2. Growth on a Renewable Source (RENEW)

A forest grows biomass (leaves, trunks, roots, animals, bacteria, etc.) using the steady energy of sunlight. A certain amount of sunlight falls on the earth each day; wherever you are you can count on an average amount year after year. This kind of energy source is called renewable.

How the sunlight is used does not affect the amount that is available. A forest that uses the sunlight grows, increasing biomass until it is using almost all the sunlight, which falls each day. When the amount of biomass growth equals the amount that dies and is decomposed, the system of the forest is in a steady state.

In the diagram (Figure II-2a), J is the steady inflow of energy, sunlight in our example. The part of the flow which goes into the system is K*JR*Q, JR, being the part of J which is available to be used. The equation:

J = JR + K*JR*Q

has been changed algebraically for the computer to:

JR = J/(1 + K*Q).

The equation for the change in Q is the growth in biomass minus the death and decomposition of biomass. The growth in biomass is proportional to the sunlight available (JR) and the amount of biomass already growing in the forest (Q): Kl*JR*Q. As in the Exponential Growth model (Figure II-1a), the coefficient K1 is a difference between coefficients K2 and K3.

The death and decomposition of biomass is a proportion (K4) of the stored biomass of forest organisms (Q): K4*Q.

Therefore, the equation for the change in forest biomass (DQ) is:

DQ = K3*JR*Q - K4*Q.

Then amount of biomass at the end of a day will be the biomass at the beginning plus the change:

Q = Q + DQ.

This program needs these three equations.

You get a graph (Figure II-2b) when you run the program showing changes in Q. The growth in biomass (Q) is exponential at first while there is more sunlight than the organisms can use. Then Q levels off at a steady state as the forest system organizes to use all the available sunlight.

Examples of Models Using Renewable Sources

This model is especially appropriate for natural systems, (forests, fields, marshes, rivers, lakes, oceans) growing on steady-flowing sources (sun, rain, wind, tides, waves). An example is successional growth on a bare field, from plants into mature forest trees. At first the weeds grow quickly, then shrubs, tree seedlings, and finally a forest with trees and plants using all the inflowing energy of the sun and rain as it becomes available.

An economic example is a business that has a steady inflow of a raw material such as leather. The business uses the leather to produce belts. The number of belts in stock increases quickly. Then the stock levels off when the number of belts being produced equals the number of belts being sold.

The economies of countries grow this way too. When the colonists came to America their civilization expanded very fast. There were many new resources available to them, such as rich soil, land, and forest wood as well as the tools and knowledge they brought with them. Early in this century growth began to level as we are were using our resources (fossil fuels as well as sun and rain) as fast as they became available.

Discussion Questions and "What If" Experiments

Discussion Question

  1. Compare and contrast systems that grow exponentially (Figure II-1) with those which grow up and then level off at a steady state (Figure II-2). (Consider the difference in the sources of energy for their growth.)

"What if" Experiments

  1. If you lived in an area with a combination of sun and rain better than in our program, how would this affect the forest growth? Prove it by changing and running the program to increase J to 60. What would the graph of Q look like if you reduced J to 30?

  2. Let's consider a successional forest, which is already at the shrub stage. Since Q is starting higher, will the graph level higher? To find out, change statement to: Q = 25

  3. If you plant and then study another forest whose decomposition rate is greater than that of the original, what will this do to the amount of biomass at its steady state? What statement in the program will you change to find out? Do it. Do the mature forests contain the same biomass at steady state? If not, which is more? Why?

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