an overview of the airs radiative transfer model...

IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 41, NO. 2, FEBRUARY 2003 303

An Overview of the AIRS Radiative Transfer ModelL. Larrabee Strow, Scott E. Hannon, Sergio De Souza-Machado, Howard E. Motteler, Member, IEEE, and

David Tobin

Abstract—The two main elements of the Atmospheric InfraredSounder Radiative Transfer Algorithm (AIRS-RTA) are describedin this paper: 1) the fast parameterization of the atmospheric trans-mittances that are used to perform the AIRS physical retrievalsand 2) the spectroscopy used to generate the parameterized trans-mittances. We concentrate on those aspects of the spectroscopy thatare especially relevant for temperature and water vapor retrievals.The AIRS-RTA is a hybrid model in that it parameterizes mostgases on a fixed grid of pressures, while the water optical depthsare parameterized on a fixed grid of water amounts. Water vapor,ozone, carbon monoxide, and methane profiles can be varied, inaddition to the column abundance of carbon dioxide.

Index Terms—Atmospheric retrievals, radiative transfer, remotesensing, spectroscopy.

I. INTRODUCTION

T HE ATMOSPHERIC Infrared Sounder (AIRS) [1] usesa physical algorithm for the retrieval of atmospheric

profiles, and consequently is dependent on an accurate, andfast, radiative transfer algorithm for computing clear-airradiances. The AIRS physical retrieval algorithm uses ap-proximately 300 channels to determine temperature, water,and ozone profiles. Additional channels are used to retrievemethane, carbon monoxide, and eventually carbon dioxide.Calls to the atmospheric infrared sounder radiative transferalgorithm (AIRS-RTA) represent the most CPU-intensive partof the operational processing, so the RTA must be fast. Thehigh spectral resolution of AIRS coupled with its low noiseshould produce retrievals that are as good, or better, than theworldwide operational radiosonde network, if the forwardmodel accuracy approaches the noise level of the instrument.

Two primary components of the AIRS-RTA determine itsaccuracy: 1) the spectroscopy used to compute atmospherictransmittances and 2) the quality of the fast model transmit-tance parameterization. We review here the basic form of theAIRS-RTA parameterization and its accuracy. A detailed expla-nation of the procedures used to generate the parameterizationcoefficients is beyond the scope of the paper.

We will also review the spectroscopy used to generate theAIRS-RTA parameterization and the associated line-by-line

Manuscript received April 29, 2002; revised October 14, 2002. This workwas supported by the National Aeronautics and Space Administration underContract NAS5-31378.

L. L. Strow, S. E. Hannon, and S. DeSouza-Machado are with the Departmentof Physics, University of Maryland—Baltimore County, Baltimore, MD 21250USA (e-mail: [email protected]).

H. E. Motteler is with the Department of Physics and the Joint Center for EarthSystems Technology, University of Maryland—Baltimore County, Baltimore,MD 21250 USA.

D. Tobin is with the Space Science Engineering Center, University of Wis-consin, Madison, WI 53706 USA.

Digital Object Identifier 10.1109/TGRS.2002.808244

(LBL) algorithms that generate the monochromatic transmit-tances required for producing the fast radiative transfer model.This discussion focuses on the characteristics that distinguishour LBL algorithms from others and will include comparisonsbetween up-welling atmospheric radiances observed withhigh-spectral resolution radiometers flying on the NationalAeronautics and Space Administration’s (NASA) ER-2 aircraftand radiances computed using our LBL algorithm.

See [1] for an overview of the AIRS instrument and [3] for de-tails on the AIRS spectral resolution and spectral response func-tions (SRFs). AIRS design parameters relevant for the radiativetransfer algorithm are 1) a 650-cm (15 m) to 2700-cm(3.7 m) spectral range with 2378 channels; 2) SRFs with fullwidths at half maximum of /1200 (0.5–2.3 cm ); and 3)noise levels on the order of 0.2 K (70% of AIRS channels havenoise less than 0.2 K, 20% have noise less then 0.1 K).

II. RADIATIVE TRANSFER

The observed AIRS radiance for channelis the integratedproduct (“convolution”) of the monochromatic radiancewith the normalized instrument SRF for channel

SRF (1)

The retrieval of atmospheric parameters from is accom-plished by varying an initial guess for the temperature andconstituent amounts until the difference between observed andcalculated radiances is minimized for some selection of chan-nels .

The monochromatic radiance leaving the top of a nonscat-tering, clear atmosphere is

(2)

The first term is the surface blackbody emission whereisthe surface emissivity and is the Planck function. Thesecond term is the atmospheric emission, followed by the down-welling atmospheric emission reflected by the surface.is thedown-welling thermal flux and the reflectance of this flux bythe surface, which we assume to be Lambertian. Reflected solarradiation is represented by the last term in this equation, where

is the solar irradiance incident at the top of the atmosphere

0196-2892/03$17.00 © 2003 IEEE

304 IEEE TRANSACTIONS ON GEOSCIENCE AND REMOTE SENSING, VOL. 41, NO. 2, FEBRUARY 2003

and is the solar reflectance by the surface. All of these termsinvolve the atmospheric layer-to-space transmittance from somepressure to space at angle , the satellite zenith angle asmeasured along the ray from the surface to the satellite

(3)

where is the optical depth per unit pressure for thegas at pressure viewed at angle . Note that the alsodepends on and the abundance of the radiatively activeatmospheric constituents, although this is not shown explicitly.

We can simplify the solar contribution by noting that the twosolar transmittances in (2) can be combined into a single, longerpath transmittance

(4)

where

(5)

A. Channel-AveragedRadiative Transfer

The AIRS forward model uses a discretized version of (2) foreach spectral channel

(6)

with 100 atmospheric layers, which is sufficiently fine to keepdiscretization errors below the AIRS noise level.is the firstatmospheric layer above the surface, which in practice is gener-ally some fraction of one of the 100 fixed pressure layers.

The channel-averaged layer-to-space transmittances in thisequation are given by

SRF (7)

AIRS channels are narrow enough that we can replace the con-volution of the Planck function with its value at channel center,which introduces errors below the 0.1 K level. The solar irra-diance term is the convolution of the AIRS SRF with a solarspectrum derived from the Atmospheric Trace Molecule Spec-troscopy (ATMOS) experiment [4]. The channel-averaged ver-sion of the reflected thermal term, will be discussedlater.

