Quantifying the biologically possible range of steady-state ... - CiteSeerX

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Biologia, Bratislava, 61/Suppl. 19: S234—S239, 2006

Quantifying the biologically possible range of steady-state soil and surface climates with climate model simulations Axel Kleidon1,2 1

Department of Geography and Earth System Science Interdisciplinary Center, University of Maryland, 2181 Lefrak Hall, College Park, MD 20742, USA; tel.:+1-301-405-3203; fax: +1-301-314-9299; e-mail: [email protected] 2 Max-Planck-Institut für Biogeochemie, Postfach 10 01 64, D–07701 Jena, Germany; tel.: +49-3641-576217; fax: +49-3641576201; e-mail: [email protected]

Abstract: The terrestrial biosphere shapes the exchange fluxes of energy and mass at the land surface. The diversity of plant form and functioning can potentially result in a wide variety of possible climatic conditions at the land surface and in the soil, which in turn feed back to more or less suitable conditions for terrestrial productivity. Here, I use sensitivity simulations to vegetation form and functioning with a global climate model to quantify this possible range of steady-states (“PROSS”) of the surface energy- and mass balances. The surface energy- and water balances over land are associated with substantial sensitivity to vegetation parameters, with precipitation varying by more than a factor of 2, and evapotranspiration by a factor of 5. This range in biologically possible climatic conditions is associated with drastically different levels of vegetation productivity. Optimum conditions for maximum productivity are close to the simulated climate of present-day conditions. These results suggest the conclusions that (a) climate does not determine vegetation form and function, but merely constrains it, and (b) the emergent climatic conditions at the land surface seem to be close to optimal for the functioning of the terrestrial biosphere. Key words: atmosphere-biosphere interactions, climate, feedbacks, maximum entropy production, vegetation

Introduction Terrestrial vegetation affects soil and surface properties over land, and thereby modulates the exchange fluxes of energy, water and carbon between the land surface and the overlying atmosphere. When compared to a bare surface, green forest canopies absorb more solar radiation, are aerodynamically rougher, and have a higher ability to transpire water. Below the ground, vegetation can reach to greater depth through the root system to explore soil moisture supply for evapotranspiration, and litter production by vegetation increases soil organic matter, which in turn increases the ability of soils to hold moisture and affects soil hydraulic conductivity. Climate model simulations of a “Desert World” show that the climate over land would be drastically different in the absence of terrestrial vegetation (Betts, 1999; Fraedrich et al., 1999; Kleidon et al., 2000) and would likely result in climatic conditions less suitable to vegetation growth (Betts, 1999; Kleidon, 2002). What these extreme sensitivity simulations demonstrate is that the climate of the land surface and soil system can operate in different steady states, depending on vegetation form and functioning. To put this into a conceptual framework, we can describe the steady state

in terms of the balances of energy, water, and carbon, characterized by the surface temperature Ts , the aggregated soil water content within the rooting zone Ws , and the amount of carbon stored in live vegetation Cveg and in the soil Csoil . The climatological surface energy balance can be expressed as follows: cp dTs /dt = Qsw,net − Qlw,net − Qsh − Qlh = 0

(1)

with cp being the heat capacity of the soil, Qsw,net the net absorption of shortwave radiation at the surface, Qlw,net the net emission of longwave radiation, Qsh the sensible heat flux, and Qlh the latent heat flux. We consider the climatic mean state only, so that eqn. (1) yields zero when averaged over a sufficiently long time period. Similarly, the steady-state surface water balance is expressed as the balance of the fluxes of precipitation P, evapotranspiration E, and runoff and drainage R: dWs /dt = P − E − R = 0

(2)

Note that the rate of evapotranspiration E is linked to the latent heat flux by E = Qlh /L, with L being the latent heat of vaporization. Finally, the simplified carbon balances of live veg-

Quantifying the biologically possible range of steady-state soil and surface climates etation and soil carbon are expressed by: dCveg /dt = GP P − RESa − LIT = 0

