operating wavelengths optimization for a spaceborne lidar measuring atmospheric co_2

Operating wavelengths optimization for a spacebornelidar measuring atmospheric CO2

Jérôme Caron1,2,* and Yannig Durand1

1European Space Agency, European Space Research and Technology Centre,Keplerlaan 1, P.O. Box 229, 2200 AG Noordwijk, The Netherlands

2Consultant from RHEA System SA

*Corresponding author: [email protected]

Received 29 June 2009; revised 27 August 2009; accepted 7 September 2009;posted 8 September 2009 (Doc. ID 113050); published 25 September 2009

The Advanced Space Carbon and Climate Observation of Planet Earth (A-SCOPE) mission, a candidatefor the next generation of European Space Agency Earth Explorer CoreMissions, aims at measuring CO2

concentration from space with an integrated path differential absorption (IPDA) lidar. We report theoptimization of the lidar instrument operating wavelengths, building on two performance models devel-oped to assess measurement random errors from the instrument, as well as knowledge errors on geo-physical and spectral parameters required for the measurement processing. A promising approach todecrease sensitivity to water vapor errors by 1 order of magnitude is reported and illustrated. The pre-sented methods are applicable for any airborne or spaceborne IPDA lidar. © 2009 Optical Society ofAmerica

OCIS codes: 010.0010, 010.0280, 010.3640.

1. Introduction

The Advanced Space Carbon and Climate Observa-tion of Planet Earth (A-SCOPE) mission, whichhas just completed assessment study, aims to mea-sure atmospheric CO2 concentration from space withan unprecedented coverage and accuracy [1]. Itslaser-based technique is a promising approach to un-ambiguously characterize the CO2 sources and sinks.A-SCOPE belongs to the second generation of spacemissions dedicated to CO2 monitoring, followingthe passive missions Orbiting Carbon Observatory(OCO) [2] and Global Greenhouse Gas Observationby Satellite (GOSAT) [3]. The A-SCOPE instrumentis a quasi-nadir-looking differential absorption lidar(DIAL). Its innovative concept, called integratedpath differential absorption (IPDA), relies on themeasurement of the laser pulse echoes reflected onthe ground surface and provides the total columnconcentration of atmospheric CO2.

The use of lidar instruments to measure CO2 isexpected to bring several advantages over passivemeasurements: they allow full day/night coverage,coverage of high latitudes during all seasons, andare less impacted by cloud cover thanks to the smallfootprint of the collimated laser beams. Further-more, their time-gated detection technique unam-biguously defines the optical path of the detectedsignal, overcoming some fundamental limitationsof passive instruments that can be impacted by, forinstance, unknown aerosol or cirrus layers [4]. Withan appropriate instrument design, a significant re-duction of the measurement biases is expected forthe IPDA concept [1]. In this paper, the optimizationof the operating wavelengths is investigated with theaim of further reducing measurement and processingerrors. Improvements are not only expected for therandom error budgets, but also for the systematicerrors that are of fundamental importance for thederivation of CO2 fluxes, which is the fundamentalscientific objective of A-SCOPE.

Differential absorption lidars emit two laser pulsesat well-defined, very close wavelengths. The first one,

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1 October 2009 / Vol. 48, No. 28 / APPLIED OPTICS 5413

called “on-line” is strongly absorbed by the soundedmolecules, while the second one, called “off-line,” isnot, and serves as a radiometric reference. Followingrecommendations of preliminary studies [1], a pulseddirect detection lidar was selected for the assessmentstudy of A-SCOPE, as well as two sets of on-/off-linewavelengths, at 1.57 and 2:05 μm. The laser wave-length adjustment was made by choosing appropri-ate CO2 absorption lines, by optimizing the valueof the CO2 differential absorption, and byminimizingboth its temperature sensitivity and water vapor in-terference. Starting from these two wavelength sets,the current paper reports on their further optimiza-tion based on substantial improvements: the spectralvariability of the requirement is considered, andsensitivities to errors in water vapor, temperature,ground pressure, scattering surface elevation, andlaser frequency are calculated using a common for-malism based on the inverse approach, where theerrors arising during the measurement processingare quantified.In Section 2, a short overview of the A-SCOPE

mission is given. A more detailed description canbe found in [1,5]. The model calculating measure-ment relative random errors (RRE) is summarizedin Section 3. The next two sections focus on the opti-mization of the IPDA operating wavelengths, eva-luating the impact of wavelength dependent require-ments (Section 4), and sensitivity to errors in proces-sing parameters (Section 5). Using the formalismintroduced in these two sections, the on-line (Sec-tion 6) and off-line (Section 7) operating wavelengthsare optimized. In Section 8, a method to further re-duce the sensitivity to water vapor errors is pre-sented and illustrated.

2. A-SCOPE Mission Overview

A-SCOPE follows a near-polar Sun-synchronizedorbit with 6h local time descending node (LTDN),at a relatively low reference altitude, in the rangeof 325 to 400km. The low altitude improves the lidarradiometric budget, while the dawn–dusk orbit pro-vides a stable thermal environment. The typicallylow Earth reflected Sun background light is furtherreduced by the measurement geometry, the solarzenith angle being always higher than 60°.The lidar instrument operates in direct detection.

