Dent-Chap11 - Fifth Edition CARTOGRAPHY Thematic Map Design...

Info iconThis preview shows pages 1–15. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 2
Background image of page 3

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 4
Background image of page 5

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 6
Background image of page 7

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 8
Background image of page 9

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 10
Background image of page 11

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 12
Background image of page 13

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Background image of page 14
Background image of page 15
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Fifth Edition CARTOGRAPHY Thematic Map Design Borden D. Dent Georgia State University gr: w WCB _ Ifl McGraw-HIII Boston Burr Ridge, IL Dubuque, IA Madison, WI New York San Francisco St. Louis Bangkok Bogota Caracas Lisbon London Madrid Mexico City Milan New Delhi Seoul Singapore Sydney Taipei Toronto Erwin Rois: called cartograms “diagrammatic maps." Today they may be called cartograms, value-by-area maps, anamorphated images, or simply spatial trans- formations. Whatever name one uses, cartograms are unique representations of geographical space. Exam— ined more closely, the value-by—area mapping tech- nique encodes the mapped data in a simple and effi- cient manner with no data generalization or loss of detail. Two forms, contiguous and noncontiguous, have become popular: Mapping requirements include the preservation of shape, orientation, contiguitv, and data that have suitable variation. Successful commu- nication depends on how well the map reader recog- nizes the shapes of the internal enun‘ieration units, the accuracy of estimating these areas, and (fleetive leg- end design. Complex forms include the two-variable map. Cartogram construction may be by manual or computer means. In either method, a careful examina— tion of the logic behind the use of the cartogram must first be undertaken. 208 PART ll Techniques of Quantitative Thematic Mapping We are accustomed to looking at maps on which the politi~ cal or enumeration units (e.g., states, counties, or census tracts) have been drawn proportional to their geographic size. Thus, for example, Texas appears larger than Rhode Island, Colorado larger than Massachusetts, and so on. The areas on the map are proportional to the geographic areas of the political units. (Only on non-equal—area projections are these relationships violated.) It is quite possible, however, to prepare maps on which the areas of the political units have been drawn so that they are proportional to some space other than the geographical. For example, the areas on the map that represent states can be constructed propor- tional to their population, aggregate income. or retail sales volume, rather than their geographic size. Maps on which these different presentations appear have been called cur- lograms, value-by-area maps, anamorphated images,‘ and spatial trunsfonmtrians. This chapter introduces this unique forrn of map. In these abstractions from geographic reality. ordinary geo- graphic area. orientation, and contiguin relationships are lost. The reader is forced to look at a twisted and distorted image that only vaguely resembles the geographic map. Yet cartograms are being used more and more by professional geographers to uncover underlying rrtathematical relations. general models. and other revealing structures} Cartogra— phers likewise use them for comrtrunicalion of these ideas. 'I‘heir evcntrral srrccess as a corrrrrrunicatiorr device rests on the ability of the map reader to restructure them back into a recognizable form. Regardless of these complexities. car— tograms are popular. Their appeal no doubt results from their attention—getting attributes. Gridlock Relative Trattic Congestion Based on Vehicle—Miles of Travel per Road Mile State areas are proportional to yearly mileage THE VALUE'BY-AREA CARTOGRAM DEFINED All value-by-area maps, or cartograms, are drawn so that the areas of the intemal enumeration units are proportional to the data they represent. (See Figures 1l.l and 11.2.) This method of encoding geographic data is unique in thematic mapping. In other thematic forms, data are mapped by se- lecting a symbol (area shading or proportional symbol, for example) and placing it in or on enumeration units. In the area cartogram, the actual enumeration unit and its size carry the information. ' Value—by-area cartograms can be used to map a variety of data. Raw or derived data, at ratio or interval scales, cen- sus data, or specially gathered data can be mapped in a car- togram. Because of the method of encoding, there is no data generalization. No data are lost through classification and consequent simplification. In terms of data encoding, the value-by—area cartogram is perhaps one of the purest forms of quantitative map, because no categorization is necessary during its preparation. Unfortunately, data retrieval is fraught with complexity, and readers may experience con- fusion because the base map has been highly generalized. 13R] FF HIS'I‘ORY Of- TH 1% METHOD As with so many other techniques in thematic mapping. it is difficult to pinpoint the beginning of the use of value— by—area maps. An early version was apparently used by Levasseur in his textbooks in both 1868 and 1875. To quote Funkhouser: Figure 11.1 Typical value—by— area cartogram. (Cartogram designed by Bernard J. vrtrtHamoml. Used by permission.) Vehicle-miles of travel per mile of road ( x 1000) _l"t 1,680 560 140 For example, Wyoming had 5.4 billion vehicle-miles driven in 1986. over 38.900 road and street miles. This yields 138.8 vehicle-miles driven per road mile. Source at data United States Bureau ol the Census, Statistical Abstract of the United States. t987 Washington D.C USGPO 1986 data a measure of tratlic congestion. ; ," ru’ajw M ss';’...,;.;\...- zi -' ‘ Note: NV, with an estimated concert attendance at over 600,000, ls excluded because at space imitations. .