The authors have provided a good response to the technical questions raised by the reviewers. The DEM optimisation method clearly has merit and the standard of the scientific work is good. I would welcome the publication of this article and research.

However, I still have some concerns over the presentation of the research. The language is difficult to follow in some locations and although copy editing will clearly improve this there are some locations where the meaning of the manuscript is open to interpretation. See specific comments below relating only to the abstract and introduction and comments by the reviewer.

Furthermore, the description of the code availability is too vague. Specifically, what are the third party components of the code, in what software was the classic CVT implementation made. What are the novel aspects of the code and what comes from a third party? The paper must comply with the GMD data policy on the link below and this section needs to be more informative than simply asking the reader to email the authors:

http://www.geoscientific-model-development.net/about/code_and_data_policy.html


Specific comments regarding section 1. Please apply the same reasoning to the other sections.

Abstract

“The topographic impacts on modifying Earth systems variability have been well recognised.” This would be simpler to understand as “The impact of topography on Earth systems variability is well recognised”

This sentence “Numerical schemes from Earth systems either use empirical parameterization as sub-grid scale and downscaling skills to express topographic endogenous processes, or rely on insecure point interpolation to induce topographic forcing, which create bias and input uncertainties” should perhaps read “Numerical schemes of Earth systems either use empirical parameterization at sub-grid scale with downscaling to express topographic endogenous processes, or rely on insecure point interpolation to induce topographic forcing, which create bias and input uncertainties”

“This article proposes a novel high-fidelity multiresolution DEM model with high-quality grids to meet the challenges of scale transformation.” I don’t understand the “with high quality grids”. Do you mean for generalising high quality topographic data?

Change “The cCVT model is then evaluated on real LiDAR-derived DEM datasets compared to the classical heuristic method.” to “The cCVT model was evaluated on real LiDAR-derived DEM datasets and compared to the classical heuristic method.”

Introduction

“However, as numerical simulation systems evolved to incorporate broader scales and finer processes to produce more fidelity predictions” I would consider using the wording more exact predictions rather than more fidelity predictions.

“Earth and environmental simulations usually adopt sub-grid scheme to exert topographical heterogeneity and rely on downscaling the finer observations to surface variables” Do you mean upscaling rather than downscaling. e.g. upscaling fine topographic observations to model surface variables. You meaning here has implication for the following sentences also.

“The topography are also commonly treated as a static boundary layer in dynamics simulations” should read “Topography is commonly treated as a static boundary layer in dynamics simulations”


“However, mesh from interpolated vertices does not necessarily comply with the terrain relief, and bed elevation errors are frequently reported as one input uncertainty” -> “However, a mesh from interpolated vertices does not necessarily comply with the terrain relief, and elevation errors are frequently reported as one input uncertainty”

“While there are many situations where dynamic conditions are stressed for stronger impacts on modifying predictions” do you mean something like “Although there are many situations where dynamic conditions have stronger impacts on modifying predictions”

Section 1.2

“with the effects that the main relief features strongly stressed while non-structural details are massively suppressed” - > “with the effects that the main relief features are strongly stressed while non-structural details are massively suppressed”

“map cognitive efforts are drawn to produce progressive data reduction” Sorry but it is not clear to me what is meant by map cognitive efforts are drawn


“Since the static topographic layer are commonly composed directly by DEM datasets to diverse simulation interests, maintaining precise surface approximation 5 for rigorous boundary conditions is more important than ‘sparse’ geomorphology representation.” - > “Since static topographic layers are commonly composed directly from DEM datasets for diverse simulation interests, maintaining precise surface approximation for rigorous boundary conditions is often more important than ‘sparse’ geomorphology representation.”

“The first class of approaches is due to the computational bottleneck consideration, that determination which combination of vertices to a TIN surface approximates the original dense DEM surface best needs exponential time” This sentence needs to be rewritten, the meaning is unclear.

