Thermodynamics of the biosphere

In nature all is harmony, A consonance fore'er agreed on...

F. Tyutchev, 1865

.It is living matter—the Earth's sum total of living organism—that transforms the radiant energy of the Sun into the active chemical energy of the biosphere. Living matter creates innumerable new chemical compounds and extends the biosphere at incredible speed as a thick layer of new molecular systems. These compounds are rich in free energy in the thermodynamic field of the biosphere. Many of the compounds, however, are unstable, and are continuously converted to more stable form. .Mechanisms, created by this way—living organisms—are principally distinct from other atomic, ionic, or molecular systems in the Earth's crust, both within and outside the biosphere.

V. Vernadsky "Biosphere", 1926

11.1. Introduction

At the beginning of the XIXth century, J.-B. Lamarque had introduced the term "Biosphere". He considered it as the "Scope of Life" and some sort of external cover for Earth. In 1875, the same term was introduced in geology by E. Süss, who distinguished the biosphere as one of Earth's covers. But V. Vernadsky was the person who first created the modern concept of the biosphere. This concept was stated in two lectures published in 1926. Later, it was further developed by Vernadsky himself and by Kostitzin (1935), Timofeev-Resovsky (1961a), Sukhachev (1967) and other Russian scientists. All this work put together allows us to speak of the Russian classical school (Svirezhev, 1974).

According to Vernadsky, the biosphere is an external Earth cover, the Scope of Life (let us recall Lamarque). But he notes also that this definition (as for the Scope of Life) is not complete. The Vernadsky biosphere includes:

• "bio-generic matter", i.e. organic and mineral substances created by living matter (for instance coal, peat, litter, humus, etc.),

• "bio-inert matter", created by living organisms together with inorganic Nature (water, atmosphere, sediment rocks).

Towards a Thermodynamic Theory for Ecological Systems, pp. 271-299 © 2004 Elsevier Ltd. All Rights Reserved.

From the point of view of thermodynamics the biosphere of our planet is a typical open system that exchanges energy and matter with Space and Earth's mantle. Certainly, both the meteoric flux and the volcanism are matter fluxes into the system, and the escaping gases and plates tectonics are typical matter fluxes out of it, but the influence of all these fluxes is negligibly small (at least, for considered periods of time). On the other hand, if we would like to consider the long-term evolution of the biosphere, all the above-mentioned slow fluxes have to be taken into account.

The biosphere is a typical "large" system with an abundance of interacting components. In addition to the methodology of large systems in the study of biosphere processes, we may also use the following two paradigms: the "atomistic" paradigm of bio-geocoenoses (BGC) and the paradigm of invariant structure of biogeochemical cycles.

(a) Bg-paradigm. While the Vernadsky concept may be considered as maximally aggregated (it is like a view of the biosphere from the outside), the concept of the BGC suggested by Sukhachev (1967) and developed by Timofeev-Resovsky (1961b) relates to the elementary units of the biosphere, a concept that is basically atomistic in nature. In accordance with the Timofeev-Resovsky definition, the BGC is a part (area) of the biosphere, which has no any essential ecological, geo-morphologic, hydrological, micro-climatic or any other borders within itself. The entire biosphere is divided by these borders on elementary systems, naturally separated from one another. Due to the reality of existence of these boundaries, the BGCs can be considered as half-isolated subsystems, the averaging inside them is quite natural. So, the BGC dynamics can be described by a comparatively small number of variables.

The BGC is also an elementary unit of biogeochemical work in the biosphere. Indeed, all the local nitrogen and phosphorus turnovers are practically closed inside the BGC (excluding denitrification); therefore, in respect to these elements, the BGC may be considered as an almost closed system. If we consider the bio-geocenotic local carbon cycle then we can see that the number of different internal paths of carbon is much higher than the number of carbon inflows and outflows connecting the given BGC with others and with the atmosphere. In other words, the internal structure of BGC is more complex than the structure of its connections with the environment—although all BGCs are connected to the single entity, the biosphere, by the atmosphere and hydrosphere. It is very important that all BGCs have the same structure of the local biogeochemical cycles; therefore, they are dynamically similar, differing from each other only by the parameters. It implies that if we describe the BGC dynamics as the dynamics of local biogeochemical cycles, then the differences between the BGCs are the differences in parameters of the same dynamic systems.

Finally, if the model of the biosphere is primarily the model of global biogeochemical cycles, then the whole biosphere can be considered as a system of loosely interacting elementary subsystems, subjected to the same dynamic laws and relations. Elementary units (subsystems) differ from each other only by different values of parameters. So, we can consider the biosphere as the statistical ensemble.

According to N. Basilevich (personal communication), there are about 50,000 BGCs on the Earth's surface. In principle, we would not have any problems if we had complete information on all the parameters of all BGCs (first of all, their spatial distribution on Earth). However, this is far from being the case. Moreover, our knowledge is unsatisfactory for the most part of the Earth's surface. The only solution is to apply methods of spatial interpolation and extrapolation of the available information (under the assumption of continuity).

