Modeling the relationships between land use and land cover ...ltm.agriculture.purdue.edu/docs/brown0369.pdf · use and land cover for modeling landscape change. Attempts to model

Journal of Environmental Management (2000) 59, 000–000doi:10.1006/jema.2000.0369, available online at http://www.idealibrary.com on

Modeling the relationships between landuse and land cover on private lands inthe Upper Midwest, USA

D. G. Brown†*, B. C. Pijanowski‡ and J. D. Duh†

This paper presents an approach to modeling land-cover change as a function of land-use change. We arguethat, in order to model the link between socio-economic change and changes in forest cover in a region thatis experiencing residential and recreational development and agricultural abandonment, land-use and land-cover change need to be represented as separate processes. Forest-cover change is represented here usingtwo transition probabilities that were calculated from Landsat imagery and that, taken together, describe aMarkov transition matrix between forest and not-forest over a ten-year period. Using a three-date land-usedata set, compiled and interpreted from digitized parcel boundaries, and scanned aerial photography for136 sites (c. 2500 ha) sampled from the Upper Midwest, USA, we test functional relationships between forest-cover transition probabilities, standardized to represent changes over a decade, and land-use conditionsand changes within sample sites. Regression models indicated that about 60 percent of the variation in theaverage forest-cover transition probabilities (i.e. from forest to not-forest and vice versa) can be predictedusing three variables: amount of agricultural land use in a site; amount of developed land use; and the amountof area increasing in development. In further analysis, time lags were evaluated, showing that agriculturalabandonment had a relatively strong time-lag effect but development did not. We demonstrate an approachto using forest-cover transition probabilities to develop spatially-constrained simulations of forest-coverchange. Because the simulations are based on transition probabilities that are indexed to a particulartime and place, the simulations are improved over previous applications of Markov transition models. Thismodeling approach can be used to predict forest-cover changes as a result of socio-economic change, bylinking to models that predict land-use change on the basis of exogenous human-induced drivers. 2000 Academic Press

Keywords: remote sensing, Markov models, land-use change, forest fragmentation.

Introduction

Models of land-use and land-cover changeare powerful tools that can be used tounderstand and analyze the important link-age between socio-economic processes asso-ciated with land development, agriculturalactivities, and natural resource managementstrategies and the ways that these changesaffect the structure and function of ecosys-tems (Turner and Meyer, 1991). We defineland use as human activity on the land(in sensu Turner et al., 1995). Land use isinfluenced by economic, cultural, political,historical, and land-tenure factors at mul-tiple scales. Land cover, on the other hand,is one of the many biophysical attributes of

ŁCorresponding author

† School of NaturalResources andEnvironment, University ofMichigan, Ann Arbor, MI48109-1115, USA

‡ College of NaturalScience, Michigan StateUniversity, East Lansing,MI 48824, USA

Received XX Month XXXX;accepted XX Month 2000

the land that affect how ecosystems function(in sensu Turner et al., 1995). In frontierregions with economies based primarily onextractive industries (e.g. developing coun-tries), land use and land cover are oftensemantically equivalent. For example, theland-use activity associated with loggingleads to a deforested land cover (Lambin,1997). Therefore, satellite images can oftenbe used to detect land-use change throughobservations of the biophysical characteris-tics of the land. However, in a post-modernand information-driven economy, like most ofthe contemporary United States and Europe,land use and land cover are less likely to beequivalent. Although forestry can be mod-eled as a land-use activity that respondsto economic, social, and demographic drivers

0301–4797/00/000000C00 $35.00/0 2000 Academic Press

2 D. G. Brown et al.

(e.g. Alig, 1986; Mauldin et al., 1999), suchdrivers do not provide direct predictors forunderstanding and modeling the amount andlocations of forests and tree-cover in all partsof a landscape. Changes in the amount ofcarbon sequestered in forests and their soils,for example, is ambiguously related to dis-persed rural residential development in adominantly agricultural landscape. Develop-ment of second homes in a forested regionmay involve little clearing of trees on largelyforested or reforesting lots, and agriculturalabandonment or conversion into residentialuses often leads to regrowth of forests (Staa-land et al., 1998; Foster and Gross, 1999).

This paper addresses the implications ofthe fundamental differences between landuse and land cover for modeling landscapechange. Attempts to model land-cover (e.g.forest-cover) change at the landscape scale asa direct function of socio-economic change(viz., Lambin, 1997), are problematic indeveloped economies. Existing models rarelyinclude the effects of land-use change onland cover explicitly. Predictive models oflandscape change in a human-inhabited land-scape must describe the social processes thataffect land use (e.g. development, agricul-tural production, tourism and recreation).Because land-use change occurs parcel-by-parcel, where the parcel is the basic unitof land ownership, information should becollected, and processes modeled, with theparcel as the basic unit. To characterize thebiophysical implications of land-use change,e.g. on biodiversity, water quality, and car-bon sequestration, the relationships betweenland use and land cover must also be quan-tified. Land-cover change is not restricted toparcel boundaries and sub-parcel represen-tation of land cover is preferable. Becauseland use and land cover are related butnot equivalent, models of landscape changeshould include this missing link. Addition-ally, by coupling land-use and land-coverchange models, such a link may provide mod-elers of land-use change with a means to useremote sensing data to help validate land-usechange models.

We start by describing an approach to mod-eling the relationship between land-use andland-cover change as distinct, but linked,processes. We then present an empirical anal-ysis of the linkage between rural residentialdevelopment, agricultural abandonment, and

changes in forest cover on private lands in theUpper Midwest USA, from the early 1970s tothe early 1990s. The specific objectives of thispaper are to:

ž present a framework for modeling thatrepresents land use and land cover sepa-rately and that characterizes the link usingMarkov transition probabilities;ž describe an approach to calculating Markov

transition probabilities from multitemporalclassified satellite imagery, when suchimagery contains some degree of classifi-cation and positional uncertainty;ž develop functional relationships between

land-cover transition probabilities andland-use change at the landscape scale;andž present a simple illustration of the appro-

ach described for the spatial simulation offorest-cover change.

Land-use and land-coverchange modeling

Models of land-use and land-cover changehave been developed to address when, whereand why land-use and land-cover changeoccurs (for good summaries of these modelssee Baker, 1989; Riebsame et al., 1994;Lambin, 1997; Theobald and Hobbs, 1998).They usually involve empirically fitting themodels to some historical pattern of change,then extending those patterns into the futurefor prediction. Because our ultimate goal isto understand the processes driving changesin the amount and distribution of forest inthe Upper Midwest, and because the amountand distribution of forest in the UpperMidwest is largely socially and economicallydetermined through the determination ofland use, we require an approach that linksthe drivers of land-use change, the associatedchanges in land ownership and use, and theresulting changes in forest cover (Figure 1).We treat land-use change as a separateprocess from land-cover (i.e. forest-cover)change. The general structure shown here,i.e. using regional and global scale driversto determine the amount of change, andgeographic and landscape scale drivers todetermine its pattern, is similar to that takenin the Conversion of Land Use and its Effects(CLUE) model of land-cover change in the

Modeling land use and land cover 3

Drivers of land-use change

Global and regional scale

Geographic landscapescale

amount

pattern

Parcel land-usechange

Forest-coverpattern and change

Figure 1. The general modeling framework used in this project. This paper focuses on the link betweenland use and forest-cover change.

tropical frontier (de Koning et al., 1999)and the Land Transformation Model (LTM)which has been used in the Upper Midwest,USA (Pijanowski et al., 2000). In this sectionwe present background information on theforest-cover modeling approach employed.

