on the interaction of gravity waves and thermal tides in the middle atmosphere fabian senf, erich...
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On the interaction of gravity waves and thermal
tides in the middle atmosphere
Fabian Senf, Erich Becker Leibniz Institute for Atmospheric Physics,
Kühlungsborn
Ulrich AchatzGoethe University,
Frankfurt (Main)
• Introduction- Gravity waves and thermal tides in the middle atmosphere
- On gravity – tidal wave interaction studies
• Model- Ray tracing method
- Experiments of different complexity
• Results- modulation of gravity-wave frequencies and phase velocities
- refraction of horizontal wave vector
- amplitude of gravity-wave force
- equivalent friction coefficients
Overview:
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• zonally averaged HAMMONIA zonal wind and temperature for north winter
dynamics of middle atmosphere
Introduction:
latitude
altit
ude
[km
]
latitude
• zonally averaged HAMMONIA zonal wind and temperature for north winter
dynamics of middle atmosphere
Introduction:
latitude
altit
ude
[km
]
latitudeBreite
tropospheric
sources
gravity wave force
meridional
circulation
adiabatic
cooling
adiabatic
warming
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drives
Meso-scale gravity waves are essential for large-scale
dynamics, but hardly resolved in complex circulation
models!
parameterizations with crude assumptions
high-resolution, mechanistic modelling
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dynamics of middle atmosphere
Introduction:
thermal tides
• planetary-scale buoyancy oscillations induced by solar heating
sun
heating
tidesnorth pole
earth
Introduction:
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zonal wind amplitude
meridional wind amplitude
HAMMONIA diurnal tides as background (from Hauke Schmidt)
Introduction:
latitude
altit
ude
[km
]
total
altit
ude
[km
]
migrating non-migrating
Introduction:
Thermal tides induce extreme changes in the conditions for
gravity wave propagation in the middle atmosphere.
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thermal tides
• interaction between gravity waves and thermal tides is not deeply understood and also not sufficiently investigated
• because most studies focus on the interaction between thermal tides and gravity-wave parameterizations!
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Past Studies of the interaction between thermal tides and gravity-wave parameterizations:
• highly idealized models: Fritts & Vincent (1987), Lu & Fritts (1993) • linear modeling: Forbes et. al. (1991); Miyahara & Forbes (1991,1994),
McLandress (1997), Meyer (1997), Ortland & Alexander (2006)
• non-linear GCM results: Mayr et. al. (1998,2001), Akmaev (2001), McLandress (2002)
Main outcome:
• shrinking of vertical phase structure
• but different effects on tidal amplitude (different source and turbulence parameterization seem to be responsible)
But, with crude assumptions:
• gravity wave parameterizations in vertical columns
• assumed: stationarity of background flow and instantaneous adjustment
Introduction:
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Our strategy:
• relaxing of the assumptions made for gravity wave propagation • successively including temporal and horizontal dependence of the background flow
• BUT, keeping other aspects as simple as possible! highly simplified lower boundary conditions (or GW sources) saturation at convective instability threshold to estimate turbulent
diffusion coefficients
Introduction:
ray tracing of gravity waves
Ray tracing in thermal tidesModel:
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waveparcel
gro
up
velo
city
cg
ray tracing and wave parcel concept
t = 1 h t = 6 h t = 10 h
zona
l win
d pr
ofile
altit
ude
longitude
c
• wave parcel: small volume of GW field
• ray tracing: following the path of wave parcel
Ray tracing in thermal tidesModel:
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ray tracing and wave parcel concept
zona
l win
d pr
ofile
c
• wave parcel: small volume of GW field
• ray tracing: following the path of wave parcel
Ray tracing equations and symmetries of WKB theory:
• transience frequency modulation
• horizontal gradients refraction
• vertical gradients
Model:
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Conventional GW Parametrization:
• transience frequency modulation
• horizontal gradients refraction
• vertical gradients
Model:
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RAPAGI – RAy PArametrization of Gravity wave Impacts:
• global ray tracing model for time-dependent flows
• conservation of wave action and diffusion according to simple saturation theory (Lindzen, 1981)
Model:
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gravity wave spectrum in use:
• 14 gravity wave fields in different directions:
- horizontal wave length with about 400 km to 600 km
- periods in the range of hours
- momentum fluxes between 0.3 to 0.5 mPa
c = 33 m/s
c = 10 m/s
Model:
• extremely simple, but reproduces average gravity wave forces
Ray tracing experiments:
Model:
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full
complex ray tracing simulation
noREF
simple ray tracing – simulation
TS
conventional vertical column
transience included transience includedno transience,instantaneously
adjusting
horizontal refraction and propagation
included
no horizontal refraction and
propagation
no horizontal refraction and
propagation
increasing complexity
Vertical column thinking
15°S latitude (TS)
• expected height of strongest gravity wave forcing
• moves downward with tidal phase
transient critical layers?
