4. Mesospheric temperatures above Spitsbergen 59
4.4. Harmonic temperature and brightness perturbations
4.4.1. Case examples of hourly perturbations
A selection of six case examples that contain distinct oscillations in the derived rotational temperatures and OH* emission brightness is shown in Fig. 4.17 to 4.19 (seepp. 94-96).
The left panels show the time series of OH(3-1) and OH(4-2) temperatures and rela-tive intensity changes of the associated Q1(1) rotational lines. Ideally, one should relate changes in the OH* brightness to the intensity changes of the selected entire emission band, which needs to be reconstructed from the observed emission lines. However, Reisin and Scheer [2001] found that the direct use of measured band intensities also gives con-sistent results in terms of brightness fluctuations. Even though, the consideration of intensity changes of a single rotational line is a further simplification, the additional consideration of the three most intense P1 rotational lines of the OH(3-1) and OH(4-2)
4.4. Harmonic temperature and brightness perturbations 91 bands did not appear to change the characteristics of the brightness fluctuations in the measurements of this work.
The right panels of Fig. 4.17 to 4.19 show normalised periodograms that were com-puted by means of a Lomb-Scargle analysis of the time series shown in the left panels.
Similarly to the Fourier analysis, the Lomb-Scargle analysis allows us to decompose the spectral harmonic components of a time dependent signal. One important difference between both methods is that the Lomb-Scargle analysis does not require an equal dis-tribution of time steps (e.g. see Press and Rybicki [1989]). Therefore, it can be directly applied to a time series that contains several data gaps. The Lomb-Scargle analysis also allows us to estimate the significance of different spectral components. Because gravity and tidal wave perturbations can only be observed for a few cycles, the significance level can be largely affected by the choice of the time window (e.g. see Oznovich et al. [1997]).
Further techniques, such as the removal of additional harmonic components in the time series, can be applied to improve the significance levels, but for the initial investigation of harmonic components in this section the Lomb-Scargle analysis is directly applied to the time series on the left panels.
It is worth noting that the qualitative characteristics of each example are kept, if we switch off the correction for the atmospheric transmission, which according to Sect. 3.8 has a particularly strong impact on the OH(4-2) temperatures. Accordingly, as long as we may suppose that the atmospheric transmission is constant with time, the observed harmonic perturbations are essentially representing the intrinsic response of the OH*
airglow layer to atmospheric waves.
Discussion of results
Figure 4.17 shows the first two examples of harmonic hourly temperature/line-intensity fluctuations in the OH(3-1) and OH(4-2) bands. Signatures of an approximate 6 h oscillation, matching with the tidal sub-harmonics, are present in the first example (Fig. 4.17a). The second example (Fig. 4.17b) is dominated by an approximate 8.5 h to 9 h oscillation, which is close to a ter-diurnal periodicity.
If we consider the periodograms on the right panels of Fig. 4.17, the dominant fre-quency component of each example is reflected in the associated power spectrum of each parameter (i.e. temperatures and line-intensities). With respect to the indicated α-significance level6, we find that almost all parameters reach at least theα = 0.5 level.
The only exception exists for the 6 h oscillation of the OH(3-1) temperatures (Fig. 4.17a:
right panel). However, we also notice that all spectral power peaks are clearly above the background level of the periodograms, while further techniques may increase the significance levels, as noted above. Therefore, we will mainly focus on the frequency
6The α level is the probability of rejecting the null hypothesis, i.e. in this case the assumption of a pure noise signal. It is related to the level of confidenceCas follows: 1−C=α
power relative to the background level in the following.
An interesting feature of both examples in Fig. 4.17 is the phase shift between tem-perature and line-intensity perturbations. In this case, temtem-perature perturbations are preceding the intensity perturbations, which according to the SG theory suggests an up-ward energy propagation as discussed above. The visual inspection of the time series confirms that leading temperature perturbations are the most common feature, which is also in agreement with the principal excitation mechanisms of tidal and gravity waves in the lower atmospheric layers. Examples of the opposite case (i.e. positive sign of η) are also shown by other studies (e.g. Ghodpage et al. [2012]), but these typically appear on rare occasions. This is also the case for the time series of this work, where only two events with preceding line-intensity perturbations were visually identified.
