the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 16 Feb 2023
Technical note: Statistical generation of climate-perturbed flow duration curves
Abstract. Assessing the robustness of a water resource system's performance under climate change involves exploring a wide range of streamflow conditions. This is often achieved through rainfall-runoff models, but these are commonly validated under historical conditions with no guarantee that calibrated parameters would still be valid in a different climate. In this note, we introduce the first statistical generation method to produce a range of plausible streamflow futures that are coherent across the full range of hydrological conditions. It relies on a three-parameter analytical representation the flow duration curve (FDC) that has been proved to perform well across a range of basins of different climate. We rigorously prove that for common sets of streamflow statistics mirroring average behavior, variability, and low flows, the parameterisation of the FDC under this representation is unique. We also show that conditions on these statistics for a solution to exist are commonly met in practice. These analytical results imply that streamflow futures can be explored by sampling wide ranges of three key flow statistics, and by deriving the corresponding FDC to model basin response across the full spectrum of flow conditions. We illustrate this method by exploring in which hydro-climatic futures a proposed run-of-river hydropower plant in eastern Turkey is financially viable. Results show that contrary to approaches that modify streamflow statistics using multipliers applied uniformly throughout a time series, our approach seamlessly represents a large range of futures with increased frequencies of both high and low flows. This matches expected impacts of climate change in the region, and supports analyses of the financial robustness of the proposed infrastructure to climate change. We conclude by highlighting how refinements to the approach could further support rigorous explorations of hydro-climatic futures without the help of rainfall-runoff models.
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Notice on discussion status
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The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
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Journal article(s) based on this preprint
Interactive discussion
Status: closed
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RC1: 'Comment on egusphere-2022-1468', Anonymous Referee #1, 23 Mar 2023
This technical note introduces a numerical framework for the statistical generation of flow duration curves and then demonstrates its relevance on a hydropower planning problem. The key idea supporting the framework is the representation of Flow Duration Curves (FDC) through a set of parameters, whose value is directly related to key streamflow statistics, e.g., mean, median, or standard deviation. By sampling in the space of these statistics (through the use of multipliers), one can then stochastically generate new FDCs.
I believe the proposed approach is novel and technically sound (including the derivations provided in the SI). Importantly, the proposed approach can indeed be useful for a variety of water management applications. The presentation is clear and the manuscript well structured. Hence, my suggestion is to proceed with a minor revision.
My only major comment concerns the ‘type’ of streamflow data that are needed to parameterise the model; a point that, in my opinion, requires a deeper discussion. For example, I believe it may be challenging to implement the framework in a catchment characterized by land use change or other anthropogenic interventions. In other words, I suspect that the use of the framework might be limited to pristine catchments (unless the framework is complemented by a process-based model that somewhat accounts for the aforementioned drivers). Another point I would discuss is the ‘safe operating space’ of the framework, intended as the amount and quality of data needed for its successful implementation. With this, I am not trying to diminish this paper (which I found interesting), but simply to understand how to best use the model it presents.
Finally, the authors may want to consider a full article (rather than a technical note), something that could be done by including the SI in the main manuscript and extending the description of the case study. I would leave this up to the authors.
Specific comments
- Abstract: “coherent across the full range of hydrological conditions”. Could you please elaborate on or clarify the meaning of this statement?
- Line 36-37: I agree with this statement, but also believe that streamflow is not the only source of uncertainty that water planners account for (water demand, for instance, is another one). This is an important caveat I would mention.
- Line 43: should it be “change”?
- Line 64. I would say a few words about the Kosugi model. It is hard to follow the next paragraph (and, hence, grasp the overall contribution) without some basic information about the model.
- Equation 1: I assume that “erfc” refers to the complementary error function, right? I would mention this explicitly in the paper.
- Line 132-133. I’m afraid I don’t fully understand this part: why is it necessary to verify this condition?
- Figure 1. I would expand the caption instead of referring the readers to the main text.
- Line 157. “Additional energy”?
- Line 161. Can you provide more details about the data you used? For instance, how long was this time series? What’s the minimum amount of data needed to make the application of this model successful?
- Line 189. What are the input variables to HYPER?
- Line 2010. What are these other functional forms?
Citation: https://doi.org/10.5194/egusphere-2022-1468-RC1 -
AC1: 'Reply on RC1', Veysel Yildiz, 16 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2022-1468/egusphere-2022-1468-AC1-supplement.pdf
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AC1: 'Reply on RC1', Veysel Yildiz, 16 May 2023
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RC2: 'Comment on egusphere-2022-1468', Anonymous Referee #2, 26 Apr 2023
Yildiz et al. introduce a new approach to generate possible future streamflow scenarios for stress testing the impacts of possible climatic changes on river systems. The approach is elegant, requiring only three parameters to modify key characteristics of the flow duration curve (mean, standard deviation and low/high flow quantile or median, coefficient of variation and low/high flow quantile). I think this approach is a nice contribution to the literature. I have a only a few suggestions for improvement.
