NASA Technical Reports Server (NTRS) 19980151106: The 4-Day Wave as Observed from the Upper Atmosphere Research Satellite Microwave Limb Sounder

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by  NASA Technical Reports Server (NTRS)

NASA/CR- 7--" 207746 /
_,,,_ ,,, United States ofAmerica
Reprinted from JOUle.NAt. ©F ATMOSPHERIC SCIENCES // 1. _'</_ - ' i
Vol. 54.No. 3. I February 1997
© 1997 American Meteorological Society
> .7'
The 4-Day Wave as Observed from the Upper Atmosphere Research Satellite
Microwave Limb Sounder
D. R. ALLEN AND J. L. STANFORD
Department of PhysicsandAstronomy. IowaState University,Ames. Iowa
L. S. ELSON, E. E FISHBEIN, L. FROIDEVAUX, AND J. W. WATERS
JetPropulsion Laboratory, CaliforniaInstitute of Technology.Pasadena. California
(Manuscript received 16February 1996,infinalform 22July 1996)
ABSTRACT
The "4-day wave" isaneastward movingquasi-nondispersive featurewithperiodnear4days occurringnear
thewinter polar stratopause. Thispaper presentsevidence of the 4-day feature inMicrowave Limb Sounder
(MLS)temperature,geopotential height,andozonedatafromthelatesouthernwintersof 1992and1993.Space-
timespectral analysesreveal adouble-peakedtemperature structure consistingofone peaknearthestratopause
andanother inthe lower mesosphere, with anout-of-phase relationship between the twopeaks. This double-
peaked structure is reminiscent of recentthree-dimensional barotropic/baroclinic instability modelpredictions
andisobserved hereforthe firsttime.The heightvariation ofthe4-dayozonesignalisshowntocompare',,,,ell
with alinear advective-photochemical tracer model. Negative regions of quasigeostrophic potential vorticil_
(PV)gradientandpositiveEliassen-Palm fluxdivergenceareshowntooccur,consistentwithinstabilitydynamics
playingarole inwave forcing. Spectralanalysesof PVderived from MLSgeopotential heightfields reveal a
4-daysignalpeaking near the polarstratopause. The three-dimensional structurc ofthe 4-day wave resembles
thepotential w)rticity "charge" concept, wherein a PVanomaly inthe atmosphere (analogous toanelectrical
charge ina dielectric material) inducesa geopotential field,a vertically oriented temperature dipole,andcir
culation aboutthe vertical axis.
1. Introduction Simon 1995) studies have examined the 4-day phenom-
enon.
The 4-day wave is a ubiquitous feature in the polar The wave has been observed in both hemispheres but
winter upper stratosphere. It was first observed in tem- is stronger in the Southern Hemisphere (Venne and Stan-
perature data as a strong 4-day signal in zonal wave- ford 1982). The horizontal phase structure is variable,
number 1 (Venne and Stanford 1979). Later studies with both poleward and equatorward momentum flux
showed that it consists of waves 1through at least 4 all events (Venne and Stanford 1982; Prata 1984; Manney
moving with the same phase speed, such that the period 1991). The wave is generally barotropic, although some
of wave 1is near 4 days. Synoptic plots of temperature episodes show strong equatorward heat flux (Randel and
reveal a quasi-nondispersive "warm pool" of air, which Lait 1991). The episodes studied by Randet and Lait
rotates eastward around the winter pole near the stra- (1991) and Lawrence and Randel (1996) reveal a dipole
topause with a 4-day rotation period (Prata 1984; Lait structure of positive and negative Eliassen-Palm flux
and Stanford 1988b; Lawrence et al. 1995). Numerous divergence associated with the 4-day wave, with the
observational (Venne and Stanford 1979, 1982; Prata positive region overlapping negative quasigeostrophic
1984; Lait and Stanford 1988b; Randel and Lait 1991; potential vorticity gradient, a signature of instability
Manney 1991; Fraser et al. 1993; Lawrence et al. 1995;
processes.
Lawrence and Randel 1996) and theoretical (Hartmann Theoretical studies have focused on instability of the
1983; Manney et al. 1988; Manney 1991; Manney and jet structure as the mechanism for 4-day wave growth.
Randel 1993: Bowman and Chen 1994; Orsolini and Hartmann (1983) and Manney et al. (1988) showed that
periods of 4-day wave growth are consistent with bar-
otropic instability of the stratospheric polar night jet.