Transition probabilities have been usedextensively for analysis and modeling ofland-use and land-cover change (Burnham,1973; Bell, 1974; Turner, 1987; Muller andMiddleton, 1994). The approach treats statetransitions as Markovian random processesthat are conditional on the initial state only.Transition models can be expressed in matrixform as:

ntC1DPnt .1/

where nt is a vector of land-area fractionsin each of m cover or use types at time t,ntC1 is the vector of land-area fractions forthe same types at tC1, and P is an mðmmatrix which expresses the probability thata site in state i at time t will transitionto state j at time tC1. The matrix P isrow-standardized, such that the sum oftransition probabilities from a given stateis always equal to one. The value of theapproach is that the transition matrix, oncespecified, can be used analytically to projectfuture landscape compositions (Jahan, 1986;Guttorp, 1995) or in simulation modelingto develop alternative landscape scenarios(Burnham, 1973; Turner, 1987). Any set ofstates (e.g. land-use or land-cover classes)can be used, provided their definitions do notchange over time, at any scale of analysis. Thechange matrix is often derived from multipletemporal classifications of land use or landcover (Bell, 1974; Turner, 1987).

The primary limitations of Markov-basedtransition probability-based models for land-use and land-cover change analyses are:(1) the assumption of stationarity in thetransition matrix, i.e. that it is constantin both time and space; (2) the assump-tion of spatial independence of transitions;and (3) the difficulty of ascribing causalitywithin the model, i.e. the transition prob-abilities are often derived empirically frommulti-temporal maps with no description ofthe process (Baker, 1989). This third limi-tation is particularly acute when land-coverchanges are under investigation, for exam-ple from remotely sensed imagery, and whenthose changes are driven by social and eco-nomic processes (Turner, 1987). To addressboth limitations 1 and 3 above, Baker (1989)suggested setting state transition probabili-ties as a function of exogenous or endogenousvariables, which vary in space and time.Equation (1) then becomes

nt�1DP[f .t, x/]nt .2/

and

pijDf .t, x/Db1X1Cb2X2CÐ Ð ÐCbsXs .3/

where pij are the elements in the matrix oftransition probabilities P, and the param-eters (e.g. bs) describe the functional rela-tionship between some set of predictor vari-ables (e.g. Xs), which can vary in both time(t) and space (x), and pij. Turner (1987)demonstrated an approach to conditioningthe changes to initial states in adjacentsites, in addition to conditioning changes onthe initial state, thereby introducing spatialdependence into the simulation (the secondlimitation).


Whereas Markov transition probabilitiesprovide a convenient analytical frameworkfor simulating land-cover change using obser-ved transitions, e.g. from remote sensing,alternative approaches are typically usedfor modeling the influence of social andeconomic drivers on land-use change. Thealternative model structures are designed tointroduce a better representation of causa-tion into the models, by relating change toeither exogenous driving variables, spatialinteraction processes, or both. Theobald andHobbs (1998) summarized two primary typesof causal land-use change models: regression-type models and spatial transition-basedmodels. The former type establishes func-tional relationships between a set of spatialpredictor variables that are used to pre-dict the locations of change on the land-scape. These include logistic regression mod-els (Landis, 1994), hedonic price models (Alig,1986; Geoghegan et al., 1997), and artificialneural networks (Pijanowski et al., 2000).The latter type of models is exemplified by

a spatial-temporal extension of the Markovtransition models referred to as cellularautomata (Deadman et al., 1993; Clarkeet al., 1997). Both types of models can beused to include geographic site and situa-tion variables in modeling change. Becausewe view land-use change as the proximatecause of forest-cover change and the resultof change in exogenous driving variables, theapproach we present here bridges land-usechange models based on functional relation-ships with human-induced exogenous driv-ing variables and the transition probabilityapproach to modeling land-cover change.

Study area and data

Our study was conducted over the UpperMidwest, USA, which includes northern por-tions of Michigan, Minnesota, and Wisconsin(Figure 2). Secondary forests, having regen-erated following nearly complete harvest ofpre-European forests in the late 19th and

Minnesota

Wisconsin

Michigan100 0 100 200 km

Towns > 20 000Sample sitesSample countiesMajor roads

N

Figure 2. The study region, showing locations of sample counties and sample sites.


early 20th centuries (Williams, 1989), coverlarge portions of the region. Three majorland-use trends are evident in the region.First, like many forested areas in the USand throughout the temperate mid-latitudes,forest-cover is increasing (Houghton et al.,1999). Forest cover increased in the region by3% between 1980 and 1993 (Schmidt, 1997;Miles and Chen, 1992; Leatherberry andSpencer, 1996). Second, the amount of farm-land in the region declined by 5% between1987 and 1997 (Census of Agriculture, 1997).Third, ownership became increasingly frag-mented into more and smaller parcels. Dur-ing the 30 years between 1960 and 1990,average private parcel sizes declined by anaverage of 1Ð2 percent per year across theregion (Brown and Vasievich, 1996).

These land-use changes are related tobroader demographic shifts occurring in ruralareas throughout the United States, includ-ing the Upper Midwest. During the 1970s,the observed growth rate in the population ofnon-metropolitan areas exceeded the growthrate of metropolitan areas for virtually thefirst time in the 20th century. Widespreadmigration out of rural areas followed inthe 1980s, due to a significant decline inthe farm economy and loss of employmentopportunities. Rural areas again saw signif-icant immigration in the 1990s, because ofa rebound in rural employment, a recessionin the early 1990s that affected urban areasmore than rural areas, and increasing inte-gration with the national and internationaleconomies through improved transportationand communications infrastructure (John-son, 1998; Johnson and Beale, 1998).

Area-frame sampling

A stratified sampling scheme, based on ademographic/economic classification of coun-ties and on locational differences withincounties relative to urban areas, lakes, majorroads and public lands, was used to selectrepresentative sample area frames. The sam-pling approach is summarized here, anddescribed in more detail by Brown andVasievich (1996). We classified county typesusing a cluster analysis based on variablesderived from a principal-components anal-ysis of county-level census and economicdata between 1960 and 1990. All counties

in the region were classified into one offour demographic/economic types, accordingto the dominant controls and patterns ofdemographic change. We selected three to sixcounties within each demographic/economictype, making a total of 17. The coun-ties selected from Michigan were Baraga,Crawford, Grand Traverse, Iosco, Luce, andMecosta; in Minnesota the counties wereCarlton, Cass, Isanti, Lake of the Woods,and Morrison; and in Wisconsin they wereAdams, Douglas, Florence, Marathon, Vilas,and Washburn (Figure 2).

