JOURNAL OF GEOPHYSICAL RESEARCH, VOL. 105, NO. E4, PAGES 9521-9537,APRIL 25, 2000
Thermal tides and stationary waves on Mars as revealed
by Mars Global Surveyor thermal emission
spectrometer
Don Banfield and Barney Conrath
Departmentof Astronomy,CornellUniversity,Ithaca,New York
John C. Pearl and Michael D. Smith
NASA GoddardSpaceFlightCenter,Greenbelt,Maryland
Phil Christensen
Departmentof Geology,ArizonaStateUniversity,Tempe
Abstract.
Atmospheric temperature retrievals from thermal emissionspectrom-
eter (TES) observedradiancesmake possiblethe most completeseparationof the
constituent wave modes evident in Mars atmosphere to date. We use all of the
data from the first aerobrakingperiod as well as the sciencephasing orbits, which
affords good sampling of the diurnal tides and stationary waves. TES retrievals of
atmospheric temperature on a grid of pressurelevels are the fundamental data set
in this study. We then fit this data to selectedFourier modes in longitude and time
for altitude, latitude, and L• bins. From this we have identified the amplitudes
and phasesof the diurnal and semidiurnaltides, the first few (gravest)stationary
waves, and a few modes which arise becauseof couplingsbetween sun-fixed tides
and topography. We also retrieve estimates of the zonal and time of day mean
temperature meridional crosssectionsand their rates of change. The zonal and
time of day mean temperature meridional crosssectionsagree with those of Conrath
et al. [this issue]to within I K wherewe can reliablyretrievethis mode (90øSto
•20øS). Heating rates of up to 2.4 K/sol wereobservedaroundthree scaleheights
above 60øS-90øSduring the Ls = 310ø - 320ø dust storm. Diurnal tide amplitudes
of greater than 8 K were observed during the Noachis and L• = 310ø - 320ø
dust storms. From Ls = 255ø - 285ø an unexplained phase reversal at two scale
heights was observedin the diurnal tide from 60øS-80øS.Convectivepenetration
abovethe unstableboundary layer may explain anomalous(180øout of phasewith
the sun) diurnal tide phasesbetween0.5 and one scaleheight abovethe subsolar
point. Semidiurnal tides are of order 2 K throughout the southern extratropics.
A stationary mode of wavenumberone was observedwith amplitude 1-4 K in the
southern extratropics. Topographically coupled tidal modes were also quantified.
1.
Introduction
this subsetof data (from the first aerobrakingperiod
phasing
orbits(SPO)ofthemission)
Mars Global Surveyor's (MGS) thermal emission (AB1)andscience
is the best yet for discerningthe different wave modes
spectrometer(TES) has been used to retrieve atmospheric temperatures as the spacecraft scanned differ-
ent locationson the planet [Conrathet al., this issue].
that exist in Mars atmosphere. That is the focusof this
work.
Waves in Mars' atmosphere have been studied from
Becausethe spacecraft was inserted slowly into its maporbit since Mariner 9 first took measurements that reping orbit using aerobraking,MGS and TES had a long
period of time to observemany different combinationsof vealed the atmospherictemperature. The diurnal thertime of day, latitude, and longitude. The result is that mal tide was easily identified in these data because of
its largeamplitude[e.g.,Pirragliaand Conrath,1974].
Conrath[1981]analyzeda subsetof the data (northern
Copyright 2000 by the American GeophysicalUnion.
Paper number 1999JE001161.
0148-0227/ 00/ 1999JE001161$09.00
winter midlatitudes)and foundwave-likeperturbations
but could not determinespecificallywhat type of wave
it was becauseof the spacecraft'ssamplingpattern. He
found it consistentwith either a traveling baroclinic
9521
9522
BANFIELD
ET AL.: MARS THERMAL
TIDES AND WAVES FROM MGS TES
wave or a stationary wave of wavenumber2. Banfield apoapsein the AB1 and SPO missionphases,TES ob-
et al. [1996]identifiedwhat appearedto be thermal
servations
scanned
the instrument
field of view across
tides and stationary wavesin infrared thermal mapper the planet, sensingmany combinations of latitude, lon(IRTM) T15 data, althoughrecentwork suggests
that gitude, and local time in a short period of time. These
the data and that portion of their work may have been sequences,which primarily coveredthe Southern Hemicorruptedby surfaceradiance[Wilson and Richardson, sphere (becauseapoapsewas always in the Southern
2000].
Hemisphere)are particularly valuable in the present
These studies of the waves present in Mars atmospherehave put usefulbut limited constraintson atmo-
work.
In Figure 1 we show the coveragein several dimen-
sphericmodels. Nayvelt et al. [1997]tried to explain sionsfor a typical sliceof data (15øofLs) from the AB1
some of the observed surface streaks in terms of station-
and SPO missionphases. Figure la showsthe coverage
ary waveobservations.Much work has been doneex- as a function of latitude and longitude. From figure la,
aminingthe connectionbetweenatmospheric
dustopac- it is apparent that the coverage is generally complete
ity andthe thermaltides[e.g.,LeovyandZurek,1979].
and uniform
However,observations
of globalwavesare scarce,a fact
whichwe hopeto partially remedywith this work. The
impactof theseresultswill leadto morefaithfulmodels
and a better understandingof the phenomenain Mars'
pole. Figure lb shows the same data as a function
of latitude and local time. In this representation it is
clear that the data north of -030øS are highly concentrated about one time of day, while south of that they
are generally complete and uniformly distributed. This
coverageseverely hampers our ability to determine the
tidal amplitudes for the Northern Hemisphere. However, a similar plot for the mapping missionphase data
would have all latitudes having observationsat exactly
2 times of day, making the tidal amplitudes significantly
harder to determine. Finally, Figure lc showsa set of
cuts in longitude and time of day for nine different latitudes. This plot again showshow the coveragein time
of day becomes sparse north of -030øS. It also shows
that where there are observations, they are generally
uniformly spacedin longitude versuslocal time. If there
were significantcorrelationsbetweenthe longitudeof an
observation and its local time, it would again be more
difficult to separate out the tidal amplitudes from the
stationary wave amplitudes.
atmosphere.
