the high accuracy atmospheric correction for hyperspectral data (hatch) model

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 41, NO. 6, JUNE 2003 1223

The High Accuracy Atmospheric Correction forHyperspectral Data (HATCH) Model

Zheng Qu, Bruce C. Kindel, and Alexander F. H. Goetz

Abstract—The High-accuracy Atmospheric Correction forHyperspectral Data (HATCH) model was developed for derivinghigh-quality surface reflectance spectra from remotely sensed hy-perspectral imaging data. This paper presents the novel techniquesapplied in HATCH. An innovative technique, a “smoothness test”for water vapor amount retrieval and for automatic spectralcalibration, is developed for HATCH. HATCH also includes anoriginal fast radiative transfer equation solver and a correlated-gaseous absorption model based on HITRAN 2000 database.Spectral regions with overlapping absorptions by different gasesare handled by precomputing a correlated- lookup table forvarious gas mixing ratios. The interaction between multiplescattering and absorption is explicitly handled through the useof the correlated- method for gaseous absorption. Finally, someresults are presented for HATCH applied to Airborne VisibleInfrared Imaging Spectoradiometer data and together withcomparison of the results between HATCH and the AtmosphereRemoval program. The limitations in HATCH include that theHATCH assumes a Lambertian surface, and adjacent effect is notconsidered. HATCH assumes aerosols to be spatially homogeneousin a scene.

Index Terms—Airborne Visible Infrared Imaging Spectora-diometer (AVIRIS), atmospheric model, Hyperion, hyperspectral.

I. INTRODUCTION

T HE HIGH-accuracy Atmospheric Correction for Hyper-spectral Data (HATCH) model is a program that derives

high-quality surface spectra from remotely sensed hyperspec-tral imaging data. One of the major purposes of hyperspectralimaging spectrometers operating in the visible and near infraredwavelengths, e.g., Airborne Visible/Infrared Imaging Spectrom-eter (AVIRIS), and Hyperion onboard the National Aeronauticsand Space Administration (NASA) Earth Observing 1 (EO-1)satellite, is to measure the spectral reflectance of the earth’s sur-face. The raw data from such spectrometers are radiances thatcontain information from the interaction of solar radiation withthe atmosphere as well as the earth’s surface. One needs to do

Manuscript received May 31, 2002; revised January 27, 2003. This work wassupported by the National Aeronautics and Space Administration under GrantNAG5-4447 and Grant NCC5-458.

Z. Qu was with the Center for the Study of Earth from Space/CIRES, Univer-sity of Colorado, Boulder, CO 80309 USA. He is now with the Department ofEarth and Atmospheric Sciences, Purdue University, West Lafayette, IN 47907USA (e-mail: [email protected]).

B. C. Kindel is with the Center for the Study of Earth from Space/CIRES,University of Colorado Boulder, CO 80309 USA (e-mail: [email protected]).

A. F. H. Goetz is with the Center for the Study of Earth from Space/CIRESand the Department of Geological Sciences, University of Colorado, Boulder,CO 80309 USA (e-mail: [email protected]).

Digital Object Identifier 10.1109/TGRS.2003.813125

atmospheric correction to separate spectral information of theearth’s surface from that of atmosphere.

The Atmosphere Removal program (ATREM) [1] has beenwidely used in the hyperspectral remote sensing community asan atmospheric correction tool for over ten years. It works fastand delivers surface reflectance retrieval with reasonable accu-racy. Yet the major techniques employed in ATREM are nowoutdated as a result of new advancements in the area of atmo-spheric radiative transfer. These include the following.

1) Malkmus band model based on HITRAN 92 database:HITRAN 2000 [2] is now available with more accuratemolecular line parameters. Also, ATREM employs themultiplication rule to handle transmittance in spectralregions where multiple gas absorption is present. Thisresults in less accurate transmittance calculation inthese regions, e.g., at 2.0m where both HO and COstrongly absorb.

2) Three-band ratioing technique for water vapor amountretrieval: The prerequisite for this technique is that thesurface reflectance spectrum is linear in wavelength in thewater vapor absorption region to be used. This introducesretrieval errors when the surface reflectance spectrum isnot linear for wavelength, for instance, when the surfacecontains iron-rich soil and/or vegetation.

