Info

USA Unplugged Home Energy Solution

Do It Yourself Solar Energy

Get Instant Access

Fig. 12.2. Log-log plot of the ratio of nitrogen to phosphorus turnover rates, R, at maximum exergy versus the logarithm of the nitrogen/phosphorus ratio, log(N/P). The plot is consistent with Vollenweider (1975).

such results for a lake eutrophication model. The ratio, R, of nitrogen (N) to phosphorus (P) cycling, which gives the highest exergy, is plotted in a logarithmic scale versus log(N/P). The plot in Fig. 12.2 is also consistent with empirical results (Vollenweider, 1975).

Of course, one cannot "inductively test" anything with a model, but the indications and correspondences with data tend to support in a general way the exergy-storage hypothesis. The cycling ratio giving the highest ascendancy is also correlated similarly to the N/P ratio (R. Ulanowicz, personal communication).

(7) Fitness. Brown et al. (1993) and Marquet and Taper (1998) examined patterns of animal body size. They explained frequency distributions for the number of species as functions of body size in terms of fitness optimisation. Fitness can be defined as the rate at which resources in excess of those required for maintenance are used for reproduction (Brown, 1995). This definition suggests channelling of resources to increase the free-energy pool. Fitness, so interpreted, may be taken as consistent with the exergy-storage hypothesis.

(8) Structurally dynamic modelling. 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 (J0rgensen, 1986, 1988, 1990, 1992a,b; Nielsen, 1992a,b; J0rgensen and Padisak, 1996; Coffaro et al., 1997; J0rgensen and de Bernardi, 1997, 1998), have been investigated to see how structural changes are reflected in free-energy changes. The latter were computed as exergy indexes (see Section 12.5). Time-varying parameters were selected iteratively to give the highest index values in a given situation at each time step (see J0rgensen and Padisak, 1996). Such informal procedures for system identification are complicated and prone to error. Final results, and whether local versus global optima are realised, etc. are very sensitive to initial choices made. Even so, at the least, it was always observed that maximum exergy index values could not be achieved without changing parameter values, i.e. without structural dynamics. The technicalities of parameter fitting aside, this overall result means that system structure must change if its free-energy storage is to be continually maximised. Changes in parameters, and thus system structure, do not only reflect changes in external boundary conditions, but also mean that such changes are necessary for the ongoing maximisation of exergy. For all the 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 maximise their exergy content.

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 optimisation to estimate parameters determining the spatial distribution of these species. He found good accordance between observations and model, as was able, using this method without calibration, to explain more than 90% of the observed spatial distribution of various species of Zostera and Ulva. Some examples of structurally dynamic models will be presented in Chapter 13.

(9) E.P. Odum's attributes. In summary, phenological progression in ecosystems, when viewed through the lens of exergy relationships, bears unmistakable resemblances to the growth of organisms, succession of communities and evolution of taxa. All these processes can be seen as proceeding on different space-time scales more or less under the exergy principles of growth as outlined in this volume (see Table 12.2 for a partial list). This list is complete in accordance with E.P. Odum's attributes (see also Table 2.5 in Section 2.4). This implies that all the characteristics of ecosystem development, summarised in E.P. Odum's attributes, comply with the maximum exergy-storage principle.

The conclusion from these examples and other examples presented in J0rgensen et al. (2000) and J0rgensen (2002b) is that they do not constitute a rigorous test of the exergy-storage hypothesis. This is impossible because exergy cannot be measured for ecological systems. They are too complex. However, through modelling and recourse to many examples, a kind of "inductive verification" is possible. That is what this section has tried to show, namely that the hypothesis provides a plausible objective function over a broad selection of actual systems and circumstances. Assistance from modelling depends on

Table 12.2

A partial list of characteristics of developed ecosystems that are in accordance with the exergy principles of this chapter

