Laser diode absorption spectroscopy for accurateCO2 line parameters at 2 μm: consequences

for space-based DIAL measurementsand potential biases

Lilian Joly,1 Fabien Marnas,2 Fabien Gibert,2 Didier Bruneau,3 Bruno Grouiez,1

Pierre H. Flamant,2 Georges Durry,1,3 Nicolas Dumelie,1

Bertrand Parvitte,1 and Virginie Zéninari1,*1Groupe de Spectrométrie Moléculaire et Atmosphérique, UMR CNRS 6089, UFR Sciences

Exactes et Naturelles, BP 1039, 51687 Reims Cedex, France2Institut Pierre Simon Laplace (IPSL), Laboratoire de Météorologie Dynamique (LMD),

UMR CNRS 8539, Ecole Polytechnique, 91128 Palaiseau Cedex, France3Institut Pierre Simon Laplace (IPSL), LATMOS, UMR CNRS 8190, CNRS-Réduit

de Verrières, B.P. 3, 91371 Verrières-le-Buisson Cedex, France

*Corresponding author: virginie.zeninari@univ‑reims.fr

Received 22 June 2009; revised 11 September 2009; accepted 11 September 2009;posted 16 September 2009 (Doc. ID 113194); published 1 October 2009

Space-based active sensing of CO2 concentration is a very promising technique for the derivation of CO2

surface fluxes. There is a need for accurate spectroscopic parameters to enable accurate space-basedmea-surements to address global climatic issues. New spectroscopic measurements using laser diode absorp-tion spectroscopy are presented for the preselected R30 CO2 absorption line (ð2001ÞIII←ð000Þ band) andfour others. The line strength, air-broadening halfwidth, and its temperature dependence have been in-vestigated. The results exhibit significant improvement for the R30 CO2 absorption line: 0.4% on the linestrength, 0.15% on the air-broadening coefficient, and 0.45% on its temperature dependence. Analysisof potential biases of space-based DIAL CO2 mixing ratio measurements associated to spectroscopicparameter uncertainties are presented. © 2009 Optical Society of America

OCIS codes: 280.1910, 300.6260.

1. Introduction

Carbon dioxide has been identified as a key green-house gas due to its significant contribution to globalwarming and climate change [1]. Limitations in ourcurrent understanding of the carbon cycle limit ourcapacity to predict future evolution of atmosphericCO2 and global temperature on the Earth. These lim-itations are mostly due to our incapacity to localize

and quantify CO2 surface sources and sinks. CO2fluxes are currently measured at the surface, butsuch measurements are scattered and difficult to ex-trapolate in larger scale using an ecosystemmodel inthe so-called “bottom–up” view [2]. CO2 concentra-tion measurements in synergism with a transportmodel can also infer CO2 surface fluxes in the“top-down” view [3], which justifies the many effortsthat are currently done to measure CO2 concentra-tion from space. Passive techniques use spectra ob-tained in the thermal infrared (AIRS, IASI) ormid-infrared (SCIAMACHY, GOSAT) domains [4–6].

0003-6935/09/295475-09$15.00/0© 2009 Optical Society of America

10 October 2009 / Vol. 48, No. 29 / APPLIED OPTICS 5475

However, the first ones provide CO2 concentration inthe upper troposphere only, far from the surfacefluxes. The latest are dependent on solar illumina-tion with inherent restrictions concerning daytimeoperation and the latitude of measurements. Thesemid-infrared passive instruments are also sensitiveto regional biases due to heterogeneous thin cloudsand aerosol layers.In this context, the pulsed differential absorption

lidar (DIAL) technique, which uses echo from theground, appears promising for global monitoring ofCO2 concentration from space. Demonstration of ac-curate DIALmeasurement from the ground has beenreported [7–9], and enhanced efforts in DIAL tech-nology for a space-based mission are on the way.Some space programs are also under study at NASA(ASCENDS) and at ESA (A-SCOPE) [10,11]. To inferaccurate surface fluxes, atmospheric CO2 concentra-tion should be determined with a 1ppm ð∼0:27%Þprecision in total column [12]. Such a measurementis demanding for a DIAL instrument (especially onthe spectral properties of the laser source). Moreover,the biases, or at least the difference in biasesbetween geographic areas, must be kept to withina fraction of ppm to retrieve accurately the CO2sources and sinks from the column measurements.This requirement implies an accurate knowledge ofthe spectroscopic parameters of the CO2 absorp-tion line.Section 2 describes the method used to infer at-

mospheric CO2 column mean mixing ratio and intro-duces the issue on CO2 line spectroscopy for accuratetotal column DIAL measurement. This leads us tothe requirements on spectroscopic parameters. InSection 3, we discuss the preselected spectral domainof investigation in the (ð2001ÞIII←ð0000ÞI band ofCO2 [13] and present a laser diode absorption spec-troscopy (LDAS) technique [14–16] for the relevantspectroscopic parameters for DIAL application: linestrength, air-broadening coefficient, and its tempera-ture dependence with a precision never reached be-fore, to the best of our knowledge. These results arethen discussed in Section 4 with respect to the re-quirements on CO2 mixing ratio accuracy.

