Quantifying Climate Feedbacks in the Middle Atmosphere Using WACCM” by Maartje Sanne Kuilman Et Al

Interactive comment on “Quantifying climate feedbacks in the middle atmosphere using WACCM” by Maartje Sanne Kuilman et al.

Anonymous Referee #2

Received and published: 1 April 2020

1 General Comments

The paper presents another application of CFRAM, a one-dimensional (mostly) radiative climate model for offline feedback analysis, in a more than a decade long series, now using output of the high top chemical climate model WACCM. In other studies it was used for example for a low top GCM (Taylor et al., 2013) or a CCM up to thermosphere (Zhu et al., 2016). When it was applied to global radiative models more than a decade ago, data transfer was straight forward but for use with complex 3D models it is essential to provide information on averaging of model output. I suppose CFRAM was applied for zonal averages at every meridional grid point and for every month of the 40 year time slices, am I right from hints only in the references? There are also a lot of other options. This has to be documented since this can contribute significantly to errors (see for example TEM-analysis mentioned by authors, line 652; Zhu et al., 2016).

First of all, the authors would like to thank the reviewer for the helpful comments.

The calculations are done at every grid point of the WACCM model after temporal means of the data of the perturbation run and the control run are taken. This means the data that go into the CFRAM calculations have the dimensions of latitude, longitude and height. A zonal mean has been done only after the calculations. This information has now been added to section 2.3:

We take the time mean of the WACCM data and perform the calculations for each grid point of the WACCM data. This means that in the end, we will have the temperature changes at each latitude, longitude and height.

The shown results are not new, they almost resemble what was found with chemical radiative convective models more than 30 years ago (e.g. Brühl and Crutzen, 1988). Concerning upper stratospheric ozone chemistry, the authors should for example read Cariolle (1983), what is written in the manuscript is a mess.

Thanks the references. The section on the changes in the ozone concentration due to the changed CO2 concentration has now been rewritten and significantly shortened, as this is not new and not the main point of our work: we are interested in the temperature response as a result of the changes in the O3 concentration in WACCM.

In general, the paper needs much more clear definitions what has been done.

It has been made clearer what has been done. Section 2.3 and 2.4 contain more information about on how the calculations are done. 2 Specific comments

The presented averages of temperature change from 12 to 80 km altitude in the abstract and also key points are confusing and not physically meaningful because several different regimes are involved. Here it would be more useful to focus on the upper stratosphere. Is the averaging mass weighted or not?

The authors agree it is better to show the temperature changes for the specific regions in the middle atmosphere. When calculating the temperature changes, we do take into account the mass of the layers as can be seen in equation (7). When doing the averaging over the different heights and latitudes, we take an ordinary average and do not account for this.

More than a decade ago is not recently (paragraph beginning with line 136). What is the spatially limited domain, please define. Provide references earlier. Merge with next paragraph and rearrange.

This has been done now.

The climate feedback-response analysis method (CFRAM) is an alternative method which takes into account that the climate change is not only determined by the energy balance at the top of the atmosphere, but is also influenced by the energy flow within the Earth’s system itself (Cai and Lu, 2009, Lu and Cai, 2009). The method is based on the energy balance in an atmosphere-surface column. It solves the linearized infrared radiation transfer model for the individual energy flux perturbations. This makes it possible to calculate the partial temperature changes due to an external forcing and these internal feedbacks in the atmosphere. It has the unique feature of additivity, such that these partial temperature changes are linearly addable.

The paragraph beginning with line 157 is confusing concerning the statements on ozone here, skip that or define clearly what are the ozone changes due to, including the altitude dependence.

Right, this is how it is stated in their paper but we understand it misses more information here. As we don’t want to do too much in detail of their study, this part has been removed.

In section 2.2 the assumptions for the other radiatively and chemically active gases should be provided. Is the double CO2 scenario with preindustrial conditions for N2O, CFCs, CH4 and NOx in the troposphere? This is also critical for the SST.

This information has been added to section 2.2:

Other radiatively and chemically active gases, such as ozone, will change because of the changes in the CO2-concentration, due to WACCM’s chemical model as well.

As we used a fixed SST from the CSEM model as forcing. The atmosphere component of CESM is the same as WACCM, but does not include stratospheric chemistry. So you are right that this is an element that we are not including in our analysis.

Section 2.3 should include how WACCM output is implemented into CFRAM, i.e. the averaging methods for space and time.

This information has been added to section 2.3:

Split Fig. 2 and Fig. 4 into more vertical sections (e.g. lower stratosphere, upper stratosphere, mesosphere). What kind of averaging?

This has now been done: see Figure on the next page. The averaging procedure has also been explained in the text:

Figure 2 shows the average change in global mean temperature for the lower stratosphere, the upper stratosphere and the mesosphere for the experiment with the changed CO2-concentration and changed SSTs. To calculate the lower stratosphere temperature changes, we take the average value of the temperature change from the tropopause – the pressure level of which is an output of WACCM – until about 24 hPa for each latitude.

The tropopause is not exactly at the same pressure level, we always take the one for the perturbation experiment which is a bit higher at some latitudes, to make sure that we don’t use values from the troposphere. We add the values for each latitude up and take the average. This average is not mass weighted. The temperature changes in the upper stratosphere and in the mesosphere are calculated in the same way, but then for the altitudes 24 hPa-1 hPa and 1 hPa-0.01 hPa respectively.

Figure 2 shows the radiative feedbacks due to ozone, water vapour, clouds, albedo and the dynamical feedback, as well as the small contribution due to the Non-LTE processes, as calculated by CFRAM. The ‘total’-column shows the temperature changes in WACCM, while the column ‘error’ shows the difference between temperature change in WACCM and the sum of the calculated temperature responses in CFRAM. In sections 3.3-3.6, we will discuss the different feedbacks separately in more detail, at this point we give an overview of the general effects and relative importance of the different feedback processes.

Figure 2 shows that the temperature change in the lower stratosphere due to the direct forcing of CO2 is around 3 K. We also observe that there is a cooling of about 1 K due to ozone feedback in the tropical region while there is a slight warming taking place in the summer hemispheres in both January and July. We also see that the temperature change in the lower stratosphere is influenced by the water vapour feedback and to a lesser degree by the cloud and albedo feedback.

In the upper stratosphere, the cooling due to the direct forcing of CO2 is with about 9 degrees considerably stronger than in the lower stratosphere. The water vapour, cloud and albedo feedback play no role in the upper stratosphere and mesosphere. The ozone feedback results in the positive partial temperature changes, of about 2 K. This means that the ozone feedback yields a radiative feedback that mitigates the cooling, which is due to the direct forcing of CO2. This has been suggested in earlier studies, such as Jonsson et al., 2004. With CFRAM, it is possible to quantify this effect and to compare it with the effects of other feedbacks in the middle atmosphere.

The picture in the mesosphere is similar. The main difference is that the temperature changes are larger, note the difference of the range for the temperature change between Fig. 2c, d and Fig. 2e,f.

The temperature response due to dynamical feedbacks is small in global average. This can be understood as waves generally do not generate momentum and heat, but redistribute these instead (Zhu et al., 2016). However, the local responses to dynamical changes in the high latitudes are large, as we will see in section 3.3. There are some small temperature responses due to non-LTE effects as well.

Figure 2: The mean temperature responses to the changes in CO2 and various feedback processes in the lower stratosphere from the tropopause height until 24 hPa (a,b), upper stratosphere from 24-1 hPa (c, d) and in the mesosphere from 1- 0.01 hPa (e,f) in July (a, c, e) and January (b, d, f) in the polar regions (90°S-70°S and 70°N-90°N), the tropics (20°S-20°N) and the global mean, for experiment with double CO2 and changed SSTs.

Figure 4 has also been changed:

Figure 4: The mean temperature responses to the changes in CO2 and various feedback processes in July (a,c) and January (b,d) in the upper stratosphere between 24 and 1 hPa, for polar regions (90°S-70°S and 70°N-90°N), the tropics (20°S-20°N) and the global mean for the experiment with double CO2 (a,b) and changed SSTs (c,d) separately.

Figure 4 shows temperature responses in the upper stratosphere for the experiment with double CO2 (a,b) and changed SSTs (c,d) separately. These temperature changes were calculated as they were for Fig. 2. Again also, the ‘total’-column shows the temperature changes as found by WACCM, the columns CO2, O3, H2O, cloud, albedo, dynamics, Non-LTE shows the temperature responses as calculated by CFRAM. Error shows the difference between temperature change in WACCM and the sum of the calculated temperature responses in CFRAM.

We learn from this figure that the effects of the changed SSTs on the middle atmosphere are relatively small as compared to the effects of changing the CO2. The changes in SSTs are responsible for large temperature changes as a result of the dynamical feedbacks especially in the winter hemispheres. A similar figure for the lower stratosphere (not shown) shows that the the temperature response to the water vapour feedback is, however, almost solely due to changes in the SSTs.

Earlier, we discussed that the sum of the two separate temperature changes in the experiment with double CO2 and changed SSTs is approximately equal to the changes observed in the combined simulation. We find that the same is true for the temperature responses to the different feedback processes.

The paragraph beginning with line 564 is confusing. I suppose you mean ozone changes induced by CO2 cooling. Ozone matters also in the infrared window.

This was indeed what was meant, the paragraph has now been rewritten.

In addition, the vertical profile of the temperature responses to the direct forcing of CO2 and the feedbacks is shown in Figure 3. Here, one can see that the increase in CO2 leads to a cooling over almost the whole middle atmosphere: an effect that increases with height. We also observe that in the summer upper mesosphere regions, the increased CO2-concentration leads to a warming. The changes in ozone concentration in response to the doubling of CO2 leads to warming almost everywhere in the atmosphere. In some places, this warming exceeds 5 K. In the polar winter the effect of ozone is small due to lack of sunlight.

Shorten the paragraph beginning with line 628.

This paragraph has now been shortened.

Changing the SSTs does not lead to a change in CO2-concentration, therefore the temperature response to changes in CO2 is not present for the run with only changed SST (Figures not shown).

You may improve the paragraph beginning with line 645 by the use of the textbook by Holton.

This section has been rewritten: As discussed in the introduction, in the middle atmosphere there is a wave driven circulation which drives the temperatures away from radiative equilibrium. Large departures from this radiative equilibrium state are seen in the mesosphere and in the polar winter stratosphere. In the mesosphere, there is a zonal forcing which yields a summer to winter transport. In the polar winter stratosphere, there is a strong forcing that consists of rising motion in the tropics, poleward flow in the stratosphere and sinking motion in the middle and high latitudes. This circulation is referred to as the Brewer-Dobson circulation (Butchart et al. 2010).

Don’t forget to mention convection around line 688.

This has now been mentioned.

The warmer sea surface temperatures enhance the activity of transient planetary waves and orographic gravity waves in the lower and middle stratosphere, for example via the amplification of deep convection (Deckert and Damaris, 2008). The changed SSTs also leads to enhanced dissipation of planetary waves, as well as orographic and non-orographic waves in the upper stratosphere.

Does Fig. 6 show the average of the 40yr time slice?

Yes, that is right. This is now mentioned explicitly in the text:

The differences in the meridional component of the residual circulation (�̅∗) between the different simulations are shown in Fig. 6. These data are averaged over the 40 years of data.

Section 3.4 has to be rearranged and improved, the key processes are missing. The reaction O+O3, the sink reaction in the Chapman chemistry, is strongly temperature dependent (see Brühl und Crutzen, 1988; Cariolle, 1983; or JPL). NO and Cl catalytic cycles matter mostly in the upper and mid stratosphere, in the mesosphere hydrogen species (e.g. OH) are most important. Check if in all calculations only CH3Cl acts as chlorine source (pre-industrial!).

Thanks for this comment and the helpful references. The section on the changes in the ozone concentration due to the changed CO2 concentration has now been rewritten and significantly shortened, as this is not new and not the main point of our work: we are interested in the temperature response as a result of the changes in the O3 concentration in WACCM.

Ozone plays a major role in the chemical and radiative budget of the middle atmosphere. The ozone distribution in the mesosphere is maintained by a balance between transport processes and various catalytic cycles involving nitrogen oxides, HOx and Clx radicals. In the upper stratosphere, NOx and Clx cycles dominate (Cariolle, 1982), while OH is of utmost importance in the mesosphere (Jonsson et al., 2004).

In this paper, we are interested in the changes in ozone concentration induced by the increased CO2 concentration and/or the changes in SST in WACCM. In the real world, the ozone concentration is not only affected by the changing CO2 concentration, but also by CFC and NOx emissions.

