recise knowledge of atmospheric transmission andcattering is gaining growing relevance for obtainingccurate surface reflectance spectra from aerospaceeasurements.1 Retrieved water vapor abundance
s often used to remove the related absorption fea-ures from the radiance reaching the sensor and evenor investigating the greenhouse effect and the en-rgy balance on the ground. Aerospace remote sens-ng of atmospheric water vapor content may beerformed with a passive microwave sensor for whichhe retrieval algorithms require data gathered overater surfaces2; with a thermal infrared sensor op-rating over land under clear-sky conditions, a cir-umstance in which retrieval accuracy is limited byhe assumed surface temperature and emissivity3; ory measurement of the solar radiation reflected by aand surface in the visible and near-infrared spectralegions.4 In fact the retrieval of water vapor contentver inland waters and the open sea shows strongnaccuracies because of the low reflectance of these
The authors are with the Institute of Applied Physics, “Nelloarrara,” Consiglio Nazionale delle Ricerche, Via Panciatichi 64,0127 - Florence, Italy. A. Barducci’s e-mail address [email protected] 11 December 2003; revised manuscript received 12
aters, which causes the measured signal to be dueainly to aerosol scattering. Measurements over
louds, which show small spectral variation in reflec-ance, are hindered by changes in the penetrationepth of the incoming solar radiation.Following a spectroscopic approach, we developed a
ew mathematical method for quantitative retrievalf vertically integrated water vapor content, largelyn the lower part of the troposphere. The algorithmas used to process both radiance spectra simulatedith the MODTRAN4 radiative transfer code andyperspectral images collected with the Airborneisible-Infrared Imaging Spectrometer �AVIRIS�ver the Cuprite mining district in southwest Ne-ada. In Section 2 we discuss the details of the pro-osed mathematical method and an additionalmpirical method to perform H2O retrievals from lab-ratory measurements obtained with the VIRS-200maging spectrometer. In Section 3 experimentalesults are compared with numerical simulations.ection 4 is devoted to conclusions and plans for fu-ure developments.
. General Description of the Algorithm
he radiance measured by a downlooking imagingpectrometer can be written as the sum of the atmo-pheric radiance �path radiance� and the directlyransmitted radiance that emerge from the observedarget.5,6 In the visible and near-infrared parts ofhe electromagnetic spectrum the measured radiance
Ll
wLtosdiScteia
sbpio
cpF
drsaniau8tm
rsiabttmsaewa�bttTa
Hemat
Fcvv of th
�k� observed in the kth spectral channel at a fixedocation obeys the following equation:
L�k� � � Ls��, ��Sk���d�
� ��Lpath��, �� � ���, ��E��, ��cos �
�
� exp����sec ���Sk���d�,
k � 1. . .N , (1)
here Ls��, �� is the at-sensor spectral radiance,path��, �� is the atmospheric path radiance, E��, �� is
he at-ground irradiance, ���� is the optical thicknessf the plane-parallel atmospheric slab from ground toensor, ���� is the surface reflectance, � is the viewingirection �the angle between the nadir and the view-ng direction�, � is the zenith distance of the Sun, andk��� is the spectral sensitivity of the kth spectralhannel. It is clear that the radiance that reacheshe sensor is modulated by the atmospheric transpar-ncy exp�����; thus it contains information pertain-ng to scattering particles �molecules and aerosols�nd absorbing gas.As suggested from previous research,7,8 the atmo-
pheric transparency depends strongly on the num-er of water vapor molecules found in the viewingath, a circumstance that allows us to retrieve thentegrated water vapor abundance from the shape ofne of its absorption bands.By means of the MODTRAN4 radiative transfer
ode,9,10 we simulated a standard atmospheric trans-arency for three water vapor amounts, as shown inig. 1. The strong dipole moment and the light hy-
ig. 1. Vertical atmospheric transmittance versus wavelength fororrespond to relative differences in the water vapor abundance aalue �corresponding to 1.46, 2.92, and 5.84 g cm2, respectively�isibility of 20 km and a rural aerosol model. Note the presence
rogen atoms that compose a water vapor moleculeesult in strong and broad absorption bands. Thepectra that we obtained indicate that, for typicaltmospheric conditions, the in-band transparencyear 940 and 1140 nm is sensitive to changes in the
ntegrated amount of water vapor, whereas the bandst 1380 and 1880 nm are often saturated. Anotherseful absorption band is that which is centered at20 nm, but the correspondingly small change inransparency with water vapor content should beeasured with higher accuracy �see Fig. 2�.To retrieve columnar amounts of water vapor from
emotely sensed radiance acquired by hyperspectralensors it is necessary to adopt some inverse model-ng of atmospheric optical parameters. Most avail-ble models11,12 represent judicious compromisesetween a faithful representation of a physical sys-em and its mathematical tractability. For example,he pressure broadening of a diatomic molecule atoderately low temperatures may be locally repre-
ented by the Elsasser �or regular� band model13–15:n infinite array of equally spaced spectral lines ofqual strength and identical shape �identical half-idths�. The distribution of energy levels for ansymmetric molecule, however, requires a statisticalor random� model, in which the lines are assumed toe randomly located. One can obtain a more realis-ic representation by assuming that the line intensi-ies are governed by a probability-density function.hen the properties of the band will be determined byweighted average of the single-line properties.The main atmospheric gases are N2�78%�, O2�21%�,2O, Ar, CO2, and O3. In the visible part of the
lectromagnetic spectrum, transparency is affectedainly by ozone and aerosol absorption below 400 nm
nd by Rayleigh and Mie scattering. Here we wanto focus our attention only on the water vapor absorp-
e water vapor amounts �MODTRAN 4 simulations�. The curvests of 0.5, 1.0, and 2.0 with respect to the standard MODTRAN 4e simulation refers to a midlatitude summer atmosphere with ae O2 absorption band at 760 nm.
