A Review of Machine Learning Approaches to Soil Temperature Estimation

Abstract

Soil temperature is an essential factor for agricultural, meteorological, and hydrological applications. Direct measurement, despite its high accuracy, is impractical on a large spatial scale due to the expensive and time-consuming process. On the other hand, the complex interaction between variables affecting soil temperature, such as topography and soil properties, leads to challenging estimation processes by empirical methods and physical models. Machine learning (ML) approaches gained considerable attention due to their ability to address the limitations of empirical and physical methods. These approaches are capable of estimating the variables of interest using complex nonlinear relationships with no assumptions about data distribution. However, their sensitivity to input data as well as the need for a large amount of training ground truth data limits the application of machine learning approaches. The current paper aimed to provide a review of ML techniques implemented for soil temperature modeling, their challenges, and milestones achieved in this domain.

1. Introduction

Soil temperature is an essential environmental parameter in earth sciences, such as meteorology and climate change; soil processes, such as evaporation, infiltration, and nutrient cycling; and agricultural purposes, such as precision farming and irrigation scheduling at many developmental stages. As an important meteorological parameter, soil temperature controls the heat transfer from the soil to the atmosphere and vice versa. In addition, agriculture applications including potential evapotranspiration, root development, crop growth, and yield of crop are affected by soil temperature variations. Soil temperature also plays a remarkable role in determining hydrological parameters, such as evaporation, precipitation, and infiltration of water through soil.

Accurate estimation of soil temperature is complicated because of the physical, chemical, and biological processes governing the soil-plant-atmosphere system [1]. Since soil temperature is highly localized and can be difficult to measure directly, indirect methods of assessing soil temperature using more easily measured variables such as air temperature and readily available weather data gained much attention.

Generally, estimation methods for soil temperature are classified into three groups (1) in situ measurements, (2) satellite observations, and (3) model-based estimates.

The most reliable method is in situ measuring using local instruments such as thermistors, thermocouples, thermocouple wires, and averaging thermocouples, which can provide accurate estimates of soil temperature. Although in situ measurements, which are necessary to validate the two other methods, can provide soil temperature with a relatively high degree of accuracy, the low density of sensors and fine spatial resolution of sampling restrict the use of point (or field) observations to map the soil temperature over a wide geographical area because of expensive equipment. In other words, continuous monitoring of soil temperature at different depths requires a variety of sensors installed at short distances to represent the spatial heterogeneity in soil temperature. However, high costs of installation and maintenance, equipment requirement, special expertise, and point measurement limit the application of these field soil temperature sensors.

Therefore, satellite sensors received significant attention over the past few decades. Yet, scaling issues and measurement depth, despite current advances, are the most considerable challenges of remote sensing techniques.

The model-based approach, including empirical and physical models, can retrieve soil temperature by surface information and weather-forcing variables. Empirical models use statistical regression techniques and parametric functions to map the soil temperature through in situ measurements. These models are simple to implement without a specific background. Although these models are useful to model soil temperature dynamics with an acceptable accuracy, the need for suitable reference samples of the desired target variable for calibration and validation of results restricts the use of the models due to the costly and time-consuming process of in situ measurements. Moreover, the estimation accuracy of reference samples can be affected by errors during the measurement process. The statistical regression-based relationship between input and output is site dependent; therefore, empirical relationships, despite their fewer input data requirements, are valid only under specific operational conditions in which the samples were collected [2,3,4]. Furthermore, varying environmental conditions in addition to some matters such as nonlinearity, outlier data, multicollinearity, and heteroscedasticity can decrease the estimation accuracy of statistical models due to the lack of physical structure.

Physical models, including agronomical models, hydrological models, earth system models, and land surface models (LSMs), are based on assumptions that simplify the real phenomena, which leads to more general use in comparison to collections of in situ measurements. However, these simplifying assumptions lead to uncertainty in estimating the soil temperature at the continental or global scales. Physical models suffer from high complexity, intensive input data requirement, and high computational cost in estimating near-real-time soil temperature, which makes accurate estimation of physical parameters challenging [5]. Additionally, errors due to forcing data and parameters potentially lead to uncertainties in the long-term monitoring of soil temperature. Although data assimilation techniques such as the land data assimilation system (LDAS) can improve the accuracy of estimates, errors due to the physics of these models are inevitable [6].

With the significant progress in computer technology, various machine learning (ML) techniques, known as computational artificial intelligence-based (AI) models with a dynamic input-output mapping approach, were developed to address the aforementioned drawbacks. These data-driven models are mathematical representations built based on training data to estimate target variables by analyzing data attributes. They are capable of approximating complex nonlinear relationships, including nonlinear, nonmonotonic, and multimodal relationships, with limited assumptions about data distribution as well as predefined conceptual relationships between input and output data because of their advanced learning strategies. Due to this property, a wide range of diverse datasets with unknown probability density functions can be used to estimate variables of interest using ML with better performance than other parametric methods [2] Moreover, multi-source usage makes ML models suitable for large-scale studies such as climate and hydrology studies. Since ML techniques rely on the relationships between model inputs and desired outputs, they can accurately represent earth processes without an explicit structure.

Unlike empirical models, ML-based outputs can be applied as important information sources to retrieve soil temperature in unsampled areas [7,8]. In addition, these methods with high computational speed and high adaptability to different inputs and configurations are superior to LSMs and Soil Vegetation Atmosphere Transfer (SVAT) models [9]. However, ML methods need a large number of samples with known target labels to capture the variability of complex systems. Other challenges are overfitting the models to the training data as well as low convergence during the learning process [10].

If an ML-based model is sufficiently trained to represent the physical process, it can provide accurate predictions of data not included in the training process, i.e., the generalization concept [11]. Thus, introducing physical principles and constraints into machine learning techniques can improve the estimation accuracy of the model by reducing the optimization search space to physically based possibilities [12,13,14]. Furthermore, applying a penalty to the optimization process because of inconsistent predictions can drive the optimization process to reduce error and generate physically meaningful results. In addition to the training process, ML models are highly dependent on input variables that are correlated with soil temperature, including climatic variables such as air temperature and precipitation, soil properties such as soil texture and land cover, and vegetation indices [15,16]. In other words, the quality and quantity of training data significantly affect the performance of ML models. As a result, the ML models are incapable of capturing the relationships between data and generalizing appropriate patterns to new datasets for small datasets, resulting in an overfitted model. In contrast, noisy data may lead to the model underfitting to the training datasets if a relatively simple learning structure is used. Furthermore, limited datasets representing specific conditions cause the model to fail to recognize true underlying patterns. A data preprocessing process, such as bias reduction, data normalization, and data size increment, can mitigate these issues, in addition to the feature selection process that determines which data are appropriate for input.

The advent of ML-based soil temperature prediction occurred when [17] used relative humidity, wind speed, and air temperature, as inputs in both single-layer and multi-layer neural networks to predict soil temperature, thereby providing a foundation for machine learning as a method for soil temperature estimation using climate variables. Since then, many studies proposed other ML models and input variables for soil temperature prediction. Given that ML models were successfully used to retrieve soil characteristics for two decades, the current research addresses the application of different machine learning methodologies in predicting soil temperature. These predictive models along with decision-support systems can alleviate the time and operational costs associated with instrumental measurements. The remainder of this paper is organized as follows. In Section 2, different artificial intelligence-based models are classified into four main categories: (i) artificial neural networks, (ii) deep learning, (iii) kernel models, and (iv) hybrid models, in which the studies carried out by these methods are assessed in detail. The limitations and future perspectives are also discussed in Section 3.

