzy: Kuchar Leszek , Broszkiewicz-Suwaj Ewa

Identyfikatory

DOI

10.37190/epe220103

• Języki publikacji: EN

Abstrakty

EN

Knowledge of the distribution quantiles of precipitation maximum amounts is required in many fields concerning engineering design or hydrological risk assessment. When the number of observation years is small, it is not possible to fit the probability distribution function to maximum values and to calculate quantiles. This paper presents a procedure for calculating the quantiles of the probability distribution of daily precipitation maximums over a year using stochastic convergence of distributions. The distribution series of random variables, defined based on the cut-off sample with the elimination of the smallest values, made it possible to determine the quantiles for times series of order α of the distribution. These values were approximated by a function from the exponential class and then extrapolated to obtain quantiles for the distribution of maxima. The resulting quantile estimates, for short time series, were corrected using the kurtosis of the data used for estimation, which leads to a very large error reduction.

Słowa kluczowe

EN

stochastic method; daily precipitation; Pareto law

PL

metoda stochastyczna; opad dobowy; prawo Pareto

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Environment Protection Engineering
• Rocznik: 2022
• Tom: Vol. 48, nr 1
• Strony: 35--50
• Opis fizyczny: Bibliogr. 26 poz., rys., tab.

Twórcy

autor

Kuchar Leszek

• Wrocław University of Environmental and Life Sciences, Department of Applied Mathematics, Grunwaldzka 53, 50-357 Wrocław, Poland

