|The manuscript has been substantially revised and most issues raised in the first round of reviews have been addressed. I think the study is certainly very interesting and worth publication. Some of the results are probably to be regarded as preliminary and will need further testing, but this is acceptable given the quite ambitious study carried out and the authors' comprehensive accounts of the limitations of their findings.|
This said, I think the manuscript could really do a better job at valuing the underpinning work if it was written in a more concise and clear way. Many sentences are rather long-winded and there are several language mistakes, including some potentially very misleading confusion in technical terms (e.g. "sensitivities" for "uncertainties" or "ranges" for "values"; some specific examples are given below). Overall this makes the text quite hard to follow. I think that the entire manuscript should be reread and revised before publication.
I also have few additional suggestions for improvement, described below. All line numbers refer to the version called "hess-2019-10-author_response-version1.pdf" (the one introduced by a short message to the editor Monica Riva).
1) P. 2 L. 39-75: I think this addition is a bit odd. The content is useful but the way it is placed here really breaks the flow of the Introduction. First, given that it is a comment on the limitations of Morris, I would place it after the use of Morris is presented in the context of this work (i.e. after lines 80-83: "...we present an application of the Morris method (...) to the Global Gradient-based Groundwater model ...") not before. Second, I would shorten it, and possibly move some of the more technical details to the methodology section (2.2.2). It is odd that 35 lines in the Introduction are dedicated to a detailed discussion of pros and contras of Morris method, while the general introduction to global groundwater models took less than 25 and the review of SA applications less than 30!
2) P. 6 L. 11-16. I would at least mention here that the robustness of parameter ranking will also be assessed, and that details of how this is done are in Appendix 1. This is an important detail of the methodology, and should at least be mentioned here. Also, either here or in the Appendix, it should be clarified where the distribution of mu* values, and hence their CIs, stem from - i.e. how bootstrapping works. I find Figure A1 somehow misleading. It seems to suggest that the CIs are relative to the distribution of the Elementary Effects (EEs) for a given sample, i.e. as if each white point referred to the individual EE calculated for a certain trajectory. However, I guess the distribution should stem from the re-sampling of the 1848 available simulations, i.e. each white point in Figure A1 is a different mu* (mean EEs) calculated from a different bootstrap resamples. This is crucial but is never really clearly stated, either in the main text or in the Appendix!
LANGUAGE AND TYPOS
P. 1 L. 20: remove "for a computationally expensive model"
P. 1 L. 40: add (I suppose): "... and CHANGES are projected to continue due to climate change"
P. 2 L. 20-22: "...have led to more widespread application e.g. (...) For this reason, existing studies of global models...". Something convoluted and unclear in this sequence. Maybe better: "... have facilitated their application e.g. (...) Still, existing studies of global models..."
P. 2 L. 105: "a Monte Carlo experiment to investigate sensitivities of simulated hydraulic head ..." This sentence is very confusing. It is unclear what it refers to and how this analysis is different from the subsequent Morris analysis. I think the confusion arises from the incorrect use of the term "sensitivities". If this sentence refers to Figure 4 and 5, then what is investigated here are the output "uncertainties", not "sensitivities", and the sentence should be rephrased as: "a Monte Carlo experiment to quantify uncertainty in simulated hydraulic head ...."
P. 3 L. 47: "calculated river discharge calculated by WaterGAP". Remove the first "calculated"
P. 3 L. 36: missing ")" after R
P. 3 L. 47: "h_swb" is undefined
P. 4 L. 4: "a flow from the cell to a surface water body is negative and positive if the opposite is true." why making things so complicated!? Replace by "a flow from the cell to a surface water body is negative and viceversa."
Figure 1: I would add "h_swb" in the Figure, given it is the most mentioned variable in the text, it would be good to have it clearly displayed in the schematic.
P. 5 L. 13: "the river conductance Criv in a steady-state groundwater model needs to be set in a way that the river is the sink for all the inflow to the grid cell (R and inflow from neighbouring cells) that is not transported laterally to neighbouring cells." Too long and hard to follow, please consider breaking into two sentences.
