Explicit simulation of reactive microbial transport with a dual-permeability, two-site kinetic deposition formulation using the integrated surface-subsurface hydrological model HydroGeoSphere

Currle, Friederike; Therrien, René; Schilling, Oliver S.

doi:https://doi.org/10.5194/egusphere-2025-372

Preprints

https://doi.org/10.5194/egusphere-2025-372

Preprints

06 Feb 2025

| 06 Feb 2025

Explicit simulation of reactive microbial transport with a dual-permeability, two-site kinetic deposition formulation using the integrated surface-subsurface hydrological model HydroGeoSphere

Friederike Currle, René Therrien, and Oliver S. Schilling

Abstract. Assessing the transport behavior of microbes in surface water-groundwater systems is important to prevent contamination of drinking water resources by pathogens. While wellhead protection area (WHPA) delineation is still predominantly based on dye injection tests and advective transport modeling, size exclusion of colloid-sized microbes from the smaller and usually less conductive pore space causes a faster breakthrough and thus faster apparent transport of microbes compared to that of solutes. To provide a tool for better assessment of the differences between solute and microbial transport in surface water-groundwater systems, we here present the implementation of a dual-permeability, two-site kinetic deposition formulation for microbial transport in the integrated surface-subsurface hydrological model HydroGeoSphere (HGS). The implementation considers attachment, detachment and inactivation of microbes in both permeability regions and allows for multispecies transport. The dual-permeability, two-site kinetic deposition implementation in HGS was verified against an analytical solution for dual-permeability colloid transport and the suitability of the model for microbial transport at the wellfield scale is illustrated in a multi-tracer flow and transport study of an idealized alluvial riverbank filtration site. In this illustrative example, the transport of reactive microbes, conservative ⁴He, and reactive ²²²Rn was simulated in parallel, allowing mixing ratios, tracer breakthrough curves and travel times to be assessed via multiple approaches. The developed simulation tool is the first integrated surface-subsurface hydrological simulator for reactive solute and microbial transport, and marks an important advancement to unlock and quantify governing microbial transport processes in riverbank filtration settings. It enables meaningful WHPA delineation and risk assessments even under extreme hydrological situations such as flood events.

Received: 27 Jan 2025 – Discussion started: 06 Feb 2025

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Journal article(s) based on this preprint

21 Oct 2025

Explicit simulation of microbial transport with a dual-permeability, two-site kinetic deposition formulation using the integrated surface–subsurface hydrological model HydroGeoSphere

Friederike Currle, René Therrien, and Oliver S. Schilling

Hydrol. Earth Syst. Sci., 29, 5383–5403, https://doi.org/10.5194/hess-29-5383-2025,https://doi.org/10.5194/hess-29-5383-2025, 2025

Short summary

Friederike Currle, René Therrien, and Oliver S. Schilling

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-372', Anonymous Referee #1, 08 Mar 2025