2. AI-Based Models for Soil Temperature Estimation

2.1. Artificial Neural Networks

An artificial neural network (ANN), which is a universal approximator for nonlinear mapping, classically comprises three layers including input, hidden, and output layers, as shown in Figure 1. The model can learn the multivariate non-linear relationships between the input and output without physical concepts and generalize them to other points [18,19]. Thus, ANNs eliminate the need for an explicit configuration of physical relationships by defining the input–output relationship, which prevents the models from errors caused by incorrect associations. Moreover, these models benefit from a relatively low computational cost due to the one-time calibration.

The most widely used variants of ANN include feed-forward neural networks (FFNNs) or multilayer perceptrons (MLPs), radial basis neural networks (RBNN), and generalized regression neural networks (GRNNs). Despite the different structures of ANN models, all of them consist of two functional components, i.e., learning and optimization processes for classifying inputs to hidden layers and to outputs, respectively. The first component, known as the input-hidden component, detects nonlinearity in the input data and classifies inputs into hidden layers by a learning algorithm (supervised or unsupervised). The second functional component, known as the hidden-output component, includes an optimization process to find the best match between the classified inputs and targets. The classified inputs are mapped to the outputs by linear projection, which adjusts the model parameters by a negative gradient algorithm by minimizing the mean square error between the ANN output and target data. ANNs are capable of dealing with a large amount of data because of the separate training process of the components. In addition, an adaptive procedure can be used to recursively update the parameters when the observational data of interest are sufficient.

ANNs are the most popular type of AI models for approximating hydrological and environmental components such as soil temperature with a long-term history. For example, ref. [20] compared the performance of three AI-based models, i.e., MLPs, GRNNs, and RBNNs, as well as multiple linear regression (MLR) in modeling monthly soil temperatures at different depths. They assessed the effect of climatic data, including relative humidity, solar radiation, wind speed, and air temperature, on the resulting soil temperature by GRNN, among which the air temperature was identified as the most effective variable. According to the results, RBNN performed better than MLP and GRNN in estimating soil temperature at depths of 5 and 10 cm, while MLR and GRNN models presented the best accuracy at 50 and 100 cm, respectively. In addition to climatic data, the effect of periodicity on model accuracy in the training, validation, and test periods was investigated, leading to a decrease in the root mean square error (RMSE) of GRNN, MLP, RBNN, and MLR by 19, 15, 19, and 15 %, respectively.

Ref. [21] used several data-intelligent ML models, i.e., ANN, extreme learning machine (ELM), and M5 Model Tree (M5 Tree), to estimate monthly soil temperatures at 5, 50, and 100 cm. The models were trained by meteorological information obtained from two stations in Turkey, including air temperature, relative humidity, wind speed, solar radiation, and periodicity. The ELM model, with the highest accuracy and lowest error, was considered the most accurate model at a depth of 50 cm.

Even though climatic data may be unavailable in some regions, most studies use meteorological parameters as input data to estimate soil temperature. For example, ref. [22] employed geographical information, i.e., latitude, longitude, and altitude as well as the calendar month, to estimate monthly soil temperature at depths of 5, 10, 50, and 100 cm using ANN, adaptive neuro-fuzzy inference system (ANFIS) and gene expression programming (GEP). According to the results, the ANFIS model provided the most accurate estimates, followed by the ANN and GEP. Ref. [23] predicted the monthly soil temperature at a depth of 10 cm by ANN over a large spatial domain with complex terrain in southwestern China. The independent variables included geographical information obtained from a digital elevation model and the Normalized Difference Vegetation Index (NDVI) derived from satellite imagery. Compared to multiple linear regressions, ANNs improved the RMSE, mean absolute error (MAE), and R2 by about 44%, 70%, and 18%, respectively.

Using Earth observation satellite data, ref. [24] evaluated the predictive capability of feed forward back propagation neural network (FFBPNN) for land surface temperature by past land surface temperature (LST) values as well as geographical characteristics. They confirmed the ability of ANN to learn and predict a non-linear complex dataset.

The aforementioned studies modeled soil temperature on a monthly time scale while daily or sub-daily resolutions are more advantageous for agricultural purposes. Moreover, the applicability of these models is limited due to the lack of environmental and atmospheric data used for soil temperature estimation. To address these issues, ref. [25] employed ANN and wavelet neural network (WNN) models to forecast soil temperature 1–7 days ahead by only surface air temperature data with hourly temporal resolution. The results showed that a wavelet transform, which decomposes the inputs into low and high-frequency components, can improve the prediction accuracy of soil temperature.

The methods of ELM, GRNN, backpropagation neural networks (BPNN), and random forests (RF) were exploited to derive half-hourly soil temperatures at depths of 2 cm, 5 cm, 10 cm, and 20 cm from datasets of air temperature, relative humidity, solar radiation, wind speed, and vapor pressure deficit [26]. Despite the desirable performance of all the models, the ELM model with a high computational speed showed more accurate results at different soil depths. Ref. [27] used the MLP model, RF, Gaussian process (GaP), and M5P models to estimate daily soil temperature in arid regions by climate data obtained from two stations, which included sunshine, wind speed, relative humidity, and air temperature. It was found that the MLP model with RMSE ranging from 3.3 to 6.3 °C performed better than the other models in estimating soil temperature at a depth of 5 cm. Ref. [28] employed MLP and MLR models to estimate the daily soil temperature at 5, 10, 20, 30, 50, and 100 cm by daily meteorological data, including relative humidity, solar radiation, air temperature, and precipitation. The results showed the superiority of MLP to MLR as well as the higher effectiveness of air temperature and humidity over other variables. Ref. [29] applied MLP and ANFIS models to estimate the daily soil temperature at two stations in Illinois, USA. A variety of weather data, including air temperature, relative humidity, dew point temperature, potential evapotranspiration, wind speed, solar radiation, and soil temperature at 10 and 20 cm depths were used to model the soil temperature. The input data for air temperature, wind speed, and solar radiation were recognized as the best data combination for both models. In addition, it was found that the MLP model outperformed ANFIS for both stations at depths of 10 and 20 cm. Ref. [30] exploited ANN, MLR, and GEP to estimate the multi-depth daily soil temperature at a station with a semiarid climate in Iran. To adopt the best input data, they used 12 combinations of meteorological data including relative humidity, wind speed, extraterrestrial radiation, sunshine hours, and minimum and maximum air temperatures. Although all models were able to estimate soil temperature, the ANN model exhibited the best performance. Ref. [31] applied ANN, WNN, and GEP models to estimate the daily soil temperature at different depths in Iran based on single-station measurements. At all depths, air temperature, radiation, and sunshine hours had the greatest effect on the soil temperature prediction. The results revealed that the best performance belonged to WNN with the lowest RMSE and highest R; however, the estimation accuracy as well as the effect of climatic factors decreased with increasing soil depth.

