Introduction

Glacial deposits are widely discovered in the late Ediacaran strata all over the world, such as the Gaskiers, Bou-Azzer, Hankalchough, et al., yet these glaciations were highly heterogeneous, spanning from 580 Ma to 560 Ma or even younger1,2,3,4. In addition, geological and paleomagnetic evidence indicate that the ice sheets might have extended to subtropical regions4,5. Recently, it was proposed that these glaciations constituted a spatially widespread and temporally continuous ice age extending to ~30–40° N/S and lasting for at least 20 million years (Myr) through 580–560 Ma6,7, and this prolonged ice age might have occurred in the context of a true polar wander (TPW) process, which could account for dramatic rates in continental latitude shifting globally8. However, either the trigger or the maintenance of the late Ediacaran ice age remains elusive. Especially for glaciation in sub-tropical regions, it is sensitive to fluctuations of atmospheric CO2 level (pCO2) and thus cannot last long9,10,11, as for the hypothesized soft snowball Earth during the Cryogenian12. Although the accretionary orogenic belts at ~580 Ma might enhance continental weathering and accordingly initiate this great late Ediacaran ice age13, it remains unclear why such a climatic condition could be maintained for more than 20 million years.

Large amplitude TPW during the late Ediacaran was recognized based on the series of paleomagnetic and secular mantle temperature reconstructions14,15,16,17,18,19,20. TPW is the reorientation of the solid Earth relative to its rotational axis, and is thus accompanied with significant changes of latitude-longitude location of continents but not much change in the relative positions between continents8,15. Such changes of continental locations could have affected the climate during the late Ediacaran6,21, as has been demonstrated for the late Paleozoic and Cenozoic ice ages22,23,24. For instance, migration of continents into and out of the tropical region due to TPW could lead to diachronous distribution of glacial deposits (e.g., North China and Laurentia) with temporal gaps, giving the illusion of a diachronous global glaciation25,26.

Other than the influence on local glaciations, TPW can also affect the global climate in at least two ways. The first is through the redistribution of surface albedo since the reflectivity of continents is much higher than that of oceans23; more continents in low-latitude regions reflect more sunlight and thus induce a cooler climate27. The second is through varying the silicate weathering rate6,28, which changes pCO2. In detail, the migration of continents from cold and dry regions (e.g., high latitudes) to warm and wet areas (e.g., low latitudes) could increase the silicate weathering rate substantially29,30,31. Besides, if continents wander from regions covered by ice sheets to ice-free tropics as occurred during the ice age, the newly exposed glacial-eroded land surface is prone to weathering, i.e., higher weatherability32. That is because continental glaciation is an effective mechanism for exposing fresh rocks by removing the surficial low-weatherability materials, and producing fine-grained materials (rock flour) with highly reactive surface (i.e., surface/volume) in the meantime33,34. This second effect of true polar wander (i.e., on silicate weathering) might be particularly important for maintaining a low pCO2 and thus sustaining a prolonged ice age in the late Ediacaran; it could also increase the terrestrial supplies of nutrients (e.g., phosphorus) into the ocean35, as inferred from widespread phosphogenic events in the Ediacaran-Cambrian transition36,37, and potentially drove the diversification of multicellular organisms and eventually led to the Cambrian explosion38,39,40.

Here, we simulate the global climate and continental weathering during the great late Ediacaran ice age by using a fully coupled atmosphere-ocean general circulation model, CESM1.2.2, and a revised weathering model from Gabet and Mudd41, as presented in Zuo et al.31. The main goal is to examine the range of pCO2 within which the global ice age with glaciers extending to subtropical regions could be sustained. Unlike the Cryogenian Snowball Earth or typical high-latitude glaciations in Phanerozoic (such as the Cenozoic glaciation in the southern hemisphere), where the breakup of supercontinent or the rise of the Tibetan Plateau are believed to play an important role5,42, this simulation is conducted in the context of late Ediacaran TPW event, showing a rapid latitudinal shifts of continents’ positions. In order to make the results more convincing, the climate and continental weathering were simulated at various pCO2 across five timeslices between 580 Ma and 560 Ma, with 5 Myr intervals (see Methods and Table S1).

