1. Introduction
Several global glaciations have occurred during the late Neoproterozoic era of Earth history (850–541 Ma) (e.g., Hoffman et al. 1998; Hoffman et al. 2017), during which both the continents and oceans were probably covered by thick ice. These extreme glacial events have been termed the snowball Earth events. Much effort has been spent on determining the threshold atmospheric CO2 concentration (pCO2) below which Earth would enter a snowball state (Chandler and Sohl 2000; Feulner and Kienert 2014; Jenkins and Smith 1999; Liu et al. 2013; Poulsen and Jacob 2004; Poulsen et al. 2001; Poulsen et al. 2002; Voigt and Marotzke 2010; Voigt and Abbot 2012; Voigt et al. 2011; Yang et al. 2012a,b). This threshold value has been estimated to be roughly between 100 and 200 ppmv [see the summary in Liu et al. (2017)] by a few atmosphere–ocean general circulation models (AOGCMs), when the solar constant was fixed to be 94% of the present-day value (Bahcall et al. 2001; Gough 1981); both the upper and lower ends of the range can change by more than a factor of 2 depending on the albedos of sea ice and land (Voigt and Abbot 2012) and the continental configuration (Liu et al. 2018) used in the model. However, none of these studies considered the influence of dust, which could have been much more prevalent than in the present day (Liu et al. 2020) due to the fact that land was not covered by vegetation (Morris et al. 2018; Puttick et al. 2018).
Liu et al. (2020) showed that the atmospheric dust loading could reach more than 10 times that of the present day. Such large amount of dust scattered and absorbed over 20 W m−2 of solar radiation, so that the surface was cooled; the annually averaged global-mean surface temperature (GMST) was reduced by >10°C under a relatively warm Precambrian climate. In previous modeling studies with CCSM3, the GMST changes by 3°C for each doubling or halving of pCO2 when the climate is relatively warm (e.g., the present-day climate). This climate sensitivity to pCO2 increases to ~6°C when the climate is cold (e.g., GMST < 0°C, but before entering a snowball state) (e.g., Liu et al. 2013; Yang et al. 2012a). Even for this high climate sensitivity, 10°C or more of cooling due to dust means that the previously obtained threshold pCO2 from AOGCMs should be nearly quadrupled if the influence of dust had been considered in the model.
The real threshold pCO2 may not be derived in such a straightforward way since the atmospheric dust loading and its radiative forcing change with the climate. For example, as the climate gets colder, more ice and snow are accumulated at the surface, which will prohibit dust emission. On the other hand, as the climate gets colder, bare soil becomes drier, which promotes dust emission (Marticorena and Bergametti 1995). Moreover, the deposition of dust onto snow and ice reduces surface albedo and will have a warming effect (He et al. 2019), which may partially or fully offset the cooling effect of atmospheric dust when snow or ice area is large. In the extreme case of global ice cover (i.e., a snowball Earth), dust has a significant warming effect by either reducing the snow or ice albedo (Abbot and Pierrehumbert 2010; Le Hir et al. 2010). In this case, even the atmospheric dust might cause significant surface warming because it is more absorptive to sunlight than the surface ice (Abbot and Halevy 2010); this effect should also exist over the high-latitude region in a non–snowball Earth climate. Liu et al. (2020) has examined the dust impact on climate only for a relative warm climate state, for which the dust had a cooling effect. Therefore, it is unclear how the dust emission and deposition will change when the Earth marches toward a snowball state, and how it will impact on the threshold pCO2. Our purpose here is to investigate the impact of the atmospheric dust loading on a cold climate and the threshold pCO2 for snowball Earth formation with an AOGCM in which the dust emission, transportation, and deposition are enabled.
2. Methods
a. Model description and experiments
The Community Earth System Model version 1.2.2 (CESM 1.2.2) developed by National Center for Atmospheric Research (NCAR) is employed in this study. It is a state-of-the-art AOGCM that simulates physical, chemical, and geobiological processes in the atmosphere, land, sea ice, ocean, land ice, and rivers (Hurrell et al. 2013). For the purpose of the current study, the land ice component is turned off due to its long time scale, as in previous studies (Liu et al. 2013; Voigt et al. 2011; Yang et al. 2012a). Ice sheets on land may affect the atmospheric dynamics by changing surface topography and may produce rock powder (which is a good dust source) by grinding the land surface. It is thus desirable to perform simulations with active land ice in the future when increased computational power will make such computationally expensive simulations feasible. For now, we consider simulating only the deposition of snow on land as a reasonable compromise, since surface snow has a high albedo and prohibits dust emission just like an ice sheet. The biogeochemical component is also inactive in our simulations.
For the atmospheric component, the Community Atmosphere Model version 4 (CAM4) is used and run with its finite volume dynamical core (Neale et al. 2010). For the land component, the Community Land Model version 4 (CLM4) is used (Oleson et al. 2010). Both CAM4 and CLM4 are run at a horizontal resolution of 1.9° × 2.5°. The ocean component [Parallel Ocean Program Ocean model version 2 (POP2); Smith et al. 2010] and sea ice component [Community Ice Code version 4.0 (CICE4); Hunke et al. 2010] are run on the same horizontal grid with a nominal 1° resolution. The grid points are uniformly spaced (with a spacing of 1.125°) along the zonal direction but nonuniformly spaced along the meridional direction; the spacing is ~0.26° near the equator, ~0.70° around midlatitudes, and ~1° near the poles. In the vertical direction, the atmosphere and ocean have 26 and 60 layers, respectively. The sea ice albedo is 0.60 (0.45 in the near-infrared and 0.75 in the visible) and the snow albedo is 0.86 (0.73 in the near-infrared and 0.98 in the visible) (Hunke et al. 2010).