Manney and Randel (1993) used a 3D instability model
Corre._7_ondingauthor address: Douglas R.Allen, Argonne Na-
to show that realistic 4-day wave growth rates exist in
tional Laboratory, Building 203,J/171. 9700South Cass Avenue,
Argonne, IL60439-4843. monthly mean background wind states only if both bar-
E-mail:drallen(a_anl.gov otropic and baroclinic components are included. Their
© 1997American Meteorological Society

1FEBRUARY 1997 ALLEN ET AL. 421
model also predicted a double-lobed structure in the ozone data from two austral late-winter time periods,
perturbation temperature field with one lobe in the upper 14 August-20 September 1992 and 9 August-16 Sep-
stratosphere and another in the lower mesosphere, with tember 1993, when MLS was viewing southward (cov-
rapid phase variation in between. erage from 80°S to 34°N).
The present paper takes advantage of the coverage
and vertical resolution of the Microwave Limb Sounder
b. Temperature data
(MLS) onboard the Upper Atmosphere Research Sat-
ellite (UARS) to examine the 4-day wave during the late MLS temperature is obtained by viewing limb emis-
austral winters of 1992 and 1993. As will be shown sion of O, at 63 GHz. The version 3 data (used here)
below, strong 4-day signals exist in MLS temperature, are retrieved on every other UARS pressure level n(the
geopotential height, and ozone. The vertical coverage UARS level-3 pressure grid is 1000 × 10 "'_hPa, where
provided by MLS allows resolution of a double-peaked n = 0,1,2,...) and have precisions ranging from 1.4 K
structure in perturbation temperature with an out-of- at 22 hPa to 3.1 K at 0.46 hPa. MLS temperatures are
phase relationship between the upper and lower peaks, used at eight pressure levels from 22 hPa to 0.1 hPa
as predicted by Manney and Randel (1993). Spectral (22, 10, 4.6, 2.2, 1.0, 0.46, 0.22, 0.1 hPa). The last two
analyses of MLS ozone reveal a 4-day signal in zonal levels are contaminated by large systematic errors and
wavenumber 1 near the polar stratopause. A linear ad- are biased by a zonal mean climatology. Wave structures
vective-photochemical model is used to calculate the estimated at these levels are attenuated and should be
ozone response to temperature and wind perturbations viewed with some caution. Validation information on
associated with the 4-day wave. The vertical variation version 3 MLS temperature is available in Fishbein et
of model ozone amplitude and phase is in good agree- al. (1996).
ment with observations of MLS ozone. Negative regions
of quasigeostrophic potential vorticity (PV) gradient and
c, Ozone data
positive Eliassen-Palm flux divergence are shown to
occur, consistent with wave forcing by instability dy- MLS ozone retrievals are obtained from limb emis-
namics. sion in two bands centered near 205 and 183 GHz. The
The 4-day feature is also shown to exist in quasi- version 3 ozone data are retrieved on every other UARS
geostrophic PV derived from MLS geopotential heights. pressure level. The 205-GHz data have smaller uncer-
The three-dimensional structure of this signal resembles tainties throughout the stratosphere, while the 183-GHz
the PV "charge" discussed by Hoskins et al. (1985) and data are less noise limited in the mesosphere. Both 205-
more recently by Bishop and Thorpe (1994). The latter and 183-GHz ozone data are used in this paper from 22
authors have also extended the concept to Ertel PV to 0.22 hPa. Validation information on version 3 MLS
(Thorpe and Bishop 1995), although the present paper ozone is available in Froidevaux et al. (1996) and Ri-
focuses on quasigeostrophic PV. In this electrostatics caud et al. (1996). Single-profile precision for ozone
analogy, a PV anomaly in the atmosphere acts like an retrievals is in the 0.1-0.4 ppmv range, depending on
electrical charge in a dielectric material, with an asso- altitude.
