remote sensing of winds and atmospheric ......remote sensing of winds and atmospheric turbulence...

REMOTE SENSING OF WINDS AND ATMOSPHERICTURBULENCE BY CROSS-CORRELATION OF

PASSIVE OPTICAL SIGNALS

A. J. Montgomery

IIT Research InstituteChicago, Illinois 60616

ABSTRACT

This paper describes a new methodfor the remote measurement of windsand atmospheric turbulence by thecross-correlation of passive opticalsignals. If small local variationsin atmospheric density, temperatureor other parameters cause fluctuationsin scattered or thermal radiationdetected by a radiometer on theground, then the cross-correlationof the fluctuations detected by tworadiometers with crossed fields otview can yield turbulence informationpertaining to the region about thisintersection point. When the fieldsof view are not quite crossed turbu-lent eddies will be convectedthrough the fields of view sequen-tially, and the transit times ofthe eddies identified by thecorrelation procedure will yieldwind information.

The successful application ofthis technique, detecting fluctu-ations in scattered sunlight, hasdemonstrated both the potential,and the present limitations ofthe method, which are discussedin this paper. Results for thepower spectrum of the fluctuationsand for winds at an altitude of 61

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REMOTE SENSING OF WINDS AND ATMOSPHERIC TURBULENCE

meters are shown, and the wind measure-ments are compared to similar measure-ments made with a standard anemometerlocated on top of a 61 meter tower.

1. INTRODUCTION

The determination of wind profiles, turbulence scales andthree dimensional wave-number components is of great importancein numerical methods of weather prediction and in clear airturbulence studies. Some type of remote sensing system is quiteclearly required if this information is to be obtained conven-iently. In the case of wind measurements which are of particularimportance in weather prediction for the tropical and subtropicalregions of the earth, measurements at a sufficient number ofgrid points over a time interval of a few hours could be obtainedonly with a satellite remote sensing system.

At this time no proven technique is available by whichwind fields may be remotely measured. However, a limited amountof wind field information may be inferred from some of theatmospheric parameters measured with presently orbitingmeteorological satellites. This problem is discussed byW. Nordberg in COSPAR Transactions No. 3, "Status Report on theApplications of Space Technology to the World Weather Watch."

This paper describes a new technique presently underdevelopment which shows promise for the remote detection ofwinds directly. Wind components have been successfullydetermined at 200 and 400 foot altitudes from the cross-correlation of output signals of two photometers located on theground with their fields of view intersecting at these altitudes.In these tests scattered sunlight was detected; however,extension of the technique to infrared measurements of watervapor, ozone or other possible atmospheric tracers is presentlybeing studied.

This technique was first suggested by M. J. Fisher (1964)and has been developed by IIT Research Institute and NASA,Marshall Space Flight Center, for the measurement of convectionspeeds and turbulent flow properties in fluid flows. Since thepower of the technique has very clearly been demonstrated inmeasurements of convection speeds, eddy scales, and eddylifetimes, in turbulent shear layers produced by an air jet,

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A. J. MONTGOMERY

(Fisher and Krause, 1967), the basic method will be describedwith reference to these successful aerodynamic tests.

In the course of this paper we shall discuss:

(1) The basic concept of the crossed-beam technique(2) Successful application to subsonic and supersonic

aerodynamic flows(3) Methods of applying the technique to the atmosphere(4) Source of atmospheric fluctuations(5) Particular problems associated with the technique

due to the unstationary nature of atmospheric phenomena(6) Initial measurements of winds and their comparison

with data from meteorological towers(7) Some future developments which are currently being

considered.

2. CROSSED-BEAM TECHNIQUE

The crossed-beam experimental configuration as used inthe aerodynamic test program is shown in Figure 1. Two collimated

IW r I= IMULTIPULIER

FLUCTUATIONSi.I-f DEFLECTORS

iy R(LI, SX)UR

NSOZZLE xI Cos B T

2 LIGHT SOURCES

Figure 1. Space Fixed Crossed Beam Test Arrangements

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beams from the two light sources shown intersect (~ = 0) at thepoint of interest in the flow. The spectral content of theradiation that is detected is selected by the optical filter ormonochromator which precedes the detector in both beams, and thewavelength has to be chosen so that there are absorption orscattering losses from the beam during its passage through theflow. Since the flow is turbulent there will be variations inthe numbers of absorbers or scattering agents along the twobeams which will cause fluctuations in the detected signals.Measurement of the cross-correlation between the signals fromthe two detectors will yield information about the fluctuationlevel in the region of intersection of the two beams in thefollowing manner. If a turbulent eddy having associated with ita higher or lower concentration of scatterers or absorbers thanthe surrounding medium passes through one of the beams it willcause fluctuations in the detected signal. Only if it passesthrough intersection point of the two beams will a zero timedelay correlated fluctuation be produced. Thus it may be shownthat the output of the correlator depends only on the propertiesof those eddies which pass through the beam intersection point.The correlation coefficient, which is normalized with respectto the uncorrelated fluctuations; depends as well on the eddyscales and the way in which the strength of the fluctuations inabsorber or scatterer concentration vary along the two beams.Let us now consider one beam displaced a distance ~ down-streamfrom the other beam. An eddy convected along the line of minimumseparation between the beams will cause fluctuations at onedetector and a correlated fluctuation at the second detector atime T later, where T is the time for the eddy to be convectedthe distance ~. Thus if the correlation between the two signalsis measured as a function of time delay, this correlation functionwill be a maximum for t = T.

