Comparing Aircraft-Based Remotely Sensed Energy Balance Fluxes with Eddy Covariance Tower Data Using...

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

JOSÉ L. CHÁVEZ AND CHRISTOPHER M. U. NEALE

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

LAWRENCE E. HIPPS

Plant, Soils and Biometeorology Department, Utah State University, Logan, Utah

JOHN H. PRUEGER

National Soil Tilth Laboratory, ARS, USDA, Ames, Iowa

WILLIAM P. KUSTAS

Hydrology and Remote Sensing Laboratory, ARS, USDA, Beltsville, Maryland

(Manuscript received 1 May 2004, in final form 18 November 2004)

ABSTRACT

In an effort to better evaluate distributed airborne remotely sensed sensible and latent heat flux esti-mates, 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 fluxmodels 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 covarianceenergy balance flux measurements. The results show latent heat flux estimates (adjusted for closure) witherrors of (mean � std dev) �9.2 � 39.4 W m�2, sensible heat flux estimate errors of 9.4 � 28.3 W m�2, netradiation error of �4.8 � 20.7 W m�2, and soil heat flux error of �0.5 � 24.5 W m�2. This good agreementwith measured values indicates that the adopted methodology for estimating the energy balance compo-nents, 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 fluxstations. In particular the flux source area model (footprint) seemed to better integrate the resulting heatflux image pixels. It is suggested that future studies test the methodology for heterogeneous surfaces understable atmospheric conditions.

1. Introduction

Reliable spatial–temporal estimation of evapotrans-piration (latent heat flux) of vegetation is very impor-tant for water management and soil moisture assess-ment in agriculture as well as in natural ecosystems.Airborne remote sensing is a powerful tool in precisionagriculture applications, such as in the estimation ofspatial evapotranspiration and yield. It is operationallyflexible, 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 sensedlatent and sensible heat flux estimates have been com-pared to surface fluxes measured with micrometeoro-logical stations such as eddy covariance, Bowen ratioenergy 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 havebeen used in the effort to compare against remotelysensed crop water consumption (Morse et al. 2001).Results have shown that the remote sensing methodsare capable of determining distributed heat fluxes withsome discrepancies (Qi et al. 1998; Moran et al. 1989).

Corresponding author address: Christopher M. U. Neale, Bio-logical and Irrigation Engineering Department, Utah State Uni-versity, Logan, UT 84322-4105.E-mail: [email protected]

DECEMBER 2005 C H Á V E Z E T A L . 923

© 2005 American Meteorological Society

Furthermore, the image pixels were selected for thecomparisons using different criteria. For instance,sometimes pixels upwind of the micrometeorologicaltower have been averaged for comparison without re-gard to the true size of the upwind contributing area(Neale et al. 2001; Moran et al. 1989). A technique toproperly integrate the remote sensing heat flux pixels isneeded for the comparisons with ground-measuredfluxes in order to validate the use of remote sensingmethodologies for accurate vegetation evapotranspira-tion estimates.

Footprint models have been developed to determinewhat area (upwind of micrometeorological-flux sta-tions) is contributing the heat fluxes to the sensors aswell as the relative weight of each particular cell insidethe footprint limits. Different footprint models havebeen proposed in the literature, basically, one-dimen-sional (1D) or two-dimensional (2D) models. Somemodels are the analytical solution to the diffusion–dispersion–advection equation (Horst and Weil 1992,1994). Other models are Lagrangian (Leclerc and Thur-tell 1990). Studies using these models were able to es-timate how contributions of upwind locations to themeasured flux depend on the height of the vegetation,height of the instrumentation, wind speed, wind direc-tion, and atmospheric stability conditions.

Because of the scale of in-field variability in heatfluxes derived from high-resolution airborne remotesensing, footprint models could be a useful tool in theintegration and comparison of these energy balancefluxes (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 ofheat flux estimated through a remote sensing method-ology in comparison with measured fluxes in corn- andsoybean fields near Ames, Iowa, during the Soil Mois-ture–Atmosphere Coupling Experiment (SMACEX) in2002. For this purpose, methods of spatially obtainingsoil heat flux as well as aerodynamic temperatures fromremote sensing and basic ground meteorological datawere developed.

2. Material and methods

Kustas et al. (2005) present an overview article pro-viding background and including their rationale for thestudy, a site description, the experimental design, thehydrometeorological conditions, and a summary of re-sults.

This section has been divided into three parts: thefirst part describes the instrumentation and data typesused in the experiment. The second part, entitled modeldevelopment phase, discusses the calibration of the soilheat flux and surface aerodynamic temperature models,

with the presentation of an iterative method to derivesurface aerodynamic resistance, using the calibratedaerodynamic temperature and with the description ofthe sensible heat flux, net radiation, and latent heat fluxmodels used to obtain the spatially distributed fluxes.The third section, entitled model verification phase, de-scribes the footprint models and statistics used to evalu-ate both the remote sensing estimates and the perfor-mance of the footprints in weighting/integrating the re-motely sensed fluxes.

a. Data description

1) REMOTE SENSING DATA

The remote sensing data consisted of high-resolutionmultispectral imagery in the visible, near-infrared, andthermal-infrared portions of the electromagnetic spec-trum. These images were calibrated and transformedinto surface reflectance and temperature images usedfor the estimation of reflected or outgoing shortwaveand longwave radiation, respectively, with both compo-nents required in the estimation of spatially distributednet radiation. Also, vegetation indices derived fromsurface reflectance were related to leaf area index(LAI), vegetation canopy height (for zero-plane dis-placement, roughness height, and aerodynamic resis-tance calculations), and fractional vegetation cover (forcalibrating the thermal imagery and account for vari-able surface emissivity effects). Surface temperaturederived from the thermal imagery was also used in theestimation of the distributed sensible heat fluxes.

