Emergent constraints on climate-carbon cycle feedbacks in the CMIP5 Earth system models



An emergent linear relationship between the long-term sensitivity of tropical land carbon storage to climate warming (γLT) and the short-term sensitivity of atmospheric carbon dioxide (CO2) to interannual temperature variability (γIAV) has previously been identified by Cox et al. (2013) across an ensemble of Earth system models (ESMs) participating in the Coupled Climate-Carbon Cycle Model Intercomparison Project (C4MIP). Here we examine whether such a constraint also holds for a new set of eight ESMs participating in Phase 5 of the Coupled Model Intercomparison Project. A wide spread in tropical land carbon storage is found for the quadrupling of atmospheric CO2, which is of the order of 252 ± 112 GtC when carbon-climate feedbacks are enabled. Correspondingly, the spread in γLT is wide (−49 ± 40 GtC/K) and thus remains one of the key uncertainties in climate projections. A tight correlation is found between the long-term sensitivity of tropical land carbon and the short-term sensitivity of atmospheric CO2 (γLT versus γIAV), which enables the projections to be constrained with observations. The observed short-term sensitivity of CO2 (−4.4 ± 0.9 GtC/yr/K) sharpens the range of γLT to −44 ± 14 GtC/K, which overlaps with the probability density function derived from the C4MIP models (−53 ± 17 GtC/K) by Cox et al. (2013), even though the lines relating γLT and γIAV differ in the two cases. Emergent constraints of this type provide a means to focus ESM evaluation against observations on the metrics most relevant to projections of future climate change.

1 Introduction

In most climate-carbon cycle projections, climate warming reduces the efficiency of anthropogenic carbon dioxide (CO2) absorption by the land and ocean [Cox et al., 2000; Friedlingstein et al., 2001, 2006]. As a result, more emitted carbon stays in the atmosphere leading to additional warming, representing a positive climate-carbon cycle feedback [Friedlingstein et al., 2001, 2003].

The long-term sensitivity of land carbon storage to future climate warming (γL) can be quantified in terms of carbon loss per unit temperature change [Friedlingstein et al., 2003], usually given in units of GtC/K. The differences in γL simulated by the models remain a key uncertainty in climate projections of the 21st century [Friedlingstein et al., 2006; Booth et al., 2012]. However, γL cannot be directly evaluated with observations, not only because the observational record is not yet long enough but also because γL relates to a theoretical reference state in the absence of climate change, which is obviously not observable. The tropics make a dominant contribution to uncertainties in γL [Raddatz et al., 2007; Huntingford et al., 2013]. Uncertainties in future projections of tropical rainfall, and in the response of ecosystems to these, are central to the overall uncertainty in the response of the land carbon cycle to climate change [Jupp et al., 2010; Rammig et al., 2010; Huntingford et al., 2013].

In a recent study, Cox et al. [2013] found a correlation between the long-term sensitivity of tropical land carbon storage to climate warming (γLT) and the short-term sensitivity of atmospheric carbon dioxide (CO2) to temperature variability on interannual time scales (γIAV). A correlation between the long-term and the short-term sensitivities can be expected if the processes that play for the long-term response are also driving the short-term fluctuations, i.e., if processes occurring on long time scales (such as vegetation dynamic) are not dominant. This is potentially the case here as both the short- and long-term responses of the tropical land to climate are predominantly driven by changes in the balance between the gross carbon fluxes, photosynthesis, and ecosystem respiration. Responses of the carbon cycle to climate anomalies are mirrored in the interannual variability (IAV) of the CO2 growth rate [Keeling et al., 1989, 1995; Francey et al., 1995]. This relationship is especially valid in the tropics, where strong variability caused by El Niño gives a spatially coherent pattern of warmer and colder years [Bousquet, 2000].

The variability of tropical temperature and atmospheric CO2 concentrations are both observable quantities, and therefore, γIAV can be directly inferred from observations. A strong correlation between γIAV and γLT therefore provides an Emergent Constraint on the long-term sensitivity of land carbon storage to climate change. More generally, emergent constraints are relationships across an ensemble of models, between some aspect of the Earth system sensitivity and an observable trend or variation in the current climate [Flato et al., 2013]. This is a relatively new area of research with some promising examples already studied in the literature, for example, constraints on the snow-albedo feedback [Hall and Qu, 2006; Qu and Hall, 2013], on Antarctic total column ozone projections [Karpechko et al., 2013], on climate sensitivity based on variations in midtropospheric relative humidity and their impact on clouds [Fasullo and Trenberth, 2012], and on the sensitivity of tropical precipitation extremes to climate change [O'Gorman, 2012].

