Testing of a New Gravity Waves Based Clear-Air Turbulence Diagnostic

The coincidence between gravity waves (GW) and clear-air turbulence (CAT) has been evident for a long time. Quite successful yet controversial attempt has been made in recent years to exploit this connection (Knox et al., 2008). This suggests that GW may be yet underestimated CAT generator. In the present paper we utilize the approach proposed by Haman (Haman, 1962). In this work Haman postulated, that GW excited by shallow convection may at certain altitude reach amplitude large enough to break and turn to turbulence due to nonlinear effects. He used a second order linear ordinary differential equation (ODE), a variant of the so called Scorer equation in order to determine the local vertical evolution of amplitude of the linear GW. This equation has coefficients which are dependent on the wind and temperature vertical profile and also on horizontal wave vector and phase velocity of GW. Therefore knowing these quantities one is able to determine vertical evolution of GW amplitude in the linear approximation and look for levels at which nonlinear effects may become important.

In order to use this approach as a CAT prognostic we have used data from the mesoscale NWP model COAMPS, run by Interdisciplinary Center of Mathematical Modeling, University of Warsaw, Poland (ICM) as the source of vertical profiles. Since shallow convection (the generator of GW in our approach) in the COAMPS model is not resolved but parameterized leaving some uncertainty regarding its spatial structure, we decided to construct a probabilistic model assuming that small disturbance in form of a spectrum of horizontal sinusoidal waves is generated everywhere at the height 1200m a.m.s.l. (it was rescaled to match terrain height properly). This spectrum is assumed uniform and isotropic and cover the approximate range of wavelengths and phase speeds corresponding to that which could be generated by shallow convection. Another issue arising immediately was where such a wave would break leading to CAT occurrence. As initial approximation we have used here an estimate of the ratio of nonlinear to linear terms magnitude in the momentum equation as a breaking criterion, though work is in progress to adapt a more robust one based on the turbulent energy production (McCann, 2001; Knox et al. 2008). In this way a total of 1820 initial (with respect to altitude) conditions for second order linear ODEs were crated for each vertical column. The sought result was the level at which the breaking criterion was fulfilled for each equation.

Using these results a scalar (index) was constructed which corresponds to expected CAT encounter inten- sity. This quantity is simply the number of broken waves within a vertical interval of certain thickness centered around the height of interest. The next step was the comparison of the results against eAMDAR data covering Europe during the period from January 2010 to May 2010 in order to select the best ones. Of course they de- pended strongly on the selected interval thickness however the best of those indices had the area under receiver operator curve (AUC) for moderate or greater MOG CAT encounters detection around 0.62. The indices were then combined using random forest method. The best of the combined indices were resulting in AUC for MOG CAT encounters on the level of 0.75 which is comparable to the performance of NOAA GTG1 as reported on rtvs.noaa.gov. These results are as yet still somewhat unstable (it happens sometimes that the random forest combination actually show AUC below 0.62) and the work towards further improvement of the method is in progress.