Geophysical Research Letters

Climate feedbacks under a very broad range of forcing



[1] An atmospheric general circulation model, coupled to a mixed layer ocean, is subjected to a broad range of forcing away from the current climate between 1/16 to 32 times current CO2 in halving/doubling steps. As climate warms climate sensitivity weakens (although not monotonically), albedo feedback weakens (driving much of the sensitivity weakening), water vapour feedback strengthens (at a rate slightly larger than it would if relative humidity remained unchanged), and lapse rate feedback increases (negatively); this latter change essentially offsetting the water vapour increases. Longwave cloud feedbacks are relatively stable (moderate and positive) across the full range; shortwave cloud feedback remains relatively weak, apart from under the coldest climates. Cloud optical property related components (from total water content, water/ice fraction and cloud thickness) remain remarkably stable. Cloud ‘amount’ feedbacks show the greatest trends: weakening as temperatures increase. Although cloud feedbacks show an overall consistency of features in different latitudes, precise patterns of changes differ substantially for different baseline climates.

1. Introduction

[2] A useful concept over small ranges of climate change is that of ‘climate sensitivity’, whereby the global temperature response is assumed to be linearly related to the radiative forcing [Randall et al., 2007]. This requires important global ‘atmospheric’ feedbacks–due to changes in water vapour, lapse rate, clouds and surface albedo–remain close to constant with temperature. Of course this assumption eventually breaks down as temperatures move far enough from the current climate [e.g., Colman et al., 1997], but it remains unclear how rapidly this occurs, how strong these feedbacks become as forcing becomes large, and even what physical processes play the dominant roles.

[3] These questions are important partly because future greenhouse gas forcing may proceed well past a mere doubling of preindustrial CO2. Although simple models indicate a ‘runaway’ water vapour feedback is not a realistic threat under foreseeable forcing, increased understanding of this and other feedback responses to strong (positive) forcing in General Circulation Models (GCMs) is at least prudent. Cloud feedbacks in particular have been found to vary in models even for relatively modest warming [Senior and Mitchell, 2000], and may eventually become dominant as forcing becomes large [Boer et al., 2003]. On the cooling side, changes under scenarios such as paleoclimates are important as climate change analogues and tests for climate sensitivity, and hence there is a need for understanding feedback behaviour under significant negative as well as positive forcing.

[4] Several studies have traced sensitivity across a broad range of forcing, but few have evaluated the underlying feedbacks. Stouffer and Manabe [2003], considering the response of a coupled GCM to an eight-fold range of CO2 (equation image to 4 times present), noted a decreasing global sensitivity with warming, which they speculated was dominated by weakened albedo feedback [see also Wetherald and Manabe, 1975]. Hansen et al. [2005], investigating GCM sensitivity to successive doubling of CO2 from equation image to 8 times present, found it to lie in a ‘trough’, with increasing values as climate both warms and cools away from the present. They also speculated that this results from albedo feedback strengthening as the climate cools and from water vapour feedback eventually becoming dominant for very warm climates. Boer et al. [2003], applying very strong forcing to a coupled model, through up to 45% solar constant increases, quantified changes in long wave (LW) and short wave (SW) ‘cloud radiative forcing’ derived feedbacks. They found that as temperature increased, LW terms remained relatively constant, whereas the SW ‘cloud’ term became large, eventually resulting in runaway warming. The role of individual feedbacks, such as that of water vapour was not, however, clear in that study, as the cloud forcing approach does not cleanly separate cloud feedback from the others, and the ‘clear sky’ term is a mixture of clear sky water vapour and lapse rate feedbacks, as well as the ‘Planck’ cooling [Soden et al., 2004].

[5] The question, then, of the variation with temperature of the basic ‘atmospheric’ feedbacks for broad forcing away from the current climate remains to be systematically considered. The present study aims to address this, using the powerful ‘perturbed radiative perturbation’ (PRP) technique, which permits the clear delineation of different feedbacks. Although limited to a single GCM it can at least provide us with a benchmark for investigating what physical processes appear important in determining feedback strength, and how these systematically vary across a broad range of climate change.

2. Experiments and Quantification of Climate Feedbacks

2.1. Models and Experiments

[6] The atmospheric model used here is a version of the Australian Bureau of Meteorology Research Centre atmospheric model [Colman et al., 2001] with the addition of mixed phase clouds [Rotstayn et al., 2000] and modified LW and SW optical properties (adopting those of Chou et al. [1998] and Sun and Pethick [2002], respectively). The radiation parameterisation is updated to the Sun Edward Slingo scheme [Sun and Rikus, 1999]. Resolution is triangular wave 47, with 17 levels in the vertical.

