IDF Curves Using the Frank Archimedean Copula
This article has a reply.
VIEW THE REPLYThis article has a reply.
VIEW THE REPLYPublication: Journal of Hydrologic Engineering
Volume 12, Issue 6
Abstract
This study aims at deriving intensity-duration-frequency (IDF) curves from bivariate rainfall frequency analysis using the copula method, which does not assume the rainfall variables to be independent or normal or have the same type of marginal distributions. The bivariate distributions are then employed to determine conditional return periods and IDF curves needed for urban drainage design. The IDF curves are tested using rainfall data from catchments in Louisiana and are also compared with those of Technical Paper 40 (TP-40) of the U.S. National Weather Service as well as those published in the literature.
Get full access to this article
View all available purchase options and get full access to this article.
References
Alila, Y. (2000). “Regional rainfall depth-duration-frequency equations for Canada.” Water Resour. Res., 36(7), 1767–1778.
Babak, N., Singh, V. P., and Yu, F. X. (1991). LADOTD 24-hour rainfall frequency maps and I-D-F curves, Louisiana Transportation Research Center, Baton Rouge, La.
Bacchi, B., Becciu, G., and Kottegoda, N. T. (1994). “Bivariate exponential model applied to intensities and durations of extreme rainfall.” J. Hydrol., 155, 225–236.
Baghirathan, V. R., and Shaw, E. M. (1978). “Rainfall depth-duration-frequency studies for Sri Lanka.” J. Hydrol., 37, 223–239.
Bell, F. C. (1969). “Generalized rainfall-duration-frequency relationships.” J. Hydr. Div., 95(1), 311–327.
Bernard, M. M. (1932). “Formulas for rainfall intensities of long durations.” Transactions, 96, 592–624.
Bouvette, T. C., Lambert, J. L., and Bedient, P. B. (1982). “Revised rainfall frequency analysis for Houston.” J. Hydr. Div., 108(4), 515–528.
Burlando, P., and Rosso, R. (1996). “Scaling and multiscaling models of depth-duration-frequency curves for storm precipitation.” J. Hydrol., 187, 45–64.
Chen, C.-L. (1983). “Rainfall intensity-duration-frequency formulas.” J. Hydraul. Eng., 109(12), pp. 1603–1621.
Chow, V. T. (1953). “Frequency analysis of hydrologic data with special application to rainfall intensities.” Univ. of Illinois Bulletin, 50(81).
Cunnane, C. (1978). “Unbiased plotting positions—A review.” J. Hydrol., 37(3), 205–222.
De Michele, C., Salvadori, G., Canossi, M., Petaccia, A., and Rosso, R. (2005). “Bivariate statistical approach to check adequacy of dam spillway.” J. Hydrol. Eng., 10(1), 50–57.
Dickinson, T. (1977). “Rainfall intensity-frequency relationships from monthly extremes.” J. Hydrol., 35, 137–145.
Dunn, C. N. (1986). “Generation of regional rainfall intensity-duration-frequency curves for Pennsylvania.” MS thesis, Pennsylvania State Univ., University Park, Pa.
Durrans, S. R., and Brown, P. A. (2002). “Development of an Internet-based rainfall atlas for Alabama.” Water Sci. Technol., 45(2), 11–17.
Favre, A.-C., El Adlouni, S., Perreault, L., Thiemonge, N., and Bobee, B. (2004). “Multivariate hydrological frequency analysis using copulas.” Water Resour. Res., 40, W01101.
Ferro, V., and Bagarello, V. (1996). “Rainfall depth-duration relationship for South Italy.” J. Hydrol. Eng., 1(4), 178–180.
Ferro, V., and Porto, P. (1999). “Regional analysis of rainfall-depth-duration equation for South Italy.” J. Hydrol. Eng., 4(4), 326–336.
Frederick, R. H., Meyers, V. A., and Auciollo, E. P. (1977). “Five- to precipitation frequency for the eastern and central United States.” NOAA Technical Memorandum NWS-Hydro-35, U.S. National Weather Service, Silver Spring, Md.
Froehlich, D. C. (1993). “Short-duration-rainfall intensity equations for drainage design.” J. Irrig. Drain. Eng., 119(5), 814–828.
Froehlich, D. C. (1995). “Long-duration-rainfall intensity equations.” J. Irrig. Drain. Eng., 121(3), 248–252.
Genest, C., and Mackay, L. (1986). “The joy of copulas: Bivariate distributions with uniform marginals.” Am. Stat., 40(4), 280–283.
Genest, C., and Rivest, L. (1993). “Statistical inference procedures for bivariate Archimedean copulas.” J. Am. Stat. Assoc., 88(424), 1034–1043.
Gert, A., Wall, D. J., White, E. L., and Dunn, C. N. (1987). “Regional rainfall intensity-duration-frequency curves for Pennsylvania.” Water Resour. Bull., 23(3), 479–486.
Grimaldi, S., Serinaldi, F., Napolitano, F., and Ubertini, L. (2005). “A 3-copula function application for design hyetograph analysis.” IAHS Publication No. 293, Int. Assoc. of Hydrological Sciences, Walling Ford, U.K.
Gringorten, I. I. (1963). “A plotting rule of extreme probability paper.” J. Geophys. Res., 68(3), 813–814.
Hargreaves, G. H. (1988). “Extreme rainfall for Africa and other developing areas.” J. Irrig. Drain. Eng., 114(2), 324–343.
Herr, H. D., and Krzysztofowicz, R. (2005). “Generic probability distribution of rainfall in space: The bivariate model.” J. Hydrol., 306, 237–264.
Hershfield, D. M. (1961). “Rainfall frequency atlas for the United States for durations from and return periods from .” Technical Paper 40, U.S. Weather Bureau, Washington, D.C.
