the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Quantifying the Regional Water Balance of the Ethiopian Rift Valley Lake Basin Using an Uncertainty Estimation Framework
Abstract. In Ethiopia more than 80 % of big freshwater lakes are located in the Rift Valley Lake Basin (RVLB), serving over 15 million people a multipurpose water supply. The basin covers an area of 53,035 km^{2}, and most of the catchments recharging these lakes are ungauged and their water balance is not well quantified, hence limiting the development of appropriate water resource management strategies. Prediction for ungauged basins (PUB) has demonstrated its effectiveness in hydroclimatic datarich regions. However, these approaches are not well evaluated in climatic datalimited conditions and the consequent uncertainty is not adequately quantified. In this study we use the Hydrologiska Byråns Vattenbalansavdelning (HBV) model to simulate streamflow at a regional scale using global precipitation and potential evapotranspiration products as forcings. We develop and apply a MonteCarlo scheme to estimate model parameters and quantify uncertainty at 16 catchments in the basin where gauging stations are available. Out of these 16, we use the 14 most reliable catchments to derive the best regional regression model. We use three different strategies to extract possible parameter sets for regionalization by correlating the best calibration parameters, the best validation parameters, and parameters that give the most stable predictions with catchment properties that are available throughout the basin. A weighting scheme in the regional regression accounts for parameter uncertainty in the calibration. A spatial crossvalidation is applied multiple times to test the quality of the regionalization and to estimate the regionalization uncertainty. Our results show that, other than the commonly used bestcalibrated parameters, the best parameter sets of the validation period provide the most robust estimates of regionalized parameters. We then apply the regionalized parameter sets to the remaining 35 ungauged catchments in the RVLB to provide regional water balance estimations, including quantifications of regionalization uncertainty. The uncertainties of elasticities from the regionalization in the ungauged catchments are higher than those obtained from the simulations in the gauged catchments. With these results, our study provides a new procedure to use global precipitation and evapotranspiration products to predict and evaluate streamflow simulation for hydroclimatically datascarce regions considering uncertainty. This procedure enhances the confidence to understand the water balance of underrepresented regions like ours and supports the planning and development of water resources.
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Interactive discussion
Status: closed

RC1: 'Comment on hess2021271', Anonymous Referee #1, 30 Jul 2021
This is a review of “Quantifying the Regional Water Balance of the Ethiopian Rift Valley Lake Basin Using an Uncertainty Estimation Framework” by Abraham et al. The paper presents a method to predict streamflow on ungauged basins in a region of Ethiopia. The method first uses behavioral parameter sets to identify parameters that are to be used in the regression analysis (for identifying relationships between parameters and catchment descriptors). A few parameter selection methods are proposed, which are then tested in regionalization using a leaveoneout approach. The authors then extend the study to include an analysis on the streamflow elasticity to better understand how changes in precipitation can affect variations in streamflow.
I found this paper to be informative about the study region, and I think there is potential to this paper. However, I think that there is a fair amount of work left before it can be considered for publication in HESS. Here are my concerns:
1. The literature review is quite outdated. Many seminal papers are presented in this paper, but a lot of work has been done in the past few years that could be used to set a clearer context to this study. For example, see Guo et al. 2021 for an uptodate review on regionalization approaches across the globe. This will also help contextualize the claim in lines 5759:
Guo, Y., Zhang, Y., Zhang, L. and Wang, Z., 2021. Regionalization of hydrological modeling for predicting streamflow in ungauged catchments: A comprehensive review. Wiley Interdisciplinary Reviews: Water, 8(1), p.e1487.
2. Lines 7789: This section is more of a description of the method. I suggest the authors better define the problem they are trying to solve and provide clear objectives. The way they are presented in the paper, the objectives are not clear to me.
3. Lines 106107: This sentence is unclear. Which global parameter sets? Which climate forcings? Please be specific. I suggest removing this "overview" paragraph and focus on a stepbystep description of the methodology. The steps can then refer to the figure to see where they fit in.
4. Figure 1: I think there are steps missing here. For example, how does the calibration fit into this process? I assume it is in the parameter estimation step, where the best set from the behavioral sets are identified, but that should be clarified. And the parameters are only computed on the gauged basins (obviously) but is there also a validation step?
5. Section 3.1: This section presents the data and catchment properties. I would suggest moving this to the “study area” section, since it deals with the data and properties of the study area.
6. Also, it would be important to state why the data are only available until 2007. Perhaps there was a decision to close gauging stations, etc., but for the reader it feels as if the study was completed on data that has not been updated in the past 14 years.
7. Lines 137140: Please state clearly which properties and data are used as catchment descriptors here. These sentences asis are pretty vague.
8. Lines 211213: Indicate that CV is the standard deviation divided by the mean.
9. The methodology presented in section 3.5 seems biased, in my opinion. At this stage, towards lines 230235, the authors explain that the three regression models (trained on parameters coming from the calibration period, validation period and “stable” parameters) are verified on the validation period only. This is problematic, because at this stage I could foresee that the regression model trained on the “best validation” parameter set would probably be the best during verification. This is because the hydroclimatic conditions play a major role in the ability to regionalize in the first place (as stated a bit further in the paper). So parameter sets that are “good” on this period, are probably going to be better in regionalization than parameters trained on other periods, simply because the hydroclimatic conditions are more similar by default (given the proximity of the catchments). I think that to even the field, the same process should have been completed by testing the regression models on the calibration period and the full period as well, to complete the experiment design. I would be fairly confident that the regression models would perform best on their corresponding training period. I suggest the authors include this analysis in a revised version to be able to analyze this aspect and contextualize the claim that one regression model is “better” than the others. This can be done by updating figure 5b, where we can see the effect I am referring to.
10. Figure 4: It is important to note that the small distributions of 5, 8, 13 and 15 are caused by the fact that they barely hit 0.5 NSE, meaning that only a few parameter sets are even allowed in this analysis. Whereas catchments with higher NSEs have many more parameter sets that are above 0.5. Perhaps one approach would have been to keep only the top 0.1 NSE from the maximum or something similar. Why keep parameter sets that have NSE values of 0.5 if some runs give 0.7 / 0.8 NSE? It seems that these are less “behavioral” than those at 0.7 if the maximum is 0.75. Perhaps keeping a fixed range vs their maximum value would allow for a better comparison.
11. Following comment #10, line 275276: “The parameters in these catchments remained insensitive” should be revised. It is not that they are insensitive. It is that the only few parameter sets with NSE > 0.5 had to have those parameter values.
12. Figure 5 is extremely vague for me, I am not sure what I am looking at even after reading the text, legend and caption a few times. Please consider displaying in another fashion or providing a more detailed interpretation.
13. Lines 297 – 315: I think these results should be provided with some sort of note that they are strongly dependent on the available dataset and that they must be taken with a grain of salt for the abovementioned reasons: 1 Not a lot of training data; 2 some catchments have a large spread of possible values due to having a NSE>>0.5, whereas others have NSE barely above 0.5, which plays on the identifiability of parameter sets.
14. Figure 8: Here the CVs are not clear to me. Why do 2 neighboring catchments have similar elasticities, but have CVs that range from essentially 0 to 180% ? a CV of 180 means that the standard deviation is 1.8x the average, so I am supposing that the precipitation is extremely low there? and neighboring catchments are very different in this regard? Please provide a bit more guidance to clarify.
15. Line 361: “With an average decrease of 0.40% from calibration to validation…” What exactly does this represent? 0.40% of the NSE value? Of another error metric? Please specify.
16. Lines 367369. Please revise following my comment #9.
17. Lines 379388: This section is restating the results. It would be beneficial to restructure the text to focus on the lessons learned from the experiment and dig deeper into the results to explain them and find links with the literature. this entire paragraph (lines 379389) only has one such sentence of interest, the last one that compares to the Beck et al. 2016 study.
18. Lines 414415: Was it really well identified, or is it simply that most parameter sets were barely able to provide 0.5 NSE (and looking at figure 3, it would seem that catchment #15 did not attain 0.5 at all in calibration)?
19. Line 442: “regress” à regression?
20. Lines 484485: This sentence kind of pops up from nowhere and has little relevance to the rest of the paper. I would suggest removing it.
Finally, the paper should be proofread by a professional English speaker as there are quite a lot of syntax errors which sometime distract from the content. In a similar vein, it is more typical to use a neutral and objective writing style to "depersonalize" the text. Instead of writing "we use the HBV model...", try to use "the HBV model was used...". I am unsure of the official HESS policy on this, but it is good practice.
Citation: https://doi.org/10.5194/hess2021271RC1 
AC1: 'Reply on RC1', Tesfalem Abraham, 06 Oct 2021
We thank Reviewer 1 for the thoughtful suggestions and constructive comments that we believe highly strengthening the quality of our study. We structured our responses directly below each reviewer comment in bold font.
This is a review of “Quantifying the Regional Water Balance of the Ethiopian Rift Valley Lake Basin Using an Uncertainty Estimation Framework” by Abraham et al. The paper presents a method to predict streamflow on ungauged basins in a region of Ethiopia. The method first uses behavioral parameter sets to identify parameters that are to be used in the regression analysis (for identifying relationships between parameters and catchment descriptors). A few parameter selection methods are proposed, which are then tested in regionalization using a leaveoneout approach. The authors then extend the study to include an analysis on the streamflow elasticity to better understand how changes in precipitation can affect variations in streamflow.
I found this paper to be informative about the study region, and I think there is potential to this paper. However, I think that there is a fair amount of work left before it can be considered for publication in HESS. Here are my concerns:
We thank Reviewer #1 for understanding the potential ideas that we tried to explain throughout the manuscript. We will incorporate all the concerns arising from the review to complete the manuscript.
1. The literature review is quite outdated. Many seminal papers are presented in this paper, but a lot of work has been done in the past few years that could be used to set a clearer context to this study. For example, see Guo et al. 2021 for an uptodate review on regionalization approaches across the globe. This will also help contextualize the claim
in lines 5759:Guo, Y., Zhang, Y., Zhang, L. and Wang, Z., 2021. Regionalization of hydrological modeling for predicting streamflow in ungauged catchments: A comprehensive review. Wiley Interdisciplinary Reviews: Water, 8(1), p.e1487.
We agree and will add more recent literature on regionalization to explain in more detail the research gaps that we address in our study including the study by Guo et al. (2021). We will clarify that, other than previous regionalization studies, we consider three possible sets of model parameters and evaluate them for their adequateness for regionalization, and use the results of multiple spatial splitsample tests to quantify the uncertainty that goes along when regionalizing parameter sets from a low number of catchments. In addition, we tried to show that globally available precipitation and potential evapotranspiration data sets can be used for regional modeling studies.
2. Lines 7789: This section is more of a description of the method. I suggest the authors better define the problem they are trying to solve and provide clear objectives. The way they are presented in the paper, the objectives are not clear to me.
Thank you, we will modify this paragraph, to make sure that our research problems and objectives are clearly stated.
3. Lines 106107: This sentence is unclear. Which global parameter sets? Which climate forcings? Please be specific. I suggest removing this "overview" paragraph and focus on a stepbystep description of the methodology. The steps can then refer to the figure to see where they fit in.
The Reviewer is referring to the statement "We apply global parameter sets and climatic forcings for…". We will clarify it by defining what we mean by global parameter sets and climatic forcing at this point.
Also, we agree with the comment and will remove the overview paragraph and provide a detailed description of the overall methodology. We will make sure that Fig 2. is referenced in the appropriate location in this section.
4. Figure 1: I think there are steps missing here. For example, how does the calibration fit into this process? I assume it is in the parameter estimation step, where the best set from the behavioral sets are identified, but that should be clarified. And the parameters are only computed on the gauged basins (obviously) but is there also a validation step?
We assume the reviewer is referring to Figure 2 because Figure 1 mentioned above is only a description of the study area. We will make sure to include the missing steps mentioned by reviewer #1. We will update the flow chart by adding the best parameter estimation steps from calibration, validation, and stable parameter sets in the “Parameter estimation in gauged catchments” box. In addition, we will clarify the best parameters selected from the validation steps.
5. Section 3.1: This section presents the data and catchment properties. I would suggest moving this to the “study area” section, since it deals with the data and properties of the study area.
Thank you – we will move that section accordingly.
6. Also, it would be important to state why the data are only available until 2007. Perhaps there was a decision to close gauging stations, etc., but for the reader it feels as if the study was completed on data that has not been updated in the past 14 years.
This is a good point. We explain that the streamflow data we collect from the Ministry of Water Irrigation and Energy (MoWIE) in Ethiopia ends in 2007. After this period, administrative structural change was made and individual basin authorities are given the mandate to collect and manage the data. Due to such changes, a long period (20082015) of data is still not available for the user, and the available ones from 2016 up to now are of poor quality than the ones we choose for our study period (19952007).
Therefore, we will make sure to update this information.
7. Lines 137140: Please state clearly which properties and data are used as catchment descriptors here. These sentences asis are pretty vague.
We will add more detail to the section to clarify the catchment descriptors that are used.
8. Lines 211213: Indicate that CV is the standard deviation divided by the mean.
We will define CV as the standard deviation divided by the mean.
9. The methodology presented in section 3.5 seems biased, in my opinion. At this stage, towards lines 230235, the authors explain that the three regression models (trained on parameters coming from the calibration period, validation period and “stable” parameters) are verified on the validation period only. This is problematic, because at this stage I could foresee that the regression model trained on the “best validation” parameter set would probably be the best during verification. This is because the hydroclimatic conditions play a major role in the ability to regionalize in the first place (as stated a bit further in the paper). So parameter sets that are “good” on this period, are probably going to be better in regionalization than parameters trained on other periods, simply because the
hydroclimatic conditions are more similar by default (given the proximity of the catchments). I think that to even the field, the same process should have been completed by testing the regression models on the calibration period and the full period as well, to complete the experiment design. I would be fairly confident that the regression models
would perform best on their corresponding training period. I suggest the authors include this analysis in a revised version to be able to analyze this aspect and contextualize the claim that one regression model is “better” than the others. This can be done by updating figure 5b, where we can see the effect I am referring to.Thank you for these helpful suggestions. It is correct that the procedure we applied to evaluate the regionalization performance was done only for the validation phase by considering this period to be a prediction phase. We recognize that the hydroclimatic conditions of each evaluation period could potentially affect their performance. We will therefore repeat the evaluation reserving one independent time slot different from the currently used calibration and validation periods to independently evaluate the three different regression models. We will carry out additional evaluations for the calibration period and for the whole simulation period as well to compare the performances in each period.
