In the manuscript titled “The Water Table Model (WTM) v2.0.1: Coupled groundwater and dynamic lake modelling”, the author present the Water Table Model comprising coupled dynamic and groundwater level components to simulate terrestrial water changes. This study fills a gap in groundwater level research due to its broad spatial (watershed to global) and temporal (monthly to millennial) scope. Compared with G3M water table elevation model, the WTM has priority in shallow underground water and lake water elevation simulation. Comparing the climate-driven water table depth at Last Glacial Maximum with present day, North America stored more water in lakes and groundwater.

There are still certain changes and clarifications that the authors should address prior to publication. For these reasons, I believe that the manuscript can be accepted for publication by the Journal of Hydrology. Below, I have some general suggestions to the authors.

General comments:

• It would be better to discuss the impact of Dupuit–Forchheimer approximation on the accuracy of water table depth simulation, such as the possible range of errors in this study. Because this study does not include vertical hydraulic infiltration, the critical infiltration process. Relevant studies can be cited to strengthen the explanation of the applicability of this assumption. For example, considering the increased computational efficiency due to this assumption, the error is not a major issue, etc. Such a discussion could address the reliability of the paper and its citation rate. If I understand correctly, only Figures 4 and 5 compared the model with the observations, but the time used for the comparison is unclear. Therefore, the overall accuracy of the model remains vague.

Specific comments:

• The three data sources for the observations of water table level are groundwater-table depth, lake extents and depths, and wetland depth (assumed to be zero). Different data sources may have measurement discrepancies and issues with the validity of assumptions. Ultimately, all three data sources are treated as equally valid and compared with the model values. Providing some evidence for this approach would enhance the credibility of the paper. The basic attributes of the observational data should also be listed in the appendix or the main text. It is uncommon to only cite the paper without any data description.

• Regarding the schematic diagram Figure A1 of the model, it appears that the soil and channel are unidirectionally coupled, meaning that under saturated soil moisture conditions, water flows from the soil to the channel/lake, but the channel/lake is impermeable, with no water returning to the surrounding soil. This situation could introduce errors. If so, could the author discuss the potential impact on this study?

• Figure 1: The elements in Figure 1 are relatively simple, it is recommended to use a textual description instead. Compared with Figure 1, Figure 2 sufficiently demonstrates the relationship between groundwater levels and soil moisture infiltration. Alternatively, the author may provide more information for the water level simulation in Figure 1. The author can decide which option is more suitable.

• Figure 2: It lacks soil moisture contours that would indicate the gradient of total hydraulic head in Darcy's law or soil pressure head ψ. In soil moisture-related studies, displaying such schematic diagrams is a common practice. Showing the gradient helps illustrate the process of the system gradually approaching equilibrium from its initial state. In this study, in other word, it would be better to draw a schematic diagram of the hydraulic gradient, which is equal to the slope of the water table and does not vary with depth below the water table.

• Figure 3: Could the author include the simulation time period in the figure caption? The same issue exists with the other figures as well. The Figure 6 simulation period is also unknown.

• Figure 4: The y-axis values in Figure 4 are very small. Please confirm that the area enclosed by the curve and the x-axis is 1. If the sum of the probabilities is not 1, please explain the reason beside the x-axis limits. Figure b shows good results. There are a few issues. The missing observations are replaced with assumed values; could the authors exclude comparisons for the missing observations from the histogram? Observations cover 11.3% of the cells within the research domain. Could the authors display the location of these 11.3% in a raster figure in the appendix? This would allow readers to intuitively understand the range shown by the histogram.  

• Figure 5: In Figure 5(a), there is a noticeable distinction in the number of observation points in the regions where both x and y axes are negative and where x is positive and y is negative. What causes this? This difference appears to be caused by interpolation. The model has a feature where many simulated data points have the same observed value. In Figure 5(b), similarly, many model simulation values have the same observed values. Please ensure that this figure has accurately excluded meaningless simulation results and explain the reasons for such discrepancies/phenome. In line #329, the discrepancies include seasonal variations in observed data, one solution would be normalized data for each season.

• Figure 6: G3M treats surface water as a static boundary condition, all water above the land surface would either evaporate or run off. Therefore, the G3M’s poor performance within +/-10m is obvious. Why choose to compare with G3M simulation results that have obvious assumption biases?

