Global sonde datasets do not support a mesoscale transition in the turbulent energy cascade

The dynamics driving Earth's weather are commonly presumed to be governed by a hierarchy of distinct dynamical mechanisms, each operating over some limited range of spatial scales. The largest scales are argued to be driven by quasi-two-dimensional turbulence, the mesoscales by gravity waves, and the smallest scales by 3D isotropic turbulence. In principle, such a hierarchy should result in observable breaks in atmospheric kinetic energy spectra at discrete points as one mechanism transitions to the next. Using global radiosonde and dropsonde datasets, we show that this view is not supported in observations. Between 200m and 8km, we find that structure functions calculated along the vertical direction display a Hurst exponent of H_v \approx 0.6, which is inconsistent with either gravity waves (H_v = 1) or 3D turbulence (H_v = 1/3). In the horizontal directions, large-scale structure functions between 200km and 1800km display a Hurst exponent of H_h \approx 0.4, which is inconsistent with quasi-geostrophic dynamics (H_h = 1). We show that these observations are instead consistent with a lesser-known theory of stratified turbulence proposed by Lovejoy and Schertzer in 1985, where at all scales the dynamics obey a single anisotropic turbulent cascade with H_v=3/5 and H_h =1/3.

Our results suggest a reinterpretation of atmospheric dynamics: rather than being controlled by a hierarchy of distinct dynamical elements, atmospheric flow should instead be thought of as a superposition of anisotropic turbulent eddies that continually cascade from large scales to small scales. We show how this view may be interpreted literally and used to construct photorealistic and quantitatively accurate simulations of atmospheric volumes, and without integration of the hydrodynamic equations. We argue that the model also provides a more intuitive basis for interpreting both the intermittent and the anisotropic aspects of the observed statistics of the atmosphere.