Infrared Radiative Effects of Increasing CO2 and CH4 on the Atmosphere in Antarctica Compared to the Arctic

We simulated the seasonal temperature evolution in the atmosphere of Antarctica and the Arctic focusing on infrared processes. Contributions by other processes were parametrized and kept fixed throughout the simulations. The model was run for current CO2 and CH4 and for doubled concentrations. For doubling CH4 the warming in Antarctica is restricted to the lowest few hundred meters above the surface while in the Arctic we find a warming in the whole troposphere. We find that the amount of water is the main driver for the differences between both polar regions. When increasing both, CO2 and CH4 from pre‐industrial values to current concentrations, and averaged over the whole troposphere, we find a warming of 0.42 K for the Arctic and a slight cooling of 0.01 K for Antarctica. Our results contribute to the understanding of the lack of warming seen in Antarctica throughout the last decades.

• We simulate the temperature development in both polar regions in the infrared and find that doubling CO 2 and CH 4 lead to opposing forcings • The different amount of water vapor shows to be responsible for the differences in warming/cooling in both polar regions • In Antarctica doubling CH 4 leads to a cooling of almost the whole troposphere, a future increase in H 2 O could invert this

Supporting Information:
Supporting Information may be found in the online version of this article. 10.1029/2023GL105600 2 of 9 effect normally increases for an increase in greenhouse gases, we could show in our previous study that for the high and cold elevated areas of central Antarctica a negative greenhouse effect is observed (Schmithüsen et al., 2015).A negative greenhouse effect means, the atmosphere emits more energy to space than it receives from the surface, leading to net-cooling of the atmospheric column.In the meantime, our observations have been confirmed by others (Chen et al., 2023;Freese & Cronin, 2021;Sejas et al., 2018;Smith et al., 2018).In Schmithüsen et al. (2015) we concentrated on CO 2 as originator for the negative greenhouse effect, later Sejas et al. (2018) pointed out that the effect of H 2 O actually exceeds that of CO 2 in this respect.The occurrence of a negative greenhouse effect depends on the temperature profile and the distribution of the constituent in question.
For instance, for CO 2 the relation between stratospheric and surface temperature is of relevance, but for H 2 O the presence and intensity of a surface inversion determines the sign of the greenhouse effect.In fact, most relevant greenhouse gases can cause a negative greenhouse effect: when a strongly emitting atmospheric layer that can radiate into space is warmer than the surface the greenhouse effect can become negative.The potential of other greenhouse gases (namely O 3 , CH 4 , N 2 O) in this respect can be seen in Schmithüsen (2015, Figure 2.1).
Our single column model used in our first study did not allow to investigate where in the atmosphere the cooling takes place and whether the negative greenhouse effect leads to a cooling of the surface in Antarctica.We have now extended our model to simulate the radiation and temperature development for all atmospheric layers and at the surface as a function of the atmospheric composition.The atmospheric temperature is determined by many factors, including the radiation in the ultraviolet/visible (UV/Vis) and in the infrared spectral region, the effects of clouds, advection, convection, and feedback processes.Since the warming/cooling by greenhouse gases occurs mainly in the infrared spectral region we restricted our studies to that region.All other processes determining the temperature development, mentioned above, were included as constant averages we name ΔT res , calculated as described below.This allowed us to perform process studies to investigate only the first-order impact of specific greenhouse gas concentrations on the temperature development.In order to avoid uncertainties of broad-band radiation parametrizations our simulations were done using a high resolution model (0.01 cm −1 , i.e., line-by-line), based on Notholt et al. (2006).
In a first step we simulated the annual temperature cycle in Antarctica and the Arctic for current greenhouse gas concentrations (CO 2 : 400 ppmv denoted "1xCO 2 "; CH 4 : 1.85 ppmv in the troposphere, decreasing above denoted "1xCH 4 "; H 2 O: based on ERA5 denoted "1xH 2 O") and compared the results to temperature profiles deduced from ERA-5 reanalysis data.In the second step we run the simulations with 2xCO 2 or 2xCH 4 .The difference between the corresponding simulations gives us the induced warming/cooling in each atmospheric layer and the surface throughout the year.In order to investigate the role of H 2 O in detail we also run the simulations with 2xCO 2 and 2xCH 4 for Antarctica with strongly increased water vapor (5xH 2 O, comparable to the Arctic) and with strongly decreased water vapor (0.2xH 2 O) for the Arctic, comparable to Antarctica.

