RESEARCH ARTICLE

 

Estimation of soil temperature for agricuitural applications in South Africa using machine-learning methods

 

 

Lindumusa Myeni^{I, II}; Tlotlisang Nkhase^III; Ramontsheng Rapolaki^{IV, V}; Zaid Bello^{VI, VII}; Mokhele E. Moeletsi^{III, VII}

^IUnit for Environmental Sciences and Management, North-West University, Potchefstroom, South Africa
^IIDepartment of Geography and Environmental Studies, School of Geo- and Spatial Sciences, North-West University, Mahikeng, South Africa
^IIIAgricultural Research Council - Natural Resources and Engineering, Pretoria, South Africa
^IVSouth African Weather Service, Marine Research Unit, Cape Town, South Africa
^VDepartment of Geography, University of the Free State, Bloemfontein, South Africa
^VIAgricultural Research Council - Grain Crops, Potchefstroom, South Africa
^VIICentre for Global Change, University of Limpopo, Sovenga, South Africa

Correspondence

 

 

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ABSTRACT

This study was undertaken to investigate the potential of using machine-learning approaches as alternative and cost-effective tools for estimating soil temperature from readily available meteorological data for agricultural applications in South Africa. Four machine-learning models - multiple linear regression, artificial neural networks, random forest and decision tree - were developed and tested to estimate daily soil temperature at six soil depths (viz. 10, 20, 30, 40, 60 and 80 cm) using meteorological data acquired from seven stations, representing diverse climatic conditions in South Africa. The data were randomly split into two parts: the first 80% of the data set was used for training, while the remaining 20% was utilised to validate the models. The results showed that soil temperature at various depths can be reasonably estimated by different generic machine-learning models, with average Nash-Sutcliffe efficiency values ranging from 0.74 for decision tree to 0.87 for random forest models and root mean square error values of less than 2.79 °C for all models. Among the evaluated models, random forest models showed the highest estimation accuracy across different soil depths and climatic conditions, with average Nash-Sutcliffe efficiency values ranging from 0.87 to 0.95. This study indicated that the performance of climate-specific models was better than that of the aggregated ones. Therefore, it is recommended that machine-learning approaches, particularly RF models, be developed for specific climatic conditions where possible to achieve better soil temperature estimations. The developed models can be applied with caution in other regions with similar climatological and pedological properties.
SIGNIFICANCE:
• This study evaluated the performance of four machine-learning models in estimating daily ST at six depths using meteorological data in diverse climatic conditions in South Africa.
• The results showed that ST at various depths can be reasonably estimated using different machine learning models, although the performance of climate-specific models was better than that of the aggregated ones.
• Among the evaluated models, RF models had the highest estimation accuracy across different soil depths and climatic conditions.

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Introduction

Soil temperature (ST) is a fundamental parameter that governs the exchange of heat, moisture and energy at land-atmosphere interfaces.¹ It also influences or governs the belowground physical, chemical and biological processes of soil, such as soil respiration, soil heat and mass transport properties, soil moisture content, microbial activity, pedogenic processes, chemical reactions, organic matter storage and mineralisation.^2-5 Furthermore, ST controls the thermodynamic equilibrium between the liquid, solid and gas phases in the pedosphere and subsequently influences the transport and fate of chemical contaminants as well as greenhouse gases.⁶ Consequently, sT plays a critical role in crop growth and may have more influence than air temperature in most cases.⁷ Specifically, the thermal conditions of the soil largely affect seed germination, root development, nutrient transformation and uptake, plant growth and crop yields.^7,8 Therefore, information about ST is crucial to inform decisions on several agricultural activities, such as the proper design of drainage and irrigation systems, selection of appropriate planting dates and optimum utilisation of pesticides and fertilisers to reduce soil and groundwater pollution.^6,9

Previous research has shown that ST varies with depth, with fluctuations in deeper layers being smaller than those near the soil surface due to their greater thermal memory and reduced sensitivity to short-term climatic variables.¹⁰ The primary drivers of ST are air temperature and solar radiation, while the secondary drivers are soil texture, soil colour, soil moisture content, thermal properties of soil (e.g. specific heat capacity and thermal conductivity), bulk density, evaporation from the soil surface, soil surface albedo and land cover.^1,6,11

