General comments:

Byrom et al. have created a clear manuscript that conveys scientifically relevant findings. They do this by expanding upon work that has highlighted a stratospheric base state dependence on CMIP6 model 4xCO2 ERF, investigating the role of O3 that plays a significant role in determining stratospheric temperatures.

They construct stratospheric ozone change experiments in NorESM2, prescribing ozone from the higher stratospheric-resolution CESM2-WACCM, to demonstrate how stratospheric temperatures change with O3 concentrations. They then calculate IRF (through offline radiative code)  and adjustments (through radiative kernels) that result from a quadrupling of CO2 from these different stratospheric states.

Through this, and by comparing methods with previous work, they show the importance of calculating IRF through offline code, and using appropriate kernels that avoid extrapolating to above the top of the  model. They further show that IRF depends on the base state of the stratosphere, due to overlapping O3 and CO2 spectral bands and stratospheric temperature. However, stratospheric temperature adjustments do not change significantly between increases and decreases of O3. Cloud adjustments result in invariant ERF, which highlights that stratospheric O3 concentrations are unlikely to explain the inter-model spread in 4xCO2 ERF.

I would like to see this published, though I have some minor concerns that I would like to see addressed.

Specific comments:

L112: on calculating the cloud adjustment as a residual, I’m not confident that A_c is being properly estimated. It seems like the same criticism levied against calculating IRF as the residual could apply to calculating A_c as a residual. Non-zero ϵ may explain the differences in cloud feedbacks shown in Figure 3. I’d like to see further justification for assuming approximately zero ϵ.

L117: It’s not clear to me how you calculate the adjustment to surface temperature change (A_T_s). I think a brief explanation is warranted, or just clarification that you used the same method as in the papers that follow the same approach.

Figure 3: especially given the small number of years (9, instead of the ~20 you might use from 30 year runs) used in calculating values in the figure, this figure could benefit from error bars to show standard errors. If error bars are very small, I think the results would still benefit from acknowledging this.

Fig. S3: CESM2 and NorESM2 are very similar, so isn’t comparing what they do here quite limiting? It might be worth clarifying this.

Technical corrections:

L17-19: Unclear sentence “However… O3”. This could read as though the base-state stratospheric temperatures and the spectral overlap of CO2 and O3 are counteracting the spread in CO2 ERF. Given what you write in your conclusions, it seems like this should be something along the lines of “The spread in CO2 IRF is explained by the impact of base-state stratospheric temperature on the emission of outgoing longwave radiation and the spectral overlap of CO2 and O3, but these do not explain the spread in CO2 ERF”.

L233-244: I think the use of brackets here leads to less clarity. This seems like a good example of what has been criticised in previous literature (https://doi.org/10.1029/2010EO450004), where parentheses are not used for clarification. I would recommend writing separate sentences e.g. for increase vs. decrease of O3 instead of trying to save space with parentheses.

Figures (generally): the figures are a bit blurry, which makes it hard to read some elements especially in Figs. 1, 3, and S3. Ideally these would be higher resolution, or the font size might be increased.

Fig. S3: why the change of colours from Fig. 3? I found it a bit harder to distinguish the shades of blue than the shades of orange.

Review of egusphere-2024-111, entitled "Investigating the role of stratospheric ozone as a driver of inter-model spread in CO₂ effective radiative forcing" by Byrom et al.

General comments

The submitted manuscript investigates stratospheric ozone as a cause of inter-model differences in stratospheric temperature, and hence its role as a contributing factor to inter-model spread in CO₂ radiative forcing. The work aims to explore whether the stratospheric temperature dependence of instantaneous radiative forcing (IRF) extends to effective radiative forcing (ERF). Using the Norwegian Earth System Model 2, the authors explore the impact of stratospheric ozone perturbation and further stratospheric temperature on the magnitude of 4xCO2 ERF and its components (IRF and rapid adjustments) via a series of well-designed fixed-SST simulations. The authors found that the systematic stratospheric ozone perturbations barely influence the spread of 4xCO2 ERF, although the effects of systematic stratospheric ozone perturbations clearly show in both the IRF and stratospheric adjusted radiative forcing (SARF) via their base-state dependence. Meanwhile, the authors also found considerable uncertainty in the IRF calculations with different methods, stemming from differences in both radiative transfer codes and the vertical coordinates (e.g., model top pressure and vertical resolutions). These results may help to better understand the large spread in the IRF and further ERF, hopefully reducing uncertainty in estimates of climate sensitivity. Overall, I found the manuscript well-organized, well-illustrated, and a good addition to the understanding of state-dependent radiative forcing. I would recommend Atmospheric Chemistry and Physics consider this article for publication after minor revisions.