Characteristics

Explanation

1. High biomass

2. High respiration, transpiration and other catabolic processes

3. Gradient development

4. High information content

5. High level of specialisation and differentiation

6. High level of adaptation and buffer capacity

7. High levels of network complexity and organisation

8. Big size of (some) organisms

9. Highly developed history

10. High indirect/direct effect ratio

11. Irreversible processes

12. Both bottom-up and top-down regulation

13. Symbioses developed

14. Diversity of processes

To utilise available nutrients and water to produce the highest stored exergy To maintain the system far from thermodynamic equilibrium The system moves as far as possible away from thermodynamic equilibrium To utilise maximally the flow of exergy and resources To utilise space and time heterogeneity to gain the highest possible level of exergy To meet the challenge of changing forcing functions A consequence of the first four characteristics To minimise specific entropy production and thereby the cost of maintenance when exergy flow becomes limiting Caused by all developmental processes A consequence of the complex network A consequence of system history To utilise all available avenues to build as much dissipative structure as possible

Two or more species move simultaneously further from thermodynamic equilibrium To utilise all available avenues to build as much dissipative structure as possible deriving a valid substitute measure for absolute exergy, an index covering the storage of both biomass and information that can be used in modelling studies to give further credential to the hypothesis. In Chapter 5 such an index—the relative exergy index—was developed.

12.5. Other ecosystem theories

Boltzmann (1905) said that the struggle for existence is a struggle for free energy available for work, which is a very close definition to the maximum exergy principle introduced in Chapter 5. Similarly, Schrodinger (1944) pointed out that organisation is maintained by extracting order from the environment. These last two principles may be interpreted as the systems that are able to gain most exergy under the given conditions, i.e. to move the farthest from thermodynamic equilibrium, will prevail. Exergy is defined as the useful or available energy of the system relative to the environment. Such systems will gain most biogeochemical energy available for doing work and therefore have most energy stored to be able to struggle for their existence. There seems to be a certain parallelism, therefore, between the three formulations of principles. However, in spite of external similarity between the MPP and the exergy principle, they are not equivalent (the differences will be discussed later on).

Boltzmann proposed that "life is a struggle for the ability to perform work", which is exergy. Referring to one of the thermodynamic identities, which can be written in verbal form:

free energy = energy — temperature • entropy that can be interpreted as (Straskraba et al., 1997) energy — disorder = energy + order.

The difference between free energy and exergy is the ability with exergy to select a case-dependent reference state.

Ecological (and biological) growth and development have very much to do with the evolution of order in the material of organised matter, and work must be done to create this order out of the background (reference state) of somewhat less order. Teleology is frequently brought into the discussion about the origins of order, in the form of "objective functions", "goal functions", "optimisation criteria", "extreme principles" and "orientors" (e.g. Muller and Leupelt, 1998). This volume's central hypothesis, exergy-storage maximisation, is one such goal function, or in Aristotelian terms, a "final cause". In this section a selection of others is reviewed, all of them being criteria for purposeful ecological growth and development. How the different approaches can be united in an ecosystem theory will be discussed in Section 12.6.

(1) Maximum biomass. Biomass is stored energy, some of which can be turned into work. This portion is exergy, the inherent order in which is taken into account through multiplication by N/s (Eq. (4.3) in Chapter 5). Eqs. (5.1) and (5.2) in Chapter 5 show even more clearly the two contributions—by N the total matter, and by Kullback's measure K of the increment of information. The ability of a species to perform work in an ecosystem, its exergy or free energy, is thus proportional not only to its information content, but also to its biomass. Margalef (1968), Straskraba (1979, 1980) and Brown (1995) have all proposed the use of biomass as an ecological goal function. As biomass is storage and has exergy, its maximisation would be at least partly consistent with the exergy-storage hypothesis. For entire systems, however, this would require different weighting factors, as shown in Eqs. (7.9) and (7.10) in Chapter 5, to account for the different information (order) inherent in the different biological species.

(2) Maximum power (for details, see Section 12.2). The transformation of energy to perform work is correlated with the amount of exergy available (stored or in passage) within the system. The more exergy is stored, the more is available to be drawn on for work at a later stage, which requires conversion from storage to through-flow. In order to achieve storage, however, there must first be boundary flows (inputs) to sequester. Ecosystems must, therefore, contain balanced mixes of diametrically opposed quantities, storages and flows. Through-flow and storage are inversely related (see "ascendancy" in Chapter 11). One can be traded for the other, as determined by the composition of organic "stores" and biotic "storers" and "processors" that in aggregate determine whole-system turnover. Rapid turnover decreases storage and increases through-flow, and vice versa. A nice link between exergy storage and work performance was demonstrated by Salomonsen (1992) for two lakes with significantly different levels of eutrophication. He showed that the exergy/maximum power ratio was approximately the same in both cases.