To put this discussion on a more formal footing, the math-ematical basis of the technique will be briefly considered.Using the coordinate system shown in Figure 1, the point of beamintersection has coordinates (x, y, z), where the y and z axisare orientated along the directions of the crossed beams.Distances from the point of intersection are denoted by , ,and C in the x, y, and z directions, respectively. The intensitymeasured by the y-axis detecting system will be given by:

Il(t) = Io exp { - K (x, y +T, z, t, X)dT (1)

where Io is the initial beam intensity and K is the extinctioncoefficient. The reduction in the intensity of the beam willresult from both absorption and scattering losses. In acompletely general case both scattering into the field of viewof the detecting system and emission from within the field of

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A. J. MONTGOMERY

view have to be considered and, in fact, are of vital importancein the application of the crossed-beam technique to atmosphericmeasurements. However, the simple theory, only, will beconsidered here.

If the extinction coefficient, K, is divided into a meanand time varying part, equation (1) can be written

I1 (t) = I0 exp l- f<K (x, y+,z) > dr> exp 1-fk(x,y+nr,z,t)dn (2)

Since the second integral in this expression will be, or can bemade to be,.very much less than unity, a linear expansion can beused, and the result obtained for the fluctuating signal at thedetector is

il(t) = -<I>k (x, y + q, z, t) dRl (3)

The signal at the second detector will be of similar form andthe covariance of the two detector signals will be given by

G(x, y, z) - 1/T fT il(t) i2 (t) dt (4)O

where T is the period of integration which ideally is ofsufficient length to yield a statistically stationary valueof G(x,y,z). Thus substituting for i1 (t) and i2 (t) we cabwrite for the covariance of the signals that

G(x, y, z) = <I1><12> rlff 1/T fT k(x, y + r, z, t)

k(x, y, z + %, t) dtdrdq (5)

The term inside the time integral is clearly the covariance ofthe fluctuations in extinction coefficient at the points (x,y + 'r, z) and x, y, z + C). which will be significantly differentfrom zero only within the correlated area about the beamintersection point. If the assumption is made that the fluctua-tions in the k do not vary appreciably over this correlation areathen the covariance of the two detector signals can be written

G(x, y, z) = <I1><12> k2 (x, y, z, t) LyLz (6)

where L and Lz are the integral length scales in the y and zdirections, respectively. This measured quantity is thereforerelated directly to the local turbulent intensities and theintegral scales at the point of intersection of the beams.

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A point to note here is that the spatial resolution isdetermined in theory by the beam diameters and that spatialresolutions obtained in turbulent intensity measurements areconsiderably less than the integral scale of the turbulence.

Other turbulent properties may be obtained from measurementsof space-time correlations. In Figure 1 the second beam isdisplaced a distance 4 in the flow direction and the covarianceof the two detector signals can be measured for different beamseparation time delays T. Fisher and Krause have shown that,to a useful degree of approximation, the space time correlationcoefficient that would be measured by two point probes locatedat the points A & B can be measured with the crossed-beam system,

r(Q , T) = G (x + ,, y, z, T) /G(x, y, z).

By measuring this space-time correlation coefficient over rangeof , and T such properties of interest as integral length scales,turbulent spectra, convection velocities, moving axis time scalesand eddy lifetimes can be obtained.

This can most easily be understood with reference to someof the experimental results that have been obtained, as shown inFigure 2. Each of the individual curves is the correlation

_,C

N 1 '- Il 1'

-I

.6 .8

T (millisecs)

1.6

Figure 2. Crossed Beam Correlation in a Subsonic Jet

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A. J. MONTGOMERY

function obtained for one particular separation of the two beams.The convection velocity can be obtained from any of these curves,with the exception of the one in which ~ = 0, by dividing theknown value of ~ by the time delay corresponding to the peak ofthe correlation function. The maximum value of the correlationfunction decreases as the beam separation increases. Thisbehavior reflects the fact that as an eddy moves downstream itgradually loses its identity. The eddy-lifetime is defined asthe time in which the envelope decreases to l/e of its initialvalue. The space correlation coefficient r(~,o), which can begenerated by noting the points at which the individual cross-correlation curves interest the = 0 axis, may be integratedover all 4 to obtain the integral scale of the turbulence, andthe cross-power spectrum may be obtained by the Fourier transformof the cross-correlation function.

It was noted in the above discussion that the choice ofoptical wavelength has to be such that there is absorption orscattering along the beam so that turbulence effects thereforeresult in fluctuations in the detected signal. In supersonicflows, where there are significant variations in air density,some measurements were made at a wavelength of 1850A where oxygenabsorbs. In subsonic flows, and in some experiments in supersonicflows, a tracer was introduced in the flow, and the fluctuationsin visible light produced by variations in the number of tracerparticles along the beam were detected.

