Modeling the Effects of Greenbelts at the Urban-Rural Fringe

Daniel G. Brown

Scott E. Page

Rick Riolo

William Rand

With funding from

BiocomplexityFirst Biennial Conference, IEMSS, Lugano, Switzerland, 26 June, 2002

SLUCE Project Goals (Spatial Land Use Change and Ecological Effects)

• Develops agent-based models of land use that will be compared with recent (~50 yrs) changes and used for evaluating future scenarios.

• Explores and implements complementary methodologies (ABM, GIS, survey research, spatial analysis, remote sensing).

Agent-Based Models

Spatial Analysis/RemoteSensing

Social Surveys and

Scenarios

Land Use Change

• Focuses on land use dynamics at the urban-rural fringe (i.e., Metro Detroit) and their ecological effects.

Agent-Based Models

Goals of this Presentation

• Present an agent-based model of land use change at the urban-rural fringe that can be used to evaluate policy options.

• Compare ABM results with a simpler mathematical model for validation.

• Evaluate the interactions between greenbelt placement and width and the process of land development.

Goals of Mathematical Model

• see what can be proved with a simple math model, and what assumptions must be made to make it tractable

• serve as comparison for the ABM, which will be able to lift these assumptions

Mathematical Model

• Assumptions– M locations on a line– N people/agents– Greenbelt

• width w

• beginning at location g > m

Model Specifications

• Location j has natural beauty q(j)

• Agents care about– distance to services : s (closer is better)– aesthetic quality: q(j)

• value of location j = u(s) + q(j)

Math Model Results

• R1: If all sites have same q, then any greenbelt prevents sprawl

• R2:If q’s vary, then a greenbelt prevents sprawl if best location outside of the greenbelt is worse than the best location inside of the greenbelt– mathematics: tradeoff between w and g

Specific Cases

• Quality decreases from the left– all greenbelts prevent sprawl

• Quality increases from the left– sprawl difficult to prevent– linear preferences: only w matters if x > M

Agent-Based Model

• Implemented using objective-C and Swarm (www.swarm.org)

• Environment– 80 by 80 lattice, each cell has

• a value of natural beauty, assigned randomly or based on defined pattern

• score for distance to service centers, based on the sum of inverse distances to the nearest 8, updated at each step

sd = 0.5 * max[2, (1/sc1) + ... + (1/sc8)]

Random pattern of

Natural Beauty

ABM: Agents• Each cell in lattice accommodates only 1

resident or service center • residents

– have attributes that describe• preference for beauty (nb)

• preference for nearness to SCs (sd)

• service centers (SC)– initial SC located in middle of left side– one new SC created near location of each

100th resident - SC follow residents

Red cells are service

centers

Location Decision

• 10 residents are created during each discrete time step.

• Residents locate by:– selecting 15 cells randomly– moving to the cell that provides the

highest utilityutilityxy = 0.5(nb*nbxy*sdxy + sd*sd2

xy) Black cells are

residents

Adding a Greenbelt• A greenbelt, an area that cannot be

developed, is defined by its starting position from the left side (g) and its width (w).

• We report the number of time steps before there are 300 developments beyond the greenbelt.

Green cells are

greenbelt

Experimental Results• Multiple runs for each experiment (n=30)

• Different parameter settings to compare with mathematical model results.1 Random Preferences and Environment2 Effects of Set Preferences

• nearness to services

• natural beauty

3 Effects of Specific Patterns in the Environment

• Each of the above run with two different values set for greenbelt start (g), 20 and 40, and width (w), 1 and 15.

1: Random Preferences/Environment• Simple probability suggests that, using random

placement of developments, the number of time steps to achieve 300 developments beyond the greenbelt should be:

• 39 when g is 20

• 59 when g is 40# Time Steps [Average (std dev)] to reach

300 developments beyond greenbelt

Greenbelt start (g)20 40

Width (w) 1 39 (1) 61 (2)15 39 (1) 60 (2)

1: Graphic Results• Results validate proper functioning of the model.• Graphics show results after 50 time steps.

Graphic illustrates one run with g=20 and w=15

2: Modifying Preferences• A: Setting a uniform preference for nearness to services

(0.5) results in a long time to cross the greenbelt.

• B: Adding a uniform preference for natural beauty (0.5) decreases time to cross greenbelt.

# Time Steps [Average (std dev)] to reach 300 developments beyond greenbelt

A: Distance to Services B: Distance & Beauty

Greenbelt start (g) Greenbelt start (g)20 40 20 40

Width (w) 1 113 (23) 275 (47) 1 86 (19) 194 (52)15 151 (26) 337 (19) 15 103 (29) 278 (39)

2: Graphic Results

• A: Development stays left of greenbelt to be near services, which causes services to locate there.

• B: Some sites to the right have higher utility because of their beauty.

Graphics illustrate one run with g=20 and w=1

3: Patterns of Natural Beauty• A: Longest crossing times are achieved (1.5 times

the random beauty pattern) with Beauty decreasing to the right.

• B: Significantly shorter crossing times with Beauty increasing to the right.

# Time Steps [Average (std dev)] to reach 300 developments beyond greenbelt

A: Beauty High on Left B: Beauty High on Right

Greenbelt start (g) Greenbelt start (g)20 40 20 40

Width (w) 1 131 (7) 320 (25) 1 44 (7) 71 (30)15 167 (15) 344 (3) 15 47 (14) 99 (62)

3: Graphic Results

• A: Comparable to math model, specific case 1, agents stay to the left.

• B: Comparable to math model, specific case 2, sites to the right are irresistible.

Graphics illustrate one run with g=40 and w=15

Conclusions• Greenbelts affect patterns of development

– trade-off between location and width

– effectiveness dependent on preferences and environment

• Comparison of results validate the agent-based model using a simple math model

• ABM can accommodate– 2- or higher dimensional world

– population with heterogeneous preferences

– real or designed environmental characteristics