1、外文资料与中文翻译Metrics of scale in remote sensing and GISMichael F Goodchild(National Center for Geographic Information and Analysis, Department of Geography, University of California, Santa Barbara)ABSTRACT: The term scale has many meanings, some of which survive the transition from analog to digital rep
2、resentations of information better than others. Specifically, the primary metric of scale in traditional cartography, the representative fraction, has no well-defined meaning for digital data. Spatial extent and spatial resolution are both meaningful for digital data, and their ratio, symbolized as
3、US, is dimensionless. US appears confined in practice to a narrow range. The implications of this observation are explored in the context of Digital Earth, a vision for an integrated geographic information system. It is shown that despite the very large data volumes potentially involved, Digital Ear
4、th is nevertheless technically feasible with todays technology.KEYWORDS: Scale, Geographic Information System , Remote Sensing, Spatial ResolutionINTRODUCTION: Scale is a heavily overloaded term in English, with abundant definitions attributable to many different and often independent roots, such th
5、at meaning is strongly dependent on context. Its meanings in “the scales of justice” or “scales over ones eyes” have little connection to each other, or to its meaning in a discussion of remote sensing and GIS. But meaning is often ambiguous even in that latter context. For example, scale to a carto
6、grapher most likely relates to the representative fraction, or the scaling ratio between the real world and a map representation on a flat, two-dimensional surface such as paper, whereas scale to an environmental scientist likely relates either to spatial resolution (the representations level of spa
7、tial detail) or to spatial extent (the representations spatial coverage). As a result, a simple phrase like “large scale” can send quite the wrong message when communities and disciplines interact - to a cartographer it implies fine detail, whereas to an environmental scientist it implies coarse det
8、ail. A computer scientist might say that in this respect the two disciplines were not interoperable.In this paper I examine the current meanings of scale, with particular reference to the digital world, and the metrics associated with each meaning. The concern throughout is with spatial meanings, al
9、though temporal and spectral meanings are also important. I suggest that certain metrics survive the transition to digital technology better than others.The main purpose of this paper is to propose a dimensionless ratio of two such metrics that appears to have interesting and useful properties. I sh
10、ow how this ratio is relevant to a specific vision for the future of geographic information technologies termed Digital Earth. Finally, I discuss how scale might be defined in ways that are accessible to a much wider range of users than cartographers and environmental scientists.FOUR MEANINGS OF SCA
11、LE LEVEL OF SPATIAL DETAILREPRESENTATIVE FRACTIONA paper map is an analog representation of geographic variation, rather than a digital representation. All features on the Earths surface are scaled using an approximately uniform ratio known as the representative fraction (it is impossible to use a p
12、erfectly uniform ratio because of the curvature of the Earths surface). The power of the representative fraction stems from the many different properties that are related to it in mapping practice. First, paper maps impose an effective limit on the positional accuracy of features, because of instabi
13、lity in the material used to make maps, limited ability to control the location of the pen as the map is drawn, and many other practical considerations. Because positional accuracy on the map is limited, effective positional accuracy on the ground is determined by the representative fraction. A typi
14、cal (and comparatively generous) map accuracy standard is 0.5 mm, and thus positional accuracy is 0.5 mm divided by the representative fraction (eg, 12.5 m for a map at 1:25,000). Second, practical limits on the widths of lines and the sizes of symbols create a similar link between spatial resolutio
15、n and representative fraction: it is difficult to show features much less than 0.5 mm across with adequate clarity. Finally, representative fraction serves as a surrogate for the features depicted on maps, in part because of this limit to spatial resolution, and in part because of the formal specifi
16、cations adopted by mapping agencies, that are in turn related to spatial resolution. In summary, representative fraction characterizes many important properties of paper maps.In the digital world these multiple associations are not necessarily linked. Features can be represented as points or lines,
17、so the physical limitations to the minimum sizes of symbols that are characteristic of paper maps no longer apply. For example, a database may contain some features associated with 1:25,000 map specifications, but not all; and may include representations of features smaller than 12.5 m on the ground
18、. Positional accuracy is also no longer necessarily tied to representative fraction, since points can be located to any precision, up to the limits imposed by internal representations of numbers (eg, single precision is limited to roughly 7 significant digits, double precision to 15). Thus the three
19、 properties that were conveniently summarized by representative fraction - positional accuracy, spatial resolution, and feature content - are now potentially independent.Unfortunately this has led to a complex system of conventions in an effort to preserve representative fraction as a universal defi
