Comparing Aircraft-Based Remotely Sensed Energy Balance Fluxes with Eddy Covariance Tower Data Using Heat Flux Source Area Functions

JoséL. Chávez Remote Sensing Services Laboratory, Biological and Irrigation Engineering Department, Utah State University, Logan, Utah

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Christopher M. U. Neale Remote Sensing Services Laboratory, Biological and Irrigation Engineering Department, Utah State University, Logan, Utah

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Lawrence E. Hipps Plant, Soils and Biometeorology Department, Utah State University, Logan, Utah

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John H. Prueger National Soil Tilth Laboratory, ARS, USDA, Ames, Iowa

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William P. Kustas Hydrology and Remote Sensing Laboratory, ARS, USDA, Beltsville, Maryland

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Abstract

In an effort to better evaluate distributed airborne remotely sensed sensible and latent heat flux estimates, two heat flux source area (footprint) models were applied to the imagery, and their pixel weighting/integrating functionality was investigated through statistical analysis. Soil heat flux and sensible heat flux models were calibrated. The latent heat flux was determined as a residual from the energy balance equation. The resulting raster images were integrated using the 2D footprints and were compared to eddy covariance energy balance flux measurements. The results show latent heat flux estimates (adjusted for closure) with errors of (mean ± std dev) −9.2 ± 39.4 W m−2, sensible heat flux estimate errors of 9.4 ± 28.3 W m−2, net radiation error of −4.8 ± 20.7 W m−2, and soil heat flux error of −0.5 ± 24.5 W m−2. This good agreement with measured values indicates that the adopted methodology for estimating the energy balance components, using high-resolution airborne multispectral imagery, is appropriate for modeling latent heat fluxes. The method worked well for the unstable atmospheric conditions of the study. The footprint weighting/integration models tested indicate that they perform better than simple pixel averages upwind from the flux stations. In particular the flux source area model (footprint) seemed to better integrate the resulting heat flux image pixels. It is suggested that future studies test the methodology for heterogeneous surfaces under stable atmospheric conditions.

Corresponding author address: Christopher M. U. Neale, Biological and Irrigation Engineering Department, Utah State University, Logan, UT 84322-4105. Email: cneale@cc.usu.edu

Abstract

In an effort to better evaluate distributed airborne remotely sensed sensible and latent heat flux estimates, two heat flux source area (footprint) models were applied to the imagery, and their pixel weighting/integrating functionality was investigated through statistical analysis. Soil heat flux and sensible heat flux models were calibrated. The latent heat flux was determined as a residual from the energy balance equation. The resulting raster images were integrated using the 2D footprints and were compared to eddy covariance energy balance flux measurements. The results show latent heat flux estimates (adjusted for closure) with errors of (mean ± std dev) −9.2 ± 39.4 W m−2, sensible heat flux estimate errors of 9.4 ± 28.3 W m−2, net radiation error of −4.8 ± 20.7 W m−2, and soil heat flux error of −0.5 ± 24.5 W m−2. This good agreement with measured values indicates that the adopted methodology for estimating the energy balance components, using high-resolution airborne multispectral imagery, is appropriate for modeling latent heat fluxes. The method worked well for the unstable atmospheric conditions of the study. The footprint weighting/integration models tested indicate that they perform better than simple pixel averages upwind from the flux stations. In particular the flux source area model (footprint) seemed to better integrate the resulting heat flux image pixels. It is suggested that future studies test the methodology for heterogeneous surfaces under stable atmospheric conditions.

Corresponding author address: Christopher M. U. Neale, Biological and Irrigation Engineering Department, Utah State University, Logan, UT 84322-4105. Email: cneale@cc.usu.edu

1. Introduction

Reliable spatial–temporal estimation of evapotranspiration (latent heat flux) of vegetation is very important for water management and soil moisture assessment in agriculture as well as in natural ecosystems. Airborne remote sensing is a powerful tool in precision agriculture applications, such as in the estimation of spatial evapotranspiration and yield. It is operationally flexible, because the system can fly on demand, weather permitting, and acquire high spatial resolution imagery (e.g., 0.2–2.0 m), depending on the study needs.

In the past, airborne and satellite remotely sensed latent and sensible heat flux estimates have been compared to surface fluxes measured with micrometeorological stations such as eddy covariance, Bowen ratio energy balance systems, and scintillometers (Gao et al. 1998; Neale et al. 2001; Moran et al. 1989, Moran 1990; Watts et al. 1998). Sometimes even lysimeters have been used in the effort to compare against remotely sensed crop water consumption (Morse et al. 2001). Results have shown that the remote sensing methods are capable of determining distributed heat fluxes with some discrepancies (Qi et al. 1998; Moran et al. 1989). Furthermore, the image pixels were selected for the comparisons using different criteria. For instance, sometimes pixels upwind of the micrometeorological tower have been averaged for comparison without regard to the true size of the upwind contributing area (Neale et al. 2001; Moran et al. 1989). A technique to properly integrate the remote sensing heat flux pixels is needed for the comparisons with ground-measured fluxes in order to validate the use of remote sensing methodologies for accurate vegetation evapotranspiration estimates.

Footprint models have been developed to determine what area (upwind of micrometeorological-flux stations) is contributing the heat fluxes to the sensors as well as the relative weight of each particular cell inside the footprint limits. Different footprint models have been proposed in the literature, basically, one-dimensional (1D) or two-dimensional (2D) models. Some models are the analytical solution to the diffusion–dispersion–advection equation (Horst and Weil 1992, 1994). Other models are Lagrangian (Leclerc and Thurtell 1990). Studies using these models were able to estimate how contributions of upwind locations to the measured flux depend on the height of the vegetation, height of the instrumentation, wind speed, wind direction, and atmospheric stability conditions.

Because of the scale of in-field variability in heat fluxes derived from high-resolution airborne remote sensing, footprint models could be a useful tool in the integration and comparison of these energy balance fluxes (net radiation, latent heat flux, sensible heat flux, and soil heat flux) with measured values. In this study, 2D footprints will be evaluated for the integration of heat flux estimated through a remote sensing methodology in comparison with measured fluxes in corn- and soybean fields near Ames, Iowa, during the Soil Moisture–Atmosphere Coupling Experiment (SMACEX) in 2002. For this purpose, methods of spatially obtaining soil heat flux as well as aerodynamic temperatures from remote sensing and basic ground meteorological data were developed.

2. Material and methods

Kustas et al. (2005) present an overview article providing background and including their rationale for the study, a site description, the experimental design, the hydrometeorological conditions, and a summary of results.

This section has been divided into three parts: the first part describes the instrumentation and data types used in the experiment. The second part, entitled model development phase, discusses the calibration of the soil heat flux and surface aerodynamic temperature models, with the presentation of an iterative method to derive surface aerodynamic resistance, using the calibrated aerodynamic temperature and with the description of the sensible heat flux, net radiation, and latent heat flux models used to obtain the spatially distributed fluxes. The third section, entitled model verification phase, describes the footprint models and statistics used to evaluate both the remote sensing estimates and the performance of the footprints in weighting/integrating the remotely sensed fluxes.

a. Data description

1) Remote sensing data

The remote sensing data consisted of high-resolution multispectral imagery in the visible, near-infrared, and thermal-infrared portions of the electromagnetic spectrum. These images were calibrated and transformed into surface reflectance and temperature images used for the estimation of reflected or outgoing shortwave and longwave radiation, respectively, with both components required in the estimation of spatially distributed net radiation. Also, vegetation indices derived from surface reflectance were related to leaf area index (LAI), vegetation canopy height (for zero-plane displacement, roughness height, and aerodynamic resistance calculations), and fractional vegetation cover (for calibrating the thermal imagery and account for variable surface emissivity effects). Surface temperature derived from the thermal imagery was also used in the estimation of the distributed sensible heat fluxes.

