Soil moisture–atmosphere coupling accelerates global warming

Domain: earth_science
Published: 2023-08-15
Editorial outcome: major_revision

Abstract
Soil moisture–atmosphere coupling (SA) amplifies greenhouse gas-driven global warming via changes in surface heat balance. The Scenario Model Intercomparison Project projects an acceleration in SA-driven warming due to the ‘warmer climate–drier soil’ feedback, which continuously warms the globe and thereby exerts an acceleration effect on global warming. The projection shows that SA-driven warming exceeds 0.5°C over extratropical land masses by the end of the 21st Century. The likelihood of extreme high temperatures will additionally increase by about 10% over the entire globe (excluding Antarctica) and more than 30% over large parts of North America and Europe under the high-emission scenario. This demonstrates the high sensitivity of SA to climate change, in which SA can exceed the natural range of climate variability and play a non-linear warming component role on the globe.

Introduction
Since the onset of the Industrial Revolution, anthropogenic emission of greenhouse gases (GHG) has caused Earth’s climate to warm measurably. Nonetheless, the rates of warming vary greatly across the globe1–3. Previous researches have revealed that regional variability is due in part to land–atmosphere coupling4–7, whereby differences in land surface conditions (e.g., soil moisture, snowpack, and vegetation cover) modulate mass fluxes and energy to the atmosphere8–16 and, furthermore, influence weather patterns and climate anomalies associated with GHG forcing. For instance, soil moisture–atmosphere coupling (SA) is linked to increased intensity and frequency of high-temperature extremes and heat waves via the impact of atmospheric warming on soil moisture in some regions17–22. However, a coherent picture of the extent to which global warming (including warming rate and heat extremes) will be impacted by SA and its time evolution under different emission scenarios remains unclear.

In order to analyze the SA effect on global warming, we employed six global climate models (CESM2, CMCC-ESM2, EC-Earth3, IPSL-CM6A-LR, MIROC6, and MPI-ESM1-2-LR)—the Land Surface, Snow and Soil Moisture Model Intercomparison Project (LS3MIP)23, the Scenario Model Intercomparison Project (ScenarioMIP)24, and the historical experiment in Coupled Model Intercomparison Project phase 6 (CMIP6)—to isolate the climatic impact of SA during the extra-tropical summer under different warming scenarios. Experiments under the same emission scenario are driven by the same forcing agents (i.e., sea surface temperature, sea ice, and CO2 concentrations). In the Land Feedback Model Intercomparison Project with prescribed Land Conditions experiment (LFMIP-pdLC) from LS3MIP, the soil moisture is fixed to its climatological state for the period 1980–2014 which is derived from historical global climate model output (Supplementary Fig. 1). Then the SA effect can be isolated from the relative differences between fully coupled experiments (historical, the SSP1-2.6, and SSP5-8.5 experiments) and LFMIP-pdLC experiment. In this study, we consider three time horizon periods: 1995–2014, 2040–2059, and 2080–2099 to represent modern, mid-term, and long-term future conditions, respectively.

Results
Under each emission scenario investigated here, SA amplifies global warming over much of Earth’s land surface (Fig. 1). Even under the most stringent GHG mitigation pathway, the SA-induced warming is considerably greater than that experienced currently (Fig. 1a, c). Centers of SA-amplified warming occur primarily within the mid-latitudes of Northern Hemisphere and the subtropical regions of Southern Hemisphere, respectively. The most extreme warming occurs over central North America (NA: 28–55°N, 88–110°W) and central and eastern Europe (EUR: 40–60°N, 20–50°E) in modern period (0.89±0.53°C and 0.56±0.41°C), which is generally consistent with Berg et al4. The warming will be up to 2.4°C in both regions in the long-term future under the very high-emission scenario (Fig. 1d). Under low-emission scenario, SA-induced warming varies little between the mid-term and long-term future projections; under the very high-emission pathway, however, warming is significantly more intense for long-term than for mid-term periods, particularly in EUR and NA. Specifically, global land-surface air temperature (excluding Antarctica) is projected to rise by 0.68°C±0.38°C owing to SA-induced warming by the end of this century, which is measurably higher than the mid-term projection (0.44°C±0.28°C; Fig. 1f). In NA and EUR, the difference between mid-term and long-term future projections is 0.67°C±0.66°C and 0.71°C±0.57°C, respectively. The area over which SA-induced warming exceeds 0.5°C (1.0°C) would increase by nearly 30% (>200%) by the end of the 21st Century compared with mid-term projections (Supplementary Figs. 2–3).

Our findings exhibit a clear uptrend in SA-induced warming in the mid-latitude Northern Hemisphere under the very high-emission pathway, with comparatively weak trends under the lower-emission scenario (Fig. 2). For the very high-emission pathway, the positive trends caused by SA over EUR (0.17°C±0.08°C per decade) and NA (0.16°C±0.09°C per decade) explain 18.5±9.7% and 18.8±10.0%, respectively, of the overall warming rate in each region (Supplementary Table 1). Clearly, the uptrend of SA-induced warming associated with very high greenhouse gases emission would accelerate the speed of global warming, and the magnitude of acceleration would increase with time. Therefore, we posit that, unless we take early action to reduce emission, SA- and GHG-induced warming would become closely coupled, resulting in a positive feedback that may hasten the approach of distinct climate range. Should the most stringent emission pathway be adopted, our results suggest SA-induced warming will weaken significantly (Fig. 2a).

Although SA contributes <10% to the likelihood of extreme high-temperature under modern conditions, this influence is likely to be strengthened over northern China and northernmost South America in the mid-term future (Fig. 3a). By the end of this century, the role of SA in the frequency and intensity of extreme high-temperature events globally is projected to rise significantly, consistent with the uptrend of SA-induced warming, and could approach 20% in the mid–high-latitude Northern Hemisphere and subtropical Southern Hemisphere (Fig. 3a). Over NA and EUR hotspots, SA would cause a rightward shift and pronounced flattening of the surface air temperature probability distribution function, representing an overall increase in the probability of extreme high-temperature over both regions (NA: +52.5%; EUR: +30.8%; Fig. 3c, d). Viewed another way, in the absence of SA-induced warming, the probability of the extreme high-temperature under the very high-emission pathway decreases by almost a third over NA and by a quarter over EUR by the end of the 21st Century.

In addition to frequency, the SA effect might also influence the intensity of extreme high-temperature; this process would impact North China and parts of South America in mid-term projections and globally in long-term projections (Fig. 3b). Our results indicate that the intensity will rise by >1.5°C globally and by as much as 8.0°C over North America and Europe. Under the most stringent emission-mitigation scenario, the relationship between SA and the intensity and probability of extreme high-temperature would weaken (Supplementary Fig. 4), suggesting that reductions in GHG emission would actively reduce the severity of such events. We note that this feature is present in all the models considered here (Supplementary Figs. 5–6). The extreme high-temperature due to SA in India is diverse among different models though the SA-driven warming is significant, which maybe associated with the large uncertainty of Indian summer monsoon precipitation25.

GHG-driven warming is projected to dry the soil column26 (Fig. 4a, b and Supplementary Fig. 7), thereby reducing evapotranspiration and allowing the ground surface to receive more solar shortwave radiation (longwave radiation is much weaker) through a reduction in cloud cover (Fig. 5a, b and Supplementary Fig. 8). Meanwhile, decreasing evapotranspiration could increase sensible heat flux from the land surface to the low-level atmosphere via decreasing the latent heat flux (Fig. 5c, d). The increasing sensible heat flux caused by the joint enhanced shortwave radiation and reduced latent heat flux trigger the nonlinear warming under severe GHG emission. Those phenomena are the strongest in the Northern mid-latitude, especially in EUR and NA, and Southern subtropical, where decreasing soil moisture can significantly change surface energy partitioning from latent heat flux to more sensible heat flux via decreasing evapotranspiration. On the contrary, there is a slight cooling effect caused by SA in a few regions, such as Sahara and Arabian Peninsula. The evapotranspiration change over those regions is negligible, while the negative cloud cover and positive shortwave radiation anomalies are generally significant, which suggests that the local evapotranspiration associated with soil moisture is not the primary factor dominating the surface energy balance. The impact of SA on surface energy over those regions may be due to the non-local effect and related to the large-scale circulation16,27.

Under the very high-emission scenario, progressively drying soil column leads to an acceleration of the decline in evapotranspiration (Fig. 4b, d), with the result of increased positive radiative budgets and thereby the acceleration of the amplified-warming, particularly over NA and EUR. Moreover, the correlation coefficient between evapotranspiration and soil moisture will increase under a drying soil background, which eventually aggravates the reduction of evapotranspiration caused by soil drying over time (Fig. 4e–h). These characteristics are not only shown in the surface soil moisture which is most directly related to evapotranspiration, but also in the root zone soil moisture (Supplementary Fig. 9). The enhanced sensitivity of evapotranspiration to soil drying lead to the increase of SA-induced non-linear warming under very high GHG emission background. The non-linear increase of SA-induced warming, combined with the GHG-warming, will make global warming to act like a snowball, corresponding to SA and other climate factors approaching a novel and unpredictable statement.

Furthermore, we decompose the SA-induced changes in surface air temperature into the following radiative forcing terms: surface albedo, evapotranspiration, shortwave transmissivity, air emissivity, aerodynamic resistance, and residual terms28 (see Methods). The primary driver of SA-induced warming is positive radiative forcing arising from the changes in evapotranspiration term and shortwave transmissivity term outlined above (Supplementary Figs. 10 and 11), which is the consequence of the decrease in evapotranspiration on shortwave radiation and sensible heat flux. Generally, the shortwave transmissivity term is larger than the evapotranspiration term for the global land in the modern period, while the effects of the two terms become equivalent in the future, especially in very high-emission scenario. Over EUR and NA in the long-term future, the combined positive radiation (sum of the above five terms) dominated by evapotranspiration term and shortwave transmissivity term will reach 33.5±14.1 and 32.8±16.7 W m−2 under high-emission scenario. Compared with the modern period (15.4±9.9 and 22.1±9.2 W m−2), the combined radiation will increase by 117.5±276.5% and 48.4±53.3% over EUR and NA. However, under low-emission scenario, although the combined radiation will also increase (23.1±5.9 and 25.3±12.6 W m−2), they are smaller than half of those in high-emission scenario.

Methods
CMIP6 models
Six global climate models in CMIP6 (CESM2, CMCC-ESM2, EC-Earth3, IPSL-CM6A-LR, MIROC6, and MPI-ESM1-2-LR) are used to analyze the impact of SA on surface air temperature. Extra-tropical summer is defined as the June–August (JJA) average in Northern Hemisphere and the December–February (DJF) average in Southern Hemisphere. Since there have been only six CMIP6 LS3MIP models published so far, we only use these six models in this article. The multi-model mean is used to remove uncertainties arising from model differences. For the majority of our analyses, we incorporated monthly data derived from all six models. Due to the lack of latent heat flux in MIROC6 model, the multi-mode mean of latent heat flux is the result of the other five models. The surface air temperature probability distribution function and extreme high-temperature are calculated from daily data for each model (no multi-model mean) separately. Because the amount of monthly data is not enough compared with daily data, we are concerned that the probability distribution function characteristics cannot be accurately captured. Meanwhile, the multi-model mean will mask the intensity distribution of extreme high-temperatures when the number of models is little. So, we used daily data to calculate the probability distribution function and extreme high-temperature probability for each model separately in Fig. 3 (MPI-ESM1-2-LR model under high-emission scenario), Supplementary Fig. 4 (MPI-ESM1-2-LR model under low-emission scenario), Supplementary Fig. 5 (CMCC-ESM2), and Supplementary Fig. 6 (IPSL-CM6A-LR). And the results showed that they had similar characteristics. In the six global climate models, CESM2, CMCC-ESM2, IPSL-CM6A-LR, and MPI-ESM1-2-LR include simulated dynamic vegetation, and EC-Earth3 and MIROC6 models do not include simulated dynamic vegetation. The surface soil moisture depth is 10 cm, and the root zone soil moisture depth is 100 cm.

