The frequency of MW events revealed by the airglow imaging observations

We expected that numerous MWs would be induced by the mountainous area located to the west of the observation site, and that these MWs would propagate to the upper mesosphere. However, only four possible MW events were identified from the airglow observations over a period of approximately 1 year and 8 months (from May 2018 to December 2019).

We consider that there are two possible reasons for the low number of MWs observed in our study. First, although MWs may be induced by the mountainous area around Mt. Fuji, their vertical propagation may be impeded by the presence of a critical level and/or a turning level on the ray path. Second, fewer MWs are induced by the mountainous area around Mt. Fuji than in other mountainous areas.

We referred to the MERRA-2 (MERRA-2 tavg3_3d_asm_Nv: 3d, 3-Hourly, Time-Averaged, Model-Level, Assimilation, Assimilated Meteorological Fields V5.12.4) reanalysis data (Gelaro et al. 2017) to verify the wind fields on the days when the stationary structures were observed. The spatial resolution of the meteorological fields is 0.5° × 0.625° and the time interval is 3 h. We checked for the presence of a critical level in the horizontal wind profile in the direction perpendicular to the line of the wavefront for each event. This verification was conducted at altitudes ranging from 1,000 m to the upper limit of MERRA-2 (60 km) from the ground.

It was confirmed that the wind field during three events (2 June 2018, 1 February, and 15 December 2019) all had a critical level in this altitude range. This finding implies that these stationary structures were not a MW that was propagating from the mountains near the observation site. On the other hand, the wind profile during an event on 6 January 2019 had no critical level. The wind direction during the event was eastward from the lower layer to an altitude of 60 km. The horizontal wavelength of the event was about 50 km and the highest background wind speed during the event was about 50 m/s at an altitude of about 10 km. The intrinsic period of the wave at that altitude was about 1,000 s, so there was also no turning level. The wind condition allowed the vertical propagation of a MW. Figure 10 shows the horizontal wind speed component, U [m/s] projected in the direction of the wind at an altitude of 1,000 m (the red line shows the mean horizontal wind data from 21:00 to 27:00 JST on 6 January 2019). As shown in Fig. 8, January 2019 was the month with the longest period of clear skies in the entire observation period; the number of days that had clear skies for at least 2 h was 22 days. On these 22 days in January 2019, the nightly mean (18:00–27:00 JST) wind was projected in the wind direction at an altitude of 1,000 m from the ground (black lines in Fig. 10). Further, conditions on 13 of these 22 days were favorable for the vertical propagation of MW into the upper atmosphere (at least up to 60 km). Moreover, the wind profile on 6 January 2019 (red line) indicated the presence of highly suitable conditions during this period. Nevertheless, only one MW event was observed during this month.

Fig. 10
figure10

Horizontal wind speed component, U [m/s], projected in the wind direction at an altitude of 1,000 m from the ground. The red line shows the mean horizontal wind data from 21:00 to 27:00 JST on 6 January 2019. Black lines show the nightly mean (18:00–27:00 JST) wind profiles projected in the wind direction at an altitude of 1000 m from the ground on 22 clear nights in January 2019

In the same manner, wind fields were checked for the rest of the observation period. The results showed that favorable conditions for the vertical propagation of MWs occurred on 28 nights over the 20 months of the observation period. Like the event on 6 January 2019, a MW with a wave vector in the east–west direction and a wavelength of about 50 km may propagate vertically in winter. However, no other MW events were observed over the Kanto area in 2018 and 2019.

Based on the obtained findings, we focused on the second hypothesis, i.e., fewer MWs are induced by the mountainous area around Mt. Fuji than in other mountainous areas, to explain the unexpectedly low number of MW events in the airglow layer. We have verified the wind profile up to 60 km (the upper limit of MERRA-2). There is an unchecked region between z = 60 km and z = 85 km (height of the airglow layer). However, horizontal wind through this region in January is likely to be eastward according to long-term observations of mesospheric wind by using radars. The peak altitude and the amplitude of the zonal wind (mesospheric jet) in January are 70–75 km and + 40 m/s, respectively (Namboothiri et al. 1999). Zonal wind above the peak altitude gradually decreases to + 20 m/s till airglow height. Thus, the mean wind profile in January would increase in the eastward direction above 60 km. The typical amplitudes of diurnal and semidiurnal tides are in order of 5–15 m/s in January (Igarashi et al. 2002). Thus, zonal wind between the gap region should stay eastward in January if the typical wind field and amplitudes of tides are assumed. We therefore employed a simple proxy to explain the generation frequency of MWs in the mountainous area around Mt. Fuji in the next section.

