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NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 1
Solar Semidiurnal Tide in the Atmosphere
Jeff ForbesDepartment of Aerospace Engineering Sciences University of Colorado, Boulder, CO 80309-0429
• Forcing of the Semidiurnal Tide
• Vertical Propagation of the Semidiurnal Tide and its Interactions with the Overlying Atmosphere
Distortion by Zonal Mean Winds Modulation by Longitude Variations in Mean Winds (Stationary Planetary Waves) Modulation by Traveling Planetary Waves (e.g., 2-day
wave)
• Solar Semidiurnal Tide in Mars’ Dusty Atmosphere
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 2
ITM System
0 km
60 km
400 km
Pole Equator
Mass Transport
Wave Generatio
n
Planetary Waves
ConvectiveGenerationof GravityWaves & Tides
Turbulence
CO2
CH4
CO2 Cooling
Ion Outflow
Solar Heating
The ITM SystemThe ITM System HEscape
Wind Dynamo
BEEnergetic Particles
B
Polar/AuroralDynamics
E
MagnetosphericCoupling
Joule Heating
H2O
solar-driven tides
O3TopographicGenerationof GravityWaves
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 3
The semidiurnal tide is just one
example from a whole spectrum of
waves that couple different
atmospheric regions and produce
observable phenomena.
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 4
0
50
100
150H
eig
ht
(km
)
UV Absorptionby O3
12local time
0 24
hea
tin
g r
ate
0latitude
+90 -90
hea
tin
g r
ate
Near-IR Absorption by H2O, latent heating
EUV Absorptionby O, O2, N2
Thermal Excitation of the Semidiurnal Tide
mean
diurnal
semidiurnal
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 5
Q = Qo + an cosnΩtLTn=1
N
∑ +bnsinnΩtLT
=Qo + An cos(nΩtLTn=1
N
∑ −φ)
12local time
0 24
hea
tin
g r
ate,
Q
In the local time frame, the heating may be represented as
Ω =2π
24
Q
nΩt+nλ −φ = const
⇒ dλdt
=−nΩn
=Cph ⇒ Cph= -Ω
Implying a zonal phase speed
Converting to universal time tLT = t + λ/Ω , we have an expression of the form
An cos(nΩtn=1
N
∑ +nλ −φ)
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 6
Solar Heating Distribution from a Space-Based Perspective
Cph= -Ω : Migrating Solar Thermal Tides
To an observer in space, it looks like the heating bulge (and the tides it generates) are fixed with respect to the Sun, and the planet is rotating beneath.
To an observer on the ground, the heating bulge, and the tides it generates, are moving westward or “migrating” at the apparent motion of the Sun.
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 7
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Meridional wind field at 103 km (April) associated with the semidiurnal tide propagating upward from the lower atmosphere, mainly excited by UV
absorption by O3 in the stratosphere-mesosphere
The tide propagates westward with respect to the surface once per day, and is locally seen as the same semidiurnal tide at all longitudes.
Courtesy M. Hagan
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 8
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NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 9
0
50
100
150H
eig
ht
(km
)
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Coupling into higher-order
shorter-wavelength modes
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Semidiurnal variation in surface pressure 6oS
Propagation to surface
Distortion by zonal mean zonal winds
UV Absorptionby O3
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TIMED/SABER Semidiurnal Tide at 100 km
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 10
Eastward Winds over Saskatoon, Canada, 65-100 km
Note thepredominance
of the semidiurnal tide at upper
levels, withdownward
phase progression.
Note the transition from easterlies (westerlies) below ~80-85 km to westerlies (easterlies) above during summer (winter), due to GW filtering and momentum deposition.
Tidal Variability
Courtesy of C. Meek and A. Manson
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 11
Longitude variations are taken into account with zonal wavenumbers s n.
A spectrum of tides thus exists, to first order representable as a linear superposition of waves of various frequencies (n) and zonal wavenumbers (s):
Cph= -nΩs
: Non-Migrating Solar Thermal Tides
s=−k
s=+k
∑ An cos(nΩt+ sλn=1
N
∑ −φ)
€
Cph =dλ
dt= −nΩ
s ∴ s > 0 ⇒ westward propagation
The waves with s ≠ n are referred to as non-migrating tides because they do not migrate with respect to the Sun to a planetary-fixed observer.
