The Atmosphere and Climate Modeling - Introduction to Carbon Capture and Sequestration - page 77

Section 5
Climate models
The physics of the climate
The fundamental principles employed in modeling the earth's climate are
well known. Climate models are based on the three fundamental princi-
ples that follow from Newton's laws: conservation of mass, conservation
of energy, and conservation of momentum. If we consider the fl ow of
material in and out a control volume, we can write a “mass balance,”
which tells us that we will accumulate mass if more material comes in
than goes out. Similar balances can be written for energy and momen-
tum. The resulting equations are commonly referred to as the Navier-
Stokes equations. Solving the Navier-Stokes equations analytically is
only possible for a very limited set of simple problems. Numerical solu-
tions to these equations are necessary for “real-world” problems.
Obtaining these numerical solutions is so sophisticated that it is a special
fi eld of science — “Computational Fluid Dynamics.” This fi eld of research
has benefi tted enormously from the extraordinary advances in computer
power and software in the past 20 years.
The number of applications of Computational Fluid Dynamics is
large. For example, if we would like to mathematically model the differ-
ences between toothpaste and water fl owing through a pipe, we need to
solve the Navier-Stokes equations parameterized with the properties of
water and toothpaste. This fi eld has had some remarkable successes.
For example, virtually all modern airplanes are completely designed on a
computer. The predictions from solutions to the Navier-Stokes equations
accurately provide the details of air fl ow around the wing of a commercial
airliner! Such details afford the design of new aircraft that are even more
safe than their predecessors. These same equations are used to forecast
the weather and to predict the climate.
At this point we would like to emphasize that, although the underlying
physics of the fl ow around an airplane and the fl ow of the atmosphere is
the same, the differences in size and complexity create enormous scien-
tifi c challenges. We would like to highlight these challenges with a short
historical perspective of the different climate models.