Bias Correction to GEV Shape Parameters Used to Predict Precipitation Extremes
Publication: Journal of Hydrologic Engineering
Volume 21, Issue 10
Abstract
Previous studies have shown that the shape parameter of the generalized extreme-value (GEV) distribution, a distribution commonly applied in precipitation frequency analysis, is difficult to estimate from short records because of sampling bias. This bias is confirmed in the present study using annual precipitation maxima data from NOAA Atlas 14, which covers much of the United States and its territories. The bias depends on record length as well as on the magnitude of the population shape parameter. Correcting sample shape parameter estimates for bias yields extreme precipitation quantiles that are more conservative (i.e., higher) than would be obtained without a correction. For example, in a test case presented here, the bias correction increased the 1- and 24-h 10,000-year quantiles by 8 and 10%, respectively. This paper presents an expression and coefficients that may be used to develop approximately unbiased GEV shape parameter estimates for regions covered by NOAA Atlas 14.
Get full access to this article
View all available purchase options and get full access to this article.
Acknowledgments
The author would like to thank NOAA’s Office of Hydrologic Development for sharing the annual precipitation maxima data for Atlas 14, Volume 10, in advance of its publication. The author also acknowledges helpful comments from several anonymous reviewers of this paper; from Angelos Findikakis, Stewart Taylor, and Matthew Waterman on a precursor to this article; and helpful suggestions from John England at the outset of this work.
References
Cavanaugh, N. R., Gershunov, A., Panorska, A. K., and Kozubowski, T. J. (2015). “The probability distribution of intense daily precipitation.” Geophys. Res. Lett., 42(5), 1560–1567.
Cheng, L., and AghaKouchak, A. (2014). “Nonstationary precipitation intensity-duration-frequency curves for infrastructure design in a changing climate.” Sci. Rep., 4, 7093.
Fisher, R. A., and Tippett, L. H. C. (1928). “Limiting forms of the frequency distribution of the largest or smallest member of a sample.” Proc. Camb. Philos. Soc., 24(2), 180–190.
Hosking, J. R. M. (2005a). “Fortran routines for use with the method of L-moments, Version 3.04.”, IBM Research Division, Yorktown Heights, NY, 33.
Hosking, J. R. M. (2005b). “Version 3.04 of the L-moments codes.” 〈http://lib.stat.cmu.edu/general/lmoments〉 (Jul. 29, 2005).
Hosking, J. R. M., and Wallis, J. R. (2005). Regional frequency analysis: An approach based on L-moments, Cambridge University Press, New York, 224.
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.
Koutsoyiannis, D. (1999). “A probabilistic view of Hershfield’s method for estimating probable maximum precipitation.” Water Resour. Res., 35(4), 1313–1322.
Koutsoyiannis, D., Kozonis, D., and Manetas, A. (1998). “A mathematical framework for studying rainfall intensity-duration-frequency relationships.” J. Hydrol., 206(1-2), 118–135.
Kunkel, E. K., et al. (2013). “Probable maximum precipitation and climate change.” Geophys. Res. Lett., 40(7), 1402–1408.
Martins, E. S., and Stedinger, J. R., (2000). “Generalized maximum-likelihood generalized extreme-value quantile estimators for hydrologic data.” Water Resour. Res., 36(3), 737–744.
National Research Council. (1994). Estimating Bounds on Extreme Precipitation Events: A Brief Assessment, National Academy Press, Washington, DC, 29.