Multispectral digital imagery was acquired over thestudy area, using the Utah State University (USU) air-borne digital remote sensing system (Neale andCrowther 1994; Cai and Neale 1999). The system com-prises three Kodak Megaplus digital frame cameraswith interference filters centered in the green (G)(0.545–0.560 �m), red (R) (0.665–0.680 �m) and near-infrared (NIR) (0.795–0.809 �m) portions of the elec-tromagnetic spectrum. The fourth camera is an Infra-metrics 760 thermal-infrared scanner (8–12 �m) thatprovides thermal-infrared radiance, used to obtain sur-face radiometric temperature images.

The high-resolution imagery was acquired on severaldifferent days during the intensive sampling period ofSMACEX 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 ThematicMapper overpasses. These regional flights covered theentire study area (approximately 12 km � 22 km) at anominal pixel resolution of 1.5 m from an altitude ofapproximately 3350 m [11 000 ft above ground level

924 J O U R N A L O F H Y D R O M E T E O R O L O G Y — S P E C I A L S E C T I O N VOLUME 6

(AGL)]. Imagery was also acquired from a lower alti-tude of 2100 m (7000 ft AGL) over selected fields con-taining energy balance stations (flux flights), resultingin a shortwave pixel resolution of 1 m. This additionalimagery was acquired on DOY 167, 169, 174, 182, 184,and 189. Tables 1 and 2 show the list of the fields con-taining the flux stations with the DOY and overpasstime (LST) along with several variables used in thecalculations. Figure 1 shows the location of the fieldsand stations in the study area. On DOY 182, the cornwas at almost full cover, while the soybean fields wereat early stages of growth, showing a mix of bare soil andgrowing canopy.

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

The shortwave images were corrected for lens-vignetting effects and geometric radial distortions inprocedures similar to those described by Neale andCrowther (1994) and Sundararaman and Neale (1997).

The individual spectral images were registered intothree band images and rectified to a 1:24 000 digitalorthophotoquad base map. The individual rectified im-ages were then mosaicked along the flight lines to formimage strips that, in turn, were stitched together to forma mosaic of the entire study area for each regionalflight.

The digital numbers of the rectified multispectral im-age strips were converted to radiance using the systemcalibration method described by Neale and Crowther(1994). These radiances were divided by the incomingsolar irradiance to obtain surface spectral reflectance.Solar irradiance in each spectral band was obtainedfrom radiance measured concurrently to the flights withan Exotech radiometer placed over a barium sulfatestandard reflectance panel with known bidirectionalproperties (Jackson et al. 1992). Examples of calibratedthree-band images can be seen in Figs. 1 and 2.

The thermal-infrared imagery was mosaicked alongthe flight lines and rectified to the high-resolutionthree-band image mosaic described above. The digitalnumbers were transformed into apparent (at sensor)temperature values using the system calibration bar atthe bottom of each image. The images were correctedfor atmospheric and surface emissivity effects usingMODTRAN version 3.0 (Berk et al. 1989), an atmo-

TABLE 1. Basic information used in the aerodynamic temperature model development.

Croptype

FlightLST DOY

Siteno.

Hc(W m�2)

Taero_inv

(°C)Ts_RS

(°C)Ta

(°C)LAI

(m2 m�2)U

(m s�1)hc

(m)Zm

(m)

C 1111 167 15.1 166.2 29.9 35.6 23.2 0.8 1.7 0.64 3.0C 1111 167 15.2 224.3 31.6 38.0 23.3 0.9 1.7 0.65 3.0S 1111 167 16.1 198.2 31.2 39.3 23.6 0.7 1.9 0.19 2.0S 1111 167 16.2 167.8 31.7 41.1 23.6 0.3 1.9 0.14 2.3C 1512 167 15.1 123.1 30.3 37.6 25.3 0.8 1.5 0.64 3.0C 1512 167 15.2 170.3 31.5 38.5 25.4 0.9 1.7 0.65 3.0S 1132 167 16.1 222.6 34.5 40.3 23.9 0.7 2.2 0.19 2.0S 1132 167 16.2 182.8 33.2 44.1 23.9 0.3 2.3 0.14 2.3C 1145 167 6 148.7 28.8 35.2 23.2 1.4 1.7 0.78 2.9C 1042 167 33 189.3 30.6 38.3 22.9 1.0 2.9 0.63 2.9C 1015 169 15.1 136.3 29.3 34.7 27.1 1.7 5.7 0.93 3.0C 1015 169 15.2 180.7 31.6 34.4 28.5 1.7 5.8 0.94 3.0C 0938 174 15.2 98.0 29.4 31.9 27.5 1.6 5.1 0.92 3.0S 0938 174 16.1 141.2 31.4 36.4 28.2 1.1 5.5 0.24 2.0S 0938 174 16.2 99.4 30.3 36.0 27.9 1.1 6.6 0.24 2.3C 1005 174 15.2 103.4 29.9 35.1 28.2 1.6 5.4 0.92 3.0S 1005 174 16.1 158.9 32.1 40.0 28.9 1.1 6.0 0.24 2.0S 1005 174 16.2 128.4 31.6 39.1 28.7 1.1 7.3 0.24 2.3C 1043 184 15.1 83.8 29.3 31.6 27.3 4.5 2.2 1.84 4.0C 1043 184 15.2 103.8 30.0 32.9 27.4 3.7 2.3 1.60 3.9S 1043 184 16.1 148.4 34.0 38.3 28.0 1.9 2.9 0.34 2.0S 1043 184 16.2 122.1 32.5 35.7 27.9 2.6 3.3 0.39 2.3C 1048 189 15.1 9.8 30.4 30.4 30.2 5.0 3.3 1.99 4.0C 1048 189 15.2 28.9 30.6 30.5 30.1 4.6 3.4 1.86 3.9S 1048 189 16.1 2.5 30.6 32.5 30.5 2.8 4.2 0.45 2.0S 1048 189 16.2 9.4 30.6 31.4 30.4 3.9 4.6 0.46 2.3


spheric radiative transfer model (software). This cor-rection 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 MODTRANmodel.

An example of a corrected at-surface temperatureimage (colored for better temperature visualization)

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

TABLE 2. Stations and data used in the verification phase.

Croptype

FlightLST DOY

Siteno.