The soil erodibility (k) is a key parameter in determining the amount of dust that can be emitted from the ground by a given wind stress (Prospero et al. 2002; Zender et al. 2003a). The value of k is determined by topographic distribution but not a simple function of local topography; it is proportional to the upstream area from which surface runoff may reach this location (Zender et al. 2003a). The rationale is that more fine-grained material will accumulate at locations where their upstream rivers pass by larger area (the geomorphic erodibility hypothesis). Therefore, in general, local topographic maxima have small erodibility values and minima have large erodibility values but the values need be adjusted according to the detailed distribution of surrounding topography. The value of k in the Amazon forest region could thus be similar to that in the Saharan deserted region (see Fig. 1c in Zender et al. 2003a), except that the former does not emit dust due to the protection by vegetation.
The value of k varies spatially between 0 and 5.7 on the present-day Earth with a global mean value of 0.15 (Zender et al. 2003a). With no detailed information available for the Neoproterozoic, a spatially uniform value is used herein; two very different values, 0.15 and 0.01875 (i.e., 0.15/8; the value 0.15 is halved three times) are tested to cover the uncertainty in dust emission. As will be described later, this latter value will give an atmospheric dust loading of ~4.4 times that of present-day value. Such dust loading is modest given that the dust loading during the last glacial maximum (~21 000 years ago) was probably twice that of the present-day value (Albani et al. 2016), even though most of the land surface was still covered by plants. Note that the global pattern of dust emission is dominated by the climate pattern and is thus not greatly affected by assuming a uniform k, although local detailed emission could be unrealistic (cf. Figs. 2a and 2c in Zender et al. 2003a). One source of the uncertainties in k comes from the fact that cyanobacteria lived on land during the Precambrian and biogenic soil crust could form at the surface (Boyce and Lee 2017; Planavsky et al. 2021). Such soil crust could prevent surface dust emission just like vegetation but could be broken much more easily than the latter by wind or water flow. Since the distribution of such soil crust is unknown, a small k is tested as described above to hopefully cover its influence on dust emission.
The Dust Entrainment and Deposition (DEAD) scheme is used for dust emission in CLM4 (Zender et al. 2003b). The Bulk Aerosol Model (BAM) scheme is used in CAM4 to calculate the dust transportation and deposition for four different size bins (0.1–1.0, 1.0–2.5, 2.5–5.0, and 5.0–10 μm in diameter) (Mahowald et al. 2006; Schulz et al. 1998). The size distribution of emitted dust is fixed in the model but the size distribution of atmospheric dust loading changes with climate conditions. The fraction of fine dust particles (0.1–2.5 μm in diameter) in the dust loading is especially sensitive to changes in precipitation (Albani et al. 2014). In CAM4, only the shortwave radiative effect of dust is considered, its longwave radiative effect and indirect effect as cloud condensation nuclei (CCN) are neglected (Albani et al. 2014; Scanza et al. 2015). Previous studies indicated that the longwave radiative effect due to dust was much smaller than the shortwave effect both at the surface (Choobari et al. 2014) and at the top of atmosphere (Albani et al. 2014). Whether this effect remains small under a very cold climate such as a near-snowball state studied here is uncertain. The indirect effect of dust is difficult to estimate, but could cause additional surface cooling (Ghan et al. 2012; Sagoo and Storelvmo 2017). The effect of dust in lowering the albedo of snow and sea ice is included in CLM4 (Oleson et al. 2010) and CICE4 (Hurrell et al. 2013).
The continental configuration employed here is appropriate for 720 Ma (Li et al. 2008), most relevant for the first of the two Neoproterozoic snowball Earth events. Without reliable reconstructed topography, the average elevation of continent is assumed to be ~400 m above sea level, which is close to the modern global mean surface elevation. To route the river runoff toward the oceans, the elevation is increased to 450 m at the center of the continents and decreases linearly toward the edges. An idealized midocean ridge approximately 2000 m high is added on the ocean floor in the Northern Hemisphere to slow down the midlatitude oceanic current. Otherwise, the current will become intense due to the lack of continents between 45° and 70°N where the atmospheric westerly is strong (see Fig. 3 below). The ocean model may become unstable when this ocean current becomes too strong according to our previous experience (Liu et al. 2013). In reality, there are almost always midocean ridges in the open ocean; adding ridges has little influence on the global surface climate and the threshold pCO2 as has been tested previously (Liu et al. 2013). Moreover, because the ocean grids converge at the two poles, there will be numerical singularities there. To avoid such singularity, one small circular continent of radius ~5° is placed at each pole. These small continents have negligible effect on the global climate and dust emission (mostly snow covered). Adding two polar continents is also the recommended approach by NCAR when simulating deep paleoclimate and has been adopted in previous studies (Liu et al. 2013, 2020). The solar constant is set to be 1285 W m−2, 94% of the present-day value (~1367 W m−2), since the sun was fainter in the past (Gough 1981). The orbit parameters for year 1990 are used. The preindustrial values of 805.6 and 276.7 ppbv are specified for CH4 and N2O concentrations, respectively. Aerosols such as black carbon, sulfate, and organic carbon are omitted because our main focus here is on the dust aerosol. All the configurations described above are similar to those in Liu et al. (2013, 2017), where the threshold pCO2 has been searched with an older version of the model, CCSM3, at a significantly lower spatial resolution.
