the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Throughfall spatial patterns translate into spatial patterns of soil moisture dynamics – empirical evidence
Christine FischerBedtke
Johanna Clara Metzger
Gökben Demir
Thomas Wutzler
Download
 Final revised paper (published on 02 Aug 2023)
 Supplement to the final revised paper
 Preprint (discussion started on 06 Jan 2023)
 Supplement to the preprint
Interactive discussion
Status: closed

CC1: 'Comment on hess2022418', ZhiShan Zhang, 20 Jan 2023
The authors collected an extensive dataset, i.e., throughfall and soil water contents on a 1‐ha temperate mixed beech forest plot in Germany 2015  2016 during the growing seasons in independent high‐resolution stratified random designs, to investigate the effect of throughfall spatial heterogeneity on the soil water response and check which other factors modify the result. The method is reliable, the result is interested, the conclusion is significant after thoroughly discussion, such as throughfall spatial patterns leave a stronger imprint on soil water dynamics than on soil water content per se. I recommend the manuscript can be published by the international journal after minor revision.
Throughfall, also called net rainfall, is a part of gross rainfall after vegetation modification. Simply, it sources from gross rainfall. However, in your linear mixed effect models to evaluate the influence of potential drivers explaining soil water content or soil water content increase, gross rainfall was removed due to strong correlation with mean throughfall. I think you neglect the most important factor of soil water content. Please the authors consider it with alternative method. Such as in your equation 1, you used median of throughfall to calculate the normalized value of the spatially distributed measurements of throughfall. I recommend you can use gross rainfall instead of median of throughfall to calculate it, you can refer to Zhang et al. (2016) and Zhao et al. (2019).
I think the manuscript is long, some contents can be deleted or moved to supplementary, such as L268274, only retain direct relevant contents. Also, the Abstract is long, need to be condensed.
Soil water content or soil moisture has a unified call in the full text. Also, the unit of soil water content should be used m3 m3 instead of %.
Many long sentences, such as L8587, L97100. The language needs to be polished.
Zhang et al. (2016) Gross rainfall amount and maximum rainfall intensity in 60minute influence on interception loss of shrubs: a 10year observation in the Tengger Desert. Scientific Reports, srep26030.
Zhao et al. (2019) Rain shadow effects of individual shrub related to crown shape in arid desert. Ecohydrology, e2076.
Citation: https://doi.org/10.5194/hess2022418CC1 
AC3: 'Reply on CC1', Anke Hildebrandt, 20 Mar 2023
Thank you for the carefull reading of the manuscript, feedback and recommendations for improvement. Below, we only respond to the recommendations suggesting changes in the article, to propose how we are going to address them.
Throughfall, also called net rainfall, is a part of gross rainfall after vegetation modification. Simply, it sources from gross rainfall. However, in your linear mixed effect models to evaluate the influence of potential drivers explaining soil water content or soil water content increase, gross rainfall was removed due to strong correlation with mean throughfall. I think you neglect the most important factor of soil water content. Please the authors consider it with alternative method. Such as in your equation 1, you used median of throughfall to calculate the normalized value of the spatially distributed measurements of throughfall. I recommend you can use gross rainfall instead of median of throughfall to calculate it, you can refer to Zhang et al. (2016) and Zhao et al. (2019).
Yes, we omitted rainfall from the analysis and only work with throughfall, which is the dominant part of the netprecipitation. We also agree that from a statistical perspective it would be possible to work with gross precipitation instead of the spatial median throughfall in the mixed effects model. However, after consideration, we believe the physically more consistent way forward is to stick with the spatial median throughfall itself. This way the same variable is partitioned to yield information about the temporal (median TF) and spatial variation (δP_TF). Also, the dependence of throughfall on rainfall is already very well established through previous research, while here we focus on the heritage of its spatial pattern.
I think the manuscript is long, some contents can be deleted or moved to supplementary, such as L268274, only retain direct relevant contents. Also, the Abstract is long, need to be condensed.
Many long sentences, such as L8587, L97100. The language needs to be polished.
Thank you. We will shorten the abstract and also revise section of the main text.
Soil water content or soil moisture has a unified call in the full text. Also, the unit of soil water content should be used m3 m3 instead of %.
Yes, we sometimes use the term soil moisture when we are referring more general to water in soil, not to the measurement. This was originally meant to improve the readability of the text. We will check for consistency once more. We also use Vol% as unit for soil water content in the Tables, and will make sure it is used consistently thoughout.
