### Abstract

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Analysis
- 3. Standard Deviations and Wave Amplitudes
- 4. Seasonal Variations
- 5. Intradecadal and Interdecadal Variations
- 6. Discussion
- 7. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[1] The long-term development of short-period gravity waves is investigated using the analysis of temperature fluctuations in the mesosphere. The temperature fluctuations are quantified by their standard deviations *σ* based on data from OH measurements at Wuppertal (51°N, 7°E) and Hohenpeissenberg (48°N, 11°E) obtained from 1994 to 2009 at 87 km altitude. The temperatures are Fourier analyzed in the spectral regime of periods between 3 and 10 min. The resulting oscillation amplitudes correlate very well with the standard deviations. Shortest periods are taken as “ripples” that are indicative of atmospheric instabilities/breaking gravity waves. In consequence the standard deviations are used as proxies for gravity wave activity and dissipation. This data set is analyzed for seasonal, intradecadal, and interdecadal (trend) variations. Seasonal changes show a double peak structure with maxima occurring slightly before circulation turnaround in spring and autumn. This is found to be in close agreement with seasonal variations of turbulent eddy coefficients obtained from WACCM 3.5. The intradecadal variations show close correlations with the zonal wind and the annual amplitude of the mesopause temperature. The long-term trend (16 years) indicates an increase of gravity wave activity of 1.5% per year. Correspondences with dynamical parameters such as zonal wind speed and summer length are discussed.

### 1. Introduction

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Analysis
- 3. Standard Deviations and Wave Amplitudes
- 4. Seasonal Variations
- 5. Intradecadal and Interdecadal Variations
- 6. Discussion
- 7. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[2] Atmospheric gravity waves (GW) are known to be important parts of middle atmosphere dynamics. They have been intensively studied since the early work of Colin Hines [*Hines*, 1960] with respect to their influences on atmospheric structure and variability [e.g., *Andrews et al.*, 1987; *Fritts and Alexander*, 2003]. They are known to control the mesospheric circulation and its changes by dissipation and momentum deposition [e.g., *Fritts et al.*, 2006]. An extensive review on the voluminous literature on GW has been given by *Fritts and Alexander* [2003]. More recent developments are described e.g., by *Preusse et al.* [2006, 2008, 2009], *Ern et al.* [2004], *Jacobi et al.* [2006], *Krebsbach and Preuße* [2007], *Wu et al.* [2006], and the references given therein.

[3] Substantial amount of work has been spent on the question as to the origin of gravity waves in the mesosphere. There are many sources in the lower atmosphere (orographic structures, weather systems), and GW upward propagation in the middle atmosphere up to the mesopause has been extensively studied e.g., by ray tracing methods [*Preusse et al.*, 2009, and references therein]. Gravity waves are subject to many influences and modifications on their way up to the mesosphere and lower thermosphere, as for instance by wind filtering in the middle atmosphere [e.g., *Alexander*, 1998]. Wavelike oscillations are also known to be excited in situ in the mesosphere by breaking gravity waves and Kelvin-Helmholtz or convective instabilities. These have exceptionally short periods and wavelengths (“ripples”), and are investigated in detail by theory and imaging experiments [e.g., *Nakamura et al.*, 1999; *Horinouchi et al.*, 2002; *Hecht*, 2004, *Hecht et al.*, 2005, 2007; *Taylor et al.*, 1997, 2007; *Shiokawa et al.*, 2009]. Gravity wave–fine structure interactions, related Kelvin-Helmholtz instabilities, and turbulence production have also been numerically studied by *Fritts et al.* [2009, and references therein].

[4] Gravity wave amplitudes in the upper mesosphere are comparatively large. At the mesopause they appear to be the strongest of all types of waves (in temperature [*Offermann et al.*, 2009]). In the lower mesosphere and upper stratosphere their amplitudes are relatively small indicating considerable wave dissipation. Gravity waves therefore appear to be linked to turbulence production and hence to eddy diffusion in the mesosphere [e.g., *Rapp et al.*, 2004].

[5] Considering the general importance of gravity waves it is interesting to study possible long-term changes. Seasonal variations have been analyzed on many occasions, and sometimes with quite different results. Annual and semiannual variations have been found with maxima at solstices or at equinox. The structures depend on the wave frequency, and can be different for different latitudes as well as different altitudes. Measurement parameter (wind, temperature) also appears to play a role. For details, see, e.g., *Manson et al.* [1999], *Jacobi et al.* [2006], *Dowdy et al.* [2007], *Offermann et al.* [2009], and *Preusse et al.* [2009], and the many references given therein. Interannual (intradecadal) and interdecadal (long-term trend) results are much more scarce. Considerable interannual variability has been observed, and there appear to be indications of solar cycle influences [e.g., *Jiang et al.*, 2006; *Jacobi et al.*, 2006]. An analysis of a limited data set at the station of Wuppertal (51°N, 7°E) was given by *Offermann et al.* [2006]. The latter data are substantially extended and analyzed in detail in the present paper.

