IMPROVING NEAR-SURFACE SOIL TEMPERATURE ESTIMATION USING EMPIRICAL AND NUMERICAL METHODS IN CROP-COVERED SURFACES

IMPROVING NEAR-SURFACE SOIL TEMPERATURE ESTIMATION USING EMPIRICAL AND NUMERICAL METHODS IN CROP-COVERED SURFACES | Authorea try { document.documentElement.classList.add('js'); } catch (e) { } var _gaq = _gaq || []; _gaq.push(['_setAccount', 'G-8VDV14Y67G']); _gaq.push(['_trackPageview']); (function() { var ga = document.createElement('script'); ga.type = 'text/javascript'; ga.async = true; ga.src = ('https:' == document.location.protocol ? 'https://ssl' : 'http://www') + '.google-analytics.com/ga.js'; var s = document.getElementsByTagName('script')[0]; s.parentNode.insertBefore(ga, s); })(); Skip to main content Preprints Collections Wiley Open Research IET Open Research Ecological Society of Japan All Collections About About Authorea FAQs Contact Us Quick Search anywhere Search for preprint articles, keywords, etc. Search Search ADVANCED SEARCH SCROLL This is a preprint and has not been peer reviewed. Data may be preliminary. 9 April 2026 V1 Latest version Share on IMPROVING NEAR-SURFACE SOIL TEMPERATURE ESTIMATION USING EMPIRICAL AND NUMERICAL METHODS IN CROP-COVERED SURFACES Authors : Thiago Duarte 0000-0002-8471-104X [email protected] , Xue-Jun Dong 0000-0003-3072-1901 , Edna Maria Bonfim-Silva , and Tonny da Silva Authors Info & Affiliations https://doi.org/10.22541/au.177574758.84614799/v1 33 views 31 downloads Contents Abstract Supplementary Material Information & Authors Metrics & Citations View Options References Figures Tables Media Share Abstract Soil temperature as an important variable in both agricultural and natural systems, influences numerous biophysical processes. Interest in simulating soil temperature remains strong, particularly when working with large areas at high temporal and spatial resolution. In this study, a method was proposed that integrates an empirical approach for estimating soil surface temperature with an explicit finite difference solution of the heat conduction equation. Two additional approaches were also evaluated for comparison. Thermal diffusivity was estimated using (i) a simple linear function and (ii) a pedotransfer function. Soil temperature was measured at a depth of 10 cm in a fully developed sesame crop field using a capacitance-based soil moisture and temperature probe. Simulations were performed at an hourly step scale, and model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Bias, and the Kling–Gupta Efficiency (KGE). The numerical method outperformed both empirical approaches, even after calibration. Considering both thermal diffusivity methods, performance metrics for the numerical approach were 0.92 (RMSE), 0.68 (MAE), -0.29 (Bias) and 0.88 (KGE). The empirical methods showed similar performance to each other but inferior results overall. After calibration, the empirical models showed slight improvement but remained inferior to the numerical method. In general, model performance was better when using the simple linear equation to estimate thermal diffusivity; however, the numerical method was less sensitive to the thermal diffusivity estimation. In conclusion, the proposed numerical method proved to be suitable for estimating near-surface soil temperature under vegetated conditions. IMPROVING NEAR-SURFACE SOIL TEMPERATURE ESTIMATION USING EMPIRICAL AND NUMERICAL METHODS IN CROP-COVERED SURFACES Abstract Soil temperature as an important variable in both agricultural and natural systems, influences numerous biophysical processes. Interest in simulating soil temperature remains strong, particularly when working with large areas at high temporal and spatial resolution. In this study, a method was proposed that integrates an empirical approach for estimating soil surface temperature with an explicit finite difference solution of the heat conduction equation. Two additional approaches were also evaluated for comparison. Thermal diffusivity was estimated using (i) a simple linear function and (ii) a pedotransfer function. Soil temperature was measured at a depth of 10 cm in a fully developed sesame crop field using a capacitance-based soil moisture and temperature probe. Simulations were performed at an hourly step scale, and model performance was evaluated using Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Bias, and the Kling–Gupta Efficiency (KGE). The numerical method outperformed both empirical approaches, even after calibration. Considering both thermal diffusivity methods, performance metrics for the numerical approach were 0.92 (RMSE), 0.68 (MAE), -0.29 (Bias) and 0.88 (KGE). The empirical methods showed similar performance to each other but inferior results overall. After calibration, the empirical models showed slight improvement but remained inferior to the numerical method. In general, model performance was better when using the simple linear equation to estimate thermal diffusivity; however, the numerical method was less sensitive to the thermal diffusivity estimation. In conclusion, the proposed numerical method proved to be suitable for estimating near-surface soil temperature under vegetated conditions. Key words: pedotransfer function, energy balance; finite difference method; numerical modelling; thermal conductivity INTRODUCTION Soil temperature is an important factor influencing numerous biological and physical processes in crops and natural systems, such as soil respiration, microbiological activity, soil water potential, root development, among others. It is used as an input parameter in many mathematical models with energy balance applications (Holmes et al. 2008) or in hydrological models that consider its effects on root water uptake (Ni et al. 2019). The dynamics of soil temperatures depend on soil depth and are strongly influenced by soil type, soil moisture, relief and surface cover. For instance, bare soil undergoes much wider temperature fluctuations than covered soil. For example, at 10 cm depth, diurnal temperature fluctuations exceeding 20 °C have been reported for bare soils, whereas amplitudes typically ranging from 10–15 °C was observed in tree-covered soil (Ni et al. 2019). Daily peak temperatures under dry soil conditions can be, on average, 7.1 °C lower beneath tree canopies than in the air, and around 4 °C higher in grassland soils than in the air (Lozano-Parra et al. 2018). Although soil temperature is important and relatively easy to measure using specific sensors or sensors associated with soil water content, difficulties may arise when dealing with large amounts of data, particularly over extensive areas, where measurements can become impractical due to cost or labor constraints. In such scenarios, a common alternative is to model soil temperature using physical, empirical, or hybrid approaches, as noted by Liang et al. (2013). In this context, near-surface soil temperature has frequently been estimated using empirical approach, such as one developed by Zheng et al. (1993), which estimates soil temperature based on air temperature and the Beer–Lambert law of attenuation of light intensity in a medium. The model introduced by Zheng et al. was first used to estimate daily soil temperature at 10 cm depth at continental scales across the United States. Later, the model was adapted by Kang et al. (2000) to predict daily spatial patterns of soil temperature at the same depth in a forested landscape with different types of cover. Kätterer and Andrén (2009) introduced additional parameters to the Kang et al. (2000) model to partition the attenuation factor into an LAI-dependent component and an independent component. Moreover, they proposed a new approach to estimate soil surface temperature (z = 0) based on air temperature and the light attenuation caused by leaf area index through the Beer–Lambert law. The empirical models mentioned above have been applied with relatively acceptable levels of accuracy, with errors lower than 3.0 °C reported by Liang et al. (2013). However, although these studies mainly focused on large-scale estimation, often with direct applications in remote sensing, some inconsistencies have been reported. For example, Paul et al. (2004) found underestimations of up to 5 °C in forested areas. In this study, we propose that near-surface soil temperature of vegetation covered areas can be estimated more accurately using the original model proposed by Kätterer and Andrén (2009) combined with a simple explicit finite-difference method. As a demonstration, soil temperature at 10 cm depth was estimated on an hourly scale in a sesame crop field, with superior results compared with previous approaches. MATERIALS AND METHODS Locality and field measurements The study was carried out in a center pivot field at the Texas A&M AgriLife Research and Extension Center at Uvalde in 2015. The local soil is Fine-silty, mixed, active, hyperthermic Aridic Calciustoll (https://soilseries.sc.egov.usda.gov/OSD_Docs/U/UVALDE.html), and the climate is classified as Humid Subtropical climate (Cfa) according to the Köppen climate classification system. Seeds of three sesame varieties (S28, S32, and S36 provided by Sesaco Co., San Antonio, Texas, USA) were planted with 101 cm of row spacing, directly on wheat stubble on 7/16/2015 (about 50 days after the harvest of a wheat crop) in the northeast quarter of the 20-ha center pivot field. The crops were managed under full- and deficit irrigation regimes, but only data from selected full-irrigation plots were used in this study. Sesame was harvested on 10/25/2015. During the growing season, soil temperature and soil water content measurements at 10 cm depth