Hc(W m�2)

Taero_inv

(°C)Tsfc_RS

(°C)Ta

(°C)U

(m s�1)LAI

(m2 m�2)hc

(m)Zm

(m)

S 1512 167 16.1 160.9 34.2 41.2 25.8 0.7 1.7 0.19 2.0S 1512 167 16.2 139.3 33.0 41.5 25.8 0.3 1.9 0.14 2.3S 1100 167 13 196.0 35.0 42.9 23.9 0.2 2.2 0.16 1.8S 1015 169 16.1 178.2 32.1 37.5 27.6 1.1 7.0 0.24 2.0S 1015 169 16.2 152.4 31.8 37.0 27.6 1.1 7.6 0.23 2.3C 1115 182 15.1 85.3 29.9 32.1 28.7 4.8 3.6 1.64 4.0C 1115 182 15.2 125.0 31.0 32.3 29.1 5.2 3.4 1.47 3.9S 1115 182 16.1 254.2 35.1 43.8 29.7 5.7 1.5 0.31 2.0C 1321 182 15.1 50.5 31.4 35.1 30.8 5.6 3.9 1.51 4.0S 1321 182 16.1 260.0 36.9 46.6 31.9 6.5 1.6 0.31 2.0C 1415 182 15.1 42.0 31.4 34.4 30.9 5.6 3.9 1.33 4.0C 1415 182 15.2 122.3 32.5 35.3 30.9 6.1 3.3 1.25 3.9C 1043 182 15.1 82.3 29.4 32.5 28.2 4.5 3.9 1.6 4.0C 1043 182 15.2 123.7 30.6 33.4 28.7 4.7 3.3 1.4 3.9S 1043 182 16.1 231.4 34.6 43.3 29.2 5.5 1.6 0.29 2.0C 1209 182 24 60.2 30.5 31.6 29.6 5.2 4.3 1.78 3.9S 1140 182 14 229.0 34.8 39.1 29.9 5.9 2.1 0.36 2.0C 1110 182 6 82.9 30.2 33.1 28.9 5.4 4.7 1.89 5.0S 1201 182 3 208.5 34.8 42.0 30.0 6.2 1.6 0.3 2.1C 1404 182 24 21.2 31.2 33.2 30.9 5.6 4.3 1.78 3.9C 0857 189 15.1 33.9 27.8 29.0 27.3 5.0 3.3 1.99 4.0C 0857 189 15.2 28.5 28.4 29.2 27.9 4.6 3.6 1.86 3.9


can be seen in Fig. 2 for the corn- and soybean fields,containing flux stations 15 and 16, respectively. All im-age processing was conducted using the ERDAS Imag-ine software. Spatial distribution of the fluxes was ob-tained using the high-resolution calibrated and georef-erenced imagery as inputs, along with ground-measured meteorological data at the towers, byprogramming the appropriate equations described be-low within ERDAS Imagine model maker and produc-ing output images of different parameters (leaf areaindex, aerodynamic temperature, soil heat flux, canopyheight, etc.).

2) GROUND DATA ENERGY BALANCE FLUXES

The basic input data used in the remote sensing–based computation of fluxes were measured at the eddycovariance energy balance flux stations in each fieldand corresponded to the 30-min period coinciding withthe aircraft overpass time. These data consisted ofmean air temperature, wind speed, vapor pressure, in-coming shortwave radiation, and instrumentationheight. The measured sensible heat fluxes were used toobtain the aerodynamic temperatures through inver-sion of the bulk aerodynamic resistance equation.Other data measured at the flux stations and used in thecomparisons 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 tem-perature.

The eddy covariance energy balance flux stationscomprised the following equipment: a Campbell Scien-tific, Inc. (CSI), CSAT3 3D sonic anemometer, a LI-COR7500 open-path CO2/H2O analyzer or a CSI KH20Krypton Hygrometer, net radiometers [Radiation andEnergy Balance System (REBS) Q7 or Kipp & ZonenCNR01 type], and soil heat flux plates completed theequipment of the energy balance stations. In addition,the stations where equipped with Apogee (modelIRTS-P) thermal-infrared radiometers (IRTs) viewingthe canopy from nadir, nominally at 5 m AGL for thecorn sites and 3 m AGL for the soybean sites. Soil heatflux was measured at each station with four soil heatflux plates distributed across the corn and soybean rowsand installed at an 6-cm depth, along with soil tempera-ture thermocouples placed within the topsoil layer. Theair temperature/relative humidity sensor (VaisalaHMP35C) was positioned 1–2 m above local terrain forsoybean fields and 2–3 m for the corn.

The energy balance fluxes for the different DOY,measured with the eddy covariance flux stations, re-sulted in a general energy balance closure of about85%. In some cases, this left a considerable amount ofenergy unaccounted for in the partitioning of net radia-tion into sensible and latent heat fluxes, which couldcause significant discrepancies in the comparisons withestimated remotely sensed heat fluxes, which forcesclosure in its methodology. The inherent error in mea-suring the sensible heat flux (H), latent heat flux (LE),net radiation (Rn), and soil heat flux (G), by ground

FIG. 2. (left) A three-band (NIR, RED, GREEN) false color reflectance image and (right) a surface temperature image for stations15 and 16 on DOY 189.


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, personalcommunication). For this reason, the measured Bowenratio at the flux stations was used to adjust the mea-sured fluxes and force closure following the proceduresuggested by Twine et al. (2000) described in Table 3.The flux data were processed using half-hour integra-tion periods described by Kustas et al. (2005) in thissame special issue. The exact standard time of the re-mote sensing image acquisition overpass was used todetermine what flux period with which to compare theestimates. The sensible and latent heat flux data forDOY 167 were acquired in flux mode and not in timeseries mode, which was the case for all other measure-ment dates.

The ground station data obtained in different fieldsand on different dates and times were divided into twogroups representing the model development and vali-dation phases of the research (Tables 1 and 2). For thedevelopment phase 26 data records were used, while 22records were used for the verification phase.

b. Model development phase

Net radiation estimates from remote sensing arefairly accurate according to Neale et al. (2001), but soiland sensible heat flux estimates need more research.Improvement in the estimation of these variables isneeded because latent heat flux is usually obtained as aresidual from the energy balance equation. In thisstudy, soil heat flux and surface aerodynamic tempera-ture models were calibrated for corn- and soybeanfields and for the conditions encountered during theexperiment to improve the remote sensing estimationof LE. The aerodynamic temperature model was usedto obtain distributed sensible heat flux.