Calculation of the Temperature Development for Current CO 2 and CH 4 Mixing Ratios
Our model is based on our line-by-line code described in Notholt et al. (2006).It has been modified to calculate the radiation and temperature development in high resolution (0.01 cm −1 ) in each of the 90 atmospheric layers in the spectral region 50 to 2,000 cm −1 (5-200 μm).
From monthly averaged ECMWF reanalysis data (ERA5) at 90°N or 90°S (Muñoz Sabater, 2019) we derived 12 temperature profiles as climatological average over 30 years ; above ∼60 km the profiles are complemented by the US-standard atmosphere.The volume mixing ratios of all trace gases other than CO 2 , CH 4 , H 2 O and O 3 are based on long-term averages from balloon soundings and satellite data originating from the Upper Atmospheric Research Satellite Correlative Measurements Program (UARS-CMP) (Peterson & Margitan, 1995).The data from the 12 monthly averaged temperature, H 2 O and O 3 profiles were spline (piecewise cubic polynomial fit) interpolated to each individual time of the simulation.The method based on monthly averages was chosen in order to simulate a smooth annual cycle that still features the predominant seasonal temperature evolution throughout the year.For consecutive years of the simulation the same 12 profiles for temperature, H 2 O and O 3 were used.Spectral data were taken from the HITRAN2008 (Rothman et al., 2009) and HITRAN2012 (Rothman et al., 2013) molecular spectroscopic databases and the ATM2019 linelist (https://mark4sun.jpl.nasa.gov/specdata.html).The line broadening was calculated using a Voigt profile (Humlicek, 1982).The H 2 O and CO 2 continuum was added, using the MT_CKD model (Mlawer et al., 2012).
Our program calculates the infrared radiation.In order to get the total atmospheric energy budget, contributions by for example, solar UV/Vis radiation, advection, clouds, convection, and feedback processes, need to be considered.We pre-calculate the sum of these contributions as difference between our long-wave simulation and a climatological temperature evolution based on ERA5 and name them temperature residuals ΔT res (z, t) as described below.
Using a starting temperature profile our model gives the upward and downward radiation in every altitude layer.
The radiation together with the heat capacity of each layer gives for each altitude z and time step Δt the long-wave change in temperature ΔT LW (z, t).The difference between the real temperature change ΔT(z, t), from the spline interpolated ERA5 data and the simulated temperature change ΔT LW (z, t) can be assigned to contributions by all other processes mentioned above, ΔT res (z, t).
The residuals ΔT res (z, t) have been calculated for all layers in the atmosphere for each month (12 profiles) and are prescribed input to the model experiments.As the heat capacity of the surface (z = z 0 ) cannot be calculated directly a substitute "surface sensitivity" is used (see Supporting Information S1).
The temperature development after a time step Δt for the new temperature T(t + Δt) can now be calculated as Using a starting profile (1 January in Antarctica; 1 July in the Arctic), the temperature change from the infrared simulation ΔT LW (z, t) is added to the previous temperature T(z, t), corrected with ΔT res (z, t), spline interpolated from the prescribed monthly ΔT res (z, t) profiles for the specific time of the year.The model runs were done for a time step Δt of 3 hrs in Antarctica and 1 hr for the Arctic, for longer time steps the calculated temperatures started to oscillate.Figure S1 in Supporting Information S1 gives an example for ΔT res (z, t), ΔT LW (z, t) and ΔT(z, t).
The difference between the ERA5-based input profiles and our simulated temperatures is within a range of ±0.1 to ±0.2 K or better (Figure S2 in Supporting Information S1).The variability is due to the use of monthly calculated ΔT res (z, Δt) and the numerical effects of the interpolation.Since we are interested in the seasonal temperature development the differences for the short term variability is not of importance.When averaging for longer periods of a few months the ERA5-data and our simulated temperatures agree within much less than ±0.05 K.This means, our simulated annual temperature cycle agrees well with the ERA5 data.We would like to point out that only one starting temperature profile has been used to simulate the temperature development for the whole year or longer, while the model is nudged by the pre-calculated temperature residuals.

