Bare Soil Surface Research Articles

Sensible Heat Observations Reveal Soil-Water Evaporation Dynamics

Abstract Soil-water evaporation is important at scales ranging from microbial ecology to large-scale climate. Yet routine measurements are unable to capture rapidly shifting near-surface soil heat and water processes involved in soil-water evaporation. The objective of this study was to determine the depth and location of the evaporation zone within soil. Three-needle heat-pulse sensors were used to monitor soil heat capacity, thermal conductivity, and temperature below a bare soil surface in central Iowa during natural wetting/drying cycles. Soil heat flux and changes in heat storage were calculated from these data to obtain a balance of sensible heat components. The residual from this balance, attributed to latent heat from water vaporization, provides an estimate of in situ soil-water evaporation. As the soil dried following rainfall, results show divergence in the soil sensible heat flux with depth. Divergence in the heat flux indicates the location of a heat sink associated with soil-water evaporation. Evaporation estimates from the sensible heat balance provide depth and time patterns consistent with observed soil-water depletion patterns. Immediately after rainfall, evaporation occurred near the soil surface. Within 6 days after rainfall, the evaporation zone proceeded > 13 mm into the soil profile. Evaporation rates at the 3-mm depth reached peak values > 0.25 mm h−1. Evaporation occurred simultaneously at multiple measured depth increments, but with time lag between peak evaporation rates for depths deeper below the soil surface. Implementation of finescale measurement techniques for the soil sensible heat balance provides a new opportunity to improve understanding of soil-water evaporation.

Retrieval of surface roughness using multi-polarized Envisat-1 ASAR data

Spatial distribution of surface roughness is very critical information for many application areas. Surface roughness is often characterized using statistical distribution. However, due to the huge complexity associated with spatial soil surfaces it is difficult to accurately characterize surface roughness over large areas using statistical distribution. Surface roughness influences SAR backscatter significantly and therefore for bare soil surfaces, surface roughness plays a critical role in determining the degree of depolarization of the SAR signal. In this paper surface roughness is retrieved using multi-polarized Envisat-1 ASAR data. The depolarization ratio [σ°VH − σ°VV] has been found to be very sensitive to surface roughness. This study demonstrates an approach that can be used to retrieve quantitative surface roughness values from a space platform without making any assumptions regarding distribution of surface roughness on the ground.

Some insight into the influence of urban ground surface properties on the air-surface exchange of total gaseous mercury

Abstract Experiments utilizing meteorologically normalized sampling conditions were used to illustrate the role and function of urban pavement, bare soil and turf grass surface properties with respect to the air-surface exchange of total gaseous Hg (TGM). After ensuring uniform meteorological effects to each surface, resultant TGM fluxes from turf grass, bare soil and pavement were specifically representative of their diverse physical and biogeochemical properties. Results spanning the entire sampling year show distinct TGM flux signatures for each surface (5.69 ± 5.79 (ng/m 2 h) for bare soil, 0.53 ± 1.25 for turf grass, 0.26 ± 0.41 for pavement). Based on medians, the surface limitations of pavement decreased TGM flux by a factor of 22 compared to bare soil and by a factor of 2 compared to turf grass. Turf surface limitations decreased TGM flux by a factor of 11 compared to bare soil. By comparing these results to a parallel study, meteorological effects were found to develop 24% of the TGM flux signature for pavement, 53% for turf and 60% for bare soil. The remaining percentage contributions to each TGM flux signature were from the cumulative surface property effects of each surface. These results suggest that the greater the TGM flux magnitude for a particular surface, the more measurements are needed under a wide variety of meteorological conditions to develop a broad understanding of its TGM flux characteristics. Seasonal observation allowed closer investigation of a large shift to TGM deposition for the turf surface during the fall season. The large shift toward deposition was suspected to be linked to the formation of a thatch layer on the unexposed soil surface just beneath the turf layer.