It measures the return from ground backscatter(hard target return), and integrates the CO2 mixingratio information over the full atmospheric verticalcolumn. From the atmospheric CO2 measurement,inversion methods are used to infer the sourcesand sinks that drive the global carbon cycle. The abil-ity of inversion methods to constrain and resolve CO2fluxes strongly improves with increasing measure-ment sensitivity at low altitude, where the fluxesare largest. The fine selection of the wavelengths of-fers the lidar instrument the needed high sensitivityto the planetary boundary layer. The two sets of op-erating wavelengths (denoted by InitialB1 and Initi-alB2) selected in the assessment study are presented

in Table 1, with the corresponding differential ab-sorption optical depths (DAODs). As required bythe IPDA concept, a small portion of the transmittedbeams is picked up and sent to the receiving channeldetector, which accurately monitors the fluctuationsin the pulse energy ratio on-line/off-line.

One observation is defined as the average of allmeasurements over a 50km path. For a low altitudeorbit, where spacecraft velocity is about 7km=s, a la-ser with a repetition rate of 50Hz results in about350 measurements to be averaged in order to obtainthe DAOD at “observation level.” Distinction is madebetween the measurement products: observation le-vel DAOD, the scattering surface elevation (SSE) re-quired to process it, and the column-averaged CO2dry air mixing ratio that requires further processing.

3. Measurement Random Errors

A dedicated performance model, calculating lidarmeasurement RRE has been developed to supportthe A-SCOPE instrument design and sizing. Thismodel first calculates the atmospheric absorptionas a function of wavelength. Then it combines theatmospheric properties with the lidar instrument,simulating the complete measurement optical path,and derives radiometric and noise performances.The following atmospheric effects are calculated: ab-sorption from CO2 and H2O, molecular Rayleighscattering, and extinction due to a median aerosoldistribution [6]. Molecular absorption is evaluatedwith spectroscopic parameters from the HITRAN04 database [7,8], except for the CO2 lines soundedby the on-line laser pulses (R18 and R30), for which[9] is used. Voigt line shapes are considered. Besides,the atmosphere is modeled with a U.S. standard pro-file [6,10], with 380ppm CO2. The DAODs calculatedwith these assumptions are presented in Table 1. Thelidar reflectivities range from 0:035 sr−1 (representa-tive of oceans) to 0:3 sr−1 (possible value on deserts)[1]. Background light is also calculated, with albedosranging from 0.11 to 0.94 and a worst case Sun ze-nithal angle of 60°.

The DAOD, denoted byΔτ, is obtained from on-lineand off-line returns and calibration signals with

Δτ ¼ −

12log

�ðSONreturn − SbgdÞðSOFF

cal − Sbgd;calÞðSOFF

return − SbgdÞðSONcal − Sbgd;calÞ

�; ð1Þ

where Sbgd and Sbgd;cal are background signals scaledto the laser return and calibration integration times,respectively. The RRE is calculated by differentiatingEq. (1) [11,12]. A sufficiently large detector dynamic

Table 1. Baseline Operating Wavelengths Sets andCorresponding Differential Absorption Optical Depths for A-SCOPE

Operating Wavelength Set InitialB1 InitialB2

On-line wavenumber [cm−1] 6361.2246 4875.6487Off-line wavenumber [cm−1] 6356.50 4875.22DAOD 0.7679 1.0989

5414 APPLIED OPTICS / Vol. 48, No. 28 / 1 October 2009

range is assumed, so that calibration signals can beset to stronger levels than the laser returns and thushave negligible noises. The following random errorcontributors are considered: shot noise from the lasersignal, shot noise from the background light, and in-trinsic detector noise. All measurements are per-formed with the same detector.

RRE ¼ δðΔτÞΔτ

¼ 1

n½2Δτ

�� σðSONreturnÞ

SONreturn − Sbgd

�2þ� σðSOFF

returnÞSOFFreturn − Sbgd

�2

þ σ2ðSbgdÞΔt

ΔtBG

�1

SOFFreturn − Sbgd

−

1

SONreturn − Sbgd

�2�½

: ð2Þ

Δt and ΔtBG are the integration times for the laserreturns and for the background measurement inthe absence of a useful signal. n is the number ofmeasurements used for averaging. S represents thevarious signals and σ their root-mean-square devia-tions, both expressed in photoelectrons:

SONreturn ¼ QeðNON

sig þNbgdÞ; ð3Þ

Sbgd ¼ QeNbgd; ð4Þ

σ2ðSONreturnÞ ¼ QeFðNON

sig þNbgd þNdetÞ; ð5Þ

σ2ðSbgdÞ ¼ QeFðNbgd þNdetÞ: ð6Þ

N are the incident photons, Qe is the detector quan-tum efficiency, and F is the detector excess noise fac-tor.Ndet is the photon flux, incident onto the detector,that would generate a shot noise having the sameamplitude as the detector noise:

Ndet ¼Qe

FΔt2

�NEPhν

�2: ð7Þ

NEP stands for noise equivalent power and is thenoise figure of merit of the detector (in W=Hz0:5), h(in joule seconds) is Planck’s constant, and ν (in in-verse seconds) is the frequency of the detected radia-tion. The RRE from Eq. (2) is directly driven by theinstrument sizing parameters: laser transmittedpower, receiver aperture diameter, and detector per-formance. Other measurement random error contri-butors are: (i) noise created by the imperfect overlapbetween on-line and off-line footprints on groundwith a spatially variable lidar reflectivity, (ii) speckle

noise, and (iii) laser frequency jitter. The main sourceof overlap noise is laser on-line /off-line pointing jit-ter. For a value of �25 μrad, considered as achievablethanks to the relaxation from the magnifying trans-mitter telescope, the error is negligible [5,13].Speckle noise can be calculated from the instrumentparameters summarized in Table 2. The number ofspeckle cells is about 9000 at 1:57 μm, and 5000 at2:05 μm, giving a RRE of about 0.00035 for bothcases. The speckle noise is weaker than shot and de-tector noises for the lowest lidar reflectivity (worstcase), but becomes significant over ground. As it isnearly independent of wavelength on small spectralranges, it has little influence on the operating wave-length optimization, and has not been included in thepresent analysis. It is included in the full instrumenterror budget presented in a separate paper [5]. Final-ly, a laser frequency jitter of a few megahertz, asachieved by candidate laser systems [14], gives anegligible RRE [5]. With a detection bandwidth of2nm, the background signal is weak, so that the ac-tual value of the background integration time ΔtBGdoes not impact the presented analysis, and has beenset toΔt. The assumed instrument parameters, sum-marized in Table 2, reflect the typical technology per-formance either available or foreseen for the missionimplementation. Detector parameters at 1:6 μm havebeen selected according to existing devices [15],while, at 2:0 μm, they are target values specifiedby ESA for ongoing technology developments. Moredetails about the A-SCOPE performance modelscan be found in [5]. The calculated random errorsare compared to spectrally variable requirementsin Section 4.

4. Spectral Variations of the Requirements

The A-SCOPE IPDA lidar provides a measurementof the total column DAOD. The CO2 total columnDAOD ΔτCO2

that is extracted from it contains allthe information about CO2 absorption in a singlenumber. ΔτCO2

is linked to the vertical distributionof CO2 concentration by an integral involving theweighting function (WF):

Table 2. Instrument Parameters used for Calculation of MeasurementRelative Random Errors

B1 (1:57 μm) B2 (2:05 μm)

Laser pulse energy [mJ] 50 50Telescope diameter [m] 1 1Receiver path transmittance 0.65 0.65Integration time Δt ¼ ΔtBG [ns] 200 200Spacecraft altitude [km] 400 400Number of measurementswithin 50km ¼ n

346 346

Field of view [mrad] 0.200 0.200Background filter bandwidth [nm] 2 2Quantum efficiency ¼ Qe 0.75 0.75Excess noise factor ¼ F 5 1.5NEP [fW=Hz0:5] 50 100


ΔτCO2¼

ZρCO2

ðpÞWFðpÞdp

¼Z

ρCO2ðpÞΔσCO2

ðpÞmdryairg

1

1þ mH2O

mdryairρH2OðpÞ

dp:

ð8Þ

ΔσCO2is a differential absorption cross section per

molecule (in square meters), mH2O and mdryair denotethe average masses of one H2O and one dry air mo-lecule (in kilograms), and g∼ 9:8m=s2 is the Earthgravity. ρCO2

is the CO2 dry air mixing ratio and isdefined by

ρCO2¼ nCO2

ndryair¼ nCO2

nairð1þ ρH2OÞ; ð9Þ

where nCO2, ndryair, and nair are numbers of molecules

per unit volume (in inverse cubic meters) and ρH2O isthe H2O mixing ratio.Due to the integral in Eq. (8), weighting functions

with a stronger contribution in the lower part of thetroposphere are more favorable to the characteriza-tion of CO2 sources and sinks that are located close tothe ground. Such weighting functions are obtainedwith pressure broadening effects: CO2 absorptionlines are extremely narrow at high elevations, whileclose to ground they are significantly widened. Inconsequence, on-line wavelengths far away fromthe line center have a larger CO2 absorption contri-bution from the lower troposphere and, for the samescientific return, will allow relaxed requirements. Onthe opposite, on-line wavelengths closer to the linecenter constrain the requirement.A goal requirement of 0:5ppm, applying to random

errors on the column-averaged CO2 dry air mixingratio measurements, was formulated for a constantpressure weighting function [1]. It includes both in-strument random errors (measurement noises, laserfrequency jitter) and random errors in ancillary data(SSE, geophysical parameters) with equal contribu-tions. The ratio Xðλon; λoff Þ can be used to rescale thisrequirement to a real set of operating wavelengths:

Xðλon; λoff Þ ¼R pgroundpPBL WFðλon; λoff ÞdpR pground0 WFðλon; λoff Þdp

; ð10Þ

where the pressure pPBL defines the upper limit ofthe planetary boundary layer, arbitrarily definedat 1km over sea level. The value pPBL ∼ 897hPahas been obtained by averaging over various repre-sentative atmospheric profiles [6,10]. The corre-sponding DAOD random error requirement,restricted to the instrument contributors, scales as

RREgoalmeasurementðλon; λoff Þ ¼

1ffiffiffi2

p 0:5380

Xðλon; λoff ÞX0

; ð11Þ

with

X0 ¼ 1 −

PPBL

P0∼ 0:1149; ð12Þ

and where P0 ¼ 1013:25hPa is the standard groundpressure. Requirements for the relative systematicerrors (RSE) are 10% of the RRE requirements, andseparate, as for RRE, into instrument and ancillarydata contributions with equal weights. For both RREand RSE, threshold requirements are 3 times higherthan goal requirements.

