Scaling turbulent atmospheric stratification. II: Spatial stratification and intermittency from lidar data

Tuck

Schertzer³

et al. 2009

Atmos. Chem. Phys.

Self Cite

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...

Section: Comparison With Other Aircraft Studiessupporting

confidence: 77%

Section: Understanding the Effects Of Vertical Aircraft Motion On Thesupporting

confidence: 73%

Section: Comparison With Other Aircraft Studiesmentioning

confidence: 99%

mentioning

confidence: 99%

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Reinterpreting aircraft measurements in anisotropic scaling turbulence

Tuck

Schertzer³

et al. 2009

Atmos. Chem. Phys.

Self Cite

“…Whereas the great majority of turbulence theories are isotropic -or at least quasi isotropic (they have the same exponents but not necessarily the same prefactors in all directions) -empirical studies of the vertical atmospheric structure, e.g., Van Zandt (1982), Schertzer and Lovejoy (1985), Dewan and Good (1986), Gardner (1994), Dewan (1997), Lilley et al (2004), Lilley et al (2008), show on the contrary that the turbulence is anisotropic, with vertical exponents different from those in the horizontal so that the stratification is scaling. They therefore require anisotropic theories such as the quasi-linear gravity wave theories -e.g.…”

Section: Cascades In Geophysical Turbulencementioning

confidence: 99%

The stochastic multiplicative cascade structure of deterministic numerical models of the atmosphere

Stolle

Nonlin. Processes Geophys.

Schertzer³

2009

Self Cite

Abstract.By direct statistical analysis we show that over almost all their range of scales and to within typically better than ±1%, atmospheric fields obtained from analyses and numerical integrations of atmospheric models have the multifractal structure predicted by multiplicative cascade models. We quantify this for the horizontal wind, temperature, and humidity fields at 5 different pressure levels for the ERA40 reanalysis, the Canadian Meteorological Centre Global Environmental Multiscale (CMC, GEM) model, as well as the National Oceanographic and Atmospheric Administration Global Forecasting System (NOAA, GFS). We investigate the additional prediction that the cascade belongs to a universal multifractal basin of attraction. By demonstrating a "Levy collapse" of the statistical moments to within ±2 to ±5% over most of the range of scales, we conclude that there is good evidence for this. Finally, we discuss how this stochastic multiplicative cascade structure can be exploited in improving ensemble forecasts.

Scaling turbulent atmospheric stratification. I: Turbulence and waves

Quart J Royal Meteoro Soc

Schertzer

Lilley

et al. 2008

Self Cite

ABSTRACT:In this first of a three-part series, we argue that the dynamics of turbulence in a stratified atmosphere should depend on the buoyancy over a wide range of vertical scales and on energy flux over a wide range of horizontal scales; it should be scaling, but anisotropic, not isotropic. We compare the leading statistical theories of atmospheric stratification which are conveniently distinguished by the elliptical dimension D s which quantifies their degree of spatial stratification. This includes the mainstream isotropic 2-D (large scales), isotropic 3-D (small scales) theory but also the more recent linear gravity wave theories (D s = 7/3) and the classical fractionally integrated flux (FIF) 23/9-D unified scaling model. In the latter, the horizontal wind has a k −5/3 spectrum as a function of horizontal wavenumber determined by the energy flux and a k −11/5 energy spectrum as a function of vertical wavenumber determined by the buoyancy force variance flux. In this model, the physically important notion of scale is determined by the turbulent dynamics, it is not given a priori (i.e. the by usual Euclidean distance). The 23/9-D FIF model is the most physically and empirically satisfying, being based on turbulent (spectral) fluxes. The FIF model as originally proposed by Schertzer and Lovejoy is actually a vast family of scaling models broadly compatible with turbulent phenomenology and with the classical turbulent laws of Kolmogorov, Corrsin and Obukov. However, until now it has mostly been developed on the basis of structures localized in space-time. In this paper, we show how to construct extreme FIF models with wave-like structures which are localized in space but unlocalized in space-time, as well as a continuous family of intermediate models which are akin to Lumley-Shur models in which some part of the localized turbulent energy 'leaks' into unlocalized waves.The key point is that the FIF requires two propagators (space-time Green's functions) which can be somewhat different. The first determines the space-time structure of the cascade of fluxes; this must be localized in space-time in order to satisfy the usual turbulence phenomenology. In contrast, the second propagator relates the turbulent fluxes to the observables; although the spatial part of the propagator is localized as before, in space-time it can be unlocalized. (It is still localized in space, now in wave packets.) We display numerical simulations which demonstrate the requisite (anisotropic, multifractal) statistical properties as well as wave-like phenomenologies. In parts II and III we will examine the empirical evidence for the spatial and temporal parts, respectively, of the model using state-of-the-art lidar data of aerosol backscatter ratios (which we use as a surrogate for passive scalar concentration).