The parameterization of the gas transmittances is quite in-volved, and will be simplified in this discussion by assumingthat the algorithm only needs to vary water and ozone transmit-tances as a function of gas amount, observation secant angle, andtemperature. This leaves us with three separate transmittanceterms; one for all gases with fixed amounts, including CO, thatwe label , one for water vapor transmittances labeled

, and one for ozone labeled . The AIRS radiativetransfer algorithm can also vary methane and carbon monoxideprofiles, and adjust the total column of CO. Since Beer’s law

is not obeyed for convolved transmittances we cannot directlycompute the total convolved transmittance in (7) as the productof the individual convolved transmittances, since

(8)

where

SRF (9)

Recovery of Beer’s law is partially possible by expressingthe individual convolved transmittances in the following way assuggested by Susskind [5]

and (10)

Using these definitions for the individual convolved transmit-tances we see in the following equation that we recover the truetotal convolved transmittance after multiplication

(11)The aforementioned relation is only correct if the canbe accurately parameterized as a function of the atmospherictemperature and gas profile, and with satellite viewing angle.The parameterization accuracy is increased if the most dom-inant gas transmittance for a given channel is formed alone,as was done for in (11). Additional details on how thecarbon monoxide and methane transmittances are handled arediscussed in [2].

Since the layer optical depth has a more linear de-pendence on temperature and gas abundance than the transmit-tance, we parameterize the layer optical depths, which are easilyformed from the layer-to-space transmittances

(12)

Most optical depths are linearly parameterized (see Section II-Cfor exceptions) as

(13)

where the constant terms are determined from least squaresregression of the above equation to a statistical set of atmo-spheric profiles. The predictors, , and regression techniquesare discussed in more detail later. The final form of the AIRS ra-diative transfer equation uses , as shown below, forin (6)

(14)

Similar, but more complicated procedures are used to developtransmittance equations for the other variable gases, carbonmonoxide, and methane. Variable COis treated as a specialcase; see Section II-F.

STROWet al.: AIRS RADIATIVE TRANSFER MODEL 305

B. Reflected Down-Welling Thermal Radiance

The down-welling thermal flux reflected by the surface isgenerally a small but not negligible term that will increase ob-served brightness temperatures by nominally 0.2 K for .This term can grow to 0.6 K in regions of low emissivity, suchas over silicate deserts.

The monochromatic down-welling thermal flux (for a clearnonscattering atmosphere) can be accurately computed usingthe standard diffusivity approximation (Goody and Yung)

(15)

where is the diffusivity angle for layer. The termin the discretized version of the radiative transfer equation (be-fore convolution with the SRFs) is, therefore

(16)

We partially rewrite this equation in terms of the layer transmit-tance

(17)

in order to clarify the following approximation to this relation.Even within the diffusivity approximation the exact computa-

tion of the above quantity takes significant time, since it requirestransmittances at different angles than the direct emission term.Moreover, since this term is quite small, significant approxima-tions may be warranted. Since most of the down-welling fluxthat ultimately is reflected back to the satellite is coming fromthe lower troposphere, Kornfield and Susskind [6] suggestedmodeling the down-welling flux as emission from a single at-mospheric layer with temperature as

(18)

where is a correction factor determined using regression overa statistical set of profiles. Note, we are using channel convolvedvalues for the transmittances in the above equation. A differentlayer temperature is used for each channel by finding whichlayer resulted in the most accurate approximation for this radi-ance term. was modeled as a linear equation with five pre-dictors; a constant, , , , and ,where is the secant of . Note that this approximation forthe reflected thermal radiation only uses transmittances that arealready computed for the larger atmospheric emission radianceterm. We estimate that this approximation for reflected thermalradiation is accurate on average to15% to 20%. In the futurewe may find that this term requires further improvements.

Fig. 1. Mean layer pressures used in the AIRS fast radiative transfer model.

C. Atmospheric Layering

The AIRS fast model uses two different layering methods tomodel the optical depths. The most intuitive is a grid of verticalslabs with constant pressure. In this case, each layer is definedby the two bounding grid pressure levels (solayers require a

level grid). The discretized version of the radiative transferequation discussed in the previous section uses this 100-layerpressure grid and ultimately all s must be available on thisgrid. All component gas transmittances, with the exception ofwater vapor for 600 channels, are parameterized on this gridwhich spans the range 1100–0.005 hPa. The 101 atmosphericpressurelevelswhich divide the atmosphere into 100 layers aredefined as

(19)

where is level number, and , , and are constants. Byfixing , , and

hPa, we can then solve for these three constants. This re-lation gives us smoothly varying layers and is fine enough tonot limit the accuracy of the radiative transfer equation. A plotof these layers is shown in Fig. 1. Note that although the levelnumbering has level 1 closest to the surface, the layer numberingscheme used in the AIRS-RTA has layer 1 closest to the satellite.

A second method for layering the atmosphere (introduced in[7] and [8]) called OPTRAN is used for600 channels that aredominated by water vapor. Water vapor amounts can vary bythree orders of magnitude in the lower troposphere, producinghigh variability in the transmittances that are difficult to param-eterize accurately. OPTRAN interpolates the atmospheric pro-file under consideration onto a grid of layers that have constantlayer-to-space water amounts. The optical depth is computedon this grid and then interpolated back to the constant pressuregrid for performing radiative transfer. The main predictor foroptical depth on the OPTRAN grid is pressure, rather than acombination of secant angle and gas amount, as is the case ona constant pressure grid. In order to achieve acceptable accura-cies with OPTRAN we used 300 grid layers of constant wateramount.


Although OPTRAN produces more accurate parameteri-zation using a smaller number of parameters for most watervapor channels, we found that a grid of constant pressurelayers worked better for the fixed gas transmittances [9].Consequently, the AIRS transmittance parameterization is ahybrid of both methods.

