validation of wind profiles measured with incoherent doppler lidar

Validation of wind profilesmeasured with incoherent Doppler lidar

Matthew J. McGill, Wilbert R. Skinner, and Todd D. Irgang

A high-resolution incoherent Doppler lidar has been constructed at the University of Michigan SpacePhysics Research Laboratory. The primary purpose of this lidar is to measure vertical profiles of thehorizontal wind field with high spatial and temporal resolution. In mid-1994 a rawinsonde system wasused to assess the performance of the lidar. The resulting comparisons of profiles from the balloons andthe lidar are shown. The comparisons show an ;2-mys rms error between the two systems. Thereasons for this error are discussed, and a sensitivity study is shown to illustrate the sensitivity of thelidar wind measurements to various system parameters. Finally, steps that are being taken to improvethe systematic errors are discussed. © 1997 Optical Society of America

Key words: Lidar, incoherent Doppler lidar, Fabry–Perot interferometer, Doppler shift, wind mea-surements, aerosol backscatter.

1. Introduction

The use of lidar technology to measure atmosphericwinds has become an important meteorological capa-bility. Currently, two primary categories of wind-sensing lidars exist: coherent and incoherent ~ordirect detection! lidar. Coherent systems use a het-erodyning technique to measure winds.1,2 This isaccomplished with a local oscillator that is mixedwith the return signal to generate a beat frequency.Changes in the beat frequency are related to changesin the wind speed. The incoherent technique di-rectly measures the Doppler shift experienced by apulse of narrowband laser light as it is scattered byeither molecules or aerosols. Incoherent detectionrequires knowledge of a zero-wind spectral positionrelative to measured Doppler-shifted spectra. A ref-erence spectrum is measured at the same time as theatmospheric spectra by the collection of light scat-tered from the outgoing optics, and this spectrumsuffers no Doppler shift. The position of the refer-ence spectrum is then subtracted from the position of

When this research was undertaken the authors were with theDepartment of Atmospheric and Space Sciences, Space PhysicsResearch Laboratory, University of Michigan, Ann Arbor, Michi-gan 48109. Matthew J. McGill is now with NASA Goddard SpaceFlight Center, Code 912, Greenbelt, Maryland 20771.Received 28March 1996; revised manuscript received 30 August

1996.0003-6935y97y091928-12$10.00y0© 1997 Optical Society of America

1928 APPLIED OPTICS y Vol. 36, No. 9 y 20 March 1997

each atmospheric spectrum to determine the line-of-sight wind. One can detect wavelength shifts by us-ing a high-resolution spectroscopic device ~typically aFabry–Perot interferometer! to examine the laser sig-nal. Aerosols provide a near-ideal scattering sourcebecause the backscattered signal is not broadenedsignificantly from the original laser bandwidth.Therefore wind measurements are obtained readilywith an incoherent lidar in regions of high aerosolloading, such as the planetary boundary layer andlower stratosphere. In the free troposphere and re-gions of the upper atmosphere, where aerosol concen-trations are small, molecular scattering can be usedto obtain wind measurements. Because of thermalbroadening, scattering from molecules does not pro-vide the sensitivity to a Doppler shift that is given byaerosols, but wind determinations are still possiblewith a molecular-scattered signal.Members of the Space Physics Research Labora-

tory at the University of Michigan have designed andbuilt an incoherent detection lidar system that usesscattering from aerosols to measure vector winds inthe lower troposphere. The first results were pub-lished in 1992.3 Since that time, a number of systemchanges have been made and a field study was per-formed.4 That field study, although successful, ledto many engineering changes, primarily to achievebetter instrument stability. In mid-1994, a balloonintercomparison was performed to ascertain the ac-curacy of the lidar measurements in the planetaryboundary layer. The results of the balloon intercom-parison showed that the instrument was operating

quite well, but there were still engineering changesneeded to optimize the system. Several fundamen-tal instrument effects, such as nonlinear detectorcounting, were not included in earlier data analysis.These effects were studied carefully and incorporatedinto a completely new, mathematically robust analy-sis routine.5 With the new analysis technique, thelidar and balloon wind profiles were found to agree towithin ;2 mys in the planetary boundary layer.This result is good, considering that further designmodifications have been identified and are being im-plemented, as discussed below.The lidar system that we describe in this paper is a

second-generation version of an original Doppler li-dar constructed at the University of Michigan.3 Assuch, the system is not optimal, and it served as anengineering prototype for a new system currently un-der construction. It is important to recognize thatthis lidar is not an optimal system ~as discussed inSections 6 and 7! and that the relatively high energyrequirements for boundary layer measurements arenot indicative of the multichannel incoherent detec-tion method in general. Rather, the purpose of thelidar system was to demonstrate that useful vectorwind measurements could be obtained in the lowertroposphere with a multichannel incoherent detec-tion method and to identify areas needing improve-ment. If vector winds could be measured in thelower troposphere, the measurement capability couldbe expanded to the upper troposphere and strato-sphere. Successful operation of the lidar has led to aproposal for a spaceborne system, and development ofa prototype system is under way.The University of Michigan lidar can measure

wind and aerosol backscatter profiles simulta-neously, during both day and night. A Fabry–Perotinterferometer system is used to resolve the aerosol-scattered spectrum and determine the Doppler shift.Figure 1 shows how the aerosol and molecular back-scatter contribute to the total return signal. Manylidars require approximations to separate the twocomponents of the return.6,7 With a multichanneldetector and a nonlinear least-squares fitting tech-nique, the Doppler shift, aerosol signal, and molecu-lar signal can be determined simultaneously anduniquely from each measured spectrum. The aero-

Fig. 1. Return signal that is due to aerosol and molecular scat-tering. Only the indicated wavelength region is imaged onto thedetector.

