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Advances in Space Research 40 (2007) 846–854

On the winter anomaly of the night-to-day ratio of ozonein the middle to upper mesosphere in middle to high latitudes

G.R. Sonnemann a,b, P. Hartogh b, Ch. Jarchow b, M. Grygalashvyly a,*, U. Berger a

a Leibniz-Institute of Atmospheric Physics at the University Rostock in Kuhlungsborn, Schloss-Str. 6, D-18225 Ostseebad Kuhlungsborn, Germanyb Max-Planck-Institute for Solar System Research, Max-Planck-Str. 2, D-37191 Katlenburg-Lindau, Germany

Received 4 November 2006; received in revised form 12 January 2007; accepted 15 January 2007

Abstract

Long-term measurements of ozone by means of the microwave technique performed at Lindau (51.66�N, 10.13�E), Germany,revealed a winter anomaly of the night-to-day ratio (NDR) which is more clearly pronounced as the so-called tertiary nighttime ozonemaximum. The domain of occurrence also differs somewhat from that of the nighttime ozone enhancement. The maximum winter-to-summer ratio amounts to a value of two to three in 70 km height. The annual variation of the NDR is modulated by oscillations of plan-etary time scale. 3D-calculations on the basis of the advanced GCM LIMA essentially reflect the observations but also show some typicaldifferences which probably result from a somewhat too humid model atmosphere in middle latitudes. We analyzed the most importantimpacts on the middle mesospheric ozone. The strongest impacts are connected with the annual variation of water vapor and theso-called Doppler-Sonnemann effect considering the influence of the zonal wind on the chemistry due to the fact that ozone is subjectedto an effective dissociation longer than molecular oxygen for an increasing solar zenith angle. Because of that the net odd oxygenproduction decreases faster than the formation of atomic oxygen from ozone which is involved in an odd oxygen destructing catalyticcycle. A shortening of the time of sunset by a west wind regime increases the nighttime ozone level relatively, whereas the daytime ozoneis less influenced by the zonal wind in the domain considered.� 2007 COSPAR. Published by Elsevier Ltd. All rights reserved.

Keywords: Tertiary ozone maximum; Mesospheric chemistry; Doppler-Sonnemann effect; DSE; Sudden stratospheric warming; Catalytic cycle

1. Introduction

A large body of publications deals with the so-calledtertiary ozone maximum (e.g., Froidevaux et al., 1996;Jarchow et al., 2000; Marsh et al., 2001; Hartogh et al.,2004; Degenstein et al., 2005; Seppala et al., 2006; Sonne-mann et al., 2006a), indeed a somewhat strange term as itreflects the historical sequence of its detection, but it doesnot relate to a geophysical cause. This was the reason tocalling it MMM (middle mesospheric maximum of ozone)in Hartogh et al., 2004. The characteristics of the MMMare summarized in the following way: it is only an effectoccurring at high latitudes close to the polar night termi-

0273-1177/$30 � 2007 COSPAR. Published by Elsevier Ltd. All rights reserv

doi:10.1016/j.asr.2007.01.039

* Corresponding author. Tel.: +49 38293 68144.E-mail address: oa009@iap-kborn.de (M. Grygalashvyly).

nator around 72 km altitude during nightime in the winterhalf of the year and extends into middle latitudes withdecreasing amplitude. Suppressing the day-to-day fluctua-tions by a smoothing procedure, the observations show astrong variation of its amplitude in the order of weeks.The MMM was interpreted by Marsh et al., 2001 in termsof stronger decline of the water vapor dissociation rate forincreasing solar zenith angle than that of molecular oxy-gen entailing an imbalance between odd oxygen (i.e., thesum of ozone and atomic oxygen) production and its lossby reactions with hydrogen radicals. This interpretationwas extended by Hartogh et al., 2004; who additionallyconsider the very slow decrease of the ozone dissociationrate with increasing solar zenith angle. The dissociation ofozone forms atomic oxygen which returns largely toozone, but it is also involved in the important odd oxygendestroying catalytic cycle:

ed.

G.R. Sonnemann et al. / Advances in Space Research 40 (2007) 846–854 847

HþO3 ! OHþO2 and

OHþO! HþO2

net: OþO3 ! 2O2

ð1Þ

Hence, this process considerably reduces the effect of oddoxygen increase with growing solar zenith angle.