ion band located at 940 nm. The total water vaporransmission may be expressed as16,17
��, T� � p��, T� e��, T� l��, T�
� c��, T� l��, T� . (2)
Here l��, T� is the percentage of radiation atten-ated by water vapor single lines,18,19 c��, T� � p��,� e��, T� is the transparency that is due to waterapor continuum absorption, and T is the tempera-ure.
Various mechanisms to explain the water vaporontinuum absorption, including contributions fromhe extreme wings of the strong rotational water va-or lines in the far infrared as well as possible �H2O�2imer contributions, have been proposed. Gener-lly, two contributions are recognized: one is due toself-broadening term and the other, the so-called
oreign broadened component, is due to the collisionsy other atmospheric gases �mainly N2, which com-rises 78% of the total�.The first factor on the right-hand side of Eq. �2�
akes into account the strong dependence of the waterapor absorption coefficient on temperature and onartial pressure in the atmosphere. The corre-ponding absorption coefficient kc��, T, e, p0� is mod-led for a mixture of H2O in N2 as follows20–31:
here Cs0��, T� is the self-broadening coefficient mol-
cules1 cm2 atm1� for water vapor, w is the densitymolecules cm3� of water vapor molecules, e is theater vapor partial pressure atm�, p0 atm� is the
otal sample pressure, and ��T� is the ratio of the2-broadening coefficient to the self-broadening.his implies that for e � 0.1 atm and p0 � 1 atm morehan 90% of the contribution to k ��, T, e, p � comes
ig. 2. Detail of the vertical atmospheric transmittance of Fig. 1 it 940 nm is most sensitive to changes in water vapor amount.
rom the self-broadening term and that kc��, T, e, p0�aries approximately as e2.In the visible–near-infrared spectral range, consid-
ring water vapor concentrations of 0.4 to 4.0 g cm2,he continuous absorption coefficient introducedbove is far below the single-line absorption coeffi-ient. In fact, single line absorption is the most im-ortant contribution to atmospheric absorption in the40-nm band, and it is rather insensitive to temper-ture and pressure profiles in the atmosphere.The monochromatic atmospheric transparency forvertical path between the ground �z � 0� and a finaleight z can be written as32–34
l��� � exp���, z�� , (4)
here optical thickness ���, z� is expressed as
���, z� � �0
z
�ext��, ��d� � �0
z
s���n���d� , (5)
here �ext��, �� represents the spectral extinction co-fficient, n��� is the density of the absorber, and s��� ishe absorber’s cross section.
The basic idea of the proposed algorithm is to usehe normalized line depth see Eq. �7� below� to esti-ate the line area by spectral integration. The line
rea is a relevant parameter from any absorptionand because it measures the total energy removedrom the radiation field as a result of the spectralroperty considered. This parameter can be reliablystimated also from the radiance spectra acquired atoderate spectral resolution; moreover, the required
n-band spectral integration helps to mitigate the ef-ects of any uncorrelated noise source.
Let us consider a remote source that emits a spec-ral radiance Lc��, �� that is not affected by contin-um as well as line absorption. At-sensor radiance
wavelength range 700–1020 nm. The absorption band centeredthe presence of the O2 absorption band located at 760 nm.