Major concern:

The authors found that the systematic stratospheric ozone perturbations barely influence the spread of 4xCO2 ERF, although the effects of systematic stratospheric ozone perturbations clearly show in both the IRF and SARF via their base-state dependence. Based on Figure 3, it is clear that the cloud adjustment offsets the stratospheric temperature dependence of the IRF and SARF. I would suspect that most cloud adjustments come from cloud changes at higher altitudes. It would be good if the author could decompose cloud adjustment into contributions from high, mixed, and low clouds, probably following Soden and Vecchi (2011). It would be even better if the authors had ISCCP simulator results available (it is totally ok if not). If the cloud adjustment comes from high altitudes, as suspected, the author could probably get the stratospheric temperature-dependent ERF by simulations only perturbing ozone within the upper stratosphere in the future.

Soden, B. J., and G. A. Vecchi (2011), The vertical distribution of cloud feedback in coupled ocean-atmosphere models, Geophys. Res. Lett., 38, L12704, doi:10.1029/2011GL047632.

Minor comments:

Lines 15-16: Are the host-model radiative transfer calculations referring to online or offline double-call calculations with the same radiative transfer codes? If yes, the authors could probably encourage model centers to provide online double-call for their simulations.

Lines 16 and 81-82: I wondered why the authors chose to use the 50% increase and decrease in stratospheric O₃ concentration instead of doubling and halving stratospheric O₃ concentration.

Lines 17-19, 240-241 & 265-268: Is the effect of the spectral overlap of CO₂ and O₃ comparable to the effect of stratospheric temperature dependence? It would probably be interesting to have a simple test with LBL codes in the future.

Lines 92-95: Can the authors provide more details for the PORT offline calculations? Are the calculations described here just offline double-call calculations? So, just two offline calculations using 1x and 4x CO2 concentrations with identical base-state from control simulation. Can the authors help to explain what “the simulations are run for 16 months with the last 12 months used to …” means?

Line 99: It would probably be better to use “temperature, water vapor, or surface albedo” instead of “stratospheric temperature, surface albedo or clouds”, since there is no cloud kernel in the radiative kernels of Soden et al. (2008).

Lines 141-144 & 157-159: It is great to see the conclusion that the magnitude of IRF varies notably between both experiments, demonstrating a dependence on the diagnostic method of choice, although this may not be very new. Even with the identical radiative kernel method, the IRF obtained from 17- and 19-levels are noticeably different. In particular, stratosphere adjustment has a strong dependence on the model top and probably vertical resolution. This is because the radiative flux perturbation due to the same temperature perturbation at higher altitudes (e.g., 1 hPa) within the upper stratosphere is larger than that of lower altitudes (e.g., 10 hPa) within the upper stratosphere. Meanwhile, the temperature cooling at higher altitudes within the upper stratosphere is usually also stronger than at lower altitudes within the upper stratosphere. Therefore, stratospheric adjustment (IRF) from 17-level kernels is smaller (larger) than that of 19-level kernels.

Lines 144-145, 171-175 & 187-191: Since the accuracy of IRF calculation from the radiative kernel method depends on the differences of radiative transfer codes and the vertical coordinate resolution (ignoring the base-state dependence), here it would be great to isolate the contribution from the difference of radiative transfer codes by interpolating (and extrapolating if necessary for surface and probably for CAM5 kernels) the three radiative kernels onto the output resolution of NorESM2-MM and redoing kernel decomposition calculations. I believe there are native model grid versions available for the three radiative kernels. With the obtained difference, it may be easy to determine whether the error is acceptable. For NorESM2-MM with a low model top, the authors could even simplify the isolation process by using 17-level kernels for the kernel decomposition calculations. Actually, the sentence in lines 173-175 suggests the difference for kernels from radiative transfer codes is small.