[7] The GCM is coupled to a mixed layer ocean, by design removing the complicating effect of feedbacks due to changes in ocean circulation. This allows rapid achievement of large surface temperature changes, and permits comparison of feedbacks defined with respect to a traditionally understood ‘equilibrium climate sensitivity’, but of course ignores the effects of possible ocean circulation changes.

[8] A total factor of 512 change was imposed on the concentration of CO2, with values of 1/16, equation image, …, 8, 16 and 32 × CO2 (with a ‘control’ value of 345 parts per million, ppm). Each factor of 2 represents a close to equal change in climate forcing (see below), with feedbacks evaluated between adjacent pairs of doubling experiments.

2.2. Feedback Analysis

[9] For a small climate perturbation the change to radiation, R, at the top of atmosphere (TOA) at a given location in the model can be written (where the tilde ‘∼’ denotes the vertical profile of a variable):

equation image

where T* is the surface temperature change applied uniformly throughout the atmosphere, Γ the lapse rate, q the specific humidity, C the cloud distribution and α the surface albedo. These radiative perturbations (normalised by the global temperature change) comprise the ‘climate feedbacks’ and are determined by offline running of the radiation code [e.g., Wetherald and Manabe, 1988] on daily archived fields. Details of these ‘PRP’ calculations are given by Colman et al. [2001] and a review of its strengths and weaknesses is given by Bony et al. [2006].

[10] The radiative impact of cloud changes can be very complex and therefore the total cloud feedback is divided here into components due to cloud fraction (i.e., the 3-D cloud distribution) and cloud optical property changes, following the method of Colman et al. [2001]. The optical property change can be divided further into components from total water content of the cloud, CW, the liquid/frozen fraction (or ‘phase’), CP and the in-cloud temperature (related directly to cloud thickness within each layer), CT. Cloud fraction changes are divided into change in total cloud ‘amount’ (CA) (as seen at the TOA) and the vertical distribution of the clouds–denoted as the cloud ‘height’, CH (see Colman et al. [2001] for details). Forcing between each pair of experiments is evaluated as a residual from TOA fluxes after all feedbacks are evaluated, and allowing for stratospheric equilibration. All calculations represent 10 year means.

3. Results and Discussion

[11] The forcing and the global ‘sensitivity’ (defined as global temperature change normalised by the forcing) as a function of temperature are shown in Figure 1. Forcing per doubling increases with CO2 baseline amount (and temperature) from below 4 Wm−2 to over 6 Wm−2 over the forcing range. Values between equation image and 8 × CO2 correspond quite closely to those from Hansen et al. [2005] (their ‘Fa’–equilibrated stratosphere without tropospheric adjustment), although for concentrations below equation image× they are systematically stronger. Global sensitivity does not vary smoothly, but shows a declining trend, being around 40% weaker in the warmest climates than the coldest. There is no compelling evidence for a ‘trough’ centred on current values [cf. Hansen et al., 2005].

Figure 1.

Global mean forcing for a doubling of CO2 (Wm−2) and sensitivity (KW−1m2) as a function of ‘baseline’ CO2 level (taken as the smaller concentration across each forcing ‘step’). Error bars show standard error. Also shown are forcing values taken from Hansen et al. [2005] (note that their ‘control’ CO2 level is specified as 291ppm, cf. 345ppm in the current experiments).

[12] Global SW and LW feedbacks are provided in Figure 2 and the meridional distribution of contributions in Figure 3. Global surface albedo feedback may be anticipated to show strong temperature sensitivity, and indeed declines from around 0.6 Wm−2 K−1 for the coldest temperatures to close to zero for the warmest, with the variation being close to linear over much of the range. This decline makes up much of the trend in sensitivity (see below). The feedback contribution from sea ice changes exceeds that for snow (over land) only at the very coldest temperatures (not shown), and sea ice feedback also declines more rapidly with increasing temperature. The reason is that for the warmer climates, sea ice disappears almost totally, whereas some snowfall persists over land areas, supporting a continued, although weakened, snow albedo feedback. The present result confirms the expectation that albedo feedback declines with decreasing sea ice/snow cover in the baseline climate, however over this range of cooling the albedo feedback at no stage becomes the dominant positive feedback, remaining, for example, weaker than that from water vapour, even at the lowest temperatures. Meridional contributions to the feedback (Figure 3a) steadily encroach equatorward and strengthen in mid latitudes as the climate cools, but with the Arctic north of 70°N showing a more abrupt on/off behaviour. Strengthening of the global albedo feedback occurs not only simply from increased areas of snow and ice, but also from it moving into regions of greater insolation. The relative importance of these two factors can be estimated by a second calculation using radiative perturbations normalised by incoming solar radiation at each point. The insolation effect is insignificant for warmer climates, but increases in importance as climate cools, accounting for ∼30% of the amplification of the albedo feedback increase in the coldest climate, relative to the current.