Three sets of experiments are carried out, with k set to 0 (no dust), 0.15/8 and 0.15, respectively. Two control simulations are run to near equilibrium (after ~2300 model years) with pCO2 = 2000 ppmv for the cases k = 0 and 0.15. The surface climate still drifts slowly [~1°C (1000 yr)−1] at the end of simulations. Since the temperature changes due to perturbations applied herein is much larger than 1°C, the slow drifting of climate is not expected to affect the analyses presented herein. Then a series of simulations are branched off from the control runs with lower and lower pCO2 until a snowball Earth is obtained. A control simulation is not performed for k = 0.15/8 and all simulations for this intermediate k are branched off from the control simulation for k = 0.15. Typically, the branch runs are continued for 300 to 500 years in order to reach quasi-equilibrium (Fig. 1). The last 100 years of data are used for analyses. All simulations are summarized in Table 1.
Time series of (a) global mean surface temperature and (b) the global fraction of sea ice for all simulations.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
Summary of results for all fully coupled runs. The two values in the k_CO2 column represent the erodibility level and CO2 concentration (ppmv), respectively. DOD, FFP, DD, WD, and DO stand for dust optical depth, fraction by mass of fine particles (0.1–2.5 μm), dry deposition rate, wet deposition rate, and total deposition over ocean, respectively.
b. Diagnosis of radiative effect of dust
We take a similar approach as in Yoshioka et al. (2007) to estimate the direct shortwave radiative effect of dust by modifying the radiation subroutines in CAM4 and operating diagnostic runs. In each time step, the radiative fluxes are calculated twice, one with the radiative function of dust turned off and the other turned on. The purpose of the former is just to output the relevant radiative fluxes. These fluxes do not participate in other model calculations. Both radiative fluxes are output and the difference between them gives us the radiative effect of dust. Five years of simulations are carried out for each case for this purpose. The radiative effect diagnosed this way does not perturb the climate like in the method below and is thus precise. (The diagnoses shown in Figs. 11, 13a, and 13e are produced this way.)
The method above is not feasible when diagnosing the changes in other fluxes such as sensible and latent heat fluxes due to dust. These flux changes can be obtained simply by subtracting the respective fluxes from coupled simulations with and without dust. However, because sea ice extent and sea surface temperature (SST) may change substantially between the runs, flux changes diagnosed this way contain the contribution due to sea ice and SST changes. Therefore, we also carry out series of AGCM calculations in which the sea ice and SST are prescribed. Even so, the diagnosed flux changes are contaminated by snow and surface temperature changes on sea ice and land. All AGCM simulations are run for 50 years and the last 10 years are used for analyses. (The flux changes in Figs. 13b–d, 13f–h, 14, and 15 are obtained using this method.)
3. Results
a. Dust emission and atmospheric dust loading
When k is 0.15, the global dust emission is ~85 700 teragrams (Tg) per year when pCO2 is 2000 ppmv, ~36 times that of the present day (2365 Tg; Albani et al. 2014). Most of the dust is emitted from subtropical regions (Figs. 2a–d) where soil is dry (Figs. 3a–d) and/or wind stress is strong (Figs. 3e–h), both of which have significant seasonal variations. Therefore, most atmospheric dust resides in the low-latitude regions in the downwind direction (Figs. 2e–h), where it is very effective in blocking the sunlight and cooling the surface. Because land area in the Southern Hemisphere is larger than that in the Northern Hemisphere, the annual emission over the former is significantly larger than that over the latter (Fig. 5a), and so is the dust loading (Fig. 5b).
(a)–(d) Surface dust emission and (e)–(h) atmospheric dust loading for four seasons; k = 0.15 and pCO2 = 2000 ppmv.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
(a)–(d) Soil moisture (unit: % by volume) and (e)–(h) surface wind stress (unit: N m−2) for four seasons; k = 0.15 and pCO2 = 2000 ppmv.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
Global dust emission decreases monotonically with the decrease of pCO2, but the rate of decrease is small before pCO2 is reduced to a very low value (Table 1). The global emission is ~77 200 Tg yr−1 when pCO2 is 140 ppmv, only ~10% smaller than when pCO2 is 2000 ppmv, but the emission decreases abruptly to ~52 900 Tg yr−1 when pCO2 is 70 ppmv. Accordingly, the dust deposition into ocean also decreases (Table 1). The change of land snow cover (Figs. 4f–j) has a significant impact on the spatial pattern of dust emission (Figs. 4a–e); the sudden decrease of global dust emission when pCO2 is lowered from 140 to 70 ppmv is consistent with the dramatic expansion of land snow cover (cf. Figs. 4i,j). Together with the equatorward expansion of snow cover, the wind stress strengthens around the equator (Figs. 4k–o), making up some of the subdued dust emission in regions covered by snow. The strengthening of winds is due to increased meridional temperature gradient within the tropical region and the strengthening of Hadley circulation (e.g., Fig. 9 of Yang et al. 2012a). Wind stress weakens in most of the mid- to high-latitude regions. However, its impact on dust emission is small since these regions are covered by snow already. Consistent with the changes of snow cover and wind stress, the latitudes of peak zonal mean dust emission shift toward the equator (Fig. 5a).
