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  • View in gallery

    Schematic diagram illustrating the resistance network for the (a) parallel and (b) series formation used in TSM scheme. Also shown is the flux partitioning between soil (subscript s) and canopy (subscript c) and some of the key model inputs. Symbols are defined in the text.

  • View in gallery

    Clumping factor Ω for corn and soybean derived from this study and Anderson et al. (2005). Details are given in the text.

  • View in gallery

    Comparison between TSM output and METFLUX observations using the series resistance network (TSMS) and parallel resistance network (TSMP) for (a) net radiation Rn, (b) soil heat flux G, (c) sensible heat flux H, and (d) latent heat flux LE, adjusted to invoke closure by residual method LERE. Symbols correspond to overpass date (DOY) and model version, namely, TSMS or TSMP.

  • View in gallery

    Soil surface temperature comparison between ground observations and TSM output. Symbols correspond to overpass date (DOY) and series and parallel model versions, TSMS and TSMP, respectively.

  • View in gallery

    Model sensitivity SX, computed via Eq. (4) to a ±20% error in LAI for both the parallel (TSMP) and series (TSMS) network.

  • View in gallery

    Canopy temperature TC and soil temperature TS computed from TSMS and TSMP under increasing fractional vegetation cover fC for DOY 167 conditions at a soybean site WC161 (see text for details).

  • View in gallery

    Output of H from TSMS and TSMP under increasing fC for DOY 167 conditions at a soybean (WC161) and corn (WC151) site.

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Utility of Remote Sensing–Based Two-Source Energy Balance Model under Low- and High-Vegetation Cover Conditions

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  • 1 Hydrology and Remote Sensing Laboratory, ARS, USDA, Beltsville, Maryland
  • | 2 National Soil Tilth Laboratory, ARS, USDA, Ames, Iowa
  • | 3 Biological and Irrigation Engineering Department, Utah State University, Logan, Utah
  • | 4 Hydrology and Remote Sensing Laboratory, ARS, USDA, Beltsville, Maryland
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Abstract

Two resistance network formulations that are used in a two-source model for parameterizing soil and canopy energy exchanges are evaluated for a wide range of soybean and corn crop cover and soil moisture conditions during the Soil Moisture–Atmosphere Coupling Experiment (SMACEX). The parallel resistance formulation does not consider interaction between the soil and canopy fluxes, whereas the series resistance algorithms provide interaction via the computation of a within-air canopy temperature. Land surface temperatures were derived from high-resolution Landsat Thematic Mapper (TM)/Enhanced Thematic Mapper (ETM) scenes and aircraft imagery. These data, along with tower-based meteorological data, provided inputs for the two-source energy balance model. Comparison of the local model output with tower-based flux observations indicated that both the parallel and series resistance formulations produced basically similar estimates with root-mean-square difference (RMSD) values ranging from approximately 20 to 50 W m−2 for net radiation and latent heat fluxes, respectively. The largest relative difference in percentage [mean absolute percent difference (MAPD)] was for sensible heat flux, which was ≈35%, followed by a MAPD ≈ 25% for soil heat flux, ≈10% for latent heat flux, and a MAPD < 5% for net radiation. Although both series and parallel versions gave similar results, the parallel resistance formulation was found to be more sensitive to model parameter specification, particularly in accounting for the effects of vegetation clumping resulting from row crop planting on flux partitioning. A sensitivity and model stability analysis for a key model input variable, that is, fractional vegetation cover, also show that the parallel resistance network is more sensitive to the errors vegetation cover estimates. Furthermore, it is shown that for a much narrower range in vegetation cover fraction, compared to the series resistance network, the parallel resistance scheme is able to achieve a balance in both the radiative temperature and convective heat fluxes between the soil and canopy components. This result appears to be related to the moderating effects of the air temperature in the canopy air space computed in the series resistance scheme, which represents the effective source height for turbulent energy exchange across the soil–canopy–atmosphere system.

Corresponding author address: Fuqin Li, USDA-ARS, Hydrology and Remote Sensing Lab., Beltsville, MD 20705. Email: fcl@hydrolab.arsusda.gov

Abstract

Two resistance network formulations that are used in a two-source model for parameterizing soil and canopy energy exchanges are evaluated for a wide range of soybean and corn crop cover and soil moisture conditions during the Soil Moisture–Atmosphere Coupling Experiment (SMACEX). The parallel resistance formulation does not consider interaction between the soil and canopy fluxes, whereas the series resistance algorithms provide interaction via the computation of a within-air canopy temperature. Land surface temperatures were derived from high-resolution Landsat Thematic Mapper (TM)/Enhanced Thematic Mapper (ETM) scenes and aircraft imagery. These data, along with tower-based meteorological data, provided inputs for the two-source energy balance model. Comparison of the local model output with tower-based flux observations indicated that both the parallel and series resistance formulations produced basically similar estimates with root-mean-square difference (RMSD) values ranging from approximately 20 to 50 W m−2 for net radiation and latent heat fluxes, respectively. The largest relative difference in percentage [mean absolute percent difference (MAPD)] was for sensible heat flux, which was ≈35%, followed by a MAPD ≈ 25% for soil heat flux, ≈10% for latent heat flux, and a MAPD < 5% for net radiation. Although both series and parallel versions gave similar results, the parallel resistance formulation was found to be more sensitive to model parameter specification, particularly in accounting for the effects of vegetation clumping resulting from row crop planting on flux partitioning. A sensitivity and model stability analysis for a key model input variable, that is, fractional vegetation cover, also show that the parallel resistance network is more sensitive to the errors vegetation cover estimates. Furthermore, it is shown that for a much narrower range in vegetation cover fraction, compared to the series resistance network, the parallel resistance scheme is able to achieve a balance in both the radiative temperature and convective heat fluxes between the soil and canopy components. This result appears to be related to the moderating effects of the air temperature in the canopy air space computed in the series resistance scheme, which represents the effective source height for turbulent energy exchange across the soil–canopy–atmosphere system.