Mapping Soil Organic Carbon Concentration for Multiple Fields with Image Similarity Analysis

Remotely sensed imagery with high spatial resolution has been used to map soil organic carbon (SOC) concentrations at a field scale with greatly increased accuracy and reduced cost compared with grid sampling. The procedure, however, requires each crop field to be sampled and mapped separately. The purpose of this study was to determine if cost could be reduced further by grouping a number of crop fields based on their image similarity, and then mapping them together as one group. Ten crop fields with a bare soil surface were selected from a 2000 NASA ATLAS image. The similarity among these fields was examined with the Ward neural network system (WNNS) using the image histogram features extracted from the image for each field. Seven fields were placed into two groups based on the coefficient of determination (R2) values computed from WNNS, with one group consisting of three fields and the second consisting of four fields. Soil samples were taken from the seven fields along with their global positioning system locations and were divided into two data sets, with one for model development and the other for result checking. Models for mapping SOC concentrations were developed for each group of fields using a single procedure. The resulting maps were checked based on soil sample sets that were not used in model development and showed good agreement between mapped values and lab‐determined values, with r2 values of 0.80 for one group of fields and 0.77 for the second group of fields. The models were greatly improved compared with the model developed for all seven fields (R2 was 0.87 and 0.91 for two groups vs. 0.63 for all fields and RMSE was 0.108 and 0.143 vs. 0.219 of SOC percentage). The model developed with similarity grouping was also compared with the model for field‐by‐field mapping and showed close agreement (R2 was 0.87 for Group 1 vs. 0.89 for Field 2 only in Group 1 and RMSE was 0.108 vs. 0.119 for the same field).

Turbulent Flux Transfer over Bare-Soil Surfaces: Characteristics and Parameterization

AbstractParameterization of turbulent flux from bare-soil and undercanopy surfaces is imperative for modeling land–atmosphere interactions in arid and semiarid regions, where flux from the ground is dominant or comparable to canopy-sourced flux. This paper presents the major characteristics of turbulent flux transfers over seven bare-soil surfaces. These sites are located in arid, semiarid, and semihumid regions in Asia and represent a variety of conditions for aerodynamic roughness length (z0m; from <1 to 10 mm) and sensible heat flux (from −50 to 400 W m−2). For each site, parameter kB−1 [=ln(z0m/z0h), where z0h is the thermal roughness length] exhibits clear diurnal variations with higher values during the day and lower values at night. Mean values of z0h for the individual sites do not change significantly with z0m, resulting in kB−1 increasing with z0m, and thus the momentum transfer coefficient increases faster than the heat transfer coefficient with z0m. The term kB−1 often becomes negative at night for relatively smooth surfaces (z0m ∼ 1 mm), indicating that the widely accepted excess resistance for heat transfer can be negative, which cannot be explained by current theories for aerodynamically rough surfaces. Last, several kB−1 schemes are evaluated using the same datasets. The results indicate that a scheme that can reproduce the diurnal variation of kB−1 generally performs better than schemes that cannot.

肥料の撒き方の違いによる斜面からの養分流出に関する研究

肥料の撒き方の違いによる斜面からの養分流出に関する研究

Mulching as a means of exploiting dew for arid agriculture?

A traditional mulching technique used in Lanzarote, Canary Islands, allows dry farming as well as pronounced water savings in irrigation. It is known to reduce evaporational losses, but is also supposed to enhance the nocturnal condensation of water vapour from the atmosphere. The mulch layer consists of porous volcanic rock fragments abundantly available on the island. The mulched surface is believed to cool rapidly and to be more hygroscopic than a bare soil surface. This was investigated during a field experiment conducted over 68 nights during different seasons in 2001 and 2002, as well as some simple laboratory measurements. It was found that nocturnal condensation on the mulch surface (max 0.33 mm) was lower than on the bare soil surface (max 0.57 mm) or any one of three alternative mulch substrates. However, a slightly stronger nocturnal cooling of the mulched as compared to the bare surface was present. It is shown that these contrary findings can be explained by the higher hygroscopicity of the dry loam soil, resulting in condensation gains beyond the strict definition of dew. Differences in plant-availability of non-hygroscopic dew water and hygroscopic water uptakes are discussed, and conditions under which mulching would show positive condensation effects are defined. This includes a theoretical section demonstrating that non-hygroscopic mulch layers of a proper thickness can provide small amounts of dew to plant roots at the mulch–soil interface. This condensation could also happen during the day and would be favoured by a high amplitude of the diurnal atmospheric moisture cycle.