Calculation of Warming/Cooling for Doubling CO 2 and CH 4
In the first step the simulations were performed for current concentrations of CO 2 and CH 4 , using the prescribed ΔT res .In the next step the simulations were repeated for 2xCO 2 or 2xCH 4 .We used the same prescribed residuals ΔT res from above, calculated for 1xCO 2 and 1xCH 4 .This allowed us to identify the contribution caused by the change in the infrared radiation separated from all other processes.In order to allow the simulations to reach equilibrium for the enhanced greenhouse gas concentrations we calculated the temperature development for a period of 3 years.We consider equilibrium to be reached once the year-to-year variation of the temperature is constantly below 0.01 K.The results shown in the next paragraphs are for year three.
Since the main infrared absorbers are H 2 O, CO 2 , CH 4 , N 2 O, and O 3 we used only these five trace gases for our simulations in order to speed up the calculations.Test runs with all 52 infrared active trace gases show an excellent agreement to within 0.01 K (Figure S3 in Supporting Information S1).
We have also applied our program to the US-Standard atmosphere (Figure S4 in Supporting Information S1).
For 2xCO 2 we find a temperature increase of 2.2 K at 2 m altitude, in good agreement with 1.95 K that can be concluded from the studies by Gillett et al. (2013) using global climate models.For these runs the water vapor feedback was considered, which means, the relative humidity was kept constant during the temperature evolution.

Results
Figures 1a and 1c show the resulting temperature differences between the simulations with 2xCO 2 and 1xCO 2 .
Figures 1b and 1d give the results for 2xCH 4 -1xCH 4 .Results are shown for absolute altitudes up to 12 km, Figure 10.1029/2023GL105600 4 of 9 S5 in Supporting Information S1 gives the corresponding results up to 90 km.When doubling CO 2 the troposphere in Antarctica shows a warming from the surface at 2.8 km altitude up to 5.5 km on average and a cooling above (Figure 1a).In the Arctic we find a warming from the surface at 0 km altitude essentially up to tropopause (8.4 km on average) and cooling above (Figure 1b).When doubling CH 4 the warming in Antarctica is restricted to the first 100-400 m above the surface at 2.8 km (the first 10-20 layers in the model, Figure 1c).Above, the atmosphere cools, except a slight warming at 8 km in January and February.For the Arctic the warming by CH 4 is found up to 10 km on average, with the exception of a slight cooling around 3-4 km around February (Figure 1d).Note that the model setup does not allow for changes in vertical or horizontal airmass mixing, or non-radiative feedback processes.Hence, any temperature signals shown are solely due to the forcing from the change in CO 2 or CH 4 .In reality, vertical and horizontal mixing would smooth the temperature signals.
As shown by Dufresne et al. (2020) the negative greenhouse effect of CO 2 depends on the spectral overlap with other greenhouse gases, particularly H 2 O.This effect can be seen when reducing the H 2 O concentration of the Arctic profiles in our simulations to 20%, comparable to Antarctica, or increasing the water content in Antarctica by a factor of 5, comparable to the Arctic conditions (Figure S6 in Supporting Information S1 shows typical H 2 O profiles).Results from these simulations are shown in Figure 2. We would like to point out that a 5× higher water amount is probably unrealistic, the water concentration could then be higher than the saturation pressure of H 2 O, but in our case it is a useful sensitivity study.
When reducing H 2 O in the Arctic to 20% we find a comparable temperature pattern forcing for 2xCH 4 as for Antarctica (compare Figure 2d with Figure 1c).The warming then remains restricted to the lowest troposphere, and a cooling is observed above.A corresponding effect is visible when increasing the water content in Antarctica by a factor of 5, leading to a much stronger warming for 2xCH 4 , comparable to the Arctic (compare Figure 2c with Figure 1d), with a warming nearly throughout the whole troposphere.Similarly, for CO 2 we see less warming of the troposphere when reducing water in the Arctic to 20% (compare Figure 2b with Figure 1b) and increased warming for 5 times H 2 O in Antarctica (Figure 2a compare to Figure 1a).Interestingly, for 5 times H 2 O Antarctica shows a slight cooling for 2xCH 4 above the surface in winter (June to August) which coincides with the strongest surface inversions in the respective model setups.