This manuscript presents the implementation of an existing dual-permeability approach to address transport of (microbial) colloids in the proprietary software HydroGeoSphere that can simulate saturated-unsaturated flow and transport coupled to surface flow and transport. The code is validated against an existing analytical solution for 1-D dual-permeability transport with linear exchange kinetics between the two domains and linear kinetic sorption in both of them. The final demonstration is a virtual test case mimicking bank filtration, in which colloidal transport is simulated together with 4He and radon as natural tracers. There is no comparison to experimental or field data.
As the manuscript’s major statement is that the authors have transferred an existing model formulation to an existing software package I see this as a technical note rather than a research article. The 1-D example is not particularly exciting from a process-insight view because the influence of different parameters on multi-permeability models has been discussed before. I have remarks on the 3-D application further down.
With respect to presenting the model extension of HydroGeoSphere, the text is written in a slightly odd way. It is not clear what was actually developed within the study, and what has already existed. I checked the HydroGeoSphere documentation, which includes colloid transport in dual-permeability models. But that might only mean that the documentation has already included the results of the present study. The only wording that directly implies model extension is in lines 175-177, where the inclusion of a first-order decay term is mentioned. Please clarify that the implementation of the Bradford et al. (2009, doi: 10.1029/2008WR007096) formulation is really specific to this study. Otherwise I am even more puzzled what the message of the manuscript is.
Let’s come to the conceptual assumptions of the Bradford et al. (2009) formulation. Dual-permeability flow and transport was introduced by Barenblatt et al. (1960, doi: 10.1016/0021-8928(60)90107-6) to address preferential flow in fractured media, and has been used to parameterize effects on heterogeneity on (flow and) solute transport, characterized by strong anomalous behavior. The concept has been presented using different names (e.g., multi-domain model, mobile-mobile model). In contrast to dual-porosity (mobile-immobile, transient storage) models, it requires solving two coupled flow problems, posing big difficulties in unique calibration if the flow behavior is quite normal. Bradford et al. (2009) reinterpreted the conceptual model to facilitate that colloids break through earlier than solutes. The latter effect is caused by size exclusion and by the fact that colloids cannot experience the velocity within pores at distances to solids smaller than half their diameter. If the colloids have the same net electrical charge as the grain surface they experience an even smaller portion of the intra-pore velocity distribution because they are repelled from the no-slip boundary. Other model formulations for colloid transport, involving reversible attachment-detachment and irreversible straining, cannot reproduce a first breakthrough before that of solutes. Bradford et al. (2009) claimed that their formulation also addresses straining, but that is not really true. In both domains, the model assumes kinetic first-order attachment and detachment. It is trivial to derive equilibrium sorption coefficients from the ratio of the detachment and attachment rate coefficients. Choosing a low detachment coefficient in the low-permeability domain still implies reversible sorption. However, straining is irreversible: particles get stuck in pore throats and never ever become mobile again. This implies that the formulation of Bradford et al. (2009) leads to very long tailing of colloid breakthrough curves with a complete recovery at infinite times, whereas models that include an elimination mechanism according to standard colloid filtration theory will have an incomplete recovery (i.e. the zeroth moment of the transfer function between the in- and output concentration in 1-D transport is smaller than unity). If you really want straining, you either choose a detachment coefficient in the less-mobile domain of zero, or you introduce a first-order elimination term. The authors have such a term, but they relate it other mechanisms than straining because they uncritically adopt the erroneous perspective of Bradford et al. (2009) that kinetic reversible mass transfer could parameterize (irreversible) straining.
Would there be a much simpler way of achieving an earlier breakthrough of colloids than of solutes without introduction of a second permeability? That is indeed possible. All you need is a retardation factor for the colloids smaller than one, and they are faster than the solutes. You would still need an irreversible straining term and (at least one) kinetic, reversible attachment-detachment term, but the model would be much simpler because you could skip coming up with two spatial permeability distributions and exchange terms of the fluids between the two domains (and the flow problem would have half the number of unknowns). Given the fact that the authors don’t want to use the dual-permeability formulation for its original purpose (addressing anomalous flow and transport in highly heterogeneous formations), and that they don’t have the data to inform such a model for its original purpose, I cannot recommend the conceptual approach chosen by the authors. It is simply an overkill, particularly in 3-D settings.
The authors promise a reactive microbial transport model in the title. This is slightly misleading. The only “reaction” term is a first-order elimination term. Many microbes of interest undergo complex dynamics due to growth, dormancy and reactivation, change in mobility corresponding to their physiological state or abundance. In the model of the authors the microbes must be introduced via the inflow and can only adsorb or vanish besides transport. They are essentially treated like dead particles. I can fully understand that the authors don’t intend to elaborate on microbial dynamics, but then they should be careful in selling they model as “reactive microbial transport model”.
As mentioned above, I am not too impressed by the 1-D tests. They mainly reproduce the work of Bradford et al. (2009), who at least had a comparison to real measurements, and of Leij and Bradford (2013). It is of course important that a code is tested against analytical solutions for model validation, but it is not a scientifically particularly exciting exercise.
The 3-D demonstration is supposed to show that the model works field-similar settings. It is not well suited to convince the reader that an integrated surface-subsurface hydrological model is needed. The test would equally well work with a pure groundwater model forced by the boundary condition at the river. In the setup, like in many bank filtration applications, the river is not really affected by groundwater flow and transport (and every HydroGeoSphere user knows that running the model as pure porous-medium model makes life much easier). A more interested application would show real feedbacks between the surface and subsurface domains, e.g., when considering transport of pathogens in a meandering stream with intensive hyporheic exchange and bank storage. That is obviously not the final application that the authors have in mind, but I would claim that the 3-D test problem could be simulated with loose coupling of the surface and subsurface domains (or even just predefining river-stage and concentration fluctuations as boundary condition).
In the 3-D test case, the authors first simulate steady-state concentrations, involving an input of (microbial) colloids from the river, ⁴He as a natural tracer for the mixing of old groundwater with river water, and ²²²Rn as age tracer. They then simulate the response to a river-stage fluctuation. Proportional to the river discharge they increase the concentration of the (microbial) colloids an of ⁴He in the river (mimicking an artificial tracer with concentration is proportional to that of the microbes). The former makes sense, whereas I am not happy about the later because ⁴He is supposed to be an indicator of mixing of old groundwater and river infiltrate, and with the pulse in the river the boundary between the two water bodies moves. While this boundary may be far away from the observation points, it is not particularly smart to create two causes of ⁴He changes. It might have been better to add a real artificial tracer to separate the signals.
As designed, the colloids break slightly earlier through than the solute tracer. The effect is not super big (4.5% earlier peak time) and well within the uncertainty of travel-time estimates in real-world studies on outlying well-head protection zones. With a longitudinal dispersivity of more than 5m (and additional dispersion caused by mobile-mobile transport), the peaks are so broad that the difference in the breakthrough curves are not particularly obvious by eye sight. The much more interesting signal is that of the radon. Here, the authors get a much earlier breakthrough. They attribute this to radon following the pressure wave (lines 433-434), but that makes physically no sense. What I believe is that the river-stage fluctuation shifts the flow pattern and by that the age distribution. Honestly, I find this phenomenon more interesting than the micobial-transport study as you see a real signal.
The results section ends with a summary/conclusion, followed by a discussion section, and then final conclusions. That’s a little bit odd, particularly since the actual conclusions are quite shallow.
In summary, I have expressed my doubts that the dual-permeability model is the best choice for transport of microbial colloids. I am convinced that you can achieve the same results computationally much cheaper. I believe that the 1-D model has too much weight given that it includes nothing new. The 3-D application does not need an integrated surface-subsurface model and does not underscore that the chosen model formulation is really needed. If there were real data that can only be interpreted with the model, the authors would have a much stronger point. This manuscript needs severe revisions to make it a significant contribution.

