Thank you very much for your encouraging feedback and the insightful suggestions for improvement. The calculation of the broadband emission temperature was a useful check on our results. We have implemented the suggestions in the manuscript and  individual comments are addressed below.

1. One important omission was that the authors talk about coupling with a slab ocean but don’t provide details.  Do you simply mean a heat sink? There are other models, even for global mean, that do a decent job – see the semi-infinite diffusion model described by MacMynowski et al. (2011).

We have added some more details to the discussion of the slab ocean simulations at line 121:

"The slab ocean model used in this study is a simple heat sink in equilibrium with the atmosphere. The depth of the slab ocean only affects the time to reach equilibrium (Kluft et al., (2019)) and is set to 10 m."

2. The discussion on lines 287 about aerosol height is interesting but, I think, not particularly relevant. The height of the aerosol layer is less important than the effective radiative height of the atmosphere (where the atmosphere optical thickness is equal to 1). This might be something you could compute for your various cases to show how the radiative height is changing.

We agree that the change in emission height is relevant for feedback and forcing. However, in this particular case, the altitude of the aerosol layer and its distance from the tropopause height are also critical. With increasing tropopause height at higher temperatures, the distance of the aerosol to the tropopause is reduced in our modelling framework because the aerosol resides at a fixed altitude. Thus, it has an increasing effect on tropospheric temperatures, precluding parts of the troposphere from participating in the radiative feedback. Pointing out this effect, which is an unrealistic behaviour of our model, is the goal of the discussion starting at line 304. This effect is related to the aerosol's physical height, not the effective emission height.

Inspired by your suggestion, we calculated the effective emission temperature of the atmosphere as a proxy to emission height. The emission height is calculated using the top of the atmosphere longwave flux and the Stefan-Boltzmann relation for a black body. We note the following:

a. In the Tg20 experiment the emission temperature decreases (w.r.t Reference) by around 2 K and 2.7 K at 280 K and 300 K surface temperature. However for 0.5XCO2 the emission temperature changes by around 1 K across the surface temperature range. These emission temperature changes reflect the longwave forcings shown in Fig. 3.

b. The emission temperature difference between 280 K and 300 K surface temperatures is around 8.8 K for the Reference, whereas it is 8 K for Tg20. Thus, the change in emission height with surface warming is not much different upon aerosol injection. This reflects the slightly smaller LW feedback under aerosol loading as shown in Fig. 4.

While this was a useful check on our results, it does not provide any novel insights. In order to keep the manuscript concise we prefer to not include these emission temperatures in the manuscript.

3. Kashimura et al. (2017) also the importance of shortwave absorption in the atmospheric column and differences added by the aerosol layer.  It would be interesting to compare your results to theirs (if applicable).

Kashimura et al. (2017) have presented a compelling study on the shortwave radiation budget at the surface after aerosol injection using a similar decompsition technique. Our analysis of the  shortwave forcing component  aligns with their results. Thus, the following reference has been added at line 178: "This is in agreement with the results by Kashimura et al. (2017), who showed that the decrease in water vapour with surface cooling results in a weaker forcing."

As we mainly focus on the longwave radiation at the top-of-the-atmosphere, other results could not be compared to their findings.

4. Your discussion in Section 6 is interesting, particularly Figure 6c.  I wonder if it would be appropriate to talk about efficacy (Hansen et al., 2005) here, as you are showing why efficacy differences may occur.

We added the following sentence to line 553: “The efficacy of stratospheric aerosol forcing, i.e., the effectiveness of a unit forcing to cause temperature changes in comparison to CO2 forcing (Hansen et al., (2005)), is greater than one at low surface temperatures, but approximately one above 295 K.”

5. There is a typo on line 367 (“fixed”).

We have corrected the typo.

Thank you very much for taking the time to review our manuscript and for the insightful suggestions for improvement. We think that the comment pointing out the missing discussion on the limitations of the study was very crucial to help the reader to appreciate insights and limitations of our study. We have modified the manuscript based on your suggestions. Replies to individual comments are below. 

