HESS Review on “Spatio-temporal soil moisture retrieval at the catchment-scale using a dense network of cosmic-ray neutron sensors” (https://doi.org/10.5194/hess-2021-25 )

1. General comments:

The paper “Spatio-temporal soil moisture retrieval at the catchment-scale using a dense network of cosmic-ray neutron sensors” by Heistermann et al., 2021 presents the first published analyses of comprehensive dataset of a dense network on Cosmic ray neutron sensors (CRNS) data and adjacent measurements, which were featured in the publication by Fersch et al., 2020 (https://doi.org/10.5194/essd-2020-48 ). The present paper is a contribution of high scientific significance as it presents a novel method for spatial interpolation of CRNS data from a network of closely positioned CRNS sensors. The study brings significant insights into the potential (and limitations) of CRNS technology to characterise spatiotemporal variability of soil water content (SWC) (i) at relatively high resolution (10m grid) and (ii) full small catchment scale (1km²) coverage.

Together with Fersch et al., 2020 this paper is a valuable scientific contribution to the way we look at SWC spatiotemporal variability with CRNS sensors. The methodological framework of the study includes the standardization of sensitivity of multiple (and diverse) CRNS sensors; it addresses thoroughly the correction of the signal for static effects and dynamic factors on the sensors’ signals; the calibration for obtaining a single N₀ for all sensors is especially valuable for further CRNS studies. Moreover, the assessment of uncertainties is thorough and openly assessed. The spatial interpolation (using unconstrained and constrained model) is one of the most important assets of the paper, as a contribution to the CRNS community.

Nevertheless, my main concerns are with the presentation quality of the paper: the length and structure of the manuscript could be substantially improved (see specific comments). Therefore, I would like to suggest major revisions.

2. Specific comments:
   • While this is a discussion paper, I would encourage the authors to be more concise and structured when presenting their findings (examples are given below). There are sections which seem to be excessively long. That would hopefully help address another issue, which is the often “downplaying” of the study findings (examples also given). Moreover, during the discussion the implications of the findings and potential benefit of the application of these novel analyses are shown/discussed but in a scattered manner throughout “Results and discussion” section. I would recommend condensing them in a subsection within “Summary and conclusions”. Below I outline specific examples:

In Section 1.2. Aims and objectives:  research questions and specific objectives of the study are presented between lines 65-95 and surely could be condensed. If you would wish to keep all the text, separate clearly in “aims and objectives” and “justification”. That would help structuring further the manuscript.

Section 4.4. has effectively three subsections “Unconstrained model”, “Constrained model” and “Forward operator”. Please give these index numbers 4.4.1. , 4.4.2 and 4.4.3. (similar to what you have done in section 4.1.). Also, lines 319-340 from subsection Unconstrained model: please try to shorten and restructure. Only in line 327 you say what you have actually done in the study and before that you give several examples (319-327). I would encourage you to first say what you did and then give the examples.

Section 5.2. between lines 473-484. – text can be shortened, and arguments presented more concisely. For example, line 472 “Clearly, the agreement is less than perfect. Still, the general pattern suggests”, can be rephrased to “While the agreement is not perfect, the general pattern suggests…”. 

In general, in Section 5: try to restructure main discussion points (5.1. to 5.5.) in a way that it follows the flow of your aims and objectives.

Section 6 Summary and conclusions (which are then called “main lessons learned along these steps”) needs to be more concise. Shortly introduce the “main lessons” and then expand on them in 6.1. and 6.2.

2.1. Section 4.3. is particularly good, as uncertainties have been very well acknowledged and explained. Moreover, the limitations of the study are thoroughly and openly discussed. However, I encourage the authors to include a short comment in discussion on the applicability and reproducibility of the set-up (of dense CRNS networks) and perhaps provide examples of what would be the minimum number of CRNS probes to be included in a similar set-up in order to assess CRNS SWC spatiotemporal variability in a reliable way at the catchment (in this case 1 km²) scale.

3. Technical corrections:
   • Figures: Improvements suggested on the following figures

Figure 1: In the legend you refer to “Climate gauge” and in caption to “Climate station” and in the text (line 169) you use the term meteorological station.  Please choose one term only. Besides, from the figure it does not become apparent where are the peaty soils within this catchment are located. From the text we understand that location 23 is on peaty soils, but what is the extend of these? Would it be possible to include the soils on this map too? May be in a separate panel? Finally, the manual samples locations: they seem to be very close to the CRNS sensors, which is ok, but visually it is impossible to distinguish how many you had around each CRNS probe. Could you include information on their number (e.g. in Table 1)?

Figure 3: Is it correct that the rover can sense neutron intensity between 7000 and 11000 cph? (this is just a question, rather than an improvement suggestion)

Figure 5: great figure. Could you include the legend also on the right panel for consistency? Also, optionally name the panels as a),b) and c), this will help you shorten the text related to that figure.

Figure 6: another very clear figure. However, I wonder why precipitation is presented as mm/6h and the SWC at the panel below in daily values? I guess it is ok if the width of the cell representing a day on the bottom panel is matched with the width 4 bars of rain.

• Tables:

Table 1: to address my comment on Figure 1, perhaps you can include an extra column to this table “Dominant soil type” or give percentage of the soil types present within each footprint.

Table 2: Under each header add the units, if applicable. That might avoid having a lengthy caption and faster to understand to readers.

• Others:

Line 9-11: Do you need to enumerate all the static effects and temporally dynamic factors in the abstract? Shorten sentence if possible.

Line 14: you mention already here “constrained interpolation”, which is great. Could you also please mention what you will refer later on as “unconstrained” to improve clarity and keep consistent?

Line 44: on “isolated” sensor footprints only. Change “only” for “mainly”, as there are already several key studies published using CRNS rovers.

Line 51-57: Am I correct that here you present the main aim of the study? If so, please restructure this paragraph first stating the main aim and then then the justification. (the content is good, but the flow can be improved).

Lines 67 – 78: The first question or specific objective has been given more space compared to questions 2 and 3. Could you please make this section more concise? In that way the “weight” of the three specific objectives seems equally distributed.

Line 94: Abbreviation FDR is not defined previously. Could you please include “Frequency domain reflectometry” here?

Line 102: change to “We then present and discuss the corresponding results (section 5)…” – as Results and Discussion are presented simultaneously.

Line 109: please provide information on what portion of the catchment is covered with grassland (in %) and forest (in %) to give a better idea of the heterogeneity in land use to which you refer in Line 60.

Line 113: Section 3.1. Overview does not add anything to point 3. Data. In fact, you state “as already pointed out”. Thus, I would remove the current Section 3.1.

Line 138-142: Section 3.3. is unnecessarily long and can be shortened to two sentences. Alternatively fuse current sections 3.3. and 3.6. as one, giving it an appropriate name. The measurements described in these two sections are used to do the continuous correction of the signal.

Line 144: “As we mention in section 1.1. we require local measurements of the soil water content and the soil bulk density” – you don’t actually mention soil bulk density in current section 1.1. Either include it there or rephrase this sentence.

Line 146: Do “several measurement techniques” refer to the techniques outlines in sections 3.4.1., 3.4.2. and 3.4.3.? If so, please change to “the following measurement techniques”.

Line 168: Current section 3.6 should be moved after current section 3.1., as the meteorological data is relevant to all the CRNS analysis. Also, see my comment on using “climatic gauge”, “climate station” or “meteorological station”.

Line 172: Section 3.7 does not really present data (since you do not use it for analysis and merely to create figure 1). I would remove this section as the information is already provided in the caption of Figure 1. Optionally, add the hyperlink from the current section 3.7 to the caption of Fig.1 .

Line 173: replace “incl.” with “including”.

Line 411: SMT100 cluster (SoilNet) should be defined/mentioned earlier, as for example in line 90. In line 431 you refer to the same as “FDR-cluster”. Choose one term and stick to it.

Line 484: “… Fig.5 is both encouraging and disappointing” – put first disappointing and then encouraging, as this is the order in which you present them afterwards. Also, why would you say disappointing about a Figure you include in a publication? Choose a different less negative word. There are several places in the manuscript where you downplay the results of your research (see my comment about line 611 for example).

Line 486: “The vertical shades in the left panel indicate that the theta (Ni) is highly uncertain.” You refer here to the percentiles, but which ones/which grey shades? The 5-95% or the 25-75% ones? Be more specific. Also you can see from this left panel that the uncertainty is larger in the wetter range and smaller in the drier range. Acknowledge that instead of saying that they all are highly uncertain. See my comments about downplaying your results.

