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On the Issues of Scale, Resolution, and Fractal Analysis in the M,Apping Sciences* 88 Volume44, Number1, February1992 port of the Committee on Transpiration and tionships between land-surface processes and clio Evaporation, 1943-44. Transactions,American Geo- mate, and the statistical analysis of large-scale clio physicalUnion 2;:638-93. mate fields. JOHANNES FEDDE1\IA is Assistant Professorof CORT WILLMOTT is Chair of the Department Geography at the University of California, Los An- of Geography and Professorof Geography and Ma- geles. He was formerly a Ph.D. student at the Uni- rine Studies at the University of Dela\vare. He also versity of Dela\vare. His researchinterests include is a member of the University:s Center for Climatic \vater balance climatology and climate/teleconnec- Research. His research interests include the rela- cion processes. On the Issues of Scale, Resolution, and Fractal Analysis in the M,apping Sciences* Nina Siu-Ngan Lam Dale A. Quattrochi Lo/lisianaState University NASA Scienceand TechnologyLaboratory, StennisSpace Center Scale and resolution have long been key issues in geography. The rapid development of anal:-.tical cartography, GIS; and remote sensing {the mapping sciences} in the last decade has forced the issues of scale and resolution to be treated formally and better defined. This paper addresses the problem of scale and resolution in geographical studies, \vith special reference to the mapping sciences. The fractal concept is introduced, and its use in identifying the scale and resolution problem is discussed. The implications of the scale and resolution problem on studies of global change and modeling are also explored. Key words: scale, resolution, fractals, mapping sciences. Scale, Resolution, and Geography areas. Some geographers rely on data obtained from satellites, yet others depend on data re- T he concept of scale is central to geography garding pollen counts and soil particles ob- (Harvey 1969; Meentemeyer 1989; Wat- tained through electronic microscopes. Diver- son 1978; Woodcock and Strahler 1987). It is sity within the discipline results in the need one of the main characteristics that portrays to address spatial problems from multiple geographic data and provides a unique percep- scales and resolutions. tion of spatial attributes as they relate to form, This variation in scales can be regarded both process, and dimension. Geographers often as a strength and weakness of the discipline. deal with spatial phenomena of various scales. Analyzing geographical phenomena using a For example, geomorphology encompasses range of scales offers a special view and meth- stUdies ranging from patterns of river net- ' odology that other disciplines seldom employ, \vorks, river basins, and coastline changes to enhancing geography's strength. To the con- potholes, cave, and gully formation based on trary, the massive amount of data needed for international, national, regional, or local analysis of spatial phenomena at various scales, scales. Climatologists study upper air circula- coupled with the possibility of applying an tion around the globe as \vell as effects of local inappropriate methodology, often leads to a climate on agricultural production and health. meaningless study. This invites criticism and Urban geography includes studies ranging confusion from within the discipline and from from analyzing the urban systems in an in~er- other related disciplines. national, national, or regional context to as- This paper does not attempt to solve issues sessing the impact of facility location on local of scale and resolution, but rather brings to- .\\.e thank Grego~. Carter, Lee De Cola, the anonymous revie,vers, and the editor for improving this paper; Clifford Duplechin a~d Mary Lee Eggart, and the LSl: graduate students for preparing the graphics; and the NASA, john C. Stennis SpaceCenter, Director's Discre- tiona~. Fund for supporting in part the development of this paper. Profession.!Geogr.pher. -1-1(1)1992, pages 88-98 tCCop.vright 1992 b~. Associationof AmericanGeographers Initial submission,April 1991;final acceptance,August 1991 Scale,Resolution, and Fractal Analysis 89 SCALE Closely related to scale is the concept of SPATIAL~ -SPATIo-~ TEMPORAL~"" -TEMPORAL resolution. Resolution refers to the smallest distinguishaoleparts in an object or a sequence (Tobler 1988),and is often determined by the ~ ~, capability of the instrument or the sampling interval used in a stUdy. A map containing data by county is considered of finer spatial resolution than a map by state. In referenceto GEOGRAPHIC OPERATIONAL CARTOGRAPHIC the three meaningsof scale,small-scale stUdies (or Observation) (or Map) usually employ data of finer spatial resolution Figure 1: Meanings of scale. than large-scalestudies. Small-scale maps, on the