NOAA (National Oceanic and Atmospheric Administration). (1978). “Probable maximum precipitation estimates, United States East of the 105th Meridian.”, U.S. National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2006a). “Precipitation-frequency atlas of the United States.” NOAA Atlas 14, Volume 2, Version 3.0, Ohio River Valley and Surrounding States, G. Bonnin, D. Martin, B. Lin, T. Parzybok, M. Yekta, and D. Riley, National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2006b). “Precipitation-frequency atlas of the United States.” NOAA Atlas 14, Volume 3: Puerto Rico and the U.S. Virgin Islands, Version 2.0, G. Bonnin, D. Martin, B. Lin, T. Parzybok, M. Yekta, and D. Riley, National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2011b). “Precipitation-frequency atlas of the United States, Hawaiian Islands.” NOAA Atlas 14 Volume 4 Version 3, S. Perica, et al., eds., National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2011c). “Precipitation-frequency atlas of the United States, selected Pacific Islands.” NOAA Atlas 14 Volume 5 Version 3, S. Perica, et al., eds., National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2011a). “Precipitation-frequency atlas of the United States.” NOAA Atlas 14, Volume 1, Version 5.0: Semiarid Southwest, G. Bonnin, et al., eds., National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2012). “Precipitation-frequency atlas of the United States, Alaska.” NOAA Atlas 14 Volume 7 Version 2.0, S. Perica, et al., eds., National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2013a). “Precipitation-frequency atlas of the United States, Midwestern States.” NOAA Atlas 14 Volume 8 Version 2.0, S. Perica, et al., eds., National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2013b). “Precipitation-frequency atlas of the United States, Southeastern States.” NOAA Atlas 14 Volume 9 Version 2.0, S. Perica, et al., eds., National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2014). “Precipitation-frequency atlas of the United States, California.” NOAA Atlas 14 Volume 6 Version 2.3, S. Perica, et al., eds., National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2015). “NOAA Atlas 14, precipitation-frequency atlas of the United States.” Volume 10 Version 2.0: Northeastern States (Connecticut, Maine, Massachusetts, New Hampshire, New York, Rhode Island, Vermont), S. Perica, S. Pavlovic, M. St. Laurent, C. Trypaluk, D. Unruh, and O. Wilhite, National Weather Service, Silver Spring, MD.
NOAA (National Oceanic and Atmospheric Administration). (2016). “Precipitation frequency data server (PFDS).” 〈http://hdsc.nws.noaa.gov/hdsc/pfds/〉 (Feb. 26, 2016).
Ohara, N., Kavvas, M. L., Kure, S., Chen, Z. Q., Jang, S., and Tan, E. (2011). “Physically based estimation of maximum precipitation over American River Watershed, California.” J. Hydrol. Eng., 351–361.
Papalexiou, S. M., and Koutsoyiannis, D. (2006). “A probabilistic approach to the concept of probable maximum precipitation.” Adv. Geosci., 7, 51–54.
Papalexiou, S. M., and Koutsoyiannis, D. (2013). “Battle of extreme value distributions: A global survey on extreme daily rainfall.” Water Resour. Res., 49, 187–201.
Pilgrim, D. H. (2001). Australian rainfall and runoff, a guide to flood estimation, Institution of Engineers, Barton, ACT, Australia.
Salas, J. D., and Obeysekera, J. (2014). “Revisiting the concepts of return period and risk for nonstationary hydrologic extreme events.” J. Hydrol. Eng., 554–568.
Serinaldi, F., and Kilsby, C. G. (2014). “Rainfall extremes: Toward reconciliation after the battle of distributions.” Water Resour. Res., 50(1), 336–352.
Serinaldi, F., and C. G., Kilsby (2015). “Stationarity is undead: Uncertainty dominates the distribution of extremes.” Adv. Water Resour., 77, 17–36.
TVA (Tennessee Valley Authority). (1995). “Flood analyses for Department of Energy Y-12, ORNL, and K-25 plants: Flood analyses in support of flood emergency planning.” ES/CNPE-95/1, Knoxville, TN.
USBR (U.S. Bureau of Reclamation). (2004). “Hydrologic hazard curve estimating procedures.”, Dam Safety Research Program, Denver.
USBR (U.S. Bureau of Reclamation). (2011). “Review of probable maximum precipitation procedures and databases used to develop hydrometeorological reports.” Denver.
U.S. DOE (U.S. Department of Energy). 2012. “Natural phenomena hazards analysis and design criteria for DOE facilities.” DOE-STD-1020-2012, Washington, DC.
U.S. NRC (U.S. Nuclear Regulatory Commission). (2013). Proc., Workshop on Probabilistic Flood Hazard Assessment (PFHA), Washington, DC.
van Oldenborgh, G. J., et al. (2013). “Annex I: Atlas of global and regional climate projections.” Climate Change 2013: The Physical Science Basis. Contribution of Working Group I to the 5th Assessment Rep. of the Intergovernmental Panel on Climate Change, T. F. Stocker, et al., eds., Cambridge University Press, Cambridge, U.K.
Water Resources Council. (1982). “Guidelines for determining flood flow frequency, bulletin 17B of the hydrology subcommittee.” Interagency Advisory Committee on Water Data, U.S. Geological Survey, Reston, VA.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 21 • Issue 10 • October 2016
Copyright
© 2016 American Society of Civil Engineers.
History
Received: Oct 13, 2015
Accepted: Mar 31, 2016
Published online: Jun 9, 2016
Published in print: Oct 1, 2016
Discussion open until: Nov 9, 2016
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.