a. General

A brief description of the coupled model is given here. For more details, see Manabe et al. (1991). It consists of general circulation models (GCMs) of the atmosphere and oceans, and a land surface model. It is global in scope, with geography as realistic as possible given its resolution. The atmospheric component has nine vertical finite difference levels. The horizontal distributions of predicted variables are represented by spherical harmonics (15 associated Legendre functions for each of 15 Fourier components) and by gridpoint values (Gordon and Stern 1982), which have a spacing of approximately 4.5° latitude by 7.5° longitude. A simple land surface model is used to compute surface fluxes of heat and water (Manabe 1969). Insolation varies seasonally, but not diurnally. Cloud cover is predicted based on relative humidity.

The finite-difference oceanic component, with a horizontal resolution of approximately 4.5° latitude by 3.75° longitude and 12 vertical levels, uses the Modular Ocean Model (MOM) code described in Pacanowski et al. (1991). This particular version of MOM is based, in turn, on a model described by Bryan and Lewis (1979). In addition to horizontal and vertical background subgrid-scale mixing, the model has isopycnal mixing as discussed by Redi (1982) and Tziperman and Bryan (1993). Convection occurs whenever the vertical stratification becomes unstable. Sea ice is predicted using a free drift model developed by Bryan (1969). It computes sea ice thickness from a thermodynamic heat balance and the advection of ice by ocean currents. The atmospheric and oceanic components of the model interact with each other once each day through the exchange of heat, water, and momentum. Because of the model's coarse resolution, it is necessary to impose flux adjustments of heat and water at the air–sea interface to maintain the model in a realistic mean state. Though these adjustments do not eliminate the model's shortcomings (Marotzke and Stone 1995), they do not change from one year to the next and are independent of the sea surface temperature and salinity anomalies that develop during the integration.

b. Surface albedo parameterization

Because the subject of this article is SAF, a description of the model's surface albedo parameterization is given. Even if it were incorporated into perfect models of the atmosphere, ocean, and land, this parameterization would not produce perfectly realistic surface albedo variations because it does not include every possible effect of variations in surface properties on local surface albedo. Its aim instead is to simulate in an easily interpretable way the average relative brightnesses of open ocean, bare land, snow, sea ice, and ice sheets.

Over ice-free ocean regions, surface albedo is prescribed as a function of latitude. Over ice-covered ocean regions, surface albedo is parameterized as a function of ice thickness and surface temperature. Figure 1a illustrates this dependence for a typical ocean point with an an ice-free albedo of 10%. Surface albedo increases with increasing ice thickness and decreasing surface temperature from the ice-free value to a maximum value of 80% for ice thicknesses greater than 1 m and temperatures lower than −10°C. Between 0 and 1 m, the dependence on ice thickness has a parabolic form. The temperature dependence in the −10°–0°C range is linear and is intended to reproduce the albedo effects of meltwater on top of the ice as well as the fact that colder ice is more likely to be covered with highly reflective snow than warmer ice (Grenfell and Perovich 1984; Allison et al. 1993; Barry 1996; Massom et al. 2001). Above 0°C, there is no temperature dependence.

Over land, the influence of snow on surface albedo is treated in a similar way to the influence of ice in the ocean. Over snow-free areas, surface albedo is prescribed according to vegetation cover and land surface type. (The impact of vegetation anomalies on surface albedo is not included in the model.) Over snow-covered land regions, surface albedo is parameterized as a function of snow depth and surface temperature. Figure 1b illustrates this dependence for a typical land point with a snow-free albedo of 20%. Surface albedo increases with increasing snow depth and decreasing surface temperature from the snow-free value to a maximum value of 60% for snow depths greater than 2 cm (water equivalent) and temperatures lower than −10°C. Between 0 and 2 cm, the dependence on snow depth has a parabolic form. The linear dependence on temperature in the −10°–0°C range is intended to take into account the fact that wet snow, more common at higher temperatures, typically has a lower albedo than completely frozen snow (Wiscombe and Warren 1980). Above 0°C, there is no temperature dependence. The model does not contain any glacial dynamics. Instead, the Greenland and Antarctic ice sheets are prescribed. However, fresh snow is allowed to accumulate on the ice sheets, and surface albedo is allowed to vary with snow depth and surface temperature in a manner similar to other land points, albeit with a much higher snow-free value (55%) and a much higher maximum value (80%) for snow depths greater than 2 cm and temperatures below −10°C (Fig. 1c). This is meant to take into account the albedo effects of fresh snow and melting on top of the glacier, such as those observed by Stroeve et al. (1997).

