Dynamics of a global-scale vegetation model

Transcription

1 ecological modelling 198 (2006) available at journal homepage: Dynamics of a global-scale vegetation model John K. Hughes a,, Paul J. Valdes a,1, Richard Betts b,2 a Bristol Research Initiative for the Dynamic Global Environment, BRIDGE, School of Geographical Sciences, University of Bristol, University Road, Bristol BS8 1SS, UK b Ecosystems and Climate Impacts, Met Office, Hadley Centre for Climate Prediction and Research, Fitzroy Road, Exeter, Devon EX1 3PB, UK article info abstract Article history: Received 2 June 2005 Received in revised form 18 May 2006 Accepted 22 May 2006 Published on line 7 July 2006 Keywords: DGVM GCM Climate modeling Vegetation An increasing number of climate modelling studies use a general circulation model (GCM) coupled to a dynamic global vegetation model (DGVM), yet the intrinsic properties of DGVMs and the feedbacks in this coupled system have not been fully investigated. Here we present details of several intrinsic properties of an established DGVM, TRIFFID, and its coupling with the Hadley Centre GCM. A new version of TRIFFID is first developed which is able to reproduce much of the behaviour of TRIFFID, yet is simple enough to be investigated analytically. This is used to show: (1) TRIFFID has a single stable equilibrium vegetation coverage, which depends on environmental conditions, (2) the dominant timescale of changes in vegetation structure is variable and is determined by environmental conditions through photosynthesis, and (3) TRIFFID damps out variability at periods less than the response timescale. From these results we conclude that the variability of the vegetation structure, and hence vegetation feedbacks can damp or amplify atmospheric variability through a shift in the response timescale, i.e. that vegetation feedbacks to the atmosphere are sensitive to the period of the atmospheric variability Elsevier B.V. All rights reserved. 1. Introduction The development of general circulation models (GCMs) during the past decade has included more realistic representations of land surface processes (see Sellers et al., 1997). Allowing dynamic changes to the vegetation structure is one of the most important of these developments, and means that vegetation structures (including vegetation distribution) are not required to be in equilibrium with the climate. The Hadley Centre GCM, HadUM3 (Gordon et al., 2000; Pope et al., 2000; Williams et al., 2001) is one of the GCMs which incorporate a dynamic global vegetation model (DGVM), the TRIFFID model (Cox et al., 1999; Cox et al., 2000). Adams et al. (2004) noted that while [TRIFFID] is fairly elegant mathematically, having only a few step func- tions and no rule-based behaviour, it remains a very complicated model which is somewhat opaque and mathematically intractable. This paper will analyse the dynamical core equations of TRIFFID in order to address this opacity, which will help in the interpretation of future simulations. In particular we will investigate which components of the core equations determine variability in land surface conditions, which will help with the understanding of land atmosphere coupling in monsoon system and will be applicable to other phenomena where land surface properties influence climate. Although this study only analyses a single DGVM, TRIFFID, the results are important for three reasons: firstly, TRIFFID is one of the most widely used DGVM in current climate research (e.g. Betts et al., 2004), secondly because of similarities it shares with other Corresponding author. Tel.: ; fax: addresses: J.K.Hughes@bristol.ac.uk (J.K. Hughes), P.J.Valdes@bristol.ac.uk (P.J. Valdes), richard.betts@metoffice.com (R. Betts). 1 Tel.: ; fax: Tel.: ; fax: /$ see front matter 2006 Elsevier B.V. All rights reserved. doi: /j.ecolmodel

2 ecological modelling 198 (2006) DGVMs, and finally because of the influence it may have on the development of future DGVMs (e.g. as part of the JULES project: In formulating a dynamic representation of global vegetation in a model it is important to consider the real world global vegetation behaviour. In an early review of dynamic global vegetation modelling, Woodward and Beerling (1997) highlight some key issues associated with developing DGVMs, specifically which physical processes should be included in the model, and the validation of DGVM properties; the long timescale involved in some components of vegetation dynamics make the issue of validation particularly problematic. In the remainder of this section different sources of evidence and theory relating to global vegetation will be reviewed. The relevant sources are diverse and we cannot hope to provide comprehensive review of all material, however the text will serve as a basic overview. It has been argued that some ecological systems are chaotic (Hastings et al., 1993; Stone and Ezrati, 1996); chaotic behaviour is largely defined by extreme sensitivity to small changes in conditions, and is therefore associated with instability. This is an important issue since whether global vegetation responds to future anthropogenic climate change in a chaotic fashion or exhibits a less risky, stable response (ignoring the potential for climate vegetation feedback processes) has