Quantifying the sources of spread in climate change experiments



[1] Energy-balance models (EBM) constitute a useful framework for summarizing the first-order physical properties driving the magnitude of the global mean surface air temperature response to an externally imposed radiative perturbation. Here the contributions of these properties to the spread of the temperature responses of an ensemble of coupled Atmosphere-ocean General Circulation Models (AOGCM) of the fifth phase of the Coupled Model Intercomparison Project (CMIP5) are evaluated within the framework of a state-of-the-art EBM. These partial contributions are quantified (in equilibrium and transient conditions) using the analysis of variance method. The radiative properties, particularly the strength of the radiative feedback to the global equilibrium surface warming, appear to constitute the most primary source of the spread. Moreover, the adjusted radiative forcing is found to play an important role in the spread of the transient response.

1. Introduction

[2] The equilibrium climate sensitivity ECS (the equilibrium mean surface air temperature response to a doubling of carbon dioxide concentration) and the transient climate response TCR (the temperature response at the time of 2 × CO2 in a 1% yr−1 CO2 increase experiment) are two metrics commonly used in climate model analysis and climate change study. The spread in their AOGCM estimates remains large from one phase of the CMIP project to another [Meehl et al., 2007]. The identification of the key mechanisms responsible for this spread and the quantification of their contributions constitute a necessary step in the improvement of climate change understanding and modeling.

[3] For a given externally imposed radiative perturbation, the first-order transient surface temperature response is driven by two main properties of the climate system: the strength of the radiative response and the ocean thermal inertia [Dickinson, 1981; Hansen et al., 1984; Wigley and Schlesinger, 1985; Knutti and Hegerl, 2008]. Previous studies, based on individual model or multimodel analysis, attempted to estimate the role of these properties in the spread of AOGCMs responses. Multimodel studies have shown that the strength of the radiative feedback due to the cloud component constitutes the primary source of differences in the equilibrium temperature response [Soden and Held, 2006; Dufresne and Bony, 2008]. However, Crook et al. [2011] suggest that the spread associated with the cloud feedback may have been overestimated due to methodological deficiencies. By decomposing the transient temperature response into the sum of contributions due to the Planck response, the forcing magnitude, the radiative feedbacks and the ocean heat uptake, Dufresne and Bony [2008] concluded that the main contributor to the spread in the TCR is the cloud feedback and that the ocean heat uptake constitutes a secondary source of spread. Such conclusion is supported by individual model studies suggesting that the atmosphere component is the major source of differences of transient responses [e.g., Williams et al., 2001; Meehl et al., 2004; Collins et al., 2007].

[4] However, by analyzing the inter-model correlation between the transient surface temperature response, the ECS and the mixing layer depth at high latitudes,Boé et al. [2009]suggested that the role of the deep-ocean heat uptake has been underestimated. The source of the spread of the transient responses is thus a topic of debate. Moreover, these studies are limited in two ways. First, they do not provide a quantitative estimate of the magnitude of the different contributions to the spread. Secondly, some key processes that can contribute significantly to the spread are not taken into account, mainly the tropospheric adjustment of the radiative forcing [Gregory and Webb, 2008; Colman and McAvaney, 2011; Crook et al., 2011] and the possible change in the global feedback strength during the transition due to the impact of the deep-ocean heat uptake on the spatial structure of the surface temperature pattern [Winton et al., 2010; Geoffroy et al., 2012b, hereinafter G12b].

[5] To overcome these two main limitations, the use of a state-of-the-art energy-balance framework and a suitable statistical method are combined in order to investigate the different contributions of each climate system parameter/property to the spread in the responses of a given set of AOGCMs. After a presentation of the EBM framework (Section 2), the statistical method is described (Section 3). This method is applied to 16 CMIP5 AOGCMs and results are presented and discussed in Section 4.