As a new atmospheric correction model, HATCH utilizes thelatest advancements in the area of radiative transfer (RT). Theseinclude the following:

1) HITRAN 2000 [2] based correlated-method, which al-lows accurate transmittance calculation in regions wheremultiple gases absorb strongly (e.g., at 2.0m where bothH O and CO strongly absorb), to accurately handle at-mospheric transmittance;

2) fast radiative transfer equation solver—multigrid discreteordinate method—to explicitly account for radiation in anonhomogeneous scattering–absorbing atmosphere;

3) novel technique called the “smoothness test” for columnwater vapor amount retrieval, which eliminates the lin-earity assumption of the surface spectra in the conven-tional three-band ratioing technique [1];

4) automatic spectral calibration of the sensors based onthe remotely sensed data only and using the “smoothnesstest” technique.

A special version of HATCH, called HATCH-2d, wasdeveloped for application to pushbroom sensors such as Hy-perion, since its spectral calibration varies from one detectorcolumn to another. Therefore, in doing atmospheric correc-tion, HATCH-2d uses the corresponding individual spectral

0196-2892/03$17.00 © 2003 IEEE

1224 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 41, NO. 6, JUNE 2003

(a) (b) (c)

Fig. 1. (a) AVIRIS image of Yerington, NV. (b) First principal component image. (c) Water vapor image derived using HATCH.

response function [Gaussian function characterized by centerwavelength and full-width-half-maximum (FWHM)] for eachdetector column instead of using one across the entire sensorarray. The automatic spectral calibration of the sensor is alsoperformed individually for each detector column.

HATCH derives surface reflectance on a pixel-by-pixel basis,since the water vapor amount varies significantly spatially.Fig. 1 shows the first principal component image of AVIRISat Yerington, NV and the water vapor image derived usingHATCH, as well as the AVIRIS image. The variability in thefirst principal component image shows its apparent connectionto the spatial variation of water vapor, in addition to surfacereflectivity variation, which indicates the necessity of thederivation on a pixel-by-pixel basis. In the following text wepresent the methodology used in HATCH and some results forHATCH applied to AVIRIS data.

In another paper in this issue [3], more results of HATCH asapplied to model data as well as AVRIS and Hyperion data arepresented.

II. M ETHODOLOGY

A. Correlated-k Method for Gaseous Absorption

The correlated- method [4], [5] for gaseous absorption cal-culation transforms the line-by-line integration over a spectralband of a radiative quantity, e.g., transmittance, into integrationover the cumulative probability distribution function of the gasabsorption coefficients. The transformed integration can, there-fore, be computed using a few quadrature points without com-promising accuracy, since the function to be integrated is trans-formed to a smooth one.

For example, if we want to compute a band-averaged trans-mittance in a wavelength interval , a straightforward wayis to compute the transmittance using line-by-line integration

(1)

where is wavelength, is the monochromatic absorptioncoefficient at wavelength , and is the path length. Sincegaseous absorption spectra in the visible and near-infrared(NIR) region consist of numerous narrow lines, the line-by-linemethod is impractical for processing remotely sensed imagingdata. For the wavelength interval , let us define the prob-ability distribution function (PDF) of as , then thecumulative probability function of is,

(2)

The cumulative probability function is a monotonic func-tion of , and the relationship between them can be inverted.The integration for the band-averaged transmittance canbe computed through integration over

(3)

Since is a relatively smooth function, the above integra-tion over can be performed using a few quadrature points.This is the -distribution method. The correlated-distributionmethod is a simple extension of thedistribution to inhomoge-neous paths

(4)

where is now a function of both path lengthand wavelength. The physical implication of (4) is that only oneexists for

a given along path length. There is extensive literature dis-cussing conditions and accuracy of the application of the corre-lated -distribution method [4]–[6], [9]. Fu and Liou [6] present

