Review of “Understanding biases and changes in European heavy precipitation using dynamical flow precursors” by Oldham-Dorrington et al.

This manuscript introduces a flow-dependent decomposition framework for analyzing heavy precipitation biases and forced changes in two major large-ensemble climate simulations (CESM2 LENS2 and MPI-GE). The paper classifies synoptic states using region-specific multivariate precursor patterns (Z500, U850, V850), enabling a novel partition of precipitation errors into dynamical (synoptic forcing occurrence) and conversion (local-scale processes converting forcing to precipitation). The authors apply this to 38 regions across Europe and all seasons.

Overall, this paper is impressively comprehensive, and the results reveal new insights into compensating biases, dynamical controls, and the physical mechanisms behind future changes in heavy precipitation frequency. The paper is clearly written, well structured, and methodologically rigorous. It will be of high interest to the climate dynamics, hydroclimate, and impacts communities. The identification of widespread compensating biases and distortions in forced changes is especially valuable for model evaluation, downscaling, and storyline applications.

I find the manuscript to be a strong and valuable contribution suitable for publication after minor revisions. My comments below aim to enhance clarity, interpretation, and broader applicability.

1. The use of the term “precursor” may inadvertently mislead readers into assuming that these synoptic patterns are derived from lead-time composites—that is, flow anomalies that occur prior to heavy precipitation. As currently implemented, the composites are constructed on the heavy precipitation day itself, meaning they represent heavy precipitation synoptic patterns rather than true temporal precursors. Although I understand the desire for continuity with earlier work (Dorrington et al., 2024), a short clarification of terminology would be helpful. Explicitly stating that the term “precursor” reflects the synoptic-scale controls on heavy precipitation rather than a temporal lead signal would prevent misinterpretation. You may also wish to reference the terminology adopted in Dorrington et al. (2024) while clarifying its slightly different meaning here.
2. A minor weakness of the manuscript is that it focuses almost exclusively on the occurrence (frequency) of heavy-precipitation days. Beyond Figure 2, there is relatively little discussion of the associated intensity (magnitude) biases or projected changes. While the emphasis on categorical heavy precipitation is scientifically justified, real-world hazards depend jointly on both frequency and magnitude. I recommend adding a short contextual discussion. Alternatively, the title and narrative could be adjusted slightly to emphasize “heavy precipitation frequency” to better reflect the paper’s scope.
3. The proposed dynamical and conversion decomposition relies on well-populated synoptic bins and robust estimates of the conditional probability as well as dynamical and conversion biases. The authors use 50-member ensembles from CESM2 and MPI-GE, but many modeling centers and CMIP6/CMIP7 simulations provide only a handful of ensemble members. To help readers assess the broader applicability of the framework, I encourage the authors to estimate the minimal ensemble size required to obtain stable decomposition results. Even a qualitative guideline or a discussion of how the required size depends on the choice of the number of synoptic bins (e.g., K = 5 K = 10) would greatly improve the usability of the method for other studies.

In short, this is a well-designed and insightful manuscript that advances our understanding of flow-dependent heavy-precipitation frequency biases and changes. With clarifications on terminology, broader discussion of intensity considerations, and guidance on ensemble-size requirements, the paper will be even more impactful and accessible to a wide interdisciplinary audience.

Review of "Understanding biases and changes in European heavy precipitation

using dynamical flow precursors" by Oldham-Dorrington et al.

The authors present an interesting framework to attribute climate model heavy precipitation biases over European regions to biases in different drivers and residual (nonlinear) terms, as well as to attribute changes in heavy precipitation to changes in drivers respectively.

The framework is comprehensive, useful and applicable to other regions and variables. It also allows for the identification of compensating biases. Overall this approach is a useful addition to the existing literature, but some clarifications about the context of existing research, the method and its limitations are required.

Major issues

1 .The authors are surprisingly ignorant of existing literature on trend and bias attribution. While the latter is indeed still limited, a large body regarding the first exists. A key methodology in this respect is dynamical adjustment, which aims at identifying (and removing) trends caused by large-scale circulation changes (Deser et al., 2016; Smoliak et al., 2015, see also Sippel et al., 2019, Vautard et al., 2023, and IPCC AR6 WG1 Chapter 10 for applications; it could be that some of the papers cited in this manuscript are also examples). A paper of particular importance here is the one by Pfahl et al (2017), decomposing changes in extreme precipitation into dynamic and thermodynamic components. While these studies have a different purpose than this one here, the approaches still deserve to be made explicit. 