In winter, the daytime the ozone concentration does notremarkably increase, rather is slightly decreases. The annu-al variation of the MMM displays some peculiarities: Theannual maximum occurs somewhat before winter solstice.In late March and April a subsidiary maximum appearsat somewhat higher altitudes than the primary maximum.In other words, there is a slight long-lasting relative mini-mum of the annual variation of the MMM occurring inFebruary. The modulations differ from year to year. How-ever, after winter solstice a strong drop of the amplitudecan frequently be registered further resulting in a decreaseof the average amplitude of the MMM in January/February.

Although, the Lyman-a radiation, which dissociateswater vapor forming odd oxygen destructing hydrogenradicals, changes with the solar rotation, the variation isnot so strong within a rotation period of 27 days (Woodset al., 2000) and the optical depth of unity will already bereached above the height of the MMM in middle and highlatitudes, particularly in winter. In other words, it cannottrigger the variation with planetary time scale, i.e., withregard to definition variations for longer than a day. Thevariation of the solar radiation is symmetric relative tothe solstices but it varies with solar activity.

Evidently, the night-to-day ratio (NDR) is closely relat-ed to the MMM, but it also relates to the change of thediurnal variation. We define as nighttime value the averagebetween sunset and sunrise, and as daytime value the meanbetween sunrise and sunset of the following day. As theduration of nighttime and daytime period changes withthe season, a systematic bias may result especially in veryhigh latitudes around the solstices. In this paper, we pres-ent both ozone measurements by means of the microwavetechnique performed in Lindau (51.66�N, 10.13�E), Ger-many, and model calculations on the basis of an advanced3D-model of the dynamics and chemistry. We discuss thefindings in terms of different influences upon the ozonechemistry.

2. Results

2.1. Observations

The microwave technique is an established tool to mon-itor the atmosphere with respect to certain measurableminor constituents such as water vapor or ozone. Thedevice as well as some results have been described, e.g.,in Hartogh and Hartmann, 1990; Hartogh et al., 1997;Seele and Hartogh, 1999; and Hartogh et al., 2004. Fig. 1shows the nighttime ozone mixing ratio at Lindau between

50 and 80 km for different height levels in 5 km steps forthe period January 1, 2003 to March 31, 2004 (blackpoints) and the running average (red lines) using a Gauss-ian function with 8 day full width half maximum (FWHM).Some gaps of the measurements have been linearly interpo-lated. The annual variation of the nighttime ozone is typi-cal. The maximum winter-to-summer ratio in 70–75 kmamounts, on average, to a factor two. The maximum valuesexceed 3 ppmv. The winter maximum was extremely highin 2003/04 compared to the maxima recorded in the otheryears. In each year a relative minimum occurs in January/February followed by an increase around March, whereasthe absolute minimum occurs in summer. The mean behav-ior of the annual variation of ozone (not shown) exhibits acamel-hump pattern in the domain of the MMM, the firsthump occurs before winter solstice and the second onearound spring equinox. A faint semiannual variationoccurs around 63–65 km, being the transition regionbetween the summer maximum in the lower mesosphereand the winter maximum in the upper mesosphere whereboth phenomena weakly influence the annual behavior.

Fig. 2 displays the night-to-day ratios for the same peri-od. The black points represent the averaged values for theindividual days employing the same procedure of smooth-ing as for Fig. 1. The red curve represents the averagebehavior according to a Fourier analysis using the first sev-en Fourier coefficients for the presentation for a seven yearmonitoring interval. Comparing this with Fig. 1 the picturehas changed. Beginning at the 65 km level a clear winter-time enhancement of the NDR occurs. The ratio is maxi-mum at 70 km with winter-to-summer values of a factortwo to three. At this altitude the summer minimum occursin August and corresponds to the annual water vapor max-imum. The ascent toward the winter maximum, also occur-ring before winter solstice, is steeper than the decenttoward the summer minimum. The mean curves showslight semiannual variations at 75 and 80 km with a domi-nant peak in April and a second slight maximum in Octo-ber, whereas the summer minimum already occurs in July.The April peak agrees with the subsidiary peak of theMMM which is located above its primary peak. The cam-el-hump-like variation is less pronounced. In the lowerpanels the ratio approaches unity, a faint enhancementstarts already at 60 km. We have to mention that, on theone hand, the 80 km panel is the most uncertain level asthe measurements could be influenced by a strong second-ary ozone maximum around 90 km and that the signal forthe daytime values is not so far from the noise level. On theother hand, the ozone values are retrieved from a heightinterval of 5 km around the depicted height level.

