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D A R G A N M . W . F R I E R S O N

U N I V E R S I T Y O F W A S H I N G T O N , D E P A R T M E N T O F A T M O S P H E R I C S C I E N C E S

Modeling the General Circulation of the Atmosphere.

Day 1: A Hierarchy of Models

In my lectures…

 We’ll study:   The “general circulation” of the atmosphere

  Large scale features of the climate

Questions like…

 Why are the rainforests and deserts of the world at similar latitudes?

Questions like…

 What determines the horizontal temperature distribution on Earth?

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Questions like…

 What determines the vertical temperature structure on Earth?

Questions like…

 How will these change with global warming?

Rainy regions get rainier, dry regions get drier

First: An Introduction to Climate Models

 Models are key to our understanding of the climate

Observed global temperatures and modeled temperatures

An Introduction to Climate Models

  Forecasts of global warming

Global temperature forecasts for different emissions scenarios

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General Circulation Models (GCMs)

 What are the components of these models?

 What are the essential physical processes that are being modeled?

 What are the simplest mathematical models that can capture the essential physics?

AGCM Components

  AGCM: Atmospheric General Circulation Model

  “Dynamics”:   Fluid equations on a rotating sphere

  “Physics”:   Radiative transfer

  Surface fluxes/boundary layer scheme   Clouds

  Moist convection

Dynamical Core of AGCMs

  Essentially just fluid equations on the rotating sphere

Dynamical Cores of AGCMs

  The “primitive equations”:

Coordinates: = (longitude, latitude, pressure) (λ, θ, p)

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Dynamical Cores of AGCMs

 Horizontal momentum eqns:

  Coriolis terms are key due to rapid rotation of Earth

Rotation/sphericity terms

Momentum equations in longitude and latitude

Dynamical Cores of AGCMs

 Horizontal momentum eqns:

Pressure gradient term

Momentum equations in longitude and latitude

Φ = gz = “geopotential”

Primitive equations

  Vertical momentum eqn. is “hydrostatic balance"

Vertical momentum equation

Hydrostatic balance

  Vertical momentum equation:

  In z-coordinates, written as:

  Key assumption: atmosphere is a very thin film   Small aspect ratio (100 km horizontal grid size)

  Cloud resolving models are “nonhydrostatic”

∂p

∂z= −ρg

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Dynamical Cores of AGCMs

 Mass conservation:

Mass conservation equation

Looks incompressible, but it isn’t. Pressure coordinates makes this form possible (requires hydrostatic balance too).

Dynamical Cores of AGCMs

  Thermodynamic equation:

Temperature changes due to compression and expansion

Dynamical Cores of AGCMs

  Source terms: where much of the complexity comes in

“Physics”

Primitive Equations Summary

  Key simplification: hydrostatic   Small aspect ratio allows this

  Pressure as a vertical coordinate allows   Simplified mass conservation equation

  Simplified pressure gradient expressions

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Simplified dynamical cores

  Linearized about background density/temperature profiles   Boussinesq equations (small density variations)

 Ocean density only varies by less than 4% globally!

  Anelastic equations (small potential temperature variations)  Atmospheric density does vary a lot, but mostly due to pressure

changes

Simplified dynamical cores

  Truncated vertical structure:   Barotropic fluid: incompressible & independent of height

  Shallow water fluid: single layer of incompressible fluid

  Two-layer fluid: two shallow water layers   Galerkin truncations

Simplified dynamical cores

  Asymptotically reduced systems   Quasi-geostrophic equations

  Weak temperature gradient equations

  Many others!