ciated vector field (independent of static stability, den-
sity, and boundary conditions) that produces "action at
d. Geopotential height data
a distance." Isolated PV charges induce geopotential
anomalies, circulation about the vertical axis, and a ver- The MLS geopotential height dataset used in this
tically oriented temperature dipole similar to observa- study is a preliminary dataset, which is not available in
tions of the 4-day wave presented in this study. version 3 but is planned in future versions. The geo-
potential height is obtained by measuring pressure as a
function of tangent-point height. Pressure is obtained
2. Microwave Limb Sounder data from the same radiances as temperature, but the radi-
ances are sensitive to pressure from 10 hPa to 0.046
a. The MLS instrument
hPa. Tangent-point altitude is determined from the ori-
The Microwave Limb Sounder is 1of 10 instruments entation of the MLS antenna, measured by an angle
on board the Upper Atmosphere Research Satellite. encoder, the UARS attitude control system, and the
MLS uses a 1.6-m scanning antenna to observe the at- ground-tracked UARS orbit determination. The pressure
mospheric limb emission simultaneously in spectral (in log pressure coordinates with atmospheric scale
bands at 63, 183, and 205 GHz (Barath et al. 1993). height 7 km) precision ranges from 5 m at 10 hPa to
These observations allow the determination of chlorine 10 m at 0.1 hPa, while the altitude precision is altitude
monoxide, ozone, water vapor, nitric acid, sulfur di- independent and isestimated to be around 100 m. Errors
oxide, temperature, and geopotential height in the strat- in geopotential height (excluding precision) arising from
osphere and mesosphere during both day and night and the tangent-point altitude are synchronized to the UARS
in the presence of stratospheric clouds and aerosols. This orbit and contaminate the zonal mean and high fre-
study analyzes temperature, geopotential height, and quencies near the diurnal tide. However, the analyses
422 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 54
Tretrieved (1992)
Period [days]
4.0 2.0 1 .3 1.0
66
37
10 31 10 31
!
22 26 22 26
1.0 .75 .50 .25 .25 .50 .75 1,0 1.0 .75 .50 ,25 .25 .50 .75 1 .0
WesLward Freq. [1/day] Eastward Westward Freq. [I/day] Eastward
(c) Tretrieved (1993) (d) Tgeoht (1993)
Period [days] Period [days]
1 0 1.3 2.0 4.@ 4.0 2.0 1.3 1 .0 1.0 1 .3 2.0 4.0 4 0 2.8 1.3 1,0
10 66
22 60
6 0 I
_C__ ",4262 t 6_64_ g_1.4106 54 Z
48__
L '4B__ Le10
D
u_n22 42_ _2.2 42_
c. L
o_ 46 37 cL4.6 37
10 31 10 : : 31
22 26 22 I I I , h 26
t. •75 .50 .25 ,25 .50 175 .0 I .0 .75 .50 i25 ,25 ,50 .75 1.0
Westward Freq. (1/day] Eastward Westward Freq. (1/day] Eastward
FIG. 1. (a) East-west power spectrum for wave 1MLS temperature (T_,._) at 72°S for 18 August-6 September
1992. Dashed contours are at 10, 20, and 30 K2day, and solid contours are from 40 to 100 K-_day by 10 K: day.
(b) Same as (a) but for temperature derived from MLS geopotential height (T_ooh,). (c),(d) Same as (a),(b) but for
2-16 September 1993.
performed in this paper (zonal wave 1,3-5-day periods) interpolation allows data to be mapped onto synoptic
have sufficiently long periods to avoid significant effects maps, which are processed every 12 hours. Satellite
from these errors. Good agreement is found on these orbital period drift generally limits the procedure to ap-
spatial and temporal scales between MLS temperature proximately l-week analysis periods. The procedure
(coined T,_,,_d in this paper) and temperature derived here is essentially a remapping in time so that periods
from MLS geopotentiai height data (Tg_oh,),as discussed longer than a week can be analyzed. Data are interpo-
in section 4a. lated onto horizontal grids of 4° latitude by 5°longitude
and onto the standard UARS pressure levels.
The twice-daily synoptic maps described above were
3. Analysis procedure
decomposed in ace and time by applying a two-di-
MLS data used in this analysis were produced by the mensional sinusoidal transform [see appendix of Ziemke
asynoptic mapping method (Salby 1982a,b; Lait and and Stanford (1990)]. Power spectral density is defined
Stanford 1988a). The specific technique used for this in this study as (2Af)-_[A2(k, to) + B2(k, to)], and am-
study is presented in detail in Elson and Froidevaux plitude is defined as [A2(k, to) + B2(k, to)]°_, where Af
(1993). Briefly, data are binned by latitude and separated is the unit bandwidth (NDAT At)-L NDAT is the number
into ascending and descending time series. The time and of data points in the ttme series (NDAT=38 for 1992,
space axes are rotated to anew coordinate system where NDAT=30 for 1993) and At is the temporal sampling
a fast Fourier transform (FFT) is applied to calculate interval (0.5 day); A(k, to) and B(k, to) are the cosine and
the spectral coefficients. An inverse transformation and sine coefficients of the discrete Fourier expansions
1FEBRUARY1997 ALLEN ET AL. 423
Tretrieved Wave 1 3-5 day Murakami (1979) to the temporal FFT coefficients and
then recombining the coefficients through an inverse
Longl rude [degrees] FFT.