Fig. 8 shows the percentage changes in O3-concentration when the CO2- concentration and/or the SSTs change. An increase in CO2, leads to an increase of ozone in most of the middle atmosphere. However, in the tropical lower stratosphere, the summer polar mesosphere, the winter and equatorial mesosphere, a decrease in ozone is seen. Fig. 8c and f show that changing the SSTs also has a significant impact on the ozone concentration. A complete account of the ozone changes is out of the scope of this paper, but the main processes responsible for ozone changes will be discussed.

Figure 8: The percentage changes in ozone concentration in July (top) and January (bottom) for (a,d) the simulation with high CO2 and SSTs, (b,e) the simulation with high CO2, (c,f) the simulation with high SSTs, all as compared to the pre-industrial control simulation, as found by WACCM. The statistical signifance and tropopause height are indicated as in Fig. 6.

Ozone chemistry is complex, however the ozone increase between 30 - 70 km can be understood primarily as a result of the negative temperature dependence of the reaction O + O2 + M à O3 + M. The fractional contribution of this processes and other loss cycles involving NOx, CLOx and NOx varies with altitude.

At altitudes between 50 and 60 km, the ozone increase is understood by less effective HOX odd oxygen destruction. The increase in O3 between 45 and 50 km can be understood as the reaction rate coefficient of the sink reaction O + O3 à 2O2 decreases. At altitudes lower than 45 km, there is a decrease of NOx abundance, which can explain the increase (Jonsson et al., 2004).

Schmidt et al. (2006) show that the decrease of ozone at the high latitudes in the summer mesosphere, is due to a decrease in atomic oxygen which results from increased upwelling. The decrease in O3 concentration in the polar winter around 0.1 hPa is due to a stronger subsidence of NO and Cl, which are both ozone-destroying constituents. The statement in line 820 is quite controversial, a lot of models lead to different results here; please check.

The caveat that all models don’t consistently reproduce the tropopause temperatures has been added.

It can be seen that changing the SSTs leads to an increase in water vapour almost everywhere in the middle atmosphere (Fig. 10c and f). In WACCM, the increase in SSTs is observed to lead a higher and warmer tropopause, which can explain this increase of water vapour. However, it should be noted that models currently have a limited representation of the processes determining the distribution and variability of lower stratospheric water vapour. Minimum tropopause temperatures aren’t consistently reproduced by climate models (Solomon et al., 2010; Riese et al., 2012). At the same time, observations are not completely clear about whether there is a persistent positive correlation between the SST and the stratospheric water vapour neither (Solomon et al., 2010).

Split the averaging region in line 903ff consistent with the new figures and the revised abstract.

The abstract and the conclusion have been revised.

4. Discussion and conclusions

In this study, we have applied the climate feedback response analysis method to climate sensitivity experiments performed by WACCM. We have examined the middle atmosphere response to CO2 doubling with respect to the pre-industrial state. We also investigated the combined effect of doubling CO2 and subsequent warming SSTs, as well as the effects of separately changing the CO2 and the SSTs.

It was seen before that the sum of the two separate temperature changes in the experiment with only changed CO2 and only changed SSTs is, at first approximation, equal to the changes observed in the combined simulation (see e.g. Fomichev et al. (2007) and Schmidt et al. (2006)). This is also the case for WACCM.

We have found that, even though changing the SSTs yields significant temperature changes over a large part of the middle atmosphere, the effects of the changed SSTs on the middle atmosphere are relatively small as compared to the effects of changing the CO2 without changes in the SSTs.

We find that the temperature change due to the direct forcing of CO2 increases with increasing height in the middle atmosphere. The temperature change in the lower stratosphere due to the direct forcing of CO2 is around 3 K while in the upper stratosphere, the cooling due to the direct forcing of CO2 is with about 9 K considerably stronger than in the lower stratosphere. In the mesosphere, the cooling due to the direct forcing of CO2 is even stronger.

Ozone responds to changes in respond to changes in CO2 and/or SSTs due to changes in chemical reaction rate constants and due to the strength of the up- and downwelling. The temperature changes caused by these changes in ozone concentration generally mitigate the cooling caused by the direct forcing of CO2. However, we have also seen in that in the tropical lower stratosphere and in some regions of the mesosphere, the ozone feedback cools these regions further.

We also have seen that the global mean temperature response due to dynamical feedbacks is small, while the local responses to the changes in dynamics are large. Doubling the CO2 leads to a stronger summer-to-winter-pole flow, which leads to cooling of the summer mesosphere and a warming of the winter mesosphere. Changing the SSTs weakens this effect in the mesosphere, but leads to temperature changes in the stratosphere and lower mesosphere.

The temperature change in the lower stratosphere is influenced by the water vapour feedback and to a lesser degree by the cloud and albedo feedback, while these feedbacks play no role in the upper stratosphere and the mesosphere.

It would also be interesting to investigate the exact mechanisms behind the feedback processes in more detail. Some processes can influence the different feedback processes, such as ozone depleting chemicals influencing the ozone concentration and thereby the temperature response of this feedback. Other studies have shown that a surface albedo change, which is associated with sea ice loss, can influence the middle atmosphere dynamics, which in turn influences the temperature response (Jaiser et al., 2013). The CFRAM cannot unravel the effects of these different processes.

There is also a need for a better understanding of how different feedbacks in the middle atmosphere affect the surface climate. As discussed in the introduction, the exact importance of ozone feedback is currently not clear While this paper focused on the temperature changes in the middle atmosphere, similar analysis can be done to quantify the effects of feedbacks on the surface climate.

In conclusion, we have seen that CFRAM is an efficient method to quantify climate feedbacks in the middle atmosphere, although there is a relatively large error due to the linearization in the model. The CFRAM allows for separating and estimating the temperature responses due an external forcing and various climate feedbacks, such as ozone, water vapour, cloud, albedo and dynamical feedbacks. More research into the exact mechanisms of these feedbacks could help us to understand the temperature response of the middle atmosphere and their effects on the surface and tropospheric climate better.

3 Technical corrections

Please define all formula letters in line 298.

This has now been done:

∆(�⃗ − �⃗) = ∆(�⃗ − �⃗)() ∗ �� ∗ � (5)

In which ∆(�⃗ − �⃗) is the difference in the shortwave radiation (�⃗) and longwave radiation (�)⃗) between the perturbation run and the control run as a flux in Wm-2, -1 while ∆(�⃗ − �⃗)() is this difference as heating rate in Ks in WACCM, with �� = with p in Pa and � = 1004 J �� the specific heat capacity at constant pressure.

In line 546 something is missing or twice. Right, this has been corrected.

Add ’high latitude’ in line 616. This has been added.

Typo in line 688. This has been corrected.

Captions of Fig. 7 to 11 can be shortened (tropopause as in Fig. 6).

Thanks for this comment, this has been implemented now.

4 References

Brühl, C. and P.J. Crutzen: Scenarios of possible changes in atmospheric temperatures and ozone concentrations due to man’s activities, estimated with a one-dimensional coupled photochemical climate model. Climate Dynamics, 2: 173- 203, 1988.

Cariolle, D.: The ozone budget in the stratosphere: results of a one-dimensional photochemical model. Planet. Space Sci., 31: 1033-1052, 1983.

Others see discussion paper. Interactive comment on “Quantifying climate feedbacks in the middle atmosphere using WACCM” by Maartje Sanne Kuilman et al.

Anonymous Referee #3

Received and published: 9 March 2020

I am sorry to say that I am still not happy with this paper in its present form.

First of all, we would like to thank the reviewer for his or her comments. We do point out that almost all of these questions were already addressed in the pre-review for this paper. Large parts of the paper have been rewritten (see also comment on reviewer #2) and we hope that the reviewer is more satisfied with the paper.

The paper is missing a clear message and many statements remain vague.

What we do in this paper is to apply a new method to quantify the temperature responses to different feedback processes that arise in response to changing the CO2-concentration. This is one of the first studies in which it is calculated how much of the temperature change in a specific place in the atmosphere is attributed to which feedback process. The method we applied here can quantify the temperature response, but to provide a complete explanation of all the responses and the exact mechanism behind all the feedback processes is outside the scope of this paper.

For example in the abstract: "feedback processes" (l 51) but which processes?

The “feedback processes” we mean chemical, physical and dynamical processes, which can feedback to the radiation and further change the temperature, in our study these processes arise due to a change in CO2 concentration.

We understand that the formulation in the abstract was maybe not very clear and the abstract has now been rewritten.

The importance of the middle atmosphere for surface and tropospheric climate is increasingly realized. In this study, we aim at a better understanding of climate feedbacks in response to a doubling of CO2 in the middle atmosphere using the climate feedback response analysis method (CFRAM). This method allows one to calculate the partial temperature changes due to an external forcing and climate feedbacks in the atmosphere. It has the unique feature of additivity, such that these partial temperature changes are linearly addable. We find that the temperature change due to the direct forcing of CO2 increases with increasing height in the middle atmosphere, with the cooling in the upper stratosphere about three times as strong as in the lower stratosphere. The ozone feedback yields a radiative feedback that generally mitigates this cooling, however in the tropical lower stratosphere and in some regions of the mesosphere, the ozone feedback cools these regions further. The temperature response due to dynamical feedbacks is small in global average, although the temperature changes due to the dynamical feedbacks are large locally. The temperature change in the lower stratosphere is influenced by the water vapour feedback and to a lesser degree by the cloud and albedo feedback, while these feedbacks play no role in the upper stratosphere and the mesosphere. We find that the effects of the changed SSTs on the middle atmosphere are relatively small as compared to the effects of changing the CO2. However, the changes in SSTs are responsible for large temperature changes as a result of the dynamical feedbacks and the temperature response to the water vapour feedback in the lower stratosphere is almost solely due to changes in the SSTs. As CFRAM has not been applied to the middle atmosphere in this way, this study also serves to investigate the applicability as well as the limitations of this method. This work shows that CFRAM is a very powerful tool to study climate feedbacks in the middle atmosphere. However, it should be noted that there is a relatively large error term associated with the current method in the middle atmosphere, which can be for a large part be explained by the linearization in the method.

CFRAM (l 54) is not known to me; I am not sure how helpful this statement is without further explanation to the readers of ACP.

Further explanation of the method is now added in the abstract (see above).

I would like to refer to Taylor et al., 2013; Song and Zhang, 2014; Hu et al., 2017; Zheng et al., 2019, who have used CFRAM as a practical diagnostic tool to analyse the role of various forcing and feedback studying surface climate change.

Response to CO2 doubling but at what time has the doubling been reached – would that not be important for the issue of stratospheric ozone? Ozone feedback is mentioned (l 63), but what is assumed for ozone in the upper stratosphere? We know upper stratospheric ozone is "recovering" over the coming decades (WMO, 2018); is this the point here?

We are not speaking here about the changes in O3-concentration due to the ozone hole, but rather changes in ozone concentration that are resulting from changes in the CO2 concentration. The ozone concentration in the control run is for pre- industrial conditions. We change the CO2 and/or the SSTs in the model and compare the two equilibrium states. In runs with the changed CO2 and/or the SSTs the ozone concentration is changed due to the changes in CO2 concentration only. The model has interactive chemistry which calculates the amount of ozone concentration.

And a "warming by 1.5 K, but in which region? Changes in dynamics play a large role (l 66) but which changes, which role? And above 0.1 hPa, which is certainly a region where an ozone feedback is expected. Above 0.1 hpa is above 60 km; this is the mesosphere.

In the earlier version of the paper, average temperature changes over the whole middle atmosphere region were taken. Although this can learn us something, we have now divided Fig. 2 for the regions: lower, upper stratosphere and mesosphere.

Several tropospheric issues are "of minor importance" (l 69), but why is this issue discussed in an abstract of a paper on the "middle atmosphere"? We investigate the temperature responses to feedback processes. Some of these processes might have an effect in the middle atmosphere, and we see that this is indeed the case for the lower stratosphere, however not for the regions above.

Further comments: l. 85-90: It should be clearly said that the middle atmosphere is *not* in radiative equilibrium in most regions; downwelling in the polar regions in winter is part of the BD circulation, and not only an "example". See e.g. Dunkerton, JAS, 1978.

This formulation was written similarly in the PhD thesis ‘The middle atmosphere and its sensitivity to climate change’ by Andreas Jonson, which I read several times while working on this paper (https://www.diva- portal.org/smash/get/diva2:198863/FULLTEXT01.pdf).

I have changed this paragraph to emphasize the role of dynamics for the temperatures in middle atmosphere.

