Biogeophysical Feedbacks and the Dynamics of Climate

M. Claussen 1. Introduction 61

Potsdam-lastimte for 2. Synergisms 62

Potsdam, Germany 3- Multiple Equilibria 64

4. Transient Interaction 66

5. Perspectives 67

References 69

1. Introduction

Traditionally, vegetation has been considered a more or less passive component of climate. For example, Alexander von Humboldt (1849) imagined the desertification of North Africa to be caused by an oceanic impact. He argues that somewhere in the "dark past," the subtropical Atlantic gyre was much stronger and flooded the Sahara, thereby washing away vegetation and fertile soil. When examining different theories of ice ages, DeMarchi (1885) concluded that the occurrence of glacial epochs does not depend on changes in the "covering of the earth's surface (vegetation)." Koppen (1936) described vegetation as "crystallized, visible climate" and referred to it as an indicator of climate much more accurate than our instruments. I interpret Koppen's statement in the sense that he considered vegetation as being completely determined by climate. If Koppen would have taken into account the possibility that vegetation could affect atmospheric and oceanic circulation, then he certainly would have sought a more "objective" parameter. In the same line of thinking, coupled atmosphere-ocean models were regarded as state-of-the-art climate models (see, for example, Cubasch et al., 1995). Global vegetation patterns in these models are kept constant in time. Only short-term plant physiology and, to some extent, fractional vegetation and leaf area are allowed to change with meteorological conditions.

Today, a more general definition of climate in terms of state and ensemble statistics of the climate system is generally accepted (see Peixoto and Oort, 1992). The climate system encompasses not only the abiotic world (atmosphere, hydrosphere, cryosphere, pe-dosphere) but also the living world, the biosphere. Interestingly, the IPCC (Houghton ct al., 1997) defines a climate model as a model which "include(s) enough of the components of the climate system to be useful for simulating the climate." This defini tion is misleading. One can successfully simulate the observed state of a system with a reduced model, e.g., the present-day climate using atmosphere-ocean models. However, the nonlinearity of the climate system could lead to multiple states under the same external forcing owing to feedbacks between all components of the system. Hence, when operating with a subset of the complete model, one could miss important aspects of the dynamics of the entire system, which I discuss for the case of vegetation-climate interaction.

A number of studies reveal that predictions of global atmospheric models are highly sensitive to prescribed large-scale changes in vegetation cover, such as removal of tropical (e.g., Henderson-Sellers et al., 1993; Polcher and Laval, 1994; Zheng and Elthair, 1997) and boreal (e.g., Bonan et al., 1992) forests. Although these studies illustrate the potential effects of massive vegetation changes on the climate system, they can hardly be validated. Therefore, Foley et al. (1994) suggest investigation of past environments such as the climate of the early to middle Holocene, some 6000-9000 years ago, for which strong differences in global vegetation pattern are amply documented (see below). I follow their reasoning and discuss mainly palaeo climate.

Generally, I review the state of the art of our knowledge of vegetation-climate interaction, where I will restrict myself to biogeophysical aspects. First, I discuss synergisms of feedbacks between various components of the climate system, with emphasis on the inclusion of vegetation. Second, I explore the nonlinear character of vegetation-climate interaction: the possibility of multiple solutions to the vegetation-climate system and, third, its consequences for the transient vegetation-climate dynamics. I do not try to seek a complete-as-possible summary; instead, I focus on gaps and perspectives in biogeophysical modeling.

GLOBAL BIOGEOCHEMICAL CYCLES IN THE CLIMATE SYSTEM

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2. Synergisms

2.1 High Northern Latitudes

Palaeobotanic evidence indicates that during the early to middle Holocene, boreal forests extended north of the modern treeline (Frenzel et al, 1992; TEMPO, 1996; Cheddadi et al, 1997). It is suggested that this migration was triggered by changes in the earth's orbit. Moreover, the migration of boreal trees is assumed to amplify the initial warming owing to the so-called taiga-tundra feedback, first discussed by Otterman et al. (1984) and Harvey (1988, 1989a,b). The albedo of snow-covered vegetation is much lower for forests than for low vegetation such as tundra, which can readily be seen from a bird's-eye view. Hence the darker, snow-covered taiga receives more solar energy than the snow-covered tundra, which, in turn, favors the growth of taiga. Later, Foley et al. (1994) analyzed the vegetation-snow-albedo feedback in more detail. By imposing an increase in forest area of some 20% as a surface condition, they find that changes in land surface conditions give rise to an additional warming of some 4 °C in spring and about 1 °C in the other seasons. Orbital forcing would produce only some 2 °C. The additional warming is caused mainly by a reduction of snow and sea-ice volume by nearly 40% and subsequent reduction in surface albedo. Further simulations using similar experimental setups but different models (TEMPO, 1996) corroborate the earlier results. These studies clearly point at the importance of vegetation-climate interaction at high northern latitudes in amplifying climate change triggered by some external forcing. Unfortunately, no attempt has been made to isolate the effect of a decrease in vegetation-snow-albedo and the sea-ice-albedo feedback. So it was not clear how much the biospheric process actually contributes to the mid-Holocene warming at high northern latitudes or whether the warming was mainly caused by a synergism between vegetation change and oceanic feedback.