In this work, we make a distinction between waves
which are highly predictable,either by being fixed in
spaceor forced directly by the sun, and those waves
which are much lesspredictableand travel at all manner of speeds.The highly predictablewaveswe consider
part of the climatology,whilethe otherwavesare what
we looselycall "weather." In this work, we focuson
the predictablewaves,leavingthe "weather"for a later
work. In section2, we discusswhich subsetof the data
we have examined and why and the properties of the
TES instrument and its atmosphericretrievals. Follow-
ingthat we definethe wavemodesthat wesolvefor and
then go on to describethe methodswe usedto estimate
amplitudesand phases. Next we presentsomeof our
results. Finally, we concludewith a discussion
of some
possibleimplicationsof theseresultsand a summaryo
2.
2.1.
Data
Set
Orbits and Coverage
2.2.
TES
over these dimensions
to near the north
Retrievals
The TES instrument is a Michelson interferometer,
measuring thermal
emission between 1600 and
200 cm -1 with a resolution of either 5 or l0 cm -1
Us-
The data we use in this study are the atmospheric ing the 15 micron CO2 absorptionband complex,atmotemperature retrievals from the MGS spacecrai•'sTES spherictemperaturescan be retrieved[e.g., Conrathet
instrument from the AB1 and SPO phasesof the mis- al., this issue]. While the instrumenthas the capabilsion, that is, before the mapping phase. After entering ity of scanningthe forward and aft limbs of the planet
the polar mapping orbit, TES was restricted to obser- to increase vertical resolution of the retrievals, we only
vationsonly at certain fixed times of day. Although favored for mapping purposes,this orbit is not well suited
for samplingtime of day variations. Becausethe diurnal variations typically dominate, it is easy for them to
alias into other modes if they are not well observed. It
may prove possibleto use the horizon sensorson the
spacecraftto infer the time of day variationsduring the
mapping phase of the mission,but that approachhas
not yet beenfully tested (T.Z. Martin, private communication, 1999).
Prior to entering the mapping phase of its mission,
the spacecraft
's orbit changedslowlywith time and afforded the instruments different views of the planet that
also changedwith time. When the spacecraftwasnear
considered
retrievalsof the (muchmorecommon)near
nadir observations.
The effective vertical
resolution
of
thesenear nadir observationsis larger than 1/2 of a
scaleheight (•5 kin). The TES team has prepareda
data set reporting the atmospherictemperatureof each
retrieval on a standard pressuregrid with a half scale
heightinterval, starting at 6.1 mbar, the referencepres-
sure we use throughoutthis work (i.e., Pi=6.1 mbar
[exp(-i/2)] for i = 0, 1,..., 8). The lowestpressurein
the grid for these near-nadir observationsis 0.11 mbar
or an altitude of four scaleheights. For pressureslower
than this, the information content of the signalis min-
imal [Conrathet al. this issue].The temperatures
are
reportedfor everynear nadir observationfrom the AB1
BANFIELD
ET AL- MARS THERMAL
TIDES AND WAVES FROM MGS TES
I
9O
I
9523
I
................
.½s}&;:;:;:;;;:;:;:;:::;'"'"•"'•:"•4•}::•:i
•:!:::
,::
..............
:::::::::::::::::::::
....................
ß
::•:ai•
*::;::•P•::.•::-;•:8
-:' .
45
:::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::::
. ...
..:...........................
-45
-9O
0
45
90
155
180
225
270
56O
515
East Longitude
Figure 1. The coverageafforded by the spacecraftduring a typical 15øLs period in the
AB1 and SPO mission phasesplotted as a function of several different dimensions. (a)
The number of observations in each of our bins as a function of latitude versus longitude
is shown. Coverageis good and roughly uniform. (b) The coverageas a function of local time versus latitude is given. Note that the coveragein the north is very poor in local time but relatively good and uniform in the south. (c) The coveragefor nine different
latitude bins as a function of longitude versuslocal time is shown. Again, note that the
north has very poor local time coverage,while the south is more uniform. Furthermore, the
observationsin the south are roughly uniformly spread over the longitude-local time plane.
and SPO phases of the mission, except at those locations where topography penetrated into the pressure
level considered for the region being observed, or the
spectrum was corrupted and uninterpretable.
The retrievals of atmospherictemperature from TES
spectra are subject to several noise sources. These include instrument noise, errors in the estimated surface
pressure,radiometric calibration of the instrument, and
assumptions about surface emissivity and atmospheric
dust opacity. The magnitudesand behavior of these error sourcesare such that all retrievals are subject to an
error of •1-2 K. Additionally, the error bars on retrieved
temperatures in the lowest scale height are dominated
by possiblesurface pressureerrors. The TES retrievals
used in this work were performed without the use of the
assumedfor the calculations[•'onrath et al., this issue].
For example, a 5% error in the surface pressurecan
lead to a 1-6 K error in the retrieved temperature for
the lowest layer, for surface temperatures of 200-260 K,
respectively[•'onrath et al., this issue].
3.
Modes
This
work
Considered
is focused
on the
wave
modes
in Mars'
atmosphere that are either constant with time and of
integral wave number in longitude (globally coherent
stationarywaves,includingthe zonal mean) or varying
with a frequencythat is an exact multiple of 1 sol-1
(solarthermal tides). We alsoincludethosetidal modes
which are not Sun-fixed but which are expected to be
Mars Orbiter LaserAltimeter (MOLA) topographyand produced by the interaction of the Sun-fixed tides with
thus likely have significanterrors in the surfacepressure longitudinal asymmetries in either the forcing or the
9524
BANFIELD
ET AL-
MARS
THERMAL
TIDES
AND
WAVES
FROM
MGS TES
901
45
-45
-9O
0
5
6
9
12
Locol
15
1S
21
24
Time
Fi•m'e 1. (continued)
topography. Finally, we also included a secula.rterm
have rr - 0, that is, no time variation. The solar tidal
which accounts for the seasonal drift in the zonal and
modes have a phase speed equal to that of the sun,
time of day mean temperatures. Generally, this term
was small over the averagingperiods; however,it was
notably large during one of the dust storms.
We have generally followedthe conventionsby Chap-
--- - 1 - Cphas
Csu,•
e ---
•• , and
are therefore
limited
to
s -- rr. Finally the tidal modes produced from inter-
actionsbetweenthe Sun-followingtides (of longitudinal wavenumberso - rr) and longitudinaIvariationsin
man and Lindzen[1970],excepto•trdefinitionof phase. heatingor topography(of longitudinalwavenumber
m)
We ca,nexpressthe perturbation temperature by
can be expressed as the sum of terms with s - So+ m
T-
}+
to),
where T is temperature, 0 is latitude, z is altitude, t is
and s- So- m [e.g.,Znrek,1976;Conrath,1976].