The weighting functions for the nominal InitialB1and InitialB2 wavelengths, as well as for variousshifts applied to the on-line wavelengths, are pre-sented in Figs. 1 and 2. In both cases, a positive spec-tral shift (in cm−1) moves the on-line laser frequencycloser to the CO2 line center. For B1 the weightingfunction amplitude is significantly changed for on-line spectral shifts as small as þ= − 0:01 cm−1. Thishigh spectral sensitivity translates into a demandingrequirement about spectral stability. A second fea-ture is the strong change in the shape of the weight-ing functions. For a laser tuned toward the linecenter, a strong maximum of sensitivity appearsaround 200hPa. It is not beneficial to the measure-ment and should be avoided. While the spectral posi-tion of the B1 on-line wavelength strongly influencesthe shape of the weighting function, for B2 the shapeis rather stable. Since the B2 CO2 line is strongerthan B1, to achieve an optimal DAOD close to unity[12], the B2 laser on-line has been chosen furtheraway from the CO2 line center. This explains theshape of the B2 weighting functions, more appropri-ate for sensing the CO2 close to ground.

By using Eq. (11), the requirements (goal andthreshold) on measurement RRE have been calcu-lated for two spectral intervals around B1 and B2,and are presented in Figs. 3 and 4. On the samegraphs, the RRE calculated with Eq. (2) is plottedwith instrument assumptions from Section 3, for var-ious lidar reflectivities and scattering surface alti-tudes. In both the B1 and B2 cases, the RREcloser to the line center increases due to the strongerabsorption and lower level of the on-line return (onthe right side of the plots), while it increases in

Fig. 1. Pressure weighting functions for the InitialB1 wavelengthset, with various spectral shifts of the on-line.


the absence of absorption (on the left side of the plots)due to the diminution of the differential signal. Thesefigures suggest possibilities for on-line optimization.The margin between the RRE in the worst operatingconditions (lowest lidar reflectivity) and the thresh-old requirements must stay positive and should bemaximized. For both B1 and B2, slightly movingthe on-line wavelengths away from the line centerimproves the situation. This possibility was notobvious for B1, since it consists of increasing theRRE: Fig. 3 shows that the requirement increasesfaster than the RRE. These possibilities of improve-ment identified by analyzing measurement errorsmust be confirmed by investigating the spectral sen-sitivity of measurement processing errors.

5. Errors Impacting the Measurement Processing

The processing required to calculate the column-averaged CO2 dry air mixing ratio introduces addi-tional errors due to uncertainties on laser frequency,SSE, spectroscopic parameters, and geophysicalparameters (temperature, pressure, humidity). Thegenerated errors can be inherently systematic (forspectroscopic parameters), or both random and sys-

tematic (general case). The sensitivities calculated inthis section serve as a basis to quantify both randomand systematic error budgets. Errors in spectroscopicparameters are known to play a significant role inthe IPDA error budget [16]. Since significant effortsare ongoing to perform improved spectroscopic char-acterizations of CO2 in spectral regions of interest forremote sensing [9,17], the associated uncertaintiesare expected to decrease in the near future, andare disregarded in this work.

The impact of uncertainties in laser frequency,SSE, temperature, pressure, and water vapor is nowcalculated with a common formalism. It is assumedthat the DAOD is given as a measurement, and thatthe errors are arising at two levels: (1) when correct-ing the DAOD from interfering gases, mainly water,and (2) when dividing it by the integrated weightingfunction to retrieve the column-averaged CO2 dry airmixing ratio:

~ρCO2¼ Δτmeasured −ΔτH2O

IWF; ð13Þ

IWF ¼Z ΔσCO2�

1þ mH2O

mdryairρH2O

�mdryairg

dp: ð14Þ

In Eqs. (13) and (14), Δτ are DAODs, ~ρCO2is the CO2

dry air mixing ratio with a ∼ sign standing for “col-umn averaged,” and IWF is the integrated weightingfunction. The DAODs, ~ρCO2

, and IWF are dimension-less quantities. The sensitivities to laser frequency orSSE knowledge errors are calculated with

δ~ρCO2

~ρCO2

¼ −

�1

ΔτCO2

dΔτH2O

dxþ 1IWF

dIWFdx

�δx; ð15Þ

where x represents laser frequency or SSE, and δx re-presents a small increment in x.Uncertainties onSSEcome from timing errors in the measurement of thelaser pulse echoes, from errors in platform pointing,or in platform location with respect to the reference

Fig. 2. Same as Fig. 1, for the InitialB2 wavelength set.