Only coupled atmosphere-vegetation models can analyze the dynamics of the feedback, i.e., the interaction between changes in vegetation structure and climate. For example, Gutman et al. (1984) and Gutman (1984, 1985) explored the idea of relating the surface parameters of an atmospheric model (e.g., albedo and water availability) to climatic variables. They used the Budyko (1974) radiative index of dryness, D, to characterize the geobotanic type of a climate zone and proposed a simple relation between albedo, water availability, and D. Later, Henderson-Sellers (1993) and Claussen (1994) coupled comprehensive atmospheric ciruclation models with (diagnostic) biorne models, i.e., with models of macro ecosystems assuming an equilibrium with climate. Hence these asynchronously coupled atmosphere-biome models can be used to assess equilibrium solutions of the system, but not system dynamics. Nevertheless, the idea of developing such models turned out to be a valuable extension of sensitivity studies based on one-way coupled models and the more simple models of Gutman et al. (1984).

Returning to the problem of the vegetation-snow-albedo feedback at high northern latitudes, i.e., the taiga-tundra feed back, one would expect this feedback to be a positive one: a reduction in surface albedo increases near-surface temperatures, which, in turn, favors growth of taller vegetation, reducing surface albedo further (see Otterman et al., 1984). The feedback is limited by topographical constraints, e.g., coast lines, or by the insolation. The studies of Claussen and Gayler (1997) and Texier et al. (1997), using different atmospheric models but the same biome model of Prentice et al. (1992), confirm the earlier assertion that the vegetation-snow-albedo feedback is positive. However, both models show a rather small northward expansion of boreal forests. This is not surprising, as the annual cycle of sea-surface temperatures (SSTs) and Arctic sea-ice volume are kept constant. Obviously, the synergism between terrestrial and marine feedbacks is missing. This has clearly been demonstrated in a study by Ganopolski et al. (1998) using a coupled atmosphere-ocean-vegetation model. They find a summer warming over the Northern Hemisphere continents of some 1.7 °C (in comparison with present-day climate) owing to orbital forcing on the atmosphere alone. Inclusion of ocean-atmosphere feedbacks (but keeping vegetation structure constant in time) reduces this signal to some 1.2 °C, whereas the taiga-tundra feedback (but now without any oceanic feedback) enhances summer warming to 2.2 °C. In the full system (including all feedbacks) this additional warming is not reduced, as one would expect from linear reasoning, but it is increased to 2.5 °C as a result of a synergism between the taiga-tundra feedback and the Arctic sea-ice-albedo feedback. Likewise, orbital forcing alone induces a wintertime cooling of some — 0.8 °C. The biogeo-physcial feedbacks alone reduce this cooling to — 0.7 °C, and the atmosphere-ocean interaction, to —0.5 °C. The synergism between the two feedbacks, however, causes a winter warming of some 0.4 °C. The warming of Northern Hemisphere winters, which is supported by reconstructions (e.g., Cheddadi et al, 1997), is often referred to as the "biome paradox." From the results of Ganopolski et al. (1998) one can conclude that the biome paradox is not a pure biospheric feedback, but it is caused mainly by the synergism between this feedback and the oceanic feedback.