2. Two-Layer EBM Framework

[6] The two-layer energy-balance model with an efficacy factor of deep-ocean heat uptake (hereafter EBM-ε) predicts the time-evolution of the mean surface air temperature responseTand the deep-ocean temperature responseT0 to an external radiative perturbation according to the following system of equations [Held et al., 2010; G12b]:

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In this framework, the climate system is described by 3 radiative parameters, the forcing reference amplitude (such as inline image), the equilibrium feedback parameter λand the efficacy factor of deep-ocean heat uptakeε, and 3 thermal-inertia parameters, the first-layer (atmosphere/land/upper-ocean) heat capacityC, the second-layer (deep-ocean) heat capacityC0 and the heat exchange coefficient between the two layers γ.

[7] Geoffroy et al. [2012a, hereinafter G12a] and G12bpropose a calibration method to derive these 6 thermal parameters from an AOGCM step-forcing experiment. They show that this simple model represents fairly the transient response of a given AOGCM to a gradual increase of CO2. The use of the EBM-εframework has several advantages. First, all parameters are adjusted consistently within a single framework. Then the inclusion of the efficacy factor of deep-ocean heat uptakeε allows a refined representation of the radiative imbalance evolution likely resulting in a better estimation of the parameters driving the transient climate change. Thus one can assume that the set of thermal parameters derived by this method can be used to quantify the contribution to the spread of the transient temperature responses simulated by a set of AOGCMs.

[8] In the following of this section, a “process-oriented” decomposition of the transient surface temperature response is proposed. This decomposition allows to quantify the contributions of each process to the magnitude of the response and provides an insight of the different mechanisms responsible for the spread ofT(t). As shown in G12b, the surface temperature response can be decomposed as the sum of three contributions: T(t) = Teq(t) + TD(t) + TU(t). The first term is the instantaneous equilibrium temperature Teq(t) =  inline image(t)/λ. The remaining contribution TU + TD is the temperature perturbation associated with the climate system heat uptake TH [Winton et al., 2010; G12a, G12b] where TU and TDare the temperature perturbations associated respectively with the upper- and the deep-ocean heat uptake (G12b). More precisely, TD can be decomposed as the sum of two contributions, inline image representing the flux to deep ocean and inline imagerepresenting the impact of the deep-ocean heat uptake on the radiative imbalance due to the modification of the temperature pattern. The four terms involved in this decomposition allows to distinguish the thermal fluxes at play in the energy balance when associated with the scale factorλ. The sum inline image represents the instantaneous rate of heat storage of the climate system, −λTHλbeing the top-of-the-atmosphere radiation imbalance. The contributionTDd is a deviation from Teqdue to the effect of the deep-ocean heat uptake on the strength of the radiative feedbacks during the transition. The sumTeq + TDd can be viewed as an apparent instantaneous equilibrium surface temperature during the transition.

[9] For the 16 CMIP5 AOGCMs studied in G12b, Figure 1a shows the scatterplot of the temperature response emulated by the EBM (calibrated with the abrupt 4 × CO2 experiment only) and the real AOGCM response at the time of 2 × CO2 (i.e. the TCR) and 4 × CO2 of the 1% yr−1 CO2 increase experiment. The multimodel mean of the AOGCMs response in the 1% yr−1 CO2 increase experiment until 2 × CO2 and that of the EBM is plotted in Figure 1b. For each AOGCM individually and on average, the difference between the response of the EBM and the real response is small supporting that the EBM framework is suitable for the present study. Note that the bias decreases during the second half of the simulations (period 70–140 yr from 2 × CO2 to 4 × CO2).

Figure 1.

(a) Scatterplot between the temperature response of the EBM and the real AOGCM response in the 1% yr−1 CO2 experiment at the time of 2 × CO2 (noted TCR, red triangles) and at the time of 4 × CO2(noted TCR4, blue circles). The TCR is calculated as the average of 7 years centered over the 70th year and the TCR4 as the average of the last 5 years of the experiment for both the AOGCM and the EBM. (b) Time-evolution of the multimodel mean of the surface temperature response (thin black) of the 1% yr−1 CO2 increase experiment until the time of 2 × CO2 (70 yr), of the EBM surface temperature response (thick black) and its decomposition in Teq(t) (red), TU (green), TDλ (purple) and TDd(blue). The vertical bars at right indicate the ±1 inter-model standard deviation for each EBM variable at the time of 2 × CO2.

