Convec'vely-­‐generated	  Gravity	  Waves	  on	  Mars	  and	  Their	  Inﬂuence	  on	  the	  Upper	  Atmosphere	
Takeshi	  Imamura	  (JAXA,	  Japan)	  Ayuka	  Watanabe	  (Univ.	  Tokyo,	  Japan)	  	  Yasumitsu	  Maejima	  (Riken,	  Japan)	

Gravity	  waves	  on	  Mars	
Gravity waves which are generated in the troposphere and propagate
to the upper atmosphere are considered to play key roles inmomentum and energy transport in the Martian atmosphere.

altitude(km)Vertical wavelike structures oftemperature (Schofield et al., 1997)	

GW	  energy	  distribuEon	  according	  to	  radio	  occultaEon	  (Creasey	  et	  al.	  2006)	
temperature(K)Horizontal wavelike structure of atmospheric density in the lower
thermosphere (Fritts et al. 2006)

The	  accelerometer	  measurements	  revealed	  density	  ﬂuctuaEons	  of	  5-­‐50%	  on	  horizontal	  scales	  of	  20-­‐200	  km	  in	  the	  lower	  thermosphere	  (100-­‐130	  km)	

Wave	  sources	
•Convective excitation / topographic excitation / geostrophic
adjustment ?
• Previous Mars GCMs assumed wave spectra in the source region
based on experience in the Earth’s atmosphere (e.g., Medvedev et al.
2011).
• Tenuous atmosphere of Mars favors strong large-scale winds near thesurface, which lead to strong topographic generation, and strong
convective activity, which leads to strong convective generation.
•Convective generation has been less studied than topographicgeneration for Martian atmosphere.	

ConvecEon	  on	  Mars	ConvecEon	  can	  be	  driven	  by	  uniform	  heaEng	  in	  the	  boundary	  layer	  and	  by	  localized	  heaEng	  of	  dust	  clouds	
Temperature	  proﬁles	  by	  radio	  occultaEon	  (Hinson	  et	  al.,	  2008)	  Regional model of dust plume ‘Rocket
dust storm’ (Spiga et al., 2013）	

*	  NighYme	  detached	  convecEve	  layers	  are	  also	  suggested	  by	  radio	  occultaEons	  (Hinson	  et	  al.,	  2013)	  Homopause	  control	• We	  take	  the	  homopause	  to	  be	  the	  alEtude	  where	  the	  eddy	  diﬀusion	  coeﬃcient	  and	  the	  molecular	  diﬀusion	  coeﬃcients	  are	  equal,	  although	  large-­‐scale	  dynamics	  also	  inﬂuences	  the	  homopause	  height.	  	  • The	  homopause	  is	  typically	  located	  near	  105	  km	  alEtude	  (100	  nbar)	  on	  Earth,	  near	  135	  km	  (10	  nbar)	  on	  Venus,	  and	  near	  125	  km	  (1	  nbar)	  on	  Mars	  (Mueller-­‐Wodarg,	  2008).	  The	  relaEvely	  low	  pressure	  at	  the	  MarEan	  homopause	  implies	  strong	  turbulent	  mixing	  in	  the	  MarEan	  upper	  atmosphere.	  	  • The	  locaEon	  of	  the	  homopause	  inﬂuences	  the	  composiEon	  of	  the	  exosphere,	  thereby	  inﬂuencing	  the	  species	  escaping	  to	  space.	

1-D photochemical model by Krasnopolsky (2002)	