D. Predictors

The layer effective optical depths are modeled as simplefunctions of various profile-dependent predictors [the terms

in (14)]. Typically these predictors are terms related tothe layer temperature, absorber amount, and viewing angle,and for OPTRAN, pressure. However, the loss of Beer’s lawmeans that the functional dependence of the transmittances onthe predictors can be quite complex, so the exact selection ofpredictors involves a combination of insight and trial-and-errortesting. In addition, the layer optical depths also depend onthe layers above them (at higher altitudes), which is a naturalconsequence of deriving the layer effective optical depths fromratios of layer-to-space transmittances.

A detailed discussion of all predictors used for all channelsand gases is beyond the scope of this paper, so instead we sum-marize the profile variables that make up the actual predictors.

The predictors are products of various powers of the fol-lowing profile variables; the secant of the path zenith angle,

, , ratios of the various gasamounts (water, ozone, methane, carbon monoxide) to their ref-erence values, and some additional variables that are nonlocalin that they depend on the profile above the layer under consid-eration. The gas amounts refer to the amount of the absorbercontained within the layer along a nadir path. To insure thatthe predictors are of the same magnitude most are ratioed ordifferenced with a layer temperature or amount from a refer-ence profile (U.S. Standard Atmosphere). For example, two pre-dictor variables that take into account the dependence of thelayer transmittances on the layers above are

(20)

and

(21)

where is the pressure, the profile water amount,and the water amount for the reference profile. Similarvariables to for ozone, carbon monoxide, and methane arealso used.

We used 11 temperature predictors in (14) that were con-structed from various products of powers of, , and . Forwater vapor optical depths the predictors include up to 13 prod-ucts of powers of , , , , and two variables similar to

but for ozone and methane. Ozone used a maximum of tenproducts of various powers of, , , and . CO and CHoptical depths each used up to ten products of four predictorsanalogous to those used for . The water vapor continuum

was parameterized with products of powers of, , and .Finally, the CO column content was parameterized with fourproducts of powers of and . The exact selection of predic-tors are available in [10]. The resulting coefficients for all 2378channels, 100 layers, and four variable gases requires 35 MB ofstorage.

Since the OPTRAN layering scheme uses a grid of constantlayer-to-space water amounts while AIRS radiative transfer ison a constant pressure grid, we calculate the OPTRAN predic-tors at the AIRS pressure layers and then linearly interpolatethem to the OPTRAN grid. We used nine predictors for OP-TRAN; a constant, , , , , , , , and ,where

(22)

and

(23)

Once these predictors are interpolated onto the OPTRAN gridthey are normalized by dividing them by a reference profile (alsointerpolated to the OPTRAN grid) to keep all predictor valuesclose to unity.

E. Regressions

The successful determination of the fast model parameteri-zation coefficients is highly dependent on weighting the var-ious terms in the regression equation (14). Recall that the at-mospheric emission from a single layer is proportional to theproduct where is a layer transmittance and isa layer-to-space transmittance. We can define a transmittanceerror as

(24)

where is the optical depth andrepresents some small frac-tional error in . A plot of this equation resembles the shape ofthe curve shown in Fig. 2. The transmittance is most sensitiveto optical depths near unity, and insensitive to small or large op-tical depths.

Consequently, during the regressions to determine the fastmodel coefficients we adjust the input optical depth to arriveat the weighted values shown in Fig. 2, except that we limit theminimum weighted to one. The final used in the re-gression is the product of the weighted values determined sep-arately for the layer optical depth and for the layer-to-space op-tical depth. To maintain the balance of (13), we must apply thesame weighting factor to the predictors.

The regression training dataset consists of 48 profiles, eachcalculated at six viewing angles between nadir and 60. The48 profiles were selected to span the expected range of profilevariability and were mostly selected from the TIGR [11] profiledatabase. Data for an additional six angles extending out to 83


Fig. 2. Weighted values used for optical depths used in regressions for fastmodel parameters.

was created for the shortwave channels because of the longerpathlengths that arise in the reflected solar term of the radiativetransfer equation. Care should be taken in using the AIRS-RTAat large solar zenith angles due to uncertainties in the true atmo-spheric path under those conditions.

The monochromatic transmittances for each profile were cal-culated using the KCARTA [12], [13] code, and included allgases contained in the 1996/1998 HITRAN [14] database (HI-TRAN 2000, Version 11.0 will be used in the near future). Pro-files for the minor gases that do not vary in the fast radiativetransfer model were set to climatological mean values.

The water vapor continuum was parameterized separatelyfrom the line spectra, since it is essentially constant over thewidth of an AIRS channel and can be removed from the in-strument convolution. This also makes it easier to parameterizethe water line spectra. In addition, it allows us to modify thewater continuum in the AIRS fast model separately from thecontributions to the water transmittances due to the line spectra.This has the practical advantage that we can easily modify thecontinuum, which is the more uncertain part of the spectrum.

To simplify the fast model, the “fixed” gas amounts were keptidentical in all the regression profiles, and only the layer tem-peratures were allowed to vary. Small variations in layer gasamount caused by the combined effects of water vapor displace-ment, gravity (as a function of latitude), and layer pathlength(required to keep the layer pressure constant) are typically lessthan 1% to 2%. We have parameterized these effects with a termwe call the “ -factor” that modifies the fixed gas optical depth

.The regression profiles are also used to compute the reflected

down-welling thermal radiance using kCARTA, generating thedataset needed to determineand in (18).

F. Variable CO

The at-launch AIRS radiative transfer algorithm allows vari-ation of the CO column amount although this capability is notpresently used in the AIRS retrieval algorithm. Climatological(hemispherical and seasonal) variations in COmixing ratio ofa few parts per million volume (ppmv) are large enough to ob-serve with AIRS, so we need the capability to compute the ef-

fects of CO on AIRS radiances when analyzing biases. In thelong term the potential for AIRS to retrieve COwill be care-fully examined.

CO should only vary globally by several percent at most,resulting in changes to the optical depth that are very linear inCO amount. For simplicity we treat COas one of the “fixed”gases and model the small variability of COas a separate ad-ditive perturbation term as follows:

CO (25)

where the are constant coefficients determined by regression,and the predictors are , , , and . COis the percentage increase or decrease in the COmixing ratiofrom our standard value of 370 ppmv. The regression for theconstants requires computing convolved monochromatic trans-mittances with our standard value for the COand with an en-hanced CO mixing ratio.

