This manuscript has been accepted for publication in ... · Dr. Axel Kleidon akleidon@bgc-jena ... 76 ion. The water limited rate is assumed to be proportional ... at a much larger

KLEIDON: OPTIMUM STOMATAL CONDUCTANCE AND CHANGE X - 1

This manuscript has been accepted for publication in Geophysical Research Letters.

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Jena, July 12, 2007

Axel Kleidon

For more information or comments, please contact:1

BIOSP

HER

IC

THEORY AND

MO

DELLING

Dr. Axel [email protected] Theory and Modelling GroupMax-Planck-Institut für BiogeochemieHans-Knöll-Str. 10 • Postfach 10 01 6407745 Jena • Germany

Ph: +49-3641-576-217 • Fax: +49-3641-577-217

http://www.bgc-jena.mpg.de/bgc-theory

GEOPHYSICAL RESEARCH LETTERS, VOL. ???, XXXX, DOI:10.1029/,

Optimized Stomatal Conductance and the Climate Sensitivity to2

Carbon Dioxide3

A. KleidonMax-Planck-Institut fur Biogeochemie, Jena, Germany4

Stomatal conductance shapes the exchange of water5

and carbon of vegetated land surfaces. Previous stud-6

ies have demonstrated that optimized stomatal function-7

ing that maximizes productivity provides a realistic de-8

scription of how stomata operate. Here I investigate9

the role of optimum stomatal functioning for the sen-10

sitivity of terrestrial productivity and land surface cli-11

mate to concentrations of atmospheric carbon dioxide12

(pCO2). I conduct sensitivity simulations with a coupled13

vegetation-climate system model with different values of14

maximum stomatal conductance at different prescribed15

levels of pCO2. The optimum in stomatal conductance16

shifts to lower values with increasing pCO2, which is con-17

sistent with observed sensitivities of stomatal density of18

leaves. If this change in optimum conditions is not taken19

into account, the climate sensitivity shows (a) a general20

underestimation of terrestrial productivity under altered21

pCO2 and (b) different sensitivities of key climatic vari-22

ables to pCO2. The climate sensitivity of land temper-23

ature for a doubling of pCO2 ranges from ∆T = 2.7 K24

to ∆T = 3.2 K, depending on whether stomata adapt25

optimally or not at all. These results demonstrate that26

the assumed ability of vegetation to adapt to its environ-27

ment can have important consequences for the simulated28

climate system sensitivity to pCO2.29

1. Introduction

Stomata, small openings in leaves, link the exchange30

of water and carbon of vegetated surfaces. In order to31

fix carbon, plants take up atmospheric carbon dioxide32

through these openings while transpiring water at the33

same time. A change in the atmospheric concentration34

of carbon dioxide (pCO2) results in an altered gradient in35

pCO2 between ambient air and the leaf’s interior, thereby36

affecting the water-and carbon exchange of the vegetated37

cover (see e.g. recent study by Long et al. [2006]). Recon-38

structions of the past stomatal densities of leaves, which39

set the maximum conductance of leaves to water and40

carbon exchange, respond to pCO2 on a time scale of41

decades (Woodward [1987]). This effect has been used42

to reconstruct past pCO2 concentrations from leaf fossils43

(Retallack [2001], Beerling and Royer [2002a], Beerling44

and Royer [2002b]).45

Several studies have shown that stomatal conductance46

and change in stomatal functioning is an important factor47

in land surface exchange fluxes and thereby affect climate48

model simulations of global change (Sellers et al. [1996],49

Copyright 2007 by the American Geophysical Union.0094-8276/07/$5.00

2


Betts et al. [1997], Douville et al. [2000]). Here I test50

whether the reconstructed change in stomatal density to51

different pCO2 reflects the optimized response of vegeta-52

tion functioning to maximize productivity under altered53

pCO2 conditions (Cowan and Farquhar [1977], Kleidon54

[2004]) and estimate the consequences for the simulated55

climate sensitivity in an Earth system model of interme-56

diate complexity.57

2. Methods2.1. The Planet Simulator

I use the Planet Simulator (PlaSim), an Earth system58

model of intermediate complexity (Lunkeit et al. [2004],59

Fraedrich et al. [2005a], Fraedrich et al. [2005b]). PlaSim60

consists of a low resolution dynamic core of T21 spectral61

resolution (corresponding to a spatial resolution of 5.6◦62

* 5.6◦ longitude/latitude), a radiative transfer scheme63

which considers absorption by water vapor and clouds,64

ozone, and carbon dioxide, a prognostic cloud scheme,65

a mixed layer ocean model, a thermodynamic sea-ice66

model, a land surface model and the SimBA dynamic67