This leavesus with three groupsof modes,rr - 0, s -
[0,1,2,...] (thestationary
modes);
rr - [1,2,3,...], s -
rr (the Sun-following
tidal modes);and rr -[1,2, 3,...],
time, ½ is (east) longitude,rr is a wavenumberin time s - rr q-m for m - [1,2,3,...] (the longitudinalvari(positiveby convention),and s is a zonalwavenumber. ation forced tidal modes), in addition to the secular
T•'s(O,z) is the amplitude of a particular wave mode. term. Note that becausewe only considerinteger val-
T•c'ul•(O,z) is the amplitudeof the secular
drift mode, ues of rr, then we can treat time as periodic with period
and to is a reference time, the mean value of t for the I sol(except
forwiththesecular
term). Essentially,
this
observations.We definethe phaseof a mode, ( using
just echoesthe fact that we are only interested in wave
modes that vary repeatably over exactly a sol. The
other combinationsof s and rr not within these groups
represent wave modes that are neither fixed to surface
If we wish to limit the modes considered to those menfeatures nor directly forced by the sun. They are the
tioned above, this limits the combinations of rr and s al- traveling waves that are usually called "weather" by
lowed. First we consideronly globally coherentmodes, most and will be the subject of our next work with
implying that s - 0, 1, 2, .... The stationary modes all this data set. In fact, to better reveal the "weather,"
(r•,s
__tan-1
•m{
Tr•'s}
•e{T•,•}
.
(2)
BANFIELD
ET AL.- MARS THERMAL
ß
o
o
o
o
o•
•
c-,4
TIDES AND WAVES FROM MGS TES
o
co
c)
o
o
o
co
o
o
o
o
i
i
co
o
9525
9526
BANFIELD
ET AL.: MARS THERMAL
we must first isolate the well-defined
variations
under
TIDES
AND WAVES
FROM
MGS TES
spectrum for every datum, we evaluated it for a lim-
ited set of locationsin longitude and time, resultingin
perhapsa factor of -•16 increasein speed(the median
fit from a given set of data. We have experimentedwith numberof observationsper bin). We used24 bins in
fits to O'max: 3 and mmax-- 3 and found that power longitude(15øbins)and 12 binsin time (2 hourbins).
scrutiny here.
Obviously,there is a limit to how many modescan be
decreasesas the mode frequencyincreases.Specifically,
the modes added by increasing from amax = 2 and
mmax= 2 to amax= 3 and mm•x = 3 only explain •6%
more of the power in these types of waves. For comparison, note that we find that the diurnal tide alone
accountsfor • 70% of the powerin thesetypesof waves.
Furthermore, the data coveragemakes it difficult to reliably retrieve fits for the high-frequencymodes. Thus,
for this work, we have limited ourselvesto amax = 2
and mmax = 2, which should contain most of the power
in the data set for these types of wave modes.
Becauseour data set is not uniformly sampledin the
longitude-time domain, aliasing is a significant problem. This can be seen heuristically in that the different
Fourier modes, while orthogonal on a uniformly sampled domain, have significant correlationsfor our limited and nonuniform sampling. Therefore power in a
given mode in the data set will have nonzero convolutions with other modes. This constitutesaliasing,power
leaking from one mode into another that is nonnegligibly correlated with the first mode for incompletesampling.
Periodogram techniques only compute the convolu-
4.
tion of the data with
Estimation
a set of modes.
The end user then
must interpret these convolutionsin terms of mode am4.1. Amplitudes and Phases
plitudeswhile being awareof the possibilitiesof aliasing.
To estimate the amplitudes of the different wave Least squaresfitting of the modesto the data goesone
modes outlined above, we used a combination of bin- step beyond the periodogram techniques,in that minning and least squaresfitting, based on the ideas of imizing the difference between model and data helps
Wu et al. [1995] (see Wu et al. [1995]for more de- separate those modes with high convolutionswith the
tails on the approach). The data set we used from data into ones that represent real power and oneswhich
the TES team was already sampled on nine distinct are more likely aliased noise. As an example, two modes
pressure levels, each separated by half a scale height, could show convolutionswith the data set that differ by
starting at 6.1 mbar. We kept that vertical sampling a few percent and are highly correlated. Using a periin our analysis. We broke the data into L• blocks of odogram technique, the end user would have difficulty
15øto resolve seasonaland dustinesschangeswell. In decidingif both are likely to have power or if one is real
testing this choice of seasonalresolution, for one sec- and the other aliased. The least squaresfitting would
tion (L• - 300ø - 320ø, whichincludesa dust storm) usethe fact that one mode would likely fit the data betwe found that 10øL• blocks yielded notably better re- ter than the other (although only marginally so) and
solved changes. For that period, we used 10øL• bins. would ascribe the power to the best fitting mode. For
It is important to include a long enoughperiod to give this reason, we choseto use least squaresfitting of the
good coverageof longitude and time of day and to aver- modesrather than periodogramtechniques.
age over lower-frequencywaves. However, too long an 4.2. Error
Bars
interval will smear out seasonal or other atmospheric
A least squares fit will return formal error bars to
behavior changes. It appears that 10ø-15øL• bins were
accompany
the retrieved parameters. However,the fora good compromisefor this TES data set.
mal
error
bars
only represent how well the model fits
We chose not to fit spherical harmonics or Hough
functions to the data for each L• and altitude bin. Be-
causeof the poor coveragein the north, the global nature of Hough functions would have resulted in poorly
constrained fits. Rather, we choseto bin the data further by latitude and then, within each of those bins,
fit Fourier series in longitude and time to the data.
This proved to be simpler and also allowed us to keep
relatively high resolution in the meridional direction,
without having to fit to high-ordersphericalharmonics.
