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  • View in gallery

    Global-mean surface air temperature change 〈T ′〉 (K) and climate sensitivity ŝ (W m−2 K−1) for the warming experiments with CGCM3 (dashed lines), CCSM2 (solid lines), and CSM1 (dotted lines). (top) Year 41–50 average of ŝ for CGCM3 and CCSM2 are shown as horizontal lines.

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    Annual-mean values of the components of the global feedback parameter Λ̂ as function of surface temperature change 〈T ′〉 between the control and 5% solar constant increase simulations. The longwave (L) and shortwave (S) cloud-free atmosphere/surface (A) and cloud (C) feedback components (color coded) are shown for the three models (characterized by different symbols).

  • View in gallery

    The evolution of the global- and annual-mean radiative flux 〈R′〉 with temperature change 〈T ′〉 for the three models (color-coded triangles). The cloud 〈RC〉 (stars) components are also shown. Open symbols give monthly mean values over the first year of integration. The direct estimate of climate forcing from (2) is marked by the heavy black arrow. The CSM1 result for a 2.5% increase in solar constant is also shown (green triangles).

  • View in gallery

    The zonally averaged structures of the local feedback parameter Λ and its components (A: clear sky, C: cloud only, S: shortwave, L: longwave) for CCSM2 and CGCM3 (open and filled symbols). Units are W m−2 K−1 and values are calculated from the average of year 41–50 simulation results. Note that the range of all of the diagrams is the same except for ΛSA.

  • View in gallery

    Geographical distribution of the local feedback parameter Λ (W m−2 K−1) and its components (A: clear sky, C: cloud only, S: shortwave, L: longwave) for CCSM2 calculated from the average of year 41–50 simulation results.

  • View in gallery

    As in Fig. 5 but for the CGCM3 results.

  • View in gallery

    The evolution of the spatial pattern of Λ as measured by the spatial correlation with the year 41–50 mean pattern. Filled and open circles are for annual-mean values, and triangles are for 10-yr means for CCSM2 and CGCM3, respectively.

  • View in gallery

    Feedback parameter Λ (shaded in W m−2 K−1) and the change in surface temperatures (contours in K) calculated from the average of years 41–50 of (a) CSM1, (b) CCSM2, and (c) CGCM3 simulation results.

  • View in gallery

    Divergent wind vectors and the corresponding velocity potential for the CCSM2 and CGCM3 models at the 200-hPa level (mean of years 41–50). (top) Control-run values and (bottom) the changes in the 5% solar constant increase simulation. Units are 103 kg m−1 s−1 and 108 kg s−1, respectively.

  • View in gallery

    The mean streamfunction associated with the divergent east–west mass circulation for the years 41–50 of the control runs of CCSM2 and CGCM3. (bottom) The change in the 5% solar constant increase run is shown. Units are 109 kg s−1.

  • View in gallery

    Longwave–cloud feedback parameter ΛLC (shaded, in W m−2 K−1) and the change in surface temperatures (contours, in K) for (a) fully coupled run and (b) the run with prescribed SSTs and sea ice.

  • View in gallery

    The difference in the divergent wind component in the 100–500-hPa layer and (top) the associated velocity potential that results from specifying smoothed SST in the western equatorial Pacific and (bottom) the corresponding difference in the Walker circulation. Units are 103 kg m−1 s−1 and 108 kg s−1, respectively.

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Local and Global Climate Feedbacks in Models with Differing Climate Sensitivities

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  • 1 International Pacific Research Center, University of Hawaii at Manoa, Honolulu, Hawaii
  • | 2 Canadian Centre for Climate Modelling and Analysis, Meteorological Service of Canada, University of Victoria, Victoria, British Columbia, Canada
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Abstract

The climatic response to a 5% increase in solar constant is analyzed in three coupled global ocean–atmosphere general circulation models, the NCAR Climate System Model version 1 (CSM1), the Community Climate System Model version 2 (CCSM2), and the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled General Circulation Model version 3 (CGCM3). For this simple perturbation the quantitative values of the radiative climate forcing at the top of the atmosphere can be determined very accurately simply from a knowledge of the shortwave fluxes in the control run. The climate sensitivity and the geographical pattern of climate feedbacks, and of the shortwave, longwave, clear-sky, and cloud components in each model, are diagnosed as the climate evolves. After a period of adjustment of a few years, both the magnitude and pattern of the feedbacks become reasonably stable with time, implying that they may be accurately determined from relatively short integrations.

The global-mean forcing at the top of the atmosphere due to the solar constant change is almost identical in the three models. The exact value of the forcing in each case is compared with that inferred by regressing annual-mean top-of-the-atmosphere radiative imbalance against mean surface temperature change. This regression approach yields a value close to the directly diagnosed forcing for the CCCma model, but a value only within about 25% of the directly diagnosed forcing for the two NCAR models. These results indicate that this regression approach may have some practical limitation in its application, at least for some models.

The global climate sensitivities differ among the models by almost a factor of 2, and, despite an overall apparent similarity, the spatial patterns of the climate feedbacks are only modestly correlated among the three models. An exception is the clear-sky shortwave feedback, which agrees well in both magnitude and spatial pattern among the models. The biggest discrepancies are in the shortwave cloud feedback, particularly in the tropical and subtropical regions where it is strongly negative in the NCAR models but weakly positive in the CCCma model. Almost all of the difference in the global-mean total feedback (and climate sensitivity) among the models is attributable to the shortwave cloud feedback component.

All three models exhibit a region of positive feedback in the equatorial Pacific, which is surrounded by broad areas of negative feedback. These positive feedback regions appear to be associated with a local maximum of the surface warming. However, the models differ in the zonal structure of this surface warming, which ranges from a mean El Niño–like warming in the eastern Pacific in the CCCma model to a far-western Pacific maximum of warming in the NCAR CCSM2 model. A separate simulation with the CCSM2 model, in which these tropical Pacific zonal gradients of surface warming are artificially suppressed, shows no region of positive radiative feedback in the tropical Pacific. However, the global-mean feedback is only modestly changed in this constrained run, suggesting that the processes that produce the positive feedback in the tropical Pacific region may not contribute importantly to global-mean feedback and climate sensitivity.