(3) Minimum specific entropy. Mauersberger (1983, 1995) proposed a "minimum entropy principle" consistent with the principle of least specific dissipation from far-from-equilibrium thermodynamics (Prigogine, 1947). Johnson (1990, 1995) investigated least specific dissipation over a wide range of ecological case studies. Aoki (1988, 1989, 1993, 1995) compared entropy production, which reflects exergy utilisation, in terms of maintenance versus exergy storage in different lake ecosystems. He found that eutrophic lakes capture and store more exergy, then subsequently use it for maintenance. This is consistent with the general observation (e.g. J0rgensen, 1982; Salomonsen, 1992) that eutrophic lakes have more biomass, thus more stored exergy but, following on from this, also greater through-flow and dissipation, though less specific dissipation, than mesotrophic or oligotrophic lakes. Biomass-specific exergy, in other words, decreases with increasing eutrophication.

(4) Maximum emergy. Odum (1983a,b) introduced another goal function, "embodied energy", later contracted to emergy. Section 7.9 has presented the idea behind this concept. Embodied energy is expressed in solar energy equivalents; see Section 7.9. Though exergy and emergy are conceptually and computationally very different quantities, and though emergy calculates how much solar energy it costs to build a structure whereas exergy expresses the actual work potential for growth once built, the two measures correlate well when computed for models (J0rgensen, 1994). The difference between the two concepts may be expressed as follows: emergy expresses the costs in solar radiation equivalent, while exergy expresses the result (the stored working capacity). When two species are compared, the ratio between the two may be very different, but when we compare entire ecosystems, it is not surprising that the costs and the results are parallel concepts. Bastianoni and Marchettini (1996) found that a natural lagoon had a high exergy/emergy ratio while a man-made wastewater lagoon had a low value. Nature is, therefore, apparently better able to utilise the emergy in order to obtain exergy than man-made systems (Bastianoni, 1998).

(5) Ascendancy. Another network measure of whole-system contributions to growth and development is ascendancy (Ulanowicz, 1986, 1997). According to this theory, in the absence of overwhelming external disturbances, living systems exhibit a propensity to increase in an "ascendant" direction (see also Chapter 9). As ascendancy is well correlated with stored exergy (J0rgensen, 2002b), maximising ascendancy is similar to maximising exergy storage. The relationship is not straightforward, however. Considering Example 6 in Section 12.4, increased cycling at steady state increases both the through-flow and storage that can be derived from boundary inputs (Patten et al., 1997). One is traded for the other, depending on the composition of components, which determines system turnover. Rapid turnover decreases storage and increases through-flow, and vice versa. As ascendancy is dominated by its extensive variable, through-flow, if this is maximised, then storage must be sacrificed accordingly in the steady-state relationship. But, as through-flow and storage are closely coupled, if through-flow is maximised so necessarily is the storage to which this may contribute. Conversely, the greater the storage in a system is, the more is available to be converted to through-flow as circumstances warrant. Maximisation of ascendancy, a measure heavily dominated by through-flow, can thus be taken as generally consistent with the exergy-storage hypothesis.

In conclusion, initially different concepts about how energy and matter are related to one another in complex systems organisation turn out in many cases—but not all—to be merely nuances in expression of the same central phenomena: that basically local negentropy production (exergy storage) opposes but enables entropy production (exergy destruction).

