Measuring Trace Gases in Plumes From Hyperspectral ... - IEEE Xplore

854

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 42, NO. 4, APRIL 2004

Measuring Trace Gases in Plumes From Hyperspectral Remotely Sensed Data Rodolphe Marion, Rémi Michel, and Christian Faye

Abstract—A method [joint reflectance and gas estimator (JRGE)] is developed to estimate a set of atmospheric gas concentrations in an unknown surface reflectance context from hyperspectral images. It is applicable for clear atmospheres without any aerosol in a spectral range between approximately 800 and 2500 nm. Standard gas by gas methods yield a 6% rms error in H2 O retrieval from Airborne Visible/Infrared Imaging Spectormeter (AVIRIS) data, reaching several tens percent for a set of widespread ground materials and resulting from an simplifying assumption of linear variations of the reflectance model within gas absorption bands and partial accounting of the gas induced signal. JRGE offers a theoretical framework consisting in a two steps algorithm that accounts for sensor characteristics, assumptions on gas concentrations and reflectance variations. It estimates variations in gas concentrations relatively to a standard atmosphere model. An adaptive cubic smoothing spline like estimation of the reflectance is first performed. Concentrations of several gaseous species are then simultaneously retrieved using a nonlinear procedure based on radiative transfer calculations. Applied to AVIRIS spectra simulated from reflectance databases and sensor characteristics, JRGE reduces the errors in H2 O retrieval to 2.87%. For an AVIRIS image acquired over the Quinault prescribed fire, far field CO2 estimate (348 ppm, about 6% to 7% rms) is in agreement with in situ measurement (345–350 ppm) and aerosols yield an underestimation of total atmospheric CO2 content equal to 5.35% about 2 km downwind the fire. JRGE smoothes and interpolates the reflectance for gas estimation but also provides nonsmoothed reflectance spectra. JRGE is shown to preserve various mineral absorption features included in the AVIRIS image of Cuprite Mining District test site. Index Terms—Hyperspectral remote sensing, reflectance, trace gases.

I. INTRODUCTION

C

HARACTERIZING surface and atmospheric properties from hyperspectral imaging spectrometry is of major importance in earth sciences. It has been successfully applied to geological, aquatic, ecological and atmospheric research [1], [2]. Manuscript received April 28, 2003; revised September 25, 2003. R. Marion is with the Département Analyse et Surveillance de l’Environnement, Laboratoire de Détection et Géophysique, Télédétection et Surveillance de l’Environnement (DASE/LDG/TSE), Laboratory of Remote Sensing of the Environment of Commissariat à l’Energie Atomique (CEA), 91680 Bruyères-le-Châtel, France and also with the joint Ecole Nationale Supérieure de l’Electronique et de ses Applications (ENSEA) Université de Cergy–Pontoise (UCP) Centre National de la Recherche Scientifique (CNRS) Image and Signal Processing Laboratory (ETIS), 95014 Cergy-Pontoise, France (e-mail: [email protected]). R. Michel is with the Laboratory of Remote Sensing of the Environment, Commissariat à l’Energie Atomique (CEA), 91680 Bruyères-le-Châtel, France. C. Faye is with the joint Ecole Nationale Supérieure de l’Electronique et de ses Applications (ENSEA) Université de Cergy–Pontoise (UCP) Centre National de la Recherche Scientifique (CNRS) Image and Signal Processing Laboratory (ETIS), 95014 Cergy-Pontoise, France. Digital Object Identifier 10.1109/TGRS.2003.820604

Hyperspectral sensors (e.g., Airborne Visible/Infrared Imaging Spectormeter (AVIRIS), HyMap, Hyperion) are passive earth-looking systems providing radiance images in the solar reflected portion of the electromagnetic radiation spectrum. Generally, they cover a spectral range included in the 400–2500-nm window with a few hundred contiguous bands about 10 nm wide. The nominal pixel size is typically a few meters. Typical, SNRs are a few hundred. As an example, the AVIRIS spectral range is 400–2500 nm, the number of bands is 224, the spectral bands are about 10 nm wide, the spatial resolution is about 20 m and the SNR is between 300 and 800 for the year 1995. The images depend on the sun irradiance, on the atmosphere, on the ground and on the system’s transfer function in a complex way (scattering, absorption, reflection, averaging) leading to a strongly nonlinear pixel (3). Fig. 1 shows a diagram of the hyperspectral observational geometry. One of the major issues of hyperspectral data processing is the joint retrieval of atmospheric gas concentrations and ground reflectance. It is essential not only for studying atmospheric properties but also for ground-based applications requiring accurate atmospheric correction [1], [2]. Several techniques have already been proposed to measure the amount of a particular gas of interest (e.g., H O, CO , O , O ) including narrow/wide ratio (N/W) [3], continuum interpolated band ratio (CIBR) [4], [5], atmospheric precorrected differential absorption (APDA) technique [6], and curve-fitting procedures [7]. These methods typically yield the total water vapor content with an accuracy of about 6% root mean square (rms) from AVIRIS data. Accuracy may decline to more than several tens percent when the ground reflectance varies nonlinearly with wavelength within gas absorption bands [6] or when other species than water are considered [8]–[10]. A more accurate estimation of gas amounts is generally required to investigate a wider range of phenomena including forest fires, volcanoes, industrial pollution. As an example, the total CO column abundance variation induced by the Quinault prescribed fire (see Section VI-B1) is less than 5% and cannot easily be measured from the mentioned methods. The main objective of this paper is to provide a comprehensive mathematical framework for the joint retrieval of gas absorber amounts and ground reflectance from hyperspectral data. We consider an aerosol-free atmosphere (Rayleigh atmosphere) and standard ground temperatures in the spectral range between approximately 800 and 2500 nm. Further developments of the method to overcome the physical limitations of this paper (e.g., aerosols effects, spectral range) are discussed in the conclusion. Hereafter, we first present the useful principles of imaging spectrometry yielding the equation of the image. We then dis-