- The Discussion claims that this method “compares favorably with existing statistical methods to perturb flows such as the delta change approach.” However, the paper does not formally compare the proposed FDC alteration approach with the delta change approach. I think it would help sell the method to include a few FDC alterations with the same mean change but different changes in the variance and low flow quantile with using the delta change method to achieve the same mean change. Seeing differences in both the streamflow time series and resulting performance impacts from the delta change method vs. different FDC alterations that achieve the same mean change would help sell the utility of this approach for climate vulnerability assessments.
- Discuss the conditions of unicity (either when they are introduced or in the Discussion section). Are these conditions likely to be met, and if so why? Where might it not be true? What are the implications of not being able to explore changes that don’t meet these conditions?
- One noted limitation in the Discussion of this FDC alteration is it does not change the length of wet and dry spells. I recommend noting this can be achieved by changing the parameters of a Markov chain-based streamflow generator (see e.g. Stagge and Moglen, 2013).
- Another limitation of the FDC approach not mentioned in the Discussion is that it cannot capture changes in seasonality, which would preclude its application in snow-dominated catchments, or perhaps monsoon systems. I recommend noting this as well. See examples in the literature from Nazemi et al. (2013) and Quinn et al. (2018).
Minor comments:
- Line 70: drop “of” after “represent”
- Line 140: change “Zenedo” to “Zenodo”
- Line 159: change “standard deviation” to “coefficient of variation”
- Line 171: drop “is” before “projected”
- Line 176: change “latin” to “Latin”
- Table 1: why not explore potential increases in the median/1st percentile or decreases in the coefficient of variation?
- Line 177: “the” is repeated
References:
Nazemi, A., Wheater, H. S., Chun, K. P., & Elshorbagy, A. (2013). A stochastic reconstruction framework for analysis of water resource system vulnerability to climate‐induced changes in river flow regime. Water Resources Research, 49(1), 291-305.
Quinn, J. D., Reed, P. M., Giuliani, M., Castelletti, A., Oyler, J. W., & Nicholas, R. E. (2018). Exploring how changing monsoonal dynamics and human pressures challenge multireservoir management for flood protection, hydropower production, and agricultural water supply. Water Resources Research, 54(7), 4638-4662.
Stagge, J. H., & Moglen, G. E. (2013). A nonparametric stochastic method for generating daily climate‐adjusted streamflows. Water Resources Research, 49(10), 6179-6193.Citation: https://doi.org/10.5194/egusphere-2022-1468-RC2 -
AC2: 'Reply on RC2', Veysel Yildiz, 16 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2022-1468/egusphere-2022-1468-AC2-supplement.pdf
Interactive discussion
Status: closed
-
RC1: 'Comment on egusphere-2022-1468', Anonymous Referee #1, 23 Mar 2023
This technical note introduces a numerical framework for the statistical generation of flow duration curves and then demonstrates its relevance on a hydropower planning problem. The key idea supporting the framework is the representation of Flow Duration Curves (FDC) through a set of parameters, whose value is directly related to key streamflow statistics, e.g., mean, median, or standard deviation. By sampling in the space of these statistics (through the use of multipliers), one can then stochastically generate new FDCs.
I believe the proposed approach is novel and technically sound (including the derivations provided in the SI). Importantly, the proposed approach can indeed be useful for a variety of water management applications. The presentation is clear and the manuscript well structured. Hence, my suggestion is to proceed with a minor revision.
My only major comment concerns the ‘type’ of streamflow data that are needed to parameterise the model; a point that, in my opinion, requires a deeper discussion. For example, I believe it may be challenging to implement the framework in a catchment characterized by land use change or other anthropogenic interventions. In other words, I suspect that the use of the framework might be limited to pristine catchments (unless the framework is complemented by a process-based model that somewhat accounts for the aforementioned drivers). Another point I would discuss is the ‘safe operating space’ of the framework, intended as the amount and quality of data needed for its successful implementation. With this, I am not trying to diminish this paper (which I found interesting), but simply to understand how to best use the model it presents.
Finally, the authors may want to consider a full article (rather than a technical note), something that could be done by including the SI in the main manuscript and extending the description of the case study. I would leave this up to the authors.
Specific comments
- Abstract: “coherent across the full range of hydrological conditions”. Could you please elaborate on or clarify the meaning of this statement?
