Using the technique described above, the parameters of 98 periodic waves were estimated. Figure 2 shows a statistical histogram of the observed horizontal wavelengths. Most of the waves had horizontal wavelengths (λH) between 120 and 160 km. The mean observed horizontal wavelength was 144.8 km with a standard deviation of 24.8 km. It is important to note that no wave had wavelengths either greater than 220 km or less than 60 km. Note that, using this technique, it is possible to observe periodic waves with horizontal wavelengths as long as 1500 km in the OI6300 images, which is the size of the projected area. Otherwise, theoretically gravity waves with wavelengths as short as the spatial resolution could be observed, but the shortest one had horizontal wavelength of ∼ 67 km.

Figure 3 shows the observed periods (τ) for the quasi-monochromatic periodic waves. Most of them ranged from 10 to 35 min, indicating that they had short periods as compared to the medium-scale gravity waves observed in the MLT region . The mean period of these waves was 21.8 min with a standard deviation of 10.6 min. No wave had a period shorter than 5 min, and only two of them had periods larger than 45 min. The lower limit makes sense, given that gravity waves cannot have intrinsic periods shorter than the Brünt–Väissälä or buoyancy period, which is ∼ 8–9 min at that altitude .

Using the periods (τ) and horizontal wavelengths (λH) from Figs. 2 and 3, the observed horizontal phase speeds (cH=λH/τ) were estimated, and the results are shown in Fig. 4. Most of the waves had phase speeds between 60 and 150 m s-1, although fewer had much larger phase speeds (up to 210 m s-1). The mean phase speed was 109.0 m s-1 with a standard deviation of 37.5 m s-1. Note that the phase speed is different from the intrinsic phase speed, from which the background wind has been subtracted e.g.,.

Comparing the wave parameters estimated in this work to the results from , one can note that the wavelengths and periods were shorter than those from Arecibo, and the periodic waves observed over São João do Cariri are faster.

The present results indicate that the periodic waves observed in the OI6300 airglow emission were faster than the waves observed in the OH layer in the MLT region over Brazil from 2000 to 2004 and during the Southern Hemisphere spring months in 2005 and in 2002 . Fast gravity waves are less susceptible to dissipative filtering by molecular viscosity, which is the main filtering mechanism in the thermosphere. In the thermosphere, kinematic viscosity and thermal diffusivity damp gravity waves individually, depending on their intrinsic frequency, vertical wavelength, and intrinsic phase speed e.g.,. However, the spatial characteristics of the gravity waves (wavelength) should be taken into account. When a gravity wave propagates into the thermosphere, the kinematic viscosity and thermal diffusivity act in order to produce damping for the wave e.g.,.

ray-traced many gravity waves from the troposphere and lower thermosphere into the thermosphere, and determined their propagation characteristics and dissipation altitudes. She found that horizontal wavelengths longer than 100 km are necessary in order for gravity waves to reach z≥ 200 km Fig. 9b from. This is consistent with our results here (shown in Fig. 4). Additionally, that work shows that the vertical wavelengths must be at least 40 km. This is also consistent with our results, because a long vertical wavelength is necessary in order for a gravity wave to be observed in the OI6300 airglow emission. In particular, a gravity wave must have λz≫ 40 km in order to be observed in the OI6300 emission layer, since the OI6300 emission layer thickness is ∼ 80 km .

In general, a gravity wave reaching z>200 km must have an intrinsic phase speed of at least 100 m s-1 . Since the wind is unknown, the intrinsic phase speeds could not be calculated. However, our range of observed phase speeds as shown in Fig. 4 is consistent with this result. Neither medium-scale nor small-scale (bands and ripples) gravity waves observed in the MLT region by airglow images in previous works have the same necessary period and wavelength patterns simultaneously. This suggests that the sources of the gravity waves observed in the OI6300 images are likely different from the sources of the MLT gravity waves. For example, these gravity waves may have their sources associated with thermospheric body forcing or heating in the lower thermosphere . Some of these waves may even be generated by the Perkins mechanism.

Figure 5 shows the propagation direction of all of the 98 periodic waves. A clear anisotropy of the propagation direction can be noticed. It seems that there are two preferential propagation directions: north and southeast. Most of the gravity waves propagated to the northeast, north or northwest. Another group of waves propagated to the southeast. Periodic waves propagating southwestward, westward and eastward were rare.

