Atmospheric CO_2 measurements with a 2 μm airborne laser absorption spectrometer employing coherent detection

Atmospheric CO2 measurements with a 2 μm airbornelaser absorption spectrometer employing

coherent detection

Gary D. Spiers,1 Robert T. Menzies,1,* Joseph Jacob,1 Lance E. Christensen,1

Mark W. Phillips,2 Yonghoon Choi,3 and Edward V. Browell4

1Jet Propulsion Laboratory, California Institute of Technology, Pasadena, California, 91109, USA2Lockheed Martin Coherent Technologies, Louisville, Colorado, 80027, USA

3National Institute of Aerospace, Hampton, Virginia, 23666, USA4NASA Langley Research Center, Hampton, Virginia, 23681, USA

*Corresponding author: [email protected]

Received 19 January 2011; accepted 10 February 2011;posted 8 March 2011 (Doc. ID 141344); published 9 May 2011

We report airborne measurements of CO2 column abundance conducted during two 2009 campaignsusing a 2:05 μm laser absorption spectrometer. The two flight campaigns took place in the CaliforniaMojave desert and in Oklahoma. The integrated path differential absorption (IPDA) method is usedfor the CO2 column mixing ratio retrievals. This instrument and the data analysis methodology provideinsight into the capabilities of the IPDA method for both airborne measurements and future global-scaleCO2 measurements from low Earth orbit pertinent to the NASA Active Sensing of CO2 Emissions overNights, Days, and Seasons mission. The use of a favorable absorption line in the CO2 2 μm band allowsthe on-line frequency to be displaced two (surface pressure) half-widths from line center, providing highsensitivity to the lower tropospheric CO2. The measurement repeatability and measurement precisionare in good agreement with predicted estimates. We also report comparisons with airborne in situ mea-surements conducted during the Oklahoma campaign. © 2011 Optical Society of AmericaOCIS codes: 010.1280, 010.3640, 280.3420, 280.3640.

1. Introduction

Observations of CO2 mixing ratios from Earth orbit,primarily in the lower and middle troposphere withmeasurement precision equivalent to 1–2 parts permillion by volume (ppmv) or better, are desired to de-fine spatial gradients of CO2, from which sources andsinks can be estimated with much reduced uncer-tainty than is presently attainable, on a spatial gridscale of order 103 km × 103 km [1–3]. AtmosphericCO2 is a long-lived gas, with sources and sinksprimarily at the surface. Consequently, a remote sen-sing technique that can emphasize the lower tropo-

spheric component or provide vertical profileswithin the troposphere is preferred.

The laser absorption spectrometer (LAS) approachoffers the potential to provide the high-accuracy CO2mixing ratio measurements with the vertical andhorizontal spatial resolution that is desired by thecarbon cycle research community. The LAS probesa well-characterized pressure-broadened absorptionline profile with one or more laser frequencies inorder to provide weighting functions suitable for re-trieving vertical profile information [4]. An LAS ap-proach to global-scale CO2 measurement from Earthorbit utilizes differentially attenuated multiwave-length backscatter from the Earth surface alongthe suborbital track, with subsequent analysis ofthe backscatter intensities at each wavelength to

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2098 APPLIED OPTICS / Vol. 50, No. 14 / 10 May 2011

retrieve CO2 mixing ratios. This is a form of the tech-nique referred to as integrated path differential ab-sorption (IPDA). An airborne LAS system utilizingthe IPDA technique can obtain mixing ratio informa-tion on a regional scale with higher spatial resolutionthan can be obtained from low Earth orbit (LEO).

Flying an airborne CO2 LAS instrument over avariety of sites offers the opportunity to demonstratethe suitability of the LAS IPDA technique, to evalu-ate the instrument technology, and to develop and re-fine the high-precision CO2 retrieval algorithms thatare the predecessors to the LEO retrieval analogues.With an airborne platform, multiple overpasses atdifferent altitudes will provide vertical profile infor-mation in addition to the inherent weighting func-tions. The instrument described in this paperutilizes an absorption line in the 2 μm ð20013←00001Þ band. The line strength is sufficiently largethat suitable differential absorption exists forhigh-sensitivity measurement over relatively short(1–2km) path lengths. Thus, CO2 mixing ratioscan be retrieved in layers with thicknesses of thesedimensions.

We provide a brief description of the basic IPDAprinciples in Section 2, followed by the airborne in-strument description (Section 3), the airborne cam-paigns that have taken place (Section 4), and thedata processing, analysis, and CO2 mixing ratio re-trieval algorithm approach (Section 5). Data fromthe 2009 airborne campaigns are the primary subjectof this paper.

2. Basic Principles

The basic concept involving the propagation of a dis-cretely or continuously tunable laser through the at-mosphere to detect and quantify the concentration ofan atmospheric gas has a long history. The specificuse of a topographic target to provide the backscat-tered signal was mentioned in [5], with a brief allu-sion to an infrared laser system that could be used ina helicopter at altitudes of a few hundred metersabove the ground. It was pointed out in [6] that, withthe use of heterodyne detection, a compact airborneLAS system operating in the infrared could be em-ployed at altitudes an order of magnitude higher. Theprinciples of the IPDA technique for two frequency-tuned transmitted (and detected) signals are asfollows. (The “on-line” signal at λ1 is tuned to a fre-quency that overlaps the CO2 absorption line of in-terest, while the “off-line” signal at λ2 is tuned to afrequency in the vicinity for which there is minimumoverlap with absorption lines.)

The instrument measurement parameter of keyimportance is the transmittance ratio, τ ¼ τon=τoff ,which relates directly to the differential absorptionoptical depth, DAOD ¼ AODon–AODoff , referring tothe optical depths encountered at the on line andoff line laser sounding frequencies:

DAOD ¼ − lnðτÞ: ð1Þ

Here we consider a double pass through the atmo-spheric path. Then the relationship between DAODand the (normalized) received power at the on-lineand off-line laser frequency channels is

lnðPon=Poff Þ ¼ −ð2DAODÞ: ð2ÞThe term “on line” in the context of this paper is notrestricted to the line center frequency, since we cantake advantage of tuning the transmitter to an opti-mum frequency within the line profile. We assume,for the purpose of this introduction of the basic prin-ciples, that (1) there is no significant contribution tothe absorption at either sounding frequency from ab-sorption lines of other gases, and (2) the offset be-tween the two sounding frequencies is sufficientlysmall such that gas continuum absorption and par-ticle extinction contributors to the optical depthproduce insignificant differential optical depth. (Theinfluences on DAOD of weak water vapor absorptionlines in the neighborhood are certainly considered inthe actual analysis.)

