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Systems Theory

Systems Theory. Pedro Ribeiro de Andrade Münster, 2013. Geoinformatics enables crucial links between nature and society. Nature: Physical equations Describe processes. Society: Decisions on how to Use Earth´s resources. How to model Natural-Society systems?.

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Systems Theory

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  1. Systems Theory Pedro Ribeiro de Andrade Münster, 2013

  2. Geoinformatics enables crucial links between nature and society Nature: Physical equations Describe processes Society: Decisions on how to Use Earth´s resources

  3. How to model Natural-Society systems? • Connect expertise from different fields • Make the different conceptions explicit If (... ? ) then ... Desforestation?

  4. “A hypothesis or theory [model] is clear, decisive, and positive, but it is believed by no one but the man who created it. Experimental findings [observations], on the other hand, are messy, inexact things, which are believed by everyone except the man who did that work” Harlow Shapley (1885-1972), American astronomer

  5. Models “[The] advantage of a mathematical statement is that it is so definite that it might be definitely wrong…..Some verbal statements have not this merit; they are so vague that they could hardly be wrong, and are correspondingly useless.” Lewis Fry Richardson (1881-1953) – first to apply mathematical methods to numerical weather prediction

  6. What is a System? • Definition: A system is a group of different components that interact with each other • Example: The climate system includes the atmosphere, oceans, polar caps, clouds, vegetation…and lots of other things

  7. How do we study systems? • Identify the components • Determine the nature of the • interactions between components

  8. Earth as a system

  9. Systems Theory • Provides a unified classification for scientific knowledge. • Enunciated by biologist Ludwig Von Bertalanffy: • 1920s: earliest developments • 1937: Charles Morris Philosophy Seminar, University of Chicago • 1950: “An Outline of General Systems Theory”, Journal for the Philosophy of Science • Scientists that introduced Systems Theory in their fields: • Parsons, sociologist (1951) • J.G Miller, psychiatrist & psychologist (1955) • Boulding, economist (1956) • Rapoport, mathematician (1956) • Ashby, bacteriologist (1958)

  10. Short History of System Dynamics The System Dynamics approach was developed in the 1960s at M.I.T. by Jay Forrester. A system in Modelica

  11. Conception of Reality • Any measurable part of reality can be modeled • Systems are represented as stocks and flows • Stocks represent energy, matter, or information • Flows connect and transport stocks • Systems are opened or closed

  12. A system • Can you identify parts? and • Do the parts affect each other? and • Do the parts together produce an effect that is different from the effect of each part on its own? and perhaps • Does the effect, the behavior over time, persist in a variety of circumstances? Source: (Meadows, 2008)

  13. slide Systems Building Blocks • Stocks • Flows • Information Links • Decision Points • Converters • Auxiliary Variables

  14. slide Stocks • “Things” that accumulate in a system • Physical or non-physical things • Value is a quantity or level • Persistent (remain even if all flows stop) • Conservation (stock units enter from environment and return to environment)

  15. slide Flows • Movement of “things” in and out of stocks • Not persistent (can be stopped and started) • Value is a rate of change (will always have a time dimension) • Flow unit = stock unit / time • The unit of measurement for a flow will always be the unit of measurement of a stockdivided byan element of time

  16. slide Stock and Flow Diagram • Stocks in boxes • Flows as straight double arrows • Information Links as thin curved arrows • Decision Points as closed in X

  17. Control Material Flaw to Stock Control Material Flaw from Stock Stock Send information from the Stock Add New information System Dynamics Modelling

  18. Shrimp farming

  19. Simple model for shrimp farm

  20. Results? Figure 7

  21. Positive Coupling Atmospheric CO2 Greenhouse effect • An increase in atmospheric CO2 causes • a corresponding increase in the greenhouse • effect, and thus in Earth’s surface temperature • Conversely, a decrease in atmospheric CO2 • causes a decrease in the greenhouse effect

  22. Negative Coupling Earth’s albedo (reflectivity) Earth’s surface temperature • An increase in Earth’s albedo causes a • corresponding decrease in the Earth’s surface • temperature by reflecting more sunlight back to • space • Or, a decrease in albedo causes an increase in • surface temperature

  23. The interesting thing to do is to put couplings together in feedback loops…

  24. Negative Feedback Loops: Electric Blankets person A’s body temperature person A’s blanket temperature person B’s blanket temperature person B’s body temperature

  25. A Positive Feedback Loop: Mixed-up Electric Blankets person A’s blanket temperature person A’s body temperature person B’s blanket temperature person B’s body temperature

  26. A Positive Feedback Loop: Mixed-up Electric Blankets Any perturbation will cause both people to adjust their blanket controls, but with undesired consequences. Ultimately, one person will freeze (become infinitely cold) and the other person to swelter (become infinitely hot).

  27. Equilibrium State: Conditions under which the system will remain indefinitely --If left unperturbed

  28. An Unstable Equilibrium State

  29. An Unstable Equilibrium State Perturbation

  30. When pushed by a perturbation, an unstable equilibrium state shifts to a new, stable state.

  31. A Stable Equilibrium State

  32. A Stable Equilibrium State Perturbation

  33. When pushed by a perturbation, a stable equilibrium state, returns to (or near) the original state.

  34. Tools for system dynamics • Dinamo • Vensim • Simile • STELLA

  35. Water in the tub • Initial stock: water in tub = 40 gallons • water in tub(t) = water in tub(t – dt) – outflow x dt • t = minutes • dt = 1 minute • Runtime = 8 minutes • Outflow = 5 gal/min

  36. Cell (description extracted from “TerraME types and functions”) Not yet

  37. Event Not yet Not yet

  38. Temporal model 1:42:00 cs:save() 1:38:07 ag2:execute( ) 1:32:10 ag1:execute( ) (1) Get first EVENT (2) Update current time 1:32:00 cs:load( ) (3) Execute the ACTION . . . (4) ACTION return value false true (5) Schedule EVENT again Source: (Carneiro et al., 2013)

  39. Observer Not yet

  40. Water in the tub • Initial stock: water in tub = 40 gallons • water in tub(t) = water in tub(t – dt) – outflow x dt • t = minutes • dt = 1 minute • Runtime = 8 minutes • Outflow = 5 gal/min

  41. Water in the tub 2 • Initial stock: water in tub = 40 gallons • water in tub(t) = water in tub(t – dt) – outflow x dt • t = minutes • dt = 1 minute • Runtime = 8 minutes • Outflow = 5 gal/min • Inflow = 40 gal every 10 min

  42. Conclusions • Two ways to increase stocks • Stocks act as delays or buffers • Stocks allow inflows and outflows to be decoupled

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