urbdp 422 urban and regional geo-spatial analysis lecture 11: modeling spatial phenomena:

URBDP 422 URBAN AND REGIONAL GEO-SPATIAL ANALYSIS

Lecture 11: Modeling Spatial Phenomena: the Land Cover Change Model

Lab: Exc. 11, Network Analysis

FEB 11, 2014

Lecture’s Objectives

• Land Cover Change Model

• Uncertainty

• Unresolved issues in modeling urban landscapes

Questions• How does urban development affect

– Hydrology? (Flooding, water supply)– Stream quality?– Salmon populations?– Bird diversity?

• What do we need to define in order to answer these questions?

Example: Percent Land Cover

100% Urban 16% Urban 3% UrbanPercent Land 1 Percent Land 2 Percent Land 3

100 % Urban

0% Mixed urban

0 % Forest

16% Urban

73% Mixed Urban

11% Forest

3% Urban

86% Mixed Urban

11% Forest

A

a

pLand

n

j

ij 1

Sum of the area of all patches of the corresponding patch type divided by total landscape area.

% TIA, % Trees, and B-IBI

B-IBI and %Trees

R 2 = 0.5978

0

10

20

30

40

50

60

0% 20% 40% 60% 80% 100%

%Trees

B-I

BI

B-IBI and %TIA

R 2 = 0.6151

0

10

20

30

40

50

60

0% 20% 40% 60% 80% 100%

%TIA

B-I

BI

Example: Aggregation Index

AI equals the number of like adjacencies divided by the maximum possible number of like adjacencies involving a specified class

High Impervious Aggregation Medium Impervious Aggregation Low Impervious Aggregation

92% Impervious Aggregation Index

72% Impervious Aggregation Index

28.5% Impervious Aggregation Index

High Medium Low

Aggregation Index and B-IBI

R 2 = 0.66

10

15

20

25

30

35

40

45

50

40 50 60 70 80 90 100

AI (Forest)

B-I

BI

R 2 = 0.60

10

15

20

25

30

35

40

45

50

40 50 60 70 80 90 100

AI (Urban)

B-I

BI

Questions• What might the consequences of development

look like in 2038?• What if

– we expand the highway system? – Or expand the light rail? – Or change development regulations?– Or… you ask me…

• What do we need to calculate to answer these questions?

Assess future land cover

• Land cover change model…

• LCCM is constructed using observed biophysical, land cover, and development data

LCCM Background

• LCCM is a multinomial Logit model based on a set of discrete choice equations of site-based land cover transitions

MU HU

LU HU

MU

Mixed Forest

HU

MU

LU

Conifer Forest

HU

MU

LU

Mixed Forest

LCCM Background

• LCCM calculates transitions probabilities for each pixel in the landscape

• Name some factors that might be associated with each transition.

MU HU

LU HU

MU

Mixed Forest

HU

MU

LU

Conifer Forest

HU

MU

LU

Mixed Forest

Land Cover Sample Variables

Landscape Composition Metrics

  Percent Urban

  Percent Light Urban

  Percent Forest

  Percent Steep Slope

Distance Metrics

  Distance to Critical Areas

  Distance to Primary Roads

  Distance to Local Roads

Landscape Configuration Metrics

All Urban Aggregation Index

Forest Aggregation Index

Development Intensity Variables

  Development Event   Geometric Mean Parcel Size

Recent Development Variables

  Commercial Area Added Time T-3

  Residential Units Added Time T-3

Indicator Variables

Below Minimum Parcel Size

  Is Inside Urban Growth Boundary

UrbanSim

UrbanSim Modules

Model Implementation

• Developed within the Open Platform for Urban Simulation (OPUS) and UrbanSim modeling platforms (Waddell 2002, Waddell et al. 2003

• Land cover change predictions were made for four counties (King, Kitsap, Piece, and Snohomish) every 4 years from 2003 to 2027.

• Model estimations were created using observed data from 1991, 1995, 1999 , and 2002

• Land cover change predictions will be generated for the Central Puget Sound region every year from 2000 to 2040.

Land Cover Transitions Modeled

k

j)β(i ts,Χ

j)β(i ts,Χj)(i

ts,Pe

e

Pst is the probability of land cover change at site s at time t.