Simple proxy to assess the frequency of MW excitation

When MWs are induced, wavy clouds, such as those shown in Fig. 11, are frequently generated on the leeward side of the mountainous area. Such clouds form when the winds in the lower atmosphere that are moving toward the orographic source contain sufficient water vapor to be saturated. These clouds have been observed frequently over Japan by the GMS-8 satellite (Bessho et al. 2016). However, if the atmosphere is dry, then there is a high possibility that wavy clouds will not appear, even if MWs are induced. Therefore, the absence of wavy clouds does not mean that MWs are not being induced. The formation of wavy clouds indicates that mountain-crossing airflow has occurred. Therefore, in this study, we assumed that MWs are induced whenever wavy clouds were formed on the leeward side of the mountains (e.g., see Fig. 11). In other words, we used the formation of wavy clouds as a proxy for the induction of MWs.

Fig. 11
figure11

Wavy clouds detected over the Tohoku area, Japan at 3:00 UT on June 22, 2018 by GMS-8

In this study, “wavy clouds” are defined as a set of three or more clouds oriented in parallel rows that are generated in the vicinity of mountainous areas. We examined the generation frequency and the spatial distribution of these wavy clouds over Japan by analyzing and visually checking color images acquired by GMS-8 in 2018. Specifically, we divided image data for Japan (3301 pixels × 2701 pixels) into smaller images (300 pixels × 300 pixels, i.e., 300 km × 300 km) and then checked if there were wavy clouds in each area. When wavy clouds were detected in a sub-image, we further subdivided the image into smaller sub-images (100 pixels × 100 pixels, i.e., 100 km × 100 km). The reason for subdividing the image into 100 km × 100 km sub-images was to investigate the generation and distribution of wavy clouds at a high spatial resolution. In addition, the direction of the wavefront, θ, and the distance between two adjacent clouds that make up a wavy cloud, i.e., the horizontal wavelength, λ, were calculated. Appendix 1 shows a detailed explanation of the procedure for deriving θ and λ.

Wavy clouds were typically stable and were continuously observed at the same location for several hours. Although the GMS-8 color image is acquired over 2.5 min, we analyzed the image data acquired every hour (taken at 9:00, 10:00, 11:00 … JST) during the day to simplify the analysis. When wavy clouds were detected in the same area in successive images, it was considered that the image represented the same event. The number of days when wavy clouds were observed was then counted for each sub-image (100 km × 100 km).

Frequency of wavy clouds over Japan

We analyzed GMS-8 color images acquired from January 2018 to December 2018 to identify wavy clouds over Japan. Figure 12a shows the occurrence frequency and spatial distribution of wavy clouds over Japan in this period. The color scale represents the number of days during which wavy clouds were observed. Wavy clouds were frequently observed over Hokkaido and the Tohoku region. Focusing on the Tohoku region, the area with the highest frequency was 79 days in 248 non-totally overcast days (Fig. 12b). In contrast, even over the highest area of the Kanto region, which is also within the FOV of our airglow imager, wavy clouds were detected only on 21 days in 239 non-totally overcast days. Furthermore, in most areas around the Kanto region, wavy clouds were detected only during approximately 10 days (Fig. 12c). These results showed that the occurrence frequency of wavy clouds differs markedly among regions, even though there are numerous mountainous areas throughout Japan.

Fig. 12
figure12

Number of days with wavy clouds in 2018 a over Japan and the surrounding area, b Tohoku region, and c Kanto region

The MERRA-2 data were used to calculate the wind velocity at an altitude of 1000 m from the ground at the center of each area and used as the background wind. Using this data set, we examined the angle between the wavefront direction and the background horizontal wind direction. Figure 13a shows the total occurrence frequency of the number of events with wavy clouds that were enumerated using this angle. The findings showed that more than 75% of wavy clouds had an angle ≥ 60°. The direction of the phase line of the wavy clouds was considered to reflect the orientation of the mountain ridgeline. Therefore, it was expected that MWs are frequently induced in regions where the angle between the direction of the background horizontal wind and the mountain ridgeline are ≥ 60°. A positive correlation was observed between the wavelength of the wavy clouds and the background wind speed (Fig. 13b). This relationship resembles the features of topographical wavy clouds reported by Fritz (1965). Although wavy clouds can be generated by a variety of mechanisms, i.e., not only by winds flowing over mountains but also by air masses colliding, frontal systems, convection, and wind shear, many of the wavy clouds detected in this study are likely to be caused by MWs.

Fig. 13
figure13

a Distribution of occurrence frequency of wavy cloud events enumerated based on the angle between the direction of the phase line of the wavy clouds and the background wind direction. b Relationship between the background wind speed at the altitude of 1000 m from the ground and the wavelength of wavy clouds detected over the Tohoku region

Relationship between topography and background wind in the lower atmosphere

The difference in the number of MWs generated over each region is considered to be the result of the interaction between topography and the synoptic horizontal wind field in the lower layers of the atmosphere. We examined the relationship between topographical features and the horizontal wind field by using geographical elevation data and meteorological reanalysis data. In this study, using the PNG Elevation Tile provided by the Geospatial Information Authority of Japan, the orientation of the mountain ridgeline (θ’) was derived from the elevation data by the method shown in Appendix 2. The orientation of the mountain ridgeline is expressed as 0° ≤ (theta ^{prime})≤ 180° (θ’ = 0° represents that the mountain ridgeline faces east-west, and the angle increases counterclockwise).

