Do you know the story of blind men and the elephant? Each man approaches the elephant and discovers a different aspect by using their sense of touch. Because one has felt the trunk, another the small tail, and another the smooth tusk, each has a different view about what the elephant is and what it looks like. Scientists often face the same problem. We each study some small aspect of the natural world and then draw conclusions about the working of nature from our study. However, our conclusions may be no more accurate than the blind man's if we do not consider the connections between our study and the broader world. For example, if we want to understand the human body, we might begin by trying to understand the workings of a cell. And, to understand the cell, it might be necessary to spend a life-time of research studying a single molecule and its functions. A competent scientist, however, will consider the connections between the molecule she is studying and the human body as she interprets her results.

Systems analysis is one of the tools that scientists use to keep track of connections among the different aspects of a problem and to recognize which ones are most important. A system to a scientist is the whole thing. It may be a cell, or a drop of water or it might be the oceans or the whole earth. However, the key to systems analysis is recognizing the "wholeness" of the object that we are studying. The scientist in her investigation of the molecule considers all other parts of the cell and the interactions between the cell and other cells not to mention the larger environment that affects the cell in so many ways. In fact if she were to try to study the molecule in total isolation, she would learn some things, but might in the end have a totally inaccurate model of the molecule and its functions in the body.

The key to systems analysis is its ability to describe complex systems in a way that draws attention to important relationships within the system. To begin one would look at a system and determine its parts (components) and the functions (processes) that occur within the system. For example, a geologist studying erosion of a stream valley might want to consider water, the stream itself, soil, rock, plants, animals, wind, rain, snow, and ice as components. Processes that are important are the flow of water, precipitation, seasonal changes, weathering of rocks, movement of rock and soil down slope, action of plants to hold soil and rain, action of animals on the banks of streams, human activity in modifying the stream and .. Of course at some point the geologist must consider which of these components and processes are most significant to his understanding of way the stream erodes its valley. One might say that microscopic animals or toxic waste in the stream are components; however, it is quite possible that neither plays an important direct effect on stream erosion.

Among the most important processes in any system will be those that control the flow of energy and matter through the system, that is the inputs and outputs of the system. In the example of the stream, inputs might be water, soil, and energy as sunlight. An output might the water, rocks and soil moved out of the valley by the stream. The idea of flow of matter and energy is so basic to understanding system functioning that three classes of systems are recognized based on the movement of energy and matter into and out of the system. An isolated system is one in which neither matter nor energy is able to enter or leave the system. The second law of thermodynamics implies that there is only one isolated system -- the universe. All other systems will permit the transfer of energy across the system boundary. There is no perfect thermos that can be used to totally isolate a system from its energy surroundings. On the other hand, it can be useful to imagine a system operating in isolation. This can be especially true for understanding chemical and physical processes that occur at a molecular level. For example it is easiest to understand evaporation and condensation in an isolated system before considering what happens when heat is added or subtracted.

A closed system is one in which energy is able to move in and out of the system, but the amount of matter remains fixed. For all practical purposes, the earth is a closed system. The planet receives constant energy input in the form of radiation from the sun and constantly emits radiation to space. However, with the exception of the addition of meteors and cosmic rays, amounts of matter that are insignificant (usually) and the loss of small amounts of hydrogen from the atmosphere, the amount of matter on Earth is fixed. Other closed systems might be a test tube that has been closed to prevent addition of material or a rocket traveling to Mars. Because the earth is a closed system, understanding behavior of this kind of system becomes very important to understanding the earth's environmental systems.

The third kind is the open system. In open systems, both matter and energy are free to enter or leave. For example, a river is an open system because water, soil, rocks, fish, etc. can enter and leave. And, of course energy is warming the river or the river warms its surroundings by losing energy as heat, not to mention the changes in energy of the stream as it flows faster or slower because of changes in the slope of the land.

(Take a moment to review these concepts before continuing. Consider the human body as a system. Name 10 components and 5 processes that are important to the body system. Is the body open, closed or isolated? How might you decide? Consider the isolation chamber used by doctors who study infectious diseases. What kind of system is it?)

Because system analysis is interested in process or change, one needs to be able to measure the process or its effects if one is to understand it. What are measured are variables. Again thinking about the stream system described above, variables that might be considered are the depth of the stream, the amount water in the stream, the speed of stream flow, the number of cattle near the stream, the per cent of land covered by vegetation, the amount of soil moved by the stream, the amount of rain that falls on the stream's drainage area, etc. A complex system will have a large number of variables that can be measured; so many that it is impossible to measure them all. One might measure the number of paramecia in the stream, but is it necessary? So a scientist using systems analysis would be forced to decide which of the variables are important to her understanding of the process that she is studying. Experience is often used to make that decision. Most important to stream erosion are climatic conditions including temperature and rainfall, the volume of water carried by the stream and the velocity of the water. One might choose to measure additional variables depending on the focus of the study or if one finds that the variables being measured are useful in predicting or explaining the behavior the system. For example, streams flowing through fields occupied by cattle are significantly different from streams that are not used by large animals. The cattle break the banks of the stream and make the stream shallower and wider. It might, therefore, be important to measure the number of cattle in the area of the stream to really understand its shape and its ability to move sediments.