[6] Gravity waves are extremely manifold as their wavelengths, periods, and propagation directions are considered. All these parameters vary with altitude, latitude, and specific location of the measurements. Data interpretation is therefore not easy, and a consistent climatology is obviously difficult to obtain. Furthermore ground based measurements lack horizontal and sometimes also vertical information. Satellite measurements are limited to gravity waves of longer wavelengths in the horizontal or vertical direction because of limited spatial resolution of limb sounders in the horizontal and nadir sounders in the vertical [e.g., *Alexander*, 1998; *McLandress et al.*, 2000; *Preusse et al.*, 2006]. These types of measurements have been performed by various satellites instruments such as MLS, LIMS, CRISTA, SABER, HIRDLS, and AMSU [*Wu and Waters*, 1996; *Fetzer and Gille*, 1994; *Eckermann and Preusse*, 1999; *Preusse et al.*, 2006, *Alexander and Ortland*, 2010; *Jiang et al.*, 2006]. (Explanation of the acronyms is given in Table 1.)

Table 1. List of AcronymsAcronym | Definition |
---|

AMSU | Advanced Microwave Sounding Unit |

AURA | NASA satellite, Earth science Projects Division |

CRISTA | Cryogenic Infrared Spectrometers and Telescopes for the Atmosphere |

DOY | Day Of Year |

ESD | Equivalent Summer Duration |

FFT | Fast Fourier Transform |

GCM | General Circulation Model |

GRIPS | Ground based Infrared P-branch Spectrometer |

HIRDLS | High Resolution Dynamics Limb Sounder |

LIMS | Limb Infrared Monitor of the Stratosphere |

MLS | Microwave Limb Sounder |

SABER | Sounding of the Atmosphere using Broadband Emission Radiometry |

TIMED | Thermosphere, Ionosphere, Mesosphere, Energetics, and Dynamics |

WACCM | Whole Atmosphere Community Climate Model |

[7] Up to now the time intervals covered by satellite measurement series are rather limited. Much longer data series are available from various ground experiments. These include radar wind measurements, Lidar intensity or temperature measurements, and airglow spectral or imaging observations of temperature or intensity [e.g., *Fritts and Alexander*, 2003; *Scheer et al.*, 2006; *Jacobi et al.*, 2006; *Hoffmann et al.*, 2011, and references therein]. High time resolution can be obtained by these techniques. Particularly high resolution has been obtained by the OH technique. Mesospheric oscillations with periods of a few minutes have been observed by OH imaging experiments [e.g., *Taylor et al.*, 2007; *Hecht et al.*, 2007].

[8] In the present paper we discuss an OH data series covering 16 years of observation (1994–2009) with a time resolution of 1.3 min taken at the station of Wuppertal (51°N, 7°E, GRIPS II instrument). In addition, six years of data taken at Hohenpeissenberg (48°N, 11°E, GRIPS I, 2004–2009) are also included. This is a large amount of data, only part of which can be discussed here. The paper is organized as follows: Section 2 describes the data and their analysis. Section 3 compares oscillation amplitudes and the standard deviations *σ*_{N} from the nightly mean temperature as a proxy for mesospheric waves. In section 4 the seasonal variations of this parameter are discussed. This includes wave breaking and eddy coefficients K_{zz} as obtained from a recent atmospheric model WACCM 3.5. Section 5 analyzes intradecadal and interdecadal variations. Section 6 discusses the results and compares them with other data. Section 7 summarizes the results.

### 2. Data and Analysis

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Analysis
- 3. Standard Deviations and Wave Amplitudes
- 4. Seasonal Variations
- 5. Intradecadal and Interdecadal Variations
- 6. Discussion
- 7. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[9] The hydroxyl (OH) layer in the upper mesosphere is centered at about 87 km altitude and is 8 km wide (full width at half maximum) [e.g., *Bittner et al.*, 2002; *Oberheide et al.*, 2006; *Mulligan et al.*, 2009; *Offermann et al.*, 2010]. The exact layer altitude is not very important for the wave analyses presented here. The OH molecules are chemically excited and emit a broad spectrum of lines at visible and near infrared wavelengths. These emissions are widely used to determine atmospheric temperatures at this altitude [e.g., *Scheer et al.*, 2006]. Such measurements are also taken at the station of Wuppertal (51°N, 7°E) by a small grating spectrometer of moderate resolution (GRIPS II). With this instrument the intensities of three P band lines at wavelengths of 1.524 *μ*m, 1.533 *μ*m, and 1.543 *μ*m are measured, from which the temperature is derived. Instrument and measurement technique are described in detail by *Bittner et al.* [2002] and *Offermann et al.* [2010]. A similar (“twin”) instrument (GRIPS I) is operated at the station of Hohenpeissenberg (48°N, 11°E) about 360 km south of Wuppertal [*Offermann et al.*, 2010, 2011]. The measurements are taken during night to avoid stray light from the sun. The fields of view are tilted northward to avoid moon interferences. Cloud-free observations were used only. The three infrared lines of one spectrum are measured within 54 s. This should be fast enough to limit the distortion of the derived temperature value by haze possibly drifting into the field of view.

