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

Developing a new general Developing a new general circulation model for circulation model for

planetary atmospheres - planetary atmospheres - how (and why!)how (and why!)

Claire NewmanClaire Newman

Kliegel Planetary Science SeminarKliegel Planetary Science SeminarMarch 1st 2005March 1st 2005

Overview of the talkOverview of the talk What is a general circulation model (GCM)?What is a general circulation model (GCM)?

Why develop a new model for planetary atmospheres: Why develop a new model for planetary atmospheres: what questions are we trying to answerwhat questions are we trying to answer??

How is this new model being developed?How is this new model being developed?

Description of the base model: the Earth-based, limited Description of the base model: the Earth-based, limited area “Weather Research and Forecasting” (WRF) modelarea “Weather Research and Forecasting” (WRF) model

Description of the changes needed to ‘globalize’ WRFDescription of the changes needed to ‘globalize’ WRF

Description of the changes needed to make ‘planetary’ Description of the changes needed to make ‘planetary’ WRFWRF

Recent results and future work: Earth, Mars and Recent results and future work: Earth, Mars and TitanTitan

What is a general circulation model What is a general circulation model (GCM)?(GCM)?

dynamics physics

Basically Newton II in 3 dimensions: force = mass x acceleration(subject to mass & energy conservation)

You can actually write downwrite 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.)

Generally is conceptually (and practically) split into two components:

Includes everything acting at a smaller scale to the dynamics, all of which is represented via

parameterizationsThis includes:

1. Small scale turbulence2. Friction at the surface3. Absorption, emission and

scattering of radiation

DU = 2V sin - 2W cos - UW + Uv tan -1 p + Fx

Dt a a X

‘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

‘Coriolis’ terms due to air parcel moving in a rotating (not inertial) frame

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

Terms due to the coordinate system rotating

Pressure gradient force per unit mass

Frictional force per unit mass - usually added in during physics, as must be parameterized

AccelerationForce / mass

Examples of physics in a GCMExamples of physics in a GCMRadiative transfer in a planetary atmosphere:

Absorption and scattering in the atmosphere

Atmospheric layer

Surface

Absorption and scattering at the surface

Solar wavelengths

Thermal wavelengths

Surface emission (~Tsurf

4)

Absorption and scattering in the atmosphere Atmospheric

emission (~T4)

Absorption and scattering at the surface

Temperature changes depend on heating rates, which Temperature changes depend on heating rates, which are determined from net fluxes, which in turn depend are determined from net fluxes, which in turn depend on temperature => many interconnected equations on temperature => many interconnected equations and many methods of solving them to find T(z)and many methods of solving them to find T(z)

Why do we need a new Why do we need a new GCM for planetary GCM for planetary

atmospheres?atmospheres?

To understand this, you first need to understand:

What questions do we What questions do we want to answer?want to answer?

EarthEarth MarsMars TitanTitan

CO2 atmospherePsurf ~ 610 PaTsurf ~ 210 K

Very eccentric orbitMajor topographyDust storms

N2 atmospherePsurf ~ 1.5x105 PaTsurf ~ 93 K

Thick haze layersMethane ‘hydrology’Slowly rotating

N2 atmospherePsurf ~ 1x105 PaTsurf ~ 288 K

Water cycleOceans & land surfaces

Dust opacities for 2001 global storm from MGS TES websiteDust opacities for 2001 global storm from MGS TES website

Onset and evolution of a Martian dust Onset and evolution of a Martian dust stormstorm

Meridional circulation strengthens

T increases inside dust cloud

SurfaceSurface

Strongwinds

Wind stress lifting: +ve feedbacks 2 - global scaleWind stress lifting: +ve feedbacks 2 - global scale

S poleS pole N poleN pole S poleS pole N poleN pole

Fairly strong associated winds and dust lifting

Very strong associatedwinds and much more dust lifting

Wind stress lifting: +ve feedbacks 1 - local scaleWind stress lifting: +ve feedbacks 1 - local scale

Storm onset & evolution: Storm onset & evolution: multiscale multiscale feedbacksfeedbacks

180° 180°120°W 60°W 120°E0° 60°E

90°N

60°N

30°N

30°S

60°S

0°

90°S

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 MarsRegions of interest on Mars

180° 180°120°W 60°W 120°E0° 60°E

90°N

60°N

30°N

30°S

60°S

0°

90°S

Potential areas of higher resolution

Regions of interest on MarsRegions of interest on Mars

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 => Model with high resolution areas within resolution areas within global domain, and global domain, and information passing information passing bothboth ways (2-way feedbacks)ways (2-way feedbacks)

