Using an optimality model to understand medium and long-term responses of vegetation water use to elevated atmospheric CO2 concentrations

Modelling results presented in this paper suggest that elevated atmospheric CO2 concentrations (eCO2) lead to reductions in leaf-level stomatal conductance and increases in water use efficiency. One consequence was a predicted increase in the perennial vegetation cover and rooting depth in water-limited regions, which provides further support to the view that the globally observed advancement of woody plants is enhanced by fossil fuel emissions. Simulated vegetation responses to eCO2 depend on time scale and climate, but generally compare well with free air CO2 enrichment experiments (FACE).


Introduction
Elevated atmospheric CO 2 concentrations (eCO 2 ) are generally expected to lead to reductions in stomatal conductance and hence leaf-scale water use (Wong et al. 1979;Drake et al. 1997). This physiological response has been incorporated into many land surface models, allowing to account for the 'physiological effect' of eCO 2 on surface temperatures in addition to the 'radiative effect' (Sellers et al. 1996;Cao et al. 2010). Several modelling studies have concluded that the physiological effect of eCO 2 on stomata may have resulted in regional and global shifts in the water balance and a general increase in river runoff (e.g. Gedney et al. 2006;Betts et al. 2007;Gopalakrishnan et al. 2011). However, other modelling studies reported that the leaf-scale effect may be offset by concurrent changes in leaf area index, dampening the reduction in vegetation water use due to eCO 2 (Piao et al. 2007;Wu et al. 2012;Niu et al. 2013) and implicated land use change or changes in solar irradiance as possible reasons for increases in continental river runoff (Oliveira et al. 2011). So far, there is only limited empirical evidence for the full range of vegetation responses to eCO 2 , but both theoretical considerations and remote sensing data have led some authors to link the observed global increase in perennial vegetation cover ('woody thickening') to increasing atmospheric CO 2 concentrations (C a ) Midgley 2000, 2012;Berry and Roderick 2002;Eamus and Palmer 2008;Donohue et al. 2013), suggesting that stomatal closure is indeed only the first step in a long cascade of potential effects of eCO 2 . These may include alterations in species compositions, perennial vegetation cover and rooting depths, which come about as the amount of transpiration required to fix a given amount of CO 2 declines with increasing atmospheric CO 2 concentrations. Such alterations are likely to only become obvious after several generations of plants, which, for perennial plants, can take decades to centuries or beyond.
Large-scale free-air CO 2 enrichment (FACE) experiments allow separation of the C a effect on different plant species from other environmental changes, which is very difficult for remote sensing observations. However, the first FACE experiments were only launched in the 1990s, focussing mainly on temperate ecosystems (Ainsworth and Long 2005), and most of them have come to an end already (Norby and Zak 2011), as they were not intended for the study of long-term vegetation dynamics in response to eCO 2 . The present study investigates whether eCO 2 might affect vegetation and the water balance differently in the medium and long term using a previously tested model that incorporates dynamic feedbacks between natural vegetation and the water balance (Schymanski et al. 2009b). Rather than prescribing vegetation response to environmental change, the model is based on the assumption that vegetation self-optimizes to maximize its 'Net Carbon Profit' (i.e. maximizing the difference between carbon acquired by photosynthesis and carbon spent on maintenance of the organs involved in its uptake) and finds the 'optimal' vegetation for given environmental conditions. Here we use this model to investigate the different time scales of vegetation response to eCO 2 .
We selected four study sites ranging from dry (waterlimited) to wet (energy-limited) conditions in Australia. At each site, we use the model to solve for the optimal vegetation under an assumed climate-CO 2 combination. We use the model runs to ask the following questions: (1) What would be the difference in predicted annual transpiration rates if only quickly varying vegetation properties (sub-annual scale) were allowed to respond to eCO 2 (medium-term response)? (2) What would be the difference in predicted annual transpiration rates if all vegetation properties were allowed to respond to increased CO 2 (long-term response)? (3) Does an increase in atmospheric CO 2 have similar effects on transpiration in all four catchments and climates for both the medium and long-term responses?

