Henning Mejer

Emergy, environ, exergy and ecological modelling

Abstract Hitherto, applied calculations of exergy for higher organisms have been based on traditional thermodynamic considerations, which did not take into account the organizational level of organisms. It seems reasonable to include such perspectives in a thermodynamic evaluation of ecosystems. Therefore, two methods that are theoretically more sound for calculations of exergy for higher organisms are proposed in this paper. The first is based upon the thermodynamic information due to genes. The method is rooted in statistical thermodynamics and should be considered the best candidate for exergy calculations of ecosystems including higher organisms. The second method is a parallel to the method used for calculation of emergy, and is based on the cost of free energy computed from an ecological network. Because this method does not consider the increase of information due to evolution, it should be considered theoretically less sound than the first mentioned method. It is, however, interesting to compare the two methods, as they to a certain extent reflect the differences between emergy and exergy. Emergy attempts, as exergy, to account for the quality of energy by the use of a transformity factor. The transformity factors for calculation of emergy are found from the network as the number of solar equivalents that it has cost to construct the considered organism. Emergy is therefore often more easy to compute, provided that the ecological network is known, while exergy after the new methods for calculations presented here seems to have a better theoretical basis. The two methods tested for calculation of exergy give different results, but the results are in the same order of magnitude. The two major problems in development of ecological models are the parameter estimation and the selection of the best model structure. The latter requires that more ecological system properties are incorporated in our models. A procedure based upon recent developments in ecosystem theory is proposed to meet this requirement. It should be considered a first approach to a theoretical improvement of the modelling procedure for development of models with more ecological properties.

Ecological buffer capacity

A new concept — the ecological buffer capacity — has been introduced to express the response of an ecosystem to changes in the loading. Either the relative or absolute stability gives this sort of information. By means of this concept, it has been attempted to show how complicated a model must be to give an acceptable description of the response to changes in the phosphorus loadings. It was found that the ecological buffer capacity increases with increasing model diversity, either expressed by means of the Shannon index or the number of state variables, but since it is of importance to include the most essential mass flows, the exergy is more suitably related to the buffer capacity than the diversity. Consequently, the exergy can be used as an expression for the buffer capacity, that is, as an expression for the response of an ecosystem to changes in the driving functions. Both the buffer capacity and the exergy can be used to select the required state variables for a model. Interchanging Pjeq (= phosphorus concentration in box j at thermodynamic equilibrium) with Pj0 (= phosphorus concentration in box j at steady state) in the exergy expression, seems to give a useful Liapunov function for the considered set of models.

EXERGY AND ECOLOGICAL BUFFER CAPACITY

Ecological model constraints imposed by chemical, physical, thermodynamical, biological and topological laws are discussed. Two aspects: thermodynamic exergy and ecological buffer capacity are brought into focus.

Examination of a lake model

Abstract A eutrophication model was validated using data from both Lyngby Lake and Glumso Lake. It was possible to calibrate the model on the basis of data obtained from measurements of Lyngby Lake during 1952–1958. During this period the lake received treated waste water that had a high nutrient concentration. The model was then used to simulate the changes of Lyngby Lake during the period 1959–1975. Beginning in 1959, the waste water was conveyed to the sea, but the nutrient concentration in the tributaries was slowly increasing. The response of the lake to the changes was described very well by the model. Approximately the same parameter values were used in studies of different lakes. An evaluation of the model seems to lead to the conclusion that long-term changes and changes in average and maximum values due to changes in forcing functions are well described by the model, but the model has still to be improved if it is to be employed to describe annual cycles. An automatic computer calibration was tested and afterwards a suggested validation procedure was applied. This procedure was used for comparison of different versions of the model.

Ecosystem as self-organizing critical systems

Abstract The paper examines the following properties which are often associated with self-organizing critical systems: (1) Is the relationship between body size and abundance for species in ecosystem a power law? (2) Will the frequency with which observed changes exceeds a given change versus the change follow a power law? (3) Will the typical frequencies of ‘avalanches’ follow a power law? (4) Can the occurrences of ‘avalanches’ according to a well-examined ecosystem model be used to explain the underlying causality? As the examinations give the clear answer ‘yes’ to all four questions, and as many other properties of ecosystems also point towards ecosystems as self-organising critical systems, it seems possible to support the hypothesis, that ecosystems are self-organizing systems.

Modelling the global cycle of carbon, nitrogen and phosphorus and their influence on the global heat balance

Abstract A model for the accumulation of CO 2 in the atmosphere has been set up, taking into consideration: (1) the global cycle of nitrogen and phosphorus: (2) the CO 2 -diffusion in the oceans with means of a multilayer śea model; (3) the ability of the oceans to take up CO 2 ; (4) the influence of the CO 2 -concentrations and of the temperature on this ability; (5) different growth rates for the consumption of fossil fuel including logistic growth; (6) the natural climatic variation. It is shown to be essential to include all these factors. The inclusion of factors (4) and (6), which have been omitted in many previous publications, is very essential to the model.

Modelling the global heat balance

Abstract A previous model of the global heat balance has been expanded by including the influence of SO2 pollution, water content of the atmosphere and cloudiness. It was found that the previous results were not changed significantly by this expansion of the model. The conclusions set up uising the previous model were still valid: (1) it is great importance to include the buffer capacity of the sea, including its dependence on pH and the temperature; (2) it is of importance to include natural climatic variations; (3) the dominanting factor is the trend in the consumption of fossil fuel.