Estimating Error in an Analysis of ForestFragmentation Change Using NorthAmerican Landscape Characterization(NALC) Data

Daniel G. Brown,* Jiunn-Der Duh,* and Scott A. Drzyzga*

We describe an approach for estimating measurement the variation in error. We demonstrate how, in a changeanalysis, predicted error can be used to identify locationserror in an analysis of forest fragmentation dynamics.that exhibit change substantially greater than the errorWe classified North American Landscape Characteriza-in value estimation. Elsevier Science Inc., 2000tion (NALC) images in four path-row locations in the

Upper Midwest to characterize changing patterns of for-est cover. To estimate error, we calculated the differences

INTRODUCTIONin values of forest fragmentation metrics for overlappingscene pairs from the same time frame (or epoch). The Over the past decade, scientific investigations into theoverlapping image areas were subdivided into landscape link between spatial landscape structure and ecologicalpartitions. We tested the effects of amount of forest cover, processes have benefited from a proliferation of land-landscape phenology, atmospheric variability (e.g., haze scape indices to characterize the spatial patterns of land-and clouds), and alternative processing approaches on scapes. Literally dozens of indices of landscape patternthe consistency of metric values calculated for the same have been developed and used to quantify spatial pat-place and approximate time but from different images. terns on the landscape (O’Neill et al., 1988; Baker andTwo of the metrics tested (average patch size and num- Cai, 1992; McGarigal and Marks, 1995; Gustafson, 1998).ber of patches) were more sensitive to image characteris- The importance of pattern in forested landscapes is welltics and contained more measurement error in a change established. Forest fragmentation and the presence ofdetection analysis than the others (percent forest cover edge affects forest species composition and diversity, pri-and edge density). Increasing the landscape partition size mary production, and suitability of the forest for habitatmoderately reduced the amount of error in landscape (Iida and Nadashizuka, 1995; Stouffer and Bierregaard,change analysis, but at the cost of reduced spatial resolu- 1995; Flather and Sauer, 1997; Laurance et al., 1997).tion. Processes used to generalize the forest map, such as Forman (1997) defined the process of fragmentation assmall-polygon sieving and majority filtering, were not “the breaking up of a habitat, ecosystem, or land usefound to consistently decrease measurement error in met- type into smaller parcels” (p. 39). For our purposes, for-ric values and in some cases increased error. Predictive est fragmentation can also refer to a quantifiable state ofmodels of error in a forest fragmentation change analysis the forest (i.e., the degree to which the forest is brokenwere developed and significantly explained up to 50% of up into a number for small parcels at any given time).

Remote sensing, especially from the Landsat-class satel-lites, has provided a wealth of data to support analysis of

* Department of Geography, Michigan State University, East landscape pattern and changes in pattern on a regionalLansing scale (Skole and Tucker, 1993; Vogelmann, 1995; Jorgen-

Address correspondence to Daniel G. Brown, School of Natural sen and Nohr, 1996; Weishampel et al., 1998).Resources and Environment, University of Michigan, 430 E. Univer-

To develop reasonable causal links between ob-sity, Ann Arbor, MI 48109-1115. E-mail: danbrown@umich.eduReceived 9 March 1999; revised 18 June 1999. served patterns on the landscape and the processes driv-

REMOTE SENS. ENVIRON. 71:106–117 (2000)Elsevier Science Inc., 2000 0034-4257/00/$–see front matter655 Avenue of the Americas, New York, NY 10010 PII S0034-4257(99)00070-X

Forest Fragmentation Dynamics 107

ing those patterns, multitemporal analyses of dynamic measurement error is affected by the amount of forestcover within the area and differences in landscape phe-patterns are necessary. Trajectories of pattern metrics

can be compared among places to infer differential nology and atmospheric variations, each of which dif-ferentially affects the classification process in differentcausal forcings and differential effects (Turner, 1990;

Dunn et al., 1991; Kitzberger and Veblen, 1999; Pan et images.The objectives of this study were to:al., 1999). The North American Landscape Characteriza-

tion (NALC) project of the Landsat Pathfinder program 1. calculate the measurement error in estimatingassembled and preprocessed triplicates of Landsat MSS change in four different metrics of forest amountimages to support land cover change analyses and re- and fragmentation as a result of differences ingional and national inventories of terrestrial carbon the characteristics of MSS scenes;stocks for the twenty-year period spanning 1972 and 2. test the effects of landscape generalization1992 (Lunetta et al., 1998; Yuan and Elvidge, 1998). The through postprocessing, to remove small-scale vari-data set consists of three images for each Worldwide ability, and scale (i.e., size of landscape units) onReference System (WRS)-2 path-row location, one the error in fragmentation metrics; andwithin each of three time frames, or epochs (1972–1975, 3. develop a statistical model to evaluate potential1985–1987, and 1990–1992). NALC data hold promise causes of error and to predict the amount of er-for supporting regional- and decadal-scale analyses from ror in a change analysis.which the processes driving landscape change can be in-

