Discriminatory Power of Heterogeneity Statistics with Respect to Error of Precipitation Quantile Estimation
Publication: Journal of Hydrologic Engineering
Volume 20, Issue 10
Abstract
At low sample size, sampling error may be reduced by pooling multiple gauge records. This creates an error component due to heterogeneity, the degree to which the pooled regional data’s quantile estimates are different from the true at-site quantiles. Heterogeneity statistics attempt to quantify the degree to which error is added due to regional heterogeneity. They are justified through elucidation of a so-called reasonable proxy relationship with error caused by heterogeneity and through the ability of heterogeneity thresholds to detect heterogeneous regions. In this paper, previous findings regarding three heterogeneity statistics are revisited; a previous finding that is superior to and is amended based on simulation experiments and upon enumeration of all possible regionalizations of a small gauge dataset across time scales from daily to monthly. Thresholds defined based on are shown to be too high for application to and new thresholds are derived for . Two nonparametric heterogeneity statistics are tested and found to achieve only the unsatisfactory performance level of .
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Acknowledgments
Data was provided by the State Climatology Office, Minnesota Department of Natural Resources, Division of Ecological and Water Resources. The writers thank Jason Giovannettone for assistance. Financial support provided by the George Mason University Presidential Scholarship is gratefully acknowledged.
References
Abida, H., and Ellouze, M. (2006). “Hydrological delineation of homogeneous regions in Tunisia.” Water Resour. Manage., 20(6), 961–977.
Adamowski, K., Alila, Y., and Pilon, P. J. (1996). “Regional rainfall distribution for Canada.” Atmos. Res., 42(1–4), 75–88.
Alila, Y. (1999). “A hierarchical approach for the regionalization of precipitation annual maxima in Canada.” J. Geophys. Res., 104(D24), 31645–31655.
Atiem, I. A., and Harmancioğlu, N. B. (2006). “Assessment of regional floods using L-moments approach: The case of the River Nile.” Water Resour. Manage., 20(5), 723–747.
Bradley, A. A. (1998). “Regional frequency analysis methods for evaluating changes in hydrologic extremes.” Water Resour. Res., 34(4), 741–750.
Burn, D. H., and Goel, H. K. (2000). “The formation of groups for regional flood frequency analysis.” Hydrol. Sci. J., 45(1), 97–112.
Dalrymple, T. (1960). “Flood frequency analyses: Manual of hydrology: Part 3. Flood-flow techniques.”, Washington, DC.
Dikbas, F., Firat, M., Cem Koc, A., and Gungor, M. (2012). “Classification of precipitation series using fuzzy cluster method.” Int. J. Climatol., 32(10), 1596–1603.
Dodangeh, E., Soltani, S., Sarhadi, A., and Shiau, J. T. (2013). “Application of L-moments and Bayesian inference for low flow regionalization in Sefidroud basin, Iran.” Hydrol. Process., 28(4), 1663–1676.
Feng, J., Yan, D., Li, C., Gao, Y., and Liu, J. (2013). “Regional frequency analysis of extreme precipitation after drought event in the Heihe River basin, northwest China.” J. Hydrol. Eng., 1101–1112.
Gabriele, S., and Chiaravalloti, F. (2013). “Using the meteorological information for the regional rainfall frequency analysis: An application to Sicily.” Water Resour. Manage. 27(6), 1721–1735.
Gaume, E., Gaál, L, Viglione, A., Szolgay, J., Kohnová, S., and Blöschl, G. (2010). “Bayesian MCMC approach to regional flood frequency analyses involving extraordinary flood events at ungauged sites.” J. Hydrol., 394(1–2), 101–117.
Greenwood, J. A., Landwehr, J. M., Matalas, N. C., and Wallis, J. R. (1979). “Probability weighted moments: Definition and relation to parameters of several distributions expressable in inverse form.” Water Resour. Res., 15(5), 1049–1054.
Guse, B. F. (2010). “Improving flood frequency analysis by integration of empirical and probabilistic regional envelope curves.” Ph.D. thesis, Faculty of Mathematics and Natural Sciences, Univ. of Potsdam, Potsdam, Germany.
Guttman, N. B., Hosking, J. R. M., and Wallis, J. R. (1993). “Regional precipitation quantile values for the continental United States computed from L-moments.” J. Clim., 6(12), 2326–2340.