P. 5, titles of Sec. 2.2.1 and 2.2.2: "choice in " should be "choice of"
P. 5 L. 66: "we apply a basic sensitivity method" Given what follows, maybe better "we calculate a basic sensitivity index"
P. 6 L. 11: "To achieve that, mu* and sigma are presented in this study in ranks". Very unclear. If I was not familiar with Morris method and the parameter ranking, I would have a hard time understand what this means.
P. 6 L. 24: "my" should be "by"
P. 6 L. 33: "equally" should be "equal"
P. 6 L. 62: "we introduce the use of a Global Hydrological Response Unit (GHRU)." should be "we introduce the use of Global Hydrological Response Units (GHRU)."
P. 6 L. 68-71: "All multipliers for a given parameter for all regions are based on the same random distribution inside a given range of uncertainty for that parameter." Again very unclear. Looking at Table 1 I would say that the same random distributions (i.e. uniform with ranges given in Table 1) are used for the parameter multipliers in all GHRUs. Is this the point? Or something else?
P. 6 L. 78: "to the mean in a cluster" maybe "to the mean in that cluster"?
P. 7 L. 2-15. This paragraph is still very unclear. First, I would swap the order of presentation. In its present form, it is unclear where the number 1848 on L. 5 comes from. I would first introduce how you determine the maximum number of model evaluations ("For 7 parameters (without ocean boundary), n GHRUs... the total number of simulation (1848)." and then explain how you select the 42 optimised trajectories ("10,000 initial trajectories were sampled in total .... are selected (Ruano et al., 2012)". Also, in the sentence "We assume 42 for the number of optimised trajectories ...", I would clarify that this is the number of elementary effects and is the variable "r" in the formula that gives N (it may not be obvious to the reader not familiar with Morris).
P. 7 L. 21-24: "Each simulation was an OAT experiment (an extended explanation of OAT and other sensitivity experiment setups and methods can be found in Pianosi et al. (2016))." Why this comment here? It is very generic and does not seem appropriate for an "experimental configuration" section. Either make it more specific or move to the methodology section?
P. 7 L. 47: "(see Sect. 4)" I would remove the reference.
P. 8 L. 1-3. Confidence intervals and bootstrapping were never mentioned before! So this sentence can only be understood if in the point was anticipated in the methodology section (see also point 2 above).
P. 8 L. 65: "to analyse the outcomes of 1848 model realisations" Vague. I'd be more specific: "to quantify the output uncertainty as given in the 1848 available model realisations"
P. 8 L. 79: "in regions of the model where..." I suppose should be "in regions of the domain where..." (unless the sentence actually refers to regions of the model input-output response surface?)
P. 9 L. 34: "independently of the applied parameter ...". This wording suggests we are only looking at regions where 100% of MC realisations behave the same. Otherwise, it should be rephrased as "for most applied parameter ...". Also, I suppose "parameter ranges" should be replaced by "parameter values" (the ranges of variability stay the same, it's the sampled values that are changing, I guess?).
Caption of Table 3: " Percentage fractions of simulated cells with parameter sensitivity mu* and parameter interaction sigma per model output h and Qswb, where the respective output is most sensitive to the listed parameter." Very convoluted, please rephrase.
P. 11 L. 41-44: "The values shown in Fig. 10 (a) should be judged with caution as they also include the regions Fig. A2 shown to be unreliable. Reliability means that due to overlapping CIs (any overlapping) the ranking of the parameters can’t be clearly determined". Unclear. Maybe "Fig. A2" should be in parenthesis? What does the side note "(any overlapping)" is expected to point at?
Caption of Figure 9: "ranked by Sigma value" - maybe the capital sigma should be a small sigma?
P. 13 L. 24-25: "statistically zero sensitivity values (overlapping CI with zero)". Unclear what the problem is. If the sensitivity index has small CI centred around zero, I would conclude that that input factor is probably uninfluential. Why this result should be regarded as problematic? If instead the CI is very large, then the estimated sensitivity index could be statistically not very reliable, and that would be problematic - regardless of the fact that the CI is centred around zero or above. Pls clarify.
P. 15: L. 76: "a feasible the number". Remove "the"
P. 16 L. 20-22: "Results of the method of Morris need to be contemplated in a ranking based scheme that relies on metrics that summarize the calculated EEs." Vague and unclear, please clarify what a "ranking based scheme" is and which "metrics" are used, or rephrase the entire sentence.