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ALMA Memo # 517

Turbulence simulations of dry and wet phase
fluctuations at Chajnantor.
Part I: The daytime convective boundary layer.

Alison Stirling, John Richer, Richard Hills, Adrian Lock 2005-04-18

Abstract:

We have performed numerical simulations of the atmosphere for typical daytime convective conditions at Chajnantor, and derived the resulting wet and dry contributions to the atmospheric phase fluctuations. The simulations show that:

• Dry phase fluctuations are concentrated in two layers -- near to the ground, and at the temperature inversion. The wet fluctuations are concentrated at the inversion, while the total phase fluctuations are more uniformly distributed within the convective layer. This is because of significant positive and negative correlations between the dry and wet refractive index fluctuations.
• The phase structure function is well described by a Kolmogorov turbulence spectrum on small scales, with a turn over on a scale of order the depth of the boundary layer.
• The variation of total r.m.s. phase with elevation shows a dependence on the square root of air mass for the total phase, but the dry component shows a linear variation with air mass, and the wet component varies as air mass to the power 0.75.

  A scaling analysis has been used to relate the r.m.s. wet and dry phase fluctuations to the vertical profiles of temperature and water vapour so that an estimate of the phase fluctuations at Chajnantor can be obtained from radiosonde data.

• Using this approach, the r.m.s. dry fluctuations along a single line of sight are found to be 100-200 um at the 25-75 percentiles respectively, and the equivalent wet fluctuations are found to lie in the range 180-530 um. The total r.m.s. path fluctuations were estimated to be 240-525 um, and we have compared these estimates with independent measurements of the total r.m.s. phase obtained from interferometric measurements (Evans et al., 2003), and these show excellent agreement.
• The correlation coefficient between total and wet phase fluctuations is estimated, and this is found to lie in the range 0.75-0.97 at the 25-75 percentiles. This suggests that, even under conditions where the dry phase fluctuations are expected to be at their highest, water vapour radiometry is expected to be able to remove a high percentage of phase fluctuationsat Chajnantor.