Risk Assessment of Hydroclimatic Variability on Groundwater Levels in the Manjara Basin Aquifer in India Using Archimedean Copulas
Publication: Journal of Hydrologic Engineering
Volume 17, Issue 12
Abstract
In this paper, a bivariate-copula-based methodology is presented to assess the risk associated with hydroclimatic variability on groundwater levels in an unconfined aquifer at the Manjara basin in India. Rank correlation analysis is used to identify the association between the El Niño–Southern Oscillation (ENSO) index, precipitation, and groundwater levels. It is found that the dependencies among the hydroclimatic variable pairs are statistically significant and the dependence structure can be modeled by using bivariate Archimedean copulas. The groundwater level or depth-to-groundwater table (DGWT) in the study region is found to be responsive toward interannual precipitation variations that are influenced by the ENSO phenomenon. For probabilistic representation of hydroclimate variables, various probability distributions are evaluated and it is found that the precipitation and DGWT are best fitted using lognormal and Weibull distributions, respectively, whereas the ENSO index is best fitted using nonparametric-based normal kernel density function. For modeling joint dependence structure of hydroclimatic variable pairs (precipitation-DGWT, ENSO index-precipitation, and ENSO index-DGWT), appropriate Archimedean copulas (viz, Ali-Mikhail-Haq, Clayton, Gumbel-Hougaard, and Frank families) are evaluated. On performing standard statistical tests, it is found that the Frank copula is best representing the joint dependence structure for all three variable pairs. Then the Frank copula-based joint distributions are used to derive conditional distributions and to perform risk analysis of groundwater levels. The study suggest that the copula-based methodology can be used effectively for modeling dependence structure of hydroclimatic variables and for risk assessment of groundwater levels under changes in hydroclimatic conditions.
Get full access to this article
View all available purchase options and get full access to this article.
References
Aghakouchak, A., Ciach, G., and Habib, E. (2010). “Estimation of tail dependence coefficient in rainfall accumulation fields.” Adv. Water Resour., 33(9), 1142–1149.
Barco, J., Hogue, T. S., Girotto, M., Kendall, D. R., and Putti, M. (2010). “Climate signal propagation in southern California aquifers.” Water Resour. Res., 46, W00F05.
Bárdossy, A. (2006). “Copula-based geostatistical models for groundwater quality parameters.” Water Resour. Res., 42(11), W11416.
Bárdossy, A., and Li, J. (2008). “Geostatistical interpolation using copulas.” Water Resour. Res., 44(7), W07412.
Central Ground Water Board (CGWB). (2009). “Groundwater information Osmanabad district Maharashtra.”, Ministry of Water Resources, New Delhi, India.
Chebana, F., and Ouarda, T. (2009). “Index flood-based multivariate regional frequency analysis.” Water Resour. Res., 45(10), W10435.
Chen, C.-C., Gillig, D., McCarl, B. A., and Williams, R. L. (2005). “ENSO impacts on regional water management: Case study of the Edwards Aquifer (Texas, USA).” Clim. Res., 28(2), 175–181.
Chowdhary, H., and Singh, V. P. (2010). “Reducing uncertainty in estimates of frequency distribution parameters using composite likelihood approach and copula-based bivariate distributions.” Water Resour. Res., 46(11), W11516.
Dijkstra, H. A. (2006). “The ENSO phenomenon: Theory and mechanisms.” Adv. Geosci., 6, 3–15.
Eltahir, E. A. B., and Yeh, P. J.-F. (1999). “On the asymmetric response of aquifer water level to floods and droughts in Illinois.” Water Resour. Res., 35(4), 1199–1217.
Fleming, S. W., and Quilty, E. J. (2006). “Aquifer responses to El Niño-Southern Oscillation, Southwest British Columbia.” Ground Water, 44(4), 595–599.
Freeze, R. A., and Cherry, J. A. (1979). Groundwater, Prentice Hall, Englewood Cliffs, NJ.
Gadgil, S., Rajeevan, M., and Francis, P. A. (2007). “Monsoon variability: Links to major oscillations over the equatorial Pacific and Indian oceans.” Curr. Sci., 93(2), 182–194.
Genest, C., and Favre, A.-C. (2007). “Everything you always wanted to know about copula modeling but were afraid to ask.” J. Hydrol. Eng., 12(4), 347–368.
Genest, C., and MacKay, J. (1986). “The joy of copulas: Bivariate distributions with uniform marginals.” Am. Stat., 40(4), 280–283.
Genest, C., and Rémillard, B. (2008). “Validity of the parametric bootstrap for goodness-of-fit testing in semiparametric models.” Ann. Inst. Henri Poincaré, 44(6), 1096–1127.
Genest, C., Rémillard, B., and Beaudoin, D. (2009). “Goodness-of-fit tests for copulas: A review and a power study.” Insurance: Math. Econ., 44(2), 199–213.
Ghosh, S. (2010). “Modelling bivariate rainfall distribution and generating bivariate correlated rainfall data in neighboring meteorological subdivisions using copula.” Hydrol. Processes, 24(24), 3558–3567.
Groundwater Survey and Development Agency (GSDA). (2009). “Dynamic groundwater resources of Maharashtra.”, Pune.
Gurdak, J. J. et al. (2007). “Climate variability controls on unsaturated water and chemical movement, High Plains aquifer, USA.” Vadose Zone J., 6(3), 533–547.
Hanson, R. T., Dettinger, M. D., and Newhouse, M. W. (2006). “Relations between climate variability and hydrologic time series from four alluvial basins across the southwestern United States.” Hydrogeol. J., 14(7), 1122–1146.