In this study, we begin to develop the theoretical basis for describing the emergent constraint reported by Cox et al. [2013]. We also extend that analysis by considering the more recent ensemble of Phase 5 of the Coupled Model Intercomparison Project (CMIP5) Earth system models (ESMs), including models with an interactive land nitrogen cycle which have the potential to change the correlation between γIAV and γLT. In addition, we use land and ocean net CO2 fluxes from the Global Carbon Project (GCP) to develop the observational constraint on γIAV, rather than the global atmospheric CO2 concentration as in Cox et al. [2013]. This allows the approach to be applied to model runs with prescribed CO2 concentrations and those with interactive atmospheric CO2, and is more directly comparable to the carbon fluxes anomalies simulated in the ESMs. The sensitivity of CO2 to tropical temperature IAV is calculated from two kinds of CMIP5 simulations: historical simulations driven by CO2 emissions and standard simulations with a prescribed 1% per year increase in CO2 concentration. We cross-check our results with models from the previous Coupled Climate-Carbon Cycle Model Intercomparison Project (C4MIP), as used in the study of Cox et al. [2013], but using the new methodology presented here.

This paper is organized as follows: Section 2 describes the models and simulations used in this study. Section 3 provides an overview of the observations that are used to evaluate the models and to constrain the projections. The theoretical basis and the methodology for an emergent constraint are presented in section 4. In section 5, the results are presented and discussed, and section 6 closes with a summary.

Table 1. CMIP5 Models
 ModelInstituteAtmospheric ResolutionOceanic ResolutionMain Reference
ACanESM2Canadian Center for Climate Modeling and Analysis, BC, CanadaT63, L35256 × 192, L40Arora et al. [2011]
BCESM1-BGCNational Center for Atmospheric Research Boulder, CO, USA0.9° × 1.25° gx1v6, L530.9° × 1.25° gx1v6, L53Gent et al. [2011]
CGFDL-ESM2MGeophysical Fluid Dynamics Laboratory, United StatesM54, L24360 × 200, L50Dunne et al. [2012]
DHadGEM-ESMet Office Hadley Center, Exeter, Devon, UKN96, L381.0°–0.3° × 1.0°, L40Collins et al. [2011]
EIPSL-CM5A-RInstitut Pierre Simon Laplace, Paris, France96 × 95, L392 × 2, L31Dufresne et al. [2013]
FMIROC-ESMJapan Agency for Marine-Earth Science and Technology, Japan; Atmosphere and Ocean Research Institute, JapanT63, L80256 × 192, L44Watanabe et al. [2011]
GMPI-ESM-LRMax Planck Institute for Meteorology, Hamburg, GermanyT63, L47GR15, L40Giorgetta et al. [2013]
HNorESM1-MENorwegian Climate Center, Norwayf19, L26gx1v6, L53Iversen et al. [2012]

2 Models and Model Simulations

In this study, we analyze the carbon cycle feedback constraints from eight ESMs participating in the CMIP5 project. CMIP5 supported the climate model projections presented in the Intergovernmental Panel on Climate Change Fifth Assessment Report and includes a large number of different experimental designs [Taylor et al., 2012]. The model data are available to the research community via the Earth System Grid Federation (ESGF). The models that are included in this study are listed in Table 1 together with their atmospheric and oceanic grids, and an appropriate reference.

Table 2. Overview of the Simulation Experiments in This Study
 ExperimentCoupling of Carbon CycleAvailable PeriodTemporal ResolutionForcing
1HistoricalFully coupled1850–2005monthlygreenhouse gases, anthropogenic and volcanic climate forcing, land use change, solar forcing, and aerosols
21%COU2Fully coupled0–140monthly1%/yr CO2 increase
31%BGCuncoupled0–140monthly1%/yr CO2 increase