- Line 36-37: I agree with this statement, but also believe that streamflow is not the only source of uncertainty that water planners account for (water demand, for instance, is another one). This is an important caveat I would mention.
- Line 43: should it be “change”?
- Line 64. I would say a few words about the Kosugi model. It is hard to follow the next paragraph (and, hence, grasp the overall contribution) without some basic information about the model.
- Equation 1: I assume that “erfc” refers to the complementary error function, right? I would mention this explicitly in the paper.
- Line 132-133. I’m afraid I don’t fully understand this part: why is it necessary to verify this condition?
- Figure 1. I would expand the caption instead of referring the readers to the main text.
- Line 157. “Additional energy”?
- Line 161. Can you provide more details about the data you used? For instance, how long was this time series? What’s the minimum amount of data needed to make the application of this model successful?
- Line 189. What are the input variables to HYPER?
- Line 2010. What are these other functional forms?
Citation: https://doi.org/10.5194/egusphere-2022-1468-RC1 -
AC1: 'Reply on RC1', Veysel Yildiz, 16 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2022-1468/egusphere-2022-1468-AC1-supplement.pdf
-
AC1: 'Reply on RC1', Veysel Yildiz, 16 May 2023
-
RC2: 'Comment on egusphere-2022-1468', Anonymous Referee #2, 26 Apr 2023
Yildiz et al. introduce a new approach to generate possible future streamflow scenarios for stress testing the impacts of possible climatic changes on river systems. The approach is elegant, requiring only three parameters to modify key characteristics of the flow duration curve (mean, standard deviation and low/high flow quantile or median, coefficient of variation and low/high flow quantile). I think this approach is a nice contribution to the literature. I have a only a few suggestions for improvement.
- The Discussion claims that this method “compares favorably with existing statistical methods to perturb flows such as the delta change approach.” However, the paper does not formally compare the proposed FDC alteration approach with the delta change approach. I think it would help sell the method to include a few FDC alterations with the same mean change but different changes in the variance and low flow quantile with using the delta change method to achieve the same mean change. Seeing differences in both the streamflow time series and resulting performance impacts from the delta change method vs. different FDC alterations that achieve the same mean change would help sell the utility of this approach for climate vulnerability assessments.
- Discuss the conditions of unicity (either when they are introduced or in the Discussion section). Are these conditions likely to be met, and if so why? Where might it not be true? What are the implications of not being able to explore changes that don’t meet these conditions?
- One noted limitation in the Discussion of this FDC alteration is it does not change the length of wet and dry spells. I recommend noting this can be achieved by changing the parameters of a Markov chain-based streamflow generator (see e.g. Stagge and Moglen, 2013).
- Another limitation of the FDC approach not mentioned in the Discussion is that it cannot capture changes in seasonality, which would preclude its application in snow-dominated catchments, or perhaps monsoon systems. I recommend noting this as well. See examples in the literature from Nazemi et al. (2013) and Quinn et al. (2018).
Minor comments:
- Line 70: drop “of” after “represent”
- Line 140: change “Zenedo” to “Zenodo”
- Line 159: change “standard deviation” to “coefficient of variation”
- Line 171: drop “is” before “projected”
- Line 176: change “latin” to “Latin”
- Table 1: why not explore potential increases in the median/1st percentile or decreases in the coefficient of variation?
- Line 177: “the” is repeated
References:
Nazemi, A., Wheater, H. S., Chun, K. P., & Elshorbagy, A. (2013). A stochastic reconstruction framework for analysis of water resource system vulnerability to climate‐induced changes in river flow regime. Water Resources Research, 49(1), 291-305.
Quinn, J. D., Reed, P. M., Giuliani, M., Castelletti, A., Oyler, J. W., & Nicholas, R. E. (2018). Exploring how changing monsoonal dynamics and human pressures challenge multireservoir management for flood protection, hydropower production, and agricultural water supply. Water Resources Research, 54(7), 4638-4662.
Stagge, J. H., & Moglen, G. E. (2013). A nonparametric stochastic method for generating daily climate‐adjusted streamflows. Water Resources Research, 49(10), 6179-6193.Citation: https://doi.org/10.5194/egusphere-2022-1468-RC2 -
AC2: 'Reply on RC2', Veysel Yildiz, 16 May 2023
The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2023/egusphere-2022-1468/egusphere-2022-1468-AC2-supplement.pdf
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Robert Milton
Solomon Brown
Charles Rougé
The requested preprint has a corresponding peer-reviewed final revised paper. You are encouraged to refer to the final revised version.
- Preprint
(1352 KB) - Metadata XML
-
Supplement
(375 KB) - BibTeX
- EndNote
- Final revised paper