the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Applying recession models for low-flow prediction: a comparison of regression and matching strip approaches
Abstract. Low flows in the Swiss Plateau are expected to occur more often, to last longer and, hence, to be more severe under climate change. To predict and manage such periods of water scarcity effectively, more precise information on the drainage behavior of catchments is required. The drainage behavior of a catchment can be characterized by recession analysis methods (RAMs; e.g., recession curves) of which several have been developed in the last decades. Their recession parameters have been related to different aquifer characteristics or more general catchment characteristics like lithology, topography, or climatology. Such parameters vary widely, and the effects of uncertainties on the model’s outcomes are diverse and complex. Despite the obvious potential of recession curves for prediction, they have so far not been used for operational low flow prediction and guidance for hazard mitigation. In addition, recession curves of slowly draining catchment states are hardly represented by current RAMs.
To fill the gap of RAMs representing slow draining catchment states we developed two novel RAMs, one fully automated and based on the matching strip method (MRC_slow), the other one (SDSC) relying on a careful expert-based selection of few recession segments with the slowest recession behavior. Alongside we used three established RAMs from the literature (one further matching strip model, linear regression and lower envelope in the discharge decay – discharge recession diagram). We applied the five RAMs on previously extracted low flow segments of 33 catchments in the Swiss Plateau and compared them on their recession curvatures, durations, and volumes. We designed a procedure that evaluates which of any selected RAMs best matches the recession behavior of individual low flow segments of a hydrograph. Applying this in a simulated prediction situation, we evaluated in retrospect, which of the five specifically selected RAMs predicted the low flow hydrographs between 2021 and 2022 most accurately.
We found the variability of recession durations and volumes between catchments to be higher than between the five RAMs. Within 30 of the 33 catchments, the order of recession durations and recession volumes was the same. Hence the different recession behaviors of the RAMs could be related to different catchment states. Upon evaluating the low flow predictions, we found that the MRC_slow approach overall performed best followed by linear regression and SDSC. However, for operational low flow prediction we recommend using four of the five RAMs. This allows for changing the recession model(s) at every timestep if the recession behavior changes. It is also possible to present predictions with a model ensemble, indicating a range of uncertainties if several models perform similarly well. The described data-driven approach and the newly developed models are, therefore, very promising for improving low flow predictions in gauged catchments.
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RC1: 'Comment on nhess-2024-78', Anonymous Referee #1, 30 Jul 2024
This study aims to address the estimation of low-flow hydrograph recession using five approaches, including two methods proposed by the authors. Analyses were conducted with daily streamflow data from 33 catchments in the Swiss Plateau. The authors present the findings from three perspectives of identified low-flow recession: 1) the duration of the recession, 2) the specific discharge volume embedded in the recession, and 3) the overall prediction performance.
The issues raised by the authors are significant; however, the manuscript is hindered by several factors: 1) illogical or incorrect interpretations with insufficient or no supporting evidence, 2) subjective descriptions based on visualization without quantification, and 3) redundant and colloquial writing, a relatively large number of grammatical issues, and unclear figure legends. These factors diminish the clarity and rigor of their findings, which are essential for a high-quality paper. Major comments regarding these key concerns are outlined below, followed by additional comments related to the analyses:
- Illogical or incorrect interpretations with insufficient or no supporting evidence:
- The authors found that most of their study sites (30 out of 33) reveal the same order of the estimated duration and discharge volume across the five employed models (i.e., REG_q05 > SDSC > MRC_slow > REG_mean > MRC_p). They claim that these results demonstrate the variance in estimation is more attributable to catchment variability rather than the models themselves. This conclusion is not logical. Such results indicate that REG_q05 consistently has the highest estimation of recession duration and volume, while MRC_p consistently has the lowest, regardless of catchment. This is clear evidence of systematic bias across models and does not provide insight into the contribution of catchment variability. To support the authors' proposal, it would be logical to show that the order of the estimated duration or volume across the 33 catchments is consistent regardless of the model used. For example, if catchment i is always estimated to have a longer duration in all five models, while catchment j always has a shorter duration, this would support the authors' hypothesis. However, such a result is not presented, and based on the results in Tables A2 and A3, this does not appear to be the case.
- Figures 4 to 6 clearly show differences in the identification of recession behavior across the five models; however, the analysis lacks a benchmark for comparison. Merely noting these differences (as stated in line 376) cannot be considered a valuable finding. The authors suggest that these differences reflect the models' abilities to represent different hydrological processes and conditions (lines 482-492), but no evidence or benchmark is presented to support this claim. Most importantly, the authors' conclusion is illogical and contradictory. They propose that a single catchment can have greater contributions from groundwater than from shallower root zones, as shown by REG_q05 and SDSC, while simultaneously having fewer contributions from groundwater than from shallower root zones, as indicated by REG_mean and MRC_p??
- There are several other interpretations that require significant improvement. Here are some but could be more: lines 362, 365, 397, 494-506, 516.
