The paper at hand presents an analysis of the influence of stochastic perturbations on the representation of wintertime blocking over Europe in a global climate model. First, it is shown that stochastic parametrizations decrease blocking frequencies, especially over Europe, and thereby deteriorate the representation of atmospheric blocking. Thereafter, the authors investigate mechanisms how the blocking frequencies over Europe are changed by the stochastic perturbations. They show that the mid-latitude jet stream and the tropical overturning circulation (i.e. the Hadley cell) are strengthened through SPPT, and argue that these changes in the mean winter circulation are responsible for the deterioration of the blocking representation. The authors claim that the changes in the midlatitude blocking representation originates from modified diabatic heating in the tropics, which impacts stationary eddies in the tropics and hence modifies the extratropical circulation, and emphasize the importance of the correct representation of the tropical circulation for atmospheric blocking.

The paper provides an interesting perspective on atmospheric blocking in the context of stochastic parametrization and is a valuable contribution to the existing literature, as it aims at providing a process-level understanding of how stochastic parametrizations affect the mean state of the model – an aspect which has not received too much attention. The presentation of the results (figures, equations, formulations, etc.), however, requires substantial revision, especially in the first parts of the paper.

General comment:

• The presentation of the results partly does not meet the required scientific standards. For example, for equations 1 and 2, the used symbols are not explained. For all figures, the units are not displayed at the color bar. In Figure 6, wind vectors are displayed, but the caption does not explain what they show. Most abbreviations are used without explanation (MJO, IFS; ECMWF, …). Together, all these aspects disturb the readability of the manuscript and can be improved without a lot of effort.

Specific comments:

• Line 8 (Abstract): I would not use the word “Surprisingly” here, as there is no indication for the reader why this should be surprising at this stage of the paper. I suggest to use a more neutral formulation, such as: “We show that the activation of …”.
• Lines 22-23: This sentence is not correct. Depending on the configuration of the blocking, winds can be particularly strong on the northern flank of the blocking (for example when the jet is deflected northward)
• Lines 27-29: It might be worthwhile to add that not only climate models, but also numerical weather prediction models struggle with predicting blocking over Europe (see for example Quinting and Vitart, 2019)
• Line 41: It was not the initial purpose of stochastic parametrizations to be an alternative to resolution increases, but to represent uncertainty in the unresolved scales. Please rephrase this sentence, as it is misleading.
• Lines 64-65: Adding to the discussion of possible dynamical reasons leading to changes of the mean state of the model, you might be interested in the two following references that deal with a process-based understanding of the impact of stochastic perturbations: Pickl et al. 2022, and Deinhard and Grams, 2023. Even though they focus on different processes, their findings fit well into the scope of your discussion.
• Lines 65-85: Consider reordering this paragraph. After line 65, it would be good to discuss the body of literature that has dealt with the impact of stochastic perturbations on different aspects of the model (i.e. MJO, ENSO, tropical cyclones, etc.) without a specific focus on the Climate Sphinx data set. After that, the research gap can be identified (i.e. connection to blocking), the question can be posed and the data set can be mentioned.
• Line 86: “With these goals in mind”: When implementing the previous comment, the reference to the research goals are much clearer.
• Line 102: How is the ensemble for the baseline simulation generated, when no stochastic perturbations are used? Please clarify.
• Lines 104-106: This sentence is not very precise. Consider rephrasing it along the following lines: “For each of the two setups, simulations have been run with different resolutions ranging from 125 km to 16 km, with decreasing ensemble size for increasing resolution.”
• Lines 109-110: Isn’t the main reason that blocking is the most frequent in winter and spring time?
• Lines 121-122: If the TL1279 simulation is not considered, please remove it from Table 1.
• Line 130: It might be helpful to add that by averaging all ensemble members, the low-resolution simulations have a larger weight than the high-resolution simulations.
• Line 138: I don’t really understand the sentence. What do you mean by “reference value for the 98^% confidence interval for 29 ensemble members”?
• Lines 147-148: This sentence is not very nice to read. Consider rephrasing this sentence along the lines: “Even though the SKEB scheme accounts for variability that is not represented in the deterministic version of the model, its impact on the model climate is negligible (Davini et al., 2017b).”
• Lines 150-151: Also here, I suggest reformulating the sentence to something like: “SPPT introduces variability by perturbing the deterministic parametrization tendencies of the temperature, specific humidity and wind fields as follows:”
• Line 158: In the context of your results, it is interesting to add that the magnitude of the SPPT-perturbations on average scale with the magnitude of the deterministic tendency, which are larger in the tropics than in the extra-tropics (see Leutbecher et al., 2017). Therefore, the most prominent effects of SPPT occur in the tropical regions.
• Lines 206-210: I cannot bring together your discussion of Figure 1a and the Figure itself. You write that the baseline model underestimates the blocking frequencies over Europe, but I mainly see white to light red colors over Europe in Figure 1a, indicating a slight overestimation of the frequencies compared to ERA5. You also describe that “the model significantly underestimates blocking at high latitudes in the Siberian region”, but overall, the reddish colors predominate. In contrast, the large biases over the East Pacific are not discussed at all. Please carefully review this paragraph.
• Lines 210-220: Even though this paragraph is important, it disturbs the discussion about the first results in Figure 1. I would suggest shifting the whole paragraph into the Methods section where also the blocking index is described, and once again refer to the issue here.
• Line 221: Again, I don’t like the term “surprisingly”, as it suggests that a different result is expected, but the reasons for the speculation are not clear to the reader. It would make sense to do this if you wrote something like “Unlike reported in REFERENCE, stochastic parametrizations do not improve the representation of … ”. However, if this is not the case, I would suggest to stick to a neutral formulation, such as “We show that stochastic parametrizations do not improve the representation of …”.
• Line 230: According to Figure 1, the blocking frequencies in the North Pacific are as large as in the North Atlantic, so please find a different motivation to focus on the North Atlantic region.
• Lines 240-244: It would be easier to understand the message of Figure 2a if the paragraph starts with a simple description of the differences between the baseline and stochastic experiments. For example: “The stochastic parametrizations result in a strengthening of the upper-tropospheric winds. This is evident for both the northern and southern hemispheres, even though they are in different solsticial conditions”.
• Lines 258-259: Can you give more details of why the strengthened Hadley circulation can explain the strengthened jet?
• Lines 260-261: As the zonal mean wind or the mean overturning circulation, also TKE and EGR are quantities to characterize the mean state of the model. Please rephrase this sentence.
• Line 268: “This is compatible with what has already been found by …”
• Lines 304-308: I suggest to shift this paragraph to the Methods section, in which the blocking index is introduced, and specify where you are using grid-point based frequencies and where you use other definitions.
• Lines 415-419: Here again, the findings of Pickl et al. 2022 are of interest, who discuss a very similar threshold-behaviour of rapidly ascending air streams that is observed with SPPT.
• Lines 449-451: I don’t understand the last part of the sentence, after the comma. Please rephrase.
• Line 452-454: I don’t fully agree with this sentence, as you do not verify if the stochastic parametrizations improve the Hadley circulation, the jet stream, etc. However, I agree that your analysis shows that the representation of blocking is affected by the tropical circulation, and hence it is important to accurately capture the latter.