global vegetation model. The model is able to realisti-68

cally capture the large-scale patterns of the present-day69

climatology.70

The photosynthetic rate of the vegetative cover is sim-71

ulated as the minimum of a light-limited and a flux-72

limited rate. The light-limited rate is proportional to73

photosynthetically active radiation, fractional leaf cover,74

and depends on atmospheric pCO2 in a logarithmic fash-75

ion. The water limited rate is assumed to be proportional76

to the rate of transpiration divided by the gradient in77

pCO2 across the leaf boundary. Vegetation productivity78

then shapes the vegetation biomass dynamics and affects79

land surface properties such as surface albedo, surface80

roughness and the rooting zone of the soil. A parameter-81

ization of maximum stomatal conductance is added to the82

standard configuration of the model by adding a unitless83

factor gs,max to the bulk formula for the computation of84

the evapotranspiration rate. Through its effects on evap-85

otranspiration it influences the water-limited rate of pho-86

tosynthesis. The standard version of the model does not87

consider the effect of maximum stomatal conductance on88

land evapotranspiration rates, i.e. gs,max = 1. Kleidon89

[2004] has shown that the optimized value of gs,max < 190

that maximizes productivity for the present-day yields in91

reasonable climatic conditions, but results in a substan-92

tial increase in productivity. More details on the model93

are provided in Kleidon [2004] and Kleidon [2006].94

2.2. Simulation Setup

A set of sensitivity simulations was conducted at val-95

ues of pCO2 = 200, 280, 360, 540, 720, and 1000 ppm. At96

each concentration of pCO2, additional simulations were97

performed for gs,max = 0.01, 0.02, 0.04, 0.10, 0.15, 0.20,98

0.30, 0.40, 0.70, and 1.00. The parameter gs,max was99

varied globally uniform, that is, regional variations in100

gs,max were not considered here. The ”Control” simula-101

tion of the present day refers to the setup of pCO2 = 360102

ppm and gs,max = 1.00. All simulations were run with a103

mixed-layer ocean and interactive, thermodynamic sea-104

ice model, but with the same glacier mask. Oceanic105

heat transport was prescribed in these simulations with106

the heat fluxes derived from a ”Control” simulation with107

prescribed climatological sea surface temperatures. The108

simulations were run with an accelerated time stepping109

scheme for terrestrial vegetation to reach the steady state110

X - 4 KLEIDON: OPTIMUM STOMATAL CONDUCTANCE AND CHANGE

within 40 model years (Kleidon et al. [2007]).111

3. Results and Discussion

The sensitivity of land averaged annual mean produc-112

tivity to gs,max and its sensitivity to pCO2 is shown in113

Fig. 1. A clear maximum is seen for all pCO2 val-114

ues, with the maximum occurring at a gs,max = 1.00115

for pCO2 = 200 ppm and subsequently lower values for116

higher values of pCO2.117

The shift to lower values of the optimum gs,max for118

higher pCO2 is consistent to the reconstructed sensitivity119

of stomatal density to pCO2 (Fig. 2). For the purpose120

of comparison of the relative sensitivity to pCO2, the121

reconstructed sensitivities are set to the optimum value122

gs,max for pCO2 = 360 ppm. This is done because the re-123

constructed sensitivity of stomatal density can be highly124

species specific, yet the simulation model represents an125

integrated value of all plants that form the whole canopy126

at a much larger scale. Fig. 2 shows that the simu-127

lated sensitivity of optimum stomatal conductance falls128

very well within the range of reconstructed sensitivities129

of stomatal density.130

The impacts of different adaptive behaviors of stom-131

atal conductance on the climate sensitivity of key vari-132

ables over land is shown in Fig. 3 for three cases: (i) the133

”Control” case is taken as the simulations where stomatal134

conductance was not adapted optimally to either present-135

day or altered pCO2 conditions (i.e. gs,max = 1.0), (ii)136

the ”Present-day” case represents the case where stom-137

atal conductance is optimized for present-day, but not138

for altered pCO2 conditions, and (iii) the ”Adapted”139

case represents the case where stomatal conductance is140

adapted for both, present-day and altered pCO2 condi-141

tions.142

The climate sensitivities of land temperature range143

from 2.7K for the ”Control” to 3.2K for the ”Adapted”144

case for a doubling of pCO2 (see Fig. 3a). This dif-145

ference in the temperature sensitivity is attributable to146

differences in the hydrologic cycle over land. While the147

sensitivity of precipitation is relatively similar among the148

