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Toward atmospheres without tops: Absorbing upper boundary conditions for numerical models
Author(s) -
Rasch Philip J.
Publication year - 1986
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.49711247415
Subject(s) - mathematics , nonlinear system , context (archaeology) , boundary value problem , equations of motion , mathematical analysis , physics , classical mechanics , geology , paleontology , quantum mechanics
The appropriate upper boundary condition (UBC) formulation for the dynamical equations used in atmospheric physics is discussed in terms of both theoretical and computational aspects. The previous work on the UBC formulation is reviewed in the context of a linear mid‐latitude primitive equation (PE) model. A new technique for constructing the UBC is introduced. The technique depends upon the existence of analytic solutions to simplifications to the equations of motion. These analytic solutions are used to construct the exact radiation UBCs (often used in tidal theory and studies of the upper atmosphere) which are non‐local in time and space. Approximate UBCs, which are local in time, are formed through rational approximations to the exact radiation UBCs. The technique is demonstrated to be effective for both Rossby and gravity modes. The UBC is tested for computational problems initially in the linear PE model, and subsequently in a forced, damped nonlinear quasi‐geostrophic model.