Overview of the talk

1. Developing a new general circulation model for planetary atmospheres - how (and why!)Claire NewmanKliegel Planetary Science SeminarMarch 1st 2005

2. Overview of the talk • What is a general circulation model (GCM)? • Why develop a new model for planetary atmospheres: what questions are we trying to answer? • How is this new model being developed? • Description of the base model: the Earth-based, limited area “Weather Research and Forecasting” (WRF) model • Description of the changes needed to ‘globalize’ WRF • Description of the changes needed to make ‘planetary’ WRF • Recent results and future work: Earth, Mars and Titan

3. What is a general circulation model (GCM)? Generally is conceptually (and practically) split into two components: physics dynamics Basically Newton II in 3 dimensions: force = mass x acceleration (subject to mass & energy conservation) Includes everything acting at a smaller scale to the dynamics, all of which is represented via parameterizations You can actually write down the complete physics of how air parcels move in a rotating frame (ignoring relativity and quantum mechanics), even if to solve the problem you need to make approximations (like ignoring small terms, working with a finite number of points, etc.) This includes: Small scale turbulence Friction at the surface Absorption, emission and scattering of radiation

4. Dynamics, e.g., the zonal (E-W) momentum equation: U, V, W = wind in E-W, N-S and vertical respectively,  = latitude, p = pressure,  = density, a = planet radius, t = time, X = E-W distance Force / mass Acceleration DU = 2V sin - 2W cos - UW + Uv tan -1 p + Fx Dt a a X Frictional force per unit mass - usually added in during physics, as must be parameterized ‘Coriolis’ terms due to air parcel moving in a rotating (not inertial) frame Terms due to the coordinate system rotating Pressure gradient force per unit mass ‘Material derivative’ = rate of change of U following an air parcel U = U(t, x, y, z) => U = U/t t + U/x x + U/y y + U/z z => U/t = U/t + U/x x/t + U/y y/t + U/z z/t By definition, U = x/t, V = y/t and W = z/t => DU/Dt = U/t + U/x U + U/y V + U/z W

5. Examples of physics in a GCM Radiative transfer in a planetary atmosphere: Temperature changes depend on heating rates, which are determined from net fluxes, which in turn depend on temperature => many interconnected equations and many methods of solving them to find T(z) Solar wavelengths Absorption and scattering in the atmosphere Atmospheric layer Atmospheric emission (~T4) Thermal wavelengths Absorption and scattering in the atmosphere Absorption and scattering at the surface Absorption and scattering at the surface Surface Surface emission (~Tsurf4)

6. Why do we need a new GCM for planetary atmospheres?To understand this, you first need to understand:What questions do we want to answer?

7. Earth Mars Titan N2 atmosphere Psurf ~ 1.5x105 Pa Tsurf ~ 93 K Thick haze layers Methane ‘hydrology’ Slowly rotating CO2 atmosphere Psurf ~ 610 Pa Tsurf ~ 210 K Very eccentric orbit Major topography Dust storms N2 atmosphere Psurf ~ 1x105 Pa Tsurf ~ 288 K Water cycle Oceans & land surfaces

8. Onset and evolution of a Martian dust storm Dust opacities for 2001 global storm from MGS TES website

9. Storm onset & evolution: multiscale feedbacks Wind stress lifting: +ve feedbacks 1 - local scale T increases inside dust cloud Strong winds Surface Wind stress lifting: +ve feedbacks 2 - global scale Meridional circulation strengthens Very strong associated winds and muchmore dust lifting Fairly strong associated winds and dust lifting S pole N pole S pole N pole

10. Regions of interest on Mars 90°N 60°N 30°N 0° 30°S 60°S 90°S 180° 120°W 60°W 0° 60°E 120°E 180° Tharsis: strong slope flows; Western boundary currents on the eastern edge Argyre and Hellas: slope flows in region of strong zonal winds and near cap edge Northern plains: relatively uninteresting

11. Regions of interest on Mars 90°N 60°N 30°N 0° 30°S 60°S 90°S 180° 120°W 60°W 0° 60°E 120°E 180° Potential areas of higher resolution