During the mid-Holocene, orbital forcing triggered a warming of the Northern Hemisphere in summer, whereas the opposite was valid for the end of the Eemian warm period some 115 ka B. P., as pointed out by Harvey (1989b) and subsequently by Gallee et al. (1992), Berger et al. (1992, 1993), and Gallimore and Kutzbach (1996). These studies show that the taiga-tundra feedback contributes significantly to the temperature response to orbital forcing. Gallimore and Kutzbach (1996) state that even a prescribed increase in surface albedo which is deduced from a biome model estimate of tundra expansion at 115 ka B. P. is sufficient to induce glaciation over northeastern Canada. (Actually, Gallimore and Kutzbach (1996) did not simulate glacial inception, just the occurrence of permanent snow cover.) deNoblet et al. (1996) support this hypothesis by using a coupled atmosphere-biome model, although they obtain just a substantial increase in snow depth, but no large-scale perennial snow cover over North Canada was obtained. Moreover, they restrict themselves to the biospheric feedbacks ignoring any synergism between land surface and sea ice (which presumably could help to get perennial snow cover).

2.2 Subtropics

While most researchers in the field agree on the relative importance of biospheric feedbacks operating at high northern latitudes, the discussion becomes more interesting and diverse as the sub-tropics are concerned. Climate reconstructions and data on fossil pollen compiled by Jolly et al. (1998), Hoelzmann et al. (1998), Petit-Maire (1996), and Anhuf et al. (1999) indicate that North Africa was much greener in the mid-Holocene than today. The Sa-haran desert was, presumably to a large extent, covered by annual grasses and low shrubs. The Sahel reached at least as far north as 23 °N, more so in the western than in the eastern part.

In their model, Texier et al. (1997) yield a positive feedback between vegetation and precipitation in this region, which is, however, much too weak to get any substantial greening (Fig. 1A). They suggest an additional (synergistic) feedback between sea-surface temperature (SST) and land-surface changes. By modifying surface conditions in North Africa (increased vegetation cover, increased areas of wetlands and lakes) Kutzbach et al. (1996) obtain some change in their model that leads to an increase in precipitation in the southeastern part of the Sahara, but almost none in the western part (Fig. IB). An upgraded version of the model used by Kutzbach et al. (1996) reveals a northward spread of vegetation also in the western part of north Africa according to Brostrom et al. (1998). Claussen and Gayler (1997) find a strong feedback between vegetation and precipitation and an almost complete greening in the western Sahara and some in the eastern part (Fig. 1C). By and large the latter model results, although far from perfect, seem to agree best with the data. Claussen and Gayler (1997) and Claussen et al. (1998) explain the positive feedback by an interaction between high albedo of Saharan sand deserts and atmospheric circulation as hypothesized by Charney (1975). They extend Charney's theory by accounting for atmospheric hydrology, i.e., moisture convergence and associated convective precipitation. [For present-day climate this feedback, or "Charney's loop," was discussed in detail by Lofgren (1995) and, independently by Claussen (1997).]

Now the question of which model is "correct" arises. To tackle this problem, deNoblet et al. (2000) compare the "extreme" — concerning the magnitude of Saharan greening—models of Claussen and Gayler (1997) and Texier et al. (1997). Both groups use the same biome model, but different atmospheric models. Moreover, the atmospheric model and the biome model are asynchronously coupled in different manners: Claussen and Gayler (1997) use the output of the climate model directly to drive the biome model, while Texier et al. (1997) take the difference between model results and a reference climate as input to the biome model. The latter, the so-called anomaly approach, prevents the coupled model from drifting to an unrealistic climate which could be induced by some positive feedbacks between biases in either model. I Ience this method is similar to the "flux correction"

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10 20 Longitude

10 25

Longitude

10 25

Longitude

C 40

S 20

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1

1

1

1

y

20 Longitude

FIGURE 1 Reduction of desert from present-day climate to mid-Holocene climate simulated by (a) the models of Texier ct al. (1997), (b) Kutzbach et al. (1996), and (c) Claussen and Gayler (1997). (a, c) are taken with modifications from deNoblet et al. (2000) and (b) with modifications from Kutzbach et al. (1996).

20 Longitude

FIGURE 1 Reduction of desert from present-day climate to mid-Holocene climate simulated by (a) the models of Texier ct al. (1997), (b) Kutzbach et al. (1996), and (c) Claussen and Gayler (1997). (a, c) are taken with modifications from deNoblet et al. (2000) and (b) with modifications from Kutzbach et al. (1996).

in coupled atmosphere-ocean models. It turns out that the difference between coupling procedures affects the results of the coupled atmosphere-biome model only marginally. Hence deNoblet et al. (2000) conclude that the differences in north Africa greening cannot be attributed to the coupling procedure; it can be traced back to different representations of the atmospheric circulation in the tropics. The atmospheric model of Claussen and Gayler (1997) somewhat overestimates the duration of the north African monsoon, while the other model of Texier et al. (1997) yields an unrealistic near-surface pressure distribution and, therefore, a too zonal circulation. The authors demonstrate why the one model yields an unrealistically arid climate and they "believe" more in the other model as the existence of a strong biogeophysical feedback in north Africa is concerned. But they cannot prove that the latter model is completely trustworthy. Hence this issue certainly needs further consideration.