Results

Constraining the range of pCO2 during the late Ediacaran ice age

According to the unambiguous rock and fossil records, the late Ediacaran ice age was not a snowball Earth glaciation43,44,45,46, which means that glaciers were unlikely to extensively extend into tropical regions (i.e., < 30°N/S) and the pCO2 should be no less than 35 ppmv (Figure S1a–e)47,48. The available paleomagnetic and geochronological data alone cannot make convincing correlations of these Ediacaran glaciations, nor could it resolve the climatic condition of late Ediacaran. A recent study interpreted these glacial records in the context of the concurrent late Ediacaran TPW event, and proposed a continuous ice age concomitant with the TPW event6. Thus, the late Ediacaran ice age was characterized by extensive glaciations in mid- to high-latitude with glaciers extending to subtropical regions, and lasting for at least 20 Myr. Under such climatic conditions, the glaciers were highly sensitive to the pCO247,48, and thus it is critical to constrain the pCO2 level during the late Ediacaran ice age.

For pCO2 of 35 ppmv, the simulated thick snow depth (>800 mm water equivalent; where glaciers are able to develop locally) in the hottest month of each hemisphere on land could explain >50% of the glacial records, and the calculated thin (<100 mm) snow covers the rest (Figure S2a–e, k). Because the highland and orbital variations are ignored in the simulations carried out herein (see Methods), both of which could enhance snow accumulation, we did not fine-tune the pCO2 further so that thick snow covers all the glacial records. When pCO2 = 35 ppmv, the annually averaged global mean surface temperatures (GMST) for 580 Ma, 575 Ma, 570 Ma, 565 Ma, and 560 Ma, are −8.1 °C, −6.7 °C, −6.2 °C, −4.3 °C, −5.9 °C (Fig. 1a and Figure S1a–e), respectively, over 17 °C colder than the preindustrial level. The large spread of GMSTs should be primarily attributed to the change of continental configuration (i.e., TPW) because the variation of solar constant from 580 Ma to 560 Ma is too small49. Generally, the larger the continental areas in the tropics (CAT, Fig. 2i), the cooler the climate due to its high surface albedo (Fig. 1a and Figure S1a–e). Thus, the GMST in 580 Ma is colder than the other runs probably because of its greatest CAT (Fig. 2i). Continental configuration in the extratropical region could also play an important role in the variation of GMST through other effects49, especially during 575-565 Ma when the changes of CAT alone fails to explain the changes of GMST. Overall, the TPW during the late Ediacaran could affect the global climate greatly.

Fig. 1: Variations of annual mean surface temperature, matching rates between simulations and observations, and sea ice depth in the Southern Hemisphere under 580–560 Ma continental configurations and various pCO2.
Fig. 1: Variations of annual mean surface temperature, matching rates between simulations and observations, and sea ice depth in the Southern Hemisphere under 580–560 Ma continental configurations and various pCO2.
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a Simulated annual mean surface temperature for pCO2 = 35 ppmv; (b) glacial matching rates between simulations and observations, in which the blue and orange dots represent the scenarios shown in Figure S1f–j and Figure S1k–o, respectively; (c) sea ice thickness in the Southern Hemisphere. Black values in panels are the pCO2 (ppmv) for the dots nearby.

Fig. 2: Weathering rates in pCO2 = 35 ppmv and carbon balance state with uniform weatherability assumptions in 580–560 Ma.
Fig. 2: Weathering rates in pCO2 = 35 ppmv and carbon balance state with uniform weatherability assumptions in 580–560 Ma.
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a–e Weathering rate when pCO2 = 35 ppmv; (f–h) Weathering rate when pCO2 has increased to the level (label on the top) in which weathering rate would be balanced by VCO2; (i) changes of continental areas in the tropics (CAT, blue line with left axis), global sum weathering rate in (a–e) (solid orange line), (f–h) (dashed orange line), and VCO2 (global sum weathering rate in 580 Ma when pCO2 = 35 ppmv) with 10% variation (shaded orange zone). The gray contour lines represent the edges of sea ice with gridbox fraction of 50% in each panel. The global sum weathering rates have been shown at the top-right in (a–h) with the unit: mol C/yr. The names of continents have been labeled in panel (a–e). NC North China, Au Australia, EA East Antarctica, WA West Africa, NA Northeast Africa, In India, SC South China, K Kalahari, B Baltica, Am Amazonia, Si Siberia, L Laurentia.

To obtain the upper bound of pCO2 for the great late Ediacaran ice age, the pCO2 is doubled (the increase of global radiative forcing is approximately the same for each doubling) multiple times until the simulated snow distribution is unable to explain the glacial records. A simple criterion is used here; the simulated climate is considered too hot if the lowest latitude at which snow exists during the hottest month of the year (i.e. snow exists perennially) is higher than the lowest latitude at which glacial record exists. Due to the uncertainty of paleolatitude reconstruction15, the lowest latitude of the glacial record is increased by 5° in each hemisphere (blue lines in Figure S1f–o). With this strategy, the upper bounds of pCO2 are found to be 70, 140, 280, 140, and 70 ppmv for 580 Ma, 575 Ma, 570 Ma, 565 Ma, and 560 Ma, respectively. At these pCO2, the simulated sea-ice edges have developed to the subtropical regions (grey lines in Figure S1f–j), comparable to the conjectured sea ice distribution from geological records6. The simulated land snow in the hottest month of each hemisphere covers all the glacial records (Fig. 1b and Figure S1f–j). Further doubling of pCO2 will drive the lowest latitudes of the simulated permanent land snow to too high values (Fig. 1b and Figure S1k–o). For example, about 50% (Fig. 1b) of sites with glacial records have no simulated permanent snow in 570 Ma (Figure S1m) and 565 Ma (Figure S1n).

Although the average latitude of sea ice edges is concordant with GMST (Figure S1a–e), the local sea-ice thickness is not. This is because the sea-ice thickness is not only determined thermodynamically by the local surface temperature, but also dynamically by the sea-ice flow. The latter is controlled by the continental configuration. In the Northern Hemisphere, little continent is present, so that the sea-ice thickness is mainly controlled by CO2 levels (GMST; Figure S1p–t). In the Southern Hemisphere, on the other hand, the continents effectively block sea-ice flow and affect sea-ice thickness. For example, the GMST in 580 Ma with 70 ppmv pCO2 is 5.2 °C colder than that of 575 Ma with 140 ppmv pCO2, but the average sea-ice thickness in the Southern Hemisphere is 2.6 m thinner (Fig. 1c and compare Figure S1p with Figure S1q). Hence, other than GMST, true polar wander also affects the sea-ice distribution directly.

Modulation of continental weathering and pCO2 by TPW

Having the simulated spatial distributions of temperature and runoff, the continental silicate weathering flux can be estimated (Fig. 2) (see Methods). At the lower bound pCO2 (35 ppmv), the weatherable regions concentrate within the warm and wet tropical region for all periods (Fig. 2a–e). Since the simulated temperature (Figure S1a–e) and runoff (Figure S2f–j, l) are similar in different continental configurations, the global total weathering flux varies almost linearly with the CAT (Fig. 2i). The calculated global weathering flux is the smallest at 575 Ma (1.41 × 1011 mol C/yr), and largest at 580 Ma (2.87 × 1011 mol C/yr). Therefore, if the volcanic outgassing remained nearly constant, TPW could drive large fluctuations of pCO2 by modulating continental silicate weathering. The fluctuations of pCO2 might be large enough such that the late Ediacaran ice age became episodic rather than continuous.

