# Fire

## Overview

This short unit about the spreading of forest fires is intended to teach some of the basics of using a simple pre-made model/simulation. While there are many benefits to using this model, the ability to physically verify the results proves to be difficult. It turns out that the rudimentary simulation of a wild fire spreading through a forest of varying densities can be implemented in a wide range of tools including NetLogo, AgentSheets, Vensim, Excel, and possibly others. Thus, this single model can teach the basics of simulation techniques like agent modeling, cellular automata, and systems dynamics without requiring students to relearn or rediscover what results to expect and allows them to focus on the methods and the techniques.

### For Teachers/TAs

• Geared a little bit towards the teachers and upper end students. Meant largerly as an intro into what we're looking at.
• Much more so geared towards the teachers than students. This is a fairly technical article and is meant to give an overview of an Agent-Based version of wildfires.

### For Students

• Parts of this article are fairly technical and mathematical, however I think there's a lot of good information here. Perhaps we could write up a summary.
• Some of the language might be tough for intro-students, however there's some fascinating information here on why cellular automata are important.

## Lecture Notes

Lecture 1

• Brief cover of wildfires, to understand the basics of what we're going to try to model
• Fires can start any number of ways (lightning, careless smokers, etc.)
• Fires can spread in many ways (more lightning, wind, dense undergrowth, etc.)
• Start covering basic dynamic modeling methods (brief overview, we'll cover Cellular Automata later)
• Cellular Automata
• Cells of a grid can be in some state
• Think of a sheet of graph paper and you can either shade in a square or not
• One cell's state may or may not affect its neighbors
• Changes based on a set of rules
• Agent Modeling
• Independent agents whose behavior is governed by sets of rules
• Systems Dynamics
• Sets of math equations govern the output of a set of graphs
• Output of equations is governed by rates

Lecture 2

• More in-depth coverage of cellular automata
• Game Of Life - canonical example [GoL on Wikipedia]
• Grid where each cell can either be alive or dead
• Cells can either be alive or dead based on the number of living/dead cells around them
• This rule controls the entire simulation and can produce some seemingly complex results
• The wildfire model we'll use is a special-case of the Game of Life
• Trees can either be alive, burning, or smoldering
• Alive trees can be caught on fire by neighboring burning trees and become burning
• Burning trees can catch neighboring alive trees on fire and can become smoldering after a certain time
• Smoldering trees can do nothing
• In the basic model, the average distance between trees (i.e. the forest's density) can be controlled
• Certain aspects can be seen by varying this control
• Lightning: where new fires can be started at a random location
• Wind: where fire has a tendency to spread in certain directions
• Wetness: where certain trees may have a decreased chance to catch on fire
• Duration of Burning: where burning trees may stay burning longer
• As with density, tuning these "knobs" can produce different behaviors

## Lab

This lab will consist of learning how to use NetLogo's wildfire model to see how minor changes in parameters can, under certain circumstances, producing wildly different results.

The student should first see the tediousness of the process of:

1. Set the desired parameter to some value
2. Run the model
3. Record the proper results into a spreadsheet
4. Increment the parameter and repeat steps (2-4)

The next step is to learn how to use NetLogo's parameter sweep ("Behavior Space") functionality to automate this process.

Ideally, when they run the manual parameter sweep they'll get results that tell them very little about how the density of the affects how much of it gets burnt. This will stress the importance of taking representative data sets to be able to accurately analyze the model.

A continuation of the lab would be to use one of the extended models (likely written by one of the TAs) and run parameter sweeps to understand how the different features can dramatically change the results.

#### Bill of Materials

As long as the students don't try to actually burn down a forest to validate these models, there is no cost for this lab.