(a)–(e) The annual mean dust emission (filled contours; unit: kg m−2 s−1) and surface wind velocities (arrows; unit: m s−1) for different pCO2. (f)–(j) Annual mean snow depth (unit: cm) and (l)–(o) anomalies of surface wind stress (unit: N m−2) for different pCO2. In (k), the annual mean surface wind stress rather than its anomaly is shown; in (l)–(o), the differences in wind stress between the respective cases and the case in (k) are shown. Note that (l)–(o) share the same color bar on the right of (l). (p)–(t) Annual mean precipitation with different pCO2. For all cases k = 0.15.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
Zonal mean (a) surface dust emission and (b) atmospheric dust loading. The solid lines are the scenarios for different pCO2 when k = 0.15, while the dashed curves represent the case when pCO2 = 280 ppmv and k = 0.15/8.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
Global atmospheric dust loading (the total weight of dust in the atmosphere) is 689 Tg when k = 0.15 and pCO2 is 2000 ppmv, ~25 times that of the present day. In contrast to surface dust emission, the atmospheric dust loading does not change monotonically with decrease of pCO2 (Table 1). The loading decreases first slightly to 658 Tg when pCO2 is reduced from 2000 to 560 ppmv, and then increases slightly to 685 and 716 Tg when pCO2 is decreased to 280 and 140 ppmv, respectively. The dust loading increases abruptly to 912 Tg when pCO2 is reduced further to 70 ppmv. The increase is mainly in the equatorial region and the whole Northern Hemisphere (Fig. 5b).
The abrupt increase of dust loading when pCO2 is reduced from 140 to 70 ppmv is clearly due to the abrupt decrease of precipitation (Figs. 4p–t) and wet deposition (Table 1). Wet deposition is responsible for removing approximately a third of atmospheric dust under warmer climate (Table 1), especially the fine dust particles (less than 2.5μm in diameter) (Zender et al. 2003b), but is only 21% under very cold climate (GMST = −22.8°C when pCO2 = 70 ppmv). The increase of dust loading in the Northern Hemisphere is likely due to the strengthening of the Hadley circulation during June–August (JJA) as pCO2 decreases (Fig. 6). The strengthened Hadley circulation not only brings dust to higher altitude, but also brings more dust from the Southern Hemisphere into the Northern Hemisphere by near-surface winds. The Hadley circulation during other seasons changes little (not shown).
(a)–(c) Dust emission and (d)–(f) Hadley circulation during JJA; pCO2 is (top) 2000, (middle) 280, and (bottom) 70 ppmv. The surface winds are also superimposed in (a)–(c). In all panels k = 0.15.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
For k = 0.15/8, dust emission and atmospheric dust loading are available for only one case (pCO2 = 280 ppmv). Both of them are reduced by a factor of ~5 compared to those for k = 0.15 (Table 1 and Fig. 5). This rate of change is similar to that obtained in Liu et al. (2020) for a warmer climate. The dust loading is 122 Tg, 4.4 times that of present-day value (~27.5 Tg) and approximately twice that of last glacial maximum (~21 000 years ago; Albani et al. 2016).
b. Climate impact of dust
When climate is warm, dust has a significant impact on the GMST; the GMST without dust is 14.5°C when pCO2 is 2000 ppmv and decreases to −2.5°C once dust is considered (k = 0.15; Figs. 7a,b). This represents a cooling of 17°C, much greater than the temperature change between the present day and the last glacial maximum (~21 000 years ago) which is only ~4.7°–8.6°C (Snyder 2016). Correspondingly, the sea ice expands from ~54° latitude to ~30° latitude (Figs. 7c,d). Therefore, dust alone could have driven a warm climate into a severe glaciation if surface erodibility k was indeed as large as 0.15. However, when pCO2 is lowered to 280 ppmv, the impact of dust on GMST becomes minor. At this pCO2, GMST without dust is −12.3°C and sea ice edges are near the tropical region already. When dust is considered (k = 0.15), the GMST decreases only slightly to −13.7°C although both the atmospheric dust loading and its optical depth are similar to when pCO2 is 2000 ppmv (Table 1). For this case, adding dust cools the tropical region but warms the polar regions (cf. the yellow and dark blue curves in Fig. 9a; see also Figs. 8d,f); the area of sea ice increases by expanding equatorward but the thickness of sea ice in polar regions decreases (Figs. 8g,i). The thinning of sea ice is mainly due to strengthened westerlies in the mid- to high latitudes (cf. Figs. 8c,a) and thus larger equatorward Ekman transport (cf. Figs. 8l,j). More discussion about this is presented in section 4b.