Start with the expression for DAOD between on-and off-line transmitted signals:

DAOD ¼Z

R2

R1ð σonðp;TÞ − σoff ðp;TÞÞnðzÞdz; ð3Þ

where R ¼ R2–R1 is the total path length or range,σon − σoff is the local differential cross section atzðcm2mol−1Þ that is a function of the pressure andtemperature, and nðzÞ is the local CO2 number den-sity. The quantity nðzÞ can be expressed as

nðzÞ ¼ qðzÞð1 − qH2OðzÞÞnairðzÞ; ð4Þ

where qðzÞ is the “dry air” volume mixing ratio ofCO2, qH2OðzÞ is the volume mixing ratio of water va-por, and nairðzÞ is the air number density. (Knowledgeof the water vapor mixing ratio is necessary in orderto derive the dry air mixing ratio of CO2.) The DAODas expressed in Eq. (3) is a functional of the numberdensity profile of CO2, with a weighting function thatis dependent on the pressure and temperature de-pendence of the CO2 absorption line profile. TheDAOD measured through a thin layer of thicknessδz at height Z in the atmosphere can be expressed as

δðDAODÞz ¼ nðzÞWFðzÞ½ðσon − σoff Þ�SURFACEδz; ð5Þ

where WFðzÞ is the normalized weighting function.The vertical weighting depends on the specific dis-placement of the on-line laser frequency from linecenter.

In principle the column-weighted dry air mixingratio, XCO2, can be derived from a measurement ofthe DAOD, along with knowledge of the spectroscopicparameters, surface pressure, atmospheric tempera-ture profile, and the water vapor profile.

There is an optimum DAOD for IPDA sounding[7–9]. If the DAOD is too large, the attenuation of

10 May 2011 / Vol. 50, No. 14 / APPLIED OPTICS 2099

the on-line signal results in insufficient signal-to-noise ratio (SNR) from the on-line detector. If theDAOD is too small, much higher overall SNR at bothchannels is required to obtain the necessary CO2measurement precision. In addition, residual sourcesof bias due to instrumental imperfections become re-latively more significant. The optimum DAOD isclose to unity.

The absorption cross section at the probing on-linefrequency is dependent on altitude due to the pres-sure broadening of the line profile, and this permitssome flexibility in achieving an optimum or near-optimum DAOD. When using the most favorablelines in the 2:05 μm band, optimum DAOD isachieved when detuning the on-line frequency twoto three (surface pressure) half-widths from line cen-ter frequency. The weighting favors the lower tropo-sphere when the on-line frequency is detuned one ormore half-widths from line center. We can use this toadvantage in the LAS IPDA technique, as mentionedabove. Detuning the on-line frequency two to threehalf-widths from line center results in selective prob-ing of the CO2 in the lower troposphere, where theCO2 mixing ratio variability of interest is the high-est. (Typical weighting functions for CO2 soundingare found in [10].) Having weighting functions thatpeak at the surface for optimum values of DAOD isof great advantage for LEO platforms as well as formeasurements from aircraft flying near the top of thetroposphere.

In the airborne measurement context, as opposedto operation from LEO, an advantage of operation inthe 2 μm CO2 band is that the DAOD values forlayers as small as ∼1–2km thickness are still suffi-ciently large for precise measurement capability.Altitude profiling can be accomplished with a se-quence of multiple overpasses of a ground track atdifferent altitudes. This quality of the 2 μmCO2 bandhas been utilized to conduct ground-based lidar ob-servations of CO2 with spatial resolution at the0:5–1km scale [11,12].

3. Uncertainties Due to the Spectroscopic andAtmospheric Modeling

Attainment of precision of the level of ∼0:3%–1% is achallenging endeavor, starting with the need to ob-tain a very high instrumental SNR within themeasurement time and involving knowledge of allspectroscopic and atmospheric quantities that mightimpact the determination of the optical depth due toCO2 absorption at a level of a few parts in 104. Dis-cussion of the impacts of spectroscopic uncertaintiesand how they affect measurement precision andmeasurement accuracy is outside the scope of thispaper. In recent years there have been several stu-dies of the line parameters for the 2:05 μm CO2band of interest here. These include studies of linestrengths (e.g., see [13–15]), air-broadened half-width and pressure shift coefficients (e.g., see [16]),and effects of line mixing on the line profiles (e.g.,see [17]). Systematic errors associated with spectro-

scopic line parameters are diminishing as a result ofthese continuing studies. However, they are still sig-nificant. The potential systematic influence of theline profile uncertainty on our airborne LAS mea-surements is discussed in Section 6. In a clear atmo-sphere, as stated above, the influential atmosphericvariables include surface pressure, temperature, andwater vapor profiles. The uncertainties associatedwith knowledge of these variables are components inthe overall error budget. (Note that the scatteringsurface elevation is important in refining the valuesof the atmospheric variables for the purpose of deriv-ing XCO2 from the lidar measurements.) Thesusceptibility of the DAOD to uncertainties in knowl-edge of atmospheric temperature and water vaporhave been discussed in [10,18]. More recently, resultsof a systematic study of residual uncertainties asso-ciated with the Advanced Space Carbon and ClimateObservation (A-SCOPE) choices of operating wave-lengths, including potential errors due to atmo-spheric modeling uncertainties, have been reported[19]. In Section 6 we summarize the impacts of theseuncertainties on the derivation of XCO2 values froma set of LAS airborne measurements.

4. Airborne CO2 LAS Instrument

The CO2 LAS instrument developed jointly by JetPropulsion Laboratory (JPL) and Lockheed MartinCoherent Technologies [20] consists of five key sub-systems: (1) the optical assembly, (2) the control elec-tronics unit, (3) the control software unit, (4) thethermal management assembly, and (5) the signalprocessing/data acquisition electronics.

The CO2 LAS transceiver approach is to utilizeheterodyne detection, implementing a narrow band-width receiver, with frequency-stabilized narrow-linewidth laser transmitters and local oscillators.The lasers are diode-laser-pumped rare-earth ion-doped crystal lasers, specifically yttrium lithiumfluoride (YLF) crystal with thulium (Tm) and hol-mium (Ho) dopants. These lasers are designed for ef-ficient lasing in the 2:05 μm spectral region. Thetransceiver consists of two separate transmit/receivechannels for the on-line and off-line components ofthe LAS measurement. The beam expander off-axistelescopes for each channel are identical in size andconfiguration, with the input optics designed to opti-mize the truncated Gaussian beam parameters formaximum heterodyne photomixing efficiency. Thetransmitter frequencies are carefully stabilized withrespect to a selected CO2 absorption line. Each chan-nel has a dedicated heterodyne detector and a cw sin-gle-frequency laser, which acts both as the transmitlaser and the local oscillator for heterodyne detectionof the return signal. The transceiver also includes aseparate low-power cw laser that provides a refer-ence for frequency offset locking of the on-line andoff-line lasers. The functional layout of the transcei-ver optical configuration is depicted in Fig. 1.