Citation: https://doi.org/10.5194/egusphere-2025-372-RC1
- AC1: 'Reply on RC1', Friederike Currle, 02 Apr 2025
  
  Dear reviewers, dear editors
  We are pleased with the feedback and would like to thank the two reviewers for the very helpful comments. None of the reviewers have risen any technical concerns related to the implementation of the code, which highlights that our code is relevant and carefully implemented. However, both reviewers have suggested some important improvements in the presentation of the verification and illustration examples of the new model implementation, which we will implement, and which will allow the manuscript to improve further. Moreover, as correctly pointed out by reviewer #1, the paper is a technical note rather than a research paper, an aspect which we would like to confirm.
  We will address all comments of reviewer #1 in a revised manuscript as outlined in detail in the supplement.
  Sincerely,
  Friederike Currle, René Therrien and Oliver Schilling
  
  Citation: https://doi.org/10.5194/egusphere-2025-372-AC1
RC2:
'Comment on egusphere-2025-372', Anonymous Referee #2, 17 Mar 2025

This manuscript outlines the inclusion of dual-permeability, two-site kinetic deposition formula for microbial transport in HydroGeoSphere (HGS). I believe this topic is relevant and of interest to the readers of EGUsphere. The manuscript is generally well-written, with the inclusions of expected sections outlining the model development, validation and illustrative application, all written in a clear manner.
As presented, my primary concern relates to the novelty and contributions of this work. How does this differentiate from other subsurface reactive transport models available – why should someone choose to use HGS over these models? I understand that the primary feature of including these equations in HGS is the inclusion with an integrated hydrologic model as opposed to solely a subsurface model, but no part of this manuscript uses or highlights the benefit of an integrated approach over subsurface-only. The authors outline the equations that govern surface flow and transport, but the verification and illustrative application do not seem to utilize the surface domain at all. Perhaps it is simulated, but the results are not presented or discussed. I think this is critical to the contributions of this work – what does this newly developed feature provide that was otherwise lacking? Perhaps a comparison between groundwater-only simulations and the integrated approaches can help demonstrate the benefit of including these equations with HGS as opposed to solely a subsurface approach.
Given this concern is critical to the contributions and novelty of this research, I feel the authors need to make significant revisions before this manuscript can be considered for publication.

Citation: https://doi.org/10.5194/egusphere-2025-372-RC2
- AC2: 'Reply on RC2', Friederike Currle, 02 Apr 2025
  
  Dear reviewers, dear editors
  We are pleased with the feedback and would like to thank the two reviewers for the very helpful comments. None of the reviewers have risen any technical concerns related to the implementation of the code, which highlights that our code is relevant and carefully implemented. However, both reviewers have suggested some important improvements in the presentation of the verification and illustration examples of the new model implementation, which we will implement, and which will allow the manuscript to improve further. Moreover, as correctly pointed out by reviewer #1, the paper is a technical note rather than a research paper, an aspect which we would like to confirm.
  We will address all comments of reviewer #2 in a revised manuscript as outlined in detail in the supplement.
  Sincerely,
  Friederike Currle, René Therrien and Oliver Schilling
  