Annual mean (a),(b) surface temperature and (c),(d) sea ice thickness for cases (top) without and (bottom) with dust; pCO2 is 2000 ppmv in all cases, and k = 0.15 in (b) and (d).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
Annual mean (a)–(c) surface winds, (d)–(f) surface temperature, (g)–(i) sea ice thickness, and (j)–(l) sea ice velocity for cases (top) without and (middle),(bottom) with dust. In all cases pCO2 is 280 ppmv; k = 0.15/8 in (b), (e), (h), and (k) and k = 0.15 in (c), (f), (i), and (l).
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
For k = 0.15/8, the GMST is −16.2°C when pCO2 is 280 ppmv. This is colder than that for k = 0.15 under the same CO2 forcing although the atmospheric dust loading is less than one-fifth of that in the latter case. Figure 9a shows that the two cases have similar surface temperature in the tropical region, but the case with more dust (k = 0.15) has much warmer temperature over the mid- to high-latitude regions than the case with less dust (k = 0.15/8). Interestingly, the global sea ice fraction is almost the same (Fig. 1b) for k = 0.15/8 and 0.15. This is likely due to the much stronger equatorward Ekman transport of sea ice in the case k = 0.15 than in k = 0.15/8, as will be discussed in more detail in section 4b.
(a) Zonal mean surface temperature and (b) vertical profiles of global mean air temperature. The cases for pCO2 equaling to 2000 and 280 ppmv are shown.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
As has already been demonstrated in Liu et al. (2020), the vertical profiles of atmospheric temperature changes significantly when substantial dust is present in the air. This is demonstrated again here in Fig. 9b. Such changes in vertical structure of temperature affects many of the surface energy fluxes and could be the major reason why the surface temperature for case k = 0.15 is not much colder than that for case k = 0. This will also be discussed in section 4.
The annual mean precipitations for k = 0.15/8 and 0.15 are ~19% and 40% less than when there is no dust (Fig. 10). The decrease of surface temperature reduces evaporation and the moisture holding capacity of atmosphere according to the Clausius–Clapeyron relationship. Ideally, the precipitation rate may change by 7% per 1°C of temperature change; in reality, both the observed and model-simulated precipitation due to global warming driven by greenhouse gases is approximately half that value (Skliris et al. 2016). The dust-induced precipitation change rate is ~4.9% °C−1 and 28.6% °C−1 for k = 0.15/8 and 0.15, respectively. The former can probably be explained partially by the temperature change, while the latter clearly cannot be explained by the temperature change. Since the model ignores the indirect effect of dust as cloud condensation nuclei and the GMST is similar for the three cases (Table 1), the significant decrease in precipitation for nonzero k must be due to suppression of convection by presence of dust. The heavy dust loading heats the lower to mid atmosphere significantly in case k = 0.15, reaching 0.6 K day−1 between 800 and 600 hPa in terms of the global mean (Liu et al. 2020). The dust heating is the strongest where the dust loading is the heaviest, and is thus not shown. This enhanced heating of the tropospheric relative to the near-surface atmosphere increases the stability of the lower atmosphere as can be inferred from the vertical gradients of the temperature profiles in Fig. 9b, and suppresses precipitation in the tropical region (Fig. 10).
(a) Annual mean precipitation without dust, and its anomalies with respect to zero-dust case when k = (b) 0.15/8 and (c) 0.15; pCO2 is 280 ppmv for all three cases.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
c. Snowball Earth bifurcation point
Without dust, the modeled Earth climate enters a snowball state when pCO2 is between 280 and 140 ppmv (Fig. 1). This is in the same range as those obtained by previous AOGCMs summarized in Liu et al. (2017), but is higher than that obtained by CCSM3, which was between 60 and 50 ppmv (Liu et al. 2013). The increased threshold pCO2 is probably because of the higher surface albedo of snow (0.86 vs 0.82) and sea ice (0.60 vs 0.53) in CESM1.2.2 than in CCSM3. When a relatively weak dust emission (k = 0.15/8) is considered, the threshold pCO2 is also between 280 and 140 ppmv. However, when a much stronger dust emission (k = 0.15) is considered, the bifurcation point is significantly lower, between 70 and 35 ppmv (Table 1 and Fig. 1). Therefore, although dust has a strong cooling effect during the warm period of the Neoproterozoic (Liu et al. 2020), most likely heavy dust could have made it harder for Earth to enter a snowball state. The main reason may be that near the snowball bifurcation point (i.e., ice and snow cover is almost global), the planetary albedo for the regions covered by ice/snow would be reduced significantly if heavy dust loading is present. Reduction of planetary albedo increases the energy input into the climate system, some of which is transmitted to the surface (see discussion in section 4a).
It is notable that the global sea ice fraction is ~60% in the no-dust case (Fig. 1b) before the snowball state, which is only slightly larger than that (~55%) in the previous study (Liu et al. 2013). But the critical sea ice fraction is near 70% or even greater than 85% in the dust cases for k = 0.15/8 and 0.15, respectively (Fig. 1b). The existence of a threshold for sea ice fraction is essentially due to the runaway ice-albedo feedback within the tropical region. Because dust is the heaviest within the tropical region (Fig. 5b), this ice-albedo feedback might be greatly weakened (also see section 4a). This delayed sea ice run away is to some extent equivalent to the experiments in Voigt and Abbot (2012), where the threshold for sea ice fraction increased from 55% to 70% when sea ice albedo was lowered from 0.75 to 0.45.
