Infrared Atmospheric Sounding Interferometercorrelation interferometry for the retrieval of

atmospheric gases the caseof H2O and CO2

Giuseppe Grieco1 Guido Masiello1 Carmine Serio1Roderic L Jones2 and Mohammed I Mead2

1CNISM Unitaacute di Ricerca di Potenza University of Basilicata Via Ateneo Lucano 10 85100 Potenza Italy2Centre for Atmospheric Science Department of Chemistry University of Cambridge Lensfield Road Cambridge CB2 1EW UK

Corresponding author seriounibasit

Received 28 February 2011 revised 13 June 2011 accepted 16 June 2011posted 29 June 2011 (Doc ID 143357) published 29 July 2011

Correlation interferometry is a particular application of Fourier transform spectroscopy with partiallyscanned interferograms Basically it is a technique to obtain the difference between the spectra of atmo-spheric radiance at two diverse spectral resolutions Although the technique could be exploited to designan appropriate correlation interferometer in this paper we are concerned with the analytical aspects ofthe method and its application to high-spectral-resolution infrared observations in order to separate theemission of a given atmospheric gas from a spectral signal dominated by surface emission such as in thecase of satellite spectrometers operated in the nadir looking mode The tool will be used to address somebasic questions concerning the vertical spatial resolution of H2O and to develop an algorithm to retrievethe columnar amount of CO2 An application to complete interferograms from the Infrared AtmosphericSounding Interferometer will be presented and discussed For H2O we have concluded that the verticalspatial resolution in the lower troposphere mostly depends on broad features associated with thespectrum whereas for CO2 we have derived a technique capable of retrieving a CO2 columnar amountwith accuracy of asymp 7parts per million by volume at the level of each single field of view copy 2011 OpticalSociety of AmericaOCIS codes 0100010 0100280 0101280 2804991

1 Introduction

The idea of using partially scanned interferogramsfor the retrieval of atmospheric parameters datesback to Kyle [1] who argued that large portions ofthe spectrum (the Fourier transform of the interfer-ogram and vice versa) could bring poor or no informa-tion for a given atmospheric parameter whereassmall ranges in the interferogram domain could con-centrate much information about the parameter athand Kyle [1] exemplified the techniques for tem-

perature whereas in Ref [2] a correlation inter-ferometer was proposed for the observation of atmo-spheric trace gases The direct inversion of smallsegments of interferometric radiances for the pur-pose of temperature retrieval was further analyzedand exemplified in [3]

In some circumstances according to [1] the inter-ferogram domain can provide a data space in whichinformation about the atmospheric thermodynami-cal state can be encoded much more efficiently thanin the spectral domain Exploiting this idea Griecoet al [4] have shown how to perform a dimensionalityreduction of high-spectral-resolution infrared obser-vations which preserves the spectral coverage of the

0003-693511224516-13$15000copy 2011 Optical Society of America

4516 APPLIED OPTICS Vol 50 No 22 1 August 2011

original spectrum Once compared to the usual wayof reducing a high amount of spectral data by simplyconsidering a sparse (optimal) selection of the spec-tral channels the methodology has shown a betterperformance mostly for the retrieval of water vapor

In this paper we consider the point of transform-ing back to the spectral domain the partial scannedinterferogram in such a way as to obtain a differencespectrum with an improved signal-to-noise ratiowhich can be used for the retrieval of atmosphericgases Depending on the interferogram range we canisolate emission features of atmospheric gases fromeg the strong surface emission In this respect thetechnique is mostly suited for nadir looking radio-metersspectrometers on board satellites becausefor this instrumentation the observed infrared radi-ance is made up by the atmospheric component plusthat of surface emission

In principle for the purpose of atmospheric para-meter retrieval according to [13] once we have in-dividuated a suitable interferogram interval therewould be no need to transform these data back tothe Fourier or spectral domain However while thisstrategy can be effective for temperature which gov-erns the emission at any spectral channels it wouldbe not effective for gases In fact the advantage of thespectral domain is that it is the right domain inwhich to recover and describe the shape or patternarising from the energy emission associated withthe vibrationndashrotation modes of a given atmosphericmolecule As an example the spectral emission pat-tern corresponding to a gas such as CO2 at anywavenumber would give an indication primarily ofthe emission by a particular line whereas the inter-ferogram at a given optical path difference (OPD) isan indication of the combined effect of emissions byall the lines in the spectrum Thus the interferogramdomain can be good for temperature retrieval be-cause we can concentrate in a single small intervalthe temperature information coming from over all ofthe spectrum However for a gas such as CO2 wecould gain advantage by looking back at the Fourierdomain in which eg we could isolate weak emissionoccurring in the hot bands in the atmospheric win-dow from the strong emission within the 14 μm CO2band Thus for particular applications such as thatconcerning CO2 and trace gases there could be anadvantage in transforming back to Fourier space asuitable partial interferogram in such a way as towork directly with a difference spectrum

Although one could in principle design a spectro-meter working on the principle of Fourier transformspectroscopy with partially scanned interferograms[2] the technique is here intended mostly as an ana-lysis tool which can be applied to a complete inter-ferogram recorded over an OPD ranging from zero toa given maximum OPD Therefore in the presentwork the full interferogram is obtained as theFourier transform of the spectrum In principle thespectrum could have been recorded either with aradiometer or a Fourier transform spectrometer

The technique will be exemplified to show how wecan handle and partly separate from the spectrumthe surface emission in order to (i) analyze the ver-tical spatial resolution of H2O retrieval and (ii) devel-op and implement a suitable scheme for the retrievalof the columnar load of CO2

The methodology will be applied to the InfraredAtmospheric Sounding Interferometer (IASI) whichis flying on board the Meteorological OperationalSatellite (MetOp) platform IASI was developed inFrance by the Centre National drsquoEtudes Spatiales(CNES) and is the first of three satellites of theEuropean Organisation for the Exploitation of Me-teorological Satellites (EUMETSAT) European PolarSystem (EPS)

The instrument spectral bandwidth covers therange from 645 to 2760 cmminus1 (362 to 1550 μm) witha sampling interval of Δσ frac14 025 cmminus1 Thus eachsingle spectrum yields 8461 data points or channelsThe calibrated IASI interferogram extends from 0 toa maximum OPD of 2 cm

As already outlined the main objective of thispaper is to illustrate demonstrate and exemplifythe potential advantages of high infrared spectral re-solution observations data analysis with partiallyscanned interferograms through the exploitationof IASI data Toward this objective we have useda forwardinverse methodology which we refer toas φ-IASI whose mathematical aspects and valida-tion have been largely documented (see eg [5ndash9])

The paper is organized as follows In Section 2 wedescribe the IASI data used for the present analysisand describe the basic aspects of the partiallyscanned interferogram approach The applicationto IASI for the purpose of how to address the problemof spatial vertical resolution of H2O retrieval closethe surface is discussed in Section 3 The applicationto IASI for CO2 retrieval is dealt with in Section 4Conclusions are drawn in Section 5

2 Methodological Background IASI Data PartialInterferograms and Transforms

A IASI Data

For the purpose of simulations we use the Chevalierdataset [10] This set is mostly used to define a prioricovariance matrices of atmospheric parameters(background information) and to build up whenneeded (IASI spectrum atmospheric state vector)pairs for the purpose of training statistical retrievalalgorithm The use of this dataset is mostly limited toSection 3

Real IASI observations (mostly used in Section 4)and related atmospheric state vectors come from the2007 Joint Airborne IASI Validation Experiment(JAIVEx) campaign [11] over the Gulf of MexicoWe have a series of six spectra for 29 April 200716 spectra for 30 April 2007 and finally three spectrafor 04 May 2007 The spectra were recorded for clear-sky fields of view selected based on high- resolutionsatellite imagery from the Advanced Very High

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4517

Resolution Radiometer (AVHRR) on MetOp and in-flight observations Furthermore the data for 29April 2007 correspond to a nadir IASI field viewwhereas those for the other two days correspond toa field of view of 2250 degrees

Dropsonde and the European Centre for MediumRange Weather Forecasts (ECMWF) model datawhich have been used for a best estimate of the atmo-spheric state during eachMetOp overpass have beenprepared and made available to us by the JAIVExteam The JAIVEx dataset contains dropsonde pro-files of temperature water vapor and ozone whichextend up to 400hPa Above 400hPa only ECMWFmodel data are available The atmospheric state vec-tors used in this study use JAIVEx dropsonde dataup to 400hPa supplemented by collocated ECMWFforecasts of temperature water vapor and ozonefrom 400hPa to 01hPa (corresponding to about65km)

The validation of the IASI retrieval algorithmfor carbon dioxide is mainly based on CO2 profilesmeasurements which during the JAIVEx campaignwere directly recorded by the University of Cam-bridge Tunable Diode Laser Absorption Spectro-meter (TDLAS) [12] instrument installed on theFacility for Airborne Atmospheric Measurements(FAAM) aircraft [11] We have a set of four CO2 pro-files covering the campaign days from 18 April to 29April 2007 This set of profiles is shown in Fig 1 Forcompleteness we have also included two in situsoundings (18 and 28 April 2007) which refer toflights over the Oklahoma target area The dates ofinterest to us are those of 29 and 30 April 2007 whenthe FAAM aircraft flew below the MetOp satellitetrack over the Gulf of Mexico The complete set ofTDLAS CO2 profiles is here shown also to have anidea of the timendashspace CO2 variability Although theprofiles show a marked difference at some pressurelevels once we consider the columnar amount ofCO2 the variability is 15parts per million by volume(ppmv)