H2	
Homopause＝80 km	

Purpose	  of	  this	  study	
• To	  clarify	  how	  eﬃciently	  convecEon	  generates	  gravity	  waves	  on	  Mars	  • To	  explain	  the	  large-­‐amplitude	  density	  ﬂuctuaEons	  observed	  during	  aerobraking	  of	  Mars	  orbiters	  • To	  understand	  how	  the	  homopause	  height	  is	  controlled	  • To	  assess	  the	  contribuEon	  of	  convecEvely-­‐generated	  waves	  on	  the	  energy	  budget	  of	  the	  thermosphere	  Method	• CombinaEon	  of	  a	  nonlinear	  regional-­‐scale	  model	  of	  convecEon	  and	  a	  linear	  soluEon	  of	  wave	  propagaEon	  in	  the	  upper	  atmosphere	  – The	  period,	  the	  wavelength	  and	  the	  amplitude	  of	  the	  waves	  generated	  by	  convecEon	  are	  found	  by	  using	  a	  2-­‐D	  regional-­‐scale	  model	  based	  on	  CReSS	  (Cloud	  Resolving	  Storm	  Simulator).	  	  – The	  esEmated	  wave	  parameters	  are	  used	  as	  the	  input	  to	  a	  linear	  wave	  model	  extending	  to	  the	  thermosphere.	  
• (LimitaEons	  of	  2-­‐D	  modeling	  will	  be	  discussed	  later)	  2-­‐D	  regional	  model	Two types of forcing:(1) Uniform heating near the surface	
(2) Localized heating representing a local dust storm
Dynamics
Model	  domain	 
Grid	  interval	 

CReSS	  version	  2.3Horizontal:	  600	  km	  VerEcal:	  0-­‐100	  km	  (sponge	  layer	  at	  100-­‐150	  km)Horizontal:	  0.5	  km	  VerEcal:	  0.25	  kmSide:	  RadiaEon	  (Localized	  heaEng)	  or	  	  	  	  Boundary	  	  	  	  	  	  	  	  	  	  	  Periodic	  (Uniform	  heaEng)	  condiEon
Top	  and	  bofom:	  Rigid	  wallDiﬀusivity

Calculated	  from	  turbulence	  kineEc	  energy	  by	  1.5th	  order	  closure	  scheme

IniEal	  condiEon

6	  hPa	  at	  the	  surface	  Neutral	  straEﬁcaEon	  below	  5	  km	  alEtude	  No	  background	  wind

IniEal	  temperature	  proﬁle	11(1) Uniform heating
300km
50  kmHeberle et al. (1993)

Sponge  layer
Grid	  interval:	  Δx=0.5km,	  Δz=0.25km	 

100  km0.25  km  thickHeating region

Neutral  layer

Heating  is  given  in  the  lowest  layer  (0.25  km  thick)  by
QMAX = 40 K/hour
to be consistent with the nighttime radiative cooling rate of the
5 km-thick boundary layer estimated by Heberle et al. (1993).

* The convective heat flux is similar to Odaka et al. (1998）.	

Structure	  of	  convecEon	  (200	  min)	
VerEcal	  velocity	  (m/s)	

Temperature	  perturbaEon	  (K)	VerEcal	  velocity	  (m/s)	

Convective velocities
are consistent with
Odaka et al. (1998）.	
Temperature	  pertrubaEon	  (K)	2-­‐D	  spectrum	  of	  verEcal	  velocity	• The	  unit	  of	  the	  spectral	  density	  used	  here	  is	  	  	   	  m2	  s-­‐2	  /	  log2(wavenumber)	  log2(frequency)	  i.e.	  the	  squared	  amplitude	  in	  each	  power	  of	  two	  of	  the	  wavenumber	  and	  frequency.	  	  • We	  take	  the	  square	  root	  of	  this	  quanEty	  as	  the	  amplitude	  for	  each	  wavenumber	  and	  frequency	  mode.	  	

buoyancy	  freq.	

2-­‐D	  spectrum	  of	  w’	  at	  60	  km	  alEtude	sound	  speed	*	  Color	  scale	  is	  log10(power)	

2-­‐D	  spectra	
Hea'ng	  rate	  =	  40	  K/h	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  4	  K/h	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  0.4	  K/h	Alt.	  
60	  km	•20	  km	

•The	  signiﬁcant	  power	  seen	  at	  frequencies	  higher	  than	  the	  buoyancy	  frequency	  at	  60	  km	  is	  afributed	  to	  turbulent	  eddies	  generated	  via	  nonlinearity	  of	  primary	  waves.	  
The	  maximum	  power	  occurs	  at	  wavelengths	  of	  10-­‐50	  km,	  being	  consistent	  with	  the	  horizontal	  scales	  of	  the	  boundary-­‐layer	  convecEve	  cells,	  and	  at	  periods	  of	  700-­‐2000	  s,	  being	  consistent	  with	  the	  turnover	  Eme	  of	  convecEon.	  	(2) Localized heating

