In this study, the authors estimated soil moisture on a few sites using a combination of multi-sourced spatiotemporal variables. The topic is interesting and definitely within the scope of the journal. However, I found a couple of major issues that significantly affected the quality and completeness of this work.

There are a few comments that the authors may consider.

Major issues:

1. As indicated by the title and throughout the manuscript, this work is aimed at predicting rut depth with relevant predictors. However, no rut depth values were predicted. Instead, the model predicted soil moisture. The performance was then evaluated by investigating the correlation between the rut depth and the predicted moisture using Kendall’s correlation coefficient.

I do not think this is the correct approach. Either you need to predict rut depth directly and compare the predictions with the measured rut depth, or you build a second model to predict rut depth using the predicted soil moisture from the previous model and then compare the predicted rut depth with the observations. Simply showing the correlation between the predicted soil moisture and the measured rut depth is not enough, as this is not an apple-to-apple comparison. Given the above reasoning, the current work is incomplete.

2. ERA5 is a very coarse product with spatial resolution at kilometer level. Given the size of the study areas shown in Figure 7, I don’t think ERA5 can provide enough useful information in terms of spatial variability. You may want to justify your selection.

3. The structure of some parts of the manuscript is very confusing. Most contents in the discussion section should be in the introduction section. You discuss results you got in the discussion section, not the motivation, existing efforts, and current gaps.

Minor issues:

1. Line 217: Why scale the τ values with 0.99 but not 0.98 or other numbers?

2. The bottom part of Figure 2: As I said previously, the comparison between RD and SWC is not fair. Instead of a comparison, what was really investigated in this manuscript is the correlation between RD and predicted SWC.

3. I suppose some of your input data items may have different spatial resolutions. Maybe consider adding some explanation of how you unify them.

4. Similar to the one mentioned in the third major issue mentioned above, some titles in section 3 may not be appropriate and are not informative. For example, 3.3 Rut depth data. If it is more about the data, it shouldn’t be in the result section.

5. Line 221: The usage of “Therefore” is confusing, as I did not see any causation between the previous sentence and the one that follows.

6. Line 346: Wrong usage of “Despite”. You talked about the advantages of the manually obtained dataset at the beginning and you recommended manual datasets at the end. I suppose “Therefore” is the correct word to use here.

The authors predicted soil moisture for a study site based on a statistical model, considering different variables (e.g., distance to water (DTW), topographic wetness index, soil moisture satellite estimates). First, they identified which variables are more related with soil moisture, then they used the identified variables for soil moisture prediction. They used two different soil moisture estimates collected in the field to validate the model (IMT and SSN). The content of the manuscript is relevant and the data collected in the field is valuable, but the results lack further interpretation and discussion. For instance, what is the physical meaning of having DTW as an important predicting variable? Is this expected? Why is DTW a better predictor in one case (IMT), but ERA-5 is the best predictor in the other case (SSN)? What are the differences in the observations that could lead to that? Also, predicted soil moisture is related with rutting depth only visually in a map. The actual relation between soil moisture and rutting depth needs to be further discussed, otherwise the title of the paper is inconsistent with what it delivers. There are many things like these that need to be better explained (outlined below). Moreover, another concern is that there are two study sites (A and B). In site A, both different measurements overlap in space, so they are comparable. In site B, the different measurements do not overlap in space, so it’s concerning to what extent they can be compared. This needs to at least be explained/discussed further in the manuscript. I hope my comments can be useful and that the authors can improve the manuscript by adding some clarifications.

Major comments:

L124, L246:  What is the explanation behind adding Year as an explanatory variable? I understand using Month and Season, as a given month or season could be consistently wetter than a different month or season. But it’s not clear to me how a different year could be important to predict soil moisture. This could be relevant in a climate change study, when you have more than 50 years of data for analysis, for instance. Here, you only have a few years of data, which are not representative of extremes, so I am not sure I understand what is the reasoning in incorporating it as an explanatory variable. Moreover, it would be interesting to comment on the discussion on the impact that variables Month or Season could have in different climates (e.g., would they be relevant in places where temperature and precipitation are constant throughout the year?)