The circulation in the troposphere is thermally driven, however this is quite different for the middle atmosphere. The air in the middle atmosphere is out of reach for convection and is not in direct contact with the Earth’s surface, which means that the middle atmosphere is dynamically stable. In the absence of eddy motions the zonal-mean temperature would relax to a radiatively determined state. However, a wave driven motions of the air drive the flow away from this state of radiative balance and in this way determine the heating and cooling patterns in the middle atmosphere (Shepherd, 2010). l 115-122: Ozone is mentioned here, but it is well established that stratospheric ozone responds to changing halogen levels (WMO 2018). This aspect can not be ignored in this study.

While the reaction of ozone to CFCs and the consequent ozone hole are very important and interesting topics in itself, this is not the topic of this study. What we do here is investigate the temperature changes that arise from the direct forcing of CO2 and the feedback processes that result from this increase in CO2. We have not investigated the effect of the depletion/recovery of ozone.

Sec. 2.3: Is this a new formulation of CFRAM or is this section just reiterating a technique used before? It looks like a new description here as there are no references to previous description of CFRAM at the top of sec 2.3.

Partly this is a new formulation. The method is based on the CFRAM method as described in Lu and Cai (2009), however the method needed to be adjusted in order to be applicable on WACCM output data. I referred to Lu and Cai at the end of the section, but have now added an additional reference at the beginning of the section. l 731-735: No, the ozone concentration is *not* controlled by the Chapman reactions "for a large part". Depending on altitude, NOx and HOx cycles are important; this is well known (check the textbook you are citing). Also chlorine compounds are relevant.

This part has been rewritten:

Ozone plays a major role in the chemical and radiative budget of the middle atmosphere. The ozone distribution in the mesosphere is maintained by a balance between transport processes and various catalytic cycles involving nitrogen oxides, HOx and Clx radicals. In the upper stratosphere, NOx and CLx cycles dominate, while hydrogen species are of most importance in the mesosphere (Cariolle, 1982). l 774: The direct influence is only possible where the chemistry not too fast, again check the Brasseur and Solomon textbook.

The section on the changes in the ozone concentration due to the changed CO2 concentration has now been rewritten and significantly shortened, as this is not new and not the main point of our work: we are interested in the temperature response as a result of the changes in the O3 concentration in WACCM.

Sec. 3.5: The feedback for stratospheric H2O is not that simple, see eg. Solomon et al., Science, 2010; Riese et al, JGR, 2012).

The caveat that all models don’t consistently reproduce the tropopause temperatures has been added.

Several points are mixed here. There might be a change in stratospheric water vapour based on changing climatic conditions and this change could have an impact on local heating/cooling but also an effect of the surface radiative forcing. These issues should be disentangled.

The CFRAM method here calculates the temperature change on the basis of the radiative changes due to changes in water vapour alone. This method doesn’t allow further disentanglement. Our results show that that the regions where there is an increase in the water vapour, there is a cooling, and vice versa. The water vapour feedback as calculated here only takes into account radiative processes, if the water vapour feedbacks on the temperature via dynamical feedbacks this would be shown as a result of the dynamical feedback. l 820: warmer tropopause: also in the tropics? (where water vapour is entering the stratosphere). Would you not expect higher SSTs causing more wave activity and thus a stronger tropical upwelling? Why is this argument not correct?

Yes, WACCM a warmer tropopause in the tropics as well (the tropopause temperature comes as an output of the model). See here the changes in tropopause temperature for the different latitudes in July.

A study by Deckert and Dameris (2008) indeed shows that higher tropical SSTs can indeed strengthen the tropical upwelling into the stratosphere. However, as explained by Solomon et al. (2010) the transport of the water vapour in the stratosphere is mainly a function of the tropopause temperature. We see that this is changing, which can explain what is seen in the model. l 815-816: Is this reduction expected from simple water vapour equilibrium (over ice) arguments? Citations?

I assume the reviewer is referring to an earlier version of the manuscript. A suggestion was made, but based on the comments of other reviewers this was taken out.

Sec 3.6 discusses feedbacks that "play only a very small role" for the middle atmosphere. Fig 12 shows that the middle atmosphere is largely grey (zero effect). But the caption tells me that the comparison is to pre-industrial conditions, so the reported "delta" is due to a change relative to pre-industrial? Then one would expect a larger signal – correct? And the discussion starting in l. 810 is not discussing "pre- industrial"; this is confusing. Yes, the delta T is the temperature change between the run with the changed SSTs and/or CO2 and pre-industrial conditions. Exactly, we see that these feedbacks (albedo and cloud) basically only effect the temperatures in the lower stratosphere and not in the upper stratosphere and the mesosphere. It would have been interesting to see a larger signal higher up in the atmosphere, but it is not there.

I speak about middle atmosphere climate sensitivity which is here used to refer to how much the middle atmosphere will cool or warm after the doubling of CO2 as compared to the pre-industrial state. Figure 12 is no different from Fig. 5 ,7, 9 and 11. It shows the temperature response to the changes in SSTs for the run with high SSTs as compared to pre-industrial conditions.

L 964-972: these lines seem to describe the overall conclusions of the paper; when I read these lines they seem to tell me that CFRAM is okay, but that some refinement is necessary. This is a rather technical statement (which would be more helpful if statements like "some" would be more specific). Most importantly however, the paper promises to talk about "quantifying (!) climate feedbacks in the middle atmosphere" – in my view this has not been achieved in this manuscript.

This is the first study in which it is calculated how much of the temperature change in a specific place in the middle atmosphere is attributed to which feedback process in response to a doubling of CO2. We succeeded in performing the calculations and indeed quantifying these temperature responses. Fig 2, 3, 4, 5, 7, 9, 11 and 12 show the quantification we aimed at achieving. Another goal of the paper was to investigate the applicability of this traditional form of method in the middle atmosphere (contrary to what is done by Zhu et al.). We have learnt that it can be used, but indeed it is not perfect. The linearization is a fundamental part of the method and leads inevitably to errors.

References:

* The current report on stratospheric ozone is WMO 2018, I suggest using this most current information (see above)

This reference is no longer there.

Brasseur and Solomon 2005: this is an excellent text book but might not give the most up to date information required here on upper stratospheric ozone

We think this fundamental relationship between the temperature and water vapor in the middle atmosphere is not out of date. We added further references in the text.

1 Quantifying climate feedbacks in the 2 middle atmosphere using WACCM 3 4 Maartje Sanne Kuilman1, Qiong Zhang2, Ming Cai3, Qin Wen1,4 5 6 1. Department of Meteorology and Bolin Centre for Climate Research, 7 Stockholm University, Stockholm, Sweden 8 2. Department of Physical Geography and Bolin Centre for Climate 9 Research, Stockholm University, Stockholm, Sweden 10 3. Department of Earth, Ocean and Atmospheric Science, Florida State 11 University, Tallahassee, Florida, USA 12 4. Laboratory for Climate and Ocean-Atmosphere Studies (LaCOAS), 13 Department of Atmospheric and Oceanic Sciences, School of Physics, 14 Peking University, Beijing, China 15 16 Corresponding author: Maartje Sanne Kuilman ([email protected]) 17 18 Key points: 19 20 • In a double CO2 climate, the direct forcing of CO2 would lead to a 21 cooling which increases with increasing height in the middle 49 Deleted: of approximately 9 K 22 atmosphere, with the cooling in the upper stratosphere about three 50 Deleted: . 23 times as strong as in the lower stratosphere. 24 Formatted: Font: Italic 25 • The ozone feedback yields a radiative feedback that generally Formatted: Normal 26 mitigates this cooling. The dynamical feedback is another important Formatted: List Paragraph, Line spacing: single 27 feedback with large effects locally, while the effects of the water vapour 51 Deleted: by warming the middle atmosphere by 28 feedback and especially the cloud and albedo feedbacks are only of 52 approximately 1.5 K. ¶ 29 importance in the lower stratosphere. 53 ¶ 30 54 Deleted: small. 31 • CFRAM is very powerful tool to study climate feedbacks in the middle Formatted: Font color: Black 32 atmosphere however, there is an error term caused by the linearization Formatted: List Paragraph 33 in the method. 55 Deleted: ¶ 34 56 ¶ 35 57 ¶ 36 58 ¶ 37 38 39 40 41 42 43 44 45 46 47 48

59 Abstract 60 Formatted: Font: Not Bold, Font color: Auto 61 The importance of the middle atmosphere for surface and tropospheric 108 Deleted: feedback processes in 62 climate is increasingly realized. In this study, we aim at a better understanding 109 Deleted: To 63 of climate feedbacks in response to a doubling of CO in the middle 2 110 Deleted: understand feedback processes 64 atmosphere using the climate feedback response analysis method (CFRAM). 111 Deleted: we use 65 This method allows one to calculate the partial temperature changes due to 66 an external forcing and climate feedbacks in the atmosphere. It has the Formatted: Font color: Black 67 unique feature of additivity, such that these partial temperature changes are 112 Deleted: We examine the middle atmosphere 68 linearly addable. We find that the temperature change due to the direct forcing113 response to CO2 doubling with respect to 69 of CO2 increases with increasing height in the middle atmosphere, with the Formatted: Font color: Auto 70 cooling in the upper stratosphere about three times as strong as in the lower Formatted: Font: 12 pt, Font color: Auto 71 stratosphere. The ozone feedback yields a radiative feedback that generally 114 Deleted: pre-industrial state in the Whole Atmosphere 72 mitigates this cooling, however in the tropical lower stratosphere and in some 115 Community Climate Model (WACCM). Globally, the 73 regions of the mesosphere, the ozone feedback cools these regions further. 116 simulated 74 The temperature response due to dynamical feedbacks is small in global Formatted: Font: 12 pt, Font color: Auto 75 average, although the temperature changes due to the dynamical feedbacks Formatted: Font color: Auto 76 are large locally. The temperature change in the lower stratosphere is 117 Deleted: decrease between 200 and 0.01 hPa (~12-80 77 influenced by the water vapour feedback and to a lesser degree by the cloud 118 km) is found to be -5.2 K in July and -5.5 K in January in 78 and albedo feedback, while these feedbacks play no role in the upper 119 WACCM. The CFRAM calculations show that the direct 120 forcing of CO2 alone would lead to an even stronger 79 stratosphere and the mesosphere. We find that the effects of the changed 121 cooling of approximately 9 K in the middle 80 SSTs on the middle atmosphere are relatively small as compared to the Formatted: Font: 12 pt, Font color: Auto 81 effects of changing the CO . However, the changes in SSTs are responsible 2 122 Deleted: in both July and January. This cooling is 82 for large temperature changes as a result of the dynamical feedbacks and the 123 being mitigated by the combined effect of the different 83 temperature response to the water vapour feedback in the lower stratosphere 124 feedback processes. ¶ 84 is almost solely due to changes in the SSTs. As CFRAM has not been applied 125 The contribution from the ozone feedback causes a 126 warming of approximately 1.5 K, mitigating the cooling 85 to the middle atmosphere in this way, this study also serves to investigate the 127 due to changes in CO2. Changes in CO2 also lead to 86 applicability as well as the limitations of this method. This work shows that 128 changes 87 CFRAM is a very powerful tool to study climate feedbacks in the middle 129 Deleted: dynamics. The changes in dynamics play a 88 atmosphere. However, it should be noted that there is a relatively large error 130 large role locally, especially above 0.1 hPa. Other 131 feedback processes, which are known to be important 89 term associated with the current method in the middle atmosphere, which can 132 in the tropospheric and surface climate, such as the 90 be for a large part be explained by the linearization in the method. 133 water vapor, albedo and cloud 91 134 Deleted: of minor importance in the middle 92 1. Introduction 135 atmosphere,although some 93 136 Deleted: seen 94 The middle atmosphere is the region of the atmosphere that encompassed Formatted: Font color: Auto 95 the stratosphere, where the temperature increases with height, from 10-50 km 137 Deleted: the stratosphere, mainly through the 96 and the mesosphere, where the temperature decreases with height, from 138 responses to sea surface temperature and sea ice 97 about 50-90 km. A classic study by Manabe and Strickler (1964) shows that 139 changes. It 98 in the troposphere, water vapour is the dominant greenhouse gas, followed by Formatted: Font color: Auto 99 CO2. Ozone is responsible for the existence of the stratosphere and the 100 reversal of the temperature gradient in the stratosphere. 101 140 Deleted: The middle atmosphere is generally 102 The circulation in the troposphere is thermally driven, however this is quite 141 controlled by radiative processes although there are 103 different for the middle atmosphere. The air in the middle atmosphere is out of 142 important exceptions. The temperature in the winter 104 reach for convection and is not in direct contact with the Earth’s surface, 143 stratosphere for example, is significantly greater than 144 what is expected from radiative equilibrium 105 which means that the middle atmosphere is dynamically stable. In the 145 considerations alone. This results from adiabatic 106 absence of eddy motions the zonal-mean temperature would relax to a 146 heating associated with downwelling at higher latitudes 107 radiatively determined state. However, wave-driven motions of the air drive 147 as a part of the Brewer-Dobson circulation (Brewer, 148 1949, Dobson, 1956). ¶ 149 Deleted: -

150 the state away from this state of radiative balance and in this way determine 151 the heating and cooling patterns in the middle atmosphere (Shepherd, 2010). Formatted: Font: Italic 152 153 Many chemical, physical and dynamical processes in the middle atmosphere 154 are still often overlooked in climate model simulations. This can be noticed 155 from the description of the experimental design in model intercomparison 156 projects as in e.g. Kageyama et al. (2017) and Taylor et al. (2012). However, 157 recently, there have been a number of studies that show the importance of the 158 middle atmosphere for the surface and tropospheric climate. It has, for 159 example, been shown that cold winters in Siberia are linked to changes in the 160 stratospheric circulation (Zhang et al., 2018).