- Subjective descriptions based on visualization without quantification (list but not exhaustive). Quantitative description is encourage: lines 359-360, 362, 365, 401-405(horizontal variance?); Supporting references is required: lines 57-58, 63-65, 184, 198, 200-201, 230, 278, 320.
- Typos, mistakes, and descriptions can be improved to address redundancy and colloquial writing (list but not exhaustive): Typos/mistakes: lines 65, 94-95, 98-99, 152-153, 179, 358; Descriptions: lines 24-27, 33, 89-91, 103-106, 141-151, 164-165, 192, 218-219, 257-258, 303-304, 307-309, 312-314.
Other comments:
- The authors are encouraged to exercise greater caution when discussing potential interpretations and ensure proper citations. For example, lines 496-498: Can a classical hydrological process, such as daily variations in evapotranspiration losses, be considered "data noise"? If so, it raises the question of what constitutes "normal data dynamics" according to the authors' understanding.
- The intercorrelation between the duration and discharge volume is suggested to be properly accounted for in the analysis.
- The selection of the study model is suggested to be reconsidered by reviewing some more recent literature. For example, numerous studies (Biswal and Marani, 2010; Shaw and Riha, 2012; Bart and Hope, 2014; Dralle et al., 2017; Jachens et al., 2020; Tashie et al., 2020) have indicated that cloud-based methods (particularly REG_mean, and most of the methods selected in this study) significantly underestimate recession decay compared to event-based methods, particularly for low flows. Additionally, certain techniques, such as the exponential time step method (ETS, Roques et al., 2017), have been proposed to improve low-flow recession estimation.
- How do the various thresholds used in Section 3.2 influence the uncertainty of the analysis?
- The meaning of ‘nonlinear-drainage behavior’ in line 365 needs to be clarified. Note that a common linear discharge-storage relationship corresponds to an exponent b=1 in equation (1), which represents an exponential decay in the hydrograph and would not be depicted as a straight line (e.g., Botter et al., 2009). The latter seems to be what the authors refer to here in Figure 4.
Bart, R., & Hope, A. (2014). Inter-seasonal variability in baseflow recession rates: The role of aquifer antecedent storage in central California watersheds. Journal of Hydrology, 519(PA), 205–213. https://doi.org/10.1016/j.jhydrol.2014.07.020
Biswal, B., & Marani, M. (2010). Geomorphological origin of recession curves. Geophysical Research Letters, 37(24), 1–5. https://doi.org/10.1029/2010GL045415
Botter, G., Porporato, A., Rodriguez-Iturbe, I., & Rinaldo, A. (2009). Nonlinear storage-discharge relations and catchment streamflow regimes. Water Resources Research, 45(10), 1–16. https://doi.org/10.1029/2008WR007658
Dralle, D. N., Karst, N. J., Charalampous, K., Veenstra, A., & Thompson, S. E. (2017). Event-scale power law recession analysis: Quantifying methodological uncertainty. Hydrology and Earth System Sciences, 21(1), 65–81. https://doi.org/10.5194/hess-21-65-2017
Jachens, E. R., Rupp, D. E., Roques, C., & Selker, J. S. (2020). Recession analysis revisited: Impacts of climate on parameter estimation. Hydrology and Earth System Sciences, 24(3), 1159–1170. https://doi.org/10.5194/hess-24-1159-2020
Roques, C., Rupp, D. E., & Selker, J. S. (2017). Improved streamflow recession parameter estimation with attention to calculation of − dQ/dt. Advances in Water Resources, 108, 29–43. https://doi.org/10.1016/j.advwatres.2017.07.013
Shaw, S. B., & Riha, S. J. (2012). Examining individual recession events instead of a data cloud: Using a modified interpretation of dQ/dt-Q streamflow recession in glaciated watersheds to better inform models of low flow. Journal of Hydrology, 434–435, 46–54. https://doi.org/10.1016/j.jhydrol.2012.02.034
Tashie, A., Pavelsky, T., & Band, L. E. (2020). An Empirical Reevaluation of Streamflow Recession Analysis at the Continental Scale. Water Resources Research, 56(1), 1–18. https://doi.org/10.1029/2019WR025448
Citation: https://doi.org/10.5194/nhess-2024-78-RC1 -
RC2: 'Comment on nhess-2024-78', Anonymous Referee #2, 24 Aug 2024
The paper compares different techniques of recession analysis, proposing two new approaches. I read the paper, compiled the detailed comments below and then read the review of Referee #1. I agree with her/his evaluation. On top of what Referee #1 already noted, some additional comments are:
1) The models are different from the definition, some related to the middle part of the recession, others to the low part. What is the use of comparing all of them together? Isn't it trivial that they differ?
2) The use of the recession models for the prediction of how a drought (low flow) could evolve in future days is, to me, the most interesting contribution of the paper. Maybe more test events could be considered and statistics should be added about errors in the discharge prediction at one and more days ahead, which would be meaningful in practice.
