On correctness of the vertical discretization in numerical weather prediction models

摘要

Well posedness of the initial value problem for vertically discretized hydrostatic equations used in European Centre of Medium-range Weather Forecasts and Irish Meteorological Service numerical weather prediction models is studied. The problem is reduced to verification of oscillatoriness of the vertical structure matrices, which depend on used vertical discretization. This checking is performed by applying the criterion of total positivity expressed in terms of connected planar networks with nonnegative real weights. The main result is a proof of the correctness of initial value problems for chosen models.