Note that we only vary the COin the regression profiles bya constant ppmv offset in every layer. This means that, in prin-ciple, CO in (25) should be the same for all layers. Ourparameterization for variable COis very accurate, far belowthe AIRS noise levels. Consequently, we expect that one couldvary the CO profile (and not just the column) to some degreeand not introduce significant errors, although we have not care-fully evaluated any potential errors that could arise under theseconditions.

This correction to the fixed gas optical depths for variableCO will generally have the same order of magnitude as the

-factor correction discussed in the previous section. The-factor correction modifies the amount of fixed gases (in-

cluding CO ) in a layer to account for displacement by highlyvariable water vapor, which must be done to keep the layerpressure constant. However, note that the-factor correctionis applied to all channels, not just those with water vaporemission, and thus must be done accurately in order to retrievevariable CO.

G. Accuracy and Performance

Fig. 3 shows the fitting errors, in brightness temperature units,for the fast transmittance regressions (middle panel). This plotdoes not include errors that may be introduced by the reflectedthermal parameterization, which are highly dependent on thesurface reflectivity. The bottom panel of Fig. 3 shows brightnesstemperature errors of the AIRS-RTA when using an independentdataset, which was a selection of 212 profiles from the TIGRdataset that were not used as fitting profiles. These 212 profileswere selected to evenly cover the globe to the extent possiblewith TIGR.

Histograms of the fast model parameterization errors for boththe dependent and independent profile dataset shown in Fig. 4show that the vast majority of channels have errors below 0.1 K.For clarity we truncated the histogramaxis a little above 0.2 K,which removes two/four channels from the histogram for the de-pendent/independent profile sets, respectively. Errors are largerfor the independent profile set, mostly for channels in regionsdominated by water that had extremely low fitting errors. On


Fig. 3. (Top) A simulated AIRS spectrum. (Middle) RMS difference betweenfast modelB(T ) and trueB(T ) for the 48 regression profiles, for five slantpaths. (Bottom) Same as middle, but using 212 independent profiles from theTIGR database.

average the mean rms error increased by about 50% to 0.04 Kwith the independent profile set. If our profile statistics are rep-resentative, spectroscopy errors (and in a few cases SRF uncer-tainties) rather than parameterization errors should dominate theuncertainties in the AIRS-RTA.

The largest errors in the fast model parameterization are fortwo to three high-altitude COchannels that have interferingwater vapor lines. These channels are easily avoided in theretrieval, since there are sufficient numbers of high-altitudeCO channels that do not have water vapor interference. TheAIRS-RTA parameterization errors are also higher than averagefor a subset of water channels centered on water vapor lines ofmedium strength in the 1250–1375-cmregion. These chan-nels are generally avoided in the retrieval because they havebroader weighting functions than channels located in-betweenspectral lines that peak at the same altitude.

The AIRS-RTA integrates the radiative transfer equationusing the 100-layer model of the atmosphere. However, theAIRS physical retrieval algorithm methodology does notrequire evaluation ofradiancederivatives for each of the 100layers (see [15, Table 1]). Temperature retrievals, for example,use 24 vertical temperature derivatives of the radiance, corre-sponding to the 24 trapezoid functions discussed in [15]. Thisapproach significantly lowers the CPU requirements on theRTA and allows the use of finite difference radiance derivatives.The AIRS-RTA can compute 12 complete AIRS spectra of all2378 channels in one second using a commodity CPU circa2001.

III. SPECTROSCOPY

This section provides a brief overview of the spectroscopyand line-by-line algorithms used in the AIRS-RTA. The spec-troscopy determines the absolute accuracy of the AIRS-RTA.A reasonable lower limit on desired errors in the AIRS-RTA isthe nominal noise level of 0.2 K, although some retrieval/as-similation schemes might require even lower biases relative to

Fig. 4. Distribution of fitting errors in the AIRS-RTA.

a model atmosphere. If the spectroscopic errors are systematicin each atmospheric layer (same percentage error) this trans-lates into a maximum error of 1% in the spectroscopy. This isa demanding requirement, since it is often difficult to obtainagreement among different laboratory measurements of molec-ular line strengths to better than 2%, and even more difficult tomeasure line shapes to this accuracy.

The AIRS high-spectral resolution is most important in thatit allows the use of channels in-between spectral lines, whichhave absorption coefficients proportional to pressure squared,that produce sharp weighting functions compared to channelson top of spectral lines. AIRS is therefore quite sensitive to theatmospheric spectral line shapes, especially for COand H Olines that have very high optical depths in the atmosphere. Wesummarize here the results of the development of improvedCO spectral line shapes, based on laboratory studies of COspectra that are in-turn validated with atmospheric emissionspectra measured by the NAST-I and S-HIS high-spectralresolution interferometer radiometers flying on NASA’s ER-2.Studies of HO line shapes are continuing, but uncertaintiesin the measurement of HO amounts in both the laboratorysetting and in the atmosphere have slowed progress in HO lineshapes, although extensive field campaigns by the DOE ARM[16] program should bear fruit in the near future.

One major consideration for COline shapes in theAIRS-RTA is the effect of line-mixing, which redistributesthe radiation of overlapping spectral lines away from whatwould be computed using noninteracting Lorentz line shapes.Line-mixing reduces the effective far-wings of these interactinglines, while increasing the line shape near the line centers.Duration-of-collision effects also considerably reduce the COline wing from Lorentz values and is especially importantin the head of the band near 2400 cm (4.3 m) thatcontains excellent temperature sounding channels. The largeeffect of Q-branch line-mixing on high-spectral resolutionnadir sounders was reported by Strowet al. [17] some yearsago and has been reviewed more recently [18]. A number ofpopular line-by-line radiative transfer algorithms (GENLN2and LBLRTM) incorporate Q-branch line mixing.


Line mixing in CO P/R-branches has received less atten-tion than Q-branch line-mixing because the P/R lines are morewidely separated than Q-branch lines and it was believed thatP/R mixing has less of an effect on the COspectrum. In ad-dition, early studies ascribed the strong sub-Lorentz behaviorof the R-branch bandhead of COat 4.3 m solely to du-ration-of-collision effects and neglected the strong influence ofP/R-branch line-mixing. GENLN2 [19], for example, modelsthe sub-Lorentz behavior of the COlines with the empiricalmodel of Cousinet al.[20], which contains 14 line shape param-eters, derived from laboratory spectra, to describe thespec-tral line shapes. Subsequently, Cousin [21] and Boissoles [22]showed the P/R-branch line-mixing was responsible for muchof the sub-Lorentz behavior of the R-branch bandhead, but theirproposed model was too inaccurate for remote sensing applica-tions.