sol backscatter is of interest not only for the informa-tion about atmospheric aerosols, but also forinformation about the state of the atmosphere, suchas the mixing-layer height.8 The benefits of concur-rent wind and aerosol measurements will prove use-ful in the modeling of aerosol transport.Although the lidar we describe in this paper was

developed only for measuring the mean wind fieldand tested only in the lower troposphere, other ap-plications are possible with some further engineeringdevelopment. This technique is applicable to all re-gions of the atmosphere, provided a system is devel-oped to use the appropriate scatterers ~i.e., aerosolsor molecules!. Applications of this wind-measuringtechnique include turbulence monitoring and pollut-ant tracking, among others. It is important to reit-erate, however, that the system that we consider inthis paper was developed as a proof of concept forfuture application. For example, a satellite-basedlidar system that concurrently measures winds andaerosols would be a powerful meteorological tool.A complete description of the instrument was pub-

lished previously5,9 and should be consulted for de-tails about the instrument design and operation. Inbrief, a pulsed, injection-seeded Nd:YAG laser fre-quency doubled to 532 nm is used as the light source.A seed laser within the Nd:YAG laser provides anarrow linewidth ~0.0045 cm21 compared with ;1cm21 for the unseeded Nd:YAG!. A high-resolutionetalon ~HRE! is used to resolve the aerosol-backscattered spectrum. The HRE is a 10-cm air-gap Fabry–Perot interferometer with a free spectralrange ~FSR! of 0.05 cm21 ~400 mys or 1.50 GHz!. Alow-resolution etalon ~LRE! is used to filter back-ground sunlight for daytime measurements. TheLRE is a Fabry–Perot interferometer with a 0.49-cmair-gap spacing and a FSR of 1.02 cm21 ~30.592 GHz!.Although not required for nighttime operation, theLRE remains in place continually to avoid disturbingthe optical alignment. The fringe pattern generatedby the HRE is imaged onto a 32-channel image planedetector ~IPD!. The detector is similar to those usedon the High Resolution Doppler Imager10,11 aboardthe Upper Atmosphere Research Satellite and theFabry–Perot instrument flown on the Dynamics Ex-plorer.12 The IPD has concentric anodes of equalareas that matches the detector to the etalon fringepattern ~equal wavelength intervals have equal ar-eas!. Only the innermost 12 channels are currentlybeing used.

2. Data Analysis

Data analysis is performed with a nonlinear least-squares fitting method. The fitting technique wasdeveloped to extract simultaneously and uniquely theDoppler shift, aerosol signal, and molecular signalfrom each measured spectrum. This inversionmethod is possible because the three components ofthe measured spectra have uniquely different func-tional shapes, as shown in Fig. 2. Although the in-version is linear in the aerosol and molecular signals,it is nonlinear in the Doppler shift. Taking advan-

20 March 1997 y Vol. 36, No. 9 y APPLIED OPTICS 1929

Fig. 2. Three different pieces of information are contained in a measured spectrum, each having a distinct functional shape @Eq. ~1!#. Aleast-squares technique can be used to determine the three parameters uniquely.

tage of the orthogonality of the three functions allowsa successful least-squares determination of the threeparameters. Furthermore, because each spectrumis fitted completely independent of all others, no un-necessary assumptions about the molecular compo-nent are required, as in the Klett algorithm.6,7

A. Instrument Model

A complete mathematical derivation of the lidar sys-tem model and inversion has been published previ-ously.5 For reference, however, the systemmodel onwhich the fitting is based is described here. Theequation being fitted in the inversion process is

N~r, j! 5ETlεDthc

OA~r!AT

4pr2DhQETOTF~n!TLRE~ j, n!

3h~ j!nC

(n50

`

!n, j sincS nNFSR

D3 expS2 p2n2DnL

2

DnFSR2 Dcos 2pnSj2 j0~r!

NFSRD

3 Fa~r! 1 v~r!expS2 p2n2DnM2

DnFSR2 DG . (1)

Values for the instrument parameters are given inTable 1, and the variables are defined as follows:j is the detector channel number,r denotes the range from the transmitter ~m!,N~r, j! is the number of counts on channel j at range

r,ET is the transmitted laser energy per pulse ~J!,ε is the pulse repetition frequency ~Hz!,Dt is the total integration time ~s!,


OA~r! is the fractional overlap of the telescope andlaser,AT is the area of the receiving telescope ~m2!,Dh is the range bin length ~m!,QE is the quantum efficiency of the detector,TO is the transmission of the optics ~excluding fil-

ters!,TF~n! is the transmission of filters,TLRE~ j, n! is the transmission of the low-resolution

etalon,nC is the number of detector channels,h~ j! is a detector normalization coefficient,DnL and DnM are the 1ye widths of the laser and

molecular linewidths ~cm21!,NFSR is the number of detector channels per HRE

FSR, andDnFSR is the wave number change per HRE FSR

~cm21!.

Table 1. Model Input Parameters

VariableName Parameter Value

ET Transmitted energy 60 mJypulseAT Telescope area 1555 cm2

Dh Range bin length 150 mQE Detector efficiency 3.2%TO Transmission of optics 5.6%TF Transmission of filters 8.6%DnL Laser 1ye width 4.59 3 1023 cm21

~1.3 3 1024 nm!DnM Molecular 1ye width 4.75 3 1022 cm21

~1.344 3 1023 nm!

Equation ~1! is correct for an incoherent lidar if oneassumes linear detector counting and a single-scattering atmosphere. Effects of multiple scatter-ing are not considered in this model because the fieldof view of the instrument is so small that multiple-scattering effects are minimal. Multiple scatteringwill really influence the measurements only if a cloudis present. It has been shown13 that even when acloud base is encountered, single scattering still ac-counts for 95% of the return signal when the laserbeam divergence is 0.5 mrad ~which is similar to thislidar system!. Also, aerosol thermal broadening,molecular absorption, turbulent broadening, andBrillouin scattering effects have been neglected be-cause of the width of the laser line and the bandwidthof the 10-cm etalon.The terms a and v in Eq. ~1! are generalized quan-

tities defined as

a~r! 5PA~p, r!bA~r!expH22 *0

r

@bA~r9! 1 bM~r9!#dr9J ,(2)

v~r! 5PM~p, r!bM~r!expH22 *0

r

@bA~r9! 1 bM~r9!#dr9J ,(3)

where bA~r! is the aerosol volume-scattering coeffi-cient ~km21!, bM~r! is the molecular volume-scattering coefficient ~km21!, PA~p, r! is the aerosolbackscatter phase function, and PM~p, r! is themolecular backscatter phase function. We notethat PA~p, r! and PM~p, r! are normalized such that1y4p ** P~u, f!sin ududf 5 1. The terms a and vdescribe the aerosol and molecular contributions tothe total return signal, assuming no absorption.By defining these generalized quantities, one can ob-tain wind measurements and aerosol backscatter esti-mates without an exact knowledge of parameters thatare difficult to determine, such as the telescope field ofview and laser beam overlap function. A useful param-eter to define is the aerosolymolecular ratio. Definedas R 5 @PA~p, r!bA~r! 1 PM~p, r!bM~r!#yPM~p, r!bM~r!,which is equivalent to ~a 1 v!yv, this ratio expressesthe relative aerosol loading of the atmosphere. A ra-tio of one represents pure molecular scattering, a ratioof two means equal amounts of aerosol and molecularscattering, and an increasing ratio represents an in-creasing aerosol concentration.The term !n, j in Eq. ~1! arises from the Fabry–

Perot transmission function and is defined as

!n, j 5 S1 2+

1 2 5D2S1 2 5

1 1 5D for n 5 0,

!n, j 5 2S12+

12 5D2S12 5

11 5D3 5n exp@24p2n2DdD

2~ j!n02# for n. 0, (4)

where + accounts for any absorptive or scatteringlosses in the etalon plates, 5 is the plate reflectivity,

and DdD~ j! is an instrument defect parameter ~seeSubsection 2.B!.The quantity j0~r! in Eq. ~1! has been defined as

j0~r! 5NFSR

DnFSRF~n0 2 nC! 2

2UH~r!n0 sin f

c G (5)

and locates the position, in channels, of the Doppler-shifted fringe pattern. The Doppler shift that is dueto the mean wind is

DnD~r! 52UH~r!n0 sin f

c, (6)

where sin f is the observation zenith angle andUH~r!is the horizontal wind velocity ~mys!. The term ~n0 2nC! in Eq. ~5! accounts for any offset in the position ofthe laser line n0 with respect to the central frequencyof the etalon nC.Finally, the transmission of the LRE is given as

TLRE~ j, n! 5 S1 2 5

1 1 5DS1 1 5E

1 2 5ED

3~12 5E!

2

12 25E cos 2pFj2 j0~r!NLRE

1 fLREG1 5E2

,

(7)

where NLRE is the number of channels per LRE FSR,fLRE is the offset between the two etalons, and 5E isan effective reflectivity. The effective reflectivity istaken from ameasured instrument response functionand serves to match the LRE model to the measuredLRE finesse. The expression for the transmission ofthe LRE @Eq. ~7!# is an approximate form of theFabry–Perot transmission function. However, be-cause the FSR of the LRE is so much greater thanthat of the HRE, use of the approximate form is bothacceptable and computationally efficient.

B. Model Calibration

In addition to the parameters given in Table 1, sev-eral other parameters are required for the forwardmodel to represent accurately the instrument re-sponse. These include detector normalization coef-ficients, the instrument defect parameter, and acorrection for nonlinear detector counting. Each ofthese effects have been described more fully,5 and inthis subsection we provide only an overview of theinstrumental quantities and how they affect the winddetermination.The illumination and sensitivity of each detector

channel are not the same, and normalization coeffi-cients are used to compensate. The detector nor-malization coefficients describe the relative responseof the detector to broad-bandwidth illumination.The detector normalizations are obtained from un-seeded laser scans that provide a broad linewidthsource ~;1 cm21! through the etalons, although con-tinuum light sources have also been used. The nor-malization coefficients should remain constant, but


can change considerably if the position of the outgo-ing laser beam or the location of the telescope focusmoves ~see Section 7!.The instrument defect term is used to tune the

interferometer model so that it matches the mea-sured instrument spectral response. The defect pa-rameter includes several effects, such as platebowing, microscopic plate defects, detector broaden-ing, and off-axis aberrations, that can broaden theinstrument function. The instrument defect term isallowed to vary with detector channel to describe thevariation of etalon finesse with channel. One candetermine the defect parameter for each channel byperforming a least-squares fitting of a HRE responsefunction. The fitting is accomplished with the sameforward model described above.Nonlinear detector counting is an important factor

in the near field. All photomultiplier type devicessuffer from this effect, which is basically a limitationon how many photons can be counted in a given timeinterval. The lidar IPD has a 260-ns dead time.This means that at most, one photon every 260 ns canbe counted on each channel of the detector. If morethan one photon is incident within that time, thesubsequent photon is not counted. As a result, thespectral shape can become distorted because chan-nels with more incident photons will be affected morethan channels with few incident photons. The effecton wind determination can be pronounced if the dataare not corrected. A suitable correction can be ob-tained if the mean time between photon events ismuch greater than the dead time ~i.e., the detector isonly slightly nonlinear!. In that case,

Nm, j 5Na, j

1 1Na, jt

Dt

, (8)

where Nm, j is the measured counts on channel j, Na, jis the counts that would be sensed if the detector werecompletely linear, Dt is the total integration time, andt is the dead time. Inverting Eq. ~8! allows one todetermine the actual count rate.The nonlinear effect is different for the reference

spectrum than for other spectra. When the laserpulse propagates through the free atmosphere, thedetector can count photons for an entire microsecond~the range-gating length is equivalent to 1 ms!. Thereference, however, receives all of its signal withinthe pulse length of the laser ~;6 ns!. Because this issignificantly less than the detector dead time, onlyone photon per pulse can be counted on each channel.Because of this, it is easy to drive the detector into anonlinear counting region. Even for the atmo-spheric spectra there is enough return signal in thefirst 100–200 m to cause nonlinear counting.Although the nonlinear counting effect can be cor-

rected, there can still be a problem when a low-level,optically thick cloud is encountered. When the laserpulse impinges on the base of a thick cloud, a strongreturn signal can result over only 6–12 ns. It has


been found that spectra in such cases cannot be cor-rected adequately as either reference spectra or at-mospheric spectra.

3. Sensitivity of Model Parameters

The forward model of the lidar system provides apowerful tool for examining the effect of variousmodel parameters on the fitted variables. As de-scribed in Section 2, there are three primary instru-mental parameters that must be known to model thesystem properly: detector normalization coeffi-cients, instrument defect function, and detector non-linearity. Our purpose in this section is to explorethe effect of systematic errors in these parametersand to determine how those errors affect the recov-ered wind measurements. Attention is also given tounderstanding how the offset of one etalon relative tothe other can produce large errors in the wind deter-minations.The results of this sensitivity study must not be

interpreted as correction factors that can be appliedto the data. If there were a known error in one of theparameters, that parameter could be recalculated orremeasured in the laboratory to correct the resultanterrors in the fitting process. Instead, the results ofthese simulations show how errors in the variousparameters affect proper determination of the windand to what accuracy each parameter must be knownso as to achieve a certain wind error. Furthermore,because each parameter was isolated and examinedseparately, the errors from each must be combinedinto a total systematic error contribution to the winderror.

A. Detector Normalization Coefficients

The detector normalization coefficients can have aprofound effect on the shape of the measured spectra,which can greatly affect the wind determination.The effect is greatest for spectra with low aerosolymolecular ratio, although it is not insignificant forspectra with higher ratios. In practice, there islikely some error in the normalizations for all chan-nels. The error in the wind w that is attributable toerror in the normalization coefficients n can be writ-ten as

sw 5 (i51

12 S]w]ni

Dsn,i, (9)

where the subscript i denotes the channel numberand sn,i is the error in the normalization coefficient.One can calculate the slope ]wy]ni using the forwardmodel and perturbing the normalization coefficientsby a known amount one channel at a time. Usingthe propagation of errors theorem, assuming randomuncertainties in the normalizations, and assumingthe detector channels are uncorrelated, we obtain

sw2 5 sn

2 (i51

12 S]w]ni

D2. (10)

Figure 3~a! shows the results of applying Eq. ~10! fordifferent values of error in the normalization coeffi-cients and different aerosolymolecular ratios. Ingeneral, Fig. 3~a! shows that, to achieve a line-of-sight wind error of less than 1 mys ~regardless of theratio! requires knowledge of the detector normaliza-tion coefficients to greater than 3%.It is important to note that the reference spectrum

will suffer from the same effects as the atmospheric~i.e., Doppler-shifted! spectra. The reference spec-trum will always appear as a high ratio ~typically aratio of between five and seven!. The actual wind ismeasured relative to the reference, and errors in thereference must be accounted for when systematic er-rors are examined. To account for reference spec-trum errors, a model reference spectrum wasconstructed and perturbed just as for the others. Wethen corrected the resulting wind errors by subtract-ing the error that was due to the reference. Thesame holds true for all the errors described in thefollowing subsections.

B. Instrument Defect Function

The instrument defect function also affects the shapeof measured spectra. The effect of errors in the de-

Fig. 3. Error in recovered line-of-sight wind for various aerosolymolecular ratios ~denoted by R! as a function of a! error in detectornormalization coefficients and b! error in instrument defect func-tion.

fect function is not as significant as for the detectornormalization coefficients but can contribute 0.2 mysor more to the total systematic errors. Just as forthe detector normalization coefficients, there is likelyto be error in the defect values for all channels.Equation ~10! can again be used to examine the effectof errors that are due to the defect function. Figure3~b! shows the resulting curves for various aerosolymolecular ratios, in which the effects for the referencespectrum have been subtracted. Overall, it can beseen that to achieve a 0.5-mys wind error, the defectfunction must be known to greater than approxi-mately 20%.

C. Detector Nonlinearity

Any attempt to generalize the effect of detector deadtime on wind and aerosolymolecular ratio determina-tions is difficult. Unlike the detector normalizationcoefficients or the instrument defect function, thedead time is presumed to be the same for all chan-nels. Also, the dead time correction is a highly non-linear function, so it is dependent on signal level. Toassume a constant laser power and to build spectra ofdifferent aerosolymolecular ratios would result in anunrealistic situation. It is also not correct simply toscale the peak count rate so that all spectra have thesame peak counts. This would result in an artificialsituation, and spectra with low ratio would have ab-normally high molecular signal levels.Despite these problems, some statement about

wind error that is due to error in the dead time isnecessary. A specific case study will suffice to illus-trate the effect, with the understanding that the deadtime effect is nonlinear. For this test, a model spec-trum was constructed with an aerosolymolecular ra-tio of 2.0, peakmeasured signal level of 12,100 counts~peaked in channel 4.3!, and a dead time of 260 ns~these are typical values!. The dead time was thenperturbed by a known amount, and the spectrumwasfitted using the perturbed dead time. The resultsare summarized in Table 2, and a dead time error of2100% represents the case of fitting the spectrumwith no dead time correction applied. As Table 2shows, almost a 1-mys error can result if no dead timecorrection is used. The error is also dependent onthe aerosolymolecular ratio, but this is difficult toquantify in a general sense. Of course, as the signal

Table 2. Errors in Wind Determination because of Errors in DetectorDead Time for Spectra with Peak Counts in Channel 4.3

Error inDead Time

~%!

Systematic Errorin Recovered Wind

~mys!

2100 0.8069250 0.4038225 0.2007210 0.0793110 20.0780125 20.1947150 20.3550


level rises, the error in the wind and the ratio willincrease regardless of the ratio.

