Mapping Settlements in the Wildland–Urban Interface: A

Decision Tree Approach

Rutherford V. PlattGettysburg College

The wildland–urban interface (WUI) is the area where human-built structures intermingle or abut wildlandvegetation. Maps of the WUI are important for resource management, particularly related to wildfire miti-gation, but are often based on spatially coarse data such as housing counts from census blocks. Here, threedecision tree models are used to create maps of human settlements for use in delineating the WUI. The firstmodel uses statistics derived from image objects; the second model uses data related to topography, amenities,and accessibility; and the third model uses all available data. The accuracy of the models was evaluated in termsof the percentage of actual structures that fall within the area delineated as settlements. Overall, the threedecision models performed similarly, although the third decision tree model was the best. For delineatingsettlements, all three decision tree models represent an improvement over a null model and the Radeloffet al. (2005) WUI mapping methodology and perform similar to the Wilmer and Aplet (2005) WUI mappingmethodology. The models are also more flexible than many existing models, as they allow users to trade offaccuracy and the size of the delineated settlement. The strategies described here can potentially yield improvedmaps of the WUI over larger areas. Key Words: dasymetric mapping, decision trees, object-oriented,wildland–urban interface.

La interfaz urbano-forestal (WUI) es el area en donde estructuras hechas por el hombre se entremezclan ocolindan con la vegetacion forestal. Los mapas de la WUI son importantes para el manejo de los recursos,particularmente en relacion con la mitigacion de los incendios forestales, pero a menudo se basan en datosde baja resolucion espacial como el recuento de viviendas por bloques censales. Aquı, tres modelos de arbolesde decisiones se utilizan para crear mapas de asentamientos humanos para su uso en la delimitacion de laWUI. El primer modelo utiliza las estadısticas derivadas de objetos de imagen, el segundo modelo utilizadatos relacionados a la topografıa, los servicios y la accesibilidad; y el tercer modelo utiliza todos los datosdisponibles. La precision de los modelos se evaluo en terminos del porcentaje de las existentes estructurasque califican dentro del area delimitada como asentamientos. En general, los tres modelos de decisionesfuncionaron similarmente, aunque el tercer modelo de arbol de decision fue el mejor. Para delimitar losasentamientos los tres modelos de arbol de decision representan una mejora sobre un modelo nulo y a lametodologıa cartografica WUI de Radeloff et al. (2005) y funcionan de manera similar a la metodologıacartografica WUI de Wilmer y Aplet (2005). Los modelos son tambien mas flexibles que muchos de losmodelos existentes, ya que permiten a los usuarios compensar la precision y el tamano del asentamiento

The Professional Geographer, 64(2) 2012, pages 262–275 C© Copyright 2012 by Association of American Geographers.Initial submission, January 2010; revised submission, June 2010; final acceptance, September 2010.

Published by Taylor & Francis Group, LLC.

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delimitado. Las estrategias descritas aquı pueden potencialmente producir mapas mejorados de la WUI enzonas mas extensas. Palabras claves: mapa dasimetrico, arboles de decision, orientacion a objetos,interfaz urbano-forestal.

T he wildland–urban interface (WUI), thearea where housing abuts or intermin-

gles with wildland vegetation, is associatedwith the vexing problems of structure lossdue to wildfire, habitat fragmentation, spreadof invasive species, and human–wildlife con-flict. An important challenge for resource man-agers is consistently and accurately mappingthe WUI. The definition of the WUI gen-erally has three components: a “community”(henceforth called settlement), wildland veg-etation, and a distance buffer representingthe area where the WUI extends beyond thesettlement (Stewart et al. 2007). Each compo-nent can be defined in a variety of ways de-pending on the purpose and assumptions ofthe study. The distance buffer, for example,has been defined as up to 2.4 km (1.5 miles)from a settlement (Healthy Forests Restora-tion Act 2003), 0.8 km (0.5 miles) from a set-tlement (Wilmer and Aplet 2005), or a variabledistance from a settlement depending on vege-tation height (Platt 2010). Wildland vegetationalso has myriad definitions, most based on veg-etation types in the National Land Cover Dataset (NLCD; Radeloff et al. 2005; Wilmer andAplet 2005; Hammer et al. 2007; Theobald andRomme 2007).

