Stability of the Vegetation-Atmosphere System in the Early Eocene Climate

So far, the transitivity of the global system has been analysed for late Quaternary (glacial, interClariy aim glacial and present-day) climate. Here, we extend this analysis to a warm, almost ice-free climate with a different configuration of continents. We use the Earth system model of the Max Planck 5 Institute for Meteorology to analyse the stability of the climate system under early Eocene and preindustrial conditions, respectively. We initialise the simulations by prescribing either dense forests or bare deserts on all continents. Starting with desert continents, an extended desert remains in Central Asia in the early Eocene climate. Starting with dense forest coverage, the Asian desert is much Updated major


Introduction
The interaction between atmosphere and vegetation may allow for multiple equilibria of the vegetation-atmosphere system pointing to intransitive dynamics in the climate system is as suggested by Lorenz (1968).Multiple equilibrium states have been detected in various model simulations when initialised with different vegetation covers.Claussen (1994Claussen ( , 1998)), Claussen and Gayler (1997), Kubatzki and Claussen (1998), Wang and Eltahir (2000), Zeng and Neelin (2000), and Rachmayani et al. (2015) find multiple state in Northern Africa, Oyama and Nobre (2003) in the Amazon region, Claussen (1998) in Central Asia, and Dekker et al. (2010)  simulations with initially more extended vegetation cover lead to a moister climate and smaller deserts than simulations initialised with sparse vegetation coverage.
The stability of the atmosphere-vegetation system depends on the climate state.For example, the intransitivity of the atmosphere-vegetation system over Northern Africa vanishes, or becomes much less pronounced, for the mid-Holocene climate in the simulations by Claussen and Gayler (1997) and Rachmayani et al. (2015), respectively.Likewise, Bathiany et al. (2012) show that the pattern of bi-stability over Northern Africa changes at different times in different location during the transition from mid to late Holocene.Such changes in the stability of the atmosphere-vegetation system may lead to abrupt changes in vegetation and climate due to a loss of stability in the regions which exhibit multiple states (Brovkin et al., 1998;Claussen et al., 1999;Renssen et al., 2003).Further, changes in the stability of the atmosphere-vegetation system may even induce abrupt changes in locations which seem to be more stable, but which are interlinked with the unstable locations (Bathiany et al., 2013a, b).
So far, most studies have assessed the stability of the atmosphere-vegetation system for interglacial or glacial climate, i.e. a climate states with permanent ice sheets.
Little is known about the transitivity of the atmosphere-vegetation system in climates that strongly differ from the current late Quaternary climate.Therefore, we explore the stability of the atmosphere-vegetation system in climate of the early Eocene.The early Eocene (about 54 to 52 Ma ago) belongs to the warmest periods in the last 65 million years.An atmospheric CO 2 concentration between 300 and 2000 ppm (Beerling and Royer, 2011) as well as a different orography and bathymetry than today led to 5 • C to 6 • C warmer tropics (Pearson et al., 2007) and to mostly ice-free poles (Zachos et al., 1992).The warm climate allowed a dense vegetation cover in almost all regions (Willis and McElwain, 2002).Even on Antarctica and in the high North, flora fossils indicate a dense tree cover (Wolfe, 1985;Eberle and Greenwood, 2012;Harrington et al., 2012;Pross et al., 2012).Using the Earth system model of the Max Planck Institute for Meteoroloy (MPI-ESM), we simulate the early Eocene climate and the pre-industrial climate.We start simula-Introduction

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Full tions from two different vegetation states, all ice-free continents are either completely covered with dense forests or with bare-soil deserts, respectively (Port et al., 2015).From these initial states, the model system is allowed to freely evolve, with dynamically interacting atmosphere, ocean, and vegetation.Depending on the initial conditions, new equilibria in the vegetation-atmosphere system are reached after some 1000 years of simulation.