The LFMIP-pdLC experiment in LS3MIP, SSP1-2.6, and SSP5-8.5 experiments in ScenarioMIP, and the historical experiment are analyzed. The LFMIP-pdLC experiment in LS3MIP is used to assess the impact of land-atmosphere coupling caused by soil moisture on weather and climate through fixing the soil moisture as their climatological state (the annual mean cycle for the period 1980–2014 derived from historical global climate model output). Then the SA effect can be isolated through the relative differences between fully coupled experiments (historical, the SSP1-2.6, and SSP5-8.5 experiments) and fixed soil moisture experiment (LFMIP-pdLC experiment)23. The ScenarioMIP reflects future climate (2015–2099) under high and low Shared Socioeconomic Pathways (SSP)24. The SSP1-2.6 experiment and r1i1p1f1 member in the LFMIP-pdLC experiment corresponds to the same low-emission scenarios (2015–2099), and the SSP5-8.5 experiment and r1i1p1f2 member in the LFMIP-pdLC experiment corresponds to the same high-emission scenarios (2015–2099).

Extreme high-temperature
The spatial distribution of extreme high-temperature (Fig. 3a, b, Supplementary Fig. 4a, b, Supplementary Fig. 5a, b, and Supplementary Fig. 6a, b) is determined by calculating the 90th percentile of surface air temperature in each grid point. And for the probability distribution function of surface air temperature over NA and EUR (Fig. 3c, d, Supplementary Fig. 4c, d, Supplementary Fig. 5c, d, and Supplementary Fig. 6c, d), regional average of surface air temperature is calculated first, and then the probability distribution function of the regional average is calculated. In order to analyze the extreme high-temperature changes driven by SA, the 90th percentile of surface air temperature in LFMIP-pdLC experiment is used as the threshold temperature in three time periods (modern, mid-term, and long-term) separately. The probability and intensity differences of surface air temperature in coupled experiment (historical, the SSP1-2.6, and SSP5-8.5 experiments) relative to the threshold temperature in LFMIP-pdLC experiment are taken as the SA effect across the three time horizon periods (modern, mid-term, and long-term).

Contribution to the warming trend
We calculated the warming trend (°C per decade, 2015-2099) of total, GHG, and SA effect on ground surface air temperature under high-emission scenario (SSP5-8.5) over the globe (excluding Antarctica), northern middle latitudes (Northern: 30–60°N, 180°W–180°E), southern subtropical latitudes (Southern: 20–40°S, 180°W–180°E), Europe (EUR: 40–60°N, 20–50°E), and North America (NA: 28–55°N, 88–110°W) in future projections (Supplementary Table 1). (1) The total contribution to the warming trend is obtained by calculating the trend of the surface air temperature in fully coupled experiment under high-emission scenario (SSP5-8.5), because the time series of this experiment included both GHG and SA effects; (2) the contribution of SA to the warming trend is obtained by calculating the trend of the difference of surface air temperature between fully coupled experiment (SSP5-8.5) and fixed soil moisture experiment (LFMIP-pdLC) under high-emission scenario, because the time series of this difference between the two experiments considered as SA effect; (3) the contribution of GHG to the warming trend is obtained by calculating the trend of the surface air temperature in fixed soil moisture experiment (LFMIP-pdLC) under high-emission scenario, because the time series of this experiment included GHG effect and excluded SA effects.

Decomposition of SA-driven changes in surface air temperature28
We decompose the changes in surface air temperature (Ta) caused by SA into the energy balance components. The change in Ta can be expressed as the sum of the changes in radiative forcing (ΔTr ad) and the changes in heat flux (ΔTc air). In this study, the Ta changes are expressed as:

ΔTa = ΔTr ad + ΔTc air (1)

In order to calculate the change of Ts caused by SA, we start with the formula of land surface energy balance:

Sn + Ln = λE + H + G (2)

where Sn and Ln are the net short-wave and long-wave radiation at the surface. λ, E, and H are the vaporization latent heat, evapotranspiration, and sensible heat flux. G is the ground heat flux, which magnitude is small and can be ignored on seasonal and longer time scales.

Sn + Ln = λE + H (3)

Sn can be expressed as:

Sn = Sτ(1 − α) (4)

where S is the solar radiation flux at atmosphere top, τ is the atmospheric short-wave transmissivity, α is the surface albedo.

According to the Stephan–Boltzmann law, the downward long-wave radiation at the land surface can be calculated roughly as:

L↓ = εa σTa4 (5)

where εa is atmospheric air emissivity, σ is the Stephan–Boltzmann constant (5.67 × 10−8 W m−2 K−4). The upward long-wave radiation is expressed as:

L↑ = (1 − εS) εa σTa4 + εS σTs4 (6)

where εS is the land surface emissivity, and it can be treated as constant of 0.95, since the εS varies very little over different land covers, around 0.95. Therefore, the net long-wave radiation at the land surface is expressed as:

Ln = L↓ − L↑ = εS εa σTa4 − εS σTs4 (7)

The sensible heat flux is expressed as:

H = ρCd/ra (Ts − Ta) (8)

where ρ is the air density (1.21 kg m−3), Cd is the air specific heat at constant pressure (1013 J kg−1 K−1), and ra is the aerodynamic resistance. Because in water-restricted areas such as arid and semi-arid regions, the change of latent heat flux is more determined by soil moisture, so latent heat flux is not written as a function of the change of Ta.

Using Eqs. (2)–(8), the surface energy balance equation can be expanded as following:

Sτ(1 − α) + εS σ εa Ta4 − εS σ Ts4 = λE + ρCd/ra (Ts − Ta) (9)

Assuming that S, λ, ρ, Cd, σ and εS are independent of Ts, it can be further differentiated the Eq. (9) with respect to Ts:

ΔTs = f1 (−SτΔα − λΔE + S(1 − α)Δτ + εS σTa4 Δεa + ρCd/ra (Ts − Ta) Δra) + f1 (ρCd/ra + 4εS σTs3) ΔTa (10)

where f1 is the Ts sensitivity to 1 W m−2 radiative forcing.

f1 = 1/(ρCd/ra + 4εS σTs3) (11)

On the right side of Eq. (10), the first term is the Ts change caused by radiative and thermodynamic forcings associated with SA-driven changes in surface albedo, evapotranspiration, short-wave transmissivity, air emissivity, and aerodynamic resistance (ΔTr ad = f1 (−SτΔα − λΔE + S(1 − α)Δτ + εS σTa4 Δεa + ρCd/ra (Ts − Ta) Δra)). The second term (f1 (ρCd/ra + 4εS σTs3) ΔTa) is the Ts change further drives a change in Ta through the surface heating rate change (ΔTr ad = f1 (ρCd/ra + 4εS σTs3) ΔTr ad). Through equations (1) and (10), Ta changes caused by SA can be decomposed into the following forms:

ΔTa = f1 (−SτΔα − λΔE + S(1 − α)Δτ + εS σTa4 Δεa + ρCd/ra (Ts − Ta) Δra) + ΔTc air (12)

Where f1 = 1/(ρCd/ra + 4εS σTs3), f1 is the Ta sensitivity to 1 W m−2 radiative forcing.

The change in surface air temperature (ΔTa) caused by SA is decomposed into radiative forcing terms by Eq. (12)28 and incorporating surface albedo (−SτΔα), evapotranspiration (−λΔE), shortwave transmissivity (S(1 − α)Δτ), air emissivity (εS σTa4 Δεa), aerodynamic resistance (ρCd/ra (Ts − Ta) Δra), and residual terms (ΔTc air). In our decomposition, we used the multi-model mean (CESM2, CMCC-ESM2, EC-Earth3, and IPSL-CM6A-LR) in our calculations. The remaining two models (MIROC6 and MPI-ESM1-2-LR) were omitted because they lack the relevant radiation input data.

Data availability
All data used in this study are freely available online. The CMIP6 model simulations are from https://esgf-node.llnl.gov/search/cmip6/.

