Observations and Modelling of Fronts and Frontogenesis

Figure 11.7 displays the probability density of these
gradients. The dotted line represents a Gaussian
distribution with the observed mean and standard deviation.
The observed kurtosis is 76, much larger than the Gaussian
value of 3. This suggests the presence of a velocity field
that strains the temperature gradients to small scales. The
large kurtosis is characteristic of processes with sharp
transitions between small and large values. It measures the
front-like nature of the surface temperature field, which is
dominated by intermittent large gradients separated by
regions of small gradients. Qualitatively similar
distributions of temperature and velocity gradients occur at
small scales in three-dimensional turbulence (Monin and
Yaglom, 1975). Calculations of the kurtosis for
distributions of average horizontal gradient over distances
from 100 m to 100 km show that the kurtosis increases sharply
below scales of 10 km, with an evident but irregular change
in dependence at a few hundred meters, roughly the vertical
scales of the surface boundary layer.
II.4.b Spectra
Figure 11.8 displays the ensemble averaged horizontal
wavenumber spectrum of 15 m horizontal temperature gradient,
band averaged to 5 bands per decade. The variability between
10 and 100 km wavelengths that is evident in the time series
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