The reference laser (Laser 3 in Fig. 1) emits a fewmilliwatts of power, while the off-line transmitter


laser (Laser 1) and the on-line transmitter laser(Laser 2) emit sufficient power for the high-precisionmeasurement of CO2 from aircraft altitudes in themiddle and lower troposphere. An onboard low-pressure CO2 gas absorption cell is used to lockthe reference laser to the CO2 Rð30Þ line of theð2001ÞIII←ð0000Þ band, with line center at4875:749 cm−1. The cell is hermetically sealed andtemperature controlled. Using phase modulationspectroscopy along with an acousto-optic modulatorin the reference laser beam path to minimize opticalfeedback from the rest of the instrument, an rmslinewidth of approximately 50kHz is achieved. Afewmilliwatts of the output from Laser 2 is combinedwith the output from the reference laser for fre-quency offset locking. Laser 2 is tunable over a rangeof several gigahertz with respect to the fixed fre-quency of Laser 3, using a piezoelectrically posi-tioned resonator end mirror. Tunability of Laser 2allows CO2 measurement flexibility through on-linefrequency adjustment. (The atmospheric CO2 linehas a pressure-broadened FWHM of very nearly4GHz at sea-level pressure.) An additional few milli-watts from Laser 2 is tapped off to act as the localoscillator (LO) for heterodyne detection of the returnon-line signal. The remaining power is passed to theinstrument on-line telescope via a polarization beamsplitter and quarter-wave retardation plate (λ=4) setto produce circular polarized light. The combinationof polarizer and retardation plate acts as the trans-ceiver transmit/receive switch for the on-line compo-nent. (An analogous approach is used for the off-linechannel.)

Offset locking is accomplished using wide-bandheterodyne photomixers that monitor the beat fre-quencies between the outputs of Laser 1 and Laser 2with respect to Laser 3 (reference laser). The fre-quency difference between two of these compactTm, Ho:YLF single-frequency lasers can be locked toan accuracy of less than 100kHz. Dating from thetime of first integrated performance tests, the on-lineand off-line lasers have been tuned to the same offsetfrequencies with respect to the CO2 Rð30Þ line at4875:749 cm−1, namely þ4:00GHz and −15:72GHzrespectively. (See the parameter listing in Table 1.)The Rð30Þ line was selected based on evaluation ofrelative sensitivities to uncertainties associated withatmospheric temperature and relative humidityprofiles, the neighborhood around Rð30Þ exhibitingminimum CO2 retrieval sensitivity to these uncer-tainties [10]. The choice of Rð30Þ as the optimum linein the 2:05 μm band has been validated in recent

Fig. 1. (Color online) LAS transceiver functional layout. DDS, direct digital synthesizer.

Table 1. JPL Airborne LAS Instrument Parameters

Parameter Value

CO2 line center frequency 4875:749 cm−1

JPL LAS ON frequency JPL LAS OFFfrequency

4875:882 cm−1

4875:225 cm−1

Laser output power 100mWTransmit/receive telescope apertures 10 cm diameterReceiver FOV (diffraction-limited) 60 μradPhotomixer type InGaAsReceiver heterodyne frequency window 10–20MHzSignal digitization 14bits=50MHz


more comprehensive wavelength optimizationstudies [19].

A frequency offset is required between the returnsignals and their corresponding local oscillators forlow-noise heterodyne detection. By pointing thetransmit beams at a known offset from nadir, the re-turn signals experience a nominally fixed Dopplershift for a given aircraft velocity, thereby eliminatingthe need for an additional frequency shifting devicein the receiver. For a platform velocity of 60m=s anda transmit angle close to nadir, the change in Dopplerfrequency shift with off-nadir pointing angle alongthe flight track, at an operating wavelength of2051nm, is about 1:0MHz=deg (i.e., angle offsetalong the aircraft motion vector). In practice the air-craft pitch angle adds to the fixed off-nadir pointingangle with respect to the LAS instrument mount-ing frame.

The transceiver assembly is mounted to a two-sided optical bench, with custom-designed opticalmounts for each of the components. This opticalbench is edge-mounted to a base plate, as picturedin Fig. 2(a). In operational configuration, the opticalbench is in a near-vertical plane, and a cover is fas-tened to the base plate. An o-ring seal allows thetransceiver environment to be held near (sea level)atmospheric pressure, with internal pressure andtemperature continuously monitored. With the coverin place, the transceiver subsystem is ready to bemounted to an aircraft interface frame [see Fig. 2(b)].Thus the assembly is contained within an enclosurewith electrical feedthroughs and optical windows.

The baseplate/enclosure assembly includes vibrationisolation.

The key airborne LAS instrument parameters aresummarized in Table 1.

5. Airborne Campaigns

The CO2 LAS instrument has been flown in four testflight campaigns beginning in summer 2006 withconsistent improvements in data processing, analy-sis, and calibration methodology in each successivecampaign.

• California: engineering checkout flights wereconducted over the Mojave desert and the PacificOcean during summer 2006.

• Virginia: five flights were conducted in Virginiain October 2007 in the joint flight campaign with theNASA Langley Research Center (LaRC)/ITT Multi-functional Fiber Laser Lidar (MFLL) instrument.

• California: multiple overpasses of the ElMirage dry lake in the Mojave desert on two daysin April 2009.

• Oklahoma: four multioverpass flight days nearthe atmospheric radiation measurement (ARM)Southern Great Plains (SGP) site, July/August2009—joint campaign with NASA LaRC/ITT andGoddard Space Flight Center (GSFC) airborneinstruments.

The instrument was installed in a Twin Otter air-craft for each of these campaigns, chartered fromTwin Otter International, Ltd. out of Grand Junc-tion, Colorado [see Fig. 3(a)]. The transceiver opticalhead was mounted over an open nadir port as pic-tured in Fig. 3(b). The installation included a rack

Fig. 2. (Color online) (a) LAS with optical bench horizontal,telescope side up, base plate in background. (b) LAS transceiverin hermetically sealed enclosure. CG, center of gravity.

