@article{fdi:010053501,
  title = {{T}owards improved criteria for hydrological model calibration : theoretical analysis of distance- and weak form-based functions},
  author = {{G}uinot, {V}. and {C}appelaere, {B}ernard and {D}elenne, {C}. and {R}uelland, {D}.},
  editor = {},
  language = {{ENG}},
  abstract = {{C}alibrating conceptual hydrological models is often done via the optimization of objective functions serving as a measure of model performance. {M}ost of the objective functions used in the hydrological literature can be classified into distance- and weak form-based objective functions. {D}istance- and weak form-based objective functions can be seen respectively as generalizations of the square error and balance error. {A}n 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. {T}he theoretical results are illustrated by two simple test cases. {W}eak 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. {I}n contrast with distance-based objective functions, they do not have the inconvenience of solution non-uniqueness. {F}inally, the need for models with internal variables bearing a physical meaning is acknowledged.},
  keywords = {{M}odel performance evaluation ; {C}alibration ; {O}bjective function ; {M}ean squared error ; {N}ash-{S}utcliffe efficiency ; {C}onceptual hydrological model},
  booktitle = {},
  journal = {{J}ournal of {H}ydrology},
  volume = {401},
  numero = {1-2},
  pages = {1--13},
  ISSN = {0022-1694},
  year = {2011},
  DOI = {10.1016/j.jhydro.2011.02.004},
  URL = {https://www.documentation.ird.fr/hor/fdi:010053501},
}