For the purpose of sensitivity analysis we havealso used ECMWFCO2 profiles [1314] obtained fromthe assimilation of the Atmospheric Infrared Radio-meter Sounder (AIRS) radiances The CO2 verticalprofiles were interpolated in space and time to the25 IASI soundings This set of 25 CO2 profiles isshown in Fig 2

Finally again for the purpose of CO2 retrieval wehave also used IASI data for a 12h global acquisitionon 17 November 2009 This dataset is the same asthat used in [15] to perform a cloud detection inter-comparison exercise

B Basics of Fourier Transform Spectroscopy withPartially Scanned Interferograms

The basic concepts of Fourier spectroscopy can befound in the appropriate texts (see eg [16]) Herewe limit ourselves to a summary of the basic defini-tions which are relevant to our methodology

In Fourier spectroscopy the spectrum rethσTHORN (with σthe wavenumber) and the interferogram cethχTHORN (with χthe OPD) constitute a Fourier pair defined by thefollowing equations (see eg [16])

rethσTHORN frac14Z thorninfin

minusinfincethχTHORN expethminus2πiσχTHORNdχ eth1THORN

cethχTHORN frac14Z thorninfin

minusinfinrethσTHORN expeth2πiσχTHORNdσ eth2THORN

with i being the imaginary unitThe spectrum and the interferogram are in prac-

tice band-limited functions therefore taking intoaccount that the interferogram is sampled up to agiven maximum OPD χmax we modify Eq (1) by in-troducing the data-sampling window WethχTHORN

rethσTHORN frac14Z thorninfin

minusinfinWethχTHORNcethχTHORN expethminus2πiσχTHORNdχ eth3THORN

360 365 370 375 380 385 390

200

300

400

500

600

700

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900

1000

1100

CO2 mixing ratio (ppmv)

Pre

ssur

e (h

Pa)

18 April 2007 (CO2 amount 3836 ppmv)

28 April 2007 (CO2 amountt 3841 ppmv)

29 April 2007 (CO2 amount 3814 ppmv)

30 April 2007 (CO2 amount 3851 ppmv)

Fig 1 In situ TDLAS measurements of the CO2 profile for theJAIVEx experiment

375 380 385 390 395 400

0

100

200

300

400

500

600

700

800

900

1000

CO2 mixing ratio (ppmv)

Pre

ssur

e (h

Pa)

29 April 200730 April 200704 May 2007

Fig 2 (Color online) CO2 mixing ratio profiles derived from theECMWF analysis and timendashspace collocated with the 25 JAIVExIASI soundings

4518 APPLIED OPTICS Vol 50 No 22 1 August 2011

with

WethχTHORN frac141 for ∣χ∣ le χmax0 otherwise

eth4THORN

where ∣ middot ∣ means the absolute value and χmax is themaximum OPD

ThemaximumOPD χmax also determines the sam-pling rate Δσ within the spectral domain Accordingto the Nyquist rule the relation is

Δσ frac14 12χmax

Δχ frac14 12ethσ2 minus σ1THORN

eth5THORN

where σ2 minus σ1 is the spectral bandwidth For IASI wehave σ1 frac14 645 cmminus1 σ2 frac14 2760 cmminus1 hence χmax frac142 cm and Δσ frac14 025 cmminus1

The fact that IASI is apodized (see eg [17]) is ofno concern here For IASI we just consider the inter-ferogram obtained from the calibrated apodizedspectrum One could also consider obtaining the com-plete interferogram corresponding to each IASI bandone at a time However for the purpose of the presentstudy the IASI spectrum is a band-limited functionover the range 645 to 2760 cmminus1 whose values areavailable at a sampling interval of Δσ frac14 025 cmminus1

According to the ShannonndashWhittaker samplingtheorem [18] in case we want to resample the spec-trum at a sampling rate lower than the original wejust have to introduce in Eq (3) a data-sampling win-dow with its new cutting point at χτ lt χmax The num-ber Mτ of independent data points that are left afterapplying this truncation is

MτMIASI

frac14 χτχmax

eth6THORN

whereas the new sampling rate in the spectraldomain involves again the Nyquist rule

Δστ frac14 eth2χτTHORNminus1Mτ

MIASIfrac14 Δσ

Δστ eth7THORN

An alternative processing approach which yieldsthe same result could be to use a suitable cardinalsine (or sinc function) interpolation in the spectraldomain This would avoid the passage through theinterferogram domain However we prefer to usethe method outlined above because it is numericallyfaster

1 Partial Interferogram

The partial interferogram can be easily introducedusing the concept of a data-sampling window appliedto the complete interferogram extending from χ frac14 0to χ frac14 χmax

Working with the spectrum in case we do not wantto be sensitive to surface emission we can use chan-nels inside strong absorption bands We can obtain

something similar with a suitable windowing of acomplete interferogram that is by considering an ap-propriate data-sampling window with a lower andupper truncation point [1]

~WethχTHORN frac141 for χτl le ∣χ∣ le χτu0 otherwise

eth8THORN

This data-sampling window removes from the spec-trum all those broad features which are representedby interferometric radiances below the left trunca-tion point χτl In fact we have

~WethχTHORN frac14 WethχTHORNτu minusWethχTHORNτl eth9THORN

where W is the boxcar window as defined in Eq (4)and the subscripts τl and τu identify the windowfunction with cutting points χτl and χτu respectivelyBecause the Fourier transform is linear withinthe spectral domain the double-truncation data-sampling window is equivalent to take the difference

dethσTHORN frac14 rχτu ethσTHORN minus rχτl ethσTHORN eth10THORN

where rχτx ethσTHORN corresponds to the spectrum obtainedby truncating the interferogram at the OPD χτx Inorder to correctly define the difference above weneed the two spectra to be sampled on the samewavenumber grid mesh This is achieved eg byzero-padding the interferogram in order to have asampling interval Δσ frac14 025 cmminus1 which is that cor-responding to the IASI data

An example of the difference spectrum dethσTHORN is ex-emplified in Fig 3 where we show the couples corre-sponding to the right-truncation points χτ frac14 0009000707 cm respectively and the spectral differencewhich corresponds to the interferogram rangefrac1200090 00707 cm It is seen that considering partial

0 0005 001minus20

0204060

a)

1000 1500 2000 2500minus005

0005

01 b)

0 002 004 006minus20

0204060

c(χ)

(W

mminus

2 srminus

1 )

c)

1000 1500 2000 2500minus005

0005

01

r(σ )

(W

mminus

2 (cm

minus1 )minus

1 srminus

1 )

d)

0 002 004 006 008minus2

0

2

optical path difference χ (cm)

e)

1000 1500 2000 2500minus002

0

002

wavenumber σ (cmminus1)

f)

Fig 3 Examples of couples (interferogram spectrum) fordifferent OPDs Couple a) b) refers to χ frac14 00090 cm and couplec) d) refers to χ frac14 00707 cm Couple e) f) exemplifies that thepartial interferogram in the range frac12χ frac14 00090 χ frac14 00707 cm cor-responds to the difference of the spectra d)ndashb)

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4519

interferograms allows us to isolate line absorptionsfrom the broad features of the spectrum

Once again the difference spectrum shown inFig 3f) could be obtained by applying an appropriatesampling function to the spectrum We have just toconsider the Fourier transform of the window func-tion ~WethχTHORN This is the difference of two cardinal sinefunctions

2χτusineth2πσχτuTHORN

2πσχτuminus 2χτl

sineth2πσχτlTHORN2πσχτl

eth11THORN

A more striking example of how we can use theconcept of the partial interferogram is provided inFig 4 where we consider the partial interferogramand the related difference spectrum correspondingto truncation points χτl frac14 065 cm and χτu frac14 068 cmThe contrast also shown in the figure with an inter-ferogram corresponding to a CO2 load equal to zerohelps us to understand how much this short segmentis dominated by CO2 emission The emission for thewhole spectrum finds a strong positive interferenceor correlation in a very short segment of the interfer-ogram This interference is caused by the regularspacing of CO2 lines In the wavenumber domainthis regular spacing has a period of about 16 cmminus1and modern satellite infrared sensors have been de-signed with a spectral resolution better than 08 cmminus1

in order to resolve the periodic structure which ismuch more marked in the ν2 CO2 band

Figure 4 shows that the interferogram intervalfrac12065 068 cm contains much of the informationabout CO2 lines In fact the difference spectrumdethσTHORN just oscillates in phase with the CO2 bandswhose intensities are amplified whereas the bandstructures of other gases are almost zeroed

One important aspect of the partial interferogramis that we reduce the bandwidth of the interferogram

and therefore we improve the signal-to-noise ratiowithin the difference spectrum

According to a well-known elementary result ofFourier spectroscopy [19] the spectral noise varianceis proportional to the interferogram bandwidthΔχ frac14 χτ2 minus χτ1 In case we consider the full interfero-gram Δχ is exactly the maximum OPD which forIASI is 2 cm As a consequence the variance of dethσTHORNis simply computed in case we know the variance ofrethσTHORN that is the radiometric noise affecting the spec-tral radiances

Let εethσTHORN be the radiometric noise affecting the fullIASI spectrum rethσTHORN for the spectrum dethσTHORN the noiseis

εΔethσTHORN frac14 εethσTHORNffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiχτ2 minus χτ1χmax

r eth12THORN

where the subscript Δ refers to the differencespectrum and χmax frac14 2 cm

However to obtain dethσTHORN we use zero padding in or-der not to modify the IASI sampling of 025 cmminus1This means that unless we consider channels thatare far apart from each other we have to take intoaccount the channel correlation