Line 605-607: While limitations are honestly acknowledged the paragraph ends on a negative note, which does not reflect the main outcome. I would recommend rephrasing along the lines “While both the unconstrained and the constrained approaches failed to fully simulate the dry are in the southwest of the SoilNet area, the constrained captured it relatively better.”

Line 611: “largely” outperform seems like an overstatement (downplaying the overall good results of your study). I would remove “largely”. If you mean that the unconstrained model outperforms during a prolonged period of time, modify text accordingly.

Line 622: typo. Change “reliably” to “reliability”.

Line 629: I understand the willingness to emphasize the “heterogeneous” in here, as it is a key word in this study. However, not entire convinced about “heterogeneous hydro-meteorological conditions”. Are you not considering that precipitation, temperature and barometric pressure measured at the climate station are all the same for all sensors? I would recommend saying “dynamic” or rephrase.

Line 725: typo. Change “August 2910” to the corresponding year.

Supplementary material is clear and neatly presented.

(I apologize for the late post. I will try to post the second part in 1 day, which is about the spatial patterns and interpolation)

1. GENERAL COMMENTS

This paper presents valuable and interesting results on a dense network of CRNS with an attempt at a uniform calibration for multiple probes. It provides both practical advice and technical insights for the calibration and application of CRNS. Overall, the authors did a great job on experiment design, data collection and analyses, simulation, and result illustration. 

2. SPECIFIC COMMENTS

2.1 Sensitivity factor was assumed to be a constant for each sensor, which seems intuitively reasonable but needs scrutiny. 

Since these factors are essential to the uniform calibration, it at least requires some citations and/or explanation. 

2.2 Please define/specify "local uncertainty". I think the "local" refers to the parameter space, not the spatial-temporal space. If I am correct, it creates some ambiguity in the text since the discussions are always related to space/time in this paper. (Line 271, 415, 665, etc.)

2.3 Please briefly explain the choice of "200 times" of the Monte-Carlo simulation on the sensitivity of N0. To my understanding, the number of simulations depends on the dimensions of the parameter space. Why are 200 times good enough to quantify the uncertainty of N0 concerning these many parameters and disturbances.

3. TECHNICAL COMMENTS

Line 26 "small spatial measurement support" and Line 330 "points of support"

Support is an important concept in defining spatial scales of soil sampling and measurements. I recommend adding a definition and citations here. This would also help to present the results on soil moisture spatial patterns in the following sections.

Line 259 "assuming a spatially uniform value of N0..." 

Modification required. Since N0 mainly depends on the sensor itself after correcting all factors (air pressure, vegetation, lattice water, etc.), it is not a spatial variable.

(To be continued.)

(continued)

1. GENERAL COMMENTS

The ideas of designing a dense network and devising a constrained model to study soil moisture variability with multiple CRNS are innovative. As pointed out by the authors, this study was limited by making various assumptions and decisions' arbitrariness. This study still made valuable contributions to applications of CRNS. The selection of the model and its parameters requires some more clarification. This paper can also be improved by considering issues on footprint and resolution.

2. SPECIFIC COMMENTS

2.4 Models

Line 88 References for the concept of geophysical inversion are needed.

Line 329 There are three parameters for a variogram model, nugget, sill, and range. The paper only emphasized the range but did not mention the other two. Please specify the parameter selections. 

Line 297 The Kriging ranges for soil moisture and bulk density are quite different. Please justify this selection.

2.5 Footprint, model parameters, and scaling

One of the unique features of CRNS is its large footprint, which could directly influence data visualization, model selection, and interpolation. The grid size for the interpolation process is 10 m * 10 m (Line 311), which is much smaller than the footprint. This implies that the modeling is not just an interpolation but also involves a downscaling process for the CRNS measurements. It is of great interest in terms of the CRNS studies. However, it also requires more clarification and cautiousness. For example, is it reasonable to use observed soil moisture, θ(N^obs), to do Ordinary Kriging with a resolution much smaller than its footprint? Does it implicitly assume that observed soil moisture values are also representative at a smaller scale?