For this study, model outputs from three simulations were analyzed and are listed in Table 1. The esmHistorical (hereafter referred to as “Historical”) experiment is a fully coupled simulation from 1850 to 2005 with historical anthropogenic emissions of CO2, atmospheric concentrations being calculated interactively by the ESM as the balance between anthropogenic emissions and uptakes by the land and ocean [Taylor et al., 2012]. The 1pctCO2 (hereafter referred to as “1%COU”) simulation is a standard idealized experiment forced with a 1%/yr increase of atmospheric CO2 concentration up to 4 × CO2, starting from the preindustrial value for 1850 of ~285 ppmv. The third simulation also considers a 1%/yr increase of CO2, but in which the carbon cycle is not affected by any climate change (esmFixClim1, hereafter referred to as “1%BGC”, the biogeochemically coupled simulation). In this latter simulation (termed as the “uncoupled run” by Friedlingstein et al. [2003, 2006]), the radiation code of the ESM sees the control preindustrial CO2 concentration (so that there is no associated climate change), but the carbon cycle otherwise sees a 1%/yr increase in atmospheric CO2. As opposed to the Historical simulation that account for all known forcings (greenhouse gases, aerosols, land use change, and volcanoes), the two 1%/yr simulations are only forced with the CO2 increase; all other forcings are held at their preindustrial levels.

From the CMIP5 models that were available on the ESGF by summer 2013, we selected those that provide both land and ocean carbon fluxes and storage for all three experiments. For details of these models, see Table 1. Table 3 lists details of the land and ocean carbon representation for each model. For comparison, we also analyzed six models from the Coupled Climate-Carbon Cycle Model Intercomparison Project (C4MIP) [Friedlingstein et al., 2006]. For C4MIP, the coupled and uncoupled simulations were forced by anthropogenic CO2 emissions for the historical period, followed by anthropogenic emissions from the Special Report on Emissions Scenarios A2 scenario [Nakicenovic et al., 2000].

Table 3. Overview of Land and Ocean Carbon Modules in CMIP5 Model
 ModelLand ModelsReferences for Land ModelOcean ModelsReferences for Ocean Models
ACanESM2CLASS2.7 and CTEM1Verseghy et al. [1993] and Arora et al. [2011]CMOCZahariev et al. [2008]
BCESM1-BGCCLM4Lawrence et al. [2011]BEC 
CGFDL-ESM2MLM3Dunne et al. [2012]MOM4Griffies et al. [2004]
DHadGEM-ESJULES and TRIFFIDCox [2001] and Clark et al. [2011]Diat-HadOCCCollins et al. [2011]
EIPSL-CM5A-RORCHIDEEKrinner [2005]PISCESAumont [2003]
FMIROC-ESMMATSIRO and SEIB-DGVMSato et al. [2007]COCOWatanabe et al. [2011]
GMPI-ESM-LRJSBACHKnorr [2000]HAMOCC5Assmann et al. [2010]
HNorESM1-MECLM4Lawrence et al. [2011]HAMOCC5Assmann et al. [2010]

3 Observations for Model Evaluation

To calculate the observational estimate of γIAV, we used land and ocean carbon fluxes from the Global Carbon Project (GCP, http://www.tyndall.ac.uk/global-carbon-budget-2010). For each year since 1959, GCP provides a global CO2 budget, reporting the fossil fuel and the land use change emission data, the observed atmospheric CO2 growth rate, an estimate of the ocean carbon uptake from four ocean biogeochemical models constrained by observed oceanic uptake data, and the land carbon uptake as the residual of atmospheric CO2 and ocean carbon fluxes [Le Quéré et al., 2013].

Annual mean temperatures from the NOAA–National Climate Data Center (NCDC, http://www.esrl.noaa.gov/psd/data/gridded/data.noaamergedtemp.html) were used to estimate the interannual variability in the tropics (30°S–30°N). This data set covers the period from 1880 to the present day at a monthly resolution [Smith et al., 2008].

4 Theoretical Basis and Methodology

4.1 Theoretical Basis for the Emergent Constraint

The change of land carbon over time, math formula, can be defined as the net carbon flux from land to atmosphere (Net Biome Productivity—NBP) that depends on the temperature (T), the atmospheric CO2 concentration (Ca), and the stored carbon on land (CL):

display math(1)

As in previous studies [Friedlingstein et al., 2003, 2006], we have implicitly assumed here that the impacts of other environmental changes, such as changes in rainfall, scale approximately linearly with the magnitude of the warming. This assumption is broadly consistent with the success of pattern scaling [Huntingford and Cox, 2000]. Linearizing equation (1) by Taylor expanding about an initial equilibrium state leads to the following:

display math(2)

where a, b, and c denote math formula and ΔCL, ΔCa  and ΔT  are changes relative to the initial state in land carbon uptake, CO2, and temperature, respectively. Rewriting equation (2) and defining the constants a, b, and c for consistency with Friedlingstein et al. [2006] gives the following:

display math(3)


display math(4.1)
display math(4.2)
display math(4.3)

