Agronomy Journal 92:847-854 (2000)
© 2000 American Society of Agronomy
SPARSE CANOPY SYMPOSIUM INTRODUCTION
A Two-Source Energy Balance Approach Using Directional Radiometric Temperature Observations for Sparse Canopy Covered Surfaces
William P. Kustas and
John M. Norman
Dep. of Soil Science, Univ. of Wisconsin, 1525 Observatory Dr., Madison, WI 53706 USA
bkustas{at}hydrolab.arsusda.gov
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ABSTRACT
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A two-source energy balance model developed to use directional radiometric surface temperature for estimating component heat fluxes from soil and vegetation has had several recent modifications to account for some of the unique properties associated with sparse canopies. Two of these changes involve the algorithms predicting the divergence of net radiation inside the canopy and how to account for clumped vegetation, which affects both the wind and radiation penetration inside the canopy and radiative temperature partitioning between soil and vegetation components. Model results with and without these modifications are compared using data collected from a sparsely vegetated row crop of cotton (Gossypium hirsutum L. cv. Delta Pine 77). It is suggested that these two new algorithms be incorporated in any two-source model applied to sparse canopies.
Abbreviations: LAI, leaf area index • RMSD, root-mean-square-difference • MB, mean-bias
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INTRODUCTION
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THE USE of directional radiometric surface temperature, TR (
), from a zenith view angle frequently involves the controversial assumption that it is equivalent to the so-called "aerodynamic temperature", TO, of the surface. TO is the temperature that satisfies the bulk resistance or "single-source" expression having the form
 | (1) |
where H is the sensible heat flux (W m-2), 
Cp is the volumetric heat capacity of air (J m-3 K-1), TA is the air temperature at some reference height above the surface (K), REX is an excess resistance associated with heat transport, and RA is the aerodynamic resistance (s m-1). A detailed discussion of the application of RA and REX with observations of TR () is given by Stewart et al. (1994).
The problem is that TO cannot be measured, so it is often replaced with an observation of TR () in Eq. [1]. However, for sparse canopies differences between TO and TR () can be > 10 degrees (e.g., Kustas, 1990). Moreover, Vining and Blad (1992) showed that use of Eq. [1] with the TR () observations at different viewing angles can significantly affect the computation of H. As a result, efforts have concentrated on ways to adjust REX to obtain good agreement with measured H. Most approaches have been empirical (e.g., Stewart et al., 1994; Kubota and Sugita, 1994) and therefore difficult to apply a priori to different surface types. Indeed, the testing of various REX formulations with experimental data indicates that single-source schemes are not applicable to partial canopy covered surfaces (Sun and Mahrt, 1995; Kustas et al., 1996; Verhoef et al., 1997; Troufleau et al., 1997; Lhomme et al., 1997).
Therefore, recent efforts have concentrated on accounting for the difference between TO and TR () using "two-source" models, which consider the effects of soil and vegetation temperatures and resistances on both TO and TR () (e.g., Lhomme et al., 1994; Norman et al., 1995; Chehbouni et al., 1996). Although two-source models are better suited for sparse canopies, the algorithms generally used for estimating soil and vegetation contributions to TR () observations and the partitioning of radiation between the soil and vegetation can have a significant effect on model predictions. Few studies have made comparisons between modeled and measured soil and vegetation temperatures and heat fluxes and hence it is difficult to assess these formulations.
In this paper the two-source model proposed by Norman et al. (1995) (hereafter referred to as N95) will be used to evaluate the effects on heat flux predictions by considering more physically-based schemes for partitioning radiation and temperatures between soil and vegetation, which is particularly relevant to sparse canopies. Required model inputs are directional radiometric temperature and its angle of view, fractional vegetation cover or leaf area index, vegetation height and approximate leaf size, solar radiation, air temperature, and wind speed. While the N95 model has satisfactorily predicted total heat fluxes over a wide range of surfaces and environmental conditions (Zhan et al., 1996), the capability of the model to compute physically realistic component heat fluxes and temperatures from the soil surface and vegetation has only recently been tested by Kustas and Norman (1999a) using micrometeorological and TR() data collected from a furrowed sparsely vegetated cotton crop located in central Arizona (Kustas, 1990). The results of this study led to two modifications which are model specific, while the other two are general in nature and apply to any two-source formulation. The implication of these new formulations on model flux predictions are discussed using the data from sparsely vegetated row crop of cotton.