Janga Reddy, M., and Ganguli, P. (2012). “Application of copulas for derivation of drought severity-duration-frequency curves.” Hydrol. Processes, 26(11), 1672–1685.
Kao, S.-C., and Govindaraju, R. S. (2008). “Trivariate statistical analysis of extreme rainfall events via the Plackett family of copulas.” Water Resour. Res., 44(2), W02415.
Kao, S.-C., and Govindaraju, R. S. (2010). “A copula-based joint deficit index for droughts.” J. Hydrol., 380(1–2), 121–134.
Leonard, M., Metcalfe, A., and Lambert, M. (2008). “Frequency analysis of rainfall and streamflow extremes accounting for seasonal and climatic partitions.” J. Hydrol., 348(1–2), 135–147.
Maity, R., and Kumar, D. N. (2008). “Probabilistic prediction of hydroclimatic variables with nonparametric quantification of uncertainty.” J. Geophys. Res., 113, D14105.
Mayer, T. D., and Congdon, R. D. (2008). “Evaluating climate variability and pumping effects in statistical analyses.” Ground Water, 46(2), 212–227.
Nelsen, R. B. (1999). An introduction to copulas, Springer, New York.
Pant, G. B., and Parthasarathy, B. (1981). “Some aspects of an association between the Southern Oscillation and Indian summer monsoon.” Meteorol. Atmos. Phys., 29(3), 245–252.
Pelckmans, K. et al. (2003). “LS-SVMlab Toolbox User’s Guide: Release 1.5.” Technical Report no., Katholieke Universiteit Leuven, Leuven-Heverlee, Belgium.
Poulin, A., Huard, D., Favre, A.-C., and Pugin, S. (2007). “Importance of tail dependence in bivariate frequency analysis.” J. Hydrol. Eng., 12(4), 394–403.
Rajeevan, M., Pai, D. S., Dikshit, S. K., and Kelkar, R. R. (2004). “IMD’s new operational models for long-range forecast of southwest monsoon rainfall over India and their verification for 2003.” Curr. Sci., 86(3), 422–431.
Ropelewski, C. F., and Halpert, M. S. (1987). “Global and regional scale precipitation patterns associated with the El Niño/Southern Oscillation.” Mon. Weather Rev., 115(8), 1606–1626.
Salvadori, G., and De Michele, C. (2004). “Frequency analysis via copulas: Theoretical aspects and applications to hydrological events.” Water Resour. Res., 40(12), W12511.
Samaniego, L., Bárdossy, A., and Kumar, R. (2010). “Streamflow prediction in ungauged catchments using copula-based dissimilarity measures.” Water Resour. Res., 46(2), W02506.
Scott, C. A., and Shah, T. (2004). “Groundwater overdraft reduction through agricultural energy policy: Insights from India and Mexico.” Int. J. Water Resour. Dev., 20(2), 149–164.
Serinaldi, F. (2008). “Analysis of inter-gauge dependence by Kendall’s , upper tail dependence coefficient, and 2-copulas with application to rainfall fields.” Stochastic Environ. Res. Risk Assess., 22(6), 671–688.
Serinaldi, F., Bonaccorso, B., Cancelliere, A., and Grimaldi, S. (2009). “Probabilistic characterization of drought properties through copulas.” Phys. Chem. Earth, 34(10–12), 596–605.
Shah, T., Molden, D., Sakthivadivel, R., and Seckler, D. (2000). “The global groundwater situation: Overview of opportunities and challenges”. International Water Management Institute, Colombo, Sri Lanka.
Sklar, A. (1959). “Functions de repartition a n dimensions et leurs marges.” Publ. Inst. Stat. Univ. Paris, 8, 229–231.
Soman, M. K., and Slingo, J. M. (1997). “Sensitivity of the Asian summer monsoon to aspects of the sea surface temperature anomalies in the tropical Pacific Ocean.” Q. J. R. Meteorolog. Soc., 123(538), 309–336.
Suykens, J. A. K., and Vandewalle, J. (1999). “Least squares support vector machine classifiers.” Neural Process. Lett., 9(3), 293–300.
Todd, D. K. (1980). Groundwater hydrology, Wiley, New York.
Trenberth, K. E. (1997). “The definition of El-Niño.” Bull. Am. Meteorol. Soc., 78(12), 2771–2777.
Vapnik, V. N., Golowich, S., and Smola, A. (1997). “Support vector method for function approximation, regression estimation, and signal processing.” Adv. Neural Inf. Process. Syst., 9, 281–287.
Webster, P. J., and Yang, S. (1992). “Monsoon and ENSO: Selectively interactive systems.” Q. J. R. Meteorolog. Soc., 118(507), 877–926.
Wilks, D. S. (1995). “Statistical methods in atmospheric sciences”. International geophysics series, Vol. 59, Academic Press, New York.
Zhang, L., and Singh, V. P. (2006). “Bivariate flood frequency analysis using the copula method.” J. Hydrol. Eng., 11(2), 150–164.
Zhang, L., and Singh, V. P. (2007). “Trivariate flood frequency analysis using the Gumbel Hougaard copula.” J. Hydrol. Eng., 12(4), 431–439.
Information & Authors
Information
Published In
Copyright
© 2012 American Society of Civil Engineers.
History
Received: Jun 26, 2011
Accepted: Dec 14, 2011
Published online: Nov 15, 2012
Published in print: Dec 1, 2012
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.