Review of « Improving Statistical Projections of Ocean Dynamic Sea-level Change Using Pattern Recognition Techniques” by Malagon-Santos et al.

The paper investigates the benefit of using pattern recognition approaches to assess statistical regional sea level projections from coupled climate model outputs. The study shows that using EOF pattern recognition and low-frequency component analysis significantly reduce errors in pattern scaling of regional ocean dynamic sea level change. The authors apply those two methods on the large ensemble MPI-GE simulations. Each member has different initial conditions. Therefore, it is possible to assess the impact of ocean initial conditions on projected dynamic sea level change. The presented results highlight the need to apply such a pattern recognition methods to reduce errors in regional emulation tools of ocean dynamic sea level change especially when a few realizations are available because of the huge computation cost.

The topic of the paper is interesting as the future generation of AOGCM will increase both atmosphere and oceans spatial resolutions. Thus, a few simulation integrations will be preferred from large ensembles because of the computational cost. Therefore, this technique may be relevant for future sea level change investigations.

I find the paper well written. It is well organized. However, the methodology part could be improved as the methodology is not easy to understand especially for a non-expert in pattern filtering. I think the authors can provide more explanations to help the reader.

Overall, the paper is well supported but some parts are unclear. For instance, I struggle to fully understand and interpret Fig1 as it lacks of explanation in the caption (see my comment below).

I find the paper very technical and I wander if Ocean Science is the right journal to publish this piece of work. I recommend a major revision for the manuscript before a possible publication.

Major comments

• When using EOF decomposition, one strong assumption is that all the modes are independent (i.e., they are orthogonal to each other). Is it really the case especially at global scale? This might be discussed in the conclusion as a limitation of the approach.
• What do you mean by ‘well separated’? (L143) How is it performed? Are you sure the initial conditions are totally different and independent? Please, clarify.
• As GMTSLR is removed, the underline hypothesis is that the model conserves volume instead of mass. Is that right? If so, this is due to the Boussinesq’s approximation. This should be clearly stated to avoid any misunderstanding.
• MPI-GE description is too succinct. Please, provide more insights. There is no mention on the spatial resolution of the MPI-GE simulations especially for the ocean part. I assume that the ocean spatial resolution is about 1° meaning that the oceans have laminar flows. If so, what is the consequence when assessing the internal variability? Are not you underestimated it? Some studies have estimated the ocean-based internal variability from a large ensemble of forced OGCM. When increasing the spatial ocean resolution, the ocean-based internal variability increases in space and time. We can expect the same behavior for the coupled internal variability. I would appreciate some discussion on this specific point in the discussion’s section.

Minor comments

L54-63: When describing the drivers of regional sea level changes, one might want to know the associated time scales of each processes. Please, clarify. This would help the reader.

L66: What do you mean by natural variability? Could you define this concept? This would help the readers.

L75: What do you mean by ‘regional emulation tools’? Please, define any new terminology.

L109-110: How many members do you need to completely cancel out the internal variability?

L297: What do you mean by ‘conventional approaches’? please, clarify.

L323-324: ‘…that appear to be linked to volcanic eruptions’. Can you bring extra explanation here or a suitable reference?

Figure1: I do not fully understand this plot. Why Sk is decreasing when pattern number is increasing? Please, clarify it and maybe extend the caption.

Figure2: Please, change SD by standard deviation. This would help the reader.

Figure 4: Are the results consistent when considering RCP 4.5 an RCP 8.5? It would be interesting to add them into the supplementary materials.

In this study the authors used large ensemble simulations from one climate model to test to what extent pattern filtering approaches help to reduce internal variability in the dynamic sea level. They then discussed the benefits of using such approach to reduce uncertainties in pattern scaling of dynamic sea level change. This is an important research topic as large ensemble simulations are computationally expensive and usually we need to deal with limited or even single ensemble from climate model.

My main comment is that the reduced regression errors (residuals) in pattern scaling after applying the pattern filtering approach are well expected as the internal variability is reduced. I agree quantifying them is useful but the current manuscript fails to demonstrate more value for using such approach prior to pattern scaling, as claimed in the title and main message. Specifically, to what extent the application of pattern filtering could change the slope α of pattern scaling? Is there a significant change? Could you please show this change not only for global maps but also for time series in key regions as examples? Afterall this is what we really obtain and need from pattern scaling.

Some minor comments below,

L21 “model disagreement” is not straightforward here – please consider rephrasing. In the context of last sentence does it refer to “climate model” or “statistical model”? should “disagreement” be “uncertainty” here?

L26 “MPI-GE” might not be familiar to some readers

L26 “so that internal variability is optimally characterized while avoiding model biases” – please consider rephrasing. We can never avoid the model bias issue. My understanding is when using single model large ensemble simulations, the externally forced signal is optimally characterized, which provides important basis to test pattern filtering methods.

L27 “pattern filtering” do you mean the “two pattern recognition methods (L23)” or specifically the “signal-to-noise maximizing EOF pattern filtering (L24)”

L66 “natural” should be “internal climate” as used in most other places – please check throughout the manuscript for this.

Figure 3 It’s unclear (1) how the number of ensembles needed is calculated; (2) what does “forced response variance” refer to. Could you please make connections to equations in section 3?