Vegetation optimality model
The model used in this study (vegetation optimality model, VOM) is a coupled water balance and vegetation dynamics model, which does not rely on any input of site-specific vegetation properties or past observations of vegetation response to environmental forcing. This model has been described elsewhere in detail (Schymanski et al. 2008b(Schymanski et al. , 2009b and the model code is available online (https://github.com/schymans/VOM). In summary, the VOM consists of a physically based multilayer soil water balance model (0.5 m thick soil layers down to an impermeable bedrock in this study) interfacing with a root water uptake model, which again interfaces with a tissue water balance and leaf gas exchange model. Water fluxes between soil layers and into the fine roots are formulated as functions of water potential gradients and resistances, while leaf gas exchange is simulated as a function of stomatal conductance and leaf-air mole fraction differences. The leaf-internal sink strength for CO 2 is modelled based on a biochemical model of photosynthesis (von Caemmerer 2000), but simplified by omitting carboxylation-limited conditions (see Supporting Information or Schymanski 2007;Schymanski et al. 2009b). For the present study, the soil water balance model was also simplified in that the catchment was represented by a rectangular block of soil rather than a linear hillslope as in Schymanski (2007) and Schymanski et al. (2009b). This was found necessary to improve consistency and robustness while parameterizing different catchment geometries (see Supporting Information for details).

Optimality, adjustable vegetation properties and associated trade-offs
The VOM approach is based on the assumption that natural vegetation has co-evolved with its environment over a long period of time leading to a composition that is optimally adapted to the conditions. Optimal adaptation is simulated by allowing dynamic adjustments of different vegetation properties at different time scales: (1) Foliage projective cover and max. rooting depth of perennial plants (decades) (2) Water-use strategies (decades) (3) Foliage projective cover of seasonal plants (daily) (4) Photosynthetic capacity and vertical fine root distributions (daily) (5) Canopy conductance (hourly) The different vegetation properties are optimized to maximize the community long-term net carbon profit (NCP), i.e. leaf CO 2 uptake minus respiration costs due to maintenance and turnover of foliage, wood and roots (Schymanski 2007;Schymanski et al. 2009b).
The canopy is represented by two 'big leaves'. One big leaf of invariant size (M A,p , m 2 big-leaf area m 22 ground area) represents perennial vegetation and another big leaf of varying size (M A,s , m 2 big-leaf area m 22 ground area) represents seasonal vegetation. As the big leaves are not assumed to transmit any light, no overlap between these two leaves is allowed, so that M A,s + M A,p ≤ 1. The seasonal vegetation is allowed to vary in its spatial extent (M A,s ), but has a limited maximum rooting depth (y r,s ¼ 1 m), while the perennial component has optimized but invariant M A,p and rooting depth (y r,p ). Maximum rooting depths are assumed to be invariant in time, but the distribution of roots within each root zone is allowed to vary on a day-by-day basis. The photosynthetic capacity in each big leaf (represented by electron transport capacity, J max25 ) is also allowed to vary from day to day, while stomatal conductivity (g s ) in each big leaf is allowed to vary on an hourly scale.
The costs and benefits in terms of NCP associated with the optimized parameters in the VOM can be separated into direct and indirect costs and benefits. The direct benefits relate to an increase in photosynthesis, e.g. by increasing big-leaf size, photosynthetic capacity or stomatal conductance. The direct costs relate to increased respiration, e.g. by increased maintenance respiration related to an increased photosynthetic capacity. The indirect benefits relate to carbon gains and losses at a later time, e.g. the consequence of increased stomatal conductance can be a prolonged period of drought-induced stomatal closure and reduced photosynthesis later. Another example is an increase in rooting depth, which has a direct maintenance cost but only an indirect benefit of allowing greater stomatal conductivity and photosynthesis during drought periods. To maximize photosynthetic carbon uptake (A g ) with a limited amount of water, transpiration should be controlled by stomata in such a way that the slope between CO 2 uptake and transpiration (∂E t /∂A g ) is kept constant during a day (Cowan and Farquhar 1977;Cowan 1982Cowan , 1986Schymanski et al. 2008a). This slope is denoted by l s and l p for seasonal and perennial vegetation, respectively. Over longer time periods, the parameters l s and l p should be sensitive to the availability of soil water and this sensitivity could be seen as a plant physiological response shaped by evolution to suit a given environment (Cowan and Farquhar 1977;Cowan 1982). In the VOM, the sensitivity of l s and l p to soil water is parametrized as and where h denotes the matric suction head in the soil while i r,s and i r,p denote the deepest soil layer accessed by roots of seasonal and perennial plants, respectively, while the summation is performed over all soil layers (i) within the rooting zone. The parameters c lf,s , c le,s , c lf,p and c le,p are assumed to represent the long-term adaptation of a plant community to its environment and are likely influenced by the species composition of the community. seasonal plants (M A,s ) and the root surface areas of perennial and seasonal plants (S Ar,p and S Ar,s , respectively) are optimized dynamically on a day-by-day basis. For a more detailed description of the optimization algorithms, see Schymanski (2007) and Schymanski et al. (2009b).
The same 30 years of meteorological forcing for each site were used in combination with different atmospheric CO 2 concentrations (C a ¼ 317, 350 and 380 ppm, representing the observed C a values in 1960, 1990 and 2005, respectively). The response to eCO 2 was then taken as the difference between the results for 350 or 380 and 317 ppm and simulated responses at different sites were compared to answer Question 3 in the Introduction.
Medium-term responses (Question 1 in the Introduction) were simulated by taking the C a ¼ 317 ppm simulations and re-running with C a ¼ 350 ppm and C a ¼ 380 ppm, while only allowing optimization of those vegetation properties that were assumed to vary at seasonal and shorter time scales (root surface areas, stomatal conductances and electron transport capacities). In other words, medium-term response refers to simulations where those variables marked as 'Constant' in Table 1 were optimized for C a ¼ 317 ppm, while all other variables were optimized for C a ¼ 350 ppm or C a ¼ 380 ppm.
To simulate long-term adaptation (Question 2 in Introduction), optimization of all vegetation parameters in Table 1 was performed independently under each C a level for each site.