Discussion
In general, when increasing the concentration of a uniformly distributed greenhouse gas, the lower atmosphere gets warmer, above a cooling results.The altitude where a warming switches to a cooling we name z w/c .The warming in the lower atmosphere results from the increased insulating effect of greenhouse gases and the increased downwards radiation from the atmosphere above (Dufresne et al., 2020).The strong absorption by for example, tropospheric H 2 O masks the emission by the surface.The top-of-atmosphere radiative loss originates from within the atmosphere, the effective emission height is determined by the amount of H 2 O.The cooling above z w/c results from the increased upward radiative loss to space.
Figure 3a shows the longwave downwards and upwards radiation for current mixing ratios of CO 2 and CH 4 (1xCO 2 and 1xCH 4 ) in Antarctica.The dotted lines give the radiation when increasing the amount of water by a factor of 5.For enhanced H 2 O the longwave downwards radiation increases within the troposphere, shifting z w/c Figure 3b shows the difference in the longwave downwards radiation for 2xCO 2 -1xCO 2 and 2xCH 4 -1xCH 4 .Note the different scaling for both trace gases.While CO 2 has a nearly constant mixing ratio throughout the whole atmosphere, the mixing ratio of CH 4 decreases with altitude.This is reflected in the radiation difference in the stratosphere which increases with altitude for 2xCO 2 -1xCO 2 while it decreases for 2xCH 4 -1xCH 4 .This increase in the downwards radiation above the tropopause leads to the well-known warming of the troposphere.
Since the stratospheric mixing ratio profiles of CO 2 and CH 4 qualitatively differ, the resulting warming of the troposphere for increased downwards radiation of CO 2 and CH 4 differ.The dotted lines in Figure 3b give the results for 5-times H 2 O.For the increased H 2 O the radiation difference decreases, caused by the masking effect of H 2 O.
Tropospheric heating caused by increasing greenhouse gases is directly coupled to increasing stratospheric downwards radiation.Sensitivity studies by doubling the mixing ratios of CH 4 or CO 2 only in the upper troposphere and stratosphere confirm the role of the downward radiation from the upper troposphere/stratosphere (Figure S7 in Supporting Information S1).If a greenhouse gas is only increasing in the troposphere, the level z w/c lowers significantly (Figures S7a and S7b in Supporting Information S1).Since for CH 4 a doubling influences the troposphere more than the stratosphere due to its decrease in mixing ratio with altitude, z w/c lowers accordingly.We conclude that the difference in the mixing ratio profiles is mainly responsible for the difference in z w/c between CO 2 compared to CH 4 .
Our studies confirm previous results (Chen et al., 2023;Dufresne et al., 2020;Sejas et al., 2018) that the amount of water is the dominant factor for the different temperature forcings when comparing Arctic and Antarctic.We also investigated how CH 4 behaves compared to CO 2 .The altitude z w/c , where the warming switches to a cooling differs, depending on the mixing ratio profiles of both trace gases.Our simulations with 5 times water for Antarctica and 0.2 times water for the Arctic further demonstrate that the specific temperature profiles in Antarctica, with sometimes higher temperatures in the stratosphere compared to the surface, are only of minor importance.
Comparing the simulated temperatures of current CO 2 and CH 4 concentrations (400 ppm CO 2 and 1.85 ppm CH 4 ) to pre-industrial values (278 ppm CO 2 and 0.75 ppm CH 4 ) results in an overall slight warming only in the first 1-2 km above the surface in Antarctica (Figure 4a).While the overall warming in Antarctica is limited to up to 4-5 km, the warming in the Arctic takes place up to 8-9 km (Figure 4b).
We have calculated the pressure weighted average of the simulated temperature changes up to 7,000 m for doubling CO 2 and CH 4 (Table 1).The overall temperature increase up to 7,000 m in the Arctic for doubling CO 2 10.1029/2023GL105600 7 of 9 with 0.81 K is much higher than what we get for Antarctica (0.16 K).For a doubling of CH 4 , in Antarctica a slight cooling of 0.06 K results compared to a warming of 0.07 K for the Arctic, when averaging up to 7,000 m.When increasing both, CO 2 and CH 4 from pre-industrial values to the current concentrations results in a warming of 0.42 K for the Arctic and 0.02 K for Antarctica.

