be disappointing, since the forcing is ‘barely’ adequate to
simulate the desired objective i.e. an accumulation of
perennial snow on continents at high northern latitudes. The
modeling strategy is then to start at 115 ka BP, when the
astronomical forcing seems most favorable, to maximize
the response of the system. Since it is difficult to modify all
the boundary conditions of the model in a coherent way so
that it aligns with the situation that existed 115 ka BP ago,
the best approach is often to maintain conditions close to
the control situation, the ‘current’ state, or rather the
‘pre-industrial’ state, such as sea level and greenhouse gases.
Often, when modelers talk about experimenting with entry
into glaciation using OAGCMs, this is in fact a simulation
with the same boundary conditions and forcings as for the
pre-industrial period except for the insolation, which is
changed to correspond to the astronomical forcing of 115 ka
BP ago. The objective is not to make an ice cap ‘grow’
(which would require a comprehensive ice cap model and
thousands of years of integration) but simply to check that
when insolation is modified, snow may accumulate in certain
locations. There is only a very distant connection between
this and the available paleoclimate observations, and therefore comparison with the data is not easy since the conditions imposed on the numerical experiment are idealized.
In general, models can only represent a small part of the
global climate system with the other parts being imposed or
ideally represented. Although their aim is to describe certain
aspects of the problem in the most realistic way possible,
they cannot claim to be exhaustive. Before embarking on
any modeling exercise, it is essential to formulate a precise
hypothesis corresponding to the selected configuration.
Taking the example above of entry into glaciation, it is not
possible to ‘simulate the start of an ice age’ in all of its
aspects. However, some questions can be formulated and an
attempt made to answer them. For example, for a general
atmospheric circulation model: ‘Taking a control situation
i.e. a pre-industrial climate as a starting point, does simply
changing the radiative forcing at the top of the atmosphere
without changing ocean surface temperatures (which would
require an ocean model), or vegetation (requiring a vegetation model), or the expansion of the ice sheet (requiring an
ice sheet model), or anything else, bring about persistent
snow cover in some northern regions?’ Formulated in this
way, it is easier to understand the gap between this and a
broad-ranging simulation of a glacial inception. More comprehensive models can answer more general questions, but
there is no ‘all-encompassing’ model. It is therefore important to correctly define the hypothesis to be tested, and to
choose the relevant model configurations to do this.
The following sections describe the major families of
climate models, from the most complex to the conceptual.
Each section gives examples of the application of these
models to paleoclimate questions.
General Circulation Models, Complex Models
of the Earth System
Equations, Discretization and Parametrization:
Example of Atmospheric General Circulation
Models
A natural approach to simulate the characteristics of the
Earth’s climate is to look at the basic equations describing
the behavior of the atmosphere and the ocean. First, we will
describe how atmospheric general circulation models
(AGCM) are constructed in order to represent the evolution
of atmospheric characteristics (temperatures, winds, precipitation, etc.) on a global scale. We know (see Chap. 1) that
at this scale, the atmospheric circulation is driven by the
differential in insolation between the equator and the poles.
The fundamental equations are therefore energy conservation, supplemented by mass conservation (of air and water),
momentum conservation and the law of perfect gases.
Conservation of energy:
DI=Dt ¼ Àp Dq
À1
=Dt
À
Á þ Q
ð25:2Þ
where
I is the internal energy per unit of mass (I = c p T, c p being the
specific heat of air at constant pressure), p is the pressure,
q is the density of the atmosphere,
Q is the heating rate of the atmosphere per unit of mass,
D/Dt is the Lagrangian (Material) derivative: D=Dt ¼
À
@
@t þ u
@
@x þ v
@
@y þ w
@
@z
u, v, w being the wind components with the dimensions
x (longitude), y (latitude) and z (altitude).
Conservation of momentum:
Dv
Dt
¼ À2X Â vÀ
1
q
grad p
ð Þ þ g þ F
ð25:3Þ
where
v = (u, v, w) is the velocity of the wind relative to the surface
of the Earth,
X is the rotational angular velocity of the Earth,
p is the atmospheric pressure,
g is the acceleration due to gravity,
F is the force exerted per unit of mass.
Conservation of mass (of air and water):
Dq
Dt
¼ q À div v
ð Þ þ C À E
ð25:4Þ
where C is the creation rate of the species under consideration, and E is its destruction rate.