Fig. 3. (a) Twin Otter aircraft. (b) LAS transceiver assemblymounted on frame and integrated onto Twin Otter above nadirport hole, with tilt angle adjusted to provide 14deg off-nadir angleduring nominal cruise conditions.


for the instrument control and data acquisitionelectronics, and a chiller for maintenance of a suita-ble optical head temperature range. A JPL inertialnavigation system/global positioning system (GPS)unit was also mounted to the aircraft frame. Forthe April 2009 flights over ElMirage, a PicarromodelG1301 in situ CO2 sensor, on loan from Picarro, Inc.[21], was also installed on the aircraft. During thefirst flight campaign in 2006, the original signal pro-cessing board was damaged and replaced by a50MHz digitizer that was readily available. The po-sitive aspect of this outcome was the capability toproduce high-resolution fast Fourier transforms(FFTs) and periodograms that provided additionalsignal diagnostics (e.g., spectral width as well aspower). The negative aspect was that the onboarddata transfer to archival memory was not fast en-ough to collect 100% of the data generated. The datacollection efficiency was only 20% during the firstcampaign. By 2009 this had increased to between40% and 50%.

In this paperwe report in particular on results fromthe 2009 flight campaigns over the Mojave and in thevicinity of theOklahomaARMSGP site. For the April2009 Mojave campaign, the aircraft flew in transit tothe Van Nuys airport, where it was maintained dur-ing the campaign. On two flight days (17 and 19April), the experiment team flew multiple El Mirageoverpasses, six overpasses at each of three altitudes.The atmospheric parameters (temperature, pressure,relative humidity) weremeasured using onboard sen-sors in order to characterize the weighting functionsused for the CO2 column mixing ratio retrievals. TheEl Mirage dry lake is elongated, ∼8km in the long di-mension, and the overpasses were oriented in this di-mension. The elevation variability across the dry lakebed in the direction of the ground track was 4–5m.The 2 μm reflectivity [bidirectional reflectance distri-bution function (BRDF) at the backscatter angle] var-ied by 30% across the dry lake. During the July/August 2009 Oklahoma campaign, the aircraft flewout of the local Ponca City airport. Flight tracksand flight altitudeswere coordinatedwith teams fromNASA LaRC/ITTand NASAGSFC, who also flew air-borne laser instruments for IPDA measurements ofcolumn CO2 mixing ratios. The flight tracks wereeast–west in direction, ∼55km in length, about10km south of Ponca City near the east end of thetrack. The tracks were a few kilometers north oftheDepartment of Energy (DOE) SGPARMsite, withthe track midpoint being ∼10km east of the DOEARM site. The surface elevation varied by ∼25moverthe length of the ground track. The ground track in-cluded wooded terrain, agricultural plots, and mean-dering river locales. The ground-track reflectivityvaried by a factor of 5, the river reflectivity being atthe low end and bare soil at the high end of the dy-namic range. Although sharp changes in reflectivity(e.g., water–land boundaries) can be problematic forIPDA systems with displacements between the on-line and off-line footprints [22], no transient differen-

tial reflectance were observed in the JPL LAS data.(The footprint centers are separated by 12 cm.) TheOklahoma campaign included four JPL flight days be-tween 31 July and 4 August, all over the same flighttrack. The same flight altitude sequence was main-tained over the course of the four flight days: fourconstant altitude overpasses, (1) 10 kilofeet (kft),(2) 9kft, (3) 7kft, and (4) 8kft. DOE radiosondes werelaunched within 4h of each day’s flights for measure-ments of vertical profiles of atmospheric temperature,pressure, and relative humidity.

Characterizations of the instrument stability andthe baseline noise spectra for each channel are criti-cally important. The instrument includes an onboard“validator”: a modified belt sander that provides aDoppler-shifted backscattering signal for each chan-nel. The validator is inserted into the LAS field ofview at convenient intervals in order to validate theoverall stability of the instrument. For example, va-lidator data were collected before and after eachoverpass during the Oklahoma overflights. Thismethodology enables the monitoring of variationsin system gain ratio at the precision level of 0.3%.The baseline noise spectrum data are also collectedat intervals during each flight. Two methods havebeen intercompared. One method for collecting noisespectra involves inserting the motionless belt sanderin the field of view (thus no heterodyne signal ap-pears). The other method involves flying over a verydark surface for intervals of time. At an off-nadir an-gle of 14 deg, the surface of an inland lake is verydark, and useful noise data can be collected usingthese targets. Detailed studies indicate that thereis no discernible difference between noise spectra(in the 10–20MHz region) obtained with these twomethods.

6. Signal Processing and Data Analysis

Our approach to data analysis and CO2 retrieval is asfollows. The LAS on-line and off-line signals aresampled, stored, and processed as described below,to calculate for various atmospheric layers the valuesof

lnðPoff=PonÞ ¼ ð2DAODÞ;

whichwe routinely call “lnðratioÞ.”Then these results,derived from the measurements, are compared withforward model predictions of DAOD for a range ofcolumn-average CO2 mixing ratios. We use the line-by-line radiative transfer model (LBLRTM) providedby Atmospheric and Environmental Research, Inc.(AER), modified to include a merged line para-meter database. In the 5 cm−1 region centered at4875:5 cm−1, a set of line parameters for CO2 andH2O provided by Toon [23] were substituted for theAER version 2.1 line parameter database. Line cou-pling/mixing coefficients [24]were included. TheToonlineparameterswere compiledusing theapproachde-scribed in [17]. The forward model is based onthis modified LBLRTM code plus the atmospheric


characterization data needed to provide the descrip-tion of the atmospheric layers being probed, specifi-cally pressure, temperature, relative humidity, andgeometric layer thickness. The onboard GPS systemprovides theaircraft positionknowledge (includingal-titude with respect to the geoid). Lacking an onboardcoboresighted laser altimeter, the surface elevationwas obtained through other means.

A. Key Properties of the Return Signal

The airborne LAS signals are a delayed self-heterodyne spectrum, since the local oscillator is de-rived from the transmitter laser by means of a beamsplitter in the path (as in Fig. 1). The self-heterodynetechnique has been used frequently to measure semi-conductor laser linewidths (e.g., see [25–27]). Thetheoretical expression for the self-heterodyne powerspectrum has been derived assuming the fluctua-tions of the optical phase to be Gaussian distributed,with the time dependence of the phase correlation ofthe recombined fields expressed as

< ½φðtÞ − φðt − τdÞ�2 >¼ jτdj=τc; ð6Þ

where τd and τc are the delay time and the coherencetime. The coherence time associated with the phasecorrelation of the recombined beams, τc, is the timefor the optical phase fluctuation to evolve over 1 rad,on average. The power spectrum consists of twoterms. The first term is the coherent mixing term,a delta-function term whose relative contribution de-cays with increasing (normalized) delay time τd=τc:

S1ðωÞ ¼ aI1I2 expð−τd=τcÞδðω − ωhÞ: ð7Þ

The second term is a modulated Lorentzian thatapproaches a standard Lorentzian with increasingτd=τc:

S2ðωÞ ¼ðaI1I2τcÞ=π

1þ ðω − ωhÞ2τ2c·�1 − exp

�−τdτc

�

×�cosðω − ωhÞτd þ

ðsinðω − ωhÞτdÞðω − ωhÞτc

��: ð8Þ

The effects of laser jitter, most probably caused byacoustic disruptions, can cause a decoupling of therelationship between laser linewidth and the phasecoherence time τc. This point was made in [28] whilereporting on observations of the shape of the powerspectrum using a cw coherent laser radar for varioustarget ranges. Laser jitter does impact the linewidthsof the LAS signals. A study of the airborne LAS sig-nals over time periods in the range 80 μs to 1ms (forτd in the range 4–20 μs) indicate sequences of indivi-dual 4K FFT delta-function-like power spectra thatcontain occasional “jumps” in center frequency ran-ging in value up to ∼200kHz. There are differencesin the opto-mechanical construction of the on-lineand off-line lasers (the off-line laser having a largerlongitudinal mode spacing), and the discriminants

and time constants of the frequency-stabilizationfeedback loops differ from each other. Consequently,the jitter effects are not identical. For typical valuesof τd during flight operations (∼15–30 μs), the on-linelaser jitter is more consequential, resulting in alarger spectral width. Typical FWHM values overtime periods of several hundred milliseconds are100–250kHz, with the off-line laser linewidths beingat the low end of this range.

The backscattered radiation takes the form of a dy-namic speckle pattern. Independent (uncorrelated)samples of the speckle are obtained as the aircraftmoves along the flight track, with speckle decorrela-tion occurring on the time scale of τdecorr ¼ d=2vacg(where d is the instrument aperture diameter, νacgis the aircraft ground speed). The integrated powerof the signal in the periodogram is related to theintensity of the return signal incident on the photo-mixer. The probability density of a collection of inde-pendent samples obeys negative exponentialstatistics [29]

PIðIÞ ¼1hIi exp

�−

IhIi

�; ð9Þ

where the mean value is hIi and the variance is hIi2.Power estimation requires an approach to mana-

ging speckle fluctuation effects. Assuming the localoscillator (LO)-induced shot noise is the dominantcontributor to the receiver noise, the heterodyneSNR, SNRH, for a matched filter receiver, can be ex-pressed as

SNRH ¼ fðδ=ðδþ 1ÞgðMTÞ1=2; ð10Þ

where δ is the signal degeneracy factor, namely themean number of signal photocounts in the coherencetime of the signal, and MT is the number of indepen-dent (speckle) samples of the signal in the timedomain [30]. This assumes a single-photomixer recei-ver, with the receiver aperture sampling no morethan a single speckle lobe. For this case, δ can becalled the carrier-to-noise ratio, CNR. (The CNR isused more broadly to include total receiver noise, ad-ditional sources being, e.g., preamp noise and bias

Fig. 4. Measurement uncertainty due to speckle fluctuationstatistics. Relative uncertainty depends on distance travelled, orspatial resolution along ground-track, independent of aircraftplatform.


circuit noise.) Obviously precision in power estima-tion demands averaging over multiple realizationsof the speckle field. Figure 4 depicts the attainablemeasurement precision versus along-track distancetravelled in the aircraft for the JPL airborne LAS in-strument with its 10 cm diameter apertures. Duringthe 2009 flight campaigns, as stated earlier, the datacollection efficiency was about 40%. This results inlonger integrations required to achieve the desiredmeasurement precision. Future instrument up-grades include faster data transfer to archivalmemory in order to achieve 100% data collectionefficiency.

B. Signal Processing, Characterization, and DAODEstimation

The intermediate frequency (IF) photomixer signalsfrom the on-line and off-line channels are amplifiedand bandwidth limited to a nominal 10–21MHz win-dow. The signals from each channel are digitizedwith a 50Msample=s, 14 bit digitizer. The samplesare transformed into the spectral domain using anFFT operation followed by conversion to periodo-grams. The commonly used “squarer” estimator [31]is used to determine the return power in each chan-nel. Both 4K and 16K FFTs have been employed inthe study of the signals. In each case, the samplingduration (80 μs for the 4K FFT, 320 μs for the 16 FFT)is shorter than the speckle decorrelation time of thesignal, τdecorr, which is ∼1ms for the nominal TwinOtter cruise speed.

A preselected number of periodograms is summed,and the remainder of the signal processing steps op-erate on a collection of these sums over g individualperiodograms. The signal power becomes a gamma-distributed random variable. The sum of k indepen-dent exponentially distributed random variables,

each of which has a mean value θ, can be describedby the gamma function, f ðx; k; θÞ, with integer valuesof k. The equation defining the probability densityfunction of a gamma-distributed random variable x is

f ðx; k; θÞ ¼ xk−1½expð−x=θÞ=θkΓðkÞ� for θ > 0;

ð11Þ

whose shape approaches Gaussian with increasing k,in accordance with the central limit theorem. For ex-ample, selecting a value g ¼ 122, 16K periodogramscorresponds to an integration over 40ms of data.Since τdecorr is ∼1ms, k is approximately 40 in thiscase. We must distinguish between g and k, since,for flights on the Twin Otter aircraft, multiple16K data samples fit within the decorrelation time.

The signal processing and data analysis algorithmfollows the steps outlined in Fig. 5. In the third boxwe list a 40ms integration, although 80 and 160msintegrations are occasionally employed in high-altitude or low surface backscatter cases. The deter-mination of the signal peak frequencies in the10–20MHz window involves several steps and qual-ity control filters. Optical alignment in the along-track direction demands identical channel 1 andchannel 2 heterodyne frequencies, the acceptable tol-erance being derived from the on-line and off-linefootprint overlap tolerance. After successful determi-nation of the channel 1 and channel 2 signal frequen-cies, an adjustment is made to compensate for thefact that the receiver gain for each channel is notstrictly flat across the 10–20MHz window, and thedeviations from flatness are not identical. This com-pensation is a very important element of the IPDAcalculation. The on-line and off-line signal peak fre-quencies move in synchronism as the aircraft moves

Fig. 5. (Color online) Flow diagram of algorithm for retrieval of column-average CO2 mixing ratio.


through atmospheric cells of various dimension,causing variability in ground speed, pitch angle,etc. Small frequency excursions over few second timeperiods are accommodated as the periodograms aresummed over longer integration times; however,periods of turbulence that result in rate of changeof signal frequency above a preset limit are filteredout of the data record. Finally, on-line and off-line sig-nal power calculations are performed, followed bynormalization steps to account for variations in slantpath length between instrument and footprint on thesurface, small variations in laser power, or othersmall drifts in channel 1 and channel 2 overall sys-tem gain. System stability is quantified through theuse of “validation” data collection periods, when anonboard backscattering validator subsystem is in-serted into the instrument field of view, interceptingthe transmitter beams. During the El Mirage andOklahoma campaigns, validator data periods pre-ceded and followed the overpasses at each altitude.