Conclusions
Our studies yield the instantaneous forcing when doubling CO 2 or CH 4 .Changes in vertical or horizontal mixing following a warming or cooling are not considered.In reality the temperature signals would smooth out.In our simulations for Antarctica we find a cooling for doubling CH 4 nearly throughout the whole troposphere, but not at the surface or in the first 100-500 m above the surface.For doubling CO 2 the Antarctic atmosphere shows a warming up to 5.5 km and cooling above.Mixing processes might lead to a slight cooling at the surface in Antarctica.Overall, other feedback processes are important for the observed temperature increases in both polar regions.While we calculated a warming of 0.95 K since pre-industrial CO 2 and CH 4 for the Arctic, the observed increase since 1960 is 2-3 K (Wendisch et al., 2023).The difference results from the various feedback processes, most importantly the melt of sea ice and the lapse rate feedback (Pithan & Mauritsen, 2014).
Our studies demonstrate that the Antarctic atmosphere is much less prone to direct radiative heating compared to the Arctic.This study could be one piece in the puzzle when understanding the lack of warming in Antarctica throughout the last decades compared to the Arctic.
Our findings are in line with Sejas et al. (2018), who concluded that for the Arctic a colder climate in the past would imply drier conditions, with a potential for a negative greenhouse effect caused by surface inversions.Our results confirm this, and show that a colder and drier Arctic could have led to a cooling by an increase in CH 4 , maintaining the cold Arctic climate conditions.In this way, our results suggest that for a sustained warming, and accompanied increase of H 2 O, the cooling by CH 4 in the Antarctic troposphere might turn into a warming, corresponding to a tipping point in the Antarctic atmosphere.This might lead to an increase in the temperature in Antarctica.

Figure 1 .
Figure 1.Temperature forcing (K) as a function of altitude throughout the year calculated for 2xCO 2 -1xCO 2 (a and c) and 2xCH 4 -1xCH 4 (b and d) for Antarctica (a and c) and the Arctic (b and d).In Antarctica the surface is at 2.8 km altitude, in the Arctic at 1 m.

Figure 2 .
Figure 2. Test simulations for Antarctica (a) and (c) and the Arctic (b) and (d).Shown is ΔT between two runs, simulated for 2xCO 2 -1xCO 2 , (a) and (b) with 5 times H 2 O for Antarctica (a) and 20% water in the Arctic (b).Panels (c) and (d) give the same test runs for 2xCH 4 -1xCH 4 .

Figure 3 .
Figure 3. (a) LWD and LWU for current CO 2 and CH 4 mixing ratios over Antarctica.The dotted lines give the results for 5 times H 2 O.(b) Difference in LWD for 2xCO 2 -2xCO 2 2 and 2xCH 4 -1xCH 4 for Antarctica.The dotted lines give the results for 5 times H 2 O.Note the different scaling for CO 2 and CH 4 .

Figure 4 .
Figure 4. Temperature forcing as a function of altitude throughout the year calculated for the comparison of current greenhouse gas concentrations (400 ppm CO 2 and 1.85 ppm CH 4 ) versus pre-industrial values (278 ppm CO 2 and 0.75 ppm CH 4 ) for Antarctica (a) and the Arctic (b).In Antarctica the surface is at 2.8 km altitude, in the Arctic at 1 m.

Table 1
Temperature Change (K) for 2xCO 2 -1xCO 2 , 2xCH 4 -1xCH 4 , and Current CO 2 and CH 4 Pre-Industrial Values, Averaged for the Atmosphere From the Surface up to 7 km Altitude and Given at 2 m Altitude