Abstract

The enigmatic Neoproterozoic geological record suggests the potential for a fully glaciated “snowball Earth.” Low-latitude continental position has been invoked as a potential snowball Earth trigger by increasing surface albedo and decreasing atmospheric CO2 concentrations through increased silicate weathering. Herein, climate response to the reduction of total solar irradiance (TSI) and CO2 concentration is tested using four different land configurations (aquaplanet, modern, Neoproterozoic, and low-latitude supercontinent) with uniform topography in the NCAR Community Atmosphere Model, version 3.1 (CAM3.1), GCM with a mixed layer ocean. Despite a lower surface albedo at 100% TSI, the threshold for global glaciation decreases from 92% TSI in the aquaplanet configuration to 85% TSI with a low-latitude supercontinent. The difference in thresholds is principally because of the partitioning of local longwave cooling relative to poleward energy transport. Additionally, dehumidification of the troposphere over large tropical continents in CAM3.1 increases direct heating by decreasing cloud cover. Continental heating intensifies the Walker circulation, enhancing surface evaporation and moistening the marine troposphere. Topography also provides an important control on snowball Earth initiation. Modern topography in the modern continental arrangement eases snowball initiation, requiring a 2% smaller reduction in TSI relative to a modern continental arrangement without topography. In the absence of potential silicate weathering feedbacks, large tropical landmasses raise the barrier to initiation of snowball events. More generally, these simulations demonstrate the substantial influence of geography on climate sensitivity and challenge the notion that the reduced continental area early in Earth history might provide a solution to the faint young Sun paradox.

1. Introduction

Several lines of geologic evidence from the mid- and late Neoproterozoic suggest the episodic occurrence of prolonged low-latitude glaciation and the possibility of a “snowball Earth” resulting from global glaciation. Cryogenian (850–630 Ma) glaciogenic sequences and diamictites are found on every continent and are frequently overlain by thick “cap” carbonate sequences. Large and chemostratographically correlated carbon isotope anomalies in these cap carbonates are thought to reflect the global nature of mid- and late Neoproterozoic glaciations (Hoffman and Schrag 2002; Macdonald et al. 2010). Iridium anomalies found at the base of cap carbonates in Africa suggest that the Marinoan glaciation episode lasted at least 3 million years, but more likely 12 million years (Bodiselitsch et al. 2005), though these results have not been duplicated in other cap carbonate sequences. Finally, the return of banded iron formations (BIFs) in the Neoproterozoic after a billion year hiatus (Hoffman and Schrag 2002; Pierrehumbert et al. 2011) has been argued to be evidence of ocean anoxia, possibly resulting from tropical pack ice interfering with and weakening wind-driven ocean circulation or total isolation of the ocean from the atmosphere by sea ice (Kirschvink 1992). Termination of snowball Earth is thought to have resulted from the buildup of atmospheric CO2 levels over millions of years as silicate weathering essentially stopped during the snowball event, while volcanic outgassing continued unabated. Supporting this suggestion, strongly negative Δ17O anomalies in Neoproterozoic sulfate minerals precipitated after termination of snowball events suggest higher CO2 levels than at any point during the Phanerozoic (Bao et al. 2008, 2009).

Not all geologic evidence is compatible with a fully frozen snowball Earth, however. Biomarker evidence of eukaryotic life dates back to the Archean (Waldbauer et al. 2009), whereas evidence of sponges exists prior to the Marinoan glaciation (Love et al. 2008). Therefore, the emergence of Metazoan life predated the snowball events, and Metazoan survival calls into question the existence of a completely glaciated ocean. Additionally, while deposition of cap carbonates is thought to reflect amplified continental weathering or the overturning of a stratified ocean following deglaciation (Hoffman and Schrag 2002), it has been questioned how these mechanisms could produce widespread and synchronous carbonate deposition (Ridgwell et al. 2003; Shields 2005).

Efforts using climate models to understand Neoproterozoic climate have only stoked the snowball debate. According to standard solar evolution models, solar luminosity during the Neoproterozoic would have been approximately 6%–7% lower than present (Gough 1981; Crowley and Baum 1993). Energy balance models (EBM) developed independently by Budyko (1969) and Sellers (1969) suggest global glaciation driven by a runaway ice–albedo feedback could result from modest reductions in solar luminosity (as little as 1.6%) after ice expands equatorward beyond a critical latitude. Improvements to EBM parameterization of heat transport and thermal diffusion made by North (1975a,b) suggested global glaciation might occur with reductions in solar luminosity closer to 7%.

Snowball Earth initiation has also been explored in a growing number of general circulation models (GCMs). Larger reductions of total solar irradiance (TSI) are typically required in GCMs to simulate a snowball state than in EBMs, suggesting that climate dynamics and feedbacks not captured in EBMs restrict ice expansion. In support of this conclusion, previous studies have identified processes including ocean heat transport (Poulsen et al. 2001; Bendtsen 2002), wind-driven ocean circulation, and cloud radiative forcing (Poulsen and Jacob 2004) that restrict sea ice growth. For example, clouds over sea ice restrict surface sensible heat loss and have a warming effect over sea ice. The ice–albedo feedback is stronger when cloud radiative forcing is excluded (Poulsen and Jacob 2004). Likewise, ocean circulation transports heat to and stabilizes the ice line. Convective mixing warms the surface ocean adjacent to the ice margin restricting ice growth, with the largest impact occurring in the winter (Poulsen et al. 2001). In contrast, the addition of sea ice dynamics promotes snowball Earth initiation (Voigt and Abbot 2012).

Nonetheless, a wide range of solar luminosity and carbon dioxide concentration thresholds for snowball initiations have been reported (Pierrehumbert et al. 2011). With Marinoan continents, the ECHAM5/Max Planck Institute Ocean Model (MPI-OM) model predicts a snowball state when solar luminosity is reduced below 96% of the modern value with preindustrial greenhouse gas concentrations (Voigt et al. 2011). With comparable but lower than preindustrial (CO2 of 100–140 ppmv) greenhouse gas concentrations, however, other models including the Fast Ocean Atmosphere Model (FOAM; e.g., Poulsen et al. 2001; Poulsen 2003), Goddard Institute for Space Studies (GISS; e.g., Chandler and Sohl 2000) model, and the Global Environmental and Ecological Simulation of Interactive Systems model (GENESIS; e.g., Jenkins and Frakes 1998; Baum and Crowley 2001, 2003) fail to simulate snowball states when solar luminosity is reduced below 94%. Yang et al. (2012b,c) find snowball states in the fully coupled Community Climate System Model, version 3 (CCSM3), model when TSI is reduced by 10%–10.5% with preindustrial greenhouse gas concentrations or by 6% with a strong greenhouse gas reduction to 17.5 ppmv CO2. A follow-up study using CCSM, version 4 (CCSM4), showed similar, but slightly less extreme, initiation thresholds (Yang et al. 2012a). Other solutions in addition to global ice cover have also been invoked to explain the geologic evidence. “Slushball” or “waterbelt” solutions (e.g., Hyde et al. 2000; Chandler and Sohl 2000; Baum and Crowley 2001, 2003; Micheels and Montenari 2008) describe a state with glaciated continents but ice-free tropical oceans and ice margins poleward of 25° latitude. In these studies, however, a large portion of land was positioned in mid- and high latitudes, at odds with paleogeographic reconstructions for the Marinoan and Sturtian glaciations (Hoffman and Li 2009). An additional solution, the “Jormungand” state—named for the serpentlike appearance of a narrow band of iceless equatorial ocean in a Hovmöller diagram—emerges when the albedo of snow-covered and bare sea ice differs sufficiently (Abbot et al. 2011). These open-ocean solutions provide an attractive explanation for glaciogenic deposits in low paleolatitudes and provide a refuge for life but may fail to account for the deposition of banded iron formations during the Sturtian glaciation [little evidence exists for BIFs in the Marinoan; see Hoffman and Li (2009)], depending on how effective the wind-driven ocean circulation is at preventing deep ocean anoxia globally.

