land cover change model for central puget sound...

Land Cover Change Model for Central Puget Sound: Land Change Predictions to 2050

Report prepared for Weyerhaeuser as part of the Puget Sound

Development and Climate Change Project

Matt Marsik and Marina Alberti Urban Ecology Research Laboratory

Department of Urban Design and Planning University of Washington

April 2010

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Table of Contents List of Tables List of Figures List of Appendices Executive Summary 1. Model Definition

1.1. Land Cover Change 1.2. Land development 1.3. Site attributes 1.4. Spatial context

2. Input Data 2.1. Development data

2.1.1. Urban Sim cache 2005-2038 2.1.2. Urban Sim cache 2041-2050

2.2. Land cover 2.2.1. Land Cover Classification

2.2.1.1. Top Level Supervised Classification 2.2.1.2. Spectral Unmixing 2.2.1.3. Non-Vegetation Classification 2.2.1.4. Urban Classes 2.2.1.5. Vegetation Classification 2.2.1.6. Wetlands, Shorelines, Open Water, and Bare Rock/Ice/Snow Classes

2.2.2. Land Cover Trajectory Analysis 2.3. Landscape patterns

3. Model Specification 3.1. Statistical Model 3.2. Transitions Modeled 3.3. Variables Considered 3.4. Model Estimation

4. Spatial Constraints 4.1. Creation of spatial masks 4.2. Urban land classes 4.3. Non-urban land classes 4.4. Application of constraints as a means of spatially segmenting the model

5. Land Cover Change Model 5.1. Input data and years modeled 5.2. Parameter Estimation 5.3. Spatial Constraints 5.4. Land Cover Validation

6. Land Cover Predictions 6.1. Dominant Landscape Changes 6.2. Types of Change 6.3. Patterns of Change

7. Conclusions 8. References

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List of Tables Table 1. Land use development types used in this study Table 2. Coefficient and significance values of generalized linear models to extend the UrbanSim cache from 2038 to 2050. Table 3. Land cover classes, abbreviations, and definitions for land cover data. Table 4. Rules applied to create top-level classes for water, vegetation and non vegetation. Table 5. Preliminary land cover classes derived from hybrid approach. Table 6. Definition of landscape metrics used in LCCM. Table 7. Land cover transitions modeled. Table 8. Input variables Table 9. Empirically derived thresholds used to determine value ranges of spatial constraints. Table 10. Validation metrics of the 2005 and 2008 predicted land cover Table 11. Observed and predicted land cover percentages of the Central Puget Sound landscape. Table 12. Rates of land cover change for predicted transitions List of Figures Figure 1. Central Puget Sound study area Figure 2. Spatial constraint masks. Figure 3. Observed land cover for Central Puget Sound Figure 4. Land cover predictions for 2005-2050 for Central Puget Sound Figure 5. Temporal changes in observed (1986 to 2007) and predicted land cover (2005 to 2050). Figure 6. Rates of land cover change for the modeled transitions. Figure 7. Kappa validation metrics List of Appendices Appendix A. Input variable definitions. Appendix B. Model parameter specification based on sampling of and model estimation from 1995 and 1999 observed land cover. Appendix C. ArcGrid syntax to calculate land cover transitions

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Executive Summary

As part of our NSF Biocomplexity Projects I and II we developed a high-resolution land-cover change model (LCCM v1.0, Hepinstall et al. 2008; Alberti et al., 2006) and integrated it with the UrbanSim model (Waddell et al. 2003; www.urbansim.org) developed for the Central Puget Sound Region (Waddell et al. 2007). The LCCM uses as a set of spatially explicit multinomial logit models of site-based land-cover transitions to predict land cover change in the Central Puget Sound region (King, Kitsap, Piece, and Snohomish). The LCCM uses UrbanSim predictions among additional input variables (derived from observed land cover) and explicitly models the interactions between land use and land cover change and environmental variables through time and space (Alberti et al. 2006). The land-cover transition probability of a 30x30m grid cell is a function of the interaction between the current land cover of the cell, its spatial context, and the spatial contagion of development. The equations for transition probabilities are estimated empirically as a function of a set of independent variables comparing land cover data at different points in time (presently for 1991, 1995 and 1999 in Puget Sound). The predicted land cover output is produced from the comparison to a statistical distribution of the probabilities for all plausible land cover transitions. The process is iterative, with the current predicted land cover (time t) as input for the next time step (t+1).

This report describes a new version of LCCM expanding the approaches and application of the land cover change model (LCCM 2.0) with an enhanced multinomial logit choice model. We have extended model predictions every three years from 2005 to 2050, thus extending the temporal scale. We used LCCM v2.0 in parallel with LCCM v1.0 to reproduce past estimations and predictions based on 1991, 1995 and 1999 land cover and ancillary data to test the new model formulation and to provide a baseline to continue the land cover predictions to 2050. New input data (e.g. landscape composition and configuration metrics) have been derived from existing 1999, 2002 and 2007 land cover data using GIS to create a database for the 1999-2007 land cover model. An updated model specification for 1995-2002 estimation and prediction has been created using the updated land cover data.

To represent land cover changes resulting from future development and land use, we have included in LCCM v2.0 input data depicting predicted development date (i.e. year of development ‘event’), development types (e.g. commercial, residential, industrial, etc) and development intensities (e.g. housing and commercial units/acre ). To extend the land cover predictions, we require updated UrbanSim output for development units and intensities, and some measure of development (i.e. land use) types for the region of interest. Since LCCM is a grid based model, these developments were used within LCCM as input data whereby they will be allocated to a grid index that corresponds to the unique parcel ID used by UrbanSim. Additionally, these data are required for the working data swap cache, in which development data are computed internally within OPUS and LCCM and spatially allocated (again, based on a grid-parcel relationship) during the prediction.

We implement the Land Cover Change Model (LCCM) using 1995, 1999 and 2002 observed land cover data for King, Pierce, Snohomish, and Kitsap counties, (Figure 1) and fifty-eight explanatory input variables (Table 6). Land cover change was simulated for 3-year time intervals from 2005 to 2050. Model output for 2005 and 2008 were compared with the 2007 observed land cover data (developed by UERL) to assess the agreement, which provided satisfactory Kappa statistics. A set of empirically-derived spatial constraints were used to realistically portray predicted urban development throughout the region. Based on the 2050

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predicted land cover, urban areas comprise about 25% of Central Puget Sound with a net gain of 6.3% from 2005. Grass and agriculture, and forest classes comprise about 5% and 51% of the landscape, with net losses of about 3% and 12%, respectively. Urban development, often at the expense of non-urban classes, is realistically constrained based on policy and topographic limits, and projected population growth.

Figure 1. Central Puget Sound study area. Land cover data are from the UERL 2007 observed land cover classification.

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1 Model Definition

1.1 Land Cover Change The land cover change model (LCCM) consists of a set of spatially explicit multinomial logit models of site-based land cover transitions. A complete description of the theoretical foundations of the model can be found in Hepinstall et al. (2008). We build on previous efforts in land cover change modeling to simulate land cover change as influenced by spatially explicit dynamic interactions between socio-economic and biophysical processes (Turner et al. 1996, Berry and Minser 1997, Wear and Bolstad 1998, Wear et al 1998). The probability of transition of a 30-m pixel from one discrete land cover class i to another cover class j is influenced by the intensity of a development predicted by UrbanSim (Waddell 2005), a set of attributes of the pixel, and the land cover composition and configuration of the neighboring pixels. UrbanSim is an agent based urban modeling approach that represents the interactions and behaviors of human agents with regard to development at the site scale (i.e. parcel and building scale. The model implements a perspective on urban development that represents a dynamic process resulting from the interaction of many actors making decisions within the urban markets for land, housing, non-residential space and transportation (Waddell 2005). The transition probability equations are estimated empirically as a function of a set of independent variables comparing land cover data ever three to four years from 1995 to 2002 (See 2.4 Land Cover). We use Monte Carlo simulation to determine whether each pixel of a specified land cover changes to another cover type or remains in its current state. Spatial constraints representing distance to roads and urban areas, industrial and manufacturing areas, an urban growth boundary and projected population densities are applied during the Monte Carlo simulation to restrict unrealistic growth of urban land covers. Land cover change equations are used to estimate the transition probabilities for each cell and the changes implemented by comparing the probabilities to a random number chosen from a uniform distribution between 0 and 1. If the transition probability to a different land cover exceeds the random value, the transition takes place. Otherwise, the grid cell maintains its current land cover. The results are the simulation of land cover change that represent any observed transitions between historic land cover.

1.2 Land development The probability that a 30-m pixel will change to another land cover type depends on the type of development predicted by the UrbanSim development model at the parcel level. Development types are associated with dominant land use and specified number of housing units, square feet of commercial, industrial and government space. Using these development templates we estimate the intensity of development events within a 5x5 pixel window (150-m cell). Parcel level attributes are allocated to the 150m grid. In this way the intensity of development in the neighboring cells positively influences land cover transition from non-urban land cover classes to urban land cover classes and from less built-up urban classes to more built-up urban classes.

1.3 Site attributes A number of biophysical attributes of the site influence directly and indirectly the land cover transition probabilities. They influence the choice of households and business of specific locations, the tradeoffs between alternative land uses, and ultimately the cost of development. Three major site biophysical characteristics are topography, soil productivity, and land erodibility. Site slope affect negatively the transition from all non-urban land cover to urban land

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cover types and from mixed urban to paved urban. Whether a site is on prime agriculture lands or not influences the probability of land cover transition. Also highly erodible sites have a lower probability to transition to developed land. Other attributes of the site are their characterization with respect to critical areas which include wetlands, areas with a critical recharging effect on aquifers used for potable water, fish and wildlife habitat conservation areas, recently flooded areas and geologically hazardous areas. Increased distance from critical areas influence positively all transitions from non urban land cover classes to urban land cover classes and from less intense urban land cover classes to more intense urban land cover classes. Among the attributes of the site that positively influence transition from non-urban to urban land cover are also its proximity to roads and other urban infrastructures which include water and drainage lines and electric utilities, natural gas and telecommunication grids. For this first version of the model, distance to infrastructure other than roads is represented by distance to existing development.

1.4 Spatial context The effects of the spatial context can be captured by a number of pattern metrics that describe the land use and land cover characteristics of the neighboring cells. Four spatial effects are considered: 1) the existing land cover and land use characteristics (both composition and spatial configuration) of the neighboring cells, 2) its location with respect to the urban to rural gradient, and 3) the proximity to most recent land conversion and most recent development event. We measured spatial context with a variable moving window of 150-m, 450-m, and 750-m resolution centered on the 30-m pixel depending on the variable of interest measured. Land cover characteristics are currently measured at 150-m resolution while land development characteristics are measured at 450-m and 750-m. We measure land cover composition and configuration using four indices: percentage landscape, dominance, mean patch size, and contagion. Estimated coefficients for each of these variables are dependent on the terminal transition. The probability of transition from one land cover type to another is higher if the surrounding cells are highly dominated by the same land cover class as the terminal transition. The transition from non-urban classes to urban classes is also more likely at the urban fringe where evenness of land cover classes is low, mean patch size of urban is low and aggregation of forest is high. Among the explanatory variables of land cover change is the position of the cell along the urban rural gradient (Wear et al 1998). Development events and land cover transition in adjacent cells influence the probability of land cover transition in a given cell. We include among the variables the percent of the area in 150-m window that has recently changed. We also include the number of residential units and square feet of commercial/industrial recently added within a 450-m window and 750-m window centered on the pixel.

2 Input Data

2.1 Development data Parcel data and relative land use attributes are preprocessed to construct a composite representation of development within a 150-m window. Parcel and building data from 2000 to 2040 were obtained from the Puget Sound Regional Council (PSRC) with attribute data including land use, number of residential building units, square footage, and year built of the existing development (Alberti et al., 2006). Cells are classified on the basis of their dominant

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land use, residential units and square feet of commercial/industrial, into ‘Development Types’ (Table 1). The development type was constructed in several steps. First land parcels are intersected with a vector grid of 150-m resolution. The parcel and building attribute data are then joined to this parcel-grid intersection. Then, the dominant land use for each 150m x 150m window is determined by calculating the largest percentage area of parcels associated with a specific land use for each development type. Dominant land use is assigned to percentage area greater than 60%. For the remaining sample units, a mix of land use is determined. We applied Principle Components Analysis to determine key components of mixed development types. These were made up primarily of Transportation, Single Family Residential, Open Space, and Other (agricultural, rural land, and water). Table 1. Land use development types used in this study (Classification scheme used by UrbanSim for Puget Sound region).