(3)

dCsoil /dt = LIT − RESh = 0

(4)

with GPP being the gross primary productivity, RESa the rate of autotrophic respiration, LIT the litter production rate, and RESh the heterotrophic respiration rate. Not included here for simplicity are the mass balances of nutrients. These balances are not independent, but strongly coupled. Vegetation productivity GPP depends on light (i.e. Qsw,net ), but also on the rate of transpiration (as a part of E) since transpiration is closely linked to the gas exchange of carbon dioxide between the air and the leaf’s interior. On the other hand, GPP and biomass Cveg affect leaf area and rooting depth, both of which affect E and Qsw,net . Furthermore, the actual rate of E affects boundary layer characteristics, including the formation of convective clouds and rainfall (e.g. Lyons, 2002). This in turn affects the amount of incoming solar radiation (as an important component of Qsw,net ) and the precipitation rate P. Even though Qsw,net and P would seem to be important drivers of the surface energy- and mass balances, these variables are in fact not independent variables. In other words, these fluxes do not determine the steady-state energy- and mass balances, but merely act as constraints that emerge from the interaction of the surface with the overlying atmosphere. These constraints limit the form and functioning of terrestrial vegetation. For instance, the actual value of P imposes an upper boundary on the rate of evapotranspiration E, and thereby on GPP. Likewise, Qsw,net imposes an upper, energetic limit on E and on the lightlimited rate of GPP. Yet it is through the diversity of plant form and functioning that many degrees of freedom are introduced to the energy- and mass balances. That is, a range of possible solutions to eqns. (1–4) exists, resulting in a range of values for Ts , Ws , Cveg and Csoil . For instance, the partitioning of carbohydrates between below- and aboveground growth (root-shoot ratio pr,s ) can vary among plants. The carbon balance constraint acts to limit the total amount of carbohydrates to be partitioned. Within this range, pr,s modulates the leaf area and the rooting characteristics of the surface, two climatologically relevant land surface properties. A high allocation to belowground growth would allow for a greater ability to access stored water in the soil. But it comes at the expense of reduced aboveground growth, resulting in less leaves. For the physical functioning of the land surface, this would result in a larger soil moisture holding capacity within the rooting zone, which potentially enhances E, but a lower leaf area index and therefore likely in a higher surface albedo, reduced vegetation cover, and a lower Qsw,net . Root-shoot partitioning is just one example of

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the moderating effects of terrestrial vegetation on land surface and climate functioning. The purpose of this paper is to provide a simple estimate for the range of steady-state climatic conditions that are “biologically possible”. I use the term “biologically possible” to refer to forms and functioning of terrestrial vegetation that result in a positive, nonzero productivity (i.e. GPP > 0). This Possible Range Of Steady States (short, “PROSS”) of the land surface energy- and mass balances will be quantified with numerical simulations with a coupled vegetation-climate system model.

Material and methods I use the Planet Simulator (PlaSim, LUNKEIT et al., 2004; FRAEDRICH et al., 2005a,b), an Earth system model of intermediate complexity. This model consists of an atmospheric component that simulates the dynamics of atmospheric motion, radiative transfer processes, and a full treatment of the atmospheric water cycle including a prognostic cloud scheme. The land component consists of a 5- layer soil temperature model, a snow model, and a “bucket” soil hydrology scheme. The model represents the land surface with a coarse resolution of about 5.6◦ × 5.6◦ lat/lon, and model equations are integrated on a time step of 40 minutes. The model is able to reasonably simulate the present-day climate (see e.g. KLEIDON, 2006). Fully integrated into the model is SimBA, a simple dynamic global vegetation model. The purpose of SimBA is to capture the first-order aspects of the interrelationship between terrestrial productivity, climate, and large-scale land surface parameters, such as surface albedo, leaf area index, canopy conductance, and rooting zone depth. In SimBA, the net rate of photosynthesis (gross primary productivity, GPP) is taken as the minimum of a light-limited and a flux-limited rate, following the approach of MONTEITH et al. (1989) and DEWAR (1997). The light-limited rate is parameterized as a function of photosynthetically active radiation, surface temperature, and fractional cover of leaves. The flux-limited rate is proportional to the gradient of carbon dioxide across the leaf-air interface and the rate of transpiration. Heterotrophic respiration is taken to be proportional to biomass, with an assumed turnover rate of 40 years. The mass balance of live biomass is then modeled using GPP, respiration, and vegetation biomass change. Vegetation biomass in turn sets the fraction of the land surface fveg that is dominated by vegetation. Land surface parameters of the climate model are then determined from a weighted sum of a value representative of a bare surface and one representative of vegetation. These parameters are: surface albedo as , soil water holding capacity of the rooting zone Ws,max (“bucket size”), surface roughness z0 , and a unitless surface conductance gs that is introduced as a multiplier in the bulk formula in the calculation of the latent heat flux. Even though this is a highly simplified representation of vegetation dynamics, it nevertheless achieves the objective of providing an interactive coupling of the vegetation-climate system. The climatic conditions affect the rate of photosynthesis, through light, temperature, and water availability. Photosynthetic activity builds up biomass, which then affects land surface parameters that in turn affect climate. A