QU et al.: HATCH MODEL 1225

a number of numerical simulations with application of the cor-related -distribution method for various problems, includingthose in solar spectrum. For our problem, i.e., radiation transferin the atmosphere in the spectrum between 0.35–2.53m andat a spectral resolution of 0.001m, the correlated -distribu-tion method can be reasonably applied. We choose the wave-length interval of 0.001 m for computing correlated-distri-bution data, so that HATCH can properly resolve the Hyper-spectral sensors’ response functions, whose FWHM values areoftentimes about 0.01m and may be even smaller with ad-vancement of the technology. The correlated-distribution datafor HATCH contains quadrature points for(denoted as here-after), as well as the corresponding absorption coefficientsfor various pressure and temperature values, and for each wave-length interval.

Besides yielding better accuracy than band models forcomputing gaseous absorption, the correlated-method alsoprovides an explicit way to accurately account for the inter-action between multiple scattering and absorption. HATCHexplicitly computes radiance and flux values for ina scattering–absorbing atmosphere by simply treating theproblem in the way it would for monochromatic radiation.Then, a summation of the radiance or flux values over thequadrature points yields the radiance or flux for the desiredspectral interval. Multiple scattering increases the effective pathlength of a photon, and consequently increases the probabilityof a photon getting absorbed during its transmission. A moreaccurate treatment of this interaction by using the correlated-method is thus expected to improve HATCH performance inthe short wavelength regions.

HATCH uses a correlated- lookup table built fromline-by-line gaseous transmittance. The transmittance iscomputed using the line-by-line code LBLRTM [7] based onHITRAN 2000 database [2]. The line-by-line calculation of thetransmittance is performed in a resolution of 0.2 of FWHMof the absorption lines using Voigt line shape [7], and thecontinuum absorption is also included in the calculation. Thelookup table is independent of the HATCH algorithm and iseasy to update once a new version of the HITRAN databasebecomes available.

The correlated -distribution data used in HATCH are com-puted in 0.001-m intervals as mentioned above. It uses adap-tive quadrature points (3, 6, 12, and 24 quadrature points). Therelatively smoother part of the transmittance spectra can be rep-resented by a smaller number of quadrature points in the cor-related- method. For example, spectra around the 0.86-m at-mospheric window region requires only three quadrature points,while spectra around the 0.94-m strong water vapor absorptionregion requires 24 quadrature points. The criterion to determinethe optimal number of quadrature points is that the-distribu-tion method differs from a line-by-line result by less than 0.0001for transmittance in a 10-km gas path with a typical atmosphericgas concentration at the surface.

For spectral regions with overlapping absorptions by differentgases, correlated-datasets are generated for various possiblegas mixing ratios. The lookup table has four dimensions, i.e.,temperature, pressure, wavelength, and gaseous mixing ratio.Though there are seven gases (O, CO , H O, CH , N O, CO,

Fig. 2. Midlatitude summer atmosphere transmittance computed fromHATCH and MODTRAN4. The results are convolved to AVIRIS responsefunctions. The top curve is the difference between MODTRAN and HATCHtransmittance, shifted upward by 1.2 for clarity.

O in the earth’s atmosphere that produce observable absorp-tion features in the 0.4–2.5-m range, only HO, O , and COcould vary significantly in the concentration in a realistic atmos-phere (note that concentration of COhas seasonal and yearlyvariation). Unlike H O and CO, however, O absorption bandsin the 0.4–2.5-m spectral region are continuum (e.g., Chappiusbands around 0.45–0.80-m region), and therefore, we do notinclude O into the correlated-distribution dataset calculation.Instead, we only compute its averaged absorption cross-section

in 0.001- m intervals. In Section II-D.1, we will briefly dis-cuss how we add contribution of Ointo the total radiation atten-uation. Now that we have only HO and CO that could vary sig-nificantly in the concentration in the 0.4–2.5-m spectral range,we can use only one mixing ratio as a variable for the lookuptable. In the spectral regions with no significant COabsorp-tion, we use the HO’s mixing ratio (H O/all gases) as a vari-able in the lookup table. In the COabsorption regions, we usethe mixing ratio between HO and CO (i.e., H O/CO ) as avariable in the lookup table, since in these regions there is verylittle absorption by any other gases.

The atmospheric optical properties (e.g., extinction coeffientsas functions of , single-scattering albedo, etc.) are first com-puted at 34 vertical grade points with pressure and temperaturevalues derived from a preassigned LOWTRAN [8] atmosphericprofile. Assuming linear variation of these optical propertiesacross the adjacent vertical grade points, the radiative quanti-ties like transmittance are computed accordingly. HATCH doesnot use the conventional homogeneous atmospheric layers in theradiative transfer calculation, because we use a new, fast radia-tive transfer equation solver for HATCH, which works on thevertical grade points. Section II-B will address this topic in de-tails. Fig. 2 gives a comparison of transmittance computed fromMODTRAN4 [9] and from HATCH for a standard midlatitudesummer atmosphere with an overhead illumination. The overalldifference between the two spectra is less than 3%.


Both models use correlated-distribution method andHITRAN database. The slight difference in the transmittancespectra may be due to different ways to discretize the verticalatmospheric profile in the radiative transfer (MODTRAN usesthe conventional optically homogeneous layers to represent theatmospheric vertical profile). For applications in atmosphericcorrection for the hyperspectral data, however, our mainconcern here is the computation speed. The major advantagefor HATCH is that it uses a much faster RT equation solver,which is detailed in the next section.

B. Radiative Transfer Equation Solver: Multigrid DiscreteOrdinates Method

Since HATCH specifically targets the atmospheric radiativetransfer problems in the visible and SWIR regions only, inorder to speed up the data processing, we use our own radiativetransfer algorithm rather than the general-purpose atmospherictransmission code MODTRAN [9].

For a scattering–absorbing atmosphere, when the adjacent ef-fect is not considered, the at-sensor radiancecan be related tothe Lambertian surface reflectanceby

(5)

where is the atmospheric path radiance; is the two-waytransmittance for the sun-surface sensor path;is the sphericalalbedo of the atmosphere; is the exoatmospheric solar irra-diance; and is the solar zenith angle.

The major computation task for HATCH for surface re-flectance retrieval on a pixel-by-pixel basis is to compute thethree radiative quantities , , and for a given solar-sensorgeometry and the tabulated water vapor amount. In order tospeed up the computation, we implemented a new method forsolving the RT equation called the multigrid discrete ordinatesradiative transfer (MGRT) method [11]. The new methoddelivers a comparable accuracy to DISORT [12], which iswidely used in RT calculation, including MODTRAN4, and isfive to ten times faster in a radiance calculation.

The new method solves the integral form of the RT equa-tion for a scattering–absorbing atmosphere and employs the lin-earity of the equation to speed up the convergence of the itera-tion process by computing the residual on fewer streams. Forexample, it solves the equation on a two-stream grid to com-pute the residual from a four-stream iteration. It generally con-verges in less than five iteration cycles. We attribute the speed ofMGRT in solving the RT equation to its use of multigrid methodin the angular space. Readers can refer to [13] for more on math-ematics of this method and for a further list of references.

The integral form of the RT equation for a plane parallel scat-tering–absorbing atmosphere can be written as follows:

(6)

where is the scattering source function

(7)

and

(8)

(9)

where , , and are optical depth, cosine of zenith angle, andazimuthal angle for the radiance;, are multiplescattering, single-scattering source function, scattering phasefunction, and extraterrestrial solar irradiance, respectively;and are cosine of zenith angle and azimuthal angle of inci-dent solar beam, respectively. We can rewrite (6) by

(10)

where is a linear operator

(11)

and the right-hand side of the linear equationis defined by

(12)

Let us use to denote the discretized in angular space,where is the number of discrete zenith angles (i.e., number ofstreams) in discretization and useand to denote the radi-ance and the right-hand side on the-stream discrete ordinategrids.

For , an initial guess of , the “defect” of the RT equationis

(13)

If we denote the “correction” to as

(14)

The correction satisfies

(15)

which has exactly the same form as (10). This allows us to it-eratively solve (15) on a coarser grid. The flow chart in Fig. 3illustrates the solution procedure for a four stream RT equation.

Table I presents the relative CPU time comparison forDISORT and MGRT when performing a radiance computationover the range 0.4–2.5m at 1-nm intervals. Fig. 4 givesaccuracy comparisons between DISORT and MGRT for amidlatitude summer atmosphere path radiance at= 1.0[Fig. 4(a)] and 0.9 [Fig. 4(b)], and = 0 , 45 , 90 , 135 ,and 180, where is the cosine of the radiance zenith angle(i.e., positive values correspond to downlooking geometry)and is the relative azimuth angle to solar beam incidentplane. The solar zenith angle is at 45. Again the wavelengthrange is between 0.4–2.5m. Results are plotted in ratiosof rms difference between MGRT and DISORT over mean,using the DISORT 24-stream results as baselines. The MGRTconvergence behavior is also shown in Fig. 4 as curves denoted


Fig. 3. Flowchart of the RT equation-solving procedure in MGRT.

TABLE ITHE RELATIVE CPU TIME COMPARISON FORDISORTAND MGRT

by “MGRT-MGRT (24 STR),” using the MGRT 24-streamresults as baselines. Note some differences shown here are dueto different treatment of atmospheric layering. DISORT dividesthe atmosphere into a number of optically homogeneous layerswhile MGRT computes radiative quantities over a number ofvertical grid points and assumes that the optical properties varylinearly across adjacent grid points.

C. Column Precipitable Water Vapor Retrieval

Column water vapor amount is one of the major uncertainfactors in the atmospheric components that affect radiation in

Fig. 4. Relative accuracy for upwelling radiance computed from MGRT ascompared to DISORT.

the 0.4–2.5-m spectral regions. Gaoet al. [1] proposed thethree-band ratioing technique for water vapor amount retrieval,which requires the surface reflectance values at the selectedthree channels to be linear in wavelength. The three-bandratioing technique works fairly well for most surface types.Yet, systematic errors are introduced for vegetation surfaces,snow/ice surfaces, and iron-rich soils, which have absorptionbands in the 0.94-m region.

The new technique, called the “smoothness test,” imple-mented here attempts to avoid the linearity assumption for thesurface reflectance. It is based on the principle often used byhyperspectral data analysis researchers that either under- oroverestimation of water vapor amount results in residual spikesin the retrieved surface reflectance. Features generated frompoor atmospheric corrections are generally rougher than theinherent surface spectral features. In other words, atmospherictransmission features contain more high-frequency componentsthan spectral reflectance features do.

Therefore, the best water vapor estimation yields thesmoothest retrieved surface reflectance in the water vaporabsorbing regions. There are quite a few criteria that can beused for a smoothness test. Our criterion is as follows. First,following (5), surface reflectance is derived for 40 discreteamounts of water vapor (the range can be specified by theuser, default is [0.5 cm, 6.0 cm])

(16)

where is the channel number for the sensor; .


Fig. 5. “Smoothness test” for water vapor retrieval. Adjacent reflectancespectra offset: 0.15.

Then, in a water vapor absorption spectral region, asmoothed reflectance spectrum is constructed accordinglyusing a truncated cosine series

(17)

where is the cosine series coefficient obtained from cosinetransform, and is the number of cosine terms is roughly deter-mined such that

(18)

We choose an empirical value of 0.4m for , such thatin this wavelength interval surface spectral features are resolvedwhile water vapor spectral features are largely smeared. Notethat the channel number is limited to channels within watervapor absorption spectral region

(19)

We originally chose the sum of the squares of the differencesin the spectral region between the two spectra and toserve as the smoothness criterion, i.e., we used

(20)

as the smoothness criterion. The minimal value ofindicatesa best retrieval. However, oftentimes in a water vapor absorp-tion region, e.g., around 0.94m, the retrieved spectrum dif-fers from the smoothed one by double-sided spikes as seenin Fig. 5, with one overcorrection and the other undercorrection.Therefore, the optimal, retrievedshould be a balance betweenthe two spikes. The criterion we choose for determining the dis-crete water vapor amount is such that

(21)

reaches a minimum value. Note the absolute value is computedafter the summation. Further, we refine the water vapor amountfrom the discrete value by linear interpolation such that

(22)

where subscript is a decimal number that corresponds to in-terpolation of discrete values of as well as . With , thecontinuous water vapor amount can be determined frominterpolation. In the same manner, with, we can computethe interpolation of the three atmospheric parameters in (16),namely, the sun-surface-sensor two-way transmittance, theatmospheric path radiance , and spherical albedo .Hence, the entire surface reflectance spectrum can be de-rived using (16).