Model
The Earth system model of the Max Planck Institute for Meteorology (MPI-ESM) consists of the atmospheric general circulation model ECHAM6 (Stevens et al., 2013), the Max Planck Institute Ocean Model MPIOM (Jungclaus et al., 2013), the land surface scheme JSBACH (Reick et al., 2013), and the ocean biogeochemistry model HAMOCC (Ilyina et al., 2013).We use ECHAM6 in a horizontal resolution is T31 (approximately 3.75 • ) and with 31 levels in the vertical.The ocean grid has a horizontal resolution of about 3 • and 40 levels in depth.
JSBACH includes a dynamic vegetation module based on a tiling approach (Brovkin et al., 2009).Vegetation is represented by eight Plant Functional Types (PFTs) which reflect present-day plant taxa (Table 1).During the early Eocene, however, plant types have been differed from today.Grass land is common today, but it did not exist during the early Eocene (Willis and McElwain, 2002).C 3 spreaded in the early to mid Miocene (20-10 Ma) (Janis, 1993), while C 4 expanded during the mid to late Miocene (Cerling et al., 1993).Instead, other plant species dominated the vegetation cover during the early Eocene which are extinct, or almost extinct, today such as paratropical rainforest or polar forest (Wolfe, 1985).In our study, we neglect any differences in plant taxa.Thus, we focus on the biogeophysical processes and their differences between early Figures

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Full Eocene and pre-industrial climate.The effect of difference between early Eocene and current plant taxa will be the focus of subsequent studies.

Early Eocene setting
For our early Eocene simulations, we use the same boundary conditions as Port et al. (2015).Orography and bathymetry are based on the maps by Bice and Marotzke (2001) which Heinemann et al. (2009) interpolated from the original resolution of 2 • times 2 • to the model resolution of T31.The orography map lacks information on subgrid orography such as slope, anisotropy, orientation, SD, maxiumum, minimum, mean elevation.Without these informations, sub-grid interactions of atmospheric flow with orography can not be parameterised in ECHAM6 (Stevens et al., 2013).Hence, we turn off the module for sub-grid orographic drag and wave generation.
In the standard version of MPIOM, the grid poles are over Greenland and Antarctica.With Eocene continents, the pole over present-day Greenland coincide with the Palaeo-Atlanic Ocean, i.e. meridians converge at this pole leading to numerical singularies.To avoid singularies, we use the setting by Heinemann et al. (2009) who placed the MPIOM north pole and south pole to the large continents of Palaeo-Asia and to Palaeo-South America, respectively.
The atmospheric CO 2 concentration is fixed to 560 ppm (Table 2), which is the lower limit of reconstructions (Zachos et al., 2001;Beerling and Royer, 2011).Methane and nitrous oxide are set to pre-industrial values in the early Eocene atmosphere and also the orbit corresponds to the pre-industrial orbit (Table 2).This approach limits the differences between the early Eocene and the pre-industrial boundary conditions to the distribution of continents, the bathymetry, the presence of ice sheets, and the atmospheric CO 2 concentration.Introduction

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Simulations
Our simulations start from the simulations by Port et al. (2015).They explore the impact of extreme land cover on the early Eocene climate and the pre-industrial climate by simulating and a "desert world" and a "forest world" for both climates, respectively.In the "desert world", no vegetation occurs on all continents during the simulated 400 years.
In the "forest world", trees cover all ice-free continents completely.
In order to separate the albedo effect of vegetation from the hydrological effect, Port et al. (2015) simulate the forest world and the desert world two times, respectively.All soils either have a homogeneous albedo of 0.1 (dark soil) or 0.4 (bright soil).In the dark soil case, soil and vegetation have about the same albedo leading to weak albedo changes by vegetation relative to bare soil.In other words, vegetation affects climate mainly through the hydrological cycle.In the bright soil case, vegetation has a much lower albedo than soil.Hence, both, the albedo effect and the hydrological effect of vegetation are pronounced.
At the end of the simulations by Port et al. (2015), climate differs significantly between the forest worlds and the desert worlds.We extend those simulations by further 1000 years.During the extended simulations, atmosphere, ocean, and vegetation interact and thus, vegetation establishes, migrates, and retreats dynamically.In the brightsoil simulations, the vegetation-atmosphere system reaches the same state when initialised with dense forest as when initialised with bare soil.As we focus on intransitive dynamics in the vegetation-atmosphere system, we exclude a detailed discussion of the bright-soil simulations in this study.Instead, we present the results for the dark-soil simulations where multiple equilibria establish depending on the initial vegetation cover in both, the early Eocene and the pre-industrial climate.Table 3 gives an overview of the considered four simulations where all soils have a low soil albedo.Introduction

