1. Introduction to Climate Models: history and basic structure Topics covered:
2. Brief history
3. Physical parametrizations

2. Definition and a healthy philosophy regarding climate models

3. The climate System

4. Brief history of climate modelling
1922: Lewis Fry Richardson
basic equations and methodology of numerical weather prediction
1950: Charney, Fjørtoft and von Neumann (1950)
first numerical weather forecast (barotropic vorticity equation model)
1956: Norman Phillips
first general circulation experiment (two-layer, quasi-geostrophic hemispheric model)
1963: Smagorinsky, Manabe and collaborators at GFDL, USA
9 level primitive equation model
1960s and 1970s: Other groups and their offshoots began work
University of California Los Angeles (UCLA), National Center for Atmospheric Research (NCAR, Boulder, Colorado) and UK Meteorological Office
1990s: Atmospheric Model Intercomparison Project (AMIP)
Results from about 30 atmospheric models from around the world
2007: IPCC Forth Assessment Report
climate projections to 2100 from numerous coupled ocean-atmosphere-cryosphere models.

5. How do they see our planet?
19 Atmospheric Levels
20 Ocean Levels

6. Met Office Unified Model level structure: more recent grids

7. HADLEY CENTRE CLIMATE MODELS

8. HiGEM2 land-sea mask and bottom topography model has 1/3 degree resolution (“eddy permitting”)

9. How are they tested?

10. Testing against Palaeo-data

11. Development of Met Office climate models
Now
ATMOSPHERE
LAND
OCEAN
ICE
SULPHUR
CARBON
CHEMISTRY
1999
ATMOSPHERE
LAND
OCEAN
ICE
SULPHUR
CARBON
1997
ATMOSPHERE
LAND
OCEAN
ICE
SULPHUR
1992
ATMOSPHERE
LAND
OCEAN
ICE
Component models
are constructed off-line
and coupled in to the
climate model when
sufficiently developed
1988
ATMOSPHERE
LAND
OCEAN
1985
ATMOSPHERE
LAND
1960s
ATMOSPHERE 6

12. The horizontal and vertical resolutions of climate models need to be high enough to avoid numerical errors and to resolve the basic dynamical and transport processes There is a trade-off between resolution and computing time, but model resolutions are increasing continually, as more computer power becomes available

13. Physical parametrizations
Momentum equation;
dV/dt = -p -2^V –gk +F +Dm
Where =1/ ( is density), p is pressure,  is rotation rate of the Earth, g is acceleration due to gravity (including effects of rotation), k is a unit vector in the vertical, F is friction and Dm is vertical diffusion of momentum
Thermodynamic equation;
dT/dt = Q/cp + (RT/p) + DH
where cp is the specific heat at constant pressure, R is the gas constant,  is the vertical velocity, DH is the vertical diffusion of heat and Q is the internal heating from radiation and condensation/evaporation;
Q = Qrad + Qcon
Continuity equation for moisture (similar for other tracers);
dq/dt = E – C + Dq
where E is the evaporation, C is the condensation and Dq is the vertical diffusion of moisture

14. Physical parametrizations in atmospheric models
Processes that are not explicitly represented by the basic dynamical and thermodynamic variables in the basic equations (dynamics, continuity, thermodynamic, equation of state) on the grid of the model need to be included by parametrizations.
There are three types of parametrization;
Processes taking place on scales smaller than the grid-scale, which are therefore not explictly represented by the resolved motion;
Convection, boundary layer friction and turbulence, gravity wave drag
All involve the vertical transport of momentum and most also involve the transport of heat, water substance and tracers (e.g. chemicals, aerosols)
Processes that contribute to internal heating (non-adiabatic)
Radiative transfer and precipitation
Both require the prediction of cloud cover
Processes that involve variables additional to the basic model variables (e.g. land surface processes, carbon cycle, chemistry, aerosols, etc)

15. Parametrized processes in the ECMWF model

16. Atmospheric models include parametrizations for:
cloud formation, microphysics and precipitation
radiative transfer (both solar and thermal)
dry and moist convection (and transport of tracers)
surface exchanges and land surface processes
drag processes (e.g. boundary layer, gravity waves)
aerosols, chemistry, carbon cycle