The objectives are addressed quantitatively throughferred and modeled. However, as with any multitemporalanalysis of image overlap areas between neighboringsatellite image data set, the nature of the data and thepath-row locations in two Upper Midwest study areas,characteristics of the images affect the results and mustone in Michigan and one on the Wisconsin/Michiganbe considered in their interpretation.border. Because each path-row has associated with itYuan and Elvidge (1998) listed seven image charac-three images (from 1972–1975, 1985–1987, and 1990–teristics that complicate attempts to detect landscape1992), we used 12 images in our analysis. Forest frag-change by comparing pairs of images. These were “1) thementation metrics calculated for an area from two im-differences in band-passes and spatial resolution, 2) spa-ages in the same epoch should yield the same value fromtial misregistration, 3) variations in the radiometric re-each image. Nonzero differences between metric valuessponse of the sensors, 4) differences in the distributionderived from images of the same epoch (within two yearsof cloud and cloud shadow, 5) variations in solar irradi-of each other) are quantified and attributed to differ-ance and solar angles, 6) variations in atmospheric scat-ences unrelated to interepochal landscape dynamics (i.e.,tering and absorption, and 7) differences in phenology”they are measurement error or noise).(p. 166). Whereas Yuan and Elvidge (1998) focused on

Our approach provides a quantitative basis for mak-pixel-by-pixel land cover change analysis in the face ofing decisions on appropriate processing steps, appro-these complicating influences, our analysis focuses on es-priate fragmentation metrics, and data fitness for use oftimating changes in the fragmentation of forest cover.NALC data or other satellite imagery in an analysisFurther complications affect change analyses applied atchange in forest fragmentation dynamics. Further, thea regional scale (i.e., involving multiple path-row loca-analysis is interpreted for insight into appropriate acqui-tions). Differences in the time of acquisition of neigh-sition strategies for monitoring and analysis of landscapeboring images within the same epoch can introduce in-change in temperate forests. By attributing cause totraepochal variation in landscape condition due tosome of the error, acquisition strategies can be designedseasonal or interannual variability.to minimize the error variation and develop a purer char-Our approach is a postclassification analysis of theacterization of ecologically significant changes in land-change in landscape pattern metrics selected to evaluatescape pattern. For error that is unavoidable, we proposeforest fragmentation. Areas within the overlap betweenan error modeling strategy that can be used to evaluateadjacent WRS path and row locations, a little more thancalculated changes in metric values against the estimated25% of scene area at the latitude of our study area, aremeasurement error. Therefore, calculated changes thatimaged twice for each epoch. We use the area within theare small relative to the estimated error can be ignoredoverlap to quantify the amount of measurement errorin favor of a focus on changes that are greater than the(i.e., “noise”) in landscape pattern metrics that is not at-estimated error.tributable to actual landscape modification between ep-

ochs (i.e., the “signal”). Knowledge of error magnitudesin such analyses can be used to distinguish actual land- STUDY AREAS AND DATAscape changes from spurious changes in metric values re-

Secondary forests, having regenerated following nearlysulting from image variability. We test hypotheses aboutcomplete harvest of pre-European forests in the latethe sources of measurement error for fragmentation met-

rics. Specifically, we hypothesize that the magnitude of nineteenth and early twentieth centuries, cover large ar-

108 Brown et al.

eas of the Upper Midwest, defined here to include data set within the region that contains 136 such areaMichigan, Minnesota, and Wisconsin. In the northern frames. Table 1 lists the numbers of area frames that fellportion of these three states, forests make up about one within each path-row location; note that area frames arehalf of the land cover, support a $24 million per year counted more than once when they fell within the sceneforest products industry, and provide wildlife habitat and overlap area. The photographs were variable in type,important ecological services, including carbon seques- quality, and concurrence with NALC image dates. Nev-tration. The most abundant forest types found in the re- ertheless, they serve as excellent data for classifying andgion are beech-maple, aspen-birch, red-white pine, and validating the forest cover maps. Because of the largejack pine. number of photos and the variety of dates, photo dates

Like many rural areas in the United States, popula- are not listed to simplify Table 1.tion in the region has been growing more rapidly in re-cent decades, especially during the 1970s and 1990s (Fu-

METHODSguitt and Beale, 1996). Population grew an average of2% per year throughout the northern half of the region Our approach to quantifying measurement error was toduring the 1970s, with some rural areas experiencing (1) classify each of the twelve images, (2) subdivide thegrowth that was much more rapid. In addition, the num- overlap study areas into landscape partitions, (3) calcu-ber of seasonal homes in the region is quite large, espe- late several forest fragmentation metrics for each of thecially in northern Lower Michigan where seasonal homes landscape partitions in each image, and then (4) evaluatemake up greater than 50% of housing units in some the differences between the landscape metrics for im-counties. This population change, along with the increas- ages of the same epoch. The differences between frag-ing relative affluence of the population and a changing mentation metric values calculated at the same placeeconomic base, contributes to landscape pattern and within the same epoch provide estimates of the measure-change in the region. ment error in fragmentation metric values that can be