serious implications. Various studies (e.g. Foley et al., 1998) have highlighted the importance of investigating DGVM stability. One possible source of evidence on the stability of global vegetation comes from mass extinction events. For the present discussion, mass extinctions may be considered as major perturbations to the environment, the response of vegetation to that perturbation offers evidence on its inherent properties. Willis and McElwain (2002), pp review evidence for mass extinction in plant taxa, concluding that plants do not appear to be as sensitive to mass extinction as animals, which suggests stability rather than inherent instability of the vegetation system. Dynamic vegetation does not have to be in equilibrium with the climatic state, and can lag behind climate variability. When dynamic vegetation is included in GCM simulations additional system memory is introduced, that acts as a low pass filter to climate variability (i.e. vegetation is not sensitive to short timescale variability). That vegetation naturally acts as a low pass filter has a well-established history in the literature of DGVM development, for example as discussed by Woodward (1987), pp , or Henderson-Sellers (1993), p In ecology, evidence for disequilibrium of vegetation has been observed in, for example, tree distributions in Europe (Svenning and Skov, 2004). Discussion of the re-colonisation of vegetation most famously takes the form of Reid s paradox, which focuses on our understanding of seed dispersal (Clark et al., 1998; Powell, 2003), and has been given new importance in the context of future climate change (Davis, 2001). Another important concept is the idea that vegetation may exhibit multiple equilibria. It is thought that such multiple equilibria require significant feedbacks within a system (i.e. the earth system; see Rial et al., 2004). Vegetation is not isolated from the rest of the climate system, and it both influences and is influenced by the atmospheric state. Vegetation feedback processes are thought to be particularly important in North Africa (Xue and Shukla, 1993), where the Sahara desert dominates the land surface and is associated with high albedo values, 20% greater than that of vegetation. If, for example, vegetation replaces bare sand as the dominant land surface type more solar energy is absorbed, resulting in a change in the monsoon circulation (which is driven by the difference in temperatures between ocean and continent) and further enhancing vegetation distributions (Charney, 1975). Vegetation also enhances the recycling of moisture, allowing further transport into the continental interior (e.g. Kutzbach et al., 1996; Zheng and Eltahir, 1998; Braconnot et al., 1999). Studies of Holocene vegetation changes in North Africa typically make use of the multiple equilibria concept (Brovkin et al., 1998; Scheffer and Carpenter, 2003): reconstructions of vegetation suggests that the Sahara was partially vegetated in the mid-holocene (Jolly et al., 1998), but between 5000 and 6000 years ago vegetation coverage changed abruptly to a desert state on a timescale of decades to centuries (de Menocal et al., 2000; Street-Perrott et al., 2000); and it has been hypothesised that both vegetated and desert states represent stable equilibria (Brovkin et al., 1998). Understanding the causes of this transition is critical to our understanding of global vegetation dynamics since it is a relatively modern and dramatic example of abrupt change and, possibly, of multiple equilibria (Brovkin et al., 1998). Most attempts to simulate the mid- Holocene greening of the Sahara under-predict the North African monsoon strength (Joussaume et al., 1999); however Claussen and Gayler (1997), and Claussen et al. (2003) are able to simulate the partially vegetated Sahara. Claussen et al. (1999) also simulate the rapid desertification of the Sahara observed using the CLIMBER2 Earth System Model of Intermediate Complexity (Petoukhov et al., 2000). Brovkin et al. (1998) estimate that approximately 3500 years ago the stability of the Saharan system changed to support only a single, desert, state and this transition was associated with a decrease of summer solar insolation below a threshold value (Claussen et al., 1999). This transition may also have been influenced by decreased intra-annual variability of vegetation fluctuations (Renssen et al., 2003), highlighting the importance of understanding vegetation dynamics. On a longer timescale vegetation during the Pliocene and Pleistocene in North Africa also underwent extensive expansions and contractions (Horowitz, 1989; Larrasoana et al., 2003), and understanding the behaviour of this region should be considered in the context of this history. Another region of interest is the boreal region, where there exist a strong contrast in albedos between snow and vegetation (e.g. Bonan et al., 1992; Brovkin et al., 2003). Here cooling may lead to further snow development and further cooling which Gallimore and Kutzbach (1996) demonstrated could play a role in glacial inception. Modelling results of Brovkin et al. (2003) suggest that feedbacks in boreal regions are too weak to support multiple equilibria at present, however Kubatzki et al. (2000) show that during the previous interglacial period (the Eemian) vegetation feedbacks may have been important in amplifying seasonal changes in the incoming solar radiation. Claussen et al. (2006) showed that in general vegetation feedbacks were an important component of the system by which relatively weak changes in the solar radiation were amplified to drive climate change. In addition to the snow-albedo feedbacks, this region may also have undergone a comparatively

