DOCSLIB.ORG

Assessing Raster Representation Accuracy Using a Scale Factor Model

Total Page：16

File Type：pdf, Size：1020Kb

Download full-text PDF Read full-text
Assessing Raster Representation Accuracy Using a Scale Factor Model Assessing Raster Representation Accuracy Using a Scale Factor Model Jeong Chang Seong and E. Lynn Usery Abstract using six equal-area projections: Interrupted Goode Homolos- Raster datasets of global and continental extent are subject to ine, Interrupted Mollweide, Wagner IV, Wagner W, Lambert error resulting from projection transformation. This paper Azimuthal Equal Area, and Oblated Equal-Area projections. examines the error problem from a theoretical perspective and They quantified and graphically depicted shape and scale dis- develops a model to calculate the extent of the errors. The tortions caused by reprojection. However, because their theoretical examination indicates that error results in two research used sample grids that were drawn on already pro- forms, areal size change of pixels and categorical error re- jected maps, the application is limited since no theoretical sulting from loss or duplication of pixels. A scale factor model, background or models to estimate and simulate the pixel value based on the horizontal and vertical scale factors of the changes in various projection change situations were pre- projection, is developed to provide a computation of the sented. It is the purpose of this research to investigate the effect resulting error from specific projections. The model is of projection distortion on raster representation at a global scale experimentally tested with the cylindrical equal area, and develop a scale factor model to simulate the effect. The sinusoidal, and Mollweide projections. Results indicate that next three sections of this paper provide a theoretical approach the model predicts error within one percent of actual values to the assessment of raster representation accuracy based on a and that the sinusoidal projection is subject to smaller errors scale factor model. The fifth section develops an experimental in projecting raster data than the other projections tested. design and tests this approach using three specific projections. After the extension of the model to other types of projections is discussed, some conclusions based on this work are provided in Introduction the last section. With society's increasingly global perspective and global mod- eling needs, raster databases of geographic phenomena and Errors in Raster Representation and Transformation processes at continental and global scales have been con- The transformation of features at regional and global extents structed using a number of different map projections. These using the raster data structure brings two distinct problems raster databases exist at a variety of resolutions and have been which may be labeled as areal size and category. The areal-size generated from many different data sources. For example, problem results from a transformation which causes the area Steinwand (1994) coded algorithms of the Interrupted Goode represented in the raster data format to be unequal to the size of Homolosine projection for coarse-resolution global data sets. the same area represented in the vector data format unless the Tobler et al. (1995) used unprojected spherical quadrilateral pixel resolution is infinitely small. Practically, rather than grids to map global population data. Also, Lowman et al. infinity, vector and raster resoll~tionsconverge to the same rep- (1999)used the Robinson projection to map tectonic and volca- resentation at a pixel size equivalent to the smallest number nic activity around the world. The U.S. Geological Survey also which can be represented in the computer, which also corres- distributes digital raster datasets to the public to assemble ponds to the smallest possible pixel size and the smallest vector global databases of vegetation, climate, land cover, and eleva- distance which can be represented between two points. tion at resolutions of one degree, one-half degree, one kilome- The category problem is that some categories may be lost or ter, and 30-arc seconds, respectively. Dobson et al. (2000) duplicated when vector features are represented in raster for- developed the LandScan population database for the world on mat. There is no loss or gain of categories among equal-area pro- a 30-arc-sec grid. These publicly available data may be in geo- jections in the vector data structure because original features graphic coordinates or a projected coordinate system. In either will remain after projection. However, the situation is quite dif- case, users who wish to combine datasets through geographic ferent in the raster data structure. Suppose there is araster data information system (GIS) software are faced with a problem of layer with a 1-km pixel resolution in the Interrupted Goode map projection transformation and little guidance concerning Homolosine projection with 255 categories and the data are the accuracy of the projection transformation process (Cliffe, reprojected to the Albers conic equal-area projection with the 2000). same 1-km pixel resolution. Unlike the flexibility of vectorrep- Usery and Seong (2001) have demonstrated that continen- resentation, the rigidity of raster representation and the require- tal areas are subject to significant distortion if raster data are ment of nearest-neighbor interpolation for categorical data projected. Steinwand et al. (1995) identified the effects of map cause the frequency of each category to be changed, sometimes projection properties on data quality in global change studies significantly. As an example, a subset of the Eurasia dataset of J.C. Seong is with the Department of Geography, Northern Photogrammetric Engineering & Remote Sensing Michigan University, 1401 Presque Isle Ave., Marquette, MI 49855 ([email protected]). Vol. 67, No. 10, October 2001, pp. 1185-1191. E.L. Usery is with the Department of Geography, University 0099-1112/01/6710-1185$3.00/0 of Georgia, 204 GGS Building, Athens, GA 30602 (usery@ 0 2001 American Society for Photogrammetry arches.uga.edu; [email protected]). and Remote Sensing PHOTOGRAMMETRIC ENGINEERING & REMOTE SENSING October 2001 1185 the global land-cover characterization (GLCC)data (Eidenshink representing the original feature's size, which yields an 80 per- and Faundeen, 1994;Lauer and Eidenshink, 1998;Brown, cent representation accuracy. 