Multispectral digital imagery was acquired over the study area, using the Utah State University (USU) airborne digital remote sensing system (Neale and Crowther 1994; Cai and Neale 1999). The system comprises three Kodak Megaplus digital frame cameras with interference filters centered in the green (G) (0.545–0.560 μm), red (R) (0.665–0.680 μm) and near-infrared (NIR) (0.795–0.809 μm) portions of the electromagnetic spectrum. The fourth camera is an Inframetrics 760 thermal-infrared scanner (8–12 μm) that provides thermal-infrared radiance, used to obtain surface radiometric temperature images.

The high-resolution imagery was acquired on several different days during the intensive sampling period of SMACEX during the months of June and July 2002. Three major flight dates were 16 June [day of year (DOY) 167], and 1 (DOY 182) and 8 (DOY 189) July, which were planned to coincide with Landsat Thematic Mapper overpasses. These regional flights covered the entire study area (approximately 12 km × 22 km) at a nominal pixel resolution of 1.5 m from an altitude of approximately 3350 m [11 000 ft above ground level (AGL)]. Imagery was also acquired from a lower altitude of 2100 m (7000 ft AGL) over selected fields containing energy balance stations (flux flights), resulting in a shortwave pixel resolution of 1 m. This additional imagery was acquired on DOY 167, 169, 174, 182, 184, and 189. Tables 1 and 2 show the list of the fields containing the flux stations with the DOY and overpass time (LST) along with several variables used in the calculations. Figure 1 shows the location of the fields and stations in the study area. On DOY 182, the corn was at almost full cover, while the soybean fields were at early stages of growth, showing a mix of bare soil and growing canopy.

The shortwave camera lens F-stop settings were f5.6 for the G and R bands and f8.0 for the NIR. The shutter speeds were mostly set to 10 ms, except for DOY 189 when they were at 15 ms. The sky conditions for all flight time periods were mostly free of clouds. Considerable atmospheric interference resulting from smoke was present during the acquisition period on DOY 189. The prevailing wind direction during all the flights was from the south-southwest.

The shortwave images were corrected for lens-vignetting effects and geometric radial distortions in procedures similar to those described by Neale and Crowther (1994) and Sundararaman and Neale (1997). The individual spectral images were registered into three band images and rectified to a 1:24 000 digital orthophotoquad base map. The individual rectified images were then mosaicked along the flight lines to form image strips that, in turn, were stitched together to form a mosaic of the entire study area for each regional flight.

The digital numbers of the rectified multispectral image strips were converted to radiance using the system calibration method described by Neale and Crowther (1994). These radiances were divided by the incoming solar irradiance to obtain surface spectral reflectance. Solar irradiance in each spectral band was obtained from radiance measured concurrently to the flights with an Exotech radiometer placed over a barium sulfate standard reflectance panel with known bidirectional properties (Jackson et al. 1992). Examples of calibrated three-band images can be seen in Figs. 1 and 2.

The thermal-infrared imagery was mosaicked along the flight lines and rectified to the high-resolution three-band image mosaic described above. The digital numbers were transformed into apparent (at sensor) temperature values using the system calibration bar at the bottom of each image. The images were corrected for atmospheric and surface emissivity effects using MODTRAN version 3.0 (Berk et al. 1989), an atmospheric radiative transfer model (software). This correction resulted in at-surface radiometric temperatures. Radiosonde observations acquired at the lidar site (fields 15 and 16) during the overflights were used to obtain the necessary input data to the MODTRAN model.

An example of a corrected at-surface temperature image (colored for better temperature visualization) can be seen in Fig. 2 for the corn- and soybean fields, containing flux stations 15 and 16, respectively. All image processing was conducted using the ERDAS Imagine software. Spatial distribution of the fluxes was obtained using the high-resolution calibrated and georeferenced imagery as inputs, along with ground-measured meteorological data at the towers, by programming the appropriate equations described below within ERDAS Imagine model maker and producing output images of different parameters (leaf area index, aerodynamic temperature, soil heat flux, canopy height, etc.).

2) Ground data energy balance fluxes

The basic input data used in the remote sensing–based computation of fluxes were measured at the eddy covariance energy balance flux stations in each field and corresponded to the 30-min period coinciding with the aircraft overpass time. These data consisted of mean air temperature, wind speed, vapor pressure, incoming shortwave radiation, and instrumentation height. The measured sensible heat fluxes were used to obtain the aerodynamic temperatures through inversion of the bulk aerodynamic resistance equation. Other data measured at the flux stations and used in the comparisons included latent heat flux, net radiation, soil heat flux, surface temperature, friction velocity, wind direction, standard deviation of wind direction, and air temperature derived from the sonic virtual temperature.

The eddy covariance energy balance flux stations comprised the following equipment: a Campbell Scientific, Inc. (CSI), CSAT3 3D sonic anemometer, a LI-COR 7500 open-path CO2/H2O analyzer or a CSI KH20 Krypton Hygrometer, net radiometers [Radiation and Energy Balance System (REBS) Q7 or Kipp & Zonen CNR01 type], and soil heat flux plates completed the equipment of the energy balance stations. In addition, the stations where equipped with Apogee (model IRTS-P) thermal-infrared radiometers (IRTs) viewing the canopy from nadir, nominally at 5 m AGL for the corn sites and 3 m AGL for the soybean sites. Soil heat flux was measured at each station with four soil heat flux plates distributed across the corn and soybean rows and installed at an 6-cm depth, along with soil temperature thermocouples placed within the topsoil layer. The air temperature/relative humidity sensor (Vaisala HMP35C) was positioned 1–2 m above local terrain for soybean fields and 2–3 m for the corn.

The energy balance fluxes for the different DOY, measured with the eddy covariance flux stations, resulted in a general energy balance closure of about 85%. In some cases, this left a considerable amount of energy unaccounted for in the partitioning of net radiation into sensible and latent heat fluxes, which could cause significant discrepancies in the comparisons with estimated remotely sensed heat fluxes, which forces closure in its methodology. The inherent error in measuring the sensible heat flux (H), latent heat flux (LE), net radiation (Rn), and soil heat flux (G), by ground systems, are shown to be 15%–20%, 15%–20%, 5%–10%, 20%–30%, respectively, according to Weaver (1990), Field et al. (1994), and L. Hipps (2003, personal communication). For this reason, the measured Bowen ratio at the flux stations was used to adjust the measured fluxes and force closure following the procedure suggested by Twine et al. (2000) described in Table 3. The flux data were processed using half-hour integration periods described by Kustas et al. (2005) in this same special issue. The exact standard time of the remote sensing image acquisition overpass was used to determine what flux period with which to compare the estimates. The sensible and latent heat flux data for DOY 167 were acquired in flux mode and not in time series mode, which was the case for all other measurement dates.