If most of these waves are assumed to be gravity waves (due to their spectral characteristics discussed in the Sect. 3.1), there are two main factors which could create this observed anisotropy. The first factor is that gravity waves are filtered by the winds in the lower to mid-thermosphere . Combined with dissipative filtering, this process mainly preserves those gravity waves propagating opposite to the neutral wind. Those gravity waves propagating in the same direction as the wind have smaller λz, which causes the effects of molecular viscosity to be enhanced, thereby causing the waves to dissipate . The second factor is that the source of the gravity waves may be anisotropic (either for each individual source or for the location of the sources relative to the observation location).

reported a long period study on wave structures observed in OI6300 airglow images over Indonesia. They found that the dominant propagation direction is to the south, which does not agree with the present observations. They also suggested that the origin of these waves was due to the penetration of gravity waves in the thermosphere.

MSTIDs generated by the Perkins instability can be observed at mid- and low latitudes during nighttime. They usually propagate in the Perkins phase front normal direction . A portion of the waves observed in this work had this characteristic. According to , even MSTIDs generated at high latitudes can reach the tropics if they propagate along this direction. Observations have confirmed this e.g.,.

For our data set here, it is not likely that the Perkins instability or the sporadic E layer instability was the main mechanism for generating the observed waves, because most of them are not heading in the Perkins phase front normal direction. There are few waves propagating eastward and westward, which could easily be explained by gravity wave source, wind and dissipative filtering processes. There is a set of waves that has Perkins' phase front direction, i.e., the waves which propagated to the southeast; however, the observations close to the Equator exclude the possibilities of these waves being generated by the Perkins process. On the other hand, the few waves propagating to the northwest could have their origin in the Perkins instability at midlatitudes, but this cannot be confirmed by using only airglow images.

The propagation direction of gravity waves observed in the mesopause region, at the same site of observation , revealed a distinct behavior, primarily, the large gravity waves, which have a well-defined propagation direction to the east and northeast. This was another reason to believe that the present waves must have their origin in the lower thermosphere.

The present data have a long period of observation, such that the seasonality and solar cycle dependence on the wave activity could be studied. Figure 6 shows the occurrence of the waves and their respective propagation direction as a function of the months. Most of the periodic waves were observed from April to October. Waves with azimuth between 337.5 and 22.5∘ were considered to be propagating northward, waves with azimuth between 22.5 and 67.5∘ were considered propagating northeastward, etc. For example, periodic waves propagating northward and northeastward only appeared during the winter months. Waves propagating southward were observed in almost all months, but only for a few events. Even though the number of observed cloudless nights (as shown at the top of the bars in Fig. 6) was reduced in the first half of the year, this can not be the reason for the present seasonality because there were more nights of observation in September, October, November and December, and few waves were observed as well.

A simple analysis of the thermospheric wind pattern is useful for understanding those results. Gravity waves propagating in the same direction as the wind may easily reach critical levels and be absorbed by the background atmosphere e.g.,. According to , the meridional wind in Brazilian equatorial region, derived from a Fabry–Pérot interferometer located at the Cajazeiras Observatory (38.56∘ W, 6.89∘ S), blows toward the south during the Southern Hemisphere winter months (June, July, and August), primarily at the beginning of the night. This is the period of the higher occurrence of the periodic waves, and most of them are propagating against the background wind; i.e., they propagated to the north. Moreover, none of the waves propagating northward were observed during the summer months (December, January, and February), when the wind was predominately blowing to the north.

In order to investigate the possible effect of solar activity on the occurrence of these waves in the thermosphere, the solar flux F10.7 cm is plotted together with the monthly occurrence of the wave events in Fig. 7. Again, the data cover almost an entire solar cycle. It seems that the occurrence of periodic waves depends on the solar activity. However, this occurrence rate does not strictly follow the solar cycle in the years 2000, 2005 and 2007. It is important to observe that in 2000, 2002 and 2006 there were 41, 75 and 42 nights observed, respectively; i.e., there were few observed nights compared to the closer years. Periodic waves observed in the OI6300 for the Northern Hemisphere were more common during the winter as well . Small-scale gravity waves, observed in the MLT at São João do Cariri , were also observed more frequently during the winter.

The magnetic activity during the time of observation is shown in Fig. 8, and most of the observed periodic waves had durations shorter than 1.5 h (not shown here). These periodic waves were mostly observed during quiet geomagnetic conditions, and the number of wave events was fairly independent of Kp for Kp =0 to 5. This suggests that these events occurred predominately during the low magnetic activity. Thus, geomagnetic activity does not appear to be an important factor for observing these wave structures in the OI6300 airglow images.