ID NAME MIN # UNITS MAX # UNITS MIN SQFT MAX SQFT DESCRIPTION R1 1 1 0 499 Residential

2 R2 2 4 0 499 Residential 3 R3 5 9 0 499 Residential 4 R4 10 15 0 499 Residential 5 R5 16 21 0 499 Residential 6 R6 22 30 0 499 Residential 7 R7 31 75 0 499 Residential 8 R8 76 2800 0 499 Residential 9 M1 1 9 500 4999 Mixed Use

10 M2 1 9 5000 24999 Mixed Use 11 M3 1 9 25000 4000000 Mixed Use 12 M4 10 30 500 4999 Mixed Use 13 M5 10 30 5000 24999 Mixed Use 14 M6 10 30 25000 4000000 Mixed Use 15 M7 31 2800 5000 99999 Mixed Use 16 M8 31 2800 100000 4000000 Mixed Use 17 C1 0 0 1 24999 Commercial 18 C2 0 0 25000 99999 Commercial 19 C3 0 0 100000 4000000 Commercial 20 I1 0 0 1 24999 Industrial 21 I2 0 0 25000 99999 Industrial 22 I3 0 0 100000 4000000 Industrial 23 GV 0 0 1 4000000 Government 24 VD 0 0 0 0 Vacant Developable 25 Ag 0 0 0 0 Agriculture 26 Forest 0 0 0 0 Forest 27 Military 0 0 0 0 Military 28 Mining 0 0 0 0 Mining 29 VU 0 0 0 0 Vacant Undevelopable After determining the dominant land use, we normalized the number of residential units and commercial/industrial square footage for each grid cell. This is accomplished by calculating the number of units and square footage per unit of parcel area. Next, the number of units and square footage are multiplied by the area of the parcel intersected by the grid cell to determine the total number of units and square footage in the 150m cell. Classification rules within each dominant

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development type category were established based on combined natural breaks of number of units and square footage of commercial and industrial built up area. The addition of residential units and non-residential square footage constitutes a new development event, from which the distances from these events are identified as new urban areas created in the current prediction year, representing the spatial context of new development. These development data are supplied to LCCM as a data cache within UrbanSim, so that for each subsequent year of prediction, following the base year of land cover, the development type is calculated. This process of generating the development type data produced square footage of commercial, industrial and governmental land uses along with the number of residential units, all for each 150m grid cell for each year of predictions. UrbanSim reads in these data, along with an index grid, from the data cache, and allocates the development data based on their tabular correspondence the index grid. In other words, the development data are spatially allocated using an 150-m index grid (the same index intersected with the parcel data) In this way, for each year of prediction, LCCM has a spatial representation of the dominant land development data that, in addition to biophysical site characteristics, helps determine land cover change in the Central Puget region.

2.1.1 Urban Sim cache 2005-2038 Attributes needed from UrbanSim output: number of residential units, non-residential square footage, land use type, unique building and parcel identifiers, and parcel square footage. To create the cache database the development data are calculated from for prediction time, the UrbanSim output from PSRC was allocated to the grid index. This index is used internally by LCCM to create needed data for each future prediction period to account for dynamic development into the future. To begin to allocate the UrbanSim data, which are output at the parcel level, to the grid index, the parcels and grid index are spatially unioned. In addition to predictions at the parcel level, UrbanSim predicts at the building level. Predicted residential units and non-residential square footage are aggregated from the building level to the parcel level by a common building identifier. The aggregated building characteristics were then joined to their respective parcel. An area-weighting approach was used to allocate the combined building-parcel attributes (residential units and square footage) based on the grid index, in which each grid cell has a unique identifier that indicates the number of residential units and square footage in each grid cell. Land use was needed to generate the development rasters and determine development types, and was aggregated to the grid index level. Development representing commercial, government, industrial and residential land uses were calculated based on the respective aggregated land use, residential units and square footage. The aggregated land use, development, residential units and square footage are combined together and the unique development types calculated according to Table 1. These data were then exported to format usable by LCCM.

2.1.2 Urban Sim cache 2041-2050 The UrbanSim cache development data were extended to 2050 using a generalized linear modeling (GLM) (Nelder and Wedderburn, 1972) approach applied to the 2000-2040 data. GLM is a flexible generalization of ordinary least squares regression that relates the linear model to the response variable via a link function with the magnitude of the variance of each measurement as a function of its predicted value. Here, GLM is used as a historic time series analysis with the idea that the spatial occurrence of each development land use can be predicted from past,

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Table 2. Coefficient and significance values of generalized linear models to extend the UrbanSim cache from 2038 to 2050. The explanation of variable codes is as follows: COMM0211Av indicates the 10-year average (AV suffix) of commercial square footage (COMM prefix) between 2002 and 2011 (0211 core date). GOVT = government square footage; IND = industrial square footage; RES = number of residential units; POPDENS#### = population density for that particular decade; MICEN = binary dummy variable to indicate inside/outside of industrial and manufacturing centers; and URBCEN = binary dummy variable to indicate inside/outside of the urban growth boundary. Significance codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1.

Estimate Std. Error t‐value Pr(>|t|) (Intercept) 1.44E+03 4.35E+02 3.303 0.000991 *** COMM0211AV ‐3.56E‐02 9.82E‐03 ‐3.621 0.000308 *** COMM2029AV 1.04E+00 8.67E‐03 120.255 <2.00e‐16 ***

Estimate Std. Error t‐value Pr(>|t|)

(Intercept) ‐6.69E+00 1.41E+02 ‐0.047 0.962GOVT0211AV 1.02E‐01 2.06E‐02 4.964 8.13E‐07 *** GOVT1120AV ‐1.99E‐01 3.55E‐02 ‐5.623 2.44E‐08 *** GOVT2029AV 1.09E+00 1.63E‐02 67.047 <2.00e‐16 *** POPDEN2030 ‐2.14E‐02 4.77E‐03 ‐4.479 8.39E‐06 *** URBCEN 2.02E+03 4.76E+02 4.252 2.31E‐05 ***


(Intercept) 7601.496 603.7323 12.591 <2.00e‐16 *** IND1120AV ‐0.37179 0.05593 ‐6.647 4.91E‐11 *** IND2029AV 1.14325 0.05586 20.468 <2.00e‐16 *** MICEN 6923.111 1072.091 6.458 1.66E‐10 ***


(Intercept) ‐0.09129 0.137644 ‐0.663 0.5073RES0211AV 0.544397 0.05127 10.618 <2.00e‐16 *** RES1120AV ‐1.51249 0.075883 ‐19.932 <2.00e‐16 *** RES2029AV 2.045952 0.048645 42.059 <2.00e‐16 *** POPDEN2000 0.000344 0.000164 2.104 0.0357 * POPDEN2020 ‐0.00067 0.00034 ‐1.959 0.0504 . observed states of the same land use, along with other ancillary predictors. During creation of these development data, rasters were created for commercial, industrial, governmental, and residential land use attributes (number of units and square footage) matching the prediction time steps for LCCM. A 10-year average was created for each land use type; for example, a 10-year average of commercial square footage was calculated from individual commercial predictions from 2002, 2005, 2008, and 2011. This process was repeated for each of the four land use types to create a time series of decadal averages. Additional predictors were decadal population density, locations of manufacturing and industrial centers, and the urban growth boundary. A GLM (Equations 1-4 below) was fit to the 2029-2038 decade of each of the four land use data

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types using a sample of previous decades land use along with ancillary data in a backwards-stepwise selection process to calculate the best-fit model (Table 2). To improve the explanatory power of the predictor variables on the dependent, the resulting models were inspected for any spurious variables, and the model refit to create an optimal prediction model. All independent variables were significant at the alpha = 0.01 level. Predictions were made using the fitted GLMs substituting the 2029-2038 averaged data for the 2020-2029 averaged data. In this way, potential future spatial expansion of these development variables is conditioned upon their historic patterns. Similar to processing of the previous set of UrbanSim data, these data were aggregated to the grid index level, combined and export to the format required by LCCM.

COMM2938 ~ COMM0211 + COMM2029 (1) GOVT2938 ~ GOVT0211 + GOVT1120 + GOVT2029 + POPDEN2030 + URBCEN (2) IND2938 ~ IND1120 + IND2029 + MICEN (3) RES2938 ~ RES0211 + RES1120 + RES2029 + POPDEN2000 + POPDEN2020 (4)

2.2 Land cover Observed land cover data (Figure 3) were taken from the Urban Ecology Research Lab in-house data repository. The observed land cover data available were from 1995, 1999, 2002, and 2007. These data were created from the classification of Landsat imagery using a mixed-method approach of supervised classification and spectral unmixing. See Alberti et al. (2004) and Hepinstall et al. (2009) for a detailed description of the data and the classification methods. The resulting classification exhibits 14 general types of land cover found throughout the Central Puget Sound region (Table 3). Table 3. Land cover classes, abbreviations, and definitions for land cover data. Class # Class Abbrev. Definition

1 Heavy Intensity Urban HU > 80% Impervious Area 2 Medium Intensity Urban MU 50-80% Impervious Area 3 Light Intensity Urban LU 20-50% Impervious Area 4 Land Cleared for

Development CDEV Cleared Land

5 Grass GR Developed Grass and Grasslands 6 Deciduous and Mixed Forest MF >80% Deciduous Trees,

10-80% each Decid./Conif. Trees 7 Coniferous Forest CF >80% Coniferous Trees 8 Clearcut Forest CC Clearcut Forest 9 Regenerating Forest REG Re-growing Forest 10 Agriculture AG Row Crops, Pastures 11 Non-Forested Wetlands NFW Wetlands Assoc. with Open Water 12 Open Water OW 13 Bare Rock/Ice/Snow BR 14 Shoreline SH

In multinomial-logit land cover change modeling, the calculation of the transition probabilities to determine future land cover change depend on observed, historic land cover change. Hence, the LCCM model specification was created using observed land cover data from 1995, and 1999, and applied to the 2002 land cover data. That is, using the model specification from the 1995 and

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1999 land cover, the model was run using the 2002 land cover data as the starting point. Validation of LCCM output for the 2005 and 2008 predicted land cover data was performed using the 2007 observed land cover data.

2.2.1 Land Cover Classification A combination of Landsat Thematic Mapper (TM) and Enhanced TM (ETM+) imagery covering the extent of the central Puget Sound region was acquired for this project. This area includes the Seattle-Everett-Tacoma Metropolitan Statistical Area and points east to the crest of the Cascade Range. Thematic Mapper (TM), an instrument of NASA distributed by the U.S. Geological Survey (USGS), is a multi-spectral, scanning radiometer carried on Landsat satellites 4 and 5. It has been providing continuous, 16-day cycle, global coverage since July 1982. TM contains six spectral bands (bands 1-5 and 7) representing the visible, near-infrared and mid-infrared wavelength regions, with a spatial resolution of 30-meters. The ETM+, launched on Landsat satellite 7 in April 1999, contains the same data parameters as TM, but has upgraded radiometric calibrations. We applied supervised classification by extracting spectral signatures from various land cover types in the summer image, using high-resolution ortho-photography for referencing the materials. The various land-cover types included dense urban surfaces (e.g. pavements, roofing surfaces), mixed-urban areas (e.g. residential), grasses, clear-cut, conifer and bare ground and agricultural lands. Training sites are digitized using the AOI tool in ERDAS Imagine. Signatures are extracted from the image using the AOI’s for each class. At each supervised classification interval, we masked water and vegetation using a three-class image comprised of water, vegetation and non-vegetation, derived from spectral unmixing, discussed below. The vegetation class was later disaggregated using spectral unmixing and seasonal change strategies, also discussed below. Our general approach to classification is both interactive and hierarchical. We start with broad classes and work within these classes to disaggregate them into more detailed classes or subclasses. We use several classification techniques throughout the process to achieve a final classification for each time step. Our starting point is a top-level classification in which each summer image is segmented into three categories: vegetation, non-vegetation, and water. This is done through a combination of spectral unmixing and supervised classification. 2.2.1.1 Top Level Supervised Classification We applied a top level supervised classification by extracting spectral signatures from various land cover types in the summer image, using high-resolution ortho-photography as a reference to locate training sites. All six spectral bands plus an NDVI band derived from the image are used in the classification. AOI’s representing vegetation and non-vegetation land cover types were digitized and signatures were extracted. These include multiple AOI’s for each of the following categories: urban, mixed urban, bare soil, deciduous, conifer, grass, green agriculture, dry grass, grasslands, & water. Signature separability scores were calculated and signatures combinations were reconfigured only when scores indicated poor separability. This classification results were recoded into vegetation (deciduous, conifer, grass, and green grass) non-vegetation (urban, mixed urban, bare soil, dry grass, and grasslands), and water.