There is a growing need for accurate ST information at high temporal and spatial resolution due to its vital role in precision agriculture and climate change adaptation.^1,2,11-14 Traditionally, ST is measured using costly and labour-intensive approaches such as thermometers, soil heat flux, time-domain reflectometry, ground-penetrating radar, thermocouples, thermistors and gamma attenuation.^4,10,12,15 Although in situ measurements provide the most accurate ST data, they only provide point measurements that do not account for spatial variability, which is essential for various agricultural purposes and many other related applications.¹⁶ Despite recent technological advancements in sensors and devices, establishing, operating and maintaining uniformly distributed station networks for in situ measurements of ST remain very expensive.¹⁷ Consequently, in situ measurements of ST at various depths are not readily available from most of the standard weather stations and are often restricted to short-term research sites with limited spatial coverage.^2,6,14,18-20 The scarcity of long-term, high-quality ST data is prominent in developing countries due to financial constraints.¹¹ Consequently, ST is often estimated indirectly using modelling and remote-sensing approaches.^2,12,16,21

Although remote-sensing approaches provide valuable ST estimates with high spatial resolution and at a relatively lower cost, their major limitation is that only a few centimetres (2-7 cm) of soil depth are sensed from satellites.^6,16 This limits the applicability of remote-sensing approaches in providing continuous ST estimates at different soil depths that are required for operational purposes, especially in areas with deep agricultural soils. As an alternative, ST is often estimated from readily available or easily measured variables such as solar radiation, air temperature and soil properties using modelling approaches.^2,6,16 It is worth noting that the complexity, data input requirements and levels of accuracy vary with different models.^2,22

Generally, models for estimating ST can be divided into two categories. The first category is mechanistic models that are based on the physical processes of energy balance and heat transfer.^4,14 However, mechanistic models are complex and data intensive, which limits their applicability for operational purposes, especially in data-scarce countries.¹² The second category is empirical models that are based on correlations with the readily available or easily measured variables using statistical methods.²² Considering that the correlations between explanatory variables and ST may not be linear, some advanced artificial intelligence methods have been successfully used to estimate ST at different depths in various countries across the world.^{4,5,12-14,19,23,24} For regions facing data constraints, the development and evaluation of alternative approaches for estimating ST using readily available data are crucial for various applications in sectors such as agriculture, environmental monitoring and management, construction and infrastructure as well as hydrology and water management.^14,19,25 In this context, machine-learning approaches have been widely proposed as cost-effective and efficient alternatives for accurate estimation of ST at different depths by developing a non-linear relationship between ST and readily available meteorological variables using data from standard weather stations.^{4,12,13,19,23}

To our knowledge, few studies have investigated the possibilities of using machine-learning methods in predicting ST in Africa, particularly in the southern African region, which is widely described as one of the major hot spots for climate change²⁶, where, in turn, the need for accurate ST estimates for the full profile at high spatial resolution is imperative to support sustainable agricultural production under changing climatic conditions in this region. The availability of continuous in situ measurements of ST acquired for at least a 2-year period at some stations of the Agricultural Research Council (ARC) that represent a wide range of South African soil types and climatic conditions provided a distinctive opportunity to investigate the applicability of machine-learning methods in estimating ST in this region. Therefore, this study aimed to assess the performance of selected machine-learning approaches, ranging from simple multiple linear regression to sophisticated techniques for estimating daily ST at different depths using meteorological data in diverse climatic conditions for agricultural applications in South Africa.

The first objective of this study was to evaluate the performance of four machine-learning models - namely multiple linear regressions (MLR), artificial neural networks (ANNs), random forests (RF) and decision trees (DTs) - in estimating daily ST at six depths across different climatic zones in South Africa. The second objective was to explore the effects of different climatic factors on the performance of each model for estimating ST. This study is expected to guide the selection of the most suitable machine-learning approaches that can be applied for accurate estimation of ST at different climatic conditions from readily available data in this region. This study is anticipated to be one of the first in this region that will contribute towards the development of improved ST forecasts, which are critical to inform efficient planning and decision-making in precision agriculture and many other related applications.