1) SOIL HEAT FLUX MODELING

Soil heat flux (G) models based on remotely sensedinputs were obtained by fitting different types of curvesto the G/Rn versus LAI dataset for the selected modeldevelopment phase data.

The distributed LAI values (LAI_RS) were obtainedfrom the calibrated high-resolution imagery using amodel developed during SMACEX (Anderson et al.2004) that was based on the Optimized Soil AdjustedVegetation Index (OSAVI; Rondeaux et al. 1996) andground samples. Equation (1) was reported to have anR2 value of 0.85 (14.9% error) and was developed foran LAI range of 0.13–5.23:

LAI_RS � �4 OSAVI � 0.8�

� �1 � 4.73E-6 EXP15.64 OSAVI�. �1�

This model was applied to the OSAVI image that wascalculated from the calibrated airborne reflectance im-age, obtaining spatially distributed LAI. The bias re-sulting from atmospheric effects mentioned in Ander-son et al. (2004) between the airborne and satellitereflectance was removed prior to applying the relation-ship above to the airborne imagery.

2) SURFACE AERODYNAMIC TEMPERATURE

MODELING

The general bulk aerodynamic resistance equationwas used to estimate H (W m�2) [Eq. (2)] based onsurface aerodynamic temperature. Because the aerody-namic temperature is not measured or easily calculatedin remote sensing applications, different authors haveopted in the past to use the remotely sensed surfacetemperature instead. Choudhury et al. (1986) foundthat these two temperatures were nearly the same fornear-neutral atmospheric conditions, but radiometricsurface temperatures were higher than aerodynamictemperatures for stable conditions and lower for un-stable conditions. According to Wenbin et al. (2004),for homogeneous and isothermal surfaces the definitionof aerodynamic, radiometric, and thermodynamic tem-peratures are equivalent, but over heterogeneous sur-faces there are differences between the aerodynamicand surface radiometric temperatures because of theunavailability of the thermodynamic surface tempera-ture to measure molecular mean kinetic energy, conse-quently leading to errors in the estimation of H, result-ing in errors in the estimation of LE from remote sens-ing. Thus, this subsection of the paper describes theparameterization that is followed to obtain the surfaceaerodynamic temperature using the remotely sensedand ground inputs.

The bulk aerodynamic resistance equation can bewritten as

H � �aCpa�Taero � Ta��rah, �2�

where �a is air density (kg m�3), Cpa is specific heat ofair � 1005 (J kg�1 K�1), Ta is average air temperature

TABLE 3. Surface energy balance closure adjustment procedure.

(Rn � G) � available energy � (H � �H ) � (LE � �LE), (a) � Bowen ratio � (H � �H )/(LE � �LE); (b)from Eqs. (a) and (b)�LE � {(Rn � G) � [(1 � ) * LE]}/(1 � ); (c)from Eqs. (b) and (c)�H � [ * (LE � �LE) � H], (d)LE (closure) � LE (measured) � �LE, (e)H (closure) � H (measured) � �H. (f)


(K), Taero is average surface aerodynamic temperature(K), which is defined for a uniform surface as the tem-perature at the height of the zero-plane displacementplus the roughness length (d � Zoh) for sensible heattransfer Zoh (m), and rah is surface aerodynamic resis-tance (s m�1) to heat transfer from Zoh to Zm [height ofwind speed measurement (m)]. For neutral atmo-spheric conditions rah is

ra �

ln�z � d

zom� ln�z � d

zoh�

uk2 , �3�

where U is the average horizontal wind velocity(m s�1), k is the von Kármán constant, which is equal to0.41, d is the zero-plane displacement height (m), andZom is the roughness length for momentum transfer(m). Here, Zoh, Zom, and d can be estimated from thecrop canopy height (hc) (Brutsaert 1982):

Zom � 0.123 hc, �4�

Zoh � 0.1 Zom, �5�

d � 0.67 hc. �6�

From the Monin–Obukhov similarity theory, rah forunstable atmospheric conditions can be expressed as

rah �

ln�Zm � d

Zoh� � �h�Zm � d

LM_O� � �h� Zoh

LM_O�

u*k,

�7�

where �h is the stability correction factor for atmo-spheric heat transfer, LM_O is the Monin–Obukhovlength scale (m), and u* is the friction velocity (m s�1);LM_O is defined as

LM_O �

�u*3Ta�aCpa

gkH, �8�

where g is gravity acceleration. The stability correctionfactor for atmospheric heat transfer �h for unstableconditions (LM_O � 0) is

�h � 2 ln�1 � x2

2 �, �9�

x � �1 � 16Zm � d

LM_O�1�4

. �10�

The friction velocity under neutral conditions (LM_O ��) is

u* �Uk

ln�Zm � d

Zom� . �11�

Considering diabatic or nonneutral conditions, thefriction velocity is

u* �Uk

ln�Zm � d

Zom� � �m�Zm � d

LM_O� � �m� Zom

LM_O� ,

�12�

where �m is the stability correction factor for momen-tum transfer. For unstable conditions it is

�m � 2 ln�1 � x

2 � � ln�1 � x2

2 � � 2a tan�x� ��

2.

�13�

Because Taero in Eq. (2) is unknown, the approachused to obtain this parameter for calibration purposeswas to invert the H equation using the H and Ta mea-sured by the flux stations and rah derived from mea-sured H. The resulting value was called inverted Taero

(Taero_inv), and was used in the modeling of Taero basedon remote sensing (RS) and ground input variables.Using Eqs. (7), (8), and (12) with H, U, and Ta mea-sured at the EC towers rah was derived, along with hc

and Zm. The resulting rah term represents an invertedrah (rah_inv).