D. Etalon Offset

It is important to keep the two etalons in resonance.The resonance condition is necessary to maintain op-timal throughput. But there is another, more sig-nificant consideration. When the two etalons arenot held in resonance, the distribution of light fallingon the detector is not uniform, which can bias thewind determination. This is exactly the conditionthat occurred in the lidar instrument during some ofthe balloon intercomparisons. Figure 4 shows a plotof recovered wind error versus relative offset ~fLRE, indetector channel units! between the two etalons.Because both the reference and the atmospheric spec-tra will be influenced by this effect, the error that isdue to a model reference spectrum has been sub-tracted to give an effective line-of-sight wind error.Figure 4 was made with the forward model and wasperformed for several values of the aerosolymolecularratio. Model spectra were constructed assumingvarious offsets between the two etalons. The mod-eled spectra were then analyzed with the assumptionthat the etalons were in resonance ~no offset!. Therecovered wind errors illustrate clearly that even asmall offset can result in a large wind error. As canbe seen, the effect is most significant for low aerosolymolecular ratios, but is not insignificant for higherratios.

4. Wind Profiles

A standard operating pattern has been developed tocollect data in three different viewing directions for 2min in each direction. Data can be collected contin-uously except during periods of precipitation. Thelidar observes to the north and west to obtain the twohorizontal wind components needed to build a hori-zontal wind vector. A 48° zenith angle results in100-m vertical resolution. Figure 5 illustrates thelidar viewing geometry. A vertical observation pro-vides an approximate check on instrument stability

Fig. 4. Error in recovered line-of-sight wind as a function of eta-lon offset for various aerosolymolecular ratios ~denoted by R!.


because vertical winds should be small except underconditions of extreme convective activity. The 2-mindata integration period is a trade-off between maxi-mum temporal resolution and gathering enough re-turn signal to have sufficiently low statistical error.It is important to note that the temporal and spatialresolutions are particular to this system only. Withfurther design work, a similar system could be devel-opedwith better resolution, both in time and space ~tostudy short time-scale turbulent effects, for example!.Figure 6 shows a typical example of the horizontal

wind field measurement capability. Each vector isproportional to the wind speed, and a 10-mys-scalevector is shown in the lower left corner for reference.The vectors are spaced 100 m apart vertically and 6

Fig. 5. Lidar viewing geometry. L.O.S., line of sight.

Fig. 6. Horizontal wind field from 12 September 1994. Vectorsare spaced 6 min apart. As denoted by the compass, the positivex axis represents east and the positive y axis represents north.For reference, a 10-mys scale is drawn in the lower left corner.

min temporally. Above the 100-m level, the lidarwinds are continuous and consistent, which is im-pressive considering that each data point is fittedindependent of all others. The 100-m level is dis-torted strongly by nonlinear detector effects ~see Sec-tion 6!. In Figure 6 the winds are seen to rotateclockwise with altitude, which is indicative of theEkman spiral. Observations of such mesoscale me-teorological phenomena demonstrate the usefulnessof the lidar as a wind-measuring tool.Although a vertical profile is obtained, it is not used

for vertical wind measurements. Vertical winds arenormally small, of the order of centimeters per sec-ond. Because the laser is stable only to approxi-mately 0.5 mys, vertical wind measurements areprecluded under normal atmospheric conditions.However, the vertical scan provides aerosol backscat-ter measurements and a check on instrument opera-tion. We note that the optical system itself does notpreclude vertical wind measurements. Indeed, theoptical system is capable of resolving Doppler shiftsof the order of a few centimeters per second; laserstability is the limiting factor.

5. Balloon Intercomparison

A rawinsonde system was brought to Ann Arbor,Michigan, to validate the incoherent Doppler lidarmeasurements. During the months of August andSeptember 1994, a National Center for AtmosphericResearch ~NCAR! Cross-Chain Loran AtmosphericSounding System ~CLASS! balloon system was collo-cated with the lidar. Forty-three balloons werelaunched successfully over several days, under vari-ous atmospheric conditions, and during differenttimes of the day. A wide range of atmospheric con-ditions was desired to determine the accuracy of lidarwind measurements under varying atmospheric con-ditions. Many balloons were launched at 2 hr inter-vals during the early morning and evening hours toobserve wind changes that generally occur duringthose time periods.14 Various atmospheric condi-tions were encountered during the period of the bal-loon campaign, including an extended period of lowaerosol content.The NCARCLASS balloon system is based on long-

range navigation ~Loran-C! technology, which wasdeveloped as a navigational aid for ships and planes.With advances in technology and an increase in thecoverage of Loran-C stations, most areas of theUnited States now have access to Loran-C signals.The NCAR developed its CLASS system in the mid-1980’s, and the CLASS system has been acceptedwidely by the meteorological community as an accu-rate method of wind profiling.Vaisala RS-80LH radiosondes were used for the

balloon intercomparison. As the balloon rises, thesonde continually transmits information to theground station. On the ground, the radiosonde dataare processed into temperature, humidity, and pres-sure estimates. The Loran-C frequencies are pro-cessed with an ANI-7000 aircraft navigator toprovide wind speed estimates. The final wind mea-

surements are 30-s averages of Loran data. Winderrors for the CLASS system are expected to be lessthan 0.5 mys in the Ann Arbor area.15After the balloon campaign, as data analysis was

begun, it was discovered that the two etalons hadcome out of resonance for an extended period of timeduring the campaign. Failure of a pressure-adjusting stepper motor connected to the etalons issuspected. This caused the balloon comparison to besplit into two groups: those balloons launched whenthe lidar was operating properly ~17 balloons! andthose launched during the period when the etalonswere not in resonance ~26 balloons!. This distinctionis necessary for two reasons. First, when the etal-ons are out of resonance, instrument throughput islowered, resulting in greater statistical error.Second, different analysis procedures had to be ap-plied to each group. When the etalons are not inresonance, a fourth parameter must be added to thefitting technique. This fourth parameter describesthe position of the peak LRE transmission relative tothat of the HRE. Although the fourth parametercan be fitted and wind measurements obtained,16 inthis paper we focus only on the balloons launchedwhen the system was operating properly and onlythree parameters were being fitted.Figure 7 shows two different lidar–balloon inter-

comparisons from a period when the two etalons wereheld in resonance. Error bars for the balloon mea-surements are not shown, but are expected to be lessthan 0.5 mys at all altitudes.15 The lidar profiles are

Fig. 7. Lidar ~solid curve! and balloon ~dashed curve! profiles fora! 2:00 UT and b! 4:00 UT, 9 September 1994. Lidar profiles arehour averages. Error bars are shown for the lidar profiles.