• Figure 7: The raster figure located in the Canada region does not have a corresponding color scale. Another way is adding a note in the caption to show thickness value. Figure 3 has the same issue.

• Figure 8: If I understand correctly, it is not very clear how accurately the model's ice cover section compares with the observations. So it is unclear of the water table change from LGM to present day, the Figure (a) shows slight increases in northern part of Northern America. In the context of overall climate change, additional evidence may be needed to support this result.

• Figure 10: During the period of 17 - 16 ka BP, groundwater shrank rapidly, while surface water remained relatively stable, with only a slight decrease. This result is quite unexpected; could the authors explain the reason?

• In the conclusion section, the results of other studies related to the significant findings of this research could be discussed here, such as the main finding of reduction trend in lake volume. For example, this article might mention similar conclusions ¹. The conclusion section also needs to be kept complete.

• If climate models with future global warming/radiation/aerosol scenarios are used as model input, it is possible to show future changes in groundwater levels and lake levels. If there are some eye-catching conclusions, this could potentially increase the citation rate of the paper.

Technical corrections:

• Line #452, “wherever the water table”, “the” is the typo.

1          Zhang, Y. & Li, Y. Evolution of lake water volume in global closed basins since the Last Glacial Maximum and its implication for future projection. Progress in Physical Geography: Earth and Environment 46, 613-629 (2022).

Review of "The Water Table Model (WTM) v2.0.1..." Callaghan etal

Overall comments and assessment:  This is an article on an interesting topic that presents a groundwater and lake model formulation.  I have some big-picture and detailed comments below, but I think the work aligns well with GMD and recommend eventual publication pending some revisions of the writing and general focus of the manuscript.



Big-picture / general comments:

The scope of this work is a bit broader than it might otherwise need to be.  I find a few general themes / messages in the work:

1. 1. A combination of a large scale groundwater parameterization similat to Fan et al and a lake model similar to Barnes et al (2021; fill-spill-merge)
   2. A robust numerical implementation of the otherwise simple (explicit FD) formulation of Fan et al using the PETSC numerical library that is also documented and open source, etc.
   3. A series of large scale simulations, including a present day north american simulation and a reconstruction or evolution of the water table since the last glacial maximum.
   4. A lengthy series of appendices that detail model inputs, assumptions and a range of equations presenting infiltration and long-term ET

While most of these themes are interesting and this clearly represents a lot of work, it is hard to tell what the central focus of the manuscript is.  Is this a possible climate application?  A model to represent present-day conditions?  (i.e. is the science / results the focus); is this a model description paper that comprehensively talks about these interactions? (i.e. is the model formulation GW-lake or GW-lake-land surface the focus); is this a numerical applications paper that talks about performance and the need for putting this framework on something like PETSC?  There are multiple GMD paper-worthy topics in here (in my opinion) and having them all in one manuscript so prominantly makes it a bit hard for the reader to follow the main themes and take-home messages and weakens the work overall.  I'm not suggesting a complete re-write of the manuscript, but some careful discussion among the authors to help focus and tighten this work around a central theme.

Detailed Comments:

