REPLY to “ Two comments on the Surface Quasigeostrophic model for the atmospheric energy spectrum , ” submitted to JAS by E . Lindborg

Surface quasigeostrophic turbulence (Held et al. 1995) is not an exotic geophysical effect, but rather a generic description of quasigeostrophic turbulence at vertical surfaces of sharp change in the mean environment (vertical boundaries are an extreme example). Tulloch and Smith (2006, 2008) argued that surface quasigeostrophic (SQG) effects are consistent with many perplexing features of the observed atmospheric energy spectrum (Nastrom and Gage 1985). In the first paper, Tulloch and Smith (2006) considered a ‘toy’ model consisting of SQG flow overlying a finite-depth region of zero potential vorticity (PV), thereby including ‘interior’ dynamics in the barest way possible. The energy spectrum that results from forcing this system at large scale nevertheless exhibits a spectral break from a −3 slope to a −5/3 slope, and a forward cascade of energy at the upper surface, both qualitatively consistent with observations at the tropopause. However, the model is far too simple to be taken as quantitatively descriptive, and its flaws are amply described the paper. Tulloch and Smith (2008) developed a more complete, but still very idealized model that includes active surfaces coupled to two interior modes. The model allows a mean baroclinic flow and thus baroclinic instability, but assumes constant buoyancy frequency (N), rigid boundaries above and below, horizontal homogeneity, and other simplifications, not the least of which is that it is still strictly quasigeostrophic. The goal of the papers is to suggest how synoptic scale baroclinic instability, combined with the sharp jump in N at the tropopause, can lead to SQG effects that are consistent with observations, not to provide quantitatively descriptive models, nor to suggest that SQG dynamics is solely responsible for the shallowing of the spectrum in the mesoscales. Lindborg (2008 — the comment to which this note is a reply) implicitly assumes that Tulloch and Smith (2006, 2008) proposed their models as complete descriptions of the observations. Based on this mistaken perception, he explicitly criticizes the idea that the models of Tulloch and Smith explain the atmospheric spectrum on two counts: