Based on my own review and the review of Anonymous Referee #1, I believe the revised manuscript is now acceptable for publication in GMD. I have attached the review from Anonymous Referee #1 below, in case you would like to make any final revisions to the text before it is submitted for publication (however these modifications will not be subject to further review). Please note that the review below will be published as part of GMDD once the manuscript has been accepted for publication.

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Anonymous Referee #1

"A new and inexpensive non-bit-for-bit solution
reproducibility test based on time step convergence
(TSC1.0)" by H. Wan et al.


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General comments:

Overall this revision is much stronger than the original and the
presentation is improved. The addition of information on the PERGRO
test and its limitations in the context of CAM5 will be useful for
many readers. In addition, I think the revised pass/fail criteria
makes more sense in the context of time integration, and look forward
to further analysis in the future.

My first three main concerns (numbered as before) have been
adequately addressed:

(1) The method itself is now better described, and I appreciate the
addition of Section 5. Several issues are now noted as being planned
future work.

(2) The authors have done a good job clarifying the scope and
applicability of the method (e.g., section 2.1). I have a better
understanding of its utility.

(3) The experimental results section now better aligns with the scope
(some experiments have been added and some deleted - and the
discussion improved).


The response to concern (4) regarding the one-sided t-test still does
not entirely make sense to me." While I agree with this sentence in
the response (page 9): "In a non-answer-changing case, while ∆RMSD can
be negative by chance for an ensemble member, it is very unlikely that
it will be negative for all members", the statement may also be true
if you replaced the word "negative" with "positive". So that leads to
the question of what makes a positive deviation more likely than a
negative deviation?

I *think* the assumption being made is that a bug in the code could
not somehow make the time stepping more accurate - which is what is
needed to make ∆RMSD negative. While that makes sense from a
theoretical standpoint, in practice (because this is a chaotic
floating point simulation), wouldn't it be safer to use the
non-directed t-test? Further, the explanation in the response (bottom
of page 9) that negative ∆RMSD should not be tested with this method
because it's solution-changing, strengthens my opinion that a fail
should be issued in this case:

"The only situation we could imagine systematically negative ∆RMSD to
occur would be the implementation of a new and more accurate set of
time stepping algorithms that featured smaller sensitivity to the step
size change of 1 s to 2 s, but yet produced very similar solutions at
1 s time step when compared to the original code. Such a case of
algorithm update would be considered a substantial code change, so
methods like TSC and PerGro would not be the most natural tests to
perform since they are designed to assure that the solutions are
unchanged."


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Specific comments:

-Is TSC 1.0 available to download or is it only available by request
from the authors?

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Technical Corrections

p.3, line 28: "characteristics" => "characteristic"

p.11, line 23: Missing article at the beginning of the sentence
"One-sided test is ..."