Across these models, a myriad of paleogeographies has been used and may in part be responsible for the range of observed sensitivities. Here, we investigate this possibility and the hypothesis that low-latitude continents facilitate snowball Earth initiation (Kirschvink 1992). Multiproxy reconstructions of Neoproterozoic geography place the bulk of the land area in the tropics and subtropics (Kirschvink 1992; Li et al. 2008; Hoffman and Li 2009), a distribution that has been considered conducive to snowball Earth initiation for three major reasons. First, land surfaces generally have higher albedo than the ocean, particularly under the relatively cloud-free descending limb of the Hadley cell in the subtropics where surface albedo has a stronger impact on planetary albedo. Second, as continental glaciers form and sea level drops, land would replace shallow seas in the tropics, further increasing albedo (Kirschvink 1992). Finally, weathering rates of silicate minerals would increase with increased land under the intertropical convergence zone, leading to an enhanced drawdown of atmospheric CO2 under a constant volcanic degassing rate (Marshall et al. 1988; Worsley and Kidder 1991).

Previous studies provide conflicting conclusions about the impact of the increased tropical landmass on global average temperatures. GCM experiments generally suggest higher global temperatures when more land is concentrated in the tropics. For example, Barron et al. (1984) show that tropical continents suppress evaporative cooling and warm the tropics and Poulsen et al. (2002) suggest mid- and high-latitude continents promote cooling by increasing snow coverage over continents and sensible heat loss from the ocean, leading to greater global ice coverage. In contrast, Voigt et al. (2011) demonstrate that the increased tropical landmass cools global temperatures in the ECHAM5/MPI-OM model by increasing planetary albedo and weakening the greenhouse effect. Here, we analyze how climate sensitivity to variation in solar luminosity and greenhouse gas forcing varies with paleogeography and describe the implications for snowball Earth initiation and more broadly the role of paleogeography in the constraints of paleoclimate sensitivity. This paper investigates the response of climate dynamics to changes in radiative forcing as a function of geography. Future work (R. P. Fiorella and C. J. Poulsen 2013, unpublished manuscript) estimates the dependence of climate feedback strengths on paleogeography across the same forcing changes.

2. Model description and setup

Snowball Earth initiation experiments were performed using the National Center for Atmospheric Research Community Atmosphere Model, version 3.1 (CAM3.1; Collins et al. 2004), consisting of an atmospheric model coupled to a 50-m mixed layer ocean model and the Community Land Model (CLM), version 3.0 (Oleson et al. 2004). A horizontal resolution of spectral T31 (~3.75°) was used in the atmospheric model, with 26 levels in the vertical direction. Zero ocean heat transport was specified everywhere for the mixed layer ocean, and dynamic adjustments to the mixed layer ocean heat flux were disabled. Sea ice is modeled purely on a thermodynamic basis with no dynamics included. To generate a better match with modern sea ice distributions, the default settings in the mixed layer ocean model in CAM3.1 add 15 W m−2 to the Northern Hemisphere ocean and remove 10 W m−2 from the Southern Hemisphere ocean; these values were set to zero in our experiments.

Neoproterozoic boundary conditions are not well constrained. Model boundary conditions were chosen to best represent the Neoproterozoic, to facilitate glaciation, and to simplify the analysis of results. Eccentricity was set to zero and obliquity was held constant at 23.5°. Carbon dioxide (280 ppm), aerosol, and ozone concentrations were set to preindustrial levels. Model default values were used for methane (1714 ppb) and nitrous oxide (316 ppb); sensitivity tests indicate this choice does not fundamentally alter the results presented here. As land plants had not evolved in the Neoproterozoic, all land vegetation was removed and the land surface specified as desert. CLM calculates the land surface albedo as a function of soil color and the moisture content of the topsoil layer. To facilitate glaciation, the lightest most reflective soil color is used, having visible/near-infrared (NIR) albedos of 0.24/0.48 when the top layer of soil is dry and decreasing to 0.12/0.24 when the top soil layer is saturated (Oleson et al. 2004). Ocean albedo is 0.06 for direct sunlight in these experiments. The albedo of sea ice increases linearly with thickness up to 1 m, at which albedos are capped at 0.67 in the visible and 0.30 for NIR wavelengths. Cold snow has an albedo of 0.91/0.63 for visible/NIR wavelengths.

We test four different continental arrangements: (i) an aquaplanet with no land, similar to the configuration used in Jenkins (1993, 1999) but with zero ocean heat transport and a mixed-layer depth of 50 m (hereafter AQP), (ii) an equator-centered rectangular supercontinent extending between 43°N and 43°S and spanning 130° in longitude (hereafter RECT), (iii) a Marinoan (~635 Ma) continental reconstruction with two large tropical continents (hereafter MAR), based on the paleogeography used in Voigt et al. (2011), and (iv) a modern continental configuration with topography removed (hereafter MOD-NT; see Fig. 5 for maps of the four geographies). The global land fraction was similar across the configurations with 32.3%, 27.8%, and 27.0% land coverage for the MOD-NT, MAR, and RECT experiments, respectively (Table 1). Low-latitude (≤30°) land fraction is 28.8%, 48.1%, and 38.5% for the MOD-NT, MAR, and RECT experiments, respectively. Land surface elevations are 100 m in these experiments.

Table 1.

Results for AQP, MOD-NT, MAR, and RECT configurations at 100% TSI and 280 ppmv CO2.

Results for AQP, MOD-NT, MAR, and RECT configurations at 100% TSI and 280 ppmv CO2.
Results for AQP, MOD-NT, MAR, and RECT configurations at 100% TSI and 280 ppmv CO2.

For the RECT, MAR, and MOD-NT configurations, atmospheric temperatures were initialized with a cosine latitudinal gradient ranging from 28°C at the equator to 12°C at the poles, and initial wind conditions were calculated using the thermal wind. Sea surface temperatures were initiated from a coupled CCSM simulation of modern climate. For runs in which TSI was varied, the model was run at 100% of the modern solar constant for 100 years, after which branch runs were performed by immediately reducing TSI to values as low as 80%. A summary of all of the runs performed in which TSI is altered is provided in Table 2. Runs in which CO2 were varied were all started with no initial ice and initial atmosphere and ocean temperatures set to 300 K everywhere and a TSI of 94%. CO2 was varied between 10 000 and 0.10 ppmv (see Table 3). A 1% reduction in TSI corresponds to a global average change in incoming solar radiation at the top of the atmosphere of 3.42 W m−2, multiplied by the fraction of shortwave (SW) radiation absorbed (i.e., 1-albedo), while each factor of 2 change in CO2 concentration represents a change in radiative forcing of approximately 2.66 W m−2 (Collins et al. 2006a). As stable climate states lacking permanent sea ice have been reported for modern TSI (e.g., Pierrehumbert et al. 2011), additional sensitivity experiments were performed when TSI was varied with no initial ice and initial atmosphere and ocean temperatures set to 300 K everywhere. Results presented here were insensitive to this change in initial boundary conditions.