The inverted Taero dataset was regressed against dif-ferent combinations of U, Ta, remotely sensed radio-metric surface temperature (Ts_RS), and LAI from re-mote sensing using multiple linear and nonlinear re-gression techniques. Both Ts_RS and LAI were obtainedby integrating the raster image spatial values in theupwind footprint using the area-of-interest (AOI) poly-gon shape of the Schmid (1994) footprint model (de-scribed in next section). To assess the accuracy of theTs_RS measurements, a comparison was performedagainst the ground-measured radiometric surface tem-perature (IRT) by the IRTs placed on the flux towers.The remote sensing accuracy in estimating LAI waspresented in the previous subsection.

In the estimation of rah, when using a RS method toobtain sensible heat flux, an adjustment for the atmo-spheric stability conditions needs to be made and LM_O

is unknown. In general, values of measured H at thesurface are not available and, therefore, there is a needfor a method to estimate rah independently of H. Toaccomplish 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 result-ing atmospheric stability correction factor values formomentum and heat transfer, along with the measuredwind speed at the flux tower and the distributed veg-etation canopy height, were used in Eqs. (7) and (12) toobtain the spatial rah raster image, which ultimately wasused along with the distributed surface aerodynamictemperature for obtaining the remotely sensed estima-tion of H. This remote sensing estimation of rah wasdenoted as rah_e, that is, estimated surface aerodynamicresistance, which was later evaluated against theground station–derived rah_inv, using one of the weight-ing/integrating and statistical methods described in thesubsection below. The same procedure was followed toevaluate the remote sensing estimation of Taero, whichwas called Taero_e. The average air temperature Ta andwind speed U, measured at the flux stations, were usedin the H and rah estimations as explained above. Thesetemperature and wind values were assumed to be con-stant over the relatively small upwind footprints usedfor the remote sensing flux calculations. Given the rela-tively uniform nature of agricultural fields and the smallspatial scale of the footprints for each flux tower, this isa reasonable assumption. The diffusive nature of theboundary layer ensures that mean air temperature andwind velocities would vary little above these surfacesover distances of only 100–200 m (the typical footprintsize).

The required hc values in Eqs. (4) and (6) were ob-tained from the remote sensing–derived OSAVI usingEqs. (14) and (15) below by Anderson et al. (2004):

hc_CORN � �1.86 OSAVI � 0.2�

� �1 � 4.82E-7 EXP17.69 OSAVI�, �14�

where hc_CORN is the corn canopy height in meters, and

hc_SOYBEAN � �0.55 OSAVI � 0.02�

� �1 � 9.98E-5 EXP9.52 OSAVI�,

�15�

where hc_SOYBEAN is the soybean canopy height inmeters.

3) NET RADIATION

The net radiation is expressed as

Rn � �1 � ��Rs � �a�Ta4 � �s�Ts

4, �16�

where Rn is the net radiation (W m�2), � is surfacealbedo, Rs is incoming shortwave radiation (W m�2)measured with pyranometers, � is the Stefan–Boltzmann constant (5.67E-08 W m�2 K�4), � is emis-sivity, and T is temperature (K), with subscripts “a” and“s” for air and surface, respectively. Surface albedo forvegetated areas was estimated using the Brest and

Goward (1987) model. This model is based on the Rand NIR band reflectance

� � 0.512RED � 0.418NIR. �17�

Equation (17) was applied spatially using the calibratedreflectance images; Ts_RS was used for Ts in Eq. (16).The RS at-sensor temperature imagery was correctedfor atmospheric effects and for surface emissivity con-sidering Hipps’ (1989) suggestions and following Brun-sell and Gillies’ (2002) procedures. The correction wasperformed assuming a bare soil and fully vegetated sur-face emissivity of 0.93 and 0.98, respectively, and thefractional vegetation cover from the scaled NormalizedDifference Vegetation Index (NDVI). The emissivityof air can be obtained from the Brutsaert (1975) equa-tion

�a � 1.24� ea

Ta�1�7

, �18�

where ea is actual vapor pressure (mb). The methodol-ogy suggested by Crawford and Duchon (1999) wasadopted to adjust Brutsaert’s leading coefficient of 1.24for cloud fraction and for the month of the year. Theadopted �a equation was

�a � �clf � �1 � clf��1.22 � 0.06 sin�mo � 2��6�

� �ea�Ta�1�7�, �19�

where clf is the cloud fraction term. This term is equalto (1 � s), with s being the ratio of the measured solarirradiance to the clear-sky irradiance. The term “mo” isthe month of the year. For clear-sky conditions theleading coefficient resulted in a value of 1.16.

4) LATENT HEAT FLUX

Spatial distribution of the fluxes for any given flightoverpass were obtained as raster image layers using theERDAS Imagine model maker on a pixel-by-pixel basisand obtaining the instantaneous latent heat flux as aresidual from the energy balance equation:

LE � Rn � G � H. �20�

c. Model verification phase

FOOTPRINT MODELS

The spatially estimated Taero, rah, H, G, LE, and Rn

that were derived from the remote sensing methodol-ogy were weighted/integrated using four differentmethods. The first footprint (FTP) was applied by Ka-harabata et al. (1997) who borrowed basic conceptssummarized by Horst and Weil (1992, 1994), but, in-stead of using the expression for the crosswind-integrated flux distribution function (which was ad-justed empirically to Lagrangian simulations), used the


actual crosswind Gaussian distribution. This resulted inthe generation of weights in the x and y direction. Thenew function is expressed as

f�x, y, Zm� �u*k

�h� Zm

LM_O�

sZms

�B�z�s

e�� y2

2�y2�

�2��y

e�� Zm

B�z�s

A�zU�x�,

�21�

where f(x, y, Zm) is the footprint or source weight func-tion, x is the upwind distance from the tower or sensorlocation, y is the crosswind distance from the axis par-allel to the wind direction (x) (m), s is a shape exponent1 for unstable conditions, 2 for very stable conditions,and 1.3–1.5 for neutral conditions. Table 4 shows theequations involved in the footprint function f(x, y, Zm).Equation (21) was implemented through a computerprogram called Flux Area Source Weights Generator(FASOWG), written in Visual Basic v6 specifically forthis study. The second method of pixel integration con-sisted in using the shape of the FASOWG FTP bound-ary as an AOI polygon to extract a simple average of allpixel values within the shape of the footprint.