0196-2892/04$20.00 © 2004 IEEE

MARION et al.: MEASURING TRACE GASES IN PLUMES

855

Fig. 1. Hyperspectral data collection. Sun-emitted electromagnetic wave L () interacts with atmospheric molecules and particles through absorption and () and atmospheric radiance L (). Radiance is scattering processes T (). At-sensor radiance L() is the sum of ground-reflected radiance L ) for spectral channel i. This signal includes spectral features of effluent plume n . band-averaged by the instrument yielding measured signal (L

cuss the potential and the limitations of the existing methods, especially when the unknown surface reflectance varies nonlinearly with wavelength within gas absorption bands. Afterward, we propose an enhanced method, named the joint reflectance and gas estimator (JRGE). It is dedicated to the measurement of trace gases within a plume corresponding to variations relatively to a given standard atmosphere model. The method takes into account all the information about gases contained in the data and yields optimized estimates. It is based on a cubic smoothing spline like surface reflectance estimator and nonlinear radiative transfer calculations. A general error model is then developed. JRGE is finally applied to both simulated and field AVIRIS data.

II. IMAGING SPECTROMETRY A. Radiative Transfer Considerations From the viewing geometry schematically shown in Fig. 1, the monochromatic radiance at the input of a downward-looking sensor can be written in a simplified form as [11]

of the atmosphere) containing gaseous species in addition to the standard atmospheric state, the at-sensor radiance becomes

(2) , is the integrated density over the plume where height of the th species, is a known geometrical parameter depending on the viewing angles (i.e., sun and sensor locations), is the known absorption coefficient (altitude-dependant) of the th species, and is the total plume is also a functransmittance. The path-scattered radiance tion of the unknown gas densities. The total atmospheric content where in the th species can be written represents the standard atmospheric density and is the unknown excess due to the plume. A hyperspectral sensor performs a band-averaging of the incoming radiance field at each channel ( is the total number of channels of the imaging system). This measure, corrupted by the additive noise , is then equal to

(1) is the radiance at the imaging where is the wavelength, is the surface reflectance, is spectrometer, the solar radiance above the atmosphere, is the total atmospheric transmittance equal to the product of the atmospheric transmittance from the sun to the earth’s surface and that from the earth’s surface to the sensor according to is the the Beer–Bouguer–Lambert law [12], and path-scattered radiance (i.e., the backscattered atmospheric radiance not reflected by the ground). In the presence of a plume located just above the ground (typically in the first kilometer

(3) where is the normalized instrument’s transfer function for channel . The spectral atmospheric features are typically decades narrower than the instrument channel width (e.g., nm wide and H O absorption bands near 1 m are about AVIRIS spectral channel width is about 10 nm). It is, thus, noteworthy that the multiplicative operator of monochromatic

856


atmospheric terms in (3) does not commute with the instrument’s averaging operator. According to the properties of surface reflectance spectra (see Section IV-A) and by defining , the measured radiance of a pixel for channel can be written

Hereafter,

we propose a method to estimate the , from (5) for which the , are , are known, and unknown, and are computed from a standard atmosphere model, and a noise model is available (see Section IV-A). III. POTENTIAL AND LIMITS OF CONVENTIONAL METHODS

(4) where

is the mean ground reflectance over the channel .

B. Influence of the Plume Gases Radiance

on the Path-Scattered

In the 400–2500-nm spectral region, there are typically seven atmospheric gases that produce observable absorption features [13]. These gases are water vapor (H O), carbon dioxide (CO ), ozone (O ), nitrous oxide (N O), carbon monoxide (CO), methane (CH ), and oxygen (O ). In the considered spectral range, ozone does not have observable absorption is not dependent on features. The path-scattered term the surface reflectance but is sensitive to the atmospheric composition, in particular aerosol and water vapor contents. At low ground reflectance, it is the major contributor to the total radiance, whereas at higher reflectance the direct reflected solar radiation dominates [6], [7]. Erroneous gas contents are retrieved if one neglects this term because it acts as a ground reflectance independent offset to the direct reflected term. depends on as noted in (2), drastically Theoretically, increasing the complexity of the model. In our approach, we determine an excess of gases due to the plume and not the total can be considered indeatmospheric content so that pendent on . To validate this assumption, the path radiance was computed with the radiative transfer code MODTRAN4 [14] in the single-scattering mode and spectrally averaged using AVIRIS radiometric properties for the year 1995 (see Section IV-A). The atmospheric state was aerosol-free US 1976 Standard Atmosphere Model and the columnar water vapor was 1.4 g/cm . The sun was at 40 and the target at sea level observed according to a nadir viewing from a sensor in space. An excess of gas was added in the first atmospheric layer for the six species listed above corresponding to typical forest fires in the emissions [15]–[17]. The maximum variation path radiance was obtained for H O (for a variation of the total column equal to about 18%) and was about six times below the noise level. Concentrations corresponding to physical phenomena for typical atmospheric gases yield a variation in the path radiance below the noise for current sensors indicating that such excesses cannot be retrieved from the path radiance itself. It is noteworthy that no excess of gas can be recovered from radiance data for pixels with near zero reflectance. The measured radiance of a pixel for channel can thus be written as

(5)

Existing methods have extensively been applied to hyperspectral data, especially AVIRIS images, to retrieve the water vapor column [18] and with less accuracy the ozone [8], the oxygen [9], and the carbon dioxide [10] columns. For a comparison between these methods, see for example [4] (for N/W and CIBR) and [6] (for CIBR and APDA). These techniques only take into account several, eventually one, measurement channels within gas absorption bands (ratioing techniques) and/or they do not systematically consider all the absorption bands (ratioing and curve-fitting techniques), and thus they do not take benefit from the whole information available. They usually do not deal with overlapping absorption bands (e.g., CO and H O bands near 2000 nm). These limitations may yield an error far greater than 10% in H O column density retrieval over some specific ground materials (see [6] and [19] for a validation of APDA over 379 reflectance spectra). A. Effect of Nonlinearity of the Reflectance Absorption Bands

