Abstract

Climate sensitivity is one of the most important metrics for future climate projections. In previous studies the climate of the last glacial maximum has been used to constrain the range of climate sensitivity, and similarities and differences of temperature response to the forcing of the last glacial maximum and to idealized future forcing have been investigated. The feedback processes behind the response have not, however, been fully explored in a large model parameter space. In this study, the authors first examine the performance of various feedback analysis methods that identify important feedbacks for a physics parameter ensemble in experiments simulating both past and future climates. The selected methods are then used to reveal the relationship between the different ensemble experiments in terms of individual feedback processes. For the first time, all of the major feedback processes for an ensemble of paleoclimate simulations are evaluated. It is shown that the feedback and climate sensitivity parameters depend on the nature of the forcing and background climate state. The forcing dependency arises through the shortwave cloud feedback while the state dependency arises through the combined water vapor and lapse-rate feedback. The forcing dependency is, however, weakened when the feedback is estimated from the forcing that includes tropospheric adjustments. Despite these dependencies, past climate can still be used to provide a useful constraint on climate sensitivity as long as the limitation is properly taken into account because the strength of each feedback correlates reasonably well between the ensembles. It is, however, shown that the physics parameter ensemble does not cover the range of results simulated by structurally different models, which suggests the need for further study exploring both structural and parameter uncertainties.

1. Introduction

Climate sensitivity, defined as the global mean equilibrium surface temperature change under a doubling of atmospheric CO2 concentration (2 × CO2), is a useful metric because it is generally well correlated with the magnitude of changes in other climatic variables. In addition, the global mean temperature change is often referenced when the target reduction of greenhouse gas (GHG) emission is discussed during policy-making processes. Thus, it is important to quantify and reduce the uncertainty in climate sensitivity. Many different approaches have been taken, from estimates based on observations to ensemble modeling studies using experienced climate as constraints. These constraints include short volcanic response, century-long instrumental records, and climate reconstructions of the last millennium (Knutti and Hegerl 2008). Paleoclimatic information further back in time has also been utilized to provide a constraint and to support or refute suggested ranges of the climate sensitivity (Edwards et al. 2007). In particular, the last glacial maximum (LGM) has received much of the attention as the forcing is relatively large and well known, and reasonably accurate quantitative reconstructions of the climate response are available.

The past and future temperature changes are linked through the so-called climate sensitivity parameter λ, defined as surface temperature change ΔTs normalized by adjusted radiative forcing F;

 
formula

Here the overbar denotes global average. Yoshimori et al. (2009, hereafter referred to as Y09) categorized previous climate-sensitivity-related studies with the LGM climate into three groups: 1) those that estimate the climate sensitivity directly from reconstructed temperature and estimates of external forcings; 2) those that validate a model’s sensitivity by comparing paleosimulations and reconstructions; and 3) those that constrain the probability distribution of the climate sensitivity with paleodata through a physics parameter ensemble (PPE). It is often assumed in studies taking the first approach that the climate sensitivity parameter is the same between the past and the future, while the second and the third approach do not assume such a universality in the parameter. The second approach accepts that paleoclimate can be used as a criterion for the model validation. In other words, it is implicitly assumed that a model’s ability to successfully simulate the past is a necessary condition of, or at least relevant to, future climate projections. The third approach uses the model ensemble to indicate the relationship between past and future climate changes. If the mechanisms causing past temperature response are unrelated to the 2 × CO2 response, then the climate sensitivity will not be constrained by the third approach.

As described in more detail in section 3, climate sensitivity is a result of feedback processes involving changes in water vapor, lapse rate, surface albedo, and clouds. A possible similarity or difference in the climate sensitivity parameter for positive and negative forcings has been discussed in many studies (Hansen et al. 1984; Broccoli and Manabe 1987; Hewitt and Mitchell 1997; Ramstein et al. 1998; Broccoli 2000; Hansen et al. 1997, 2005), but the strength of individual feedbacks have only been quantified more recently by Crucifix (2006) and Y09. Crucifix analyzed four different atmosphere–ocean (AO) general circulation models (GCMs), finding that three models show smaller sensitivity to the LGM forcing than to the 2 × CO2 forcing while one model shows the opposite. This asymmetry and model difference are both attributed to the shortwave cloud feedback. Hargreaves et al. (2007) showed that 80% of their PPE members exhibited weaker sensitivity to lowered GHG level than to elevated GHG level. In their study, however, the processes behind this asymmetry were not investigated. Y09, on the other hand, rigorously investigated feedbacks in both LGM and 2 × CO2 experiments and confirmed that a similar asymmetry occurs through the shortwave cloud feedback. Their conclusion is, however, based on one model with a single parameter set. The purpose of this study is to identify important feedbacks responsible for the nonlinearity in the climate sensitivity parameter between cold past and warm future experiments, in a PPE updated from Hargreaves et al. (2007), and examine whether or not the results obtained by Y09 are robust in much larger parameter space. In addition, we investigate whether the difference between other structurally different models presented by Crucifix (2006) may be captured at the level of individual feedbacks by simply varying parameter values in a single model. Furthermore, the study reveals some of the fundamental behavior of our model that appeared extensively in the Intergovernmental Panel on Climate Change Fourth Assessment Report (IPPC AR4) in the context of past, present, and future climate (Solomon et al. 2007).

In the next section, the model and PPE are briefly described. One of the challenges of performing the feedback analysis on ensemble experiments is to find a suitable simplified method with reasonable accuracy. For example, the method employed by Y09 would require 36 000 years of radiative transfer calculation for the results presented in the following. Although technical, the methodological exploration is crucial and is presented in section 3. The results obtained by the feedback analysis are then presented in section 4, followed by the conclusion in section 5. Some notes on the feedback analysis method are added in the appendix.

