the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
| 25 Nov 2025
Hierarchical sedimentary architecture governs basin-scale solute dispersion: From pre-asymptotic dynamics to uncertainty propagation
Abstract. Real aquifers are structured as hierarchical sedimentary systems, where multi-scale heterogeneity and geometric connectivity jointly govern groundwater flow and solute migration. Although the general influence of heterogeneity has been extensively investigated, the scale-dependent effects of hierarchical organization, particularly under basin-scale flow conditions, remain inadequately quantified. In this study, we reconstructed a series of three-dimensional heterogeneous sedimentary architectures at the basin scale and performed numerical simulations to explore dispersion behavior. The results reveal that the geometry and connectivity of dominant lithofacies at macroform scales control macro-dispersion, while finer-scale heterogeneity has only a secondary influence on plume evolution. Furthermore, the evolution of macro-dispersion is characterized by a prolonged pre-asymptotic phase, far exceeding that observed at classical sites such as Borden, indicating that basin-scale solute transport remains non-ergodic over extended times and distances. Uncertainty analysis further identifies a distinct buffering effect inherent to basin systems, in which the aggregation of numerous flow pathways dampens realization-to-realization variability caused by local heterogeneity. When integrated with previously reported laboratory- and sandbox-scale results from the same site, these findings establish a mechanistic and transferable framework linking hierarchical sedimentary architecture to multi-scale dispersion and uncertainty. This framework advances theoretical understanding of non-Fickian transport and provides practical guidance for large-scale modeling and groundwater management in data-limited regions.
Competing interests: One of the (co-)authors is a member of the editorial board of Hydrology and Earth System Sciences.
Publisher's note: Copernicus Publications remains neutral with regard to jurisdictional claims made in the text, published maps, institutional affiliations, or any other geographical representation in this paper. While Copernicus Publications makes every effort to include appropriate place names, the final responsibility lies with the authors. Views expressed in the text are those of the authors and do not necessarily reflect the views of the publisher.- Preprint
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Status: open (until 06 Jan 2026)
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RC1: 'Comment on egusphere-2025-5652', Anonymous Referee #1, 28 Nov 2025
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AC1: 'Reply on RC1', Wanli Ren, 06 Jan 2026
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Response to comments from Anonymous Referee #1
Overview of Anonymous Referee #1:
This paper, based on real basin study area, systematically analyzes the scale effects of solute transport and dispersion in heterogeneous aquifers using a hierarchical sedimentary framework and numerical simulation. Overall, the manuscript has a good topic selection and relatively advanced research methods, aligning with research frontiers in non-Fick solute transport in heterogeneous aquifers. Through detailed results presentation and comprehensive discussion, it provides practical guidance for large-scale modeling and groundwater management in data-limited regions. However, there is still some space for improvement in areas such as writing format, methodological hypotheses, quantification of results, and the applicability of the research.
Reply: We sincerely thank the reviewer for the constructive and insightful comments, which helped us improve the manuscript in terms of clarity, methodological transparency, quantification of key findings, and applicability. In the revised manuscript we will address each of his/her observations/suggestions.
Specific comments:
（1）In the Abstract and Discussion sections, authors mentioned "…prolonged pre-asymptotic phase, far exceeding that observed at classical sites such as Borden.", it is suggested that quantitative metrics can be provided here to make the difference in solute transport characteristics between sites and basins more intuitive. Furthermore, the authors mentioned "mechanistic and transferable framework" and "practical guidance" at the end of the Introduction section, but these are broad descriptions. A more accurate and intuitive expression would be better, such as which observable parameters are most important for predictable diffusion indices.
Reply: We agree. In the revised Abstract and Discussion, we will add some quantitative metrics to make the difference in pre-asymptotic transport behavior more intuitive. Specifically, we will report characteristic time/distance to reach quasi-asymptotic behavior, or time-evolution of effective dispersivity, or slope/plateau behavior, and will provide a direct comparison with classical sites (e.g., Borden). In addition, we will refine the statements “mechanistic and transferable framework” and “practical guidance” by replacing broad descriptions with more operational wording.