In the subsonic case very good agreement was obtained withhot wire measurements, and this comparison also demonstrated thehigh spatial resolution that may be obtained using the crossed-beam technique. No comparison of the supersonic results withpreviously measured values is possible, since these measurementsrepresent an advance in state of the art.

3. ATMOSPHERIC MEASUREMENTS

In the atmosphere the use of artificial light sources wouldbe most undesirable since this would severely limit the appli-cation of the technique. Natural, distributed sources fall intothree categories

a) Scattered Sunlightb) Thermal Emissionc) Non-Thermal Emission (for example, airglow).

Figure 3 shows the atmospheric radiation background for twoaltitudes. During daylight hours scattered sunlight predominatesfor wavelengths shorter than approximately 3 microns. At nightscattered starlight, scattered moonlight and airglow are themain sources of radiation in the visible and near infraredportion of the spectrum.

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2 CONDITIONS: ZENITH ANGLE * 45m - EXCELLENT VISABILITY

c 10 - REGION REGION OF 30dK SCATTER- THERMAL F BODY ENVE-

SEA16 ED SOLAR EMISSION LOPELEVEL RADIATION

/'- . ~a213 KBLACK

UO~ X A t N~~~ BODY 4 / LOPE

10 KM

4 6 8 1 2 4 6 810 20 40 60

WAVELENGTH, p. (micron)

zI.o

Q I AAA TMOSPHERIC-- 8 -- 2T RATRANSMISSION,

3[ .SEA LEVEL

4 6 8 1 2 4 6 8 10 20 40 60

WAVELENGTH, /. (micron)

Figure 3. Emission Spectrum of Atmospheric RadiationBackground for Two Altitudes.

To apply the crossed-beam technique to atmospheric measure-ments, the correlated portion of the detected fluctuationssignals must be of such a magnitude that it can be pulled outof the noise in a reasonable integration time. The noise signalwill consist of uncorrelated fluctuations from parts of the beamaway from the intersection point, detector noise and shot noiseassociated with the mean level of radiation incident upon thedetector. Ideally the design of the optical system would ensurethat the predominant source of noise is due to atmosphericfluctuations, but if narrow spectral bandwidths have to be usedin the infrared portion of the spectrum this may not be possible.

Even if the uncorrelated atmospheric fluctuations are thepredominant noise source, it may not be possible to isolate thecorrelated portion of the signal in a reasonable integration time.The nonstationary nature of atmospheric phenomena limits theintegration time, so that, if there are too many eddies alongthe field-of-view of the detector which significantly contributeto the atmospheric fluctuation level, it may not be possible'pull out' the correlated signals by the cross-correlation,within times for which stationary conditions can be consideredto obtain. For this reason, it is necessary to be selective inthe type of measurement that is made so that the number of eddies

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A. J. MONTGOMERY

along the detector field-of-view which significantly contributeto the measured fluctuation level is limited.

In fact it would be difficult to choose a measurementwavelength for which there are equal contributions to the detectedsignal from different altitudes but the contribution fromdifferent altitudes is difficult to determine without a morecomprehensive knowledge of turbulence scales, and temporalvariations in density, aerosol concentration and temperature.

It was shown previously that the covariance of the signalsfrom two detectors with crossed fields-of-view is given by

G(x, y, z) = <I 1 ><I2 >>7(x, y, z, t) LyLz

This expression contains the square of the extinction-coefficientfluctuations and the product of two scale lengths. The magnitudeof the extinction coefficient fluctuations will usually begreater near the ground because the air density and the aerosolconcentration are greater, and because of the turbulence generatedby flow over uneven terrain. On the other hand, the turbulencescales are less so that there will be a compensating effect, andthe altitude region which contributes most significantly to thefluctuating signal is not clear-cut. There are obviously somesevere problems in reliably computing contributions to thefluctuations from different altitudes, and this point will beclarified in the discussions of particular cases which follow.

3.1 Scattered Sunlight Measurements

A photometer on the ground pointing upwards willreceive radiation which is scattered into its field-of-view byboth air molecules and aerosol particles. The mean signal levelrecorded will depend on the elevation and azimuth of the field-of-view of the photometer relative to the angle of the sun andupon the meteorological conditions. Because of the presence oftemperature and corresponding density variations in the airwhich will be convected through the photometer field-of-viewby winds, there will be fluctuations superimposed upon the meanphotometer output signal. The magnitude of these fluctuationswill depend on the scales of these eddies and the absolute magni-tude of the air density and/or aerosol density variations. Fora constant eddy scale and percentage variation in scattererconcentration, the decrease in air density with height willreduce the molecular scatter contribution to the fluctuationlevel at the detector by a factor of 10 for eddies at analtitude of 8 kilometers as compared to fluctuations at groundlevel. The aerosol fluctuation contribution under similarconditions will fall off much more rapidly because of the muchquicker relative decrease in aerosol concentration with altitude.

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Using the turbid atmosphere model of Elterman (1964) the detectedsignal will be down a factor of 10 at an altitude of 1 kilometer.