Equation (3) is as proposed by Friedlingstein et al. [2003, 2006], except for the first term on the left-hand side. It is, however, vital to include this “inertial” term as it enables us to relate short-term variability to long-term sensitivity. To show this, we consider the following two limits:

  1. On long (centennial) time scales, the interannual variability in the carbon cycle is much smaller than the long-term changes which means that math formula and the first term in equation (3) is negligible. The resulting equation is the one published by Friedlingstein et al. [2003, 2006] and describes the long-term change of land carbon uptake depending on the change in temperature and atmospheric CO2:
    display math(5)
    From equation (5), γL, or its regional equivalents such as γLT  for the tropics, can be calculated as in previous studies [Friedlingstein et al., 2003, 2006].
  2. On short (interannual) time scales, changes in the long-term trend will be close to zero (ΔCL ~ 0, ΔCa = 0) and the second term in equation (3) is now negligible. This limit gives a relationship between the long-term sensitivity of land carbon storage to climate change γL  and the short-term sensitivity of the net atmosphere to land carbon flux to interannual temperature variations, math formula:
    display math(6)
    Here as elsewhere in this paper, the subscript “L” represents “Land” and the subscript “NBP” denotes the “Net Biome Productivity”. Equation (6) is in the spirit of the Fluctuation-Dissipation Theorem [Leith, 1975; Bell, 1980] as it is a relationship between the equilibrium sensitivity of the system to external forcing, and the fluctuations in the unperturbed system.

However, equation (6) does not in itself imply an observational constraint on γL, for two reasons. First, in general, the NBP of a region is poorly known so that γNBP is not well constrained by observations. Second, the time scale τ  is not known a priori. We follow Cox et al. [2013] to overcome these problems. By focusing specifically on tropical land (30°N–30°S), it is possible to get an estimate of γNBP based on the interannual variability in atmospheric CO2, making use of the strong evidence that interannual variability in CO2 is dominated by interannual variability in the NBP of tropical land [Denman et al., 2007; Schneising et al., 2014]. This implies assuming math formula, where here ΔCO2 is the interannual variability in CO2, and ΔT is the interannual variability in temperature. Under this assumption, equation (6) becomes

display math(7)

where the subscript “LT” now applies specifically to land in the tropics. Given an estimate of τ, equation (7) provides a constraint on the long-term sensitivity from the observable  γIAV .

The outstanding issue is therefore the estimation of τ, which is the subject of ongoing research. The Fluctuation-Dissipation Theorem (FDT) indicates that  τ could in principle be derived from the correlogram relating fluctuations in tropical temperature to fluctuations in atmospheric CO2, by integrating across all lag periods between these two variables [Bell, 1980]. Unfortunately, the time series data available from observations are invariably too short for this pure FDT approach to provide a useful constraint [Kirk-Davidoff, 2009].

As an alternative, we could assume that tropical land carbon behaves approximately like a one-box store with a single turnover time. In this case,  τ  becomes the carbon turnover time, defined as the size of the store (i.e., the total vegetation plus soil carbon in the tropics) divided by the annual flux of carbon flowing through that store (i.e., the Net Primary Productivity in the tropics). Previous studies have shown that the turnover times for land carbon differ substantially across ESMs [Anav et al., 2013], and we would therefore not expect a plot of γLT against γIAV  to fit around a single straight line in the way that Cox et al. [2013] describe for the C4MIP models.

In fact, equation (7) implies that the linear relationship between γLT and γIAV  reported by Cox et al. [2013] in turn implies a near constant value of τ across the model ensemble. As the turnover time for tropical land carbon also differs for the C4MIP models (although to a lesser degree than for the CMIP5 models), this strongly suggests that the τ value relating γLT to γIAV  is not determined by the turnover rates of tropical land carbon, but instead by a time scale that is common to all of the C4MIP model runs.

