Apr 20, 1985 - mont et al., 1972; Thomas et al., 1977; Rowlett et al., 1978]. A common feature in all of ... gravity wave energy [Hines, 1960]. Rowlett et al. used ...
JOURNAL OF GEOPHYSICAL
RESEARCH, VOL. 90, NO. D2, PAGES 3881-3888, APRIL 20, 1985
Tidal Oscillationsin the Atmospheric Sodium Layer P. P. BATISTA,B. R. CLEMESHA,D. M. $IMONICH, AND V. W. J. H. KIRCHHOFF Instituto de Pesquisas Espaciais-INPE,ConselhoNacional de Desenvolvimento Cientificoe Tecnolrgico-CNPq,S•o Jos• dos Campos,Brazil The vertical distribution of atmosphericsodium has been measuredat S•o Jos• dos Campos (23øS, 46øW) over a total of about 20 completediurnal cyclesbetweenApril and August 1981. Average time variations of the sodium density show strong oscillationswith 12- and 24-hour periods.Both the diurnal and semidiurnalcomponentsof the oscillation display large amplitudesand a 180ø phaseinversion near the layer peak. Thesefeaturesare interpretedin terms of the propagationof tidesin the layer, taking into account the interaction between the tide and the minor constituent layer. It is shown that the vertical wind is the most important factor that determinesthe amplitude of the oscillationin sodiumdensityat a fixedheight,thusmaking it possibleto estimatethe phaseand amplitudeof the wind oscillationsover a
limitedheightrange.Diurnalandsemidiurnal verticalwindamplitudes of 2-6 cm s- • and5-20 cms-•, respectively,have been inferred. The 12-hour component shows vertical phase propagation with a wavelengthof ~ 50 km, in agreementwith recent theories.The 24-hour component,however,shows
characteristics of an evanescent mode insteadof the expectedS•.• mode.Maximum upwardvertical velocityoccursat about 2100 LT at all heightsfor the diurnal componentand at 0600 and 1800LT at 85 km for the semidiurnalcomponent.Theseresultsappear to be the first reported measurementsof tidally inducedverticaldisplacements in the mesopause region.
INTRODUCTION
sodium were obtained with the lidar beam pointed to the
The atmospheric sodium distribution was first observedat S•o Jos• dos Campos,Brazil (23øS,46øW), in 1972 [Kirchhoff and Cieraesha,1973]. Even theseearly measurementsshowed wavelike structuresin the sodiumprofile, varying slowly with time. Kirchhoff and Clemesha [1973] suggestedthat these structuresmight be produced by the propagation of tides in the layer. The presenceof wavelike structuresin the sodium layer has also been reported by several other authors [Blamont et al., 1972; Thomaset al., 1977; Rowlett et al., 1978]. A
zenith, but some measurements were made with the beam
pointing alternatelyto three differentpositionsin the sky, and the resultsof a study of horizontal motions in the layer were publishedby Clemeshaet al. [1980, 1981]. Although the presenceof oscillationswith periods greater
than 10 hours had been noticed in most of the data obtained, the study of these oscillationswas restrictedby the fact that sodiummeasurementswith the laser radar were obtained only during nighttime, for which the longer seriesof data lasted for lessthan • 11 hours. Since 1981, improvementsin the radar common feature in all of these structures is their downward equipmenthave made it possibleto measuresodium density motion with time, consistentwith the upward propagation of during daytime. With this improvement the study of long gravity wave energy [Hines, 1960]. Rowlett et al. useddigital seriesof data, lasting for severaldays, becamepossible.The filtering techniquesto processthe sodium profiles. This enfirst results of these measurements[Clemesha et al., 1981] abled them to isolatethe main gravity wave modespresentin showed the presenceof a strong oscillation with a 12-hour the layer. Oscillationswith vertical wavelengthsof 10.9 km, period and, at some heights, the presenceof an oscillation 6.3km, and 5.2km anda verticalphasevelocityof 1.8km h- • were identified. The relationship between the perturbations with a 24-hour period. It is well known that atmospherictides play an important observedin the sodium and in the atmosphericdensity at role in the mesopauseregion [Chapman and Lindzen, 1970; Urbana, Illinois, has been studied by Shelton et al. [1980], Forbes, 1982a, b]. However, their main characteristicsrathe who used Chiu and Ching's [1978] linear theory for the responseof atmosphericlayers to gravity waves.More general principal propagation modes and the absolute and relative expressionsfor the responseof atmosphericlayers to gravity amplitudes between the main components,phases,and vertical wavelengths--are not yet well known. Most of the waves have been developedby Sheltonand Gardner [1981]. measurements of tides in the mesopauseregion have been This theory helped to interpret the variations observedin the obtained in terms of the horizontal wind fields mainly by sodium layer, and a large number of gravity waves, with periodsvarying from 85 to 500 min and vertical wavelengths meansof meteor radar, MST radar, and the partial reflection technique[Forbes, 1984]. Furthermore, much of the data has from 4.8 to 25 km, wereidentified.However, as pointedout by Shelton and Gardner in their longer seriesof measurements been obtained at northern hemispheremid-latitudes.The purpose of this paper is to report the study of tides by means of (more than 10 hours), oscillations with longer periods atmeasurementsof sodium density variations. Tidal oscillations tributed to tides were also present. causeperturbations in the sodium layer, which extends from A number of studieshave been carried out using the data 76 to 105 km, and therefore by studying the sodium density from S•o Jos• dos Campos. Simonichet al. [1979] studied the ß
