Modeling project and study on Martian atmospheric convection

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Modeling project and study on Martian atmospheric
convection

• Masatsugu Odaka
• Hokkaido University, Japan
• odakker_at_gfd-dennou.org

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Contents

• Overview of activities of our research group
• Our scientific interests and numerical modeling
  projects
• Introduce my previous and future work
• Numerical simulation of Martian dry convection by
  using an anelastic model (Odaka, 2001)
• Numerical simulation of Martian moist convection
  and development quasi-compressible
  non-hydrostatic model

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Our scientific interests

• Geophysical Fluid Dynamics (GFD) and numerical
  simulation
• Fluid dynamics in Earth and planetary sciences
• Meteorology and oceanography
• Solid earth sciences (mantle convection and lava
  flow)
• MHD dynamo in the Earths core
• Planetary atmospheres
• Solar nebula dynamics

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Why planetary atmospheres?

• Interested in unique atmospheric phenomenon which
  are not observed in the Earth
• 4-days circulation in Venus
• Global dust storm in Mars
• Grate red spot and cloud belts in Jupiter
• Investigate how our theory is universal or not
• Understand atmospheric phenomenon of the Earth by
  comparing with those of another planets

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To study planetary atmosphere

• Numerical simulation is a powerful approach.
• The amount of observational data of planetary
  atmospheres is small.
• To understand simulation results and confirm
  whether those are appropriate or not,
• Compare with observations (but it is limited)
• Compare with those obtained by
• Using reduced system model
• Adapting same model (with different physical
  processes) for the Earth

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Recent problems on numerical model

• Backgrounds
• Specialization and development of computers
• Recent model becomes to be complicated.
• Consists of a number of lines of numerical codes
  with huge amount of output data
• Recognizing what is going on in it is becoming
  harder and harder.
• In the older ages, different phenomena described
  by a set of similar equations can be understand
  in the similar way.
• Nowadays, only those who know the particular
  aspect of a climate model know that.
• It is not useful for comparative study on
  planetary atmospheres.

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What kind of model is desired?

• Easy to trace
• Users are assumed to follow the codes
• Easy to change
• both to simplify and to complicate
• Users are assumed to change the codes
• Module structure to put or remove processes
• Easy data manipulation
• Free and open

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Modeling project of our laboratory and
collaborators (GFD Dennou Club)

• Data manipulation
• gtool4 netCDF convention and gt4f90io
• http//www.gfd-dennou.org/arch/gtool4/
• Dennou-Ruby, GPHYS, GAVE
• http//www.gfd-dennou.org/arch/ruby/
• Hierarchical models
• SPMODEL, GMS, DCPAM
• Cover a set of models with a standardized form of
  coding
• High performance models for simple GFD situations
• ISPACK (used in SPMODEL)

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Hierarchical modelshttp//www.gfd-dennou.org/arch
/dcmodel/

• Spectral fluid models
• dcpam
• SPMODEL
• Finite difference fluid models
• GMS
• deepconv
• Energy model
• Oboro

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SPMODEL

• A set of typical spectral models in GFD.
• Try to improve readability of source code
• Takehiro et al. 2002
• http//www.gfd-dennou.org/arch/spmodel/
• Define and prepare spectral operators
• Fourier and Legendre transformation in ISPACK
  (Ishioka, 2002) is used.
• For a given geometry, a set of spectral functions
  and transformations, derivatives, and so on are
  prepared.
• Eliminate indices from variables
• Fortran 90 features
• Operators and variables
• A standardized way of coding
• Data I/O gt4f90io

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SPMODEL coding style

• Variables
• xy_Var grid data
• w_Var spectral data
• Transformation function
• w_xy(xy_Var) spectral transformation
• xy_w(w_Var) inverse transformation
• Operator function
• xy_GradLon_w(w_Var) gradient(longitude)
• xy_GradLat_w(w_Var) gradient(latitude)
• w_Div_xy_xy(xy_Var,xy_Var) horizontal divergence
• w_Jacobian_w_w(w_Var,w_Var) Jacovian
• w_Lapla_w(w_Var) Laplacian

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An example of SPMODELSpherical shallow water
model
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An example of SPMODELSpherical shallow water
model

