Journal of Atmospheric and Solar-Terrestrial Physics 127 (2015) 37–50

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Tidal signatures in temperatures derived from daylight lidar soundingsabove Kühlungsborn (54°N, 12°E)

M. Kopp n, M. Gerding, J. Höffner, F.-J. LübkenLeibniz Institute of Atmospheric Physics at the Rostock University, Schlossstraße 6, 18225 Kühlungsborn, Germany

a r t i c l e i n f o

Article history:Received 23 April 2014Received in revised form18 June 2014Accepted 5 September 2014Available online 10 September 2014

Keywords:Daylight-capable lidarTemporal variationTideMesosphere lower thermosphereStratosphere

x.doi.org/10.1016/j.jastp.2014.09.00226/& 2014 Elsevier Ltd. All rights reserved.

esponding author.

a b s t r a c t

We have developed a new Rayleigh–Mie–Raman (RMR) lidar at the mid-latitude station in Kühlungsborn(54°N, 12°E) for analyzing geophysical phenomena at day and night, e.g., temperature tides andNoctilucent Clouds. For this study we have used about 3100 h of data since April 2011 with additionaldata from summer 2010. The RMR lidar was in operation day and night in addition to the existingdaylight-capable potassium resonance lidar. We show for the first time an overview of the altitudestructure and seasonal variation of temperature tides, observed with lidars between 40 and 100 kmaltitude at a mid-latitude site. There is a gap around 80 km altitude due to a decreasing signal-to-noiseratio during the day. We derive mean tidal amplitudes and phases with 24-, 12-, and 8-h period. In mostof the months, the diurnal component dominates the other tidal components with mean amplitudes of1–2 K in the stratopause region (45–55 km altitude), where it is up to three times higher thansemidiurnal and terdiurnal tidal amplitudes. The diurnal tide is damped at ∼60 km altitude. In themid-mesosphere (65–70 km) diurnal, semidiurnal, and terdiurnal tidal components have comparablemean amplitudes of about 1–1.5 K, except around the equinoxes. Around the mesopause the diurnal tidedominates again, with mean amplitudes of about 4 K, but with a large variability. The seasonal variationshows a conspicuous structure below ∼65 km altitude with tidal amplitudes small in summer and largearound the equinoxes. This structure vanishes above ∼65 km. There, the amplitude increases in summer.The measured tidal amplitudes and phases are compared with the MERRA (Modern Era Retrospectiveanalysis for Research and Applications) reanalysis data. Repeated soundings in subsequent years allow toexamine the year-to-year variation. The data from March in both 2012 and 2013 show a prominentdiurnal tide at around 45 km altitude with amplitudes about three times larger than in the other months.The short-term variability can be examined from continuous lidar operations during clear-sky periods. Ina case study we show a large variability of the tidal amplitudes, especially the 8-h variation. This can onlybe examined due to a good temporal coverage of the lidar data.

& 2014 Elsevier Ltd. All rights reserved.

1. Introduction

Solar thermal tides have an enormous impact on dynamicprocesses of the mesosphere lower thermosphere (MLT) regionand also for coupling mechanisms of different atmospheric layers.These atmospheric tides are global-scale waves inducing varia-tions, e.g., in wind and temperature fields with diurnal, semidiur-nal, and also higher periodic oscillations. Comparable to otherwaves, thermal tides propagate upwards with amplitudes growingwith altitude. Thermal tides are classified into migrating tides(sun-synchronous and westward propagating) and non-migrating(not sun-synchronous) tides. Solar heating due to the absorptionof solar radiation by trace gases (such as water vapor in thetroposphere, ozone in the stratosphere and around the

mesopause, as well as oxygen above 90 km altitude) is the mainexcitation mechanism of migrating thermal tides (e.g., Chapmanand Lindzen, 1970; Forbes, 1984). Prominent processes for theexcitation of non-migrating tides are longitudinal differences intropospheric latent heat release and radiative heating (e.g., Haganand Forbes, 2002; Zhang et al., 2010a), and also non-linearinteractions between migrating tides and other waves(Oberheide et al., 2002). Theoretical numerical modeling of tidesis performed by numerous modelers (e.g., McLandress, 2002;Achatz et al., 2008; Du and Ward, 2010; Zhang et al., 2010b). Tidalinformation from observations are mainly provided by satellitemeasurements (e.g., Talaat and Lieberman, 1999; Oberheide et al.,2006; Huang et al., 2010; Pancheva et al., 2009) and by ground-based measurements, mainly from radars (e.g., Hoffmann et al.,2010; Lu et al., 2011; Jacobi, 2012). Early studies focussed ondiurnal and semidiurnal tides, while the terdiurnal tidal compo-nent attains interest in the literature and is increasingly being

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analyzed, e.g., by the help of ground-based wind radars (e.g.,Teitelbaum et al., 1989; Beldon et al., 2006) or by satelliteobservations (e.g., Pancheva and Smith, 2013).

Only few publications deal with temperature variations derivedby ground-based lidar observations. Daytime lidar soundings inthe mesosphere are still technically challenging and only per-formed at a few stations worldwide (e.g., Chen et al., 1996; vonZahn et al., 2000; Chu et al., 2001; Klekociuk et al., 2003; Höffnerand Lautenbach, 2009). Thus, observed tides being extracted fromlidar temperatures are sparse. There are also few examples duringpolar nights. For example, Lübken et al. (2011) analyzed thermaltides in the summer mesopause region above Davis (69°S, 78°E). Inanother case, Fong et al. (2014) presented winter temperaturetides between 30 and 110 km at McMurdo (78°S, 167°E).

At mid-latitudes (about 40°N) most observations of tides bydaylight temperature lidars are performed between ∼80 and105 km (States and Gardner, 2000b; She et al., 2002; Fricke-Begemann and Höffner, 2005; Yuan et al., 2010). Gille et al.(1991) analyzed tidal components from daylight (nighttime)Rayleigh lidar measurements between 30 and 60 km (80 km) atBiscarrosse, France (44°N, 1°W) for two winter months. Never-theless, the extraction of tidal waves from lidar temperatures withperiods longer than 12-h is rare. Therefore, we have developed anew Rayleigh–Mie–Raman (RMR) lidar at the IAP in Kühlungsborn(54°N, 12°E) for probing altitudes of ∼40–75 km under full daylightconditions and high solar elevation angles of up to 60°. Routinesoundings at day and night with the new RMR lidar started inApril 2011, plus some initial soundings in summer 2010. As aconsequence, about 3100 h of lidar soundings until October 2013are considered in this publication. Additional soundings are per-formed with a daylight-capable potassium resonance lidar measuringtemperatures between ∼80 and 100 km altitude. Thus, a diurnalcoverage is achieved over an altitude range of ∼40–100 km. Admit-tedly, there is a gap in our measured data from both lidars at around80 km due to a low signal-to-noise ratio during the day.

