Application of exergy as ecological indicator and goal function in ecological modelling

Model every system and if it not modelable make it modelable.

Sven Erik J0rgensen (changed from Galilei)

A vision without action is just a dream; an action without a vision just passes time; a vision with an action changes the world.

Nelson Mandela

13.1. Introduction

Exergy has been applied in order to improve two important tools for environmental management, namely assessment of ecosystem integrity and ecological models.

About 15 years ago, the environmental managers proposed to find ecological indicators that were able to assess the integrity of ecosystems, or you may say "take the pulse" of the ecosystem. The idea was to be able not only to assess (preferably quantitatively) a few indicators of the ecosystem integrity, but also (if possible) to come up with a diagnosis. If the ecosystem is not sound, what would we name the disease? It was realised that the first step in a process of cure would be to set up a quantitative diagnosis. How bad was the eutrophication or the toxic substance pollution for instance? Exergy and specific exergy have been applied as ecological indicators:

1. by comparison and integrity assessment of eutrophied lakes (J0rgensen, 2002b),

2. by comparison and integrity assessment of coastal zones (J0rgensen, 2002b),

3. by integrity assessment of Mondego Estuary in Portugal (Marques et al., 2002),

4. by integrity assessment of Chinese lakes (Xu et al., 2000),

5. as ecological indicators for coastal lagoons in Europe (ISPRA, 2001),

6. for integrity assessment of different farming systems (J0rgensen, 2002b),

7. for integrity assessment in a situation where toxic contamination of ecosystems has taken place.

Towards a Thermodynamic Theory for Ecological Systems, pp. 325-349 © 2004 Elsevier Ltd. All Rights Reserved.

The application of exergy as ecological indicator is presented in Section 13.2 where the relationship between exergy and ecosystem integrity will be discussed, and in Section 13.3 where Example 1 in the above list is used to illustrate the application.

If we follow the general modelling procedure, we will attain a model that describes the processes in the focal ecosystem, but the parameters will represent the properties of the state variables as they are in the ecosystem during the examination period. They are not necessarily valid for another period because we know that an ecosystem can regulate, modify and change them, if a response to the change in the prevailing conditions is needed, determined by the forcing functions and the interrelations between the state variables. Our present models have rigid structures and a fixed set of parameters, reflecting that no changes or replacements of the components are possible. We need, however, to introduce parameters (properties) that can change according to changing forcing functions and general conditions for the state variables (components) to continuously optimise the ability of a system to move away from the thermodynamic equilibrium. So, we may hypothesise that the change of these properties (parameters) can be accounted for in our model by the use of an ecological goal function. The idea currently is to test if a change of the most crucial parameters produces a higher goal function of the system and, if that is the case, to use that set of parameters.

The types of models that can account for the change in species composition as well as for the ability of the species, i.e. the biological components of our models, to change their properties, i.e. to adapt to the prevailing conditions imposed on the species, are sometimes called structurally dynamic models in order to indicate that they are able to capture structural changes. They may also be called the next or fifth generation of ecological models to underline that they are radically different from previous modelling approaches and can do more, namely describe changes in species composition or changes in the properties of the species.

It could be argued that the ability of ecosystems to replace present species with other better fitted species can be considered by the construction of models that encompass all actual species for the entire period that the model attempts to cover. This approach has, however, two essential disadvantages. The model becomes first of all very complex, as it will contain many state variables for each trophic level. It also implies, of course, that the model will contain many more parameters that have to be calibrated and validated and this will introduce high uncertainty into the model's results and will render the application of the model very case-specific (Nielsen, 1992a,b). In addition, the model will still be rigid and, having continuously changing parameters, even without changing the species composition will not give the model the property of the ecosystems (Fontaine, 1981). It can be shown to be very important that ecological models reflect the flexibility and adaptability that characterise organisms. If a model includes many rigid state variables (species), there will only be one species that will have a combination of properties that gives the best chance for survival in a given situation. The other species will have a combination of the properties that makes survival and growth more difficult, and they cannot become complete (Nielsen, 1992a,b).

Several goal functions have been proposed, but only very few models that account for change in species composition or for the ability of the species to change their properties within some limits have been developed.

Bossel (1992) applies maximisation of a benefit or satisfaction index based on balancing weighted surplus orientor satisfactions on a common satisfaction scale. The approach is used to select the model structure of continuous dynamic systems and is able to account for the ecological structural properties. The approach seems very promising, but has unfortunately not been applied to ecological systems except in three cases.

Straskraba (1979) uses a maximisation of biomass as the governing principle. The model computes the biomass and adjusts one or more selected parameters to achieve the maximum biomass at every instance. The model has a routine which computes the biomass for all possible combinations of parameters within a given realistic range. The combination that gives the maximum biomass is selected for the next time step and so on.

Exergy has been used most widely as a goal function in ecological models. It has been applied up to now in 13 case studies, where significant changes in the species composition or the properties of the species were observed: for four shallow lakes—S0bygard Lake, Denmark (J0rgensen, 2002b), Glums0 Lake, Denmark (J0rgensen, 2002b), Mogan Lake, Turkey (Zhang et al., 2003a,b) and Lake Balaton, Hungary (J0rgensen and Padisak, 1996); two population dynamic models (J0rgensen, 2002b); for Mondego Estuary, Portugal (J0rgensen et al., 2002a); for Lake Annone Italy (J0rgensen and de Bernardi, 1997); for the Lagoons of Venice (Coffaro et al., 1997); to explain the success and failure of biomanipulation (J0rgensen and de Bernardi, 1998); to explain the intermediate disturbance hypothesis (J0rgensen and Padisak, 1996); to explain the change in the properties of Darwin's finches (J0rgensen and Fath, in press) and to explain the hysteresis in the shift from submerged vegetation and to phytoplankton-dominated eutrophication and back again to submerged vegetation by reduction of the nutrient input (Zhang et al., 2002). For all 13 case studies, the models were able to simulate the observed changes with a standard deviation similar to other model studies.

