Soil temperature is a critical parameter in soil science, agriculture, meteorology, hydrology, and water resources engineering, and its accurate and cost-effective determination and prediction are very important. Machine learning models are widely employed for surface, near-surface, and subsurface soil temperature predictions. The present study employed a properly designed one-dimensional convolutional neural network model to predict the hourly soil temperature at a subsurface depth of 0–7 cm. The annual input dataset for this model included eight hourly climatic features. The performance of this model was assessed using a wide range of evaluation metrics and compared to that of a multilayer perceptron model. A detailed sensitivity analysis was conducted on each feature to determine its importance in predicting the soil temperature. This analysis showed that air temperature had the greatest impact and surface thermal radiation had the least impact on soil temperature prediction. It was concluded that the one-dimensional convolutional model performed better than the multilayer perceptron model in predicting the soil temperature under both normal and hot weather conditions. The findings of this study demonstrated the capability of the model to predict the daily maximum soil temperature.

Accurate soil temperature prediction in cold climates is crucial for optimizing agricultural practices, hydrological processes, water resource management, minimizing frost damage, and mitigating flood risks. The capacity of deep learning methods to capture intricate patterns and relationships in climate data enhances the accuracy of soil temperature predictions and offers substantial benefits for reducing climate change impacts. In the present study, a comparative analysis of different deep learning techniques, including long short-term memory (LSTM), convolutional neural network (CNN), and multi-layer perceptron (MLP), for predicting the soil temperature is provided. The study examined cold climate areas across Canada, from snowy regions to Arctic conditions. Input datasets were considered both as time series and shuffled order. To comprehensively evaluate the predictive approaches for soil temperature, four machine learning (ML) models—CNN, LSTM, MLP in time series, and MLP on shuffled data—were employed. The results showed ML models using input data as time series have struggled with accurate soil temperature prediction, especially in very cold and polar climates, likely due to the presence of ice layers on the soil, limiting fluctuations near the freezing point. The normalized RMSE (NRMSE) for the CNN, LSTM, and MLP was calculated to be 8.6%. 7.4%, and 6.9%, respectively, and the scatter index (SI) for CNN, LSTM, and MLP was calculated to be 1.0%, 0.9%, and 0.9%, respectively. On the other hand, MLP-shuffled that employs shuffled input data outperformed others with an NRMSE of 5.4% and an SI of 0.7%, by creating a generalized data representation, free from presentation sequence bias. This study showed that predicting soil temperature in very cold climates poses a challenge for machine learning, yet the MLP-shuffled model excels, attaining superior accuracy through the creation of a generalized data representation independent of the sample sequence.

A numerical simulation has been carried out to study the interaction of a cavitation bubble and an elastic membrane. Boundary element method is used to simulate the physics of the membrane between two fluids which are assumed to be same (water) for simplicity. The intent of this paper is to clearly investigate the bubble–membrane interaction. Elasticity of the membrane plays an important role on the behavior of the bubble. For example, a bubble near a ‘stiff’ membrane (high elasticity), jets toward it (the same as the rigid boundary). The influence of two main parameters, namely, dimensionless distance of the bubble center to the membrane initial position (H′) and the dimensionless elasticity of the membrane (E′) are discussed. We have considered the dimensionless distance of the bubble center to the membrane initial position in the range of 0.5 ⩽ H′ ⩽ 1 and a membrane of dimensionless elasticity in the range of 0.01 ⩽ E′ ⩽ 10. An increase in H′ leads to a decrease in the membrane displacement from its initial position. Also, increasing of E′ leads to a change in the behavior of the bubble from spherical collapse to jetting toward the membrane (in a same H′) and decreasing in membrane displacement.