n the
Lf
Tb
wa
opdL
fri
H
i�lmaswsfpnwi
wbLim
Fcobnsnc ver a
s��, �� is related to emitted radiance Lc��, �� asollows:
Ls��, �� � Lc��, �� c��� l��, �� . (6)
he normalized line depth ���� at wavelength � cane reliably estimated as
���� �Lc��, �� c��� � Ls��, ��
Lc��, �� c���� 1 � l��, �� ,
(7)
hich yields the fraction of monochromatic powerbsorbed by the atmospheric slab.In Fig. 3 we schematically depict the measurement
f the line area. Lc��, �� c��� represents the ex-ected continuum intensity; thus normalized lineepth ���� no longer depends on emitted radiancec��, �� or on continuous absorption c���.Assuming that the shape of a single spectral line
or a homogeneous path in a single absorbing gas isepresented by the Lorentz profile, line depth ����ntegrated on spectral window �� is given by
A � ���
����d� � ��� [1 � exp(
1� �
�
ST����
���e����
�� � �0�2 � ���e�����2 n���d�)]d�. (8)
ig. 3. The basic idea of the proposed algorithm is to use residualentered at 940 nm. This value is used for estimating the line areaf the ideal spectral radiance as dimmed by continuous absorptiony use of samples of the observed spectral radiance Ls��, �� nearegligible. At least two samples, one on the blue flank and the othtraight line. The interpolated radiance is then used as an esonabsorption channels, and the curves with triangle symbols indicode for a standard midlatitude summer atmosphere for an obser
ere � is the ray path and
ST����
�
��e����
�� � �0�2 � ���e�����2
s the parametric expression of the line profileLorentz shape�, which depends on line strength S,ine center frequency �0, and the half-width at half-
aximum �� that is related to collision broadeningnd Einstein’s spontaneous emission. The linetrength depends mainly on gas temperature T,hich in turn changes with height in the atmo-
phere.35 Line-width parameter �� instead is aunction of altitude through the water vapor’s partialressure e being thermodynamic Doppler broadeningegligible. To account for the whole spectral bande have to sum all single-line contributions blended
n the observed spectral signature:
A � ���(1 � exp��
j�1
M � �Sj
�
��jN�
��j � �j0�2 � ���j�
2��)d�,
(9)
here we have considered in the sum the total contri-ution from M single lines, each one described by theorentz profile of Eq. �8�. The unknown N� � �� n���d�
s the integrated amount of absorbers, namely, theass of absorbers in an atmospheric column of uni-
ntensity ���� that corresponds to the water vapor absorption bandpectral integration. The line-area estimation requires knowledge, Lc ��, �� c ���, at any � within the line. This value is obtainedings of the line at a wavelength where line absorption becomesthe red flank, are selected to permit the fitting of an interpolatione of continuum intensity. The straight line holds two nearbyradiance spectrum simulated by a MODTRAN4 radiative transfert 1.5 km over the ground.
ary cross section. It is worth noting that in expres-ion �9� we have obtained an approximate relationshiphat may even depend on the assumption of single-linerofiles that are independent of height. The assump-ion of line profiles that are independent of heightolds true only for uniform atmosphere in which tem-erature and pressure do not change with altitude.owever, this circumstance is partially verified in our
ase because we are considering airborne observationsf the Earth’s surface from a relative height �above theround� that was a limited range �3–20 km�. Thepproximate result of expression �9� can also be ac-epted for unsaturated lines, in which case the expo-ent on the right-hand side of Eq. �8� can be expandeds a power series stopped to the first order. One mayompute the double integral �in frequency k and posi-ion �� thus obtained by carrying out the frequencyntegral as a first step. As a result of this first inte-ration the dependence on �k of the line profile is can-eled out and an outcome proportional to Sn��� isbtained. We point out that line strengths S of tran-itions embedded in the near-infrared water-vaporand under consideration are almost insensitive to themall temperature variations encountered in the at-osphere when the height is changed within the afore-entioned range. In fact, S is regulated mainly by
opulation distribution in the two levels of the molec-lar transition. Population ratio P is governed byoltzmann’s law:
P �g1
g0exp�
�E10
KT���� ,
here, as can be shown, transition energy �E10 is farbove typical atmospheric KT��� values at any height. Hence the exponential term is estimated in itssymptotic region where its T derivative is vanishing,hus making line strength S constant with height.
ig. 4. Typical cross-section spectrum for an H2O molecule, deingle-line contributions that occur in the absorption band.
or typical airborne remote-sensing applications allhe above reasons and approximations are verified ateast partially, thus giving likelihood to the approxi-
ate relationship in expression �9�.If the chosen spectral interval �� covers the exten-
ion of the absorption band, then one can equiva-ently take the limits of integration of expression �9�rom � to �� without introducing significant error.
typical cross-section spectrum for the H2O moleculederived from the HITRAN 2000 database10� is shownn Fig. 4.