We chose two study areas in the Upper Midwest, attributed to image characteristics, processing, and/or in-corresponding to two areas of overlap between adjacent traepochal temporal variation. We compared magnitudesNALC scene areas (i.e., same row, neighboring paths). of error in four metrics to image characteristics, testedThe study areas were selected in northern Lower Michi- the effects of several image processing procedures, andgan (hereafter referred to as “study area A”) and north- evaluated hypotheses about some of the causes of mea-ern Wisconsin on the border with Michigan (hereafter surement error to build models for predicting thereferred to as “study area B”) because of extensive forest amount of error at a particular place for a given paircover in each, but with differences in relative amount of images.(Fig. 1). The two scene overlaps each cover an area ofbetween 860 kha to 870 kha. As of the early 1990s, study Image Classificationarea A (WRS-2 paths 21 and 22 on row 29) had about

We used a combination of digital number (DN) thresh-56% forest cover. At the same time, study area Bolds and unsupervised classification to assign pixels to(WRS-2 paths 24 and 25 on row 28) was about 83% for-one of four classes: forest, nonforest, water, and otherest covered.(which includes clouds and cloud shadows). In the firstWe obtained all NALC images covering these twostep, thresholds were identified for each image on vari-study areas, twelve in all (three epochs, four path-rowous spectral channels and channel combinations to iden-locations). The dates of the NALC images for these fourtify features that occurred at spectral extremes. Thresh-scenes are given in Table 1. The NALC data set is de-olds were set through interactive interpretation of eachscribed in more detail elsewhere (Lunetta et al., 1998).individual scene. Cloud shadows were identified using aIn support of image classification and accuracy as-threshold on the average DN value of MSS channels 1sessment, we scanned, georeferenced, and mosaiced ae-and 2 (visible). A threshold was defined for each imagerial photographs for sample area frames located through-on MSS channel 4 (near-infrared), below which all areasout the sample scenes. The area frames corresponded towere assigned to the water class. Because of some ambi-blocks of nine square survey sections and were betweenguity between the water and shadow classes, areas identi-2.0 kha and 2.4 kha in size. Eight area frames were se-fied as water were given precedence over cloud shadowlected within each of several counties throughout the re-areas. Pixels were classified as clouds if they had DNsgion, some of which fell outside the images used for thisabove a set threshold on the third “tasseled cap” compo-study. The sampling strategy for the area frames is de-nent, sometimes called the “yellowness” index (Jensen,scribed in detail by Brown and Vasievich (1996). Aerial1996). Finally, areas affected by haze were identified us-photographs at scales between approximately 1:15,000ing an upper and lower threshold on this same tasseledand 1:70,000 were collected for three dates, correspond-cap index, after it had been processed with a low-passing to each of the NALC epochs. Thirty-eight area

frames were used to support this investigation from a filter for smoothing. DN values of areas identified as

Forest Fragmentation Dynamics 109

Figure 1. Study areas A and B. Classified land cover from image pairs in the 1990s epoch. Whiteoutlines indicate landscape partitions in each of the study areas.

hazy were adjusted using histogram matching with non- reasonable, especially for the broadleaf and mixed conif-erous/broadleaf forests that dominate the study regionhazy areas in the visible MSS channels to reduce the at-

mospheric effect on the subsequent image classification (World Wildlife Fund, 1999). Each of the aerial photo-mosaics was divided in half horizontally. The northern(Richter, 1990).

Areas not classified as clouds, cloud shadows, or wa- half of each site was used for cluster labeling and thesouthern half for accuracy assessment. Therefore, the ae-ter were classified using the iterative self-organizing data

analysis routine (ISODATA) to assign each pixel to one rial photo for the southern half of each site was maskedduring cluster labeling.of between 50 and 70 spectrally homogenous clusters

(Jain, 1989). Classes were labeled as forest or nonforest After classification of forest and nonforested classeswas complete, the water, cloud, and cloud shadow masksthrough on-screen comparison of spectral cluster loca-

tions with corresponding aerial photographs. Forest was were added back to the classified image. To maintain aconsistent study area through all of our analyses, thedefined as having greater than 40% tree canopy cover.

Although common land cover classifications use a 10% cloud and cloud shadow masks were combined for allimages covering a particular study area. This meant thatthreshold (Anderson et al., 1976), we used the higher

threshold to exclude areas that were less likely to func- for study area A, for example, there were six potentialcloud and cloud shadow masks that were combined totion as forest ecosystems. The 40% threshold is more

Table 1. Dates of North American Landscape Characterization (NALC)images used for this study

Number ofAir Photo

Path Row 1970s Datea 1980s Date 1990s Date Samples

24 28 17 July 1975 12 July 1985 27 June 1990 1825 28 26 June 1974 22 July 1986 5 August 1991 821 29 1 August 1975 8 August 1985 9 August 1991 1622 29 9 June 1973 28 June 1985 15 July 1991 11

a Landsats 1, 2, and 3 used the WRS-1 path-row locations, but the images were reprojectedinto WRS-2 scene locations as part of the NALC project. In some cases, imagery from a differentdate was used to supplement the 1970s image by creating an image mosaic. Where this occurred,the date of the dominant image is given to economize space.