Fig. 3. Measurement RRE for various SSE and ground lidar re-flectivities, as a function of the on-line position. Goal and thresholdrequirements are given for comparison. The InitialB1 wavelengthset is assumed.



geoid. Sensitivities to temperature knowledge errorsare calculated with a similar equation:

δ~ρCO2

~ρCO2

¼ −

�1

ΔτCO2

dΔτH2OðTðzÞ þ δTÞdδT

þ 1IWF

dIWFðTðzÞ þ δTÞdδT

�δT; ð16Þ

but assuming that a constant offset δT is added to thewhole profile. The temperature derivatives are calcu-lated with respect to this constant offset. It has beenpointed out [4] that real temperature errors tend tocompensate each other statistically along the verticaldirection. It is possible to handle correctly such effectsby using, for instance, the covariance matrix methodwith data from the European Center for Medium-range Weather Forecasting (ECMWF). The constanttemperature offset approach followed here is not aim-ing at calculating the impact of real temperatureerrors, but rather at quantifying properly their spec-tral variations.Besides, it gives ameaningful figure ofmerit that was used in recent sensitivity studies [16].Finally, sensitivities to ground pressure or water

vapor errors are evaluated with

δ~ρCO2

~ρCO2

¼ −

�1

ΔτCO2

dΔτH2O½yðzÞð1þ εÞ�dε

þ 1IWF

dIWF½yðzÞð1þ εÞ�dε

�ε; ð17Þ

assuming that the whole pressure or water vaporprofiles yðzÞ are multiplied by a constant scaling fac-tor 1þ ε. The derivatives in Eq. (17) are taken withrespect to ε. For the pressure, this approach is sug-gested by the equation of hydrostatic equilibrium.If the profile pðzÞ verifies this equation, the profilekpðzÞ also verifies it for any constant positive factork, for mathematical reasons. The calculated watervapor sensitivity suffers from similar limitationsas temperature sensitivity, and does not describe realerrors with high accuracy. It is only used to quantifyrelative spectral improvements in the impact ofwater vapor errors. The sensitivities to pressure andto elevation changes are redundant to some extent.However, both kinds of perturbation have slightlydifferent impacts, as an elevation change is a trunca-tion of the atmospheric profile, whereas a pressurechange is a scaling. They aim to address differentkinds of errors, such as SSE retrieval errors, errorsin the interpolation of pressures on ground, or fore-cast inaccuracy.

When evaluating the previous equations forsensitivity to laser frequency, SSE, temperature, orpressure, it is noticed that the first term in the equa-tions (linked to water DAOD) usually gives a smallercontribution. This is a direct consequence of the verylow water DAOD for the considered operating wave-lengths. Similarly, the off-line wavelength position

Table 3. Calculated Performances for the Baseline A-SCOPE Wavelength Sets

Operating Wavelength Set InitialB1 InitialB2

RRE (SSE ¼ 0km, lidar reflectivity ¼ 0:035 sr−1) 0.00138 0.00255Goal / threshold RRE requirements 0:00069=0:00208 0:00153=0:00458

Sensitivity to

on-line spectral position [MHz−1] −0:001001 −0:000591elevation increment [km−1] 0.0928 0.2171temperature increment [K−1] 0.000773 −0:002058fraction error in pressure [−] −0:735 −1:653fraction error in water mixing ratio [−] 0.00368 0.00547

Fig. 5. Relative variations in column-averaged CO2 dry air mix-ing ratio sensitivity to knowledge errors in various processingparameters, as a function of the on-line position. The InitialB1wavelength set is assumed. Relative spectral changes in therequirement are given for comparison. Fig. 6. Same as Fig. 5, for the InitialB2 wavelength set.


has a very small impact, and all the sensitivity comesfrom the on-line position. For the sensitivity to watervapor errors, the situation is different. Equivalentamounts of error come from both terms in Eq. (17),with similar contributions from on-line and off-linewavelengths. In the next sections, numerical resultsfor the sensitivities are presented and discussed.

6. On-line Wavelength Optimization

The sensitivities of the column-averagedCO2 mixingratio to the following parameters have been calcu-lated: laser on-line frequency, SSE, temperature,ground pressure, and water vapor. Calculations havebeen repeated for six different climatic contexts de-fined in [6,10]. For each source of errors, Table 3 pre-sents the worst values obtained while varying theclimatic assumptions, at the nominal on-line wave-lengths. These numbers represent the contributionof measurement processing to the A-SCOPE errorbudgets. The relative spectral variations of the sen-sitivities when the on-line wavelengths are changedare presented in Figs. 5 and 6. At the nominal on-linevalues, all curves converge to one. For each curve, theworst case obtained when varying the atmosphericconditions is plotted. This explains some eventualdiscontinuities in the slopes of the curves. The rela-tive spectral variations of the requirement are alsopresented, for comparison.From these curves, it is apparent that most sensi-

tivities have the same spectral variations as the re-quirement, except the spectral and temperaturesensitivities. For B1, Fig. 5 invalidates the perfor-mance improvement proposed in Section 4 by tuningthe on-line away from the line center. The gain in theRRE budget is largely offset by a strong increase intemperature sensitivity. In addition, the improve-ment in the spectral sensitivity is not so high as couldbe initially expected: the gain due to the decrease inthe DAOD spectral slope is attenuated by the de-crease of the DAOD, so that the relative sensitivityis still significant. The InitialB1 on-line wavelength

position was found to be very close to an optimum,and it was decided to keep it unchanged. By contrast,the change in the on-line position proposed for B2 inSection 4 is clearly confirmed by Fig. 6. When tuningthe on-line farther away from the line center, not onlydoes the margin between the RRE and the require-ment increase, but both spectral and temperaturesensitivities decrease significantly. Lacking the ac-tual values of knowledge errors about wavelengthand temperature, an equal weight was given to bothsensitivities by adding them quadratically. An im-proved position for the B2 on-line was then foundat 4875:59 cm−1. The performances associated to thisnew wavelength are summarized in Tables 4 and 5,in the “B2 (new on-line)” column.