Avoid the use of non-scientific terms like greedy, weeding

“The second class of approach is due to the consideration of TIN surface from feature points do not necessarily warrants best approximation to the original dense DEM, for feature points are commonly selected through some local metric.” I did not understand this sentence.

“The purpose of this article is to devise a multiresolution DEM model that considers optimized surface approximation and guaranteed grid quality. The quality grid is demanded by the aforementioned easy incorporation with the simulation systems. Multiresolution is an effective paradigm to model scale diversity (Du et al., 2010; Guba et al., 2014; Ringler et al., 2011; Weller et al., 2016), among those promising plans, we are especially fascinated by the centroidal Voronoi tessellations 4 (CVTs) method for the intuitive way to redistribute samples with a designated function (Du et al., 1999; Du et al., 2010; Ringler et al., 2011), and develop CVT to an optimized surface transformation method to realize multiresolution terrain model” - > “The purpose of this article is to devise a multiresolution DEM model that optimises surface approximation and guaranteed grid quality, where the quality grid is demanded by the aforementioned easy incorporation with simulation systems. Multiresolution is an effective paradigm to model scale diversity (Du et al., 2010; Guba et al., 2014; Ringler et al., 2011; Weller et al., 2016). Amongst a number of promising approaches, we are especially fascinated by the centroidal Voronoi tessellations (CVTs) method as an intuitive way to redistribute samples with a designated function (Du et al., 1999; Du et al., 2010; Ringler et al., 2011) to develop an optimized surface transformation method to realize multiresolution terrain models.”


“The selection of feature points have important morphological structures embedded, computed (such as D8 flow algorithm) or auxiliary input morphological lines have been proved to have significant influence on the quality of transformed DEM surface” I’m not sure what you mean here, should this read something like “The selection of feature points can have a significant influence on the quality of the transformed DEM surface by embedding morphological structures such as those from D8 flow algorithms and auxiliary morphological lines.”

“For the discrete TIN surface, we compute robust mean curvature as incident property. Upon this discrete spatial domain and property domain, the CVT loops and make discrete set equalized from both domains. Spatial equalization warrants a quasi-uniform quality TIN grid, while the intrinsic property domain equalization warrants distribution of the discrete facets conforms to inherent terrain variation. It thus a total different approach to DEM generalisation and we called it curvature CVT (cCVT)” I’m sorry but I don’t understand this sentence.

“Existing CVT implementation often undertake clustering approach. However, clustering over discrete sets suffers from numeric issues such as zigzag boundaries, invalid cluster cells (Valette et al., 2008), and limited grid quality.” - > Existing CVT implementations often undertake a clustering approach. However, clustering over discrete sets suffers from numeric issues such as zigzag boundaries, invalid cluster cells (Valette et al., 2008) and limited grid quality.”

Dear Xinqiao Duan,

Many thanks for your revised manuscript and please accept my apologies for the delay in processing. It is my great pleasure to accept the manuscript given the revisions you have made. I have a few technical points below relating to the conclusions that you might want to consider, however I believe the contribution of the article is now very clear.

Kind Regards,
Jeff Neal

Technical corrections

Change
"Although there are many situations where dynamic conditions are stressed for stronger impacts on modifying predictions"
to
"Although there are many situations where dynamic conditions are stressed as stronger impacts on predictions"



Conclusions

Change
"Evaluation of the cCVT multiresolution DEM model on Earth and environmental systems in wide ranged domains and scales is a topic for future studies."
to
Evaluation of the cCVT multiresolution DEM model on Earth and environmental systems over a wide range of domains and scales is a topic for future studies.

Finally, you need to give some context to the final sentence of the conclusions. I believe Ringler et al. are describing the tyranny of chasing ever finer resolution in earth system models at great computational cost. But this would not be clear from the sentence because tyranny could mean almost anything (for example that Earth system modelling is a bad thing per say), so this sentence would not convey the good point you wish to make.