Code availability
Analysis and figure generation were performed using NCL and MATLAB. The code and scripts of the five figures in the paper are available from Zenodo: https://doi.org/10.5281/zenodo.7928584.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "This study presented potentially original findings on the role of land-atmosphere coupling as an amplifier of GHG warming over some regions, with this amplifying effect stronger under the high emission scenario. The presentation is overall clear.\nHowever, before the manuscript can be accepted, the authors need to address the following major concerns (about the interpretation of results and the methodology used) and minor comments.\nMajor concerns:\n1) While the authors emphasized the positive LA contributions to warming over NA and EUR, they didn’t explain why these positive LA contributions are strong primarily over these regions. In fact, there are also negative LA contributions to warming over Africa (except southern part) in Fig. 1. The authors need to analyze and explain the results over Africa (except southern part) in a similar way (to ensure that the authors’ arguments are robust).\nSimilarly, the LA contributions to extreme high temperatures are negative over most of Africa and India (Fig. 3). Some explanations are also needed.\n2) Lines 356-365 discussed the method to compute GHG and LA contributions to the total warming, but it is not obvious what these terms exactly represent. The authors need to present and discuss these individual contributions for the “modern” period. From Fig. 2, it seems that the LA-driven temperature difference (warming) is quite large over NA in the “modern” period. The question is: is this LA-driven large difference realistic? – at least some comparisons with any prior studies are needed.\nTo further ensure that the methodology is appropriate, the authors should add the results for the period of 1900-1919 (when GHG forcing is weak) - if such model simulation results are available.\n3) Eq. (1) is the primary equation used to explain the mechanisms for the results, and hence the assumptions used to derive this equation should be presented. For instance, it is unclear how the downward and upward longwave radiation variations are computed.\nMinor comments:\n4) the use of the term “Snowball effect” in the title does not seem appropriate, as there are both positive and negative LA contributions to warming (see major comment 1).\n5) for Table S1, provide the scenario used. Furthermore, provide the range (i.e., min and max) for each value (from the various model results).\n6) mention in the text how the “globe” is defined? – does it include Antarctic and Greenland?\n7) Lines 333-337: provide more details on LFMIP-pdLC.", "reviewer_2": "The paper “Snowball effect of land-atmosphere coupling on global warming” explores the role of land-atmosphere feedbacks on projections of surface air temperature by comparing the outputs from LS3MIP experiment with the historical and future projections with SSP1-2.6 and SSP5-8.5.\nThe results indicate that the land surface has a compounding effect on the global warming due to the feedbacks between the land and the atmosphere. Specifically, over high latitudes, the fully coupled models show a decrease in evaporation and decrease in cloud cover which cause an increase in radiation at the surface and an increase in sensible heating that led to an increase in surface air temperature and compounds the effects of greenhouse gasses.\nThe paper is logically organized which makes it easy to follow. The experiment design is interesting, and the results provide insights into the coupling between the land and the atmosphere and its impact on future projects of temperature. Based on this, the paper is well suited for Nature Communications and merits publication. Despite these positive aspects, the paper is not particularly clear in defining certain aspects of the work and there needs to be some discussion about the uncertainly in the models. Based on this, here are a few suggestions for improvement.\nFirst, there are a few places in the paper that need some clarification. For example, in lines 50-56 it provides a brief overview of the LS3MIP experiment and how the models are used to derive the results. I found this section to be confusing and it would benefit for a little bit more detail about the LS3MIP experiment. Specifically, it uses the climatology from 1980-2014 for soil moisture, but does it also change soil temperature, snow cover and other lands surface states? What impacts does changing some aspects of the land surface model but not others have on the model simulations?\nLine 104-106 is also a bit confusing. What is meant by “LA will switch from its role as an agent of internal climate variability to one in which LA is tied directly to GHG emissions”? This statement is problematic on many levels and should be revised. It is unclear on what is meant by “agent” and how LA is “tied directly to GHG”.\nLine 329 was confusing as it is unclear by what is meant by “monthly data will affect the distribution of extreme temperature probability”. Is this referencing the fact that the monthly data will not show as high of a value as daily data due to temporal averaging? If so, then it is still unclear exactly how this was resolved given that some models provide daily data and others only have monthly data.\nLines 345-351 are very confusing, and I am not completely sure I understand what is going on.\nAre you doing a regional scale analysis (e.g., multiple grid cells within a certain range of the center grid cell) or is it just a grid cell analysis? Using without LA interactions as the threshold temperature only works if you are comparing the differences between without LA and with LA across the three time periods (modern, mid-term and long-term). I think that is what is being done here, but it is difficult to understand.\nExtended Data Fig. 1 (Lines 412-415) was not helpful and difficult to see any relationship given the monthly frequency of the data. Consider revising so that it can clearly show the difference between the two model runs (uncoupled, coupled) that you are trying to emphasize here.\nExtended Data Fig. 9 (Lines 471-481) was very interesting and clearly shows the attribution of the change from the coupled and uncoupled models. Consider trying to highlight this more in the paper.\nLastly, and most importantly, there needs to be a broader discussion about the uncertainty of LA coupling in models and how it has the potential to spin out of control and not provide realistic representation of coupling (Dirmeyer, 2013; Roundy et al., 2013; Santanello et al., 2015). Therefore, there is always the potential that what is being shown here is not necessarily an indication of what will happen in a future climate with increased GHG, but could just be coupled models snowballing into an unrealistic coupling state due to limitations of parameterization in the land surface and atmospheric models.\nDirmeyer, P. a. (2013). Characteristics of the water cycle and land–atmosphere interactions from a comprehensive reforecast and reanalysis data set: CFSv2. Climate Dynamics, 41(3–4), 1083–1097. https://doi.org/10.1007/s00382-013-1866-x\nRoundy, J. K., Ferguson, Craig R., & Wood, Eric F. (2013). Impact of land-atmospheric coupling in CFSv2 on drought prediction. Climate Dynamics, 1–14. https://doi.org/10.1007/s00382-013-1982-7\nSantanello, J. A., Roundy, J., & Dirmeyer, P. A. (2015). Quantifying the Land–Atmosphere Coupling Behavior in Modern Reanalysis Products over the U.S. Southern Great Plains. Journal of Climate, 28(14), 5813–5829. https://doi.org/10.1175/JCLI-D-14-00680.1", "reviewer_3": "Review for „Snowball effect of land–atmosphere coupling on global warming“ by Qiao et al.\nSummary\n=======\nQiao et al. analyse 6 CMIP6 climate model simulations under 2 emission scenarios and the historical period in comparison with their LFMIP-pdLC simulations under LS3MIP to isolate and study the impact of LA coupling on the warming in the 21st century from the overall warming. The authors show that the impact of soil moisture and snow cover change due to GHG changes will enhance the global warming in case oft he high emission scenario.\nThe topic oft he study is relevant for understanding the contribution of LA coupling to climate change in global climate model simulations under different GHG scenarios. But it needs major revision prior to publication.\nMajor comments:\n===============\n1) The study complements the publication Zhou, S., Williams, A.P., Lintner, B.R. et al. Diminishing seasonality of subtropical water availability in a warmer world dominated by soil moisture–atmosphere feedbacks. Nat Commun 13, 5756 (2022). https://doi.org/10.1038/s41467-022-33473-9 , however this study is not cited.\n2) The title is gimmickry („snowball effect“) and not covering the study („effect of land–atmosphere coupling“), the study only analyses the soil moisture and snow cover effect on the global warming, not the land-atmosphere coupling effect.\n3) This study needs to account at least for the root zone soil moisture. Showing the 10 cm soil moisture in Fig 4 is not sufficient for the goal of this study, it needs tob e at least 1m. E.g. Fig. 4 shows only about 1-2 kg/m² in soil moisture change 100 years, i.e. 1-2 mm in 10 cm of soil, i.e. 2.5-5% oft the porosity. Further Evapotransipartions uses the root zone, not the top 10 cm.\n4) It is necessary to distinguish regions with latent heat flux limited by soil moisture and those limited by radiation, because they will result in different land atmosphere coupling paths. Only under soil moisture limitation the soil moisture impacts the temperature. This is very well seen in the results by Qiao et al. but not discussed. Include this in the analyses.\nIn Detail:\n==========\n1. „Snowball“ in the frame of climate research is associated with the „Snowball Earth“ and therefore the „snowball effect“ even though meaning something different may lead to the wrong attention. Please change the title to fit the study (see summary) and not to be gimmickry.\n2. Lines 44-48: Something is missing here. It is not clear how many models etc without jumping to the methods section\n3. Line 51: LFMIP simulations are not „uncoupled“. It is important to name here LFMIP so nobody is confused with uncoupled LMIP ( Bart Van den Hurk et al. Geoscientific Model Development, DOI 10.5194/gmd-9-2809-2016)\n4. Change lines 55-56, e.g.: „For the LFMIP experiment, land-surface forcing comprises the annual mean cycle of soil moisture and snow cover for the period 1980–2014 derived from historical global climate model output by fixing their climatological state to remove long-term trends and inter-annual variability (Extended Data Fig. 1)“. This is because not the land surface state but the soil moisture and snow cover are fixed, which is essential fort he analyses because this means that the surface energy fluxes and land surface temperature can change in LFMIP.\n5. Lines 55: the LA effect cannot be isolated , only that of soil moisture and snow cover.\n6. Line 57-58: Why do you use 20year climatologic periods instead of 30year periods? You are looking at soil moisture and ET changes, not only temperature. See e.g. Liersch et al 2020 Environ. Res. Lett. 15 104014 DOI 10.1088/1748-9326/aba3d7 and Hawkins, E., & Sutton, R. (2016). Connecting Climate Model Projections of Global Temperature Change with the Real World, Bulletin of the American Meteorological Society, 97(6), 963-980. Retrieved Feb 28, 2023, from https://journals.ametsoc.org/view/journals/bams/97/6/bams-d-14-00154.1.xml\n7. Line 60/61: Change to „Under each emission scenario investigated here, LA due to soil moisture and snow cover amplifies global warming over much of Earth’s land surface (Fig. 1).“\n8. Lines 63-68: Mention here the reasons for those regions. It is not surprising to find the amplification in regions which will become increasingly soil moisture limited in evapotranspiration.\n9. SAT: Use the ESGF abbreviation tas , not SAT, which is rather uncommon.\n10. Line 337: Delete „Such as“\n11. All Figs with „LA induced“ differences (e.g. Fig. 4, Extended Figs. 7,8,10): Name that these are CMIP6 and LFMIP difference plots (as in Fig. 1)\n12. Line 34: Too many references, some ore doubling the statement. References 2,3,6 and 7 are superficial.\n13. Reference 8 has the wrong first author. It should be Berg et al.\n14. Line 41: Decide to cite reference 22 or 24 because they are not providing any extra information needed for your study.\n15. Figure 8: Why is figure 8 only in the extended data when your title is about land-atmosphere coupling?