Spatial Metadata and GIS for Decision Support

Transcription

1 Proceedings of the 29th Annual Hawaii International Conference on System Sciences - I996 Spatial Metadata and GIS for Decision Support David W. S. Wong Geography & Earth Systems Science George Mason University Fairfax, VA U.S.A. C. Victor Wu Department 0; Geography Sam ford University Birmingham, AL lj.s.a Abstract The proliferation of GZS technology has great& increased the access to and the usage of spatial data. Making maps is relatively easy even for those who do not have much cartographic training. Nonetheless, the concerns for spatial data quality among GZS and spatial data users have just began to sprout, partly because information about spatial data quality is not readily available or useful. Metadata, which refer to data describing data, include the quality and accuracy information of the data. The Federal Geographic Data Committee has proposed content standards of metadata for spatial databases. However, the standards are not adequate to document the spatial variation in data quality in geographic data. This paper argues that information about the quality of spatial data over a geographical area, which can be regarded as spatial metadata, should be derived and reported to help users of spatial data to make intelligent spatial decisions orpolicy formulations. While cartographers focus on the representation of spatial data qualily and statisticians emphasize the quantitative measures of data quality, this paperproposes that GZS are logical tools to assess certain types of error in spatial databases because GZS are widely used to gather, manipulate, analyze, and display spatial data. A framework is proposed to derive several vpes of data quality information using GZS. These fypes of quality information include positional accuracy, completeness, attribute accuracy and to some extent logical consistency. However, not eve y type of spatial metadata can be derived from GIS. Some of them have to be obtained by some exogenous processes. Regardless of the sources of spatial metadata, they should be stored as part of the spatial databases, and treated as decision aid to assist data users. The paper concludes with an example showing how spatial metadata can provide insight in identijling poor neighborhoods forfurtherpolicyfonnulation. Introduction Thanks to the advancements in Geographic Information Systems (GIS) technology and the recent development in telecommunication facilities, spatial databases have become easily accessible and the uses of spatial databases have greatly increased. Quite often, users of spatial data rely on GIS to store, manipulate, analyze, and display their spatial data Maps are the most common form of output from GIS to represent spatial data for a wide variety of purposes, including decision making and policy formulation. However, as Monmonier [l] points out, users of spatial data should concern the quality of data which in turn affects the confidence of decision or the success of policies. Thus the needs to document data quality emerge. Metadata are information about data, and spatial data include the cartographic data representing the spatial features and the attribute data describing the characteristics of the spatial features. The Federal Geographic Data Committee (FGDC) has proposed metadata standards for spatial data [2]. One aspect of the metadata standards is the inclusion of information about the accuracy of the spatial database. Descriptions and summary statistics about data accuracy are included in the current metadata standards, and are applied to the whole spatial database uniformly. However, the quality of data, in most instances, varies spatially. The positional accuracy of a spatial feature, or the accuracy of an attribute in one location is not the same as in another location. Thus in a spatial database, the quality measure of spatial data for an area may not be applicable to data describing other areas. The standards fail to take into account this nature of spatial data and are far from adequate to provide useful accuracy information for spatial data to data users. Spatial scientists and geographers do realize that the quality of spatial data varies from one location to the other, and they have been developing techniques and frameworks to visualize the quality of data through various cartographic means. However, /96 $ IEEE 557

2 most efforts either emphasize on the techniques of representing data quality information, or deriving data quality measures. Very few researchers investigate how to derive, assess, and represent data quality in and by GIS, the environment in which spatial data are captured, stored, analyzed, and represented. In this paper, we argue that some useful and important metadata for spatial database are spatial in nature, and thus, similar to any spatial data, they can be stored and manipulated by GIS, and displayed by spatial media such as map. Furthermore, some spatial metadata can be derived with the help of GIS. In the following section, we will point out the inadequacies of the current metadata standards for spatial data. We will also provide a brief description of the cartographic approach and the statistical approach to data quality. Then, we will identity