To estimate how much TPW via modifying continental weathering could have affected pCO2, here we assume that pCO2 was 35 ppmv at the beginning of late Ediacaran ice age (i.e., 580 Ma) and the volcanic CO2 outgassing rate (VCO2) was exactly balanced by the continental weathering. Moreover, VCO2 is assumed to be constant throughout the late Ediacaran, and all other sources (e.g., weathering of organic carbon) and sinks (e.g., burial of organic carbon) of CO2 are neglected. VCO2 is thus estimated to be 2.87 × 1011 mol C/yr, quite low compared to the present-day value (4.5 × 1012 mol C/yr)29,31. This is understandable since 1) a relatively low value of pCO2 is used to estimate the global weathering rate, 2) the surface slope, which is important for erosion and weathering influx, is near zero in the current model setting, and 3) the continents are assumed to composed of granites, which are more difficult to weather than basalts (see Methods). In fact, previous studies also argued low VCO2 in the late Neoproterozoic50,51, whereas the volcanic activities remain largely unconstrained52. Nevertheless, the detailed value of VCO2 should not affect our conclusion since the main purpose of the current work is to see how the weathering rate varies during the late Ediacaran TPW event, and whether pCO2 can be maintained within the range of sustaining a prolonged non-snowball Earth ice age.

At pCO2 = 35 ppmv, the calculated weathering rates for 575-560 Ma (Fig. 2b–e) are all lower than the assumed VCO2 (Fig. 2a), with that for 560 Ma nearest to VCO2 (Fig. 2i). This means that the pCO2 in these periods would increase to a higher level until the warmer and wetter climate pushes the weathering rate back to the assumed VCO2. Calculations show that the pCO2 (GMST) in 575 Ma, 570 Ma, and 565 Ma had to be as high as 560 ppmv (6.3 °C), 560 ppmv (6.9 °C), and 280 ppmv (4.7 °C), respectively, in order for the carbon cycle to reach an approximate new balance (Fig. 2f–i; Table S1). These high pCO2 all exceed the appropriate pCO2 range determined in the last section, and the associated sea-ice edges would retreat to ~45°–55° latitudes (Fig. 2f–h). So, if we only consider the effects of climate (pCO2) on the weathering rate, the late Ediacaran ice age would have been interrupted due to decreasing CAT and thus weathering rate by TPW.

On the other hand, intensity of continental silicate weathering could be enhanced by exposing more chemically reactive rocks from higher glaciated latitudes. The enhanced continental weathering rate during ~580–560 Ma is also indicated by the strontium isotope records7,53. Due to TPW, some previously glaciated continents might be moved to the low-latitude region and become ice-free (mainly in Laurentia and Amazonia, see red framed regions in Fig. 3). These continental areas are denoted as deglaciated continental areas (DCA) hereafter. The surface of DCA would be characterized by brecciated rock fragments with large surface-to-volume ratios, increasing the weathering rate. To consider this effect, we recalculate the weathering rates and the equilibrium pCO2 for 575-565 Ma (Fig. 3a–e, k) by assuming that the weatherability of DCA had increased to 10 times of initial level based on the soil records in the Last Glacial Maximum (LGM)33.

Fig. 3: Weathering rate and pCO2 with the increased weatherability of deglaciated continental areas (DCA).
Fig. 3: Weathering rate and pCO2 with the increased weatherability of deglaciated continental areas (DCA).
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a–e Weathering rate and equilibrium pCO2 with weatherability in DCA (regions framed in red) has increased to 10 times of initial level when pCO2 = 35 ppmv in 580 Ma; (f–j) same as (a–e) but the pCO2 = 70 ppmv in 580 Ma. All equilibrium pCO2 has been tagged on the top of each panel. The gray contour lines represent the edges of sea ice with gridbox fraction of 50%. The global sum weathering rates have been shown at the top-right of each panel with the unit: mol C/yr. The (k, l) represent changes of the global sum weathering rate in (a–e and f–j), respectively, and the VCO2 (global sum weathering rate in 580 Ma) with 10% variation (shaded orange zone).

