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2. Determination of potential energy (Ep) from GPS/MET profiles
We have extracted fluctuating components of temperature, T’, from a single GPS/MET profile by applying a high-pass filter with a cutoff at 10 km. We also calculated N2 by differentiating the temperature profile for adjacent three heights. As the GPS/MET profiles are already low-pass filtered in order to reduce noise, where the cut-off of the filter is tuned to pass phase variations of the GPS signal corresponding to vertical scale of 2 to 3 km in the stratosphere and approximately 200 m in the lower troposphere [Rocken et al., 1997]. Accordingly, T’ in the stratosphere consists of temperature fluctuations having a vertical scale between 2-3 km and 10 km. Then, we have calculated the temperature variance, and estimated the potential energy Ep=1/2(g/N)2(T’/T)2 by using the observed N2. We have noticed that the enhanced amplitudes of T’ above about 45 km are unrealistically large. Therefore, we have restricted the maximum height range of the analysis below about 45 km.
2.1 Comparison of Seasonal Variations of Ep and Ek from GPS/MET and ST Radar Data
Using GPS/MET data, we have determined the monthly mean values of Ep in a height range of 15-20 km around the MU radar in Shigaraki, Japan (34.9oN, 136.0oE), and the ST radar at the White Sands Missile Range, New Mexico (32.4oN, 106.4oW) [Tsuda et al., 2000; Nastrom et al., 2000]. Then, we have compared the seasonal variations of Ep with the climatological behavior of the kinetic energy Ek due to gravity waves obtained from long-term observations with MU and WS in 1985-1989 and 1991-1996, respectively. We have found a good consistency of the seasonal variations between Ep and Ek with an enhancement in winter months.
It is noteworthy that the ratio of Ep to Ek agrees reasonably well with a theoretical prediction assuming linear gravity waves, although the difference in the vertical and horizontal resolutions between GPS/MET and the MU radar measurements should be investigated in more detail. These comparisons imply that the utilization of the GPS/MET profiles in the study of stratospheric gravity wave activity has been verified at these specified radar sites.
2.2 Global Distribution of Ep at 20-30 km in November-February.
We have analyzed distributions of Ep as functions of latitude, longitude and seasons between 15 and 45 km. We have separated a year into four seasons, that is, March to April, May to August, September to October, and November to February. Then, we have calculated Ep from the individual GPS/MET temperature profiles, collected during April 1995 and February 1997.
First, we have determined the latitude-longitude distribution of Ep in the 20-30 km height region in northern hemisphere winter months (from November to February), when the largest number of GPS/MET data was collected (a total of 4,569 data out of 10,853). (see Plate 1 of Tsuda et al. [2000]; or Fig. 1 on page VIII of SPARC Newsletter No. 13, 1999). Note that only few data points were obtained around tropical Africa, and a larger amount of data was collected at middle and high latitudes due to the configuration of the satellite orbits and the distribution of the ground reference sites. Large Ep values (exceeding 6 J/kg) are mostly detected at low latitudes from 25oN to 25oS centered around the equator, and they are particularly enhanced over the regions where active convection is expected, such as over the Indonesian archipelago, the Indian ocean, Eastern Atlantic Ocean, and South America. This result strongly suggests that atmospheric waves are actively generated by tropical convection. The Ep values at midlatitudes (higher than 30o) are generally larger in the northern (winter) hemisphere. However, the Ep values at low latitudes could partially be contributed by equatorial waves that add a zonally symmetric bias.
We have also analyzed longitudinal distributions of Ep at 20-30 km during November and February. Since we are interested in the differences in Ep between continents and oceans, considering the orographic effects, we have focused on a latitude band from 30oN to 60oN where the topography can be classified into continents (65o-130oW and 0o-145oE) and oceans (0o-65oW and 130oW-145oE). There is a tendency for Ep to be larger over continents than oceans. In particular, Ep was enhanced over North America, while it was depressed in the central Pacific. These land-sea contrasts in Ep could be attributed to the effects of mountain lee waves caused by an interaction between topography and surface winds [Tsuda et al., 2000].
2.3 Latitude Distribution of Ep at 15-45 km
We have selected a height range between 15 km and 45 km, and defined five overlapping height regions with a 10 km thickness starting from 15 km and an increment of 5 km. It is noteworthy that the noise on the L2 band of GPS signals considerably increased when anti-spoofing (A/S) encryption of the GPS signals was turned on [Rocken et al., 1997]. Then, effects of ionospheric correction produce artificial fluctuations in the GPS/MET temperature profiles, which could be recognized down to about 30 km. Therefore, we use here only data during prime times under A/S-off conditions for a study of the height variations of Ep distributions. Fig. 1 shows latitudinal variations of Ep in the five altitude ranges, where individual Ep values are averaged every 10o in 18 latitude bands [Tsuda et al., 2000]. The latitudinal distribution of the GPS occultation events, as shown in a histogram in Fig. 1, is nearly symmetric relative to the equator, with the maximum around 30o in each hemisphere. However, it was significantly reduced at latitudes higher than 70o. Therefore, the analyzed results in the polar regions may not be statistically significant.
In the 20-30 km layer in Fig. 1, we have detected the largest value of Ep in the low latitudes, where the latitude range of the enhanced Ep is wider in November-February than in other seasons. Moreover, the Ep values at midlatitudes are larger in the winter hemisphere, which is more evident in May-August, while in equinox (September-October) Ep in the midlatitudes was nearly the same between the northern and southern hemispheres. In the overlying altitude regions, the enhanced peak of Ep near the equator tends to disappear, but the Ep at higher latitudes becomes larger.
It is remarkable that in September-October the latitudinal distribution of Ep is symmetric between the northern and southern hemispheres in the entire height ranges. However, near solstices the Ep distribution involves a large hemispheric asymmetry at middle and high latitudes, which is more pronounced in May-August. There are also differences in the Ep distribution between the June and December solstices. For example, Ep values at 40o-70oS in May-August are significantly larger than those at 40o-70oN in November-February. Conversely, Ep values at 40o-70oS in November-February are smaller than those at 40o-70oN in May-August. These results suggest that the latitudinal distribution of the gravity wave activity in the stratosphere depends on hemisphere as well as on season.
Figure 1 Latitudinal variations of the zonally averaged Ep and standard deviation at 15-45 km in three seasons. Number of GPS/MET profiles is shown in a histogram, whose total is 1608, 1430 and 1836, respectively. Results in March-April are not shown here, because number of the GPS/MET profiles under A/S-off conditions was insufficient (430).
2.4 Height Variations of Ep
We have determined height variations of Ep in the equatorial region (10oS-10oN) and at midlatitudes (40o-60o). The Ep values decrease between 20 km and 25-30 km altitude, which is more evident at low latitudes, and show a gradual and rapid increase at 25-35 km and above 35 km, respectively. A strong annual variation with maximum in winter is detected in both northern and southern hemispheres, although large hemispheric differences are recognized. On the other hand, seasonal variations are not evident in the equatorial region.