110 Brown et al.

Table 2. Classification Accuracies

1970s 1980s 1990s

Path Row Nmin PCC Kappa PCC Kappa PCC Kappa

21 29 314 72.5 0.492 78.8 0.596 81.6 0.60422 29 205 78.5 0.618 85.6 0.742 91.2 0.84324 28 317 75.0 0.397 82.0 0.533 83.6 0.53625 28 131 75.6 0.452 72.7 0.315 81.2 0.440

Accuracies are given as the percentage of randomly selected pixels correctly classified (PCC)compared to class assignments made through aerial photo interpretation. Also listed is theminimum number of accuracy assessment sample points used for images in a given path-row(Nmin) and the kappa statistic for each error matrix.

create one consistent mask across all images in all maximum number of square landscapes that could fitepochs. into each study area. The three landscape sizes were ap-

A set of between 15 and 25 control points was ran- proximately 2.5 kha (nine survey sections; displayed indomly identified within the southern half of each photo- Fig. 1), 9.3 kha (approximately equal to a Jeffersonianmosaic. The points were overlain on the aerial photo- survey township), and 21 kha in size. Study area A wasgraphs and assigned to a class using photo interpretation partitioned into 325, 83, and 35 nonoverlapping land-for each epoch. Error matrices were constructed to com- scapes, respectively; study area B was partitioned intopare the class identified for each sample site through ae- 250, 65, and 25 landscapes, respectively. The landscaperial interpretation with the class assigned to those sites partitions served as the basic units of analysis for as-through cluster labeling. The error matrices are summa- sessing the error in the change of fragmentation metrics.rized in Table 2 using percent correctly classified and the The forest fragmentation in each landscape partition waskappa statistic. summarized using patch-based metrics. Although regu-

One pattern in the image accuracies is worth noting. larizing the landscape partitions simplified our analysis,Image accuracy tended to improve as the image date be- irregularly sized and shaped partitions (e.g., watersheds)came more recent. Images from the 1970s all had accu- could be used. When using irregular partitions, however,racies less than 80%, whereas images from the 1990s all care should be taken in interpreting results as some met-had accuracies greater than 80%. This trend may be re- rics exhibit a scale effect (i.e., values are sensitive tolated to the availability of concurrent aerial photographs. changes in the size of the units).At earlier dates, the dates of available aerial photographstended to be less concurrent with the satellite image

Metric Calculationdates. Another possible explanation relates to imageFour metrics of forest fragmentation were selected forquality, which is generally known to be better in MSSthe analysis (Table 3). All metrics were calculated for allimages from Landsat 5 than from Landsat 1.images and all landscape partitions. All metrics were cal-culated using FRAGSTATS (McGarigal and Marks,Landscape Partitioning1995). Real change in the percentage of a landscape thatOne way to approach the analysis of changing landscapeis forested (PF) relates directly to habitat destruction andpatterns is to summarize changes in forest fragmentationto the amount carbon sequestered in the landscape. Thefor an entire region (e.g., one number indicating the ratenumber of patches (NP) and mean patch size (MPS) areof change of a pattern characteristic for the entire re-related to one another and to the percent of the land-gion). However, to identify locations of most rapidscape that is forested. Taken together, actual values ofchange and to evaluate the potential causes of change,these metrics provide information about the degree tothe analysis needs to be geographically disagreggated inwhich the forest is in many small patches or few largesome way. For our analysis, we disaggregated by subdi-patches. Edge density (ED) focuses on the amount ofviding the regional landscape into equally sized andedge in the landscape. Because forest edge affects micro-shaped landscape partitions for which forest fragmenta-climate and resource availability, different species tendtion and change metrics were calculated. The use ofto view edges in different ways. Real changes in edgelandscape partitions facilitates the mapping and monitor-density on a landscape will favor some species while pen-ing of the regional geographic patterns of forest fragmen-alizing others. Although we recognize that the use oftation.landscape partitions to calculate metrics will tend to biasEach of our two study areas was subdivided intothe values of NP and MPS because of the truncation ofsquare landscape partitions at three different levels of ag-large patches (Hunsaker et al., 1994), the validity of met-gregation to evaluate the influence of landscape size on

the measurement error in the metrics. We delineated the ric sensitivity analysis should be relatively unaffected by

Forest Fragmentation Dynamics 111

Table 3. Landscape Patterns Metrics Used to Assess Forest Fragmentation

Metric Abbreviations Definition

Percent forest PF Percentage of the landscape covered by forestNumber of patches NP Number of forest patchesMean patch size MPS Average size of forest patchesEdge density ED Length of forest/nonforest edge4landscape area

such bias because we are differencing metric values cal- To compare the amount of error between metrics, wecompared RE values among metrics.culated for landscapes of equal size.