The exposure of DCA due to TPW is sufficient to maintain strong silicate weathering and thus low pCO2. Model results show that the global weathering rates would be high enough to balance VCO2 when pCO2 is increased slightly from 35 ppmv to 70 ppmv for 575–565 Ma when the effect of DCA is considered (Fig. 3b–d). The 70 ppmv is a safe pCO2 for 575-565 Ma to maintain continuous late Ediacaran ice age as demonstrated above (Figure S1f–j). If the effect of DCA is not considered, doubling the pCO2 from 35 to 70 ppmv would only increase the global weathering rate by 26%, 24%, and 10% for 575, 570, and 565 Ma, respectively (Table S1). In contrast, the effect of DCA would additionally enhance the global weathering rate by another 57%, 53%, and 15% for the three periods, respectively (Table S1). That is, the effect of DCA on the global weathering rate is approximate twice the effect of doubling pCO2 from 35 ppmv to 70 ppmv.

Choosing a different value for VCO2 does not affect the conclusion above. For example, VCO2 would be 3.34 × 1011 mol C/yr (Fig. 3f) if pCO2 was 70 ppmv (still low enough to maintain the required glaciation as described in the previous section) rather than 35 ppmv at 580 Ma. Again, doubling pCO2 from 70 ppmv to 140 ppmv would be sufficient to drive a global weathering rate high enough to balance VCO2 in 575–565 Ma, if the effect of DCA is considered (Fig. 3g–i, l, and Table S1). The pCO2 level of 140 ppmv is still within the acceptable range to sustain glacial condition during 575–565 Ma (Figure S1g–i). Given the fact that both CAT and DCA are controlled by continental configuration, we propose that TPW should play a vital role in sustaining the late Ediacaran ice age between 580 Ma and 560 Ma.

Discussion

Although some uncertainties remain in the current study, such as the unavailability of a land ice model in CESM 1.2.2 due to high computational demand (Methods). However, using the extent of permanent snow on land as a substitute for the extent of ice sheets is based on the physical understanding that ice can grow only when snow can survive the summer, and that ice cannot grow much beyond this snowline. This is generally true for large-scale continental ice sheets which flow slowly but not applicable to small mountain glaciers which often flow quickly into snow-free regions without being melted. Thus, the variation of land ice distribution could be delineated well by the distribution of permanent snow as demonstrated by an offline glacier simulation (Methods and Figure S3). Such a way of inferring land ice distribution is generally acceptable in the literature especially when the timescale of interest is much longer than the timescale of glaciers so that glaciers are always in equilibrium with the forcing54. The estimated pCO2 ranges for glaciations may change when different climate models and (or) orbital parameters are employed48,55. Even when the estimated pCO2 ranges for the Ediacaran ice age change significantly, the calculated CO2 volcanic outgassing and weathering rate of newly exposed continents would also change proportionally with pCO231 which thus may not jeopardize the effect of TPW on sustaining the ice age presented here. Moreover, some glacial deposits (e.g., at ~35°N in Australia), used to constrain the range of pCO2, are also highly uncertain6. Furthermore, the lithology should be highly variable on the Earth’s surface but is assumed to be uniformly felsic in this preliminary study; the effect of erupted basaltic rocks, which is ten to hundreds of times more reactive than felsic rocks56, due to rifting of Laurentia57,58 is also ignored.