 

Study site description

Seven stations of the ARC were selected to develop and evaluate the performance of selected machine-learning approaches (Figure 1). These stations represent four different agro-climatic zones based on the Köppen-Geiger climate classification, namely BSk (arid, steppe and cold), Cwb (temperate, dry winter and warm summer), BSh (arid, steppe and hot) and Cfa (temperate, without dry season and hot summer).²⁷ Detailed characteristics, climatic conditions and periods of available daily data from each station are presented in Table 1. The selection of these stations was based on the availability of quality ST data at different depths and corresponding meteorological data. All selected stations are located in agricultural lands where ST information is crucial for precision agriculture as climate variability and change continue to threaten the sustainability of agriculture in this region.

 

Methods and materials

Selected machine-learning models for soil temperature estimation

Four selected machine-learning approaches for ST estimation (i.e. MLR, ANN, RF and DT) were evaluated. The selection of these approaches was based on their different structures, learning processes, complexity levels and assumptions. Moreover, these selected machine-learning approaches have been successfully applied over a wide range of climatic conditions across different countries.^4,6,23 Brief descriptions of the machine-learning approaches that were used for the estimation of ST in this study are provided in the supplementary material.

Data collection and processing

Daily measurements of ST at six different depths (viz. 10, 20, 30, 40, 60 and 80 cm), along with minimum air temperature (T_min in °C), maximum air temperature (T_max in °C), solar irradiance (R_s in MJ/m²), wind speed (U in m/s), minimum relative humidity (RH_min in %), maximum relative humidity (RH_max in %) and rainfall (mm) at each station, were extracted from the ARC databank (https://www.agroclimate.agric.za/WP/Wp/). Detailed information regarding the climate databank of ARC and the measurement descriptions has been reported by Moeletsi et al.²⁹

The retrieved data underwent a data quality control process to examine for missing values, rate of change, consistency, extreme values and sensor drift, as well as to identify and remove erroneous, suspicious and improbable values, following the procedures of Allen et al.³⁰ and Myeni et al.³¹ Only data sets that passed our quality check were used for the evaluation of selected machine-learning approaches in this study.

Training and testing of models

The selected machine-learning approaches were trained and evaluated for two different scenarios. For each soil depth, all ST data were grouped, regardless of climatic zones, and then used to train and test generic models for specific depths (Scenario 1), which are hereafter referred to as aggregated models. Furthermore, all ST data from the same depth and climatic zone were grouped and then used to train and test models for specific climatic zones and depths (Scenario 2).

The meteorological data were standardised by subtracting the mean and scaling to unit variance, as machine-learning approaches perform better when numerical variables are scaled to the standard range, following a similar procedure as Gómez-Escalonilla et al.³² Under each scenario, the data set was split into two parts randomly: the first 80% of the data set was used for training, while the remaining 20% of the data set was utilised for testing the models. All model training and predictions for this study were carried out using the Scikit-learn package in the Python programming language. A systematic process was used to test pairwise and higher-order combinations of different explanatory variables (meteorological variables). Only the combinations that computed the best output for each model were selected based on the highest adjusted coefficient of determination (r²).^5,23,24 After this exercise, rainfall and wind speed (U) were eliminated from input variables, as they had no significant influence on the outputs of the models at a 95% significance level.