nocturnal
and seasonal sodium
variations
variations, one can obtain information about tides in this
based on over 5
years of data. Simultaneousmeasurementsof sodiumdensity height range. Twenty-four-hourmeasurementsof atmospheric and severalnightglow emissionlines were reported by Ciera- sodium have been reported by only two groups. Clemeshaet eshaet al. [1979]. Most of the measurementsof mesospheric al. [1982] analyzed 24-hour sodium density measurements taken in two sequencesbetweenthe 5th and 8th and the 11th and 15th of May 1981. Granier and Megie [1982] also reportCopyright 1985 by the AmericanGeophysicalUnion. ed diurnal and nocturnal measurements of mesospheric sodium,but they did not study the time evolution of the proPaper number 4D 1302. 0148-0227/85/004D- 1302505.00 file. Their emphasiswas on the day-to-night differencesin the 3881
3882
BATISTA ET AL.' TIDAL OSCILLATIONS IN THE ATMOSPHERIC SODIUM LAYER
12
0
12
0
12
0
12
0
12
0
12
0
I
I
T
[
T
•
•
I
I
I
•
I
•
I1•
I
•
II
DAY
9
•0
•
DAY
6
7
8
9
DAY
I i
12
13
14
15
MAY/81
DAY
13
14
15
16
17
JULY/81
DAY
3
5
6
4
I___1i2 0I _ 112 0I
0
APR/81
•
12
I
0
MAY/81
7
I
I
12
8
I
0
I
12
AUG / 81
I
0
I
12
0
LOCAL TIME (HOUR)
Fig. 1. Available sodiumdensitydata for the five sequences of 24-hour measurements.
abundance and the upper and lower scale heights of the sodiumlayer. In this paper the measurements of Clerneshaet al. [1982] are analyzedtogetherwith sequences of observationsobtained in April, July, and August 1981.Emphasisis given to the time evolution of the profile averagedover all the available data from April to August.Diurnal and semidiurnalcomponentsof the oscillationare separatedand independentlystudied. EXPERIMENTAL
RESULTS
The data analyzedin this paper were obtainedfrom April 9 to August 8, 1981. Height resolutionwas 1 km, and profiles were taken at approximately15-min intervals.These profiles wereinterpolatedat eachexacthour to generatea sequenceof hourly mean profiles. Information about the laser radar and the data acquisitionprocesscan be found in Simonichet al. [1979] and Clerneshaet al. [1982]. In Figure 1 we show the five periodsduring which the data were obtained. Data gaps are caused by bad weather conditions or failuresin the equipment.It can be seenthat runs of more than 4 and 4.5 days of continuous measurementswere obtainedin May and August1981,respectively. Contour plots of sodiumdensityfor three completedays in August 1981 are shown in Figure 2, where the isoplethsare
the sodium density over a period of severaldays will be considered.
Figure 3 showsthe averaged24-hour variation of sodium density for all data gathered during the periods shown in Figure 1. To obtain this averagevariation, the hourly mean profileswere averagedfor all days having data at that time. Becausesome daytime data were rather noisy, a weighted averagingschemein which the weightwas proportionalto the reciprocalof the probabledata error was used.The probable data error was based on photon-counting statistics in the usualway. After averaging,the data were smoothedby taking a 3-km runningmean in heightand a 3-hour runningmean in time. A histogramshowingthe number of hourly mean profiles used to calculatethe generalhourly mean is also shown in the figure.The followingfeaturescan be observed: 1. Sodium density isoplethsaway from the peak layer--
0.5, 1.2,and 3 x 109 m-3 on theuppersideand2 and3 x 109
on the lower side--oscillate regularly with a dominant 12hour period. 2. In the lower part of the layer, below 85 km, the 24-hour period dominates. 3. Sodium densitydecreasesduring the daytime hours on the upper side of the layer, mainly around noon. But there is alsoevidenceof a decreasenear midnight. givenin 109 atomsm-3. The variationin the heightof the 4. Near the peak of the layer the diurnal and semidiurnal oscillations are not obvious, but there is a variation with maxsodium isopleths---corresponding to densitiesof 1, 2, and 3 X 109 m-3, with maximaand minimaoccurringapproxi- imum densityoccurringat around 0600 LT. mately every 12 hours--indicates the presenceof a semidiurnal oscillation.Below 85 km the presenceof a density minimum is observed around 0 and 3 LT, and a maximum r-• 20 occursaround 12 and 15 LT, which indicatesa strongerdiurnal variation at these heights.In addition to these regular • ,o variationsobservedon individual days there are also apparently random variations,suchas short-periodfluctuations,fast increasesor decreases of the sodiumdensityin variousheight IOO ranges,or statisticalfluctuations associatedwith the measurements process.In order to avoid these random fluctuations and to make the tidal effectsclearer,the averagebehavior of ß
,-M 9O i
85
I
0
6
12 18 0 508
81
6
12 18 0 60881
6
12 18 0
8o
o
3
6
9
12
15
18
21
70881
LOCAL TIME (hour)
LOOAL TIME (HOUR)
Fig. 2. Sodiumdensityisopleths in unitsof 109 m-3 for August5-7, 1981.