some aspects of spatial data quality that can be derived using GIS. We will also demonstrate how the spatial information of data quality, which is the spatial metadata, can be crucial to facilitate spatial decisions. Are metadata for spatial data spatial? Metadata for spatial data can provide important information about spatial databases. One type of information should be included iu metadata is data quality. The spatial data quality report, which is included in the Spatial Data Transfer Standards (SDTS) [3], should at least consist of five portions covering lineage, positional accuracy, attribute accuracy, logical consistency, and completeness. The lineage portion describes the source of materials and methods of derivation used to create the digital databases. The history of the production process should also be included. The position accuracy portion reports the discrepancies between the locations of objects and features stored in the spatial databases and the real world locations. Attributes accuracy concerns the errors in describing the aspatial characteristics of spatial features. Logical consistency refers to the accuracy in the structure of encoding spatial features. Completeness concerns the spatial and subject matter coverage of the databases. Each of these aspects in spatial data quality is crucial to enable the correct use of spatial data, to help users decide if particular spatial database is appropriate for specific purposes, and to warn the users to what extent they should trust the data. The Federal Geographic Data Committee (FGDC) is in charge of coordinating the development of content standards for metadata for spatial data [2]. The standards have been and will be adopted by all federal agencies, most public agencies, and most private organizations disseminating spatial data. Figure 1 represents the major features of the standards of metadata for spatial data proposed by FGDC. Besides information about the organization of spatial databases, spatial referencing, and spatial entity and attribute, a very important component of metadata included in the FGDC standards is the quality of spatial data represented by the above five aspects outlined in SDTS [3]. Figure 1 also describes the proposed components to be included in the metadata standards for spatial data quality. Please note that besides attribute accuracy, logical consistency, completeness, positional accuracy, and lineage, cloud cover is also a component in the standards for data quality. However, since the amount of cloud cover is only applicable to remotely sensed data and aerial photos, but not applicable to other types of data, thus cloud cover is not a required component in the standards. It is true that some aspects of spatial data quality information, such as lineage, can be applied to the whole geographical database. However, the quality of data varies spatially due to problems in data collection (or capture), compilation, analysis, and representation. For instance, because cloud cover exists in a remotely sensed image, the data for certain areas covered by clouds in the database may be less accurate than the data describing other regions. Quite ohen, socioeconomic data are gathered by sampling and not all regions are sampled to the same extent. Thus sampling error is different from regions to regions. Some spatial data are derived from summary or statistical measures. Due to different degrees of generalization, these summary statistics may not have the same degree of accuracy over the region. Despite the fact that metadata standards proposed by FGDC define the details of spatial data quality, they fail to accommcdate the spatial variation of data quality, which is a very important aspect of spatial data quality. It is clear that positional accuracy, attribute accuracy, and logical consistency of spatial data may vary from one location to another in spatial databases. Even for completeness, the details of spatial coverage vary over different regions in geographical databases. But the metadata standards only allow one set of description for the whole database. Table 1 describes the components proposed for the standards for attribute accuracy. For instance, in section of the standards about Quantitative Attribute Accuracy Assessment, a value or an estimate will be assigned to summarize the accuracy of entities in the whole spatial database, and no measures documenting the spatial variation of data quality can be incorporated into the content standards. Because spatial data quality is not uniform over space, it is necessary to derive measures or schemes to document the spatial variation of data quality so that they can be treated as part of the metadata. 558