Since neural network (NN)-based soil temperature models are location-specific, they cannot be extended to other locations because of the unique relationships between soil temperature and climate conditions at the training location. However, it is possible to build spatially distributed temperature models if sufficient temperature data are initially known. In this regard, ref. [32] used an ensemble approach using machine learning techniques such as ANN, decision tree (DT), and k-nearest neighbors (k-NN) to predict spatially distributed land surface temperatures from a given dataset of land temperature at known locations. The statistical indices showed good performance of the proposed model built by DT, variable ridge regression (VRR), and conditional inference tree (CIT).

Some studies evaluated the efficiency of ML models for predicting soil temperature only at shallow depths, while the relationship between effective parameters and soil temperature changes with the depth of the soil temperature sample, leading to a need for multi-depth evaluation. In this regard, ref. [33] used an ANN and a co-active neuro-fuzzy inference system (CANFIS) to predict the soil temperature at two locations in Iran at depths from 5 to 100 cm using only air temperature data. The resulting models performed better for shallower sample depths, and stations in dry climates. The authors hypothesized that moisture in humid climates may act as a thermal insulator, interfering with the relationship between the air and soil temperatures. Ref. [34] modeled soil temperature at depths from 5 to 100 cm at Mersin station, Turkey, by using ELM, ANN, classification and regression trees (CRT), and the group method of data handling (GMDH). They also investigated the models’ sensitivity to the input variables, including air temperature, solar radiation, wind speed, relative humidity, and soil temperature. According to the results, the ELM performed best among all the models. The models for shallow soil temperature performed best and were found to rely only on the climate input of air temperature; while at deeper depths, more input variables (namely wind speed and solar radiation) were required.

The aforementioned studies used input data that associate concurrent climate parameters, and each individual set of measurements stands on its own, with no inherent connection in time to other data points. This data structure makes it necessary to introduce other techniques to account for time-related behavior. The simplest technique to account for seasonal cycles in soil temperature is to include the month of the year and, optionally, the day as well, as another input parameter. With this approach, ref. [35] investigated soil temperatures in Adana, Turkey, at five depths from 5 to 100 cm. The soil temperature was modeled using linear regression (LR) and nonlinear regression (NLR) as well as a feedforward neural network using different input sets depending on the season: air temperature, depth, and month were used year-round, and in the hot season atmospheric pressure, and solar radiation inputs were added. The results revealed the superior performance of FFNN over linear and nonlinear models. In addition, the results did not show any change in the model performance with sample depth for the neural network. Ref. [36] modeled soil temperature data from across Turkey using ANN, ANFIS, and MLR models. The study found that monthly soil temperature could be predicted using monthly minimum and maximum air temperatures, soil depth, calendar month number, and monthly precipitation. The models were built using all soil temperature data from different soil depths and climate regions, which would implicitly have different relationships with the climate input variables. The success of the models, especially the ANFIS model, indicates that these differences could be accounted for using the inputs of climate variables and soil depth, allowing for a model that was not intrinsically tied to a single location or soil depth. [37] used ANN models to predict soil temperature at locations across Turkey using the input climate parameters of solar radiation, sunshine duration, and air temperature; location parameters of altitude, latitude, and longitude; and time parameters of month and year. The best performing model was for the 20 cm depth, and the 100 cm depth model performed marginally worse. The inclusion of the year in the input is an interesting choice: it limits the models’ applicability to make predictions for the future, where the year will, by nature, be outside the range used for training the model. However, within the range of historical data, using year as an input variable allows the model to account for changes in seasonal patterns from year to year. Including only the month and day in the input variables inherently assumes that the seasonal patterns do not vary from year to year; however, natural variation in weather patterns as well as climate change contradict this assumption.

Another way of accounting for time without assuming identical yearly patterns is to use a sliding window approach. With this method, the soil temperature at a given time is modeled with an input of climate variables from the same time and from one or more previous time steps. Ref. [38] modeled the soil temperature at two study sites in Iran using MLPs and support vector machines (SVMs) with and without optimization via the firefly algorithm (FFA). The input climate variables (air temperature, wind speed, relative humidity, and sunshine hours) from the current day, the previous day, and, in some models, the day prior to that were all used as model inputs. The study concluded that using two days of previous data led to the best results, and the models that used FFA outperformed the standalone models without optimization. Ref. [39] investigated two stations in different climate regions of Iran, with sampling depths ranging from 5 to 100 cm. They used seasonal autoregressive integrated moving average (SARIMA), a linear stochastic approach, with seasonal standardization and spectral analysis in preprocessing. This model was compared to three machine learning models, i.e., ELM, self-adaptive evolutionary ELM (SaE-ELM), and ANFIS, and was shown to outperform them. The SARIMA model showed no loss of quality for deeper soil temperatures and performed moderately better at deeper depths.

One difficulty in the sliding window approach is that it makes assumptions about the lag time between the causal climate variable and the effect on soil temperature (namely, lag times equal to or less than the window length). The actual lag times may be long or follow complex patterns. Along with building several machine learning models to predict hourly soil temperatures at their sites in Iran, ref. [40] used wavelet decomposition to assess the coherence between various climate parameters and soil temperature. They observed that air temperature and soil temperature were highly coherent at a periodicity of 4 to 8 h for a soil depth of 5 cm, and 8 to 16 h at depths of 10 and 30 cm. Relative humidity and soil temperature were coherent at a periodicity of 16 to 64 h for 5 cm depth, and 4 to 8 h for 10 and 30 cm depths. While most studies examine soil temperature over larger time scales (i.e., daily, not hourly), the different periodicities between different climate variables and soil temperatures imply that the best sliding window models of soil temperature would need to include data from many different previous time steps. Furthermore, the fact that the periodicity of different climate variables changed in opposite directions upon changing the soil depth indicates that the sliding window would have to be different for models predicting temperatures at different depths.

Compared with other artificial intelligence models, ANNs can better extract the hidden features of big data. However, they are usually based on single data feature extraction without accounting for the spatiotemporal patterns of the data, which leads to a decrease in the prediction accuracy of soil temperature. In this regard, increasing the neural network depth can improve the optimization rate and model expression such as in deep learning (DL) models [41], which are discussed in the next section. A list of studies related to soil temperature estimation by ANN models is given in

Table 1. A list of studies carried out to estimate soil temperature by ANNs.