7. Off-line Wavelength Optimization

As already mentioned, the off-line has a limited im-pact on spectral, SSE, temperature, and pressuresensitivities. In this regard, the selection of the off-line wavelength is uncritical, as it offers little oppor-tunity to decrease or improve the performances. Tothe contrary, the off-line can introduce significanterrors in the measurement due to water concentra-tion uncertainties (as well as any other interferingmolecule). To minimize this effect, the off-line wave-lengths used for the assessment study have beenselected in a spectral region with low water inter-ference, such that the remaining water absorptionsof the on-line and off-line compensate each other.

The relative spectral change of the ratio betweenwater sensitivity and the requirement, calculatedwith Eqs. (11) and (17), is presented in Figs. 7 and 8as a function of the off-line position. The worst casevalues obtained over six atmospheric profiles [6,10]have been used for water sensitivity. The relativespectral change in the ratio between the RRE andthe requirement has also been plotted, so as to checkthe impact in the measurement RRE budget due tooff-line changes. For B2, the previously optimizedon-line at 4875:59 cm−1 was used.

Table 4. Optimized Operating Wavelength Sets for A-SCOPEa

Operating wavelength set B1 (optimized) B2 (new on-line) B2 (optimized)

On-line wavenumber [cm−1] 6361.2246 4875.59 4875.59Off-line wavenumber [cm−1] 6360.948 4875.22 4875.386DAOD 0.7525 0.4484 0.4126

aNew on-line follows optimization of on-line as described in Section 6; optimized lines follow optimization of off-line as described inSection 7.

Table 5. Calculated Performances For Optimized Wavelengths Sets

Operating Wavelength Set B1 (optimized) B2 (new on-line) B2 (optimized)

RRE (SSE ¼ 0km, lidar reflectivity ¼ 0:035 sr−1) 0.00141 0.00172 0.00187Goal/threshold RRE requirements 0:00068=0:00203 0:00166=0:00497 0:00164=0:00492

Sensitivity To

on-line spectral position [MHZ−1] −0:001021 −0:000456 −0:000495elevation increment [km−1] 0.0895 0.2450 0.2413temperature increment [K−1] 0.000737 −0:001189 −0:001358fraction error in pressure [−] −0:712 −1:859 −1:831fraction error in water mixing ratio [−] 0.00334 0.00618 0.00455


For B1, an off-line of around 6361:0 cm−1, muchcloser to the on-line, was investigated. The ratio be-tween the RRE and the threshold requirement is66.4% at 6356:50 cm−1. Because of the small remain-ing margin for the RRE, it was decided to tolerateonly a relative increase of 5% in this ratio. The off-line was chosen accordingly, at 6360:948 cm−1, witha ratio RRE over the requirement of 69.7% and a de-crease of about 7% in the ratio between sensitivity towater vapor and the requirement. For B2, the ratioRRE over the threshold requirement is 34.6% at4875:22 cm−1, so that a larger relative increase of10% could be tolerated. The resulting off-line wave-length is 4875:386 cm−1, with a decrease of about 25%in the ratio between water vapor sensitivity and therequirement.The expected IPDA performances have been recal-

culated for these two new off-lines, and are presentedin Tables 4 and 5. The resulting optimized sets ofwavelengths show significant improvements thatwere obtained without assumptions about the valuesof knowledge errors on the processing parameters.In this regard, small further improvements mightstill be possible that should be considered in futuremission phases.

8. Approach to Cancel Water Sensitivity

Because of pressure broadening effects, the sensitiv-ities to spectral variations and to SSE or pressureerrors, calculated in Eqs. (15) and (17), are varyingin opposite directions. When moving away fromthe line center, the DAOD spectral slope and the re-quired spectral stability are decreasing. At the sametime, the part of the absorption taking place close tothe ground is increasing and the DAOD measure-ment is becoming more sensitive to SSE and pres-sure errors. Only a compromise can be obtainedbetween these errors.

By contrast, a significant improvement in the sen-sitivity to temperature and water vapor errors can beexpected with an appropriate wavelength selection.Temperature sensitivity is strongly changing bothwith the selected CO2 absorption line [18] and withthe exact on-line position with respect to the center ofthis line [16]. As previously mentioned, it does notdepend significantly on the off-line wavelength. Inthe following, new on-line wavelengths have been se-lected, not only to optimize temperature sensitivity,but also to achieve a situation where water sensitiv-ity can be efficiently canceled with an appropriatechoice of the off-line wavelength. The present sectionaims to discuss further this possibility, which is, toour knowledge, not mentioned in the literature.

Sensitivity to water vapor is specific in that on-lineand off-line water optical depths have the same orderof magnitude. It is, in principle, possible to find off-line wavelengths such that the water DAOD cancelsout. But this approach is not optimal to achieve lowwater sensitivity, since water vapor is also used torescale the measurements from total air to dry air.The two water contributions are illustrated by the

Fig. 7. Relative variations in the ratio between water vaporsensitivity and threshold requirement, and in the ratio betweenmeasurement RRE and threshold requirement, as a function ofthe off-line position. The InitialB1 wavelength set is assumed.