Corresponding author address: Markus Stowasser, IPRC/SOEST, University of Hawaii at Manoa, 1680 East–West Rd., Post Bldg. 401, Honolulu, HI 96822. Email: stowasse@hawaii.edu

Abstract

The climatic response to a 5% increase in solar constant is analyzed in three coupled global ocean–atmosphere general circulation models, the NCAR Climate System Model version 1 (CSM1), the Community Climate System Model version 2 (CCSM2), and the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled General Circulation Model version 3 (CGCM3). For this simple perturbation the quantitative values of the radiative climate forcing at the top of the atmosphere can be determined very accurately simply from a knowledge of the shortwave fluxes in the control run. The climate sensitivity and the geographical pattern of climate feedbacks, and of the shortwave, longwave, clear-sky, and cloud components in each model, are diagnosed as the climate evolves. After a period of adjustment of a few years, both the magnitude and pattern of the feedbacks become reasonably stable with time, implying that they may be accurately determined from relatively short integrations.

The global-mean forcing at the top of the atmosphere due to the solar constant change is almost identical in the three models. The exact value of the forcing in each case is compared with that inferred by regressing annual-mean top-of-the-atmosphere radiative imbalance against mean surface temperature change. This regression approach yields a value close to the directly diagnosed forcing for the CCCma model, but a value only within about 25% of the directly diagnosed forcing for the two NCAR models. These results indicate that this regression approach may have some practical limitation in its application, at least for some models.

The global climate sensitivities differ among the models by almost a factor of 2, and, despite an overall apparent similarity, the spatial patterns of the climate feedbacks are only modestly correlated among the three models. An exception is the clear-sky shortwave feedback, which agrees well in both magnitude and spatial pattern among the models. The biggest discrepancies are in the shortwave cloud feedback, particularly in the tropical and subtropical regions where it is strongly negative in the NCAR models but weakly positive in the CCCma model. Almost all of the difference in the global-mean total feedback (and climate sensitivity) among the models is attributable to the shortwave cloud feedback component.

All three models exhibit a region of positive feedback in the equatorial Pacific, which is surrounded by broad areas of negative feedback. These positive feedback regions appear to be associated with a local maximum of the surface warming. However, the models differ in the zonal structure of this surface warming, which ranges from a mean El Niño–like warming in the eastern Pacific in the CCCma model to a far-western Pacific maximum of warming in the NCAR CCSM2 model. A separate simulation with the CCSM2 model, in which these tropical Pacific zonal gradients of surface warming are artificially suppressed, shows no region of positive radiative feedback in the tropical Pacific. However, the global-mean feedback is only modestly changed in this constrained run, suggesting that the processes that produce the positive feedback in the tropical Pacific region may not contribute importantly to global-mean feedback and climate sensitivity.

Corresponding author address: Markus Stowasser, IPRC/SOEST, University of Hawaii at Manoa, 1680 East–West Rd., Post Bldg. 401, Honolulu, HI 96822. Email: stowasse@hawaii.edu

1. Introduction

Forecasts of how the global climate may change over the next century in response to standard scenarios of anthropogenic perturbation of atmospheric composition have now been conducted in a large number of comprehensive coupled ocean–atmosphere models. For example, the Intergovernmental Panel on Climate Change (IPCC) third assessment report (Houghton et al. 2001) featured results from 80-yr simulations of the global-mean surface warming due to a 1% yr−1 growth of atmospheric CO2 conducted using 19 different models. The transient climate response of these simulations varies from about 1.3° to 3.8°C.

The surface temperature increase realized in a particular model in such an experiment is considered to depend on (i) the radiative forcing of the climate produced by the change in CO2; (ii) the climate sensitivity of the model, which connects the magnitude of the surface warming to that of the radiative perturbation; and (iii) the rate of ocean heat uptake that acts to delay the realization of the surface warming. Climate sensitivity appears to be a reasonably robust quantity for a particular model with only modest dependence on the forcing pattern and the climate state (e.g., Hansen et al. 1997; Senior and Mitchell 2000; Watterson 2000; Boer and Yu 2003a, b; Meehl et al. 2004). Differences in the equilibrium climate sensitivity among current models are quite large, however, and this accounts for much of the uncertainty in the predictions of warming over the next century and beyond (e.g., Cess et al. 1990; Watterson et al. 1999; Houghton et al. 2001; Colman 2003).

We investigate issues relating to climate sensitivity, climate feedback, and climate forcing in simulations with three state-of-the-art global climate models, namely the National Center for Atmospheric Research (NCAR) Climate System Model version 1 (CSM1), the Community Climate System Model version 2 (CCSM2), and the Canadian Centre for Climate Modelling and Analysis (CCCma) Coupled General Circulation Model version 3 (CGCM3). Initial conditions for the experiments are taken from long control runs of the models and an instantaneous 5% increase in the solar constant is imposed. The models are subsequently integrated for 50 or 100 years, in parallel with a continuation of the control runs over the same period.

The first issue considered is the estimation of the equilibrium climate sensitivity, which is attained when the model has come into equilibrium with the imposed forcing using relatively short transient model integrations. We follow Boer and Yu (2003a, b) in diagnosing local climate feedbacks in the experiments and separating these feedbacks into components associated with changes in shortwave and longwave radiation, and to atmosphere/surface (clear sky) and cloud changes. The feedbacks are determined for each year of the integration, and the transient evolution and the approach to stable values is evaluated.

In these experiments, the top-of-atmosphere climate forcing can be straightforwardly determined from a knowledge of the net solar flux in the control runs. In experiments with other climate forcing mechanisms (such as a change in the concentrations of well-mixed greenhouse gases or aerosol distributions) diagnosing the forcing is more difficult. Gregory et al. (2004) propose that global-mean climate forcing can be estimated by regressing the top-of-atmosphere radiative change against the change in surface temperature during a transient integration. We will compare the radiative forcing inferred this way with our more direct calculations.