Within each county we selected eight areaframes, or sites, that were 3 by 3 surveysections, or approximately 2500 ha, in size.The sites selected within counties were strat-ified by proximity (near or not-near) to majorroads, public lands, large lakes (greater than4 ha), and urban areas (any that were delin-eated on 1:24 000 scale topographic quadran-gles). Nearness was defined using a set bufferdistance around each feature, ensuring thatsamples were taken both inside and outsidethe buffer. We set buffer distances, essen-tially working hypotheses of the influences ofeach feature, as follows: 8 km for roads, 5 kmfor public lands, 3 km for lakes, and 8 kmfor urban areas. Sites were positioned so thateach site fell entirely within one county. Siteswere not selected if they contained a substan-tial proportion (i.e. greater than 30 percent) ofurbanized area, public land, or water. A totalof 136 sample sites was identified (Figure 2).

Land-use data

The land-use data we used were interpretedfrom parcel maps and aerial photography,and we mapped by parcel for the 136 samplesites for each of three dates (early 1970s,early–mid 1980s, and early 1990s). Parcelboundaries (Figure 3a) were digitized fromplat books that are published periodicallyfor each county at a scale of approximately1:51 000 (e.g. Accurate Publishing, 1993 andRockford Map Publishers, 1990). To ensurethat parcel boundaries overlaid, parcels weredigitized completely from the 1990s maps andedited, by deleting or adding boundary lines,to create the 1970s and 1980s maps. Aerialphotography (Figure 3b) ranged in scalebetween approximately 1:15 000 and 1:70 000and was scanned at the equivalent of 2 m


Figure 3. Data for one of the 136 sample sites mapped for this study. (a) Parcel boundaries digitizedfrom published plat books. (b) Scanned and rectified aerial photograph mosaics. (c) Three major classes ofinterpreted land use based on the primary classification (white is undeveloped, light gray is agriculture, darkgray is developed). (d) Forest cover classified from NALC data (white is not-forest, gray is forest, black iswater or cloud).


ground resolution, rectified, and mosaiced foreach site at each date.

Each parcel was assigned a primary andsecondary land-use code from among 27 dif-ferent categories, but our analysis simplifiesthe categories to focus on developed, undevel-oped, and agricultural uses (Figure 3c). Thequality of the land-use class assignments wasevaluated using three-date composites. Threedifferent types of transitions were flaggedthrough a database query and revisited byan interpreter to evaluate and, if needed,change the classifications at all three dates.First, several transitions were identified asunlikely in any event (e.g. transitions frommost developed to undeveloped or agricul-tural uses). Second, overlay polygons thathad a different class assignment in each ofthe three dates were flagged. Finally, overlaypolygons were re-visited if they started thestudy period as one class, changed to a sec-ond class in the second time interval, thenreverted to the first class in the third period.This quality control procedure was used toidentify and fix the most obvious classifica-tion problems.

Forest-cover data

Land cover was characterized across theentire region using the North AmericanLandscape Characterization (NALC) dataproduced from Landsat Multispectral Scan-ner (MSS) triplicates corresponding to threetime periods similar to those of the land-usedata: 1972–1975, 1985–1987, and 1990–1992.Our region spans about 20 MSS scenes. TheNALC data set (Lunetta et al., 1998) has aspatial resolution of 60 m and a target spatialuncertainty (measured as root mean squarederror) of less than one pixel (i.e. 60 m).Because the actual reported spatial error inthe scenes was not always less 60 m, andbased on our informal assessment of imageregistration quality, their spatial registrationposed a challenge for change analysis.

We used a combination of digital-number(DN) thresholds and unsupervised classifica-tion to assign pixels to one of four classes:forest, non-forest, water, and other (whichincludes clouds and cloud shadows). Brownet al. (2000) described the image-processingand classification procedures in detail. In the

first step, thresholds were identified inter-actively for each image on various spectralchannels and channel combinations to iden-tify clouds, cloud shadows, and water. Areasaffected by haze were also identified usingDN thresholds and were adjusted accordingto a method described by Richter (1990) toreduce the atmospheric effect on the subse-quent image classification.

Areas not classified as clouds, cloudshadows, or water were classified using theiterative self-organizing data analysis rou-tine (ISODATA) to assign each pixel to oneof between 50 and 70 spectrally homoge-nous clusters (Jain, 1989). Classes werelabeled as forest or non-forest through on-screen comparison of spectral cluster loca-tions with corresponding aerial photography.Forest was defined as having greater than40% tree canopy cover, which is a reasonablethreshold for the broadleaf and mixed conifer-ous/broadleaf forests that dominate the studyregion (World Wildlife Fund, 1999). We usedthe aerial photo-mosaics to support imageclassification and accuracy assessment. Theaccuracy of the classifications correspondingto the study sites ranged from 66Ð7 to 94Ð5%.Accuracies tended to be lower in the 1970speriod and higher in the 1990s period (Brownet al., 2000). Forest-cover data were labeled‘missing’ if a site was more than 50% cloud-covered.

Methods

The empirical analysis involved developinga statistical model of the forest transitionprobabilities, aggregated by site, as a func-tion of the types and magnitudes of land-useand parcel-size change within the 136 samplesites. We also calculated the change in a met-ric of the local spatial pattern of the forest.The transition probabilities were then used ina demonstration of an approach to simulatingforest-cover change.

Calculating transition probabilities

Two transition probability values were usedto quantify forest change for the 136 sam-ple sites. The values quantify the ratesof transition between forest and not-forest


.pfnf / and vice versa .pnff /. Because misclas-sification and misregistration in the forest-cover maps can negatively affect traditionalchange-detection methods, we used a proba-bilistic change-detection approach to quantifyforest change. Using a 5 by 5 moving window,we calculated the proportion of forest withinthe window for each pixel location to createa map of forest probability, called pft, fromforest maps of each of the three dates. Theforest and not-forest transition probabilitiesbetween two dates (tD1 and tD2) were thendefined as:

pnffD.1�pf 1/ðpf 2 .4/

pfnfDpf 1ð.1�pf 2/ .5/

where pnff is the probability of a pixel thatchanged from not-forested to forested, pfnf

is probability of a pixel that changed fromforested to not-forested, pf 1 is the proportionof forest in the 5 by 5 window of a pixel indate 1, and pf 2 is the proportion of forest inthe 5 by 5 window of a pixel in date 2. If acell was classified as either water or clouds ineither time period, that cell did not contributeto the calculation of pnff and pfnf .