C. Contributors to Error Budget

The spectral line parameters, including the lineshape, are obvious potential contributors to systema-tic error. The Rð30Þ line centered at 7845:749 cm−1 isthe selected CO2 line for the differential absorptionmeasurement. As described earlier, the on-line andoff-line laser frequencies are derived from a referencelaser stabilized to the Rð30Þ line center in a low-pressure cell. At present it appears that there isagreement on the line intensities of Rð30Þ and itsneighbors to within 1%, based on spectroscopic inves-tigations reported during the last five years [13–15].The line profile modeling, for all the CO2 bands in the1:6 μm and 2:05 μm regions, is continuing to evolve.There is general agreement that the Voigt line shapeassumption is not sufficient to attain accuracy at the1% level, and line mixing effects must be included(e.g., see [17]). Further discussion of the line shapeissue follows in Section 7.

Contributors to the random error budget andmitigation methods include

• SNR (on-line and off-line)Several authors have determined the optimum

value of DAOD that minimizes relative error in itsmeasurement, using on-line and off-line SNR asparameters (e.g., see [7–9]). From a random errorminimization point of view, the optimal single-passDAOD is ∼1 and the on-line-to-off-line transmittedenergy ratio is ∼4 for most efficient use of the lidarenergy aperture product. In practice, for the 2009 ElMirage and Oklahoma campaigns (particularly ElMirage), the layer thicknesses being probed weresuch that the measured DAODs were in the range0.15–0.35, i.e., significantly less than optimum fora given total transmitted energy. Further discussionfor the particular campaigns follows in Section 7.

• Aircraft altitude uncertainty (use onboard GPSfor aircraft location)

• Overall channel 1 and channel 2 system gainvariability (monitor laser transmitter power in realtime; conduct validator measurements at each flightaltitude)

• Laser frequency stability (rely on laser lockloop stability, rely on reference laser stabilizationto CO2 line center frequency)

• Surface elevation and variability (eliminate bymeasuring DAOD in layers defined by aircraft alti-tudes; alternatively use aircraft altitude and digitalelevation model data)

• Footprint overlap (prealignment verification onground; monitor the channel 1 and channel 2 back-scatter signal Doppler shift offset for along-trackcomponent)

• Atmosphere: uncertainty in knowledge of pres-sure, temperature, relative humidity profiles [utilizecalibrated onboard sensors; use available surfacedata, radiosonde data, tower data; choice of Rð30Þline and on-line, off-line frequencies mitigates effectsof T, RH uncertainties]

The contributors to the overall error and their im-pacts on the error budget are listed in Table 2. As onewould expect, the entries are quite similar to thosefound in an error budget table for an IPDA systemin LEO (e.g., see [18]); however, it is important to re-cognize that some contributors are much more signif-icant for a system on an airborne platform.

7. Measurement Results: El Mirage and OklahomaCampaigns

A. El Mirage

The main purpose of the mid-April 2009 El Mirageflight campaign was to evaluate the stability and re-peatability that could be obtained when flying over aflat surface with nearly uniform high albedo. Theweather was stable during this mid-April 2009 per-iod. Sensors aboard the aircraft provided measure-ments of T, p, and RH at the 2kft, 6kft, and 8kftflight levels, which were 616m, 1850m, and 2549mabove the dry lake surface, respectively. The atmo-spheric parameters were very nearly the same dur-ing the two days. These atmospheric parameterswere used in the LBLRTM forward model to providepredictions of the relevant layer DAOD values for arange of CO2 column-average mixing ratios. The 6kftand 8kft series of overpasses were the objects of thedata analysis, for reasons stated earlier. The analysisconcentrated on the precision of the measured DAODof the layer bounded by the 6kft and 8kft overpasses.

Table 3 provides a summary of the lnðratioÞ mea-surement stability and repeatability for theElMirageflights. Therewere six overpassesat eachaltitude, thedata collection portion of each overpass covering aground-track length of 8km. For this ground-tracklength, the speckle fluctuation limit on the over-pass-average SNR is ∼200. (The data summary inTable 3 does not include the first overpass at each al-titude. The first overpass at each altitude was treated


as a “pilot training” overpass, the aircraft speed andattitude typically being much more stable after thefirst overpass.) The standard deviation, in DAODunits, is a measure of the repeatability of the “over-pass-average” measurements. The standard devia-tion of the double-pass DAOD measurement for the6–8kft layer ranges from 0.011 to 0.012. The limitdue to speckle fluctuation statistics, as stated above,would be ∼0:007. This measurement precision resultis consistent with prediction based on the contribu-tions to the error budget listed in Table 2. Note that2 ðDAODÞ through the full midlatitude troposphere is∼1:8 for this on-line/off-line frequency pair. The mea-surement precision within each set of overpasses at afixed altitude is equivalent to ∼0:7% of full tropo-spheric (double-pass) DAOD. From day to day, wesee a 2 ðDAODÞ measurement difference of 0.024across the 300m thick 6–8kftlayer. This is a ratherlarge fraction of the double-pass DAOD across thisthin layer. However, it is encouraging to note thatour day-to-day repeatability, expressed as a percen-tage of the full tropospheric column equivalent, is∼1:3%. This is a measure of the extent to which wewere able to control and mitigate the impacts of thepotential source of error/uncertainty listed in Table 2.

Comparison of the measured DAOD values withthose predicted by our forward model indicated aconsistent systematic offset. The CO2 mixing ratiovalues that were used in the forward model were pro-

vided by in situ Picarro instrument measurements atflight altitudes. The measured DAOD values werehigher than predicted by the forward model. The off-set from the LBLRTM forward model prediction is afactor of 1.4. In other words, the retrieved column-average CO2 mixing ratio values, based on the air-borne LAS measurements, are high by a factor of1.4. Somewhat surprisingly, the measured DAOD va-lues in the 2 –6kf t layer were also offset from theLBLRTM forward model prediction by the same fac-tor. This offset is discussed further in the followingparagraphs.