3 Table 1: Contents Standards for Spatial Metadata: Attribute Accuracy (adopted from FGDC, 1994) 2.1 Attribute Accuracy -- au assessment of the accuracy of the identification of entities and assignment of attribute values m the data set. Type:Compound Attribute Accuracy Report -- an explanation of the accuracy of the identification of the entities and assignments of values in the data set and a description of the tests used. Type: text Domain free text Quantitative Attribute Accuracy Assessment -- a value assigned to summarize the accuracy of the identification of the entities and assignments of values in the data set aud the identification of the test yielded the value. Type: compoulld Attribute Accuracy Value -- an estimate of the accuracy of the identification of the entities and assignments of attribute values in the data set. Type: text Domain: Unknown free text Attribute Accuracy Explanation -- the identification of the test that yielded the Attribute Accuracy Value Type: text Domaim free text I Metadata I Attribute Accuracy LOgiCal collsistency Completeness Positional Accuracy Lineage Cloud Cover Figure 1. Components of the Content Standards for Digital Geospatial Me&data. (Adopted from Susan Stitt (1994) Graphical Representation of the Federal Geographic Data Committee s Content Standards for Digital Geospatiall Metadata. Technology Transfer Center, National Biological Survey. 559

4 The need for spatial metadata A commonly adopted assumption in geographic information processing is that the source data are uniform in characteristics [4]. The uniformity notion can be expanded to include the uniformity in data quality. This may be the spirit adopted by the FGDC in specifying the metadata standards. On the other hand, it is well recognized that the quality of spatial data varies spatially, and it is also necessary to document the spatial variation in data quality [5]. Cartographers have devoted a great deal of effort to represent data quality through cartographic means, though many subareas await further investigations [6]. The focus of this theme of research is to develop framework symbology, and tools to represent the accuracy or the amount of error in spatial data. The results in this area are likely resulted in graphical techniques to represent uncertainty or the magnitude of error in data [7,8]. Emerging technologies such as animation, sonitication, video and new media for communication provide potentials for novel representations of data quality information [9, lo]. Recent research has extended to investigate how data quality can affect the outcomes of spatial decision making [ 111. On the contrary, spatial statisticians focus on identifying the source of error [ 121 in different stages of geographic information processing, on building procedures and models to document and quantify error, and on assessing the effect of error (error propagation) in statistical analysis [ 131. (For those who are interested in the statistical approach to spatial data quality, please refer to [ 141. However, this approach is withdrawn from the context of how spatial data are most commonly handled, manipulated, stored, displayed, and used. While statisticians and cartographers have both made valuable contributions to the research on spatial data quality, the research along these two tracks are ad hoc in nature. They describe or portray the error in spatial data with numbers or graphics, but are less concerned about the uses of data quality information. Data quality information should be reported to assist data users to use the database efficiently and appropriately, similar to software packages that are accompanied by manuals to assist users using the package properly. Data quality information is especially important to those who rely on spatial data to make decision or formulate policy. Therefore, Wu and Buttenfield [lo] point out that data quality information should be treated as a decision aid in data processing. In other words, many decisions in data processing should be made in reference to data quality information. There are two implications of the above statement. The first implication is that data quality information should be adequate to judge the fitness of the data for specific usage [ The second implication requires the data quality information to be thorough but to the point such that concerns for data quality will not severely interfere with the operation of spatial data processing. Given what we have argued above, it is natural and logical that spatial metadata report spatial variation of data quality. This type of information may greatly affect the analysis results in many instances. Furthermore, metadata should accompany spatial databases, so that the data quality information is always available in the course of spatial data processing. To accommodate these two notions, we propose the concept of spatial metadata in addition to metadata for spatial data. Despite the wording, the true distinction between these two concepts is that spatial metadata are spatial in nature - they vary by location. One should be able to derive some types of spatial metadata &om GIS operations and render spatial metadata with maps. On the other hand, metadata for spatial data may not be mappable. The standards proposed by FGDC are metadata standards for spatial data, but are not standards for spatial metadata. Most users of spatial data unlikely have access to sophisticated tools, or knowledge of error modeling in spatial data. It is also becoming more frequent that these data users are using GIS to store, manipulate, and display spatial data. Making the data quality information readily available is extremely important to these users. Since data quality information should be part of the metadata, the rest of this paper will focus on how spatial metadata, but not metadata for spatial data can be made available to data users by using GIS. Deriving data quality information in GIS In general, data quality information is not easy to obtain. NCDCDS [5] specifies the conditions under which tests should be performed to evaluate the quality of data. However, the NCDCDS document does rr ~f provide the details in performingthose tests and evaluations. It just states that some kind of tests or assessments are required. The fundamentals of data quality information are left to statisticians who have tried to keep track of error that may occur during the spatial data processing procedure. Griflith [ 121 discusses the sources of error in different stages of creating spatial data. Ma.