3 Application 1 Sensitivity of Water Vapor Retrievalto Broad Spectral Components

As stated throughout this paper one important as-pect of the partial interferogram methodology is thatit can separate line emissions of atmospheric gasesfrom the bulk emission of the underlying surface

This can be used to check the sensitivity of a givenretrieved atmospheric parameter to the two compo-nents above atmospheric and surface emissions Foratmospheric gases this sensitivity is particularly in-teresting close to the surface Surface channels arenormally located in the atmospheric window andtherefore they are free from strong gas absorptionbands In window channels weak gas emission canexist which is particularly the case for water vaporHowever this weak emission is masked by the back-ground radiation

Considering only leading terms in the radiativetransfer equation the background emission at thetop of the atmosphere can be written as

ϵethσTHORNBethTgTHORNτo eth13THORN

where ϵethσTHORN is the surface emissivity B (Tg) is theblackbody Planck function computed at the tempera-ture of the surface Tg and τo is the total transmit-tance along the atmospheric path from the groundto the satellite

The sensitivity of a retrieval to variations of a gi-ven retrieved parameter at a pressure-altitude levelcan be assessed with the methodology of averagingkernels [62021] These have the advantage of ad-dressing both the effect of the observations (infraredradiance) and that of the background covariancematrix or a priori information

065 0655 066 0665 067 0675 068minus5

0

5

optical path difference χ (cm)

c(χ)

(W

mminus

2 srminus

1 )

a)

1000 1500 2000 2500minus002

minus001

0

001

002

wavenumber (cmminus1)

d(σ)

(W

mminus

2 (cm

minus1 )minus

1 srminus

1 )

b)

Interferogramzero CO

2 interferogram

Fig 4 a) Example of partial interferogram in the range frac12χ frac14065 χ frac14 068 cm for a case of a CO2 load equal to 0 and 385ppmvrespectively and b) difference spectrum dethσTHORN corresponding to thecase with a CO2 load equal to 385ppmv

4520 APPLIED OPTICS Vol 50 No 22 1 August 2011

Figure 5a) shows the averaging kernels for watervapor in the range of 1025 to 900hPa This case wasproduced by considering a tropical model of the atmo-sphere The surface emissivity was set to theMasudaemissivity model for the sea surface [22] Forwardmodel calculations were performed with the σ-IASImodel [78] The background a priori covariancematrix was computed based on climatology [10] Theresult shown in Fig 5a) considers the full IASI spec-tral coverage and data points (8461 IASI channels)It is seen that the retrieval is sensitive to moistureclose to the surface at least to the moisture justabove the planetary boundary layer

The question is then posed of whether the resultshown in Fig 5a) can be improved or not in casewe separate the atmospheric emission from the back-ground radiation

Toward this objective let us consider the interfero-metric radiances belonging to the partial interfero-gram frac1200090 2 cm In this way we remove the headof the interferogram from the data that is the por-tion of data around the zero path difference Accord-ing to the discussion in Subsection 2B1 this has theeffect of removing from the spectrum the broad andsmooth component of Eq (13) that is Earthrsquos surfaceemission and continuum atmospheric emission aswell

The new averaging kernels computed with thepartial interferogram are shown in Fig 5b) It is seenthat the removal of broad emission componentsmakes the situation much worse than the case inwhich we do not remove this background spectral sig-nal The sensitivity to lower moisture is almost zer-oed and the averaging kernels fail to peak to theright atmospheric level

At a first glance one could think that the sensitiv-ity to water vapor close to the surface is an effect ofthe surface emissivity alone In fact it can be shown(eg [23]) that the emissivity modulation preventsthe Jacobian from getting to zero at the surface level

However in the present exercise the effect of emis-sivity modulation can be eliminated from the bulkbackground emission just by setting it to the valueof 1 at each channel

We have redone the averaging kernels computa-tions but this time using ϵethσTHORN frac14 1 They are shownin Fig 6 which can be compared to Fig 5 It is seenthat the emissivity modulation has an important ef-fect in enhancing the sensitivity to H2O variationsclose to the surface However this is not the only ef-fect as Fig 6 clearly shows that a sensitivity to watervapor still exist in a case of a perfect blackbody back-ground emission Looking again at Eq (13) we seethat a smooth term which can be responsible of im-proving the sensitivity to H2O variations in the loweratmosphere is the total transmittance τo Evidentlythe weak line and continuum absorption of H2O arecapable of modulating the emission from the surfaceto an extent that is still capable of adding its finger-print to the averaging kernels

We see that by using the concept of the partial in-terferogram we have found a very interesting resultThis result leads us to conclude that the spatialvertical resolution for water vapor retrieval close tothe surface is dependent on broad features of the spec-trum and is not a consequence of a better spectralresolution

4 Application 2 The Case of CO2 Retrieval

The partial interferogram shown in Fig 4 for a casewith and without CO2 load helps us to understandthat the CO2 signature at 067 cm has to be propor-tional or a function of the CO2 concentration

Transforming back to the spectral domain the par-tial interferogram we obtain the difference spectrum

minus01 0 01 02 03

0

100

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500

600

700

800

900

1000

AK for H2O

Pre

ssur

e (h

Pa)

a)

minus01 0 01 02 03

0

100

200

300

400

500

600

700

800

900

1000

AK for H2O

Pre

ssur

e (h

Pa)

b)

Fig 5 (Color online) Example of IASI averaging kernels for H2Ofor a tropical atmospheric model for the pressure range 1025 to900hPa a) Averaging kernels computed considering the full IASIspectral coverage and channels Panel b) is the same as a) but nowthe averaging kernels have been computed with a partial interfer-ogram extending in the range of frac1200090 2 cm The results havebeen obtained with the Masuda emissivity for the sea surface

minus01 0 01 02 03

0

100

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1000

AK for H2O

Pre

ssur

e (h

Pa)

a)

minus01 0 01 02 03

0

100

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900

1000

AK for H2O

Pre

ssur

e (h

Pa)

b)

Fig 6 (Color online) Same as Fig 5 but now the computationshave been performed considering the surface emissivity equal to 1at each channel

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4521

shown in Fig 4b) where the CO2 periodic line pat-tern is amplified For the purpose of illustration ofhow we can take advantage of this amplification letus consider Fig 7 which for a spectral segmentaround the wavenumber 809 cmminus1 shows dethσTHORN forsix IASI nadir observations along with two referencesynthetic dethσTHORN-spectra corresponding to a CO2 mix-ing ratio of 300 and 450ppmv respectively It is seenthat the six IASI spectra are nicely trapped in be-tween the two reference spectra The IASI spectrawere recorded in April 2007 and for that period theglobal average value for CO2 was 38410 ppmv ac-cording to the NASA Earth System MonitoringLaboratory (Global Monitoring Division eg seehttpwwwesrlnoaagovgmdccggtrends) The tworeference spectra shown in Fig 7 are based on an at-mospheric state vector obtained by inverting one ofthe six IASI spectra

Figure 7 shows that the peaks of the harmonicfunction which result from backtransforming thepartial interferogram in the range frac12065 068 cm area function of the CO2 amount This suggests that thedifference spectrum dethσTHORN can be used to develop andimplement suitable retrieval procedures for CO2

For the present analysis we focus on a simple buteffective statistical regression approach for the esti-mation of the CO2 columnar amount In deriving theprocedure we will make the assumption that theshape of the CO2 profile is uniform with altitudethat is a constant mixing ratio at each pressure le-vel This is equivalent to assume a priori informationabout the CO2 as is usual in any retrieval methodol-ogy The effect of this assumption will be dealt with inSubsection 4B1

An analysis for the search of the channels that arebest linearly correlated with the CO2 columnaramount shows that there are many and a few of them

are almost insensitive to surface emissivity andtemperature

Four of these good channels have been identifiedand they correspond to the wavenumbers 7852580925 97675 and 2105 cmminus1 respectively Forthese channels an example of the functional relation

qCO2frac14 f ethdethσTHORNTHORN eth14THORN

is shown in Fig 8 for a case of noiseless radiances Itis seen that the relation is almost perfectly linearthat is

qCO2frac14 f ethdethσTHORNTHORN asymp a times dethσTHORN thorn b eth15THORN

The above channels correspond to wing regions ofstrong absorption bands or to moderate absorptionbands In general channels inside strong absorptionbands show a behavior that is largely nonlinear

As said the linear behavior shown in Fig 8 corre-sponds to an ideal case with no noise added to theobservations Even in this situation the linear rela-tion is not perfect although the approximation isgood How good it is can be assessed by computingthe standard deviation of the linear best fit to thenoise-free data points For the four channels abovethis is not greater than 13ppmv This value is a sortof inherent error which affects the estimation of qCO2

through the linear approximation of Eq (15) The va-lue of 13ppmv can be thought of as the ultimateaccuracy of the method which cannot be reduced tozero even by averaging because it is related to thelinearization error

With radiances affected by noise the estimation ofthe columnar amount of CO2 through Eq (15) can bemuch larger than the intrinsic value of 13ppmv Theestimation error can be computed through the usualrule of variance propagation

808 8085 809 8095 810 8105 811 8115 812minus25

minus2

minus15

minus1

minus05

0

05

1

15

2

25

3x 10

minus3

wavenumber (cmminus1)

∆ r(

σ) (

W m

minus2 (

cmminus

1 )minus1 s

rminus1 )

