|Title||The development and testing of a new two-time-level semi-Lagrangin scheme (SETTLS) in the ECMWF forecast model|
|Year of Publication||1999|
|Secondary Title||Technical Memorandum|
|Place Published||Shinfield Park, Reading|
|Type of Work||Technical Memorandum|
A new treatment of the two-time-level semi-Lagrangian scheme is presented which avoids extrapolation in time of the velocities used for the computation of trajectories and for the non-linear terms of the evolution equations. Extrapolation in time is used in the original two-time-level scheme in order to make it centered in time and therefore second-order accurate. This time extrapolation can lead to instabilities. In the new scheme the second order accuracy is achieved by means of a Taylor series expansion to second order the departure point of the semi-Lagrangian trajectory thus avoiding extrapolation of the first-order term. The estimate of the second order term in this expansion is obtained by means of a stable time extrapolation from the previous time step and therefore the scheme is named "Stable Extrapolation Two-Time-Level Scheme" or SETTLS. We diagnosed some cases of noise in forecast fields as arising from an instability of the time extrapolation in the version of the two-time-level semi-Lagrangian scheme used operationally at ECMWF between December 1996 and April 1998 and show that the noise can be removed by the use of the SETTLS scheme.