Fig. 3. Sodium density isopleths for the average of all data
(April-August1981).The curvesare givenin unitsof 109 m-3. The histogramshowsthe numberof daysincludedin the average.
BATISTA ET AL.' TIDAL OSCILLATIONS IN THE ATMOSPHERIC SODIUM LAYER
3883
In order to emphasizethe amplitude of the oscillations,the data of Figure 3 were plotted in the form of a time variation of density at each height. The results are shown in Figure 4, where the sodium density is normalized by the 24-hour
averagefor each 2-km interval. Values of ANa/•la around 30% and 40% are typical away from the peak of the layer, and very high values(even > 100%) occur at the lower edge. Near the peak the amplitudesare weak but not negligible.For the semidiurnaloscillationa clear vertical phasepropagation can be seen,with a phasereversaloccurringnear to the layer peak. DISCUSSION
2
NNa 8O
•Na I
Interaction of the SodiumLayer With the Tide
The presenceof oscillationswith 12- and 24-hour periodsis a clear indication of the existenceof tides in the sodium layer. However, certain featuresof the oscillations,such as the large amplitudesand the 180ø phase inversion near the peak, can only be explainedby taking into accountthe interactionof the layer with the tide. This can be done by consideringthe conti-
0
0
6
12
18
0
6
12
18
0
LOCAL TIME (HOUR)
Fig. 4. Normalized average24-hour sodiumdensityvariationsfor all data (April 9-August 8, 1981). Tilted lines represent apparent phase propagation.Variations are representedat 2-km height intervals.
nuityequations for the majorandminorconstituents haying densitiesN and n, respectively.We assume an atmospheric wave with period T propagating in the atmosphere. Production and loss terms, whose diurnal variation might lead to periodic variations in the sodium density, are not considered in the continuity equation. Several chemical time constants have been calculated by Kirchhoff and Clemesha [1983a], showingthat at and above 86 km these are larger than 1000
hoursat noon and 75 hoursat midnight.The effectsof Na + ions are not considered, since the available measurements in-
dicate that their concentrationis only about 10% of that of the neutral Na in the height region of interest. The possible effect of a source modulation
on the calculated
sodium
den-
Linearizing(1), we have
c•-• c3 Qh•non )=•c3 (h•o )+(1 l•odNo dz n1 odnoh dz,IT (2) where W is the vertical velocity. This relation was presented by Dudis and Reber [1976]. Assumingtemporal variationsgiven by exp (i2•t/T), (2) becomes
An no-AN NoF•-• iT(1 ;odno dz N1 OdNoh •zz 'JW
(3)
sities has been investigated by Kirchhoff and Clemesha Dudis and Reber [1976] took advantage of the simple rela[1983b]. It is shown that the time constantinvolved is very tion betweenW and AN/No, given by Hines [1960] for longlarge, and the correspondingdensitychangesare negligible.In addition we assume that the diffusion time of the minor conperiod and low vertical wavelengthgravity waves,in order to derive a unique relationshipbetweenthe perturbationsin the stituent in the major constituent is large compared with T. This assumptionis justified by the analysis of Kirchhoff and minor and major constituent densities. An analogous approach has been given by Chiu and Ching [1978]. For tides, Clemesha[1983b], who have shown that the diffusion time constant is several days. With these assumptionswe expect however, the relationship between W and AN/No is not simple. It depends on the height and on the propagation that the simple dynamical model that follows is a good approximation for the sodium variations, except at the lower mode.Thus, (3), which relatesAn/nowith AN/No and W, must edgeof the layer. In this casethe velocitiesof the two constit- be considered. uents willbeequal(•). Therefore thedivergences oftheveloci- Sheltonet al. [1980] used Chiu and Ching's[1978] formula ties in the continuity equationsfor N and n can be equated. to study the special case of gravity wave propagation in the Thus we have sodium layer. Sheltonand Gardner [1981] made a more general study of the responseof atmosphericlayers to atmospheric 1 dn 1 dN (1) waves.They showedthat, for a wave period T lessthan the n dt N dt diffusion time of the minor constituent,the perturbation denwhere sity of the latter can be describedby a combination of an d • oscillationand a distortion of the basicprofile. +v-v From (3) it is seen that An/no is given by the sum of dt c•t two terms: Ti -- AN/No and T2 -= iT/2•r((1/no)(dno/dz) From the viewpoint of a Lagrangian observerthe fractional -(1/No)(dNo/dz))W. The T1 term is simply the atmospheric variation in the densityof the minor constituentwill be equal density perturbation, but T2 depends on the period of the to the fractional variation of the atmosphericdensity.For an oscillation, on the vertical wind, and on the difference of the Eulerian observer,who measuresthe density at a fixed point inversesof the scale heights of the minor and major constitin the atmosphere,this is not true. Writing the densitiesn and uents.It is important to note that for constituentsdistributed N as a sum of a basic profile depending only on z, plus a as layers, as in the caseof sodium, the term in parenthesesin wave-induced term, we have (3) is positivebelow the layer peak (dno/dz> 0 and dNo/dz < 0); above the peak the sign of the term reverses(dno/dz< 0 N(?, t) = No(z) + AN(F, t) _
andI(1/no)(dno/dz)l > I(1/No)(dNo/dz)l). Thusr 2willleadW by
n(?,t) = no(z) q- An(?,t)
•r/2 above the layer peak and lag by •r/2 below. Furthermore,
3884
BATISTAET AL.: TIDAL OSCILLATIONS IN THE ATMOSPHERIC SODIUMLAYER 8O 7O "-'
6O
Z
40
I--
30
O
IOO --e
ß
• 90
•> I
I
I
80
85
90
I ß
I
95 ß
_
ß ß ß
8O
ß
0
-3o
$
6
9
12
15
18
21
LOCAL TIME (hour)
-4o
HEIGHT ( km )
Fig. 5. Amplitude of the term T2 of equation (3) for T = 24 hour,
W = 5 cms- a,andtheaveragesodiumprofileno(Z ) for all data.