Research	Models	Output	Input	Soil Depth	Performance Criteria	Best Model(s)
[20]	MLP, GRNN, RBNN, MLR	Monthly soil temperature	Relative humidity, solar radiation, wind speed, air temperature, soil temperature	5, 10, 50, 100 cm	RMSE, MAE, R2	RBNN at depths of 5 and 10 cm, MLR at depth of 50 cm, GRNN at depth of 100 cm
[21]	ANN, ELM, M5 Tree	Monthly soil temperature	Air temperature, relative humidity, wind speed, solar radiation, periodicity	5, 50, 100 cm	R, RMSE, MAE, WI, NSE, LMI	ELM
[22]	ANN, ANFIS, GEP	Monthly soil temperature	Latitude, longitude, altitude, number of months	5, 10, 50, 100 cm	R2, RMSE, MAE	ANFIS
[23]	ANN	Monthly soil temperature	Latitude, longitude, elevation, topographic wetness index, NDVI	10 cm	RMSE, MAPE, R2
[24]	FFBPNN	Land surface temperature at 14 years’ interval	A sequence of past LST values, latitude, longitude	-	R, MSE
[25]	ANN, WNN	Next 1 to 7 day soil temperature	Surface air temperature	5, 10, 20, 30 cm	RMSE	WNN
[26]	ELM, GRNN, BPNN, RF	Half-hourly soil temperature	Air temperature, wind speed, relative humidity, solar radiation, and vapor pressure deficit	2, 5, 10, 20 cm	RMSE, MAE, NSE, R	ELM
[27]	MLP, RF, GP, M5P	Daily soil temperature	Sunshine hours, wind speed, relative humidity, air temperature	5 cm	MAE, RMSE, R	MLP
[28]	MLP, MLR	Daily soil temperature	Air temperature, solar radiation, relative humidity, precipitation	5, 10, 20, 30, 50, 100 cm	R, RMSE, MAE	MLP
[29]	MLP, ANFIS	Daily soil temperature	Air temperature, relative humidity, dew point temperature, potential evapotranspiration, wind speed, solar radiation, soil temperature	10, 20 cm	NSE, RMSE, MAE, APE	MLP
[30]	GEP, ANN, MLR	Daily soil temperature	Relative humidity, wind speed, extraterrestrial radiation, sunshine hours, minimum and maximum air temperature	5, 10, 20, 30, 50, 100 cm	R2, RMSE	ANN
[31]	ANN, WNN, GEP	Daily soil temperature	Air temperature, solar radiation, pressure, soil depth, periodicity	10, 20, 30, 50, 100 cm	R, MAE, RMSE, AIC, Taylor diagrams	WNN
[32]	An ensemble approach based on ANN, MARS, CIT, DT, ICR, k-NN, LAR, NNLS, NCPQR, PCA, Lasso, VRR, PPR	Land Surface Temperature	Latitude, longitude, temperature		Total computation time, RMSE, R2	Model built by DT, VRR, and CIT.
[33]	ANN, CANFIS	Daily soil temperature	Air temperature	5, 10, 20, 30, 50, 100 cm	RMSE, R	ANN
[34]	ELM, ANN, CRT, GMDH	Monthly soil temperature	Air temperature, relative humidity, solar radiation, wind speed	5, 10, 50, 100 cm	RMSE, R2	ELM
[35]	FFBPNN, LR, NLR	Monthly soil temperature	Air temperature, atmospheric pressure, solar radiation, depth, month	5, 10, 20, 50, 100 cm	MAPE, R	FFBPNN
[36]	ANN, ANFIS, MLR	Monthly soil temperature	Minimum and maximum air temperature, calendar month number, depth of soil, precipitation	5, 10, 20, 50, 100 cm	RMSE, MAE, R2	ANFIS
[37]	FFNN	Monthly mean soil temperature	Altitude, latitude, longitude, month, year, solar radiation, sunshine duration, air temperature	5, 10, 20, 50, 100 cm	RMSE, R
[38]	SVM, MLP, SVM-FFA, MLP-FFA	Soil temperature	air temperature, relative humidity, sunshine hours, wind speed	5, 10, 20 cm	RMSE, MAE, R	MLP-FFA
[39]	SARIMA, ELM, SaE-ELM, ANFIS	Daily soil temperature	Soil temperature	5, 10, 20, 30, 50, 100 cm	RMSE, MAPE, R2	SARIMA
[40]	ANFIS, SVM, RBNN, MLP optimized by the FFA, SFO, SSA, and PSO algorithms	Hourly soil temperature	Air temperature, relative humidity, solar radiation, wind speed	5, 10, 30 cm	NSE, RMSE, MAE, R2, PBIAS	ANFIS-SFO

Abbreviation: Willmott Index of Agreement (WI), Legates and McCabe index (LMI), Mean Squared Error (MSE), Absolute Percentage Error (APE), Akaike Information Criterion (AIC), Multivariate Adaptive Regression Spline (MARS), Independent Component Regression (ICR), Least Angle Regression (LAR), Non Negative Least Square (NNLS), Non Convex Penalized Quantile Regression (NCPQR), Principal Component Analysis (PCA), Projection Pursuit Regression (PPR), SunFlower Optimization (SFO), Salp Swarm Algorithm (SSA), Particle Swarm Optimization (PSO), Nash–Sutcliffe Efficiency (NSE), Percent Bias (PBIAS), Mean Absolute Percentage Error (MAPE).

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2.2. Deep Learning

Traditional neural network models are incapable of processing big data and have limited generalization ability and scalability. Moreover, their slow training process and easy falling into local optima are other weaknesses of standard neural networks. Therefore, ref. [42] developed deep learning (DL) models to deal with large multi-feature data through a multiple hidden layer structure. Compared to traditional neural networks, DL models, which are known as large-sized neural networks, as shown in Figure 2, have strong computing power which can automatically extract high level features from low level input data by intermediate layers with learning complex nonlinear functions in different fields such as search engines and image recognition. Since soil has extremely complex and nonlinear structural characteristics, DL models are more effective in analyzing soil particle size and soil texture than traditional models [16,43]. In addition, these methods simulate land-atmosphere interactions without complex knowledge governing physical models. These models can efficiently process future data with a high computational speed and integrate more data to improve prediction accuracy through additional learning. However, an inappropriate sample size of the input data may cause overfitting, thereby decreasing the prediction accuracy.

The most common DL models for environmental prediction include spatial models (Convolutional Neural Networks, CNNs by [44]), temporal models (Long Short-Term Memory networks, LSTMs by [45]) and spatial–temporal models (Convolutional LSTM, ConvLSTM by [46]).

The CNN, as a classical data-driven DL model, provides a powerful feature extraction tool to improve the predictive process by identifying the spatial features of data in multiple arrays. However, the CNN model, with decreasing number of layers, performs poorly in feature extraction. To address this issue, ref. [47] developed the residual network (ResNet) by introducing the residual block to construct deep neural networks.

LSTM models, which are a type of recurrent neural networks (RNN), are applied to deal with sequential data in order to predict the time series of target variables by learning from past observations. Therefore, these models, which are able to simulate nonlinear dynamic systems with minimal input data, retain the advantageous information of long-term time series data across multiple time steps. Although RNN is well suited for simulating time series data because it preserves the information of previous time steps through internal self-looped cells, the problem of gradient disappearance occurring in the long-range memory of the original RNN restricts its applicability in predicting targets. To overcome this problem, ref. [45] used a gate mechanism to obtain information in an RNN-based LSTM network model. However, LSTM neglects the learning of backward features, which leads to the development of the Bidirectional LSTM (BiLSTM) network model by combining backward and forward LSTMs.

The CNN and LSTM models only capture spatial and temporal variations, while the target variables have a correlation between space and time. This problem was solved via the ConvLSTM model, which is a combination of the CNN and LSTM models. Unlike the CNN and LSTM models, ConvLSTM using the output of the previous layer as the input for the next layer is capable of extracting both temporal and spatial features by a convolution layer at the same time without decreasing the map size.

Some researchers exploited CNN, LSTM, and ConvLSTM models to estimate and predict the soil temperature. For example, ref. [48] modeled soil temperature using persistence forecast (PF), BPNN, LSTM, and CNN trained with data decomposed using ensemble empirical mode decomposition (EEMD). They investigated three sites in Switzerland, at depths between 5 and 30 cm. The EEMD-based models provided the best results, and no model performance differences were noted between depths. Ref. [49] built on this work, focusing on the proposed EEMD-Conv3d model and extending it to predict spatiotemporally distributed soil temperature by air temperature data. The model showed the best performance among the Conv (2d and 3d), ConvLSTM, EEMD-Conv2D, and EEMD-ConvLSTM models.

