A finite‐element scheme for the vertical discretization of the semi‐Lagrangian version of the ECMWF forecast model

摘要: A vertical finite-element (FE) discretization designed for the European Centre Medium-Range Weather Forecasts (ECMWF) model with semi-Lagrangian advection is described. Only non-local operations are evaluated in FE representation, while products of variables physical space. With only to be integrals. An integral operator derived based on Galerkin method using B-splines as basis functions compact support. Two versions have been implemented, one piecewise linear (hat functions) and other cubic B-splines. No staggering dependent employed space, making well suited use advection. The two scheme compared finite-difference (FD) schemes both Lorenz Charney–Phillips linearized model. The give more accurate results than FD phase speeds most gravity waves. Evidence shown that suffer less from computational mode staggering, although temperature geopotential held at same set levels too. As a result, reduce level noise forecasts full They also by about 50% persistent cold bias lower stratosphere present (i.e. operational ECMWF before its replacement version described here) improve transport stratosphere. Copyright © 2004 Royal Meteorological Society