However, since the eddy scales increase with altitude,the ability to detect fluctuations at an altitude of 1 kilometerby the cross-correlation of the photometer signals with theexperimental arrangement shown in Figure 4 may not be moredifficult than if the measurements are made with the beamscrossed at an altitude of 50 meters to detect fluctuations atthis level. In fact since scattering at low altitudes isdominated by atmospheric aerosols, and the aerosol concentrationdecreases very quickly with altitude as shown by the aerosolscattering coefficient in Figure 5, we expect the low altitudefluctuations to predominate and, for this reason, the experimentspresently being carried out are aimed towards the measurements ofwinds and turbulence at altitudes up to about 1000 meters bydetection of scattered sunlight.

In this discussion I have somewhat glossed over theorigin of the fluctuations in scattered sunlight except to saythat they are due to fluctuations in concentrations of aerosolsand air molecules. Direct sunlight will be scattered by moleculesand aerosols in the field-of-view of the detector so if there isa density increase or increase in concentration of aerosols in avolume element of the field-of-view, there will be an incrementalincrease in the direct scattered signal. However, light scatteredinto the field-of-view at higher altitudes may be scattered outof the beam and an increase in density or aerosol concentrationin a volume element would therefore cause a decrease in detectorsignal. In addition there will be a contribution from multiplescattering into the 'beam'. The relative values of thesedifferent contributions will depend strongly on the atmosphericconditions and the angle of the sun with respect to the directionof view of the photometers.

If the direct scattered sunlight predominates it wouldbe possible to obtain a positive correlation even in the completeabsence of fluctuations in scatterer concentration in the regionof the beam intersection point. The sunlight reaching thisregion has traversed a long path through the atmosphere andtherefore there will be intensity fluctuations. Similarfluctuations will be present in the scattered sunlight whichcould result in a significant correlation between the twodetected signals. However, when there is a lateral separationbetween the two beams as is necessary in wind measurement,this effect is minimized.

Midwest Research Institute (St. John, A. D. andGlauz, W. D. 1968) have performed some calculations to determinethe relative contributions to the fluctuations in the detectedsignal. However, multiple scattering was not included, andfurther work is definitely necessary in this area.

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A. J. MONTGOMERY

SEPARATION OF BEAMS OUT OFPLANE OF PAPER PERMITS NORMALWIND COMPONENT TO BEDETERMINED

DIRECT SUNLIGHT

ATMOSPHERICRADSCATION INHOMOGENITIESSCATTERED INTOFIELD OF VIEWOF DETECTORBY AEROSOLSAND AIRMOLECULES

PHOTOMETER (> PHOTOMETER # 2

Figure 4. Application of Crossed Beam Technique to Measurementof Atmospheric Winds and Turbulence

E

0-t3

10- 4 10- I 100

AEROSOL (Mie) SCATTERING COEFFICIENT (km -

)

Figure 5. Aerosol (Mie) Scattering Coefficient vs. Altitude forVisible Wavelengths

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3.2 Thermal Emission

Although successful measurements have been madedetecting scattered sunlight in the visible portion of thespectrum, this particular method is restricted to substantiallycloudless sky conditions. If an isolated cloud enters thefield-of-view of the detecting system there is an increase by afactor of the order of 5 in the detected signal. With a responseextending down to 0.01 cycles per second the recorded ac signalwill also increase to a level which will be dependent upon therate of movement of the cloud. When the cloud fills the field-of-view a main source of signal fluctuations will be thenonuniformities in the cloud itself.

If this signal were recorded the power associated withthe fluctuations due to clouds would generally dominate thesignals, and spurious cross-correlations would be measured.However, if clouds are in the field-of-view for only a smallfraction of the recording time then this effect can be eliminatedby setting the signal at zero whenever a cloud is in the field-of-view of either photometer system.

Potentially these problems can be largely overcome ifwater vapor is used as a tracer and measurements are made inthe vicinity of the water vapor absorption band at 6.3 microns.The exact choice of wavelength will determine the relativesignal received from volume elements at different distancesfrom the detecting system. ESSA is presently studying thisproblem.

Measurements of wind profiles at higher altitudescould be made by detecting the thermal emission of ozone at9.6 microns. Some preliminary calculations (Krause et al.,1966) indicate that fluctuations of the order of 0.01% could bedetected with 8 inch collector optics and state-of-the-artdetectors. We are presently studying these approaches and planfield tests to determine their potential and to further increasethe usefulness of the crossed-beam technique as applied toatmospheric measurements.

4. MEASUREMENTS OF SCATTERED SUNLIGHT FLUCTUATIONS

The photometer systems used in the atmosphere measurementsof scattered sunlight have the following specifications:

Frequency Response Variable within range 0.01-300 HzMean Signal/RMS Noise 10OField-of-View 5-30 minutes of arcSpectral Response 0.4-1 micronSpectral Bandpass Variable (minimum 500A)

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A. J. MONTGOMERY

Details of the design of the photometer system are given in the appendix. A photograph of one of the photometers is shown in Figure 6 and the instrumentation van in Figure 7.

