Introduction to climate modeling

ECOLMAS Course 1-4 April 2008

Course description

• Goal: To equipe you with a comfortable basic knowledge in the trade of climate modeling

• Course web site: http://www.geo.uni-bremen.de/~apau/ecolmas_modeling2

Recommended reading:General

• Hartmann, Dennis L.: Global Physical Climatology. Academic Press, 1994.

• Ruddiman, William F.: Earth‘s Climate. Past and Future. Freeman, 2001.

Recommended reading:Modeling

• Trenberth, Kevin E. (ed.): Climate System Modeling, Cambridge University Press, 1992.

• McGuffie, K. and A. Henderson-Sellers: Forty years of numerical climate modeling, International Journal of Climatology 21, 1067-1109 (2001).

• Washington, Warren M. and Parkinson, Claire L.: An Introduction to Three-Dimensional Climate Modeling. 2nd edition. University Science Books, Sausalito, California, 2005.

What is climate?

Climate‘s what we expect, but weather‘s what we get.

(Larry Riddle)

What is climate?

• Climate is about the expected values of the meteorological elements (“climatic elements“) at a location during a certain month or season– temperature, precipitation, wind, pressure,

cloudiness, humidity usually at the surface of the Earth

– annual means, distribution through the year as well as interannual variability

What is the climate system?

Vegetation

Atmosphere

Ice

Ocean

Landsurface

From Apollo 17 flight, 7 December 1972

Conceptual model of the climate system

Figure 1-5 (bottom) from Ruddiman (2001)

Conceptual model of the climate system

• Complexity of real climate system can be organized and simplified in a conceptual model

Engineer’s point of view: the climate system running as a machine

But what are the connections between the various components it is made of?

Interactions between climate system components

Energy exchange in different forms:

• Sensible heat flux

• Latent heat flux– Related to evaporation/precipitation and water flux in

the atmosphere, salt transport in the ocean

• Momentum flux– E.g. associated with wind energy

What is a model?Models are• smaller than reality (finite number of processes, reduced size of

“phase space”)• simpler than reality

(description of processes is idealized)• closed, whereas reality is open (infinite number of external, unpredictable forcing factors

is reduced to a few specified factors)(Hans von Storch)

• Examples of models– models build to scale (houses, cars, …)– map, sketch or drawing– numerical model

• conceptual• quasi-realistic, surrogate of reality

• Models put numbers on ideas (W. F. Ruddiman)

http://www.miniatur-wunderland.de/

Why use climate models?

• To formulate and test hypothesis• To have an independent way to test whether a

particular theory can explain the (proxy-) data• To understand past climates

– response to climate forcings– couplings and feedbacks between climate system

components

• To relate present climate to human activities• To make predictions for the future

Types of models

• Atmospheric general circulation models (AGCMs)

• Ocean general circulation models (OGCMs)• Sea-ice and land ice models • Vegetation models• Biogeochemical models• Marine ecosystem models

First numerical model

• First description of a method for constructing a weather forecast by means of numerical calculation was published by Richardson (1922)

Basics of numerical models

1. State variables

2. Fundamental equations

3. Parameterization

4. Discretization

5. Numerical solution

State variables

• Many variables can be thought of as a “concentration“ or “property per unit volume“.

• Fluxes then have dimensions of “property per unit time and area”.

Examples of state variables

• Ocean– Temperature

– Salinity

– Pressure

– Current velocity

• Atmosphere– Temperature

– Density

– Humidity

– Cloud water content

– Pressure

– Wind velocity

Fundamental equations• Conservation of momentum

(horizontal) velocity (winds, currents)• Conservation of mass (“principle of continuity”)

vertical velocity, humidity, salinity• Conservation of energy (“first law of

thermodynamics”)temperature

• Equation of statedensity (air, sea water)

Parameterization in climate models

• Sub-gridscale processes, or processes that cannot be derived from „first principles“, must be parameterized– e.g. thundercloud formation, soil moisture

transfer in the atmosphere, eddies and convection in the ocean

Discretization

Most common in ocean models:

• “Finite difference” method in time

• “Finite difference” or “finite volume” method in space