  Citation: https://doi.org/10.5194/egusphere-2025-372-AC2

Interactive discussion

Status: closed

RC1:
'Comment on egusphere-2025-372', Anonymous Referee #1, 08 Mar 2025

This manuscript presents the implementation of an existing dual-permeability approach to address transport of (microbial) colloids in the proprietary software HydroGeoSphere that can simulate saturated-unsaturated flow and transport coupled to surface flow and transport. The code is validated against an existing analytical solution for 1-D dual-permeability transport with linear exchange kinetics between the two domains and linear kinetic sorption in both of them. The final demonstration is a virtual test case mimicking bank filtration, in which colloidal transport is simulated together with 4He and radon as natural tracers. There is no comparison to experimental or field data.
As the manuscript’s major statement is that the authors have transferred an existing model formulation to an existing software package I see this as a technical note rather than a research article. The 1-D example is not particularly exciting from a process-insight view because the influence of different parameters on multi-permeability models has been discussed before. I have remarks on the 3-D application further down.
With respect to presenting the model extension of HydroGeoSphere, the text is written in a slightly odd way. It is not clear what was actually developed within the study, and what has already existed. I checked the HydroGeoSphere documentation, which includes colloid transport in dual-permeability models. But that might only mean that the documentation has already included the results of the present study. The only wording that directly implies model extension is in lines 175-177, where the inclusion of a first-order decay term is mentioned. Please clarify that the implementation of the Bradford et al. (2009, doi: 10.1029/2008WR007096) formulation is really specific to this study. Otherwise I am even more puzzled what the message of the manuscript is.
Let’s come to the conceptual assumptions of the Bradford et al. (2009) formulation. Dual-permeability flow and transport was introduced by Barenblatt et al. (1960, doi: 10.1016/0021-8928(60)90107-6) to address preferential flow in fractured media, and has been used to parameterize effects on heterogeneity on (flow and) solute transport, characterized by strong anomalous behavior. The concept has been presented using different names (e.g., multi-domain model, mobile-mobile model). In contrast to dual-porosity (mobile-immobile, transient storage) models, it requires solving two coupled flow problems, posing big difficulties in unique calibration if the flow behavior is quite normal. Bradford et al. (2009) reinterpreted the conceptual model to facilitate that colloids break through earlier than solutes. The latter effect is caused by size exclusion and by the fact that colloids cannot experience the velocity within pores at distances to solids smaller than half their diameter. If the colloids have the same net electrical charge as the grain surface they experience an even smaller portion of the intra-pore velocity distribution because they are repelled from the no-slip boundary. Other model formulations for colloid transport, involving reversible attachment-detachment and irreversible straining, cannot reproduce a first breakthrough before that of solutes. Bradford et al. (2009) claimed that their formulation also addresses straining, but that is not really true. In both domains, the model assumes kinetic first-order attachment and detachment. It is trivial to derive equilibrium sorption coefficients from the ratio of the detachment and attachment rate coefficients. Choosing a low detachment coefficient in the low-permeability domain still implies reversible sorption. However, straining is irreversible: particles get stuck in pore throats and never ever become mobile again. This implies that the formulation of Bradford et al. (2009) leads to very long tailing of colloid breakthrough curves with a complete recovery at infinite times, whereas models that include an elimination mechanism according to standard colloid filtration theory will have an incomplete recovery (i.e. the zeroth moment of the transfer function between the in- and output concentration in 1-D transport is smaller than unity). If you really want straining, you either choose a detachment coefficient in the less-mobile domain of zero, or you introduce a first-order elimination term. The authors have such a term, but they relate it other mechanisms than straining because they uncritically adopt the erroneous perspective of Bradford et al. (2009) that kinetic reversible mass transfer could parameterize (irreversible) straining.
Would there be a much simpler way of achieving an earlier breakthrough of colloids than of solutes without introduction of a second permeability? That is indeed possible. All you need is a retardation factor for the colloids smaller than one, and they are faster than the solutes. You would still need an irreversible straining term and (at least one) kinetic, reversible attachment-detachment term, but the model would be much simpler because you could skip coming up with two spatial permeability distributions and exchange terms of the fluids between the two domains (and the flow problem would have half the number of unknowns). Given the fact that the authors don’t want to use the dual-permeability formulation for its original purpose (addressing anomalous flow and transport in highly heterogeneous formations), and that they don’t have the data to inform such a model for its original purpose, I cannot recommend the conceptual approach chosen by the authors. It is simply an overkill, particularly in 3-D settings.
The authors promise a reactive microbial transport model in the title. This is slightly misleading. The only “reaction” term is a first-order elimination term. Many microbes of interest undergo complex dynamics due to growth, dormancy and reactivation, change in mobility corresponding to their physiological state or abundance. In the model of the authors the microbes must be introduced via the inflow and can only adsorb or vanish besides transport. They are essentially treated like dead particles. I can fully understand that the authors don’t intend to elaborate on microbial dynamics, but then they should be careful in selling they model as “reactive microbial transport model”.
As mentioned above, I am not too impressed by the 1-D tests. They mainly reproduce the work of Bradford et al. (2009), who at least had a comparison to real measurements, and of Leij and Bradford (2013). It is of course important that a code is tested against analytical solutions for model validation, but it is not a scientifically particularly exciting exercise.
The 3-D demonstration is supposed to show that the model works field-similar settings. It is not well suited to convince the reader that an integrated surface-subsurface hydrological model is needed. The test would equally well work with a pure groundwater model forced by the boundary condition at the river. In the setup, like in many bank filtration applications, the river is not really affected by groundwater flow and transport (and every HydroGeoSphere user knows that running the model as pure porous-medium model makes life much easier). A more interested application would show real feedbacks between the surface and subsurface domains, e.g., when considering transport of pathogens in a meandering stream with intensive hyporheic exchange and bank storage. That is obviously not the final application that the authors have in mind, but I would claim that the 3-D test problem could be simulated with loose coupling of the surface and subsurface domains (or even just predefining river-stage and concentration fluctuations as boundary condition).
In the 3-D test case, the authors first simulate steady-state concentrations, involving an input of (microbial) colloids from the river, ⁴He as a natural tracer for the mixing of old groundwater with river water, and ²²²Rn as age tracer. They then simulate the response to a river-stage fluctuation. Proportional to the river discharge they increase the concentration of the (microbial) colloids an of ⁴He in the river (mimicking an artificial tracer with concentration is proportional to that of the microbes). The former makes sense, whereas I am not happy about the later because ⁴He is supposed to be an indicator of mixing of old groundwater and river infiltrate, and with the pulse in the river the boundary between the two water bodies moves. While this boundary may be far away from the observation points, it is not particularly smart to create two causes of ⁴He changes. It might have been better to add a real artificial tracer to separate the signals.
As designed, the colloids break slightly earlier through than the solute tracer. The effect is not super big (4.5% earlier peak time) and well within the uncertainty of travel-time estimates in real-world studies on outlying well-head protection zones. With a longitudinal dispersivity of more than 5m (and additional dispersion caused by mobile-mobile transport), the peaks are so broad that the difference in the breakthrough curves are not particularly obvious by eye sight. The much more interesting signal is that of the radon. Here, the authors get a much earlier breakthrough. They attribute this to radon following the pressure wave (lines 433-434), but that makes physically no sense. What I believe is that the river-stage fluctuation shifts the flow pattern and by that the age distribution. Honestly, I find this phenomenon more interesting than the micobial-transport study as you see a real signal.
The results section ends with a summary/conclusion, followed by a discussion section, and then final conclusions. That’s a little bit odd, particularly since the actual conclusions are quite shallow.
In summary, I have expressed my doubts that the dual-permeability model is the best choice for transport of microbial colloids. I am convinced that you can achieve the same results computationally much cheaper. I believe that the 1-D model has too much weight given that it includes nothing new. The 3-D application does not need an integrated surface-subsurface model and does not underscore that the chosen model formulation is really needed. If there were real data that can only be interpreted with the model, the authors would have a much stronger point. This manuscript needs severe revisions to make it a significant contribution.