The second footprint model (third method of pixelintegration) was a Flux Source Area Model (FSAM)used by Schmid (1994), based on the Horst and Weil(1992) model (coded in FORTRAN). FSAM generatesthe FTP weights for the source area and the approxi-mate dimensions of the FTP area for an area that con-tributes up to 90% of the sensed fluxes by the instru-

mentation. It includes the crosswind-integrated flux asHorst and Weil (1992, 1994)

F�x, y, Zm� � Dy�x, y�.Fy�x, Zm�, �22�

where F(x, y, Zm)is the footprint weight function, Dy(x, y)is the crosswind distribution function, and Fy(x, Zm) isthe crosswind-integrated function.

Measured H, Ta, U, Zm, hc, wind direction, and stan-dard deviation of wind direction values at the flux sta-tion were used to obtain the size, shape, and weights ofthe FTP for the conditions during the half-hour inte-gration period corresponding to the remote sensingaircraft overpass. Once the weights were generated(FASOWG, FSAM) as output text files, the files wereimported into ERDAS Imagine and converted into araster image to facilitate spatial operations using theERDAS modeler maker. After carefully consideringthe wind direction at the time of each remote sensingoverpass, the weights image was georectified to thethree-band image, resulting in a raster image with thesame geographic coordinate system as the latent andsensible heat flux images. The weights image was mul-tiplied to the flux, Rn, Taero, and rah images using Imag-ine modeler maker to obtain as output the weightedheat flux, Rn, Taero, and rah images within the FTPboundaries. Pixels histograms were extracted from theimage table attributes in ERDAS Imagine and inte-grated in an Excel spreadsheet, by adding the result ofmultiplying each class by its frequency in the histogram,thus, obtaining the weighted-integrated pixel values.These values were then compared to the corresponding

TABLE 4. Equations involved in Kaharabata et al.’s (1997) footprint model.

B � ��1�s�1�2 ��3�s��1�2, A ��1�s�3�2 ��3�s��1�2

s. Parameters A and B appear in the vertical distribution equation [Dz(x, z)] for a

diffusing scalar that applies a power-law and surface similarity to help define the vertical flux shape; � is the gamma function,

Dz(x, z) � [e�(z/B�z)�s]/(A�z), �y is the crosswind spread of the plume, �y � x�� h(x), �� is the wind fluctuation, h � 1 for x � 13 m,and h � �0.100538 ln(x) � 0.562162 (where x in kilometers), and for 13 m � x � 10 km; U(x) is the velocity of streamwiseplume advection [vertical integration of the product of local wind speed u(z) and Dz(x, z)]; �z is the vertical spread of the plume

�z ��1�s�1�2 ��3�s�1/2

��2�s�z, z is the mean plume height for dispersion from a surface source, obtained from

dz

dx�

k

�ln�p�z � d�

Zom�� m� pz

LM_O�� h� pz

LM_O�. The parameter p varies between 1.53 � p � 1.57 for s values between 1 � s � 2,

and can be computed through p � {s[�(2/s)/�(1/s)]s}1/(1�s), or z using the Horst and Weil (1994) approximation for neutralconditions

x ≅ z ln� z

Zom�.

The stability correction for momentum �m � �5pz

LM_O, for LM_O � � 0,

U�z� �u

*k �ln�c�z � d�

Zom� � �m� cz

LM_O��, �c � 0.562�.


ground station–measured fluxes to evaluate the remotesensing methodology. AOI polygons were drawn fol-lowing the boundary of the FSAM footprint area, andsimple pixel arithmetic averages were extracted forcomparison to the corresponding measured values. Thisbecame the fourth method of pixel weighting/integration.

d. Statistical analysis

Finally, the evaluation of the different models (equa-tions) and FTP integrating methods was carried outcomparing the mean bias error (MBE) and root-mean-square error (RMSE). These are the mean and stan-dard deviation errors, respectively. Their definitionsfollow:

MBE �1n �

i�1

n

X�M�i � X�O�i, �23�

where n is the number of pairs compared, X(M)i is themodeled (estimated) value, and X(O)i is the observedor measured value. A positive MBE means that themodel overestimated the reference value;

RMSE �� 1n � 1 �

i�1

n

�X�M�i � X�O�i � MBE�2.

�24�

3. Results and discussion

Examples of graphical representations of the FSAMand FASOWG FTPs are shown in Figs. 3 and 4. In thisstudy conditions were unstable, resulting in shorter orsmaller FTPs. Also Figs. 3 and 4 clearly show how theFTPs distribute heat flux weights across the sourcearea. The FASOWG FTP model concentrated theweights closer to the flux stations than the FSAMmodel. Figure 5 presents both FTP AOIs over a LAIimage, showing the differences in their spatial integra-tion. Figure 6 shows the energy balance componentsimages for stations 15.1, 15.2, and 16.1 for DOY 182,with the transparent outline of the FSAM FTP laid overthe image to allow for visualization of the variabilitywithin and around the FTP. Results are individuallydiscussed below.

a. Surface temperature

Figure 7 shows a comparison of surface temperaturesbetween the RS and IRT measurements, which resultedin an excellent agreement (R2 � 0.927). The correlationis very high for surface temperatures up to about 38°Cand lower for the range of 38°–41°C. The agreement isevidence of proper thermal imagery calibration. Thedisagreement at higher temperatures corresponds tomore sparse vegetation cases and possibly to differ-

FIG. 3. FSAM footprint (left) lateral and (right) plan view for flux station 15.1 (corn) under unstable atmospheric conditions ofDOY 182.


ences in the footprint observed by the IRT and RSthermal scanner, that is, the IRT looked at an area 1.5m in diameter (3 m east of the EC tower), while the RSthermal scanner pixel size was 6 m for the high-altitudeflight and 4 m for the low-altitude flight. At low LAIvalues this effect would be largest. A low biomass pres-ence was observed on DOY 167 on both corn- andsoybean fields. When data from DOY 167 were re-moved 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 linearand a logarithmic model being the best fit (R2 � 0.732),

G � �0.3324 � ��0.024 LAI�

� �0.8155 � �0.3032 ln�LAI��Rn. �25�

Figure 8 displays the curve fitting and shows that Eq.(25) applies for LAI values between 0.3 and 5. Addi-

FIG. 5. FSAM (longer) and FASOWG (shorter) footprint AOIs for stations 15.1 and 15.2 in the cornfield, oriented according toaverage 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. 4. FASOWG footprint (left) lateral and (right) plan view for station 15.1 on DOY 182.