Study sites and site-specific data
The four study sites chosen were all part of the OzFlux network [Ozflux is the Australian and New Zealand Flux Research and Monitoring Network (http://www. dar.csiro.au/lai/ozflux/index.html), which is part of a global network coordinating regional and global analysis of observations from micro-meteorological tower sites (Fluxnet, http://www.fluxnet.ornl.gov/fluxnet/index. cfm)]. The sites span a climatic gradient from semi-arid to humid. The OzFlux sites are long-term monitoring sites for canopy scale CO 2 and water vapour exchange. These sites were Virginia Park (VIR) and Cape Tribulation (CT) in Queensland, Tumbarumba (TUM) in New South Wales and Howard Springs (HS) in the Northern Territory. The geographic locations, vegetation types and key climatic properties of the different sites are summarized in Table 2, while satellite-derived dynamics of foliage projective cover (FPC, fraction of ground area occupied by vertical projection of foliage) is illustrated in Fig. 1. Catchment and soil properties at the different sites are given in Tables 3 and 4.
Meteorological data for the sites were obtained from the Queensland Department of Natural Resources, Mines and Water [SILO Data Drill (http://www.nrm.qld. gov.au/silo)]. The data set contained, among others, daily totals of global solar radiation, precipitation, and class A pan evaporation, daily maxima and minima of air temperature and daily values for atmospheric vapour  Table 1. Optimized vegetation properties in the VOM and their assumed time scales of variation. Subscripts p and s denote perennial and seasonal vegetation, respectively. Canopy conductance is optimized indirectly, as it depends on environmental conditions, J max25 and l, the latter of which is determined by the c l. . . parameters using Eqs. (1) and (2).

Symbol
Description Dynamics

Simulated and observed FPC dynamics
Mean FPC (the sum of the area fractions covered by the perennial and seasonal big leaves, M a,s + M a,p ) responded positively to eCO 2 in all simulations (Table 5), but obviously to a very small extent where FPC was already close to 1 at low C a (TUM and CT). At these light-limited sites, the model simulated an unexpectedly (and unrealistic) low perennial fractional cover (M A,p ) of 0.28-0.29 for TUM and 0.24-0.25 for CT. On the other hand, simulated seasonal fractional cover (M A,s ) was high and largely invariant at these sites, resulting in almost full cover when both seasonal and perennial fractional covers were combined ( Fig. 1). Figure 1 also illustrates that the simulations do capture seasonality and inter-annual variability of satellite-derived FPC estimates at the drier sites (e.g. years 1998-99 at VIR or 2003-04 at HS), and the lack of seasonality at the wetter sites (TUM and CT). However, the model predicts full cover on many occasions when satellitederived FPC is below 0.8 or even 0.5 (at VIR). Note that the simulations under eCO 2 suggest a clear increase in perennial FPC (base lines in Fig. 1) at the two drier sites.