We will also update Figure 5b, by including the evaluation of regionalization performance in the calibration periods and for the whole simulation periods.
10. Figure 4: It is important to note that the small distributions of 5, 8, 13 and 15 are caused by the fact that they barely hit 0.5 NSE, meaning that only a few parameter sets are even allowed in this analysis. Whereas catchments with higher NSEs have many more parameter sets that are above 0.5. Perhaps one approach would have been to keep only the top 0.1 NSE from the maximum or something similar. Why keep parameter sets that have NSE values of 0.5 if some runs give 0.7 / 0.8 NSE? It seems that these are less “behavioral” than those at 0.7 if the maximum is 0.75. Perhaps keeping a fixed range vs their maximum value would allow for a better comparison.
Thank you for this important point. As stated by reviewer #1, we used behavioral parameter sets resulting a NSE above 0.5 resulting in different remaining numbers of parameter sets. For catchments #5, #8, #13, and #15, 741, 25, 593, and 2,877 parameter sets remain after applying the threshold. With 593 parameter sets and larger, we have reason to assume that the distributions of model parameters and NSE values of catchments #5, #13, and #15 are not biased by a low sample size despite being just slightly above the 0.5 NSE level. We will provide this information to the revised manuscript and add to the discussion of the revised manuscript that the distributions derived from the remaining parameter sets of catchment #8 might be biased by a low sample.
However, we prefer to remain with the thresholdbased separation of behavioral and nonbehavioral parameter sets as a thresholdbased approach helps to explicitly state under which minimum performance requirements, i.e. NSE ≥ 0.5, our regionalization by the CVweighted regression was conducted.
11. Following comment #10, line 275276: “The parameters in these catchments remained insensitive” should be revised. It is not that they are insensitive. It is that the only few parameter sets with NSE > 0.5 had to have those parameter values.
We will make sure to revise as suggested.
12. Figure 5 is extremely vague for me, I am not sure what I am looking at even after reading the text, legend and caption a few times. Please consider displaying in another fashion or providing a more detailed interpretation.
Thank you. We will prepare Figure 5 again in a more readable format and clarify it in the caption.
13. Lines 297 – 315: I think these results should be provided with some sort of note that they are strongly dependent on the available dataset and that they must be taken with a grain of salt for the abovementioned reasons: 1 Not a lot of training data; 2 some catchments have a large spread of possible values due to having a NSE>>0.5, whereas others have NSE barely above 0.5, which plays on the identifiability of parameter sets.
We will rewrite this paragraph to clarify that our results are only based on available streamflow data and on the global forcing datasets.
14. Figure 8: Here the CVs are not clear to me. Why do 2 neighboring catchments have similar elasticities, but have CVs that range from essentially 0 to 180% ? a CV of 180 means that the standard deviation is 1.8x the average, so I am supposing that the precipitation is extremely low there? and neighboring catchments are very different in this regard? Please provide a bit more guidance to clarify.
Thank you! These are important questions. The reviewer is referring to the extreme differences that we found for the wettest year CVs resulting in neighboring catchments. The differences in CV are found for the ungauged catchment numbers 22 and 28 and gauged catchment #05 in Figure 8. As we explained in lines 440443, the precipitation in the ungauged catchments number 22 and 28 is very low compared to gauged catchment #05 as shown in Table S2 and Table 2. In addition, the catchments properties in the ungauged regions are highly different that influences the 14 sets of model parameters derived from the regionalization that increased the resulting CV values. We see extreme differences in annual precipitation values of 928.9 mm, and 631.7 mm in the ungauged catchments number 22 and 28 respectively that is highly different from 1319.6 mm in the gauged catchment #05 (Table S2 and Table 2). Such extreme differences in precipitation together with other catchment properties will cause high variability of the regionalized discharge even in the neighboring catchments. In addition to precipitation variability, this effect is linked with the remoteness of the most of gauged catchments used to establish the regional model as we noted in lines 440443. We will expand our elaborations accordingly in the revised version of the manuscript.
15. Line 361: “With an average decrease of 0.40% from calibration to validation…” What exactly does this represent? 0.40% of the NSE value? Of another error metric? Please specify.
Thank you. We meant the change of the average NSE values from calibration to validation by “an average decrease of 0.40 % from calibration to validation” it is. We will make sure to clarify this.
16. Lines 367369. Please revise following my comment #9.
Will do.
17. Lines 379388: This section is restating the results. It would be beneficial to restructure the text to focus on the lessons learned from the experiment and dig deeper into the results to explain them and find links with the literature. this entire paragraph (lines 379389) only has one such sentence of interest, the last one that compares to the Beck et al. 2016 study.
Thank you for the suggestion! We will update this paragraph accordingly making sure to cite relevant literature supporting our experiment.
18. Lines 414415: Was it really well identified, or is it simply that most parameter sets were barely able to provide 0.5 NSE (and looking at figure 3, it would seem that catchment #15 did not attain 0.5 at all in calibration)?
With 2,877 parameter sets with NSE ≥ 0.5, we believe that the derived distributions are representative and that our conclusions on the identifiability of the model parameters for catchment #15 are valid. Please see our response to comment 10 of this review.
19. Line 442: “regress” à regression?
Yes.
20. Lines 484485: This sentence kind of pops up from nowhere and has little relevance to the rest of the paper. I would suggest removing it.
We will remove the sentence.
Finally, the paper should be proofread by a professional English speaker as there are quite a lot of syntax errors which sometime distract from the content. In a similar vein, it is more typical to use a neutral and objective writing style to "depersonalize" the text. Instead of writing "we use the HBV model...", try to use "the HBV model was used...". I am unsure of the official HESS policy on this, but it is good practice.
Thank you. We will perform a professional language check. In addition, we will recheck the HESS policy for the writing style. Both styles are quite often used in different scientific journals and we picked the preference of using the first person pronoun.
Reference
Guo, Y., Zhang, Y., Zhang, L. and Wang, Z.: Regionalization of hydrological modeling for predicting streamflow in ungauged catchments: A comprehensive review, Wiley Interdiscip. Rev. Water, 8(1), 1–32, doi:10.1002/wat2.1487, 2021.
Citation: https://doi.org/10.5194/hess2021271AC1

AC1: 'Reply on RC1', Tesfalem Abraham, 06 Oct 2021

RC2: 'Comment on hess2021271', Anonymous Referee #2, 26 Aug 2021
This manuscript was challenging to assess. The transferability of model parameters calibrated at gauged locations to ungauged locations using a regionalization approach where parameters are estimated using catchment properties able to estimated at the ungauged catchment is, in many ways, wellworn territory, as the authors also note (L4558). Much of the discussion in Section 5.2 also points to results that are consistent with previous studies. In my opinion, there has been inconsistent success demonstrated in previous studies as to the utility of this approach and the results presented here are no different than previous studies have found.
The question then is both whether the approach presented here represents such a difference from past studies as to be a substantial departure from past practices that it would be of value to report the results and that the study area and catchments are sufficient to make broader conclusions about this potential new approach.
From what I am able to understand about the approach and the catchments, neither of these meet the criteria so as to make a substantial and broader contribution to our understanding of why or how we might improve on regionalization approaches for parameter estimation at ungauged locations.
My recommendation is based on a number of what I see as serious methodological and evaluation questions as well as a highly complimentary presentation of a limited application of the approach to only a small number of catchments. I describe these issues in more detail below. If the manuscript does receive a recommendation other than Reject, I also offer additional minor and editorial comments that the authors need to consider in their revision.
(1) Broader contribution of the work
(1a) The use of weighted least squares (L200), although not necessarily a substantial advance, is what I believe to be the novel aspect of the study. Perhaps if this were emphasized more in the introduction and concentrated in more detail with the existing studies, it might become more clear that this is a more substantial contribution that the impression I was left with. Otherwise, this being mentioned is more detail so later in the discussion paper (in the methods) contributes to this point being lost. I would also be more explicit as to how this work differs from Wagener and Wheater (2006) and the followon studies that have cited that paper.
(1b) I do not agree that this work is novel because these approaches have only been applied in datarich regions (L5658). In my opinion, the reason these methods have been applied in datarich areas is to test the limits of these approaches. Even then, the results have certainly been mixed. Certainly, you could have chosen a more datarich area to test this approach and then removed streamgauges to understand the effects of gauges on the performance of the method.
(1c) Linked to Comment 1b, it is difficult to make broader conclusive statements about the utility of this approach when only 16 (or 14) catchments are being used. Either way, for a regionalization study, 1416 gauges is a very limited number. I realize that 2 catchments were removed because they were poor performing, which reduced the number of catchments to 14. I am not sure if removing these 2 catchments was the correct thing to do here; are they poorly performing because the underlying model is not a good representation? Were these locations removed just to improve your own study results? It seemed as though there was not a solid technical reason to remove these gauges from the study.
(2) Methodological and evaluation concerns
(2a) I missed where nonlinear regressions are being used in conjunction with weighted (linear) least squares (L200)? I see later in L218 that the nonlinear regression is discussed but with not much justification or explanation as to why this is the case.
The form of Equation 10 looks like the form of a regression equation when the regression was performed in log space and then transformed back to normal space. In other words, the logs of the response and predictor variables were taken to linearize the relation between them (to better ensure the assumption of a linear relation for the regression) and then the regression was performed on the logtransformed variables.
Of course, an additive model in log space is a multiplicative model in normal space. So to get the values back to normal space, Equation 10 is what the regression equation looks like when the additive linear model is retransformed back to normal space.
Seeing that you do not mention anywhere that you performed the regression on the logs of the response and predictor variables, I am not understanding why you would apply the nonlinear equation shown in Equation 10 for this reason. More justification is then needed for the application of Equation 10 to the data.
(2b) Keep in mind NSE values less than 0 have the interpretation that the mean of the data is a better model than the model being proposed (in this case, the regionalization model is worse than simply using the mean of the data as the model). NSE values less than 0.5 are likely poor fits and those less than 0.25 are approaching the case where would have been better off using the mean of the observed data instead of the regionalization approach. You make the statement on L383 that “79% of the catchments had a NSE > 0”; however, I do not believe this is a statement that puts the method in a positive light. Surely you could find a simpler model (even the drainage area ratio, perhaps) that would achieve the same success as having 80% of the model results better than using the mean of the data. The reverse of the statement on L383 means that 3 catchments (20%) of the 14 catchments did have an NSE < 0 using this regionalization method. How would one in practice guarantee that they were applying the regionalization to an ungauged location where the method would not provide a worse estimate than the mean of the data?
(2c) In calculating the NSE based on the actual values of flow, what were the range of flow values? If no attempt to balance the weight of the high and low flows in the NSE calculation, the NSE itself would be most affected by the fit of the model at the highest flows, and thus the NSE may only be a reflection of how well the parameters are estimating flows for the largest flows. For example, a difference of 0.1 cms and 5 cms would be a poor fit but if your high flow values are large (on the order of 100s or 1000s of cms) a difference of 4.9 cms would register as an excellent fit for NSE and this fit  simply by the numerical calculation of the NSE  would swamp any of the fits at the low flows since the differences squared would be so much less. Would it not be better to compute the NSE on the logs of the streamflows? Or at least split the flows into high, low, and mid flows so that these issues of scale are not affecting the interpretation of fit?
(2d) There are no regression equations provided or regression diagnostics for the equations so that one could assess whether these are valid regression equations with statistically significant explanatory variables. To use these regression equations in prediction mode and calculate uncertainty and prediction intervals (which is done in Section 4.2), the behavior of the regression equations must adhere to the properties of a linear regression (statistically significant explanatory variables, homoscedastic residuals, uncorrelated and normallydistributed residuals, and uncorrelated explanatory variables).
(2e) In Equation 8, the weights are described as 1/CV (the reciprocal of the CV; L213). I was having difficulty understanding this. The CV = standard deviation / mean; the reciprocal is then mean / standard deviation. The weights in a weighted least squares regression are, ideally, 1 / variance. How then were you able to achieve a weight equal to 1 / variance by using the inverse of the CV? This needs to be clarified in more detail so the reader can follow along.
(2f) For insensitive parameters (Figure 4), such as Mmaxeas, it seems it would be advantageous to incorporate this knowledge somehow into your regionalization scheme, although it would be unclear how this would hold up for ungauged locations. On L432433, the statement is made “Our study shows the insensitivity of model parameters to be related to catchment properties.” I am not sure how that can be. If a parameter is insensitive to model calibration, then it would have no preference for the value; therefore, why would one expect this parameter to be estimable or predictable? Would it not be better to just simply randomly generate a value for this parameter from a uniform distribution of values given the parameter range in Table 3?
Then in an ungauged location, how would one be able to predict whether this was a catchment that was insensitive to the parameter Mmaxeas or if it was one of the 3 catchments (figure 4) that was highly sensitive to this parameter?
Could you simplify your regionalization by only regionalizing sensitive parameters and then assigning a random, uniformly distributed value to the insensitive parameters?
(2g) The use of the word “stable” parameter set is not very clear. The definition of the “stable” parameter set is the set of parameters that “shows the smallest difference between the calibration and validation NSE”. But this does not consider also picking the parameter set with the highest NSE as well. It also does not explain how the validation period has a higher NSE than the calibration period for some catchments. Lastly, how does this criteria help in determining the best parameter set for regionalization? What is the benefit of transferability when you have a “stable” set of parameters at one location? In other words, what would be the guarantee that a parameter set will work well at another location just because it is “stable”?
(2h) Section 3.5: I am not understanding the validation and selection of the parameter sets (L229233). From what I could understand, the parameter sets are tested on the validation phase and in leaveoneout mode. What is the leaveoneout method not sufficient itself to assess the performance of the method? Also, it would seem a longer period of calibration (one that includes both of what you term the calibration and validation periods) provide better parameter estimates? I am not understanding why the leaveoneout approach to measure uncertainty is not enough to evaluate the approach?
It is also unclear in the methods when calibration and validation are used. You could use Figure 2 to clarify this. From my reading, in Figure 2, you could modify the box “regional regression” to read “regional regression using calibration parameters” and then “evaluation of the regression procedure using validation and leave one out”. Although, as I note, I do understand why the validation and leaveoneout are both used.
(3) For these methodological reasons given in (2), there are a number of questions related to the results and interpretations:
(3a) Figure 3 shows that the model performs better in the validation phase for some catchments, which is quite puzzling. Why would parameters perform better under validation rather than calibration for some catchments? I believe this needs to be explained thoroughly, unless I am not understanding the methods, in which case, this needs to be better explained in the methods.
(3b) The sections on elasticity and uncertainties would need to be evaluated after the comments in (2) are addressed, as I am not sure the methods themselves were applied in a manner consistent with the assumptions of linear regression nor am I certain the nonlinear regression was needed because a logtransform of the data did not appear to be used.
(3c) Figure 5a: Please add a 1to1 line on the figure so that the reader can determine for themselves how much worse the regionalization method performs. By presenting the x and yaxes at different starting locations, it gives the impression that the methods are somewhat similar, unless the reader looks carefully at the axes values.
(3d) The conclusions discuss how identifiable parameters are able to be reasonably well reproduced but one cannot know a priori which parameters are identifiable at an ungauged location. How would one be able to apply this conclusion in practice then, when a leaveoneout approach is not possible? How would one know which parameters are sensitive and insensitive and at which catchments are there exceptions? Otherwise, this proposed method does not seem to very useful in practice.
(4) The data statement is inadequate. Please note the EGU data policy: https://www.hydrologyandearthsystemsciences.net/policies/data_policy.html. Having the streamflow data “available upon request” is not consistent with the EGU data policy. If the data are not publicly accessible, a detailed statement as to why this is the case must be stated. Otherwise, the data needs to be placed in a public repository and cited.
Minor Comments:
L152: There should be a clear statement here that these 3 parameters are also calibrated, much like it is stated in line 169. Consider modifying it to read “Three calibrated parameters…”
Table 2: The headings are not formatted for easy readability and cut off midword.
Figure 3  add the abbreviations Cal, Val, and Stb to the caption.
Line 361: Decrease of 0.4% in what?
Line 367: What model was 3 regressions? Were there not 6 parameters to estimate via regression? Or do you mean there were 3 explanatory variables in each regression model? If the equations were shown, this would help clarify the number of regressions.
L368: What is the “optimal regional model”? I have not seen this term defined anywhere else in the text?
L369371: How is the “spatial crossvalidation” different from the “LeaveOneOut method”? Only the leaveoneout method was described earlier as a validation method. In L377378, how could a robust spatial crossvalidation be completed with only 14 (or 16) catchments?
L373: The text states that “this method is more stable and more resilient to errors…” but an explanation would be needed here, as I am not convinced this is the case.
L379: Change to read: “A scatter plot of monthly NSE values between parameters estimated from the model calibration and parameters regionalized from the regression equations show…”
Lines 446452: No evidence is offered to support these points.
Citation: https://doi.org/10.5194/hess2021271RC2 
AC2: 'Reply on RC2', Tesfalem Abraham, 06 Oct 2021
We thank Reviewer 2 for her/his comments and suggestions that will highly strengthen the quality of the study. In the following, we show our responses directly below the Reviewer’s comments in bold font.
This manuscript was challenging to assess. The transferability of model parameters calibrated at gauged locations to ungauged locations using a regionalization approach where parameters are estimated using catchment properties able to estimated at the ungauged catchment is, in many ways, wellworn territory, as the authors also note (L4558). Much of the discussion in Section 5.2 also points to results that are consistent with previous studies. In my opinion, there has been inconsistent success demonstrated in previous studies as to the utility of this approach and the results presented here are no different than previous studies have found.
The question then is both whether the approach presented here represents such a difference from past studies as to be a substantial departure from past practices that it would be of value to report the results and that the study area and catchments are sufficient to make broader conclusions about this potential new approach.
From what I am able to understand about the approach and the catchments, neither of these meet the criteria so as to make a substantial and broader contribution to our understanding of why or how we might improve on regionalization approaches for parameter estimation at ungauged locations.
We thank the reviewer for the general assessment and her/his questions arising on the novelty of this paper. In the following, we clarify the novelty that we believe we had in this paper to our best knowledge, that has not been explored by previous studies. As the reviewer already mentioned, most of the regionalization approaches are proposed and tested with large samples of gauged catchments, only a few also discussed the regionalization using fewer catchments, e.g. 10 catchments in Wagener and Wheater (2006). However, in Ethiopia dense networks of gauging stations are lacking, a situation very similar to other developing countries and regions. Therefore, the aim of our study is not to present an entirely new method, but instead, we want to adapt (see discussions in the following) the commonly used regionalization approach such that we can use it to help the understanding of water balances in the Ethiopian Rift Valley Basin with the reality of low data availability. Arising from our adaptions, the novelties of our approach are as follows:
i) As the reviewer noted towards L4558, we discussed the general approaches that have been used for predictions in ungauged basins. However, we showed a different approach by analyzing the impact of using different parameter sets for regionalization. Other than the typical approach of using the bestcalibrated parameters of the gauged catchments (e.g. Wagener and Wheater, 2006), we extract three possible parameter sets for regionalization. Although previous work already considered multiple similar parameter sets for regionalization (Livneh and Lettenmaier, 2013), to our knowledge the differences of using the bestcalibrated parameter, the best parameter set in the validation period, and the most stable parameter set considering their performance in calibration and validation period have not yet been explored. Using a spatial split sample test, we show that the best parameter sets of the validation provide better estimates of regionalized parameters than the commonly used bestcalibrated parameters.
ii) We express the uncertainty of model parameters going along with using a low sample of catchments for regionalization: Due to the low number of gauged catchments in the Ethiopian Rift Valley Basin, the relationships between model parameters and catchment attributes consist of just 14 points. Therefore, the resulting regionalization can be expected to remain uncertain. We quantify its uncertainty by applying the spatial split sample test 14 times leaving out once each of the catchments and therefore obtain 14 regionalization parameter sets that express the uncertainty of regionalized model parameters in our datasparse region. We are aware of the possibility to regionalize hydrological signatures but recent work showed that their information content is limited (Addor et al., 2018) and that their regionalization should go along with considering discharge observation uncertainties (Westerberg et al., 2016). Nevertheless, to our knowledge, there has not been an uncertainty quantification of regionalization parameters in a datasparse region like ours. Other than regionalized signatures, our regionalized model parameters will allow to run the model with climate projections.
iii) We show that applying our model with input data derived from global products (MSWEP, GLEAM) can provide acceptable discharge simulations for both gauged and ungauged catchments. In addition, we show the difference of this approach than the previous ones by the application of global data products to provide acceptable regional model in datasparse regions. The acceptable simulation results that we obtain in the gauged catchments and with the spatial splitsample test indicate that global products can be used as model inputs to provide reasonable simulations in datasparse regions. In addition, our regionalized parameters are distinct to those of globally regionalized parameter sets such as the HBV parameters (Beck et al., 2016) indicating that even if only sparse data is available, they can improve regional hydrological simulations.
In Section 5.2 the reviewer is referring to two studies by Goshime et al. (2020) and Abebe et al. (2010). “Much of the discussion in Section 5.2 also points to results that are consistent with previous studies. In my opinion, there has been inconsistent success demonstrated in previous studies as to the utility of this approach and the results presented here are no different than previous studies have found.”
We thank the reviewer for these points. In L405406, we tried to show the consistency of highly sensitive parameters (β, F_{C}, and L_{P}) to the previous study in the region (Goshime et al., 2020). In addition, in line L407409 we discussed the interaction between parameters that could cause the insensitivity of some model parameters. However, we believe these studies are substantially different from ours considering the abovementioned (iiii). We will clarify this in the revised manuscript and include the respective literature.
My recommendation is based on a number of what I see as serious methodological and evaluation questions as well as a highly complimentary presentation of a limited application of the approach to only a small number of catchments. I describe these issues in more detail below. If the manuscript does receive a recommendation other than Reject, I also offer additional minor and editorial comments that the authors need to consider in their revision.
(1) Broader contribution of the work
(1a) The use of weighted least squares (L200), although not necessarily a substantial advance, is what I believe to be the novel aspect of the study. Perhaps if this were emphasized more in the introduction and concentrated in more detail with the existing studies, it might become more clear that this is a more substantial contribution that the impression I was left with. Otherwise, this being mentioned is more detail so later in the discussion paper (in the methods) contributes to this point being lost. I would also be more explicit as to how this work differs from Wagener and Wheater (2006) and the follow on studies that have cited that paper.
Thank you. We will make sure to emphasize more on the weighted least square and mention existing relevant literature in the introduction. The difference of our approach to Wagener and Wheater, (2006) and following studies (Lane et al., 2021; Singh et al., 2014) is that we extract three possible parameter sets to show the difference of regionalization performance derived from using the bestcalibrated parameter, the best parameter set in the validation period, and the most stable parameter sets as we described more in (i) above and in subsection 3.3 of the manuscript.
(1b) I do not agree that this work is novel because these approaches have only been applied in datarich regions (L5658). In my opinion, the reason these methods have been applied in datarich areas is to test the limits of these approaches. Even then, the results have certainly been mixed. Certainly, you could have chosen a more datarich area to test this approach and then removed stream gauges to understand the effects of gauges on the performance of the method.
Thank you for this point. This sentence will be clarified; we will make sure to provide more detail about the observed hydroclimatic data limitation in our region. Using the available global data sets, we showed the possibility and reliability of a regional modeling approach including a quantification of the uncertainty that remains due to the data limitations of our study region. We will clarify this, too, in the revised version of the paper.
(1c) Linked to Comment 1b, it is difficult to make broader conclusive statements about the utility of this approach when only 16 (or 14) catchments are being used. Either way, for a regionalization study, 1416 gauges is a very limited number. I realize that 2 catchments were removed because they were poor performing, which reduced the number of catchments to 14. I am not sure if removing these 2 catchments was the correct thing to do here; are they poorly performing because the underlying model is not a good representation?
Thank you. As we stated in L8388 there are low numbers of gauged catchments in the Ethiopian Rift Valley Basin, and this comment is consistent with the response provided above on the low sample of catchments for regionalization in (ii). As stated by the reviewer in (1c) we removed 2 catchments. We mentioned in L188190 that the reason for their removal was their poor performance due to the fast flow processes and the occurrence of wetlands immediately above the gauge in catchments #06 and #12, respectively. The model structure does not consider these processes and would therefore provide unrealistic results. We will clarify this in the revised version of the paper.
Were these locations removed just to improve your own study results? It seemed as though there was not a solid technical reason to remove these gauges from the study.
Please see the comment above.
(2) Methodological and evaluation concerns
(2a) I missed where nonlinear regressions are being used in conjunction with weighted (linear) least squares (L200)? I see later in L218 that the nonlinear regression is discussed but with not much justification or explanation as to why this is the case.
The form of Equation 10 looks like the form of a regression equation when the regression was performed in log space and then transformed back to normal space. In other words, the logs of the response and predictor variables were taken to linearize the relation between them (to better ensure the assumption of a linear relation for the regression) and then the regression was performed on the logtransformed variables.
Of course, an additive model in log space is a multiplicative model in normal space. So to get the values back to normal space, Equation 10 is what the regression equation looks like when the additive linear model is retransformed back to normal space.
Seeing that you do not mention anywhere that you performed the regression on the logs of the response and predictor variables, I am not understanding why you would apply the nonlinear equation shown in Equation 10 for this reason. More justification is then needed for the application of Equation 10 to the data.
We explained this already in L216220 of the submitted manuscript, however, our elaborations may not be clear enough. We will clarify the misunderstanding and try to give more explanation about the nonlinear regression option we propose. In this study, we apply the weighted linear regression between the catchment properties (independent variables) and model parameters (response variable). We choose the linear regression for the correlating multiple catchment properties with the model parameter as shown in Table S1. However, we chose a nonlinear regression equation on the normal scale (not logscale) if there is only one catchment property correlating with a model parameter. For instance in Table S1, we can see that L_{P }is correlated only with Elevation in such cases we applied the nonlinear regression.
In addition, to increase the representation of more identifiable catchments, we applied a weighted regression on the normal scale. We are aware of the possibility to do nonlinear regression on the logtransformed scale however, the correlation coefficient of L_{P}_{ }with Elevation is superior on the normal scale than the logtransformed ones that can provide a better regression model on the normal scale. Furthermore, we will make sure to include more discussion about the relationships between the catchment properties and model parameters that form the regression model.
(2b) Keep in mind NSE values less than 0 have the interpretation that the mean of the data is a better model than the model being proposed (in this case, the regionalization model is worse than simply using the mean of the data as the model). NSE values less than 0.5 are likely poor fits and those less than 0.25 are approaching the case where would have been better off using the mean of the observed data instead of the regionalization approach. You make the statement on L383 that “79% of the catchments had a NSE > 0”; however, I do not believe this is a statement that puts the method in a positive light. Surely you could find a simpler model (even the drainage area ratio, perhaps) that would achieve the same success as having 80% of the model results better than using the mean of the data. The reverse of the statement on L383 means that 3 catchments (20%) of the 14 catchments did have an NSE < 0 using this regionalization method. How would one in practice guarantee that they were applying the regionalization to an ungauged location where the method would not provide a worse estimate than the mean of the data?
It is correct that our regionalization approach resulted in low performance in few evaluation catchments. However, in the study, we focus on the challenges in regionalization in datalimited conditions showing the applicability of global forcing data for the regionalization of data sparseregions considering the resulting uncertainties. Using the best validation parameters, the regression model does not perform well in three catchments as discussed in L383. However, the median value of NSE for the 14 catchments is 0.56 that we believe is a sufficient performance in regionalization that started with an NSE threshold of 0.5 and above (Fig. 5b). Therefore, we believe our approach provides a basis for regional model estimation and uncertainty quantification for low catchment numbers in the datasparse regions.