A second argument concerns the missing interaction with the ocean. Therefore, Kutzbach and Liu (1997) provide simulations using an asynchronously and partially coupled atmosphere-ocean model (no freshwater fluxes, no dynamic sea-ice model). They find an increase in north African monsoon precipitation as a result of increased SST in late summer bringing the model in closer agreement with palaeo data. Similarly, Hewitt and Mitchell (1998), using a fully coupled atmosphere-ocean model, observe an increase in precipitation over north Africa, but still not as intense as data suggest. They assume that missing biospheric feedbacks caused their model "failure." Ganopolski et al. (1998) have readdressed this issue using a coupled atmosphere-vegetation-ocean model in different combinations (as atmosphere-only model, atmosphere-vegetation model, atmosphere-ocean model, and fully coupled model). They conclude that in the subtropics, the biospheric feedback dominates (Fig. 2) while the synergism between this feedback and an increase in monsoon precipitation owing to increased SST adds only little.

The model of Ganopolski et al. (1998) is the only "true" climate model according the IPCC definition as it includes all components of the climate system relevant to describe mid-Holocene climate. However, it has a rather coarse horizontal resolution. Hence to be certain of their results, one must confirm that these results are independent of the model resolution.

3. Multiple Equilibria

As the interaction between components of the climate system is nonlinear, one might expect multiple equilibrium solutions. Gut-man et al. (1984) and Gutman (1984, 1985) found only unique, steady-state solutions in their zonally averaged model. (Actually, they regarded their results as "tentative and merely as an illustration of the suggested approach," because of the simplicity of their model.) The possibility of multiple equilibria in the 3-dimen-sional atmosphere-vegetation system was discovered later by Claussen (1994) and subsequently analyzed in detail by Claussen (1997, 1998) for present-day climate, i.e., present-day insolation and SST. Two solutions to the atmosphere-vegetation system appear: the arid, present-day climate and a humid solution resembling more the mid-Holocene climate, i.e., with a Sahara greener than today, albeit less green than in the mid-Holocene (Fig. 3).

0 60 120 180 240 300 ATM + OCE

120 180 240 300

0 60 120 180 240 300 ATM + OCE + VEG

120 180 240 300

60 120 180 240 300

-0.9 -0.8 -0.4 -0.2 -0.1 -0.05 0.05 FIGURE 2 Reduction of desert from present-day climate to mid-Holocene climate simulated by Ganopolksi et al. (1998). The color labels refer to differences in (nondimensional) fractional coverage of desert between today and 6000 years before present. Desert fractions are diagnosed from annual mean precipitation and temperature obtained by the atmosphere-only model (ATM) and the atmosphere-ocean model (ATM + OCE) using present-day land-surface conditions. Desert fractions are predicted from vegetation dynamics by using the atmosphere-vegetation model (ATM + VEG) and the fully coupled model (ATM + OCE + VEG).

FIGURE 3 Multiple equilibria computed for present-day climate (a) and for the climate of the last glacial maximum (c). For mid-Holocene conditions, only one solution is obtained (b). A summary of the results of Claussen (1997) (a), Claussen and Gayler (1997) (b), and Kubatzki and Claussen (1998) (c).

FIGURE 3 Multiple equilibria computed for present-day climate (a) and for the climate of the last glacial maximum (c). For mid-Holocene conditions, only one solution is obtained (b). A summary of the results of Claussen (1997) (a), Claussen and Gayler (1997) (b), and Kubatzki and Claussen (1998) (c).

The two solutions differ mainly in the subtropical areas of north Africa and, but only slightly, in central east Asia. The possibility of multiple equilibria in the atmosphere-vegetation system of North-west Africa has recently been corroborated by Wang and Eltahir (2000) and Zeng and Neelin (2000) by using completely different models of the tropical atmosphere and dynamic vegetation.

Interestingly, the stability of the atmosphere-vegetation system seems to change with time: experiments with mid-Holocene vegetation yield only one solution, the green Sahara (Claussen and Gayler, 1997), while two solutions exist for the Last Glacial Maximum (LGM) (Kubatzki and Claussen, 1998).