Reference at 300 ppmvReference at 450 ppmvIASI observations

Fig 7 (Color online) Example of IASI difference spectra dethσTHORNobtained by Fourier backtransforming the partial interferogramsin the interval frac12χ frac14 065 χ frac14 068 cm The two reference spectrashow that the sinusoid peaks are proportional to the CO2 columnaramount

minus800 minus600 minus400

300

350

400

450σ=78525 cmminus1

d(σ) (W mminus2 (cmminus1)minus1 srminus1)times 106

CO

2 col

umn

amou

nt (

ppm

v)

minus1800 minus1600 minus1400 minus1200

300

350

400

450σ=80925 cmminus1

d(σ) (W mminus2 (cmminus1)minus1 srminus1)times 106

CO

2 col

umn

amou

nt (

ppm

v)

minus300 minus200 minus100

300

350

400

450σ=97675 cmminus1

d(σ) (W mminus2 (cmminus1)minus1 srminus1)times 106

CO

2 col

umn

amou

nt (

ppm

v)

20 30 40 50

300

350

400

450σ=2105 cmminus1

d(σ) (W mminus2 (cmminus1)minus1 srminus1)times 106

CO

2 col

umn

amou

nt (

ppm

v)

Fig 8 Linear dependence of CO2 columnar amount on dethσTHORNfor four channels selected in regions of weak-moderate CO2

absorption

4522 APPLIED OPTICS Vol 50 No 22 1 August 2011

varethqCO2THORN frac14 a2varethdethσTHORNTHORN eth16THORN

where varethsdotTHORN stands for varianceUsing Eq (12) the variance of dethσTHORN is simply

computed in case we know the variance of rethσTHORN thatis the radiometric noise affecting the spectral ra-diances For the case at hand the bandwidth is re-duced by the factor 2=eth068 minus 065THORN frac14 2=003 Thusthe noise for the difference spectrum is scaled downby a factor equal to eth2=003THORN1=2 frac14 8165

However as stated in Subsection 2B1 becausewe use zero padding to obtain dethσTHORN we have to takeinto account channel correlation unless we considerchannels that are far apart from each other For thecase at hand a slight correlation of 035 still existsbetween the couple of channels 78525 cmminus1 and80925 cmminus1

In practice once we have an estimation from eachsingle channelwe can formavariance-weightedaver-age over the four channels in order to obtain a betterestimate with improved variance Let CΔ be the cov-ariance matrix of the difference spectrum computedat the four channels at hand (this is a matrix 4 times 4)and let A be the diagonal matrix whose diagonal ele-ments are the a coefficients for the four channelsThen the covariance matrix of the four estimates ofqCO2

from the four channels respectively is Cq frac14ACΔA0 with the prime meaning transpose For sim-plicity let q frac14 ethq1 q2 q3 q4THORN0 be the vector formedwith the four estimates of the columnar CO2

amount corresponding to the channels 78525 cmminus180925 cmminus1 97675 cmminus1 2105 cmminus1 respectively avariance-weighted average q is obtained by

q frac14X4ifrac141

wiqi eth17THORN

with

wi frac14Cminus1

q ethi iTHORNP4ifrac141 C

minus1q ethi iTHORN eth18THORN

and finally the variance of q is

varethqTHORN frac14X4ifrac141

X4jfrac141

wiwjCqethi jTHORN eth19THORN

Note that the covariance CΔ depends on the noisecharacteristics of the instrument alone whereas thematrixA can be computed in simulation for any givenatmospheric vector therefore Cq and the weightswi

canbe computed in advanceFor IASI and for a typicaltropical atmosphere the weights are 020 058 008and 014 for the channel at 78525 cmminus1 80925 cmminus197675 cmminus1 2105 cmminus1 respectively and ethvarethqTHORNTHORN1=2is approximately 7ppmv Also note that asshown in Fig 8 while the slope for the channel at78525 cmminus1 is positive the slope for the channel at80925 cmminus1 is negative therefore the two estima-tions for qCO2

are anticorrelated with help to furtherreduce the variance

To sum up the procedure is capable of an accuracyof about

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi132 thorn 72

pfrac14 71ppmv at each single

pixel of the 2 times 2 pixel matrix of the IASI instanta-neous field of view (IFOV) Note that the intrinsicterm of13ppmv is a linearization noise and cannotbe reduced to zero by averaging Once averaged overthe four pixels inside each single IFOV the accuracybecomes

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi132 thorn 72=4

pfrac14 37ppmv

A Sensitivity of the Statistical Regression to CO2

Variability and Potential Interfering Factors

The two coefficients a b of the linear fit may dependon the atmospheric state vector The dependence canbe analyzed by considering the sensitivity of dethσTHORN fora given channel σ to a generic atmospheric param-eter The noise-normalized sensitivity to a param-eter X can be computed according to

SXΔ frac14

1εΔethσTHORN

partdethσTHORNpartX

eth20THORN

where εΔethσTHORN is the radiometric noise affecting the dif-ference spectrum dethσTHORN The above sensitivity expres-sion says how much larger is the noise-normalizedvariation of the signal for a unitary perturbation ofa generic atmospheric parameter X Note that ingeneralX can a be a scalar (eg surface temperatureand emissivity in which case the sensitivity is a sca-lar function of the wavenumber σ or a vector (egtemperature profile water vapor profile) in whichcase the sensitivity is a matrix

For the purpose of comparison the above sensitiv-ity can be also defined for the case of the spectrumrethσTHORN

SX frac14

1εethσTHORN

partrethσTHORNpartX

eth21THORN

As stressed in Subsection 2B1 the observationalnoise is different for rethσTHORN and dethσTHORN

We expect that in case X is the CO2 mixing ratioprofile the sensitivity SXΔ is by far larger thanSX and conversely in case X is a potential interferingfactor In other words we expect that the differentia-tion of the spectrum while improving the sensitivityto the CO2 mixing ratio reduces the sensitivity to theremaining state vector components surface emissiv-ity and temperature temperature profile and watervapor profile

That this is in fact the case is shown by the series offigures from Fig 9 to Fig 11 which refer to a tropicalatmosphere model Figure 9 shows that the differen-tiation of the spectrum improves the sensitivity toCO2 by a factor of 5 and more everywhere alongthe vertical

Conversely Fig 10 shows that dethσTHORN is much lesssensitive than rethσTHORN to surface emissivity and tempera-ture In particular dethσTHORN at 78525 and 97675 cmminus1 isalmost insensitive to any variation in the surfacetemperature and emissivity

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4523

For the temperature the situation is similar tothat shown for surface emissivity and temperatureIn particular the sensitivity tends to be lower inthe middle-lower troposphere where we have thebulk of CO2 concentration Concerning the dethσTHORN spec-trum Fig 11 shows that the channel at 80925 cmminus1

is the one most sensitive to temperature variationsfor the case of dethσTHORN To see how much let us considera temperature perturbation ΔT of thorn2K at eachlayer along the profile The corresponding noise-normalized variation ΔethdethσTHORNTHORN=εΔethσTHORN is given accord-ing to Eq (20) by

ΔethdethσTHORNTHORNεΔethσTHORN

frac14 STΔΔT eth22THORN

which when computed at 80925 cmminus1 gives 073Thus the variation of the signal dethσTHORN is below the

noise level Conversely if we perform the same calcu-lation for the case of the spectrum rethσTHORN we obtain

ΔethrethσTHORNTHORNεethσTHORN frac14 STΔT eth23THORN

which once computed at 80925 cmminus1 yields the va-lue 442 This means that the variation in the signalis four times the noise level at 80925 cmminus1 andhence rethσTHORN is largely affected from the temperatureperturbation as expected

The same results as those shown for temperatureare obtained for water vapor The sensitivity of dethσTHORNto water vapor perturbations is by far much less thanthat corresponding to the spectrum rethσTHORN The resultsare not shown for the sake of brevity

B CO2 Retrieval Validation

The methodology to retrieve CO2 has been applied tothe 25 JAIVEx spectra and the results are exempli-fied in Fig 12 To apply the methodology we have toperform the following steps for each single spectrum

1 obtain the atmospheric state vector for thegiven spectrum

2 with the state vector defined at step 1 com-pute a set of spectra corresponding to differentvalues of CO2 columnar amount four reference spec-tra (eg at 300 350 400 and 450ppmv) are enough

3 transform the reference spectra to differencespectra dethσTHORN and compute the coefficients a and bof the linear regression for each channel

4 transform the given IASI spectrum to the dif-ference IASI spectrum and use the linear regressioncomputed at the step above to obtain the estimationof the CO2 columnar amount at each channel and

5 combine the four estimates corresponding tothe four channels as explained in Section 4 to obtainthe final estimate for the given IASI observation

0 2000 4000 6000 8000

0

100

200

300

400

500

600

700

800

900

1000

Sensitivity SX (ppvminus1)

Pre

ssur

e (h

Pa)

a)

0 2000 4000 6000 8000

0

100

200

300

400

500

600

700

800

900

1000

Sensitivity SX∆ (ppvminus1)

b)

78525 cmminus1

80925 cmminus1

97675 cmminus1

2105 cmminus1

78525 cmminus1

80925 cmminus1

97625 cmminus1

2105 cmminus1

Fig 9 For the four channels listed in the legend a) shows sen-sitivity of rethσTHORN and b) shows sensitivity of dethσTHORN to the CO2 mixingratio profile

600 800 1000 1200 1400 1600 1800 2000 22000

100

200

300

400

wavenumber (cmminus1

)

