Gravity wave activity in the troposphere and lower stratosphere: An observational study of seasonal and interannual variations

Authors

  • Yongfu Wu,

    1. State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing, China
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  • Wei Yuan,

    Corresponding author
    1. State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing, China
    • Corresponding author: W. Yuan, State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing 100190, China. (wyuan@spaceweather.ac.cn)

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  • Jiyao Xu

    1. State Key Laboratory of Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences, Beijing, China
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Abstract

[1] An 11 year (1998-2008) temperature and wind data set obtained over Annette Island (55.03°N, 131.57°W) is used to examine gravity wave activity and their seasonal and interannual variations in gravity wave activity. Vertical wave number spectra of normalized temperature and wind fluctuations are calculated and are compared with the predictions of gravity wave saturation models. Results indicate that there are serious discrepancies between our measurements and earlier observational results at present stage of study of vertical wave number spectra. The correlation coefficients between tropospheric and stratospheric temperature spectral parameters are very small, suggesting that the result is in agreement with previous studies. Time series of total wave energy reveal clear seasonal and interannual variations. Maximum wave energy amplitudes occur near winter of each year in the troposphere and near summer of each year in the stratosphere. Specifically, the maximum wave energy amplitudes in the troposphere show a close correspondence with the maximum occurrence rate of dynamical instability. In addition, the maximum wave energy amplitudes in the stratosphere also show a close correspondence with the maximum occurrence rate of convective instability.

1 Introduction

[2] Vertical profiles of atmospheric wind and temperature in the troposphere and middle atmosphere exhibit fluctuations with vertical scales ranging from a few tens of meters to a few tens of kilometers, which are now widely thought to be due principally to a field of gravity waves. VanZandt [1982] pointed out that the observed spectra tend to have the same shape and power spectral density regardless of seasons, meteorological conditions, and geographical locations. Subsequently, motivated by observations of “universal” spectrum, various gravity wave saturation models have been developed, including linear instability [Dewan and Good, 1986; Smith et al., 1987], nonlinear wave-wave interaction [Weinstock, 1990], Doppler spreading [Hines, 1991; Gardner, 1994], and saturated-cascade similitude theory [Dewan, 1997].

[3] During the past two decades, a number of authors have examined the characteristics and variability of the atmospheric spectra using a variety of atmospheric wind and temperature observations from different platforms, including measurements from radiosondes [Tsuda et al., 1991; Allen and Vincent, 1995; Nastrom et al., 1997; Nastrom and VanZandt, 2001], MST radar [Smith et al., 1985; Fritts et al., 1988; Tsuda et al., 1989], rocket [Dewan et al., 1984; Wu and Xu, 2006], and satellite [Wang et al., 2000]. A universal spectrum and several gravity wave saturation modes have been proposed [VanZandt, 1982; Dewan and Good, 1986; Smith et al., 1987; Weinstock, 1990; Hines, 1991; Gardner, 1994; and Dewan, 1997]. However, observed spectra are usually compared with the models of Dewan and Good [1986] and Smith et al. [1987], including slope and amplitude.

[4] Allen and Vincent [1995] have pointed out that although the agreement between theory and experiment appears to have been accepted already, the shapes and amplitudes of vertical wave number power spectra can vary with geographic position and time. Moreover, the extent of these variations is not well known at present and the available data set of high-resolution radiosonde measurements is ideal for addressing the problem. Therefore, our first purpose in this study is to use an 11 year (February 1998 to December 2008) radiosonde data set conducted at Annette Island (55.03°N, 131.57°W), US, to examine the characteristics of vertical wave number spectra of normalized temperature and wind fluctuations in the troposphere and lower stratosphere. During the past decade, the gravity wave activity and its seasonal and interannual variations have been studied primarily at tropical-Ocean sites and at midlatitude continental sites, using radiosonde observations [Alexander and Vincent, 2000; Vincent and Alexander, 2000; Zhang and Yi, 2007]. However, very little information on the seasonal and interannual variations of total wave energy E(=KE + PE) at midlatitude sites is currently available. Therefore, our second purpose is to study the seasonal and interannual variations of total wave energy E at this midlatitude site using the same high-resolution radiosonde measurements.