Ref. [50] predicted the soil temperature in Ottawa, Canada, at depths between 0 and 7 cm. They used a wide variety of models and input variables in order to form a comprehensive view on the best possible models for soil temperature prediction. Their modeling methods included LRs, k-NNs, DT-based models, SVMs, stacking methods, MLP, DL, and ANFIS models. The input variables were the air temperature, precipitation, surface pressure, evaporation, wind speed, dew point temperature, solar radiation, and thermal radiation. The three best-performing models were the DL model, MLP, and stacking model; the choice of the best model among the three depended on the size of the dataset and the computational requirements. These three models were used in a sensitivity analysis to determine the most relevant input parameters, which were identified as air temperature and solar radiation.

Ref. [51] used 30 measurement stations across the US, representing different climates. BiLSTM was used to model soil temperatures at these locations, which trains models with data points from both previous and future time steps. BiLSTM outperformed the other models at all but the shallowest depth, demonstrating that using climate variables and time data together eliminate the decreased effectiveness of models at deep depths. The study also explicitly shows the correlation of different climate variables with soil temperatures at different depths, all of which decrease with increasing depth except for month and day. This is in keeping with the result from ANNs that using current climate variables without time data leads to less accurate models at greater depths.

Ref. [52] proposed an embedded network prediction model based on the gated recurrent unit (GRU), a modified type of LSTM, to learn the features of the historical soil temperature at local and global scales. By comparing the model with ANN, ELM, and LSTM, it was concluded that the proposed model outperformed the other models in predicting multi-depth soil temperature at different time points, including 6 h, 12 h, and 24 h.

Ref. [53] compared the performance of ML-based models, including the DL model and RBNN, with conventional approaches for soil temperature interpolation in southeast Canada. According to the results, the spline deterministic spatial interpolation method, even with increasing the spline nonlinearity, failed to provide the spatial distribution for the soil temperature and soil water content. On the other side, the ML models could capture the spatial variability of soil temperature even in sharp transition areas. It should be noted that deep learning, with a normalized RMSE of 9.0% and R² of 89.2%, outperformed the RBNN. A list of studies related to soil temperature estimation by DL models is given in

Table 2. Studies conducted to model soil temperature using DL techniques.

Research	Models	Output	Input	Soil Depth	Performance Criteria	Best Model(s)
[48]	EEMD-CNN, PF, BPNN, LSTM, EEMD-LSTM	Next 1, 3, 5 day’s soil temperature	Soil temperature at different depths and areas	5, 10, 30 cm	MSE, RMSE, MAE, R2	EEMD-CNN, EEMD-LSTM
[49]	EEMD-Conv3d, Conv2D, Conv3D, ConvLSTM, EEMD-Conv2D, EEMD-ConvLSTM	Next 1, 3, 5 day’s soil temperature	Soil temperature	7 cm	MSE, RMSE, MAE, R2, MAPE	EEMD-Conv3d
[50]	LR, ridge regression, Lasso, ENet, DT, RF, k-NN, XGBoost, SVM, gradient boosting, stacking methods, MLP, DL, ANFIS	Hourly soil temperature	Air temperature, precipitation, surface pressure, evaporation, wind speed, dew point temperature, solar radiation, thermal radiation	7 cm	MAE, MSE, RMSE, R2, MAPE	DL, MLP, stacking model
[51]	BiLSTM, LSTM, DNN, RF, SVR, LR	Hourly soil temperature	Maximum and minimum air temperature, wind speed, solar radiation, maximum and minimum relative humidity, vapor pressure, dew point temperature	5, 10, 20, 50, 100 cm	RMSE, MAE, R2	BiLSTM
[52]	GRU-based model, ANN, ELM, LSTM	Soil temperature at different time points (6 h, 12 h, 24 h)	Historical soil temperature	5, 10, 15 cm	RMSE, MAE, MSE, R2	GRU-based model
[53]	RBFN, DL, spline deterministic spatial interpolation method	Soil temperature	Soil temperature, soil moisture, climate data	10 cm	RMSE, NRMSE, SI, MAPE, Bias, R2, MAE, NSE, VAF, AIC, MSE, MaxE	DL

Abbreviation: Deep Neural Network (DNN), Support Vector Regression (SVR), Normalized RMSE (NRMSE), Scatter Index (SI), Variance Accounted For (VAF), Maximum Residual Error (MaxE).

.

2.3. Kernel Models

Kernel functions play a significant role in machine learning because of their simplicity and generality. Various kernel function embedded models were developed to capture non-linear relationships among which the support vector machine (SVM) is a well-known kernel model. This model was originally developed for classification purposes in which a classification hyperplane is obtained by maximizing the margin between different classes as shown in Equation (1) [54].

$$wx+b=0$$

(1)

where w is a weighting vector, x is the independent input vector, and b indicates the bias. To distinguish negative and positive samples, the hyperplane provides two dashed lines w·x + b = −1 and w·x + b = 1 with a maximum distance of $\frac{2}{\parallel w\parallel }$. The optimization function is also expressed as follows:

$$\left\{\begin{array}{c}\min \frac{1}{2}{\parallel w\parallel }^2\\ y_i\left(w{x}_i+b\right)\ge 1, i=1,2,\dots l\end{array}\right.$$

(2)

where y is the dependent output vector and l is the number of samples.

SVMs models, which are based on the statistical learning theory, can solve inverse problems by past data to obtain variables of interest forward in time. To predict the variables of interest, these models formulate quadratic optimization by structural risk minimization (SRM) instead of empirical risk minimization (ERM), which is their outstanding characteristic, to ensure a global optimum [55]. This ML-based approach, considered a sparse method without being affected by dimensionality, utilizes the generation error bound and intensive loss function, leading to precise predictions. Furthermore, SVMs can resist noises and generalize concepts under limited data conditions [56]. However, kernel function selection is a challenging stage of their learning process. In addition, the scale and speed of the learning process can be other limiting factors of SVM, especially for real-time data.

SVM models, because of their high processing speed and the need for fewer training data besides appropriate performance, recently gained attention for extracting geo-/bio-physical parameters. For example, ref. [57] developed an SVM-based model comprising an annual average soil temperature prediction model and a daily soil temperature amplitude prediction model to retrieve the daily soil temperature. The annual average of humidity, wind speed, radiation, soil, and air temperature are employed to train the annual average soil temperature prediction model and the daily soil temperature amplitude prediction.

Despite the significant role of soil temperature in meteorological, ecological, and hydrological processes, studies did not address soil temperature evaluation with fine temporal resolution in data-scarce regions. Furthermore, most studies employed air temperature as an input training dataset to estimate soil temperature while a significant correlation was observed between soil temperature drop and soil moisture rise. To this end, ref. [58] exploited the SVM model along with an extreme gradient boosting system (XGBoost), RF, and MLP to predict the spatiotemporal variability of soil temperature in the Indian Himalayan Region (IHR) by hourly and half-hourly time series data, including rainfall, soil moisture, soil temperature, air temperature, relative humidity, vapor pressure deficit, and solar radiation. Different input data combinations were utilized to estimate the soil temperature: Meteorological parameters, Meteorological parameters + rainfall, Meteorological parameters + soil moisture, and Meteorological parameters + rainfall + soil moisture. Among the models, XGBoost showed the best performance, followed by RF, MLP, and SVM. Moreover, the addition of soil moisture, unlike rainfall, to meteorological data improved the estimation accuracy significantly.