[10] The OH temperatures show strong variations on a wide range of time scales, reaching from minutes to decades. One recurrent variation with large amplitude is the seasonal change. An example for Wuppertal is shown in Figure 1. Mean nightly temperatures are given. They are low in summer and high in winter which is due to the large scale circulation. The seasonal variation is modeled by an harmonic analysis (solid line in Figure 1) with seven free parameters: mean temperature T_{0}, three amplitudes A_{1},A_{2},A_{3} for annual, semiannual, and terannual components, and the corresponding phases. Figure 1 shows the data of 2005. This year is chosen because it is near the middle of our data window analyzed and because the terannual component of the harmonic fit is well visible as relative increases around DOYs 100 and 250, respectively. Seasonal analyses for years 1987–2008 have been described by *Offermann et al.* [2010], and some long-term trends have been obtained.

[11] Here we analyze the temperature measurements from 1994 to 2009 for the fastest oscillations detectable by our technique. One infrared spectrum is taken every 1.3 min. As an example a data set resulting from 16 spectra in a 21 min interval is shown in Figure 2. Oscillation periods down to 2.6 min can be determined according to the Nyquist theorem.

[12] The data are analyzed on a nightly basis. Owing to the time resolution of our instrument the data are fairly noisy. This is partly due to the intensity fluctuations of the three infrared lines used. Their noise is amplified by the nonlinear retrieval method used to determine the temperature [*Bittner et al.*, 2002]. As a measure of the temperature fluctuations we use the standard deviation *σ*_{N} from the nightly mean temperature. These *σ*_{N} values can be occasionally quite large (40 K). They contain both the noise and the atmospheric variations due to waves and “ripples” (see below).

[13] The objective of our analysis is to separate the waves from the noise. For this purpose we use a spectral analysis (FFT). As the noise can be much larger than the amplitudes of the atmospheric waves, it cannot be excluded that some noise fluctuations are mistaken as waves by the spectral analysis. To avoid a distortion of our results we use the following procedure: We perform an FFT analysis not only for the temperatures, but at the same time also for the intensities of all three infrared lines. A wave identified in the temperatures is accepted as valid only if it shows up in the intensities of the lines as well. An example is shown in Figure 2. For all subsequent analyses we use data sets of 16 data points, i.e., 16 measured intensity spectra for the FFT. The three FFT spectra of the three lines are averaged and compared to the temperature FFT spectrum. This is shown in Figure 3 for the temperature and intensity data of Figure 2. An FFT analysis of 16 data points yields amplitudes of eight spectral elements (21 min, 10.4 min, 6.9 min, 5.2 min, 4.2 min, 3.5 min, 3 min, and 2.6 min). We do not use the two end points of the spectrum. We count a wave event as valid only if (1) the temperature spectrum has a relative maximum at a given spectral position, i.e., the amplitude at this point is 5% larger than at its two neighbor positions, and (2) if the mean intensity spectrum has a corresponding maximum at the same spectral position. For the example given in Figure 3 this is the case at the period of 6.9 min. However, we also count an event as valid if the intensity maximum does not occur at the same spectral position as that of the temperature but at the neighbor position. In the example given in Figure 3 this occurs at 3 min and 3.5 min, respectively. The reason is the limited spectral resolution of our FFT. This may attribute a wave to a spectral position or to its neighbor if the wave period is about in the middle. Thus Figure 3 counts two maxima in total.

[14] Our analysis method is fairly conservative. It is justified as follows: If in the atmosphere there is a wave in the temperature this also causes a wave in the three intensity lines used by us. This is because temperature enters the equation of OH level excitation (exponentially). In general temperature variations and those of the intensities seen in the data may not be independent. There are three cases to consider: (1) If the mean of three intensity lines shows a wavelike structure and a temperature wave results (and vice versa) we count this as a valid event. (2) If there is an oscillation in the temperature but not in the intensities there are three possibilities: either the intensities have been disturbed too strongly (for instance by some noise) or the intensities have compensated to some extent, or there is no real wave in the temperature at all, i.e., it is accidental. In each of these cases the event/time interval considered is discarded as a candidate for containing a temperature wave. (3) There is an oscillation seen in the intensities, but not in temperature. This may for instance happen if the intensities are modulated in a wavelike form by some obstacle (cloud) in the field of view. In this case the three lines are changed by the same factor, and the retrieval algorithm does not yield a temperature change. Also this type of event is discarded.