Sen

sitiv

ity to

em

issi

vity

a) SX

SX∆

600 800 1000 1200 1400 1600 1800 2000 22000

2

4

6

8

wavenumber (cmminus1

)Sen

sitiv

ity to

Sur

face

Tem

p (

Kminus1 )

b) SX

SX∆

Fig 10 Sensitivity of rethσTHORN and dethσTHORN to a) surface emissivity andb) surface temperature for the four channels at 78525 8092597675 and 2105 cmminus1

0 01 02 03 04

0

100

200

300

400

500

600

700

800

900

1000

SX (Kminus1)

Pre

ssur

e (h

Pa)

a)

0 01 02 03 04

0

100

200

300

400

500

600

700

800

900

1000

SX∆ (Kminus1)

b)

78525 cmminus1

80925 cmminus1

97675 cmminus1

2105 cmminus1

78525 cmminus1

80925 cmminus1

97625 cmminus1

2105 cmminus1

Fig 11 For the four channels listed in the legend a) shows thesensitivity of rethσTHORN and b) shows the sensitivity of dethσTHORN to thetemperature profile

4524 APPLIED OPTICS Vol 50 No 22 1 August 2011

The atmospheric state vector can be obtained inmany ways radiosonde observations ECMWF short-forecast or analysis retrieval from IASI observa-tions or combinations of these For the presentanalysis the atmospheric state vector has been re-trieved directly from IASI observations

The results shown in Fig 12 are compared to qCO2

columnar amount values as computed by ECMWFCO2 profiles (see Fig 2) obtained from the assimila-tion of AIRS radiances As stated in Subsection 2Athe CO2 vertical profiles were interpolated in spaceand time to the 25 IASI soundings For each IASICO2 channel the computation of qCO2

from a givenCO2 mixing ratio profile is performed according to

qCO2frac14

Rpupi

SCO2ΔqethpTHORNdpRpupi

SCO2Δdp eth24THORN

where qethpTHORN is the CO2 mixing ratio profile at pres-sure p and the sensitivity-weighting function corre-sponds to the given channel The columnar amount isobtained for any single channel and the final value iscomputed as shown in Eq (17) In this way the com-putation parallels the ones we perform to obtain theIASI estimate and gives a value that can be com-pared to the observations

From Fig 12 we see that the ECMWF productstend to slightly overestimate the IASI observationsComparing the average values for the three dayswe have

bull 29 April 2007 3884ppmv (ECMWF) versus3845ppmv (this work)

bull 30 April 2007 3879ppmv (ECMWF) versus3848ppmv (this work) and

bull 4 May 2007 3860ppmv (ECMWF) versus3833ppmv (this work)

It is seen that both AIRS-based ECMWF and IASIretrievals tend to evidence a decreasing trend of CO2from April to May although as said ECMWF seemsto be upward biased with respect to IASI

The above values can be also compared to the glob-ally averaged marine surface monthly mean valueof CO2 which for April 2007 is 38410ppmv (and38394ppmv for May 2007) according to the NASAEarth System Monitoring Laboratory (Global Moni-toring Division eg see httpwwwesrlnoaagovgmdccggtrends)

However a further check of the quality of our CO2retrieval has been obtained by a comparison ofIASI products with in situ TDLAS CO2 profilesThe TDLAS instrument (see Subsection 2A) was in-stalled on the FAAM aircraft and the set of CO2 pro-files recorded during the campaign is shown in Fig 1It should be stressed that these CO2 observationscover the part of the atmosphere (approximately200 to 900hPa) to which our methodology is mostlysensitive (see eg Fig 9) Therefore they providethe most important and accurate test about the relia-bility and accuracy of our methodology

According to these in situ observations we showthat the columnar amount for 29 April 2007 is3814ppmv against an average value as estimatedfrom the six IASI soundings of eth3845 32THORNppmvFor 30 April 2007 for which we have the largest setof IASI soundings (16 IASI spectra) we have a colum-nar amount of 3851ppmv from TDLAS to be com-pared to the value of eth3846 20THORNppmv from IASI(this last value have been averaged over the 16 IASIsoundings) We see that the agreement is very goodparticularly for 30 April 2007 when we have a betterspatial coverage of the target area with 16 IASIsoundings

The TDLAS columnar amount for CO2 is alsoshown in Fig 12 which gives more evidence thatthe ECMWF analysis tends to overestimate the CO2columnar amount If we compare ECMWF to TDLASfor 30April 2007 forwhichTDLASgot an observationdown to the surface we see that ECMWF differs fromTDLAS in the lower troposphere This is the result ofthe fact that satellite observations are not sensitive tonear-surface concentration of atmospheric gases (seealso the discussion in Section 3) The TDLAS profileevidences a fact that is well known to the science com-munity that is that in nonpolluted areas the sea-level amount of CO2 is less than that observed inthe free atmosphere above the planetary boundarylayer (eg see also httpwwwesrlnoaagovgmdccggtrends)

Finally a further consistency check of the CO2columnar amount as derived from our methodologycan be obtained by comparing the variability of the25 estimates (that is their standard deviation) tothe accuracy for any single estimate which has beenassessed to be asymp71ppmv (see Section 4) In fact be-cause of the limited timendashspace span of the JAIVExcampaign it is unlikely that the CO2 columnaramount has remarkably changed its value Thus

0 5 10 15 20 25370

380

390

400

410

420

Number of IASI spectrum

qC

O2 (

ppm

v)a)

0 5 10 15 20 256

7

8

Number of IASI spectrum

Err

or (

ppm

v)

b)

IASI 29 April 2007IASI 30 April 2007IASI 04 May 2007ECMWF analysisTDLAS 29 April 2007TDLAS 30 April 2007

Fig 12 CO2 columnar amount for the 25 IASI spectra of theJAIVEx experiment The figure also provides a comparison withthe CO2 columnar amount from the AIRS-based ECMWFanalysisand TDLAS instrument onboard the FAAM aircraft b) Estimationerror for the IASI estimates [same symbols as in panel a)]

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4525

For the temperature the situation is similar tothat shown for surface emissivity and temperatureIn particular the sensitivity tends to be lower inthe middle-lower troposphere where we have thebulk of CO2 concentration Concerning the dethσTHORN spec-trum Fig 11 shows that the channel at 80925 cmminus1

is the one most sensitive to temperature variationsfor the case of dethσTHORN To see how much let us considera temperature perturbation ΔT of thorn2K at eachlayer along the profile The corresponding noise-normalized variation ΔethdethσTHORNTHORN=εΔethσTHORN is given accord-ing to Eq (20) by

ΔethdethσTHORNTHORNεΔethσTHORN

frac14 STΔΔT eth22THORN

which when computed at 80925 cmminus1 gives 073Thus the variation of the signal dethσTHORN is below the

noise level Conversely if we perform the same calcu-lation for the case of the spectrum rethσTHORN we obtain

ΔethrethσTHORNTHORNεethσTHORN frac14 STΔT eth23THORN

which once computed at 80925 cmminus1 yields the va-lue 442 This means that the variation in the signalis four times the noise level at 80925 cmminus1 andhence rethσTHORN is largely affected from the temperatureperturbation as expected

The same results as those shown for temperatureare obtained for water vapor The sensitivity of dethσTHORNto water vapor perturbations is by far much less thanthat corresponding to the spectrum rethσTHORN The resultsare not shown for the sake of brevity

B CO2 Retrieval Validation

The methodology to retrieve CO2 has been applied tothe 25 JAIVEx spectra and the results are exempli-fied in Fig 12 To apply the methodology we have toperform the following steps for each single spectrum

1 obtain the atmospheric state vector for thegiven spectrum

2 with the state vector defined at step 1 com-pute a set of spectra corresponding to differentvalues of CO2 columnar amount four reference spec-tra (eg at 300 350 400 and 450ppmv) are enough

3 transform the reference spectra to differencespectra dethσTHORN and compute the coefficients a and bof the linear regression for each channel

4 transform the given IASI spectrum to the dif-ference IASI spectrum and use the linear regressioncomputed at the step above to obtain the estimationof the CO2 columnar amount at each channel and

5 combine the four estimates corresponding tothe four channels as explained in Section 4 to obtainthe final estimate for the given IASI observation

0 2000 4000 6000 8000

0

100

200

300

400

500

600

700

800

900

1000

Sensitivity SX (ppvminus1)

Pre

ssur

e (h

Pa)

a)

0 2000 4000 6000 8000

0

100

200

300

400

500

600

700

800

900

1000

Sensitivity SX∆ (ppvminus1)

b)

78525 cmminus1

80925 cmminus1

97675 cmminus1

2105 cmminus1

78525 cmminus1

80925 cmminus1

97625 cmminus1

2105 cmminus1

Fig 9 For the four channels listed in the legend a) shows sen-sitivity of rethσTHORN and b) shows sensitivity of dethσTHORN to the CO2 mixingratio profile

600 800 1000 1200 1400 1600 1800 2000 22000

100

200

300

400

wavenumber (cmminus1

)

Sen

sitiv

ity to

em

issi

vity

a) SX

SX∆

600 800 1000 1200 1400 1600 1800 2000 22000

2

4

6

8

wavenumber (cmminus1

)Sen

sitiv

ity to

Sur

face

Tem

p (

Kminus1 )

b) SX

SX∆

Fig 10 Sensitivity of rethσTHORN and dethσTHORN to a) surface emissivity andb) surface temperature for the four channels at 78525 8092597675 and 2105 cmminus1