The ground station data obtained in different fields and on different dates and times were divided into two groups representing the model development and validation phases of the research (Tables 1 and 2). For the development phase 26 data records were used, while 22 records were used for the verification phase.

b. Model development phase

Net radiation estimates from remote sensing are fairly accurate according to Neale et al. (2001), but soil and sensible heat flux estimates need more research. Improvement in the estimation of these variables is needed because latent heat flux is usually obtained as a residual from the energy balance equation. In this study, soil heat flux and surface aerodynamic temperature models were calibrated for corn- and soybean fields and for the conditions encountered during the experiment to improve the remote sensing estimation of LE. The aerodynamic temperature model was used to obtain distributed sensible heat flux.

1) Soil heat flux modeling

Soil heat flux (G) models based on remotely sensed inputs were obtained by fitting different types of curves to the G/Rn versus LAI dataset for the selected model development phase data.

The distributed LAI values (LAI_RS) were obtained from the calibrated high-resolution imagery using a model developed during SMACEX (Anderson et al. 2004) that was based on the Optimized Soil Adjusted Vegetation Index (OSAVI; Rondeaux et al. 1996) and ground samples. Equation (1) was reported to have an R2 value of 0.85 (14.9% error) and was developed for an LAI range of 0.13–5.23:
i1525-7541-6-6-923-e1
This model was applied to the OSAVI image that was calculated from the calibrated airborne reflectance image, obtaining spatially distributed LAI. The bias resulting from atmospheric effects mentioned in Anderson et al. (2004) between the airborne and satellite reflectance was removed prior to applying the relationship above to the airborne imagery.

2) Surface aerodynamic temperature modeling

The general bulk aerodynamic resistance equation was used to estimate H (W m−2) [Eq. (2)] based on surface aerodynamic temperature. Because the aerodynamic temperature is not measured or easily calculated in remote sensing applications, different authors have opted in the past to use the remotely sensed surface temperature instead. Choudhury et al. (1986) found that these two temperatures were nearly the same for near-neutral atmospheric conditions, but radiometric surface temperatures were higher than aerodynamic temperatures for stable conditions and lower for unstable conditions. According to Wenbin et al. (2004), for homogeneous and isothermal surfaces the definition of aerodynamic, radiometric, and thermodynamic temperatures are equivalent, but over heterogeneous surfaces there are differences between the aerodynamic and surface radiometric temperatures because of the unavailability of the thermodynamic surface temperature to measure molecular mean kinetic energy, consequently leading to errors in the estimation of H, resulting in errors in the estimation of LE from remote sensing. Thus, this subsection of the paper describes the parameterization that is followed to obtain the surface aerodynamic temperature using the remotely sensed and ground inputs.

The bulk aerodynamic resistance equation can be written as
i1525-7541-6-6-923-e2
where ρa is air density (kg m−3), Cpa is specific heat of air = 1005 (J kg−1 K−1), Ta is average air temperature (K), Taero is average surface aerodynamic temperature (K), which is defined for a uniform surface as the temperature at the height of the zero-plane displacement plus the roughness length (d + Zoh) for sensible heat transfer Zoh (m), and rah is surface aerodynamic resistance (s m−1) to heat transfer from Zoh to Zm [height of wind speed measurement (m)]. For neutral atmospheric conditions rah is
i1525-7541-6-6-923-e3
where U is the average horizontal wind velocity (m s−1), k is the von Kármán constant, which is equal to 0.41, d is the zero-plane displacement height (m), and Zom is the roughness length for momentum transfer (m). Here, Zoh, Zom, and d can be estimated from the crop canopy height (hc) (Brutsaert 1982):
i1525-7541-6-6-923-e4
i1525-7541-6-6-923-e5
i1525-7541-6-6-923-e6
From the Monin–Obukhov similarity theory, rah for unstable atmospheric conditions can be expressed as
i1525-7541-6-6-923-e7
where ψh is the stability correction factor for atmospheric heat transfer, LM_O is the Monin–Obukhov length scale (m), and u* is the friction velocity (m s−1); LM_O is defined as
i1525-7541-6-6-923-e8
where g is gravity acceleration. The stability correction factor for atmospheric heat transfer ψh for unstable conditions (LM_O < 0) is
i1525-7541-6-6-923-e9
i1525-7541-6-6-923-e10
The friction velocity under neutral conditions (LM_O ∼ ∞) is
i1525-7541-6-6-923-e11
Considering diabatic or nonneutral conditions, the friction velocity is
i1525-7541-6-6-923-e12
where ψm is the stability correction factor for momentum transfer. For unstable conditions it is
i1525-7541-6-6-923-e13

Because Taero in Eq. (2) is unknown, the approach used to obtain this parameter for calibration purposes was to invert the H equation using the H and Ta measured by the flux stations and rah derived from measured H. The resulting value was called inverted Taero (Taero_inv), and was used in the modeling of Taero based on remote sensing (RS) and ground input variables. Using Eqs. (7), (8), and (12) with H, U, and Ta measured at the EC towers rah was derived, along with hc and Zm. The resulting rah term represents an inverted rah (rah_inv).

The inverted Taero dataset was regressed against different combinations of U, Ta, remotely sensed radiometric surface temperature (Ts_RS), and LAI from remote sensing using multiple linear and nonlinear regression techniques. Both Ts_RS and LAI were obtained by integrating the raster image spatial values in the upwind footprint using the area-of-interest (AOI) polygon shape of the Schmid (1994) footprint model (described in next section). To assess the accuracy of the Ts_RS measurements, a comparison was performed against the ground-measured radiometric surface temperature (IRT) by the IRTs placed on the flux towers. The remote sensing accuracy in estimating LAI was presented in the previous subsection.

In the estimation of rah, when using a RS method to obtain sensible heat flux, an adjustment for the atmospheric stability conditions needs to be made and LM_O is unknown. In general, values of measured H at the surface are not available and, therefore, there is a need for a method to estimate rah independently of H. To accomplish this, the following procedure was adopted: using rah from Eq. (3) as an initial condition, Eqs. (2), (7), (8), (9), (12), and (13) were iterated until rah values converged. Once this condition was satisfied, the resulting atmospheric stability correction factor values for momentum and heat transfer, along with the measured wind speed at the flux tower and the distributed vegetation canopy height, were used in Eqs. (7) and (12) to obtain the spatial rah raster image, which ultimately was used along with the distributed surface aerodynamic temperature for obtaining the remotely sensed estimation of H. This remote sensing estimation of rah was denoted as rah_e, that is, estimated surface aerodynamic resistance, which was later evaluated against the ground station–derived rah_inv, using one of the weighting/integrating and statistical methods described in the subsection below. The same procedure was followed to evaluate the remote sensing estimation of Taero, which was called Taero_e. The average air temperature Ta and wind speed U, measured at the flux stations, were used in the H and rah estimations as explained above. These temperature and wind values were assumed to be constant over the relatively small upwind footprints used for the remote sensing flux calculations. Given the relatively uniform nature of agricultural fields and the small spatial scale of the footprints for each flux tower, this is a reasonable assumption. The diffusive nature of the boundary layer ensures that mean air temperature and wind velocities would vary little above these surfaces over distances of only 100–200 m (the typical footprint size).