2. Model and experiments

The model used in this study is an atmospheric GCM coupled to a slab-type mixed layer ocean model. The model also contains land surface and sea ice components. The atmosphere and land surface components are identical to those in the fully coupled model with an ocean GCM known as the Model for Interdisciplinary Research on Climate 3.2, medium-resolution version [MIROC3.2(medres)] in the IPCC AR4, except that the horizontal resolution used here for our PPE is T21 (~5.6°) rather than T42 (~2.8°). For computation of radiative forcing and construction of radiative kernels (section 3c), the original T42 version of the model is used so as to compare with more accurate analysis in Y09. The atmosphere has 20 vertical sigma levels, and the ocean is represented by a motionless 50-m layer with a heat capacity. A simple thermodynamic sea ice model is employed without dynamics. The MIROC3.2 model has been used in many previous studies (e.g., Nozawa et al. 2005; Kimoto 2005; Ohgaito and Abe-Ouchi 2007; Yanase and Abe-Ouchi 2010), and we refer readers to K-1 Model Developers (2004) for a detailed description of the full-ocean coupled version of the model and Y09 for a description of the slab-ocean coupled version of the model.

To understand the model behavior in a large, but realistic, parameter space and to examine the sensitivity of simulated results to the choice of uncertain model parameters, an ensemble of 40 model versions at T21 resolution is constructed, each member of which has different sets of values for 13 model parameters (Table 1). The number of varied parameters is reduced from 25 in Annan et al. (2005) because little sensitivity was found to now-fixed parameters. The size of the ensemble is reasonable, but not ideal, and is limited by computational resources. A priori parameter values are specified within a realistic range using Latin hypercube sampling (McKay et al. 1979). Parameters are then constrained by seasonally averaged observational data during the course of the preindustrial equilibrium simulation (CTRL) using the ensemble Kalman filter technique (Annan et al. 2005). Updates of these procedures from Annan et al. (2005) and Hargreaves et al. (2007) are described in Yokohata et al. (2010) including representation of the effect of ocean heat transport (q flux). The q flux differs between ensemble members but is identical between experiments except for small zonal redistribution, following Broccoli (2000), associated with different ocean area in the past. Hargreaves and Annan (2009) also used the same ensemble.

Table 1.

List of perturbed parameters: the range for 36 members used for the analysis is presented and that for the original 40 members is indicated with asterisk if different (see text).

List of perturbed parameters: the range for 36 members used for the analysis is presented and that for the original 40 members is indicated with asterisk if different (see text).
List of perturbed parameters: the range for 36 members used for the analysis is presented and that for the original 40 members is indicated with asterisk if different (see text).

All experiments are listed in Table 2. We study equilibrium states: the model is spun up at least 20 years for each experiment, and 20-yr stable simulations after the spinup are used for the analysis. A factor times the preindustrial CO2 level is specified in the R2 × CO2 experiment. The LGM experiment is set to simulate the climate of the last glacial maximum in which appropriate GHG concentrations, ice sheets, and orbital parameters are prescribed for those about 21 000 years ago, according to the Paleoclimate Modelling Intercomparison Project (PMIP2) protocol (Braconnot et al. 2007). These experiments are designed to investigate similarities and differences between past and future climate sensitivity parameters and feedback processes. In addition, some further experiments are performed to more deeply investigate the dependence of feedbacks and the climate sensitivity parameter to different types of climate forcing. The LGMGHG experimental protocol is the same as the CTRL experiment but with the GHGs changed to LGM levels and is devised to separate the effect between GHG and ice sheet (with minor orbital) forcing. The LGMICE experiment is the same as the CTRL experiment except with ice sheets and orbital parameters changed to LGM conditions. The exact values of the boundary conditions for the CTRL, LGM, and LGMGHG experiments are presented in Table 1 of Y09. The CTRL experiment serves as a reference for the R2 × CO2, LGM, LGMGHG, and LGMICE experiments. To investigate the dependence of feedbacks and climate sensitivity on the background climate state we perform the LGM2 × CO2 experiment, where the atmospheric CO2 mixing ratio at the LGM is doubled with all other boundary conditions identical to the LGM experiment, and compare the results with those from the R2 × CO2 experiment. Note that this state dependency of feedbacks was not investigated in Y09. Members that blow up during the integration or have trends larger than 0.05 K yr−1 for the last 20 years of the integration are excluded (but most of trends are much smaller) as they have not reached the equilibrium. The R2 × CO2 experiment is used as a surrogate of the 2 × CO2 experiment, as in Hargreaves and Annan (2009), because this quality control would reduce the number of members from 40 to 32, otherwise. Thirty-one members commonly available in the R2 × CO2 and 2 × CO2 experiments confirm a linear relation in the global mean temperature response. Consequently, 36 members commonly available in all experiments listed in Table 2 are analyzed.

Table 2.

List of T21 physics parameter ensemble: “PI” denotes preindustrial conditions.

List of T21 physics parameter ensemble: “PI” denotes preindustrial conditions.
List of T21 physics parameter ensemble: “PI” denotes preindustrial conditions.

3. Feedback analysis

a. Definition

As a way to understand physical mechanisms of surface temperature response to applied forcing, it is useful to quantify the contribution of individual feedback processes to the radiative flux change at the top of the atmosphere (TOA) (Hansen et al. 1984; Schlesinger 1988). Net radiation at the TOA, N, at any given time may be written as a function of radiative forcing constituents xi and meteorological fields μj:

 
formula

Examples of xi and μj are atmospheric CO2 concentration and snow albedo, respectively. The change in net radiation is then written as

 
formula

where F is the adjusted radiative forcing at the TOA. If we assume that changes in meteorological fields are functions of the global mean surface temperature change alone such that

 
formula

we have

 
formula

where

 
formula

is called the climate feedback parameter. More explicitly,

 
formula

where P, q, Γ, A, and C denote the Planck response, water vapor, lapse rate, surface albedo, and cloud feedbacks, respectively. At equilibrium, the left side of (5) becomes zero on the global average; thus, the total feedback parameter Λ and climate sensitivity parameter λ are linked through the relationship:

 
formula

In the current study, rapid stratospheric adjustments are included in forcing F (=Fa), but rapid tropospheric adjustments are included in feedbacks Λ, unless noted otherwise. Here adjustments occur without changing the global mean surface temperature when radiative perturbation is applied. The stratosphere-adjusted radiative forcing of each experiment computed with the original T42 version of the model is presented in Fig. 1a (cf. Y09 and Fig. 6.5 of Jansen et al. 2007) and is used to evaluate λ and Λ. Recent studies have shown, however, that the tropospheric adjustment occurs with CO2 forcing primarily through cloud changes (Hansen et al. 2005; Gregory and Webb 2008; Andrews and Forster 2008; Andrews et al. 2009) and it is often considered as a part of forcing. Therefore, in places we also evaluate λ and Λ with the troposphere–stratosphere adjusted forcing (Fs) and discuss the implications for the results. In practice, Fs and the total feedback parameter are calculated as the intercept and slope of the regression line (5), respectively, from the first 20 years of spinup integrations starting from a corresponding reference state (Gregory et al. 2004).

Fig. 1.

Annual and zonal mean forcing and response with respect to the corresponding reference climate (Table 2): (a) stratosphere-adjusted radiative forcing and (b) surface air temperature. The radiative forcing for LGM, LGMGHG, and LGMICE is taken from Y09. In both (a),(b) R2 × CO2 is doubled to facilitate the comparison with LGM2 × CO2. In (b) the thick lines show the ensemble means and the thin lines show ±1 standard deviation of the ensemble.

Fig. 1.

Annual and zonal mean forcing and response with respect to the corresponding reference climate (Table 2): (a) stratosphere-adjusted radiative forcing and (b) surface air temperature. The radiative forcing for LGM, LGMGHG, and LGMICE is taken from Y09. In both (a),(b) R2 × CO2 is doubled to facilitate the comparison with LGM2 × CO2. In (b) the thick lines show the ensemble means and the thin lines show ±1 standard deviation of the ensemble.

b. Method

There are several different techniques to diagnose the strength of individual feedbacks Λj (Bony et al. 2006). To select the most suitable method for the PPE of future climate and paleoclimate experiments, we examine several candidate methods. Here the different techniques are explained. The method which closely follows the mathematical definition of the feedback is the partial radiative perturbation (PRP) method (Hansen et al. 1984; Wetherald and Manabe 1988). In this method, variables that are associated with each feedback process of interest from perturbed experiments are substituted into offline radiation code of the model with reference climate taken from the control experiment. The subsequent change in radiation at the TOA is diagnosed as the strength of the feedback. Readers are referred to Y09 for the details of the procedure including cancellation of decorrelation errors (Colman and McAvaney 1997). While this method should provide the most accurate estimate, it requires the storage of a substantial amount of model output, the use of an offline version of the radiation code of the model, and a relatively complicated procedure. Thus, it may be impractical for the diagnosis of feedbacks for multimodel or multiparameter ensembles. Therefore, various reduced methods, which require a more modest amount of model output and lower computational resources, have been proposed. Of these, the classical method is to calculate cloud radiative forcing (CRF) (Cess and Potter 1988; Cess et al. 1990; Cess et al. 1996; Tsushima et al. 2005) in which the effect of cloud changes is evaluated as the difference in the radiation change at the TOA between total sky and clear sky. This convenient method was criticized by Soden et al. (2004) because the CRF is contaminated by noncloud contribution, although it is still useful because a direct comparison can be made with observations. For feedback analysis in the shortwave spectral region, the approximate PRP (APRP) method was recently proposed and has been shown to reproduce, with high precision, results made by the PRP method (Taylor et al. 2007). The APRP represents the atmosphere as a single layer of clear-sky and overcast regions with bulk optical properties; surface albedo, cloud, and clear-sky feedbacks are separately evaluated. Taylor et al. (2007) demonstrated that this method is superior to previously proposed other reduced methods, including Yokohata et al. (2005a). As the vertical distribution of water vapor, temperature, and clouds has a large effect on the radiation balance, simplification of longwave feedback analysis by representing the atmosphere as one or two layers has not been very successful (Yokohata et al. 2005b).

Recently, a method using radiative kernels was proposed that accurately reproduces the results by the PRP method in both shortwave and longwave regions (Soden and Held 2006; Shell et al. 2008; Soden et al. 2008). Radiative kernels are collections of information on radiation changes at the TOA under unit perturbation. These normalized radiation changes are scaled by the actual changes in simulations to estimate the feedback strength. For example, the radiative kernel for surface albedo is constructed by first calculating the radiation change due to a perturbation of surface albedo by 1%, and then the strength of albedo feedback in a perturbed experiment is estimated by multiplying the simulated albedo change to the kernel. The radiation code is used only when kernels are first constructed. Once kernels are available, the method requires only monthly mean model output. The noncloud contributions in the CRF are estimated using kernels, and the cloud feedback is evaluated by subtracting them from the CRF. In the next subsection, the method of constructing radiative kernels using the radiation code of the MIROC model is briefly described.

c. Construction of kernels

It is expected that the use of a radiation code identical to that used in the model simulations, and avoiding vertical interpolation when applying the kernels to model output, would give better results than using kernels from other models. Kernels are constructed with the T42 version of the model for comparison with the PRP results of Y09. Details of the procedure follow Soden et al. (2008) and Shell et al. (2008). First, kernels with idealized warming perturbations (K+) with respect to the CTRL are constructed. The surface and air temperatures are increased by 1 K, and water vapor is increased by the amount equivalent to 1-K warming under a fixed relative humidity, separately for each grid point. Corresponding net radiation changes at the TOA, taking downward as positive, are stored as kernels. We also construct a set of kernels with 1-K cooling perturbations (K) with respect to the CTRL and another set of kernels with 1-K warming perturbations with respect to the LGM . The essential feature of kernels (K+) from other models, as described in Soden et al. (2008), is captured and it is summarized in the appendix together with some differences. While the temperature and albedo kernels are scaled linearly by simulated changes in corresponding fields, the water vapor kernel is scaled linearly by changes in the logarithm of simulated amount of water vapor. The horizontally interpolated radiative kernels from T42 to T21 are used for the analysis of the T21 PPE.