The CO line shape model for P/R-branch mixing and dura-tion-of-collision effects used in the AIRS-RTA was developedby Tobin [23] and has been refined more recently by Machadoet al. [24]. Tobin used laboratory spectra provided by JohnJohns [25] to develop an approximation for the combined effectsof P/R-branch line-mixing and duration-of-collision effectsthat was physically based, had as few adjustable parameters aspossible, and was sufficiently accurate for atmospheric remotesensing applications. This theory uses the same energy-gapscaling theory for rotational relaxation that has been successfulin Q-branch studies, and adds a two-parameter adjustmentfor duration-of-collision effects that follows the approach ofBirnbaum [26], [27]. He was able to accurately model bothroom and low-temperature COspectra in the R-branch bandhead with only three adjustable parameters, two parameterizingduration-of-collision effects, and one that scales the rotationalrelaxation that determines line-mixing.

P/R-branch line-mixing and duration-of-collision effectsshould also affect CO line shapes in the strong 15-mbands that are used for atmospheric temperature sounding.Duration-of-collision effects should be identical to what weobserved in the band. However, at 15m these effects areharder to observe because the various CObands in this regionare more spread apart than in the 4-m region. We expectP/R-branch line-mixing to be approximately half as strong inthe 15- m bands than in the 4.3-m bands. The 4.3-m bandsare primarily bands that only have even, or odd, rota-tional levels present. The 15-m bands of CO are primarily

type bands which haveall rotational levels present in thestates. The end result is that half of the rotationally inelastic

molecular collisions transfer the molecule to rotational statesthat are not connected to a radiative transition, and thus thesecollisions do not contribute to line mixing. This is in contrastto the situation in bands where all rotational states areconnected to a radiative transition, so all rotationally inelasticcollisions can lead to line mixing.

Our 15- m CO line shape uses the duration-of-collision pa-rameters derived from COspectra at 4.3 m, but computesline-mixing appropriate for and bands. We use anenergy-gap scaling law for the rotational relaxation that is pa-rameterized by ensuring that the scaling law reproduces the ob-served linewidths as a function of, the rotational state quantum

Fig. 5. Laboratory spectrum of COin the 15-�m region and percent errors inthe computed absorption coefficients for this spectrum. This spectrum was 766torr of CO , 15-cm path length, at 296.7 K.

number. Details of these calculations, and comparisons to labo-ratory data, can be found in [23] and [24]. Other line-by-line al-gorithms use various approximations for the far-wing COlineshape. GENLN2, for example, uses the empirical Cousin [20]far-wing line shape for the COline shape, both at 4.3 and 15

m, although Cousin derived the empirical parameters for thisline shape using 4.3-m spectra. Consequently, GENLN2 over-estimates the effect of line-mixing at 15m, since it uses aparameterization to model the band line wings at 15m.

Fig. 5 shows our observed minus computed absorption coef-ficients for a laboratory spectrum of COin the 15- m region.The theory summarized above is labeled Q-, P/R-Mixing in thisfigure, which also shows results for the Cousin line shape, thestandard Lorentz line shape, and a line shape that uses Q-branchmixing with Lorentz for the P/R-branch lines of the strongbands. The center of the strong Q-branch at 720 cmis notwell-modeled in any of these cases because the transmittancespectrum used for this figure was saturated in that region. Ourline shape model calculation in this figureused no adjustableparameters.The duration-of-collision parameters from the4.3- m band were used, along with a standard computationof line-mixing that used a single parameter derived fromQ-branch spectra that is constant for all bands with Q-branches.This result indicates that line-by-line codes using the Cousinline shape at 15 m will overestimate line-mixing (computedbrightness temperatures will be too large in a region with apositive lapse rate).

A. Validation With Aircraft Observations

Figs. 6 and 7 show comparisons between computed and ob-served brightness temperature spectra in the 15-m region forthe WINTEX (Winter EXperiment) and the CLAMS (Chesa-peake Lighthouse and Aircraft Measurements for Satellites) air-craft campaigns. The WINTEX observations were made withthe NPOESS/NASA-Langley NAST-I interferometer flying onNASA’s ER-2 during March 1999. Atmospheric conditions inthe vicinity of a colocated radiosonde launch during this flight


Fig. 6. Observed minus computed spectrum in the longwave CObands.Observed spectrum taken by NAST-I on NASA’s ER-2 during the WINTEXfield campaign. The computed spectrum used the profile from a colocatedradiosonde. The�markers in the top panel denote channels in between spectrallines, and the same channels are denoted with circles in the bottom panel.

were very uniform and largely clear. The computed spectra usedthe radiosonde (CLASS sonde) profile and line-by-line calcula-tions of the radiance, one using our P/R-Mixing algorithm andthe other using the Cousin parameterization for the COlineshape.

The CLAMS measurements were made with the Universityof Wisconsin’s Scanning-HIS interferometer, aboard the ER-2on July 17, 2001 off the coast of Wallops Island, VA, undernominally clear conditions. The CLAMS calculations usedthe ECMWF (European Centre for Medium-Range WeatherForecasts) forecast/analysis model fields for the profile.The Scanning-HIS flew a regular flight pattern that covered11 ECMWF 0.5 grid cells. The calculations shown in thebottom of Fig. 7 are the biases for approximately 3500 indi-vidual fields of view covering the 11 ECMWF grid cells. These3500 points represent 77% of the Scanning-HIS observations.The remaining 23% of the observations were discarded be-cause of cloud/land contamination. In addition, the computedsea-surface temperature was adjusted by approximately 0.5to obtain agreement between observed and computed meansea-surface temperature (window channels). This adjustmentensures that the observed minus computed plot emphasizeserrors in the atmospheric transmittances.