We suggest that the most likely candidate for such a time scale is related to the rate of climate change, which is largely determined by the common scenario of increases in CO2 emissions prescribed in all of the C4MIP models [Friedlingstein et al., 2006]. Similarly, the CMIP5 simulations analyzed in this paper experience a common time scale associated with the prescribed 1% per year increase in atmospheric CO2, which differs slightly from the scenario time scale of the C4MIP models.

Our working hypothesis is therefore that the CMIP5 models will also fit around a straight line in the γLT and γIAV  space, but that this straight line may have a different gradient to that for the C4MIP models, owing to the different scenarios prescribed in each of these intercomparison exercises. The analysis presented in the remainder of this paper allows this hypothesis to be tested and most importantly assesses whether the emergent constraint on γLT as reported by Cox et al. [2013] is robust to changes in the ESM model generation and the prescribed climate change scenario.

4.2 Methodology

As in Friedlingstein et al. [2003, 2006], we apply equation (5) separately to the tropical land carbon in the coupled and uncoupled simulations:

display math(8.1)
display math(8.2)

where ΔTT is the change in the average tropical near-surface temperature (over land and ocean between 30°N and 30°S), and the superscripts “c” and “u” denote the coupled and uncoupled simulations, respectively.

In contrast to Cox et al. [2013], we use the coupled (1%COU) and uncoupled (1%BGC) 1%/yr simulations to estimate ΔCL. As the CO2 concentration is prescribed to be identical in the coupled and uncoupled runs, math formula equals math formula. In addition, we follow Friedlingstein et al. [2003, 2006] in assuming math formula. Although there may be small temperature changes in the uncoupled simulations, for example, due to CO2-induced changes in the distribution of vegetation, these are negligible compared to the temperature changes in the coupled simulations (1% to less than 5% depending on the ESM). Under these assumptions, the equations for the coupled and uncoupled changes can be subtracted to yield an expression for γLT which depends on the difference between the tropical land carbon storage of the coupled (1%COU) and uncoupled (1%BGC) simulations, and the temperature change in the coupled simulation

display math(9)

The changes in these variables are computed for the tropical band (30°N–30°S) as the difference between year 110 and year 30 after the start of the simulation at 1850 CO2 concentration levels.

In order to calculate the short-term fluctuation, land and ocean CO2 annual fluxes and tropical annual mean temperature from the models and the observations are detrended using an 11 year running mean, as in Cox et al. [2013]. The gradient of the least squares linear regression between anomalies in the CO2 growth rate and the tropical temperature defines γIAV. An advantage of calculating γIAV from the annual mean land and ocean CO2 fluxes is that the tropical temperature does not have to be aligned to the annual increment in CO2 [Jones and Cox, 2005; Cox et al., 2013], as both are already centered in time in the middle of each year.

To assess robustness, γIAV is calculated from both the Historical and the 1%COU simulation. For the Historical simulation, we exclude data for 2 years following large volcanic eruptions (Mount Agung, 1963; El Chichon, 1982; and Mount Pinatubo, 1991), as Cox et al. [2013], and calculate γIAV over the period 1960 to 2005 in both models and observations. In the 1%COU simulation, a reference period from 40 to 90 years after the start of the simulation in 1850 is chosen, thus representing a warmer climate than today. We have tested the robustness of this choice by calculating γIAV (and γLT above) also for different periods, which yielded very similar results (not shown).

5 Results

5.1 Climate-Carbon Cycle Feedback Constraints in CMIP5 Models

In both experiments with prescribed CO2 (i.e., 1%COU and 1%BGC), all models were forced by 1% increase of CO2 until quadrupling, except the GFDL-ESM2M model simulation, which stopped increasing CO2 at the time of CO2 doubling (year 80) and kept the CO2 concentration thereafter. The results for GFDL-ESM2M are therefore not comparable to the other models after year 80. The simulated tropical temperature change in the CO2 prescribed coupled simulations (1%COU) shows significant differences among the models at the time of CO2 quadrupling (year 140 in Figure 1c), ranging from around 3 to 5 K (excluding GFDL-ESM2M). CESM1-BGC and NorESM1-ME show a slower increase in tropical temperature than the other five models.

Figure 1.

Quantities used to diagnose γLT. Cumulative tropical land carbon uptake for (a) the coupled simulation, (b) the uncoupled simulation, and (c) the projected tropical (30°N–30°S) mean near-surface air temperature (tas) change in the prescribed CO2 coupled simulation (1%COU), for the CMIP5 models listed in Table 1. The simulations are forced by 1%/yr rise in CO2 until quadrupling, except in the GDFL-ESM2M model, which prescribed a constant CO2 after doubling. Vertical red lines show the interval over which γLT was calculated.