1991 1995 1999

2002 2007 Figure 3. Observed land cover for Central Puget Sound

2.2.1.2 Spectral Unmixing Linear spectral unmixing was applied to the same image (without the NDVI band) to derive end member fraction images for non-vegetation, vegetation, and shade. End members were identified by analyzing a sub-sample of the image in spectral space (through an n-dimensional viewer) and locating clusters of pixels that bounded the majority of pixels in band space. End members were selected based on the following criteria: 1) they must exist as unique spectra that bound the majority of the pixels in the data cloud, 2) they must exist on a general linear plane between the other end members and 3) they are not extreme pixels. Some of the literature regarding end member selection suggests using the extreme pixels that bound all other pixels in mixing space. This, however, may be inappropriate for several reasons. Extreme end members can be thought of as statistical outliers. They do not represent the end of mixing space but rather pixels that do not occur very often such as clouds. Typically, extreme pixels exist on the far end of a vector delineating the mixing space between itself and two other end members. Using these spectra instead of the pure pixels that bound the majority of the data may cause skewed results. End member selection yielded three general end members representing non-vegetation (soil and urban pixels), vegetation (agricultural fields), and shade (water) (Table 4). Spectra for these end members were extracted and used as inputs into the linear unmixing model. Running the model produces a series of fraction images, one for each end member and an RMS image representing model error for each pixel. The vegetation end member image was normalized for shade by dividing it from the sum of itself and the non-vegetation image. The shade normalized vegetation image, the raw end-member fraction images, and the results of the supervised classification were used in the following rules to divide the image into vegetation, non-vegetation, and water. Table 4. Rules applied to create top-level classes for water, vegetation and non vegetation. Water Shade EM >= .75 and Veg EM <= .20 Vegetation Shade Normalized Veg > .80 and/or

pixel is Veg in supervised classification. Non-Vegetation All other pixels

2.2.1.3 Non-Vegetation Classification The first step in the Non-vegetation classification is to classify clear-cut patches. Previous experience with Landsat in this area indicate that clear cuts are often spectrally confused with urban classes and are thus hard to separate with a high level of accuracy. Clear cuts do, however, exist as large homogenous patches and have temporal characteristics that are quite different from urban objects. A recent clear cut will have very little vegetation, but will have been forested in earlier images and exhibit re-growth in later images. Our collection of images from numerous time steps provided an opportunity to take advantage of temporal patterns that help separate classes that are difficult using single date spectra alone. To classify clear cuts, we created a stacked raster file with bands 3, 4, 5, and 6 from the date of classification and the two endpoints of our study period, 1985 and 2002. We then apply a supervised classification using signatures from urban, mixed urban, dry grass, grasslands, bare soil and clear cuts. The result of this classification is masked so that only those pixels classified as “non-vegetation” in the top-level classification are included. A 7x7 focal majority filter is then

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applied to the masked image so that only pixels classified as non-vegetation are impacted by the filter. The results of the filter were converted to a binary image, where clear cuts are assigned a value of one and everything else is zero. These pixels are considered classified as clear-cut and do not receive further consideration at this point. By and large, this process was able to identify the clear-cut patches and sharply reduced the number of mis-classified pixels. Another common problem in urban remotes sensing is the spectral confusion between bare soil and urban surfaces. Within our study area, there are numerous agricultural areas that often have tilled or unplanted fields and are spectrally similar to urban areas. However, similar to clear cuts, the temporal characteristics of agricultural areas are quite different from urban pixels in that they typically go back and forth from vegetated to non-vegetated. In order to capture this pattern, we calculated the variance of band 4 for all the summer images combined. This variance band was stacked with 6 spectral bands for each summer image. We hypothesized that agricultural areas would display greater variance in the near-infrared portion of the spectrum than would urban areas. A supervised classification was run using signatures for urban, mixed urban, dry grass, grasslands, and agricultural bare soil. The classification was masked by the non-vegetation pixels and a 3x3 majority filter was applied. Again, this filtering only affects pixels identified as non-vegetation in the top-level classification.

2.2.1.4 Urban Classes Spectral unmixing is once again applied to the summer image using a refined set of end members representing urban, vegetation and shade. The methodology for extracting signatures was the same as in the top-level classification. This time, however, only pixels that contained 100% of urban materials were considered as potential end members from the area in feature space that previously had been identified as non-vegetation. Locating spectral end members for urban surfaces presents a unique problem in that there is a tremendous degree of spectral variance among urban reflectance. Previous research has shown that pure impervious surfaces tend to lie along an axis of low to high albedo spectrum. As a result, pure urban pixels often exist without actually being end members because they fall somewhere between low and high albedo (non-vegetation) end members (Small 2001, Wu and Murray 2002). Furthermore, the low and high albedo pixels at the end of this range may represent end members but not necessarily distinct urban end members. For example, the low albedo end member is spectrally similar to shade and is therefore hard to differentiate. Similarly, high albedo spectra could be from clouds, bare soil or a bright urban surface. To further confound this problem, pixels that are a mixture of impervious surface and vegetation, for instance, will contain some degree of shade. Using a low albedo end member as an impervious proxy will most likely model this shade component as impervious surface, when in reality it can not be determined whether the shade is caused by a building, tree or is in fact part of the impervious surface spectra. From our experience, bare soil does not seem to exist as a truly distinct urban end member in spectral space, but rather exists along the same vector between the urban end member and shade/water end member (Alberti et al., 2004). This plane extends from high albedo bare soil/urban surface to low albedo bare soil/urban surface to water. The pixels along this plane (except for water pixels at the end of the plane) are some combination of urban surface, bare soil

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and shade. Because the supervised classification separates whole pixel bare soil from urban pixels, it can be assumed (from the accuracy assessment) that most bare soil pixels in the image are already classified and removed from the analysis. Furthermore, because the shade fraction image is solved to derive impervious estimates, it can be assumed that urban pixels along this plane will be estimated at close to 100 percent impervious. This leaves pixels that contain both impervious surface and bare soil to be somewhat difficult to detect. Since there was little evidence that bare soil existed as an end member distinct from urban end members, it is inappropriate to use it in a spectral unmixing model with an urban end member. Therefore, if an urban pixel does contain bare soil, this component will most likely be modeled as shade and impervious surface during the unmixing.

2.2.1.5 Vegetation Classification The first step in the vegetation classification is to separate vegetation pixels into Forest and Grass/shrub/green agriculture. Using the same summer image + NDVI used in the top level classification, a supervised classification is run using several vegetation signature resulting in a two class image comprised of either forest pixels or grass, shrub, crops pixels. Once masked by the vegetation pixels classified in the top-level classification, the grass/shrub/crops pixels are considered classified. A file consisting of bands 3, 4, 5, and 6 from the leaf-off and leaf-off image is generated for the particular year of classification. A supervised classification is run using signatures for conifer and mixed forest classes. The resulting classification is made by those pixels identified as forest in the previous step. The classification is then compiled using the following rules resulting in 9 classes (Table 5). Table 5. Preliminary land cover classes derived from hybrid approach. Class Definition Heavy Intensity Urban > 80% Impervious Area Medium Intensity Urban 50-80% Impervious Area Light Intensity Urban 20-50% Impervious Area Grass Developed Grass and Grasslands Deciduous and Mixed Forest

>80% Deciduous Trees, 10-80% each Decid./Conif. Trees

Coniferous Forest >80% Coniferous Trees Clearcut Forest Clearcut Forest Bare Soil Non-vegetated Open Water Water 2.2.1.6 Wetlands, Shorelines, Open Water, and Bare Rock/Ice/Snow Classes Several land cover classes were derived from ancillary GIS data. Open water (lake or pond, ditch or canal, stream or river, bay, estuary, gulf, ocean/sea, and reservoir), non-forested wetlands (marsh, wetland, swamp, bog, and cranberry bog), shoreline (tidal, mud, sand, and gravel flats), and ice/snow (glacier or permanent snowfield) were derived from 1:24,000 scale Digital Line Graph (DLG) data. 2.2.2 Land Cover Trajectory Analysis

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A full description of the land cover trajectory analysis is described in (Hepinstall et al., 2009). The 9 classes resulting from the land cover classification analysis (Table 5) for multiple dates (1986, 1991, 1995, 1999, and 2002) were used to constrain possible changes to those that made intuitive sense. For example, Heavy Urban in 1986 would not be expected to become Coniferous Forest in any later date. Specific rules detailing allowable landscape trajectories were developed.

Table 6. Definition of landscape metrics used in LCCM. Landscape Metrics Equations

Pland Sum of the area of all patches of the corresponding patch type, divided by total landscape area. (Pland is calculated in a 5 x 5 pixel moving window

A

a

PpLand

n

jij

i

∑=== 1

Mean Patch Size Sum of the areas of all patches of class type i divided by the number of patches. (Patch Size calculated on the entire study landscape at once and MPS is then calculated by sampling the Patch Sizes in a 5 x 5 pixel moving window)

Aggregation Index The number of like adjacencies in the target class, divided by the maximum number of like adjacencies of that class. (Aggregation index is calculated in a 5 x 5 pixel moving window)

Shannon Evenness Index Measures the negative difference between the observed Shannon’s Diversity Index divided by the maximum Shannon’s Diversity Index for m number of patch types. (SHEI is calculated in a 5 x 5 pixel moving window)

Specific rules were developed for each of the target final land cover classes (Table 3). Bare Soil in the preliminary classification was split in to Cleared for Development (if one of the developed classes at a later date), Agriculture (if bare soil or grass in later dates), or Clearcut (if a forest class and above 300 m elevation). Because of slight yearly environmental differences (primarily wetness) between satellite images, the exact separation between urban land cover classes is variable, leading to temporal sequences such as HU-MU-LU-MU-HU. Two image dates, 1991 and 1999 were chosen as base classifications from which to determine when urban land cover classes for the other dates were incorrect. Urban Classes were constrained to maintain or increase

i

n

jij

n

a

MPS∑== 1

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intensity over time. If there was a disagreement between 1991 and 1999 urban classes, 1999 prevailed. Regenerating Forest was derived from the Clearcut in the previous time step. Clearcut was constrained to only occur above 300 m elevation and have been forested in the previous time step.

2.3 Landscape patterns Land cover data are processed to compute four landscape indices adapted from three landscape ecology metrics to characterize the landscape patterns (O’Neil et al. 1988, Turner 1989). The indices are computed for each Landsat image (Table 6): mean patch size (mps), the size of individual land cover patches averaged over all patches of a given class; pLand., the proportion of the landscape area occupied by each cover type; Shannon’s Evenness Index, the deviation from the maximum possible landscape evenness and is calculated using all 14 land cover classes; and Aggregation Index, the percent of possible like adjacencies of a focal class (maximum when focal class is in a single compact patch). The indices are computed with Fragstats version 3.3 (McGarigal and Marks, 1995) (www.umass.edu/landeco/research/fragstats/fragstats.html). For calculating these metrics, we use a moving window of 150-m resolution (5 x 5 pixels) centered on the 30-m cell to assign neighboring values to each 30-m cell.

3 Model Specification

3.1 Statistical Model LCCM’s specifications are described in Alberti et al. (2006). We define the probability of the transition of any land cover 30-m cell as a function of the interaction between the current land cover of the cell, its spatial context, and the spatial contagion of development. The land cover change model is structured to predict the probability of a single cell changing from one discrete land cover to another class as a function of present land cover class of that cell, a set of attributes of the cell, and the specific development event predicted by the development model within the cell. The model incorporates the spatial context of the 30-m cell by assigning to the cell the landscape composition and configuration of a 150-m window centered on the 30-m cell and determining the distance of the cell from recent and predicted development transitions. The probability of land cover for a grid cell changing from the original class i to class j is estimated using a series of multinomial logit models (Turner et al. 1996). The model is composed of two sets of multinomial logit equations of land cover change that occur to sites initially in non urban land cover (forest, grass, clear cuts and bare soil) and land cover change that occur to sites initially in urban land cover (mixed urban and paved urban). The probability of transition of a pixel of initial land cover i at time t having the same land cover class at time t+1 (j=0) or changing to one of the other land cover classes (j = 1…J) can be written as a multinomial logit:

Jj ,...,1= (5)

∑=

= J

js

X

X

ijs

j

e

eP)(

(

'

'

)β

β

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Where:

Pij is the probability of land cover at a given grid cell at time t having the same cover class at time t+1 or changing to another cover class. βj is a vector of estimated logit coefficients. J is the number of land cover states.

3.2 Transitions Modeled Possible land cover transitions were constrained by several assumptions. Land cover transitions between date pairs were constrained to those which are plausible (Table 7) as observed from a trajectory analysis of the historical land cover data. Six classes were assumed to not change between dates. Clear-cut forest was assumed to all convert to Regenerating Forest in the next time step. Parcel abandonment, where a parcel might revert to grass/shrub and eventually forest if not covered with impervious surface was explicitly not modeled. Six transition equations were developed (Table 5). Each starting land cover class has plausible development transitions as depicted in the table.

