## 1 Introduction  
Soil temperature (T\({}_{\mathrm{s}}\)), as a consequence of the combined effect of hydrothermal circulation in both the atmosphere and the land surface, is an important factor in atmospheric-ecological-environmental systems [1, 2, 3]. T\({}_{\mathrm{s}}\) has significant impacts on the energy balance of global atmospheric-ecological-environmental systems [4, 5], thereby directly affecting the growth and development of plants [6]. Under natural conditions, T\({}_{\mathrm{s}}\) is influenced by other environmental factors such as atmospheric temperature, vegetation type, soil moisture, and topography, which together cause the spatial and temporal variations in \(\rm T_{s}\)[7]. Given its importance and complexity, accurate prediction of \(\rm T_{s}\) is of substantial value in both scientific research and practical applications [8,9]. However, the current approaches for measuring \(\rm T_{s}\) are generally complicated, costly, and time consuming [1], which make the wide range monitoring of \(\rm T_{s}\) inaccessible in many countries, especially for undeveloped countries. The incomplete \(\rm T_{s}\) data caused by this predicament presents an obstacle to the estimation and analysis of \(\rm T_{s}\) conditions and poses a significant challenge for accurate \(\rm T_{s}\) prediction on a large scale [10]. The prevailing approaches for \(\rm T_{s}\) measurements can be divided into three major categories, each of which has its own advantages and disadvantages. The first category is the in situ monitoring of \(\rm T_{s}\) with equipment installed in meteorological stations, which allows the actual \(\rm T_{s}\) to be recorded in real-time [11,12]. However, considering the geographical limitation and the economic cost of constructing meteorological stations and the potential data deficiencies due to equipment problems, this approach is not suitable for studies covering various regions [13]. The second category is the estimation of \(\rm T_{s}\), which consists of the interpolation method, the Newhorl model estimation, and direct estimation. The interpolation method estimates \(\rm T_{s}\) at any depth based on known \(\rm T_{s}\) at similar depths through certain formulas [14]. The Newhorl model estimation method uses air temperature plus a fixed value to roughly estimate \(\rm T_{s}\) at a certain depth. For instance, [PERSON] [15] obtained the \(\rm T_{s}\) values at a depth of 50 cm indirectly by adding 2.5 \({}^{\circ}\)C to the mean yearly temperature. The direct estimation method simply uses the \(\rm T_{s}\) from known depths to represent \(\rm T_{s}\) at unknown depths [16]. Although approaches in the second category can solve certain problems in \(\rm T_{s}\) measurements to some extent, differences in several factors such as soil depth, elevation, and environment are not considered during estimation, which certainly have impacts on \(\rm T_{s}\). Therefore, these methods may be suitable for the local scale, but results obtained from them are not universally applicable and cannot be generalized [17]. Therefore, it is necessary to find methods that are applicable to a large-scale range. The third category is to establish a regression equation for \(\rm T_{s}\) calculation. Research has verified similar patterns in the variations between \(\rm T_{s}\) and air temperature [18,19], and therefore relationships between the two temperatures can be used for \(\rm T_{s}\) calculation at various depths through regression equations [20]. Some studies even consider the impacts of geographical factors (e.g., longitude, latitude, and elevation) on \(\rm T_{s}\) and build a multiple linear regression equation to quantify the impact of each geographical factor on \(\rm T_{s}\)[21]. Although approaches in this category overcome the deficiencies of the methods in the other two categories, there are still disadvantages in these approaches as \(\rm T_{s}\) are not necessarily linearly related to geographical factors [22], which might lead to significant biases during calculation [23].