Figure 1: it looks like in Site1, IMT, SSN measurements and trials overlap spatially. In Site 2, it looks like the IMT measurements were performed in a different location than SSN + trials. This needs to be clearly stated in the methods section. In the results/discussion section, this issue needs to be addressed as well. I would like to see the Kendall’s correlations (e.g., Figure 5 and 6) drawn separately for site 1 and Site 2. Maybe for Site 1, correlations could be better than Site 2, because of the spatial variations in sampling locations. It could be that you decide to focus on the results mainly from Site 1, because the measurements are more consistent there.

In the methods section, it’s not clear to me the timing between different measurements and trials. IMT were collected monthly between Sep 2019 and Oct 2020 (L113). The SSN time coverage is not clear. The trials were conducted on Mar 2021 and Oct 2020 (L189 and L190). But then, in the results section, in Figure 3, it looks like trials were conducted in Mar 2021 and maybe Oct 2022? Please state in the Methods section clearly the time coverage between each measurement and trial. Isn’t it relevant that with SSN you have measurements during/after the trials, whereas for IMT, you only have measurements before the trials? This should be mentioned and the impacts of this different coverage in time should be discussed.

Section 3.1: discuss for instance whether IMT and SSN are recording the same variable or not. According to the methods section, IMT measures soil moisture at 6cm, whereas SSN at 10cm. Is this a big difference or not?

L159: How accurate is the ERA5-Land soil moisture retrieval? The resolution is 9 km x 9 km! So your site is mainly only covered by only one pixel. I think this mismatch in spatial resolution should be mentioned in the discussion when analyzing the results.

L161: Moreover, you stated that the ERA-5 is based on ground-based observations as well. I assume that the data is more accurate for regions where there are ground-based observations, and less accurate for regions where there are not. Was ground-based soil moisture data near your study sites used to “calibrate”/inform the ERA-5 product?

Figure 3: are these time series from Site 1, Site 2, or both? Please make this clear.

Figure 3: based on the Kendall’s coefficients, it looks like correlations in green/layer2/deeper soil are higher than correlations in blue/layer1/top soil. I think it’s important to mention that in the results section. And to discuss it in the discussion session.

3.2. Soil moisture models: for SSN, the most important variable was DTW25 and for IMT, the most important variable was SWC_ERA. Can you explain why these variables turned out to be the most important ones? Was this what you expected? Are there physical reasons for that? You could maybe discuss this more in the Discussion section.

L280-281: I think it’s important to mention in the text that none of the models were significant for Trial 2. In the end, you made the decision of which model to use based on Trial 1. It’s important to discuss more in the Discussion about these differences in Trial 1 and Trial 2.

Figure 7: I am not sure it is fair to use a model to predict soil moisture in trial 1 and trial 2, if you just used the data from trial 1 to train the model. Please discuss this.

The analysis of Figure 7 in general is a bit too shallow. Please discuss more the results of the model. Are predicted soil moisture and rut depth consistent? What is the correlation between these two variables?*** Are the results of the model what you expected? Is the spatialization really relevant here (i.e., are there heterogeneities that the spatial model was able to represent?). And I ask this particularly because I didn’t understand Figure 1: for site B, the measurements of IMT and SSN do not overlap. How did you compare them? If you compared them regardless of the spatial variability, maybe spatial variability is actually not that relevant here.

***One way to check the correlation between two variables that have different units is to use the Spearman rank correlation. It takes into account the ranking between the different variables, not their absolute values.

Can you use the results of the model to actually predict rut depth? If not, please at least discuss this and why not. Otherwise, I think the title of the paper needs to be updated, because in the end rut depth was not predicted as stated in the title.

L315-320: you discuss the relation between rutting and DTW reported by other studies. But, in your study, what were the outcomes in terms of rutting depth and relation with DTW? This is not clear.

There seems to be important differences between Trial 1 and Trial 2, and they have different conditions (wet/dry). Would precipitation data be useful as a proxy for rut depth as well? If yes, comment about this in the discussion. If not, just ignore this comment.

In section 4.1. Importance of predictive systems, you mention the importance of “predictive systems”, and, by that, I understand that one could use the methodology described in the paper to predict rut depth in the future. And one of the highlights of the methodology here is that it incorporates the temporal variability, by using the ERA-5 product. However, ERA-5 data could not be used to predict rutting depth in the future, given that the ERA-5 data is for the present, it is not a forecast for the future. And this brings back the question as to whether precipitation could be an important proxy, because, for precipitation, there are forecasts available.