12.6. Towards a consistent ecosystem theory

The properties of ecosystems can only be revealed using a pluralistic view. It is therefore not surprising that there are many different ecosystem theories published in the scientific literature. It is, on the other hand, necessary to try to unite the theories and examine if they are tied up in contradictions or form a pattern that can be used to give a better understanding of the nature of ecosystems and to solve the global environmental problems. The goal is to give a common framework of reference for further development of a more profound and comprehensive ecosystem theory than the one we are able to present today. The pattern should serve as a "conceptual diagram", which can be used as a basis for further discussion of how ecosystems behave. We are still in an early stage of an ecosystem—theoretical development—and it may be argued that this attempt is premature, but experience from modelling has taught us that it is better to conclude one's thoughts in a conceptual diagram at an early stage and then be ready to make changes than to let all modelling efforts wait until all details are known, as this will never be the case due to the immense complexity of Nature (J0rgensen, 2001b, 2002b). Moreover, recent development in ecosystem theory has made it possible to conclude that the theories presented here are indeed consistent and supplementary.

The centre of the pattern presented below is the tentative Fourth Law of Thermodynamics, but it cannot be excluded that other tentative laws could be the core of an ecosystem theory. What can we conclude from these (tentative) laws about ecosystem properties? Can we, as is known from physics, formulate a limited number of laws and explain a very large number of observations (J0rgensen, 2001b, 2002b; see also Chapter 1)? This question has been answered with a clear "yes" in this volume. The recent development in system ecology represents a paradigm shift. The paradigm that is now receding has dominated our culture for several hundred years. It views the universe as a mechanical system composed of elementary building blocks. The new paradigm is based on a holistic worldview. The world is seen as an integrated whole and recognises the fundamental interdependence of all phenomena.

The support for the validity of the tentative law in its present formulation (see Section 12.3) is strong and may be summarised in the following three points:

1. It may be considered a translation of Darwin's theory to thermodynamics and is consistent with the basic, thermodynamic laws. The selected organisation is the one that offers most "survival" and may be measured as exergy.

2. The application of the hypothetical law in models gives (many) results that are consistent with ecological observations (see Section 12.3 of this chapter, J0rgensen, 2002b, and Chapter 13).

3. It is possible to validate models that describe the change in properties of the components, the so-called structurally dynamic models, by application of exergy as a goal function (see Section 12.3 and Chapter 13).

We need a number of different complementary approaches to explain ecosystems, which is not surprising as much simpler physical phenomena, light, for instance, need two different descriptions, namely, as waves and as particles. Several ecosystem theories have been presented in the scientific literature during the last 2-3 decades; see Section 12.5. At first glance they look very different and seem to be inconsistent, but a further examination reveals that they are not so different and that it should be possible to unite them in a consistent pattern. It has been accepted by the system scientists since 1998/1999 but, as a result of two meetings in 2000, one in Porto Venere, Italy, in late May and one in Copenhagen, in early June in conjunction with the American Society of Limnology and Oceanography meeting, it can now be concluded that a consistent pattern of ecosystem theories has been formed. Several system ecologists agreed on the pattern presented below as a working basis for further development in system ecology. This is of the utmost importance for progress in system ecology because, with a theory in hand, it will be possible to explain many rules that are published in ecology and applied ecology that again explain many ecological observations, as has been discussed in Sections 12.3-12.5 and will be discussed further in Chapter 13. We should, in other words, be able to attain the same theoretical basis that characterises physics: a few basic laws, which can be used to deduce rules that explain observations. It has, therefore, also been agreed that one of the important goals in system ecology would be to demonstrate (prove) the links between ecological rules and ecological laws.

The first contribution to a clear pattern of the various ecosystem theories came from the network approach used often by Patten. He has shown by a mathematical analysis of networks in steady state (representing, for instance, an average annual situation in an ecosystem with close to balanced inputs and outputs for all components in the network) that the sum of through-flows in a network (which is maximum power) is determined by the input and the cycling within the network. The input (the solar radiation) again is determined by the structure of the system and its biomass (the stored exergy is a function of the biomass distributed over the structure). Furthermore, the more the complexity of the structure, the more maintenance is needed. Therefore, the more exergy dissipated, the greater the inputs are. Cycling, on the other hand, means that the same energy (and correspondingly, exergy) is utilised better in the system, and therefore more biomass distributed over the structure (exergy) can be formed without increase of the inputs. It has been shown previously that more cycling means an increased ratio of indirect to direct effects, while increased input does not change the ratio of indirect to direct effects; see Chapters 13 and 14.