Statistical analysis

The root mean square error (RMSE, °C), mean absolute error (MAE, °C), Nash-Sutcliffe efficiency (nSe) and concordance correlation coefficient (CCC) were used to evaluate the performance of the model for the estimation of ST (°C) at different depths and were calculated using the following equations:

where i is the data pair index, n is the number of observations, ST_e (°C) is the estimated ST from the model, ST₀ is the observed ST, ST₀ is the mean of ST_o, ST_e is the mean of S T_e, p is the correlation coefficient between the two variables, and σ_o and σ_e are the variances of S T_o and ST_e, respectively. A linear regression between ST_e and ST_o values was also computed:

where the slope (m) was used as a measure of accuracy and c (°C) is the y-intercept. The coefficient of determination (r²) was considered as a measure of precision. Based on these statistics, RMSE, MAE and c values approaching 0, and NSE , CCC , r² and m values approaching 1, indicate better model performance.⁴

 

Results and discussion

Description of meteorological and soil temperature data

The descriptive statistics of daily meteorological and ST data used for the training and testing of the machine-learning models are provided in Table 2. The results showed that ST at a 10 cm depth ranged between 4.80 °C and 39.50 °C with a mean of 21.26 °C, while at an 80 cm depth, it varied between 8.50 °C and 34.60 °C with a mean of 21.51 °C.^13,18 Furthermore, the results also showed that the standard deviations of ST decreased with soil depths, thereby suggesting the minimal variability of temperatures at deeper soil layers compared to surface layers due to the substantial effects of atmospheric conditions on ST at topsoil layers, as also reported in previous studies.^6,14,15,18 Nevertheless, the data illustrate diverse climatic conditions which are crucial for developing and testing machine-learning models that are efficient in estimating ST at various depths over diverse climatic regions.

Correlation analysis between weather variables and soil temperature at different depths

The results of the average correlations between weather variables and ST at various depths across all stations are presented in Figure 2. The results show that ST at different depths is highly correlated with air temperature, particularly with T_min and T_max. Furthermore, the results also indicate that R_s had a significant and positive correlation with ST and emerged as the second most influential variable after air temperature, supporting the findings of previous studies.^11,13,23 This finding is probably due to R_s being the major source of soil heat and energy required for soil evaporation. Thus, high evaporation rates due to greater R_s result in drier and warmer ST. In addition, rainfall, relative humidity and wind speed were not significantly correlated with ST at any depth (p < 0.05), as has been found in previous studies.^18,23

The results of this study are in agreement with those of previous studies, confirming that the influence of meteorological variables on ST gradually decreased with soil depth.^13,14,18,20 For example, the correlation of T_max with ST reduced from 0.78 at a depth of10 cm to 0.64 at 80 cm.^13,14,18,20 The significant correlations between weather variables and ST at various depths indicate that these variables could be used confidently as predictors of ST.

Evaluation of machine-learning models

Comparison of the selected machine learning models at different depths

Generic models were developed following the procedure explained for Scenario 1 under 'Data collection and processing' section. Overall, the results indicated that relationships between observed and estimated STs at various depths by different machine learning models were reasonable, with average NSE values ranging from 0.74 for DT models to 0.87 for RF models and RMSE values of less than 2.79 °C for all models (Figures 3-6; Table 3). The average MAE values ranged from 1.50 °C for RF models to 2.06 °C for DT models. The scatter plots illustrated that all the generic models tended to overestimate low ST and underestimate high temperatures, although the overall agreement between observed and estimated ST was reasonable.

The NSE values ranged between 0.79 and 0.90 for the topsoil (10 cm), while for the bottom layers (80 cm), they ranged between 0.69 and 0.84, while the RMSE and MAE values varied for different models and were not statistically different across the depths. This suggests that the efficiency of all generic models decreased with the increase in soil depth. Generally, soil moisture content increases with soil depth; therefore, higher-than-expected moisture in deep soil layers may have reduced the correlations between meteorological variables and ST, leading to relatively lower model predictability.¹⁵ Moreover, the relatively high accuracy of the evaluated models at topsoil layers could be due to high correlations of meteorological variables with ST at the surface compared to deeper soil layers, supporting the findings of previous studies.^{4,11,14,19,20,24} However, this study contradicts some of the previous studies that reported the increased performance levels of the machine learning models with soil depth. These studies argued that this was mainly due to a stronger memory of the ST at deeper soil layers as a result of the minimal influence of surface meteorological conditions, which in turn increases its predictability.^12,14,15