There is also a wide spread in the tropical land carbon storage among the CMIP5 models (Figure 1), which is of the order of 117–381 GtC for the coupled (1%COU, Figure 1a) and 182–788 GtC for the uncoupled (1%BGC, Figure 1b) simulations. Due to holding CO2 at 2 × CO2 after the time of concentration doubling (year 80), the evolution of tropical land carbon storage of GFDL-ESM2M flattens in both simulations after atmospheric CO2 stabilization.

From the difference of coupled and uncoupled simulations, the climate-carbon cycle sensitivity γLT can be quantified in terms of carbon loss per unit temperature increase. γLT values for each model are listed in Table 4. Confirming the findings of previous studies [Cox et al., 2000; Friedlingstein et al., 2001, 2006; Arora et al., 2013], all models show a negative γLT. However, there is a wide range of results in γLT, ranging from −6.7 GtC/K in CESM1-BGC to −116.4 GtC/K in GFDL-ESM2M.

Table 4. Overview of the Derived Sensitivities γLT and γIAV, Listed for Each Model
 ModelγLT (GtC/K) bγIAV Historical (GtC/yr/K) a, cγIAV 1%COU (GtC/yr/K) c
  1. a

    The uncertainty is given as the standard deviation.

  2. b

    Calculated from equation (9), as the difference of cumulated land carbon flux between the coupled (1%COU) and uncoupled (1%BGC) simulation.

  3. c

    Correlation between the global CO2 IAV from land plus ocean carbon fluxes and tropical (30°N–30°S) temperature IAV.

ACanESM2−74.3−7.4 ± 1.1−16.2 ± 1.2
BCESM1-BGC−6.70.2 ± 1.1−3.5 ± 0.8
CGFDL-ESM2M−116.4−12 ± 1.6−13.1 ± 2.1
DHadGEM-ES−60.2−5.9 ± 0.7−7.9 ± 1.5
EIPSL-CM5A-LR−22.9−3.7 ± 1−6.6 ± 1.6
FMIROC-ESM−58.4−6.9 ± 1.7−10.7 ± 1.4
GMPI-ESM-LR−78.3−0.5 ± 0.9−6.9 ± 0.6
HNorESM1-ME−7.2−0.8 ± 0.9−2.9 ± 0.7
IOBS-−4.4 ± 0.9-

It is interesting to note that CESM1-BGC and NorESM1-ME simulate the weakest climate change impact on tropical land carbon storage. The CLM4 land surface model, used in both of these ESMs (Table 3), includes an interactive nitrogen cycle. Therefore, in these models, warming not only leads to carbon loss from enhanced soil decomposition but also a counteracting carbon gain due to enhanced photosynthesis associated with increased soil nitrogen availability. The overall effect depends on the balance between these two effects but is always lower (less negative γLT) than in carbon-only models [Thornton et al., 2007, 2009; Zaehle et al., 2010].

The γIAV is calculated over the period 1960–2005 for the historical simulations (Figures 2a, 2c, 2e, and 3) for consistency with the CO2 observational data that we used, and over the period year 40 to year 90 from the 1%COU simulations (Figures 2b, 2d, 2f, and 4). The variability of both carbon fluxes and tropical temperature is found to vary widely across the ESMs (range in Figures 2-4), as does the strength of the correlation between CO2 IAV and temperature IAV (linear regression in Figures 3 and 4). The γIAV varies from zero (nonsignificant) for CESM1-BGC to −12 GtC/yr/K for GFDL-ESM2M, with a multimodel average of −4.6 GtC/yr/K.

Figure 2.

Quantities used to diagnose γIAV, each displayed in the applied period. Anomalies of the (a and b) global land carbon flux, (c and d) global ocean carbon flux, and (e and f) tropical near-surface temperature calculated from the Historical simulation in Figures 2a, 2c, and 2e and from the 1%COU simulation in Figures 2b, 2d, and 2f, for CMIP5 models listed in Table 1.

Figure 3.

(a–i) Correlation between the IAV of the sum of the global land and ocean CO2 fluxes and tropical temperature from Historical, shown for each model and the observations. Numbers indicate single years and colored lines are the best fit linear regression excluding the years after volcanic eruptions.