So far, no other regions on earth in which multiple equilibria could evolve on a large scale have been identified Levis et al. (1999) seek multiple solutions to the atmosphere-vegetation-sea-ice system at high northern latitudes. Their model converges to one solution in this region corroborating the earlier assertion (Claussen, 1998) that multiple solutions manifest themselves in the subtropics, mainly in north Africa.

Why do we find multiple solutions in the subtropics, but none at high latitudes—and why for the present-day and LGM climates, but not for mid-Holocene climate? Claussen et al. (1998) analyze large-scale atmospheric pattern in present-day, mid-Holocene, and LGM climates. They find that velocity potential patterns, which indicate divergence and convergence of large-scale atmospheric flow, differ between arid and humid solutions mainly in the tropical and subtropical regions. It appears that the Hadley-Walker circulation slightly shifts to the west. This is consistent with Charney's (1975) theory of albedo-induced desertification in the subtropics. Moreover, changes in surface conditions directly influence vertical motion, and thereby large-scale horizontal flow, in the tropics (Eltahir, 1996), but hardly at middle and high latitudes (e.g., Lofgren, 1995a,b). For the mid-Holocene climate, the large-scale atmospheric flow is already close to the humid mode, even if one prescribes present-day land surface conditions. This is caused by differences in insolation: in the mid-Holocene boreal summer, the Northern Hemisphere received up to 40 W m~2 more energy than today, thereby strengthening African and Asian summer monsoon (Kutzbach and Guetter, 1986). During the LGM, insolation was quite close to present-day conditions.

A more ecological interpretation of multiple equilibria is given by Brovkin et al. (1998). They develop a conceptual model of vegetation-precipitation interaction in the western Sahara which is applied to interpret the results of comprehensive models. The conceptual model finds three solutions for present-day and LGM climate; one of these, however, is unstable to infinitesimally small perturbations. The humid solution is shown to be less probable than the arid solution, and this explains the existence of the Sahara desert as it is today. For mid-Holocene climate, only one solution is obtained. Application of the conceptual model to bios-pheric feedbacks at high latitudes (Levis et al., 1999) yields only one solution for the present-day conditions.

Are multiple equilibria just a matter of the atmosphere-vegetation system, or do they occur also in the atmosphere-ocean-vegetation system? So far, we have not yet found multiple solutions in the model of Ganopolski et al. (1998). (The model attains multiple solutions associated with multiple states of the thermohaline convection.) I blame this deficit on the coarse resolution of this model, because north Africa is represented by just three grid boxes, Sahara, Sudan, and tropical north Africa. Subsequently,

Saharan precipitation in the coarse model of Ganopolski et al. (1998) is less sensitive to changes in land-surface conditions than the west Saharan precitpitation in the model used by Claussen (1997, 1998). On the other hand, the study of Ganopolski et al. (1998) shows that the biogeophysical feedback in north Africa is mainly a vegetation-atmosphere feedback. Therefore, I assume that our conclusion from coupled vegetation-atmosphere models should generally be valid, i.e., also vegetation-atmosphere-ocean models (with finer horizontal resolution) should exhibit multiple equilibria in the north African region.

4. Transient Interaction

The discussion of multiple equilibria seems to be somewhat academic. However, the existence of these could explain abrupt transitions in vegetation structure (Claussen et al., 1998; Brovkin et al., 1998). If global stability changes in the sense that one equilibrium solution becomes less stable to finite amplitude perturbations than the others, then an abrupt change of the system from the less stable to a more stable equilibrium is to be expected. Brovkin et al. (1998) find in their conceptual model that the green solution becomes less stable around 3.6 ka B.P. Keeping in mind that the variability of precipitation is larger in humid regions than in arid regions of north Africa (e.g., Eischeid et al., 1991), one would expect a transition roughly between 6 and 4 ka BP.

In fact, there is evidence that the mid-Holocene wet phase in north Africa ended around 5.0-4.5 ka B.P. even in the high continental position of the east Sahara (Pachur and Wtinnemann, 1996; Pachur and Altmann, 1997). Petit-Maire and Guo (1996) present data suggesting that the transition to present-day's arid climate did not occur gradually, but in two steps with two arid periods, at 6.7-5.5 and 4-3.6 ka B.P. Other reconstructions indicate that freshwater lakes in the eastern Sahara began to disappear from 5.7 to 4 ka B. P., when recharge of aquifers ceased at the end of the wet phase (Pachur and Hoelzmann, 1991). Pachur and

Years before present

FIGURE 4 Development of vegetation fraction in the Sahara (full line, left ordinate) as response to changes in insolation of the Northern Hemisphere during boreal summer (dashed line, right ordinate). The abscissa indicates the number of years before present. Figure 4 is taken with modifications from Claussen et al. (1999).