161 Other studies show that the representation of ozone in climate models affects 162 climate change projections (Dietmüller et al., 2014; Noda et al., 2017; Nowack 163 et al., 2015, 2018;). It has been found that the ozone representation can result 164 in up to a 20% difference in simulated global mean surface warming (Nowack 165 et al., 2015), although the exact importance of changes in ozone seems to be 166 dependent on both the model and the scenario (Nowack et al., 2015) and is 167 not found by all studies (Marsh et al., 2016).

168 Neglecting the effect of ozone may lead to a significant underestimation of the 169 temperature during past climate if we compare with available paleoclimate 170 reconstructions (Ljungqvist et al, 2019), and may also alter the future climate 171 projections in different CO2 scenarios. As the effect is found to be rather large 172 in some studies, and absent in other, there is a need for a better 173 understanding of the behaviour of the middle atmosphere in response to 174 changing CO2 conditions, as the ozone concentration is influenced by this. 175 176 Ozone is an example of a climate feedback, a process that changes in 177 response to a change in CO2-concentration and in turn dampens or amplifies 178 the climate response to the CO2 perturbation. These climate feedbacks are a 179 challenging subject of study, as observed climate variations might not be in 180 equilibrium, multiple processes are operating at the same time and moreover 181 the geographical structures and timescales of different forcings differ. 182 However, feedbacks form a crucial part of understanding the response of the 183 atmosphere to changes in the CO2-concentration.

184 Various methods have been developed to study these feedbacks, such as the 185 partial radiative perturbation (PRP) method, the online feedback suppression 186 approach and the radiative kernel method (Bony et al., 2006 and the 187 references therein). These methods study the origin of the global cimate 188 sensitivity (Soden and Held, 2006; Caldwell et al., 2016; Rieger et al., 2017). 189 The focus of these methods is on changes in the global mean surface 190 temperature, global mean surface heat and global mean sensible heat fluxes 191 (Ramaswamy et al., 2019).

192 These methods are powerful for this purpose; however, they are not suitable 195 Deleted: purpose, 193 to explain temperature changes on spatially limited domains. They neglect 194 non-radiative interactions between feedback processes and they only account

196 for feedbacks that directly affect the radiation at the top of the atmosphere 197 (TOA).

198 The climate feedback-response analysis method (CFRAM) is an alternative 243 Deleted: Recently, a new climate feedback analysis 199 method which takes into account that the climate change is not only 244 method has been developed, which is an offline 245 diagnostic tool: the 200 determined by the energy balance at the top of the atmosphere, but is also 201 influenced by the energy flow within the Earth’s system itself (Cai and Lu, 246 Deleted: ). With this method, one can calculate the 247 temperature changes on a spatially limited domain: it is 202 2009, Lu and Cai, 2009). The method is based on the energy balance in an 248 possible to isolate partial temperature changes due to 203 atmosphere-surface column. It solves the linearized infrared radiation transfer 249 an external forcing and internal feedbacks in the 204 model for the individual energy flux perturbations. This makes it possible to 250 atmosphere. The partial temperature changes are 251 linearly addable; their sum is equal to the total 205 calculate the partial temperature changes due to an external forcing and these252 temperature change (Cai and Lu, 2009, Lu and Cai, 206 internal feedbacks in the atmosphere. It has the unique feature of additivity, 253 2009).¶ 207 such that these partial temperature changes are linearly addable. 254 ¶ 255 CFRAM 208 209 As a practical diagnostic tool to analyse the role of various forcing and Formatted: Font color: Black 210 feedback, CFRAM has been used widely in climate change research on 256 Deleted: exchange between the Earth’s system and 257 outer space 211 studying surface climate change (Taylor et al., 2013; Song and Zhang, 2014; 212 Hu et al., 2017; Zheng et al., 2019). 258 Deleted: . 213 214 This method has been applied to study the middle atmosphere climate 215 sensitivity as well (Zhu et al., 2016). In Zhu et al. (2016), the CFRAM method 259 Deleted: study 216 has been adapted and applied to both model output, as well as observations. 260 Deleted: that study 217 The atmospheric responses during solar maximum and minimum are studied Formatted: Font: Italic 218 and it is found that the variation in solar flux forms the largest radiative Formatted: Font: Italic 219 component of the middle atmosphere temperature response. 220 261 Deleted: , 221 In the present work, we apply CFRAM to climate sensitivity experiments 262 Deleted: They study the 222 performed by the Whole Atmosphere Community Climate Model (WACCM), 263 Deleted: e 223 which is a high-top global climate system model, including the full middle 264 Deleted: find 224 atmosphere chemistry. We investigate the effects of doubling the CO2- 265 Deleted: They show that increasing CO2 cools the 225 concentration and the accompanying sea surface temperature changes on the266 middle atmosphere, while the changes in O3- 226 temperature changes in the middle atmosphere as compared to the pre- 267 concentration lead to a cooling in some regions of the 268 middle atmosphere and to a warming in others. 227 industrial state. We discuss the total responses and feedbacks, as well as 228 those that are induced by doubling CO2 and changes in the sea surface 229 temperature and sea ice distribution separately. 230 231 2. The model and methods 232 233 2.1 Model description

234 The Whole Atmosphere Community Model (WACCM) is a chemistry-climate 235 model, which spans the range of altitudes from the Earth’s surface to about 236 140 km (Marsh et al., 2013). The model consists of 66 vertical levels with 237 irregular resolution, ∼1.1 km in the troposphere above the boundary layer, 238 1.1–1.4 km in the lower stratosphere, 1.75 km at the stratosphere and 3.5 km 239 above 65 km. The horizontal resolution is 1.9◦ latitude by 2.5◦ longitude.

240 WACCM is a superset of the Community Atmospheric Model version 4 241 (CAM4) developed at the National Center for Atmospheric Research (NCAR). 242 Therefore, WACCM includes all the physical parameterizations of CAM4

269 (Neale et al., 2013), and a well-resolved high-top middle atmosphere. The 270 orographic gravity wave (GW) parameterization is based on McFarlane 271 (1987). WACCM also includes parameterized non-orographic GWs, which are 272 generated by frontal systems and convection (Richter et al., 2010). The 273 parameterization of non-orographic GW propagation is based on the 274 formulation by Lindzen (1981).

275 The chemistry in WACCM is based on version 3 of the Model for Ozone and 276 Related Chemical Tracers (MOZART). This model represents chemical and 277 physical processes from the troposphere until the lower thermosphere. 278 (Kinnison et al., 2007). In addition, WACCM simulates chemical heating, 279 molecular diffusion and ionization and gravity wave drag.

280 2.2 Experimental set-up

281 In this study, we first perform a simulation under pre-industrial conditions and 282 take this experiment as a control run, forced with pre-industrial ocean surface 283 conditions such as sea surface temperature and sea ice (referred to SSTs 284 from now on), see table 1. The pre-industrial CO2-concentration is set as 280 285 ppm, the SSTs are from the CMIP5 pre-industrial control simulation by the 286 fully coupled earth system model CESM (Hurrel et al., 2013). The atmosphere Formatted: Font: Italic 287 component of CESM is the same as WACCM, but does not include 288 stratospheric chemistry.

289 We also run a perturbation experiment by doubling the CO2 concentration to 290 560 ppm from pre-industrial level. In WACCM, the CO2-concentration does 291 not double everywhere in the atmosphere. Only the surface level CO2 mixing 292 ratio is doubled, and elsewhere in the atmosphere is calculated according to 293 WACCM’s chemical model. Other radiatively and chemically active gases, 294 such as ozone, will change because of the changes in the CO2-concentration, 295 due to WACCM’s chemical model as well.

296 For the double CO2 simulation, we run two experiments by using two SSTs 297 forcing, one is keeping the pre-industrial SSTs unchanged, and another one 298 from a double CO2 equilibrium simulation by CESM. To investigate the effect 299 of SSTs, we further run a simulation for only using the SST forcing from the 300 coupled CESM for double CO2 condition, but keep the CO2-concentration as 301 280 ppm. All the simulations are run for 50 years, of which the last 40 years 302 are used for analysis.

303 Table 1. Set-up of the model experiments.

Experiment CO2 SSTs from CESM equilibrum run Pre-industrial 280 ppm PI control CO2 and SSTs high 560 ppm Double CO2 run CO2 high 560 ppm PI control SSTs high 280 ppm Double CO2 run

304 2.3 Climate feedback-response analysis method (CFRAM)

305 In this study, we aim to understand and quantify the different climate 353 Deleted: 306 feedbacks that may play a role in the middle atmosphere in a high CO2 307 climate. For this purpose, we apply a climate feedback-response analysis 308 method (CFRAM). 309 310 As briefly discussed in the introduction, traditional methods to study climate 311 feedbacks are based on the energy balance at the top of the atmosphere 312 (TOA). This means that the only climate feedbacks that are taken into account 313 are those that effect the radiative balance at the TOA. However, there are 314 other thermodynamic and dynamical processes that do not directly affect the 315 TOA energy balance, while they do yield a temperature response in the 316 atmosphere. 317 318 Contrary to TOA-based methods, CFRAM considers all the radiative and non- 319 radiative feedbacks that result from the climate system due to response to an 320 external forcing. This means that CFRAM starts from a slightly different 321 definition of a feedback process. Note also that as the changes in temperature 322 are calculated simultaneously, the vertical mean temperature or lapse rate 323 feedback per definition do not exist in CFRAM. 324 325 Another advantage of CFRAM is that it allows for measuring the magnitude of 326 a certain feedback in units of temperature. We can actually calculate how 327 much of the temperature change is due to which process. The ‘climate 328 response’ in the name of this method refers to the changes in temperature in 329 response to the climate forcings and climate feedbacks. 330 331 The mathematical formulation of CFRAM is based on the conservation of total 332 energy (Lu and Cai, 2009). At a given location in the atmosphere, the energy 354 Deleted: . 333 balance in an atmosphere-surface column can be written as: Formatted: Font: Italic 334 335 �⃗ = �⃗ + �⃗ + �⃗ − �⃗ − �⃗ + �⃗ (1) 336 337 �⃗ represents the vertical profile of the net long-wave radiation emitted by the 338 different layers in the atmosphere and surface. �⃗ is the vertical profile of the 339 solar radiation, which is absorbed by these layers. �⃗ is the convergence of 340 total energy in each layer due to turbulent motions, �⃗ is convergence of 341 total energy into the layers due to convective motion. �⃗ is the large-scale 342 vertical transport of energy from different layers to others. �⃗ is the large- 343 scale horizontal transport within the layers and �⃗ is the work done by 344 atmospheric friction. 345 346 Due to an external forcing (in this study, the change in CO2-concentration 347 and/or change in SSTs), the difference in the energy flux terms then 348 becomes: 349 350 ∆�⃗ = ∆�⃗ + ∆�⃗ + ∆�⃗ + ∆�⃗ − ∆�⃗ − ∆�⃗ + ∆�⃗ (2) 351 352 In which the delta (∆) stands for the difference between the perturbation run