2. Methodology for Integrated CO2 DIALMeasurements from Space

In this study, we assume a spaceborne DIAL instru-ment in a nadir viewing configuration that collectsground surface returns along the satellite track. TheDIAL technique uses only two wavelengths, oneemitted on a CO2 absorption line (on) and anotherin a spectral region free of absorption (off). Assumingthat the contribution of other constituents in the at-mosphere is negligible, the single-path differentialoptical thickness due to CO2 absorption can beinferred from a comparison of the two lidar opticalpowers:

τ ¼ 12ln�Poff

Pon

�þ C; ð1Þ

where Poff and Pon are the ground returned powersfor the on and off lines, respectively, and C is an in-strumental differential parameter [17].

This differential optical thickness can also beexpressed as a function of atmospheric parameterswith

τ ¼Zpsurf

0

ρðpÞWFðpÞdp; ð2Þ

where ρ is the CO2 mixing ratio, psurf is the atmo-spheric pressure at the reflecting surface, and WFis the differential pressure-weighting function

WFðpÞ ¼ naðpÞð~σonðpÞ − ~σoff ðpÞÞ�−∂z∂p

ðpÞ�: ð3Þ

Assuming hydrostatic equilibrium, WF can be writ-ten as

WFðpÞ ¼ ~σonðpÞ − ~σoff ðpÞmagð1þmw=maρwðpÞÞ

; ð4Þ

where na ¼ p=½kTðpÞð1þ ρWðpÞÞ� is the dry-air den-sity, ~σi is the absorption cross section at the laser line,ρW is the water vapor mixing ratio, ma and mw arethe dry-air and water molecular masses, p and T arethe atmospheric pressure and temperature, and k isthe Boltzmann constant.

Thus, an atmospheric column-average dry-air CO2mixing ratio can be inferred by

�ρ ¼ τR psurf0 WFðpÞdp : ð5Þ

Equation (5) shows that the same accuracy has to bereached for the lidar measurement (τ) and for the dif-ferential weighing function, which depends on atmo-spheric and spectroscopic parameters. In particular,the absorption line cross section has to be known towithin 0.27% along the DIAL laser beam path.

3. Laser Diode Absorption SpectroscopyMeasurements in the 2 μm CO2 Absorption Band

A. Selection of the Spectral Domain of Investigation

The selection of the relevant CO2 absorption lines forDIAL measurements depends on five major criteria:

• the availability of laser sources reaching thespecifications needed in terms of power (or energy),spectral properties, and beam quality for space plat-form operation. The following study focuses on 1.6and 2 μm domains where promising laser sources aresuitable for a space mission [18–22];

• the absence of interference with absorptionlines of other species, especially water vapor;

• a minimum in temperature sensitivity, whichmeans that the energy of the lower state of the

5476 APPLIED OPTICS / Vol. 48, No. 29 / 10 October 2009

CO2 transition,E00, is around 200 to 400 cm−1 (see Ap-pendix B in Gibert et al. [9]);• an optimal differential optical thickness, τ ∼ 1,

due to CO2 absorption along the path tominimize thestatistical error on DIAL measurement [23];• a WF peaking near the surface, i.e., a high sen-

sitivity to the lowest atmospheric layers to observeconcentration gradients linked to CO2 surface fluxes.This requires a laser line positioning on the wing of aCO2 absorption line [17].

The four first guidelines are addressed in Menziesand Tratt [13]. With respect to optimal differentialoptical thickness, the use of strong intensity CO2 ab-sorption lines, mainly present in the 2 μm domain, isrequired. As a result, the R30 CO2 absorption line at4875:75 cm−1 in the (ð2001ÞIII←ð0000ÞI band of CO2 isone of the most suitable lines for DIAL measurementfrom space.

B. Experimental Setup and LDAS Methodology

The CO2 molecular spectra in the 2:05 μm region arerecorded at high resolution with a diode laser spec-trometer (Fig. 1). The laser source is a commercialcontinuous-wave distributed feedback (DFB) diodelaser purchased from Nanoplus (Germany). The sidemode suppression ratio is higher than 30dB. Theaverage output power is ∼10mW and the laser line-width is usually lower than 10MHz FWHM. The to-tal tuning range with temperature and current is6 cm−1. The continuous tuning range with current (atconstant temperature) is approximately 1 cm−1, overwhich there are no mode hops. This point is of parti-cular interest to properly reconstruct the absorptionbaseline, as the laser sweeps the molecular transi-tion over a spectral range that is large enough toyield zero-absorption signals at the end and at thebeginning of the scanning interval. The laser wave-length is temperature stabilized by means of a Pel-tier thermo-element and is driven by a low noisecurrent supply. A low-frequency ramp at 100Hz isused to scan the diode laser wavelength over the se-lected absorption lines by amodulation of the drivingcurrent.Five absorption lines of the ð2001ÞIII←ð0000ÞI band

of the CO2 molecule are reachable in the tunabilityrange of the Nanoplus device. Weak lines of the

ð2001ÞII←ð0000ÞI band of 13CO2 and 18O12C16O arealso present. These lines have not been studied herebut were taken into account in the retrieval process.The experimental setup is based on [14,15]. The laserbeam is separated into two parts by a beam splitter.One is coupled to a confocal Fabry—Perot interfe-rometer for frequency calibration (free spectral range0:0095 cm−1). The other one, the main beam, passesthrough the absorption cell.