Years before present

FIGURE 4 Development of vegetation fraction in the Sahara (full line, left ordinate) as response to changes in insolation of the Northern Hemisphere during boreal summer (dashed line, right ordinate). The abscissa indicates the number of years before present. Figure 4 is taken with modifications from Claussen et al. (1999).

Hoelzmann (personal communication) suggest that climate change at the end of the mid-Holocene was faster in the western than in the eastern Sahara. Indeed, deMenocal et al. (2000) report of an abrupt decline in aeolian dust transport off the Northwest African Atlantic coast 5500 years ago. This reconstruction is consistent with the hypothesis of multiple equilibria in the western, not in the eastern Sahara.

The arguments above are based on studies of the system at or in the vicinity of an equilibrium state. Only with fully coupled, dynamic vegetation models can one explore the time evolution of biogeophysical feedbacks. Claussen et al. (1999) analyze the transient structures in global vegetation pattern and climate using the coupled atmosphere-ocean-vegetation model of Ganopolski et al. (1998), but with a dynamic vegetation module. Their simulations clearly show (not just suggest) that subtle changes in orbital forcing triggered changes in north African climate which were then strongly amplified by biogeophysical feedbacks in this region. The timing of the transition, which started at around 5.5 ka B.P. in the model (Fig. 4), was governed by a global interplay between atmosphere, ocean, sea ice, and vegetation. The interplay is affected by a change in tropical SST and by the synergisms between bios-pheric and oceanic feedbacks, mentioned in Section 2.1, which influence the large-scale meridional temperature gradient. Hence the abrupt desertification—abrupt in comparison with the subtle change in orbital forcing—is a regional effect. The timing of it depends, however, on global processes. Whether tropical SST or biospheric feedbacks at high northern latitudes dominate the latter has still to be evaluated.

5. Perspectives

The investigation of biospheric feedbacks using coupled vegetation-climate models has just started. Therefore, it is too early to arrive at a conclusion, which, in its true sense, always implies some "closure." Instead, I try to "open" this issue further.

So far it has been recognized that there are biogeophysical feedbacks which affect the (global) climate system. However, as outlined above, theoretical analyses of biogeophysical feedbacks often focus on synergisms instead of feedbacks. The influence of several biogeophysical feedbacks, having included their synergism with other, for example, oceanic feedbacks, on the climate system is simulated without paying attention to the role of individual feedbacks. To illustrate the problem, I briefly recall the classical feedback analysis presented by, for example, Schlesinger (1988) and Peixoto and Oort (1992), and I extend their analysis to include synergisms.

Let us assume that the state of the climate system depends on external forcing, E, such as insolation and anthropogenic land cover change, and internal processes //,. Any external forcing E will change the state of the climate system defined in terms of extensive variables S. Hence S = G E, where G is a sensitivity factor or sometimes referred to as a gain. Without any feedback, the response of the system would be S0 = G0 E. With feedbacks,

FIGURE 5 A schematic view on the linear feedback analysis (a,b) and its extension to synergisms (c). G and G0 represent the gain of a system with and without any feedback, respectively. S is the response of the system to an external forcing E. H, (i = 1, 2, 3) are internal or feedback processes. Hi2 and H2} are synergistic processes between H, and H2 and H2 and H„ respectively, which modify the output H, S {i = 1,2,3,). S is the response of the nonlinear system. Synergisms between more than two internal processes are omitted in this sketch, (a) and (b) are taken with modifications from Peixoto and Oort (1992).