4. Discussion
a. Cooling and warming effects of dust
Atmospheric dust is known to cool the surface by blocking the sunlight. However, our simulation results above demonstrate clearly that its cooling effect disappears and a global warming effect even appears under a very cold climate. In this section, we try to understand these two opposing effects of dust by diagnosing the related energy fluxes.
The changes in energy fluxes due to presence of dust can be relatively easily diagnosed for the three cases with pCO2 = 280 ppmv since the GMSTs are approximately similar whether there is dust or not (Table 1); the GMSTs for the cases with k = 0.15 and 0.15/8 are only 1.4° and 3.9°C lower than that for the case with k = 0 (i.e., no dust), respectively. Especially notable is that the case with more dust (k = 0.15) produces warmer climate than the case with less dust (k = 0.15/8). This does not happen for a relatively warm climate, as shown in Liu et al. (2020) where the GMSTs in all simulations were higher than −6°C. In a cold climate, ice/snow area is large. Dust is less reflective than ice and snow; more sunlight will be absorbed over ice- and snow-covered regions in the presence of dust aerosols or dust deposits on snow and ice.
Enhanced absorption of sunlight due to dust is most clearly seen from the changes in planetary albedo and the net downward shortwave radiation at the top of atmosphere (TOA) (Fig. 11). For strong dust emission (k = 0.15), the planetary albedo is significantly reduced over the mid- to high-latitude regions compared to cases with weak or no dust emission (Fig. 11c). This reduction is mainly due to absorption of sunlight by atmospheric dust since the reduction in surface albedo is small in most regions (Fig. 12). In many regions around 30° latitude, the surface albedo actually increases by more than 40% due to expansion of sea ice and snow coverage when dust is turned on (Fig. 12). Dust increases the planetary albedo within the tropical region where there is almost no snow or ice (Fig. 11). Averaged over the globe, the dust particles decrease planetary albedo by 0.41% and 2.86% for k = 0.15/8 and 0.15, respectively, and the net downward shortwave radiation at TOA increases by 1.02 and 7.84 W m−2, respectively. Note that the changes in both planetary albedo and shortwave radiation are diagnosed using the precise method of Yoshioka et al. (2007); an additional set of radiative fluxes is calculated online at each time step by ignoring the influence of dust (see more detail in section 2b). That is, the values in Fig. 11 are not the differences in albedo or radiative fluxes between k = 0.15/8 and k = 0 or between k = 0.15 and k = 0, but rather diagnosed in the cases for k = 0.15/8 or 0.15. The results mean that Earth absorbs more energy from the sun than when there is no dust in cold climates, similar to what has been suggested by Abbot and Halevy (2010) for a snowball Earth. The much larger increase in energy absorption for k = 0.15 than for k = 0.15/8 is a good indicator why climate in the former is warmer than that in the latter.
The changes in (a),(c) planetary albedo and (b),(d) net downward shortwave radiation at TOA due to dust. Positive is downward for (b) and (d). The gray contour lines represent the edges of sea ice with gridbox fraction of 50% in each panel. In all cases pCO2 = 280 ppmv; (left) k = 0.15/8 and (right) k = 0.15.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
The difference in (a),(c) surface albedo and (b),(d) downward shortwave radiation at the surface between the dust case (k = 0.15/8 and 0.15) and no-dust case (k = 0). Positive is downward for (b) and (d), and note that the global mean labeled at the top right of these two panels count only the positive values over the globe, different from those in Fig. 11. For all cases pCO2 = 280 ppmv; (left) k = 0.15/8 and (right) k = 0.15.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
Reduction of surface albedo is less than 0.05 in the case for k = 0.15/8 but can be greater than 0.1 between 30° and 45°N in the case for k = 0.15 (Fig. 12c). This is due to presence of dust impurities in snow over both land and sea ice and in the sea ice itself; the mass mixing ratio of dust can reach ~5 × 10−3 kg kg−1 in snow and ~0.1 × 10−3 kg kg−1 in surface sea ice (the upper 5 cm; not shown). This modeling result is broadly in line with the reduction in snow albedo by volcanic tephra observed by Dadic et al. (2013), where a mass mixing ratio around 10−3 kg kg−1 can lower the albedo of snow by more than 0.2. In some regions around 40° latitudes, the reduction of surface albedo exceeds 0.2. This is due to thinning of sea ice (Figs. 8g–i) and disappearance of land snow (not shown). But in some regions around 25° latitude, surface albedo increases substantially (>0.4), due to the equatorward expansion of sea ice.