We chose10øbinsin latitude, which still afforded good
coveragefor most latitudes, yet resolvedthe latitudinal
variations
well.
the existing data. It includesno estimateof aliasing
possibilities. To include this, we modeledthe error bars
using a Monte Carlo technique. We took the observing pattern for each set of Ls, altitude and latitude
bins that we were fitting, and manufacturedmany sets
of synthetic data with 2 K observational errors. Then
by examining the standard deviations of the retrieved
mode amplitudes, we estimated the combinedeffects of
the noisein the data, as well as the gapsin the coverage
contributing to aliasing. This approach is probably effective in estimating the relevant error bars, but it does
have shortcomings. Our choiceof temperature retrieval
observationalerror is almost certainly an oversimplifi-
Finally, instead of fitting the longitude-time Fourier
seriesdirectly to all the raw data, we further binned it cation. We noted above that the observational error
in the longitude and time dimensions.This allowedus is larger near the surface becauseof surfaceradiance,
to greatly speedup the fitting process,without sacrific- and the poorly known (pre-MOLA) topography.Thus
ing accuracy.That is, instead of evaluatingthe Fourier a constant 2 K observationalerror for all altitudes prob-
BANFIELD
ET AL.: MARS
THERMAL
TIDES
AND WAVES
FROM
MGS TES
9527
ably overestimates the errors at high altitudes and un-
any latitudes. There are two gaps (Ls = 285ø- 300ø
and Ls = 320ø - 360ø) in the data set.
ing of this approachis that it only accountsfor aliasing
This mode is the quantity that is presented in the
among the modesthat are being fit. Heuristically,this zonal mean, time mean crosssections,suchas by •'oncan be understood in that the least squaresfit divides rathet al. [this issue].However,the approachusedin
the observedpower between the modes being fit. The that and other works simply averagesmany observaobservational noise, combined with the incomplete ob- tions together, ignoring the possibility of aliasing and
serving pattern causesleakage between the modes, or waves. Our work can be usedto estimatethe magnitude
aliasing. Because the power is only divided between of these possible effects and thus an estimate of the erthe modes being fit, the aliasing is only accountedfor ror bars on those profiles. We carefully computedzonal
derestimates
them at low altitudes.
Another
shortcom-
between those modes. To minimize this problem, we
typically fit out to Smax= 2, the results of which suggested that there is significantly less power at higher
wavenumbers. Therefore we are likely accounting for
most of the power that could be aliasing into the im-
portant (low wavenumber)modes.
5.
Results
Here we present our results. The format of the presentation is crosssectionsof mode amplitude and phase
as a function of altitude and latitude. We present a
set of these cross sections, an individual plot for each
means using the same subsetsof data and the same bin
sizesas were usedby •'onrath et al. [this issue](not
shown)and foundour resultsto agreewith theirsquite
well where we can determinea reliable result. The typical standard
deviation
of the differences between our
results and theirs in the valid regionswas •1 K. This
meansthat the samplingthroughout the AB1 and SPO
missionphasesis uniform enoughin longitudeand time
of day that the simple meansof the data are representative of completely and uniformly sampled means. However, keepin mind that this is only true in thoseregions
wherewe havebeenableto determinea reliableresult,
or south of •20øS. North of this we are not able to es-
L s bin. The phase(being a circular variable) is rep-
timate the strength of the other modes and can make
resentedby color on these plots, with a spectrum that
wraps around also in a circular fashion. Amplitude is
representedboth by contoursand alsoby the saturation
of the color• the contoursyielding readable values.
Regionsthat are left blank on theseplots were filtered
out for one of severalreasons.The strongestreasonthat
we left a region blank was due to the least squaresfit
being ill determined. This typically resulted from there
no estimateasto the accuracyof the simpleaverages
of
the data at thoselatitudes. Usingour estimates,error
barsof 5 K or moreare possible
in the zonalaverages
of •'onrathet al. [thisissue]for the northernlatitudes.
The seasonal progressionof this mode shows the
SouthernHemisphere
warmingand losingits latitudinal gradient from Ls = 180ø-
255ø.
The latitu-
dinalgradientevenreverses
(warmerat the pole)for
beingfewerfilled bins (in longitudeand time) than the
number of modes being fit. The regionsaffectedby this
Ls: 255ø - 285ø, then returnsto beingwarmerat the
equatorby L s = 30ø. A notablewarmingoccursfrom
were at all latitudes in the north and near the ground. Ls: 225ø - 240ø, coincident
with a largedust storm
Another reasonthat we left regionsblank on these plots in Noachis[Smithet al. this issue].A smallerbut still
was that the retrieved amplitude of the mode was less notablewarmingalsooccursat Ls = 310ø-320ø, which
than the estimate
of the error bars on that
mode.
That
is, that mode is consistent with a value of zero. The
amplitude for the mode that we retrieved in those locations may be correct, but we choseto cut those values
from the plot to ensure that the values displayed are
significant. This constraintfiltered out the resultsfrom
regionsthat were just north of the valid results shown
in the plots to near the equator. Finally, we did not display values which had error bars associatedwith them
greater than 5 K. This typically cut values which were
anomalouslyhigh in the retrieval, and only a few scattered locations were effected. Because of these factors,
our plots only extend from the south pole to 10øN.
is also coincident with a smaller dust storm north and
northwestof Argyrewhichstartedat Ls: 309ø [Smith
et al. this issue]. Still further pursuingthe similarities between the observeddust opacity from Smith et
al. [thisissue]and theseresults,we seethat the cooler
SouthernHemispheretemperaturesfrom Ls = 0ø - 30ø
(compared
to similarsolarinputat Ls = 180ø- 195ø)
are again consistentwith the reduceddust opacity observed
at that
time.
5.2. Zonal Mean,
or:0, s=0
Time Mean Secular Trend:
We also fit a secular trend to the zonal and time mean
5.1.
Zonal Mean, Time Mean:
rr = 0, s = 0
temperature distribution, which is depicted in Figure 3.
The zonal mean, time mean mode, a: 0, s = 0 ap- This mode is important to fit becauseit has signifipears in Figure 2. Note that for this mode, phase is cant amplitude, and without including it in the fit, it
undefined, so it appears in black and white. For many could easily alias into other modes. The structure of
values of Ls, we were only able to constrain this mode this mode is enlightening as well. It mainly echoesthe
well as far north as •20øS. We were also unable to conseasonalchangesnoted in the zonal and time mean term
strain this mode well in the lowest half scale height at above,that of slowwarming in the south during south-
9528
BANFIELD
ET AL.'
MARS THERMAL
TIDES
AND WAVES
FROM
MGS TES
o
t.c)
r,q
I
o
II
I
¸
¸
o
z
:.....