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Model description
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A detail description of the original N95 model can be found in Norman et al. (1995). Other versions of the model adapted to use multiple-view angle TR() observations is described in Kustas and Norman (1997). Changes to several of the original N95 formulations to account for temporal variations in net radiation divergence through the canopy layer and in the soil heat flux-soil net radiation ratio are described in Kustas et al. (1998). Additional modifications were made recently based on the analysis of Kustas and Norman (1999a) using micrometeorological and TR() data collected from a furrowed sparsely vegetated cotton crop located in central Arizona (Kustas, 1990). These modifications to the N95 model were validated by Kustas et al. (2000) under a wider range of vegetative cover and soil moisture conditions than is normally exhibited in field data using a comprehensive plant-environment (PE) model Cupid (Norman and Campbell, 1983; Norman and Arkebauer, 1991), which simulates radiation exchange, turbulent fluxes and TR() for plant canopies. Cupid accommodates all the generality inherent in a comprehensive PE model by using parameterizations of important processes at the leaf level (cm) and integrating mechanistic equations to the canopy level (10–100 m). Cupid simulated TR() values for low, moderate, and high vegetation cover, under moisture stressed and wet soil conditions and low and high wind speeds were used by the modified N95 model to predict surface fluxes and compare with Cupid output. The r2 values for sensible heat flux, H, and latent heat flux, LE, were 0.85 and 0.90, respectively, indicating that the N95 model can account for a significant portion of the variation in heat fluxes.
Modifications to the N95 model formulations, which can significantly influence flux predictions for sparse canopy covered surfaces include: (i) replacing the commonly used Beer's Law expression for estimating the divergence of net radiation through the canopy layer with a more physically-based algorithm; (ii) adding a simple method to address the effects of clumped vegetation on radiation divergence and wind speed inside the canopy layer, and radiative temperature partitioning between soil and vegetation components; (iii) adjusting the magnitude of the Priestley-Taylor (Priestley and Taylor, 1972) coefficient 
PT used in estimating canopy transpiration; and (iv) formulating a new estimation for soil resistance to sensible heat flux transfer, RS. The later two changes are model specific and are not described here (see Kustas and Norman, 1999a). The two former changes can be applied to any two-source scheme and are discussed below.
Many two-source models use exponential extinction of net radiation (i.e., Beer's Law) for estimating the partitioning of net radiation, RN, between the soil, RN,S, and canopy, RN,C, namely,
 | (2a) |
 | (2b) |
where the value of 
typically ranges between 0.3 and 0.6 (Ross, 1981). Experience has revealed that this is only appropriate for canopies of nearly full cover and contains significant systematic errors for sparse canopies with relatively hot soil surfaces. Using exponential extinction formulations for net radiation, namely Eq. [2a] and [2b], assumes that attenuation and scattering of solar radiation dominate the profile of net radiation in the canopy. If canopies are sparse so that soil surface temperature can be more than 20°C above vegetation temperature, then errors occur because of the contribution of soil thermal radiation to net radiation. For a leaf area index (LAI) on the order of 0.5 with differences in soil and vegetation temperatures on the order of 20°C, net radiation absorbed by the soil surface and canopy calculated using Beer's Law approach can lead to relative errors of 
15 and 40% for the soil and canopy, respectively.
A more physically-based algorithm for estimating the divergence of RN avoids the problem with exponential extinction of net radiation by considering the transmission of direct and diffuse shortwave radiation separately from the transmission of long-wave radiation through the canopy (Campbell and Norman, 1998). Since the reflection and absorption of radiation in the visible and near-infrared wavelengths is markedly different for vegetation and soils, the visible and near-infrared albedos of the soil and vegetation were evaluated separately before combining to give an overall shortwave albedo. The equations for estimating the transmission and reflection of direct and diffuse shortwave radiation are described in Chapter 15 of Campbell and Norman (1998). With an incoming shortwave radiation observation, the net shortwave radiation balance for the soil (SN,S) and canopy (SN,C) are computed; then the net long-wave radiation balance for the soil (LN,S) and canopy (LN,C) are estimated. The long-wave balance for the soil-vegetation-atmosphere system is derived by calculating diffuse radiation transmission to the soil and absorption by the canopy (Ross , 1975). A simpler formulation of the net long-wave radiation balance than described in Ross (1975) uses a single exponential equation to describe the transmission for both the soil and canopy,
 | (3a) |
 | (3b) |
where the extinction coefficient, L 
0.95, is similar to the extinction coefficient for diffuse radiation under low vegetation, that is, LAI 
0.5 (Campbell and Norman, 1998) and LC, LS, and Lsky are the long-wave emissions from the canopy, soil and sky, respectively. LC and LS are computed from the Stefan-Boltzmann equation using canopy and surface soil temperatures estimated by the model and Lsky is estimated from shelter level air temperature and vapor pressure (Brutsaert, 1982). Thus Eq. [2a] and [2b] are replaced by visible and near-infrared radiation penetration equations from Chapter 15 of Campbell and Norman (1998) combined with Eq. [3a] and [3b] above for computing RN,S and RN,C (i.e., RN,S = SN,S + LN,S and RN,C = SN,C + LN,C).