‘J ‘— tam; Elvis Concerts Attendance per State, 1970 — 1977 Source: Stanley, Davld E.,wlth Frank Cottey. The Elvis Encyclopedia. Santa Monlca, 0A.: General Publlshing Group, Inc , 1994. W These include colored bar graphs showing the number of inhabitants per square kilometer of the countries of Eu- rope, the school population per hundred inhabitants. the number ot'kilometers of railroad per hundred square kilo— meter of territory, em; squares proportional to the extent of surfaces, population, budget, commerce, merchant ma- rine of the countries of Europe, the squares being grouped about each other in such a manner as to correspond to their geographical position. (Author‘s emphasis)3 Although not called a value-by—area cartogram by Lev- asseur, the appearance of the actual graph seems to support the idea that it was indeed such a cartogram. Others have traced the idea of the cartogram to both France and Ger- many in the late nineteenth and early twentieth centuries re- spectively.4 Erwin Raisz was certainly among the first American cartographers to employ the idea; he wrote on the subject 50 years ago.5 Cartogram construction techniques were treated by Raisz through several editions of his text- book on cartography.6 In 1963, Waldo Tobler discussed their theoretical underpinnings, most notably their projec- tion system, and concluded that they are maps based on un- known projections.7 Cartograms have been used in texts and in the classroom to illustrate geographical concepts; their role in communication situations has been investigated.8 Since their introduction, cartograms have been used in atlases and general reference books to illustrate geographi- cal facts and concepts,9 but no book has been devoted en- tirely to these interesting maps. This chapter treats area cartograms only. Linear trans— formations (such as in Figure 1.8 in Chapter 1) are also possible, but are not discussed here. @ 1995 Andrew Dent and Linda Tumbull C HA PTE R 11 The Cartogram: Value-By-Area Mapping 209 Figure 11.2 Elvis concerts attendance per state, 1970—77. A contiguous value-by-area cartogram showing unique data. This map reveals that unique and rarely mapped data can be the subject of cartogram mapping and can attract unusual attention. (Map compiled by Andrew Dent and Linda Tumbull, Georgia State University. Used by permission.) Attendance per state 10,000 —- Note: DE, Dc, ID, MT. NH, ND, VT, WY, AK = 0 NJ data are unavailable. TWO BASIC FORMS EMERGE Two basic forms of the value-by-area cartogram have emerged: contiguous and noncontiguous. (See Figure 11.3.) Each has its own set of advantages and disadvantages, which the designer must weigh in the context of the map’s purpose. Contiguous Cartograms In contiguous cartograms, the internal enumeration units are adjacent to each other. Although no definitive research exists to support this position, it appears likely that the con— tiguous form best suggests a true (i.e., conventional) map. With contiguity preserved, the reader can more easily make the inference to continuous geographical space, even though the relationships on the map may be erroneous. Making the cartogram contiguous, however, can make the map more complex to produce and interpret, for both man— ual and computer solutions. Several advantages may be listed for the contiguous form: 1. Boundary and orientation relationships can be maintained, strengthening the link between the cartogram and true geographical space. 2. The reader need not mentally supply missing areas to complete the total form or outline of the map. ' 3. The shape of the total study area is more easily preserved. The disadvantages of the contiguous form include: 1. Distortion of boundary and orientation relationships can be so great that the link with true geographical space becomes remote and may confuse the reader. 210 PART II Techniques of Quantitative Thematic Mapping Figure 11.3 Contiguous and noncontiguous cartograms. Contiguous cartograms like (a) are compact, and boundary relations are attempted. In noncontiguous cartograms, such as (b), enumeration units are separated and positioned to maintain relatively accurate geographic location. 2. The shapes of the internal enumeration units may be so distorted as to make recognition almost impossible. Noncontiguous Cartograms The noncontiguous cartogram does not preserve boundary relations among the internal enumeration units. The enu- meration units are placed in more or less correct locations relative to their neighbors. with gaps between them. Such cartograms cannot convey continuous geographical space and thus require the reader to infer the contiguity feature. There are nonetheless certain advantages in using non- contiguous cartograms: 1. They are easy to scale and construct. 2. The true geographical shapes of the enumeration units can be preserved. 3. Areas lacking mapped quantities (gaps) can be used to compare with the mapped units, for quick visual assessment of the total distribution.10 The disadvantages of the noncontiguous cartogram include: 1. They do not convey the continuous nature of geographical space. 2. They do not possess an overall compact form, and it is difficult to maintain the shape of the entire study area. MAPPING REOLJIREMENTS Communication with cartograms is difficult at best, be— cause it requires the reader be familiar with the geographic relations of the mapped space: the total form of the study area as well as the shapes of the internal enumeration units. This task may not be too difficult for students in the United States when the mapped area is their homeland and the in- ternal units are states, but how many students in this coun— try are familiar with the shapes of the Mexican states or those of the African nations? Likewise. are European stu- dents that knowledgeable about the shapes of the Canadian provinces or the states of the United States? On the other hand. by the very fact that they are unfamiliar with the mapped areas, map readers may pay more attention to the map than they otherwise would. The situation can even be complex when mapping close to home. How many Tennessee residents know or could recognize the shapes of the counties in Tennessee? Georgia has 159 counties, Texas more than 200. Fortunately, most professional cartographers realize