the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Influence of bank slope on sinuosity-driven hyporheic exchange flow and residence time distribution during a dynamic flood event
Yiming Li
Uwe Schneidewind
Stefan Krause
Hui Liu
Abstract. This study uses a reduced-order two-dimensional (2-D) horizontal model to investigate the influence of riverbank slope on the bank storage and sinuosity-driven hyporheic exchange flux (HEF) along sloping alluvial riverbanks during a transient flood event. The Deformed Geometry Method (DGM) is applied to quantify the displacement of the sediment-water interface (SWI) along the sloping riverbank during river stage fluctuation. This new model approach serves as the initial step to consider complicated floodplain morphologies in physics-based models for better predictions of HEF. Several controlling factors, including sinuosity, alluvial valley slope, and river flow advective forcing and duration of flow are incorporated in the model to investigate the effects of bank slope in aquifers of variable hydraulic transmissivity. Compared to simulations of a vertical riverbank, sloping riverbanks were found to increase the HEF. For sloping riverbanks, the hyporheic zone (HZ) encompassed a larger area and penetrated deeper into the alluvial aquifer, especially in aquifers with smaller transmissivity (i.e., larger aquifer hydraulic conductivity or smaller specific yield). Furthermore, consideration of sloping banks as compared to a vertical river bank can lead to both underestimation or overestimation of the pore water residence time. The impact of bank slope on residence time was more pronounced during a flood event for high transmissivity aquifer conditions, while it had a long-lasting influence after the flood event in lower transmissivity aquifers. Consequently, this decreases the residence time of HEF relative to the base flow condition. These findings highlight the need for (re)consideration of the importance of more complex riverbank morphology as control of hyporheic exchange in alluvial aquifers. The results have potential implications for river management and restoration and the management of river and groundwater pollution.
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Yiming Li et al.
Status: final response (author comments only)
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RC1: 'Comment on hess-2023-29', Anonymous Referee #1, 29 May 2023
The authors present an interesting modelling exercise on hyporheic exchange between river water and groundwater as function of river bank slope. This is an overlooked variable but highly relevant in the outer world. I made many remarks in the manuscript itself that are major to minor. My major overall concern is that the RESULTS chapter is a very, very hard read. It repeatedly took me two times reading to understand the meaning of sentences or text parts. This is largely due to the fact that the authors use the symbols and abbreviations instead of the hydrological terms. I therefore ask for a complete rewriting of this chapter where the features observed are explained in terms of hydrological processes. Attention should also be paid to the related figures and their captions as these are hard to grasp, too. I did make less small remarks in this chapter for this reason.
The DISCUSSION chapter is meagre. The authors do not convince that slope is an important attribute when it comes to associated biogeochemical processes. The authors should provide some examples to illustrate this. They may also realise that many drinking water abstractions are situated in alluvial valleys of hilly or mountainous catchments. What does this mean and what is the impact of an abstraction? This is worth to be discussed under this chapter.
Another topic is whether the authors deal with phreatic or confined aquifers when it comes to propagation of hydraulic pressure. This makes a big difference and is relevant in the field but not addressed at all. I also ask them to discuss the other case in the DISCUSSION chapter (in terms of differences and similarities).
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AC1: 'Reply on RC1', Zhang Wen, 19 Jul 2023
(1) The authors present an interesting modelling exercise on hyporheic exchange between river water and groundwater as function of river bank slope. This is an overlooked variable but highly relevant in the outer world. I made many remarks in the manuscript itself that are major to minor. My major overall concern is that the RESULTS chapter is a very, very hard read. It repeatedly took me two times reading to understand the meaning of sentences or text parts. This is largely due to the fact that the authors use the symbols and abbreviations instead of the hydrological terms. I therefore ask for a complete rewriting of this chapter where the features observed are explained in terms of hydrological processes. Attention should also be paid to the related figures and their captions as these are hard to grasp, too. I did make less small remarks in this chapter for this reason.
Reply: By rewriting, we will reduce the abbreviations or symbols in the main text with keeping those that are widely used throughout the paper (such as SWI, HZ and HEF). For example, we will replace “RTD”, “Γd”, “d**(t)” and “A**(t)” by “travel time”, “transmissivity of aquifer”, “penetration distance of HZ” and “extent of HZ”, respectively. Furthermore, the figures and their captions will be revised as well to be clearer.
