Estimation Of Soil Heat Flux Research Articles

Ensemble machine learning for interpretable soil heat flux estimation

Soil heat flux (SHF) is a key component of the surface energy balance and driver of soil physiochemical and biological processes. Accurate estimation of soil heat flux is challenging due to variations in soil composition, overlying vegetation density and phenology, and highly variable environmental forcings. Existing SHF process-based and data-driven estimation methods have focused on midday landscape scale estimates that correspond to satellite acquisitions, despite the high variability that SHF displays at diurnal scales and throughout the growing season. Recently developed data-driven techniques have emphasized pre-determined predictor variables, with model complexity and predictor selection not carefully evaluated, leaving a gap in our understanding of what information is required to accurately predict SHF. Here we developed and evaluated a suite of ensemble machine learning (ML) models to quantify the ability of meteorological and remote sensing data to predict SHF variability at half-hourly temporal resolution throughout a growing season, producing a comprehensive evaluation of the importance of predictor set composition for SHF estimation at high temporal resolution. We compared this suite of machine learning models to six semi-empirical models and found that the machine learning models broadly outperformed the existing models in capturing diurnal variability across the growing season for four agro-ecosystems (soybean, corn, sorghum, and miscanthus). Crop-specific ML models were able to capture over 86% of the variability in SHF using only two predictor variables, pointing to the need for careful evaluation of predictor sets to identify synergistic combinations. ML models developed using pooled data across all crops captured almost 80% of SHF variability using three predictors, demonstrating the power and generalizability of these methods independent of crop type. Shapley additive explanations (SHAP) were used to examine model interpretability, providing insights into the typically opaque ML modelling process and interaction of predictor variables. Models trained with fewer input variables tended to display more linear and interpretable feature attribution, motivating the use of interpretability as an important consideration in parsimonious model selection. These results provide a robust demonstration of the ability of ML to capture the variability in SHF at sub-hourly resolution across growing seasons spanning a wide range of phenological variation for unique agricultural systems. This study provides a comprehensive evaluation of predictor requirements for model performance, guiding future applications that will take advantage of the next generation of satellite-based observing systems, or in-situ proximal observations of vegetation status and meteorological conditions.

Global land surface evapotranspiration monitoring by ETMonitor model driven by multi-source satellite earth observations

Evapotranspiration (ET) is an essential ecohydrological process linking the land surface energy, water and carbon cycles, and plays a critical role in the earth system. ET remains one of the most problematic components of the water cycle to be determined due to the heterogeneity of the landscape and the complexity of driving factors. The satellite-based earth observation is expected to provide ET information at large-scales. However, accurate global ET information, with spatially and temporally continuous coverage at moderate-to-high resolution, is still scarce. In this paper, a combined model, called ETMonitor, with multi-process parameterizations, was improved and applied to estimate the global ET, mainly using the biophysical and hydrological parameters/variables retrieved from satellite observations. The ETMonitor model was improved in several aspects in this study to generate the global ET datasets during 2000–2019 at daily/1-km resolution, including: 1) adopting high temporal resolution surface water cover and snow/ice cover as input, to simulate the impact of their seasonal change on ET variation; 2) parameterizing the impact of soil moisture on plant transpiration and soil evaporation using high resolution soil moisture, which was downscaled to 1-km resolution from the coarse resolution data retrieved from microwave remote sensing observation; 3) involving a better soil heat flux estimation to reduce its impact on the uncertainty of estimated ET; 4) being calibrated based on global ground flux observations to achieve better accuracy. The estimated daily ET was validated based on the global in situ observations at site scale across various ecosystems, with overall high correlation (0.75), low bias (0.08 mm d-1), and low root mean square error (0.93 mm d-1). It had good ability to partition total ET to plant transpiration and soil evaporation indicated by the good agreement with the ground isotope measurements in a growing season at one site in the northwest China. The estimated global ET was cross-validated by comparing with other existing ET products, and it showed the global ET estimated by ETMonitor could capture the expected global ET patterns both in space and in time. It also indicated the superiority of the ET product by ETMonitor in the following aspects: capability in capturing the seasonal dynamics of waterbody evaporation and sublimation; better performance in capturing the spatial variation of ET in the irrigated cropland regions and mountain regions with complex terrain than other global ET products, e.g., the GLEAM and MOD16 ET products; capability of ET component partitioning at high spatial (1-km) and high temporal (daily) resolutions with good accuracy. The estimated plant transpiration, soil evaporation, canopy rainfall interception loss, and water body evaporation and snow sublimation accounted for 61.54 % (±0.44 %), 19.08 % (±0.54 %), 13.54 % (±0.49 %), and 5.84 % (±0.24 %), respectively, of the total ET on global average. The ETMonitor global ET dataset could provide important information on studies of global terrestrial water and energy cycles and climate change studies, and water resources management at global and regional scales.