The differences in the feedbacks among the three models are also investigated. The NCAR models have some of the lowest values of global-mean climate sensitivity among the current generation of models. The sensitivity of the CCCma model, although almost twice as large, falls in the middle of the range of model sensitivities considered in Houghton et al. (2001). We compare the clear-sky and cloud feedbacks among the models and examine the pattern of feedbacks in relation to the geographical distribution of the surface warming in each model. An additional experiment with prescribed SST investigates the effect of the structure of the tropical Pacific sea surface temperature warming on the local feedbacks and on global climate sensitivity.

The models employed are described in section 2 and the formalism used to diagnose the climate feedbacks is reviewed in section 3. Section 4 discusses results for global-mean feedbacks and climate sensitivity. Section 5 presents results concerning the geographical distribution of the feedbacks, and section 6 considers results pertaining to the tropical Pacific. Conclusions are summarized in section 7.

2. Models and experiments

The three coupled ocean–atmosphere, global general circulation models used in this study are CSM1, CCSM2, and CGCM3. Detailed descriptions of CSM1 and CCSM2 are given in Boville and Gent (1998) and Kiehl and Gent (2004), respectively. A number of climate change integrations, involving a variety of scenarios, have been documented for versions of the NCAR CSM (Boville and Gent 1998; Meehl et al. 2000; Boville et al. 2001; Dai et al. 2001). The differences in the atmosphere component of CCSM2 and CSM1 include an updated prognostic cloud water scheme (Rasch and Kristjánsson 1998; Zhang et al. 2003), a generalization of the cloud overlap in the radiation code (Collins 2001), and a more accurate formulation of water vapor radiative effects (Collins et al. 2002). Cloud fraction is diagnosed similarly in both model versions based on a generalization of the scheme introduced by Slingo (1987), with variations described in Kiehl et al. (1998) and Rasch and Kristjánsson (1998). The CCSM integrations reported here were performed at the International Pacific Research Center (IPRC) and were begun from initial conditions provided by NCAR from their control runs. The simulations were performed at T31 resolution with 18 levels in the vertical for CSM1 and 26 levels for CCSM2.

The CGCM3 integrations were performed at CCCma and initialized from the control run of that model. Earlier versions of the CCCma coupled global climate model (CGCM1 and CGCM2) and the results of climate change integrations using these model versions are described in Flato et al. (2000) and Boer et al. (2000) and references therein. CGCM3 incorporates a new version of the atmospheric component (AGCM3) as discussed in Scinocca and McFarlane (2004). For the present study CGCM3 was run at T47 horizontal resolution and 32 vertical levels with physics calculations on the 96 × 48 linear grid.

The NCAR CSM1 and CCCma version 1 model (CGCM1) are among the models whose climate sensitivities, based on calculations with mixed layer ocean components, are compared in chapter 9 of Houghton et al. (2001). The equilibrium sensitivities of the models, as measured by the global-mean surface temperature change for a doubling of atmospheric CO2 concentration, is 2.0°C for CSM1 (T42 resolution), which is nearly the smallest of any model considered, and 3.5°C for CGCM1, which is close to both the mean and median of all the model results. The results discussed later in the present paper suggest that this difference in climate sensitivity between the NCAR and CCCma model families persists in the later versions, specifically the NCAR CCSM2 and CCCma CGCM3.

For each of the three models considered here, a control integration and a forced climate change integration from the same initial state are performed. The climate change is forced by an instantaneous 5% increase in the solar constant over that used in the control simulation. For CSM1 and CCSM2 the model integrations extend for 50 years, while for CGCM3 the integrations extend for 100 years.

The global-mean climate forcing due to the 5% solar constant increase is about 12 W m−2 for each of the three models considered. This can be compared to the forcing from a doubling of CO2 concentration, which is typically found to be about 4 W m−2. The solar constant change imposed here thus represents a fairly large perturbation and is chosen to produce a climate change signal that could be diagnosed accurately in the presence of natural variability. Boer et al. (2005) examined the response of the CSM1 to a wide range of increases (2.5%–45%) in the solar constant. They found that the climate sensitivity is only a very weak function of the forcing level up to about 10% increases. Thus conclusions drawn from the 5% perturbation are expected to be applicable as well to either smaller or modestly larger climate forcings.

3. Forcing and feedback

Following Boer and Yu (2003b), the time-averaged column-integrated energy equation is written as
i1520-0442-19-2-193-e1
where R is the top-of-atmosphere (TOA) net downward flux, h is the heat storage in the atmosphere and underlying land or ocean, and A is the convergence of horizontal heat transport in the atmosphere and ocean; X′ = XX0 indicates the difference in the value of a variable between the perturbed X and control X0 simulations. The radiative perturbation R′ is expressed as two terms, namely, a radiative feedback g = (RR*) = ΛT ′, written as linear function of surface temperature change, and a radiative forcing, f = (R*R0), representing the externally imposed perturbation to the radiative balance. Here R* is the radiative flux for the same conditions of atmospheric temperature, pressure, moisture, etc., as for R0 (i.e., as for the control run, but with the incident solar radiation at the TOA increased by 5%).

a. Forcing

The calculation of the radiative forcing in the experiments is straightforward. For R = S + L, the TOA downward shortwave and longwave radiative components, the control run value of S is S0 = (1 − α0)Σ, where Σ is the solar input and α0 the planetary albedo. For a 5% increase in solar constant with other quantities retaining their control run values, S* = 0.05(1 − α0)Σ and L* = L0 so that
i1520-0442-19-2-193-e2
This is the “instantaneous TOA” radiative forcing and can be diagnosed accurately from a knowledge of the net downward TOA solar flux control run, So. Another widely used definition of climate forcing (advocated by the IPCC) is the “adjusted tropopause” forcing, that is, the change in the net downward flux at the tropopause induced by the climate perturbation after allowing the stratospheric temperature to adjust radiatively. The adjusted-tropopause forcing for the present solar constant increase is reduced somewhat over the instantaneous-TOA forcing due to the absorption of the solar beam in the stratosphere. This effect is partly compensated by the increased downward flux at the tropopause due to the warmer adjusted stratosphere. For our solar constant perturbation the fractional difference between climate forcing defined relative to TOA and the adjusted-tropopause value is bounded by the fraction of the solar beam absorbed above the tropopause, which is less than 0.05 (Lacis and Hansen 1974).