15300km
50  kmHeatingrate

Sponge  layer
Grid	  interval:	  Δx=0.5	  km,	  Δz=0.25km	 

100  km120min

3  km  thickHeating region
Heatingrate

Time5km
Neutral  layer

60km/30km  wide

Maximaum  heating  QMAX = 20 K/hour
based on Spiga et al. (2013)
Horizontal  distanceNo	  radiaEvely-­‐acEve	  dust	  is	  included	Structure	  of	  convecEon		  (200	  min)	

VerEcal	  velocity	  (m/s)	Temperature	  (K)		  (50	  min)		  (100	  min)	

2-­‐D	  spectra	
Peak	  hea'ng	  rate	  =	  20	  K/h	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  	  2	  K/h	
Width	  of	  hea'ng	  region	  =	  60	  km	

Width	  of	  hea'ng	  region	  =	  30	  km	

•Similar	  to	  the	  uniform	  heaEng	  model,	  but	  the	  contribuEon	  in	  a	  3-­‐D	  atmosphere	  should	  be	  much	  less.	  	1-D linear wave solution	
The	  verEcal	  structures	  of	  speciﬁc	  wave	  modes	  seen	  in	  the	  convecEon	  models	  are	  solved	  using	  a	  full-­‐wave	  model	  (e.g.,	  Hickey	  et	  al.	  2000;	  Schubert	  et	  al.	  2003).	  The	  model	  solves	  the	  linearized	  equaEons	  of	  conEnuity,	  momentum,	  and	  energy	  for	  a	  compressible	  atmosphere.	  Waves	  are	  forced	  near	  the	  surface	  by	  a	  periodic	  heaEng.	  	  • Wave	  amplitudes	  are	  scaled	  so	  that	  the	  maximum	  amplitude	  of	  the	  horizontal	  wind	  in	  the	  model	  domain	  is	  equal	  to	  the	  horizontal	  phase	  velocity.	  Since	  the	  wave	  modes	  studied	  in	  this	  study	  all	  have	  amplitudes	  large	  enough	  for	  saturaEon	  at	  high	  alEtudes,	  giving	  marginally-­‐saturated	  amplitudes	  enables	  evaluaEon	  of	  wave	  dissipaEon	  in	  the	  region	  where	  the	  inﬂuence	  of	  molecular	  dissipaEon	  dominates.	  	  • The	  physical	  domain	  extends	  from	  0	  km	  to	  500	  km.	  	  • RadiaEve	  damping	  is	  considered	  (Eckermann	  et	  al.	  2011).	  
•HeaEng	  rate	

wave-induced drift	

Total	
sensible heat flux divergence	wave-inducedpressure gradients	

viscous heating	Finding	  the	  homopause	• Given	  a	  gravity	  wave	  saturated	  via	  convecEve	  breaking,	  the	  wave-­‐
induced	  turbulent	  diﬀusion	  coeﬃcient	  is	  given	  by	  (Lindzen	  1981)	  kc 4
D =γ
2HN 3

• where	  k	  is	  the	  horizontal	  wavenumber,	  c	  is	  the	  horizontal	  phase	  velocity,	  H	  is	  the	  scale	  height,	  and	  N	  is	  the	  buoyancy	  frequency.	  	  • The	  eﬃciency	  parameter	  γ,	  which	  was	  not	  included	  in	  Lindzen's	  (1981)	  original	  formulaEon,	  accounts	  for	  the	  spaEally	  and	  temporally	  localized	  character	  of	  the	  turbulence.	  Although	  the	  value	  of	  γ	  is	  highly	  uncertain,	  previous	  modeling	  studies	  adopted	  γ=	  0.2	  (Barnes	  1990;	  Theodore	  et	  al	  1993;	  Joshi	  1995).	  Here	  we	  further	  consider	  the	  spaEally	  and	  temporally	  localized	  character	  of	  gravity	  waves,	  and	  tentaEvely	  adopt	  γ	  =	  0.1.	  	  • Finding	  the	  alEtude	  where	  the	  turbulent	  diﬀusion	  coeﬃcient	  D	  is	  equal	  to	  the	  molecular	  diﬀusion	  coeﬃcient,	  we	  obtain	  the	  homopause	  height.	  VerEcal	  structure	