were performed using a set of 5-TM soil sensors (Decagon Devices, Inc. Pullman, WA, USA) from 09/02/2015 to 10/25/2015 in two full-irrigated plots planted with variety S36 and S28 and the data was recorded with EM-50 dataloggers (Decagon Devices, Inc. Pullman, WA, USA) at 30-minute intervals and later averaged to 1-hour intervals. During the crop cycle, LAI was measured four times (representing the growth stages of early bloom, late bloom, initial dry down, and late dry down) using a destructive sampling method. In each measurement, three plants were chosen randomly from within a 0.28 ha plot area and different organs such as leaves, stems and reproduction structures were separated and the one-sided leaf area was measured using a LI-3100 Area Meter (LI-COR, Inc., Lincoln, NE, USA). Then, biomass of different types of organs was measured after oven-drying. The relationship between the leaf dry weight and specific leaf weight was determined, and then the total leaf area and LAI were calculated. An exponential model was fitted to the LAI data, as shown in equation 1. During the soil temperature measurement period, leaf area index (LAI) changed from 4.86 to 1.49 m 2 m -2 (Fig. 1). \(\text{LAI\ }_{\text{sesame}}=\ 5.191\times exp\left\{-0.5\left[\ln\left(\frac{\frac{\text{DAP}}{58.486}}{0.376}\right)\right]^{2}\right\}\) 1 where DAP represents days after planting (day). Fig. 1 Seasonal variation of leaf area index in a sesame field at Uvalde, Texas in 2015. The vertical dashed lines represent the time period during which the soil temperature was measured. Three different approaches were used to simulate soil temperature at 10 cm depth, two empirical and one numerical-empirical. The empirical models were those proposed by Kang et al. (2000) and modified by Kätterer & Andrén (2009), as described below. The equation proposed by Kang et al. (2000) is written as: \(k_{z}=\left(\frac{\pi}{D\left(\theta\right)p}\right)^{1/2}\) 2.1 where t is time (day); T surf is soil surface temperature (°C); D(θ) is thermal diffusivity (cm 2 s -1 ); p is the period of temperature variation (s), defined as 24 × 60 × 60, to represent daily variations ; k LB is the extinction coefficient set as 0.45; and z is soil depth (cm). The equation proposed by Kätterer & Andrén (2009) is written as follows: not-yet-known not-yet-known not-yet-known unknown \(T_{t}\left(z\right)=T_{t-1}\left(z\right)+\left[{T_{\text{surf}}-T}_{t-1}\left(z\right)\right]\text{αexp}\left(-k_{z}z\right)\exp\left(-k_{\text{lai}}\text{LAI}_{t}\right)\) 3 In the Kätterer and Andrén (2009) model, the attenuation of temperature is partitioned into two components: one dependent on LAI (k lai ) and the other independent of LAI (α), resulting in the following parameter values for mineral soils: α = 0.24 and k lai = 0.15. The soil surface temperature was calculated according to Kätterer & Andrén (2009): \(T_{\text{surf}}=T_{a}\left[s_{1}+\left(1-s_{1}\right)\exp\left(-s_{2}\left(LAI-\text{LAI}_{\text{ref}}\right)\right)\right]\), 4 where T a is air temperature (°C); LAI is leaf area index (m 2 m -2 ); LAI ref is the reference leaf area index (m 2 m -2 ). LAI ref is defined as the LAI of a reference crop at meteorological stations (LAI = 3.0 m 2 m -2 ); and s 1 and s 2 are model parameters for mineral soils with values of 0.95 and 0.40, respectively. The third approach combines the empirical soil surface temperature estimation (eq. 4) with the numerical solution of the heat diffusion equation, as described below. The numerical method consisted of solving the partial differential equation of heat conduction. \(\frac{\partial T\left(z,t\right)}{\partial t}=\frac{\partial}{\partial z}\left[D\left(\theta\right)\frac{\partial T}{\partial z}\right]\), 5 where T (z,t) is soil temperature at depth z and time t (°C); D(θ) is thermal diffusivity as function of soil water content (cm 2 s -1 ); z is soil depth (cm); and t is time (s). Equation 5 was discretized using the explicit method (Reichardt and Godoi, 1973), yielding: \(T_{i}^{j+1}=T_{i}^{j}+\left[\frac{\mathrm{\Delta}t}{\left(\mathrm{\Delta}z\right)^{2}}\right]\left[D_{i+\frac{1}{2}}^{j}\left(T_{i+1}^{j}-T_{i}^{j}\right)-D_{i-\frac{1}{2}}^{j}\left(T_{i}^{j}-T_{i-1}^{j}\right)\right]\), 6 where \(T_{i}^{j}\)is the temperature at layer i and time step j ; \(T_{i}^{j+1}\)is the temperature at layer i and time step j + 1; Δt is the time step (s); Δz is layer thickness (cm);\(D_{i+\frac{1}{2}}^{j}\) is the thermal diffusivity between layer i and i + 1, calculated as an arithmetic mean; and\(D_{i-\frac{1}{2}}^{j}\ \)is the thermal diffusivity between layers i - 1 and i . The surface temperature was calculated using equation 4. For the simulation, the soil profile was divided into 100 layers, each 1.0 cm thick (Δz = 1.0 cm). The time step was set to Δt = 0.5 s. In this case, the