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

Abstract

Abstract. Rock moisture, which is a hidden component of the terrestrial hydrological cycle, has received little attention. In this study, frequency domain reflectometry is used to monitor fluctuating rock water content (RWC) in a sandstone cave of the Yungang Grottoes, China. We identified two major cycles of rock moisture addition and depletion, one in summer affected by air vapour concentration and the other in winter caused by freezing–thawing. For the summer-time RWC, by using the long short-term memory (LSTM) network and the SHapley Additive exPlanations (SHAP) method, we find relative humidity, air temperature and wall temperature have contributions to rock moisture, and there is a good match between predicted and measured RWC using the three variables as model inputs. Moreover, by using summer-time vapour concentration and the difference between dew point temperature and wall temperature as input variables of the LSTM network, which belongs to physics-informed machine learning, the predicted RWC has a better agreement with the measured RWC, with increased Nash–Sutcliffe efficiency (NSE) and decreased mean absolute error (MAE) and root mean square error (RMSE). After identifying the causal factors of RWC fluctuations, we also identified the mechanism controlling the inter-day fluctuations of vapour condensation. The increased vapour concentration accompanying a precipitation event leads to transport of water vapour into rock pores, which is subsequently adsorbed onto the surface of rock pores and then condensed into liquid water. With the aid of the physics-informed deep learning model, this study increases understanding of sources of water in caves, which would contribute to future strategies of alleviating weathering in caves.