1. I find the analysis presented by the authors to be sound generally. There are also some interesting results shown, such as the temperature dependence of the aerosol net radiative effects. However all of the findings seem to me to be quite limited by the simple model setup, which ignores the effects of clouds. The reader is left to wonder what the actual sensitivities are in nature, with revisions in the numbers presented that may well be significant, particularly regarding masking of surface emissions (as it is no longer the surface being masked but colder cloud tops)? The analysis is also not global but rather represents mainly the deep tropics, with an incoming insolation of 409.6 W/m2 assumed. A broadly defined surface albedo of 0.2 is imposed, again departing significantly from the real world, to account for the absence of clouds. These again seem to be pretty substantial caveats, particularly in estimates of surface emission masking by aerosols. One also wonders about effects at high latitudes, where the surface and upper atmosphere temperature are more comparable. Are we overestimating global effects by focusing on tropical conditions? The question then is can an analysis be readily conducted in which these caveats are accounted for? To me the clear answer seems to be yes, one could simply perform a nudged AMIP simulation with a realistic accounting of stratospheric aerosols versus a control simulation (or ensemble) with none. In cases where additional physical interpretation is then needed, simulations with konrad might play an important role - or perhaps direct interpretation from the simulation will be tractable. But on its own, the modeling setup used in the present version of the work seems to provide quite limited insight.

We agree with the reviewer that cloud effects could alter our results quantitatively. We deliberately choose to quantify only the clear-sky radiative forcing and feedback to stratospheric aerosol, following similar studies on CO2 forcing and feedback which also restrict themselves to the clear-sky effects (Kluft et al. (2019), (2021), Seeley and Jeevanjee (2021), Jeevanjee et al. (2021)).

While this is certainly a limitation of our study we think the understanding of the clear-sky effect is a necessary prerequisite to understand possible modulations of the radiative forcing through clouds. We therefore think that our contribution to the understanding of the clear-sky effect is of merit. To emphasize the concentration on clear-sky more clearly, we changed the title to “Surface Temperature Dependence of Stratospheric Sulfate Aerosol Clear-Sky Forcing and Feedback.” 

Regarding the suggestion to perform AMIP simulations, we respectfully disagree that they would provide an objectively better framework for addressing the problem in our paper. Firstly, AMIP simulations cannot serve as test bed for feedback due to the fixed SST, and AMIP+4K simulations are in their own way problematic substitutes for feedback calculations due to their unrealistic SST patterns. Secondly, AMIP simulations would not have allowed for such a broad range of densely sampled SST boundary conditions. While it would be possible to bin grid points by temperature and use this as a substitute for sampling the full range of SST, these grid points would also differ in their climatological surface albedo, cloudiness, integrated water vapor, vertical moisture distribution, temperature profile, tropopause height, aerosol load, insolation, etc. Even with konrad at hand as interpretative guide, it is hard to pin down variations in forcing and feedback to variations in one input. 

We believe that 1D-RCE studies can provide more than just very limited insight into climate systems. Our goal is to describe basic dependencies of forcing and feedback on surface temperature and to shed light on effects that arise from the spectral nature of the aerosol scattering. konrad is an appropriate tool for this question. Other studies have yielded very insightful results despite being limited to the 1D-RCE domain, such as Manabe and Wetherald (1967), Dacie et al. (2019), Bourdin et al. (2021).

We now explicitly mention the limitations and discuss their consequences, starting at line 364. Kindly refer to comment 7 for more details. 

Minor Comments:

2. Abstract doesn’t say what data/models are used? Some information on methods to contextualize the analysis should be included.

We agree that this information would be helpful for the reader. The modified line 3 of the abstract reads: "Using a one-dimensional radiative-convective equilibrium model, we quantify the contributions to clear-sky forcing and feedback from absorbing and re-emitting longwave radiation, stratospheric heating, and enhanced stratospheric water vapour."

3. 18: are there no references for the longwave offset?

We have added a reference for Andronova et al., (1999) in line 17. In their paper, they presented both shortwave and longwave radiative forcing by volcanic aerosol. 

We also added the following in the introduction: "Andronova et al. (1999) showed that the longwave component of the stratospheric sulfate aerosol ("aerosol" hereafter) forcing increases with surface temperature but did not provide an explanation"

and in line 200:

"This is in agreement with the observation that humidity has a very weak influence on the aerosol longwave forcing by Andronova et al. (1999)."

4. 22: perhaps expand as to how differences in stability project onto a feedback, via clouds?

We believe that the description of prior work on the effect of tropospheric stability on the feedback is not necessary to apprehend the results of the current study and would be a diversion to the reader. In konrad, the tropospheric stability under clear-sky conditions is determined by the surface temperature only, as the lapse rate is constrained to be moist adiabatic.

We now explicitly mention the absence of stability changes in our model konrad in the discussion in line 231 and 355.

Regarding the impact on clouds, kindly refer to our reply to comments 1 and 7.

5. 23: perhaps expand - what purely radiative effects?