3 454 ecological modelling 198 (2006) rapid shift in vegetation composition since there is strong evidence that glacial ecosystems had much greater productivity than at present and supported large mammals such as woolly mammoths (Mammuthus primigenius); this vegetation is commonly referred to as mammoth steppe (Walker et al., 2001). Guthrie (2001) hypothesise that subtle climatology changes and vegetation feedbacks were essential in maintaining mammoth steppe, and this phenomena should perhaps be studied within the paradigm of stability analysis and multiple equilibria. On an abstract level, the idea of stabilising vegetation feedbacks in the climate system is illustrated by the conceptual model known as Daisyworld. Originally introduced by Watson and Lovelock (1983). Daisyworld simulates the competition between two species of vegetation with environmental feedbacks. The most important result from Daisyworld is the ability of vegetation to alter the climate in a self-regulating way (i.e. homeostasis) leading to global temperatures, which remain constant over a large range of solar luminosities. Since Daisyworld was first proposed by Watson and Lovelock (1983) the model has been extended to investigate the impact of more complex ecosystem dynamics though the general conclusion remains unaffected (Lenton and Lovelock, 2001). When Daisyworld is expanded to include two dimensions of space on a sphere, the model is capable of simulating catastrophic shifts to a low-latitude desert equilibrium (Ackland et al., 2003); however even with increased model complexity the self-regulating behaviour characteristic of Daisyworld remains. The effect of representing the spatial dimension for capturing sudden shifts in ecosystems was also demonstrated in the more realistic study of van Nes and Scheffer (2005). The parallels between Daisyworld and the real climate system (as represented in GCMs) are discussed by Lenton and Betts (1998) and Betts (1999) demonstrates the self-beneficial behaviour of vegetation in a GCM. The main value of Daisyworld however is not as a qualitative, predictive tool, but in its relation to the general methodology of earth system science (Schellnhuber, 1999; Lenton and Wilkinson, 2003). In order to appreciate the behaviour of TRIFFID in the wider context of other DGVMs a number of models are now reviewed. The inter-comparison of DGVMs by Cramer et al. (2001) explores differences between models, and also develops a framework with which to relate results generated from one model to the group of DGVMs. The six DGVMs considered by Cramer et al. (2001) are: TRIFFID (Cox, 2001), SDGVM (Woodward et al., 1998), LPJ (Sitch, 2000; Sitch et al., 2003), VECODE (Brovkin et al., 1997), HYBRID (Friend et al., 1997), and IBIS (Foley et al., 1996; Kucharik et al., 2000); some properties of these DGVMs will now be reviewed, though a systematic investigation of the dynamics of each DGVM has yet to be completed, and instead the approach taken by Cramer et al. (2001) typifies the methodology generally adopted: that of integrative studies of responses to realistic climate patterns. LPJ and HYBRID use a bottom-up approach to the simulation of vegetation. This method assumes that vegetation on the scale of DGVMs exhibit the same dynamics as individual plants (Sitch, 2000). The extent to which ecological processes are scale dependent is a focus of current ecological research (van Gardingen et al., 1997), however it is thought that different physical and biological processes influence vegetation structure at different scales (Delcourt et al., 1983). HYBRID simulates individual trees and a layer of grass, competing for light, moisture and nitrogen within a grid box (Friend et al., 1997). The bottom-up approach is computationally expensive, prohibiting the use of HYBRID interactively in a GCM (Cramer et al., 2001; Sitch, 2000). In response to the computational expense of HYBRID, the LPJ DGVM simulates plant functional types (PFTs) rather than the individual plants (Sitch, 2000; Smith et al., 1997). The PFT population sizes are then used to scale from patch to grid box scale, and therefore LPJ uses individual based vegetation dynamics theory to simulate changes in the vegetation composition; in LPJ vegetation compete for light and moisture. The dynamics of bottom-up models are by their nature largely intractable to mathematical analysis (though it would be possible to conduct idealised experiments and analyse the heuristic properties). In contrast TRIFFID, SDGVM, IBIS and VECODE adopt a heuristic modelling approach, whereby the land surface properties relevant to GCM simulations, e.g. surface albedo, or roughness length, are modelled directly (Cox, 2001). IBIS simulates grid box vegetation in two layers: tree canopy and grass level canopy. Within each canopy PFTs compete for light and moisture. Trees can also act to shade