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Full 3 Results and discussion

Early Eocene climate
The warm and humid early Eocene climate favours dense vegetation cover in almost all regions.Only in Central Asia and in southern Africa, deserts remain in the DE simulation (Fig. 1).Subtropical semi-deserts establish in South America, North America, and Australia.In these arid and semi-arid regions, pronounced differences in vegetation cover emerges between the DE simulation and the FE simulation (Fig. 2).
In the semi-desert in western North America (marked in Fig. 2), the desert cover is larger by 0.43 in the FE simulation than in the DE simulation and precipitation is smaller by 0.52 mm day −1 (70 %) (Fig. 3c).In the semi-desert in southern South America, desert cover is larger by 0.19 and precipitation is smaller by 0.5 mm day −1 (43 %) in the FE simulation (Fig. 3b).The differences on the American continents are counterintuitive because starting from dense forest leads to a larger desert in these regions than starting from bare soil.This result disagrees with all simulations previously mentioned in the introduction.Later, we will discuss the mechanism causing these bi-stabilities.
In the semi-desert in southern Africa (marked in Fig. 2), desert cover is smaller by 0.12 at the end of the FE simulation than at the end of the DE simulation (Fig. 3d).However, considering the trend of −0.04 and 0.07 per 100 years at the end of the FE and DE simulation, the difference in vegetation cover may not be significant.
In the Asian desert, the differences in the vegetation cover are most pronounced.
At the southern edge of the desert, more grass and trees remain in the FE simulation than in the DE simulation (Fig. 2).At the beginning of the FE simulation, the dense forest transpires 1.35 mm day −1 leading to an evapotranspiration of 1.7 mm day −1 and a precipitation of 1.8 mm day −1 in Central Asia (Fig. 3a).During the FE simulation, precipitation is sufficient to maintain a large part of the vegetation cover which preserves high transpiration rates and strong precipitation.By the end of the FE simulation, desert cover amounts to 0.43 and precipitation to 0.82 mm day −1 in Central Asia.Introduction

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Full At the beginning of the DE simulation, evapotranspiration in Central Asia is ten times weaker than at the beginning of the FE simulation and precipitation is six times smaller (Fig. 3a).Starting from this dry climate, only little vegetation establishes preserving a dry climate in Central Asia.At the end of the DE simulation, desert cover in Central Asia is larger by 0.36 than in the FE simulation and precipitation weaker by 0.6 mm day −1 .
In both, the FE and the DE simulation, soil have an albedo of 0.1 which is similar to the albedo of vegetation.Hence, the albedo effect of vegetation is weak and the multiple stable vegetation-atmosphere states in Central Asia result from a hydrological feedback.As vegetation increases precipitation in Central Asia mostly during the Asian monsoon (Fig. 4), we suggest that vegetation enhances water recycling leading a stronger Asian monsoon and to more precipitation relative to bare soil and feeding back to vegetation growth.
Above, we show that the semi-deserts on the American continents are larger in the simulation with initial forest cover than in the simulation with initial desert.To identify the driving mechanism for this bi-stability, we analyse the impact of vegetation on the large scale atmospheric circulation in further detail.Following Claussen (1997), we compute the velocity potential at 200 hPa which is an indicator of large scale, upper-air divergence and convergence, and hence, convection and subsidence in the tropics.The separation of the horizontal wind, V , in the rotational component, V Ψ , and in the divergent component, V χ , yields (1) The divergent part of the wind is the gradient of the velocity potential, χ , ∇χ = V χ . (2) Hence, the divergent part of the large scale wind is directed towards the strongest increase in the velocity potential.This relation implies that air flows from the centre of negative velocity potential to the centre of positive velocity potential.Therefore, upper Introduction