Huff, F. A., and Angel, J. R. (1989). “Frequency distributions and hydroclimatic characteristics of heavy rainstorms in Illinois.” Bulletin 70, Illinois State Water Survey, Champaign, Ill.
Huff, F. A., and Angel, J. R. (1992). “Rainfall frequency atlas of the Midwest.” Bulletin 71, Illinois State Water Survey, Champaign, Ill.
Institution of Engineers. (1958). “Australian rainfall and runoff.” First Rep. of the Stormwater Standards Committee.
Joe, H. (1997). Multivariate models and dependence concepts, Chapman and Hall, New York.
Kelly, K. S., and Krzysztofowicz, R. (1997). “A bivariate meta-Gaussian density for use in hydrology.” Stochastic Hydrol. Hydraul., 11(1), 17–32.
Kothyari, U. C., and Garde, R. J. (1992). “Rainfall intensity-duration-frequency formula for India.” J. Hydraul. Eng., 118(2), 323–336.
Koutsoyiannis, D. (1996). Statistical hydrology, National Technical University Press, Athens, Greece.
Koutsoyiannis, D., Kozonis, D., and Manetas, A. (1998). “A mathematical framework for studying intensity-duration-frequency relationships.” J. Hydrol., 206, 118–135.
Long, D., and Krzysztofowicz, R. (1992). “Farlie-Gumbel-Morgenstern bivariate densities: Are they applicable in hydrology?” Stochastic Hydrol. Hydraul., 6(1), 47–54.
Long, D., and Krzysztofowicz, R. (1995). “A family of bivariate densities constructed from marginals.” J. Am. Stat. Assoc., 90(340), 739–746.
Maksimov, V. A. (1964). “An outstanding rainstorm in the Donbas.” Soviet hydrology: Selected paper, No. 1, American Geophysical Union, Washington, D.C. (English translation).
Miller, J. F., Frederick, R. H., and Tracey, R. J. (1973). “Precipitation-frequency atlas of the western United States.” NOAA Atlas II, National Weather Service, Silver Spring, Md.
Naghavi, B., Singh, V. P., and Yu, F. (1991). LADOTD 24-hour rainfall frequency maps and I-D-F curves, Louisiana Transport Research Center, Baton Rouge, La.
Naghavi, B., Singh, V. P., and Yu, F. X. (1993). “Development of rainfall frequency maps for Louisiana.” J. Irrig. Drain. Eng., 119(6), 1066–1080.
Nelsen, R. B. (1999). An introduction to copulas, Springer, New York.
Niemczynowicz, J. (1982). “Areal intensity-duration-frequency curves for short term rainfall events in Lund.” Nord. Hydrol., 13, 193–204.
Oyebande, L. (1982). “Deriving rainfall intensity-duration-frequency relationships fro regions with inadequate data.” Hydrol. Sci. J., 27(3/9), 353–367.
Reich, B. M. (1963). “Short-duration rainfall intensity estimates and other design aids for regions of sparse data.” J. Hydrol., 1(1), 3–28.
Salvatori, G., and De Michele, C. (2004). “Frequency analysis via copulas: Theoretical aspects and applications to hydrological events.” Water Resour. Res., 40(12), W12511.
Sherman, C. W. (1931). “Frequency and intensity of excessive rainfalls at Boston, Massachusetts.” Transactions, 95, 951–960.
Singh, K., and Singh, V. P. (1991). “Derivation of bivariate probability density functions with exponential marginals.” Stochastic Hydrol. Hydraul., 5, 55–68.
Sivapalan, M., and Bloschl, G. (1998). “Transformation of point rainfall to areal rainfall: Intensity-duration-frequency curves.” J. Hydrol., 204, 150–167.
Sklar, A. (1959). “Fonctions de Repartition à n Dimensions et Leurs Marges.” Publ. Inst. Stat. Univ. Paris, 8, 229–231.
Sreedharan, K. E., James, E. J., and Saseendran, S. A. (1990). “Regional rainfall depth-duration-frequency analysis for Southwest India.” J. Inst. Eng. (India), Part AG, 70, 187–192.
Trupl, J. (1959). “Relationships between intensities of short duration rainfalls and occurrence of thunderstorms.” Rep., Hydraulics Research Institute, Prague-Podbala, Czechoslovakia.
Vieira, D. B., and abd de Souza, C. Z. (1985). “Analysis of the relation intensity-duration-frequency of heavy rains for Ribierao Preto.” ICID Bull., 34(1), 49–55.
Yue, S. (2000a). “Joint probability distribution of annual maximum storm peaks and amounts as represented by daily rainfalls.” Hydroscience Journal, 45(2), 315–326.
Yue, S. (2000b). “The Gumbel logistic model for representing a multivariate storm event.” Adv. Water Resour., 24(2), 179–185.
Yue, S. (2000c). “The Gumbel mixed model applied to storm frequency analysis.” Water Resour. Manage., 14(5), 377–389.
Yue, S., Ouarda, T. B. M. J., Bobée, B., Legendre, P., and Bruneau, P. (1999). “The Gumbel mixed model for flood frequency analysis.” J. Hydrol., 226, 88–100.
Zhang, L. (2005). “Multivariate hydrological frequency analysis and risk mapping.” Ph.D. dissertation, Louisiana State Univ., Baton Rouge, La.
Zhang, L., and Singh, V. P. (2006). “Bivariate flood frequency analysis using the copula method.” J. Hydrol. Eng., 11(2), 150–164.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 12 • Issue 6 • November 2007
Pages: 651 - 662
Copyright
© 2007 ASCE.
History
Received: Sep 27, 2005
Accepted: Apr 10, 2007
Published online: Nov 1, 2007
Published in print: Nov 2007
Authors
Metrics & Citations
Metrics
Citations
Download citation
If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download.