Furthermore, our objective is not to create a new regionalization technique however, we try to introduce regionalization methods that can be adapted to datasparse regions by using global datasets. Poor performances of parameter regionalization are also reported by previous studies. A study showing regionalization of HBV parameters using the 10 most similar donor catchments has resulted in a median daily NSE value of 0.02 and monthly NSE of 0.17 in the 1113 evaluation catchments globally (Beck et al., 2016). Other studies also showed poor performance of hydrologic signatures during multiple regression. For example, a study by Zhang et al., (2018) has performed with a NSE value of 0.16 for the multiple regression of slope. They also found an NSE value of 0.06 while regionalizing the slope of the flow duration curve using a logtransformed multiple linear regression in the leaveoneout approach. The same study has also shown NSE < 0 performance of signature regionalization using a hydrologic model (SIMHYD) on 605 catchments in Australia. Therefore, the abovementioned difficulties in regression of model parameters coupled with the use of global data products in a datasparse region can be expected to result in considerable uncertainty. However, our approach provides good reason to assume that acceptable median NSE value can be obtained despite low catchment numbers.
(2c) In calculating the NSE based on the actual values of flow, what were the range of flow values? If no attempt to balance the weight of the high and low flows in the NSE calculation, the NSE itself would be most affected by the fit of the model at the highest flows, and thus the NSE may only be a reflection of how well the parameters are
estimating flows for the largest flows. For example, a difference of 0.1 cms and 5 cms would be a poor fit but if your high flow values are large (on the order of 100s or 1000s of cms) a difference of 4.9 cms would register as an excellent fit for NSE and this fit – simply by the numerical calculation of the NSE  would swamp any of the fits at the low flows since the differences squared would be so much less. Would it not be better to compute the NSE on the logs of the streamflows? Or at least split the flows into high, low, and mid flows so that these issues of scale are not affecting the interpretation of fit?Thank you for these valuable points. We did not attempt to balance the weight of the high and low flows in this study. Throughout the 14 catchments, we have highly variable ranges of flow. For instance in catchment #05 flow ranges from 0 m^{3}/s to 700 m^{3}/s. For the revised manuscript, we will explore if the use of a more balanced logNSE would improve our results.
(2d) There are no regression equations provided or regression diagnostics for the equations so that one could assess whether these are valid regression equations with statistically significant explanatory variables. To use these regression equations in prediction mode and calculate uncertainty and prediction intervals (which is done in
Section 4.2), the behavior of the regression equations must adhere to the properties of a linear regression (statistically significant explanatory variables, homoscedastic residuals, uncorrelated and normallydistributed residuals, and uncorrelated explanatory variables).We will make sure to provide the regression equation with their prediction intervals. Since several weighted regression equations were derived (i.e. 14 regression equations for every nine parameters), we will provide them with their R^{2} in the supplement in an extra xlsx file.
(2e) In Equation 8, the weights are described as 1/CV (the reciprocal of the CV; L213). I was having difficulty understanding this. The CV = standard deviation / mean; the reciprocal is then mean / standard deviation. The weights in a weighted least squares regression are, ideally, 1 / variance. How then were you able to achieve a weight equal to 1 / variance by using the inverse of the CV? This needs to be clarified in more detail so the reader can follow along.
In the weighted regression procedure, higher weights are assigned for more identifiable catchments by considering their performance and variability during parameter estimation. In our approach, given behavioral parameter sets, different catchments showed different parameter variability. Using a weight 1/CV or 1/variance, both cases would result in a similar result. For a parameter, introducing a constant (the mean) into the regression will not change the relative weights to each catchment since the scaling factor is the same, meaning that the regression will remain the same. However, by doing this there is an advantage to compare the weights of a catchment for different parameters because using 1/CV removes the influence of magnitude and units of a parameter.
(2f) For insensitive parameters (Figure 4), such as Mmaxeas, it seems it would be advantageous to incorporate this knowledge somehow into your regionalization scheme, although it would be unclear how this would hold up for ungauged locations. On L432433, the statement is made “Our study shows the insensitivity of model parameters to be related to catchment properties.” I am not sure how that can be. If a parameter is insensitive to model calibration, then it would have no preference for the value; therefore, why would one expect this parameter to be estimable or predictable? Would it not be better to just simply randomly generate a value for this parameter from a uniform
distribution of values given the parameter range in Table 3?Then in an ungauged location, how would one be able to predict whether this was a catchment that was insensitive to the parameter Mmaxeas or if it was one of the 3 catchments (figure 4) that was highly sensitive to this parameter?
Could you simplify your regionalization by only regionalizing sensitive parameters and then assigning a random, uniformly distributed value to the insensitive parameters?
Thank you for this helpful remark. As shown in Figure 4, M_{MAXBAS}_{ }showed insensitivity in all catchments except #05 and #08_{}that are sensitive towards the lower values. For the estimation of parameters in the ungauged catchments, we will incorporate the reviewer's suggestion by generating random values for the insensitive parameters in their parameter range to test if they can improve the regional model evaluation.
Throughout line L423432, we discussed already the interaction between catchment properties and model parameters. For instance, the insensitivity of K_{1}and K_{2} is directly attributed to the small drainage area and slope of catchments in #08 and #10. Whereby the increase in K_{1} and K_{2 }may not affect the outflow condition due to the resulting less soil moisture in the upper and lower reservoirs. We also provided an example for this in L427432. Therefore, our statement in L432433 refers to the influence of catchment properties on the model parameter identifiability.
(2g) The use of the word “stable” parameter set is not very clear. The definition of the “stable” parameter set is the set of parameters that “shows the smallest difference between the calibration and validation NSE”. But this does not consider also picking the parameter set with the highest NSE as well.
Thank you for these points. We will clarify that stable parameters are those that are showing the smallest difference between the calibration and validation NSE as we defined in Eq. 6. We tried to answer the concerns of the reviewer (but not in detail), by picking the most stable parameter set by considering their performance in calibration and validation period in L8283. We will make sure to explain better that we have already picked parameter set with the highest NSE while selecting stable parameter sets.
It also does not explain how the validation period has a higher NSE than the calibration period for some catchments.
This comment is consistent with our response to question (3a) below.
Lastly, how does this criteria help in determining the best parameter set for regionalization? What is the benefit of transferability when you have a “stable” set of parameters at one location? In other words, what would be the guarantee that a parameter set will work well at another location just because it is “stable”?
Our regional model was tested for parameters derived from the calibration, validation, and the most stable parameter sets. This approach produces three regional models for our study region that would increase the chance to choose the best parameter set for regionalization. In addition, our approach produces a reliable model by reducing the uncertainty that could be propagating from using single parameter sets.
Concerning the transferability of stable parameter sets, our entire procedure shows the possibility to produce a spatially evaluated robust regional model.
(2h) Section 3.5: I am not understanding the validation and selection of the parameter sets (L229233). From what I could understand, the parameter sets are tested on the validation phase and in leaveoneout mode. What is the leaveoneout method not sufficient itself to assess the performance of the method? Also, it would seem a longer period of calibration (one that includes both of what you term the calibration and validation periods) provide better parameter estimates? I am not understanding why the leaveoneout approach to measure uncertainty is not enough to evaluate the approach?
In L229233 we present the regional models derived from using catchment properties and model parameters. However, in our split sample test, that we apply before the regionalization, we use three types of best parameters (from calibration, validation, and the most stable parameters sets). We then used these three parameter sets to produce three regression models in the leaveoneout procedure, and select the one performing best (as shown in Figure 5b). Using parameters exclusively from a (even longer) calibration period goes along with the risk of regionalizing overfitted parameters, which is shown by our analysis that identifies the best validation parameter set at the superior set for regionalization. We will clarify this in the revised version of the manuscript in addition with a stricter evaluation of the regional model following the remarks of reviewer #1.
It is also unclear in the methods when calibration and validation are used. You could use Figure 2 to clarify this. From my reading, in Figure 2, you could modify the box “regional regression” to read “regional regression using calibration parameters” and then “evaluation of the regression procedure using validation and leave one out”. Although, as I note, I do understand why the validation and leaveoneout are both used.
Regarding the calibration and validation periods, we mentioned in Section 3.3., L180181, that the calibration period is set from 1995–2002 and the validation period is from 2003–2007. In addition, we will make sure to mention this in Figure 2. We will also modify the box to read “regional regression using calibration parameters” and then “evaluation of the regression procedure using validation and leave one out”.
(3) For these methodological reasons given in (2), there are a number of questions related to the results and interpretations:
(3a) Figure 3 shows that the model performs better in the validation phase for some catchments, which is quite puzzling. Why would parameters perform better under validation rather than calibration for some catchments? I believe this needs to be explained thoroughly, unless I am not understanding the methods, in which case, this
needs to be better explained in the methods.Thank you for this point. We have used behavioral parameter ranges (parRANGE) during calibration with NSE ≥ 0.5, from which we select the best validation parameter. Therefore, from these samples, there will be a possibility of one best parameter set which can perform better than the bestcalibrated parameter sets in some catchments. However, we agree with the concerns of the reviewer that, on the normal calibration and validation, using a single parameter set, the best parameters of the calibration period will eventually show superior performance than the validation period. We will add this critical point to the discussion of the revised paper.
(3b) The sections on elasticity and uncertainties would need to be evaluated after the comments in (2) are addressed, as I am not sure the methods themselves were applied in a manner consistent with the assumptions of linear regression nor am I certain the nonlinear regression was needed because a logtransform of the data did not appear to be used.
We will make sure to update this section based on the comment in (2). The comment regarding the selection of the regression options is consistent with the response in (2a).
(3c) Figure 5a: Please add a 1to1 line on the figure so that the reader can determine for themselves how much worse the regionalization method performs. By presenting the x and yaxes at different starting locations, it gives the impression that the methods are somewhat similar, unless the reader looks carefully at the axes values.
Thank you. We will make sure to add a 11 line.
(3d) The conclusions discuss how identifiable parameters are able to be reasonably well reproduced but one cannot know a priori which parameters are identifiable at an ungauged location. How would one be able to apply this conclusion in practice then, when a leaveoneout approach is not possible? How would one know which parameters are sensitive and insensitive and at which catchments are there exceptions? Otherwise, this proposed method does not seem to very useful in practice.
Thank you for this remark, which we think, is a misunderstanding. Every regionalization study relies on a set of donor catchments where discharge observations are available. For those catchments, model parameters have to be obtained by inverse parameter estimation, during which parameter sensitivities can be obtained. If wellidentifiable, more reliable regional relationships can be obtained for those parameters using the most dominant catchment attributes. Either large or low samples of catchments, a leaveoneout procedure should always be possible, too. We will rephrase this part of the conclusions for clarification.
(4) The data statement is inadequate. Please note the EGU data policy: https://www.hydrologyandearthsystemsciences.net/policies/data_policy.html. Having the streamflow data “available upon request” is not consistent with the EGU data policy. If the data are not publicly accessible, a detailed statement as to why this is the case must be stated. Otherwise, the data needs to be placed in a public repository and cited.
Thank you! We obtained streamflow data from the Ethiopian Ministry of Water Irrigation and Energy (MoWIE) by formal request, and they do not allow sharing the data among 3^{rd} parties. In case if anyone wants, this data can be acquired through a formal request. So, we will make sure to add a detailed statement of why data is not publicly available.
Minor Comments:
L152: There should be a clear statement here that these 3 parameters are also calibrated, much like it is stated in line 169. Consider modifying it to read “Three calibrated parameters…”
We will modify this as stated in L152.
Table 2: The headings are not formatted for easy readability and cut off midword.
We will make sure to update the headings in a more readable format.
Figure 3  add the abbreviations Cal, Val, and Stb to the caption.
We will add them.
Line 361: Decrease of 0.4% in what?
Thank you. We meant the change of the average NSE values from calibration to validation. We will make sure to clarify this.
Line 367: What model was 3 regressions? Were there not 6 parameters to estimate via regression? Or do you mean there were 3 explanatory variables in each regression model? If the equations were shown, this would help clarify the number of regressions.
Thank you. We used the three bestestimated parameters from calibration, validation, and stable sets as shown in L192196. Using these parameters, we derive three regional models for 14 catchments that reproduce the nine HBV parameters as shown in Figure 6. However, in Figure 6 we have presented nine parameters reproduced from using only the bestvalidated parameters. Therefore, the threeregression models refer to the regional models deriving from using the best parameters of calibration, validation, and stable parameters sets. We will provide the equation of the regression models, please also refer to the reply to comment (2d).
L368: What is the “optimal regional model”? I have not seen this term defined anywhere else in the text?
In this regard, the “optimal regional model” is the best regional model derived from using the best parameters of calibration, validation, and stable sets. The comparison of these optimal regional model performances was shown in Figure 5b, where the NSE of a regional model derived from using the bestvalidated parameter has shown superiority over the other two. We will make sure to define this term throughout the paper for more clarity.
L369371: How is the “spatial crossvalidation” different from the “LeaveOneOut method”? Only the leaveoneout method was described earlier as a validation method. In L377378, how could a robust spatial crossvalidation be completed with only 14 (or 16) catchments?
Thank you for these points. Throughout this paper, we used these two terms interchangeably and they are not different from each other. Both terms describe the spatial validation of the regionalized model by leaving out one catchment at a time by producing a 14regression model that quantifies the uncertainty of regionalization as well.
The comment/question referring to L377378, about robust crossvalidation using 1416 catchment is consistent with our response in (ii) above.
L373: The text states that “this method is more stable and more resilient to errors…” but an explanation would be needed here, as I am not convinced this is the case.
Thank you. We will make sure to explain this more.
L379: Change to read: “A scatter plot of monthly NSE values between parameters estimated from the model calibration and parameters regionalized from the regression equations show…”
Thank you. We will make sure to change this.
Lines 446452: No evidence is offered to support these points.
We will make sure to add relevant literature that supports these statements.
