On the Application of Trajectory Methods in Numerical Forecasting

Abstract

On the basis of a comparison between the results so far obtained by the usual numerical methods in physical weather prediction and the graphical methods it is likely that certain defects in the present forecast methods are due to the Eulerian technique. The possibilities for the use of a quasi-Lagrangian technique are investigated, and it is found that such a technique is possible and becomes especially simple when combined with a space-smoothing which eliminates the shorter fast moving waves in the spectrum. The Lagrangian method of computation is described in the barotropic case and also for a simplified two-parameter baroclinic model.

Conservative Semi-Lagrangian Scheme Applied to One-Dimensional Shallow Water Equations

“…Since 1959, semi-Lagrangian schemes have been studied by Wiin-Nielsen (1959) and many other scientists. Most semi-Lagrangian schemes employing backward trajectories have been reviewed by Staniforth and Côté (1991).…”

Equivalence of Semi-Lagrangian and Lagrange-Galerkin Schemes Under Constant Advection Speed

“…Schemes based on characteristics for hyperbolic PDEs have been proposed by Courant-Isaacson-Rees in [3] and have prompted the development of a number of specific techniques, including Semi-Lagrangian (SL) methods, which have first appeared in the framework of Numerical Weather Prediction problems (see the pioneering paper [18] and the review [15]). SL methods have another well estabilished field of application in plasma physics, where their use has been suggested in [2] and widely studied since (see, e.g., [1,8,16]), and their popularity is also growing in other fields such as general Computational Fluid Dynamics (CFD) problems, Hamilton-Jacobi equations and level-set methods [7,17], conservation laws [13].…”

3D ALE Finite-Element Method for Two-Phase Flows With Phase Change

“…The semi-Lagrangian method has its own history dating from the end of the 1950's ( [98]) and the beginning of the 1960's ( [49] and [79]). However, the use of such a methodology for modeling fluid flow problems came later in the 1980's through the work of [78] and [73], in which predominately convective problems were investigated.…”