Estimation of surface energy fluxes from remotely sensed data over Akure, Nigeria

The spatial variation and composition of surface energy fluxes across different land use over Akure, Nigeria has been investigated using the Surface Energy Balance Algorithm for Land (SEBAL) approach. In 1984, built up area had the lowest net radiation with a mean value of 472.56 W/m2, while the highest net radiation was over the forested area (mean value of 528.93 W/m2). For sensible heat flux, the highest values were observed over the built-up areas with a mean of 245.5 W/m2 and the lowest values over the forested areas (mean value of 160.5 W/m2). Latent heat flux was highest over the forested area with a mean value of 304.1 W/m2 while the built-up area had the lowest latent heat (mean value of 164.3 W/m2). Similar spatial distribution of the surface energy fluxes was observed in 2014. This shows that the distribution of the surface energy fluxes across Akure varies based on the features of the different land covers. Error analysis showed poor estimation of soil heat flux from SEBAL. SEBAL model can be applied for the estimation of surface energy fluxes in areas of sparse ground station data and can also reveal the spatial variation of the energy fluxes.

Regional surface soil heat flux estimate from multiple remote sensing data in a temperate and semiarid basin

The regional surface soil heat flux (G0) estimation is very important for the large-scale land surface process modeling. However, most of the regional G0 estimation methods are based on the empirical relationship between G0 and the net radiation flux. A physical model based on harmonic analysis was improved (referred to as model) and applied over the Heihe River Basin northwest China with multiple remote sensing data, e.g., FY-2C, AMSR-E, and MODIS, and soil map data. The sensitivity analysis of the model was studied as well. The results show that the improved model describes the variation of G0 well. Land surface temperature (LST) and thermal inertia (Γ) are the two key input variables to the HM model. Compared with in situ G0, there are some differences, mainly due to the differences between remote-sensed LST and the in situ LST. The sensitivity analysis shows that the errors from-7 to-0.5K in LST amplitude and from-300 to 300J m-2 K-1 s-0.5 in Γ will cause about 20% errors, which are acceptable for G0 estimation.

In Situ Thermistor Calibration for Improved Measurement of Soil Temperature Gradients

Core Ideas Soil temperature gradients are important for soil (latent) heat flux estimation. Heat‐pulse sensor thermistors' temperature differences were on the order of 0.2°C. In situ calibration reduced uncertainty between thermistors to about 0.06°C. In situ calibrated offsets between thermistors were similar to laboratory results. Offsets were found to change very little over a 5‐yr period. Accurate measurement of soil temperature gradients is important for the estimation of soil heat flux and latent heat flux, both major components of the surface energy balance. Soil temperature gradients are commonly measured using heat‐pulse sensors equipped with thermistors. In this study, individual thermistors showed absolute temperature differences on the order of 0.2°C when placed under uniform temperature conditions. These differences compromised measurement of soil temperature gradients over small depth increments and/or conditions with relatively minor variation in temperatures. An in situ calibration approach was found to reduce the uncertainty between thermistors to about 0.05°C in a vineyard under arid conditions. In situ calibration results were similar to laboratory results before and after field deployment for temperatures ranging between 4 and 60°C. Thermistor offsets were found to change very little over a 5‐yr period, indicating that pre‐ or post‐laboratory calibration could be sufficient. The in situ approach can be useful when calibration prior to field deployment is unavailable and/or sensor failure prevents post‐field calibration.