Corresponding author address: Fuqin Li, USDA-ARS, Hydrology and Remote Sensing Lab., Beltsville, MD 20705. Email: fcl@hydrolab.arsusda.gov

1. Introduction

Satellite-derived radiometric surface temperature (TR) is a key boundary condition for most remote sensing–based energy balance models (Kustas and Norman 1996). However, this radiometric surface temperature is not equivalent to the aerodynamic surface temperature (TO) that is associated with heat transport at the effective source height, particularly for partial canopy–covered surfaces (Chehbouni et al. 1996). Efforts to adjust model parameters in order to consider differences between TO and TR have been largely empirical (e.g., Mahrt and Vickers 2004), although when calibrated with in situ data, it can provide reliable estimates (Chávez et al. 2005). More physically based schemes not requiring in situ calibration have been recently proposed and evaluated (e.g., Su et al. 2001), including data from the Soil Moisture–Atmosphere Coupling Experiment (SMACEX) (Su et al. 2005), indicating reliable performance under most conditions. In effect, these latter schemes attempt to consider the difference in the role of the vegetation canopy and underlying soil on heat transport and radiative temperature.

This is the concept behind the two-source model (TSM), which was developed to make use of remotely sensed (radiometric) surface temperature and fractional vegetation cover for computing soil and vegetated canopy temperatures and heat fluxes (Norman et al. 1995). The model contains parameterizations that explicitly treat the radiative and convective heat exchanges from the soil and canopy elements, taking into account the key factors influencing both the surface radiative and aerodynamic temperatures. In comparison to other types of formulations, TSM is shown to be robust for a wide range of landscape and hydrometeorological conditions (Kustas et al. 1996; Zhan et al. 1996; Kustas and Norman 1997). There have also been revisions to TSM, providing applications to a wider range of environmental conditions (Kustas and Norman 1999a, 2000)

The SMACEX field campaign was conducted in concert with the Soil Moisture Experiment 2002 (SMEX02) between mid-June and mid-July (Kustas et al. 2003, 2005). Both soil moisture and vegetation cover conditions changed dramatically during the field experiment. Therefore, this dataset provides a unique opportunity for evaluating the two TSM resistance formulations originally proposed by Norman et al. (1995) in order to assess their performance under a full range of canopy cover and soil moisture conditions.

In this paper, the two resistance formulations of energy exchange (see Fig. 1)—one allowing interaction between the soil and vegetation (series version) and the other neglecting such interactions (parallel version)—were examined. Flux footprint models are also applied to establish the upwind pixels largely influencing the scale of the tower-based flux measurements. Results from both the parallel and series resistance parameterizations used in TSM, defined by TSMP and TSMS, respectively, are compared to tower-based flux measurements. In addition, the sensitivity and model stability of TSMP and TSMS to errors in a key input variable fractional vegetation cover is analyzed. The output of soil and vegetation canopy component heat fluxes and temperatures are compared and contrasted.

2. Model description

A detailed description of the original TSM series and parallel formulations can be found in Norman et al. (1995). A unique feature of the modeling strategy is that the solution is attained through balancing both the radiative temperature and convective (turbulent) heat fluxes of the soil and vegetated canopy components. Several revisions have been made more recently in order to accommodate a wider range of land cover and environmental conditions. These modifications are briefly summarized below with the algorithms described in greater detail in the appendix.

Most of the modifications improve the capability of TSM to partition radiative and convective fluxes between the soil and vegetation canopy components under more heterogeneous cover conditions. For radiation, revisions include replacing the Beer’s law–type expression used to derive net radiation for soil and canopy components with a more physically based algorithm developed by Campbell and Norman (1998). This new algorithm considers the divergence properties of longwave and shortwave radiation separately through the canopy layer instead of simply using an exponential decay of net radiation.

A clumping factor, affecting both radiation and turbulent heat exchange, has been introduced into the model because over many landscapes vegetation is clumped, resulting in the nonuniform distribution of leaf area within a pixel. This has a different effect on radiation divergence and wind decay inside the canopy air space relative to uniformly distributed vegetated canopies (Kustas and Norman, 1999a, b, 2000). This is particularly the case for row crops, where the vegetation may, depending on spacing and crop type, intercept 70%–80% of the radiation that is absorbed by the same crop randomly distributed over the same field (Campbell and Norman 1998). Chen and Cihlar (1995) and Kucharik et al. (1999) proposed a convenient way to estimate radiation extinction for clumped vegetation where the leaf area index (LAI) and fractional vegetation cover ( fC) used in the LAI–fC exponential relation is multiplied by a clumping factor Ω (see the appendix). This clumping factor Ω can also be used in formulations affecting the wind and, hence, the resistance to heat exchange for the soil and canopy components (Kustas and Norman 1999a, b, 2000).