17. Clouds and precipitation
GCMs cannot resolve clouds, but a knowledge of their amount and properties is important for the calculation of radiation fields and precipitation
A GCM therefore needs a cloud parametrization. These have evolved in time with increasing complexity:
Earliest (and simplest) cloud parametrization
cloud amount = 0 if grid box is unsaturated
cloud amount = 1 if grid box saturated (and excess humidity is rained out)
Diagnostic schemes
cloud amount is diagnosed from the model variables
Prognostic schemes
cloud amount is a prognostic variable, with tendency terms that enable the changes in cloud amount to be calculated (from new parametrizations…)

20. Prognostic cloud scheme in the ECMWF model
Linking the parametrizations to provide the rate terms in the above equations

21. Radiation

22. Radiative transfer: clouds
earliest schemes used-ray tracing in shortwave and emissivity approximation in longwave
cloud radiative properties were fixed
no treatment of aerosols
modern schemes use the “two-stream equations” which enable scattering to be included as well as calculation of radiative properties of clouds and aerosols
The effect of particle size, phase (whether water or ice) and shape (ice crystals) can then be parametrized
important for investigating the indirect effect of aerosols on cloud radiative properties

23. Convection
The first convection schemes simply adjusted the temperature profile to remove super-adiabatic layers
Most contemporary convection schemes use a mass-flux approach, with buoyant plumes entraining and detraining to reach different levels.
Yanai et al. (1973)
Arakawa and Scubert (1974)
Gregory and Rowntree (1990)
Important processes to be included are the effects of saturated downdraughts and momentum transport
e.g. Gregory, Kershaw and Inness (1997)

24. Schematic of an ensemble of cumulus clouds.
Convection scheme
Schematic of an ensemble of cumulus clouds.
From Yanai et al. (1973)
Cloud mass fluxes.
 denotes the entrainment of environmental air into the cloud
 denotes the detrainment of cloud air into the environment
MC is the cloud mass flux
From Yanai et al. (1973)

25. Surface processes
Surface schemes are needed to calculate the fluxes of heat, moisture and momentum between the surface and atmosphere and to calculate surface temperature and other variables
Over the oceans, the schemes are quite simple
Over land, models now contain quite detailed representations of evaporation, interception and vertical transfers of heat and moisture in the soil
For example, MOSES I (in the Met Office Unified Model) includes a model of stomatal control of evaporation
MOSES 2 also explicitly treats subgrid patchiness of the landscape with a tile scheme

26. Surface Hydrology in Met Office Surface Exchange Scheme (MOSES)

27. Representation of orography; the importance of resolution
The upper figure shows the surface orography over North America at a resolution of 480km, as in a low resolution climate model.
The lower figure shows the same field at a resolution of 60km, as in a weather forecasting model.
Remember that orographic processes are highly non-linear.

28. Orographic processes
The effect of details of the surface orography that are not resolved by the model’s grid must be parametrized
Processes that are known to be important include low level flow blocking and gravity wave drag
The sub-gridscale variability of the orography is used to drive the parametrizations

29. Mean and standard deviation of orographic heights at two resolutions
NWP model: 60km
Climate model: 250km
Mean: explicitly resolved by the model
Standard deviation: used to drive the parametrizations

30. Orographic drag schemes typically include two effects
Low-level flow blocking and separation
Gravity waves:
Long waves which may propagate into the stratosphere
These were the only waves that were represented in the first generation of gravity wave drag schemes

31. Aerosols: Saharan dust

32. Further reading Books;
Washington, W.M. and Parkinson, C.L., An introduction to three dimensional climate modeling. Oxford University Press
Trenberth, K.E.,1995. Climate system modeling. Cambridge University Press
Randall, D.A General circulation model development. Academic Press
Houghton, J.T. et al., Climate change 2001; the scientific basis. Cambridge University Press. (Working Group 1 contribution to the IPCC Third Assessment )
Web pages;
ECMWF seminars:
AMIP:
GFDL:
NCAR:
GISS:
Met Office: