@misc{74893,
  author = {M. Hortal},
  title = {The development and testing of a new two-time-level semi-Lagrangin scheme (SETTLS) in the ECMWF forecast model},
  abstract = {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.},
  year = {1999},
  journal = {ECMWF Technical Memoranda},
  number = {292},
  pages = {17},
  month = {11/1999},
  publisher = {ECMWF},
  address = {Shinfield Park, Reading},
  url = {https://www.ecmwf.int/node/10017},
  doi = {10.21957/ap8qpeghx},
  language = {eng},
}