Comparing Figs. 1a,b, simulated sea ice is generally more reflective of sunshine than snow on land. For example, below −10°C, thick sea ice, presumably snow covered at these low temperatures, has an albedo of 80%. Deep snow on land in the same temperature range has a smaller albedo—60%. Though deep fresh snow on a flat unvegetated land surface has a similar albedo to snow-covered ice, the maximum albedo of snow-covered land regions is deliberately set to a lower value because relatively dark vegetation sometimes rises above the top of the snowpack in the real climate, particularly in heavily forested regions, reducing typical surface albedos of snow-covered land areas (see, e.g., Robock 1980).

a. SAF

The left column in Fig. 2 shows the quasi-equilibrium SAT increase that takes place as a result of CO₂ doubling in the VA experiment. The geographical and seasonal distribution of the warming is a familiar one (see e.g., Manabe and Stouffer 1980). There is significantly more warming in high latitudes during all seasons, with the largest polar amplification seen during fall and winter in both hemispheres. The high-latitude warming is smallest during summertime in both hemispheres, with spring lying between these two extremes. SAF plays a significant role in generating the poleward amplification pattern seen in the left column in Fig. 2. This is apparent by examining the SAT increase that takes place as a result of CO₂ doubling in the FA experiment (Fig. 2, right column). When SAF is suppressed, the warming in high latitudes is drastically reduced, with little poleward amplification seen during summer and spring in either hemisphere.

The effect of SAF may be quantified by examining the VA/FA ratio of the CO₂-induced warming (dashed lines, Fig. 3). There is about twice as much warming near the SH sea ice zone in the VA experiment during all seasons. The SAF amplification decreases poleward of the ice margin to about 50% over Antarctica. It also decreases equatorward to values of about 20% in the Tropics. In the NH during winter, spring, and fall, the amplification rises gradually from 20% at about 30°N to more than 70% at the pole. During NH summer, an amplification of about 60% is more concentrated over the Arctic.

Consistent with a strong positive SAF, the climate in the VA experiment with doubled CO₂ has markedly less snow and ice, increasing the net incoming insolation in the mid- to high latitudes of both hemispheres (Fig. 4). In the NH, the reduction in snow over land rather than the reduction in sea ice contributes most to the change in incoming shortwave during winter and fall. During spring, the reduction in snow and ice contribute about equally, while in summer, a reduction in Arctic sea ice is responsible for most of the increase in shortwave radiation, snow cover being negligible at this time of year except over the Greenland ice sheet. In the SH, the increase in shortwave radiation can be traced almost exclusively to a reduction in sea ice, with a slight change in the albedo of the Antarctic ice sheet making a small contribution during SH summer.

With the exception of September–October–November (SON, hereafter all 3-month units will be denoted by an acronym composed of the first letter of each respective month), the peak warming ratios of Fig. 3 are larger in the SH than the NH. This is probably due partly to the fact that snow albedo feedback plays a large role in the overall NH SAF, whereas the SH SAF is overwhelmingly dominated by sea ice reductions. Since the albedo contrast between sea ice and open ocean is greater than the the albedo contrast between snow and bare land (Fig. 1), the effect of SAF is somewhat larger in the SH.

It is clear from Figs. 3 and 4 that the effects of SAF are largest in the areas where the surface albedo changes as a result of CO₂ doubling in the VA experiment. The sea ice reduction is responsible for nearly all the change in incoming insolation in the SH, and the largest ratios in the SH are seen in the sea ice zone. Similarly, in the NH, the large effect of the decrease in snow cover during SON, DJF, and MAM is seen in large warming ratios in the mid- to high latitude areas where snow is found during these seasons. When snow disappears in NH summer, the largest ratios become confined to the Arctic, where a large decrease in sea ice albedo takes place.