12. The big questions for Mars (I) • How do dust storms begin and evolve, and why do some become global? • How do flows associated with the large topography interact with the global circulation? Need higher resolution just in regions where local slopes and circulations may be crucial Must consider multi-scale feedbacks: look at local dust lifting and the effect on the local and global circulation, which in turn affects further lifting => Model with high resolution areas within global domain, and information passing both ways (2-way feedbacks)

13. Interannual variability in Mars’s atmosphere ‘Storm season’ Dust opacity Brightness temperature ‘Storm season’ Areocentric longitude Ls Areocentric longitude Ls From Liu et al. JGR 2003

14. The big questions for Mars (II) • What determines the variability in the Martian dust cycle and hence climate? • What was the climate like in the past, & does this help us understand present geological features? • When and where was water stable at the surface, and where would subsurface water deposits be? Need to look at interannual variability and/or changes over long timescales => Need efficient and accurate (mass and angular momentum conserving) model

15. Clouds on Titan Titan imaged over 9 days in the K’ filter (centered at 2.12 m) which sees down to the surface and troposphere, using the AO system at Keck. (Images scaled to the brightest point in each case.)

16. The big questions for Titan (I) • What controls when and where methane clouds form? Want to use higher resolution just over regions where clouds form now (and over other cloud-formation regions in other seasons) => Need a model capable of placing high resolution regions with the global domain

17. “Spinning up” Titan’s atmosphere The atmosphere can gain/lose angular momentum from/to the surface When a GCM is ‘spun up’ this transfer must average to zero over a year Results from the LMD Titan GCM, from Hourdin et al., Icarus 1995

18. The big questions for Titan (II) • How much does interaction with the surface affect the atmospheric circulation? • What determines the equatorial superrotation? • How variable is Titan’s circulation and albedo (at different wavelengths) over the long Titan year? A long Titan year and thick atmosphere (high dynamical inertia) mean long spin-up times => Need a model which is fast, and accurate over the integration times required => Experiments to explore sensitivities and study variability take a long time

19. The Weather Research and Forecasting (WRF) model • Mesoscale (limited area) model for weather research and forecasting on Earth • Developed by NCAR in collaboration with other agencies (NOAA, AFWA, etc.) • Aim: to produce a reliable mesoscale model, to be used for real-time forecasting and as a research tool, with improvements being worked into new releases

20. Features of WRF Mass in kg (x1018) 5.20354 • Dynamics conserve mass and angular momentum - highly accurate • Highly parallel code => efficient • Large suite of physics parameterizations and a modular form => flexible • Uses Arakawa C-grid 5.20350 0 125 250 375 500 Days V V V T T T U U U U V V V T T T U U U U V V V U = zonal (E-W) velocity point V = meridional (N-S) velocity point T T T U U U U T = temperature / mass point V V V

21. Features of WRF (cont.) • Nesting capability: • 2-way nesting capability: Mother domain Mother domain Child 2 ‘Grandchild’ Child siblings Child 1 1-way nesting 2-way nesting

22. The usual approach - how mesoscale WRF runs: b) its initial and boundary conditions being provided by a separateglobalmodel a) place nests within a mesoscalemodel (WRF), with • Interface between global and mesoscale models is one-way => no feedbacks from small to larger scale • Unless specially designed to match, often have different dynamics and/or physics - inconsistent • Interface is also ‘messy’, e.g., must view output from the two models using different tools Separate global model WRF Drawbacks:

23. Globalising WRF gives a highly accurate & efficientglobal model, in which we can place 1- & 2-waynests So we are basically using WRF’s nesting abilities to nest all the way down from global

24. Changes required for global WRF • Allow use of a latitude-longitude grid WRF is set up for conformal rectangular grids (such as polar stereograhic) where the map to real world scaling factor is the same in the x as in the y direction We still need a rectangular grid, but one which will reach from the south to the north pole => lat-lon grid

25. If dx = gap between grid points in map coordinates, and dX = actual distance (in meters), then dX = (1/mx) dx and likewise dY = (1/my) dy Original WRF Global WRF • Lat-lon grid => x = a, y = a, => dx = a d, dy = a d, whereas dX = a cos d, dY = a d => mx = dx/dX = sec, my= dy/dY = 1 => mx ≠ my => Needed to identify which map scale factor was required in all equations where ‘m’ appeared, and reintroduce map scale factors where they previously cancelled (so were omitted) Conformal grid => for all map projections available (mercator, polar stereographic, etc.), mx = my at all points => Only one map scale factor (m) used, and omitted altogether when mx and my cancelled