(2) The DISCUSSION chapter is meagre. The authors do not convince that slope is an important attribute when it comes to associated biogeochemical processes. The authors should provide some examples to illustrate this. They may also realise that many drinking water abstractions are situated in alluvial valleys of hilly or mountainous catchments. What does this mean and what is the impact of an abstraction? This is worth to be discussed under this chapter.
Reply: We will provide more examples in the discussion to illustrate that the bank slope is important for biogeochemical processes. For example, we will compare the current RTD results to those of previous research (Derx et al., 2014; Song et al., 2020) to reveal the impacts of bank slope on the removal of dissolved carbon and hot moments of (de)nitrification activities. Also, we will revise Figure 8 to 11 to highlight that bank slope is also important to be considered when accessing the hot locations of biogeochemical processes.
As for the groundwater usage in some area with topographic slope, it is truly worth discussion in this chapter. In general, a stronger abstraction of groundwater will lead to a lower groundwater table, which makes the riparian aquifer to gain water from river more easily, and form a larger area of hyporheic zone as well as a longer travel time of river water in the aquifer. We will refine these discussions and add them in the revised version.
(3) Another topic is whether the authors deal with phreatic or confined aquifers when it comes to propagation of hydraulic pressure. This makes a big difference and is relevant in the field but not addressed at all. I also ask them to discuss the other case in the DISCUSSION chapter (in terms of differences and similarities).
Reply: The current version of manuscript only focused on the un-confined aquifer (phreatic aquifer) and did not address the confined condition. Because the elastic specific yield coefficient of groundwater in confined aquifer is much smaller than the gravitational one in phreatic aquifer, the confined aquifer is expected to be more conductive for the propagation of hydraulic pressure than phreatic aquifer. We will build a confined models in the revised version as a contrast, to illustrate the differences and similarities of hyporheic exchange processes between confined and phreatic aquifers.
Citation: https://doi.org/10.5194/hess-2023-29-AC1
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AC1: 'Reply on RC1', Zhang Wen, 19 Jul 2023
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RC2: 'Comment on hess-2023-29', Anonymous Referee #2, 14 Jul 2023
Li et al. explore the role of bank slope and channel flow dynamics on the temporal evolution of sinuosity-driven hyporheic exchange. To this end, a series of metrics are used: fluxes, hyporheic zone extent, and mean residence time. As a novel contribution, the authors use a deformed geometry method implemented in COMSOL to mimic the effect of a sloping bank.
Main Comments:
The manuscript is generally well-written. I suggest revising the text to improve clarity (see my comments below). For example, the methods introduce equations (line 200) with variables that need to be clearly defined. Also, I suggest making the introduction more succinct to focus on the actual study.
In its current form, this manuscript requires significant revisions, and I wonder if this is a contribution suited for publication in HESS. In the following, I describe the aspects that support my conclusion and provide a few suggestions to address them.
- After reading the current manuscript, I tried to answer the question: is the work making a significant or incremental contribution to our understanding of hyporheic processes? In other words, did I learn something new that wasn’t in Gomez-Velez et al. (2017)? Based on the current version of this manuscript, my answer is “no.” This work adds additional complexity to capture the effect of the sloping bank; however, the approach includes strong assumptions that might defeat its purpose. For example:
- The deformed geometry method (DGM) proposed here ignores the primarily vertical fluxes within the wedge cut by the moving boundary, which is still assumed vertical. Is this a reasonable assumption, and what are the implications? The importance of the bank slope highlighted by Liang et al. (2018), Doble et al. (2012), and others for cross-sectional, partially saturated models results from the vertical component of the exchange and the migration of the air-water interface. These processes are ignored here; therefore, I wonder whether the current model addresses these issues. Reproducing the simulations from Gomez-Velez et al. (2017) is helpful for completeness and verification; however, I suggest that the authors use a 3D version of this conceptual model to verify the appropriateness of their 2D reduced-complexity model and the implemented DGM.
- Within the dimensionless context, the metrics show only mild differences with the bank slope. Cases with significant differences require a $\Gamma_d$ of 100, which is relatively uncommon in natural systems (see Figure 2A in Gomez-Velez et al. (2017)). The authors need more clarity about their definition of “significant” differences caused by the bank slope and put this in the context of physical and biogeochemical processes and observations. Based on these results, I would conclude that representing the slope of the banks (with the Authors' conceptualization) does not have significant implications for the exchange flux and other metrics.
- The most novel aspect of this manuscript relates to using a deformed geometry method; however, there is no detail about its implementation.