We modified the sentence to expand on what we mean by purely radiative effects. The sentence at line 28 now reads: "In addition to circulation and pattern effects, purely radiative effects, such as longwave absorption and re-emission by greenhouse gases, have been found to cause a state dependence of forcing and feedback to changes in CO2 levels."

6. 27: it is unclear to me if you are alluding to different feedbacks to aerosol loading or different feedbacks in other processes (e.g. clouds) in the presence or absence of aerosol loading.

We agree that the sentence is confusing. The sentence at line 31 has been modified to read: "In this work we explore if such a state dependence of radiative forcing and feedback also exists for stratospheric sulfate aerosol ("aerosol" hereafter), and if the radiative effects from stratospheric aerosol loading may modify different radiative feedbacks in the atmosphere."

7. 60: there is no mention of the drawbacks of using a single column model for this exercise yet they are substantial. For example, clouds are not even considered in the simulations. Yet cloud masking is likely a central consideration in aerosol-climate interactions. Masking effects between high clouds and the surface. They also may depend strongly on latitude.

We agree that the manuscript was lacking a discussion in this regard. The following text has been added to discuss the limitations of our methodology at line 369:

"The simple conceptual model used for our study enables an understanding of the physics behind the temperature dependence of aerosol forcing and feedback and their quantification in such an idealized setting. However, the realism of the setting is limited in particular by a) the assumptions of tropical atmospheric conditions and b) the neglection of cloud effects. Despite the simplicity of the 1D-RCE approach, forcing and feedback estimates obtained with konrad and similar tools are in general very similar to estimates using general circulation models. For example, 1D-RCE estimates of the clear sky feedback are robustly close to −2.2 W m−2 K−1 (Manabe and Wetherald, 1967; Kluft et al., 2019; Koll and Cronin, 2018; Koll et al., 2023), while estimates from CMIP models lie between about −1.9 and −2.2 W m−2 K−1 (Held and Shell, 2012; Zelinka et al., 2020; Vial et al., 2013; Koll et al., 2023). The usefulness of studying averaged atmospheric conditions for Earth is partly related to Earth’s OLR being an approximately linear function of surface temperature. This characteristic implies that the impact of radiative forcing is very similar for warm and cold climates (Koll and Cronin, 2018). Adding clouds to our study would likely change the results quantitatively. Clouds would reduce the aerosol’s SW forcing depending on their albedo, and the LW forcing depending on their emission temperature. For the case of the feedback, both aerosol and clouds mask feedback from surface emissions, so that the feedback-weakening effect of aerosol could be reduced in the presence of clouds. However, we expect that the idealized study presented here provides a useful background for potential future attempts to assess the temperature dependence of stratospheric aerosol forcing on Earth."

8. 120: it is noteworthy that coupling a single-column model to a slab ocean also does not really diagnose climate sensitivity accurately since it does not allow for changes in coupled dynamics and associated patterns of response.

We agree that coupling a single column model to a slab ocean does not give a complete estimation of climate sensitivity when compared to more complex members of the model hierarchy. Our reason to use slab ocean simulations is to estimate climate sensitivity more accurately than possible from just fixed surface temperature simulations, within the scope of our experimental setup.

In order to not mislead the reader on the objectives of this study, we have added the following in the introduction at line 49. "We do not aim to provide strictly quantitative statements about the actual magnitude of clear-sky aerosol forcing and feedback in nature. Instead, we aim for a mechanistic understanding of the clear-sky radiative changes instigated by stratospheric sulfate aerosol and how they shape the forcing and feedback at climate states with different surface temperatures. Hence, the numbers we provide should not be mistaken for estimates of the real-world radiative feedback or climate sensitivity."

Thank you for your insightful feedback. We think your comments were particularly helpful for emphasising the important findings from the study. We have implemented most of your suggestions and reply to the comments individually below.

Major Comments

1. A key theme and insight of this work is that the state-dependence of the aerosol forcing is equivalent (by Clairaut's theorem) to the aerosol dependence of the feedback parameter. This should be brought to the fore, and ideally articulated in a displayed equation so that this point does not escape the reader's attention. Note that this phenomenon was recently explored in detail for CO2 forcing by Xu and Koll, "CO2‐Dependence of Longwave Clear‐Sky Feedback Is Sensitive to Temperature", GRL 2024, which should be cited. Their application of Clairaut's theorem is in the second line after their Eqn (6).

We agree that this finding deserves more elaboration and more focus. We cited Xu and Koll (2024), added a discussion on Clairaut's theorem (including an equation) to section 5.2, and brought this finding out more clearly in the abstract.

