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

Aircraft measurements of the horizontal wind have consistently found transitions from roughly k −5/3 to k −2.4 spectra at scales Δ x c ranging from about 100–500 km. Since drop sondes find k −2.4 spectra 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 is H z ≈ 0.57 ± 0.02, close to the theoretical prediction of the 23/9D turbulence model which predicts H z = 5/9 = 0.555…. This model also predicts that isobars and isoheight statistics will diverge after Δ x c ; 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 Δ x c ≈ 160, 125 km, (transverse, longitudinal). These results thus give strong direct support to the 23/9D scaling stratification model.