Citation: https://doi.org/10.5194/egusphere-2025-372-RC1
- AC1: 'Reply on RC1', Friederike Currle, 02 Apr 2025
  
  Dear reviewers, dear editors
  We are pleased with the feedback and would like to thank the two reviewers for the very helpful comments. None of the reviewers have risen any technical concerns related to the implementation of the code, which highlights that our code is relevant and carefully implemented. However, both reviewers have suggested some important improvements in the presentation of the verification and illustration examples of the new model implementation, which we will implement, and which will allow the manuscript to improve further. Moreover, as correctly pointed out by reviewer #1, the paper is a technical note rather than a research paper, an aspect which we would like to confirm.
  We will address all comments of reviewer #1 in a revised manuscript as outlined in detail in the supplement.
  Sincerely,
  Friederike Currle, René Therrien and Oliver Schilling
  
  Citation: https://doi.org/10.5194/egusphere-2025-372-AC1
RC2:
'Comment on egusphere-2025-372', Anonymous Referee #2, 17 Mar 2025

This manuscript outlines the inclusion of dual-permeability, two-site kinetic deposition formula for microbial transport in HydroGeoSphere (HGS). I believe this topic is relevant and of interest to the readers of EGUsphere. The manuscript is generally well-written, with the inclusions of expected sections outlining the model development, validation and illustrative application, all written in a clear manner.
As presented, my primary concern relates to the novelty and contributions of this work. How does this differentiate from other subsurface reactive transport models available – why should someone choose to use HGS over these models? I understand that the primary feature of including these equations in HGS is the inclusion with an integrated hydrologic model as opposed to solely a subsurface model, but no part of this manuscript uses or highlights the benefit of an integrated approach over subsurface-only. The authors outline the equations that govern surface flow and transport, but the verification and illustrative application do not seem to utilize the surface domain at all. Perhaps it is simulated, but the results are not presented or discussed. I think this is critical to the contributions of this work – what does this newly developed feature provide that was otherwise lacking? Perhaps a comparison between groundwater-only simulations and the integrated approaches can help demonstrate the benefit of including these equations with HGS as opposed to solely a subsurface approach.
Given this concern is critical to the contributions and novelty of this research, I feel the authors need to make significant revisions before this manuscript can be considered for publication.