[10] Figure 1b also represents the decomposition of the multimodel mean surface temperature response in Teq, TU, TDλ, and TDd. The mean TCR and the mean ECS are respectively of the order of 2 K and 3.5 K. The inter-model standard deviation of the ECS (about 1 K) is larger than the standard deviation of the TCR (about 0.4 K) because the ocean heat uptake reduces the spread [Raper et al., 2002]. This results from the dependency between Teq and the negative contribution TH. In particular, both are scaled by a factor 1/λ. The term THis dominated by the deep-ocean heat uptake temperature representing the flux to deep oceanTDλ, with an ensemble mean amplitude of −1 K. The mean amplitude of TDd is as large as the mean amplitude of TUwith a value of about −0.3 K but is associated with a larger spread, suggesting a non negligible role of the efficacy factor of deep-ocean heat uptake to the spread.

[11] The decomposition of the transient surface temperature response presented here is different from the one of Dufresne and Bony [2008]. Their decomposition is expressed with respect to the Planck feedback parameter λP rather than the total feedback parameter λ, which gives within the framework of a zero-layer EBM:

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where λi is the feedback parameter associated with the feedback i and κ the ocean heat uptake efficiency. Assuming that λP is model independent, the spread of each term is then associated with one parameter only but depends also on T (i.e. on all parameters). Hence the contribution of each single parameter to the variance of T can not be quantitatively assessed based on this equation. A quantification of the contribution of each physical parameter to the spread of the temperature responses may be derived based on the statistical method described in the next section.

3. Statistical Method

[12] The contribution of each thermal property to the spread of the multimodel global surface warming in the 1% yr−1 CO2 experiment is investigated via a multifactor analysis of variance (ANOVA) [e.g., Christensen, 1996, p. 331]. The parameters driving a transient climate change are assumed to be the 6 parameters of the EBM-ε. The transient temperature response Tis a time-dependent function of these 6 parameters:

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The function fis assumed to be the analytical solution of the EBM-ε described in G12b. For each of the 16 AOGCMs used in this study, the calibrated values of the 6 parameters are summarized in Tables 1 and 2 of G12b.

[13] In order to estimate the contribution of each parameter to the spread of T, we need to allow each parameter to vary individually. For this purpose, an ensemble of N0 = 166 values of the temperature response {Ti,j,k,l,m,n} is computed at each time step by considering all possible combinations of the AOGCM parameters:

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where the subscript i denotes that the forcing parameter value is the one of the ith AOGCM and similarly for j, k, l, m, n. Following the analysis of variance method, Tis decomposed in the sum of one-variable functions:

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where Iis an interaction term (including first-order interactions, second-order, etc.). This decomposition is exact butI is potentially significant. The best approximation of T over the set of values considered is then obtained by computing, from the {Ti,j,k,l,m,n}, the mean value inline image, the function inline image such that:

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and similarly, the functions inline image to inline image, where N1, …, N6 denotes respectively the number of values taken by the parameters inline image, …, γ (in our case, N1 = … = N6 = 16). The interaction term I can then be estimated as a residual from equation (6).

[14] The variance Var(T) of the ensemble {Ti,j,k,l,m,n} can be decomposed as the following:

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where inline image denotes the estimated contribution of the parameter x to the variance of {Ti,j,k,l,m,n}:

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Note that the term inline image is somewhat more complicated and not explicitly written here [see, e.g., Christensen, 1996]. In the case of two models, the present method is equivalent to the factorial method [Montgomery, 2005] used by Teller and Levin [2008] to evaluate the relative contributions of thermodynamic conditions and microphysical characteristics to variations in precipitation.