（2）The last part of the Introduction section is the structure of the paper. It is suggested that word "part" can be changed to "section,", and that the title of the Section 2 can be changed to "methods". Section 2.2.1 should be renamed to "Sedimentary heterogeneity parameters" or "Sediment heterogeneity parameters."
Reply: We agree and will revise the structure and terminology accordingly. We will replace “part” with “section” in the Introduction section, and will rename Section 2 to “Methods,” and revise Section 2.2.1 to “Sedimentary heterogeneity parameters” (or “Sediment heterogeneity parameters”) for consistency and clarity.
（3）In the text, background information and existing research should be described using the present or past tense; the Methods section of the paper should use the past tense or passive voice; the Results/Discussion section should use the present tense. Please make the corresponding modifications throughout the paper.
Reply: We appreciate this guidance. We will systematically revise verb tense usage throughout the manuscript.
（4）57 boreholes were used to construct 20 km × 22 km × 50 m models in this study. While this is a common practice in basin scale modeling, its representativeness still needs to be effectively evaluated since this research focuses on the heterogeneity of the aquifer. It is recommended that the authors supplement the relevant content in the manuscript.
Reply: We agree that representativeness should be explicitly evaluated given the study’s focus on heterogeneity. We will add a dedicated discussion in Section 2.1.
（5）A constant porosity of 0.35 is not sufficiently for facies ranging from gravel to clay, but this simplification is acceptable if the research objective is solely to resolve the control of the K-field and architecture on dispersions. It is recommended that the assumptions for this parameter be explicitly stated in Section 2.4.3, and that any potential biases introduced by these assumptions be briefly discussed in the discussion section. Similarly, setting Dij=0 implies that macrodispersion is only caused by non-uniform velocity fields. This is reasonable for studying pre-asymptotic behavior of structural controls, but it might underestimate dispersion compared to real systems. It is recommended to add discussion of this aspect in the parameter settings and Discussion section.
Reply: We agree. We will explicitly state the constant porosity assumption in Section 2.4.3 and clarify that this simplification is reasonable to identify the structural and K-field controls on macrodispersion. Similarly, setting Dij=0 implies that dispersion arises solely from non-uniform velocity fields (macrodispersion driven by heterogeneity/architecture), which is appropriate for diagnosing pre-asymptotic structural controls but could underestimate total dispersion relative to real aquifers where local dispersivity and molecular diffusion contribute. These limitations and applicability boundaries will also be discussed in both the Section 2.4 and the Discussion Section.
（6）The existing Uncertainty analysis section is a "scenario analysis" What is the basis for setting up the comparison groups for volume proportion and conductivity? In other words, is this reasonable in terms of geological conditions? Please provide further explanation or emphasize the application scenario of this setting to enhance the guiding significance of the conclusions.
Reply: We agree with the reviewer’s characterization and will revise the manuscript accordingly.
（7）In the Results section, please focus on "presentation + brief explanation". Lengthy discussions about cross-scale or literature comparison can be systematically elaborated in the Discussion section to avoid repetition and redundancy of the text.
Reply: We will streamline the Results section to focus on key outputs and concise explanations, and will move extended cross-scale interpretation and literature comparison to the Discussion Section.
（8）There are several grammatical issues in the text. For example, line 93, "less than < 1‰" should be modified to "< 1‰"；Line 175，"Scale-II" is recommended to be consistently referred to as "Scale II"; line 320，"…dispersivity shows a power…" is recommended to modified as "dispersivity exhibits a power-law increase with time.". Therefore, it is recommended that the authors carefully revise and polish the English writing throughout the manuscript.
Reply: Thank you for pointing these out. We will perform a comprehensive language polishing throughout the manuscript, including terminology consistency and grammar.
（9）In Figure 3, it is recommended to also mark key information such as the location of the Nen River and its upstream and downstream relationships.
Reply: We agree and will update Figure 3.
（10）In Figure 2, it is suggested that "phreatic water aquifer" in the title should be changed to "phreatic aquifer" directly.
Reply: We agree and will revise the Figure 2 title to “phreatic aquifer” as suggested.
（11）Regarding flow field calibration (in Figure 5), it is currently stated that "The simulated water levels show good agreement... closely following the 1:1 line.". although the trend looks good on the graph, but specific values such as RMSE, NRMSE, and R² are missing.