The radiative exchange algorithms used in the model apply to vegetative canopies with leaves randomly distributed over the surface. When the leaves are not randomly distributed over the surface, but clumped as in the case of row crops, they may only intercept 70 to 80% of the radiation in comparison to the same crop randomly distributed over the surface (Campbell and Norman, 1998). Models to estimate radiation extinction for row crops have been developed (e.g., Gijzen and Goudriaan, 1989), but are rather complex and require additional information about the surface which will not be available operationally. An alternative is to use the same formulations described above, but with LAI multiplied by a clumping factor 
, namely LAI, (Chen and Cihlar, 1995). Campbell and Norman (1998) suggest for strongly clumped canopies, is a function of the solar zenith angle, 
S (radians), and can be estimated by the following expression:
 | (4) |
where (0) is the clumping factor when the canopy is viewed at nadir and D is the ratio of vegetation height vs. width of clumps.
The clumping factor must also be included in the expression that estimates the fraction of soil surface and vegetation temperatures contributing to the TR() observation. With the use of a single emissivity to represent the combined soil and vegetation, the ensemble directional radiometric temperature, TR(), is related to the fraction of the radiometer view occupied by soil vs. vegetation expressed as
 | (5) |
where TC and TS are the thermodynamic temperatures of the vegetation canopy and soil surface, respectively, and are assumed to represent spatially weighted averages of the sunlit and shaded portions of the canopy and soil, respectively, and n 4 (Becker and Li, 1990). The fraction of the field of view of the infrared radiometer occupied by canopy, f(), depends upon the view zenith angle, , canopy type and fraction of vegetative cover, fC. f() can be estimated from canopy architecture and view angle; but for many vegetated surfaces for a random or clumped canopy, a spherical leaf angle distribution can be assumed, and with an estimate of LAI,
 | (6) |
The value of (0) can be estimated with general knowledge of LAI and the fractional cover of the canopy. For the cotton crop used by Kustas and Norman (1999a), LAI 0.4 and fractional cover, fC 0.24. If the vegetation were randomly distributed and the leaf angle distribution approximated a spherical distribution, the canopy gap fraction from the zenith would be exp(-0.5 LAI) 0.82 and the fraction of the nadir view occupied by the vegetation would be 0.18. In actuality the vegetation is clumped along the furrows so the field LAI of 0.4 corresponds to a local LAI (LAIL) within the vegetated region of LAIL = LAI/fC 1.7. If all the leaves contained within the vegetated region are randomly distributed, then the transmission of this vegetated region is fC exp(-0.5 LAIL). The fraction of the nadir view occupied by the soil is fC exp(-0.5 LAIL ) + (1 - fC ) 0.86 so that exp(-0.5 LAI) 0.86 yielding (0) 0.75. The angular dependence of given by Eq. [4] is reasonable for cross-row directions, but obviously is not representative of the along-row direction. A more general approach for obtaining clumping factors from canopy architecture is given by Kucharik et al. (1999).
