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© Crown copyright Page 1
Distribution of water vapour in the turbulent atmosphere
Atmospheric phase correction for ALMA
Alison Stirling
John Richer & Richard Hills (Cambridge)
October 2006
© Crown copyright Page 2
Contents
ALMA and the phase correction problem
Sources of atmospheric phase fluctuations
Simulations of realistic atmospheres
Phase correction strategies
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ALMA
Atacama Large Millimeter ArrayInterferometer with 50 x 12 m antennasCovers baselines between 100 m - 10 kmFrequency range between 31.3 - 950 GHz
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Phase correction for interferometers
Smith Weintraub equation for refractive index of air:
Dry WetPath length calculated by integrating refractive index along the line of sightFluctuations in path length typically of order 250 microns (30 degrees at 90GHz)
= E1 E2*
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Minimising atmospheric phase contamination - 1
Envisat, MERIS sensor: Maximum water vapour
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Minimising atmospheric phase contamination - 2
Water vapour radiometry Measures atmospheric brightness temperature in 4-
8 channels close to 183 GHz emission lineOnly sensitive to the wet component of phase Continuous monitoring along astronomical line of
sightRetrieval dependent on temperature and water
vapour profile with heightComplicated by the presence of hydrometeor (liquid
cloud, ice crystals)
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Minimising atmospheric phase contamination - 3
Fast Switching
Look at point source, zero phase between antennas, Use to deduce atmospheric component of differential phase Sensitive to total phase variation Off-target so reduces integration time Not looking at same field of view Intermittent, so phase accuracy decays with time
Phase retrieval algorithm sensitive to structure of atmosphere
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Sources of atmospheric phase fluctuations
Planetary Waves•Rossby•Kelvin
GOES 6.7 microns 21 September 2006
Condensation and evaporation•Cloud processes•Differential latent and sensible heating at surface
Turbulent mixing across a gradient•Convection via surface heating•Mechanical turbulence driven by wind shear•Mountain wave breaking
1000 km scales
100 km scales
10 km scales
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What causes atmospheric phase fluctuations?
Mixing across a gradient contd…
•Turbulent mixing initially acts to increase inhomogeneity
•Variance depends on gradient
•The mixing acts to decrease the gradient (and so the variance)
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Understanding phase fluctuations
Focus on: ALMA site Convection and mechanical turbulence
Simulate atmosphere over a 24 hour periodUse data collected from the site to drive simulations
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Large Eddy Model
Solves the Navier-Stokes equations on a grid
Explicitly resolves larger scale turbulent eddies
On sub-grid scale assumes a Kolmogorov -5/3 energy cascade to smaller scales where it is dissipated
Carries pressure and temperature as state variables
All phases of water included (vapour, cloud, ice, snow)
Simple radiative transfer model to include the effects of radiative heating and cooling
Insert winds, energy sources (eg from ground, or large-scale winds)
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Forcing and initial conditions
0730 Local time
25m resolution 4 x 4 x 3 km domain, horizontally periodic
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Time variation of water vapour
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Late morning, early afternoon
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Late afternoon
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Morning evolution of temperature & water vapour
0900 1000 1100 1200
w
1130
Mean potentialtemperature
Mean watervapour
r.m.s. potentialtemperature
r.m.s. watervapour
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Evening evolution of temperature and water vapour
1600 1700 1800 1900
w
1730
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Refractive index fluctuations
1100 hours 2000 hours
Wet
Dry
Total
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Horizontal phase distribution
Dry
Wet
Total
Local Time
0930 1130 1330 1530 1730
4km
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Spatial structure function
0930 1130 1330 1530 1730
Local time
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Variation of r.m.s. phase with time of day
Wet x Total
Dry x Total
Wet x Dry
Wet
Dry
Total
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Possible phase correction strategies
Just use Fast Switching
Just use WVR
Use FS to obtain an estimate for the dry phase, and use WVR to determine wet phase
Issues:Frequency of Fast Switching
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Combining fast switching and wvr - 1
(NB no instrument noise added)
Wind speed 4 m/s
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Combining fast switching and wvr-2
0930
1130
1330
1530
Frequency: 113GHzTslew = 1.39 sTcal = 0.11 s(Holdaway 2001)
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Summary
Large eddy simulations can be used to quantify the components of phase fluctuations
Fluctuations located at surface and inversion
Dry fluctuations typically ¼ amplitude of wet
Structure function shape can be preserved at night
Dry and wet fluctuations are anti-correlated, effect most pronounced at night
Combined WVR – FS allows FS cycle time to quadruple