A Lagrangian Advection Scheme Using Tracer Points

Abstract

ABSTRACT A new quasi-Lagrangian advection scheme with similarities to the so-called Particle-In-Cell methods bas been introduced with the purpose of describing advection processes in atmospheric modelling in an accurate way. The new Full Particle In Cell (FPIC) scheme has been tested and compared with other advection schemes commonly used in atmospheric modelling. The first tests deal with plane passive advection in a non-deforming as well as in a strongly deforming flow. In these cases, the FPIC scheme is compared with a traditional semi-Lagrangian advection method. The new scheme has the advantage of being exact for linear advection and in the case of non-linear advection, much less damping is seen than with the semi-Lagrangian scheme. In order to investigate if the FPIC scheme behaves reasonably in the atmospheric dynamical environment, it has been fully implemented in a shallow water model including orography and with semi-implicit treatment of gravity wave terms. Also in this case, the scheme behaves as well as, or better than, traditional schemes. As it is intended to use the FPIC scheme for advection of water vapour and liquid water in a GCM, a test of advection of a positive definite, sharply varying, passive tracer in the shallow water model has been carried out. For the same reason, the FPIC scheme has also been tested for passive advection on the sphere. It turns out that the scheme also behaves excellently in these cases. Among the advantages of FPIC are: no CFL (Courant-Friedrichs-Levy) criterion limits the length of the time step, the scheme can be formulated so that it is approximately mass conserving and high accuracy is still obtained when the resolution is decreased in order to reduce the computational cost. Furthermore, the scheme is positive definite. The most serious limitation of the scheme is that if demands more memory than traditional schemes.