
^{1}Université ParisEst, Ecole des Ponts ParisTech, LEESU, MarnelaVallée, France ^{2}McGill U., Physics dept, Montreal, Canada Abstract. 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 quasigeostrophic 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 quasigeostrophic limitations, to go in fact from scale analysis to scaling analysis in order to derive better analytical models. In this direction, we derive vorticity equations in a space of (fractal) dimension D=2+H_{z} (0 ≤ H_{z} ≤ 1), which corresponds to a first step in the derivation of a dynamical alternative to the quasigeostrophic approximation and turbulence. The corresponding precise definition of fractional dimensional turbulence already demonstrates that the classical 2D and 3D turbulence are not the main options to understand atmospheric dynamics. Although (2 + H_{z})D turbulence (with 0 < H_{z} < 1) has more common features with 3D turbulence than with 2D turbulence, it has nevertheless very distinctive features: its scaling anisotropy is in agreement with the layered pancake structure, which is typical of rotating and stratified turbulence but not of the classical 3D turbulence. Citation: Schertzer, D., Tchiguirinskaia, I., Lovejoy, S., and Tuck, A. F.: Quasigeostrophic turbulence and generalized scale invariance, a theoretical reply, Atmos. Chem. Phys., 12, 327336, doi:10.5194/acp123272012, 2012. 
