The authors propose an improved version of a patch-based CNN that can include the terrain features at multiple scales, to predict the maximum inundation depths for several catchments and rainfall events.

Moreover, they show that the model benefits from transfer learning, even with little data.

The paper is overall well presented and with some interesting and original conclusions.

However, there are also several minor changes that I believe would further improve the strengths of the paper and that must be addressed before publication.

General comments:

In the introduction, there is no mention of other DL models for flood prediction.

I would add a longer section that includes the recent developments not only for CNN-based models with terrain generalizability. 

You could, for example, add some of the following:  (Fraehr et al., 2023; Bentivoglio et al., 2023; Berkhahn and Neuweiler, 2024; Liao et al., 2023; Burrichter et al., 2023; He et al., 2023).

In the introduction, you argue that there's a lack of generalizability to unseen case studies but then you also cite several papers that tackle this issue. While I agree that generalizability to unseen case studies is still an area of research, I would not frame it exactly as a gap in the research.

This applies also to the generalizability for both terrain and rainfall that you mention in the abstract (lines 3-5) as there are already papers that deal with it, such as do Lago et al. (2023).

Same goes for the idea of "contextual information". I would argue that this idea only/mainly applies to case studies with higher spatial resolution, as you have in your experiments.

Thus in does not seem fit for a gap in the literature. I would try to reformulate this gap by arguing that for high spatial resolution domains would benefit from including the information at lower spatial resolutions, because there are certain patterns in the topography that cannot be captured with patch-based models that use high-resolution data.

The paper misses all formulas employed in the model. Despite the sufficiently clear Figures 2 and S1, I would recommend adding the key equations employed by your model and also some equations for the metrics that you employ.

All testing metrics are reported via the MSE, which makes the physical interpretation unclear. I would suggest changing the testing metrics to either root mean squared error or mean absolute error, which can both be in meters instead of meters squared.

It's also not clear to me why you consider the MSE only for water depths larger than 0.1 m. This would make more sense for determining a spatial metric, which might be strongly influenced by those small values. But I would keep the regression metric (whichever you end up considering) evaluated over the whole domain, without thresholds.

Moreover, you should include some metric to assess the spatial accuracy, for example with the critical success index, which was used in several previous studies (e.g., Löwe et al., 2021; do Lago et al., 2023; Bentivoglio et al., 2023). 

Please also define all the metrics you employ before you discuss the results.

I think sections S1 and S2 can be merged within the main text, since they both include some useful information and they are not that long.

I also think Table S1 should be included in the main manuscript as it shows a valuable comparison with another model, which is generally lacking in the rest of the paper.

On this regard, I believe your paper would benefit by comparing with the study from Guo et al. 2021, which you cite several times. You also state that you outperform this model (line 350), so I would add a longer analysis if you want to claim that, comparing for example different metrics over the whole test dataset, on both models.

Specific comments:

Line 6: it is not clear what you refer to with contextual information. This becomes more clear only later on in the paper, but since it's one of your main improvements I would try to clarify it better also in the abstract. 

This idea of "context" also emerges when you describe your model in section 2. In a similar fashion, I would clarify better what you mean by context.

For example, in line 76 "... extract and combine the information from the high-resolution local patch, its context and the rainfall times series to emulate the corresponding flood map" the term context seems very generic. You could use the notion of multi-scale spatial features (that you use in line 79) to help you clarify (or substitute) your notion of context.

Line 54: I would add in the patch-based methods also the CGAN from do Lago et al. (2023).

line 71: I would add at least a reference here.

End of introduction: not necessarily needed but you could add a paragraph that specifies how the rest of the paper is structured.

Line 103: you mention that you include an RNN because it allows you to model rainfall for different events' duration, yet you only consider events of 1 hour. Moreover, depending on the type of RNN you are using (which is not clear from the architecture) you might have a number of outputs which depend on the length of your input sequence, despite it is true that your RNN in theory works with any input length. How would you deal with input hyetographs that have different durations?