The “offset” between measured DAOD values andforward model predictions had been noticed duringprior flights in 2006 and 2007. The El Mirage cam-paign results permitted a more accurate determina-tion of the offset, due to improvements in calibration/validation methodology and the availability of theonboard Picarro instrument data. Experienceindicated that the offset was robust. There was no

Table 2. CO2 Measurement Uncertainty/Error Budget

Error SourceUncertainty/Assumption

MeasurementError (% full

column DAOD)

MeasurementError

(ppmv CO2) Comments

AtmosphereSurface pressure 1hPa 0.15 0.6 Eliminate by measuring DAOD in

layers bounded by multiple-leveloverflights

Pressure at aircraft altitudes 1:5hPa 0.22 0.9Temperature profile 2K 0.11 0.4 Applicable to Rð30Þ lineWater vapor mixing ratio:(1) conversion to dry

CO2 (2) H2O lineinterference

10% in“tropical”

atmosphere(worst case)

0.1 0.1 0.4 0.4 Inferred CO2 error can be ∼3 times lessfor LEO than for low flying aircraftmeasurements, due to water vaporvertical profile

Aerosol and thin cloud spectralscattering/extinction

negligible negligible Negligible spectral variability ofscattering within Δλ ∼ 0:3nm

SurfaceSurface elevation 3m 0.1 0.4 Eliminate by measuring DAOD in layers

bounded by multiple-level overflightsAircraft PositionAircraft altitude (GPS) 3m 0.1 0.4 Relative error depends on layer thickness

Laser TransmitterPower transmitted 0.5% 0.75 3 Use validator to monitor driftsFrequency knowledge/control 2MHz 0.08 0.3 On-line frequency offset from line centerSystem Gain Ratio Stability 0.5% 0.75 3 Use validator to monitor relative drift in

channel 1/channel 2 system gain ratioPointingControl/knowledge 25=100 μrad 0.01 negligible Heterodyne drives this; N/A for aircraft

On-line/Off-Line Pointing OffsetControl/knowledge of

along-track pointing offsetnegligible Use channel 1 and channel 2 heterodyne

signal difference frequency asdiagnostic

Table 3. Summary of ln�ratio� � 2�DAOD� Measurement Stabilityover El Mirage, Mean Value, and Standard Deviation (SD)

for Multiple Overpasses at Each Altitude

AtmosphericLayer

17 April2ðDAODÞ

17 AprilSD

19 April2ðDAODÞ

19 AprilSD

6–8kft layer(δz ¼ 699m)

0.173 0.012 0.197 0.011


indication that the magnitude of the offset was af-fected by surface type or atmospheric conditions.An exhaustive analysis of potential causes of this off-set eliminated the data analysis algorithm as theculprit.

Two likely sources of the offset were identified, onecontributing to a greater extent than the other. Thefirst source is related to the fact that, at Twin Otteraltitudes, the surface scatter sources are not in thefar field. In other words, the instrument optics arefixed and focused at infinity; thus, at ranges less than∼3km, the optics are somewhat out of focus. Evi-dence of this condition manifests itself in that theoff-line return signal does not decrease with increas-ing altitude as inverse range squared in the altituderange covered by the Twin Otter flights (range to sur-face 600–3000m). The dependence on range to sur-face, R, is very close to 1=R rather than 1=R2 up to∼2600m. In other words, the system receiving effi-ciency is range-dependent, increasing linearly withrange up to 2:6km. From 2.6 to 2:9km the slope de-creases; however, the receiving efficiency has not yetreached its asymptote. This is well-understood beha-vior for monostatic coherent lidars, as documented inthe literature (e.g., see [32]). A small mismatch be-tween the off-line and on-line channel receiving effi-ciency functions (e.g., due to small differences in therespective photomixer active surface geometries)causes a range-dependent lnðPon=Poff Þ that can mas-querade as an absorbing gas. A contribution to theDAOD of about 0:1km−1 due to this effect would fullyaccount for the observed offset. For example, as therange to the surface increases from 2 to 3km, thisamounts to a change in the on-line/off-line channelresponsivity ratio of ∼10%. The second source ofthe offset is related to the distortions of the absorp-tion line profile due to line mixing effects. Estimatesof the magnitude of this effect, based on recent spec-troscopic studies (e.g., see [15,17]) lead us to inferthat this source could contribute only a small fractionof the observed offset.

B. Oklahoma

The 2009 flight campaign in the vicinity of the DOESGP site occurred in the July/August time frame,31 July through 4August. This campaign featured co-ordinated flights with other airborne CO2 measure-ment teams. A NASA LaRC team gathered profiledata using the Atmospheric Vertical Observation ofCO2 in the Earth’s Troposphere (AVOCET) in situCO2 measurement system [33,34] onboard the NASALangley UC-12 aircraft, conducting spiral ascentsonce daily. NASA GSFC [35] and NASA LaRC/ITT[36] teams were flying in other aircraft, with their re-spective laser IPDA instrumentation. The individualdata analysis groups were firewalled from each otherduring the campaign. Each of the airborne IPDAgroups flew over a common east–west (fixed latitude)ground track, approximately 50km in length, at anumber of fixed altitudes. The JPL Twin Otteroverflights occurred in sequence at 10, 9, 7, and

8kft altitudes over the same east–west ground trackon four days, midday time period on each day. Theoverpass-average altitudes relative to the geoid as in-dicated by the onboard GPS varied by about �50mfrom day to day. Average altitudes (above mean sealevel) were approximately as follows: (1) 7kft ¼2260m, (2) 8kft ¼ 2590m, (3) 9kft ¼ 2910m,10kft ¼ 3235m.

Radiosondes launched daily during this period pro-vided pressure, temperature, and relative humidityprofiles up to at least 10km altitude. A weightingfunction example for the 31 July atmosphere, asmeasured by the sonde for that day, is shown in Fig. 6,for the JPL LAS on-line/off-line frequency pair.Figure 6 points out graphically that (a) the LAS ismuch more sensitive to a CO2 molecule in the lowertroposphere than at higher altitudes and that (b) thelayers that were probed by these aircraft overflightsare a small fraction of the total troposphere depth.

A major objective of this Oklahoma campaign wasdemonstration of the ability to measure column-weighted CO2 mixing ratio for columns that ex-tended to the surface in addition to layers boundedby the aircraft overflight altitudes. The analysis ofthe LAS Oklahoma campaign data included the in-corporation of a range-to-ground algorithm that in-corporated the Shuttle Radar Topography MissionDigital ElevationModel data set for the ground-tracktopography, in lieu of data from an onboard laseraltimeter. The surface elevation varied from approxi-mately 290–320m over the ground track. Conse-quently, it was mandatory to account for thetopographic variability in the CO2 column retrievalsfor columns extending to the surface. In contrastwith the El Mirage case, the surface type and 2 μmreflectivity was quite variable along the groundtrack, as displayed in Fig. 7. It is clear that theon-line and off-line signals are highly correlated overa wide range of surface reflectivity, the power ratio

Fig. 6. Weighting function, wðzÞ, for the LAS on-line, off-linefrequency pair: 31 July 2009 atmosphere in vicinity of ARM SGPOklahoma site.


showing no surface reflectivity influence. Two nota-ble (high and low reflectivity) points along theground track are highlighted in Fig. 7. Relativelyhigh reflectivity is seen when the ground trackpasses over a bare field consisting of dry soil. The op-posite extreme occurs when the ground track passesover a meandering river.