Despite the increase in absorption at TOA when dust is present, the sunlight absorbed at the surface is reduced and causes cooling. To understand why the k = 0.15 case is warmer than the k = 0.15/8 case, the energy fluxes at the surface are diagnosed by additional experiments in which sea surface temperature and sea ice are fixed to those for k = 0. In this way, the energy flux changes due to surface feedbacks (e.g., changes in temperature and sea ice) are minimized. For these experiments, we again apply the same technique as in Yoshioka et al. (2007) to diagnose precisely the direct radiative forcing of dust at the surface. Dust reduces the global mean shortwave radiation received at the surface by 10.1 and 31.6 W m−2 for k = 0.15/8 and 0.15, respectively (Figs. 13a,e). However, because the vertical temperature structure changes significantly when dust is present (Fig. 9b), the surface gains energy by reducing the outward sensible and latent heat fluxes and receiving more clear-sky longwave radiative flux from above (Fig. 13). These fluxes can only be diagnosed by subtracting the respective variables between AGCM cases with dust and case without dust. The energy loss due to sensible heat flux is reduced by 4.0 and 10.8 W m−2 in terms of global mean for k = 0.15/8 and 0.15, respectively; for the latent heat flux, the values are 2.5 and 7.2 W m−2. The change in downward longwave radiative flux is negligible when k = 0.15/8, while it increases by 4.7 W m−2 when k = 0.15. The summation of these fluxes cancels more than two-thirds of the direct radiative forcings at the surface by dust.
(a),(e) The direct radiative forcing of dust and the changes of (b),(f) sensible heat flux (c),(g) latent heat flux, and (d),(h) downward clear-sky longwave radiative flux (DLRF) at the surface due to dust. The values here are diagnosed from experiments with prescribed SST and sea ice. For (a), (d), (e), and (h), negative means the surface receives less energy from above; for (b), (c), (f), and (g), negative means the surface loses less energy to the atmosphere above. For all cases pCO2 = 280 ppmv; (left) k = 0.15/8 and (right) k = 0.15.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
Moreover, both the cloud cover and the cloud water and ice path decrease, increasing shortwave radiation but decreasing longwave radiation received at the surface, causing a net increase of ~1.0 W m−2 for both k = 0.15/8 and 0.15 (Fig. 14). Therefore, without the feedback of ocean temperature and sea ice dynamics, the net forcings by dust to the surface are −2.6 and −7.2 W m−2 for k = 0.15/8 and 0.15, respectively. Note that the diagnosed sensible, latent, and longwave radiative fluxes over both land and sea ice may not represent the forcing of a warm atmosphere accurately because their surface temperature changes significantly when dust is considered (Figs. 15a,c); all three fluxes are affected by surface temperature. However, because the tropical temperatures are similar between cases for k = 0.15/8 and 0.15 (Fig. 9a), the large difference between Figs. 13f–h and Figs. 13b–d (especially over tropical oceans) is still a good indicator of strong positive forcings of dust for k = 0.15 relative to those for k = 0.15/8.
The changes of (a),(d) shortwave, (b),(e) longwave, and (c),(f) net cloud forcings at the surface due to dust. The values here are diagnosed from experiments with prescribed SST and sea ice. For all cases pCO2 = 280 ppmv; (left) k = 0.15/8 and (right) k = 0.15.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
Changes in surface temperature between the cases with dust (k = 0.15/8 and 0.15) and without dust (k = 0), calculated from the prescribed-SST AGCM runs. pCO2 = 280 ppmv for all cases. The white regions represent the open ocean (no sea ice) that the SST is prescribed.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
From the diagnostics above, it seems that dust in the case of k = 0.15 has a much more negative effective forcing (cooling effect) on the surface than of k = 0.15/8. However, the temperature over sea ice increases by as much as 5° and 1.5°C in the cases of k = 0.15 and 0.15/8 (Figs. 15a,c), respectively, even though SST is prescribed to that of case k = 0; such changes make the diagnosed atmospheric longwave radiative forcing anomaly over sea ice–covered regions in Fig. 13h greatly underestimated. If the temperature over sea ice had not changed, the surface would have emitted less blackbody radiation by approximately 5.9 and 1.1 W m−2 for k = 0.15 and k = 0.15/8, respectively. When these corrections are considered, the surface cooling effect by dust is now −1.3 W m−2 for both k = 0.15 and 0.15/8. The reduction of sensible and latent heat fluxes should have also been underestimated but the magnitude of underestimation cannot be calculated as simply, although it is reasonable to think that the underestimation is more severe for the case k = 0.15 than for k = 0.15/8. Therefore, a smaller total cooling effect for the case k = 0.15 than the case k = 0.15/8 is expected, although not quantitatively obtained.
b. Thinning of polar sea ice
Significant thinning of polar sea ice is obtained for k = 0.15 (Fig. 8i) compared to k = 0 (Fig. 8g). The thinning of polar sea ice is most likely due to enhanced equatorward Ekman transport as has been clearly demonstrated in Figs. 8j–l. The fact that the polar sea ice is thinner than midlatitude sea ice in Fig. 8i indicates that the effect of Ekman transport dominates that of temperature, since polar temperature is still colder than the midlatitude temperature in this case (Fig. 9a). The warmer polar surface temperature for k = 0.15 than for k = 0 (Fig. 9a) should not be important for sea ice thinning because the temperature there is very low in either case; sea ice will grow to ~1000 m thick in both cases if there is no equatorward ice transport and oceanic heat transport (which is indeed negligible in high-latitude regions). In fact, the thermal growth of sea ice is actually faster in the former than in the latter due to thinner sea ice thickness in the former (diagnosed from the AOGCM runs; not shown). The enhanced Ekman transport in the k = 0.15 case is due to the very strong westerlies in the mid- to high-latitude regions (Figs. 8a–c), which themselves are due to strong meridional temperature gradient in the middle atmosphere in the k = 0.15 case (Fig. 16). This change in westerlies is also observed in the AGCM runs (not shown), indicating that it is a direct influence of dust on the atmospheric circulation rather than the feedbacks of ocean and sea ice. The enhanced equatorward transport of sea ice also produces leads (not shown), which, together with the darkening of snow on sea ice by dust, decrease the surface albedo in the polar region as shown in Fig. 12c.
