This manuscript presents an uncoupled inversion approach to estimate soil hydraulic and solute transport parameters from electromagnetic induction measurements made during an infiltration experiment. The consideration of solute transport in addition to water flow is relatively novel and should be of interest to the community.

After reading this manuscript, I am left with a range of concerns that are described in the general and specific comments below. Although I am generally supportive of this type of research, I can currently not recommend this manuscript for publication. To address my comments and concerns, additional analysis may be required and considerable rewriting would be necessary. I am unsure whether this still is in the realm of a major revision, but I decided to go with this recommendation.

GENERAL COMMENTS

1. Considerable previous work is available discussing the use of geophysical data to parameterize hydrological models. It has been argued that the uncoupled inversion strategy used here may provide biased hydraulic parameters because errors as well as assumptions (e.g. smoothness) from the EMI inversion can propagate to the estimated water content and solute content distributions. In such cases, the use of coupled inversion has been advocated. I think that this approach may also be advantageous in your case. It should be made clear in the manuscript why the current inversion approach was selected, and why it is expected to not suffer from the problems that have led some researchers to prefer a coupled inversion approach when the aim is to parameterize a hydrological model with geophysical data. Given the used EMI-inversion approach with smoothing in space and time, I have difficult time to believe that uncoupled inversion does not lead to problems.
2. A synthetic modelling experiment would help to support the presented results. It would not only help to confirm that the uncoupled inversion approach is able to provide realistic parameter estimates, but it would also help to address other concerns addressed in the specific comments below, such as the information content of the measurements to reliably estimate 8 hydraulic parameters of two different layers from the limited number of available measurements, as well as the separation of the solute and the infiltration front.
3. Although I also wish that EMI measurements could be treated as quantitative measurements, this is still not the case. As detailed in several studies, the application of EMI inversion requires the correction of the measured ECa data for expected shifts and offsets, as for example discussed in von Hebel et al. (2014) and some of his follow-up work. Such a calibration was not considered in this study, and I find this problematic. The authors argue that this only leads to problems with the estimated saturated water content, but I am not convinced by this.

SPECIFIC COMMENTS

Line 17. For most journals, a single-paragraph abstract is required. Please check.

Line 21. Consider reformulating this sentence to make clear that this is the aim of the study.

Line70. Although I understand where you are going, I think this sentence should be improved (e.g. “also” and “proper” do not really seem to fit here).

Line 86. The studies cited here are mostly focused on saturated systems and the estimation of the soil hydraulic conductivity. Perhaps it would be more appropriate to focus on studies that have attempted to estimate the full set of hydraulic parameters required to describe flow and transport in unsaturated soils.

Line 96. In my opinion, efficiency and number of electrodes are not such a good reason to discard the ERT method. If 1D models are assumed, the amount of electrodes could be substantially reduced. However, relatively large electrode separations would be required to obtain sensitivity at depth. The sensitivity distribution with depth is much more favorable in case of EMI, which enables a more compact experiment.

Line 105. Consider rewriting here. The apparent electrical conductivity DOES represent the electrical conductivity distribution with depth. However, there is no direct relation and there are many distributions that can provide the same apparent conductivity. Perhaps use “…does not directly provide information…”.

Line 159. The text is confusing here. Two altitudes are provided. Consider rewriting.

Line 172. Perhaps it would be good to already mention the water content at the start of the experiment here.

Line 181. Please provide manufacturer of these sensors.

Line 182. How does this compare to the pore water electrical conductivity of the remaining water content? Both the initial water content and this information is essential to evaluate whether the first infiltration experiment can be evaluated solely in terms of water content variations.

Line 183. Can you be more precise about the measurement schedule? I guess you mean 1 hour irrigation and a break of 1 hour, but I am not sure.

Line 184. I guess it was 2000 dm3 on 16 m2? Perhaps already provide units in mm (or m) given that you will be using 1D modelling afterwards.

Line 210. This text confuses me. Were multiple experiments performed? Why average water volume? Please clarify.

Line 218. Is there an S in the equation, or is this a typo? If yes, please describe what it represents?

Line 229. To be able to reproduce the simulations, I think you should describe the layers that you assumed in the EMI inversion in more detail.

Line 230. This text is confusing because it suggests that models are constrained in space by neighbors. In my understanding, there is only 1 model with 7 layers here. Correct? Is there a constraint on the layer-by-layer variation? It is clearer later in the text, but please improve text here already.

