%0 Journal Article
%9 ACL : Articles dans des revues avec comité de lecture répertoriées par l'AERES
%A Guinot, V.
%A Cappelaere, Bernard
%A Delenne, C.
%A Ruelland, D.
%T Towards improved criteria for hydrological model calibration : theoretical analysis of distance- and weak form-based functions
%D 2011
%L fdi:010053501
%G ENG
%J Journal of Hydrology
%@ 0022-1694
%K Model performance evaluation ; Calibration ; Objective function ; Mean squared error ; Nash-Sutcliffe efficiency ; Conceptual hydrological model
%M ISI:000290072000001
%N 1-2
%P 1-13
%R 10.1016/j.jhydro.2011.02.004
%U https://www.documentation.ird.fr/hor/fdi:010053501
%> https://www.documentation.ird.fr/intranet/publi/2011/05/010053501.pdf
%V 401
%W Horizon (IRD)
%X Calibrating conceptual hydrological models is often done via the optimization of objective functions serving as a measure of model performance. Most of the objective functions used in the hydrological literature can be classified into distance- and weak form-based objective functions. Distance- and weak form-based objective functions can be seen respectively as generalizations of the square error and balance error. An analysis of the objective functions shows that: (i) the calibration problem is transformed from an optimization problem with distance-based objective functions into a root finding problem for weak form-based functions; (ii) weak form-based objective functions are essentially less prone to local extrema than distance-based functions; (iii) consequently, they allow simple gradient-based methods to be used; (iv) parameter redundancy can be assessed very simply by superimposing the contour lines or comparing the gradients of two objective functions of similar nature in the parameter space; and (v) simple guidelines can be defined for the selection of the calibration variables in a conceptual hydrological model. The theoretical results are illustrated by two simple test cases. Weak form-based approaches offer the potential for better-posed calibration problems, through the use of a number of independent criteria that matches the dimension of the identification problem. In contrast with distance-based objective functions, they do not have the inconvenience of solution non-uniqueness. Finally, the need for models with internal variables bearing a physical meaning is acknowledged.
%$ 062