(a) Zonal mean annual temperature and (b) zonal winds. The results are from the fully coupled runs.
Citation: Journal of Climate 34, 16; 10.1175/JCLI-D-20-0803.1
c. Limitations of the model
The model employed here has some limitations in simulating both dynamic and radiative processes related to dust. One of the major limitations may be that the indirect effect of dust acting as cloud condensation nuclei is omitted. In reality, the dust aerosols promote the formation of small cloud droplet and enhance cloud albedo (Su et al. 2008). So the simulations herein may have underestimated the cloud radiative effect (Fig. 13) due to dust. Another limitation may be that spherical dust particles have been assumed when calculating the dust radiative forcing. Field observations show that most dust particles have nonspherical shapes (Gao and Anderson 2001; Okada et al. 2001) and are better absorbers of solar radiation than spherical particles (Wang et al. 2013). Also, Kok et al. (2017) argued that the current model approach might overestimate the cooling effects of dust by having too large a proportion of fine-size dust. These uncertainties make it difficult to ascertain the net radiative effect of dust even in the present Earth (Ginoux 2017). CESM1.2.2 also omits the formation of soil crust by either physical or biological processes (Belnap and Lange 2001). Although the wide range of surface erodibility tested here might have encompassed the relevant uncertainty, its influence on the spatial variability of k could not be tested realistically. These limitations are faced by most if not all of the current climate models. Nonetheless, the model employed herein captures the essential effect of dust and our simulations should still provide useful information about the possible influence of dust on the initiation of snowball Earth events.
5. Conclusions
The change of atmospheric dust loading in different climates and the influence of dust on the initiation of Neoproterozoic snowball Earth events are investigated using the fully coupled Earth system model CESM1.2.2. Globally uniform surface erodibility is used, and two values, k = 0.15 and 0.15/8, are tested. The findings are as follows:
The dust emission decreases as climate becomes colder due to increasing snow coverage of land surface but atmospheric dust loading increases slightly. The atmospheric dust loading increases abruptly by as much as 39% when the climate is cooled to a near-snowball state due to dramatically decreased precipitation.
The net cooling effect of dust is negligible when the climate is very cold (e.g., global sea ice fraction is greater than 60%). When pCO2 = 2000 ppmv, GMST is reduced by ~17 K if surface erodibility k is increased from 0 (no dust) to 0.15. However, when pCO2 = 280 ppmv, GMST is reduced by only 1.4°C for the same variation of k. Moreover, the case with a much smaller k (= 0.15/8) produces a colder (by 2.5°C) climate than the case for k = 0.15, although the dust loading of the former is only one-fifth of that of the latter. The two cases (k = 0.15/8 and 0.15) have very similar tropical climate but the latter has warmer temperature in the mid- to high-latitude regions, even warmer than that in the no dust case. The most important reason that the dust cases do not have much colder climate than the no dust case is that under cold climate, in which surface albedo is high, adding dust in the atmosphere reduces the global planetary albedo. The solar energy absorbed by atmospheric dust is transferred to the surface through a few processes, either directly or indirectly; the warm atmosphere increases longwave radiation to the surface, reducing shortwave cloud forcing and upward sensible and latent heat fluxes at the surface. They have all contributed to warming the mid- to high-latitude regions in the k = 0.15 case.
The mid- to high-latitude westerlies are greatly enhanced and polar sea ice thinned when atmospheric dust loading is high. This is because the meridional temperature gradient in the middle atmosphere over the mid- to high-latitude regions is greatly enhanced when heavy dust loading is present. The strong westerlies promote the equatorward Ekman transport of sea ice and thin the sea ice in the polar region
Dust makes it more difficult for Earth to enter a snowball state. When there is no dust, the threshold pCO2 for Earth to enter a snowball state is between 280 and 140 ppmv. The threshold pCO2 is also between 280 and 140 ppmv for k = 0.15/8 but decreases to between 70 and 35 ppmv when k = 0.15.
Acknowledgments
Y. Liu benefited from discussion with Jing Li at Peking University on the radiative effect of dust. We thank all three anonymous reviewers for their constructive comments. The simulations were performed on the High-Performance Computing Platform of Peking University. Y. Liu is supported by the National Natural Science Foundation of China under Grant 41875090. Y. Liu and Y. Hu are supported by the National Natural Science Foundation of China under Grant 41761144072. P. Liu is supported by the China Postdoctoral Science Foundation under Grants 2021M690142 and 2021T140629.
Data availability statement
All data analyzed in the paper are stored on a personal server and will be available upon request from the first or corresponding authors.
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