Fig. 5 shows the retrieved reflectance spectra in the watervapor absorption regions using AVIRIS data and their corre-sponding smoothed spectra. The fourth pair of spectra (thicksolid line) from top corresponds to the proper water vaporamount derived by this technique.

In [3], results from HATCH applied to model simulated datashow that HATCH reflectance retrievals are insensitive to liquidwater content in vegetation cover if the 0.940-m band is usedfor retrieval, but not if 1.14-m band is used for the retrieval.

Once the water vapor amount at the first pixel is derived, thenext adjacent pixel can use this value as an initial guess and thesmoothness test needs to be performed only for a few differentwater vapor amounts to find the proper water vapor value.

D. Aerosols and Other Gases

1) Aerosols: In the NIR wavelengths, where molecular scat-tering is weak, aerosol scattering is the major contributor to at-mospheric path radiance. A good aerosol model should encom-pass a variety of types of aerosols that differ in their spectralproperties.

HATCH uses the Air Force Geophysics Laboratory’s(AFGL) standard aerosol data [14] for tropospheric aerosols.MODTRAN 3 [10] aerosol vertical profiles are used. One func-tion in HATCH is to allow different aerosol types to be mixedexternally, e.g., a mixture of oceanic and urban aerosols can beused for coastal regions. Hence, more accurate accounting ofpath radiance for short wavelength region can be achieved. Theuser needs to specify the aerosol types (oceanic, urban, rural,or continental) and their mixing ratio, as well as the surfacevisibility.

Use of the correlated-method allows us to integrate in astraightforward way all scattering, both due to molecules andaerosols, together with absorption into our RT model describedin Section II-B, e.g., extinction coefficientas a function ofat a certain grade point is computed from

(23)

where is the value for all gases except O; andare the absorption cross-section and the number density for O,respectively; and are the absorption cross section andthe number density for aerosols, respectively; and is theRayleigh extinction coefficient.


The Rayleigh scattering term is computed using an empiricalequation from MODTRAN [9]

km

(24)where , , are pressure in hectopascals, temperature inKelvin, and wavenumber in units per centimeter, respectively.

2) CO and CH : Both CO and CH have strong absorp-tion bands in the infrared spectral regions. Most of these bandsoverlap with water vapor absorption bands. Different mixing ra-tios between HO and CO (i.e., H O/CO or that betweenH O and CH (i.e., H O/CH could result in different bandabsorption coefficients. The amounts for these gases in HATCHare user adjustable variables. Since the correlated-lookup tableconsists of a dimension for mixing ratio, e.g., mixing ratio be-tween H O and CO (i.e., H O/CO for CO absorption re-gions, or that between HO and CH (i.e., H O/CH for CHabsorption regions, the overlapping absorption is automaticallytaken into consideration for HATCH through interpolation ofthe mixing ratio.

E. Spectral Calibration Using Known Atmospheric AbsorptionFeatures

Even after the water vapor amount is fine-tuned by thesmoothness test, the derived reflectance spectra often showsystematic spectral features in the water vapor absorptionregions. These are believed to be result partially from wave-length calibration shifts during the flight. By shifting the centerwavelengths up to 3 nm in 0.1-nm intervals and by shiftingFWHM of the spectrometer up to2 nm in 0.1-nm intervalsin the strong water vapor absorption regions and the oxygen-Aband, HATCH searches for the smoothest retrieved spectrum.The smoothest spectrum, determined by the same criterion usedfor water vapor retrieval, should result in the proper wavelengthshift. Our experiments show that the spectral shift determinedthis way is mostly independent of water vapor amount andpixel location. The center wavelength shift and FWHM shiftare performed in turns and the loop goes for two cycles.