Figure 2.

Global mean SW and LW feedbacks (Wm−2K−1) as a function of global temperature. (a and b) Water vapour, q, cloud, C, lapse rate, LR, albedo, a, water vapour plus lapse rate, q + LR and the ‘Planck’ response, T* (the last of these referring to the right hand y axis). (c and d) Cloud feedback components from cloud amount and height, CA, CH, water content and phase, CW, CP and cloud thickness, CT. Refer to equation (1) and text for definitions of feedback terms. Error bars show standard errors of the (10 year) means. The dashed line in Figure 2b shows the feedback strength which would occur from water vapour if RH remained unchanged across each forcing step.

Figure 3.

Zonal mean contributions to global feedbacks (Wm−2K−1) for a subset (every second pair) of the forcing steps. (a) Surface albedo, (b) LW water vapour, (c) lapse rate, (d) SW cloud and (e) LW cloud.

[13] The water vapour feedback is shown in Figures 2a and 2b. The SW term is relatively ‘flat’, but the dominant LW strength roughly doubles over the more than 20°C temperature range. The meridional pattern of LW contributions (Figure 3b) shows a disproportionate increase from the relatively cloud free subtropics, particularly for the warmest temperatures. Much of the marked tropical ‘dip’ is from masking by clouds (not shown), which becomes stronger with increased temperature. There is also a substantial increase in the feedback in the extra tropics. Indeed, in the northern hemisphere the absolute increase in water vapour strength is reasonably constant between subtropics and pole, representing a very much larger relative increase compared to the tropics.

[14] Soden and Held [2006] demonstrated that for the current climate, GCM water vapour feedback strength is overall consistent with a close to unchanged relative humidity (RH) (or more precisely, with a small decline in global RH). In the present experiments, global mean RH indeed varies only modestly (by 6% of its mean value overall) with an initial decline with warming, but changing to small increases in the very warmest climates (not shown). The dotted line in Figure 2b shows the feedback expected if RH remained unchanged between the analysed ‘pair’ of climates. Consistent with the discussion above, the bulk of the water vapour feedback can be explained by unchanged RH, but its strength is below that of unchanging RH for cool climates, moving to above it as the climate warms–i.e. RH trends accelerate the rate of change of water vapour feedback with warming.

[15] Global lapse rate feedback also becomes stronger (more negative) as global temperature rises (Figure 2b). Figure 3c shows this to be partly due to increases in positive tropical and subtropical contributions (arising since over much of this region lapse rate remains at close to saturated adiabatic) and partly from decreased negative contributions at high latitudes. These latter contributions arise over cold land/sea ice where temperature inversions are decreasing in strength with warming, particularly in winter [Colman, 2003]. The poleward shift in the crossover between positive and negative contributions in both hemispheres are consistent with a retreat in sea ice and snow cover. For the warmest climates, virtually no negative contributions at all are seen.

[16] Water vapour and lapse rate feedback are known to be related across models in the current climate regime, with a degree of offsetting between the two, in part due to their opposing effects in the tropical upper troposphere [Randall et al., 2007]. The present findings extend this much further, showing virtually no change in the combined feedback across the full range of warming (more than 20K). The importance of the stabilising effect of lapse rate feedback is underscored by the fact that without it, in the warmest climate the feedbacks total around 3.6 Wm−2 K−1, sufficient for runaway warming. The behaviour of the combined water vapour/lapse rate feedback noted here is consistent with Boer et al. [2003], who found almost unchanged (clear sky) combined water vapour/lapse rate/Planck feedback. What is perhaps surprising from the current findings is quite how closely the two feedbacks cancel across such a broad range of forcing when, for example, when lapse rate trends come from differing processes at different latitudes. That issue is to be the subject of further study.