Figure 4.18a shows one example of a preceding intensity perturbation event. Accord-ing to the periodogram, the oscillation is dominated by a ter-diurnal component. Again, all parameters show a low significance (i.e. higherαvalues) but with the ter-diurnal line-intensity component peaking above the background level in the periodogram. Only the ter-diurnal oscillation of the OH(4-2) temperatures is not evident in the periodogram, but if we compare their maximum and minimum values with the OH(3-1) temperatures in the time series, we still find characteristics of a ter-diurnal oscillation.
While the SG theory gives an explanation for the time delay between temperature and brightness perturbations, the vertical shifts in the OH* Meinel bands imply a further delay in the airglow response between different OH* Meinel bands. In comparison to the vertical shift of about 3 km between the maximum responses in brightness and temper-ature altitudes of the same emission band, the vertical shift between two adjacent OH*
Meinel bands is typically in the order of a few hundred metres as stated earlier. This implies that the time delay between the OH(3-1) and (4-2) bands should be smaller compared to the delay between the temperature/line-intensity responses of the same band. With respect to the first two examples (Fig. 4.17), the temperature/line-intensity delays are roughly in the order of 1 h to 3 h, which makes the detection of an even smaller phase shift difficult due to the hourly resolution and short duration of the signals.
This also gives an explanation why the temperature and line-intensity changes appear to be in phase between both OH* Meinel bands. The situation looks slightly different in the third example (Fig. 4.18a), if we look at the shifted maxima between OH(3-1) and OH(4-2) temperatures around 04:00 to 05:00 (UTC). In contrast, no significant phase shift is evident between the associated line-intensity fluctuations.
Another example of a phase shift between OH(3-1) and OH(4-2) temperatures is shown in Fig. 4.18b. Interestingly, the leading OH(3-1) temperatures are quite evident in this example, but we also notice that a similar phase shift is again missing between the fluctuations of both line-intensities. In terms of the SG theory, this implies that the bottom side profile altitudes of the OH(3-1) and OH(4-2) emissions, which are most
4.4. Harmonic temperature and brightness perturbations 93 sensitive in their brightness fluctuations, are less distinct compared to their profile peak altitudes, which are more sensitive in their temperature responses.
Figure 4.19a gives another example of pronounced oscillations in temperatures and line-intensities that could be observed during a 24 h observational period. The interest-ing feature of this example is a transition from an approximate semi-diurnal frequency to a higher 6-8 h frequency during the day, while both frequencies lie in the tidal frequency range.
Figure 4.19b shows an even larger time range of several days where exceptional weather conditions allowed for almost continuous observations. Pronounced temperature / line-intensity oscillations exist that are superimposed by a coherent change in both param-eters at daily time scales. The coherent large scale response in both paramparam-eters indi-cates an interesting feature, which we will get back to at the end of the next chapter in Sect. 5.11.3. With regard to the Lomb-Scargle analysis, the corresponding low frequency component reaches spectral power values as high as P(flow) = 45 in the periodogram, which is clearly above the values of the higher frequencies. Despite the large time win-dow compared to the previous examples, we also notice a 9.1 h frequency component in OH(3-1) and OH(4-2) line-intensities in the periodogram close to the α = 0.5 level.
Similarly to the second example in Fig. 4.17b, this frequency is close to a ter-diurnal oscillation. In this context, Oznovich et al. [1997] suggest that ”terdiurnal oscillations are a common feature of the winter polar mesopause, possibly the most recurring distur-bance of the region”. Despite the slightly lower frequency in our example, this may also indicate a dominant ter-diurnal feature during the considered period, which is evident for the line-intensities at least. The missing signature of a ter-diurnal temperature oscil-lation in the periodogram is probably related to the smaller amplitudes of temperature versus line-intensity perturbations.