Physics of AGCMs

  Climate models have some very complex parameterizations of physical processes   Radiative transfer   Convection

  Clouds

 We’ll describe general ideas of how these are parameterized

  And talk about simple ways to parameterize these effects as well

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Radiative transfer

  Sun warms the Earth (primarily at the surface) – “shortwave radiation”

  Surface emits infrared radiation

  Atmosphere absorbs & re-emits “longwave radiation”

Radiative transfer models

  Clear sky radiative transfer is essentially a solved problem

 Divide electromagnetic spectrum into bands

  Solar absorption and scattering by H2O, CO2, O3, O2, clouds, aerosols

  Longwave absorption and emission by H2O, CO2, O3, N2O, CH4, CFC-11, CFC-12, CFC-113, HCFC-22, aerosols, clouds

  Very computationally expensive!   ~50% of the total CPU usage is running the radiation code

Cloud schemes

  Clouds have two primary effects on the climate:   Blocking solar radiation

  Trapping longwave radiation

  Relative importance vary based on depth of clouds

Shallow clouds cool, High clouds can warm

Clouds schemes

 Warming and cooling effects of clouds nearly cancel in the current climate

  Cloud interactions are the most uncertain process in GCMs   Lead to the largest differences between models

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Moist convection schemes

  Convection = vertical overturning due to density differences

  Air rises if it’s warmer than it’s surroundings

  Atmosphere is strongly heated from below, leading to large amounts of convection

  Ocean is heated from above:

key difference between atmosphere and ocean!

Warm ocean water is confined within a few 100 meters of the surface

Moist convection schemes

 Moisture condensation serves as a large heat source within the atmosphere (tomorrow’s lecture)

  Rising air condenses, which gives air extra buoyancy

  Classic multiscale problem:   Cloud scale is a few km (at most), grid scale is 100 km

Moist Convection Schemes

  Convection schemes are based on models of sub-grid scale entraining plumes of different widths

  Eventually global cloud resolving models will eliminate the need for cumulus parameterization

 We’ll talk about simple ways to do moist convection later this week   Anything connected to moisture is fundamentally a multiscale

problem

Additional AGCM Parameterizations

  Surface flux/boundary layer schemes   How much evaporation & heat flux comes off the ocean/land

  How heat, moisture and momentum are distributed in the turbulent boundary layer

  Typically based on turbulent closures with empirical data

 Gravity wave drag parameterizations   Momentum fluxes from sub-grid scale breaking of waves

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What Models Don’t Parameterize (yet)

  Carbon cycle

 Dynamic vegetation

 Dynamic ice-sheet models

  Interactive chemistry (e.g., ozone chemistry)

  Aerosol effects on cloud formation

Simplified physics GCMs

  There is value in developing GCMs with simplified physics:   Easier to understand   Easier to reproduce results

  Results more robust (less sensitive to parameters)

  Less computational expense

  Test ground for theories of the general circulation

Simplified GCM Experiments

 Nature has only provided us with one planet

  Computer models allow us to explore a range of imaginary planetary climates:   Ocean-covered planets   Planets with different rotation rates,

radius, solar heating

  Certain physical effects suppressed or enhanced

Simplified GCM Experiments

  See Held (2005, BAMS) for biological analogy:   In biology, hierarchy occurs naturally: bacteria, fruit flies, lab

mice, etc

  This has allowed rapid progress in understanding molecular biology, the genome, etc

  In atmospheric science, we have to create our own hierarchies   Have to additionally argue that the simplified models are

worth studying though

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An Idealized AGCM

 Held-Suarez model (1994, BAMS)

  Radiation and convection parameterized as

Warmer than Teq => cooling Cooler than Teq => warming

That’s it

An Idealized AGCM

  Equilibrium distribution is what radiation and convection would produce without dynamics

Latitude

Temperature Potential Temperature

Latitude

Equator is hotter than observed Pole is colder than observed Constant stratospheric temperature

Roughly moist adiabatic vertical structure

An Idealized AGCM

  Instantaneous surface pressure:

An Idealized AGCM

  Instantaneous surface pressure:

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An Idealized AGCM

  Potential temperature climatology

From Held and Suarez (1994)

Circulation transports heat poleward and upward

An Idealized GCM

  Zonal winds

versus observations:

An Idealized GCM

 Held-Suarez model has been used to study:   Annular modes of extratropical variability (Gerber and Vallis)

  Sensitivity of extratropical circulation to tropopause height (Williams; Lorenz and DeWeaver)

  Winds in equatorial troposphere (Kraucunas and Hartmann)

  Stratosphere-troposphere coupling (Reichler, Kushner and Polvani)

Next time…

 What determines the vertical structure of temperature on Earth

 How simplified AGCMs can be used to study this

  An introduction to moisture