0 90 180 270 360 As a comparison to the MLS temperature measure-
8/14/92
ments, temperature was also calculated from MLS geo-
potential height using the hydrostatic approximation T
= R-tO(l)/O(ln p), with R = 287 J kg ' K-_ (dry air gas
constant) and constant vertical spacing d(ln p) = 0.387
(determined from UARS standard pressure surfaces).
Quasigeostrophic potential vorticity q' and potential
vorticity gradient _, were calculated using the spherical
8123/92 formulation of Matsuno (1970):
q, ±[®'- +
= f: (cos_b (p;)_
fa:[cos_ cos,/,\ y
f2a2 [Po*[l ]
+-p?t- oJ:j (2)
9/01/92 211 cos_b
a
Here u is the zonal wind, Po = Pooe-:m, Poois the density
at the surface (1000 hPa), z is the log-pressure coor-
dinate, A is longitude, f is the Coriolis parameter, and
l-Iis the earth's angular frequency. Overbars denote zon-
al means, primes denote deviation from the zonal mean,
9/11/92
and subscripts denote partial derivatives. The Brunt-
V/iis_iila parameter and atmospheric scale height were
given the constant values N_ = 4 × 10 4s--2and H =
7 km; q' was calculated from MLS geopotential height
data, while _,.was calculated from U. K. Meteorological
Office (UKMO) zonal winds. MLS data were not used
in the calculation of _, due to the known inaccuracy in
9120/92 r , , the zonal mean geopotential height (see section 2d).
FIG.2.Time vslongitude plotof 7".,.....,.jat 64°Sand 1hPa (48 UKMO horizontal winds and temperatures on UARS
km) filteredforwave 1and3-5 dayperiods(eastwardandwestward)
pressure surfaces, obtained from the Goddard Space
for14August-20 September 1992.Dashed contours arefrom -4 to
0Kby I K.Solid contours are from 1to4 Kby 1K. Flight Center Distributed Active Archive Center
(DAAC), were interpolated with a cubic spline onto
horizontal grids of 4° latitude by 5° longitude. These
{T., qS., ff_+}(x, t) winds and temperatures were used in the calculation of
_;.and also in the tracer model discussed in section 4c.
The quasigeostrophic Eliassen-Palm (EP) flux vector
= E E [A+(k, w) cos(kx --- cot)
and the EP flux divergence were calculated with the
k=O _=0
following spherical formulation:
+ B+(k, w) sin(kx _+oJt)]. (1)
Here T, (I), and /z are temperature, geopotential, and F = (F_,, F_) = poa cosga(--ff_v', _fv'-_--_) (4)
ozone mixing ratio; +(-) refers to westward (eastward)
components; t is time; x is zonal distance; Ax is the 1 O OF.
zonal grid interval of 2wa cos4)/72; k is the zonal wave- V.F - a cos_ba¢ (c°s_bF_) + "--_"Oz (5)
number; oJ is the angular frequency; a is the earth's
radius; and _bis latitude. A 1-2-1 running mean was Here u' and v' (meridionai wind) are calculated from
applied in frequency space to power spectral density, MLS geopotential heights (using the geostrophic ap-
but not to amplitude. The time mean was removed be- proximation) and T' is from MLS-retrieved tempera-
fore applying the FFT to focus the analysis on traveling tures. In the EP flux diagram (Fig. 11), the vector com-
waves. ponents are multiplied by 2rra cos(b. This factor ac-
Filtered time series in this study were produced by counts for the spherical geometry of the earth to make
first applying the bandpass filter response function (with the arrow pattern look nondivergent if and only if _7.F
half-amplitude points at 3 and 5 day periods) given by = 0 (see Edmon et al. 1980).
424
JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUMI2 54
TreLrieved Waves 1-3 3-5 day (1 hPa)
FIG. 3. Polar stereographic plots of MLS temperature at 1hPa filtered for waves 1-3 and 3 5 day eastward periods for 22-29 August
1992. Latitude circles are at 20°, 40°, 60°, and 80°S with the South Pole at the center. Eastward direction isclockwise with 0 longitude on
the positive vertical axis. Dashed contours are from -5 to 0 K by I K. Solid contours are from 1to 8 K by 1K.
4. Results 1992. The mode makes at least five revolutions around
a. Temperature the pole with a rotation period near 3.8 days.
