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Atmospheric Tides: Linking Deep Tropical Convection to Ionosphere-Thermosphere

Variability

• Briefly discuss migrating vs. non-migrating tides.

• Demonstrate relationship between the global distribution of troposphere deep tropical convection (and latent heating), and excitation of the eastward-propagating diurnal tide with zonal wavenumber = 3 (DE3) [and other tidal components].

• Illustrate DE3 and wave-4 longitude structures in the lower thermosphere (90-110 km), and upper thermosphere and ionosphere (ca. 400 km)

• Reveal sea-surface temperature variability as a source of ionospheric variability

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Troposphere Solar Heating as a Driver for Ionospheric Variability?

• Earth’s atmosphere 0-500 km is a single connected system.

• Latent heating and other processes (e.g., heating by H2O absorption) excite a spectrum of waves (tides, planetary waves, gravity waves, Kelvin waves, etc.) that carry amplified tropospheric signals throughout the atmosphere.

• Analysis of these signals can inform us about tropospheric processes and changes.

foF2

Global Distribution of Solar Heating from a Space-Based Perspective

To an observer in space, it looks like the bulge isfixed with respect to the Sun, and the planet is rotating beneath it.

In the local (solar) time frame, the heating may be represented as

heating = Qo + an cosnΩtLTn=1

N

∑ +bnsinnΩtLT

=Qo + An cos(nΩtLTn=1

N

∑ −φ)

Local time, tLT

“localperspective”

€

Ω=2π

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diurnal, (n = 1), semidiurnal (n = 2), etc. tides

To an observer in space, it looks like the bulge is fixed with respect to the Sun, and the planet is rotating beneath it.

To an observer on the ground, the bulge is moving westward at the apparent motion of the Sun. It is sometimes said that the bulge is ‘migrating’ with the apparent motion of the Sun with respect to an observer fixed on the planet.

Since this thermal forcing is periodic, it can excite a wave, called a “thermal tide”, that can propagate from the lower atmosphere up into the upper atmosphere where it is dissipated.

This is what things look like if the solar heating is the same at all longitudes.

Converting to universal time tLT = t + /Ω , we have

heating = Qo + An cos(nΩtn=1

N

∑ +n −φ)

Cph =ddt

=−nΩn

= -Ω Implying a zonal phase speed

Taking into account longitude effects involves replacing n with s n and

summing over s as well

Remember this for later,

with s = 1

For solar heating that varies with longitude, a spectrum of tides is produced that consists of a linear superposition of waves of various frequencies (n) and zonal wavenumbers (s):

implying zonal phase speeds

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.

Transforming back to local time:

€

Cph =dλ

dt= −nΩ

s ∴ s > 0 ⇒ westward propagation

At any given longitude, we have a sum of waves that defines the local time pattern of heating, as

before; however, this pattern now changes with longitude.

s=−k

s=+k

∑ An,sn=1

N

∑ z,θ( )cos nΩt+ s −φn,s z,θ( )( )

s=−k

s=+k

∑ An,sn=1

N

∑ z,θ( )cos nΩtLT + s−n( ) −φn,s z,θ( )( )

Similarly, at any given local time, we have a sum of waves that defines the

longitude dependence of heating at that local time.

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-3 0 2 5

Diurnal Latent Heating and Lower Thermosphere Response

“Decomposition” of the diurnal heating rates yields

a spectrum of diurnal waves, which, when

superimposed, yields the pattern to the left.

This wave spectrum propagates upward, and evolves with height since

the various waves are affected differently by background winds and

dissipation. They superimpose at high

altitudes to give a pattern like the one to the left

Annual-mean height-Integrated (0-15 km) diurnal heating rates (K day-1) from

NCEP/NCAR Reanalysis ProjectDominant zonal wavenumber representing low-latitude

land-sea contrast on Earth is m = 4

diurnal harmonic of

solar radiation

Modulation by dominant

zonal wavenumber

m = 4

m = 1

(short vertical wavelength)

s = +5s = -3

Spectrum of Diurnal Tides Excited by Latent Heating Due to Tropical Convection, Modulated by Land-Sea Contrast

eastwardpropagating

westwardpropagating

€

cos nΩt + sλ( ) × cos mλ( ) → cos Ωt − 3λ( ) + cos Ωt + 5λ( )

€

Cph = −nΩ

s= −Ω

s±m

n = 1

s = n = 1

“DE3”

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El-Niño-type conditions

Normal conditions

Source: SSTs are from the NCEP Version 2.0 OI Global SST analyses

Other Factors Also Determine the Global Distribution of Latent Heating, e.g., Sea-Surface Temperature

Kelvin Wave

DE3 Temperature Amplitude Distribution, August 2002, from TIMED/SABER Measurements

Tn,s cos nΩt+ s −φn,s⎡⎣ ⎤⎦

Tn,s cos nΩtLT + (s−n) −φn,s⎡⎣ ⎤⎦becomes

How Does the Wave Appear from Sun-Synchronous Orbit?