In addition to classification, SVM can be used for regression purposes, which is known as support vector regression (SVR). The basis of SVR is the iterative process of the sequential minimal optimization (SMO) algorithm [59]. Similar to SVM, SVR, which can capture nonlinear relationships between input and output variables, is used to estimate soil temperature due to its robustness to noise and generalization ability under conditions with limited reference samples [60]. Ref. [61] investigated soil temperature at depths from 10 to 100 cm at five different locations across Iran, ranging from hyper-arid to hyper-humid. SVR models were built with and without an input corresponding to the month of the year, and the models containing the month parameter were found to be more accurate, especially in deeper layers. Furthermore, the results showed that SVR models were better in deep layers than in shallow ones while MLR models could predict daily soil temperature at surface layers with relatively good accuracy.

Ref. [62] assessed the accuracy of SVR and Elman neural network (ENN) as well as SVR and ENN coupled with the firefly algorithm (SVR-FFA and ENN-FFA) and the krill herd algorithm (SVR-KHA and ENN-KHA) in modeling soil temperature at depths of 5, 10, 20, 30, 50, and 100 cm. Various meteorological data combinations were evaluated under five scenarios, which included (air temperature), (air temperature, sunshine), (air temperature, sunshine, relative humidity), (air temperature, sunshine, relative humidity, wind speed), and (air temperature, sunshine, relative humidity, wind speed, pressure deficit). With the best performance at 10 cm soil depth, all models showed a decrease in error from 5 to 10 cm and an increase from 10 to 100 cm. Additionally, optimization algorithms provided relatively satisfactory results in modeling soil temperature, especially at lower depths.

Ref. [63] estimated the daily soil temperature at depths of 5, 10, 20, and 50 cm for two stations with semiarid and humid climates in Turkey by Bayesian Tuned Support Vector Regression (BT-SVR), Bayesian Tuned Gaussian Process Regression (BT-GPR), and LSTM models. A variety of daily meteorological indicators, including cloudiness, air temperature, relative humidity, precipitation, and pressure, were used as input variables, and soil temperature at different depths was the output variable. To increase the accuracy, the study used a novel scheme based on the Bayesian optimization method to optimize the parameters of kernel functions of the GPR and SVR models. A number of kernel functions were used for GPR, such as constant, linear, polynomial, squared exponential, rational quadratic, power, and Matern-3, as well as linear, polynomial, Gaussian, and sigmoid functions for SVR. Among the models, the BT-GPR model exhibited the highest accuracy for both stations at depth of 5 cm.

Table 3. Studies conducted to model soil temperature using kernel functions.

Research	Models	Output	Input	Soil Depth	Performance Criteria	Best Model(s)
[57]	SVM	Daily soil temperature	Humidity, wind speed, radiation, soil temperature, air temperature, time of year	5, 10, 20, 50, 100 cm	RMSE, MAE, R2
[58]	XGBoost, SVM, RF, MLP	Hourly and half-hourly soil temperature	Rainfall, soil moisture, soil temperature, air temperature, relative humidity, vapor pressure deficit, solar radiation	15 cm	R2, MAE	XGBoost
[61]	SVR, MLR	Daily soil temperature	Minimum and maximum air temperature, solar radiation, relative humidity, dew point temperature, atmospheric pressure	10, 30, 100 cm	NRMSE, MBE, NSE, R2, WR2	SVR
[62]	SVR, ENN, SVR-FFA, ENN-FFA, SVR-KHA, ENN-KHA	Daily soil temperature	Air temperature, sunshine hours, relative humidity, wind speed, pressure deficit	5, 10, 20, 30, 50, 100 cm	RMSE, MARE, R2	SVR-KHA
[63]	LSTM, BT-SVR, BT-GPR	Daily soil temperature	Cloudiness, air temperature, relative humidity, precipitation, pressure	5, 10, 20, 50 cm	R2, RMSE, MAE	BT-GPR

Abbreviation: Mean Bias Error (MBE), Weighted Coefficient of Determination (WR²).

presents a list of studies carried out to model soil temperature using kernel function embedded models.

2.4. Hybrid Models

Despite considerable progress achieved in dealing with dynamic, non-stationary, and non-linear data by AI methods, the single models suffer from insufficient accuracy in some cases of environmental simulation. To overcome the limitations of any single method, coupled prediction models were developed to improve the accuracy in both the prediction and optimization stages by incorporating the superior features of individual models.

Adaptive neuro-fuzzy inference systems (ANFIS), which are a combination of ANN and fuzzy logic, comprise an important category of hybrid models (Figure 3). These models map input variables to output targets through an ensemble of membership functions and if-then rules. Although ANFIS can predict target variable dynamics with limited input requirements and acceptable prediction accuracy, the long-term generalization capability of NN is restricted by the ad hoc nature of fuzzy logic rules. Moreover, additional pre-processing requires extensive time and frequency domain computations. However, ANFIS is one of the most popular models for simulating and predicting environmental components such as soil temperature. Ref. [64] built several ANFIS models for soil temperature prediction to explore different optimization schemes. Using only air temperature as an input variable, the models predicted soil temperature at locations in North Dakota, U.S., at 10 cm depth. The optimization schemes were the PSO, SSA, grey wolf optimizer (GWO), genetic algorithm (GA), dragonfly algorithm (DA), grasshopper optimization algorithm (GOA), and a proposed hybrid SSA-GOA algorithm including a mutation phase (mSG). The proposed optimization scheme resulted in a model with improved predictive power over other ANFIS models, though the convergence time was longer than for most optimization schemes except GOA.

Ref. [65] extended a historical record of 1827 days of soil temperature data from two sites in Illinois, US, each with data at 10 and 20 cm depths. The data were extended using MLP and ANFIS with and without PSO as well as auto-regressive moving average (ARMA). To account for seasonal variation, some models were built using data preprocessed with spectral analysis or wavelet decomposition to remove the seasonal periodic component. The ARMA model combined with spectral analysis outperformed the AI techniques for both depths.

Ref. [66] applied ANFIS, dynamic evolving neurofuzzy inference system (DENFIS), WNN, and multivariate adaptive regression spline (MARS) to predict land surface temperature using NDVI, normalized difference built-up index (NDBI), normalized difference bareness index (NDBaI), normalized difference water index (NDWI), urban index (UI), and elevation. According to the results, ANFIS showed the best performance in training and test periods with RMSE of 0.78 °C and 0.36 °C, respectively.

In [67], the performance of ANFIS model against a time-series-based model, i.e., bi-linear model, was evaluated for daily soil temperature retrieval at different soil depths (5, 10, 50, and 100 cm) by daily recorded soil temperature. Furthermore, two hybrid models built by combining ANFIS with bi-linear and wavelet analyses were developed to improve the retrieval accuracy of soil temperature. Based on the soil temperature results, the ANFIS model demonstrated better performance than the bi-linear model as well as the hybrid models were superior to classical models. In addition to local evaluation, an external analysis was implemented to assess the performance of ANFIS in modeling soil temperature at 5 and 50 cm depths by soil temperature data at 10 and 100 cm, respectively, and vice versa, denoting the positive effect of soil temperature data at another depth in retrieving soil temperature at target depth.

