6-мавзу. Математик моделлаштириш элемент­лари

e) Concerning the way to consider the parameters' variability, the following stand out:

1. 
   models with global (or lumped) parameters;
   
2. 
   models with distributed parameters.
   

In the case of the models with lumped parameters, the values that characterize the system's structure, the value of the input and output fluxes as well as the state values are constant for the whole system, while for the models with distributed parameters, the same values are variable in space.
The models with global parameters are used when:

• 
  the system's degree of homogeneousness is high;
  
• 
  the system's structure is relatively unknown, and the system's internal states either are not accessible for measurements, either do not present practical interest.
  

Such models may be used for example for the discharge evaluation in a certain section on the river. The input elements (precipitations, temperatures) or the system's states (the humidity of the soil) are averaged on the river basin surface, its heterogeneous structure being ignored.
The simplifying hypotheses, which stand at the basis of the models with global parameters, lead to a more reduced degree of accuracy, but the results obtained are in many situations satisfactory.
In case of high heterogeneity of the system, the parameters of the corresponding models may not be considered constant, but variable in space, resulting models with distributed parameters; the system is discretized spatially (and not functionally) in quasi-homogeneous areas, each area being characterized by its own values of the parameters. There must be mentioned however that within an area the parameters have a global character, just like the input data or the state variables that have values averaged on each one of these areas.
The first models with distributed parameters in hydrologic sciences have been used for modelling groundwater resources, the aquifers being characterized by a hydraulic conductivity variable in space. For mathematical modelling, the study domain is discretized; each element of the mesh can have at the limit a specific value of hydraulic conductivity, recharge from precipitation or of the storage coefficient.
Subsequently, the models with distributed parameters have begun to be used for surface runoff modelling as well. The river basins are divided in quasi-homogeneous areas (cultivated areas, surfaces covered with forests, impermeable zones etc), each area having its own transformation structure and its own parameters.
Due to the large number of parameters of the distributed models, the parameters have generally a physical meaning and may be obtained insitu. The models with distributed parameters lead to a greater precision of modelling, but they present difficulties from the point of view of parameters evaluation.