Both Figs. 6 and 7 exhibit the same general error in the Cousinline shape in the 710–740-cm region. Although these dif-ferences are relatively small, they are 5–10 times greater thanthe AIRS accuracy requirements. It is also encouraging thatwe see the same improvements in the observed minus com-puted radiances using different instruments (NAST-I, S-HIS)and different sources for the atmospheric profile (radiosondes,ECMWF model data). The more irregular structures in theseobserved minus computed spectra are either due to an inade-quate temperature profile at higher altitudes, or due to watervapor lines that are in error either due to the spectroscopy, ormore likely, due to uncertainties in the water vapor profile. We

Fig. 7. Observed minus computed spectra (mean errors shown). Observedspectra recorded by the Scanning-HIS spectrometer on the ER-2 during theCLAMS campaign. The computed spectra used ECMWF forecast/analysisfields for the profiles. The� markers in the top panel denote channels inbetween spectral lines, and the same channels are denoted with circles in thebottom panel.

expect higher errors at line centers where much of the atmo-spheric emission originates high in the atmosphere near the air-craft. The radiosonde errors may be larger at these high alti-tudes ( 50 hPa), contributing some of the observed differencesin the WINTEX case. In addition, neither the radiosonde northe ECMWF profiles are appropriate for the temperature pro-file very close to the aircraft where the air path temperature isprobably modified by the local aircraft environment. The goodagreement between observed and computed brightness temper-atures near 720 cm in the CLAMS case is surprising, and pos-sibly fortuitous, since this emission also originates close to theplane.

Fig. 8 is the WINTEX spectrum shown earlier, but now in the4.3- m temperature sounding region where line-mixing is verystrong. Again, the calculations were done for both the Cousinline shape and our P/R-branch line shape. The better agreementfor our P/R-branch calculation is attributed to better laboratorydata that was used to compute the three adjustable parameters(two for duration-of-collision and one for line-mixing) and toour more physically based treatment of line-mixing and dura-tion-of-collision effects inside the band. Similar differences be-tween these two line shapes have been seen in other aircraftspectra.

Finally, we show observed minus computed spectra in thewater vapor region, Fig. 9. The bottom panel in this plot showsobserved minus computed spectra for the WINTEX spectrumdiscussed earlier, and for a clear-sky spectrum taken by theHIS interferometer on the ER-2 during the CAMEX-1 (Con-vection and Moisture EXperiment) in 1993. Both spectra werecomputed using a colocated radiosonde profile. The key fea-ture of these calculations is the relatively good agreement in-be-tween spectral lines (lower altitude water) and the poor, and vari-able, agreement on top of spectral lines (high-altitude water).Errors in-between lines of 2 K near 1600 cm are a con-sequence of changes to CKD 2.4, the water vapor continuum,


Fig. 8. Observed minus computed spectrum around the shortwave COFt.sounding channels. Observed spectrum taken by NAST-I on NASA’s ER-2during the WINTEX field campaign. The computed spectrum used the profilefrom a colocated radiosonde.

Fig. 9. Observed minus computed spectrum in wavenumber regionsdominated by water vapor. (Top) Observed spectrum taken by NAST-I onNASA’s ER-2 during the WINTEX field campaign. (Bottom) Observed minuscomputed spectra for the WINTEX spectrum shown above (blue) and for aspectrum taken during the CAMEX-1 campaign (red).

from earlier versions. If CKD 2.3 is used instead, the errorsnear 1600 cm are reduced by more than 1 K. Comparisonsbetween the CAMEX-1 spectrum and a water vapor continuumdeveloped by Strowet al. [28] show even better agreement inthis spectral region. The AIRS-RTA discussed here uses CKD2.4, but later versions will use a new continuum based on CKD2.4, combined with the results of [28] and the analysis of AIRSvalidation data.

We expect the radiative transfer calculations on top of lines tobe more accurate than calculations between lines, since the cal-culations between lines are dominated by the water vapor con-tinuum, which is always difficult to measure in the laboratory

Fig. 10. Observed minus computed brightness temperatures shown in Fig. 9,but plotted against the computed water vapor brightness temperature. This plotshows that the obs-calc errors are smaller for the higher temperature (loweraltitude) channels where the radiosonde profile is expected to be more accurate.

relative to the water vapor line strengths and widths. We there-fore attribute the poor agreement on top of lines to uncertaintiesin the sonde water vapor profiles at high altitudes, which arecommonly acknowledged to contain high errors.

Fig. 10 is a scatter plot of the observed minus computedbrightness temperatures versus the computed brightness tem-perature for the WINTEX case. This plot emphasizes that mostof the differences between observed and computed spectraare at the lower temperatures, although there are significantdifferences at the band center near 1600 cmthat are severalKelvin, which as stated above are significantly reduced usingCKD 2.3 instead of CKD 2.4.

B. kCARTA and UMBC-LBL

The monochromatic atmospheric transmittances that formthe core of the AIRS-RTA are computed using the kCARTAline-by-line algorithm [12], [13]. kCARTA computes trans-mittances and/or radiances from compressed lookup tables ofatmospheric transmittances, resulting in very fast computationtimes. kCARTA is an extensively documented [13] FORTRAN77 program that is available from the authors. The compressedlookup tables that accompany kCARTA require600 MB ofstorage space.

The kCARTA lookup table transmittances were computedwith a custom line-by-line (LBL) algorithm developed by theauthors, which we call UMBC-LBL. The only real requirementon the UMBC-LBL is to compute kCARTA’s static lookup ta-bles of compressed transmittances. These tables only changewhen improvements are made to the molecular line parametersor gas cross-sections, an infrequent occurrence. Since speed isnot an important issue for UMBC-LBL we can accurately modelboth Q-, and P/R-branch mixing in UMBC-LBL, and not relyon perturbation solutions. At present UMBC-LBL includes COline-mixing for 12 Q-branch and 12 P/R-branch bands. The P/R-


branch bands also include a duration-of-collision term discussedearlier. A detailed description of UMBC-LBL is available [29].