Spectral plots of T_,,_,_d for zonal wavenumbers 2and
Space-time spectral decomposition is a useful tool 3 (not shown here) for the 1992 event show signals at
for isolating the 4-day wave from other atmospheric 1 hPa with eastward periods of 2.0 and 1.3 days, re-
signals. Figure la presents a periodogram for zonal spectively. These sinusoidal components move at the
wavenumber 1power spectral density (defined in sec- same phase speed of the wave 1, 4-day signal and com-
tion 3 and hereafter called power) for MLS-retrieved bine with wave 1 to form a "warm pool" of air at 1
temperature (hereafter T,,,_,,,_) at 72°S latitude for 18 hPa (coupled with a slightly less prominent "cold
August-6 September 1992. A clear 4-day eastward pe- pool") that rotates around the pole with a period near
riod signal exists near 1hPa (48 km), and asomewhat 4 days. This feature is shown in Fig. 3, where T,_,,_,._
weaker signal occurs near 0.22 hPa (60 km). These sig- data have been filtered over 14 August-20 September
nals are also evident in temperature derived from MLS 1992 for waves 1-3 and eastward rotation periods of
geopotential height (hereafter T_o,,) in Fig. Ib,although 3-5 days. (Wave 4and higher were not analyzed because
the lower signal maximizes near 2.2 hPa (42 km). An the frequency of interest, 4 days divided by integer
even stronger 4-day signal is found during 2-16 Sep- wavenumber, is near or outside the Nyquist limit of
tember 1993 in both T_,_,_._(Fig. lc) and Tgoo_,(Fig. approximately 1day L) The warm pool rotates around
ld). The 4-day signal dominates the traveling wave the pole as an identifiable entity throughout the record
spectra for this time period with two lobes centered near shown displaying the quasi-nondispersive (soliton-like)
2.2 hPa (42 km) and 0.22 hPa (60 km). Sections 4d and nature of the feature.
4f further discuss the validity of the 4-day signal in The perturbation temperature (T_,,,.,J amplitude for
terms of uncertainty and statistical significance. wave 1 and 3.8-day eastward period is plotted in Fig.
The 1992 4-day wave event was further isolated by 4a for the 1992 4-day wave event. A large lobe exists
filtering a 38-day series of T_,_,o.,_for zonal wavenumber in the upper stratosphere, peaking near 48 km and 72°S
1and periods (both eastward and westward) of 3-5 days with maximum amplitude of 4.2 K. A smaller upper
and plotting on a Hovm611er (time vs longitude) diagram lobe is centered at 60 km and 68°S. This double-lobed
for 64°S and I hPa (Fig. 2). The 4-day wave amplitude structure is similar to that predicted by the instability
increases over the first 10 days and remains constant study of Manney and Randel (1993). In their results,
for another 10days before dissipating near 1September the upper lobe is larger and extends well into the mes-
1 FEBRUARY 1997 A L LE N E T A I.. 425
(a) Tretrieved (1992) that the two peaks constitute one entity. The 1993 series
also reveals this vertical temperature dipole (Fig. 5b).
Here the lower peak has a strong wave 1structure that
66 [
begins near 48 km and descends to 42 km over this
8-day period. The upper feature, which maximizes near
60
60 kin, is approximately 180° out of phase with the
lower feature. The quadrupole pattern produced by the
4s
two out-of-phase lobes remains stable for at least two
42 weeks, through the end of the UARS month (16 Sep-
tember 1993), when MLS changed tonorthward viewing
37
(coverage from 80°N to 34°S).
25 b. Geopotential
-BO 70 -80 -50 -40 -30 -20 The vertical temperature dipole structure seen in Fig.
Latitude [degrees] 5 suggests that the perturbation geopotential amplitude
should increase with height throughout the region of the
lower temperature lobe and decrease with height in the
region of the upper lobe. This is confirmed in Fig. 6a,
which shows the geopotential amplitude for the 1992
(b) TreLrieved (1993) series for eastward moving wave 1with a period of 3.8
days. The signal maximizes near 57 km, at the boundary
66 I between the warm and cold anomalies (see Fig. 5a), and
decreases above it. The 1993 geopotential amplitude
(Fig. 6b) peaks near 48 km, consistent with the pertur-
54 bation temperature structure for that series (Fig. 5b).
The geopotential signal decreases with altitude more
rapidly in the 1993 time series, due to a larger-amplitude
upper temperature lobe in 1993 than in 1992. The me-
37 ridional structure shown here is similar to previous ob-
servations of the 4-day wave in geopotential height
(Manney 1991; Lawrence and Randel 1996).
25 !\ L l I I l
-80 -70 -60 -50 -40 -30 -20 c. Ozone
Latitude [degrees] Other than the unpublished conference report by Ran-
del et al. (1992), the present paper is the first to present
FIG. 4. (a) Y,_,,,,,_j amplitude for wave t and 3.8-day eastward period
for 18 August 6 September 1992. Contours are every 10% interval observations of the 4-day wave in ozone. Periodograms
of the maximum (4.2 K), with values higher than 50% shaded. (b) for wave 1 MLS ozone (both 205- and 183-GHz data)
T,....... aamplitude for wave 1and 3.75-day eastward period for 2-16 at 72°S during 18 August-6 September 1992 are pre-
September 1993. Contours are every 10% of the maximum (5.8 K),
sented inFig. 7. A 4-day peak exists near the stratopause
with values higher than 5()% shaded.
