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models have been instrumental in increasing our understanding of the climate system
and in the development of new parameterizations and methods of evaluating sensitivity
for more complex and realistic models" .
The central idea is that the solar radiation input is completely compensated in the
long run by the earth's radiation output. Since temperature is, roughly speaking, (e.g.
via the Stefan-Boltzmann law) linked to the energy, it should be possible to compute
the evolution of long term means from the energy balance. First models of this type
were proposed by Budyko ([Budyko (1969)]) and Sellers [Sellers (1969)]' and we refer
to [Ghil/Childress (1987), North et al. (1981), Henderson-Sellers/McGuffie (1987)] for
expository presentations as well as further literature.
The dominating feedback mechanism in an energy balance model is the ice-albedo
effect, which is of destablizing nature. Very roughly, expanding ice-sheets lead to a
higher reflectivity, which lowers the planetary absorption and consequently temperature
decreases, hence the ice and snow formation will be enhanced. Similarly, retreating icesheets allow a higher absorption of solar energy, which induces further melting of ice
and snow due to an increase in temperature. It is therefore of major interest, how the
(model) system responds to changes in the incoming solar radiation flux, a question,
which is usually addressed by introducing a nonnegative parameter, the so-called solar
constant.
Most energy balance models assume a direct linkage between albedo and temperature, which is questionable considering the long response times of the huge continental
ice-sheets. As a result, these models exhibit on the one hand, too high a sensitivity
with respect to changes in the solar radiation, as far as the transition to a deep freeze
climate is concerned, but on the other hand they are nevertheless not capable to reproduce the glacial/interglacial cycles. Therefore, there have been occasional attempts
[Bhattacharya et al. (1982), Hetzer/Schmidt (1995), Hetzer (1995)] to overcome this
difficulty by linking the albedo to a weighted temperature, which takes the temperature
history over, say, ten thousand years into account. Of course, the heat storage term of
the system is also directly affected by the amount of ice-formation, and so one should
employ the same approach for that term.
One can distinguish energy balance models by the choice of the albedo function.
Budyko-type models employ a step-function that has one discontinuity at the so-called
models have been instrumental in increasing our understanding of the climate system
and in the development of new parameterizations and methods of evaluating sensitivity
for more complex and realistic models" .
The central idea is that the solar radiation input is completely compensated in the
long run by the earth's radiation output. Since temperature is, roughly speaking, (e.g.
via the Stefan-Boltzmann law) linked to the energy, it should be possible to compute
the evolution of long term means from the energy balance. First models of this type
were proposed by Budyko ([Budyko (1969)]) and Sellers [Sellers (1969)]' and we refer
to [Ghil/Childress (1987), North et al. (1981), Henderson-Sellers/McGuffie (1987)] for
expository presentations as well as further literature.
The dominating feedback mechanism in an energy balance model is the ice-albedo
effect, which is of destablizing nature. Very roughly, expanding ice-sheets lead to a
higher reflectivity, which lowers the planetary absorption and consequently temperature
decreases, hence the ice and snow formation will be enhanced. Similarly, retreating icesheets allow a higher absorption of solar energy, which induces further melting of ice
and snow due to an increase in temperature. It is therefore of major interest, how the
(model) system responds to changes in the incoming solar radiation flux, a question,
which is usually addressed by introducing a nonnegative parameter, the so-called solar
constant.
Most energy balance models assume a direct linkage between albedo and temperature, which is questionable considering the long response times of the huge continental
ice-sheets. As a result, these models exhibit on the one hand, too high a sensitivity
with respect to changes in the solar radiation, as far as the transition to a deep freeze
climate is concerned, but on the other hand they are nevertheless not capable to reproduce the glacial/interglacial cycles. Therefore, there have been occasional attempts
[Bhattacharya et al. (1982), Hetzer/Schmidt (1995), Hetzer (1995)] to overcome this
difficulty by linking the albedo to a weighted temperature, which takes the temperature
history over, say, ten thousand years into account. Of course, the heat storage term of
the system is also directly affected by the amount of ice-formation, and so one should
employ the same approach for that term.
One can distinguish energy balance models by the choice of the albedo function.
Budyko-type models employ a step-function that has one discontinuity at the so-called