Within Gas

The reflectance spectrum of enstatite (sample IN-10B, particle size 45–125 m) was chosen as a reference (from the Jet Propulsion Laboratory (JPL), Pasadena, CA, spectral library) for demonstration purpose because of the high error of standard methods for this material. A radiance pixel was simulated using MODTRAN4 in the single-scattering mode with the following entries: aerosol-free US 1976 Standard Atmosphere Model with an excess of water vapor equal to 3500 ppm in the first atmospheric kilometer (to simulate a vapor plume), solar zenith angle of 40 , target at sea level and nadir viewing sensor located above the atmosphere. Noise was added to the computed signal using the radiometric characteristics of AVIRIS instrument for the year 1995 (see Section IV-A). We used a three-channel APDA nm FWHM nm technique (reference channels nm FWHM nm, measurement chanand nel: nm FWHM nm) applied to the 940-nm water vapor absorption band [Fig. 2(a)] (FWHM is the full width at half-maximum). APDA first performs a linear interpolation of within absorption bands. This assumption yields an overestimation of reaching about 43% in the center of the 940-nm absorption band leading to an estimated H O excess equal to 12 880 ppm instead of 3500 ppm. It corresponds to a relative error in the first atmospheric layer equal to 268%. This error reported to the total atmospheric H O content is about 41%. This overdetermined value is due to the parabolic shape of enstatite near 940 nm. This demonstrative example illustrates the fact that the usual assumption of linear variations within absorption bands may yield large errors. This of huge amount of error can be reduced by averaging all the water absorption channels between 880 and 1000 nm to form


857

portance for CO retrieval with absorption bands located in low SNR spectral regions. IV. JRGE: THEORETICAL DEVELOPMENTS

(a)

In the following, we propose a comprehensive method that systematically takes into account the whole information of interest included in the data to retrieve gas absorber amounts and ground reflectance. It is based on a mathematical description of the physical characteristics of the signal. The developed algorithm is a two steps algorithm which first estimates the surface reflectance and then the densities of the plume gases. It is of major importance to note here that the obtained interpolated reflectance is only used to better estimate the densities of the gases. Once the atmospheric parameters are retrieved, the surface reflectance is inverted using (5) without smoothing the data and, thus, preserving the surface features (see Section VI-B2). A. Physical Constraints and Assumptions

(b) Fig. 2. (a) H O retrieval around the 940-nm absorption band (gray line) over material enstatite (black line). APDA linear interpolation (black stars) yields overestimation of reflectance and 41% overdetermined H O content. JRGE-proposed method better fits parabolic enstatite shape (white circles) and reduces error on H O to 6% (see text for details). (b) H O and CO overlapping absorption bands near 2000 nm (respectively, white circles and black stars) yield complex radiance pattern (gray line). Contrary to previous standard algorithms, JRGE addresses that point in a simultaneous gases retrieval procedure.

a broad water vapor absorption channel (see Section VI-A1). Unfortunately, this procedure mainly reduces the influence of measurement noise but not the error due to the assumed linear model of the reflectance. B. Effect of Overlapping Absorption Bands Conventional methods generally use the assumption of separated gas absorption bands and estimate each separately. However, absorption bands may overlap [Fig. 2(b)] so that one may be in need for a more comprehensive method retrieving simultaneously the . C. Effect of Noise Conventional ratioing methods use few reference channels located at each side of the absorption bands in order to interpolate the surface reflectance. The interpolation, thus, drastically depends on the noise in these reference channels. They do not benefit from the whole signal to minimize the influence of noise during the reflectance interpolation procedure. This point is generally negligible for H O retrieval but may be of high im-

We consider the following physical constraints and assumptions. • From imaging spectrometry theory [2], surface reflectance spectra do generally not include hyperfine absorption features. For current hyperspectral sensors (e.g., AVIRIS, HyMap, and Hyperion), the surface reflectance can, thus, be considered as a spectrally smooth function of wavelength. This assumption allows: 1) to consider mean reflectance values in each spectral channel in (4) and 2) the construction of the proposed estimator. The validity of this assumption is discussed in Sections V-A and VI-A2. • Estimates of the minimum and maximum values of (respectively, and ) are available. As an exrepresents with ample, the user may suggest that an accuracy of 20%, 30%, or 100% or may give values depending on the studied phenomenon (e.g., forest fire, volcano, industrial plants). This requirement allows the selection of the measurement (or absorption) channels (see Section IV-B). • A noise model is assumed to be available. The total noise on the measured radiance in channel results from two independent noise contributions: 1) the inherent photon noise and 2) the instrument’s noise. The total noise can be modeled by an additive Gaussian white-noise process with zero mean and a standard deviation equal to ; the noises in the different channels are supposed to be statistically independent [20]. The photon noise is estimated from the conversion factor of photons to signal and the instrument’s noise can be defined as the standard deviation of the dark signal measured during the image acquisition ([20] and [21] for AVIRIS sensor specifications) so that an estimate of the noise standard deviation is available for each channel of each pixel. Typical SNR values are greater than 500 over much of the spectral range for 1995 AVIRIS data (between 300 and 800). • Gases of interest are known and characterized by their absorption coefficient , calculated from spectroscopic data obtained in [22].

