State of the Art in the Application of Models

The shortcomings of modelling were, however, also revealed. It became clear that the models were rigid in comparison with the enormous flexibility, which was characteristic of ecosystems. The hierarchy of feedback mechanisms that ecosystems possess was not accounted for in the models, which made the models incapable of predicting adaptation and structural dynamic changes. Since the mid-1980s, modellers have proposed many new approaches, such as (1) fiizzy modelling, (2) examination of catastrophic and chaotic behaviour of models, and (3) application of goal functions to account for adaptation and structural changes. Application of objective and individual modelling, expert knowledge and artificial intelligence offers some new additional advantages in modelling. Chapter 9 discusses when it is advantageous to apply these approaches and what can be gained by their application. All these recent developments may be called the fifth generation of modelling.

Table 1.2 reviews types of ecosystems that have been modelled by biogeochemical models up to the year 2000. An attempt has been made to indicate the modelling effort by using a scale from 0 to 5 (see the table for an explanation of the scale).

Table 1.3 similarly reviews the environmental problems which have been modelled until today. The same scale is applied to show the modelling effort as in Table 1.2. Besides biogeochemical models. Table 1.3 also covers models used for the management of population dynamics in national parks and steady-state models applied as ecological indicators (see Section 6.4). It is advantageous to apply goal functions in conjunction with a steady-state model to obtain a good ecological indication, as proposed by Christensen (1991: 1992). This is touched on in Chapter 9, where various goal functions and their application are presented.

Table 1.2. Biogeochemical models of ecosystems

Ecosystem Modelling effort


Lakes, reservoirs, ponds Estuaries Coastal zone Open sea Wetlands Grassland Desert Forests

Agricultural land Savanna

Mountain lands (above timberline) Arctic ecosystems


5: Very intense modelling effort, more than 5(1 different modelling approaches can be found in the literature.

4: Intense modelling effort, 20-50 different modelling approaches can be found in the literature;

4-5: May be translated to class 4 but on the edge of an upgrading to class 5:

3: Some modelling effort, 6-19 different modelling approaches are published;

2: Few (2-5) different models that have been fairly well studied have been published:

1: One good study and/or a few not sufficiently well calibrated and validated models;

0: Almost no modelling efforts have been published and not even one well studied model.

Note that the classification is based on the number of different models, not on the number of case studies where the models have been applied; in most cases the same models have been used in several case studies.

Table 1.3. Models of environmental problems

Problem Modelling effort

Oxygen balance




Heavy metal pollution, all types of ecosystems


Pesticide pollution of terrestrial ecosystems


Other toxic compounds include ERA


Regional distribution of toxic compounds


Protection of national parks


Management of populations in national parks


Endangered species (includes population dynamic models)


Ground water pollution


Carbon dioxide/greenhouse effect


Acid rain


Total or regional distribution of air pollutants


Change in microclimate


As ecological indicator


Decomposition of the ozone layer


Health-pollution relationships


*See Table 1.2 for explanation of scale.

*See Table 1.2 for explanation of scale.

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