Figure 6. Photometer Trailers (by Courtesy of MSFC)

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cd w

C *w

o o •H •U >~, CO W

4-1 0) C 4-> QJ U

6 D 5 o 4-1 w > , C PQ

0)

3 bO

•H Pn

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A. J. MONTGOMERY

Power spectral density measurements of the fluctuationsunder clear sky conditions are shown in Figures 8, and in Figure9 these results are replotted with the ordinate - power spectraldensity x frequency. In this second plot the area underneaththe curve in a particular frequency interval, Af, is directlyproportional to the energy in this frequency interval. Theseresults were obtained by playing back the recorded signalsthrough a variable bandpass filter and measuring the outputlevel with a RMS voltmeter. It can be seen that the fluctuationsfollow quite closely a -6.5 power law down to frequencies lessthan 0.1 cycles per second. The roll off beyond 0.01 cyclesper second is due in part to the high pass filter which reducesthe amplitude of the signal 3db at 0.01 cycles per second andwinds down at the rate of 6db per octave.

10-16

10-17

10-18 -

U

c"

a)

E0

10- 19

10- 20

10-21

10-22

10-2310.001 0.01 0.1 I 10 100

f, cps

.-Figure 8. Single Beam Power Spectrum 1 vs. f

Af

539

o POWER SPECTRUMA NOISE CALIBRATION

SLOPE- 5/3


E

.0

40

20

0 a I a

0.001 0.01 0.1 I 10f,cps

Figure 9. Single-Beam Power Spectrum, f 1 vs. foaf

A line of slope -5/3 is also shown in Figure 8 and it isevident that the results differ significantly from the -5/3dependence that would be expected in point measurements. Thisis not an unexpected result because of the integration alongthe line of sight. The contribution of an eddy, being convectedthrough the field-of-view of the photometer system, to the fluc-tuating signal will be proportional to both the variation inthe number of scatterers associated with the eddy, and the sizeof the eddy measured along the field-of-view of the detectingsystem. Because the contributions from different eddies areuncorrelated then the resulting rms fluctuation from n eddiesalong the line of sight will only be n times the contributionof a single eddy. This intuitive argument would indicate thata -8/3 power law might be expected. At this time

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A. J. MONTGOMERY

there is no proven explanation of the -6.5/3 power law that isactually measured, however, if the turbulent eddies were elongatedin the flow direction, such a reduction in the power dependancecould be observed. The effect of the increase in eddy scalesand the decrease in the magnitude of the fluctuations withaltitude would also be expected to change the power spectrum,but no attempt has yet been made to study the way in which thesevariables would effect it.

5. CROSSED-BEAM MEASUREMENTS OF WINDS

Since atmospheric crossed-beam measurements detectingscattered sunlight are continuing at the present time this paperis a status report of the results obtained to date. Successfulwind measurements have been made, and this success has gone handin hand with the development of suitable statistical methods toreduce the effects of non-stationarity in the data.

The geometry of the crossed-beam arrangement used in theatmospheric tests is shown in Figure 10. The location and

ANEMOMETER(

T61 m

AWIND

DIRECTION

"R #2

PHOTOMETER # I

Figure 10. Geometry at Atmospheric Crossed Beam Arrangement.

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1


viewing direction of the photometers are usually made to liein two parallel vertical planes which are chosen to beapproximately perpendicular to the wind direction. Most of themeasurements to date have been made with the two beams crossedat an altitude corresponding to the top of the meteorologicaltower. Thus a direct comparison between the wind measured withan anemometer on top of the tower and that obtained from thecrossed-beam measurements is possible. It should be noted thatthe altitude at which the wind is in fact measured depends onthe wind direction. If the wind direction is perpendicular tothe parallel vertical planes containing the lines of sight ofthe detector systems, then the altitude of measurement will bethe height at which the beams would intersect if the two verticalplanes were coincident. For all other wind directions an eddycan only traverse both 'beams' at a different altitude determinedby the angle between the beams and the wind direction. Since ina practical case both the wind speed and the wind direction willbe varying, the result obtained with the crossed-beam systemrepresents a complex type of averaging over both altitude andtime. If the wind direction is fairly constant within + 200 ofthe plane of the beams then the altitude region over whTch theaveraging will take place will be small, and the crossed-beammeasurement can be considered to yield an average wind velocityat the crossing altitude.

Before describing some of the experimental results that havebeen obtained some comments about the fluctuation records, andthe data processing are in order. Under clear skies the signalfluctuations with a bandpass from 0.01 - 10 Hz are typically ofthe order of 1% of the mean signal level. Although this factis not completely established, the fluctuation levels appear tobe less after a rain when the ground is still damp. This is notat all unlikely since the aerosol concentrations near the groundwould be lower under these circumstances. In a 45 minute recordit is usually found that there are portions of the record inwhich the fluctuation level is considerably higher than theaverage. Sometimes there is an obvious cause for this, such asa car going by on a nearby dirt road raising a considerable dustcloud which drifts through the detector field-of-view. At othertimes there is no apparent reason for the increased activity.In any case, if a straight averaging procedure were used in thedata processing, the portions of the record in which the fluctua-tions are large tend to dominate the correlation results.

To avoid this problem the data are processed in the computerin 6 minute segments, and the time averaged cross product isnormalized with respect to the rms levels in that segment of therecord before the pieces are averaged through the entire record.In other words, the correlation function is found for each segmentand this procedure successfully prevents any particular piecefrom dominating the entire record.

