**6. Atmospheric gravity waves in the troposphere**

evaporation of the cloud liquid water and settled down. The pressure jump was generated in the dry sector of the vapour front in the mid-troposphere. The back trajectory analysis of the air particle [39] depicted in **Figure 9** showed that the air particle in the East China Sea during the meteotsunami event came from mainly two or three regions. The warm moist air mainly came from South China Sea, Indochina Peninsula and Bengal Bay. Those air particles moved northeast along with the high-pressure system located in the Philippines, and lifted orographically over the inland area of the South China (region 'SW' and 'S'). Other particles came from upper dry air of northwest Eurasian continent or along with the subtropical jets via Tibetan Plateau (region 'NE' and 'E'). Further analysis in **Figure 10** showed that the anomalous mass of the moist air in the lower troposphere was transported from the tropical regions within 3 days before the meteotsunami event on March 31, 1979. The peak value of the moisture transport in the end of March (~200 kgm/s) was much greater than the peak value in the summer monsoon season (~150 kgm/s). The massive transport of the lower moist air into inland China can be seen especially in the late winter and early spring (February–April) for nearly every year. In the same period, the secondary oscillations larger than 1.0 m in amplitude were

**Figure 10.** The northward component of water vapour flux across the line of South China coasts (22.5N, 105–120E) after the vertical integration between 850- and 1000-hPa isobar surface. Red line indicates the 3-day average from 6-h data in

the year 1979. Blue line indicates the 10-day average of climatic value for 55 years (1958–2012) [26].

**Figure 9.** Air particle distribution into East China Sea. The left panel indicates the analysis area with initial particles located in region X. The middle panel shows the distribution of the individual particles 72 h before the meteorological tsunami over the East China Sea. The colour markers indicate the altitude of each air particles. The right panel indi-

cates the particle proportion in each sector shown in the left panel [26].

24 Tsunami

The atmospheric gravity waves are also one of the typical processes to generate pressure disturbance in the sea level, travelling with a long disturbances. There are two mechanisms supporting such characteristics of the atmospheric gravity wave: wave duct [40] and wave CISK [41]. The stable lower troposphere with an increasing wind in a vertical direction is overtopped with an unstable layer in the mid-troposphere as illustrated in **Figure 11** [10]. The Richardson number Ri

$$Ri = \frac{N^2}{\left(dU \wedge dz\right)^2} \tag{9}$$

is generally used to see the atmospheric stability, where *N* = the Brunt-Väisälä frequency and *U* = horizontal velocity. Such vertical structure reflects the wave energy and traps the gravity waves towards the long distance [40, 42, 43]. The potential for downward or upward propagation of mid-tropospheric internal gravity waves may be assessed from the inequality of the linear gravity wave theory [43, 44].

$$N > \frac{2\pi U}{\lambda} \tag{10}$$

where *λ* = the horizontal wavelength of internal gravity wave. The depth of the wave duct D is described as

$$D = \mathcal{A}\_{\varepsilon} \left( \frac{1}{4} + \frac{1}{2}n \right) \qquad \qquad (n = 0, 1, 2, \dots), \tag{11}$$

where *λz* denotes the vertical wave length. Using the wind speed at critical level *Uc*, the *λz* can be approximated as

$$
\lambda\_{\pm} \approx 2\pi \frac{U\_c - U}{N} \tag{12}
$$

The wave CISK denotes the coupling between the gravity wave and convection. The convergences associated with the gravity wave force the moist convection while convection heating provides the energy for the wave [26, 41, 45].

**Figure 11.** Schematic of the generation and the propagation of the atmospheric gravity wave in the presence of the wave-ducting layer, and the enhancement of the ocean long wave. A case study for widespread meteorological tsunami on Mediterranean and Black Sea, in June 2014 (Šepić et al., 2015) [10].