2.2. Calculations

We use our new GCM LIMA (Leibniz-Institute modelof the Middle Atmosphere) for the calculations. The modelis described in Berger and Lubken, 2006; Sonnemann et al.,2006b. The main difference between the older model COM-

Fig. 1. Nighttime ozone mixing ratio at Lindau between 50 and 80 km for different height levels with 5 km space for the period 1st January 2003 to 31stMarch 2004 (black points) and the running average (red lines) using a Gaussian function with 8 day full width half maximum (FWHM).

848 G.R. Sonnemann et al. / Advances in Space Research 40 (2007) 846–854

MA-IAP (see also Sonnemann and Grygalashvyly, 2005and the quotations in it) and LIMA is the fact that the firstmodel calculates climatological averages whereas LIMAuses real temperature and horizontal wind data up to35 km altitude from assimilation of ECMWF (EuropeanCenter for Medium Weather Forecast) data. The dynami-cal model has a new architecture, it employs so-called sim-plex or three-angle coordinates advantageous for thegravity wave parametrization. This model is able to calcu-late the propagation of planetary waves and creates suddenstratospheric warmings (SSW).

Fig. 3 shows, according to Fig. 2, the NDR at 51.25�Nat the same altitudinal levels and additionally at 72 km.The calculations yielded a clear winter anomaly of theNDR beginning already at 60 km (the scale has been chan-ged). The amplitudes are generally somewhat too largecompared with the observations and the modulations are

stronger than in the measurements. With increasing heightup to 75 km the NDR rises. The behavior at 75 km ismarked by strong variations in winter 2003/04. The day-time values are somewhat too small. A possible cause couldbe too humid air compared with the real atmosphere in theconsidered period, particularly decreasing the daytimeozone concentration. The NDR responds sensitively tosmall errors in the absolute density of the daytime values.Water vapor has a large latitudinal gradient in middle lat-itudes increasing toward low latitudes. Consequently, a toostrong meridional mixing by tidal waves could enhance thewater vapor mixing ratio at middle latitudes. The integra-tion of the system during sunset also seems to be an intri-cate problem because, in order to limit the computertime, one commonly uses relatively large integration timesteps. This is generally a drawback of all global models.However, we reduced the time step to 2 min in this calcula-

Fig. 2. The same state of affairs as Fig. 1 but for the night-to-day ratio (NDR). The black points represent the slidingly averaged values for the individualdays, the read curve displays the mean behavior according to a Fourier analysis for a seven year monitoring interval exhibiting the first seven Fouriercoefficients.

G.R. Sonnemann et al. / Advances in Space Research 40 (2007) 846–854 849

tion. We mention that the model does not work interactive-ly. This will particularly influence the behavior during SSWevents, especially in the domain above 80 km but not sostrongly below this altitude (Sonnemann et al., 2006b).Although we use a model assimilating real data, the currentstate of the real atmosphere cannot accurately and com-pletely be mirrored by it. Despite these critical remarks,the model qualitatively mirrors the winter anomaly of theNDR.

Fig. 4 displays the NDR at 70 km altitude at differentlatitudes. The amplitude increases from middle to high lat-itudes. There is no winter anomaly at low and equatoriallatitudes but an annual variation reflecting the variationof water vapor. The summer values at 61.25�N are influ-enced by the polar day conditions. There is only a relativelyslight diurnal variation of ozone. Outwardly, the picturerecalls the winter anomaly of the plasma in the D-layer also

having a occurrence border in middle latitudes (close to40�) and showing variations of planetary time scale (e.g.,Offermann, 1980; Taubenheim, 1983). However, the alti-tude is more than 20 km lower for the winter anomaly ofthe NDR and the dynamics in the middle mesosphere aredifferent than that of the lower thermosphere.

3. Discussion

Evidently, the interpretations of the MMM mentionedin the Section 1 are not extensive enough to explain thephenomenon. Also the increase of the winter-to-summerratio of the NDR compared with that of the MMM refersto different influences, because the daytime values indicaterather a winter minimum rather than a maximum or showno distinct annual variations as does the ozone referencemodel (Keating et al., 1990) showing a slight maximum

Fig. 3. NDR for the same state of affairs as depicted in Fig. 2 but calculated by means of the GCM LIMA.