A revised version of the soil resistance formulation proposed in Norman et al. (1995) is now applied. In the original formulation, the wind speed near the soil surface is used with two coefficients assumed to be constant for a wide variety of surface conditions. In the revised algorithm, Kustas and Norman (1999a, 2000) show that the temperature difference between the soil and canopy, in addition to the wind, affects the rate of heat transport or resistance, hence, the coefficients can vary (see the appendix).

Initially, the partitioning of available energy between latent and sensible heat flux for the vegetated canopy is achieved using the Priestley–Taylor approach, and is reduced under conditions of stress, which presumably would appear in the radiometric temperature and resulting TSM-estimated soil and canopy temperatures. However, a more gradual change in the Priestley–Taylor parameter αPT is now implemented, which decreases its value in increments to accommodate stressed vegetation conditions, similar to canopy resistance (McNaughton and Jarvis 1991). In addition, Kustas and Norman (1999a, 2000) find that αPT for the canopy may be larger than 1.3 under certain environmental conditions, which is supported by field data (Baldocchi 1994).

3. Data and site description

a. Site description

SMACEX was conducted in and around the Walnut Creek watershed (WCW) near Ames, Iowa, between 15 June and 8 July 2002 (Kustas et al. 2003, 2005). The WCW area was the primary focus of SMACEX, containing a network of 14 meteorological-flux (METFLUX) towers located within the area and multiple flight tracks flown by the Canadian Twin Otter for evaluating spatial variability in fluxes across the study area. Details of the flux measurement activities are provided in Prueger et al. (2005).

b. Data

In this paper, two Landsat-7 Enhanced Thematic Mapper (ETM) scenes, one Landsat-5 Thematic Mapper (TM) scene and one aircraft scene were used to provide remotely sensed imagery encompassing the WCW study area. The remotely sensed data provide imagery on nearly a weekly basis, spanning vegetated canopy cover from 25% to 50% on 16 June [day of year (DOY) 167], 50% to 75% on 23 June (DOY 174), 75% to 90% on 1 July (DOY 182), and to essentially full cover, namely, 85% to 100% on 8 July (DOY 189). A detailed description and analysis for converting the raw remotely sensed data from the Landsat satellite to land surface temperature TR and narrowband reflectances, used in deriving vegetation indices, is given by Li et al. (2004). Chávez et al. (2005) provide a description of the aircraft data. The pixel resolutions of the land surface temperature images from the Landsat-5 and -7 scenes were 120 and 60 m, respectively, while the aircraft-based instrument yielded 6-m resolution. The aircraft radiance values were aggregated to 60-m pixel size so that TSM output would be comparable to the output using the Landsat resolutions. The vegetation indices, Normalized Difference Water Index (NDWI) from Landsat and Optimized Soil Adjusted Vegetation Index (OSAVI) from the aircraft, as well as the commonly used Normalized Difference Vegetation Index (NDVI), were resampled to the same pixel resolution as land surface temperature. The relationships between these vegetation indices and model variables fC, LAI, and canopy height hC are described in Anderson et al. (2004).

Details concerning the measurement and processing of the METFLUX tower data during SMACEX are described in Prueger et al. (2005). Twelve of the 14 flux towers were fully operational during the main field campaign. At each METFLUX tower site, air temperature and vapor pressure measurements were taken nominally at 2.5 m above ground level (above soil surface, expressed as AGL in the rest of the paper) over corn, and ∼1.5 m AGL over soybean. Eddy covariance measurements (including mean wind speed) in corn were taken from ∼3 m AGL before the end of June, and at ∼4 m AGL after, while in soybean, these measurements remained at ∼2 m AGL during the whole campaign. Local meteorological data that are required by the model, which include solar radiation, air temperature, vapor pressure, and wind speed, were taken from the METFLUX towers at the time of satellite overpasses. At some METFLUX towers without solar radiation observations, the solar radiation measurements were used from the nearest tower. Wind direction was also used to estimate the upwind flux footprint/source area as described below.

Crop height hC and LAI were sampled 3–4 times during the field experiment at 31 WCW field sites. Details of the sampling strategy/technique and analysis of the results can be found in Anderson et al. (2004). Equations for interpolating between measurement days were also derived from the results of Anderson et al. (2004).

Soil surface temperature was measured by an infrared radiometer [Apogee model IRTS-P, ∼60° field of view (FOV)] mounted from 0.10 (in soybean) to 0.30 (in corn) m AGL between the rows at an oblique (∼45°) viewing angle. With a 60° FOV and 45° view angle, measurement heights of 0.10 and 0.30 m yield an elliptical target area, with a major/minor axis of 0.35/0.16 and 1.0/0.50 m, respectively. The measurements were temperature corrected according to a procedure outlined by Bugbee et al. (1999), and were adjusted for emissivity based on Li et al. (2004).

4. Model input and validation data

a. Vegetation clumping

Radiometric surface temperature and fractional vegetation cover serve as key boundary conditions in TSM. As discussed and analyzed in detail by Anderson et al. (2005) for the SMACEX region, clumping of the vegetation can significantly influence radiometric temperature partitioning between soil and canopy temperature components and heat fluxes. This result is in agreement with an earlier study applying TSM over a cotton row crop with fractional cover of approximately ∼0.25 (Kustas and Norman 1999a). An algorithm for estimating the clumping factor Ω is described in the appendix.