The large-scale motions with meso-α scale, synoptic scale or monsoon scale provide the structure of wave-ducting layer or wave CISK. In June 2014 event, the expansion of the waveducting layer generates and propagates the atmospheric gravity waves. The synoptic weather pattern and the sea level oscillation in that event are shown in **Figure 12** [10]. According to the Šepić et al. (2015) [10], the synoptic structure can be summarized as follows: first, inflows of warm and dry air from Africa in the low troposphere (~850 hPa); second, a strong south-west jet stream in the middle troposphere (~500 hPa) and the presence of the unstable layer between 600 and 400 hPa isobar [10]. The first pattern appeared at Menorca Island, Spain, in the west of the Mediterranean Sea, and the area of the wave propagation moved eastward [10]. The area of the high wind speed in the middle troposphere was located east of the trough.

The cold or dry sector of the cold or stationary front can satisfy the wave-CISK or wave-duct structure very well. In February 2009 event in the west Kyushu in **Figure 13**, Japan, a train of the pressure wave was generated in the north sector of the stationary front under both mechanisms of wave duct and wave CISK. The warm moist air lifted by the mountain effect in South China mixed with the dry air of the mid-troposphere from the south of the Himalaya mountain range. The mixed air generated the unstable layer in the mid-troposphere and covered above the East China Sea. The trough extended from the Siberia and the subtropical high-pressure system generated the latitudinal convergence over the area of the unstable midtroposphere [26]. The wave length of the pressure waves ranged 30–100 km with the period of 20–60 min including the eigen oscillation mode in various bays in that area.

Multiscale Meteorological Systems Resulted in Meteorological Tsunamis http://dx.doi.org/10.5772/63762 27

The wave CISK denotes the coupling between the gravity wave and convection. The convergences associated with the gravity wave force the moist convection while convection

**Figure 11.** Schematic of the generation and the propagation of the atmospheric gravity wave in the presence of the wave-ducting layer, and the enhancement of the ocean long wave. A case study for widespread meteorological tsuna-

The large-scale motions with meso-α scale, synoptic scale or monsoon scale provide the structure of wave-ducting layer or wave CISK. In June 2014 event, the expansion of the waveducting layer generates and propagates the atmospheric gravity waves. The synoptic weather pattern and the sea level oscillation in that event are shown in **Figure 12** [10]. According to the Šepić et al. (2015) [10], the synoptic structure can be summarized as follows: first, inflows of warm and dry air from Africa in the low troposphere (~850 hPa); second, a strong south-west jet stream in the middle troposphere (~500 hPa) and the presence of the unstable layer between 600 and 400 hPa isobar [10]. The first pattern appeared at Menorca Island, Spain, in the west of the Mediterranean Sea, and the area of the wave propagation moved eastward [10]. The area

The cold or dry sector of the cold or stationary front can satisfy the wave-CISK or wave-duct structure very well. In February 2009 event in the west Kyushu in **Figure 13**, Japan, a train of the pressure wave was generated in the north sector of the stationary front under both mechanisms of wave duct and wave CISK. The warm moist air lifted by the mountain effect in South China mixed with the dry air of the mid-troposphere from the south of the Himalaya mountain range. The mixed air generated the unstable layer in the mid-troposphere and covered above the East China Sea. The trough extended from the Siberia and the subtropical high-pressure system generated the latitudinal convergence over the area of the unstable midtroposphere [26]. The wave length of the pressure waves ranged 30–100 km with the period of

of the high wind speed in the middle troposphere was located east of the trough.

20–60 min including the eigen oscillation mode in various bays in that area.

heating provides the energy for the wave [26, 41, 45].

26 Tsunami

mi on Mediterranean and Black Sea, in June 2014 (Šepić et al., 2015) [10].

**Figure 12.** Propagation of the meteotsunamigenic synoptic pattern of 2014 together with the maximum heights of corresponding sea level oscillations at the times of the meteotsunami events. Left panels are 850 hPa air temperature, middle panels are 500 hPa wind and right panels are distribution of the unstable layer (Ri <0.25) in the mid-troposphere. (Šepić et al., 2015) [10].

**Figure 13.** Weather condition of meteorological tsunami around the cold front on February 25, 2009. The surface weather chart (left), wavy clouds by satellite IR image (middle) and unstable layer covered with the East China Sea (right) [26].