References
Van Stan, II, J. T., Gutmann, E., and Friesen, J. (Eds.): Precipitation Partitioning by Vegetation: A Global Synthesis, Springer International Publishing, Cham, https://doi.org/10.1007/9783030297022, 2020.Citation: https://doi.org/10.5194/hess2022418AC3

AC3: 'Reply on CC1', Anke Hildebrandt, 20 Mar 2023

RC1: 'Comment on hess2022418', Anonymous Referee #1, 22 Feb 2023
This manuscript is an ambitious attempt to link spatial variability of throughfall with soil moisture, using an extremely detailed dataset and innovative throughfall interpolation technique. The results are explained well.
The statistical treatment is relatively heavy, in that there are multiple normalizations, rank transformations, and perevent terms. Interpreting results is difficult as a result. Some additional discussion on this point would be helpful, as would more precision in the presentation of results. In general, the statistical treatment makes it impossible to determine how much difference throughfall variation makes for soil moisture. Detransforming after analysis or repeating the analysis with raw variables and generalized linear models that do not require preanalysis transformations are two options that would make the results more useful.
With a few mild assumptions, this manuscript appears to have enough data to do a full water balance of the soil, including deep percolation during events and transpiration between events. Those are probably for the future, but maybe they can be added easily here for a richer description of the importance of spatial variability of throughfall.
Detailed comments:
L98 I suggest adopting “macroporosity” as it is here, instead of “air capacity” as most other places—that term is much less used.
L207 for how many events were there trends, and were those trends interpretable?
L218 citation should be Zimmerman et al. (2009). I found this sentence confusing and in need of explanation. I think it should say “we chose the estimator that gave median theta of 0.455” to match the box in Fig S1. If I understand this correctly, I think it means that you assumed the data were normally distributed and chose the estimator to match that, and that you feel confident in doing so because octile skew was never outside of [2…2]. The manuscript would be better if that logic (or the correct logic) is described here. I also wonder what it means for the best estimator to vary. Is there something to infer about spatial structure of throughfall in each event?
L225 how many outliers were removed, which events were they in, and is it interpretable as to why they are outliers? The answers to these questions would help readers understand the consequences of the removals.
L233 how exactly did you check? By whether theta was about 0.455?
L235 L444 why not use cokriging, given the finding of correlation with local canopy density and distance to tree?
L241 please resolve the conflict between this assertion of skew and previous assertion of no skew, necessary for adoption of gaussian assumptions in variogram model fitting.
L251 and elsewhere: naming deltaP, TF, and theta variables as “spatial pattern” is confusing because spatial pattern is a property of all locations, not of a single location. An example of how this term is problematic is L323: patterns cannot be correlated with each other, and there is really only one pattern for each time.
L263 normalizing predictor variables is a very important decision that affects model selection and interpretation. Unfortunately, it is difficult to interpret here because “normalize” does not have a consistent meaning and the exact transformation is not specified (Fig 5 axis labels suggest z transform). Was the transformation parametric, and, if so, how well is that choice justified given the rank transformation used on many other variables, including most response variables? Why were all transformations necessary? Axis labels fig 5 and 6 suggest the response variables were also transformed, but that is not mentioned in the methods. Finally, the results and discussion should acknowledge the transformed nature of the analyses when making interpretations.
Tables 2, 3, and S5: except for the sign, it is redundant to present both t and p. It would be better to see effect size to help judge importance of these relationships, not just consistency of them. I do not understand what is literally meant by “variables are scaled such that the tvalue indicates the effect strength” (Table 3 caption), because I do not know what “strength” means in this context. I think this sentence confuses consistency of the
Tables: what is the meaning of italics and bold?
Fig 2 grouping by storm size is not necessary; please consider whether a scatterplot—with storm size as the independent variable—would give richer information.
L315 n=11 or n=3 as fig 4?
L345 Table S6 is missing
Fig 56 are the z scale transformations simply for these figures or are all statistical analyses also z scaled for the independent and dependent variables?
L420 it would be good to show at least some data vs. kriged surfaces; readers have no way to know how to judge this now except this sentence in the discussion. L422 the previous sentence says the real variation was not maintained.
