Joint horizontal-vertical anisotropic scaling, isobaric and isoheight wind statistics from aircraft data

• Published in: Geophysical research letters Vol. 39; no. 11
• Main Authors: Pinel, J., Lovejoy, S., Schertzer, D., Tuck, A. F.
• Format: Journal Article
• Language: English
• Published: Washington, DC Blackwell Publishing Ltd 01-06-2012; American Geophysical Union; John Wiley & Sons, Inc
• Subjects: Aircraft; aircraft observations; Earth sciences; Earth, ocean, space; Environmental Sciences; Exact sciences and technology; Geophysics; Global Positioning System; Horizontal; Isobars; Mathematical models; Nonlinear systems; Satellite navigation systems; scaling; Spectra; Statistics; turbulence; wind; Structure function; models; spectra; stratification; joints; fractal dimension; turbulence; trajectory; Global Positioning System; winds; Aircraft observation; prediction; statistics
• ISSN: 0094-8276; 1944-8007
• DOI: 10.1029/2012GL051689

Aircraft measurements of the horizontal wind have consistently found transitions from roughly k−5/3 to k−2.4 spectra at scales Δxc ranging from about 100–500 km. Since drop sondes find k−2.4spectra in the vertical, the simplest explanation is that the aircraft follow gently sloping trajectories (such as isobars) so that at large scales, they estimate vertical rather than horizontal spectra. In order to directly test this hypothesis, we used over 14500 flight segments from GPS and TAMDAR sensor equipped commercial aircraft. We directly estimate the joint horizontal‐vertical (Δx, Δz) wind structure function finding ‐ for both longitudinal and transverse components ‐ that the ratio of horizontal to vertical scaling exponents isHz ≈ 0.57 ± 0.02, close to the theoretical prediction of the 23/9D turbulence model which predicts Hz = 5/9 = 0.555…. This model also predicts that isobars and isoheight statistics will diverge after Δxc; using the observed fractal dimension of the isobars (≈1.79 ± 0.02), we find that the isobaric scaling exponents are almost exactly as predicted theoretically and Δxc ≈ 160, 125 km, (transverse, longitudinal). These results thus give strong direct support to the 23/9D scaling stratification model.
Key Points
TAMDAR data analysis gives strong support to anisotropic scaling
At large horizontal lags, aircraft on isobars measure vertical fluctuations
Wind statistics from constant altitude and isobaric levels are not equivalent