Figure 2: I would add a reference to more complete version of the architecture that is in the supplementary material, as it helps clarifying how do the scaled dot-product attention and the multi-context fusion work.

I would also specify somewhere (and not only in the manuscript) that you don't only take the DEM as input, but also other several ones (despite obtained from the DEM).

line 107: I think that section S1 can be merged with section 2.5, since it is quite small and would help understanding right away what the normalized accumulated rainfall is.

Section S1: it is not clear if Pmin refers to the event with the least accumulated rainfall for all simulations (training and testing) or just the training ones.

line 108: adding the adjective "locality-aware contextual" to the output of the attention, makes it seem like there is another operation in between. Consider removing it for clarity.

line 110: please define what you consider as upsampling layer.

line 135: i assume that the upscaling is done via a sort of mean pooling, but in the text it's not clear if you are using another strategy.

line 147: i suppose you mean that the model should be equivariant to rotations, i.e., a rotation of the input should result in an equivalent rotation of the output.

It would be interesting to also see what is the effect of adding this data augmentation to your training dataset (either in the results section or in the supplementary material).

line 156: normalization and min-max scaling are not equivalent. Min-max scaling is a type of normalization. Please clarify it in the text.

sections 4 and 5.1 can probably be merged with section 3.

lines 210-211: the shape notation seems to range from 1 to 9 instead of from 1 to 3, cfr. Fig. 3. In general, the notation $P_ms$ seems confusing at times.

Figure 5: I am not convinced by the overlapping of pie charts and violin plots. I would either separate them in two figures so that the pie chart becomes clearer or improve the legend for the pie chart.

lines 230-237: I think Table S1 should be included in the main manuscript as it shows a valuable comparison with another model, which is generally lacking in the rest of the paper.

line 245: you mention that the resolution for Singapore is 2m. Does this mean that the large-scales are at 4 and 8 meters now? Shouldn't this affect the performance of your deep learning model, since you are capturing different processes now?

Section 6.1.1: did you also keep the same learning rate? Generally a high learning rate might cause your model's weights to deviate substantially from the pre-trained model.

Figure 7: I would specify that this figure is using the transferred model.

lines 367-368: I got a bit confused with the term different topographical features. You could maybe use some different term such as "a broader variety of topographical features".

lines 368-369: do you have any supporting data for this claim? I don't recall seeing in the manuscript any analysis on the amount of overlapping or over-sampling.

lines 386-392: I am not sure this analysis adds much to the discussion, though I agree that there is a lack of a common benchmark dataset.

Maybe consider also merging discussions and conclusions since there are some overlaps and the conclusions themselves are not too long.

Technical corrections:

line 43: there seems to be an extra "("

References:

Bentivoglio, R., Isufi, E., Jonkman, S. N., and Taormina, R.: Rapid spatio-temporal flood modelling via hydraulics-based graph neural networks, Hydrology and Earth System Sciences, 27, 4227–4246, https://doi.org/10.5194/hess-27-4227-2023, 2023.

Berkhahn, S. and Neuweiler, I.: Data driven real-time prediction of urban floods with spatial and temporal distribution, Journal of Hydrology X, 22, 100 167, 2024.

Burrichter, B., Hofmann, J., Koltermann da Silva, J., Niemann, A., and Quirmbach, M.: A Spatiotemporal Deep Learning Approach for Urban Pluvial Flood Forecasting with Multi-Source Data, Water, 15, 1760, 2023.

do Lago, C. A., Giacomoni, M. H., Bentivoglio, R., Taormina, R., Gomes, M. N., and Mendiondo, E. M.: Generalizing rapid flood predictions to unseen urban catchments with conditional generative adversarial networks, Journal of Hydrology, p. 129276, https://doi.org/https://doi.org/10.1016/j.jhydrol.2023.129276, 2023.

Fraehr, N., Wang, Q. J., Wu, W., and Nathan, R.: Supercharging hydrodynamic inundation models for instant flood insight, Nature Water, 1, 835–843, 2023.

He, J., Zhang, L., Xiao, T., Wang, H., and Luo, H.: Deep learning enables super-resolution hydrodynamic flooding process modeling under spatiotemporally varying rainstorms, Water Research, 239, 120 057, 2023.

