On the mathematical treatment of energy balance
climate models
Jesus Ildefonso Dfaz
Departamento de Matematica Aplicada
Universidad Complutense de Madrid
28040 Madrid
SPAIN
1. Introduction.
Climate models have different characteristics than weather prediction models: the
time scale is completely different (centuries versus days or weaks) and their main goal is
also complementary (prognostic in the weather prediction and diagnostic in the case of
climate models). Climate models were introduced in order to understand past and future
climates and their sensitivity on a few of relevant features (which a quantitative analysis
reduces to some parameters).
Two of the most important ingredients of the models concern the Solar radiation Ra
(short-wave energy from Sun) and the Earth radiation Re (long-wave radiation escaping
into space). The consideration of other features under different degree of accuracy introduces a hierarchy in the class of climate models. So, according to the time variable
the models are classified into equilibrium and dynamical models. With respect to the
space variable the models are called as O-D zero-dimensional (if only the mean Earth
temperature is analized), 1-D latitudinal or vertical models, 2-D horizontal or meridional
plane models and so up the most sophisticated 3-D General Circulation model. More
complex models have been also considered in the literature by coupling the study of the
Earth temperature with different phenomena from the Glaceology, Celestial Mechanics,
Geophysics, etc. (see the monographs of Ghill and Childress [1987], North [1993] and
Henderson-Sellers and Mc Guffie [1987]).
In this work we shall pay attention to the mathematical treatement of some horizontal
energy balance models generalizing the models introduced (independently) by Budyko
[1969] and Sellers [1969].
NATO ASI Series. Vol. 148
The Mathematics of Models for Climatology
and Environment
Edited by Jesus Ildefonso Of.z
© Springer-Verlag Berlin Heidelberg 1997
climate models
Jesus Ildefonso Dfaz
Departamento de Matematica Aplicada
Universidad Complutense de Madrid
28040 Madrid
SPAIN
1. Introduction.
Climate models have different characteristics than weather prediction models: the
time scale is completely different (centuries versus days or weaks) and their main goal is
also complementary (prognostic in the weather prediction and diagnostic in the case of
climate models). Climate models were introduced in order to understand past and future
climates and their sensitivity on a few of relevant features (which a quantitative analysis
reduces to some parameters).
Two of the most important ingredients of the models concern the Solar radiation Ra
(short-wave energy from Sun) and the Earth radiation Re (long-wave radiation escaping
into space). The consideration of other features under different degree of accuracy introduces a hierarchy in the class of climate models. So, according to the time variable
the models are classified into equilibrium and dynamical models. With respect to the
space variable the models are called as O-D zero-dimensional (if only the mean Earth
temperature is analized), 1-D latitudinal or vertical models, 2-D horizontal or meridional
plane models and so up the most sophisticated 3-D General Circulation model. More
complex models have been also considered in the literature by coupling the study of the
Earth temperature with different phenomena from the Glaceology, Celestial Mechanics,
Geophysics, etc. (see the monographs of Ghill and Childress [1987], North [1993] and
Henderson-Sellers and Mc Guffie [1987]).
In this work we shall pay attention to the mathematical treatement of some horizontal
energy balance models generalizing the models introduced (independently) by Budyko
[1969] and Sellers [1969].
NATO ASI Series. Vol. 148
The Mathematics of Models for Climatology
and Environment
Edited by Jesus Ildefonso Of.z
© Springer-Verlag Berlin Heidelberg 1997