For estimating accurate values of Ω, ground measurements of LAI and the fractional amount of interrow spacing that is covered by the crop canopy fVEG are needed (Anderson et al. 2005). Typically, such detailed observations are not available and indirect methods must be relied upon, such as remotely sensed vegetation indices. With areally averaged LAI measurements 〈LAI〉 from Anderson et al. (2004), an estimate of the fractional amount of vegetation cover occupying interrow spacing fVEG came via NDVI as described in Choudhury et al. (1994),
i1525-7541-6-6-878-e1
where NDVImax is the NDVI for complete vegetation cover and NDVImin is the NDVI for bare soil. NDVImax and NDVImin were assigned values of 0.89 and 0.1, respectively, based upon the NDVI histogram analysis of each remotely sensed scene. The coefficient a is a function of leaf orientation distribution within the canopy, where erectophile to planophile canopies have values between 0.6 and 1.25. A value of 0.625 was used in the current investigation.
For clumped vegetation, it is assumed that fVEG, estimated via Eq. (1), represents the fractional amount of interrow bare soil occupied by vegetation, and not the bare soil that is seen through the canopy elements along the rows. Then the local leaf area index LAIL (LAI within the row crop) is computed as LAIL = 〈LAI〉/fVEG. The total amount of soil viewed at nadir (i.e., viewing angle ϕ = 0) fS is estimated as the combined fraction of the bare soil area in the interrows (1 − fVEG) and the fraction of bare soil seen through the canopy elements along the rows ( fSR), so that (Anderson et al. 2005)
i1525-7541-6-6-878-e2
where
i1525-7541-6-6-878-e3

Hence, the actual fractional vegetation cover fC (=1 − fS) is computed via Eq. (A2). The view angle dependency of Ω is described in the appendix (see Anderson et al. 2005).

This approach is not as reliable as the procedure used by Anderson et al. (2005) and yields a less dynamic range, but the resulting values illustrated in Fig. 2 are comparable, with the largest discrepancy under lower cover conditions. Therefore, the method can be used when ground measurements of fVEG are not available. The impact of the two estimates of Ω on TSM-calculated fluxes is evaluated and discussed.

b. Estimating source area

The focus of this paper is to use the tower-based flux measurements to evaluate the utility of the TSM using a parallel versus a series resistance network for computing fluxes. Therefore, an estimate of the flux footprint or upwind source area contributing to the METFLUX tower measurements was considered essential for selecting those TSM output (pixels) that were estimated to significantly contribute to the measurements. The flux footprint models that were employed in this study are those described by Schuepp et al. (1990) and Kormann and Meixner (2001). Other footprint models were also employed by Chávez et al. (2005), and yielded relatively small differences in footprint estimation from those selected here. The results from the two models were quite similar for the corn and soybean sites (because the flux measurement heights above the canopy elements were similar), indicating that the maximum flux density typically occurred at ∼20 m upwind, with greater than 50% of the total flux originating within 60 m of the observation sites and up to 80% of the flux being within 120 m of the METFLUX tower sites. Thus, TSM output for one to two pixels in the upwind direction was used under most conditions.

Under some circumstances, several surrounding pixels were also averaged to account for errors in registering the satellite and aircraft imagery. Most of the METFLUX tower sites were located in relatively homogeneous fields. However, using the footprint model did improve comparisons between TSM output and METFLUX observations for some of the Walnut Creek (WC) sites that were more variable in their vegetation canopy cover conditions. This was particularly the case for 1 July (DOY 182), when surface soil moisture was very low because of an extended dry-down period. For example, the TSM output of LE for adjacent pixels surrounding the METFLUX tower in the WC03 and WC25 sites varied by ∼50–100 W m−2. Thus, without the footprint estimation, a greater than 50 W m−2 difference with measured LE could result from not selecting the appropriate pixels contributing to the measured flux.

c. Flux measurement uncertainty

Typically, the eddy covariance technique will undermeasure the turbulent fluxes, which has been attributed to many different factors (Massman and Lee 2002). The degree of undermeasurement is often related to the so-called closure ratio—the ratio of turbulent heat fluxes to the available energy, CR = (H + LE)/(Rn − G). At the time of the remote sensing observations, the flux measurements show that the ratio CR was usually 0.80–0.90. Under daytime conditions, Prueger et al. (2005) found a CR of ∼0.8 for both the corn and soybean sites. However, the TSM scheme, as well as any land surface models, conserves energy, hence, this situation can lead to unavoidable bias errors in the comparison between the model-estimated and measured fluxes.

To resolve this problem, Twine et al. (2000) suggested taking the Bowen ratio H/LE as being correct and, with reliable Rn and G measurements, recomputed the eddy heat fluxes so that the residual energy was distributed through the Bowen ratio [this will be called the Bowen ratio (BR) method]. Recently, Brotzge and Crawford (2003) observed that the eddy covariance approach had the lowest CR values and tended to undermeasure LE relative to the Bowen ratio technique (using gradients of air temperature and water vapor) under high evaporative conditions. This suggests that the residual energy should be assigned to LE [this will be called the residual (RE) method].

Prueger et al. (2005) compared the network-averaged METFLUX output of Rn, H, and LE with the aircraft-based measurements, and found close agreement in Rn and H, but significantly larger scatter in LE. When closure was problematic for either the tower- or aircraft-based measurements, having a residual, Rn − G − H − LE ≈ 100 W m−2, Prueger et al. (2005) showed that it was associated with significant differences in estimates of LE from the tower and aircraft. While this is not definitive evidence that the undermeasurement problem with eddy covariance is caused by the water vapor flux (Anderson et al. 2005), adjustments to both H and LE via the BR method may not always be warranted. Factors contributing to a lack of closure include measurement errors, source area mismatch between available energy and eddy flux measurements, and the neglecting of heat storage and energy for photosynthesis (Meyers and Hollinger 2004). Because it has not been established how best to reconcile nonclosure in eddy flux observations, model–measurement comparisons will be performed without closure and closure using both the BR and RE methods.

5. Results and discussion

The parallel and series resistance formulations used in the TSM scheme, denoted by TSMP and TSMS, respectively, were evaluated at each METFLUX site. Because differences in the resistance formulations largely affect the partitioning of the turbulent heat fluxes, the results for Rn and G from TSMP and TSMS were similar, with points scattered around the 1:1 line for Rn, but with a more noticeable bias between modeled and measured G (Figs. 3a and 3b). Both TSMP and TSMS yield an overall root-mean-square difference (RMSD) and mean absolute difference (MAD) on the order of 20 W m−2, which results in a mean absolute percent difference of less than 5% (see Table 1 for definitions of the difference statistics). For G, differences with the observations are greater with an overall RMSD of approximately 30 W m−2, yielding a MAPD of ∼30%. A significant contribution to the differences is an overall bias between modeled and measured G, with both TSMP and TSMS overestimating G, except on 16 June (DOY 167). Ground measurements indicated relatively wet soils from precipitation a few days prior to DOY 167, followed by the significant drying of surface soil moisture until a return of rainfall in the WCW area starting on 4 July (DOY 185) (Prueger et al. 2005). This is likely to affect the fraction of soil net radiation conducted into the soil [Eq. (A16)]. A calibration of the coefficient in Eq. (A16) would remove the bias, similar to the results from Chávez et al. (2005).

For the sensible heat flux H, differences between TSMP and TSMS output versus METFLUX observations illustrated in Fig. 3c indicate a slight underestimate, and not a substantial difference between resistance formulations. The difference statistics reported in Table 1 suggest slightly better results using TSMS. The difference statistics are reported for both H measured by the eddy covariance system HM and the measured H adjusted for closure with the BR method HBR. Differences with HBR are generally larger, but the relative difference as quantified by MAPD is not because HBR > HM. Overall, the RMSD and MAD values with HM are on the order of 35 and 30 W m−2, and ∼50 and 40 W m−2 with HBR, respectively. In either case (i.e., comparisons using HM or HBR) the MAPD values are on the order of 35% for TSMS and 40% for TSMP.

For the latent heat flux LE, the best agreement between TSM output and METFLUX observations occurs when LE, measured by the eddy covariance system LEM, is modified for closure by the residual method LERE. The statistics in Table 1 show no significant difference in the performance between TSMS and TSMP for estimating LERE. Much greater RMSD values result when comparing TSMS and TSMP output with LEM. This difference, however, is mainly the result of a significant bias, not an increase in scatter with LEM, with output from TSMS and TSMP being ∼100 W m−2 higher, on average (Table 1). Forcing closure with the BR method results in a slight increase in the difference statistics for TSMP, but no real change in the TSMS results, except for a minor increase in MAPD. Overall, the MAPD values between TSMS output and LEM, LEBR, and LERE decrease from ≈35% to ≈10%, while for TSMP the decrease is from ≈40% to 15%, and finally 10%, respectively. Forcing closure for the eddy covariance measurements either by the BR or RE method significantly reduces discrepancies in the estimation of the heat fluxes, also found by other SMACEX studies (Anderson et al. 2005; Crow et al. 2005; Su et al. 2005).

The difference statistics between TSMS and TSMP versus the METFLUX observations were also evaluated separately for each crop. The METFLUX measurements indicated that the largest differences between corn and soybean were in the turbulent heat fluxes H and LE (Prueger et al. 2005). The RMSD, MAD, and MAPD values for H and LE tended to be higher for corn relative to soybean. The greatest difference was in MAPD values for H, where MAPD ≈ 45% for corn using both model formulations, while for soybean MAPD ≈ 20% and 30% using TSMS and TSMP, respectively. Although both model formulations yielded higher RMSD values for corn (≈50 W m−2) compared to those for soybean (≈40 W m−2), with higher measurements of LE over corn, the MAPD values were similar, namely, ≈10%. Therefore, overall, and relative to the magnitude of the fluxes, the performance of TSM was similar for both crops.

An analysis of flux partitioning between the soil and vegetated canopy components from TSMP and TSMS suggests there are slight differences, mostly in the soil surface energy balance under lower crop cover (DOY 167 and 174). The comparison of canopy and soil sensible and latent heat fluxes indicates that HS values are generally higher and LES values are slightly lower for DOY 167 and 174 from TSMS compared to TSMP. The average difference in HS is ≈ 15 W m−2 and in LES is 10 W m−2. As a result, the average soil Bowen ratio HS/LES for the 2 days from TSMS and TSMP is ≈ 0.88 and 0.75, respectively.

Although there were no measurements of the soil and canopy heat flux components (latent and sensible heat fluxes), there were soil surface temperature measurements provided by an infrared radiometer. Comparison (Fig. 4) of the TS from the radiometer with that derived from TSMS and TSMP yield similar results (RMSD ∼4°C) and are reasonable for the first 3 days, considering the significant mismatch in pixel resolution from the imagery (60–120 m) and the relatively small area sampled by the IRTS-P sensors. The outliers significantly underestimating TS on DOY 189 are a result of the fact that the Landsat TR values for most of the sites were less than air temperature, a condition under which the TSM scheme has difficulty computing TS values that are significantly higher than air temperature.