[15] Such an ANOVA method does not require the parameters to be independent to assess their individual contribution to the variance. If independence does not occur, however, the interpretation of the results is somewhat more complicated. In particular, the total variance Var(T) that is decomposed in the ANOVA method may not be equal to the multimodel sample variance of the temperature response σT2. Note also that one alternative could be to consider groups of (dependent) parameters. If this option is chosen, however, the question addressed is not the same, as one assesses the contribution of “groups of parameters” to the variance, which is different to the contribution of “individual parameters” to the variance. This phenomenon are not really problematic here, as clear dependences between the parameters considered are not observed. More precisely, the correlation between each couple of parameters but one is consistent with zero (G12b). The only exception involves λ and γ, but the correlation in this case mainly comes from one outlier model.

4. Contributions of the Physical Parameters

[16] The frequency distributions of the TCR and the ECS obtained for all-parameter combinations ensemble (166 elements for the TCR and 162 elements for the ECS) are shown in Figure 2. Both distributions are highly skewed with a long tail due to the nonlinear relationship between the climate sensitivity and the feedback factor [Knutti and Hegerl, 2008]. The time-evolution of the variance of the inter-modelσT2and of the all-parameter combinations ensembleVar(T) for T(t) and Teq(t) is represented in Figure 3a. The variance of Teq(t) increases as a square function of time and roughly similarly for T(t). In each case, the spread of the all-parameter combinations ensemble is larger than the inter-model spread (see alsoFigure 2). Nevertheless, the all-parameter combinations variancesVar(T) and Var(Teq) (e.g. respectively 1.24 K2 and 6.31 K2 at 4 × CO2) are well within the 5–95% confidence interval of their respective inter-model spread (respectively 0.47 to 1.63 K2 and 2.70 to 9.27 K2 at 4 × CO2). Figures 3b and 3cshow the time-evolution of the contributions associated with the thermal parameters and the interaction term to the spread ofT(t). Note that the contributions to Teq(t) do not vary in time. The magnitude of the different contributions to the TCR and the ECS are summarized in Figure 3d. The interaction term explains about 3% and 1% of the spread respectively of the TCR and of the ECS. These low values suggest that the analysis of variance decomposition is accurate to quantify the contributions to the spread in the responses.

Figure 2.

Probability density functions of the TCR (black) and the ECS (red) obtained for all combinations of the parameters of the set of AOGCMs. The vertical lines at bottom indicate the individual model analytical values of the TCR (black) and the ECS (red).

Figure 3.

(a) Time-evolution of the variances of the multimodel analytical surface temperature responseσT2(black, dashed), and of the all-parameter combinations surface temperature responseVar(T) (black, solid) and equilibrium temperature response (red). Time-evolution (over 140 yr) of the contribution (%) to the spread of the transient surface temperature responses associated with (b) the radiative parameters inline image, λ, and ε and (c) the thermal inertia parameter C, C0 and γ. The contribution of the interaction term is also plotted (dashed black line) in Figure 3c. (d) Contribution of each parameters and of the interaction term to the ECS and the TCR.

[17] The equilibrium temperature response is a function of the adjusted radiative forcing and the equilibrium radiative feedback parameter only. Their respective contributions to the spread of the ECS are respectively of 12% and 87%. The inter-model spread of the radiative feedback parameter is by far the main contributor to the spread of the ECS. The methodology presented here could be extended to quantify the contribution of each independent radiative feedback (water vapor plus lapse rate, cloud and surface albedo) by using a decomposition of the global radiative feedback parameter. Similarly, a decomposition of the adjusted radiative forcing could be performed in order to evaluate the contribution of the fast adjustments to the spread.

[18] During the transition, the total contribution of inline image and λ is reduced due to the role of the other parameters. After few decades, λ remains the main contributor to the spread, but less strongly than in equilibrium, with a value of 56% at the time of 2 × CO2. On the contrary, the transient contribution of inline imageis enhanced in comparison with the equilibrium one. It decreases with time and reach a value of the order of 26% after 70 years of simulations. This emphasizes the importance of the forcing magnitude during a climate transition and the uncertainty associated with the tropospheric adjustment. Note that this result can be understood in the zero-layer EBM mentioned above. In this framework, inline image while inline image. Assuming that κ does not vary, the (normalized) sensitivity of the TCR to λ is smaller than that of the ECS. From a more quantitative point of view, this result can be obtained by applying a simplified decomposition of the variance based on Taylor series.