Citation: https://doi.org/10.5194/egusphere-2025-372-RC2
- AC2: 'Reply on RC2', Friederike Currle, 02 Apr 2025
  
  Dear reviewers, dear editors
  We are pleased with the feedback and would like to thank the two reviewers for the very helpful comments. None of the reviewers have risen any technical concerns related to the implementation of the code, which highlights that our code is relevant and carefully implemented. However, both reviewers have suggested some important improvements in the presentation of the verification and illustration examples of the new model implementation, which we will implement, and which will allow the manuscript to improve further. Moreover, as correctly pointed out by reviewer #1, the paper is a technical note rather than a research paper, an aspect which we would like to confirm.
  We will address all comments of reviewer #2 in a revised manuscript as outlined in detail in the supplement.
  Sincerely,
  Friederike Currle, René Therrien and Oliver Schilling
  
  Citation: https://doi.org/10.5194/egusphere-2025-372-AC2

Peer review completion

AR: Author's response | RR: Referee report | ED: Editor decision | EF: Editorial file upload

ED: Reject (02 Apr 2025) by Heng Dai

ED: Reconsider after major revisions (further review by editor and referees) (03 Apr 2025) by Heng Dai

AR by Friederike Currle on behalf of the Authors (15 May 2025) Author's response Author's tracked changes Manuscript

ED: Referee Nomination & Report Request started (03 Jun 2025) by Heng Dai

RR by Anonymous Referee #2 (24 Jun 2025)

RR by Anonymous Referee #3 (25 Jul 2025)

Suggestions for revision or reasons for rejection

This is a very interesting paper, and highly relevant to HESS's diverse readership. It presents a very complex model that generalizes dual permeability flow in a river bed to bacterial residence in the fluid and solid bulk. It is well written, clearly presented, and overall of high quality. The main aspects I found that need improvement are: 1. The model presentation, specifically clearly presenting how each specific aspect is incorporated within the equations, yet not only in the parameterization part, but also on how each process is depicted as a functional form within the equation. 2. What is the added value of the bacterial parametrization implementation, making the observed results differ from other models like colloidal transport or sorption, as the results themselves are not different in a noticeable way? I’m sure there are differences, but the paper will benefit from outlining them explicitly.
The specific comments are as follows:
The abstract is well-written and provides motivation for the study, as well as its aims. I would suggest adding the implications of this study, specifically, what are “meaningful WHPA delineation and risk assessments even under extreme hydrological situations such as flood events.”
Lines 35-45 provide an excellent motivation.
Line 48: Does diffusion really play a role for bacteria? Maybe for 0.1 μm, but it will not have any effect on the process of early breakthrough
Line 62: “secondary energy minimum” is not defined.
General remark for the introduction: The introduction is well-written and clear; however, there are not many references to actual experimental results, nor to the possible parameters that may govern these experiments on bacterial/viral migration in porous media. Are there no relevant experiments in the literature?
Line 118: “by a modified form of Richards' equation.” What are the modifications? I know that a detailed model will be presented later, but a brief preview of where we differ from the Richards equation can make the following part of the model easier to understand.
Line 130: “k” is generally noting the permeability or intrinsic permeability. Consider using a different notation for the relative permeability or adding a subscript, as it is more related to occupancy of the fluid within the porous structure and less to the actual permeability, which is included in the hydraulic conductivity. I believe that in any case, it should be written as k_rl.
Also, is the code implementing the model available in a repository or on GitHub? In the “Code and Data availability” section, the links lead to the input files, but I couldn’t access the trial version of HydroGeoSphere even after the extensive verification stage.
Equations 10-14: This section as a whole, and the equations part specifically, are not presented in a way that allows the reader to understand the model. Each specific equation represents a different aspect: equations 10 and 11 refer to the high and low concentration transport, respectively, and equations 12 and 13 refer to the density. Although the sentence preceding this one states this aspect, it requires the reader to understand it without specific guidance. I recommend dividing the equations according to their representation (separating them into 10 and 11, 12 and 13, and 14 alone) and providing a detailed explanation for each part, marking the role of each aspect in the equation, rather than just referring to each parameter within it. As an example, take the important aspect of the “microbial inactivation in the liquid and solid phases” marked by 𝜆, the first-order sink term. This is the extension of the authors’ from a colloidal model to a bacterial model; hence, it is a seminal aspect in the study. Why not explain why the structure of 𝜆𝑠l𝜌𝑏l𝑠l marks the decay form in the solid? When the model is complex, an effort should be made to guide the reader on the role of each aspect in the model.

Equation 17 is a tensorial ADE with an exchange and sink term, and since this is a known form, it’s easier to follow. However, I believe that equation 18, which depicts the exchange between the surface to the subsurface, heavily relies on the previous section. Yet this is not clearly explained.