The climate forcing f in (2) is obtained straightforwardly from the control-run net solar flux. A comparably accurate determination of the climate forcing in a doubled CO2 experiment would be considerably more complicated. State-of-the-art models can be expected to have planetary albedos (and hence shortwave net radiative fluxes) close to that observed. Thus, the global-mean climate forcing for a change in solar constant should be very similar among models, which is not necessarily the case for other climate perturbations.

The smooth distribution of Σ is modulated by the planetary albedo α0 to give the geographical pattern of S0, and hence of f (not shown). The planetary albedo is generally larger, corresponding to smaller forcing, over land than over oceans. For the three models considered in the present study, the annual-mean, global-mean climate forcing due to the increase in solar constant is between 11.9 and 12.1 W m−2 (see Table 1).

b. Feedback

The radiative response expressed as a linear function of temperature change defines the feedback parameter Λ with
i1520-0442-19-2-193-e3
where all quantities are functions of location and time. The feedback parameter is further decomposed into clear-sky (ΛA) and cloud (ΛC) feedbacks, as well as into shortwave (ΛS) and longwave (ΛL) components, to give the nine components:
i1520-0442-19-2-193-e4
The clear-sky components can be easily computed by using the model’s clear-sky diagnostics of the net longwave and shortwave flux at the TOA.

4. Global-mean feedback and climate sensitivity

Taking the global average (indicated by angular brackets) of (1) gives
i1520-0442-19-2-193-e5
where 〈A′〉 = 0 on the global average and the global feedback parameter Λ̂= 〈ΛT ′〉/〈T ′〉 is a average of the local feedback weighted by the temperature change, with 〈Λ〉 ≠Λ̂. For a system in equilibrium, 〈dh′/dt〉 goes to zero, and the three representations of the globally averaged response of the system are related as
i1520-0442-19-2-193-e6
where ŝ = −1/Λ̂ is the climate sensitivity parameter linking global mean forcing to global-mean temperature response. Senior and Mitchell (2000) and Boer and Yu (2003a) report that, in earlier versions of the Hadley Centre and CCCma models, Λ̂and ŝ are only very slowly varying functions of time as the climate approaches equilibrium after forcing is stabilized at a constant value. In these earlier CCCma model experiments discussed by Boer and Yu (2003a), the variation is on the order of 10%–20% over a 1000-yr simulation. The equilibrium climate sensitivity of models can also depend on the forcing level, as discussed in Boer et al. (2005). Nevertheless, a knowledge of Λ̂ and hence ŝ gives a measure of the global climate sensitivity of a model, which is useful for scaling results, calibrating simpler models, and for comparing the behavior of different models.

Figure 1 displays the time series of annual-mean, global-mean surface air temperature change, 〈T ′〉, and the climate sensitivity, ŝ, for the three models considered here.

In each model the diagnosed climate sensitivity, ŝ, varies rapidly over the first few years but approaches a fairly stable value over the rest of the integration. The horizontal lines in the top panel of Fig. 1 show the values of ŝ based on the average of years 41–50 of the NCAR and CCCmm model integrations. After the first 20 years or so, the diagnosed annual-mean value of the sensitivity is within a few percent of the year 41–50 mean, although there is some indication of a weak increasing trend in the sensitivities. The behavior of the NCAR and CCCma models differ in the first few years, with the diagnosed sensitivity dropping from larger values in the CCCma model but rising over the same period in the NCAR model.

The present study will concentrate on our estimates of the equilibrium climate feedbacks and sensitivity, but the behavior of the climate simulations in the first few years after the switch-on of the solar forcing perturbation may be worthy of additional investigation. The introduction of stratospheric aerosols by major volcanic eruptions produces a rather sudden and widespread climate forcing with a tropospheric effect expected to be somewhat similar to a change in the solar constant. Our results in Fig. 1 suggest that, even with perfect data, the climate sensitivity diagnosed in the way described here from a short-lived transient volcanic forcing event may differ significantly from the equilibrium climate sensitivity.

Figure 2 displays the annual-mean values of Λ̂ and its components as functions of the annual global-mean surface air temperature change relative to the control run. The various components may evolve rapidly during the first few years but settle into a slow drift after about the first decade. The trend with time (or, equivalently, increasing warming) is for the magnitudes of each of the feedbacks to reduce.

The difference in climate sensitivity between the CCCma and NCAR models in Fig. 1 (top panel) is reflected in the differences in the global mean feedback parameter Λ̂ in Fig. 2 (black triangles and dots). The four components of the feedback are also plotted individually. All of the individual feedback components differ only slightly between the two NCAR models (closed and open circles).

The CGCM3 longwave cloud feedback component Λ̂LC (purple triangles) is very similar to those of the NCAR models (correspondingly colored circles) as is the clear-sky shortwave component Λ̂SA (green triangles and circles). However, the CGCM3 longwave clear-sky Λ̂LA (blue triangles) is slightly stronger negative than those of the NCAR models.

The top part of Table 1 gives the global average forcing obtained “directly” from (2) together with the global climate feedback and its components calculated from (5) in the form
i1520-0442-19-2-193-e7
The results are for averages over years 41–50 of the simulations. Results of an additional calculation for CGCM3 using averages over years 91–100 are also given. The difference in the shortwave cloud feedback component Λ̂SC in Table 1 and in Fig. 2 (orange symbols) accounts for most of the difference in net feedback, and hence climate sensitivity, between models.

a. Regression approach

Gregory et al. (2004) propose a method to calculate the anticipated equilibrium global-mean temperature increase, 〈T ′e〉, the global feedback parameter, Λ̂, and the global-mean forcing, 〈f〉, in transient simulations using only the evolving surface temperatures and TOA radiative imbalances. We use the present set of simulations to see how well this method works compared with the “direct” determinations discussed above. Figure 3 plots 〈R′〉 versus 〈T ′〉 (triangles) and the straight lines are obtained by a least squares linear regression:
i1520-0442-19-2-193-e8
Provided the fit is good, we have from (5) that a = Λ̂ and b = 〈f〉. That is, the slope a of the regression line gives the feedback parameter and the y intercept gives the forcing. At equilibrium 〈R′〉 = 〈dh/dt〉 = 0 and the equilibrium temperature change is the x axis intercept with 〈T ′e〉 = −b/a = −〈f〉/Λ̂ = ŝf〉.

