Accurate pressure gradient calculations in hydrostatic atmospheric models

Abstract

Most models of atmospheric flow which use the primitive equations require a diagnostic equation to determine local total pressure. In hydrostatic models, this equation is the vertically integrated hydrostatic equation. A frequently used approximation to this integration is to hold the temperature constant within model layers yielding a linear proportionality between Op or Mir (Exner’s function) and Az. This procedure yields static pressures with errors on the order of 10−3mb.