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.Correspondence to: S. Lovejoy (lovejoy@physics.mcgill.ca) 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 (| z/ x|) of the aircraft as a function of lag x and of scale invariant lag x/ z 1/H z .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 propose...

[1] The problem of turbulence is ubiquitous in the Earth sciences, astrophysics and elsewhere. Virtually the only theoretical paradigm that has been seriously considered is strongly isotropic in the sense that scaling exponents are the same in all directions so that any remaining anisotropy is ''trivial.'' Using 235 state-of-the-art drop sonde data sets of the horizontal wind at %5 m resolution in the vertical, we show that the atmosphere is apparently outside the scope of these isotropic frameworks. It suggests that anisotropy may frequently be strong requiring different scaling exponents in the horizontal and vertical directions.

[1] We apply multifractal analysis using exponents H 1 , C 1 , and a to straight and level stratospheric flight legs of the ER-2 high-altitude research aircraft in the inner vortex (defined as having wind speed <30 ms À1). The quantities so analyzed were ozone, wind speed s and temperature T, with the more gappy NO y data being analyzed by H 1 alone. The results for ozone, wind, and temperature are presented as time-dependent data on the three possible planes of the exponents and are compared for the different variables. We relate values of H 1 found in January observations of NO y to those found for ozone. Inner vortex mixing does not remove the small-scale polar stratospheric cloud-induced antipersistence (negative correlation between neighboring intervals for all choices of interval) in ozone by mid-March. Given that large particles were in evidence on all flights examined up to and including 7 March (although in greatly decreased numbers compared to January), this is reasonable. The value of a for ozone did, however, show an increase by mid-March, consistent with the widespread ozone loss evident from time series of histograms of ozone and methane. The histograms also demonstrate that inhomogeneity, with long tails in the probability distributions, is maintained throughout at the 15-25% level in both species. Interpretation is made in terms of polar stratospheric cloud (PSC) induced antipersistence competing with persistence induced by the large-scale insolation field, with the balance increasingly favoring the latter as time proceeds. Results are compared with inner vortex data obtained during earlier ER-2 flights in the Antarctic (1987) and in the Arctic (1989). The inner vortex over Antarctica showed significant increases in H 1 (O 3 ) and a during mid to late September. The correlated increases are consistent with latitudinal excursions of the outer vortex after the cessation of PSC processing, with increased solar exposure increasing H 1 (O 3 ) and a greater variety of filaments increasing a(O 3 ). It is concluded that the results have implications for the calculation of photochemical ozone loss in the vortex as a function of time and show that the combined effects of Bolgiano-Obukhov k À11/5 vertical scaling and Kolmogorov k À5/3 horizontal scaling predict the scaling behavior of wind speed observed by the aircraft. Rates of change of scaling exponents are linked to horizontal mixing rates and are combined with rates of change of methane to estimate diabatic descent and ozone loss rates for the inner vortex.