Simulations by the Community Atmosphere Model (CAM) and 15 other climate models suggest that climate sensitivity is linked to continental middle to high latitude present-day springtime albedo. We compare 1 × CO2 and 2 × CO2 CAM simulations against similar simulations with snow cover fraction purposely increased. Greater snow cover fraction leads to higher albedo and lower temperatures at 1 × CO2 but has less influence at 2 × CO2 when little snow remains due to global warming. This makes the simulation with higher albedo at 1 × CO2 more sensitive to increased CO2, in agreement with past work. We show that the wide variation in simulated snow-albedo feedbacks and climate sensitivities among 15 other models correlates well with variations in the continental middle to high latitude present-day springtime albedo, in agreement with our CAM results. The development of more accurate snow and albedo parameterizations should improve model estimates of climate sensitivity.
 A large portion of Earth's continental surfaces is covered by snow on a seasonal basis. Snow-covered surfaces have shortwave all-sky albedos that often exceed 0.7, while snow-free values rarely exceed 0.3. This large difference in surface albedo activates a positive feedback known as the snow-albedo feedback (SAF), which acts in both the seasonal context and the climate change context. In this feedback, warmer temperatures melt snow, thereby lowering the surface albedo, increasing the surface absorbed radiation, and enhancing the original warming [e.g., Qu and Hall, 2007].
Hall  calculated from climate model simulations that the SAF over continents together with the ice-albedo feedback over oceans may account for half the high-latitude temperature response to doubled CO2 in the Northern Hemisphere (NH). Winton  averaged the SAF and ice-albedo feedback from transient CO2 simulations of 12 CMIP3 models (coupled Atmosphere-Ocean General Circulation Models (AOGCMs) in the World Climate Research Programme's (WCRP's) Coupled Model Intercomparison Project phase 3 (CMIP3)). Winton found a global feedback at the surface near 0.3 W m−2 K−1, of which three-quarters originated in the NH with roughly equal continental and oceanic contributions. (In equilibrium simulations the NH would contribute less than three-quarters of the feedback due to greater melting of the slower-responding Southern Hemisphere sea-ice (A. Hall, personal communication, 2007)).
Hall and Qu  expressed the SAF as the change in net shortwave radiation, Q, relative to changes in the surface air temperature, Ts:
where the subscript SAF emphasizes that equation (1) accounts for the radiative response to surface albedo, αs, only. Incoming solar radiation at the top of the atmosphere, Itoa, is assumed constant and positive down. The term , where αp is planetary albedo, introduces atmospheric attenuation on the effect of changing αs, assuming constant concentrations of shortwave absorbers such as water vapor and clouds. Surface processes enter the calculation as relative changes in the surface albedo in response to changing surface temperatures, .
 Springtime contributes about half the NH SAF on simulated climate change because insolation and snow extent are both large in that season [Hall, 2004]. Qu and Hall  established that springtime mean simulated ≅ 0.5 over NH continents with little variation across CMIP3 models and reasonable agreement with observations. In contrast, corresponding values of vary widely across models from about −0.015 to −0.005 K−1 (observational estimate just under −0.010 K−1 [Hall and Qu, 2006]). Also Roesch  showed that CMIP3 models have distinctly more pronounced systematic present-day albedo biases over snow-covered than over snow-free areas and Bony et al.  showed that the largest intermodel scatter in CO2-induced warming occurs in the high latitudes. In search for an explanation, Qu and Hall  determined that a model's bias for low(high) αs in snow-covered areas reduces(increases) the albedo contrast between snow-covered and snow-free surfaces and weakens(strengthens) its SAF relative to other models. This result suggests that developing parameterizations that describe Earth's continental surfaces more accurately relative to observations (αs in particular) may improve the simulation of feedbacks and climate sensitivity.
 The wide range of values across climate models has led us to investigate further into the relationship between αs, , and climate sensitivity (formally defined as the simulated equilibrium change in global surface air temperature, ΔTsglobal, due to a doubling in concentration of atmospheric CO2 [Kiehl et al., 2006]). We begin within the idealized framework of a climate model coupled to a slab ocean model. We examine the sensitivity of climate sensitivity to surface albedo by modifying the model's calculation of snow cover fraction. The results have more general implications when we include in the analysis output from 15 CMIP3 AOGCM simulations.