The results further showed that the RF and ANN models performed better than the MLR and DT models at multiple depths, which is consistent with other previous studies.^1,15,20 However, RF models showed better performance than ANN models at most soil depths,

with NSE values ranging from 0.84 to 0.90 compared to 0.83 to 0.89 for the ANN models. These findings suggest that RF models had the highest estimation accuracy among the evaluated generic models across different soil depths. On average for the temperature of the whole soil profile, the RF exhibited the lowest RMSE (1.98 °C) and MAE (1.50 °C) and the highest CCC (0.93) and NSE (0.87), outperforming the rest of the models.^1,15,20 The DT models showed relatively poor efficiency, particularly for estimating ST at deeper soil layers (below 30 cm), with NSE values of less than 0.75.¹⁴ Furthermore, this study confirmed that the MLR models had limited capabilities of capturing non-linearity between meteorological variables and ST due to their simple and linear structures.^5,14 These findings are in accordance with those of previous studies that have reported that the performances of the different machine-learning approaches vary with their structures, learning capabilities and prediction power.^14,23,24

Comparison of the selected machine-learning models at different climatic zones

The generic models were developed for specific climatic zones following the procedure explained for Scenario 2, under 'Data collection and processing' section. The average performances of each machine learning model at different climatic zones are presented in Table 4. Detailed information on the performance of the climate-specific models per depth is presented in Supplementary table 1.

Among the evaluated models, RF had the highest estimation accuracy across different climatic zones, with average NSE values ranging from 0.90 (BSk and Cfa) to 0.95 (Cwb), and average RMSE values varying between 1.06 °C (BSk) and 1.74 °C (Cwb). These findings demonstrate the capability of the RF model in providing accurate estimates of ST across a wide range of climatic zones (i.e. arid and humid) in this region. In contrast, among the evaluated models, DT gave the worst performance in the estimation of ST across different climatic zones, with average NSE values ranging from 0.80 to 0.89 and RMSE values varying between 1.46 °C and 2.33 °C.

In accordance with the findings of Dong et al.¹¹ and Bayatvarkeshi et al.²⁴, our results show that the accuracy of models varies across different climatic conditions, with better model performance observed under temperate, dry winter and warm to hot summer climatic conditions (Cwb and Cfa) compared to cold or hot semi-arid zones (BSk and BSh). The better model performances in subtropical climatic conditions could be attributed to smaller differences between soil and air temperatures, which led to stronger correlations and improved model predictions.^15,24 The variation of model performances across different climatic zones could be attributed to the capabilities of specific models in capturing the influence of dominating factors, such as weather conditions, geographical and environmental factors as well as soil properties on St in certain regions.^11-13 Although machine-learning models are black boxes and lack explicit scientific principles (e.g. physical processes of heat transfer), the results show that the direction of error in ST estimates with depth varies by region. This is probably due to the dominance of morphological and climatic factors influencing ST variations in specific regions as well as the learning capabilities of the model used.

Implications and applicability of the study

Our findings show that the accuracy of ST estimates by generic models decreases with soil depth, probably due to the influence of soil physical properties and the relatively low correlation of meteorological variables in deep soils. This suggests that including soil properties such as soil organic matter, soil texture and soil water content could improve the accuracy of ST estimates at deeper layers.¹¹ Our findings demonstrate that ST at different depths could be reliably estimated from meteorological data using machine-learning approaches and RF should be prioritised for more accurate estimates.

The accuracy of models varies across different climatic conditions, with better model performances observed under subtropical climatic conditions. This suggests that the characteristics and predictability of ST vary across different climatic zones, limiting the transferability of machine-learning models across different regions with distinct physiographic conditions, mainly in terms ofclimatological and pedological properties.¹⁴ Our findings also indicate that the overall performance of climate-specific models was better than that of the aggregated ones. This suggests that machine-learning models, particularly RF, should be developed for specific climatic conditions where possible for better ST estimations. Given that local models are more accurate (presented in Supplementary table 2), the development of station-specific RF models will be beneficial for the gap-filling of ST data using readily available climate data from stations at locations facing data discontinuity.