The design of the forward operator and the optimization argument is innovative since it provides a way of downscaling CRNS measurement to almost any arbitrary scale/resolution, which may be only limited by computational capacity. 

The design of the dense network made the footprints of CRNS largely overlapped, which provides extra information about soil moisture spatial patterns. This may also make it logically possible and reasonable to do the downscaling and to improve the interpolation. Can the overlaps be used for results validation?  

3. TECHNICAL COMMENTS

Line 262 Eq. 1 

Recommendation: replace comma with semicolon, i.e. theta(N_i; N₀)

To my understanding, N_i is a variable, and N₀ is a parameter in Eq. 1.

Line 350 delete extra "suitable"

Line 622 reliably -> reliability

Review of HESS 2021-25 “Spatio-temporal soil moisture retrieval at the catchment-scale using a dense network of cosmic-ray neutron sensors”

General comments:

This manuscript describes the first ever attempt to use multiple CRNS to estimate catchment-scale soil moisture, including temporal and spatial variations. The research conducted is of interest and importance to the research community, even if the findings are somewhat marginal in their advancement of practical application. While the paper is well-organized and written, it is excessively long and tedious to read. I understand that the authors wish to share the minutia of their novel methodology, but as written the paper is difficult to read and seems more akin to a grant proposal than a scientific manuscript.

I dislike the goal of the project to match the pattern rather than absolute values (stated in Line 434) and the general avoidance of quantifying differences or variability in the estimated and measured soil moisture values. I understand why the authors have chosen this approach, but I also think that the use of the absolute values of measured and estimated volumetric water content would be useful to present to the scientific community. Relative values only provide so much information.

For these reasons, I suggest the authors make major revisions to the manuscript before it can be accepted for publication.

Specific comments:

Section 2: The authors mention in passing the presence of very shallow groundwater, but do not mention how this likely has significant effects on their CRNS measurements. This issue should be addressed much more thoroughly.

Additionally, the authors should provide the textural and SOM information for samples taken near each CRNS (texture) and for each mixed sample (SOM). Providing an average catchment-scale value is not acceptable, and readers cannot be expected to read every cited paper to find this information, which could easily be incorporated into Table 2. Further, the estimated gravimetric water content values > 1.0 g/g shown in Figure 4b are unrealistic, unless you are considering a highly organic soil. However, based on the information presented, it is impossible to determine the soil type near CRNS 21 and 23.

Table 2: In addition to including information regarding soil texture and SOM for each site, the authors should include some indication of the variability of the values shown for each site. Also, bulk density values are incredibly low, less than 1 kg/L in most cases. Including the SOM content in this table would make those values look less suspect, if indeed the SOM content is extremely high. If not, the authors need to address the very low bulk density values reported.

Figure 5: How does the variability in θ_i^obs during Monte Carlo simulations compare to the variability observed in measured volumetric water content from thermo-gravimetric samples? Could the authors provide mean uncertainty values for Monte Carlo θ(N_i) and θ_i^obs? It is difficult to estimate these values from Figure 5 alone.

Line 525 and Figure 6a: Reference evapotranspiration is different than potential evapotranspiration, but the terms are used interchangeably in the text. Make sure all instances are changed to “reference.”

Line 543: It would be good, again, if the authors would quantify this uncertainty.

Figure 9. The results shown in this figure are underwhelming. I expected that the highly concentrated CRNS sensors would be able to provide a closer match in spatial soil moisture distribution to the SoilNet measurements. The lack of spatial agreement with SoilNet soil moisture values, even with a high concentration of CRNS that is unlikely to replicated in practice, is surprising and a bit disappointing. If the CRNS are unable to provide useful spatially explicit information, what is the benefit of using these extremely expensive sensors rather than many cheaper in-situ sensors or downscaled remote sensing data? Also, I would be more interested in a time series figure showing the mean field-scale volumetric water content for each of the three scenarios- unconstrained, constrained, and SoilNet. I suspect that the constrained and unconstrained values would be far more similar to one another than to the SoilNet values.

Line 595: While I agree that the current application of a large number of CRNS in a small area is interesting, I do not think it is economically feasible or sustainable. The authors should at least mention the cost prohibitive nature of this study.

Technical corrections:

Line 301: Should read “how the availability of sampling locations affected N₀ calibrations,

Line 725: Should read “from August 2019"