On the positivity of mass in commonly used numerical transport schemes

Abstract Numerical transport schemes used in atmospheric models only approximate the evolution of the real mass continuity equation. The inaccuracies introduced by discretization schemes result, amongst other things, in the appearance of fictitious “holes” in the mass field, i.e. places where the concentration is locally negative. In this article we compare the behaviour of various numerical schemes that are commonly used in atmospheric models, the remedies that are often applied to prevent the appearance of unphysical holes, and their side effects on the evolution of a transported field.

[1]  W. Grabowski,et al.  The multidimensional positive definite advection transport algorithm: nonoscillatory option , 1990 .

[2]  P. Smolarkiewicz,et al.  The multidimensional positive definite advection transport algorithm: further development and applications , 1986 .

[3]  Yasuo Tatsumi,et al.  A Spectral Limited-area Model with Time-dependent Lateral Boundary Conditions and Its Application to a Multi-level Primitive Equation Model , 1986 .

[4]  W. Moxim,et al.  Tracer simulation using a global general circulation model: Results from a midlatitude instantaneous source experiment , 1978 .

[5]  William Bourke,et al.  A multi-level spectral model. I. Formulation and hemispheric integrations , 1974 .

[6]  Philip J. Rasch,et al.  On Shape-Preserving Interpolation and Semi-Lagrangian Transport , 1990, SIAM J. Sci. Comput..

[7]  Richard B. Rood,et al.  Numerical advection algorithms and their role in atmospheric transport and chemistry models , 1987 .

[8]  Roger Daley,et al.  A Baroclinic Finite-Element Model for Regional Forecasting with the Primitive Equations , 1979 .

[9]  P. Rasch,et al.  Two-dimensional semi-Lagrangian trans-port with shape-preserving interpolation , 1989 .

[10]  P. Rasch,et al.  Computational aspects of moisture transport in global models of the atmosphere , 1990 .

[11]  A. Robert.  A Semi-Lagrangian and Semi-Implicit Numerical Integration Scheme for the Primitive Meteorological Equations , 1982 .

[12]  F. Shuman,et al.  An Operational Six-Layer Primitive Equation Model , 1968 .

[13]  P. Smolarkiewicz.  A Simple Positive Definite Advection Scheme with Small Implicit Diffusion , 1983 .