Line 146: I was just wondering if the authors have any idea why there is a close agreement between cloud adjustment from the two different methods.

Lines 146-148: If I understood Smith et al. (2020a) correctly, the cloud adjustment in Smith et al. (2020a) was obtained by using APRP for SW and PRP for LW, and there is no liquid water path adjustment for the CO₂ cloud adjustment calculation. It would be great to double-check it.

Lines 205-206 & 221-226: These sentences suggest a ~8K temperature difference at 10 hPa, and correspondingly, there is a 0.8 W m^-2 spread in the IRF. The resulting IRF sensitivity to temperature matches very well with the around -0.1 W m^-2 K^-1 (slopes) shown in Fig 1C and Fig S2 in He et al. (2023). As the online IRF difference (4 W m^-2) reported by He et al. (2023) includes both contributions from radiative transfer code difference and base-state difference, it may be better to compare the 0.8 W m^-2 spread here with the ~2 W m^-2 spread in offline IRF calculation with identical radiative transfer code (e.g., Fig 1B in He et al. (2023)). Meanwhile, I hope the authors can discuss cloud adjustment more. Apparently, we can see the stratospheric temperature dependence in both IRF and SARF. The offsetting effects of cloud adjustment are the reason why the stratospheric temperature dependence does not extend to the ERF. It feels like the cloud adjustment probably mainly occurs for high clouds, which could be closely related to the response of tropopause to ozone perturbation. It would be good if the author could decompose cloud adjustment into contributions from high, mixed, and low clouds, probably following Soden and Vecchi (2011). It would be even better if the authors had ISCCP simulator results archived. If the guess is correct, the authors could probably avoid the high cloud response (or tropopause response) by limiting the ozone perturbation within the upper stratosphere. In that case, the authors could probably get the stratospheric temperature-dependent ERF.

Lines 254-255: It is because of the offsetting effects of cloud adjustment.

Lines 255-256: It could be expected, considering the similarities between CESM2 and NorESM2.

Lines 263-265: I wondered why the authors expect a large spread in the magnitude of stratospheric temperature adjustment. It looks like Fig S6 in He et al. (2023) shows almost no difference in the stratospheric adjustments obtained from piClim-4xCO2/piClim-control and amip-4xCO2/amip simulations.

Recent studies have argued that a large component of the CO2 IRF spread in CMIP models can be explained by documented large spread in stratospheric base state temperatures. This manuscripts serves as an important follow-up, testing whether differences in stratospheric O3 can explain the documented stratospheric temperature spread and thus the CO2 forcing spread. The authors find the answer is no.  It’s a well written, interesting study. But before it can be accepted I recommend the authors address my comments below that touch on interpretation of results and providing more details/explanations in certain places.

General: I agree that Stratospheric O3 differences cannot explain the spread in 4xCO2 ERF, based on the results presented here. But I think the authors are too quick to discount the effect of differing Stratospheric O3 on the spread in IRF.  As noted a few comments below, I’d argue that a slightly deeper dive into the He et al. Results suggests the two papers may be more comparable than the authors suggest.  

Introduction Section: To address the relevance of this study’s results to the question of CMIP spread, it would be helpful answer how realistic is the range of 0.5 StratO3 to 1.5 StratO3 relative to the actual range of StratO3 across CMIP models. Is there a considerable spread in Strat O3 across CMIP models? I was under the (maybe incorrect) impression that O3 is prescribed in CMIP atmosphere-only simulations. In which case, the hypothesis that Strat O3 spread explains the CMIP Strat. T spread would be wrong. Some comments/explanation along these lines would be helpful.

