Hydrology and Earth System Sciences www.hydrol-earth-syst-sci.net 1027-5606 1607-7938 13 4 2009 10.5194/hess-13-503-2009 http://www.hydrol-earth-syst-sci.net/13/503/2009/ http://www.hydrol-earth-syst-sci.net/13/503/2009/hess-13-503-2009.html http://www.hydrol-earth-syst-sci.net/13/503/2009/hess-13-503-2009.pdf 503 517 2009-04-24 Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods W. Castaings william.castaings@imft.fr D. Dartus F.-X. Le Dimet G.-M. Saulnier IMFT UMR 5502 (CNRS, INP, UPS), Université de Toulouse, 31400 Toulouse Cedex, France LJK UMR 5224 (CNRS, INPG, UJF, INRIA), Grenoble Universités, 38041 Grenoble Cedex 9, France EDYTEM, UMR 5204, Université de Savoie, 73376 Le Bourget du Lac Cedex, France European Commission, Directorate-General Joint Research Centre, Institute for the Protection and Security of the Citizen, Econometrics and Applied Statistics Unit, T.P. 361, 21020 Ispra (VA), Italy Variational methods are widely used for the analysis and control of computationally intensive spatially distributed systems. In particular, the adjoint state method enables a very efficient calculation of the derivatives of an objective function (response function to be analysed or cost function to be optimised) with respect to model inputs. <br><br> In this contribution, it is shown that the potential of variational methods for distributed catchment scale hydrology should be considered. A distributed flash flood model, coupling kinematic wave overland flow and Green Ampt infiltration, is applied to a small catchment of the Thoré basin and used as a relatively simple (synthetic observations) but didactic application case. <br><br> It is shown that forward and adjoint sensitivity analysis provide a local but extensive insight on the relation between the assigned model parameters and the simulated hydrological response. Spatially distributed parameter sensitivities can be obtained for a very modest calculation effort (~6 times the computing time of a single model run) and the singular value decomposition (SVD) of the Jacobian matrix provides an interesting perspective for the analysis of the rainfall-runoff relation. <br><br> For the estimation of model parameters, adjoint-based derivatives were found exceedingly efficient in driving a bound-constrained quasi-Newton algorithm. The reference parameter set is retrieved independently from the optimization initial condition when the very common dimension reduction strategy (i.e. scalar multipliers) is adopted. <br><br> Furthermore, the sensitivity analysis results suggest that most of the variability in this high-dimensional parameter space can be captured with a few orthogonal directions. A parametrization based on the SVD leading singular vectors was found very promising but should be combined with another regularization strategy in order to prevent overfitting. Bannon, P. R.: Hydrostatic adjustment: Lamb's problem, J. Atm. Sci., 52, 1743–1752, 1995. Bruijnzeel,~L A.: Hydrological functions of tropical forests: not seeing the soil for the trees?, Agr. Ecosyst. Environ., 104, 185–228, doi:10.1016/j.agee.2004.01.015, 2004. Costa,~M H.: Large-Scale Hydrological Impacts of Tropical Forest Conversion, in: Forests, Water and People in the Humid Tropics, edited by: Bonell,~M. and Bruijnzeel,~L A., Cambridge University Press, Cambridge, 590–597, 2004. Dill,~K A. and Bromberg,~S.: Molecular driving forces, Garland Science, New York, 2003. Dolman,~A J., Silva Dias,~M A F., Calvet, J-C., Ashby,~M., Tahara,~A S., Delire,~C., Kabat,~P., Fisch,~G F., and Nobre,~C A.: Meso-scale effects of tropical deforestation in Amazonia: preparatory LBA modelling studies, Ann. Geophys.