1999) was reprojected from the Interrupted Goode Homolosine The error occurs when the original shape is distorted. lf a projection to the Albers equal-area conic projection and the projection changes an original shape severely, we may expect geographic latitude and longitude system. The subset covered an increased error. The number of categories and spatial auto- the latitude range of 47.1" N through N 53.7"and the longitude correlation also affect the error. If there is only one category, the range of 15.3"E through E 32.0"with 37 global ecosystem land- highest possible spatial autocorrelation, the frequency will be cover categories. The reprojection result showed 2.7 percent the same as the total number of pixels. On the contrary, if there and 35.5 percent errors when the data were reprojected to the are many categories in low spatial autocorrelation, projection Albers equal-area conic projection and geographic latitude1 may bring significant frequency changes. Error varies directly longitude system, respectively. with the spatial autocorrelation of the image; lower spatial The difference among categorical value frequencies autocorrelation yields lower accuracy and higher spatial auto- occurring at the projection stage is not easily visible because correlation yields higher accuracy. At small spatial extents, as the total area is retained in the projected image if an output pro- with local raster databases, the error will not be as significant jection is an equal-area projection. However, the error is obvi- as with global databases because of relatively small shape dis- ous when the frequency of each category is compared between tortions. In global-scale databases, significant error is expected the two images (Usery and Seong, 2001). Categorical values due to the severe shape distortion required to maintain areal may be gained or lost depending on the resulting shape of the equivalency. reprojected features and the arrangement of raster pixels. Modeling the Accuracy of Raster Representation of Equal-Area Characteristics of Categorical Errors in Raster Representation Projectsons In an equal-area projection, a feature on the globe projected to a Equivalency can be maintained by distorting shape. Specifi- flat surface should be represented with its original size. If the cally, when the multiplication of the vertical and horizontal feature's size is not represented correctly, the difference scale factors is 1.0,equivalency is maintained (Bugayevskiy et between the original size and the projected size is the extent of al., 1995; Yang et al., 2000). In most map projections, the hori- the error. zontal and vertical scale factors are represented as mathemati- In Figure 1, assume the symbol 'x' is the center of each cell. cal equations. The change of horizontal and vertical scales If a rasterization algorithm uses the feature in the vector repre- results in shape change of features. If a vector data structure is sentation occurring at the center of a pixel for representing the used, the change of scales does not affect the representation of pixel in the raster representation, features may be ignored. In categories because all features will be represented in the pro- the case of projection A, the XI,x2, ~4,and x5 features are lost. jected vector database. However, if a raster database is used, Projection B shows a feature loss of only ~5.However, features severely reduced features may be ignored because they are not also may be over-represented as in projection B, where ~2is large enough to be represented by a pixel that is much larger duplicated. Therefore, the total error extent is composed of the than the reduced feature size. Figure 2 shows the relationship pixels that are ignored and those that are over-represented. In between scale change and raster representation. Original fea- other words, the accuracy of raster representation is the size of tures are shown in distorted shape in thinner lines. New raster- correct categorical representation.
Load more

Recommended publications
  • Mollweide Projection and the ICA Logo Cartotalk, October 21, 2011 Institute of Geoinformation and Cartography, Research Group Cartography (Draft Paper)
    Mollweide Projection and the ICA Logo CartoTalk, October 21, 2011 Institute of Geoinformation and Cartography, Research Group Cartography (Draft paper) Miljenko Lapaine University of Zagreb, Faculty of Geodesy, [email protected] Abstract The paper starts with the description of Mollweide's life and work. The formula or equation in mathematics known after him as Mollweide's formula is shown, as well as its proof "without words". Then, the Mollweide map projection is defined and formulas derived in different ways to show several possibilities that lead to the same result. A generalization of Mollweide projection is derived enabling to obtain a pseudocylindrical equal-area projection having the overall shape of an ellipse with any prescribed ratio of its semiaxes. The inverse equations of Mollweide projection has been derived, as well. The most important part in research of any map projection is distortion distribution. That means that the paper continues with the formulas and images enabling us to get some filling about the liner and angular distortion of the Mollweide projection. Finally, the ICA logo is used as an example of nice application of the Mollweide projection. A small warning is put on the map painted on the ICA flag. It seams that the map is not produced according to the Mollweide projection and is different from the ICA logo map. Keywords: Mollweide, Mollweide's formula, Mollweide map projection, ICA logo 1. Introduction Pseudocylindrical map projections have in common straight parallel lines of latitude and curved meridians. Until the 19th century the only pseudocylindrical projection with important properties was the sinusoidal or Sanson-Flamsteed.
