Developing a new general circulation model for planetary atmospheres - how (and why!) Claire Newman Kliegel Planetary Science Seminar March 1st 2005

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

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.) (Discrete problem rather than continuous) This includes: Small scale turbulence Friction at the surface Absorption, emission and scattering of radiation

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

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 Atmospheric layer Absorption and scattering in the atmosphere Atmospheric emission (~T4) Absorption and scattering in the atmosphere Thermal wavelengths Absorption and scattering at the surface Absorption and scattering at the surface Surface Surface emission (~Tsurf4)

Why do we need a new GCM for planetary atmospheres 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?

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

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

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 1 - why circ strengthens 2 - why can’t put high resn everywhere Meridional circulation strengthens Very strong associated winds and much more dust lifting Fairly strong associated winds and dust lifting S pole N pole S pole N pole

Regions of interest on Mars 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

Regions of interest on Mars 0° 30°S SAY RE RESN HERE!! 60°S 90°S 180° 120°W 60°W 0° 60°E 120°E 180° Potential areas of higher resolution

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)

Interannual variability in Mars’s atmosphere ‘Storm season’ Dust opacity Brightness temperature Brightness temp = T for sig fraction of lower atm, with info content centred on ~0.5mbar (~25km) ‘Storm season’ Areocentric longitude Ls Areocentric longitude Ls From Liu et al. JGR 2003

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

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.)

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

“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

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

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

Features of WRF Mass in kg (x1018) 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 5.20354 5.20350 125 250 375 500 Days V V V T T T U U U U Better than 4 parts in e5, and no trend 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

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 2-way nesting capability:

The usual approach - how mesoscale WRF runs: b) its initial and boundary conditions being provided by a separate global model a) place nests within a mesoscale model (WRF), with Separate global model WRF Drawbacks: 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

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

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 Need rectangular and pole to pole => need lat lon NB - mercator will never reach pole; polar stereographic can’t meet at both poles READ!!

Original WRF Global WRF => mx ≠ my mx = my at all points 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 MORE?? NO!

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 CHANGE 2nd!! 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’

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 -> 0 also, 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

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

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 testing to look at wave propagation etc.

North pole North pole South pole South pole 1. Initial wind pattern for solid body rotation over the poles North pole North pole Overpole test results South pole South pole

Wind pattern after 1 1/2 days

Wind pattern after 4 1/2 days

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

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

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)

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.

Northern summer solstice: GFDL Mars GCM and WRF without dust

Northern summer solstice: Oxford Mars GCM and WRF without dust

Southern spring equinox: GFDL Mars GCM and WRF without dust

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

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

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

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

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)