In the manuscript titled “ LISFLOOD-FP 8.2: GPU-accelerated multiwavelet discontinuous Galerkin solver with dynamic resolution adaptivity for rapid, multiscale flood simulation”, the authors develop the new LISFLOOD-FP 8.2 version integrates GPU parallelised dynamic and the DG2 solver (GPU-MWDG2) to simulate tsunami-induced flooding. It shows progressively larger speedups over the GPU-DG2 simulations from 𝐿 ≥ 10. There are still certain changes and clarifications that the authors should address prior to publication. There are still certain changes and clarifications that the authors should address prior to publication. I believe that the manuscript can be accepted for publication by the GMD after minor revision. Below, I have some general comments for the authors.

General comments:

• The paper describes an innovative GPU-MWDG2 solver, so section 2.1 is the core of the calculation method in this paper. To help readers understand the detailed clarification on certain algorithmic. It is recommended that the authors provide some key portions of the code or pseudo-code as appendix. This is merely a suggestion and does not affect the validity of the paper's arguments.
• The paper could benefit from a deeper analysis of the trade-offs between accuracy and efficiency when choosing different error thresholds (ε). The choice of ε = 10-4 vs. 10-3 shows efficiency improvements, more discussion is needed on when to choose one over the other in practical scenarios.
• Figure 7 and Figure 10 are comparisons between GPU-MWDG2 and GPU-DG2, there is no description of the dashed line in the figure caption. The comparison between the two in terms of computational performance is not intuitive enough.
• The paper touches on the scalability of the solver but could provide a more forward-looking discussion of future applications. For example, how would this solver perform in larger simulations involving urban flooding, river flooding that require coupling with other environmental models? A brief discussion of scalability in more complex, coupled systems could enhance the paper's impact.

Specific comments:

• It is very rare for DOIs and data links to appear in an abstract.
• Line #219-#220, ensure consistency in the formatting of references. For example, "Kesserwani et al. (2023)" is used multiple times but isn't always consistent in placement or citation style.
• Figure Legends Overlap: In some figures, such as Figure 4(b), the legends and lines overlap, making it difficult to interpret the data. Please revise the figures to ensure clarity.

Review of 

LISFLOOD-FP 8.2: GPU-accelerated multiwavelet discontinuous Galerkin solver with dynamic resolution adaptivity for rapid, multiscale flood simulation

This paper validates the accuracy and efficiency of a new version of the LISFLOOD-FP inundation model that provides dynamical multiscale grid adaptivity by incorporating the previously developed GPU-MWDG2 solver. The previous version of LISFLOOD-FP only allowed static adaptivity, based on the initial conditions.  

The results suggest that the new, adaptive, LISFLOOD-FP is both accurate and efficient (up to 4.5 times faster). The paper represents a significant advance in efficient flood modelling using the standard 2D shallow water equation model. I also believe the paper will be interesting for more general readers, who want to better understand dynamically adaptive methods.  

Most of my questions and suggestions are aimed at making the paper more understandable and higher impact by clarifying basic properties of the method, however I also have some concerns about the tolerance and validation of the method.

Questions:

1. The abstract should be revised to be clearer for non-expert users of the LISFLOOD-FP models.

(a) It would be helpful to specify that the model is based on the two-dimensional shallow water equations (not the multilayer three-dimensional shallow water equations used in ocean and atmosphere modelling).

(b) More details on the error threshold are needed in the abstract and Section 1.  Is epsilon a relative error threshold that controls all prognostic variables, or just some variables?  What does it measure or control? Or perhaps it is a relative error threshold for the tendencies? Please clarify what epsilon measures/controls and how it set.  See also question 3 below: the results don’t seem to show that epsilon controls the error of the prognostic variables.

(c) How is the refinement level L defined? Is it a dyadic (power of 2) refinement of a coarsest grid? What is the coarsest grid? How does the number of computational elements depend on L? Does the non-adaptive simulation use the same L (but with no adaptivity)?

(d) It would be helpful to make more general conclusions about the efficiency of the adaptive method, rather than reporting results for a specific example. What determines the refinement level where the adaptive method is faster? How should the tolerance epsilon be set to achieve an acceptable balance of efficiency and accuracy for a given application?

2. Introduction

(a) Par 3: Low order finite volume discretizations are typically used because the goal is to preserve various mimetic properties of the discretization (e.g. conservation of mass to machine precision, ensuring that there is nos spurious generation of vorticity from a uniform vorticity field). This is considered essential for climate modelling, for example.  Does LISFLOOD-FP discretely conserve mass and other mimetic properties? Does the adaptive version retain these conservation properties? If not, why are mimetic properties like mass conservation not important?

(b) Par 5: How should the number of retained computational modes scale with the error threshold? This can usually be calculated for adaptive wavelet methods, based on the order or accuracy of the wavelets and dimensionality of the problem (2 in this case).

(c) Par 5: What is special about L=9?  Can you make more general claims about efficiency? Is the time step fixed for all scales?

3. Section 3

The RMS errors presented in Tables 3 to 6 do not confirm that the tolerance actually controls the error of either the height or velocity variables.  A valid dynamically adaptive wavelet method should be characterized by the fact the tolerance controls the error: error should ideally be proportional to tolerance, or, at least the error should decrease significantly when the tolerance is decreased by a factor of 10. In many cases the results  show the error decreases by 10-30% or so, and in at least cases the error actually grows, which is concerning since it suggests that epsilon does not control the error of the simulation (at least for these choices of epsilon).  

These results merit much more discussion and explanation if they are intended to validate the error control of the adaptive method. It would be very helpful to consider a wider set of tolerances epsilon for large L (e.g. 1e-1, 1e-2, 1e-3, 1e-4, 1e-5, 1e-6 or another suitable set of 6 or more epsilon values) to properly understand how and if epsilon controls the error of the prognostic variables.