\n16. How ist he albedo changing? Due to snow and moisture or also due to dynamic vegetation in the models?\n17. Do the models include simulated dynamic vegetation (i.e. LAI growth and root growth due to atmospheric and soil moisture conditions)? Add this information."}, "author_response": "Responses to NCOMMS-22-53760-A\nReviewer #1:\nReviewer Comment\nThis study presented potentially original findings on the role of land-atmosphere\ncoupling as an amplifier of GHG warming over some regions, with this amplifying\neffect stronger under the high emission scenario. The presentation is overall clear.\nHowever, before the manuscript can be accepted, the authors need to address the\nfollowing major concerns (about the interpretation of results and the methodology used)\nand minor comments.\nReply\nWe thank the reviewer for the positive comments on original findings of this\nmanuscript. We have revised the manuscript in accordance with the reviewer’s\ncomments. Below please find our point-to-point response to the comments.\nMajor Comments:\nReviewer Comment\n1. While the authors emphasized the positive LA contributions to warming over NA and\nEUR, they didn’t explain why these positive LA contributions are strong primarily over\nthese regions. In fact, there are also negative LA contributions to warming over Africa\n(except southern part) in Fig. 1. The authors need to analyze and explain the results\nover Africa (except southern part) in a similar way (to ensure that the authors’\narguments are robust). Similarly, the LA contributions to extreme high temperatures are\nnegative over most of Africa and India (Fig. 3). Some explanations are also needed.\nReply\nFirstly, we changed title to “Soil moisture-atmosphere coupling accelerates global\nwarming” in the revised manuscript because the LFMIP-pdLC experiment only reflects\nthe effect of fixed soil moisture.\nThe warming effect of soil moisture-atmosphere coupling (SA) is most intensive\nover NA and EUR, so we emphasize the SA-warming in the two regions. About the\nrelevant explanation, we have illustrated by Figs. 4-5 and Supplementary Figs. 8-11.\nActually, this manuscript is organized as two parts: Part 1 is about facts (Figs. 1-3;\nSupplementary Figs. 1-7) and Part 2 is about the relevant explanations (Figs. 4-5;\nSupplementary Figs. 8-11).\nFig. 4 demonstrates the most weakening of evapotranspiration in NA and EUR,\nwhich conduce to the most increase of sensible heat flux because of the intensive SA\nover the two regions. If we consider the net energy of ground surface and low-\natmosphere as a cake, the less evapotranspiration increases surface receiving shortwave\nradiation (the anomalous longwave radiation is much weaker, Supplementary Fig. 8 in\nthe revised manuscript) through a reduction in cloud cover (Figs. 5a-b in the revised\nmanuscript), which enlarges the energy cake. On the other way, the less\nevapotranspiration also leads to more energy transferred from latent heat flux to the\nsensible heat flux (Figs. 5c-d in the revised manuscript), especially over those dry-wet\ntransition regions such as NA and EUR. Bigger slice of the bigger cake conduces to the\nstrongest positive sensible heat flux over NA and EUR, which thereby become a soil\nmoisture-warming hotspot. Following the comment, we have strengthened the\nexplanation in the revised manuscript (Page 11 Lines 166-177: GHG-driven warming\nis projected to dry the soil column26 (Figs. 4a–b and Supplementary Fig. 7), thereby\nreducing evapotranspiration, allowing the ground surface to receive more solar\nshortwave radiation (longwave radiation is much weaker) through a reduction in cloud\ncover (Figs. 5a-b and Supplementary Fig. 8). Meanwhile, decreasing\nevapotranspiration could increase sensible heat flux from the land surface to the low-\nlevel atmosphere via decreasing the latent heat flux (Figs. 5c-d). The increasing sensible\nheat flux caused by the joint enhanced shortwave radiation and reduced latent heat flux\nconduce to the nonlinear warming under severe GHG emission. Those phenomena are\nthe strongest in the Northern mid-latitude and Southern subtropical, especially in EUR\nand NA, where decreasing soil moisture can significantly change more surface energy\nallocation from latent heat flux to sensible heat flux via decreasing evapotranspiration.).\nSecondly, the negative warming effect of SA over African Sahara is much weaker\nin comparison with those positive warming, we did not specially discuss the\nphenomenon in the manuscript. The soil moisture anomalies over Sahara is generally\nvery small due to the extremely dry condition and the models may not capture the\nplausibly local impact of SA. On the other way, based on the Fig. 5 and Supplementary\nFig. 8 in the revised manuscript, we can find that the evapotranspiration anomalies over\nSahara is very little while the negative cloud cover and positive shortwave radiation\nanomalies are generally significant, which suggests that the local evapotranspiration\nassociated with soil moisture is not the major factor dominating the surface energy.\nThe impact of SA on the surface energy over Sahara is non-local and related to the large-\nscale circulation anomalies, which may be the reason for the positive shortwave\nradiation whereas negative sensible heat flux anomalies with the local little\nevapotranspiration anomaly (Berg et al., 2017; Zhou et al.,2022). Overall, the negative\nsensible heat flux, which may due to the non-local LA impact, conduces to the negative\nsurface air temperature anomalies and less extreme high-temperature events over\nSahara. Following the suggestion, we add the relevant content in the revised manuscript\n(Pages 11-12 Lines 177-183: On the contrary, there is a slight cooling effect caused by\nSA in a few regions, such as Sahara and Arabian Peninsula. The evapotranspiration\nchange over those regions is very little, while the negative cloud cover and positive\nshortwave radiation are generally significant, which suggests that the local\nevapotranspiration associated with soil moisture is not the primary factor dominating\nthe surface energy. The impact of SA on surface energy over those regions may be due\nto the non-local effect and related to the large-scale circulation (Berg et al., 2017;\nZhou et al.,2022).)\nFinally, about the negative extreme high-temperature anomalies over India in long-\nterm future, as pointed out by the reviewer, we do not expect it because the surface air\ntemperature anomaly is positive though it is not significant in the multi-model mean\n(Figs. 1c-d). Furthermore, there are great differences among different models in India\n(negative in MPI-ESM1-2-LR (Figs. 3a-b), positive in CMCC-ESM2 (Supplementary\nFigs. 5a-b) and little change in IPSL-CM6A-LR (Supplementary Figs. 6a-b)), which\nmay be the consequence of the large uncertainty of Indian summer monsoon\nprecipitation (Prasanna 2016).\nIn MPI-ESM1-2-LR model, the SA negative effect on extreme high-temperature\nover India and North Africa can be explain through the morphological changes of PDF\n(Explained Fig. 1). Specifically, the PDF of surface air temperature over India and\nNorth Africa does not change significantly by SA, and shifted slightly to the left,\nespecially in the long-term future, which suggests that the SA effect on extreme high-\ntemperature in these regions is slight.\nWe added the relevant description in the manuscript.\nPage 9 Lines 148-151: The extreme high-temperature due to SA in India are diverse\namong different models though the SA-driven warming is significant, which may be\nrelevant the large uncertainty of Indian summer monsoon precipitation (Prasanna et al.,\n2016)\nReference\nPrasanna, V. Assessment of South Asian Summer Monsoon Simulation in CMIP5-\nCoupled Climate Models During the Historical Period (1850–2005). Pure Appl.\nGeophys. 173, 1379–1402 (2016). https://doi.org/10.1007/s00024-015-1126-6.\nBerg, A., Lintner, B., Findell, K. & Giannini, A. Soil Moisture Influence on Seasonality\nand Large-Scale Circulation in Simulations of the West African Monsoon. Journal\nof Climate30, 2295-2317, doi:10.1175/jcli-d-15-0877.1 (2017).\nZhou, S. et al. Diminishing seasonality of subtropical water availability in a warmer\nworld dominated by soil moisture-atmosphere feedbacks. Nat Commun 13, 5756,\ndoi:10.1038/s41467-022-33473-9 (2022).\nReviewer Comment\n2. Lines 356-365 discussed the method to compute GHG and LA contributions to the\ntotal warming, but it is not obvious what these terms exactly represent. The authors\nneed to present and discuss these individual contributions for the “modern” period.\nFrom Fig. 2, it seems that the LA-driven temperature difference (warming) is quite large\nover NA in the “modern” period. The question is: is this LA-driven large difference\nrealistic? – at least some comparisons with any prior studies are needed. To further\nensure that the methodology is appropriate, the authors should add the results for the\nperiod of 1900-1919 (when GHG forcing is weak) - if such model simulation results\nare available.\nReply\nAccording to the reviewer’s suggestion, we revised and described the contribution\nto warming trend in more detail. Meanwhile, it is important to note that the\ncontributions to warming trend is the warming rate by total, GHG, and SA effect, not\nthe cumulative warming.\nPage 21 Lines 328-344: Contribution to the warming trend. We calculated the\nwarming trend (°C/decade) of total, GHG, and SA effect on ground surface air\ntemperature under high-emission scenario (SSP5-8.5) over globe (not include\nAntarctica), northern middle latitudes (Northern: 30–60°N, 180°W–180°E), southern\nsubtropical latitudes (Southern: 20–40°S, 180°W–180°E), Europe (EUR: 40–60°N,\n20–50°E), and North America (NA: 28–55°N, 88–110°W) in future projections (2015-\n2099). (1) The total contribution to the warming trend is obtained by calculating the\ntrend of the surface air temperature in fully coupled experiment under high-emission\nscenario (SSP5-8.5), because the time series of this experiment included both GHG\nand SA effects; (2) the contribution of SA to the warming trend is obtained by\ncalculating the trend of the difference of surface air temperature between fully coupled\nexperiment (SSP5-8.5) and fixed soil moisture experiment (LFMIP-pdLC) under high-\nemission scenario, because the time series of this difference between the two\nexperiments considered as SA effect; (3) the contribution of GHG to the warming trend\nis obtained by calculating the trend of the surface air temperature in fixed soil moisture\nexperiment under high-emission scenario (LFMIP-pdLC), because the time series of\nthis experiment included GHG effect and excluded SA effects.\nWe revised the description of the contribution to warming trend in manuscript.\nPage 6 Lines 102-106: For the very high-emission pathway, the positive trends caused\nby SA over EUR (0.17 ± 0.08 °C pre decade) and NA (0.16 ± 0.09 °C pre decade)\ncorrespond to 18.5 ± 9.7% and 18.8 ± 10.0%, respectively, of the overall warming rate\nin each region (Supplementary Table 1).\nSupplementary Table 1| Contributions to the warming trend (°C/decade). The\nwarming trend of total, GHG, and SA effect on ground surface air temperature under\nhigh-emission scenario (SSP5-8.5) over globe (not include Antarctica), northern\nmiddle latitudes (Northern: 30–60°N, 180°W–180°E), southern subtropical latitudes\n(Southern: 20–40°S, 180°W–180°E), Europe (EUR: 40–60°N, 20–50°E), and North\nAmerica (NA: 28–55°N, 88–110°W) in future projections (2015-2099). The warming\nuncertainty is obtained by calculating the standard deviation of multiple models.\nGlobe Northern Southern EUR NA\nGHG 0.68±0.13 0.77±0.17 0.57±0.11 0.74±0.21 0.69±0.17\nSA 0.05±0.03 0.09±0.05 0.03±0.02 0.17±0.08 0.16±0.09\nTotal 0.73±0.13 0.86±0.14 0.60±0.12 0.91±0.16 0.86±0.15\nFor the phenomenon that SA-driven temperature difference (warming) is quite\nlarge over NA in the “modern” period in Fig. 2 and Fig. 1f (grey bars). the SA-driven\n0.83±0.51 ℃ warming in NA in the modern period is smaller than or equivalent to\nthat in Berg et al. (2014) , in which SA does lead to more than 2℃over North America\nin 1971-2000 using the GFDL climate model (Explained Fig. 2). We have also added\nrelevant quote and explanation in the manuscript.\nPage 4 Lines 67-71：The most extreme warming occurs over central North America\n(NA; 28–55°N, 88–110°W) and central and eastern Europe (EUR; 40–60°N, 20–50°E)\nin modern period (0.89 ± 0.53°C and 0.56 ± 0.41°C), which is generally consistent with\nBerg et al14. The warming will up to 2.4°C in the two regions in the long-term future\nunder the very high emission scenario (Fig. 1d).