X is the y x m matrix of the y independent variables and a unitary constant associate with each m site with initial class i.

ij is a vector of estimated logit coefficients.

k is the number of land cover states.

Observed 1991 Observed 1995 Predicted 1999 Observed 1999

Land Cover Change Model

1991 (t0) Land cover class

1995 (t1) Land cover class

Land cover Change (LCC)

Set of all possibleLand cover transitions

1999 (t2) Land cover class (predicted)

Aggregation Index of Conifer - sample of light urban to medium urban

- Sample of conifer to light urban

Land Cover Change Model

1991 (t0) Land cover class

1995 (t1) Land cover class

Land cover Change (LCC)

Stratified 10% random Sample of 30 m pixels

Sample spatialData layers, export to database

Set of all possibleLand cover transitions

Aggregation Index of Conifer - sample of light urban to medium urban

- Sample of conifer to light urban

Land Cover Change Model

Aggregation Index of Light Urban - sample of light urban to medium urban

- Sample of conifer to light urban

Land Cover Change Model

1991 (t0) Land cover class

1995 (t1) Land cover class

Land cover Change (LCC)

Stratified 10% random Sample of 30 m pixels

Sample spatialData layers, export to database

Multinomial Logit used to estimate equations for Land cover transition

Set of all possibleLand cover transitions

Land Cover Change Model

1991 (t0) Land cover class

1995 (t1) Land cover class

Land cover Change (LCC)

Stratified 10% random Sample of 30 m pixels

Sample spatialData layers, export to database

Multinomial Logit used to estimate equations for Land cover transition

Set of all possibleLand cover transitions

One set of equations for each land cover class including No Change3

Spatial data sets as potential explanatory

variables of LCCPixel-level probabilitiesof land cover transition from unique combination of input variables for each equation

Map Transitionprobabilities

1991 Land cover class

1999 (t2) Land cover class (predicted)

Land Cover Change Model

1991 (t0) Land cover class

1995 (t1) Land cover class

Land cover Change (LCC)

Stratified 10% random Sample of 30 m pixels

Sample spatialData layers, export to database

Multinomial Logit used to estimate equations for Land cover transition

Set of all possibleLand cover transitions

One set of equations for each land cover class including No Change3

Spatial data sets as potential explanatory

variables of LCCPixel-level probabilitiesof land cover transition from unique combination of input variables for each equation

Monte Carlo simulation to randomlyDetermine which transition (includingNo Change) occurs and where

Map Transitionprobabilities

1991 Land cover class

1999 (t2) Land cover class (predicted)

Land Cover Change Model

1991 (t0) Land cover class

1995 (t1) Land cover class

Land cover Change (LCC)

Stratified 10% random Sample of 30 m pixels

Sample spatialData layers, export to database

Multinomial Logit used to estimate equations for Land cover transition

Set of all possibleLand cover transitions

One set of equations for each land cover class including No Change3

Spatial data sets as potential explanatory

variables of LCCPixel-level probabilitiesof land cover transition from unique combination of input variables for each equation

Monte Carlo simulation to randomlyDetermine which transition (includingNo Change) occurs and where

Compare predicted with observed

Map Transitionprobabilities

1991 Land cover class

1999 (t2) Land cover class (predicted)

1999 (t2) Land cover class (observed)

Land Cover Change Model

1991 (t0) Land cover class

1995 (t1) Land cover class

Land cover Change (LCC)

Stratified 10% random Sample of 30 m pixels

Sample spatialData layers, export to database

Multinomial Logit used to estimate equations for Land cover transition

Set of all possibleLand cover transitions

One set of equations for each land cover class including No Change3

Spatial data sets as potential explanatory

variables of LCCPixel-level probabilitiesof land cover transition from unique combination of input variables for each equation

Monte Carlo simulation to randomlyDetermine which transition (includingNo Change) occurs and where

Spatially-constrain output Using observed rules of urban development patterns

Compare predicted with observed

Map Transitionprobabilities

1991 Land cover class

1999 (t2) Land cover class (predicted)

1999 (t2) Land cover class (observed)