Fath and Patten (2000) used these results to determine the development of various variables used as goal functions (exergy, power, entropy, etc.). An ecosystem is of course not setting goals, but a goal function is used to describe the direction of development an ecosystem will take. Their results can be summarised as follows:

1. Increased inputs (more solar radiation is captured) mean more biomass is distributed over the same structure, more exergy stored, more exergy degraded and, therefore, also means higher entropy dissipation, more through-flow (power), increased ascendancy, but no change in the ratio indirect to direct effect or in the retention time for the energy in the system = total exergy stored in the system/input exergy per unit of time.

2. Increased cycling implies the same biomass is distributed over a more complex structure, more exergy stored, more through-flow, increased ascendancy, increased ratio of indirect to direct effect, increased retention but no change in exergy degradation.

Almost simultaneously J0rgensen et al. (2000) published a paper, which claims that ecosystems manifest three growth forms (see also Section 12.3):

I. Growth of physical structure (biomass), which is able to capture more of the incoming energy in the form of solar radiation, but also requires more energy for maintenance (respiration and evaporation).

II. Growth of the complexity of network, which means more cycling of energy and matter.

III. Growth of information (more developed plants and animals with more genes), from r-strategists to K-strategists, that wastes less energy but also usually carries more information.

These three growth forms may be considered as an integration of E.P. Odum's attributes, describing changes in an ecosystem associated with development from the early to the mature stage; eight of the most applied attributes associated with the three growth forms should be mentioned (for the complete list of attributes see Table 2.5). These changes are the following:

1. Ecosystem biomass (biological structure) increases.

2. More feedback loops (including recycling of energy and matter) are built.

3. Respiration increases.

4. Respiration relative to biomass decreases.

5. Bigger animals and plants (trees) become more dominant.

6. The specific entropy production (relative to biomass) decreases.

7. The total entropy production will first increase and then stabilise on approximately the same level.

8. The amount of information increases (more species, species with more genes, the biochemistry becomes more diverse).

Growth form I covers attributes 1, 3 and 7. The biomass increases according to attribute 1, which implies that the respiration also increases because it costs more exergy to maintain more biomass. This also means that the entropy production will increase.

Growth form II covers 2 and 6. When the network increases, there will be more feedback mechanisms available for regulation of the network. The energy and matter will thereby circle to a higher extent, which means that more biomass can be supported with the same total input and output of the exergy.

Growth form III covers the attributes 4, 5, 7 and 8. Bigger and more developed species will take over according to growth form III. It implies more biomass in relation to respiration and while the total entropy production is not changed the specific entropy production is decreasing.

Holling (1986)—see Fig. 12.3—has suggested how ecosystems progress through the sequential phases of renewal (mainly growth form I), exploitation (mainly growth form II), conservation (dominant growth form III) and creative destruction. The latter phase also fits into the three growth forms but will require further explanation. The creative destruction phase is a result of either external or internal factors. In the first case (for instance, hurricanes and volcanic activity), further explanation is not needed, as an ecosystem has to use the growth forms under the prevailing conditions that are determined by external factors. If the destructive phase is a result of internal factors, the question is "why would a system be self-destructive?"

A possible explanation is: a result of the conservation phase is that almost all nutrients will be contained in organisms, which implies that there are no nutrients available to test new and possibly better solutions to move further away from thermodynamic equilibrium or, if expressed in Darwinian terms, to increase the probability of survival. This is also implicitly indicated by Holling, as he talks about creative destruction.

Therefore, when new solutions are available, it would, in the long run, be beneficial for the ecosystem to decompose the organic nutrients into inorganic components, which can be utilised to test the new solutions. The creative destruction phase can be considered as a method to utilise the three other phases and the three growth forms more effectively in the long run (J0rgensen and Fath, submitted). This is indicated in the figure as "trend of each further cycle" and it is shown that the ecosystem is moving towards a higher specific

Fig. 12.3. Holling's four phases of ecosystems, described in terms of biomass versus specific exergy. The presentation is inspired by Ulanowicz (1997).

exergy (and maybe biomass), if the inorganic components are available to form more biomass for each cycle.