1-hr averages. The lidar data were averaged for sev-eral reasons. Averaging reduces measurementnoise, which is important in the higher altitude levelswhere signal level decreases rapidly. Averagingalso extends the lidar profile over the duration of theballoon flight. Because the balloons were set to riseslowly ~to obtain many points in the boundary layer!,a typical balloon took over a half-hour to rise throughthe boundary layer. Thus, we minimized the differ-ence between instantaneous point measurements forthe balloon and longer volume averages for the lidarby averaging.The error bars plotted on the lidar profiles in Fig. 7

illustrate two important considerations for this lidarsystem. First, the error bars generally increasewith height because of the decrease in return signal.A decreasing signal causes the statistical error toincrease. Second, the error bars are smaller wherethe aerosol content is larger, even at higher altitudes.This second point demonstrates that, for this partic-ular system, wind measurements become more diffi-cult as aerosol content decreases. Thus, in regionsof low aerosol content, the lidar data will becomenoisy whereas the balloon data remain unaffected bythe change in aerosol content. For this reason,development is under way to augment the aerosolwind-measuring receiver with a molecular wind-measuring counterpart.It is important to briefly discuss why the wind data

are shown as horizontal vector winds ~and vectorcomponents! rather than as radial velocities. Al-though many wind profilers display radial velocities,the intent of this instrument was to measure thehorizontal vector wind field. As other profilers, thelidar fundamentally measures radial velocities ~seeFig. 5!. The conversion between radial and vectorvelocities is a simple geometric conversion, and inthat sense, the difference between radial and vectorvelocities is small. Although radial velocity is thefundamental quantity, the purpose of the lidar was tomeasure accurately horizontal vector winds, and thepurpose of the Loran-tracked balloons was to validatethe vector wind measurements. Future compari-sons will likely involve a radar profiler ~such as a915-MHz boundary-layer profiler!, but we believethat the rawinsondes provided a satisfactory valida-tion of the instrument operation.

6. Discussion of Wind Errors

Shown in Fig. 8~a! is the mean difference betweenlidar and balloon profiles ~lidar wind minus balloonwind! for all 17 balloons launched during the periodwhen the two etalons were in resonance. The meandifference is greatest near the ground and decreasesto a constant error with increasing altitude. Thelidar detector nonlinearity effect is greatest for thelowest altitudes and is likely the most significantfactor contributing to the difference. However, sev-eral of the balloons had difficulty acquiring a goodLoran signal lock until the sonde had risen 200 or300 m, which could influence the balloon profiles inthe lower levels. Figure 8~b! shows the correspond-


ing rms difference between the lidar and balloon pro-files. Again, the error is large at low altitudes wherethe detector nonlinearity effect is significant. Theerror decreases with altitude as the nonlinearity ef-fect decreases. The error then begins to increaseagain as the signal level begins to dropwith increasedaltitude. Given the laser instability and detectornonlinearity issues, a rms error of ;2 mys in themid-altitude regions is considered excellent. Theoverall difference between the two techniques israther small when one considers the difference be-tween instantaneous point measurements and longervolume measurements. Slight differences betweenthemeridional and zonal components of the rms errorare attributed to subtle differences in the detectornormalization coefficients, which were assumed con-stant, but have been shown to have changed slightlyover time ~see discussion below!.There are four points that need consideration with

regard to possible causes of error between the balloonand lidar wind profiles. First, the lidar makes time-averaged measurements over a volume, rather thaninstantaneous point measurements. In this sense,the lidar is perhaps more representative of the meanstate of the atmosphere. Second, there is always thepossibility that the balloon measurements are incor-rect. No attempt was made to track the balloonsindependently and verify their accuracy. Third, thelidar measurements assume a horizontal homogene-ity of the wind field. We obtained a horizontal windprofile by measuring in one direction for 2 min andthen measuring in a different direction for 2 moreminutes to obtain the two components needed tobuild a horizontal wind vector. The assumption isthat the mean wind does not change over the 4-minmeasurement period or over the distance separatingthe two volumes being sampled. Furthermore, thelidar–balloon comparisons could suffer from nonho-mogeneity of the wind field. That is, the balloonsdrift away from the lidar measuring site and could besampling in regions quite distant from the regionbeing sampled by the lidar. Fourth, lower-altitudewinds measured by the two techniques could differ

Fig. 8. Mean lidar–balloon wind difference and rms wind differ-ence. Graphs are a composite of 17 balloon profiles during periodswhen the two etalons were held in resonance.

because of surface effects. Winds in the lowest al-titudes are affected strongly by local topography,buildings, and trees. This effect is reduced athigher altitudes where the wind flow generally be-comes more uniform. The point measurements ofthe balloon could, therefore, be quite different fromthe volume-averaged lidar measurements at loweraltitudes.There are two types of errors that contribute to

the error in the measured lidar winds, and it isimportant to understand fully the causes and im-plications of each. Statistical error is determinedsolely by the number of measured photons. Thelidar is photon counting, so Poisson statistics apply,and more photons translate to less error in the mea-surement.5 Because the return signal drops off as1yr2 with altitude, the wind error is expected toincrease linearly with altitude, assuming the signallevel dominates over background. As shown inFig. 8~b!, the error increases above 700 m, which isdue primarily to a decreasing signal level. To de-crease the statistical error requires either more sig-nal or averaging of data into longer time periods.Because more photons cannot be collected due tonear-field detector nonlinearity, the only way to de-crease the statistical error is to average the dataover longer periods. Instrumental error affectshow well the least-squares fit can approximate theactual data. The accuracy of the fit depends pri-marily on three instrument parameters, as dis-cussed in Subsection 2.B: detector normalizationcoefficients, an etalon defect function, and a detec-tor dead time. To avoid biasing the fit, these threeparameters must be well known from laboratorycalibration measurements, as discussed in Section3.Errors in the detector normalization coefficients