This article focuses entirely on improvingthe first aspect of the WUI definition: humansettlements in sparsely settled areas. Settle-ments include structures, roads, lawns, andother features. The areal extent of settlementsis typically derived either from distance tostructure locations or from socioeconomicdata. Structure locations can be estimatedfrom well location data available from the statedivisions of water resources (Aspinall 2004)or by digitizing structure location from high-resolution imagery. Unfortunately, structurelocation data sets are often incomplete, out ofdate, or prohibitively expensive to develop overlarge extents. For these reasons, many maps ofsettlements rely instead on socioeconomic data.For example, settlements can be mapped usingparcel data, which are consistently collected bycounty assessors, up to date, although not al-ways publicly available in geographic informa-tion system (GIS)-ready form. Housing countsfrom census data can also be used to map settle-

ments, but in sparsely populated areas censusblocks are very large and contain a large amountof undeveloped land. In these areas, estimatesof housing location or housing density areoften misleading—locally densely developed orundeveloped areas will effectively be “averagedaway” within a large census block. Shortof knowing the exact location of structures,one way to achieve improved areal estimatesof settlements is with techniques related todasymetric mapping.

Dasymetric mapping is the division of spaceinto zone boundaries that reflect the underly-ing statistical variation of a particular variable(Eicher and Brewer 2001). Typically, dasymet-ric mapping disaggregates coarse-resolutionquantitative data to a finer resolution usingancillary data sources (Mennis and Hultgren2006). An example illustrates the dasymetricmapping process at its simplest: Imagine a mapof housing density based on census tract hous-ing counts. The housing density estimates arepoor because there are areas within the cen-sus blocks (e.g., ponds and parks) where housescannot exist. The underlying statistical varia-tion of housing density would be better rep-resented if the ponds and parks had a housingdensity of zero and the remaining zones hada higher density. Dasymetric techniques typi-cally use remote sensing data or other publiclyavailable data sets (e.g., road data, land coverdata, cadastral data) to derive weights or rulesfor distributing the population within zones(Cockings, Fisher, and Langford 1997; Eicherand Brewer 2001; Chen et al. 2004; Reibeland Bufalino 2005; Maantay, Maroko, andHerrmann 2007). The weights or rules aretypically derived from “expert knowledge” orassumptions about the distribution of the vari-able of interest, although they can also be de-rived from empirical sampling (Mennis 2003;Mennis and Hultgren 2006).

Strategies for mapping the WUI eitheremploy very simple dasymetric mapping ornone at all to delineate settlements. The mostspatially extensive attempt to date to delineatethe WUI, the WUI assessment (Radeloffet al. 2005), maps the intermix WUI (wherestructures mix with wildland vegetation) andinterface WUI (where structures abut wildland

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vegetation) across the coterminous UnitedStates using an overlay of block data fromthe 2000 Census and vegetation data fromthe NLCD. Using this method, settlementsare defined as the 2000 Census blocks witha housing density of one structure per 16.2hectares (40 acres) or more. The Radeloff et al.study did not employ dasymetric mapping,as it did not attempt to alter or refine censusblock boundaries. In contrast, Wilmer andAplet (2005) and Theobald and Romme (2007)used a similar technique but employed simpledasymetric mapping—the removal of publicland before calculating housing density.