Stomatal conductance, roots and evapotranspiration
In all simulations, stomatal conductance decreased in response to elevated CO 2 concentrations (C a ) ( Table 5). Except for the driest site, the simulated medium-term response of evapotranspiration (E T , sum of transpiration by perennial and seasonal vegetation plus soil evaporation) was a decrease in the order of 10-80 mm year 21 for an increase in C a of 63 ppm (Fig. 2). The simulated long-term response, in contrast, ranged from a slight decrease (10-25 mm year 21 ) to increases in E T by up to 70 mm year 21 (Fig. 2) when increasing C a from 317 to 380 ppm. The largest increase at the HS site was accompanied by an increase in perennial vegetation rooting depth (from 4.5 to 5 m) and M A,p (from 0.3 to 0.39) in the model. For all other sites, simulated rooting depths of perennial vegetation were at 2 m and invariant (data not shown). For the driest site (VIR), simulated perennial FPC increased from 0.22 to 0.28, with a corresponding increase in transpiration by perennial plants (E t,p in the second part of Table 5), but this was accompanied by a decrease in transpiration by seasonal vegetation and soil evaporation (E t,s and E s , respectively, in the second part of Table 5), resulting in a very small sensitivity of total E T to C a at this site. In general, the predictions considering long-term adaptation led to higher E T rates than those considering medium-term adaptation only (Fig. 2). Simulated root area indices (RAI) had a tendency to increase with C a in the water-limited catchments and to decrease in the energy-limited catchments. The increases in RAI with C a at the water-limited sites were much more pronounced in the medium-term adaptation scenario (up to 100 % increase) than for long-term adaptation (up to 25 % increase, Table 5).
Medium-term simulations. Transpiration responses were partly offset by opposite responses in soil evaporation, which was strongly correlated with surface soil moisture (Q 1 , top 50 cm, Fig. 3A). Figure 3A also illustrates that in the medium-term simulations, surface soil moisture decreased at the driest site (VIR), changed very little at the intermediate site (HS) and increased at the energylimited sites (TUM and CT) in response to increasing C a . Simulated trends in root area indices (RAI p and RAI s for perennial and seasonal vegetation, respectively) were relatively similar to those in transpiration rates, except at HS, where a strong increase in RAI s coincided with little change in E t,s (Fig. 3A).
Long-term simulations. Simulated soil moisture increased slightly at all sites (all changes ,5 %, Photosynthesis and water-use efficiency Table 5 and Fig. 3A and B show the following additional trends: (1) Photosynthetic capacities (J max25 ) and CO 2 assimilation rates (A g ) increased with C a in all simulations, with a stronger increase in A g for seasonal vegetation in the medium term, but a stronger increase for perennial vegetation in the long term. These trends were consistent across all four sites.  Table 5. Simulated responses to increasing atmospheric CO 2 concentrations (C a ). First column in each block gives the actual values (for C a ¼ 317 ppm), while subsequent columns contain deviations (in %) from these values. Negative differences marked in red font. 'Medium-term response', constant vegetation properties (see Table 1) were optimized for C a ¼ 317 ppm; 'Long-term adaptation', all vegetation properties were optimized for the respective C a . P, precipitation; Q, drainage and runoff; E T , evapotranspiration (transpiration + soil evaporation) 1 ; E t , transpiration 1 ; E s , soil evaporation 1 ; G s , big-leaf CO 2 stomatal conductance 2 ; WUE, water-use efficiency (total A g /total E t ); iWUE, intrinsic WUE [average (A g /G s )]; M A , fractional cover of big leaf; A g , CO 2 uptake rate 1 ; J max25 , leaf electron transport capacity 2 ; l p and l s , median of ∂E t /∂A g ; RAI, root area index (fine root surface area per ground area); Q 1 , soil saturation degree in top soil layer; Av(Q), average saturation degree within the rooting zone of perennial vegetation. All magnitudes given as averages (l p and l s : median values) over last 5 years of simulation. Note that at steady-state, total P ¼ total Q + total E T . However, in the simulations for VIR, soil water storage (saturated + unsaturated) varies by up to 1000 mm on a decadal scale, and in fact decreased in the last 5 years of the simulation by roughly 500 mm, explaining the mean annual imbalance of 100 mm at this site (see Fig. 2 in the SI). 1 Per m 2 ground area; 2 per m 2 projected leaf area. with seasonal vegetation at each site, and increased linearly with increasing atmospheric CO 2 at all sites with up to 24 % increase at 380 ppm compared with 317 ppm, both under medium and long-term adaptation.
(3) The median values of the slope between CO 2 uptake and transpiration (l ¼ ∂E t /∂A g ) give an indication whether water is used more or less conservatively. The lower the values of l, the more water use is limited to times favourable for higher WUE (e.g. high relative humidity of the air and light availability) and hence the more conservative the water use. Simulated l p and l s (for perennial and seasonal vegetation, respectively) generally decreased with increasing C a at the water-limited sites (VIR and HS), while they increase with C a at the energy-limited sites (TUM and CT). This effect is slightly more pronounced under long-term adaptation but equally clear under medium-term adaptation.
Direct comparison of relative changes in response to eCO 2 under medium and long-term adaptation scenarios reveals clear differences only for drainage (Q), total evapotranspiration (E T ), transpiration by perennial and seasonal vegetation (E t,p and E t,s , respectively), FPC, CO 2 assimilation rate (A g ), the water-use strategy indicator l and RAI, as summarized in Table 6. As mentioned before, E T was generally higher under long-term adaptation and hence drainage was lower, compared with medium-term adaptation. This was largely caused by a stronger increase in FPC of perennial plants under long-term adaptation. CO 2 assimilation rates (A g ) increased stronger than FPC, and generally stronger under long-term adaptation. Root area index was generally lower under long-term adaptation at the two water-limited sites (VIR and HS). Table 6 also reveals that, at the drier sites, simulated vegetation used more water under eCO 2 , which was partly compensated for by decreases in soil evaporation, while at the wetter sites, the changes were reversed. CO 2 assimilation (A g ) at the drier sites also benefited more from eCO 2 than at the wetter sites, translating into an almost proportional scaling of WUE with atmospheric CO 2 in the simulations (relative sensitivities ranging between 0.6 for the wettest site and 1.2 for the driest site).