This paper is organized as follows: In Section 2 we describe thenew lidar instrument as well as the available lidar data. Section 3explains the method for deriving tidal parameters from our lidardata. In Section 4 we present the altitude structure of amplitudesand phases for October 2011, and for all available data from 2010 to2013. We also show short-term variations for October 2011.Furthermore, we present an estimation of the seasonal variationof tidal parameters. The measured amplitudes and phases arecompared with MERRA reanalysis data in Section 5. Finally, themain results will be discussed in Section 5 and summarized inSection 6.

2. Description of instruments and data

We have developed a new daylight-capable Rayleigh–Mie–Raman (RMR) lidar (Gerding et al., 2010) in addition to the existingRMR lidar for nighttime temperature soundings (e.g., Alpers et al.,2004; Rauthe et al., 2006; Gerding et al., 2008). An injection-seeded Nd:YAG laser is used as the transmitting power laser in thelidar system. The seeder is locked to an iodine absorption line toachieve high frequency stability needed for the narrow-bandoptical filters in the detector. A beam widening telescope is usedto reduce the laser beam divergence down to about 60 μrad. Thebeam widening telescope actually enables only one-wavelengthoperation at 532 nm. The laser beam is transmitted co-axially intothe atmosphere. Daylight observations require special filteringtechniques that reduce the high background coming fromthe sun.

Spatial filtering by a small Field of View (FOV) and narrow-bandspectral filtering with Fabry–Perot–Etalons (FPE) are applied. The

new RMR lidar has a FOV of about 62 μrad compared to the powerlaser divergence, resulting in a lower background compared totypical (i.e. much larger) FOVs. Due to turbulence in the atmo-sphere, a fast real-time beam-stabilization has to be used tostabilize the laser beam within the small FOV (Eixmann et al.,2014). We adopted a technique first developed and implementedfor the mobile IAP iron lidar (Höffner and Lautenbach, 2009). Theremaining jitter of the beam axis is about 5 μrad during the dayand less at night.

Spectral filtering for suppression of the solar background isachieved by applying a narrow-band interference filter (IF) andtwo Fabry–Perot–Etalons. The full-width-half-maximum (FWHM)of the IF is about 130 pm. Both etalons have similar opticalproperties with a free-spectral-range (FSR) of 120 pm (140 pm)and a FWHM of about 4 pm (4.5 pm) for the first (second) etalon,respectively. The FWHM of the etalon is in the range of theDoppler-broadening of the backscattered Rayleigh signal. There-fore, the transmission (T) of the etalons depends on the actualDoppler-broadening of backscattered light ( >T 90% at 100 K and

<T 80% at 350 K), i.e. on the atmospheric temperature profile. Analtitude dependent transmission correction needs to be applied forabsolute temperature calculation. This will be implemented in thenear future. In this paper we mainly deal with temperaturedeviations from the mean profile. It can be shown that thesystematic error for temperature deviations by ignoring thecorrection is about 5% of the temperature variation, i.e. thesystematic error is much smaller than the statistical uncertainty.We report in detail about the effect of narrow-band FPE filters ontemperature calculation in a prospective publication.

Soundings by RMR lidar are complemented by potassiumresonance lidar measurements between 80 and 100 km altitudeuntil September 2012. The potassium lidar uses a narrow-bandalexandrite laser for scanning the Doppler broadened atomicpotassium-D1 line at a wavelength of 770 nm (von Zahn andHöffner, 1996). The potassium lidar achieved daylight capabilityin 2002 due to the development of a Faraday-Anomalous-Disper-sion-Optical-Filter (FADOF) (e.g. Fricke–Begemann et al., 2002;Höffner and Lautenbach, 2009). The temperature profiles with thecombined lidars are calculated every 15 min with 2 h integrationtime and a vertical resolution of 1 km.

Fig. 1 shows a temperature profile from the daylight RMR lidarand the potassium lidar on 30 September 2011. The exampleshows a nearly continuous profile from ∼38 to 96 km altitude. Itdemonstrates the capability of both lidars to operate at noon andat high solar elevation (∼33°, integration time 09:30–11:30 Uni-versal Time, UT). Measured data of both lidars show a strong wavestructure with a temperature minimum around 83 km, eventhough there is still a small gap and no overlap of the profiles.The statistical uncertainty is less than 3 K below 70 km, and lessthan 10 K below 78 km as well as around 90 km altitude. For theother regions the uncertainty in this particular profile is largerthan 10 K (and less than 20 K). In the subsequent tidal analysis, weomit all data with uncertainty larger than 10 K.

In Fig. 2, a time series of temperature variations from multipledaylight measurements (29 September to 3 October, 2011) isshown. Absolute temperatures (Fig. 2a) and temperature devia-tions from the daily mean (Fig. 2b) are calculated for the upperstratosphere and mesosphere at night and day. The temperatureprofiles of the RMR lidar reach up to 85 km during the night andup to 75 km during the day. They are complemented by data of thepotassium lidar (∼80–100 km at night, ∼85–95 km at day). Asshown in Fig. 2a, absolute temperatures in the mesopause regionare as low as 160 K.

Wave structures with different periods are clearly visible in thewhole altitude region (Fig. 2b). For this example the uncertainty ofthe temperatures is limited to 10 K, so the gap around 80 km is

Fig. 1. Temperature profiles on 30 September, 2011 for daylight RMR (blue) andpotassium lidar (red) with an integration time of 2 h. The statistical uncertainty ismarked as grey area. Solid lines mark regions with uncertainty less than 10 K,dashed lines mark regions with uncertainty between 10 and 20 K. The latter areignored in further analysis. The black line is a temperature profile from COSPARInternational Reference Atmosphere, CIRA-86, Fleming et al. (1990). (For inter-pretation of the references to color in this figure caption, the reader is referred tothe web version of this article.)

Table 1Statistic of RMR (potassium) lidar observations. Each observation is longer than 6 h,i.e., suitable for tidal analysis.

Month Year Observation time (hours)

June 2010 268 (259)July 176

April 2011 168 (184)June 146 (129)October 182 (126)

January 2012 108 (87)March 157May 171 (138)June 105July 188 (108)August 162 (89)

March 2013 130April 153May 102June 207July 273August 196September 98October 115

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larger than in the example above (Fig. 1). The data for this studyare collected from routine soundings between April 2011 andOctober 2013, along with two months of summer data in 2010.

Up to now, a good data coverage has been achieved for spring,summer, and autumn months (see Table 1). During winter, no dataare available for November, December and February due to badweather conditions in these months. For the monthly compositeswe only used periods of more than 90 h per month for the tidalanalysis, except for the data of January and August 2012 (potas-sium lidar) with a slightly shorter total observation time than 90 h.Each observation lasted for at least 6 h. In total, 3100 h areavailable to derive tidal signatures from lidar measurements. InSection 3 we demonstrate the data analysis by using an example ofOctober 2011.

3. Method of data analysis – tidal composite analysis of lidardata

It is obvious from Fig. 2 that the temperature variations show asuperposition of various gravity and tidal waves. In the context ofthis paper we name all waves with periods of 24-, 12-, or 8-h as a

Fig. 2. Series of continuous lidar observations (about 84 h, 29 September–3 October, 201The integration time is 2 h with a statistical uncertainty of maximal 10 K. Grey areas marthis periods are given in Universal Time (UT). Times for tidal analysis given as Local-So

tide, even if the particular modes of the waves cannot be identifiedfrom lidar data. We demonstrate our method of data analysis forOctober 2011 (i.e., 30 September–24 October.). For this month,182 h (within 9 days) of lidar soundings are used to perform acomposite analysis. In this particular case, the lidar was inoperation 84 % of the time. The available temperature data areaveraged for each particular local time and altitude.

Fig. 3a shows absolute temperatures during night and day inthe upper stratosphere and mesosphere. Non-Local-Solar-Time(non-LST) synchronous waves are largely removed by theaveraging process. We subtracted the single daily mean profileto get temperature deviations. Temperature fluctuations of theindividual days are averaged depending on LST (Fig. 3b), result-ing in a time series with a resolution of 30 min for each altitudebin. Harmonic fits of a superposition of diurnal, semidiurnal,and terdiurnal tidal components are applied to these timeseries.

Figs. 3c and d show the temperature fluctuations and fits at 50and 60 km for October 2011. The fitted variations with 24-, 12-,and 8-h period (blue lines) show good agreement to the observedvariation (red lines with error bars) at both altitudes. The errorbars combine statistical uncertainties, error of measurements, andnatural variability. Fig. 3e shows the corresponding fitted tem-perature deviations for the whole altitude range, which nicely

1). Absolute temperatures (a) and temperature deviations from the daily mean (b).k the nocturnal measurement time for a lidar without daylight capability. Times forlar-Time (LST).

Fig. 3. Composite of temperature soundings (i.e. 30 September–24 October 2011). Data averaged with respect to Local-Solar-Time (LST). Absolute temperatures during nightand day in the upper stratosphere and mesosphere (a). Temperature deviations from the daily mean (b). Individual temperatures (black) at 50 km (c) and 60 km altitude(d) with mean values (red, with error bars) and harmonic fit (combined fit of 24-, 12-, and 8-h tidal components, blue line). Error bars combine statistical uncertainties (errorof measurement) and natural variability. Corresponding fitted temperature deviations for 24-, 12-, and 8-h tidal components (e). Residuals after subtraction of the tidalcomponents (f). (For interpretation of the references to color in this figure caption, the reader is referred to the web version of this article.)

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reproduces the original deviation shown in Fig. 3b. Fig. 3f presentsthe residuals after subtraction of the fitted tidal components. Noremaining dominant waves can be seen in the residual data. Theresults are omitted at around 80 km altitude due to an incompletediurnal coverage. The method is also described by Lübken et al.(2011), analyzing thermal tides at polar latitudes.

4. Results of tidal analysis

In this section we present monthly mean amplitudes andphases for October 2011 in comparison with parameters obtainedduring different periods to study the variability of tidal ampli-tudes. Afterwards, we show mean tidal parameters for individual

Fig. 4. Measured tidal amplitudes (a) and phases (b) for the 24-h (blue), 12-h (red),and 8-h (green) components in October 2011. (For interpretation of the referencesto color in this figure caption, the reader is referred to the web version of thisarticle.)

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months derived from all available data. Furthermore, the gooddata coverage allows an estimate of the seasonal variation of tidalamplitudes and phases for the selected heights.

Fig. 4 presents monthly mean tidal amplitudes (a) and phases(b) for the 24-, 12-, and 8-h components, calculated from allmeasurements of October 2011 (i.e. 30 September–24 October).The figure clearly shows a dominant diurnal tidal component at∼40–60 km altitude compared to the semidiurnal and terdiurnalcomponents. Moreover, the 24-h component shows maximalamplitudes near the stratopause at ∼48 km (∼3 K), and decreasingamplitudes above. Semidiurnal amplitudes are up to ∼1.5 K,comparable to the terdiurnal amplitudes. The semidiurnal tidedecreases between ∼40 and 55 km, whereas the terdiurnal tideincreases slightly in this altitude range. At altitudes between ∼60and 70 km, diurnal amplitudes vary between ∼0.5 and 1.5 K, andare smaller than below. Semidiurnal and also terdiurnal ampli-tudes generally increase compared to altitudes below, and are bothlarger than the diurnal amplitudes. The semidiurnal componenthas two maxima (∼3 K) around 65 km and 73 km. Above 90 km,amplitudes of the diurnal and semidiurnal tide increase, e.g., up to∼8 K at 93 km (12-h). The terdiurnal component is also larger

Fig. 5. Short-term variability of measured tidal amplitudes and phases for the 24-h (a),plotted for the whole period in Fig. 4.

compared to lower heights, but generally decreases. The data isomitted above ∼95 km due to a decreasing signal-to-noise ratio.