As an example, a pixel location with pf 1D1(100% of forest in date 1) and pf 2D1 (100%of forest in date 2), the probabilities of thepixel changing from not-forested to forestedand from forested to non-forested [pnff andpfnf ] are both zero, while a pixel location withpf 1D0Ð6 (60% of forest in date 1) and pf 2D0Ð3(30% of forest in date 2), the probabilitiesof the pixel being changed from not-forestedto forested and from forested to not-forested(pnff and pfnf ) are 0Ð12 and 0Ð42, respectively.To represent the transition probabilities ofeach of the 136 sites, we calculated theaverage value of pnff and pfnf across all thepixels in each sample site.

Calculation of the transition probabilitiesrequired a pairing of NALC images for eachsample site over each of the two time inter-vals. The pairs of NALC images representedvariable time intervals ranging from 4 to13 years in length. We decade-standardizedthe transition probabilities using matrix alge-bra (Jahan, 1986). pnff and pfnf were definedas above, such that

PD[

1�pfnf pfnfpnff 1�pnff

]D[

a bc d

]. .6/

For any given time interval (x) that P rep-resents, the decade-standardized transitionprobabilities (pŁnff and pŁfnf ) become:

pŁfnfD�2�10/xb..aCd�R/10/x

�.aCdCR/10/x/R

.7/

pŁnffD�2�10/xc..aCd�R/10/x

�.aCdCR/10/x/R

.8/

whereRD

√a2C4bc�2adCd2 .9/

Hereafter, pŁnff and pŁfnf are referred to as NFFand FNF.

Table 1 lists the average values for thesetwo variables across all 136 sites and foreach time interval. Although there are otherreasons that a place can switch from not-forest to forest (i.e. planting) and from forestto not-forest (i.e. natural disturbance such asfire), we expect that the majority of suchswitches are due to forest regrowth andclearing, respectively.

Measuring forest pattern

In order to quantify the spatial pattern offorest cover, we use a very simple metric thatdescribes the tendency of forested pixels tooccur next to other forested pixels. The met-ric, called pff , is the site-average proportionof forested pixels among the eight neighbor-ing pixels of any forested pixel (Riitters et al.,1999). The value of pff ranges from 0 to 1;where 0 indicates that all the forest pixels,if there are any, are isolated, and 1 indicatesthat the landscape is completely covered by aseamless cover of forest.

The change variable associated with pffwas DPFF (Table 1), which refers to thedecade-standardized change in pff valuesover the interval [i.e. .pff 2–pff 1/ divided bythe number of years in the interval andmultiplied by ten]. Because the decadalchange in pff was so small (one percentagepoint or less, on average) we did not modelDPFF as a function of land-use change.However, we did use pff to constrain spatialsimulations in forest cover (described below).Rather than estimate the change in pff overa decade, however, we assumed that the


Table 1. Site variables with mean values for each of the two time-periods represented in this study

Abbreviation Description 1970s 1980smean mean

Forest-cover variables

FNF Probability that a forest pixel transitioned to non-forested 0Ð305 0Ð265NFF Probability that a non-forest pixel transitioned to forest 0Ð453 0Ð489DPFF Decade-standardized change in PFF 0Ð002 0Ð011

Development variables

DEV1I Initial proportion of site area with development in primary 0Ð047 0Ð070DEV Decadal rate of development (sum of all three levels of increase 0Ð310 0Ð300APSI Initial geometric mean of parcel size .m2/ 137 552 103 488DAPS Decadal rate of change in mean parcel size �0Ð221 0Ð090

Agriculture variables

AGI Initial proportion of site area with agriculture in primary or secondary 0Ð460 0Ð440AGDEV Decade-standardized proportion of agriculture converting to development 0Ð019 0Ð029AGUNDV Decade-standardized proportion of agriculture abandoned 0Ð099 0Ð129AGAPSI Initial mean (geometric) agricultural parcel size 290 928 226 989DAGAPS Decadal rate of change in mean agriculture parcel size 5Ð08 6Ð655

value remained constant in our examplesimulations.

Regression model at the site scale

Because we have measured the land-use andforest-cover change at a number of sites (136)and over multiple time periods (2), the com-piled data set represents a panel that can beanalyzed using methods for panel data anal-ysis developed by econometricians (Hsiao,1989). Our basic goal in developing the modelis to test for linear functional relationshipsat the site-scale between two response vari-ables (NFF and FNF) and land-use changepredictor variables selected to describe theprocesses of development and agriculturalconversion and abandonment in the studyregion. Because the number of time periodswas small (i.e. 2), and the data exhibited asignificant degree of temporal dependence,we estimated conservative models using theaverage values between the two time periodsfor all variables (Hall and Cummins, 1999).The response variables NFF and FNF weretransformed using the arc-sine transforma-tion (where the transformed value of Y issin�1 Y1/2) to address the problem of non-uniform variance common in proportion vari-ables (Draper and Smith, 1981).

Our basic hypothesis was that land-use change, in particular development andagricultural conversion, predicts forest-cover

change, and that parcel sizes and changes inparcel sizes are important covariates in thoserelationships. Therefore, the models were setup to evaluate change in the transformedvalues of forest-cover change over a ten-yearperiod as a function of the changes in, andinitial conditions of, the amounts and parcelsizes of developed and agricultural land usesover the period (Table 1). The developmentvariables refer to the initial proportion of areacoded as developed in the primary (DEV1I)classification, initial geometric mean of par-cel sizes (APSI), the decadal rate of changein parcel sizes (DAPS), and the proportionof area increasing its level of development,normalized to a decade (DEV). For the lattervariable, we identified two kinds of change inthe land-use classification that qualified as‘increasing level of development’: (1) parcelsthat initially had no development in the pri-mary or secondary classification that addeddevelopment to their primary or secondaryclass; and (2) parcels that initially haddevelopment in the secondary but not pri-mary classification that added developmentin the primary class. The agriculture vari-ables describe the initial proportion of the siteclassified (primary or secondary) as agricul-ture (AGI), the initial geometric mean of thearea of agricultural parcels (AGAPSI), andthe ten-year rate of change in the size of agri-cultural parcels (DAGAPS). Change in agri-cultural land use was characterized by theproportion of agricultural areas, defined by


AGi, that converted to development (AGDEV)or undeveloped uses (AGUNDV), normalizedto a ten-year period. Because the AGDEVand AGUNDV variables were conditional onhaving some amount of agriculture presentinitially, and because the area in agriculturewas small or zero in many sites, the effectsof these variables were explored separatelyfrom the full model.

Simulating forest cover

We demonstrate the use of the Markovtransition matrix and the PFF metric ofspatial pattern in forest cover through asimple simulation exercise using a single site.Given an initial map of forest cover by gridcell and a two by two transition matrix, anew map of forest cover can be created bychanging the proper number of forest cellsto not-forest, according to the FNF value,and the proper number of not-forest cellsto forest, according to the NFF value. Forexample, if the map contains 100 forest cellsand 200 non-forested cells and has FNFD0Ð25and NFFD0Ð50, then a random selection of25 forested cells can be switched to not-forestand a random selection of 100 non-forest cellscan be switched to forest.

