the Creative Commons Attribution 4.0 License.
the Creative Commons Attribution 4.0 License.
Physics-informed machine learning for understanding rock moisture dynamics in a sandstone cave
Kai-Gao Ouyang
Gang Mei
Hong-Bin Yan
Ran Niu
Li Wan
Yijian Zeng
Abstract. Rock moisture, which is considered as a hidden component of the terrestrial hydrological cycle, has received little attention. In this study, the frequency-domain reflectometry (FDR) is used to obtain fluctuating rock water content in a sandstone cave of the Yungang Grottoes, China. We identified two major cycles of rock moisture addition and depletion, one in the summer and the other in the winter. By using the LSTM (Long Short-Term Memory) network and the SHAP (SHapley Additive exPlanations) method, relative humidity, air temperature and wall temperature are found to have contributions to rock moisture in the summer. By using vapor concentration and the difference between dew point temperature and wall temperature as two input variables of the LSTM network, the predicted rock water content has a very good agreement with the measured rock water content, with the Nash–Sutcliffe efficiency coefficient (NSE) being as high as 0.978. Because the two new input variables are factors directly controlling vapor condensation, they provide informative priors to the deep learning model and improved prediction performance. After identifying the causal factors of rock water content fluctuations, we also identified the mechanism controlling the multi diurnal vapor condensation. The increased vapor concentration accompanying a precipitation event leads to transport of water vapor into rock pores, which is subsequently adsorbed onto the surface of rock pores and then condensed into liquid water. With the aid of the deep learning model, this study increases understanding of sources of water in caves, which would contribute to future strategies of alleviating weathering in caves.
Kai-Gao Ouyang et al.
Status: final response (author comments only)
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RC1: 'Comment on hess-2022-403', Anonymous Referee #1, 19 Dec 2022
This paper investigates the dynamics of rock moisture in a cultural heritage site in China. Based on an analysis of soil moisture sensor measurements, the main outcome of the study is that wetting of the rocks during the summer period is mainly caused by water absorption from the water vapor in the atmosphere. Also a wetting and drying cycle is observed during winter due to freezing and thawing. The interpretation of the results is based on sensitivity analyses of a trained LSTM and an LSTM trained on a set of available direct measurements is compared with an LSTM that is trained on variables that are derived from measurements and that are more directly related to condensation processes such as the wall temperature and dew point temperature. The latter LSTM is called a physics-informed LSTM. The LSTMs are trained on a dataset of one year and are then used to predict the other year.
The obtained insights are interesting and could also be of relevance for the management, protection of the heritage site. I would propose that the authors also give some ideas on how these insights could be used for these purposes.
There are a few general questions that need to be addressed.
1) the paper is based on a 2-years time series of rock moisture measurements by only one single sensor. What is the value of such a single sensor time series? Can the results be transferred to other locations? I can imagine that one does not want to disturb such heritage sites with a lot of sensors but wouldn’t it be possible to find a few locations where sensor measurements would not cause a disturbance? Or would you expect a big difference when you place the sensors in a sand layer that you put in thermal contact with the wall so that the wall temperature of the sand is similar to that of the rock? Is a 2-years period sufficiently long? I think these are questions that need to be addressed and discussed in the paper.
2) the description of the LSTMs is not clear and the reason for also presenting the RNN is not clear since it is not used in the paper.
3) the physics-informed LSTM performed a bit better than the other LSTM but the improvements are not very impressive. Could you find examples where you would expect a much larger improvement? Even though the match between the measurement and LSTM is impressive, they remain a black box and it is not so clear to me why the LSTMs are needed in this paper. What is their role? Doing a sensitivity analyses, you found that precipitation did not explain the rock moisture dynamics and comparing model fits of physics-informed LSTMs with non-informed LSTMs you found that absorption of vapor is the main process. But, can’t this be inferred as well from time series analyses, e.g. covariance, wavelet, analyses? If the purpose is to obtain an understanding of the processes, what are the advantages of using LSTMs in comparison with other more classical methods? Could the parameters or weights that are obtained by training the LSTM be interpreted and used to explain the behavior of the system?
4) I was confused about the winter period. Was it also used to train the LSTM? There is a discussion on the sensor measurements during the winter period but I could not find a discussion on the performance of the LSTMs for this period.
Abstract:
There were a few points unclear in the abstract.
