Simulation• A “model” that is a simulation of a past or

potential event

• Typically the models are not considered general (simpler models may be)

• Relies on knowledge of the mechanisms behind the processes that created the event

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Simulations are Used In:

• Volcanic eruption processes

• Flood dynamics

• Land slides

• Earthquakes

• Disease propagation

• Oil spills

• Species population dynamics

• Social dyanmis

Validation?

• Past Events:– Can ground-truth based but how

generalizable are they?

• Future Events:– How to ground-truth?

• Best case:– Model based on past events, ground-truth,

then extend into the future carefully

Civil Engineering

• Civil engineering is based on what has worked in the past

• New structures are built based on:– Understanding of materials– Books of “margins of error” based on what

has worked and not worked in the past– Simulations of potential scenarios

Tacoma Narrows Bridge

• http://www.youtube.com/watch?v=j-zczJXSxnw

• After the Tacoma narrows bridge collapsed, all suspension bridges had to be checked for harmonic oscillations against the typical winds in the area

• Today, this is just one of the simulations that are used to test structures in different situations.

Simulation Models

• NASA’s Perpetual Ocean– http://svs.gsfc.nasa.gov/vis/a000000/

a003800/a003827/

• NASA Simulation of aerosols:

Animations (Simulations?)

• Tsunamis:– http://www.youtube.com/watch?

v=_bCTa5su8II– http://www.youtube.com/watch?

v=WgpXzwLuGDo

When to simulate?

• Completely hypothetic scenarios

• Really minimal data

• Temporal process -> compelling animations

• The process is believed to be well understood (simulations are typically mechanistic)

• When the problem can be simplified enough to run on available hardware!

• Educational

Methods

• Agent-Based

• Cellular automaton

• Agent:– Typically a point– Has “attributes”: health, size, age, sex, etc.– Behaves independently

• Moves, feeds, breeds, dies

– Can “interact” with other agents– Can “interact” with its envrionment

Agent Based Modelswww.anylogic.com

Environmental Science

• Spatially Explicit Individually Based Models (SEIBM)– Each “object” in the model represents one

individual

• Spatially Explicit Population Based Models (SEPBM)– Each “object” represents N individuals

Simple Model

• All Agents– X– Y

• Predator– Hunger

• Prey– Health

Prey 1

Prey 1

Prey 1Pred 1

How it works

• Move agents

• Agent interactions– Prey

• Update attributes– Hunger– Birth– Death

Movement

• Each agent has an x, y coordinate

• Moves to a new position based on:– Random movement– Directed movement– Terrain– Forces: wind, water, slope

Random

Directed

Lagrangian Movement

“Walking”

• Random Walk– Brownian Motion: pseudo-random

movement of particles when interacting with other particles

• “Directed Walk”– Movement toward a resource

• Lévy flight foraging hypothesis – Line lengths drawn from a “heavy tailed”

distribution

Interactions

• Agents interact with each other:– Breed– Feed– Interact with distance < some minimum

• Agents interact with the environment:– Feed on grass

Agents Update Attributes• Hunger/Health go down without food• Birth happens at some cycle if conditions

are correct• Death

– If Hunger/Health are too high/low– Age > maximum– Conditions too harsh

• Also can:– Grow– Learn– Bloom, senesce

Life Cycle

Birth

Youth

Adult

Death

Individually Based Models

• Crowds– http://www.lsi.upc.edu/~npelechano/

MACES/MACES.htm

• Princeton’s migration studies:– http://icouzin.princeton.edu/leadership-

collective-behavior-and-the-evolution-of-migration/

• Agent Based Traffic Model– http://www.cs.unc.edu/~wilkie/

Cellular Automata

• Monitor what is in each “cell”– Typically:

• Each raster has the number of individuals of one type (or amount of available veg)

– Can also include:• Land cover, barriers, water vs. land, etc.• Difficulty to cross area• Open vs. protected areas

Tools

• NetLogo

• HexSim

• MASON Multi-Agent Simulation Toolkit

• Repast

• Programming!– Python– Java

• Books: “Agent-Based Models of Geographical Systems”

Python SEIBM• Very simple model

• Includes 2 classes: – Animal (prey and predators)– Veg (grass)

SEIBM – Main Script

• Imports: Tkinter, time, random, Veg, Animal

• Setup the GUI

• Initialize animal objects in an array

• Loop forever:– Update each object– Redraw the window– Let Python process events (mouse clicks)– Sleep for a bit