2. Another key insight of this paper seems to be in lines 202-221, and in particular lines 218-221 regarding the enhanced Ts-dependence of aerosol IRF relative to CO2. But only indirect evidence for this interpretation is provided (Fig. 2). Could the authors simply plot the change in spectrally-resolved emission temperatures under aerosol forcing (with coarse spectral resolution as in Fig. 2) to illustrate that aerosol forcing emanates from the IR window whilst CO2 forcing does not? Also, note that it is not just the absorption spectrum of sulfate aerosol which matters for this, but also the fact that sulfate aerosols are concentrated in the stratosphere (Fig. 1) rather than being well mixed.

In our model setup, the current coupling between konrad and RRTMG only gives a broadband flux output in the longwave and shortwave. Thus, unfortunately spectrally-resolved emission temperatures cannot be calculated, and we resort to indirect evidence and a mechanistic explanation.

We agree that the difference in vertical distribution of the aerosol and CO2 is important besides the absorption spectrum. To make this clearer we have rephrased line 227 to "To summarize, the fact that aerosol forcing exhibits a pronounced surface temperature dependence while CO2 forcing does not, arises from two factors: aerosol absorbs inside the atmospheric emission window whereas CO2 does not, and aerosol is concentrated in the lower stratosphere, whereas CO2 is well-mixed throughout the atmosphere."

3. I appreciated seeing the explicit compensation between SW and LW aerosol forcing in Fig. 3. I've always wondered what this looks like. It seems that the LW component cancels about 1/3 of the SW component. Would the authors agree with this? If so it might be a nice rule of thumb to popularize. If this has been noted or illustrated before, then those references should be provided.

The compensation ranges all the way from 35% - 70%. This is because, between 280 K - 300 K, the shortwave component changes only around 0.5 and 1 W/m^2, whereas the longwave component increases by 1.5 and 3 W/m^2 for Tg10 and Tg20 respectively.

We added the following sentences to line 229: The longwave forcing offsets around 1/3 to 2/3 of the SW forcing, where this ratio increases with surface temperature and aerosol load as shown in Fig. 3(d). Note that konrad does not represent tropospheric adjustments, which are therefore not included in this estimate."

To emphasize this pointing we are adding the new panel (d) to the original Figure 3. 

4. Sections 6 and 7 are useful checks on the forcing-feedback framework and are worth including, but seem unrelated to the main points of the paper. Perhaps they could be relegated to an Appendix or SI?

We agree that Sections 6 and 7 are not central to the flow of the paper and have moved them to appendices.

5. From Fig. 5 and Table 1 it seems that the H2O adjustment is quite small, perhaps a 5% effect or so. Could the authors quantify this in a general way, so that readers have a sense of how negligible this effect is?

Due to the dependence of temperature on other components and the total longwave forcing, the contribution from water vapour adjustment ranges from around 4% to 7%.

We added this information to line 199.

Minor comments

1. What ozone profile (if any) was used in the konrad simulations? If nonzero and fixed in pressure, how might this affect tropopause height?

We use a fixed vertical distribution of ozone in pressure space following the RCEMIP protocol (Wing et al., (2018)). Hence, the amount and distribution of ozone remains the same irrespective of the atmospheric state. The above information has been added to the model description at line 73.

Dacie et al. (2019) studied how changes in the ozone profile affect the tropopause temperature and height. They show that in agreement to previous studies using other models,  when the ozone profile is shifted upward (as expected from surface warming), the tropopause increases in height and decreases in temperature due to a reduction of radiative heating in this region.

2. Eqn 4 is the Cess sensitivity, and should perhaps be referred to as such.

We now mention the Cess sensitivity in line 114, and also added that calculating the feedback with the slab ocean model is also referred to as "Charney sensitivity" (line 121)

3. The color bar showing aerosol extinction in the left side of Fig. 1 is unsatisfying, as no units or color bar label are provided. Could the authors be more precise about what they mean by extinction, and then add a color bar to make the plot quantitative?

We have modified Fig. 1(a) to represent a line plot of the aerosol extinction coefficient at 550 nm to make it quantitative.

4. The decomposition of forcing state-dependence into abs, delta T and delta q is is given in Table 1, whilst the analogous decomposition for the feedback (which should be closely related by Clairaut's theorem) is illustrated in a Figure (Fig. 5). Any reason why the forcing results should not also be in a figure, rather than a table?

To maintain consistency, we have replaced Table 1 with a corresponding figure. We have excluded Tg10 from the same for visual clarity and no important information is lost.