Altitude (km)horizontal	  wavelength	  =	  50	  km,	  	  period	  =	  900	  s	
300

300

300

250

250

250

200

200

200

150

150

150

100

100

100

50

50

50

00-500 -250
0250 500
Heating rate (K/day)

0-3 -2 -1 0 1 2
Phase (radian)

30 0.05 0.1 0.15 0.2
Fractional density amplitude

Uniform	  hea'ng	  model	  with	  nominal	  hea'ng	  rate	

The	  amplitude	  seen	  in	  the	  convecEon	  model	  is	  10	  Emes	  larger	  than	  that	  required	  for	  saturaEon.	  à	  Amplitude	  in	  the	  thermosphere	  is	  determined	  by	  saturaEon	  at	  lower	  alEtudes.	  
Turbopause	  height	  is	  calculated	  to	  be	  132	  km	  	Altitude (km)

300

300

300

250

250

250

200

200

200

150

150

150

100

100

100

50

50

50

00-500 -250
0250 500
Heating rate (K/day)

0Altitude (km)-3 -2 -1 0 1 2
Phase (radian)

30 0.05 0.1 0.15 0.2
Fractional density amplitude

300

300

300

250

250

250

200

200

200

150

150

150

100

100

10050505000-100 -50
050 100
Heating rate (K/day)

0-3 -2 -1 0 1 2
Phase (radian)

3

00.05
0.1
Fractional density amplitude

horizontal	  wavelength	  =	  50	  km	  period	  =	  900	  s	  	  àTurbopause	  height=	  132	  km	  	horizontal	  wavelength	  =	  50	  km	  period	  =	  2000	  s	  	  àTurbopause	  height=	  110	  km	  	Waves	  in	  weaker	  heaEng	  case	Altitude (km)Uniform	  hea'ng	  model	  with	  10%	  hea'ng	  rate	
300

300

300

250

250

250

200

200

200

150

150

150

100

100

100

50

50

50

00-15

0-3 -2 -1 0 1 2
Phase (radian)

30 0.01 0.02 0.03 0.04
Fractional density amplitude-10 -505
Heating rate (K/day)horizontal	  wavelength	  =	  20	  km	  period	  =	  2000	  s	  	  àTurbopause	  height=	  93	  km	  	Medvedev	  et	  al.	  (2011)	

LimitaEon	  of	  2-­‐D	  modeling	The	  dominant	  horizontal	  wavelength	  (tens	  of	  kilometers)	  and	  the	  period	  (tens	  of	  minutes)	  are	  determined	  by	  the	  basic	  characterisEcs	  of	  convecEon,	  which	  would	  be	  largely	  unchanged	  in	  the	  three-­‐dimensional	  atmosphere.	  	  • The	  amplitude	  in	  the	  thermosphere	  is	  limited	  by	  saturaEon	  in	  most	  of	  the	  cases.	  Once	  saturated,	  the	  result	  in	  the	  alEtude	  region	  where	  molecular	  diﬀusion	  dominates	  does	  not	  depend	  on	  the	  source	  strength.	  	  • Considering	  these	  points,	  the	  conclusions	  drawn	  from	  the	  current	  2-­‐D	  model	  are	  expected	  to	  be	  largely	  unchanged	  in	  a	  3-­‐D	  atmosphere.	  	  (Of	  course,	  3-­‐D	  modeling	  is	  indispensable	  for	  determining	  the	  realisEc	  source	  spectrum	  and	  the	  wave	  amplitude	  over	  all	  alEtudes.	  Nonlinear	  cascade	  in	  convecEon	  should	  generate	  other	  spaEal	  scales	  and	  resultant	  other	  wave	  modes.)	  	•Summary	•••••

Generation of fast gravity waves by intense convection due to low
atmospheric density was suggested. Such waves are potentially
important in the upper atmosphere due to less damping.
The suggested amplitudes of atmospheric density are consistent withthe observations during aerobraking of Mars orbiters.
Convectively-generated waves seem to explain the observed
homopause height, although other dynamical processes can also
contribute.
The heating and cooling caused by the gravity waves can besignificant in the lower thermosphere.
The suggested fast waves have vertical wavelengths of several tensof kilometers, and thus they are difficult to be detected in verticalprofiles of temperature and winds.