Techniques related to dasymetric mappingtechniques could potentially be used to delin-eate settlements for mapping the WUI. For ex-ample, remotely sensed imagery could be usedto find areas where structures are likely to exist(e.g., bright or spectrally heterogeneous areas).Alternatively, other ancillary data sources couldbe used to identify areas likely to contain struc-tures. Past research has indicated that certainfactors (e.g., distance to employment oppor-tunities, zoning) shape population patterns inboth urban and rural areas. Research has alsoindicated that amenities such as ski resorts (Du-ane 1999), public lands (Riebsame, Gosnell,and Theobald 1996), and space and seclusion(Davis, Nelson, and Dueker 1994) provide ahigh quality of life that might override eco-nomic considerations of where to live (Rudzitisand Streatfield 1993; Rudzitis 1999). In addi-tion, scenic natural resources such as forests,riparian areas, and lakeshores draw low-densitydevelopment and are also ecologically valuable(Ball 1997; Myers et al. 2000; Hansen et al.2002). Population growth in rural counties ofthe northern Rockies is associated with areas ofmountainous topography, forest cover, precipi-tation, and conserved land (Rasker and Hansen2000). Because population is tightly coupledwith housing, it makes sense that factors re-lated to topography, accessibility, and amenitiesdrive and constrain the location of settlements.At the time of publication of this article, how-ever, such variables had rarely if ever been usedto refine maps of settlements within counties.

In this article, three maps of settlementswere developed for the mountainous westernhalf of Boulder County, Colorado. The mapswere created using models calibrated with de-cision trees, a strategy for partitioning datainto homogenous groups based on the explana-

tory variables that best distinguish the variationof the independent variable (Breiman et al.,1984). The maps use techniques similar todasymetric mapping but for simplicity presenta nominal variable (settlement vs. nonsettle-ment) rather than a continuous variable (e.g.,housing density). The first decision tree model(DT-Objects) was calibrated with remotelysensed imagery. In this model, object statisticsderived from 1-m digital ortho quarter quads(DOQQs) were used to delineate settlements.The second model (DT-Characteristics) wascalibrated with variables related to topography,accessibility, and amenities at a resolution of30 m. The third model (DT-All) was calibratedwith both remotely sensed data and data relatedto topography, accessibility, and amenities. Theproject has the following goals: (1) comparethe three decision tree models, a null model,and two existing WUI models in terms of theirability to delineate settlements; and (2) evaluatethe relationship between location of structuresand variables related to object statistics, ameni-ties, accessibility, and topography. The deci-sion tree approach represents a robust strategyfor developing WUI maps and produces logi-cal rules that could potentially be extended toother areas.

Methods

Study AreaThe study area for this project is the privateland within the mountainous areas of Boul-der County, Colorado (Figure 1). This studyarea was chosen for several reasons. First, it isdata rich; in particular, digitized locations ofstructures are available to calibrate and validatethe models. Second, the mountainous areas ofBoulder County are a quintessential WUI envi-ronment containing widespread exurban devel-opment and several small former mining towns,including Nederland, Ward, and Jamestown.The public land surrounding these areas is pri-marily managed by the U.S. Department ofAgriculture (USDA) Forest Service, the Bu-reau of Land Management (BLM), the Na-tional Parks Service (NPS), and the BoulderCounty and City Open Space and MountainParks. Because virtually all structures in thestudy area abut or intermingle with wildlandvegetation, this study is able to focus on the“human settlement” component of the WUI.

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Mapping Settlements in the Wildland–Urban Interface 265

Figure 1 Study area of the mountainous area in Boulder County, Colorado. (Color figure available online.)

Decision TreesDecision trees were used to delineate settle-ments within the study area. Decision trees area set of nonparametric techniques that derivea series of rules to classify cases into discretegroups. A common statistical classifier, logis-tic regression, fits a logistic curve to describethe relationship between an independent vari-able and the probability of class membership. Incontrast, decision trees do not assume a mono-tonic relationship between independent anddependent variables. They are able to modelcomplex nonlinear relationships and interac-tions between independent variables. Studiessuggest that decision trees might yield bet-ter classification accuracy than traditional sta-tistical classifiers such as maximum likelihood(Friedl and Brodley 1997) and result in a sub-stantial reduction in data dimensionality (Borakand Strahler 1999).