Consistently, PF was the quantity least sensitive toerror and MPS was most sensitive. PF and ED both ex-Characterizing Measurement Errorhibit only moderate degrees of variation due to imageBecause the difference between metric values should bedifferences. Both have an average RE across all imagesidentical when calculated from two images of the sameof less than 35% of the mean value. Although there isepoch, a nonzero difference is attributable to measure-substantial variation in RE between image pairs, thesement error (noise) in the context of an interepochaltwo metrics were consistently lowest in terms of theirchange analysis (i.e., where the goal is to measure arelative error.change signal). Our measure of error, therefore, is the

MPS had an average RMSE across all images thatdifference between metric values calculated for the samewas greater than one and a half times the mean MPSlandscape partition within the same epoch. For eachvalue. This suggests that because of its sensitivity to im-metric, we summarized the errors across all landscapeage characteristics, in addition to a tendency to have a

partitions using the root mean squared error (RMSE). highly skewed distribution, MPS is a poor choice as aRMSE is a summary measure of the average magnitude metric of landscape fragmentation change. However, be-of error, without reference to the direction or bias of the cause the NP metric is inversely proportional to MPSerror. RMSE is reported in the units of the metric it and NP is less sensitive to image characteristics, NP is asummarizes. To standardize the measure of error for good alternative for characterizing the degree to whichcomparison between landscape metrics, RMSE values the landscape is made up of many small patches versusare divided by the mean of the metric values obtained fewer large patches.in both images of a pair. This calculation yields a quan-tity that summarizes the relative amount of error (RE), Effect of Landscape Sizeexpressing the RMSE as a proportion of the average By summarizing landscape patterns over larger areasmetric value. (i.e., using larger landscape partitions), the effects of er-

rors on the metric values should be reduced because er-rors will tend to average out. This is especially true ofRESULTSspatial misregistration errors. By increasing landscape

Comparison of Metrics size, in essence, spatial resolution in the pattern analysisTable 4 lists the RMSE and RE values calculated for is traded for more confidence that the numbers are accu-each metric in each image pair. Each entry in the table rate. Further, one goal of landscape pattern change anal-is a summary of errors across all landscape partitions cal- ysis is to identify areas on the landscape that are chang-

ing more rapidly. The detail with which areas of rapidculated from a pair of images within the same epoch.

Table 4. RMSE and RE for Image Pairs Covering the Same Study Area atthe Same Time Period

PF NP MPS ED

Epoch RMSE RE RMSE RE RMSE RE RMSE RE

Study area A1970s 30.38 0.68 122.29 1.15 58.74 2.46 25.15 0.521980s 14.34 0.27 56.40 0.78 64.97 1.84 21.20 0.441990s 13.24 0.23 65.14 0.80 42.29 1.32 18.58 0.37

Study area B1970s 3.13 0.04 10.72 0.48 245.90 0.89 4.96 0.201980s 4.05 0.05 9.12 0.42 287.60 1.14 5.18 0.181990s 7.35 0.09 17.25 0.85 411.43 1.49 10.96 0.39

Calculated using 2.5 kha landscape partitions

112 Brown et al.

Figure 2. The effect of increasing landscape partition size on error in fragmentation metrics.

forest fragmentation or agglomeration can be identified one partition reduced the RE calculated at 9.2 kha from2.25 to 0.47, and indicated an error reduction from thewill be reduced with larger landscape partitions.

We compared the errors in metric differences for 2.5 kha partition size, which was consistent with all otherdates at both study areas.both study areas at three different landscape partition

sizes to test the hypothesis implicit above that increasinglandscape size reduces error. Figure 2 illustrates the ef- Effects of Sieving and Filteringfects of increasing the landscape partition size on the er- It can be tempting to generalize classified images for re-ror calculated for each metric in each study area in each gional scale analysis by removing the smallest patches.epoch. Errors in NP and MPS are reported as RE, be- This is especially true if the smallest patches are sus-cause changing partition size will naturally lead to an in- pected of being the most error-prone in a change analy-crease in the mean of both NP and MPS. This changing sis. We applied map generalization methods to our im-mean will affect RMSE by increasing it with the mean; ages to test the implicit assumption that through maphowever, RE will not be biased in this way. Error levels generalization the accuracy of a change analysis will bein PF and ED are reported as RMSE because they are improved.both density measures that are divided by landscape area Image-processing packages provide two commonand do not exhibit this scale effect. methods for generalizing a classified image to make it