-Italy, 17, 1095–1110, 1999. Dutton,~J A.: The Ceaseless Wind, an Introduction to the Theory of Atmospheric Motion, Dover Publications, New York, 1986. Gedney,~N. and Valdes,~P J.: The effect of Amazonian deforestation on the Northern Hemisphere circulation and climate, Geophys. Res. Lett., 27(19), 3053–3056, 2000. Henderson-Sellers,~A., Dickinson,~R E., Durbidge,~T B., Kennedy,~P J., McGuffie,~K., and Pitman,~A J.: Tropical deforestation – Modeling local-scale to regional-scale climate change, J Geophys. Res., 98(D4), 7289–7315, 1993. Holton,~J R.: An Introduction to Dynamic Meteorology, 2nd edn., Academic Press, New York, 1979. Lamb, H.: Hydrodynamics, 6th edition, Dover, New York, 1945. Landau,~L D. and Lifshitz,~E M.: Course of Theoretical Physics, 6, Fluid Mechanics, Pergamon Press, Oxford, 1987. Lydolph, P. E.: Climates of the Soviet Union. World Survey of Climatology, volume 7, Elsevier, Amsterdam-Oxford-New York, 1977. Makarieva, A. M. and Gorshkov, V. G.: Biotic pump of atmospheric moisture as driver of the hydrological cycle on land, Hydrol. Earth Syst. Sci., 11, 1013–1033, 2007. McEwan,~M J. and Phillips,~L F.: Chemistry of the Atmosphere, Edward Arnold, London, 1975. Moore,~N., Arima,~E., Walker,~R., and Ramos da Silva,~R.: Uncertainty and the changing hydroclimatology of the Amazon, Geophys. Res. Lett., 34, L14707, doi:10.1029/2007GL030157, 2007. Nobre,~C A., Sellers,~P J., and Shukla,~J.: Amazonian deforestation and regional climate change, J Climate, 4, 957–988, 1991. Roy,~S B. and Avissar,~R.: Impact of land use/land cover change on regional hydrometeorology in Amazonia, J Geophys. Res., 107(D20), 8037, doi:10.1029/2001JD000662, 2002. Salati, E. and Vose, P. B.: Amazon Basin – A system in equilibrium, Science 225, 129–138, 1984. Silva Dias,~M A F., Rutledge,~S., Kabat,~P., Silva Dias,~P L., Nobre,~C., Fisch,~G., Dolman,~A J., Zipser,~E., Garstang,~M., Manzi,~A O., Fuentes,~J D., Rocha,~H R., Marengo,~J., Plana-Fattori,~A., Sá,~L D A., Alvalá,~R C S., Andreae,~M O., Artaxo,~P., Gielow,~R., and Gatti,~L.: Cloud and rain processes in a~biosphere atmosphere interaction context in the Amazon Region, J Geophys. Res., 107(D20), 8072, doi:10.1029/2001JD000335, 2002. Tennekes,~H. and Lumley~J L.: A~First Course in Turbulence, The MIT Press, Cambridge MA, 1990. Tijm, A. B. C. and Van Delden, A. J.: The role of sound waves in sea breeze initiation, Q. J. Roy. Meteorol. Soc., 125, 1997–2018, 1999. Van Delden, A.: Linear dynamics of hydrostatic adjustment to horizontally homogeneous heating, Tellus, 52B, 380–390, 2000. Van Kampen,~N G.: Stochastic Processes in Physics and Chemistry, North Holland Publishing Company, Amsterdam, 1983. Van der Molen,~M K., Dolman,~A J., Waterloo,~M J., and Bruijnzeel,~L A.: Climate is affected more by maritime than by continental landuse change: a~multiple-scale analysis, Global Planet. Change, 54, 128–149, 2006. Von Hann,~J.: Lehrbuch der Meteorologie, Verlag von Christian Hermann Tauchnitz, Leipzig, 1915. Wallace,~J. M. and Hobbs,~P V.: Atmospheric Sciences, an Introductory Survey, Academic Press, Orlando FL, 1977. Walter,~H.: Die Vegetation der Erde in oeko-physiologischer Betrachtung, Fisher, Jena, 1964. Walter,~H. and Lieth,~H.: Klimadiagramm Weltatlas, Gustav Fisher, Jena, 1967. Werth,~D. and Avissar,~R.: The local and global effect of Amazon deforestation, J Geophys. Res., 107(D20), 8087, doi:10.1029/2001JD000717, 2002.