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:

Fabian Senf @

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:

Fabian Senf @

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

Fabian Senf @

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:

Fabian Senf @

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!

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THE END!

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

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Ergebnisse:

Refraktion des horizontalen Wellenvektors

Westwind-Jet

Ostwind-Jet

NP / Winter

SP / Sommer

EQ

u0