Japan-France planetary atmospheric modeling workshop,
2015/05/14, Kobe Univ.

A GCM for the stratosphereof Jupiter being developedin the Max Planck InstituteTakeshi Kuroda
Tohoku University

A.S. Medvedev, J. Sethunadh,
P. Hartogh

Max Planck Institute for Solar System Research

Background of the development:

JUICE-SWI (Sub-MillimetreInstrument)• PI: Paul Hartogh (MPS), with the science andinstrumental cooperation of Japan (NICT)• The main objective of a sub-millimetre wave
instrument is to investigate the structure,composition and dynamics of the middle
atmosphere of Jupiter and exospheres of itsmoons, as well as thermophysical properties of thesatellites surfaces. (from Yellow Book)• JUICE-SWI is highly sensitive to CH4, H2O, HCN, COand CS in Jupiter’s stratosphere.
• From CH4 molecular lines, vertical temperature
profiles and wind velocities can be measured.
• CO and CS, which are chemically stable, can beused as tracers for the investigations ofatmospheric flows (general circulation anddynamical processes).

Collision of
ShoemakerLevy 9[HST, 1994]:
Origin ofH2O, CS, COand HCN?

Atmosphere of Jupiter
Vertical structure: observed by Galileo Probe• Thermosphere(<10-3hPa)• Stratosphere(102～10-3hPa)• Troposphere(104-5～102hPa)- With cloud layers- Driven by theinternal heat source.

[Seiff et al., 1998]

Here we focus on the stratosphere.

Jupiter’s stratosphere

Temperature and zonal
wind fields observed by
Cassini/CIRS• Affected by radiative processes
by molecules in stratosphere, as
well as eddies enhanced fromthe troposphere.
(cf. troposphere: convection cellstructures transport the energyand momentum)• The estimation from the thermal
wind equation and cloud tracking(for lower boundary wind speed)
shows the existence of fast zonal
wind jets of 60-140 m s-1 at 23N
and 5N.
[Flasar et al., 2004]

Radiative processes in Jupiter’sstratosphere• CH4: Absorber of the solar radiation• CH4, C2H2, C2H6, collision-induced
transitions of H2-H2 and H2-He:
Effective in the infrared cooling.

We have developed a bandradiative transfer model for
Jupiter’s stratosphere for the fastand effective calculations in theGCM (correlated k-distributionapproach).

Mixing ratios ofhydrocarbons from a
photochemical model[Moses et al., 2005]

Radiative band model
Band

IR(infrared)/SO(solar)

Wavenumber
range [cm-1]

Molecules

12345678910111213
1415
1617IRIR
IRIRIRIR
IR, SO
IR, SO
IR, SO
IR, SO
SO
SO
SO
SO
SO
SO
SO

10-200200-400
400-600
600-700
700-860
860-960
960-1200
1200-1400
1400-1700
1700-2100
2100-3450
3450-4800
4800-6300
6300-7800
7800-9200
9300-10800
10800-11800

CH4, H2-H2, H2-He
CH4, H2-H2, H2-He
CH4, H2-H2, H2-He
CH4, C2H2, H2-H2, H2-He
C2H2, C2H6, H2-H2, H2-He
CH4, C2H6, H2-H2, H2-He
CH4, H2-H2, H2-He
CH4, H2-H2, H2-He
CH4, H2-H2, H2-He
CH4, H2-H2, H2-He
CH4, H2-H2
CH4, H2-H2
CH4, H2-H2
CH4, H2-H2
CH4, H2-H2
CH4, H2-H2
CH4, H2-H2

Coordinate• Correlated kdistribution approach• We made a table of kdistributions in 13
pressure grids (logequal interval between
10-3 and 103 hPa), 3
temperature grids (100,150 and 200 K) for 17
wavenumber bands.

• The atmospheric composition of molecules (1000 ppmv of CH4, 1ppmv of C2H2, 10 ppmv of C2H6, 86.4 % of H2, 13.6 % of He) is fixedin making the table.