This study used a particular tree growingmethod called classification and regression trees(CRT; Breiman et al. 1984). CRT finds thresh-olds of the independent variables that split datainto groups that are as “pure” (homogeneous)as possible in terms of the dependent variable.The splits are based on the Gini method, whichcalculates impurity based on the squared prob-abilities of the cases belonging to a dependentvariable category. The tree continues to growuntil either (1) the tree grows to a maximum offive levels, a commonly used cutoff to maintainmodel parsimony, or (2) splitting the data re-sults in an improvement in impurity (squaredprobability of an area containing a structure)

of less than 0.0001. This fully grown tree hasthe smallest possible “risk” (the proportion ofmisclassified cases adjusted for prior probabili-ties and any defined misclassification costs). Toavoid overfitting, the trees are then pruned byremoving nodes (rules) to create the smallesttree that does not increase risk by more thanone standard error. Generally, pruning resultsin a vastly simplified set of classification rules,with a minimal increase in risk.

To calibrate and validate the decision treemodels, a supervised classification strategy wasused. A data set of 13,908 points was compiledwhere points represent (1) the actual locationof the 6,954 structures and (2) a random sampleof 6,954 points. The random sample representsall private land beyond 200 m from a structure.The actual locations of structures were digi-tized by Boulder County Land Use in 2003,using DOQQs and on-the-ground GlobalPositioning System readings. The pointsrepresent the estimated center of the buildingfootprint. Because areas with a density lowerthan one structure per 16.2 ha are commonlyconsidered outside a community (U.S. Depart-ment of Agriculture and U.S. Department ofthe Interior 2001; Radeloff et al. 2005; Wilmerand Aplet 2005), and thus not part of theWUI, structures that were more than 576 mfrom another structure were removed. Underthis definition, two or more adjacent 16.2-ha2

parcels with structures at the center wouldcount as a community, but a more dispersedset of structures would not. The decision treeswere used to distinguish the “structure” points

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from the “nonstructure” points, after whichthe models were applied to the landscape asa whole to delineate settlements. A randomlyselected 80 percent of the points were includedin the calibration procedure, and the remaining20 percent were reserved for validation.

DT-ObjectsThe first decision tree model was calibratedwith object statistics derived from 1-mblack-and-white 1999 U.S. Geological Survey(USGS) DOQQs. USGS DOQQs were usedbecause they are the same images used todigitize individual structures, are available freeof charge for large areas, and require less com-putational power to process than multispectraldata of comparable resolution. DefiniensProfessional 5.0 (Definiens AG, Munich,Germany) was used to segment the image intoobjects and calculate object statistics, a strategyknown as object-oriented image analysis (OBIA).OBIA is the segmentation and classificationof homogeneous image polygons, or objects,rather than individual pixels. Whereas tradi-tional classification typically relies exclusivelyon spectral and textural data, OBIA also utilizesspatial relationships between objects, shapecharacteristics of objects, and a wide variety ofstatistics related to spectral and textural charac-teristics of objects. Studies have suggested thatOBIA techniques are better (or at minimumno worse) than traditional pixel classifica-tion methods (Willhauck 2000; Civco et al.

2002; Oruc, Marangoz, and Buyuksalih 2004;Whiteside and Ahmad 2005; Platt and Rapoza2008). Decision tree models are likely to beeffective in sorting through and identifying thespectral, spatial, textural, and contextual objectstatistics for image classification (Laliberte,Fredrickson, and Rango 2007).