ratio\(r=\frac{D\times\mathrm{\Delta}t}{{\mathrm{\Delta}x}^{2}}\ \)must be lower than 0.5 to ensure numerical stability. Thus, for each 1-hour step, 7200 smaller time steps were computed. The bottom boundary temperature was set to 25 °C. Figure 2 illustrates the one-dimensional spatial and temporal discretization scheme adopted in this study. not-yet-known not-yet-known not-yet-known unknown Fig. 2 Schematic representation of the one-dimensional soil heat conduction model. The diagram only shows ten layers (n = 10), but in the model, the soil profile (L = 100 cm) was discretized into N = 100 layers (Δz = 1 cm). The temporal discretization was Δt = 0.5 s. The thermal diffusivity (D(θ)) required for the previously described methods was calculated using two approaches. The first was the pedo-transfer function presented by Arkhangelskaya and Lukyashchenko (2018), described below: \(k_{0}=\left(1.464826-2,446,390a\right)\times 10^{-7}\) 7.1 \(\theta_{0}=0.312884-0.007097sand-535,120k_{0}+0.002017silt\) 7.2 \(b=0.684129-2,033,140a\) 7.3 \(D\left(\theta\right)=\ k_{0}+aexp\left[-0.5\left(\frac{\ln\left(\frac{\theta}{\theta_{0}}\right)}{b}\right)^{2}\right]\) 7.4 where k 0 is the thermal diffusivity of dry soil; a is the difference between the maximum thermal diffusivity at the optional water content θ 0 and that of dry soil; b is the half-width of the peak of D(θ). The second approach is a simple linear equation estimated based on reference values for silt-clay soils reported in Wijk and de Vries (1966) (p. 110). The fitted equation is\(D\left(\theta\right)=0.0086\theta\ +\ 0.0026\). Statistical analysis The methods described in the previous section were compared using the Root Mean Square Error (RMSE), Mean Absolute Error (MAE), Bias, and the Kling–Gupta Efficiency (KGE), as described below: \(MAE=\frac{1}{n}\sum_{i=1}^{n}\left|P_{i}-O_{i}\right|\) 9 \(Bias=\frac{1}{n}\sum_{i=1}^{n}\left(P_{i}-O_{i}\right)\) 10 \(KGE=1-\sqrt{\left(r-1\right)^{2}+\left(\alpha-1\right)^{2}+\left(\beta-1\right)^{2}}\) 11 \(r=\frac{\sum{\left(O_{i}-\overline{O}\right)\left(P_{i}-\overline{P}\right)}}{\sqrt{\sum{\left(O_{i}-\overline{O}\right)^{2}\sum\left(P_{i}-\overline{P}\right)^{2}}}}\) 12 \(\alpha=\frac{\sigma_{P}}{\sigma_{O}}\) 13 \(\beta=\frac{\overline{P}}{\overline{O}}\) 14 where: O i is the observed value for the i -th data point; P i is the predicted value for the i -th data point; Ō is the mean of observed values;\(\overline{P}\) is the mean of predicted values; n is the total number of observations; σ o is the standard deviation of observations, σ P is standard deviation of predictions. RESULTS AND DISCUSSION The soil temperature estimation results obtained from the different approaches are presented in Figure 3, with their corresponding statistical performance summarized in Figure 4. Two important observations can be made. First, the numerical method outperformed both the Kang and Kätterer and Andrén models, yielding lower RMSE, MAE and Bias, and higher KGE. The average values, considering both thermal diffusivity methods, were 0.923, 0.683, -0.294 and 0.881, respectively. The Kang and the Kätterer and Andrén models performed very similarly, with a slight superiority in the former, with the KGE error values being 0.820 and 0.781, respectively. The second observation concerns the thermal diffusivity performance. All the three evaluated methods performed better when the simple linear equation based on method of Wijk and de Vries (1966) was used to estimate thermal diffusivity. The general trend between the two methods was an increase in RMSE, MAE and Bias errors, and reduction in KGE. However, overall, the proposed numerical method was less affected by the thermal diffusivity method. On the average, the reduction of the KGE metric was 8.94, 3.63 and 0.39 %, for Kätterer and Andrén, Kang and Numerical methods, respectively. Therefore, although the equation developed by Arkhangelskaya and Lukyashchenko (2018) was derived from a relatively large dataset covering diverse textural classes, it appears that their model does not accurately represent the thermal diffusivity of the local soil examined in this study. This highlights the importance of choosing the correct model to represent soil thermal diffusivity with notable effect of final results. In this case, a more general and broadly applicable function based on Wijk and de Vries’s appeared to be more suitable and should be preferable. Fig. 3 Relationship between simulated and measured soil temperature at 10 cm depth of a sesame field obtained using three modeling methods (rows) that incorporate different approaches to estimating thermal diffusivity (columns). Fig. 4 Statistical performance of soil temperature models using different approaches for calculating D(θ). RMSE: root mean square error; MAE: mean absolute error; KGE: Kling–Gupta efficiency; D(θ): thermal diffusivity (cm 2 s -1 ). An example of hourly simulation over a one-week period is shown in Figure 5. It is evident that the proposal numerical method was able to capture soil temperature dynamics more effectively than the other tested models. In addition, there is a visual similarity between Kang and the Kätterer and Andrén models in predicting soil temperature. This suggests that these models may be more suitable for representing daily, or seasonal temperature variations, as shown, for example in Paul et al. (2004) and Liang et al. (2014). Fig. 5 Example of hourly simulation results over one week (09/02/2015 – 09/08/2015) in a sesame field, using the three evaluated methods in combination with the Wijk and de Vries thermal diffusivity equation. The errors observed in the Kang and Kätterer, and Andrén models may also be associated with the need for calibration of their empirical parameters. Therefore, to assess whether local calibration could improve model performance, we calibrated the models using an independent dataset obtained from another sesame field plot from our site. In the Kang model, only the k LB parameter (Equation 2) was calibrated, whereas in the Kätterer and Andrén model, the parameters α and kₗₐᵢ were adjusted (Equation 3). The surface temperature function remained unchanged. The calibrated equations and corresponding simulation results are presented in Figure 6 and Table 1. In general, the errors decreased after calibration compared to the original unadjusted models. However, even after calibration, the empirical models still exhibited higher errors than the numerical method. In the Kang model, the calibrated parameter values differed slightly from those in the original study; for instance, the original k LB value was 0.45, whereas the calibrated value was 0.3364. In contrast, for the Kätterer and Andrén (2009) model, although the calibrated α parameter was very similar to the original value, the calibrated k lai parameter converged to zero (Table 1). The parameter α represents the attenuation factor of the temperature gradient between air and soil. It was initially proposed to partition the overall attenuation factor into two components: one dependent on leaf area index (LAI) through k lai and another independent of LAI through α. According to the authors, this approach was necessary to improve the performance of the original model due to substantial discrepancies between measured and simulated temperatures. Therefore, the calibrated k lai value of zero appears unreasonable, as it implies that LAI would provide no contribution to temperature attenuation. Table 1. Calibrated parameters and statistical performance of soil temperature models using Wijk and de Vries equation for calculating D(θ). Original Calibrated Kang k LB = 0. 45 k LB = 0. 3163 816 1.217 0.882 -0.355 0.795 Kätterer and Andrén α = 0.24 k lai = 0.15 α = 0.3320 k lai = 0.000 816 1.141 0.843 -0.335 0.840 n: number of data used in calibration step. α: attenuation factor independent of LAI; k lai : attenuation factor dependent of LAI coefficient ; k LB : extinction coefficient for the Beer-Lambert law; D(θ): thermal diffusivity (cm 2 s -1 ). Fig. 6 Relationship between simulated and measured soil temperature at 10 cm depth obtained using Kang et al. (2000) and Kätterer and Andrén (2009) model after calibration. The prediction of soil temperature has been carried out using different approaches, including machine learning methods (Feng at al. 2019), empirical approaches (Zhang et al. 2022), and numerical methods (Naranjo-Mendoza et al. 2018). Among numerical techniques, the explicit finite difference method is generally simpler to formulate and implement than the implicit method, while often providing comparable performance (Pérez et al. 2024). The explicit approach was adopted in this study because it is straightforward to implement computationally and does not require high computational cost, while maintaining accurate estimates (Naranjo-Mendoza et al., 2018). In the work of Naranjo-Mendoza et al. (2018), the soil temperature in a grass-covered urban area was simulated using analytical methods and finite-differences method with different boundary conditions. The result showed that the finite-difference method using air temperature as upper boundary condition outperformed both short and long-term temperature predictions when compared with the analytical methods and with the finite-difference approach that used surface heat flux as the upper boundary condition. More complex and physically based models are available in the literature, such as Trench (Buckley et al., 2023), HYDRUS (Radcliffe and Šimůnek, 2018), and the model proposed by Naranjo-Mendoza et al. (2018). These models provide a more comprehensive representation of soil heat