Comment on "Reinterpreting aircraft measurement in anisotropic scaling turbulence" by Lovejoy et al. (2009)

Abstract

Abstract. Recently, Lovejoy et al. (2009) argued that the steep ∼k −3 atmospheric kinetic energy spectrum at synoptic scales ( 1000km) observed by aircraft is a spurious artefact of aircraft following isobars instead of isoheights. Without taking into account the earth's rotation they hypothesise that the horizontal atmospheric energy spectrum should scale as k −5/3 at all scales. We point out that the approximate k −3 -spectrum at synoptic scales has been observed by a number of non-aircraft means since the 1960s and that general circulation models and other current models have successfully produced this spectrum. We also argue that the vertical movements of the aircraft are far too small to cause any strong effect on the measured spectrum at synoptic scales.Aircraft measurements (Nastrom and Gage, 1985) show that the atmospheric kinetic energy wavenumber spectrum has a transition from an approximate k −3 -range, at scales from several hundred kilometres to several thousand kilometres (synoptic scales), to an approximate k −5/3 -range at scales from about five hundred kilometres down to one kilometre (mesoscales). Structure function analyses from aircraft measurements (e.g. Cho and Lindborg 2001) are also consistent with this result. Recently, Lovejoy et al. (2009) argued that the observed steep spectrum at synoptic scales is an artefact of the vertical motions of the aircraft. According to the authors' own hypothesis the horizontal kinetic energy spectrum should scale as k −5/3 from the very smallest scales of micro turbulence up to the very largest scales of planetary motions Correspondence to: E. Lindborg

Spectral structure of mesoscale winds over the water

“…As illustrated in Gage and Nastrom (1986) (their Figure 1), the source for enstrophy injection at the largescale end of the k −3 region of the spectrum is the geostrophic turbulence that is related to the baroclinic instability, and the source of the energy injection at the small-scale end of k −5/3 could be the buoyancy force such as gravity waves (Gage and Nastrom, 1986) or convective cloud systems (Lilly, 1983). This theory for quasi-two-dimensional (2D) turbulence was first presented by Kraichman (1967) and Batchelor (1969), supported over time by numerous theoretical, numerical and experimental studies, including Lilly and Petersen (1983), Gage and Nastrom (1986), Lindborg (1999), Shivamoggi (2000), Tung and Orlando (2002) and Lindborg et al (2010). Experiments also suggested that the mesoscale 2D flow has some isotropy characteristics, reflected as the lateral and meridional wind components having very similar spectral form (Gage and Nastrom, 1986;Högström et al, 1999;Larsén et al, 2011).…”

“…The spectral behaviour of the wind speed in the mesoscale range, from a few kilometres to hundreds of kilometres, or from a few minutes to hours, is not only a fundamental atmospheric research topic (e.g. Gage and Nastrom, 1986;Lindborg, 1999;Lindborg et al, 2010;Högström et al, 1999), but also important for practical use in wind energy applications. Modern wind farms are of the size of tens of kilometres, which means that the power spectrum in the mesoscale range is an important measure of accuracy for short-term forecasting (Vincent et al, 2010) as well as extreme wind estimation .…”

Why anisotropic turbulence matters: another reply

“…2 Scaling Isotropic versus scaling anistropic turbulence: the debate 2.1 Discussion 15 Over the last twenty-five years there have been two competing statistical turbulent frameworks for atmospheric dynamics the "isotropy primary" (IP) "standard model" which postulates first isotropy and only then scaling and the "scaling primary" (SP) model. While the former implies at least two regimes separated by a "dimensional transition": a small scale regime of isotropic 3-D turbulence and a large scale regime 20 of isotropic 2-D turbulence, the latter implies wide range scaling but with different exponents in the horizontal and vertical directions.…”

Quasi-geostrophic turbulence and generalized scale invariance, a theoretical reply

“…It is ironical that the source of the present debate on intermediate scale atmospheric dynamics presumably corresponds to the importation into meteorology of two successive techniques from hydrodynamics at two different periods. In order to focus the present paper on this question and therefore on the limitations of the theory of quasi-geostrophic turbulence (QGT, Charney, 1971) and show how to overcome them, let us first reject the second claim of Lindborg et al (2010), LT-NCG hereafter, that models may overcome limitations of a theory because in a very general manner models are obtained by introducing further constraints into a given theoretical framework, e.g. boundary conditions, discretization of partial differential equations, subgrid modelling and other parametrizations.…”

“…Lindborg et al (2010) claim that the apparent spectrum power law E(k) ≈ k −3 on scales ≥ 600 km obtained with the help of commercial jetliner trajectory deviations (GASP and Mozaic databases) could not be brought into question (Lovejoy et al, 2009a), because this spectrum corresponds to "a well known theory of quasi-geostrophic turbulence developed by Charney (1971)". Lindborg et al (2010) also claim that "limitations [of this theory] have been relaxed in many of the modern models of atmospheric turbulence". We show that both claims are irrelevant and that generalized scale invariance (GSI) is indispensable to go beyond the quasi-geostrophic limitations, to go in fact from scale analysis to scaling analysis in order to derive better analytical models.…”