We use a White-type multipass cell that provides atotal of 203:8 cm path length (4 × 50 cm plus 3:8 cm)for the intensity measurements and a 1003:8 cm pathlength for the air-broadening coefficient measure-ments (20 × 50 cm plus 3:8 cm). The cell is adjust-able temperature wise and was used for measure-ments between room temperature (295K) and 210K(−63 °C, 1 °C total uncertainty). Two photodiodes areused for the detection of the two signals, which aresent to a personal computer (PC) for data acquisitionvia a Data Translation DT9832 16 bit ADC converter.The carbon dioxide was supplied by the Air LiquideCompany as well as the dry air, each with a statedpurity of 99.999%. The pressure inside the absorp-tion cell is measured with an uncertainty of 0.5%(full-scale value) using two MKS Baratron (Model122BA) manometers with 10 and 1000Torr full scale.The variation of temperature and pressure duringthe measurement is negligible since each measure-ment takes 0:5 s.

For each line under study, we recorded about 30spectra at various pressures from 2 to 14hPa for in-tensity measurements and from 50 to 1000hPa forair-broadening measurements. In the latter case, theCO2 concentration was around 1%. To retrieve thespectroscopic parameters of the line, we apply a non-linear least-squares fit to the molecular transmissionusing a Voigt profile for the modeling of the lineshape. The fitting procedure has been carefully de-scribed elsewhere [14,15]. The use of other types ofprofile such as Rautian–Sobelman or Galatry profileshow that even if the residual term was sometimeslower than the one obtained with the Voigt profile,the influence on the retrieved parameters was lessthan 0.5%, i.e., the same as the statistical error ofthe intensity measurements. Therefore, we use aVoigt profile to fit the experimental data:

~σðνÞ ¼ SγDπ

y

�ln 2π

�1=2

Zþ∞

−∞

expð−u2Þy2 þ ðx − uÞ2 du; ð6Þ

where y ¼ ðln 2Þ1=2γ=γD and x ¼ ðln 2Þ1=2ðν − ν0Þ=γD, Sis the line intensity, γ is the Lorentzian line half-width at half-maximum (HWHM), γD is the DopplerHWHM bandwidth, η is the temperature parameter,E00 is the energy of the lower state of the transition,and the subscript 0 denotes the standard conditionsof temperature and pressure:

Fig. 1. Block diagram of the experimental setup used for LDASmeasurements [15].

10 October 2009 / Vol. 48, No. 29 / APPLIED OPTICS 5477

S ¼ S0

�T0

T

�exp

�−E00hck

�1T−

1T0

��; ð7Þ

γ ¼ γ0PP0

�T0

T

�η; ð8Þ

γD ¼ ν0ð2 ln 2kT=mÞ1=2=c: ð9Þ

C. LDAS Measurements Between 4873 and 4879 cm−1

Examples of the CO2 R30 transition at 4875:75 cm−1

are displayed in Fig. 2. The line intensity and half-width are derived from the fitting procedure as de-scribed in [14,15]. Residual terms do not exceed 0.2%.The fitted value was very close to the HITRAN value[24], which is intermediate between the data re-ported in [25,26].The line intensities are measured in units of

cm−1=ðmolecule cm−2Þ at the temperature of eachspectrum, using the total measured pressure. Theline intensity for each spectrum is then standardizedto T0 ¼ 296K with Eq. (7) so the measurements from

the various spectra can be averaged. Then, the lineintensity for the pure 12C16O2 isotopomer is obtainedby dividing the line strength by the isotopic fraction0.984204. Our uncertainty corresponds to one stan-dard deviation obtained by averaging the measure-ments at 296K for each line. Errors from pressureand temperature uncertainties result in ∼0:1% inthe total error budget, the main part coming from theinversion (baseline, absorption line Voigt fit).