Minor comments:

L15-16: “(…) to model the response variable, in-situ soil water content” -> “(…) to model the soil water content” – I see no need for the “response variable”, as it is a very vague term.

L20: “(…) as well as temporal components such as numeric variables derived from date and (…)” – “numeric variables” is too vague.

L34: I find it a bit strange to put a reference in a middle of a statement. “Soil compaction as a consequence of harvesting operations (Eliasson, 2005; etc) is detrimental to a (…)”. What is the statement that these citations refer to?

Section 2.1.3. Soil maps: what is the information on these soil maps? Is it soil texture? Please state it.

L60: Agren et al. (2021), used -> without the comma

L91: when you mention the predictor variables here, it would be nice to have an idea of which variables are these. For instance, add in parenthesis (e.g., topographic indexes, soil texture)

I think it would make the paper much clearer if you added a sub-section in the beginning of Material and Methods called “Study design” or “Study overview”. In this section, you could present Figure 2, and you write in a little bit more detail what is written as the caption of Figure 2. I think having an overview of the study design before reading the technicalities of the methods section would be very helpful.

L110-111 and L117-118: both are “known to be temporally wet or sensitive machine traffic” – it’s repetitive. Add this sentence only one time referring to both sites.

L143: what SPI stands for?

L148: how is “Basin” a variable? Is it the basin area?

L154: how were you “able to gather maps” ? What is the source for these maps?

L149-L150: I couldn’t find any justification for re-sampling to 15m x 15m based on Agren et al. (2014). Please explain where this number comes from. Also, in general, please add clarification on how datasets with different spatial resolutions were merged.

I think the methods section is too long. Some steps are described as a “recipe” instead of a scientific paper. For instance:

L130: “ (…) inserted into the attributed of a shapefile”, L169: “(…) merged with in-situ data” – these small technical steps of merging/formatting two datasets don’t need to be detailed.

I would avoid using full sentences to describe the names of variables. For instance, in L138-139, “(…) of the following sizes: 0.25 ha (DTW025), 1.00ha (DTW1), 4.00 ha (DTW4)”. In L 153-155: “(…) scale of 1:5,000 from forest site surveys (Soil05).” In L156-157, “(…) scale of 1:50,000 are available for the entirety of North Rhine-Westphalia (Soil50)”

L159-162: I would rephrase it as: “ERA-5 Land is a global (…) , including soil moisture [m³ m^-3] at the top soil layer (0-7cm) and at a depth of 7-28 cm. The soil moisture at the top soil layer is retrieved by assimilating satellite and ground-based observations”. The names of the variables Volumetric soil water layer 1 and 2 are not relevant. I don’t think you use them further in the manuscript. If you do, then you can add their names in parenthesis, but if not, I see no reason why they should be mentioned.

In Figure 2, in the second row (predictors), there are some gray lines in the back, which seem to be connecting “soil maps” and the ERA graph to “add data”. However, I assume “topogr. indices” and “Month Season” are supposed to be included as well?

Figure 3: a legend on the side with the colors and the names of the variables would be helpful.

Figure 3: no need to say “the figure displays”

Figure 3: the names ‘layer 1’ and ‘layer 2’ are not really relevant here. I think it would be more relevant to provide what these layers refer to: layer 1 (top soil) and layer 2 (7-28cm depth).

L232-233: “Soil water content was measured (…) August 2020” – I consider this fits in Methods, not Results.

2.2 Rut depth data: make it clear here what is different between Trials 1 and 2. Trial 1 is in a wet condition and Trial 2 is in a dry environment, right? That’s why it is expected that SWC1 > SWC2. This makes the interpretation of Figure 6 afterwards easier.

Figure 6: what does the black lines and the black values refer to? Make it clear in the caption.

L346: but in site 2, the locations of IMT and SSN are different.

L272: “SWC_PRED proved to be a better predictor of rut depth”, particularly for Trial 1 (in wetter conditions).

L317: ground water -> groundwater

L316-318: 65% + 93% is more than 100%. I don’t think I understand this sentence. Please reformulate it.

L316-318: proximity to groundwater and DTW are two different things, no?

Discussion: section 4.1. Importance of predictive systems: I think I would move this in the very end of the discussion.