the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Elasticity curves describe streamflow sensitivity to precipitation across the entire flow distribution
Bailey J. Anderson
Manuela I. Brunner
Louise J. Slater
Simon J. Dadson
Abstract. Streamflow elasticity is a simple approximation of how responsive a river is to precipitation. It is represented as a ratio of the expected percentage change in streamflow for a 1 % change in precipitation. Typically estimated for the annual median streamflow, we here propose a new concept in which streamflow elasticity is estimated across the full range of streamflow percentiles in a large-sample context. This “elasticity curve” can be used to develop a more complete depiction of how streamflow responds to precipitation. We find three different elasticity curve types which characterize this relationship at the annual and seasonal timescales in the USA, based on two statistical modelling approaches, a panel regression which facilitates causal inference and a single catchment model which allows for consideration of static attributes. Type A describes catchments where low flows are the least and high flows are the most responsive to precipitation. The majority of catchments at the annual, winter, and fall timescales exhibit this behavior. Type B describes catchments where the response is relatively consistent across the flow distribution. At the seasonal timescale, many catchments experience a consistent level of response across the flow regime. This is especially true in snow-fed catchments during cold months, when the actual elasticity skews towards zero for all flow percentiles while precipitation is held in storage. Consistent response is also seen across the majority of the country during spring when streamflow is comparatively stable and in summer when evaporation demand is high and soil moisture is low. Finally, Type C describes catchments where low flows are the most responsive to precipitation change. These catchments are dominated by highly flashy low flow behavior. We show that the curve type varies separately from the magnitude of the elasticity. Finally, we demonstrate that available water storage is likely the key control which determines curve type.
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Bailey J. Anderson et al.
Status: final response (author comments only)
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RC1: 'Comment on hess-2022-407', Keirnan Fowler, 12 Jun 2023
This paper examines the common concept of streamflow elasticity and takes it one step further, examining the sensitivity of different flow percentiles to changes in precipitation. This means the impact of climate changes can be examined separately for high flows and low flows. I find this to be a worthwhile extension to an existing widely-used method. It allows the elasticity concept to be more closely related to problems of societal interest such as ecological sensitivity to changes in low flows and impacts on infrastructure due to changes in high flows.
I find the manuscript to be close to publication standard already. The methods used are rigourous, the writing is usually quite clear, the findings are well supported by quality figures, and the paper is relatively complete. I offer the following comments, in the hope of improving the paper from its already high standard. Points 1 and 7 are editorial (and thus subjective) and are suggestions only.
1. OVERALL FRAMING OF PAPER. I think the abstract and introduction could be improved to frame the paper better and increase its impact. To me, the paper should primarily aim to be an introduction to a new concept (or, more precisely, a new variant on an existing concept), as per the existing line 400: "The intention of this paper is to provide an introduction to the concept [of elasticity curves] in a large-sample context". If this is indeed the goal, then the authors ought to aim to clearly establish: (1) the importance of the existing method; and (2) the need for the new method, couched in terms of the limitations of the existing method. Neither of these aims are achieved very well in the existing abstract and introduction.
Specifically, the tone of the introduction seems to take for granted that the existing method is important; it does not clearly explain its significance or what questions can be/have been answered by the method in the past. Likewise, although the introduction does go some way to answering (2) (line 62-63), it waits too long to do so and does not go into sufficient detail (saying only "abnormally high and low flows are associated with the greatest strain on hydrological systems"). Can we get a lot more detail here? Eg. for high flows, it could acknowledge/discuss that infrastructure is often designed according to estimates of flooding potential, so any changes to this potential are very important; likewise low flows are important eg. for riverine ecology among other things. Articulating these factors will help the reader understand why the new method is important, which will motivate them to keep reading. In my view, it is crucial to do this early, before they lose interest.
As for the abstract, the majority of the text is spent trying to articulate the different catchment "types" that have been defined for the example application. This would be fine if the paper was about a new system for classifying catchments. But if the paper is about introducing the concept of elasticity curves, then this detail is unexpected and unhelpful in the abstract. The abstract needs to be about the method, not this particular application. Readers can read the full paper if they want this sort of detail. My suggestion would be to focus the abstract on the importance/significance of the method and what it adds; limit the results to a handful (say two or three) things that were learned in the specific application. Note, existing text in the conclusion section, Line 427 - 434, contains some of the above elements and could be adapted for the abstract.
2. CLARITY OF METHOD. I feel there is a strong possibility of readers misunderstanding the method. Specifically, the focus on different flow percentiles (or ranges of percentiles) may lead readers to believe that the method only focusses on precipitation that falls during the relevant percentile/range. For example, the reader might believe that the method is asking "how sensitive is low flow to precipitation that falls concurrently with times of low flow?" whereas my understanding is that the intent is to use the same seasonal or annual average of precip & PET regardless of which flow percentile is in view. Is this correct? Can the authors make this clearer please? Perhaps via some more concrete examples? An explanatory figure may also help.
