A two-parameter Budyko function to represent conditions under which evapotranspiration exceeds precipitation

Greve, Peter; Gudmundsson, Lukas; Orlowsky, Boris; Seneviratne, Sonia I.

doi:https://doi.org/10.5194/hess-20-2195-2016

Articles | Volume 20, issue 6

https://doi.org/10.5194/hess-20-2195-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

https://doi.org/10.5194/hess-20-2195-2016

© Author(s) 2016. This work is distributed under
the Creative Commons Attribution 3.0 License.

Articles | Volume 20, issue 6

Research article

|

08 Jun 2016

Research article |

| 08 Jun 2016

A two-parameter Budyko function to represent conditions under which evapotranspiration exceeds precipitation

Peter Greve, Lukas Gudmundsson, Boris Orlowsky, and Sonia I. Seneviratne

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Final revised paper (published on 08 Jun 2016)
Preprint (discussion started on 16 Jul 2015)

Interactive discussion

Status: closed

AC: Author comment | RC: Referee comment | SC: Short comment | EC: Editor comment

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RC C2948: 'Referee comment for "The Budyko framework beyond stationarity" by Greve et al.', Fernando Jaramillo, 03 Aug 2015
- AC C4187: 'Author response', Peter Greve, 09 Oct 2015
RC C3015: 'Review', Anonymous Referee #2, 06 Aug 2015
- AC C4188: 'Author response', Peter Greve, 09 Oct 2015
RC C4371: 'Interesting computation but (in my opinion) a flawed approach', Anonymous Referee #3, 23 Oct 2015

Peer-review completion

AR: Author's response | RR: Referee report | ED: Editor decision

ED: Reconsider after major revisions (05 Nov 2015) by Roger Moussa

AR by Peter Greve on behalf of the Authors (16 Dec 2015) Author's response Manuscript

ED: Referee Nomination & Report Request started (24 Dec 2015) by Roger Moussa

RR by Anonymous Referee #2 (22 Jan 2016)

Suggestions for revision or reasons for rejection

The authors have improved the manuscript, yet many major comments of the different reviewers were not correctly addressed/implemented. Overall the revision seems rushed.
I still believe that some of the derivation should be further explained and justified, in particular the assumption in eq. 6 dE/dEp=0, which we know is incorrect (Complementary relationship). Also the steady state assumption used on monthly time scales (even whil including storage) deserves a discussion. There are some implied time scale assumptions there (stepwise varying storage on monthly time scales or annual time scales whereas in reality E, P and runoff constrain the water balance and thus "y0".

Specific comments:
- l10: change beside precipitation: it is always precipitation that generates the storage, it is a matter of time scale considered. Maybe something like beside monthly precipitation (but this is specific to the monthly analysis)
- l11: upward rotation is unclear
- l13: in which monthly or annual E exceeds monthly or annual P
- l19: sth is missing here: Before and after Budyko ..
- l21: replace surprisingly
- l35: could be made, replace with has been made. L34 to 37 seem out of place
- l43: replace numerically reproduced by maybe best fitted (not the same expression)
- l46: steady-ste conditions is confusing because then there is a dS/dt equation. What about dividing into two sentences?
- l52: change beside precipitation (see above)
- in equation 2 you should include groundwater flow in and out (not storage of GW) and say that you neglect it or take large watersheds so that the contribution is small (perimeter vs area contribution) (this was in my previous review)
- l69: how do you define EP, there are multiple definitions (see Lhomme 2000) (this was in my previous review)
- You need to justify your steady state assumption (especially on monthly time scales), this is clearly not obvious.
- l78: Ep being a natural constraint: replace constraint by upper bound on
After eq 5 add i.e. in very humid environments
After eq 6 add i.e. in very dry environments
Eq 6 is wrong (see previous review), we know that based on the complementary relationship, the slope is only zero in very wet conditions, not dry ones.
Please justify more.
- l101: be more explicit: say that this is storage that you are capturing with y0
- l107: corresponding to the original Budyko function: not exactly: best fit
- l110->114: maybe you should mention how you can have both storage dependence and steady state assumption.
- eq 10 is wrong (mentioned in my previoius review) take two parabolic ciuves shifted and this is obvious. Instead: - (P-E)_min <= -P_min + E_max
- l169: play an important role in E and runoff
- l170-171: change besides P
-l204: reframe other water sources than P: be more explicit: this is storage that you are looking at
- l 175 for the Ep estimate say what assumptions are made on rs, ra and albedo
- l180: multi-year mean: replace by climatological
l189-191: The lower correlations are also due to phenology which is not included in your method and should be discussed (at least one sentence)