the futility of mapping little-known places with cartograms. Cartograms can present a unique view of geographical space. Raisz stated many years ago that cartograms “may serve to right common misconceptions held by even well— informed people.”ll Harris and McDowell have suggested that the value-by—area map is a good way to teach about ge- ographical distributions.” Tentative evidence indicates that map readers can obtain information from value-by-area maps as effectively as from more conventional forms. For this to happen, however, certain qualities of the true geo- graphic base map must be preserved during transformation. The first of these is the shape quality. Preservation of the general shape of the enumeration units is so crucial to com- munication that the cartogram form should not be used un— less some approximation of true shape can be achieved. Conventional thematic maps are developed by placing graphic symbols on a geographic base map. Regardless of the form of the thematic presentation, the symbols are tied to the geographical unit with which the data are associated. Thus, for example, graduated symbols are placed at the cen— ters of the states. Value-by-area maps, however, are unique in that the thematic symbolization also forms the base map. In a way, the enumeration units are their own graduated symbols, in addition to carrying the information of the “fin—f conventional base map. On an original geographic base map of, for example, the United States, each state contains four kinds of information—size, shape, orientation, and contiguity. (See Figure‘ll.4.) In value—by—area mapping, only size is transformed; the other elements are preserved as nearly as possible. Contiguity is somewhat special and may not be as important as the others in map reading. Individual unit shapes on the cartogram must be similar to their geographical shapes. It is through shape that the reader identifies areas on the cartogram. Shape is a bridge that allows the reader to perceive the transformation of the original. (See Figure 11.5.) If the reader cannot recognize shape, confusion results and comprehension is difficult, if Original Geo raphical pace Operation Size (area) -—> Transformed ~r---——-———v ——> > Preserved — ~-— > Shape — ——i 4—) Transformed (Preservation attempted) - > Orientation > Preserved > Preserved Contiguity [ -> Transformed Overall shape approximated »' through generalization l Transformation Original geographical Visual cues C HAPTE R 11 The Cartogram: Value—By-Area Mapping 211 not lost altogether. The designer’s problem is deciding how far it is possible to go along a continuum between shape preservationand shape transformation before the enumera- tion unit becomes unrecognizable to the majority of readers. Geographical orientation is another important element in value-by—area mapping. Orientation is the internal arrangement of the enumeration units within the trans- formed space. Because the reader must be familiar with the geographic map of the study area to interpret a cartogram properly, the cartographer must strive to maintain recogniz— able orientation. When distortion of internal order occurs, communication surely suffers. How frustrating it would be to see Michigan below Texas! Figure 11.4 Ideal cartographic operations in value-by-area mapping. Cartogram Both contiguous and noncontiguous Noncontiguous Contiguous Both contiguous and noncontiguous Noncontiguous Figure 11.5 The importance of shape in cartogram design. Shape preservation provides necessary visual cues for efficient reader recognition of original spatial units. Reader recognition of units Transformation Accurate shape not attempted No visual cues — 212 PART II Techniques of Quantitative Thematic Mapping Contiguity as an element in cartogram development re- lates, of course, only to the contiguous form. When produc- ing this kind, it is desirable to maintain as closely as possi- ble the original boundary arrangement from true geographical space. Of the elements mentioned thus far— shape, order, and contiguity—it appears that contiguity is the least important in terms of communication. It is likely that map readers do not use understanding of geographic boundary arrangements in reading cartograms. How many of us, for example, know how much of Arkansas is adjacent to Texas? On noncontiguous varieties, of course, contiguity per se cannot be preserved. It is possible, however, to main- tain loose contiguity by proper positioning of the units, al- though gaps remain between the units. Of the qualities mentioned (shape, order, and contiguity), shape is by far the most important. Use the value~by~area cartogram technique only where the reader is familiar with the shapes of the internal enumeration units. Do not overesti— mate the ability of the reader in this regard. Well—designed legends can be helpful, as discussed later in this chapter. Data Limitations Although value-by-area maps present numerous possibili— ties for the communication of thematic data, they are not without their limitations. Within the three principal ways of symbolizing data for thematic maps—point. line. and area——cartograms fall most comfortably into the category of area. Area is the element that must vary within the car— togram. so there are obvious limits outside of which one should not attempt this kind of representation. The limits are dictated by the data and their variability. It would be fruitless to map data that are exactly proportional to the areas of the enumeration units of the geographic base. (See Figure 11.0.) The cartogram would then replicate the origi- nal. At the other extreme, there could be a single enumera— tion unit having the same area as the entire “transformed” space, in which case no internal variation would be shown. No cartogram (or any other map) would be needed. Within these general limits, there exists a range of possibilities. The chief goal of the cartogram is to illustrate a thematic distribution in dramatic fashion, which requires that the data be compatible with the map‘s overall purpose. The data set should be compared to the enumeration units on the geo- graphical base. If reversal is evident (large states having small numerical