Instantaneous fluctuations of temperature and moisture in the upper troposphere and tropopause region. Part 2: Structure functions and intermittency

Probability density functions (p.d.f.s) in MOZAIC instantaneous fluctuations of temperature, relative and absolute humidity with various spatial resolutions had shown signs of intermittency. This appears to have originated either from turbulence or certain physical processes (e.g. gravity waves, deep convection) that bring air masses of different origin close together or from air mass boundaries within the averaging volumes, at which the thermodynamical properties show a discontinuity and are nearly independent on both sides of the boundary. In the present paper, we derive a stochastic model for the observed p.d.f.s in the tropopause region and compare the p.d.f.s of the fluctuations in the atmosphere to small-scale Rayleigh-Benard convection p.d.f.s with similar shapes. In both cases, intermittency originates from rare events of large amplitude super-posed unto a Gaussian background. The peculiar ogival shape of some of the distributions results from the sampling procedure, and the ogival character becomes more pronounced with increasing spatial resolution. Analysis of structure functions up to order three reveals that the MOZAIC data represent an intermediate state between large-scale two-dimensional and small-scale three-dimensional inertial range turbulence. This can be visualised by the scale interaction of the typical length of MOZAIC flight legs and the sampling rate (and hence also spacing). While night legs belong to and exceed the synoptic scale, the events causing intermittency have a scale roughly corresponding to the sampling scale which is clearly sub-synoptic. Our results are directly relevant for the development of stochastic cloud-microphysical schemes in general circulation and weather forecast models.