%& Arno and Bitterlich [ 161 attempts to track the error involved in digitizing. There are existing models to capture the error involved in different stages of spatial data processing [17]. However, in many situations, GIS can help to evaluate the accuracy of spatial data. Positional accuracy Since GIS can incorporate spatial data from different sources, of different formats, and of different degrees of 560

5 accuracy, they provide ideal environments to assess the positional accuracy of spatial databases. GIS can also be very powerful tools to show data users the magnitude that the data deviate from more reliable data sources. For example, the Digital Line Graphs (DLG) and the Topologically Integrated Geographic Encoding and Referencing System (TIGER) are two popular digital databases disseminated by federal agencies concerning general cartographic features. To evaluate the accuracy of these two line databases, users can import the data into a GIS package using an aerial ortho photo, SPOT image or similar type of remotely sensed data of the same area as the background. Superimposing the three data sources can tell users which type of data is more accurate and reliable in certain areas. The positional discrepancies derived from overlaying diherent data sources vary among regions. Summarizing the discrepancies over the whole spatial database by a single measure will loose the spatial variation of data quality information. Discrepancies data over the area can be and should be stored in the line database, or in general the geographical feature database, as part of the spatial metadata information. Figure 2 is an illustration of this concept. The DLG and TIGER for a small section of Fairfax City, Virginia are imported and displayed in ArcView. A TIFF image generated from an aerial photo is put in the background. DLG provides more details and thus is more accurate than TIGER. However, the DLG is still far from accurate in terms of positional accuracy when compared with the image. Substantial positional discrepancies between the DLG and the image can be recognized in this small region. Conceptually, these discrepancies can be captured in terms of some statistics to reflect the discrepancies. These statistics can further be manipulated, stored, and also displayed together with the spatial data to reflect the positional accuracy of geographical features in the spatial database. Note that this type of positional accuracy information is not uniform for the whole database. The Fairfax City example that shows significant variation of data quality over the region (Figure 2) is the norm rather than the excepuon. Completeness and logical consistency Similar strategy can be used to evaluate the completeness of spatial databases. Using the DLG, TIGER, and aerial photo in Figure 2 as an example again, the DLG seems to have better coverage in certain sections than the TIGER. But in other areas, the situation is just the opposite. Definitely, the completeness of database is very much related to how recent the database has been updated. In general, TIGER is more recent that many DLG coverages, but still may not be as recent as many aerial photos. GIS can be used to compare different data sources and derive completeness information for spatial databases. Theoretically, when spatial databases are imported to GIS in which topological relationships are stored or extracted, ditterent data sources can be compared to derive data quality information about the logical consistency of spatial data. However, topological structure and relationship in geographical features are modeled and captured implicitly in most GIS. Some systems have particular features or functions that may assisthe evaluation or testing of logical consistency in the database. Since the process to assess logical consistency in GIS is relatively system-dependent, it is not feasible to derive a general framework to be implemented in GIS to derive logical consistency information. Attribute accuracy To assess attribute accuracy, the concept can be the same as assessing the data quality in aspects such as positional accuracy and completeness. Basically, in the GIS environment, we can compare the attribute data from different sources or different formats with prior knowledge about which data sources are more reliable. Comparing the database in question with the more reliable data sources can yield data quality information. However, the operation can be very different from the previous procedures, depending very much upon the source