value or vice versa), the cartogram is likely to be worthy of execution. Two measures, the linear regression and rank-order correlation indices, provide a degree of quantita- tive support. Unfortunately, these methods fall short in that they provide only overall indices of association; they do not indicate variation or agreement between data pairs within the total set. A statistical regression analysis may prove useful, but arbitrary limits must still be selected. More infomial ways of determining appropriateness are easily workable. Whatever procedure is chosen to determine the appro- priateness of a data set for cartogram construction, such a determination should always be made before such a map is ORIGINAL GEOGRAPHICAL SPACE Appropriate appropriate appropriate Figure 11.6 Data limitations and value—by-area mapping. If the original data lead to spatial transformation that is unchanged from the original (as on the left), the value—by-area tecluriquc is inappropriate. Also inappropriate would be those cases resulting in only one enumeration unit remaining after transformation (as in the center). Most suitable would be those instances when original data are transformed into new spatial arrangements dramatically different from the original (as on the right). begun. Those not familiar with such maps often launch into a construction, only to find the results rather disappointing. If the map does not illustrate the distribution in a visually dramatic way, it is best abandoned. COMMUNICATING WITH CARTOG RAMS Success in transmitting information by the value-by-area technique is not guaranteed. There are at least three prob— lem areas: shape recognition, estimation of area magnitude, and the stored images of the map reader. The designer should be familiar with the influences of each on the com— munication task. RECOGNIZING SHAPES It is by the shape of objects around us that we recognize them. We often identify three-dimensional objects by their silhouettes, and we can label objects drawn on a piece of paper by the shapes of their outlines. This holds true for recognition of outlines on maps. For example, South America can be seen as distinct from the other con- tinents. The shape qualities of objects that make them more recognizable are simplicity, angularity, and regular- ity.13 Simple geometric forms such as squares, circles, and triangles are easily identified. Shapes to which we can at— tach meaning are also easy to identify. In the production of value—by«area maps, the cartogra- pher ordinarily attempts to preserve the shapes of the enu— meration units. How this is done is crucial to the effective— ness of the map. Many of the elements that identify the shape of the original should be carried over to the new gen- eralized shape on the cartogram. The places along an out- line where direction changes rapidly appear to be those that carry the most information about the form’s shape.l4 There- fore, such points on the outline should be preserved in mak— ing the new map. These points can be joined by straight lines without doing harm to the generalization or to the reader’s ability to recognize the shape. (See Figure 11.7.) Figure 11.7 Straight-line generalization of the original shape. Important shape cues are concentrated at points of major change in direction along the outline, as indicated here in the upper drawing. These points should be retained in transformation as a guide in the development of a reasonable straight-line generalization to approximate the original shape. as done here in the lower drawing. CHAPTE R 11 The Cartogram: Value-By-Area Mapping 213 L ESTIMATING AREAS Because each enumeration unit in a cartogram is scaled di- rectly to the data it represents, no loss of information has occurred through classification or simplification. If any error results, it is to be found somewhere else in the com- munication process—most likely in the reader’s inability to judge area accurately. The psychophysical estimation of area magnitudes is influenced by the shapes of the repre— sentative areas used in the map legend. Research suggests that for effective communication of area magnitudes, the shapes of the enumeration units should be irregular polygons (not amorphous shapes) and that at least one square legend symbol should be used at the lower end of the data range.15 It is best to provide three squares in the legend, one at the low end, one at the middle, and one at the high end of the data range. Of course, the overall communication effort may fail because the distor- tions from true shapes brought about by the method can in- terfere with the flow of information. A COMMUNICATION MODEL It has been stressed thus far that couununicating geographic inl’orn‘iation with cartograms is difficult unless certain rules are followed. First. shape—recognition clues along the out- line of enumeration units must be maintained. Second, if the cartographer cannot assume that the reader knows the true geographical relationships of the mapped area, a geo- graphic inset map must be included. Third. the cartographer should provide a well-designed legend that includes a rep— resentative area at the low end of the value range. These three design elements are placed in a generalized communication model of a value-by-area cartogram in Fig- ure 11.8.16 In this View, design strategies should accommo~ date the map—reading abilities of the reader. In Step 1, all the graphic components are organized into a meaningful hi- erarchical organization so that the map’s purpose is clear. Accurate shapes of the enumeration units are provided in Step 2 by retaining those outline clues that carry the most information—4m places where the outline changes di- rection rapidly. In the United States, people are exposed from early child- hood to maps of the country through classroom wall maps, road maps, television. and advertising. Recently, satellite pho— tographs have added to the already clear images of the coun— try‘s shape in the minds of the population. How well these images are formed vaiies from individual to individual. Some people have well-formed images not only of the shape of the United States, but also of the individual states; others have difficulty choosing the correct outline from several possible ones. Successful cartogram communication may well rest on the accuracy of the reader’s image of geographical space. Without a correct image, the reader cannot make the neces- sary match between cartogram space and geographical space. Confusion results if this connection is not made quickly. 