Estimation of Soil Heat Flux over the Northern Tibetan Plateau based on in-situ Soil Temperature and Moisture Data

Estimation of Soil Heat Flux over the Northern Tibetan Plateau based on in-situ Soil Temperature and Moisture Data

Assessment of a Remote Sensing Energy Balance Methodology (SEBAL) Using Different Interpolation Methods to Determine Evapotranspiration in a Citrus Orchard

A surface energy balance algorithm for land (SEBAL) for estimating evapotranspiration (ET) has been parameterized and tested in a 400-ha drip irrigated citrus orchard. Simultaneously, during three growing seasons, energy fluxes were measured using Eddy Covariance. Instantaneous fluxes obtained with SEBAL using 10 images from Landsat-5 were compared with the measured fluxes. The Perrier function was the best method for properly estimating the roughness momentum length for discontinuous canopies, as in citrus orchards. Crop height was estimated using LIDAR data. In general, SEBAL performed well for net radiation estimation but failed in soil heat flux estimation. Latent heat estimations from the SEBAL model had a relative root mean square error (rRMSE) of 0.06 when compared with measurements obtained by Eddy Covariance. Three procedures were tested for up-scaling the instantaneous ET estimates from SEBAL to daily ET values: 1) assuming the fraction between the actual ET and the reference ET is constant throughout the day; 2) using actual local crop coefficient curves; and 3) using an up-scaling factor where the fraction of hourly ET to daily ET equals the ratio of hourly to daily global solar radiation. This last method gave acceptable results for daily ET estimations $({\bf rRMSE} = {\bf 0.09})$ and for 15-day ET $({\bf rRMSE} = {\bf 0.19})$ , and its main advantage is that no local data are required. It is concluded that the SEBAL methodology can be successfully applied for determining actual ET, even in discontinuous citrus canopies. However, additional parameterizations of momentum roughness length were needed in order to obtain reliable ET determinations.

Soil heat flux and day time surface energy balance closure at astronomical observatory, Thiruvananthapuram, south Kerala

Soil heat flux is an important input component of surface energy balance. Estimates of soil heat flux were made in the year 2008 using soil temperature data at Astronomical Observatory, Thiruvananthapuram, south Kerala. Hourly values of soil heat flux from 00 to 24 LST are presented for selected days typical of the winter, pre-monsoon, SW monsoon and NE monsoon seasons. The diurnal variation is characterized by a cross-over from negative to positive values at 0700 h, occurrence of maximum around noon and return to negative values in the late evening. The energy storage term for the soil layer 0–0.05 m is calculated and the ground heat flux G ∗ is estimated in all seasons. Daytime surface energy balance at the surface on wet and dry seasons is investigated. The average Bowen’s ratio during the wet and dry seasons were 0.541 and 0.515, respectively indicating that considerable evaporation takes place at the surface. The separate energy balance components were examined and the mean surface energy balance closure was found to be 0.742 and 0.795 for wet and dry seasons, respectively. When a new method that accounts for both soil thermal conduction and soil thermal convection was adopted to calculate the surface heat flux, the energy balance closure was found to be improved. Thus on the land surface under study, the soil vertical water movement is significant.

An improved empirical method for large spatial scale surface soil heat flux estimations

In this paper, a novel method to simulate soil heat flux for large spatial scale is proposed. This method is constructed with the ratio of soil heat flux and net radiation (G0/Rn) and surface characteristic parameters, such as ratio vegetation indices, surface temperature, surface shortwave infrared reflectance, soil moisture content, solar zenith angle. Field calibration is carried out using measured data in 2009 from Yingke, Huazhaizi, Arou, and Dayakou stations located in Heihe River Basin, Northwest of China. The estimated soil heat flux is compared with field observation data from Yingke and Arou stations in 2008. The overall deviation basis and correlation coefficient between the soil heat flux estimation and measured data are 13.4% and 0.804 in the Yingke station and 12.5% and 0.893 in the Arou station respectively, and also the correlation coefficient are 0.905 in the Maliantan station and 0.817 in the Binggou station respectively. Results indicated that the proposed method performed well in Heihe River Basin. This new method could be an optimal choice to estimate surface soil heat flux for large spatial scale in the future.