(1.0 hPa), coincident with the T,........L..amaximum at the
same altitude, see Fig. la. A 2-day eastward period sig-
osphere. However, T,_,n_d is largely climatology at 66 nal exists at 2.2 hPa; the source of this signal is unknown
kin, forcing zonally asymmetric wave amplitudes to and is not thought to be related to the 4-day wave. The
zero; therefore, the abrupt fall-off with height above 60 2-day feature does not exist in spectra from 5 to 20
km in Fig. 4a may not be real. The 1993 series also September 1992.
displays a double-lobed structure (Fig. 4b), with maxima To ascertain the relationship between the 4-day fea-
near 42 km, 76°S (amplitude of 5.8 K) and 60 km, 80°S. ture in ozone and the other atmospheric variables, a
Manney and Randel (1993) also predict rapid vertical linear advective-photochemical model was used to cal-
phase variation between the two lobes. Such behavior culate the ozone response to temperature and meridional
can be explicitly seen in height versus longitude plots wind perturbations associated with the 4-day wave. The
of T,e,,_e_aat 72°S, filtered for waves 1-3 and eastward procedure combines the linearized thermodynamic and
rotation periods of 3-5 days. Figure 5a presents 8days ozone continuity equations to obtain an expression for
during the peak amplitude of the 1992 time series. The the ozone mixing ratio (Hartmann and Garcia 1979;
plots reveal a warm anomaly near 48 km bounded above Rood and Douglass 1985; Randel 1990, 1993). Because
by a cold anomaly near 60 km. This dipole pattern con- the 4-day wave amplitudes in the various components
tinues throughout the 4-day wave life cycle, suggesting (T, u, v, and/,) are observed to be much less than their
426
JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 54
(a)
TreLrieved W 1-3, 3-5 day (22-29 August 1992)
66 7 • '....:iI i :66I 66
60 60 60
54 54 54
_48 48 4st 48
N 42
42 42t 42
_ 37 37 37 : 0 37
31 , 1_/22/,92 31 /2 /9 31 , _/24492 31 , _/25/,92
260 901802703602E 90 t80 270' II'I:'360 26 ! 90180270360 260 90 180 270 360
Longitude
66t,'"_ '..:._.... t 66
66 _ :::ii_
60 [.q_/ .... o :.:b'A 60
48 : ':.) 48
42 42 42 ..:i¸ ( L 4_4s::::
37 _' 37 37
3t : , , f-q_ 27/,9i _:: : '" 31
26 ,: 8/ _F/-_92 -.._. , _Z29 / 9;_P----
260 90 180 270 360 261 90 180 270 360 90 180 271_ 360 '260 90 180 270 360
(b)
Tretrieved W 1-3, 3-5 day (4-11 September 1992)
66
60
H 54
54 : : :I:II: :II' 54 54 :::'
,-M : .I : :IIIII-:: : I
_48
4 8 ['I: :: 4 S :::I: :" :'[:'::' 4 8 ....
-_ 42
_ 37 37 .i. :) 37 ::!!::: !:":!":
31 , 9/ 4/93 31 '.': ' 31 ".::!:: "i
260 90180270360260 9018027036026 90180270360260 [ v 90 t8?0/270.376/903
Longitude
66 66 ' ........ ..... :.
...... 'I '
60
I___ _
54 54 ":' ':i'": I_\_" \\\ -.i:
48 48 :?::::: : 48 ::::::.ii::!::::(": i:....
42 42 iiI
)_I "IIIII_
37 :rltII-:I: t 437842__.:i:;:i:(: C::ill ii _
31 31[ • ...... ' _ /
26 ...." , qg/9/,93 fl 26 ..... '......9,/10/,9..3/ 31 _ _9,111/93 _"
260 90180 270360 90 180 270 360 90 180 270 360 260 90 180 27_ 360
FIG. 51(a) T,,,,,_ on a height vs longitude grid at 72°S filtered for waves 1-3 and 3-5-day eastward rotation period for 22-29 August
1992. (b) Same as (a) but for 4-11 September 1993. Contours are every 1 K with solid (dashed) line having positive (negative) values.
