Soil Thermal Inertia Research Articles

A Two-Source Normalized Soil Thermal Inertia Model for Estimating Field-Scale Soil Moisture from MODIS and ASTER Data

Soil moisture (SM) is a crucial component for understanding, modeling, and forecasting terrestrial water cycles and energy budgets. However, estimating field-scale SM based on thermal infrared remote-sensing data is still a challenging task. In this study, an improved Flexible Spatiotemporal DAta Fusion (FSDAF) method based on land-surface Diurnal Temperature Cycle (DTC) model (DFSDAF) was proposed to fuse Moderate Resolution Imaging Spectroradiometer (MODIS) and Advance Spaceborne Thermal Emission and Reflection Radiometer (ASTER) land-surface temperature (LST) data to generate ASTER-like LST during the night. The reconstructed diurnal LST data at a high spatial resolution (90 m) was then utilized to drive a two-source normalized soil thermal inertia model (TNSTI) for the vegetated surfaces to estimate field-scale SM. The results of the proposed methods were validated at different observation depths (2, 4, 10, 20, 40, 60, and 100 cm) over the Zhangye oasis in the middle region of the Heihe River basin in the northwest of China and were compared with the SM estimates from the TNSTI model and other SM products, including AMSR2/AMSR-E, GLDAS-Noah, and ERA5-land. The results showed the following: (1) The DFSDAF method increased the accuracy of LST prediction, with the determination coefficient (R2) increasing from 0.71 to 0.77, and root mean square error (RMSE) decreasing from 2.17 to 1.89 K. (2) the estimated SMs had the best correlation with the observations at the 10 cm depth (with R2 of 0.657; RMSE of 0.069 m3/m3), but the worst correlation with observations at the 40 cm depth (with R2 of 0.262; RMSE of 0.092 m3/m3); meanwhile, the modeled SMs were significantly underestimated above 40 cm (2, 4, 10, and 20 cm) and slightly overestimated below 40 cm (60 and 100 cm); in addition, the field-scale SM series at high spatial resolution (90 m) showed significant spatiotemporal variation. (3) The SM estimates based on the TNSTI for the vegetated surfaces are more capable of characterizing the SM status in the root zone (~80 cm) or even deeper, while the SMs from AMSR2/AMSR-E, GLDAS-Noah, or ERA5-land products are closer to the SM in the surface layer (the depth is less than 5 cm). The TNSTI provided favorable data supports for hydrological model simulations and showed potential advantages for agricultural refinement managements and smart agriculture.

Surface energy budget at Curiosity through observations and column modeling

Diurnal ground surface temperatures (Tg) and the five major terms of the surface energy budget (SEB) are displayed from hourly Mars Science Laboratory observations and from column model simulations in four contrasting cases along the Curiosity traverse. Tg and the SEB terms are otherwise well simulated on regolith near the landing spot and on rocky Pahrump Hills, but the residual in observation-based SEB (~downwelling longwave radiation) shows unexplained peaks in the morning and evening and simultaneously model-Tg is too cold. Enhanced or diurnally variable crater dust does not help but diurnally variable soil thermal inertia (suggested by Fourier analysis of observed Tg) reduces both defects at both sites. Sand on the steep Namib dune is instead homogeneous, defects here being reduced by taking into account slope effects. Regolith at the 2018 dust storm site appears inhomogeneous, with the SEB terms and Tg relatively well simulated even in this case of extremely heavy dust load.

Evaluating and improving simulations of diurnal variation in land surface temperature with the Community Land Model for the Tibetan Plateau.

This study evaluated and improved the ability of the Community Land Model version 5.0 (CLM5.0) in simulating the diurnal land surface temperature (LST) cycle for the whole Tibetan Plateau (TP) by comparing it with Moderate Resolution Imaging Spectroradiometer satellite observations. During daytime, the model underestimated the LST on sparsely vegetated areas in summer, whereas cold biases occurred over the whole TP in winter. The lower simulated daytime LST resulted from weaker heat transfer resistances and greater soil thermal conductivity in the model, which generated a stronger heat flux transferred to the deep soil. During nighttime, CLM5.0 overestimated LST for the whole TP in both two seasons. These warm biases were mainly due to the greater soil thermal inertia, which is also related to greater soil thermal conductivity and wetter surface soil layer in the model. We employed the sensible heat roughness length scheme from Zeng, Wang & Wang (2012), the recommended soil thermal conductivity scheme from Dai et al. (2019), and the modified soil evaporation resistance parameterization, which was appropriate for the TP soil texture, to improve simulated daytime and nighttime LST, evapotranspiration, and surface (0–10 cm) soil moisture. In addition, the model produced lower daytime LST in winter because of overestimation of the snow cover fraction and an inaccurate atmospheric forcing dataset in the northwestern TP. In summary, this study reveals the reasons for biases when simulating LST variation, improves the simulations of turbulent fluxes and LST, and further shows that satellite-based observations can help enhance the land surface model parameterization and unobservable land surface processes on the TP.

