Vertical Wavelengths of Downward Phase Propagating Gravity Waves Determined by Vertical Fluctuation of Idealized Radiosonde Balloons

This paper investigates the limitation in calculating the vertical wavelength of downward phase propagating gravity waves from the vertical fluctuation of idealized radiosonde balloons in a homogeneous background environment. The wave signals are artificially observed by an idealized weather balloon with a constant ascent rate. The apparent vertical wavelengths obtained from the moving radiosonde balloon are compared to the true vertical wavelength obtained from the dispersion relation, both in the no-wind case and in the constant-zonal-flow case. The node method and FFT method are employed to calculate the apparent vertical wavelength from the sounding profile. The difference between the node apparent vertical wavelength and the true vertical wavelength is attributed to the fact that the ascent rate of the balloon and the downward phase speed induce a strong Doppler-shifting bias on the apparent vertical wavelength from the observation records. The difference between the FFT apparent vertical wavelength and the true vertical wavelength includes both the Doppler-shifting bias and the mathematical bias. The extent to which the apparent vertical wavelength is reliable is discussed. The Coriolis parameter has negligible effects on the comparison between the true vertical wavelength and the apparent one.Significance StatementThe purpose of this study is to discuss the Doppler-shifting bias induced by the ascent rate of radiosonde balloon when measuring the apparent vertical wavelengths of downward phase propagating gravity waves from the vertical fluctuation of idealized radiosonde balloons. This is an easily omitted problem. However, it can dramatically affect the gravity wave diagnosis when the ascent rate profile is treated as a quasi-instantaneous data. Further, such uncertainty could lead to remarkable errors in other derived wave propagating properties (e.g., phase velocity, which is the key input parameter in gravity wave parameterization).