(b) Hypothesis of the invariant structure of biogeochemical cycles. The second paradigm is based on the hypothesis of the invariant structure of biogeochemical cycles. In other words, the structure of interrelations, along which biogeochemical flows, water and energy are circulated, does not depend on the size of the system itself, or on its geographical location; only the values of flows change. Therefore, in accordance with this concept, we can consider the whole terrestrial vegetation pattern as some united ecosystem described by some average parameters, not differing structurally, for instance, from a forest ecosystem.

However, these two approaches should lead to the same result, as the difference between them is the difference between thermodynamics and statistical mechanics, i.e. the difference in the methods of averaging.

Continuing further study of the biosphere problem, we suggest using the following three basic axioms (see also Svirezhev, 1998a, 1999):

1. The contemporary state of the biosphere is stationary.

2. This state is stable in Lyapunov's sense.

3. This state is structurally stable.

In the process of the study we implement two scientific paradigms: Vernadsky's concept of the biosphere and the evolutionary (Darwinian) paradigm. The evolutionary paradigm gives us the possibility to assert that the current state of the biosphere is the result of the evolutionary process, in that natural selection chooses this state from multiple virtual variants. Therefore, any biosphere model should possess some properties of selectivity, i.e. it should be the non-linear model with multiple equilibriums.

It is obvious that the model has also to comply with the different laws of conservation (energy, matter and momentum), since the biosphere is practically a closed system (with respect to matter) and a "through-flow" system (with respect to energy). The latter means that perhaps the biosphere is a typical dissipative structure.

The model should not be contradictory from the thermodynamic point of view, since the biosphere is an open system far from thermodynamic equilibrium.

An application of these "selective" criteria allows us to assume that such a model would adequately describe the dynamics of the biosphere.

11.2. Comparative analysis of the energetics of the biosphere and technosphere

The biosphere as an open thermodynamic system exists due to a permanent flow of solar energy. Earth receives 3.5 X 1024 J of solar energy annually that maintains the work of the climatic machine. The function of the "green cover" results in 5.5 X 1021 J/year of new biomass. Thus, although vegetation is the main concentrator and transformer of solar energy in the biosphere, it uses only 0.16% of solar energy for the creation of a new biomass. The rest is spent on the process of transpiration by leaves, providing water and nutrient transport, etc. Approximately 60% of it is immediately used for respiration and the remaining 40% is the annual global production, which is equal to 2.3 X 1021 J/year (Svirezhev and Svirejeva-Hopkins, 1998).

The energetic characteristics of the biosphere have not significantly changed since the beginning of the era of vascular plants (about one billion years ago). The efficiency coefficient of the autotrophic component, the functioning of which provides the energetic basis for evolution of animals, is equal to h = 2.3 X 1021/3.5 X 1024 < 0.66%.

Stability of the biosphere is maintained by the permanent dissipation of energy. In other words, the biosphere is a typical dissipative system. This energy flow provides a steady state for 1.84 X 1018 g of living biomass (or 3.5 X 1022 J), and animal biomass constitutes only 0.8% of it, i.e. 1.46 X 1016 g. Animals consume only 3% of the NPP (7.35 X 1019 J/year) (Smil, 1991) that maintains both the metabolism of living matter and its diversity. The latter is the information basis of evolution.

At the present time, Earth's technosphere (our technological civilisation) spends about 3 X 1020 J/year to provide its functioning and evolution (Svirezhev and Svirejeva-Hopkins, 1998). This is mainly the energy of fossil fuels and nuclear energy. A share of "pure" biosphere energy (hydropower station and firewood) in this balance is small (~ 5%).

It is obvious that Homo sapiens is a component of both the biosphere and technosphere. If we consider humans as animals, then all human energetic requirements are satisfied through food, and the annual energy food demand per individual is 4 X 109 J. For the current population size of Homo sapiens (< 6 X 109 individuals) annual energy food demand is equal to 2.4 X 1019 J/year. By comparing these values we see that the energy demand of mankind (as a biological species) is currently equal to one-third of the total biological energy of the biosphere which is accessible to animals (7.35 X 1019 J/year). Fig. 11.1 represents the dynamics of food energy demand for mankind, using the reconstruction of human population growth from the Neolithic era. Until the Neolithic revolution, when man changed his behaviour from gathering to producing food, he was part of the biosphere, no different from other animals.

At the time of the Neolithic revolution the human population included 4 X 106 individuals, and required the energy supply of 1.6 X 1016 J/year, which was 0.022% of the total energy flow for all animals.

According to the physical theory of fluctuations (Landau and Lifshitz, 1995) the probability of fluctuation which could cause the elimination of Homo sapiens is equal to:

[energy demand for human population "1 energy supply for all animals J T 1.6 X 1016

7.35 X 1019

FrOm NeOlithic times until the beginning Of industrial revOlutiOn (at the edge Of the XVIIIth and XIXth centuries) with its Own sOurce Of energy (fossil fuels), Man had been Only a part Of the biOsphere. Humans were cOmpeting with Other species, and had increased their energy demand up tO 4 X 1018 J/year, sO that the prObability Of their eliminatiOn decreased until Pr0 = exp[—4 X 1018/7.35 X 1019] < 94.8%. LOOking at these

GJ/year

2.4-1010

0.8-109

1.4-109

4-109

1.6107

1800 2000 years

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