We used MERRA-2 reanalysis data to examine the horizontal wind directions in the lower layer of the atmosphere. We adopted this wind field as a synoptic wind field. The wind velocity at an altitude of about 1000 m from the ground at the center of each elevation tile was calculated using these data. We defined the wind direction as being 0° when the wind blows eastward, with the angle increasing counterclockwise.

The acute angles between the horizontal wind directions and the direction of the mountain ridgelines (θ′) that were deduced using the above method were calculated for the entire world; we defined this angle as α. As mentioned in section “Frequency of wavy clouds over Japan”. 60° ≤ α ≤ 90° is considered to be favorable for inducing wavy clouds, i.e., over-mountain airflow, which is the primary source of MWs. Figure 14 shows the annual ratio, P, which satisfies the condition, 60° ≤ α ≤ 90° around Japan. Wind data at 10:30, 13:30, and 16:30 JST were used for this calculation because we wanted to compare the findings against the wave cloud occurrence frequency, which is derived from GMS-8 color images acquired during the day. The isolated data points surrounded by zero are omitted from this plot. The findings showed that these areas were highly consistent with the observed wavy cloud counts shown in Fig. 12. High values were clearly observed in the Tohoku and Hokkaido regions, and low numbers were clearly observed around the Kanto region.

Fig. 14
figure14

Annual occurrence of the condition satisfying 60° ≤ α ≤ 90°. The annual occurrence of 60° ≤ α ≤ 90° was calculated using 2920 wind values. The size of each cell was 40 km × 40 km. This value indicates the ratio for which favorable conditions occur for the induction of wavy clouds

The findings presented in Fig. 14 are consistent with the distribution of the occurrence frequency of wavy clouds. The simple proxy, (alpha), is considered to be well suited for predicting MW hotspots around the world. We estimated the global distribution of α in the same manner that was used to produce Fig. 14 and present the results in Fig. 15. The range of world elevation data used to derive α was between 70.6° S and 70.6° N and 180.0° W and 180.0° E. Importantly, all 3-h average wind data (8 wind values/day) are used in this calculation. Colored plots were observed in all of the major mountainous areas around the world (Fig. 15). For example, numerous colored plots were shown in the Andes and Antarctic Peninsula regions (surrounded by red circles in Fig. 15), which are well known sources of MWs. However, the findings showed that major mountainous areas are not “permanent” hot spots for wavy clouds. Indeed, the annual ratio of α in these regions being 60° ≤ α ≤ 90° is about 25–50%. In the high and mid-latitudes of the Northern Hemisphere, there are many locations where the ratio is > 25%, which is as high as that in the MW hotspots. In low-latitude regions, such as Mexico, northern Africa, southern India, and Southeast Asia, there are regions where the ratio is > 50%. Importantly, this plot merely shows the distribution of potential wavy cloud hot spots, i.e., the locations at which the active induction of MWs by over-mountain airflow may occur. Thus, it will be important to confirm the actual frequency of MWs being propagated into the upper atmosphere at these sites by further observations.

Fig. 15
figure15

Same as Fig. 14, except that the map shows the distribution of (alpha) at a global scale. The Andes Mountains and the Antarctic Peninsula are indicated by red circles

Comparison with model results

Sato et al. (2009) examined the origins of mesospheric gravity waves and the associated vertical flux in zonal momentum using a high-resolution global spectral climate model (KANTO model). Their model resolution was T213 (triangular truncation at wavenumber 213, which corresponds to about 60 km) in the horizontal direction and 300 m in the vertical direction. The horizontal wavelength resolved in the KANTO model is ≥ 188 km (Watanabe et al. 2008). Momentum flux is well suited for use as a diagnostic tool for estimating the effects of gravity waves because it is conserved, unless wave generation and/or dissipation occur (Eliassen and Palm 1961). Comparing their results with our Fig. 15 shows that the findings of the two studies are in good agreement in the Andes and the Antarctic Peninsula (red circles) where the effects of topographic gravity waves are dominant. On the other hand, Fig. 15 also shows that there are numerous small-scale (~ 80 km) hot spots in the mid-latitude regions of the Northern Hemisphere. The effect of such small areas on the atmospheric circulation is difficult to estimate in model calculations due to the limitations imposed by the spatial resolution of most models. However, we consider that the total contribution of these small areas is likely to be larger than that estimated in the study of Sato et al. (2009). Therefore, we expect that if the MWs that are induced in these small areas can propagate to the upper mesosphere, the total effects of those small excitation sources on circulation in the middle atmosphere are not negligible. In future work, we will investigate the propagation process of MW from small terrains and its impact on the upper atmosphere.

It is therefore considered necessary to conduct observations in order to verify how many MWs excited by such small areas can propagate to the upper mesosphere.

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