214 PART l l Techniques of Quantitative Thematic Mapping HEADER TASKS Understand map purpose. step 1 Recognize statistical units. Step 2 CARTOGRAPHER TASKS Provide total map organization to suit purpose. Provide shapes with meaningful cues from original geographical shapes. Figure 11.8 Cartographer and reader tasks in a generalized value-by-area cartogram communication model. Many of the steps are likely to occur simultaneously, not sequentially—especially Steps 2 through 5. (Source: Borden D. Dent, “Communication Aspects of Value-by-Area Cartogramr, "American Cartographer 2 [l975]:154—68.) Use mental map of mapped Provide an inset map of Use statistical areas with straight-line segments. Provide a legend containing at least an anchor stimulus in the low end of the value Use other cartographic language elements efficiently. Provide labelinr , explanatory statements, other geographical cues. Step 3 geographical base to area‘ augment mental map. Make magnitude estimation of statistical areas. Step 4 range. Compare mental map of geographical area and Step 5 cartog ram. “ LI? M“— Respond to cartogram message. Step 6 In Step 3, the readers search through the represented ge— ographic areas in an attempt to match what they see with their stored images.” Because the reader’s stored images may be inaccurate, the designer should include a geo— graphic map of the cartogram area in an inset map. The map reader in Step 4 estimates the magnitudes of the enumeration units by comparing them with those pre— sented in the legend. Effective legend design makes this task easier. Anchor stimuli in the legend should be squares, including at least one at the low end of the value range. In Step 5. written elements, strch as labels and explana— tor‘y notes, are included to assist the map reader in identifying parts of the map that may be unfamiliar at fast. Finally, the designer should be willing to restructure the message to make the communication process better (Step 6). Inasmuch as the cartographer may not know what the reader thinks, because the cartagrapher and reader are usually separated in time and space, the first five tasks become even more important. Advantages and Disadvantages Unfortunately, cartograms have not been studied in enough detail to reveal exactly what impresses map readers about them or exactly how they are read. Preference—testing research has discovered that cartograms do communicate spa— tial information, are innovative and interesting, display re- Be willing to restructure message to effect desired response. r‘narkable style, and present a generalized picture of reality. Value-by-area maps are often stimulating, provoke consider— able thought, and show geographical distributions in a way that stresses important aspects. On the other hand, they are viewed as difficult to read, incomplete, unusual, and different from reader’s preconceptions of geographical space. Probably the most serious drawback is that no established methodology leads to consistent results. No two people devise identical car- tograms of the same area. (This may be considered a strength rather than a drawback.) For the unnamed map reader, the new configurations can cause visual confusion, detracting from the purpose of the map rather than adding to it. lhe advantages of this thematic mapping technique . . .13 are. l. T o shock the reader with unexpected spatial peculiarities. 2. To develop clarity in a map that might otherwise be cluttered with unnecessary detail. 3. To show distributions that would, if mapped by conventional means, be obscured by wide variations in the sizes of the enumeration areas. Disadvantages include: 1. Some map readers may feel repugnance at the “inaccurate” base map that results from the study. a «35-1 .2, a . Sui k m 2. Map readers may be confused by the logic of the method unless its properties are clearly identified. 3. Specific locations may be difficult to identify because of shape distortion of the enumeration areas. TWO-VARIAB LE CARTOG RAMS The discussion thus far has concerned only the use of a sin— gle data set (variable), but it is possible to illustrate two or more data sets on a single cartogram. For example, on a cartogram of the United States in which the states are repre— sented proportional to their populations, the cartographer can render individual states by gray tones, as on a choro- pleth map. The state areas may be represented as belonging to classes in another distribution. (See Figures 11.9 and 11.10.) This appears to be a very compatible representation of two distributions, as both relate to area. A choropleth map presupposes an even distribution throughout each enu- meration unit, as does a cartogram. This form of two-vari- able value-by-area cartogram has been used successfully in mapping the spatial variation of socioeconomic data in Australian cities. ‘9 ()ther second variables can be accommodated on car- tograms by graduated point-symbol schemes. The second distribution can be represented by placing a graduated sym~ bol within each enumeration unit of the cartogram. The reader must make the visual-intellectual comparison between the size of the enumeration unit and the size of the scaled symbol. This may be difficult for some readers at first. Al- though little research has been done on either method, it CHAPTER 11 The Cartogram: Value-By-Area Mapping 215 is a high degree of mathematical association between the two data sets. They certainly deserve further inquiry. Another use related to two-variable mapping is to show how much of a total area is occupied by internal geographic divisions. (See Figure 11.11.) In this instance, the reader is asked to compare area proportions, and shape preservation is not often of central concern. The sizes of the internal areas are drawn proportional to the data being mapped. CARTOGRAM CONSTRUCTION There are two