Land Cover Change Model

1991 (t0) Land cover class

1995 (t1) Land cover class

Land cover Change (LCC)

Stratified 10% random Sample of 30 m pixels

Sample spatialData layers, export to database

Multinomial Logit used to estimate equations for Land cover transition

Set of all possibleLand cover transitions

One set of equations for each land cover class including No Change3

Spatial data sets as potential explanatory

variables of LCCPixel-level probabilitiesof land cover transition from unique combination of input variables for each equation

Monte Carlo simulation to randomlyDetermine which transition (includingNo Change) occurs and where

Spatially-constrain output Using observed rules of urban development patterns

Compare predicted with observed

Compare predicted with observed

Map Transitionprobabilities

1991 Land cover class

1999 (t2) Land cover class (predicted)

1999 (t2) Land cover class (observed)

Observed and Predicted Land Cover Change for Central Puget Sound 1986-2027

0%

20%

40%

60%

80%

100%

1986 1991 1995 1999 2002 2003 2007 2011 2015 2019 2023 2027

Obs Obs Obs Obs Obs Pred Pred Pred Pred Pred Pred Pred

Regerating Forest

Clearcut Forest

Coniferous Forest

Mixed Forest

Agriculture

Grass

Light Urban

Medium Urban

Heavy Urban

1995-1999spec fileall 4 counties

Sources of Agreement and Errors in Predicted Landscape

*Derived using methods from Pontius et al. 2004 Ecological Modeling 179

0

10

20

30

40

50

60

70

80

90

100

1 2 4 8 10

Resolution as multiple of pixel side

Perc

en

t o

f L

an

dscap

e disagreement due toquantity LCCM

disagreement due tolocation LCCM

agreement due tolocation LCCM

agreement due toquantity LCCM

agreement due tochance LCCM

Integrated Geo-Spatial Models

Alberti and Waddell 2001.

Model and Null Percent Correct at Multiple Scales*:Predictions of 1999 Landscape from 1991-95

*Derived using methods from Pontius et al. 2004 Ecological Modeling 179

50

55

60

65

7075

80

85

90

95

1001 2 4 8 10

Resolution as multiple of pixel side

Perc

en

t o

f L

an

dscap

e

LCCM Asymptote

NULL Asymptote

NULL % Correct

LCCM % Correct

Partitioning the Model

Spatial Segmentation

Spatial Dependence

Spatial structure may occur due to:

a) positive spatial autocorrelation among the locations and/or

b) spatial dependence due to human and ecological responses to underlying environmental conditions

(Wagner and Fortin 2005)

Modeling Spatial Pattern

k

j)β(i ts,Χ

j)β(i ts,Χj)(i

ts,Pe

e

k

)sδty jβ(i ts,Χ

)ty jβ(i ts,Χ)ty j(i

ts,Pe

e ss

Uncertainty• We need to identify and quantify uncertainty in land

cover change models– Uncertainty can lead to propagation of error when

connecting to other models

• Problem of equifinality (Beven 1990)– multiple parameter sets can produce “optimal model” and

“reasonable” results

• Research objective: To identify and quantify sources of uncertainty in input data and model structure, and produce ensemble model predictions of land cover change

Types of Uncertainty in LCCM

• Input data– Measurement errors

• Systematic errors– Spatial resolution and sampling design

• Model structure

• Stochasticity– Random number generators

Types of Uncertainty in LCCM

Proposed Uncertainty Approach for LCCM

• Combination of Bayesian melding (Raftery et al. 1995) and Bayesian model averaging (Hoeting et al. 1999)

Multinomial logit model

Model Estimation

Model Prediction

Bayesian Model Averaging

Bayesian Melding

Output

Step 1:

Step 2:

Step 3:

Implications for Future Models

- Problem definition

- Multiple actors

- Time

- Space

- Feedback

- Uncertainty

Modeling the Urban Landscape

- Multiple actors Models need to explicitly represent the diversity of actors to be realistic

- Time Dynamic models, representing time explicitly are more realistic

- Space Spatial resolution depends on the appropriate resolution at which phenomena occur

- Feedback It is important to consider key feedback mechanisms among variables driving the model dynamic

- Uncertainty Models should treat uncertainty explicitly to assess model results