•1-
I'q
('xl
*--
0
•1-
I-q
('xl
,--
ß•-
0
I-q
('xl
,--
0
'•-
I'D
C'•
•--
0
I
I
t'
ß
,•- I-q CXl •- 0
,•- I-q CXl •-- 0
,•- I-q 0,,I •-- 0
,•- I-q 0,,I ,-- 0
(SH 01ooS)opn!lV
'•-
I'D CXl ,-- 0
BANFIELD
,q--
i,q
ET AL'
O,,l
,-
o
MARS THERMAL
,q--
i,q
eq
•--
TIDES AND WAVES FROM MGS TES
o
o
o
o
,q--
i,,.-)
eq
,--
o
,q--
i,q
eq
•--
o
,q--
i,,--)
exl
,--
o
,q--
i,,--)
exl
•--
o
,q--
i,,--)
exl
•--
o
,q--
i,q
c-q
,-
o
,q--
i,q
eq
,--
o
,q--
i,,--)
cx,i
,-
o
,q--
i,,--)
cx,i
•--
o
(S•H 8iooS) 8pn:•!:•lV
9529
9530
BANFIELD
ET AL.: MARS THERMAL
TIDES AND ¾VAVES FROM MGS TES
ern springand slowcoolingin the southduringsouth- with heightnear the top of our domain,althoughin
makesthissomewhat
amern fall. However, it also showsa very large warm- the tropicsthe poorcoverage
ing(2.4K/sol)in thehighsouthern
latitudes,
centered biguous.It is perhapsmostclearlyevidentin Figat •2.5 scaleheightsaltitudeduringthe smallerdust ure 4 for L s - 240ø and the two mostequatorward
stormnearArgyre(Ls: 310ø - 320ø).Thereis alsoa latitudes. This phenomenonoccursroughlyequatorcentered
hint of an elevatedheatingrate duringthe Noachisdust ward of 50øS,with the strongestexpression
storm(Ls: 225ø- 240ø)•but thisis muchmoresubtle aroundL• -- 270ø, southernsummer. If the heating
nearthe surface,tidal theorypredicts
than that evidentduringthe smallerLs: 310ø - 320ø is all deposited
advance
(maxima
occurring
earlierin theday)
storm. This is even more surprisingin light of the a phase
fact that the seasonaltemperaturetrends are working with heightat all altitudesnearthe equatoranda veragainstthe warmingat Ls = 310ø - 320ø, whilethey tical wavelengthof •35 km [e.g.,Zuve/•,1976]. This is
would enhancethat during L• : 225ø- 240ø. Per- consistent with the behavior we see from the bottom to
hapsthis is indicatingsomething
verydifferentabout
the middle
the dust distribution or the resulting diabatic circula-
top. Perhaps this behavior at high altitude is indicative of heating significantly removed from the surface.
Furthermore, the apparent phase advance with height
tion in these two dust storms.
of our domain
near the bottom
5.3.
Sun-Synchronous
Tides
5.3.1. Diurnal Tide' cr- 1, s- 1. Plate 1 shows
the amplitude and phase of the sun synchronous,diurnal tide. More locations are left blank on these plots
than on those for the zonal and time of day mean mode
becausethe amplitudes of this mode are much smaller
and more often lessthan the error bars at a given location. However, throughout much of the Southern Hemisphere,the diurnal tide is well resolvedby the TES data.,
with amplitudes of order 4 K.
In the southern extratropics• for most of the Ls values we cover, we generally see a constant phase of
but
of the domain
not with
starts
that
near the
with a local maxi-
mum near midnight, directly out of phasewith the sun.
While this can not be a direct leakage of surfaceradi-
anceinto this level of the retrieval (becauseit is 180øout
of phase),it may still be an artifact of the retrievalprocess. Surface effects have been identified as a possible
sourceof error by the TES team, but the exact magnitude is difficult to quantify. This low-altitude phase
advance with height may also be a real phenomenon.
We will return to this topic in section 6.
There are two aspects of this mode in the latitudes
in which it vertically propagates which are interesting. The first is that this region extends to •60øS
fbr some œs values. Simple tidal theory predicts that
vertical propagation stops at 30øS, although modeling
•90ø(maximum at about 1800 LT, green in Plate 1).
In that latitude range, this mode is expected to lag
the sun and not propagate vertically, as we observe. work [Wilson and Ha•iltor•, 1996] showsit extending
There is a significant departure from this behavior from somewhat poleward of 30ø, particularly into the winter
L• = 255 ø - 285 ø, poleward of •50øS and above two hemispheredue to the strong westerliesthere. The secscaleheights. In this region, we seethe amplitude signif- ond aspect of interest is that the amplitude does not
icantly decrease(downto •2 K)• and the phasechange seem to grow with height inversely with the density to
to leadingthe sunby •90 ø(maximumat about 0600 LT, maintain a constant energy flux through the domain.
purple in Plate 1). Becausethe amplitudedecreases
in Instead, the amplitude is roughly constant with height
that region, it is conceivablethat our retrieval of phase near the tropics, perhaps decreasingwith height at more
is less significant even though it exceedsthe associated values of L• than increasing. This is probably indicaerror bars. However, Figure 4 demonstrates that this tive of either the distribution of forcing for this mode
is not the case. Figure 4 shows normalized tempera- or converselyits damping. Both of theseaspectsof this
ture variations
about their means as a function of altidominant tidal mode are intriguing and need further
tude versus local time, fbr four 10ølatitude bins near the
exploration.
south pole for L.• = 240ø - 255ø and L• - 270ø- 285ø.
Out,side of the latitude band where the mode appears
The phase reversal for the southernmost 30øof latitude
to propagate vertically, it is interesting to note the disis evident for the L.• : 270ø - 285ø plots, while it is tribution of amplitude as a function of location and seaclearly absent from the earlier ones. Shown in this man- son. The amplitude is very high at the same locations
ner, it is evident that this phase reversal is a significant and the same season as the large Noachis dust storm
result and not an artifact of the relatively small am- near L•: 225ø - 240ø. This is expected, as a large dust
plitude in that region. •re will return to this topic in opacity should indicate a strong coupling between the
section 6.
solar forcing and the atmosphere'sthermal response.
Nearer the equator, the other structure we see in this
This range of Ls in fact exhibits amplitudesin excessof
mode's phase is what appears to be a phase advance 8 K as high as four scaleheightsabovethe surface,per(maxima occurring earlier in the day, color changing haps suggestingthat the dust is well mixed very high
from red to greenin Plate 1) with height near the bot- into the atmosphere. The amplitude decreasesagain as
tom, and a phaseregression(maxima occurringlater in the seasonsadvance, in concert with the dust opacity,
until at L• : 310ø- 320ø it shows amplitude > 8 I(
the day, color changingfrom green to red in Plate l)
BANFIELD
ET AL.- MARS THERMAL
TIDES
AND WAVES FROM
MGS TES
oI
0
0
0
0
0
x
•pnl:!dwv
o
!
