GEOG 110 – Lab #2 – Modeling Growth and Decay DynamicsLinear Growth or DecayExponential Growth or DecayLogistic GrowthExponential Growth and DecayLogistic GrowthGEOG 110 – Lab #2 – Modeling Growth and Decay DynamicsDue Date: 11:59 pm September 30, 2005Objectives: Become familiar with three behavior patterns that are present in manydynamic systems; linear growth or decay, exponential growth or decay,and logistic growth. Learn how to translate the mathematicalrepresentations of these patterns into STELLA models.Background: As you should have learned from Lab #1, identifying the components of asystem and the linkages between them is just one part of constructing amodel. An equally critical activity is defining the rules that govern thesystem. This is usually done by specifying a set of equations that statewhat the system will do under a given set of conditions. In the graphicallanguage of STELLA, this is the act of replacing those question marks inthe Model view with equations (or sometimes a graph element, which stilldictates an x - y relationship, and is used in the instance when a crediblemathematical expression of the relationship cannot be found).In environmental science, we tend to learn of these equations orrelationships through observations: We measure some variables ofinterest, look at the sort of plot they produce when graphed on two axes, ifpossible hypothesize an equation that describes the observed behavior, andthen test it to see if it is a useful model of the phenomenon. There are fivecommon behavior patterns that you should become familiar with to helpyou construct environmental models in STELLA:- Linear growth or decay- Exponential growth or decay- Logistic growth- Overshoot and collapse- OscillationIn this exercise, we will examine the first three of these common behaviorpatterns in detail.Resources: This lab exercise does not include the background and theory required foryou to understand the origins and applicability of these behavior patterns.For that information, you should look to material from the lectures andChapter 2 (pp. 28-65) of the course text. At this point, you should havealready have successfully completed Lab #1, and you should have thebasic familiarity with STELLA required to build the simple models forthis exercise. If you need to refer to resources to help you with the detailsof using STELLA, refer back to those suggested for Lab #1. From thispoint onward, the lab exercises will not be provided in step-by-step detail,1because the focus from this point onward will be on what the modelsrepresent, not on the nuts and bolts of constructing them.Procedure: This second exercise (and subsequent exercises) features slightly lessspecific instructions. If you cannot recall how to before some basicoperation in STELLA, refer back to lab exercise #1 or refer to theresources referred to therein.Linear Growth or Decay1. Get STELLA started and open up the lake model you constructed forLab #1. Conveniently, that lake model is a system that features a stockthat displays linear behavior using the equations and values wespecified. You can compare our system to the generic linear systemdiagram (Figure 2.3, p. 34) from the course text and see the structuralsimilarity. Recall that your system should look like this:2. Run the model using the values we specified last time(Precipitation=25 m3/time, Evaporation=20 m3/time, initial lakevolume=100 m3) and have a look at the output. Is the system’s stock(the lake) displaying linear growth or decay with these values?3. Change just one of the two processes’ values such that the systemdisplays the opposite behavior (i.e. either growing or decaying at theopposite rate to which it did previously). There are two possible waysyou can accomplish this.4. You may recall that the Run Specs for our model were set so that themodel would run for 12 time steps. Experiment with changing thelength of the simulation (i.e. number of time steps in the model run) tosee what the final value of the stock is at the end of model runs ofdifferent lengths.Exponential Growth or DecayIn order to experiment with exponential behavior, we are going to add afurther process to our lake model. It was always a little odd that the onlyway water left our lake was through evaporation. Let’s assume that ourlake also has a dam on it, and that it has an open gate to release water fromthe lake in proportion to how full the lake is.25. Set the both the Precipitation and Evaporation rates to 20 m3/time. Bydoing this, we are making our lake a steady state system that will notdisplay any further linear behavior.6. Add another process that removes water from the your lake stock,which you can call Outflow. You can slide the Evaporation processupward a little, place Outflow below it. This process is quiteanalogous to that shown in Figure 2.8 of the course textbook(described on pp. 39-40), so you can use that as a guide to help youconstruct this. Add the appropriate converter (name it Flow Rate) andthe necessary connectors too. You should create something that lookslike this:You’ll need to select some existing model elements and slide themaround a little to get it to look organized and neat like this. 7. As you can see from the question marks in the figure above, I’mlooking at my model in the Model view, and the question marks tellme that Outflow and Flow Rate both need some values filled in so as todefine their behavior. Set the Flow Rate to 0.5/time (by typing 0.5 inthe box and clicking the Units button to set the units). Set the Outflowto Flow_Rate*your_lake by using the controls in the dialog (either byclicking on the model objects in the Required Inputs or by typing themout, and the * by clicking on the appropriate button or typing it out).8. Set the Run Specs to run the model from time steps 0 to 12, withDT=0.25. Set the Sim Speed to 1 real secs = 1 unit time so you canwatch the model run. Maximize your Lake Graph so you can see theplot, and Run the model. Your Lake Graph plot should looksomething like this:39. Save this model as youronyen-lab2-exp.stm in your course directory atthis point, so I can see you’ve successfully built