Here, W (C) refers to warm (cold) anomalies.
respective zonal mean values (T' << T, etc.), we use a The photochemical relaxation rate, F, and the linearized
linearized thermodynamic equation, ozone response to small temperature perturbations, O,
are shown in Fig. 8a, adapted from Hartmann and Garcia
T; + aT" + v'T,. + w'S = 0
(1979), who studied ozone transport by planetary waves
1 in the winter stratosphere using a iinearized fl-plane
S = _[Ktr + HL], (6) model centered at 60°. Radiative damping of the tem-
perature perturbations is neglected, since the radiative
where w' is the vertical wind component, K = R/c,, = timescale is of order 10 days in the region of interest
2/7, and H = 7 km; and a linearized ozone continuity (26-57 km) [see Hartmann and Garcia (1979)], while
equation, the advective timescale [k(_ - c)]-' isof order 1-2 days
from 26 to 42 km, and the photochemical timescale F-'
/x; + n/z_' + v'/2,. + w'/2: = -r/._' - OT'. (7)
is less than 1 day from 42 to 57 km. Radiative heating
1 FEBRUARY 1997 A L LE N E T A L. 427
(a) Geopotential (1992) (0 - ib)T + _V
M = (9)
F+ia
=--#, -#iris a =- k(n - c) b =---k(n - c)#:/S.
!-
Figure 8b presents the resulting model ozone ampli-
_ 54 tude for the wave 1,3.8-day period signal at 60°S (thick
# 48 solid line). Also plotted are the observed ozone ampli-
tudes at 60°S for 205-GHz (thin solid) and 183-GHz
_ 42
(dashed) data. Error bars on the observed data were
_ 37 calculated using the procedure described in section 4d.
Reasonable agreement is found between the observed
and model amplitudes, with low values in the middle
stratosphere and lower mesosphere, and a maximum in
the upper stratosphere (near 42 km). Results from a
-BO --70 -60 -50 -aO -30 purely advective model (F = O = 0) and a purely
Latitude [degrees] photochemical model [/G,,, = (O/F) T,,,,, see Randel
(1990)] show a transition region between dynamical and
photochemical control from approximately 37 to 49 km,
where both dynamics and photochemistry play an im-
portant role.
(b) Geopotential (1993) The phase of the model and observed 4-day feature
is provided in Fig. 8c. Good agreement exists between
66 I I/I I the 205-GHz observed phase and the model throughout
!- the stratosphere, while the 183-GHz observed phase
agrees with the model in the lower mesosphere but di-
_ 54 verges somewhat in the stratosphere. As mentioned in
# 48 section 2c, the 205-GHz data have smaller uncertainties
in the stratosphere, while the 183-GHz data are less
_ 42
noise limited in the mesosphere, so the phase results
_ 37 - shown here are consistent with the data quality.
The good agreement (at least to first order) between
I_ 31 -- model and observations suggests that the observed
3 25 I I 4-day signal in ozone is produced largely by the coupled
effects of constituent advection by the 4-day wave per-
-80 -70 -60 -50 -40 -30 -20
turbation winds in the presence of zonal-mean constit-
Latitude [degrees]
uent gradients and photochemical processes associated
FIG. 6. (a) MLS geopotential amplitude for wave 1 and 3.8-day with the 4-day wave perturbation temperature and mix-
eastward period for 18 August-6 September 1992. (b) Same as (a) ing ratio anomalies.
but for 2-16 September 1993, 3.75-day eastward period. Contours
are at every 10% interval of the maximum with values higher than
50% shaded. d. Uncertainty in 4-day wave amplitude
In order to assess the uncertainty in the 4-day wave
amplitude calculation, a random number generator was
from ozone perturbations has also been neglected, as in
used to make a noise dataset with level 3AT format
Randel (1990, 1993), since it is likely small compared
to changes due to advection. Solving Eq.(6) for w' and (along-track, evenly spaced in time) with values be-
substituting into Eq.(7) gives the following differential tween -0.5 and +0.5 (arbitrary units), giving a root
equation for/_': mean square (rms) variation of 0.29. This represents the
random noise in a given MLS measured quantity with
+ -
an rms error (defined here as uncertainty) of 0.29. These
data were passed through the asynoptic mapping routine
described in section 2and synoptic maps were produced.
