6-мавзу. Математик моделлаштириш элемент­лари

g) According to the number of the input and output components, the models may be classified in:

1. 
   monovariable;
   
2. 
   multivariable.
   

One input and one output characterize monovariable models, while multivariable models have more input and one or more output.
An example of monovariable model in hydrology is the use of average global precipitation at the scale of a watershed, representing a unique input value in the hydrological models. If one associates to each station a Thiessen polygon, then one obtains a multivariable model, with more input values. Similar considerations may be made concerning the zoning of the aquifer's recharge.
h) From the parameters number point of view, the following models stand out:

1. 
   non-parametrical models;
   
2. 
   parametrical models.
   

Tables as well as curves or sets of curves, represented graphically or whose ordinates are defined numerically belong to the category of non-parametrical models. One can give as examples of non-parametrical models: the operation rules of a reservoir, the SSARR curves, rules for water allocation etc. The weighted function defined by discrete values (for example the unit hydrograph) is another example of non-parametrical model.
The input-output models for which the transformation of the input in output values is expressed under analytical form as well as the input-states-output models, written as state equations, are examples of parametrical models; the studied processes are described by differential equations, in the case of the models with global parameters, or by equations with partial derivates, in the case of the models with distributed parameters. The equations' coefficients represent the parameters, which must be estimated; the more robust the model, the more a smaller number of parameters must be calibrated (the principle of the parameters' parsimony). The transfer function, analytically defined, is another example of parametrical model.
The weighting function defined by discrete values is a non-parametrical model. It may be transformed in a relatively simple way in a parametrical model, looking for analytically defined curves, which fit well the weighting function's ordinates.
If the analytical expression of the weighting function is known, its parameters may be determined directly through optimisation.