26. Changes required for global WRF • Deal with polar boundary conditions V V Place v points at poles, with v there = 0 Nothing is allowed to pass directly over the poles - atmospheric mass is pushed around the pole in longitude instead - and no fluxes can come from the polar points when calculating variables U T U T U V V T T U U U V V • Deal with instabilities at the model top The basic mesoscale WRF model generally only reached a maximum of ~30km, plus was regularly (and frequently) forced by a separate GCM However, ‘standalone’ global WRF will develop upper level instabilities due to spurious wave reflection at the model top if these are not damped in some way - we must therefore introduce a ‘sponge layer’

27. Changes required for global WRF • Avoid instabilities due to E-W distance between grid points becoming small near poles This is a problem due to the CFL (Courant Friedrichs Lewy) criterion: ∆ t < ∆ x / U where U is the fastest moving wave in the problem => As ∆ x -> 0, ∆ t must -> 0also, which is very expensive => a) Use a small ∆ t (far less than needed to satisfy at the equator), OR b)Increase largest effective scale ∆ x by filtering out smaller wavelengths (e.g. retaining only wavenumber 1 at the pole itself) Usual method in GCMs is to use a polar Fourier filter

28. Changes for planetary WRF Models are generally very Earth-specific! • Remove ‘hardwired’ planet-specific constants - instead use parameters which vary with planet • Change ‘Earth time’ to ‘general planet time’ • Allow orbital parameters to be specified • Add physics parameterizations where needed

29. Results: for Earth (up to 3.) • Solid-body rotation test(for a non-rotating planet!) including solid body rotation over the poles • Held-Suarez standard test of a dynamical core: Newtonian relaxation to typical tropospheric temperature profiles with Rayleigh friction (winds slowed towards zonal mean) increasing with height • Polvani-Kushner extension to Held-Suarez: added a simple stratosphere with cooling over winter pole • Further testingto look at wave propagation etc.

30. 1. Initial wind pattern for solid body rotation over the poles North pole North pole South pole South pole

31. Wind pattern after 1 1/2 days

32. Wind pattern after 4 1/2 days

33. 2. The Held-Suarez test: a. Zonal mean T averaged over last 1000 days Global WRF Expected result

34. 2. The Held-Suarez test: b. Zonal mean u averaged over last 1000 days Global WRF Expected result

35. 3. Polvani-Kushner - in initial stages (up to 380 days, but need average over last 9000 days of 10000 day experiment) Zonal mean u in global WRF at 380 days Expected zonal mean u (average over last 9,000 days)

36. Results: for Mars (up to 3.) • No CO2 condensation, no atmospheric dust, no topography, diurnally-averaged heating • Added topography, diurnal cycle • Mars with a realistic (but prescribed) atmospheric dust content and with a CO2 cycle • Mars with interactive dust lifting and transport • High resolution nests over Hellas, Tharsis, etc.

37. Northern summer solstice: GFDL Mars GCM and WRF without dust

38. Northern summer solstice: Oxford Mars GCM and WRF without dust

39. Southern spring equinox: GFDL Mars GCM and WRF without dust

40. Ls = 190°: global WRF zonal mean T, u & wind MGS TES zonal mean T MGS TES zonal mean u

42. Results: for Titan (up to 1.) • Prescribed haze distribution • Include interactive haze production and transport using a microphysics scheme • Add methane cloud microphysics • Introduce photochemistry schemes

43. Prescribed haze distribution: some results we will compare with: Northern winter solstice Northern spring equinox a. Meridional streamfunctions produced by the LMD Titan GCM b. Zonal mean zonal winds produced by the LMD Titan GCM

44. Conclusions • Global, planetary WRF is a highly efficient and accurate global model in which high resolution 2-way nests can be embedded • It has performed (and is performing) well in general tests (e.g. mass conservation) and tests used for other Earth GCMs (e.g. Held-Suarez) • Initial Mars results (no dust or CO2 cycle) match those from other Mars GCMs

45. Conclusions • Ongoing work includes Mars with realistic dust and a CO2 cycle, and spinning up Titan’s atmosphere (including running in parallel on a beowulf cluster)