All three models show an approximately linear relation between 〈R′〉 and 〈T ′〉 with the exception of the early years of the integrations, which exhibit a positive offset of 〈R′〉 above the best-fit regression line. The cloud 〈RC〉 (stars) components are also plotted. The differences in 〈R′〉 are dominated by the cloud components whereas the clear-sky components are in reasonable agreement among the models. The two NCAR models exhibit negative values of 〈R′〉 of about 6 W m−2, which contrasts with weakly negative values for CGCM3. The differences in 〈RC〉 are reflected in the slopes of the regression lines (the global feedback parameter) and the x axis intercept (the equilibrium temperature change) all of which are measures of climate sensitivity from (6). The regression yields values of 〈T ′e〉 of around 5 K for both NCAR models. For the CGCM3 a larger warming of around 9 K is estimated. Without actually performing much longer runs it is not possible to be certain how accurate these estimates of equilibrium warming are. However, they suggest that the models have realized more than 85% of the estimated equilibrium global-mean warming over the first 50 years of integration.

Table 1 lists the values of the global feedback parameter and the clear-sky and cloud feedback components obtained both directly and by the regression method. The indirectly calculated values of the forcing 〈f〉 of about 9 W m−2 for the NCAR models differ considerably from the direct values of 12 W m−2. This 25% disagreement compares with something less than 7% for the CCCma results. The direct and indirect calculations of each of the individual feedbacks are also much closer for the CCCma model than for the NCAR models. Boer et al. (2005) note that, not surprisingly, the regression approach is not suitable for very large forcing values when the relationship between 〈R′〉 and 〈T ′〉 becomes nonlinear. This motivates us to also show results in Fig. 3 for an experiment with the CSM1 with a 2.5% increase in solar constant (described in Boer et al. 2005). In this case the regression method yields a forcing estimate of 4.6 W m−2 compared to a directly determined value of 6 W m−2, again a difference of about 25%. The result is that the indirect method apparently underestimates the forcing by about one-quarter for the NCAR models. There is considerably better agreement in the two methods for CGCM3.

These results indicate that the Gregory et al. (2004) regression approach may have some practical limitation in its application, at least for some models. It is striking that our analysis shows such a large difference in the behavior among the individual models in this respect. The CCCma model has a radiative imbalance that does scale reasonably linearly with the realized surface warming over the entire experiment. The NCAR models, on the other hand, show a very strong departure from this linear relation during the early years of the experiment. It would be interesting to repeat this analysis for other models and see if a similar range of behavior appears and whether the form of the radiative imbalance-versus-realized warming relation correlates with other aspects of model sensitivity.

5. Geographical pattern of the feedback

The geographical pattern of the feedback is expressed as the local contribution Λl to the global feedback parameter such that Λ̂= 〈Λl〉. From (1)
i1520-0442-19-2-193-e9
The subscript l is omitted in the following discussion. Here we will present annual-mean values of the feedback diagnosed from years 41–50 of each of the simulations. The zonal-mean values of the feedback, [Λ], and its components for CCSM2 and CGCM3 are compared in Fig. 4. A map of the feedback and components for CCSM2 is shown in Fig. 5 and for CGCM3 in Fig. 6. The CSM1 results (not shown) are reasonably similar to those from CCSM2.

Figure 4 shows that the difference in the global-mean total feedback, 〈Λ〉 is attributable mainly to differences in the Tropics and subtropics where the NCAR model’s feedback is much more negative than that of the CCCma model. The meridional variation of three of the four individual components Λ̂SA, Λ̂LA, and Λ̂LC, are quite similar for the two models, but the shortwave cloud feedback Λ̂SC is quite different in the two models, particularly in the latitude belt 30°S–30°N.

To provide objective comparisons of the feedbacks between the models some simple calculations have been performed, starting with the full annual-mean feedback values depicted in Figs. 5 and 6. We decompose a given field, X, into the global mean 〈X〉, the zonal mean of the deviation from the global mean [X]+ = [X] − 〈X〉 and remaining component X* = X − [X] so that X = 〈X〉 + [X]+ + X*. Then, writing the difference between the two models as d = YX with Y = ΛNCAR, X = ΛCCCma for Λ or any of its components, the mean-square difference is 〈d2〉 = 〈d2 + 〈[d]+2〉 + 〈d*2〉 where the terms measure, respectively, the differences in global means, in the meridional structure, and of the remaining geographical pattern. The spatial correlations are
i1520-0442-19-2-193-e10
giving the overall spatial correlation and the correlations of the meridional structures and the remaining geographical patterns with + symbolizing the deviations from the global average. Note that ([X]+)+ = [X]+ and (X*)+ = X*.

For each component of the feedback Table 2 presents the global-mean values and then the mean-square difference and correlation measures of similarity between the models. As noted earlier, the 〈d2 values in Table 2 show that there is good agreement of global-mean values of ΛA and ΛL between the models, but considerable disagreement in ΛS and ΛC, largely ascribable to differences in ΛSC.

Despite the visual impression that the patterns of Λ are broadly similar for the two models shown in Figs. 5 and 6, the objective measures in Table 2 indicate very substantial differences with the overall correlation of Λ between the two models being only 0.06. Interestingly, not only is the spatial correlation of Λ between CCSM2 and CGCM3 small, it is only a modest 0.53 between CCSM2 and CSM1 (not shown). These global spatial measures include area weighting and so discount the visually prominent high-latitude features.

It is the tropical differences in Λ that are most important in determining the global mean, and in the Tropics the differences between models are especially notable in components involving solar cloud feedback. The negative feedback in CCSM2 is associated with an increase in low cloud cover over the oceans in two bands north and south of the equator. By contrast, the CGCM3 shows a slight decrease in cloud cover in this region (not shown).

While the patterns of ΛLC do not agree particularly well, their zonally and globally averaged values are comparatively small. Longwave cloud feedbacks, although differing in detail, all show a distinctive feature of strong positive feedback in the tropical Pacific due to enhanced convection and the associated increase in high cloud cover. This is investigated in section 6.