(a)
08:00 12:00 16:00 20:00
160 170 180 190 200
OH* rotational temperatures from hourly averaged spectra
T (K)
OH(3−1) OH(4−2)
05 Jan−2011 0.008
0.01 0.012 0.014
I (AU)
Intensity of rotational Q 1(1) line
0 2 4 6 8 10 12
0 2 4 6 8
f(1/day)
P(f)
Lomb−Scargle normalised periodogram
α =0.5 α =0.1
T; OH(3−1) I; OH(3−1) T; OH(4−2) I; OH(4−2)
(b)
20:00 00:00 04:00 08:00 12:00
160 170 180 190 200 210
OH* rotational temperatures from hourly averaged spectra
T (K)
OH(3−1) OH(4−2)
08 Jan−2012 0.01
0.015 0.02 0.025
I (AU)
Intensity of rotational Q1(1) line
0 2 4 6 8 10 12
0 2 4 6
f(1/day)
P(f)
Lomb−Scargle normalised periodogram
α =0.5 α =0.1 α =0.05
T; OH(3−1) I; OH(3−1) T; OH(4−2) I; OH(4−2)
Figure 4.17.: Two examples of temperature perturbations that lead line-intensity pertur-bations. Left panels: OH(3−1), OH(4−2) temperatures and Q1(1) line-intensities (arbitrary units). The temperature error bars indicate the fitting error of the hourly averaged spectrum. The uncertainty in the measured intensity is expressed in terms of the standard deviation of noise in the spectral domain. Right panels: Normalised Lomb-Scargle periodograms of temperatures and intensities (see legend) referring to the same time window of the displayed time series.
4.4. Harmonic temperature and brightness perturbations 95 (a)
00:00 04:00
200 210 220 230
OH* rotational temperatures from hourly averaged spectra
T (K)
OH(3−1) OH(4−2)
09 Feb−2009 5
6 7 8x 10−3
I (AU)
Intensity of rotational Q 1(1) line
0 2 4 6 8 10 12
0 1 2 3 4 5
f(1/day)
P(f)
Lomb−Scargle normalised periodogram
α =0.5 α =0.1
T; OH(3−1) I; OH(3−1) T; OH(4−2) I; OH(4−2)
(b)
04:00 08:00 12:00 16:00
180 190 200 210 220 230
OH* rotational temperatures from hourly averaged spectra
T (K)
OH(3−1) OH(4−2)
03 Dec−2009 4
5 6 7 8 9
x 10−3
I (AU)
Intensity of rotational Q 1(1) line
0 2 4 6 8 10 12
0 2 4 6
f(1/day)
P(f)
Lomb−Scargle normalised periodogram
α =0.5 α =0.1 α =0.05
T; OH(3−1) I; OH(3−1) T; OH(4−2) I; OH(4−2)
Figure 4.18.: (a): Line-intensity perturbations lead temperature perturbations.
(b): OH(3-1) temperature perturbations lead OH(4-2) temperature perturbations. Same designations as used in Fig. 4.17.
(a)
16:00 00:00 08:00 16:00 00:00 08:00 160
170 180 190 200
OH* rotational temperatures from hourly averaged spectra
T (K)
OH(3−1) OH(4−2)
29 Dec−2011 30 Dec−2011 0.01
0.015 0.02 0.025
I (AU)
Intensity of rotational Q 1(1) line
0 2 4 6 8 10 12
0 2 4 6
f(1/day)
P(f)
Lomb−Scargle: 28−Dec 10:00 to 29−Dec 07:00 (UTC)
α =0.5 α =0.1 T; OH(3−1) I; OH(3−1) T; OH(4−2) I; OH(4−2)
0 2 4 6 8 10 12
0 2 4 6
f(1/day)
P(f)
Lomb−Scargle: 29−Dec 07:00 to 30−Dec 12:00 (UTC)
α =0.5 α =0.1
(b)
00:00 00:00 00:00 00:00
160 180 200 220 240
OH* rotational temperatures from hourly averaged spectra
T (K)
OH(3−1) OH(4−2)
22 Dec−2013 24 Dec−2013 26 Dec−2013 28 Dec−2013 0.005
0.01 0.015 0.02 0.025 0.03
OH relative peak intensity
Irel
2 4 6 8 10 12 0
2 4 6 8
f(1/day)
P(f)
Lomb−Scargle normalised periodogram
α =0.5 α =0.1
T; OH(3−1) I; OH(3−1) T; OH(4−2) I; OH(4−2)
Figure 4.19.: (a): Example of frequency change in hourly perturbations. (b): Low fre-quency modulation (daily scale) superimposed by hourly perturbations.
Same designations as used in Fig. 4.17.