Assessing shallow groundwater level using RTI model and long-term MODIS data in Ejina Basin, Northwest China

The present study aims to exploit the thermal inertia model to assess the shallow groundwater level distribution, as an attempt to address agricultural water shortage and ecological degradation in arid and semi-arid regions. Apparent thermal inertia (ATI) model is one of the most commonly used and successfully implemented models, whereas in some cases, the scales of the results achieved on different dates are inconsistent, which poses a serious difficulty when monitoring soil moisture over time. To address this restriction, we introduce a soil moisture indicator, called RTI, which derives an approximation of soil thermal inertia, from flexible multi-temporal MODIS observations covering a 2-year period. Taking the Ejina Basin in arid area as an example, to more accurately assess the shallow groundwater level distribution, ATI and RTI models were adopted based on the long time series MODIS data to assess the multi-temporal soil moisture content in the study area. The data of groundwater level measured by observation well and thermal inertia were employed to generate scatter diagrams. Subsequently, a nonlinear equation was developed. Based on the thermal inertia, the temporal and spatial distribution map of the shallow groundwater level in the whole study area was generated with the inverse calculation of the nonlinear equation. It was found that the shallow groundwater level distribution in Ejina Basin tended to be shallower from south to north, as well as from summer to winter. As revealed from the results, both ATI and RTI models can effectively assess the shallow groundwater level in arid areas. The RTI model could better reflect the seasonal changes of soil moisture content and groundwater level.

Estimating catchment scale soil moisture at a high spatial resolution: Integrating remote sensing and machine learning

Soil moisture information is important for a wide range of applications including hydrologic modelling, climatic modelling and agriculture. L-band passive microwave satellite remote sensing is the most feasible option to estimate near-surface soil moisture (~0–5 cm soil depth) over large extents, but its coarse resolution (~10s of km) means that it is unable to capture the variability of soil moisture in detail. Therefore, different downscaling methods have been tested as a solution to meet the demand for high spatial resolution soil moisture. Downscaling algorithms based on the soil thermal inertia relationship between diurnal soil temperature difference (ΔT) and daily mean soil moisture content (μSM) have shown promising results over arid and semi-arid landscapes. However, the linearity of these algorithms is affected by factors such as vegetation, soil texture and meteorology in a complex manner. This study tested a (i) Regression Tree (RT), an Artificial Neural Network (ANN), and a Gaussian Process Regression (GPR) model based on the soil thermal inertia theory over a semi-arid agricultural landscape in Australia, given the ability of machine learning algorithms to capture complex, non-linear relationships between predictors and responses. Downscaled soil moisture from the RT, ANN and GPR models showed root mean square errors (RMSEs) of 0.03, 0.09 and 0.07 cm3/cm3 compared to airborne retrievals and unbiased RMSEs (ubRMSEs) of 0.07, 0.08 and 0.05 cm3/cm3 compared to in-situ observations, respectively. The study showed encouraging results to integrate machine learning techniques in estimating near-surface soil moisture at a high spatial resolution.

Disaggregating satellite soil moisture products based on soil thermal inertia: A comparison of a downscaling model built at two spatial scales