• https://orcid.org/0000-0002-4157-0910

autor

Broszkiewicz-Suwaj Ewa

• https://orcid.org/0000-0001-9346-0118

Bibliografia

• [1] BZYMEK B., JAROSIŃSKA E., The effects of catchment surface sealing on stormwater runoff, J. Techn., 2012, 109 (4), 41–57 (in Polish).
• [2] ROMANIAK A., Assessment of the relation between atmospheric precipitation and rainwater runoff for various urban surfaces, J. Water Land Dev., 2017, 32 (1–3), 87–94. DOI: 10.1515/jwld-2017-0010.
• [3] KAŹMIERCZAK B., KOTOWSKI A., The influence of precipitation intensity growth on the urban drainage systems designing, Theor. Appl. Clim., 2014, 118 (1–2), 285–296. DOI: 10.1007/s00704-013-1067-x.
• [4] LARSEN A.N., GREGERSEN I.B., CHRISTENSEN O.B., LINDEJ J., MIKKELSEN P.S., Potential future increase in extreme one-hour precipitation events over Europe due to climate change, Water Sci. Techn., 2009, 60 (9), 2205–2216. DOI: 10.2166/wst.2009.650.
• [5] JENNINGS D.B., JARNAGIN S.T., Changes in anthropogenic impervious surfaces, precipitation and daily streamflow discharge: a historical perspective in a mid-atlantic subwatershed, Land. Ecol., 2002, 17 (5), 471–489.
• [6] VALTANEN M., SILLANPAA N., SETATA H., Effects of land use intensity on stormwater runoff and its temporal occurrence in cold climates, Hydr. Proc., 2014, 28 (4), 2639–2650. DOI: 10.1002/hyp.9819.
• [7] DIETZ M.E., Low impact development practices: A review of current research and recommendations for future directions, Water Air Soil Poll., 2007, 186, 351–363. DOI: 10.1007/s11270-007-9484-z.
• [8] KOTOWSKI A., KAŹMIERCZAK B., DANCEWICZ A., Modeling precipitation for sewer sizing, Institute of Fundamental Technological Research, Polish Academy of Sciences, Warsaw 2010 (in Polish).
• [9] DIETZ M.E., CLAUSEN J.C., Stormwater runoff and export changes with development in a traditional and low impact subdivision, J. Environ. Manage., 2008, 87 (4), 560–566. DOI: 10.1016/j.jenvman.2007.03.026.
• [10] GLASER R., BRÁZDIL R., PFISTER C., DOBROVOLNY P., BARRIENDOS VALLVE M., BOKWA A., CAMUFFO D., KOTYZA O., LIMANÓWKA D., RACZ L., RODRIGO F.S., Seasonal temperature and precipitation fluctuations in selected parts of europe during the sixteenth century, Clim. Change, 1999, 43, 169–200. DOI: 10.1023/A:1005542200040.
• [11] KHARIN V.V., ZWIERS F.W., Estimating extremes in transient climate change simulations, J. Clim., 2005, 18 (8), 1156–1173. DOI: 10.1175/JCLI3320.1.
• [12] FRANCIS T., Extreme Precipitation Analysis at Sizewell: Final Report, MetOffice, UK, 2011.
• [13] HOSKING J.R.M., WALLIS J.R., Parameter and quantile estimation for the generalized Pareto distribution, technometrics, 1987, 29 (3), 339–349, http://www.jstor.org/stable/1269343
• [14] KAŹMIERCZAK B., WDOWIKOWSKI M., Maximum rainfall model based on archival pluviographic records- case study for Legnica (Poland), Per. Polyt. Civil Eng., 2016, 60 (2), 305–312, DOI: 10.3311/PPci.8341.
• [15] KUCHAR L., BROSZKIEWICZ-SUWAJ L., Quantile estimation of probability distributions for maximum daily precipitation and short time series of observational data, [In:] T. Kałuża (Ed.), Modelling of hydrological processes, Modelling issues in the water management sector, Bogucki Wydawnictwo Naukowe, Poznań 2020, 55–66 (in Polish).
• [16] FORESTIERI A., LO CONTI F., BLENKINSOP S., CANNAROZZO M., FOWLER H.J., NOTO L.V., Regional frequency analysis of extreme rainfall in Sicily (Italy), Int. J. Clim., 2018, 38, e698–e716. DOI:10.1002/joc.5400.
• [17] LI L., YAO N., LIU D.L., SONG S., LIN H., CHEN X., LI Y., Historical and future projected frequency of extreme precipitation indicators using the optimized cumulative distribution functions in China, J. Hydr., 2019, 124170, DOI: 10.1016/j.jhydrol.2019.124170.
• [18] KUCHAR L., Using WGENK to generate synthetic daily weather data for modelling of agricultural processes, Math. Comp. Symul., 2004, 65, 69–75. DOI: 10.1016/j.matcom.2003.09.009.
• [19] KUCHAR L., Weather generation with a new approach to rainfall variance estimation and seasonal correlation of variables for crop production modelling, Agrophys., 2011, 1 (4), 40–46.
• [20] KUCHAR L., IWANSKI S., JELONEK L., SZALINSKA W., Application of spatial weather generator for the assessment of climate change impacts on a river runoff, Geografie, 2014, 119 (1), 1–25.
• [21] MILLARD S.P., NEERCHAL N.K., Environmental statistics with S-PLUS, CRC Press, Boca Raton 2000.
• [22] WALPOLE R.E., MYERS R.H., MYERS S.L., YE K., Probability and statistics for engineers and scientists, 7th Ed. Prentice Hall, New York 2002.
• [23] KUCHAR L., IWAŃSKI S., Evaluation of multisite synthetic data generated by spatial weather generator and long climate data series, EKO-DOK 2018 E3S Web of Conferences, 2018, 44, 00083. DOI: 10.1051/e3sconf/20184400083.
• [24] GUMBEL E.J., The statistics of extremes, Columbia University Press, New York 1960.
• [25] STEDINGER J.R., VOGEL R.M., FOUFOULA-GEORGIOU E., Frequency analysis of extreme events, [In:] D.R. Maidment (Ed.), Handbook of hydrology, McGraw-Hill, 1993.
• [26] KOTOWSKI A., KAŹMIERCZAK B., Probabilistic models of maximum precipitation for designing sewerage, J. Hydrom., 2013, 14 (6), 1958–1965. DOI: 10.1175/JHM-D-13-01.1.