Five of the presented hypotheses to describe ecosystem growth and development are examined with respect to three growth forms:

A. The entropy production tends to be minimum (this is proposed by Prigogine (1947, 1980) for linear systems at steady non-equilibrium state, not for systems that are far from equilibrium). It is applied by Mauersberger (1983, 1995) to derive expressions for bioprocesses at a stable stationary state. See Section 12.5 and Chapter 3.

B. Natural selection tends to make the energy flux through the system a maximum, so far as compatible with the constraints to which the system is subject (Odum, 1983a,b). This is also called the MPP (see Section 12.2).

C. Ecosystems will organise themselves to maximise the degradation of exergy (Kay, 1984).

D. A system that receives a through-flow of exergy will have a propensity to move away from thermodynamic equilibrium, and if more combinations of components and processes are offered to utilise the exergy flow, the system has the propensity to select the organisation that gives the system as much stored exergy as possible; see Sections 12.1 and 12.3 (J0rgensen and Mejer, 1977, 1979; Mejer and J0rgensen, 1979; J0rgensen, 1982, 1997, 2002b).

E. An ecosystem will have a propensity to develop towards a maximisation of the ascendancy (Ulanowicz, 1986); see Section 12.5 and Chapter 9.

The usual description of ecosystem development illustrated, for instance, by the recovery of Yellow Stone Park after fire, an island born after a volcanic eruption, reclaimed land, etc., is well covered by Odum (1969): at first the biomass increases rapidly which implies that the percentage of captured incoming solar radiation also increases. But since species diversity of plants at the first stage of succession is very low, there are a lot of lacunas in the ability of plants to capture solar radiation in necessary spectral intervals. Moreover, vegetation cover at this stage has not developed a storey structure that naturally decreases its ability to capture incoming radiation, in particular diffusive radiation and radiation, which has already passed through upper storeys. In this time the energy needed for maintenance increases with growth of biomass and flux of metabolic heat increases too. But the heat must be dissipated and for this the mechanism of transpiration is insufficient: in addition, the mechanism of turbulence transport is needed. The latter can be provided by the sufficiently complex architecture of vegetation cover. There are not such types of possibilities at this stage; therefore, the possibilities of simple biomass growth (form I) are quickly exhausted. It is obvious that the information component of exergy is very small, and the value of exergy is determined by the enthalpy of biomass, i.e. captured exergy is equal to captured energy.

Finally, we note that the through-flow (of useful energy), exergy dissipation and the entropy production also increase due to the increased need of energy for maintenance.

Growth form II becomes dominant at the next stage of succession when the ecosystem structure begins to be complicated, although there is an overlap of the two growth forms. Further unstructured growth of biomass does, therefore, not increase the specific exergy of biomass. The complication of structure leads to increase of the information component of exergy and increase of biomass diversity. The role of different species in the ecosystem and their influence on such important general characteristics as, for instance, stability becomes more and more different in comparison with the first stage of proportional simple growth. This means that their biomasses are diversified, and their specific exergies differ more and more from each other. The ecosystem can still improve the ecological network and can still replace r-strategists by K-strategists, small animals and plants with bigger ones, etc. However, growth form II does not require more exergy for maintenance. Exergy degradation is, therefore, not increasing but is maintained on a constant level.

Finally, if growth forms I and II are typical microevolutionary processes (an ecosystem succession belongs to such a type), then growth form III is a macroevolutionary process a when the genotype information is changed as a result of mutations and consequent natural selection, so that the number of non-nonsense genes increases, and less developed species could be more developed. Let us keep in mind the so-called Cope's law: the later descendent may be increasingly larger than its ancestors. For instance, the horse is today much bigger than the horse fossils from 20-30 million years ago.

The accordance with the five descriptors + specific entropy production and the three growth forms based on this description of ecosystem development is shown in Table 12.3.