1) summer and winter cycles of moisture addition and depletion are mentioned but no information is given about the underlying processes leading to these cycles
2) LSTMs are used to predict soil moisture. But, it is not clear whether different LSTM’s are used for summer and winter and whether different input variables are used for the two different seasons.
3) vapor concentration and the difference in dew point temperature and wall temperature are informative input variables to predict rock moisture. It is mentioned that they improved the prediction performance but it is unclear compared to what the predictions were improved.
4) what are ‘multi-diurnal fluctuations’?
5) Causal factors of rock moisture fluctuations were identified. But, it is not clear which fluctuations the authors are referring to. Fluctuations in a season or diurnal fluctuations? Can causal factors explaining the moisture fluctuation in a season be used to explain the diurnal fluctuations?
Introduction: I was confused by the word use ‘cave’. It can be either an underground camber or it can be a cavity in a face of a cliff. Looking at the pictures later, it seems that the latter definition is the one applicable here. This difference is important to understand where air temperature, humidity are measured or defined. Furthermore, are air humidity and temperature measured in these caves or in the free atmosphere at some distance from the caves? I suppose that there will also be an exchange of moisture and sensible heat between the free air and the wall of the cliff and that the humidity temperature in the cavities will be different from that in the free atmosphere. I think you need to elaborate on this and explain better where air humidity, atmospheric conditions, etc. are measured and how those measurements are influenced or influence the rock moisture.
Ln 57: You want to investigate the relation between atmospheric conditions and the rock moisture content in caves. But where are the atmospheric conditions measured? In the caves or above the soil surface in the free atmosphere?
Ln 70-75: Make clear here whether you are referring to air temperature and humidity in the caves.
Study site and methods:
I think that a conceptual figure that shows the ‘different forms of water’ and the different ‘sources of these forms’ would be helpful.
Figure 3 and Figure 4 should be made conform with each other. An output layer is missing in figure 4. The notation in the text should match with the notation used in figures 3 and 4. The equations in the text were mixed up.
Ln 155: Dimensions of the weight matrices should be given.
Ln 185: equations for mean absolute error and root mean square error are not correct.
Results:
Rock moisture increases with increasing vapor concentration, also when wall temperature is higher than the dew point temperature. Is that caused by the fact that the water potential in the rock is much lower than the water potential of free water? The dew point gives the temperatures at which vapor starts condensing on a flat surface. But, wouldn’t vapor also condense in a dry porous medium when the temperature is above the dew point temperature but the vapor concentration is above the equilibrium vapor concentration in the free air space that is in contact with the water in the porous medium? This equilibrium vapor concentration would be calculated from the water potential in the porous medium using the Kelvin equation.
Citation: https://doi.org/10.5194/hess-2022-403-RC1 - AC1: 'Reply on RC1', Xiao-Wei Jiang, 17 Feb 2023
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RC2: 'Comment on hess-2022-403', Oliver Sass, 06 Mar 2023
This is an excellent paper on rock moisture in sandstone caves of a cultural heritage site. The authors point out that rock moisture is a hidden component of the terrestrial hydrologic cycle" and I fully agree. The authors use a FDR moisture sensor for measuring rock water content (RWC) over approx. 2 years and meteorological measurements to explain the observed RWC fluctuations. They use a machine learning algorithm to assess the explanatory potential of each meteorological factor and find that air humidity and dewpoint temperature explain a large part of the observed fluctuations. RWC is extremely well predicted from input variables (e.g. Fig. 6). This is a very interesting an unique result. I recommend acceptance after very minor revision.
(I must note that I'm a specialist on rock moisture but I don't have the expertise to assess the quality of the machine learning approach.)Specific comments:
L104-106: I can confirm from my own work that on-site calibration of RWC measurements is difficult and that the relationship is linear in approximation.
L222-224: "The decreasing low liquid water content induced by freezing indicates that rock moisture in spring and autumn belongs to movable bound
water that could be responsible for chemical weathering." I cannot follow this reasoning. Consider to leave this out, or explain better why you think this.L231, L253, L261: I'm not sure if precipitation can in fact be discarded as an input factor of RWC. There cannot be a direct correlation between P and RWC as the up and down of single precipitation events does not reach the rock surfaces in the caves. If the water seeped through the rock, it would reach the surfaces (a) with a considerable time lag, (b) in a greatly smoothed temporal course. Have you tried to feed in e.g. a running average of precipitation with a temporal shift of several days (or weeks) into your model?
