Abstract
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 (|Δz/Δx|) of the aircraft as a function of lag Δx and of scale invariant lag Δx/Δz1/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.
Highlights
Aircraft are commonly used for high resolution studies of the dynamic and thermodynamic atmospheric variables and they are indispensable for understanding the statistical structure of the atmosphere in the horizontal direction
We examine in detail the characteristics of 16 horizontal tropospheric aircraft legs with an aim to systematically determining the consequences of the anisotropic turbulence on the vertically fluctuating trajectories
We argued that while the fractal regime was presumably dominated by turbulence, that the highly variable transition point from Htr ≈1/3 to Htr ≈1 depended on the level of turbulence, the slopes of the isobars and perhaps even the pilot and autopilot
Summary
Aircraft are commonly used for high resolution studies of the dynamic and thermodynamic atmospheric variables and they are indispensable for understanding the statistical structure of the atmosphere in the horizontal direction. For the ER-2, the fractality of the trajectory could be traced to a combination of turbulence and the plane’s autopilot which kept the plane near a constant Mach number of 0.7, effectively enforcing long range correlations between the wind and the aircraft altitude The interpretation of such data requires assumptions about the turbulence and the mainstream turbulence theories are virtually all isotropic – or at least “quasi isotropic”, i.e. with at most “trivial” (scale independent) anisotropies – whereas on the contrary the atmosphere apparently displays “scaling anisotropy”. If – as these studies suggest – the turbulence really is anisotropic with different horizontal and vertical exponents, one must find new ways to interpret the aircraft measurements and to estimate the true statistics and horizontal exponents While this was partially accomplished in the Lovejoy et al (2004) study of the special ER-2 stratospheric aircraft, it is important to generalize the results and test them on the somewhat different tropospheric aircraft data which attempt to follow isobars rather than isomachs (surfaces of constant Mach number). At the larger scales, we obtain the different isobaric spectrum (which below we argue is the same as the vertical spectrum)
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