FIGURE 5 A schematic view on the linear feedback analysis (a,b) and its extension to synergisms (c). G and G0 represent the gain of a system with and without any feedback, respectively. S is the response of the system to an external forcing E. H, (i = 1, 2, 3) are internal or feedback processes. Hi2 and H2} are synergistic processes between H, and H2 and H2 and H„ respectively, which modify the output H, S {i = 1,2,3,). S is the response of the nonlinear system. Synergisms between more than two internal processes are omitted in this sketch, (a) and (b) are taken with modifications from Peixoto and Oort (1992).

however, one has to assume that the response S of the full system is modified by some internal or feedback processes H;, triggered by S. The output (Ef/)s- of these internal processes feeds into the system such that (see Fig. 5)

The factor G„ H, is called feedback /. Hence G = G0 I (1 - 2/). Peixoto and Oort (1992) note that this analysis is based on the assumption that there exist no synergisms, i.e., interaction among feedbacks. To extend their analysis one could define a multidimensional transfer function G which includes not only feedbacks but also synergisms between feedbacks. Formally, one may write S = GE, where S is the response of the full system, and

S = G0E + (l]/)s + (m)s + (im^S + • • •, where /; indicate the synergism between two processes F/and //(with i /), and/,,;, between H„ HP and f/.(with i t4 j k). As for feedbacks, we can differentiate between positive, i.e., amplifying synergisms, if/, > 0, and negative ones, if f < 0. It is worth noting that this analysis depends on the reference state chosen. Generally, gain G and response S differ no matter whether we apply the external forcing E or — E.

For illustration, I have calculated feedbacks/, and synergisms/,, from model results summarized in Ganopolski et al (1998) for mid-Holocene temperature changes. By inspecting Table 1, it becomes clear why the so-called biome paradox, mentioned in Section 2.1, is not a pure "biome" paradox, but arises from the synergism between biogeophysical and oceanic feedbacks. The feedback analysis shows positive feedbacks/, and/. Hence both, the atmosphere-ocean feedback / and the atmosphere-vegetation feedback f2, tend to "oppose" wintertime cooling by enhancing radiative forcing; however, they are not strong enough to produce a warming. The response of the system without synergisms would produce a cooling with respect to today's climate, i.e., AS = S(6k) -S(0k) < 0, where S(6k) = S0(6fc)/(1-/,-/). It is the synergism /¡2 between these feedbacks that produces a wintertime warming, indicated in Table 1 by AS = S(6k) ~ S(0k) > 0 and fu > >kU

Berger (1999) uses the factor-separation technique proposed by Stein and Alpert (1993) to exlore feedbacks and synergisms. Work in progress suggests that both methods, my extension of the classical feedback analysis and the factor-separation technique, are similar and that they yield the same results if properly normalized.

In this context, it should be emphazised that the problem of synergisms has been overlooked in the investigation of anthropogenic land cover change. Generally these experiments are undertaken as sensitivity experiments, i.e., the response of the atmosphere to (prescribed) changes in land cover is analyzed. Hence these experiments do not really belong to the category of feedback experiments. However, if longer time scales are considered, the (prescribed) changes in land cover could trigger changes in natural vegetation in regions not directly affected by anthropogenic land use (e.g., Brovkin et al., 1999) and, perhaps even more importantly, they could trigger synergisms with other feedbacks. For example, work in progress (Ganopolski et al, 2000) suggests that, using the model of Ganopolski et al (1998), the effect of tropical deforestation differs, if we allow for oceanic feedbacks. In temperate regions we find a summer warming in the case of fixed SST, but a summer cooling in the case of an interactive ocean.

Biogeophysical feedbacks can lead to multiple equilibria of the climate system and they influence the (transient) dynamics of the climate system. This has been shown—meanwhile by three com

TABLE 1 Oceanic Feedback Factors,/, Biogeophysical Feedback Factors,/, and their Synergism,/ ,, for Temperature Changes on Average over the Northern Hemisphere (NH), the Northern Hemisphere Continents (NHL), and the Southern Hemisphere (SH) during Boreal Summer (June, July, August), Boreal Winter (December, January, February) and on Annual Average in Response to a Change in Orbital Parameters from 6000 Years Ago to Today

Temperature

TABLE 1 Oceanic Feedback Factors,/, Biogeophysical Feedback Factors,/, and their Synergism,/ ,, for Temperature Changes on Average over the Northern Hemisphere (NH), the Northern Hemisphere Continents (NHL), and the Southern Hemisphere (SH) during Boreal Summer (June, July, August), Boreal Winter (December, January, February) and on Annual Average in Response to a Change in Orbital Parameters from 6000 Years Ago to Today

