Download Lecture 3: A basic modelling primer

A basic modelling primer
Details for Today:
DATE:
BY:
14th October 2004
Mark Cresswell
FOLLOWED BY:
Practical
69EG3137 – Impacts & Models of Climate Change
Lecture Topics
• Introduction (what is a model?)
•
•
•
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Modelling philosophy
The systems approach to modelling
Systems analysis
Climate model basics
• Suggested reading
• Assignment 1 set today
INTRODUCTION
Introduction #1
What is a Model?
• A necessarily simplified abstraction of the realworld
• Comprises the known fundamental sources of
causality within a natural system
• Disregards factors of little or no importance
• Uses assumptions
• Uses parameterisations where factors are not
known or hard to calculate
Introduction #2
What is a Model?
• A climate model must attempt to describe the
climate system in terms of basic physical,
chemical and biological principles (laws)
• The model becomes a series of equations
expressing these laws
• Equations must be solved rapidly for individual
grid-points and for many time integrations
Introduction #3
What is Modelling?
• A process such as weathering (by wind or rain) may be
represented mathematically by the inputs (water),
outputs (sediment solution) and weathering action
involved. An entire system is a collection of processes
(like the climate system for example) - each one defined
by a set of rules at the simplest level or complex
equations and physics at a higher level. The
mathematical representation of the dynamics of real
world systems is known as simulation modelling.
Modelling Philosophy
Modelling Philosophy #1
• It has been suggested that the most useful links
between a theory and a model are mediated
through imagination (Harvey, 1969)
models
imagin ation
theory
Modelling Philosophy #2
There are three broad categories of model as outlined by
Hardisty, 1995:
• Natural analogues. The use of actual events or
objects occurring in different times or different
places to help examine what has, is or will
happen to a particular system
• Hardware or physical models. A range of
materials (often natural) is used
• Mathematical models. A range of deterministic
or stochastic approaches based upon the solution
of equations, rules and algorithms.
Modelling Philosophy #3
Example of a very basic model
ou tpu t
i npu t
fu ncti on
state varia ble
Modelling Philosophy #4
When modelling a dynamic process (like the climate) we are
concerned with the following paradigm:
Future value (or state) = present value + change
We may also consider the following re-arrangement:
Change = future value – present value
Modelling Philosophy #5
The MOST important principle of modelling
The Systems Approach
The Systems Approach #1
• Complex systems (such as the climate or
ecosystem) may be disassembled into smaller
sub-systems, each of which has individual inputs
and outputs
• By breaking down a large system in this way, we
can study and model individual components
more easily. This strategy is known as the
systems approach
• Many natural systems blur into other systems
making the demarcation of a system (and hence
the limits of the model boundary) a difficult
issue
The Systems Approach #2
• Since the 1970s there has been a shift (in the
environmental sciences) to a dynamical systems
approach after the realisation that models can
evolve in time as the processes and sub-systems
they represent change and evolve.
• The study of the functioning and composition of
systems is known as systems analysis (Hardisty
et al., 1995). Systems analysis is very closely
allied to modelling as system construction is an
early phase in modelling itself
Systems Analysis
Systems Analysis #1
• There are four phases
• Phase 1: The lexical phase. This requires the (a)
definition of the system boundaries; (b) selection
of system components (more correctly referred
to as state variables); and (c) estimation of the
value (state) of the state variables. Huggett
(1980) calls these stages system closure,
entitation and quantitation respectively
Systems Analysis #2
• Phase 2: The parsing phase. This involves
defining the relationships of the state variables
of the system in a mathematical way.
Relationships may be deterministic (a single
value) or stochastic (a more probabilistic or
random value).
• Deterministic model solutions provide a single
outcome - with no estimate of error or
probability
• Stochastic models provide both probabilities and
estimates of skill and reliability
Systems Analysis #3
• Phase 3: The modelling phase. The first step is
model construction which requires that changes
in controlling and state variables are well
understood. The second step is running the
model.
• In advanced global climate model simulations
the ocean model is coupled to the atmospheric
model
• Less advanced (and hence less computationally
intensive) climate models run atmospheric
models with oceanic persistence or climatology
Systems Analysis #4
• Phase 4: The analysis phase. This is where the
model is validated – when we compare the
model output against actual observations. Once
we are happy the model performs well, we can
begin to trust its outputs
• Observational data used for validation of climate
models is often referred to as reanalysis
• ECMWF produces ERA-15 (1979-1993)
• ERA-15 however is flawed and hence climate
models have been affected as a result
Climate model basics
Climate model basics #1
• Radiation: input, output and absorption of solar
radiation and the emission of infrared radiation
• Dynamics: movement of energy around the
globe by oceans and winds - both horizontal and
vertical
• Surface processes: effects of sea- and land-ice,
snow, vegetation, albedo, emissivity and surfaceatmosphere energy exchanges
• Chemistry: chemical composition of the
atmosphere
• Resolution: both in time and space
Climate model basics #2
Fundamental equations solved in GCMs
• Conservation of energy (first law of thermodynamics):
– Input energy = increase in internal energy + work done
• Conservation of momentum (Newton’s second law of
motion):
– Force = Mass x Acceleration
• Conservation of mass (the continuity equation)
• Ideal gas law
Climate model basics #3
1. Conservation of momentum
Dv
 2  v  1p  g  F
Dt
2. Conservation of mass

D
   v  C  E
Dt
3. Conservation of energy

DI
d -1
 p
Q
Dt
dt
4. Ideal gas law

p  RT
Suggested reading
Text Books
Hardisty J, Taylor DM and Metcalfe SE (1995). Computerised environmental modelling: A practical
introduction using Excel. Published by John Wiley & Sons, England.
Berry J and Houston K. (1995). Mathematical modelling. Published by Edward Arnold, London
Giordano F, Weir M and Fox W. (1997). A first course in mathematical modeling. Published by
Brooks and Cole, California.
Deaton M and Winebrake J. (1999). Dynamic modelling of environmental systems. Published by
Springer Verlag, New York
Assignment 1 Set Today
Climate change is influenced by complex interlinked
processes. This interactive model lets you explore the
system and how we can change it, simply by moving
controls with your mouse and observing the effect
instantly on plots ranging from emissions to impacts. The
calculation methods are based on those used in the recent
Intergovernmental Panel on Climate Change Third
Assessment Report, implemented efficiently in the java
language to work within your web browser.
http://www.chooseclimate.org/jcm/index.html
The model can be accessed from the J:\ drive: J:\EG3137\JCM\Index.html
Some additional resources relating to climate change in Africa can be found at:
http://www.grida.no/climate/vitalafrica/english/index.htm
http://www.newscientist.com/hottopics/climate/climate.jsp?id=ns99992811
http://news.bbc.co.uk/2/hi/world/africa/2220584.stm
http://www.defra.gov.uk/environment/climatechange/ccafrica-study/