The objective measures show a much closer agreement between models for the geographical structures of clear-sky components. The change in albedo due to the retreat of snow and sea ice cover is clearly seen in the shortwave component ΛSA. The longwave feedback ΛLA includes a negative contribution due to the increase in IR blackbody emission into space as surface temperature increases and also a positive contribution from water vapor–temperature feedback.

Once established early in the simulation, the geographical pattern of Λ for a particular model is robust and evolves only modestly with time. Figure 7 gives the spatial correlation of the year 41–50 mean Λ with annual (circles) and 10-yr mean (triangles) values over the 50 years of the integration.

The main features of the geographical distribution of Λ have developed by year 10 of the integration and both models exhibit spatial correlations of greater than r = 0.9 for 10-yr mean patterns after the first decade.

6. Feedback in the tropical Pacific

While the local feedback parameter, Λ, is negative over much of the globe, a region of positive feedback stands out in the tropical Pacific in all three model results, although its location and extent differs in each. This feature is largely, but not entirely, attributable to the longwave cloud feedback ΛLC (see Figs. 5 and 6) and is connected to a permanent El Niño–like warming in the models as the global-mean temperature rises. Boer et al. (2004) argue that this region of positive feedback also operates to produce the La Niña–like pattern that is seen in simulations of the Last Glacial Maximum (LGM) with CGCM2 and some other models (in response to a negative climate forcing in this case). In addition to the obvious regional implications for an El Niño–like response in the Pacific (e.g., Meehl 1996), there is the possibility that the mechanism leading to the tropical Pacific positive feedback patch acts to significantly affect the global feedback and increase climate sensitivity. Alternatively, this mechanism may only produce a modification of the feedback pattern without significantly affecting the global average.

The El Niño–like nature of the warming pattern is a consequence of basin-scale equatorial ocean dynamics according to Boer and Yu (2003c) who show, in an earlier version (CGCM1) of the CCCma coupled model, that both the region of positive feedback in the tropical Pacific and the El Niño–like temperature response are absent in a simulation with a mixed layer or thermodynamic-only ocean component. Meehl et al. (2000) examine the surface temperature response in global warming simulations with atmospheric models coupled to a mixed layer ocean to suppress the effects of ocean dynamics; their results suggest that the development of the permanent El Niño–like warming in the tropical Pacific might enhance the global-mean surface warming by 5% and that the El Niño–like warming response in the model was attributed to cloud feedbacks interacting with the radiative forcing. Of course, observations of the interannual variability in the real world show that globally averaged surface temperatures are anomalously warm during an El Niño event (e.g., Nicholls 1992), but the two situations are not necessarily parallel. In particular, Yu and Boer (2002) show that the mean El Niño–like warming pattern in CGCM1 is sustained by oceanic heat transports into the region, while observational results suggest that oceanic heat transports are away from the region in the usual transient El Niño event.

The feedback parameter and the change in surface temperature in the tropical Pacific region are shown in Fig. 8 for all three of the present model warming experiments.

The tropical Pacific region of positive Λ is associated with an El Niño–like SST warming pattern in the central Pacific for CSM1, in the western Pacific for CCSM2, and in the central eastern Pacific for CGCM3. The region of positive feedback is surrounded by comparatively strong negative feedback in the NCAR models, and this serves to localize the temperature maximum in that region. By contrast, the CGCM3 feedback pattern is broader, less localized, and less congruent to the temperature pattern. In all of the models the largest longwave cloud feedback is associated with the greatest changes in surface temperature. Most previous global warming simulations have exhibited a mean El Niño–like warming (e.g., Meehl and Washington 1996; Timmermann et al. 1999; Boer et al. 2000; Cai and Whetton 2000), but there are exceptions with some models simulating a bland tropical SST change pattern (Meehl et al. 2000) or even a La Niña–like pattern (Noda et al. 1999).

Rewriting (1) and then assuming that the change in oceanic heat storage in the Tropics is comparatively small, we obtain
i1520-0442-19-2-193-e11
This highlights the connection to the change in energy convergence, A′, in the atmosphere and ocean. Here R′ = RA + C′, where RA is the cloud-free change in radiative flux and C′ is the change in cloud radiative forcing.

Atmospheric energy transport is closely connected to the the divergent flow in the Tropics (Boer and Sargent 1985; Trenberth et al. 2000). Figure 9 plots the control run 200-hPa divergent wind vectors and associated velocity potential for CCSM2 and CGCM3 together with the change in these quantities for the 5% solar constant increase experiment. The regions of divergence in the control simulations are associated with regions of warm sea surface temperatures and high latent heat release and the flux of energy is toward cold continental and oceanic regions. These patterns are clearly related to the upper-tropospheric components of the Hadley–Walker circulation. The Walker circulation in the equatorial east–west plane over the Pacific is represented by the streamfunction associated with the divergent east–west wind component uD for the equatorial band 5°N–5°S calculated as ψ(p, λ) = ∫p0 uD dp/g. This is plotted for the control runs for CCSM2 and CGCM3 in the top panels of Fig. 10. The bottom panels show the changes in ψ in the perturbed experiments for both models.

Large centers of upper-tropospheric divergence (and lower-tropospheric convergence) in the central and western equatorial Pacific warm pool region are apparent in the control runs of both models. The equatorial eastern Pacific cold tongue is associated with upper-tropospheric convergence. The associated Walker circulation is distinctly stronger in CGCM3 than in CCSM2.

In the perturbed runs the overall strength of the Walker circulation is reduced in CGCM3. In the CCSM2, by contrast, the upper-tropospheric divergence strengthens in the western Pacific warm pool and the Walker circulation is actually slightly enhanced, leading to an increase in convection and high cloud cover in this region. Both models simulate an increased convergence over the Indian Ocean and Southeast Asia, but this feature is again more pronounced in CGCM3.

Much of the geographical structure of the feedback in the tropical Pacific is associated with the longwave cloud component, ΛLC, which is strongly positive in the western Pacific in the CCSM2 simulation (see Fig. 5). To investigate the importance of air–sea interactions in determining the ΛLC distribution, a separate integration with prescribed SSTs was performed. In particular, the CCSM2 model was run with exactly the same 5% increase solar constant but with prescribed SSTs and sea ice concentrations. These were taken from the original 5% perturbation simulation everywhere except in a region of the western Pacific bounded by 8°S–8°N, 140°–220°E. Here the SST was prescribed as the control run value plus a warming field based on the original 5% perturbation model results, but smoothed in this region to suppress zonal gradients in the warming, while retaining the average surface temperature increase over the region.