The halfwidths are measured in units of cm−1 atthe temperature of each spectrum. The halfwidths is-sued from the fitting procedures are plotted as afunction of pressure. An example for the R30 transi-tion at various temperatures is given in Fig. 3. Theslope of the regression line corresponds to the broad-ening coefficient in cm−1=atm at temperatures from−62 °C to ambient temperature. The broadening coef-ficient, at the reference temperature 296K and pres-sure 1013hPa, is given by Eq. (8) with p ¼ p0 ¼1013hPa and T0 ¼ 296K:

γðTÞ ¼ γ0ð296KÞ�296T

�η; ð10Þ

which can be written as

ln γðTÞ ¼ −η lnðTÞ þ lnðγ0ð296ÞÞ þ η lnð296Þ: ð11Þ

The tunability of the Nanoplus diode laser enables usto study five CO2 lines of the ð2001ÞIII←ð0000ÞI bandlying between 4873 and 4879 cm−1. The corre-sponding line intensities using the Voigt profile arereported in Table 1 and compared with recent experi-mental determinations and calculations [25–27]. Ouruncertainties correspond to one standard deviationas obtained by an averaging of the measurements.We also report in Table 1 the uncertainties for theprevious determinations when available. Our linestrength results are in good agreement with other ex-perimental data. The difference between ourdata and [25,26] does not exceed 0.7% for any ofthe five lines. Our results are often between these va-lues. On the other hand, these data are different fromthe HITRAN data (up to 16% difference). The nextHITRAN update will include the Toth data [27]and will be more accurate. The R26 line data arequite in agreement with a previous experiment ledby our team with another diode laser setup in 2004[28]. The results obtained in the present paper are

4875.65 4875.75 4875.850.75

0.8

0.85

0.9

0.95

1T

rans

mis

sion

4875.65 4875.75 4875.850.75

0.8

0.85

0.9

0.95

1

4875.65 4875.75 4875.85−5

0

5x 10 −3

1/ λ (cm −1)

Res

idua

l

4875.65 4875.75 4875.85−5

0

5x 10 −3

1/ λ (cm −1)

Exp.Fit

(a) (b)

Fig. 2. Examples of recorded absorption spectra for the CO2 R30transition at 4875:75 cm−1. Experimental and fitted Voigt shapesare presented. The residual term, i.e., the experimental valueminus the theoretical value from Voigt line shape is shown atthe bottom. Experimental conditions are (a) p ¼ 3:71mbar,T ¼ 293K, L ¼ 203:8 cm and (b) p ¼ 166:1mbar, T ¼ 295K,L ¼ 1003:8 cm. CO2 mixing ratio is 0.009.

Table 1. Absolute Line Intensities for CO2 in the 2:05 μm Region at 296K and Comparison with Previous Determinationsa

LineSigma(cm−1)

S0ð10−22 cm−1=ðmolecule:cm−2ÞÞThis Work HITRAN 2004 [24] Diff. (%) Regalia-Jarlot et al. [25] Diff. (%) Toth et al. 2006 [26] Diff. (%)

R26 4873.1290 1.984(7) 2.295 −16 1.996(40) −0:6 1.985(15) −0:1R28 4874.4481 1.747(9) 2.019 −16 1.760(35) −0:7 1.745(15) 0.1R30 4875.7487 1.507(6) 1.741 −16 1.509(30) −0:1 1.504(11) 0.2R32 4877.0305 1.278(7) 1.474 −15 1.284(26) −0:5 1.273(11) 0.4R34 4878.2932 1.060(12) 1.225 −16 1.065(21) −0:5 1.057(8) 0.3a The numbers in parentheses are the uncertainties on the last digit.

5478 APPLIED OPTICS / Vol. 48, No. 29 / 10 October 2009

the most accurate regarding the uncertainties (0.4%for the R30 line).The study of the CO2 line intensities was extended

to the determination of the air-broadening coeffi-cients. The halfwidth of the lines issued from the fit-ting procedure are plotted as a function of pressure.The slope of the regression line corresponds to thebroadening coefficient in cm−1=atm. The correspond-ing air-broadening coefficients are reported in Table 2and compared with previous results. Our experimen-tal results are in agreement to within 5% and 3%,respectively, with HITRAN and Toth et al. [29]. Theuncertainty on the air-broadening coefficient ob-tained at 296K is 1.8% for the R30 line, so the studywas extended to lower temperatures that reproduceatmospheric conditions. The Neperian logarithm ofthe broadening coefficients obtained at various tem-peratures using the Voigt profile are plotted as afunction of − lnðTÞ in Fig. 4. Using Eq. (11), we cal-culated air-broadening coefficients, γ, γ0ð296KÞ, andthe associated temperature parameter η for the R26,R28, and R30 lines (Table 2). The uncertainty on theair-broadening coefficient at 296K for the R30 line islow (0.15%). The same conclusion applies for η whose

uncertainty is lower than 0.45% for the R30 line.Note that the temperature dependence of air-broadening coefficient η ¼ 0:78 is constant in the HI-TRAN database. Assuming the same η parameterwhatever the transition is seems to be relevant, butthe parameter must be lowered to 0.66.

4. Discussion: Potential Biases on DIALMeasurements Because of Spectroscopy Uncertainty

To fulfill accurate and reliable CO2 flux retrievalsusing CO2 column dry-air mixing ratio, two condi-tions are required:

– the precision must reach ∼1ppm to signifi-cantly improve the “top-down”model inversions. Sys-tematic bias must be then lower than this limitationto prevent from error on the global carbon budget peryear [3,12].