0 01 02 03 04

0

100

200

300

400

500

600

700

800

900

1000

SX (Kminus1)

Pre

ssur

e (h

Pa)

a)

0 01 02 03 04

0

100

200

300

400

500

600

700

800

900

1000

SX∆ (Kminus1)

b)

78525 cmminus1

80925 cmminus1

97675 cmminus1

2105 cmminus1

78525 cmminus1

80925 cmminus1

97625 cmminus1

2105 cmminus1

Fig 11 For the four channels listed in the legend a) shows thesensitivity of rethσTHORN and b) shows the sensitivity of dethσTHORN to thetemperature profile

4524 APPLIED OPTICS Vol 50 No 22 1 August 2011

The atmospheric state vector can be obtained inmany ways radiosonde observations ECMWF short-forecast or analysis retrieval from IASI observa-tions or combinations of these For the presentanalysis the atmospheric state vector has been re-trieved directly from IASI observations

The results shown in Fig 12 are compared to qCO2

columnar amount values as computed by ECMWFCO2 profiles (see Fig 2) obtained from the assimila-tion of AIRS radiances As stated in Subsection 2Athe CO2 vertical profiles were interpolated in spaceand time to the 25 IASI soundings For each IASICO2 channel the computation of qCO2

from a givenCO2 mixing ratio profile is performed according to

qCO2frac14

Rpupi

SCO2ΔqethpTHORNdpRpupi

SCO2Δdp eth24THORN

where qethpTHORN is the CO2 mixing ratio profile at pres-sure p and the sensitivity-weighting function corre-sponds to the given channel The columnar amount isobtained for any single channel and the final value iscomputed as shown in Eq (17) In this way the com-putation parallels the ones we perform to obtain theIASI estimate and gives a value that can be com-pared to the observations

From Fig 12 we see that the ECMWF productstend to slightly overestimate the IASI observationsComparing the average values for the three dayswe have

bull 29 April 2007 3884ppmv (ECMWF) versus3845ppmv (this work)

bull 30 April 2007 3879ppmv (ECMWF) versus3848ppmv (this work) and

bull 4 May 2007 3860ppmv (ECMWF) versus3833ppmv (this work)

It is seen that both AIRS-based ECMWF and IASIretrievals tend to evidence a decreasing trend of CO2from April to May although as said ECMWF seemsto be upward biased with respect to IASI

The above values can be also compared to the glob-ally averaged marine surface monthly mean valueof CO2 which for April 2007 is 38410ppmv (and38394ppmv for May 2007) according to the NASAEarth System Monitoring Laboratory (Global Moni-toring Division eg see httpwwwesrlnoaagovgmdccggtrends)

However a further check of the quality of our CO2retrieval has been obtained by a comparison ofIASI products with in situ TDLAS CO2 profilesThe TDLAS instrument (see Subsection 2A) was in-stalled on the FAAM aircraft and the set of CO2 pro-files recorded during the campaign is shown in Fig 1It should be stressed that these CO2 observationscover the part of the atmosphere (approximately200 to 900hPa) to which our methodology is mostlysensitive (see eg Fig 9) Therefore they providethe most important and accurate test about the relia-bility and accuracy of our methodology

According to these in situ observations we showthat the columnar amount for 29 April 2007 is3814ppmv against an average value as estimatedfrom the six IASI soundings of eth3845 32THORNppmvFor 30 April 2007 for which we have the largest setof IASI soundings (16 IASI spectra) we have a colum-nar amount of 3851ppmv from TDLAS to be com-pared to the value of eth3846 20THORNppmv from IASI(this last value have been averaged over the 16 IASIsoundings) We see that the agreement is very goodparticularly for 30 April 2007 when we have a betterspatial coverage of the target area with 16 IASIsoundings

The TDLAS columnar amount for CO2 is alsoshown in Fig 12 which gives more evidence thatthe ECMWF analysis tends to overestimate the CO2columnar amount If we compare ECMWF to TDLASfor 30April 2007 forwhichTDLASgot an observationdown to the surface we see that ECMWF differs fromTDLAS in the lower troposphere This is the result ofthe fact that satellite observations are not sensitive tonear-surface concentration of atmospheric gases (seealso the discussion in Section 3) The TDLAS profileevidences a fact that is well known to the science com-munity that is that in nonpolluted areas the sea-level amount of CO2 is less than that observed inthe free atmosphere above the planetary boundarylayer (eg see also httpwwwesrlnoaagovgmdccggtrends)

Finally a further consistency check of the CO2columnar amount as derived from our methodologycan be obtained by comparing the variability of the25 estimates (that is their standard deviation) tothe accuracy for any single estimate which has beenassessed to be asymp71ppmv (see Section 4) In fact be-cause of the limited timendashspace span of the JAIVExcampaign it is unlikely that the CO2 columnaramount has remarkably changed its value Thus

0 5 10 15 20 25370

380

390

400

410

420

Number of IASI spectrum

qC

O2 (

ppm

v)a)

0 5 10 15 20 256

7

8

Number of IASI spectrum

Err

or (

ppm

v)

b)

IASI 29 April 2007IASI 30 April 2007IASI 04 May 2007ECMWF analysisTDLAS 29 April 2007TDLAS 30 April 2007

Fig 12 CO2 columnar amount for the 25 IASI spectra of theJAIVEx experiment The figure also provides a comparison withthe CO2 columnar amount from the AIRS-based ECMWFanalysisand TDLAS instrument onboard the FAAM aircraft b) Estimationerror for the IASI estimates [same symbols as in panel a)]

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4525

The atmospheric state vector can be obtained inmany ways radiosonde observations ECMWF short-forecast or analysis retrieval from IASI observa-tions or combinations of these For the presentanalysis the atmospheric state vector has been re-trieved directly from IASI observations

The results shown in Fig 12 are compared to qCO2

columnar amount values as computed by ECMWFCO2 profiles (see Fig 2) obtained from the assimila-tion of AIRS radiances As stated in Subsection 2Athe CO2 vertical profiles were interpolated in spaceand time to the 25 IASI soundings For each IASICO2 channel the computation of qCO2

from a givenCO2 mixing ratio profile is performed according to

qCO2frac14

Rpupi

SCO2ΔqethpTHORNdpRpupi

SCO2Δdp eth24THORN

where qethpTHORN is the CO2 mixing ratio profile at pres-sure p and the sensitivity-weighting function corre-sponds to the given channel The columnar amount isobtained for any single channel and the final value iscomputed as shown in Eq (17) In this way the com-putation parallels the ones we perform to obtain theIASI estimate and gives a value that can be com-pared to the observations

From Fig 12 we see that the ECMWF productstend to slightly overestimate the IASI observationsComparing the average values for the three dayswe have

bull 29 April 2007 3884ppmv (ECMWF) versus3845ppmv (this work)

bull 30 April 2007 3879ppmv (ECMWF) versus3848ppmv (this work) and

bull 4 May 2007 3860ppmv (ECMWF) versus3833ppmv (this work)

It is seen that both AIRS-based ECMWF and IASIretrievals tend to evidence a decreasing trend of CO2from April to May although as said ECMWF seemsto be upward biased with respect to IASI

The above values can be also compared to the glob-ally averaged marine surface monthly mean valueof CO2 which for April 2007 is 38410ppmv (and38394ppmv for May 2007) according to the NASAEarth System Monitoring Laboratory (Global Moni-toring Division eg see httpwwwesrlnoaagovgmdccggtrends)

However a further check of the quality of our CO2retrieval has been obtained by a comparison ofIASI products with in situ TDLAS CO2 profilesThe TDLAS instrument (see Subsection 2A) was in-stalled on the FAAM aircraft and the set of CO2 pro-files recorded during the campaign is shown in Fig 1It should be stressed that these CO2 observationscover the part of the atmosphere (approximately200 to 900hPa) to which our methodology is mostlysensitive (see eg Fig 9) Therefore they providethe most important and accurate test about the relia-bility and accuracy of our methodology

According to these in situ observations we showthat the columnar amount for 29 April 2007 is3814ppmv against an average value as estimatedfrom the six IASI soundings of eth3845 32THORNppmvFor 30 April 2007 for which we have the largest setof IASI soundings (16 IASI spectra) we have a colum-nar amount of 3851ppmv from TDLAS to be com-pared to the value of eth3846 20THORNppmv from IASI(this last value have been averaged over the 16 IASIsoundings) We see that the agreement is very goodparticularly for 30 April 2007 when we have a betterspatial coverage of the target area with 16 IASIsoundings

The TDLAS columnar amount for CO2 is alsoshown in Fig 12 which gives more evidence thatthe ECMWF analysis tends to overestimate the CO2columnar amount If we compare ECMWF to TDLASfor 30April 2007 forwhichTDLASgot an observationdown to the surface we see that ECMWF differs fromTDLAS in the lower troposphere This is the result ofthe fact that satellite observations are not sensitive tonear-surface concentration of atmospheric gases (seealso the discussion in Section 3) The TDLAS profileevidences a fact that is well known to the science com-munity that is that in nonpolluted areas the sea-level amount of CO2 is less than that observed inthe free atmosphere above the planetary boundarylayer (eg see also httpwwwesrlnoaagovgmdccggtrends)

Finally a further consistency check of the CO2columnar amount as derived from our methodologycan be obtained by comparing the variability of the25 estimates (that is their standard deviation) tothe accuracy for any single estimate which has beenassessed to be asymp71ppmv (see Section 4) In fact be-cause of the limited timendashspace span of the JAIVExcampaign it is unlikely that the CO2 columnaramount has remarkably changed its value Thus