Despite these precautions, spurious correlations are stillsometimes obtained which make identification of the peak in the

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A. J. MONTGOMERY

correlation function corresponding to the wind speed ambiguous.The so-called statistical error is utilized to help solve thisproblem. In simple terms a correlation function is found foreach six minute piece of data throughout the record. Thesecorrelation functions are averaged and the rms variation in thevalue of the correlation function is found for each time delay.It is this rms variation, suitably weighted to obtain the desiredstatistical certainty in the result, which is called thestatistical error.

Ideally, if a stationary situation existed, the statisticalerror would decrease as the square root of the number of piecesincluded; however, it is found in the atmospheric data that theerror begins to decrease, but after some time period (usuallybetween 30 minutes and one hour) the error either oscillates orstarts to increase again. The integration time is thereforechosen as the time in which the statistical error reaches itsminimum value.

Figure (11-14) shows some of the results obtained which havebeen previously presented by Stephens, Sandborn and Montgomery.Figure 11 is the result for a zero separation case with the fields-of-

.I

.1

< .0oWm 1.0

T Dcn

I so0 |l .0

.0 4

0 DURATION OF ,

8 OBSERVATION= 112.5 min //

6 -TOWER HEIGHT = 122 m /--STATISTICAL

1 / ERROR

)2

2

4 S..

-.06 -

DATA TAKEN UNDERCLEAR SKIES ATM.SF.C. AUG. 1967

I I

cuCROSS-BEAMCORRELATIONCURVE

-30 -20 -10 0 10

TIME DELAY (sec)

DETECTOR I

~ J TOWER

OmRAEc1

DETECTOR 2

TESTARRANGEMENT

20 30

Figure 11. Cross Correlation Function - Zero Beam Separation

543

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ft .

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view of the two detectors intersecting at an altitude corres-ponding to the top of the meteorological tower at MSFC. No windinformation is of course available from this measurement. Thecorrelation coefficient is quite small- 0.05 and the peak onlyslightly exceeds the statistical error. However, the peak doesoccur accurately at t = 0 as would be expected in this measure-ment. The statistical error is associated, of course, with thevalue of the correlation function; hence with a 90% probabilitythe correlation function at zero time delay is 0.05 + 0.03.This statistical probability results from the choice of weighingfactor applied to the rms variations in the correlation function.Plotting the results in this manner is used for ease of present-ation.

The remaining wind measurements were made at the ColoradoState University meteorological test site in the North PlatteRiver Valley, located in northeastern Colorado, approximatelyfifteen miles east of the first major pressure rise of theRocky Mountains.

Figure 12 shows the anemometer data plotted as a first orderprobability density of velocity, and the correlation functionplotted in terms of a wind velocity. Since the beam separationwas 30 meters the long tail of the cross-correlation curve

TESTARRANGEMENT

DETECTOR I TOWER

30m

,16_____________ _ {j 8 DIRECTION IDETECTOR 26 80 RANGEi-- BEAM SEPARATION 3 30 m

E _\ DURATION OF OBSERVATION = I hr II minL<Z O Z TOWER HEIGHT =61 m

a] .12 - X U60 | DATA TAKEN UNDER CLEAR SKIESn P<); AT CSU SEPT 67

U)

r CROSS BEAM CORRELATION CURVE.08 - '_ 40 , J

0 i

m !_J S__STTATISTICAL ERROR

.. <..04 r X 2 -i -- FIRST ORDER PROBABILITYWZ DENSITY OF VELOCITY ASna. MEASURED BY ANEMOMETER

Li 0 I l I I I , i , , iO 1 2 3 4 5 6 7 8 9 10 1I 12

mWIND VELOCITY( -'c)

0 15.0 7.5 5.0 3.8 3.0 2.5

TIME DELAY (sec)

Figure 12. Light Wind Case , 3 mph.

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A. J. MONTGOMERY

represents delay times from 2.5 to 5 seconds as compared withthe 5-30 second time delay range covered by peak. Thus thistail results from the method of presentation and is notsignificant. There is quite good agreement between theanemometer and the crossed-beam results although the winds werelight and variable.

Higher wind cases are shown in Figure 13 and 14 in which,once again, good agreement is shown between the anemometer andthe crossed-beam results. In Figure 13 the statistical erroris relatively small and the correlation coefficient at the peakis large. Under these windy conditions a greater concentrationof aerosols might be expected to be present close to the ground,and this could weight the results by increasing the contributionto the fluctuating signal from low altitudes. This would havethe effect of decreasing the number of eddies along the field-of-view of the photometers which contribute significantly tothe fluctuation level, and therefore increase the correlationcoefficient.

BEAM SEPARATION --96 mDURATION OF OBSERVATION = I HR

.30 - 30 TOWER HEIGHT - 61 m

a: 1211 r An DATA TAKEN UNDER CLEARSKIES AT C.S.U. JAN 68 TEST

,[a W ARRANGEMENT

m Z 0O DETECTOR I/ .20 W)Z CROSS-BEAM N DR N

LO .20 20 _CORRELATION CURVE 9 E

0 C-c2

0 i) -FIRST ORDERm m PROBABILITY DENSITY

z W OF VELOCITY ASI._-4 N .10 i l o MEASURED BY ANEMOMETER

., STATISTICAL ERROR

0 4 8 12 16 20 24 28 32 36 40

WIND VELOCITY ( se)

I I I I I I IL -1 -J L L ' I I 24.4 12.0 8.0 6.0 4.8 4 3.4 3.0 2.7 2.4

TIME DELAY (sec)

Figure 13. Medium Wind Case ' 20 mph.