3) Linking the regression models, or even better the recession characteristics, to catchment properties would be indeed very interesting and useful for understanding and practice (e.g., estimation of recession characteristics in ungauged catchments). With the analysis done on 33 catchments, something could be done in this paper already. For example, analyses could be added on the results stratified by catchment area, geology, topography and climate.
Overall I've found the paper quite difficult to read, maybe because I've not applied this kind of models before. But the paper should be readable by non-experts in recession analysis too. I've tried to indicate where I was confused in the following comments.
Detailed comments:
Line 103: What are the "two main groups"? I would suggest to add some more details on the difference between the identification of MRC and the analytical recession analysis. What is the objective of the latter?
Line 105: so only MRC are of interest here, with two classes of methods? I am confused.
Line 116: which method has been criticized to be too subjective? All methods for MRC identification?
Line 121: "developped"
Line 176: isn't this a limitation of the study? Shouldn't the analysis also consider several alternative extraction methods, since the results depend so strongly on it?
Line 206: what are the two analytical methods? If the Authors mean REG_mean and REG_q05, these are estimations of two characteristics of the same model of Equation (1), i.e., the trend of average values of dQ/dt vs. Q and the trend of the low values of dQ/dt vs. Q.
Lines 222-227: MRC_p should be described. Knowing that an EXCEL spreadsheet exists is not enough.
Lines 228-240: the procedure is hard to follow for me. What is the relative value assigned to the last segment? How is the threshold to exclude steeper parts identified? I am confused here.
Line 244, Eq. (3): this is the linear reservoir equation. It corresponds to dQ/dt = -c*Q. So MRC_slow is a linear model for the recession. That's ok but the text seems to refer to a more complex model.
Line 248: what are the fitted variables? Are they Q_0 and c? I don't get how the procedure for the horizontal transposition works. Probably because I didn't understand the previous part of the method.
Line 295: for the recession curve plot it would be better to plot logQ vs. t to identify linear vs. non linear recessions.
Line 300: here the parameter c of Equation (3) is called regression coefficient but I didn't get that it was evaluated through a regression analysis. And I finally see that the Authors also know that log(c) is equivalent to log(a) when b=1 (linear reservoir). But it is very confusedly said.
Lines 306-310: why are recession volumes and duration useful to compare between models? I would have expected the shape of the MRC (as described by a and b) to be more important.
Line 337: how is the RAM an independent variable? Isn't it a method?
Figure 4: why not plotting the lines in a log-linear plot so to show the non linearity of some of the curves?
Figures 4 and 5: The meaning of slopes and intercepts in both recession curve plots and recession plots should be stated clearly.
Line 358: what does "curvature" mean here? I guess the Authors refer to the slope of the curves. The curvature would be meaningful to analyse in a log-linear plot.
Line 369: it is trivial that MRC_slow and MRC_p have a slope 1 in the recession plot. They are linear models.
Line 395: it appears that the recession volumes are determined by the identified recession duration. What is the meaning of these volumes? In other words, how shall we interpret the fact that the REG_q05 volume is the greatest when REG_q05 identifies the lowest part of the recession curve?
Figure 6: the difference of volume between methods does not seem very interesting to me. Maybe it would be better to show the differences between catchments (maybe catchment area could be used in the x axis).
Figure 7: is this analysis done for the 2021-2022 drought event? If so it should be indicated in the figure and text. It is unclear to me how well can we predict discharge in the future days, based on this plot.
Figure 9: it is not so easy to understand what the figure shows. For instance, I don't understand the meaning of the size of the points (should we consider the biggest ones as more informative?)
Line 481: I don't get how the order of the models in terms of duration and volume suggests that "the variances between the models can be attributed to various catchment states and characteristics".
Lines 482-492: if all recession typologies occur in all catchments, are the RAMs useful? Can we distinguish between catchments? And between events?
Line 510: isn't it trivial that SDSC fits better the recession segments than REG_q05, in calibration, given many more degrees of freedom? But it may be worse in prediction.
Lines 531-536: maybe also change in connectivity could cause the breakpoints in SDSC.
Line 545: isn't it trivial that, of the four automated models, MRC_slow and REG_q05 should represent best the low end of the recessions?
Lines 563-569: I don't understand.
Line 571: here finally I understand the meaning/usefulness of the backward prediction. It should be stated before.
Section 5.3: on top of MAPEcor, the Authors should add a measure of the error in the discharge prediction at one or more days ahead, which is more meaningful in practice.
Lines 582-586: linking the regression models, or even better the recession characteristics, to catchment properties is indeed very interesting and, with the analysis done in 33 catchments, it could be done in this work. Would it be possible to add some analyses on the results stratified by catchment area, geology, topography and climate?
Lines 594-597: I can't follow the reasoning here. How can the order of the models in terms of duration and volume suggest that "the variability between the catchments is higher than between the models"? And how can "this suggest that the differences between the models can be allocated to different catchment states"?
Citation: https://doi.org/10.5194/nhess-2024-78-RC2
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