[5] This paper is organized as follows. We begin by describing the experimental data and analysis procedures in section 2. Our observational results and discussions are presented in section 3. The conclusions are given in section 4.

2 Experimental Data and Analysis Methods

[6] An 11 year (1998–2008) temperature and wind data set obtained from 7590 high-resolution balloon soundings at Annette Island (55.03°N, 131.57°W), US, is used to study gravity wave activity and seasonal and interannual variations of total wave energy in the troposphere and lower stratosphere. Table 1 summarizes the number of balloon soundings launched in each month used in this paper from February1998 to December 2008. The balloon soundings were launched twice per day at 1100 and 2300 UT and were recorded at 6 s intervals which correspond, approximately, to 30 m height resolution given the approximate 5 m/s ascending rate of the balloon. We interpolate the temperature and wind data set at 50 m height intervals using a cubic spline function in order to obtain equally spaced data points. The temperature and wind data with height resolution of 50 m are used to derive vertical wave number spectra of normalized temperature and wind fluctuations as well as total wave energy.

Table 1. The Number of Balloon Soundings in Each Month Used in This Paper From February 1998 to December 2008
YearJFMAMJJASOND
19980445148584703029354226
1999283340334352494138273523
2000314242415051544833453832
2001474539444847545738333646
2002483641455050473738373942
200341454052480443925272335
2004353127434851514736352228
2005243448465755575439423441
2006503540465553475636373840
200732383852545451574539360
200848360434944474545263632

[7] Further, we restrict the analysis to the height ranges of 1.65–8.00 km in the troposphere and 18.00–24.35 km in the lower stratosphere, giving a 6400 m height range. This tropospheric height range beginning at 1.65 km is selected in order to exclude planetary boundary layer effects [Nastrom et al., 1997; Nastrom and VanZandt, 2001]. This stratospheric height range beginning at 18.00 km is selected in order to exclude the possible effect of the tropopause on the vertical wave number spectra of the normalized temperature and wind fluctuations. Between 1998 and 2008, about 70% of all balloon soundings reached a height of 24.35 km. Figure 1 displays an example of temperature (Figures 1a and 1c) and Brunt-Väisälä frequency squared (Figures 1b and 1d) profiles observed on 14 October 2000 (Figures 1a and 1b) and 30 October 2000 (Figures 1c and 1d). The Brunt-Väisälä frequency squared N2 is

display math(1)

where T is the temperature, g is the acceleration due to gravity, and Γ is the adiabatic lapse rate. The temperature profile in Figure 1a is relatively simple. The temperature decreases from the surface layer to a distinct tropopause at around 10.35 km, which is marked by a large increase in N2 profile in Figure 1b. In contrast, the temperature and N2 profiles in Figures 1c and 1d are complex and are usually not clearly recognized. The main tropopause is seen to occur at about 16.8 km, consistent with a large increase in N2 in Figure 1d. However, there is also a zone of high stability (a secondary tropopause) located at 11.3 km and which has a corresponding maximum in N2. The region between 11.3 and 16.8 km is a transition region between purely tropospheric behavior below and purely stratospheric behavior above.

Figure 1.

(a and c) An example of temperature, and (b and d) N2 profiles measured on 14 October (Figures 1a and 1b) 2000 and 30 October (Figures 1c and 1d) 2000. The thick vertical bars on the N2 profiles show the mean values of N2 and the height ranges used in spectral analysis.

