page 1© crown copyright distribution of water vapour in the turbulent atmosphere atmospheric phase...

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Distribution of water vapour in the turbulent atmosphere

Atmospheric phase correction for ALMA

Alison Stirling

John Richer & Richard Hills (Cambridge)

October 2006

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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