or nature of error in attributes. Wong and Wu [ 181 argue that one source of attribute data inaccuracy is due to the spatial aggregation process. Quite often, spatial decision and analysis rely upon spatially aggregated data, such as census tract data. When data are aggregated spatially, a smoothing or generalization process is underway. Therefore, the aggregated data retain less detailed information. Error is introduced during the generalization process. In general, highly aggregated data are less reliable than disaggregated data, and the magnitude of aggregation error varies geographically, sometimes in a significant manner. Thus, aggregation error can be regarded as spatial metadata. Wong and Wu [18] have proposed an approach to evaluate aggregation error primarily for vector format data in GIS. Several indices indicating spatial aggregation error. The approach basically compares data of different scales or resolutions. It is assumed that disaggregated data such as the block group data are more reliable that aggregated data such as census tract [ 19, 201. Thus discrepancies between the layer of census tract data and the layer of census block group data can reflect the aggregation error, and these statistics can be regarded as data quality information and be part of the spatial metadata. Wong and Wu [ 181 demonstrate that these statistics can be mapped to provide users information about the reliability of the data. 561

6 Their work is an example showing that spatial metadata can be derived in the GIS environment. Storing and displaying spatial metadata However, not all the spatial data quality information can be derived from GIS. In fact, most tests for spatial data quality are not supported by existing GIS functionality, and therefore need to be performed outside the GIS environment. Statisticians (for example, [12]) has identified various sources of error in spatial data attributes. One major source is sampling error, which is related to sampling size. Besides, the process through which spatial data are compiled is also error-prone. Various statistics capturing different types of error can be derived during the process of data processing. This type of data quality information can be and should be stored as part of the spatial databases [21, 221. If these data quality measures vary geographically, they should be treated as spatial metadata. For instance, the size of samples used to tabulate data can be documented during the data gathering process. US Census of Population and Housing Summary Tape File (STF) 3A includes two variables indicating what percentage of the population and housing units are being sampled in each census area1 unit to compile the STF 3A data. These sampling percentages vary significantly over the census area. In general, the data are more reliable if these percentages are high. Other data quality statistics for each individual area1 unit may also be compiled during the data gathering and processing steps. They should be stored in the database to serve as spatial metadata. There are many variables in the census population and housing database. The sampling statistics reported in STF 3A can be applied to all census variables to indicate the quality of data in respecto sampling issue. However, there are other sources of error affecting data quality, and these sources of error may not be applied uniformly to all census variables or all attributes of a spatial database. In other words, within a spatial database, the quality of data may varies among different attributes recorded by the database. Reliability statistics or data quality measures for each variables can be derived too. Examples are the aggregation error measures proposed by Wong and Wu [18]. These measures can be calculated for many census variables for each areal unit reported in census. Thus, each variable in a spatial database can have a quality measure attached to it. Because the positional accuracy of geographical features varies across space, therefore conceptually, we can measure the positional error of each geographical feature and store that information in the database as an additional attribute of the feature. However, practically, it may not be feasible or necessary to attach a quality measure to each geographical feature, such as each line segment or each point location, in a spatial database. A more reasonable strategy is to evaluate a specific feature type for different regions rather than for each location. This regional approach to document data quality measures can also be applied to record logical consistency and completeness information. Given today s computational technology and advancement, some data quality measures can be derived in GIS in real time theoretically. Practically, the bottleneck is to develop efficient procedures in GIS that can calculate data quality measures by comparing data from different sources and di&rent formats. This is unfortunately a less recognized area in GIS, and has not been developed sufficiently. On the other hand, many statistics about spatial data quality are derived exogenously, such as the percentages being sampled in the census STF 3A. These statistics are kept inthe spatial database as additional feature attributes or as additional elements to