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Results:
ph
ase
vel
oci
ty
altit
ude
[km
]
velocity [m/s]
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Results:
Vertical column thinking
is NOT appropriate for tides due to frequency modulation!
less critical layer filtering!
15°S latitude (TS)
ph
ase
vel
oci
ty
altit
ude
[km
]
velocity [m/s]
15°S latitude (TS)
altit
ude
[km
]
velocity [m/s]
Understanding frequency modulation:
• simplified equations:
Results:
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• local positive tendency of wind leads to increase of phase speed
• local negative tendency of wind leads to decrease of phase speed
t = 1 h
t = 4 h
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• horizontal phase velocity follows the shape of the background (BG) wind
(Contours: BG Wind)longitudinal variations of phase velocity
longitude
altit
ude
[km
]
[m/s]
Results:
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• meridional gradients of the zonal wind induce refraction of gravity waves into the jet maximum in which their travel time is minimized
longitude
latit
ude
refraction of horizontal wave vectors
Results:
latitude
altit
ude
[km
]
latitude
average gravity wave flow
arrows: average group velocity,colors: initial meridional position,contours: wind in wave direction
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Results:
OW
N
S
OW
N
S
latitude
altit
ude
[km
]
latitude
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OW
N
S
OW
N
S
average gravity wave flow
arrows: average group velocity,colors: initial meridional position,contours: wind in wave direction
Results:
meridional displacement
• displacements of 50° in latitude occur often!• displacements larger than 100° in latitude are possible!
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Results:
Results:
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amplitude of zonal diurnal gravity wave force
latitude
altit
ude
[km
][m/s per day]
48454239363330272421181512963
• conventional GW parameterizations extremely overestimate zonal GW drag amplitude
• simulations without horizontal refraction slightly overestimate zonal GW drag amplitude
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tidal wind
force
• e.g.180° phase shift
• projection on tidal wind
• force on tidal amplitude
Results:
phase relation between force and tides
tidal wind• e.g. 90° phase shift
• projection on tidal acceleration
• advancing of tide
• force on phase structureforce
• projections of the diurnal gravity wave force on
- tidal wind
real part of equivalent friction coefficient
if positive: local decrease of tidal amplitude
- tidal acceleration
imaginary part of equivalent friction coefficent
if negative: local vertical shrinking tidal phase structure
Results:
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2420161284-4-8-12-16-20-24
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• conventional parameterizations extremely over-estimate the decrease of tidal amplitude
latitude
altit
ude
[km
]
real parts of equivalent friction coefficients
[per 106 s]
Results:
2420161284-4-8-12-16-20-24
• conventional parameterizations mainly over-estimate the decrease of tidal vertical wave length
Results:
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latitude
altit
ude
[km
]
imaginary parts of equivalent friction coefficients
[per 106 s]
Summary:
• WKB theory and ray tracing has been used describing propagation and dissipation of a spectrum of GWs
• monthly averaged data + diurnal tides from HAMMONIA as background for GW propagation
• comparison with conventional GW parameterizations show:
overestimation of GW drag
• frequency modulation reduces diurnal gravity wave forces
• horizontal refraction leads to formation of wave guides and large meridional displacements
• GW drag induces decrease of tidal vertical wave length and amplitude
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Thank you for your attention!
Breite
Höh
e [k
m]
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Ergebnisse:
Refraktion des horizontalen Wellenvektors
Westwind-Jet
Ostwind-Jet
NP / Winter
SP / Sommer
EQ
u0
Schnitt in Stratopause