– the interregional biases must be 1 order of mag-nitude lower than the accuracy, i.e., ∼0:1ppm. Inter-regional biases may consist in systematicdifferent dry-air CO2 mixing ratio measurementbetween two regions (spatial resolution 1000 km×1000 km). That affects directly the accuracy of inter-regional fluxes and then of surface sources and sinksestimates [11].

These requirements consider a constant pressure-weighting function (WF) with a relative cumulatedweighting function of 11% in the atmosphericboundary layer (ABL) (0 < z < 1km or 1013 > p >894hPa).

Using HITRAN 2004 and data from the presentpaper, we computed the single-path vertical atmo-spheric transmission for the lower 60km above thesurface for the R30 CO2 absorption line [Fig. 5(a)].On- and off-line are positioned at 4875.63 and4875:05 cm−1, respectively, to get an optimal opticaldepth [Fig. 5(b)]. WF is not constant and the cumu-lated weighting function in the ABL increases up to18% [Fig. 5(c)]. Then, the precision and the bias onthe total column measurement can be relaxed to1.6 and 0:16ppm, respectively.

From Eq. (5) we can see that a total column DIALmeasurement is sensitive to two main types of error:

0 200 400 600 800 10000

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0.09

p (mbar)

γ (c

m−1

)

−62 ° C−45 ° C−25 ° C−3° C22 ° C

Fig. 3. Halfwidths γ of the CO2 R30 transition (in the 2 μm) as afunction of pressure. The halfwidth is calculated using a Voigt fit.

Table 2. Experimental Values of Air-Broadening Coefficients at 296K and Comparison with Previous Determinationsa

γ0ðcm−1=atmÞ at 296K η

Thisworkb

HITRAN2004 [24]

Diff.(%) Toth et al. 2008 [27]

Diff.(%) This workc This workc HITRAN 2004 [24]

Diff.(%)

R26 0.0727(3) 0.0692 4.8 0.0704(14) 3.2 0.0727(3) 0.656(20) 0.78 −19R28 0.0714(13) 0.0687 3.8 0.0699(14) 2.1 0.0713(2) 0.662(17) 0.78 −18R30 0.0703(13) 0.0684 2.7 0.0693(14) 1.4 0.0702(1) 0.657(3) 0.78 −19R32 0.0691(10) 0.0681 1.4 0.0688(14) 0.4R34 0.0675(10) 0.0678 −0:4 0.0684(13) −1:3

aThe numbers in parentheses are the uncertainties on the last digit. Note that the results for R28 at low temperatures were not suffi-ciently accurate and the η value was determined only from the three higher temperatures. The results for R32 and R34 were also notaccurate enough since the absorption was weaker and weaker with the temperature decrease.

bUsing Voigt profile fitting procedure of the line intensity (from Fig. 6).cUsing Eq. (11) and Fig. 4.

10 October 2009 / Vol. 48, No. 29 / APPLIED OPTICS 5479

errors due to DIAL differential optical depth mea-surements, i.e., instrumental random and systematicerrors, and errors on WF calculations. The WF ran-dom error resulting from errors on surface pressure,

humidity, and temperature vertical profiles have al-ready been reported elsewhere [11,13,17]. The dry-air CO2 mixing ratio error results in 0:5ppm for a1hPa of surface pressure error, 0.3 and 0:1ppm fortemperature and humidity errors using the covar-iance error matrix of ARPEGE, the French NWPmodel. All together, these errors are ∼0:6ppm lowerthan the precision requirements of 1ppm.

Assuming a perfect knowledge of the meteoro-logical variables, an error δX on a spectroscopicparameter will yield a bias on the retrieved CO2 mix-ing ratio:

δρðpsurf ;TðpÞ; δXÞ ¼ τR psurf0 WFðp;TðpÞ; δXÞdp

−τR psurf

0 WFðp;TðpÞ; δX ¼ 0Þdp :

ð12Þ

Except for the line strength parameter, which yieldsto a constant bias, the bias is dependent on the tem-perature profile through the calculation of the ab-sorption cross section and on the surface pressure(including altitude effect) that sets the limit of theWF integration. The bias is also dependent on thewater vapor content but with a much lower sensitiv-ity, not to be discussed here.

−5.7 −5.6 −5.5 −5.4 −5.3−2.75

−2.7

−2.65

−2.6

−2.55

−2.5

−2.45

−2.4

−2.35

−ln(T)

ln(

γ)

R30R26R28

Fig. 4. Halfwidths γ of R26, R28, and R30 CO2 transitions (in the2 μm) band as a function of temperature (logarithmic scale). Theslope of the linear fit enables the determination of the temperatureparameter of the CO2 absorption line η. The halfwidths are calcu-lated using a Voigt fit.