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Full air diverges in the centre of negative velocity potential and converges in the centre of positive velocity potential.Below the divergence, air rises and below the convergence, air subsides.Figure 5a shows a bipolar pattern in the velocity potential at 200 hPa at the end of the DE simulation.The centre of positive velocity potential indicates subsidence over the tropical Atlantic Ocean, while the centre of negative velocity potential implies convection over the western Pacific Ocean.Over Central Asia, positive velocity potential prevails indicating subsidence over this region.
In the FE simulation, velocity potential pattern differs from the DE simulation (Fig. 5b).In Central Asia more vegetation remains in the FE simulation than in the DE simulation.
The additional vegetation enhances convection over this region as indicated by the negative velocity potential.With a stronger convection over Asia, the amplitude of the velocity potential pattern increases and the pattern shifts westwards relative to the DE simulation indicating different large scale atmospheric circulations in both simulations.
With a different global atmospheric circulation, precipitation differs significantly between the FE and the DE simulation (Fig. 6).At the west coast of the American continents, precipitation is weaker in the FE simulation leading to less vegetation in the semi-arid regions in western North America and southern South America.In other words, the multiple vegetation-atmosphere states in these semi-arid regions seem to be connected to the multiple vegetation-atmosphere states in Central Asia.
Such a connection of multiple vegetation states in several regions, so far, has not been found for the present-day climate.Claussen (1997) simulates a shift in the atmospheric circulation with different vegetation states in the Sahara.However, the shifted atmospheric circulation affects the vegetation in the Sahara only.
The question remains which mechanism links the multiple stable vegetation states in Central Asia and on the American continents.Both regions are connected through the Walker circulation.In the present-day climate, the Walker circulation describes the zonal atmospheric circulation over the subtropical Pacific Ocean.In combination Introduction

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Full with the zonal ocean circulation in the Pacific Ocean, the Walker circulation forms the El Niño-Southern Oscillation.
In the early Eocene simulations, the strong bipolar pattern in the velocity potential is associated with a zonal circulation similar to the tropical Walker circulation today: air rises over the western Pacific Ocean and subsides over the eastern Pacific Ocean (Fig. 5).In the FE simulation, this bipolar pattern is more pronounced indicating that vegetation in central Asia enhances the convection branch of the Walker circulation relative to the DE simulation.Due to continuity reasons, stronger convection in Asia causes stronger subsidence over the American continents and, therefore, less vegetation in the American subtropics.

Pre-industrial climate
In the pre-industrial Sahel, more vegetation remains in the FP simulation than establishes in the DP simulation (marked region in Fig. 2).Time series of desert cover and precipitation in the Sahel illustrate that desert cover is smaller by 0.21 at the end of the FP simulation than at the end of the DP simulation and precipitation is about two times stronger (Fig. 7).
In comparison to the stability of the vegetation-atmosphere system in the early Eocene climate, only the vegetation in the Sahel is bistable indicating that globally connected bi-stabilties in several regions are absent in the pre-industrial climate.To identify the reason for the different stability of the vegetation-atmosphere system in the early Eocene and in the pre-industrial climate, we analyse the velocity potential at 200 hPa in Fig. 8.The positive velocity potential over the Sahel implies that subsidence prevails over this region.Even the additional vegetation in the FP simulation does not enhance convection.Presumably, the subsidence over the Sahel prevents vegetation from inducing strong convection.
As vegetation fails to enhance convection over the Sahel, the global atmospheric circulation is almost the same in the FP simulation and the DP simulation leading to only weak differences in precipitation between both simulations (Fig. 9).Especially outside Introduction