25 Modeling and Paleoclimatology
325
simulate the desired objective i.e. an accumulation of
perennial snow on continents at high northern latitudes. The
modeling strategy is then to start at 115 ka BP, when the
astronomical forcing seems most favorable, to maximize
the response of the system. Since it is difficult to modify all
the boundary conditions of the model in a coherent way so
that it aligns with the situation that existed 115 ka BP ago,
the best approach is often to maintain conditions close to
the control situation, the ‘current’ state, or rather the
‘pre-industrial’ state, such as sea level and greenhouse gases.
Often, when modelers talk about experimenting with entry
into glaciation using OAGCMs, this is in fact a simulation
with the same boundary conditions and forcings as for the
pre-industrial period except for the insolation, which is
changed to correspond to the astronomical forcing of 115 ka
BP ago. The objective is not to make an ice cap ‘grow’
(which would require a comprehensive ice cap model and
thousands of years of integration) but simply to check that
when insolation is modified, snow may accumulate in certain
locations. There is only a very distant connection between
this and the available paleoclimate observations, and therefore comparison with the data is not easy since the conditions imposed on the numerical experiment are idealized.
In general, models can only represent a small part of the
global climate system with the other parts being imposed or
ideally represented. Although their aim is to describe certain
aspects of the problem in the most realistic way possible,
they cannot claim to be exhaustive. Before embarking on
any modeling exercise, it is essential to formulate a precise
hypothesis corresponding to the selected configuration.
Taking the example above of entry into glaciation, it is not
possible to ‘simulate the start of an ice age’ in all of its
aspects. However, some questions can be formulated and an
attempt made to answer them. For example, for a general
atmospheric circulation model: ‘Taking a control situation
i.e. a pre-industrial climate as a starting point, does simply
changing the radiative forcing at the top of the atmosphere
without changing ocean surface temperatures (which would
require an ocean model), or vegetation (requiring a vegetation model), or the expansion of the ice sheet (requiring an
ice sheet model), or anything else, bring about persistent
snow cover in some northern regions?’ Formulated in this
way, it is easier to understand the gap between this and a
broad-ranging simulation of a glacial inception. More comprehensive models can answer more general questions, but
there is no ‘all-encompassing’ model. It is therefore important to correctly define the hypothesis to be tested, and to
choose the relevant model configurations to do this.
The following sections describe the major families of
climate models, from the most complex to the conceptual.
Each section gives examples of the application of these
models to paleoclimate questions.
General Circulation Models, Complex Models
of the Earth System
Equations, Discretization and Parametrization:
Example of Atmospheric General Circulation
Models
A natural approach to simulate the characteristics of the
Earth’s climate is to look at the basic equations describing
the behavior of the atmosphere and the ocean. First, we will
describe how atmospheric general circulation models
(AGCM) are constructed in order to represent the evolution
of atmospheric characteristics (temperatures, winds, precipitation, etc.) on a global scale. We know (see Chap. 1) that
at this scale, the atmospheric circulation is driven by the
differential in insolation between the equator and the poles.
The fundamental equations are therefore energy conservation, supplemented by mass conservation (of air and water),
momentum conservation and the law of perfect gases.
Conservation of energy:
DI=Dt ¼ Àp Dq
À1
=Dt
À
Á þ Q
ð25:2Þ
where
I is the internal energy per unit of mass (I = c p T, c p being the
specific heat of air at constant pressure), p is the pressure,
q is the density of the atmosphere,
Q is the heating rate of the atmosphere per unit of mass,
D/Dt is the Lagrangian (Material) derivative: D=Dt ¼
À
@
@t þ u
@
@x þ v
@
@y þ w
@
@z
u, v, w being the wind components with the dimensions
x (longitude), y (latitude) and z (altitude).
Conservation of momentum:
Dv
Dt
¼ À2X Â vÀ
1
q
grad p
ð Þ þ g þ F
ð25:3Þ
where
v = (u, v, w) is the velocity of the wind relative to the surface
of the Earth,
X is the rotational angular velocity of the Earth,
p is the atmospheric pressure,
g is the acceleration due to gravity,
F is the force exerted per unit of mass.
Conservation of mass (of air and water):
Dq
Dt
¼ q À div v
ð Þ þ C À E
ð25:4Þ
where C is the creation rate of the species under consideration, and E is its destruction rate.
25 Modeling and Paleoclimatology
325