Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 13 12 2009 10.5194/hess-13-2299-2009 http://www.hydrol-earth-syst-sci.net/13/2299/2009/ http://www.hydrol-earth-syst-sci.net/13/2299/2009/hess-13-2299-2009.html http://www.hydrol-earth-syst-sci.net/13/2299/2009/hess-13-2299-2009.pdf 2299 2314 2009-12-03 Copula based multisite model for daily precipitation simulation A. Bárdossy bardossy@iws.uni-stuttgart.de G. G. S. Pegram Institute of Hydraulic Engineering, University of Stuttgart, Stuttgart, 70569, Germany Civil Engineering Program, University of KwaZulu-Natal, Durban, South Africa From the point of view of multisite stochastic daily rainfall modelling, there are two new ideas introduced in this paper. The first is the use of asymmetrical copulas to model the spatial interdependence structure of the rainfall amounts together with the rainfall occurrences in one relationship. The second is in the evaluation of the (necessary but often ignored) congregating behaviour of the higher values of simulated rainfall; this evaluation is performed by calculating the entropy of the observations at all the near equilateral triangles that can be formed from the sequences at the gauge sites, as a function of their mutual separation distance. It turns out that the model captures the qualities desired and offers a fresh approach to a relatively mature problem in hydrometeorology. Akaike, H.: A new look at the statistical model identification, IEEE T. Automat. Contr., 19(6), 716–723, 1974. Apipattanavis, S., Podestá, G., Rajagopalan, B., and Katz, R W.: A semiparametric multivariate and multisite weather generator, Water Resour. Res., 43, W11401, doi:10.1029/2006WR005714, 2007. Bárdossy, A.: Copula-based geostatistical models for groundwater quality parameters, Water Resour. Res., 42, W11416, doi:10.1029/2005WR004754, 2006. Bárdossy, A. and Li, J.: Geostatistical interpolation using copulas, Water Resour. Res., 44, W07412, doi:10.1029/2007WR006115, 2008. Fang, H.-B., Fang, K.-T., and Kotz, S.: The meta-elliptical distribution with given marginals, J. Multivariate Anal., 82, 1–16, 2002. Herr, D. and Krzysztofowicz, R.: Generic probability distribution of rainfall in space: The bivariate model, J. Hydrol., 306, 237–264, 2005. Joe, H.: Multivariate models and dependence concepts, Chapman Hall, Boca Raton, 1997. Linhart, H. and Zucchini, W.: Model Selection, Wiley, New York, 1986. Matalas, N.: Mathematical assessment of synthetic hydrology, Water Resour. Res., 3(4), 937–945, 1967. Mehrotra, R. and Sharma, A.: Preserving low-frequency variability in generated daily rainfall sequences, J. Hydrol., 345, 102–120, 2007. Mehrotra, R., Srikanthan, R., and Sharma, A.: A comparison of three stochastic multi-site precipitation occurrence generators, J. Hydrol., 331, 280–292, 2006. Nelsen, R.: An introduction to copulas, Springer Verlag, New York, 1999. Pegram, G. and James, W.: A Multivariate Multi-lag Autoregressive Model for the Generation of Operational Hydrology, Water Resour. Res., 8, 1074–1076, 1972. Press, W., Teukolsky, S., Vetterling, W., and Flannery, B.: Numerical recipes in Fortran, Cambridge University Press, Cambridge, England, 1992. Salvadori, G., Michele, C D., Kottegoda, N., and Rosso, R.: Extremes in nature. An approach using copulas, Springer, New York, 2007. Serinaldi, F.: Copula-based mixed models for bivariate rainfall data: an empirical study in regression perspective, Stoch. Env. Res. Risk. A., 23, 677-693, 2009. Serinaldi, F.: Multisite generalisation of a daily stochastic precipitation generation model, Stoch. Env. Res. Risk A., 22, 671–688, 2008. Sklar, A.: Fonctions de répartition à N dimensions et leurs marges, Publ. Inst. Stat. Paris, 8, 229–131, 1959. Srikanthan, R.: Stochastic Generation of Daily Rainfall Data at a Number of Sites, CRC for Catchment Hydrology, Technical Report 05/7, 7, 66, Monash University, 2005. Srikanthan, R. and McMahon, T. A.: Stochastic generation of annual, monthly and daily climate data: A review, Hydrol. Earth Syst. Sci., 5, 653–670, 2001. Srikanthan, R. and Pegram, G.: A Nested Multisite Daily Rainfall Stochastic Generation Model, J. Hydrol., 371(1–4), 142–153, 2009. Thomas, H. and Fiering, M.: Mathematical synthesis of streamflow sequences for the analysis of river basins by simulation, Design of Water Resources Systems, Harvard University Press, Cambridge, MA, USA, Chapter~12, 1962. Wilks, D.: Multisite generalisation of a daily stochastic precipitation generation model, J. Hydrol., 210, 178–191, 1998.