Within the framework of Definiens Pro-fessional 5.0, the object segmentation processis based on a number of parameters relatedto scale, color, shape, smoothness, and com-pactness (Definiens Professional 5.0 User Guide2006). The scale parameter is a unitless num-ber that controls the size of image objects.The color and shape parameters dictate therelative influence of spectral information andshape in creating object boundaries. The shapeparameter is defined by the smoothness andcompactness parameters. Compactness is cal-culated as the ratio of the border length andthe square root of the number of object pix-els. Smoothness is calculated as the ratio of theborder length and the shortest possible borderlength derived from the bounding box of animage object. Because there is no optimum setof parameters, a standard practice is to selectparameters through trial and error. The fol-lowing parameters were iteratively selected toderive objects: scale, 50; color, 0.7; shape, 0.3;smoothness, 0.5; compactness, 0.5. These pa-rameters yielded objects that captured individ-ual structures and surrounding infrastructure(Figure 2).

Figure 2 Detail of image segmentation before (left) and after (right).

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Table 1 Variables derived from image objects

Spectral characteristics Shape Texture

Max pixel value Length GLCM contrastMean difference to scene Area including inner polygons GLCM std devStd dev Area GLCM meanMinimum pixel value Area excluding inner polygons GLCM homogeneityMean of outer border Perimeter GLCM entropy

Number of edges GLCM correlationBorder lengthWidthShape indexCompactness (polygon)Border indexCompactness (generic)RoundnessLength of longest edgeElliptic fitRectangular fitAverage length of edgesAsymmetryDensityLength/widthStd dev of length of edgesNumber of inner objectsMain direction

Note: Haralick’s gray-level cooccurrence matrix (GLCM) describes how different combinations of pixel values occurwithin an object (Haralick, Shanmugam, and Dinstein 1973).

The segmentation procedure produced ob-jects of variable size (M = 747 m2, SD = 683m2). Within the objects, a total of thirty-five ob-ject statistics were calculated, each related to aspectral characteristic, texture, or shape of theobjects (Table 1; see Definiens Professional 5.0User Guide 2006 for further details). The objectstatistics were then assigned to the points thatfell inside (6,954 representing structures and6,954 representing nonstructures). The cali-bration points were then used to calibrate thedecision tree model to develop rules for dis-tinguishing the structure points from the non-structure points.

DT-CharacteristicsThe second decision tree model was calibratedon site characteristics related to topography(slope, topographic position, solar radiation),amenities (percentage canopy cover, distancefrom stream, distance to trailhead, distance topublic lands), and accessibility (distance to road,distance to city; Table 2). Rasters representingthese variables were derived from commonlyavailable data sets from the USGS, USDA For-est Service, and Boulder County Land Use. All

rasters have a spatial resolution of 30 m. It washypothesized that houses would most likely bebuilt in areas of low slope, close to the city, inareas that receive lots of sunlight, in valleys, inopen canopy areas, on south-facing slopes, onareas close to roads and trails, and near streams(Table 2). As with the object statistics, thesite characteristics were assigned to the points(6,954 representing structures and 6,954 rep-resenting nonstructures). As with DT-Objects,the calibration points were then used to cali-brate the decision tree.

DT-AllThe third decision tree model was calibratedon the same validation points, using the datafrom both DT-Objects (object statistics) andDT-Characteristics (topography, accessibility,and amenities).

Delineation of Settlements from DecisionTree RulesDecision trees are made up of a series ofrules, each associated with the proportion ofobservations that belong to a particular class.

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Table 2 Topography, accessibility, and amenities variables

Name Description Source data

Slope Slope (degrees) USGS 30 m DEMDist2city Distance to Boulder by roads USDA Forest Service road dataRadiation Total annual solar radiation received by site USGS 30 m DEMTPI Topographic position index∗ (Jenness 2006) USGS 30 m DEMCancover Canopy cover (%) LANDFIREPublanddist Euclidean distance to public land (m) Boulder County public lands dataRoaddist Euclidean distance to closest road (m) USDA Forest Service road dataDisttrail Distance to trailheads along roads USDA Forest Service and Boulder County Open

Space Trail dataStreamdist Euclidean distance to stream (m) USGS streams

Note: Topographic position index (TPI) is calculated as the difference between a cell and the neighborhood of the cell.If TPI is positive, it is higher than the surrounding neighborhood (for large neighborhoods, interpreted as a ridge or hill);if it is negative it is lower than the surrounding neighborhood (for large neighborhoods, interpreted as a valley). TPI isstrongly scale dependent; in this case a 1,000-m circular neighborhood is used. USGS = U.S. Geological Survey; USDA= U.S. Department of Agriculture; DEM = digital elevation model.