The body on attributing local surface climate model biases to large-scale biases is much less developed, but there also initial studies exist (e.g., Respati et al., 2024 on drivers of tropical rainfall biases; Addor et al., 2016 and Maraun et al., 2021 in a bias correction context; Wang et al. 2014 on causes of SST biases). Relevant is also Maraun et al. (2017) who argue that understanding the causes of climate model biases is key to a credible bias correction.

These strands of literature need to be discussed in the introduction. 

More general, statements about "previous literature" (line 241) should be backed up by actual references to the literature. 

2. I am not quite sure whether equation A3 (line 579) really is useful to understand the influences of model biases on the representation of trends. In many situations, model biases may be time invariant, but, e.g, feedback processes can induce time-varying climate model biases (e.g. Maraun, 2012). Does equation A3 give useful results in such a situation? As far as I understand, biases are implicitly assumed to be time invariant.

3. Is it useful to apply PCA to create the scalar index defining the extremeness of the precursors? PCA is linear and based on the correlation matrix and may not capture the asymmetries and tail behaviour in the "precursor" time series. This choice should at least be discussed.

4. I am not convinced by the term "precursor". Precursor definitely has a temporal prediction aspect to it. E.g., there is a community working on identifying precursors to natural hazards such as earth quakes or health issues such as epileptic seizures. If I understand correctly though, the precursors are evaluated on the same day as the precipitation event, i.e., there is no prediction in time. I would suggest to replace precursor by predictor, which is commonly used in regression analysis and does not necessarily imply predictions in time. Another, even more neutral term would be covariate.

Further comments

Line 25: I am missing a discussion of large-scale circulation errors (and projection uncertainties) along the line of the discussions in Shepherd, 2014, in particular given the scope of the paper. 

Line 38: "enhancing some processes disproportionately" sounds odd.

Line 77: evaluate, not validate. A climate model cannot be validated, but only evaluated. 

Line 137: "described there in full" is not necessary.

Line 191: "categorical occurrence". This is tautological and sounds odd or pretentious.

Line 241: then cite the literature!

Line 252: "whereas MPI-GE struggles to sufficiently convert any synoptic precursor into heavy precipitation". This sounds overly negative and subjective. The difference between the two models is quantitative, not qualitative.

Line 253: "bias budget" sounds strange.

Figure 3: I am surprised by the inferred regions: e.g. heavy precipitation in East Anglia (highest for north-easterly flow) behaves very different to precipitation over the West of England, Wales or Ireland (highest for south-westerly flow). Why are they combined in the same region?

Figure 4: the labeling is odd. The i) (meaning 1) can easily be misinterpreted as the letter i. In the caption, replace quiver by arrow. You are talking to climate scientists, not mathematicians. 

Figure 5a,b: add ERA5 to label Psk

References

Addor, N., Rohrer, M., Furrer, R., & Seibert, J. (2016). Propagation of biases in climate models from the synoptic to the regional scale: Implications for bias adjustment. Journal of Geophysical Research: Atmospheres, 121(5), 2075-2089.

Deser, C., Terray, L., & Phillips, A. S. (2016). Forced and internal components of winter air temperature trends over North America during the past 50 years: Mechanisms and implications. Journal of Climate, 29(6), 2237-2258.

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Maraun, D. (2012). Nonstationarities of regional climate model biases in European seasonal mean temperature and precipitation sums. Geophysical Research Letters, 39(6).

Maraun, D., Shepherd, T. G., Widmann, M., Zappa, G., Walton, D., Gutiérrez, J. M., ... & Mearns, L. O. (2017). Towards process-informed bias correction of climate change simulations. Nature Climate Change, 7(11), 764-773.

Maraun, D., Truhetz, H., & Schaffer, A. (2021). Regional climate model biases, their dependence on synoptic circulation biases and the potential for bias adjustment: A process‐oriented evaluation of the Austrian regional climate projections. Journal of Geophysical Research: Atmospheres, 126(6), e2020JD032824.

Pfahl, S., O’Gorman, P. A., & Fischer, E. M. (2017). Understanding the regional pattern of projected future changes in extreme precipitation. Nature Climate Change, 7(6), 423-427.

Respati, M. R., Dommenget, D., Segura, H., & Stassen, C. (2024). Diagnosing drivers of tropical precipitation biases in coupled climate model simulations. Climate Dynamics, 62(9), 8691-8709.

Sippel, S., Meinshausen, N., Merrifield, A., Lehner, F., Pendergrass, A. G., Fischer, E., & Knutti, R. (2019). Uncovering the forced climate response from a single ensemble member using statistical learning. Journal of Climate, 32(17), 5677-5699.

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