858


• Terms and are computed using a standard atmosphere model (chosen from the location of the scene) with a line-by-line radiative transfer code before applying sensor’s averaging. B. Channel Selection The proposed method considers three types of channels (Fig. 3). 1) Measurement Channels: Measurement (or absorption) channels are the channels of the imaging system sensitive to variations in the amount of trace gases. First, an equivalent and reflectance is computed from the data (Fig. 3) (5) under the assumption of zero (6) is related to the radiance The associated standard deviation by . Similarly, the minstandard deviation imum and the maximum values of the reflectance (respectively, and ) are computed from the assumed variations and of and (5) (7)

(8)

which represent the envelope of the possible values of the real reflectance (Fig. 3). The measurement channels are then defined . to be those for which 2) Saturated Channels: A channel is considered to be (a factor three is introsaturated if its radiance is below duced in order to diminish the number of outliers). Within the 400–2500-nm spectral region, saturated channels are generally located near 1400 and 1900 nm where H O strongly absorbs. 3) Reference Channels: The channels not selected as measurement or saturated channels are referred to as reference channels. C. Surface Reflectance Estimator This section describes the procedure used to estimate the surface reflectance from the radiance signal. 1) Construction of the Smoothing Spline Estimator: In agreement with physical constraints and assumptions (see of the surface reflectance in Section IV-A), an estimator channel is computed as

(9) where denotes the are weighting coefficients, is a regusecond derivative of conlarization parameter discussed in Section IV-C2, and tains all the values. The first term in (9) controls the fidelity to the data and the second term the global smoothness of the estimator. is called a smoothing spline estimator and is known

Fig. 3. Spectral channels definition and selection. Standard atmospheric parameters and physical assumptions (see text for details) yield equivalent, minimum, and maximum estimates of reflectance from radiance signal ~ ) variations (respectively, black stars, and gray shape). (~ below noise define reference channels. Radiance below noise yields saturated channels. Gas-dependant channels are referred to as measurement channels. JRGE interpolation (white circles) constraints depend on channel type.

0

to be a natural cubic spline with knots at the observation points [23]–[27]. A cubic smoothing spline with knots in is a piecewise cubic polynomial where pieces join -continuously at the points , i.e., satisfies the following conditions: , where • On each interval and is a polynomial of degree . is -continuous on . • is called natural if it is linear on the end • In addition, and . intervals The weights used to estimate the reflectance are given by the following: • in the reference channels (in concordance with weighted least squares theory); in the measurement and saturated channels. • Those weights allow to smooth the noise on within the reference channels and to interpolate the reflectance elsewhere. Equation (9) can be simplified if the natural cubic spline is represented with its value-second derivative form [28]. Let de(the superscript is matrix note the vector the vector (by transposition) and ). definition, a natural cubic spline has Define for , and let be in size with entries a tridiagonal matrix , and a tridiagonal matrix in size with entries . and specify a natural cubic spline if and only if the condition is satisfied and then (10) By substituting matrix form as

by

in (10), (9) can be rewritten in (11)


where lution of (11) yields

and

diag

859

. Reso-

Thus, Newton’s method can be used with increments in given by

(12) By defining (6) that

diag

(19)

, we can write from where

and

Then, by defining , the surface reflectance estimator can be expressed as a function of the measured radiance and the path radiance by

From [24], the matrix is positive definite and it is is also a positive defeasy to show that is a strictly inite matrix which induces that the function ; it guarantees the global converincreasing function for gence to the root . Setting between five and 30 experimentally yields a rapid convergence (typically five iterations) of the method when considering AVIRIS data. Note that is chosen according to the noise level in the absorbing regions, and thus it is not adapted to the entire spectral domain (see Section VI-B2 and the conclusion for a discussion).

(13) D. Gas Concentrations Estimator We obtain a surface reflectance estimator for a given value of the smoothness parameter . 2) Choice of the Smoothness Parameter : controls the tradeoff between the fidelity to the data and the global smoothness of the reflectance estimator. If it is too small, the model fits the noise and if it is too large then some of the original signal is known and may be damped. In our study, the noise level then the regularization parameter can be determined using the discrepancy principle [29]. Statistically, the weighted residual sum of squares between the data and the true surface reflectance should be equal to

In this section, we compute simultaneously the estimates of the gases of interest as (20) with

(14) For the surface reflectance estimate , the weighted residual sum of squares is (15) is chosen to minimize considering (15) we have

. By using the chain rule and by

where in the measurement channels and elsewhere. We use a Newton’s method for minimization to solve estimated vector . Indeed, (20) for the this method is particularly adapted because (20) is strongly nonand because the Jacobian and the linear toward the Hessian matrices (respectively, and ) can be comvector of increments is given puted analytically. The by (21)

(16) By multiplying (12) by ating with respect to we obtain

where

and

are equal to

and by differenti(22)

.. . (17)

Setting

then gives .. .

(18) where the minimization with respect to is equivalent to the minimization with respect to . This scheme ensures the positivity of and also permits to take a large range of values.

.. .

.. .

(23)

Starting with , the process is iterated until convergence leads to variis reached, that is when the added increment ations in the concentrations of the gases lower than a tolerance. Note that in practice, only the measurement channels are retained in the calculation.

860


V. ERROR ANALYSIS

matrices

We define the

For comparison with standard methods which estimate the in the total gas column, we define the retrieval error gaseous species relatively to the total amount by

and

.. .

.. .

.. .

.. .

as

.. .

(30)

(24) This overall error can be decomposed into three main sources of errors affecting the retrieval algorithm. We have labeled these as the algorithmic error, the noise measurement error, and the model error. The algorithmic error is due to the algorithm only, the noise measurement error is due to the physical noise on the data and the model error is induced by uncertainties in , the instrument’s the model parameters (e.g., response function, the instrument’s calibration, the radiative transfer model, etc.). Those errors are described below and evaluated in Section VI-A2.

