Application of Copulas to Modeling Temporal Sampling Errors in Satellite-Derived Rainfall Estimates
Publication: Journal of Hydrologic Engineering
Volume 12, Issue 4
Abstract
The dependence between temporal sampling error in satellite-derived rainfall estimates and rainfall rate is of scientific and practical interest. We explore the use of copulas to construct the needed joint distribution between the sampling error and the corresponding rainfall rate. Our approach is to first estimate the marginal distribution functions in a parametric way, and then use these with a number of copula functions in search of the one most appropriate. We use maximum likelihood to estimate the parameters of the copulas. We select the best-fitted parametric copula function as the one that gives the largest likelihood. Our findings have important implications for the interpretation and propagation studies of remote sensing precipitation uncertainties.
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Acknowledgments
The writers wish to thank Dr. Brian R. Nelson for providing the rainfall data set. This research was supported by the U.S. National Oceanic and Atmospheric Administration Office of Global Programs through Grant No. UNSPECIFIEDNA57WHO517 to the second writer, by the National Aeronautics and Space Administration (NASA) through Grant No. NASANAG5-9664, and the NASA Earth System Science Fellowship to the first writer. The second writer also acknowledges the support of the Rose and Joseph Summers Professorship Endowment.
References
Bell, T. L., and Kundu, P. K. (2000). “Dependence of satellite sampling error on monthly averaged rain rates: Comparison of simple models and recent studies.” J. Clim., 13, 449–462.
Gebremichael, M., and Krajewski, W. F. (2004). “Characterization of the temporal sampling error in space-time averaged rainfall estimates from satellites.” J. Geophys. Res., 109, D11110.
Gebremichael, M., and Krajewski, W. F. (2005a). “Effect of Temporal Sampling on Inferred Rainfall Spatial Statistics.” J. Appl. Meteorol., 44(10), 1626–1633.
Gebremichael, M., and Krajewski, W. F. (2005b). “Modeling distribution of temporal sampling errors in area-time averaged rainfall estimates.” Atmos. Res., 73, 243–259.
Ha, E., and North, G. R. (1999). “Error analysis for some ground validation designs for satellite observations of precipitation.” J. Atmos. Ocean. Technol., 16, 1949–1957.
Huffman, G. J. (1997). “Estimates of root-mean-square random error for finite samples of estimated precipitation.” J. Appl. Meteorol., 36, 1191–1201.
Huffman, G. J., et al. (1997). “The global precipitation climatology project (GPCP) combined precipitation dataset.” Bull. Am. Meteorol. Soc., 78(1), 5–20.
Huffman, G. J., et al. (2001). “Global precipitation at one-degree daily resolution from multisatellite observations.” J. Hydrometeor., 2, 36–50.
Joe, H. (1997). Multivariate models and dependence concepts, Chapman & Hall, London.
Kunsch, H. R. (1989). “The jackknife and the bootstrap for general stationary observations.” Ann. Stat., 17, 1217–1241.
Nelsen, R. B. (1999). An introduction to copulas, Springer, New York.
Nelson, B. R., Krajewski, W. F., Kruger, A., Smith, J. A., and Baeck, M. L. (2003a). “Archival precipitation data set for the Mississippi River Basin: Development of a GIS-based data browser.” Comput. Geosci., 29(5), 595–604.
Nelson, B. R., Krajewski, W. F., Kruger, A., Smith, J. A., and Baeck, M. L. (2003b). “Archival precipitation data set for the Mississippi river basin: Algorithm development.” J. Geophys. Res., 108(D22), 8857.
Nelson, B. R., Krajewski, W. F., Smith, J. A., Habib, E., and Hoogenboom, G. (2005). “Archival precipitation data set for the Mississippi River Basin: Evaluation.” Geophys. Res. Lett., 32(18), L18403.
Nijssen, B., and Lettenmaier, D. P. (2004). “Effect of precipitation sampling error on simulated hydrological fluxes and states: Anticipating the global measurement satellites.” J. Geophys. Res., 109, D02103.
Oki, R., and Sumi, A. (1994). “Sampling simulation of TRMM rainfall estimation using radar-AMeDAS composites.” J. Appl. Meteorol., 33, 1597–1608.
Sorooshian, S., Hsu, K., Gao, X., Gupta, H. V., Imam, B., and Braithwaite, D. (2000). “Evaluation of PERSIANN system satellite-based estimates of tropical rainfall.” Bull. Am. Meteorol. Soc., 81, 2035–2046.
Steiner, M. (1996). “Uncertainty of estimates of monthly areal rainfall for temporally sparse remote observations.” Water Resour. Res., 32, 373–388.
Steiner, M., Bell, T. L., Zhang, Y., and Wood, E. F. (2003). “Comparison of two methods for estimating the sampling-related uncertainty of satellite rainfall averages based on a large radar dataset.” J. Clim., 16(22), 3759–3778.
Tawn, J. A. (1988). “Bivariate extreme value theory: Models and estimation.” Biometrika, 75, 397–415.
Yilmaz, K. K., Hogue, T. S., Hsu, K.-L., Sorooshian, S., Gupta, H. V., and Wagener, T. (2005). “Intercomparison of rain gauge, radar, and satellite-based precipitation estimates with emphasis on hydrologic forecasting.” J. Hydrometeor., 6, 497–517.
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© 2007 ASCE.
History
Received: Oct 12, 2005
Accepted: Nov 26, 2006
Published online: Jul 1, 2007
Published in print: Jul 2007
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