Measurement Measurement of Atmospheric Turbulenceof Atmospheric Turbulence

by Means of Light, Sound, and Radio Wavesby Means of Light, Sound, and Radio Waves

Andreas MuschinskiAndreas Muschinski

Dept. of Electrical and Computer EngineeringDept. of Electrical and Computer Engineering

University of Massachusetts AmherstUniversity of Massachusetts Amherst

Observing the Turbulent Atmosphere:Observing the Turbulent Atmosphere:

Sampling Strategies, Technologies, and ApplicationsSampling Strategies, Technologies, and Applications

NCAR, Boulder, CO, 28-31 May 2008NCAR, Boulder, CO, 28-31 May 2008

OverviewOverview

IntroductionIntroduction

Wave propagation through turbulence: the basicsWave propagation through turbulence: the basics

Anisotropy in optical surface-layer turbulenceAnisotropy in optical surface-layer turbulence

Vertical-velocity biases observed with radars and sodarsVertical-velocity biases observed with radars and sodars

OutlookOutlook

OverviewOverview

IntroductionIntroduction

Wave propagation through turbulence: the basicsWave propagation through turbulence: the basics

Anisotropy in optical surface-layer turbulenceAnisotropy in optical surface-layer turbulence

Vertical-velocity biases observed with radars and sodarsVertical-velocity biases observed with radars and sodars

OutlookOutlook

Light, sound, and radio waves Light, sound, and radio waves in the optically clear atmospherein the optically clear atmosphere

Do not propagate along straight linesDo not propagate along straight lines

Change their amplitudes, phases, and angles-of-arrival Change their amplitudes, phases, and angles-of-arrival deterministically and randomly in space and timedeterministically and randomly in space and time

Carry information about mean values and fluctuations of wind, Carry information about mean values and fluctuations of wind, temperature, density, pressure, humidity, and refractive index.temperature, density, pressure, humidity, and refractive index.

Differential downward ray-bendingDifferential downward ray-bending

can make the sun look squeezed …can make the sun look squeezed …

Here comes the sun …Here comes the sun …

Number of dipoles: Number of dipoles: 18,43218,432

Peak power:Peak power:1.5 MW1.5 MW

Beam width:Beam width:0.8 deg0.8 deg

… … or otherwise deformed.or otherwise deformed.

From Pernter and Exner, From Pernter and Exner, Meteorologische OptikMeteorologische Optik (1910, p. 194) (1910, p. 194)

Upward ray-bending can make Upward ray-bending can make

you see water puddles on a dry road …you see water puddles on a dry road …

Road mirageRoad mirage

Near Bonneville Speedway, UT, August 2005Near Bonneville Speedway, UT, August 2005

From Pernter and Exner, From Pernter and Exner, Meteorologische OptikMeteorologische Optik (1910, p. 127) (1910, p. 127)

From Pernter and Exner, From Pernter and Exner, Meteorologische OptikMeteorologische Optik (1910, p. 128) (1910, p. 128)

Random ray-bending can create Random ray-bending can create

changing patterns at the bottom ofchanging patterns at the bottom of

a swimming pool …a swimming pool …

OverviewOverview

IntroductionIntroduction

Wave propagation through turbulence: the basicsWave propagation through turbulence: the basics

Anisotropy in optical surface-layer turbulenceAnisotropy in optical surface-layer turbulence

Vertical-velocity biases observed with radars and sodarsVertical-velocity biases observed with radars and sodars

OutlookOutlook

Valeryan TatarskiiValeryan Tatarskii

Tatarskii, V. I., 1961:Tatarskii, V. I., 1961:

Wave Propagation in a Turbulent Medium.Wave Propagation in a Turbulent Medium.

McGraw-Hill, New York, 285 pp. McGraw-Hill, New York, 285 pp.

Tatarskii, V. I., 1971: Tatarskii, V. I., 1971:

The Effects of the Turbulent Atmosphere on Wave Propagation.The Effects of the Turbulent Atmosphere on Wave Propagation.