Table 7. Land cover transitions modeled. (Full land cover class names and abbreviations listed in Table 2). Land Cover Change

Model

Equation Base Year

No Change Choices

HU HU Equation 1 MU MU HU Equation 2 LU LU HU MU

CDEV CDEV Equation 3 GR GR HU MU LU MF CF Equation 4 MF MF HU MU LU GR CC Equation 5 CF CF HU MU LU GR CC

CC REG REG REG

Equation 6 AG AG HU MU LU WET WET WAT WAT BR BR SH SH

3.3 Variables Considered A total of fifty-eight variables were considered (Table 8) in the multinomial logit equations to model the six land cover change equations (Table 7). These variables were selected to measure various aspects of the landscape including: site attributes, site location (distance to variables);

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landscape composition; landscape configuration; and change variables (development events, recent development) (Alberti et al., 2006).

Table 8. Input variables (n = 58, including the Equation-specific constant) potentially used in the multinomial logit equations.

Variable Description Variable

Name Variable Description Variable

Name

Equation-Specific Constant ALT Landscape Composition Metrics: Within 150x150m (5x5 Pixel)

Window Floodplain PFLD

Surrogate Development Event Variable (Urbansim) Steep Slope PSLP Development Since Time 1 DE Streams PSTR

Landscape Composition Metrics: Within 150x150m (5x5 Pixel) Window Wetlands PWET

Clearcut And Regenerating Forest PCC Critical Areas PCRI Deciduous And Mixed Forest PMF Coniferous Forest PCF Development Intensity Variables Agriculture PAG Housing Density 1991 HD1 Grass PGR Com Den 1991 CD1 Heavy Urban PHU Total Improved Value TIV Medium Urban PMU Light Urban PLU Recent Development Variables Water PWA 450 M Neighborhood Window Same PES Comm Area Added 15 Window 88-91 C450 Resid. Units Added 15 Window 88-91 H450

Landscape Configuration: Distance Metrics 750 M Neighborhood Window Agriculture Source Area DAG Comm Area Added 25 Window 88-91 C750 Forest Source Area DTIM Resid. Units Added 25 Window 88-91 H750 Wetlands DWET Critical Areas DCRI Dummy Variables Public Lands DPUB Developed In 1991 DT1 Distance To Development In Time 1 DDT1 Binary Below Min Parcel Size BLMZ Freeways DFRE Is Timberlands TBL Primary Roads DPRD Is Public Lands PUB All Non-Local Roads DNLR UERL Devtype: Residential DRES Local Roads DLOC UERL Devtype: Commercial DC Central Business District DCBD UERL Devtype: Industrial DI

Landscape Configuration Metrics: Within At 150x150m (5x5 Pixel) Window UERL Devtype: Mixed Use DMU

Heavy Urban Mean Patch Size HMPS UERL Devtype: Open Space/Undev. DOS

Medium & Light Urban Mean Patch Size MMPS Is Steep Slope SSLP All Urban Mean Patch Size AMPS Inside/Outside Urban Growth Line UGL Forest Mean Patch Size FMPS Grass Mean Patch Size GMPS Urban And Paved Aggregation Index HAI Mixed Urban Aggregation Index MAI All Urban Aggregation Index AAI Forest Aggregation Index FAI Grass Aggregation Index GAI 1991 Shannon Evenness SHEI Geometric Mean Parcel Size (2000) PSG

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3.4 Model Estimation To incorporate a longer time period of land cover change, the model estimation for LCCM was generated from observed land cover transitions between 1995 and 1999 land cover data. Plausible transitions were identified from a trajectory (or transition) image calculated between 1995 and 1999 land cover. A plausible transition is one that is logical and commonly occurs (e.g. conversion from grass to mixed forest or light urban) and that comprises at least 0.5% of the landscape in the transition image. Whereas the conversion from heavy urban to coniferous forest in a three year time step is highly improbable and not realistic in this region. There are 26 plausible land cover transitions (Table 5). A stratified, random sample of 1000 points was created for each plausible transition, which were aggregated together and used to subset all fifty seven input variables by this sampling scheme for model estimation. Input variables were chosen for inclusion based on their Student’s t-statistic. Unless they contributed qualitative explanatory power any statistically insignificant variables were removed from each submodel. For example, in the submodel for conversion to heavy urban, a variable representing commercial and industrial may remain

4 Spatial Constraints

4.1 Creation of spatial masks A series of spatial masks (Figure 2) or constraints were used to realistically allocate the land cover transitions based on the calculated transition probabilities. These constraints enforced limits primarily to urban expansion based on observed limitations (Table 9) with the historic land cover data. Urban areas from the 2002 land cover were extracted to analyze the value ranges of elevation, slope and distance to urban and road metrics within these areas. An urban mask was created using two standard deviations from mean values for distance to roads, distance to urban areas in 2002, elevation, and slope. This mask is applied to all the urban classes (heavy, medium, and light).

4.2 Urban land classes Heavy urban can occur within a spatial mask representing manufacturing and industrial areas, and is further restricted by from occurring on agriculture, grass and mixed forest, as direct conversion from these classes in unlikely, as observed from the empirical land cover data. Medium and light urban are restricted by a mask of the respective population density for the current decade. For example, in the 2005-2008 predictions, the 2000 population density was used; 2011-2017, 2010 population density and so on.

4.3 Non-urban land classes Medium and light urban are both restricted from agriculture, and medium urban from mixed forest. Again, these constraints were devised based on the empirical land cover data. The mixed forest class is restricted from transitioning to grass, coniferous forest and clearcut forest , as mature coniferous forest does not normally transition to mixed forest, and mixed forest areas are not clearcut for timber production. Mixed forest, regenerating forest, and agriculture are left unconstrained. Areas of non-forested wetlands, snow, rock, ice, shoreline, and water remain consistent through time.

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Table 9. Empirically derived thresholds used to determine value ranges of spatial constraints. Minimum Maximum Mean Standard

Deviation Mean+3*STD Mean+2*STD

Elevation 0.00 560.00 98.53 69.17 306.04 236.87Slope 0.00 69.10 3.46 4.18 16.00 11.82Distance to Roads 0.00 6460.04 93.09 281.19 936.67 655.48Distance to Urban 1991‐2002 0.00 2906.29 26.20 69.24 233.91 164.67Population Density 2000 0.00 1500610.00 2306.73 4823.88 16778.37 11954.49Population Density 2010 0.00 729522.00 995.47 2135.03 7400.56 5265.53Population Density 2020 0.00 662438.00 1109.65 2329.24 8097.37 5768.13Population Density 2030 0.00 829501.00 1210.75 2667.43 9213.04 6545.61Population Density 2040 0.00 1065380.00 1326.31 3077.80 10559.71 7481.91

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4.4 Forest regeneration Regeneration of forest from clear-cut to mixed and coniferous forest was determined using forest practices application (FPA) spatial data from Washington Department of Natural Resources (DNR) (2009) cross-referenced with forest stand dynamic ages reported by Franklin et al., (2002). The Washington DNR FPA data categorized timber stands as even-age, uneven-age and salvage classes, which they defined a harvest rotation cycle. A temporal lagging (top row in table below) was created from these harvest cycles and the stand regeneration dynamics proposed by Franklin et al., (2002). For example, if a pixel is determined to be regenerating forest in the 2005 prediction, has an even-age harvest cycle of 15 years, and was coniferous forest in 1991, then the pixel reverts to coniferous forest in 2005. Otherwise the pixel is tested to see if it is an uneven or a salvage harvest cycle and mixed forest. If not the pixel remains as regenerating forest. The explicit rules are provided in Appendix C. In this way, regenerating forest can be converted back to mixed and coniferous forest using established harvest cycles and stand dynamics. Year Lag 3 15 20 25

Year Previous Year

Even‐Age Harvesting

Uneven‐Age Harvesting

Salvage Harvesting

2005 2002 1991 1986 19862008 2005 1991 1986 19862011 2008 1995 1991 19862014 2011 1999 1995 19912017 2014 2002 1999 19912020 2017 2005 1999 19952023 2020 2008 2002 19992026 2023 2011 2005 20022029 2026 2014 2008 20052032 2029 2017 2011 20082035 2032 2020 2014 20112038 2035 2023 2017 20142041 2038 2026 2020 20172044 2041 2029 2023 20202047 2044 2032 2026 20232050 2047 2035 2029 2026

4.5 Application of constraints as a means of spatially segmenting the model Urban growth is constrained according to distance to roads and from existing urban areas observed in the 2002 land cover data. These empirical constraints coupled with the predicted population densities of 2010 to 2040 spatially segment the allocation of urban transitions whereby medium and heavy urban will occur closed to existing urban areas and roads and light urban (suburban and exurban land covers) occur based on forecast distribution of population densities and road densities.

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Elevation Slope Distance to Roads Distance to Urban Areas 2002

2 sigma Urban Mask UGB and MI centers Population Density 2000 Population Density 2010 Figure 2. Spatial constraint masks. The following is a description of the mask codes: UGB = urban growth boundary; MI = manufacturing and industrial centers. Both data layers are available from the Puget Sound regional Council.

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Population Density 2020 Population Density 2030 Population Density 2040

Agriculture Protected Public Lands Timber Mask Washington DNR FPA Mask Figure 2 continued. Spatial constraint masks.

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5 Land Cover Change Model

5.1 Input data and years modeled A run of the Land Cover Change Model (LCCM) was made using 1995, 1999 and 2002 observed land cover data for King, Pierce, Snohomish, and Kitsap counties, (Figure 1). GIS data sources used to develop the explanatory variables are listed in Table 6. Land cover change was simulated for 3-year time intervals (2005, 2008, 2011, 2014, 2017, 2020, 2023, 2026, 2029, 2032, 2035, 2038, 2041, 2044, 2047, and 2050). Model output for 2005 and 2008 were compared with the 2007 observed land cover data (developed by UERL) to assess the agreement between model predictions and the observed land cover.

5.2 Parameter Estimation The multinomial logit equations were calculated using the discrete choice module of the UrbanSim modeling system. Variables were added systematically for each set of land cover transitions. Parameter estimates (Appendix B) were applied to spatially explicit variables to obtain probabilities for each 30-m cell in our study area. Land cover transition equations for each starting land cover type were summed and standardized to 1. Based on the estimated coefficients and variables specified in the model specification, LCCM calculates probabilities for each modeled land cover transition. Monte Carlo random sampling was used to determine which land cover transition was selected. These probabilities were compared against a Monte Carlo simulation (i.e. generated surface of random numbers) of calculated threshold probabilities. If the transition probability calculated by LCCM exceeded that calculated by the Monte Carlo draw, then the transition occurred; otherwise the land cover state remained constant. The comparisons to the Monte Carlo draws were spatially constrained using a series of spatial masks calculated using distance to roads, distance to urban areas observed in the 2002 land cover, an urban growth boundary with locations of major manufacturing and industrial areas, and predicted population densities generated from population forecasts produced by the PSRC. This process created the final land cover predictions.

5.3 Spatial Constraints The spatial constraint masks (Figure 2) reflect realistic limits to urban growth in the Central Puget Sound region. Based on empirical thresholds for elevation, slope, distance to urban areas and roads, and predicted population density, predicted future urban expansion is allocated in accordance with urban areas observed in the historic land cover maps. In this way, transitions to urban covers do not occur unrestrained, but follow simple empirical relationships based on historic data reflecting the limited available space for growth based on both a growth management act limiting the spatial extent of development and the physical constraints of the Puget Sound region; mountains (and hence topographic controls) to the east and the Puget Sound to the west. Masks for non-urban conversions also stem from observed historic constraints such as the limited availability of agricultural and timber lands, and protected public lands, which serve to allow non-urban land covers to occur.

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5.4 Land Cover Validation The accuracy (i.e. model validation, Table 10, Figure 7) of the predictions was determined using the observed 2007 land cover. There are two type of agreement between observed and predicted land cover change that are important to consider. First is the agreement between the amount of change observed and the amount of change predicted for each land cover type. Second is the locational agreement between the observed and predicted change. Because the model uses the observed amount of change between 1995 and 1999 to parameterize the statistical model, the amount of change predicted should closely match what was observed, assuming no deviation in change rates. Table 10. Validation metrics of the 2005 and 2008 predicted land cover using the 2007 observed land cover as the reference land cover.