Table 2.

Summary of TSI model experiments performed and result of run when terminated after years indicated. TSI is listed as a percentage of the modern value.

Summary of TSI model experiments performed and result of run when terminated after years indicated. TSI is listed as a percentage of the modern value.
Summary of TSI model experiments performed and result of run when terminated after years indicated. TSI is listed as a percentage of the modern value.
Table 3.

Summary of CO2 model experiments performed and result of run when terminated after years indicated.

Summary of CO2 model experiments performed and result of run when terminated after years indicated.
Summary of CO2 model experiments performed and result of run when terminated after years indicated.

In all cases, the model was run until the surface temperature trend over a 20-yr period was less than 1°C century−1, signifying a quasi-equilibrium state was reached. Particularly for experiments near the bifurcation point between snowball and intermediate ice states, we integrated several simulations for additional time to ensure these equilibria were stable (Tables 2 and 3). Unless otherwise noted, results shown here represent averages of the final 20 years of model integration. Average sea ice margin positions were determined by taking the inverse sine of the total hemispheric ocean fraction after masking the land.

3. Results

a. Climate sensitivity to TSI changes

At 100% TSI, the mean annual surface temperatures are similar for all four geographies, ranging between 272.4 and 274.0 K (Table 1). In all cases, the surface temperatures are highly zonal because of the lack of topography, with some asymmetries near the edges of continents (Figs. 1a–d), presumably a result of land–sea thermal contrasts. An equator-to-pole temperature gradient of 70 K is simulated. Equatorial and polar temperatures average around 295 and 225 K for all four geographies, respectively. Global surface albedo varies from a maximum of 0.356 for the MAR geography to a minimum of 0.310 for the AQP geography because of differences in land and snow/ice distribution. Atmospheric dynamics and associated cloud distributions result in a range of planetary albedo between the geographies at 100% TSI that is more than 5 times smaller than the surface albedo range (0.406 for AQP and 0.397 for MOD-NT), and as a result surface temperatures only vary by 1.6 K. The mean climatological positions of sea ice are also similar for all four geographies, ranging from a maximum equatorward extent of 39.7°N and 39.3°S (RECT) to a minimum equatorward extent of 42.7°N and 40.5°S (MOD-NT).

Fig. 1.

Zonally and annually averaged surface temperatures at (a) 100% and (b) 95% TSI for the AQP, MOD-NT, MAR, and RECT experiments. At 100% TSI, the four geographies have a highly similar temperature structure with mean annual tropical and polar temperatures around 295 and 225 K, respectively. At 95% TSI, the temperature structures of the four geographies diverge—AQP temperatures are at least 15 K lower than the MOD-NT, MAR, and RECT geographies at all latitudes.

Fig. 1.

Zonally and annually averaged surface temperatures at (a) 100% and (b) 95% TSI for the AQP, MOD-NT, MAR, and RECT experiments. At 100% TSI, the four geographies have a highly similar temperature structure with mean annual tropical and polar temperatures around 295 and 225 K, respectively. At 95% TSI, the temperature structures of the four geographies diverge—AQP temperatures are at least 15 K lower than the MOD-NT, MAR, and RECT geographies at all latitudes.

When TSI is reduced to 95%, prominent differences between the AQP and MOD-NT, MAR, and RECT simulations emerge. Despite a 13% lower surface albedo at 100% TSI than the MAR geography, the AQP configuration shows the highest sensitivity of surface temperature and ice position to TSI reduction (Fig. 2). AQP equatorial temperatures decrease to 278 K, and polar temperatures decrease to 190 K, yielding an increased equator-to-pole temperature gradient of 88 K. In contrast, equatorial and polar temperatures fall to 285–290 and 200–210 K for the three geographies with land. As TSI is further reduced, AQP surface temperatures decrease the most rapidly with TSI, but the MOD-NT, MAR, and RECT climatologies diverge as ice expands equatorward and show a greater range of sensitivity at lower TSI values (Fig. 2). For example, at 90% TSI the MOD-NT configuration has an average surface temperature 4.3 K lower than the MAR and 7.2 K lower than the RECT simulations. Differing sea ice cover is associated with temperature differences. MOD-NT has the largest ice extent at this TSI (Fig. 2c), particularly in the Southern Hemisphere where there is less land, followed by MAR that has slightly greater ice expansion in the Northern Hemisphere compared to RECT. As a result, planetary albedo increases more in the MOD-NT and MAR cases than in the RECT case at 90% TSI. Annual average land surface temperatures for the MOD-NT, MAR, and RECT cases are all above 273 K at 93% TSI and too warm to support land glaciers, though experiments with higher elevations may.

Fig. 2.

(a) Mean annual surface temperature, (b) mean annual ice margin, and (c) surface and (d) planetary albedos as a function of TSI. A strong bifurcation notes the transition to a snowball state for each configuration as TSI is decreased. AQP enters the snowball state most readily (TSI < 92%), followed by MOD-NT, MAR, and RECT when TSI is reduced below 88%, 86%, and 85%, respectively.

Fig. 2.

(a) Mean annual surface temperature, (b) mean annual ice margin, and (c) surface and (d) planetary albedos as a function of TSI. A strong bifurcation notes the transition to a snowball state for each configuration as TSI is decreased. AQP enters the snowball state most readily (TSI < 92%), followed by MOD-NT, MAR, and RECT when TSI is reduced below 88%, 86%, and 85%, respectively.

As a result of these varying sensitivities, the threshold TSI for snowball state initiation differs between geographies. Though the configurations with land concentrated in the low latitudes have slightly higher initial surface albedo at 100% TSI, both surface and planetary albedo for the AQP configuration increases more rapidly with reductions in TSI and is higher at TSI below 100% (Figs. 2c,d). All four configurations exhibit a strong bifurcation in temperature and ice coverage at the transition between partial and global ice coverage. AQP enters the snowball state at the highest solar constant, transitioning to full ice coverage between 92% and 91% TSI. The snowball transitions occur at 88%, 86%, and 85% of modern TSI for the MOD-NT, MAR, and RECT configurations. Across the AQP, MOD-NT, and MAR experiments, the reduction in TSI necessary to induce a snowball state increases with the low-latitude land fraction. Despite having less low-latitude land area than MAR, the RECT configuration experiences global sea ice cover at a lower TSI, suggesting that continentality also impacts snowball initiation.