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ED: Reconsider after major revisions (25 Jan 2016) by Roger Moussa

AR by Peter Greve on behalf of the Authors (04 Mar 2016)

ED: Referee Nomination & Report Request started (12 Mar 2016) by Roger Moussa

RR by Anonymous Referee #4 (04 May 2016)

Suggestions for revision or reasons for rejection

A two-parameter Budyko function to represent conditions under which evapotranspiration exceeds precipitation
by P. Greve, L. Gudmundsson, B. Orlowsky, and S. I. Seneviratne Hydrol. Earth Syst. Sci. Discuss., 12, 6799-6830, 2015
based on hess-2015-234-author_response-version2.pdf

I have been asked to evaluate the above manuscript for final publication in HESS in view of the interactive discussion.
Overall I am quite positive about the achievements of the manuscript. The first major achievement is the derivation of the new seasonal time scale Budyko framework from quite general assumptions in line of the Fu 1981 derivation. The second achievement is that this framework allows to analyze the seasonal water balance as a function of the aridity index within a general Budyko framework.
While these achievements by itself should warrant publication in HESS, however, the authors did not satisfactorily address all critical comments of the reviewers. I came up with similar concerns when reading the revised version of the manuscript as the reviewers (whose comments I read afterwards). As the achievements are substantial, I believe it is sufficient to reformulate critical passages and add one or two paragraphs to the discussion. Therefore, I recommend acceptance, after implementation of the following critical points:

a) the framework is not predictive – if I understand correctly, the critical new parameter which is defined by y0 = E – P / Ep depends on E itself – therefore it can not be determined a priori. The Budyko function or the Fu curve with the commonly accepted value for w = 2.6 allows to predict E from P and Ep alone. Therefore the framework allows to analyse the seasonal course of E in hindcast as shown in Figures 7-9. As I noted earlier this is in itself quite an achievement (see Fig. 9). This point needs to be stated clearly and at central position within the manuscript – abstract – section interpreting the new parameter - conclusions.

b) In the abstract it is being argued that runoff assessment is critical. However, only E is being determined by the framework. Please show how runoff can be determined within the framework – it might be obvious but a worked example (in Michael Roderick style) for the two examples shown in Fig. 9 would be very beneficial and would clearly help the reader how to make use of the proposed framework.

c) Discuss what makes the proposed framework different from the ones cited in the introduction. This point was already remarked by the first reviewer but was not implemented.

d) The second reviewer asked if y0 is being determined for each month. In Figure 9 and 7 it seems that k and y0 are constant. Please make this point clear.

Minor comments
Figure 8b) (Original Budyko) → from the text it should be Fu 1981 curve.
Adjust the Short Summary

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RR by Anonymous Referee #2 (13 May 2016)

ED: Publish subject to minor revisions (Editor review) (16 May 2016) by Roger Moussa

AR by Peter Greve on behalf of the Authors (24 May 2016) Manuscript

ED: Publish as is (26 May 2016) by Roger Moussa

AR by Peter Greve on behalf of the Authors (27 May 2016) Author's response Manuscript

Short summary

The widely used Budyko framework is by definition limited to steady-state conditions. In this study we analytically derive a new, two-parameter formulation of the Budyko framework that represents conditions under which evapotranspiration exceeds precipitation. This is technically achieved by rotating the water supply limit within the Budyko space. The new formulation is shown to be capable to represent first-order seasonal dynamics within the hydroclimatological system.