2005 2008Kappa 0.85 0.83Kno 0.76 0.73Klocation 0.83 0.79Kquantity 0.77 0.77Kstandard 0.74 0.71 Several composite measures of model validation were calculated using IDRISI software and an excel spreadsheet developed by G. Pontius (Pontius 2001, Pontius et al. 2004). Kappa is a statistic that attempts to remove the chance (random) agreement between two maps (usually a classified map that is being tested for accuracy and a “truth” map). Because of the confusion between agreement due to class quantity observed/predicted and the agreement between the location in observed and predicted land cover, two variants on the standard Kappa statistic, Kno, and Klocation, were also calculated. Kno is the agreement of the two maps (the proportion of pixels in the predicted map that agree with the observed map) corrected for chance agreement divided by perfect agreement (1.0) corrected for chance agreement. Klocation is a measure of the locational agreement between the predicted observed maps. Table 7 presents these measures (along with the traditional Kappa) for 2005 and 2008. Agreement is higher for 2005 predicted land cover than for 2008 since the prediction for each time step is based on the previous time step’s prediction. That is, with the 2008 predicted land cover, it is an additional time step further from the 2002 land cover, which was the starting land cover base for the predictions. The overall Kappa statistics for the 2005 and 2008 predicted land covers were high at 0.85 and 0.83 indicating good agreement with the 2007 land cover classification. K location and K quantity provide a better representation of the distribution of error respective of spatial location and amount per land cover class. As seen here, the predicted land cover do better predicting location of land cover that is slightly higher than the quantity of change. These metrics represent agreement with the observed land cover for the near term prediction (i.e. within the eight years of the start of the prediction). We do not assume these agreement values to remain high as the prediction year increases towards 2050 and we cannot assume a linear decrease in the Kappa values. We are currently investigating Bayesian melding uncertainty analysis (Sevkicova et al 2007; Raftery et al 1995) to address the temporal decay of uncertainty. Another approach would be to apply extended Kappa metrics developed by Pontius and Petrova (2010). They devised a

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technique to extrapolate the anticipated accuracy of land cover predictions to any future time point. Using past land cover information to simulate present land cover, an observed measurement of predictive accuracy will anticipate how accurately future land cover is predicted. The method is based on the assumption that model accuracy decays towards randomness with future predictions at a decay rate conditioned upon prior model performance. This approach would provide a time series of uncertainty metrics for each prediction time period; the method incorporates past and present observed and predicted land cover data and uncertainty metrics to calculate future uncertainty estimations; applicable at multiple resolutions.

a.

b. Figure 7. Kappa validtion metrics for 2005 (a) and 2008 (b) predicted land covers compared to 2007 land cover classifciation.

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6 Land Cover Predictions

6.1 Dominant Landscape Changes We see a succession of urban transition from light to medium to heavy urban cover (Figure 4 and 5). This makes sense given the limited area for urban expansion constrained by the biophysical environments. There is finite area for urban areas to expand as evidenced by empirical historic land cover change. Coniferous forest dominants the predicted landscape decreasing from less than a third to slightly less than a quarter of the landscapes. Agriculture and clear-cut forest suffer the largest losses, while mixed forest and grass decrease to moderate percentages.

6.2 Types of Land Cover Change The total area in urban classes steadily increased from 1991 to 2002 (Table 11, Figures 4 and 5), while the area in grass, agriculture, and deciduous and mixed forests steadily declined. Coniferous forest area declined from 1991 to 1995, but returned to 1991 levels in 1999 and 2002. Some of this observed change may have been confusion between the two forest classes in the 1995 classification because of poor image quality from the 1995 summer image. However, the predicted loss of conifer forest was much greater than that observed in 1999 and 2002 (Figure 3 and 5). This is likely because of the change in the observed trend between 1991-95 and 1995-1999-2002. Similarly, the observed trend of decreasing area in grass seen from 1995 to 2002 was not reflected in the predicted land cover (Table 9). Urban land cover conversion plateaus after 2029-2032 transitions reflecting a limit on the amount of the landscape available for construction of the urban environment. From the empirical, historic relationships of urban areas and elevation, future urbanization is predicted to observe those constraints currently in place. For example, urbanization is limited by elevation and slope In this way urban expansion is constrained by physical constraints (e.g. elevation, slope) and demographic variables (e.g. predicted population). By 2050 (Table 9) urban expansion (comprised of 10.2% HU, 7.8% MU, and 9.2% LU) is predicted to be 23% of the total Central Puget Sound landscape. This reflects a net gain of 6.8% and 1.8% for heavy and medium urban, with a 3.2% loss for light urban from the 2005 prediction. The landscape will be almost 46% forest cover, consisting of 7.4% MF, 28.7% CF, 0.4% CC, and 9.7 REG. From 2005 predicted percentages, mixed, coniferous, and clear-cut forest lose 6.6%, 2%, and 3.8% respectively. Grass and agriculture will compose slightly more than 12% total cover, with 12.4% and 0.03% of the landscape, respectively, with losses of 7% and 1.7 from 2005. The remaining classes (CDEV, NFW, OW, BR, and SH) comprise 18.4% of the landscape with no net gain or loss from 2005.

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Table 9. Observed and predicted land cover percentages of the Central Puget Sound landscape. Refer to Table 3 for description of land cover class codes. Observed Predicted Land Class 1986 1991 1995 1999 2002 2007 2005 2008 2011 2014 2017 2020 2023 2026 2029 2032 2035 2038 2041 2044 2047 2050

HU 1.37 1.72 2.05 2.58 3.32 3.77 4.32 5.09 5.73 6.27 6.72 7.12 7.49 7.83 8.17 8.50 8.81 9.12 9.42 9.67 9.91 10.16

MU 3.46 4.69 5.26 5.06 6.01 7.11 5.29 5.15 5.17 5.30 5.49 5.74 6.02 6.28 6.54 6.77 6.96 7.13 7.32 7.52 7.66 7.76

LU 3.51 5.10 6.22 7.49 8.30 7.64 8.64 8.63 8.55 8.41 8.23 7.99 7.72 7.44 7.15 6.85 6.56 6.27 5.95 5.65 5.39 5.15

GR 8.14 7.92 8.94 6.92 5.36 5.89 6.94 7.64 8.61 9.31 9.85 10.26 10.61 10.91 11.16 11.37 11.58 11.75 11.94 12.13 12.27 12.41

AG 2.41 3.19 2.17 2.05 1.70 2.10 1.05 0.54 0.29 0.18 0.12 0.09 0.07 0.05 0.05 0.04 0.04 0.04 0.04 0.03 0.03 0.03

MF 20.66 18.26 18.44 14.97 14.00 12.38 14.04 13.31 12.32 11.37 10.51 10.25 9.64 9.22 8.84 8.39 8.38 8.06 7.78 7.44 7.27 7.36

CF 36.21 31.90 28.95 30.24 30.71 27.64 32.22 31.60 31.30 31.13 31.01 30.46 30.32 30.10 29.91 29.85 29.42 29.35 29.25 29.22 29.11 28.74

CC 3.80 1.59 1.48 1.41 4.20 1.22 0.42 0.44 0.41 0.40 0.40 0.40 0.40 0.40 0.39 0.39 0.39 0.39 0.39 0.39 0.39 0.39

REG 2.95 4.37 5.92 7.27 8.03 13.12 8.75 9.27 9.29 9.30 9.34 9.37 9.41 9.44 9.48 9.51 9.54 9.57 9.59 9.62 9.64 9.67

CDEV 0.07 0.28 0.21 0.20 0.07 0.03 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06 0.06

NFW 0.42 0.34 0.34 0.34 0.34 0.35 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34 0.34

OW 9.39 10.01 9.84 9.50 9.78 9.89 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78 9.78

BR 7.46 10.51 10.07 11.87 8.07 8.74 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04 8.04

SH 0.18 0.11 0.11 0.11 0.11 0.12 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11 0.11

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2005 2008 2011 2014

2017 2020 2023 2026

Figure 4. Land cover predictions for 2005-2050 for Central Puget Sound

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2029 2032 2035 2038

2041 2044 2047 2050

Figure 4 continued. Land cover predictions for 2005-2050 for Central Puget Sound

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Figure 5. Temporal changes in observed (1986 to 2007) and predicted land cover (2005 to 2050). Total percentage of landscape occupied by urban classes steadily increases throughout the predicted time period. Table 9 and Figure 5 show the percentages of the landscape occupied by each land cover class. Heavy urban increases rapidly from the start of the predictions until 2026, when it slightly increases for each prediction period. Medium urban follows an opposite trend with a slow increase from 2005 to about 2023, after which a more rapid increase is observed, at the expense of light urban. Light urban cover increases at the onset of prediction until a decrease after 2020. These decreases in conversion to urban about the mid 2020s into the 2030s results from the decrease in the availability of other classes to be converted based on the combination of the urban and population density constraints, primarily affecting medium and light urban. The conversion to non-urban classes show opposite trends as their urban counterparts, due to the fact these classes are being converted to the urban classes. Conversion to grass from agriculture and the forest classes shows a drastic decline after 2008-2011 transition pair, then decreasing steadily to 2050. This trend is mimicked by the conversion to mixed forest and to a lesser extent by the conversion to coniferous forest. Regenerating forest consumes most of the transitioning mixed and coniferous forest cells, which doubles in spatial extent at the end of the predictions. Clear-cut forest diminished rapidly, turning to regenerating forest. Agriculture all but disappears throughout the predictions occupying less than 1% of the landscape. As are the types of land cover conversion important, so are the rates of change. Rates of change for most of the transitioning classes are highest at the onset (in the earliest years of predictions)

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of the simulation (Figure 6 and Table 12). Heavy and light urban, and clear-cut forest all exhibit a steady decreasing rate of change with an exponential form quickly reaching asymptote in the first third of the prediction sequence. Medium urban shows a slight increase in its change rate with a plateau into the mid 2020s, afterwards the conversion rates decrease similarly to the other urban classes. The declining trends of the urban classes, in particular, again reflect the realistic constraint on urban development given the current empirical limits governed by topographic controls, growth management policies (reflected in the urban growth boundary) and by the predicted population densities. Grass, mixed forest and coniferous forest show similar declining trends in rates of change, with the forest class having peak rates of change during the 2011-2014 date pair, and grass showing an undulating change rate between the mid 2010s to the mid 2030s. This can be explaining by the temporal lagging of the spatial constraints applied to the conversion of grass to other classes. Without the temporal lag grass was aggressively converted to other cover types, which seemed unrealistic given the current and potential expense of suburban and exurban development, which maintains a significant amount of grass cover.

Figure 6. Rates of land cover change for the modeled transitions. See Table 3 for description of land class codes.

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Table 12. Rates of land cover change for predicted transitions expressed as percentage per year (% yr-1). Transitions based on observed transitions between 1995 and 1999 land covers. Land cover codes: HU = Heavy urban; MU = Medium urban; LU = Light urban; GR = Grass and pasture; MF = Mixed forest; CF = Coniferous forest; CC = Clearcut forest; REG = Regenerating forest. Transition Years

2005 2008 2011 2014 2017 2020 2023 2026 2029 2032 2035 2038 2041 2044 2047

Transition Type 2008 2011 2014 2017 2020 2023 2026 2029 2032 2035 2038 2041 2044 2047 2050

MU‐>HU 0.1979 0.1631 0.1364 0.1161 0.1037 0.0978 0.0916 0.0892 0.09 0.0855 0.0837 0.0835 0.068 0.0679 0.0678

LU‐>MU 0.1619 0.1753 0.1795 0.1768 0.1779 0.18 0.1703 0.1622 0.1567 0.1397 0.1323 0.1354 0.1234 0.1039 0.0912

AG‐>MU 0.0036 0.0011 0.0004 0.0001 4E‐05 2E‐05 7E‐06 1E‐06 4E‐06 0 0 0 1E‐06 0 0

CF‐>MU 0.0037 0.0037 0.0033 0.0028 0.0026 0.0023 0.0019 0.0016 0.0013 0.0011 0.0009 0.001 0.0009 0.0007 0.0006

Total >MU 0.1693 0.1801 0.1832 0.1797 0.1806 0.1823 0.1722 0.1638 0.158 0.1408 0.1333 0.1365 0.1243 0.1046 0.0918

GR‐>LU 0.0926 0.083 0.0717 0.0438 0.0301 0.0239 0.0183 0.0149 0.0121 0.0098 0.008 0.0068 0.0049 0.0034 0.0027

AG‐>LU 0.0086 0.0028 0.0008 0.0003 8E‐05 3E‐05 1E‐05 3E‐06 1E‐06 0 1E‐06 4E‐06 0 0 0

MF‐>LU 0.1233 0.1022 0.0824 0.0835 0.0769 0.0671 0.054 0.0433 0.0362 0.026 0.0219 0.0199 0.0149 0.0109 0.0091

CF‐>LU 0.0827 0.0628 0.0463 0.0344 0.026 0.0204 0.0145 0.0105 0.008 0.0057 0.0046 0.0038 0.0027 0.0021 0.0016

Total >LU 0.3072 0.2508 0.2011 0.162 0.133 0.1114 0.0868 0.0688 0.0563 0.0415 0.0345 0.0305 0.0225 0.0164 0.0135