The required hc values in Eqs. (4) and (6) were obtained from the remote sensing–derived OSAVI using Eqs. (14) and (15) below by Anderson et al. (2004):
i1525-7541-6-6-923-e14
where hc_CORN is the corn canopy height in meters, and
i1525-7541-6-6-923-e15
where hc_SOYBEAN is the soybean canopy height in meters.

3) Net radiation

The net radiation is expressed as
i1525-7541-6-6-923-e16
where Rn is the net radiation (W m−2), α is surface albedo, Rs is incoming shortwave radiation (W m−2) measured with pyranometers, σ is the Stefan–Boltzmann constant (5.67E-08 W m−2 K−4), ɛ is emissivity, and T is temperature (K), with subscripts “a” and “s” for air and surface, respectively. Surface albedo for vegetated areas was estimated using the Brest and Goward (1987) model. This model is based on the R and NIR band reflectance
i1525-7541-6-6-923-e17
Equation (17) was applied spatially using the calibrated reflectance images; Ts_RS was used for Ts in Eq. (16). The RS at-sensor temperature imagery was corrected for atmospheric effects and for surface emissivity considering Hipps’ (1989) suggestions and following Brunsell and Gillies’ (2002) procedures. The correction was performed assuming a bare soil and fully vegetated surface emissivity of 0.93 and 0.98, respectively, and the fractional vegetation cover from the scaled Normalized Difference Vegetation Index (NDVI). The emissivity of air can be obtained from the Brutsaert (1975) equation
i1525-7541-6-6-923-e18
where ea is actual vapor pressure (mb). The methodology suggested by Crawford and Duchon (1999) was adopted to adjust Brutsaert’s leading coefficient of 1.24 for cloud fraction and for the month of the year. The adopted ɛa equation was
i1525-7541-6-6-923-e19
where clf is the cloud fraction term. This term is equal to (1 − s), with s being the ratio of the measured solar irradiance to the clear-sky irradiance. The term “mo” is the month of the year. For clear-sky conditions the leading coefficient resulted in a value of 1.16.

4) Latent heat flux

Spatial distribution of the fluxes for any given flight overpass were obtained as raster image layers using the ERDAS Imagine model maker on a pixel-by-pixel basis and obtaining the instantaneous latent heat flux as a residual from the energy balance equation:
i1525-7541-6-6-923-e20

c. Model verification phase

1) Footprint models

The spatially estimated Taero, rah, H, G, LE, and Rn that were derived from the remote sensing methodology were weighted/integrated using four different methods. The first footprint (FTP) was applied by Kaharabata et al. (1997) who borrowed basic concepts summarized by Horst and Weil (1992, 1994), but, instead of using the expression for the crosswind-integrated flux distribution function (which was adjusted empirically to Lagrangian simulations), used the actual crosswind Gaussian distribution. This resulted in the generation of weights in the x and y direction. The new function is expressed as
i1525-7541-6-6-923-e21
where f (x, y, Zm) is the footprint or source weight function, x is the upwind distance from the tower or sensor location, y is the crosswind distance from the axis parallel to the wind direction (x) (m), s is a shape exponent 1 for unstable conditions, 2 for very stable conditions, and 1.3–1.5 for neutral conditions. Table 4 shows the equations involved in the footprint function f (x, y, Zm). Equation (21) was implemented through a computer program called Flux Area Source Weights Generator (FASOWG), written in Visual Basic v6 specifically for this study. The second method of pixel integration consisted in using the shape of the FASOWG FTP boundary as an AOI polygon to extract a simple average of all pixel values within the shape of the footprint.
The second footprint model (third method of pixel integration) was a Flux Source Area Model (FSAM) used by Schmid (1994), based on the Horst and Weil (1992) model (coded in FORTRAN). FSAM generates the FTP weights for the source area and the approximate dimensions of the FTP area for an area that contributes up to 90% of the sensed fluxes by the instrumentation. It includes the crosswind-integrated flux as Horst and Weil (1992, 1994)
i1525-7541-6-6-923-e22
where F(x, y, Zm)is the footprint weight function, Dy(x, y) is the crosswind distribution function, and (x, Zm) is the crosswind-integrated function.

Measured H, Ta, U, Zm, hc, wind direction, and standard deviation of wind direction values at the flux station were used to obtain the size, shape, and weights of the FTP for the conditions during the half-hour integration period corresponding to the remote sensing aircraft overpass. Once the weights were generated (FASOWG, FSAM) as output text files, the files were imported into ERDAS Imagine and converted into a raster image to facilitate spatial operations using the ERDAS modeler maker. After carefully considering the wind direction at the time of each remote sensing overpass, the weights image was georectified to the three-band image, resulting in a raster image with the same geographic coordinate system as the latent and sensible heat flux images. The weights image was multiplied to the flux, Rn, Taero, and rah images using Imagine modeler maker to obtain as output the weighted heat flux, Rn, Taero, and rah images within the FTP boundaries. Pixels histograms were extracted from the image table attributes in ERDAS Imagine and integrated in an Excel spreadsheet, by adding the result of multiplying each class by its frequency in the histogram, thus, obtaining the weighted-integrated pixel values. These values were then compared to the corresponding ground station–measured fluxes to evaluate the remote sensing methodology. AOI polygons were drawn following the boundary of the FSAM footprint area, and simple pixel arithmetic averages were extracted for comparison to the corresponding measured values. This became the fourth method of pixel weighting/integration.

d. Statistical analysis

Finally, the evaluation of the different models (equations) and FTP integrating methods was carried out comparing the mean bias error (MBE) and root-mean-square error (RMSE). These are the mean and standard deviation errors, respectively. Their definitions follow:
i1525-7541-6-6-923-e23
where n is the number of pairs compared, X(M)i is the modeled (estimated) value, and X(O)i is the observed or measured value. A positive MBE means that the model overestimated the reference value;
i1525-7541-6-6-923-e24

3. Results and discussion

Examples of graphical representations of the FSAM and FASOWG FTPs are shown in Figs. 3 and 4. In this study conditions were unstable, resulting in shorter or smaller FTPs. Also Figs. 3 and 4 clearly show how the FTPs distribute heat flux weights across the source area. The FASOWG FTP model concentrated the weights closer to the flux stations than the FSAM model. Figure 5 presents both FTP AOIs over a LAI image, showing the differences in their spatial integration. Figure 6 shows the energy balance components images for stations 15.1, 15.2, and 16.1 for DOY 182, with the transparent outline of the FSAM FTP laid over the image to allow for visualization of the variability within and around the FTP. Results are individually discussed below.

a. Surface temperature

Figure 7 shows a comparison of surface temperatures between the RS and IRT measurements, which resulted in an excellent agreement (R2 = 0.927). The correlation is very high for surface temperatures up to about 38°C and lower for the range of 38°–41°C. The agreement is evidence of proper thermal imagery calibration. The disagreement at higher temperatures corresponds to more sparse vegetation cases and possibly to differences in the footprint observed by the IRT and RS thermal scanner, that is, the IRT looked at an area 1.5 m in diameter (3 m east of the EC tower), while the RS thermal scanner pixel size was 6 m for the high-altitude flight and 4 m for the low-altitude flight. At low LAI values this effect would be largest. A low biomass presence was observed on DOY 167 on both corn- and soybean fields. When data from DOY 167 were removed from the analysis the agreement with the IRT, readings increased to R2 = 0.965.