- The SI section is almost a copy of the methods from Gomez-Velez et al. (2017). I leave this issue for the Editor to resolve, but there should be a balance between credit and completeness. To some degree, it feels like the SI could be replaced by a sentence like “We use the same methods, equations, and metrics described in Gomez-Velez et al. (2017). The only difference is the implementation of a deformed geometry method to capture the dynamic evolution of the wetting front along the sloping banks,” followed by the exact details of the moving boundary equation (y(x,t) in the manuscript) and the explanation of the deformed geometry method.
General comments:
Line 20-21: “This new model approach serves as the initial step to consider complicated floodplain morphologies in physics-based models for better predictions of HEF…” is inaccurate. This model is a refinement of a reduced-complexity model, but the literature is full of significantly more complex models that capture the complexities of banks and floodplains.
Lines 53-55: I need clarification on this statement, which seems conceptually incorrect. I suggest rewording for clarity.
Line 200: You need to define the parameters used here. You could use the conceptual figure from the SI.
Citation: https://doi.org/10.5194/hess-2023-29-RC2 -
AC2: 'Reply on RC2', Zhang Wen, 19 Jul 2023
Main Comments:
(1) The manuscript is generally well-written. I suggest revising the text to improve clarity (see my comments below). For example, the methods introduce equations (line 200) with variables that need to be clearly defined. Also, I suggest making the introduction more succinct to focus on the actual study.
Reply: Thanks for your comments and suggestions, we will add the definitions of the variables in every equation throughout the paper, and introduce more actual field study succinctly in the Introduction section as you suggested.
(2) In its current form, this manuscript requires significant revisions, and I wonder if this is a contribution suited for publication in HESS. In the following, I describe the aspects that support my conclusion and provide a few suggestions to address them.
After reading the current manuscript, I tried to answer the question: is the work making a significant or incremental contribution to our understanding of hyporheic processes? In other words, did I learn something new that wasn’t in Gomez-Velez et al. (2017)? Based on the current version of this manuscript, my answer is “no.”
Reply:
Thanks for reviewer’s comments and suggestions. Firstly, our paper does have new outcomes that have not been addressed by Gomez-Velez et al. (2017). Here are some examples :
1. This study reveals the impacts of bank slope on HEF and HZ in the aquifers with lower transmissivity, which has not been addressed in Gomez-Velez et al. (2017).
- This study reaches the conclusion that the aquifer transmissivity determines the impact time of bank slop on the residence time distribution (RTD), which can be more specifically and briefly represented as: for a higher transmissivity aquifer, the impacts of bank slope on RTD were observed only during the dynamic flood event. However, long-lasting impacts can be found after the flood event for low transmissivity aquifers. All the above findings have not been observed in Gomez-Velez et al. (2017).
- This study finds that the impact pattern of bank slope on RTD is also influenced by the location along the sinuous river. For example, including bank slope will lead to generally shorter residence times around cut bar (x = 0) but longer residence times around point bar (x = λ). This is a new understanding and has not been addressed by Gomez-Velez et al. (2017) or any other research.
This work adds additional complexity to capture the effect of the sloping bank; however, the approach includes strong assumptions that might defeat its purpose. For example: The deformed geometry method (DGM) proposed here ignores the primarily vertical fluxes within the wedge cut by the moving boundary, which is still assumed vertical. Is this a reasonable assumption, and what are the implications? The importance of the bank slope highlighted by Liang et al. (2018), Doble et al. (2012), and others for cross-sectional, partially saturated models results from the vertical component of the exchange and the migration of the air-water interface. These processes are ignored here; therefore, I wonder whether the current model addresses these issues. Reproducing the simulations from Gomez-Velez et al. (2017) is helpful for completeness and verification; however, I suggest that the authors use a 3D version of this conceptual model to verify the appropriateness of their 2D reduced-complexity model and the implemented DGM.
Reply: As for the reasonability of the assumption of using Boussinesq equation and DMG to capture the migration of wet front: the assumptions are the same to those used in Liang et al. (2018), the model dimension of which is extended to 2-D in our study accounting for the morphology characteristics of river (sinuosity) and ambient groundwater gradient. Besides, our model framework, flow equation and corresponding assumptions have also been wildly used in previous numerical research focused on the same topic, such as Boano et al. (2014) and Gomez-Velez et al. (2013; 2017), etc; particularly, the DMG has been successfully implemented and proved to be accurate in Liang et al. (2018). Thus, the assumption in our model is reasonable to support the implementation of the research goal.