and mass transfer processes and are preferable in situations requiring fine temporal resolution or a more complete solution of the surface energy balance – particularly at the upper boundary condition – although they require a larger number of inputs, such as solar radiation, air temperature, rainfall, wind speed, and relative humidity, which are the external factors determining soil temperature. In the present study, the upper boundary condition is prescribed using the empirical approach proposed by Kätterer and Andrén to calculate the soil surface temperature. This simplification avoids solving the full surface energy balance and assumes that soil temperature dynamics are primarily driven by conductive heat transfer. Consequently, the governing equation (Eq. 5) accounts only for heat conduction in the soil profile. Other processes that may influence soil temperature, such as convective heat transport associated with water movement or vapor fluxes, are not explicitly represented in the model (Kirkham and Powers, 1972). Despite these simplifications, the proposed numerical model showed satisfactory performance at the hourly timescale for shallow depths (10 cm). Therefore, it is expected to perform comparably at coarser temporal resolutions, particularly on daily timescale (Naranjo-Mendoza et al. 2018). Hence, the proposed approach may be suitable for applications in remote sensing studies and land surface modeling where computational efficiency and simplicity are required. CONCLUSION Soil temperature can be simulated using approaches ranging from simple empirical formulations to fully numerical solutions. In this study, a hybrid numerical–empirical method was developed that integrates an empirical estimation of soil surface temperature with an explicit finite difference solution of the heat conduction equation. Application of the model at 10 cm depth in a vegetated sesame field demonstrated its ability to accurately reproduce hourly soil temperature dynamics. The results demonstrate that the proposed approach outperformed purely empirical methods while maintaining low computational complexity. Because the upper boundary condition is solved empirically, the method may not be suitable for situations that require a more detailed representation of the energy balance between the soil surface and the overlying atmosphere. However, it provides an efficient alternative for estimating near-surface soil temperature at hourly or longer time scales and represents a practical approach for applications requiring reliable soil temperature simulations under vegetated conditions. REFERENCES Arkhangelskaya, T., & Lukyashchenko, K. (2018). Estimating soil thermal diffusivity at different water contents from easily available data on soil texture, bulk density, and organic carbon content. Biosystems Engineering, 168, 83–95. https://doi.org/10.1016/j.biosystemseng.2017.06.011 Feng, Y., Cui, N., Hao, W., Gao, L., & Gong, D. (2019). Estimation of soil temperature from meteorological data using different machine learning models. 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Climate Research, 2(3), 183–191. https://doi.org/10.3354/cr002183 Supplementary Material File (image1.emf) Download 67.99 KB File (image3.emf) Download 26.29 MB File (image4.emf) Download 105.69 KB File (image5.emf) Download 116.43 KB File (image6.emf) Download 5.83 MB Information & Authors Information Version history V1 Version 1 09 April 2026 Copyright This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License Keywords energy balance finite difference method numerical modelling pedotransfer function thermal conductivity Authors Affiliations Thiago Duarte 0000-0002-8471-104X [email protected] Federal University of Rondonopolis View all articles by this author Xue-Jun Dong 0000-0003-3072-1901 Texas A&M AgriLife Research and Extension Center, Uvalde, TX 78801 USA View all articles by this author Edna Maria Bonfim-Silva Federal University of Rondonopolis View all articles by this author Tonny da Silva Federal University of Rondonopolis View all articles by this author Metrics & Citations Metrics Article Usage 33 views 31 downloads .FvxKWukQNSOunydq8rnd { width: 100px; } Citations Download citation Thiago Duarte, Xue-Jun Dong, Edna Maria Bonfim-Silva, et al. IMPROVING NEAR-SURFACE SOIL TEMPERATURE ESTIMATION USING EMPIRICAL AND NUMERICAL METHODS IN CROP-COVERED SURFACES. Authorea . 09 April 2026. DOI: https://doi.org/10.22541/au.177574758.84614799/v1 If you have the appropriate software installed, you can download article citation data to the citation manager of your choice. Simply select your manager software from the list below and click Download. For more information or tips please see 'Downloading to a citation manager' in the Help menu . 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