For example, a single decision tree rule mightstate that of points that are more than 90 mfrom roads and more than 15 m from publicland, 84 percent represent nonstructures and16 percent represent structures. In this exam-ple, all cells more than 90 m from roads andmore than 15 m from public land would beclassified as nonstructures because the 84 per-cent proportion is above the 50 percent cutpoint (the proportions are used as a proxyfor probability). The 50 percent cut point isarbitrary and in fact does not represent theactual proportion of cells containing a struc-ture; whereas 50 percent of the calibrationpoints represent structures, only a small per-centage of cells in the landscape actually containstructures. By design, the delineated settlementwas overpredicted to minimize errors ofomission.

All maps were produced using 30-m gridcells. The input data for DT-Characteristicsis already represented in 30-m grid cells, butthe objects used as input to DT-Objects are ofvariable size and based on 1-m orthophotos. Tomake the maps comparable, the image objectswere converted to a 30-m grid, using the cen-ter point rule in cases where multiple objectsintersect a grid cell.

Model Comparison and EvaluationAfter delineating the settlements, the modelswere compared using three techniques: (1) a vi-sual comparison, (2) classification matrices, and(3) a graph of the percentage of structures that

fall within settlements (high is better) versusthe percentage of study area classified as set-tlements (low is better). This graph allows themodels to be compared at every possible cutpoint, not just 50 percent. For reference, themodels are compared to a null model, wherethe percentage of land in settlements is equal tothe correctly classified structures. The modelsare also compared to the settlements defined bytwo existing WUI mapping strategies: Radeloffet al. (2005) and Wilmer and Aplet (2005).

Results

DT-ObjectsVariables with the most explanatory power ap-pear earlier in the tree and more frequently(Lagacherie and Holmes 1997). The most im-portant variable for the DT-Objects tree ismaxpixel (Figure 3): A point has a higher prob-ability of representing a structure when themaxpixel value is high. Farther down the tree,variables related to object texture appear fre-quently. When gray-level cooccurence matrix(GLCM) contrast, GLCM stddev, and GLCMentropy are high, this indicates that the pixelvalues within the object are heterogeneous. Itmakes intuitive sense that structure points tendto be located in objects that are heterogeneouswith some bright pixels, as structures have a va-riety of building materials, some of which (e.g.,cement, bare ground) are highly reflective andsome of which (e.g., asphalt, most shingles) aredark. Variables related to shape (e.g., length)

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Figure 3 Decision tree for DT-Objects. Each node (shown as a rectangle) includes a variable andthreshold value. Values greater than the threshold are split to the right, whereas values less than or equalto the threshold are split to the left. Terminal nodes (shown as ovals) include the probability that a pointrepresents a structure.

are also important but appear less frequentlythan texture. For example, points in objectswith high maxpixel value that also have lowlength (e.g., are compact) are likely to repre-sent structures.

DT-CharacteristicsThe second decision tree model, DT-Characteristics, shows that only a few variablesare important for distinguishing the classes. Atthe top of the tree, roaddist is the most impor-tant variable (Figure 4). Farther down the tree,slope and publanddist are also important.

The rules can be interpreted as follows:Structures tend to be within 92 m of the roadnetwork. Structures also tend to be located inareas directly adjacent to public land. Indeed,many of the few structures located far fromroads are within 15 m of public land. Struc-tures tend to be located on land with less than16 degrees slope in places farther than 36 mfrom a road.