L426 the technique to estimate the variogram is irrelevant; the question is whether the assumptions of Kriging are useful in this application. Neither Voss nor Lark established that it is, so I do not agree with citing them here. Just because the data can be modeled by variograms does not mean Kriging assumptions hold, and there are good reasons to believe that throughfall does not vary smoothly in space. As the first attempt to use Kriging quantitatively for interpolation, the burden is on the current manuscript to establish the applicability of the technique. A more detailed discussion of the Kriging in light of what the literature says about spatial variability would be an important addition. For example, one issue that is not addressed here is the role of sampler size in spatial variability estimates and interpolation.
Technical corrections:
L108 surely the small mountain does not move
L124 minimize
L127 points
L127 the immediate vicinity
L164 depths
L166 location
L206 smaller than
L214 served
The Supplement table numberings are confusing: e.g., “Table S1 / S4.”
Fig S3 the axis is mislabeled and should be “CQV”
L275 is a redundant Table caption and can be deleted. Same for L275, L283284, L296297, L338, L350, L359, L366.
L332 “event sizes”; L333 “posthoc test of a oneway ANOVA” isn’t literally correct.
L359, L378 it would be clearer to say added, not stored
L379 I don’t think “factors…were related to” is what was intended
L442 I don’t understand “next to”
L484 “weak”
Citation: https://doi.org/10.5194/hess2022418RC1 
AC1: 'Reply on RC1', Anke Hildebrandt, 20 Mar 2023
We thank the reviewer for the very insightful feedback on the manuscript. Here we respond to the more critical feedback, suggestions for changes of analysis, figures and tables to state how we will address it in the revision. We will give a comprehensive pointbypointresponse with the revision.
The statistical treatment is relatively heavy, in that there are multiple normalizations, rank transformations, and perevent terms. Interpreting results is difficult as a result. Some additional discussion on this point would be helpful, as would more precision in the presentation of results. In general, the statistical treatment makes it impossible to determine how much difference throughfall variation makes for soil moisture. Detransforming after analysis or repeating the analysis with raw variables and generalized linear models that do not require preanalysis transformations are two options that would make the results more useful.
We agree. The statistical treatment renders it difficult to follow and we will improve the communication in the next version. Regarding the specific concern on data transformation. The mixed effects models, used to test how spatial fields of throughfall affected soil moisture response, did not strictly require transformations. Instead, we transformed data for the following reasons:
 We separated mean and spatial deviation from the mean in order to be able to distinguish between, e.g. precipitation event size and the spatial distribution of the throughfall. This allowed us to pool the data across events. The same is true for the soil water content.
 We ztransformed the data in order to be able to compare the effect sizes. The advantage will be seen more in the next version of the manuscript, where we present the effect sizes.
In the new version we will more clearly state how data were transformed and explain why.
With a few mild assumptions, this manuscript appears to have enough data to do a full water balance of the soil, including deep percolation during events and transpiration between events. Those are probably for the future, but maybe they can be added easily here for a richer description of the importance of spatial variability of throughfall.
Yes, there are several manuscripts in preparation dealing with the overall water balance of the forest plot, which turned out to be more complex than we expected. Therefore, the focus is really on different challenges. For example, determining transpiration from the soil water balance is not trivial in general (Hupet et al., 2003, Jackisch et al., 2020). In our case, we also observed species interacting belowground. We sincerely think that separating those narratives helps focusing the message, and we therefore prefer to focus on the effect of throughfall on soil water response.
How many precipitation events were there trends, and were those trends interpretable?
Somewhat less than half of the events had spatial trends (Table S2). We found those trends difficult to interpret. They changed direction with time, were of varying strength and occurred in small as well as in large events. Canopy cover had no spatial trend (Table S2). Spatial trends may have been related to the interaction of slope aspect and wind direction. We will add the reference to the Table in the supplement.
Why not use cokriging, given the finding of correlation with local canopy density and distance to tree?
The kriging was performed for throughfall. This was done, because throughfall and soil moisture cannot be assessed at the same location. There was no relation between throughfall and distance to the next tree (Table S5). The latter was only the case for soil water content. There was a relation between canopy cover and throughfall. Thus, it is true that cokriging with canopy cover would theoretically be possible. However, unfortunately, the canopy cover was only assessed at the throughfall locations, and not at the soil sensor locations. We therefore cannot apply cokriging to support kriging to sensor locations.