The impact of uncertainty in the clumping factor on TSM output was evaluated. TSM output using the Ω values from Anderson et al. (2005) was compared to output from using our estimates of the Ω values (see Fig. 2). The greatest differences in model output resulting from the Ω value used (primarily in H and G) are for the lower vegetated canopy cover cases, particularly for DOY 167. The MAPD using the two estimates of Ω for G is ∼5%, but is more pronounced for TSMP than TSMS for H, where MAPD ∼10% and 3%, respectively. As the vegetation cover increases and discrepancies between the estimates of Ω values decrease, with MAPD values dropping to or below 5%. If no clumping factor is used, or Ω = 1, then the most significant change in TSM output is in H (relative to its magnitude), with the greatest impact on TSMP. For the first 3 days with partial cover and Ω = 1, output of H from TSMS increases by ≈10 W m−2 or, nominally, 10%, on average, while H from TSMP increases by ≈30 W m−2 or ≈25%. This indicates that the series resistance formulation is less sensitive to the value of Ω than the parallel version.

The clumping factor affects the surface heat fluxes mainly through fC as expressed in Eq. (A2) and LAI in Eqs. (A19)(A20). In this paper, fC is calculated from LAI, which is estimated from the satellite-based NDWI and the aircraft-based OSAVI (Anderson et al. 2004). Error in fC/LAI estimation will lead to inaccuracies in the partitioning of the radiative temperature between soil and vegetative canopy components via Eq. (A1), which, in turn, can lead to significant errors in flux computations, particularly at higher fractional cover conditions (Anderson et al. 2005). Therefore, the sensitivity and stability of TSMP and TSMS to errors in the vegetation amount expressed in LAI or fC are examined.

According to Anderson et al. (2004), uncertainty in estimating LAI from satellite NDWI and aircraft OSAVI was 18% and 15%, respectively. Therefore, LAI was assigned a ±20% variation from the original estimate for each tower site. The sensitivity in model output was evaluated for H because LE is solved by a residual for the soil and also indirectly through the Pristley–Taylor formulation for the canopy. The sensitivity SX was computed as a ratio,
i1525-7541-6-6-878-e4
where H±20% is the sensible heat flux from the model having a ±20% deviation from the original LAI and associated output HOrig, and with the quantity multiplied by 100 for converting to a percentage. The sensitivity analysis was run over all 12 tower sites, and for the first 3 days having partial vegetation cover and surface temperatures that are higher than the air temperature.

The results of the sensitivity analysis are illustrated in Fig. 5, which shows the average SX values for all 12 sites. The corn sites generally had slightly higher SX values than soybean (a few percent) because the corn had higher LAI values, and, hence, experienced larger relative changes in cover. However, the variations are not significant enough to report or illustrate separately in the figure. The SX values from TSMP are at least twice that of TSMS, with the greatest sensitivity for DOY 182. The SX values were 15%–20% and 5%–10% for TSMP and TSMS, respectively. The greater sensitivity for both resistance schemes for DOY 182 is due the fact that of the 3 days, the relative change in LAI is the largest and an extended dry down resulted in the lowest surface soil moisture conditions occurring DOY 182.

To understand the factors causing the greater sensitivity of TSMP to variations in vegetation cover conditions, model temperature components of the soil and vegetation from both resistance schemes were analyzed by incrementally increasing fractional cover from fC = 0.1 to 1. With radiometric surface temperature and meteorological conditions from DOY 167 and tower site WC161, this provided a maximum surface air temperature difference for evaluating model response.

The results illustrated in Fig. 6 indicate a gradual increase in soil temperatures for both TSMP and TSMS, with increasing fC. The canopy temperatures remain essentially constant until a threshold value fC is reached, resulting in a sharp increase in TC, particularly for TSMP. Moreover, at a slightly higher fC TSMP can no longer maintain a balance for both the radiative temperature and turbulent heat fluxes for the soil and vegetated canopy components and, hence, find a “physical” solution. For TSMS, this threshold is reached at higher fC, and the increase in TC is not as rapid as with TSMP output. Furthermore, a physical solution is attainable through to an fC of ∼0.8. This slower response to changes in fC with TSMS seem to be related to the moderating effects of the air temperature in the canopy air space TAC, defined in the series resistance scheme as the effective source height for turbulent energy exchange across the soil–canopy–atmosphere system (see Fig. 1). This series resistance network parameterization, which allows interaction between the soil and canopy via TAC, more effectively limits the rise in TS, while at the same time it computes a realistic TC in order that a balance in radiative temperature and turbulent heat fluxes can be achieved at the higher fC values.

The range in fC over which the two resistance forms of TSM produce a physical solution is a way of assessing model “stability.” In other words, the capability of the model to compute fluxes under a wide range of fractional cover and/or radiometric surface temperature conditions. As is evident in the results of the canopy and soil temperature computations, TSMS maintained physical solutions for a significantly broader range in fC values. In Fig. 7, the effect of variation in fC on TSMP and TSMS output of H for a representative corn (WC151) and soybean (WC161) flux tower sites is shown using DOY 167 conditions. For both corn and soybean tower sites, H from TSMP increases more rapidly than TSMS with an increase in fC, especially after the fC threshold is reached, where as the increase in H is much more dramatic and quickly reaches an fC value having no physical solution. Not only is the fC threshold higher for TSMS, but, also, a physical solution is attained for fC that is slightly larger than 0.8, close to a full canopy cover condition. This stability analysis suggests that the TSMS is more robust and can be applied to a wide range of environmental conditions. A similar conclusion was made by Kustas et al. (2004) when applying TSM with simulated fluxes and surface temperatures from a detailed soil–plant–atmosphere model (Cupid; Norman and Campbell 1983) under a wide range of vegetation cover and soil moisture conditions.