Reference
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Addor, N., Nearing, G., Prieto, C., Newman, A. J., Le Vine, N. and Clark, M. P.: A Ranking of Hydrological Signatures Based on Their Predictability in Space, Water Resour. Res., 54(11), 8792–8812, doi:10.1029/2018WR022606, 2018.
Beck, H. E., van Dijk, A. I. J. M., de Roo, A., Miralles, D. G., McVicar, T. R., Schellekens, J. and Bruijnzeel, L. A.: Globalscale regionalization of hydrologic model parameters, Water Resour. Res., 52(5), 3599–3622, doi:10.1002/2015WR018247, 2016.
Goshime, D. W., Absi, R., Haile, A. T., Ledésert, B. and Rientjes, T.: BiasCorrected CHIRP Satellite Rainfall for Water Level Simulation, Lake Ziway, Ethiopia, J. Hydrol. Eng., 25(9), 05020024, doi:10.1061/(asce)he.19435584.0001965, 2020.
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Singh, R., Archfield, S. A. and Wagener, T.: Identifying dominant controls on hydrologic parameter transfer from gauged to ungauged catchments  A comparative hydrology approach, J. Hydrol., 517, 985–996, doi:10.1016/j.jhydrol.2014.06.030, 2014.
Wagener, T. and Wheater, H. S.: Parameter estimation and regionalization for continuous rainfallrunoff models including uncertainty, J. Hydrol., 320(1–2), 132–154, doi:10.1016/j.jhydrol.2005.07.015, 2006.
Westerberg, I. K., Wagener, T., Coxon, G., McMillan, H. K., Castellarin, A., Montanari, A. and Freer, J.: Uncertainty in hydrological signatures for gauged and ungauged catchments, Water Resour. Res., 52(3), 1847–1865, doi:10.1002/2015WR017635, 2016.
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Citation: https://doi.org/10.5194/hess2021271AC2

AC2: 'Reply on RC2', Tesfalem Abraham, 06 Oct 2021
Interactive discussion
Status: closed

RC1: 'Comment on hess2021271', Anonymous Referee #1, 30 Jul 2021
This is a review of “Quantifying the Regional Water Balance of the Ethiopian Rift Valley Lake Basin Using an Uncertainty Estimation Framework” by Abraham et al. The paper presents a method to predict streamflow on ungauged basins in a region of Ethiopia. The method first uses behavioral parameter sets to identify parameters that are to be used in the regression analysis (for identifying relationships between parameters and catchment descriptors). A few parameter selection methods are proposed, which are then tested in regionalization using a leaveoneout approach. The authors then extend the study to include an analysis on the streamflow elasticity to better understand how changes in precipitation can affect variations in streamflow.
I found this paper to be informative about the study region, and I think there is potential to this paper. However, I think that there is a fair amount of work left before it can be considered for publication in HESS. Here are my concerns:
1. The literature review is quite outdated. Many seminal papers are presented in this paper, but a lot of work has been done in the past few years that could be used to set a clearer context to this study. For example, see Guo et al. 2021 for an uptodate review on regionalization approaches across the globe. This will also help contextualize the claim in lines 5759:
Guo, Y., Zhang, Y., Zhang, L. and Wang, Z., 2021. Regionalization of hydrological modeling for predicting streamflow in ungauged catchments: A comprehensive review. Wiley Interdisciplinary Reviews: Water, 8(1), p.e1487.
2. Lines 7789: This section is more of a description of the method. I suggest the authors better define the problem they are trying to solve and provide clear objectives. The way they are presented in the paper, the objectives are not clear to me.
3. Lines 106107: This sentence is unclear. Which global parameter sets? Which climate forcings? Please be specific. I suggest removing this "overview" paragraph and focus on a stepbystep description of the methodology. The steps can then refer to the figure to see where they fit in.
4. Figure 1: I think there are steps missing here. For example, how does the calibration fit into this process? I assume it is in the parameter estimation step, where the best set from the behavioral sets are identified, but that should be clarified. And the parameters are only computed on the gauged basins (obviously) but is there also a validation step?
5. Section 3.1: This section presents the data and catchment properties. I would suggest moving this to the “study area” section, since it deals with the data and properties of the study area.
6. Also, it would be important to state why the data are only available until 2007. Perhaps there was a decision to close gauging stations, etc., but for the reader it feels as if the study was completed on data that has not been updated in the past 14 years.
7. Lines 137140: Please state clearly which properties and data are used as catchment descriptors here. These sentences asis are pretty vague.
8. Lines 211213: Indicate that CV is the standard deviation divided by the mean.
9. The methodology presented in section 3.5 seems biased, in my opinion. At this stage, towards lines 230235, the authors explain that the three regression models (trained on parameters coming from the calibration period, validation period and “stable” parameters) are verified on the validation period only. This is problematic, because at this stage I could foresee that the regression model trained on the “best validation” parameter set would probably be the best during verification. This is because the hydroclimatic conditions play a major role in the ability to regionalize in the first place (as stated a bit further in the paper). So parameter sets that are “good” on this period, are probably going to be better in regionalization than parameters trained on other periods, simply because the hydroclimatic conditions are more similar by default (given the proximity of the catchments). I think that to even the field, the same process should have been completed by testing the regression models on the calibration period and the full period as well, to complete the experiment design. I would be fairly confident that the regression models would perform best on their corresponding training period. I suggest the authors include this analysis in a revised version to be able to analyze this aspect and contextualize the claim that one regression model is “better” than the others. This can be done by updating figure 5b, where we can see the effect I am referring to.
10. Figure 4: It is important to note that the small distributions of 5, 8, 13 and 15 are caused by the fact that they barely hit 0.5 NSE, meaning that only a few parameter sets are even allowed in this analysis. Whereas catchments with higher NSEs have many more parameter sets that are above 0.5. Perhaps one approach would have been to keep only the top 0.1 NSE from the maximum or something similar. Why keep parameter sets that have NSE values of 0.5 if some runs give 0.7 / 0.8 NSE? It seems that these are less “behavioral” than those at 0.7 if the maximum is 0.75. Perhaps keeping a fixed range vs their maximum value would allow for a better comparison.
11. Following comment #10, line 275276: “The parameters in these catchments remained insensitive” should be revised. It is not that they are insensitive. It is that the only few parameter sets with NSE > 0.5 had to have those parameter values.
12. Figure 5 is extremely vague for me, I am not sure what I am looking at even after reading the text, legend and caption a few times. Please consider displaying in another fashion or providing a more detailed interpretation.
13. Lines 297 – 315: I think these results should be provided with some sort of note that they are strongly dependent on the available dataset and that they must be taken with a grain of salt for the abovementioned reasons: 1 Not a lot of training data; 2 some catchments have a large spread of possible values due to having a NSE>>0.5, whereas others have NSE barely above 0.5, which plays on the identifiability of parameter sets.
14. Figure 8: Here the CVs are not clear to me. Why do 2 neighboring catchments have similar elasticities, but have CVs that range from essentially 0 to 180% ? a CV of 180 means that the standard deviation is 1.8x the average, so I am supposing that the precipitation is extremely low there? and neighboring catchments are very different in this regard? Please provide a bit more guidance to clarify.
15. Line 361: “With an average decrease of 0.40% from calibration to validation…” What exactly does this represent? 0.40% of the NSE value? Of another error metric? Please specify.
16. Lines 367369. Please revise following my comment #9.
17. Lines 379388: This section is restating the results. It would be beneficial to restructure the text to focus on the lessons learned from the experiment and dig deeper into the results to explain them and find links with the literature. this entire paragraph (lines 379389) only has one such sentence of interest, the last one that compares to the Beck et al. 2016 study.
18. Lines 414415: Was it really well identified, or is it simply that most parameter sets were barely able to provide 0.5 NSE (and looking at figure 3, it would seem that catchment #15 did not attain 0.5 at all in calibration)?
19. Line 442: “regress” à regression?
20. Lines 484485: This sentence kind of pops up from nowhere and has little relevance to the rest of the paper. I would suggest removing it.
Finally, the paper should be proofread by a professional English speaker as there are quite a lot of syntax errors which sometime distract from the content. In a similar vein, it is more typical to use a neutral and objective writing style to "depersonalize" the text. Instead of writing "we use the HBV model...", try to use "the HBV model was used...". I am unsure of the official HESS policy on this, but it is good practice.
Citation: https://doi.org/10.5194/hess2021271RC1 
AC1: 'Reply on RC1', Tesfalem Abraham, 06 Oct 2021
We thank Reviewer 1 for the thoughtful suggestions and constructive comments that we believe highly strengthening the quality of our study. We structured our responses directly below each reviewer comment in bold font.
This is a review of “Quantifying the Regional Water Balance of the Ethiopian Rift Valley Lake Basin Using an Uncertainty Estimation Framework” by Abraham et al. The paper presents a method to predict streamflow on ungauged basins in a region of Ethiopia. The method first uses behavioral parameter sets to identify parameters that are to be used in the regression analysis (for identifying relationships between parameters and catchment descriptors). A few parameter selection methods are proposed, which are then tested in regionalization using a leaveoneout approach. The authors then extend the study to include an analysis on the streamflow elasticity to better understand how changes in precipitation can affect variations in streamflow.
I found this paper to be informative about the study region, and I think there is potential to this paper. However, I think that there is a fair amount of work left before it can be considered for publication in HESS. Here are my concerns:
We thank Reviewer #1 for understanding the potential ideas that we tried to explain throughout the manuscript. We will incorporate all the concerns arising from the review to complete the manuscript.
1. The literature review is quite outdated. Many seminal papers are presented in this paper, but a lot of work has been done in the past few years that could be used to set a clearer context to this study. For example, see Guo et al. 2021 for an uptodate review on regionalization approaches across the globe. This will also help contextualize the claim
in lines 5759:Guo, Y., Zhang, Y., Zhang, L. and Wang, Z., 2021. Regionalization of hydrological modeling for predicting streamflow in ungauged catchments: A comprehensive review. Wiley Interdisciplinary Reviews: Water, 8(1), p.e1487.
We agree and will add more recent literature on regionalization to explain in more detail the research gaps that we address in our study including the study by Guo et al. (2021). We will clarify that, other than previous regionalization studies, we consider three possible sets of model parameters and evaluate them for their adequateness for regionalization, and use the results of multiple spatial splitsample tests to quantify the uncertainty that goes along when regionalizing parameter sets from a low number of catchments. In addition, we tried to show that globally available precipitation and potential evapotranspiration data sets can be used for regional modeling studies.
2. Lines 7789: This section is more of a description of the method. I suggest the authors better define the problem they are trying to solve and provide clear objectives. The way they are presented in the paper, the objectives are not clear to me.
Thank you, we will modify this paragraph, to make sure that our research problems and objectives are clearly stated.
3. Lines 106107: This sentence is unclear. Which global parameter sets? Which climate forcings? Please be specific. I suggest removing this "overview" paragraph and focus on a stepbystep description of the methodology. The steps can then refer to the figure to see where they fit in.
The Reviewer is referring to the statement "We apply global parameter sets and climatic forcings for…". We will clarify it by defining what we mean by global parameter sets and climatic forcing at this point.
Also, we agree with the comment and will remove the overview paragraph and provide a detailed description of the overall methodology. We will make sure that Fig 2. is referenced in the appropriate location in this section.
4. Figure 1: I think there are steps missing here. For example, how does the calibration fit into this process? I assume it is in the parameter estimation step, where the best set from the behavioral sets are identified, but that should be clarified. And the parameters are only computed on the gauged basins (obviously) but is there also a validation step?
We assume the reviewer is referring to Figure 2 because Figure 1 mentioned above is only a description of the study area. We will make sure to include the missing steps mentioned by reviewer #1. We will update the flow chart by adding the best parameter estimation steps from calibration, validation, and stable parameter sets in the “Parameter estimation in gauged catchments” box. In addition, we will clarify the best parameters selected from the validation steps.
5. Section 3.1: This section presents the data and catchment properties. I would suggest moving this to the “study area” section, since it deals with the data and properties of the study area.
Thank you – we will move that section accordingly.
6. Also, it would be important to state why the data are only available until 2007. Perhaps there was a decision to close gauging stations, etc., but for the reader it feels as if the study was completed on data that has not been updated in the past 14 years.
This is a good point. We explain that the streamflow data we collect from the Ministry of Water Irrigation and Energy (MoWIE) in Ethiopia ends in 2007. After this period, administrative structural change was made and individual basin authorities are given the mandate to collect and manage the data. Due to such changes, a long period (20082015) of data is still not available for the user, and the available ones from 2016 up to now are of poor quality than the ones we choose for our study period (19952007).
Therefore, we will make sure to update this information.
7. Lines 137140: Please state clearly which properties and data are used as catchment descriptors here. These sentences asis are pretty vague.
We will add more detail to the section to clarify the catchment descriptors that are used.
8. Lines 211213: Indicate that CV is the standard deviation divided by the mean.
We will define CV as the standard deviation divided by the mean.
9. The methodology presented in section 3.5 seems biased, in my opinion. At this stage, towards lines 230235, the authors explain that the three regression models (trained on parameters coming from the calibration period, validation period and “stable” parameters) are verified on the validation period only. This is problematic, because at this stage I could foresee that the regression model trained on the “best validation” parameter set would probably be the best during verification. This is because the hydroclimatic conditions play a major role in the ability to regionalize in the first place (as stated a bit further in the paper). So parameter sets that are “good” on this period, are probably going to be better in regionalization than parameters trained on other periods, simply because the
hydroclimatic conditions are more similar by default (given the proximity of the catchments). I think that to even the field, the same process should have been completed by testing the regression models on the calibration period and the full period as well, to complete the experiment design. I would be fairly confident that the regression models
would perform best on their corresponding training period. I suggest the authors include this analysis in a revised version to be able to analyze this aspect and contextualize the claim that one regression model is “better” than the others. This can be done by updating figure 5b, where we can see the effect I am referring to.Thank you for these helpful suggestions. It is correct that the procedure we applied to evaluate the regionalization performance was done only for the validation phase by considering this period to be a prediction phase. We recognize that the hydroclimatic conditions of each evaluation period could potentially affect their performance. We will therefore repeat the evaluation reserving one independent time slot different from the currently used calibration and validation periods to independently evaluate the three different regression models. We will carry out additional evaluations for the calibration period and for the whole simulation period as well to compare the performances in each period.