Geography also impacts the global-mean surface temperature at the bifurcation point; the minimum surface temperature without global ice cover is 233.3 K for AQP but 237.2 K for RECT. Similarly, the latitude of the maximum ice extent before the transition to global ice cover for AQP is closer to the equator (10.6°N and 9.4°S) than for any of the other configurations. Maximum ice extents for each configuration are provided in Table 1. We note that while all configurations show Jormungand-like states with ice equatorward of about 15° latitude, only the AQP configuration shows a true Jormungand state in these experiments. The Jormungand climate state is characterized by both (i) stable ice margins equatorward of 25° latitude and (ii) clear separation from other climate states by an additional bifurcation, the Jormungand bifurcation (Abbot et al. 2011; Voigt and Abbot 2012). The low-latitude ice states in the MOD-NT, MAR, and RECT configurations are not separated from higher-latitude ice states by an additional bifurcation, and thus are not Jormungand states. In the following sections, we address the energetic and dynamical differences leading to the highly varied responses in reduction of radiative forcing and snowball Earth initiation to differences in geography.

b. Climate sensitivity to CO2 changes and comparison with changes in TSI

In this section, we investigate the extent to which our results are sensitive to altering radiative forcing through TSI rather than greenhouse forcing. Yang et al. (2012c) point out that the spatial pattern of forcing by changes in CO2 is uniform, while TSI changes have a stronger absolute forcing in the tropics than at the poles (their Fig. 8a). To test this, we present experiments for all four geographies in which CO2 concentrations are varied between 10 000 and 0.01 ppm and TSI is fixed at 94%. A summary of these runs is presented in Table 3. The CO2 runs show the same pattern of sensitivity observed in the TSI runs, with progressively larger reductions in CO2 concentrations required for snowball initiation in the AQP, MOD-NT, MAR, and RECT geographies.

We calculate the change in radiative forcing for all of the TSI and CO2 runs relative to a reference point of 100% TSI and 280 ppm CO2 to directly compare the impacts of both radiative forcing methods. Each doubling of CO2 is estimated to have a total radiative forcing change of 2.66 W m−2 (Collins et al. 2006a). Forcing by TSI changes is calculated by multiplying the change in the solar constant by (1 albedo)/4, using the albedo for each case at 100% TSI. Simulated climates converge for intermediate forcings whether TSI or CO2 is altered (Fig. 3). Under larger and smaller forcing net forcings from this reference point, however, CO2 has a greater climatic effect than TSI. Ice-free states are simulated at smaller global forcing increases when CO2 is increased compared to when TSI is increased because high-latitude forcing is stronger for the same increase in global radiative forcing. Likewise, initiating snowball states requires a greater decrease in global radiative forcing when CO2 is reduced compared to when TSI is reduced because the decrease in tropical radiative forcing is smaller for equal global forcing reductions by CO2 reductions than for TSI reductions (Fig. 3). Additionally, snowball states are not simulated through reductions in CO2 alone at 94% TSI for the MAR and RECT geographies, despite a 10 W m−2 greater decrease in global radiative forcing. These results highlight the importance of tropical energy balance in controlling the initiation of snowball states.

Fig. 3.

Comparison of runs in which TSI and CO2 were varied for all four geographies. (a)–(d) The annual average surface temperature (K) and (e)–(h) the annual average ice line position. Direct comparison of CO2 and TSI forcing was achieved by calculating the radiative forcing change from a common reference point of 100% TSI and 280 ppm CO2. For the same global forcing, snowball states are harder to initiate when CO2 is reduced compared to when TSI is reduced, with snowball states not simulated for the MAR and RECT geographies through CO2 reduction alone with TSI fixed at 94%. Similarly, ice-free states are more readily simulated with CO2 increases compared to TSI increases for the same global forcing. This trend is principally related to the zonal pattern of radiative forcing induced by each method of altering global radiative forcing.

Fig. 3.

Comparison of runs in which TSI and CO2 were varied for all four geographies. (a)–(d) The annual average surface temperature (K) and (e)–(h) the annual average ice line position. Direct comparison of CO2 and TSI forcing was achieved by calculating the radiative forcing change from a common reference point of 100% TSI and 280 ppm CO2. For the same global forcing, snowball states are harder to initiate when CO2 is reduced compared to when TSI is reduced, with snowball states not simulated for the MAR and RECT geographies through CO2 reduction alone with TSI fixed at 94%. Similarly, ice-free states are more readily simulated with CO2 increases compared to TSI increases for the same global forcing. This trend is principally related to the zonal pattern of radiative forcing induced by each method of altering global radiative forcing.

c. Tropical energy balance changes

Low-latitude continents are thought to facilitate global ice cover by reducing absorbed shortwave radiation through increased surface albedo (Kirschvink 1992; Hoffman and Schrag 2002). Our results suggest differently: particularly in the deep tropics, the net shortwave radiation received at the surface is greater for geographies with more tropical land despite a higher surface albedo because of the near absence of clouds over large landmasses. These trends in shortwave radiation absorbed support the idea that atmospheric conditions can be more important than the surface for setting the planetary albedo and are consistent with modern observations that atmospheric reflection accounts for approximately 90% of observed planetary albedo (Donohoe and Battisti 2011). Equatorward of 10°, absorbed shortwave radiation is 30 and 20 W m−2 higher for the RECT and MAR geographies than for the AQP geography (Fig. 4a). Longwave radiation shows an even larger disparity between the RECT and AQP geographies, with emission being approximately 40 W m−2 higher in these latitudes in the RECT case (Fig. 4b). Clouds are universally cooling in the tropics at 100% TSI, but the amount of cooling varies by 20–30 W m−2 between the geographies, with the AQP and MOD-NT geographies having the most negative cloud forcing (Fig. 4c). This difference in cloud forcing results from stark differences in tropical cloud fraction between geographies (Fig. 5). Cloud fractions over land, particularly in the subtropics, tend to remain below 0.3 while exceeding 0.6 over the oceans at comparable latitudes. The presence of continents also reduces cloud fractions over the ocean near land (Figs. 4e and 5), increasing cloud radiative forcing over the ocean. This effect is most pronounced in the RECT case, where cloud forcing over the ocean in the deep tropics is 20 W m−2 higher than in the AQP case at 100% TSI.

Fig. 4.

Components of global energy balance (W m−2) at 100% TSI for all four geographies. (a) Net surface shortwave radiation absorbed, (b) net surface longwave radiation emitted, (c) total cloud forcing, (d) total greenhouse forcing (difference in upwelling clear-sky longwave radiation at the top of the atmosphere and the surface), and (e) cloud forcing over the ocean. Geographies with large amounts of tropical land area (i.e., MAR and RECT) have higher net shortwave radiation in the deep tropics than geographies with little or no tropical land area (i.e., AQP) primarily a result of lower cloud fraction. This energy disparity is ameliorated by increased longwave emission and a smaller greenhouse forcing for the high land configurations, leading to similar tropical temperatures across all four geographies.

Fig. 4.

Components of global energy balance (W m−2) at 100% TSI for all four geographies. (a) Net surface shortwave radiation absorbed, (b) net surface longwave radiation emitted, (c) total cloud forcing, (d) total greenhouse forcing (difference in upwelling clear-sky longwave radiation at the top of the atmosphere and the surface), and (e) cloud forcing over the ocean. Geographies with large amounts of tropical land area (i.e., MAR and RECT) have higher net shortwave radiation in the deep tropics than geographies with little or no tropical land area (i.e., AQP) primarily a result of lower cloud fraction. This energy disparity is ameliorated by increased longwave emission and a smaller greenhouse forcing for the high land configurations, leading to similar tropical temperatures across all four geographies.

Fig. 5.

