3:00 PM - 3:15 PM
[MTT43-06] Continuous excitation of atmospheric free oscillation by cumulus heating
★Invited Papers
Keywords:atmospheric free oscillation, cumulus convection, Lamb waves, infrasound
Existence of Broadband Continuous Excitation of the Earth's Atmospheric Free Oscillation
A framework that linearizes the governing equations of the Earth's atmospheric motion, assumes periodicity in the direction of time and longitude, and separates variables in the vertical and latitudinal directions has been used as a framework for the consideration of atmospheric tides and other atmospheric waves (e.g., Chapman and Lindzen 1970). The eigenvalue (equivalent depth) of the vertical structure equation is about 10 km, and the horizontal velocity of the corresponding wave is the speed of sound (about 330 m/s). The horizontal structure equation is known as the Laplace Tidal Equation (LTE), and its modal solutions have been investigated in detail by Longuet-Higgins (1968), and they can be roughly classified into the slow westward propagating "Rossby mode" and the "gravity wave mode" with a large phase velocity. Corresponding to these modes, it has been known that there exist eastward propagating waves called "4-day waves" (zonal wavenumber 2), "5-day waves" and "10-day waves" (zonal wavenumber 1), which are associated with the Rossby mode, and "33-hour waves", which are associated with the global gravity wave mode (Kelvin mode with zonal wavenumber 1). Sakazaki and Hamilton (2020, J.Atmos.Sci), using global atmospheric reanalysis data, further showed that gravity wave modes with wavenumbers up to 10 or more are excited. On the other hand, Nishida et al (2014, Geophys.J.International) analyzed dense barometer data deployed in the eastern United States and found that Lamb waves are constantly excited from wavenumber 20 to about 1200. Lamb waves, which are trapped in the lower atmosphere and propagate horizontally at the speed of sound, correspond to gravity waves when considered globally with LTE, and their vertical structure is exactly the same as the eigenfunctions of the "vertical structure equation" mentioned earlier. Taken together, these results suggest that modes with an equivalent depth of 10 km are constantly excited in the Earth's atmosphere, almost continuously, from global modes with wavenumber of 1 to high wavenumber modes with wavenumber of 1000 or more.
Possibility of excitation by cumulus clouds
In this paper, we assume that cumulus convection is a possible source of excitation of the broadband atmospheric free oscillations described above. The first reason is that cumulus convection is an isolated disturbance with a spatial scale of about 1 km, so it can be a broadband wave source with a spatial range of wavenumber from 0 to 10,000. Second, since cumulus clouds have a lifetime of about one hour and there are large fluctuations in the heating structure even during their life cycle, they can be a broadband wave source with a frequency ranging from zero to several mHz in time.
Excitation of Lamb wave vertical modes by cumulus heating
When the atmosphere is heated, the direct response is the generation of sound waves, and the response after this propagates vertically contributes to the excitation of Lamb waves and the subsequent internal gravity waves Bannon (1995) showed that no surface pressure remains after the hydrostatic adjustment following heating. However, since the atmosphere above the heat source is displaced upward, positive heating results in a positive pressure anomaly as a contribution to the Lamb wave vertical mode. It can be seen that the amplitude can generally be estimated by the pressure response of the atmosphere confined to a vertical region of about scale height.
Estimation of Amplitude
Based on the above discussion, we estimated the heating response of the atmosphere in the vertical layer by referring to the current Earth observation facts about the number and lifetime of cumulus clouds. The results depend on the estimate of the Q-value of the atmospheric free oscillation, but the amplitude of the Lamb wave of Nishida et al (2013) and the global mode of Sakazaki and Hamilton (2020) can be generally explained. The details will be discussed in the day.
A framework that linearizes the governing equations of the Earth's atmospheric motion, assumes periodicity in the direction of time and longitude, and separates variables in the vertical and latitudinal directions has been used as a framework for the consideration of atmospheric tides and other atmospheric waves (e.g., Chapman and Lindzen 1970). The eigenvalue (equivalent depth) of the vertical structure equation is about 10 km, and the horizontal velocity of the corresponding wave is the speed of sound (about 330 m/s). The horizontal structure equation is known as the Laplace Tidal Equation (LTE), and its modal solutions have been investigated in detail by Longuet-Higgins (1968), and they can be roughly classified into the slow westward propagating "Rossby mode" and the "gravity wave mode" with a large phase velocity. Corresponding to these modes, it has been known that there exist eastward propagating waves called "4-day waves" (zonal wavenumber 2), "5-day waves" and "10-day waves" (zonal wavenumber 1), which are associated with the Rossby mode, and "33-hour waves", which are associated with the global gravity wave mode (Kelvin mode with zonal wavenumber 1). Sakazaki and Hamilton (2020, J.Atmos.Sci), using global atmospheric reanalysis data, further showed that gravity wave modes with wavenumbers up to 10 or more are excited. On the other hand, Nishida et al (2014, Geophys.J.International) analyzed dense barometer data deployed in the eastern United States and found that Lamb waves are constantly excited from wavenumber 20 to about 1200. Lamb waves, which are trapped in the lower atmosphere and propagate horizontally at the speed of sound, correspond to gravity waves when considered globally with LTE, and their vertical structure is exactly the same as the eigenfunctions of the "vertical structure equation" mentioned earlier. Taken together, these results suggest that modes with an equivalent depth of 10 km are constantly excited in the Earth's atmosphere, almost continuously, from global modes with wavenumber of 1 to high wavenumber modes with wavenumber of 1000 or more.
Possibility of excitation by cumulus clouds
In this paper, we assume that cumulus convection is a possible source of excitation of the broadband atmospheric free oscillations described above. The first reason is that cumulus convection is an isolated disturbance with a spatial scale of about 1 km, so it can be a broadband wave source with a spatial range of wavenumber from 0 to 10,000. Second, since cumulus clouds have a lifetime of about one hour and there are large fluctuations in the heating structure even during their life cycle, they can be a broadband wave source with a frequency ranging from zero to several mHz in time.
Excitation of Lamb wave vertical modes by cumulus heating
When the atmosphere is heated, the direct response is the generation of sound waves, and the response after this propagates vertically contributes to the excitation of Lamb waves and the subsequent internal gravity waves Bannon (1995) showed that no surface pressure remains after the hydrostatic adjustment following heating. However, since the atmosphere above the heat source is displaced upward, positive heating results in a positive pressure anomaly as a contribution to the Lamb wave vertical mode. It can be seen that the amplitude can generally be estimated by the pressure response of the atmosphere confined to a vertical region of about scale height.
Estimation of Amplitude
Based on the above discussion, we estimated the heating response of the atmosphere in the vertical layer by referring to the current Earth observation facts about the number and lifetime of cumulus clouds. The results depend on the estimate of the Q-value of the atmospheric free oscillation, but the amplitude of the Lamb wave of Nishida et al (2013) and the global mode of Sakazaki and Hamilton (2020) can be generally explained. The details will be discussed in the day.