We will also update Figure 5b, by including the evaluation of regionalization performance in the calibration periods and for the whole simulation periods.
10. Figure 4: It is important to note that the small distributions of 5, 8, 13 and 15 are caused by the fact that they barely hit 0.5 NSE, meaning that only a few parameter sets are even allowed in this analysis. Whereas catchments with higher NSEs have many more parameter sets that are above 0.5. Perhaps one approach would have been to keep only the top 0.1 NSE from the maximum or something similar. Why keep parameter sets that have NSE values of 0.5 if some runs give 0.7 / 0.8 NSE? It seems that these are less “behavioral” than those at 0.7 if the maximum is 0.75. Perhaps keeping a fixed range vs their maximum value would allow for a better comparison.
Thank you for this important point. As stated by reviewer #1, we used behavioral parameter sets resulting a NSE above 0.5 resulting in different remaining numbers of parameter sets. For catchments #5, #8, #13, and #15, 741, 25, 593, and 2,877 parameter sets remain after applying the threshold. With 593 parameter sets and larger, we have reason to assume that the distributions of model parameters and NSE values of catchments #5, #13, and #15 are not biased by a low sample size despite being just slightly above the 0.5 NSE level. We will provide this information to the revised manuscript and add to the discussion of the revised manuscript that the distributions derived from the remaining parameter sets of catchment #8 might be biased by a low sample.
However, we prefer to remain with the thresholdbased separation of behavioral and nonbehavioral parameter sets as a thresholdbased approach helps to explicitly state under which minimum performance requirements, i.e. NSE ≥ 0.5, our regionalization by the CVweighted regression was conducted.
11. Following comment #10, line 275276: “The parameters in these catchments remained insensitive” should be revised. It is not that they are insensitive. It is that the only few parameter sets with NSE > 0.5 had to have those parameter values.
We will make sure to revise as suggested.
12. Figure 5 is extremely vague for me, I am not sure what I am looking at even after reading the text, legend and caption a few times. Please consider displaying in another fashion or providing a more detailed interpretation.
Thank you. We will prepare Figure 5 again in a more readable format and clarify it in the caption.
13. Lines 297 – 315: I think these results should be provided with some sort of note that they are strongly dependent on the available dataset and that they must be taken with a grain of salt for the abovementioned reasons: 1 Not a lot of training data; 2 some catchments have a large spread of possible values due to having a NSE>>0.5, whereas others have NSE barely above 0.5, which plays on the identifiability of parameter sets.
We will rewrite this paragraph to clarify that our results are only based on available streamflow data and on the global forcing datasets.
14. Figure 8: Here the CVs are not clear to me. Why do 2 neighboring catchments have similar elasticities, but have CVs that range from essentially 0 to 180% ? a CV of 180 means that the standard deviation is 1.8x the average, so I am supposing that the precipitation is extremely low there? and neighboring catchments are very different in this regard? Please provide a bit more guidance to clarify.
Thank you! These are important questions. The reviewer is referring to the extreme differences that we found for the wettest year CVs resulting in neighboring catchments. The differences in CV are found for the ungauged catchment numbers 22 and 28 and gauged catchment #05 in Figure 8. As we explained in lines 440443, the precipitation in the ungauged catchments number 22 and 28 is very low compared to gauged catchment #05 as shown in Table S2 and Table 2. In addition, the catchments properties in the ungauged regions are highly different that influences the 14 sets of model parameters derived from the regionalization that increased the resulting CV values. We see extreme differences in annual precipitation values of 928.9 mm, and 631.7 mm in the ungauged catchments number 22 and 28 respectively that is highly different from 1319.6 mm in the gauged catchment #05 (Table S2 and Table 2). Such extreme differences in precipitation together with other catchment properties will cause high variability of the regionalized discharge even in the neighboring catchments. In addition to precipitation variability, this effect is linked with the remoteness of the most of gauged catchments used to establish the regional model as we noted in lines 440443. We will expand our elaborations accordingly in the revised version of the manuscript.
15. Line 361: “With an average decrease of 0.40% from calibration to validation…” What exactly does this represent? 0.40% of the NSE value? Of another error metric? Please specify.
Thank you. We meant the change of the average NSE values from calibration to validation by “an average decrease of 0.40 % from calibration to validation” it is. We will make sure to clarify this.
16. Lines 367369. Please revise following my comment #9.
Will do.
17. Lines 379388: This section is restating the results. It would be beneficial to restructure the text to focus on the lessons learned from the experiment and dig deeper into the results to explain them and find links with the literature. this entire paragraph (lines 379389) only has one such sentence of interest, the last one that compares to the Beck et al. 2016 study.
Thank you for the suggestion! We will update this paragraph accordingly making sure to cite relevant literature supporting our experiment.
18. Lines 414415: Was it really well identified, or is it simply that most parameter sets were barely able to provide 0.5 NSE (and looking at figure 3, it would seem that catchment #15 did not attain 0.5 at all in calibration)?
With 2,877 parameter sets with NSE ≥ 0.5, we believe that the derived distributions are representative and that our conclusions on the identifiability of the model parameters for catchment #15 are valid. Please see our response to comment 10 of this review.
19. Line 442: “regress” à regression?
Yes.
20. Lines 484485: This sentence kind of pops up from nowhere and has little relevance to the rest of the paper. I would suggest removing it.
We will remove the sentence.
Finally, the paper should be proofread by a professional English speaker as there are quite a lot of syntax errors which sometime distract from the content. In a similar vein, it is more typical to use a neutral and objective writing style to "depersonalize" the text. Instead of writing "we use the HBV model...", try to use "the HBV model was used...". I am unsure of the official HESS policy on this, but it is good practice.
Thank you. We will perform a professional language check. In addition, we will recheck the HESS policy for the writing style. Both styles are quite often used in different scientific journals and we picked the preference of using the first person pronoun.
Reference
Guo, Y., Zhang, Y., Zhang, L. and Wang, Z.: Regionalization of hydrological modeling for predicting streamflow in ungauged catchments: A comprehensive review, Wiley Interdiscip. Rev. Water, 8(1), 1–32, doi:10.1002/wat2.1487, 2021.
Citation: https://doi.org/10.5194/hess2021271AC1

AC1: 'Reply on RC1', Tesfalem Abraham, 06 Oct 2021

RC2: 'Comment on hess2021271', Anonymous Referee #2, 26 Aug 2021
This manuscript was challenging to assess. The transferability of model parameters calibrated at gauged locations to ungauged locations using a regionalization approach where parameters are estimated using catchment properties able to estimated at the ungauged catchment is, in many ways, wellworn territory, as the authors also note (L4558). Much of the discussion in Section 5.2 also points to results that are consistent with previous studies. In my opinion, there has been inconsistent success demonstrated in previous studies as to the utility of this approach and the results presented here are no different than previous studies have found.
The question then is both whether the approach presented here represents such a difference from past studies as to be a substantial departure from past practices that it would be of value to report the results and that the study area and catchments are sufficient to make broader conclusions about this potential new approach.
From what I am able to understand about the approach and the catchments, neither of these meet the criteria so as to make a substantial and broader contribution to our understanding of why or how we might improve on regionalization approaches for parameter estimation at ungauged locations.
My recommendation is based on a number of what I see as serious methodological and evaluation questions as well as a highly complimentary presentation of a limited application of the approach to only a small number of catchments. I describe these issues in more detail below. If the manuscript does receive a recommendation other than Reject, I also offer additional minor and editorial comments that the authors need to consider in their revision.
(1) Broader contribution of the work
(1a) The use of weighted least squares (L200), although not necessarily a substantial advance, is what I believe to be the novel aspect of the study. Perhaps if this were emphasized more in the introduction and concentrated in more detail with the existing studies, it might become more clear that this is a more substantial contribution that the impression I was left with. Otherwise, this being mentioned is more detail so later in the discussion paper (in the methods) contributes to this point being lost. I would also be more explicit as to how this work differs from Wagener and Wheater (2006) and the followon studies that have cited that paper.
(1b) I do not agree that this work is novel because these approaches have only been applied in datarich regions (L5658). In my opinion, the reason these methods have been applied in datarich areas is to test the limits of these approaches. Even then, the results have certainly been mixed. Certainly, you could have chosen a more datarich area to test this approach and then removed streamgauges to understand the effects of gauges on the performance of the method.
(1c) Linked to Comment 1b, it is difficult to make broader conclusive statements about the utility of this approach when only 16 (or 14) catchments are being used. Either way, for a regionalization study, 1416 gauges is a very limited number. I realize that 2 catchments were removed because they were poor performing, which reduced the number of catchments to 14. I am not sure if removing these 2 catchments was the correct thing to do here; are they poorly performing because the underlying model is not a good representation? Were these locations removed just to improve your own study results? It seemed as though there was not a solid technical reason to remove these gauges from the study.
(2) Methodological and evaluation concerns
(2a) I missed where nonlinear regressions are being used in conjunction with weighted (linear) least squares (L200)? I see later in L218 that the nonlinear regression is discussed but with not much justification or explanation as to why this is the case.
The form of Equation 10 looks like the form of a regression equation when the regression was performed in log space and then transformed back to normal space. In other words, the logs of the response and predictor variables were taken to linearize the relation between them (to better ensure the assumption of a linear relation for the regression) and then the regression was performed on the logtransformed variables.
Of course, an additive model in log space is a multiplicative model in normal space. So to get the values back to normal space, Equation 10 is what the regression equation looks like when the additive linear model is retransformed back to normal space.
Seeing that you do not mention anywhere that you performed the regression on the logs of the response and predictor variables, I am not understanding why you would apply the nonlinear equation shown in Equation 10 for this reason. More justification is then needed for the application of Equation 10 to the data.
(2b) Keep in mind NSE values less than 0 have the interpretation that the mean of the data is a better model than the model being proposed (in this case, the regionalization model is worse than simply using the mean of the data as the model). NSE values less than 0.5 are likely poor fits and those less than 0.25 are approaching the case where would have been better off using the mean of the observed data instead of the regionalization approach. You make the statement on L383 that “79% of the catchments had a NSE > 0”; however, I do not believe this is a statement that puts the method in a positive light. Surely you could find a simpler model (even the drainage area ratio, perhaps) that would achieve the same success as having 80% of the model results better than using the mean of the data. The reverse of the statement on L383 means that 3 catchments (20%) of the 14 catchments did have an NSE < 0 using this regionalization method. How would one in practice guarantee that they were applying the regionalization to an ungauged location where the method would not provide a worse estimate than the mean of the data?
(2c) In calculating the NSE based on the actual values of flow, what were the range of flow values? If no attempt to balance the weight of the high and low flows in the NSE calculation, the NSE itself would be most affected by the fit of the model at the highest flows, and thus the NSE may only be a reflection of how well the parameters are estimating flows for the largest flows. For example, a difference of 0.1 cms and 5 cms would be a poor fit but if your high flow values are large (on the order of 100s or 1000s of cms) a difference of 4.9 cms would register as an excellent fit for NSE and this fit  simply by the numerical calculation of the NSE  would swamp any of the fits at the low flows since the differences squared would be so much less. Would it not be better to compute the NSE on the logs of the streamflows? Or at least split the flows into high, low, and mid flows so that these issues of scale are not affecting the interpretation of fit?
(2d) There are no regression equations provided or regression diagnostics for the equations so that one could assess whether these are valid regression equations with statistically significant explanatory variables. To use these regression equations in prediction mode and calculate uncertainty and prediction intervals (which is done in Section 4.2), the behavior of the regression equations must adhere to the properties of a linear regression (statistically significant explanatory variables, homoscedastic residuals, uncorrelated and normallydistributed residuals, and uncorrelated explanatory variables).
(2e) In Equation 8, the weights are described as 1/CV (the reciprocal of the CV; L213). I was having difficulty understanding this. The CV = standard deviation / mean; the reciprocal is then mean / standard deviation. The weights in a weighted least squares regression are, ideally, 1 / variance. How then were you able to achieve a weight equal to 1 / variance by using the inverse of the CV? This needs to be clarified in more detail so the reader can follow along.
(2f) For insensitive parameters (Figure 4), such as Mmaxeas, it seems it would be advantageous to incorporate this knowledge somehow into your regionalization scheme, although it would be unclear how this would hold up for ungauged locations. On L432433, the statement is made “Our study shows the insensitivity of model parameters to be related to catchment properties.” I am not sure how that can be. If a parameter is insensitive to model calibration, then it would have no preference for the value; therefore, why would one expect this parameter to be estimable or predictable? Would it not be better to just simply randomly generate a value for this parameter from a uniform distribution of values given the parameter range in Table 3?
Then in an ungauged location, how would one be able to predict whether this was a catchment that was insensitive to the parameter Mmaxeas or if it was one of the 3 catchments (figure 4) that was highly sensitive to this parameter?
Could you simplify your regionalization by only regionalizing sensitive parameters and then assigning a random, uniformly distributed value to the insensitive parameters?
(2g) The use of the word “stable” parameter set is not very clear. The definition of the “stable” parameter set is the set of parameters that “shows the smallest difference between the calibration and validation NSE”. But this does not consider also picking the parameter set with the highest NSE as well. It also does not explain how the validation period has a higher NSE than the calibration period for some catchments. Lastly, how does this criteria help in determining the best parameter set for regionalization? What is the benefit of transferability when you have a “stable” set of parameters at one location? In other words, what would be the guarantee that a parameter set will work well at another location just because it is “stable”?
(2h) Section 3.5: I am not understanding the validation and selection of the parameter sets (L229233). From what I could understand, the parameter sets are tested on the validation phase and in leaveoneout mode. What is the leaveoneout method not sufficient itself to assess the performance of the method? Also, it would seem a longer period of calibration (one that includes both of what you term the calibration and validation periods) provide better parameter estimates? I am not understanding why the leaveoneout approach to measure uncertainty is not enough to evaluate the approach?