d. Performance

A comparison of various methods applied to the 2 × CO2 experiment of the T42 standard model is summarized in Fig. 2. This shows that the APRP method well reproduces the PRP result for the shortwave feedback, and the kernel (K+) method well reproduces the PRP results for both shortwave and longwave feedbacks, consistent with previous studies. The sign of global mean longwave cloud feedback is incorrectly estimated with the method proposed by Yokohata et al. (2005b). Next, we examine the performance of the APRP and kernel methods for paleoclimate applications.

Fig. 2.

Comparisons between various feedback analysis methods for T42 2 × CO2 experiments: (a) shortwave (SW) water vapor feedback; (b) longwave (LW) water vapor (WV) and lapse rate (LR) feedbacks; (c) SW cloud feedback; (d) LW cloud feedback; (e) surface albedo feedback; and (f) Planck response. PRP (APRP) denote partial radiative perturbation (approximate PRP). Results of PRP are from Y09. The K+ kernels are used. CRF and Y05 denote cloud radiative forcing and the method proposed by Yokohata et al. (2005b). “Blackbody” denotes the response estimated by assuming earth–atmosphere as a blackbody (see appendix). Values in the bracket represent the global average.

Fig. 2.

Comparisons between various feedback analysis methods for T42 2 × CO2 experiments: (a) shortwave (SW) water vapor feedback; (b) longwave (LW) water vapor (WV) and lapse rate (LR) feedbacks; (c) SW cloud feedback; (d) LW cloud feedback; (e) surface albedo feedback; and (f) Planck response. PRP (APRP) denote partial radiative perturbation (approximate PRP). Results of PRP are from Y09. The K+ kernels are used. CRF and Y05 denote cloud radiative forcing and the method proposed by Yokohata et al. (2005b). “Blackbody” denotes the response estimated by assuming earth–atmosphere as a blackbody (see appendix). Values in the bracket represent the global average.

The global mean feedback strength obtained by three different methods for T42 2 × CO2, LGMGHG, and LGM experiments are presented in Table 3. Based on our own experience, we place a rather subjective criteria for the required precision of ~0.1 W m−2 K−1, but it turns out to be a reasonable one to distinguish the difference between experiments in section 4. The error is measured here as a departure from the PRP results by Y09 using the same data. It is shown that the APRP method is superior to the kernel method for the shortwave feedback analysis (Table 3). This is probably because the APRP takes nonlinearity of the climate response to the forcing into account while the kernel method extrapolates a linear tangential increment. In addition, the kernel for surface albedo induces errors if applied when orbital configuration and thus insolation are different from the reference climate because the effect of albedo changes on radiation is certainly different under different insolation. Therefore, we conclude that APRP is the most suitable method for our shortwave feedback analysis. For longwave feedbacks, the precision of the kernel method for lapse rate, cloud, and the Planck response is acceptable (Table 3). The water vapor feedback, however, may suffer from substantial errors depending on which kernel, K+ or K, is used owing to nonlinearity of this feedback. The results indicate that the precision is ensured as long as appropriate kernels, that is, K+ for the warming experiment (2 × CO2) and K for cooling experiments (LGMGHG and LGM), are used.

Table 3.

A comparison between PRP, APRP, and radiative kernel (K+ and K) methods for the feedback analysis in T42 experiments. Feedbacks are q: water vapor, Γ: lapse rate, A: albedo, C: cloud, and P: Planck response; SW (LW) denote shortwave (longwave) components. Units are W m−2 K−1. Values that differ from the corresponding PRP analysis by more than 0.1 W m−2 K−1 are highlighted in bold. Details of the experiments are described in, and values of PRP are taken from, Y09. Note that APRP is not applicable for the longwave feedbacks.

A comparison between PRP, APRP, and radiative kernel (K+ and K−) methods for the feedback analysis in T42 experiments. Feedbacks are q: water vapor, Γ: lapse rate, A: albedo, C: cloud, and P: Planck response; SW (LW) denote shortwave (longwave) components. Units are W m−2 K−1. Values that differ from the corresponding PRP analysis by more than 0.1 W m−2 K−1 are highlighted in bold. Details of the experiments are described in, and values of PRP are taken from, Y09. Note that APRP is not applicable for the longwave feedbacks.
A comparison between PRP, APRP, and radiative kernel (K+ and K−) methods for the feedback analysis in T42 experiments. Feedbacks are q: water vapor, Γ: lapse rate, A: albedo, C: cloud, and P: Planck response; SW (LW) denote shortwave (longwave) components. Units are W m−2 K−1. Values that differ from the corresponding PRP analysis by more than 0.1 W m−2 K−1 are highlighted in bold. Details of the experiments are described in, and values of PRP are taken from, Y09. Note that APRP is not applicable for the longwave feedbacks.

Strong support for the validity of the analysis method is provided when the total feedback parameter calculated from stratosphere adjusted radiative forcing and simulated temperature change is reproduced by the sum of individual feedbacks as indicated by Eq. (8). Figure 3 shows the scatterplot of these two different estimates together with the one-to-one line. Apart from the LGMICE experiment, the results lie close to the line. This is because we use different kernels for the different experiments: K+ for the R2 × CO2 experiment, K for the LGM, LGMGHG, and LGMICE experiments, and for the LGM2 × CO2 experiment. From the available data alone, the cause of the deviation from the line for the LGMICE experiment is not clear. The interpretation of temperature response and the total feedback parameter for the LGMICE experiment is complicated because a large fraction of temperature change is caused by the elevated LGM ice sheet surface, which is not at all related to the feedback processes. This also applies to the LGM experiment, but the fractional effect is much smaller under the large influence of GHG forcing, as described in the next section, and it is less subjective to unforced internal variability. Nevertheless, the existence of a strong positive correlation in the LGMICE suggests the usefulness of the analysis as long as some caution is taken in the interpretation.