In all but one instance of the six pairs of images and more aesthetically pleasing and remove the smallestfour metrics, increasing the landscape partition size mod- patches. One approach, sieving, simply recodes smallerately reduced the error, confirming that increased par- patches to the class with which they share their longesttition size resulted in reduced error. The one case of in- border. The other approach, filtering, changes everycreasing error with increasing partition size (between 2.5 pixel to the majority class found within a specified searchkha and 9.3 kha in study area B in the 1980s) was an window around each pixel. Sieving alters only pixels thatanomaly. The anomaly was caused by the fact that one are in small patches, whereas filtering has the potentialof the partitions had only one forest patch that encom- to alter all pixels.passed most of the partition in one image of the pair. Figure 3 illustrates the effects that sieving at threeThis very large patch was subdivided into two patches in levels of polygon size and filtering at two window sizesthe other image of the pair, resulting in a very large dif- had on the error in a change analysis. In all cases, error

is summarized using RE to facilitate comparisons acrossference in MPS for that one partition. Removing that

Forest Fragmentation Dynamics 113

Figure 3. The effect of postprocessing methods on error in fragmentation metrics. Sieve 1, Sieve 3, and Sieve 10 indicateprocessing by removing forest patches less than 1, 3, and 10 ha in size, respectively. Filter 3 and Filter 5 indicate pro-cessing with a majority filter kernel 333 and 535 pixels in size, respectively.

different degrees of postprocessing, because the mean of consistency with which landscape pattern metrics can beestimated. If the goal is estimating change in forestall metrics is affected by sieving and filtering.

Sieving and filtering clearly do not consistently re- cover, for example, the analysis suggests that such post-processing approaches are more likely to increase thanduce the amount of error in a change analysis. With the

exception of study area B in the 1990s epoch, the errors decrease the error in the change estimate.in the estimates of PF were consistently higher in imagepairs that were sieved or filtered. The effects of filtering A Model of Error in Metric Differencestended to be more pronounced than the effects of siev- We hypothesize three measurable influences on error ining. Estimates of change in NP tended to be positively assessments of change in forest fragmentation metrics.affected by sieving and filtering. Although the actual First, we hypothesize that error in forest fragmentationnumber of patches in each image decreases through siev- metrics will be higher where the land cover in a land-ing and filtering, the estimates of change in NP tended scape partition is more evenly divided among forestedto be less affected by error when they have been pro- and nonforested covers (i.e., 50% forest cover). Rathercessed in this way. The influence of sieving and filtering than describing some physical characteristic of the re-on MPS and ED tended to be inconsistent, suggesting mote sensing system, our first hypothesis holds that pat-that their effect on error was sensitive to the characteris- tern metrics tend to be less sensitive to minor perturba-tics of the image being processed. tions when the landscape is dominated by one land cover

This analysis suggests that extreme care should be or another. Second, we hypothesize that the degree totaken in applying postprocessing methods designed to which haze is present in either of the images of a pairgeneralize an image or map when the goal is pattern- will display a positive relationship with magnitude of er-based change analysis. In addition to biasing the absolute ror in a change analysis based on that image pair. Finally,numbers (i.e., decreasing estimates of PF, ED, and NP we hypothesize that where the images are acquired un-and increasing estimates of MPS), sieving and filtering der more divergent phenological conditions, the error in

their estimates of changing fragmentation levels will bealgorithms have differential levels of influence on the

114 Brown et al.

higher. We assume that the other sources of error inclassification and pattern analysis will be minor relativeto these. We neutralized the influence of differences incloud and cloud shadow area by using the same mask forall images at a site.

To test these hypotheses, we built a statistical modelof error and tested the model for significance in ex-plaining the error magnitudes for each pattern metricacross all landscape partitions in all epochs and bothstudy areas. To account for the relative amount of forestcover, we used the average estimated amount of forestcover in a partition from both images in the pair as apredictor variable with a second-order polynomial form(i.e., percent forest and the percent forest squared wereboth used in the equation). Our hypothesis suggests thatbelow a 50% forest cover, increasing forest cover shouldresult in increasing error; above a 50% cover, increasingcover should result in decreasing error. The second-orderpolynomial can approximate this relationship.

Figure 4. Change in average composite NDVI throughHaze in the partitions was accounted for by identi-an average growing season for the three ecoregions infying two levels of haziness on the “yellowness” indexthe study areas (Northern Lakes and Forests, North(i.e., third tasseled cap channel) through DN thresh- Central Hardwoods, and Southern Michigan Till Plain;

olding. The haziest class was weighted 1.0 and the sec- Omernik, 1987). NDVI values were averaged for eachJulian date from composite AVHRR images from be-ond haziest class was weighted 0.5. The weighted sum oftween 1982 and 1991 (Eidenshink and Faundeen,the area in the two haze classes was calculated to pro-1994).duce an index of haziness in a given partition. To esti-

mate the influence of haze on the comparison of two ep-ochs, we used the union of the two haziness masks as an

between images. We present models using both phe-estimate of the amount of area that was hazy in either nology variables for comparison.image. Model coefficients were estimated using multiple