Regions of downward phase progression with altitude arefound for all tidal components. For the diurnal tide the phaseprogression is in general downward up to 53 km altitude with aphase speed of about �2.6 km/h (vertical wavelength of ∼62 km)and downward above 90 km altitude (�1.3 km/h, ∼31 km). Inbetween, the phase progression is to some extent disturbed andchanges direction. Phase shifts are partly related to small ampli-tudes in the corresponding altitude range. The reader should notethat small amplitudes will cause large uncertainty in the fittingalgorithm, thus, making the associated phase values in these casesquestionable. Semidiurnal and terdiurnal phases propagate down-ward over large altitude ranges (40–90 km). Regions of reversephase progression (upward) are visible at 51–55 km (12-h), and56–59 km (8-h). The 12-h phase speed is about �1.4 km/h below70 km with a corresponding vertical wavelength of ∼17 km.Between ∼86 and 95 km altitude, the 12-h phase propagatesslower with altitude (�1.1 km/h, vertical wavelength of 13 km)compared to altitudes below. The phase speed of the terdiurnalcomponent is about �2.2 km/h (vertical wavelength of ∼18 km)below 70 km and similar between 85 and 90 km.

There is only limited knowledge about the short-term varia-bility of tidal parameters (days to weeks), because, e.g., satellitestypically average 1–2 months of data. To study the variability oftidal amplitudes with time we now separate the data set into twoperiods, namely 30 September–3 October (interval I, ∼84 h of totalsounding time) and 14–24 October (interval II, ∼98 h of totalsounding time), as shown in Fig. 5. The diurnal tidal componentdominates at altitudes of 40–60 km. Amplitudes are similar forboth time intervals up to ∼50 km (Fig. 5a). Above, between 50 and60 km, amplitudes of the 24-h component decrease, stronger forinterval I and less for interval II. Between 60 and 70 km the 24-hamplitudes vary strongly with altitude (0.2–3 K). The 24-h com-ponent shows temporal phase shifts above 60 km (not illustratedhere). Amplitudes in the separated intervals are larger than in thetotal interval. This can be explained by considering the phasesduring both intervals which change by about 9 h at 60 km altitude.This phase shift reduces mean tidal amplitudes compared to theshort period data. Above 70 km a detailed analysis is no longerpossible due to increasing errors (not shown, cf. Fig. 4), but ingeneral, the 24-h tide seems to be larger in interval II compared tointerval I. Amplitudes of the 12-h component show larger varia-tions with time compared to the 24-h component at low altitudes

12-h (b), and 8-h (c) single components. The error bars are omitted for clarity, but

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(40–50 km, see Fig. 5b). Between 62 and 65 km altitude, theamplitudes are similar in both intervals. Again, as found for the24-h component, the 12-h component shows temporal phaseshifts above 65 km (not illustrated here). Amplitudes in theseparated intervals are larger than the total interval (phase shiftduring both intervals by about 4 h at 70 km altitude). This phaseshift reduces mean tidal amplitudes compared to the short perioddata. Similar to the 12-h tide, the 8-h tide also shows a largervariation with time compared to the 24-h component in thelowest altitude range (40–50 km). In interval I the amplitudesare higher on average for the terdiurnal component compared to

Fig. 6. Altitudinal variation of monthly mean tidal amplitudes, 24-h (blue), 12-h (red), anbars are mean values of the single fitted monthly uncertainties from 2010 to 2013. (For inthe web version of this article.)

the amplitudes in interval II (∼50–55 km, 60–75 km, and partlyabove 85 km altitude, Fig. 5c). Terdiurnal tidal amplitudes areenhanced in interval I (up to 2 K at 53 km) and reduced in intervalII (∼0.5 K). Above 60 km altitude, terdiurnal amplitudes increase inboth periods with largest amplitudes in interval I. Obviously, theterdiurnal component is more prominent at the beginning of theperiod and vanishes at the end of the month. A general behaviorconcerning the different altitude ranges can be seen: the diurnal(semidiurnal) tidal component dominates at altitudes between 40and 60 km (above 60–75 km). The 8-h component typically has

d 8-h (green). The particular years and observation hours are listed in Table 1. Errorterpretation of the references to color in this figure caption, the reader is referred to

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the smallest amplitudes, but gets important at some altitudes andintervals, e.g., in the first interval at 50–55 km and 60–75 km.

Beside these case studies on selected short intervals, our lidardata allow to examine the height variation of tidal parameters as afunction of season. In the following, we describe monthly ampli-tudes and phases. Fig. 6 shows monthly mean amplitudes for allavailable data since April 2011 (plus some additional data fromsummer 2010). The weather conditions allow soundings mostly inspring, summer, and autumn. In general, below ∼55 km altitudemost months show higher amplitudes for the diurnal (∼1–2 K)

Fig. 7. Altitudinal variation of monthly mean tidal phases, 24-h (blue), 12-h (red), and 8-hthe 24-h tide are partly plotted modulo 24-h to avoid phase shifts. Similarly for the 12-2010 to 2013. (For interpretation of the references to color in this figure caption, the re

than for the semidiurnal (∼0.5–1 K) and the terdiurnal (∼0.5 K)component. March (∼4.5 K) and October (∼2.5 K) clearly showhigher diurnal amplitudes than the other months at these alti-tudes. For the semidiurnal component, lowest amplitudes areobserved in June (∼0.5 K), whilst they are about three times higherin March/April and also in September/October. Amplitudes of theterdiurnal component are also low in summer (June, less than0.2 K), and larger in spring (∼0.5 K) and autumn (∼1 K). Up to now,tidal amplitudes for winter can only be calculated for January2012. The typical feature of a dominating diurnal tide at lower

(green). The particular years and observation hours are listed in Table 1. Phases forh and 8-h tide. Error bars are mean values of the fitted monthly uncertainties fromader is referred to the web version of this article.)

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altitudes (below ∼60 km) is not observed in January 2012. In thismonth, semidiurnal (diurnal) amplitudes are nearly constant(∼1 K) up to 50 km (60 km), terdiurnal amplitudes are vanishingat 45 km, but increase above. A pronounced maximum of thesemidiurnal component, which does not appear in any othermonth, is found in January 2012 at ∼55 km altitude (∼4 Kamplitude). The data from January may have been influenced bySudden Stratospheric Warming (SSW) events, occurring in themeasurement period of January 2012. In general, above 55 km andup to 65 km altitude, amplitudes of the diurnal componentdecrease in most of the months, showing lowest amplitudes inthe late summer (July/August, ∼0.5 K), and maxima in January(∼5 K) and April (∼2.5 K). The maxima in autumn are lesspronounced. Amplitudes of the semidiurnal tide generally increasewith height, showing also a pronounced summer minimum withlowest amplitudes in the late summer (July/August, ∼0.5 K), and

Fig. 8. Seasonal variation of monthly tidal amplitudes for the 24-h (blue), 12-h (red), anMonthly mean values from 2010 to 2013 are calculated for all data listed in Table 1. Errwhole observation time for January and August (f) is slightly shorter (∼90 h) than for theto color in this figure caption, the reader is referred to the web version of this article.)

maxima in March/April, and September/October (up to 3 K).Terdiurnal amplitudes increase less with height, also revealing aminimum in summer (June–August), and maxima in autumn (upto 1 K). At these altitudes (55–65 km) January amplitudes show astronger increase compared to other months as seen especially forthe 24- and 8-h components (24-h maximum: ∼5 K, 8-h max-imum: ∼4 K). Between 65 and 70 km altitude, amplitudes of allcomponents typically increase again. Above 80 km (∼85–90 km),amplitudes of all components decrease in most cases, whereasabove ∼90 km, amplitudes tend to increase, again. Error bars tendto be larger at these upper heights.

Fig. 7 shows the altitudinal variation of monthly mean phasesfor all available data. At low altitudes (∼40–60 km) the phaseprogression of the diurnal component is typically downward in allmonths. Above ∼60 km, there is a change of phase progressionfrom downward to upward propagation in all months, but altitude

d 8-h (green) tidal components provided from RMR (a–e) and potassium (f) lidar.or bars are mean values of the fitted monthly uncertainties from 2010 to 2013. Theother months considered for the tidal analysis. (For interpretation of the references

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and strength of the phase shift vary between the months. Thephase shift occurs in January at ∼55 km, between April and Augustand also in October at ∼65–70 km, and in March and September at∼60 km. At altitudes above 85 km, phases are nearly constant inJanuary, April, May, and August, and downward in June, July and tosome extend in October. The semidiurnal tide shows a downwardphase progression for all months at altitudes between ∼40 and65 km, except for January where the downward phase progressionis only up to 55 km. In some months the phase gradient changesabove, showing, e.g., upward progression in January, April andJune.

Between 85 and 95 km altitude the phase progression of the12-h component is typically downward or nearly constant (June

Fig. 9. Seasonal variation of monthly tidal phases for the 24-h (blue), 12-h (red), and 8-hmean values from 2010 to 2013 are calculated for all data listed in Table 1. Error bars are mdata is partly missing. (For interpretation of the references to color in this figure captio

and July). In comparison to the semidiurnal component, the phasepropagation of the terdiurnal component is more disturbed, partlydue to the lower amplitudes of the terdiurnal component. Thisresults in a larger uncertainty for the phase. At altitudes below∼75 km, phases are nearly constant (March until June) or down-ward progressing (January, July until October). Between 85 and95 km altitude, phases are roughly constant in January, April, andOctober, whilst they propagate downward in May until August.

Beside this height variation of tidal amplitudes and phases,Figs. 6 and 7 already show the seasonal variation of tides. This canbe seen more clearly in Figs. 8 and 9. Different altitude rangesbetween 45 and 90 km are presented (mean values across 5 kmvertical range). As already seen in Figs. 6 and 7, in the stratopause

(green) tidal components provided from RMR (a–e) and potassium (f) lidar. Monthlyean values of the fitted monthly uncertainties from 2010 to 2013. At some altitudesn, the reader is referred to the web version of this article.)

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region (45–55 km) the diurnal tide dominates compared to the 12-h and 8-h components (Fig. 8a and b). Diurnal amplitudes arenearly constant (1.5 K) from May to August, and increase aroundequinoxes. As explained above, January has a slightly reduceddiurnal amplitude, potentially affected by the SSW in 2012.Semidiurnal amplitudes are lowest in summer and again increasearound equinoxes. Seasonal variations of the terdiurnal amplitudesare similar to the semidiurnal tidal amplitudes (e.g. the increasearound autumn equinox), but less pronounced. Between 50 and65 km altitude (Fig. 8b–d), the semi- and terdiurnal tidal ampli-tudes are roughly similar in summer, but smaller for the terdiurnaltide in spring and autumn. For the 8-h tide the largest amplitudesare observed in October (∼1 K) and lowest in June (less 0.2 K). Inthe mid-mesosphere the semidiurnal and terdiurnal componentbecome more and more important compared to the diurnalvariation. At altitudes between 55 and 65 km (Fig. 8c and d)diurnal amplitudes decrease compared to below, whereas semi-diurnal amplitudes generally increase. Amplitudes of all compo-nents show a pronounced seasonal variation with a minimum insummer. This can be seen up to ∼65 km altitude. Between 60 and70 km, esp. the 24-h and 12-h tidal components have similaramplitudes (except around equinoxes and January). In summerthey typically increase again up to 70 km altitude (Fig. 8e). In theupper mesosphere (Fig. 8f) diurnal amplitudes are again largerthan the others for almost all months. Very large amplitudes arefound in April (∼14 K) and August (∼6.5 K). The whole observationtime for August is slightly shorter (∼90 h) than for the othermonths considered for the tidal analysis.

At a given height range the phase of the 24-h tidal componentis nearly constant over the months and varies slightly around17 LST (16 LST) at altitudes between 45 and 55 km (55–60 km), seeFig. 9a–c. Above 60 km the monthly phase variation is largercompared to altitudes below. The phase of the 24-h component isoffset by about 6 h (May–October). Generally, the phases of thesemidiurnal and the terdiurnal tide vary stronger compared to thediurnal tide. With increasing altitudes the phase variations be-come larger. At some altitudes the data are in some extendomitted, because small amplitudes hinder the phase calculation.In the mesopause region (Fig. 9f) the data coverage is limited,because the data are only available for January, April to August,and October.

Weather conditions and continuous lidar operation enablerepeated soundings in subsequent years, i.e. allow to examinethe year-to-year variation. In a case study we show the data fromMarch 2012 to 2013, because the most remarkable altitude profiles(Fig. 10) are observed in March. The amplitudes are similar in bothyears for all tidal components. Here, a prominent diurnal tide isfound at around 46 km altitude with amplitudes nearly threetimes larger than in other months (∼5 K), in both 2012 and 2013.Diurnal amplitudes decrease with height (above 46 km), whereasthe semidiurnal component shows increasing amplitudes up to60 km. Terdiurnal amplitudes are roughly constant with altitude.Above 58 km (54–63 km) amplitudes are higher for semidiurnalthan for diurnal variations in March 2012 (2013). Another diurnalpeak (∼4 K at 54 km) is found in March 2012. These two yearsreveal similar features for all tidal components. We thereforeconclude that the tidal features presumable vary little from yearto year. We note that the similarity of the tidal amplitudes in 2012and 2013 is also observed in other months, although less pro-nounced. However, a detailed study of the year-to-year variabilityof tidal amplitudes and phases is beyond the scope of this paper.The year-to-year persistency of our main results also implies thatthey are not significantly influenced by instrumental effects.

5. Discussion

Temperature fluctuations can be measured by lidars with ahigh temporal and vertical resolution. Our new, daylight-indepen-dent lidar data set covering ∼3100 h gives an insight into the localtidal structure between 40 and 100 km altitude at Kühlungsborn(54°N, 12°E). Nevertheless, we cannot distinguish between migrat-ing and non-migrating tides as well as local sun-synchronouswaves in lidar data from a single location. In contrast, space-borneinstruments like satellites provide global structures with a limitedlocal time coverage. However, satellite's tidal measurements needsignificant amount of sampling time to cover 24-h variations atone location and, thus, have great difficulties conducting tidalvariability study. Thus, a combination of both, satellites andground based techniques are desirable for analyzing tidal signa-tures. Ward et al. (2010) show good agreement between satelliteand ground based tidal wind signatures in the CAWSES (Climateand Weather of the Sun-Earth System) tidal campaign. A compar-ison of our extensive temperature data set with other parameters(e.g., wind data) and also with satellite data is planned for thefuture.

For a direct comparison of our measurements with an inde-pendent data set we calculated mean amplitudes and phases fromModern Era Retrospective Analysis for Research and Applications(MERRA), cf. Rienecker et al. (2011). The MERRA data set deliversan un-interrupted three-hourly data set each day (at 00:00 UT,03:00 UT, etc.) and is, in contrast to the lidar, not limited to clear-sky conditions. In this version, the horizontal grid resolution is1.25°�1.25° with a number of 42 pressure levels and a top levelpressure of 0.1 hPa (∼65 km). See http://gmao.gsfc.nasa.gov/research/merra/intro.php for a description of the MERRA dataand method. The altitudes are given in pressure units for MERRA.Thus, for a comparison with the lidar data, altitudes are con-verted in geometric altitudes via the approximated formula:

= −Z H P Pln ( / )0 , with the scale height H¼7 km, pressure P, andreference pressure =P 1013 hPa0 . We use the same months con-sidered for the lidar observations, see Fig. 11. The MERRA data aredivided into three altitude ranges (a) 44–51 km, (b) 51–57 km, and(c) 57–65 km. In general, the MERRA data show a dominatingdiurnal tide at altitudes below 60 km. The amplitudes are up to∼2.2 K for the 24-h component, ∼0.6 K for the 12-h component,and small (∼0.3 K) for the 8-h component. Mean values of tidalamplitudes and also the phase progression agree roughly with ourlidar observations. The terdiurnal variation is smaller than in ourdata, potentially due to the lower temporal resolution of MERRA.The monthly mean composites of MERRA do not reproduce theseasonal variation with smallest amplitudes in summer as found inour data. As seen in the lidar data the diurnal tide in MERRAtypically decreases with altitude. The 12-h and 8-h componentsare roughly constant, i.e., do not show a significant increase withaltitude, as observed by lidar especially at equinox.

Fig. 12 shows an altitude profile (October 2011) of MERRAamplitudes and phases for the 24-, 12-, and 8-h componentsbetween 40 and 65 km. In general, the height structure is similarto the lidar data (Fig. 4). The diurnal variation dominates thesemidiurnal and terdiurnal variation. As mentioned before, thelargest amplitudes (up to ∼2.5 K) for the diurnal tide are observedat around 50 km. In agreement with the lidar data from October2011 (Fig. 4), the tidal phases from MERRA show a downwardprogression for all components.

Overall for this time period between 2011 and 2013, the MERRAdata do not show the general increase of amplitudes aroundequinoxes in the monthly mean composite and underestimatesthe terdiurnal tide, which is seen in our lidar data. Albeit, thedominating diurnal tide as well as the phase behavior is inagreement with our data.

Fig. 10. Year-to-year comparison of tidal amplitudes (March 2012 and 2013) for the24-h (blue), 12-h (red), and 8-h (green) tidal components. Error bars combinestatistical uncertainties (photon noise) and natural variability. (For interpretation ofthe references to color in this figure caption, the reader is referred to the webversion of this article.)

Fig. 11. Seasonal variation of monthly tidal amplitudes and phases for the 24-h (blue), 12from 2010 to 2013, sampled comparable to the lidar data set for all months with lidapproximated formula (see text for details). (For interpretation of the references to colo

Fig. 12. Monthly tidal amplitudes and phases for the 24-h (blue), 12-h (red), and8-h (green) tidal components from MERRA data of October 2011 (see Fig. 4 for acomparison with lidar amplitudes and phases). Geometric altitudes are calculatedvia an approximated formula, see text for details. (For interpretation of thereferences to color in this figure caption, the reader is referred to the web versionof this article.)

M. Kopp et al. / Journal of Atmospheric and Solar-Terrestrial Physics 127 (2015) 37–50 47

At mid-latitudes, diurnal, semidiurnal, and terdiurnal tideshave been observed before in wind data (e.g., Hoffmann et al.,2010; Lu et al., 2011) and in temperature data (e.g., States and

-h (red), and 8-h (green) tidal components of the MERRA data. Monthly mean valuesar data. Altitude ranges are shown in geometric altitudes and calculated via anr in this figure caption, the reader is referred to the web version of this article.)

M. Kopp et al. / Journal of Atmospheric and Solar-Terrestrial Physics 127 (2015) 37–5048

Gardner, 2000b) of the mesosphere and lower thermosphere.Most of these data sets cover only a part of the region describedhere, or do not consider all tidal components. Precise temperaturesoundings in the mesosphere and lower thermosphere are rare, asthey require regular daytime lidar soundings. They are extremelychallenging and only performed at few stations. Most of theinformation derived from lidar temperatures are subject to theMLT region (e.g., Fricke-Begemann and Höffner, 2005; Yuan et al.,2010).