Lack of high spatial resolution soil moisture data is a major limitation in many regional scale hydrologic, climatic and agricultural applications. The available satellite soil moisture data products are too coarse and unable to cater for this resolution requirement. Downscaling coarse spatial resolution satellite soil moisture retrievals is a feasible option to meet the required level of spatial resolution for those applications. The main focus of this study is to compare two soil thermal inertia-based downscaling models, built by using long-term time records of (i) point scale in-situ data and, (ii) 25 km resolution Global Land Data Assimilation System (GLDAS) land surface model outputs. The developed models were tested over Goulburn River catchment in the Upper Hunter Region of NSW, Australia to downscale Soil Moisture Active Passive (SMAP) 36 km radiometric product into 1 km resolution.The downscaled SMAP product from both models produced encouraging results with unbiased root mean square errors (ubRMSEs) of 0.07–0.10 cm3/cm3, against in-situ field data, and an average ubRMSEs of 0.07 cm3/cm3 when compared to the National Airborne Field Experiment 2005 (NAFE'05) soil moisture retrievals. Both models showed promising results over semi-arid regions in estimating soil moisture at a high spatial resolution, but with their own strengths and weaknesses. The findings here provide useful insights on the robustness of the soil thermal inertia relationship across scales and the effects of the model resolution to the downscaled soil moisture estimates. The approach demonstrated encouraging results over semi-arid regions in estimating soil moisture at a high spatial resolution.

An analytical method to evaluate the impact of vertical part of an earth-air heat exchanger on the whole system

Abstract This paper presents a simplified analytical model within numerical results to determine the thermal balance of Earth-Air Heat Exchanger (EAHE). The EAHE is a device which uses the principle of soil thermal inertia used for ventilation in buildings. It has three sections: a vertical section at the entrance, an horizontal section in the area of soil thermal inertia and a vertical section at the exit, also considered as area in soil thermal inertia. The assessment for the heat algebrical gain at the vertical section of air entrance in the EAHE is established. In this study, the initial conditions of the problem are obtained and the temperature equation specified model is solved analytically, by considering that the vertical part of an EAHE or a vertical EAHE is under periodic fluctuations in both ambient air temperature and soil temperature. The model can predict the air temperature variation along vertical and horizontal section of the tube for any hour of the day and can be used for a vertical EAHE. It can also determine the daily or annualy mean and amplitude of the total cooling or heating effect of the tube. Numerical results are graphically presented, discussed and compared to experimental datas.

Improving Estimation of Soil Moisture Content Using a Modified Soil Thermal Inertia Model

There has been substantial research for estimating and mapping soil moisture content (SMC) of large areas using remotely sensed images by developing models of soil thermal inertia (STI). However, it is still a great challenge to accurately estimate SMC because of the impact of vegetation canopies and vegetation-induced shadows in mixed pixels on the estimates. In this study, a new method was developed to increase the estimation accuracy of SMC for an irrigated area located in YingKe of Heihe, China, using ASTER data. In the method, an original model of estimating bare STI was modified by decomposing a mixed pixel into three components, bare soil, vegetated soil, and shaded soil, as well as extracting their fractions using a spectral unmixing analysis and then deriving their fluxes. Moreover, the 90 m spatial resolution thermal images were scaled down to the 15 m spatial resolution by data fusion of a discrete wavelet transform (DWT) and re-sampling using the nearest neighbor method (NNM). The modified model was compared with the original model based on the mean absolute error (MAE) and relative root mean square error (RRMSE) between the SMC estimates and observations from 30 validation soil samples. The results indicated that compared to the original model based on the parallel dual layer, the modified STI model based on the serial dual layer statistically significantly decreased the MAE and RRMSE of the SMC estimates by 63.0–63.2% and 63.0–63.5%, respectively. The 15 m spatial resolution thermal bands obtained by the DWT data fusion provided more detailed information of SMC but did not significantly improve its estimation accuracy than the 15 m spatial resolution thermal bands by re-sampling using NNM. This implied that the novel method offered insights on how to increase the accuracy of retrieving SMC estimates in vegetated areas.

Soil Thermal Inertia Effect on Shallow Basement Energy Performance in Different Morocco Climates

Abstract This study deals with the energy performance of a shallow basement in six climates ranging from cold to desert climate. A case study of a partially buried house located in the hot semi-arid climate of Marrakech (Morocco) is first monitored during 2 months in summer and 2 months in winter. A trnsys model of this house was built and validated against the monitoring results. Simulation results show that the annual thermal load of the partially buried house is always lower than that of the corresponding above ground building house except for the Atlantic climate. Indeed, burying the house at 1.2 m reduces its annual thermal load by 19% at least in the Mediterranean climate and by about 39% in the cold climate.