Reply: Quantitative metrics are indeed necessary. We will add these metrics to support the statement of good agreement.
Citation: https://doi.org/10.5194/egusphere-2025-5652-AC1
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AC1: 'Reply on RC1', Wanli Ren, 06 Jan 2026
reply
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RC2: 'Comment on egusphere-2025-5652', Anonymous Referee #2, 19 Dec 2025
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The comment was uploaded in the form of a supplement: https://egusphere.copernicus.org/preprints/2025/egusphere-2025-5652/egusphere-2025-5652-RC2-supplement.pdf
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AC2: 'Reply on RC2', Wanli Ren, 06 Jan 2026
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Response to comments from Anonymous Referee #2
Overview of Anonymous Referee #2:
This study combined borehole soil sampling, groundwater level data, and groundwater flow and transport modeling to examine the impact of subsurface heterogeneity on dispersion at the basin-scale. Overall, the dataset and modeling framework are promising, and the study has the potential to make a valuable contribution once the issues below are addressed.
Reply: We appreciate the reviewer’s general impression on the value of our manuscript. We will update the manuscript considering his/her valuable feedback. Below we addressed all the comments and suggestions.
Major comments:
（1）The novelty and knowledge gap can be better articulated. In particular, the current introduction may not set the stage for this study well. Consequently, the three research objectives lack literature review support and strong motivations.
- For instance, the reviewer would be curious what motivated the author to perform an uncertainty analysis. Was it because existing literature shows a wide range of different observations in the field? Was it because a new model was used and the model involved some uncertain parameters whose uncertainty is unknown? Was it because there has been an inconsistency between existing observations and models? Or something else?
- Another example is why did they want to quantify the relative contributions of sedimentary architectural attributes, hydraulic statistics, and source size? There seems to be no well-organized discussions on the existing knowledge about how these three factors control the dispersion processes under field-representative aquifers and large-scale flow fields.
- A similar question arises for the uncertain proportion part.
Reply: We appreciate the specific request for a clearer articulation of the novelty, the knowledge gap, and the motivations behind our research objectives—particularly the uncertainty analysis and the attribution of controlling factors. We will strengthen the Introduction Section to more clearly articulate the specific knowledge gaps in scale-dependent solute dispersion under basin-scale hierarchical heterogeneity conditions, and the novelty of our approach in addressing those gaps. For the uncertainty analysis part, we will revise the section title and add some information to explicitly state this scope (e.g., “Scenario-based uncertainty propagation of dispersivity”) and to avoid ambiguity about the traditional UQ framework.
（2）The writing and logical flow can be improved through substantial revisions. Please see the specific comments for some examples.
Reply: We appreciate this comment. We will systematically revise the manuscript according to the specific comments.
（3）The manuscript involves quite a number of jargons and unclear sentences, which may require clarification or rephrasing. Below are some examples:
- “ From pre-asymptotic dynamics to uncertainty propagation”
- “geometric connectivity”
- “general influence”
- “hierarchical organization”
- “Although the general influence of heterogeneity has been extensively investigated, the scale-dependent effects of hierarchical organization, particularly under basin-scale flow conditions, remain inadequately quantified.”
- “lithofacies”
- “macroform scales”
- “macro-dispersion”
- “finer-scale heterogeneity”
- “ Non-ergodic”
- “basin-scale structure”
- “macroscopic spreading and dispersion across scales”
- “A total of 57 boreholes … were collected”
- “To bias-correct parameter estimates affected by incomplete exposure of sections, …”
Reply: We appreciate these specific comments. In fact, many of the terms exemplified here are specialized in hydrogeology research area. Providing extensive supplementary explanations might compromise the readability of the entire text. However, based on this comment, In the revised manuscript, we will try to reduce jargon and improve clarity in the revised manuscript.
As for specific comments, we will make one-on-one revisions and provide detailed responses in the revised manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-5652-AC2
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AC2: 'Reply on RC2', Wanli Ren, 06 Jan 2026
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CC1: 'Comment on egusphere-2025-5652', Giacomo Medici, 20 Dec 2025
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General comments
Very good research on aquifer heterogeneities in geological porous media. Please, find my suggestions to improve the manuscript.
