Lecture 3

1. Lecture 3 BSC 417/517 Environmental modeling

2. FEEDBACK! • A feedback loop in a dynamic system can be defined as a closed-loop circle of cause and effect • Conditions in one part of the system cause results elsewhere in the system, which in turn influence conditions • Learn to identify these in models by their spatial relationship

3. Feedback • Definition: “Feedback is a process whereby some proportion of the output signal of a system is passed (fed back) to the input. This is often used to control the dynamic behavior of the system”

4. The ideal feedback loop in non-Stella iconography

5. Positive and negative • Types of feedback are: • Negative feedback: which tends to reduce output (but in amplifiers, stabilizes and linearizes operation); • Positive feedback: which tends to increase output; or • Bipolar feedback: which can either increase or decrease output

6. First, a bit on the history of feedback • Negative feedback was applied by Harold Stephen Black to electrical amplifiers in 1927 • In 1921,  Black joined the forerunner of Bell Labs, in New York City, working on elimination of distortion • After six years, Black invented the negative feedback amplifier commuting to work aboard the ferry • Basically, the concept involved feeding systems output back to the input as a method of system control • The principle has found widespread applications in electronics, including industrial, military, and consumer electronics, weaponry, analog computers, and such biomechanical devices as pacemakers • Forerunner: thermostats, railroad engines

7. History of feedback: cybernetics • Norbert Wiener • Formalized the notation and scientific process of feedback as “communication and control” within systems, including computer, human, and animal systems • The foundation of computing and various modern sciences • Systems biology • Ecology • Process optimization • Environmental modeling

8. Ol Norbert

9. History of feedback: cybernetics • Forerunner of Norbert Wiener: Arturo Rosenblueth • A Mexican researcher and physician whose 1943 paper Behavior, Purpose and Teleology, proposed that behavior controlled by negative feedback, applied to either animal, human or machine was a fundamental principle of systems

10. Norbert Wiener: your bedtime reading • 1948, Cybernetics: Or the Control and Communication in the Animal and the Machine. Cambridge, MA: MIT Press. • 1950, The Human Use of Human Beings. Da Capo Press. • 1966, Nonlinear Problems in Random Theory. MIT Press. • 1966, Generalized Harmonic Analysis and Tauberian Theorems. MIT Press. • 1966, God & Golem, Inc.: A Comment on Certain Points Where Cybernetics Impinges on Religion. MIT Press. • 1988, The Fourier Integral and Certain of its Applications (Cambridge Mathematical Library). Cambridge Univ. Press. • 1994, Invention: The Care and Feeding of Ideas. MIT Press.

11. Positive feedback • An amplifying system • A system that responds to perturbation in the same direction as the perturbation • May lead to “unstable equilibrium” and explosive conditions • Acceleration of effects leading to big changes

12. Examples • The familiar audio screech in the positive loop between microphone and amplifier • Increasing temperatures leading to melting of the ice caps leading to reduced reflection of the sun’s rays leading to further warming • The hyperbolic growth of the world population observed till the 1970s has recently been correlated to a non-linear second order positive feedback between the demographic growth and technological development • Technological growth - increase in the carrying capacity of land for people - demographic growth - more people - more potential inventors - acceleration of technological growth - accelerating growth of the carrying capacity - the faster population growth - accelerating growth of the number of potential inventors - faster technological growth - hence, the faster growth of the Earth's carrying capacity for people, and so on • Feed or Feedback, by A. Duncan Brown • Positive loop between agriculture and population

14. Example: permafrost melting • From U of Michigan project • http://sitemaker.umich.edu/section2_group1/arctic_issues__permafrost • The Terrestrial Carbon Cycle Climate Feedback

15. Permafrost

17. Details • Warmer temperatures in the Artic have begun to thaw the arctic permafrost, a layer of soil that has been frozen since before the last ice age • It contains frozen organic matter that has been preserved by the ice, historically making the permafrost layer a carbon sink that contains 14% of the total carbon in the world’s soils (Christiansen 1995). A recent estimate suggests that if all of the carbon stored in permafrost were released into the atmosphere, the CO2 levels in the atmosphere would double • The warmer than average temperatures recorded in this region in the last couple of decades have been indirectly causing the permafrost to change from a CO2 sink to a CO2 source (Oechel 1993) and has increased methane emissions as well (Christiansen 1995) • This is being directly caused by an increase in soil drainage and aeration from temperature increases (PBS 2004) • The effect of photosynthesis as a stabilizing factor in the process, through the increased exposure of vegetation to the atmosphere, is not expected to reach the levels CO2 out gassing any time soon, so the thawing of this layer has created a positive feedback loop known as the Terrestrial Carbon Cycle Climate Feedback (Oechel 1993)

18. Impact • As this cycle feeds into itself, the thawing of the permafrost layer becomes an even greater issue. • Much of the infrastructure of Alaska is built on this ancient permafrost and now that it is thawing, the water is starting to drain away and the ground is subsiding, causing once solid structures such as roads and buildings to crack and lean. • This problem has become more wide spread and a greater concern throughout the Arctic as time has progressed (Armstrong 2003). • Permafrost thawing and longer warmer seasons allows water that was previously contained to flow away and more evaporation throughout the year. • The thawing is literally “uncorking” lakes so that the water is flowing out of Alaska and into the open oceans (Riordan 2006). • 15% of the surface water in Alaska has been lost to this outflow in the last 50 years (PBS 2004).

19. Couple of examples in biology • Contractions in childbirth • When a contraction occurs, oxytocin (a hormone) is released into the body, which stimulates further contractions, resulting in contractions increasing in amplitude and frequency • Blood clotting • The loop is initiated when injured tissue releases signal chemicals which activate platelets in the blood. • An activated platelet releases chemicals which activate more platelets, causing a rapid cascade and the formation of a blood clot

21. More examples • So-called “vicious cycles”: poverty, hunger, debt • Converse: “virtuous cycles”: education, agricultural productivity, clean water, health, money • Hyperbolic or exponential growth (second order behavior) is often driven by positive feedback • Many examples in biology and population

23. Negative feedback F-

24. Negative feedback • System tending toward equilibrium • In biology, we often use the term “homeostasis” • Perturbations to the system are counteracted by the system’s response • Thermostats in machine and animal • Many biological and ecological processes, because nature tends to “self-regulate” or react to oppose factors that destabilize the system • And that’s a very good thing

25. Negative feedback

26. More on negative feedback • In biology…

28. Recognizing negative feedback • “Nature responds” often cited for human induced change that is counteracted by environmental systems • Often linked to unintended consequences