Figure 4.

As for Figure 3, but using 1%COU simulations. Note that there is no observation panel here.

The observed γIAV, derived from the sum of the GCP land and ocean fluxes versus the IAV of tropical (30°S–30°N) temperature from NCDC data, yields a γIAV of −4.4 ± 0.9 GtC/yr/K with a correlation coefficient of r = −0.60 (Figure 3i). This compares with the value quoted by Cox et al. [2013] of 5.1 ± 0.9 GtC/yr/K, using a different method based on annual mean CO2 concentrations rather than fluxes, and for a slightly longer period (1960–2010). GFDL-ESM2M and CanESM2 have the highest values of γIAV of −12 GtC/yr/K and −7.4 GtC/yr/K, respectively (Figures 3a and 3c). CESM1-BGC and NorESM1-ME show the smallest γIAV, 0.2 GtC/yr/K and −0.8 GtC/yr/K (Figures 3b and 3h), which is much lower than the observations. These two models also show weak correlation between CO2 IAV and temperature IAV (r = 0.03 and r = −0.14, respectively).

Plotting γLT against γIAV reveals the emergent constraint identified by Cox et al. [2013], and we do this for both the Historical simulations and the 1%COU simulations (Figure 5) to test for robustness. In both cases, there is evidence of a linear relationship between γLT and γIAV, which holds for all the models apart from MPI-ESM-LR. This model shows a surprising net negative correlation between variations in soil respiration and temperature, most likely due to a strong suppression of soil respiration under reducing soil moisture, which overwhelms the usual increase in soil respiration with warming [Ciais et al., 2005; Reichstein et al., 2007; Zaehle et al., 2010]. As a result, MPI-ESM-LR has unusually high soil carbon in dry regions, which is vulnerable to climate change (Figure 5a). It therefore seems that MPI-ESM-LR does not fit on the γIAV γLT correlation line (Figure 5a) as its short-term response is driven by different processes (the suppression of heterotrophic respiration by soil aridity) than the long-term response (decline in net primary productivity and hence in carbon storage). We have excluded MPI-ESM-LR when calculating the best fit linear regression.

Figure 5.

(a) The long-term sensitivity of tropical land carbon storage to climate warming (γLT) versus the short-term sensitivity of atmospheric CO2 to interannual temperature variability (γIAV) for the CMIP5 and C4MIP models. The red line shows the best fit line across the CMIP5 models using the Historical simulation. The vertical dashed lines show the range of the observed γIAV according to Figure 3. (b) PDF for γLT. The solid line was derived after applying the IAV constraint to the models while the dashed line is the prior PDF derived purely from the models, before applying the IAV constraint. Red lines show PDFs for CMIP5 models and black lines and symbols are for C4MIP models. (c and d) Same as Figures 5a and 5b but with γIAV calculated from the 1%COU simulations.

Interestingly, although both CESM1-BGC and NorESM1-ME include nitrogen limitations [Lawrence et al., 2011], these two models appear to fit the same line as the carbon-only models. This suggests that the inclusion of the nitrogen cycle does not change the relationship between the short- and long-term responses of tropical land carbon to climate, even though these models yield much lower values of γIAV and γLT.

In the Historical experiment, the models can be constrained by the calculated observational estimate of γIAV  = −4.4 ± 0.9 GtC/yr/K. Without the observational constraint, all models would be equally likely to give the true γLT in both experiments, which is shown as the dashed red lines in Figures 5b and 5d as a probability density function (PDF, calculated following Cox et al. [2013]). Using the observed γIAV as constraint, a conditional PDF can be calculated. This is achieved by integrating over a contour PDF, which follows from multiplying the PDF of the observations and the PDF of the regression line. This conditional PDF gives a sharper peak with slightly less negative values and a much tighter range on the γLT. The conditional PDF gives γLT = −44 ± −14 GtC/K, whereas the unconditional PDF gives γLT = −49 ± 40 GtC/K for the CMIP5 models in the Historical experiment (Figure 5b).

5.2 Comparison With C4MIP Models

To test for robustness, we compare our results to the findings of Cox et al. [2013] who derived a similar constraint from C4MIP models (Figure 5a, black symbols). The correlation between γLT and γIAV across the C4MIP (r = 0.98) models is as tight as for the CMIP5 models but the slope is slightly different. Most importantly, the best fit linear regression lines intercept close to the observational range and therefore give a similar emergent constraint on γLT. The calculated conditional PDF gives −53 ± −17 GtC/K for the C4MIP models as compared to −44 ± −14 GtC/K for the CMIP5 ESMs.