Discussion
The model presented here and its components have been tested at the HS site in previous publications (Schymanski et al. , 2008a(Schymanski et al. , b, 2009b and further detailed tests are required before projections into the future are attempted. The simulations presented in this paper are intended as answers to the question what might be the response of vegetation to eCO 2 at different temporal and spatial scales IF vegetation were to adapt in a way to maximize its NCP in the long term. In other words, the model is used as a tool to understand the implications of an optimality hypothesis on possible responses of vegetation to eCO 2 in different climates. Therefore, no attempts were made to improve any of the model results by parameter tuning or changes to the model structure. In that respect, one advantage of optimality-based models is that they simulate the adaptation of plants to their environment based on a principle that is not expected to change as the environment changes and hence their performance for predictions into the future is not expected to be fundamentally worse than that for predicting the past.

Ecological relevance of community-scale optimality
The origins of the community-scale optimality hypothesis adopted in the VOM can be traced back to Lotka (1922), who proposed that natural selection would yield communities that maximize their throughput of energy, Odum and Pinkerton (1955) who postulated that climax communities balance their primary productivity and maintenance cost while maximizing their biomass and Odum (1969), who extended the hypothesized goal of succession to include preservation of nutrients and protection from external perturbations by complex interactions including mutualism, commensalism and others. Maximization of the NCP can be seen as an approach to quantify the maximum amount of energy (in the form Figure 2. Simulated mean annual evapotranspiration rates for different atmospheric CO 2 concentrations (C a ). 'Medium-term' refers to simulations where constant vegetation properties (see Table 1) were optimized for C a ¼ 317 ppm, while dynamic vegetation properties were optimized for the respective C a . 'Long-term' refers to simulations where all vegetation properties were optimized for the respective C a . The horizontal black dashed lines are a visual guide to see the change relative to the E T rates at 317 ppm C a .
AoB PLANTS www.aobplants.oxfordjournals.org & The Authors 2015 of assimilated carbon) that can be available within the ecosystem to support any such processes. It can been argued that natural selection does not act at the ecosystem level but instead acts on individuals and it has been shown on theoretical grounds that optimal resource use by competing plants is not equivalent to optimal resource use by a community of plants (Cowan 1982). However, consideration of more complex interactions in ecosystems resulted in the emergence of system-wide extrema in productivity or resource use (Loreau 1998) while the debate about the effects of natural selection at higher organizational levels is ongoing (Fussmann et al. 2007;Frank 2013;Pruitt and Goodnight 2014). A discussion of the consistency of optimality hypotheses with ecological theories is beyond the scope of this paper, but an overview of different optimality approaches relevant to ecohydrology can be found in Schymanski et al. (2009a).