FIG. 6. Distributed energy balance components for stations 15.1, 15.2 (corn), and 16.1 (soy-bean) (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.


tional G models based on remotely sensed vegetationindices 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 forbroadcast grain crops and alfalfa, both with differentcanopy structures. The developed soil heat flux equa-tion was applied to the selected verification phasedataset, resulting in an average estimation error (MBE)of �0.5 W m�2 and an rmse of 24.5 W m�2 when theFSAM FTP was used as the weighting/integratingmethod, (Table 5). Figure 9 shows the predicted soilheat flux against the measured values for the validationdataset. Some of the scatter is attributed to the com-parison of essentially a point measurement with thespatial estimates from the remote sensing G model in-tegrated using the FTP. Another source of error maybe from the error in LAI estimation (about 15%) andresulting error propagation.

c. Surface aerodynamic temperature

The best Taero model resulting from the multiple re-gression procedures was based on Ta, Ts_RS, U, andLAI_RS as shown below (R2 � 0.766):

Taero_e � �0.534 Ts_RS� � �0.39 Ta� � �0.224 LAI_RS�

� �0.192 U� � 1.67. �26�

Table 5 shows the results from applying Eq. (26) to theverification phase data. The MBE and rmse valueswere 0.2° and 0.9°C, respectively, for the FSAM FTPintegration method. Figure 10 plots the values of pre-dicted 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 esti-mates for low biomass stands (the asymptotic part ofthe model) and uncertainties in Ts_RS for the same lowbiomass stands (maybe there is a need for greater �s

correction). On the other hand, it could be an indica-tion that empirical equations for Taero need to be de-veloped separately for corn and soybean canopies be-cause of differences in their structure and canopyheight vis-à-vis the LAI. Given that for real nonuni-form surfaces Taero is effectively a parameter, the em-pirical fit with these properties is actually rather good.

d. Surface aerodynamic resistance

Figure 11 and Table 5 show the comparison of theestimated rah (rah_e) against inverted values from mea-sured H that is adjusted for closure. The iterativemethod seems to work because the estimated values

FIG. 7. Airborne- vs ground-measured surface temperaturecomparison.

FIG. 6. (Continued)


match the referenced values with an estimation error of�0.16 � 2.8 s m�1 (MBE � rmse) for the FSAM FTPmethod (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 about10% difference in rah (1.5–2.0 s m�1) would result in anH error of only 9%–10%. The need for accurate spatialTaero and Ta estimations to obtain proper distributed Hestimates 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 forclosure and 6.5 � 29.5 W m�2 with adjustments forclosure using G from RS, respectively. Closure adjust-

ments on measured H and LE were made using G fromRS to characterize the error introduced by the mea-surement because the heat fluxes come from the up-wind FTP area and measured G represents only a pointmeasurement. In any case, these relatively good retriev-als of H result from the good estimation of rah and Taero.The H rmse values reflect the rather small variabilityintroduced by the Taero and rah models (error propaga-tion) mostly for larger values. This can be seen in Fig.12 where the estimated and measured H that are ad-justed for closure are compared.

f. Net radiation

The remote sensing estimation of net radiation wasreasonably good with errors of �4.8 � 20.7 W m�2 for

FIG. 8. Soil heat flux logarithmic curve fitting.

TABLE 5. Statistical errors from comparing airborne remote sensing estimates against ground-derived values, and weighted/integratedusing different methods. Note: The subscript e in the variables indicate the estimated RS. LEnc is the EC measured LE, not adjustedfor closure.

Pixel weightingintegrating method

Taero_e

(°C)rah_e

(s m�1)G_e

(W m�2)Rn_e

(W m�2)H_e

(W m�2)LE_e

(W m�2)LEnc

(W m�2)

A MBE � 0.2 0.2 0.4 3.2 2.2 1.4 54.6B MBE � �0.2 0.1 �1.6 0.0 �1.6 3.0 56.3C MBE � 0.2 0.2 �0.5 �4.8 9.4 �9.2 44.0D MBE � 0.1 0.2 0.9 �1.5 10.0 �12.5 40.7

A RMSE � 0.9 2.4 21.7 25.6 33.5 39.6 49.7B RMSE � 0.7 2.7 22.2 27.7 32.9 48.3 53.8C RMSE � 0.9 2.8 24.5 20.7 28.3 39.4 45.6D RMSE � 0.6 2.4 22.1 26.5 30.6 49.2 56.6

Method: A � FASOWG FTPB � FASOWG AOIC � FSAM FTPD � FSAM AOI


the FSAM FTP (Table 5). This is well within the 5%–10% error in typical net radiation measurements. Thecomparison with measured values is shown in Fig. 13.The bias is very small and could come from estimationerrors in albedo and air emissivity and, to a smallerextent, the variability in the net radiation measure-ments at a spot (point measurement) versus the inte-grated values within the footprints.

g. Latent heat flux

The LE estimates from RS are compared in Tables 5with measured LE that is adjusted and not adjusted forenergy 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 re-mote sensing procedure is a residual from the energy

balance equation; thus, closure is inherent. Given theuncertainty in eddy covariance measurements of LE(Weaver 1990; Field et al. 1994), the agreement is verygood. The errors were �9.2 � 39.4 W m�2 for theFSAM FTP integration, well within the margin of errorof the ground station measurements. This is an excel-lent result because of the small bias, and it is evidencethat the remote sensing procedure can provide goodestimates of the distributed latent heat fluxes. The biasdecreased to �5.6 � 28.7 W m�2 when the closure wasperformed using G estimated from remote sensing(Table 6 and Fig. 16). The bias at smaller values of LEin Figs. 14 and 16 can be attributed to errors resultingfrom larger values of H and G.

