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Using Modelling to Address Problems

This seminar outline explores the process of building models, applying them in problem-solving, quantifying uncertainty, and integrating data. Key topics include model controls, integration of data, and constraints on model structure. The session covers principles of qualitative formulation, modelling processes, and the Global Carbon Cycle model. It also delves into specifying equations, analysis techniques, and Fusion Analysis. The seminar summary highlights the importance of functional forms in model behavior, handling parameter uncertainty, utilizing models for management, and data assimilation processes.

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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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