b. Soil heat flux

The curve fitting of different models to the G/Rn versus LAI dataset resulted in a combination of a linear and a logarithmic model being the best fit (R2 = 0.732),
i1525-7541-6-6-923-e25
Figure 8 displays the curve fitting and shows that Eq. (25) applies for LAI values between 0.3 and 5. Additional G models based on remotely sensed vegetation indices and identified in the literature were also tested. These models did not provide as good a fit to the data, mostly because of the fact that they were developed for broadcast grain crops and alfalfa, both with different canopy structures. The developed soil heat flux equation was applied to the selected verification phase dataset, resulting in an average estimation error (MBE) of −0.5 W m−2 and an rmse of 24.5 W m−2 when the FSAM FTP was used as the weighting/integrating method, (Table 5). Figure 9 shows the predicted soil heat flux against the measured values for the validation dataset. Some of the scatter is attributed to the comparison of essentially a point measurement with the spatial estimates from the remote sensing G model integrated using the FTP. Another source of error may be from the error in LAI estimation (about 15%) and resulting error propagation.

c. Surface aerodynamic temperature

The best Taero model resulting from the multiple regression procedures was based on Ta, Ts_RS, U, and LAI_RS as shown below (R2 = 0.766):
i1525-7541-6-6-923-e26
Table 5 shows the results from applying Eq. (26) to the verification phase data. The MBE and rmse values were 0.2° and 0.9°C, respectively, for the FSAM FTP integration method. Figure 10 plots the values of predicted Taero (Taero_e) against inverted Taero (Taero_inv) for the validation dataset, showing a very good match (R2 = 0.9). Some bias occurs for higher Taero values, possibly related to uncertainties in the LAI_RS estimates for low biomass stands (the asymptotic part of the model) and uncertainties in Ts_RS for the same low biomass stands (maybe there is a need for greater ɛs correction). On the other hand, it could be an indication that empirical equations for Taero need to be developed separately for corn and soybean canopies because of differences in their structure and canopy height vis-à-vis the LAI. Given that for real nonuniform surfaces Taero is effectively a parameter, the empirical fit with these properties is actually rather good.

d. Surface aerodynamic resistance

Figure 11 and Table 5 show the comparison of the estimated rah (rah_e) against inverted values from measured H that is adjusted for closure. The iterative method seems to work because the estimated values match the referenced values with an estimation error of −0.16 ± 2.8 s m−1 (MBE ± rmse) for the FSAM FTP method (R2 = 0.84). According to a sensitivity analysis, a 1° error in Taero (about 3.2% difference in Taero) or Ta would result in an H error of about 50%, while an about 10% difference in rah (1.5–2.0 s m−1) would result in an H error of only 9%–10%. The need for accurate spatial Taero and Ta estimations to obtain proper distributed H estimates is evident.

e. Sensible heat flux

In Tables 5 and 6 the H estimation error was 9.4 ± 28.3 W m−2 for the FSAM FTP with adjustments for closure and 6.5 ± 29.5 W m−2 with adjustments for closure using G from RS, respectively. Closure adjustments on measured H and LE were made using G from RS to characterize the error introduced by the measurement because the heat fluxes come from the upwind FTP area and measured G represents only a point measurement. In any case, these relatively good retrievals of H result from the good estimation of rah and Taero. The H rmse values reflect the rather small variability introduced by the Taero and rah models (error propagation) mostly for larger values. This can be seen in Fig. 12 where the estimated and measured H that are adjusted for closure are compared.

f. Net radiation

The remote sensing estimation of net radiation was reasonably good with errors of −4.8 ± 20.7 W m−2 for the FSAM FTP (Table 5). This is well within the 5%–10% error in typical net radiation measurements. The comparison with measured values is shown in Fig. 13. The bias is very small and could come from estimation errors in albedo and air emissivity and, to a smaller extent, the variability in the net radiation measurements at a spot (point measurement) versus the integrated values within the footprints.

g. Latent heat flux

The LE estimates from RS are compared in Tables 5 with measured LE that is adjusted and not adjusted for energy balance closure (Figs. 14 and 15, respectively). The agreement is much better when closure is forced, because of the fact that the LE obtained from the remote sensing procedure is a residual from the energy balance equation; thus, closure is inherent. Given the uncertainty in eddy covariance measurements of LE (Weaver 1990; Field et al. 1994), the agreement is very good. The errors were −9.2 ± 39.4 W m−2 for the FSAM FTP integration, well within the margin of error of the ground station measurements. This is an excellent result because of the small bias, and it is evidence that the remote sensing procedure can provide good estimates of the distributed latent heat fluxes. The bias decreased to −5.6 ± 28.7 W m−2 when the closure was performed using G estimated from remote sensing (Table 6 and Fig. 16). The bias at smaller values of LE in Figs. 14 and 16 can be attributed to errors resulting from larger values of H and G.

h. Footprints

The error statistics of Table 5 showed that, in general, the FSAM footprint resulted in an integration of the fluxes that closer matched (lower MBE and rmse) the measured values. The integration method did not make a significant difference in the case of Taero, rah, and G. In general, either of the FTPs appeared to better weight/integrate the heat fluxes than the simple arithmetic averages, indicating FTPs should be used to properly compare and/or validate the spatially distributed fluxes obtained from remote sensing with ground-measured fluxes.

4. Conclusions

The corn- and soybean fields in the study area presented a good range of vegetation cover (leaf area index) for the estimation of net radiation, soil heat flux, and sensible heat flux with remote sensing, as well as for the methodology. Soil moisture levels were not limiting and, therefore, the available energy (RnG) predominantly went to LE (evapotranspiration) rather than to heating the air (H). However, more H was generated over the soybean fields, which were in an earlier stage of growth than most cornfields in the area.

Surface temperature was well estimated by the airborne thermal scanner when compared to IRT readings on the ground. The aerodynamic temperature modeling, using surface radiometric temperature, horizontal wind speed, leaf area index, and air temperature, resulted in very low estimation errors, with a slight overprediction of 0.2 ± 0.9°C. The surface aerodynamic resistance was well estimated with prediction errors of −0.2 ± 2.8 s m−1. The fitted logarithmic soil heat flux model showed the best coefficient of determination, 0.732, among several of the models that were tested, and in the verification process underpredicted measured G by −0.5 ± 24.5 W m−2. The sensible heat fluxes that were obtained were estimated with errors of 9.4 ± 28.3 W m−2. Net radiation was estimated to −4.8 ± 20.7 W m−2, which validates the remote sensing methodology and corroborates previous research results in the retrieval of this variable. Further improvements in the calibration of the airborne thermal infrared imagery for surface emissivity and improved estimates of albedo and the emissivity of the air should reduce the bias further.

The lack of energy balance closure for the eddy covariance flux measurements led us to adjust for closure to obtain meaningful comparisons of H and LE with the corresponding airborne remote sensing estimates. The spatial estimation of the latent heat flux (LE or ET) resulted in errors of just −9.2 ± 39.4 W m−2. The bias was decreased further when remotely sensed G values were used to estimate the available energy for closure (−5.6 ± 28.7 W m−2). This is a low bias error, but may partially hide the fact that the variability that is introduced by the point G measurements was removed by using the remote sensing values in forcing closure.