Table 6. Alternative Operating Wavelengths sets for A-SCOPE

Operating Wavelength Set AlternativeB1 AlternativeB2

On-line wavenumber [cm−1] 6332.68 4874.59Off-line wavenumber [cm−1] 6332.27 4874.9425DAOD 0.7284 0.7453

Fig. 9. Proposed on-line/off-line set achieving cancellation ofwater sensitivity at 1.57 micrometers, with CO2 and H2O opticaldepths.


two terms in the right-hand side of Eq. (17). In orderto clarify their role, we write

ΔτH2O ¼Z ð1þ εÞρH2O

1þ kð1þ εÞρH2O

ΔσH2O

mdryairgdp; ð18Þ

IWF ¼Z

11þ kð1þ εÞρH2O

ΔσCO2

mdryairgdp; ð19Þ

with

k ¼ mH2O

mdryair: ð20Þ

Evaluating the derivatives with respect to ε gives ex-plicit expressions for the two contributors:

dΔτH2O

dε

�ε¼0

¼Z ρH2O

ð1þ kρH2OÞ2ΔσH2O

mdryairgdp; ð21Þ

dIWFdε

�ε¼0

¼Z

−kρH2O

ð1þ kρH2OÞ2ΔσCO2

mdryairgdp: ð22Þ

These two expressions, when inserted in Eq. (17),determine the water sensitivity of the CO2 mixing ra-tio. We see that the right-hand side of Eq. (21) has thesame sign as the water DAOD, while the right-hand

side of Eq. (22) is negative. If a small positive value ofwater DAOD is achieved, then it is possible to finetune the wavelengths such that both contributorscancel each other, giving a perfect cancellation of sen-sitivity to water.

This possibility was investigated for the InitialB1and InitialB2 wavelength sets. But since the on-linewater optical depth was initially extremely low, witha DAOD even negative for B1, it was not possible tofind suitable off-line wavelengths. Other CO2 absorp-tion lines, for which this cancellation scenario isachieved, have been identified. The proposed newwavelength sets are called “AlternativeB1” and “Al-ternativeB2.” Their exact values obtained after opti-mization are presented in Tables 6 and 7, with asummary of the associated performances. Thesetwo new sets of wavelengths show similar perfor-mances as the optimized B1 and B2 sets of Tables 4and 5 for most aspects. A remarkable improvement isfound for water sensitivity, which is reduced by a fac-tor of ∼10 for B1, and by a factor of ∼50 for B2. Thetemperature sensitivity is also improved by morethan 50% for B2, while being roughly unchangedfor B1. These improvements are obtained for theworst case values of sensitivities over six atmo-spheric profiles [6,10]. The position of these new wa-velengths with respect to the CO2 and H2Oabsorption spectra is presented in Figs. 9 and 10.As expected, the obtained H2O optical depths areslightly stronger than the minimum attainable va-lues, with stronger values for the on-line than theoff-line, a necessary condition to achieve the watersensitivity cancellation. The validity of these newwavelengths for a spaceborne lidar needs further in-vestigation to be confirmed, using more accuratemodels of the temperature and water profile errors,as well as improved spectroscopic parameters.Nevertheless, the feasibility of the water sensitivitycancellation is clearly demonstrated.

9. Conclusion

A-SCOPE, a candidate for the next generation ofEarth Explorer Core Missions, aims at measuringthe CO2 concentration from space with a pulsedIPDA lidar. In this paper, the two sets of operatingwavelengths initially proposed for the lidar (on-linesat 6361:2246 cm−1 and 4875:6487 cm−1, with off-linesat 6356:50 cm−1 and 4875:22 cm−1) are analyzed inlight of the recently completed assessment study.Measurement random errors are compared to

Table 7. Calculated Performances for Alternative Wavelengths Sets

Operating Wavelength Set AlternativeB1 AlternativeB2

RRE (SSE ¼ 0km, lidar reflectivity ¼ 0:035 sr−1) 0.00139 0.00187Goal/threshold RRE requirements 0:00064=0:00193 0:00157=0:00470

Sensitivity to

on-line spectral position [MHz−1] 0.001102 0.000477elevation increment [km−1] 0.0862 0.2317temperature increment [K−1] 0.000720 0.000677fraction error in pressure [−] −0:690 −1:800fraction error in water mixing ratio [−] 0.00032 −0:00011

Fig. 10. Proposed on-line/off-line set at 2.05 micrometers, sameas Fig. 9.


spectrally variable requirements. Sensitivities toknowledge errors on laser frequency, surface scatter-ing elevation, temperature, ground pressure, andwater vapor are calculated with a common formalismthat quantifies the errors occurring in measurementprocessing. Based on this analysis, optimized posi-tions for the A-SCOPE wavelengths are given. A pro-mising method is also proposed to reduce further theimpact of water uncertainties. New operating wave-lengths sets are calculated (on-lines at 6332:68 cm−1

and 4874:59 cm−1, with off-lines at 6332:27 cm−1 and4874:9425 cm−1), with a water sensitivity reduced bya factor of 10 at 1:57 μm, and by a factor of 50 at2:05 μm. The temperature sensitivity is also 50% low-er at 2:05 μm, with other performances unchanged.The presented methods are applicable to anyIPDA lidar.Significant improvements have been predicted in

the A-SCOPE performance. The results presentedfor 380ppm CO2 can be extrapolated to account forfuture higher CO2 concentrations. The RRE budgetwill slightly decrease at 1:57 μm, and increase at2:05 μm (the DAOD coming closer or departing fromits optimal value [12]), influencing the optimal on-line position. RRE requirements are unchanged, asare all sensitivities except water sensitivity, whichdepends on both CO2 and H2O DAODs. To achievethe proposed cancellation scenario, the H2O DAODwill have to be slightly higher, with a correspondingchange in the off-line position.

