Deep learning and vine copula-based sequencing: approaches under investigation for forecasting soil temperature dynamics

Accurate soil temperature forecasting remains challenging due to (1) capturing complex nonlinear relationships between atmospheric variables and soil thermal dynamics across depths, and (2) balancing short-term accuracy with long-term reliability under increasing climate variability. To address this, the first systematic comparison of vine copulas and deep learning models (Long Short-Term Memory (LSTMs), Convolutional Neural Networks (CNNs), Gated Recurrent Units (GRUs)) for multi-depth forecasting (5, 10, 30, and 50 cm) were presented across forecasting horizons (1, 7, 15, and 30 days) in semi-arid regions. Vine copulas were employed for their proven ability to model multivariate dependencies, while deep learning models were selected for their temporal pattern recognition capabilities. In this study, air temperature, sunshine duration, and relative humidity-selected based on Kendall's Tau-were used as input variables to evaluate model accuracy for forecasting horizons of 1, 3, 5, and 7 days (deep learning) and lag times of 1, 3, 5, and 7 days (vine copulas). Deep learning models, particularly CNNs, performed well in soil temperature forecasting. For 1-day predictions, CNNs (3-day sequence) achieved near-perfect accuracy (NSE = 0.99, RMSE = 0.43-1.11 degrees C) across 5-30 cm depths. Their strong performance persisted for 7-day forecasts (NSE > 0.96, RMSE < 2.19 degrees C), with optimal results at 30 cm (MAE = 0.67-1.14 degrees C). GRUs (7-day sequence) excelled in 30-day forecasts (NSE = 0.85-0.88), except at 50 cm, where LSTMs performed slightly better (NSE = 0.80). Performance declined predictably with longer horizons but maintained NSE > 0.82 across all configurations. However, the vine-based approach consistently outperformed deep learning models at various depths and time lags. The C-vine and R-vine models demonstrated the best forecasting accuracy across all depths. While deep learning reduced error rates by an average of 55%, the vine-based approach achieved even greater improvements-approximately 72%, 58%, 71%, and 72% based on RMSE values for 30-day forecasts. Overall, the vine-based method performed best at all depths with a lag-1 configuration, highlighting its potential for environmental and agricultural applications.