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Scaling turbulent atmospheric stratification. III: Space–time stratification of passive scalars from lidar data

In this third and final part of the series, we concentrate on the temporal behaviour of atmospheric passive scalars. We first recall that—although the full (x, y, z, t) turbulent processes respect an anisotropic scale invariance—that due to advection—the generator will generally not be a diagonal matrix. This implies that the scaling of (1‐D) temporal series will generally involve three exponents in real space: 1/3, 1/2, 3/5, for spectra βτ = 5/3, 2, 11/5, with the first and last corresponding to domination by advection (horizontal and vertical respectively), and the second to pure temporal development (no advection). We survey the literature and find that almost all the empirical βτ values are indeed in the range 5/3 to 2. We then use meteorological analyses to argue that, although pure temporal development is unlikely to be dominant for time‐scales less than the eddy turnover time of the largest structures (about 2 weeks), an intermittent vertical velocity could quite easily explain the occasionally observed βτ ≈ 2 spectra.