410
c) Development of new mathematical and computational techniques, not only in the field of
numerical analysis, but also in the realm of data acquisition and treatment. This includes not
only new statistical tools: Expert system modelling is also an emerging alternative (Cheeseman
and Oldford, 1994). Stochastic modelling is also coming into age with interesting applications
to climate science (Wiesenfeld and Moss, 1995).
First of all, a physical definition of climate will be presented. Later on, problems in the
mathematical description will be considered (Haltiner 1970, Pedlosky 1987).
Physically speaking, climate can be defined as some spatio-temporal average of the
energy budget determined by the global mechanisms that transport, distribute and store the
incoming Solar energy. Therefore, the "natural" approach to climate modelling is to formulate
the so-called "energy balance models" (EBM) (Budyko, 1969; Sellers, 1969). The contribution
of vulcanism has sensible effects on certain observation scales in this budget. Moreover,
anthrapiceffects must be taken into account, for man-made energy manipulation can easily
interfere with the natural cycles (Herring and Hobbs, 1994). As a consequence, the idea of
control must be seriously incorporated in climatic studies.
Climate modelling is achieved though the selection of some descriptors, usually called
state variables. These are macroscopic quantities whose evolution in time and space is observed
from a theoretical viewpoint. A catalogue of these variables follows:
a) In the case of short and medium range studies, air temperature, sea surface temperature
(SST), water vapor in the atmosphere and salinity of the sea water, as well as C02 and ~
concentrations, are the most usual state variables in addition to wind, marine current and
pressure fields. In this case climate modelling is best achieved though some variations of
general circulation models (GCM). Tradition in climatic studies analyzes their evolution in 30year long cycles, though the tendency exists to consider shorter time intervals, even to the limit
of deterministic weather prediction, in order to include sharper and finer variations in the realm
of climate science.
b) In the case of long range studies, as is the case of paleoclimatic ones, the following are more
adequate variables: Temperature at the thermocline bottom and various traces of dissolved or
trapped gases (e.g. the ratio [018]/[016])in ice records. This is a consequence of some
considerations to be made later on.
The evolution of the state variable values is described by the set of physical laws they
obey to (Bjerknes, 1904). The mathematization of these laws is often difficult to separate from
their formulation itself (Hal tiner, 1970). In any case, three sets a/problems are found:
a) The choice of the right Mathematics and the formulation of basic results. Problems in this
group include existence and uniqueness results for various classes of equations, several types
of estimates reflecting the physical soundness of the hypotheses, etc. (Diaz and Lions, 1993).
b) Computational questions arise in a natural way, given the relative scarcity of analytic
solutions (Dfaz and Lions, 1993; Hernandez, Pacheco and Garcia, 1983a; Lions, 1991) for
most sets of equations as soon as a minimal complexity is reached. On the other hand,
computational power is increasing in such a way that some problems can be viewed in a
different way. As an example, rounding error analyses, with a 64-bit arithmetic could yield
place to problems of storage and data retrieval of large mathematical structures.
c) Spatial and temporal limits of the system and boundary conditions deduced from them.
A climatic study of the Canary Islands from the modelling point of view starts with the
difficulty of determining the system limits: The Archipelago lies in a very complicated interface
(Figure 2) between the A(~ores anticyclonic gyre dominating the Central Atlantic Ocean and the
huge continental mass of the Saharian Desert. The main observable features are: the cold
c) Development of new mathematical and computational techniques, not only in the field of
numerical analysis, but also in the realm of data acquisition and treatment. This includes not
only new statistical tools: Expert system modelling is also an emerging alternative (Cheeseman
and Oldford, 1994). Stochastic modelling is also coming into age with interesting applications
to climate science (Wiesenfeld and Moss, 1995).
First of all, a physical definition of climate will be presented. Later on, problems in the
mathematical description will be considered (Haltiner 1970, Pedlosky 1987).
Physically speaking, climate can be defined as some spatio-temporal average of the
energy budget determined by the global mechanisms that transport, distribute and store the
incoming Solar energy. Therefore, the "natural" approach to climate modelling is to formulate
the so-called "energy balance models" (EBM) (Budyko, 1969; Sellers, 1969). The contribution
of vulcanism has sensible effects on certain observation scales in this budget. Moreover,
anthrapiceffects must be taken into account, for man-made energy manipulation can easily
interfere with the natural cycles (Herring and Hobbs, 1994). As a consequence, the idea of
control must be seriously incorporated in climatic studies.
Climate modelling is achieved though the selection of some descriptors, usually called
state variables. These are macroscopic quantities whose evolution in time and space is observed
from a theoretical viewpoint. A catalogue of these variables follows:
a) In the case of short and medium range studies, air temperature, sea surface temperature
(SST), water vapor in the atmosphere and salinity of the sea water, as well as C02 and ~
concentrations, are the most usual state variables in addition to wind, marine current and
pressure fields. In this case climate modelling is best achieved though some variations of
general circulation models (GCM). Tradition in climatic studies analyzes their evolution in 30year long cycles, though the tendency exists to consider shorter time intervals, even to the limit
of deterministic weather prediction, in order to include sharper and finer variations in the realm
of climate science.
b) In the case of long range studies, as is the case of paleoclimatic ones, the following are more
adequate variables: Temperature at the thermocline bottom and various traces of dissolved or
trapped gases (e.g. the ratio [018]/[016])in ice records. This is a consequence of some
considerations to be made later on.
The evolution of the state variable values is described by the set of physical laws they
obey to (Bjerknes, 1904). The mathematization of these laws is often difficult to separate from
their formulation itself (Hal tiner, 1970). In any case, three sets a/problems are found:
a) The choice of the right Mathematics and the formulation of basic results. Problems in this
group include existence and uniqueness results for various classes of equations, several types
of estimates reflecting the physical soundness of the hypotheses, etc. (Diaz and Lions, 1993).
b) Computational questions arise in a natural way, given the relative scarcity of analytic
solutions (Dfaz and Lions, 1993; Hernandez, Pacheco and Garcia, 1983a; Lions, 1991) for
most sets of equations as soon as a minimal complexity is reached. On the other hand,
computational power is increasing in such a way that some problems can be viewed in a
different way. As an example, rounding error analyses, with a 64-bit arithmetic could yield
place to problems of storage and data retrieval of large mathematical structures.
c) Spatial and temporal limits of the system and boundary conditions deduced from them.
A climatic study of the Canary Islands from the modelling point of view starts with the
difficulty of determining the system limits: The Archipelago lies in a very complicated interface
(Figure 2) between the A(~ores anticyclonic gyre dominating the Central Atlantic Ocean and the
huge continental mass of the Saharian Desert. The main observable features are: the cold