Lecture 9 Notes  October 14, 2004

Energy Balance Climate Model

Time rate of change of stored energy (depends on inertia) = 
    Net Radiative Flux (Fin - Fout) +
    Northward Heat Flux Convergence +
    Heat Flux from Land to Sea along latitude

The models solves this equation for land and ocean temperature at each latitude. The first line in the equation is zero when the climate is at an equilibrium. The model includes the greenhouse effect in the way it computes the outgoing longwave radiation, it specified albedo uniquely for land, ocean and ice/snow covered surfaces.
land distrirbution
On the left is the geometry for the model. There is a fraction of land and ocean at each latitude. The model can be thought of as computing the temperature over land and ocean separately, except that the two media are then coupled by the heat flux along latitudes from land to sea or vice versa.  The rate of heat exchange between land and ocean is weighted by the land/ocean fraction, so that a small ocean fraction can only have a small influence on the adjacent land.

The north-south and land-ocean heat transports are both computed from temperature gradients. This is an oversimplifciation of the real world and is called a parameterization by modelers. Heat moves from warm to cold places.

The ocean depth is just 30 m so the timescale for the climate to adjust to a new equilibrium is 10-20 yrs. Sea ice grows over the ocean when the ocean temperature tries to drop below freezing. Also there is a parameterizations that accounts for snow on land. The model simply adjusts its surface albedo when the land temperature drops below freezing, as if it has snow cover.

The land/ocean distribution and the incoming solar radiation (abbreviated insolation) are inputs to the model.

The model does not have clouds or circulation

You can run this model with a web interface at

The next three collections of figures are from the class exercisese. First is the control or modern day climate. Next is the future climate subject to an increase in greenhouse gas concentrations equivalent to altering the net radiative flux by 2 W/m2. Finally the third is for a climate 500 million years ago where the land/ocean distribution is different and the solar constant is reduced by 3%.
500 million bp
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Contact the instructor at: atms211@atmos.washington.edu

Last Updated: 9/29/2004