Fire is a pulsing model, which includes a switch. When the grass (Q) has grown up to a critical mass (G1), then the fire switches on. When the grass has burned down so low (G2) there is no longer enough to burn, the fire switches off. As the fire burns, it releases nutrients, which stimulate growth and are bound up in the grass again. (Figure III-13).

In the program (Table III-13) the fire switch is turned on when Q>G1 (see statement). G2 is the quantity of grass left after the fire. G1 and G2 are thresholds and are shown at the top of the switch symbol in the figure.

The total nutrients in the system (TN) include the nutrients in the soil (N) plus those bound up in the grass (F*Q). When the grass (Q) is burned, all the nutrients in the burned grass return to the soil: that is, the nutrients in the soil are the total nutrients minus the nutrients bound-up in the unburned grass (N-TN-F*Q).

Statements draw lines from the values Q and N had right before the fire to their values right after the fire. When these are red, they illustrate the fire dramatically.

Examples of Switch Models

Many natural systems have fire as part of their normal pattern. Pine forests in southeastern U.S., chaparral in southern California and the Mediterranean, and grasslands around the world have this pattern. Sometimes fire comes every 4 or 5 years as in our Southeast; sometimes it's every hundred or so as in the lodgepole pine forest in Yellowstone National Park. A spurt of growth follows the fire, as the nutrients are recycled into the soil.

An economic example is a buildup of inventories in a store to a certain amount, followed by a sale to sell most of them. N might be the empty hangers and shelves ready to take more clothes.

"What if" Experimental Problems

1. Does the forest pulse more or less often if more nutrients are added to the system? What would you increase in the program to find out? Do it and explain the result.
   


2. If the fire were put out by firefighters when it had burned about three-quarters of the grass, what would happen to the timing of the pulse? Change the program so that when the fire comes Q goes down to 0.75 of G1. Run the program. Was your hypothesis right?
   


3. What happens to a fire-cycle system if fire is kept out completely? Eliminate statement to see.
   


4. Lower the sun and rain (I) to one-half. How often does fire come?

COMPUTER MINIMODELS AND SIMULATION EXERCISES FOR SCIENCE AND SOCIAL STUDIES

Howard T. Odum* and Elisabeth C. Odum+
* Dept. of Environmental Engineering Sciences, UF
+ Santa Fe Community College, Gainesville

Center for Environmental Policy, 424 Black Hall
University of Florida, Gainesville, FL, 32611
Copyright 1994

Autorização concedida gentilmente pelos autores para publicação na Internet
Laboratório de Engenharia Ecológica e Informática Aplicada - LEIA - Unicamp
Enrique Ortega
Mileine Furlanetti de Lima Zanghetin
Campinas, SP, 20 de julho de 2007