Line 246. I wonder whether there is any support for the time-lapse inversion strategy implemented here. You are penalizing changes in space as strong as changes in time by using a single regularization parameter. Is this realistic? The literature on time-lapse ERT inversion is substantially larger. Has this approach been considered for ERT?

Line 248. At this point, it would be good to describe how the desired value of the regularization parameter was determined.

Line 284. It is not clear to me how the water content was obtained here. Did you use Eq. (1) and assumed a fixed pore water conductivity equal to the applied tap water? How was the permittivity converted to water content in this case?

Line 287. What kind of optimization procedure was used? Or do you mean here that the optimization implemented in Hydrus was used? In any case, it would be good to mention the optimization strategy.

Line 294. At this point, I am missing two important aspects. First, it would be good to discuss whether all fifteen hydraulic parameters were optimized. If yes, I would recommend reflecting on the identifiability of all these parameters. Is there sufficient information? This is particularly doubtful for the bedrock in case of the TDR measurements since it does not contain a sensor. Second, I think you need to clarify how the initial conditions were specified. Only with this information, it is possible to reproduce your model set-up.

Line 304. This seems to suggest that the same dispersivity was assumed for the three layers? A short justification would be appropriate.

Figure 3. Please emphasize that the modelling is related to the EMI inversion only in the caption. You have multiple inversions in your approach. I also think that more reflection is required on the relatively poor fit provided here. To what extent can this be related to the lack of calibration of the EMI measurements (see general comments).

Line 321. I assume that a set of EMI measurements before the infiltration is also available. I think it would be good to also include these measurements here and use them to reflect on the initial conditions.

Line 328. If the topsoil is saturated and the bedrock remains dry (i.e. no changes), I wonder where all the water applied after the third irrigation is going? Is it flowing laterally? This would be problematic because of the 1D model used to describe water flow.

Line 335. In case of TDR, I assume that this is the mean value from the four sensors? I propose to include error bars to reflect the spatial variability of the measured bulk conductivity obtained with TDR.

Line 347. I find it optimistic to state that a mean error of 16 mS m-1 is acceptable. The entire range of inverted bulk electrical conductivity is from 0 to 60. Would an accuracy of 0.15 cm3cm-3 (range of 0 – 0.45) be acceptable? I think some more critical reflection is required here.

Line 352. This is correct. Based on this observation, it was concluded that corrections are required before meaningful EMI inversion results can be obtained.

Line 377. It would be desirable to also show the fit to the tensiometer data.

Line 379. For the EMI-based inversion, I assume that the data presented in Figure 4 were converted to water content and used for the inversion? I think this should be emphasized more because one may obtain the impression that the two depths presented in Figure 6 were used only.

Line 380. I think this information should be provided in the methods and not in the results (see specific comment for Line 294).

Line 381. Units are missing for the hydraulic parameters. Also make sure that they are consistent with the parameters presented in Table 1. I assume that the units of hydraulic conductivity are not consistent, otherwise the bedrock would be the most conductive.

Line 384. Please also provide a simulated water content distribution like Figure 4. I am particularly interested in seeing the development in the bedrock layer.

Line 404. Make sure to indicate which parameters were fixed during optimization.

Figure 7. Consider changing the legend. I think you should use the horizon names and not the method names. This suggests that the two depths were inverted independently, which is hopefully not the case.

Figure 8. Would be good to also present measurements at t=0. How do the initial conditions of the second experiment compare to those of the first experiment?

Line 432. I wonder whether this can be interpreted as a separation of the infiltration front and the solute front. This is expected to happen, especially if the soil is relatively wet at the start of the experiment. Given that the background electrical conductivity at depth is much higher in Figure 9 than in Figure 4, this may be the case.

Line 454. This could be supported by using the error bars to represent the variability in the four measurements.

Line 463. This seems to suggest that only two depths were extracted from the EMI inversion. It is not clear to me why the information in Figure 9 was not used during the optimization. I would say that one of the key advantages of EMI is that we obtain more depth information compared to TDR, but this aspect does not seem to be considered here.

Review of ‘In-situ estimation of soil hydraulic and hydrodispersive properties by inversion of Electromagnetic Induction measurements and soil hydrological modeling’ by  Giovanna Dragonetti, Mohammad Farzamian, Antonio Coppola, Angelo Basile, and Fernando Monteiro Santos

The paper presents a way to interpret electromagnetic induction data (i.e., bulk soil electrical conductivities) estimate soil hydraulic properties in the field, at roughly the scale of the soil profile. The paper argues this is relevant for optimizing water use in irrigated agriculture. It reports on field experiments involving infiltration of solute-free water to monitor the wetting front, followed by infiltration with saline water to monitor the effect of the salt on the electrical conductivity. An attempt is made to derive plot-scale (not field-scale) soil hydraulic and solute transport parameters to assess the potential of non-invasive EM measurements for practical applications in irrigated agriculture without exploring this in detail. 