Total annual average cloud fraction for all four geographies at 100% TSI. Cloud fractions are highest over regions of vigorous convection over the ocean and lower in the subtropics and particularly over land. Cloud fractions are notably low over MAR and RECT geographies resulting from the presence of large continents in the subtropics, though cloud fractions are low over the entirety of the RECT continent, while cloud fractions remain higher in the deep tropics over the smaller continents of the MAR geography.

Fig. 5.

Total annual average cloud fraction for all four geographies at 100% TSI. Cloud fractions are highest over regions of vigorous convection over the ocean and lower in the subtropics and particularly over land. Cloud fractions are notably low over MAR and RECT geographies resulting from the presence of large continents in the subtropics, though cloud fractions are low over the entirety of the RECT continent, while cloud fractions remain higher in the deep tropics over the smaller continents of the MAR geography.

Geography alters tropical energy balance, as shown by the large disparities in surface shortwave absorption and longwave emission between cases. The higher sensitivity of AQP to TSI reduction is related to its larger dependence on greenhouse forcing to maintain energy balance (Fig. 6). Specific humidity q and surface temperature T are tightly coupled through the Clausius–Clapeyron equation in all of our simulations (Fig. 7a). Reductions in TSI reduce direct solar heating linearly, while greenhouse forcing decreases nearly exponentially above the bifurcation points for all geographies (Fig. 6d). Therefore, TSI reductions have the strongest impact on global temperatures in AQP resulting from its large greenhouse forcing term in the tropical energy balance. In contrast, a larger proportion of the energy budget is radiatively direct in the configurations with land. As a result, these cases show lower sensitivities to TSI reductions than AQP. Among configurations with land, the RECT (MOD-NT) configuration has the largest (smallest) radiatively direct energy budget portion (Figs. 4 and 6) and shows the lowest (highest) sensitivity in q to changes in TSI (Fig. 7b). Tight qT coupling suggests dynamical differences between the experiments affect the energy partitioning that drives the different sensitivities to changes in TSI observed. Additionally, we explore the relative strength of different climate feedbacks and how they contribute to the observed climate sensitivity in future work.

Fig. 6.

Weighted area average (from 30°N to 30°S) components of the surface energy balance (W m−2) as a function of TSI for all four geographies. (a) Net surface shortwave radiation absorbed, (b) net surface longwave radiation emitted, (c) total cloud forcing, and (d) total greenhouse forcing (difference in upwelling clear-sky longwave radiation at the top of the atmosphere and the surface). At 100% TSI, the AQP and MOD-NT configurations are more reliant on greenhouse forcing to maintain tropical temperatures and are most sensitive to decreases in TSI as the amount of atmospheric water vapor decreases with TSI. Cloud forcing in the MAR and RECT configurations are more positive by approximately 10 W m−2 prior to snowball initiation and higher absorbed shortwave fluxes that decrease less rapidly than greenhouse forcing.

Fig. 6.

Weighted area average (from 30°N to 30°S) components of the surface energy balance (W m−2) as a function of TSI for all four geographies. (a) Net surface shortwave radiation absorbed, (b) net surface longwave radiation emitted, (c) total cloud forcing, and (d) total greenhouse forcing (difference in upwelling clear-sky longwave radiation at the top of the atmosphere and the surface). At 100% TSI, the AQP and MOD-NT configurations are more reliant on greenhouse forcing to maintain tropical temperatures and are most sensitive to decreases in TSI as the amount of atmospheric water vapor decreases with TSI. Cloud forcing in the MAR and RECT configurations are more positive by approximately 10 W m−2 prior to snowball initiation and higher absorbed shortwave fluxes that decrease less rapidly than greenhouse forcing.

Fig. 7.

Vertically integrated water vapor as a function of (a) average global surface temperature (K) and (b) TSI from 30°N to 30°S for all four geographies. At 100% TSI, vertically integrated water vapor is notably lower for high tropical land configurations MAR and RECT, with the RECT geography having 35% less tropical atmospheric water vapor than the AQP geography. Temperature and specific humidity are tightly coupled in (a), as vertically integrated water vapor flows average global surface temperature as suggested by the Clausius–Clapeyron equation. As TSI is reduced, however, the rate of decrease of vertically integrated water vapor in (b) is higher for AQP than the other configurations with land since the energy budget has a larger greenhouse forcing term.

Fig. 7.

Vertically integrated water vapor as a function of (a) average global surface temperature (K) and (b) TSI from 30°N to 30°S for all four geographies. At 100% TSI, vertically integrated water vapor is notably lower for high tropical land configurations MAR and RECT, with the RECT geography having 35% less tropical atmospheric water vapor than the AQP geography. Temperature and specific humidity are tightly coupled in (a), as vertically integrated water vapor flows average global surface temperature as suggested by the Clausius–Clapeyron equation. As TSI is reduced, however, the rate of decrease of vertically integrated water vapor in (b) is higher for AQP than the other configurations with land since the energy budget has a larger greenhouse forcing term.

d. Amplified Walker-like circulation in configurations with high tropical land area

For clarity, we focus on the differences between the AQP and RECT configurations to assess the impact of large land–sea contrasts on zonal circulation patterns in the deep tropics. AQP shows strong upward motion at all longitudes to about 350 hPa (Fig. 8). The atmosphere is nearly saturated at the surface and in the upper troposphere. In contrast, RECT shows strong and deeper upward motion over the ocean (to about 250 hPa) but strong radiatively driven subsidence in the upper- and midtroposphere over the continent, limiting upward motion to the boundary layer and leading to low relative humidity over the continent. Relative humidity drops below 5% over the western third of the continent. Temperatures over the oceans decrease with altitude following the moist adiabatic lapse rate, while dry subsiding air over the continent warms near the dry adiabatic lapse rate during adiabatic descent. As a result of this increased lapse rate as well as increased direct solar heating in the absence of clouds, temperatures at the surface are warmer than they would be were there no continent. Surface winds advect this warm dry continental air over the oceans, increasing surface evaporation (Fig. 9). Though higher amounts of land decrease the total water flux from tropical oceans, evaporation is more efficient over the ocean in the MAR and RECT cases. Warmer global temperatures and enhanced ocean surface water fluxes yield higher specific humidity over the oceans for the RECT configuration than for the AQP at lower TSIs, particularly in the mid- and upper troposphere (Fig. 8) where water vapor has a more potent greenhouse effect relative to the boundary layer (Held and Soden 2000). The MAR and MOD-NT configurations also show a Walker cell, but both are weaker than the RECT cell as the amount of contiguous land in the deep tropics is lower and land–sea contrasts are less extreme.

Fig. 8.

Annually and meridionally (between 5°N and 5°S) averaged longitudinal/height cross sections of vertical pressure velocities (mb day−1) and relative humidity (%) for the (a),(b) AQP and (c),(d) RECT geographies at 95% TSI. Black contour lines in (b) and (d) indicate specific humidity in 1 g kg−1 intervals. Vertical pressure velocities in the AQP configuration are ubiquitously negative in the troposphere, suggesting vigorous upward motion at all longitudes in the annual average. In contrast, the RECT configuration shows strong upward motion over the oceans but strong subsidence in the free troposphere, limiting weaker upward motion to the boundary layer over the continent. Likewise, the troposphere is near saturation at the surface and near the tropopause in the AQP experiment at all longitudes, while the troposphere is near saturation in the boundary layer and tropopause over the ocean but is markedly drier over the continent, particularly over the continent’s western half. Over the ocean, near-surface specific humidity is nearly 3 times higher in the RECT experiment than in the AQP experiment. Additionally, higher specific humidity in the midtroposphere of the RECT experiment results in greenhouse forcing less sensitive to TSI than in the AQP case.