The data from the JPL LAS instrument were pro-cessed, and following the processing effort, intercom-parisons were made with the LaRC in situ CO2profiles. In this context, a brief description of thein situ measurement technique and operations isprovided here. AVOCET uses a modified LI-CORmodel 6252 nondispersive infrared gas analyzer-based sampling system with dual sample cells toachieve high CO2 measurement precision by compar-

ing the differential absorption between the sampledair and a calibrated reference gas that is traceableto the World Meteorological Organization primarycalibration standards maintained at the NationalOceanic and Atmospheric Administration ClimateMonitoring and Diagnostics Laboratory in Boulder,Colorado. During ambient sampling, air was continu-ously drawn throughaRosemountprobe, a permeablemembrane dryer to remove H2O, the LI-COR analy-zer, and then through the diaphragmpump. Frequentbut short calibrations with well-documented andstable calibration gases, critical to achieving bothhigh precision and accuracy, were accomplished byperiodically (∼15 minutes) flowing calibration gasthrough the instrument’s sample cell. The systemwasoperated at a constant mass flow rate (500 cm3min−1)and pressure (250Torr) and had a CO2 measurement

Fig. 7. On-line (blue) and off-line (red) signal power and powerratio versus time during 31 July 2009 during west-to-east overpassat 10kft altitude.

Fig. 8. Atmospheric CO2 profiles over Oklahoma ARM SGPvicinity from airborne in situ measurements during spirals.

Fig. 9. (a) Column-average CO2 mixing ratio retrieval, 31 July 2009, aircraft west-to-east overpass at 10kft altitude. Overpass-averageretrieval, 382ppmv. Column boundaries: upper (aircraft altitude) 3177m overpass average, lower (surface elevation) 302m ground-trackaverage. (b) Column-average CO2 mixing ratio retrieval, 4 August 2009, aircraft east-to-west overpass at 9kft altitude. Overpass-averageretrieval, 393ppmv. Column boundaries: upper (aircraft altitude) 2960m overpass average, lower (surface elevation) 302m ground-trackaverage.


precisionof≤0:1parts in106 (ppm) (�1σ) andaccuracyof �0:25ppm for 1Hz sampling rates. AVOCET CO2measurements were made from a maximum altitudeof 8km to below 300m above ground level. AllAVOCET measurements were integrated with GPSlatitude, longitude, and altitudemeasurementsmadeon the UC-12.

The LAS data processing proceeded in two steps.First, the analysis concentrated on the precision andday-to-day repeatability of themeasuredDAODof thelayer bounded by the 10 and 7kft overpasses. (A datasystem problem on 2 August precluded the 7–10kftDAOD measurement.) The resulting DAOD valuesand the retrieved CO2 column abundance valuesindicated a low day-to-day variability in this layer,column-average mixing ratio differences being lessthan the measurement precision limit of 8ppmv inthis layer. The objective of the second step in the ana-lysis was the column abundancemeasurement for thecolumn extending to the surface. With the averagesurface elevation over the ground track being∼300m,the average column height over the 10kft flight trackwas ∼2900m. Even including the uncertainty asso-ciated with range-to-surface determination (as inTable 2), the longer path length provided reduced re-lative uncertainty in derived column-average mixingratio, i.e., an overpass-average precision in the range3–4ppmv. The day-to-day variability in the (surfaceto 3:2km) column average was observed to be signifi-cantly larger than the measurement uncertainty, i.e.,the IPDAmeasurements indicated that therewas sig-nificant midday CO2 mixing ratio variability in thelower troposphere over the course of the 31 Julythrough 4 August time period, the difference incolumn-weighted mixing ratio between 31 July and4 August being nearly 10ppmv.

Comparisons between the LAS-measured column-weighted mixing ratios and the AVOCET profilesconfirmed our conclusions of very little variabilityin the CO2 mixing ratios within the 7–10kft layer,while significant variability occurred at the lower al-titudes. TheAVOCET-derived profiles shown inFig. 8also provided a means to evaluate the LAS-derivedmissing ratio offset and compare with the El Mirageresult. Using the AVOCET column-average mixingratios in the 7–10kft (2260–3235m above mean sealevel) altitude layer as “truth,” the derived offset was1.37. This confirmed our belief that the offset isstable, robust, independent of, e.g., surface type oratmospheric state. Thus, we systematically removedthe offset in the retrievals of weighted-column CO2mixing ratio. The resulting weighted-column CO2mixing ratios between surface and aircraft levelare shown in Fig. 9 for two cases: (a) 31 July, 10kftoverpass, and (b) 4 August, 9kft overpass. The Fig. 9results correspond to an integration time of 10 s(600m along-track spatial resolution). The uncer-tainty for this spatial resolution is primarily dueto speckle fluctuations statistics, with standard de-viation of 5ppm. The standard deviation due tospeckle fluctuation is ∼0:6ppm for the overpass-

average retrievals, which is a minor contributor tothe estimated 3–4ppm uncertainty due to the othersources of uncertainty in the overall budget (as listedin Table 2).

8. Conclusions

We have demonstrated airbornemeasurements of at-mospheric CO2 using a 2:05 μm LAS instrument andthe IPDA method. The level of precision of the mea-sured DAOD due to tropospheric CO2 is equivalent toapproximately 4ppmv in a weighted column throughthe troposphere. Day-to-day repeatability of mea-sured DAOD in atmospheric layers has been demon-strated to be at the same level as the measurementprecision.

As a result of comparisons with calibrated airbornein situ sensors and extensive investigation of LAS in-strument characteristics and data processing meth-odology, we have concluded that the retrieved valuesof DAOD in lower tropospheric layers exceed modelpredictions by a consistent factor that is due primar-ily to an instrument optical effect. Given the stabilityof the instrument optics, we can precisely determinethis offset over the range of altitudes covered by theTwin Otter and calibrate it out. The resulting retrie-vals indicate that we were able observe day-to-dayvariability in the lower tropospheric column-weighted CO2 with an uncertainty of 4ppm. Specklefluctuations add to the measurement uncertainty foralong-track averaging intervals less than a kilo-meter. We believe that, if the scattering surface isin the far field of the instrument, the predominantcontributor to the observed offset disappears.

The demonstrated capability of this airborne in-strument adds validity to the capability to imple-ment the NASA Active Sensing of CO2 Emissionsover Nights, Days, and Seasons mission in the2020 time frame.

This researchwas carried out at the JPL,CaliforniaInstitute of Technology, under contract with theNational Aeronautics and Space Administration(NASA).

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Atmospheric CO_2 measurements with a 2 μm airborne laser absorption spectrometer employing coherent detection