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Using Modelling to Address Problems

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?

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Using Modelling to Address Problems

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

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

  9. 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…

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

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

  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

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