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Commentary Connecting mathematical ecosystems, real-world ecosystems, and climate science Only about one-half of the annual anthropogenic CO2 emissions remain in the atmosphere, and the remainder is absorbed by terrestrial ecosystems and the oceans (Le Quere et al., 2013). Many factors including climate, nitrogen (N) deposition, and forest recovery following disturbance contribute to the terrestrial carbon (C) sink, but modeling analyses of the twentieth century C cycle attribute much of the C uptake to enhanced plant productivity arising from higher atmospheric CO2 concentration, the so-called ‘CO2 fertilization’ response (Sitch et al., 2008; Piao et al., 2013). Model projections over the twenty-first century also highlight the importance of CO2 fertilization to reduce the accumulation of anthropogenic CO2 emissions in the atmosphere (Friedlingstein et al., 2006, 2014). Free-air CO2 enrichment (FACE) experiments in forest ecosystems reveal such productivity gains (Norby et al., 2010). However, detection of these changes in the natural world has been elusive. Models of the terrestrial biosphere remain a key means to understand the historical C cycle and to make projections of the future. In this issue of New Phytologist, Zaehle et al. (2014, pp. 803– 822) assess how well these models perform in comparison with FACE experiments.

biosphere (termed the carbon–concentration feedback in climate science literature). Climate change reduces this C accumulation, because of lower net primary production (NPP) and increased heterotrophic respiration (termed the carbon–climate feedback). This conceptualization of the C cycle in ESMs was first quantified for the Intergovernmental Panel on Climate Change (IPCC) fourth assessment report (AR4) and remains largely unchanged for the fifth assessment report (AR5) (Fig. 2a). However, the question remains: how well does this mathematical representation of the terrestrial C cycle represent the real world? For instance, it has long been recognized that ESMs overestimate the CO2 fertilization response by failing to account for N limitation of NPP (Hungate et al., 2003). Indeed, the inclusion of an N cycle in the CLM4 reduces the C gain with CO2 enrichment, seen also in other models with coupled C–N cycles (Zaehle et al., 2010; Zhang et al., 2011). The models used for AR5 lack C–N biogeochemistry, except for the CLM4, but are the C–N models themselves a step forward, or are they merely different compared with the C-only class of models? Addressing this is critical in light of recommended amounts of permissible anthropogenic CO2 emissions to limit planetary warming to 2°C (IPCC, 2013). There are many tools to assess model performance. Models are routinely evaluated against eddy covariance flux datasets, both at individual tower sites (St€ockli et al., 2008) and with empirically upscaled global flux datasets (Bonan et al., 2011), but these do not necessarily test underlying processes in the model or responses to perturbations. Some model evaluations exploit the annual cycle of atmospheric CO2 (Cadule et al., 2010), inter-annual variability

‘How, then, do we interpret model simulations of a twentyfirst century Earth?’

Models of Earth’s climate have traditionally emphasized geophysical processes. Chief among these are: clouds, radiation, and convection; ocean–atmosphere coupling; sea ice; and, soil moisture–precipitation coupling. The advent of Earth system models (ESMs) – with representation of coupled physics, chemistry, and biology – has moved the study of the terrestrial C cycle and terrestrial ecosystems to the forefront of climate science. In these models, climate and atmospheric CO2 co-evolve based on anthropogenic CO2 emissions and terrestrial and marine feedbacks. Fig. 1 illustrates the C cycle simulated by one ESM – the Community Earth System Model and its terrestrial component model, the Community Land Model (CLM4). In the absence of climate change, higher atmospheric CO2 concentrations over the twentieth century drive an accumulation of C in the terrestrial Ó 2014 The Author New Phytologist Ó 2014 New Phytologist Trust

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Fig. 1 Terrestrial carbon (C) cycle simulations over the twentieth century using the Community Land Model (CLM4). Shown are simulations forced with historical CO2 concentrations and CO2 and climate for C-only (a) and carbon–nitrogen (C–N) (b) configurations of the model. See Piao et al. (2013) for a description of the simulation protocol and model analyses. New Phytologist (2014) 202: 731–733 731 www.newphytologist.com

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Carbon-climate feedback, γL (Pg C K–1)

Carbon-concentration feedback, βL (Pg C ppm–1)

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AR4 (b)

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(Piao et al., 2013), or response to large-scale drought (Reichstein et al., 2007). Ecosystem experiments have been conducted in relation to soil warming, CO2 enrichment, N addition, and throughfall exclusion. Zaehle et al. (2014) show how such experiments with real world ecosystems inform the mathematical ecosystems depicted in models. Zaehle et al. (2014) used 11 ecosystem models to investigate the effects of N availability on the response of forest productivity to elevated CO2 at two FACE sites – a deciduous broadleaf forest at Oak Ridge National Laboratory and the evergreen needleleaf Duke Forest. Multi-model comparisons typically reveal divergent responses across models. Although quantification of model uncertainty is useful, scientific advancement requires that such comparisons provide insight to the underlying processes causing the divergent model responses. Indeed, Medlyn et al. (2011) espoused the need to not just describe model simulations, but also to characterize models in terms of process parameterizations and assumptions to correctly interpret the results. De Kauwe et al. (2013) identified key assumptions in modeling the response of stomatal conductance to elevated CO2, and Zaehle et al. (2014) similarly did that for plant productivity. A key motivation for the study of Zaehle et al. (2014) is that the NPP enhancement with elevated CO2 declined over the length of the Oak Ridge experiment but was sustained over 10 yr at the Duke site. The model simulations show that we have much to learn about New Phytologist (2014) 202: 731–733 www.newphytologist.com