Accounting for soil porosity improves a thermal inertia model for estimating surface soil water content

Soil thermal inertia (P), a property that controls the temporal variation of near-surface temperature, has been used to estimate surface water content (θ) in remote sensing studies. The accuracy of θ estimates, however, is affected by surface soil porosity (n). We hypothesize that n can be derived using a simple linear n-P relationship of a dry surface soil layer, and that accounting for n improves the accuracy of θ estimation using a P(θ) model. The P of a surface layer was measured by using the heat pulse method during a drying period, and the feasibility of estimating θ with a P(θ) model that included n was explored. The approach was also tested with published P values derived from meteorological data and MODIS data against in situ θ measurements at two field sites in Arizona, USA. The results on a partially vegetated shrubland indicated that by using the P-derived n, the P(θ) model provided more accurate θ estimates than by using the literature n values. Discrepancies between modeled θ and in situ θ measurements were observed at small θ values, which were caused in part by the fact that the modeled θ represented soil layers a few millimeters thick, while the in situ measurements represented θ at the 5-cm depth. The new n-P function has potential for estimating surface θ accurately using multi-scale P data on bare soils or on sparsely vegetated lands.

Intercomparison of two trapezoid-based soil moisture downscaling methods using three scaling factors

ABSTRACTThis paper compared two soil moisture downscaling methods using three scaling factors. Level 3 soil moisture product of advanced microwave scanning radiometer for EOS (AMSR-E) is downscaled from 25 to 1 km. The downscaled results are compared with the soil moisture observations from polarimetric scanning radiometer (PSR) microwave radiometer and field sampling. The results show that (1) the scaling factor of normalized soil thermal inertia (NSTIs) and vegetation temperature condition index (VTCI) are better than soil evaporative efficiency in reflecting soil moisture; (2) for method 1, NSTIS is the best in the downscaling of soil moisture. For method 2, VTCI is the best; (3) no significant differences of the correlation coefficients (R2) and the biases were found between the two methods for the same scaling factors. However, method 2 shows a better potential than method 1 in the time-series applications of the downscaling of soil moisture; (4) compared with the relationship between the area-averaged soil moisture of AMSR-E and that of PSR, R2 of the 6 sets of the downscaled soil moisture almost do not decrease, which suggests the validity of the downscaling of soil moisture with the two downscaling methods using the three scaling factors.

Performance analysis on a large scale borehole ground source heat pump in Tianjin cultural centre

In this paper, the temperature distribution of the geothermal field for the vertical borehole ground-coupled heat pump was tested and analysed. Besides the borehole ground-coupled heat pump, the system composed of the ice storage, heat supply network and cooling tower. According to the operation data for nearly three years, the temperature constant zone is in the ground depth of 40m -120m with a temperature gradient of about 3.0°C/100m. The temperature of the soil dropped significantly in the heating season, increased significantly in the cooling season, and reinstated in the transitional season. With the energy balance design of the heating and cooling and the existence of the soil thermal inertia, the soil temperature stayed in a relative stable range and the ground source heat pump system was operated with a relative high efficiency. The geothermal source heat pump was shown to be applicable for large scale utilization.

Role of Soil Thermal Inertia in Surface Temperature and Soil Moisture‐Temperature Feedback

AbstractA conceptual model based on the surface energy budget is developed to compute the sensitivity of the climatological mean diurnal amplitude and mean daily surface temperature to the soil thermal inertia. It uses the diurnal amplitude of the net surface radiation, the sensitivity of the turbulent fluxes to the surface temperature and the soil thermal inertia. Its performance is evaluated globally with numerical simulations using the atmospheric and the land surface modules of a state‐of‐the‐art climate model. The only regions where the thermal inertia has a limited impact are the moist regions. In dry areas, together with the stability of the boundary layer it plays a major role. It also has a significant impact at high and midlatitudes especially in winter when the turbulent fluxes are weak. In semiarid regions, the soil moisture exhibits a high day‐to‐day variability strongly correlated to the evaporation and the day‐to‐day variability of the surface temperature is generally explained by the soil moisture via its control on the evaporation. However, the soil moisture via its control on the thermal inertia reduces the impact of the day‐time evaporative cooling by reducing the nocturnal cooling. This newly identified moisture‐related negative feedback can reduce the variability of the surface temperature in semiarid regions by up to a factor of 2. The model also provides a simple framework to understand the role of the thermal properties in the frequent cold bias identified in stratified stable atmospheric situations in the northern midlatitudes.