describe the geographical characteristics of the spatial features, the size of the spatial databases will grow significantly. It is true that the cost for massive data storage is falling everyday. The problem falls on the ability of the general users in dealing with huge databases, and in identifying pertinent information in huge spatial databases. A related technical and operational issue is how to store and organize the spatial database efficiently to include the spatial metadata information. This issue cannot be addressed thoroughly here given the length and focus of this paper. The most common purpose of using GIS is probably for map generation. In the context of metadata, GIS can be very useful to display spatial metadata. Cartographers have indepth discussions on using cartographic tools and skills to display and visualize spatial data quality information. As long as the spatial metadata are either stored as part of the spatial database or derived in the GIS environment, GIS can use various means to display data quality information [6]. It is not necessary to discuss all the cartographic details here, though new tools and techniques are developing for visualizing data quality. Spatial data quality, decision making and policy analysis Recent research has indicated how the display of data of different quality has impacts on decision making [l 11. However, the displays do not show the data quality information but data of different quality levels. In the following section, we will use an example to demonstrate how spatial metadata can be very uselul and important to make spatial decisions and policy. 562

7 Many studies try to identity poverty areas so that public and social policies can be targeted toward these areas. Sometimes, these areas are known as the underclass regions [23,24] in which residents are suffered from persistent adverse socioeconomic conditions. VeIy often, socioeconomic variables in census data are used to identify such regions in a metropolitan area. Just like most socioeconomic studies, the underclass study treats census data as reliable facts rather than information with certain degree of error or inaccuracy. Thus the underclass areas discovered using census data may not be the real adverse areas. Figure 3 shows two maps. The one on the right shows the per capita income ($) of Washington, DC, reported from 1990 Census of Population and Housing [25]. The categories are defined by quantiles. The northwest (NW) quadrant of DC is generally regarded as the more aflluent area, and this map verities this general impression. However, at the lower middle section of the NW quadrant, a census tract has extremely low per capita income. Most analyses may come to a conclusion that this census tract is the problem area and needs help, while all neighboring census tracts are in relatively good condition. However, if the analyst is given spatial metadata, such as the map on the left (in Figure 3), which shows the percent of population sampled, the analyst may be skeptical about the information of the very low per capita income in that so-called problem tract in NW and the very high per capita income in the rest of NW census tracts. Because the percentages of population sampled during the census are so low in the problem tract (10% or lower versus 20% in some areas), the per capita income data may not be that reliable. The low income tract may have a per capita income not as low as the map shows, while the neighboring affluent tracts in NW, especially those with low percentage sampled, may not be as rich as they look on the map. For decision or policy makers concerning the poverty issue, they should also include data quality information to identify areas that need assistance. Percentage sampled is in fact spatial metadata, and the map is an example how spatial metadata can be presented like other spatial data. Conclusion Currently, GIS have been used primarily to make maps based upon data stored in the systems. Very often, these maps are used in the spatial decision and policy making processes, with very little concern about the quality of (data deriving) the information. Metadata describe different aspects of data, including the quality of data. Metadata for spatial data are supposed to be helpful to evaluate the reliability and usefulness of spatial data. But the metadata content standards proposed by FGDC cannot capture the spatial variation of spatial data, and there is a need to develop metadata to reflect this spatial dimension of data quality. This paper argues that in addition to metadata for spatial data, it is necessary to develop spatial metadata, which can reflect the geographical differences in data quality. Some of these spatial data quality statistics can only be derived during the spatial data processing procedure, and they should be stored in the spatial databases. When these databases are manipulated in GIS, the data quality information will be available to data users. Since GIS can incorporate different sources of spatial data of various quality levels, this paper proposes different methods that can be used in GIS to compare data of different levels of accuracy to derive quality information in different aspects. Further, because spatial metadata are spatial