In looking at systems, one can see that some systems remain constant or nearly constant over time. The human body between the ages of 20 and 60 changes very little. One important variable, body temperature, except when we are ill, remains near 98.6° F. This temperature is considered the steady state condition of the body and is so essential to good health that even a deviation of 1° is a sure indication of illness. An oven can be set to a variety of steady states depending on the temperature you want. As this example implies, a system need not have a single possible steady state.

When describing steady state, it is important to define the time span that one is considering. Earth's climate system has been at steady state for last few million years when considered over a long time frame such as periods > 25,000 years. It is in a period of extensive glaciation and average temperature has remained low. However, on the shorter term, less than 10,000 years, climate is quite variable with temperature fluctuating 5 to 10° F in a few 10's of years in some parts of the earth. This would seem to imply that the earth's climate steady state is not tightly controlled (can fluctuate significantly) or that there are two steady states and that the earth climate system fluctuates between warmer and colder steady states while maintaining a more or less constant average on a longer time scale.

Understanding the steady state of a system, if it has one, is extremely important if one is to accurately describe the system. It is also important to know if the steady state is stable or unstable. This is a difficult concept because we obviously would expect steady states to be stable -- isn't that what steady means. Yes and no. The difference between stable and unstable steady states is the ability of a system to return to the steady state if something happens to force the system to move away from steady state conditions. The steady state temperature of the human body is a stable steady state. If you start to exercise, your body produces more heat and your body temperature may rise slightly. However, you also begin to sweat which cools your body and reduces the temperature to its normal level. The oven (when it is on) will be at a stable steady state with respect to temperature because it has a thermostat that controls the input of energy. If temperature rises above the set level, the burner/heating element is turned off. If temperature falls below steady state, the heating element is turned on. Soda water in an open bottle is an example of an unstable steady state. So long as nothing upsets the bottle, the carbon dioxide remains in the water and the soda retains a steady state concentration of CO2. However, if you shake or bang the bottle, gas bubbles will form rapidly and leave the system.

Systems that are at stable steady state are said to be at dynamic equilibrium. These systems have the ability to "correct" for changes in their environment This ability is expressed in a law known as Le Chatellier's Principle which states that when a system at dynamic equilibrium is stressed, it will change to minimize the effects of the stress. Stress used in this context means a change that affects the state of the system.

It is easiest to understand Le Chatellier's Principle by considering simple systems like a mixture of liquid water and ice. Approaching the problem from the point of view of systems analysis, we could say that the components of the system are water as liquid and ice, and the container. The system will be closed so the only input or output is energy, in this case heat. The processes are melting or freezing and the transfer of heat to and from the container. The important variables are the number of molecules in liquid and solid states (amount of liquid and ice) and the temperature of the system. The stress we will apply is a small amount of heat.

As you know if you heat ice, it will melt more quickly. So, because we have stressed the system, it will change and the number of liquid molecules will increase. We can write this in equation form

Ice + Heat <=====> Liquid

(I show it as a reversible change because we know increasing entropy favors forming the liquid, but decreasing potential energy favors forming ice.) The equation implies that heat is being stored in the liquid. If that is true, the removal of heat from the system will .... yes, that's right .... lower the temperature of the system. And, if temperature drops, some of the liquid molecules will change back to ice. The net effect is that so long as some ice remains in system, the temperature remains the same because additional heat is stored in the molecules that change from the solid to liquid state. From Le Chatellier's point of view, the system has acted to minimize the effect of the stress by converting the heat to potential energy stored in the liquid molecules. In effect the system has "tried" to prevent a temperature rise by allowing the ice to melt. In this example, the steady state does change by changing the ratio of solid to liquid molecules and so cannot be considered perfectly stable. However, it is entirely stable with respect to temperature. In fact, ice water is one of the most accurate constant temperature systems known. I think you can also predict that this might have a tremendous impact on cold weather climates near water. So long as ice and liquid remain present, what is the lowest temperature the water will experience? What is the highest? If heat is removed from the water, how does it respond and what effect does this have on temperature?)

