Download Models, science and the real world

Using Modelling to
Address Problems
Scientific Enquiry in Biology and the
Environmental Sciences
Modelling Session 2
Seminar 2 outline
• What is the process for building a model?
• How are models applied in problem solving
situations?
• How is uncertainty quantified and
attributed?
• What parts of the model are critical controls
on model behaviour?
• How can data and models be integrated?
Constraints on model
structure
• Realism - the degree to which model structure
mimics the real world
• Precision - the accuracy of model predictions
(output)
• Generality - the number of systems and
situations to which the model correctly applied
The process of modelling
1. Objectives: identify the system, the questions, the stopping rule,
ultimate goals
2. Hypotheses: develop specific hypotheses and graphical description
of the model
3. Mathematical formulation: convert qualitative hypotheses into
mathematical equations
4. Coding and verification: convert equations to code and develop
numerical framework
5. Initial conditions, parameters and calibration: set start
conditions, calibrated rate constants
6. Analysis and evaluation: execution, qualitative and quantitative
checks, falsification
Principles of qualitative
formulation





Identify state variables
Identify flows among state variables
Identify the controls on flow rates
Identify auxiliary and driving variables
Identify the time-step
The modelling process
 Calibration – determination of model
parameters
 Corroboration - testing model output
 Sensitivity analysis – how do inputs
relate to outputs
 Residual analysis - what might explain
model failure
The Global Carbon Cycle – a simple model
Fossil
Fuels (7 per yr) &
volcanoes
Atmosphere (750)
Litterfall/
sedimentation
Vegetation (700)
Ocean
(50 in surface,
40000 at depth)
Respiration
Photosynthesis
Combustion
Soils (1500)
Sediments
75,000,000
The Global Carbon Cycle – a simple model
Fossil
Fuels (7 per yr) &
volcanoes
Atmosphere (750)
Litterfall/
sedimentation
Vegetation (700)
Respiration
Photosynthesis
Combustion
Soils (1500)
Influence
Global
temperature
Specifying equations
• Photosynthesis is a saturation equation on
atmospheric CO2 concentration
• Respiration is an exponential function of
temperature
• The pre-industrial C cycle is calibrated at a
steady-state
• But the parameters are not well known…
The global C cycle
“The breathing forest model”
www.sei.se/forests/index.htm
Data Assimilation
MODELS
OBSERVATIONS
-Capable of interpolation
MODELS
& forecasts
-Subjective & inaccurate?
-Clear confidence limits
OBSERVATIONS
-Incomplete, patchy
-net fluxes
FUSION
ANALYSIS
Complete ANALYSIS
with clear confidence
limits & capable of forecasts
Seminar 2 summary
• The importance of functional forms in
model behaviour
• Parameter uncertainty can be translated into
predictive uncertainty
• Models can be used as management tools
for control
• Data assimilation is a process for optimally
combining models with observations