[17] For cloud feedbacks, with the possible exception of SW feedback for the coldest climates, no particularly marked sensitivity to temperature is found (Figures 2a and 2b). LW cloud feedback trends are markedly less than those for water vapour or lapse rate. What variation there is comes from a weak decline in (negative) LW cloud fraction term (Figure 2d), partially offset by a decline in the large (positive) cloud water component. Indeed the decline in the latter (13% drop over the full warming) may be in turn a reflection simply of decreases in high cloud amounts (15% reduction). The net SW cloud feedback (Figure 2a) shows overall decline with temperature, but with considerably more ‘volatility’ apparent. Note, however, it is difficult to attribute significance to the details of the ‘sawtooth’ variation across the middle temperature range as sampling uncertainties (arising from large interannual variability) are as large as the variation between doubling steps,. Again, the cloud water component (Figure 2c) is close to constant across the full forcing range, but now there is a slow decline in the (negative) phase feedback. Given the strongly non-linear dependence of both SW and LW cloud optical properties with cloud water and ice contents [Colman et al., 2001], the weak variation in cloud optical feedbacks over a 25K range in global temperature is striking. Cloud fraction feedback in the SW shows probably the greatest change with temperature for any cloud component: a sustained decline which is responsible for much of the overall decrease in strength in net SW cloud feedback. Note, however, that the SW cloud feedback remains relatively weak, consistently smaller than that from surface albedo in this model, so makes a weaker contribution to the overall decline in sensitivity with temperature.

[18] Meridional contributions to global cloud feedbacks (Figures 3d and 3e) show a great deal of variation in magnitude and pattern, but there are some consistent trends. The strong negative (positive) contributions to SW (LW) feedback at Southern mid-latitudes move systematically poleward as temperatures increase, in line with a poleward migration in storm tracks and associated cloudiness. A similar (although somewhat less clear) trend is seen in the northern hemisphere. The tropics and subtropics show some systematic increase/decrease with temperature for the LW/SW feedbacks, although peaks and troughs of contributions vary considerably. These can be tracked to changes in contributions from cloud fraction, with the individual optical property feedbacks revealing smoother, more consistent trends (not shown).

4. Summary and Conclusions

[19] The present study analyses atmospheric feedbacks over a broad range of climate forcing, viz varying between 1/16 and 32× current CO2. Associated temperature change was 25K. It highlights a number of features about model feedbacks across such a range, some of which has been the subject of speculation in other studies, or has been noted in comparisons between different models for a smaller range in forcing.

[20] 1. Surface albedo feedback decreases close to linearly with increasing temperature, with the term due to sea ice change declining more rapidly with temperature than from snow over land. This is the main source of weakening sensitivity in this model.

[21] 2. Water vapour and lapse rate closely offset one another over the full range of temperature change. Northern extratropical contributions to water vapour feedback (Figure 3b) increase as quickly as those in the tropics. RH changes explain feedback strengthening which is slightly greater than if it remained unchanged. Tropical lapse rate feedback increases rapidly, and high latitude negative contributions weaken, contract poleward, then virtually disappear as the climate warms.

[22] 3. Cloud feedback variations with temperature are modest. Optical property contributions to feedback vary only weakly for both SW/LW. Cloud fraction feedbacks show more sensitivity to temperature, and the SW term in particular systematically weakens with warming. The meridional characteristics of cloud feedbacks show consistent poleward progression in changes associated with northern and southern storm tracks. Tropical and subtropical contributions show gross consistency (e.g. in sign and overall magnitude) and suggestions of an overall trend in magnitude in both SW/LW, but the changes in patterns of the contributions are complex. Despite this complexity, in the global mean only modest trends are seen in net cloud feedback.

[23] The feedbacks will also, of course, depend upon other aspects of the climate, particularly the ocean. Similar analysis would need to be done for fully coupled models to confirm consistency of behaviour or feedbacks across such a large range of forcing. Furthermore, the results are for a single model only. Variation in feedbacks, particularly for clouds, could be significantly different in other models as evidenced by their range in climate sensitivity [e.g., Randall et al., 2007]. However the current study should provide a baseline for comparison for such investigations.


[24] This work was partially supported by the Australian Climate Change Science Program, administered by the Department of Climate Change. The authors thank Zhian Sun for helpful discussion and for performing radiation code and line-by-line comparisons, and Martin Dix, Simon Grainger and an anonymous reviewer for their helpful comments.