In the Introduction, the authors appear to tweak their interpretation of the literature to suit their needs, resulting is some claims that are debatable or even incorrect. I noticed numerous self-citations. In fact 28 of 59 references (47%) are self-citations! I think this is a record in my multiple decades as a reviewer. It probably would not hurt to look at the works of others to have a more balanced overview of the state of knowledge. A few examples are detailed below. 

l. 51-58. Richards’ equation (RE) applies at the Darcy scale. The smallest scale at which it can be applied is the scale of the representative elementary volume. The largest scale is not as well defined, but it is clear that at some point the proportionality between the water flux density and the hydraulic gradient will break down because of soil heterogeneity, different flow directions within the volume of interest, etc. The fact that RE is used at the filed scale does not imply it is assumed that it is valid there, but that there is no alternative yet. This can be gleaned from the way RE is used at the field scale: the problem is used to one dimension, and it is hoped the properties of the soil and the vegetation (usually a crop) were chosen such that the results reflect the field scale, without actually modeling the entire field.

The author’s statement that the ADE is assumed to be valid at any scale is incorrect. There is a rich literature spanning several decades (especially in groundwater hydrology but also in soil physics) about the increase of the dispersion coefficient with solute travel distance, and concepts such as the fractional advection-dispersion equation and Continuous Time Random Walk have been proposed to remedy the problem. The dilution theory proposes a different mixing process than diffusion. In soil physics, the solute spreading proportionality to the square root of time (for steady flow) consistent with the ADE has been challenged. Its alternative, stochastic-convective solute spreading, lets solute spread proportional to time. A google-scholar search with these terms will provide ample references.

l. 67-69. It is unclear to me why the authors believe that different properties of soil layers are more important for solute transport than they are for soil water flow or root water uptake (or density of the root network, for that matter).

l. 70-83. I agree (and so do others) that lab-based soil hydraulic properties often transfer poorly to the field. But field method often have a limited range, which creates a risk when the soil dries out. Also, soil layering, soil heterogeneity within layers, spatial variation of the infiltration rate during an experiment, preferential flow, etc. all end up indiscriminately in the soil hydraulic properties determined from field experiments. This paper focuses on field measurements and aims to obtain from those the soil hydraulic properties at a more relevant, but at this point in the paper still poorly defined, scale. With this in mind, the paper cannot not ignore these issues because they are highly relevant for it. They should therefore be thoroughly discussed, not ignored.

l. 96. ‘a field scale’ change to ‘the field scale’

l. 107-112. Quite recently, HESS published a paper related to the subject discussed here (Kim Madsen van't Veen, Ty Paul Andrew Ferré, Bo Vangsø Iversen, and Christen Duus Børgesen, Hydrol. Earth Syst. Sci., 26, 55–70, https://doi.org/10.5194/hess-26-55-2022, 2022). It would be nice to discuss this paper as well. If I am not mistaken, that paper does not delve into the soil hydraulic properties, but they examine the details of the measurements and the data inversion in some detail.

l. 122-130. There seems to be a contradiction here. Even if you are able to find field-scale soil hydraulic properties with non-invasive techniques, you propose to verify these with small-scale sensors (TDR probes and tensiometers). But to obtain field-scale data with those you will have to install them at many locations at multiple depths, which will disturb the soil layers and the flow paths. Only later in the paper we learn that you are actually only monitoring smaller plots, with sensors at two depths on four locations, away from the area in which you use the non-invasive techniques, without moving the CMD instrument over the field. Please bring this section of the text in agreement with the experimental setup.

l. 167. This is the first time you mention the size of the plots. It appears to me that your frequent use of the term ‘field scale’ above was a bit misleading. You ae working on the plot scale, not the field scale. I do not believe this invalidates the work, or that the experiments were performed on too small a scale, I just think the terminology you use is unfortunate.

l. 184. 2000 liters of water translates to 125 mm, is that correct? I am optimistic that the design of your experiment ensured a uniform infiltration over the plot area.

l. 199-200. This makes sense, but are you sure that the digging required to install the sensors did not affect the water flow pattern and wetting front velocity? In other words: are your reference profiles representative of the profile under the CMD mini-Explorer? I admit I do not really know how to avoid this, except by digging up the entire plot. But perhaps you installed the invasive sensors some time before to let the soil settle, perhaps aided by some wetting-drying cycles? I cannot tell from the text.