[8] Now, we describe our procedure for spectral analysis. Dewan and Grossbard [2000] showed that the analysis procedure used by Nastrom et al. [1997] did not include “prewhitening/postcoloring” and that their results were contaminated by an artifact not previously discussed in the literature. Therefore, we apply the “prewhitening/postcoloring” procedure in this paper. First, the means and linear trends are removed from the normalized temperature, zonal wind, and meridional wind profiles. Then the normalized temperature, zonal wind, and meridional wind profiles are prewhitened by means of a differentiating filter given by

display math(2)

where xi and yi are the data series before and after prewhitening, and β is taken to be 1. Second, a cosine tape window is applied to the differenced data. The differenced profiles are then transformed to the power spectral density using the fast Fourier transform routine. Finally, the power spectra densities of the prewhitened data, Fpw, are adjusted to compensate the effect of the differencing and the cosine taper window.

[9] The post-colored spectra, Fpwpc(m), are given by

display math(3)

where pwpc is prewhitening/postcoloring, mi is the ith wave number, and M is number of data points.

3 Observational Results and Discussions

[10] Our purposes in this section are to examine the characteristics of vertical wave number spectra of normalized temperature and zonal and meridional wind fluctuations and to assess the seasonal and interannual variations of total wave energy using all vertical profiles of temperature and zonal and meridional wind in the troposphere and the lower stratosphere. To do this, we first calculate individual vertical wave number spectra of each normalized temperature and zonal and meridional wind fluctuations. Then these individual vertical wave number spectra of normalized temperature and zonal and meridional wind fluctuations are averaged arithmetically to increase confidence level in the spectral power. Finally, the total wave energy is obtained from the vertical wave number spectra of normalized temperature and zonal and meridional wind fluctuations.

3.1 Mean Spectra

[11] The mean spectra of normalized temperature fluctuations in the troposphere and the lower stratosphere obtained from 5287 balloon soundings are shown in Figure 2. The dashed straight line in Figure 2 is predicted by the linear saturation theory of Dewan and Good [1986] and Smith et al. [1987] with the spectral slope of −3.0. The two mean normalized temperature spectra in Figures 2a and 2b exhibit several significant features. First, in the wave number range of 1.09 × 10−3–5.00 × 10−3 cyc/m, the two mean normalized temperature spectra have slopes near −2.73 in the troposphere and −2.70 in the lower stratosphere, which is consistently smaller than the slope of −3 predicted by the linear saturation theory. The wave number of 5.00 × 10−3 cyc/m corresponds to half the Nyquist wave number due to the 50 m resolution. In this wave number range of 1.09 × 10−3–5.00 × 10−3, the aliasing effects should be insignificant. The sudden decrease in the slope at the right-hand end of the spectra is probably due to aliasing, as described by Allen and Vincent [1995]. Second, the spectral amplitude in the troposphere is consistently larger than the expected prediction by as much as a factor of about 2.0 but the spectral amplitude in the lower stratosphere is consistently less than theoretical prediction. Third, the two mean spectra exhibit clear discontinuities in the slopes to less negative values at small wave numbers of 3.13 × 10−4 (cyc/m) in the troposphere and of 4.69 × 10−4 (cyc/m) in the lower stratosphere. This yields an estimate of the dominant vertical wavelength at these heights of math formula in the troposphere and math formula in the lower stratosphere. The dominant vertical wavelengths of 3.2 km in the troposphere and 2.1 km in the lower stratosphere are consistent with earlier observational results. Fritts et al. [1988] showed that the dominant vertical wavelength was λ* = 21/3/m* = 2.5 − 3.0 km in the troposphere and λ* = 21/3/m* = 2.5 − 2.9 km in the lower stratosphere for velocity and temperature data, respectively. They are also close to the value of λ* = 2.0 km in the temperature field in the troposphere and the lower stratosphere reported by Tsuda et al. [1991] as well as to the value of λ* = 2.4 km and λ* = 2.7 km in the temperature field in the troposphere and the lower stratosphere reported by Allen and Vincent [1995]. It must be pointed out, however, that the conversion from dominant vertical wave number m to dominant vertical wavelength λ is not the same as used by other authors, some, including the observations presented here, use λ = 1/m [Tsuda et al., 1991; Allen and Vincent, 1995], others use λ = 21/3/m [Fritts et al., 1988]. This is important to bear in mind when we discuss the dominant vertical wavelength.

Figure 2.