Line 80-90. Although it’s clear if you read table S1, I recommend the authors make it clearer in this section of the text that stratospheric O3 is reduced (or increased) by 50% in both the perturbed 4xCO2 simulation and in the corresponding control pre-industrial simulation, thereby ensuring the new O3 filds act only to alter the base state and not as a forcing adjustments itself.

Line 150-190: I appreciated the authors nuanced discussion about the application of radiative kernels for diagnosing the stratospheric adjustment. Their arguments logically make sense. But do we have any proof that their estimate of the stratospheric adjustment using the CESM kernel is more representative of the model’s true adjustment compared to the previous uses of kernels applied in e.g. Smith et al.?  The fact that the residual-derived cloud adjustment matches the alternative Smith et al method is maybe promising, but as a residual calculation, it is difficult to pinpoint potential canceling biases. For instance, it’s possible both the stratospheric adjustment and some other adjustments have equal and opposite errors.  

If we assume the authors are correct in their statement that it is best to use kernels from the host model, it would be helpful if they also gave a recommendation about how kernels should best be used when being applied across multiple models to evaluate inter-model spread. Although its not a focus of this paper, a brief comment would be helpful since this is a common use of kernels and there is not currently a radiative kernel available for every host model.

Line 220-226: First, the authors state that their range in IRF across experiments of 0.8 W/m2 is much smaller than the 4 W/m2 IRF spread that He et al. Finds across the online double calls.  This is true. But the authors should keep in mind that He et al. Does not claim all of that spread is due to the base state. They claim “more than half” (presumably the r^2 ~ 0.67 is what they are basing this on) of the spread is explained by the base state but not all of it. I recommend the authors factor this in when comparing the He et al. result to their own findings.  

Further, I’d argue that a fairer comparison between the spread in this paper and the spread in He et al. would be a comparison to the offline calculations of their figure 1C (rather than their 1B) where the IRF spread is subject only to base state differences and not to differences in radiative transfer algorithms across models, as is the case in this present study.  In the He et al. figure 1C it appears ~14 degreesK  of 10 hPa stratospheric temperature spread across models corresponds to 1.3 W/m2 of IRF spread.  Since the 10 hPa temperatures in this study range from -3K to +4K relative to the standard case (line 205), and this corresponds to a 0.8 W/m2 spread in IRF across the experiments, it would appear the StratT vs IRF spread results are actually quite comparable between the two studies from this perspective.  Does this impact the overall conclusions that the authors would draw about the importance of StratO3 spread to IRF spread?  

Line 231-244: It is interesting to consider the relative importance of StratO3 effect on CO2 forcing through overlap with CO2 vs through stratospheric temperature effects. Do the authors have a relative sense of this? It’s difficult to imagine a setup that could address this for ERF, but for IRF one could presumably perform an offline radiative transfer calculation with PORT where StratO3_x0.5 or StratO3_x1.5 is imposed but Stratospheric temperatures are prescribed in all cases from a StratO3_x1 climate as a way to isolate the spectral overlap effects from the stratospheric temperature base state secondary effects.

Line 253-255: There appears to be a misinterpretation here. The fact that A_Tstrat remains the same size across experiments would actually support the IRF enhancement/reduction extending all the way to ERF rather than prevent it (As ERF = IRF + A_Tstrat + other adjustments). In order for the IRF enhancement/reduction not to extend to ERF, there needs to be an equal but opposite compensation in the enhancement/reduction of a different adjustment.  In Figure 3, this seems to occur largely through the cloud adjustment term.  i.e. the IRF is larger than the standard experiment for the StratO3x0.5 case while the A_c is smaller than standard. Likewise the IRF is smaller than the standard experiment for StratO3x1.5 while the corresponding A_c is larger than standard.  I recommend the authors rephrase this section to emphasize the A_c term changes rather than focusing on the static magnitude of A_Tstrat. I further recommend the authors explore why A_c has this apparent sensitivty to StratO3.  It would help us understand whether the ERFs lack of sensitivity is due to the specific characteristics of stratospheric O3 or if ERF is just not sensitive to stratospheric temperature base states more generally.