Fricke-Begemann and Höffner (2005) presented the 24-h, 12-h,and 8-h tidal wave perturbations in temperatures around themesopause region (∼80–105 km) at two stations for one montheach (Tenerife, 28°N, November 2000 and Kühlungsborn, 54°N,February 2003). In this case study, Fricke-Begemann and Höffner(2005) found that the amplitude of the diurnal tide aboveKühlungsborn is in most altitudes less than half of the semidiurnalamplitude in winter. We have used the same potassium lidar forthe mesopause region as Fricke-Begemann and Höffner (2005)have before, but we have widely extended the data base.

States and Gardner (2000b) show the seasonal variation oftides observed by a sodium lidar from February 1996 to January1998 at another mid-latitude station, Urbana, Illinois (40°N,88°W). The seasonal variation of the tides is similar in spring,summer, and autumn. The 24-h variation is reduced in winter asalso reported by Fricke-Begemann and Höffner (2005) and seen inour data set. Yuan et al. (2010) presented a study of diurnal tidalperturbations in temperatures by a sodium lidar (∼5000 h) andTIMED/SABER observations above Fort Collins (41°N, 105°W). Incontrast to States and Gardner (2000b), the tidal amplitudes showan annual variation with a maximum in February.

As mentioned above, Fricke-Begemann and Höffner (2005)found a lower diurnal than semidiurnal tide in winter, as wellseen in our new lidar data (January). Furthermore, Yuan et al.(2010) reported a summer minimum (2–3 K), which is also seen inour lidar data. They found propagating diurnal tides observed withthe lidar near equinox, and trapped modes during solstice. TheSABER data in this study show maxima (6–7 K) in spring (March)and autumn (September), and minima in summer and winter(around solstices) as known from classical theory (Forbes, 1982a).As mentioned above, we found a similar seasonal behavior withmaxima in April (14 K) and late summer (August, 6.5 K) in the newlidar data. We also see trapped modes in winter (January) with amaximum near 24 LST. The seasonal variation in the MLT region ismainly controlled by the combination of zonal mean winds andsolar heating (McLandress, 2002). Hagan and Roble (2001) re-ported that the differences in phases between the infrared andultraviolet forcing could have an impact on the seasonal variationof the tidal amplitudes. Furthermore, nonlinear interactions be-tween the migrating diurnal tide and stationary planetary waves(SPW1) can produce trapped diurnal tidal modes. The maximumof SPW1 is found in winter and early spring in the northernhemisphere at middle latitudes, potentially initiating the largediurnal amplitudes in the MLT region. Forbes and Hagan (1988)presented differences in the diurnal tide propagation betweensolstice and equinox. Large atmospheric dissipation effects on thediurnal tide propagation during solstice could excite more eva-nescent modes due to mode coupling. Here, the dominant Houghmode (1, 1) couples into the first symmetric and asymmetricevanescent Hough modes (1, �2) and (1, �1). Thus the verticalwavelength increases (Yuan et al., 2010). This is also seen in ourMLT data at winter solstice.

The semidiurnal tidal phase during summer near Fort Collinsshows large vertical wavelengths in the mesopause region (Yuanet al., 2008), similar to our observations. During January andOctober we observe much shorter vertical wavelengths of thesemidiurnal tide, which is also reported by Fricke-Begemann and

Höffner (2005) for an earlier Kühlungsborn data set, but not, e.g.,by Yuan et al. (2008). This indicates that above our site the higher-order Hough modes (e.g. H2.10–H2.17) play a larger role comparedto Fort Collins.

Very few studies cover the height range below 80 km. Gilleet al. (1991) analyzed tidal components from Rayleigh lidarmeasurements between 30 and 80 km at Biscarrosse, France(44°N, 1°W) for winter (November 1988 and January 1989). Fordaylight conditions their lidar only covers heights below 60 km.Similar to our observations, they found constant amplitudesbetween 35 and 60 km (2–3 K) for the diurnal variation, but twiceas large as in our data set. Vice versa, the semidiurnal variation hasbeen found smaller in the Biscarrosse data (∼2.5 K). The Januarytidal amplitudes in our data may have been influenced by suddenstratospheric warmings (SSWs) occurring in 2012. This result isconsistent with WACCM (Whole Atmosphere Community ClimateModel) simulations in the mesosphere and lower thermosphereregion. Tidal amplitudes of the 12-h migrating solar tide areenhanced during SSWs due to changes in ozone forcing andnonlinear planetary wave interaction (Pedatella et al., 2012).

Dudhia et al. (1993) reported a local maximum of ∼3 K (at50 km) observed for the 24-h tide at mid-latitudes. They analyzeddata from Improved Stratospheric And Mesospheric Sounder(ISAMS) on Upper Atmosphere Research Satellite (UARS) between20 and 80 km in a winter period (December 5, 1991–January 13,1992). Again, the amplitudes of diurnal variation in the strato-pause region are about twice as large as in our wintertime data.But also ISAMS data show a dominating semidiurnal tide, in goodagreement to our observations, potentially again reflecting theinfluence of SSW.

Sakazaki et al. (2012) reported diurnal tides derived fromSABER and MERRA reanalysis data. At mid-latitudes, double-maxima with 2–3 K in the upper stratosphere (near 50 km) occurin January. For the diurnal tide, amplitude maxima are found nearthe stratopause in all months (January, April, July, and October), aswe see in our lidar data. A constant phase is obvious in this regionat ∼18 LT throughout the year, in good agreement with our resultsfrom lidar and MERRA data.

In most months, our lidar data set shows diurnal tides dom-inating up to ∼60 km. But above, amplitudes of the diurnal tidedecrease, perhaps due to the fact that the tides are trapped.Trapped tides are predicted poleward of 30° latitude and receivethe strongest excitation by absorption of ozone at ∼45 km altitude(e.g.,). The semidiurnal tide dominates compared to the diurnaltide and partly shows an exponential growth with height, e.g., inOctober. A vertical wavelength of about 62 km is derived for thediurnal component from phase progression of about �2.6 km /h(Fig. 5). This vertical wavelength indicates negative Hough modes(only existing for diurnal tides) and is in agreement with theore-tical expectations (e.g., Forbes and Garett, 1978). Our observationsare consistent with model results from Lindzen (1990), showingthat most of the diurnal forcing goes into these negative, non-propagating modes.