simulations, the sensitivity of evapotranspiration is in-149

sensitive to pCO2 in the ”Adapted” case, but increases150

with pCO2 in the other two cases. This means that the151

net convergence of atmospheric moisture transport over152

land increases in the ”Adapted” case. Also, the lack of153

enhanced evapotranspiration rates in this case is likely154

to cause the increase in temperature sensitivity shown155

in Fig. 3a. The sensitivity in evapotranspiration is mir-156

rored in the sensitivity of cloud cover over land, with157

cloud cover increasing with pCO2 in the ”Control” and158

the ”Present-Day” cases, but declining in the ”Adapted”159

case. This decline in cloud cover in the ”Adapted” case160

results in an increase in net radiative forcing (not shown)161

that adds further to the increased temperature sensitiv-162

ity. However, due to the uncertainty in cloud cover and163

precipitation sensitivities among climate models, these164

sensitivities may depend on the specific climate model165

used.166

These sensitivities can be interpreted by the co-167

limitation of GPP by light and carbon uptake. The168

optimum in gs,max shifts to lower values with increas-169

ing pCO2 since the greater gradient across the leaf-air170

boundary interface allows for the same uptake of CO2171

with less water. The resulting reduction in ET leads to172

a temperature increase, and less cloud cover. This sen-173

sitivity is consistent with previous studies (e.g. Sellers174


et al. [1996]), but the change in stomatal conductance is175

not prescribed, but rather obtained from optimization.176

There are clearly some limitations of this study. In the177

present implementation of the optimization, gs,max is as-178

sumed to be a globally uniform parameter. This could be179

improved by performing a multidimensional optimization180

at every grid cell of the model. Another aspect not con-181

sidered here is the time scale at which maximum stom-182

atal conductance could adjust under a transient change183

in pCO2. The observations by Woodward [1987] suggest184

that it may happen at a relatively short time scale so that185

the optimization may in fact be a reasonable approxima-186

tion for the transient case as well.187

Other vegetation parameters could adapt as well, such188

as the root-shoot ratio or canopy roughness, but these are189

held constant here. Both aspects are likely to lead to an190

underestimation of productivity under the altered forc-191

ing, and it would be necessary to consider these other as-192

pects as well in the representation of a fully adaptive ter-193

restrial biosphere in climate model simulations of global194

change.195

4. Summary and Conclusion

Sensitivity simulations with a coupled vegetation-196

climate model demonstrated that the optimum stomatal197

conductance of the vegetative cover shifts to lower val-198

ues for higher levels of pCO2. This optimum response199

and the associated climatic impacts are largely consistent200

with reconstructed sensitivities of stomatal density and201

previous modelling studies. This confirms that an opti-202

mization approach seems to be reasonable in representing203

the adaptive behavior of terrestrial vegetation in the cli-204

mate system. Furthermore, it provides further indication205

that stomatal conductance indeed adapts optimally to its206

environment, and that this has important consequences207

for the climate sensitivity to pCO2 over land.208

This result has implications for the interpretation of209

changes in stomatal density in paleoclimatological recon-210

structions. A change (or no change) in stomatal density211

in the past may also reflect adaptation to other driv-212

ing factors, e.g. global warming by an increase in atmo-213

spheric methane. This would alter the energy- and water214

balances at the surface and may thereby affect the re-215

sulting optimum value of stomatal conductance. If this216

were the case, differences in stomatal density could not217

necessarily be converted into pCO2 concentrations. This218

would, however, require further testing with additional219

model simulations.220

Acknowledgments. This research was in part sup-221

ported by the National Science Foundation through grant222

ATM0513506. The author thanks Dana Royer and Richard223

Betts for their constructive reviews.224

References

Beerling, D. J., and D. L. Royer (2002a), Reading a co2 signal225

from fossil stomata, New Phytologist, 153, 387–397.226

Beerling, D. J., and D. L. Royer (2002b), Fossil plants as indi-227

cators of the phanerozoic global carbon cycle, Annu. Rev.228

Earth Planet. Sci., 30, 527–556.229

Betts, R. A., P. M. Cox, S. E. Lee, and F. I. Woodward (1997),230

Contrasting physiological and structural vegetation feed-231

backs in climate change simulations, Nature, 387, 796–799.232

Cowan, I. R., and G. D. Farquhar (1977), Stomatal function-233

ing in relation to leaf metabolism and environment, in In-234

tegration of activity in the higher plants, edited by D. H.235


Jennings, pp. 471–505, Cambridge University Press, Cam-236

bridge, UK.237

Douville, H., S. Planton, J. F. Royer, D. B. Stephenson,238

S. Tyteca, L. Kergoat, S. Lafont, and R. A. Betts (2000),239

Importance of vegetation feedbacks in doubled CO2 climate240

experiments, J. Geophys. Res., 105, 14,841–14,861.241

Fraedrich, K., H. Jansen, E. Kirk, U. Luksch, and F. Lunkeit242

(2005a), The Planet Simulator: Towards a user friendly243

model, Z. Meteorol., 14, 299–304.244

Fraedrich, K., H. Jansen, E. Kirk, and F. Lunkeit (2005b),245

The Planet Simulator: Green planet and desert world, Z.246

Meteorol., 14, 305–314.247

Kleidon, A. (2004), Optimized stomatal conductance of veg-248

etated land surfaces and its effects on simulated produc-249

tivity and climate, Geophys. Res. Lett., 31, L21,203, doi:250

10.1029/2004GL020769.251

Kleidon, A. (2006), The climate sensitivity to human appro-252

priation of vegetation productivity and its thermodynamic253

characterization, Glob. Planet. Ch., 54, 109–127.254

Kleidon, A., K. Fraedrich, and C. Low (2007), Multiple steady-255

states in the terrestrial atmosphere-biosphere system: a re-256

sult of a discrete vegetation classification?, Biogeosciences257

Discussion, 4, 687–705.258

Long, S. P., E. A. Ainsworth, A. D. B. Leakey, J. Noes-259

berger, and D. R. Ort (2006), Food for thought: lower-260

than-expected crop yield stimulation with rising CO2 con-261

centrations, Science, 312, 1918–1921.262

Lunkeit, F., K. Fraedrich, H. Jansen, E. Kirk, A. Kleidon,263

and U. Luksch (2004), Planet Simulator reference manual,264

available at http://puma.dkrz.de/plasim.265

Retallack, G. J. (2001), A 300-million-year record of atmo-266

spheric carbon dioxide from fossil plant cuticles, Nature,267

411, 287–290.268

Sellers, P. J., et al. (1996), Comparison of radiative and phys-269

iological effects of doubled atmospheric CO2 on climate,270

Science, 271, 1402–1406.271

Woodward, F. I. (1987), Stomatal numbers are sensitive to in-272

creases in co2 from pre-industrial levels, Nature, 327, 617–273

618.274

Wynn, J. G. (2003), Towards a physically based model of CO2-275

induced stomatal frequency response, New Phytologist, 157,276

394–398.277

A. Kleidon, Max-Planck-Institut fur Biogeochemie, Post-278

fach 10 01 64, 07701 Jena, Germany. (akleidon@bgc-279

jena.mpg.de)280


0

2

4

6

8

ytivitcu

dor

Pm/

Cg( 2

)d/

0.01 0.10 1.00Stomatal Conductance

200 ppm

280 ppm

360 ppm

540 ppm

720 ppm

1000 ppm

Figure 1. Sensitivity of terrestrial gross primary pro-ductivity (GPP) to maximum stomatal conductance fordifferent levels of atmospheric pCO2 concentrations, asindicated.

0.0

0.2

0.4

0.6

0.8

1.0ecnatc

ud

no

C latam

otS

200 400 600 800 1000

pCO2

optimalW87-herbariumW87-experimentBR02-eqn2aBR02-eqn3aBR02-eqn4bW03-eqn8

Figure 2. Comparison of the sensitivity of optimalstomatal conductance to observed sensitivities of Wood-ward [1987] (W87) and different relationships reportedin Beerling and Royer [2002a] (BR02) and Wynn [2003](W03). The reconstructed relationships are plotted suchthat they yield the same value as the optimum value ofthe model simulation for the present-day pCO2 concen-tration of 360ppm.


2.0

2.5

3.0

3.5

4.0

noitati

picerP

200 400 600 800 1000

pCO2

1.0

1.5

2.0

2.5

3.0

noitari

psnart

opav

E

200 400 600 800 1000

pCO2

30

35

40

45

50

revo

C d

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C

ppmppm

ControlPresent-DayAdapted

mm/d mm/d

%a. b.

c. d.12

14

16

18

20

22

erutare

pme

T

°C

Figure 3. Sensitivity of annual means of (a) near surfaceair temperature, (b) cloud cover, (c) precipitation and(d) evapotranspiration averaged over land to atmosphericpCO2 for the ”Control” model simulations (dashed lines),the simulations in which stomatal conductance is opti-mized for the present-day pCO2 only (”Present-Day”,dotted line), and the simulations for which stomatal con-ductance is optimized to the prescribed pCO2 concentra-tion (”Adapted”, solid line).

This manuscript has been accepted for publication in ... · Dr. Axel Kleidon akleidon@bgc-jena ... 76 ion. The water limited rate is assumed to be proportional ... at a much larger

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