Fig. 8.

Annually and meridionally (between 5°N and 5°S) averaged longitudinal/height cross sections of vertical pressure velocities (mb day−1) and relative humidity (%) for the (a),(b) AQP and (c),(d) RECT geographies at 95% TSI. Black contour lines in (b) and (d) indicate specific humidity in 1 g kg−1 intervals. Vertical pressure velocities in the AQP configuration are ubiquitously negative in the troposphere, suggesting vigorous upward motion at all longitudes in the annual average. In contrast, the RECT configuration shows strong upward motion over the oceans but strong subsidence in the free troposphere, limiting weaker upward motion to the boundary layer over the continent. Likewise, the troposphere is near saturation at the surface and near the tropopause in the AQP experiment at all longitudes, while the troposphere is near saturation in the boundary layer and tropopause over the ocean but is markedly drier over the continent, particularly over the continent’s western half. Over the ocean, near-surface specific humidity is nearly 3 times higher in the RECT experiment than in the AQP experiment. Additionally, higher specific humidity in the midtroposphere of the RECT experiment results in greenhouse forcing less sensitive to TSI than in the AQP case.

Fig. 9.

(a) Total surface water flux (Pg s−1) and (b) surface water flux normalized by the ocean fraction [Pg s−1 (ocean fraction)−1] from 30°N to 30°S for all four geographies as a function of TSI. At 100% TSI, surface water flux is highest for the AQP configuration but falls most rapidly with TSI. Surface water flux normalized by the ocean fraction shows evaporation in tropical oceans is more efficient for the MAR and RECT configurations than for the AQP configurations.

Fig. 9.

(a) Total surface water flux (Pg s−1) and (b) surface water flux normalized by the ocean fraction [Pg s−1 (ocean fraction)−1] from 30°N to 30°S for all four geographies as a function of TSI. At 100% TSI, surface water flux is highest for the AQP configuration but falls most rapidly with TSI. Surface water flux normalized by the ocean fraction shows evaporation in tropical oceans is more efficient for the MAR and RECT configurations than for the AQP configurations.

Higher moisture contents over the RECT ocean imply the potential for greater latent heat release, driving deeper convection. Convective precipitation rates are double those over the ocean at 95% and 93% TSI in the RECT geography compared to AQP. Deeper convection and increased atmospheric moisture content changes the vertical distribution of clouds (Fig. 10) and may be responsible for the increased cloud forcing over the oceans in the RECT case compared to the AQP case. As noted above, clouds are nearly absent over the continent, but over the oceans midlevel cloud cover decreases and high-level cloud cover increases in the tropics and subtropics (Fig. 10). With higher moisture contents, low-level clouds tend to have a stronger impact on shortwave forcing because of higher optical depth, while high-level clouds tend to have a stronger warming effect through increased longwave forcing (Hartmann 1994). As a result, the shift in the vertical distribution of clouds results in 20–40 W m−2 more shortwave warming in the RECT case, while longwave warming is only reduced by 10–15 W m−2, suggesting that the enhanced Walker circulation warms the deep tropics by 5–30 W m−2 by altering the cloud distribution.

Fig. 10.

Difference between RECT and AQP vertical cloud fractions at 95% TSI. Both (left) zonally averaged differences and (right) longitudinal differences in the deep tropics (10°N–10°S) are shown. Contour interval is 0.05 and negative values are shaded. The Walker circulation simulated decreases the amount of low- and midlevel clouds and increases the amount of high-level clouds, increasing the shortwave cloud forcing in the tropics by 20–40 W m−2, while only decreasing the longwave cloud forcing by 10–15 W m−2.

Fig. 10.

Difference between RECT and AQP vertical cloud fractions at 95% TSI. Both (left) zonally averaged differences and (right) longitudinal differences in the deep tropics (10°N–10°S) are shown. Contour interval is 0.05 and negative values are shaded. The Walker circulation simulated decreases the amount of low- and midlevel clouds and increases the amount of high-level clouds, increasing the shortwave cloud forcing in the tropics by 20–40 W m−2, while only decreasing the longwave cloud forcing by 10–15 W m−2.

The Hadley circulation also shows variability with paleogeography. The Hadley circulation is stronger for the AQP configuration and is weaker for each of the MOD-NT, MAR, and RECT geographies at TSIs of 100%, 97%, and 95%. As in prior studies, the mass streamfunction of the mean meridional circulation increases in the tropics as TSI is reduced prior to the initiation of snowball states (Poulsen and Jacob 2004; Voigt and Marotzke 2009; Yang et al. 2012c). Strong differences persist between all geographies at all TSIs, however. For example, the Hadley circulation is stronger at 100% TSI for the AQP case than it is for any other configuration even at 95% TSI. Differences between paleogeographies and the seasonal maximum strength of the Hadley cells are larger than implied by the annual mean (Yang et al. 2012c), but the lack of a consistent trend between NH Hadley cell strength in austral summer and SH Hadley cell strength in boreal summer with paleogeographic arrangement suggests that poleward energy transport by the Hadley circulation is not a dominant mechanism for restricting ice expansion at high TSIs. Direct comparison of different geographies at the same TSI may be compromised since the ice position evolves differently across geographies. Strong land–sea contrasts with tropical continents do, however, strengthen the mean zonal circulation and result in an anomalously strong Walker circulation. Coupled with enhanced longwave cooling over tropical continents, strengthened tropical zonal circulation likely decreases the efficiency of poleward heat transport, resulting in tropical temperatures and an ice line position that is less sensitive to changes in radiative forcing. This finding is consistent with energy balance model predictions (Held and Suarez 1974).

In future work (R. P. Fiorella and C. J. Poulsen 2013, unpublished manuscript), we show that the reduced climate sensitivity in the RECT case to changes in TSI and CO2 relative to the climate sensitivity observed in the AQP cases is principally because of (i) a stronger surface albedo feedback in the AQP case, resulting from a larger contrast between the ocean and the sea ice than between land and snow and (ii) a more rapid decay of the water vapor feedback strength with TSI for the AQP case, resulting in stronger ice line responses to TSI perturbations at high TSI. The more strongly positive water vapor feedback in the AQP configuration relative to the other configurations at high TSI may play a role in inducing the Jormungand state in this configuration.

e. Effect of topography in the modern simulations

To assess the impact of topography on snowball initiation, we performed additional simulations using the modern continental arrangement with modern topography (MOD-WT). Including topography lowers the snowball Earth initiation threshold from 90% in the MOD-WT case to 88% in the MOD-NT case. At TSI higher than the bifurcation point, however, mean annual surface temperature and surface and planetary albedo remain similar (Fig. 11), indicating that the change in the bifurcation point cannot be explained by a difference in global albedo.

Fig. 11.

(a) Mean annual surface temperature (K) and (b) ice margin latitude for the MOD-WT and MOD-NT experiments as a function of TSI. Albedos are tightly coupled to temperature and are not shown. Adding topography to the MOD-NT continental configuration raises the snowball bifurcation point from 88% to 90% modern TSI; though above the bifurcation points, little difference exists between global surface temperature and ice margin latitude.