0 5 10 15 20 25370

380

390

400

410

420

Number of IASI spectrum

qC

O2 (

ppm

v)a)

0 5 10 15 20 256

7

8

Number of IASI spectrum

Err

or (

ppm

v)

b)

IASI 29 April 2007IASI 30 April 2007IASI 04 May 2007ECMWF analysisTDLAS 29 April 2007TDLAS 30 April 2007

Fig 12 CO2 columnar amount for the 25 IASI spectra of theJAIVEx experiment The figure also provides a comparison withthe CO2 columnar amount from the AIRS-based ECMWFanalysisand TDLAS instrument onboard the FAAM aircraft b) Estimationerror for the IASI estimates [same symbols as in panel a)]

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4525

the variability we observe among the 25 estimateshas to be just a result of random variations becauseof instrument noise As a consequence we have tofind that this variability has to agree with the accu-racy of each single estimate We have found that thevariability is 718ppmv which can be compared tothe expected accuracy of 71ppmv This definitelyshows that our in-depth error analysis takes cor-rectly into account all the important random noisesources which affect the IASI observations FromFig 12 it is also evident that we observe in adjacentIASI pixels peak-to-peak variations of 20ppmvwhich are unlikely to be an effect of spatial varia-tions The fact is that with an accuracy of 71ppmvthe 3σ interval has a width of 426ppmv thereforepeak-to-peak variations of 20ppmv are consistentwith the expected random fluctuations

1 Sensitivity to the a Priori CO2 Profile

Throughout Section 4 to Subsection 4B we have as-sumed that the shape of the CO2 profile is uniformwith altitude that is a constant mixing ratio at anypressure level Thus a final important aspect wewant to address is the sensitivity of our method tothe a priori CO2 profile shape we assume in order toperform the radiative transfer calculations whichare used to compute the regression coefficientsin Eq (15)

It has to be stressed that the choice of an a prioriCO2 profile (background information or whatsoever)has to be done in any retrieval method we either con-sider retrieving the CO2 mixing ratio profile or itscolumnar amount Depending on how this a priori isconsistent with the true atmospheric parameter wewant to retrieve it can introduce a bias in the finalestimate This section provides an assessment of theorder of magnitude of this further bias

Toward this objective we have redone the compu-tation for the JAIVEx experiment but now the shapeof the CO2 profile is no longer uniform with altitudebut it is determined according to the shape of theCO2 profiles of the ECMWFanalysis (see Fig 2) Thischoice allows us to simulate realistic situationsalthough by a comparison with TDLAS we knowthat the ECMWF CO2 profile shape is in error inthe lower troposphere Each IASI sounding has beencoupled with its collocated ECMWFCO2 profile Thisprofile is scaled to a prescribed CO2 amount qCO2

through

qsethpTHORN frac14qCO2

times qecmwf ethpTHORNRpupi

qecmwf ethpTHORNdp eth25THORN

As before allowing qCO2to vary in a prescribed range

of values we have a set of scaled profiles qsethpTHORN whichare used to perform the computation of the regres-sion coefficients in Eq (15)

In Fig 13 the 25 IASI JAIVEx estimates obtainedin this way are compared to those corresponding toCO2 profiles with a uniform shape It is seen from this

figure that the difference between the two sets is ofthe order of 1ppmv less than the intrinsic accuracyof the method itself As outlined in Subsection 4Bthe reason of this slight positive difference is that theECMWF analysis tends to overestimate the CO2amount in the lower troposphere

We conclude this section by showing a first IASICO2 map corresponding to two IASI orbits for the per-iod 17ndash18 November 2009 The CO2 column amounthas been averaged over the four pixels for each IASIIFOV therefore the expected accuracy of each esti-mate is of the order of asymp37ppmv The map of theseresults is shown in Fig 14 The map is intended tobe illustrative of the capability of the method andnot to draw significant results about CO2 variabilitywhich deserves a more complete analysis in terms oftimendashspace coverage However we see that the mappresented in Fig 14 captures very well the positivegradient close to the coasts and is largely in agree-ment with the globally averaged value for that timewhich was around 386ppmv As already observed in

0 5 10 15 20 25370

380

390

400

410

Number of IASI sounding

q CO

2 (pp

mv) a)

0 5 10 15 20 250

05

1

15

2

Number of IASI sounding

Diff

eren

ce (

ppm

v)

b)

Uniform shapeNonuniform shape

Difference

Fig 13 Checking the sensitivity of our CO2 columnar amountretrieval amount to the assumed shape for the CO2 profile(uniform or not with altitude) The exercise shown in the figuresconsiders the 25 IASI soundings of the JAIVEx experiment Thedifference in panel b) is (nonuniform)ndash(uniform)

ppmv

370 375 380 385 390 395 400 405 410

Fig 14 (Color online) IASI CO2 map for portions of two orbitson 17 November 2009

4526 APPLIED OPTICS Vol 50 No 22 1 August 2011

Subsection 4B when commenting on the results inFig 12 we can see also from the present map thatthere are adjacent pixels for which we observe a var-iation of up to 10ndash20ppmv As already said oneshould consider that with an accuracy of 37ppmvthe3σ interval has a width of 222ppmv Thereforethe large variability seen in some part of the map isstill statistically consistent with the accuracy of themethodology In addition one should consider thatwhile for the JAIVEx experiment clear sky has beencarefully checked also with satellite imagery of thetarget area for the case shown in Fig 14 clear skyhas been diagnosed with an IASI stand-alone cloudscene tool [824] and therefore cloud contaminationis likely to occur in some pixels and hence introducespurious variability This variability is eliminated byconsidering monthly maps which have also the effectof reducing meteorological variability

5 Conclusions

Exploiting basic concepts of correlation interferome-try also known as Fourier transform spectroscopywith partially scanned interferograms we have de-veloped and discussed a methodological frameworkwhich can be used to develop retrieval algorithmswith IASI data for atmospheric gases The methodol-ogy has been illustrated and exemplified with simu-lated and real IASI observations

Taking advantage of the fact that the concept of apartial interferogram over a given range frac12χ1 χ2 isequivalent to differentiate two spectra at a spectralresolution determined by the two OPDs χ1 and χ2according to the well-known Nyquist rule we haveset up a general scheme that allows us to isolate lineemissions from those potentially interfering of thesurface

The concept of the partial interferogram has beenthen used to show that

bull close to the surface the vertical spatialresolution of the retrieved water vapor profile is onlydetermined by broad feature in the spectrum and

bull an efficient statistical regression procedure forthe retrieval of the CO2 columnar amount can be de-signed based on correlation interferometry

The capability of the CO2 retrieval method hasbeen exemplified and demonstrated with the use ofIASI data It has been shown that the method canprovide a CO2 columnar amount with an accuracyof asymp 7ppmv at the level of the single IASI IFOVThe particularly appealing advantage of this methodis the capability to isolate the effect of CO2 lines fromother possible interfering effects and improve the sig-nal-to-noise ratio also by a factor 5 and more whichallows us to look at wing regions of the CO2 absorp-tion bands and weak lines in the hot bands located inthe atmospheric windows Unlike strong absorptionregions weak absorption bands behave linearly un-der variations of the CO2 amount

Finally it has to be stressed that the concept ofcorrelation interferometry can be easily extendedto other minortrace gases such as CO CH4 andN2O an objective which is under present investiga-tion by the authors

The IASI has been developed and built under theresponsibility of the Centre National drsquoEtudesSpatiales (CNES France) It is flown on-board theMetOp satellites as part of the EUMETSAT PolarSystem The IASI L1 data are received throughthe EUMETCast near-real-time data distributionservice We thank Dr Stuart Newman (Met Office)for providing the JAIVEx data The JAIVEx projecthas been partially funded under EUMETSAT con-tract EumCO061596PS The FAAM BAe 146 isjointly funded by the Met Office and the Natural En-vironment Research Council The US JAIVEx teamwas sponsored by the National Polar-orbiting Opera-tional Environmental Satellite System IntegratedProgram Office and the National Aeronautical SpaceAdministration (NASA)

References1 T G Kyle ldquoTemperature soundings with partially scanned

interferogramsrdquo Appl Opt 16 326ndash332 (1977)2 H W Goldstein R N Grenda M H Bortner and R Dick

ldquoCIMATS a correlation interferometer for the measurementsof atmospheric trace speciesrdquo in Proceedings of the 4th JointConference on Sensing of Environmental Pollutants (AmericanChemical Society 1978) pp 586ndash589

3 W L Smith H B Howell and H M Woolf ldquoThe use ofinterferometric radiance measurements for sounding theatmosphererdquo J Atmos Sci 36 566ndash575 (1979)

4 G Grieco G Masiello and C Serio ldquoInterferometric vsspectral IASI radiances Effective data-reduction approachesfor the satellite sounding of atmospheric thermodynamicalparametersrdquo Int J Remote Sens 2 2323ndash2346 (2010)

5 G Masiello and C Serio ldquoDimensionality-reduction approachto the thermal radiative transfer equation inverse problemrdquoGeophys Res Lett 31 L11105 (2004)

6 A Carissimo I De Feis and C Serio ldquoThe physical retrievalmethodology for IASI the δ-IASI coderdquo Environ Model Soft-ware 20 1111ndash1126 (2005)

7 U Amato G Masiello C Serio and M Viggiano ldquoThe σ-IASIcode for the calculation of infrared atmospheric radiance andits derivativesrdquo Environ Model Software 17 651ndash667 (2002)

