| 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.
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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.