## 1 Introduction
Therefore, it is necessary to explore a more efficient method to perform the calculation. In recent years, machine learning algorithms have been widely used in studies for estimating hydrological and meteorological indicators, such as air temperature [24], dew point temperature [25], precipitation [26], solar radiation [27], diffuse solar radiation [28], and evapotranspiration [29,30], among which an artificial neural network (ANN) is probably the most common machine learning algorithm used for modeling. For \(\rm T_{s}\) estimation, ANN has been applied in different areas of the world by scholars. The first study on record for estimating \(\rm T_{s}\) with machine learning algorithms was carried out by [PERSON] et al. [31], in which \(\rm T_{s}\) at three depths (i.e., 10, 50, and 150 cm) were estimated with ANN models. [PERSON] [32] evaluated the potential of ANN in daily and yearly \(\rm T_{s}\) estimation in Athens and Dublin, and the research concluded that the ANN model had an adequate performance in estimating \(\rm T_{s}\). [PERSON] [33] applied an ANN model to estimate monthly \(\rm T_{s}\) at multiple depths in Adana, Turkey, and the result showed that ANN was a suitable model for estimating \(\rm T_{s}\). [PERSON] et al. [34] utilized ANN and multiple linear regression model to estimate daily \(\rm T_{s}\) at six soil depths, in which they found that temperature and relative humidity (RH) were the most influential parameters affecting \(\rm T_{s}\) estimation among mete orological factors. Although the ANN model is widely used by everyone for estimating \(\mathrm{T_{s}}\), as scholars continue their research, it was found that the ANN model is not necessarily better than other machine learning algorithms in estimating \(\mathrm{T_{s}}\). Therefore, it becomes more meaningful to keep investigating new models to improve the estimation performance. Recent advances of newly developed machine learning algorithms have enabled scholars to evaluate and compare the capabilities of various algorithms in estimating \(\mathrm{T_{s}}\), e.g., M5 model tree (M5 Tree), random forests (RF), M5P model tree (M5P), multiple linear regression (MLR) model, support vector machine (SVM) model, and extreme learning machine (ELM) model, etc. [PERSON] et al. [2] compared the capabilities of ELM, ANN, and M5 Tree in modeling monthly \(\mathrm{T_{s}}\) at 5, 50, and 100 cm depths, and they found that the ELM model would be a more desirable tool for estimating \(\mathrm{T_{s}}\) at a wide range of depths. [PERSON] et al. [35] reported that the adaptive neuro-fuzzy inference system (ANFIS) provided superior results in monthly \(\mathrm{T_{s}}\) estimation than ANN and gene expression programming (GEP) with data from 31 stations in Iran. [PERSON] et al. [36] estimated monthly \(\mathrm{T_{s}}\) at different soil depths (i.e., 5, 10, 20, 50, and 100 cm) using nonlinear regression and MLR models, and obtained the most accurate results at the depth of 5 cm. [PERSON] et al. [37] evaluated the capabilities of ELM and RF models in estimating half-hourly \(\mathrm{T_{s}}\) for maize fields, and they concluded that the ELM model had better estimated performance. [PERSON] et al. [38] utilized MSP, MLP, and RF models to estimate daily \(\mathrm{T_{s}}\) in arid regions, the results of which showed that MLP outperformed other models with better performance metrics. [PERSON] et al. [39] also compared the modeling capabilities of MLP, MLR, and radial basis neural networks (RBNN) for monthly \(\mathrm{T_{s}}\) estimation at different soil depths, with inconsistent results obtained depending on depth. At depths of 5 and 10 cm, the RBNN model had the best estimating accuracy among all models used, while at other soil depths (50 and 100 cm), MLR performed better. [PERSON] et al. [40] applied SVM and multivariate adaptive regression splines (MARS) to estimate month-by-month \(\mathrm{T_{s}}\) for 30 stations in Iran, and it was found that MARS outperformed the SVM model.