Intro to system diagrams and behavior

Consider the Elkhorn River as a system. There are many reasons you might want to understand how it behaves, foremost of which might be the desire to understand its flooding behavior. The adjacent air photo gives one view of part of the system. In trying to understand its behavior many question can be generated. What features/components can be recognized? What are some of the factors that determine how the different components behave? How do these factors interact? This is a good example of a complex 'system'.

In constructing a system diagram you are trying to identify what the pieces are and how they are linked together for a particular system. One way to think of this is that you are making a mental map of how the system works. You can use the metaphor of a puzzle (metaphors are extremely useful in science). To start with we will define three puzzle pieces, each with their own shape.

Pieces of the puzzle = system diagram elements.

• reservoirs = rectangles.
• transfer processes = spigots.
• controlling variables = ovals.

In class exercise: an introduction to system modeling using the hydrologic 'cycle'. It often helps to start with what you are most familiar with. We will have you get into groups, and then take the three types of puzzle pieces described above, fill them in with appropriate reservoirs and transfer process and link them with arrows into a diagram of the hydrologic cycle. Include everybody's name on the resulting system diagram.

In this course we will focus a lot of attention on three systems/'cycles' - hydrologic, rock, and carbon cycles.

Closed versus open systems.

The standard rock cycle - is it open or closed?

Garbage in, leachate out - the importance of the recognizing the difference between closed and open systems.

Is the earth a closed system?

Is a mineral a closed system?

Remember that a system is a human artifact of convenience. If your system is open you can always try to expand its boundary, so that it becomes more complete and less closed.

Closed versus open models and uncertainty. When modeling a system you try to include the most important components and variables. The degree to which you haven't included components and variables that influence system behavior might be considered the degree of openness. What do you think is the relationship between certainty about or confidence in a system model and how open or closed it is?

Equilibrium versus non-equilibrium states.

In an equilibrium state the system is not changing, in a non-equilibrium state it is.

Perturbations and forcings both cause a system to change (ie. disturb the equilibrium): perturbation = sudden, forcing = gradual. Can you think of geoscience examples of what might be perturbations and what might be forcings for a grasslands ecosystem? How about for a sandy coastline such as Padre island?

Stable and non-stable equilibriums.

An example of glaciers and end moraines.

Do natural systems spend much time in an equilibrium state?

Feedback loops.

Some of you may have encountered the distinction between independent and dependent variables. A change in the independent variable causes a change in the dependent variable. For example, an increase in temperature usually causes more of a solid (like salt) to dissolve in water. You don't think that an increase in the amount that is dissolved causes the temperature to change. However, how about two variables that are codependent, coupled?

Positive and negative couplings:

positive feedback = paired negative couplings or positive couplings.

negative feedback = a negative and positive paired coupling.

consider how is oxygen level and fish population may be linked in a fish tank.

examples of geoscience couplings with feedback - are they positive or negative:

• extent of sea ice and local atmospheric temperature in polar region.
• photosynthetic respiration and carbon dioxide level in atmosphere.

Exploring feedback behavior in graph space:

• your text has a good example on page 22 dealing with noise level and anger. A very interesting point to realize here is that this type of analysis can be used in many situations, not just to understand earth systems. Think of how fights 'escalate'.
• exploring this behavior in graph space consists of mapping, for two variables the nature of their feedback. This will consist of two lines/curves, one describing how x is a function of y and the other of how y is a function of x. Then imagine some perturbation in x or y that starts the system responding. You will keep track of how it responds in increments, literally in steps. If the perturbation is in y then find the value of x on the x as a function of y curve. That x will then trigger a new level in y. Draw a line to that y. That y will trigger a new level of x. Draw a line to that x. The result will be a series of steps that track the evolution of the system. Note that points of intersection between the two curves represent equilibrium points.
• for this graph try identifying the three equilibrium points and then figure out which ones are 'stable' and which ones aren't.

Boundaries and transfer processes.

How are system components defined?

Examples of important boundaries:

• earth's surface:
• rock-atmosphere
• water-atmosphere
• cell wall.
• skin.
• core versus mantle.
• groundwater table.
• a storm front.

What are some processes that transport material across a boundary from one reservoir to another?

Permeable versus impermeable boundaries, selective permeability.

Surface energy, bubbles and hexagons.