1. Page 1© Crown copyright Distribution of water vapour in the turbulent atmosphere Atmospheric phase correction for ALMA Alison Stirling John Richer & Richard Hills (Cambridge) October 2006

2. Page 2© Crown copyright Contents ALMA and the phase correction problem Sources of atmospheric phase fluctuations Simulations of realistic atmospheres Phase correction strategies

3. Page 3© Crown copyright ALMA  Atacama Large Millimeter Array  Interferometer with 50 x 12 m antennas  Covers baselines between 100 m - 10 km  Frequency range between 31.3 - 950 GHz

4. Page 4© Crown copyright Phase correction for interferometers Smith Weintraub equation for refractive index of air: Dry Wet Path length calculated by integrating refractive index along the line of sight Fluctuations in path length typically of order 250 microns (30 degrees at 90GHz) = E1 E2*

5. Page 5© Crown copyright Minimising atmospheric phase contamination - 1 Envisat, MERIS sensor: Maximum water vapour

6. Page 6© Crown copyright Minimising atmospheric phase contamination - 2 Water vapour radiometry  Measures atmospheric brightness temperature in 4- 8 channels close to 183 GHz emission line  Only sensitive to the wet component of phase  Continuous monitoring along astronomical line of sight  Retrieval dependent on temperature and water vapour profile with height  Complicated by the presence of hydrometeor (liquid cloud, ice crystals)

7. Page 7© Crown copyright 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

8. Page 8© Crown copyright 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

9. Page 9© Crown copyright 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)

10. Page 10© Crown copyright Understanding phase fluctuations Focus on:  ALMA site  Convection and mechanical turbulence  Simulate atmosphere over a 24 hour period  Use data collected from the site to drive simulations

11. Page 11© Crown copyright 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)

12. Page 12© Crown copyright Forcing and initial conditions 0730 Local time 25m resolution 4 x 4 x 3 km domain, horizontally periodic

13. Page 13© Crown copyright Time variation of water vapour

14. Page 14© Crown copyright Late morning, early afternoon

15. Page 15© Crown copyright Late afternoon

16. Page 16© Crown copyright Morning evolution of temperature & water vapour 0900 1000 1100 1200 w 1130 Mean potential temperature Mean water vapour r.m.s. potential temperature r.m.s. water vapour

17. Page 17© Crown copyright Evening evolution of temperature and water vapour 1600 1700 1800 1900 w 1730

18. Page 18© Crown copyright Refractive index fluctuations 1100 hours2000 hours Wet Dry Total

19. Page 19© Crown copyright Horizontal phase distribution Dry Wet Total Local Time 0930 1130 1330 1530 1730 4km

20. Page 20© Crown copyright Spatial structure function 0930 1130 1330 1530 1730 Local time

21. Page 21© Crown copyright Variation of r.m.s. phase with time of day Wet x Total Dry x Total Wet x Dry Wet Dry Total

22. Page 22© Crown copyright 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

23. Page 23© Crown copyright

24. Page 24© Crown copyright Combining fast switching and wvr - 1 (NB no instrument noise added) Wind speed 4 m/s

25. Page 25© Crown copyright Combining fast switching and wvr-2 0930 1130 1330 1530 Frequency: 113GHz Tslew = 1.39 s Tcal = 0.11 s (Holdaway 2001)

26. Page 26© Crown copyright 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