Finally, the required value of the first derivative of

(31)

is given by (32)

can then be computed from (27), and the noise measurement error in the gaseous species is defined by

A. Algorithmic Error

(33)

The algorithmic error in the gaseous species is systematic and results from the assumption of smoothness of the reflectance and from the interpolation procedure. It is defined as (25) and it will be evaluated for unnoisy simulated signals. B. Noise Measurement Error covariance matrix In this section, we estimate the of the resulting random error in the estimate of the densities covariance matrix of the as a function of the known noise on the measured radiance . We define the function by (26) A first-order expansion of

.. .

about

yields

C. Model Error It is noteworthy to recall here that this paper does not deal with the effect of aerosols and high thermal emission of the ground that may yield significant bias in the estimates of the (see Section VI-B1). Errors in the instrument spectral calibraand in tion and gas line parameters may also yield errors in the estimate of the reflectance (Fig. 6). Those errors are instrument and model dependent, and their treatment requires a prior analysis not addressed in the present study. Lack of description of those uncertainties may yield a shift in the smoothing parameter resulting in a systematic error in the estimated gas concentrations and reflectance spectra. VI. VALIDATION JRGE has been validated using both simulated data and AVIRIS images acquired during the 1994 Quinault prescribed fire and over Cuprite Mining District in 1997. A. Validation on Simulated Data

(27) where is the matrix of the first partial derivative of the function with respect to . From Section IV-D, the vector minimizes the least squares measure (28) where is an implicit function. From (13) and (26) and by differentiating , we obtain

(29)

1) Comparison With APDA for Water Vapor Retrieval: For this comparison, the JPL and the Johns Hopkins University (JHU), Baltimore, MD, spectral libraries were employed. These databases consist of measured reflectance spectra for 430 mineral samples (from JPL), at which we added 41 soil samples, 45 manmade samples, four vegetation samples, and five water samples (from JHU). Radiance spectra were simulated using MODTRAN4 in the following conditions: aerosol-free US 1976 Standard Atmosphere Model with an excess of water vapor equal to 3500 ppm in the first atmospheric kilometer (to simulate a vapor plume), solar zenith angle of 40 , a target at sea level, and a nadir viewing sensor located above the atmosphere. Radiances were then averaged according to the AVIRIS instrument specifications for the year 1995 and related system noise was added to the computed signals. Retrieval of the water vapor content was performed with a three-channel APDA nm FWHM nm technique (reference channels


(a)

861

(b)

(c)

Fig. 4. AVIRIS images of Quinault prescribed fire (47.32 N, 124.27 W, AVIRIS 092194, run 10, scene 1, flight altitude: 20 km). (a) = 568:65 nm. West–northwest plume includes high concentrations of aerosols with typical high radiance value. (b) CO concentrations map computed for pixels with 0:1 within CO absorption bands. (Area A) Pixels not affected by burn. (Area B) Beach section (sand only) not affected by burn. (Area C) reflectance Beach section (sand only) under smoke plume. (Area D) High concentrations of aerosols near fire. (Black area) Algorithm not applied. (c) = 2057:50 nm. Near-infrared image within CO absorption band. Slight radiative effect of aerosols within plume and hot fire pixels are discernible (see text for details).

TABLE I COMPARISON BETWEEN APDA AND JRGE FOR WATER VAPOR RETRIEVAL. JRGE SIGNIFICANTLY REDUCES ERROR IN H O ESTIMATE A SET OF WIDESPREAD SURFACE MATERIALS YIELDING APDA, PARTICULARLY LARGE ERRORS [6], [19]. JRGE ENHANCEMENT FACTOR IS ABOUT TWO FOR WHOLE DATABASE (SEE TEXT FOR DETAILS)

and

nm FWHM nm, measurement channel: nm FWHM nm), a broad-channel APDA technique (obtained by averaging all the water vapor absorption channels between 880 and 1000 nm), and the proposed JRGE method. Results are reported in Table I. JRGE and APDA yield compatible results. For the seven materials yielding the largest errors for APDA, the spectral shape of the reflectance within the 940-nm water vapor absorption band is fitted by the JRGE method [Fig. 2(a)] with an accuracy of a few percent and the quality of the resulting determination of water vapor content is enhanced by a six average factor. For the whole database, the accuracy of JRGE for water vapor retrieval is 2.87%, yielding a 2 enhancement factor. 2) Error Analysis: The effects of algorithmic error and noise measurement error on the determination of water vapor and carbon dioxide concentrations have been investigated by simulation (Table II). For water vapor, we used the simulation described above and for carbon dioxide an excess of 525 ppm was added to ambient conditions corresponding to the same variation of the total column as for water vapor (i.e., about 18%). For each molecule, two series of radiance spectra were simulated, one with additive

FOR

TABLE II ANALYSIS OF ERRORS (JRGE). ERRORS ESTIMATED FROM (25) AND (33) USING JPL AND JHU SPECTRAL LIBRARIES. DATABASE RMSE IS STANDARD DEVIATION OF RETRIEVAL ERROR (24)

noise and another one without noise. We used (33) to compute on the noisy radiances and (25) to compute on the unnoisy radiances. Algorithmic error and noise measurement error are closed so that no significant improvement may be obtained from further algorithmic developments. Quadratic summing of errors are consistent with uncertainties estimated with both simulated and real data (Table I and Section VI-B1). Considering the whole database the estimated accuracy of JRGE is equal to 2.87% for H O and 5.14% for CO . The method yields relatively better results for H O because of a better SNR within H O absorption bands and because the main

862


TABLE III CO ESTIMATION AND COMPARISON WITH IN SITU MEASUREMENT (SEE FIG. 4 FOR AREAS LOCATION)

(a)

Fig. 5. AVIRIS image ( = 1211:33 nm) of Cuprite Mining District (37.20 N, 117.62 W, AVIRIS 061997, run 2, scene 4, flight altitude: 21 km) and location of extracted pixels (see text for details).