S236 more detailed description of SimBA is given in KLEIDON (2006). In order to evaluate the range of steady-state climates that are biologically possible, we conduct a series of sensitivity simulations with the model in which we vary vegetationrelated model parameters. The model parameters and the range over which these were varied are: maximum stomatal conductance gs,max (gs,max = 0.01, . . . , 1.00), canopy roughness z0,c (z0,c = 0.1m, . . . , 10.0m), root-shoot ratio pr,s (pr,s = 0.01, . . . , 0.99) and a parameter pgrow which describes how much of the productivity is allocated to biomass growth (pgrow = 0.01, . . . , 1.00). These parameters are varied in a globally uniform manner. While this is clearly unrealistic, we chose this setup here in order to yield a consistent model setup. Sea surface temperatures are prescribed in the simulations. Each sensitivity simulation was started with zero vegetation biomass and was then run for an equivalent of 200 years in order for the biomass pools to reach a steady state. The mean climatic state is then determined from averaging model output over the last 10 years. In total, more than 100 sensitivity simulations were performed where these parameters were modified within the given ranges. The model’s standard setup for the presentday (the “Control”) uses values of gs,max = 1.00, z0,c = 2m, pr,s = 0.50, and pgrow = 1.00. Another simulation with a “Desert World” setup (as in KLEIDON et al., 2000) was performed that is void of terrestrial vegetation. The reader is referred to PAVLICK & KLEIDON (2006) for more details regarding the simulation setup and model validation.

A. Kleidon

Fig. 1. Possible range of global mean land surface temperature and soil wetness within the rooting zone and the associated value of vegetation productivity in gC m−2 d−1 . Each symbol represents the average from one sensitivity simulation.

Results The possible range of steady-state conditions of the land surface is investigated in terms of the annual means averaged over all land areas. Even though the consideration of global land means is a gross simplification that cannot capture the large geographic variation of climatic conditions across regions, it is used here to demonstrate the concept and to provide a first estimate of PROSS. Figure 1 shows PROSS in terms of surface temperature and soil wetness (mean soil moisture content divided by soil moisture holding capacity of the rooting zone). The sensitivity simulations span a range of annual mean land temperatures of about 15–19 ◦C, and a range of soil wetness values of ≈ 0 to 55%. Mean soil wetness is most sensitive to the value of root-shoot partitioning, as expected. Stomatal conductance shapes most strongly the variation of global land temperature. This can be understood directly as the result of differing levels of latent cooling (see variation of E in Fig. 4 and discussion below). Associated with these differences in surface climate is a wide range of contrasting configuration of the terrestrial carbon balance, as shown in Fig. 2. The PROSS of the surface energy balance spanned by the sensitivity simulations is shown in Fig. 3. Note that the climatological mean energy balance constraint, Qsw,net = Qlw,net + Qsh + Qlh is indicated by the dotted lines in Fig. 3. Total absorbed solar radiation varies by about 20 W m−2 . Under this con-

Fig. 2. Possible range of steady states of the global mean terrestrial carbon balance, in terms of the average amounts of carbon stored in vegetation biomass and the soil. The ”Desert World” simulation (black star) is, by definition, located at carbon pool sizes of zero kgC m−2 .

straint of absorbed solar heating, the range of possible values for radiative and turbulent cooling is about 30 W m−2 . The corresponding PROSS of the annual mean water balance is shown in Fig. 4. The set of points (P, E)

Quantifying the biologically possible range of steady-state soil and surface climates

Fig. 3. Possible range of steady states of the terrestrial energy balance, in terms of annual means of net emission of longwave radiation and turbulent fluxes (sum of the sensible and latent heat fluxes).