[15] Our selection criterion thus is strict as quite a few (small) waves may be lost. It has, however, the advantage to exclude strong noise fluctuations in the temperature signal from being accidentally taken as real temperature waves. We have checked on this effect by dropping the requirement that an intensity maximum must be seen simultaneously with the temperature maximum. As expected the amplitudes given in Figure 4 below went up. The changes were moderate: between 10% and a factor 2.3.

[16] Our method thus yields lower limits for wave occurrence and wave amplitudes. It does not give a climatology as it is biased for instance toward high temperature amplitudes. This is, however, not a limitation for the present analysis as this studies relative variations, only.

[17] To obtain a general impression of the temperature spectra we have analyzed the data of all nights available in year 1997 which we use as a test year here. Again, data sets of 21 min length have been used. Amplitudes are very different and can be substantial (see Figure 3). We therefore calculate for a given oscillation period a mean amplitude per night which is weighted by the occurrence frequency. Resulting mean spectra are shown in Figure 4 for various times of the year 1997. The curves give means of three months each which are moved in steps of two months through the year (i.e., JFM, MAM, MJJ, JAS, SON, NDJ). The error bars are errors of the mean.

[18] The amplitudes are between 1 K and 5 K, which is typical also of other years. It is interesting to note an increase of amplitudes from long to short periods in Figure 4. This is essentially determined by the occurrence frequencies of the oscillation periods as the amplitudes are rather similar (±5%, decreasing from long to short periods). The increase is seen in a similar way in other years, too (1997–2009).

[19] Only part of the oscillations in Figure 4 can be gravity waves as these can exist only at periods longer than the Brunt-Väissällä period (5 min). Following suggestions by *Taylor and Hapgood* [1990], *Taylor et al.* [1997], *Hecht* [2004], and *Hecht et al.* [2007] we assume as a working hypothesis that our 3 min periods are “ripples” that are indicative of atmospheric instabilities. This is discussed in detail in section 6.1 below. The curves in Figure 4 indicate a seasonal variation of the amplitudes with greatest values in late summer and autumn. This will be discussed in detail below (section 4).

[20] We have checked whether the maximum criterion “5% larger than at its two neighbor positions” might be too weak. We have raised that value in steps up to 40%. This should decrease the mean amplitudes in Figure 4. It does as expected. The changes are, however, moderate. Up to a 20% criterion they are 7–25%. For the 40% criterion they are 50% to a factor 1.4. The relative form of the spectra remains about the same in all cases.

[21] We have also checked whether the increased maximum criteria affect the long-term correlation of the short-period proxy *σ*_{a} and the longer-period proxy *σ*_{N} discussed below (first and second paragraphs in section 4, and Figure 9). It is found that the long-term *σ*_{a} curve in Figure 9 is essentially unchanged in its relative structures. The correlation coefficients between *σ*_{a} and *σ*_{N} are slightly reduced by 4% in the 20% case and by 13% in the 40% case.

[22] It needs to be mentioned that the temperature changes shown in Figure 2a are very large, and high amplitudes result in Figure 3. This is not a common feature. These data rather were chosen to give a pronounced example. In general amplitudes larger than 25 K amount only to a few percent of occurrence for the periods shown in Figure 4. Temperature changes of 50 K or more within 1.3 min occur in less than 4% of the cases.

[23] The complexities of airglow wave structures in the upper mesosphere including line-of-sight cancellations have recently been demonstrated by *Snively et al.* [2010]. They show how difficult it is to analyze in detail spatial and temporal structures especially for measurements from a single station. We do not attempt this here but rather study the long-term stability or variation of our signatures.

