Need for Numerical Developments within COSMO J Need for Numerical Developments within COSMO J. Steppeler, DWD Zurich 2005

The development of LM numerics Klemp Wilhelmson Runge Kutta Semi-Lagrangian main Competitor of RK Consideration in the medium range future: Global nh

Reasons for the success of KW Simple robust method comparable in cost and accuracy to Euler Centred difference Competitive methods (SL) had (and have) problems in realising the efficiency gain they achieve in hydrostatic models as no efficient 3-d Helmholtz solver has yet been found. With continued research into SI- methods this situation need not stay the same

Grid Structure and Time Integration With Klemp Wilhelmson Method

The Runge Kutta scheme (NCAR) t+dt RK is a two time level 3rd order in time scheme, involving substepping for fast waves Spacial order is 3 or 5 (upstream differencing) Approximation conditions concern vert. coordiante and phys. interface Semi-lagrange: 2nd order in time, 3rd order in space, could be easier to achieve efficiency with large dt t

Considerations for RK Accuracy 3rd order sufficient for practical purposes, if approximation conditions are fulfilled Efficiency as KW As a rather new method RK is not sufficiently investigated, in particular it would be nice to have more practical examples showing the advantages of the increased order in forecast mode

Numerical research Tends to be long term Even for easy to program methods development time is often conted in years Is often associated with model reprogramming After lack of relevant developments models tend to stop existence

Vanished model Missing Numerical research HIRLAM NH modelling MC2 Further development of SL eta Problems of Z Tapp/White NH-instabilities In institutes as NCAR or UKMO there is a planned change of model generations

Considerations for COSMO Approximation conditions for RK scheme: delta h < delta z or use LM_Z Physics interfaceanalog to what is done for Orography Increase of the efficiency of RK: Semi implicit methods e.t.c. More validation of RK against other methods, such as KW, SL

Global nh, the replacement of LM in the medium term

Saving factors of Discretisations Finite Volumes: 1 Baumgardner Order2: 1 Baumgardner Order3: 1 Great circle grids: RK, SI, SL 1 now 3 seem possible Tiled grids: 1.5 Serendipidity grids 3 Unstructured Conservation