Fig. 2 Scientific advancement of carbon cycle–climate coupling in Earth system models (ESMs). (a) Land carbon–concentration and carbon–climate feedback parameters for 11 models used in the Intergovernmental Panel on Climate Change (IPCC) fourth assessment report (AR4) (Friedlingstein et al., 2006) and nine models in IPCC AR5 (Arora et al., 2013). Shown are the individual models (symbols) and the multi-model mean (star). The two shaded symbols show results from two AR5 ESMs that used the Community Land Model (CLM4). The methodology used to derive these feedback parameters differs between AR4 and AR5, so they are not directly comparable. (b) A synergy of observations, theory, process parameterizations, and ESMs is needed to gain confidence in carbon cycle– climate projections.

CO2 regulation of NPP and how to formulate this in models. Most of the models replicated the initial NPP enhancement at both sites, but failed to adequately replicate long-term trends at either site. Most models showed signs of progressive N limitation, with progressively smaller NPP enhancement because of N limitation at Oak Ridge, but only three of the 11 models correctly simulated the magnitude of the decline. The models largely failed to reproduce the sustained NPP enhancement observed at the Duke experiment. Six of the models have been used to simulate temporal trends in the global C cycle. One in particular, the CLM4 shown in Fig. 1, has a low NPP enhancement with elevated CO2. How, then, do we interpret model simulations of a twenty-first century Earth? The models represent hypotheses of how the Earth system functions and codify an understanding of C cycle–climate coupling, but must always be interpreted in light of uncertainty. Just as the dieback of the Amazon rainforest over the twenty-first century simulated by the Hadley Centre model (Cox et al., 2000) stimulated much research on the sensitivity of tropical rainforests to drought, the importance of CO2 fertilization and C–N biogeochemistry to meet permissible anthropogenic CO2 emissions to limit planetary warming will stimulate much research. What should that research entail? Comparisons with experimental manipulations are necessary, but will not provide all the answers. We should not expect global models, which by necessity are generalizations of richly complex systems, to exactly replicate Ó 2014 The Author New Phytologist Ó 2014 New Phytologist Trust

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site-scale experiments given the complexity of factors operating at each site. It may be more appropriate to evaluate models with comparisons to syntheses that emerge from a meta-analysis of experiments. For example, site-specific N addition experiments with the CLM4 highlight deficiencies in the model’s N cycle and guide model improvements, but are subject to the vagaries of the particular sites (Thomas et al., 2013a). Synthetic global-scale N addition experiments, representing more idealized and generalized responses rather than site-specific responses, equally inform model needs (Thomas et al., 2013b). The advent of models of the Earth system, including its terrestrial ecosystems, has placed plant ecology at the center of climate science. Climate science advances in a systematic framework with successive generations of models evaluated in model inter-comparison projects (so-called MIPs; e.g. Fig. 2a). It is likely that most ESMs will include C–N biogeochemistry for the IPCC sixth assessment report, that more MIPs will be performed in search of greater scientific understanding, and that the frontiers of global terrestrial biosphere modeling, such as phosphorus cycling, microbial models of decomposition, photosynthetic and respiratory temperature acclimation, and crop management, will eventually be included in ESMs. Greater attention must be given to understanding processes, rather than model projections of the future. Model development and evaluation must embrace a synergy of ecological observations, theory to explain the observations, numerical parameterizations to mathematically describe that theory, and ESM simulations to test implications for climate change (Fig. 2b). We still have much to learn about the complexity of terrestrial ecosystems, their interactions in the Earth system, and how to mathematically formulate ecosystem responses to global change. Obtaining these answers challenges ecologists – observationalists, experimentalists, theoreticians, and modelers – and climate scientists to craft a truly interdisciplinary framework to advance planetary ecology. Gordon B. Bonan National Center for Atmospheric Research, Boulder, CO 80307, USA (tel +3034971613; email [email protected])

References Arora VK, Boer GJ, Friedlingstein P, Eby M, Jones CD, Christian JR, Bonan G, Bopp L, Brovkin V, Cadule P et al. 2013. Carbon–concentration and carbon– climate feedbacks in CMIP5 Earth system models. Journal of Climate 26: 5289– 5314. Bonan GB, Lawrence PJ, Oleson KW, Levis S, Jung M, Reichstein M, Lawrence DM, Swenson SC. 2011. Improving canopy processes in the Community Land Model version 4 (CLM4) using global flux fields empirically inferred from FLUXNET data. Journal of Geophysical Research 116: G02014. Cadule P, Friedlingstein P, Bopp L, Sitch S, Jones CD, Ciais P, Piao SL, Peylin P. 2010. Benchmarking coupled climate-carbon models against long-term atmospheric CO2 measurements. Global Biogeochemical Cycles 24: GB2016.