in nature, GIS are logically the ideal tools to display spatial metadata along with other spatial data to assist spatial decision making and policy formulation. Though the examples used in this paper are relatively simplistic, they are primarily for illustrative purpose. The ideas in this paper can be developed further to be applied to more complicated situations. There are still many problems in deriving and displaying spatial metadata [21]. These problems include the storage issue, the structure of spatial database, and the dynamic query of spatial data quality information. However, to facilitate the generating and reporting of spatial metadata, we should develop capabilities in GIS to assess the magnitude of spatial data error of various types to facilitate data users and GIS users to determine ifthe data are appropriate and trustworthy. References [l] Monmonier, M. (1993) Exploring the Quality of Enumeration-Area Data with Graphic Scripts Cartographica 30(2): [2] Federal Geographic Data Committee (1994) Content Standardsfor Digital Geospatial Metadata, FGDC. [3] NIST (National Institute of Standards and Technology) (1992) Federal Information Processing Standards. Publication I73 (Spatial Data Transfer Standard).Washington,D.C.:U.S. Department of Commerce. [4] Burrough, P.A. (1986) Principles of Geographical Information Systems for Land Resources Assessment. Oxford: Clarendon Press. [5] NCDCDS (National Committee for Digital Cartographic Data Standards) (1988) Digital Cartographic Data Quality The American Cartographer 15(l):

8 [6] Buttenfield, B. P. (1991) Visualizing Cartographic Metadata. NCGIA Research Initiative 7: Visualization of Spatial Data Quality, Scientific Report for the Specialist Meeting 8-12 June 1991, Castine, Maine. NCGIA Technical Paper 91-26, Santa Barbara:UCSB, pp.cl7 - ~26. [7] Beard, M. K., B. P. Buttenfield, and S. B. Clapham (1991) NCGIA Research Initiative 7: Visualization of Spatial Data Quality, Scientific Report for the Specialist Meeting 8-12 June 1991, Castine, Maine. NCGIA Technical Paper 91-26, Santa Barbara: UCSB. [8] McGranaghan, M. (1993) A Cartographic View of Spatial Data Quality. Cartographica, 30(2): [9] Fisher, P. F. (1993) Visualizing Uncertainty in Soil Maps by Animation, Cartographica 30(2): [lo] Wu, C.V., and Buttentield, B. P., 1994, Spatial Data Quality and its Evaluation, Computer, Environment, and Urban Systems, 18(3). [ 1 l] Leitner, M. (1995) The Visualization of Data Quality in Cartographic Displays and its Impact on Decision Making - A Test Design Paper presented at the 1995 Annual Meeting of the Association of American Geographers, Chicago, IL. [12] Griffith, D. A. (1991) Data Quality and Visualization: A Position Paper. NCGIA Research Initiative 7: Visualization of Spatial Data Quality, Scientific Report for the Specialist Meeting 8-12 June 1991, Castine, Maine. NCGIA Technical Paper 91-26, Santa Barbara: UCSB, pp.c77 - ~84. [13] Heuvelink, G. and P. Burrough (1989) Propagation of Errors in Spatial Modelling with GIS, International Joumalfor Geographical Information Systems 3: [ 141 Veregin, H., 1989, A Taxonomy of Error in Spatial Databases, NCGIA Technical Paper 89-12, UCSB, Santa Barbara. [ 151 Chrisman, N.R. (1986) Obtaining Quality Information of Digital Data, Proceedings, Auto- Carto-I, Volume 1. London, U.K. [ 161 M&ni, G., Amo, M. and W. Bitterlich (1989) Observations and Comments on the Generation and Treatment of Error in Digital GIS Data, in M. F. Goodchild and S. Gopal (ed) Accuracy of Spatial Databases. London Taylor and Francis, [17] Goodchild, M. F. and S. Gopal (1989) Accuracy of Spatial Databases. London: Taylor and Francis [18] Wong, D.W.S. and C.V. Wu (1995) Qualityof Aggregated Spatial Data - a Guidance for Decision, Proceedings, Fourth International Conference on Computers in Urban Planning and Urban Management, July l l-14,1995, Melbourne, Australia. [19] Fotheringham,A. S. andd. W. S. Wong(1991) The Modifiable Areal Unit Problem in Multivariate Statistical Analysis, Environment and Planning A 23, Openshaw, S. (1984) The Modijable Area1 Unit Problem. Concepts and Techniques in Modem Geography, Number 38., Geo Books, Norwich. [21] Guptill, S. C. (1989) Inclusion of Accuracy Data in a Feature Based, Object-Oriented Data Model, in M. F. Goodchild and S. Gopal (ed) Accuracy of Spatial Databases. London: Taylor and Francis, [22] Maki, R. J. (1991) Storing Data Reliability Information within the Digital Chart of the World Database. NCGIA Research Initiative 7: Visualization of Spatial Data Quality, Scientific Report for the Specialist Meeting 8-12 June 199 1, Castine, Maine. NCGIA Technical Paper 91-26, Santa Barbara: UCSB, pp.cll5 - ~123. [23] Hughes, M.A. (1989) Misspeaking Truth to Power: A Geographical Perspective on the Underclass Fallacy Economic Geography 65(3): [24] Hughes, M.A.(1990) Formation of the Impacted Ghetto: Evidence from Large Metropolitan Areas, 1970-l 980 Urban Geography 11(3): [25] Bureau ofthe Census (1991) 1990 Census of Population and Housing: Summay Tape File 3 on CD-ROM. Washington: The Bureau. 564

9 Figure 2: Comparson of TIGER, DLG, and Image (part of Fairfax City, VA) 565

10 Figure 3. Maps of Percent Population Sampled (left) and Per Capita Income (right), Washington, D.C. 566