AG‐>GR 0.1179 0.0465 0.0212 0.0102 0.0049 0.0023 0.0013 0.0007 0.0003 0.0002 0.0001 8E‐05 4E‐05 2E‐05 2E‐05

MF‐>GR 0.5165 0.4716 0.0581 0.0594 0.1168 0.0847 0.1164 0.0719 0.1002 0.0589 0.0313 0.0275 0.023 0.0168 0.0232

CF‐>GR 0.1725 0.188 0.1783 0.1662 0.1626 0.1493 0.1423 0.1255 0.1251 0.1116 0.1076 0.1168 0.1143 0.1089 0.1093

Total >GR 0.8069 0.7061 0.2575 0.2358 0.2843 0.2363 0.26 0.198 0.2256 0.1707 0.139 0.1443 0.1373 0.1257 0.1325

GR‐>MF 0.316 0.3239 0.3739 0.1478 0.0856 0.0716 0.0625 0.0517 0.048 0.0405 0.0379 0.0285 0.0236 0.0168 0.0152

AG‐>MF 0.0077 0.0036 0.0015 0.0006 0.0002 8E‐05 2E‐05 5E‐06 0 1E‐06 0 0 0 0 0

CF‐>MF 0.009 0.011 0.0116 0.013 0.0104 0.0082 0.0059 0.0047 0.004 0.0033 0.0032 0.0032 0.0029 0.0025 0.0024

Total >MF 0.3326 0.3385 0.387 0.1614 0.0962 0.0799 0.0684 0.0565 0.0521 0.0438 0.0411 0.0317 0.0265 0.0193 0.0176

GR‐>CF 0.2747 0.2939 0.3034 0.2153 0.1723 0.1593 0.1433 0.1308 0.1252 0.1147 0.1129 0.1132 0.1095 0.1028 0.1027

CF‐>CC 0.028 0.0219 0.0167 0.0127 0.0105 0.0089 0.0074 0.0064 0.0054 0.0047 0.004 0.0041 0.0038 0.0034 0.0031

CC‐>REG 0.0032 0.0047 0.0036 0.0024 0.0018 0.0013 0.001 0.0008 0.0007 0.0005 0.0004 0.0004 0.0004 0.0003 0.0003

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6.3 Patterns of Change Much of the conversion to heavy and medium urban cover types (Figure 4) occurs within the urban growth boundary (Figure 2) with the additional restrictions imposed by topographic controls (i.e. elevation and slope). These two classes provide most of the infill within the urban growth boundary, which may be accurate given current policy in place to curb excessive growth and the costs of expanding these covers types beyond their current spatial domain. In addition to this urban constraint, the distribution of predicted population densities, which was based on 2000 population densities distributed by census tract, restricted the expansion of light urban (i.e. residential neighborhood and suburban/exurban) development outside of currently developed urban areas. Perhaps a more realistic approach is to model the re-definition of the census tracts as the population increases in the Central Puget Sound region. In this way, population densities, thus light urban development, would more accurately reflect the anticipated population of the region. Expansion of grass and mixed forest, two cover types commonly associated with residential development, occur along the fringes of current development outside the dense urban core, and in the suburban and exurban areas. Conversions to coniferous, clear-cut and regenerating forests are restricted to current timber lands, dominating much of the exurban landscape east of the developed heavy-medium urban metro core. A potential limitation is the assumption that the current timber lands will remain designated as such into the future, without the addition or subtraction of areas for timber harvest. Some minor conversion of these cover types do occur outside of the exurban areas, within designated green spaces or protected public lands, which have been observed empirically from the historic land cover data.

7 Conclusions High spatial resolution land cover predictions are made to 2050 for the Central Puget Sound region. Using a multinomial logit statistical model and a unique combination of development and biophysical empirical input data, to emphasize site characteristics and economic and demographic influences, are used calculate the probability of land cover transition based on historic land cover change. Using realistic urban and non-urban growth constraints, in 2050 the Central Puget Sound region is composed of approximately 25% urban cover, and 57% forested and managed land cover. These land cover prediction scenarios developed here provide a moderate view of land cover change in the region for the next 45 years. These land cover predictions can be used in conjunction with other forecast data (e.g. climate and hydrologic change data) to determine the impacts of possible land cover changes in a coupled human-natural system.

8 References Alberti, M., Weeks, R., and S. Coe. 2004. Urban Land Cover Change Analysis for the Central

Puget Sound: 1991-1999. Journal of Photogrammetry and Remote Sensing 70:1043-1052.

Alberti, M., C. Redman, J. Wu, J. Marzluff, M. Handcock, J. Anderies, P. Waddell, D. Fox, H. Kautz, J. Hepinstall. 2006. Urban landscape patterns and global environmental change (GEC): Complex dynamics and emergent properties. International Human Dimension of Global Climate Change. Spring 2006.

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Alberti, M., J. Marzluff, M. Handcock, P. Waddell. 2006. Biocomplexity I Final Report. National Science Foundation.

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Hepinstall, J.A., M. Alberti and J.M. Marzluff. 2008. Predicting land cover change and avian community responses in rapidly urbanizing environments. Landscape Ecology 23 (10): 1257-1276.

Hepinstall-Cymerman J., Coe S., Alberti M. 2009. Using Urban Landscape Trajectories to Develop a Multi-Temporal Land Cover Database to Support Ecological Modeling. Remote Sensing. 1(4):1353-1379.

McGarigal, K. and Marks, B. J. 1995. FRAGSTATS: Spatial Pattern Analysis Program for Quantifying Landscape Structure. Gen. Tech. Rep. PNW-GTR-351. Pacific Northwest Research Station, USDA-Forest Service, Portland.

Nelder, John; Wedderburn, Robert. 1972. "Generalized Linear Models". Journal of the Royal Statistical Society. Series A (General) 135 (3): 370–384.

O'Neill, R. V., J. R. Krummel, R. H. Gardner, G. Sugihara, B. Jackson, D. L. DeAngelis, B. T. Milne, M. G. Turner, B. Zygmunt, S. W. Christensen, V. H. Dale and R. L. Graham. 1988. Indices of landscape pattern. Landscape Ecology. 1(3): 153-162.

Pontius, R G. 2000. Quantification error versus location error in the comparison of categorical maps. Photogrammetric Engineering & Remote Sensing 66(8) p.1011-1016.

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Turner, M. 1989. Landscape ecology: the effect of pattern on process. Annual Review Ecological Systems, 20, pp.171-197.

Turner, M.G. ,David N. Wear, Richard O. Flamm. 1996. Land Ownership and Land-Cover Change in the Southern Appalachian Highlands and the Olympic Peninsula. Ecological Applications, 6(4) 1150-1172.

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Waddell, P., Borning, A., Noth, M., Freier, N., Becke, M., Ulfarsson, G. (2003), Microsimulation of Urban Development and Location Choices: Design and Implementation of UrbanSim, Networks and Spatial Economics, 3, 43-67.

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Wear, D.N., and P. Bolstad. 1998. Land Use Changes in Southern Appalachian Landscapes: Spatial Analysis and Forecast Evaluation. Ecosystems 1(6):575-594.

Wear, D.N., Monica G. Turner, Robert J. Naiman. 1998. Land Cover Along an Urban-Rural Gradient: Implications for Water Quality. Ecological Applications, 8(3):619-630.

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Appendix A. Input variable definitions. The model uses the following logit variables: (Xpixel,k is the k-th explanatory variable X for pixel pixel).

• ALT = alternative_specific_constant for each modeled equation modeled Note on Transformations:

A. All percentage variables are ARCSIN(square root(x)) transformed and the variable grids have been transformed as well

B. All distance variables are ln (x) / 10 transformed Definitions: Attributes (changed from Invariants) – base data either used directly or used as base data for calculating Computed Invariants or Variables Computed Invariants - calculated once, before any model runs, do not need (at this point in the model specification) to be re-calculated at any point during the run) Intermediate Computed Variables – variables that are calculated during the run and are intermediate steps to calculating the Computed Variables Computed Variables – variables that are computed each time step, have been transformed from Legend

1. BOLD_FACE_UPPER_CASE is a standard variable name and the name of an ArcGIS float file

2. bold_lower_case is the long _name 3. normal text is the explanation of how calculated

Output from time step x - 1 Land cover base data

• LCTx = land cover at time = x. Fourteen land cover classes (See Table 3 for class number values and names).

Attributes (Currently base data that does not change).

• TIV = land_value_per_acre – ln_bounded( cell.total.improved.value + 1) / 10a • PSG = geometric_mean_of_parcel_within_150_grid_cell – πX( PARCEL) /

10000000a • VUE = is_in_view – if VUE == 1 then 1 else 0 • UGL is_outside_urban_growth_boundary – if UGL == 1 then 1 else 0 • BMLZ = is_on_minimum_lot_size if BMLZ == 1 then 1 else 0 • PUB = is_on_public – if PUB == 1 then 1 else 0 • TBL = is_on_timberland – if TBL == 1 then 1 else 0 • STR = is_stream_river – if STR == 1 then 1 else 0 • FLD = flood_plain – if FLD == 1 then 1 else 0 • WET = wetlands – if WET == 1 then 1 else 0 • SLP = percent_slope

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• CBD b = central_business_district – if CBD == 1 then 1 else 0 • CRITb = critical_area – if CRI == 1 then 1 else 0 • PARMTSQ = parcel_size_meter_squared - parcel size as of 2002 in meters squared • FREE – freeways – freeways • NLOCRDS – all_roads_but_local – all roads except local roads • LOCRDS – local_roads – local roads only • PRDS – primary_roads – primary roads

a- division to standardize range of input variables for multinomial logit modeling. b- attributes that may be modified by UrbanSim in the future. Computed Invariants

A) Landscape Composition Invariants • PSTR = percentage_of_streams_pixels_within_150_grid_cell – (sum over p in

cell.150m, if STR == 1 else 0) / 25 • PFLD = percentage_of_flood_plain_pixels_within_150_grid_cell – (sum over p in

cell.150m, if FLD == 1 then 1 else 0) / 25 • PWET = percentage_of_wetland_pixels_within_150_grid_cell – (sum over p in

cell.150m, if WET == 1 else 0) / 25 • PSLP = percent_of_pixels_greater_than_25%_slope_within 150_grid_cell – (sum

over s in cell.150m, if SLP == >25 then 1 else 0) / 25 • PCRI = percent_of_pixels_in_critical_areas_within 150_grid_cell – (sum over s in

cell.150m, if CRI == 1 else 0) / 25 B) Distance Invariants • DTIM = ln_distance_to_forest_source_area – ln (( pixel.distance to nearest pixel

where TBL == 1 ) + 1) / 10a • DWET = ln_distance_to_wetland – ln ((distance to WET == 1 in meters) + 1) / 10a • DSTR = ln_distance_to_stream – ln ((distance to STR == 1 in meters) + 1) / 10a • DCRI = ln_distance_to_critical_area - ln (( pixel.distance to nearest pixel with CRIT

== 1 ) + 1) / 10a • DCBD = ln_distance_to_central_business_district – ln ((distance in meters to nearest

pixel where CBD == 1) + 1) / 10a a- division by 10 to standardize range of input variables for multinomial logit modeling. Computed Variables

A) Land Use Computed Variables (Time-step change in Development type is provided by UrbanSim in the current implementation) • DRES = development_type_residential – if DEVT ge 1 and le 8 then 1 else 0. • DC = development_type_commercial – if DEVT == 17,18,19 then 1 else 0. • DI = development_type_industrial – if DEVT == 20, 21, or 21 then 1 else 0. • DMU = development_type_mixed_use – if DEVT ge 9 and le 16 then 1 else 0. • DOS = development_type_open_space – if DEVT == 24, 26, 29 then 1 else 0.