F. A Posteriori Polishing of Reflectance Spectra

HATCH-derived reflectance spectra, though improved afterspectral calibration process, still contain some systematic errors.A systematic transmittance adjustment spectrumis derivedfrom the data itself using a similar method as that presentedby [15]. The adjustment spectrumis then multiplied by thesun-surface-sensor two-way transmittanceto get the adjustedtwo-way transmittance

(25)

The procedure to derivegoes as follows. First, an ensembleof no less than 1000 pixels are selected randomly across thescene. Each derived surface reflectance spectrum is approxi-mated by an artificially smooth curve constructed from a trun-cated cosine series. Then, the optimum adjustment spectrumis obtained in a least squares sense such that with a single ad-justment spectrum applied to two-way transmittance for all

Fig. 6. Maximal wavelength deviation from mean center wavelengths forHyperion.

Fig. 7. Errors associated with retrieval of a spectrally flat 50% reflector usingthe average spectral calibration of the Hyperion detector in the HATCH model.“Left” and “Right” correspond to detector column at left and right edge of thedetector array, respectively.

pixels without regard to water vapor amount, the resulting re-flectance spectra ensemble has the smallest rms difference fromthat of artificial, smooth curves aforementioned.

Apparently, the accuracy of the derived adjustment spectrummainly depends on how the surface spectra differ from each

other among the ensemble of selected pixels. In a scene domi-nated by only one terrain type, the derived adjustment spectrum

may be less accurate and should be used with caution. Thisprocess is optional for the user.

G. HATCH-2d: Application to Pushbroom Sensors Such asHyperion

The pushbroom sensors (e.g., Hyperion onboard EO-1) aredifferent from optomechanical sensors (e.g., AVIRIS). We willtake Hyperion as an example in the following.

Each column of pixels in Hyperion data corresponds to anindividual detector that has its own response function charac-terized by its center wavelength and FWHM. Using the Hy-perion response functions for the detector arrays, we plot inFig. 6 the maximum deviation from mean center wavelengthvalues across the sensor for Hyperion. Using the mean centerwavelength spectrum as a basis, across the detector arrays, thecenter wavelengths may deviate from the mean values by upto 2.4 nm. Experiments show that a mere 0.1-nm miscalibra-tion in center wavelength can result in up to 5% error in sur-face reflectance retrieval [16]. Therefore, it is necessary to usethe individual spectral response function for each detector in-stead of using one across the entire sensor. Fig. 7 shows er-rors associated with retrieval of a spectrally flat 50% reflector


Fig. 8. Image of 09-30-1999 AVIRIS overflight at Boulder, CO.

using the average spectral calibration of the Hyperion detector inthe HATCH model. In this experiment, ignoring response func-tion differences among detectors in Hyperion could result in upto 8% reflectance retrieval errors around 0.94-m water vaporregions.

The spectral calibration procedure for pushbroom sensorsneeds to be carried out on a column-by-column basis as theresponse function shift (i.e., shift in center wavelength and inFWHM) for each detector can have different magnitudes anddirections. Therefore, in HATCH-2d, the spectral calibrationis performed on a column-by-column basis. This increasesthe computation burden significantly. HATCH-2d speeds upthe procedure by utilizing the fact that the response functionshift varies gradually across the entire detector array, becauseadjacent detectors always experience very close physicalcondition changes. Hence, the response function shift can befound quickly if the shift values of the adjacent column is usedfor initial guess.

Thanks to absorption features of O, H O, CH , and CO atvarious spectral regions, HATCH-2d is able to handle possiblespectral miscalibration separately for each spectral region. Forexample, O band around 0.76m is used for spectral calibra-tion for wavelengths between 0.6–0.86m, while the 1.14-mwater vapor absorption region is used for spectral calibration forwavelengths between 1.06–1.25m, etc.

Fig. 9. HATCH- and ATREM-derived, as well as ASD-measured, surfacereflectance for soil at AVIRIS image site A.