Validation of two soil heat flux estimation techniques against observations made in an engineered urban green space

In highly developed landscapes, the soil heat flux that results from changes in land cover determines, in part, the extent to which urban climatic conditions can be modulated (e.g. retrofitting cities with new, engineered green spaces to reduce urban heat island effect). In this paper, temperature-dependent (TD) and temperature-independent (TI) soil heat flux models are validated against 6 days of measurements made in an engineered urban green space. The results suggest that the TI model (heat flux plate method) represents the observations better than the temperature-dependent one, which consistently overestimates soil heat flux at night and during the dusk-dawn period. Moreover, a sensitivity analysis reveals that the TD model is more sensitive to the selection of thermal conductivity and heat capacity values than the TI model. It can be concluded that the TI model is a more robust predictive tool, and especially in urban applications where soil properties may be highly uncertain.

Spatio-temporal surface soil heat flux estimates from satellite data; results for the AMMA experiment at the Fakara (Niger) supersite

This paper describes a method that employs Earth Observation (EO) data to calculate spatiotemporal estimates of soil heat flux, G, using a physically-based method (the Analytical Method). The method involves a harmonic analysis of land surface temperature (LST) data. It also requires an estimate of near-surface soil thermal inertia; this property depends on soil textural composition and varies as a function of soil moisture content. The EO data needed to drive the model equations, and the ground-based data required to provide verification of the method, were obtained over the Fakara domain within the African Monsoon Multidisciplinary Analysis (AMMA) program. LST estimates (3 km × 3 km, one image 15 min −1) were derived from MSG-SEVIRI data. Soil moisture estimates were obtained from ENVISAT-ASAR data, while estimates of leaf area index, LAI, (to calculate the effect of the canopy on G, largely due to radiation extinction) were obtained from SPOT-HRV images. The variation of these variables over the Fakara domain, and implications for values of G derived from them, were discussed. Results showed that this method provides reliable large-scale spatiotemporal estimates of G. Variations in G could largely be explained by the variability in the model input variables. Furthermore, it was shown that this method is relatively insensitive to model parameters related to the vegetation or soil texture. However, the strong sensitivity of thermal inertia to soil moisture content at low values of relative saturation (<0.2) means that in arid or semi-arid climates accurate estimates of surface soil moisture content are of utmost importance, if reliable estimates of G are to be obtained. This method has the potential to improve large-scale evaporation estimates, to aid land surface model prediction and to advance research that aims to explain failure in energy balance closure of meteorological field studies.

Effects of the soil heat flux estimates on surface energy balance closure over a semi-arid grassland

Soil heat flux is important for surface energy balance (SEB), and inaccurate estimation of soil heat flux often leads to surface energy imbalance. In this paper, by using observations of surface radiation fluxes and soil temperature gradients at a semi-arid grassland in Xilingguole, Inner Mongolia, China from June to September 2008, the characters of the SEB for the semi-arid grassland were analyzed. Firstly, monthly averaged diurnal variations of SEB components were revealed. A 30-min forward phase displacement of soil heat flux (G) observed by a fluxplate at the depth of 5-cm below the soil surface was conducted and its effect on the SEB was studied. Secondly, the surface soil heat flux (Gs) was computed by using harmonic analysis and the effect of the soil heat storage between the surface and the fluxplate on the SEB was examined. The results show that with the 30-min forward phase displacement of observed G, the slope of the ordinary linear regression (OLR) of turbulent fluxes (H+LE) against available energy (Rn-G) increased from 0.835 to 0.842, i.e., the closure ratio of SEB increased by 0.7%, yet energy imclosure of 15.8% still existed in the SEB. When Gs, instead of G was used in the SEB equation, the slope of corresponding OLR of (H+LE) against (Rn-Gs) reached 0.979, thereby the imclosure ratio of SEB was reduced to only 2.1%.