1. Introduction: The intro starts with a nice motivation on the changes of terrestrial water storage over geologic time scales.  It defines the need for a GW+lake model that can run over much longer timescales than the current literature provides.  My feeling is that in the paragraph around line 65 the authors might keep this focus   instead of diving into anthropogenic impacts, etc.  I recommend expanding this out (if this is the focus the authors decide to go with), and focusing on the details of the work that will enable these types of simulations.  In other words, I feel this paragraph is where the manuscript starts to split into a few different directions losing the nice focus it had in the rest of the intro.  Additionally, the authors might also consider the conceptual framework of Condon et al WRR 2021 (figure 4) as a way to further classify the space their work sits within.
2. There are a number of really short paragraphs that are distracting to the reader.  Examples include lines 81-83 (perhaps leave this to the model / data availability statement or put in a footnote); lines 94-97; lines 266-268; lines 269-271
3. Comparison to observations for the present-day simulation:  The model comparisons to water table observations as currently written are very hard to follow and in my opinion do not support the message of the manuscript.  Figure 5 is confusing and looks like it might actually contain plotting errors or artifacts.  In (A) he pattern and striped lines (some horizontal and vertical, some at 45-deg angles) look like there might be an aliasing issue or even something numerical going on.  The values, even when plotted as head (incuding topography, in B) in which some of the areas that should have heads over 1km are below sea level.  These graphs plus the associated analysis need to be carefully reviewed and possibly reconsidered.  I understand the need to compare models to observations but this section as presented does not instill confidence in the model formulation.  Perhaps other benchmarks could be used with the model?  Are there analytical solutions to which the model could be compared that might also serve as unit tests for the code framework?
4. What is the impact of including lakes in the simulation?  This is discussed in text (lines 343-352) but an approach might be simulate with and without the lake model (or with a simpler approach the removes water) to show the difference spatially and using something like histograms.
5. LGM simulation.  This section is in my opinion pretty novel.  Very few efforts have tried to simulate dynamics across these spatial temporal scales (e.g. Lemieux et al) and this section ties well into the motivation for the work.
6. Uncertainty.  Parameter uncertainty is a primary challenge in these types of modeling studies.  It seems that one advantage of a simplified / reduced physics model is the ability to run very rapid simuations that include parameter sensitivity and uncertainty.  This would greatly enhance the work to provide understanding of what parameters might be driving outputs and to address the substantial uncertainty in the assumptions made around the geologic framework.  If this is outside the scope of the work, it would be very helpful to provide discussion of uncertainty and how it might impact the results and conclusions.

Reed Maxwell

Princeton University

This paper presents a Water Table Model (WTM) designed to simulate the dynamic interactions between surface water and groundwater levels. The model exhibits notable innovation and has the potential to attract researchers interested in long-term simulations. The writing is clear and well-organized, making the study accessible and comprehensible. However, there are several critical areas that require further attention and revision to enhance the manuscript's rigor and applicability. Specifically, the manuscript would benefit from a deeper exploration of uncertainties related to key inputs, consideration of human water usage, and a more detailed discussion of parameter sensitivity and initialization approaches.

1. Uncertainty in evapotranspiration (ET) estimation: One of the key inputs for the WTM is evapotranspiration (ET), which is widely recognized as a challenging and uncertain variable in hydrological modeling. Given the significant impact of ET on water table dynamics, it is crucial to discuss the extent to which ET uncertainty may affect the water table estimation. I recommend including a sensitivity analysis or discussion on how variations in ET estimations could influence the water table simulations.
2. Effect of Water Depth on Heat Storage and Evaporation: The paper does not clarify whether the effect of water depth on heat storage within water bodies has been considered in the evaporation computation. Heat storage significantly impacts evaporation rates, especially across different seasons. Shallow water bodies, with less thermal inertia, experience more rapid temperature changes, while deeper bodies retain heat longer. These variations affect seasonal evaporation rates. The authors should address how water depth and thermal storage are factored into the model or discuss the potential integration of these elements to improve the model's accuracy.
3. Inclusion of human water usage: The current WTM does not account for human water usage, including agricultural irrigation, industrial demand, and urban development, all of which heavily rely on both surface water and groundwater resources. This omission could significantly limit the model’s applicability in real-world scenarios where human activities play a critical role in water table dynamics. It is recommended that the authors consider integrating a component to represent human water usage or at least provide a discussion on how such factors could be incorporated in future model developments.
4. Initialization of the water table: The manuscript lacks clarity on how the initial water table is set in the WTM simulations. It would be beneficial to discuss whether surface water body products from satellite remote sensing (e.g., JRC-GSW, https://global-surface-water.appspot.com) could be utilized for initialization purposes. Additionally, for simulations extending over thousands of years, it is essential to clarify the approach used for initializing the water table and how this might impact long-term model outcomes.
5. Simulation of Flooding and Inundation Processes: The manuscript currently does not provide sufficient detail on whether the WTM is capable of simulating flooding and inundation processes under transient state conditions. The ability to model these processes would significantly enhance the utility and applicability of the model, particularly given the increasing frequency and severity of flood events due to climate change and anthropogenic activities. This represents a highly promising area of application, especially for regions prone to extreme hydrological events. A detailed discussion in this regard could greatly expand the potential impact and use cases of the model.
6. Parameterization and uncertainty analysis: The WTM involves substantial parameterization and a large number of model parameters. It is critical to assess how parameter uncertainty might influence the model results. A more detailed uncertainty analysis or discussion is recommended to understand the robustness of the model outcomes and provide guidance on parameter calibration and sensitivity.