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Computed Variables A) Landscape Composition Computed Variables • PES = percentage_pixels_of_same_land_cover_class_within_150_grid_cell – arcsin(

square root ((sum over p in cell.150m, if LCTx == focal_cell_land_cover) / number of valid (not water) pixels in 150 m window ))

• PHU = percentage_of_heavy_urban_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 1) / number of valid (not water) pixels in 150 m window ))

• PMU = percentage_of_medium_urban_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 2) / number of valid (not water) pixels in 150 m window ))

• PLU = percentage_of_light_urban_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 3) / number of valid (not water) pixels in 150 m window ))

• PGR = percentage_of_grass_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 5) / number of valid (not water) pixels in 150 m window ))

• PMF = percentage_of_decid_and_mixed_forest_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 6) / number of valid (not water) pixels in 150 m window ))

• PCF = percentage_of_coniferous_forest_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 7) / number of valid (not water) pixels in 150 m window ))

• PCC = %_of_clearcut_and_regen_forest_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 8) / number of valid (not water) pixels in 150 m window ))

• PAG = percentage_of_agriculture_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 10) / number of valid (not water) pixels in 150 m window ))

• PWA = percentage_of_water_pixels_within_150_grid_cell – arcsin( square root ( (sum over p in cell.150m, if LCTx == 12) / 25 ))

B) Distance Computed Variables • DAG = ln_distance_to_agricultural_area– ln (( pixel.distance to nearest pixel with

ag_mps > 400 30-m pixels) + 1) / 10a • DDT1 = ln_distance_to_development– ln ((distance in meters to nearest pixel with

LCT1 le 3) + 1) / 10ab • DFRE = ln_distance_to_freeway– ln ( pixel.distance from FREE == 1) + 1) / 10ab • DPRD = ln_distance_to_primary_roads– ln (( pixel.distance from PRIM == 1) + 1) /

10ab • DNLR = ln_distance_to_all_roads_but_local– ln_bounded( pixel.distance NLOCAL

== 1 + 1) / 10ab • DLOC = ln_distance_to_local_roads – ln (( pixel.distance from LOCAL == 1 ) + 1) /

10ab a- division by 10 to standardize range of input variables for multinomial logit modeling. b- currently these variables are derived from 2002 GIS data and are not modified by either the LCCM or UrbanSim.

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Computed Variables C) Landscape Metric Computed Variables • HAI = aggregation_index heavy_urban_within_150_grid_cell – arcsin(sqrt(hu_ai /

100)). See Table 4 for AI equation. • MAI = aggregation_index medium_and_light_urban_within_150_grid_cell –

arcsin(sqrt(mlu_ai / 100)) . See Table 4 for AI equation. • AAI = aggregation_index all_urban_within_150_grid_cell – arcsin(sqrt(au_ai / 100)).

See Table 4 for AI equation. • FAI = aggregation_index _forest_within_150_grid_cell – arcsin(sqrt(forest_ai / 100)).

See Table 4 for AI equation. • GAI = aggregation_index_grass_within_150_grid_cell – arcsin(sqrt(grass_ai / 100)).

See Table 4 for AI equation. • HMPS = ln_mean_patch_size_heavy urban_within_150_grid_cell – ln (hu_ps + 1) /

10a • MMPS = ln_mean_patch_size_medium_low_urban_within_150_grid_cell – ln

(MLU_PS + 1) / 10a • AMPS = ln_mean_patch_size_all urban_within_150_grid_cell – ln (ALLU_PS + 1) /

10a • FMPS = ln_mean_patch_size_forest_within_150_grid_cell – ln (FOREST_PS + 1) /

10a • GMPS = ln_mean_patch_size_grass_within_150_grid_cell – ln (GRASS_PS + 1) / 10a • SHEI = Shannon_evenness_index_within_150_grid_cell – arcsin(sqrt(LC_SHEI)) –

See Table 4 for SHEI equation. • SHEI_MOD = Shannon_evenness_index_within_150_grid_cell –

arcsin(sqrt(LC_SHEI)) – See Table 4 for SHEI equation. a- division by 10 to standardize range of input variables for multinomial logit modeling.

D) Land Use Computed Variables (Supplied from UrbanSim output, base GRID CELL size is 150 m)

• DE – development_event – development event in Development Grid in the past three years inclusive of the current year (e.g., base year = 1991, include development events from 1988, 1989, 1990, and 1991)

• DT1 = developed_in_time_1 – if LCT == 1,2, or 3 then 1 else 0 • HD1 = housing_density_per_acre– ln ( residential, condo, and apartment number of

units in current year / number of acres + 1) / 10 a (5.55975 converts 150 m UrbanSim GRID CELLS to acres)

• CD1 = commercial_density – ln ( commercial square feet in current year / number of acres + 1 ) / 10 a (5.55975 converts 150 m UrbanSim GRID CELLS to acres)

• HOUSE_ADD = n_residential_units_recently_added_by_parcel - the number of residential units added in the last three years inclusive of the current year (Intermediate Computed Variable)

• COMM_ADD = commercial_sqft_recently_added_by_parcel - the number of commercial square feet added in the last three years inclusive of the current year (Intermediate Computed Variable)

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Computed Variables D) Land Use Computed Variables (continued) • H450 = n_residential_units_recently_added_within_450m_window – the number of

residential units added in the last three years inclusive of the current year: ln (n_residential_units_recently_added_within_450_window_cell + 1) / 10a

• C450 = commercial_sqft_recently_added_within_450m_window – the number of commercial square feet added in the last three years inclusive of the current year: ln (commercial_sqft_recently_added_within_450m_window + 1) / 10a

• H750 = n_residential_units_recently_added_within_750m_window – the number of residential units added in the last three years inclusive of the current year: ln (n_residential_units_recently_added_within_450m_window + 1) / 10a

• C750 = commercial_sqft_recently_added_within_750m_window– the number of commercial square feet added in the last three years inclusive of the current year: ln (commercial_sqft_recently_added_within_750m_window + 1) / 10a

a- division by 10 to standardize range of input variables for multinomial logit modeling.

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Appendix B. Model parameter specification based on sampling of and model estimation from 1995 and 1999 observed land cover. A. Conversion to Heavy Urban (HU).

From Land Cover Class: MU LU GR MF

To Land Cover Class: HU HU HU HU

Variable Name Variable Description

ALT Equation-Specific Constant 15.297 8.988

Development Event Variable (Urbansim)

DE Development Since Time 1 Landscape Composition Metrics: Within 150x150m (5x5 Pixel) Window

PCC Clearcut And Regenerating Forest PMF Deciduous And Mixed Forest 3.716 -1.597 -3.259 PCF Coniferous Forest 2.019 PAG Agriculture -1.703 PGR Grass 0.478 -3.462 PHU Heavy Urban 5.668 PMU Medium Urban 6.602 PLU Light Urban -6.106 PES Same -4.290 PWA Water

Landscape Composition Metrics: Within 150x150m (5x5 Pixel) Window PFLD Floodplain PSLP Steep Slope -1.505 -1.837 -1.059 PSTR Streams -1.263 PWET Wetlands -0.682 -1.366 PCRI Critical Areas

Landscape Configuration: Distance Metrics DAG Agriculture Source Area 0.940 DTIM Forest Source Area 1.888 DWAT Water 6.238 1.907 DWET Wetlands DCRI Critical Areas DPUB Public Lands 2.438 2.503 DDT1 Distance To Developed In Time 1 DFRE Freeways 2.758 DPRD Primary Roads 0.281 DNLR All Non-Local Roads 2.569 DLOC Local Roads -0.891 -2.139 DCBD Central Business District -4.276

Landscape Configuration Metrics: Within At 150x150m (5x5 Pixel) Window AMPS All Urban Mean Patch Size 2.718 0.705 FMPS Forest Mean Patch Size GMPS Grass Mean Patch Size 1.031 HMPS Heavy Urban Mean Patch Size MMPS Medium Urban Mean Patch Size

HAI Urban And Paved Aggregation Index MAI Mixed Urban Aggregation Index 3.126

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From Land Cover Class: MU LU GR MF

To Land Cover Class: HU HU HU HU

AAI All Urban Aggregation Index 0.000 0.000 FAI Forest Aggregation Index GAI Grass Aggregation Index 0.000 SHEI Shannon Evenness Index PSG Geometric Mean Parcel Size (2000)

Development Intensity Variables HD1 Housing Density Time 1 -4.129 CD1 Com Den Time 1 TIV Total Improved Value

Recent Development Variables 450 M Neighborhood Window

C450 Comm Area Added Time 1 – 3 years H450 Residential Units Added Time 1 – 3 years

750 M Neighborhood Window C750 Comm Area Added Time 1 – 3 years 0.353 0.371 H750 Residential Units Added Time 1 – 3 years

Dummy Variables DT1 Developed In Time 1

BLMZ Binary Below Min Parcel Size -0.296 -0.403 CRIT Critical Areas TBL Is Timberlands PUB Is Public Lands -0.638 1.111

DRES Devtype: Residential -0.541 -1.068 -0.449 DC Devtype: Commercial DI Devtype: Industrial 0.784

DOS Devtype: Open Space/Undev. 0.488 0.411 DMU Devtype: Mixed Use -0.515 -1.134 SSLP Is Steep Slope -0.835 UGL Inside/Outside Urban Growth Line 0.797 1.479 1.678

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B. Conversion to Medium Urban (MU). From Land Cover Class: MU LU GR MF AG

To Land Cover Class: MU MU MU MU MU


ALT Equation-Specific Constant 7.000 7.294 16.215 12.705 3.730



PCC Clearcut And Regenerating Forest PMF Deciduous And Mixed Forest -2.531 -2.937 -1.357 PCF Coniferous Forest -0.919 -3.196 PAG Agriculture PGR Grass -1.154 -8.603 -3.460 -4.717 PHU Heavy Urban 1.876 -1.053 PMU Medium Urban 4.481 5.061 PLU Light Urban -3.826 0.628 PES Same -0.952 8.621 1.442 PWA Water

Landscape Composition Metrics: Within 150x150m (5x5 Pixel) Window PFLD Floodplain 0.364 PSLP Steep Slope -0.908 -1.151 -3.004 PSTR Streams -0.708 PWET Wetlands -0.641 PCRI Critical Areas 0.197

Landscape Configuration: Distance Metrics DAG Agriculture Source Area -0.608 DTIM Forest Source Area 0.780 DWAT Water DWET Wetlands DCRI Critical Areas 2.338 DPUB Public Lands 1.050 DDT1 Distance To Developed In Time 1 DFRE Freeways DPRD Primary Roads 1.248 DNLR All Non-Local Roads -0.843 DLOC Local Roads -0.717 -1.785 DCBD Central Business District -3.000

Landscape Configuration Metrics: Within At 150x150m (5x5 Pixel) Window AMPS All Urban Mean Patch Size 1.018 0.804 FMPS Forest Mean Patch Size GMPS Grass Mean Patch Size 0.408 -0.804 HMPS Heavy Urban Mean Patch Size MMPS Medium Urban Mean Patch Size

HAI Urban And Paved Aggregation Index

MAI Mixed Urban Aggregation Index -2.035E-04

AAI All Urban Aggregation Index 1.888E-04 1.891E-04 2.786E-04 FAI Forest Aggregation Index GAI Grass Aggregation Index -1.036E-05

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From Land Cover Class: MU LU GR MF AG

To Land Cover Class: MU MU MU MU MU

SHEI Shannon Evenness Index 0.663 PSG Geometric Mean Parcel Size (2000) -0.238 1.370

Development Intensity Variables HD1 Housing Density Time 1 CD1 Com Den Time 1 1.251 TIV Total Improved Value


C450 Comm Area Added Time 1 – 3 years H450 Residential Units Added Time 1 – 3 years 2.423

750 M Neighborhood Window C750 Comm Area Added Time 1 – 3 years H750 Residential Units Added Time 1 – 3 years 0.453 -2.294


BLMZ Binary Below Min Parcel Size -0.395 CRIT Critical Areas 1.026 TBL Is Timberlands PUB Is Public Lands

DRES Devtype: Residential -0.290 -0.285 DC Devtype: Commercial DI Devtype: Industrial

DOS Devtype: Open Space/Undev. DMU Devtype: Mixed Use -2.488 SSLP Is Steep Slope UGL Inside/Outside Urban Growth Line 0.338 0.848 0.719

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C. Conversion to Light Urban (LU). From Land Cover Class: LU GR MF CF AG

To Land Cover Class: LU LU LU LU LU


ALT Equation-Specific Constant 6.156 17.393 9.807 13.444 6.925



PCC Clearcut And Regenerating Forest PMF Deciduous And Mixed Forest PCF Coniferous Forest PAG Agriculture PGR Grass -1.374 1.175 -3.237 PHU Heavy Urban -2.650 PMU Medium Urban 2.013 1.455 PLU Light Urban 0.905 2.570 1.351 PES Same -1.431 PWA Water

Landscape Composition Metrics: Within 150x150m (5x5 Pixel) Window PFLD Floodplain 1.536 PSLP Steep Slope -1.108 -0.349 -1.203 -2.704 PSTR Streams PWET Wetlands PCRI Critical Areas