6 Summary

An observation-based emergent constraint for the long-term sensitivity of land carbon storage to future climate warming (γLT) has been derived from an ensemble of eight Earth system models (ESMs) participating in the Fifth Phase of the Coupled Model Intercomparison Project (CMIP5). The γLT cannot be directly derived from observations, yet it remains a key uncertainty in climate projections of the 21st century. A previous study by Cox et al. [2013] based on models participating in the Coupled Climate-Carbon Cycle Model Intercomparison Project (C4MIP) has already shown that the long-term climate sensitivity γLT is highly correlated with the short-term sensitivity of atmospheric carbon dioxide (CO2) to temperature variability (γIAV).

In this paper, a mathematical formulation for the emergent constraint between γLT and γIAV has been developed, which shows that the long- and short-term sensitivities are approximately related to each other through a time scale τ.

To test whether the emergent constraint holds in an ensemble different than C4MIP, a subset of eight ESMs was selected from the larger CMIP5 ensemble because the necessary output (surface downward CO2 flux, carbon mass flux out of the atmosphere due to net biosphere production on land, and near-surface air temperature) was provided from two simulations with fully coupled carbon cycle (Historical and 1%COU) and one where the carbon cycles was insensitive to climate change (1%BGC). The first experiment is a historical simulation where the carbon cycle is fully coupled and CO2 emissions calculated interactively (Historical). In the second simulation, CO2 is prescribed with a 1%/yr increase until quadrupling, starting at a preindustrial value of ~285 ppmv (1%COU), except in one model (GFDL-ESM2M) where the forcing stabilized at a doubling of CO2.

A tight correlation across the CMIP5 models between the sensitivity of land carbon storage to warming (γLT) and the short-term sensitivity of atmospheric CO2 to tropical temperature variability (γIAV) is found. The only obvious divergence from the relationship is the MPI-ESM-LR model, which shows a unique positive correlation between anomalies in temperature and soil respiration, which seems at odds with observations. This model was therefore excluded from our linear regression. The two ESMs with an interactive nitrogen cycle (NorESM1-ME and CESM-BGC) produce the lowest values of γLT  along with unrealistically low values of γIAV, but still broadly fit the best fit emergent relationship.

Overall, a linear correlation between γLT and γIAV is derived from both the Historical and the 1%COU CMIP5 model ensemble, thus confirming previous results found for the C4MIP ensemble [Cox et al., 2013]. However, this straight line in the γLT and γIAV  space has a different gradient in all three ensembles, owing to the different scenarios prescribed in each of these intercomparison exercises. The time scale τ in the theoretical framework for the emergent constraint is therefore most likely related to the rate of climate change, which is largely determined by the particular scenario imposed for each of the ensembles.

Constraining both ensembles with observations results long-term sensitivities, γLT, that are very similar (CMIP5: −44 ± 14 GtC/K and C4MIP: −53 ± 17 GtC/K). It therefore seems that this emergent constraint is robust to changes in the model ensemble, to the experimental design (i.e., whether the CO2 concentration is prescribed or interactive), and to the scenario prescribed.

Emergent constraints of this type, between observable aspect of variability and long-term Earth System Sensitivities, offer a very promising approach to reduce the uncertainties in climate change projections. We hope that this paper will act as some stimulus for others to search for emergent constraints among the growing ensemble of complex ESMs that are now becoming available for analysis.


This work was funded by the European Commission's Seventh Framework Programme, under grant agreement 282672, the “Earth system Model Bias Reduction and assessing Abrupt Climate change (EMBRACE)” project, and the DLR “Earth System Model Validation (ESMVal)” project. We acknowledge the World Climate Research Program's (WCRP) Working Group on Coupled Modeling (WGCM), which is responsible for CMIP, and we thank the climate modeling groups for producing and making available their model output. For CMIP, the U.S. Department of Energy's Program for Climate Model Diagnosis and Intercomparison provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We thank ETH Zurich for help in accessing data from the ESGF archive. Thanks also to Chris Jones and Colin Prentice for their helpful reviews, and Eddy Robertson and Mattia Righi for constructive discussions and comments.