Understanding the k-5/3 to k-2.4 spectral break in aircraft wind data

A fundamental issue in atmospheric dynamics is to understand how the statistics of fluctuations of various fields vary with their space-time scale. The classical - and still “standard” model - dates back to Kraichnan and Charney’s work on 2-D and geostrophic (quasi 2-D) turbulence at the end of the 1960’s and early 1970’s. It postulates an isotropic 2-D turbulent regime at large scales and an isotropic 3D regime at small scales separated by a “dimensional transition” (once called a “mesoscale gap”) near the pressure scale height of ≈10 km. By the early 1980’s a quite different model emerged, the 23/9-D scaling model in which the dynamics were postulated to be dominated (over wide scale ranges) by a strongly anisotropic scale invariant cascade mechanism with structures becoming flatter and flatter at larger and larger scales in a scaling manner: the isotropy assumptions were discarded but the scaling and cascade assumptions retained. Today, thanks to the revolution in geodata and atmospheric models - both in quality and quantity - the 23/9-D model can explain the observed horizontal cascade structures in remotely sensed radiances, in meteorological “reanalyses”, in meteorological models, in high resolution drop sonde vertical analyses, of lidar vertical sections etc. All of these analyses directly contradict the standard model which predicts drastic “dimensional transitions” for scalar quantities. Indeed, until recently the only unexplained feature was a scale break in aircraft spectra of the (vector) horizontal wind somewhere between about 40 and 200 km. However - contrary to repeated claims - and thanks to a reanalysis of the historical papers - the transition that had been observed since the 1980’s was not between k^-5/3 and k^-3 but rather between k^-5/3 and k^-2.4. By 2009, the standard model was thus hanging by a thread. This was cut when careful analysis of scientific aircraft data allowed the 23/9-D model to explain the large scale k-2.4 regime as an artefact of the aircraft following a sloping trajectory: at large enough scales, the spectrum is simply dominated by vertical rather than horizontal fluctuations which have the required k^-2.4 form. Since aircraft frequently follow gently sloping isobars, this neatly explains the last obstacle to wide range anisotropic scaling models finally opening the door to an urgently needed consensus on the statistical structure of the atmosphere. However, objections remain: at large enough scales do isobaric and isoheight spectra really have different exponents? In this presentation we attempted to study this issue in more detail than before by analyzed data measured by commercial aircrafts through the Tropospheric Airborne Meteorological Data Reporting (TAMDAR) system over CONUS during year 2009. The TAMDAR system allows us to calculate the statistical properties of the wind field on constant pressure and altitude levels. Various statistical exponents were calculated (velocity increment in terms of horizontal, vertical displacement, pressure and time) and we show here what we learned and how this analysis can help with solving this question.