Nonparametric Approach for Bivariate Drought Characterization Using Palmer Drought Index
Publication: Journal of Hydrologic Engineering
Volume 11, Issue 2
Abstract
A drought is usually represented by duration and severity, and may last several months or years. Multidimensional characteristics of a drought make univariate analysis unable to reveal the significant relationship among drought properties. Furthermore, historical records tend to be too short to fully evaluate drought characteristics. A practical method was proposed in this study to estimate the bivariate return period of droughts based on the use of synthetic data to overcome the above considerations. The bivariate return period of droughts is dependent on the drought interarrival time and the joint distribution of drought properties. A nonparametric method was employed in this study to estimate the joint distribution of drought properties. The historical droughts in the Conchos River Basin, Mexico were evaluated based on their return period estimated by the proposed method. The proposed method allowed a better understanding of the joint probabilistic behavior of droughts beyond the limitation of the univariate/parametric frequency analysis.
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Acknowledgments
This study is based upon works supported by SAHRA (Sustainability of semi-Arid Hydrology and Riparian Areas) at the University of Arizona under the STC Program of the National Science Foundation, Agreement No. NSFEAR-9876800. Dr. Bart Nijssen and Dr. Donald Davis at the University of Arizona and Dr. Javier Aparicio at Mexican Institute of Water Technology (IMTA) provided valuable comments. The comments of two anonymous reviewers considerably improved the manuscript. All contributions are gratefully acknowledged.
References
Alberts, T., and Karunamuni, R. J. (2003). “A semiparametric method of boundary correction for kernel density estimation.” Stat. Probab. Lett., 61, 287–298.
Bowman, A., and Azzalini, A. (1997). Applied smoothing techniques for data analysis: The kernel approach with -plus illustrations, Oxford University Press, New York.
Bras, R. L., and Rodríguez-Iturbe, I. (1984). Random functions and hydrology, Addison-Wesley, Reading, Mass.
Chow, V. T., Maidment, D. R., and Mays, L. W. (1988). Applied hydrology, McGraw–Hill, New York.
Dracup, J. A., and Kendall, D. R. (1990). “Floods and droughts.” Climate change and U.S. water resources, P. E. Waggoner, ed., Wiley, New York, 243–267.
Dracup, J. A., Lee, K. S., and Paulson, E. G. (1980). “On the definition of droughts.” Water Resour. Res., 16(2), 297–302.
González, J., and Valdés, J. B., (2003). “Bivariate drought recurrence analysis using tree rings reconstructions.” J. Hydrologic Eng., 8(5), 247–258.
Haan, C. T. (2002). Statistical methods in hydrology, The Iowa State University Press, Ames, Iowa.
Harrell, F. E., and Davis, C. E. (1982). “A new distribution free quantile estimator.” Biometrika, 69(3), 635–640.
International Boundary and Water Commission. (2002). “Deliveries of waters allotted to the United States under Article 4 of the United States–Mexico Water Treaty of 1944.” U.S. Section Rep., El Paso, Tex.
Kelly, M. E. (2001). “The Rio Conchos: A preliminary overview”. Texas Center for Policy Studies, Austin, Tex. ⟨http://www.texascenter.org/borderwater/⟩
Kim, T., and Valdés, J. B. (2003). “Nonlinear model for drought forecasting based on a conjunction of wavelet transforms and neural networks.” J. Hydrologic Eng., 8(6), 319–328.
Kim, T., and Valdés, J. B. (2005). “Synthetic generation of hydrologic time series based on nonparametric random generation.” J. Hydrologic Eng., 10(5), 395–404.
Kim, T., Valdés, J. B., and Aparicio, J. (2002). “Frequency and spatial characteristics of droughts in the Conchos River Basin, Mexico.” Water Int., 27(3), 420–430.
Kim, T., Valdés, J. B., and Yoo, C. (2003). “Nonparametric approach for estimating return periods of droughts in arid regions.” J. Hydrologic Eng., 8(5), 237–246.
Lall, U. (1995). “Recent advance in nonparametric function estimation: Hydrologic application.” Rev. Geophys., 33(S), 1093–1102.
Lall, U., and Moon, Y. (1993). “Kernel flood frequency estimators: Bandwidth selection and kernel choice.” Water Resour. Res., 29(4), 1003–1015.
Mathier, L., Perreault, L., Bobe, B., and Ashkar, F. (1992). “The use of geometric and gamma-related distributions for frequency analysis of water deficit.” Stochastic Hydrol. Hydr., 6(4), 239–254.
Oliveria, J. T. D. (1975). “Bivariate extremes: Extensions.” Bull. Internat. Statist. Inst., 46(2), 310–319.
Palmer, W. C. (1965). “Meteorological drought.” Research Paper No. 45, U.S. Weather Bureau, Washington, D.C.
Scott, D. W. (1992). Multivariate density estimation: Theory, practice and visualization, Wiley, New York.
Sen, Z. (1976). “Wet and dry periods of annual flows series.” J. Hydraul. Div., Am. Soc. Civ. Eng., 102(10), 1503–1514.
Sharma, A. (2000). “Seasonal to interseasonal rainfall probabilistic forecasts for improved water supply management: Part 3—A nonparametric probabilistic forecast model.” J. Hydrol., 239, 249–258.
Shiau, J., and Shen, H. W. (2001). “Recurrence analysis of hydrologic droughts of differing severity.” J. Water Resour. Plan. Manage., 127(1), 30–40.
Silverman, B. W. (1986). Density estimation for statistics and data analysis, Chapman and Hall, New York.
Smakhtin, V. U. (2001). “Low flow hydrology: A review.” J. Hydrol., 240, 147–186.
Stedinger, J. R., Vogel, R. M., and Foufoula-Georgiou, E. (1993). “Frequency analysis of extreme events.” Handbook of hydrology, D. R. Maidment, ed., McGraw–Hill, New York, 18.1–18.66.
Yevjevich, V. (1967). “An objective approach to definitions and investigations of continental hydrologic droughts.” Hydrology Papers, 23, Colorado State Univ., Fort Collins, Colo.
Yue, S., Ouarda, T. B. M. J., and Bobée, B. (2001). “A review of bivariate gamma distributions for hydrological application.” J. Hydrol., 246, 1–18.
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.
Information & Authors
Information
Published In
Journal of Hydrologic Engineering
Volume 11 • Issue 2 • March 2006
Pages: 134 - 143
Copyright
© 2006 ASCE.
History
Received: Feb 18, 2004
Accepted: Mar 11, 2005
Published online: Mar 1, 2006
Published in print: Mar 2006
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