the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Development of InterGrid Cell Lateral Unsaturated and Saturated Flow Model in the E3SM Land Model (v2.0)
Gautam Bisht
Lingcheng Li
Dalei Hao
Donghui Xu
Abstract. The lateral transport of water in the subsurface is important in modulating the terrestrial waterenergy distribution. Although few land surface models have recently included lateral saturated flow within and across grid cells, it is not a default configuration in the Climate Model Intercomparison Project version 6 experiments. In this work, we developed the lateral subsurface flow model with both unsaturated and saturated zones in the Energy Exascale Earth System Model (E3SM) Land Model version 2 (ELMv2.0). The new model, called ELM_{lat}, was benchmarked against PFLOTRAN, a 3D subsurface flow and transport model, for three idealized hillslopes that included a convergent hillslope, divergent hillslope, and titled Vshape hillslope with variably saturated initial conditions. ELM_{lat} showed comparable performance with PFLOTRAN in terms of capturing the dynamics of soil moisture and groundwater table for the three benchmark hillslope problems. Specifically, the mean absolute errors (MAE) of the soil moisture in the top five layers between ELM_{lat} and PFLOTRAN were within 1 % ± 4 % and the MAE of water table depth were within ± 0.3 m. Next ELM_lat was applied to the Little Washita experimental watershed to assess its prediction of groundwater table, soil moisture, and soil temperature. The spatial pattern of simulated groundwater table depth agreed well with the global groundwater table benchmark dataset generated from a global model calibrated with long term observations. The effects of lateral groundwater flow on the energy flux partitioning were more prominent in low land areas with shallower groundwater tables, which the difference of simulated annual surface soil temperature could reach 0.4–0.5 °C at low land areas between ELMv2.0 and ELM_{lat}. Incorporating lateral subsurface flow in ELM improves the representation of the subsurface hydrology which will provide a good basis for future largescale applications.
Han Qiu et al.
Status: open (until 22 Jun 2023)

RC1: 'Comment on egusphere2023375', Anonymous Referee #1, 09 May 2023
reply
This is a review of "Development of InterGrid Cell Lateral Unsaturated and Saturated Flow Model in the E3SM Land Model (v2.0)" by Qiu et al.
The authors describe the development of a saturated lateral flow parameterization for betweengridcell water movement. The modified model is compared to a fully 3d subsurface flow model.
Derivation of equations
In general, I thought that the derivation of the moisture movement equations could be improved. Around line 105, the authors reference Oleson et al. [2013], which describes the conservation of mass in one dimension that is used in the CLM model. But their equation 7 is not what is found in Oleson et al., and instead is written in the general 3d form. The authors here use the index n to denote different control volumes, before switching to an index k used to describe the layers of the 1d soil structure. I think it would be more clear to either 1) describe the 3d equations first, then show how the specific 1d case leads to the ELM/CLM equations described in Oleson et al., or follow Oleson et al. and then show how the 3d equations are used to define the new term in equation 14.
Regarding the equations describing the lateral flux, e.g. 14 and following, the areas used to convert between fluxes and volumes should be clarified to show whether they are actual surface areas, or projected areas. The appropriate area is the area that is normal to the direction of the flux. This is why I found the description of equation 16 confusing. I don't think describing the fluxes relative to z' (the rotated z axis) make sense. This is still a 1d column model, with the nodes aligned verticaly, therefore the fluxes in the column are all in the vertical. Presumably the coupling to the atmosphere also occurs in the vertical. It would be more clear to me to note that a cosine arises in equation 16 due to the projected area of the surface being smaller than the surface area by a cosine factor.
I would also like to know if the presence of z in equation 15 is correct. I understood the gravity term in the modified Darcy equation to be the sin(theta) term.
Why does equation 17 not have a similar form as equation 15? Also, I would like to see the calculation of the transmissivity T described here rather than simply referenced.
What is the size of the contribution of the unsaturated lateral flow term, for both the benchmarking and application simulations? It would be useful to indicate the relative importance of this term, and whether this impacts the simulations significantly. It would seem to be straightforward to turn off this flux to test this issue.
Evaluation over lww
A comparison to a LWW PFLOTRAN simulation would have been interesting. Given that PFLOTRAN was used in the benchmarking section, why was it not used in the evaluation section?
The WTD map in figure 8 shows that the addition of lateral flow helps to better resolve the uphill/downhill differences in water table depth, but there are still significant differences relative to the Fan WTD map. The authors note that calibration of the f_d parameter to give a better match to the Fan WTD map may not be fruitful due to differences in climate forcing. But given the relatively large differences, it would be informative to do a sensitivity test for the f_d parameter. For example, is there a value of f_d that further lowers the water table depth, and better resolves the riparian areas as shown in the Fan map?
Statements such as "The effects of WTD changes on the energy fluxes were more pronounced at low elevation cells, especially at the stream and its surrounding cells. The delivery of the groundwater through the lateral flow to the valleys supported higher LH while reducing the SH compared with ELMv2.0 which has little spatial WTD variations" do not appear to be well supported by figure 9. Instead of highlighting the differences between the uphill and downhill areas apparent in figure 8, figure 9 shows spatial patterns having broad domainwide patterns. Why do the water table patterns in figure 8 show much more structure? For example, larger LH values do not appear consistently in the riparian areas. Similarly, the patterns in the difference maps only show scattered points rather than a clear riparian pattern. Why is this?