    [Show full text]
  • An Efficient Technique for Creating a Continuum of Equal-Area Map Projections
    Cartography and Geographic Information Science ISSN: 1523-0406 (Print) 1545-0465 (Online) Journal homepage: http://www.tandfonline.com/loi/tcag20 An efficient technique for creating a continuum of equal-area map projections Daniel “daan” Strebe To cite this article: Daniel “daan” Strebe (2017): An efficient technique for creating a continuum of equal-area map projections, Cartography and Geographic Information Science, DOI: 10.1080/15230406.2017.1405285 To link to this article: https://doi.org/10.1080/15230406.2017.1405285 View supplementary material Published online: 05 Dec 2017. Submit your article to this journal View related articles View Crossmark data Full Terms & Conditions of access and use can be found at http://www.tandfonline.com/action/journalInformation?journalCode=tcag20 Download by: [4.14.242.133] Date: 05 December 2017, At: 13:13 CARTOGRAPHY AND GEOGRAPHIC INFORMATION SCIENCE, 2017 https://doi.org/10.1080/15230406.2017.1405285 ARTICLE An efficient technique for creating a continuum of equal-area map projections Daniel “daan” Strebe Mapthematics LLC, Seattle, WA, USA ABSTRACT ARTICLE HISTORY Equivalence (the equal-area property of a map projection) is important to some categories of Received 4 July 2017 maps. However, unlike for conformal projections, completely general techniques have not been Accepted 11 November developed for creating new, computationally reasonable equal-area projections. The literature 2017 describes many specific equal-area projections and a few equal-area projections that are more or KEYWORDS less configurable, but flexibility is still sparse. This work develops a tractable technique for Map projection; dynamic generating a continuum of equal-area projections between two chosen equal-area projections.
    [Show full text]
  • Rcosmo: R Package for Analysis of Spherical, Healpix and Cosmological Data Arxiv:1907.05648V1 [Stat.CO] 12 Jul 2019
    CONTRIBUTED RESEARCH ARTICLE 1 rcosmo: R Package for Analysis of Spherical, HEALPix and Cosmological Data Daniel Fryer, Ming Li, Andriy Olenko Abstract The analysis of spatial observations on a sphere is important in areas such as geosciences, physics and embryo research, just to name a few. The purpose of the package rcosmo is to conduct efficient information processing, visualisation, manipulation and spatial statistical analysis of Cosmic Microwave Background (CMB) radiation and other spherical data. The package was developed for spherical data stored in the Hierarchical Equal Area isoLatitude Pixelation (Healpix) representation. rcosmo has more than 100 different functions. Most of them initially were developed for CMB, but also can be used for other spherical data as rcosmo contains tools for transforming spherical data in cartesian and geographic coordinates into the HEALPix representation. We give a general description of the package and illustrate some important functionalities and benchmarks. Introduction Directional statistics deals with data observed at a set of spatial directions, which are usually positioned on the surface of the unit sphere or star-shaped random particles. Spherical methods are important research tools in geospatial, biological, palaeomagnetic and astrostatistical analysis, just to name a few. The books (Fisher et al., 1987; Mardia and Jupp, 2009) provide comprehensive overviews of classical practical spherical statistical methods. Various stochastic and statistical inference modelling issues are covered in (Yadrenko, 1983; Marinucci and Peccati, 2011). The CRAN Task View Spatial shows several packages for Earth-referenced data mapping and analysis. All currently available R packages for spherical data can be classified in three broad groups. The first group provides various functions for working with geographic and spherical coordinate systems and their visualizations.