Predicting System Behavior

One of the goals of systems analysis is to be able to predict system behavior. To do this, scientists look for instances of cause and effect within the system. For example, in the ice-water system an input of heat caused ice to melt. It can also be said that melting ice caused heat to be removed from the system. Both processes, adding heat and melting effect each other. This is an example of feedback. Feedback occurs when two processes (usually measured as changes in two variables) are interdependent. Another example of feedback would be the ability of your body to sense the surface temperature of your skin, If it is low, more blood is sent to the surface areas of your body to keep them warm. So the flow of blood regulates the body's surface temperature and the body's surface temperature regulates the flow of blood. Feedback in a system is important if the system is to maintain a stable steady state. However, not all feedback systems produce stable steady states. Consider the person who begins to smoke. The nicotine in the cigarette produces certain chemical changes in the body and creates a sense of need (dependence) for more nicotine. The person smokes more which creates additional need, which causes the person to smoke more, etc. Although other factors such as cost and health also affect the system, the simple system does not predict a stable steady state even though there is feedback. The earth's climate also has numerous feedback mechanisms, some that act to create stable steady states and others which are unstable. The feedback between ice cover and climate is an example of feedback that produces a potentially unstable result. If ice cover increases, it will cause more radiation to be reflected into space, cooling the planet. Trace the effect that this will have on the amount of ice and on climate.

When considering the effects of feedback on the system, it is important to determine if the feedback is positive or negative, and if the feedback is tight or loose. Feedback is said to be positive when both dependent relationships between two interdependent variables are negative or both are positive. It is an algebraic determination. Multiply two positives and the result is positive. Multiply two negatives and the result is also positive. A negative feedback is one in which one dependent relationship is positive and the other negative. The feedback in the ice-water system is negative. The feedback in the ice cover-climate system is positive because increased ice reduces temperature and increased temperature will reduce ice -- both relationships are negative. Determine the sign of feedback in smoker system.  It is possible to show that negative feedback always acts to stabilize the system.  Positive feedback is more interesting because it may create either stable or unstable steady states.

A system at a stable steady state with tight feedback has the potential to maintain nearly constant conditions. Loose feedback might maintain the steady state, but with much more fluctuation. Obviously if you are trying to cook, it is important to have tight feedback controlling the temperature of your oven. I once had a stove in which the thermostat was broken. If I set the temperature at 350, the oven temperature would fluctuate between 200 and 600. Not very satisfactory if you are trying to cook in the oven. It is often important, therefore, to not only think about the presence or absence of feedback in a system and its sign, but how tightly if constrains the behavior of the system. A stable steady state that is maintained by averaging against wild fluctuations may fit the definition of a stable steady state, but is not really very stable.

Visualizing the system (Creating system models)

One of the powers of the system approach is that once one begins to describe the system, it is possible to present a relatively simple visual representation of the system called a flow chart. The flow chart is designed to describe the movement of energy and/or matter through the system by relating process and variables in a way that presents the connections among them. Typically one uses labeled boxes or ovals to represent variables and arrows to indicate process. I will ask you to follow this convention when you present your work on an exam, in practice session or in your project.

It is probably easiest to understand by looking a some examples, using a simple system, ice and liquid water, first and a more complicated system like the stream described above later. A flow chart of the ice-water system would need to consider the processes of heat transfer and melting/freezing and the variables temperature, energy input, amount of ice (or liquid) in the system. The flow chart might look like this:

The arrow between energy input and temperature represents the process of energy transfer and the + sign implies that an increase in energy input causes an increase in temperature. The arrow from temperature to amount of ice represents the effect of increased temperature on the amount ice which is negative because it causes melting. The arrow from ice to temperature represents the release of heat as ice forms and potential energy stored in liquid water is converted to heat. The formation of ice, therefore, acts to raise temperature and so the sign is positive. Because arrows are shown indicating interdependence between the amount of ice and temperature, the system includes feedback. By "multiplying" the signs one can determine that the feedback is negative. Any time one can use a flow chart to recognize potential feedback in the system, one recognizes a potential for steady state within the system.

The more complex flow chart representing the erosional system of a stream includes more variables and processes. The chart does a good job of presenting the important relationships that control erosion in a very simple and very concise manner. I'd like to draw your attention to a couple ideas included in the chart. First, a variable may be acted on by several processes. For example the velocity of the stream is controlled by the slope of the stream, the volume of the stream, and the sediment load. Of these only sediment load is related to velocity by an interdependent relationship indicating feedback. This feedback in the erosion system is a very significant aspect of how streams affect their valleys. Geologists now recognize that streams have an "equilibrium" load dependent on the velocity and volume of the stream. If a stream is carrying more than this load, sediments are deposited in the stream channel. If the stream has less, it will add sediment to its load leading to more rapid erosion. The underload situation is common downstream from dams which remove sediments from water by slowing the flow. Water on the downstream side of the dam works to re-establish the equilibrium load by eroding material from the stream bed and banks. In populated areas, this can cause significant property damage.

A second point is my choice not to show a sign related to climate and its effect on producing loose rock and soil that might be carried by the stream. Climate clearly affects the amount of material available. However, climate is not a strictly defined variable. If the interest of the flow chart was to establish the climatic effects on erosion, then one would need to describe climate more exactly with a number of variables like temperature, rainfall, number of days with frost, etc.

Reading questions:  1. Consider a tree as a system.  Name important components, variables, and processes that impact the ability of the tree to survive.
                                2. Give an example of a system that employs feedback to limit system variability.

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