Improvement of EDR forecast by new terms in TKE-equation and by MOS using in situ observations

One exercise for the aviation forecast at German Weather Service (DWD) is the prediction of turbulence. New standards by ICAO and users require an improvement of the turbulence forecast method.

The Ellrod index (product of deformation and vertical wind-shear) and the EDR (eddy dissipation rate of the turbulent kinetic energy, TKE) are calculated based on the NWP- model COSMO_EU .However, the Ellrod index often over forecasts the turbulence and the EDR frequently misses turbulence events. Within a project at DWD, turbulence forecast should be improved by pushing two intentions.

In the first step a prognostic TKE scheme in COSMO_EU is considered. In the lower troposphere (below FL210) the comparison of the model EDR and the ACARS EDR measurements show a correlation since the turbulent length scale depends on the height. Especially for the upper troposphere (above FL210), new source terms are added to the TKE equation. These terms are derived from a larger sub-grid scale circulation (in contrast to smaller turbulence-scale in traditional boundary layer schemes) due to occurrence of horizontal and vertical wind shears, orographic blocking and gravity wave breaking and convection. Further physical processes could be improved by the additional terms, e.g., the TKE advection.

In a second step, the physical discrepancies of NWP should be minimized by post processing - the model output statistic (MOS). The procedure follows stepwise forward multiple regression algorithms with a polynomial coefficient - fitted to each predictor. In the beginning, a one-predictor-equation is calculated using the predictor showing the highest linear correlation to the predictand. The error of the one-predictor-equation (residual) then will be the new predictand. The predictor with the highest correlation to the residual is selected as second predictor, and so on. The predictors are direct outputs of NWP-model. The predictands are measured by commercial aircrafts (maxEDR) available over the USA. Therefore, COSMO_EU was nested over US domain in order to produce appropriate model output.

The results for a short period are satisfying. The shear term based on direct model output indicates correlation and offers variance reduction. The linear regression equation (MOS), improves the forecasted turbulence. We will investigate two half winter years.