    [Show full text]
  • 5–21 5.5 Miscellaneous Projections GMT Supports 6 Common
    GMT TECHNICAL REFERENCE & COOKBOOK 5–21 5.5 Miscellaneous Projections GMT supports 6 common projections for global presentation of data or models. These are the Hammer, Mollweide, Winkel Tripel, Robinson, Eckert VI, and Sinusoidal projections. Due to the small scale used for global maps these projections all use the spherical approximation rather than more elaborate elliptical formulae. 5.5.1 Hammer Projection (–Jh or –JH) The equal-area Hammer projection, first presented by Ernst von Hammer in 1892, is also known as Hammer-Aitoff (the Aitoff projection looks similar, but is not equal-area). The border is an ellipse, equator and central meridian are straight lines, while other parallels and meridians are complex curves. The projection is defined by selecting • The central meridian • Scale along equator in inch/degree or 1:xxxxx (–Jh), or map width (–JH) A view of the Pacific ocean using the Dateline as central meridian is accomplished by running the command pscoast -R0/360/-90/90 -JH180/5 -Bg30/g15 -Dc -A10000 -G0 -P -X0.1 -Y0.1 > hammer.ps 5.5.2 Mollweide Projection (–Jw or –JW) This pseudo-cylindrical, equal-area projection was developed by Mollweide in 1805. Parallels are unequally spaced straight lines with the meridians being equally spaced elliptical arcs. The scale is only true along latitudes 40˚ 44' north and south. The projection is used mainly for global maps showing data distributions. It is occasionally referenced under the name homalographic projection. Like the Hammer projection, outlined above, we need to specify only
    [Show full text]
  • Bibliography of Map Projections
    AVAILABILITY OF BOOKS AND MAPS OF THE U.S. GEOlOGICAL SURVEY Instructions on ordering publications of the U.S. Geological Survey, along with prices of the last offerings, are given in the cur­ rent-year issues of the monthly catalog "New Publications of the U.S. Geological Survey." Prices of available U.S. Geological Sur­ vey publications released prior to the current year are listed in the most recent annual "Price and Availability List" Publications that are listed in various U.S. Geological Survey catalogs (see back inside cover) but not listed in the most recent annual "Price and Availability List" are no longer available. Prices of reports released to the open files are given in the listing "U.S. Geological Survey Open-File Reports," updated month­ ly, which is for sale in microfiche from the U.S. Geological Survey, Books and Open-File Reports Section, Federal Center, Box 25425, Denver, CO 80225. Reports released through the NTIS may be obtained by writing to the National Technical Information Service, U.S. Department of Commerce, Springfield, VA 22161; please include NTIS report number with inquiry. Order U.S. Geological Survey publications by mail or over the counter from the offices given below. BY MAIL OVER THE COUNTER Books Books Professional Papers, Bulletins, Water-Supply Papers, Techniques of Water-Resources Investigations, Circulars, publications of general in­ Books of the U.S. Geological Survey are available over the terest (such as leaflets, pamphlets, booklets), single copies of Earthquakes counter at the following Geological Survey Public Inquiries Offices, all & Volcanoes, Preliminary Determination of Epicenters, and some mis­ of which are authorized agents of the Superintendent of Documents: cellaneous reports, including some of the foregoing series that have gone out of print at the Superintendent of Documents, are obtainable by mail from • WASHINGTON, D.C.--Main Interior Bldg., 2600 corridor, 18th and C Sts., NW.
    [Show full text]
  • Portraying Earth
    A map says to you, 'Read me carefully, follow me closely, doubt me not.' It says, 'I am the Earth in the palm of your hand. Without me, you are alone and lost.’ Beryl Markham (West With the Night, 1946 ) • Map Projections • Families of Projections • Computer Cartography Students often have trouble with geographic names and terms. If you need/want to know how to pronounce something, try this link. Audio Pronunciation Guide The site doesn’t list everything but it does have the words with which you’re most likely to have trouble. • Methods for representing part of the surface of the earth on a flat surface • Systematic representations of all or part of the three-dimensional Earth’s surface in a two- dimensional model • Transform spherical surfaces into flat maps. • Affect how maps are used. The problem: Imagine a large transparent globe with drawings. You carefully cover the globe with a sheet of paper. You turn on a light bulb at the center of the globe and trace all of the things drawn on the globe onto the paper. You carefully remove the paper and flatten it on the table. How likely is it that the flattened image will be an exact copy of the globe? The different map projections are the different methods geographers have used attempting to transform an image of the spherical surface of the Earth into flat maps with as little distortion as possible. No matter which map projection method you use, it is impossible to show the curved earth on a flat surface without some distortion.
