Correctness of the vertical discretization in hydrostatic atmospheric models

This study is about properties of the vertical structure matrices of hydrostatic atmospheric models. The main focus of this research is the influence of these matrices on the well-posedness of vertically discretized initial value problems for linearized hydrostatic atmospheric equations. One of the results obtained states that the vertical structure matrices arising in the usual local vertical discretizations have oscillatory properties, which ensure the positivity of their spectrum and completeness of the set of eigenvectors. In such cases, well-posedness of the initial value problems considered is proved analytically. Another result is a relation between locality of the vertical approximation and well-posedness. Based on numerical experiments it is shown that greater non-locality can lead to ill-posed initial value problems. Copyright (C) 2008 Royal Meteorological Society