These results appear to validate this methodology for estimating the spatial variations of energy balance components using airborne high-resolution multispectral imagery. It is important to note that good retrievals of aerodynamic temperatures are critical in this process. Herein they were obtained empirically, using available measured fluxes for the development of the model, and, thus, should be considered specific for the two crop types and stability conditions that are encountered at the study site.

The comparison of estimated to measured values was performed using both footprint models and simple averages. In general, for the surface conditions encountered and under unstable atmospheric conditions both of the footprint models that were tested (FSAM and FASOWG) performed better than the simple AOI polygon averages. Footprint weights should definitely be used for integrating remotely sensed fluxes over heterogeneous surfaces. The FSAM model by Schmid (1994) is recommended because the higher weights are distributed further upwind from the flux stations, and the footprint is larger. To further test the footprint effectiveness on weighting/integrating the spatially distributed fluxes, it is recommended that cases with stable atmospheric conditions and significant surface heterogeneity conditions be included.

Acknowledgments

This paper was funded through NASA’s Global Water and Energy Cycle Program under Contract NAG5-11673. Support for the research was also provided by the Utah Agricultural Experiment Station, the Organization of American States, and the Remote Sensing Services Laboratory, Department of Biological and Irrigation Engineering at Utah State University. Thanks to Dr. Martha Anderson, Dr. Gilberto Urroz, Dr. Harikishan Jayanthi, and graduate students Ricardo Griffin, Tapan Pathak, Deepak Lal, and Kyle Andreason who provided assistance.

REFERENCES

  • Anderson, M. C., Neale C. M. U. , Li F. , Norman J. M. , Kustas W. P. , Jayanthi H. , and Chavez J. , 2004: Upscaling ground observations of vegetation water content, canopy height, and leaf area index during SMEX02 using aircraft and Landsat imagery. Remote Sens. Environ., 92 , 447464.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berk, A., Bernstein L. S. , and Robertson D. C. , 1989: MODTRAN: A moderate resolution model for LOWTRAN 7. Geophysics Laboratory, Bedford, Maryland, Rep. GL-TR-89-0122, 37 pp.

  • Brest, C. L., and Goward S. N. , 1987: Driving surface albedo measurements from narrow band satellite data. Int. J. Remote Sens., 8 , 351367.

  • Brunsell, N. A., and Gillies R. , 2002: Incorporating surface emissivity into a thermal atmospheric correction. Photogramm. Eng. Remote Sens. J., 68 , 12631269.

    • Search Google Scholar
    • Export Citation
  • Brutsaert, W., 1975: On a drivable formula for long-wave radiation from clear skies. Water Resour. Res., 11 , 742744.

  • Brutsaert, W. H., 1982: Evaporation into the Atmosphere. D. Reidel Publication, 299 pp.

  • Cai, B., and Neale C. M. U. , 1999: A method for constructing three dimensional models from airborne imagery. 17th Biennial Workshop on Color Photography and Videography in Resource Assessment, Reno, NV, American Society for Photogrammetry and Remote Sensing and Department of Environmental and Resource Science, University of Nevada.

  • Choudhury, B. J., Reginato R. J. , and Idso S. B. , 1986: An analysis of infrared temperature observations over wheat and calculation of latent heat flux. Agric. For. Meteor., 37 , 7588.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Crawford, T. M., and Duchon C. E. , 1999: An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling longwave radiation. J. Appl. Meteor., 38 , 474480.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Field, R. T., Heiser M. , and Strebel D. E. , 1994: Measurements of surface fluxes. The FIFE Information System, Summary Document. [Available on-line at http://www.esm.versar.com/FIFE/Summary/Sur_flux.htm.].

  • Gao, W., Coulter R. L. , Lesht B. M. , Qiu J. , and Wesely M. L. , 1998: Estimating clear-sky regional surface fluxes in the Southern Great Plains atmospheric radiation measurement site with ground measurements and satellite observations. J. Appl. Meteor., 37 , 522.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hipps, L., 1989: The infrared emissivity of soil and Artemisia tridendata and subsequent temperature corrections in a shrub-steppe ecosystem. Remote Sens. Environ., 27 , 337342.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Horst, T. W., and Weil J. C. , 1992: Footprint estimation for scalar flux measurements in the atmospheric surface layer. Bound.-Layer Meteor., 59 , 279296.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Horst, T. W., and Weil J. C. , 1994: How far is far enough?: The fetch requirements for micrometeorological measurement of surface fluxes. J. Atmos. Oceanic Technol., 11 , 10181025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jackson, R. D., Clarke T. R. , and Moran M. S. , 1992: Bidirectional calibration results of 11 Spectralon and 16 BaSO4 reference reflectance panels. Remote Sens. Environ., 40 , 231239.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaharabata, S. K., Schuepp P. H. , Ogunjemiyo S. , Shen S. , Leclerc M. Y. , Desjardins R. L. , and MacPherson J. I. , 1997: Footprint considerations in BOREAS. J. Geophys. Res., 102 , D24,. 2911329124.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kustas, W. P., Hatfield J. L. , and Prueger J. H. , 2005: The Soil Moisture–Atmosphere Coupling Experiment (SMACEX): Background, hydrometeorological conditions, and preliminary findings. J. Hydrometeor., 6 , 791804.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leclerc, M. Y., and Thurtell G. W. , 1990: Footprint prediction of scalar fluxes using a Markovian analysis. Bound.-Layer Meteor., 52 , 247258.

  • Moran, M. S., 1990: A satellite-based approach for evaluation of the spatial distribution of evapotranspiration from agricultural lands. Ph.D. dissertation. University of Arizona, 223 pp.

  • Moran, M. S., Jackson R. D. , Raymond L. H. , Gay L. W. , and Slater P. N. , 1989: Mapping surface energy balance components by combining LandSat Thematic Mapper and ground-based meteorological data. Remote Sens. Environ., 30 , 7787.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morse, A., Allen R. G. , Tasumi M. , Kramer W. J. , Trezza R. , and Wright J. L. , 2001: Application of the SEBAL methodology for estimating evapotranspiration and consumptive use of water through remote sensing. Idaho Department of Water Resources and University of Idaho, Department of Biological and Agricultural Engineering Final Report to the Raytheon Systems Company and the Earth Observation System Data and Information System Project, 142 pp.

  • Neale, C. M. U., and Crowther B. , 1994: An airborne multispectral video/radiometer remote sensing system: Development and calibration. Remote Sens. Environ., 49 , 187194.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neale, C. M. U., Hipps L. E. , Prueger J. H. , Kustas W. P. , Cooper D. I. , and Eichinger W. E. , 2001: Spatial mapping of evapotranspiration and energy balance components over riparian vegetation using airborne remote sensing. Proceedings of the Remote Sensing and Hydrology 2000 Symposium, M. Owe et al., Eds., IAHS, Publication 267, 311–315.

  • Qi, J., and Coauthors, 1998: Estimation of evapotranspiration over the San Pedro riparian area with remote sensing and in situ measurements. Special Symp. on Hydrology, Phoenix, AZ, Amer. Meteor. Soc., CD-ROM, 1.13.

