| 04 May 2026
Soil hydrological modelling as a tool to scale EMI-estimations to direct measurements of soil water content distributions in an infiltration experiment
Abstract. This study explores the possibility of integrating electromagnetic induction, EMI, measurements with hydrological modelling to characterize soil hydraulic behaviour during an infiltration process at the transect scale. A controlled 10-hour irrigation experiment was conducted on bare sandy soil in Italy, where time-lapse apparent electrical conductivity, σa, readings were collected along a 24 m transect. Direct soil water content observations were obtained on soil samples at sites spaced 1 m apart and at five depths. Contextually, EMI readings were taken by a CMD Mini Explorer sensor and inverted to estimate bulk electrical conductivity, σb, distributions over time, which were subsequently converted to as many water content, θ, distributions through a site-specific θ–σb calibration relationship derived from independent TDR measurements taken in the upper 25 cm of soil during the infiltration experiment. Soil hydraulic properties (SHPs) for the two soil horizons of the soil profile were independently measured using the tension infiltrometer method (TIM). Two sets of hydrological simulations were carried out using a dynamic Richards-equation-based model, adopting either auger-measured initial water content profiles with the original SHPs, or EMI-estimated initial water content profiles with SHPs scaled by adjusting the saturated water content. Results show that the EMI-estimated water content distributions can effectively reproduce infiltration dynamics when appropriately scaling initial conditions and SHPs. Within this framework, scaling the SHPs and assigning initial conditions consistent with EMI observations enables the conversion between the high-frequency, microscopic description obtained from point-scale measurements and the low-frequency, macroscopic description provided by EMI monitoring. In the proposed approach, the hydrological model provides a physically based interpretative framework for understanding what an EMI sensor observes during infiltration experiments and allows for reconciling nonlinear temporal evolution of θ distributions as observed by point scale measurements and estimated by EMI during wetting front propagation without the need for empirical scaling relationships. The findings extend the results of Dragonetti et al. (2022), demonstrating that EMI monitoring combined with physically based modelling provides a robust framework for interpreting infiltration processes and estimating SHPs non-invasively at the field scale.
Dear Editor, Dear Authors,
Thank you for the invitation to review the article entitled “Soil hydrological modelling as a tool to scale EMI-estimations to direct measurements of soil water content distributions in an infiltration experiment”.
I commend the authors for their work. The manuscript reflects substantial field and modelling efforts and demonstrates a thorough understanding and careful investigation of this important topic. Nonetheless, I have both specific and more general questions and concerns regarding the presented approach, which I believe should be addressed before considering this work for publication in leading journal such as HESS.
L23 – 25 Consider avoiding “microscopic” and “macroscopic” in this context.
L33 “worldwide”, I agree, and references should reflect this. At the moment there seems to be a bias towards the authors’ – Italian work, in the first paragraphs but also throughout the manuscript. This also results in a lack of references where the authors possibly did not have suitable works.
L136 As I side note about the ERT, I think ERT is the strong choice for monitoring infiltration processes: autonomous and more stable time-lapse measurement, arguably also higher vertical resolution, and control on the data quality. While the list of advantages and disadvantages is long and case-specific, the wider use of ERT in time-lapse applications is clear and should be kept in mind.
L141 “EMI still needs inversion if the goal is to obtain σa distribution.” Did you mean σb?
L142 “model-space calibrations are more widely used”. The supporting references continue to be from the authors or collaborators, which weakens the introduction and raises some concerns. I would not agree on this, for example.
L165 In Dragonetti et al. (2022), if I understand correctly, the EMI data (σa) or inverted model (σb) were not scaled (e.g., relative to the TDR) but the inverted σb model was converted into moisture content with a laboratory calibration (θ - σb)? This way EMI is converted into moisture content but the - investigated - effect of the footprint is maintained.
L182 “ the hydrological model itself could provide a consistent framework to reconcile the two seemingly different observations from TDR and EMI by appropriately scaling the initial water contents observed by the two techniques and the saturated water contents of their respective water retention curves.” Yes, but this would mean having the wrong saturated water contents? And possibly a hydraulic conductivity curve that (although apparently similar) compensate for this? This part is a bit convoluted and I am not sure I can follow it.
L234 Consider specifying if you use a GPS or some manual markers to track the continuous Mini Explorer measurements?
L260 – EQ1 I think there is a typo, the denominator should have a minus sign?
L279 Consider clarifying how the undisturbed samples are collected, considering the predominant sand content and the relevance of the samples (bulk density and thus moisture contents, saturated moisture content analysis, also laboratory electrical calibration?).
L321 Regarding the regularization, yes, I agree on the differences and possible specific advantages of a sharp regularization. However, I also think that the key aspects remain how many measurements are available, as well as their independence and error. Consider balancing these theoretical aspects with more specific details, for example, would it be good to see the inversion misfits associated with the six measurements on each position?