Section 3.1. A paragraph should be added explaining how well the synthetic experiment matches natural conditions and which natural conditions it replicates.
Line 279. Correct the term: “low+high-permeability”
Line 282. Can you provide the integral evaluation for the analytical solution in an appendix?
Figure 2. Looking at the BTC and colloidal adsorption to the column, the results are strikingly similar to the solute sorption-desorption process in soil. Can the authors comment on what the observable difference is stemming from the colloidal nature of this simulation, specifically referring to the various scenarios in Table 1, and even more specifically, to scenario 2, where the decay rate is introduced?
Furthermore, what is the reasoning for providing a decay rate of ~2 hours for a pulse of 2 hours? Wouldn’t it make a competing aspect where, prior to attachment, there will be a decay in considerable values? And isn’t that the explanation for the rapid decay with the depth, namely, that the exchange can only occur at the upper layers, prior to the decay occurring over time?
Can the authors comment on the model's sensitivity to various parameters? Which is more dominant: the exchange rate, conductivity difference for the dual permeability, or perhaps the reactive components of the attachment\detachment?

Line 399: What were the steady-state criteria?
Figure 4. Is it possible to present the figures with a logarithmic color map? This will enable a better separation for concentration variation, allowing for the estimation of the model's sensitivity.
Line 439: In a way, this sentence: “The simulated concentrations show faster transport of microbes due to size exclusion compared to the slower bulk transport of solutes like 4He,” could have easily been written for colloidal transport, and if we focus only on the velocity aspect, then it could be written for sorption scenarios. I believe that an effort should be made to explain how the behavior of bacteria in the model's results differs from that of colloids or solute sorption. The implementation of the bacterial aspect in the model is presented, as is the specific implementation; however, the variation in these aspects on the results from colloid transport with sorption is not discussed. The only aspect I notice is the decay rate, but it is not sufficiently stated in the context of the results.

Figure 5. Add the “Days” as a label to the x-axis

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RR by Anonymous Referee #1 (26 Jul 2025)

Suggestions for revision or reasons for rejection

This manuscript is the revision of a manuscript that I have reviewed before on implementing a dual-permeability approach to address transport of (microbial) colloids in the proprietary software HydroGeoSphere that can simulate saturated-unsaturated flow and transport coupled to surface flow and transport. Upon the revision, the authors have added a new demonstration case that extends the Abdul (1985) benchmark of HydroGeoSphere, which includes coupled surface runoff and subsurface flow and transport, to include transport of microbial colloids. Such a testcase was requested by both reviewers of the original manuscript. However, I am still not convinced.
In my previous review I have explained that the dual-permeability model was originally developed for completely different questions, namely to address flow and transport in highly heterogeneous media (including karst systems) by an effective model that does not resolve the heterogeneity. The dual-permeability specific coefficients (second permeability, division of the pore space, exchange coefficient) are typically calibrated by fitting anomalous behavior in both flow (e.g., different head responses in nearby piezometers connected to karst features and not) and transport (e.g., double peaks, extended tailing). None of that applies to the examples of the authors, and it was obviously also not the intension of Bradford et al. (2009), who reinterpreted the approach to address size-exclusion of colloids by introduction of a second permeability. I find it odd that the manuscript contains zero critical discussion of the underlying conceptual assumptions, even after my review (, which I don’t want to reiterate). The literature is full of dual-permeability papers that are entirely differently motivated, and the authors simply ignore.
I have expressed my skepticism that the dual-permeability approach is really needed in my previous review. Unfortunately, the demonstration cases of the authors don’t show that the results obtained could not be obtained by a traditional particle-transport code with single permeability, attachment, detachment, and straining. The authors did not make any effort to make this comparison. They only show that the computationally very demanding and difficult to calibrate dual-permeability approach has successfully been implemented. But it is only an improvement when it leads to a qualitative difference to existing approaches. (A hardly detectable peak in a breakthrough curve does not convince me that the effort is worthwhile.) Thus, I stick to my recommendation to go without the scientifically boring 1-D verification against an analytical solution in the main article (it can be moved to supplementary material and briefly mentioned in the main text) and perform a real effort to reproduce the same results (e.g., of the Abdul test case) with a single-permeability model and the usual parameterizations for particle transport. Please demonstrate that there is a real difference!
I also believe that the authors should discuss the issue of calibration in a more systematic way. While it is true that any complex model is difficult to calibrate, the introduction of the second permeability plus fractions and exchange terms in a setting that does not show anomalous flow and solute-transport behavior is an add-on to the already existing complexity. The fact that the authors use exactly the same boundary conditions in both domains might help to some extent. Unlike in karst-applications of the dual-permeability domain, the velocity fields in the two domains are doomed to be identical to a fixed factor and the heads are actually completely identical in the way the authors handle the model, at least in the saturated part of the subsurface domain. The factor of the velocities is the ratio of conductivities, and the effective single conductivity of the dual-permeability model is the fraction-weighted arithmetic average. This might be seen as a chance, as a single-domain flow calibration might be a good starting point. To get the ratio of the two conductivities and the fractions of the two domains, and the exchange coefficient for transport (that for flow should be insensitive with identical head fields) requires solute-transport information sensitive to that [which I have not seen in the applications of the authors], and the coefficients for attachment, detachment, and straining from particle measurements. The chances are super high that model calibration is very ambiguous, and I honestly don’t see how the authors could obtain crucial model parameters independently from concentration data.
Minor stuff
1. Line 83: At the end of the traditional approaches, you should at least mention what is not possible in these approaches.
2. Somewhere where you discuss the Bradford (2009) model: Explain where the dual-permeability model really comes from, and how Bradford reinterpreted it.
3. Lines 86-87: “… to occur in the small-pore, low velocity regions … occurs in the large-pore, high-velocity region”. It’s not the region that is small.
4. Line 119: Helium is not a radioactive compound. It is the product of alpha-decay, but you simply treat it as conservative compound.
5. Equation 12, and lines 185-186: What is the reasoning behind assuming a mass exchange between the solid parts of the high- and low-permeability domains? Is don’t see any physical mechanism that could do that.
6. Equation 17: the divergence of flux should be written with a nabla operator followed by a scalar-product dot (\cdot in LaTeX)
7. Line 205: The upside-down triangle is the nabla operator, which may represent the gradient (typically of a scalar field) OR the divergence of a vector field. It is not always the gradient.
8. Section 3: see above. Move that to supplementary material.
9. Line 261: You don’t need a transverse dispersivity in a 1-D problem.
10. Line 276: If the first-order decay coefficients are supposed to include straining they should not be identical in both domains.
11. Line 288: That the analytical solution contains no colloid exchange between the two solids is not a restriction, as this exchange makes physically no sense to begin with.
12. Line 385 and vey often thereafter: Like in the title, I would remove the word “reactive” when you talk about transport of microbes. There are no chemical reactions involved.
13. Lines 404 and 407: Just talk about “microbes”, you don’t really consider their species.
14. Lines 408-409: You can be more specific here. I assume that the spots in the stream bed where the microbes pop up are locations with infiltrating conditions. There locations have largely to do with the discretized bathymetry of the channel.
15. Lines 422-433, discussion of figure 4: I am pretty sure that that the ratio between high- and low-K contributions remains constant because the boundary conditions of the two domains are the same: Qhigh/Qlow = w_h*K_high/(w_l*K_l), which here is simply 10%
16. Lines 437 and 444: You faithfully talk about size exclusion, but that is not how the model is really formulated. You have simply an irreversible attachment in the low-K region, which you may use to parameterize the effects that are in reality caused by size exclusion.
17. Line 450: “As second illustrative example for coupled microbial and solute transport”
18. Lines 514-515: Why do you refer to bacteriophages? You don’t simulate viruses attacking bacteria.
19. Lines 522-523: If the decay coefficient is supposed to represent straining, it should be different in the two domains. You did this better in the Abdul testcase.
20. Lines 554-555: Your model formulation does NOT restrict microbial transport to the high-permeability pore space. There is also microbial transport in the low-K region.
21. Lines 564-565: See above. There is no demonstration that the dual-permeability formulation is really needed (and a single-permeability model could not get the job done.)
22. Discussion: See my major remarks above
23. Lines 589-590: Sorry, but the dual-permeability issues come on top of all the other issues in calibrating surface-water-groundwater model. So this is not an excuse.
24. Line 621: The transport is preferential in the high-K region also for solutes. You need the irreversible attachment in the low-K region to make this formulation represent straining.
25. Lines 624-626: You did not show with your applications that the dual-permeability approach is really needed.