Moreover, it has been found possible to improve the parameter estimation by the use of exergy. If one parameter is not known with sufficient accuracy, it is possible to find this parameter as the value which yields the highest exergy for the model of the ecosystem considered (J0rgensen, 1995b, 2002b). For eutrophication models it has furthermore been attempted to combine a normal calibration of some parameters with a determination of the combination of other parameters that gives the highest exergy (J0rgensen, 2001a).

Finally, it should be mentioned that it is possible to obtain a better calibration of models developed for ecosystems that show seasonal changes of species composition, for instance a eutrophication model, where the phytoplankton and zooplankton species in the spring, summer and fall are often different. The usually applied calibration procedure determines one parameter set covering the entire year, while we, by the use of exergy optimisation, can find the current change of parameters that reflects the change of species composition, the so-called succession. Not surprisingly the application of a current optimisation of the exergy will therefore offer a better conformity between model simulations and observations (J0rgensen et al., 2002c; Zhang et al. 2003a,b). Exergy optimisation is, of course, only used for the parameters of the organisms, while physical-chemical parameters are calibrated according to the normally applied procedure. Only the living components show flexibility and adaptability.

As seen from this overview, the exergy maximisation is a useful tool in modelling and can offer some clear advantages in obtaining good model results. One case study, namely the change in the beak size of Darwin's finches, has been selected to illustrate this structurally dynamic type of model and these applications in modelling. It is presented in Section 13.5.

13.2. Exergy and specific exergy as ecological indicators

More and more environmental managers include ecological considerations in their management strategy, and they have therefore asked ecologists and system ecologists the following question: how can we express that an ecosystem is ecologically sound and measure it? The doctor of medicine attempts to express the health condition of his patient by the use of indicators such as, for instance, the blood pressure, the temperature, the kidney function, etc. The environmental manager is similarly searching for ecological indicators that can assess the ecosystem integrity. As an ecosystem is a very complex system, it is not surprising that it is not an easy task to find good ecological indicators to give the appropriate information on the ecosystem integrity, although many ecologists and system ecologists have been and are working with this problem.

Rapport (1995) even uses the phrases "to take nature's pulse", "the problem of detecting diseases in nature" and "clinical ecology" to stress the parallelism to human pathology.

von Bertalanffy (1942, 1952) characterised the evolution of complex systems in terms of four major attributes:

(1) progressive integration (entails the development of integrative linkages between different species of biota and between biota, habitat and climate),

(2) progressive differentiation (progressive specialisation as systems evolve biotic diversity to take advantage of abilities to partition resources more finely and so forth),

(3) progressive mechanisation (covers the growing number of feedbacks and regulation mechanisms),

(4) progressive centralisation (it probably does not refer to a centralisation in the political meaning, as ecosystems are characterised by short and fast feedbacks and decentralised control, but to the more and more developed cooperation among the organisms (the Gaia effect) and the growing adaptation to all other components in the ecosystem).

Costanza (1992) summarises the concept definition of ecosystem integrity as the following integrity: (1) homeostasis, (2) absence of disease, (3) diversity or complexity, (4) stability or resilience, (5) vigour or scope for growth and (6) balance between system components. He emphasises that it is necessary to consider all or at least most of the definitions simultaneously. Consequently, he proposes an overall system integrity index, HI = VOR, where V is system vigour, O the system organisation index and R the resilience index. With this proposal Costanza probably touches on the most crucial ecosystem properties covering ecosystem integrity.

Measures of integrity should reflect the two aspects of the organisational state of an ecosystem: functional and structural. Function refers to the overall activities of the ecosystem. Structure refers to the interconnection between the components of the system. Measures of function would indicate the amount of energy being captured by the system.

It could be covered by measuring the exergy captured by the system. Measures of structure would indicate the way in which energy is moving through the system. The exergy stored in the ecosystem could be a reasonable indicator of the structure. If an ecosystem is able to maintain its organisation far from thermodynamic equilibrium in spite of the changing environmental condition, the ecosystem is said to have integrity. If an ecosystem is unable to maintain its organisation then it has lost its integrity. Integrity is, therefore, associated with the ability of the system to reach and maintain its optimum operating point.

Table 13.1 summarises a set of ecological indicators (referred from Kay, 1991). As seen, the stressed system has flows that are about 20% less (except export that drops by about 8%, but measured relative to the import, it even increases), the biomass drops about 35% and the ascendancy drops by slightly more than 20%.

Exergy expresses, in accordance with Chapter 5, the biomass of the system and the genetic information, which this biomass is carrying. Only a relative exergy index, however, can be calculated. It measures the relative, approximate distance from thermodynamic equilibrium, but it is only based on the ecological components included in the calculation. It includes the exergy embedded in the ability to make ordering processes, which are carried out by the information stored in the genes. Exergy also expresses the energy needed to decompose the system into inorganic matter (Svirezhev, 1992), and the work the system can perform by a proper use of these decomposition processes.

Table 13.1

Ecosystem indicators for the Crystal River March Gut Ecosystem

Table 13.1

Ecosystem indicators for the Crystal River March Gut Ecosystem



Stressed ecosystem





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