Fig. 6. Recompositionof the variations of the sodium density with time and height,consideringonly the average,diurnal,and semidiurnal components.Contour levelsare given in units of 109 atoms m-3
the absolutevalue of (1/no)(dno/dz) -(1/No)(dNo/dz) is typically larger below the point wherethe signchanges. In order to estimatethe relativeimportanceof Tx and T2,it is necessaryto considerno(z)as the averagesodiumprofile of our data and to ascribereasonablevaluesto AN/No and W. In Figure 5 the amplitudeof T2is shownfor a 24-hour period
a reconstruction,usingonly the 12- and 24-hour components, shownin Figure 6. Figure 7 shows(in percentage)the ratios (Ad(zo)/Ao(zo) and As(zo)/Ao(zo) ) betweenthe amplitudesof the diurnal and semidiurnal componentsand the average24-hour sodiumdensity, respectively.Regionswith differentbehaviorsare emphasized. with a verticalwind amplitudeof 5 cm s- x and a density In region I, Ad is greater than As but decreasesrapidly with perturbation of 5%. These values are reasonable for vertical increasingheights.In regionII, Asis greaterthan Aa. Aa varies windsand densityperturbationsat uppermesospheric heights. from about 5% to 20% and Asfrom about 10% to 30%. Near It is seenthat the contributionof T2 to An/nois very large. the layer peak (region III), both As and Aa are small but Values of 60% for An/no are reached at the bottom of the nonvanishing,with Aa greaterthan As,and the phasechanges layer.The value of AN/No is alsoshownfor comparison.How rapidly with height. This region also displaysa differentbethis term will sumwith or subtractfrom T2will dependon the havior of the phases,so it is classifiedas region III. In region relativephasebetweenW and AN/No. If the phaseof AN/No IV, above the layer peak, the amplitudesof both diurnal and leads W by 90ø, AN/No will increasethe amplitudeof An/no semidiurnalcomponentsincreaserapidly with height,AsIAo aboveand decreaseit below the layer peak.The joint effectof going from 30% to 80% and Ad/Ao increasingfrom 15% to
Tx and T: is importantin determiningthe inversionpoint in
30%.
the phase of An/no. The experimental data show that this height is between92 and 98 km. A larger contribution of AN/No would movethe phasereversalheightout of this inter-
At this point the questionmight be asked as to whether or not the average of data taken over a period of almost 5 months is really representativeof winter conditionsor whether it is merely the result of a seriesof randomly phased oscillations. In order to verify this point, we have made partial averages,consideringonly the longest sequencesof data. In Figure 8 are shown the average 24-hour contour plots of sodium density for May 11-15, 1981 (Figure 8a) and for
val. This factsupportsthe conclusion that T: is dominant. Separationin Components
Although the semidiurnalperiod is dominant over most of the height range, the presenceof a diurnal oscillationis also visible,mainly at the lower edgeof the layer. For a quantitativestudy of the phasesand amplitudesof the diurnal and semidiurnalcomponentsthe least square method has been used to fit the following function to the measuredsodiumdensitiesfor eachheightz0:
ß DIURNAL
ø SEMIDIURNAL
2n
Ao(zo) + AJzo) cos (t- q0JZo)) 2n
+ A,(zo) cos • (t-- qb,(Zo) ) (4) where Ao(zo),Aa(zo)and A,(zo) are the average,diurnal, and semidiurnal amplitudes, respectively, and qba(Zo) and qb,(Zo) are phasesof thediurnalandsemidiurnal components. 800 20 40 60 80 I00 126 140 Fitting only diurnal and semidiurnalcomponents, neglectAMPLITUDE/AVERAGE (%) ing higherfrequencies, is justifiedby the fact that thesetwo componentsare clearly dominant. The fact that only the 12Fig. 7. Ratios between measured lms diurnal and semidiurnal and 24-hour componentsare important is demonstratedby amplitudes and the steady component of density as a function of the similaritybetweenthe originaldata shownin Figure3 and height.
