Climate, mathematics, and the Canary Islands
Jose M. Pacheco* and N. Hayek**
* Departamento de Matematicas
Universidad de Las Palmas de Gran Canaria
Campus de Tafira Baja
35017 Las Palmas, Spain
** Universidad de La Laguna I Academia Canaria de Ciencias.
La Laguna (Tenerife), Spain
O. Introduction.
It is difficult to provide a simple definition of climate. A vague idea, matching the
intuitive notion of the layman, is the following: Climate is an average state of the
atmospheric weather. Such a definition must be made precise enough in order to establish the
ranges of spatial and temporal variability involved in it for a scientific study of the problem
(Figure 1).
Four main concepts are taken into account in order to understand what climate is:
a) A notion of temporal durability. Thus, climate can be considered as some expected and
characteristic feature of the spatial domains under consideration. Therefore, climate modelling
has in some sense a more diagnostic character than weather studies, where prognostic features
are predominant.
b) The just cited spatial domains are defined, as a rule, in a loose way; so boundary conditions
incorporated in models are difficult to define and to formulate. The mathematical framework
is that of free boundary problems. Land topography must be included among the limiting
conditions in climatic studies.
c) The mathematical description of climate is achieved through the analysis of some
dynamical spatio-temporal equilibrium in the values of the climatic variables.
d) A statistical interpretation of the three above points: This is the basis of any climatic
classification.
Perturbations in the perception of any of these four concepts is generically known as
climate change, and thus introduces a general philosophy on how to perform climate change
experiments.
Global climate and climate change modelling has such a degree of complexity that the
task lies beyond the limits of today's Mathematics and Computer Science (Lions,1991).
Therefore, partial approaches are needed, focusing mainly on the following points:
a) To identify and to understand in depth the various physical processes involved between the
different fluid envelopes of the Earth (Feistel, 1993). These include not only the atmosphere,
but also the world ocean and ice caps, as well as their vertical stratifications.
b) Adequate mathematical modelling for the physical processes, depending on the underlying
physics and the appropriate scaling of the phenomena under consideration (Giorgi, 1995; Liu
and Yang, 1994; Lorenz, 1969; North, 1993; Vannitsem and Nicolis, 1994).
NATO AS) Series, Vol.) 48
The Mathematics of Models for Climatology
and Environment
Edited by Jesus Ildefonso Diaz
© Springer-Verlag Berlin H~ide)berg 1997
Jose M. Pacheco* and N. Hayek**
* Departamento de Matematicas
Universidad de Las Palmas de Gran Canaria
Campus de Tafira Baja
35017 Las Palmas, Spain
** Universidad de La Laguna I Academia Canaria de Ciencias.
La Laguna (Tenerife), Spain
O. Introduction.
It is difficult to provide a simple definition of climate. A vague idea, matching the
intuitive notion of the layman, is the following: Climate is an average state of the
atmospheric weather. Such a definition must be made precise enough in order to establish the
ranges of spatial and temporal variability involved in it for a scientific study of the problem
(Figure 1).
Four main concepts are taken into account in order to understand what climate is:
a) A notion of temporal durability. Thus, climate can be considered as some expected and
characteristic feature of the spatial domains under consideration. Therefore, climate modelling
has in some sense a more diagnostic character than weather studies, where prognostic features
are predominant.
b) The just cited spatial domains are defined, as a rule, in a loose way; so boundary conditions
incorporated in models are difficult to define and to formulate. The mathematical framework
is that of free boundary problems. Land topography must be included among the limiting
conditions in climatic studies.
c) The mathematical description of climate is achieved through the analysis of some
dynamical spatio-temporal equilibrium in the values of the climatic variables.
d) A statistical interpretation of the three above points: This is the basis of any climatic
classification.
Perturbations in the perception of any of these four concepts is generically known as
climate change, and thus introduces a general philosophy on how to perform climate change
experiments.
Global climate and climate change modelling has such a degree of complexity that the
task lies beyond the limits of today's Mathematics and Computer Science (Lions,1991).
Therefore, partial approaches are needed, focusing mainly on the following points:
a) To identify and to understand in depth the various physical processes involved between the
different fluid envelopes of the Earth (Feistel, 1993). These include not only the atmosphere,
but also the world ocean and ice caps, as well as their vertical stratifications.
b) Adequate mathematical modelling for the physical processes, depending on the underlying
physics and the appropriate scaling of the phenomena under consideration (Giorgi, 1995; Liu
and Yang, 1994; Lorenz, 1969; North, 1993; Vannitsem and Nicolis, 1994).
NATO AS) Series, Vol.) 48
The Mathematics of Models for Climatology
and Environment
Edited by Jesus Ildefonso Diaz
© Springer-Verlag Berlin H~ide)berg 1997