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The development and testing of a new two‐time‐level semi‐Lagrangian scheme (SETTLS) in the ECMWF forecast model
Author(s) -
Hortal Mariano
Publication year - 2002
Publication title -
quarterly journal of the royal meteorological society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.744
H-Index - 143
eISSN - 1477-870X
pISSN - 0035-9009
DOI - 10.1002/qj.200212858314
Subject(s) - extrapolation , computation , taylor series , series (stratigraphy) , trajectory , lagrangian , noise (video) , mathematics , scheme (mathematics) , nonlinear system , term (time) , range (aeronautics) , computer science , algorithm , mathematical analysis , physics , geology , image (mathematics) , materials science , composite material , paleontology , quantum mechanics , astronomy , artificial intelligence
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 the trajectories and for the nonlinear terms of the evolution equations. Extrapolation in time is used in the original two‐time‐level scheme in order to make it centred in time and therefore second‐order accurate. This time‐extrapolation can lead to instabilities. In the new scheme the secondorder accuracy is achieved by means of a Taylor series expansion to second order around the departure point of the semi‐Lagrangian trajectory thus avoiding extrapolation of the first‐order term. The estimate of the secondorder term in this expansion is obtained by means of a stable time extrapolation from the previous time step and therefore the scheme is named the ‘Stable Extrapolation Two‐Time‐Level Scheme’ or SETTLS. Some cases of noise in forecast fields, arising from an instability of the time extrapolation in the version of the two‐time‐level semi‐Lagrangian scheme used operationally at the European Centre for Medium‐Range Weather Forecasts (ECMWF) between December 1996 and April 1998, are diagnosed; it is shown that the noise can be removed by the use of the SETTLS. Copyright © 2002 Royal Meteorological Society.