ways of producing value—by-area cartograms: manually and by computer technology. At present, more maps are probably generated by manual methods. MANUAL METHODS Manual techniques for the construction of value—by—area maps are quite simple. Suppose a cartographer wishes to construct a cartogram of total United States population. First, the total population is recorded for each state. The cartographer must then decide what the total area for the transformation is to be, and what proportion of the total population is represented by each state. Then the area for each state is computed on the basis of its share. (See Table 11.1.) Drafting can then begin. The cartographer must draft each state, preserving the shapes of the states while making their areas conform to the values computed. Of course, exact shapes are not preserved in contiguous cartograms. World Population Millions 3-40 Denmark r Canada \ Norway 9 Netherlands \ Sweden I 77 . 160 I. / Fl d .249-289 Ireland 9 9mm -—- In an \ Poland I 853 Czech. J apan France .Swnz' . ‘ Romania ' / — Bulgaria ~ Austria l Hun a Spain /Greece 9 '3’ Israel nary Yugoslavia I . lndla 'Mex1co Egypt @— Brazll . Chile — — Argentina 8 - . . . . outh Africa Screntific Authorship Percent of World Total Australia 1.0 ' I5— .1 Countries have been drawn proportional to their percent of world total. New Zealand Figure 11.9 Contribution of countries to world scientific authorship. (Source: Anthony R. deSouza, “Scientific Authorship and Technological Potential” (editorial), Journal of Geography [July/August 1985]: I38. Reprinted by permission of the National Council for Geographic Education. Population layer added later and not part of the original map. 216 PART ll Techniques of Quantitative Thematic Mapping Figure 11.10 Value-by- American Indian Population area cartogram with Distribution of American Indian superimposed distribution. Population in the Contiguous United States Placing a second variable over 1990 a population cartogram may reveal interesting new patterns, or patterns not evident if mapped on geographical space. Experimentation is the key idea. Here it is clear that American Indians are concentrated in these states having relatively small total population (except California). Percent oi U.S. total Indian population residing in each state .21 - 1.5 State areas drawn proportional 2.0 - 4.3 to 1990 total population 7.2 - 10-9 2.000.000 13_o . 13.5 Data sources: Population from United States Census of Population. 1990; indlan population tram United States Bureau oi Indian Affairs. United States Department at the matter. 1990 data. Only states with reservations and trust © Borden D. Dent. 1992 lands are mapped. States with no euch lands had populations accounting tor only it percent oi total Indian population In the contiguous United some. Figure 11.11 Cartogram to show geographical proportion. Distribution of Metropolitan In this presentation SMAs are drawn Effective Buying income proportional to their buying power and are Louisiana shown relative to the total buying power of the state. Shapes of the SMAs are not as important in this form of cartogram, . Total State EBI = 45 billion dollars although relauve locauon ls. exandria : Total of all SMA EBI = 35 billion doiiars Metropolitan Statistical Areas are represented proportional to their 1987 EBI Houma- Thibodaux Data source: 5 + MM. i988. "Survey oi Buying Power" Map copyright Borden 0. Dent. 1989 To facilitate the drafting of the states, it is convenient to for the cartogram (this unit size is selected simply because of begin by computing what some small areal division repre- the convenience of obtaining this grid paper). By dividing sents in terms of population. For example, the population of the population determined for each .01 square inch unit into every .01 square inch can be calculated by dividing the total the state’s total population, the number of these .01 count- population into the total number of square inches determined ing units can be ascertained. The cartographer need only .1980 Population Number of State Counting Units Alabama 3,890,006 60 Alaska 400,481 6 Arizona 2,717,866 42 Arkansas 2,285,513 35 California 23,668,562 350 Colorado 2,888,834 46 Connecticut 3,107,576 49 Delaware 595,225 9 Florida 9,739,992 154 Georgia 5,464,265 88 Hawaii 965,935 15 Idaho 943,935 15 ‘Illinois 11,418,461 175 Indiana 5,490,179 84 Iowa 2,913,387 46 Kansas 2,363,208 35 Kentucky 3,661 ,433 57 Louisiana 4,203,972 67 Maine 1.124.660 18 Maryland 4,216,446 67 Massachusetts 5 ,737,037 91 Michigan 9,258,344 147 Minnesota 4,077,148 63 Mississippi 2,520,638 39 Missouri 4,917,444 77 CHAPTER 11 The Cartogram: Value—By-Area Mapping 217 ‘ a i 1980 . State . Population 786,690 ' 14, Montana _. ' Nebraska 1,570,006 25 3 Nevada 799,184 14 New Hampshire 920,610 14 New Jersey. 7,364,158 116 New Mexico 1,299,968 21 New York 17,557,288 277 North Carolina 5,874,429 91 North Dakota 652,695 11 Ohio 10,797,419 168 Oklahoma 3,025,266 49 Oregon 2,632,663 42 Pennsylvania 11,866,728 186 Rhode Island 947,154 14 South Carolina 3,1 19,208 49 South Dakota 690,178 .11 Tennessee 4,590,750 74 Texas 14,228,383 242 Utah 1 ,461,()37 25 Vermont 511,456 11 Virginia 5,346,279 84 Washington 4,130,163 67 West Virginia 1,949,644 32 Wisconsin 4,705,335 74 Wyoming 470,816 7 Total population (excluding District of Columbia and Puerto Rico) = 222,670,654. Total map area adopted in cartogram = 35 sq in. Counting unit size adopted for project = .01 sq in. Total number of counting units = 3,500. For each state, a ratio of the state’s population to the national population was determined. The ratio was applied to the 3,500 total counting units to compute the number of units assigned to the state. For computation in this table, population figures were rounded to the nearest thousand. arrange these small counting units until the shape of the state is approximated. (See Figure 11.12.) After the shape is achieved, the cartographer may wish to check the accuracy of the state’s area by a quick planimeter measurement. Digi- tal readout planimeters are available for such uses. Each state’s shape is adjusted and fitted to adjacent states until the cartogram is completed. The shape of the entire