Fig. 4. Possible range of steady states of the terrestrial water balance, in terms of the annual means of precipitation and evapotranspiration. Also shown for comparison is the 1 : 1 line and a linear best fit line.

from the sensitivity simulations fall on a straight line, with a best fit of E = –1.50 + 1.37 · P (r2 = 0.99), in units of mm/d. Extrapolated to E = 0 results in a value of P = 1.09 mm d−1 , which would be the rate of precipitation in the absence of any continental evapotranspiration. In this case, continental runoff (and atmospheric

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moisture convergence) would balance precipitation, i.e. R = 1.09 mm d−1 . The fact that the slope is greater than 1 indicates that continental runoff decreases with increased P (as a result of increased E), and attains values of R = 0.76 mm d−1 at P = 2 mm d−1 and R = 0.39 mm d−1 at P = 3 mm d−1 . However, at values above P ≈ 2.5 mm d−1 , a deviation from the linear relationship can be seen that converges to the 1:1 slope. This means that the increased intensity of continental recycling of moisture with higher values of E and the associated decoupling of local water sources from the large-scale atmospheric moisture convergence saturates at high values of P. Also indicated in Figs 1–4 is the effect of the associated climates on simulated vegetation productivity. These conditions vary widely, from near zero productivity (symbols filled by light colors) to a maximum of about 3.5 g C m−2 d−1 (symbols filled with dark colors). In all diagrams, the “Control” simulation (indicated by the white star) is reasonably close to the simulations that are associated with maximum productivity. Discussion The sensitivity simulations are clearly highly simplified. The model is one of intermediate complexity, emphasizing first-order effects and interactions. The simulation setup is simplified in that vegetation parameters were varied in a globally uniform manner. Many other effects of the terrestrial biosphere on soil and land surface functioning were not included here. For instance, the value of plant available water and soil conductivity depend on the amount of organic matter. As shown in Fig. 2, the amount of simulated soil carbon varies drastically among the simulations, which would imply very different soil properties and nutrient cycling characteristics. These aspects were also not considered here, but would clearly affect the results. Despite these shortcomings, the model simulations nevertheless confirm the main point of this paper, that there is a wide range of possible steady-state solutions to terrestrial surface energy-, water-, and carbon balance that depends on the emergent shape and functioning of the terrestrial biosphere. This view is notably different to the more traditional viewpoint that the climate system operates in one or a few (multiple) steady states [e.g. see Budyko (1969) with respect to the snow- albedo feedback, e.g. Claussen, 1998 and Wang, 2004 for vegetation-climate interactions]. The results presented here also show that the wide range of possible steady state solutions of the terrestrial energy-, water-, and carbon balance have different implications for the productivity of the terrestrial biosphere. Since the “Control” climate is close to one yielding maximum productivity, it seems that the terrestrial biosphere self-organizes itself into a steady-state of maximum productivity. While optimization principles have been used before, they have been used pri-

S238 marily with respect to plant or stand scale, e.g. with respect to root-shoot partitioning (Thornley, 1969; Thornley, 1972), stomatal functioning (Cowan & Farquhar, 1977; Cowan, 1977), optimum nitrogen distribution in canopies (Field, 1983; Dewar, 1996), and rooting depth (Kleidon & Heimann, 1998; Kleidon, 2004b). The difference in this study is that largescale atmospheric feedbacks are explicitly included in the optimization process, so that the resulting maximum emerges at the planetary scale. The resulting notion that the present-day climate is optimal for the productivity of the terrestrial biosphere is similar to the Gaia hypothesis of Lovelock (1972), which states that the Earth’s climate is regulated for and by the biosphere. More importantly, the maximization of productivity is consistent with the fundamental thermodynamic principle of Maximum Entropy Production (MEP, e.g. Ozawa et al., 2003; Dewar, 2003; Dewar, 2005; Kleidon & Lorenz, 2005) as applied to the Earth’s biosphere (Kleidon, 2004a; Kleidon, 2004c; Kleidon & Fraedrich, 2005). Since productivity balances respiration in steady state, a maximization of productivity is equivalent with the maximization of respiration, which in turn measures the dissipative nature of the terrestrial biosphere. Maximization in photosynthetic activity then corresponds to a maximization of biotic entropy production. This places the maximization of GPP on a fundamental principle, one that applies not only to biological processes, but also to purely physical processes such as atmospheric turbulence (e.g. Paltridge, 1975; Paltridge, 1978; Ozawa & Ohmura, 1997; Lorenz et al., 2001; Kleidon et al., 2003; Kleidon et al., 2006). However, further evaluations and comparison to observations would be necessary to confirm that present-day climatic conditions are indeed optimal to the terrestrial biosphere. An attempt in doing so is given in Pavlick & Kleidon (2006). Optimal functioning of the terrestrial biosphere has important consequences for the impacts of perturbations and change on land surface functioning (Kleidon, 2004a). This is schematically shown in Fig. 5. When a steady-state is perturbed, the state of the land surface deviates from the optimum. As a response of the coupled system, the overall feedback to the perturbation is negative, that is, it is going to bring the conditions back to the optimum (Fig. 5 top). This is an inherent property associated with MEP and optimality. When conditions change on longer time scales, for instance in response to interannual variability, glacialinterglacial changes or future changes associated with elevated concentrations of atmospheric carbon dioxide, then the optimal properties associated with vegetation form and functioning are likely to shift (Fig. 5 bottom). An inadvertent consequence of this is that if the adaptability of vegetation behavior is not considered, the dissipative activity of the terrestrial biosphere under change can only be underestimated, resulting in bi-