Also significant is the extent to which large effects of SAF are seen in Fig. 3 outside the areas where surface albedo changes. There is about 50% more warming in Antarctica in all seasons, in spite of the fact that the albedo of the Antarctic ice sheet hardly changes even in summer (Fig. 4); more than 2°C of the annual-mean SAT increase simulated over Antarctica in the VA model is attributable to SAF. There is also about 20% more warming in the deep Tropics during all seasons in the VA model, in spite of the total absence of any CO₂-induced change in surface albedo in the VA model in this region. This corresponds to a warming difference of about 0.5°C (see Fig. 5). The warming attributable to SAF in areas outside the regions directly affected by it must occur because atmospheric and possibly oceanic motion diffuse the heat anomaly away from the sea ice and snow zone. A detailed analysis of this effect is beyond the scope of this paper. However, evidence of it can also be seen in other modeling studies. Ingram et al. (1989) noticed that the Tropics warm less in climate change modeling experiments where sea ice extent is prescribed, and Broccoli (2000) quantified the simulated impact of the NH ice sheets of the last glacial maximum on tropical SSTs.

b. Ice thickness feedback

The seasonal distribution of the CO₂-induced warming in areas covered by sea ice in the VA model (Fig. 2, left column) does not match the seasonal distribution of the increased solar radiation at the surface (Fig. 4). The Arctic warming is largest in NH fall and winter, when sunshine is weakest, and the CO₂-induced change in incoming solar radiation due to sea ice reduction is minuscule. Similarly, the warming in the Southern Ocean is largest in SH fall and winter, also when the least increase in incoming solar radiation due to sea ice albedo feedback occurs.

Analyzing an atmospheric model similar to the present one coupled to a mixed layer model of the ocean, Manabe and Stouffer (1980) highlighted the importance of the CO₂-induced change in sea ice thickness in modulating the seasonal distribution of climate change. Robock (1983), analyzing an energy balance model, also highlighted the importance of this “ice thickness feedback.” The CO₂ increase, the humidity increase, and the decrease in surface albedo all act to increase the downward radiative fluxes at the surface throughout the year. However, during icemelt season (spring and summer), almost all of this additional energy goes into melting more ice, with a relatively small effect on surface temperature. The loss of sea ice in spring and summer then leads to significantly thinner ice throughout the icepack when it grows again in fall and winter. This facilitates more sensible heat transfer from the warm ocean to the frigid atmosphere during fall and winter, generating a large increase in SAT. The sensible heat increase is very effective in generating warming near the surface during fall and winter because the polar atmosphere is so stratified during these seasons, so that all of the effects of the sensible heat flux change are concentrated in the lowest layers of the atmosphere.

Because the FA climate change experiment lacks SAF, much of the seasonal variation in the quasi-equilibrium warming seen in this experiment can be attributed to the ice thickness feedback alone. Comparing the left and right columns in Fig. 2, the seasonal variations in the positions of the warming maxima in areas covered by sea ice are very similar in the FA model. Thus the conclusion of Robock (1983), based on an energy-balance model, that ice thickness feedback is the main determinant of the seasonal distribution of warming in sea ice–covered regions even when SAF is present, is supported by this study using full-blown general circulation models of the atmosphere and ocean.

In winter and fall of both hemispheres, there is a large degree of polar amplification of the climate change signal in the experiment without SAF, with nearly 3 times as much warming in high latitudes than in the Tropics. However, on an annual-mean basis, polar amplification in the FA model is much smaller, being hardly detectable in the SH, and somewhat apparent in the NH (Fig. 5). In the VA model, on the other hand, the annual-mean polar amplification is dramatic, with nearly twice as much warming in the SH high latitudes as in the Tropics, and more than twice as much warming in the NH high latitudes. This indicates that to a first-order, SAF is the reason more warming generally occurs at high latitudes, with ice thickness feedback being the mechanism determining how this additional warming is distributed seasonally. This is reasonable, since SAF actually increases the solar energy absorbed in high latitudes, while ice thickness feedback is a nonradiative feedback that mainly redistributes energy within the system.

a. Direct effect of SAF on SAT anomalies

The solid lines in Fig. 3 show the VA/FA ratio of zonal-mean standard deviation of seasonal-mean local SAT in the internal variability experiments for all four seasons. This metric provides a quantitative assessment of the impact of SAF on the typical magnitudes of SAT anomalies at the smallest scale resolved by the model. If the ratios are much larger than one, SAF significantly amplifies local internal variability. In the NH, SAF seems to have little effect on internal variability, with the ratios being close to one for all seasons except spring. Approximately 15% more springtime SAT variability occurs in the extratropics in the experiment with SAF. This amplification can be traced entirely to the continents. In the SH, the effect of SAF is visible during all seasons and is especially pronounced near the sea ice margin, where there is typically a 20% enhancement of local SAT variability. Comparing the solid and dashed lines in Fig. 3, the relatively weak effect of SAF on local internal variability contrasts starkly with the large effect of SAF on climate change at all latitudes during all seasons. Also significant is the large influence of SAF on the externally forced SAT anomaly in the Arctic. This NH sea ice albedo feedback is largely absent in the internal variability case. SAF only amplifies local internally generated NH SAT variability significantly through snow albedo feedback in the spring.