Soil Heat Flux Modeling Using Artificial Neural Networks and Multispectral Airborne Remote Sensing Imagery

The estimation of spatially distributed crop water use or evapotranspiration (ET) can be achieved using the energy balance for land surface algorithm and multispectral imagery obtained from remote sensing sensors mounted on air- or space-borne platforms. In the energy balance model, net radiation (Rn) is well estimated using remote sensing; however, the estimation of soil heat flux (G) has had mixed results. Therefore, there is the need to improve the model to estimate soil heat flux and thus improve the efficiency of the energy balance method based on remote sensing inputs. In this study, modeling of airborne remote sensing-based soil heat flux was performed using Artificial Neural Networks (ANN). Soil heat flux was modeled using selected measured data from soybean and corn crop covers in Central Iowa, U.S.A. where measured values were obtained with soil heat flux plate sensors. Results in the modeling of G indicated that the combination Rn with air temperature (Tair) and crop height (hc) better reproduced measured values when three independent variables were considered. The combination of Rn with leaf area index (LAI) from remote sensing, and Rn with surface aerodynamic resistance (rah) yielded relative larger overall correlation coefficient values when two independent variables were included using ANN. In addition, air temperature (Tair) may be a key variable in the modeling of G as suggested by the ANN application (r of 0.83). Therefore, it is suggested that Rn, LAI, rah and hc and potentially Tair be considered in future modeling studies of G.

Comparison and Analysis of Empirical Equations for Soil Heat Flux for Different Cropping Systems and Irrigation Methods

We evaluated the performance of four models for estimating soil heat flux density (G) in maize (Zea mays L.) and soybean (Glycine max L.) fields under different irrigation methods (center-pivot irrigated fields at Mead, Nebraska, and subsurface drip irrigated field at Clay Center, Nebraska) and rainfed conditions at Mead. The model estimates were compared against measurements made during growing seasons of 2003, 2004, and 2005 at Mead and during 2005, 2006, and 2007 at Clay Center. We observed a strong relationship between the G and net radiation (Rn) ratio (G/Rn) and the normalized difference vegetation index (NDVI). When a significant portion of the ground was bare soil, G/Rn ranged from 0.15 to 0.30 and decreased with increasing NDVI. In contrast to the NDVI progression, the G/Rn ratio decreased with crop growth and development. The G/Rn ratio for subsurface drip irrigated crops was smaller than for the center-pivot irrigated crops. The seasonal average G was 13.1%, 15.2%, 10.9%, and 12.8% of Rn for irrigated maize, rainfed maize, irrigated soybean, and rainfed soybean, respectively. Statistical analyses of the performance of the four models showed a wide range of variation in G estimation. The root mean square error (RMSE) of predictions ranged from 15 to 81.3 W m-2. Based on the wide range of RMSE, it is recommended that local calibration of the models should be carried out for remote estimation of soil heat flux.

Long-term estimation of soil heat flux by single layer soil temperature

Soil heat flux is one of the important components of surface energy balance. In this study, long-term estimation of soil heat flux from single layer soil temperature was carried out by the traditional sinusoidal analytical method and the half-order time derivative method of Wang and Bras [Wang and Bras (1999) J Hydrol 216:214-226]. In order to understand the characteristics of soil heat flux and to examine the performances of the two methods, a field experiment was conducted at a temperate and humid grassland in Cork, Ireland. Our results show that the soil heat flux had the same magnitude as the sensible heat flux at this grassland site. It was also demonstrated that the analytical method did not predict the soil heat flux well because the sinusoidal assumption for the temporal variation in soil heat flux was invalid. In contrast, good agreement was found between the soil heat flux measurements and predictions made by the half-order time derivative method. This success suggests that this method could be used to estimate soil heat flux from long-term remotely sensed surface temperature.