BATISTA ET AL.' TIDAL OSCILLATIONS IN THE ATMOSPHERIC SODIUM LAYER
3885
August3-8, 1981 (Figure 8b). It is noted that the main characteristics(the strong semidiurnaloscillationwith a downward
phasepropagationat the 1, 2, 3, and 4 x 109 atomsm-3 density levels and the density increase at the lower edge around 15 hours) are presentin both setsof data. It is clear then that the average oscillations are characteristicsof the winter mesosphereat our latitude. Height variations of the phasesof the diurnal and semidiurnal componentsare shown for the general averagein Figures 9a and 9b, respectively(filled circles).It is noted that the phaseshift of 180ø near the layer peak occursin both diurnal and semidiurnal components.This phase change occurs over the range of heightsbetween92 km and 96 km. For the sake of continuity the phasevariation is repeatedwith a 180ø shift below the peak (dotted lines, open circles).The semidiurnal component shows vertical phase propagation with a wavelength of • 50 km. The phase of the diurnal component, on the other hand, showsno vertical propagation and is fixed at • 3 hours on the upper side of the layer and at • 15 hours on the lower side. Close to the peak of the layer the phasesof both the semidiurnal and diurnal componentsshow anomalous behavior. This is to be expectedbecause,in this region, the two terms of (3) make contributionsof the same order of magnitude. This region is delineated by horizontal lines in Figure 9. The phasesof the diurnal and semidiurnalcomponentsof the oscillation for the August 3-8, 1981, sequenceare also shownin Figures 9a and 9b, respectively(triangles).It can be seen that the phase of the semidiurnal component for the 5-day sequenceis very similar to that of the average. The phase of the diurnal component for the 5-day sequenceis similar to that of the averageabove the layer peak but highly variable below the peak. This is not surprisingin view of the well-known day-to-day variability of the 24-hour tide. From the previousdiscussionit can be concludedthat most of the sodiumdensityvariationscan be explainedas the effect of tidal propagationon the layer, as describedby (3). The 180ø phaseshiftjust above the peak, as well as the large amplitudes of An/no,are consistentwith the dominanceof the term T2 in 11.05.81 - 15.05.81 lOO
90
(a)
80
o
6
12
18
-r90
6 LOCAL
bl
12
18
TIME{hour)
Fig. 8. Sodium densityisoplethsfor the (a) May 11-15, 1981, sequenceand for the (b) August 3-8, 1981, sequence.The contours are
givenin unitsof 109m-3
•
9
12
15
18
21
LOCAL TIME (hour)
moor 95
(b) 90 85800
Fig. 9. Variationsin the phasesof (a) diurnaland (b) semidiurnal componentsof sodiumdensitywith height.Open circles,time of mini-
mum density;filledcircles,time of maximumdensityfor the AprilAugustaverage.Triangles,the samefor the August3-8, 1981, sequence.
(3). Near the layer peak, where T2 is small, An/no •s proportional to AN/No. At the extremitiesof the layer, An/no is mainly a consequenceof the vertical wind, leading 90ø in phaseon the upper side and lagging90ø on the lower side. Using this fact and making certain assumptions,we can obtain information about the amplitudeand phaseof the vertical wind responsiblefor the variation in An/no. Since far from the peak T• >>T•, equation(3) can be approximatedby
no=2•r dz No •zz',] w An• iT(nl_o dno 1dNo•
(5)
Using the experimentallydeterminedsemidiurnaland diurnal componentsof An/no and 1/no' dno/dzfrom the average profile togetherwith 1/No'dNo/dz taken as the reciprocalof the scaleheight for a standard atmosphere,it becomespossible to estimatethe vertical wind W. Obviously, the larger the ratio betweenT: and T•, the better will be the estimatefor W. The results of such an analysisare shown in Figure 10 for the diurnal and semidiurnal cases.The horizontal strip with no data correspondsto the proximity of the layer peak where the approximation is not valid. Typical values for the amplitude of the diurnal wind (Figure 10a) are between2 and 4 cm on the upper side. Figure 10b showsthe inferred semidiurnal
4
0
:3
wind wheretypicalamplitudesare between5 and 10 cm s- • on the lower side and 10 to 20 cm s-• on the upper side.
v
lOO
•-
0
s- • on the lowersideof thelayerandbetween4 and 6 cm s- •
3. o8.81 - 8.o8.81 •
(a)
Shaded areas correspondto very high values. These values appear becausethe measuredperturbationsAn/no are larger than predictedby linear theory. Nonlinear variationsare important near the peak and extremitiesof the layer [seeShelton and Gardner, 1981]. Variations, nondynamicalin origin, can also contribute to these amplitudes.There appear to be no measurementsof vertical tidal wind velocitiespublishedin the literature with which we can usefullycompare our results.Our estimatedvelocitiesdo, however,appear to be consistentwith those measuredby MST radar (B. B. Balsley, personal communication, 1983).
3886
BATISTA ET AL.: TIDAL OSCILLATIONS IN THE ATMOSPHERIC SODIUM LAYER
2 0 -2 -4
o6 -4 -2 0
4
Forbes' winter model there would be a phase difference of
6
about
(a)
2 hours.