The main reason for the larger effect of SAF on climate change is the differing geographical structures of internally generated and externally forced climate variations. While the externally forced SAT anomaly has the same sign everywhere, internal SAT variations are not nearly so geographically coherent. In the NH extratropics, for example, the typical correlations between local internal SAT variations and SAT variations averaged over the extratropics are quite small for all seasons (Table 1), never rising above 0.25. The typical correlations between local SAT variations and SAT variations averaged over the extratropics poleward of 30°S are similarly small in the SH. This implies that the local SAT variations in the regions of both hemispheres potentially most affected by SAF typically have a spatial scale much smaller than the two extratropical zones poleward of 30°N–30°S. These relatively small-scale anomalies are therefore damped by horizontal heat exchange with surrounding regions as well as radiative fluxes at the top of the atmosphere. This horizontal damping dilutes the effects of radiative damping processes such as SAF on local internal SAT variations, and reduces the impact of eliminating SAF in the FA experiment. When the smaller-scale internal SAT anomalies most affected by horizontal damping are eliminated by averaging SAT over the entire extratropics, the effect of SAF increases substantially (cf. the left two bars in each panel in Fig. 6). This is particularly true in the NH during MAM, and in the SH during all seasons. This confirms that horizontal damping is partially responsible for the small impact of SAF on local internal SAT variability seen in Fig. 3.

The effect of SAF on internal extratropical-mean variations is still not as large as its effect on the CO₂-induced SAT anomaly during any season (cf. the right two bars in each panel in Fig. 6), despite the fact that some horizontal damping effects are eliminated by averaging the internal SAT variations over the extratropics. This difference occurs because horizontal damping of extratropical-mean SAT anomalies is still possible through heat exchange with the Tropics across 30° and 30°S. This effect is likely to be more significant in the case of internal variability than externally forced climate change, as internal tropical temperature anomalies are not necessarily correlated with their extratropical counterparts, whereas the CO₂-induced warming occurs at all latitudes.

The effect of SAF on local internal variability may also be smaller than its effect on externally forced climate change partly because of the ice thickness feedback discussed in section 4b. It has been noted before that the apparent impact of a positive feedback mechanism is amplified by the presence of another positive feedback (Hall and Manabe 1999; Robock 1983). The presence of this positive ice thickness feedback enhances the apparent impact of SAF in the CO₂-doubling context. On the other hand, the ice thickness feedback is weak in the internal variability case because internally generated SAT variations are not as large as the warming due to a doubling of CO₂ and are associated with correspondingly smaller changes in ice thickness. The sensible heat flux through the ice is proportional to the reciprocal of the ice thickness, so that small perturbations in ice thickness result in proportionately smaller perturbations to sensible heat flux than the sensible heat flux increase caused by a large reduction in ice thickness. There is therefore little enhancement of the apparent impact of SAF on internal variability due to the ice thickness feedback.

b. Strength of SAF in isolation from other damping mechanisms

While the final impact of SAF on internally generated SAT anomalies is attenuated mainly because it is diluted by horizontal damping, it is possible that the radiative effects of SAF are similar in the internal variability and CO₂-doubling contexts, even if the final impact of the feedback on SAT anomalies is different when combined with other damping processes. To examine the strength of SAF in isolation, the classic climate sensitivity framework relating changes in climate variables to changes in outgoing longwave and incoming shortwave radiation is used (see, e.g., Cess and Potter 1988). According to this framework, the strength of radiative feedbacks can be quantified in terms of a climate sensitivity parameter λ:

View Expanded

where F is the outgoing longwave radiation, T_s is the SAT, and Q is the net incoming shortwave radiation. The subject of this paper being SAF, we focus here on the SAF contribution to dQ/dT_s:

View Expanded

where (∂Q/∂T_s)_SAF is the variation in net incoming shortwave radiation with SAT due to surface albedo changes and α_s is the surface albedo. The partial derivative ∂Q/∂α_s is simply the variation in net incoming solar radiation with surface albedo. This is determined by cloud and incoming solar radiation fields. Of course, clouds will vary in association with internally generated and externally forced climate anomalies, so that ∂Q/∂α_s may not be exactly constant. How long-term variations in cloudiness may indirectly modulate SAF is an interesting and complex topic for future research, but is beyond the scope of this paper. Instead, the focus here is on the process most central to SAF itself: the relationship between surface albedo and SAT [i.e., the dα_s/dT_s term of Eq. (2)]. In the internal variability case, this relationship may be diagnosed by regressing surface albedo onto SAT in the VA model (Fig. 7, gray bars). In the sensitivity case, this relationship may be diagnosed by dividing the VA model's CO₂-induced change in surface albedo by the CO₂-induced change in SAT (Fig. 7, black bars). It is customary in this type of feedback analysis to analyze global-mean quantities. However, NH and SH extratropical means are first analyzed in this study to reveal potentially meaningful differences between the behavior of SAF in the two hemispheres.

In the SH, systematically smaller changes in surface albedo occur on a per degree celsius basis in the CO₂-doubling case during all seasons. This is due to the ice thickness feedback, which increases the SAT anomaly associated with a given change in surface albedo stemming from a sea ice reduction. As noted above, this feedback is strong for the CO₂-induced anomaly, but weak for internal variations. Unfortunately the ice thickness feedback contaminates the relationship between surface albedo and SAT in the climate change context. Since SAF in the SH is overwhelmingly controlled by changes in sea ice (Fig. 4), this makes it very difficult to quantify SH SAF in the climate change context by examining a time series dominated by internal variability.

At times of year when sea ice rather than snow variations are the main factor behind SAF in the NH, SAF also behaves very differently in the sensitivity and variability contexts, though for different reasons than in the SH. In the sensitivity context, large reductions in Arctic sea ice thickness are the most important factor behind SAF in the NH during JJA, when snow practically disappears as a result of the CO₂ increase (Fig. 4). On the other hand, internal Arctic SAT variations are relatively small during JJA and to the extent that they do affect underlying ice thickness, they do not do so enough to cause substantial changes in the surface albedo. An examination of the standard deviation of JJA surface albedo in the VA internal variability experiment (not shown) reveals that most of the very small amount of surface albedo variability in the NH occurring at this time of year takes place over the Greenland ice sheet. Here the melting snow on top of the glacier causes surface albedo excursions depending on its depth and temperature (see bottom panel in Fig. 1). Since Greenland accounts for a very small portion of the total area of the NH extra-tropics, this explains why minuscule surface albedo changes are associated with a 1°C internal SAT anomaly (Fig. 7, top panel), while a relatively large surface albedo change per degree celsius warming occurs in the CO₂ doubling context.

Why do NH summertime internal SAT anomalies lead to such small sea ice albedo anomalies in the Arctic, while their SH counterparts are associated with large sea ice albedo excursions? (For example, compare the internal variability surface albedo–SAT relationships during NH and SH summer, i.e., the JJA gray bar in the top panel of Fig. 7 to the DJF gray bar in the bottom panel of the figure). The NH sea ice is largely hemmed in by the boundaries of the Arctic basin, while the boundary of SH ice is not constrained by land at any longitude. The thickness of the ice at the SH ice margin is therefore much thinner than the ice at the northern edges of the North American and Eurasian continents. So internal SAT anomalies in the SH can much more easily affect the areal extent of the SH icepack and hence the overall albedo of the SH extratropics by melting or forming small amounts of ice at the SH ice margin. In the NH, free variations in ice extent at all longitudes are not possible until the climate warms enough to retract the ice margin from the Arctic basin perimeter. This is rare in the unperturbed climate, even during summertime. In SON, DJF, and MAM, the internal sea ice albedo variability also makes a small contribution to the overall NH surface albedo variability, most of which is produced by variations in snow amount. The reason again is that the icepack boundary in the NH is constrained at most longitudes to the boundaries of the Arctic basin. This accounts for the minuscule impact of sea ice albedo feedback on internal Arctic SAT variability during all seasons (Fig. 3).