III. RESULTS

The data we used for this experiment is a 1999 AVIRISover flight at Boulder, CO. Fig. 8 shows the scene. At site A(soil surface), a simultaneous surface reflectance measurementwas taken at time of AVIRIS overflight. Reflectance spectraretrieved by ATREM and HATCH are plotted together withthe surface measurement in Fig. 9 with a 15% reflectance shiftfor clarity. Improvement in reflectance values calculated by


HATCH over ATREM at the wings of the strong absorptionregions around 1.38, 1.9, and 2.5m is apparent This isprimarily attributable to the use of the correlated-method andthe new HITRAN database that more accurately accounts forgaseous absorption.

Fig. 9 also shows the spectrally calibrated HATCH spectrumdescribed above, which is much smoother and better matchesthe surface measurement. The difference between the retrievedsurface reflectance spectrum and surface measured one inthe short wavelength around 0.5m can partly be attributedto the relatively inaccurate sensor calibration in this spectralregion and partly to the adjacency effect that is not included inHATCH’s RT model.

More HATCH results and quantitative comparisons withother atmospheric correction models are presented in [3].

IV. CONCLUSION

With implementation of recent advancements in atmosphericradiative transfer, the HATCH algorithm shows improvementsin many aspects over ATREM. These include better perfor-mance in spectral regions of strong water vapor absorptionand improvements in the treatment of the overlapping of watervapor absorption by COand CH . The automatic spectralcalibration capability has proved to be a promising functionfor HATCH to handle the problematic residual atmosphericfeatures in derived reflectance. It has to be noted, however, thatHATCH assumes Lambertian surfaces, and the adjacent effectis not considered in the model.

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Zheng Qu received the B.S. degree from the Uni-versity of Science and Technology of China, Hefei,China, in 1991, and the M.S. degree from the Instituteof Atmospheric Physics, Chinese Academy of Sci-ences, Beijing, China, in 1994, both in atmosphericphysics, and the Ph.D. degree in atmospheric sciencefrom the University of Chicago, Chicago, IL, in 1999.

He is currently a Research Associate with theDepartment of Earth and Atmospheric Sciences,Purdue University, West Lafayette, IN. He was withthe Center for the Study of the Earth from Space,

Cooperative Institute for Research in the Environmental Sciences, Universityof Colorado, Boulder, and was involved with the atmospheric correction forremotely sensed hyperspectral data. His current research interests includethree-dimensional radiative transfer in the atmosphere, atmospheric correction,and radiation models in the GCM.

Bruce C. Kindel received the B.A. degree fromthe University of Colorado, Boulder, in 1992, witha double major in environmental, population andorganizmic biology and economics.

In 1992, he joined the Center for the Study of Earthfrom Space, Cooperative Institute for Research in theEnvironmental Sciences, University of Colorado. Hiscurrent research interests concern various aspects ofhyperspectral remote sensing including atmosphericcorrection, radiometric and spectral calibration, andfield calibration and characterization methods.

Alexander F. H. Goetzreceived the B.S. degree inphysics, in 1961, the M.S. degree in geophysics, in1962, and the Ph.D. degree in planetary science, in1967, all from the California Institute of Technology,Pasadena.

In 1968, he joined AT&T Bell Laboratories(Bellcomm), Washington, DC, and was involvedwith the Apollo program as Principal Investigator onexperiments on Apollo 8 and 12. In 1970, he joinedthe National Aeronautics and Space AdministrationJet Propulsion Laboratory (JPL), Pasadena, CA, and

moved to earth observations. He has been a Principal Investigator or teammember on Landsats 1, 2, and 7, Skylab, Shuttle (STS-2), and EO-1. In 1980,he was one of the originators of the imaging spectrometry program at JPLout of which came AIS and AVIRIS. In 1985, he joined the faculty of theUniversity of Colorado, Boulder, as Professor as well as Director of the Centerfor the Study of the Earth from Space, Cooperative Institute for Research inEnvironmental Sciences, University of Colorado. He is also a Cofounder andChairman of Analytical Spectral Devices, Inc., Boulder, CO.

the high accuracy atmospheric correction for hyperspectral data (hatch) model

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