Ref. [68] evaluated the applicability of ANN, ANFIS, and GP in simulating monthly soil temperature at different depths by using weather data at two stations in Turkey. The climatic data used to model soil temperature were air temperature, relative humidity, solar radiation, wind speed, and soil temperature at different depths (10, 20, and 100 cm). The results illustrated the superior performance of GP in comparison with ANN and ANFIS in estimating the soil temperature at 10, 50, and 100 cm. By including periodicity (month of the year) as another input variable, considerable improvement was achieved in the accuracy of the models.

Ref. [69] used ANN, CANFIS, WNN, and wavelet transformation combined with CANFIS (WCANFIS) to retrieve soil temperatures at 5, 10, 20, 30, and 100 cm by air temperature data. The results indicated the suitable performance of WCANFIS followed by ANN, CANFIS, and WNN. In addition, the minimum and maximum errors were obtained for the depth of 20 and 100 cm, respectively. Long-term soil temperature data are required to model soil temperature, which restricts the prediction models in most situations due to insufficient stations recording soil temperature [35]. To address this gap, ref. [70] used short-time soil temperature data recorded by thermal sensors along with air temperature, environmental parameters, and soil properties to model soil temperature at 5 and 10 cm by ANN, ANFIS, and MLR. The air temperature was found to be the most effective parameter in soil temperature modeling. In addition, the best performance belonged to ANFIS, followed by ANN and MLR, respectively.

In addition to ANFIS, researchers developed other hybrid models by combining ANN, SVM, DL, etc. For example, two ML-based models, FFBPNN and GEP, a time-series-based model, fractionally autoregressive integrated moving average (FARIMA), and two hybrid models, FFBPNN-FARIMA and GEP-FARIMA, were used to estimate the daily soil temperature at depths of 5, 10, 50, and 100 cm [71]. To generalize the models to different climate classes, the stations were selected in arid, semi-arid, and very humid climates. At all depths, the ML-based models outperformed the time-series-based model, and the hybrid models were superior to classical models.

In order to overcome the generalization issues of classical standalone models, optimization algorithms, such as GA, GWO, and PSO were integrated into the models to develop strong knowledge-based predictive systems. In this regard, some researchers addressed the lack of optimization algorithms by developing optimized AI techniques. Ref. [72] evaluated the performance of three hybrid models including SVM, MLP, and ANFIS boosted by the slime mold algorithm (SMA), PSO, and spotted-hyena optimizer (SHO) in forecasting daily soil temperature at 5, 15, and 30 cm in a semi-arid region of Punjab, India. Since the performance of ML models highly depends on the input variables, a gamma test (GT) was performed to determine the optimal input dataset for ML models, resulting in an optimal combination of relative humidity, wind speed, solar radiation, and air temperature. Among the models, SVM-SMA provided the best accuracy in predicting the soil temperature at depths of 5, 15, and 30 cm, respectively. To improve the ELM performance in estimating the daily soil temperature at depths of 5, 10, 20, 30, 50, and 100 cm, ref. [73] used the SaE algorithm to optimize the parameters of ELM’s hidden node. The input variables included the daily minimum, maximum, and average air temperatures because of their high correlations with soil temperature data at all depths. Despite the desirable behavior of both ELM and SaE-ELM against ANN and genetic programming (GP), the hybrid model showed slightly better performance with a lower mean absolute bias error (MABE) and a higher correlation coefficient (R). Ref. [74] employed a hybrid multi-layer perceptron algorithm integrated with the firefly optimizer algorithm (MLP-FFA) to predict soil temperature at multiple depths, including 5, 10, 20, 50, and 100 cm, using soil depth, periodicity (or the respective month), atmospheric pressure, air temperature, and solar radiation as model predictors. They compared the results with MLP model and found MLP-FFA model had better performance than the standalone MLP model. Ref. [75] employed ENN, which is a type of dynamic recurrent neural network, in combination with the gravitational search algorithm (GSA) and ant colony optimization (ACO) to improve the estimation accuracy of daily soil temperature. The hybrid models, i.e., ENN-GSA and ENN-ACO, exploited optimization algorithms to train the ENN’s parameters. The training data were mean temperature, maximum temperature, minimum temperature, dew point temperature, wind speed, relative humidity, precipitation, sunshine, and soil temperature at depths of 5, 10, 50, and 100 cm, which were used under different scenarios, including temperature-based, other meteorological parameters-based, and combined-based scenarios. Although hybrid models outperformed the classical ENN, the ENN-GSA was identified as the best-performing model at all depths. In addition, the highest accuracy was achieved at the full-input pattern for both standalone and hybrid models.

In spite of the fact that ANNs are suitable models for soil temperature prediction, there are a number of problems related to their application, including the scaling problem, the intensive computational effort, and the local minimum. To address these issues, Gill and [76] developed an ANN-based model boosted by genetic algorithm to predict daily soil temperature at depths of 5, 10, and 30 cm by air temperature and rainfall as well as past soil temperature data. The results showed that the developed model was successful in predicting soil temperature.

Table 4. Studies conducted to estimate soil temperature using hybrid models.

Research	Models	Output	Input	Soil Depth	Performance Criteria	Best Model(s)
[64]	ANFIS, ANFIS-SSA, ANFIS-GOA, ANFIS-mSG, ANFIS-GWO, ANFIS-PSO, ANFIS-GA, ANFIS-DA	Daily soil temperature	maximum, average, and minimum air temperature	10 cm	RMSE, STD, MAE, RMSRE, AAPRE, R2, NSE	ANFIS-mSG
[65]	MLP, ANFIS, MLP-PSO, ANFIS-PSO, ARMA	Daily soil temperature	Average, minimum, maximum, median, standard deviation, coefficient of variation, skewness, kurtosis, first quarter, and third quarter	10, 20 cm	R2, MAE, RMSE, MAPE	ARMA
[66]	MARS, WNN, ANFIS, DENFIS	Land surface temperature	NDVI, NDBI, NDWI, NDBaI, UI, elevation	-	R2, RMSE, MAE	ANFIS
[67]	ANFIS, bi-linear model, hybrid models based on ANFIS, bi-linear, and wavelet analysis	Daily soil temperature	Soil temperature	5, 10, 50, 100 cm	RMSE, MAE, KGE	ANFIS model combined with bi-linear and wavelet analysis
[68]	ANN, ANFIS, GP	Monthly soil temperature	Air temperature, relative humidity, solar radiation, wind speed, month of year, soil temperature at different depths	10, 20, 100 cm	RMSE, MARE, R2, NSE	GP
[69]	ANN, CANFIS, WNN, WCANFIS	Soil temperature	Air temperature	5,10,20,30, 100 cm	NSE, RMSE, CRM	WCANFIS
[70]	ANN, ANFIS, MLR		Air temperature, soil temperature, environmental parameters, soil properties	5, 10 cm	R2, MAPE	ANFIS
[71]	FARIMA, FFBPNN, GEP GEP-FARIMA, FFBPNN-FARIMA	Daily soil temperature	Historical records of soil temperature data	5, 10, 50, 100 cm	RMSE, MAE, RRMSE	GEP-FARIMA
[72]	SVM, MLP, and ANFIS hybridized with SMA, PSO, and SHO	Daily soil temperature	Relative humidity, wind speed, solar radiation, air temperature	5, 15, 30 cm	MAE, RMSE, IS, NSE, R, WIA, radar chart, scatter plots, box-whisker plot, Taylor diagram	SVM-SMA
[73]	ELM, SaE-ELM, ANN, GP	Daily soil temperature	Minimum, maximum, and average air temperature	5, 10, 20, 30, 50, 100 cm	MAPE, RMSE, R	SaE-ELM
[74]	MLP, MLP-FFA	Monthly soil temperature	Soil depth, periodicity (or the respective month), air temperature, atmospheric pressure, solar radiation	5,10,20,50, 100 cm	RMSE, MAE, MAPE, MBE, Taylor diagram	MLP-FFA
[75]	ENN-GSA, ENN-ACO	Daily soil temperature.	Mean temperature, maximum temperature, minimum temperature, dew point temperature, wind speed, relative humidity, precipitation, sunshine hours, soil temperature	5, 10, 50, 100 cm	RMSE, RRMSE, R2, a-20 index	ENN-GSA
[76]	ANN- based model boosted by genetic algorithm	Daily soil temperature	Air temperature, rainfall, past soil temperature data	5, 10, 30 cm	Error value

