Implementation of an improved horizontal diffusion scheme into the Méso-NH Günther Zängl Laboratoire d’Aérologie / University of Munich 7 March 2005

The problem of computing numerical diffusion in a valley

The modified diffusion scheme (Zängl, 2002, MWR 130, )  Diffusion of temperature and moisture is computed truly horizontally at all model levels where this is possible without intersecting the topography  This is accomplished by linear vertical interpolation between the model levels  As in the standard diffusion scheme, perturbation fields are used for computing diffusion Near the surface, diffusion is still calculated along the model surfaces, but…

The modified diffusion scheme (cont.)  …the diffusion coefficient depends on the local curvature of the topography; essentially, the diffusion is retained in the direction along a valley but switched off in the cross-valley direction  Moreover, the leading metric term of the coordinate transformation is taken into account (correction with the local vertical temperature gradient); this makes the diffusion independent from the vertical gradient of the large-scale (background) field

Application: The valley wind circulation in the Alpine Inn Valley Setup  3 nested model domains, horizontal resolutions 20/4/1 km  40 model layers, lowermost half-level at 20 m AGL, top near 18 km  Idealized large-scale conditions: homogeneous temperature field, no large-scale pressure gradients and winds, low humidity (idealized high-pressure situation)  Radiation is computed for October 15  Simulation is started at midnight and integrated over 30 hours  Modification of surface heat flux computation (upper limit of 0.2 for the flux Richardson number)  Topographic effects on downward longwave radiation switched off (overestimated slope effects; problem corrected in MASDEV 4.6)

Topography of the third model domain Thalreit Nieder- breitenbach

Observations of the valley wind circulation in the Inn Valley (reproduced from Pamperin and Stilke, 1985) Dashed lines: upvalley wind; solid lines: downvalley wind

Assessment of the impact of the new diffusion scheme (including the other modifications) Wind field at 230 m AGL, t = 16h (afternoon) New diffusionOriginal diffusion

New diffusionOriginal diffusion Wind field at 230 m AGL, t = 30h (sunrise 2nd day)

New diffusionOriginal diffusion Cross-sections of potential temperature, t = 30h (sunrise 2nd day)

New diffusionOriginal diffusion The noise even develops over a smooth idealized 2D-mountain! Atmosphere at rest with standard-atmosphere temperature profile, mountain height 1500 m, half-width 5 km,  x=1 km, results at t=24h

t = 14ht = 16h In this idealized case, the generation of the noise starts at the tropopause between t = 12 h and t = 14h and then spreads downward

t = 14ht = 24h Vertical wind speeds reach up to 3 m/s (colour scale ranges from -1 m/s to 1 m/s)

Summary  The modified diffusion scheme strongly reduces the syste- matic errors of numerical diffusion over steep topography  In the free atmosphere, the truly horizontal computation of temperature diffusion suppresses the development of numerical instabilities under weak-wind conditions  Within valleys, the inclusion of the leading term of the coordinate transformation renders the diffusion indepen- dent from the accuracy of the large-scale fields and therefore improves the representation local temperature inversions  The modified diffusion scheme is essential for a realistic simulation of Alpine valley-wind systems