\nFinally, the model simulation in the period of 1900-1919 are not available because\nthe LFMIP-pdLC experiment period is 1980-2099. As our response in the above, the\nSA-warming in the modern time is consistent with the previous studies, so we could\nbelieve the warming in the future is reliable to some extent.\nReference\nBerg, A., et al. Impact of Soil Moisture–Atmosphere Interactions on Surface\nTemperature Distribution. Journal of Climate 27, 7976-7993, doi:10.1175/jcli-d-\n13-00591.1 (2014).\nReviewer Comment\n3. Eq. (1) is the primary equation used to explain the mechanisms for the results, and\nhence the assumptions used to derive this equation should be presented. For instance,\nit is unclear how the downward and upward longwave radiation variations are computed.\nReply\nBecause the decomposition of surface air temperature changes caused by SA\nthrough surface energy balance was referenced Zeng et al. (2017), the specific\nderivation process was not given in this manuscript. Nevertheless, we have added the\nderivation process to the Materials and Methods as suggested by the reviewer.\nPages 21-25 Lines 345-422: Decomposition of SA-driven changes in surface air\ntemperature. The surface energy balance controls land–atmosphere interactions. There\nare two dominant factors in driving the changes of land-surface air temperature (T ):\na\nfirst, the radiative and thermodynamic variations of land surface acts directly on land-\nsurface temperature (T ), the change of T interacts on T locally through radiative (for\ns s a\nexample, long wave radiation) and non-radiative (for example, sensible heat) fluxes\n( ); second, the change in atmospheric circulation (for example, advection of cold\n𝑟𝑎𝑑\na\n∆\nn\n𝑇\nd𝑎 warm air masses) acts more directly on T\na\n( ). That is:\n𝑐𝑖𝑟\n∆𝑇𝑎 (1)\n𝑟𝑎𝑑 𝑐𝑖𝑟\nWe first estimate the change\n∆\nin\n𝑇\naT\ns=\nas\n∆\nso\n𝑇\nc𝑎iate\n+\nd w\\∆\ni\n𝑇\nt𝑎h the SA-induced radiative and\nthermodynamic forcings because the land-surface energy budget is calculated at the\n∆\nland-surface layer. The land-surface energy balance is given by:\n(2)\nwhere is the net shortwa\n𝑆\nv𝑛e\n+\nra\n𝐿\nd𝑛iat\n=\nion\n𝜆 𝐸\nat\n+\nth\n𝐻\ne s\n+\nur\n𝐺\nface, is the net longwave\nradiatio\n𝑆\nn𝑛 at the surface, is the latent heat of vaporizati\n𝐿\no𝑛n, E is evapotranspiration,\nH is the sensible heat flux and G is the ground heat flux, which can be neglected due\n𝜆\nto its small magnitude on seasonal and longer timescales. Equation (2) can be\nrewritten as:\n(3)\n, , and H, are given a 𝑆 s𝑛: +𝐿𝑛 = 𝜆𝐸 +𝐻\n𝑆𝑛 𝐿𝑛 (4)\nwhere S is the solar radiation flu\n𝑆\nx𝑛 a\n=\n𝑆\n𝜏 (\nt\n1\nop\n−\no\n𝛼\nf a\n)\ntmosphere, τ is the atmospheric\nshortwave transmissivity, α is the surface albedo.\nAs most of atmospheric water vapor is confined near the surface, some empirical\nequations can provide very good estimates of downward longwave radiation\nworldwide using surface observations. According to the Stephan–Boltzmann law,\ngiven atmospheric air emissivity ( ), the downward longwave radiation at the land\nsurface can be estimated roughly a\n𝜀\ns𝑎\n10\n(5)\n4\nwhere is the Stephan–Boltzman\n𝐿\nn↓ c\n=\non\n𝜀\ns𝑎ta\n𝜎\nn\n𝑇\nt𝑎, and equals 5.67×10-8 Wm-2 K-4.\nis atmo 𝜎 spheric air emissivity and its variation is dri 𝜎 ven by changes in atmospheric 𝜀𝑎\nwater vapour and clouds.\nThe upward longwave radiation is given by\n(6)\n4 4\nwhere is the land-surf\n𝐿\na↑c\n=\n(e e\n1\n−\nis\n𝜀\nsi\nv𝑠i\n)ty\n𝜀\n.𝑎 N\n𝜎𝑇\no𝑎te\n+\nthe\n𝜀\n𝑠l\n𝜎\nan\\𝑇\nd𝑠-surface emissivity also\nchanges\n𝜀\nswith land cover, soil moisture and snow cover. Here we treat it as a\n𝜀\nsconstant\nof 0.95 for simplicity, as satellite-observed surface emissivity varies little over mostly\nvegetated surfaces and changes only slightly from 0.95 among different land covers.\nThus, the net longwave radiation over the land surface is given by\n(7)\n4 4\nThe sensible heat flux is 𝐿 𝑛gi = ve 𝐿 n ↓b − y: 𝐿↑ = 𝜀𝑠𝜎(𝜀𝑎𝑇𝑎 −𝑇𝑠 )\n(8)\n𝜌𝐶𝑑(𝑇𝑠−𝑇𝑎)\nwhere is the air density (1.21 𝐻kg= m-3), 𝑟𝑎 is the specific heat of air at constant\npressure\n𝜌\n(1013 J kg-1 K-1) and is the ae\n𝐶\nro𝑑dynamic resistance at 2 m height.\nMaking use of equations (2\n𝑟\n)𝑎–(8), the surface energy balance equation is expanded\ninto the following form:\n(9)\n4 4\n(𝑇𝑠−𝑇𝑎)\nAssuming that S,𝑆 𝜏(, 1−, 𝛼), +𝜀 𝑠 a𝜎n(d𝜀 𝑎𝑇𝑎 a−re𝑇 i 𝑠 nd)e=pe𝜆n𝐸de+nt 𝜌o𝐶f 𝑑 ,𝑟 w𝑎 e further\ndifferentiate the eq\n𝜆\nuat\n𝜌\nion\n𝐶\n(𝑑9) w\\𝜎\nith res\\𝜀\np𝑠ect to , giving the c\\𝑇\nh𝑠ange :\n𝑇𝑠 𝑇𝑠\n1 4 𝜌𝐶𝑑(𝑇𝑠 −𝑇𝑎)\n∆𝑇𝑠 = (−𝑆𝜏∆𝛼−𝜆∆𝐸 +𝑆(1−𝛼)∆𝜏+𝜀𝑆𝜎𝑇𝑎∆𝜀𝑎 + 2 ∆𝑟𝑎)\n𝑓𝑠 𝑟𝑎\n(10)\n3\n𝜌𝐶𝑑⁄𝑟𝑎+4𝜀𝑆𝜎𝜀𝑎𝑇𝑎\nwhere is an energy redist+rib𝜌u𝐶ti𝑑o⁄n𝑟𝑎 f+a4c𝜀t𝑆o𝜎r,𝑇 𝑠 3 giv∆e𝑇n 𝑎 by:\n𝑓𝑠 (11)\n3\nrepresents the land-sur\n𝑓\nf𝑠ac\n=\n𝜌\ne t\n𝐶\ne\n𝑑\n⁄\n𝑟\nm𝑎\n+\n4\n𝜀\ns𝑆e\n𝜎\nr\n𝑇\nat\ns𝑠itivity to 1 W m−2 radiative forcing\n−1\n𝑓\na𝑠t the land surface.\ntemperature change due to radiative and thermodynamic forcings associated with SA-\ncaused changes in surface albedo, evapotranspiration, shortwave transmissivity, air\nemissivity and aerodynamic resistance (\n𝑟𝑎𝑑\n∆𝑇𝑠 = (1⁄𝑓)(−𝑆𝜏∆𝛼−𝜆∆𝐸 +\n). The second term ( )\n3\n4\n𝜌𝐶𝑑(𝑇𝑠−𝑇𝑎) 𝜌𝐶𝑑⁄𝑟𝑎+4𝜀𝑆𝜎𝜀𝑎𝑇𝑎\n𝑆qu(1an−tif𝛼ie)s∆ t𝜏he+ s𝜀tr 𝑆 o𝜎n𝑇g 𝑎 c∆o𝜀u 𝑎 p+ling be𝑟t𝑎 2 ween∆ 𝑟𝑎) and . On the one h𝜌a𝐶n𝑑d⁄,𝑟 𝑎i+t 4re𝜀𝑆v𝜎e𝑇a𝑠 3 ls ∆th𝑇a 𝑎 t\nvaries with due to SA-induced chan 𝑇 g𝑎e in air 𝑇 a𝑠dvection, such as the SA-perturbed 𝑇 𝑠\nadvection of𝑇 c𝑎old and warm air masses ( ). On the other\n3\n𝑐𝑖𝑟\n𝜌𝐶𝑑⁄𝑟𝑎+4𝜀𝑆𝜎𝜀𝑎𝑇𝑎\n𝑐𝑖𝑟\nhand, it also shows that the change in ∆ 𝑇fu 𝑠 rth=er d𝜌r𝐶iv𝑑e⁄𝑟s𝑎 a+ 4c𝜀h𝑆a𝜎n𝑇g𝑠 3 e ∆in𝑇 𝑎 via the\nchange in surface heating rate ( 𝑇𝑠 ). Usi𝑇n𝑎g equations (1)\n3\n𝑟𝑎𝑑\n𝜌𝐶𝑑⁄𝑟𝑎+4𝜀𝑆𝜎𝑇𝑠\n𝑟𝑎𝑑\nand (10), surface air temperatur∆e 𝑇c 𝑎 hang=es𝜌 c𝐶a𝑑u⁄𝑟s𝑎e+d4 b𝜀𝑆y𝜎 𝜀S𝑎A𝑇𝑎 3 c∆an𝑇𝑠 be decomposed into the\nfollowing forms:\n(12)\n1 4 𝜌𝐶𝑑(𝑇𝑠−𝑇𝑎) 𝑐𝑖𝑟\n∆W𝑇h 𝑎 e=re 𝑓(−𝑆𝜏∆𝛼−𝜆∆𝐸 +𝑆(1−, 𝛼)∆𝜏 r+ep𝜀r 𝑆 e𝜎se𝑇n 𝑎 t∆s 𝜀th 𝑎 e+ land-s𝑟𝑎u 2 rface∆ 𝑟a 𝑎 ir) t+em∆p𝑇e 𝑎 rature\n3 −1\nsensitivi\n𝑓\nty\n=\n𝜌\n1\n𝐶\n𝑑⁄\n𝑟\n𝑎\n+\n2 r\na\n𝜀\n𝑆\n𝜎\nt\n𝜀\n𝑎\n𝑇\n𝑎\n𝑓\nthe land surface.\nThe change in surface air temperature ( ) caused by SA is decomposed into\nradiative forcing terms by equation (12) 31 a\n∆\nn\n𝑇\nd𝑎 incorporating surface albedo ( ),\nevapotranspiration ( ), shortwave transmissivity ( ), air emissivity\n−𝑆𝜏∆𝛼\n( ), aerodyn−a𝜆m∆i𝐸c resistance ( ), a𝑆n(d1 r−esi𝛼d)u∆al𝜏 term ( ).\n4\n𝜌𝐶𝑑(T𝑠−T𝑎)\n𝑐𝑖𝑟\nR𝜀e 𝑆 f𝜎e𝑇re 𝑎 n∆c𝜀e 𝑎 𝑟𝑎 2 ∆𝑟𝑎 ∆𝑇𝑎\nZeng, Z. et al. Climate mitigation from vegetation biophysical feedbacks during the\npast three decades. Nature Climate Change 7, 432-436, doi:10.1038/nclimate3299\n(2017).\nMinor Comments:\nReviewer Comment\n4. the use of the term “Snowball effect” in the title does not seem appropriate, as there\nare both positive and negative LA contributions to warming (see major comment 1).\nThe SA-warming occurs over most parts of the world while the SA-cooling only\noccurs in parts of Sahara, western Asia, and Greenland. Furthermore, the warming\nstrength is much stronger than the cooling. So for global scale, SA play a warming role\non land surface air temperature.\n“Snowball” in this manuscript means the SA-warming will increase over time with\ngreater GHG-warming in SSP5-8.5 (Fig. 2), which makes global warming\naccelerating―just like a snowball downhill on the snowy mountain getting bigger and\nbigger. Nevertheless, reviewer #3 thinks that “snowball” is easy to be confused with\n“snowball Earth”. Additionally, we further checked the LFMIP-pdLC experiment and\nfound it only fixed soil moisture (do not fix snow cover).\nTherefore, we revised the title to “Soil moisture-atmosphere coupling accelerates\nglobal warming” in the revised manuscript.\nReviewer Comment\n5. for Table S1, provide the scenario used. Furthermore, provide the range (i.e., min and\nmax) for each value (from the various model results).\nReply\nThe future scenario in Table S1 is high-emission scenario (SSP5-8.5). We have\nadded explanation in the table title. Meanwhile, we calculated the warming trend of\neach model, and gave the uncertainty by calculating the standard deviation of multiple\nmodels in the table (the revised table can be seen in the reply for the major comment\n2). Thanks.\nReviewer Comment\n6. mention in the text how the “globe” is defined? – does it include Antarctic and\nGreenland?\nReply\nmanuscript (Page 2 Line 25; Page 4 Lines 75-76; Page 6 Lines 93-94; Page 21 Line\n330). Thanks.\nReviewer Comment\n7. Lines 333-337: provide more details on LFMIP-pdLC.\nReply\nFollowing the comment, we have provided a more detailed description of LFMIP-\npdLC experiment in the Introduction and Materials and Methods in the revised\nmanuscript.\nPage 3 Lines 51-57: For the Land Feedback Model Intercomparison Project with\nprescribed Land Conditions experiment (LFMIP-pdLC) in LS3MIP, which the soil\nmoisture is fixed to its climatological state (the annual mean cycle for the period 1980–\n2014 derived from historical global climate model output, Supplementary Fig. 1). Then\nthe SA effect can be isolated from the relative differences between fully coupled\nexperiments (historical, the SSP1-2.6, and SSP5-8.5 experiments) and LFMIP-pdLC\nexperiment.\nPage 19 Lines 297-305: The LFMIP-pdLC experiment in LS3MIP is used to assess the\nimpact of land-atmosphere coupling caused by soil moisture on weather and climate\nthrough fixing the soil moisture as their climatological state (the annual mean cycle for\nthe period 1980–2014 derived from historical global climate model output,\nSupplementary Fig. 1).Then the SA effect can be isolated from the relative differences\nbetween fully coupled experiments (historical, the SSP1-2.6, and SSP5-8.5 experiments)\nand fixed soil moisture experiment (LFMIP-pdLC experiment).\nReviewer Comment\nThe paper “Snowball effect of land-atmosphere coupling on global warming”\nexplores the role of land-atmosphere feedbacks on projections of surface air\ntemperature by comparing the outputs from LS3MIP experiment with the historical and\nfuture projections with SSP1-2.6 and SSP5-8.5. The results indicate that the land\nsurface has a compounding effect on the global warming due to the feedbacks between\nthe land and the atmosphere. Specifically, over high latitudes, the fully coupled models\nshow a decrease in evaporation and decrease in cloud cover which cause an increase in\nradiation at the surface and an increase in sensible heating that led to an increase in\nsurface air temperature and compounds the effects of greenhouse gasses.\nThe paper is logically organized which makes it easy to follow. The experiment\ndesign is interesting, and the results provide insights into the coupling between the land\nand the atmosphere and its impact on future projects of temperature. Based on this,\nthe paper is well suited for Nature Communications and merits publication. Despite these\npositive aspects, the paper is not particularly clear in defining certain aspects of the\nwork and there needs to be some discussion about the uncertainly in the models. Based\non this, here are a few suggestions for improvement.\nReply\nWe thank the reviewer for the positive comments on the presentation and novelty\nof this manuscript. we have modified this article in accordance with the reviewer’s\ncomments. Especially, we added the discussion about the uncertainty of the models in\nthe Discussion and Conclusion, and described the experiment design and methods\nintroduction in more detail in the materials and methods. Below please find our point-\nto-point response to your comments.\nReviewer Comment\n1. First, there are a few places in the paper that need some clarification. For example,\nin lines 50-56 it provides a brief overview of the LS3MIP experiment and how the\nmodels are used to derive the results. I found this section to be confusing and it would\nbenefit for a little bit more detail about the LS3MIP experiment. Specifically, it uses the\nclimatology from 1980-2014 for soil moisture, but does it also change soil temperature,\nsnow cover and other lands surface states? What impacts does changing some aspects\nof the land surface model but not others have on the model simulations?\nReply\nFirstly, we changed title to “Soil moisture-atmosphere coupling accelerates global\nwarming” in the revised manuscript because the LFMIP-pdLC experiment only reflects\nthe effect of fixed soil moisture.\nIn the LFMIP-pdLC experiment, changes in soil moisture over time are replaced\nby their climatology state (the annual mean cycle for the period 1980–2014 derived\nfrom historical global climate model output) to remove their interannual variability and\nlong-term trends, other land surface elements (such as soil temperature, snow cover,\nand vegetation) are not fixed. So, the soil moisture-atmosphere coupling (SA) effect\ncan be isolated from the differences between the fully coupled experiments (historical,\nthe SSP1-2.6, and SSP5-8.5 experiments) and LFMIP-pdLC experiment (fixed soil\nmoisture).\nFollowing the comment, we have modified the description of this experiment in\nmore detail.\nPage 3 Lines 51-57: For the Land Feedback Model Intercomparison Project with\nprescribed Land Conditions experiment (LFMIP-pdLC) in LS3MIP, which the soil\nmoisture is fixed to its climatological state (the annual mean cycle for the period 1980–\n2014 derived from historical global climate model output, Supplementary Fig. 1). Then\nthe SA effect can be isolated from the differences between the fully coupled\nexperiments (historical, the SSP1-2.6, and SSP5-8.5 experiments) and LFMIP-pdLC\nexperiment.\nReviewer Comment\n2. Line 104-106 is also a bit confusing. What is meant by “LA will switch from its role\nas an agent of internal climate variability to one in which LA is tied directly to GHG\nemissions”? This statement is problematic on many levels and should be revised. It is\nunclear on what is meant by “agent” and how LA is “tied directly to GHG”.\nReply\nThe meaning of this sentence is that soil moisture-atmosphere coupling as a kind\nof internal climate variability is originally little affected by external forcing.\nHowever, SA will be more closely related to higher GHG emission in the future.\nAccording to the comment, we have deleted the sentence in the revised manuscript\nbecause of the plausible potential confusion for readers.\nReviewer Comment\n3. Line 329 was confusing as it is unclear by what is meant by “monthly data will affect\nthe distribution of extreme temperature probability”. Is this referencing the fact that the\nmonthly data will not show as high of a value as daily data due to temporal averaging?\nIf so, then it is still unclear exactly how this was resolved given that some models\nprovide daily data and others only have monthly data.\nReply\nOur presentation is not clear enough in here, because amount of monthly data is\nnot enough compared with daily data, we are concerned that the probability distribution\nfunction (PDF) characteristics cannot be accurately captured. Meanwhile, the multi-\nmodel mean will mask the intensity distribution of extreme high-temperatures when the\nnumber of models is little. So, we used daily data to calculate the PDF and extreme\nhigh-temperature probability for each model (do not multi-model mean) separately in\nFig. 3 (MPI-ESM1-2-LR model under high-emission scenario), Supplementary Fig. 4\n(MPI-ESM1-2-LR model under low-emission scenario), Supplementary Fig. 5\n(CMCC-ESM2), and Supplementary Fig. 6 (IPSL-CM6A-LR). And the results showed\nthat they had similar characteristics.\nWe have modified the description of time-scale in more detail.\nPages 18-19 Lines 279-291: The surface air temperature probability distribution\nfunction and extreme high-temperature were calculated from daily data for each model\n(do not multi-model mean) separately. Because amount of monthly data is not enough\ncompared with daily data, we are concerned that the probability distribution function\ncharacteristics cannot be accurately captured. Meanwhile, the multi-model mean will\nmask the intensity distribution of extreme high-temperatures when the number of\nmodels is little. So, we used daily data to calculate the probability distribution function\nand extreme high-temperature probability for each model (do not multi-model mean)\nseparately in Fig. 3 (MPI-ESM1-2-LR model under high-emission scenario),\nSupplementary Fig. 4 (MPI-ESM1-2-LR model under low-emission scenario),\nSupplementary Fig. 5 (CMCC-ESM2), and Supplementary Fig. 6 (IPSL-CM6A-LR).\nAnd the results showed that they had similar characteristics.\nReviewer Comment\n4. Lines 345-351 are very confusing, and I am not completely sure I understand what\nis going on. Are you doing a regional scale analysis (e.g., multiple grid cells within a\ncertain range of the center grid cell) or is it just a grid cell analysis? Using without LA\ninteractions as the threshold temperature only works if you are comparing the\ndifferences between without LA and with LA across the three time periods (modern,\nmid-term and long-term). I think that is what is being done here, but it is difficult to\nunderstand.\nReply\nFor the description of regional scale and grid cells, we didn't describe them very\nclearly. The spatial distribution of extreme high-temperature (Figs. 3a-b,\nSupplementary Figs. 4a-b, Supplementary Figs. 5a-b, and Supplementary Figs. 6a-b) is\ndetermined by calculating the 90th percentile of surface air temperature in each spatial\ngrid point. And for the probability distribution function of surface air temperature over\nNA and EUR (Figs. 3c-d, Supplementary Figs. 4c-d, Supplementary Figs. 5c-d, and\nSupplementary Figs. 6c-d), regional average of surface air temperature is calculated\nfirst, and then the probability distribution function of the regional average is calculated.\nThe reviewer's understanding about threshold temperature is correct. We have\nmodified those description in more detail in the revised manuscript.\nPages 20-21 Lines 313-327: Extreme high-temperature. The spatial distribution of\nextreme high-temperature (Figs. 3a-b, Supplementary Figs. 4a-b, Supplementary Figs.\n5a-b, and Supplementary Figs. 6a-b) is determined by calculating the 90th percentile of\nsurface air temperature in each spatial grid point. And for the probability distribution\nfunction of surface air temperature over NA and EUR (Figs. 3c-d, Supplementary Figs.\n4c-d, Supplementary Figs. 5c-d, and Supplementary Figs. 6c-d), regional average of\nsurface air temperature is calculated first, and then the probability distribution function\nof the regional average is calculated. In order to analyze the extreme high-temperature\nchanges driven by SA, the 90th percentile of surface air temperature in LFMIP-pdLC\nexperiment is used as the threshold temperature in three time periods (modern, mid-\nterm, and long-term) separately. The probability and intensity differences of surface air\ntemperature in coupled experiment (historical, the SSP1-2.6, and SSP5-8.5 experiments)\nrelative to the threshold temperature in LFMIP-pdLC experiment are taken as the SA\neffect across the three time periods (modern, mid-term, and long-term).\nReviewer Comment\n5. Supplementary Fig. 1 (Lines 412-415) was not helpful and difficult to see any\nrelationship given the monthly frequency of the data. Consider revising so that it can\nclearly show the difference between the two model runs (uncoupled, coupled) that you\nare trying to emphasize here.\nReply\nThe original figure is the regional average (North America), which masks a lot of\ndifferences. As suggested by the reviewer, we selected a grid in North America to\nredraw the figure (as shown in the below). It can be found the difference of soil moisture\nbetween the fully coupled and fixed soil moisture experiments is distinct. The original\nfigure has been replaced by the below figure in the revised manuscript.\nSupplementary Fig. 1| The multi-model mean of surface (top) and total (bottom)\nmonthly soil moisture (kg/m2) periods (1980–2099) for a grid in North America\nunder high-emission scenario. Red lines represent fully coupled simulations\n(historical experiment in 1980-2014, and SSP5-8.5 experiment in 2015-2099); black\nlines represent fixed soil moisture simulations (LFMIP-pdLC in 1980-2099).\nReviewer Comment\n6. Supplementary Fig. 9 (Lines 471-481) was very interesting and clearly shows the\nattribution of the change from the coupled and uncoupled models. Consider trying to\nhighlight this more in the paper.\nReply\nWe added the relevant description about attribution of the changes in manuscript.\nThanks\nPages 14-15 Lines 224-234: Generally, the shortwave transmissivity term is larger than\nthe evapotranspiration term for the global land in the modern period, while the effects\nof the two terms become equivalent in the future, especially in very high emission\nscenario. Over EUR and NA in the long-term future, the combined positive radiation\n(sum of the above five terms) dominated by evapotranspiration term and shortwave\ntransmissivity term caused by SA will reach 33.5±14.1 and 32.8±16.7 W/m2 under high-\nemission scenario. Compared with the modern period (15.4±9.9 and 22.1±9.2 W/m2),\nthe combined radiation will increase by 117.5±276.5% and 48.4±53.3%. However,\nunder low-emission scenario, although the combined radiation will also increase\n(23.1±5.9 and 25.3±12.6 W/m2), they are smaller than half of those in high-emission\nscenario.\nReviewer Comment\n7. Lastly, and most importantly, there needs to be a broader discussion about the\nuncertainty of LA coupling in models and how it has the potential to spin out of control\nand not provide realistic representation of coupling (Dirmeyer, 2013; Roundy et al.,\n2013; Santanello et al., 2015). Therefore, there is always the potential that what is being\nshown here is not necessarily an indication of what will happen in a future climate with\nincreased GHG, but could just be coupled models snowballing into an unrealistic\ncoupling state due to limitations of parameterization in the land surface and atmospheric\nmodels.\nReply\nThere is indeed a potential to spin out of control and not provide realistic\nrepresentation of coupling due to model uncertainty which limitations of\nparameterization in the land surface and atmospheric models in a future climate with\nincreased GHG. As reflected in the references (recommended by the reviewer), land-\nsurface processes such as precipitation and evapotranspiration are very important to soil\nmoisture, while precipitation and evapotranspiration often tend to be more uncertain in\nclimate models. Therefore, in the fully coupled model, the deviation due to limitations\nof the parameterization in the land-atmosphere coupling will make the surface air\ntemperature present greater uncertainty with the projected time.\nNevertheless, our previous study (Qiao et al., 2022, Explained Fig. 3) shows that\nmost of the selected models have reasonable simulation on soil moisture, so the future\nsimulation is basically reliable. Meanwhile, by analyzing the uncertainty of\nscenarioMIP in CMIP6, Lehner et al. (2020) showed that the uncertainty of surface air\ntemperature projection was mainly affected by internal variability and model\nuncertainty (in their paper, model uncertainty refers to climate response uncertainty,\nwhich includes the uncertainty caused by limitations of the parameterization in the land-\natmosphere coupling) in the early stage, but with the projected time, the proportion of\ninternal variability and model uncertainty would decrease, while the scenario\nuncertainty would gradually increase and become the most important part (Explained\nFigs. 4 and 5 below). Scenario uncertainty means that lack of knowledge of future\nradiative forcing that arises primarily from unknown future greenhouse gas emissions\n(Lehner et al., 2020).\nConsequently, we added relative discussion about climate projection uncertainty in\nthe end of this manuscript.\nPages 17-18 Lines 263-267: Additionally, although the models we used in this research\nhave high reliability in historical simulation of soil moisture (Qiao et al., 2022), and we\nreduced the uncertainty by multi-model mean, it is noted that the results may have some\nprojection uncertainty considering limitations of the parameterization in land-\natmosphere coupling (Dirmeyer, 2013; Roundy et al., 2013; Santanello et al., 2015) and\nscenario uncertainty (Lehner et al., 2020).\nReference\nLehner, F., Deser, C., Maher, N., Marotzke, J., Fischer, E. M., Brunner, L., Knutti, R.,\nand Hawkins, E.: Partitioning climate projection uncertainty with multiple large\nensembles and CMIP5/6, Earth Syst. Dynam. 11, 491–508, doi.org/10.5194/esd-\n11-491-2020. (2020).\nReviewer # 3:\nReviewer Comment\nReview for “Snowball effect of land–atmosphere coupling on global warming” by\nQiao et al.\nSummary\nQiao et al. analyse 6 CMIP6 climate model simulations under 2 emission scenarios\nand the historical period in comparison with their LFMIP-pdLC simulations under\nLS3MIP to isolate and study the impact of LA coupling on the warming in the 21st\ncentury from the overall warming. The authors show that the impact of soil moisture\nand snow cover change due to GHG changes will enhance the global warming in case\nof the high emission scenario.