Clumping of the vegetation will also affect the wind speed inside the canopy layer and above the soil surface. This in turn will affect the magnitude of soil resistance, RS, and canopy resistance, RC, to heat transfer. Therefore, (0) is also included the equations of Goudriaan (1977) for predicting the wind speed near the soil surface, which assumes an exponentially decaying function of the form (see Appendices A and B in Norman et al., 1995 for details),
 | (7) |
where the extinction coefficient a is estimated from
 | (8) |
uS (m s-1) is the wind speed near the soil surface at height z (typically between 0.05–0.2 m), hC (m) is the canopy height, uC (m s-1) is the wind speed at the top of the canopy and wC (m) is the mean canopy leaf width. This same system of equations is used in the estimation of mean wind speed near the canopy elements for computing RC but with height z typically 0.8 hC , and the extinction coefficient a adjusted for vegetation clumpiness by using LAIL , namely,
 | (9) |
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The data
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The data used in the present analysis were collected from a furrowed row crop (cotton, Gossypium hirsutum L.) with field dimensions of 1500 m east-west and 300 m north-south located in Maricopa Farms in central Arizona (33.08°N, 111.98°W). The experiment ran from 10 June 1987, day of year (DOY) 161 to 14 June 1987, DOY 165. Detailed description of the micrometeorological instrumentation, agronomic and radiometric temperature measurements made in the cotton field are given by Kustas et al. (1989, 1990) (see also Kustas, 1990 and Kustas and Norman, 1999a). The ground-based radiometric temperature observations of sunlit and shaded soil and sunlit canopy were used to derive average canopy and surface soil temperatures as well as composite TR() values.
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Results and discussion
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Assessing Model Performance
Model performance in predicting the heat fluxes was quantified via the root-mean-square-difference (RMSD) as suggested by Willmott (1982). Another statistic, the mean-bias (MB) was computed by averaging the differences between N95 model predictions using the original vs. new net radiation and clumping factor formulations, and was also used to compare both original and new N95 model predictions with observations (Kustas and Norman, 1999a). The MB statistic will be particularly useful when comparing predicted vs. measured component temperatures. A negative (positive) value indicates the model underestimates (overestimates) the observed flux or temperature, on average. Similarly when comparing output using new vs. original model formulations a negative (positive) value indicates the new model version has lower (higher) flux predictions compared to the original, on average.
Parallel vs. Series Model Resistance Formulation
The N95 model has two formulations of the resistance network describing energy exchanges between soil and vegetative canopy components and the surrounding air. One is described as a "parallel" resistance arrangement where scalar fluxes from the soil/substrate and vegetative canopy do not interact and hence the soil surface temperature does not depend on canopy vegetative temperature. The second formulation is the "series" resistance arrangement (see Appendix A in Norman et al., 1995), which is the more traditional approach of having the heat fluxes from the soil/substrate and canopy layers influencing the temperature in the canopy air space and thus permitting interaction between soil and vegetation components (e.g., Shuttleworth and Wallace, 1985). Calculations with the N95 model using both the parallel and series resistance network by Kustas and Norman (1999a) indicated significantly better agreement with the observations were obtained using the series resistance network. This result is supported by other studies applying two-source formulations to sparse canopies (e.g., Blyth and Harding, 1995). Additionally, there is controversy surrounding the formulation using the parallel resistance scheme (Lhomme and Chehbouni, 1999; Kustas and Norman, 1999b), which can be avoided by using the series resistance approach. Therefore only the results with the series resistance network are presented.
Comparison of New vs. Original N95 Model Formulation
To assess the impact of the new net radiation divergence algorithm and clumping factor on model output both the new (N95N) and original (N95O) model formulations contain the recent modifications to the magnitude of the Priestley-Taylor coefficient PT used in estimating canopy transpiration and the new formulation for estimating soil resistance to sensible heat flux transfer, RS, developed in Kustas and Norman (1999a). Hence the differences between N95N and N95O are that Eq. [3a]–[3b] are used to partition radiation between the canopy and soil, clumpiness of the vegetation taken into account via Eq. [4] is used in adjusting the algorithms outlined in Eq. [5] to [9].
Comparisons of canopy net radiation, RN,C, soil net radiation, RN,S, and soil heat flux, G, predicted by N95N and N95O are illustrated in Fig. 1
. Mean-bias values are + 35 W m-2 for RN,C, -35 W m-2 for RN,S and -10 W m-2 for G. Thus with the new formulations for net radiation partitioning between soil and vegetation, namely Eq. [3a] and [3b], 35 W m-2 higher RN,C and lower RN,s on average is predicted even though 0.75 is used in the new radiation formulations; using < 1 actually reduces radiation absorbed by the canopy. However, soil surface temperatures were 20 to 30 degrees higher than canopy temperatures (see Fig. 4)
resulting in relatively high LN,C values to be computed via Eq. [3b]. This can be accounted for in Beer's Law formulation, namely Eq. [2b], by increasing the extinction coefficient , but this would be an empirical correction and hence cannot be done a priori.