850 G.R. Sonnemann et al. / Advances in Space Research 40 (2007) 846–854

in summer at 70 km and at 50�N. There are at least threeimportant influences which have to be taken into account.

One is that the temperature shows an annual variationin the upper mesosphere above about 65 km with largestvalues in winter but this general behavior is interruptedby SSW events resulting in a cooling of the upper meso-sphere/mesopause region. The chemical reaction rates aretemperature-dependant and entail an ozone decrease ifthe temperature increases. This should reduce the winter-time enhancement of ozone but to a different degreebetween daytime and nighttime ozone. However, the effectis insignificant close to the turning point of the annual tem-perature variation at 65 km where the annual variation ofthe temperature is very small. The influence of SSW onthe chemistry was investigated by Sonnemann et al.,2006b. They found that a SSW is able to modulate theozone concentration at the domain of the MMM.

Also very important is the annual variation of watervapor. The summer-to-winter ratio amounts to a factorof two in the region of the MMM (e.g., Seele and Hartogh,1999; Sonnemann et al., 2005). But the winter minimum of

water vapor occurs in late winter and may influence thesubsidiary ozone maximum around the spring equinox.The water vapor concentrations are still relatively highwhen the annual maximum of the MMM appears. Despitethe phase delay of the annual variation of water vapor, thereduction of the hydrogen radical production by it has thesame rank or is even stronger than the influence bythe increasing solar zenith angle in winter. But the hydro-gen radicals impact both the daytime and the nighttimeozone concentration so that a prediction about theresponse of the NDR on changing humidity is not simple.The characteristic time of the odd hydrogen familyamounts to several hours so that the daytime productionof hydrogen radicals under smaller solar zenith anglesinfluences the concentration during sunset when the imbal-ance increases, but the absolute production of hydrogenradicals and atomic oxygen from the photolysis of molecu-lar oxygen also declines then. The absolute production isultimately decisive for the nighttime ozone level. A factorof two of the ratio of the dissociation rates of molecularoxygen to that one of water vapor occurs, depending on

Fig. 4. NDR at 70 km at different latitudes calculated by the GCM LIMA.

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height, for a solar zenith angle of about 60�–70� (Hartoghet al., 2004; Sonnemann et al., 2006a). As the formation ofhydrogen radicals depend on the product JH2O[H2O] it can-not be distinguished which factor cases the variation.

In order to interpret the MMM and the winter anomalyof the NDR the most surprising finding concerns the influ-ence of the wind system. It changes principally from sum-mer to winter from an east wind to a west wind system,from a mean flow directed toward the pole to a mean flowtoward the equator, and from an upward to a downwardtransport. In the MMM region the vertical wind mainlydetermines the transport of long-living source gases suchas water vapor, whereas the characteristic times of thechemical active families are too small to be remarkablyinfluenced by the slow mean vertical wind. A meridionaltransport of the nighttime ozone can be important particu-larly in the vicinity of the polar night terminator when itslifetime increases due to the absence of strong lossprocesses.

The strongest influence results from the zonal wind.Sonnemann, 2001 introduced the photochemical Dopplereffect abbreviated with DSE (Doppler-Sonnemann effect)

in Sonnemann et al., 2006c. This effect considers the influ-ence of the zonal wind on the chemistry within a moving airparcel. The photochemical system is excited diurnally bythe solar insolation. It was discovered by Sonnemann andFichtelmann, 1987 and has been investigated in a largenumber of articles (see also Sonnemann and Gry-galashvyly, 2005 and the quotations therein) that the pho-tochemical system represents a nonlinear driven chemicaloscillator which can come into resonance if the eigen fre-quency of the system agrees with the enforcing frequencyof solar insolation. This can happen below the mesopausebut it depends on different parameters such as humidity,temperature, ratio of day-to-night hours, etc. The zonalwind changes the period of solar insolation. It becomeslonger when the wind blows against the rotation of theEarth. It becomes shorter for a wind in direction of theplanet’s rotation. This takes place in a wintry west windsystem. The change of the period under climatologicalmean conditions amounts to +4 and �7 h within the strongmesospheric summer and winter jets. The arising problemfor the domain of the MMM consists in the fact that thecharacteristic time of the chemical system amounts to only

852 G.R. Sonnemann et al. / Advances in Space Research 40 (2007) 846–854

a few hours – in other words, the period of insolation is farfrom the eigen period of the chemical system.