Israel Program for Scientific Translation, Jerusalem, 472 pp.Israel Program for Scientific Translation, Jerusalem, 472 pp.

Rytov, S. M., Y. A. Kravtsov, and V. I. Tatarskii, 1986-89:Rytov, S. M., Y. A. Kravtsov, and V. I. Tatarskii, 1986-89:

Principles of Statistical Radiophysics, Vols. 1-4.Principles of Statistical Radiophysics, Vols. 1-4.

Springer, Berlin.Springer, Berlin.

The inhomogeneous Helmholtz equationThe inhomogeneous Helmholtz equation

Maxwell equationsMaxwell equations

Time-harmonic fieldsTime-harmonic fields

Simplified constitutive parameters (Simplified constitutive parameters (μμ==μμ00, , σσ=0, =0, εε varies with location) varies with location)

Wave equationWave equation

(Inhomogeneous) Helmholtz equation(Inhomogeneous) Helmholtz equation

Methods to solve the inhomogeneous Helmholtz equationMethods to solve the inhomogeneous Helmholtz equation

Eikonal equationEikonal equation

Born approximationBorn approximation

Rytov approximationRytov approximation

Parabolic equationParabolic equation

Eikonal equation and transport equationEikonal equation and transport equation

Eikonal equation and transport equationEikonal equation and transport equation

(cont.’d)(cont.’d)

Refraction and diffractionRefraction and diffraction

Eikonal equationEikonal equation

(geometrical optics, “ray tracing”)(geometrical optics, “ray tracing”)

Describes refraction but not diffractionDescribes refraction but not diffraction

Approximates variances and frequency Approximates variances and frequency spectra of optical angle-of-arrival spectra of optical angle-of-arrival (AOA) fluctuations very well if aperture (AOA) fluctuations very well if aperture diameter is larger than twice the diameter is larger than twice the Fresnel lengthFresnel length

Born approximationBorn approximation

Describes both refraction and diffractionDescribes both refraction and diffraction

Very good approximation for radio-wave Very good approximation for radio-wave backscatter from clear-air refractive-backscatter from clear-air refractive-index perturbationsindex perturbations

Fraunhofer approximation valid if Fraunhofer approximation valid if turbulence is Bragg-isotropicturbulence is Bragg-isotropic

Fresnel approximation (or higher-order Fresnel approximation (or higher-order approximation) necessary if turbulence approximation) necessary if turbulence not Bragg-isotropic of in case of not Bragg-isotropic of in case of scatter from interfacesscatter from interfaces

Turbulence in the inertial range (in a nutshell)Turbulence in the inertial range (in a nutshell)

Optical angle-of-arrival fluctuations Optical angle-of-arrival fluctuations

(from theory of eikonal fluctuations)(from theory of eikonal fluctuations)

Horse Farm, Amherst, MA, 19 June, 2005Horse Farm, Amherst, MA, 19 June, 2005

““Seeing” the ground cooling after sunsetSeeing” the ground cooling after sunset

Boulder Atmospheric Observatory, September, 2006Boulder Atmospheric Observatory, September, 2006

Sequence of Sequence of

snapshotssnapshots

of single lightof single light

30 frames / s30 frames / s

Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007: Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007:

Angle-of-arrival anemometry […]. Angle-of-arrival anemometry […]. J. Opt. Soc. Am. AJ. Opt. Soc. Am. A, , 2424, 3478-3492., 3478-3492.

Random ray-bending (lateral and vertical)Random ray-bending (lateral and vertical)

Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007: Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007:

Angle-of-arrival anemometry […]. Angle-of-arrival anemometry […]. J. Opt. Soc. Am. AJ. Opt. Soc. Am. A, , 2424, 3478-3492., 3478-3492.

Frequency spectrum of AOA fluctuationsFrequency spectrum of AOA fluctuations

Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007: Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007:

Angle-of-arrival anemometry […]. Angle-of-arrival anemometry […]. J. Opt. Soc. Am. AJ. Opt. Soc. Am. A, , 2424, 3478-3492., 3478-3492.