Specific comments
Lines 35-87. Any link between hierarchical sedimentary architecture and sequence stratigraphy?
Lines 37-40. “Decades of field investigations…scale-dependent transport parameters”. Insert recent research that discusses the link between parameterization of heterogeneous aquifers and plume migration:
- Agbotui, P.Y., Firouzbehi, F., Medici, G. 2025. Review of effective porosity in sandstone aquifers: insights for representation of contaminant transport. Sustainability, 17(14), 6469.
- Tellam, J.H. and Barker, R.D., 2006. Towards prediction of saturated-zone pollu tant movement in groundwaters in fractured permeable-matrix aquifers: the case of the UK Permo-Triassic sandstones. https://doi.org/10.1144/GSL.SP.2006.263.01.01.
Lines 90-114. You need to insert more detail on the sedimentological nature of your deposits. Fluvial? Which kind of system?
Line 120. “lithofacies-types”. Please, provide detail on the sedimentary environment.
Line 203. Very well-known equation that we teach to MSc students. I would delete it.
Figures and tables
Figure 1. Make letters on the map larger.
Figure 1. Increase the graphic resolution for all the three images.
Figure 4. Two general head boundary and one specified flux boundary? Please, improve the figure.
Figure 5a. Make also here letters on the map larger.
Figure 5a. Increase the graphic resolution for this map.
Figure 5b. Report complete error statistics (e.g., ME, MAE, RMSE etc etc) on the graph.
Citation: https://doi.org/10.5194/egusphere-2025-5652-CC1 -
AC3: 'Reply on CC1', Wanli Ren, 06 Jan 2026
reply
Response to comments from community
Overview:
Very good research on aquifer heterogeneities in geological porous media. Please, find my suggestions to improve the manuscript.
Reply: We sincerely thank the reviewer for the positive assessment of our work and for the constructive suggestions. We will carefully considere all comments and revise the manuscript and figures accordingly.
Specific comments:
（1）Lines 35-87. Any link between hierarchical sedimentary architecture and sequence stratigraphy?
Reply: We appreciate this important suggestion. We will add a short discussion in the Introduction clarifying how hierarchical sedimentary architecture can be interpreted within a sequence-stratigraphic framework. What we can explain here is that sequence stratigraphy usually focuses on bounding surfaces and stacking patterns (e.g., channel-belt，or floodplain aggradation) that can organize architectural elements; while our workflow focuses on architecture quantified from borehole-constrained facies transitions and mean-length statistics, rather than explicitly mapping sequence-bounding surfaces.
（2）Lines 37-40. “Decades of field investigations…scale-dependent transport parameters”. Insert recent research that discusses the link between parameterization of heterogeneous aquifers and plume migration:
- Agbotui, P.Y., Firouzbehi, F., Medici, G. 2025. Review of effective porosity in sandstone aquifers: insights for representation of contaminant transport. Sustainability, 17(14), 6469.
- Tellam, J.H. and Barker, R.D., 2006. Towards prediction of saturated-zone pollu tant movement in groundwaters in fractured permeable-matrix aquifers: the case of the UK Permo-Triassic sandstones. https://doi.org/10.1144/GSL.SP.2006.263.01.01.
Reply: We agree these references strengthen the motivation for architecture-aware parameterization and its implications for plume migration. We will add both references and explicitly tied them to our discussion on how effective parameterization can bias migration predictions when heterogeneity and connectivity are not adequately represented.
（3）Lines 90-114. You need to insert more detail on the sedimentological nature of your deposits. Fluvial? Which kind of system?
Reply: We appreciate this specific comments. We will expand the “Overview of the study area” section to include a clearer depositional-system description.
（4）Line 120. “lithofacies-types”. Please, provide detail on the sedimentary environment.
Reply: Thank you. We have provided brief sedimentological interpretations for each lithofacies class (Scale I) and for the aggregated units (Scale II). Perhaps such a description is not sufficient to fully explain the sedimentary environment, we will insert a short paragraph after the lithofacies definitions describing depositional meaning and environment.
（5）Line 203. Very well-known equation that we teach to MSc students. I would delete it.
