possible outcomes of feedback loops Possible choices: –Arrived at stable end state –Never settles down in a stable end state but oscillates –Never reaches any stable end state What kind of feedback loops would produce these options?
Equilibrium States If system is in equilibrium it will not change unless it is disturbed two types: stable, unstable
Stable Equilibrium (within limits) system will return to old equilibrium state
Unstable Equilibrium small perturbations will dramatically affect the state of the system
Some Mathematical Conventions y = f(x) means that y is a function of an independent variable x mathematicians plot the independent variable on the abscissa (horizontal axis) and the dependent variable on the ordinate (vertical axis) physicists and other scientists are not always that rigid!
Two Equilibrium Points Both conditions have to be fulfilled Daisy coverage affects surface temperature Surface temperature affects daisy coverage under which conditions is the system in equilibrium?
External Forcing of the Daisy World System Forcing: outside influence on the system (e.g., insolation, chemical composition of the climate system etc.) How does Daisy World respond to external forcings ?
How will Insolation changes affect the Daisy World ?
Effects of Daisy Feedback biological albedo feedback positive and negative feedback loop two equilibrium positions (one stable, one unstable) resulting equilibrium is generally not optimum growth temperature for daisies presence of daisies lowers planetary temperatures
Effects of Daisy Feedback (cont.) Dampens effects of external forcings feedback factor f quantifies feedback effect Stability of equilibria changes