simulate permanent snow cover using only a simple atmospheric model because of the absence of positive feedback
mechanisms. It can be seen here that while a simple evaluation can lead to a better understanding of the system, it is
also only the start of an extensive exploration of increasingly
complex models to find the one that best fits with the data.
Paleoclimate simulation is not only used to evaluate the
models used for climate predictions over the next century.
This would be an extremely narrow application, especially
given the time scales that can be handled by these models.
The starting point for the development of paleoclimate
modeling is the assumptions applied when interpreting the
data. A paleoclimate model seeks to formalize the assumptions based on the physical principles of the climate system
and to test whether these principles can explain the observed
climate variations. It is clear then that the models can be
extremely varied depending on the data they are trying to
interpret. Indeed, even though the components of the climate
system are all interdependent, which is a defining feature of
this system, it is not always necessary to represent them all
in detail in order to reproduce an observed phenomenon. In
fact, it is more interesting to isolate the processes or key
components responsible for a phenomenon. This is one of
the approaches to paleoclimate modeling which tries to build
a ‘minimal’ model to explain a phenomenon. This is very
different from the models used to predict the climate of the
next century, but these approaches are important to provide a
better understanding of the climate system and its evolution.
Modeling can also highlight the importance of a particular
forcing or process. By comparing experiments which include a
certain process or forcing with experiments which exclude it, it
is possible to study its impact and identify which mechanisms
explain this impact. These ‘sensitivity experiments’ are not
necessarily very realistic but they complement the more realistic simulations of paleoclimates, by helping to better understand them. One example, in Section “General Circulation
Models, Complex Models of the Earth System”, an attempt is
made to understand the impact of ice caps versus the impact of a
lower atmospheric CO 2 concentration on the climate of the Last
Glacial Maximum (LGM). In order to understand this, simulations are created where the ice caps of the LGM are placed in
the context of the current CO 2 concentration, and also where the
CO 2 concentration of the LGM is positioned with the current
ice caps. Although these simulations do not correspond to real
situations, they provide a better understanding of the simulated
glacial climate by imposing both ice cap and CO 2 concentration
forcings from the LGM.
This chapter starts by presenting the basic concepts of
modeling, definitions essential to our understanding of
models and the digital experiments used in climatology and
paleoclimatology. We then focus on the three main families
of paleoclimate models: the most complex general circulation models, climate models of intermediate complexity, and
conceptual models. For each of these families of models, we
give examples of their use in paleoclimatology.
Some Basic Modeling Concepts
Vocabulary
Before showing how climate modeling contributes to the
study of past climates, it is useful to define the concept of a
model. Indeed, this word has quite different meanings in the
various scientific disciplines. In general, a ‘model’ is a
representation of a set of scientific ideas, formulated within
as rigorous a framework as possible, which explains a
complete set of phenomena. The model is judged to be even
more effective when it is simple and concise, and when it
offers a maximum number of solutions. It becomes quantitative when it is based on mathematical relationships. When
we talk about climate modeling, we mean ‘physical’ models
of the climate system incorporating a set of mathematical
equations that trace the evolution of the system from a
starting position within boundary conditions. It is therefore a
system of first-order differential equations, which can generally be written in the following form:
dX t
ð Þ
dt
¼ f X t
ð Þ; t
ð
Þ
ð25:1Þ
where X(t) is a vector dimension N which provides an
overall description of the state of the model at each instant t,
and f(X, t) is a function of X and of time t which describes
the evolution of the system. The dimension N of the vector X
(t) thus represents the ‘size’ of the model, which is sometimes called the ‘number of degrees of freedom’ of the
system, and the space of dimension N of all the vectors X is
called ‘the phase space’. If the state of the system is known
at a given instant t 0 , denoted by X 0 = X(t 0 ) and called the
‘initial condition’, then Eq. (25.1) makes it possible to know
the state of the system at all times.
When referring to a climate model, we may imagine a
very ‘complex’ system, with a large number of degrees of
freedom. This is often the case, but not always. Indeed, it is
important to highlight two contradictory aspects of climate
modeling. On the one hand, modeling aims to improve our
understanding of how the system functions, and on the other
hand, it is trying to provide the best possible representation
of it. In order to explore and understand what is happening
within a system of equations, it is preferable that the number
of degrees of freedom N be small. Conversely, to achieve a
good representation of a system as complex as the climate,
the number of degrees of freedom N needs to be large and
will be limited only by computing power. Although both of
these qualify as modeling, the second case is more
320
M. Kageyama and D. Paillard
mechanisms. It can be seen here that while a simple evaluation can lead to a better understanding of the system, it is
also only the start of an extensive exploration of increasingly
complex models to find the one that best fits with the data.