study area must be roughly preserved throughout. This is not difficult but is time-consuming and often frus- trating. It is wise to construct the larger enumeration units first, then the smaller ones. If odd shapes result, the non- contiguous cartogram may be selected. A question is often raised about how to treat enumera— tion areas with zero value. It is this author‘s opinion that having two or three areas with zero value should not pre— vent the map from being made. Those areas having zero values should be omitted from the cartogram, but their names should be listed in a note at the bottom of the map as having zero values so that they could not be mapped. This informs the map reader that they were not forgotten. In a sense, this “other” space of the cartogram areas with zero value has simply collapsed. Perhaps there are other solu- tions, but this author knows of none. Constructing a noncontiguous cartogram involves a slightly different procedure after computations are made. A conventional (generalized, if desired) base map is drawn. By using an optical reducer—enlarger, the states can be repro- duced at their proportionate sizes relative to one that has the same size as on the true base map.20 After the individual state areas are determined and rough shapes are formed, the cartographer positions the state outlines on a draft map to form the shape of the total study area. Relative geographical position of each state is sought. The newly sized states may be positioned in accordance with the centers of the states on a conventional map. Of course, the advantage of the noncon- tiguous form is the preservation of individual state shapes. 218 PART 11 Techniques of Quantitative Thematic Mapping Total enumeration unit I I I I I I I1 Generalized enumeration unit Figure 11.12 Constructing the cartogram. Small counting units are used to “build” the size and shape of the enumeration units (e.g., countries, states, counties) in Step 1. Step 2 involves smoothing to the approximate final shape. COMPUTER SOLUTIONS Computer programs are available for the generation of con— tiguous spatial transformations, notably one by Tobler,” and another by two Russian cartographers, Gusein-Zade and Tikunov.22 The chief drawback of these programs is their inability to preserve shapes accurately, because the goal is to achieve contiguity and equal densities through— out. They also reduce flexibility in design. For the noncon— tiguous type, the size of polygons can be scaled in a variety of ways, including the use of optical reducer-enlarger pro- jectors and photocopiers. Cartograms, and especially computer solutions, can take many forms. Perplexed by what he thought to be inadequate mapping of the British census, social geographer and car- tographer Daniel Dorling has experimented with a variety of forms to represent census statistics. He has said, for exam- ple, “The information in the census concerns not land but people and households. In visualizing these, a primary aim can be that each person and each household is given equal - . heirmain disadvantage [of cartograrnsl is that they are 'V _unfarniljar,-but weido not» learn from ‘ source'rDaniflDoi-ling, “Map Design-for Census Mapping.” The Cartographic- Journal 30 (1993):}16'7—188. representation in the image.”23 His solution, which was fa- cilitated by computer, was to draw a circle in each ward in Britain so that each circle was proportional to the popula- tion that it represented. Each circle was placed as nearly as possible to its original geographical neighbor as possible. This solution is quite unique and the final image provides a startling view of the‘population. At least one author suggests that computer solutions may not be desirable because “the novelty of an automated ap— proach may lead to intemperate haste in its utilization, whereby both the merits and weaknesses of topological trans- formation may be subrnerged in the deluge of products.”24 As in other computer applications in cartography, the machine can greatly reduce time and drudgery of production. but it must not replace or interfere with the designer’s choices. NOTES 1. V. S. T ikunov. “Anamorphated Cartographic Images: Historical Outline and Construction Techniques,” Cartography ‘17 (1988): 1—8. . Peter Haggett, The Geographer-Kr Art (Oxford, England: Blackwell, 1990), pp. 55—56. 3. H. Gray Funkhouser, “Historical Development of the Geographical Representation of Statistical Data,” Osiris 3 (1937): 269—403: quotation from p. 355. 4. John M. Hunter and Jonathan C. Young, “A Technique for the Construction of Quantitative Cartograms by Physical Accretion Models,” Professional Geographer 20 (1968): 402—6. 5. Erwin Raisz, “The Rectangular Statistical Cartogram,” Geographical Review 24 (1934): 292—96. 6. Erwin Raisz, General Cartography 2nd ed. (New York: McGraw—Hill, 1948), pp. 257—58; and Erwin Raisz, Principles of Cartography (New York: McGraw—Hill, 1962), pp. 215—21. 7. Waldo R. Tobler, “Geographic Area Map Projections,” Geographical Review 53 (1963): 59—78; see also Waldo R. Tobler, Map Transformations of Geographic Space (unpublished Ph.D. dissertation, Department of Geography, University of Washington, Seattle, 1961), p. 146. 8. Borden D. Dent, “Communication Aspects of Value- by-Area Cartograms,“ American Cartographer 2 (1975): 154—68. 9. There are numerous examples of such atlases. The following are particularly interesting: Tony Loftas, eds Atlas of the Earth (London England,: Mitchell Beazley, to 1972); Reziue Van Chi—Bonnardel, The Atlas of Africa (New York: Free Press, 1973); and Michael Kidron and Ronald Segal, The State of the World Atlas (New York: Simon and Schuster, 1981); cartograms have also been used to explore ways of presenting census data, as found in Danial Dorling, “Map Design for Census Mapping, The Cartographic Journal 30 (1993):l67—83. 10. Judy M. Olson, “Noncontiguous Area Cartograms,” Professional Geographer 28 (1976): 371—80. 11. Raisz, “The Rectangular Statistical Cartogram,” pp. 292—96. 12. Chauncey Harris and George B. McDowell, “Distorted Maps. A Teaching Device," Journal of Geography 54 (1955): 286—89. 13. Borden D. Dent, “A Note on the Importance of Shape in Cartogram Communication,” Journal of Geography 71 (1972): 393—401. 