IV. SUMMARY

This paper provides an overview of the AIRS radiativetransfer algorithm, covering both the spectroscopy and the fastparameterization of the radiative transfer used in the retrievalof atmospheric profiles from AIRS observed radiances. Inaddition, we have presented summaries of the results offield experiments using aircraft observations of high-spectralresolution radiances that validate the spectroscopy used inthe AIRS-RTA. These results suggest that the AIRS-RTA hasaccuracies approaching the 0.2 K level for channels dominatedby CO . Accuracies of the AIRS-RTA for water vapor channelsare more difficult to ascertain, although in-between spectrallines field measurements suggest errors on the order of 1 K orbetter in most spectral regions. RTA accuracies for higher alti-tude water channels (line centers) are difficult to validate withaircraft measurements. However, the spectroscopy relevant toradiative transfer at the centers of water lines should be quiteaccurate, since these parameters are relatively easy to measurein the laboratory, and have been studied extensively in the lastseveral years.

The results of the work presented here are available fromthe authors in the form of two packages: 1) a version of theAIRS-RTA (fast model) [10] that can operate outside of theAIRS retrieval system; and 2) the kCARTA pseudo line-by-lineradiative transfer algorithm [13].

The AIRS validation effort [30] will provide a number of op-portunities for validation of the AIRS-RTA, although reachingthe 0.2K level of accuracy will always be challenging.

ACKNOWLEDGMENT

The authors thank the European Centre for Medium-RangeWeather Forecasts (ECMWF) for use of forecast and analysismodel fields for validation of the AIRS forward model (CLAMSexperiment). They also thank J. Johns (NRC-Ottawa, retired) forthe laboratory spectra of CO.

REFERENCES

[1] H. H. Aumann, M. T. Chahine, C. Gautier, M. D. Goldberg, E. Kalnay,L. M. McMillin, H. Revercomb, P. W. Rosenkranz, W. L. Smith, D. H.Staelin, L. L. Strow, and J. Susskind, “AIRS/AMSU/HSB on the Aquamission: Design, science objectives, data products, and processing sys-tems,”IEEE Trans. Geosci. Remote Sensing, vol. 41, pp. 253–264, Feb.2003.

[2] S. E. Hannon and L. L. Strow, “The AIRS radiative transfer algorithm,”,to be published.

[3] L. L. Strow, S. E. Hannon, M. Weiler, K. Overoye, S. L. Gaiser, andH. H. Aumann, “Prelaunch spectral calibration of the Atmospheric In-frared Sounder (AIRS),”IEEE Trans. Geosci. Remote Sensing, vol. 41,pp. 274–286, Feb. 2003.

[4] M. Geller, “A high-resolution atlas of the infrared spectrum of the Sunand the Earth atmosphere from space: Key to identification of solar fea-tures,” NASA, Tech. Rep. NASA Ref. Pub. 1224, vol. III, 1992.

[5] J. Susskind, J. Rosenfield, and D. Reuter, “An accurate radiativetransfer model for use in the direct physical inversion of HIRS 2 andMSU temperature sounding data,”J. Geophys. Res., vol. 88, no. C13,pp. 8550–8568, 1983.

[6] J. Kornfield and J. Susskind, “On the effect of surface emissivity ontemperature retrievals,”Mon. Weather Rev., vol. 105, pp. 1605–1608,1977.

[7] L. M. McMillin, L. J. Crone, M. D. Goldberg, and T. J. Kleespies, “At-mospheric transmittance of an absorbing gas 4:OPTRAN: A computa-tionally fast and accurate transmittance model for absorbing gases withfixed and variable mixing ratios at variable viewing angles,”Appl. Opt.,vol. 34, pp. 6269–6274, 1995.

[8] L. M. McMillin, L. J. Crone, and T. J. Kleespies, “Atmospheric transmit-tance of an absorbing gas 5: Improvements to the OPTRAN approach,”Appl. Opt., vol. 34, pp. 8396–8399, 1995.

[9] S. Hannon, L. L. Strow, and W. W. McMillan, “Atmospheric infraredfast transmittance models: A comparison of two approaches,” inProc.SPIE Conf. 2830, Optical Spectroscopic Tech. Instrument. Atmospher.Space Res. II, 1996.

[10] S. E. Hannon and L. L. Strow. (2002) SARTA: The stand-alone airs radiative transfer algorithm. Univ. Maryland Balti-more County, Dept. Physics, Tech. Rep. [Online]. Available:http://asl.umbc.edu/pub/rta/sarta.

[11] V. Achard, “Trois problemes cles de l’analyze 3D de la structurethermodinamique de l’atmosphere par satellite: Mesure du contenuen ozone: classification des masses d’air; modelization hyper rapidedu ransfert radiatif,” Ph.D. dissertation, LMD, Ecole Polytechnique,Palaiseau, France, 1991.

[12] L. L. Strow, H. E. Motteler, R. G. Benson, S. E. Hannon, and S.De Souza-Machado, “Fast computation of monochromatic infraredatmospheric transmittances using compressed look-up tables,”J. Quant.Spectrosc. Rad. Trans., vol. 59, no. 3–5, pp. 481–493, 1998.

[13] S. De Souza-Machado, L. L. Strow, H. E. Motteler, and S. E.Hannon. (2002) kCARTA: An atmospheric radiative transferalgorithm using compressed lookup tables. Univ. Maryland Bal-timore County, Dept. Physics, Tech. Rep. [Online]. Available:http://asl.umbc.edu/pub/rta/kcarta.

[14] L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P. Ed-wards, J. M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana, J. Y. Mandin, J.Schroeder, A. McCann, R. R. Gamache, R. B. Wattson, K. Yoshino, K. V.Chance, K. W. Jucks, L. R. Brown, V. Nemtchinov, and P. Varanasi, “TheHITRAN molecular spectroscopic database and HAWKS (HITRAN at-mospheric workstation): 1996 edition,”J. Quant. Spectrosc. Rad. Trans.,vol. 60, pp. 665–710, 1998.

[15] J. Susskind, C. D. Barnet, and J. M. Blaisdell, “Retrieval of atmosphericand surface parameters from AIRS/AMSU/HSB data in the presence ofclouds,” IEEE Trans. Geosci. Remote Sensing, vol. 41, pp. 390–409,Feb. 2003.

[16] G. M. Stokes and S. E. Schwartz, “The Atmospheric Radiation Mea-surement (ARM) Program programmatic background and design of thecloud and radiation testbed,”Bull. Amer. Meteorol. Soc., vol. 75, pp.1201–1221, 1994.

[17] L. L. Strow and D. Reuter, “Effect of line mixing on atmospheric bright-ness temperatures near 15�m,” Appl. Opt., vol. 27, p. 872, 1988.