Paleoclimate simulation is not only used to evaluate the
models used for climate predictions over the next century.
This would be an extremely narrow application, especially
given the time scales that can be handled by these models.
The starting point for the development of paleoclimate
modeling is the assumptions applied when interpreting the
data. A paleoclimate model seeks to formalize the assumptions based on the physical principles of the climate system
and to test whether these principles can explain the observed
climate variations. It is clear then that the models can be
extremely varied depending on the data they are trying to
interpret. Indeed, even though the components of the climate
system are all interdependent, which is a defining feature of
this system, it is not always necessary to represent them all
in detail in order to reproduce an observed phenomenon. In
fact, it is more interesting to isolate the processes or key
components responsible for a phenomenon. This is one of
the approaches to paleoclimate modeling which tries to build
a ‘minimal’ model to explain a phenomenon. This is very
different from the models used to predict the climate of the
next century, but these approaches are important to provide a
better understanding of the climate system and its evolution.
Modeling can also highlight the importance of a particular
forcing or process. By comparing experiments which include a
certain process or forcing with experiments which exclude it, it
is possible to study its impact and identify which mechanisms
explain this impact. These ‘sensitivity experiments’ are not
necessarily very realistic but they complement the more realistic simulations of paleoclimates, by helping to better understand them. One example, in Section “General Circulation
Models, Complex Models of the Earth System”, an attempt is
made to understand the impact of ice caps versus the impact of a
lower atmospheric CO 2 concentration on the climate of the Last
Glacial Maximum (LGM). In order to understand this, simulations are created where the ice caps of the LGM are placed in
the context of the current CO 2 concentration, and also where the
CO 2 concentration of the LGM is positioned with the current
ice caps. Although these simulations do not correspond to real
situations, they provide a better understanding of the simulated
glacial climate by imposing both ice cap and CO 2 concentration
forcings from the LGM.
This chapter starts by presenting the basic concepts of
modeling, definitions essential to our understanding of
models and the digital experiments used in climatology and
paleoclimatology. We then focus on the three main families
of paleoclimate models: the most complex general circulation models, climate models of intermediate complexity, and
conceptual models. For each of these families of models, we
give examples of their use in paleoclimatology.
Some Basic Modeling Concepts
Vocabulary
Before showing how climate modeling contributes to the
study of past climates, it is useful to define the concept of a
model. Indeed, this word has quite different meanings in the
various scientific disciplines. In general, a ‘model’ is a
representation of a set of scientific ideas, formulated within
as rigorous a framework as possible, which explains a
complete set of phenomena. The model is judged to be even
more effective when it is simple and concise, and when it
offers a maximum number of solutions. It becomes quantitative when it is based on mathematical relationships. When
we talk about climate modeling, we mean ‘physical’ models
of the climate system incorporating a set of mathematical
equations that trace the evolution of the system from a
starting position within boundary conditions. It is therefore a
system of first-order differential equations, which can generally be written in the following form:
dX t
ð Þ
dt
¼ f X t
ð Þ; t
ð
Þ
ð25:1Þ
where X(t) is a vector dimension N which provides an
overall description of the state of the model at each instant t,
and f(X, t) is a function of X and of time t which describes
the evolution of the system. The dimension N of the vector X
(t) thus represents the ‘size’ of the model, which is sometimes called the ‘number of degrees of freedom’ of the
system, and the space of dimension N of all the vectors X is
called ‘the phase space’. If the state of the system is known
at a given instant t 0 , denoted by X 0 = X(t 0 ) and called the
‘initial condition’, then Eq. (25.1) makes it possible to know
the state of the system at all times.
When referring to a climate model, we may imagine a
very ‘complex’ system, with a large number of degrees of
freedom. This is often the case, but not always. Indeed, it is
important to highlight two contradictory aspects of climate
modeling. On the one hand, modeling aims to improve our
understanding of how the system functions, and on the other
hand, it is trying to provide the best possible representation
of it. In order to explore and understand what is happening
within a system of equations, it is preferable that the number
of degrees of freedom N be small. Conversely, to achieve a
good representation of a system as complex as the climate,
the number of degrees of freedom N needs to be large and
will be limited only by computing power. Although both of
these qualify as modeling, the second case is more
320
M. Kageyama and D. Paillard