CO absorption bands near 2000 nm are partially overlapped by a saturated H O band (Fig. 3) limiting the accuracy of the reflectance interpolation in this region.

(b)

B. Validation on AVIRIS Data 1) Carbon Dioxide Retrieval for the 1994 Quinault Fire Smoke Plume: The proposed method has been applied to an AVIRIS image [Fig. 4(a)] acquired on September 21, 1994, during the Quinault prescribed fire (47.32 N, 124.27 W, AVIRIS 092194, run 10, scene 1, flight altitude: 20 km). This image is part of the SCAR-C (Smoke Cloud and Radiation—California) experiment conducted in September 1994 in the Pacific Northwest of the United States. A detailed description of the campaign is given by [15] and [30]. At the time of image acquisition, in situ measured ambient CO column was in the range 345–350 ppm [38] and the excess due to the burn in the 400-m thick plume decreased downwind from about 120–40 ppm in the image [15]. JRGE has been applied to pixels having an average reflectance value within CO absorption bands greater or equal to 0.1 [Fig. 4(b)] because of the low SNR is this spectral region and fire pixels were excluded. The expected accuracy is about 5% to 6% rms (see Section VI-A2). The following four areas are obtained from the estimated CO concentrations map: • Area A: pixels not affected by the burn, • Area B: beach section (sand only) not affected by the burn, • Area C: beach section (sand only) under the smoke plume (located about 2 km downwind the fire), • Area D: area close to the fire with large CO underestimation.

(c) Fig. 6. Theoretical (from JPL spectral library), smooth interpolated and retrieved reflectance spectra for pixels mainly composed of (a) muscovite (pixel A), (b) kaolinite (pixel B), and (c) alunite (pixel C). Sharp features near 940 and 1140 nm may be due to both errors in AVIRIS wavelength calibrations and incorrect water vapor line parameters used in H O transmittance calculations (see Section V-C).

Retrieved values are reported in Table III. Values for area A are in agreement with ground truth and standard deviation is about 6% to 7%. Comparison of values for areas B and C (same ground material) shows an underestimation of the CO column equal to about 5.35% due to aerosols. Area D corresponding to high densities of aerosols [Fig. 4(a)] shows a large CO under-


estimation. Areas C and D include heavy smoke and clouds. As solar radiation near 2000 nm cannot go through clouds it is not possible to retrieve CO for those areas. A slight radiative effect of aerosols and hot fire pixels [Fig. 4(c)] are discernible in the near-infrared CO absorption region. 2) Surface Reflectance Retrieval at Cuprite Mining District: The second validation of JRGE has been conducted on an AVIRIS image (Fig. 5) of Cuprite Mining District acquired on June 19, 1997, (37.20N, 117.62W, AVIRIS 061997, run 2, scene 4, flight altitude: 21 km) under very clear atmospheric conditions. The objective was to demonstrate the effectiveness of the method to retrieve broad and fine surface mineral absorption features as well as to verify that no artificial features are added to the derived surface reflectance spectra. The area of Cuprite in southwestern Nevada has been widely used as a test case by the hyperspectral remote sensing community and its geologic and alteration properties have been mapped in detail (e.g., [31] and [32]). JRGE has been applied to retrieve water vapor amounts and surface reflectance spectra. Three pixels have been extracted (Fig. 5) corresponding to pixels mainly composed of muscovite (pixel A), kaolinite (pixel B), and alunite (pixel C). Results are reported in Fig. 6(a)–(c) where the interpolated for gas estimation and nonsmoothed reflectance obtained from (5) are shown together with theoretical values (from JPL spectral library). The interpolated reflectance near water vapor absorption bands does not exhibit any water residual or artificial features. It is used to derive accurate gas absorber amounts. Once the atmospheric parameters are retrieved, the surface reflectance spectra are inverted using (5) without smoothing the data and, thus, preserving the surface features. Hence, JRGE recovers the broad muscovite absorption feature in the 800–1200-nm range Fig. 6(a), the fine koalinite doublet Fig. 6(b) and alunite absorption features Fig. 6(c) in the 2000–2500-nm range. Note that the interpolated reflectance has no physical significance far from the water vapor absorption region because the smoothness is chosen according to the noise level in this parameter region, and thus it is not adapted to other wavelengths (see next section). However, in the presented cases, no surface absorption features are smoothed out because is small due to the high SNR in the water vapor absorbing region. VII. CONCLUSION A new theoretical framework for the retrieval of both ground reflectances and trace gas amounts from hyperspectral remotely sensed data has been presented. The method yields an enhancement factor equal to about two in H O retrieval accuracy on simulated data in comparison with conventional methods, and the surface absorption features are successfully recovered from real AVIRIS data. It can, thus, be used to enhance existing atmospheric correction techniques for ground-based applications (e.g., geology). The total CO column has been recovered from AVIRIS data with an accuracy of about 6% to 7% for pixels without any aerosol and with a reflectance greater or equal to 0.1 within gas absorption bands (better accuracy should be achieved from images acquired at lower altitude and with better SNR). The