grass, but grass is able to access water as it enters the soil before trees can. Successful PFTs (determined by largest carbon accumulation) crowd out less successful PFTs (Foley et al., 1996). TRIFFID simulates dynamic vegetation structure as the fractional coverage and carbon density of up to five PFTs in each grid box. In TRIF- FID PFTs compete horizontally whilst, shrub automatically displaces grasses, and trees displace grasses and shrubs. TRIF- FID models competition between grasses and between trees explicitly using modified Lotka-Volterra competition equations. Using this approach the grass PFT with the larger carbon density will dominate the grass PFT with the lower carbon density. SDGVM also predicts ecosystem-scale photosynthesis rates and stomatal conductance (Beerling et al., 1997; Woodward et al., 1998). VECODE is comparatively a simple model, predicting the fractional contributions of grass, tree and bare soil, and net primary productivity (NPP) at a particular grid box using an empirically derived function sensitive to precipitation and temperature (Brovkin et al., 1997; Lieth, 1975). VECODE was developed for use in the Earth System Model of Intermediate Complexity: CLIMBER2 (Petoukhov et al., 2000). In their inter-comparison study Cramer et al. (2001) force the DGVMs with the simulated climate response to estimated anthropogenic emissions between 1850 and 2100 (as predicted by the HadCM2 GCM), and with predicted future atmospheric CO 2 changes. The response of the DGVMs was measured in terms of the various carbon fluxes, including NPP, and in spite of the different modelling approaches taken by each DGVM the different models showed similar responses to the prescribed climate change: all DGVMs responded with increased rates of NPP. The nature of the experiment meant that it was impossible to decompose the small-scale variability in NPP rates into internal (DGVM driven) and external (climate driven) components. A benefit of the approach adopted by TRIFFID is that the dynamics of the vegetation properties can be (and are) represented as a small number of equations. This set of equations can be interrogated to better understand the core dynamic

4 ecological modelling 198 (2006) properties of the model, and their implications on the variability of climate. Previous studies have focussed on quantitative predictions (e.g. simulating atmospheric CO 2 variability, Jones and Cox, 2001; or response to climate change, Cramer et al., 2001); here we will focus on some of the dynamic properties, which underlie these studies. In Section 2 a simplified version of the TRIFFID dynamic equations are derived, s-triffid, in order to investigate the behaviour of TRIFFID. It is shown that the core dynamics of TRIFFID are reproduced by s-triffid. In Section 3 s-triffid is analysed and the characteristic timescale of s-triffid (and hence TRIFFID) is related to environmental conditions. Dynamical stability of s-triffid is also demonstrated. The response of s-triffid to environmental variability is investigated, and is related to the inherent timescale. Section 4 analyses a full complexity GCM simulation of recovery from a global perturbation to vegetation coverage (using TRIFFID) in order to validate results from s-triffid. The implications of these results are discussed in Section Simple model description TRIFFID runs at the same horizontal resolution as HadUM3: 2.50 latitude by 3.75 longitude. TRIFFID differentiates vegetation into five different plant functional types (PFTs): broadleaf tree, needleleaf tree, shrub, C3 type grass, and C4 type grass. Each PFT occupies a variable percentage of a grid box, affecting the grid box mean surface albedo and roughness length. The surface properties of a grid box therefore reflects the contributions of several different PFTs, and the residual fraction (bare soil). There also exist in TRIFFID static representations of land ice, urban regions, and inland lakes, however these are static and can and will be ignored in this paper. Broadleaf tree competes for space with needleleaf tree. Shrub is automatically displaced by the presence of either tree PFT. Grasses are assumed to be displaced by both trees and shrub, and compete for space with the other grass type. TRIFFID assumes that grass PFTs influence each other according to a form of the Lotka-Volterra competition equations (see Cox, 2001), the same is assumed for the tree PFTs. The structure of TRIFFID constrains this competition to the stable co-existence solution of the Lotka-Volterra competition equations (Hughes et al., 2004). This produces a smooth transition of PFTs across horizontal boundaries, which is more appropriate for GCM resolution than discrete boundary transitions (Svirezhev, 2000). For a PFT to achieve dominance of a grid box in TRIFFID it requires a higher net carbon assimilation rate than its competitors (Hughes et al., 2004). Carbon assimilation rates are predicted from the environmental conditions, using the photosynthesis models of Collatz et al. (1991) and Collatz et al. (1992). In order to represent the dynamics of TRIFFID in a fully self-contained set of equations it is necessary to introduce two assumptions. Most importantly it is necessary to assume that the grid box considered is dominated by a single