Mean vertical wave number spectra of normalized temperature fluctuations in the (a) troposphere and in the (b) lower stratosphere. The dashed straight line in Figures 2a and 2b is predicated by the linear saturation theory of Dewan and Good [1986] and Smith et al. [1987].

[12] We examine the normalized temperature spectra sorted by season (winter and summer). We first group the individual normalized temperature spectra into “summer (June, July, and August) and winter (December, January, and February)” before averaging. Then the seasonal mean spectra of normalized temperature fluctuations are calculated. The seasonal mean spectra are displayed in Figure 3. We can see that in the wave number range of 1.09 × 10−3–5.00 × 10−3 cyc/m, there is no seasonal variation.

Figure 3.

Seasonal mean vertical wave number spectra of normalized temperature fluctuations in the (a) troposphere and in the (b) stratosphere. The curves labeled “summer” and “winter” are mean spectra obtained from June, July, and August and from December, January, and February.

[13] The mean vertical wave number spectra of zonal and meridional wind fluctuations in the troposphere and the lower stratosphere are shown in Figure 4. The dashed straight line in Figure 4 is predicted by the linear saturation theory of Dewan and Good [1986] and Smith et al. [1987] with the spectral slope of −3.0. In the wave number range of 1.09 × 10−3–5.00 × 10−3 cyc/m, the tropospheric slopes in Figures 4a and 4c are −4.09 and −4.44 and the stratospheric slopes in Figures 4b and 4d are −3.50 and −3.51, which is significantly steeper than the slope of −3 predicted by the linear saturation theory. The spectral amplitudes in Figures 4a–4d show a large difference between observation (the solid line) and theory (dashed straight line). At the wave number 5.00 × 10−3 (cyc/m), the observational amplitudes are about 1 order of magnitude smaller than the theoretical amplitudes. The reason for this is not fully understood because we do not know how these wind data are obtained from original record.

Figure 4.

Mean vertical wave number spectra of (a) zonal and (c) meridional wind fluctuations in the troposphere and (b) zonal and (d) meridional wind fluctuations in the lower stratosphere. The dashed straight line is predicted by the linear saturation theory of Dewan and Good [1986] and Smith et al. [1987].

[14] Except for the observational results of vertical wave number spectra of wind fluctuations discussed by Pfenninger et al. [1999], the authors are aware of no such steeper slopes occurring in the troposphere and lower stratosphere. Pfenninger et al. [1999] gave a review of their wind spectra and noted “the wind spectra have a much steeper slope than the temperature spectra. We suspect that this is a result of the proprietary filtering process employed during the data acquisition which excessively attenuates the high vertical wave number components of the spectrum.” Our wind spectra are very similar to those obtained by Pfenninger et al. [1999]. Thus, we think that it is also possible that our wind data used in this paper greatly attenuate the high vertical wave number components of the wind spectra.

3.2 Correlation Slopes and Amplitudes Between the Troposphere and Stratosphere

[15] If gravity waves generated in the troposphere propagate upward without breaking or saturation processes, filtering effects, there should be a significant correlation in the spectral properties of the two regions. Pfenninger et al. [1999] examined their temperature spectra and obtained the correlation values of 0.11 for the slope and 0.19 for the amplitude [see Pfenninger et al., 1999, Figure 8]. The two correlation coefficients are very small, suggesting that little coherence exists between waves in the troposphere and waves in the stratosphere. In contrast, Nastrom et al. [1997] examined their Fu + v spectra and obtained significant correlation values of 0.40 for the slope and 0.52 for the amplitude, suggesting that the tropospheric and stratospheric spectra are composed of waves that have a common source. Following Pfenninger et al. [1999] and Nastrom et al. [1997], we examine the correlation coefficients of the normalized temperature spectra. The result of analysis is illustrated in Figure 5. Figure 5 shows the correlation coefficient is 0.04 for the slope and 0.05 for the amplitude. The t test shows that at the 99% level of significance, there is no detectable significance of the slope and amplitude. The insignificant correlations show that the spectra in the troposphere and the lower stratosphere are composed of waves that have different source.