Liao, Y., Wang, Z., Chen, X., and Lai, C.: Fast simulation and prediction of urban pluvial floods using a deep convolutional neural network model, Journal of Hydrology, 624, 129 945, https://doi.org/https://doi.org/10.1016/j.jhydrol.2023.129945, 2023.

Löwe, R., Böhm, J., Jensen, D. G., Leandro, J., and Rasmussen, S. H.: U-FLOOD – Topographic deep learning for predicting urban pluvial flood water depth, Journal of Hydrology, 603, 126 898, https://doi.org/https://doi.org/10.1016/j.jhydrol.2021.126898, 2021.

This paper proposes a new machine learning architecture for predicting pluvial flood maps with the aim of achieving better transferability of the models between catchments. The authors also explore the value of transfer earning when applying the model to a new city.

The paper is generally interesting and the suggested approaches are quite innovative. I do however have several major criticisms that I think should be addressed before publishing. These are:

1. The paper makes a number of methodological innovations, but their value is not demonstrated anywhere. How do we know if e.g. the combination of three encoders is responsible for the more spatially balanced prediction errors than Guo 2021 or the RNN time series encoder with normalisation? I think some comparisons between old and new model architecture that help us understand what has actually improved + why, should be included in the paper. The transfer learning results could be shortened to make space in the paper.
2. The use case of the approach is not fully clear to me. I can agree with climate impact studies, while I think that the value of urbanisation studies has not been demonstrated. I think the latter would require implementing some changes in the terrain or the runoff behaviour of the same city and testing if the model can still predict the flood maps. This can be addressed by either clarifying the framing in the introduction/discussion, or by including additional results.
3. Like R1, I also think that some of the supporting information clearly belongs into the paper (Section S2, Take S1)

Detailed comments

Line 58-66: Another approach to including context information is to engineer features that provide this information on the pixel level. For example providing flow accumulations or similar as input. I'm lacking a sentence on why you think this approach is not good enough and some references to related work (e.g. Pham 2020, Zhao 2020, there might be newer work that provides better examples)

Line 108: Section S1 belongs into the paper. Why is scaling applied to the RNN output (which will be in some latent space) and not the input?

Line 142: the reason for including imperviousness in some of the other models is that it enables us to distinguish that some pixels generate more runoff than others. That is not related to the terrain features that you describe here. In fact, as far as I can see, you are relying on the "glass surface assumption" when calculating runoff. It would be good to clarify this

Line 153: Actually, the UFlood paper makes quite a big effort to avoid overlaps between training and validation patches. You can criticise it for using the validation data for both test and validation, but the validation data were fully independent from the training data

Line 159: This is very interesting. It implies that the convolution kernels must be learning differences between the features, not the absolute values. I think this should be elaborated more in the paper. Do we also see better performance in the results for Zurich? Could we get the same or better results by using localized terrain data (terrain minus minimum elevation in the patch)?

Line 214: How do you define wet cells? Based on the labels, predictions or both?

Line 302:

Don't we see in the figures that the models even after transfer learning perform quite a bit worse than in Zurich, and therefore we have not yet succeeded in creating models that can be applied in other cities?

I'm addition, in Figure 7 I'm missing the results for Luzern and Singapore without transfer learning, so that we can see the impact of the transfer. 

References

Pham, B.T., Luu, C., Phong, T. Van, Trinh, P.T., Shirzadi, A., Renoud, S., Asadi, S., Le, H. Van, von Meding, J., Clague, J.J., 2020. Can deep learning algorithms outperform benchmark machine learning algorithms in flood susceptibility modeling? J. Hydrol. 592, 125615. https://doi.org/10.1016/j.jhydrol.2020.125615

Zhao, G., Pang, B., Xu, Z., Peng, D., Zuo, D., 2020. Urban flood susceptibility assessment based on convolutional neural networks. J. Hydrol. 590, 125235. https://doi.org/10.1016/j.jhydrol.2020.125235