    [Show full text]
  • Maps and Cartography: Map Projections a Tutorial Created by the GIS Research & Map Collection
    Maps and Cartography: Map Projections A Tutorial Created by the GIS Research & Map Collection Ball State University Libraries A destination for research, learning, and friends What is a map projection? Map makers attempt to transfer the earth—a round, spherical globe—to flat paper. Map projections are the different techniques used by cartographers for presenting a round globe on a flat surface. Angles, areas, directions, shapes, and distances can become distorted when transformed from a curved surface to a plane. Different projections have been designed where the distortion in one property is minimized, while other properties become more distorted. So map projections are chosen based on the purposes of the map. Keywords •azimuthal: projections with the property that all directions (azimuths) from a central point are accurate •conformal: projections where angles and small areas’ shapes are preserved accurately •equal area: projections where area is accurate •equidistant: projections where distance from a standard point or line is preserved; true to scale in all directions •oblique: slanting, not perpendicular or straight •rhumb lines: lines shown on a map as crossing all meridians at the same angle; paths of constant bearing •tangent: touching at a single point in relation to a curve or surface •transverse: at right angles to the earth’s axis Models of Map Projections There are two models for creating different map projections: projections by presentation of a metric property and projections created from different surfaces. • Projections by presentation of a metric property would include equidistant, conformal, gnomonic, equal area, and compromise projections. These projections account for area, shape, direction, bearing, distance, and scale.
    [Show full text]
  • Map Projections and Coordinate Systems Datums Tell Us the Latitudes and Longi- Vertex, Node, Or Grid Cell in a Data Set, Con- Tudes of Features on an Ellipsoid
    116 GIS Fundamentals Map Projections and Coordinate Systems Datums tell us the latitudes and longi- vertex, node, or grid cell in a data set, con- tudes of features on an ellipsoid. We need to verting the vector or raster data feature by transfer these from the curved ellipsoid to a feature from geographic to Mercator coordi- flat map. A map projection is a systematic nates. rendering of locations from the curved Earth Notice that there are parameters we surface onto a flat map surface. must specify for this projection, here R, the Nearly all projections are applied via Earth’s radius, and o, the longitudinal ori- exact or iterated mathematical formulas that gin. Different values for these parameters convert between geographic latitude and give different values for the coordinates, so longitude and projected X an Y (Easting and even though we may have the same kind of Northing) coordinates. Figure 3-30 shows projection (transverse Mercator), we have one of the simpler projection equations, different versions each time we specify dif- between Mercator and geographic coordi- ferent parameters. nates, assuming a spherical Earth. These Projection equations must also be speci- equations would be applied for every point, fied in the “backward” direction, from pro- jected coordinates to geographic coordinates, if they are to be useful. The pro- jection coordinates in this backward, or “inverse,” direction are often much more complicated that the forward direction, but are specified for every commonly used pro- jection. Most projection equations are much more complicated than the transverse Mer- cator, in part because most adopt an ellipsoi- dal Earth, and because the projections are onto curved surfaces rather than a plane, but thankfully, projection equations have long been standardized, documented, and made widely available through proven programing libraries and projection calculators.
    [Show full text]
  • Adaptive Composite Map Projections
    IEEE TRANSACTIONS ON VISUALIZATION AND COMPUTER GRAPHICS, VOL. 18, NO. 12, DECEMBER 2012 2575 Adaptive Composite Map Projections Bernhard Jenny Abstract—All major web mapping services use the web Mercator projection. This is a poor choice for maps of the entire globe or areas of the size of continents or larger countries because the Mercator projection shows medium and higher latitudes with extreme areal distortion and provides an erroneous impression of distances and relative areas. The web Mercator projection is also not able to show the entire globe, as polar latitudes cannot be mapped. When selecting an alternative projection for information visualization, rivaling factors have to be taken into account, such as map scale, the geographic area shown, the mapʼs height-to-width ratio, and the type of cartographic visualization. It is impossible for a single map projection to meet the requirements for all these factors. The proposed composite map projection combines several projections that are recommended in cartographic literature and seamlessly morphs map space as the user changes map scale or the geographic region displayed. The composite projection adapts the mapʼs geometry to scale, to the mapʼs height-to-width ratio, and to the central latitude of the displayed area by replacing projections and adjusting their parameters. The composite projection shows the entire globe including poles; it portrays continents or larger countries with less distortion (optionally without areal distortion); and it can morph to the web Mercator projection for maps showing small regions. Index terms—Multi-scale map, web mapping, web cartography, web map projection, web Mercator, HTML5 Canvas.
