|Lecture 9 Notes October 14, 2004
Energy Balance Climate Model
Time rate of change of stored energy (depends on
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.
Net Radiative Flux (Fin - Fout) +
Northward Heat Flux Convergence +
Heat Flux from Land to Sea along latitude
|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%.