DT-AllThe third decision tree model is calibrated withboth of the aforementioned data sets. As in

DT-Objects, maxpixel appears at the top of thetree (Figure 5). Roaddist appears on the secondlevel. On the third level, object statistics suchas GLCM contrast, length, and perimeter areimportant. On the lowest levels, topographicposition index (TPI), publanddist, and GLCMstddev help distinguish structures from non-structures.

Model Comparison and ValidationTo compare the models, maps were developedusing the 50 percent cut point and visually com-pared (only a subset shown here; Figure 6).The map confirms that the models are success-ful in identifying the areas that contain struc-tures but also illustrate some error (e.g., ac-tual structures located outside of the delineatedsettlement).

The models were then compared and vali-dated using classification matrices constructedwith the 20 percent of the observations re-moved from the calibration procedure. Again,the 50 percent cut point was used. For DT-Objects, it was found that 71.9 percent of thepoints representing structures were correctlyidentified and that 71.1 percent of the points

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Figure 4 Decision tree for DT-Characteristics. Each node (shown asa rectangle) includes a variable and thresh-old value. Values greater than the thresholdare split to the right, whereas values lessthan or equal to the threshold are splitto the left. Terminal nodes (shown asovals) include the probability that a pointrepresents a structure.

representing not containing structures werecorrectly identified (Table 3).

For the DT-Characteristics model, it wasfound that 80.6 percent of the points repre-senting structures were correctly identified andthat 60.4 percent of the points not representingstructures were correctly identified (Table 4).Compared to DT-Object, DT-Characteristics

did a better job identifying points that representstructures but also predicted that many pointsare likely to represent structures when in factthey do not.

The DT-All model was found to be thebest of the three but only marginally (Ta-ble 5). It was found that 80.8 percent of thepoints representing structures were correctly

Figure 5 Decision tree for DT-All. Each node (shown as a rectangle) includes a variable and thresholdvalue. Values greater than the threshold are split to the right, whereas values less than or equal tothe threshold are split to the left. Terminal nodes (shown as ovals) include the probability that a pointrepresents a structure.

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Figure 6 Detail of settlement map. DT = decision tree. (Color figure available online.)

identified and that 70 percent of the pointsnot representing structures were correctlyidentified.

The three models were then compared andvalidated using a variation on a receiver operat-ing characteristic (ROC) curve (Figure 7). Likea traditional ROC curve, the y axis shows theaccuracy—also called true positive or 1-error ofomission. In this study, it can be interpreted as

the percentage of nonremote structure points(i.e., within 576 m of another point) that fallwithin cells classified as settlements. The x axisshows the percentage of all cells classified assettlements. This can be interpreted similarlyto the false positive rate or 1-error of commission,as only a small (but unknown) percentage of theland area includes structures and surroundinginfrastructure.

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Figure 7 Receiver operating characteristic (ROC) curve showing the trade-off between “true positive”rate (i.e., the percentage of nonremote structure points within settlements) and the percentage of thestudy area classified as settlements. DT = decision tree. (Color figure available online.)

The greater the area under the curve in Fig-ure 7, the better the model. For reference, thecurve of a hypothetical model with no pre-dictive power (null model) would fall alongthe diagonal line (Figure 7); the percentage ofcells classified as settlements is equal to thepercentage of structures that fall within thesettlements area. Also, for reference, two ex-

Table 3 Classification matrix for DT-Objects

Predicted

ObservedNot a

structure Structure%

correct

Not a structure 948 385 71.1Structure 385 985 71.9Overall percentage 49.3% 50.7% 71.%

isting WUI mapping strategies (Radeloff et al.2005; Wilmer and Aplet 2005) have been placedon the graph as single points.

