Generalized diagram of the Earth system

Systems Notation

= system component

= positive coupling

= negative coupling

Positive Coupling

Car’s gas pedal Car’s speed

Amount of foodeaten

Body weight

A change in one component leads to a change of the same direction in the linked component

Positive Coupling

AtmosphericCO2

Greenhouseeffect

• 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

Negative Coupling

Car’s break system

Car’s speed

Exercise Body weight

A change in one component leads to a change of the opposite direction in the linked component

Negative Coupling

Earth’s albedo(reflectivity)

Earth’ssurface

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

Increasing carbon dioxide: forcing (long term)

Volcanic eruption: perturbation (short term)

childrens’noise

parents’ anger

negative coupling

positive coupling

person A’sbodytemperature

person A’sblankettemperature

Negative Feedback Loops:Electric Blankets

person B’sblankettemperature

person B’sbodytemperature

person A’sbodytemperature

person A’sblankettemperature

A Positive Feedback Loop:Mixed-up Electric Blankets

person B’sblankettemperature

person B’sbodytemperature

A simplified climate system: Daisyworld

Average Temperature = 30 oC No clouds, no ocean Soil = light gray (absorbs some light) Life = white daisies (reflects all light) Sun = like Earth’s Daisy growth = changes with temperature

Albedo: measure of reflectivity of a surface, expressed as a % of reflected insolation to incoming insolation.

(Christopherson, Elemental Geosystems, 2004)

albedo = 0.5

albedo=0.75

Systems diagram explicitly including albedo

Systems diagram

Response of average surface temperature to daisy coverage

22.5 °C

5 °C40 °C

completely covered planet

Equilibrium States: Graphical Determination

1. Overlay the two graphs (this is the graphical way of setting them equal to each other).

2. The points where they meet are equilibrium points.

3. Draw a systems diagram to determine whether each one is stable or unstable.

The Faint Young Sun Problem

Kasting et al., Scientific American (1988)

More H2O

Systems diagram

Response of average surface temperature to daisy coverage

External Forcing: the response of Daisy World

1. Assume that the external forcing is an increase in solar luminosity

2. The effect of temperature on daisy coverage should not change (this depends on the physiology of daisies)

3. The effect of daisy coverage on temperature should change: for the same daisy coverage, higher temperature