Introduction to Spatial Modeling

Michael F. GoodchildUniversity of California

Santa Barbara

Spatial modeling

• What is it?• Why do it?• Spatial modeling and spatial analysis

– an example

• Types of modeling• Organizing and thinking about the options

Definitions

• A model– a representation of something real– of a real process operating on the Earth's surface

• social or physical

– a design process conceived by a human• to search for the best alternative

• A digital representation– everything reduced to 0s and 1s– in software and data– executed on a computer

• a computational model

A spatial model

• A model of some process operating in space (and time)– there is variation across the space (and through

time)– location is important

• the results of modeling change when locations change• locations must be known

Models can also be analog

• Executed physically• Scaled to practical size

– scale factor is critical– scaled in space and time

• compressed and accelerated

(X,Y)

(wi,xi,yi)

Find (X,Y) to minimize:

i iii YyXxw

2/122

The Varignon Frame

Scale and digital models

• Digital models don't have a scale factor– but they operate at limited spatial resolution

• Spatial resolution is a critical factor– it determines:

• what is left out of the model• the cost of collecting data and running the model

– it contributes to the model's accuracy• the degree of uncertainty about the real world created by

the model

• Temporal resolution is important for the same reasons

2000

1970

1940

1910

A B C

D

A BC

D

Fred

MaryJohn

Why do it?

• It is better than experimenting on the real thing– surgery students and cadavers

• the digital cadaver

– highway traffic simulation– global CO2

• Evaluating "what if" scenarios• Gaining public interest and acceptance

Analyze or model?

• Analysis:– static, one point in time– searching for patterns, anomalies– generating ideas and hypotheses– evaluating

• Modeling:– may be dynamic, multiple points in time– implementing ideas and hypotheses

• to compare to the real world

– experimenting with scenarios

Simulations

• 1.8 vehicles per driveway• Driver behavior influenced by:

– lane width– slope– view distances– traffic control mechanisms– information feedback– driver aggressiveness

• 770 homes– clearing times > 30 minutes

2D clip

3D clip

Policy implications

• Addition of new outlets• Better deployment of traffic control resources• Understanding the risk• Reduce cars used per household• Problems of shut-ins, elderly, latch-key kids

Types of modeling

• Static or dynamic?– are there time steps?– are they iterated?

• does the model loop?• output of one step becomes the input of the next• how are the initial conditions defined?

– is there a real process to emulate?

Static model example

• The Universal Soil Loss Equation– prediction of soil erosion– from potentially knowable inputs

• Five inputs, one output

Is USLE a spatial model?

• No, point inputs and point output– it doesn't matter where the points are– this could be done in Excel

• downloadable procedure at http://www.co.dane.wi.us/landconservation/uslepg.htm

• So why use a GIS?– calculation of inputs

• slope from DEM

– inputs in map form– output in map form– integration with other GIS operations

Social, physical, or integrated?

• Social:– a model of some process operating among

humans• or animals

• Physical:– a model of some natural process operating in the

environment• Integrated:

– a model of the interaction of social and physical processes

• land cover change, driven by humans, impacting the environment

Individual or aggregate?

• Modeling each individual separately– data-intensive

• impossible for many physical processes

– accurate

• Modeling the behavior of aggregates– quick, cheap– the only option when individual data are

confidential

• Illustrations from:

Geovisualization of Human Activity Patterns Using 3D GIS: A Time-Geographic ApproachMei-Po Kwan and Jiyeong Lee

Identifying Ethnic Neighborhoods with Census Data: Group Concentration and Spatial Clustering: John R. Logan and Wenquan Zhang

The Steinitz framework

• Models at various stages of the decision-making or problem-solving process

Landscape Change Model by Carl Steinitz

CHANGEMODELS

IMPACTMODELS

DECISIONMODELS

DATA

INFORMATION

KNOWLEDGE

DATA

INFORMATION

KNOWLEDGE

1. How should the landscapebe described?

2. How does the landscapeoperate?

3. Is the landscape workingwell?

4. How might the landscapebe altered?

5. What differences might thechanges cause?

6. Should the landscapebe changed?

REPRESENTATIONMODELS

PROCESSMODELS

EVALUATIONMODELS

Land

scap

eA

sses

smen

tLa

ndsc

ape

Inte

rven

tion

How do models manage space?

• As a raster– cellular models

• As vector objects– possibly moving– object-oriented models

How do models manage time?

• As discrete intervals– fixed in time

• As a continuum– rates of change and movement

Cellular models

• Raster-based– but the raster could be irregular

• Each cell has a number of potential states• Rules determine changes in the states of

raster cells– based on the states of other (often neighboring)

cells– Game of Life

Planning Scenario Visualization and Assessment: A Cellular Automata Based Integrated Spatial Decision Support SystemRoger White, Bas Straatman, and Guy Engelen

Lots of options and potential

• How to organize?– how to think about the alternatives?

• Visual– a picture is worth a thousand words– people like to think visually

• especially if pictures can be translated directly into models

• STELLA– boxes and arrows

Modeling Spatial Information

SOILS

ELEVATION

VEGETATION

RAIN FALL

SLOPE

EROSIONPOTENTIAL

EROSIONHAZARD

Overlay and combine values according to the Boolean rule If (A.EQ.1).AND.(B.GT.2) then C=1 else C=0

A groundwater example

• http://www.esri.com/news/arcuser/0704/files/modelbuilder.pdf

• Alan Glennon and Rhonda Pfaff• Tutorial

Conceptual Model

Visual Representation

Script

(VBA, Python, AML, Avenue)

GIS execution

Initial conditions, parameters, rules

Maps, tables, charts

What are the operations/nodes?

• Any operation on spatial data– any GIS operation

• Many thousands of possibilities– more than 400 entries in Toolbox– plus all the desktop operations

Raster-only options

• Map algebra– Dana Tomlin's Cartographic Modeling

• Focal– operations on a cell across layers

• not strictly spatial

• Global– operations on all cells

• Local– operations on a cell and its neighbors

• Zonal– operations on a cell and contiguous cells of the same

attribute value

PCRaster and its language

• Developed at the University of Utrecht– by Peter Burrough and colleagues

• Simple algebraic language– C = A + B– equivalent to FocalAdd A and B to get C

• CA models can be written in the language– along with many other social and physical process

models– see http://pcraster.geog.uu.nl/ for examples etc.

A more comprehensive option

• P A Longley, M F Goodchild, D J Maguire, and D W Rhind, 2001. Geographic Information Systems and Science. New York: Wiley.

A six-way conceptual classification

• Query and reasoning• Measurement• Transformation• Descriptive summary• Optimization• Hypothesis testing

Queries and reasoning

• Real-time answers to geographic questions– Where is…?– What is this?– How do I get from here to here?

• Based on alternative views of a database

Measurements

• Area• Distance• Length• Perimeter• Slope, aspect• Shape

Transformations

• Buffering• Points in polygons• Polygon overlay• Spatial interpolation• Density estimation

City limits

Areas reachable in 5 minutes

Areas reachable in 10 minutes

Other areas

Courtesy of Dick Block

Descriptive summary

• Centers• Measures of spatial dispersion• Spatial dependence• Fragmentation• Fractional dimension

Optimization

• Design to achieve specific objectives• Location of central point-like facilities to serve

dispersed demand• Location of linear facilities• Design of boundaries for elections

Hypothesis testing

• Geographic objects as a sample from a population– what is the population?

• The independence assumption– the First Law of Geography– failure to find spatial dependence is always a Type

II error– hell is a place with no spatial dependence