However, the characteristic time of the chemical systemranges in the order of the time of sunset when the dissoci-ation rates decrease very rapidly. During the night, allatomic oxygen is converted into ozone or it returns tomolecular oxygen by odd oxygen destructing catalyticcycles and to a small part by direct recombination of theodd oxygen constituents. The most important catalyticcycle is given by (1) introduced in the first section of thispaper. Atomic oxygen is the most abundant odd oxygenspecies in the domain of the MMM during the daytime.Ozone and atomic oxygen have the same concentrationat about 60 km altitude; below that height ozone beginsto dominate. Although ozone increases strongly towardthe night, the odd oxygen concentration, i.e., the sum ofozone and atomic oxygen, decreases considerably.

Fig. 5 exhibits the diurnal variations of ozone, atomicoxygen and their sum at 70 km for three consecutive daysbetween November 22 and 24, 2003 for the same latitudeas considered before. The figure demonstrates the strongdecline of odd oxygen and atomic oxygen during sunset,already beginning after their daytime maximum. The smallincrease of ozone during the night results from ozone trans-port by tidal winds. The largest part of odd oxygen is lostat sunset. At 75 km height only a few percent of atomicoxygen forms to ozone after sunset. The reason is thatthe atomic oxygen formation from the dissociation ofmolecular oxygen slows down strongly with an increasingsolar zenith angle and with it the only important net oddoxygen production term. But essentially the photolysis ofozone declines slowly, resulting in the formation of atomicoxygen. The formation of atomic oxygen in the photolysisreaction is not a net odd oxygen production process as theodd oxygen constituent ozone is lost thereby. Althoughatomic oxygen mainly returns to ozone within a so-calledzero cycle, it is involved in the catalytic cycle of destructing

Fig. 5. Diurnal variations of ozone, atomic oxygen, and odd oxygenmixing ratios at 70 km altitude at 51.25�N between November 22nd and24th 2003 calculated by the GCM LIMA.

odd oxygen. To reach the highest nighttime ozone level, thetime of sunset would have to be shortened. Exactly thishappens in a wintry west wind, whereas during the daytimethe zonal wind has only a small influence on the chemistry.Sonnemann and Grygalashvyly (2003) obtained prciselythis result in a 3D-model study basing on COMMA-IAP.Sonnemann and Grygalashvyly (2003) found an increaseof the nighttime ozone of more than 60% in the domainof the west wind jet when calculating first using the fullwind system and then with a zero zonal wind. However,they did not discuss it in terms of change during sunset.The current wind during the sunset period influenced bythe strong tidal wind component is decisive for the systemresponse. A strong mesospheric west wind jet was estab-lished in November/December 2003 with maximum tempo-ral wind velocities up to 160 m s�1 around 60 km altitudeat midnight in the beginning of December. The time of sun-set shortens by two-third for this value. The wind speeddeclined to 60–80 m s�1 above 70 km and to 20 m s�1

above 80 km so that its influence on the chemistry decreas-es accordingly. A major SSW occurred during the end ofDecember. The mesospheric wind jet confines the effectand then ozone at lower altitudes becomes the dominantconstituent, which decreases the relative effect accordingly.

Fig. 6 shows an example of diurnal variations of the suc-ceeding days displayed in Fig. 5 if proceeding in the man-ner described before. The calculation runs with thecomplete wind system and then puts the zonal wind to zero.Two model days later we compare the result with that runwithout a changed zonal wind. After a period of one daythe system is approximately in a new state for the constit-uents and families with short lifetime (few hours) but theperturbation of the equation of continuity is still small.The figure makes clear that the relative deviation behavesnot so uniformly as in the example displayed in Sonne-mann and Grygalashvyly (2003) using the climatologicalmean model but it shows the tendency of the nighttime

Fig. 6. Relative deviation of ozone for the same period as shown in Fig. 5if calculating with the full wind system and with zero zonal wind.R = ([O3]with�[O3]without)/[O3]with*100 in [%].