Hosking, J. R. M. (1990). “L-moments: Analysis and estimation of distributions using linear combinations of order statistics.” J. Roy. Stat. Soc. Ser. B, 52(1), 105–124.
Hosking, J. R. M. (2014). “Regional frequency analysis using L-moments.” R package, version 3.0, 〈http://CRAN.R-project.org/package=lmomRFA〉.
Hosking, J. R. M., and Wallis, J. R. (1997). Regional frequency analysis: An approach based on L-moments, Cambridge University Press, New York.
Hosking, J. R. M., Wallis, J. R., and Wood, E. F. (1985). “Estimation of the generalized extreme- value distribution by the method of probability-weighted moments.” Technometrics, 27(3), 251–261.
Huff, F. A., and Angel, J. R. (1992). “Rainfall frequency atlas of the Midwest.”, Illinois State Water Survey, Champaign, IL.
Hussain, Z. (2011). “Application of the regional flood frequency analysis to the upper and lower basins of the Indus River, Pakistan.” Water Resour. Manage., 25(11), 2797–2822.
Jingyi, Z., and Hall, M. J. (2004). “Regional flood frequency analysis for the Gan-Ming River basin in China.” J. Hydrol., 296(1–4), 98–117.
Kar, A. K., Goel, N. K., Lohani, A. K., and Roy, G. P. (2011). “Application of clustering techniques using prioritized variables in regional flood frequency analysis—Case study of Mahanadi basin.” J. Hydrol. Eng., 213–223.
Kjeldsen, T. R., Smithers, J. C., and Schulze, R. E. (2002). “Regional flood frequency analysis in the KwaZulu-Natal province, South Africa, using the index-flood method.” J. Hydrol., 255(1–4), 194–211.
Kyselý, J., and Picek, J. (2007). “Regional growth curve and improved design value estimates of extreme precipitation events in the Czech Republic.” Clim. Res., 33(3), 243–255.
Kyselý, J., Picek, J., and Huth, R. (2007). “Formation of homogeneous regions for regional frequency analysis of extreme precipitation events in the Czech Republic.” Studia Geophysica et Geodaetica, 51(2), 327–344.
Lettenmaier, D. P., Wallis, J. R., and Wood, E. F. (1987). “Effect of regional heterogeneity on flood frequency estimation.” Water Resour. Res., 23(2), 313–323.
Lin, G. F., and Chen, L. H. (2006). “Identification of homogeneous regions for regional frequency analysis using the self-organizing map.” J. Hydrol., 324(1–4), 1–9.
Lindley, D. V., and Smith, A. F. M. (1972). “Bayes estimates for the linear model.” J. Roy. Stat. Soc. Ser. B, 34(1), 1–41.
Marx, L., and Kinter, J. L., III. (2007). Estimating the representation of extreme precipitation events in atmospheric general circulation models using L-moments, Center for Ocean-Land Atmosphere Studies, Calverton, MD.
Modarres, R. (2008). “Regional frequency distribution type of low flow in north of Iran by L-moments.” Water Resour. Manage., 22(7), 823–841.
Modarres, R., and Sarhadi, A. (2011). “Statistically-based regionalization of rainfall climates of Iran.” Global Planet. Change, 75(1–2), 67–75.
Ngongondo, C. S., Xu, C. Y., Tallaksen, L. M., Alemaw, B., and Chirwa, T. (2011). “Regional frequency analysis of rainfall extremes in southern Malawi using the index rainfall and L-moments approaches.” Stochastic Environ. Res. Risk Assess., 25(7), 939–955.
Norbiato, D., Borga, M., Sangati, M., and Zanon, F. (2007). “Regional frequency analysis of extreme precipitation in the eastern Italian Alps and the August 29, 2003 flash flood.” J. Hydrol., 345(3–4), 149–166.
Noto, L. V., and Loggia, G. L. (2009). “Use of L-moments approach for regional flood frequency analysis in Sicily, Italy.” Water Resour. Manage., 23(11), 2207–2229.
Nuñez, J. H., Verbist, K., Wallis, J. R., Schaefer, M. G., Morales, L., and Cornelis, W. M. (2011). “Regional frequency analysis for mapping drought events in north-central Chile.” J. Hydrol., 405, 352–366.
Padoan, S. A., Ribatet, M., and Sisson, S. A. (2009). “Likelihood-based inference for max-stable processes.” J. Am. Stat. Assoc., 105(489), 263–277.
