# Modeling Soil Temperature with Fuzzy Logic and Supervised Learning Methods
## 1 Introduction  
Soil temperature is an important environmental parameter that controls numerous biological, chemical, and physical processes within the soil system [1, 2]. It has a direct influence on plant growth, seed germination, microbial activity, and the uptake of water and nutrients. A reliable estimation of soil temperature is therefore crucial not only for improving agricultural productivity and optimizing irrigation scheduling, but to support environmental assessments. Conventional methods--especially in situ sensors--provide accurate measurements, but are often expensive and limited in their spatial and temporal coverage. This has led to a growing interest in predictive models as practical and cost-effective alternatives [3]. Soil temperature also serves as a valuable indicator for understanding broader ecosystem dynamics that are closely linked to agricultural, hydrological, and ecological processes. A variety of modeling approaches have been developed to estimate it, including thosebased on heat flux equations [4], coupled heat and moisture transfer models [5], and models that account for topographic and vegetative features [6]. However, in regions with limited observational data, or when measurements at multiple depths are required, conventional methods may become impractical due to logistical and financial constraints [7]. In such cases, artificial intelligence (AI)-based models offer a promising alternative, as they are able to capture complex, nonlinear interactions between multiple environmental variables, and thus improve the accuracy and efficiency of soil temperature predictions [8; 9; 10]. AI-based models have been increasingly and successfully used in a wide range of agricultural applications in recent years [11; 12; 13; 14], and their use has become particularly prominent in the prediction of soil temperature. Among these, fuzzy logic-based approaches--especially the Mamdani fuzzy inference system (MFIS) and the adaptive neuro-fuzzy inference system (ANFIS)--offer interpretable modeling frameworks capable of capturing imprecise and uncertain relationships between variables, making them well-suited for modeling soil temperature dynamics. For instance, [PERSON] and [PERSON] [15] developed the multilayer perceptron (MLP) and ANFIS models to estimate daily soil temperature at the Champaign and Springfield stations in Illinois. Similarly, [PERSON] et al. [16] employed the ANFIS model to estimate soil temperature at six different depths across three climatically diverse regions. The performance of the ANFIS was systematically evaluated against conventional regression-based methods, with results indicating superior predictive accuracy and robustness across varying climatic conditions. In addition, various machine learning methods, including artificial neural networks (ANNs), deep learning (DL), kernel-based models, and hybrid techniques, have demonstrated their performance in modeling soil temperature dynamics under different environmental conditions. ANNs, especially in the prediction of soil temperature within hydrological and meteorological modeling, are among the most widely used machine learning techniques due to their proven superior performance in numerous studies. For instance, [PERSON] et al. [17] developed an ANN model using five years of meteorological data collected from a weather station in Canada. The model used daily rainfall, potential evapotranspiration, and the day of the year as inputs to estimate daily soil temperatures at depths of 10, 50, and 150 cm. [PERSON] and [PERSON] [18] proposed an improved method for predicting morning and evening soil temperatures at depths of 5 cm and 10 cm, using minimum historical soil temperature data. [PERSON] et al. [19] estimated daily soil temperatures at six depths (5, 10, 20, 30, 50, and 100 cm) in an arid region of Iran using both ANN and multivariate linear regression models, driven by mean daily meteorological inputs, such as air temperature, solar radiation, relative humidity, and precipitation.