It is also unclear in the methods when calibration and validation are used. You could use Figure 2 to clarify this. From my reading, in Figure 2, you could modify the box “regional regression” to read “regional regression using calibration parameters” and then “evaluation of the regression procedure using validation and leave one out”. Although, as I note, I do understand why the validation and leaveoneout are both used.
(3) For these methodological reasons given in (2), there are a number of questions related to the results and interpretations:
(3a) Figure 3 shows that the model performs better in the validation phase for some catchments, which is quite puzzling. Why would parameters perform better under validation rather than calibration for some catchments? I believe this needs to be explained thoroughly, unless I am not understanding the methods, in which case, this needs to be better explained in the methods.
(3b) The sections on elasticity and uncertainties would need to be evaluated after the comments in (2) are addressed, as I am not sure the methods themselves were applied in a manner consistent with the assumptions of linear regression nor am I certain the nonlinear regression was needed because a logtransform of the data did not appear to be used.
(3c) Figure 5a: Please add a 1to1 line on the figure so that the reader can determine for themselves how much worse the regionalization method performs. By presenting the x and yaxes at different starting locations, it gives the impression that the methods are somewhat similar, unless the reader looks carefully at the axes values.
(3d) The conclusions discuss how identifiable parameters are able to be reasonably well reproduced but one cannot know a priori which parameters are identifiable at an ungauged location. How would one be able to apply this conclusion in practice then, when a leaveoneout approach is not possible? How would one know which parameters are sensitive and insensitive and at which catchments are there exceptions? Otherwise, this proposed method does not seem to very useful in practice.
(4) The data statement is inadequate. Please note the EGU data policy: https://www.hydrologyandearthsystemsciences.net/policies/data_policy.html. Having the streamflow data “available upon request” is not consistent with the EGU data policy. If the data are not publicly accessible, a detailed statement as to why this is the case must be stated. Otherwise, the data needs to be placed in a public repository and cited.
Minor Comments:
L152: There should be a clear statement here that these 3 parameters are also calibrated, much like it is stated in line 169. Consider modifying it to read “Three calibrated parameters…”
Table 2: The headings are not formatted for easy readability and cut off midword.
Figure 3  add the abbreviations Cal, Val, and Stb to the caption.
Line 361: Decrease of 0.4% in what?
Line 367: What model was 3 regressions? Were there not 6 parameters to estimate via regression? Or do you mean there were 3 explanatory variables in each regression model? If the equations were shown, this would help clarify the number of regressions.
L368: What is the “optimal regional model”? I have not seen this term defined anywhere else in the text?
L369371: How is the “spatial crossvalidation” different from the “LeaveOneOut method”? Only the leaveoneout method was described earlier as a validation method. In L377378, how could a robust spatial crossvalidation be completed with only 14 (or 16) catchments?
L373: The text states that “this method is more stable and more resilient to errors…” but an explanation would be needed here, as I am not convinced this is the case.
L379: Change to read: “A scatter plot of monthly NSE values between parameters estimated from the model calibration and parameters regionalized from the regression equations show…”
Lines 446452: No evidence is offered to support these points.
Citation: https://doi.org/10.5194/hess2021271RC2 
AC2: 'Reply on RC2', Tesfalem Abraham, 06 Oct 2021
We thank Reviewer 2 for her/his comments and suggestions that will highly strengthen the quality of the study. In the following, we show our responses directly below the Reviewer’s comments in bold font.
This manuscript was challenging to assess. The transferability of model parameters calibrated at gauged locations to ungauged locations using a regionalization approach where parameters are estimated using catchment properties able to estimated at the ungauged catchment is, in many ways, wellworn territory, as the authors also note (L4558). Much of the discussion in Section 5.2 also points to results that are consistent with previous studies. In my opinion, there has been inconsistent success demonstrated in previous studies as to the utility of this approach and the results presented here are no different than previous studies have found.
The question then is both whether the approach presented here represents such a difference from past studies as to be a substantial departure from past practices that it would be of value to report the results and that the study area and catchments are sufficient to make broader conclusions about this potential new approach.
From what I am able to understand about the approach and the catchments, neither of these meet the criteria so as to make a substantial and broader contribution to our understanding of why or how we might improve on regionalization approaches for parameter estimation at ungauged locations.
We thank the reviewer for the general assessment and her/his questions arising on the novelty of this paper. In the following, we clarify the novelty that we believe we had in this paper to our best knowledge, that has not been explored by previous studies. As the reviewer already mentioned, most of the regionalization approaches are proposed and tested with large samples of gauged catchments, only a few also discussed the regionalization using fewer catchments, e.g. 10 catchments in Wagener and Wheater (2006). However, in Ethiopia dense networks of gauging stations are lacking, a situation very similar to other developing countries and regions. Therefore, the aim of our study is not to present an entirely new method, but instead, we want to adapt (see discussions in the following) the commonly used regionalization approach such that we can use it to help the understanding of water balances in the Ethiopian Rift Valley Basin with the reality of low data availability. Arising from our adaptions, the novelties of our approach are as follows:
i) As the reviewer noted towards L4558, we discussed the general approaches that have been used for predictions in ungauged basins. However, we showed a different approach by analyzing the impact of using different parameter sets for regionalization. Other than the typical approach of using the bestcalibrated parameters of the gauged catchments (e.g. Wagener and Wheater, 2006), we extract three possible parameter sets for regionalization. Although previous work already considered multiple similar parameter sets for regionalization (Livneh and Lettenmaier, 2013), to our knowledge the differences of using the bestcalibrated parameter, the best parameter set in the validation period, and the most stable parameter set considering their performance in calibration and validation period have not yet been explored. Using a spatial split sample test, we show that the best parameter sets of the validation provide better estimates of regionalized parameters than the commonly used bestcalibrated parameters.
ii) We express the uncertainty of model parameters going along with using a low sample of catchments for regionalization: Due to the low number of gauged catchments in the Ethiopian Rift Valley Basin, the relationships between model parameters and catchment attributes consist of just 14 points. Therefore, the resulting regionalization can be expected to remain uncertain. We quantify its uncertainty by applying the spatial split sample test 14 times leaving out once each of the catchments and therefore obtain 14 regionalization parameter sets that express the uncertainty of regionalized model parameters in our datasparse region. We are aware of the possibility to regionalize hydrological signatures but recent work showed that their information content is limited (Addor et al., 2018) and that their regionalization should go along with considering discharge observation uncertainties (Westerberg et al., 2016). Nevertheless, to our knowledge, there has not been an uncertainty quantification of regionalization parameters in a datasparse region like ours. Other than regionalized signatures, our regionalized model parameters will allow to run the model with climate projections.
iii) We show that applying our model with input data derived from global products (MSWEP, GLEAM) can provide acceptable discharge simulations for both gauged and ungauged catchments. In addition, we show the difference of this approach than the previous ones by the application of global data products to provide acceptable regional model in datasparse regions. The acceptable simulation results that we obtain in the gauged catchments and with the spatial splitsample test indicate that global products can be used as model inputs to provide reasonable simulations in datasparse regions. In addition, our regionalized parameters are distinct to those of globally regionalized parameter sets such as the HBV parameters (Beck et al., 2016) indicating that even if only sparse data is available, they can improve regional hydrological simulations.
In Section 5.2 the reviewer is referring to two studies by Goshime et al. (2020) and Abebe et al. (2010). “Much of the discussion in Section 5.2 also points to results that are consistent with previous studies. In my opinion, there has been inconsistent success demonstrated in previous studies as to the utility of this approach and the results presented here are no different than previous studies have found.”
We thank the reviewer for these points. In L405406, we tried to show the consistency of highly sensitive parameters (β, F_{C}, and L_{P}) to the previous study in the region (Goshime et al., 2020). In addition, in line L407409 we discussed the interaction between parameters that could cause the insensitivity of some model parameters. However, we believe these studies are substantially different from ours considering the abovementioned (iiii). We will clarify this in the revised manuscript and include the respective literature.
My recommendation is based on a number of what I see as serious methodological and evaluation questions as well as a highly complimentary presentation of a limited application of the approach to only a small number of catchments. I describe these issues in more detail below. If the manuscript does receive a recommendation other than Reject, I also offer additional minor and editorial comments that the authors need to consider in their revision.
(1) Broader contribution of the work
(1a) The use of weighted least squares (L200), although not necessarily a substantial advance, is what I believe to be the novel aspect of the study. Perhaps if this were emphasized more in the introduction and concentrated in more detail with the existing studies, it might become more clear that this is a more substantial contribution that the impression I was left with. Otherwise, this being mentioned is more detail so later in the discussion paper (in the methods) contributes to this point being lost. I would also be more explicit as to how this work differs from Wagener and Wheater (2006) and the follow on studies that have cited that paper.
Thank you. We will make sure to emphasize more on the weighted least square and mention existing relevant literature in the introduction. The difference of our approach to Wagener and Wheater, (2006) and following studies (Lane et al., 2021; Singh et al., 2014) is that we extract three possible parameter sets to show the difference of regionalization performance derived from using the bestcalibrated parameter, the best parameter set in the validation period, and the most stable parameter sets as we described more in (i) above and in subsection 3.3 of the manuscript.
(1b) I do not agree that this work is novel because these approaches have only been applied in datarich regions (L5658). In my opinion, the reason these methods have been applied in datarich areas is to test the limits of these approaches. Even then, the results have certainly been mixed. Certainly, you could have chosen a more datarich area to test this approach and then removed stream gauges to understand the effects of gauges on the performance of the method.
Thank you for this point. This sentence will be clarified; we will make sure to provide more detail about the observed hydroclimatic data limitation in our region. Using the available global data sets, we showed the possibility and reliability of a regional modeling approach including a quantification of the uncertainty that remains due to the data limitations of our study region. We will clarify this, too, in the revised version of the paper.
(1c) Linked to Comment 1b, it is difficult to make broader conclusive statements about the utility of this approach when only 16 (or 14) catchments are being used. Either way, for a regionalization study, 1416 gauges is a very limited number. I realize that 2 catchments were removed because they were poor performing, which reduced the number of catchments to 14. I am not sure if removing these 2 catchments was the correct thing to do here; are they poorly performing because the underlying model is not a good representation?
Thank you. As we stated in L8388 there are low numbers of gauged catchments in the Ethiopian Rift Valley Basin, and this comment is consistent with the response provided above on the low sample of catchments for regionalization in (ii). As stated by the reviewer in (1c) we removed 2 catchments. We mentioned in L188190 that the reason for their removal was their poor performance due to the fast flow processes and the occurrence of wetlands immediately above the gauge in catchments #06 and #12, respectively. The model structure does not consider these processes and would therefore provide unrealistic results. We will clarify this in the revised version of the paper.
Were these locations removed just to improve your own study results? It seemed as though there was not a solid technical reason to remove these gauges from the study.
Please see the comment above.
(2) Methodological and evaluation concerns
(2a) I missed where nonlinear regressions are being used in conjunction with weighted (linear) least squares (L200)? I see later in L218 that the nonlinear regression is discussed but with not much justification or explanation as to why this is the case.
The form of Equation 10 looks like the form of a regression equation when the regression was performed in log space and then transformed back to normal space. In other words, the logs of the response and predictor variables were taken to linearize the relation between them (to better ensure the assumption of a linear relation for the regression) and then the regression was performed on the logtransformed variables.
Of course, an additive model in log space is a multiplicative model in normal space. So to get the values back to normal space, Equation 10 is what the regression equation looks like when the additive linear model is retransformed back to normal space.
Seeing that you do not mention anywhere that you performed the regression on the logs of the response and predictor variables, I am not understanding why you would apply the nonlinear equation shown in Equation 10 for this reason. More justification is then needed for the application of Equation 10 to the data.
We explained this already in L216220 of the submitted manuscript, however, our elaborations may not be clear enough. We will clarify the misunderstanding and try to give more explanation about the nonlinear regression option we propose. In this study, we apply the weighted linear regression between the catchment properties (independent variables) and model parameters (response variable). We choose the linear regression for the correlating multiple catchment properties with the model parameter as shown in Table S1. However, we chose a nonlinear regression equation on the normal scale (not logscale) if there is only one catchment property correlating with a model parameter. For instance in Table S1, we can see that L_{P }is correlated only with Elevation in such cases we applied the nonlinear regression.
In addition, to increase the representation of more identifiable catchments, we applied a weighted regression on the normal scale. We are aware of the possibility to do nonlinear regression on the logtransformed scale however, the correlation coefficient of L_{P}_{ }with Elevation is superior on the normal scale than the logtransformed ones that can provide a better regression model on the normal scale. Furthermore, we will make sure to include more discussion about the relationships between the catchment properties and model parameters that form the regression model.
(2b) Keep in mind NSE values less than 0 have the interpretation that the mean of the data is a better model than the model being proposed (in this case, the regionalization model is worse than simply using the mean of the data as the model). NSE values less than 0.5 are likely poor fits and those less than 0.25 are approaching the case where would have been better off using the mean of the observed data instead of the regionalization approach. You make the statement on L383 that “79% of the catchments had a NSE > 0”; however, I do not believe this is a statement that puts the method in a positive light. Surely you could find a simpler model (even the drainage area ratio, perhaps) that would achieve the same success as having 80% of the model results better than using the mean of the data. The reverse of the statement on L383 means that 3 catchments (20%) of the 14 catchments did have an NSE < 0 using this regionalization method. How would one in practice guarantee that they were applying the regionalization to an ungauged location where the method would not provide a worse estimate than the mean of the data?
It is correct that our regionalization approach resulted in low performance in few evaluation catchments. However, in the study, we focus on the challenges in regionalization in datalimited conditions showing the applicability of global forcing data for the regionalization of data sparseregions considering the resulting uncertainties. Using the best validation parameters, the regression model does not perform well in three catchments as discussed in L383. However, the median value of NSE for the 14 catchments is 0.56 that we believe is a sufficient performance in regionalization that started with an NSE threshold of 0.5 and above (Fig. 5b). Therefore, we believe our approach provides a basis for regional model estimation and uncertainty quantification for low catchment numbers in the datasparse regions.