Frequency spectrum of AOA fluctuationsFrequency spectrum of AOA fluctuations

(measured, lateral and vertical)(measured, lateral and vertical)

Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007: Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007:

Angle-of-arrival anemometry […]. Angle-of-arrival anemometry […]. J. Opt. Soc. Am. AJ. Opt. Soc. Am. A, , 2424, 3478-3492., 3478-3492.

““Seeing” the wind speed transverse to the line of sightSeeing” the wind speed transverse to the line of sight

Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007: Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007:

Angle-of-arrival anemometry […]. Angle-of-arrival anemometry […]. J. Opt. Soc. Am. AJ. Opt. Soc. Am. A, , 2424, 3478-3492., 3478-3492.

Random ray-bending (lateral and vertical)Random ray-bending (lateral and vertical)

Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007: Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007:

Angle-of-arrival anemometry […]. Angle-of-arrival anemometry […]. J. Opt. Soc. Am. AJ. Opt. Soc. Am. A, , 2424, 3478-3492., 3478-3492.

““Seeing” quasi-periodic changes Seeing” quasi-periodic changes

in the vertical temperature gradient (gravity waves)in the vertical temperature gradient (gravity waves)

Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007: Cheon, Y., V. Hohreiter, M. Behn, and A. Muschinski, 2007:

Angle-of-arrival anemometry […]. Angle-of-arrival anemometry […]. J. Opt. Soc. Am. AJ. Opt. Soc. Am. A, , 2424, 3478-3492., 3478-3492.

METCRAX: Looking for “atmospheric seiches” METCRAX: Looking for “atmospheric seiches”

in the Atmospheric Meteor Craterin the Atmospheric Meteor Crater

OverviewOverview

IntroductionIntroduction

Wave propagation through turbulence: the basicsWave propagation through turbulence: the basics

Anisotropy in optical surface-layer turbulenceAnisotropy in optical surface-layer turbulence

Vertical-velocity biases observed with radars and sodarsVertical-velocity biases observed with radars and sodars

OutlookOutlook

Nastrom, G. D., and T. E. VanZandt, 1994: Mean vertical motions seen by Nastrom, G. D., and T. E. VanZandt, 1994: Mean vertical motions seen by

radar wind profilers. radar wind profilers. J. Appl. Meteor.J. Appl. Meteor., , 3333, 984-995., 984-995.

Downward bias in vertical velocities Downward bias in vertical velocities

observed with VHF radars in the free troposphereobserved with VHF radars in the free troposphere

Coulter, R. L., and M. A. Kallistratova, 2004: Two decades of progress in Coulter, R. L., and M. A. Kallistratova, 2004: Two decades of progress in

SODAR techniques […]. SODAR techniques […]. Meteorol. Atmos. Phys.Meteorol. Atmos. Phys., , 8585, 3-19., 3-19.

Upward bias in vertical velocities Upward bias in vertical velocities

observed with a sodar in the lower CBLobserved with a sodar in the lower CBL

Geophysical causesGeophysical causes

of biases in vertical clear-air radar or sodar windsof biases in vertical clear-air radar or sodar winds

Nonzero covariance between local Cn2 and local w (due to gravity Nonzero covariance between local Cn2 and local w (due to gravity waves in the stable free troposphere, Nastrom and VanZandt 1994)waves in the stable free troposphere, Nastrom and VanZandt 1994)

Horizontal advection of asymmetrically corrugated interfaces Horizontal advection of asymmetrically corrugated interfaces (“KHI bias”, Muschinski 1996)(“KHI bias”, Muschinski 1996)

Nonzero covariance between local Cn2 and local w (“intermittency flux” Nonzero covariance between local Cn2 and local w (“intermittency flux” or “reflectivity flux” in the CBL, Muschinski et al., to be published)or “reflectivity flux” in the CBL, Muschinski et al., to be published)

Muschinski, A., 1996: Possible effect of Kelvin-Helmholtz instability on VHF Muschinski, A., 1996: Possible effect of Kelvin-Helmholtz instability on VHF radar observations of the mean vertical wind. radar observations of the mean vertical wind. J. Appl. MeteorJ. Appl. Meteor., ., 3535, 2210-, 2210-2217.2217.

