Reinterpreting aircraft measurements in anisotropic scaling turbulence S. Lovejoy^{1}, A. F. Tuck^{2}, D. Schertzer^{3,4}, and S. J. Hovde^{2}^{1}Physics, McGill University, 3600 University st., Montreal, Que. H3A 2T8, Canada

^{2}NOAA Earth System Research Laboratory, Chemical Sciences Division, 325 Broadway, Boulder CO 80305-3337, USA

^{3}CEREVE, Université Paris Est, France

^{4}Météo France, 1 Quai Branly, Paris 75005, France

Received: 05 Nov 2008 – Published in Atmos. Chem. Phys. Discuss.: 04 Feb 2009

Accepted: 30 Nov -0001 – Published: 13 Jul 2015

Abstract. Due to both systematic and turbulent induced vertical fluctuations, the
interpretation of atmospheric aircraft measurements requires a theory of
turbulence. Until now virtually all the relevant theories have been isotropic
or "quasi isotropic" in the sense that their exponents are the same in all
directions. However almost all the available data on the vertical structure
shows that it is scaling but with exponents different from the horizontal:
the turbulence is scaling but anisotropic. In this paper, we show how such
turbulence can lead to spurious breaks in the scaling and to the spurious
appearance of the vertical scaling exponent at large horizontal lags.

We demonstrate this using 16 legs of Gulfstream 4 aircraft near the top of
the troposphere following isobars each between 500 and 3200 km in length.
First we show that over wide ranges of scale, the horizontal spectra of the
aircraft altitude are nearly *k*^{-5/3}. In addition, we show that the
altitude and pressure fluctuations along these fractal trajectories have a
high degree of coherence with the measured wind (especially with its
longitudinal component). There is also a strong phase relation between the
altitude, pressure and wind fluctuations; for scales less than
≈40 km (on average) the wind fluctuations lead the pressure and
altitude, whereas for larger scales, the pressure fluctuations leads the
wind. At the same transition scale, there is a break in the wind spectrum
which we argue is caused by the aircraft starting to accurately follow
isobars at the larger scales. In comparison, the temperature and humidity
have low coherencies and phases and there are no apparent scale breaks,
reinforcing the hypothesis that it is the aircraft trajectory that is
causally linked to the scale breaks in the wind measurements.

Using spectra and structure functions for the wind, we then estimate their
exponents (β, *H*) at small (5/3, 1/3) and large scales (2.4, 0.73).
The latter being very close to those estimated by drop sondes (2.4, 0.75) in
the vertical direction. In addition, for each leg we estimate the energy
flux, the sphero-scale and the critical transition scale. The latter varies
quite widely from scales of kilometers to greater than several hundred
kilometers. The overall conclusion is that up to the critical scale, the
aircraft follows a fractal trajectory which may increase the intermittency of
the measurements, but doesn't strongly affect the scaling exponents whereas
for scales larger than the critical scale, the aircraft follows isobars whose
exponents are different from those along isoheights (and equal to the
vertical exponent perpendicular to the isoheights). We bolster this
interpretation by considering the absolute slopes (|Δ*z*/Δ*x*|) of the aircraft as a function of lag Δ*x* and of scale
invariant lag Δ*x*/Δ*z*^{1/Hz}.

We then revisit four earlier aircraft campaigns including GASP and MOZAIC
showing that they all have nearly identical transitions and can thus be
easily explained by the proposed combination of altitude/wind in an
anisotropic but scaling turbulence. Finally, we argue that this
reinterpretation in terms of wide range anisotropic scaling is compatible
with atmospheric phenomenology including convection.

**Citation:** Lovejoy, S., Tuck, A. F., Schertzer, D., and Hovde, S. J.: Reinterpreting aircraft measurements in anisotropic scaling turbulence, Atmos. Chem. Phys., 9, 5007-5025, doi:10.5194/acp-9-5007-2009, 2009.