545


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w. 1-- -Y.-' -STATISTICAL ERROR1-4

-.08 w) t/ A' CROSS -BEAM CORRELATION CURVE

'L L 3 BEAM SEPARATION= 117.5m.06 : \Z j DURATION OF OBSERVATION

L) < os~. : 45 minU, Uo0o - ! i >, TOWER HEIGHT = 61m

.04 Ir 2 DATA TAKEN UNDER CLEARo 5 04 FIRST ORDER SKIES AT CSU DEC 67o PROBABILITY

jZw .02 DENSITY OFL .02 uJ> I VELOCITY AS0 MEASURED BYwzLi ANEMOMETER

O 0

-I I I

V 2 3 4 5 6 7 8 9 10WIND VELOCITY (s-)

I I . .58.8 29.6 19.6 14.7 11.8

TIME DELAY(sec)

Figure 14. Low Wind - Large Beam Separation Case.

The results described above are summarized in the followingtable. There is encouragingly good agreement between t'he crossed-beam and the anemometer results. The field tests are continuingand it is hoped that results presently being analyzed willshow the same promise of the results described in this paper.

6. FUTURE DEVELOPMENT OF THE CROSSED-BEAM TECHNIQUE

The immediate future developments of the crossed-beamtechnique have to be directed towards exploring the potentialand the limitations of the method. For example, in order toremove some of the ambiguities which sometimes arise indetermining the peak in the correlation function which correspondsto the wind speed, a multiple beam system is being developed.This will permit results for several beam separations to beobtained simultaneously, and in addition, because the beam willperforce be in a fan configuration, the wind direction can alsobe found if the correlation maxima are sufficiently well defined.

546

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To avoid the limitations imposed on the present systemunder the cloudy skies the potential of infrared measurementshas to be explored. The physics of the problem in terms of try-ing to define the altitude contributions to the fluctuatingsignals in both the scattered sunlight and infrared cases hasto be studied. This would permit estimates to be made of thealtitude resolution and maximum altitudes for which useful winddata may be obtained.

Some new approaches in terms of the data reduction methodshave to be developed. The use of the derivatives of the signalsto effectively flatten the frequency spectra and narrow thecorrelation peak is presently being tried. Further examinationof the statistical error, and the relative errors betweencorrelations for different time delays obtained from the samedata record have to be examined.

7. CONCLUSIONS

The potential future development of the crossed-beamtechnique once the feasibility of its application to atmosphericmeasurements has been demonstrated is very great. There are alarge number of different types of measurements, some of whichhave been discussed above, that can usefully be made which willcontribute to the understanding of atmospheric phenomena, andto improvement in weather forcasting.

Successful ground tests should be followed by measurementsfrom aircraft. Clear air turbulence is of great importance asfar as its effect on aircraft operations is concerned, and muchcould be learned of this phenomena by crossed-beam measurementsfrom an aircraft. Of course in the aircraft case, instead ofthe fluctuations being produced by turbulence eddies beingconvected through stationary beams, the fluctuations will belargely produced by the movement of the "beams" or photometerfield's of view through regions of atmospheric turbulence. Thefluctuation frequencies will be considerably different. Alsoin the aircraft case, time delay tricks as illustrated in Figure15 may remove the necessity of having two photometers separatedin space.

The two photometers are mounted on a stabilized platformand have an angle e between their respective fields of view.If the turbulence structure is assumed to be frozen, then thefluctuations detected by photometer #1 originating from a heighth above the aircraft will be repeated in signal from photometer#2 a time T later, where T is the distance d divided by the veloc-ity of the aircraft. The altitude region of interest can there-fore be studied by selecting the appropriate time interval T.To obtain wind speeds it is necessary to separate the photometerfields of view in a direction perpendicular to the plane of the

548

A. J. MONTGOMERY

.BEAM NO. I

t=0 t=TPOSITION # I POSITION # 2

4 WIND VEL. COMR U

:co -CIRCLES INDICATE "BEAM" (FIELD OF VIEW)CROSS- SECTIONS AT ALTITUDE h

Figure 15. Scanning System Concept - For Particular WindSpeed u and Beam Separation ~ We have Time Tfor Line of Eddies Originally in Beam #1 toReach Beam #2. At Height, h, Beam Delay is T,so a Maximum Correlation is Recorded For ThisTime Delay. With a Fan of Beam Giving Numberof Different 0's the Wind Component as aFunction of Altitude May Be Measured.

paper. An ambiguity is introduced here which can only be resolvedby use of a fan of "beams" from one of the photometer systems.This problem has been discussed by Krause et al. (1966) and byKrause (1967) and will not therefore be considered further here.

The logical development of the technique through an aircraftoperation phase together with the study of spectral regions inwhich signals are detected and which could be utilized by down-ward looking systems, would then enable the potential of satelliteexperiments to be accurately assessed.

