Based on the positive reviews and minor technical comments from the reviewers, I now request that the authors incorporate these changes into the manuscript. Please review HESS guidelines for the presentation of equations to ensure that the manuscript is properly formatted.

I thank the authors for the incorporation of most of the comments from the editor and reviewers; however, some comments from the editor and reviewers have not been fully addressed:

1) As noted in the Editor comments, the authors are to ensure that the manuscript adheres to all HESS guidelines found in: http://www.hydrology-and-earth-system-sciences.net/for_authors/manuscript_preparation.html. There are several aspects that do not appear to conform to these standards even in the revised version:

a) Given the large number of equations and variables in the manuscript, the authors adhere to all guidelines throughout the manuscript.

b) Abbreviations must be spelled out on their first introduction in the figure captions, tables, abstract, and main body of the text.

c) Figure captions must be stand alone and describe all aspects of the figures, including abbreviations. The first letter of the first word of the captions should be abbreviated.

2) As noted by Reviewer 2, the use of the English language is not perfect. The reviewer gave some examples of this that were corrected by the authors; however, these were meant as examples. I have found more in my reading of the revisions that are too numerous to outline. Please carefully read the manuscript with a keen eye towards grammar and wording. In some cases, sentences are missing the word "the" in front of nouns (see p. 1, line 26, should read "on the running mean...", and there is confusion of prepositions (see p. 2, lines 2 and 7, "to" should be changed to "with"). These are only examples and the authors should carefully read the entire manuscript to resolve grammatical issues and improve readability.

I believe, as do the reviewers, that this is a meaningful contribution to the literature and an important topic that is appropriate for HESS; however, the manuscript cannot be accepted until these issues are resolved.

Unfortunately, the authors did not respond to all of my earlier comments and I must return the manuscript again for minor revisions. Whereas the manuscript has been improved, there are still revisions needed and the manuscript cannot be accepted until these items are resolved.

1 - I previously asked the authors to please review the HESS manuscript guidelines to ensure that the manuscript was in compliance; however, there are many places where the guidelines have not been followed - particularly for equations and symbols. Specific guidelines for equations and symbols are below. The authors must take note particularly for items (a), (b), and (d). The notation used in the equations and text need to be revisited based on the guidelines.

The full set of manuscript guidelines are here: http://www.hydrology-and-earth-system-sciences.net/for_authors/manuscript_preparation.html.

"a. Equations should be numbered sequentially with Arabic numerals in parentheses on the right-hand side, e.g. (1), (2), etc. If too long, split them accordingly. If there are chemical formulae included (i.e. reactions), please number them (R1), (R2), etc. When using Word, the equation editor and not the graphic mode should be used under all circumstances.
b. Multi-letter variables should be avoided. Instead use single-letter variables with subscript (e.g. ERMS instead of RMSE, or ET instead of ET). Single-letter variables or parameters and user-defined function symbols should be italic (e.g. x, Y, β, f(x)). Multi-letter variables, if they cannot be avoided, should be roman.
c. Common, explicitly defined, functions should not be italic, whether their symbols are single-letter (e.g. Γ(x) for the gamma function, B(y, z) for the beta function) or multi-letter (e.g. ln x, exp(x + y)).
d. Textual subscripts or superscripts should not be italic (e.g. xmax, Tmin where "max" and "min" stand for maximum and minimum, respectively).
e. Mathematical constants should not be italic (e.g. e = 2.718…, π = 3.141…, i2 = −1). Also, mathematical operators should not be italic (e.g. dx in integrals and derivatives, Δγ for the difference operator on γ).
f. Vectors and vector functions should be bold and italic (for single-letter variables). In particular, vectors are usually denoted with lower-case letters (e.g. x, ω as vectors; f(x) as a vector function of a vector variable). Matrices should be identified in bold with upper-case letters (e.g. A as matrix; AB as the product of matrices A and B, AT as the transpose of A, and A as the determinant of a square matrix A).
g. To distinguish between random variables and their realizations, use upper-case symbols for the former and lower-case ones for the latter (e.g. P{X = x}).
h. Do not use the hyphen (-) as a minus or subtraction sign; use the en dash (–) instead. Also do not use the letter x or the symbol * as a multiplication sign; either use the symbol × or middle dot (·) between numerals, or use a thin space (or even no space) between variables.
i. For simple expressions in the body of the text, use slash (/) to denote division (e.g. (x + y)/2η) rather than a fraction with a horizontal division line."

2 - Please review again the requirements for figures. See last sentence below in the guidelines for figure composition.

"Figure composition: It is important for the production process that separate figures are submitted. Composite figures containing multiple panels should be collected into one file before submission. The figures should be labelled correctly with Arabic numerals (e.g. fig01, fig02). They can be submitted in *.pdf, *.ps, *.eps, *.jpg, *.png, or *.tif format and should have a resolution of 300 dpi. The width should not be less than 8 cm. A legend should clarify all symbols used and should appear in the figure itself, rather than verbal explanations in the captions (e.g. "dashed line" or "open green circles")."

3 - The grammar still needs improving. It is disappointing that there are so many errors remaining after several revisions. I recommend the authors read the manuscript again to improve clarity. Here are only some of the changes that are needed based on my reading. Please note that is only a partial list. Submit a version of the revised manuscript showing track changes so that I can confirm these changes were made and see evidence that other areas of the text were reviewed and revised by the authors.

p. 1,

l. 21: ‘ones’ to ‘results’
l. 23 and 25: ‘it’ to ‘the proposed technique’
l. 25 ‘values’ to ‘value’

p. 2

l. 12: add so that sentence reads “latitudes on a global scale”
l. 23: add so that sentence reads “referred to as the established approach”
l. 32: delete ‘approach’

p. 3

l. 5: sentence should read, “This technique is referred to in the text as…”
l. 21: You have already spelled out EVA earlier so only use abbreviation here.

p. 4

l 4: should read “has mean equal to zero and variance equal to 1”; the use of ‘null average’ is awkward
l 9: Move ‘for example’ in front of “A simple test”
l 11: The use of GEV and Gx is confusing. Choose one notation for the GEV and use throughout the manuscript
l 15: an example of where x and y are not italics and should be according to the submission guidelines

p. 5

l 8: Pgns does not appear to be defined

p. 6

l 5: x should be italics, add comma at the end of pgx(x), define “it”, change “that” to “thusly”
l 8: EA and EVA are very close to each other in abbreviation and could lead to confusion by readers. Consider changing. Remove quotes around ‘dual’
l. 17 x and y are not italics

p. 7

l 3: according to the manuscript guidelines, Eq. should be placed in front of (2)
l. 8: put commas around “respectively”
Question about notation: What does the ‘0’ in the subscripts mean?

p. 8

l 4: “about” to “of”
l 5: delete “the” in “variations in the climate”
l. 6: check guidelines if a posteriori needs to the italics. Also, the dash should be removed.

p. 9

l 5: “rough” is capitalized in the equations and should be also capitalized in the text
l. 8: Commas around “in general”

p. 12

l 15: Annual maxima of what?
l. 28: Should read “GEV and GPD”
l 28: Should read “Eqs. (7) and (15), respectively”

p. 13, l 13: What figure are you referring when you point to panels (c) and (d)?

p. 14

l 2: Should read: “error associated with the stationary…”
l 6: delete comma