The Surface Energy Budget Computed at the Grid‐Scale of a Climate Model Challenged by Station Data in West Africa

AbstractIn most state‐of‐the‐art climate models, systematic errors persist in the representation of the rainfall seasonality, near surface air temperature, and surface energy budget over West Africa, even during the dry season. Most biases are related to an incorrect latitudinal position of the monsoon structures. To disentangle the role of the large‐scale dynamics from that of the physical processes in these biases, simulations are performed with the LMDZ general circulation model in which the horizontal winds are nudged toward reanalysis. Wind nudging greatly improves the position of the ITCZ as well as the representation of the components of the surface energy budget directly impacted by the water budget and hence facilitates a more systematic analysis of remaining biases associated with the physics in the model. The great potential of wind nudging to compare the energetics of the atmospheric column in climate models at grid cell scale with station observations, even for coarse grid models, is then shown. Despite the improved water advection and rainfall seasonality in the nudged simulations, errors consisting in a cold bias during the dry season over Sahel, an underestimated seasonal variation of surface albedo, and an overestimation of the solar incoming flux remain. The origin of these remaining biases is further investigated by conducting a series of dedicated sensitivity experiments. Results highlight the key role of the soil thermal inertia, the turbulent mixing efficiency, the surface albedo, and the aerosols and clouds radiative effects in the representation of meteorological 2m‐variables and surface energy budget.

The Effect of Vegetation on the Remotely Sensed Soil Thermal Inertia and a Two-Source Normalized Soil Thermal Inertia Model for Vegetated Surfaces

The estimation of soil thermal inertia (STI) (P) on the vegetated surface is a challenging task due to the difficulty in acquiring soil temperature under vegetation. In most cases, mixed surface temperature (T) is used to replace soil temperature ( ${\rm T}_{\rm s}$ ) to estimate P. Inevitably, errors are introduced because of the effect of vegetation. In this paper, on the basis of a simplified STI concept and an operational algorithm of surface temperature separation, the differences of STI estimated from ${\rm T}_{\rm s}$ , vegetation temperature ( ${\rm T}_{\rm v}$ ) and T were quantified. When there is large difference between T and ${\rm T}_{\rm s}$ (as much as 10 K), the mean absolute percentage difference (MAPD) between STI estimated from ${\rm T}_{\rm s}$ ( ${\rm STI}_{{\rm S}}$ ) and STI estimated from T ( ${\rm STI}_{{\rm M}}$ ) can reach 60%. A normalized STI ( ${\rm STI}_{{\rm N}}$ ) to account for the vegetated surface was proposed in terms of the linear mixing theory, which can be used to estimate the relative soil water (SW) content. Under the condition that the wilting point of the soil moisture and the saturated soil moisture are known for an area, SW content can then be calculated from ${\rm STI}_{{\rm N}}$ . The comparisons of the relationships between soil moisture from the advanced microwave scanning radiometer-earth observing system and ${\rm STI}_{{\rm S}},{\rm STI}_{{\rm V}},{\rm STI}_{{\rm M}}$ , and soil moisture estimated from ${\rm STI}_{{\rm N}}$ show that ${\rm STI}_{{\rm N}}$ is the best indicator of soil moisture, with the highest correlation coefficient $({\rm R}^{2})$ of 0.64 and 0.75 for the two validation domains.

Representing the Australian Heat Low in a GCM Using Different Surface and Cloud Schemes

The high insolation during the Southern Hemisphere summer leads to the development of a heat low over north-west Australia, which is a significant feature of the monsoon circulation. It is therefore important that General Circulation Models (GCMs) are able to represent this feature well in order to adequately represent the Australian Monsoon. Given that there are many different configurations of GCMs used globally (such as those used as part of the Coupled Model Intercomparison Project), it is difficult to assess the underlying causes of the differences in circulation between such GCMs. In order to address this problem, the work presented here makes use of three different configurations of the Australian Community Climate and Earth System Simulator (ACCESS). The configurations incorporate changes to the surface parameterization, cloud parameterization, and both together (surface and cloud) while keeping all other parameterized processes unchanged. The work finds that the surface scheme has a larger impact on the heat low than the cloud scheme, which is caused by differences in the soil thermal inertia. This study also finds that the differences in the circulation caused by changing the cloud and surface schemes together are the linear sum of the individual perturbations (i.e., no nonlinear interaction).

Evapotranspiration based on equilibrated relative humidity (ETRHEQ): Evaluation over the continental U.S.