### 3. Standard Deviations and Wave Amplitudes

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Analysis
- 3. Standard Deviations and Wave Amplitudes
- 4. Seasonal Variations
- 5. Intradecadal and Interdecadal Variations
- 6. Discussion
- 7. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[24] For a given time interval (e.g., one night) we calculate a mean temperature and the deviations from this mean. The corresponding standard deviation *σ*_{N} is a convenient parameter to estimate the magnitude of the temperature fluctuations in that time interval. These fluctuations contain contributions from genuine atmospheric noise, instrumental noise, gravity waves of various oscillation periods, and possibly other fast waves as tides and fast planetary waves. Figure 5 shows nightly standard deviations *σ*_{N} for the recent years in Wuppertal (black curve). The scatter of the *σ*_{N} data is fairly large and the data have therefore been smoothed by a 50-point Savitzky-Golay algorithm which has a good resolution [*Savitzky and Golay*, 1964]. This type of smoothing is used in all pictures given here if not stated differently. The error is estimated to ±0.7 K. The resulting values in Figure 5 are high and still quite variable. There are two major variations: a long-term change over several years, and a pronounced shorter variation during the course of the year which appears to recur in a similar manner each year. Either variation must have specific reasons beyond simple noise, because it is hard to believe that atmospheric and/or instrumental noise could have the time dependences shown. Especially interesting is the intra-annual variation which shows a pronounced peak in autumn and a smaller peak in spring. This pattern is seen in most of the years analyzed (see also Figure 9 below). To study whether this is a general structure or a feature specific to the Wuppertal measurement site, we have added a second data set to Figure 5 (red curve). It shows *σ*_{N} values measured by our twin instrument GRIPS I at Hohenpeissenberg. Note that this curve has been shifted upwards by 10 K to better distinguish it from the Wuppertal curve. The *σ*_{N} values at the two places are fairly similar, those at Hohenpeissenberg being somewhat larger. The intra-annual variations with the two peaks mentioned are found at Hohenpeissenberg, too. Hence, these features are general structures, indeed.

[25] Gravity wave activity is believed to influence the mesosphere and its circulation [e.g., *Holton*, 1983; *Jiang et al.*, 2006]. This should somehow be linked to our *σ*_{N} values. As gravity waves can have periods and wavelengths of very different magnitudes it needs to be determined which wave has which effect? We start here with the shortest periods we can measure as described in section 2. Afterwards we compare them with *σ*_{N} which covers somewhat longer periods.

[26] As mentioned before, we use the year 1997 as a test year. To express the amplitudes of the short periods in terms of standard deviations we calculate an equivalent standard deviation *σ*_{a} for the shortest oscillations. For this we calculate for each period i (i = 1–6) given in Figure 3 the mean amplitude ā_{i} in a given night. Only nights with more than five data sets of 21 min available are considered. Parameter *σ*_{a} is then calculated from equation (1).

The resulting *σ*_{a} values are used as a measure of short-period wave/oscillation activity. These values are plotted for all nights in 1997 versus *σ*_{N} in Figure 6. A close correlation is obtained with a correlation coefficient r = 0.91. The slope of the regression line is 0.38 K/K. If the whole smoothed data set 1994–2009 discussed below is used, the respective numbers are r = 0.94 and slope = 0.40 K/K.

[27] The time dependence of *σ*_{N} and *σ*_{a} during the course of the year 1997 is shown in Figure 7. As shown by the slope of the line in Figure 6*σ*_{a} amounts to about 40% of *σ*_{N}. A 20-point smoothing has been applied for the two curves. The two curves are nearly parallel, i.e., their relative variations are very similar. This indicates that the regression line in Figure 6 is representative of all parts of the year. The errors are about ±0.3 K for *σ*_{a} and ±0.7 K for *σ*_{N}.

[28] The parameter *σ*_{a} is a cumulative measure of the amplitudes of the six oscillation periods. It remains to be determined whether or not the amplitudes of the individual periods also behave similarly, or whether certain periods might show a peculiar behavior. This might happen because the shortest periods (3–4.2 min) may be of other origin than the longer periods (6.9–10.4 min) (ripples versus gravity waves, see section 6.1, 6.2). To check on this we plotted the amplitudes of the six periods similarly as in Figure 7 and smoothed them accordingly. These mean curves are shown in Figure 8 together with those of *σ*_{a} and *σ*_{N} as references. The estimated errors are ±0.7 K for *σ*_{N}, and between ±0.25 K and ±0.35 K for the other curves. The curves are quite similar and follow more or less the main features of *σ*_{a} and *σ*_{N} with their flat maximum in spring and a more pronounced maximum in late summer. Figure 8 shows that *σ*_{a} and also *σ*_{N} is a reasonable representation of the oscillation activity at these short periods.

[29] These results demonstrate a significant contribution of the very short period wavelike structures to the nightly data variance. About 40% of *σ*_{N} can be ascribed to them. The remaining variance must be due to other longer-period gravity waves, noise, etc. The importance of the short oscillations is further discussed in section 6.

### 4. Seasonal Variations

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Analysis
- 3. Standard Deviations and Wave Amplitudes
- 4. Seasonal Variations
- 5. Intradecadal and Interdecadal Variations
- 6. Discussion
- 7. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[30] Temperature standard deviations *σ*_{N} as shown in Figure 5 are available at Wuppertal back to 1994. This 16 year data record is shown in Figure 9. A 50-point smoothing has been used. Errors are as in Figure 5. The modulation structure with one or two peaks per year is seen in almost all of the years. Superimposed is a long-term increase 1994–2004 with an apparent trend break around 2004, and a decrease in the following years. The whole data set 1994–2009 shows a positive trend of (0.29 ± 0.02) K/a (dashed line in Figure 9). The size of the seasonal peaks is very variable (see also Figure 5).