## Evaluation

#### CRS Questions

• Which of these is a reasonable method for simulating Wild Fires?
1. A technique called "systematic dynamical conflagration"
2. Going out back campus and ....
3. Coding all the properties of wood into a program
4. A technique called "cellular automata"
• What is another name for "Cellular Automata"?
1. Automated Telecomune
2. Tessellation Automata
3. Biological Automated Simulation
4. Systems Dynamics
• Who is credited for doing some of the first work in Cellular Automata?
1. Stephen Wolfram
2. John von Neumann
3. Alan Turing
4. Stanislaw Ulam

#### Quiz Questions

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## Scheduling

This should be very early in the semester as it is a fairly simple and short topic. Given its simplicity, it should only be a single week.

## Concepts and Techniques

This unit should teach the basics of using someone else's model, as well the importance of conducting multiple runs with different parameters in order to gain an accurate understanding of the effect of the model.

## General Education Alignment

• Analytical Reasoning Requirement
• Abstract Reasoning - From the [Catalog Description] Courses qualifying for credit in Abstract Reasoning typically share these characteristics:
• They focus substantially on properties of classes of abstract models and operations that apply to them.
• This unit deals almost entirely will quantitative reasoning, and would be hard to expand into the abstract world.
• They provide experience in generalizing from specific instances to appropriate classes of abstract models.
• Parameter sweeping (one of the primary goals of this unit) can be used in almost every instance of computational simulations. In this sense it can be expanded from this specific model to others, yet it is more of a quantitative method of analysis than it is abstract.
• They provide experience in solving concrete problems by a process of abstraction and manipulation at the abstract level. Typically this experience is provided by word problems which require students to formalize real-world problems in abstract terms, to solve them with techniques that apply at that abstract level, and to convert the solutions back into concrete results.
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• Quantitative Reasoning - From the [Catalog Description] General Education courses in Quantitative Reasoning foster students' abilities to generate, interpret and evaluate quantitative information. In particular, Quantitative Reasoning courses help students develop abilities in such areas as:
• Using and interpreting formulas, graphs and tables.
• This unit is intended to teach the student how to gather data using a specific tool and analyze that data to come to some conclusion.
• Representing mathematical ideas symbolically, graphically, numerically and verbally.
• The student will need to create a lab write-up in which they express why they went about collecting the necessary amount of data. They will also need to include examples of said data and an explanation of what conclusion(s) can be drawn from that data.
• Using mathematical and statistical ideas to solve problems in a variety of contexts.
• While this unit deals almost entirely with a single tool, the idea of parameter sweeping is necessary in every form of simulation and is thus applicable in a wide range of contexts.
• Using simple models such as linear dependence, exponential growth or decay, or normal distribution.
• This wildfire model clearly shows how the number of burned trees is directly dependent on certain features of the forest (density, wetness, etc) and how minor changes in those features can dramatically change the outcome.
• Understanding basic statistical ideas such as averages, variability and probability.
• At the end of this unit the student should be able to understand that one cannot make sufficiently accurate conclusions about a model with only a single data set.
• Making estimates and checking the reasonableness of answers.
• In the beginning of the lab portion of this unit, the student should take a guess at what the result will be when the density of the forest is varied. After running a number of trials, they should be able to easily assess the accuracy of they're answer as well as the reasonableness of their results from the lab.
• Recognizing the limitations of mathematical and statistical methods.
• The student should clearly note that this model of wildfires is far from indicative of how they actually happen. It should be stressed that this model is simply proof of concept for showing the profound effect a single variable can have on the overall results.
• Scientific Inquiry Requirement - From the [Catalog Description] Scientific inquiry:
• Develops students' understanding of the natural world.
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• Strengthens students' knowledge of the scientific way of knowing — the use of systematic observation and experimentation to develop theories and test hypotheses.
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• Emphasizes and provides first-hand experience with both theoretical analysis and the collection of empirical data.
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## Scaffolded Learning

The NetLogo model(s) in question are easy to use and easy to witness the effect of changing parameters to obtain different results. As well there are fairly clear extensions for the student inclined towards taking those steps.

## Inquiry Based Learning

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