The diurnal case displays an unexpectedlack of vertical phasepropagation.Maximum densitiesoccur at ~ 3 hours on the upper side and at ~ 15 hours on the lower side of the layer. Both classical[Chapmanand Lindzen,1970] and Forbes
models(seeFigure11)predictthe dominanceof the Sx,xmode with a 20-30 km vertical wavelength at low latitudes. The dominanceof the evanescentmodes is predictedonly for mid and high latitudes. On the other hand our results do not preclude the existenceof propagating modes on individual \
!
o -io
I00 2 40
-(io
days.Largeday-to-dayphasevariationof theSx,xmodecould
-2o
•
(b)
t--- 90
causeits disappearanceafter severaldays averaging.The wellknown phasevariability of the diurnal tide has beencommented on by severalauthors.Woodman[1977] suggested that the
diurnaltide wasreallya randomquasiperiodic oscillation,and Spizzichino[1969] has found oscillationsvarying from 17 to 35 hours.The diurnal tide spectrumis not a sharp peak at 24 hours but a wide-band spectrum with periods varying from
800
6
12
~ 17 to ~ 35 hours.
18
LOCAL TIME (hour)
Fig. 10. Vertical velocityas givenby equation(5): (a) diurnal and
(b) semidiurnal. Contourlevelsare givenin cm s-x. Horizontalstrip without values correspondsto the part of the layer where the approximationmade in equation(3) is not valid.
Vertical wind models predict the amplitude of the semidiurnal vertical wind varying almost exponentially from around1 cm s- x at 80 km to 20 cm s- x at 105 km (F model) and a more rapid increasewith height for the LH model.The amplitudeincreasewith height for the diurnal vertical wind is lessthan for the semidiurnal.The F model predictsan ampli-
tudeof about4 cm s-] at ~ 80 km, increasing to 6 cm s-] at
~ 100km and decreasing above.Our estimate of the semi-
ComparisonsWith Tidal Models
diurnalwind,rangingfrom5 to 20 cm s- x,andfor thediurnal wind,rangingfrom2 to 6 cm s-•, agreeswith the predictions
We have shown that the average 24-hour variation of above 90 km; however, below 90 km our estimate is greater sodiumdensitycan be explainedas a consequence of the joint effect of tidal atmospheric density variations and the vertical for the semidiurnalcomponentand lessfor the diurnal. wind. Becauseof this dependenceon two distinct parameters, it is not possible,in principle, to arrive at unique values for either AN/No or W. Neverthelessthe dominanceof the term o /•N/N (30ø)F a /•N/N (23,6ø)LH associatedwith the vertical wind far from the peak has enß W (30 ø) f ß W (23.6 ø) LH abled us to estimate W with some confidence. Furthermore, if
only dynamical variations are presentnear the layer peak, in this height range, An/no must follow AN/No. A comparison with tidal models and with other measurements
x
DATA
SEMIDIURNAL '
,-
•
I
I
must be made
• 95 • in the W and AN/No fields.In Figure 11 are shownthe phases of An/no as well as the phasesof AN/No and W for the equinoctial model of Forbes [1982a, b; hereafterF model] and for the model of Lindzen and Hong [1974; hereafter LH model]. This last model is only for the semidiurnal case. The figure also shows, with dotted lines, the expectedAn/no variation 80 xx:l 0 3 6 9 12 that would be producedby the effectof W alone.Valuesof W PHASE (HOUR OF MAXIMUM DENSITY) for the latitude of 30ø were obtained from the tables given by Forbes and Gillette [1982], and the correspondingvalues of DIURNAL AN/No were provided by J. M. Forbes (private communication, 1983). Vertical phase propagation with wavelengths I00 x ranging from 30 to 60 km is the main feature of the semix diurnal models. The vertical wavelength of the semidiurnal component of sodium density variation is ~ 50 km, in good agreementwith the models.Near the layer peak the phaseof An/nois closeto the phaseof AN/No for both models.There is 85 excellentagreementbetweenthe phaseof our measuredAn/no and the Forbes model for the vertical wind, with the expected 80 I I I I ;z/2 phase shifts. Between 81 and 91 km the phases agree 0 3 6 9 12 15 18 21 within 30 rain, and on the top side of the layer there is a PHASE (HOUR OF MAXIMUM DENSITY) consistentphasedifferenceof about 1 hour at heightsfrom 98 Fig. 11. Phasesof sodiumdensityas comparedwith phasesof to 104 km. It should be noted, however,that the time periods AN/N o and W for modelsLH, Lindzenand Honq [1974], and F, over which our sodium measurementswere made correspond Forbes[1982a, hi. The broken line showsthe phaseof W shiftedby more closelyto winter than to equinox and that had we used 90 ø.