Figure 5.

(a) Slope and (b) amplitude of normalized temperature spectra in the troposphere versus those in the lower stratosphere.

3.3 Slope and Amplitude of the Normalized Temperature Spectra

[16] The spectral slope and amplitude are two main parameters describing the characteristics of the spectrum. We calculate the spectral slopes in the wave number range from 1.09 × 10−3 to 5.00 × 10−3 cyc/m and the spectral amplitudes at m = 2.5 × 10−3 cyc/m for all soundings. The histograms of the spectral slope are revealed in Figure 6, which shows that they both are approximately normally distributed. Further, Figure 6 shows that the steepest and shallowest slopes are −5.75 and 0.50 in the troposphere and −5.02 and −0.31 in the lower stratosphere, respectively. These data show that there is considerable variability in the slope from one flight to another.

Figure 6.

Histograms of the spectral slopes of normalized temperature spectra and their best fit Gaussian distribution in the (a) troposphere and in the (b) lower stratosphere.

[17] The histograms of the spectral amplitude in Figure 7 also show that they both are approximately normally distributed. Figure 7 shows that at m = 2.5 × 10−3 cyc/m, the maximum and minimum amplitudes are −5.55 and −5.63 in the troposphere and −3.34 and −3.13 in the lower stratosphere, respectively. These data also show that there is considerable variability in the amplitude.

Figure 7.

Histograms of the spectral amplitudes of normalized temperature spectra and their best fit Gaussian distribution in the (a) troposphere and in the (b) lower stratosphere.

[18] Similar variability in both slope and amplitude to Figures 6 and 7 is also obtained by balloon, lidar, and rocket [Senft and Gardner, 1991; Nastrom et al., 1997; Pfenninger et al., 1999; Wu and Xu, 2006]. As described by Fritts and Alexander [2003] “There are, in addition, many reasons to expect that the spectrum will also exhibit considerable variability spatially and temporally because of various sources, filtering environments, quasi-discrete waves, and gravity wave interactions with larger scales of motion”, it is therefore not surprising that there is considerable variability in both slope and amplitude of the individual spectrum.

3.4 Wave Energy

[19] We examine the seasonal and interannual variability in wave energy by computing the monthly-mean values of potential and kinetic energies.

[20] The potential energy density is given by

display math(4)

[21] The kinetic energy density is given by

display math(5)

[22] The total wave energy density is given by

display math(6)

where u ′ 2 and v ′ 2 are the monthly-mean values of zonal and meridional wind variances and are obtained from the zonal and meridional wind spectra, respectively, math formula is the monthly-mean values of the normalized temperature variance and is obtained from the normalized temperature spectra. The overbars in equations (4) and (5) show the total zonal, meridional, and normalized temperature variances in the wave number range of 1.09 × 10−3–5.00 × 10−3 cyc/m.

[23] We first calculate the monthly-mean values of math formula, math formula, and math formula in the wave number range of 1.09 × 10−3–5.00 × 10−3 cyc/m from the monthly-mean spectra of the zonal, meridional, and normalized temperature fluctuations. Then we substitute the monthly-averaged values of math formula, N2, and g into equations (4) and (5). Finally, the seasonal and interannual variations in E are smoothed by applying a five-point running mean. The resulting monthly-mean profiles of wave energy are shown in Figure 8. It is the wave energy time series, shown in Figure 8 that exhibits seasonal and interannual variations with time, with maximum wave energy amplitudes occur near winter of each year in the troposphere in Figure 8a and near summer of each year in the lower stratosphere in Figure 8b.

Figure 8.

Time series of monthly-mean wave energy in the (a) troposphere and in the (b) lower stratosphere observed during an 11 year period.