[19] The efficacy ε is the third factor that contributes most to the TCR spread with a 2 × CO2 value of 8%. This supports Winton et al.'s [2010] finding that ε needs to be taken into account in EBM studies. Finally, the spread of the TCR is mostly due to the radiative parameters λ, inline image and ε with a total value of about 90%. Note that they are also the main contributors to the spread of TU, TDλ and TUd (not shown). The efficacy ε is the main contributor for TDd whereas the spread of TU and TDλ is mainly dominated by λ.

[20] The contribution of γis of the same order than the contribution of ε, with a value of 6% at 70 yr. However, by excluding the GISS-E2-R model that is an outlier forγ (G12b), the contribution of this parameter is reduced to 5% and the contribution of ε increased to 10%. Note that without this model, λ and inline imagecontribute respectively to 54% and 28%. The time-evolution of the contribution ofγ is similar to the one of ε, both being associated with a common process, the deep-ocean heat uptake. The contribution ofC0 increases in time and decreases back after few centuries (not shown). This contribution is very small with a value of about 1% at 70 yr. As expected, the contribution of C is negligible after few years. Indeed, TU contributes little to the magnitude of Tand is characterized by a very small inter-model spread. During the first years, for which the variance is negligible, the spread is mainly explained byC and inline image. This may be due to the fact that initially, the temperature tendency is equal to inline image/C. Note that the contribution associated with ε, C0 and C, even if small for long (unrealistic) time-integration, doesn't tend towards 0 whereas the one associated withγ does. Indeed, the asymptotic temperature response deviation associated with the ocean heat uptake TTeq is equal to (C + εC0)/λ and is independent of γ.

5. Conclusion

[21] In this paper, it is shown that the combination of an energy-balance framework and the analysis of variance method allows to quantify the sources of the spread in climate change experiments. Disregarding that radiative processes are not independent of ocean processes, our results strongly support that atmospheric processes constitute the major source of uncertainty in climate model projections. These uncertainties manifest themselves in several ways, primarily in the strength of the radiative feedbacks to the surface warming but also in the tropospheric adjustment and to a lesser extent in the strength of the local radiative feedbacks in the region where the warming is slowed by deep-ocean heat uptake relatively to other regions. The results presented here are consistent with the conclusion ofDufresne and Bony [2008]. They concur that the spread in the transient temperature response is mainly due to the radiative feedbacks, secondly to the forcing and then to the ocean heat uptake. Note that the method used in both studies are similar in the sense that they are based on an energy-balance framework.

[22] However, contrary to Dufresne and Bony [2008], the present study supports an increased importance of the role of the adjusted radiative forcing as a contributor and a very small contribution of the ocean heat uptake. The latter may be explained by the addition of the efficacy factor that damps the previous estimates of the contributions associated with the heat exchange coefficient. The adjusted radiative forcing is found to contribute to about one fourth of the spread in the transient temperature response. This result emphasizes the importance of studying the processes involved in the fast tropospheric adjustment.


[23] We gratefully thank the anonymous reviewer for useful comments that helped us to improve the manuscript. Gilles Bellon, Hervé Douville, Julien Boé and Laurent Terray are also thanked for helpful discussions. This work was supported by the European Union FP7 Integrated Project COMBINE. We acknowledge the World Climate Research Programme's Working Group on Coupled Modelling, which is responsible for CMIP, and the U.S. Department of Energy's Program for Climate Model Diagnosis and Intercomparison which provides coordinating support and led development of software infrastructure in partnership with the Global Organization for Earth System Science Portals. We thank the climate modeling groups for producing and making available their model output.

[24] The editor thanks the anonymous reviewer for assistance in evaluating this paper.