\nThe topic of the study is relevant for understanding the contribution of LA coupling\nto climate change in global climate model simulations under different GHG scenarios.\nBut it needs major revision prior to publication.\nReply\nWe thank the reviewer for the positive comments on the topic. We have revised the\nmanuscript in accordance with the reviewer’s comments. Below please find our point-\nto-point response to the comments.\nMajor Comments:\nReviewer Comment\n1. The study complements the publication Zhou, S., Williams, A.P., Lintner, B.R. et al.\nDiminishing seasonality of subtropical water availability in a warmer world dominated\nby soil moisture–atmosphere feedbacks. Nat Commun 13, 5756 (2022).\nhttps://doi.org/10.1038/s41467-022-33473-9 , however this study is not cited.\nReply\nWe read this paper thoroughly, which suggested that the soil moisture–atmosphere\nfeedbacks can influence the seasonal water availability changes by changing the large-\nscale atmospheric circulation in a warmer climate using the same experiment (LFMIP-\npdLC) in CMIP6. Specifically, during the dry season in subtropical regions and the\nAmazon, declining soil moisture reduces evapotranspiration, which can increase\nsurface water availability by modulating large-scale atmospheric circulation (soil\nmoisture-atmosphere effect on circulation: reduced evaporative cooling caused by\ndeclining soil moisture further amplifies land surface warming, and the associated land-\nocean warming contrast strengthens surface pressure differences between ocean and\nland, which drives anomalous ocean-to-land moisture transport and enhances moisture\nconvergence over land). Our study focuses on the local soil moisture-atmosphere\ncoupling (SA) effect while Zhou et al. emphasize the non-local effect of SA, which is\ndeserve to discussed. Therefore, we have added the relevant discussion in the revised\nmanuscript. Thanks for the information.\nPage 17 Lines 259-263: Here we emphasize the local effect of SA on surface air\ntemperature while the latest research shows that SA can also affect the large-scale\natmospheric circulation under the global warming background (Zhou et al., 2022). In\nthis view, the joint contribution of local and non-local SA effect on global land warming\nneeds to be further investigated.\nReviewer Comment\n2. The title is gimmickry (“snowball effect”) and not covering the study (“effect of\nland–atmosphere coupling”), the study only analyses the soil moisture and snow cover\neffect on the global warming, not the land-atmosphere coupling effect.\nReply\n“Snowball” in this manuscript means the SA-warming will increase over time with\ngreater GHG-warming in SSP5-8.5 (Fig. 2), which makes global warming\naccelerating―just like a snowball downhill on the snowy mountain getting bigger and\nbigger.\nThe LFMIP-pdLC experiment originally designed to assess the land-atmosphere\ncoupling by fixing soil moisture and snow cover in the designed stage (Bart et al., 2016).\nHowever, in the running stage, this experiment only fixed soil moisture and snow cover\ndid not fix (Explained Fig 6, https://wiki.c2sm.ethz.ch/LS3MIP/Tier1Experiments).\nFurthermore, In order to verify whether the snow cover is fixed, we presented time\nseries of snow cover in different models over Europe in LFMIP-pdLC experiment\n(Explained Fig 7), all models have the obviously interannual variabilities and decadal\nvariations. Therefore, the experiment reflected the land-atmosphere coupling effect\ndriven by soil moisture.\nSince soil moisture effect is included in land-atmosphere coupling, but land-\natmosphere coupling does not only contain soil moisture effect (such as land use,\nvegetation, and snow cover). Therefore, in order to describe our research more\naccurately, we modified “land-atmosphere coupling (LA)” to “soil moisture-\natmosphere coupling (SA)” in the title and main text.\nSo, we change the title: “Soil moisture-atmosphere coupling accelerates global\nwarming” in the revised manuscript.\nReviewer Comment\n3. This study needs to account at least for the root zone soil moisture. Showing the 10\ncm soil moisture in Fig 4 is not sufficient for the goal of this study, it needs to be at\nleast 1m. E.g. Fig. 4 shows only about 1-2 kg/m² in soil moisture change 100 years, i.e.\n1-2 mm in 10 cm of soil, i.e. 2.5-5% of the porosity. Further Evapotranspiration uses\nthe root zone, not the top 10 cm.\nReply\nWe chose shallow soil moisture (10 cm) for analysis because surface soil moisture\nhas a closer relationship with evapotranspiration and can directly interact with the\natmosphere.\nWe also investigated the root zone soil moisture (100 cm) as suggested by the\nreviewer (Supplementary Fig. 9 in revised manuscript). The changes of root zone soil\nmoisture and its positive correlation with evapotranspiration are similar to those in the\nshallow soil moisture. We also added some description in manuscript.\nPage 14 Lines 209-211: These characteristics are not only shown in the surface soil\nmoisture, which is most directly related to evapotranspiration, but also in the root zone\nsoil moisture (Supplementary Fig. 9).\nAs for the shallow soil moisture change is only about 1-2 kg/m² mentioned by the\nreviewer, we can find that the seasonal fluctuation in surface soil moisture over NA is\nabout 5 kg/m2 (Supplementary Fig. 1). In this view, the change is not small.\nFinally, evapotranspiration in this manuscript refers to evapotranspiration of land\nsurface, including evaporation of land surface and transpiration of vegetation, which is\nalso a variable used in most land surface processes.\nReviewer Comment\n4. It is necessary to distinguish regions with latent heat flux limited by soil moisture\nand those limited by radiation, because they will result in different land atmosphere\ncoupling paths. Only under soil moisture limitation the soil moisture impacts the\ntemperature. This is very well seen in the results by Qiao et al. but not discussed.\nInclude this in the analyses.\nReply\nAccording to our study, the SA effect makes surface air temperature increase in\nmost parts of the world (Fig. 1), which is mainly due to the decrease of\nevapotranspiration caused by SA. The decreasing evapotranspiration will enlarge the\nsolar shortwave reaching the ground and increase sensible heat flux (Fig. 4 and Fig. 5b\nin the revised manuscript). Nevertheless, there is still a large regional difference in\nwarming strength caused by SA. The difference of the warming strength is mainly\ndepending on whether soil moisture anomalies can significantly change the allocation\nof latent heat flux and sensible heat flux via evapotranspiration. We can find that soil\nmoisture can decrease latent heat flux significantly in the Northern mid-latitude and\nSouthern subtropical, especially in EUR and NA (Figs. 5c-d in the revised manuscript),\nin which the warming degree are most.\nAccording to the reviewer's suggestion, we added analyze of different region with\nlatent heat flux limited by soil moisture and those limited by radiation.\nPage 11 Lines 174-177:The increasing sensible heat flux caused by the joint enhanced\nshortwave radiation and reduced latent heat flux conduce to the nonlinear warming\nunder severe GHG emission. Those phenomena are the strongest in the Northern mid-\nlatitude and Southern subtropical, especially in EUR and NA, where decreasing soil\nmoisture can significantly change more surface energy allocation from latent heat flux\nto sensible heat flux via decreasing evapotranspiration.\nIn Detail:\nReviewer Comment\n1. Snowball in the frame of climate research is associated with the “Snowball Earth”\nand therefore the “snowball effect” even though meaning something different may lead\nto the wrong attention. Please change the title to fit the study (see summary) and not to\nbe gimmickry.\nReply\nPlease see our response to Major Comments 2, and we change the title as follow:\n“Soil moisture-atmosphere coupling accelerates global warming”.\nReviewer Comment\n2. Lines 44-48: Something is missing here. It is not clear how many models etc without\njumping to the methods section.\nReply\nThanks, the specific models used in this manuscript are added in the main text.\nPage 3 Lines 44-46: In order to analyze the SA effect on global warming, we employed\nsix global climate models (CESM2, CMCC-ESM2, EC-Earth3, IPSL-CM6A-LR,\nMIROC6, and MPI-ESM1-2-LR)…\nReviewer Comment\n3. Line 51: LFMIP simulations are not “uncoupled”. It is important to name here LFMIP\nso nobody is confused with uncoupled LMIP ( Bart Van den Hurk et al. Geoscientific\nModel Development, DOI 10.5194/gmd-9-2809-2016).\nReply\nWe have revised the description about LFMIP-pdLC experiment. Meanwhile, we\nused “fixed soil moisture experiment / LFMIP-pdLC experiment” instead of “uncouple\nexperiment” in the revised manuscript, thanks.\nPage 3 Lines 51-57: For the Land Feedback Model Intercomparison Project with\nprescribed Land Conditions experiment (LFMIP-pdLC) in LS3MIP, which the soil\nmoisture is fixed to its climatological state (the annual mean cycle for the period 1980–\n2014 derived from historical global climate model output, Supplementary Fig. 1). Then\nthe SA effect can be isolated from the relative differences between fully coupled\nexperiments (historical, the SSP1-2.6, and SSP5-8.5 experiments) and LFMIP-pdLC\nexperiment.\nReviewer Comment\n4. Change lines 55-56, e.g.: “For the LFMIP experiment, land-surface forcing\ncomprises the annual mean cycle of soil moisture and snow cover for the period 1980–\n2014 derived from historical global climate model output by fixing their climatological\nstate to remove long-term trends and inter-annual variability (Supplementary Fig. 1)”.\nThis is because not the land surface state but the soil moisture and snow cover are fixed,\nwhich is essential for the analyses because this means that the surface energy fluxes and\nland surface temperature can change in LFMIP.\nReply\nWe have revised the description about LFMIP-pdLC experiment in manuscript.\nThe details of the modification can be seen in the previous reply and reply of Major\nComment #2.\nReviewer Comment\n5. Lines 55: the LA effect cannot be isolated , only that of soil moisture and snow cover.\nReply\nWe have revised the description about LFMIP-pdLC experiment in manuscript.\nThe details of the changes can be seen in our response to Major Comment #2 and Detail\nComment #3.\nReviewer Comment\n6. Line 57-58: Why do you use 20year climatologic periods instead of 30year periods?\nYou are looking at soil moisture and ET changes, not only temperature. See e.g. Liersch\net al 2020 Environ. Res. Lett. 15 104014 DOI 10.1088/1748-9326/aba3d7 and Hawkins,\nE., & Sutton, R. (2016). Connecting Climate Model Projections of Global Temperature\nChange with the Real World, Bulletin of the American Meteorological Society, 97(6),\n963-980. Retrieved Feb 28, 2023, from\nhttps://journals.ametsoc.org/view/journals/bams/97/6/bams-d-14-00154.1.xml.\nReply\nAlthough a longer reference period may increase the robustness of the conclusion\nand better represent the climate state, there is no perfect choice of reference period as\nHawkins and Sutton (2016) pointed out. In this study, we analyzed the same period as\nthe Sixth Assessment Report (AR6) of IPCC Working Group I. In AR6, the experts\nanalyzed climate change mainly for three time periods: the modern (1995-2014), the\nmid-term (2040-2059), and the long-term (2080-2099). Because most researches on\nclimate change are based on parameters set by AR6, which makes it convenient to\ncompare and discuss with other studies.\nReviewer Comment\n7. Line 60/61: Change to: Under each emission scenario investigated here, LA due to\nsoil moisture and snow cover amplifies global warming over much of Earth’s land\nsurface (Fig. 1).\nReply\nThanks, we have modified this sentence as reviewer’s suggestion in the revised\nmanuscript (Page 4 Lines 62-63: Under each emission scenario investigated here, soil\nmoisture-atmosphere coupling (SA) amplifies global warming over much of Earth’s\nland surface (Fig. 1).).\nReviewer Comment\n8. Lines 63-68: Mention here the reasons for those regions. It is not surprising to find\nthe amplification in regions which will become increasingly soil moisture limited in\nevapotranspiration.\nReply\nWe have discussed this comment in Major Comment 4, and we added some\ndescription in here. The details of the changes can be seen in our response to Major\nComment #4.\n9. SAT: Use the ESGF abbreviation tas, not SAT, which is rather uncommon.\nReply\nWe have modified the abbreviation in manuscript, thanks.\n10. Line 337: Delete „Such as.