Sensitivity analysis and parameter estimation for distributed hydrological modeling: potential of variational methods

By W. Castaings, D. Dartus, François-Xavier Le Dimet, G. Saulnier. 2009

68 citations recorded by the source corpus.

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. 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 Thore basin and used as a relatively simple (synthetic observations) but didactic application case. 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. 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. 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.

Subfields: Global and Planetary Change, Ocean Engineering, Water Science and Technology

View Paper: https://www.semanticscholar.org/paper/a1e81eab19925b5457228b90ad34a0ac6a76faf0

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Citations in the corpus

Advancing data assimilation in operational hydrologic forecasting: progresses, challenges, and emerging opportunities (2012, methodology): “Besides its application in MPC or MHE, adjoint modeling has been applied to more sophisticated hydrologic models, e.g., in Castaings et al. (2009) for a first order sensitivity analysis of an overland flow model.”
Global sensitivity analysis in hydrological modeling: Review of concepts, methods, theoretical framework, and applications (2015, unknown): “For example, Castaings et al. (2009) and Cibin et al. (2010) showed that the global SA of parameters can provide much more information for parameter identification and estimation.”
A Review on Global Sensitivity Analysis Methods (2014, unknown): “Such approaches are commonly used in solving large environmental systems as in climate modeling, oceanography, hydrology, etc. (Cacuci [9], Castaings et al. [13]).”
Introduction to Sensitivity Analysis (2008, unknown): “[3, 4, 48].”