“ “KHI bias”KHI bias”

Muschinski, A., 1996: Possible effect of Kelvin-Helmholtz instability on VHF Muschinski, A., 1996: Possible effect of Kelvin-Helmholtz instability on VHF radar observations of the mean vertical wind. radar observations of the mean vertical wind. J. Appl. MeteorJ. Appl. Meteor., ., 3535, 2210-, 2210-2217.2217.

“ “KHI bias”KHI bias”

Frehlich, R. G., Y. Meillier, M. L. Jensen, and B. Balsley, 2004: A statistical Frehlich, R. G., Y. Meillier, M. L. Jensen, and B. Balsley, 2004: A statistical description of small-scale turbulence in the low-level nocturnal jet. description of small-scale turbulence in the low-level nocturnal jet. J. Atmos. J. Atmos. SciSci., ., 6161, 1079-1085., 1079-1085.

Small-scale intermittency:Small-scale intermittency:

Lognormality of local epsilon and local CT2Lognormality of local epsilon and local CT2

Muschinski, A., Frehlich, and B. Balsley, 2004: Small-scale and large-scale Muschinski, A., Frehlich, and B. Balsley, 2004: Small-scale and large-scale intermittency in the nocturnal boundary layer and the residual layer. intermittency in the nocturnal boundary layer and the residual layer. J. Fluid J. Fluid Mech.Mech., , 515515, 319-351., 319-351.

Small-scale intermittency:Small-scale intermittency:

Joint lognormality of local epsilon and local CT2Joint lognormality of local epsilon and local CT2

Intermittency flux and sodar velocity biasIntermittency flux and sodar velocity bias

Muschinski, A., M. Behn, V. Hohreiter, and Y. Cheon, 2007: Vertical fluxes of Muschinski, A., M. Behn, V. Hohreiter, and Y. Cheon, 2007: Vertical fluxes of

the temperature structure variable […]. Unpublished manuscript.the temperature structure variable […]. Unpublished manuscript.

Upward flux of local CT2 (sodar reflectivity) Upward flux of local CT2 (sodar reflectivity)

in the lower CBL (measured with sonics)in the lower CBL (measured with sonics)

Coulter, R. L., and M. A. Kallistratova, 2004: Two decades of progress in Coulter, R. L., and M. A. Kallistratova, 2004: Two decades of progress in

SODAR techniques […]. SODAR techniques […]. Meteorol. Atmos. Phys.Meteorol. Atmos. Phys., , 8585, 3-19., 3-19.

Upward bias in vertical velocities Upward bias in vertical velocities

observed with a sodar in the lower CBLobserved with a sodar in the lower CBL

OverviewOverview

IntroductionIntroduction

Wave propagation through turbulence: the basicsWave propagation through turbulence: the basics

Anisotropy in optical surface-layer turbulenceAnisotropy in optical surface-layer turbulence

Vertical-velocity biases observed with radars and sodarsVertical-velocity biases observed with radars and sodars

OutlookOutlook

OutlookOutlook

Faster data acquisitionFaster data acquisition Faster computationFaster computation Better sensorsBetter sensors Better theoretical understandingBetter theoretical understanding Better numerical simulationsBetter numerical simulations Better data assimiliation.Better data assimiliation.

Better observations and predictions.Better observations and predictions.

U.S. Army Research Office (ARO)U.S. Army Research Office (ARO)

National Science Foundation (NSF)National Science Foundation (NSF)

NOAA Earth Systems Research Laboratory (ESRL)NOAA Earth Systems Research Laboratory (ESRL)

National Center of Atmospheric Research (NCAR)National Center of Atmospheric Research (NCAR)

Jerry and Linda ParosJerry and Linda Paros

… … for their generous support!for their generous support!

Thanks to …Thanks to …