Structurally dynamic modeling

Dynamic models whose structure changes over time are based on non-stationary or time-varying differential or difference equations. We will refer to these as structurally dynamic models. A number of such models, mainly of aquatic systems (Jorgensen, 1986, 1988, 1990; Nielsen, 1992a,b; Jorgensen and Padisak, 1996; Coffaro et al., 1997; Jorgensen and de Bernardi, 1997, 1998), but also as population dynamic models (Jorgensen, 2002) and terrestrial systems (Jorgensen and Fath, 2004) have been investigated to see how structural changes are reflected in exergy changes. The technicalities of parameter fitting aside, this overall result means that system structure must change if its eco-exergy storage is to be continually maximized. Changes in parameters, and thus system structure, not only reflect changes in external boundary conditions, but also mean that such changes are necessary for the ongoing maximization of exergy. For all models investigated along these lines, the changes obtained were in accordance with actual observations (see references). These studies therefore affirm, in a general way, that systems adapt structurally to maximize their content of eco-exergy. The shortcomings of assessing the exergy content of an ecosystem have been discussed above. At least in models the applicability of the exergy calculations have shown their more practical use, which can be explained by a robustness in the model calculations.

It is noteworthy that Coffaro et al. (1997), in his structural-dynamic model of the Lagoon of Venice, did not calibrate the model describing the spatial pattern of various macrophyte species such as Ulva and Zostera, but used exergy-index optimization to estimate parameters determining the spatial distribution of these species. He found good accordance between observations and model, as was able by this method without calibration, to explain more than 90 percent of the observed spatial distribution of various species of Zostera and Ulva. Box 6.4 gives an illustration of a structurally dynamic model (SDM).

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