• do it1,n
• w_Zeta_A w_Zeta_B 2 dt !
  Vorticity equation
• ( - w_Div_xy_xy( ( xy_Coli xy_w(w_Zeta)
  ) xy_GradLon_w(w_Chi) / R0,
• ( xy_Coli
  xy_w(w_Zeta) ) xy_GradLat_w(w_Chi) / R0) / R0
• w_Jacobian_w_w( w_xy( xy_Coli
  xy_w(w_Zeta) ), w_Psi ) / R02 )
• w_D_A w_D_B 2 dt ! Divergence
  equation
• ( w_Div_xy_xy( ( xy_Coli xy_w(w_Zeta)
  ) xy_GradLon_w(w_Psi) / R0,
• ( xy_Coli xy_w(w_Zeta)
  ) xy_GradLat_w(w_Psi) / R0 ) / R0
• w_Jacobian_w_w( w_xy( xy_Coli
  xy_w(w_Zeta) ), w_Chi ) / R02
• - w_Lapla_w( Gravw_H w_E ) / R02
  )
• w_H_A w_H_B 2 dt ! Mass
  conservation
• ( - w_Div_xy_xy( xy_w(w_H)
  xy_GradLon_w(w_Chi) / R0,
• xy_w(w_H)
  xy_GradLat_w(w_Chi) / R0 ) / R0
• w_Jacobian_w_w( w_H, w_Psi ) / R02
  )
• w_Zeta_B w_Zeta w_D_B w_D w_H_B
  w_H

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Model list in SPMODEL

• 1D
• KdV equation
• 2D
• Channel models of barotoropic and shallow water
  with several boundary conditions
• Convection models of several boundary conditions
• Equatorial ß plane
• Barotropic and Shallow water spherical model
• 3D
• Boussinesq Fluid in a Spherical Shell
• MHD in a Spherical Shell
• We are going to test SPMODEL framework for
  developing a GCM (DCPAM).

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DCPAM (Dennou Club Planetary Atmospheric Model)

• Three-dimensional atmospsheric model
• Constructing 3D primitive dynamical core based on
  SPMODEL
• 1D, 2D, 3D under the same coding rule.
• System for exchanging physical processes
• System for exchanging vertical descretization
  CP-grid to L-grid
• Current status
• Dynamical core is developed and Held and Suarez
  (1994) test is performed.
• http//www.gfd-dennou.org/arch/prepri/2005/hokudai
  /morikawa/poster/pub/

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GMS (grid modeling system)

• The same way as SPMODEL but for finite difference
  models
• Nakano and Nakajima
• Define and prepare operators by the use of
  structured variable
• Variables are defined as structured.
• Functions (such as adding, subtracting, ...)
  should be prepared and explicit memory handling
  are needed.
• http//ruby.gfd-dennou.org/workshop200403/masuo/
• Sorry, in Japanese only

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deepconv

• A non-hydrostatic model
• Nakajima, 1994
• Based on anelstic system
• Fortran77 source code
• Applied for Mars (Odaka, 2001)
• Next version model is under construction
• Based on quasi-compressible system
• Not include topography
• Consider to apply for not only the Earth but also
  Mars, Jupiter condition
• Use Fortran90 and coding style as like SPMODEL
• Variables are not defined as structured.

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deepconv coding stylewith C-grid

• Variables
• ss_Var data on scalar grid point
• fs_Var data on flux grid point (x)
• sf_Var data on flux grid point (y)
• Transformation function
• fs_Avrage_ss(ss_Var) scalar to flux grid point
• ss_Average_fs(fs_Var) flux to scalar grid point
• Operator function
• fs_dx_ss(ss_Var) gradient(x-direction)
• ss_dx_fs(fs_Var) gradient(x-direction)
• ss_Div_fs_sf(fs_Var,sf_Var) horizontal divergence

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deepconv

• Current status
• Dry model is developed.
• Use 2nd order centered difference for advection
• Try to introduce 4th order centered scheme and
  consider another advection scheme.
• Several test runs are now performed.
• Sound wave propagation
• Scalar advection by uniform flow
• Isolated thermal flow
• http//www.gfd-dennou.org/arch/deepconv/arare/samp
  le/
• Sorry, in Japanese only

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My scientific research

• Previous work
• Numerical simulation of Martian dry convection by
  using an anelastic model (Odaka, 2001)
• http//www.gfd-dennou.org/arch/prepri/2001/dps/mar
  sconv/pub/
• Future plan
• Numerical simulation of Martian moist convection
  and development quasi-compressible
  non-hydrostatic model

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MotivationMoist convection in early Mars

• Whether did warm climate in early Mars realize or
  not?
• No due to CO2 condensation
• Kasting (1991)
• Yes scattering effect by CO2 ice clude
• Forget Pierrehumbert (1997)
• How about cloudiness and cloud distribution are ?
• Is the circulation pattern is similar to that of
  terrestrial moist convection or not?

Colaprete and Toon, 2003 J. Geophys. Res. 108.
E4, 5025, Fig.7.
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Problems

• Introduction of CO2 condensation
• Atmospheric mass is significantly changed.
• Conservation of mass must be treated carefully.
• Which governing equations is appropriate?
• Quasi-compressible of fully compressible?
• Which vertical coordinate?
• Now under consideration