L263 normalizing predictor variables is a very important decision that affects model selection and interpretation. Unfortunately, it is difficult to interpret here because “normalize” does not have a consistent meaning and the exact transformation is not specified (Fig 5 axis labels suggest z transform). Was the transformation parametric, and, if so, how well is that choice justified given the rank transformation used on many other variables, including most response variables? Why were all transformations necessary? Axis labels fig 5 and 6 suggest the response variables were also transformed, but that is not mentioned in the methods. Finally, the results and discussion should acknowledge the transformed nature of the analyses when making interpretations.
Yes, thank you for catching this. We did indeed apply a parametric ztransformation to all variables, including the response variable. We will add this information. As mentioned above, this was done to allow better interpretation of the effect sizes of the mixed effects models. We also agree that this motivation should be better stated.
Note that rank transformation was only done to differentiate between effect of the spatial mean like event size or general soil moisture state, and the spatial pattern, as stated above. We will make an effort to point the reader to this.
Tables 2, 3, and S5: except for the sign, it is redundant to present both t and p. It would be better to see effect size to help judge importance of these relationships, not just consistency of them. I do not understand what is literally meant by “variables are scaled such that the tvalue indicates the effect strength” (Table 3 caption), because I do not know what “strength” means in this context.
This is true and also relates to the main comment stating that the interpretation of the results is difficult and agrees with Reviewer 2. We therefore present results differently in the revision, showing the effect size of each factor for the selected model. Figure R1.1 shows an example. With all variables being ztransformed, the slope estimate indicates the influence of the specific predictor on the response variable.
Figure R2.1: Factors influencing local soil water content response after rainfall (Δθ_{i}, i.e. difference between soil water content after and before each precipitation event). Shown are the slope estimates (dots) and their standard errors (lines) for the best linear mixed effects model including all events. Stars indicate the pvalues (*** p < 0.001; ** p < 0.01; * p < 0.05). Variables are zscaled such that the slope estimate reflects how strongly the predictor affects the soil moisture response.
Abbreviations: TF – throughfall; SWC – soil moistureFig 2 grouping by storm size is not necessary; please consider whether a scatterplot—with storm size as the independent variable—would give richer information.
Yes, good point. We will do this.
L420 it would be good to show at least some data vs. kriged surfaces; readers have no way to know how to judge this now except this sentence in the discussion.
We can add a figure showing kriged surfaces of a small and a large event to the appendix, to show the variation, and also demonstrating how the number of sensor locations decreases when in large compared to small events.
L426 the technique to estimate the variogram is irrelevant; the question is whether the assumptions of Kriging are useful in this application. Neither Voss nor Lark established that it is, so I do not agree with citing them here. Just because the data can be modeled by variograms does not mean Kriging assumptions hold, and there are good reasons to believe that throughfall does not vary smoothly in space. As the first attempt to use Kriging quantitatively for interpolation, the burden is on the current manuscript to establish the applicability of the technique. A more detailed discussion of the Kriging in light of what the literature says about spatial variability would be an important addition. For example, one issue that is not addressed here is the role of sampler size in spatial variability estimates and interpolation.
What we meant to say is that both applied method and the number of sensor locations adhere to the state of the art for derivation of the throughfall variogram that is next used for kriging. We will reformulate. We also can mention here the crosscorrelation which yielded satisfactory results, plus refer to sampler size. We will however try to keep this section compact, partly to accommodate the other reviewer. However, we agree that the uncertainties need to be discussed.
References
Hupet, F., Lambot, S., Feddes, R. A., van Dam, J. C., and Vanclooster, M.: Estimation of root water uptake parameters by inverse modeling with soil water content data, Water Resources Research, 39, 2003.
Jackisch, C., Knoblauch, S., Blume, T., Zehe, E., and Hassler, S. K.: Estimates of tree root water uptake from soil moisture profile dynamics, Biogeosciences, 17, 5787–5808, https://doi.org/10.5194/bg1757872020, 2020.
Citation: https://doi.org/10.5194/hess2022418AC1

AC1: 'Reply on RC1', Anke Hildebrandt, 20 Mar 2023

RC2: 'Comment on hess2022418', Anonymous Referee #2, 06 Mar 2023
The manuscript presents the results of a study of the effects of redistribution of precipitation by throughfall on the soil water content spatial distribution in a temperate forest experimental plot. The study is based on data measured in a robust and intensive sampling scheme together with values interpolated by spatial statistical methods (kriging) . This innovative combination of measurement and statistical inference allows the authors to get simultaneous values of each variables at the same location.
