CLIMATE MODELING
Jules Kouatchou
GWU - Department of Mathematics
NASA-GSFC : ESDCD
December 6, 1996
The weather is concerned with detailed instantaneous states
of the atmosphere and with the day-to-day evolution of
individual synoptic systems.
The climate is generally thought of as the average
weather or the average behavior of the land-ocean-atmosphere-cryosphere
system over some relatively long period of time; it is not
associated with the detailed sequence of daily fluctuations
we commonly refer to as "weather".
In fact the prediction of the climate is treated in the
same way as the prediction of the weather. While in
weather prediction, the concern is with predicting the
change in the weather, that is the actual temporal
evolution of the dependent parameters (temperature,
humidity, pressure, precipitations, clouds, etc.) climate
is concerned with the long term statistical properties
of the same quantities. We can speak of the climate of a
day-night cycle, month, season, year, decade, or even longer
period.
Joseph and Pharaoh
The story of Joseph and Pharaoh that happened around 1700 BC in Egypt
help us to understand why it is important to study the
climate.
One night, the king of Egypt had a dream. He dreamt that
he was standing by the River Nile, while seven fat cows
came up out of the river and began to feed on the grass.
Then seven other cows came up; they were thin and bony.
They came and stood by the other cows on the river bank, and
the thin cows ate up the fat cows.
In the morning, the king of Egypt was worried so he sent for all
the magicians and wise men of Egypt. He told them his
dream, but no one could explain it to him.
One of the servants of Pharaoh told him that there is a man
name Joseph, now in prison, that has the ability to interpret
dreams. The king sent for Joseph, and he was immediately
brought from prison. The king told Joseph his dream.
Joseph gave him the following interpretation. The seven
fat cows are seven years, years of good harvest. The seven
thin cows represent seven years of famine, no crop will
grow. Joseph continued by saying that there will be in
Egypt seven years of great plenty and after seven years
of famine.
After the words of Joseph, the king of Egypt took the
decision to appoint some officials that will be charge of
collecting and storing food during the seven good years
so that food will be a reserve supply for the country
during the seven years of famine.
Fom this simple story, we can learn that the climate was
predicted over a 14 year period. Since the prediction did
include a time of severe drought, necessary steps were
take to protect the population.
We can formulate the goal of climate study:
- to provide a reliable, verified forecasting of key
variables such as temperature and rain fall on a
regional, time-evolving basis
- in case of major events (drought, storm, etc.),
take appropriate measures
The climate is modulated by both extenal and internal
factors.
- External
- General factors
- solar radiation
- sphericity of the earth
- earth's motion around the sun and its rotation
- existence of continents and oceans
- Regional and local factors
- distance to the sea
- topography
- vegetation cover
- nature of the underlying surface
- proximity to lakes
- Internal
- Intrinsic properties of the atmosphere :
composition, various instabilities.
- General circulation
We can also add Human Activities as factors that influence
the climate. The influence on the climate due to human
activities becan with a prediction made by the Swedish
chemist, Svante Arrhenius, in 1896. Arrhenius took note
of the industrial revolution the getting underway and realized
that the amount of carbone dioxide being released into the
atmosphere aws increasing. His understanding of the
role carbone dioxide in heating the Earth, led him
to predict that if atmospheric carbone dioxide doubled, Earth
would become several degree warmer.
Among human activities, we can mention :
- Industrialization leads to release of CO2 in the
atmosphere. The direct consequence is the heating
of the Earth.
- Patterns of land use (urbanization, agriculture,
overgrazing, deforestration) changes surface albedo
evapotranspiration and runof and causes aerosols.
- Rapid growth of the world population
- Large-scale nuclear war : could lead to very large
injections of soot and dust causing transient
surface cooling lasting from weeks to months, depending
on the nature of the exchange and on how many fires
were started.
Problem :The actions of human are not
predictable in any deterministic sense.
So it difficult to include human factors in the study of
climate.