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ED: Publish subject to minor revisions (review by editor) (27 Jul 2025) by Heng Dai

AR by Friederike Currle on behalf of the Authors (06 Aug 2025) Author's response Author's tracked changes Manuscript

ED: Publish as is (18 Aug 2025) by Heng Dai

AR by Friederike Currle on behalf of the Authors (19 Aug 2025)

Journal article(s) based on this preprint

21 Oct 2025

Explicit simulation of microbial transport with a dual-permeability, two-site kinetic deposition formulation using the integrated surface–subsurface hydrological model HydroGeoSphere

Friederike Currle, René Therrien, and Oliver S. Schilling

Hydrol. Earth Syst. Sci., 29, 5383–5403, https://doi.org/10.5194/hess-29-5383-2025,https://doi.org/10.5194/hess-29-5383-2025, 2025

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Friederike Currle, René Therrien, and Oliver S. Schilling

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Supporting Information datasets for article: "Explicit simulation of reactive microbial transport with a dual-permeability, two-site kinetic deposition formulation using the integrated surface-subsurface hydrological model HydroGeoSphere" Friederike Currle, René Therrien, and Oliver S. Schilling https://doi.org/10.4211/hs.401dedd41b7040808482019759abc42c

Friederike Currle, René Therrien, and Oliver S. Schilling

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We present a new approach to simulate the transport of microbes in river-aquifer systems in the integrated hydrological model HydroGeoSphere. Compared to existing models, the advantage of the new implementation lies in the consideration of all relevant parts of the water budget and the flexibility to simulate in parallel the reactive transport of several microbial species and solutes. The new developed tool enables to improve our understanding of pathogen transport in river-groundwater systems.


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