The phenological difference between two images linear regression. Each model was estimated across 1,725was measured in two ways. First, we differenced NDVI pooled observations, where each observation was a dif-values, calculated from the MSS images and averaged ference in fragmentation metric values calculated fromacross the study area, as a measure of the phenological an image pair for the same landscape partition in thedifference within each epoch. This provides an overall same epoch. All image pairs in study areas A and B, withmeasure of the difference in how “green” the landscape 325 and 250 partitions (2.5 kha in size), respectively, andwas when the images of a pair are acquired. Figure 4 at each of the three time epochs were used in modelillustrates the change in NDVI from AVHRR through an estimation. Although we do not report separate modelsaverage growing season, averaged over a 10-year period, for simplicity, models developed separately for eachin the three ecoregions covered by our study areas. Al- study area resulted in similar strengths (as indicated bythough there are geometric and subpixel cloud errors as- t-tests) and directions (as indicated by the signs on thesociated with the AVHRR data, regional variation in coefficients) as the pooled model.NDVI can be well approximated because these local For three of the four metrics, the models supportsources of variation tend to be averaged out. The ecore- the hypotheses regarding sources of error in metric val-gions were defined by Omernik (1987) and the NDVI ues (Table 5). For PF, NP, and ED, error is significantlydata we used were described by Eidenshink and Faun- higher where a partition is evenly divided between forestdeen (1994). Differences in NDVI cannot be used to and nonforest, where haze is more prevalent, and wherecharacterize error in a long-term change analysis applica- the average NDVI values of the two images are moretion, however, because some interepochal differences in divergent. The MPS model indicates similar relationshipsNDVI necessarily reflect, in addition to phenological dif- with haziness and NDVI differences, but an opposite re-ferences, actual land cover change that is the target sig- lationship with percent forest (i.e., error is lowest wherenal in an interepochal change analysis. To make the a partition is closer to 50% forest cover). The MPSmodel more applicable to long-term change analysis, we model is the weakest in terms of explanatory power (r2

substituted the difference in Julian date of the images, is 0.179) and suffers from non-normally distributed resid-as if they were taken in the same year, for differences uals, whereas residuals for the other models exhibit nor-

mal distributions. Therefore, the MPS model is the leastin NDVI to account for seasonal phenological differences

Forest Fragmentation Dynamics 115

Table 5. Results of Multiple Linear Regression to Model Error in Fragmentation Change Metrics

PF NP MPS ED

Coefficient t Coefficient t Coefficient t Coefficient t

Models using difference in image NDVI to represent phenologyIntercept 27.93 24.61 227.00 23.79 66.99 1.61 28.98 24.23Average PF 0.45 8.65 2.03 9.33 27.27 25.75 0.71 10.99(Average PF)2 20.005 211.19 20.02 212.81 0.092 8.97 20.006 212.29Haze 0.12 15.13 0.42 12.96 1.092 5.78 0.06 6.37Diff NDVI 1.99 25.22 7.56 23.04 3.05 1.59 1.00 10.29

F 423.84 453.23 94.94 106.08Significance F 2.7E-254 6.4E-267 4.78E-73 7.51E-81Adjusted R2 0.495 0.512 0.179 0.196

Models using difference in Julian date to represent phenologyIntercept 24.87 22.54 29.85 21.24 75.54 1.78 210.59 24.90Average PF 0.37 6.46 1.71 7.20 27.40 25.86 0.67 10.41(Average PF)2 20.004 29.54 20.02 211.25 0.09 8.95 20.01 211.61Haze 0.06 6.38 0.20 5.51 1.01 5.21 0.02 2.10Diff date 0.30 15.82 1.01 12.66 0.37 0.86 0.23 10.78

F 284.02 307.81 94.40 109.14Significance F 1.3E-187 8E-200 1.17E-72 5.77E-83Adjusted R2 0.396 0.416 0.179 0.201

reliable of the four. The models of error in PF and NP landscape patterns and changes in those patterns are af-fected by errors in the classifications. Until now, littleare strongest in terms of significance and explanatoryhas been known about the way in which image errorspower, each explaining about one half of the variation inpropagate through an analysis of pattern and change. Weerror. The weakness of the MPS and ED models suggesthave presented a method for assessing this error propa-that other factors are driving variations in the error ofgation and applied it to the analysis of changing levels ofthese metrics, a topic for future research.forest fragmentation in two Upper Midwest study areas.Because images from different epochs may exhibit

