The annual production of artificial energy consumed by the anthroposphere constitutes about 3 x 10 J yr 1, which is ~12% of the global terrestrial NPP. If all the energy is transformed into heat, then the annual production of entropy is ^_Art« 1 x 1018JK-1 yr-1, which is comparable with some entropic flows in the biota (e.g., with flows caused by uptake of CO2 and release of O2).

Now the biosphere and anthroposphere are in the state of strong competition for common resources, such as land area and fresh water. Contamination of the environment and reduction of the biota diversity are the consequences of the competition.

Since the biosphere (considered as an open thermo-dynamic system) is in dynamic equilibrium, then all entropy flows have to be balanced too. Therefore, the entropy excess, which is created by the anthroposphere, has to be compensated by means of two processes: (1) reduction of the biota and degradation of the biosphere, and (2) change in the work of the Earth's climate machine (in particular, an increase in the Earth's mean temperature). Note that in any case it is desirable to include the entropic flow SArt into the total balance of entropy for both, the atmosphere and biota, but we shall assume that the anthropogenic impact concentrates only on the biota. Then ¿B = ¿D°M + ¿Work + ¿Art. By assuming that equalities ¿_ab(C02) + ¿_ba(02) ~ 0 and ¿D°M ^ = o hold in this case also, we get the follow ing simplified equation:

The total flow of transpiration can be represented as |?ba(H20)| = bB, where B is the total mass of biota (in d.w. of DOM) and b = |qBA(H2O)|/B is the specific intensity of transpiration (in g H2O g-1 d.w.), which is constant. We implicitly assume here that the power of transpiration 'pump' is proportional to the biomass of plant.

On the other hand, since this value of water is necessary to transpire in order to create P units of a new biomass (P = NPP in d.w.), then |qBA(H2O)| = pP, where p is the amount of transpired water, which is necessary for creating 1 g of biomass. Therefore, the coefficient P/B = b/p. It is known that the P/B coefficient is a biome-specific value; apparently, we can let it be a constant. Since |qBA(H2O)| = 4.8 x 1019g H2Oyr-1, B = 1.86 x 1018gd.w. and P = 1.4 x 1017gd.w.yr-1, then b = 25.8 gH2Og-1 d.w. per year, p = 343 g H2Og-1 d.w., and P/B = 0.075 yr-1. So, S(H2O) = -0.221 x 103BJK-1yr-1 or S(H2O) = -2.93 x 103 PJK-1

Let us consider the entropic flow Ssb, which is proportional to area Aveg covered by vegetation. Since vegetation covers the globe by a relatively thin layer, then the equality ^_sb = aB or ^_sb = [a/(P/B)] P are rather plausible hypotheses. The value of a is easily found from eqn [8]: a = 28.5J K-1 per g d.w. per year.

The entropic flow SWork = [ftr(DOM)]P = [ftr(DOM)(P/B)]B, so that SWork = 60.4ftP = 4.53ftB.

Finally, eqn [11] is rewritten as dVd/ ~ ( -192 + 4.530)B + ,SArt

This equation allows us to estimate different critical bounds of the impact of humankind on the biosphere. The impact may be manifested through: (a) increase in energy, E = TBSArt leads to decrease in the total biomass, B; (b) increase in energy inhibits the NPP, that is, B = B(E), SB/SE < 0 and P = P(E), SP/SE < 0. The simplest form of these functions may be linear, B = Bnat(l -E/EcBnt) and P = Pnat (l -E/EcPnt), where Bnat = 1.86 x 1018g and Pnat = 1.4 x 1017g are natural (without anthropogenic impact) values of biomass and NPP, EBrit and EPrit are critical values of energy with respect to the biomass and NPP (they vanish at these values).

The biota is living if dSB/di < 0; therefore, the upper bound for human energy production, E is

EcritS

Ecrit S

where £B = TB(192 - 4.53ft)Bnat, £P= TB(25.5 - 0.604ft) x 102 Pnat. In the previous section, we gave some meaningful interpretation to the parameter ft, but here ft is regarded as a free parameter.

Example 1. The lower bound of ft is ft* = 29 (see Exergy), which is equivalent to full disappearance of the biosphere of vascular plants. From eqn [13] we get, for ft = 29: £b « 3.2 x 1022J yr-1. In order to estimate E®it we assume that this value is equal to the full enthalpy of biota, that is, EBrit « 3.2 x 1022Jyr-1, then E* « (1/2)EBrit = 1.62 x 1022Jyr-1. Today humans are consuming about 3.24 x 1020J annually. If humans would be doubling their energy consumption by every decade, then they would reach and exceed this bound during the next 70 years.

Example 2. The work performed annually by the biota

P nat then

(1 -E/EL) where PnM Wb = WT(1 -£/£p.iJ, where Wgnat = hooM^Pnat - 1 x 1023 J yr -1 is the work of the 'natural' biota. Therefore, the relative work corresponding to the bound E* is Wb7WT = Eprit/ (£frit + CP). One of the possible estimations of Wg/ Wgat — 0.95, that is, only 5% of the potential work of the biosphere can be used to maintain its structure (in particular, animals) and its evolution; the rest is spent to turn the 'wheels' of the global biogeochemical cycles, so that £P(/3) = 0.0526£prit. By substituting this value into eqn [13], we get E* = 0.05£prit. We assume that Eprit is equal to the total enthalpy of the NPP -2.44 x 1021Jyr—1, then E* = 1.22 x 1020Jyr—1. By comparing this value with the current energy uptake, 3 x 10 Jyr— , we see that we already have serious problems today.

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