Modeling project and study on Martian atmospheric convection

1. Modeling project and study on Martian atmospheric convection Masatsugu Odaka Hokkaido University, Japan odakker@gfd-dennou.org

2. 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

3. 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 Earth’s core • Planetary atmospheres • Solar nebula dynamics

4. 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

5. 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

6. 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.

7. 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

8. 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)

9. Hierarchical modelshttp://www.gfd-dennou.org/arch/dcmodel/ • Spectral fluid models • dcpam • SPMODEL • Finite difference fluid models • GMS • deepconv • Energy model • Oboro

10. 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

11. 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

12. An example of SPMODEL:Spherical shallow water model

13. An example of SPMODEL:Spherical shallow water model do it=1,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 ) / R0**2 ) 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 ) / R0**2 & • - w_Lapla_w( Grav*w_H + w_E ) / R0**2 ) 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 ) / R0**2 ) w_Zeta_B = w_Zeta ; w_D_B = w_D ; w_H_B = w_H w_Zeta = w_Zeta_A ; w_D = w_D_A ; w_H = w_H_A end do

14. 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 β 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).

15. 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/

16. 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

17. 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.

18. 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

19. 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/sample/ • Sorry, in Japanese only

20. 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/marsconv/pub/ • Future plan • Numerical simulation of Martian moist convection and development quasi-compressible non-hydrostatic model

21. Motivation:Moist 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.

22. 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