We thank the reviewer for the constructive comments, which helped us improve the clarity and presentation. We address each comment point-by-point below.

We indicate the reviewer’s comments in bold and the text modifications in blue.

1) Line 8: The “mSWE-GNN” developed by the authors stands for the “multi-scale hydraulic graph neural network”. While “SWE” may be short for shallow water equations, strictly speaking, it is not the same as “hydraulic”.

We agree that “SWE” refers to the shallow water equations, while “hydraulic” is a broader term. We modified “multi-scale hydraulic graph neural network” to “multi-scale shallow-water-equation graph neural network” as recommended.

2) Line 16, Figure 11, and Table 2: The Pearson’s r is not good measure of correlation in this case, because it is sensitive to outliers and is not applicable when two variables do not show a clear linear pattern. The Spearman’s correlation coefficient could be a better choice in this case.

We agree with the reviewer that Pearson’s correlation can be sensitive to outliers and assumes linear dependence. In the experiments, all data pairs for which a clear correlation exists (i.e., between CSI and ARME) tend to follow a linear relationship, as also suggested by similar values of both coefficients. In the revised manuscript, we now report Spearman’s ρ both in line 16 and Figure 11. In Table 2, we kept both metrics to present a more complete picture of the correlations.

3) Lines 25-28: It should be noted that the uncertainty in model evaluation should not be ignored given the sampling uncertainty over limited space and time. The authors can refer to the paper below for more information about the limitations of some commonly used evaluation metrics in flood modeling.

We thank the reviewer for this suggestion. We now explicitly acknowledge the limitations of deterministic evaluation metrics in flood modeling, which gives further motivation for requiring probabilistic flood maps.

Lines 26-28 now read as:

“Further uncertainties can appear when quantifying the statistical fit of a model with limited data and treating metrics as deterministic (Huang and Merwade, 2024).”

4) Lines 30-32: Too many references are used here. It is suggested to remove some old ones.

As recommended by the reviewer, we removed the older references in lines 30-32, keeping up to a maximum of two entries per uncertain input.

These lines now read as:

“Building probabilistic hazard maps remains challenging as the number of uncertain variables can be large, particularly for dike breaching, where additional geotechnical properties must be considered. Uncertainties include breach location (D’Oria and Maranzoni, 2019; Westerhof et al., 2023), breach width (Mazzoleni et al., 2014; de Moel et al., 2014), breach development time (Apel et al., 2006; Ferrari et al., 2020), failure time (D’Oria and Maranzoni, 2019), and failure mechanism (D’Oria and Maranzoni, 2019; Mazzoleni et al., 2014).”

5) It is suggested to add a list of acronyms mentioned in the manuscript. The full term of the acronym only needs to be presented the first time it appears, e.g., ARME and CSI.

We appreciate this suggestion. We added a list of acronyms at the beginning of the manuscript. In addition, we ensured that all acronyms (e.g., ARME, CSI) are defined in full only upon their first appearance, in the abstract, and in the conclusions.

6) Figure 1: It would be helpful to explain the terms like “Z_ee” in the figure or figure caption.

We have updated the captions of Figures 1 and 3 to explicitly define the symbol Z_ee (elevation of elevated elements).

Figure 1 caption (modified part) now reads as:

“… a) Hydraulic structures such as elevated elements and canals are inputs. The difference between elevated elements (z_ee) and the terrain (z_i) is treated as an additional edge feature. …”

Figure 3 caption (modified part) now reads as:

“… For each edge (i,j) that intersects an elevated element, we determine the feature as the difference in elevation from that of the element (z_ee) to that of the source node i (z_i).”

7) Lines 113-114: What is “p” in the superscript, and how to determine the value of “p”.

We have clarified that p denotes the number of previous time steps used as dynamic inputs in the autoregressive formulation. This number is a hyperparameter which we set to be p=2 (lines 264-265). We selected this value based on previous studies (Bentivoglio et al., 2025).

Lines 115-116 now read as:

“…U^t-p:t are dynamic node features for time steps t-p to t, with p indicating the number of previous times steps given as input, and E are edge features.”

8) Figure 3: Is it necessary to force the mesh to align with the boundaries of structures and riverbanks?

For the coarse meshes, it is not strictly necessary to align its boundaries with structures and riverbanks, as they only need to roughly represent that flow runs in a preferential direction (given, for example, by a canal). Preliminary experiments showed little difference between including them or not.

9) Line 163: The u0_hat instead of u0 are the predicted hydraulic variables.

We thank the reviewer for identifying this inconsistency. The text has been corrected to use û₀ to indicate predicted hydraulic variables.

10) Figure 5: Please add the units for both longitudes and latitudes.

We have added the appropriate units to both longitude and latitude axes in Figure 5.

11) Figure 7(d): What is the definition of the roughness coefficient?

We have clarified that the roughness coefficient we used is based on White-Colebrook’s formula. It is the one employed for running the official simulations used by the Dutch government (VNK). The proposed model works independently of the roughness coefficient type.

Figure 7 caption now reads as:

“… d) represents the distribution of the White-Colebrook roughness coefficient, with higher values indicating urban areas”

12) Table 1: The numbers after “±” are standard deviations or standard errors? For the MAE in the validation dataset, how could 1.41-1.72 < 0?

The values after “±” represent standard deviations, not standard errors. The reason why the standard deviation is higher than the mean is that there are some simulations with much larger errors, which skew the standard deviation to larger values than the mean.

We have clarified this explicitly in the table caption, which now reads as:

“Training and testing metrics for the mSWE-GNN on dike ring 41, reporting mean and standard deviation for the mean absolute error (MAE) and critical success index for a water depth threshold ). HD073, ND234, and ND111 are three test locations along the dike perimeter and RP stands for return period. Arrows indicate whether higher (↑) or lower (↓) values are better.”

13) Line 344: Please correct the text “outlier Contrarily”.

Thank you for catching this typo. The text has been corrected to read simply “Contrarily”.

We thank the reviewer for their detailed and insightful comments. We addressed each comment in the attached supplement.