While the SAF resulting from sea ice clearly behaves differently in the sensitivity and variability contexts in both hemispheres, SAF resulting from snow on land behaves similarly. Suggestions of this can be seen in the surface albedo–SAT relationship when snow on land is the main contributor to SAF (SON, DJF, and MAM in the NH, according to Fig. 4). During these seasons, much closer agreement between the internal variability and CO₂ doubling cases is seen in the surface albedo–SAT relationships. However, this cannot be considered definitive evidence because some SAF due to sea ice occurs during these seasons in the CO₂-doubling context (Fig. 4). Moreover, though the area of the Arctic is small compared to the entire extratropics, most of the Arctic SAT increase seen in fall, winter, and spring in the VA CO₂ doubling experiment (Fig. 2, left column) is a result of thinner ice during these seasons, which in turn results from strong surface albedo feedback and melting during summer, as discussed in section 4b. The SAT data used to calculate the black bars in the top panel in Fig. 7 is therefore somewhat contaminated by ice thickness feedback effects even during SON, DJF, and MAM, when SAF due to sea ice is relatively weak (Fig. 4).

To test the idea that SAF due to snow might behave in the same way in internal variability and external forcing contexts, the surface albedo–SAT relationship is examined in NH snow-covered regions only (Fig. 8, top panel). The CO₂-doubling case is discussed first (black bars). A 1°C warming anomaly over snow-covered areas is associated with the smallest surface albedo reduction during fall and winter, a somewhat larger reduction during spring, and the largest reduction during summer.

The seasonal dependence of the surface albedo–SAT relationship is similar to the seasonal dependence of the snow depth–SAT relationship (Fig. 8, bottom panel). The same 1°C warming is associated with the smallest snow depth reduction during fall and winter, a somewhat larger snow depth reduction during spring, and the largest snow depth reduction during summer. The seasonal dependence of the snow depth–SAT relationship is likely traceable to the fact that accumulation is the dominant factor affecting the size of the snowpack during fall and winter, while melting is the dominant factor affecting its size during spring. In winter and fall, the warming reduces snow mostly because the line between rain and snow moves poleward, whereas in spring, warm temperatures are associated with less snow mostly because more of the snowpack melts. A 1°C warm SAT anomaly during spring produces more snowmelt than a 1°C warm SAT anomaly during fall and winter reduces snow accumulation because in spring temperatures are high enough that the increased melting affects much of the snowpack. In fall and winter, on the other hand, the poleward retreat of the rain/snow line only reduces snow accumulation at the snow margin. The only snow found in the NH during summer in the model is on the Greenland ice sheet. The values shown in Fig. 8 for JJA therefore pertain exclusively to the dynamics of the summertime snow budget over Greenland. The warming has a very large effect on snow depth and surface albedo here because the mean summertime SATs hover very close to freezing all over the ice sheet, so that the warming causes both snowmelt and a reduction in the precipitation falling as snow rather than rain.

The relationship in NH snow-covered areas between internally generated SAT anomalies and anomalies of surface albedo and snow depth (Fig. 8, gray bars) shows precisely the same seasonal dependence as the relationships in the context of external forcing (black bars), suggesting identical mechanisms are at work in determining the SAT, surface albedo, and snow depth relationships in the two cases. Moreover, the magnitudes of the surface albedo and snow depth anomalies associated with a 1°C SAT anomaly are in reasonably close agreement for all seasons whether the anomaly is externally forced or internally generated. Identical analyses to that shown in Fig. 8, but for the Eurasian and North American snowpack separately (not shown), give very similar results. This indicates that the simulated snow albedo feedback operates in much the same way in the internal variability and CO₂-doubling contexts.

a. Measuring sea ice albedo feedback in the SH

In section 5 it was demonstrated that in the SH, SAF behaves very differently in the internal variability and CO₂-doubling contexts. How then to extract information about SH SAF in the context of equilibrium climate sensitivity from a time series such as the scenario run or the observed record that contains both internal variability and a transient response to external forcing? It is clear from Fig. 9 that toward the beginning of the scenario run, the SAT and surface albedo variability in both hemispheres is mostly internally generated, whereas by the end of the experiment most of the variations can be traced to external forcing. So is there a point in the scenario run when the signatures of external forcing become strong enough that they dominate the SH SAF statistics? If so, is the climate in close enough equilibrium with the external forcing that the SAF statistics resemble those of equilibrium climate change?