and etalon defect function can affect the fitting, buttheir effects can be eliminated by measuring properlythose parameters in the laboratory. The detectordead time also has a pronounced effect on the fitting.The dead time correction is different for the referencethan for other spectra, because the reference receivesall its signal within the pulse length of the laser ~;6ns! compared with a full microsecond for the otherspectra. This makes it difficult to compensate forthe effect because the zero-wind reference spectrumcan be affected independently of the Doppler-shiftedspectra. In general, however, the reference spec-trum count rate is low enough that it can be fittedaccurately. The near-field range, however, receivessuch a high return signal that the dead time correc-tion cannot compensate properly. As a result, thenear-field spectra tend to have a greater error whenfitted, which quickly decreases with altitude as thecount rate, and therefore the severity of the dead timeeffect, decreases. This is also seen in Fig. 8~b!,where the error is large at 100 m and decreases up toapproximately 500 m. This error is likely attribut-able to the detector nonlinearity. The only way toeliminate this error is to either lower the transmittedintensity so that all ranges remain linear or to re-

place the present photomultiplier-type detector witha CCD-style detector. A decrease in the transmittedintensity is not desirable because this would decreasethe far-field return beyond useful limits. Therefore,research is under way to install a CCD detectionsystem. A change to a CCD detector system wouldalso allow a tenfold increase in quantum efficiency.The result would be a decrease in statistical errorsand an extension of useful measurements to higheraltitudes.A different cause of instrumental error is attribut-

able to the fundamental design of the system. Be-cause it was decided to use aerosol return to measurewinds, a 10-cm etalon spacing was chosen for thissystem. This allows full resolution of the aerosol-backscattered signal, but not the molecular signal, asshown in Fig. 1. Therefore wind measurementswith small error can be made only when aerosol re-turn is sufficient to provide a sharp spectral shape.This modeling of the lidar system has shown that thewind error is dependent on aerosol backscatter, andas the aerosolybackscatter ratio drops below ;1.2,the error in measured winds increases dramatically.This modeling is supported by actual measurements,as shown in Fig. 9, that show the measured horizon-tal wind component error as a function of both thecount rate ~statistical error! and the fitted aerosolybackscatter ratio ~related to instrumental error!.Figure 9 is a composite over several days of data, andto emphasize the effects of these two parameters onthe wind error, only the lower count rates and theaerosolybackscatter ratios are shown. We do not in-tend to imply that only the count rates or the aerosolybackscatter ratios shown in Fig. 9 are measured bythe lidar. What we show in the figure is that a verylow aerosolybackscatter ratio, which corresponds to avery low aerosol loading of the atmosphere ~a veryreal measurement condition!, cannot provide ade-quate wind errors with a 10-cm etalon. At highercount rates and higher aerosolybackscatter ratios,however, the lidar can measure horizontal wind com-ponents with approximately a 1-mys accuracy. Achange in the etalon plate spacing would allow this

Fig. 9. Wind error as a function of signal level and aerosolymo-lecular ratio.


effect to be minimized and is being considered for thefuture.

7. Lessons Learned

Several significant considerations were borne out bythe lidar–balloon intercomparison. An in-depth ex-amination of each problem encountered is importantto showwhere system improvements should bemade.In most cases, the necessary improvements have al-ready been made or are under way. The balloonintercomparison highlighted many necessary engi-neering and data analysis changes needed to providea more stable instrument and yield more accuratewind measurements.Prior to the balloon intercomparison, overlap of the

two etalons had not been considered critical becauseof the large difference in FSR between them. Webelieved that if the two etalons drifted out of reso-nance, the total throughput would just drop slightly.In fact, the throughput can drop significantly and thewind determination can become strongly biased, asshown in Subsection 3.D. The modeling of the lidarreturn with the forward model clearly illustrates theimportance of maintaining resonance between theetalons. Although the etalons are normally held inresonance with a pressure-adjusting stepper motor,failure of that motor at a crucial time demonstratedthe need for better or more frequent system monitor-ing. More important, the operational method ofmaintaining optimal overlap of the two etalons mustbe as accurate as possible to ensure that resonance ismaintained.Detector normalization coefficients had previously

been assumed constant, both in altitude and withviewing direction. This has proved not to be thecase. Because of an imperfect internal alignmentbetween the primary and secondary telescope mir-rors, different viewing directions image to slightlydifferent points. This results in differing illumina-tion on the etalons for different viewing directions.The result is a set of detector normalization coeffi-cients that vary with altitude and viewing direction.This can, and has, been accounted for in the datacollected during the balloon intercomparison. Whatwas not anticipated, however, is that the normaliza-tion coefficients can change over time. This can bedue to a disturbance of the instrument or if the posi-tion of the output beam changes slightly when thelaser flash lamp is changed. Because the angles in-volved are small, a slight change in the position of theoutgoing beam or the image point of the telescope canchange the normalization coefficients. During thecourse of the balloon intercomparison, data for nor-malization coefficients were collected only threetimes, and those data show that the normalizationsdid change slightly between measurements. Asshown in Subsection 3.A, small changes in the nor-malization coefficients can have a large effect on theproper wind determination. It is imperative, there-fore, that the normalization coefficients be measuredregularly so that changes can be incorporated into thedata analysis.


Laser stability and detector nonlinearity effectswere two primary sources of error in the lidar system.The only way to solve the laser frequency stabilityproblem is to obtain a new laser with a moretemperature-stable, seed-injecting laser. Prior tothe balloon campaign, the issue of detector nonlin-earity was never considered significant. However,an examination of measured signal levels versusthose predicted by the forward model clearly showeda significant near-field effect that reduced the mea-sured signal. Ultimately, detector nonlinearity wasfound to be the source, and a reasonable correctioncan be made to the data. The detector nonlinearityeffect can be removed by the replacement of thephotocathode-type device with a solid-state CCD de-vice, which was to be done by early 1997.The balloon comparison identified several design

changes that are needed to improve measurementaccuracy. These changes are under way and shouldbe completed in 1997. During this time, the systemwill also be changed to operate at 355 nm, to addresseye safety issues. The upgraded lidar system willfeature enhanced system stability and greater opticalefficiency and will allow for a significant improve-ment in the wind measurements.