Editorial comments:
L121: Write tan together (without spaces, otherwise it looks like four different variables). I my pdf, several other formula seem to be slightly disturbed.
L206-208: A lot of repetitive words in this section: Simplify to: "... indicating that this slight change is a result of the fluctuating rock water content. Therefore, we believe that the FDR readings reflect the actual change of water content in the rock."
L210-211: Simplify to: "This pattern of fluctuation is a direct consequence of freezing-thawing, ..."
L250-252: Put numbers in brackets behind the parameters: "The mean absolute SHAP values are in descending order: air relative humidity (0.0087), air temperature (0.0032)..." and so on
Entire Paper: The term rock water content is quite frequent; consider to use the abbreviation RWC.
Citation: https://doi.org/10.5194/hess-2022-403-RC2 -
AC2: 'Reply on RC2', Xiao-Wei Jiang, 07 Mar 2023
Response to Reviewer #2
This is an excellent paper on rock moisture in sandstone caves of a cultural heritage site. The authors point out that rock moisture is a hidden component of the terrestrial hydrologic cycle" and I fully agree. The authors use a FDR moisture sensor for measuring rock water content (RWC) over approx. 2 years and meteorological measurements to explain the observed RWC fluctuations. They use a machine learning algorithm to assess the explanatory potential of each meteorological factor and find that air humidity and dewpoint temperature explain a large part of the observed fluctuations. RWC is extremely well predicted from input variables (e.g. Fig. 6). This is a very interesting and unique result. I recommend acceptance after very minor revision.
(I must note that I'm a specialist on rock moisture but I don't have the expertise to assess the quality of the machine learning approach.)
Response: Thanks for your positive assessment on our study.
Specific comments:
L104-106: I can confirm from my own work that on-site calibration of RWC measurements is difficult and that the relationship is linear in approximation.
Response: It is true that on-site calibration of RWC measurements is difficult and we just use the apparent RWC in the current study.
L222-224: "The decreasing low liquid water content induced by freezing indicates that rock moisture in spring and autumn belongs to movable bound water that could be responsible for chemical weathering." I cannot follow this reasoning. Consider to leave this out, or explain better why you think this.
Response: Thanks for pointing out the problem. We will fix it in the revision.
L231, L253, L261: I'm not sure if precipitation can in fact be discarded as an input factor of RWC. There cannot be a direct correlation between P and RWC as the up and down of single precipitation events does not reach the rock surfaces in the caves. If the water seeped through the rock, it would reach the surfaces (a) with a considerable time lag, (b) in a greatly smoothed temporal course. Have you tried to feed in e.g. a running average of precipitation with a temporal shift of several days (or weeks) into your model?
Response: If infiltrating precipitation can reach the caves, the lagged response of rock moisture to precipitation can be identified by the LSTM model. In fact, there is no fractures in our monitoring site and we believe that infiltrating precipitation can reach the site. We tried to use the SHAP model to confirm that the rock moisture has no correlation with precipitation infiltration, but is controlled mainly by air humidity.
Editorial comments:
L121: Write tan together (without spaces, otherwise it looks like four different variables). I my pdf, several other formula seem to be slightly disturbed.
Response: Sorry for the incorrect forms of the formula due to transformation of a docx file into a pdf file. We will fix this problem in the revision.
L206-208: A lot of repetitive words in this section: Simplify to: "... indicating that this slight change is a result of the fluctuating rock water content. Therefore, we believe that the FDR readings reflect the actual change of water content in the rock."
Response: Thanks for your suggestion. We will fix it in the revision.
L210-211: Simplify to: "This pattern of fluctuation is a direct consequence of freezing-thawing, ..."
Response: Thanks for your suggestion. We will fix it in the revision.
L250-252: Put numbers in brackets behind the parameters: "The mean absolute SHAP values are in descending order: air relative humidity (0.0087), air temperature (0.0032)..." and so on
Response: Thanks for your suggestion. We will fix it in the revision.
Entire Paper: The term rock water content is quite frequent; consider to use the abbreviation RWC.
Response: Thanks for your suggestion. We will use this abbreviation in the revision.