The curves of the three models are visuallysimilar to each other and lie above the diag-onal line (null model). Starting in the upperright-hand corner of Figure 7, it is clear that

Table 4 Classification matrix forDT-Characteristics

Predicted

ObservedNot a

structure Structure%

correct

Not a structure 839 551 60.4Structure 196 1,206 86.0Overall percentage 37.1% 62.9% 73.2

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Table 5 Classification matrix for DT-All

Predicted

ObservedNot a

structure Structure%

correct

Not a structure 989 423 70.0Structure 273 1,146 80.8Overall percentage 44.6% 55.4% 75.4

if 100 percent of the study area is a commu-nity, then 100 percent of the structures willbe within a the community. By applying anyof the three decision tree models, settlementscan be shrunk to 75 percent of the study areawhile retaining ∼95 percent of the structures.The Wilmer and Aplet (2005) model performssimilarly. A null model with no predic-tive power, by contrast, would retain only75 percent of the structures. Continuing downthe curve, DT-All and DT-Characteristics al-low us to shrink the settlements to 50 percentof the study area while retaining ∼90 percentof the structures, whereas DT-Objects retainsonly ∼82 percent of the structures. The Rade-loff et al. (2005) model retains 70 percent ofthe structures at 50 percent of the study areaand so is less accurate by this standard thanthe three decision tree models. At the bot-tom of the curve, DT-All allows us to shrinkthe settlements to 20 percent of the study areawhile retaining ∼75 percent of the structures,whereas DT-Objects and DT-Characteristicsretain only ∼62 percent of the structures. Theresults show that overall DT-All is the most ac-curate model, although the advantage dependson the particular cut point.

Discussion and Conclusions

In western Boulder County, Colorado, the lo-cation of structures is related to characteris-tics such as distance to road, distance to publicland, and slope, as well as to spectral charac-teristics (e.g., maxpixel), texture (e.g., GLCMcontrast), and shape (e.g., length). These in-dependent variables were successfully used toconstruct maps of settlements in the WUI, sim-ilar in nature to dasymetric maps. The “best” ofthe three decision tree models depends on thespecific application. For small refinements ofthe estimate of structure location, the perfor-mance of the three decision tree models is simi-

lar; all three models can reduce the settlementsto 75 percent of the study area while retain-ing ∼95 percent of the structures. In this case,the DT-Characteristics model might be “best”because acquiring and processing the data forthis model is straightforward. For larger refine-ments, however, the DT-All model performsbetter than the others (higher accuracy at agiven size of delineated settlements). Unfor-tunately, calculating object-level statistics re-quires time, computational power, and expen-sive software.

The modeling strategies described in thisstudy represent a potential step forward in con-sistently mapping the WUI. In the study area,the strategies more accurately delineate settle-ments than the Radeloff et al. (2005) method,although they are not as conceptually simpleor as easily extended to large areas. The strate-gies are more flexible (if not better) than theWilmer and Aplet (2005) method because theyallow users to trade off accuracy and size of thedelineated settlement.

To apply the decision tree models to largerareas, it would be important to first evaluatethe relationships and rules to see if they ex-tend to other places. Many of the relationshipsand rules might indeed apply broadly to otherplaces, especially in the Rocky Mountain Re-gion. It is expected that across the country, mostsettlements would be spectrally heterogeneouswith some highly reflective elements. Further-more, it is expected that settlements would beclose to roads and on relatively low slopes. Ifthe relationships hold, the decision tree rulescould be used in conjunction with census blockhousing counts to create improved maps ofhousing density, which could be overlaid onlayers of wildland vegetation to create a fullWUI map. Some regional differences willdoubtless emerge, however, that could com-plicate general applicability. For example, thestudy area is amenity-rich and has exten-sive public land that constrains development.The relationship between public land and lo-cation of settlements could be very differ-ent in a nonmountainous environment, in anarea with less extensive public lands, or inan area with different zoning practices fromthe study area. Exploring the regional differ-ences would be a rich area of study. Shouldmajor regional differences in these relation-ships exist, it would be important to extend

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the method presented here to allow “rules” tovary spatially. Even if large-scale applicabilityshould ultimately prove difficult, the processof creating the decision tree models is itselfvaluable, as it helps reveal the characteristics(topographic, accessibility related, amenity re-lated, and spectral) that are associated with set-tlements. �

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