Furthermore, our objective is not to create a new regionalization technique however, we try to introduce regionalization methods that can be adapted to datasparse regions by using global datasets. Poor performances of parameter regionalization are also reported by previous studies. A study showing regionalization of HBV parameters using the 10 most similar donor catchments has resulted in a median daily NSE value of 0.02 and monthly NSE of 0.17 in the 1113 evaluation catchments globally (Beck et al., 2016). Other studies also showed poor performance of hydrologic signatures during multiple regression. For example, a study by Zhang et al., (2018) has performed with a NSE value of 0.16 for the multiple regression of slope. They also found an NSE value of 0.06 while regionalizing the slope of the flow duration curve using a logtransformed multiple linear regression in the leaveoneout approach. The same study has also shown NSE < 0 performance of signature regionalization using a hydrologic model (SIMHYD) on 605 catchments in Australia. Therefore, the abovementioned difficulties in regression of model parameters coupled with the use of global data products in a datasparse region can be expected to result in considerable uncertainty. However, our approach provides good reason to assume that acceptable median NSE value can be obtained despite low catchment numbers.
(2c) In calculating the NSE based on the actual values of flow, what were the range of flow values? If no attempt to balance the weight of the high and low flows in the NSE calculation, the NSE itself would be most affected by the fit of the model at the highest flows, and thus the NSE may only be a reflection of how well the parameters are
estimating flows for the largest flows. For example, a difference of 0.1 cms and 5 cms would be a poor fit but if your high flow values are large (on the order of 100s or 1000s of cms) a difference of 4.9 cms would register as an excellent fit for NSE and this fit – simply by the numerical calculation of the NSE  would swamp any of the fits at the low flows since the differences squared would be so much less. Would it not be better to compute the NSE on the logs of the streamflows? Or at least split the flows into high, low, and mid flows so that these issues of scale are not affecting the interpretation of fit?Thank you for these valuable points. We did not attempt to balance the weight of the high and low flows in this study. Throughout the 14 catchments, we have highly variable ranges of flow. For instance in catchment #05 flow ranges from 0 m^{3}/s to 700 m^{3}/s. For the revised manuscript, we will explore if the use of a more balanced logNSE would improve our results.
(2d) There are no regression equations provided or regression diagnostics for the equations so that one could assess whether these are valid regression equations with statistically significant explanatory variables. To use these regression equations in prediction mode and calculate uncertainty and prediction intervals (which is done in
Section 4.2), the behavior of the regression equations must adhere to the properties of a linear regression (statistically significant explanatory variables, homoscedastic residuals, uncorrelated and normallydistributed residuals, and uncorrelated explanatory variables).We will make sure to provide the regression equation with their prediction intervals. Since several weighted regression equations were derived (i.e. 14 regression equations for every nine parameters), we will provide them with their R^{2} in the supplement in an extra xlsx file.
(2e) In Equation 8, the weights are described as 1/CV (the reciprocal of the CV; L213). I was having difficulty understanding this. The CV = standard deviation / mean; the reciprocal is then mean / standard deviation. The weights in a weighted least squares regression are, ideally, 1 / variance. How then were you able to achieve a weight equal to 1 / variance by using the inverse of the CV? This needs to be clarified in more detail so the reader can follow along.
In the weighted regression procedure, higher weights are assigned for more identifiable catchments by considering their performance and variability during parameter estimation. In our approach, given behavioral parameter sets, different catchments showed different parameter variability. Using a weight 1/CV or 1/variance, both cases would result in a similar result. For a parameter, introducing a constant (the mean) into the regression will not change the relative weights to each catchment since the scaling factor is the same, meaning that the regression will remain the same. However, by doing this there is an advantage to compare the weights of a catchment for different parameters because using 1/CV removes the influence of magnitude and units of a parameter.
(2f) For insensitive parameters (Figure 4), such as Mmaxeas, it seems it would be advantageous to incorporate this knowledge somehow into your regionalization scheme, although it would be unclear how this would hold up for ungauged locations. On L432433, the statement is made “Our study shows the insensitivity of model parameters to be related to catchment properties.” I am not sure how that can be. If a parameter is insensitive to model calibration, then it would have no preference for the value; therefore, why would one expect this parameter to be estimable or predictable? Would it not be better to just simply randomly generate a value for this parameter from a uniform
distribution of values given the parameter range in Table 3?Then in an ungauged location, how would one be able to predict whether this was a catchment that was insensitive to the parameter Mmaxeas or if it was one of the 3 catchments (figure 4) that was highly sensitive to this parameter?
Could you simplify your regionalization by only regionalizing sensitive parameters and then assigning a random, uniformly distributed value to the insensitive parameters?
Thank you for this helpful remark. As shown in Figure 4, M_{MAXBAS}_{ }showed insensitivity in all catchments except #05 and #08_{}that are sensitive towards the lower values. For the estimation of parameters in the ungauged catchments, we will incorporate the reviewer's suggestion by generating random values for the insensitive parameters in their parameter range to test if they can improve the regional model evaluation.
Throughout line L423432, we discussed already the interaction between catchment properties and model parameters. For instance, the insensitivity of K_{1}and K_{2} is directly attributed to the small drainage area and slope of catchments in #08 and #10. Whereby the increase in K_{1} and K_{2 }may not affect the outflow condition due to the resulting less soil moisture in the upper and lower reservoirs. We also provided an example for this in L427432. Therefore, our statement in L432433 refers to the influence of catchment properties on the model parameter identifiability.
(2g) The use of the word “stable” parameter set is not very clear. The definition of the “stable” parameter set is the set of parameters that “shows the smallest difference between the calibration and validation NSE”. But this does not consider also picking the parameter set with the highest NSE as well.
Thank you for these points. We will clarify that stable parameters are those that are showing the smallest difference between the calibration and validation NSE as we defined in Eq. 6. We tried to answer the concerns of the reviewer (but not in detail), by picking the most stable parameter set by considering their performance in calibration and validation period in L8283. We will make sure to explain better that we have already picked parameter set with the highest NSE while selecting stable parameter sets.
It also does not explain how the validation period has a higher NSE than the calibration period for some catchments.
This comment is consistent with our response to question (3a) below.
Lastly, how does this criteria help in determining the best parameter set for regionalization? What is the benefit of transferability when you have a “stable” set of parameters at one location? In other words, what would be the guarantee that a parameter set will work well at another location just because it is “stable”?
Our regional model was tested for parameters derived from the calibration, validation, and the most stable parameter sets. This approach produces three regional models for our study region that would increase the chance to choose the best parameter set for regionalization. In addition, our approach produces a reliable model by reducing the uncertainty that could be propagating from using single parameter sets.
Concerning the transferability of stable parameter sets, our entire procedure shows the possibility to produce a spatially evaluated robust regional model.
(2h) Section 3.5: I am not understanding the validation and selection of the parameter sets (L229233). From what I could understand, the parameter sets are tested on the validation phase and in leaveoneout mode. What is the leaveoneout method not sufficient itself to assess the performance of the method? Also, it would seem a longer period of calibration (one that includes both of what you term the calibration and validation periods) provide better parameter estimates? I am not understanding why the leaveoneout approach to measure uncertainty is not enough to evaluate the approach?
In L229233 we present the regional models derived from using catchment properties and model parameters. However, in our split sample test, that we apply before the regionalization, we use three types of best parameters (from calibration, validation, and the most stable parameters sets). We then used these three parameter sets to produce three regression models in the leaveoneout procedure, and select the one performing best (as shown in Figure 5b). Using parameters exclusively from a (even longer) calibration period goes along with the risk of regionalizing overfitted parameters, which is shown by our analysis that identifies the best validation parameter set at the superior set for regionalization. We will clarify this in the revised version of the manuscript in addition with a stricter evaluation of the regional model following the remarks of reviewer #1.
It is also unclear in the methods when calibration and validation are used. You could use Figure 2 to clarify this. From my reading, in Figure 2, you could modify the box “regional regression” to read “regional regression using calibration parameters” and then “evaluation of the regression procedure using validation and leave one out”. Although, as I note, I do understand why the validation and leaveoneout are both used.
Regarding the calibration and validation periods, we mentioned in Section 3.3., L180181, that the calibration period is set from 1995–2002 and the validation period is from 2003–2007. In addition, we will make sure to mention this in Figure 2. We will also modify the box to read “regional regression using calibration parameters” and then “evaluation of the regression procedure using validation and leave one out”.
(3) For these methodological reasons given in (2), there are a number of questions related to the results and interpretations:
(3a) Figure 3 shows that the model performs better in the validation phase for some catchments, which is quite puzzling. Why would parameters perform better under validation rather than calibration for some catchments? I believe this needs to be explained thoroughly, unless I am not understanding the methods, in which case, this
needs to be better explained in the methods.Thank you for this point. We have used behavioral parameter ranges (parRANGE) during calibration with NSE ≥ 0.5, from which we select the best validation parameter. Therefore, from these samples, there will be a possibility of one best parameter set which can perform better than the bestcalibrated parameter sets in some catchments. However, we agree with the concerns of the reviewer that, on the normal calibration and validation, using a single parameter set, the best parameters of the calibration period will eventually show superior performance than the validation period. We will add this critical point to the discussion of the revised paper.
(3b) The sections on elasticity and uncertainties would need to be evaluated after the comments in (2) are addressed, as I am not sure the methods themselves were applied in a manner consistent with the assumptions of linear regression nor am I certain the nonlinear regression was needed because a logtransform of the data did not appear to be used.
We will make sure to update this section based on the comment in (2). The comment regarding the selection of the regression options is consistent with the response in (2a).
(3c) Figure 5a: Please add a 1to1 line on the figure so that the reader can determine for themselves how much worse the regionalization method performs. By presenting the x and yaxes at different starting locations, it gives the impression that the methods are somewhat similar, unless the reader looks carefully at the axes values.
Thank you. We will make sure to add a 11 line.
(3d) The conclusions discuss how identifiable parameters are able to be reasonably well reproduced but one cannot know a priori which parameters are identifiable at an ungauged location. How would one be able to apply this conclusion in practice then, when a leaveoneout approach is not possible? How would one know which parameters are sensitive and insensitive and at which catchments are there exceptions? Otherwise, this proposed method does not seem to very useful in practice.
Thank you for this remark, which we think, is a misunderstanding. Every regionalization study relies on a set of donor catchments where discharge observations are available. For those catchments, model parameters have to be obtained by inverse parameter estimation, during which parameter sensitivities can be obtained. If wellidentifiable, more reliable regional relationships can be obtained for those parameters using the most dominant catchment attributes. Either large or low samples of catchments, a leaveoneout procedure should always be possible, too. We will rephrase this part of the conclusions for clarification.
(4) The data statement is inadequate. Please note the EGU data policy: https://www.hydrologyandearthsystemsciences.net/policies/data_policy.html. Having the streamflow data “available upon request” is not consistent with the EGU data policy. If the data are not publicly accessible, a detailed statement as to why this is the case must be stated. Otherwise, the data needs to be placed in a public repository and cited.
Thank you! We obtained streamflow data from the Ethiopian Ministry of Water Irrigation and Energy (MoWIE) by formal request, and they do not allow sharing the data among 3^{rd} parties. In case if anyone wants, this data can be acquired through a formal request. So, we will make sure to add a detailed statement of why data is not publicly available.
Minor Comments:
L152: There should be a clear statement here that these 3 parameters are also calibrated, much like it is stated in line 169. Consider modifying it to read “Three calibrated parameters…”
We will modify this as stated in L152.
Table 2: The headings are not formatted for easy readability and cut off midword.
We will make sure to update the headings in a more readable format.
Figure 3  add the abbreviations Cal, Val, and Stb to the caption.
We will add them.
Line 361: Decrease of 0.4% in what?
Thank you. We meant the change of the average NSE values from calibration to validation. We will make sure to clarify this.
Line 367: What model was 3 regressions? Were there not 6 parameters to estimate via regression? Or do you mean there were 3 explanatory variables in each regression model? If the equations were shown, this would help clarify the number of regressions.
Thank you. We used the three bestestimated parameters from calibration, validation, and stable sets as shown in L192196. Using these parameters, we derive three regional models for 14 catchments that reproduce the nine HBV parameters as shown in Figure 6. However, in Figure 6 we have presented nine parameters reproduced from using only the bestvalidated parameters. Therefore, the threeregression models refer to the regional models deriving from using the best parameters of calibration, validation, and stable parameters sets. We will provide the equation of the regression models, please also refer to the reply to comment (2d).
L368: What is the “optimal regional model”? I have not seen this term defined anywhere else in the text?
In this regard, the “optimal regional model” is the best regional model derived from using the best parameters of calibration, validation, and stable sets. The comparison of these optimal regional model performances was shown in Figure 5b, where the NSE of a regional model derived from using the bestvalidated parameter has shown superiority over the other two. We will make sure to define this term throughout the paper for more clarity.
L369371: How is the “spatial crossvalidation” different from the “LeaveOneOut method”? Only the leaveoneout method was described earlier as a validation method. In L377378, how could a robust spatial crossvalidation be completed with only 14 (or 16) catchments?
Thank you for these points. Throughout this paper, we used these two terms interchangeably and they are not different from each other. Both terms describe the spatial validation of the regionalized model by leaving out one catchment at a time by producing a 14regression model that quantifies the uncertainty of regionalization as well.
The comment/question referring to L377378, about robust crossvalidation using 1416 catchment is consistent with our response in (ii) above.
L373: The text states that “this method is more stable and more resilient to errors…” but an explanation would be needed here, as I am not convinced this is the case.
Thank you. We will make sure to explain this more.
L379: Change to read: “A scatter plot of monthly NSE values between parameters estimated from the model calibration and parameters regionalized from the regression equations show…”
Thank you. We will make sure to change this.
Lines 446452: No evidence is offered to support these points.
We will make sure to add relevant literature that supports these statements.
Reference
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Citation: https://doi.org/10.5194/hess2021271AC2

AC2: 'Reply on RC2', Tesfalem Abraham, 06 Oct 2021
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Tesfalem Abraham
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