Table 12.3

An accordance between the growth forms and the proposed descriptors

Growth form I Growth form II Growth form III

Table 12.3

An accordance between the growth forms and the proposed descriptors

Growth form I Growth form II Growth form III

Exergy storage

Up

Up

Up

Power/through-flow

Up

Up

Up

Ascendancy

Up

Up

Up

Exergy destruction

Up

Equal

Equal

Retention time

Equal

Up

Up

Entropy production

Up

Equal

Equal

Exergy/biomass = specific exergy

Equal

Up

Up

Entropy/biomass = specific entropy production

Equal

Down

Down

Ratio indirect/direct effects

Equal

Up

Up

Based upon the results, it is possible to formulate the following hypothesis, which unites the five hypotheses:

"Ecosystem development in all stages will move away from thermodynamic equilibrium and select the components and the organisation that yields the highest flux of useful energy through the system and the most exergy stored in the system. This corresponds also to the highest ascendancy."

12.7. Some final comments

(1) In general, growth means increase in system size, while development is an increase in organisation independent of system size. Growth is measured as mass or energy change per unit of time, while storage-specific growth is measured in 1/units of time. Development may take place without any change (growth) in biomass. Ulanowicz (1986) uses "growth" and "development" as extensive and intensive aspects of the same process; they may often co-occur. In thermodynamic terms, a growing system is one moving away from thermodynamic equilibrium. At the state of equilibrium the system cannot do any work. All its components are inorganic, have zero free energy (exergy) and all gradients are eliminated. Everywhere in the universe there are structures and gradients resulting from growth and developmental processes cutting across all levels of organisation. A gradient is understood as a difference in an intensive thermodynamic variable, such as temperature, pressure, altitude or chemical potential. Second-law dissipation acts to tear down the structures and eliminate the gradients, but it cannot operate unless the gradients are established in the first place. Structure and organisation can be expressed in different units, such as number of state variables, number of connections in an interactive web and kJ of exergy, which corresponds to distance from thermodynamic equilibrium. Biological systems, especially, have many possibilities for moving away from equilibrium, and it is important to know along which pathways among the possible ones a system will develop. This leads to the following hypothesis, formulated in accordance with J0rgensen et al. (2000):

"If a system receives an input of exergy, it will utilise this exergy to perform work. The work performed is applied to: (1) maintain the system, dissipating the residue as heat (degraded exergy) to the system's surroundings, (2) move the system further from thermodynamic equilibrium, reflected in growth of gradients, and if more than one pathway to depart from equilibrium is offered, the one yielding the most work, and ultimately moving the system far away from thermodynamic equilibrium under the prevailing conditions, i.e. giving the most ordered structure, tends to be selected."

This is a restatement and expansion of J0rgensen and Mejer (1977). A paradox appears to exist in conflicting criteria, the joint storage maximisation of the two diametrically opposed properties storage that is build-up and dissipation, or teardown. This chapter has tried to resolve this paradox in an ecological context, and in the process expose the complexity of the interplay between thermodynamics and the growth of order in ecosystems and the ecosphere.

(2) Application of intuitively clear concepts, such as "input", "captured", "dissipation" and "degradation", which seems so clear in application to energy, induces certain difficulties in the case of exergy; in spite of that exergy can be considered as extensive a state variable as energy. In order to avoid these difficulties, we would like to come up with some analogue of them.

It is known that the total exergy of ecosystem is described by expression (3.1), Ex = exkNk, where exk are specific exergies. We assume the following:

1. Let hdet be a specific enthalpy of detritus and exgen the specific genetic exergy of kth species biomass. Then in the process of ecosystem microevolution (succession)

t!1 k passing from the first stage of growth (form I), which at Ex(t) = hdet ^k Nk(t) until the dynamic equilibrium, which at its value Exeq = £k exgenNkq.

2. Exergy in the process of its degradation decreases to the initial value hdet^kNk.

In the framework of this formalism exergy is produced within the system as entropy; it can be imported and exported using such material carriers as energy and matter.

This page is intentionally left blank

Chapter 13

Was this article helpful?

0 0
Getting Started With Solar

Getting Started With Solar

Do we really want the one thing that gives us its resources unconditionally to suffer even more than it is suffering now? Nature, is a part of our being from the earliest human days. We respect Nature and it gives us its bounty, but in the recent past greedy money hungry corporations have made us all so destructive, so wasteful.

Get My Free Ebook


Post a comment