Characterizing Millimeter Wavelength Atmospheric Fluctuations at the South Pole

1
Characterizing Millimeter Wavelength Atmospheric
Fluctuations at the South Pole

• William L. Holzapfel (UCB)
• In collaboration with
• R. Shane Bussmann (UCB)
• Chao-Lin Kuo (JPL)
• ACBAR team

2
Atmosphere CharacterizationWhy do we care?

• Atmospheric noise limits the sensitivity of
  ground-based mm-wavelength imaging experiments
• By characterizing the atmosphere, we have a
  quantitative method to compare observation sites
  around the world and predict effect of
  atmospheric fluctuations on new generation of
  experiments

3
Atmospheric Transmission
4
Why Water Vapor?

• Atmosphere is described by a uniform sky
  brightness with small spatial fluctuations due to
  water vapor
• Dry components of atmosphere (e.g. N2 and O2) are
  well-mixed and produce only a constant signal
  which is removed by differential imaging
• Water vapor is nearly uniformly distributed, but
  also fluctuates in its mass fraction, producing
  brightness temperature fluctuations which can not
  be removed by differential imaging

5
Model Spatial Component

• Kolmogorov power law derived from conservation
  of kinetic energy
• Independent of turbulence mechanism

input scale
A large vortex generates smaller ones, and so
on..
k-11/3
Power
viscosity kicks in
k (wavenumber)
6
Model Temporal Evolution

• Taylor (1938) Frozen Turbulence Hypothesis (FTH)

w

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

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Analysis

• Convert 3D power spectrum of turbulence,
  P3D(kx,ky,kz), to 2D angular power spectrum P(a)
  Bsky2(e) (ax2 ay2)-b/2
• Assume values of wind velocity to convert 2D
  angular power spectrum to 1D correlation
  function, C(?)
• Compare the observed correlations between array
  elements in ACBAR data with the model.
• Fit four free parameters of the model power law
  index, b amplitude, Bsky2(e) wind vector
  components, wF and we

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Example Correlation Matrices
150 GHz data May 30, 2002Note difference with
chop direction
Model (L)
Model (R)
Data (R)
Data (L)
Pair ADf-16De0
Pair DDf0De-16
Pair EDf-16De-16
Pair FDf16De-16
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Measured Spectral Index

• We expect to be in the 3D regime of Kolmogorov
  model ? b11/3
• Plot of model-fitted spectral index as a function
  of day

• b 4.1/-0.6 close to 11/3

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Cumulative Distribution Functionsfor Amplitude
40 GHz
Python Austral Summer
274 GHz
219 GHz
ACBAR Austral Winter
150 GHz
From Lay Halverson, 2000

• 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

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Angular Wind Vector, Plots

• Altitude of emission reasonable consistency with
  radiosonde derived water vapor pressure profiles
  adds to confidence in model

Model fit emission elevation
Radiosonde water vapor profile
12
Preliminary Conclusions

• Correlation analysis with ACBAR data probes to
  the lowest atmosphere amplitudes (no obvious
  instrument noise floor as in LH, 2000)
• Kolmogorov-Taylor model provides a good fit to
  the atmospheric fluctuations seen by ACBAR.
• Median amplitude at the South Pole in winter is
  20 mK2 rad-5/3, compared to 130 mK2 rad-5/3
  during summer at South Pole and 8000 mK2 rad-5/3
  at the Atacama desert in Chile (LH2000). (Uses
  WV emissivity to scale to 150 GHz)

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3D ? 2D Angular Power Spectrum

• The 2D angular power spectrum, P(a), can be
  obtained by integrating the third spatial
  dimension of the 3D power spectrum
• This can be re-written asP(a) Bsky2(e) (ax2
  ay2)-b/2
• Bsky2(e), b are two of the four free parameters
  of model

a angular wave number
b/2
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Amplitude Analysis Scaling Between Frequencies

• AT (Atmospheric Transmission) code used to
  understand scaling of amplitudes between
  frequencies.

Frequency 40 GHz 150 GHz 219 GHz 274 GHz
DTCMB2 0.67 mK2 rad-5/3 20. mK2 rad-5/3 160 mK2 rad-5/3 860 mK2 rad-5/3
DTRJ2 0.62 mK2 rad-5/3 6.7 mK2 rad-5/3 17. mK2 rad-5/3 31. mK2 rad-5/3
Dt2 (normalized to 40GHz) 1 0.05 0.022 0.02
Results here still somewhat tentative Need better
understanding of AT code, numbers above
calculated under conditions of Mauna Kea
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Methodology

• Fit four free parameters power law index, b
  amplitude, Bsky2(e) wind vector components, wF
  and we
• Minimize difference between observed data and the
  theoretical correlation matrix generated from
  model by varying parameters of model

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Instrument Background

• Data acquired using ACBAR, the Arcminute
  Cosmology Bolometric Array Receiver (Runyan et.
  al, 2002)
• Primary science goal is precise measurement of
  high-l CMB power spectrum at 150 GHz (Kuo et. al
  2002)

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Arcminute Cosmology Bolometer Array Receiver
16-element array
Corrugated feed horns
Cooled to 240mK He3/He3/He4 Fridge
4K
350mK
240mK
FET
Spider web Bolometers
120K
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Geometrical Situation

• A sheet of atmospheric turbulence is observed at
  height h, thickness ?h, and is in the presence of
  a wind vector w

From Lay Halverson, 2000

• Blobs of water vapor within that sheet whose
  spatial spectrum can be described by a Kolmogorov
  power law
• Small scale of turbulence fluctuations compared
  to ?h means we observe the 3-D regime of
  Kolmogorov power law b11/3