355 and the control run. 356 357 CFRAM takes advantage of the fact that the infrared radiation is directly 358 related to the temperatures in the entire column. The temperature changes in 359 the equilibrium response to perturbations in the energy flux terms can be 360 calculated. This is done by requiring that the temperature-induced changes in 361 infrared radiation to balance the non-temperature induced energy flux 362 perturbations. 363 364 Equation (2) can also be written as: 365 366 ∆�⃗ − �⃗ + ∆�� = 0 (3) 367 368 The term ∆(�⃗ − �⃗) we can calculate as the longwave heating rate and the 369 solar heating rate are output variables of the model simulations. We take the 370 time mean of the WACCM data and perform the calculations for each grid 371 point of the WACCM data. This means that in the end, we will have the 372 temperature changes at each latitude, longitude and height. 373 374 We then calculate the difference in these heating rates for the perturbation 375 simulation and the control simulation. 376 377 We use the term ∆�⃗ − �⃗ to calculate the dynamics term ∆��. 378 379 ∆�� = −∆�⃗ − �⃗ (4) 380 381 WACCM provides us with a heating rate in Ks-1. For the CFRAM calculations, 382 we need the energy flux in Wm-2. We can calculate the energy flux by 383 multiplying with the mass of different layers in the atmosphere and the specific 384 heat capacity. 385 ⃗ ⃗ 386 ∆(� − �⃗) = ∆(� − �⃗)() ∗ �� ∗ � (5) 387 Formatted: Font: 12 pt, Not Bold, Font color: Black 388 In which ∆(�⃗ − �⃗) is the difference in the shortwave radiation (�⃗) and Formatted: x_body, Line spacing: At least 12,65 389 longwave radiation (�)⃗) between the perturbation run and the control run as a pt -2 ⃗ -1 390 flux in Wm , while ∆(� − �⃗)() is this difference as heating rate in Ks in 391 WACCM, with �� = with p in Pa and � = 1004 J �� the 392 specific heat capacity at constant pressure. Formatted: Font: 11 pt, Bold, Font color: Auto 393 394 WACCM includes a non-local thermal equilibrium (non-LTE) radiation scheme 395 above 50 km. It consists of a long-wave radiation (LW) part and a short-wave 396 radiation (SW) part which includes the extreme ultraviolet (EUV) heating rate, 397 chemical potential heating rate, CO2 near-infrared (NIR) heating rate, total 398 auroral heating rate and non-EUV photolysis heating rate. 399 Therefore, we split the term ∆�⃗ − �⃗ in an LTE and a non-LTE term: 402 Deleted: ¶ 400 401 ∆�⃗ − �⃗ = ∆(�⃗ − �⃗) + ∆(�⃗ − �⃗) (6)

403 404 WACCM provides us with the total longwave heating rate as well as the total 405 solar heating rate and the non-LTE longwave and shortwave heating rates for ⃗ 406 the different runs. This means that we can calculate the term ∆(� − �⃗) 407 as well, where we again need to convert our result from Ks-1 to Wm-2: 408 ⃗ ⃗ 409 ∆(� − �⃗) = ∆(� − �⃗)() �� ∗ � (7) 410 411 This term can be inserted in equation (3): 412 ⃗ ⃗ 413 ∆(� − �⃗) + ∆(� − �⃗) + ∆�� = 0 (8) 414 415 The central step in CFRAM is to decompose the radiative flux vector, using a 416 linear approximation. 450 Deleted: a 417 418 We start by decomposing the LTE infrared radiative flux vector ∆�⃗ 419 ��⃗ 420 ∆�⃗ = ∆� + ∆�⃗ + ∆�⃗ + ∆�⃗ + ∆�⃗ + ∆�⃗ (9) ��⃗ 421 ⃗ ⃗ ⃗ ⃗ ⃗ 422 where ∆� , ∆� , ∆� , ∆� , ∆� are the changes in infrared 423 radiative fluxes due to the changes in CO2, ozone, water vapour, albedo and 424 clouds, respectively. 425 426 For equation (9), we assumed that radiative perturbations can be linearized by 427 neglecting the higher order terms of each thermodynamic feedback and the 428 interactions between these feedbacks. This is also commonly done in the 429 PRP method (Bony et al., 2006). 430 ⃗ 431 The term ∆� represents the changes in the IR radiative fluxes related to the ⃗ ⃗ 432 temperature changes in the entire atmosphere-surface column. The matrix ⃗ 433 is the Planck feedback matrix, in which the vertical profiles of the changes in 434 the divergence of radiative energy fluxes due to a temperature change are 435 represented. 436 437 We calculate this feedback matrix using the output variables of the 438 perturbation and the control run of WACCM and inserting these in the CFRAM 439 radiation code: atmospheric temperature, surface temperature, reference 440 height temperature, ozone, surface pressure, solar insolation, downwelling 441 solar flux at the surface, net solar flux at the surface, dew point temperature, 442 cloud fraction, cloud ice amount, cloud liquid amount, ozone and specific 443 humidity. 444 445 Similarly, the changes in the LTE shortwave radiation flux can be written as 446 the sum of the change in shortwave radiation flux due to the direct forcing of 447 CO2 and the different feedbacks: 448 ⃗ ⃗ ⃗ ⃗ ⃗ ⃗ 449 ∆� = ∆� + ∆� + ∆� + ∆� + ∆� (10)

451 452 Similarly, to equation (9), we perform a linearization. 453 454 Substituting (9) and (10) in equation (8) yields: 455 ��⃗ 456 ∆�⃗ − �⃗ + ∆�⃗ − �⃗ + ∆�⃗ − �⃗ + ∆�⃗ − �⃗ + ∆�⃗ − �⃗ − ∆� ��⃗ 457 +∆ �⃗ − �⃗ + ∆�� = 0 (11) 458 459 This can be written as: 460 ⃗ 461 ∆� = +∆ �⃗ − �⃗ + ∆�� (12) 492 Deleted: ➝ ⃗ 462 463 Equation (12) can be solved for the individual temperature perturbations. We 464 calculate the temperature changes due to the direct effect of CO2 as well as 465 the different feedback processes. 466 −1 ��⃗ ⃗ ⃗ 467 ∆� = ∆� − � (13) ��⃗ ��2 468 469 This can be done in a similar way for the different feedback processes: 470 −1 ��⃗ ⃗ ⃗ 471 ∆� = ∆� − � (14) ��⃗ �3 472 −1 ��⃗ ⃗ ⃗ 473 ∆� = ∆� − � (15) ��⃗ �2� 474 −1 ��⃗ 475 ∆� = ∆�⃗ − �⃗ (16) ��⃗ �� 476 −1 ��⃗ 477 ∆� = ∆�⃗ − �⃗ (17) ��⃗ �� 478 479 The factors ∆�⃗ − �⃗ , ∆�⃗ − �⃗ , ∆�⃗ − �⃗ , ∆�⃗ − �⃗ and 480 ∆�⃗ − �⃗ are calculated by inserting the output variables from WACCM in 481 the radiation code of CFRAM. Here, one takes the output variables from the 482 control run, apart from the variable that is related to the direct forcing or the 483 feedback. 484 485 This means that for the direct forcing of CO2, one takes the CO2 from the 486 perturbation run, while one takes the other variables from the control run. For 487 the ozone feedback, one takes the ozone from the perturbation run. For the 488 water vapour feedback, one takes the specific humidity, surface pressure, 489 surface temperature and dew point temperature. While for the albedo 490 feedback, one takes the downwelling solar flux at surface and net solar flux at 491 surface from the perturbation run and the other variables from the control run.

493 For the cloud feedback, one takes the cloud fraction, cloud ice and cloud 494 liquid amount from the perturbation run. For all these feedbacks, one takes 495 the other variables from the control run. 496 497 Similarly to equations (13)-(17), we also calculate the temperature change 498 due to non-LTE processes and the dynamical feedback. We already 499 calculated the terms ∆ �⃗ − �⃗ and ∆�� in (4) and (7). 500 −1 ��⃗ 501 ∆� = ∆�⃗ − �⃗ (18) ��⃗ ��−�� 502 −1 ��⃗ 503 ∆� = ∆�� (19) ��⃗ 504 505 The calculated partial temperature changes can be added, their sum being 506 equal to the total temperature change. It is important to note that this does not 507 mean that the individual processes are physically independent of each other. 508

509 ∆� = + ∆� + ∆� + ∆� + ∆� + ∆� + ∆� 510 (20) 511 The linearization done for equations (9) and (10) introduces an error between 512 the temperature difference as calculated by CFRAM and as seen in the model 513 output. Another source of error is that the radiation code of the CFRAM 514 calculations is not exactly equal to the radiation code of WACCM. 515 516 ∆� = ∆� − ∆� (21) 517 518 For more details on the CFRAM method, please refer to Lu and Cai (2009). 519 520 Note that the method used in this study differs from the Middle Atmosphere 541 Deleted: slightly 521 Climate Feedback Response Analysis Method (MCFRAM) used by Zhu et al. 522 (2016). The major difference is that in this study, we perform the calculations 523 using the units of energy fluxes (Wm-2) instead of converting to heating rates 524 (Ks-1). Another difference is that our method is not applicable above 0.01 hPa 525 (~80 km), while Zhu et al. (2016) added molecular thermal conduction to the 526 energy equation, to perform the calculations beyond the mesopause. 527 528 3. Results 529 530 3.1 Temperature responses in a double CO2 scenario 531 532 In section 2.2, it was discussed that four experiments were performed with 533 WACCM: a simulation with pre-industrial conditions, a simulation with 534 changed SSTs only, a simulation with only a changed CO2-concentration and 535 a final simulation with both changed SSTs and CO2-concentration. 536 537 Figure 1 shows the zonal mean temperature changes for the different 538 experiments with respect to the pre-industrial state, as modelled by WACCM. 539 As shown in earlier studies, we observe that an increase in CO2 causes a 540 cooling in the middle atmosphere with the exception of the cold summer upper

542 mesosphere region (Akmaev, 2006). We also observe that changing the SSTs 543 alone, while leaving the CO2-concentration at the pre-industrial levels (Fig 1c 544 and 1f) also yields significant temperature changes over a large part of the 545 middle atmosphere, and contributes to the observed warming in the cold 546 summer mesopause region. 547 548 In line with Fomichev et al. (2007) and Schmidt et al. (2006), we find that the 549 sum of the two separate temperature changes in the experiment with changed 550 CO2 only and changed SSTs only is approximately equal to the changes 551 observed in the combined simulation. Shepherd (2008) has explained this 552 phenomenon as follows: climate change affects the middle atmosphere in two 553 ways: either radiatively through in situ changes associated with changes in 554 CO2 or dynamically through changes in stratospheric wave forcing, which are 555 primarily a result of changing the SSTs (Shepherd, 2008). Even though the 556 radiative and dynamic processes are not independent, at first approximation, 557 these processes are seen to be additive (Sigmond et al., 2004, Schmidt et al., 558 2006, Fomichev et al., 2007). 559

560 561 Figure 1: The total change in temperature in July (top) and January (bottom) 562 for (a,d) the simulation with high CO2 and SSTs, (b,e) the simulation with high 563 CO2, (c,f) the simulation with high SSTs, all as compared the pre-industrial 564 control simulation. The dotted regions indicate the regions where the data 565 reaches a confidence level of 95%. The black line indicates the tropopause 566 height for the runs with changed CO2-concentration and SSTs (a,d), with 567 changed CO2-concentration (b,e) and with changed SSTs (c,f). 568 569 The CFRAM makes it possible to separate and estimate the temperature 570 responses due to an external forcing and various climate feedbacks, such as 571 ozone, water vapour, cloud, albedo and dynamical feedbacks. Note that for 572 the ozone, water vapour, cloud and albedo feedback, we can only calculate 573 the radiative part of the feedback. 574 575 Because we are using an atmosphere-only model, in our experiment, the 576 external forcing is either the change in CO2-concentration or the change in 577 SSTs or both. In an atmosphere-ocean model (such as CESM) and, of

