Characterizing Millimeter Characterizing Millimeter Wavelength Atmospheric Wavelength Atmospheric

Fluctuations at the South PoleFluctuations at the South Pole

William L. Holzapfel (UCB)William L. Holzapfel (UCB)

In collaboration with:In collaboration with:R. Shane Bussmann (UCB)R. Shane Bussmann (UCB)

Chao-Lin Kuo (JPL)Chao-Lin Kuo (JPL)ACBAR teamACBAR team

Atmosphere Atmosphere Characterization:Characterization:Why do we care?Why do we care?• Atmospheric noise limits the sensitivity of Atmospheric noise limits the sensitivity of

ground-based mm-wavelength imaging ground-based mm-wavelength imaging experimentsexperiments

• By characterizing the atmosphere, we By characterizing the atmosphere, we have a quantitative method to compare have a quantitative method to compare observation sites around the world and observation sites around the world and predict effect of atmospheric fluctuations predict effect of atmospheric fluctuations on new generation of experimentson new generation of experiments

Atmospheric TransmissionAtmospheric Transmission

Water Vapor Emission

Dotted = 0.5mm pwvSolid = 0.1mm pwv

Frequency (GHz)

Total Atmosphere Transmission

Brown = 0.5mm pwvBlack = 0.0mm pwv

Frequency (GHz)

Why Water Vapor?Why Water Vapor?

• Atmosphere is described by a uniform sky Atmosphere is described by a uniform sky brightness with small spatial fluctuations due to brightness with small spatial fluctuations due to water vaporwater vapor

• Dry components of atmosphere (e.g. NDry components of atmosphere (e.g. N22 and O and O22) ) are well-mixed and produce only a constant are well-mixed and produce only a constant signal which is removed by differential imagingsignal which is removed by differential imaging

• Water vapor is nearly uniformly distributed, but Water vapor is nearly uniformly distributed, but also fluctuates in its mass fraction, producing also fluctuates in its mass fraction, producing brightness temperature fluctuations which can brightness temperature fluctuations which can not be removed by differential imagingnot be removed by differential imaging

Model: Spatial ComponentModel: Spatial Component

• Kolmogorov power law: derived from Kolmogorov power law: derived from conservation of kinetic energyconservation of kinetic energy

• Independent of turbulence Independent of turbulence mechanismmechanism

k (wavenumber)

Powerk-11/3

viscosity kicks in

input scale

A large vortex generates smallerones, and so on..

Model: Temporal EvolutionModel: Temporal Evolution

• Taylor (1938): Frozen Turbulence Taylor (1938): Frozen Turbulence Hypothesis (FTH)Hypothesis (FTH)

w

• Small scale turbulence velocity is Small scale turbulence velocity is much smaller than either global much smaller than either global advection flow (advection flow (ww) or chopper speed) or chopper speed

AnalysisAnalysis• Convert 3D power spectrum of turbulence, Convert 3D power spectrum of turbulence,

PP3D3D((kkxx,,kkyy,,kkzz), to 2D angular power spectrum P(), to 2D angular power spectrum P(αα) = ) = BBskysky

22(() () (ααxx22+ + ααyy

22))-b/2-b/2

• Assume values of wind velocity to convert 2D angular Assume values of wind velocity to convert 2D angular power spectrum to 1D correlation function, C(power spectrum to 1D correlation function, C(θθ))

• Compare the observed correlations between array Compare the observed correlations between array elements in ACBAR data with the model.elements in ACBAR data with the model.

• Fit four free parameters of the model : power law Fit four free parameters of the model : power law index, b; amplitude, Bindex, b; amplitude, Bskysky

22((); wind vector components, ); wind vector components, wwΦΦ and and wwεε

Example Correlation Example Correlation MatricesMatrices

150 GHz data – May 30, 2002Note difference with chop direction

Model (L) Model (R)Data (L) Data (R)

Pair A:-16’:0’

Pair D:0’:-16’

Pair E:-16’:-16’

Pair F:+16’:-16’

Measured Spectral IndexMeasured Spectral Index

• We expect to be in the 3D regime of We expect to be in the 3D regime of Kolmogorov model Kolmogorov model b=11/3 b=11/3

Plot of model-fitted spectral index as a function Plot of model-fitted spectral index as a function of dayof day

• b = 4.1+/-0.6 close to b = 4.1+/-0.6 close to 11/311/3

Cumulative Distribution Cumulative Distribution FunctionsFunctionsfor Amplitudefor Amplitude

Python: Austral Summer

ACBAR: Austral Winter

40 GHz

•The ACBAR data show no noise floor•Median 150 GHz winter amplitude is 20 mK2 rad-5/3

•Median summer amplitude scaled to 150 GHz ~ 130 mK2 rad-5/3

Winter atmosphere is more stable than summer

From Lay & Halverson, 2000

219 GHz274 GHz

150 GHz

Angular Wind Vector, PlotsAngular Wind Vector, PlotsAltitude of emission: reasonable consistency Altitude of emission: reasonable consistency with radiosonde derived water vapor with radiosonde derived water vapor pressure profiles adds to confidence in modelpressure profiles adds to confidence in model

Model fit emission elevationModel fit emission elevation Radiosonde water vapor profileRadiosonde water vapor profile

Preliminary Conclusions:Preliminary Conclusions:• Correlation analysis with ACBAR data probes to Correlation analysis with ACBAR data probes to

the lowest atmosphere amplitudes (no obvious the lowest atmosphere amplitudes (no obvious instrument noise floor as in L&H, 2000)instrument noise floor as in L&H, 2000)

• Kolmogorov-Taylor model provides a good fit to Kolmogorov-Taylor model provides a good fit to the atmospheric fluctuations seen by ACBAR.the atmospheric fluctuations seen by ACBAR.

• Median amplitude at the South Pole in winter is Median amplitude at the South Pole in winter is 20 mK20 mK22 rad rad-5/3-5/3, compared to 130 mK, compared to 130 mK22 rad rad-5/3-5/3 during summer at South Pole and 8000 mKduring summer at South Pole and 8000 mK22 rad rad--

5/35/3 at the Atacama desert in Chile (L&H2000). at the Atacama desert in Chile (L&H2000). (Uses WV emissivity to scale to 150 GHz)(Uses WV emissivity to scale to 150 GHz)