Cover crop evapotranspiration under semi-arid conditions using FAO dual crop coefficient method with water stress compensation

Cover cropping is a common agro-environmental tool for soil and groundwater protection. In water limited environments, knowledge about additional water extraction by cover crop plants compared to a bare soil is required for a sustainable management strategy. Estimates obtained by the FAO dual crop coefficient method, compared to water balance-based data of actual evapotranspiration, were used to assess the risk of soil water depletion by four cover crop species (phacelia, hairy vetch, rye, mustard) compared to a fallow control. A water stress compensation function was developed for this model to account for additional water uptake from deeper soil layers under dry conditions. The average deviation of modelled cumulative evapotranspiration from the measured values was 1.4% under wet conditions in 2004 and 6.7% under dry conditions in 2005. Water stress compensation was suggested for rye and mustard, improving substantially the model estimates. Dry conditions during full cover crop growth resulted in water losses exceeding fallow by a maximum of +15.8% for rye, while no substantially higher water losses to the atmosphere were found in case of evenly distributed rainfall during the plant vegetation period with evaporation and transpiration concentrated in the upper soil layer. Generally the potential of cover crop induced water storage depletion was limited due to the low evaporative demand when plants achieved maximum growth. These results in a transpiration efficiency being highest for phacelia (5.1 g m −2 mm −1) and vetch (5.4 g m −2 mm −1) and substantially lower for rye (2.9 g m −2 mm −1) and mustard (2.8 g m −2 mm −1). Taking into account total evapotranspiration losses, mustard performed substantially better. The integration of stress compensation into the FAO crop coefficient approach provided reliable estimates of water losses under dry conditions. Cover crop species reducing the high evaporation potential from a bare soil surface in late summer by a fast canopy coverage during early development stages were considered most suitable in a sustainable cover crop management for water limited environments.

Evaporation from three water bodies of different sizes and climates: Measurements and scaling analysis

Evaporation from small reservoirs, wetlands, and lakes continues to be a theoretical and practical problem in surface hydrology and micrometeorology because atmospheric flows above such systems can rarely be approximated as stationary and planar-homogeneous with no mean subsidence (hereafter referred to as idealized flow state). Here, the turbulence statistics of temperature ( T) and water vapor ( q) most pertinent to lake evaporation measurements over three water bodies differing in climate, thermal inertia and degree of advective conditions are explored. The three systems included Lac Léman in Switzerland (high thermal inertia, near homogeneous conditions with no appreciable advection due to long upwind fetch), Eshkol reservoir in Israel (intermediate thermal inertia, frequent strong advective conditions) and Tilopozo wetland in Chile (low thermal inertia, frequent but moderate advection). The data analysis focused on how similarity constants for the flux-variance approach, C T / C q , and relative transport efficiencies R wT / R wq , are perturbed from unity with increased advection or the active role of temperature. When advection is small and thermal inertia is large, C T / C q < 1 (or R wT / R wq > 1) primarily due to the active role of temperature, which is consistent with a large number of studies conducted over bare soil and vegetated surfaces. However, when advection is significantly large, then C T / C q > 1 (or R wT / R wq < 1). When advection is moderate and thermal inertia is low, then C T / C q ∼ 1. This latter equality, while consistent with Monin–Obukhov similarity theory (MOST), is due to the fact that advection tends to increase C T / C q above unity while the active role of temperature tends to decrease C T / C q below unity. A simplified scaling analysis derived from the scalar variance budget equation, explained qualitatively how advection could perturb MOST scaling (assumed to represent the idealized flow state).

A possibilistic approach to soil moisture retrieval from ERS synthetic aperture radar backscattering under soil roughness uncertainty

Radar remote sensing of bare soil surfaces has been shown to be very useful for retrieving soil moisture. However, the error on the retrieved value depends on the accuracy of the roughness parameters (RMS height and correlation length). Several studies have demonstrated that these parameters show a high variability within a field, and therefore a lot of soil roughness profiles need to be measured to obtain accurate estimates. However, in an operational mode, soil roughness measurements are not available and therefore, for different types of tillage, roughness parameters are ill known. Possibility theory offers a way of handling this type of uncertainty, by modeling roughness parameters by means of possibility distributions. Inverting the integral equation model then leads to a possibility distribution for soil moisture. After transforming these possibilities into probabilities, mean soil moisture values and the uncertainty thereupon (given by the standard deviation) are obtained. It is found that the uncertainty depends on the wetness state of the soil. An application of our possibilistic retrieval algorithm to field observations at two sites in Belgium and one site in Italy resulted in accurate soil moisture observations (RMS error less than 6 vol %).