Abbreviation: Standard Deviation (STD), Root Mean Squared Relative Error (RMSRE), Average Absolute Percent Relative Error (AAPRE), Kling-Gupta Efficiency (KGE), Coefficient of Residual Mass (CRM), Relative RMSE (RRMSE), Mean Bias Error (MBE).

presents a list of studies conducted to estimate soil temperature using hybrid models.

Ultimately,

Table 5. Strengths and weaknesses of different ML-based models [42,77,78].

Model	Strength	Weakness
ANN	Easy to implement Few parameters Relatively low computational cost Able to learn the multivariate non-linear relationships	Sensitive to dimensionality of data Need for preliminary setting of neurons and functions easy falling into local optima Lack of considering spatiotemporal patterns of data scaling problem
DL	Highly effective for complex applications Able to learn complex underlying patterns in data Flexible to data variations over time and space Strong computing power High computational speed	Difficult to interpret High computational cost Large dataset requirement
Kernel-based	Highly effective for data classification Handling non-linear relationships Handling high dimensional data High accuracy Preventing overfitting	Sensitive to kernel function Parameter tuning requirement Computationally expensive for large datasets High memory usage
Hybrid	Improving retrieval accuracy Able to handle complex systems with large dataset requirement Flexibility Robustness	High computational requirements Increased complexity Selecting the suitable algorithms

summarizes the weaknesses and strengths of different ML-based models to make a comparison as follows:

3. Input Dataset

Three general categories of input variables are used to train ML-based models, including climate data, time series of soil temperature, and a combination of soil temperature time series and climatic data. Climate variables applied to ML models are relative humidity (average, maximum, and minimum), solar radiation, wind speed, air temperature (average, maximum, and minimum), vapor pressure deficit, sunshine hours, precipitation, dew point temperature, potential evapotranspiration, evaporation, atmospheric pressure, and cloudiness. According to the studies, air temperature was identified as the most effective variable in predicting soil temperature [20,28,31,50,70,73]. The importance of climate variables such as solar radiation, relative humidity, precipitation, and soil moisture is disputed between different studies; this may be because the effect of moisture on soil temperature varies with the soil depth and the type of climate. However, most studies demonstrated that both relative humidity and solar radiation are more effective than other variables [28,31,40,50]. Moreover, [58] showed a significant correlation between soil temperature and soil moisture than soil temperature and precipitation.

The models using climate parameters are less effective at greater depths, where aboveground climate has a decreased impact and the effect of previous temperatures is correspondingly increased. It can be due to the relationships between climate parameters and soil temperature change with the soil depth. Therefore, the inclusion of periodicity (number of days, months, and years) as another input variable led to a considerable improvement in estimation accuracy, especially at deeper soil depths [20,61,68]. In addition, combining current climate conditions with temporal information is recommended for the best results for deep soil temperature predictions [24,51].

4. Conclusions and Future Outlook

Soil temperature is a key factor affecting the physical, chemical, and biological properties of soil. In addition to meteorological variables, soil temperature depends on topographic conditions and soil characteristics. The complex interactions between these variables make the estimation of soil temperature challenging.

Direct measurement of soil temperature by instruments such as thermistors, thermocouples, and thermocouple wires on a large spatial scale is impractical because it is an expensive and time-consuming process. Therefore, soil temperature is mainly estimated using physically and statistically based models with a tradeoff between resolution, accuracy, and computational efficiency.

Physically based models, despite their wide use in soil temperature estimation, are complex with intense data requirement. On the other hand, the empirical approach is a simple method that requires less input data; however, the statistical regression-based relationship between input and output is site dependent. The limitations of the above methods led to the development of data-driven ML techniques, such as ANN, DL, and SVM, to estimate the soil temperature at multiple depths.

ANNs, as the most widely used data-driven models, are capable of capturing nonlinear data trends but these models are used to extract single data features without learning spatiotemporal patterns. DL techniques can address this issue by increasing the depth of neural networks. However, the prediction accuracy may decrease as a result of an inadequate sample size of the input data. Although the use of kernel function embedded models such as SVMs ensures a global optimum, the selection of kernel functions restricts their application. These traditional ML models have some drawbacks, including ANN’s low generalization performance, ANFIS’s need for accurate weighting of the membership function, ELM’s large training datasets requirement, and SVM’s high sensitivity to hyper-parameter selection, which limit their applications.

The best ML technique for soil temperature retrieval generally depends on training datasets, model structure, and target level of accuracy. Based on studies carried out to estimate soil temperature, DL models, such as BiLSTM and LSTM, showed better performance than other models. After that, ANFIS exhibited the best performance followed by SVM, WNN, ELN, and ANN. On the other hand, most studies found that hybrid models, which are mostly standalone models boosted by optimization algorithms, were superior to classical models. In addition to hybrid models with optimization schemes, a new generation of standalone AI-based models has the potential to offer promising alternatives to traditional models because of their flexibility.

In addition, combining current climate conditions with time information is necessary for the best results, especially for deep soil temperature predictions. In this regard, improving both machine learning and statistical methods to account for periodicity increases the accuracy of the soil temperature prediction. If modeling for deeper soil depths can be brought up to the standard currently achieved by models for shallow depths, it may be possible to reduce the number of climate variables needed as input. This can simplify the process of soil temperature prediction and make the models more generalizable to different climates. For this purpose, there are several approaches. The simplest approach is to add the month to the set of input climate variables. This method should be easy to implement for any model using the current climate conditions for prediction. It relies on seasons being relatively consistent in terms of temperature and timing from year to year. Another approach is the sliding window approach, which uses climate variables from previous time steps as the additional input variables. The current conditions are, thus, situated in a broader context in time without any assumptions about the season. The sliding window approach relies on choosing a window that is appropriate for the lag time between climate conditions and their effect on soil temperatures. In complex models, lag times between climate variables and soil temperatures may not be the same, nor may lag times between a variable and soil temperatures at different depths. Future studies should address these issues. Moreover, remote sensing observations of soil properties such as moisture content and vegetation cover can be combined with machine learning models as a future perspective to achieve more accurate soil temperature estimation. In addition, the transferability of models over different regions and climates can be more explored to determine the effective factors on the model’s performance in soil temperature retrieval across various soil types and climates.