The big questions for Mars (I)The big questions for Mars (I) How do dust storms begin and evolve, and How do dust storms begin and evolve, and

why do some become global?why do some become global? How do flows associated with the large How do flows associated with the large

topography interact with the global topography interact with the global circulation?circulation? Need higher resolution just in

regions where local slopes and circulations may be crucial

Bri

ghtn

ess

tem

per

atu

re

Du

st o

pac

ity

Areocentric longitude Ls Areocentric longitude Ls

‘Storm season’

‘Storm season’

From Liu et al. JGR 2003From Liu et al. JGR 2003

Interannual variability in Mars’s Interannual variability in Mars’s atmosphereatmosphere

The big questions for Mars (II)The big questions for Mars (II) What determines the variability in the What determines the variability in the

Martian dust cycle and hence climate?Martian dust cycle and hence climate?

What was the climate like in the past, & What was the climate like in the past, & does this help us understand present does this help us understand present geological features?geological features?

When and where was water stable at the When and where was water stable at the surface, and where would subsurface surface, and where would subsurface water deposits be? water deposits be? Need to look at

interannual variability and/or changes over long timescales

=> Need efficient and => Need efficient and accurate (mass and accurate (mass and angular momentum angular momentum conserving) modelconserving) model

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.)

Clouds on TitanClouds on Titan

The big questions for Titan (I)The big questions for Titan (I) What controls when and where methane What controls when and where methane

clouds form?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 => Need a model

capable of placing capable of placing high resolution high resolution regions with the regions with the global domain global domain

““Spinning up” Titan’s Spinning up” Titan’s atmosphereatmosphere

Results from the LMD Titan GCM, from Hourdin et al., Icarus 1995

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

The big questions for Titan (II)The big questions for Titan (II) How much does interaction with the surface How much does interaction with the surface

affect the atmospheric circulation?affect the atmospheric circulation?

What determines the equatorial What determines the equatorial superrotation?superrotation?

How variable is Titan’s circulation and How variable is Titan’s circulation and albedo (at different wavelengths) over the albedo (at different wavelengths) over the long Titan year?long Titan year? A long Titan year and thick atmosphere (high dynamical inertia) mean long spin-up times

=> Experiments to explore sensitivities and study variability take a long time

=> Need a => Need a model which is model which is fast, and fast, and accurate over accurate over the integration the integration times requiredtimes required

The Weather Research The Weather Research and Forecasting (WRF) and Forecasting (WRF)

modelmodel Mesoscale (limited area) model for weather Mesoscale (limited area) model for weather

research and forecasting on Earthresearch and forecasting on Earth

Developed by NCAR in collaboration with other Developed by NCAR in collaboration with other agencies (NOAA, AFWA, etc.)agencies (NOAA, AFWA, etc.)

AimAim: to produce a reliable mesoscale model, to : to produce a reliable mesoscale model, to be used for real-time forecasting be used for real-time forecasting andand as a as a research tool, with improvements being worked research tool, with improvements being worked into new releasesinto new releases

Features of WRFFeatures of WRF Dynamics conserve mass Dynamics conserve mass

and angular momentum and angular momentum - highly accurate - highly accurate

Highly parallel code Highly parallel code => efficient => efficient

Large suite of physics Large suite of physics parameterizations and a parameterizations and a modular form => flexible modular form => flexible

Uses Arakawa C-gridUses Arakawa C-gridV

V V

V

V

V

V V V

VV V

U U U U

U UUU

U UUU

TT T

TT T

TT TU = zonal (E-W) velocity pointV = meridional (N-S) velocity pointT = temperature / mass point

5.20354

5.203502500 500125

Mass in kg (x1018)

375Days

Features of WRF (cont.)Features of WRF (cont.)

2-way 2-way nesting nesting capability:capability:

Nesting capability:Nesting capability:

Mother domain Mother domain

Child

Child 1

Child 2siblings

‘Grandchild’

1-way nesting 2-way nesting

The usual approach - how mesoscale The usual approach - how mesoscale WRF runs:WRF runs:a) place nests within a mesoscale model (WRF), with

b) its initial and boundary conditions being provided by a separate global model

1. Interface between global and mesoscale models is one-way => no feedbacks from small to larger scale

2. Unless specially designed to match, often have different dynamics and/or physics - inconsistent

3. Interface is also ‘messy’, e.g., must view output from the two models using different tools

Drawbacks:

WRF Separate global model

Globalising WRF gives a Globalising WRF gives a highly highly accurateaccurate & & efficientefficient globalglobal model, in which we can model, in which we can place 1- & place 1- & 2-way2-way nestsnests

So we are basically using WRF’s nesting So we are basically using WRF’s nesting abilities to abilities to nest all the way down from globalnest all the way down from global