2.1. CAM Simulations
 We present output from four simulations with the Community Atmosphere Model version 3 (CAM3) [Collins et al., 2006] coupled to a slab ocean model (SOM) [Kiehl et al., 2006]. The SOM operates with prescribed ocean heat fluxes derived from a CAM3 simulation with prescribed sea-surface temperatures (SSTs). CAM3 is coupled to the Community Land Model version 3 (CLM3) [Dickinson et al., 2006]. The CLM3 has a global dry soil moisture bias connected to incorrect partitioning of the ground and canopy latent heat fluxes. We include a set of hydrology changes that improve this partitioning and lead to large changes in the continental branch of the hydrologic cycle (transpiration, ground and canopy evaporation, surface and sub-surface runoff) [Lawrence et al., 2007]. Due to an oversight the CLM3 does not allow for snow aging except in snow deep enough to have 5 layers (deeper than about 0.5 m). Fully implemented snow aging would have lowered the albedo for older snow. It turns out that the CLM3 already underestimates springtime albedo in snow-covered areas relative to satellite estimates [Lawrence and Chase, 2007].
 We performed our CAM3 simulations with T42 horizontal resolution (about 2.81° in latitude and longitude), 26 levels in the vertical, and a 20-minute time step. The simulations include a pair of control and a pair of sensitivity simulations. Each pair includes a 30-year 1 × CO2 (355 ppmv) and a 50-year 2 × CO2 (710 ppmv) simulation. Initial conditions and ocean heat fluxes come from spun up 1 × CO2 simulations that used climatological SSTs. We show average output from the last 20 years of the simulations.
 The sensitivity change involves the CLM3 fractional snow cover parameterization, which directly affects the surface albedo in snow-covered regions. The effective surface albedo is a linear combination of snow albedo and soil albedo, weighted by the snow cover fraction [Oleson et al., 2004]. The default relationship between snow cover, fsno (fraction), and snow depth, zsno (m), is:
Equations (2) and (3) generate fsno values near the low and high ends of the range of available snow parameterizations. Equation (3) generates larger fsno than equation (2) for all snow depths greater than zero. Also equation (3) has a faster rate of change in fsno than equation (2) for snow depths less than about 0.1 m. We refer to these parameterizations and the corresponding simulations as CLM3 and Y97, respectively (Table 1).
Table 1. Models and Simulations Included in This Study and Described in Section 2
 To assess the generality of the CAM results, we also analyze model output from 15 CMIP3 AOGCMs that have completed the 100-year A2 scenario simulation for the 21st century. The concentration of atmospheric CO2 averages about 395 ppmv and 750 ppmv in the first and in the last 20 years of the simulations, respectively [Meehl et al., 2006]. We include one randomly selected ensemble member per model (Table 1).
 In our analysis we work directly with surface albedo values in order to compare CAM3 and the CMIP3 models fairly, without assessing whether individual models account for masking by vegetation, snow aging, etc. Such differences among CMIP3 models lead to snow cover biases relative to observations that are not always related to the biases in albedo or snow water equivalent [Roesch, 2006].
 We calculate spatiotemporal averages of albedo as a ratio of the average reflected to average incident shortwave radiation to avoid the nonlinearities introduced when averaging the ratio directly (similarly for averages of other ratios, such as ).
3. Results and Discussion
3.1. CAM Results
 Following the method of Hall and Qu , we show output from 30 to 90°N over land in April. We find that larger snow fraction, fsno, in the Y97 than in the CLM3 simulations leads to higher surface albedo, αs, and lower surface temperature, Ts (Table 2). Higher αs from snow means greater albedo contrast between snow-covered and snow-free surfaces. This strengthens and the SAF [Qu and Hall, 2007], and enhances ΔTsglobal, the warming from 1 × CO2 to 2 × CO2 or climate sensitivity. But can greater sensitivity in Y97 be attributed to increased fsno at 1 × CO2 and to increased fsno at 2 × CO2 equally?
Table 2. Simulated Ts, αs, and for the CAM Simulations Listed in Table 1a
Annual Ts (K)
April αs (K)
April Ts (K)
Δαs/ΔTs × 100
Annual Ts is averaged over land and ocean.
1 × CO2
2 × CO2
 The Y97 and CLM3 2 × CO2 simulations have less total snow on the ground than the corresponding 1 × CO2 simulations, so they simulate more similar near-surface conditions, e.g. αs, Ts, and Tsglobal, than at 1 × CO2 (Table 2). This means that much of the difference in climate sensitivity between the Y97 and CLM3 simulations originates in the more different states of the 1 × CO2 simulations. This emphasizes the potential role of the present-day simulation in shaping a model's climate sensitivity at elevated CO2, in agreement with earlier published work.