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 12
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EQ116 km
50
100
150
Hei
gh
t (k
m)
Interaction with (modulation by) longitude variation in
background wind field(s = 1 only)
UV Absorptionby O3
s = 2(SW2)
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Coupling into sum and difference
secondary waves
s = 1(SW1)
s = 1,3(SW1,3)
Interaction with (modulation by) longitude variation in
background wind field(s = 1 only)
cos(λ)cos(2Ωt+ 2λ)→ cos(2Ωt+ 3λ) + cos(2Ωt+ λ)
SW2migrating
semidiurnaltide
SW1“difference”
SW3“sum”
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SW1 Observed over South Pole, 92 km 200
Cph =2Ω
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EQ116 km
5-year mean Semidiurnal Amplitude Temperatures, TIMED/SABER
SW1 SW3
SW0SW4
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 13
Zonal Mean Winds due to Dissipation of Semidiurnal Tides
Angelats i Coll and Forbes, 2002
SW2 +SW1 + SW3
SW2 only
SW1 + SW3
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 14
The total atmospheric response to solar forcing is the result of constructive and destructive interference between migrating and
nonmigrating tidal components, giving rise to a different tidal response at each longitude.
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TIMED/SABERSemidiurnal
Temperatures110 km
April 2004
Zhang et al., 2006
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 15
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NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 16
50
300
350
Hei
gh
t (k
m)
UV Absorptionby O3
Coupling into sum and difference
secondary waves
s = 59.6 h
s = -116 h
400
Interaction with (modulation by) Quasi-Two-Day Wave (QTDW)
with s = 3
s = 2(SW2)
Penetration into upper thermosphere &
ionosphereInteraction with (modulation by) Quasi-Two-Day Wave (QTDW)
with s = 3
cos(0.5Ωt+ 3λ)cos(2Ωt+ 2λ) → cos(2.5Ωt+ 5λ) + cos(1.5Ωt−λ)SW2
migratingsemidiurnal
tide
Eastwards = 1 16.0 h“difference”
Westwards = 5 9.6 h
“sum”
QTDW Modulation of Semidiurnal Meridional Wind AmplitudeIn the E-Region, EISCAT (Huskonen et al., 1995).
NCAR TIME-GCM: QTDW Modulation of Semidiurnal TideGenerates Sideband Waves that Propagate Above 100 km.
Palo, Roble & Hagan, Earth Planets Space, 51, 629-647, 1999
Do these waves beat with the semidiurnal tide generated in-situ in the thermosphere?
QTDW reflected in Critical Plasma Frequency
Are the above results due to modulation of the equatorial fountain by dynamo electric fields?
Is the dynamo driven directly by the 2-day wave, or by a 2-day modulated semidiurnal tide?
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 17
Solar Semidiurnal Tide in the DustyMars Atmosphere
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 18
The Model
• Time-dependent global model of the mutually-interactive semidiurnal tide and zonal mean circulation;
• Parameterization employed to handle convective instability -- eddy diffusivity introduced to keep wave amplitude at stable limit.
• Heating rates used based on observed dust distributions; validated against surface pressure perturbations measured by Viking-1and Viking-2 landers.
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 19
0
50
100
150
200H
eig
ht
(km
)
UV Absorptionby O3
s = 2(SW2)Solar radiation
absorption by dust
s = 2(SW2)
Solar Semidiurnal Tide in Mars’ Atmosphere, Ls = 270, High Dust ( ~ 2.3)
~60% density perturbationsat 122 km in aerobraking regime
~80 K
‘whole atmosphereresponse’
Solar Semidiurnal Tide in Earth’s Atmosphere, Ozone Heating
Solar Semidiurnal Tide in Mars’ Atmosphere, Dust Heating
To what degree does the solar semidiurnal tide contribute to the observed density
changes at aerobraking altitudes in connection with dust storms?
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 20
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Semidiurnal Temperature Perturbation
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 21
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Eddy diffusion Coefficient
due to Breaking Semidiurnal Tide
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 22
Zonal Mean Acceleration of the Atmosphere due to the Dissipating Semidurnal Tide
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Zonal Mean Zonal Wind, Low Dust Zonal Mean Zonal Wind Difference, = 2.3
NCAR Advanced Study Program (ASP) Seminar, February 13, 2008 23
• The semidiurnal tide and its effects are pervasive and ubiquitous in Earth’s atmosphere
• There are new things to be learned, and probably, to be discovered
• The semidiurnal tide is just one example from a whole spectrum of waves that couple different atmospheric regions and produce observable phenomena.
• The solar semidiurnal tide is important in vertically-coupling Mars’ atmosphere, with potential importance to aerobraking.
CONCLUDING REMARKS
Solar Semidiurnal Tidein the Atmosphere