L334 OK the stability of the non-irrigated part, did you also check the water mass balance or other aspects more directly related to the inversion of the dynamic part?
L363 Regarding the negligible lateral fluxes, I don’t think horizontal variability is needed to have lateral fluxes, right? For example, the two layers with different Ks could already induce a preferential lateral flow? Consider rephrasing to support your assumption.
L378 Regarding the bottom boundary condition, if I understand correctly, you estimated the negative hydraulic head based on the height difference between water table and profile boundary condition? This is ok for the positive heads, but I am not sure this is correct for the negative ones…
L405 The comparison between measurements (samples and EMI) and simulations that used the respective initial conditions from samples and EMI (plus SHP and described boundary conditions) makes sense to me. The scaling based on the averages at the different depths is not convincing or straight forward though. It seems a convoluted solution that would address but also mix both the footprint – sensitivity part (target here) and many other aspects, including, for example, an offset (wrong measurements that would need calibration) in one or more of the six EMI datasets, or even calibration (conductivity – moisture content) at different depths.
Fig3 I like and agree on showing the apparent conductivity values. The figure is intuitive and summarizes the EMI acquired datasets. My two doubts are:
1) I cannot appreciate significant changes after the first three hours. Possibly only the HCP32 shows an increase from 3h to 5h, but other shallow datasets (VCP) do not support this, right?
2) the deep HCP datasets do not show any particular variation, despite the shallow dynamics, do you suspect some balancing mechanism in the deeper region?
Therefore, I do not particularly agree with your interpretation at L424 on the evident increase in both VCP and HCP.
L426 values of lambda between 1 and 5, consider commenting on how robust and general (or case-specific) this choice could be.
Fig4 The infiltration looks ok, apart from the above concerns related to the absence of significant data changes in the deeper part (>= 50 cm depth) and later times (> 3 h), which the time-lapse inversion seems to highlight? Any estimates of the misfit for the HCP71 and HCP118 with the final – 9h model?
L441 “Figure 5 shows the soil-specific σb-θ calibration obtained by the TDR readings, as described in the section 2.2. Building of the site-specific ρb-θ relationship.” Did the EMI conversion use this calibration or a laboratory one from the samples at different depths?
L460 The spatial part of this paragraph is generally accepted in my opinion, I surely agree with the authors on this. What I think is missing is that it is not just a spatial aspect, but also the specific conductivity model; meaning that talking about different spatial scales and resolutions can be misleading in my opinion, as the EMI sensitivity varies, and could be relatively sensitive to a thin layer or object, as long as it is very conductive. To me, and the authors likely agree, the two things cannot be separated. This, however, hinders a bit the generalization of these comparisons, and the idea of reasoning in terms of spatial frequency, scaling, and low-pass filters. Consider addressing this aspect, possibly moving the paragraph to the discussion.
L471 – L483 No EMI here, correct? It is auger-based simulations (with SHP from TIM) compared to the successive auger measurements. If so, consider clarifying that in the caption of figure 7. Figure 8 is already good.
L490 - L497 Trying to summarize the different parts: the EMI-based was calibrated with the TDR measurements at the surface; then, their moisture estimates were scaled with the auger values (averages by depths); and the derived saturated water content (SHP for the simulation) was scaled with this additional factor, while the other the hydraulic parameters were taken and fixed from the tension infiltrometer measurements? It may be me, but this is hard to follow, also on its physical or methodological motivations. What is the physical or methodological meaning of the scaling factor for the saturated water content?
Fig9 1) I think that the effect of the scaling factor could be added to all the subplots, it remains readable in my opinion. 2) Would it make sense to add the auger values here for comparison (when and where available)?
In general, EMI estimates and simulations are similar in terms of moisture range, but the profiles – trends differ on their specific features (changes both vertically and in time). I do not agree much on the “very similar representation of the wetting front propagation” (L500).
Fig11 OK, this is an important figure, the comparison looks good. What I notice though is that the results introduce a significant lateral smoothing, right? Compared for example with auger values in the left panel of figure 8. My guess would be that lateral homogeneity of the SHP and of the EMI scaling can explain this. However, some assumptions seem necessary to define some statistically robust SHP and scaling factors, or even the TDR - EMI calibration itself. Therefore, my doubts are not on the specific choices but on the general contradictions of the approach, for example stressing the vertical smoothing of the inversion, but then introducing general scaling, calibration, and SHP. While I am not an expert, I wonder whether a 2D model with a more classical data assimilation approach would represent a less arbitrary and more data-based work flow. The authors did not introduce or discuss the existing literature on data assimilation, and related ERT or hydrogeophysics modeling studies. This weakens the motivation and general value of this approach in my opinion.
Finally, the overlap with the work by Dragonetti et al. (2022) is also concerning. The addition of the EMI scaling part, with the concerns outlined above, does not seem to me a substantial or sufficient methodological difference.