 We seek to confirm our CAM result that present-day albedo may partly control a model's climate sensitivity. We plot , ΔTs, and ΔTsglobal against present-day surface albedo, αsPD for the 15 CMIP3 models listed in Table 1 (Figure 1). Following Hall and Qu , we average these variables over continental regions from 30 to 90°N in April. Only ΔTsglobal is globally and annually averaged. Our averages include the first (low CO2) and last (high CO2) twenty years of the A2 scenario simulations. Each symbol in the plots represents averaged output from one of the CMIP3 models.
Figure 1a suggests a relationship between αsPD and (correlation coefficient r = −0.66, significant at the 99% confidence level). In particular, higher values of αsPD correlate well with stronger , the surface term of the SAF in agreement with Qu and Hall . Much of the signal in this relationship originates primarily in the 45 to 60°N zone and secondarily in the 60 to 75°N zone (not shown).
 Similarly, αsPD correlates well with ΔTs (Figure 1b) and ΔTsglobal (Figure 1c) where r = 0.65 (significant at the 99% confidence level) and r = 0.50 (significant at the 90% confidence level) in the respective relationships. Strictly speaking we cannot refer to ΔTsglobal as climate sensitivity because ΔTsglobal does not represent equilibrium warming at CO2 doubling; however, we assume that the transient and equilibrium model sensitivities correlate well. Then these results suggest the same relationship between the middle to high latitude present-day springtime albedo and climate sensitivity as found in CAM. Furthermore, surface albedos across the 15 CMIP3 models differ more at present-day than with elevated CO2 (not shown) in agreement with more pronounced albedo biases found over snow-covered areas than over snow-free areas [Roesch, 2006].
 We are unable to reproduce the corresponding temperature relationship found in earlier studies, e.g., Spelman and Manabe  (summarized in the last sentence of section 3.1 above), possibly because models in the 1980s used simpler representations of the ocean and sea-ice relative to contemporary models. The intermodel range in simulated temperatures in contemporary models originates partly in increased complexity in the parameterizations representing ocean and sea-ice physics.
 In a review article, Bony et al.  state that intermodel differences in cloud feedbacks explain much of the range of simulated climate sensitivity, but that the water vapor-lapse rate and surface albedo feedbacks contribute substantially. We have confirmed with idealized CAM simulations that the snow-albedo feedback in particular plays a significant role in the simulated climate sensitivity. More generally we have shown that across CMIP3 models the intermodel difference in middle to high latitude present-day springtime albedo explains much of the intermodel scatter in , the surface term of the snow-albedo feedback. Qu and Hall  came to the same conclusion using albedo from snow-covered surfaces only.
 Surface albedo in snow-covered regions emerges as a critical factor controlling climate sensitivity. Still, model developers face large uncertainty in simulating the primary variable determining snow albedo, the snow itself. Many climate models still neglect or misrepresent the effects on the surface albedo of snow aging, particle deposition on snow, sub-grid scale areas that are snow free, and plants masking snow-covered surfaces [Flanner et al., 2007; Bony et al., 2006]. Our idealized CAM simulations indicate that the selection between two equally justifiable snow cover parameterizations can lead to a 0.2 K difference in climate sensitivity.
 Across CMIP3 models, it is the scatter in simulated albedos that led us to the strong relationship between simulated present-day albedo and global warming. Given this relationship, an observational estimate of the albedo of 0.32 (averaged over 30 to 90°N over land in April [Lawrence and Chase, 2007]) narrows the ensemble of CMIP3 climate sensitivities to a best guess of about 3.25 K (Figure 1c). If the albedo-to-warming relationship could be derived from observations in the seasonal context [Hall and Qu, 2006], then one might truly narrow the expected climate sensitivity range, as Tsushima et al.  (∼3.0 K), Annan and Hargreaves  (∼2.9 K), and others have tried using various observationally-based constraints.
 We acknowledge the modeling groups for making their simulations available for analysis, the Program for Climate Model Diagnosis and Intercomparison (PCMDI) for collecting and archiving the CMIP3 model output, and the WCRP's Working Group on Coupled Modelling (WGCM) for organizing the model data analysis activity. The WCRP CMIP3 multi-model dataset is supported by the Office of Science, U.S. Department of Energy. We thank an anonymous reviewer, Alex Hall, Guo-Yue Niu, Marika Holland, and Jeff Kiehl for helpful comments. The CAM simulations were performed on National Center for Atmospheric Research (NCAR) supercomputers. NCAR is sponsored by the National Science Foundation.