[24] Fritts and Alexander [2003] showed that two most important gravity wave sources for the middle atmosphere are convection and wind shear. Following Fritts and Alexander [2003], we examine the atmospheric stability. The Richardson number, Ri, can be used as convenient measure of convective and dynamical stability, respectively. The Richardson number Ri is

display math(7)

where u and v are the zonal and meridional winds. Convective instability occurs when N2 < 0, while dynamical instability occurs when 0 < Ri < 0.25. First, we determine the gradients ∂T/∂z, ∂u/∂z, and ∂v/∂z by a cubic spline function over 300 m using values for every 50 m. Then we substitute the N2, ∂u/∂z, and ∂v/∂z into equation (5) and calculate the occurrence rate of dynamical instability, which is defined by math formula, where Ndi denotes the number of occurrences of dynamical instability in a month and No denotes the total number of observations in a month. A similar exercise using N2, ∂u/∂z, and ∂v/∂z yields the occurrence rate of convective instability, which is defined by math formula, where Nci denotes the number of occurrences of convective instability in a month and No denotes the total number of observations in a month. Finally, the occurrence rate of dynamical instability or convective instability is smoothed by applying a five-point running mean

[25] The smoothed profile of occurrence rate of dynamical instability, together with the observed variation in E in the troposphere, is shown in Figure 9. There is a clear positive correlation between the occurrence rate of dynamical instability and E. The correlation coefficient is 0.79. The t test shows that the correlation coefficient of 0.79 is significant at the 99% level. This suggests that in the troposphere the larger value of wind shear and smaller positive value of Brunt-Väisälä frequency squared, N2, are the main excitation source of the seasonal and interannual variations in E. It must be noted, however, that since the high wave number components of the wind fluctuations are excessively filtered, the actual occurrence rate of dynamical instability may be underestimated. A similar analysis is also made for studying the relationship between the convection instability and E in the troposphere, but no clear correlation is found. Thus, they will not be shown.

Figure 9.

(a) Time series of monthly-mean wave energy and (b) occurrence rate of dynamical instability in the troposphere observed during an 11 year period.

[26] To investigate the relationship between the occurrence rates of convective or dynamical instability with E in the lower stratosphere, we further calculate the occurrence rate of convective and dynamical instability similar to those in the troposphere. The smoothed profile of occurrence rate of convective instability, together with the observed variation in E in the lower stratosphere, is shown in Figure 10. We see from Figure 10 that there is also a clear positive correlation between the occurrence rate of convective instability and E. The correlation coefficient is 0.64. The t test shows that the correlation coefficient of 0.64 is significant at the 99% level. This suggests that in the lower stratosphere the convective instability is the main excitation source of the seasonal and interannual variations in E. As described above, since the high wave number components of the wind fluctuations are excessively filtered, the actual occurrence rate of convective instability may be underestimated. A similar analysis is also made for studying the relationship between the dynamical instability and E in the lower stratosphere, but we do not find a clear correlation between dynamical instability and E. Thus, they will not be shown.

Figure 10.

(a) Time series of monthly-mean wave energy and (b) occurrence rate of convective instability in the lower stratosphere observed during an 11 year period.

3.5 The Ratio of Kinetic Energy to Potential Energy

[27] As described in section 3.4, the monthly-mean values of kinetic energy and potential energy have been calculated in the troposphere and lower stratosphere. Now, we use a five-point running mean to remove small-scale noise in the profiles of kinetic energy and potential energy. The ratio of kinetic energy to potential energy (R) is shown in Figure 11. The mean ratio is 0.73 in the troposphere, which is the same value as Zhang and Yi [2007] reported at Wuhan station, China, and is difficult to be explained from the gravity wave theory. This implies a more complex wave field than what is assumed in most current models. On the other hand, a more interesting result is that the mean ratio is 1.75 in the lower stratosphere, which is close to 1.6 obtained by Vincent and Alexander [2000]. This mean ratio of about 1.6 obtained from radiosonde shows the wave field is dominated by inertia-gravity waves (the intrinsic frequency ω ≈ the inertial frequency f) rather than high-frequency waves (the intrinsic frequency ω > > the inertial frequency f), as described by Vincent and Alexander [2000].

Figure 11.