Reply: We agree. We will remove the explicit equation from the main manuscript and retained only a concise description of the method, variables, and the appropriate citations.
Figures and tables
Reply: We will make one-by-one revisions and provide detailed responses in the revised manuscript.
Citation: https://doi.org/10.5194/egusphere-2025-5652-AC3
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AC3: 'Reply on CC1', Wanli Ren, 06 Jan 2026
reply
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- 1
This paper, based on real basin study area, systematically analyzes the scale effects of solute transport and dispersion in heterogeneous aquifers using a hierarchical sedimentary framework and numerical simulation. Overall, the manuscript has a good topic selection and relatively advanced research methods, aligning with research frontiers in non-Fick solute transport in heterogeneous aquifers. Through detailed results presentation and comprehensive discussion, it provides practical guidance for large-scale modeling and groundwater management in data-limited regions. However, there is still some space for improvement in areas such as writing format, methodological hypotheses, quantification of results, and the applicability of the research. Below are my specific suggestions.
（1）In the Abstract and Discussion sections, authors mentioned "…prolonged pre-asymptotic phase, far exceeding that observed at classical sites such as Borden.", it is suggested that quantitative metrics can be provided here to make the difference in solute transport characteristics between sites and basins more intuitive. Furthermore, the authors mentioned "mechanistic and transferable framework" and "practical guidance" at the end of the Introduction section, but these are broad descriptions. A more accurate and intuitive expression would be better, such as which observable parameters are most important for predictable diffusion indices.
（2）The last part of the Introduction section is the structure of the paper. It is suggested that word "part" can be changed to "section,", and that the title of the Section 2 can be changed to "methods". Section 2.2.1 should be renamed to "Sedimentary heterogeneity parameters" or "Sediment heterogeneity parameters."
（3）In the text, background information and existing research should be described using the present or past tense; the Methods section of the paper should use the past tense or passive voice; the Results/Discussion section should use the present tense. Please make the corresponding modifications throughout the paper.
（4）57 boreholes were used to construct 20 km × 22 km × 50 m models in this study. While this is a common practice in basin scale modeling, its representativeness still needs to be effectively evaluated since this research focuses on the heterogeneity of the aquifer. It is recommended that the authors supplement the relevant content in the manuscript.
（5）A constant porosity of 0.35 is not sufficiently for facies ranging from gravel to clay, but this simplification is acceptable if the research objective is solely to resolve the control of the K-field and architecture on dispersions. It is recommended that the assumptions for this parameter be explicitly stated in Section 2.4.3, and that any potential biases introduced by these assumptions be briefly discussed in the discussion section. Similarly, setting Dij=0 implies that macrodispersion is only caused by non-uniform velocity fields. This is reasonable for studying pre-asymptotic behavior of structural controls, but it might underestimate dispersion compared to real systems. It is recommended to add discussion of this aspect in the parameter settings and Discussion section.
（6）The existing Uncertainty analysis section is a "scenario analysis" What is the basis for setting up the comparison groups for volume proportion and conductivity? In other words, is this reasonable in terms of geological conditions? Please provide further explanation or emphasize the application scenario of this setting to enhance the guiding significance of the conclusions.
（7）In the Results section, please focus on "presentation + brief explanation". Lengthy discussions about cross-scale or literature comparison can be systematically elaborated in the Discussion section to avoid repetition and redundancy of the text.
（8）There are several grammatical issues in the text. For example, line 93, "less than < 1‰" should be modified to "< 1‰"；Line 175，"Scale-II" is recommended to be consistently referred to as "Scale II"; line 320，"…dispersivity shows a power…" is recommended to modified as "dispersivity exhibits a power-law increase with time.". Therefore, it is recommended that the authors carefully revise and polish the English writing throughout the manuscript.
（9）In Figure 3, it is recommended to also mark key information such as the location of the Nen River and its upstream and downstream relationships.
（10）In Figure 2, it is suggested that "phreatic water aquifer" in the title should be changed to "phreatic aquifer" directly.
（11）Regarding flow field calibration (in Figure 5), it is currently stated that "The simulated water levels show good agreement... closely following the 1:1 line.". although the trend looks good on the graph, but specific values such as RMSE, NRMSE, and R² are missing.