Nontraditional hypsometric equation

TL;DR

This paper improves the hypsometric equation by including nontraditional terms, leading to more accurate geopotential height calculations from tropical rawinsonde data, revealing significant biases related to zonal wind direction.

Contribution

It introduces a corrected hypsometric equation with nontraditional terms, enhancing the accuracy of geopotential height estimations from tropical profiles.

Findings

Nontraditional terms significantly affect geopotential height calculations.

Zonal wind direction influences traditional geopotential height biases.

Errors at 500 hPa can reach at least 0.5 m, impacting tropical flow analysis.

Abstract

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.