Some consequences of simplifying assumptions
The results presented here revealed that the model does not reproduce the correct partitioning between perennial and seasonal vegetation at the two energy-limited sites (CT, TUM) examined. This is likely due to the fact that the only advantage of perennial vegetation in the present model is the ability to develop root systems deeper than 1 m. When rainfall is abundant throughout the year, and deep roots are not useful for increasing the long-term NCP, seasonal vegetation would have an additional advantage in the model of being able to reduce their FPC and associated maintenance costs on the rare and short occasions of insufficient water availability and be favoured over perennial vegetation. More realistic partitioning could likely be achieved if the advantage of being tall for light capture was considered in the model. Given that total FPC fell only very rarely below 0.99 at the wet sites (TUM and CT, Fig. 1) we expect that any such modifications would just shift the dominance from seasonal to perennial vegetation in the simulations, but not affect the overall fluxes very much. As discussed below, the big-leaf simplification complicates comparisons between simulated and observed leaf-scale properties. These may be further complicated by the neglect of carboxylation-limited photosynthesis in the VOM. Both simplifications were adopted to reduce computational burden in a model where optimal adaptation is computed using a large number of model runs. Given the prior performance of the model and its components (Schymanski et al. , 2008a(Schymanski et al. , b, 2009bLei et al. 2008), we assume that the structure of the costs and benefits of the optimized vegetation properties is captured adequately despite the simplifications.

Effect of spatial scale on eCO 2 responses
The effect of eCO 2 on evapotranspiration (E T ) has been known to decrease with increasing scale from leaf to canopy to catchment (Leuzinger et al. 2011). Our modelling results identify several mechanisms that may be responsible for this scale effect by buffering the leaf-scale reduction in transpiration at larger scales. First and most importantly, the reduction in leaf-scale transpiration with increasing atmospheric CO 2 causes more water to remain in the soil, which can either drain away and contribute to stream flow (as assumed in most papers Figure 3. Relative changes in evaporative fluxes and RAI vs. relative changes in (A) surface soil moisture for medium-term and (B) FPC in long-term adaptation. E t , transpiration; E s , soil evaporation; Q 1 , relative saturation in the top 0.5 m of soil; RAI, root area index. Subscripts p and s refer to perennial and seasonal vegetation, respectively. Dashed lines link points belonging to a given site (codes following Table 2) and atmospheric CO 2 concentration (subscripts to side codes). mentioned in the introduction) or be utilized by additional leaves or plants, especially in water-limited environments. The latter is supported by the general increase in simulated average FPC (Table 5), consistent with observational data compiled by Norby and Zak (2011), expressing the strongest increase in leaf area index for sites with initially low leaf area index and in line with conclusions drawn from remote sensing data by Donohue et al. (2013). In addition to increased drainage and/or FPC, the increase in soil moisture resulting from a decrease in transpiration may result in increased soil evaporation (E s ). This is indicated in the simulations for the energy-limited sites TUM and CT in Table 5, where both simulated soil moisture and soil evaporation rates increased with increasing C a . However, in the simulations for the water-limited sites (VIR and HS), increased transpiration and associated decreases in soil moisture and/or increases in ground shading due to increased FPC led to an overall reduction in soil evaporation in response to eCO 2 . In fact, the control on soil evaporation at the two water-limited sites shifted from soil moisture feedback in the medium-term simulations (Fig. 3A) to foliage cover feedback in the long-term simulations (Fig. 3B), whereas soil evaporation remained soil moisture controlled at the energy-limited sites (Table 5), where total FPC was close to 1 in all simulations (Fig. 1).

Long-term vs. medium-term responses
In addition to the dampening of leaf-scale reductions in transpiration at larger spatial scales, our modelling results also suggest a clear time-scale dependency at some of the sites and for some variables. Except for the driest site (VIR), the simulations representing medium-term  Table 6. Relative CO 2 sensitivities in medium and long-term response scenarios derived from Table 5. Values indicate relative change per relative change in C a as C a was increased from 317 to 380 ppm. A value of, for example, 0.7 indicates that the relative response of this variable was 70 % of the relative change in C a , i.e. 14 % increase for a 20 % increase in C a . Negative values marked in red font. 'med.', constant vegetation properties (see Table 1) were optimized for C a ¼ 317 ppm; 'long', all vegetation properties were optimized for C a ¼ 380 ppm. adaptation, i.e. where slowly varying vegetation properties (years-decades) were kept constant, showed a stronger reduction in evapotranspiration (E T ) at eCO 2 than simulations representing long-term adaptation, i.e. where all vegetation properties were optimized to the respective C a . In fact, at one of the sites (HS), longterm adaptation was predicted to lead to a dramatic reversal from an initial decrease in E T by 30 mm year 21 in the medium-term to an increase by 100 mm year 21 in the long term, mainly caused by an increase in perennial vegetation cover and maximum rooting depth (Fig. 2). Except for the wettest site, there was a general shift in water use from seasonal to perennial vegetation between the medium-term and long-term adaptation simulations. Interestingly, the simulations showed a stronger increase in CO 2 assimilation in response to eCO 2 for seasonal plants compared with perennial plants in the medium-term, but a dramatic reversal, i.e. much stronger increases for perennial plants when long-term adaptation was considered. This was mainly due to increases in FPC for perennial plants in the long-term adaptation simulations, which were not permitted by design in the medium-term adaptation simulations. This implicates eCO 2 as a direct contributor to 'woody thickening'. In the present model, establishment of saplings and the effect of fires were not considered, so the reasons for the woody encroachment simulated here must be different from those suggested by Bond and Midgley (2000).