[18] L. L. Strow, “CO Q-branch spectral line shapes for atmospheric re-mote sensing,” inHigh Spectral Resolution Infrared Remote Sensing forEarth’s Weather and Climate Studies, A. Chedin, M. T. Chahine, and N.A. Scott, Eds. New York: Springer-Verlag, 1993, pp. 459–475.

[19] D. P. Edwards, “Genln2: A general line-by-line atmospheric transmit-tance and radiance model,” National Center for Atmospheric Research,Boulder, CO, NCAR Tech. Note 367+STR, 1992.

[20] C. Cousin, R. Le Doucen, C. Boulet, and A. Henry, “Temperature de-pendence of the absorption in the region beyond the 4.3�m band headof CO : 2: N and O broadening,”Appl. Opt., vol. 24, p. 3899, 1985.

[21] C. Cousin, R. Le Doucen, C. Boulet, A. Henry, and D. Robert, “Linecoupling in the temperature and frequency dependencies of absorptionin the microwindows of the 4.3�m CO band,”J. Quant. Spectrosc. Rad.Trans., vol. 36, p. 521, 1986.

[22] J. Boissoles, C. Boulet, L. Bonamy, and D. Robert, “Calculation of ab-sorption in the microwindows of the 4.3�m CO band from an ECSscaling analysis,”J. Quant. Spectrosc. Rad. Trans., vol. 42, p. 509, 1989.

[23] D. C. Tobin, “Infrared spectral lineshapes of water vapor and carbondioxide,” Ph.D. dissertation, Univ. Maryland Baltimore County, Balti-more, MD, 1996.

[24] S. De Souza-Machado, L. L. Strow, D. Tobin, H. Motteler, and S. E.Hannon, “Improved atmospheric radiance calculations using COp/r-branch line mixing,” inProc. Euro. Symp. Aerospace Remote SensingEuropto Series, Sept. 1999.

[25] J. W. C. Johns, “Private communication:�m CO spectra,” unpublished,1992.

[26] G. Birnbaum and E. R. Cohen, “Theory of line shape on pressure-in-duced absorption,”Can. J. Phys., vol. 54, p. 593, 1976.

[27] G. Birnbaum, “The shape of collision broadened lines from resonanceto the far wings,”J. Quant. Spectrosc. Radiat. Transfer, vol. 21, pp.597–607, 1979.


[28] L. L. Strow, D. C. Tobin, W. W. McMillan, S. E. Hannon, W. L. Smith,H. E. Revercomb, and R. Knuteson, “Impact of a new water vapor con-tinuum and line shape model on observed high resolution infrared radi-ances,”J. Quant. Spectrosc. Rad. Trans., vol. 59, no. 3–5, pp. 303–317,1997.

[29] S. De Souza-Machado, L. L. Strow, D. Tobin, H. E. Motteler, and S.E. Hannon. (2002) UMBC-LBL: An algorithm to compute line-by-linespectra. Univ. Maryland Baltimore County, Dept. Physics, Tech. Rep.[Online]. Available: http://asl.umbc.edu/pub/rta/umbclbl.

[30] E. Fetzer, L. M. McMillin, D. Tobin, H. H. Aumann, M. R. Gunson, W.W. McMillan, D. E. Hagan, M. D. Hofstadter, J. Yoe, D. N. Whiteman,J. E. Barnes, R. Bennartz, H. Vomel, V. Walden, M. Newchurch, P. J.Minnett, R. Atlas, F. Schmidlin, E. T. Olsen, M. D. Goldberg, S. Zhou, H.Ding, W. L. Smith, and H. Revercomb, “AIRS/AMSU/HSB validation,”IEEE Trans. Geosci. Remote Sensing, vol. 41, pp. 418–431, Feb. 2003.

L. Larrabee Strow received the B.S. degree inphysics from the University of Maryland—Balti-more County (UMBC), Baltimore, in 1974, andthe M.S. and Ph.D. degrees in physics from theUniversity of Maryland, College Park, in 1977 and1981, respectively.

He is currently a Professor with the Departmentof Physics, UMBC. His research interests includemolecular spectroscopy, especially spectral lineshapes, and atmospheric remote sensing. He is amember of the AIRS Science Team.

Scott E. Hannonreceived the B.A. and M.S. degreesfrom the University of Maryland—Baltimore County(UMBC), Baltimore, in 1986 and 1990, respectively,all in physics.

Since then, he has been with the UMBC workingon topics related to atmospheric physics, with a focuson the development of a fast-forward model for theAIRS instrument.

Sergio De Souza-Machado received the B.S.degree in math/physics from the College of Wooster,Wooster, OH, in 1988, and the M.S. and Ph.D.degrees in physics from the University of Maryland,College Park, in 1990 and 1996, respectively.

He is currently an Assistant Research Scientistwith the Department of Physics, University of Mary-land—Baltimore County, Baltimore. His researchinterests include atmospheric physics, focusing onradiative transfer and molecular spectroscopy, aswell as plasma physics.

Howard E. Motteler (M’88) received the B.S.degree in mathematics from the University of PugetSound, Tacoma, WA, in 1980, the M.S. degree incomputer science from Purdue University, WestLafayette, IN, in 1982, and the Ph.D. degree incomputer science from the University of Maryland,College Park, in 1987.

He is currently a Research Associate Professor atJoint Center for Earth Systems Technology, Univer-sity of Maryland—Baltimore County (UMBC), Bal-timore, while remaining affiliated with the UMBC’s

CSEE Department. His current research interests are in the areas of scientificcomputation and applications in atmospheric science, including passive infraredand microwave sounding and radiative transfer calculations.

David Tobin received the B.S., M.S., and Ph.D. de-grees from the University of Maryland—BaltimoreCounty, Baltimore, in 1991, 1993, and 1996, respec-tively, all in physics.

He is currently a Researcher at the CooperativeInstitute for Meteorological Satellite Studies,Space Science and Engineering Center, Universityof Wisconsin, Madison. His current researchincludes involvement with ground-, aircraft-, andsatellite-based FTIR programs, the AtmosphericRadiation Measurements program, and the Atmo-

spheric Infrared Sounder.

an overview of the airs radiative transfer model...

Documents