Remote estimation of thermal inertia and soil heat flux for bare soil

A method is presented which allows thermal inertia (the soil heat capacity times the square root of the soil thermal diffusivity, C h D h ), to be estimated remotely from micrometeorological observations. The method uses the drop in surface temperature, T s, between sunset and sunrise, and the average night-time net radiation during that period, for clear, still nights. A Fourier series analysis was applied to analyse the time series of T s. The Fourier series constants, together with the remote estimate of thermal inertia, were used in an analytical expression to calculate diurnal estimates of the soil heat flux, G. These remote estimates of C h D h and G compared well with values derived from in situ sensors. The remote and in situ estimates of C h D h both correlated well with topsoil moisture content. This method potentially allows area-average estimates of thermal inertia and soil heat flux to be derived from remote sensing, e.g. METEOSAT Second Generation, where the area is determined by the sensor’s height and viewing angle.

Soil heat flux under irrigated, partially irrigated wheat and bare vertisol in relation to varying soil moisture and leaf area index at Pune

Soil heat flux as a function of moisture content in the drying cycles both under irrigated and partially irrigated wheat and in bare black vertisol was studied to relate temporal changes in soil heat fluxes to changes in leaf area index (LAI), soil water content and meteorological parameters. Moisture content dropped as low as 1 to 5 percent by weight at surface layer and 5 to 10 percent by weight at subsurface layers when irrigation was shut off under partially irrigated plot. The peak weekly mean global, net and reflected radiation during the crop growing season in this semi-arid region goes as high as 655, 361 and 179 Wm-2 respectively in the year 1996-97 and 700, 366 and 137 Wm-2 respectively during the year 1997-98. Soil temperature at 1430 hours IST ranged from 27 to 40°C at the surface (5.0 cm) layer under irrigated condition. It was 7 to 10° C and 2 to 3° C higher in the surface and subsurface layers respectively under partially irrigated wheat during the drying cycle. The upward soil heat flux ranged from -3.3 to -29.7 Wm-2 at 0730 hours IST, whereas downward heat flux at 1430 hours IST ranged between 8.4 to 33.9 Wm-2 under irrigated condition. Under partially irrigated condition it varied from -0.7 to -9.2 Wm-2 at 0730 hours IST and from 10.4 to 20.9 Wm-2 at 1430 hours IST; whereas it varied from -4.2 to -17.6 Wm-2 at 0730 hours IST and 6.7 to 24.7 Wm-2 at 1430 hours IST, under bare soil. The maximum mean heat fluxes into 5-20 cm soil depth under irrigated, partially irrigated and the bare soil were 10.2, 5.0 and 6.5 Wm-2 and 9.2, 7.1, and 6.7 Wm-2 respectively in the years 1996-97 and 1997-98. Soil temperature at 1430 hours IST both for irrigated wheat and bare vertisol and global radiation with soil temperature at 0730 hours IST under partially irrigated wheat were found to be the best predictors of soil heat flux. The relationships between soil heat flux and soil water content at different depth intervals along with LAI and other meteorological parameters could be used for estimation of soil heat flux, both for irrigated and partially irrigated wheat and bare soil.

Surface Energy Budget at Amdo on the Tibetan Plateau using GAME/Tibet IOP98 Data.