6. Summary and conclusions

The parallel and series resistance algorithms used in the two-source model (TSMP and TSMS, respectively) using radiometric surface temperature from satellite and aircraft sensors as input were both evaluated using local meteorological flux (METFLUX) tower observations. The analysis showed that both the TSMP and the TSMS output of the sensible and latent heat fluxes agreed to within 50 W m−2 of METFLUX observations when closure is enforced with the eddy covariance measurements of H and LE, with the best agreement coming from assigning all of the residual to latent heat flux. Application of a flux footprint model for estimating the upwind pixels largely contributing to the METFLUX observation resulted in a closer agreement with the observations, particularly for inhomogeneous sites having greater pixel variability in the fluxes.

Output of the component fluxes from the vegetated canopy and soil from TSMP and TSMS indicates a slight discrepancy in the partitioning of sensible and latent heat for the soil, with the TSMS tending to yield a slightly higher HS and lower LES than those of TSMP. Both modeling schemes provide estimates of TS that were comparable to observations at each METFLUX site. Considering the mismatch in pixel resolution (60–120 m) between the imagery and the local measurements (1 m<), a 4°C discrepancy for a 20°C range in TS is considered reasonable.

Vegetation clumping also affects model output, with TSMP being more sensitive to uncertainty in the clumping factor Ω than TSMS. The impact of clumped vegetation on other two-source modeling schemes needs to be considered in light of the present findings, particularly those for approaches that simulate soil and canopy temperatures and can, thereby, be compared with radiometric surface temperature measurements as a means of validation (Crow et al. 2005).

Model sensitivity and stability analyses show that TSMS is less sensitive to the leaf area index/fractional vegetation cover LAI/fC, and is more stable at different vegetation conditions. This seems to be due largely to the moderating effect of the air temperature in the canopy air space as it is used in the series resistance network, allowing for stabilizing interactions between soil and vegetative canopy components to take place.

Although there does not appear to be a large absolute difference in the performance of either the parallel or series resistance formulations used in TSM for estimating the surface fluxes under a wide range of crop canopy cover conditions during SMACEX, the TSMP output certainly appears to be more sensitive to variations in model inputs, such as the clumping factor Ω. This was further investigated by performing an analysis of sensitivity and stability of TSM to a key input variable, LAI/fC. The results indicate that TSMS is generally more robust and applicable under a wider range of environmental conditions.

Acknowledgments

Funding provided by NASA Grant NRA 00-OES-07 from the NASA Terrestrial Hydrology Program, made possible the SMACEX project. Logistical support from the USDA ARS National Soil Tilth Lab and the SMEX02 project were critical in the success of the SMACEX field campaign.

