Towards improved criteria for hydrological model calibration : theoretical analysis of distance- and weak form-based functions Guinot, V. /Cappelaere, Bernard Delenne, C. Ruelland, D. Model performance evaluation Calibration Objective function Mean squared error Nash-Sutcliffe efficiency Conceptual hydrological model 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. 2011 text https://www.documentation.ird.fr/hor/fdi:010053501 fdi:010053501 Guinot V., Cappelaere Bernard, Delenne C., Ruelland D.. Towards improved criteria for hydrological model calibration : theoretical analysis of distance- and weak form-based functions. 2011, 401 (1-2), 1-13 EN