Expression �9� represents the fundamental rela-ionship for our retrieval algorithm: using Eq. �7�,e compute a line-area estimate from experimentalata �hyperspectral image�. This estimate is thenompared with the theoretical expectation of expres-ion �9�; thus an optimal estimate of the integratedmount of water vapor, N� , can be inferred. Figure 5hows the main structure of our model. Using Eq.7� for line-area estimation requires knowledge of thedeal spectral radiance Lc��, �� c��� as dimmed by theontinuous absorption only, at any � within the line.his end is achieved by use of the samples of thebserved spectral radiance near the shoulders of thenvolved absorption line at wavelengths where theine absorption becomes negligible. At least twoamples, one on the blue flank and the other on theed flank, are selected, thus allowing us to fit a suit-ble interpolation line. The interpolated radiance ishen used as an estimate of continuum intensity.et us note that this approach is markedly different
rom the standard channel-rationing techniques thatre employed, for example, in the Moderate-esolution Imaging Spectroradiometer �MODIS� al-orithm theoretical base document.36 The maindvantage of our algorithm is that it does not requireny lookup tables to generate columnar amounts ofater vapor because it numerically finds the best
from the HITRAN 2000 database. The spectrum contains all
rived
atttv
ptt�tt
batcwpfmrMdglotw
3
Tarpaoc
aagqts�
wWtttsp
sfa
Nas
Far�eiag
bundance N� to fit the theoretical predic-ion expressed in expression �9� with the experimen-al value indicated in Eq. �7�. The converging solu-ion N� � �� n���d� is the integrated amount of waterapor held in path �.Another important property of this algorithm is its
oor sensitivity to the albedo of the target from whichhe radiation comes. This valuable property is dueo the circumstance that the basic model parameter��� is retrieved as a line-to-continuum radiance ra-io, suppressing any slowly varying physical quantityhat affects the spectrum of at-sensor radiance.
It is worth noting that the scattering of radiationy aerosol and molecules may affect both the widthnd the depth, and hence the line area, of an absorp-ion feature. In particular, the at-sensor radianceontribution due to once-scattered radiation �up-elling path radiance� certainly contains a water va-or absorption feature that is shallower than thatound in the reflected radiation that is directly trans-itted to the sensor, because of its shorter equivalent
ay path through the atmosphere �traveled air mass�.ultiply scattered radiation, however, may contain a
eeper water vapor absorption line than the at-round reflected radiation, given its longer equiva-ent ray path in the lower atmosphere. In summary,ne can state that one should carefully correct scat-ering effects to gain exact estimates of columnarater vapor abundance.
ig. 5. Flow diagram showing the main steps of the retrievallgorithm. Starting from radiometrically corrected data �spectraladiance�, the 940-nm line area is computed according to Eq. �7�see text�. Then the line area is estimated from the theoreticalxpectation of expression �9�; an H2O cross-section spectrum isntroduced from the HITRAN 2000 database. Finally the two linereas are compared by numerical analysis and the vertically inte-rated water vapor abundance is computed.
. Simple Modeling
he main drawback of our model for H2O integratedbundance computation is the requirement of high-esolution cross-section spectrum as well as the im-licit calculation burden. To arrange for a fasterlthough approximate estimate, we derived from theriginal algorithm a simpler procedure, hereinafteralled the simple model.
In Section 2 we demonstrated that the line area isrelevant quantity for the retrieval of water vapor
bundance. One step of our method was the inte-ration of optical thickness �H2O��, z�, or a relateduantity, over a certain spectral interval �H2O wherehe H2O absorption feature is localized. If we as-ume that �H2O��, z� is a separable function of spectraland spatial z variables, it is easily to find that
��H2 O
�H2O��, z�d� � ��H2 O
sH2O���d� ��1
nH2O���d� ,
(10)
here the symbols are defined as in Sections 1 and 2.e can also assume that the second integration on
he right-hand side of expression �10� is expressed ashe product of two amounts: the first is related tohe columnar abundance N� H2O of water vapor and theecond one concerns the way in which the water va-or concentration is distributed in path length �1:
��1
nH2O���d� � N� H2O ��1
fH2O���d� . (11)
This calculation can be repeated for a different ab-orption line of any other atmospheric constituent,or instance O2, that is a gas at constant mixing ratio,s are CO2, N2O, CO, and CH4:
��O2
�O2��, z�d� � �
�O2
�O2���d� �
�1
nO2���d�
� N� O2 ��O2
�O2���d� �
�1
fO2���d�. (12)
ow we define �mis as the line-area ratio for the twobsorbers considered here, which can be computedtarting from the measurements
The same ratio �mod can be predicted from a suit-ble theoretical model of atmospheric radiativeransfer, yielding in ray path�2
�mod �
��H2O
�H2O��, z�d�
��O2
�O2��, z�d�
�
�N� H2O�mod ��H2O
�H2O���d� ��2
fH2O���d�
N� O2 ��O2
�O2���d� �
�2
fO2���d�
. (14)
Let us note that, because O2 has a fixed mixingatio, the amount N� O2
remains constant even if theath length is changed. The ratio between Eqs. �13�nd �14� reduces to
�mis
�mod�
��H2O
�H2O��, z�d�
��O2
�O2��, z�d�
�
�N� H2O�mis��1
fH2O���d� ��2
fO2���d�
�N� H2O�mod��2
fH2O���d� ��1
fO2���d�
. (15)
f the two ray paths coincide,
�mis
�mod�
�N� H2O�mis
�N� H2O�mod, (16)
rom which the columnar abundance �N� H2O�mis can beetrieved:
�N� H2O�mis � �N� H2O�mod
�mis
�mod. (17)
. Results and Data Processing
o test the performance of the proposed algorithm wettempted to estimate water vapor contents fromVIRIS data collected on 25 June 1987 over the Cu-rite mining district in southwest Nevada located at7°45� North �latitude� and 117°6� West �longitude��.igure 6 shows an image �gray-scale� of the observedcene from which we can recognize some cloudsright, bottom� with their corresponding shadows.
