Overall review

This paper by Pfleiderer et al. aims to improve our ability to decompose climate trends into thermodynamic and dynamical components, with a focus on surface temperature trends in the Northern Hemisphere. The first one is to determine whether statistical methods are able to quantify dynamically induced trends in climate model data by comparing their outcomes to a set of nudged climate models experiment, considered to be the ground truth. Once this is validated, the statistical methods and another set of nudged experiments are applied to ERA5 data to actually determine the contribution of dynamical changes to the surface temperature trends in the northern mid-latitudes.

The paper is highly relevant and timely, and it provides an important assessment of dynamical adjustment techniques. Beyond its specific results, the framework developed could be applied to a wider range of climate variables, such as precipitation or extreme events.

The use of nudged simulations with no external forcing is a particularly smart approach to isolate the dynamical influence on surface temperature trends. Since such experiments are difficult to construct for observational datasets (though the AMIP + nudging above 700 hPa approach seems promising), validating statistical methods is crucial, and this paper does so effectively.

The manuscript is generally well written, although it can be hard to follow at times. Some sections, particularly on the analogues method, would benefit from clearer explanations. Also, the two main objectives, though related, are presented somewhat independently and could be more tightly connected in the structure of the paper. For example the authors could emphasize that the first objective is used to strengthen our confidence in the second objective.

Despite some concerns I have about the paper (detailes below), I think this paper is almost suitable for publication in WCD, but requires some work, notably to improve clarity. For these reasons I suggest to accept this paper with minor revisions.

Main comments

1. Comparability between methods

One of my main concerns is the comparibility between the different statistical methods. Indeed, each method uses a different set of predictor variables:

• Ridge regression uses the streamfunction
• Circulation analogues use sea-level pressure
• Direct effect analysis and U-Net use z500

This makes it difficult to assess whether differences in performance are due to the method itself or the choice of input variables. It would be helpful for the authors to comment on this explicitly. If the best predictor was chosen for each method, this should be clarified.

2. Lack of information on trend estimation, significance and uncertainty

Maybe I have missed it but I couldn't find a mention on how the trends were computed. In addition, such a study would benefit from statistical tests on trend significance and uncertainty, especially for the second objective which aims to provide robust estimates. As all methods provide an estimate of surface temperature directly, trends statistics could be computed for all cases. Moreover, it might make sense to evaluate skill metrics only for statistically significant trends.

3. Section 2.3.2 (circulation analogues) lacks clarity

The description of the analogue method is quite confusing. As someone who is not familiar with circulation analogues, I cannot say I have understood what it is from that section. Please revise it to make it clearer. Here are the points that made it unclear to me:

• “Analogues” are not clearly defined when first mentioned (line 155).
• It is unclear what the 80 possible choices for analogues refer to - days, years, months?
• What are these 50 out of 80 choices? I did not understand this paragraph
•  Line 128: "Once the Euclidian distances are determined" at that point there is no indication that a Euclidian distance is computed, or why and on what it is computed.
• Line 169: analogues are now defined but this should be done earlier

Maybe this is also the case for the UNET paragraph, but as I am more familiar with UNETs it was easier to follow.

4. Are the UNET Predictions Truly Circulation-Induced Temperature Changes?

• Line 213 describes the UNET model as predicting a temperature field with an estimate of the daily non-stationary normal removed. However, this doesn't necessarily isolate the circulation-induced component. The paper assumes that the resulting anomaly is circulation-induced, but this should be justified more clearly.
• If the previous point is justified (which I am sure it is) why not use the method from Rigal et al. (2019) directly to estimate circulation-induced temperature changes?
• Is the UNET performing well to reproduce this anomaly field?
• Why not use the UNET to predict the nudged experiment directly, which serves as the ground truth for the comparison later

Also, it is unclear what “CESM2 transient simulations” refers to. Do these include historical + SSP runs?

Minor comments

• Table 1: I fail to understand how R2 values can be positive. Could you please explain?
• Figure 4: How are thermodynamic trends obtained? Are they estimated directly (e.g., from the ridge regression method) or as a residual (total trend minus dynamical trend)?
• Line 185: To be consistent with the text, maybe consider using Y_orth instead of Y_perp
• Line 270: “to weak trends” should be corrected to “too weak trends”.

Review of WCD paper “The contribution of circulation changes to summer temperature…” by. Pfleiderer et al.

Overall, the paper is well structured and well documents a thorough study on different methods of estimating the role of atmospheric circulation changes to trends in the northern midlatitudes.

My overall recommendation would be publication after some revisions, which are generally minor.

General remarks:

My main query with this paper is the interpretation of the nudged simulations as a “benchmark”. This is an excellent approach to include but I’m not wholly convinced that this is necessarily a gold standard in term of attributing the changes due to circulation.

The nudging approach is elegant, and the demonstration in Figure 2 clearly shows that impact of the thermodynamic forcing on the global scale. However, on smaller scales I am less sure that the nudging strictly represents the contemporaneous circulation driven anomalies. A couple of conceptual examples of the potential issues are as follows:

1. In Figure 3 the nudged anomalies are consistently higher than those predicted by the individual methods over the Eurasian continent in the summer. The nudging constrains all seasons (not just summer) so there are likely to be other factors that are modified by the nudging that contribute to these – particularly soil moisture but also other factors such as vegetation, snow melt etc.. These depend on seasons preceding the summer in question. In general these are small but there is the potential for these to have a local influence over time that systematically enhances the temperature response. I suppose these can be summarised as being model “feedbacks” (from other seasons and any associated integrated response) that are explicitly not captured by any of the statistical estimates but are implicitly included in the nudged “benchmark”.
2. The second point is regarding the nudging to winds in the lower troposphere – here the nudging is performed on short timescales and, despite only forcing winds, the dominance of thermal wind balance on synoptic scales means that the nudging will have an effective local temperature forcing. This adjustment will be fast but, for example, any thermodynamic feedbacks that occur between say the land and the atmosphere (for example the strengthening of an anticyclonic high over continents during summer) will show up as being due to the “circulation” when in reality there is a non-negligible impact from thermodynamics. These should not be as well captured by the statistical methods as the information and feedbacks are not directly included but must be elucidated from the data output. Of course, on global scales (i.e. in terms of GMST) this will have no impact but in terms of estimating the “circulation” contribution to local temperature changes, the thermodynamic contribution to thermal wind balance adjustment will be attributed to “circulation”.

Neither of these examples particularly undermines the nudged simulations but do highlight how they are fundamentally different from the statistical approaches, as they implicitly include more thermodynamic effects adn feedbacks.

This may explain why the distibutions of the trends are systematically underestimated (e.g. the distrubutions on the right of Figure 3 and in Figure D2) in all the statistical approaches as they do not include the feedbacks and adjustments that are implicit in the nudged runs. At present there is only a discussion of the limitations of the statistical methods but I think discussing the limitation fo the nudged approach would also be useful to include.

I am sure the authors can directly discuss and address these differences and I think this would strengthen the interpretation of the results.

Minor comments:

Figure 3: This is a bit messy in the version I have– more details on the KDE plots on the right would be usefukle (along with axis labels etc).

Section 2.3.4: I don’t quite follow why the SLP would not be detrended as the “forced response” is small. It this important? Surely it would be better to include, unless the results are sensitive to this? I also may have misunderstood this, in which case a brief clarification might help.

I want to end on a positive: I think this is a very interesting paper!