[31] We have added in Figure 9 the long-term developments of *σ*_{a} (blue) and of the amplitudes of our shortest oscillation (3 min, red). This is because we want to check again on possible differences between the shortest oscillation (3 min) taken as an indication of ripples and the other oscillations contained in *σ*_{a} (see Sections 6.1, 6.2). The attribution of the 3 min period to ripples is discussed in Section 6.1 below. The errors of the two curves are ±0.2 K and ±0.25 K, respectively. There are several data gaps in these curves. They mostly occur because only nights with more than five data sets have been used for improved statistics. The curves follow the major structures of *σ*_{N} quite well. The correlation of *σ*_{N} with *σ*_{a} has a coefficient r = 0.94. The slope of the regression line is 0.40. The correlation coefficient of the 3 min amplitudes with *σ*_{N} is r = 0.88 (slope is 0.26). That of the 3 min amplitudes with *σ*_{a} is r = 0.94 (slope is 0.66). This close relationship of the three parameters is interesting and allows using one (*σ*_{N}) for the others. (If unsmoothed data are correlated the coefficients are between 0.57 and 0.88.) A trend of (0.12 ± 0.01) K/a is obtained by fitting a linear regression to the *σ*_{a} data (not shown in Figure 9). The corresponding numbers for the 3 min oscillation are (0.061 ± 0.008) K/a. The *σ*_{N} data series of Hohenpeißenberg (Figure 5) appears to show a trend different from that at Wuppertal. This series is, however, too short to draw significant conclusions.

[32] In an attempt to understand the nature and variability of the seasonal peaks of *σ*_{N} we have calculated a seasonal mean, i.e., the average of all years shown in Figure 9. The result is given in Figure 10. The data are again very variable and have therefore been smoothed by a 50-point running mean (red curve; the error is about three times the thickness of the line). This mean curve exhibits a seasonal structure as expected from the single years. There is a pronounced late summer peak around DOY 237 and a smaller and broader peak in spring around DOY 108.

[33] We have compared this to the turnaround times (times of zonal wind reversal) in the middle stratosphere (20 hPa altitude). The autumn reversal is at about DOY 244. The spring reversal shows a trend from DOY 110 to DOY 130 between 1988 and 2008. These times are indicated in Figure 10 by vertical dashed (black) lines and by a horizontal black arrow. These times are taken from *Offermann et al.* [2010, Figure 13]. Zonal wind reversal at the altitude of the OH measurements is of greater interest, but cannot be so easily determined. Radar wind measurements nearest to Wuppertal are taken at Juliusruh (55°N, 13°E). They are available at 94 km altitude [*Offermann et al.*, 2010, Figure 15] and show a spring reversal with a trend from DOY 148 to DOY 136 in the time interval 1993–2008. This is indicated by red dashed vertical lines and a red horizontal arrow in Figure 10. The mean value of the autumn turnaround of the radar winds near the mesopause is difficult to determine [*Offermann et al.*, 2010]. We therefore use corresponding radar data at somewhat lower altitude (80 km) from *Keuer et al.* [2007]. They find the autumn reversal near DOY 255 (red vertical dashed line in Figure 10) with a small tendency to shift toward later times.

[34] We thus find that the maxima of the temperature standard deviation *σ*_{N} occur before the circulation reversal in the stratosphere (at 20 hPa) as well in spring as in autumn. This applies even stronger to the mesosphere near the OH altitude. It should be noted that in the upper mesosphere the time of turnaround does not change much with altitude.

[35] It is widely believed that gravity waves propagating upwards in the middle atmosphere tend to break and produce turbulence in the 80–90 km altitude regime. This can be seen, for instance, in the recent WACCM 3.5 whole atmosphere model. This model uses a parameterization of both orographic and nonorographic GW. Details of the parameterization are described by *Garcia et al.* [2007]. The parameterization of nonorographic waves now includes variable GW sources that depend on frontal systems and convection calculated in the model [*Richter et al.*, 2010]. In the upper mesosphere parameterized GW dissipation leads to eddy diffusion of potential temperature and constituents which can be represented as vertical diffusion with coefficient K_{zz} (see *Garcia et al.* [2007, Appendix A4] for a description of the formulation). Figure 11 shows monthly mean K_{zz} averaged over a four-member ensemble of WACCM simulations over the period 1987 to 2005. These simulations were conducted as part of the Stratospheric Processes and their Relation to Climate 2nd Chemistry-Climate Model Validation (SPARC CCMVal-2) activity [*Eyring et al.*, 2010; *Morgenstern et al.*, 2010].