  • Rondeaux, G., Steven M. , and Baret F. , 1996: Optimisation of soil-adjusted vegetation indices. Remote Sens. Environ., 55 , 95107.

  • Schmid, H. P., 1994: Source areas for scalars and scalar fluxes. Bound.-Layer Meteor., 67 , 293318.

  • Sundararaman, S., and Neale C. M. U. , 1997: Geometric calibration of the USU videography system. Workshop on Videography and Color Photography for Resource Assessment, Proc. of the 16th Biennial Workshop, Bethesda, MD, American Society for Photogrammetry and Remote Sensing.

  • Twine, T. E., and Coauthors, 2000: Correcting eddy-covariance flux underestimates over a grassland. Agric. For. Meteor., 103 , 229317.

    • Search Google Scholar
    • Export Citation
  • Watts, C., Chehbouni A. , Kerr Y. H. , Bruin H. , Hartogensis O. , and Rodriguez J. , 1998: Sensible heat flux estimates using AVHRR and scintillometer data over grass and mesquite in Northwest Mexico. Special Symp. on Hydrology, Phoeniz, AZ, Amer. Meteor. Soc., CD-ROM, 2.5.

  • Weaver, H. L., 1990: Temperature and humidity flux-variance relations determined by one-dimensional eddy correlation. Bound.-Layer Meteor., 53 , 7791.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wenbin, M., and Coauthors, 2004: A scheme for pixel-scale aerodynamic surface temperature over hilly land. Adv. Atmos. Sci., 21 , 125131.

Fig. 1.
Fig. 1.

Flux tower field locations marked by squares over mosaicked airborne three-band reflectance imagery acquired during the regional flight of 1 Jul 2002 (DOY 182).

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 2.
Fig. 2.

(left) A three-band (NIR, RED, GREEN) false color reflectance image and (right) a surface temperature image for stations 15 and 16 on DOY 189.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 3.
Fig. 3.

FSAM footprint (left) lateral and (right) plan view for flux station 15.1 (corn) under unstable atmospheric conditions of DOY 182.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 4.
Fig. 4.

FASOWG footprint (left) lateral and (right) plan view for station 15.1 on DOY 182.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 5.
Fig. 5.

FSAM (longer) and FASOWG (shorter) footprint AOIs for stations 15.1 and 15.2 in the cornfield, oriented according to average wind direction and laid over the LAI imagery of DOY 182. LAI values reported in m2 m−2. The stars show the station locations, station 15.1 to the east and station 15.2 to the west.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 6.
Fig. 6.

Distributed energy balance components for stations 15.1, 15.2 (corn), and 16.1 (soybean) (stations marked by the red square symbol in front of the FTP), at 1221 LST DOY 182. FSAM AOI polygons overlaid on the images. Legend units in W m−2.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 7.
Fig. 7.

Airborne- vs ground-measured surface temperature comparison.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 8.
Fig. 8.

Soil heat flux logarithmic curve fitting.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 9.
Fig. 9.

Comparison of the remote sensing soil heat flux estimates with measured values. The subscript (e) stands for “estimated” and (C) for the FSAM FTP weighting/integrating method.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 10.
Fig. 10.

Comparison of RS estimation of aerodynamic temperature against inverted values from measured H.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 11.
Fig. 11.

Surface aerodynamic resistance model predictions compared to inverted aerodynamic resistance using H closure (rah_c).

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 12.
Fig. 12.

Comparison of RS estimates of H vs measured values adjusted for closure.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 13.
Fig. 13.

Comparison of RS estimates of Rn (Rn_e), integrated with the FSAM FTP, vs measured values.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 14.
Fig. 14.

Comparison of LE estimates from remote sensing with measured fluxes adjusted for closure.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 15.
Fig. 15.

Comparison of LE estimates from remote sensing with measured fluxes not adjusted for closure.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Fig. 16.
Fig. 16.

Comparison of LE estimates from remote sensing with measured values adjusted for closure using Rn and G estimated from RS.

Citation: Journal of Hydrometeorology 6, 6; 10.1175/JHM467.1

Table 1.

Basic information used in the aerodynamic temperature model development.

Table 1.
Table 2.

Stations and data used in the verification phase.

Table 2.
Table 3.

Surface energy balance closure adjustment procedure.

Table 3.
Table 4.

Equations involved in Kaharabata et al.’s (1997) footprint model.

Table 4.
Table 5.

Statistical errors from comparing airborne remote sensing estimates against ground-derived values, and weighted/integrated using different methods. Note: The subscript e in the variables indicate the estimated RS. LEnc is the EC measured LE, not adjusted for closure.

Table 5.
Table 6.

Statistical errors from comparing airborne RS estimates against ground-measured H and LE adjusted for closure using G from RS estimates, and integrated using different methods. The subscript e indicates estimated RS.

Table 6.
Save
  • Anderson, M. C., Neale C. M. U. , Li F. , Norman J. M. , Kustas W. P. , Jayanthi H. , and Chavez J. , 2004: Upscaling ground observations of vegetation water content, canopy height, and leaf area index during SMEX02 using aircraft and Landsat imagery. Remote Sens. Environ., 92 , 447464.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Berk, A., Bernstein L. S. , and Robertson D. C. , 1989: MODTRAN: A moderate resolution model for LOWTRAN 7. Geophysics Laboratory, Bedford, Maryland, Rep. GL-TR-89-0122, 37 pp.

  • Brest, C. L., and Goward S. N. , 1987: Driving surface albedo measurements from narrow band satellite data. Int. J. Remote Sens., 8 , 351367.

  • Brunsell, N. A., and Gillies R. , 2002: Incorporating surface emissivity into a thermal atmospheric correction. Photogramm. Eng. Remote Sens. J., 68 , 12631269.

    • Search Google Scholar
    • Export Citation
  • Brutsaert, W., 1975: On a drivable formula for long-wave radiation from clear skies. Water Resour. Res., 11 , 742744.

  • Brutsaert, W. H., 1982: Evaporation into the Atmosphere. D. Reidel Publication, 299 pp.

  • Cai, B., and Neale C. M. U. , 1999: A method for constructing three dimensional models from airborne imagery. 17th Biennial Workshop on Color Photography and Videography in Resource Assessment, Reno, NV, American Society for Photogrammetry and Remote Sensing and Department of Environmental and Resource Science, University of Nevada.

  • Choudhury, B. J., Reginato R. J. , and Idso S. B. , 1986: An analysis of infrared temperature observations over wheat and calculation of latent heat flux. Agric. For. Meteor., 37 , 7588.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Crawford, T. M., and Duchon C. E. , 1999: An improved parameterization for estimating effective atmospheric emissivity for use in calculating daytime downwelling longwave radiation. J. Appl. Meteor., 38 , 474480.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Field, R. T., Heiser M. , and Strebel D. E. , 1994: Measurements of surface fluxes. The FIFE Information System, Summary Document. [Available on-line at http://www.esm.versar.com/FIFE/Summary/Sur_flux.htm.].