8. Conclusions

In mid-1994 a comparison of wind profiles obtainedwith an incoherent Doppler lidar and a NCARCLASS balloon systemwas performed. The purposeof the intercomparison was to assess the accuracy ofthe lidar wind measurements and to point outchanges that could be made to improve the lidar mea-surements. In both respects, the intercomparisonwas highly successful.The primary result of the balloon intercomparison

was to illustrate the inadequacy of the lidar dataanalysis routine that was being used. An entirelynew, physically correct, mathematically robust anal-ysis method was developed. The forward modelused in this analysis method has proved powerful asa predictive model to ascertain the effects of varioussystem parameters on the wind determination. Ashas been shown, large wind errors can be caused bysmall errors in certain system parameters. The sen-sitivity of the wind determination to these parame-ters had not been appreciated previously. As aresult, steps have been taken to ensure that theseparameters are measured more accurately and moreoften.The intercomparison also pointed out several in-

strument changes that could be made to improve theaccuracy of the lidar measurements. A change to aCCD-style detector will help eliminate near-field de-tector counting problems. The use of a CCD detectorwill also increase the system throughput by a factorof 10 or more, which will reduce greatly the statisticalerrors and extend the measurements to higher alti-tudes. CCD’s are not without potential problems ei-ther, but as long as the full-well capacity is notexceeded, a CCD should provide a tremendous im-provement over the IPD. An improved telescope im-

aging system will eliminate variations in the imagedlight that have been shown to occur because of inter-nal telescope alignment problems. Both of these en-gineering changes are under way, with completionscheduled for late 1997.Notwithstanding these problems, data obtained

during the balloon intercomparison clearly illustratethe potential for incoherent Doppler lidar as a wind-measuring tool. Wind profiles have been shown thatillustrate the measurement capability and the use-fulness of the lidar measurements. The resultingballoon comparisons showed that a rms error of ;2mys was attained in regions of the boundary layerwhere detector nonlinearity was not an issue. Giventhe need for further engineering changes, as pointedout, an ;2-mys rms error is considered good.

This research was supported by NASA grantNAG1-1331.

References1. F. F. Hall, Jr., R. M. Huffaker, R. M. Hardesty, M. Jackson,

T. R. Lawrence, M. J. Post, R. Richter, and B. F. Weber, “Windmeasurement accuracy of the NOAA pulsed infrared Dopplerlidar,” Appl. Opt. 23, 2503–2506 ~1984!.

2. M. J. Post and R. E. Cupp, “Optimizing a pulsed Doppler lidar,”Appl. Opt. 29, 4145–4158 ~1990!.

3. V. J. Abreu, J. E. Barnes, and P. B. Hays, “Observations ofwinds with an incoherent lidar detector,” Appl. Opt. 31, 4509–4514 ~1992!.

4. K. W. Fischer, V. J. Abreu, P. J. Samson, and M. J. McGill,“Measurement of aerosol loading profiles and mixing layerheights in Atlanta, Georgia, during the 1992 SORP-ONA fieldstudy,” in Tunable Diode Laser Spectroscopy, Lidar, and DIALTechniques for Environmental Industrial Measurements, A.Fried, D. K. Killinger, and H. I. Schiff, eds., Proc. SPIE 2112~1993!.

5. M. J. McGill, W. R. Skinner, and T. D. Irgang, “Analysis tech-niques for the recovery of winds and backscatter coefficientsfrom a multiple channel incoherent Doppler lidar,” Appl. Opt.36, 1253–1268 ~1997!.

6. J. D. Klett, “Stable analytical inversion solution for processinglidar returns,” Appl. Opt. 20, 211–220 ~1981!.

7. J. D. Klett, “Lidar inversion with variable backscatteryextinc-tion ratios,” Appl. Opt. 24, 1638–1643 ~1985!.

8. F. J. Marsik, K. W. Fischer, T. D. McDonald, and P. J. Samson,“Comparison of methods for estimating mixing height usedduring the 1992 Atlanta Field Intensive,” J. Appl. Meteorol.34, 1802–1814 ~1995!.

9. K. W. Fischer, V. J. Abreu, W. R. Skinner, J. E. Barnes, M. J.McGill, and T. D. Irgang, “Visible wavelength Doppler lidar formeasurement of wind and aerosol profiles during day andnight,” Opt. Eng. 34, 499–511 ~1995!.

10. P. B. Hays, V. J. Abreu, M. E. Dobbs, D. A. Gell, H. J. Grassl,and W. R. Skinner, “The High-Resolution Doppler Imager onthe Upper Atmosphere Research Satellite,” J. Geophys. Res.98, 10713–10723 ~1993!.

11. P. B. Hays and J. Wang, “Image plane detector for Fabry–Perot interferometers: physical model and improvementwith anticoincidence detection,” Appl. Opt. 30, 3100–3107~1991!.

12. T. L. Killeen, B. C. Kennedy, P. B. Hays, D. A. Symarrow, andD. H. Ceckowski, “Image plane detector for the Dynamics Ex-plorer Fabry–Perot interferometer,” Appl. Opt. 22, 3503–3513~1983!.

13. Y. Benayahu, A. Ben-David, S. Fastig, and A. Cohen, “Cloud-droplet-size distribution from lidar multiple-scattering mea-surements,” Appl. Opt. 34, 1569–1578 ~1995!.

14. L. Mahrt, “The early evening boundary layer transition,” QJRMeteorol. Soc. 107, 329–343 ~1981!.

15. R. M. Passi and C. Morel, “Wind errors using the worldwideLoran network,” J. Atmos. Ocean. Technol. 4, 690–700 ~1987!.

16. M. J. McGill and W. R. Skinner, “Use of multiple Fabry–Perotinterferometers in an incoherent Doppler lidar,” Opt. Eng. 36,139–145 ~1997!.


validation of wind profiles measured with incoherent doppler lidar

Documents