PFT, i.e. that we can ignore the effects of one PFT on another, thereby allowing us to consider only a single PFT and its associated differential equations. In order to test the validity of this assumption a default simulation of HadUM3 (which includes TRIF- FID) was analysed. This simulation modelled pre-industrial climate, with modern distributions of land and solar forcing, and atmospheric concentration of carbon dioxide of 287 ppmv. After the initial spin-up phase of the experiment, 30 years of integration were completed. When the tree distributions were analysed it was found that for 94% of all tree coverage there is less than 5% of another tree PFT present in the grid box. When grass distributions were analysed it was found that for 96% of all grass coverage there was less than 5% of another grass PFT present in the grid box; hence the assumption that a grid box is dominated by a single PFT is reasonable. The other assumption required is that the local loss of carbon through leaf fall (the litterfall rate) is linearly proportional to the vegetation carbon density, which is an approximation of the carbon turnover rates (see Cox, 2001; Hughes et al., 2004). In formulating a simple version of TRIFFID (s-triffid) the carbon assimilation rate is prescribed, and is one of the forcing conditions of the model. Calculating the carbon assimilation rate within s-triffid would introduce further complexity, which would not aid the present investigation. Modelling carbon assimilation explicitly would also require the specification of alternative prognostic fields, namely those involved in the surface energy balance. With these assumptions the equations of the dynamic core of TRIFFID become: dc dt = (1 ) C (2.1) d dt = (1 ) (2.2) C 1 C C max C C = min C C max C min <C<C max (2.3) min 0 C C min where is the net primary productivity (NPP; kg C m 2 s 1 ), and is the flux of carbon into the terrestrial biosphere. C is the vegetation carbon density (kg C m 2 ). C max and C min are the maximum and minimum carbon densities, and are prescribed for a given PFT (Table 1); is the fractional coverage of the PFT for the particular grid box; is the natural disturbance rate (Table 1), and is reproduced from Cox (2001); is a spreading function which governs the distribution of carbon between increasing fractional coverage,, and increasing the carbon density, C; represents the rate of litterfall (s 1 ), and is derived through an iterative process, with the target of maximising the agreement between the full complexity TRIFFID and s-triffid (Fig. 1). By fitting s-triffid to TRIFFID through the choice of a single value of no additional dynamical properties are introduced to the model. In using Eq. (2.3) we are adapting the usual form of which is a function of leaf area index (LAI). By assuming that there is a 1:1 mapping between LAI and carbon density (and adopting an approach similar to Huntingford et al., 2000) it is possible to re-write the TRIFFID equations and eliminate LAI, greatly reducing the mathematical complexity (thus forming a third simplification). The equations presented here are similar to those used by Huntingford et al. (2000), however the links to TRIFFID were not discussed there. Huntingford et al. (2000) used their model to investigate the response of the terrestrial biosphere to anthropogenic

5 456 ecological modelling 198 (2006) Table1 Values of the constants for each PFT Broadleaf Needleleaf C3 grass C4 grass Shrub (s 1 ) C max (kg C m 2 ) C min (kg C m 2 ) These are given in Cox et al. (2000), howeverc max and C min values are derived from Cox et al. (2000) using the equations included in Hughes et al. (2004). CO 2 emissions, whilst the internal dynamics of the vegetation model are discussed here. In order to validate s-triffid the predicted fractional coverage from TRIFFID is compared against those from s-triffid. Experiments show that of all the components in both TRIFFID and s-triffid the fractional coverage has the longest associated timescales; the dominance of the fractional coverage timescale was also demonstrated by Huntingford et al. (2000). Dynamic systems theory therefore suggests that we concentrate our investigation on the fractional coverage. In order to test s-triffid against TRIFFID the NPP data simulated in the full complexity version of TRIFFID are used to drive s-triffid. The NPP data was stored at 30 min timesteps during a fully coupled climate simulation using HadUM3. The comparison is of fractional coverage of C4 type grass for a grid box in Australia, which exhibits high variability. In this region only C4 type grass and bare soil exist, and bare soil is calculated as the residual coverage after C4 type grass and does not affect the dynamics of C4 type grass. A single dominant PFT in TRIFFID is also more similar to s-triffid in which the equations represent only a single PFT (for simplicity of analysis). Fig. 1a shows the fractional coverage predicted by s-triffid and TRIFFID using the same NPP values. Fig. 1b shows the differences in fractional coverage between the two versions. It is seen that s-triffid provides an excellent reproduction of the variability of TRIFFID vegetation structure, with a typical discrepancy of less than 2%. Other case studies have been completed with success (testing different PFT types and forcing climatologies), however space requirements meant we chose to present only one experiment, and from a region that presented the most demanding validation of s-triffid. We therefore have good confidence in the ability of Eqs. (2.1) (2.3) to represent the dynamics of TRIFFID; analysis of equilibrium distributions of vegetation in s-triffid is unnecessary since this would only test the ability to simulate steady state coverage (given NPP and litterfall rates) and not whether the dynamics of s-triffid accurately correspond to TRIFFID. In the next section the behaviour of s-triffid is investigated. 