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Fig. 1 Comparison of canopy net radiation, RN,C, and soil net radiation, RN,S, and soil heat flux, G, predicted by the original N95 model version (solid circles), N95O, (except for modifications to resistance to heat transfer from the soil, RS, and Priestley-Taylor coefficient, PT, used in estimating canopy transpiration) and the new version, N95N, (open squares) which includes the new net radiation divergence formulation and clumping factor (see also Kustas and Norman, 1999a). Time along the abscissa is in Mountain Standard Time (MST)
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Fig. 4 Soil surface temperatures, TS, and canopy temperatures, TC, predicted by N95O and N95N model versions vs. observed radiometric temperatures of the soil surface and canopy components (see text). Line represents perfect agreement
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The soil sensible, HS, and latent, LES, heat fluxes and canopy sensible, HC, and latent, LEC, heat fluxes from both model versions are shown in Fig. 2
. For the soil component, the MB value is negligible (i.e., -1 W m-2) for HS , but more significant for LES where MB -20 W m-2. The N95O model predicts an average LES, <LES> 110 W m-2; thus a MB of approximately -20 W m-2 yields 20% change using N95N. For the vegetative canopy, MB values are -20 W m-2 for HC and +50 W m-2 for LEC. Since HC < 0, the negative MB value actually means that N95N predicts a higher heat flux is being advected towards the canopy. In both cases, these differences in HC and LEC predictions cause approximately a 30% change from N95O output. Including the effect of clumpiness on wind speed estimates inside the canopy resulted in less than a 10% change in RS and RC estimates on average. Consequently, the differences in heat flux predictions between N95N and N95O are mainly the result of a bias in net radiation balances between soil and canopy and a significant bias in predicted canopy temperatures (see below).
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Fig. 2 The soil sensible, HS, and latent, LES, heat fluxes and canopy sensible, HC, and latent, LEC, heat fluxes from both N95O (solid circles) and N95N (open squares) model versions. Time along the abscissa is in Mountain Standard Time (MST)
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The statistical results comparing predicted and observed total fluxes from N95N and N95O formulations are listed in Table 1
. The higher RMSD values for the turbulent fluxes, H and LE, and G using the N95O version are mainly the result of significantly larger magnitudes of MB. This is also obvious when plotting observed vs. predicted heat fluxes from both model versions, especially for LE (Fig. 3)
. Further indications that N95N heat flux predictions are more reliable is given by the RMSD and MB values comparing predicted canopy, TC, and soil, TS, temperatures with observations (see Table 1). Although the N95O version is slightly better in predicting TS, N95N significantly outperforms N95O in predicting TC. Observed vs. predicted TS and TC for both versions are illustrated in Fig. 4. Additionally, N95N estimates of the partitioning of available energy for the soil (i.e., RN,S - G) between HS and LES and the relative contributions of LES and LEC to the total LE are more physically realistic than N95O results. This is supported by the comparison of the average component fluxes estimated from Kustas (1990) with the results from the present study in Table 2
(see also Kustas and Norman, 1999a).
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Table 1 Statistical results comparing N95O vs. N95N model predicted vs. observed surface fluxes and soil and canopy temperatures
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Fig. 3 Total sensible, H, and latent, LE, heat fluxes predicted by N95O and N95N model versions vs. observed heat fluxes. Line represents perfect agreement
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Conclusions
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The results from this study support changes to two commonly used parameterizations in two-source energy balance models. These modifications have the largest impact on two-source flux predictions under sparse canopy-covered conditions. One replaces the commonly used Beer's Law expression for estimating the divergence of net radiation through the canopy layer with a more physically-based algorithm. The other is a simple method to address the effects of clumped vegetation on radiation divergence, radiative temperature partitioning between soil, and vegetation and on the wind speed inside the canopy layer. With data from a furrowed cotton crop, these two modifications result in better overall model performance in surface heat flux predictions and soil and canopy temperature estimation.
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ACKNOWLEDGMENTS
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This study would not have been possible without the cooperation and assistance of the personnel at the Maricopa Agricultural Research Center and the USDA-ARS U.S. Water Conservation Laboratory in Phoenix, Arizona.
Received for publication September 15, 1999.
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TOP
ABSTRACT
INTRODUCTION