[36] The data in Figure 11 are from 19 years of free model runs for an altitude of 85 km. Results at 90 km and 95 km altitude look essentially the same, however, the values are somewhat larger. The eddy coefficients show a pronounced seasonal variation with a high peak in autumn and a slightly broader and smaller peak in spring. This structure is similar to that seen in the temperature standard deviations in Figure 10. The eddy peak values in April, May, and September in Figure 11 (DOYs 105, 135, and 258) are given in Figure 10 as vertical dash-dotted green lines. They occur near to the turnaround times and hence near to the *σ*_{N} maxima.

[37] In Figure 11 we have added for comparison the turbopause altitudes as derived by *Offermann et al.* [2007] (errors are a few km and are given in detail in their Figure 6). At a fixed observation height (e.g., 90 km) one would expect high gravity wave amplitudes if the turbopause is at low altitude, and vice versa. We have therefore reversed the scale in Figure 11 for better comparison with K_{zz}. A close correspondence of the two curves is seen. It suggests that around months 4, 5, and 9 there is considerable gravity wave activity leading to strong turbulence production.

[38] We have also compared the monthly eddy values in Figure 11 with monthly mean *σ*_{N} values computed from Figure 10. Again, the two curves are quite similar. The correlation coefficient is 0.71 at 99% significance. The similarity is important as data from a global model (WACCM) are compared here to measurements taken at a local station (Wuppertal). These results together with those of Figures 6–9 suggest that our *σ*_{N} parameter is related to gravity wave activity as well as gravity wave breaking, and we will therefore tentatively use it as a corresponding proxy in the following. It should be mentioned that the very short period structures (ripples) are also expected to collapse into turbulence [e.g., *Hecht et al.*, 2007].

[39] It is interesting to note that there is a similar correspondence of our K_{zz} and *σ* values derived from SABER data [*Offermann et al.*, 2009, Figure 8] at lower altitudes (70–80 km). There is, however, only one seasonal K_{zz} maximum at these altitudes. It occurs in summer (July) and meets a corresponding maximum in the SABER data, indeed. This shows that the seasonal structures are very variable with altitude which is discussed below (section 6.3).

### 5. Intradecadal and Interdecadal Variations

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Analysis
- 3. Standard Deviations and Wave Amplitudes
- 4. Seasonal Variations
- 5. Intradecadal and Interdecadal Variations
- 6. Discussion
- 7. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[40] In addition to the pronounced seasonal variations of the temperature standard deviations *σ*_{N} there are substantial long-term changes as shown by Figure 9. There is a decadal increase until 2003/2004 and a subsequent decrease toward 2009. In addition, there appear to be intradecadal variations superimposed. To separate these variations from the seasonal variations and to show the structures more clearly Figure 12 presents yearly mean values of *σ*_{N}. These are calculated from 1 January to 31 December and are plotted in the middle of the year in Figure 12. In order to increase the time resolution of this analysis we have shifted the data series by half a year and calculated corresponding yearly means from 1 July to 30 June of the next year. These are plotted at the end of the year in Figure 12. For comparison Figure 12 shows corresponding annual amplitudes A_{1} of the harmonic analyses described above (red curve).The error of *σ*_{N} is about double the size of the symbols. The error of A_{1} is ±1.6 K according to *Offermann et al.* [2010, Figure 4].

[41] The increasing or decreasing trends of *σ*_{N} before and after 2004 are shown in Figure 12 by linear regression lines. Fit intervals are 1 July 1994 to 1 January 2004, and 1 January 2004 to 1 January 2009, respectively. The differences of the measured data points and the fit lines (residues) show values of several Kelvin and thus are relatively large.

[42] A linear fit line has also been drawn to the A_{1} data in Figure 12 (1994–2009), and substantial residues are seen here, too. A weak trend break at 2004 is found in the A_{1} data as well. It is, however, so weak that it is disregarded here.

[43] It is very interesting to note that the two types of residues in Figure 12 are in antiphase with each other, i.e., a positive residue in *σ*_{N} corresponds to a negative one in A_{1}, and vice versa. We have calculated the correlation coefficient to be r = −0.63 with a significance of 99%. The slope of the corresponding regression line is −0.47 K/K.

[44] If a fit is calculated for the whole *σ*_{N} data set in Figure 12 its slope is (0.32 ± 0.13) K/a. The slope of the corresponding A_{1} fit line is −0.042 K/a. The correlation of these data is marginal with a correlation coefficient of −0.38. The gradient of the regression line is –0.17 K/K. It has the same sign as the corresponding value of the residues but is quite a bit smaller.