G.R. Sonnemann et al. / Advances in Space Research 40 (2007) 846–854 853

enhancement of ozone when considering the zonal wind.Above 72 km the behavior becomes quite odd. The firstand the second considered days behave completely differ-ently although the dynamical parameter had not essentiallychanged. This response could result from the nonlinearbehavior of the odd oxygen–odd hydrogen system. Around80 km frequently a deep ozone minimum was observed andalso calculated (e.g., Fussen et al., 2000; Kaufmann et al.,2003; Hartogh et al., 2004) entailing a sensitive responseof the NDR to small changes of the system parameters.Also the possibility of a bistable behavior of the chemicalsystem was discussed by Yang and Brasseur, 1994 and Har-togh et al., 2004. In the lower domain the system respondsas expected. As Figs. 2 and 3 show, the annual variation fitsbest the observations at 65 km whereas for the higher pan-els the agreement is not so good.

During major SSW the west wind changes into a sum-mery east wind system, prolonging the time of sunsetreducing the nighttime ozone level. However, the decreaseof the temperature has the tendency to enhance the ozonelevel so that the resulting effect is damped or even reversed.As the zonal wind during daytime does not strongly affectozone, ozone increases during daytime when the tempera-ture decreases, reducing the NDR. The entire effect pos-sesses a more complicated course as the water vaporconcentration also changes within a period of SSW. Westate that on average a reduction of the nighttime ozoneconcentration and a decline of the NDR may result. Themore frequently occurring SSW after winter solstice isreflected by the average variation of ozone and the NDRdecreasing in this time. SSW and the planetary wave activ-ity modulates the annual variation of ozone and its NDR.The DSE has a considerable influence on the mesosphericnighttime ozone concentration and the NDR. Our modeldoes not yet operate completely interactively and doesnot consider the feedback of the chemical heating rates tothe dynamics. The chemical heating would lessen the verti-cal wind when employing an interactive operating model.As discussed in Sonnemann et al. (2006b) there is a discrep-ancy between observations and model output in the lowerthermosphere but an agreement in the domain below, sothat the incomplete interactive coupling does not stronglyinfluence the domain below 80 km.

4. Summary

Long-term measurements of ozone by means of themicrowave technique in middle latitudes at Lindau broughtevidence that during winter the night-to-day ratio (NDR)of ozone is strongly enhanced. The effect starts at about65 km and extends up to 75 km. The winter-to-summerratio of the NDR amounts to a maximum factor of twoto three at 70 km altitude. The annual variation of theNDR is marked by an asymmetry with highest valuesbefore winter solstice and a less steep descent after the max-imum than the preceding increase. The annual variationshows modulations with a planetary timescale. 3D-calcula-

tions on the basis of an advanced model of the dynamicsand chemistry particularly designed to investigate theMLT-region reflect the main findings, although in detailsome noticeable differences still occurred. There are differ-ent influences on the annual variation of the NDR and thenighttime middle mesospheric maximum (MMM) ofozone. A first interpretation took into consideration thefaster decrease of the water vapor dissociation rate thanthat one for molecular oxygen for increasing solar zenithangle entailing an imbalance between odd oxygen lossand its production. The dissociation rate of ozone decreas-es the most slowly. The annual variation of water vaporand the temperature also impact ozone. The winter mini-mum of water vapor furthers the ozone increase, whereasthe wintertime increase of the temperature acts in exactlythe opposite way, but its influence is reduced by the factthat the domain of the NDR anomaly is located close tothe region of reversal of the annual temperature variation.The zonal wind seems to have the strongest influence due tothe Doppler-Sonnemann effect (DSE). At sunset the wintrywest wind system conveys an air parcel more quicklythrough this period and shortens the time of effective oddoxygen destruction by the catalytic cycles. This effectresults from the imbalance between the net odd oxygenproduction by the dissociation of molecular oxygen andthe ozone dissociation rate transforming only one odd oxy-gen constituent into another. Atomic oxygen is theninvolved in the odd oxygen destroying catalytic cycle. Sud-den stratospheric warmings (SSW) entail considerable aer-onomy changes impacting the NDR and the MMM, partlyexplaining the annual asymmetry of the phenomena andthe variations of planetary time scale.

Acknowledgement

This work was supported by the Deutsche Forschungs-gemeinschaft (DFG) grant So268/4.

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