3. s-triffid results Since the previous section has shown that s-triffid captures the dynamics of TRIFFID, analysis of s-triffid is now presented with the goal of elucidating the behaviour of TRIFFID. In s-triffid the initial rate of growth of fractional coverage from bare soil is given by r, where r is defined as: r = C (3.1) Fig. 1 (a) The predicted fractional coverages of C4 type grass using s-triffid (thin, pale line) and TRIFFID (thick, black line). (b) The difference between TRIFFID and s-triffid between simulated fractional coverage of C4 type grass. For this simulation a value of = 8.0e 9 year 1 gave a good agreement between TRIFFID and s-triffid. It can be shown from (2.2) that the fractional coverage,, has logistic solutions. This means that r (as defined in Eq. (3.1)) is the intrinsic growth rate of the fractional coverage (see Gotelli, 1998, p. 100), and also determines the time taken to expand from an initially small coverage to the steady state coverage. The re-growth time, g, is related as: [ ] g = 1 1 r ln final 1 1 initial 1 (3.2)

6 ecological modelling 198 (2006) Fig. 3 Power spectrum of the fractional coverage of broadleaf tree PFT when forced with a data set of NPP exhibiting white noise. Fig. 2 Stability properties of s-triffid, derived from Eqs. (2.1) (2.3), in terms of fractional coverage vs. the rate of change of fractional coverage. where initial is the initial fractional coverage and final is the final fractional coverage. Eq. (3.1) shows that r (and therefore g) is a function of the net primary productivity (NPP), since the carbon density, C, and the spreading function,, are ultimately determined by the NPP value. Fig. 2 shows fractional coverage against the rate of change of fractional coverage, using Eqs. (2.1) (2.3). Fig. 2 shows that two equilibrium points exist for s-triffid: an unstable equilibrium at 0% coverage, and a stable equilibrium at = C/. The non-zero equilibrium is stable because a perturbation (either positive or negative) will result in the system returning to the equilibrium point, unlike the 0% coverage equilibrium, i.e. if the system is perturbed above the stable equilibrium the rate of change of fractional coverage is negative and fractional coverage returns towards the equilibrium point. When s-triffid is integrated with constant values of NPP and, the steady state fractional coverage is a constant value, which is confirmed by the stability analysis shown in Fig. 2. To investigate how s-triffid interacts with atmospheric variability s-triffid was forced with an artificial data set of 10,000 years of NPP exhibiting white noise variability around a mean value with parameter choices corresponding to broadleaf tree; this NPP data set was generated with a random number generator. A 10,000-year simulation is computationally too expensive for a GCM and TRIFFID cannot, at present, be run offline. Running TRIFFID in HadUM3 would not force TRIFFID with a white noise spectrum, complicating the analysis; therefore s-triffid provides a unique method of investigating these timescales. Fig. 3 shows the power spectrum of vegetation fractional coverage changes, from the 10,000-year simulation. Fig. 3 shows that s-triffid damps out variability for periods less than 100 years. One hundred years is approximately equal to the intrinsic timescale (1/r), and because these timescales are all related, the damping timescale is a function of envi- ronmental conditions (Eq. (3.1)). Therefore, vegetation in TRIF- FID will not respond to atmospheric variability less than the damping timescale and so vegetation feedback mechanisms involving changes in the fractional coverage will be sensitive to the timescale of atmospheric variability. The implication of this is that changes to the damping timescale, driven by changes in the environment, can effectively couple or decouple vegetation feedbacks from climate variability; i.e. whether TRIFFID responds to climate variability by altering its structure and potentially amplifying the original climate response or not depends on the timescale of the climate perturbation and the damping timescale, but a change in the damping timescale could change the system response from damping to amplification of climate variability. 4. GCM analysis In order to further verify that results from s-triffid can be related to TRIFFID a transient perturbation experiment was completed with TRIFFID dynamically coupled into the HadSM3 GCM. HadSM3 is a version of HadUM3 which explicitly simulates the atmospheric circulation but the ocean is repre- Fig. 4 Global average fractional coverage of the different PFTs throughout the 300 GCM simulation.