In order to constrain the selection of cellsto switch, such that the resulting map pat-tern is more realistic, we use PFF as anobjective-function to constrain the simula-tion of forest and non-forest transitions. Weassumed that PFF remained constant overtime. The spatial constraint required creationof multiple realizations of forest-cover changeand retaining the realization having the clos-est PFF value to that of the initial forest map.To ensure that the simulation approachedthe objective-function efficiently, we appliedheuristics to the simulation. Because switch-ing land-cover types of grid cells that werenear the edges of existing forest patchestended to increase the value of PFF, andfurther from patch edges tended to decreasePFF, the percentage of forest within a threeby three window of each cell was used toprioritize cells for alteration. This priori-tization was combined with an adjustablerandomization indicator (RI). When RI wasclose to zero (i.e. no randomness), cells witha smaller percentage of like-classed neigh-bors had a higher priority of switching. The

resulting simulated forest map had clusteredforest patches that retained the higher PFFvalues of the observed landscape. When RIwas large, land-cover change became ran-dom, and generated a sporadic map patternwith a lower PFF value. By altering the mag-nitude of RI, the simulation approached theobjective-function more effectively and effi-ciently. However, to generate more realisticpatterns when the value of NFF or FNF waslarge, a sequential simulation algorithm wasimplemented to re-evaluate the cell priorityafter a certain amount of cells was altered. Inthis case, we recalculated cell priority afterone-tenth of the transitions had been made,to correspond to an annual time-step. Sev-eral equal-probable forest-cover maps, whichrepresent the same intial forest map andidentical values of NFF, FNF, and PFF, weregenerated by automatically fine-tuning themagnitude of RI with the sequential simula-tion algorithm.

Results

According to our Landsat-based analysis,average forest cover in the sample sitesremained constant between the early 1970sand early–mid 1980s (about 53%) but increa-sed to about 57Ð5 percent by the early 1990s.This increasing forest cover was reflectedin a higher probability of forest regrowth(NFF) than forest clearing (FNF), and wasaccompanied by an average increase in thespatial aggregation of forest pixels (i.e. DPFFis positive; Table 1). Table 1 also high-lights the land-use trends that are evi-dent in our sample sites. The average site-proportion in development (primary classi-fication) increased from 4Ð7 percent in theearly 1970s to 7Ð0 percent in the early-mid1980s. On average, about 30 percent of theareas of sites experienced some from of devel-opment during each period. The proportionof site-areas used for agriculture decreasedfrom 46 percent in the early 1970s to 44percent in the early-mid 1980s. The ratesat which agricultural land was abandonedand/or developed both accelerated betweenthe 1970s and 1980s (Table 1), such thatbetween the early–mid 1980s and the early1990s, three percent of agricultural land wasconverted to development and 13 percent con-verted to undeveloped. The latter figure may


be a somewhat exaggerated measure of aban-donment because it does not account for newland being brought into production or thepossibility that rotational fallow land mightbe labeled undeveloped. Overall, parcel sizestended to decline in the 1970s, possibly due tomore rapid immigration. Agricultural parcelstended to increase in average size, proba-bly through the preferential loss of smallerfarms.

Site-scale regression analysis

Table 2 presents the results of the regressionanalysis for estimating the probabilities ofconversion over a ten-year period both fromforest to not-forest (FNF; Table 2a) and fromnot-forest to forest (NFF; Table 2b). Bothmodels were estimated using 135 of the 136sites, because one site was too cloud-coveredin both time periods. The significant predictorvariables in the two models were the same:DEV1I, DEV, and AGI (P<0Ð04 in all cases).The adjusted R2 for the models was 0Ð621 forFNF (Table 2a) and 0Ð587 for NFF (Table 2b).The residuals for both models were not foundto exhibit significant heteroskedasticity. Forthe FNF model LM testD0Ð02 (PD0Ð887) andfor the NFF model LM testD0Ð192 (PD0Ð661).

The influence of the developed land-usevariables on forest cover was fairly straight-forward. Where there was more land area

Table 2. Results of the site scale regressionanalysis

(a) Dependent variable: arcsine transform of FNF

Variable Estimated Standard t-statisticcoefficient error (P-value)

DEV1I 0Ð607 0Ð123 4Ð94 (0Ð000)DEV 0Ð155 0Ð065 2Ð39 (0Ð018)APSI �0Ð145E-08 0Ð419E-07 �0Ð347 (0Ð972)DAPS 0Ð029 0Ð019 1Ð51 (0Ð134)AGI 0Ð454 0Ð038 12Ð05 (0Ð000)C 0Ð260 0Ð026 10Ð17 (0Ð000)

(b) Dependent variable: arcsine transform of NFF

Variable Estimated Standard t-statisticcoefficient error (P-value)

AGI �0Ð361 0Ð032 �11Ð25 (0Ð000)AGAPSI 0Ð680E-07 0Ð645E-07 1Ð05 (0Ð294)DAGAPS 0Ð632E-03 0Ð474E-03 1Ð33 (0Ð185)DEV1I �0Ð319 0Ð109 �2Ð92 (0Ð004)DEV �0Ð113 0Ð054 �2Ð11 (0Ð037)C 0Ð943 0Ð029 32Ð59 (0Ð000)

developed initially, or experiencing some kindof development during the period, the prob-ability of forest clearing was greater andthe probability of forest regrowth was lower.This relationship generally confirms thatdeveloped uses, defined here to include res-idential, retail/office, industrial/warehouse,infrastructure/transportation, institutional,outdoor recreation and mining/extractive, arenegatively related to forest cover on thelandscape. However, because the analysis isaggregated by site, these results do not nec-essarily indicate direct causation.

The role in the models of the initial amountof agricultural land at a site was strongand somewhat complicated. Amount of initialagricultural land use was related positivelyto forest clearing and negatively to forestregrowth. We suspected that AGI was servingas a surrogate for other variables. To explainthe effect of AGI in more detail we examinedits relationship to both the proportion of thesite that is underlain by prime agriculturalsoils, based on STATSGO soils data (NationalSoil Survey Center, 1994), and AGUNDV.Together, prime soils and the proportion ofagricultural lands abandoned were stronglyrelated to (both P<0Ð000), and predictedabout one-third of the variation of, AGI(adjusted R2D0Ð35). This suggests that siteswith more agricultural activity tended tobe more productive and, therefore, also lesslikely to be abandoned and to give way toforest regrowth.

