1. Using Modelling to Address Problems Scientific Enquiry in Biology and the Environmental Sciences Modelling Session 2

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?

3. 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

4. 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

5. 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

6. 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

7. Fossil Fuels (7 per yr) & volcanoes Atmosphere (750) Vegetation (700) Ocean (50 in surface, 40000 at depth) Sediments 75,000,000 Soils (1500) The Global Carbon Cycle – a simple model Litterfall/ sedimentation Respiration Photosynthesis Combustion

8. Fossil Fuels (7 per yr) & volcanoes Atmosphere (750) Vegetation (700) Soils (1500) The Global Carbon Cycle – a simple model Litterfall/ sedimentation Respiration Photosynthesis Combustion Global temperature Influence

9. Specifying equations Photosynthesis is a saturation equation on atmospheric CO 2 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…

10. The global C cycle “The breathing forest model” www.sei.se/forests/index.htm

11. Data Assimilation MODELSOBSERVATIONS FUSION ANALYSIS MODELS -Capable of interpolation & forecasts -Subjective & inaccurate? OBSERVATIONS -Clear confidence limits -Incomplete, patchy -net fluxes ANALYSIS Complete with clear confidence limits & capable of forecasts

12. 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