the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 17 Oct 2022
Technical note: Displacement variance of a solute particle in heterogeneous confined aquifers with random aquifer thickness fields
Abstract. In this work, the problem of regional-scale transport of inert solutes in heterogeneous confined aquifers of variable thickness is analyzed in a stochastic framework. A general stochastic methodology for deriving the variance of the displacement of a solute particle is given based on the two-dimensional depth-averaged solute mass conservation equation and the Fokker-Planck equation. The variability in solute displacement is attributed to the variability in hydraulic conductivity and aquifer thickness. Explicit results for the solute displacement variance in the mean flow direction are obtained assuming that the fluctuations in log hydraulic conductivity and log thickness of the confined aquifer are second-order stationary processes. The results show that variation in hydraulic conductivity and aquifer thickness can lead to nonstationarity in the covariance of flow velocity, making longitudinal macrodispersion anomalous and increasing linearly with travel time at large distances.
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Status: closed
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RC1: 'Comment on hess-2022-298', Anonymous Referee #1, 08 Nov 2022
I have tried to read this paper multiple times now and every time find myself frustrated. I am highly litterate in terms of mathematically dense papers, but I found this paper next to impossible to make my way through. I do not usually write grumpy reviews, but this will be one. I have three major concerns that lead me to recommend that this paper be rejected.
(1) My first and likely biggest issue is going from equation (1) to (2). Any time you average and ADE equation like the one the authors have you will have a mean and fluctuation of the things that vary. In this case concentration, velocity and depending on the nature of the dispersion coefficient that also. Where are all of these gone? They don't just dissappear as it seems that they do in equation (2) Â - i.e. it's fine to say that the average of the fluctuation of concentration is zero, but the average of the product of concentration and velocity fluctuations is not. Indeed this is exactly what leads to things like macrodispersion and deviations from standard behaviors. Where have these gone here? There is no discussion of them and none of the assumptions I see in the problem setup suggest they do not exist or are negligible. This is the starting point of the paper and frankly makes me feel like the authors are departing from a faulty point from the getgo.
(2) As I noted I am someone who writes and reads a lot of papers with pretty dense and complex mathematics in it, but I found a lot of what the authors present extremely hard to follow, where in some places there is abundant detail and in others serious gaps.
(3) Last but not least, even if everything is right (which I cannot verify) I struggle to see the real importance of this paper and thus am hesitant to see it published in such a high level journal such as HESS which is one of the top journals in our field. Much of the paper feels a little archaic in nature and while I love theoretical papers with full mathematics I also feel that something clear should be gained by ellaborating it and I just do not see that here.
I'm sorry for being grumpy, but I also feel that the authors put me in this place with poor presentation and a lack of clear motivation and setup of the problem they're really trying to tackle. Based on my reading I believe the paper should be rejected and not published in HESS. Perhaps with some rewriting and really ensuring all the presentation is correct and consistent another more specific journal would be better suited to this type of work.
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Citation: https://doi.org/10.5194/hess-2022-298-RC1 - AC2: 'Reply on RC1', Chuen-Fa Ni, 06 Jan 2023
- AC4: 'Reply on RC1', Chuen-Fa Ni, 06 Jan 2023
- AC1: 'Comment on hess-2022-298', Chuen-Fa Ni, 11 Nov 2022
-
RC2: 'Comment on hess-2022-298', Anonymous Referee #2, 18 Dec 2022
My impression is that the novelty that this work brings is scarce. Probably this is partially due to the presentation of the derivation and the results that is quite confusing. I suggest the authors revise completely the paper by improving the description of the mathematical approach and by relating it to the state-of-art to underline the advancements introduced by the study. I also suggest revising the figures that presently are of poor quality and not so explicative. I ask the authors to rethink the graphical representation of the results and to add more graphical insights to help the comprehension. In summary, I suggest major revisions to the manuscript even if I'm aware that the sum of all the revisions would lead to a very different version of the manuscript.Â
Citation: https://doi.org/10.5194/hess-2022-298-RC2 - AC3: 'Reply on RC2', Chuen-Fa Ni, 06 Jan 2023
- AC5: 'Reply on RC2', Chuen-Fa Ni, 06 Jan 2023
Status: closed
-
RC1: 'Comment on hess-2022-298', Anonymous Referee #1, 08 Nov 2022
I have tried to read this paper multiple times now and every time find myself frustrated. I am highly litterate in terms of mathematically dense papers, but I found this paper next to impossible to make my way through. I do not usually write grumpy reviews, but this will be one. I have three major concerns that lead me to recommend that this paper be rejected.
(1) My first and likely biggest issue is going from equation (1) to (2). Any time you average and ADE equation like the one the authors have you will have a mean and fluctuation of the things that vary. In this case concentration, velocity and depending on the nature of the dispersion coefficient that also. Where are all of these gone? They don't just dissappear as it seems that they do in equation (2) Â - i.e. it's fine to say that the average of the fluctuation of concentration is zero, but the average of the product of concentration and velocity fluctuations is not. Indeed this is exactly what leads to things like macrodispersion and deviations from standard behaviors. Where have these gone here? There is no discussion of them and none of the assumptions I see in the problem setup suggest they do not exist or are negligible. This is the starting point of the paper and frankly makes me feel like the authors are departing from a faulty point from the getgo.
(2) As I noted I am someone who writes and reads a lot of papers with pretty dense and complex mathematics in it, but I found a lot of what the authors present extremely hard to follow, where in some places there is abundant detail and in others serious gaps.
(3) Last but not least, even if everything is right (which I cannot verify) I struggle to see the real importance of this paper and thus am hesitant to see it published in such a high level journal such as HESS which is one of the top journals in our field. Much of the paper feels a little archaic in nature and while I love theoretical papers with full mathematics I also feel that something clear should be gained by ellaborating it and I just do not see that here.
I'm sorry for being grumpy, but I also feel that the authors put me in this place with poor presentation and a lack of clear motivation and setup of the problem they're really trying to tackle. Based on my reading I believe the paper should be rejected and not published in HESS. Perhaps with some rewriting and really ensuring all the presentation is correct and consistent another more specific journal would be better suited to this type of work.
Â
Citation: https://doi.org/10.5194/hess-2022-298-RC1 - AC2: 'Reply on RC1', Chuen-Fa Ni, 06 Jan 2023
- AC4: 'Reply on RC1', Chuen-Fa Ni, 06 Jan 2023
- AC1: 'Comment on hess-2022-298', Chuen-Fa Ni, 11 Nov 2022
-
RC2: 'Comment on hess-2022-298', Anonymous Referee #2, 18 Dec 2022
My impression is that the novelty that this work brings is scarce. Probably this is partially due to the presentation of the derivation and the results that is quite confusing. I suggest the authors revise completely the paper by improving the description of the mathematical approach and by relating it to the state-of-art to underline the advancements introduced by the study. I also suggest revising the figures that presently are of poor quality and not so explicative. I ask the authors to rethink the graphical representation of the results and to add more graphical insights to help the comprehension. In summary, I suggest major revisions to the manuscript even if I'm aware that the sum of all the revisions would lead to a very different version of the manuscript.Â
Citation: https://doi.org/10.5194/hess-2022-298-RC2 - AC3: 'Reply on RC2', Chuen-Fa Ni, 06 Jan 2023
- AC5: 'Reply on RC2', Chuen-Fa Ni, 06 Jan 2023
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