Addressing these questions allows an assessment of the practicality of extracting information about SAF's contribution to SH climate sensitivity from the observed record. This is done by examining the evolution of the regression of SH surface albedo onto SH SAT over the course of the scenario run (Fig. 10). This statistic changes in a similar way for all seasons. When the regression calculation is based on data from the beginning of the scenario run, it matches reasonably well the regression for pure internal variability measured in the VA internal variability experiment. This holds true as long as no scenario run data are used past about 1970. Internal climate variations therefore dominate the regression statistic well into the latter part of the twentieth century despite the fact that the external forcing over the entire twentieth century is significant. The signatures of external forcing take so long to emerge in the SH because of the slow response time scale of the SH climate system. This slow response time has been noted in numerous transient climate change experiments (e.g., Manabe et al. 1991; Dai et al. 2001), and is due to the deep convection in the Southern Ocean, which results in a large effective thermal inertia in this region.

As 100-yr segments ending beyond 1970 are used, the regression rises slowly for all seasons. During JJA and SON, it reaches the value characteristic of equilibrium climate change when the regression calculation is based on data for 100-yr segments ending beyond about 2030. During DJF and MAM, it overshoots its 2 × CO₂ value, peaking for 100-yr segments ending in the early to mid-twenty-first century. Then it slowly decreases so that when the calculation is based on a 100-yr segment ending in 2094, the regression is reasonably close to the 2 × CO₂ value. The regression overshoots because much of the SH extratropical atmosphere during the early twenty-first century has warmed somewhat in response to the external forcing. However, the Southern Ocean, being the component of the climate system with the most thermal inertia, still has not warmed much and the Southern Ocean's sea ice has decreased by a correspondingly small amount (see Fig. 9). When the small surface albedo change is regressed onto the relatively large SAT change, the result is a value closer to zero than the 2 × CO₂ value. Eventually the Southern Ocean equilibrates with the overlying atmosphere, sea ice retreats, and the surface albedo–SAT statistics begin to resemble those of equilibrium sensitivity.

Based on this analysis in Fig. 10, it is likely impossible to estimate SH SAF by examining the observed climate record until well into the twenty-first century because SH climate takes decades to respond to external forcing. The signatures of internal variability and the transient response to the external forcing contaminate the SAF statistics during some seasons until nearly the end of the twenty-first century.

b. Measuring snow albedo feedback in the NH

In section 5 it was demonstrated that in the NH, the SAF due to snow on land behaves very similarly in the internal variability and CO₂-doubling contexts. In this section, it is shown that this similarity, together with the high degree of thermodynamic equilibrium of NH continental climate with external forcing, can be exploited to extract information about equilibrium climate sensitivity from a time series such as the scenario run or the observed record that contains both internal variability and a transient response to external forcing.

Figure 11 shows scatterplots of seasonal-mean surface albedo versus seasonal-mean SAT for NH snow-covered regions. During each season, the two variables are tightly correlated, falling on a fairly straight line. Moreover, the overall slope in each panel agrees nearly perfectly with the equilibrium relationship between surface albedo and SAT in the CO₂-doubling context. This suggests the NH climate over snow-covered land areas in a high degree of thermodynamic equilibrium with the external forcing throughout the scenario run.

The surface albedo–SAT regression agrees with the 2 × CO₂ value regardless of the time period—and mix of internal variability and externally forced variation—of the scenario run chosen. The cluster of points toward the upper left of each panel corresponds mostly to data from the first century and a half of the scenario run, when external forcing is weak and internal variations dominate the variability. The rest of the points derive principally from the rest of the experiment, when external forcing is large. The slopes of these two collections of points agree very well during every season, consistent with the fact that the simulated behavior of SAF in NH snow-covered land areas is the same in the internal variability and CO₂-doubling contexts.

Even if snow albedo feedback behaved very differently in the internal variability and CO₂-doubling contexts, external forcing in a region in thermodynamic equilibrium with it would dominate the statistics as soon as the externally forced anomaly becomes larger than the internal variability. In the case of snow albedo feedback, however, the signatures of internal variability do little to contaminate the surface albedo–SAT relationship, so that it is not necessary to wait until the externally forced anomaly becomes larger than internal variability. This raises the possibility that the present-day climate record may be adequate to achieve a statistically significant estimate of the real climate's SAF in the equilibrium climate sensitivity context. The satellite record of snow cover extends back to 1967, during which time a decrease in NH snow cover has been observed (Robinson 1997, 1999). Figure 12 demonstrates that this time series is likely to be more than long enough to measure the SAF in the climate sensitivity context, assuming it is possible to estimate both surface albedo and SAT using the satellite data. As more and more of the scenario run data going back in time from 2003 are used to calculate the regression between surface albedo and SAT over snow-covered areas, the regression converges reasonably well to the 2 × CO₂ value for all seasons once data from the early 1980s is included.