Suppression of Radon Exhalation from Soil by Covering with Clay-mixed Soil

The effectiveness of bentonite-mixed soil as a barrier to radon exhalation from soil is investigated experimentally at a closed uranium mine in Japan. Continuous observations of radon flux from a clay-covered soil surface and a bare soil surface were conducted for a period of 80 days. The mean radon flux from the clay-covered plot was one fifth of that from the bare plot, demonstrating that the clay-mixed soil is effective as a boundary suppressing radon exhalation from the contaminated soil. Numerical analyses using a one-dimensional radon transport model for an unsaturated soil for the dry weather conditions confirmed the effectiveness of the clay-mixed soil cover under a range of weather conditions.

A Takagi–Sugeno Fuzzy Rule-Based Model for Soil Moisture Retrieval From SAR Under Soil Roughness Uncertainty

Radar remote sensing has shown its potential for retrieving soil moisture from bare soil surfaces. Since the backscattering process is also influenced by soil roughness, the characterization of this roughness is crucial for an accurate soil moisture retrieval. However, several field experiments have shown a large variability of the roughness parameters. Describing these parameters by means of possibility distributions allows to account for their uncertainty. Verhoest et al. introduced a retrieval procedure which calculates from these uncertain roughness parameters the possibility distribution of retrieved soil moisture, from which a soil moisture value and uncertainty upon the retrieval are estimated. The main disadvantage of their technique is the high computational demand, which hampers an operational application. In this paper, a fuzzy modeling approach, which is based on fuzzy rules of the Takagi-Sugeno type, is introduced that accurately simulates the soil moisture and the uncertainty upon its retrieved value as obtained by the possibilistic procedure

Field-Supported Verification and Improvement of a Passive Microwave Surface Emission Model for Rough, Bare, and Wet Soil Surfaces by Incorporating Shadowing Effects

To investigate the potential of passive microwave techniques for observing the atmosphere over land, it is important to understand the nature of emissions from the land surface. The heterogeneity of large-scale land surface emissions has been cited as a major impediment in conducting observations of the atmosphere over land. Many models, both theoretical and empirical, have been developed to explain the surface emission with varying degrees of success. In the past, most field-supported research in soil observations using microwave techniques has concentrated on lower frequencies (L-band). This paper reports on a study, supported by field data, that seeks to improve our understanding of surface emission at various frequencies using passive microwave radiometers. This provides a crucial link between remote sensing of the land surface and the atmosphere. We show that it is important to consider shadowing associated with rough wet surfaces. By incorporating shadowing effects, the advanced integral equation model (AIEM) shows remarkable agreement with observations at all frequencies and polarizations. Although the roughness parameters obtained during our experiment correspond to very rough conditions, by including shadowing effects the AIEM model is able to transition from the not so rough natural condition as observed from space to the very rough as obtained during field experiments

Germination and seedling establishment of two annual grasses on lichen-dominated biological soil crusts

Biological soil crusts dominated by lichens are common components of shrub-steppe ecosystems in northwestern US. We conducted growth chamber experiments to investigate the effects of these crusts on seed germination and initial seedling establishment of two annual grasses; the highly invasive exotic Bromus tectorum L. and the native Vulpia microstachys Nutt. We recorded germination time courses on bare soil and two types of biological soil crusts; one composed predominantly of the lichen Diploschistes muscorum (Scop.) R. Sant. (lichen crust) and the other comprised of an assortment of lichens and mosses (mixed crust). Final germination on the lichen crust for both grass species was about a third of that on the bare soil surface. Mean germination time (MGT) was 3–4 days longer on the lichen crust compared with the bare soil. In contrast, there was no difference in germination percentage or MGT between the mixed crust and bare soil, and results were similar for both grass species. For both species, root penetration of germinating seeds on the lichen crust was lower than on the bare soil or mixed crust surfaces. The combined effects of the lichen crust on germination and root penetration resulted in an overall reduction in seedling establishment of 78% for V. microstachys and 85% for B. tectorum relative to the bare soil treatment. Our results clearly demonstrate that lichen-dominated biological soil crust can inhibit germination and root penetration, but the extent of these effects depends on the composition of the crust.