•'
PO
C•
•--
0
•'
•0
Cq
,--
0
•
r,r'j 0,4 '.-- 0
•
r,r'j 0,,I ,,-' 0
•
r,r'j 04
(S:lH@lOOS)
@pnl!llV
,,-' 0
9531
9532
BANFIELD ET AL.' MARS THERMAL TIDES AND WAVES FROM MGS TES
ug '•'•i•::'::•:"'•':::'•;:':•'•:';
•'•:'•:':•'":':•;•:;':'::•'•
.......... ::"•'
"•:'•'•,
'•:•i
•i'•iil
•i}•::•:•5
!•:':
':.........................
LiD:.:':.•
....
•":"::'":'""
•':•':':'::;:•::':'•'•
........ .
'•;•g2•
:.:
......................
•'",•"-';•::n;•."•::c&•
•. --.
.
0
•
•
•
•
0
o
__1
(%1
(SlH alooS)apn!llV
'--
0
BANFIELD
ET AL.'
MARS
THERMAL
TIDES
AND •VAVES
FROM
MGS TES
9533
o
I
x
o
o
•
o
.•
-U•6 x
aPnl!ldLu¾
0
0
o
o
I
II
...
v" i
0
z
u• o
o
I
o
o
i
I
o
o
0
o
•
(SlH @I•S) @pnl!•l¾
I'O
Oq
,--
0
9534
BANFIELD
ET AL.- MARS THERMAL
TIDES AND WAVES FROM MGS TES
o
o
I
o
V .
._øt5 oo
o
I
ml-
•
oq
,-
o
apn)dldt.u¾
o
o
o
o
0
I
I
o
I
o
I
o
00
I
,•'
•
Oq ,-
0
•-
.'•
Cq ,-- 0
•
•'D r•l
,-
0
•'
•'D Cq ,-
0
•1- •0
Oq ,-
0
BANFIELD ET AL.: MARS THERMAL TIDES AND WAVESFROM MGS TES
9535
over a broadregionof the southernextratropics,two or is not straightforward,the si•nplestexpectationwould
morescaleheightsup. This periodonceagaincoincidesbe that the semidiurnal mode might be comparable to
with one of the other significantdust stormsalready the diurnal mode, especially during dust storms. This
identifiedby TES retrievals[Smith et al. this issue]. appearsto not be the casefrom the presentanalysis,
This dust storm appears to excite a high-amplitude di- with the typical amplitude of the diurnal mode being
urnal tide even higher than that during the Noachis of order 5 K in the southern extratropics, while that of
dust storm, perhaps suggestingthat the dust was more tile semidiurnal mode is HI K. Nevertheless, this is not
at altitude
than below.
inconsistentwith observationsof large semidiurnal sur-
concentrated
Wilson and Hamilton [1996]presentmodel simula- facepressuresignals,as the long verticalwavelengthof
tions which we can directly compare with one of these the semidiurnal mode helps enhanceits surfacepressure
seasonalplots. Wilsonand Hamilton[1996,Figure16a] signaloverthat of the diurnalmode(with its relatively
show a cross section like ours for L s = 270 ø and low short vertical wavelength).
dustiness. The agreement in amplitude is generally
good. We find a large amplitude near the surface, perhaps 8 K or more below one scale height. Their results
indicate an amplitude of roughly 5 K or more in that region, then decreasingto a minimum of -•1 K near three
scale heights and increasingagain above that. This is
very similar to our results, where we seea minimum amplitude of HI K between two and three scale heights.
5.4.
Stationary
Waves
The stationary wavemodeshaveno time of day variation or or-
0. We fit the s-
land
s-
2 modes to
the data. The s - I mode, shown in Plate 3, has a typ-
ical amplitudethroughoutthe SouthernHemisphereof
•2 K, with somelocations clearly exceeding4 K, perhapsa few as high as 8 K. The spatial structureof the
WilsonandHamilton[1996,Figure16d]showthe phase amplitude is difficult to connectwith any simpleidea,
of the zonal wind oscillation being essentiallyconstant
from 30øS poleward. This is the time in which we find
the phase reversal with height at two scale heights in
the temperature signal. While Wilson and Hamilton's
plot is for zonal wind and ours is for temperature, there
is an apparent discrepancyhere betweentheir modeling
and our results for this particular season. However, in
generalfor other valuesof L s, our resultsagreewith the
but its seasonal variation shows an obvious correlation
tide far outside of the tropics.
5.3.2.
Semidiurnal Tide: cr- 2, s- 2. This
mode, the semidiurnal tide shownin Plate 2, is interesting in that it is typically much smaller in amplitude than
might be expected. We were able to reliably determine
the amplitude of this mode for •50% of tile altitudes
with enhanced amplitude.
and latitudes in tile SouthernHemisphere.The regions
where we could not determine the amplitude reliably
were either too sparsely observedor the amplitude was
too small to distinguishit from noise. Throughout the
southern extratropics, a typical amplitude of this mode
is HI K. Within the tropics the amplitude is larger,
reaching .08 K three scale heights above the equator.
The amplitude is greatest over the equator, and it could
be growing with height as quickly as a factor of 2 for
each one to two scale heights. This is notably similar
within one quadrant of longitudein the SouthernHemi-
with the smaller Ls - 310ø - 320ø dust storm. During
this time, the amplitude of this mode is 4 K or more
from 40øSto 80øS,centeredat two scaleheightsof altitude, about 4 timesthe amplitudein thoseregionsfrom
just 10øofL• earlier. There is alsosomehint that this
mode•samplitude is enhancedduring the Noachisdust
storm but perhapsonly by a factor of 2 or less. During
simulationsof Wilson and Hamilton (and with theory) the Ls - 310ø-320 ø dust storm, the phaseof this mode
and show no vertical phase propagation of the diurnal is also anomalous and consistentthroughout the region
Smith et al. [thisissue]presentmapsof dustopacity
during both of thesedust storms. Their resultsshow
that the zonal distribution
of dust in the Noachis dust
storm is roughlyuniformpolewardof 40øS,while the
L• - 310ø- 320ø storm is almost completelycontained
sphere.It is quite likely that this ditt•rencein the longitudinal distributionof dust in thesetwo stormscan
explainthe differencesobservedin their stationarywave
amplitudes.This invitesfurtherstudyinto the specifics
of the dust heatingand the generationof thesestationary wave modes.
Hollingsworthand Barnes[1996]and Nayvelt et al.
[1997]both modeledstationarywavesin Mars atmosphere.In agreementwith our results,they both found
to thep-•/2 thatispredicted
forconservation
ofenergy that the Southern Hemisphere is dominated by the
flux for a vertically propagatingmode.
s = 1 mode. We have not displayedthe s = 2 mode,
We know of no published estimates of the latitudealtitude
behavior
of the semidiurnal
tide of Mars.