i.iJ N •½) x
BATISTAET AL.: TIDAL OSCILLATIONS IN THE ATMOSPHERIC SODIUMLAYER
3887
(a)
Simulations
(b)
As has alreadybeendiscussed, a knowledgeof An/nois not sufficientfor us to make a unique determinationof AN/No and W. On the other hand, given a set of values of W and AN/N o, it is always possibleto simulate An/no in order to checkhow well the model agreeswith the experimentalresults. Some of these simulationsare shown in Figure 12. For the sake of comparisonwe reproduce,in Figure 12a, the experimentally determinedsemidiurnalvariation. Note that Figure 12a is a reconstruction
of the diurnal
variation
-.,,=-..,-
57
100
4
in which all
9o
periodsother than 12 hours have been excluded.Values for W
and AN/No, basedon classicaltidal theory have been calculated by using the method and tablesgiven by Chapmanand Lindzen [1970]. Figure 12b shows the simulation for the
8o 0
6
12
(c)
18
0
6
LOCAL TIME (hour)
12
18
(d)
Fig. 12. Comparison betweenthe experimental semidiurnal oscilclassical S•.,•.mode.In orderto get amplitudessimilarto the (a) reconstruction of the observedones,it was necessary to multiply AN/N o and W by lationin the sodiumlayerand simulations: oscillation, usingonlythe 12-hourlmsfit; (b)simulation 2. Note that this model does not reproducethe 180ø phase semidiurnal usingtheS2,2 mode;(c)simulation usingtheS2, ½mode;(d)simula-
inversionnear the peak. The reasonfor this is that the model
tion usingF model.
predictsa low ratio betweenW (cms-•) andAN/No (%), so that the wind-inducedoscillationis alwayssmallerthan that producedby the densityoscillation.Figure 12c showsthe sim-
The amplitude increaseswith height, but the rate of increaseis
ulationwith the S•.,½model.This modelyieldsverticalwave- lessthan that predictedby the models. lengths consistentwith the measurements,but the calculated
The resultsfor the diurnal componentare unexpected.Tidal
amplitudesof W and AN/No had to be multiplied by 4 to theory [Chapman and Lindzen, 1970; Forbes, 1982a] predicts obtain An/no of the same magnitude as the measurements. the dominanceof the S•,• modewith wavelength of --•25km This simulation
is more consistent with
the measurements
at low latitudes.
Our measurements
are more consistent
with
(Figure 12a) than the previousone, but the absolutephases disagree,and the increaseof the amplitudewith heightis less than observedin the measurements.Figure 12d shows the simulationfor the model of Forbes [1982b] at 30ø latitude. Amplitudessimilar to the observedones(Figure 12a) are obtainedat almostall heights,and as pointedout in the previous section,there is good agreementin the vertical wavelength
the existenceof a very long wavelength vertical wind with maximum upward velocity at --•21 hours. Vincent and Ball [1981], measuring horizontal winds at Townsville, Australia (19øS,147øE),also a low-latitude station, reported that in win-
and phase.
ationsin the weak S•,• componentcauseit to vanishin our SUMMARY AND CONCLUSIONS
By means of an analysis of continuous 24-hour measurements of mesosphericsodium densitytaken over a total of 20 daysbetweenApril and August 1981it is concludedthat (1) strong oscillationswith 12 and 24 hour periodsare present at the sodium layer; (2) most of the characteristicsof the oscillations can be explained by tidal propagation in the layer, taking into account the interaction of the layer with the atmosphericwaves; (From this interaction it follows that the vertical wind effectis very important in determiningthe sodium variation at a fixed height.) (3) this strong effect makes it possibleto estimatethe vertical motion of the layer; (The valuesfound for W were 2-6 cm
s-• for the diurnalcomponentand 5-20 cm s-• for the semidiurnal.) (4) the vertical wavelength for the semidiurnal tide was found to be about 50 km, and the averagediurnal wavelength was much greater than the layer width; (Maximum density occuredat 3 hours on the upper side of the layer and at 15 hourson the lower side.) (5) tidal models for W and AN/No can be testedby their effectson the layer. It is interestingto note that the measuredsemidiurnalvertical wavelengthis consistentwith recenttidal models[Forbes, 1982b], which predict the semidiurnaltide at the mesopause
heightasbeinga sumof S2.2,S2.4,S2.6 modes.The measured phaseagreeswith the equinox rather than the winter model.
tertimethe S•,• modeweakens,givingplaceto the dominance of evanescentmodes. It is possible that a similar situation exists at our latitude and that large day-to-day phase variaverage variation. Another unexpectedfeature of the diurnal oscillation is the very rapid change with height in its amplitude in the region of 80 km. It is possiblethat photochemical effectsproducea 24-hour variation at the bottom of the layer [Kirchhoff, 1983], although in this case, minimum density shouldbe expectedat sunriseinsteadof 0300 as observed.It is also possiblethat an interactionbetweenthe tide and chemistry might be occurringin such a way as to amplify the tidal oscillation;this possibilityis under investigation. REFERENCES
Blamont,J. E., M. L. Chanin, and G. Megie, Vertical distributionand temperature profile of the night time atmospheric sodium layer obtained by backscatter,Ann. Geophys.,28, 833-838, 1972. Chapman, S., and R. S. Lindzen, AtmosphericTides, D. Reidel, Hingham, Mass., 1970. Chiu, Y. T., and B. K. Ching, The responseof atmosphericand lower ionosphericlayer structuresto gravity waves,Geophys.Res.Lett., 5, 539-542, 1978.