Ratio (R) of kinetic energy to potential energy in the (a) troposphere and in the (b) lower stratosphere. The dashed lines show the mean values of R.

[28] There are some other radiosonde observations of the ratio of kinetic energy to potential energy (R). Geller and Gong [2010] showed the mean R is about 2 to 3 in the troposphere and about 1.5 to 2.5 in the lower stratosphere. Pfenninger et al. [1999] reported that the kinetic energy was almost always larger than potential energy by at least a factor of 4 in the troposphere and lower stratosphere. Nastrom et al. [1997] showed that the mean R was about 2.5 in the troposphere and 5 in the stratosphere. Nastrom and VanZandt [2001] further showed that the mean R was 3.1 in the troposphere and 6.2 in the stratosphere as suggested. Zhang and Yi [2007] argued that the observed mean R varied from 0.46 to 0.73 in the troposphere and from 1.31 to 3.44 in the stratosphere. De la Torre et al. [1999] found that the mean R was about 5 in the stratosphere. These observational results are obviously inconsistent with our observational results.

4 Conclusions

[29] We have presented a spectral analysis of temperature and zonal and meridional wind profiles based on an 11 year data set from February 1998 to December 2008 observed in the troposphere and lower stratosphere over Annette Island (55.03°N, 131.57°W), US. The observations are used to examine gravity wave activity and its variations with time. The spectral analysis leads to the following conclusions.

  1. [30] The slopes of the mean vertical wave number spectra of the normalized temperature fluctuations in the wave number range from 1.09 × 10−3 to 5.00 × 10−3 cyc/m are about −2.73 in the troposphere and about −2.70 in the lower stratosphere, which is consistently smaller than the slope of −3 predicted by current gravity wave saturation models. The spectral amplitude in the troposphere is found to be consistently larger than expected by as much as a factor of about 2.0, but the spectral amplitude in the lower stratosphere is consistently less than expected by theoretical prediction. The results from our analysis are inconsistent with some earlier observational results.

  2. [31] The zonal and meridional wind spectra reveal much steeper slope compared to the theoretical prediction. At the wave number 5.00 × 10−3 cyc/m, the observational amplitudes are about 1 order of magnitude smaller than the theoretical amplitudes. These observed results are inconsistent with earlier observational results.

  3. [32] For the normalized temperature spectra, the correlation coefficient between slopes is about 0.04 and between the amplitudes is about 0.05. The insignificant correlation shows that the tropospheric and stratospheric normalized temperature spectra may be composed of waves that have different source.

  4. [33] Time series of total wave energy reveal clear seasonal and interannual variations. Maximum wave energy amplitudes occur near winter of each year in the troposphere and near summer of each year in the stratosphere.

  5. [34] The maximum wave energy amplitudes in the troposphere show a close correspondence with the maximum occurrence rate of dynamical instability. The correlation coefficient is 0.79. This suggests that in the troposphere the larger value of wind shear and smaller positive value of Brunt-Väisälä frequency squared, N2, are main excitation source of the seasonal and interannual variations in total wave energy.

  6. [35] The maximum wave energy amplitudes in the stratosphere also show a close correspondence with the maximum occurrence rate of convective instability. The correlation coefficient is 0.64. This suggests that the convective instability is the main excitation source of the seasonal and interannual variations in total wave energy.

  7. [36] The ratio of kinetic energy/potential energy is about 0.73 in the troposphere and is difficult to be explained from the gravity wave theory. On the other hand, the ratio of kinetic energy/potential energy is about 1.75 in the lower stratosphere, which is close to 1.6. This suggests that wave field is dominated by inertia-gravity waves, rather than high-frequency waves.

Acknowledgments

[37] The provision of data by National Weather Service Sounding is gratefully acknowledged. We also thank the three anonymous reviewers for their valuable suggestions. This work is supported by the Chinese Academy of Sciences (KZZD-EW-01-2), the National Science Foundation of China (41274153, 41229001), the National Important Basic Research Project of China (2011CB811405), and the project is also supported by the Specialized Research Fund for State Key Laboratories.