The authors thank the industrial consortia thathave been in charge of the assessment study, namely,Astrium Germany and Thales Alenia Space. Theauthors are also grateful for many useful discussionswith the Mission Assessment Group (MAG) mem-bers, in particular Gerhardt Ehret (German Aero-space Center, Institute for Atmospheric Physics,Oberpfaffenhofen, Germany), Pierre Flamant (Labo-ratoire de Météorologie Dynamique, Palaiseau,France), Sanders Houweling (Netherlands Institutefor Space Research, Utrecht, Netherlands), François-Marie Bréon (Laboratoire des Sciences du Climat etde l’Environnement, Gif-sur-Yvette, France) and Ro-bert Menzies (Jet Propulsion Laboratory, Pasadena,California, USA).

References and Notes

1. “A-SCOPE—Advanced Space Carbon and Climate Observa-tion of Planet Earth, Report For Assessment,” ESA-SP1313/1 (European Space Agency, 2008), http://esamultimedia.esa.int/docs/SP1313‑1_ASCOPE.pdf.

2. Orbiting Carbon Observatory (OCO), http://oco.jpl.nasa.gov/.3. Global Greenhouse Gas Observation by Satellite (GOSAT),

http://www.gosat.nies.go.jp/.

4. E. Dufour and F. M. Breon, “Spaceborne estimate of atmo-spheric CO2 column by use of the differential absorptionmeth-od: error analysis,” Appl. Opt. 42, 3595–3609 (2003).

5. J. Caron, Y. Durand, J.-L. Bezy, and R. Meynart, “Performancemodeling for A-SCOPE, a spaceborne lidar measuring atmo-spheric CO2,” Proc. SPIE 7479 (in press).

6. Reference Model of the Atmosphere, issued for A-SCOPEassessment study (ESA internal document, 2007, availableon request).

7. L. S. Rothman, C. P. Rinsland, A. Goldman, S. T. Massie, D. P.Edwards, J.-M. Flaud, A. Perrin, C. Camy-Peyret, V. Dana,J.-Y. Mandin, J. Schroeder, A. McCann, R. R. Gamache, R.B. Wattson, K. Yoshino, K. V. Chance, K. W. Jucks,L. R. Brown, V. Nemtchinov, and P. Varanasi, “The HITRANmolecular spectroscopic database and Hawks (HITRAN atmo-spheric workstation): 1996 edition,” J. Quant. Spectrosc.Radiat. Transfer 60, 665–710 (1998).

8. L. S. Rothman, D. Jacquemart, A. Barbe, D. C. 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).

9. R. A. Toth, L. R. Brown, C. E. Miller, V. M. Devi, and D. C.Benner, “Spectroscopic database of CO2 line parameters,”J. Quant. Spectrosc. Radiat. Transfer 109, 906–921 (2008).

10. Atmospheric profiles (temperature, pressure, water vapor) aretaken from G. P. Anderson, S. A. Clough, F. X. Kneizys, J. H.Chetwynd, and E. P. Shettle, “AFGL Atmospheric ConstituentProfiles (0–120km),” AFGL-TR-86-0110 (Air Force Geophy-sics Laboratory, (1986).

11. R. M. Schotland, “Errors in the lidar measurement of atmo-spheric gases by differential absorption,” J. Appl. Meteorol.13, 71–77 (1974).

12. E. E. Remsberg and L. L. Gordley, “Analysis of differentialabsorption lidar from the Space Shuttle,” Appl. Opt. 17,624–630 (1978).

13. A. Amediek, A. Fix, G. Ehret, J. Caron, and Y. Durand, “Air-borne lidar reflectance measurements at 1.57 microns in sup-port of the A-SCOPE mission for atmospheric CO2,” Atmos.Meas. Tech. Discuss. 2, 1487–1536 (2009).

14. 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).

15. InGaAs APD Ref. 30645 (Perkin Elmer).16. G. Ehret, C. Kiemle, M. Wirth, A. Amediek, A. Fix, and

S. Houweling, “Space-borne remote sensing of CO2, CH4,and N2O by integrated path differential absorption lidar: asensitivity analysis,” Appl. Phys. B 90, 593–608 (2008).

17. L. Joly, F. Gibert, B. Grouiez, A. Grossel, B. Parvitte, G. Durry,and V. Zeninari, “A complete study of CO2 line parametersaround 4845 cm−1 for Lidar applications,” J. Quant. Spectrosc.Radiat. Transfer 109, 426–434 (2008).

18. 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).


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