Changes required for Changes required for globalglobal WRFWRF

Allow use of a latitude-longitude gridAllow use of a latitude-longitude grid

We still need a rectangular grid, but one which will reach from the south to the north pole=> lat-lon 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

Original WRF Global WRF

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

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

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)

Changes required for Changes required for globalglobal WRFWRF

Deal with polar boundary conditionsDeal with polar boundary conditions

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

Deal with instabilities at the model topDeal with instabilities at the model top

VV

V V

VV

U U U

U UU T T

T T

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’

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 filterUsual method in GCMs is to use a polar Fourier filter

Avoid instabilities due to E-W distance between Avoid instabilities due to E-W distance between grid points becoming small near polesgrid points becoming small near poles

Changes required for Changes required for globalglobal WRFWRF

Changes for Changes for planetaryplanetary WRF WRF

Remove ‘hardwired’ planet-specific constants - Remove ‘hardwired’ planet-specific constants - instead use parameters which vary with planetinstead use parameters which vary with planet

Change ‘Earth time’ to ‘general planet time’Change ‘Earth time’ to ‘general planet time’

Allow orbital parameters to be specifiedAllow orbital parameters to be specified

Add physics parameterizations where neededAdd physics parameterizations where needed

Models are generally Models are generally veryvery Earth-specific! Earth-specific!

Results: for Earth (up to Results: for Earth (up to 3.)3.)

1.1. Solid-body rotation testSolid-body rotation test (for a non-rotating planet!) including solid body rotation over the poles

2.2. Held-Suarez standard test of a dynamical coreHeld-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

3.3. Polvani-Kushner extension to Held-SuarezPolvani-Kushner extension to Held-Suarez: : added a simple stratosphere with cooling over winter pole

4.4. Further testingFurther testing to look at wave propagation etc.

1. Initial wind pattern for solid body rotation over the poles

North pole

South poleSouth pole

North pole

Wind pattern after 1 1/2 days

Wind pattern after 4 1/2 days

2. The Held-Suarez test:2. The Held-Suarez test:

a. Zonal mean T averaged over last 1000 days

Global WRF Expected result

2. The Held-Suarez test: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 3. Polvani-Kushner - in initial stages (up to 380 days, but need average over need average over last 9000last 9000 days of days of 1000010000 day experiment) 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 Results: for Mars (up to 3.)3.)

1.1. No CONo CO22 condensation, no atmospheric dust, no condensation, no atmospheric dust, no topography, diurnally-averaged heatingtopography, diurnally-averaged heating

2.2. Added topography, diurnal cycleAdded topography, diurnal cycle

3.3. Mars with a realistic (but Mars with a realistic (but prescribedprescribed) ) atmospheric dust content and with a COatmospheric dust content and with a CO22 cycle cycle

4.4. Mars with interactive dust lifting and transportMars with interactive dust lifting and transport

5.5. High resolution nests over Hellas, Tharsis, etc.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

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

MGS TES zonal mean u

Results: for Titan (up to Results: for Titan (up to 1.)1.)

1.1. Prescribed haze distributionPrescribed haze distribution

2.2. Include interactive haze production and Include interactive haze production and transport using a microphysics schemetransport using a microphysics scheme

3.3. Add methane cloud microphysicsAdd methane cloud microphysics

4.4. Introduce photochemistry schemesIntroduce photochemistry schemes

Northern winter solstice Northern spring equinox

1.1. Prescribed haze distribution: some results we will compare with:Prescribed haze distribution: some results we will compare with:

a. Meridional streamfunctions produced by the LMD Titan GCM

b. Zonal mean zonal winds produced by the LMD Titan GCM

ConclusionsConclusions Global, planetary WRF is a highly efficient Global, planetary WRF is a highly efficient

and accurate global model in which high and accurate global model in which high resolution 2-way nests can be embeddedresolution 2-way nests can be embedded

It has performed (and is performing) well It has performed (and is performing) well in general tests (e.g. mass conservation) in general tests (e.g. mass conservation) and tests used for other Earth GCMs (e.g. and tests used for other Earth GCMs (e.g. Held-Suarez)Held-Suarez)

Initial Mars results (no dust or COInitial Mars results (no dust or CO22 cycle) cycle) match those from other Mars GCMsmatch those from other Mars GCMs

ConclusionsConclusions Ongoing work includes Mars with realistic dust and Ongoing work includes Mars with realistic dust and

a COa CO22 cycle, and spinning up Titan’s atmosphere cycle, and spinning up Titan’s atmosphere (including running in parallel on a beowulf cluster)(including running in parallel on a beowulf cluster)