In order to explore more directly the effectsof agricultural land conversion and develop-ment on the changes in forest cover, rela-tionships between the probability of forestregeneration (NFF) and AGUNDV and DEVwere examined together for the subset of sitesthat had some initial level of agriculturaldevelopment (i.e. AGI>0). For this assess-ment, we used a fixed-effects model thattreated each site-period as a separate obser-vation, and allowed us to include time-lags inthe analysis (Hall and Cummins, 1999). Theresults indicated a strong positive relation-ship between NFF and AGUNDV .P<0Ð000/and a strong negative relationship betweenNFF and DEV .P<0Ð000/. The agricul-tural abandonment (AGUNDV) in the priortime period exhibited a significant positive,although less strong, relationship to forestregrowth .PD0Ð028/, but development (DEV)in the prior period was not strongly related


to regrowth .PD0Ð498/. The same variableswere significantly related to FNF, but thesigns were all reversed. This analysis showsthat, on sites with some agriculture present,current development and agricultural aban-donment in the previous and current ten-yearperiods predict the amount of forest regrowthand clearing (adjusted R2D0Ð211 and 0Ð260,respectively). Although the initial amount ofarea under agricultural management withina site (AGI) serves as a reasonable nega-tive surrogate for agricultural marginality,abandonment, and, ultimately, the probabil-ity of forest regrowth, rates of agriculturalabandonment relate strongly to the prob-ability of regrowth. Further, there appearsto be a longer time-lag for regrowth follow-ing abandonment than for clearing followingdevelopment.

In all cases (Tables 2a and 2b), initialaverage parcel size and changes in averageparcel size were not significantly correlatedwith forest regrowth or clearing. Althoughparcel sizes may indicate something aboutthe type of land management on a parcel, ifsuch an effect occurs it is not strong enoughto appear when parcels are aggregated intospatial landscape sites.

Simulation example

Figure 4 displays the results of an initialsimulation example to illustrate the applica-tion of the statistical models generated here.Figure 4a is an initial forest-cover map, takenfrom one of our sample sites in the early1970s time frame. If we know somethingabout the probability of forested areas totransition to non-forested land covers (FNF)and vice versa (NFF), then we can simulatethe landscape at some future time. Given themodels in Table 2, we can estimate the val-ues of NFF and FNF, using information thatwe may have or have estimated about theland-use change that is occurring in the site.In this case we use the observed transitionprobability values for illustration purposes:NFFD0Ð263 and FNFD0Ð485.

Figure 4b represents a random selection ofroughly 26 percent of the non-forested areasand 48 percent of the forested areas for tran-sition. Because the switches were selected atrandom, the resulting map pattern was toopatchy and not very realistic. It assumes that

the process of conversion occurs at randomlocations within the site. Constraining thesimulation such that the landscape patternthat results after the simulation has the samepff value as the initial landscape, resulted inFigures 4c and 4d. Although the maps inFigure 4c and 4d resulted from the samemagnitude of forest and not-forest swappingas 4b, the map pattern is preserved, and is,at least visually, more realistic.

Discussion and conclusions

Land-use and land-cover change inthe Upper Midwest, USA

The changes in forest cover that we observedwithin our sample sites are consistentwith the general increase in forest coverobserved in the forest inventory conductedby the USDA Forest Service (Stone, 1997)and throughout the temperate mid-latitudeforests (Houghton et al., 1999). At the sametime, our sites experienced both an increasein the area of developed uses and a decreasein agricultural uses. These trends are con-sistent with changes occurring in a broadrange of rural areas throughout the USA,particularly those experiencing dispersedrural recreational and residential develop-ment, including the Colorado Front Range(Theobald et al., 1996) and the SouthernAppalachians (Turner, 1990) among otherregions.

Our results suggest that agricultural activ-ities and development are strongly relatedto the forest-cover change processes thatwe observed through remote sensing. In ouraggregated landscapes (2500 ha), much of thechange in forest cover occurring between theearly 1970s and the early 1990s was pre-dicted on the basis of the amount of landused for agriculture and development, andthe rate at which development was increasingon the landscape (Table 2). All of these vari-ables were positively related to forest clearingand negatively related to forest regrowth.Because much of the study area is marginallyproductive as agricultural land, the areaswith a lot of agricultural land use were thosethat tended to have the best soils and werealso those that were, therefore, least likelyto be abandoned. At the scale of sites, parcel


Figure 4. Application of transition probabilities for forest-cover simulation. Cover types are displayed usingthe same legend as in Figure 3. (a) Initial forest-cover map. (b) Simulation of forest-cover change withoutspatial constraint (NFFD0Ð263 and FNFD0Ð485). (c and d) Simulations of identical forest-cover changeprobabilities as (b), but with spatial pattern constrained to PFFD0Ð688.

sizes bear no direct relationship with changesin forest cover.

Value and limitations of theapproach

The strengths of the relationships betweenforest-cover change processes and the amou-nts and changes in agricultural and developed

land uses in this region suggest that there ispromise for the proposed modeling approach.Land use and land cover are clearly linkedto one another. However, we argue thatmapping and modeling them as separate pro-cesses is both more theoretically defensibleand practical. As an example, consider thequestion of the effects of rural residential andrecreational development on carbon storage


in trees and their associated soils. The pro-cess is driven by demand for residential andrecreational land and governed by a mar-ket, which uses the parcel as its basic unit.Trees and forests are important aesthetic andenvironmental components of this residentialland, often enhancing its value. However, inmost cases, trees do not cover entire parcels,sometimes occurring in patches that spanparcel boundaries, and representing, at best,a secondary use of lands that are otherwiseused for hunting cabins, permanent resi-dences, seasonal residences, or other recre-ational activities. If we model the economicconditions giving rise to such development, adirect prediction of the effects on forest coveris unlikely to be obtained. Similarly, if weobserve changes in tree cover, e.g. via satel-lite remote sensing, the relationship of suchchanges to the demand for land for variouspurposes is ambiguous. Our approach, there-fore, serves as a bridge between models thatpredict changes in land use, e.g. development(Alig, 1986; Landis, 1994; Clarke et al., 1997;Geoghegan et al., 1997), and assessments ofthe impacts on land covers that provide envi-ronmental services, e.g. forests. The approachcould be extended to look at the effects ofurban sprawl on various environmentally-significant land covers.

The linear functional relationships estab-lished between land-cover change and landuse, through regression analysis, confirmthat land use and land-use change can beused to predict changes in the amount offorest cover at the landscape scale. Thesimple models developed here were basedon the average land use, land-use change,and land-cover change conditions for twotime-periods (1970s and 1980s). This tem-poral aggregation limited our ability to testfor time-lags and temporal non-stationarityin the models. However, we did demonstratethe value of including time-lags in the modelsfor exploring temporally dynamic relation-ships. The data used to generate the modelswere also spatially aggregated, which reducestheir ability to directly reflect the parcel byparcel nature of land-use change.