In Fig. 7 a false-color water vapor columnar abun-ance map that we retrieved by applying this algo-ithm is shown. Note that the columnar water vaporalue becomes small over clouds and highly variablever the clouds’ shadow. This behavior may be ex-lained if we observe that clouds are atmospheric bod-
es far above the ground with a relatively high albedo,hich reflect light through a short atmospheric pathith little water vapor content. In this way the
ignal-to-noise ratio of image data is high but the in-egrated line depth is small. In our belief the waterapor retrieval over clouds has to be a matter for future
ig. 6. AVIRIS image �gray-scale� utilized to test the algorithm.he image was collected on 25 June 1987 over the Cuprite miningistrict in southwest Nevada located at 37° 45� N and 117° 6� W.
ig. 7. Column water vapor image over the scene shown in Fig. 6.he image is presented in false colors: red indicates low-bundance areas ��0.2 g cm2�; blue shows areas of greater abun-ance ��0.9 g cm2�. Note that there is, below the water vaporbundance distribution, a memory effect that is due to the topo-raphic scene. This behavior may be explained by noting thatbove higher �smaller� terrain features the light travels through ahorter �longer� atmospheric path with little �great� water vaporontent, thus generating different estimations of the correspondingater vapor integrated abundance. This effect may be used to
nfer the elevation of the ground and, as a consequence, the heightf the water vapor column.
istNdn
vAddtstigima
thonwsa
aarc
ahaclr
FawC
nvestigation because for optically thick clouds the ab-orption effect may be slightly enhanced owing to mul-iple scattering of solar radiation within the clouds.ote that the water vapor map of Fig. 7 contains someetails of the original observed scene, an effect con-ected to the topography of the scene.Figure 8�a� compares horizontal profiles of water
apor abundance �along the same line crossing theVIRIS image� as retrieved from the two algorithmseveloped here. As can be seen, the two indepen-ent estimates agree fairly well. However, the wa-er vapor columnar abundance estimated with theimple model is on average noisier and greater thanhose computed with the other method. This behav-or is also confirmed from the corresponding histo-rams �empirical probability-density function� shownn Fig. 8�b�. The curve that corresponds to the first
ethod �thinner curve� has a mean of 0.71 g cm2
nd a standard deviation of 0.040 g cm2. The curve
ig. 8. �a� Horizontal profiles of water vapor abundance alonglgorithms. The two independent estimates show fair agreementith the simple model �darker curve� are on average noisier and grorresponding traces of water vapor columnar abundance.
hat corresponds to the simple method �thicker curve�as a mean of 0.89 g cm2 and a standard deviationf 0.098 g cm2. In our belief this behavior origi-ates from the too-coarse resolution of the AVIRIS,hich samples the involved oxygen line with one
pectral channel alone, hence making the the line-rea estimation uncertain.The tiny standard deviation of the computed H2O
bundance suggests that the retrieval algorithm isccurate and stable, and it also proves that the de-ived water vapor abundance is rather insensitive tohanges of surface reflectance.
To better investigate the stability of the proposedlgorithm with respect to target albedo variation, weave used the MODTRAN 4 code to simulate radi-nce spectra that correspond to different targets withonstant albedo. The model utilized was the mid-atitude summer model, with 20 km of visibility andural extinction.
ame line crossing the AVIRIS image as retrieved from the twowever, the water vapor columnar abundance estimates computed
r than those computed with the other method �lighter curve�. �b�
Figure 9 shows the vertically integrated water va-or abundance retrieved from simulations, which isndependent of the surface albedo. The maximumeviation from the expected horizontal straight line is
Table 1. Main Characteristics of the VIRS-200 Imaging Spectrometer
Type Push-broomNumber of channels 20 of 240 selectableFree spectral range ��m� 0.4–1.0 �2.5-nm FWHM�Instantaneous field of view �mrad� 1.0Spatial sampling interval �mrad� 1.33Cross-track samples 512Scan rate �scans�s� 12, 20, 30Quantization accuracy 10 bitsSignal-to-noise ratio �at albedo 0.5� 20�400
ig. 9. Behavior of water vapor abundance g cm2� with changinhe simulations were performed with the MODTRAN 4 code andisibility and rural extinction for several values of target albedo.bundance values are rather independent of the surface albedo, a
ig. 10. Ratio of path radiance and at-sensor radiance without pahe MODTRAN 4 code.