The comparisons to observations (figures 10 and 11) do not seem to add much insight into the relative model behaviors. Given the authors choice to not calibrate the models, I don't think it can be stated that the differences between the observations are due to model structure. For example, the A121 differences in figure 10 might be smaller if the f_d parameter in ELMv2.0 model had been calibrated. The statement that both models "were able to capture the major fluctuations and wetting/drying cycles of soil moisture (SM)" seems overstated. The rain events are generally captured, but the magnitude of the reponse, and the drydown rate is generally poor. What information are the authors trying to give to the reader with these figures? Similarly for figure 12; one does not need to perform a model simulation to be aware that shallower water tables will typically have colder temperatures, higher LH, and lower SH than deeper water tables. Any two model versions having different water table depths would presumably show this behavior. I don't see that this figure adds any additional insight to the results.
Citation: https://doi.org/10.5194/egusphere2023375RC1 
CC1: 'Comment on egusphere2023375', Xubin Zeng, 27 May 2023
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The manuscript is well written, with interesting results. The conclusions can be further strengthened by addressing the following concerns.
(1) The anisotropic ratio for the hydraulic conductivity (K_x/K_z) was set as 1 for the CH and DH cases, but it was set as 10 for the VH case, without any justifications. At least, the authors should perform sensitivity tests using the ratio of 10 for the CH and DH cases and using the ratio of 1 for the VH case, and briefly discuss the results.
Similarly, it is unclear what this ratio is for the LWW case and what the justification is (as dx = 1 km here versus 10 m for the three idealized cases).
(2) The authors proposed the lateral fluxes for both unsaturated and saturated flow in Eq. (14). To understand the importance of such fluxes, the authors should compare the magnitudes of lateral flux versus vertical fluxes for the unsaturated zone and saturated zone separately for the three idealized cases.
(3) For the TWW case, while it is probably acceptable not to compare the results with observed streamflow, the authors should at least compare runoff time series between the two simulations. For instance, how does the lateral flux affect the timing of peak runoff?
Minor comments:
(4) Line 189: porosity is 0.43 but soil moisture is greater than 0.43 in Fig. 5. Clarify.
(5) Line 219: explain how you obtain the atmospheric forcing data at 1 km grid size from the original 1/8 degree data.
(6) Line 225: revise “Google Earth Engine (Gorelick et al. 2017)” by “Google Earth Engine (GEE; Gorelick et al. 2017)”
(7) Provide and briefly discuss the correlation between Fig. 8b and Fig. 8c. Also provide simple statistics (e.g., root mean square errors) in each panel in Figs. 10 and 11.
Citation: https://doi.org/10.5194/egusphere2023375CC1 
RC2: 'Comment on egusphere2023375', Anonymous Referee #2, 01 Jun 2023
reply
The authors have the original idea of considering horizontal groundwater flow in the source/sink terms of the equation. While these are interesting results, I believe the paper could be improved by considering the following points.
About the equation
To clarify the difference between ELMlat and PFLOTRAN, it should be noted that the unsaturated horizontal flow is the results of one previous step.
Equation 16 makes sense if flux includes the surface area of the terrain, but I can't determine that with the current description.
Equation 17 is correct in the equation itself, but does it not have to account for slope gradient as in equation 15? Need a description of why unsaturated horizontal flow is considered but saturation is not.
Regarding the model benchmarkThe authors mentioned that the moisture retention curves used in ELM and PFLOTRAN are different, but why not show how much they differ? Showing the results of the fitting would be helpful for the discussion.
Regarding the resultsWhat is the reason for using top 5 layers in the comparison with PFLOTRAN as far as Figure 5 is concerned, I think it would be a fair assessment to include up to about top 10 layers. Also, what is the reason for using MAE? It tend to be small because the denominator is larger than the numerator. Why not present other indicators as well?
I understand that Figures 6 and 7 are ELMlatPFLOTRAN. If so, some discussion of the CH and DH soil moisture and groundwater table results is needed; ELMlat has less soil moisture on the down hill and more on the up hill than PFLOTRAN, even though the groundwater table is too flat compared to PFLOTRAN. Is this solely due to the water retention curve? Need to describe the difference in equations and the effect of the solution method.
Regarding Figure 9, from Figure 8, the groundwater table is deeper near the watershed boundary, but even in such locations, does the soil temperature decrease, LH increase, and SH decrease? Are these results consistent? Results and discussion on whether horizontal unsaturated flow has an effect and how the seasonal planar distribution varies are needed.
Minor comments
Line 127 may be clearer in Figure 1 than in Figure 2
I think (d) in Figure 10 is a mistake for A149.
The equation numbers are not bracketed: lines 106, 116, 126, 128, 143.
FigureA1 should be the result of all layers, not top 5 layers.
FigureA2 does not have results for (d),(e),(f).
FigureA3 has all figures marked as (a).
Line 540 is Soil MoistureâBased (I noticed this by accident)Citation: https://doi.org/10.5194/egusphere2023375RC2
Han Qiu et al.
Han Qiu et al.
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