\nReply\nWe have modified this sentence according to the reviewer's suggestion.\n11. All Figs with “LA induced” differences (e.g. Fig. 4, Extended Figs. 7,8,10): Name\nthat these are CMIP6 and LFMIP difference plots (as in Fig. 1).\nReply\nWe have modified this description according to the reviewer's suggestion. We used\n“soil moisture-atmosphere coupling (SA)” instead of “LA”, and “fixed soil moisture\nexperiment / LFMIP-pdLC experiment” instead of “uncouple experiment” in the\nrevised manuscript.\n12. Line 34: Too many references, some ore doubling the statement. References 2,3,6\nand 7 are superficial.\nReply\nWe have deleted those references. Thanks.\n13. Reference 8 has the wrong first author. It should be Berg et al.\nReply\nThanks, we have revised this reference.\n14. Line 41: Decide to cite reference 22 or 24 because they are not providing any extra\ninformation needed for your study.\nReply\nWe have deleted those references. Thanks.\n15. Figure 8: Why is figure 8 only in the Supplementary when your title is about land-\natmosphere coupling?\nReply\nWe have put the key information in the Supplementary Fig. 8 into main text as Fig.\n5 in the revised manuscript as suggested by reviewer. A more detailed description has\nalso been added in the revised manuscript.\nPages 11-12 Lines 166-183: GHG-driven warming is projected to dry the soil\ncolumn26 (Figs. 4a–b and Supplementary Fig. 7), thereby reducing evapotranspiration,\nallowing the ground surface to receive more solar shortwave radiation (longwave\nradiation is much weaker) through a reduction in cloud cover (Figs. 5a-b and\nSupplementary Fig. 8). Meanwhile, decreasing evapotranspiration could increase\nsensible heat flux from the land surface to the low-level atmosphere via decreasing\nthe latent heat flux (Figs. 5c-d). The increasing sensible heat flux caused by the joint\nenhanced shortwave radiation and reduced latent heat flux conduce to the nonlinear\nwarming under severe GHG emission. Those phenomena are the strongest in the\nNorthern mid-latitude and Southern subtropical, especially in EUR and NA, where\ndecreasing soil moisture can significantly change more surface energy allocation from\nlatent heat flux to sensible heat flux via decreasing evapotranspiration. On the\ncontrary, there is a slight cooling effect caused by SA in a few regions, such as Sahara\nand Arabian Peninsula. The evapotranspiration change over those regions is little,\nwhile the negative cloud cover and positive shortwave radiation are generally\nsignificant, which suggests that the local evapotranspiration associated with soil\nmoisture is not the primary factor dominating the surface energy (Supplementary Fig.\n8 and Fig 5c-d). The impact of SA on surface energy over those regions may be due to\nthe non-local effect and related to the large-scale circulation.\n16. How is the albedo changing? Due to snow and moisture or also due to dynamic\nvegetation in the models?\nReply\nIn the six climate models, CESM2, CMCC-ESM2, IPSL-CM6A-LR, and MPI-\nESM1-2-LR models include simulated dynamic vegetation, and EC-Earth3 and\nMIROC6 models do not include simulated dynamic vegetation. So, in the former four\nclimate models, the surface albedo is also related to dynamic vegetation caused by soil\nmoisture. The albedo change has been calculated by formula 12 (Materials and Methods)\nin Supplementary Figs. 10 and 11a, which mainly reflects the influence of albedo\nchanging caused by soil moisture on surface air temperature. We can find, no matter\nwith or without dynamic vegetation, the effect of albedo changing on surface air\ntemperature is very weak.\n17. Do the models include simulated dynamic vegetation (i.e. LAI growth and root\ngrowth due to atmospheric and soil moisture conditions)? Add this information.\nReply\nFor the six models used in this manuscript, CESM2, CMCC-ESM2, IPSL-CM6A-\nLR, and MPI-ESM1-2-LR models include simulated dynamic vegetation, and EC-\nEarth3 and MIROC6 models do not include simulated dynamic vegetation. We have\nadded relevant information in the revised manuscript.\nPage 19 Lines 291-295: Six global climate models in CMIP6 (CESM2, CMCC-ESM2,\nEC-Earth3, IPSL-CM6A-LR, MIROC6, and MPI-ESM1-2-LR) are used to analyze the\nimpact of SA on surface air temperature, which CESM2, CMCC-ESM2, IPSL-CM6A-\nLR, and MPI-ESM1-2-LR models include simulated dynamic vegetation, and EC-\nEarth3 and MIROC6 models do not include.\nREVIEWERS' COMMENTS\nReviewer #1 (Remarks to the Author):\nThe authors have satisfactorily addressed my concerns. The manuscript can be accepted after\naddressing the following minor comments.\n(1) In the derivation of Eq. (10), the change of latent heat flux (LH) is used directly, while the\nchange of sensible heat flux is written as a function of the change of (T_s – T_a). In contrast, in\nthe popular Penman-Monteith equation derivation, the change of LH is also written as a function of\nthe change of T_a. please add a few sentences to justify the decision (of using the change of LH\ndirectly in Eq. (10) without explicitly considering its dependence on the change of T_a).\n(2) In the last term of Eq. (10) and in lines 404, 407, and 409, replace “rho C_d/r_a + 4 epsilon_s\nsigma T_s ^3” by f_s for simplicity, as f_s is clearly defined in Eq. (11).\n(3) The language needs to be significantly improved. Just taking Abstract as an example:\n“….warming globle …. (not include …of SA on climate change ….and make a nonlinear …”\nshould probably be:\n“….warms globle …. (excluding …of SA to climate change ….and play a nonlinear …”\nReviewer #2 (Remarks to the Author):\nOverall, the authors did a good job of addressing my concerns. One area of minor concern is that\nthe authors did a good job of addressing my concern related to “uncertainty of LA coupling in\nmodels” in the response document but the amount of discussion that made it into the paper was\nminimal (Lines 263-267). Specifically, I think the discussion would be improved if the authors\nadded one or two more lines to this discussion arguing why they think the results are still relevant\neven with these uncertainties (I think they are still relevant and useful). The authors can get these\nadditional lines by summarizing the arguments made in the response document.\nReviewer #3 (Remarks to the Author):\nDear Liang Qiao et al.,\nthanks for the very good revision of your manuscript. You answered all my comments satisfyingly.\nSo I recommend its publication.\nThe following minor corrections are required:\nIt needs somebody checking the spelling and language, sometimes verbs (e.g. line 46, line 70) or\nletters are missing. Fig. 3c has overlapping x-axes.\nI am looking forward to see the published manuscript.\nResponses to NCOMMS-22-53760B\nReviewer #1:\nReviewer Comment\nThe authors have satisfactorily addressed my concerns. The manuscript can be accepted\nafter addressing the following minor comments.\nReply\nWe thank the reviewer for the positive comments and recognition of the\nconclusions. Below please find our point-to-point response to the comments.\nReviewer Comment\n(1) In the derivation of Eq. (10), the change of latent heat flux (LH) is used directly,\nwhile the change of sensible heat flux is written as a function of the change of ( ).\nIn contrast, in the popular Penman-Monteith equation derivation, the change 𝑇 o𝑠f − LH 𝑇𝑎 is\nalso written as a function of the change of . please add a few sentences to justify the\ndecision (of using the change of LH directl\\𝑇\ny𝑎 in Eq. (10) without explicitly considering\nits dependence on the change of ).\nReply 𝑇𝑎\ndoes affect latent heat, but in water-restricted areas such as arid and semi-arid\nregio\\𝑇\nn𝑎s, the change in LH is more determined by soil moisture, so LH is not written as\na function of the change of .\nWe have added explana\\𝑇\nt𝑎hion in the revised manuscript according to the reviewer's\nsuggestion.\nPage 23 Lines 388-390: Because in water-restricted areas such as arid and semi-arid\nregions, the change of latent heat flux is more determined by soil moisture, so latent\nheat flux is not written as a function of the change of .\n𝑇𝑎\nReviewer Comment\n(2) In the last term of Eq. (10) and in lines 404, 407, and 409, replace “\n” by for simplicity, as is clearly defined in Eq. (11). 𝜌𝐶𝑑⁄𝑟𝑎 +\n3\n4𝜀𝑆𝜎𝑇𝑠 𝑓𝑠 𝑓𝑠\nReply\nThanks, we have used the abbreviation of in relevant equations according to\nthe reviewer's suggestion (Page 24 Lines 406, 40\n𝑓\n9𝑠, 411).\n(3) The language needs to be significantly improved. Just taking Abstract as an example:\n“….warming globle …. (not include …of SA on climate change ….and make a\nnonlinear …”, should probably be: “….warms globle …. (excluding …of SA to\nclimate change ….and play a nonlinear …”\nReply\nThanks, we have checked and modified the grammar in the revised manuscript.\nSuch as:\nPages 2 Lines 20: “predicts” to “projects”\nPages 2 Lines 21: “warming” to “warms”\nPages 2 Lines 25: “not include” to “excluding”\nPages 2 Lines 27: “on” to “to”\nPages 2 Lines 28: “make a non-linear warming role” to “play a non-linear warming\ncomponent role”\nPages 2 Lines 32: “have” to “has”\nPages 2 Lines 33: “the rate of warming varies” to “the rates of warming vary”\nPages 2 Lines 34: “Previous research has” to “Previous researches have”\nPages 2 Lines 36: “the fluxes of mass” to “mass fluxes”\nPages 3 Lines 49: added “— to isolate the climatic impact of SA”\n……\nReviewer #2:\nReviewer Comment\nOverall, the authors did a good job of addressing my concerns. One area of minor\nconcern is that the authors did a good job of addressing my concern related to\n“uncertainty of LA coupling in models” in the response document but the amount of\ndiscussion that made it into the paper was minimal (Lines 263-267). Specifically, I think\nthe discussion would be improved if the authors added one or two more lines to this\ndiscussion arguing why they think the results are still relevant even with these\nuncertainties (I think they are still relevant and useful). The authors can get these\nadditional lines by summarizing the arguments made in the response document.\nReply\nWe thank the reviewer for the positive comments and recognition of the\nconclusions. We have modified and added relevant discussion about uncertainties in the\nrevised manuscript.\nPage 17 Lines 263-270: Finally, the results may have some projection uncertainty\nconsidering the limitations of the parameterization in SA (Dirmeyer, 2013; Roundy et\nal., 2013; Santanello et al., 2015) and scenario uncertainty due to the lack of knowledge\nof future radiative forcing (Lehner et al., 2020). Nevertheless, the models we used in\nthis research have high reliability in the historical simulation of soil moisture (Qiao et\nal., 2022), and we reduced the uncertainty by multi-model mean. Meanwhile, different\nsingle models have similar results for the acceleration in SA-driven warming in the\nfuture projection. So, the conclusion that SA amplifies greenhouse gas-driven global\nwarming is relatively reliable and robust.\nReviewer #3:\nReviewer Comment\nDear Liang Qiao et al., thanks for the very good revision of your manuscript. You\nanswered all my comments satisfyingly. So I recommend its publication. The following\nminor corrections are required: It needs somebody checking the spelling and language,\nsometimes verbs (e.g. line 46, line 70) or letters are missing. Fig. 3c has overlapping x-\naxes. I am looking forward to see the published manuscript.\nReply\nWe thank the reviewer for the positive comments and recognition of the\nconclusions. We adjusted the x-axes in Fig. 3c, and we have checked and modified the\nspelling and grammar in the revised manuscript. Such as:\nPages 2 Lines 20: “predicts” to “projects”\nPages 2 Lines 21: “warming” to “warms”\nPages 2 Lines 25: “not include” to “excluding”\nPages 2 Lines 27: “on” to “to”\nPages 2 Lines 28: “make a non-linear warming role” to “play a non-linear warming\ncomponent role”\nPages 2 Lines 32: “have” to “has”\nPages 2 Lines 33: “the rate of warming varies” to “the rates of warming vary”\nPages 2 Lines 34: “Previous research has” to “Previous researches have”\nPages 2 Lines 36: “the fluxes of mass” to “mass fluxes”\nPages 3 Lines 49: added “— to isolate the climatic impact of SA”\nPages 3 Lines 51: deleted “each”\nPages 3 Lines 52: “For” to “in”\nPages 3 Lines 53: “in” to “from”\nPages 3 Lines 54: deleted “which”, “the annual mean cycle”\nPages 3 Lines 54: added “which is”\nPages 3 Lines 58: “used the three climatology periods during” to “consider three time\nhorizon periods”\nPages 4 Lines 68: deleted “the”\nPages 4 Lines 73: “will” to “will be”\n……"}]

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