However, the main purpose of this study is not to accurately confine the pCO2, but to demonstrate how continental silicate weathering and thus pCO2 might have varied with the fast change of continental configuration between 580 Ma and 560 Ma within a coherent framework. Through the simulations of climate and continental silicate weathering, we argue that high global weathering rate and low pCO2 could be maintained even though the continental configuration varied significantly due to TPW. On the one hand, the TPW might move continents out of the tropical region, lowering the global weathering rate. On the other hand, the TPW moved previously glaciated continents into the tropical region and induced deglaciation, which provided highly reactive fresh rocks, enhancing silicate weathering. This enhanced weathering rate (Figs. 2, 3 and Table S1) and associated increased nutrients runoff also propose a potential mechanism for the abundance of phosphate deposits during the late Ediacaran37, a phenomenon previously attributed to the equatorial upwelling regime36,59. If the continental configuration had remained as it was at 580 Ma without TPW, the geological evidence that indicates no glaciers on Laurentia located polar regions but several glaciers on the tropical continent Baltica during 570–560 Ma6, seems uninterpretable based on the simulated climate (Figure S1f–o and S2a–e). Furthermore, the weathering rate should have decreased after 580 Ma, when assuming TPW had not occurred, as the glaciers developed based on observations. This feedback would likely inhibit the glaciation, particularly in light of the large igneous province (CO2 outgassing) recognized during late Ediacaran58. Thus, the modeling results suggest that the pCO2 might have been lower than 280 ppmv during the late Ediacaran ice age, and that a prolonged ice age could have been sustained within the TPW event. In summary, the late Ediacaran TPW event, by rapidly moving previously glaciated continents to the tropics, kept a high continental weathering rate and accordingly a low pCO2, warranting a prolonged ice age with glaciers extending to subtropical regions. Finally, the sustained high weathering rate also enhanced the nutrient level in the ocean, which in turn might have triggered the diversifications of multicellular organisms, such as the White Sea assemblage of Ediacara biota60, followed by the emergences of animals38, and ultimately led to the Cambrian explosion59,61.

Methods

Model configuration

The climate is simulated with the Community Earth System Model version 1.2.2 (CESM 1.2.2), a state-of-the-art three-dimensional model that includes the atmosphere, land, ocean, sea ice, land ice, river, and coupler components62. The land ice constituent is not activated here due to its long timescale and high computational demand as in previous studies63,64. As a climate indicator for the glacial period, ice sheets on land may increase weatherability by grinding the land surface. It is thus desirable to involve land ice simulation when computational power allows in the future. For the current study, the simulated land snow acts as a reasonable compromise, since surface snow also has high albedo and climate requirements as ice sheets. The weatherability of the land surface is prescribed in the weathering model in which the ice sheet grinding effect is considered as described below. For the purpose of the current study, the land and ocean biogeochemical components are also inactive.

For the atmospheric component, the three-dimensional Community Atmosphere model version 4 (CAM4) is used and run with its finite volume dynamical core65. The land component, Community Land Model version 4 (CLM4), simulates processes related to snow coverage, water storage, etc.66. CAM and CLM4 are operated with T31 grid with a horizontal resolution of 3.75° × 3.75°. The ocean component (Parallel Ocean Program version 2, POP2)67 and sea ice component (Community Ice CodE version 4.0, CICE4)68 are run with g37 grid with a uniform 3.6° spacing in the zonal direction and variable spacing (0.6°–3.4°) in the meridional direction. The atmosphere and ocean have 26 and 60 layers in the vertical direction, respectively. Such model and resolution configurations are typically selected for paleoclimate studies64.

The silicate weathering is calculated using a model essentially the same as that of Park et al.29 but with parameters (e.g., erosion rate constant and runoff sensitivity of dissolution rate) re-tuned to reduce the bias in global total weathering flux31,69. The model was derived originally from the framework of Gabet and Mudd41, which considers the processes of regolith generation and physical erosion in the vertical direction and is thus able to reflect the influence of supply-limit and kinetically limited conditions simultaneously. The silicate weathering rate in our model depends on the surface temperature, runoff, surface slope, and lithology, with the former two estimated from CESM1.2.2 simulations and the latter two prescribed as described in the next section.

To demonstrate the permanent snow is an appropriate compromise to represent the land glacier distribution, the Ice-Sheet and Sea-Level System Model (ISSM) version 4.17 has been employed to operate an offline simulation (Figure S3). ISSM is a thermomechanical ice-sheet model based on the unstructured mesh and finite element method70. The simulated temperature and precipitation by CESM1.2.2 have been used as the boundary conditions for the ice sheet calculation in the ISSM following the algorithm elaborated in Wei et al.71.

Experimental Setup

We used five continental configurations that reconstructed for 580 Ma, 575 Ma, 570 Ma, 565 Ma, and 560 Ma to cover the late Ediacaran ice age period and involve the TPW effects15. Without reliable information on topography, the average elevation of continents is assumed to be ~400 m above sea level which is close to that of the present day. The elevation is raised to 450 m at the continental center and gradually decreases toward the edges to direct river flow into the ocean eventually. The land surface is set to the desert since the land plants have not appeared before Cambrian72. The depth of the ocean is assumed to be 4000 m globally with an ~2000 m idealized mid-ocean ridge on the ocean floor to improve the convergence of the POP2.

To simulate the late Ediacaran ice age climate state, in which some glacial deposits have been found in ~30–40° latitudes6, the CO2 mixing ratio is firstly set to 35 ppmv under five continental configurations based on previous Neoproterozoic glacial simulations with the same model47,48,64. The solar constant is set to 1297.84 W/m2, 1298.39 W/m2, 1298.93 W/m2, 1299.48 W/m2, and 1300.02 W/m2 for 580–560 Ma, with a linear increasing rate of ~0.04% per 5 million years73. The orbital parameters are assumed to be the same as that in the year 1990. The CH4 and N2O levels are prescribed to 805.6 and 276.7 ppbv, respectively, as those in preindustrial. The aerosols are beyond the scope of this study and thus are all omitted, although some of them may have significant climate effects during the Precambrian63. The pCO2 = 35 ppmv runs reach equilibrium states after 2000 model years (Figure S4) and the global mean net radiation at the top of the atmosphere (TOA) is < ±0.3 W/m2. To find the range of acceptable pCO2 at which simulated snow thickness at hottest month is consistent with geological records, we have carried out doubling pCO2 climate simulations from 35 ppmv for 580 Ma (70 and 140 ppmv), 575 Ma (70, 140, 280, and 560 ppmv), 570 Ma (70, 140, 280, and 560 ppmv), 565 Ma (70, 140, and 280 ppmv), and 560 Ma (70 and 140 ppmv), respectively. Each pCO2 doubling run is branched off from the former lower pCO2 equilibrium state and continued for at least 300 years so that the net radiation at TOA is < ±0.3 W/m2. The above setting strategy and method are similar to our previous modeling studies of the Neoproterozoic glacial episode74.

Although the ocean carbon reservoir is huge, its contribution to pCO2 is likely negligible on the geologic timescale. When the Earth system reaches equilibrium, pCO2 is only determined by the outgassing rate and the silicate weathering rate (neglecting possible long-term change of organic burial rate), whether or not the oceanic carbon reservoir changes75. Although the ocean carbon reservoir will change in our simulations due to varied silicate weathering rates, it is unnecessary to know how it changes since pCO2 will always evolve into a value so that the climate is appropriate to bring silicate weathering rate equals to the outgassing rate, as we deduced pCO2 in Figs. 2 and 3. Thus, we treat marine carbon reservoirs as a controlling variable in the simulations.

In the weathering model, the initial lithology is assumed to be globally felsic (acid volcanic rock). The surface slope is set to 0.00025 according to the algorithm in Maffre et al.76 under the flat topography setting here. This slope value is about a quarter of the present value, which may be appropriate because of the reduced orogenesis during the Proterozoic77. Although the real lithology and slope are probably different from the prescribed values here, these two factors may change little over 580–560 Ma. So, the main conclusions in this study may not be jeopardized as long as they are treated as fixed parameters and the relative weathering rates between different runs are untouched.

When ignoring the land sheet griding effect on the newly exposed land surface the weatherability of rock should be identical during late Ediacaran ice age. The weathering rate could be easily estimated based on the temperature and runoff from the climate model (results in Fig. 2). However, considering the dramatic TPW in different geological times, continents move from ice-covered regions to tropical ice-free zones (DCA) where the weathering rate may increase due to glacial grinding effect (results in Fig. 3b–d, g–i). To simplify the calculations, the continents where the calculated annual mean surface temperature increase to >0 °C from the former (5 Myr before) cold state are defined as the DCA in this study. Here we have increased the weatherability of DCA by 10 times of initial value, based on the soil records in the Last Glacial Maximum and modeling studies33,34. As the result, the increased silicate weathering rate may significantly increase to maintain the low pCO2 and late Ediacaran ice age.