Technical comments:

• Line 27: GCM stands for “Global Circulation Models” and not “Global Climate Models”
• Lines 29-30: Consider choosing a different formulation here, as it is not clear what you mean with “moderate”. Do you mean that only little progress has been made in the field of blocking?
• Line 39: “trade-off” instead of “trade off”
• Line 45-46: “more accurately”: The propagation of errors cannot be represented more accurately, but it can be accounted for.
• Line 54: “MJOs”: Introduce the term Madden-Julian-Oscillation after the first usage of the abbreviation. Further, there is no plural of the MJO (leave out the “s”).
• Line 56 and other instances: “Northern Atlantic”: Please use “North Atlantic”, as this is much more common on the literature.
• Line 62: Introduce “Integrated Forecasting System”
• Lines 56-58: Please rephrase the second part of the sentence, along the lines: “… weather regimes, which are recurring and quasi-stable patterns of regional weather conditions …”
• Line 75: “atmospheric circulation” instead of “atmospheric circulations”
• Line 89: “dynamical” or “process-oriented” instead of “mechanistic”
• Line 94: Introduce the meaning of Climate SPHINX at the earliest appearance.
• Line 99: “considered here” instead of “here considered”
• Line 120: “scale-aware” instead of “scale aware”
• Line 127: Delete “in fact”
• Line 138: Add information of the equation, i.e. what is <x₁>, σ₁
• Line 143 and 147: For the claim “The SKEB scheme”, you use different references in two occasions. Please either unify these citations, or leave them out the second time. Further, I placing the reference at the end of the sentence.
• Line 146: As above, please introduce the symbols and terms that you are using in the equation
• Line 156: Use “independent patterns” instead of “independent perturbations”
• Lines 166-170: You use the term “particular” very often in this paragraph. Please avoid such repetitions.
• Line 172: Add GHGN and GHGS in brackets after “northward” and “southward”, respectively.
• Lines 178 and 180: Add units after φ_N = φ₀ + 15 (i.e. φ_N = φ₀ + 15° lat) and in equation 6 (-10m °lat^-1)