Requirement : Any Climate Model must
necessarily contain a so-called "what if" scenario. What if
the amount of CO2 released into the atmosphere doubles?
What if the tropical forest disappears? What if there is
an increase of volcano activities?
To find out how climate is studied, we need to know if
- it is possible to reproduce physically in a
laboratory the processes that make up the planet's
climate.
The processes that make up a planet's climate are too large
and too complex to be reproduced so we can not rely on this
approach.
- it is possible to design a model that involves all
the "components" of the climate system and that gives acceptable
prediction of the climate.
Yes. But how?
An impossible challenge?
Before answering the question how climate is studied,
we must mention some problem arising in weather study.
The atmosphere changes every millisecond. The atmosphere
is typically unstable. By unstable system we mean a system
whose future state following a slight disturbance will
diverge from what its future state would have been without
disturbance. Unstable systems may be potentially unpredictable thus
weather has limited deterministic predictability. In fact
meteologists found from theoretical consideration and
experience that usefull detailed weather prediction of
beyond about 10 days is impossible using current
observations.
Weather is concerned with day-to-day analysis of the
atmosphere but climate is associated with longer period.Is
the longer-term climate prediction thus a hopeless task?
NO! Although day-to-day weather is not predictable far
in advance, some success can be obtained in predicting
average conditions for an external period.
Example : In the statistical-mechanical
theory of gazes, although we cannot predict the behavior
of individual molecules, we accurately predict the expected
mean state and variance of an ensemble of molecules
for some sets of conditions.
Another reason that climate predictions for longer periods
may be possible is that the climate system is subject to
forcing processes that may be of overriding importance
for some time or space scale. The presence of forcing
implies that some aspects of climate may be predictable
on those time scales where the forcing and its response
are important.
Methods
There are two majors approaches to study the climate
- Data Analysis : Study of historical data from
satellites, ground stations, oceanographic soundings,
ice cores, flood records, excavation (fossils), etc.
- Modelling Studies
- Statistical Parametric Models whose goal
is to fit parameters to available data
- Numerical Models that solve physical/fluid
dynamic equations that represent processes
governing the system.
With Data Analysis and Statistical Models we can not
answer the question WHAT IF? For instance what if the amount
of CO2 doubles.
Hence we use Numerical Models to study climate.
These use equations of momentum, energy and mass
conservation to simulate the earth's atmosphere and
climate. The equations are believed to represent the
physical, chemical, and biological processes governing
the climate system for the scales of interest.
They have two major subcomponents :
- Dynamics : deals with the motion namely velocities,
pressure gradiant calculations, advection i.e. state
of the atmosphere.
- Physics : deals with sub-grid scale processes that
affect the state of the atmosphere, namely solar
radiation, longwave radiation, cloudiness,
precipitation, suface energy balance.
You can view on this picture
(ps file) the major components of the Mathematical simulation
of climate. The domain within the dashed curve corresponds to
the physics, and the outside domain to the dynamics and other
factors.
The equations modeling the climate are coupled non
linear partial differential equations containing
spacial and temporal derivatives. Solving them numerically
implies
- Marching in time : temporal discretization
- Calculating in space at each time space : spacial discretization
- Finite difference --> the globe is divided
into mesh.
- Spectral techniques --> a variable is described
as a combination of spectral waves.
It is the use of both Mathematics and high-speed computers
that makes it possible to simulate various physical processes
occurring in the climate system, allowing a better understanding
of the working of the atmosphere, hydrosphere and cryosphere.
To validate a Climate Model we check:
- Ability of the model to simulate today's climate.
The seasonal cycle is one good test because
the temperature changes are larger, on a
hemispheric average, than the change from
ice age to an interglacial period.
- Isolating individual physical components of the model,
such as its parameterizations, and testing them
against reality. For instance, one can check whether
the model's parametrized cloudiness statistics
matches the observed cloudiness statistics of a
particular box.
- Model's ability to reproduce the diverse climates
of the ancien earth or even of other planets.