The longwave cloud feedback parameter ΛLC and the temperature change for the two cases are shown in Fig. 11. The smoothing of the temperature change pattern has a strong influence on ΛLC; the strong positive center in the western Pacific wanes and even becomes slightly negative, consistent with of the results of Boer and Yu (2003c) for a mixed layer ocean. Here, the significant effects are restricted to the region where the smoothing is applied. The signal is not so striking in Λ itself since ΛSC increases and partially counteracts the change in ΛLC (not shown).

From (11) we may approximate the change between the two cases as δR′ ≈ −δA′ ≈ δC′ ≈ δΛ〈T ′〉 so that
i1520-0442-19-2-193-e12
and the change in feedback is approximately connected to a change in transport and cloud forcing.

Despite the difference in Λ in the tropical Pacific in these two experiments the global mean feedback, and hence the climate sensitivity, changes only slightly, from −2.3 W m−2 K−1 in the coupled model case to −2.2 W m−2 K−1 with prescribed smoothed SSTs. This suggests that in the full coupled model the positive feedback associated with the SST maximum is more than balanced by enhanced negative feedback elsewhere. The implication is that the tropical Pacific maximum of feedback and the associated El Niño–like warming pattern has only a fairly small (∼5%) effect on the global-mean climate sensitivity and, moreover, it might actually result in larger negative feedback elsewhere and so lead to reduced climate sensitivity. This contrasts with Meehl et al. (2000) who find that allowing a model to include the permanent El Niño–like response enhances climate sensitivity by ∼5%.

Figure 12 shows the difference in the 100–500-hPa divergent flow and in the Walker circulation for the two cases. The Walker circulation is suppressed in the simulation where the temperature is smoothed. The fully coupled CCSM2 produces a feedback that involves a temperature-gradient-driven regional circulation regime (Lindzen and Nigam 1987) that intensifies the upward vertical motion of the regional Walker circulation. This leads to an increased cloud cover in the western Pacific and to the strong ΛLC feedback in this region. The influences, as already seen in the feedback pattern, are mostly restricted to the region where the smoothing was applied. However, the zonal cell over the central North Pacific, which descends over regions at the west coast of North America and East Asia, shows an enhanced convergence in the eastern part, suggesting some degree of long-range dynamical influence of the suppressed zonal temperature gradients in the tropical Pacific. Accompanying this upper-tropospheric signal is a sea level pressure anomaly over the eastern North Pacific (not shown). This is in agreement with other studies that suggest a close relationship between sea level pressure anomalies in the North Pacific and rainfall and convection anomalies over the tropical western Pacific via dynamical atmospheric teleconnection processes (e.g., Lu 2001; Deser et al. 2004).

7. Summary

The vertically integrated energy budget equation was the basis for the analysis of the climate feedbacks in three contemporary coupled global climate models, two versions of the NCAR CCSM (CSM1 and CCSM2) and the CCCma CGCM3. The models employed are similar in their spatial resolution and basic numerical formulation but differ in the subgrid-scale parameterization of physical processes. Previous experience with the NCAR and CCCma model families suggested that the models span a significant range in total global-mean climate sensitivity, a point confirmed in the present study.

Climate feedbacks are diagnosed by comparing control simulations with climate change simulations forced by a switch-on 5% increase in the solar constant. While solar constant changes are not expected to be important over the next few centuries, the imposed forcing has the virtue that it is straightforward to implement in climate models. Since the forcing depends on the planetary albedo in the control simulation and since most models will have very similar albedos, a change in solar constant will produce global-mean radiative climate forcing of very similar magnitude in models. The geographical pattern of the forcing will also be similar for models that have a realistic distribution of albedo. Finally, the climate forcing may be simply and accurately diagnosed by scaling the net shortwave fluxes in the control run. By contrast, greenhouse gas and albedo driven climate change scenarios may be expected to produce somewhat different radiative forcings in different models and to require special calculations to obtain the forcings.

The experiments analyzed here involve fairly short integrations (50 or 100 years) and the climates are still warming at the end of the simulations. However, we estimated that over 85% of the equilibrium warming has been realized after 50 years of integration. Both the global mean and the geographical pattern of the climate feedback adjust to stable values after about two decades of integration. The values of climate forcing and climate sensitivity obtained directly from the simulations are compared with those deduced indirectly by regressing the global-mean TOA radiative imbalance against global-mean temperature change. The directly calculated global-mean forcing is very nearly the same for all models. The indirect estimate of the forcing compares well with the direct value for CGCM3 but underestimates the forcing by about 25% for both of the NCAR models.

The results presented here reveal that the global-mean behavior of the CCCma and NCAR model families differ in at least three respects. First, the equilibrium climate sensitivity is almost a factor of 2 larger in the CGCM3. Secondly, the adjustment to the shock of the of solar constant increase differs in that the diagnosed sensitivity is initially large in CGCM3 and drops rapidly by the third year, while the opposite occurs (i.e., a rapidly rising diagnosed sensitivity) in both NCAR models. One implication is that the global cooling seen in the transient response to volcanic eruptions may not be directly related to the equilibrium climate sensitivity. Finally, the diagnosed TOA radiative imbalance scales fairly linearly with the realized global-mean surface warming for the CGCM3 but there are substantial departures from this linear relationship in the NCAR models, even in an experiment with fairly modest climate forcing. It would be interesting to compare these aspects of the model behavior in similar experiments in a wide variety of climate models.

The geographical patterns of annual-mean climate feedback in the NCAR and CCCma models appear visually somewhat similar, with negative feedback over most of the globe and regions of positive feedback at high northern latitudes and around Antarctica due to the snow and ice albedo effect. Positive feedback is also found in the tropical Pacific—each model has a tropical Pacific “hot spot” of positive feedback coinciding with a local maximum in surface temperature warming.