The statistical treatment is scientifically sound and the conclusions drawn are supported by the results obtained. I recommend the publications of the paper after a minor revision that should address the following points.
Detailed comments
The abstract is a little bit long, some of the results are duplicated as those regarding the effect of soil water distribution on soil water dynamic (lines 2933 and lines 3537so the authors can consider to shorten it..
The authors use air capacity (lined 21,188) and macroporosity (line 98) : I would suggest using a unique term to avoid misunderstanding
There exist some confusion on using the terms δPTF ; δθpre and δθpost do they refer to normalized variables; spatial distribution , spatial pattern?
Data on event topsoil seems in figure S3 seem not to follow a clear concave decreasing relationship with mean soil water content as said in line 298299. Indeed, the variation around SWC equal to 20 is positive. I hesitate these results support the statements of lines 298299.. As it is no longer discussed in the paper, it might be deleted. What does it mean “enhance” soil water content variation?
Discussion of GLM model on the soil water response is rather complex. Particularly interpretation of the interactions of fixed effects in lines 376378 and figure 6. A clearer a more detailed explanation (also in the legend of figure 6) would make easier to the reader understand the foundations of the final statement. “Locally drier soil increased soil water storage in wet, but decreased it in dry times”
Section 3.2 is entitled “spatial pattern of throughfall” while it also includes results on soil water content variation.
Technical corrections
Line 53, line 518 and others: what do the authors want to say by using “next to” ?
Line 484: I think it is weak instead of week
Citation: https://doi.org/10.5194/hess2022418RC2 
AC2: 'Reply on RC2', Anke Hildebrandt, 20 Mar 2023
We thank the reviewer for the positive feedback to the manuscript and constructive recommendations. Below we respond to the main concerns to show how we are going to address them in the revision.
The abstract is a little bit long, some of the results are duplicated as those regarding the effect of soil water distribution on soil water dynamic (lines 2933 and lines 3537so the authors can consider to shorten it..
Yes, we agree. We can formulate the results part in a more compact manner.
There exist some confusion on using the terms δPTF ; δθpre and δθpost do they refer to normalized variables; spatial distribution , spatial pattern?
Thank you for pointing this out. Indeed, both reviewers found that the normalization of variables was not easy to follow and we will make an effort to better motivate this in the revision.
Data on event topsoil seems in figure S3 seem not to follow a clear concave decreasing relationship with mean soil water content as said in line 298299. Indeed, the variation around SWC equal to 20 is positive. I hesitate these results support the statements of lines 298299.. As it is no longer discussed in the paper, it might be deleted. What does it mean “enhance” soil water content variation?
It is true that concave is probably not the best way to describe this form. We want to demonstrate how soil water content spatial variation (CQV, on the yaxis, the typo will be corrected in the revision) changes with the spatial median (xaxis). At the same soil water content, post event soil water content has higher spatial variation than the preevent, especially in drier soils. This shows that precipitation events do imprint on the soil water content pattern. But surprisingly at the same time, the soil water contents does not correlate with the input, which suggests that other factors are active. We will reformulate and make sure to connect to this in the discussion.
Discussion of GLM model on the soil water response is rather complex. Particularly interpretation of the interactions of fixed effects in lines 376378 and figure 6. A clearer a more detailed explanation (also in the legend of figure 6) would make easier to the reader understand the foundations of the final statement. “Locally drier soil increased soil water storage in wet, but decreased it in dry times”
Agreed, we admittedly struggled when writing this section. We will work on it once more, trying to make the interpretation more accessible. We will also change the name of the groups in Fig 6a and 6b. Furthermore, in response to this comment and comments by Reviewer 1, we will change the presentation of the mixed effects model results. Instead of giving the results in a Tables 3 and 4, we will visualize the effect sizes as shown in Figure R2.1.
Figure R2.1: Factors influencing local soil water content response after rainfall (Δθ_{i}, i.e. difference between soil water content after and before each precipitation event). Shown are the slope estimates (dots) and their standard errors (lines) for the best linear mixed effects model including all events. Stars indicate the pvalues (*** p < 0.001; ** p < 0.01; * p < 0.05). Variables are zscaled such that the slope estimate reflects how strongly the predictor affects the soil moisture response.
Abbreviations: TF – throughfall; SWC – soil water contentCitation: https://doi.org/10.5194/hess2022418AC2

AC2: 'Reply on RC2', Anke Hildebrandt, 20 Mar 2023