VIR
Since all photosynthesis was modelled as C3 photosynthesis, the reasons for the woody thickening emerging from the model runs are also not related to physiological differences between woody C3 and herbaceous C4 plants, as suggested by Higgins and Scheiter (2012). In the VOM, perennial vegetation has the advantage of potential access to deeper soil water and can freely expand its FPC, whereas seasonal vegetation has a fixed rooting depth of 1 m and cannot exceed an FPC fraction of 1 minus the fractional cover of perennial vegetation. By its effect on WUE, eCO 2 acts to shift water-limited environments more towards energy-limited conditions, where the usually taller perennial plants have a selective advantage.

Effect of eCO 2 on stomatal control
An apparently paradox result is the negative correlation between trends in l ¼ ∂E/∂A and RAI. At the waterlimited sites, l decreases with increasing C a (indicating more conservative water use), but RAI increases, while at the energy-limited sites, l increases under eCO 2 (indicating less conservative water use) while RAI decreases. This can be better understood when looking at the combined effects of changes in C a and l on transpiration rates. If everything else stays constant, increasing values of l increase transpiration rates. However, at high constant values of l, eCO 2 would commonly reduce transpiration rates (Fig. 4A) while at low constant values of l, eCO 2 could also lead to an increase in transpiration rates (Fig. 4B). This is due to the non-linear effect of C a on the shape of the A g (g s ) curve and hence on the slope l ¼ ∂E/∂A. In the medium-term adaptation simulations, l only responds to changes in soil moisture, i.e. reduction in transpiration under eCO 2 leads to increased soil moisture and hence increased l and transpiration rates, representing a negative feedback loop. Conversely, increase in transpiration under eCO 2 at low values of l would decrease soil moisture and hence decrease l, resulting again in a negative feedback loop. In the long-term  Table 5).
adaptation simulations, the response of l to soil moisture is optimized for maximum NCP, along with all other vegetation properties. The results suggest that l should not be expected to scale with C a in any straightforward way, as assumed by, for example, Katul et al. (2010), but is only part of the whole plant adaptation to its environment (Buckley and Schymanski 2014).

Effect of eCO 2 on photosynthesis and WUE
Another apparently paradoxical result is that, contrary to previously employed approaches (e.g. Prentice et al. 2011), where the assumption of constant c i /c a ratios resulted in decreased biochemical capacity (expressed as V cmax ) in response to eCO 2 , the simulations here all resulted in increasing biochemical capacity (J max25 ) with increasing c a . This is in contrast to general findings in FACE studies, where leaf-scale biochemical parameters, J max and V cmax , have been found to decrease under eCO 2 (Ainsworth and Long 2005). This observed down-regulation of photosynthetic capacity is generally attributed to nutrient limitation or insufficient carbon sink capacity (Ainsworth and Long 2005;Leakey et al. 2009), neither of which are considered in the VOM. In contrast, the VOM results suggest that higher net carbon uptake rates could be achieved with higher J max25 under eCO 2 . In this context, it is important to consider that the VOM simulates the properties of a 'big leaf', representing aggregated canopy properties rather than leaf-scale properties, whereas decreases in J max under eCO 2 have been reported at the leaf scale (see above), with a simultaneous increase in leaf area index, even for relatively closed canopies (Norby and Zak 2011). These simultaneous responses may well have led to an overall increase in canopy-scale photosynthetic capacity (as predicted in the present study) despite decreases at the leaf scale. Note that the big-leaf representation of the canopy and the neglect of nutrient limitation are also features of many global scale models (e.g. Prentice et al. 2011), so their apparent consistency with leaf-scale observations of decreasing V cmax and/or J max under eCO 2 may not be a good indication for the correct representation of acclimation to eCO 2 . The most coherent response to eCO 2 across all simulations is an increase in WUE and iWUE (assimilation rate divided by stomatal conductance), with relative responses varying between 0.6 and 1.2 (Table 6), i.e. roughly doubling WUE for a doubling in atmospheric CO 2 concentration. This coincides with the range observed using FACE (Table 7). In a study focussing on two FACE sites (Duke and Oak Ridge), De Kauwe et al. (2013) found that 11 state of the art process-based ecosystem models produced relative responses of WUE to eCO 2 between 0.24 and 0.88 while the observed relative responses were 0.65 and 0.93 at the two sites. It is remarkable that the unmodified optimality model employed here produced such a robust eCO 2 sensitivity across four very contrasting catchments, that was in close agreement with general trends in FACE results, while more empirically based models with direct parametrizations of stomatal sensitivity to eCO 2 , partly based on other FACE experiments, produced much more scatter with a tendency to under-estimate the response of WUE to eCO 2 .