Fig. 11.

(a) Mean annual surface temperature (K) and (b) ice margin latitude for the MOD-WT and MOD-NT experiments as a function of TSI. Albedos are tightly coupled to temperature and are not shown. Adding topography to the MOD-NT continental configuration raises the snowball bifurcation point from 88% to 90% modern TSI; though above the bifurcation points, little difference exists between global surface temperature and ice margin latitude.

In addition to regional cooling and increased albedo over high elevation regions (e.g., the Tibetan, Andean, and South African plateaus), the addition of topography reduces the equator-to-pole temperature gradient by up to 15 K. This change is attributed to increases in subtropical albedo and decreases in midlatitude albedo (particularly in the Northern Hemisphere), which change the albedo distribution without changing planetary albedo (Fig. 12b). The meridional distribution of albedo changes in response to a decrease (increase) of cloud cover (Fig. 12c) and snow depth (Fig. 11d) in the midlatitudes (subtropics). Though Fig. 12 shows results for 90% TSI, the trend shown is present for all TSI above the bifurcation point between non-snowball and snowball states. The magnitude of this albedo change increases with decreasing TSI, driving an increasingly small equator-to-pole temperature gradient relative to MOD-NT in the MOD-WT simulations as TSI is reduced to the bifurcation points.

Fig. 12.

Contour difference plots between MOD-WT and MOD-NT for (a) surface temperature (K), (b) planetary albedo, (c) cloud fraction, and (d) snow depth (m, liquid water equivalent) at 90% TSI. Adding topography reduces the equator-to-pole temperature gradient in (a) by raising subtropical albedo and lowering midlatitude albedo in (b), particularly in the Northern Hemisphere where the majority of modern land is located. Albedo changes are driven by changes in cloud cover and snow depth in (c) and (d).

Fig. 12.

Contour difference plots between MOD-WT and MOD-NT for (a) surface temperature (K), (b) planetary albedo, (c) cloud fraction, and (d) snow depth (m, liquid water equivalent) at 90% TSI. Adding topography reduces the equator-to-pole temperature gradient in (a) by raising subtropical albedo and lowering midlatitude albedo in (b), particularly in the Northern Hemisphere where the majority of modern land is located. Albedo changes are driven by changes in cloud cover and snow depth in (c) and (d).

This redistribution of albedo alters the top of the atmosphere radiative balance, warming the midlatitudes and cooling the subtropics in MOD-WT. Temperatures in the Northern Hemisphere midlatitudes increase by 15 K. Ice expands more rapidly with the reduction in TSI with a decreased meridional temperature gradient as a negative global temperature perturbation plunges a larger area below freezing, causing greater expansion of sea ice. This effect is especially apparent as ice encroaches into the tropics where the meridional temperature gradient is weaker than in the subtropics and midlatitudes. Furthermore, easier initiation of snowball states associated with more efficient poleward energy transport relative to longwave cooling is predicted by EBMs (Held and Suarez 1974).

4. Discussion

The forcings required to initiate a snowball state for all continental configurations tested here require reductions in TSI below expected Neoproterozoic values based on the standard solar evolution model. Therefore, our results do not directly support the “hard snowball” hypothesis, though it is possible the radiation receipt at the surface may have been lower through mechanisms other than reduced solar irradiance, such as an increase in volcanic aerosols or a lower concentration of greenhouse gases than used in these simulations. Our results using CAM3.1 do suggest, however, that if Neoproterozoic glaciations were global, the concentration of land in the tropics was unlikely to be the facilitating factor. The omission of ocean and sea ice dynamics, factors that are known to affect snowball Earth initiation (Poulsen et al. 2001; Poulsen and Jacob 2004; Voigt and Abbot 2012), are the limitations of our study but do permit exploration of a wider range of paleogeographies and forcings through increased computational efficiency. Additionally, the mechanism facilitating lower climate sensitivities in configurations with large tropical landmasses may vary in different models, however; for example, Poulsen et al. (2002) use FOAM and conclude that tropical landmasses inhibit snowball initiation, but experiments using the ECHAM5/MPI-OM tropical landmasses encourage snowball initiation (Voigt et al. 2011).

Land surface albedos in these simulations are lower than those in previous studies. Desert soil albedos (0.35 and 0.51 in the visible and near-infrared) in FOAM (e.g., Poulsen et al. 2001; Poulsen 2003) and GENESIS (e.g., Jenkins and Frakes 1998; Baum and Crowley 2001, 2003) are based on the Biosphere–Atmosphere Transfer Scheme (Dickinson et al. 1993). Surface albedos in the GISS model [0.35 in both visible and near-infrared; Hansen et al. (1983)] are slightly lower in the near-infrared than FOAM or GENESIS. Land albedo may play a strong role in setting the strength of the Walker circulation observed through modulating the intensity of radiatively driven subsidence over the continent as well as the size of the radiatively direct portion of the surface energy budget. Land surface albedos in the Neoproterozoic are poorly constrained, but albedos lower than those in modern deserts might be reasonable as a result of widespread deposition of flood basalts due to the rifting of Rodinia (Li et al. 2008; Hoffman and Li 2009) or land surface coverage by terrestrial microbial communities (Lenton and Watson 2004; Knauth and Kennedy 2009).

The impact of paleogeography on snowball initiation within one model may be as large as the variation between models. For example, snowball initiation experiments for modern continents with modern topography with CCSM3 (CAM3.1 coupled to dynamic ocean and sea ice models; Collins et al. 2006b) by Yang et al. (2012b) yield a snowball state with a reduction between 10% and 10.5% TSI; our experiments predict a snowball state with a reduction between 10% and 11% TSI. In contrast, larger TSI reduction is required for the RECT geography in CAM3.1 than required in FOAM for a similar idealized supercontinent (Poulsen and Jacob 2004). In Poulsen and Jacob (2004), a CO2 concentration of 140 ppm was used, reducing greenhouse radiative forcing by 2.7–3.7 W m−2 (Myhre et al. 1998; Collins et al. 2006a). Assuming a fairly low planetary albedo of 0.3 near the bifurcation point, however, the extra 6% reduction in TSI necessary to initiate a snowball Earth in our experiments represents a 14.4 W m−2 change in top of the atmosphere radiative forcing, indicating snowball states are more difficult to simulate in CAM3.1. Finally, much larger reductions in TSI for snowball Earth initiation are required herein than for experiments performed in ECHAM5/MPI-OM for both the modern (Voigt and Marotzke 2009) and Marinoan (Voigt et al. 2011) continental configurations. Additionally, land temperatures for all MAR and RECT experiments at or above 90% TSI and for all MOD-NT experiments at or above 93% TSI are too warm to support land glaciers, matching results from FOAM (Poulsen et al. 2002) and GENESIS (Jenkins and Frakes 1998) but contrasting with results from ECHAM5/MPI-OM (Voigt et al. 2011). Conditions amenable to low-latitude glaciation, however, are also strongly related to the elevation and topography used in the model (Pollard and Kasting 2004).