Landscape Configuration: Distance Metrics DAG Agriculture Source Area -0.755 DTIM Forest Source Area 0.721 DWAT Water DWET Wetlands DCRI Critical Areas 1.810 0.638 DPUB Public Lands 1.761 DDT1 Distance To Developed In Time 1 DFRE Freeways DPRD Primary Roads DNLR All Non-Local Roads -0.897 -2.352 DLOC Local Roads -0.809 -1.355 DCBD Central Business District -2.285 -5.640

Landscape Configuration Metrics: Within At 150x150m (5x5 Pixel) Window AMPS All Urban Mean Patch Size FMPS Forest Mean Patch Size GMPS Grass Mean Patch Size 0.517 0.387 HMPS Heavy Urban Mean Patch Size MMPS Medium Urban Mean Patch Size

HAI Urban And Paved Aggregation Index MAI Mixed Urban Aggregation Index -1.628E-04 AAI All Urban Aggregation Index 2.192E-04 8.253E-05 2.250E-04 FAI Forest Aggregation Index GAI Grass Aggregation Index 2.697E-05

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From Land Cover Class: LU GR MF CF AG

To Land Cover Class: LU LU LU LU LU

SHEI Shannon Evenness Index -0.647 PSG Geometric Mean Parcel Size (2000) -0.536 -0.456

Development Intensity Variables HD1 Housing Density Time 1 CD1 Com Den Time 1 TIV Total Improved Value 0.577


C450 Comm Area Added Time 1 – 3 years H450 Residential Units Added Time 1 – 3 years 1.826

750 M Neighborhood Window C750 Comm Area Added Time 1 – 3 years H750 Residential Units Added Time 1 – 3 years -2.198


BLMZ Binary Below Min Parcel Size CRIT Critical Areas 0.716 TBL Is Timberlands PUB Is Public Lands 0.780

DRES Devtype: Residential DC Devtype: Commercial DI Devtype: Industrial

DOS Devtype: Open Space/Undev. DMU Devtype: Mixed Use SSLP Is Steep Slope UGL Inside/Outside Urban Growth Line

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D. Conversion to Mixed Forest (MF), Conifer Forest (CF), Grass (GR) or Clearcut (CC). From Land Cover Class: GR MF AG GR CF GR MF CF AG MF CF

To Land Cover Class: MF MF MF CF CF GR GR GR GR CC CC


ALT Equation-Specific Constant 14.922 6.07812 6.350 16.169 7.563 3.252 7.511

Surrogate Development Event Variable (Urbansim)

DE Development Since Time 1 0.801 Landscape Composition Metrics: Within 150x150m (5x5 Pixel) Window

PCC Clearcut And Regenerating Forest 6.194 4.082 1.463 PMF Deciduous And Mixed Forest 2.685 5.595 1.819 PCF Coniferous Forest 2.109 3.277 -0.405 1.941 PAG Agriculture PGR Grass 3.596 3.779 PHU Heavy Urban -4.935 PMU Medium Urban -4.027 -2.648 PLU Light Urban -0.698 PES Same -2.633 PWA Water

Landscape Composition Metrics: Within 150x150m (5x5 Pixel) Window PFLD Floodplain 0.590 PSLP Steep Slope -0.361 PSTR Streams -0.949 PWET Wetlands 1.376 -0.878 PCRI Critical Areas -0.185 -0.167 -0.275

Landscape Configuration: Distance Metrics DAG Agriculture Source Area 1.683 5.015 -2.160 1.587 DTIM Forest Source Area -1.622 -1.271 -0.698 DWAT Water 6.279 DWET Wetlands 3.002 2.131 DCRI Critical Areas DPUB Public Lands 2.867 3.529 4.539 DDT1 Distance To Developed In Time 1 DFRE Freeways -2.345 DPRD Primary Roads 3.864

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From Land Cover Class: GR MF AG GR CF GR MF CF AG MF CF


DNLR All Non-Local Roads DLOC Local Roads 3.010 1.462 2.025 DCBD Central Business District 2.227 12.366 0.109

Landscape Configuration Metrics: Within At 150x150m (5x5 Pixel) Window AMPS All Urban Mean Patch Size -2.373 FMPS Forest Mean Patch Size -0.400 GMPS Grass Mean Patch Size -0.126 -2.996 HMPS Heavy Urban Mean Patch Size MMPS Medium Urban Mean Patch Size -0.427

HAI Urban And Paved Aggregation Index MAI Mixed Urban Aggregation Index AAI All Urban Aggregation Index FAI Forest Aggregation Index GAI Grass Aggregation Index -6.012E-05 6.629E-05 7.217E-07 SHEI Shannon Evenness Index 2.653 -0.251 PSG Geometric Mean Parcel Size (2000) 1.695 1.378 0.005

Development Intensity Variables HD1 Housing Density Time 1 CD1 Com Den Time 1 TIV Total Improved Value -0.532 -0.704 -0.354


C450 Comm Area Added Time 1 – 3 years H450 Residential Units Added Time 1 – 3 years

750 M Neighborhood Window C750 Comm Area Added Time 1 – 3 years H750 Residential Units Added Time 1 – 3 years


BLMZ Binary Below Min Parcel Size -0.518 -0.939 CRIT Critical Areas TBL Is Timberlands PUB Is Public Lands 1.899 0.783 0.728

DRES Devtype: Residential 0.746

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From Land Cover Class: GR MF AG GR CF GR MF CF AG MF CF


DC Devtype: Commercial DI Devtype: Industrial

DOS Devtype: Open Space/Undev. 0.681 DMU Devtype: Mixed Use SSLP Is Steep Slope UGL Inside/Outside Urban Growth Line -0.684

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Appendix C. ArcGrid python syntax to calculate land cover transitions based on spatial constraints. # Import system modules import sys, string, os, win32com.client # Create the Geoprocessor object gp = win32com.client.Dispatch("esriGeoprocessing.GpDispatch.1") # Setting OverWriteOutput to True allows geoprocessing tools to overwrite # the output if it already exists. gp.OverWriteOutput = 1 # Check out Spatial Analyst extension license gp.CheckOutExtension("Spatial") # set workspaces InWorkSpace = "U:/users/mmarsik/lccm/data/output/lc2038_from_9599/probabilities" OutWorkSpace = InWorkSpace gp.Workspace = InWorkSpace # set raster analysis environment settings gp.Mask = "U:/users/mmarsik/lccm/data/1_GIS/partitions/partitions" gp.Extent = "U:/users/mmarsik/lccm/data/1_GIS/partitions/partitions" gp.CellSize = 30 #<-- change manually if needed # create dictonary of input years ##years = ["2005", "2008", "2011", "2014", "2017", "2020", "2023", "2026", "2029", "2032", "2035", "2038", "2041", "2044", "2047", "2050"] years = ["2005", "2008"] ##years = ["2005", "2008", "2011", "2014", "2017", "2020"] ##years = ["2023", "2026", "2029", "2032", "2035", "2038", "2041", "2044", "2047", "2050"] for year in years: ## if year == "2005": # create output land cover raster name OutLC = "lc%s" % year # create previous year from current year prevyr = "lc%s" % str(int(year)-3)

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# set popdens year if year == "2005" or year == "2008": pdens = "pdens00" elif year == "2011" or year == "2014" or year == "2017": pdens = "pdens10" elif year == "2020" or year == "2023" or year == "2026" or year == "2029": pdens = "pdens20" elif year == "2032" or year == "2035" or year == "2038": pdens = "pdens30" else: pdens = "pdens40" # set timber year if year == "2005" or year == "2008": tmbryear = "lc1986" elif year == "2011" or year == "2014": tmbryear = "lc1991" elif year == "2017": tmbryear = "lc1995" elif year == "2020": tmbryear = "lc1999" else: tmbryear = "lc%s" % str(int(year)-21) # set fpa even age year if year == "2005" or year == "2008": evenyear = "lc1991" elif year == "2011": evenyear = "lc1995" elif year == "2014": evenyear = "lc1999" else: evenyear = "lc%s" % str(int(year)-15) # set fpa uneven age year

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if year == "2005" or year == "2008": unevenyear = "lc1986" elif year == "2011": unevenyear = "lc1991" elif year == "2014": unevenyear = "lc1995" elif year == "2017" or year == "2020": unevenyear = "lc1999" else: unevenyear = "lc%s" % str(int(year)-21) # set fpa salvage year if year == "2005" or year == "2008" or year == "2011": salvgyear = "lc1986" elif year == "2014" or year == "2017": salvgyear = "lc1991" elif year == "2020": salvgyear = "lc1995" elif year == "2023": salvgyear = "lc1999" else: salvgyear = "lc%s" % str(int(year)-24) try: ## calcExp = "con(probs2005_1 >= rnd2005_1 & (urbmsk2 == 1 | uga_micen == 1) & protect <> 1 & ag <> 1 & lc02 <> 3 & lc02 <> 5 & lc02 <> 6 & lc02 <> 7, 1, \ ## con(probs2005_2 >= rnd2005_2 & (urbmsk2 == 1 & pdens00 == 1) & protect <> 1 & ag <> 1 & lc02 <> 5 & lc02 <> 6 & lc02 > 1, 2, \ ## con(probs2005_3 >= rnd2005_3 & (urbmsk2 == 1 & pdens00 == 1) & protect <> 1 & ag <> 1 & lc02 > 2, 3, \ ## con(probs2005_5 >= rnd2005_5 & protect <> 1 & lc02 > 4, 5, \ ## con(probs2005_6 >= rnd2005_6 & protect <> 1 & lc02 > 4 | (probs2005_9 >= rnd2005_9 & tmbr == 1 & lc86 == 6), 6, \ ## con(probs2005_7 >= rnd2005_7 & lc02 <> 6 & protect <> 1 & lc02 > 4 | (probs2005_9 >= rnd2005_9 & tmbr == 1 & lc86 == 7), 7, \ ## con(probs2005_8 >= rnd2005_8 & protect <> 1 & lc02 <> 6 & lc02 > 4, 8, \

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## con(probs2005_9 >= rnd2005_9 & protect <> 1 & lc02 > 4, 9, \ ## con(probs2005_10 >= rnd2005_10 & protect <> 1 & lc02 > 4, 10, lc02)))))))))" % year calcExp = "con(probs"+year+"_1 >= rnd"+year+"_1 & (urbmsk2 == 1 | uga_micen == 1) & protect2 == 0 & ag <> 1 & "+prevyr+" <> 3 & "+prevyr+" <> 5 & "+prevyr+" <> 6 & "+prevyr+" <> 7, 1, \ con(probs"+year+"_2 >= rnd"+year+"_2 & (urbmsk2 == 1 & "+pdens+" == 1) & protect2 == 0 & ag <> 1 & "+prevyr+" <> 5 & "+prevyr+" <> 6 & "+prevyr+" > 1, 2, \ con(probs"+year+"_3 >= rnd"+year+"_3 & (urbmsk2 == 1 & "+pdens+" == 1) & protect2 == 0 & ag <> 1 & "+prevyr+" > 2, 3, \ con(probs"+year+"_5 >= rnd"+year+"_5 & protect2 == 0 & "+prevyr+" > 4, 5, \ con(probs"+year+"_6 >= rnd"+year+"_6 & protect2 == 0 & "+prevyr+" > 4 | (probs"+year+"_9 >= rnd"+year+"_9 & (tmbr == 1 & "+tmbryear+" == 6) | (fpa == 15 & "+evenyear+" == 6) | (fpa == 20 & "+unevenyear+" == 6) | (fpa == 25 & "+salvgyear+" == 6)), 6, \ con(probs"+year+"_7 >= rnd"+year+"_7 & "+prevyr+" <> 6 & protect2 == 0 & "+prevyr+" > 4 | (probs"+year+"_9 >= rnd"+year+"_9 & (tmbr == 1 & "+tmbryear+" == 7) | (fpa == 15 & "+evenyear+" == 7) | (fpa == 20 & "+unevenyear+" == 7) | (fpa == 25 & "+salvgyear+" == 7)), 7, \ con(probs"+year+"_8 >= rnd"+year+"_8 & protect2 == 0 & "+prevyr+" <> 6 & "+prevyr+" > 4, 8, \ con(probs"+year+"_9 >= rnd"+year+"_9 & protect2 == 0 & "+prevyr+" > 4, 9, \ con(probs"+year+"_10 >= rnd"+year+"_10 & protect2 == 0 & "+prevyr+" > 4, 10, "+prevyr+")))))))))" ## print calcExp gp.SingleOutputMapAlgebra_sa(calcExp, OutLC) print "Done calc'ing new land cover: %s" % OutLC except: # If an error occurred print the messages. print gp.GetMessages()

land cover change model for central puget sound...

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