A. Kleidon

Fig. 5. Conceptual diagram to illustrate how optimized vegetation responds to (top) perturbation and (bottom) climatic change.

ases in the simulated climate sensitivity. For instance, imagine the case where conditions in a particular region would turn drier in a scenario of change. This would result in a shift in the factors that limit photosynthesis, with water becoming more limiting while light becomes less important. The vegetative cover is likely to respond to this change by shifting growth patterns towards more belowground growth to explore a wider range of the soil column for water. Even though the overall effect of change may nevertheless result in a lower overall productivity, the shift in growth pattern will compensate this reduction in productivity to some extent. Such adaptive behavior would be constrained to take place within the possible range of steady-states (i.e. subject to the surface energy-, water-, and carbon balance constraints) and subject to a characteristic time scale. Nevertheless, adaptive behavior in this context would have important implications for vegetation feedbacks to global change in that non-adaptive behavior would necessarily result in an emphasis of the negative impacts of global change (as in the case of e.g. Cox et al., 2000). Acknowledgements The author thanks Ryan PAVLICK for help with the simulations and discussions. This research is supported by the National Science Foundation through grant ATM336555. References BETTS, R.A. 1999. Self-beneficial effects of vegetation on climate in a ocean-atmosphere general circulation model. Geophys. Res. Lett. 26: 1457–1960.

Quantifying the biologically possible range of steady-state soil and surface climates BUDYKO, M.I. 1969. The effect of solar radiation variations on the climate of the Earth. Tellus 21: 611–619. CLAUSSEN, M. 1998. On multiple solutions of the atmospherevegetation system in present-day climate. Glob. Ch. Biol. 4: 549–559. COWAN, I.R. 1977. Stomatal behaviour and environment. Adv. Bot. Res. 4: 117–128. COWAN, I.R. & FARQUHAR, G.D. 1977. Stomatal functioning in relation to leaf metabolism and environment, pp. 471–505. In: JENNINGS, D. H. (ed.), Integration of activity in the higher plants, Cambridge University Press, Cambridge, UK. COX, P.M., BETTS, R.A., JONES, C.D., SPALL, S.A. & TOTTERDELL, I.J. 2000. Acceleration of global warming due to carbon-cycle feedbacks in a coupled model. Nature 408: 184– 187. DEWAR, R.C. 1996. The correlation between plant growth and intercepted radiation: an interpretation in terms of optimal plant nitrogen content. Ann. Bot. 78: 125–136. DEWAR, R.C. 1997. A simple model of light and water use efficiency for Pinus radiata. Tree Physiol. 17: 259–265. DEWAR, R.C. 2003. Information theory explanation of the fluctuation theorem, Maximum Entropy Production, and selforganized criticality in non-equilibrium stationary states. J. Physics A 36: 631–641. DEWAR, R.C. 2005. Maximum entropy production and the fluctuation theorem. J. Physics A 38: 371–381. FIELD, C.B. 1983. Allocating leaf nitrogen for the maximization of carbon gain: leaf age as a control on the allocation program. Oecologia 56: 341–347. FRAEDRICH, K., JANSEN, H., KIRK, E. & LUNKEIT, F. 2005a. The planet simulator: Green planet and desert world. Z. Meteorol. 14: 305–314. FRAEDRICH, K., JANSEN, H., KIRK, E., LUKSCH, U. & LUNKEIT, F. 2005b. The planet simulator: Towards a user friendly model. Z. Meteorol. 14: 299–304. FRAEDRICH, K., KLEIDON, A. & LUNKEIT, F. 1999. A green planet versus a desert world: Estimating the effect of vegetation extremes on the atmosphere. J. Clim. 12: 3156–3163. KLEIDON, A. 2002. Testing the effect of life on Earth’s functioning: How giant is the Earth system? Clim. Ch. 66: 271–319. KLEIDON, A. 2004a. Beyond Gaia: Thermodynamics of life and Earth system functioning. Clim. Ch. 66: 271–319. KLEIDON, A. 2004b. Global datasets of rooting zone depth inferred from inverse methods. J. Clim. 17: 2714–2722. KLEIDON, A. 2004c. Optimized stomatal conductance of vegetated land surfaces and its effects on simulated productivity and climate. Geophys. Res. Lett. 31: L21203. KLEIDON, A. 2006. The climate sensitivity to human appropriation of vegetation productivity and its thermodynamic characterization. Glob. Planet. Ch. (in press) KLEIDON, A. & FRAEDRICH, K. 2005. Biotic entropy production and global atmosphere-biosphere interactions, pp. 173–190. In: KLEIDON, A. & LORENZ, R. D. (eds), Non-equilibrium thermodynamics and the production of entropy: Life, earth, and beyond, Springer Verlag, Berlin, Heidelberg. KLEIDON, A. & HEIMANN, M. 1998. A method of determining rooting depth from a terrestrial biosphere model and its impacts on the global water- and carbon cycle. Global Change Biol. 4: 275–286.