ess than 1%, a comfortable stability that waseached after subtraction of the radiation componentackscattered by the atmosphere �path radiance�rom the total at-sensor radiance. In this way theistortions of the line area that are due to large-anglecattering events were strongly reduced.We have also tested the algorithm’s stability, uti-
izing simulated radiance from targets �e.g., a mapleeaf spectrum� whose reflectance changes with wave-ength. This test showed that the algorithm’s per-ormance is not corrupted by inclusion of a spectrallyelective target.To comprehend the effect of atmospheric scattering
n this kind of band measurement, we have plotted inig. 10 the ratio of the path radiance and the ground’seflected radiance directly transmitted to the sensor
ctral ground radiance transmitted to the sensor at 20-km altitude.a midlatitude summer geographic seasonal model with 20 km ofresults show that the retrieved vertically integrated water vapore observed maximum change is less than 1%.
diance versus wavelength. The calculation was performed with
g speusedThe
th ra
viesnt
tep2or
s4owmai
2OHg
FsrcictcP
smi67srap
wtv
FViTa
ersus the wavelength. As can be seen, this rationcreases toward line center owing to the augmentedxtinction coefficient that dims the farthest radiationources �the ground reflected radiance� while theearest ones remain visible �backscattered contribu-ions that originate near the sensor�.
To test the empirical simple model for H2O re-rievals we also used a VIRS-200 imaging spectrom-ter to collect in-field data. The VIRS-200 is aush-broom imaging spectrometer equipped with a-dim array �CCD� of photosensitive elements andperating in the visible–near-infrared spectralange. The sensor digitizes 20 of the 240 available
Table 2. Spectral Configuration of the VIRS-200 Imaging Spectrometer
ig. 11. Spectral transmittance �dashed curve� retrieved from VIIRS-200 channels. Note the location of the O2 absorption ba
ntroduction of two linear interpolations, the first VIRS-200 channhis spectrum is compared with total transmittance �solid curvetmosphere with 20-km visibility and for a vertical path length.
pectral channels, which are uniformly spaced from00 to 1000 nm in 2.5-nm steps. The wavelengthsf the 20 recorded channels, which are digitizedithin 10-bit accuracy, are freely chosen. Theain sensor characteristics are detailed in Table 1,
nd additional information concerning this sensors given elsewhere.37,38
The selected spectral configuration for the VIRS-00 instrument was aimed to allow us to observe the2 absorption band located at 688 nm and the two2O absorption bands centered at 695 and 719 nm, as
iven in Table 2.Measurements were performed in October 2003 at
lorence, Italy, near 11:00 a.m. local time. We ob-erved the sky’s diffuse radiation �downwelling pathadiance� from ground level. Observations wereompleted with dark-signal measurements. Exper-mental data were averaged and corrected for theorresponding dark signal and the spectrally and spa-ially coherent noise pattern by means of a flat-fieldalibration procedure developed by Barducci andippi.39
Figure 11 shows a spectrum of transmittance mea-ured with VIRS-200 data. This spectrum was nor-alized to continuum introducing two linear
nterpolations, the first in the VIRS-200 channel from84.75 to 712.25 nm and the second from 712.25 to44.75 nm. The spectrum was compared with atmo-pheric transmittance simulated by the MODTRAN 4adiative transfer code for a rural midlatitude wintertmosphere with 20 km of visibility and for a verticalath.Applying the procedure described in Eq. �17�, firste estimated �mis and then we computed �mod from
he simulated spectrum to retrieve a columnar waterapor abundance �N� H2O�mis of 2.10 g cm2.
00 measurement. Symbols indicate wavelength positions of thet 688 nm. This spectrum was normalized to a continuum byom 684.75 to 712.25 nm and the second from 712.25 to 744.75 nm.ulated with the MODTRAN 4 code for rural midlatitude winter
he problem of estimating the abundance of impor-ant atmospheric constituents �e.g., water vapor�rom remotely sensed hyperspectral images has beenxamined. A new spectroscopic method for the re-rieval of atmospheric columnar water vapor at highpatial resolution was developed, and its perfor-ance and formulation were discussed. The algo-
ithm compares the observed and expectedtheoretical� line areas to calculate the integratedbundance of the absorber over the ray path traveledy the sensed radiation. To maintain the mathe-atical formulation of the procedure as simple as
ossible, we neglected the dependence of the crossection’s spectrum on atmospheric pressure and tem-erature �profile� for the absorption line. Early re-ults obtained from processing of the water vaporbsorption line at 940 nm as extracted from a hyper-pectral image gathered by the AVIRIS were de-icted, and they proved the effectiveness of theroposed algorithm.We tested an additional empirical retrieval proce-
ure with data gathered by the VIRS-200 imagingpectrometer to arrange for a faster although approx-mate estimate. This simpler retrieval algorithmoes not require a priori knowledge of the cross-ection spectrum of the absorption line to retrieve theolumnar abundance of the related constituent.his method is based on the contemporary observa-
ion of two absorption lines, one of which, that orig-nated from an atmospheric absorber at a fixed
ixing ratio, is used as reference to compensate forost of effects of the viewing geometry and the total
ir mass traveled by the observed radiation. In ourests we chose as a reference the oxygen absorptionine located near 760 nm.