Fig. 3.

Estimated feedback parameters (Λ) from feedback analyses and simulations; also plotted is the one-to-one line.

Fig. 3.

Estimated feedback parameters (Λ) from feedback analyses and simulations; also plotted is the one-to-one line.

4. Result

a. Temperature response

Figure 4 shows the relation between climate sensitivity estimated from the R2 × CO2 experiment and the magnitude of the temperature response in the other experiments. Climate sensitivities of the T21 ensemble members are higher than the IPCC AR4 estimate of 2–4.5 K (66% confidence interval) but cover a wide range at the higher end. As stated in Yokohata et al. (2010), an addition of a new constraint in the ensemble Kalman filter resulted in slightly higher climate sensitivities than the previous PPE (Hargreaves et al. 2007). There are high correlations except for the LGMICE experiment, which was not carried out in the previous PPE. As the LGMICE forcing is a part of the LGM forcing, the low correlation of the LGMICE experiment indicates that ice sheet and orbital forcing introduces noise when the climate sensitivity is to be constrained from the LGM climate. Zonal mean temperature changes are shown in Fig. 1b. This shows that tropical cooling in the LGM experiment is mostly due to lowered GHG while comparable or larger contribution is given by ice sheet and orbital forcing in high latitudes. Little polar amplification is seen in the LGM2 × CO2 experiment compared to the R2 × CO2 experiment, consistent with the state dependence of feedbacks discussed later, in section 4d.

Fig. 4.

Annual and global mean temperature changes from corresponding reference climate (Table 2). Climate sensitivity is estimated by doubling the temperature response in the R2 × CO2 experiment. Signs are inverted for LGM, LGMGHG, and LGMICE.

Fig. 4.

Annual and global mean temperature changes from corresponding reference climate (Table 2). Climate sensitivity is estimated by doubling the temperature response in the R2 × CO2 experiment. Signs are inverted for LGM, LGMGHG, and LGMICE.

b. Overview of the feedback analysis on the parameter ensembles

Figure 5 shows the ensemble mean of each feedback strength. Consistent with Fig. 3, the total feedback parameter estimated from simulations and feedback analyses agree well (FDBK and SIM, Fa). The combined water vapor and lapse rate feedback exhibits by far the strongest positive feedback with nearly the same strength across the experiments. The approximate constancy of combined water vapor and lapse rate feedback has an important implication for changes in the hydrological cycle and atmospheric circulation. On the global average, condensation heating must be balanced by radiative damping, but the latter cannot be varied easily by changing temperature contrast between the surface and aloft because the change in water vapor feedback counteracts against it. This relation, therefore, could possibly constrain precipitation and upward tropical mass flux changes (cf. Allen and Ingram 2002; Held and Soden 2006; Vecchi and Soden 2007). The albedo feedback also exhibits nearly the same strength across the experiments, consistent with the result of Y09. This is partly because the globally averaged value of albedo feedback is generally small. At high latitudes, however, the effect of snow/ice albedo feedback is amplified by other coexisting positive feedback processes, and surface temperature change is also influenced by other factors (Y09). From Fig. 5, it is clear that the difference in the total feedback parameter between the experiments is primarily due to the difference in the shortwave cloud feedback, in agreement with the single-model result by Y09. What is new here and discussed further in the following subsections is that apart from the LGM2 × CO2 experiment the difference in the total feedback parameter is reduced considerably when it is evaluated with the troposphere–stratosphere adjusted forcing (SIM, Fs).

Fig. 5.

Mean strength of individual feedback parameters for each ensemble: error bars represent ±1 standard deviations of ensemble members. Feedbacks (abscissa labels) are q + Γ: water vapor + lapse-rate, A: albedo, C: cloud, P: Planck response, and FDBK (SIM) is total feedback estimated as a sum from feedback analyses (from simulations). SW (LW) denote shortwave (longwave components) and Fa (Fs) denote total feedback computed with the stratosphere-adjusted (troposphere–stratosphere-adjusted) forcing.

Fig. 5.

Mean strength of individual feedback parameters for each ensemble: error bars represent ±1 standard deviations of ensemble members. Feedbacks (abscissa labels) are q + Γ: water vapor + lapse-rate, A: albedo, C: cloud, P: Planck response, and FDBK (SIM) is total feedback estimated as a sum from feedback analyses (from simulations). SW (LW) denote shortwave (longwave components) and Fa (Fs) denote total feedback computed with the stratosphere-adjusted (troposphere–stratosphere-adjusted) forcing.

It is of interest to know which feedback process is responsible for the ensemble spread in each experiment. Figure 6 shows the fractional contribution of individual feedbacks to the variance of the total feedback in each ensemble. It is calculated for each experiment separately by

 
formula

following Boer and Yu (2003), Webb et al. (2006), and Yokohata et al. (2010). Here j and k are indices identifying each feedback and ensemble member, respectively, while n is the total number of ensemble members; is the ensemble variance of the total feedback; the overbar denotes the ensemble mean. Positive (negative) Vj indicate positive (negative) correlations between Λj and Λ. In all experiments, the largest contribution to the variance of the total feedback is made by the difference in the shortwave cloud feedback among ensemble members. The contribution of the longwave cloud feedback is not negligible, however. Interestingly, it appears that the contribution of the albedo feedback tends to reduce the ensemble spread in all experiments. This is probably an artifact caused by the fact that ensemble members that have larger warming in low and mid latitudes via cloud feedback result in fractionally smaller albedo feedback that operates only in high latitudes.