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KLEIDON, A. & LORENZ, R.D. (eds) 2005. Non-Equilibrium Thermodynamics and the Production of Entropy: Life, earth, and beyond. Springer Verlag, Berlin, Heidelberg. KLEIDON, A., FRAEDRICH, K. & HEIMANN, M. 2000. A green planet versus a desert world: Estimating the maximum effect of vegetation on land surface climate. Clim. Ch. 44: 471–493. KLEIDON, A., FRAEDRICH, K., KIRK, E. & LUNKEIT, F. 2006. Maximum entropy production and the strength of boundary layer exchange in an atmospheric general circulation model. Geophys. Res. Lett. 33: L06706. KLEIDON, A., FRAEDRICH, K., KUNZ, T. & LUNKEIT, F. 2003. The atmospheric circulation and states of maximum entropy production. Geophys. Res. Lett. 30: 2223. LORENZ, R.D., LUNINE, J.I., WITHERS, P.G. & MCKAY, C.P. 2001. Titan, mars and earth: Entropy production by latitudinal heat transport. Geophys. Res. Lett. 28: 415–418. LOVELOCK, J.E. 1972. Gaia: A new look at life on earth. Oxford University Press, Oxford, UK. LUNKEIT, F., FRAEDRICH, K., JANSEN, H., KIRK, E., KLEIDON, A. & LUKSCH, U. 2004. Planet Simulator reference manual. Available at http://www.mi.uni-hamburg.de/Planet Simulator.216.0.html. LYONS, T.J. 2002. Clouds prefer native vegetation. Meteorology and Atmospheric Physics 80: 131–140. MONTEITH, J.L., HUDA, A.K.S. & MIDYA, D. 1989. RESCAP: a resource capture model for sorghum and pearl millet, pp. 30– 34. In: VIRMANI, S. M., TANDON, H.L.S. & ALAGARSWAMY, G. (eds), Modelling the growth and development of sorghum and pearl millet, ICRISAT Research Bulletin 12, Patancheru, India. OZAWA, H. & OHMURA, A. 1997. Thermodynamics of a globalmean state of the atmosphere – a state of maximum entropy increase. J. Clim. 10: 441–445. OZAWA, H., OHMURA, A., LORENZ, R.D. & PUJOL, T. 2003. The second law of thermodynamics and the global climate system – a review of the Maximum Entropy Production principle. Rev. Geophys. 41: 1018. PALTRIDGE, G.W. 1975. Global dynamics and climate – a system of minimum entropy exchange. Q. J. Roy. Meteorol. Soc. 101: 475–484. PALTRIDGE, G.W. 1978. The steady-state format of global climate. Q. J. Roy. Meteorol. Soc. 104: 927–945. PAVLICK, R. & KLEIDON, A. 2006. Is terrestrial productivity at its maximum for present-day conditions? (submitted to Tellus B.) THORNLEY, J.M. 1969. A model to describe the partitioning of photosynthate during vegetative plant growth. Ann. Bot. 33: 419–430. THORNLEY, J.M. 1972. A balanced quantitative model for root: shoot ratios in vegetative plants. Ann. Bot. 36: 431–441. WANG, G. 2004. A conceptual modeling study on biosphereatmosphere interactions and its implications for physically based climate modeling, J. Clim. 17: 2572–2583.