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Fig. 7.17. The energy amplifier ratio, R is defined as the ratio of output B to control flow C. It means that R = 10 in this case (from J0rgensen, 2002b).

where the generalised flow or the ecoflow, indicated as (dNk/dt), is multiplied with the specific useful work, i.e. (DGk/Nk), simply seems to be a conversion to solar energy equivalents of the free energy. The increase in biomass in Eq. (9.1) is a conversion to the free energy flow, and the definition of embodied energy is a further conversion to solar energy equivalents.

Embodied energy is, as seen from these definitions, determined by the biogeochemical energy flow into an ecosystem component, measured in solar energy equivalents. The stored emergy, Em, per unit of area or volume to be distinguished from the emergy flows can be found from:

k=i where the specific emergy, emk, is the quality factor, which is the conversion to solar equivalents, as illustrated in Table 7.1 and Fig. 7.16, and Nk is the concentration expressed per unit of area or volume.

The emergy concept could be formally explained from the point of view of equilibrium thermodynamics. In fact, in a statistical equilibrium system without any constraints (except perhaps the conservation of the total number of particles) the equilibrium distribution is uniform. If we consider the trophic chain as such a system then the state Np = ••• = Np must be in equilibrium, but this contradicts trophic pyramids observed in reality. This contradiction can be resolved by weighing the biomasses in such a way that the equilibrium condition holds for the weighed biomasses. The specific emergy could be such a weighing factor, so that em1 Np = em2Np = ••• = emnNn. (9.3)

The calculations by Eq. (9.2) reduce the difference between stored emergy and stored exergy, which as we showed can also be found with a good approximation as the sum of concentrations multiplied by a quality factor. The quality factor for exergy accounts for the information embodied in the various components of the system (detailed information is given in Chapter 5), while the quality factor for emergy accounts for how much solar energy it has cost to form the various components. Emergy thereby calculates how much solar energy (which is our ultimate energy resource) it has cost to obtain one unit of biomass of various organisms, while exergy accounts for how much "first class" energy (energy which can do work) the organisms possess as a result of the complex interactions in an ecosystem. Both concepts attempt to account for the quality of the energy. Emergy does this by looking into the energy flows in the ecological network to express the energy costs in solar equivalents. Exergy does it by considering the amount of information (which also contains first class energy able to do work, as was shown in Chapter 5) that the components have embodied.

The differences between the two concepts may be summarised as follows:

(1) Emergy has no clear reference state, which is not needed as it is a measure of energy flows, while exergy is defined relative to the environment (see also Chapter 5).

(2) The quality factor of exergy is based on the content of information, while the quality factor for emergy is based on the cost in solar equivalents.

(3) Exergy is better anchored in thermodynamics and has a wider theoretical basis.

(4) The quality factor emk may be different from ecosystem to ecosystem, and in principle it is necessary in each case to assess the quality factor based on an energy flow analysis, which is sometimes cumbersome to make.

The quality factors listed in Table 7.1 or in Brown and Mc Clanahan (1992) may be used generally as good approximations. The quality factors used for computation of exergy (see Chapter 5) require knowledge of the non-nonsense genes (information content) of various organisms, which is sometimes surprisingly difficult to assess. A number of exergy quality factors have been found. From a theoretical point of view they can be used generally. Further comparisons of the two concepts will be presented in Chapter 12.

In his book "Environmental Accounting—Emergy and Environmental Decision Making" (Odum, 1996), H.T. Odum has used calculations of emergy to estimate the sustainability of the economy of various countries. As emergy is based on the cost in solar equivalents, which is the only long-term available energy, it seems to be a sound first estimation of sustainability.