Despite the superficial similarity of the feedback patterns in the models, the spatial correlation coefficient between the feedback fields of CCSM2 and CGCM3 is actually quite low. The feedback was decomposed into shortwave and longwave/clear-sky (atmosphere/surface) and cloud components. The mean-square differences and spatial correlations between the models were computed for each component. The clear-sky components have reasonably large correlation coefficients and, indeed, the clear-sky feedback maps look quite similar for the CCCma and NCAR models. The low spatial correlation and large mean-square difference between the total feedback patterns in the models is largely a consequence of a marked difference in the shortwave cloud feedback component in the Tropics and subtropics. The NCAR models have strong negative shortwave cloud feedback over most of the band between 30°S and 30°N due to an increase in low-cloud cover over the oceans in bands north and south of the equator. This contrasts with a slight decrease in cloud cover and a weak positive shortwave cloud feedback in CGCM3. The result is that the NCAR models exhibit stronger negative global-mean feedback than does CGCM3, resulting in a considerably lower climate sensitivity.

All three models display a local maximum in surface warming and a region of positive total feedback in the tropical Pacific region. However, the models differ in the zonal structure of the simulated surface warming, with results ranging from a mean El Niño–like warming in the eastern Pacific in the CGCM3 to a peak warming in the far western Pacific in the CCSM2 model. A separate global warming simulation for the CCSM2 was performed in which the zonal gradients in the temperature response pattern in the tropical Pacific were suppressed. In this simulation the region of positive feedback in the tropical Pacific is absent, but the global-mean negative feedback is about 5% greater than that in standard experiment. The implication is that the coupled atmosphere–ocean processes that lead to the tropical region of positive feedback and the associated SST maximum only modestly influence the global-mean climate sensitivity, and might actually act to slightly reduce the global sensitivity.

Acknowledgments

The authors acknowledge the assistance of Ping Liu and Weijun Zhu with the NCAR model runs. This research was supported by the Japan Agency for Marine-Earth Science and Technology (JAMSTEC) through its sponsorship of the International Pacific Research Center.

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Fig. 1.
Fig. 1.

Global-mean surface air temperature change 〈T ′〉 (K) and climate sensitivity ŝ (W m−2 K−1) for the warming experiments with CGCM3 (dashed lines), CCSM2 (solid lines), and CSM1 (dotted lines). (top) Year 41–50 average of ŝ for CGCM3 and CCSM2 are shown as horizontal lines.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 2.
Fig. 2.

Annual-mean values of the components of the global feedback parameter Λ̂ as function of surface temperature change 〈T ′〉 between the control and 5% solar constant increase simulations. The longwave (L) and shortwave (S) cloud-free atmosphere/surface (A) and cloud (C) feedback components (color coded) are shown for the three models (characterized by different symbols).

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 3.
Fig. 3.

The evolution of the global- and annual-mean radiative flux 〈R′〉 with temperature change 〈T ′〉 for the three models (color-coded triangles). The cloud 〈RC〉 (stars) components are also shown. Open symbols give monthly mean values over the first year of integration. The direct estimate of climate forcing from (2) is marked by the heavy black arrow. The CSM1 result for a 2.5% increase in solar constant is also shown (green triangles).

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 4.
Fig. 4.

The zonally averaged structures of the local feedback parameter Λ and its components (A: clear sky, C: cloud only, S: shortwave, L: longwave) for CCSM2 and CGCM3 (open and filled symbols). Units are W m−2 K−1 and values are calculated from the average of year 41–50 simulation results. Note that the range of all of the diagrams is the same except for ΛSA.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 5.
Fig. 5.

Geographical distribution of the local feedback parameter Λ (W m−2 K−1) and its components (A: clear sky, C: cloud only, S: shortwave, L: longwave) for CCSM2 calculated from the average of year 41–50 simulation results.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 6.
Fig. 6.

As in Fig. 5 but for the CGCM3 results.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 7.
Fig. 7.

The evolution of the spatial pattern of Λ as measured by the spatial correlation with the year 41–50 mean pattern. Filled and open circles are for annual-mean values, and triangles are for 10-yr means for CCSM2 and CGCM3, respectively.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 8.
Fig. 8.

Feedback parameter Λ (shaded in W m−2 K−1) and the change in surface temperatures (contours in K) calculated from the average of years 41–50 of (a) CSM1, (b) CCSM2, and (c) CGCM3 simulation results.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 9.
Fig. 9.

Divergent wind vectors and the corresponding velocity potential for the CCSM2 and CGCM3 models at the 200-hPa level (mean of years 41–50). (top) Control-run values and (bottom) the changes in the 5% solar constant increase simulation. Units are 103 kg m−1 s−1 and 108 kg s−1, respectively.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 10.
Fig. 10.

The mean streamfunction associated with the divergent east–west mass circulation for the years 41–50 of the control runs of CCSM2 and CGCM3. (bottom) The change in the 5% solar constant increase run is shown. Units are 109 kg s−1.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 11.
Fig. 11.

Longwave–cloud feedback parameter ΛLC (shaded, in W m−2 K−1) and the change in surface temperatures (contours, in K) for (a) fully coupled run and (b) the run with prescribed SSTs and sea ice.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Fig. 12.
Fig. 12.

The difference in the divergent wind component in the 100–500-hPa layer and (top) the associated velocity potential that results from specifying smoothed SST in the western equatorial Pacific and (bottom) the corresponding difference in the Walker circulation. Units are 103 kg m−1 s−1 and 108 kg s−1, respectively.

Citation: Journal of Climate 19, 2; 10.1175/JCLI3613.1

Table 1.

The global-mean forcing 〈f〉 (W m−2), the feedback parameter Λ̂, and its atmosphere/surface (clear sky) Λ̂A and cloud Λ̂C components (W m−2 K−1) obtained directly and by the regression method. The direct calculations use averages over years 41–50 or 91–100 as indicated, and for the regression calculation 50 and/or 100 years of data are used.

Table 1.
Table 2.

The global-mean values of the feedback parameter Λ̂ and its components for the averages of years 41–50 for the CCSM2 and CGCM3 (W m−2 K−1). Also given are the mean-square differences and spatial correlations between CCSM2 and CGCM3 results in global means, meridional structure, and of the remaining geographical pattern.

Table 2.
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