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APPENDIX

Overview of the Two-Source Model and Principal Modifications

In the two-source model, the remote sensing–based radiometric surface temperature is the composite temperature of soil and canopy and could be expressed as
i1525-7541-6-6-878-ea1
where TR is satellite- or aircraft-derived radiometric surface temperature, TC is canopy temperature, TS is soil temperature, and fC(ϕ) is fractional vegetation cover with view angle ϕ, estimated by
i1525-7541-6-6-878-ea2
where Ω is a clumping factor to account for nonhomogeneous canopy cover, such as row crops (see below).
The sensible heat flux is partitioned between the vegetated canopy (HC) and soil (HS),
i1525-7541-6-6-878-ea3
and when the soil surface and vegetation canopy fluxes are taken to be in parallel with each other (see Fig. 1), HC and HS are expressed as
i1525-7541-6-6-878-ea4
and
i1525-7541-6-6-878-ea5
where ρCP is the volumetric heat capacity of air, TA is the air temperature, rAH is the resistance to heat transfer between the surface and the reference location where the air temperature and other atmospheric data are measured, and rS is the resistance to heat flow in the boundary layer immediately above the soil surface. The resistances rAH and rS are estimated via
i1525-7541-6-6-878-ea6
i1525-7541-6-6-878-ea7
where ZU and ZT are the measurement heights for wind speed and air temperature, respectively; dO is displacement height, estimated as a fraction of canopy height hC (i.e., dO = 2/3hC); the roughness length for momentum ZOM is taken as a fraction of canopy height (i.e., ZOM = 1/8hC); and the roughness length for heat ZOH is taken as a fraction of ZOM (ZOH = ZOM/7) to account for the less efficient transport of heat versus momentum near the canopy elements (Garratt and Hicks 1973). The stability functions ψH and ψM are for heat and momentum, respectively (Brutsaert 1982), and uS is the wind speed at a height above the soil surface where the effect of soil surface roughness is minimal (i.e., ∼0.05–0.10 m AGL), with typical values for the constants a and b of approximately 0.004 and 0.012, respectively. An estimate of uS is computed from an exponential decay function from Norman et al. (1995). Kustas and Norman (1999a, 2000) revised Eq. (A7) by considering a is a function of the temperature difference between the soil and canopy, based on Kondo and Ishida (1997), with a = c(TSTC)1/3, where c ∼0.0025. In addition, b can vary depending on soil roughness and higher turbulent intensity in the canopy air space (Sauer et al. 1995).
For the series model, when the soil and canopy fluxes interact with each other (see Fig. 1), HC and HS are expressed as
i1525-7541-6-6-878-ea8
with
i1525-7541-6-6-878-ea9
and
i1525-7541-6-6-878-ea10
where TAC is the air temperature in canopy–air space, rA is the aerodynamic resistance to heat transfer with ZOH = ZOM in Eq. (A6) because rX, the total boundary layer resistance of the complete canopy of leaves, accounts for the less efficient transport of heat versus momentum near the canopy elements and is estimated by a semiempirical relation (see Norman et al. 1995).
The surface energy balance can be expressed as
i1525-7541-6-6-878-ea11
where Rn is net radiation, RnS is net radiation at soil surface, RnC is net radiation at vegetation canopy, LE is latent heat flux, and G is soil heat flux. The energy balance for the soil and vegetated canopy components are expressed as
i1525-7541-6-6-878-ea12
i1525-7541-6-6-878-ea13
In Norman et al. (1995), the Priestley–Taylor formula was used to partition the latent heat fluxes between the vegetation canopy and the soil as
i1525-7541-6-6-878-ea14
where αPT is the Priestley–Taylor parameter(∼1.3), fG is the fraction of the LAI that is green (typically fG = 1), Δ is the slope of the saturation vapor pressure verses temperature curve, and γ is the psychrometer constant (∼0.066 kPa C−1).
Through the energy balance model, latent heat fluxes from soil surface is solved as a residual,
i1525-7541-6-6-878-ea15
with G, estimated as a fraction of RnS,
i1525-7541-6-6-878-ea16
where CG ∼0.35, and has been expressed as a function of time to accommodate known temporal variation in this “constant” (Santanello and Friedl 2003).
In the revised two-source model, the separation of net radiation between canopy and soil is through a physically based model based on Campbell and Norman (1998). This can be expressed as
i1525-7541-6-6-878-ea17
i1525-7541-6-6-878-ea18
where S is solar radiation, τS is solar transmittance in the canopy, αS is soil albedo, αC is canopy albedo, LnS and LnC are longwave radiation for soil and canopy, respectively, and are estimated via the following expression:
i1525-7541-6-6-878-ea19
i1525-7541-6-6-878-ea20
where LSky, LS, and LC are longwave radiation from the sky, soil, and canopy, and can be calculated from air, soil, and canopy temperature, and κL is an extinction coefficient. Campbell and Norman (1998) described how to estimate the transmittance, albedo, and extinction coefficients for soil and canopy.
A simplified model for clumped vegetation given in Campbell and Norman (1998) was developed for forested canopies (Kucharik et al. 1999):
i1525-7541-6-6-878-ea21
where the view zenith angle ϕ = 0 for a nadir view and ϕ = 90 for a horizontal view, which is perpendicular to nadir, hence, Ω(90) ∼1. The k and p variables are empirical coefficients that depend on plant spacing and crown dimensions (Kucharik et al. 1999). Anderson et al. (2005) modified algorithms estimating both k and Ω(90) for row crops because these coefficients will also vary azimuthally.

Fig. 1.
Fig. 1.

Schematic diagram illustrating the resistance network for the (a) parallel and (b) series formation used in TSM scheme. Also shown is the flux partitioning between soil (subscript s) and canopy (subscript c) and some of the key model inputs. Symbols are defined in the text.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM464.1

Fig. 2.
Fig. 2.

Clumping factor Ω for corn and soybean derived from this study and Anderson et al. (2005). Details are given in the text.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM464.1

Fig. 3.
Fig. 3.

Comparison between TSM output and METFLUX observations using the series resistance network (TSMS) and parallel resistance network (TSMP) for (a) net radiation Rn, (b) soil heat flux G, (c) sensible heat flux H, and (d) latent heat flux LE, adjusted to invoke closure by residual method LERE. Symbols correspond to overpass date (DOY) and model version, namely, TSMS or TSMP.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM464.1

Fig. 4.
Fig. 4.

Soil surface temperature comparison between ground observations and TSM output. Symbols correspond to overpass date (DOY) and series and parallel model versions, TSMS and TSMP, respectively.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM464.1

Fig. 5.
Fig. 5.

Model sensitivity SX, computed via Eq. (4) to a ±20% error in LAI for both the parallel (TSMP) and series (TSMS) network.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM464.1

Fig. 6.
Fig. 6.

Canopy temperature TC and soil temperature TS computed from TSMS and TSMP under increasing fractional vegetation cover fC for DOY 167 conditions at a soybean site WC161 (see text for details).

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM464.1

Fig. 7.
Fig. 7.

Output of H from TSMS and TSMP under increasing fC for DOY 167 conditions at a soybean (WC161) and corn (WC151) site.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM464.1

Table 1.

Difference statistics between METFLUX measurements and TSM output of net radiation (Rn), soil heat flux (G), and sensible (H) and latent heat (LE) fluxes using series (TSMS) and parallel (TSMP) resistance formulation. Note: HM and LEM are the H and LE eddy covariance measurements without adjusting for lack of closure, HBR and LEBR are the H and LE modified by the Bowen ratio method to force closure and LERE modified LEM using the residual method as closure, RnM − GM − HM = LERE, and n is the number of observations.

Table 1.
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