7 458 ecological modelling 198 (2006) sented thermodynamically as a slab ocean model (Williams et al., 1999). At the start of the experiment the atmosphere is initialized in a pre-industrial state, whilst vegetation was set to global bare soil conditions. Global desert experiments are well established as valid studies of global vegetation modelling (e.g. Betts, 1999; Kleidon et al., 2000). Vegetation in TRIF- FID then re-grows and HadSM3 simulates 300 years of the response of the system. During the experiment vegetation is influenced by and influences the atmospheric state. Fig. 4 shows the average vegetation fractional coverage over all land masses throughout the GCM simulation. Initially C3 and C4 type grasses rise to dominance, accounting for 70% of the surface area. As shrubs re-grow the grasses (especially C3 type grass) are displaced, and as the forests re-grow shrubs are displaced (by about 15%). Of the two tree PFTs broadleaf trees re-grow most substantially over 300 years and are close to the pre-industrial equilibrium coverage (20%; as calculated from previous simulations). The pre-industrial equilibrium coverage of needleleaf trees is approximately 8% and assuming this region does not exhibit multiple equilibria (this assumption is supported by Brovkin et al., 2003), it is clear that the modelled re-growth of the needleleaf forests (which characterize boreal regions) require longer simulations to reach a steady state than the 300 years. The pre-industrial equilibrium coverage of C3 grass, C4 type grass and shrub are 15%, 9% and 23%, respectively, and comparison against Fig. 4 shows that the re-growth of needleleaf forest would most likely be an expansion of needleleaf tree into regions dominated by shrub at the end of the simulation. Fig. 4 demonstrates the long timescales associated with TRIFFID components with substantial lags in vegetation properties (>300 years). In order to quantify the re-growth timescales associated with vegetation types it is assumed that the initial growth period can be reasonably modelled by solutions of the logistic equation: (t) = ˇ e { t/} (4.1) Fig. 5 Estimates of the response time for each PFT as a function of 1.5 m air temperature and precipitation rate. (a) Broadleaf tree; (b) needleleaf tree; (c) C3 type grass; (d) C4 type grass; (e) Shrub.

8 ecological modelling 198 (2006) Table 2 Average response time properties for each PFT calculated from the transient GCM simulation PFT Mean (year) Std (year) g (90%) ± std (year) g (99%) ± std (year) Broadleaf ± ± 87.5 Needleleaf ± ± 47.0 C3 grass ± ± 0.5 C4 grass ± ± 0.5 Shrub ± ± 12.0 where ˇ and are assumed to be constants and is the response timescale; Eq. (4.1) assumes therefore that the re-growth of vegetation can be approximated by a single timescale for the whole period of re-growth of a PFT. The assumption of logistic growth is justified by the underlying equations of TRIFFID, but climate variability means this is only an approximation. The characteristic is calculated for each PFT re-growth curve using standard least squares curve fitting to the simulated fractional coverage. Only the initial period of re-growth is used, since during this period it is reasonable to assume that more dominant PFTs (i.e. for grass PFTs: shrubs and trees) have not re-grown to substantial enough coverage to seriously affect the growth rate. Grass timescales were estimated using the first 3 years of fractional coverage, shrub from 50 years of data and tree values were estimated using the whole 300 years. For each value calculated the mean 1.5 m air temperature, precipitation and NPP was also calculated. Fig. 5 shows the estimated response timescales, plotted in climate space, there is a visible (if rather complex) relationship between the position in climate space (i.e. the environmen- Fig. 6 Simulated net primary productivity values as a function of 1.5 m air temperature and precipitation rate, for each plant functional type. (a) Broadleaf tree; (b) needleleaf tree; (c) C3 type grass; (d) C4 type grass; (e) Shrub.