Fig. 6.

Fractional contribution of individual feedbacks to the variance of the total feedback in each experiment. By definition, feedbacks in each experiment add up to 1: feedback labels as in Fig. 5.

Fig. 6.

Fractional contribution of individual feedbacks to the variance of the total feedback in each experiment. By definition, feedbacks in each experiment add up to 1: feedback labels as in Fig. 5.

c. Forcing dependency of the climate sensitivity parameter

To investigate further details of the difference in individual feedbacks under different forcings, we first compare the R2 × CO2 and LGMGHG experiments (Fig. 7). A majority of ensemble members, 33 out of 36, have smaller climate sensitivity parameter (λ) and total feedback parameter (ΛSIM) for the LGMGHG forcing than for the R2 × CO2 forcing when they are calculated with the stratosphere-adjusted forcing (Fa). This is consistent with Hargreaves et al. (2007). The total feedback parameter calculated as the sum of individual feedbacks (ΛFDBK) reproduces this asymmetry only for 23 out of 36 members, likely associated with the limited accuracy of the analysis. We suggest that these asymmetries are explained by the asymmetry in the shortwave cloud feedback in which 33 out of 36 members have smaller values (ΛC,SW) for the LGMGHG forcing than for the R2 × CO2 forcing. The λ and ΛSIM become less asymmetric (27, instead of 33, are smaller) when the troposphere–stratosphere adjusted forcing (Fs) is used in their estimate. This may suggest that the asymmetry of ΛC,SW occurs through rapid tropospheric adjustments, rather than as a response to the global mean surface temperature change. Unfortunately, the asymmetry of cloud adjustments cannot be verified as variables needed for the analysis were not stored during the spinup phase. Albedo and cloud feedbacks exhibit relatively large ensemble spread. There are good correlations in these feedback strengths across individual members. In other words, members that have large feedback strength for the LGMGHG forcing also have large feedback strength for the R2 × CO2 forcing in each feedback. These results provide a physical basis for constraining the range of warm future climate change based on cold past climate change.

Fig. 7.

Decomposition of global mean feedbacks: R2 × CO2 vs LGMGHG. The variable λ indicates climate sensitivity parameter. Feedback parameters are ΛSIM: climate feedback parameter (Λ) estimated from simulations, ΛFDBK: for Λ estimated as a sum from feedback analyses, q + Γ: water vapor + lapse rate, A: albedo, C: cloud, and P: the Planck response; λ is determined from ΛSIM and SW (LW) denote shortwave (longwave) components. Crosses (+) and circles (o) in λ and ΛSIM are calculated with the stratosphere-adjusted forcing and troposphere–stratosphere-adjusted forcing, respectively; also plotted are the one-to-one lines.

Fig. 7.

Decomposition of global mean feedbacks: R2 × CO2 vs LGMGHG. The variable λ indicates climate sensitivity parameter. Feedback parameters are ΛSIM: climate feedback parameter (Λ) estimated from simulations, ΛFDBK: for Λ estimated as a sum from feedback analyses, q + Γ: water vapor + lapse rate, A: albedo, C: cloud, and P: the Planck response; λ is determined from ΛSIM and SW (LW) denote shortwave (longwave) components. Crosses (+) and circles (o) in λ and ΛSIM are calculated with the stratosphere-adjusted forcing and troposphere–stratosphere-adjusted forcing, respectively; also plotted are the one-to-one lines.

The comparison between the R2 × CO2 and LGM experiments is shown in Fig. 8. All ensemble members exhibit smaller λ and ΛSIM for the LGM forcing than for the R2 × CO2 forcing when they are calculated with Fa. Consistent with Fig. 5, the shortwave cloud feedback is responsible for the smaller sensitivity to the LGM forcing. The λ and ΛSIM become much more symmetric (27, instead of 36, are smaller) when they are calculated with Fs. One must be cautious, however, of interpreting the tropospheric “adjustments” when the forcing includes instantaneous change of topography due to the LGM ice sheets. The comparison between λ and ΛSIM reminds us of the important fact that constraining the total feedback parameter does not immediately result in a substantial narrowing of the uncertainty in climate sensitivity parameter because of the inverse relation between the two. Thus, there is some limitation on constraining the climate sensitivity from the LGM climate, but good correlations between the LGM and R2 × CO2 experiments in individual feedbacks are encouraging. Again, these results support the approach of constraining the range of warm future climate change based on cold past climate change. However, there is a possibility of underestimation if the climate sensitivity parameter deduced from proxy data alone is extrapolated, as suggested by Hargreaves et al. (2007), unless tropospheric adjustments are included in the forcing.

Fig. 8.

As in Fig. 7, but for R2 × CO2 vs LGM.

Fig. 8.

As in Fig. 7, but for R2 × CO2 vs LGM.

The ensemble results for the latitudinal distribution of the shortwave cloud feedback strength are in agreement with the results from the T42 version of the model (not shown). The asymmetric response in the shortwave cloud feedback between cooling and warming experiments is pronounced in the mid to high latitude Northern Hemisphere (~50°–60°N), north of equator, and in the midlatitude Southern Hemisphere (~50°S). Although the climate sensitivities of the T21 versions of the model are all higher than the T42 version (4.0 K), their behavior is shown to be very similar. Y09 hypothesized that a shift of the temperature-dependent mixed-phase cloud region plays a key role in the asymmetry as well as changes in evaporation likely associated with snow and sea ice cover. A similar behavior in the Southern Ocean is simulated by Colman and McAvaney (2009), and they pointed out a shift of storm track as a cause. It is future work to thoroughly investigate the underlying physical mechanisms and their relevance to tropospheric adjustments.