  • Gao, W., Coulter R. L. , Lesht B. M. , Qiu J. , and Wesely M. L. , 1998: Estimating clear-sky regional surface fluxes in the Southern Great Plains atmospheric radiation measurement site with ground measurements and satellite observations. J. Appl. Meteor., 37 , 522.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Hipps, L., 1989: The infrared emissivity of soil and Artemisia tridendata and subsequent temperature corrections in a shrub-steppe ecosystem. Remote Sens. Environ., 27 , 337342.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Horst, T. W., and Weil J. C. , 1992: Footprint estimation for scalar flux measurements in the atmospheric surface layer. Bound.-Layer Meteor., 59 , 279296.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Horst, T. W., and Weil J. C. , 1994: How far is far enough?: The fetch requirements for micrometeorological measurement of surface fluxes. J. Atmos. Oceanic Technol., 11 , 10181025.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Jackson, R. D., Clarke T. R. , and Moran M. S. , 1992: Bidirectional calibration results of 11 Spectralon and 16 BaSO4 reference reflectance panels. Remote Sens. Environ., 40 , 231239.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kaharabata, S. K., Schuepp P. H. , Ogunjemiyo S. , Shen S. , Leclerc M. Y. , Desjardins R. L. , and MacPherson J. I. , 1997: Footprint considerations in BOREAS. J. Geophys. Res., 102 , D24,. 2911329124.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Kustas, W. P., Hatfield J. L. , and Prueger J. H. , 2005: The Soil Moisture–Atmosphere Coupling Experiment (SMACEX): Background, hydrometeorological conditions, and preliminary findings. J. Hydrometeor., 6 , 791804.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Leclerc, M. Y., and Thurtell G. W. , 1990: Footprint prediction of scalar fluxes using a Markovian analysis. Bound.-Layer Meteor., 52 , 247258.

  • Moran, M. S., 1990: A satellite-based approach for evaluation of the spatial distribution of evapotranspiration from agricultural lands. Ph.D. dissertation. University of Arizona, 223 pp.

  • Moran, M. S., Jackson R. D. , Raymond L. H. , Gay L. W. , and Slater P. N. , 1989: Mapping surface energy balance components by combining LandSat Thematic Mapper and ground-based meteorological data. Remote Sens. Environ., 30 , 7787.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Morse, A., Allen R. G. , Tasumi M. , Kramer W. J. , Trezza R. , and Wright J. L. , 2001: Application of the SEBAL methodology for estimating evapotranspiration and consumptive use of water through remote sensing. Idaho Department of Water Resources and University of Idaho, Department of Biological and Agricultural Engineering Final Report to the Raytheon Systems Company and the Earth Observation System Data and Information System Project, 142 pp.

  • Neale, C. M. U., and Crowther B. , 1994: An airborne multispectral video/radiometer remote sensing system: Development and calibration. Remote Sens. Environ., 49 , 187194.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Neale, C. M. U., Hipps L. E. , Prueger J. H. , Kustas W. P. , Cooper D. I. , and Eichinger W. E. , 2001: Spatial mapping of evapotranspiration and energy balance components over riparian vegetation using airborne remote sensing. Proceedings of the Remote Sensing and Hydrology 2000 Symposium, M. Owe et al., Eds., IAHS, Publication 267, 311–315.

  • Qi, J., and Coauthors, 1998: Estimation of evapotranspiration over the San Pedro riparian area with remote sensing and in situ measurements. Special Symp. on Hydrology, Phoenix, AZ, Amer. Meteor. Soc., CD-ROM, 1.13.

  • Rondeaux, G., Steven M. , and Baret F. , 1996: Optimisation of soil-adjusted vegetation indices. Remote Sens. Environ., 55 , 95107.

  • Schmid, H. P., 1994: Source areas for scalars and scalar fluxes. Bound.-Layer Meteor., 67 , 293318.

  • Sundararaman, S., and Neale C. M. U. , 1997: Geometric calibration of the USU videography system. Workshop on Videography and Color Photography for Resource Assessment, Proc. of the 16th Biennial Workshop, Bethesda, MD, American Society for Photogrammetry and Remote Sensing.

  • Twine, T. E., and Coauthors, 2000: Correcting eddy-covariance flux underestimates over a grassland. Agric. For. Meteor., 103 , 229317.

    • Search Google Scholar
    • Export Citation
  • Watts, C., Chehbouni A. , Kerr Y. H. , Bruin H. , Hartogensis O. , and Rodriguez J. , 1998: Sensible heat flux estimates using AVHRR and scintillometer data over grass and mesquite in Northwest Mexico. Special Symp. on Hydrology, Phoeniz, AZ, Amer. Meteor. Soc., CD-ROM, 2.5.

  • Weaver, H. L., 1990: Temperature and humidity flux-variance relations determined by one-dimensional eddy correlation. Bound.-Layer Meteor., 53 , 7791.

    • Crossref
    • Search Google Scholar
    • Export Citation
  • Wenbin, M., and Coauthors, 2004: A scheme for pixel-scale aerodynamic surface temperature over hilly land. Adv. Atmos. Sci., 21 , 125131.

  • Fig. 1.

    Flux tower field locations marked by squares over mosaicked airborne three-band reflectance imagery acquired during the regional flight of 1 Jul 2002 (DOY 182).

  • Fig. 2.

    (left) A three-band (NIR, RED, GREEN) false color reflectance image and (right) a surface temperature image for stations 15 and 16 on DOY 189.

  • Fig. 3.

    FSAM footprint (left) lateral and (right) plan view for flux station 15.1 (corn) under unstable atmospheric conditions of DOY 182.

  • Fig. 4.

    FASOWG footprint (left) lateral and (right) plan view for station 15.1 on DOY 182.

  • Fig. 5.

    FSAM (longer) and FASOWG (shorter) footprint AOIs for stations 15.1 and 15.2 in the cornfield, oriented according to average wind direction and laid over the LAI imagery of DOY 182. LAI values reported in m2 m−2. The stars show the station locations, station 15.1 to the east and station 15.2 to the west.

  • Fig. 6.

    Distributed energy balance components for stations 15.1, 15.2 (corn), and 16.1 (soybean) (stations marked by the red square symbol in front of the FTP), at 1221 LST DOY 182. FSAM AOI polygons overlaid on the images. Legend units in W m−2.

  • Fig. 7.

    Airborne- vs ground-measured surface temperature comparison.

  • Fig. 8.

    Soil heat flux logarithmic curve fitting.

  • Fig. 9.

    Comparison of the remote sensing soil heat flux estimates with measured values. The subscript (e) stands for “estimated” and (C) for the FSAM FTP weighting/integrating method.

  • Fig. 10.

    Comparison of RS estimation of aerodynamic temperature against inverted values from measured H.

  • Fig. 11.

    Surface aerodynamic resistance model predictions compared to inverted aerodynamic resistance using H closure (rah_c).

  • Fig. 12.

    Comparison of RS estimates of H vs measured values adjusted for closure.

  • Fig. 13.

    Comparison of RS estimates of Rn (Rn_e), integrated with the FSAM FTP, vs measured values.

  • Fig. 14.

    Comparison of LE estimates from remote sensing with measured fluxes adjusted for closure.

  • Fig. 15.

    Comparison of LE estimates from remote sensing with measured fluxes not adjusted for closure.

  • Fig. 16.

    Comparison of LE estimates from remote sensing with measured values adjusted for closure using Rn and G estimated from RS.

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