The problem of model parameter estimation is always associated with a prior problem of model structure choice or identification (e.g. Beck et al., 1990, for their discussion of identifiability in water quality modeling). The methods available depend on whether a linear or non-linear model structure is chosen. The theory of parameter estimation is well developed for linear systems but not for non-linear systems. However, although most hydrological systems are essentially non-linear, much has been achieved using the theories of linear systems analysis.
The essence of the parameter estimation problem is that, given some time series of measurements for the inputs (U) and outputs (Y) of the system of interest, and given some chosen model G(U, θ) where θ are parameters of the model, it is necessary to identify values of θ so as to minimize some criterion of error (index of goodness of fit, objective function or loss function) in reproducing the observations Y. The problem may be extended in...
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Mathematical models; Modeling of water resources systems; Model predictions: uncertainty; Models: distribution models of catchment hydrology
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Beven, K. (1998). Models: Parameter estimation. In: Encyclopedia of Hydrology and Lakes. Encyclopedia of Earth Science. Springer, Dordrecht . https://doi.org/10.1007/1-4020-4497-6_162
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