578 course, in reality the changes in sea surface temperature and sea ice 579 distributions are responses to the changed CO2-concentration. 580 581 Figure 2 shows the average change in global mean temperature for the lower 628 Deleted: ¶ 582 stratosphere, the upper stratosphere and the mesosphere for the experiment 629 Deleted: middle atmosphere between 200 583 with the changed CO2-concentration and changed SSTs. To calculate the 630 Deleted: 0.01 hPa (12-80 km) 584 lower stratosphere temperature changes, we take the average value of the 631 Deleted: The ‘total’-column shows 585 temperature change from the tropopause – the pressure level of which is an 586 output of WACCM – until about 24 hPa for each latitude. 632 Deleted: in WACCM. It is found that 587 633 Deleted: change in global mean 588 The tropopause is not exactly at the same pressure level, we always take the 634 Deleted: the middle atmosphere between 200 and 0.01 589 one for the perturbation experiment which is a bit higher at some latitudes, to 635 hPa 590 make sure that we don’t use values from the troposphere. We add the values 636 Deleted: this 591 for each latitude up and take the average. This average is not mass weighted. 637 Deleted: is approximately -5.5 K in July 592 The temperature changes in the upper stratosphere and in the mesosphere 638 Deleted: -5.2 K in January in WACCM. 593 are calculated in the same way, but then for the altitudes 24 hPa-1 hPa and 594 1 hPa-0.01 hPa respectively. 595 596 Figure 2 shows the radiative feedbacks due to ozone, water vapour, clouds, 639 Deleted: also 597 albedo and the dynamical feedback, as well as the small contribution due to 598 the Non-LTE processes, as calculated by CFRAM. The ‘total’-column shows 640 Deleted: The 599 the temperature changes in WACCM, while the column ‘error’ shows the 600 difference between temperature change in WACCM and the sum of the 601 calculated temperature responses in CFRAM. In sections 3.3-3.6, we will 602 discuss the different feedbacks separately in more detail, at this point we give 603 an overview of the general effects and relative importance of the different 604 feedback processes. 605 606 Figure 2 shows that the temperature change in the lower stratosphere due to 670 Deleted: It can be seen that the direct forcing of the changed CO -concentration alone, as calculated by 607 the direct forcing of CO2 is around 3 K. We also observe that there is a cooling 671 2 672 CFRAM, would lead to an even stronger cooling in the 608 of about 1 K due to ozone feedback in the tropical region while there is a slight673 middle atmosphere. Globally, the cooling would be 609 warming taking place in the summer hemispheres in both January and July. 674 approximately 9 K in both July and January. The cooling 610 We also see that the temperature change in the lower stratosphere is 675 is being mitigated by the combined effect of the different 676 feedbacks. ¶ 611 influenced by the water vapour feedback and to a lesser degree by the cloud ... [1] 612 and albedo feedback. 668 Deleted: ozone feedback causes significant warming, 669 by heating the middle atmosphere globally by 613 ... [2] 662 Deleted: . It has been suggested in earlier studies 614 In the upper stratosphere, the cooling due to the direct forcing of CO2 is with 615 about 9 degrees considerably stronger than in the lower stratosphere. The Moved (insertion) [1] 616 water vapour, cloud and albedo feedback play no role in the upper Formatted: Font color: Black 617 stratosphere and mesosphere. The ozone feedback results in the positive 663 Deleted: response to 618 partial temperature changes, of about 2 K. The picture in the mesosphere is 619 similar. The main difference is that the temperature changes are larger, note 664 Deleted: in the CO2-concentration will yield 620 the difference of the range for the temperature change between Fig. 2c, d and 621 Fig. 2e,f. 622 623 The ozone feedback generally yields a radiative feedback that mitigates the 665 Deleted: will mitigate 624 cooling, which is due to the direct forcing of CO2. This has been suggested in 666 Deleted: ( 625 earlier studies, such as Jonsson et al., 2004. With CFRAM, it is possible to Formatted: Font: Italic 626 quantify this effect and to compare it with the effects of other feedbacks in the 667 Deleted: ). 627 middle atmosphere.

677 678 The temperature response due to dynamical feedbacks is small in global Formatted: Font: 12 pt 679 average. This can be understood as waves generally do not generate 680 momentum and heat, but redistribute these instead (Zhu et al., 2016). 681 However, the local responses to dynamical changes in the high latitudes are Formatted: Font: 12 pt 682 large, as we will see in section 3.3. There are some small temperature 697 Deleted: ¶ 683 responses due to non-LTE effects as well. 698 ¶ 684 699 While clouds, albedo and water vapour feedbacks are 700 of crucial importance for the tropospheric and surface 685 The error term is relatively large. In CFRAM, we assumed that the radiative 701 climate, in the middle atmosphere their role is very 686 perturbations can be linearized by neglecting the higher order terms of each 702 small globally. The feedback due to water vapour shows 687 thermodynamic feedback and the interactions between these feedbacks, this 703 some contribution locally, as will be discussed in section 704 3.6. 688 yields an error. Cai and Lu (2009) show that this error is larger in the middle 689 atmosphere than for similar calculations in the troposphere. In the middle Formatted: Font: Italic 690 atmosphere, the density of the atmosphere is smaller, which leads to smaller Formatted: Font: Italic 691 numerical values of the diagonal elements of the Planck feedback matrix. As 692 a result, the linear solution is very sensitive to forcing in the middle 693 atmosphere. Another part of the error is due to the fact that the radiative we 705 Deleted: scheme. The scheme 694 use in CFRAM is relatively simple, as compared to the one that is used in 695 WACCM. 696

707 Deleted: Figure 2 does not only show the global mean 708 temperature responses, but also those in the polar 709 regions and the tropics to give a more complete picture. 710 It can be seen that the total temperature response in 711 WACCM in the winter polar region (-7.7 K) is much 712 stronger than in the summer polar region (-4.6 K) during 713 July, resulting in 3.1 K difference. In January, there is 714 also a larger temperature response in the winter polar 715 region as compared to the summer polar region, 716 although the difference in the temperature response is 717 only 0.6K. ¶ 718 ¶ 719 It is observed that the total temperature change in the 720 polar regions during the local winter is stronger than 721 that in local summer. At the same time, the cooling due 722 to the direct forcing of CO2 alone is stronger in the 723 summer polar region than in the winter polar region. 724 The strong CO2 cooling effect in the summer polar 725 region is mitigated by the warming caused by the ozone 726 feedback. ¶ 727 ¶

706

728 Figure 2: The mean temperature responses to the changes in CO2 and 729 various feedback processes in the lower stratosphere from the tropopause 730 height until 24 hPa (a,b), upper stratosphere from 24-1 hPa (c, d) and in the 731 mesosphere from 1-0.01 hPa (e,f) in July (a, c, e) and January (b, d, f) in the 732 polar regions (90°S-70°S and 70°N-90°N), the tropics (20°S-20°N) and the 733 global mean, for experiment with double CO2 and changed SSTs. 734 735 In addition, the vertical profiles of the temperature responses to the direct 757 Deleted: response to various 736 forcing of CO2 and the feedbacks are shown in Figure 3. Here, one can see Formatted: Subscript 737 that the increase in CO2 leads to a cooling over almost the whole middle 758 Deleted: is 738 atmosphere; an effect that increases with height. We also observe that in the 759 Deleted: : 739 summer upper mesosphere regions, the increased CO2-concentration leads 740 to a warming. The changes in ozone concentration in response to the 760 Deleted: Ozone 741 doubling of CO2 leads to warming almost everywhere in the atmosphere. In 761 Deleted: a 742 some places, this warming exceeds 5 K. In the polar winter the effect of ozone 743 is small due to lack of sunlight. 744 745 There is also a relatively large temperature response to the changes in 746 dynamics. In Fig. 3, it can be seen that there is a cooling in the summer 762 Deleted: 747 mesosphere, while there is warming in the winter mesosphere. The water 748 vapour, cloud and albedo feedback play only a very small role in the middle 749 atmosphere, as we observed in Figure 2. The Non-LTE effects are also small, 750 but start to play a small role above 0.1 hPa, the exact mechanism of which is 751 outside the scope of this paper. 752

753 754 Figure 3: Vertical profiles of the temperature responses to the changes in CO2 755 and various feedback processes in July (top) and January (bottom) for the 756 experiment with double CO2 and changed SSTs in the atmosphere between

763 200 and 0.01 hPa, for regions from 50° N/S polewards and the tropics (20°S- 764 20°N), as calculated by CFRAM. 765 776 Deleted: Figure 4 shows temperature responses

766 767 Figure 4: The mean temperature responses to the changes in CO2 and 768 various feedback processes in July (a,c) and January (b,d) in the upper 769 stratosphere between 24 and 1 hPa, for polar regions (90°S-70°S and 70°N- 770 90°N), the tropics (20°S-20°N) and the global mean for the experiment with 771 double CO2 (a,b) and changed SSTs (c,d) separately. 777 Deleted: Again 772 773 774 775

778 Figure 4 shows temperature responses in the upper stratosphere for the 779 experiment with double CO2 (a,b) and changed SSTs (c,d) separately. These 780 temperature changes were calculated as they were for Fig. 2. Again also, the 781 ‘total’-column shows the temperature changes as found by WACCM, the 818 Deleted: The 782 columns CO2, O3, H2O, cloud, albedo, dynamics, Non-LTE shows the 819 Deleted: The 783 temperature responses as calculated by CFRAM. Error shows the difference 784 between temperature change in WACCM and the sum of the calculated 785 temperature responses in CFRAM. 786 787 We learn from this figure that the effects of the changed SSTs on the middle 788 atmosphere are relatively small as compared to the effects of changing the 789 CO2. The changes in SSTs are responsible for large temperature changes as 790 a result of the dynamical feedbacks, especially in the winter hemispheres. A 791 similar figure for the lower stratosphere (not shown) shows that the 792 the temperature response to the water vapour feedback is, however, almost 793 solely due to changes in the SSTs. 794 795 Earlier, we discussed that the sum of the two separate temperature changes 796 in the experiment with double CO2 and changed SSTs is approximately equal 797 to the changes observed in the combined simulation. We find that the same is 798 true for the temperature responses to the different feedback processes. 799 800 In the rest of the paper, we discuss the temperature responses to the direct 801 forcing and the various feedbacks during July and January in further detail. 802 803 3.2 Temperature direct response to CO2 804 805 Figure 5 shows the zonal mean temperature change due to the increase in 806 CO2. We see that increasing CO2 leads to a cooling almost everywhere in the 807 middle atmosphere, except at the high latitudes in the cold summer upper 808 mesosphere. The higher the temperature, the more cooling there is taking 809 place due to the increasing CO2-concentration (Shepherd, 2008). The reason 810 for this is that the outgoing longwave radiation strongly depends on the Planck 811 blackbody emission (Zhu et al., 2016). 812

820 Deleted: ¶ 821 Figure 4: The mean temperature responses to the 822 changes in CO2 and various feedback processes in July 823 (a,c) and January (b,d) in the atmosphere between 200 813 824 and 0.01 hPa, for polar regions (90°S-70°S and 70°N- 814 Figure 5: Temperature changes to direct CO2 forcing in July (left) and January 825 90°N), the tropics (20°S-20°N) and the global mean for the experiment with double CO (a,b) and changed 815 (right) for the high CO2 simulation as compared to pre-industrial control 826 2 827 SSTs (c,d) separately. ¶ 816 simulation, as calculated by CFRAM. The black line indicates the tropopause 828 Deleted: In 817 height for the runs with changed CO2-concentration. 829 Deleted: , we

830 831 Changing the SSTs does not lead to a change in CO2-concentration, therefore 832 the temperature response to changes in CO2 is not present for the run with 833 only changed SST (Figures not shown). 875 Deleted: We observed that the temperature responses 834 876 to CO2 and changed SST are approximately linearly 877 additive, which means that the temperature response to 835 3.3 Dynamical feedback 878 CO2 in the combined experiment is equal to the 836 879 temperature response to CO2 alone. 837 Ozone is the largest feedback, which mitigates the cooling due to the direct 838 CO2 forcing in most parts of the middle atmosphere (Fig. 2). Climate change 839 affects stratospheric ozone through changes in middle atmospheric chemistry, 840 through changes in dynamics or a combination of these two factors. To 841 understand how the ozone concentration is changing, it is necessary to 842 understand how the dynamics in the middle atmosphere is altered in a double 843 CO2 climate. Therefore, we will first go into the dynamics of the middle 844 atmosphere and the temperature responses to dynamical changes.

845 As discussed in the introduction, in the middle atmosphere there is a wave 880 Deleted: The transport of air in the stratosphere and 846 driven circulation which drives the temperatures away from radiative 881 mesosphere is controlled by the the Brewer-Dobson 882 circulation (BDC). The Brewer-Dobson circulation 847 equilibrium. Large departures from this radiative equilibrium state are seen in 848 the mesosphere and in the polar winter stratosphere. In the mesosphere, 849 there is a zonal forcing, which yields a summer to winter transport. In the polar 850 winter stratosphere, there is a strong forcing that consists of rising motion in Formatted: Font color: Auto 851 the tropics, poleward flow in the stratosphere and sinking motion in the middle 852 and high latitudes. This circulation is referred to as the ‘Brewer-Dobson 883 Deleted: The BDC in the mesosphere spans from the 853 circulation’ (Butchart et al. 2010). 884 summer to the winter pole Formatted: Font color: Auto 854 The zonal mean residual circulation forms an important component of the 855 mass transport by the BDC. It consists of a merional (�̅∗) and a vertical (� ∗) 885 Deleted: �̅∗ 856 component as defined in the Transformed Eulerian Mean (TEM) framework. 857 The residual circulation consists of a shallow branch which controls the 858 transport of air in the tropical lower stratosphere, as well as a deep branch in 859 the mid-latitude upper stratosphere and mesosphere.