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Dataset Description

• Data were collected during the austral winter of
  2002
• Approximately 200 files over that period, each
  constituting roughly six hours of continuous
  observation 100 GB data

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Comparison to Previous Studies

• Similar atmosphere characterization done by
  Lay and Halverson (2000), but
• Their dataset spanned the austral summer. It is
  expected that the colder temperatures of the
  winter will produce lower fluctuation amplitudes
  compared to the summer
• The correlation analysis capitalizes on the large
  number of array elements and sensitivity of ACBAR
  and allows us to probe the fluctuation amplitude
  well below the detector noise, even during the
  best weather

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Amplitude Measurements

• Log plot of 150 GHz amplitude as a function of
  time
• Triangles represent observations where Kolmogorov
  model fails (15 of data)

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Angular Wind Vector Measurements

• Need to use high signal-to-noise observations
  because angular wind-speed determination is poor
  for low amplitude fits
• Half the data survive the SNR cut
• Current limiting factor in angular wind vector
  measurements is component perpendicular to motion
  of chopper

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Application to SPT

• Tom Crawford (U. Chicago) is running observing
  strategy simulations for design of South Pole
  Telescope
• The median fluctuation amplitude and scale height
  of the water vapor during winter observations are
  critical numbers in these simulations

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Minimize c2

• Schematic representation of data processing
• IDL AMOEBA routine used to adjust free input
  parameters of model to minimize c2

Data vectors xi, xj
Model
Calculate the averaged correlation
Bsky2(e), b, wf, we
Cq(t,wf,we), Bsky2(e),b
ltxixTjgt
Mode removal matrix P
PltxixTjgtPt
P ltCTijgt Pt
Compare
c2
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Validity of Model

• For 85 of the observations, the
  Kolmogorov-Taylor model fits the data very well
• For the other 15, the data exhibit anomalously
  high amplitude fluctuations that do not fit the
  KT model. These observations are identified via
  a c2 cut

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Angular Wind Vector (cont.)

• Both wind direction and speed are fairly constant
  as function of altitude (based on radiosonde
  data)
• We can compare ACBAR angular wind-speed to
  radiosponde linear wind-speed to obtain a rough
  estimation of the scale height of the emission
• Accuracy is limited by determination of
  chopper-perpendicular angular wind-speed

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Data Processing, Part 3

• Perform mode removal project out a second order
  polynomial to remove large scale power
• Resultant correlation matrix is ready for
  comparison to model

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Angular Offset Values
pair ?F ?e Pair ?F ?e Pair ?F ?e
A -16 0 E -16 -16 I 32 -16
B -32 0 F -32 -16 J 48 -16
C -48 0 G -48 -16
D 0 -16 H 16 -16
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Theoretical Correlation Matrix

• How do we compare observed correlation matrix,
  ltxixjTgt to theoretical correlation function,
  C(?)?
• Assuming stationary noise, construct a
  theoretical correlation matrix, CTij, from C(?)
• Apply identical mode removal to CTij
• Resulting theoretical correlation matrix can be
  directly compared to ltxixjTgt

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Data Processing, Part 2

• Statistical correlation depends only on the
  relative displacement of the channels
  correlation matrices corresponding to pairs of
  array elements with identical relative
  displacements and operating at the same frequency
  are averaged together
• Very few observations demonstrate changes over
  the span of the 6 hour observation average all
  correlation matrices in an observation together
  to improve SNR

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Data Processing, Part 1

• xi and xj are each 128 element data vectors (or
  sweeps) to be correlated
• Subtract telescope offset (averaged over many
  sweeps) from each sweep
• The 128x128 element correlation matrix calculated
  from the data vectors is defined as ltxixjTgt

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Calculating, ?, the Angular Lag

• ? is set by observing strategy
• ?F and ?e are fixed according to the angular
  separation of the array elements being correlated
• wF and we, the two components of the wind vector,
  are the final two free parameters in the model

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2D Angular PS ? C(?)

• C(?) Fourier Transform(P(a))
• ? is measured in the reference frame of the
  fluctuations
• Given the temporal lag, t, chopper angular speed,
  ?, and the wind angular speed (wF,we) in the F
  (azimuth) and e (elevation) directions, ? is
  given by

2p
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Goals of Research

• Verify accuracy of Kolmogorov model of
  atmospheric turbulence by comparing to data
• Characterize parameters of model for the entire
  2002 austral winter
• Check consistency of results with other data
  (e.g. radiosonde weather balloons, previous
  similar studies)

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Model Spatial Temporal

• We expect to see a frozen pattern of Gaussian
  noise with Kolmogorov spectrum blown through the
  telescope beams by wind or the chopper motion in
  a certain direction, similar to this

Blobs of water vapor
Python Experiment (From Lay Halverson, 2000)
Unfortunately, signal-to-noise is usually much
lower than what is shown here.
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Calibration

• Voltage signal ? CMB temperature units
• Use known flux of planets to get absolute
  conversion
• Mars, 2001 5 error Venus, 2002 8 error
• Skydips used to characterize transmission of
  atmosphere
• Total uncertainty of 10 for 2002 CMB observations

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Observation Strategy

• A chopping flat mirror sweeps the telescope beam
  over 3o across the sky at a rate of 0.3 Hz and at
  constant elevation
• Each 3o sweep is binned into a vector (x) of 128
  temperature measurements for each of the 16
  detectors
• Data vectors from two array elements form the
  foundation of the correlation analysis

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Water Vapor Characteristics

• Radiosonde weather balloon data were taken once
  per day at the South Pole during the winter of
  2002.

Pwv RH P0 exp(-To/T)

• Data on pressure, temperature, relative humidity,
  and wind speed and direction as functions of
  altitude

Most water vapor pressure exists below 2km.