Physics-informed machine learning for understanding rock moisture dynamics in a sandstone cave
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)
RC1: 'Comment on hess-2022-403', Anonymous Referee #1, 19 Dec 2022
- AC1: 'Reply on RC1', Xiao-Wei Jiang, 17 Feb 2023
RC2: 'Comment on hess-2022-403', Oliver Sass, 06 Mar 2023
- AC2: 'Reply on RC2', Xiao-Wei Jiang, 07 Mar 2023
RC3: 'Comment on hess-2022-403', Anonymous Referee #3, 09 Mar 2023
- AC3: 'Reply on RC3', Xiao-Wei Jiang, 10 Mar 2023
Kai-Gao Ouyang et al.
Data of rock water content and atmospheric conditions https://doi.org/10.5281/zenodo.7382895
Kai-Gao Ouyang et al.
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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.
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.
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.