860 Both of these branches are driven by atmospheric waves. In the winter 861 hemisphere, planetary Rossby waves propagate upwards into the 862 stratosphere, where they break and deposit their momentum on the zonal 863 mean flow, which in turns induces a meridional circulation. The two-cell 864 structure in the lower stratosphere, which is present all-year round, is driven 865 by synoptic waves. The circulation is also affected by orographic gravity wave 866 drag in the stratosphere and by non-orographic gravity wave drag in the upper 867 mesosphere (Oberländer et al., 2013).

868 Most climate models show that the BDC and the upwelling in the equatorial 869 region will speed up due to an increase in CO2-concentration (Butchart el al., 870 2010). It has been shown that the strengthening of the Brewer-Dobson 871 circulation in the lower stratosphere is caused by changes in transient 872 planetary and synoptic waves, while the upper stratospheric changes are due 873 to changes in the propagation properties for gravity waves (Oberländer et al., 874 2013).

886 It has been explained that the increased stratospheric resolved wave drag is 887 caused by an increase of the meridional temperature gradient in the 888 stratosphere, which leads to a strengtening of the upper flank of the 889 subtropical jets. This in turn shifts the critical layers for Rossby wave breaking 890 upward, which allows for more Rossby waves to reach the lower stratosphere, 891 where they break and deposit their momentum, enhancing the BDC 892 (Shepherd and McLandress, 2011)

893 The differences in the meridional component of the residual circulation (�̅∗) 918 Deleted: changes 894 between the different simulations are shown in Fig. 6. These data are 919 Deleted: for 895 averaged over the 40 years of data. Figure 6b and 6e show that only 920 Deleted: 6. 896 doubling the CO2 leads to a stronger pole-to-pole flow in the mesosphere. 897 Changing the SSTs also leads to changes in the residual circulation as can be 898 seen in Fig. 6c and 6f. Oberländer et al. (2013) have shown that the rising 899 CO2-concentration affects the upper stratospheric layers, while the signals in 900 the lower stratosphere are almost completely due to changes in sea surface 901 temperature.

902 The warmer sea surface temperatures enhance the activity of transient 903 planetary waves and orographic gravity waves in the lower and middle 904 stratosphere, for example via the amplification of deep convection (Deckert 921 Deleted: . 905 and Damaris, 2008). The changed SSTs also leads to enhanced dissipation of Formatted: Font: Italic 906 planetary waves, as well as orographic and non-orographic waves in the 922 Deleted: plantery 907 upper stratosphere. 923 Deleted: als

908 924 Deleted: ¶ 925 ¶ 926 ¶ 927 ¶

909 910 Figure 6: The changes in transformed Eulerian-mean residual circulation 911 horizontal velocity �̅∗ in July (top) and January (bottom) for (a,d) the 912 simulation with high CO2 and SSTs, (b,e) the simulation with high CO2, (c,f) 913 the simulation with high SSTs, all as compared to pre-industrial control 914 simulation, as found by WACCM. The dotted regions indicate the regions 915 where the data reaches a confidence level of 95%. The black line indicates 916 the tropopause height for the runs with changed CO2-concentration and SSTs 917 (a,d), with changed CO2-concentration (b,e) and with changed SSTs (c,f).

928 We are interested in the temperature responses due to the dynamical 929 feedbacks in the different experiments. These temperature responses are 930 shown in Figure 7. Figure 7b and 7e show that there is cooling in the summer 931 mesosphere, while there is warming in the winter mesosphere, which is 932 consistent with a stronger summer-to-winter pole flow.

933 Figure 7c and 7f show the temperature responses due to changes in the 934 SSTs. It is seen that there is mostly a warming in the summer mesosphere 935 and mostly a cooling in the winter hemisphere, which would weaken the effect 936 of the changed CO2-concentration. Most of the temperature responses in the 937 lower stratosphere are caused by the changes in SSTs, as expected.

959 Deleted: ¶ 960 ¶ 961 ¶

938

939 Figure 7: Temperature responses to changes in dynamics, as calculated by 940 CFRAM, in July (top) and January (bottom) for (a,d) the simulation with high 941 CO2 and SSTs, (b,e) the simulation with high CO2, (c,f) the simulation with 942 high SSTs, all as compared to pre-industrial control simulation. The 962 Deleted: The black line indicates the tropopause height 943 tropopause height is indicated as in Fig. 6. 963 for the runs with changed CO2-concentration and SSTs 964 (a,d), with changed CO2-concentration (b,e) and with 965 changed SSTs (c,f). 944 In summary, doubling the CO2 leads to a stronger pole-to-pole flow in the 945 mesosphere, which leads to cooling of the summer mesosphere and a 946 warming of the winter mesosphere. Changing the SSTs weakens this effect, 947 but leads to temperature changes in the stratosphere and lower mesosphere. 966 Deleted: The ozone concentration in the middle 967 atmosphere is for a large part determined by so-called 968 Chapman reactions, in which molecular oxygen (O2) is 948 3.4 Ozone feedback 969 photodissociated to two atomic oxygen atoms, which 949 970 may recombine in a three-body process or react with 950 Ozone plays a major role in the chemical and radiative budget of the middle 971 molecular oxygen to produce ozone (Brasseur and 972 Solomon, 2005).¶ 951 atmosphere. The ozone distribution in the mesosphere is maintained by a 973 ¶ 952 balance between transport processes and various catalytic cycles involving 974 Changes in the circulation and dynamical transport 975 have a significant impact on the ozone distribution 953 nitrogen oxides, HOx and Clx radicals. In the upper stratosphere, NOx and Clx 976 (Salby et al., 2011, Weber et al., 2011). The O3- 954 cycles dominate (Cariolle, 1982), while OH is of utmost importance in the 977 concentration is further determined by interactions 955 mesosphere (Jonsson et al., 2004). 978 between other chemical constituents, which are also 956 979 impacted when the CO2-concentration is increased 980 (Brasseur and Solomon, 2005). ¶ 957 In this paper, we are interested in the changes in ozone concentration Formatted: Font: Italic 958 induced by the increased CO2 concentration and/or the changes in SST in Formatted: Font: Italic

981 WACCM. In the real world, the ozone concentration is not only affected by the 982 changing CO2 concentration, but also by CFC and NOx emissions. 983 984 Fig. 8 shows the percentage changes in O3-concentration when the CO2- 985 concentration and/or the SSTs change. An increase in CO2, leads to an 986 increase of ozone in most of the middle atmosphere. However, in the tropical 987 lower stratosphere, the summer polar mesosphere, the winter and equatorial 988 mesosphere, a decrease in ozone is seen. Fig. 8c and f show that changing 989 the SSTs also has a significant impact on the ozone concentration. A 990 complete account of the ozone changes is out of the scope of this paper, but 991 the main processes responsible for ozone changes will be discussed. 992

993 1017 Deleted: The dotted regions indicate the regions where 994 Figure 8: The percentage changes in ozone concentration in July (top) and 1018 the data reaches a confidence level of 95%. The black 995 January (bottom) for (a,d) the simulation with high CO2 and SSTs, (b,e) the 1019 line indicates the tropopause height for the runs with 1020 changed CO2-concentration and SSTs (a,d), with 996 simulation with high CO2, (c,f) the simulation with high SSTs, all as compared1021 changed CO2-concentration (b,e) and with changed 997 to the pre-industrial control simulation, as found by WACCM. The statistical 1022 SSTs (c,f). 998 signifance and tropopause height are indicated as in Fig. 6. 1023 Deleted: The

999 1024 Deleted: in ozone due to an increase in CO2, has been 1000 Ozone chemistry is complex, however the ozone increase between 30 - 70 1025 shown to 1001 km can be understood primarily as a result of the negative temperature Formatted: Font color: Black 1002 dependence of the reaction O + O2 + M à O3 + M. The fractional contribution Formatted: Font color: Black 1003 of this processes and other loss cycles involving NOx, CLOx and NOx varies Formatted: Font color: Black 1004 with altitude. 1005 Formatted: Font color: Black 1006 At altitudes between 50 and 60 km, the ozone increase is understood by less 1026 Deleted: (Jonsson et al., 2004). In the upper 1027 stratosphere, 1007 effective HOX odd oxygen destruction. The increase in O3 between 45 and 50 1008 km can be understood as the reaction rate coefficient of the sink reaction O +1028 Deleted: is slowed down, and leads to an Formatted: Subscript 1009 O3 à 2O2 decreases. At altitudes lower than 45 km, there is a decrease of 1010 NOx abundance, which can explain the increase (Jonsson et al., 2004). 1029 Deleted: (Bekki 1011 Formatted: Subscript 1012 Schmidt et al. (2006) show that the decrease of ozone at the high latitudes in the summer Formatted: Font: 12 pt, Not Italic, Font color: Auto 1013 mesosphere, is due to a decrease in atomic oxygen which results from 1030 Deleted: ., 2011). The 1014 increased upwelling. The decrease in O3 concentration in the polar winter 1015 around 0.1 hPa is due to a stronger subsidence of NO and Cl, which are both Formatted: Font: 12 pt 1016 ozone-destroying constituents. 1031 Deleted: ¶ 1032 Deleted: (Schmidt et al., 2006).

1033 1069 Moved up [1]: ¶ 1034 The temperature responses due to the ozone feedback are shown in Figure 91070. In 1035 It can be seen that there is a warming in the regions, where there is an Formatted: Font color: Black 1036 increase of the O3-concentration, while there is a cooling for the regions with a1071 Deleted: addition to changes in the chemistry in the 1037 decrease of the O3-concentration. However, this is not the case for the winter1072 middle atmosphere, we have seen that the dynamics 1073 are changing, which leads to changes in the ozone 1038 polar region, where there is no sunlight. Note that the temperature responses 1074 concentration. The BDC affects the O3-concentration 1039 to the changes in CO2- and O3- concentration behave differently in this 1075 directly, but also determines the amount of ozone 1040 respect: the temperature responses due to the direct forcing of CO2 follow the1076 depleting species. The decrease in the ozone 1077 concentration in the tropical lower stratosphere is due to 1041 temperature distribution quite closely, while the temperature responses due to1078 an acceleration of the BDC. In a similar fashion, the 1042 O3 follow the ozone concentration, as also seen by Zhu et al., (2016). 1079 ozone concentration in middle and high latitudes is 1043 1080 increased (Braesicke et al., 2018). As can be seen in 1081 Fig. 8, the decrease of the O3-concentration in the 1082 tropical upper troposphere region is mainly associated 1083 with changes in the SSTs. ¶

1044 1045 Figure 9: Temperature responses to changes in O3-concentration, as 1046 calculated by CFRAM, in July (top) and January (bottom) for (a,d) the run with 1047 high CO2 and SSTs, (b,e) the run with high CO2, (c,f) the run with high SSTs, 1048 all as compared to pre-industrial conditions. The tropopause height is 1084 Deleted: The black line indicates the tropopause height 1049 indicated as in Fig. 6. 1085 for the runs with changed CO2-concentration and SSTs 1086 (a,d), with changed CO2-concentration (b,e) and with 1050 1087 changed SSTs (c,f). 1051 3.5 Water vapour feedback 1052 1053 Water vapour plays a secondary but not negligible role in determining the 1054 middle atmosphere climate sensitivity. In Figure 3, we saw the temperature 1055 responses to the different feedbacks between 20°S and 20°N in July and 1056 January for changes in both the SSTs and the CO2-concentration. It can be 1057 seen that in the lower stratosphere, H2O contributes considerably to the 1088 Deleted: part of 1058 cooling in this region. Above 30 hPa, the water vapour contribution to the 1089 Deleted: is 1059 energy budget is negligible, as also seen by Fomichev et al. (2007). 1090 Deleted: main 1060 1091 Deleted: agent instead of CO2 1061 Figure 10 shows how the water vapour is changing in the middle atmosphere 1062 if the CO2-concentration and/or the SSTs are enhanced. In WACCM, 1092 Deleted: Increasing 1063 increasing the CO2-concentration alone leads to a decrease of water vapour 1064 in most of the middle atmosphere (Fig. 10 b and f). 1093 Deleted: . This is due to the 1065 1066 The amount of water vapour in the stratosphere is determinged by transport 1067 through the tropopause as well as by the oxidation of methane in the 1068 stratosphere itself. The transport of the water vapour in the stratosphere is

