INTEGRATING TOOLS FOR SURFACE WATER QUALITY MANAGEMENT - Integrating GIS, Remote Sensing, and Mathematical Modelling for Surface Water Quality Management - page 54

Model Type and Solution Techniques
According to Dahl and Wilson 1997, when models are classified by the modelled ecosystem,
distinctions are made between lake models, river models etc. Models can, however, be categorized by
other criteria as mentioned earlier. The categorization of models according to their mathematical
description and the (solution) techniques used to solve them is seen in Figure (3-2) , this classification
distinguishes between steady state and dynamic models, black box and fundamental models,
continuous and discrete time models and between deterministic and stochastic models. Furthermore
models are classified according to the dimension of the model (1D, 2D or 3D). For most problems
many kinds of models can be used. In general, the simplest model structure that is able to solve the
problem is chosen. The choice of model structure is further determined by presence of data, technical
and personal resources, computer capacity etc.
Figure (3-2): Categorization of models according to their mathematical description and the (solution) techniques
(After Dahl and Wilson, 2000)
Classification of Models According to Mathematical Description:
1. Steady State / Dynamic Models
A steady-state model involves only algebraic equations as opposed to dynamics models which,
incorporating derivatives, can model evolving conditions with time and/or space. Statistical regression
models which describe only the averaged status of the lake given constant inputs and external loading
forcing functions are typical steady-state models. For applications steady-state models are appropriate
where either the dynamics are very fast or very slow compared with the time scale of interest. In the
case of fast dynamics, equilibrium values can be used in the model and in the case of slow dynamics,
initial conditions can be employed with little loss of accuracy.
2. Input - Output / Physically Based Models
In a black box or data-driven model , both structure and parameter values are determined by the data
and any prior knowledge about the system is not utilized. A characteristic feature of black box models
is that they require large amounts of data to get good results. On the other hand, traditional modelling
of physical processes is often named physically-based modelling or (knowledge -driven modelling)
because it tries to explain the underlying processes. In a physically based model the structure of the
system, developed from known scientific laws, is the base for the model. The structure is normally
built up by a number of subsystems and the interactions between them. Unknown parameters in the
model are determined by statistical methods to get good agreement between model results and actual
data. As opposed to a black box model, the parameters in a physically based model have a physical
meaning. A physically based model can be used with more confidence for extrapolation outside the
area of observations than an empirical model. As an example of such models is a hydrodynamic model
based on Navier-Stocks partial differential equations numerically solved using finite difference
scheme.