20、ning characteristic of digital databases. When such databases are created directly from paper maps, by digitizing or scanning, it is possible for all three properties to remain correlated. But in other cases the representative fraction cited for a digital database is the one implied by its positiona
21、l accuracy (eg, a database has representative fraction 1: 12,000 because its positional accuracy is 6 m); and in other cases it is the feature content or spatial resolution that defines the conventional representative fraction (eg, a database has representative fraction 1:12,000 because features at
22、least 6 m across are included). Moreover, these conventions are typically not understood by novice users - the general public, or children - who may consequently be very confused by the use of a fraction to characterize spatial data, despite its familiarity to specialists.SPATIAL EXTENTThe term scal
23、e is often used to refer to the extent or scope of a study or project, and spatial extent is an obvious metric. It can be defined in area measure, but for the purposes of this discussion a length measure is preferred, and the symbol L will be used. For a square project area it can be set to the widt
24、h of the area, but for rectangular or oddly shaped project areas the square root of area provides a convenient metric. Spatial extent defines the total amount of information relevant to a project, which rises with the square of a length measure.PROCESS SCALEThe term process refers here to a computat
25、ional model or representation of a landscape-modifying process, such as erosion or runoff. From a computational perspective,a process is a transformation that takes a landscape from its existing state to some new state, and in this sense processes are a subset of the entire range of transformations
26、that can be applied to spatial data.Define a process as a mapping b (x,)=( a (x,) where a is a vector of input fields, b is a vector of output fields, is a function, t is time, is later in time than , and x denotes location. Processes vary according to how they modify the spatial characteristics of
27、their inputs, and these are best expressed in terms of contributions to the spatial spectrum. For example, some processes determine b(x, ,) based only on the inputs at the same location a(x, ), and thus have minimal effect on spatial spectra. Other processes produce outputs that are smoother than th
28、eir inputs, through processes of averaging or convolution, and thus act as low-pass filters. Less commonly, processes produce outputs that are more rugged than their inputs, by sharpening rather than smoothing gradients, and thus act as high-pass filters.The scale of a process can be defined by exam
29、ining the effects of spectral components on outputs. If some wavelength s exists such that components with wavelengths shorter than s have negligible influence on outputs, then the process is said to have a scale of s. It follows that if s is less than the spatial resolution S of the input data, the
30、 process will not be accurately modeled.While these conclusions have been expressed in terms of spectra, it is also possible to interpret them in terms of variograms and correlograms. A low-pass filter reduces variance over short distances, relative to variance over long distances. Thus the short-di
31、stance part of the variogram is lowered, and the short-distance part of the correlogram is increased. Similarly a high-pass filter increases variance over short distances relative to variance over long distances.L/S RATIOWhile scaling ratios make sense for analog representations, the representative
32、fraction is clearly problematic for digital representations. But spatial resolution and spatial extent both appear to be meaningful in both analog and digital contexts, despite the problems with spatial resolution for vector data. Both Sand L have dimensions of length, so their ratio is dimensionles
33、s. Dimensionless ratios often play a fundamental role in science (eg, the Reynolds number in hydrodynamics), so it is possible that L/S might play a fundamental role in geographic information science. In this section I examine some instances of the L/S ratio, and possible interpretations that provid
34、e support for this speculation.- Todays computing industry seems to have settled on a screen standard of order 1 megapel, or 1 million picture elements. The first PCs had much coarser resolutions (eg, the CGA standard of the early 198Os), but improvements in display technology led to a series of mor
35、e and more detailed standards. Today, however, there is little evidence of pressure to improve resolution further, and the industry seems to be content with an L/S ratio of order 103. Similar ratios characterize the current digital camera industry, although professional systems can be found with rat
36、ios as high as 4,000.- Remote sensing instruments use a range of spatial resolutions, from the 1 m of IKONOS to the 1 km of AVHRR. Because a complete coverage of the Earths surface at 1 m requires on the order of 1015 pixels, data are commonly handled in more manageable tiles, or approximately recta
37、ngular arrays of cells. For years, Landsat TM imagery has been tiled in arrays of approximately 3,000 cells x 3,000 cells, for an L/S ratio of 3,000.- The value of S for a paper map is determined by the technology of map-making, and techniques of symbolization, and a value of 0.5 mm is not atypical.
