GLUE uncertainty analysis of hybrid models for predicting hourly soil temperature and application wavelet coherence analysis for correlation with meteorological variables

Accurate prediction of soil temperature (T_s) is critical for efficient soil, water and field crop management. In this study, hourly T_s variations at 5, 10, and 30 cm soil depth were predicted for an arid site (Sirjan) and a semi-humid site (Sanandaj) in Iran. Existing machine learning models have high performance, but suffer from uncertainty and instability in prediction. Therefore, GLUE approach was implemented to quantify model uncertainty, while wavelet coherence was used to assess interactions between T_s and meteorological parameters. Standalone machine learning models (adaptive neuron fuzzy interface system (ANFIS), support vector machine model (SVM), radial basis function neural network (RBFNN), and multilayer perceptron (MLP)) were hybridized with four optimization algorithms (sunflower optimization (SFO), firefly algorithm (FFA), salp swarm algorithm (SSA), particle swarm optimization (PSO)) to improve T_s prediction accuracy and reduce model uncertainty. For both arid and semi-humid sites, ANFIS-SFO produced the most accurate performance at studied soil depths. At best, hybridization with SFO (ANFIS-SFO, MLP-SFO, RBFNN-SFO, SVM-SFO) decreased RMSE by 5.6%, 18%, 18.3%, and 18.2% at 5 cm, 11.8%, 10.4%, 10.6%, and 12.5% at 10 cm, and 9.1%, 12.1%, 13.9%, and 14.2% at 30 cm soil depth compared with the respective standalone models. GLUE analysis confirmed the superiority of hybrid models over the standalone models, while the hybrid models decreased the uncertainty in T_s predictions. ANFIS-SFO covered 95%, 94%, and 96% observation data at 5, 10, and 30 cm soli depths, respectively. Wavelet coherence analysis demonstrated that air temperature, relative humidity, and solar radiation, but not wind speed, had high coherence with T_s at different soil depths at both sites, and meteorological parameters mostly influenced T_s in upper soil layers. In conclusion, uncertainty analysis is a necessary and powerful technique to obtain an accurate and realistic prediction of T_s. In contrast, wavelet coherence analysis is a useful tool to investigate the most effective variables that strongly affect predictions.