Radiative band modelMolecules(infrared)

Collisioninduced
transitions(infrared)

For solar
absorption

Line spectra(1 hPa, 150K)• Molecular lines of CH4, C2H2
(600-860 cm-1) and C2H6(700-960 cm-1): FromHITRAN2008 [Rothman etal., 2009].
• Voigt profile is used for thecalculation of line
spectrum, with wing cutoffof 35 cm-1 for all molecules.
• Collision-induced
transitions of H2-H2 and H2He: From Borysow [2002](H2-H2) and Borysow et al.
[1988] (H2-He).

Radiative band modelCH4 line spectra (3450-4800 cm-1)

About k-distribution[e.g. Liou, 2002]

k-distribution of the line spectra• For fast calculations of fluxes, the line spectrum in each band isordered to be a monotone increasing function.
• The absorption and emission by molecules in each band arecalculated with 12 k-distribution integration points per a molecule(144 points in the bands the lines of 2 molecules are overlapped).
• The effects of collision-induced transitions are added.

1-D calculation

Setting

1-D calculation with equally-spaced 60 layers between 10-3
and 103 hPa has been performed.
Temperature

Component• Temperature:‘Mean state’ from
Galileo Probeobservation[Yelle et al., 2001]• Component:
From 1-D
photochemical
model [Moses etal., 2005]
2 kinds of results(Models A and C)

1-D calculation(Solid: Band, Dashed: Line-by-line)

Heating/cooling rates• Calculation of solar radiation:
Assumed zenith angle of 0°• Differences between band andline-by-line calculations are verysmall.
• Mid- and far-infrared radiation(10-960 cm-1): Dominant forcooling below ~2.5×10-3 hPa.
• CH4 infrared radiation (9602000 cm-1): Can be dominant forcooling above ~2.5×10-3 hPa,and very small effects below.
• Heating/cooling rates in upper
stratosphere strongly dependon the composition.

1-D calculation(Solid: Band, Dashed: Line-by-line)‘Model A’
component‘Model C’
component

Sensitivity of molecules(infrared cooling)
About the effect of cooling in
10-2100 cm-1:• C2H2 is dominant above~0.03 hPa (up to ~3 K/day).
• C2H6 is dominant between
0.03-10 hPa (up to ~0.2
K/day in this height region).
• Collision-induced transitions
are dominant below ~10hPa (up tp ~0.03 K/day).
• CH4 can be dominantaround the boundary tothermosphere, but its effectis small in most of thestratosphere.

1-D calculation

Total heating/cooling rate
(in comparison with a preceding study)

Total day-mean heating&cooling rates
in comparison with Yelle et al. (2001)[Yelle et al., 2001]• Our calculations of day-mean net
heating and cooling rates are in agood agreement with the results ofYelle et al. (2001), with radiativeequilibrium.
• Above 0.1 hPa, our cooling rates
exceed the heating rates, mainly due
to stronger cooling by C2H2 in ourmodel. (due to the lack of non-LTEeffects…?)

1-D calculation(From the difference ofheating/ cooling rates fordifferent temperature)

Radiative relaxation time

Cross correlation of subsolar latitude with thehemispheric temperature contrast (40°N40°S) from IRTF observation (1979—2001)[Simon-Miller et al., 2006]

Daytime & nighttime,
Models A and C components

250hPa(~2.5 years)

20hPa(~1 year)• The hemispheric temperature contrast
lags the solar forcing longer introposphere (~2.5 years) than instratosphere (~1 year), which means
the radiative relaxation time should be
longer in troposphere.
• Our model shows qualitatively
consistent results with the observation,
while a preceding study [Conrath et al.,1990] does not.