Fair agreement between the two estimates wasbserved, even if the water vapor columnar abun-ance estimated with the simple empirical model wasn average noisier and slightly more biased �greater�han that computed with the other algorithm. Thisehavior originated from the too coarse resolution ofhe AVIRIS, which sampled the O2 line with onepectral channel alone, hence making the line-areastimation uncertain.We also verified that the columnar water vapor
etrieved with the new spectroscopic method was in-ensitive to variations in surface spectral reflectance,rovided that scattering contributions to the at-ensor radiance are reliably corrected or were smallnough that they do not greatly affect the observedine shape.
eferences1. M. D. King, Y. J. Kaufman, W. P. Menzel, and D. Tanre,
“Remote sensing of cloud, aerosol, and water vapor propertiesfrom the moderate resolution imaging spectrometer �MODIS�,”IEEE Trans. Geosci. Remote Sens. 30, 2–27 �1992�.
2. W. P. Elliotad and J. Gaffen, “On the utility of radiosondehumidity archives for climate studies,” Bull. Am. Meteorol.Soc. 72, 1507–1520 �1991�.
3. J. Susskind, J. Rosenfield, and D. Reuter, “Remote sensing of
weather and climate parameters from HIRS2�MSU on TIROS-N,” J. Geophys. Res. 89, 4677–4697 �1984�.
4. V. Carrere and J. E. Conel, “Recovery of atmospheric watervapor total column abundance from imaging spectrometer dataaround 940 nm—sensitivity analysis and application to Air-borne Visible Infrared Imaging Spectrometer �AVIRIS� data,”Remote Sens. Environ 44, 179–204 �1993�.
5. R. Bennartz and J. Fischer, “Retrieval of columnar water vaporover land from backscattered solar radiation using the Me-dium Resolution Imaging Spectrometer,” Remote Sens. Envi-ron. 78, 274–283 �2001�.
6. E. B. Knipling, “Physical and physiological basis for the reflec-tance of visible and near-infrared radiation from vegetation,”Remote Sens. Environ. 1, 155–159 �1970�.
7. B. C. Gao and A. F. H. Goetz, “Column atmospheric watervapor and vegetation liquid water retrievals from airborneimaging spectrometer data,” J. Geophys. Res. 95, 3549–3564�1990�.
8. Y. J. Kaufman and B. C. Gao, “Remote sensing of water vaporin the nearer IR from EOS�MODIS,” IEEE Trans. Geosci.Remote Sens. 30, 871–884 �1992�.
9. G. P. Anderson, F. X. Kneizys, J. H. Chetwynd, J. Wang, M. L.Hoke, L. S. Rothman, L. M. Kimball, R. A. McClatchey, E. P.Shettle, S. A. Clough, W. O. Gallery, L. W. Abreu, and J. E. A.Selby, “FASCODE�MODTRAN�LOWTRAN: past�present�future,”presented at the 18th Annual Review Conference on Atmo-spheric Transmission Models, Hanscom Air Force Base, Mass.,6–8 June 1995.
0. L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Messie, D. P.Edwards, J. M. Flaud, A. Perri, C. Camy-Peyret, V. Dana, J. Y.Mandin, J. Schroeder, A. McCann, R. R. Gamach, R. B. Watt-son, K. Yoshino, K. V. Chance, K. W. Jucks, L. R. Brown, V.Nemtchinov, and P. Varanasi, “The HITRAN molecular spec-troscopic database and HAWKS �HITRAN Atmospheric Work-station�: 1996 edition,” J. Quant. Spectrosc. Radiat. Transfer60, 665–710 �1998�.
1. W. Malkmus, “Random Lorentz band model with exponential-tailed S-1 line intensity distribution function,” J. Opt. Soc. Am.57, 323–329 �1967�.
2. S. A. Clough, F. X. Kneizys, G. P. Anderson, E. P. Shettle, J. H.Chetwynd, L. W. Abreu, L. A. Hall, and R. D. Worsham, “FAS-COD3: spectral simulation,” in Proceedings of InternationalRadiation Symposium, Lille, France, 18–24 August 1988, J.Lenoble and J. F. Geleyn, eds. �Deepak, Hampton, Va., 1988�,pp. 372–375.
3. M. D. King, W. P. Menzel, Y. J. Kaufman, D. Tanre, B.-C. Gao,S. Platnick, S. A. Ackerman, L. A. Remer, R. Pincus, and P. A.Hubanks, “Cloud and aerosol properties, precipitable water,and profiles of temperature and water vapor from MODIS,”IEEE Trans. Geosci. Remote Sens. 41, 442–458 �2003�.
4. S. A. Ackerman, “Remote sensing aerosols using satellite in-frared observations,” J. Geophys. Res. 102, 17069–17079�1997�.