Further development of the models isneeded, based on the analysis presented here.First, the addition of more time periods, e.g.1960s and 1990s, will facilitate analysis ofthe functional relationships in more detail.Specifically, more time periods will permit

more formal evaluation of the influence oftime-lags through estimation of fixed- and/orrandom-effects models of land-cover dynam-ics. Second, in the case of predicting NFF,the use of time-lags and information aboutsite-quality might improve the prediction ofregrowth. We observed the existence of atime-lag in the relationship between agri-cultural abandonment and forest regrowth,but have an insufficient number of sites toevaluate differences in regrowth lags by site.Third, analysis at the parcel scale is requiredto validate the relationships found at thesite scale and to provide more detailed infor-mation about the processes that give riseto the relationships observed. Specifically, astatistical model of Markov transition proba-bilities at the parcel scale, like that presentedhere for the site scale, would facilitate finelydetailed simulation of forest cover, givenparcel-based maps of land use and land-use change. Finally, alternative modelingapproaches might be more appropriate in thisapplication. Specifically, regression trees, adecision tree-based analysis that is robustto missing values (Michaelson et al., 1994),could be used to isolate specific types of sitesand the change occurring on them. For exam-ple, with a regression tree it would be possibleto first identify the influence of amount ofagricultural land use, then, on those sitesthat have agricultural land use, evaluate theinfluence of agricultural land use conversionto development or abandonment.

Estimation of forest-cover change probabil-ities from land-use information provides animportant conceptual link that can be usedto generate forest-cover change simulationson the basis of land-use change predictions.The simulation approach demonstrated herecan be linked to models that predict land-use change over large areas for estimationof the effects on forest cover. We demon-strated the use of the Markov transitionprobabilities in a simulation model that cre-ates and updated forest-cover map given esti-mated probabilities that are specific to thattime and place (Figure 4). By estimating theMarkov transition probabilities as a functionof land-use change variables, we relax theassumption inherent in most Markov-basedmodels, that the transition probabilities arespatially and temporally stationary, and weimprove the interpretability of the model.Because the spatial patterns of forest clearing


and regrowth are not random, the simula-tion requires a spatial constraint. Here wehave demonstrated the application of a sim-ple spatial constraint based on the pff valuedescribed above. By simulating the forestchanges that adhere to the estimated transi-tion probabilities and to the target pff value,it is possible to produce multiple realizationsof the possible forest landscapes that couldresult given land-use change.

The simulation presented here is meantonly as an example and could be improved.First, we intend to work with alternative sim-ulation algorithms for generating spatially-constrained simulations, including simulatedannealing, to achieve better results. Fur-ther, the simulations could be constrainedon the basis of parcel boundaries, such thatindividual parcel land-use changes can beused to simulate forest cover within individ-ual parcels. If simulations are constrainedby parcel boundaries, additional spatial con-straints could be added. For example, anyclearing of the forest that is expected withthe development of a parcel could be con-strained to occur along the road frontage ofthe property and any remaining forest couldbe maintained towards the back of the prop-erty to reflect real processes. Finally, morethan two class transitions could be modeled toallow for the inclusion of other land-cover cat-egories (e.g. wetlands, grassland, impervious,etc.). The trade-off with all of these suggestedimprovements is that they demand additionalcomputational resources in order to producemore realistic forest-cover simulations.

Conclusion

The amount of forest cover on the landscapeshas broad-ranging implications, from ame-lioration of climatic extremes and decreasedenergy usage in local urban areas, to seques-tration of carbon and potentially dampen-ing the effects of global climate changebrought on by anthropogenic greenhouse-gasemissions on the global scale. In order tounderstand and model forest-cover dynamicswithin developed countries, it is necessary tolink those dynamics to the social and eco-nomic drivers of land-use change. We haveargued that models of land-use change canbe linked to critical land-cover outcomes (like

forest cover) through the use of Markov land-cover transition probabilities, that are calcu-lated as a function of land-use conditions andland-use change. This step in the evolutionof Markov simulation models, such that tran-sition probabilities are variable, and can beestimated in time and space, improves boththeir practicality and their ability to repre-sent causal processes. A simple simulationwas presented as an example. We expect thatsimulations like that presented could be usedto predict patterns of forest cover over largeareas for which estimates of land use andland-use change are available. Deriving suchestimates from models of land-use change,that are driven by exogenous variables, canprovide a system for the assessment of futureforest-cover impacts of economic, social, andpolicy changes. This paper provides a keystep in the development of such a system.

Acknowledgements

This work has been support by a grant fromNASA’s Land-Cover and Land-Use Change Pro-gram (NAG5-6042) and a cooperative agreementwith the USDA Forest Service North Central For-est Experiment Station (#23-95-50). We appreciatethe database help provided by Sean Savage andthe statistical advice of Emily Silverman; but allresponsibility for errors in the execution of theresearch lies with the authors. We also thankthe many people who worked on the data entryrequired for this project: Rebecca Boehm, EmilyClark, Scott Drzyzga, Bob Goodwin, Todd Jones,Jason Krawcyzk, Brad Shellito and Aron Thomas.

References

Accurate Publishing. (1993). Atlas and Plat Book:Mecosta County, MI. Battle Lake, MN: AccuratePublishing.

Alig, R. J. (1986). Econometric analysis of thefactors influencing forest acreage trends in thesoutheast. Forest Science 32, 119–134.

Baker, W. L. (1989). A review of models of land-scape change. Landscape Ecology 2, 111–133.

Bell, E. J. (1974). Markov analysis of land usechange: Application of stochastic processes toremotely sensed data. Socioeconomic PlanningSciences 8, 311–316.

Brown, D. G., Duh, J. D. and Drzyzga, S. (2000).Estimating error in an analysis of forest frag-mentation change using North American Land-scape Characterization (NALC) Data. RemoteSensing of Environment 71, 106–117.

Brown, D. G. and Vasievich, J. M. (1996). A studyof land ownership fragmentation in the upper


midwest. In Proceedings, GIS/LIS ‘96 Confer-ence, Denver, CO., pp. 1199–1209. Bethesda,MD: American Society for Photogrammetry andRemote Sensing.

Burnham, B. O. (1973). Markov intertemporalland use simulation model. Southern Journalof Agricultural Economics July, 253–258.

Census of Agriculture (1997). Washington, D.C.:U.S. Dept. of Agriculture, National AgriculturalStatistics Service.

Clarke, K. C., Gaydos, L. and Hoppen, S. (1997).A self-modifying cellular automaton model ofhistorical urbanization in the San Francisco Bayarea. Environment and Planning B 24, 247–261.

Deadman, P., Brown, R. D. and Gimblett, H. R.(1993). Modelling rural residential settlementpatterns with cellular automata. Journal ofEnvironmental Management 37, 147–160.

de Koning, G. H. J., Veldkamp, A. and Fresco, L. O.(1999). Exploring changes in Ecuadorian landuse for food production and their effects on nat-ural resources. Journal of Environmental Man-agement 57, 221–237, doi:10.1006/jema.1999.0305.