FIG. 10. Comparison of RS estimation of aerodynamictemperature against inverted values from measured H.

TABLE 6. Statistical errors from comparing airborne RS esti-mates against ground-measured H and LE adjusted for closureusing G from RS estimates, and integrated using different meth-ods. The subscript e indicates estimated RS.

Pixel weightingintegrating method

H_e

(W m�2)LE_e

(W m�2)

A MBE � 1.9 2.7B MBE � �1.8 4.3C MBE � 6.5 �5.6D MBE � 9.8 �11.2

A RMSE � 32.0 34.0B RMSE � 33.9 40.5C RMSE � 29.5 28.6D RMSE � 33.1 41.3

Method: A � FASOWG FTPB � FASOWG AOIC � FSAM FTPD � FSAM AOI

FIG. 9. Comparison of the remote sensing soil heat flux esti-mates with measured values. The subscript (e) stands for “esti-mated” and (C) for the FSAM FTP weighting/integrating method.

FIG. 11. Surface aerodynamic resistance model predictionscompared to inverted aerodynamic resistance using H closure(rah_c).


h. Footprints

The error statistics of Table 5 showed that, in gen-eral, the FSAM footprint resulted in an integration ofthe fluxes that closer matched (lower MBE and rmse)the measured values. The integration method did notmake a significant difference in the case of Taero, rah,and G. In general, either of the FTPs appeared to betterweight/integrate the heat fluxes than the simple arith-metic averages, indicating FTPs should be used to prop-erly compare and/or validate the spatially distributedfluxes obtained from remote sensing with ground-measured fluxes.

4. Conclusions

The corn- and soybean fields in the study area pre-sented a good range of vegetation cover (leaf area in-dex) for the estimation of net radiation, soil heat flux,and sensible heat flux with remote sensing, as well asfor the methodology. Soil moisture levels were not lim-

iting and, therefore, the available energy (Rn � G) pre-dominantly went to LE (evapotranspiration) ratherthan to heating the air (H). However, more H wasgenerated over the soybean fields, which were in anearlier stage of growth than most cornfields in the area.

Surface temperature was well estimated by the air-borne thermal scanner when compared to IRT readingson the ground. The aerodynamic temperature model-ing, using surface radiometric temperature, horizontalwind speed, leaf area index, and air temperature, re-sulted in very low estimation errors, with a slight over-prediction of 0.2 � 0.9°C. The surface aerodynamic re-sistance was well estimated with prediction errors of�0.2 � 2.8 s m�1. The fitted logarithmic soil heat fluxmodel showed the best coefficient of determination,0.732, among several of the models that were tested,and in the verification process underpredicted mea-sured G by �0.5 � 24.5 W m�2. The sensible heatfluxes that were obtained were estimated with errors of9.4 � 28.3 W m�2. Net radiation was estimated to �4.8� 20.7 W m�2, which validates the remote sensing

FIG. 12. Comparison of RS estimates of H vs measured valuesadjusted for closure.

FIG. 13. Comparison of RS estimates of Rn (Rn_e), integratedwith the FSAM FTP, vs measured values.

FIG. 14. Comparison of LE estimates from remote sensing withmeasured fluxes adjusted for closure.

FIG. 15. Comparison of LE estimates from remote sensing withmeasured fluxes not adjusted for closure.


methodology and corroborates previous research re-sults in the retrieval of this variable. Further improve-ments in the calibration of the airborne thermal infra-red imagery for surface emissivity and improved esti-mates of albedo and the emissivity of the air shouldreduce the bias further.

The lack of energy balance closure for the eddy co-variance flux measurements led us to adjust for closureto obtain meaningful comparisons of H and LE with thecorresponding airborne remote sensing estimates. Thespatial estimation of the latent heat flux (LE or ET)resulted in errors of just �9.2 � 39.4 W m�2. The biaswas decreased further when remotely sensed G valueswere used to estimate the available energy for closure(�5.6 � 28.7 W m�2). This is a low bias error, but maypartially hide the fact that the variability that is intro-duced by the point G measurements was removed byusing the remote sensing values in forcing closure.

These results appear to validate this methodology forestimating the spatial variations of energy balance com-ponents using airborne high-resolution multispectralimagery. It is important to note that good retrievals ofaerodynamic temperatures are critical in this process.Herein they were obtained empirically, using availablemeasured fluxes for the development of the model, and,thus, should be considered specific for the two croptypes and stability conditions that are encountered atthe study site.

The comparison of estimated to measured values wasperformed using both footprint models and simple av-erages. In general, for the surface conditions encoun-tered and under unstable atmospheric conditions bothof the footprint models that were tested (FSAM andFASOWG) performed better than the simple AOIpolygon averages. Footprint weights should definitelybe used for integrating remotely sensed fluxes over het-

erogeneous surfaces. The FSAM model by Schmid(1994) is recommended because the higher weights aredistributed further upwind from the flux stations, andthe footprint is larger. To further test the footprint ef-fectiveness on weighting/integrating the spatially dis-tributed fluxes, it is recommended that cases with stableatmospheric conditions and significant surface hetero-geneity conditions be included.

Acknowledgments. This paper was funded throughNASA’s Global Water and Energy Cycle Program un-der Contract NAG5-11673. Support for the researchwas also provided by the Utah Agricultural ExperimentStation, the Organization of American States, and theRemote Sensing Services Laboratory, Department ofBiological and Irrigation Engineering at Utah StateUniversity. Thanks to Dr. Martha Anderson, Dr. Gil-berto Urroz, Dr. Harikishan Jayanthi, and graduatestudents Ricardo Griffin, Tapan Pathak, Deepak Lal,and Kyle Andreason who provided assistance.

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Comparing Aircraft-Based Remotely Sensed Energy Balance Fluxes with Eddy Covariance Tower Data Using...

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