Clemesha,B. R., V. W. J. H. Kirchhoff, D. M. Simonich, H. Takahashi, and P. P. Batista, Simultaneous observations of sodium den-
sityandtheNaD, OH(8, 3),andOI5577-/•nightglow emissions, ,/. Geophys.Res.,84, 6477-6482, 1979. Clemesha, B. R., V. W. J. H. Kirchhoff, D. M. Simonich, H. Takahashi, and P. P. Batista,Spacedlidar and nightglowobservations of an atmosphericsodiumenhancement,J. Geophys.Res.,85, 34803484, 1980. Clemesha, B. R., V. W. J. H. Kirchhoff, D. M. Simonich, and P. P. Batista,Mesosphericwindsfrom lidar observationsof atmospheric sodium,J. Geophys.Res.,86, 868-870, 1981. Clemesha, B. R., D. M. Simonich, P. P. Batista, and V. W. J. H. Kirchhoff, The diurnal variation of atmosphericsodium, J. Geophys.Res.,87, 181-186, 1982.
3888
BATISTA ET AL.: TIDAL OSCILLATIONS IN THE ATMOSPHERIC SODIUM LAYER
Dudis, J. J., and C. A. Reber, Composition effectsin thermospheric gravity waves,Geophys.Res. Lett., 3, 727-730, 1976. Forbes, J. M., Atmospherictides, 1, Model descriptionand resultsfor the solar diurnal component, J. Geophys. Res., 87, 5222-5240, 1982a.
Forbes, J. M., Atmospheric tides, 2, The solar and lunar semidiurnal components,J. Geophys.Res.,87, 5241-5252, 1982b. Forbes, J. M., Middle atmospheric tides, J. Atrnos. Terr. Phys., in press, 1984. Forbes, J. M., and D. F. Gillette, A compendiumof theoretical atmospherictidal structures,1, Model descriptionand explicit structures due to realistic thermal and gravitational excitation, Rep. 82, Air Force Geophys.Lab., HanscomAFB, Mass., 1982. Granier, C., and G. Megie, Daytime lidar measurementsof the mesosphericsodiumlayer, Planet. SpaceSci.,30, 169-177, 1982. Hines, C. O., Internal atmospheric gravity waves at ionospheric heights,Can. J. Phys.,38, 1441-1481, 1960. Kirchhoff, V. W. J. H., Atmospheric sodium chemistryand diurnal variations: An update, Geophys.Res.Lett., 10, 721-724, 1983. Kirchhoff, V. W. J. H., and B. R. Clemesha, Atmospheric sodium measurementsat 23øS,J. Atrnos.Terr. Phys.,35, 1493-1498, 1973. Kirchhoff, V. W. J. H., and B. R. Clemesha,The atmosphericneutral sodiumlayer, 2, Diurnal variations,J. Geophys.Res.,88, 442-450, 1983a.
Kirchhoff, V. W. J. H., and B. R. Clemesha, The dissipation of a sodium cloud, Planet. Space.Sci., 31,369-372, 1983b. Lindzen, R. S., and S. Hong, Effects of mean winds and horizontal temperature gradients on solar and lunar semidiurnal tides in the atmosphere,J. Atrnos.Sci.,31, 1421-1466, 1974. Rowlett, J. R., C. S. Gardner, E. S. Richter, and C. F. Sechrist, Jr.,
Lidar observationsof wavelike structure in the atmosphericsodium layer, Geophys.Res.Lett., 5, 683-686, 1978. Shelton, J. D., and C. S. Gardner, Theoretical and lidar studiesof the density responseof the mesosphericsodium layer to gravity wave perturbations,Aeron.Rep. 99, Univ. Ill., Urbana, 1981. Shelton, J. D., C. S. Gardner, and C. F. Sechrist,Jr., Density response of the mesosphericsodium layer to gravity wave perturbations, Geophys.Res.Lett., 7, 1069-1072, 1980. Simonich, D. M., B. R. Clemesha, and V. W. J. H. Kirchhoff, The mesosphericsodium layer at 23øS: Noctural and seasonal variations,J. Geophys.Res.,84, 1543-1550, 1979.
Spizzichino, A., l•tude experimentale des vents dans la haute atmosph6re,1, Ann. G•ophys.,25, 697-720, 1969. Thomas, L., A. J. Gibson, and S. K. Bhattacharyya,Lidar observations of the horizontal variation in the atmosphericsodiumlayer, J. Atrnos.Terr. Phys.,39, 1405-1409, 1977. Vincent, R. A., and S. M. Ball, Mesosphericwinds at low- and midlatitudes in the southern hemisphere,J. Geophys.Res., 86, 91599196, 1981.
Woodman, R. F., Mesosphericwinds at equatorial latitudes. A review on observationalaspects,J. Atrnos.Terr. Phys.,39, 941-958, 1977. P. P. Batista, B. R. Clemesha, V. W. J. H. Kirchhoff, and D. M. Simonich,Instituto de PesquisasEspaciais-INPE, ConselhoNacional de Desenvolvimento Cientifico e Tecno16gico-CNPq, Caixa Postal 515, 12200 S5o Jos6dos Campos, SP, Brazil.
(ReceivedFebruary 27, 1984; revisedJuly 13, 1984; acceptedJuly 17, 1984.)