Modified perpendicular drought index (MPDI): a real-time drought monitoring method

Soil moisture and vegetation growth are the most direct and important indicators of drought events and, therefore, an understanding of vegetation and soil spectral behavior is critical to the drought estimation. Recently, Ghulam et al. [Ghulam, A., Qin, Q., Zhan, Z., 2006. Designing of the perpendicular drought index. Environmental Geology, doi:10.1007/s00254-006-0544-2 (accessed March 8, 2007).] established the Perpendicular Drought Index (PDI) that is based on an extensive analysis of spatial distribution features of soil moisture in NIR-Red spectral space. In this paper, an improved drought monitoring method, the Modified Perpendicular Drought Index (MPDI), is developed introducing vegetation fraction, which takes into account both soil moisture and vegetation growth. To validate the drought indices proposed by this paper, Enhanced Thematic Mapper Plus (ETM+) and MODerate Resolution Imaging Spectrometer (MODIS) images from different times registered over different eco-systems with various drought conditions are used to calculate the PDI and MPDI over ground measuring points. The PDI and MPDI are then compared to an in-situ drought index obtained from field measurements made synchronously with the satellite overpass, including the bulk soil moisture content at different soil depths, field moisture capacity, wilting coefficient, etc. It is evident from the results that the PDI and the MPDI is highly accordant with in-situ drought values with the highest correlation ( R 2 = 0.8134) found between the MPDI and an in-situ drought index derived from 0–20 cm mean soil moisture. This study concludes that the PDI and the MPDI provide quite similar results for bare soil surfaces, especially in the early stages of vegetation growth. However, the MPDI demonstrates a much better performance in measuring vegetated surfaces since it takes into account both soil moisture and vegetation growth in the modeling process. The MPDI has the potential to provide a simple and real-time drought monitoring method in the remote estimation of drought phenomena.

Evaluation of MOD16 algorithm using MODIS and ground observational data in winter wheat field in North China Plain

AbstractEvapotranspiration (ET) is an important factor for understanding hydrological processes and climate dynamics. Remote sensing is considered as the most promising tool for estimation of ET over a large spatial scale. The purpose of this study is to analyse and evaluate the MOD16 algorithm, developed by Nishida et al. (2003a,b), in winter wheat fields by using MODIS land products, MOD11‐land surface temperature and MOD13‐standard normalized difference vegetation index (NDVI), as well as observations at the Yucheng Experimental Station, China in 2002. The original MOD16 is a dual‐source ET model in which the evaporation fraction (EF) for bare soil surface is estimated using the VI‐Ts diagram method, and EF for vegetation is determined by a function of canopy resistance, aerodynamic resistance and air temperature. We analysed a radiation budget sub‐model and found that the estimate for solar radiation is acceptable only on cloud‐free days. We also found that, in the original MOD16, seasonal variations of minimum canopy resistance and physiological temperatures are not considered, which results in overestimation of canopy resistance when leaf area index (LAI) is less than 2·5. Because the strong unstable thermal stratification over the dry bare soil surface is ignored in the original algorithm, wind speed is overestimated and aerodynamic resistance above the vegetation surface is underestimated. We then modified the original MOD16 algorithm. The result shows that both EF and ET for vegetation estimated with the modified algorithm are in consistent with both the observations of an eddy covariance system and the calculations using the Penman‐Monteith method. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Effects of microbiotic crusts under cropland in temperate environments on soil erodibility during concentrated flow

AbstractSeveral studies illustrate the wind and water erosion‐reducing potential of semi‐permanent microbiotic soil crusts in arid and semi‐arid desert environments. In contrast, little is hitherto known on these biological crusts on cropland soils in temperate environments where they are annually destroyed by tillage and quickly regenerate thereafter. This study attempts to fill the research gap through (a) a field survey assessing the occurrence of biological soil crusts on loess‐derived soils in central Belgium in space and time and (b) laboratory flume (2 m long) experiments simulating concentrated runoff on undisturbed topsoil samples (0.4 × 0.1 m2) quantifying the microbiotic crust effect on soil erosion rates. Three stages of microbiotic crust development on cropland soils are distinguished: (1) development of a non‐biological surface seal by raindrop impact, (2) colonization of the soil by algae and gradual development of a continuous algal mat and (3) establishment of a well‐developed microbiotic crust with moss plants as the dominant life‐form. As the silt loam soils in the study area seal quickly after tillage, microbiotic soil crusts are more or less present during a large part of the year under maize, sugar beet and wheat, representing the main cropland area. On average, the early‐successional algae‐dominated crusts of stage 2 reduce soil detachment rates by 37%, whereas the well‐developed moss mat of stage 3 causes an average reduction of 79%. Relative soil detachment rates of soil surfaces with microbiotic crusts compared with bare sealed soil surfaces are shown to decrease exponentially with increasing microbiotic cover (b = 0·024 for moss‐dominated and b = 0·006 for algae‐dominated crusts). In addition to ground surface cover by vegetation and crop residues, microbiotic crust occurrence can therefore not be neglected when modelling small‐scale spatial and temporal variations in soil loss by concentrated flow erosion on cropland soils in temperate environments. Copyright © 2007 John Wiley &amp; Sons, Ltd.