549

V g


ACKNOWLEDGEMENTS

In preparing this review paper I have drawn heavily on thework of my colleagues at IIT Research Institute, and friends andassociates at Marshall Space Flight Center and Colorado StateUniversity.

The overall effort has been funded by NASA, George C. Mar-shall Space Flight Center. Dr. Fritz Krause is the NASA projectmonitor and he has made many significant technical contributionsto this work.

The atmospheric crossed-beam instrumentation has been fabri-cated by IIT Research Institute while the recording and ancillaryinstrumentation has been supplied by MSFC. Check out and thefirst crossed-beam measurements were made by IIT Research Insti-tute at Marshall Space Flight Center, and Colorado State Universityhas been responsible for the field test program carried out inColorado. All the digital data reduction has been done on MSFCcomputers.

It is not possible to acknowledge all the people who havemade significant contributions to this program, however, particu-lar mention should be made of M. J. Fisher and E. H. Klugman atIIT Research Institute, F. R. Krause and J. Heaman, R. R. Jayroeand J. B. Stephens at MSFC.and V. Sandborn at Colorado StateUniversity.

REFERENCES

Elterman, L., (1964), "Atmospheric Attenuation Model, 1964,in the Ultraviolet, the Visible and the Infrated Windowsfor Altitudes to 50 km," Environmental Research PaperNo. 46, AFCRL.

Fisher, M. J., (1964), "Measurement of Local Density Fluctua-tions in a Turbulent Shear Layer," IITRI Project Sug-gestion No. 64-107NX.

Fisher, M. J. and Krause, F. R., (1967), "The Crossed-BeamCorrelation Technique," J. Fluid Mech. 28, 705-717.

Krause, F. R., Hu, S. S. and Montgomery, A. J., (1966),"On Cross-Beam Monitoring of Atmospheric Winds andTurbulence with Two Orbiting Telescopes," NASATMX-53538.

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A. J. MONTGOMERY

Krause, F. R., (1967), "A Passive Optical Technique forRemote Sensing of Horizontal Wind Profiles andAtmospheric Turbulence," Presented at Forty-eighthAnnual Meeting of the-American Geophysical Union.

St. John, A. D. and Glauz, W. D., (1968), "Study ofAtmospheric and AAP Objectives of Cross-BeamExperiments," NASA Contractor Report NASACR-61191.

Stephens, J. B., Sandborn, V., Montgomery, A. J. "RemoteWind Detection With the Cross Beam Method at TowerHeights", Presented at the Third National Conferenceon Aerospace Meteorology May 6-9 (1968). NewOrleans, La.

APPENDIX

DESIGN OF PHOTOMETERS FOR SCATTERED SUNLIGHT MEASUREMENTS

Optical Design -- The optical design of photometer system wasbased on the following specifications:

Frequency ResponseMean Signal/RMS NoiseField of ViewSpectral ResponseSpectral Bandpass

0.001-300 cps1045 - 30 minutes of arc0.4 - 1 micronVariable (minimum 500A)

The system is shown schematically in Figure Al. The objective

CHOPPER

OBJECTIVE

a F-

UI I v

-u I-vG

Figure Al. Optical System Schematic

551


(collector) lens has an aperture 17.5 cm and a focal lengthof 47.4 cm. The field stop which defines the field of viewof the photometer is located in the focal plane of the collectorlens, and is preceded by the chopper. To avoid any possibleproblems of nonuniform fields combined with variations insensitivity over the detector area, a field lens is includedwhich images the exit pupil of the objective on to the detector.

The chopper which has square blades is rotated by its motorapproximately 3600 rpm and with 20 blades produces a signalfrequency of 1200 cps. Use of such a chopper prevents the 1/fnoise of the silicon diode detector or of the preamplifier beingthe dominant noise source at low frequencies. It also preventsslow drifts, due for example to temperature changes, from beingmisinterpreted as a low frequency signal component.

Because the intensity of the radiation reaching the detectoris relatively high, advantage could be taken of the much greaterquantum efficiency available with a silicon diode as compared toa vacuum phototube or photodiode. The detector used is anEG&G SGD-444 silicon photodiode the quantum efficiency of whichis compared to common photoemissive surfaces in Figure A2.

100

80

SGD- 444

60

LC

40

20

I ,·II L LJI

oI ...0...._ .1..._2 _·2 0.4 0, 0.8 1.0 1.2

X, V

Figure A2. Comparison of Quantum Efficiencies of SeveralPhotodetectors

552

A. J. MONTGOMERY

Electronic Signal.Processing--The signal processing electronicsare shown in Figure A3. The signal from the detector is pre-amplified before being demodulated and the AC part of thedemodulated signal is filtered and amplified. With the low-passand high-pass filters in their zero position the passband isfrom 0.01 - 300 cps. Both the a.c. and the d.c. signals arerecorded on magnetic tape using an Ampex CP100 tape recorder.

CHOPPER

-100 - TO APE

IOO0 4-TO TAPE

Figure A3. Block Diagram of Signal Processing Chain.

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remote sensing of winds and atmospheric ......remote sensing of winds and atmospheric turbulence...

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