= 4 for DE3

SABER Temperature Residuals, August, LST = 1300, 110 km

Raw temperature residuals (from the mean) exhibit the wave-4 pattern anticipated for a dominant eastward-

propagating s = -3 diurnal tide.

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The Ionospheric Dynamo

e-

e-

O+

B

O2+, NO+

Vn

€

ω− >> νenω+ ~ ν in

€

ω+,− =B | e |m+,−

€

ω− >> νenω+ >> ν in

equipotentialline

Global electrostatic field set up by dynamo action

€

∇×B =J

μ0∇ ⋅J = 0

J =σE =σ −∇Φ + Vn ×B[ ]

€

V+,− =E×B

B2

F-Region200-1000 km

E-Region100-150 km

CHAMP electron densities (~400 km) reveal wave-4 structures due to DE3 driving of the ionospheric dynamo

Maui Yamagawa

Much of the longitude variability is thought to arise from land-sea modulation of the excitation of thermal tides that propagate to the thermosphere. DE3 gives rise to a wave-4 longitude structure when interfering with the sun-synchronous tide, DW1; similarly, DE2 gives rise to a wave-3 structure when interfering with DW1.

CHAMP Neutral Temperatures Also Reveal Connections to Troposphere Excitation of Tidal Waves

DE3 = eastward-propagating diurnal tide with zonal wavenumber = 3DE2 = eastward-propagating diurnal tide with zonal wavenumber = 2DW1 = westward-propagating diurnal tide with zonal wavenumber = 1 (Sun-synchronous)

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DE3

SE2

Solar Cycle Dependence of DE3 and SE2

SE2 produced by land-sea modulation of semidiurnal component of solar heating, but also nonlinear

interaction between DE3 and DW1!

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Neutral Densities During Solar Minimum, 7 days in August, 2008

Non-symmetric wave-4 and non-anti-phasesuggests SE2, not DE3

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Neutral Densities During Solar Minimum, 11-17 December 2008

CHAMP, 332 km

GRACE, 476 km

CHAMP & GRACE co-planar

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Basic data: Monthly median foF2 values between 15-16 hr LT from the ionosondes located in Maui and Yamagawa 1960-1993, and calculate the following ratio.

Due to the location of these stations with respect to the wave-4structure maxima and minima, the above ratio is used as a proxy for the amplitude of the wave-4 structure.

Solar cycle and seasonal variabilities are removed, leaving a time series that consists of foF2RATIO monthly anomalies.

Compare yearly extreme value of ONI and the extreme value of foF2 ratio anomalies in the subsequent five months.

Oceanic Niño Index (ONI) gives SST anomalies due to the ENSO

Long-term Variations in Ionospheric Wave-4

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Yearly extreme value of ONI (red) and the extreme value of foF2 ratio anomalies in the subsequent five months (black) from January 1960 to June 1993 [Pedatella and Forbes, 2009].

Changing sea surface temperatures are thought to reflect changes in latent heat forcing of DE3, which creates wave-4 in the ionosphere

through dynamo electric fields.

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CONCLUSIONS

• Earth’s atmosphere 0-500 km is a single connected system.

• Latent heating and other processes (e.g., heating by H2O absorption) excite a spectrum of waves (tides, planetary waves, gravity waves, Kelvin waves, etc.) that carry amplified tropospheric signals throughout the atmosphere.

• Signatures of these waves appear in neutral densities and temperatures near the exobase, and throughout the ionosphere.

• Analysis of these signals can inform us about tropospheric processes and changes.

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Back-up Slides

From 2002-2008 monthly mean TEC data, the measured wave-4 amplitude is compared with the ratio of TEC values at the locations of Maui and Yamagawa

To the extent that these curves agree, the assumption of using the foF2 ratio between Maui and Yamagawa is

a reasonable proxy for wave-4 amplitude