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Cox PM, Betts RA, Jones CD, Spall SA, Totterdell IJ. 2000. Acceleration of global warming due to carbon-cycle feedbacks in a coupled climate model. Nature 408: 184–187. De Kauwe MG, Medlyn BE, Zaehle S, Walker AP, Dietze MC, Hickler T, Jain AK, Luo Y, Parton WJ, Prentice IC et al. 2013. Forest water use and water use efficiency at elevated CO2: a model-data intercomparison at two contrasting temperate forest FACE sites. Global Change Biology 19: 1759–1779. Friedlingstein P, Cox P, Betts R, Bopp L, von Bloh W, Brovkin V, Cadule P, Doney S, Eby M, Fung I et al. 2006. Climate–carbon cycle feedback analysis: results from the C4MIP model intercomparison. Journal of Climate 19: 3337– 3353. Friedlingstein P, Meinshausen M, Arora VK, Jones CD, Anav A, Liddicoat SK, Knutti R. 2014. Uncertainties in CMIP5 climate projections due to carbon cycle feedbacks. Journal of Climate 27: 511–526. Hungate BA, Dukes JS, Shaw MR, Luo Y, Field CB. 2003. Nitrogen and climate change. Science 302: 1512–1513. IPCC. 2013. Stocker TF, Qin D, Plattner G-K, Tignor M, Allen SK, Boschung J, Nauels A, Xia Y, Bex V, Midgley PM, eds. Summary for policymakers. Climate change 2013: the physical science basis. Contribution of Working Group I to the fifth assessment report of the Intergovernmental Panel on Climate Change. Cambridge, UK & New York, NY, USA: Cambridge University Press. Le Quere C, Andres RJ, Boden T, Conway T, Houghton RA, House JI, Marland G, Peters GP, van der Werf G, Ahlstr€om A et al. 2013. The global carbon budget 1959–2011. Earth System Science Data 5: 165–185. Medlyn BE, Duursma RA, Zeppel MJB. 2011. Forest productivity under climate change: a checklist for evaluating model studies. Wiley Interdisciplinary Reviews: Climate Change 2: 332–355. Norby RJ, Warren JM, Iversen CM, Medlyn BE, McMurtrie RE. 2010. CO2 enhancement of forest productivity constrained by limited nitrogen availability. Proceedings of the National Academy of Sciences, USA 107: 19368–19373. Piao S, Sitch S, Ciais P, Friedlingstein P, Peylin P, Wang X, Ahlstr€om A, Anav A, Canadell JG, Cong N et al. 2013. Evaluation of terrestrial carbon cycle models for their response to climate variability and to CO2 trends. Global Change Biology 19: 2117–2132. Reichstein M, Ciais P, Papale D, Valentini R, Running S, Viovy N, Cramer W, Granier A, Ogee J, Allard V et al. 2007. Reduction of ecosystem productivity and respiration during the European summer 2003 climate anomaly: a joint flux tower, remote sensing and modelling analysis. Global Change Biology 13: 634– 651. Sitch S, Huntingford C, Gedney N, Levy PE, Lomas M, Piao SL, Betts R, Ciais P, Cox P, Friedlingstein P et al. 2008. Evaluation of the terrestrial carbon cycle, future plant geography and climate-carbon cycle feedbacks using five Dynamic Global Vegetation Models (DGVMs). Global Change Biology 14: 2015–2039. St€ockli R, Lawrence DM, Niu G-Y, Oleson KW, Thornton PE, Yang Z-L, Bonan GB, Denning AS, Running SW. 2008. Use of FLUXNET in the Community Land Model development. Journal of Geophysical Research 113: G01025. Thomas RQ, Bonan GB, Goodale CL. 2013a. Insights into mechanisms governing forest carbon response to nitrogen deposition: a model–data comparison using observed responses to nitrogen addition. Biogeosciences 10: 3869–3887. Thomas RQ, Zaehle S, Templer PH, Goodale CL. 2013b. Global patterns of nitrogen limitation: confronting two global biogeochemical models with observations. Global Change Biology 19: 2986–2998. Zaehle S, Friedlingstein P, Friend AD. 2010. Terrestrial nitrogen feedbacks may accelerate future climate change. Geophysical Research Letters 37: L01401. Zaehle S, Medlyn BE, De Kauwe MG, Walker AP, Dietze MC, Hickler T, Luo Y, Wang Y-P, El-Masri B, Thornton P et al. 2014. Evaluation of 11 terrestrial carbon–nitrogen cycle models against observations from two temperate Free-Air CO2 Enrichment studies. New Phytologist 202: 803–822. Zhang Q, Wang YP, Pitman AJ, Dai YJ. 2011. Limitations of nitrogen and phosphorous on the terrestrial carbon uptake in the 20th century. Geophysical Research Letters 38: L22701. Key words: carbon cycle, climate change, CO2, Earth system model, stomata, stomatal conductance.

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Connecting mathematical ecosystems, real-world ecosystems, and climate science.

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