We consider two approaches to managing error indifferences in NDVI that are not related to error, butsuch an analysis: (1) minimizing the error and (2) esti-rather to actual landscape change, comparisons of phe-mating the magnitude of the error so that it can be in-nology should use a measure of seasonal differences thatcorporated into the analysis. One way to minimize theis independent of long-term change. As a surrogate forerror is to improve the image processing and classifica-phenological development we tested the difference in Ju-tion procedures. For example, improved atmosphericlian dates of two images. On average NDVI tends to in-correction algorithms to account for variable hazinesscrease through a growing season (Fig. 4). There is not amay yield some benefits. Because much has been writtenlinear relationship between Julian date and averageon classification procedures, we do not address this issueNDVI, so the variables are not perfect surrogates. How-further. We explored other potential approaches to min-ever, Julian date is a variable that is easily acquired andimizing error in an analysis of changing forest fragmenta-applied in an analysis of change.tion patterns. One approach is to aggregate the land-Substituting Julian date for average NDVI as a mea-scape, averaging out and therefore reducing local scalesure of phenology resulted in a reduction in significanceerrors. Our analysis indicates that the errors in an analy-and explanatory power for PF and NP, and only a slightsis of changing landscape patterns will be moderately re-increase for MPS and ED (Table 5). In nearly everyduced by increasing the landscape unit size. The obviouscase, the explanatory variables retained the significancetrade-off, however, is that the spatial detail availableand direction of their relationships with error in each offrom the results of the analysis is reduced.the metrics. Therefore, although Julian date is an imper-

Another approach to minimizing error that we ex-fect measure of phenological development, models of er-plored was to sieve or filter the classified image to re-ror in PF and NP retain moderate levels of explanatorymove small patches, which one may suspect of beingpower with that surrogate (about 40% of the variation ex-more prone to error than large patches. Our analysis in-plained).dicates that by generalizing the forest cover map in thisway, errors in an analysis of changing landscape pattern

DISCUSSION AND CONCLUSIONS are not consistently reduced. In fact, some metrics, mostnotably the percent forest cover, suffer from increasedBecause classifications of satellite imagery into land

cover types are never completely accurate, analyses of error when the images are processed in this way.

116 Brown et al.

Figure 5. Application of error model to fragmentation change analysis using NP metric in study area A:(a) metric values calculated for 1980s epoch; (b) metric values calculated for 1990s epoch; (c) differencesbetween epochs; (d) errors estimate using the model in Table 5; (e) the ratio of the difference and theestimated error.

Finally, error can be reduced through carefully With a reasonable estimate of error, it is possible toperform a change analysis by differencing two metric val-planned image acquisitions. We have found that the sea-

sonally variable phenology of a temperate landscape af- ues from different temporal epochs and highlight onlythose changes that are greater than the amount offects characterizations of landscape pattern. By regularly

monitoring average phenological conditions (for example, change estimated to result from image errors and differ-ences. Figure 5 illustrates an example of this approachusing coarse spatial resolution but fine temporal resolu-

tion NDVI image), it might be possible to select images examining the change in NP in study area A between the1980s and 1990s epochs. Figures 5a and b show thefor paired analysis on the basis of similarities in pheno-

logical condition. Similarly, haze might be reduced number of patches in each landscape partition for eachepoch. Figure 5c is the calculated difference betweenthrough monitoring atmospheric conditions and selecting

images on the basis of minimum haze. This would re- epochs. Figure 5d is the predicted error in that differ-ence using the equation in Table 5. Finally, Figure 5equire a multisensor strategy to image acquisition, taking

advantage of the multiple sensors currently available and shows landscape partitions for which the difference be-tween epochs exceeds the predicted error (i.e., the ratioplanned for launch.

The second major approach to managing error in an of difference to error is greater than one). All such parti-tions are then classed into two categories: those that haveanalysis of changing landscape pattern is to estimate the

amount of error and consider that error when interpret- a ratio of difference to error between 1 and 2 and thethose with a ratio greater than two.ing the results of a change analysis. To estimate error,

we have proposed a model of error in pattern metrics By applying the error models in the manner illus-trated in Fig. 5, an analysis of changing landscape pat-that considers three predictor variables: the amount of

forest in the landscape, the haze in the images, and the terns can incorporate uncertainties in the data and avoidascribing to spurious values of change a real landscapedifferences in phenology in a pair of images. Through

multiple linear regression, we demonstrate that these change cause. Such an approach should improve the use-fulness of an analysis in which landscapes are identifiedthree variables can significantly explain up to about 50%

of the error variation in a metric change analysis. with change or no-change conditions.

Forest Fragmentation Dynamics 117

ages for mapping of landscape and biological diversity in theThe research described in this article was supported by NASA’s Sahel. Int. J. Remote Sens. 17:91–109.Office of Earth Science under the Land Cover and Land Use Kitzberger, T., and Veblen, T. T. (1999), Fire-induced changesChange program (Grant #NAG5-6042). We acknowledge the

in northern Patagonian landscapes. Land. Ecol. 14:1–15.receipt of Landsat data from the North American LandscapeLaurance, W. F., Laurance, S. G., Ferreira, L. V., Rankin-deCharacterization (NALC)–Landsat Pathfinder Project and

Merona, J. M., Gascon, C., and Lovejoy, T. E. (1997), Bio-AVHRR data from the Global Land 1-KM AVHRR Project. Themass collapse in Amazonian forest fragments. Science 278:School of Natural Resources and Environment at the University1117–1118.of Michigan provided publication support.

Lunetta, R. S., Lyon, J. G., Guindon, B., and Elvidge, C. D.(1998), North American Landscape Characterization dataset

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