Although air temperatures and R_s were key factors influencing ST the findings of this study confirm that including other meteorological factors (high and low correlation variables) as inputs improved the accuracy of the machine-learning models.^11,14 However, the explanatory variables should be selected with caution to avoid overfitting, reduce unnecessary data input and maintain low model efficiency, due to the complex relationships between the inputs and output caused by irrelevant variables. Given that machine-learning models are highly sensitive to the training data, it is crucial to develop more robust models for accurate estimation of ST using long-term, large data sets from multiple agro-climatic conditions.

For agricultural applications, the next logical step will be to develop and validate an RF-based model to estimate ST in the field, using standard meteorological data acquired from the nearby weather station. From these ST estimates, various indices with implications for precision agriculture can be computed and used to inform decision-making (e.g. suitable planting dates) within the context of sustainable agriculture and climate adaptation. Although the focus of this study was on estimating ST for agricultural applications, its findings can be useful to inform the choice of the most suitable machine-learning approaches that can be applied for accurate estimation of ST for various other applications.

 

Conclusions

This study was undertaken to evaluate the performance of four machine-learning models as alternative and cost-effective tools for estimating daily ST at six depths from meteorological data in diverse climatic conditions for agricultural applications in South Africa. The results show that air temperature and R_s were the key variables influencing the variability of ST and their effects gradually decreased with soil depth. The results also show that the accuracy of ST estimates by aggregated models decreases with soil depth due to the influence of soil physical properties and the relatively low correlation of meteorological variables at deeper soil layers. The results reveal that the accuracy of models varies across different climatic conditions, and better model performance was observed under subtropical climatic conditions due to minimal differences between ST and air temperature.

The findings of this study demonstrate the capabilities of RF models in providing reasonable estimates of ST over diverse climatic conditions for agricultural and related applications in South Africa. The findings also show that the characteristics and predictability of ST vary across different climatic zones, limiting the transferability of machine-learning models across different regions. This suggests that, although generic models provided acceptable results in predicting ST, the use of local or climate-specific models should be prioritised for more accurate estimates. Given the continuous evolution of machine-learning approaches with improved capabilities, it is recommended that the efficiency of other new and innovative machine-learning models be explored. Therefore, the continuous development and testing of new machine-learning approaches using large data sets from various climatic regions are recommended for improved ST estimates. Despite that, machine-learning techniques such as RF are promising approaches for the provision of reliable ST estimates that are crucial to inform efficient planning and decision-making for precision agriculture and many other applications where ST information is essential. Due to the range of climatic conditions in which these models were developed and validated, they can be applied with caution in other regions with similar climatological and pedological properties.

 

Acknowledgements

The ARC-Natural Resources and Engineering is gratefully acknowledged for providing data.

 

Funding

Funding from the South African National Research Foundation (grant no. CSRP230503101419) is gratefully acknowledged.

 

Data availability

The data supporting the results of this study are available upon request to the corresponding author.

 

Declarations

We have no competing interests to declare. We have no AI or LLM use to declare.

 

Authors' contributions

L.M.: Conceptualisation, methodology, software, validation, formal analysis, writing - original draft preparation, writing - review and editing. T.N.: Methodology, software, validation, formal analysis, writing -original draft preparation, writing - review and editing. R.R.: Validation, writing - review and editing. Z.B.: Validation, writing - review and editing. M.E.M.: Validation, writing - review and editing. All authors read and approved the final manuscript.

 

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Correspondence:
Lindumusa Myeni
Email: lindumusa.myeni@nwu.ac.za

Received: 19 Mar. 2024
Revised: 09 Apr. 2025
Accepted: 09 Apr. 2025
Published: 29 May 2025

 

 

Editors: Jennifer Fitchett, Pfananani Ramulifho
Funding: South African National Research Foundation (CSRP2330503101419)

 

 

Supplementary Data

The supplementary data is available in pdf: [Supplementary data]