A large portion of the initiation threshold range can be attributed to model differences in albedo parameterizations (Pierrehumbert et al. 2011). Ice albedos in FOAM exceed ice albedos in CAM3.1 by approximately 0.10, suggesting a stronger ice–albedo feedback in FOAM than CAM3.1 with all else equal. Supporting this conclusion, setting both FOAM and CAM ice albedos to 0.6 yields identical initiation thresholds (Pierrehumbert et al. 2011). Comparison between ECHAM5 and CAM3.1 is more challenging. CAM3.1 tracks snow on sea ice and assigns a higher albedo to snow-covered sea ice, however, while ECHAM5 does not. Therefore, a stronger ice–albedo feedback may in part explain the difference between our results in CAM3.1 and reported ECHAM5/MPI-OM results (Voigt and Marotzke 2009; Voigt et al. 2011). The initiation of snowball states in the ECHAM5 model remains easier than in CAM3.1 when ECHAM5 snow and sea ice albedos are set to CAM3.1 values, highlighting the importance of intermodel differences in atmospheric dynamics, cloud forcing, and sea ice dynamics (Pierrehumbert et al. 2011; Voigt and Abbot 2012).

Differences in the complexity between the models used to approach the snowball problem also certainly play a role in expanding the range of initiation thresholds. The absence of dynamic ocean circulation and sea ice are the limitations of our study. Previous studies using both diffusive energy balance models (Rose and Marshall 2009) and general circulation models (Poulsen et al. 2001) find that ocean heat transport stabilizes sea ice margins at higher latitudes. As a result, the addition of ocean heat transport to our model would imply increased TSI thresholds for global glaciation. The addition of sea ice dynamics may limit the stabilizing effect of ocean heat transport, however (e.g., Voigt and Abbot 2012). Experiments by Yang et al. (2012b) show a rapid transition between a stable state with about 40% sea ice coverage and one with about 60% ice coverage when CO2 concentration is reduced from 70 to 50 ppm at 94% TSI, a change in radiative forcing of about 1.3 W m−2 (Collins et al. 2006a). Global ice coverage occurs when CO2 is further lowered to 17.5 ppm, suggesting this high ice coverage state is only stable in a small parameter space. Curiously, this rapid transition was not observed when TSI is lowered instead of CO2. Yang et al. (2012b) attribute this to the latitudinal dependence of solar radiative forcing compared to the latitudinal independence of greenhouse forcing for well-mixed greenhouse gases, using a modified EBM to show that when the ice line expands equatorward of 20°, the sensitivity due to solar forcing is stronger than the sensitivity due to greenhouse gas forcing.

Unlike the results in Abbot et al. (2011), we do not find a rapid transition between ice-free conditions and the Jormungand state. The immediate transition between an ice-free state and the Jormungand state is attributed to model deficiencies associated with the idealized configuration of CAM [aquaplanet with no aerosols, modified greenhouse gas concentrations, and no ocean heat transport detailed further in Pierrehumbert et al. (2011)]. In our experiments, different geographies may shrink the envelope of climate parameters favorable to initiating the Jormungand state and may be responsible for the absence of the strong bifurcation between ice-free conditions and the Jormungand state. Radiative forcing by TSI was never high enough to simulate an ice-free state in our experiments (the highest CO2 cases do have some seasonal ice in winter, but the summer hemisphere is ice free), but states with stable ice latitudes intermediate to ice-free and Jormungand states likely result from a smaller reduction in radiative forcing in the extratropics from TSI reductions relative to the reduction in radiative forcing resulting from reduced greenhouse gas concentrations. For the same reduction in global radiative forcing, reductions in greenhouse forcing affect all latitudes similarly, while the impact of TSI reductions is most pronounced in the tropics because of the latitudinal dependence of solar insolation (Yang et al. 2012b,c).

A final attractive aspect of the low-latitude continent snowball Earth initiation theory was that as glaciers formed on land, the sea level would drop, exposing continental shelves and further increasing surface albedo as land replaces the ocean. Rather, our results suggest as sea level drops and shallow seas in the tropics are replaced by land, snowball Earth initiation becomes more difficult as continental interiors dry, land–sea contrast becomes more pronounced, and a Walker-style circulation intensifies.

Additionally, our results challenge the recent claim that the faint young Sun paradox may be resolved by decreased surface albedo associated with decreased land area instead of increased greenhouse gas concentrations (Rosing et al. 2010). Based on results from a single-column radiative–convective model, Rosing et al. (2010) propose less emerged continents and decreased biogenic cloud condensation nuclei in the Archean eon sufficiently lower the planetary albedo to obviate the faint young Sun problem, though both their interpretation of geochemical evidence and assumption of dramatically reduced cloud condensation nuclei have been challenged. Furthermore, our results using CAM3.1 show that the addition of continents reduces planetary albedo through water vapor and cloud adjustments and results in planetary warming. Dynamical differences between the AQP and other configurations all suggest a colder planet when land is removed, making the faint young Sun paradox more severe in CAM3.1. The radiative–convective model used by Rosing et al. (2010) would not have simulated the mechanism by which AQP is shown to have greater climate sensitivity to changes in TSI.

Future work (R. P. Fiorella and C. J. Poulsen 2013, unpublished manuscript) analyzes climate feedback strengths and their sensitivity to TSI and CO2 changes using radiative kernels. We show that paleogeography has significant impacts on the water vapor and surface albedo feedback strengths in particular. As a result, estimates of paleoclimate sensitivity that fail to consider changes in paleogeography may be biased.

5. Conclusions

Our simulations do not support the hypothesis that increased tropical landmass would facilitate initiation of a snowball Earth event. While raising surface albedo, large tropical landmasses alter the partitioning of energy in the tropics such that the global climate is less sensitive to reductions in top of the atmosphere shortwave forcing. The energy budget in an aquaplanet configuration has a stronger dependence on greenhouse forcing, while the energy budget of the modern (no topography), Marinoan, and rectangular supercontinent configurations show stronger dependence on direct radiative forcing. As greenhouse forcing decreases exponentially with temperature following specific humidity scaling by the Clausius–Clapeyron equation, direct top of the atmosphere shortwave forcing decreases linearly with incremental decreases in TSI. When there is a high degree of land–sea contrast in the deep tropics, an amplified Walker circulation reduces tropical temperature sensitivity to changes in TSI, enhances evaporation over the tropical oceans, and maintains a stronger greenhouse effect at reduced TSI than when no land is present. Topography also provides a strong control on snowball Earth initiation. Including topography in a modern continental configuration lowered the TSI threshold for snowball Earth initiation by up to 2% by altering cloud and snow coverage and the meridional albedo gradient, reducing the equator-to-pole temperature gradient, in agreement with energy balance model predictions.

More generally, this study demonstrates that paleogeography and paleotopography can have a significant impact on climate sensitivity by repartitioning energy in the climate system. As a result, paleogeography and paleotopography must be considered when using paleoclimate records to estimate climate sensitivity to changing atmospheric CO2.

Acknowledgments

We thank C. Jablonowski and C. M. Bitz for helpful discussions and C. M. Bitz and C. Shields for technical assistance. M. L. Jeffery, B. J. Yanites, C. R. Tabor, T. M. Gallagher, and R. Feng provided comments improving an early draft of this paper. This material was supported by the National Science Foundation Graduate Research Fellowship under Grant 2011094378 to RPF and a BP Geosciences Fellowship to RPF. Model simulations were performed on the National Center for Atmospheric Research supercomputer Bluefire and on local clusters at the University of Michigan. We thank Dorian S. Abbot and an anonymous reviewer for insightful comments improving this manuscript.

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