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Full Northern Africa and over continents, precipitation differences are small.Hence, further multiple stable vegetation states in other regions than Northern Africa are absent.
In short, the large scale atmospheric circulation limits the multiple stable vegetationatmosphere states to North Africa.In the early Eocene climate, the bi-stability in central Asia affects subtropical deserts on the American continents because the atmospheric circulation allows vegetation in Central Asia to enhance the Asian monsoon and to shift global atmospheric circulation.The different stability of the vegetation-atmosphere system in the early Eocene and in the pre-industrial climate indicates that the location of the bi-stability relative to the atmospheric circulation determines the large scale extent of the bi-stability.
As a final note, we point to the sensitivity of our results to the soil albedo.We here assume a soil albedo of 0.1 which is almost the same as the albedo of vegetation.Due to the low soil albedo, we exclude the albedo effect of vegetation and isolate the hydrological effect.Previous studies identified the albedo effect as the major driver for multiple stable vegetation-atmosphere states in the Sahel (Charney, 1975;Charney et al., 1977;Claussen and Gayler, 1997).Other than in those studies, the bi-stabilities in our study are driven by the hydrological effect of vegetation highlighting the importance of the hydrological effect.

Conclusions
In our early Eocene simulation, we have found multiple climate states that emerge from the intransitivity of the global climate system which are triggered by different initial conditions.These multiple states differ from those detected in similar simulations of the pre-industrial climate.In the simulations of the early Eocene climate, a desert in Central Asia is much larger in simulations initialised with bare continents than in simulations initialised with densely forested continents.This difference results from the interdepence of vegetation and precipitation leading to a positive hydrological feedback.Most notably, the large-scale atmospheric circulation differs for the different initial Introduction

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Full vegetation covers which leads to larger coastal deserts in North and South America in the simulation with initially forested continents.
In our simulations, we focused on the biogeophysical processes and associated intransitivity of the atmosphere-vegetation system.We neglected any differences between plant taxa and used pre-industrial plant functional types (PFTs) for the early Eocene climate simulation.We assume that adjusting PFTs to early Eocene taxa will not change our results drastically even though the bi-stability in the Asian vegetation cover is associated with grasses.Grasses ocurred rarely during the early Eocene but, from the modelling point of view, grass behaves similar to herbs and fern which grew plentifully during that time (Utescher and Mosbrugger, 2007).Testing the sensitivity of our results to the used PFTs is subject to future studies.
In our pre-industrial simulations, the multiple stable vegetation-atmosphere states are predominately limited to Northern Africa.With the present-day distribution of continents, subsidence prevails over Northern Africa, and vegetation induces only weak convection thereby affects the large-scale atmospheric circulation only marginally.During the early Eocene, however, an Asian desert forms which is located in a region with large-scale upper-air divergence.In this region, vegetation induces convection and shifts large scale atmospheric circulation leading to further multiple stable vegetation states on the American continents.The different regional extent of multiple vegetation-atmosphere states in the early Eocene climate and in the pre-industrial climate suggest that climate and distribution of continents determines the stability of the vegetation-atmosphere system as well as the mechanisms causing multiple stable vegetation-atmosphere states.Understanding the sensitivity of multi-stabilities to constantly changing boundary contitions, such as climate and continents, deepens our knowledge about intransitive dynamcis in the climate system.Introduction

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Figure 1 .Figure 2 .Figure 3 .
Figure 1.Desert cover in the DE simulation.The average over the last 30 years of the simulation is shown.Green indicates a minimum desert cover.Blue refers to semi-desert conditions.Yellow marks desert regions.

Figure 4 .
Figure 4. Annual cycle of precipitation in early Eocene Central Asia.The respective region is marked in Fig. 2. Lines refer to the FE simulation (green) and the DE simulation (orange).The average over the last 30 years of each simulation is considered.