Zaliapin and Ghil (2010) pointed out the importance of nonlinearity of the climate feedback parameter with respect to temperature perturbation when trying to estimate climate sensitivity, especially when the linear response is close to zero. Weak nonlinearity of the climate sensitivity parameter with respect to radiative forcing or the climate feedback parameter with respect to temperature perturbation has been demonstrated in previous studies (Colman and McAvaney 1997; Hansen et al. 2005; Colman and McAvaney 2009) and in Fig. 7. Table 4 quantifies this effect in our ensemble experiments. Interestingly, these analyses all suggest a negative quadratic term for the feedback equation (coefficient d in Table 4) in contrast to the positive values that Zaliapin and Ghil (2010) proposed. Over a broad range of temperatures, a negative quadratic term would result in instability or, perhaps more reasonably, suggest that even higher-order terms would need to be considered. However, in our experiments, the quadratic term is very small compared to the substantial linear term, so has little impact on the equilibrium climate sensitivity.

Table 4.

Nonlinearity of climate sensitivity and feedback estimated from the LGMGHG, CTRL, and R2 × CO2 experiments by fitting quadratic equations: ΔTs = aF + bF2, and F = cΔTs + dTs)2. Values in the parentheses are obtained with the troposphere–stratosphere-adjusted forcing, rather than the stratosphere-adjusted forcing.

Nonlinearity of climate sensitivity and feedback estimated from the LGMGHG, CTRL, and R2 × CO2 experiments by fitting quadratic equations: ΔTs = aF + bF2, and F = cΔTs + d(ΔTs)2. Values in the parentheses are obtained with the troposphere–stratosphere-adjusted forcing, rather than the stratosphere-adjusted forcing.
Nonlinearity of climate sensitivity and feedback estimated from the LGMGHG, CTRL, and R2 × CO2 experiments by fitting quadratic equations: ΔTs = aF + bF2, and F = cΔTs + d(ΔTs)2. Values in the parentheses are obtained with the troposphere–stratosphere-adjusted forcing, rather than the stratosphere-adjusted forcing.

d. State dependency of the climate sensitivity parameter

Similar analyses are conducted for the difference between the R2 × CO2 and LGM2 × CO2 experiments, which reflects the influence of the background climate (Fig. 9). All ensemble members exhibit smaller λ and ΛSIM for a CO2 increase with respect to the LGM reference climate than to the CTRL reference climate. This is independent of the choice of Fa or Fs for the forcing. There is a cancellation in the asymmetry in the shortwave and longwave cloud feedbacks. Figure 10 shows the zonal mean feedback strength normalized by the global mean temperature change. In the LGM2 × CO2 experiment, the snow and sea ice distributions change in midlatitudes but do not change significantly in the Arctic due to the cold LGM reference climate, resulting in a smaller albedo feedback in the Arctic but a similar global mean. The difference in ΛFDBK is attributed to the combined water vapor and lapse rate feedback (Fig. 9).

Fig. 9.

As in Fig. 7, but for R2 × CO2 vs LGM2 × CO2.

Fig. 9.

As in Fig. 7, but for R2 × CO2 vs LGM2 × CO2.

Fig. 10.

Differences in water vapor (q), lapse-rate (Γ), and albedo (A) feedbacks between R2 × CO2 and LGM2 × CO2 ensemble means.

Fig. 10.

Differences in water vapor (q), lapse-rate (Γ), and albedo (A) feedbacks between R2 × CO2 and LGM2 × CO2 ensemble means.

In Fig. 10, the R2 × CO2 experiment exhibits much stronger lapse rate feedback in the Arctic. The water vapor feedback is also stronger in that experiment in high latitudes. These two feedbacks primarily reflect local temperature changes, but contribute to the global mean feedback difference of the two experiments. Both albedo and lapse rate feedbacks are stronger in the R2 × CO2 experiment in the Arctic, even when they are normalized by local temperature changes (not shown). This implies that they contribute to the stronger Arctic amplification in the R2 × CO2 experiment. On the other hand, the water vapor feedback is similar in the two experiments in the Arctic when it is normalized by local temperature changes (not shown). This implies that the water vapor feedback is affected by albedo and lapse rate feedbacks through local temperature changes. Taken together, the feedback and climate sensitivity are state dependent.

In previous studies, it was shown that global mean water vapor and lapse rate feedbacks are negatively correlated across models (Colman 2003; Soden and Held 2006) due to the relation in the vertical distribution of moisture and temperature. Y09 also showed that the sum of water vapor and lapse rate feedbacks are nearly constant for 2 × CO2, LGMGHG, and LGM experiments. In the three experiments, a fractionally stronger forcing in high latitudes in the LGM experiment with respect to the 2 × CO2 and LGMGHG experiments induces more positive lapse rate feedback in high latitudes at the expense of less water vapor feedback in low latitudes. There is a strong anticorrelation between the two feedbacks across all 180 ensemble members, and their meridional compensation is again confirmed here (Fig. 11). Members of the LGM2 × CO2 experiment are, however, shifted systematically from the regression lines of other experiments. This is related to the feedbacks in high latitudes where water vapor and lapse rate feedbacks in the ensemble means are positively correlated (not shown). Therefore, the latitudinal behavior of these two feedbacks is different for different forcing and climate states.

Fig. 11.

Relation between global mean water vapor and lapse rate feedbacks.

Fig. 11.

Relation between global mean water vapor and lapse rate feedbacks.

5. Conclusions

We have, for the first time, evaluated all of the major feedback processes for an ensemble of GCM paleoclimate simulations. We conclude that the combined use of the APRP method for the shortwave feedback and the kernel method for the longwave feedback are most suitable for such analyses. Whereas Crucifix (2006) compared feedbacks for four structurally different AOGCMs including MIROC3.2; he analyzed only cloud radiative forcing and the residual as to longwave feedbacks. In the current study, water vapor and lapse rate feedbacks are quantified explicitly, and cloud feedback, rather than cloud radiative forcing, is evaluated.

