Based on the updated text and the authors’ response to reviewers I suggest that the text is returned to the authors for major revision based on my comments. The text is in my opinion far from ready for publication. I will explain below:

• I fully agree with reviewer 1 that the methods used here need a thorough introduction, preferably in a separate methods section. The authors have largely ignored this reviewer suggestion because the methods are apparently described in a GJI paper under review. However, the GJI paper is not yet accessibly to Esurf readers, and, even if it was, the methods need more introduction here in order for this to a stand-alone-contribution. Please provide a methods section after the introduction in order to clarify to the readers how exactly the radial basis functions are used.
• The quality of the written English is still too poor, and it has not improved during revision. If improving the English is problematic for the author team they must seek professional help before resubmitting the text. I list a few examples below these general comments, but following up on those is not enough, as the text need thorough revision.
• The citation style is wrong in many cases, e.g. in lines 33, 51, 63, 129, 156.
• The text is in often fragmented with paragraphs of one or two sentences (e.g. lines 144-146, 273-277, 326-328).
• Regarding structure, I would like to see sections 2-5 as subsections of a results section.

line 24: Please add an extra s to ‘asses’.
line 34: ‘… highly accurately’ – please explain what you mean by this.
line 43: ‘…gain further access to mass transport’ do you mean something like ‘in order to gain further knowledge/insight/information on mass transport…’
line 51-55: This needs further explanation
line 63: ‘…has been applied by us…’ In this study? If so, present tense is more appropriate. If not please give reference.
lines 86-94: These bullet points were added in revision, but they are full of grammatical errors and typos.
line 112: doesn’t -> does not
lines 119-127: Why all the hyphens in this paragraph?
line 141: ‘thus’ -> ‘whereby’ and ‘was’->’is’
line 142: ‘is’ -> ‘are’
lines 144-146: This looks to be a figure caption in the wrong place.
line 172: delete ‘has’
line 176: delete ‘thus’
line 223: ‘it’s’ -> ‘its’
line 230: ‘find out’ -> ‘determine’
line 233 and elsewhere: ‘have been found’ – the use of passive voice should be reduced.
line 245: ‘Still it remains difficult’?
line 256: Please make sure to correct this one also
line 308: ‘Their’?
line 312: Please rephrase this too.

Many thanks for preparing the revised version of the manuscript.
As associate editor, I recommend the paper to be published.
However, it is not clear to me how the reference to the unpublished paper by yourself should be handled at this stage. The editorial office will guide us though this.

Dear Authors,
Thank you for all your hard work editing and modifying your paper. I am now delighted to inform you that it has been accepted for final publication in ESurf. There is one outstanding issue of how to cite an unpublished paper - that may become published by the time the proof reading process is finished - or the editorial office can advise (a pre-print server could be an alternative solution).
All the best and once again thank you,
Tom Coulthard