The
as its amplitudeis typically < 1 K throughoutthe re-
gionwherewecanretrieveit. The twomodeling
works
Viking landers yielded good data sets of the semidiur- suggest
that the s = 2 modeis morepowerfulin the
nal pressurevariations with time. These showedsignif- NorthernHemisphere,whichis not accessible
with this
icant semidiurnal amplitudes, strongly increasingtheir subsetof data. Banfieldet al. [1996]reportedstation-
amplitudesduring global dust storms [e.g., Leovyand ary wavesfroman analysisof IRTM T15, but their reZurek, 1979]. While the relationshipof surfacepres- suitsregardingthe meanstateare likelycorruptedby
sure amplitude to temperature perturbation amplitudes
surface
radiance[WilsonandRichardson,
2000].
9536
5.5.
BANFIELD
Topography-Coupled
ET AL.: MARS THERMAL
TIDES AND WAVES FROM MGS TES
Tidal Modes
It showsan amplitudeof •01K throughoutthe southern
extratropics,with amplitudesincreasinginto the NorthThe modes which arise from the interaction
between
ern
Hemisphere.Aside from this, we know of no other
the sun-fixedtidal modesand longitudinal asymmetries
yet
published
model runs with whichto comparethese
(e.g., topography)were also simultaneouslyfit in this results.
study. In general, these modes are significantlysmaller
than those discussedabove and do not presentany clear
spatial structures. Becauseof this, we have not graphically presented any of them here• The largest of these
modes in our results for the Southern Hemisphere was
the a = 1, s = -1 mode, which we found to have
an amplitude of •01.5 K, with larger values starting to
showup in the northernmostlimits of our retrieval (i.e.,
•025øS).Thesenorthernmostvalueshavethe largesterror bars, but values of 2-4 K repeatably appear near
25øS. This a:
1, s = -1 mode propagates eastward
at the same speed as the sun moves westward. It includes the eastward propagating diurnal Kelvin mode
of previousworks[e.g., Zurek, 1976]which,unlikeour
fits, has a well-defined latitudinal structure, confinedto
the tropics.
The next smaller mode in this group is the a = 1,
s = 0 mode. This mode has a period of I sol but
no longitudinal variations, essentially a pulsing of the
atmosphere, with the same phase of oscillation at all
longitudes. Typical Southern Hemisphere extratropics values for this mode are •01 K, again with indications that the amplitude increasesto the north starting
around 25øS. This mode also clearly showsan increase
in amplitude during the L s = 310ø - 320ø dust storm,
with amplitudes throughout the southern extratropics
of •02 K, and growing to nearly 4 K above three scale
heights near the South Pole. Interestingly, this mode
shows no appreciable change during the Noachis dust
storm.
Similar behavior is seen in the a = 2, s = 0 mode,
which has a period of one half of a sol and again no
longitudinal variations. Typical southern extratropical
amplitudes are •01 K, again increasingto the north beyond •025øS.This mode also showsa strong increasein
amplitude during the Ls = 310ø- 320ø dust storm, with
amplitudes of •02 K typical throughout the south, and
amplitudes exceeding4 K over two scale heights near
the South
Pole.
The remainingfive modeswe fit (i.e., (a = 1, s = 2),
(a= 1, s=3), (a=2, s= 1), (a=2,.s=3),
(a=2,
s = 4) ) were all typically lessthan or on the order of
6.
Discussion
These results, extracted from the AB1 and SPO TES
data, shouldprovidestrongconstraintsfor the numerousatmosphericmodelsthat the communitynow has.
Additionally,they may be usedto try to infer details
of the state of Mars atmosphere.We expectthat tidal
and stationary wave modelswill be appliedto these
data, and estimatesof the distributionof forcingand
dissipationwill be sharpened.
In this work, we identifiedtwo puzzlingdetailsof
the observationsthat we will explore. The first was
the apparent phase reversal of the diurnal tide from
L• - 255ø- 285ø abovetwo scaleheights,south of
•60øS (seePlate 1). We do not havean explanation
for this phenomenon;however,we have considered
the
possibilitythat it is evidenceof a criticallayer. If the
windsat thisheightwerestrongenough
easterlies
(westward)to matchthe phasespeedof the sun,it is possible that the expression
of the tide mightshowa phase
reversal and an amplitude decreaseabove the critical
layer, matching the observations. The thermal winds
canbe inferredfrom the zonaland time meantemperature fields, except for the addition of the winds at the
surface. Using the thermal winds from Conrath et al.
[thisissue],wecaninferwhatsurface
windspeeds
would
berequiredto producethiscriticallayer.Nearthepole,
the winds are very modest,10 m/s at 85øS.Further
north, this hypothesis
becomes
moreunlikely.At 75øS
a surfacewind of 45 m/s is required, and at 65øS a
surfacewind of 70 m/s is required. Thereforewe find
this hypothesishighly unlikelyto be correct(without
widespreaddust stormsevident at that time, whichwas
not the case)and leavethis phenomenon
unexplained.
The second phenomena that we noted was also in
the diurnal
tide mode.
We noted that
this mode's
phase1/2 scaleheight abovethe surfacewas 180øout
of phasewith the Sun (seePlate 1). It showsa temperature maximum near local midnight. Linear tidal
theory suggeststhat an atmosphere heated from be-
1 K throughout the southernextratropics, but they all
also suggestedlarger amplitudesto the north.
low should show a phase advance(temperaturemaxima movingtowardearlierlocaltimes) as onemovesup
WilsonandHamilton[1996]discuss
the importanceof abovethe surface,with the lowestlevelshavinga maxi-
these modes and present some model calculations sug-
gestingthat many of them probably occurin Mars' atmosphere. They suggestthat the a: 1, s: -1 and
a = 2, s = -2 modesmay be the strongestof this class
of wave at many times of year. They present a plot
mum just after local noon, sincethat is where and when
the energy is deposited. We mentioned above that it is
possiblethat this is an artifact of the retrieval process
being corruptedby surfaceradiance. However,it may
be a real phenomenon. The southernmost latitude at
[Wilsonand Hamilton,1996, Figure 17a]of the tem- which we see the phase advancewith height appears
perature amplitude crosssectionof the a: 1, s: -1 to be moderately well correlatedwith the progression
mode which compares very favorably with our results. of the subsolarlatitude through the seasons.However,
BANFIELD
ET AL.:MARSTHERMAL
TIDESANDWAVES
FROMMGSTES
9537
the strengthof thiseffectdoesnot seemwellcorrelated rr = 0, s = 1 wasobservedwith amplitude1-4 K in
coupledtide
with dust opacity. For example,the dust opacitywas the southernextratropics.Topographically
highestfromL8 = 225ø- 240ø, yet duringthistimewe modes were also quantified.
observe
no significant
phaseadvance
with heightat the
bottom of our domain and near the equator.