1094 mainly a function of the tropopause temperature (Solomon et al., 2010). In Formatted: Font: Italic 1095 WACCM, we see a decrease in temperature in the tropical tropopause for the 1096 double CO2 experiment in WACCM of about -0.25 K. The cold temperatures 1097 in the tropical tropopause lead to a reduction of water vapour of between 2 1098 and 8% due to freeze-drying in this region. Formatted: Font: Italic 1099 Formatted: Not Highlight 1100 It can be seen that changing the SSTs leads to an increase in water vapour 1101 almost everywhere in the middle atmosphere (Fig. 10c and f). In WACCM, the1130 Deleted: The 1102 increase in SSTs is observed to lead a higher and warmer tropopause, which1131 Deleted: leads 1103 can explain this increase of water vapour. However, it should be noted that 1132 Deleted: There is 1104 models currently have a limited representation of the processes determining 1133 Deleted: considerable decrease in 1105 the distribution and variability of lower stratospheric water vapour. Minimum 1134 Deleted: in the winter polar stratosphere in the 1106 tropopause temperatures aren’t consistently reproduced by climate models 1135 experiment with only doubling CO2. The 1107 (Solomon et al., 2010; Riese et al., 2012). At the same time, observations are Formatted: Font: Italic 1108 not completely clear about whether there is a persistent positive correlation 1109 between the SST and the stratospheric water vapour neither (Solomon et al., Formatted: Font: Italic 1110 2010). 1136 Deleted: phenomenon 1111 1137 Deleted: seen for the experiment with double CO2 and 1138 changed SSTs. Formatted: Font: Italic

1112 1113 Figure 10: The percentage changes in water vapour mixing ratio in July (top) 1114 and January (bottom) for (a,d) the run with high CO2 and SSTs, (b,e) the run 1115 with high CO2, (c,f) the run with high SSTs, all as compared to pre-industrial 1116 conditions, as found by WACCM. The statistical significance and tropopause 1139 Deleted: The dotted regions indicate the regions where 1117 height are indicated as in Fig. 6. 1140 the data reaches a confidence level of 95%. The black 1141 line indicates the tropopause height for the runs with 1118 1142 changed CO2-concentration and SSTs (a,d), with 1119 Figure 11 shows the temperature responses due to the changes in water 1143 changed CO2-concentration (b,e) and with changed 1120 vapour as calculated by CFRAM. It can be seen that the regions where there 1144 SSTs (c,f). 1121 is an increase in the water vapour, there is a cooling, and vice versa. This has1145 Deleted: . 1122 been explained as an increase (decrease) in water vapour in the middle 1146 Deleted: (decrease) 1123 atmosphere leads to an increase (decrease) in longwave emissions of water 1147 Deleted: (warming). An 1124 vapour in the mid and far-infrared, which leads to a cooling (warming) 1125 (Brasseur and Solomon, 2005). Higher up in the atmosphere, there are large 1126 percentage changes in water vapour, but the absolute concentration of water 1127 is small there, which explains why there is no temperature response to these 1128 changes. 1129

1148 1149 Figure 11: Temperature responses to changes in H2O-concentration in July 1150 (top) and January (bottom) for (a,d) the run with high CO2 and SSTs, (b,e) the 1151 run with high CO2, (c,f) the run with high SSTs, all as compared to pre- 1152 industrial conditions, as calculated by CFRAM. The tropopause height is 1181 Deleted: The black line indicates the tropopause height 1153 indicated as in Fig. 6. 1182 for the runs with changed CO2-concentration and SSTs 1183 (a,d), with changed CO2-concentration (b,e) and with 1154 1184 changed SSTs (c,f). 1155 3.6 Cloud and albedo feedback 1156 1157 It is known that feedbacks due to changes in clouds and surface albedo play a 1158 crucial role in determining the tropospheric and surface climate (Boucher et 1159 al., 2013, Royer et al., 1990). We have seen in Figure 2 that these feedbacks 1160 play only a very small role in the middle atmosphere temperature response to 1161 the doubling of CO2. and SSTs. However, there are some small radiative 1162 effects from the cloud and albedo feedback, that are the result of the changes 1163 in SSTs, as shown in Figure 12. 1164 1165 Changes in SSTs yield an overall increase in the cloud cover in the upper 1166 troposphere, while this is not the case if one only increases the CO2 1167 concentration. We see that in the tropical region there is a warming due to 1168 changes in clouds, while there is a cooling at higher latitudes in July (see 1169 Figure 12a). In January, the pattern looks slightly different (see Figure 12c). 1170 These temperature changes are due to changes in the balance between the 1171 increased reflected shortwave radiation and the decrease of outgoing 1172 longwave radiation. 1173 1174 We also see an effect of the changes in surface albedo in the stratosphere 1175 (see Figure 12 b and d). The temperature responses shown in Figure 12 b 1176 and d are due to radiative changes. The decrease in surface albedo would 1177 cause less shortwave radiation being reflected. We suggest that this leads to 1178 the cooling seen in the summer polar stratosphere, but more research is 1179 needed. 1180

1185 1186 Figure 12: Temperature responses to changes in cloud (left) and albedo 1187 (right) in July (top) and January (bottom) for the run with high SSTs as 1188 compared to pre-industrial conditions, as calculated by CFRAM. The 1189 tropopause height is indicated as in Fig. 6. 1214 Deleted: black line indicates the 1190 1215 Deleted: for the runs with changed SSTs. 1191 4. Discussion and conclusions 1192 1193 In this study, we have applied the climate feedback response analysis method 1194 to climate sensitivity experiments performed by WACCM. We have examined 1195 the middle atmosphere response to CO2 doubling with respect to the pre- 1196 industrial state. We also investigated the combined effect of doubling CO2 and 1197 subsequent warming SSTs, as well as the effects of separately changing the 1198 CO2 and the SSTs. 1199 1200 It was seen before that the sum of the two separate temperature changes in 1216 Deleted: also have seen 1201 the experiment with only changed CO2 and only changed SSTs is, at first 1202 approximation, equal to the changes observed in the combined simulation Formatted: Font color: Text 1 1203 (see e.g. Fomichev et al. (2007) and Schmidt et al. (2006)). This is also the Formatted: Font color: Text 1 1204 case for WACCM. 1217 Deleted: cooling 1205 Formatted: Font color: Text 1 1206 We have found that, even though changing the SSTs yields significant Formatted: Font color: Text 1, Subscript 1207 temperature changes over a large part of the middle atmosphere, the effects 1218 Deleted: alone would lead to a cooling of about 9 K 1208 of the changed SSTs on the middle atmosphere are relatively small as 1219 between 200 and 0.01 hPa (~10-80 km), for both 1209 compared to the effects of changing the CO2 without changes in the SSTs. 1220 January and July. However, the cooling in this region for 1210 1221 the experiment 1211 We find that the temperature change due to the direct forcing of CO2 Formatted: Font color: Text 1

1212 increases with increasing height in the middle atmosphere. The temperature 1222 Deleted: a high CO2 and SSTs is only 5.2 K 1213 change in the lower stratosphere due to the direct forcing of CO2 is around 3 K1223 Deleted: January and 5.5 K

1224 while in the upper stratosphere, the cooling due to the direct forcing of CO2 is 1274 Deleted: July. This means that 1225 with about 9 K considerably stronger than in the lower stratosphere. In the Formatted: Subscript 1226 mesosphere, the cooling due to the direct forcing of CO2 is even stronger. 1275 Deleted: being mitigated by the combined effect of the 1227 1276 different feedback processes. ¶ 1228 Ozone responds to changes in respond to changes in CO2 and/or SSTs due 1277 ¶ 1278 Different chemical components, 1229 to changes in chemical reaction rate constants and due to the strength of the 1230 up- and downwelling. The temperature changes caused by these changes in 1279 Deleted: particular ozone, 1231 ozone concentration generally mitigate the cooling caused by the direct 1280 Deleted: atmospheric density (due to changes in 1281 temperature) and 1232 forcing of CO2. However, we have also seen in that in the tropical lower 1233 stratosphere and in some regions of the mesosphere, the ozone feedback 1282 Deleted: (Schmidt et al., 2006). The ozone feedback 1283 counteracts the cooling effect, by mitigating the cooling 1234 cools these regions further. 1284 due to 1235 Formatted: Font color: Auto 1236 We also have seen that the global mean temperature response due to 1285 Deleted: CO2 by approximately 1.5 K in both July and 1237 dynamical feedbacks is small, while the local responses to the changes in 1286 January.¶ 1238 dynamics are large. Doubling the CO2 leads to a stronger summer-to-winter- 1287 ¶ 1239 pole flow, which leads to cooling of the summer mesosphere and a warming 1288 The 1240 of the winter mesosphere. Changing the SSTs weakens this effect in the 1289 Deleted: increases in most parts of 1241 mesosphere, but leads to temperature changes in the stratosphere and lower Formatted: Font color: Black 1242 mesosphere. 1290 Deleted: middle atmosphere, with 1243 Formatted: Font color: Black 1244 The temperature change in the lower stratosphere is influenced by the water 1291 Deleted: biggest change 1245 vapour feedback and to a lesser degree by the cloud and albedo feedback, 1246 while these feedbacks play no role in the upper stratosphere and the Formatted: Font color: Black 1247 mesosphere. 1292 Deleted: around 1 hPa. The ozone decreases 1248 Formatted: Font color: Black 1249 It would also be interesting to investigate the exact mechanisms behind the 1293 Deleted: certain parts 1250 feedback processes in more detail. Some processes can influence the Formatted: Font color: Black 1251 different feedback processes, such as ozone depleting chemicals influencing 1294 Deleted: . The temperature response of the ozone 1252 the ozone concentration and thereby the temperature response of this 1295 feedback follows the concentration of O3. The ozone 1253 feedback. Other studies have shown that a surface albedo change, which is 1296 feedback leads to a stronger warming for the case 1254 associated with sea ice loss, can influence the middle atmosphere dynamics, 1297 where only the CO2-concentration is changed, while the 1298 changes in SSTs weaken this effect in the mesosphere. 1255 which in turn influences the temperature response (Jaiser et al., 2013). The 1256 CFRAM cannot unravel the effects of these different processes. Formatted: Font color: Auto 1257 1327 Deleted: role of the water vapour feedback in the 1328 middle atmosphere is generally quite small. However, 1258 There is also a need for a better understanding of how different feedbacks in ... [3] 1259 the middle atmosphere affect the surface climate. As discussed in the 1303 Deleted: some regions of 1260 introduction, the exact importance of ozone feedback is currently not clear 1304 Deleted: , mainly as 1261 While this paper focused on the temperature changes in the middle 1326 Deleted: result of changing SSTs. Changing the SSTs... [4] 1262 atmosphere, similar analysis can be done to quantify the effects of feedbacks1312 Deleted: surface 1263 on the surface climate. 1325 Deleted: feedbacks are of crucial importance for the... [5] 1264 1317 Deleted: , that are 1265 In conclusion, we have seen that CFRAM is an efficient method to quantify 1266 climate feedbacks in the middle atmosphere, although there is a relatively 1318 Deleted: result of 1267 large error due to the linearization in the model. The CFRAM allows for 1319 Deleted: changed SSTs 1268 separating and estimating the temperature responses due an external forcing1320 Deleted: ¶ 1269 and various climate feedbacks, such as ozone, water vapour, cloud, albedo 1321 Deleted: 1270 and dynamical feedbacks. More research into the exact mechanisms of these1322 Deleted: some refinement of the method 1271 feedbacks could help us to understand the temperature response of the 1323 Deleted: necessary to reduce the 1272 middle atmosphere and their effects on the surface and tropospheric climate 1324 Deleted: this region 1273 better.

1329 1330 Acknowledgements 1372 Deleted: Acknowledgement¶ 1331 1332 The computations and simulations were performed on resources provided by 1333 the Swedish National Infrastructure for Computing (SNIC) at National 1334 Supercomputer Center (NSC) in Linköping. 1335 1336 Hamish Struthers NSC is acknowledged for assistance concerning technical 1337 aspects in making the WACCM code run on NSC supercomputer Tetralith. 1338 We thank Qiang Zhang for helping to make the radiation model code 1339 applicable to WACCM model data. 1340 1341 Competing interests Formatted: Font: 12 pt, Bold

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