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. 

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Physics-informed machine learning for understanding rock moisture dynamics in a sandstone cave

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Physics-informed machine learning for understanding rock moisture dynamics in a sandstone cave