Parida, B. P., and Moalafhi, D. B. (2008). “Regional rainfall frequency analysis for Botswana using L-moments and radial basis function network.” Phys. Chem. Earth, 33(8–13), 614–620.
Perica, S., et al. (2013). NOAA Atlas 14: Precipitation-frequency atlas of the United States, version 2.0, Vol. 8, National Oceanic and Atmospheric Administration, Washington, DC.
Pham, H. X., Shamseldin, A. Y., and Melville, B. W. (2013). “Statistical properties of partial duration series and its implication on regional frequency analysis.” J. Hydrol. Eng., 1471–1480.
Rao, A. R., and Srinivas, V. V. (2006). “Regionalization of watersheds by fuzzy cluster analysis.” J. Hydrol., 318(1–4), 57–79.
R Foundation for Statistical Computing. (2012). R: A language and environment for statistical computing, Vienna, Austria.
Rianna, M., et al. (2012). “Definition of homogeneous regions through entropy theory.” Proc., ThirdSTAHY Int. Workshop on Statistical Methods for Hydrology and Water Resources and Management, Proc., 3rd Statistical Hydrology (STAHY) Int. Workshop Association of Hydrological Sciences, Wallingford, U.K.
Saf, B. (2010). “Assessment of the effects of discordant sites on regional flood frequency analysis.” J. Hydrol., 380(3–4), 362–375.
Santos, J. F., Portela, M. M., and Pulido-Calvo, I. (2011). “Regional frequency analysis of droughts in Portugal.” Water Resour. Manage., 25(14), 3537–3558.
Satyanarayana, P., and Srinivas, V. V. (2009). “Regional frequency analysis of annual precipitation in data-sparse regions using large-scale atmospheric variables.” Proc., Symp. HS.2 at the Joint Int. Association of Hydrological Sciences (IAHS) and Int. Association of Hydrogeologists (IAH) Convention, Wallingford, U.K.
Seckin, N., Cobaner, M., Yurtal, R., and Haktanir, T. (2013). “Comparison of artificial neural network methods with L-moments for estimating flood flow at ungauged sites: The case of East Mediterranean River basin, Turkey.” Water Resour. Manage., 27(7), 2103–2124.
Smithers, J. C., and Schulze, R. E. (2001). “A methodology for the estimation of short duration design storms in South Africa using a regional approach based on L-moments.” J. Hydrol., 241(1–2), 42–52.
Srinivas, V. V., Tripathi, S., Rao, A. R., and Govindaraju, R. S. (2008). “Reigonal flod frequency analysis by combining self-organizing feature map and fuzzy clustering.” J. Hydrol., 348(1–2), 148–166.
Stein, C. (1956). “Inadmissibility of the usual estimator for the mean of a multivariate normal distribution.” Proc., 3rd Berkeley Symp. on Mathematical Statistics and Probability, Vol. 1, University of California Press, Berkeley, CA, 197–206.
Szolgay, J., Parajka, J., Kohnová, S., and Hlavĉová, K. (2009). “Comparison of mapping approaches of design annual maximum daily precipitation.” Atmos. Res., 92(3), 289–307.
Um, M. J., Yun, H., Cho, W., and Heo, J. H. (2010). “Analysis of orographic precipitation on Jeju-Island using regional frequency analysis and regression.” Water Resour. Manage., 24(7), 1461–1487.
Viglione, A., Laio, F., and Claps, P. (2007). “A comparison of homogeneity tests for regional frequency analysis.” Water Resour. Res., 43(3), 1241–1249.
Vogel, R. M., and Fennessey, N. M. (1993). “L moment diagrams should replace product moment diagrams.” Water Resour. Res., 29(6), 1745–1752.
Yang, T., et al. (2010). “Regional frequency analysis and spatio-temporal pattern characterization of rainfall extremes in the Pearl River basin, China.” J. Hydrol., 380(3–4), 386–405.
Zrinji, Z., and Burn, D. H. (1994). “Flood frequency analysis for ungauged sites using a region of influence approach.” J. Hydrol., 153(1–4), 1–21.
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Journal of Hydrologic Engineering
Volume 20 • Issue 10 • October 2015
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© 2015 American Society of Civil Engineers.
History
Received: Mar 23, 2014
Accepted: Dec 11, 2014
Published online: Jan 27, 2015
Discussion open until: Jun 27, 2015
Published in print: Oct 1, 2015
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