    [Show full text]
  • Map Projections
    MAP PROJECTIONS Methods of presenting the curved surface of the Earth on a flat map. MAP PROJECTIONS On your notebook paper, create a graphic organizer as illustrated below…Title it MAP PROJECTIONS Map Name Illustration Strength Weakness Used For?? Are all Maps created equally? Imagine trying to flatten out a globe; you would have to stretch it here, compress it there. Because of this, it is quite common for sizes, shapes, and even distances to be misrepresented in the transition from three dimensions to two. Large distortion if you are looking at a hemisphere or the entire world. Smaller distortion/inaccuracies - At the scale of a city or even a small country, Mercator Projection Cylinder shape Meridians stretched apart & parallel to each other instead of meeting at the poles. Landmasses at high latitudes appears LARGER Landmasses at lower latitudes appears relatively SMALLER. Conic Projection Designed as if a cone had been placed over the globe. Arctic regions portrayed accurately. Further you get from the top of the cone, the more distorted sizes and distances become. Great for aeronautical plotting - latitudes are more accurate. Flat Plane/Azumithal Projection Distances measured from the center are accurate. Distortion increases as you get further away from the center point. Used by airline pilots & ship navigators to find the shortest distance between 2 places. Equal Area Map Projection An interrupted view of the globe. Land masses are proportional - giving the correct perspective of size. Not usable for navigation - longitude & latitude are stretched apart in order to conform to sizes. Gall-Peters Projection Landmasses in this projection are kept accurate and in proportion.
    [Show full text]
  • Cylindrical Projections 27
    MAP PROJECTION PROPERTIES: CONSIDERATIONS FOR SMALL-SCALE GIS APPLICATIONS by Eric M. Delmelle A project submitted to the Faculty of the Graduate School of State University of New York at Buffalo in partial fulfillments of the requirements for the degree of Master of Arts Geographical Information Systems and Computer Cartography Department of Geography May 2001 Master Advisory Committee: David M. Mark Douglas M. Flewelling Abstract Since Ptolemeus established that the Earth was round, the number of map projections has increased considerably. Cartographers have at present an impressive number of projections, but often lack a suitable classification and selection scheme for them, which significantly slows down the mapping process. Although a projection portrays a part of the Earth on a flat surface, projections generate distortion from the original shape. On world maps, continental areas may severely be distorted, increasingly away from the center of the projection. Over the years, map projections have been devised to preserve selected geometric properties (e.g. conformality, equivalence, and equidistance) and special properties (e.g. shape of the parallels and meridians, the representation of the Pole as a line or a point and the ratio of the axes). Unfortunately, Tissot proved that the perfect projection does not exist since it is not possible to combine all geometric properties together in a single projection. In the twentieth century however, cartographers have not given up their creativity, which has resulted in the appearance of new projections better matching specific needs. This paper will review how some of the most popular world projections may be suited for particular purposes and not for others, in order to enhance the message the map aims to communicate.
    [Show full text]
  • The Mercator Projection: Its Uses, Misuses, and Its Association with Scientific Information and the Rise of Scientific Societies
    ABEE, MICHELE D., Ph.D. The Mercator Projection: Its Uses, Misuses, and Its Association with Scientific Information and the Rise of Scientific Societies. (2019) Directed by Dr. Jeff Patton and Dr. Linda Rupert. 309 pp. This study examines the uses and misuses of the Mercator Projection for the past 400 years. In 1569, Dutch cartographer Gerard Mercator published a projection that revolutionized maritime navigation. The Mercator Projection is a rectangular projection with great areal exaggeration, particularly of areas beyond 50 degrees north or south, and is ill-suited for displaying most reference and thematic world maps. The current literature notes the significance of Gerard Mercator, the Mercator Projection, the general failings of the projection, and the twentieth century controversies that arose as a consequence of its misuse. This dissertation illustrates the path of the institutionalization of the Mercator Projection in western cartography and the roles played by navigators, scientific societies and agencies, and by the producers of popular reference and thematic maps and atlases. The data are pulled from the publication record of world maps and world maps in atlases for content analysis. The maps ranged in date from 1569 to 1900 and displayed global or near global coverage. The results revealed that the misuses of the Mercator Projection began after 1700, when it was connected to scientists working with navigators and the creation of thematic cartography. During the eighteenth century, the Mercator Projection was published in journals and reports for geographic societies that detailed state-sponsored explorations. In the nineteenth century, the influence of well- known scientists using the Mercator Projection filtered into the publications for the general public.
    [Show full text]