• Line 182: “occurrence” instead of “timing and positioning”
• Line 230: “motivated” instead of “supported”
• Line 324: “it becomes clear that” instead of “it becomes clear how”.
• Line 332: “larger” instead of “greater”
• Line 337: “use” instead of “implementation”
• Line 432: “To determine underlying mechanisms …” instead of “Underlying mechanisms …”

References:

Deinhard and Grams, 2023: https://egusphere.copernicus.org/preprints/2023/egusphere-2023-1938/

Leutbecher et al, 2017: https://rmets.onlinelibrary.wiley.com/doi/abs/10.1002/qj.3094

Pickl et al, 2022: https://rmets.onlinelibrary.wiley.com/doi/10.1002/qj.4257

Quinting and Vitart, 2019: https://agupubs.onlinelibrary.wiley.com/doi/10.1029/2018GL081381

General comment

The paper assess the impact of stochastic parameterization on the blocking representation in a climate model. Although the study is in general well written, I have several concerns about the results and their interpretation, which are stated below.

Specific comments

Several times the authors state that the blocking frequency is underestimated in climate models, in particular over Europe (e.g. L28). This serves as a main motivation for the study. However, I don’t see this underestimation in the baseline simulations presented in Fig. 1. If anything I would say the blocking frequency is slightly overestimated over Europe. Furthermore, the baseline model seems to have a much larger problem over the north Pacific with respect to blocking. Hence, the motivation and the focus on the European/Atlantic region is not evident to me.

While the blocking frequency is compared to observations (ERA5), features of the mean state circulation (explored in Figures 2-5) is not. There, only the differences between baseline and stochastic runs are compared, which seem systematic and physically understandable, but rather small. I would like to see how these differences compare to the mean state model biases with respect to the ERA5 analysis.

The statement that an analysis grouped by resolution did not reveal significant differences (L130) deserves more explanation. This would be surprising and contradicting previous studies mentioned on L35, even on the same dataset. Figures to supposedly show this are presented in the supplement. However, I wonder if the figures S2-S4 are really correct. They seem bit-wise identical. After staring at them for several minutes I could not spot a single pixel which is different. This seems unrealistic and should be checked. If it is really true, I wonder what the explanation is and why the increasing resolution is here not beneficial for blocking simulation.

The authors state that there are several methods of blocking detection (L161), which can lead to significantly different results. The study however only uses one method. I wonder how robust the findings are and if they can be reproduced if another method was used.

It is not plausible that scales of 500-2000km, which are used in the SPPT correlation patterns represent the sub-grid variability (L158). I would rather argue that they represent flow-dependent biases of the parameterizations which are correlated over the size of weather systems. I think the authors should better explain why such large correlation patterns are used in the model setup and why the authors hypothesize that they may beneficially effect the blocking representation as suggested in L30-L47 (see also last comment).

Along those lines, I don’t see why the impact of the stochastic parameterizations, especially SPPT would decrease with increased resolution (L126). SPPT uses large spatial and temporal correlation patterns that modify the tendencies from the parameterizations in a similar way, regardless the resolution.

L206: I can’t follow the description here. Overestimation means red, right? So I do see an overestimation over the Pacific south at around 40°N. I don’t see an underestimation over Europe and also not over Siberia. I do see a pronounced underestimation over the north Pacific and Alaska. Very confusing.

L223: I don’t agree. The anomaly over Siberia has also gotten worse with the stochastic parameterization.

The authors consistently attribute the detrimental changes in blocking frequency seen in the stochastic runs to changes in the mean circulation, caused by SPPT. A retuning of the model is suggested (L441). Suppose one did that, do the authors expect any impact of the stochastic parameterization on blocking if the mean state was not changed? Are there any reasons for investigating this further, given that higher resolution simulations don’t seem to affect blocking (L130, or does it?) and stochastic physics is used as “a cheaper alternative to increasing resolution” (L41). Some discussion on those issues would be helpful.

Minor comments

L59: what is seen

The section “In this paper…” of the introduction should be the last part. I suggest to move the paragraph L76-L85 up.

L143: SKEB is not part of Buizza et al., 1999

L154: large-scale water processes -> microphysics

L181: I don’t quite understand this paragraph. In particular the choices of rejecting some events seem arbitrary.

L406: “anomalous”. Do we really know that? Or is it just altered compared to the baseline runs?

Some new results are also presented in the conclusion section (L428). I find that confusing.

Fig 1: I don’t understand what you mean by shaded contours.

Section 2.4: What is Fourier transformed? I assume only the time? And then it is transformed back with only time scales between 2-6 days maintained?