Fig. 5. (a) Single-path atmospheric transmission for the lower 60km considering CO2 (black line) and H2O (gray line) absorption linesbetween 4873 and 4877 cm−1. We considered standard conditions (STA) for temperature, pressure, and humidity profiles and a constantCO2 mixing ratio of 370ppm. On (CO2 absorbed) and Off (non absorbed) laser line positioning on the wing of the CO2 R30 absorption lineare indicated. (b) Differential optical thickness due to CO2 absorption. (c) Differential weighting function (WF). (d) Cumulated weightingfunction as a function of pressure. ABL: atmospheric boundary layer.

5480 APPLIED OPTICS / Vol. 48, No. 29 / 10 October 2009

Using a Voigt profile of the CO2 line cross section,numerically evaluated by the Humlicek algorithm[30], we calculated the biases as a function of the re-flecting surface pressure for the CO2 R30 line withdifferent temperature profiles: standard, tropical,and subarctic winter. The error considered onγ0ð0:15%Þ and on ηð0:45%Þ correspond to the spectro-scopic measurement accuracies reported in this pa-per (see Table 2). The error considered on pshift,the pressure shift coefficient (2.6%) corresponds tothe measurement accuracy of Toth et al. [29]. Themeasurement biases are presented in Fig. 6 as afunction of the reflecting surface pressure, between500 and 1000hPa, for the three temperature profiles.

For the standard T profile and a surface pressureof 1000hPa, the bias due to the error on γ0 is0:37ppm, the bias for an error on η is 0:1ppm, andthe bias for an error on the pressure shift coefficientis 0:5ppm. The 0.4% accuracy on S0 brings an addi-tional bias of 1:47ppm. The rms value of these sys-tematic errors is 1:6ppm, which is just equal tothe requirement on the global bias.

If we consider now the bias difference (in absolutevalue) between the extreme profiles (tropical andsubarctic winter) at a constant surface pressure1000hPa, we obtain differential biases of 0:025ppmfor the error on γ0, 0:065ppm for the error on η, and0:025ppm for the error on the pressure shift coeffi-cient. The total differential bias caused by the regio-nal difference in temperature is 0:074ppm.

Conversely, if we consider the bias difference forthe standard temperature profile between regionswhere the surface pressure is 1000 and 900hPa(1km altitude difference), we obtain differentialbiases of 0:02ppm for the error on γ0, 0:015ppm forthe error on η, and 0:03ppm for the error on pshift, thepressure shift coefficient. The total differential biascaused by a surface pressure difference of 100hPa is0:039ppm. Note that the surface pressure differenceconsidered here, which includes altitude difference,is higher than the difference for regions with differ-ent synoptic conditions (high and low pressuresystems).

These results are summarized in Table 3. Similarsimulations have been made to analyze the sensitiv-ity of E00 uncertainty. The results show a negligibleeffect of E00 biases (within the current accuracy of0:1 cm−1). The combined differential biases, relatedto temperature and pressure effects, are 0:084ppm.It is lower than the targeted value of 0:16ppm.

5. Conclusion

Space-based differential absorption lidar for CO2concentration measurements is a promising techni-que for the derivation of surface fluxes. We addressedthe issue of the required precision on the R30 CO2absorption line spectroscopic parameters for a 1ppmaccuracy on total column CO2 mixing ratio. A near-infrared diode laser spectrometer was used to obtainprecise and accurate data on CO2 line intensities andair-broadening coefficients using a commercial diodelaser. The spectroscopic parameters of the fiveCO2 lines between 4873 and 4879 cm−1 have beencarefully determined in terms of line strengths,

Table 3. Mean Interregional Biases on Total Column CO2 Mixing Ratio Measurements Because of Biases in Spectroscopic Parametersa

Spectroscopic Parameters and Potential Biasesηðþ0:45%Þ γ0ðþ0:15%Þ pshiftðþ2:7%Þ

Sign (δρ) Sign (δp × δT × δη) Sign (δp × −δT × δγ0) Sign (−δp × δT × −δpshift)

Differential bias δρΔpHP�LP(ppm) þ0:015 þ0:021 −0:029

δρΔTTRO�SAW(ppm) þ0:065 −0:025 −0:024

aThe results are for different regions of high and low reflecting surface pressure (LP ¼ 900hPa, HP ¼ 1000hPa) and tropical (TRO) andsubartic (SAW) temperature profiles.

−0.5 −0.45 −0.4 −0.35

500

600

700

800

900

1000

STASAWTRO

−0.3 −0.25 −0.2 −0.15 −0.1 −0.05

500

600

700

800

900

1000

Ref

lect

ing

surf

ace

pres

sure

(hP

a)

−0.5 −0.45 −0.4 −0.35 −0.3

500

600

700

800

900

1000

Bias (ppm)

γ0

η

pshift

(a)

(b)

(c)

Fig. 6. Biases on CO2 mixing ratio (in ppm) due to the spectro-scopic uncertainties that remain after the present study (takenwith a positive sign) in (a) γ0 air-broadening coefficient at296K, (b) η temperature parameter, and (c) pshift pressure shiftas a function of the pressure of the reflecting surface and for dif-ferent temperature profiles: standard (STA), subartic (SAW), andtropical (TRO).