Temperature

Boreal summer

NH,

- 1.61

+ 1.65

+ 2.75

+ 1.72

+ 2.54

NH

- 1.38

+ 0.95

+ 2.42

+ 0.85

+ 1.57

SH

- 1.41

+ 0.21

+ 3.13

-0.11

+ 0.78

Boreal winter

NHl

i 0.84

+ 0.47

+ 2.93

-0.41

+ 0.39

NH

+ 0.73

+ 0.20

+ 2.80

-0.21

+ 0.58

SH

+ 0.50

+ 0.02

+ 2.39

-0.16

+ 0.53

Annual average

NHl

- 0.30

+ 1.06

+ 2.82

+ 0.39

+ 1.19

NH

-0.19

+ 0.56

+ 2.63

+ 0.20

+ 0.96

SI I

- 0.55

+ 0.11

+ 2.77

-0.11

+ 0.69

Values of/,/,/; are scaled by a factor of 103. AS indicates the difference between the response of the linear system without any synergism and the present-day signal. AS is the difference between the mid-Holocene and present-day response of the full system.

Values of/,/,/; are scaled by a factor of 103. AS indicates the difference between the response of the linear system without any synergism and the present-day signal. AS is the difference between the mid-Holocene and present-day response of the full system.

pletely different models—for the atmosphere-vegetation system, but not yet for the complete climate system. Hence, we must consider the existence of multiple equilibria as a hypothesis awaiting further analysis and palaeo climate simulations.

Validation, of course, is a major problem in this field. So far, I have discussed mainly palaeo climate simulations. For a good reason: in many papers on biosphere-climate interaction, validation is not really considered. Instead, models being calibrated to present-day climate are applied to scenario experiments. These experiments are interesting from the academic point of view. However, their value for an assessment of future climate is limited.

Often, validation is done separately. On the one side, modules which simulate near-surface energy, moisture, and momentum fluxes in an atmospheric model are evaluated against data (e.g., in the frame of PILPS, the Project for the Intercomparsion of Land surface Parameterizations Schemes; Henderson-Sellers et al., 1995). On the other side, vegetation models are tested by inter-comparison with other models (Cramer et al, 2000). This can be only a first step, which is quite appropriate as long as atmospheric models and vegetation models are not directly coupled; for example, if the two models do not share the same module of soil hydrology. If validation of fully coupled models is considered, in particular validation of continental-scale vegetation dynamics, then comparison of model results with palaeo climate reconstructions is the only way. As a side effect, this approach has the advantage that climate modelers do not need to rely on "soft" data, i.e., proxy-data from which the state of the atmosphere is derived indirectly. Instead, biospheric variables appear as (prognostic) state variables of the climate system model and can be used for direct validation. The PMIP, the Palaeoclimate Modelling Intercompari-son Project (Joussaume and Taylor, 1995), provides a proper framework for this effort.

Finally, biogeophysical feedbacks and biogeochemical feedbacks are closely related (Schimel, 1998). Ignoring biogeochemical feedbacks seems to be reasonable for periods of nearly constant atmospheric composition, which presumably do not exist. Even throughout the last 6000-8000 years, atmospheric C02 concentrations have increased by some 20 ppm (Indermiihle et al, 1999). The assumption that this increase is caused by the decline in boreal forests and subtropical (mainly north African) grassland and savanna is not at variance with reconstructions of 5M C values by Indermiihle et al. Hence one may suspect that the decline in vegetation during the last 6000-8000 years which has amplified the long-term cooling via biogeophysical feedbacks and synergisms has also weakend the cooling trend via biogeochemical feedbacks.

The interaction between biogeophysical and biogeochemical feedbacks is quite subtle: while the latter tends to be negative through its interaction with greenhouse gases, the former can be either positive or negative, depending on whether changes in vegetation structure affect evaporation or albedo more strongly. It would be an interesting task to explore the spatial and temporal dynamics of the biogeophysical-biogeochemical interplay. Presumably, there are regions on earth in which, depending on external forcing and earth's history, the one or the other dominates. I

bet that, by solving this riddle, will we will find the answer to the question of climate-system stability which is a prerequisite for assessing the resilience of the present-day climate to large-scale perturbation such as the continuing release of fossil fuel combustion products into the atmosphere or the fragmentation of terrestrial vegetation cover.

Acknowledgments

This chapter could not have been written without the fruitful discussion within the CLIMBER group, in particular with Victor Brovkin, Andrey Ganopolski, Claudia Kubatzki, Stefan Rahmstorf, and Vladimir Petoukhov. Furthermore, I thank André Berger, Université Catholique Louvain la Neuve, for constructive comments. This work is partially funded by the European Union, Contract ENV4-CT97-0696.

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