[45] We have increased the time resolution of the analysis of the whole *σ*_{N} data set by calculating trends on a monthly basis instead of an annual basis. The results are shown in Figure 13. The monthly trends are near the slope of the entire data set of 0.32 K/yr. They are, however, not constant during the year but show seasonal variations with a broad maximum in late summer/autumn and another one in spring/early summer (see the hatched areas in Figure 13; the horizontal bar from February to November is meant to guide the eye). There are pronounced minima in February and November. These structures are not too conclusive considering the error bars. Nevertheless, the two broad maxima may be interpreted as time periods of increasing gravity wave activity and hence of dynamical forcing, if we assume our standard deviations *σ*_{N} as proxies for wave breaking. The seasonal structure is similar to the general GW structure seen in Figure 10. To indicate this, the mesosphere turnaround times shown in Figure 10 are also shown in Figure 13 as red dashed vertical lines. It is apparent that the two maxima in Figure 13 occur at the same times or somewhat earlier than those in Figure 10. Hence, if our *σ*_{N} is indicative of GW breaking a large and increasing part of it occurs before turnaround.

[46] We have checked whether the long-term trends would influence the seasonal variation of *σ*_{N} (Figure 10). Therefore we divided our data set in two subsets: 1994 to 2001 and 2002 to 2009, respectively. Corresponding seasonal variations were determined as in Figure 10 (not shown here). The curve of the later time interval is a few K above that of the earlier interval because of the trend increase in nine years. Otherwise the seasonal variation has not much changed in this time span. This was to be expected from Figure 13.

### 7. Summary and Conclusions

- Top of page
- Abstract
- 1. Introduction
- 2. Data and Analysis
- 3. Standard Deviations and Wave Amplitudes
- 4. Seasonal Variations
- 5. Intradecadal and Interdecadal Variations
- 6. Discussion
- 7. Summary and Conclusions
- Acknowledgments
- References
- Supporting Information

[78] Fluctuations of mesospheric temperature and winds have frequently been taken as proxies for atmospheric gravity waves. Here we use temperature standard deviations during the night (*σ*_{N}) as indicators of gravity wave activity. Hydroxyl (OH) temperature measurements at Wuppertal (51°N, 7°E) and Hohenpeissenberg (48°N, 11°E) are analyzed. Furthermore, data in windows of 21 min length are Fourier analyzed and yield oscillation amplitudes for periods between 3 and 10 min. These amplitudes are expressed by their equivalent standard deviation *σ*_{a} for comparison with *σ*_{N}. Standard deviations *σ*_{a} and *σ*_{N} are found closely correlated.

[79] The mean duration of the nightly measurements is approximately 5 h. Wave periods up to this length are therefore covered by *σ*_{N}. Hence, relatively short to very short waves/oscillations are analyzed here. The shortest periods (3 min) in their majority cannot be gravity waves as these mostly exist at periods longer than the Brunt-Väissällä period (5 min). They are therefore interpreted as “ripples” that result from atmospheric instabilities/gravity wave breaking. Parameter *σ*_{a} thus contains ripples and short-period gravity waves. There is a close correlation between the ripples (3 min amplitudes), *σ*_{a}, and *σ*_{N}. Therefore these parameters are taken here as proxies for gravity waves and breaking gravity waves. This is supported by a close relationship with turbulent eddy coefficients obtained from a general circulation model (WACCM 3.5). Hence, the picture suggested here is that gravity wave activity in general is accompanied by a certain amount of wave breaking/dissipation at the altitudes of our measurements. This leads us to use the standard deviations to study variations of the forcing of dynamics/circulation in the mesosphere.

[80] Time variations of *σ*_{N} (and *σ*_{a,} 3 min amplitudes) are observed on seasonal, intradecadal, and interdecadal (trend) scales. Seasonal variations show on the mean two relative maxima near (somewhat before) circulation turnaround in spring and autumn. This has been found in 13 years of Wuppertal data and in very similar form in several years of simultaneous measurements at Hohenpeissenberg. A similar seasonal variation has recently been obtained from a gravity wave analysis of SABER data. A physical relationship of gravity wave maxima and times of circulation reversal needs to be determined, though.

[81] There is an extradecadal (trend) variation of *σ*_{N} seen as a long-term increase (16 years). Similar variations are found in the zonal wind speed and the annual component A_{1} of the seasonal temperature variation. The intradecadal changes as well as the extradecadal variations of the zonal wind closely correlate with the parameter *σ*_{N}.

[82] The long-term increase of *σ*_{N} is 1.5%/year, which means a corresponding increase of long-term gravity wave activity. This appears to lead to an increase of zonal wind speed of 0.5 m/s per year at 87.5 km altitude and 55°N. This trend value allows estimating a change in summer length at the mesopause. An increase results that is in qualitative agreement with an increase of the Equivalent Summer Duration (ESD) reported in the literature.

[83] In summary, we observe changes of several dynamical parameters that appear compatible with considerable variations and a long-term increase of the activity of short-period gravity waves in the mesosphere.