863

obtained accuracy would be enough to map the CO excess induced by the fire [15], but the signal is still masked by the aerosol smoke that yields an underestimation of the gas concentration. Further developments should, thus, allow the monitoring of numerous geophysical phenomena with relatively low gas emission. The operational use of the method is limited by its development in an aerosol-free atmosphere. A more realistic radiative transfer model [33]–[35] should be used in a total column retrieval approach to take account of multiple scattering, aerosol, and adjacency effects and, thus, in allowing JRGE to be applicable below 800 nm under realistic atmospheric conditions. Researchers interested in the estimation of a smooth reflectance spectra over the entire spectral range (spectral polishing) and not only around gas absorption bands may consider JRGE as a theoretical basis that could be expanded with the use of multiple smoothness parameters [36], [37]. ACKNOWLEDGMENT The authors would like to thank the anonymous reviewers for their useful comments. REFERENCES [1] P. J. Curran, “Imaging spectrometry—Its present and future Rôle in environmental research,” in Imaging Spectrometry—A Tool for Environmental Observations, J. Hill and J. Mégier, Eds. Brussels, Belgium: ECSC-EEC-EAEC, 1994, pp. 1–23. [2] A. F. H. Goetz, “Imaging spectrometry for earth remote sensing,” in Imaging Spectroscopy: Fundamentals and Prospective Applications, F. Toselli and J. Bodechtel, Eds. Brussels, Belgium: ECSC-EEC-EAEC, 1992, pp. 1–19. [3] R. Frouin, P.-Y. Deschamps, and P. Lecomte, “Determination from space of atmospheric total water vapor amounts by differential absorption near 940 nm: Theory and airborne verification,” J. Appl. Meteorol., vol. 29, pp. 448–460, 1990. [4] V. Carrère and J. E. Conel, “Recovery of atmospheric water vapor total column abundance from imaging spectrometer data around 940 nm—Sensitivity analysis and application to Airborne Visible/Infrared Imaging Spectrometer (AVIRIS) data,” Remote Sens. Environ., vol. 44, pp. 179–204, 1993. [5] Y. J. Kaufman and B.-C. Gao, “Remote sensing of water vapor in the near IR from EOS/MODIS,” IEEE Trans. Geosci. Remote Sensing, vol. 30, pp. 871–884, Sept. 1992. [6] D. Schläpfer, C. C. Borel, J. Keller, and K. I. Itten, “Atmospheric precorrected differential absorption technique to retrieve columnar water vapor,” Remote Sens. Environ., vol. 65, pp. 353–366, 1998. [7] B.-C. Gao and A. F. H. Goetz, “Column atmospheric water vapor and vegetation liquid water retrievals from airborne imaging spectrometer data,” J. Geophys. Res., vol. 95, no. D4, pp. 3549–3564, 1990. [8] D. Schläpfer, J. Keller, and K. I. Itten, Imaging Spectrometry of Tropospheric Ozone and Water Vapor, E. Parlow, Ed. Rotterdam, The Netherlands: A. A. Balkema, 1996, pp. 439–446. [9] R. O. Green, D. A. Roberts, and J. E. Conel, “Characterization and compensation of the atmosphere for the inversion of AVIRIS calibrated radiance to apparent surface reflectance,” in Proc. 6th Annu. JPL Airborne Earth Science Workshop. Pasadena, CA, 1996, pp. 136–146. [10] S. M. De Jong and T. G. Chrien, “Mapping volcanic gas emissions in the mammoth mountain area using AVIRIS,” in Proc. 6th Annu. JPL Airborne Earth Science Workshop. Pasadena, CA, 1996, pp. 75–80. [11] W. Esaias, “Earth Observing System,” NASA, Washington, DC, Instrument Panel Rep., vol. IIb, 1986. [12] K. N. Liou, An Introduction to Atmospheric Radiation. New York: Academic, 1980, vol. 26. [13] B.-C. Gao, K. H. Heidebrecht, and A. F. H. Goetz, “Derivation of scaled surface reflectances from AVIRIS data,” Remote Sens. Environ., vol. 44, pp. 165–178, 1993.

