S-shapedness for energy balance climate models of
Sellers-Type
Georg Hetzer
Department of Mathematics
Auburn University, AL 36830,
USA
1. Introduction.
Climate models are distinguished by the relative importance they attach to the different components and processes of the climate system. One finds the so-called energy
balance climate models at the bottom on a scale of models of increasing complexity, and
coupled general circulation models of atmosphere and oceans at the top on that scale.
General circulation models are based on first principles of physics (conservation of
energy, momentum and mass) and are intended to simulate the atmospheric or oceanic
motion as well as the transport of energy and mass. They lead to very large, complex
systems of partial differential equations, which have been the subject of quite intensive
computational efforts by several groups of climate modelers (d. [Washington/Parkinson
(1986)] for further references). Only recently, J .L. Lions, R. Temam and S. Wang ([Wang
(1990/91, 1992a,b), Lions/Teman/Wang (1992a,b,c)]) have started to focus systematically on the mathematical foundations of such systems, and they have dealt with the
well-posedness and certain dynamical aspects (such as the existence of an attractor or
an approximate inertial manifold).
Despite of all this progress, there is still a need for simple phenomenological settings, and energy balance models surely belong in that category. They account only for
the most fundamental processes of the climate system, the radiation streams and the
equator-to-pole energy transports, and even these are incorporated in a rather crude
heuristical way. Nevertheless, Henderson-Sellers and McGuffie have rightfully pointed
out in their primer on climate modeling [Henderson-Sellers/McGuffie (1987)] that "these
NATO ASI Series. Vol. 148
The Mathematics of Models for Climato'ogy
and Environment
Edited by Jesus I1defonso Diaz
© Springer·Verlag Berlin Heidelberg 1997
Sellers-Type
Georg Hetzer
Department of Mathematics
Auburn University, AL 36830,
USA
1. Introduction.
Climate models are distinguished by the relative importance they attach to the different components and processes of the climate system. One finds the so-called energy
balance climate models at the bottom on a scale of models of increasing complexity, and
coupled general circulation models of atmosphere and oceans at the top on that scale.
General circulation models are based on first principles of physics (conservation of
energy, momentum and mass) and are intended to simulate the atmospheric or oceanic
motion as well as the transport of energy and mass. They lead to very large, complex
systems of partial differential equations, which have been the subject of quite intensive
computational efforts by several groups of climate modelers (d. [Washington/Parkinson
(1986)] for further references). Only recently, J .L. Lions, R. Temam and S. Wang ([Wang
(1990/91, 1992a,b), Lions/Teman/Wang (1992a,b,c)]) have started to focus systematically on the mathematical foundations of such systems, and they have dealt with the
well-posedness and certain dynamical aspects (such as the existence of an attractor or
an approximate inertial manifold).
Despite of all this progress, there is still a need for simple phenomenological settings, and energy balance models surely belong in that category. They account only for
the most fundamental processes of the climate system, the radiation streams and the
equator-to-pole energy transports, and even these are incorporated in a rather crude
heuristical way. Nevertheless, Henderson-Sellers and McGuffie have rightfully pointed
out in their primer on climate modeling [Henderson-Sellers/McGuffie (1987)] that "these
NATO ASI Series. Vol. 148
The Mathematics of Models for Climato'ogy
and Environment
Edited by Jesus I1defonso Diaz
© Springer·Verlag Berlin Heidelberg 1997