References
It is possible
that thisphenomenon
canbe explained Banfield, D., A.D. Toigo, A. P. Ingersoll, and D. A. Paige,
by convective
overshoot.
Nearmidday,particularlyat
Martian weather correlation length scales, Icarus, 119,
the subsolarlatitudes, the martian boundarylayer is
heatedvery strongly.This raisesthe possibility
that
convective
plumescouldpenetratesignificantly
intothe
stableatmosphere
abovethe convecting
boundarylayer.
This would effectivelycool this layer (whichis neces-
sarilywarmerthanan adiabatfromthe surface).The
coolingwouldbe strongest
whenthe boundarylayeris
heatedmost strongly,near localnoon,preciselywhat
our analysisshows.Thus it is possiblethat we are see-
ing this convective
overshoot
followthe subsolar
lati-
130-143, 1996.
Chapman, S. and R. S. Lindzen, Atmospheric Tides, 200pp.,
Gordon and Breach, Newark, N.J., 1970.
'
Conrath, B. J., Influence of planetary-scale topography on
the diurnal thermal tide during the 1971 Martian dust
storm, J. Atmos. Sci., $$, 2430-2439, 1976.
Conrath, B. J., Planetary-scale wave structure in the Martian atmosphere, Icarus, •8, 246-255, 1981.
Conrath, B. J., J. C. Pearl, M.D. Smith, W. C. Maguire,
S. Dason, M. S. Kaelberer, and P. R. Christensen, 1999,
Mars Global Surveyor thermal emission spectrometer
(TES) observations:Atmospherictemperaturesduring
tude around the southern summer and affect the atmo-
Aerobraking and sciencephasing, J. Geophys.Res., this
spheric
layerbetween1/2 and1 scaleheightabovethe issue.
surface
(5-10km),almostreversing
theapparent
phase Hollingsworth,
J. L., and J. R. Barnes, Forced stationary
planetary waves in Mars's winter atmosphere, J. Atmos.
of the diurnal tide. Confirmation of this may exist in
Sci.• 55, 428-448, 1996o
B., and R. W. Zurek, Thermal tides and Martian
landertemperatureentryprofiles,or radiooccultation Leovy, C.
profiles,
but isprobably
bestobserved
by upwardlookinginfraredsounding
[Smithet al.,1996].Its potential
dust storms: Direct evidence for coupling, J. Geophys.
implicationsare alsounexplored.
Res., 8•, 2956-2968, 1979.
Nayvelt, L., P. J. Gierasch, and K. H. Cook, Modeling and
observations of Martian stationary waves, J. Atmos. Sci.,
5•, 986-1013, 1997.
7.
Pirraglia, J. A., and B. J. Conrath, Martian tidal pressure
Summary
and wind fields obtained from the Mariner 9 infrared spec-
We havedeterminedthe amplitudeand phaseof wave
troscopyexperiment,J. Atmos. Sci., $1,318-329, 1974.
modesin the Martian atmospherebasedon TES obser- Smith, M.D., B. J. Conrath, J. C. Pearl, and E. A. Ustivationsof atmospheric
temperatures
fromthe AB1 and nov, Retrieval of atmospherictemperaturesin the Martian planetary boundary layer using upward-lookinginSPO MGS data. The amplitudes and phasesof the
frared spectra, Icarus, 12•, 586-597, 1996.
diurnal and semidiurnaltides, the first few (gravest) Smith, M.D., B. J. Conrath, J. C. Pearl, and P. R. Chris-
stationarywavesand a few modeswhichare couplings tensen, 1999, Mars Global Surveyor thermal emission
between sun-fixed tides and topography are included.
Estimates of the zonal and time of day mean temperature meridional crosssectionsand their rates of change
finish the modes considered.
spectrometer(TES) observations
of dust opacityduring
aerobrakingand sciencephasing,J. Geophys.Res., this
issue.
Wilson,R. J., and K. Hamilton,Comprehensive
modelsimulation of thermal tides in the Martian atmosphere, J.
The zonal and time of day mean temperaturemeridAtmos. Sci., 55, 1290-1326, 1996.
ional crosssectionsagreewith thoseof Conrathet al. Wilson, R. J., and M. I. Richardson,The Martian atmo[thisissue]
to within1 K wherewecanreliablyretrieve sphereduring the Viking Mission,1: Infrared measure-
this mode(90øSto •20øS). Outsideof this region,po-
ments of atmospherictemperaturesrevisited, Icarus, in
press, 2000.
tential errors due to the simple averagingemployedby Wu, D. L., P. B. Hays,and W. R. Skinner,A leastsquares
Conrathet al. [thisissue]cannotbe estimated.Heating method for spectralanalysisof space-timeseries,J. At-
ratesofupto 2.4K/sol wereobserved
aroundthreescale mos. Sci., 52, 3501-3511, 1995.
heightsabove60øS-90øS
duringthe L8 = 310ø - 320ø Zurek, R. W., Diurnal tide in the Martian atmosphere,J.
dust storm. Diurnal tide amplitudesof > 8 K wereob-
servedduringthe Noachisand L•:
310ø - 320ø dust
Atmos. Sci., $$, 321-337, 1976.
D. Banfield and B. J. Conrath, Department of Astronomy,
storms. From L• - 255ø - 285ø an unexplainedphase Cornell University,420 SpaceSciences,Ithaca, NY 14853.
reversalat [wo scaleheightswasobservedin the diur- (e-mail:[email protected].
cornell.edu)
nal tide from 60øS-80øS. Convective penetration above
P. Christensen,Department of Geology,Arizona State
the unstableboundary layer may explain anomalous University,Box 871404,Tempe,AZ 85287.
(180øout
of phasewiththesun)diurnaltidephases
be- J. C. Pearl and M.D. Smith, NASA/Goddard Space
tween0.5 and 1 scaleheightabovethe latitudesaround Flight Center,Code690, Greenbelt,MD 20771.
the subsolarpoint. Semidiurnaltidesare of order2 K (Received
August11, 1999; revisedDecember
16, 1999;
throughoutthe southernextratropics.Stationarywave acceptedJanuary 4, 2000.)