### 7.10. Summary of the ecological important issues

We are now able to describe how an ecosystem is working from a thermodynamic point of view. The maintenance of the ecological structure and the organisms forming the structure of the ecosystem requires a supply of exergy, which is lost as heat to the environment. If more exergy is supplied than needed for maintenance of the status quo, the surplus exergy is stored as more biomass, the more effective and complex network, or more information. It is stored to meet an unexpected period of shortage and to increase the sum of buffer capacities. The structure was named by Prigogine the dissipative structure, because it is permanently dissipating energy (converting exergy to anexergy—"destroying" exergy). It can be shown to be a consequence of the thermodynamic laws and a few other realistic assumptions (for instance, all organisms have a similar chemical composition, which biochemistry has shown us is the case) that an ecosystem will have a considerable number of various organisms with a very high chemical potential (many complex biochemical compounds with a high content of information, for instance hormones) and therefore also a high content of free energy. The latter is consistent with Boltzman's statement: the struggle for life is first of all a struggle for free energy.

It is possible to show that a Prigogine-like theorem is valid for a trophic chain in a mature ecosystem. An early-stage ecosystem (see Table 2.5) will quickly try to build as much biomass as possible, because the biomass will, as a parabolic antenna, capture as much electromagnetic photons (solar radiation) as possible, i.e. capture as much exergy as possible. The mature system on the other hand already captures the possible amount of solar radiation (about 75-80%) and has therefore in its further development to attempt to save exergy. The entropy production will tend to its possible minimum and the biomass of the chain will tend to its possible maximum. Prigogine's thermodynamics seems valid for mature ecosystems, i.e. ecosystems that have reached a dynamic "almost" steady state. It may also be expressed by exergy terms: the trophic chain tends to minimise the exergy spent for maintenance in order to have more surplus exergy to store in the ecosystem. It can even be shown that in a trophic chain the specific exergy (exergy/biomass) tends to increase through a food chain. Zooplankton has higher specific exergy (higher ^-value) than phytoplankton and fish again has higher specific exergy than zooplankton. Nature has a certain degree of randomness that implies that this rule is general but exceptions can of course be found.

When an ecosystem starts at an early state, the appearance of living biomass implies that some thermodynamic machine such as the biochemical cycles begins to work. The system starts to evolve away from the thermodynamic equilibrium: more and more exergy is stored/accumulated in the system and the process continues until all the matter is transferred from non-living to living matter. As for biomass the residence time is not infinite; biochemical cycling of the corresponding elements has to take place. As the system moves away from thermodynamic equilibrium, it can be shown that the trophic chain meets bifurcation points and that the system selects the branch that gives the highest exergy.

Which among many possibilities does a trophic chain select in its effort to move as far away from thermodynamic equilibrium as possible? To answer this question, two useful concepts are introduced: degree of adaptation = the ratio of living biomass to total organic matter and quality of adaptation = specific mean exergy = the total exergy of the system/total organic matter of the system. The maximum specific exergy = the quality of adaptation is reached at a certain level of organic matter where the utilisation of the organic matter (the degree of adaptation) is close to one. Further, an addition of organic matter implies that the quality of adaptation = the specific mean exergy is declining and the utilisation coefficient is only increased slightly (see Figs. 7.14 and 7.15). This is consistent with Kaufman's statement: biological systems operate at the edge of chaos to be able to utilise the available resources at the optimum. An overexploitation of the resources will involve oscillations that will become more and more violent and finally the system will become chaotic. An attempt to increase the specific exergy beyond what the system can bear implies an overexploitation of the lower levels in the food chain and a chaotic system is the result. An ecosystem finds, in other words, a suitable balance of the various levels in the trophic chain.

Emergy measures the cost of energy expressed as solar equivalents, while exergy gives the result of the solar radiation in a form of energy that can do work. It is interesting (see, for instance, J0rgensen, 2002b) that natural systems usually have a low emergy/exergy ratio, while man-made systems have a high ratio emergy/exergy. Natural systems are, in other words, more effective in getting exergy out of solar radiation. This is also consistent with the Prigogine-like theorem. It is recommendable to apply both emergy and exergy as ecological indicators. Emergy gives the cost, exergy the result and the ratio gives the efficiency.

Chapter 8