contrary, often contain lower or coarser resolution data than large-scalemaps. Finally, gether important points regarding scale and phenomenaoperating at a smaller scale, such resolution in light of recent developments, and as potholes and caves, require data of finer proposes the use of fractals for analyzing spa- resolution. Because large-scale studies (geo- tial phenomena encompassing various scales. graphic or observation scale)involving fine res- With appropriate methodology and sufficient olution are rather uncommon, scale and reso- attention to the problem of scale, we believe lution are often blended together and loosely that the geographical perspective derived from referred to as "scale," although it is recognized analysis using differing scales can contribute that a large-scale stUdy does not necessarily in many \vays to an understanding of various mean that it has a coarser resolution, and vice spatial phenomena. This is particularly im- versa. In this paperthe notion of the resolution portant in relating earth processes or other is generally implied whenever the term scale spatial and environmental phenomena within is used. the context of global dynamics (e.g., the In- ternational Geosphere/Biosphere Program). Controversies over the exact definition and Methodological Issues Related to measurement of scale and resolution exist Scale and Resolution (Woodcock and Strahler 1987). Some clarifi- cation of terminology, therefore, is necessary. Severalmethodological dilemmas surrounding The term scale may include all aspects-spa- the scale and resolution issue can be summa- tial, temporal, or spatio-temporal (Fig. 1). In rized here. First, different spatial processes this paper \ve focus on spatial scale. There are operate at different scales,and thus interpre- at least three meanings of scale. First, the term tations based on data of one scale may not scale may be used to denote the spatial extent apply to another scale (Harvey 1968, 1969; of a study (i.e., geographic scale or scale of Stone 1972).The noted "ecological fallacy" in observation). For example, a spatial analysis spatial analysis,making inferences about phe- of land use across the entire United States is nomenaobserved at differing scalesor imply- considered a large-scale study, as compared to ing finer resolution from coarser resolution a land use plan for a city. This definition of data, atteststo this problem. A simple example scale is quite different from the second use by Robinson (1950) sho\vs that correlations called cartographic scale, where a large-scale between t\vo variables,measured IQ and race, map covers smaller area but generally with decreased from 0.94 to 0.73, and finally to more detail, and a small-scale map covers 0.20, as resolution increased from census re- larger area \\1th less detail. The third usage of gion, to state, and to individual study scales scale refers to the spatial extent at which a (Openshaw 1984). particular phenomenon operates (i.e., opera- Because spatial patterns are usually scale tional scale). For example, mountain-building specific, inferring spatial process from spatial processes operate at a much larger scale than pattern is perplexing; this is illustrated by the that of river pothole formation. These three well-known dilemma of different processes meanings of scale, however, are often mixed leading to the same spatial pattern (Harvey and used vaguely in the literature. 1969;Turner et al. 1989b). Moreover, a spatial -~ 90 Volume44, Number1, February1992 pattern may look clustered at one scale but and landscape patterns, and to utilize fully random at another. For example,the mortality remote sensingand GIS. pattern of leukemia cancer in China appears In an integrated GIS and remote sensing randomly distributed if based on county-level system, data of various types, scales,and res- data; if the data are aggregatedand reported olutions are used. How will the analytical by province, a clustered geographicalpattern methods and results be affected by different results (Lam et al. 1989).Depending upon the scalesand resolutions?What is the relationship scale of observation, therefore, processesthat betweenscale and accuracy?The selection of appearhomogeneous at a small scale may be- an appropriate scale is also influenced by the comeheterogeneous at a largerscale. This may techniques used to extract information from be exemplified by patterns of coniferous for- remote sensingdata. The factors of scale and ests infested \vith pine bark beetle blight. At resolution, therefore, have become a major re- a small spatial scale, the patterns of infected searchdirection in GIS and remote sensing. individual trees or groups of trees \\.ithin the forest are not evident, becausethe pattern of insect damage becomesintegrated as part of A Brief Description of
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