5. M. E. Thomas and R. J. Nordstrom, “Line shape model fordescribing infrared absorption by water vapor,” Appl. Opt. 24,3526–3530 �1985�.
6. C. Prabhakara, G. Dalu, and V. G. Kunde, “Estimation of seasurface temperature from remote sensing in the 11-to-13-�mwindow region,” J. Geophys. Res. 79, 5039–5045 �1974�.
7. C. G. Kilsby, D. P. Edwards, R. W. Saunders, and J. S. Foot,“Water-vapor continuum absorption in the tropics: aircraftmeasurements and model comparisons,” Q. J. R. Meteorol. Soc.118, 715–748 �1992�.
8. M. I. Mishchenko, L. D. Travis, R. A. Khan, and R. A. West,“Modeling phase function for dust-like tropospheric aerosolsusing a shape mixture of randomly oriented polydisperse sphe-roids,” J. Geophys. Res. 102, 16831–16847 �1997�.
9. W. B. Grant, “Water vapor absorption coefficient in the
2
2
2
2
2
2
2
2
2
2
3
3
3
3
3
3
3
3
3
3
8–13-�m spectral region: a critical review,” Appl. Opt. 29,451–462 �1990�.
0. Q. Ma and R. H. Tipping, “Water vapor continuum in themillimeter spectral region,” J. Chem. Phys. 93, 6127–6139�1990�.
1. Q. Ma and R. H. Tipping, “The atmospheric water vapor con-tinuum in the infrared: extension of the statistical theory ofRosenkranz,” J. Chem. Phys. 93, 7066–7075 �1990�.
2. Q. Ma and R. H. Tipping, “A far wing line shape theory and itsapplication to the water continuum absorption in the infraredregion. I,” J. Chem. Phys. 95, 6290–6301 �1991�.
3. Q. Ma and R. H. Tipping, “A far wing line shape theory and itsapplication to the water vibrational bands. II,” J. Chem.Phys. 96, 8655–8663 �1992�.
4. Q. Ma and R. H. Tipping, “A far wing line shape theory and itsapplication to the foreign-broadened water continuum absorp-tion. III,” J. Chem. Phys. 97, 818–828 �1992�.
5. K. K. Lehmann and A. M. Smith, “Where does overtone inten-sity come from?” J. Chem. Phys. 93, 6140–6147 �1990�.
6. I. J. Barton, “Infrared continuum water vapor absorption co-efficients derived from satellite data,” Appl. Opt. 30, 2929–2934 �1991�.
7. M. E. Thomas, “Infrared- and millimeter wavelength contin-uum absorption in the atmospheric windows: measurementsand models,” Infrared Phys. 30, 161–174 �1990�.
8. R. E. Roberts, J. E. A. Selby, and L. M. Biberman, “Infraredcontinuum absorption by atmospheric water vapor in the8–12-�m window,” Appl. Opt. 15, 2085–2090 �1978�.
9. P. Chylek and D. J. W. Geldart, “Water vapor dimers andatmospheric absorption of electromagnetic radiation,” Geo-phys. Res. Lett. 24, 2015–2018 �1997�.
0. D. R. Cutten, “Extension of water vapor continuum absorptionto the 4.5–5.0 �m region,” Infrared Phys. 19, 663–667 �1979�.
1. H. R. Gordon, “Atmospheric correction of ocean color imageryin the Earth Observing System era,” J. Geophys. Res. 102,17081–17106 �1997�.
2. J. S. Accetta and D. L. Shumsker, eds., The Infrared andElectro-Optical System Handbook �SPIE, Bellingham, Wash.,�1993�, Vols. 1–8.
3. F. M. Henderson and A. J. Lewis, eds., Manual of RemoteSensing �American Society of Photogrammetry and RemoteSensing, Bethesda, Md., 1983�, Vols. I and II.
4. K. Mathew, C. M. Nagarini, and A. S. Kirankumar, “Split-window and multi-angle methods of sea surface temperaturedetermination: an analysis,” Int. J. Remote Sensing 22,3237–3251 �2001�.
5. S. J. English, C. Guillou, C. Prigent, and D. C. Jones, “Aircraftmeasurements of water vapor continuum absorption at milli-metre wavelengths,” Q. J. R. Meteorol. Soc. 120, 603–625�1994�.
6. B.-C. Gao and Y. J. Kaufman, “Derivation of columnar atmo-spheric water vapor amount from MODIS near-IR channels,”presented at the International Geoscience and Remote Sens-ing Symposium, Honolulu, Hawaii, 24–28 July 2000.
7. A. Barducci and I. Pippi, “The airborne VIRS for monitoringof the environment,” in Sensors, Systems, and Next-Generation Satellites, H. Fujisada, ed., Proc. SPIE 3221,437–446 �1998�.
9. A. Barducci and I. Pippi, “Analysis and rejection of systematicdisturbances in hyperspectral remotely sensed images of theEarth,” Appl. Opt. 40, 1464–1477 �2001�.
