the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
A rainfall-tracking travel time distribution model to quantify mixing and storage release preference in a large shallow lake by two-year stable isotopic data
Abstract. Lake Taihu is the largest eutrophic lake in China that is shallow and connected to a dense river network. Severe eutrophication is frequently observed in Lake Taihu due to excess pollutant loadings. Understanding water cycle dynamics is essential for investigating this problem. The travel time distribution (TTD), residence time distribution (RTD) and storage selection (SAS) function describing how water is stored, mixed and released in the lake provide fundamental information on water cycle dynamics. In this study, a rainfall mixing model is established and coupled with the age master equation model to estimate the time-variant TTDs and RTDs of rainwater, river water and all water in Lake Taihu based on the two-year high-resolution isotopic data. In the rainfall mixing model, a novel rainfall mixing factor is introduced to quantify the mixing of rainwater with older lake water. The estimated range of travel time varies between 2–4 months and 7–9 months, depending on lake volume. Lake Taihu shows an inverse storage effect, i.e., the release preference shifts toward younger water when lake volume is large. The results of rainfall mixing model reveal distinct patterns and control factors between the TTDs of rainwater and river water, with rainwater contributing to 15 %–25 % of outflow. Then, the SAS functions of rainwater and river water are analyzed, which are controlled by different source zones and flow patterns. Temporal variation of spatial distribution of deuterium isotope composition illustrates storage release preference is controlled by the variation of horizontal flow paths and velocities in the lake.
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RC1: 'Comment on egusphere-2024-1513', Anonymous Referee #1, 11 Jul 2024
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Review of “A rainfall-tracking travel time distribution model to quantify mixing and storage release preference in a large shallow lake by two-year stable isotopic data” by Mao et al submitted to Hydrology and Earth System Sciences
In my opinion, the manuscript will be a great addition to the journal and be of interest to its readers. Mao et al targets the variations in time and in space of residence time and travel time at Lake Taihu, China, by processing and analyzing measurements of deuterium in the lake. Temporal scales in lakes have been correlated to water quality issues, therefore knowing how long a water parcel remains in the lake depending on the meteorological conditions will provide a clearer picture on how to better manage water quality in Taihu Lake. For example, their results show that depending on the inflow of water (through rivers and rain) the travel time can decrease by half.
However, I recommend the manuscript to be brought back to the authors for revisions for the following reasons:- There have been publications mentioning Lake Taihu’s residence time. I am thinking for example of Xu et al 2009 (https://doi.org/10.4319/lo.2010.55.1.0420), Xu et al 2015 (https://doi.org/10.1021/es503744q) and Paerl et al 2014 (https://doi.org/10.1371/journal.pone.0113123). Interestingly the value of residence time is not consistent among these publications, but they remain below the 1 year mark. I think the manuscript would benefit by including a comparison and a possible explanation of the discrepancy between the publications.
- There are portions of paragraph in Section 5 that appear contradictory to the results described in the abstract. For example, at the end of Section 5.2.1, lines 477-478, Mao et al states that “older water parcels may have greater chances leaving the system than younger water parcels”. However, in the abstract it is stated that “the release preference shifts toward younger water when lake volume is large”. A reorganization of the subsections would help to make things clearer.
- In the introduction, lines 51-52, the authors mention that only Smith et al. 2018 applied the travel time distribution theory to a lake. Unless the authors were implicitly focusing on the usage of isotopic compound, I disagree with the authors. Temporal scales have been addressed in previous work in lakes. For example, Rueda and Cohen, 2005 (https://doi.org/10.4319/lo.2005.50.5.1638) looked at variation in space and time of residence time in an embayment of Lake Ontario, Canada.
- The authors mention the spatio-temporal variations of the time scales are controlled by horizontal velocities on several occasions (in the abstract and in the conclusion), they did not discuss past work identifying the flow field at Lake Taihu. The manuscript would benefit from including comparisons with past work on average flow field in Lake Taihu Liu et al. 2018 (doi:10.3390/w10060792) shows for example a rather complex average flow field, which would definitely hinder the flow of water from inflow to outflow.
I noticed a couple of typos in the text:
- Figure 2: There is no sampling point 2. I assume it is supposed to be where sampling point 32 is.
- Line 304: If I understand properly, s_rain(t,tau) is the volume of rain water aged tau, and not s(t,tau).
- Line 499: please replace “board range” with “broad range”.
- Line 505: please replace “Lake” with “lake”.
Citation: https://doi.org/10.5194/egusphere-2024-1513-RC1 -
AC1: 'Reply on RC1', Rong Mao, 15 Jul 2024
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Please find the attached document for our point-by-point replies.
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RC2: 'Comment on egusphere-2024-1513', Paolo Benettin, 19 Jul 2024
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This manuscript introduces a travel time model that deals with the problem of tracking water age in hydrologic systems characterised by multiple input fluxes. This is relevant for lake studies, which typically have 2 inputs (river inflow and rainfall). The authors apply the model to the case study of Lake Taihu, China, and calibrate the model parameters against 24 monthly values of mean isotope composition of the lake water. The authors use the calibrated model to discuss water age dynamics and rain/river water partitioning within the lake and the output fluxes.
I anticipate that, while I appreciate this work, I am afraid there are major technical issues in the solution proposed by the authors that prevents publication of the current version of the paper, but I think that similar results produced under alternative – and possibly simpler solutions may be worth of publication.
The authors touch on a very interesting and challenging problem that is multiple-input tracking in lumped models. Most of the water transit time literature (see the review work that myself and many colleagues have written in 2022, https://doi.org/10.1029/2022WR033096) dealt with systems with one single input, i.e. rainfall. Therefore, the effort put in place by the authors fills an important gap and is to be credited. The text, while needing some English proofread, is understandable and the approach undertaken by the authors appears rigorous and is described in full detail.
A key point of the paper is a new solution to the tracking of multiple sources within a lumped model. The authors call their solution “Rainfall mixing” or “rainfall tracking”. I think this solution is problematic on some fronts:
- The manuscript seems to often confound space with age. Lumped age models do not explicitly account for space. The effects of physical processes (like advection and dispersion) can be effectively reproduced by using a lagged transit time distribution or SAS function, but those processes are not directly modelled. Similarly, water age models do not account for any physical mixing within the storage and they only prescribe how the output fluxes remove waters of different ages from the storage (which is why the community tends to speak about “random sampling” rather than “well mixing”). The idea that rainfall water is well mixed with pre-existing lake water while river water is not is unsuitable to this lumped framework and should rather be translated into SAS language and equations. Translating the different transport processes of two very different inputs into a single SAS function may be challenging and highlights the limitations of lumped water age models.
- The rainfall mixing approach is difficult to understand and after reading it multiple times I still am not sure I could follow all the steps. My understanding is that ultimately the “candidate” beta-shaped SAS functions are checked at any time step and if some constrain is not respected, they are modified. The effect of this transformation is difficult to follow, but I think it generally increases the amount of young water released to the outflow, to effectively simulate the “preferential” release of rain water. The manuscript should clarify the effect of this modification more explicitly, for example by showing some examples of candidate and modified SAS function or by showing a simulation with and without those constraints. I think it is also important that this more complex approach is justified in terms of model performance, i.e. that the model with the modification performs significantly better than a “traditional” model.
- Monthly time steps for the solution of the water age balance using the Euler Forward scheme is potentially coarse. I invite the authors to verify that the numerical accuracy is not compromised by the use of large time steps.
I believe these major issues need to be addressed before discussing additional minor comments. However, I reiterate that an improved or simplified multiple-input tracking system would likely make the paper worthy of publication.
Citation: https://doi.org/10.5194/egusphere-2024-1513-RC2 -
AC2: 'Reply on RC2', Rong Mao, 24 Jul 2024
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We sincerely appreciate your valuable comments. After several days of careful analysis, we are confident in informing you that we have addressed all of your major comments, and will make thorough revisions based on them. Your valuable suggestions have greatly helped improve the quality of our manuscript.
Below is a brief summary of the modifications we will make in the revised manuscript. For detailed replies to your comments, please refer to the attached file.
(1) We derived a new analytical solution for the SAS function that successfully integrates the transport of rainwater and river water into a single SAS function, as you suggested. Therefore, steps for checking the 'candidate' beta-shaped SAS functions can be removed. We defined a new variable, the "event rain water threshold age", which is crucial for determining the shape of the new SAS function.
With this new SAS function, the TTD, RTD, and SAS function can be calculated using methods from traditional TTD literature. After that, the volumes of rain water and river water in the lake and outflows can be partitioned using the rainfall mixing factor. Therefore, the new SAS function will make our model simpler, easier to understand, and more straightforward to implement.
(2) Regarding the issue of large time steps, we have conducted an error analysis for different time steps: dt=1,0.5,0.25, 0.125 months. The deuterium concentration increases slightly with smaller time steps. Based on the results of error analysis, we will revise our manuscript using the model with a smaller time step of dt=0.25 month and add a paragraph to discuss the error caused by different time steps.
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