Mukhtarov et al. (2009) reported the global (50°S–50°N)structure, seasonal, and inter-annual variability of the migratingdiurnal tide derived from SABER/TIMED temperature measure-ments between 20 and 120 km (January 2002–December 2007).As discussed above, they also reported that below 70 km heightthe first symmetric trapped (1, �2) mode is dominating andamplifies around 50 km. Above this height mainly the symmetricpropagating (1, 1) mode exists, as the trapped tidal mode (1, �2)decays beyond this altitude. The diurnal phase is constant duringthe considered six years and is in agreement with our data close to16 LT. At mid-latitudes, diurnal amplitudes from SABER are be-tween 4.5 and 5.5 K (near 40°). In the SABER data, the seasonalvariation is dominated by a main annual variation (maximum

M. Kopp et al. / Journal of Atmospheric and Solar-Terrestrial Physics 127 (2015) 37–50 49

during summer) and a secondary semi-annual variation withequinoctial maxima. Our lidar data do not show a pronouncedannual variation, but clearly a semi-annual variation. We have noreasonable explanation regarding the missing annual variation inour data at these altitudes. Perhaps this is because our lidarobservations are performed at higher mid-latitudes (54°N). SABERsamples up to maximal 50°N. Furthermore, only local variationscan be derived from lidar measurements, but not the differentmodes of the tide. At higher altitudes (90 km) the semi-annualvariability with maxima during equinoxes dominates, similar toour observations.

There are few publications dealing with the terdiurnal tidalcomponent compared to the diurnal and semidiurnal tidal com-ponent. Direct solar heating of the lower and also the middleatmosphere is mentioned as the source for the terdiurnal tide(Chapman and Lindzen, 1970). Further processes are described byTeitelbaum et al. (1989) like a non-linear interaction between the24-h and 12-h tidal components, or an interaction between the24-h component and gravity waves, or a combination of more thanone mechanism. For example Pancheva and Smith (2013) found aclear seasonal variability of the terdiurnal tide at mid-latitudeswith maxima at equinoxes and winter from 8 years of SABER data(2002–2009). Our observation of the seasonal variation of theterdiurnal temperature tide also shows a maximum at equinoxes(esp. autumn). The observation is in general agreement with winddata from mid-latitudes. Similar to us, Beldon et al. (2006) as wellas Smith (2000) observed largest amplitudes of the terdiurnal tidein autumn or around equinoxes, using radar or UARS satellite data,respectively.

6. Summary and conclusions

We have reported a first data set of temporal variations (24-,12-, and 8-h periods) in temperatures from daylight lidar observa-tions between 40 and 100 km. In this study local tides are analyzedusing data between 2010 and 2013 at IAP in Kühlungsborn (54°N,12°E). Soundings with the new daylight-capable Rayleigh–Mie–Raman lidar reach up to approximately 75 km during the day andup to 85 km during the night, complemented by a potassiumresonance lidar above 80 km. Harmonic fits including diurnal andhigher tidal components cover most of the observed total varia-tion. The three tidal components (24-, 12-, and 8-h) are presentduring most months.

In general, the altitudinal variation shows a dominating diurnaltide in the stratopause region (∼1–2 K at 45–55 km). Above 55–60 km the diurnal tide is more or less damped. At ∼65–70 km alltidal components have comparable amplitudes (∼1–1.5 K). Largermean amplitudes (∼4 K for the dominating diurnal tide) as well asa greater variability are seen around 90 km.

Due to the good temporal coverage, continuous lidar soundingsenable studying the short-term variability of the different tidalcomponents. Short period tides (i.e., the 8- and 12-h) in October2011 show differences (greater amplitudes) compared to the meanstate. This is similar to the month-to-month variation, being aswell greater for the 8- and 12-h than for the 24-h variation.Obviously, intermittent sources and propagation conditions play alarger role for the semidiurnal and terdiurnal tide compared to thediurnal tide.

The seasonal variation of the diurnal and semidiurnal (terdiur-nal) tidal amplitudes shows maxima in spring and autumn(autumn) up to ∼65 km. This is in agreement with theoreticalexpectations, mentioning direct heating by solar light absorptionby ozone and water vapor. Equinox conditions create the bestsource for a semidiurnal variation. This is shown by the roughlysemi-annual variation of the 12-h component already in the

stratosphere. Wind conditions around the stratopause favor thepropagation of the semidiurnal tide in spring and autumn, whileamplitudes remain constant in summer, indicating at least partialwave dumping. In the upper mesosphere/lower thermosphere(85–90 km), diurnal amplitudes increase again. A high seasonalvariability of diurnal and terdiurnal amplitudes is obvious in theupper mesosphere indicating the relevance of (time-dependent)wind filtering for the propagation of tidal waves from the strato-sphere to the mesopause region. Unfortunately, a detailed seasonalvariation for this altitude region cannot be described due to thelimited data set.

In most months upward propagating tides are found high up tothe lower thermosphere. For October 2011, the diurnal componentshows a downward phase progression with altitude (below∼55 km) of about ∼�2.6 km/h, corresponding to a vertical wave-length of 62 km. In theoretical expectations this vertical wave-length indicates negative Hough modes. Semidiurnal and terdiur-nal phase progression is roughly downward over the wholealtitude range, 40–90 km (12-h: �1.4 km/h, 17 km, and 8-h:�2.2 km/h, 18 km). In the upper mesosphere the 12-h phaseprogression is slightly slower (�1.1 km/h, 13 km) compared tolower altitudes.

The comparatively large amplitude of the semidiurnal tide inthe January stratopause region appears due to the influence ofSSW. As described in literature, the enhanced amplitudes aremaybe due to changes in ozone forcing and non-linear planetarywave interactions.

MERRA reproduces our observations of mean tidal amplitudesand phases below ∼60 km altitude. Nevertheless, the seasonalvariation is damped compared to our results in these two and ahalf years of data. The terdiurnal variation may be underestimateddue to the limited temporal resolution of the MERRA data set.

The seasonal and altitudinal variation of tidal sources andpropagation conditions cannot only be revealed by temperaturedata. In the future, the seasonal variation and short term varia-bility should be further analyzed by means of additional data setsand the continuation of lidar studies.

Acknowledgments

The authors gratefully acknowledge Dieter H.W. Peters forhelpful discussions. We thank Torsten Köpnick and Michael Priest-er for the maintenance and operation of the lidar systems at IAP.We also wish to thank Sebastian Mitreiter representing all stu-dents for their numerous hours of lidar operation. This researchhas been partly supported by the Deutsche Forschungsge-meinschaft (DFG) under Grant GE 1625/2-1.

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