Prediction of karst spring discharge using LSTM with Bayesian optimisation hyperparameter tuning: a laboratory physical model approach

Estimating spring discharge in karst aquifers is challenging due to non-linear and non-stationary hydrological processes caused by spatial and temporal variations. This study mimicked the phenomenon by simulating spring discharge using a laboratory physical model. The hydrological processes adopted in the simulation include systems such as infiltration, fissure-conduit, and drainage. We then recorded spring discharge and precipitation values from the simulated model along side the corresponding air temperature and humidity-in order to analyse the time series behaviour of the system. To estimate spring discharge from the simulation, a deep learning algorithm is developed taking temperature, humidity and precipitation as the input. In this work, the Bayesian optimisation was used to sweep through a range of hyperparameter values to search for the top 5 optimal training options for a Long Short Term Memory (LSTM) neural network. In addition, XGBoost was employed to identify the key predictors of spring discharge, resulting in enhanced predictability. The results show that LSTM-1, LSTM-2, LSTM-3, and LSTM-4 are the recommended recurrent neural network designs for predicting spring discharge using all three input parameters. LSTM-1, LSTM-2, and LSTM-3 network architectures are optimal for utilising two input variables: precipitation intensity and temperature. LSTM-5 has shown that a single parameter is inadequate for estimating spring discharge. The LSTMs yielded an RMSE value of similar to 0.04, as well as a R2\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${R}<^>{2}$$\end{document} value of similar to 98.01%. The study showed that using different input parameters, the suggested LSTM model can effectively simulate spring discharge in a karst environment.