3. GREATER JUSTIFICATION OF "CAUSAL" NATURE OF ANALYSIS. The panel regression model is described as a "causal" model (eg. line 152). Can the authors please provide more justification for this? I am not an expert in this area, so I am looking for more information here - it seems to me as if this method is a variant on linear regression, with additional care to hold confounding factors constant. However, even if the authors manage to hold every available confounding factor constant, it does not resolve the problem that correlation does not imply causation. Have other authors made similar claims of panel regression, and what is their reasoning? Given there exist specialised causation methods (ie. methods that were directly formulated to try to distinguish correlation and causation such as https://doi.org/10.1126/science.1227079), it is not a claim that I would be making lightly. Even if the authors agree with me, this is no reason to change to experimental design; merely the way it is described.
4. JUSTIFICATION OF TWO METHODS. The results of the two methods are very close (a key difference is the uncertainty bounds, but these may be closer than they look - see following point). The results are so close that one wonders whether the two methods are actually doing almost the same thing. Two recommendations arise from this:
- Are both methods really needed? They are taking up valuable real-estate and they really detract from the story because it becomes more about comparing the methods rather than reflecting on what the results actually mean in this first-of-its-kind study. Perhaps one of the methods could be moved to an appendix?
- If the authors elect to keep both methods, I suggest they bolster their justification for why the two methods are different.
5. REPORTING OF UNCERTAINTY. If the authors elect to retain both methods, then the following becomes relevant. With respect to Figure 2: At first glance, the uncertainty bounds appear to be the key difference between the two methods. However, the comparison is apples with oranges, and if the authors correct this then the uncertainty bounds may be much more similar. Specifically, for the panel model, the confidence intervals are plotted, whereas for the single catchment models, IQR is plotted, which is a lot closer to prediction intervals (which plot uncertainty about individual predictions) than it is to confidence intervals (which plot uncertainty about the underlying assumed relationship). Is it possible to retain the IQR for the single catchment models and then swap to prediction intervals for the panel regression?
6. LIMITATIONS. Regarding line 320-322, this speaks to a significant limitation here: the method assumes a flow response in the same time period. So it might be that certain flows are very sensitive to changes in climate, but if this sensitivity is subject to a delay longer than the time period used, this will not be detected here. Is this true? If so, I suggest this be included / discussed.
7. EDITING FOR EASIER COMPREHENSION: Overall the text of the paper is admirably concise, but it's still very dense. I suggest the authors review the existing text specifically to try to make it easier to comprehend. One technique that might help is the use of tables since these facilitate a visual structure to the information. This is a suggestion only - I understand that this can be time-consuming to do!
ADDITIONAL MINOR COMMENTS, BY LINE:
Figure 1b: I think there's potential for confusion here: the line is monotonic increasing, but the unfamiliar reader might wonder whether it *must* be so, or whether it could be different. For example, the median (purple) point here could have higher elasticty than both the high and low flow, yes? If so, consider changing the figure to a non-monotic relationship to make it clear this is a possibility.
Line 111-12: "We estimated ... catchment boundary". Perhaps rephrase for better clarity.
Line 116: Unclear. Does "we recalculated these values in order to accurately represent the time period of the analysis" mean "we recalculated these because the existing dataset did not cover our desired period"?
Line 118: Would the sentence "Annual values..." fit better after the sentence that follows it? Also "fall into corresponding “years”" - is "water years" the intention here?
Figure 3: Unclear that column c is the same as Fig 2, partly because it is named differently. I suggest to name it exactly the same previously ("clusters") and potential add the words "(from Figure 2)" to make this explicit. I realise the current title is aiming to clarify normalised versus non-normalised but I feel this clarification can occur in the Figure 3 caption.
Line 365: The introduction of example catchments interrupts the flow of the paper. Could this be done in the methods section instead?
Citation: https://doi.org/10.5194/hess-2022-407-RC1 - AC1: 'Reply on RC1', Bailey Anderson, 05 Jul 2023
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RC2: 'Comment on hess-2022-407', Anonymous Referee #2, 04 Jul 2023
- AC2: 'Reply on RC2', Bailey Anderson, 05 Jul 2023
Bailey J. Anderson et al.
Model code and software
Elasticity_curve_analysis: initial release of code for generating and analysing elasticity curve data Bailey Anderson https://doi.org/10.5281/zenodo.7391227
Bailey J. Anderson et al.
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