  This study corrects the hypsometric equation by restoring the nontraditional
terms to relax the hydrostatic approximation. The nontraditional terms include
one Coriolis term and two metric terms in the vertical momentum equation. The
hypsometric equations with and without the nontraditional correction are used
to calculate the geopotential height of pressure levels using more than 300,000
selected tropical rawinsonde profiles. With westerlies between two pressure
levels, the thickness of the layer increases, which reduces the upward pressure
gradient forces to balance the upward nontraditional Coriolis forces; the
opposite is true for easterlies. Hence, zonal winds are negatively correlated
with traditional geopotential height biases aloft. At 500 hPa, for example,
traditional geopotential height error in the tropical troposphere is on the
order of at least 0.5 m, which is considerable with respect to geopotential
height variability in tropical large-scale flow, on the order of 10 m to 15 m.