864


[14] F. X. Kneizys, L. W. Abreu, G. P. Anderson, J. H. Chetwynd, E. P. Shettle, A. Berk, L. S. Bernstein, D. C. Robertson, P. Acharya, L. S. Rothman, J. E. A. Selby, W. O. Gallery, and S. A. Clough, “The MODTRAN 2/3 Report and LOWTRAN 7 MODEL,” Ontar Corp., North Andover, MA, 1996. [15] P. V. Hobbs, J. S. Reid, J. A. Herring, J. D. Nance, R. E. Weiss, J. L. Ross, D. A. Hegg, R. D. Ottmar, and C. Liousse, “Particle and trace-gas measurements in the smoke from prescribed burns of forest products in the pacific northwest,” in Biomass Burning and Global Change, J. S. Levine, Ed. Cambridge, MA: MIT Press, 1996, vol. 2, pp. 697–715. [16] J. D. Nance, P. V. Hobbs, and L. F. Radke, “Airborne measurements of gases and particles from an Alaskan wildfire,” J. Geophys. Res., vol. 98, no. D8, pp. 14 873–14 882, 1993. [17] R. C. Harriss, G. W. Sachse, J. E. Collins, J. L. Wade, K. B. Bartlett, R. W. Talbot, E. V. Browell, L. A. Barrie, G. F. Hill, and L. G. Burney, “Carbon monoxide and methane over Canada: July–August 1990,” J. Geophys. Res., vol. 99, no. D1, pp. 1659–1669, 1994. [18] R. O. Green, V. Carrère, and J. E. Conel, “Measurement of atmospheric water vapor using the Airborne Visible/Infrared Imaging Spectrometer,” in Proc. Image Processing. Sparks, NV, 1989, pp. 31–44. [19] C. C. Borel and D. Schläpfer, “Atmospheric pre-corrected differential absorption techniques to retrieve columnar water vapor: Theory and simulations,” in Proc. 6th Annu. JPL Airborne Earth Science Workshop. Pasadena, CA, 1996, pp. 13–21. [20] R. O. Green, J. E. Conel, J. S. Margolis, C. Chovit, and J. Faust, “In-flight calibration and validation of the Airborne Visible/Infrared Imaging Spectrometer (AVIRIS),” in Proc. 6th Annu JPL Airborne Earth Science Workshop. Pasadena, CA, 1996, pp. 115–126. [21] G. Vane, W. M. Porter, H. T. Enmark, S. A. Macenka, M. P. Chrisp, T. Chrien, L. Steimle, G. C. Bailey, D. C. Miller, J. S. Bunn, R. E. Steinkraus, R. W. Hickok, J. H. Reimer, J. R. Heyada, S. C. Carpenter, W. T. S. Deich, and M. Lee, “Airborne Visible/Infrared Imaging Spectrometer (AVIRIS),” NASA/JPL, Pasadena, CA, Tech. Rep. 87-38, Nov. 1987. [22] L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J.-Y. Mandin, J. Schroeder, A. Mccan, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, and P. Varanasi, “The Hitran molecular spectroscopic database and hawks (Hitran atmospheric workstation): 1996 edition,” J. Quant. Spectrosc. Radiat. Transf., vol. 60, no. 5, pp. 665–710, 1998. [23] C. H. Reinsch, “Smoothing by spline functions,” Numer. Math., vol. 10, pp. 177–183, 1967. [24] C. DeBoor, A Practical Guide to Splines. New York: Springer-Verlag, 1978. [25] G. Wahba, “Smoothing noisy data with spline functions,” Numer. Math., vol. 24, pp. 383–393, 1975. [26] G. Kimeldorf and G. Wahba, “A correspondence between Bayesian estimation on stochastic processes and smoothing by splines,” Annu. Inst. Statist. Math., vol. 41, pp. 495–502, 1970. [27] G. Wahba, “Improper priors, spline smoothing, and the problem of guarding against model errors in regression,” J. R. Statist. Soc., vol. 40, no. B, 1978. [28] P. J. Green and B. W. Silverman, Nonparametric Regression and Generalized Linear Models, London, U.K.: Chapman & Hall, 1994. [29] H. W. Engl, M. Hanke, and A. Neubaur, Regularization of Inverse Problems. Amsterdam, The Netherlands: Kluwer, 1996. [30] Y. J. Kaufman, L. A. Remer, R. D. Ottmar, D. E. Ward, R.-R. Li, R. Kleidman, R. S. Fraser, L. Flynn, D. McDougal, and G. Shelton, “Relationship between remotely sensed fire intensity and rate of emission of smoke: SCAR-C experiment,” in Biomass Burning and Global Change, J. S. Levine, Ed. Cambridge, MA: MIT Press, 1996, vol. 2, pp. 685–696. [31] M. J. Abrams, R. P. Ashley, A. F. H. Goetz, and A. B. Kahle, “Mapping of hydrothermal alteration in the Cuprite mining district, Nevada, using aircraft scanner images for the spectral region 0.46–2.36 m,” Geology, vol. 5, pp. 713–718, 1977. [32] R. P. Ashley and M. J. Abrams, “Alteration mapping using multispectral images—Cuprite Mining District Geological Survey Esmeralda County,” USGS, Sioux Falls, SD, Open File Rep. 80-367, 1980.

[33] S. Chandrasekhar, Radiative Transfer. New York: Dover, 1960. [34] D. Tanré, M. Herman, P. Y. Deschamps, and A. de Leffe, “Atmospheric modeling for space measurements of ground reflectances, including bidirectional properties,” Appl. Opt., vol. 18, no. 21, pp. 3587–3594, 1979. [35] D. Tanré, M. Herman, and P. Y. Deschamps, “Influence of the background contribution upon space measurements of ground reflectance,” Appl. Opt., vol. 20, no. 20, pp. 3676–3684, 1981. [36] C. Gu and G. Wahba, “Minimizing GCV/GML scores with multiple smoothing parameters via the Newton method,” J. Sci. Stat. Comput., vol. 12, no. 2, pp. 383–398, 1991. [37] S. N. Wood, “Modeling and smoothing parameter estimation with multiple quadratic penalties,” J. R. Statist. Soc. B, vol. 62, no. 2, pp. 413–428, 2000. [38] P. V. Hobbs, private communication.

Rodolphe Marion was born in Paris, France, in 1976. He received the Ing. degree in electronics engineering in 2000 from Ecole Nationale Supérieure de l’Electronique et de ses Applications (ENSEA), Cergy-Pontoise, France. He is currently pursuing the Ph.D. degree at the Laboratory of Remote Sensing of the Environment of Commissariat à l’Energie Atomique (CEA), Bruyères-le-Châtel, France, and at the joint ENSEA-UCP-CNRS Image and Signal Processing Laboratory (ETIS), Cergy-Pontoise, France, in the field of hyperspectral data analysis. His topics of interest include research and teaching in digital image and signal processing as well as new methodological developments for hyperspectral imagery.

Rémi Michel received the Ing. degree and the M.S. degree from Ecole Supérieure d’Optique (Sup’Optique), Orsay, France, in 1993, and the Ph.D. degree from the University of Orsay, in 1997. His research interests focus on remote sensing of crustal deformation, INSAR, optical subpixel correlation, and hyperspectral imagery.

Christian Faye was born in Paris, France, in 1953. He graduated from Ecole Nationale Supérieure de l’Electronique et de ses Applications (ENSEA), Cergy-Pontoise, France, in 1976, received the M.Sc. degree in information processing in 1977 and the Ph.D. degree in physics in 1986, both from the University of Orsay, Orsay, France. In mid-1977, he joined the Central Research Laboratory of the Thomson-CSF company (now Thales), Corbeville, France, for three years, where he took part in the development of the recordable optical disk. He then worked for five years in the Aeronautics division of the SAGEM company simulating advanced aircraft systems. In 1989, joined ENSEA as an Associate Professor in physics, where he is conducting his research activity in the joint ENSEA-UCP-CNRS Image and Signal Processing Laboratory (ETIS). In 1998, he became the Head of the International Relations of ENSEA. His current research topics include medical and industrial gamma imagery as well as remote sensing, and more generally, multiimage and multisignal processing applied to inverse problems in physics. Dr. Faye is a member of the French Optical Society and European Physical Society.