8 G Grieco G Masiello M Matricardi C Serio D Summa andV Cuomo ldquoDemonstration and validation of the φ-IASI inver-sion scheme with NAST-I datardquo Q J R Meteorol Soc 133217ndash232 (2007) available online at httponlinelibrarywileycomdoi101002qj162pdf

9 GMasielloCSerioACarissimoandGGriecoldquoApplicationofϕ-IASI to IASI retrieval products evaluation and radiativetransfer consistencyrdquo Atmos Chem Phys 9 8771ndash8783(2009) available online at wwwatmos‑chem‑physnet987712009

10 F Chevallier ldquoSampled database of 60 levels atmospheric pro-files from the ECMWF analysisrdquo Technical report ECMWFEUMETSAT SAF programme research report 4 (EuropeanCentre for Medium Range Weather Forecasts 2001)

11 Facility for Airborne Atmospheric Measurements ldquoJoint air-borne IASI validation experiment (JAIVEX)rdquo httpbadcnerc acukdatajaivex

12 T Gardiner M I Mead S Garcelon R Robinson N SwannG M Hansford P T Woods and R L Jones ldquoA lightweight

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4527

Subsection 4B when commenting on the results inFig 12 we can see also from the present map thatthere are adjacent pixels for which we observe a var-iation of up to 10ndash20ppmv As already said oneshould consider that with an accuracy of 37ppmvthe3σ interval has a width of 222ppmv Thereforethe large variability seen in some part of the map isstill statistically consistent with the accuracy of themethodology In addition one should consider thatwhile for the JAIVEx experiment clear sky has beencarefully checked also with satellite imagery of thetarget area for the case shown in Fig 14 clear skyhas been diagnosed with an IASI stand-alone cloudscene tool [824] and therefore cloud contaminationis likely to occur in some pixels and hence introducespurious variability This variability is eliminated byconsidering monthly maps which have also the effectof reducing meteorological variability

5 Conclusions

Exploiting basic concepts of correlation interferome-try also known as Fourier transform spectroscopywith partially scanned interferograms we have de-veloped and discussed a methodological frameworkwhich can be used to develop retrieval algorithmswith IASI data for atmospheric gases The methodol-ogy has been illustrated and exemplified with simu-lated and real IASI observations

Taking advantage of the fact that the concept of apartial interferogram over a given range frac12χ1 χ2 isequivalent to differentiate two spectra at a spectralresolution determined by the two OPDs χ1 and χ2according to the well-known Nyquist rule we haveset up a general scheme that allows us to isolate lineemissions from those potentially interfering of thesurface

The concept of the partial interferogram has beenthen used to show that

bull close to the surface the vertical spatialresolution of the retrieved water vapor profile is onlydetermined by broad feature in the spectrum and

bull an efficient statistical regression procedure forthe retrieval of the CO2 columnar amount can be de-signed based on correlation interferometry

The capability of the CO2 retrieval method hasbeen exemplified and demonstrated with the use ofIASI data It has been shown that the method canprovide a CO2 columnar amount with an accuracyof asymp 7ppmv at the level of the single IASI IFOVThe particularly appealing advantage of this methodis the capability to isolate the effect of CO2 lines fromother possible interfering effects and improve the sig-nal-to-noise ratio also by a factor 5 and more whichallows us to look at wing regions of the CO2 absorp-tion bands and weak lines in the hot bands located inthe atmospheric windows Unlike strong absorptionregions weak absorption bands behave linearly un-der variations of the CO2 amount

Finally it has to be stressed that the concept ofcorrelation interferometry can be easily extendedto other minortrace gases such as CO CH4 andN2O an objective which is under present investiga-tion by the authors

The IASI has been developed and built under theresponsibility of the Centre National drsquoEtudesSpatiales (CNES France) It is flown on-board theMetOp satellites as part of the EUMETSAT PolarSystem The IASI L1 data are received throughthe EUMETCast near-real-time data distributionservice We thank Dr Stuart Newman (Met Office)for providing the JAIVEx data The JAIVEx projecthas been partially funded under EUMETSAT con-tract EumCO061596PS The FAAM BAe 146 isjointly funded by the Met Office and the Natural En-vironment Research Council The US JAIVEx teamwas sponsored by the National Polar-orbiting Opera-tional Environmental Satellite System IntegratedProgram Office and the National Aeronautical SpaceAdministration (NASA)

References1 T G Kyle ldquoTemperature soundings with partially scanned

interferogramsrdquo Appl Opt 16 326ndash332 (1977)2 H W Goldstein R N Grenda M H Bortner and R Dick

ldquoCIMATS a correlation interferometer for the measurementsof atmospheric trace speciesrdquo in Proceedings of the 4th JointConference on Sensing of Environmental Pollutants (AmericanChemical Society 1978) pp 586ndash589

3 W L Smith H B Howell and H M Woolf ldquoThe use ofinterferometric radiance measurements for sounding theatmosphererdquo J Atmos Sci 36 566ndash575 (1979)

4 G Grieco G Masiello and C Serio ldquoInterferometric vsspectral IASI radiances Effective data-reduction approachesfor the satellite sounding of atmospheric thermodynamicalparametersrdquo Int J Remote Sens 2 2323ndash2346 (2010)

5 G Masiello and C Serio ldquoDimensionality-reduction approachto the thermal radiative transfer equation inverse problemrdquoGeophys Res Lett 31 L11105 (2004)

6 A Carissimo I De Feis and C Serio ldquoThe physical retrievalmethodology for IASI the δ-IASI coderdquo Environ Model Soft-ware 20 1111ndash1126 (2005)

7 U Amato G Masiello C Serio and M Viggiano ldquoThe σ-IASIcode for the calculation of infrared atmospheric radiance andits derivativesrdquo Environ Model Software 17 651ndash667 (2002)

8 G Grieco G Masiello M Matricardi C Serio D Summa andV Cuomo ldquoDemonstration and validation of the φ-IASI inver-sion scheme with NAST-I datardquo Q J R Meteorol Soc 133217ndash232 (2007) available online at httponlinelibrarywileycomdoi101002qj162pdf

9 GMasielloCSerioACarissimoandGGriecoldquoApplicationofϕ-IASI to IASI retrieval products evaluation and radiativetransfer consistencyrdquo Atmos Chem Phys 9 8771ndash8783(2009) available online at wwwatmos‑chem‑physnet987712009

10 F Chevallier ldquoSampled database of 60 levels atmospheric pro-files from the ECMWF analysisrdquo Technical report ECMWFEUMETSAT SAF programme research report 4 (EuropeanCentre for Medium Range Weather Forecasts 2001)

11 Facility for Airborne Atmospheric Measurements ldquoJoint air-borne IASI validation experiment (JAIVEX)rdquo httpbadcnerc acukdatajaivex

12 T Gardiner M I Mead S Garcelon R Robinson N SwannG M Hansford P T Woods and R L Jones ldquoA lightweight

1 August 2011 Vol 50 No 22 APPLIED OPTICS 4527

near-infrared spectrometer for the detection of trace atmo-spheric speciesrdquo Rev Sci Instrum 81 083102 (2010)

13 RJEngelenSSerrarandFChevallierldquoFourdimensionaldataassimilation of atmospheric CO2 using AIRS observationsrdquo JGeophys Res 114 D03303 (2009)

14 G Masiello M Matricardi and C Serio ldquoThe use of IASI datato identify systematic errors in the ECMWF forecasts of tem-perature in the upper stratosphererdquo Atmos Chem Phys 111009ndash1021 (2011)

15 L Lavanant N Fourrieacute A Gambacorta G Grieco SHeilliette F I Hilton M-J Kim A P McNally H NishihataE G Pavelin and F Rabier ldquoComparison of cloud productswithin IASI footprints for the assimilation of cloudy ra-diancesrdquo Q J R Meteorol Soc (to be published)

16 R J Bell Introductory Fourier Transform Spectroscopy(Academic 1972)

17 U Amato D De Canditiis and C Serio ldquoEffect of apo-dization on the retrieval of geophysical parameters fromFourier-transform spectrometersrdquo Appl Opt 37 6537ndash6543(1998)

18 E A Robinson and M T Silvia Digital Foundation of TimeSeries Analysis Wave-Equation Space-Time Processing Vol 2(Holden-Day 1981)

19 H M Pichett and H L Strauss ldquoSignal-to-noise ratio inFourier spectrometryrdquo Anal Chem 44 265ndash270 (1972)

20 G Backus and F Gilbert ldquoThe resolving power of gross Earthdatardquo Geophys J R Astron Soc 16 169ndash205 (1968)

21 C D Rodgers Inverse Methods for Atmospheric SoundingTheory and Practice Series on Atmospheric Oceanic andPlanetary Physics Vol 2 (World Scientific 2000)

22 K Masuda T Takashima and Y Takayama ldquoEmissivityof pure and sea waters for the model sea surface in the infra-red window regionsrdquo Remote Sens Environ 24 313ndash329(1988)

23 A M Lubrano G Masiello M Matricradi C Serio andV Cuomo ldquoRetrieving N2O from nadir-viewing infrared spec-trometersrdquo Tellus B 56 249ndash261 (2004)

24 G Masiello C Serio and H Shimoda ldquoQualifying IMGtropical spectra for clear skyrdquo J Quant Spectrosc RadiatTransfer 77 131ndash148 (2003)

4528 APPLIED OPTICS Vol 50 No 22 1 August 2011