As for using 3-D model: Thanks for your good suggestions. A 3-D model requires the utilization of the Richards equation, which is a totally different equation with different assumptions to the Boussinesq equation in our manuscript. Since we have 0.5 million grids in our 2-D model to avoid the numerical error, a dimensionality upgrade to 3-D version will lead to an extremely huge number of grids, then the computational burden will not be well handled, especially when the non-linear vertical-integrated ADE and RTD equations have to be used in this study.
Despite the neglect of the vertical flux, we think our modeling study still has its significant scientific contribution, which is in fact not dependent on the vertical flux. For example, our study reveals that the bank slope only has the significant effect on hyporheic exchange in low transmissivity aquifer. However, the bank slope should be always considered when assessing the dynamic of RTD for all kind of transmissivity of aquifer.
(3) Within the dimensionless context, the metrics show only mild differences with the bank slope. Cases with significant differences require a $\Gamma_d$ of 100, which is relatively uncommon in natural systems (see Figure 2A in Gomez-Velez et al. (2017)). The authors need more clarity about their definition of “significant” differences caused by the bank slope and put this in the context of physical and biogeochemical processes and observations. Based on these results, I would conclude that representing the slope of the banks (with the Authors' conceptualization) does not have significant implications for the exchange flux and other metrics.
Reply: Thanks for your suggestions. As you suggested, we will redefine the “significant” impact of this study, and put the implication of results more in the context of physical and biogeochemical process and observation. Firstly, the impact of bank slope on hyporheic exchange flux and hyporheic zone can be significant For example, there are ten simulation scenarios when the bank slope can increase the maximum net flux by 10 percentage, and three scenarios by 30 percentage, as shown in Figure 4. Secondly, Figure 8 to 11 already show that the impact of bank slope on RTD can be significant during flood event and after flood event for high-transmissivity and low-transmissivity aquifers, respectively, please see the corresponding explanations at Lines 524-532 in the submission version. As stated above, we would conclude that representing the bank slope does have implications for the exchange flux and other metrics.
The most novel aspect of this manuscript relates to using a deformed geometry method; however, there is no detail about its implementation.
Reply: Agree, we will add more mathematical statement about the implement of Deformed Geometry Method in the SI.
The SI section is almost a copy of the methods from Gomez-Velez et al. (2017). I leave this issue for the Editor to resolve, but there should be a balance between credit and completeness. To some degree, it feels like the SI could be replaced by a sentence like “We use the same methods, equations, and metrics described in Gomez-Velez et al. (2017). The only difference is the implementation of a deformed geometry method to capture the dynamic evolution of the wetting front along the sloping banks,” followed by the exact details of the moving boundary equation (y(x,t) in the manuscript) and the explanation of the deformed geometry method.
Reply: Thank for your careful review on our manuscript. The logical and construction of model implementation are similar to those of Gomez-Velez et al. (2017) and Singh et al. (2019), But it is not a copy of any of previous research. The duplicate checking of this manuscript (or the plagiarism detection report) from HESS can prove it. Again, we appreciate your kindly suggestion, and will revise that chapter in the revised version.
General comments:
Line 20-21: “This new model approach serves as the initial step to consider complicated floodplain morphologies in physics-based models for better predictions of HEF…” is inaccurate. This model is a refinement of a reduced-complexity model, but the literature is full of significantly more complex models that capture the complexities of banks and floodplains.
Reply: Agree, we will modify that sentence and make a clear statement that this paper is the first research focusing on the impact of bank slope on hyporheic exchange process for a sinuosity-driven river corridor.
Lines 53-55: I need clarification on this statement, which seems conceptually incorrect. I suggest rewording for clarity.
Reply: Agree, we will revise that sentence.
Line 200: You need to define the parameters used here. You could use the conceptual figure from the SI.
Reply: Agree, we will add the definition of all the parameters here in the revised version of manuscript.
Citation: https://doi.org/10.5194/hess-2023-29-AC2
- After reading the current manuscript, I tried to answer the question: is the work making a significant or incremental contribution to our understanding of hyporheic processes? In other words, did I learn something new that wasn’t in Gomez-Velez et al. (2017)? Based on the current version of this manuscript, my answer is “no.” This work adds additional complexity to capture the effect of the sloping bank; however, the approach includes strong assumptions that might defeat its purpose. For example:
Yiming Li et al.
Yiming Li et al.
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