9 460 ecological modelling 198 (2006) tal state) and the predicted response timescale (). It should be noted that when ˇ = ( 1 1) then Eq. (4.1) is the analytical solution of the vegetation dynamics and =1/r. In this initial case the re-growth of a tree PFT from 0% to 90% coverage, with = 100 years, would take 230 years (and re-growth to 99% would take 461 years; from Eq. (3.2)). The values estimated from the GCM simulation for broadleaf tree, however, range between 30 and 124 years, which correspond to re-growth times (to 90%) of between 69 and 286 years. The range of response timescales and re-growth times associated with each PFT during the experiment are given in Table 2. Fig. 6 shows averaged annual NPP rates plotted for each PFT in climate space. When the environmental sensitivity of NPP is compared to the re-growth timescale for broadleaf tree (Figs. 6a and 5a, respectively) it is clear that high NPP correspond to low, in agreement with the s-triffid analysis (i.e. Eq. (3.1)); however for other PFTs the relationship is not as clear. Needleleaf tree and C4 type grass are broadly consistent with the relationship, but Shrub, for example, actually appears to associate high NPP with slow response timescales. Rather than disproving the NPP relationship (which is clearly demonstrated for broadleaf trees) the other PFTs suggest than annual average NPP values may not be the best variable for comparison; average NPP during the growing season would probably be preferable, however due to the length of the GCM simulation only annual averages were retained. The reason for the success of comparison between Figs. 5a and 6a is due to the fact that broadleaf tree responds to climate variability on a slower timescale than grasses or shrub (i.e. it is acting as a low pass filter). If we accept that C4 type grass supports the NPP relationship it may be due to the fact that C4 type grass is typically found in the tropics, and experience weaker climate seasonality. 5. Discussion/conclusions In the present study the dynamical properties of the TRIFFID dynamic global vegetation model (DGVM) have been investigated. We have focussed on the interaction between atmospheric variability and variability of the land surface distributions. In answer to the question what causes variations of the vegetation distributions in TRIFFID? it is now clear that variability is driven by atmospheric perturbations. TRIFFID is dynamically stable and is not a source of noise. TRIFFID is not, however, completely passive to the atmospheric variability and attenuates variations above a cut-off frequency. This cut-off frequency has not been explicitly specified in TRIFFID and is not constant. The cut-off frequency is related to the time taken to re-grow from initially small coverage, and is also equivalent to the intrinsic timescale. These timescales in TRIFFID are functions of the net primary productivity (NPP; kg C m 2 s 1 ), which is determined by the balance between photosynthesis and photorespiration. Both these processes depend on the environmental conditions, including the atmospheric concentration of carbon dioxide. This relationship between response timescales and environmental conditions was demonstrated in a transient GCM experiment (Section 4). The cut-off frequency introduces a mechanism by which climate variability is coupled or de-coupled from vegetation feedback mechanisms, i.e. there exists a variable frequency at which vegetation structure switches between responding and attenuating climate variability, potentially amplifying climate sensitivity if it responds. Correct cut-off frequencies are then critical for the coupling of vegetation and the climate system. The long timescale associated with tree PFTs in TRIFFID is comparable to the thermal inertia timescale of the oceanic mixed layer and may suggest something analogous to the phenomena of harmonic resonance. The importance of the response timescale of vegetation on the North African monsoon, specifically the simulation of the mid-holocene humid period, also requires further investigation. In Section 4 results of a pre-industrial perturbation experiment using the full version of TRIFFID were presented and it was shown that the re-growth timescales of grass PFTs for a pre-industrial perturbation experiment were 0.5 and 0.6 years for C3 and C4 type grass, respectively. Shrub PFT had a characteristic regrowth timescale of 7.6 years. In a study of the variability of satellite derived NDVI, a measure of land surface greenness, Jarlan et al. (2005) showed that vegetation in the Sahel region exhibits significant variability in the periods of 6.2, 4.5, and 3.6 years. These periods are greater than the response timescale of grass PFTs in TRIFFID, however they are close to the response timescale of shrub PFT (7.6 years; Section 4). Preindustrial simulations show the Sahel region to be dominated by grass PFT (Betts et al., 2004), however grass PFTs have associated timescales of 0.5 and 0.6 years. A better match between observed timescales (Jarlan et al., 2005) and the timescales presented here would occur if shrub dominated this region, and Betts et al. (2004) show that the model under-predicts the amount of grass, shrub and trees in this region. Further tests of the spectral properties of TRIFFID may be achieved through the interdependence of the different timescales in TRIFFID, i.e. by attempting to validate the inherent timescale by validating the re-growth timescale. Validation of the timescales of tree re-growth is difficult because it requires grid box scale observations of vegetation. Hughes et al. (2004) showed that TRIFFID reproduces the large-scale recovery timescale of needleleaf tree cover after the 1908 Tunguska meteorite event, to the extent that the observations of this event allow. TRIFFID adopts a heuristic perspective, in contrast to a bottom-up version of individual-based models. The heuristic perspective may be formulised as the hypothesis that largescale land surface properties can be directly simulated. TRIF- FID conceptualises terrestrial vegetation is as a volume of carbon: carbon is added to vegetation through photosynthesis, and is lost by litterfall and photorespiration. From this formulation the coupling of environmental conditions to the timescales of vegetation is logical. It is clear, however, that both approaches (heuristic and bottom-up approaches) are necessary and useful investigative tools. It has been shown that TRIFFID is dynamically stable; however it is not established whether stability is more or less realistic than instability. In addition we have highlighted the division between inherent DGVM stability and stability of the climate system. By investigating the importance of global vegetation dynamics within the climate system, global vegetation modelling offers the potential of fresh insight into the biosphere-stability debate.

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