1-D calculation
Equation of solar heating ratein Conrath et al. [1990]

k-distribution

Radiative relaxation time
• The radiative relaxation timeby Conrath et al. [1990] wasshown to be longer in upper
atmosphere, which
contradicts the observations.
• It is because their model issimple and theheating/cooling rate isexpressed to be proportional
to the atmospheric density(pressure), which should
underestimate the radiative
effects in upper atmosphere.
← At the peaks of spectra, theabsorption coefficient becomesalmost constant against thepressure. (except the peaks,proportional to pressute)1-D calculation
Different latitudes(with observations)Radiative-convective
equilibrium temperature

Different components (Model A, Model C,
Model A with twice more/less C2H2 and C2H6)• Radiative-convective equilibrium temperature is close to the observed verticalprofiles, except the upper stratosphere (due to the lack of non-LTE effects…?)• In higher latitude, the equilibrium temperature is several Kelvins colder thanthe equator in overall. Note that the radiative effects of hazes are not included
now, which may affect the temperature in high latitudes to increase.
• In the upper stratosphere, it is sensitive to the components.

Development of the Jupiter
Current descriptions
stratospheric GCM• Log-pressure coordinate in vertical• 41 equally-spaced log-pressure levels in 0.01-1000 hPa (fromcloud-top level to upper troposphere)• Horizontal resolution of 240×180 grid points (1.5°×1°) inlongitude and latitude, correspondingly• Radiative parameterization with Newtonian
Teq is definedcooling, which relaxes the simulated temperature from this result
toward the prescribed equilibrium Teq• With different radiative
relaxation time τrad: fromConrath et al. (1990) tothis study
Newtonian coolingDevelopment of the Jupiterstratospheric GCM Why the high-resolution
Rossby radius of deformationis required?

Comparison with different planets [Showman et al., 2010; Sethunadh, 2014]• The buoyancy force dominates the inertia for motions with the horizontal
extent shorter than the Rossby radius of deformation.
• To simulate wave-mean flow interactions properly, GCMs must resolve
motions shorter than the Rossby radius of deformation.
• Rossby radius of deformation is small for cold (small T), fast-rotating(large f ), and massive (large g) planets like gas giants.

Development of the Jupiter
Current results
stratospheric GCM
τrad=105 s for all height τ profile of this studyrad(too strong in lower)

Temperature

Zonalwind• It is seen thattemperatureadjusts closely tothe prescribed Teq
under the strong
radiative forcing.
• The zonal windjets extend intothe lower
stratosphere andsteeply decaywith height.

(Lower boundary wind velocity is defined from Cassini/VIMS cloud tracking)Development of the Jupiter
Current results
stratospheric GCM
τrad=105 s for all height τ profile of this study
rad(too strong in lower)• With larger τradTemperature

Zonalwind(corresponding toConrath’s) thecalculation fails
very rapidly withtemperature
droppingcontinuously.
• With τrad= 106 s,
simulations werevery sensitive tothe initial
temperature
disturbances.

(Lower boundary wind velocity is defined from Cassini/VIMS cloud tracking)Development of the Jupiter
Current results
stratospheric GCM
Zonal wind distribution
at 30hPa using thevertical profile ofradiative relaxation
time in this study
Now the implementationof the k-distribution
radiation code of thisstudy into the GCM isongoing!
(Lower boundary wind velocity is defined from Cassini/VIMS cloud tracking)Summary

Publication about the k-distribution radiation code and 1-D calculations:
Kuroda et al., Icarus 242, 149-157, 2014 “Parameterization of radiative
heating and cooling rates in the stratosphere of Jupiter”.

• A fast and effective band model for Jupiter’s stratosphere was developed,
calculating the heating/cooling rates in a good accuracy in comparison with theline-by-line calculations.
• The band model showed radiative equilibrium in the middle of Jupiter’sstratosphere. In the upper stratosphere, the heat balance is very sensitive to themixing ratios of hydrocarbons.
• It also showed that the radiative relaxation time becomes shorter in upper
atmosphere, which is consistent with observations [Simon-Miller et al., 2006] andcorrects the theoretical error in a preceding study [Conrath et al., 1990].
• Radiative-convective equilibrium temperature was calculated for different latitudes
and composition. In low-latitude region, it is close to the observed temperature
profiles.
• Radiative effects of stratospheric hazes are not included in the current version,
which should be considered to implement in the future, as well as the non-LTE
effects for upper stratosphere.
• Now we are starting the study with a Jupiter’s stratospheric GCM which requires ahigh resolution. Implementation of this radiation code to the GCM is now ongoing.