14. Ibid. 15. Borden D. Dent, “Communication Aspects,“ pp. 154—68. 16. Ibid. [7. Searching stored nrap images was addressed in an early paper: Borden 1). Dent, “Postulatcs on the Nature of Map Reading" (paper presented at the annual meeting of the Georgia Academy of Science, l97()). 18. T. L. C. Griffin, “Cartographic Transformation 01‘ the Thematic Map Base," Cartography 1 1 (1980): 163-74. 19. Ibid. 20. ()lson, “Noncontiguous Area Cartograms,” pp. 371—80. 21. Waldo R. 'l‘obler, “A Continuous Transformation Useful for Districting," Annals (New York Academy of Sciences) 219 (1973): 215—20. 22. Sabir M. Gusein~Zadc and Vladimir S. Tikunov, “A New Technique for Constructing Continuous Cartograms," Cartography and Geographic Information Systems 20 (1993): 167—73. 23. Dorling, “Map Design for Census Mapping," pp. 167—83; see also Daniel Dorling, “Visualizing Changing Social Structure from a Census," Environment and Planning 27 (l995):353—78; and Daniel Dorling, “Cartograms for Visualizing Human Geography,” in eds. Hilary M. Hearnshaw and David Unwin, Visualization in Geographical Information Systems, (New York: Wiley, 1994), pp. 85—102. 24. Griffin, “Cartographic Transformation,” pp. 163—74. GLOS SARY cartogram name applied to a variety of representations; used synonymously with value—by—area map or spatial transformation, p. 208 contiguous cartogram a value-by-area map in which the internal divisions are drawn so that they join with their neighbors, p. 209 C HAPTE R 11 The Cartogram: Value—By-Area Mapping counting unit small spatial unit used in the manual preparation of value—by—area maps, p. 216—217 noncontiguous cartogram a value—by—area map in which the internal divisions are drawn so that their boundaries do not join their neighbors; internal units appear to float in mapped space, p. 210 orientation the internal arrangement of the enumeration unit within the total transformed region; cartogram communication relies heavily on the map reader’s knowledge of the geography of the study area, p. 211 shape quality a bridge allowing the reader to perceive the new value-by-area transformation of the original geographic base map; shape recognition is critical— without it, confusion results and communication fails, p. 210 two-variable value-by-area cartogram a value—hy—area map on which a second, related variable is mapped using area shading (chorograrns) or graduated symbols, p. 215 value-by-area map name applied to the form of map in which the areas of the internal enumeration units are scaled to the data they represent. p. 208 READINGS FOR FURTHER UNDERSTANDING Burrill, Meredith. “Quickie Cartograms.“ Professional Geographer 7 (1955): 6—7. Cole, John P., and Cuchlaine A. M. King. Quantitative Geography. London: Wiley, 1968. Cuff, David J., John W. Pauling, and Edward T. Blair. “Nested Value—by-Area Cartograms by Synrbolizing Land Use and Other Proportions.” C artographica 21 (1984): 1—8. Dent, Borden D. “A Note on the Importance of Shape in Cartogram Communication.” Journal of Geography 71 (1972): 393—401. . “Communication Aspects of Value—by-Area Cartograms.” American Cartographer 2 (1975): 154—68. Eastman, J. R., W. Nelson, and G. Shields. “Production Considerations in Isodensity Mapping.” Cartographica 18(1981): 24—30. Getis, Arthur. “The Determination of the Location of Retail Activities with the Use of a Map Transformation.” Economic Geography 39 (1963): 1—22. Griffin, T. L. C. “Cartographic Transformation of the Thematic Map Base." Cartography 11 (1980): 163—74. . “Recognition of Areal Units on Topological Cartograms.” American Cartographer 10 (I983): 17—28. Haro, A. S. “Area Cartogram ol‘ the SMSA Population of the United States.” Annals (Association of American Geographers) 58 (1968): 452—60. 220 PART [1 Techniques of Quantitative Thematic Mapping Harris, Chauncey. “The Market as a Factor in the Localization of Industry in the United States.” Annals (Association of American Geographers) 44 (1954): 315—48. , and George B. McDowell. “Distorted Maps, 21 Teaching Device.” Journal of Geography 54 (1955): 286—89. Hunter, John M., and Melinda S. Meade. “Population Models in the High School.” Journal of Geography 70 (1971): 95—104. , and Johnathan C. Young. “A Technique for the Construction of Quantitative Cartograms by Physical Accretion Models.” Professional Geographer 20 (1968): 402—6. Kelly, J. “Constructing an Area—Value Cartogram for New Zealand’s Population.” New Zealand Cartographic- Journal 17 (1987): 3—10. Kidron, Michael, and Ronald Segal. The State of the World Atlas. New York: Simon and Schuster, 1981. Loftas, Tony, ed. Atlas oft/1e Earth. London, England: Mitchell Beazley. 1972. Monmonier, Mark S. Maps, Distortion, and Meaning. Association of American Geographers. Resource Paper No. 75—4. Washington. DC: Association of American (.icographcrs. '1977. . “Nonlinear Reprojection to Reduce the Congestion ot‘Syinbols on Thematic Maps.“ Canadian Cartography): 14 (1977): 35447. Olson, Judy M. “Noncontiguous Area Cartograms.” Professional Geographer 28 (1976): 371—80. . Raisz, Erwin. “The Rectangular Statistical Cartogram_ Geographical Review 24 (1934): 292—96. » . General Cartography. New York: MCGraw—Hifl; 1948. . Principles of Cartography. New York: McGraw~ Hill, 1962. 9’ Rowley, Gwyn. “Landslide by Cartogram.” Geographica Magazine 45 (1973): 344. . “The World: Upside Down, Inside Out.” The Economist, December 22, 1984, pp. 19~24. Tobler, Waldo R. Map Transformations of Geographic Space. Unpublished Ph.D. dissertation. Seattle: University of Washington, Department of Geography, 1961. “A Continuous Transformation Useful for Districting.” Annals (New York Academy of Sciences) 219 (1973): 215—20. . “Geographical Area and Map Projections." Geographical Review 53 (1963): 59—78. 'l‘ufte, Edward R. The Visual Display of Quantitative Information. Cheshire, CT: Graphics Press, 1983. Van Chi-Bonnardel, Rczine. The Atlas ofAfrica. New York: Free Press. 1973. ...
View Full Document

{[ snackBarMessage ]}

Page1 / 15

Dent-Chap11 - Fifth Edition CARTOGRAPHY Thematic Map Design...

This preview shows document pages 1 - 15. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online