10 October 2009 / Vol. 48, No. 29 / APPLIED OPTICS 5481

air-broadening coefficients, and variation with tem-perature. The results presented in this study are dif-ferent from HITRAN 2004 but agree with the mostrecent experimental data obtained by Fourier trans-form spectroscopy. The parameters of the R30 line ofthe (ð2001ÞIII←ð000Þ band are given with good accu-racy of 0.4% for the line strength, 0.15% for the air-broadening coefficient, and 0.45% for its temperatureparameter. Assuming the same accuracy of 2.6%for the pressure shift as Toth et al. [29], these accura-cies are sufficient to reach a 1ppm accuracy onCO2 total column content and negligible inter-regional biases lower than 0:1ppm. These results aretherefore encouraging for a lidar CO2 spatial mis-sion, however, a more accurate study of the impactof the biases on the surface sources and sinks esti-mates must be performed to validate or refine themeasurement requirements.

The authors thank Barbara Poty and ThomasDecarpenterie for their help with the spectroscopicmeasurements.

References1. IPCC Fourth Assessment Report: Climate Change 2007— The

Physical Science Basis (Cambridge U, Press, 2007).2. F. Miglietta, B. Gioli, R. W. A. Hutjes, and M. Reichstein, “Net

regional ecosystem CO2 exchange from airborne and ground-based eddy-covariance, land-use maps and weather observa-tions,” Glob. Change Biol. 01219, doi:10.1111/j.1365-2486.2006 (2007).

3. P. J. Rayner and D. M. O’Brien, “The utility of remotely sensedCO2 concentration data in surface source inversions,” Geo-phys. Res. Lett. 28, 175 (2001).

4. Atmospheric Infrared Sounder (AIRS), airs.jpl.nasa.gov.5. “Scanning imaging absorption spectrometer for atmospheric

chartography (SCIAMACHY),” www‑iup.physik.uni‑bremen.de/sciamachy.

6. “Greenhouse gases observing satellite “IBUKI” (GOSAT),”www.jaxa.jp/projects/sat/gosat/index_e.html.

7. G. J. Koch, B. W. Barnes, M. Petros, J. Y. Beyon, F. Amzajer-dian, J. Yu, R. E. Davis, S. Ismail, S. Vay, M. J. Kavaya, andU. N. Singh, “Coherent differential absorption lidar measure-ments of CO2,” Appl. Opt. 43, 5092–5099 (2004).

8. F. Gibert, P. H. Flamant, D. Bruneau., and C. Loth, “Two mi-crometer heterodyne differential absorption lidar measure-ments of the atmospheric CO2 mixing ratio in the boundarylayer,” Appl. Opt. 45, 4448 (2006).

9. F. Gibert, P. H. Flamant, J. Cuesta, and D. Bruneau. “Vertical2 μm heterodyne differential absorption lidar measurementsof mean CO2 mixing ratio in the troposphere,” J. Atmos.Ocean. Technol. 25, 1477–1499 (2008).

10. “Active sensing of CO2 emission over nights, days, and seasons(ASCENDS),” cce.nasa.gov/ascends.

11. “Advanced space carbon and climate observation of planetEarth (A-SCOPE),” report for assessment (2008), www.esa.int/esaLP/SEMUE0AWYNF_LPearthexp_0.html.

12. C. E. Miller, D. Crisp, P. L. DeCola, S. C. Olsen, J. T. Rander-son, A. M. Michalak, A. Alkhaled, P. Rayner, D. J. Jacob,P. Suntharalingam, D. B. A. Jones, A. S. Denning,M. E. Nicholls, S. C. Doney, S. Pawson, H. Boesch, B. J. Connor,I. Y. Fung, D. O’Brien, R. J. Salawitch, S. P. Sander, B. Sen,P. Tans, G. C. Toon, P. O. Wennberg, S. C. Wofsy, Y. L. Yung,and R. M. Law, “Precision requirements for space-basedXCO2

data,” J. Geophys. Res. 112, D10314, doi:10.1029/2006JD007659, (2007).

13. R. T. Menzies and D. M. Tratt, “Differential laser absorptionspectrometry for global profiling of tropospheric carbon diox-ide: selection of optimum sounding frequencies for high-precision measurements,” Appl. Opt. 42, 6569–6577 (2003).

14. V. Zéninari, B. Parvitte, L. Joly, T. Le Barbu, N. Amarouche,and G. Durry, “Laboratory spectroscopic calibration of infra-red tunable laser spectrometers for the in situ sensing ofthe Earth and Martian atmospheres,” Appl. Phys. B 85,265–272 (2006).

15. L. Joly, F. Gibert, B. Grouiez, A. Grossel, B. Parvitte, G. Durry,and V. Zéninari, “A complete study of line parameters around4845 cm−1 for lidar applications,” J. Quant. Spectrosc. Radiat.Transfer 109, 426–434 (2008).