Synthesis and comparison with FACE results
In summary, the results presented in this study suggest that the primary effects of eCO 2 are a reduction of stomatal conductance and an enhancement of CO 2 assimilation. The former leads to reduced transpiration  Table 7. Documented vegetation responses to eCO 2 vs. model predictions. Relative responses were deduced from reported relative change in vegetation property divided by relative change in C a (e.g. for FACE experiments running at 580 ppm, relative change in C a would be 580/380 2 1 ¼ 0.5. FACE, free-air CO 2 enrichment; WTC, whole tree chamber. Sources: 1 Ainsworth and Long (2005)  per leaf area and an initially elevated soil moisture (Fig. 5), leading to increased drainage in energy-limited catchments. However, in water-limited catchments, elevated soil moisture is likely to result in increasing leaf area, while enhanced assimilation allows for the production of more and deeper roots, all of which would act to allow the vegetation to increase the light absorption by the canopy. The net effect is to either maintain, or even enhance, transpiration per unit ground area and to reduce soil moisture and drainage. Note that the relative increase in assimilation per unit ground area is very similar to relative increase in atmospheric CO 2 concentrations at the dry sites (VIR, HS) but at the wet sites, the response in assimilation to a 20 % increase in atmospheric CO 2 is more than halved, at around 10 % (Fig. 6).
The recent review of the FACE literature by Norby and Zak (2011) reveals that many of the long-term effects of eCO 2 predicted in the present study have already been observed experimentally, most notably increases in leaf area index, tree rooting depths and soil moisture. The observed responses are summarized in Table 7, which also indicates that the simulations presented here, both the medium and long-term adaptation scenarios, correspond very closely to general trends observed in FACE experiments. This is particularly remarkable given that most of the FACE data stems from experiments in temperate climates and managed ecosystems, whereas our model simulations refer to natural vegetation in semi-arid to tropical ecosystems. Both model simulations and FACE results illustrate a remarkable convergence in Figure 5. Summary of effects of eCO 2 on vegetation and water resources for constant climate. Effects specific to either water-limited or energylimited catchments are in the respective coloured boxes. Note that decrease in transpiration per unit leaf area has an initial effect on increasing soil moisture in all catchments, whereas initially increased soil moisture and enhanced assimilation results in increasing leaf area and increased transpiration per ground area at the water-limited sites, reversing the initial effect on soil moisture. Figure 6. Relative response of transpiration, CO 2 assimilation and their ratio to a 20 % increase in atmospheric CO 2 concentrations at constant climate, assuming long-term adaptation. some vegetation responses to eCO 2 across biomes and time scales, such as decreasing stomatal conductance, increasing WUE and in dry regions at least, an increase in the leaf area index.

Conclusions
The present analysis of the effects of eCO 2 on the economics of vegetation water use and carbon gain suggests that the assumption of optimal vegetation leads to results that are similar to observed patterns. From those results we also conclude that eCO 2 may be responsible for a large part of the globally observed shift towards more perennial vegetation ('woody thickening'). The study provides theoretical support for an eCO 2 -vegetation feedback that has the capacity to dampen reductions in vegetation water use as a result of stomatal down-regulation by allowing more leaf area and/or plants to thrive in water-limited environments. Considering different time scales of adaptation for different vegetation properties, the study separates responses to eCO 2 likely occurring at different temporal scales and suggests that reductions in water use due to stomatal down-regulation should be expected in the shorter term, while unchanged or even increased water use due to an increase in leaf area, plant abundance and potentially rooting depths may result in the longer term in water-limited systems. This suggests that the still common assumption that eCO 2 will generally reduce vegetation water use due to reductions in leaf-level stomatal conductance is not justified in water-limited catchments.

Contributions by the Authors
S.J.S. conceived and carried out the research, analysed the data and wrote the text in frequent collaboration with M.L.R. M.S. contributed thoughts and ideas, and helped develop and focus the text at various stages.

Conflict of Interest Statement
None declared.