38、 A map sheet 1 m across thus achieves an L/S ratio of 2,000.- Finally, the human eyes S can be defined as the size of a retinal cell, and the typical eye has order 108 retinal cells, implying an L/S ratio of 10,000. Interestingly, then, the screen resolution that users find generally satisfactory co
39、rresponds approximately to the parameters of the human visual system; it is somewhat larger, but the computer screen typically fills only a part of the visual field.These examples suggest that L/S ratios of between 103 and 104 are found across a wide range of technologies and settings, including the
40、 human eye. Two alternative explanations immediately suggest themselves: the narrow range may be the result of technological and economic constraints, and thus may expand as technology advances and becomes cheaper; or it may be due to cognitive constraints, and thus is likely to persist despite tech
41、nological change.This tension between technological, economic, and cognitive constraints is well illustrated by the case of paper maps, which evolved under what from todays perspective were severe technological and economic constraints. For example, there are limits to the stability of paper and to
42、the kinds of markings that can be made by hand-held pens. The costs of printing drop dramatically with the number of copies printed, because of strong economies of scale in the printing process, so maps must satisfy many users to be economically feasible. Goodchild 2000has elaborated on these argume
43、nts. At the same time, maps serve cognitive purposes, and must be designed to convey information as effectively as possible. Any aspect of map design and production can thus be given two alternative interpretations: one, that it results from technological and economic constraints, and the other, tha
44、t it results from the satisfaction of cognitive objectives. If the former is true, then changes in technologymay lead to changes in design and production; but if the latter is true, changes in technology may have no impact.The persistent narrow range of L/S from paper maps to digital databases to th
45、e human eye suggests an interesting speculation: That cognitive, not technological or economic objectives, confine L/S to this range. From this perspective, L/S ratios of more than 104 have no additional cognitive value, while L/S ratios of less than 103 are perceived as too coarse for most purposes
46、. If this speculation is true, it leads to some useful and general conclusions about the design of geographic information handling systems. In the next section I illustrate this by examining the concept of Digital Earth. For simplicity, the discussion centers on the log to base 10 of the L/S ratio,
47、denoted by log L/S, and the speculation that its effective range is between 3 and 4.This speculation also suggests a simple explanation for the fact that scale is used to refer both to L and to S in environmental science, without hopelessly confusing the listener. At first sight it seems counterntui
48、tive that the same term should be used for two independent properties. But if the value of log L/S is effectively fixed, then spatial resolution and extent are strongly correlated: a coarse spatial resolution implies a large extent, and a detailed spatial resolution implies a small extent. If so, th
49、en the same term is able to satisfy both needs.THE VISION OF DIGITAL EARTHThe term Digital Earth was coined in 1992 by U.S. Vice President Al Gore Gore, 19921, but it was in a speech written for delivery in 1998 that Gore fully elaborated the concept (www.dgitalearth.govPl9980131 .html): “Imagine, for example, a young child going to a Digital Earth exhibit at a local museum. After donning a headmounted display, she sees Earth as it appears from space. Using a data glove, she zooms in, using higher and higher lev
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