l. 207-211. How enthusiastic will farmers be if you propose to them to apply saline water to their irrigated plots if they have high-quality irrigation water available? And how well does your method perform in plots that are already salinized to some degree?

l. 220. For a paper that argues against lab experiments, it is surprising to see that you need to determine some model parameters in the lab after all. From what I understand, these parameters are indispensable for any location where you want to apply your method, so in addition to the effort you reported here, these laboratory measurements need to be carried out as well, and probably for every soil layer. But your emphasis on transferability to the field implies you need to know the spatial variation of these parameters as well. All in all, how much additional time, money, and resources are necessary for this aspect of the work?

l. 222 ‘concentrations, Cl-, to sigma-w’. Unclear. Do you mean ‘concentrations of Cl- to sigma-w’?

l. 331 (Fig. 4). Does the wedge at about 0.3 m depth in the first four hours of the experiment perhaps indicate that preferential flow rapidly carried water to this depth, wetting it faster than the top soil? It appears in Fig. 9 as well. The dispersivity of the top soil in Table 1 is very high, which points to the possibility of very non-uniform vertical flow rates consistent with preferential flow.

l. 336-339. And in addition you have the difference between disturbed and undisturbed soil in this case. Would it have been worthwhile to apply the EMI sensor above the TDRs, or would the metallic sensor have corrupted the measurements even if they had been temporarily shut off?

l. 361. The difference between the water contents is not slight, especially if it is used to time and optimize irrigations. See the comment on Fig. 6 below.

l. 370 (Fig. 6). If the differences between TDR and EMI are indicative of the error of the EMI, than the water availability in the root zone will be severely underestimated, so the use of such data in irrigation optimization will be very limited unless the farmer learns by experience to interpret the data correctly. But then, all this effort is unnecessary: even without all the modeling I suspect a farmer will figure this out after a few growing seasons. I find it difficult to reconcile this result with the rationale expressed in the Introduction.

l. 380. Fixing the residual water content at zero (or at any other value) affects the ability of the retention curve to adapt its sigmoid shape (Groenevelt, P. H. and Grant, C. D.: A new model for the soil-water retention curve that solves the problem of residual water contents, Eur. J. Soil Sci., 55, 479–485, https://doi.org/10.1111/j.1365-2389.2004.00617.x, 2004)

l. 381-382. So, apparently you need to know a priori the soil hydraulic properties of the deeper soil, presumably measured on soil cores in the lab. This is the second instance where considerable additional effort is needed for your field method to be operational. Should the conclusion therefore not be that field-only methods are not realistic and a substantial effort in the laboratory is needed as well? In addition, these extra requirements muddle the scales on which you purport to work, and negate your claim that you can work with non-invasive, fast techniques.

l. 384-385. On what basis can you claim the difference between the observations at 40 cm is acceptable and the EMI estimates at 20 cm were proper? As I argue above, the differences lead to large errors in the estimation of plant-available water in the root zone. Your statement in l. 401-403 about the different flows for EMI- and TDR-based properties illustrates my point.

l. 404 (Table 1). The values of n seem high for a silty loam, as does the saturated water content. In the A-horizon, there could be an effect of tillage, but in the B-horizon I am not sure what is going on.

l. 470 (Fig. 11)  Do you have an explanation for the dip in Cl concentrations after 2 hours for the EMI-based estimates?

l. 489. I readily believe if you measure solute concentrations in an entire field you can find such high dispersivities because they represent the soil spatial variability. But how large are the columns you mention? Several square meters diameter perhaps, possibly with preferential flow paths?

l. 518-525. Are these claims tenable if you need to have available the soil hydraulic properties of the deeper subsoil and calibrated parameters of your electrical conductivity model? Also, the discrepancy between the water contents is such that the calculated flows differ widely, as you state yourself.

l. 530-531. In solute transport studies in the unsaturated zone, the dispersivity is not that important because the flow dynamics determine most of the transport. In groundwater hydrology, with much less variable flows, the dispersivity is indeed important.

l. 554. I agree that you can cover a large area with EM methods. But your study did not use that advantage. Given the differences in the water contents, could one perhaps argue that repeated use of the same EM device by the same operator on the same field(s) could lead to an empirical ‘feel’ to time irrigations based on EM data alone, without a full-fledged monitoring and modelling effort behind it? An operational use of the instrument, so to speak.