In the east of Tibetan Plateau, Amdo, the surface energy flux measurement with eddy correlation technique was conducted during the Intensive Observation Period (IOP) of GEWEX Asian Monsoon Experiment (GAME). This study is a preliminary analysis on surface energy budget at Amdo with these data. There is a remarkable change in sensible and latent heat fluxes between pre-monsoon season and summer monsoon season. In the pre-monsoon, the ground surface and the surface layer were very dry. The specific humidity was 2 to 4 g/kg and the sensible heat flux was dominant. As the monsoon progresses, the surface becomes wet due to almost daily precipitation. Accordingly, the sensible heat flux decreases and the latent heat flux increases. In the beginning of September, nearly the end of the summer monsoon, the latent heat flux exceeds the sensible heat flux. The ground heat flux at the surface was estimated using the observed soil temperature profile with the aid of the thermal conductive equation. The computed ground heat flux corresponds to the residual of the surface energy balance in the daytime. But disagreement occurred in the evening, when the surface temperature rapidly decreases. On the daily averaged bases, the surface energy balance is not well closed. In terms of closure ratio, the value in a typical clear day was 67%. Another rough estimation of soil heat flux is made, in which the heat needed to melt the soil water and to heat up the soil layer was calculated. According to this, it was estimated that about 30 W/m2 (20% of net radiation) of soil heat flux was required on average over April 20 to July 20, but the measured soil heat flux was only 5.7 W/m2.

A long-term study of soil heat flux under a forest canopy

International programmes such as EUROFLUX focus on the analysis of long-term fluxes and energy budgets in the biosphere. Reliable estimates of hourly energy budgets require an accurate estimation of soil heat flux, that is often non-negligible even in a forest, and can be predominant during the night. Over long periods of time such as one to several months, its contribution can also be significant. The present work has been carried out to get good estimates of the soil heat flux in a maritime pine stand in the southwest of France, one of the 15 EUROFLUX sites. Using a whole year’s worth of data, soil heat flux was estimated by a two-step version of the null-alignment method using soil temperature, water content and bulk density measurements between the soil surface and a depth of 1 m. A data subset was firstly used to estimate and model the soil thermal conductivity at various depths. The full data set was then used with the modelled conductivity to estimate heat storage between the surface and a reference depth, and calculate the heat flux at the soil surface. Throughout the investigated year and at a 30 min time scale, the soil heat flux represents 5–10% of the incident net radiation, i.e. 30–50% of the net radiation over the understorey. Cumulative values from September 1997 to March 1998 reach a maximum of −70 MJ m −2, which represents nearly 50% of the cumulative values of transmitted net radiation (140 MJ m −2) over the same period. These estimates of soil heat flux allowed the energy budgets of the whole stand and the understorey to be closed, and showed that the storage terms are significant not only at a 30 min time scale but also at longer time scales (a few weeks). An attempt was finally made to model soil heat flux from meteorological data, which has rarely been done for a forest soil and over a long-term data set. In most of the existing models, soil heat flux is taken as a fraction of net radiation or sensible heat flux. Here, the litter acts as a mulch at the soil surface so that the only significant terms of the energy balance at this level are soil heat flux, transmitted net radiation and turbulent sensible heat flux. Soil heat flux is shown to be a linear combination of (1) net radiation above the understorey with a clear dependence of the coefficient on the soil cover fraction, and (2) the difference between the air and litter temperatures, with little influence of soil water content or wind speed on the coefficient.

Soil heat flux estimation based on the finite-difference form of the transient heat flow equation

Soil heat flux ( G) often aids in interpreting the response of plants to the growing environment, but methods of estimating G are needed that require limited soil temperature and physical property information. This study describes a method for estimating G by implicitly solving the finite-difference form of the transient heat flow equation for the apparent daily thermal conductivity. The derived apparent thermal conductivity and measured soil temperature gradient are applied to Fourier's law for estimating G. This method requires the measurement of soil bulk density and daily water content (for volumetric heat capacity) and hourly temperatures at three depths. Hourly G measured by heat flux plates buried at depths of 0.05 m in apple and peach orchards and 0.03 m in a barley stubble field were compared with G estimated using the harmonic method and our proposed finite-difference method. The finite-difference method performed better, as indicated by a smaller root-mean-square error (r.m.s.e.), than the harmonic method for 71 of the 83 daily data sets used in this study. The average r.m.s.e. in estimating hourly G for the 83 data sets was 10.9 W m −2 for the finite-difference method and 16.3 W m −2 for the harmonic method. Daily net warming or cooling of the soil was correctly estimated for 95% of the data sets using the finite-difference method. The harmonic method, however, results in no net warming or cooling of the soil when deviations are not accounted for in the periodicity.