Citation: https://doi.org/10.5194/hess-2022-403-AC2
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AC2: 'Reply on RC2', Xiao-Wei Jiang, 07 Mar 2023
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RC3: 'Comment on hess-2022-403', Anonymous Referee #3, 09 Mar 2023
This paper investigates the dynamics of rock moisture in a sandstone cave and describes the relationship between rock moisture, surface and air temperature, and relative humidity and precipitation. The main and innovative methodology used by the authors is an FDR soil moisture probe to derive the dynamics of rock moisture. For the analysis of the influencing variables, the authors use 4 months of hourly data from one year as training data for an LSTM model to predict the hourly water content in the rock during 4 months in the second year. The most important results are that the water content in the rock is subject to seasonal fluctuations. It increases in seasons with high humidity and high temperatures. Using the SHAP values shows that precipitation is not used as a predictor variable by the LSTM. However, the LSTM has high prediction scores (NSE) based on measurements of humidity and temperature variables, which is consistent with theoretical principles.
(I am not a specialist in rock moisture dynamics or LSTM but understand a bit about modeling and ML techniques and am confident about my knowledge in field soil moisture measurements and soil vapor adsorption.)
In my opinion, the topic is very interesting and I agree with the authors that it is necessary to make progress in this field and to explore new measurement methods. Also, their results make a lot of sense from a theoretical point of view. Unfortunately, however, I have doubts about the methodology and data analysis which need to be addressed first before minor points could be discussed.
I suggest major revision for the following reasons:
- TDR soil moisture probes have apparently been used already by other authors in this field to measure rock moisture dynamics (l. 48f, l.100f) but the authors state they "attempt to use the FDR for monitoring rock moisture in the field for the first time" (l. 56). Since this methodology is used in a new application setting, I strongly recommend giving more details about the sensor installation procedure. (l.97 ff). For me, it is not clear if the sensor is placed into holes drilled into the wall to be in close proximity/enclosed by the wall. This should be additionally added as a picture in Figure 2. I consider this an essential piece of information since it is known in the soil science community that contact between the sensor and (soil) parent material is crucial to obtain valid records of the (soil) moisture level.
- Additionally, I feel more information is needed on the sensor's measurement sensitivity as well as the temperature sensitivity of the sensor. Although it is stated that FDR is “less influenced by temperature” (l. 55f) compared to TDR I suggest adding more information about the temperature effect. Ideally, a sensor calibration to temperature would be cited or performed under controlled conditions to exclude the possibility that Temperature has a dominant influence on the FDR reading, particularly because it varies only between 0.010 and 0.030 (1-3% volumetric moisture).
- The application of LSTM (as a Machine learning technique) is currently a hot topic and widespread in the scientific community but I am not sure if the use of this method is really necessary for the data analysis in this study. The results obtained from the LSTM have NSE scores as high as 0.958 and 0.97. From what I have been taught, such high scores usually need to be investigated very cautiously. Therefore I wanted to clarify again that the LSTM was trained on a different period than the one shown in Figure 6? Please also provide information on the scores for the training data.
- Another possibility for achieving in such high NSE would be, that the predictor variables are very highly correlated with the dependent variable (rock moisture), so the model has a very "easy task". I quickly reviewed the data from the .pdf document provided by the authors on Zenodo (only 226 observations because I copied them out of the .pdf format) and it looks like all variables are highly correlated and correlations are all significant. These results would question i) the need to use such a sophisticated method (LSTM) and ii) more generally, the validity of the FDR sensor data as used in this study (because of a possible temperature effect that is superimposed on the rock moisture measurement). I suggest to at least include additionally to the LSTM statistically more simple (and easier to interpret) scores of the relationship between all predictor variables and the rock water content.
Therefore, before continuing the review process I strongly recommend to I) clarify the installation procedure of the FDR probe, ii) clarify the sensitivity of the instrument to temperature, and if the sensitivity is constant in time and iii) check for their whole data set, how strongly the variables are correlated to figure out if the use of LSTM is even necessary, or if the effect of the variables on the FDR reading is direct.
Citation: https://doi.org/10.5194/hess-2022-403-RC3 -
AC3: 'Reply on RC3', Xiao-Wei Jiang, 10 Mar 2023
The comment was uploaded in the form of a supplement: https://hess.copernicus.org/preprints/hess-2022-403/hess-2022-403-AC3-supplement.pdf
Kai-Gao Ouyang et al.
Data sets
Data of rock water content and atmospheric conditions Kai-Gao Ouyang, Xiao-Wei Jiang, Gang Mei, Hong-Bin Yan, Ran Niu, Li Wan, Yijian Zeng https://doi.org/10.5281/zenodo.7382895
Kai-Gao Ouyang et al.
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