Draper, N. R. and Smith, H. (1981). AppliedRegression Analysis. New York: John Wiley andSons.

Foster, B. L. and Gross, K. L. (1999). Temporaland spatial patterns of woody plant establish-ment in Michigan old fields. American MidlandNaturalist 142, 229–243.

Geoghegan, J., Wainger, L. A. and Bockstael, N. E.(1997). Spatial landscape indices in a hedonicframework: An ecological economics analysisusing GIS. Ecological Economics 23, 251–264.

Guttorp, P. (1995). Stochastic Modeling of Scien-tific Data. New York: Chapman and Hall.

Hall, B. H. and Cummins, C. (1999). Time SeriesProcessor Version 4Ð5. User’s Guide. Palo Alto,CA: TSP International.

Houghton, R. A., Hackler, J. L. and Lawrence, K. T.(1999). The U.S. carbon budget: Contributionsfrom land-use change. Science 285, 574–578.

Hsaio, C. (1989). Analysis of Panel Data. NewYork: Cambridge University Press.

Jahan, S. (1986). The determination of stabilityand similarity of Markovian land use changeprocesses: A theoretical and empirical analysis.Socio-Economic Planning Science 20, 243–251.

Jain, A. K. (1989). Fundamentals of Digital ImageProcessing. Englewood Cliffs, NJ: Prentice Hall.

Johnson, K. M. (1998). Renewed PopulationGrowth in Rural America. Research in RuralSociology and Development 7, 23–45.

Johnson, K. M. and Beale, C. L. (1998). The RuralRebound. Wilson Quarterly 12, 16–27.

Lambin, E. F. (1997). Modelling and monitoringland-cover change processes in tropical regions.Progress in Physical Geography 21, 375–393.

Landis, J. D. (1994). The California UrbanFutures Model: A new-generation of metropoli-tan simulation-models. Environment and Plan-ning B 21, 399–420.

Leatherberry, E. C. and Spencer, J. S. (1996).Michigan Forest Statistics, 1993. Resource Bull.

NC-170. St. Paul, MN: USDA Forest Service,North Central Forest Experiment Station.

Lunetta, R. S., Lyon, J. G., Guindon, B. andElvidge, C. D. (1998). North American Land-scape Characterization dataset developmentand data fusion issues. Photogrammetric Engi-neering and Remote Sensing 64, 821–829.

Mauldin, T. E., Plantinga, A. J. and Alig, R. J.(1999). Determinants of land use in Maine withprojections to 2050. Northern Journal of AppliedForestry 16, 82–88.

Michaelson, J., Schimel, D. S., Friedl, M. A.,Davis, F. W. and Dubayah, R. C. (1994).Regression tree analysis of satellite and terraindata to guide vegetation sampling and surveys.Journal of Vegetation Science 5, 673–686.

Miles, P. D. and Chen, C. M. (1992). MinnesotaForest Statistics, 1990. Resource Bull. NC-141.St. Paul, MN: USDA Forest Service, NorthCentral Forest Experiment Station.

Muller, M. R. and Middleton, J. (1994). A Markovmodel of land-use change dynamics in theNiagara Region, Ontario, Canada. LandscapeEcology 9, 151–157.

National Soil Survey Center (1994). State Soil Geo-graphic (STATSGO) Data Base. Misc. Pub. No.1492. Fort Worth, TX: US Dept. of Agriculture,Soil Conservation Service.

Pijanowski, B. C., Gage, S. H., Long, D. T. andW. E. Cooper. (2000). A land transformationmodel for the saginaw bay watershed. In Land-scape Ecology: A Top Down Approach (J. Sander-son and L. D. Harris, eds), pp. 183–198. BocaRaton, FL: Lewis Publishers.

Richter, R. (1990). A faster atmospheric correc-tion algorithm applied to Landsat TM images.International Journal of Remote Sensing 11,159–166.

Riebsame, W. E., Parton, W. J., Galvin, K. A.,Burke, I. C., Bohren, L., Young, R. and Knop, E.(1994). Integrated modeling of land use andcover change. Bioscience 44, 350–356.

Riitters, K. H., Wickham, J. D., Jones, K. B.and O’Neill, R. V. (1999). Global survey offorest fragmentation. Abstracts, InternationalAssociation for Landscape Ecology, 5th WorldCongress, Snowmass Village, CO. Fort Collins,CO: IALE, p. 130.

Rockford Map Publishers (1990). Land Atlas andPlat Book: Grand Traverse County, Michigan.Rockford, IL: Rockford Map Publishers, Inc.

Schmidt, T. L. (1997). Wisconsin Forest Statistics,1996. Resource Bull. NC-183. St. Paul, MN:USDA Forest Service, North Central ForestExperiment Station.

Staaland, H., Holand, O., Nellemann, C. andSmith, M. (1998). Time scale for forest regrowth:Abandoned grazing and agricultural areas insouthern Norway. Ambio 27, 456–460.

Stone, R. N. (1997). Great Lake States ForestTrends, 1952–1992. In Lake States RegionalForest Resources Assessment: Technical Papers.GTR NC-189. St Paul, MN: USDA Forest Ser-vice, North Central Forest Experiment Station.

Theobald, D. M., Gosnell, H. and Riebsame, W. E.(1996). Land use and landscape change in the


Colorado mountains II: A case study of the EastRiver Valley, Colorado. Mountain Research andDevelopment 16, 407–418.

Theobald, D. M. and Hobbs, N. T. (1998). Fore-casting rural land-use change: A comparison ofregression- and spatial transition-based models.Geographical and Environmental Modelling 2,65–82.

Turner, B. L. and Meyer, W. B. (1991). Land useand land cover in global environmental change:Considerations for study. International SocialSciences Journal 130, 669–667.

Turner, B. L., Skole, D., Sanderson, S., Fischer, G.,Fresco, L. and Leemans, R. (1995). Land-Use and Land-Cover Change Science/ResearchPlan. Joint publication of the InternationalGeosphere-Biosphere Programme (Report

No. 35) and the Human Dimensions of GlobalEnvironmental Change Programme (ReportNo. 7). Stockholm: Royal Swedish Academy ofSciences.

Turner, M. G. (1987). Spatial simulation of land-scape changes in Georgia: A comparison of threetransition models. Landscape Ecology 1, 29–36.

Turner, M. G. (1990). Landscape changes in ninerural counties in Georgia, USA. Photogram-metric Engineering and Remote Sensing 56,379–386.

Williams, M. (1989). Americans and Their Forests:A Historical Geography. Cambridge: CambridgeUniversity Press.

World Wildlife Fund (1999). Forests for Life Page.15 June, 1999 <http://www.panda.org/forests4life/whatisforest.htm>.

Documents

Modeling the relationships between land use and land cover ...ltm.agriculture.purdue.edu/docs/brown0369.pdf · use and land cover for modeling landscape change. Attempts to model