The mathematical equivalence of multi-level and vertically integrated numerical forecasting models

It is shown that, if the equations for an n-level model are averaged, the resulting equations have mathematical forms which, under certain conditions, are identical with those of the vertically integrated n-parameter model. The implications for the temperature and ɷ-profiles are discussed in order to achieve exact mathematical equivalence. A physically consistent vertically integrated model yields temperature and w-profiles which depart from those required for mathematical exactness, yet appears to lead to more realistic results.