An Investigation of the Lunar Semidiurnal Tide in the Atmosphere

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Abstract

Surface observations of the lunar semidiurnal tidal oscillations in geopotential height (at equator: amplitude ≈65 cm, phase lag ≈3O min), temperature (at Batavia: amplitude ≈0.008 K, phase lag ≈46 min), and wind (at Mauritius: amplitude U ≈ 1 cm sec⁻¹, V ≈ 1.2 cm sec⁻¹, phase lags: U ≈ 7⅔, V ≈ 3 hr) are presented. At most locations the tidal oscillation in surface pressure is observed to vary annually such that the amplitude remains relatively constant throughout the year while the phase lag varies so that it reaches maximum values during the months November–February and minimum values during the months May–August [November–February: amplitude (at equator) ≈ 61 cm, phase lag ≈ 1⅓ hr; May–August: amplitude (at equator) ≈ 72 cm, phase lag ≈ ⅓ hr]. The equations of tidal theory with Newtonian cooling are derived starting with the usual equations of dynamic meteorology. Data on the stability of the atmosphere indicate that seasonal variations in mesospheric temperatures act in the summer months to create an increased “barrier” to wave propagation, in the Schrödinger equation sense. Calculations using the empirical atmospheric stability curves, but without Newtonian cooling, give results in reasonable agreement with the observations, both of the annually averaged tidal effects and the annual variation of these effects. The addition of Newtonian cooling acts to disturb the agreement in the annual variations, but this is not taken to be serious as there are many uncertainties in the Newtonian cooling parameter. Calculations of vertical energy flux give results in good agreement with the notion of an annually changing mesospheric barrier. The phase lag in the surface pressure oscillation is shown to be a consequence of the upward energy flux. Finally, a simple analytical study is presented to see the effects of various atmospheric barriers.

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