The rms variation in the synoptic maps is 0.19, which
is 65% of the input value. The decrease is mainly due
to interpolation to a regular horizontal grid. Fourier de-
= 0. (8)
composition was then applied to isolate the amplitude
To relate p.' to T' and v', we write (_', T', v') = (M, of the wave !, 3.8-day component from 500 different
T, V) e_*''-''_, where M, T, and V denote complex-valued time series, each randomly generated. This Monte Carlo
perturbation amplitudes. From this, procedure yielded rms variations in amplitude of 0.018
428 JOURNAL OF THE ATMOSPHERIC SCIENCES VOLUME 54
(a)
205 GHz Ozone (b) 183 GHz Ozone
Pec;od [days] Per'od [days]
4.0 2.0 t .3 .0 1.0 1 3 2.0 4.0 4.0 2.0 1.3 1 0
60 .22 • --60
54
48_
42
37 46 37
10 31 10 ' 31
1 ._ ,75 50 .25 25 .50 .75 1.0 1 .0 •75 50 .25 .25 .5@ .75 1.0
Westward Fceq [1/day] Eastward Westward Freq. [1/day] Eastward
FIG. 7. (a) East-west power spectrum for wave 1 MLS ozone (205 GHz) at 72°S for 18 August-6 September
1992. Contour increment is 0.02 ppmvZ.day. Dashed lines are from 0.02 to 0.08 ppmv-%day. Solid lines are from
0.10 to 0.20 ppmvZ.day. (b) Same as (a) but for 183-GHz MLS ozone.
for the 1992 simulated series (38 time components used, frequencies, a posteriori statistics must be used (Madden
72 longitudes) and 0.020 for the 1993 simulated series and Julian 1971).] The null hypothesis is made that any
(30 time components used, 72 longitudes). The uncer- spectral peak at 4 days is due to random sampling fluc-
tainty in amplitude is 0.018/0.29 --_1/16 times the un-
tuations. Under this hypothesis, the ratio of spectral peak
certainty in the level 3AT data for 1992 and 1/14 for to nearby spectral background can be estimated statis-
1993. The difference between 1/16 and 1/14 is due to tically. For the Fourier transform spectra used here, chi-
the different bandwidth used in each year. This method squared statistics are employed to estimate the maxi-
can now be used to obtain estimated uncertainties in mum peak to background ratio that will occur in 95%
4-day wave amplitudes observed in MLS temperature of the cases for random sampling fluctuations• If the
and ozone.
observed peak exceeds this ratio, with 95% confidence
The estimated uncertainty in version 3 MLS temper- the spectral feature can be said to be statistically sig-
ature at 1 and 2.2 hPa is 3.4 and 2.2 K, respectively nificant.
(Fishbein et al. 1996). The estimated wave 1, 3.8-day Figures 9a,b show the Tre,,_o,edspectra at 2 and 0.2
eastward period amplitude uncertainty in the lower peak hPa during 2-16 September 1993. These are plotted
of Fig. 4a (1992) is 3.4/16 = 0.21 K, which is much without smoothing in Figs. 9a,b and correspond to the
smaller than the observed amplitude of 4.2 K. In 1993 smoothed plot shown in Fig. lc. Also indicated by
the uncertainty in the lower peak (Fig. 4b) is 2.2/14 = dashed lines in Fig. 9 are the estimated background and
0.16 K, which is much less than the observed amplitude 95% confidence limit (for two degrees of freedom, ap-
of 5.8 K. This Monte Carlo analysis shows that the propriate to this case of unsmoothed Fourier transform
observed amplitudes are not significantly affected by spectral estimates). Both features easily satisfy a priori
random noise in the data. statistical significance.
This method was also used to obtain estimated errors The 1992 temperature spectral 4-day peak, shown
for 205- and 183-GHz MLS ozone data. The error bars
smoothed in Fig. la, reveals a strong peak centered at
shown in Fig. 8b were computed using the above for- 1hPa that also easily exceeds the a priori 95% confi-
mulation along with data uncertainties at different pres- dence limit (not shown here). The weaker temperature
sure levels as given by Froidevaux et al. (1996). peak at 0.22 hPa is close to a stronger lower-frequency
feature. By examination of unsmoothed spectral results
e. Statistical assessments (not shown here), it can be shown that the 0.22-hPa
4-day peak also meets the criterion for a priori statistical
Because the 4-day wave is a well-established atmo- significance.
spheric phenomenon (see references in the introduc- The 183-GHz ozone spectrum at 1 hPa for 1992
tion), statistical assessment of the 4-day features found (shown smoothed in Fig. 7b) is plotted unsmoothed in
here can be made on the basis of apriori statistics (Mad- Fig. 9c. The 4-day peak exceeds the 95% confidence
den and Julian 1971). Briefly, before analysis it is de- limit and isjudged statistically significant. The 205-GHz
cided to examine spectral features near 4-day periods. ozone 4-day peak at 1 hPa (Fig. 7b) also exceeds the
[If spectral peaks are examined at previously unreported 95% confidence limit (not shown here)•