Influence of crop residues on trifluralin mineralization in a silty clay loam soil

Trifluralin is typically applied onto crop residues (trash, stubble) at the soil surface, or onto the bare soil surface after the incorporation of crop residues into the soil. The objective of this study was to quantify the effect of the type and amount of crop residues in soil on trifluralin mineralization in a Wellwood silty clay loam soil. Leaves and stubble of Potato (Solanum tuberosum) (P); Canola (Brassica napus) (C), Wheat (Triticum aestivum) (W), Oats (Avena sativa), (O), and Alfalfa (Medicago sativa) (A) were added to soil microcosms at rates of 2%, 4%, 8% and 16% of the total soil weight (25 g). The type and amount of crop residues in soil had little influence on the trifluralin first-order mineralization rate constant, which ranged from 3.57E-03 day−1 in soil with 16% A to 2.89E-02 day−1 in soil with 8% W. The cumulative trifluralin mineralization at 113 days ranged from 1.15% in soil with 16% P to 3.21% in soil with 4% C, again demonstrating that the observed differences across the treatments are not of agronomic or environmental importance.

Surface heat budget on green roof and high reflection roof for mitigation of urban heat island

In this study, the surface temperature, net radiation, water content ratio, etc., of green roofs and high reflection roofs are observed. The heat and water budget are compared to each other. In the daytime, the temperature of the cement concrete surface, the surface with highly reflective gray paint, bare soil surface, green surface and the surface with highly reflective white paint are observed to be in descending order. On a surface with highly reflective white paint, the sensible heat flux is small because of the low net radiation due to high solar reflectance. On the green surface, the sensible heat flux is small because of the large latent heat flux by evaporation, although the net radiation is large. On the cement concrete surface and the surface with a highly reflective gray paint, the sensible heat fluxes have almost the same values because their solar reflectance is approximately equal. These tendencies of the sensible heat flux accord with the pitch relation of the surface temperature. Methods to estimate the quantity of evaporation, evaporative efficiency, heat conductivity, and thermal capacity are explained, and the observation data is applied to these methods.

Evaluating parameterizations of aerodynamic resistance to heat transfer using field measurements

Abstract. Parameterizations of aerodynamic resistance to heat and water transfer have a significant impact on the accuracy of models of land – atmosphere interactions and of estimated surface fluxes using spectro-radiometric data collected from aircrafts and satellites. We have used measurements from an eddy correlation system to derive the aerodynamic resistance to heat transfer over a bare soil surface as well as over a maize canopy. Diurnal variations of aerodynamic resistance have been analyzed. The results showed that the diurnal variation of aerodynamic resistance during daytime (07:00 h–18:00 h) was significant for both the bare soil surface and the maize canopy although the range of variation was limited. Based on the measurements made by the eddy correlation system, a comprehensive evaluation of eight popularly used parameterization schemes of aerodynamic resistance was carried out. The roughness length for heat transfer is a crucial parameter in the estimation of aerodynamic resistance to heat transfer and can neither be taken as a constant nor be neglected. Comparing with the measurements, the parameterizations by Choudhury et al. (1986), Viney (1991), Yang et al. (2001) and the modified forms of Verma et al. (1976) and Mahrt and Ek (1984) by inclusion of roughness length for heat transfer gave good agreements with the measurements, while the parameterizations by Hatfield et al. (1983) and Xie (1988) showed larger errors even though the roughness length for heat transfer has been taken into account.