ATM S 211 Lecture Notes #2

Lecture 2 Notes October 4, 2004

Why do we study the climate as a system? It is complex, involving interactions between many pieces. An alternative approach is to reduce a system to its components, or building blocks, and study them. This is called a reductionist approach. For example, clouds are a component of the climate system. Understanding clouds is essential to understanding climate, but a cloud alone can tell us a limited amount about the whole climate system. Clouds are also systems themselves. A component of the climate can be a system of its own.

We use systems diagrams, or feedfback loops, to describe the flow of a system. Remember that each successive component of a system must be linked, or coupled, to the previous one. The text in the boxes of a feedback loop should describe the state (like temperature or salinity) or a behavior (like evaporation or the greenhouse effect) of the system. A boxed item should not specify how the state is changing, so it should not contain a specific action. Instead the item must be able to either increase or decrease.

Because the lower box contains a specific action, the following is an example of a bad (one that doesn't make sense) feedback loop:

bad feedback loop

Here is an example of a good (at least it is correctly drawn) feedback loop:

The water vapor feedback loop is positive and therefore yeilds an unstable equilibrium if considered in isolation. When the system is perturbed or forced (perturbation is often used for a short lived disturbance, like say a volcano, while forcing is used for a disturbance that is applied over many years or continuously, like increasing carbon dioxide), is there a runaway effect? It would runaway if the water vapor feedback acted alone, but the real climate has many other systems that act at the same time. Other systems may keep the system in check. For example, on Earth air temperature is constrained by other feedback processes that are negative:

The "Something Else" could be radiation, as we will learn in Chap 3. There is a danger in drawing conclusions about the whole system from a single loop. These loops are instructive but we must recognize their limitations. It is important to consider the whole system when predicting climate. Yet, we would have a tangled mess of feedback loops if we tried to diagram the whole climate system.

Is climate prediction hopeless? The stakes are high and so we are motivated to try. However, a numerical model is a better tool for predicting climate. We will discuss comprehensive climate models later in the course. Next we consider an imaginary planet with a single system that describes almost the whole climate.

We study Daisyworld to reinforce concepts about feedback, stability, and multiple equilibria. The primary Daisyworld system has just two components, surface temperature and daisy coverage. Temperature depends inversely on daisy coverage because daisies have high albedo, or reflectivity, so the coupling from daisies to temperature is negative. We let daisies depend on temperature with a more complex relationship that involves two possible couplings: Daisy coverage increases with increasing temperature provided the temperature is below the optimum temperature for daisies. Above that temperature, daisy coverage declines with increasing tempearture. There is a minimum and a maximum temperature where there are no daisies whatsoever. The feedback loop is either positive or negative provided the temperature allows for some daisies to live.

Daisyworld feedback loops

We can combine these two graphs to graphically find the equilibria:
graphical equilibria

The intersection to the left of the optimum temperature is a stable equilibrium and the one to the right is unstable. Practically speaking the temperature never spends any time above the optimum because the positive feedback rapidly changes the temperature for this range. If the temperature is somehow made larger than the temperature of the unstable equilibrium, then the planet will rapidly heat up until all the daisies are gone. If the temperature is somehow made to be between the equilibrium and the unstable equilibrium, the planet will rapidly cool until all the daisies are gone. The climate is stable when all the daisies are gone. The reason is swept under the rug in the text but there is another feedback loop that influences temperature here. It is negative, but not too strong so that it overwhelms the strong daisy-temperature feedback. If there are no daisies, it is the only feedback.

If we consider a change to the climate where the solar luminosity is altered, the curve that represents the temperature dependence on daisies will shift (left if solar luminosity is lowered and right if it is increased).

There is still the matter of the slope and the intercept points for the temperature dependence on daisy coverage. These numbers necessarily depend on the negative feedback that is swept under the rug. We must face them if we want to compute actual numbers. The book chooses something reasonable to give earth-like temperatures.

Are there multiple equilibria in the real climate? Maybe. The Greenland ice core gives us a proxy record of temperature with some large rapid fluctuations during the ice ages that may be evidence of multiple equilibria. The leading theory explains these flips in the temperaure record as evidence of "on" and "off" cycles of the global ocean heat conveyer (circulations that transport heat from the tropics to the northern North Atlantic near Greenland). My description is oversimplified for now. The idea is controversial too. We will return to this later in the course.

Notes on chap 3 will appear in tomorrow's lecture notes.

Back to Schedule

Contact the instructor at: atms211@atmos.washington.edu
Last Updated: 8/4/2004