16. L. Joly, B. Parvitte, V. Zéninari, and G. Durry, “Development ofa compact CO2 sensor open to the atmosphere and based onnear-infrared laser technology at 2:68micron,” Appl. Phys. B86, 743–748 (2007).

17. G. Ehret, C. Kiemle, M.Wirth, A. Amediek, A. Fix, and S. Hou-weling, “Space-borne remote sensing of CO2, CH4, and N2O byintegrated path differential absorption lidar: a sensitivityanalysis,” Appl. Phys. B. 90, 593–608 (2008).

18. G. J. Koch, J. Y. Beyond, F. Gibert, B. W. Barnes, S. Ismail,M. Petros, P. J. Petzar, J. Yu, E. A. Modlin, K. J. Davisand,and U. N. Singh, “Side-line tunable laser transmitter for dif-ferential absorption lidar measurements of CO2: design andapplication to atmospheric measurements,” Appl. Opt. 47,944–956 (2008).

19. J. Yu., B. C. Trieu, E. A. Modlin, U. N. Singh, M. J. Kavaya,S. Chen, Y. Bai, P. J. Petzar, and M. Petros, “1J=pluse Q-switched 2 μm solid state laser,”Opt. Lett. 31, 462–464 (2006).

20. M. Raybaut, A. Berrou, A. Godard, A. Mohamed, M. Lefebvre,F. Marnas, D. Edouart, P. Flamant, A. Bohman, P. Geiser, andP. Kaspersen, “High brightness 2 μm source based on a type IIdoubly resonant ECOPO,” presented at the Advanced SolidState Photonics: 2009 OSA Optics and Photonics Congress,Denver, Colorado, USA, 1–4 Feb. 2009.

21. A. Amediek, A. Fix, M. Wirth, and G. Ehret, “Development ofan OPO system at 1:57 μm for integrated path DIAL measure-ment of atmospheric carbon dioxide,” Appl. Phys. B 92,295–302 (2008).

22. D. Sakaizawa, C. Nagasawa, T. Nagai, M. Abo, Y. Shibata,M. Nakazato, and T. Sakai, “Development of a 1:6 μm differ-ential absorption lidar with a quasi phase-matching opticalparametric oscillator and photon-counting detector for thevertical CO2 profile,” Appl. Opt. 48, 748–757 (2009).

23. D. Bruneau, F. Gibert, P. H. Flamant, and J. Pelon, “Comple-mentary study of differential absorption lidar optimization indirect and heterodyne detection,” Appl. Opt. 45, 4898–4906(2006).

24. L. S. Rothman, D. Jacquemart, A. Barbe, D. Chris Benner,M. Birk, L. R. Brown, M. R. Carleer, C. Chackerian, Jr.,K. Chance, L. H. Coudert, V. Dana, V. M. Devi, J.-M. Flaud,R. R. Gamache, A. Goldman, J.-M. Hartmann, K. W. Jucks,A. G. Maki, J.-Y. Mandin, S. T. Massie, J. Orphal, A. Perrin,C. P. Rinsland, M. A. H. Smith, J. Tennyson, R. N. Tolchenov,R. A. Toth, J. Vander Auwera, P. Varanasi, and G. Wagner,“The HITRAN 2004 molecular spectroscopic database,” J.Quant. Spectrosc. Radiat. Transfer 96, 139–204 (2005).

25. L. Regalia-Jarlot, V. Zéninari, B. Parvitte, A. Grossel, X.Thomas, P. Von Dr Heydden, and G. Durry, “A complete studyof the line intensities of four bands of CO2 around 1.6 and2:0 μm: A comparison between Fourier transform and diodelaser measurements,” J. Quant. Spectrosc. Radiat. Transfer101, 325–336 (2006).

26. R. A. Toth, L. R. Brown, C. E. Miller, V. M. Devi, andD. C. Benner, “Line strengths of 12C16O2 : 4550–7000 cm−1,”J. Mol. Spectrosc. 239, 221–242 (2006).

5482 APPLIED OPTICS / Vol. 48, No. 29 / 10 October 2009

27. R. A. Toth, L. R. Brown, C. E. Miller, V. M. Devi, andD. C. Benner, “Spectroscopic database of CO2 line parameters:4300–7000 cm−1,” J. Quant. Spectrosc. Radiat. Transfer 109,906–921 (2008).

28. V. Zéninari, A. Vicet, B. Parvitte, L. Joly, and G. Durry, “In situsensing of atmospheric CO2 with laser diodes near 2:05 μm: aspectroscopic study,” Infrared Phys. Technol. 45, 229–237(2004).

29. R. A. Toth, C. E. Miller, V. M. Devi, D. C. Benner, and L. R.Brown, “Air broadened halfwidth and pressure shift coeffi-cients of 12C16O2 bands: 4750−7000 cm−1,” J. Mol. Spectrosc.246, 133–157 (2007).

30. J. Humlicek, “An efficient method for evaluation of the com-plex probability function. The Voigt function and its deriva-tive,” J. Quant. Spectrosc. Radiat. Transfer 21, 309–313(1979).

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