Despite using model ensemble members covering a much larger parameter space, the essential results on the forcing dependency of feedbacks are consistent with those obtained by Y09 in which only one model with a single parameter set was used. This indicates that those results were robust and the tuned default parameter set of MIROC3.2 T42 is producing representative results. In particular, the difference in the climate sensitivity parameter for the R2 × CO2 and LGM forcing is attributed to the different strength of the shortwave cloud feedback. The asymmetry of the shortwave cloud feedback in response to positive and negative radiative forcing is also confirmed by the majority of ensemble members. By identifying important feedbacks and adding an explanation for the temperature response in a similar PPE, this study has further explained the results of Hargreaves et al. (2007).

This study reveals that the feedback and climate sensitivity parameters depend on the nature of the forcing and background climate state. The forcing dependency arises through the shortwave cloud feedback, while the state dependency arises through the combined water vapor and lapse rate feedback in our ensembles. Their forcing dependency, however, diminishes if rapid tropospheric adjustments are considered as a part of forcing while the state dependency remains. This is not just a matter of counting adjustments as forcing or feedbacks but of understanding fundamentals of the climate system response. The current analysis is limited on the details of physical processes behind it, and further research is warranted.

In principle, the past climate sensitivity parameter can be calculated from proxy-derived temperature and model-calculated stratosphere-adjusted radiative forcing. Care must be exercised, however, when one blindly extrapolates the past climate sensitivity parameter to the future or applies such a simple energy balance argument to an extended period of time span (Lea 2004; Hansen et al. 2008). It is equally important to stress that our analysis also reveals that many feedback processes operate in a similar fashion between cold past and warm future, and does not preclude the use of LGM climate as a future constraint as long as the limitation is properly taken into account (Köhler et al. 2010). Here the similarity refers to the approximate linear relation in the strength of each feedback across ensemble members between the warming and LGM experiments. Limitations include that the cloud feedback operates differently and the ensemble spread of climate sensitivity parameter for the warming experiment is much larger than for the LGM experiment.

Our PPE spans a small range of uncertainty compared to the structurally different models presented by Crucifix (2006). There, one out of four models exhibits a larger climate sensitivity parameter due to the shortwave cloud feedback for the LGM forcing than for the 2 × CO2 forcing. In contrast, all of our ensemble members exhibit smaller shortwave cloud feedback and climate sensitivity parameters for the LGM forcing. Parameter ensembles are useful to really understand model behavior and limits and to examine whether results obtained by a single parameter set are robust. Thus, it is clear that PPE is necessary but not sufficient, and more attention needs to be paid to the structural uncertainty. Combined studies comparing PPE from structurally different models, such as in Yokohata et al. (2010) but incorporating paleoclimate simulations, are recommended. The use of the troposphere–stratosphere-adjusted forcing for multimodel analysis in such studies would be also useful.

Acknowledgments

We thank the developers of the MIROC model. Technical advice from K. Shell during the construction of radiative kernels and comments from two anonymous reviewers are greatly appreciated. We wish to extend our thanks for access to the computational resources of the NIES supercomputer system (NEC SX-8R/128M16). The developers of the freely available software, Ferret and NCL, are also acknowledged. This work was supported by the Global Environment Research Fund (S-5) of the Japanese Ministry of the Environment and the Kakushin program of MEXT.

APPENDIX

Supplementary Information on Feedback Analysis

a. MIROC kernels

The basic features of the MIROC kernels (Fig. A1) are similar to other models. For example, the clear-sky temperature kernel has large negative value in low latitudes, where the emission temperature is relatively high and small negative values near the tropopause where emissivity is small. Small negative values also appear in polar regions where emissivity and temperature are both low. Emission from the upper troposphere is effectively lost to space because little is intercepted above that level. The sensitivity (flux change per degree warming) is enhanced near the cloud top in the total-sky temperature kernel. The clear-sky water vapor kernel is large in the moist tropics and also in the upper troposphere where there is a large temperature contrast from the surface—an important factor for the greenhouse effect. The reason for the large sensitivity in the upper troposphere is also due to the large fractional increase of water vapor at cold temperatures. Interception by clouds is seen in the total-sky water vapor kernel. There are, however, some differences from other models in the total-sky kernels presumably due to the difference in background cloud distribution: there is generally larger sensitivity in the lower troposphere in the temperature kernel and a second maximum near 700 hPa in the water vapor kernel of MIROC. Note that similar color schemes to Figs. 2 and 5 of Soden et al. (2008) are adopted for visual comparison.

Fig. A1.

Radiative kernels for (a) surface temperature with total and clear skies; air temperature (b) under clear-sky conditions and (c) under total-sky conditions; water vapor (d) under clear-sky conditions and (e) under total-sky conditions. All kernels correspond to K+. Net downward radiative flux is taken as positive. Values are interpolated vertically on pressure levels after normalization by mass for display purposes.

Fig. A1.

Radiative kernels for (a) surface temperature with total and clear skies; air temperature (b) under clear-sky conditions and (c) under total-sky conditions; water vapor (d) under clear-sky conditions and (e) under total-sky conditions. All kernels correspond to K+. Net downward radiative flux is taken as positive. Values are interpolated vertically on pressure levels after normalization by mass for display purposes.

b. Blackbody response

The Planck response may be calculated by approximating the earth–atmosphere system as a blackbody (Fig. 2):

 
formula

where σ is Stefan–Boltzmann constant and Te is the effective emission temperature, which is estimated from the outgoing longwave radiation (OLR) such that

 
formula

Te is estimated in both reference and perturbed experiments, and the resulted Planck responses are averaged. Note that Wetherald and Manabe (1988) assumed a graybody in which Planck response is calculated by

 
formula

where ε is the bulk emissivity obtained by

 
formula

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Footnotes

*

Current affiliation: National Institute for Environmental Studies, Tsukuba, Japan.