AbstractA novel method of estimating evapotranspiration (ET), referred to as the ETRHEQ method, is further developed, validated, and applied across the U.S. from 1961 to 2010. The ETRHEQ method estimates the surface conductance to water vapor transport, which is the key rate‐limiting parameter of typical ET models, by choosing the surface conductance that minimizes the vertical variance of the calculated relative humidity profile averaged over the day. The ETRHEQ method, which was previously tested at five AmeriFlux sites, is modified for use at common weather stations and further validated at 20 AmeriFlux sites that span a wide range of climates and limiting factors. Averaged across all sites, the daily latent heat flux RMSE is ∼26 W·m−2 (or 15%). The method is applied across the U.S. at 305 weather stations and spatially interpolated using ANUSPLIN software. Gridded annual mean ETRHEQ ET estimates are compared with four data sets, including water balance‐derived ET, machine‐learning ET estimates based on FLUXNET data, North American Land Data Assimilation System project phase 2 ET, and a benchmark product that integrates 14 global ET data sets, with RMSEs ranging from 8.7 to 12.5 cm·yr−1. The ETRHEQ method relies only on data measured at weather stations, an estimate of vegetation height derived from land cover maps, and an estimate of soil thermal inertia. These data requirements allow it to have greater spatial coverage than direct measurements, greater historical coverage than satellite methods, significantly less parameter specification than most land surface models, and no requirement for calibration.

An Empirical Method of Estimating Soil Thermal Inertia

A method of estimating soil thermal inertia (STI), which uses midday soil heat flux (Gm) and diurnal surface temperature amplitude as the inputs, is presented in the paper.Gmis achieved from an empirical relationship between net radiation (Rn) and soil heat flux (G). To validate the STI method, a method proposed by Verhoef, which requires STI and a Fourier series analysis on surface temperature, is used to estimate diurnalG. By comparing diurnalGestimates and diurnalGmeasurements, the STI method is evaluated indirectly. The results show that the diurnal curve ofGestimates can coincide with that ofGmeasurements for bare soil, with the correlation coefficient (R2) of 0.64, bias of 10.1 W·m−2, and root mean squared errors (RMSE) of 40.9 W·m−2. For the vegetated surface,R2is 0.56, bias is −11.9 W·m−2, and RMSE is 49.2 W·m−2. The large uncertainty in the estimation ofGmresulting from the wider variation of the empirical relationship between Rn andGand the difference between mixed surface temperature and soil surface temperature may be the two primary factors for the larger deviation of the diurnal shape and the magnitude betweenGestimates andGmeasurements for the vegetated surface.

Estimation of soil thermal inertia from geostationary Meteosat Second Generation (MSG) data

The soil thermal inertia is an important parameter in remote sensing monitoring of soil heat flux and soil moisture, while its quantitative estimation from remote sensing data is still a great challenge. Most past methods use data at specific time points, which are limited to the local times of satellite passes and sensitive to single moment observation error. Moreover, most of these methods need field measurements as extra parameters. In this paper, to overcome these deficiencies, the least square adjustment real thermal inertia analytical (LSA-TI) model is proposed to estimate real thermal inertia by making full use of the high-frequency land surface temperature (LST) measurements from geostationary satellites (i.e. Meteosat Second Generation, MSG). The thermal inertia values in North African region are calculated using this method as MSG sequences of LST measurements are adopted as the only inputs.

A method to estimate diurnal surface soil heat flux from MODIS data for a sparse vegetation and bare soil

Summary This paper proposes a mathematical method based on a one-dimensional diffusion equation to derive diurnal variation of surface soil heat flux using cloudless MODIS data for a sparse vegetation and bare soil. Diurnal variation of the surface temperature and near-surface real soil thermal inertia are both simulated from the MODIS data. The study was carried out for the Yingke oasis plains area and the Arou alpine meadow area, which are located in the midstream and upstream, respectively, of the Heihe River Basin. Statistical results showed that the proposed method performs well to estimate soil heat flux for both study areas. In the oasis plains case, the coefficient of determination (R2) was 0.958 and the index of agreement (d) was 0.989. In the alpine meadow case, the coefficient of determination (R2) was 0.972 and the index of agreement (d) was 0.993. Close agreement of the estimated surface soil heat flux with measured observations indicates that the method is promising. Future work will focus on scaling this mathematical method to create a diurnal surface soil heat flux map.