Waldo R. Tobler
Waldo Rudolph Tobler (November 16, 1930 – February 20, 2018) was an American-Swiss geographer and cartographer. Tobler is regarded as one of the most influential geographers and cartographers of the late 20th century and early 21st century. He is best known for coining what has come to be referred to as Tobler's first law of geography. He also coined what has come to be referred to as Tobler's second law of geography.
Tobler's career had a major impact on the development of quantitative geography, and his research spanned and influenced the study of any discipline investigating geographic phenomena. He established the discipline of analytical cartography, contributed early to Geographic information systems (GIS), and helped lay the groundwork for geographic information science (GIScience) as a discipline. He had significant contributions to computer cartography and was one of the first geographers to explore using computers in geography. In cartography, he contributed to the literature on map projections, choropleth maps, flow maps, cartograms, animated mapping. His work with analytical cartography included contributions to the mathematical modeling of geographic phenomena, such as human movement in the creation of Tobler's hiking function. Tobler's work has been described as ahead of its time, and many of his ideas are still unable to be fully implemented due to limitations of technology.
Tobler held the positions of professor of geography and professor of statistics at University of California, Santa Barbara and was an active professor emeritus at the Department of Geography until his death.
Early life
Tobler was born in Portland, Oregon, in 1930 to parents Verner Tobler and Hanny Urech Tobler.<ref name="ToblerAutobiography">Template:Cite book</ref><ref name="Thoits2018" /> His father was a Swiss consular employee, and this granted Waldo Tobler both Swiss and United States citizenship.<ref name="Karan2000">Template:Cite book</ref><ref name="ToblerAutobiography" /><ref>Template:Cite book</ref><ref name="Unwin2019">Template:Cite journal</ref> His father's career resulted in moves to Seattle when Waldo Tobler was young, and later to Washington, D.C., when World War II started.<ref name="Clarke1">Template:Cite journal</ref><ref name="Thoits2018" /> During World War II, his father's duties included reporting on the treatment of German Prisoners of War held in the United States.<ref name="ToblerAutobiography" /> Tobler attended junior high school in Chevy Chase, Maryland, while his father was stationed in Washington, D.C.<ref name="ToblerAutobiography" />
In May 1945, after the Allied victory in Europe, the family returned to Europe by boat from Boston, Massachusetts to Le Havre France, then by train to Paris, and finally to his parents' native Switzerland.<ref name="ToblerAutobiography" /> His father was then stationed in Budapest, and Tobler attended boarding school for a year in Zurich, where he learned German, then public high school in St. Gall, and Bern.<ref name="ToblerAutobiography" /><ref name="Thoits2018" /> Geographers Pradyumna Prasad Karan and Cotton Mather speculated that this frequent moving in early life may have influenced Tobler's later career choices and passion for geography.<ref name="Karan2000" /> Tobler later stated that these early travels may have contributed to a career in geography.<ref name="ToblerAutobiography" />
Military service
When Tobler turned 18 in 1948, Switzerland wanted to draft him into the Swiss Army.<ref name="ToblerAutobiography" /> To avoid the Swiss draft, Tobler traveled to France and joined the United States Army in 1948.<ref name="ToblerAutobiography" /><ref name="Clarke1" /><ref name="Thoits2018" /><ref name="Dow1992" /> A native speaker of English, Swiss German, and French, the military trained him to speak Russian to serve as an interpreter for the Counterintelligence Corps.<ref name="Thoits2018">Template:Cite news</ref> During his time in the military, he served as both an intelligence analyst and an interpreter in Europe (mostly in Austria) during the Korean War, and participated in interviewing Austrian Prisoners of War who had been released from the Soviet Union.<ref name="Karan2000" /><ref name="Clarke1" /><ref name="Yang2018">Template:Cite web</ref> Tobler described this activity as "little more than industrial espionage."<ref name="ToblerAutobiography" /> He left the military in 1952 and used his G.I. Bill to attend university.<ref name="Dow1992">Template:Cite web</ref>
Education and field
After leaving the military, Tobler attended classes at University of British Columbia in Vancouver, Canada.<ref name="Karan2000" /><ref name="Dow1992" /> Here, Tobler was introduced to Canadian Geographer John Ross Mackay, who Tobler convinced to allow him to take advanced cartography classes as a freshman.<ref name="Karan2000" /><ref name="Flowerdew2011">Template:Cite book</ref> After two years at the University of British Columbia, Tobler transferred to the University of Washington in Seattle, from which he received his B.A. (1955), M.A. (1957), and PhD (1961), all in geography.<ref name="Karan2000" /><ref name="AAG1">Template:Cite web</ref> Tobler returned for his PhD only after receiving a National Science Foundation fellowship to fund his studies.<ref name="ToblerAutobiography" />
At the Department of Geography, University of Washington, Tobler participated in the quantitative revolution of the late 1950s, working with geography professors Edward Ullman and William Garrison.<ref name="Flowerdew2011"/><ref name="Wilson2015">Template:Cite news</ref> Here, he became one of many of Garrison's grad students (dubbed the "space cadets") who would go on to be highly influential geographers.<ref name="Unwin2019" /><ref name="AAG2015">Template:Cite web</ref><ref name="Getis1">Template:Cite journal</ref> His master's thesis is titled "An Empirical Evaluation of Some Aspects of Hypsometric Colors", and his dissertation "Map Transformations of Geographic Space".<ref name="Thesis">Template:Cite web</ref>
Career and academic organizations
Student jobs
While the GI Bill funded much of Tobler's undergraduate courses, he took on several jobs during this time. As an undergraduate student, Tobler was offered positions on research expeditions to the Arctic.<ref name="ToblerAutobiography" /> However, he turned down this position for a higher-paying job as a mucker in an underground gold mine in British Columbia. Tobler also worked parking cars part-time in Seattle and as a fire lookout in Seattle's Cedar River watershed. Tobler indicated that his choice to work in these positions rather than participate in research expeditions influenced his later specialization in geography. If he had taken the research position, he likely would have been a physical geographer.<ref name="ToblerAutobiography" />
After graduating with his B.S. in geography, Tobler was offered a position as a cartographic assistant at the University of Washington, which enabled him to pursue his master's degree.<ref name="ToblerAutobiography" />
System Development Corporation
In 1957, after obtaining his master's degree, Tobler began work for the System Development Corporation (SDC), a spinoff of the RAND Corporation, in Santa Monica, California.<ref name="ToblerAutobiography" /><ref name="Clarke1" /><ref name="Barns2006">Template:Cite journal</ref><ref name="Barnes2007">Template:Cite journal</ref> Here, Tobler worked on developing the Semi-Automatic Ground Environment (SAGE) system, a system that combined both RADAR and computers to detect Soviet bomber aircraft, coordinate interceptor aircraft, and ultimately prevent a Soviet nuclear first strike.<ref name="ToblerAutobiography" /><ref name="Barnes2007" /> Tobler's job entailed creating plastic overlay maps for Radar screens to train RADAR operators during exercises.<ref name="ToblerAutobiography" /><ref name="Clarke1" /> These maps were created manually but printed using computers such as the IBM 704.<ref name="Barnes2007" /> With these, SDC experimented with duplication and generating maps using computers directly. Tobler's experience here influenced his later academic publications and research on computer and analytical cartography.<ref name="Barns2006"/><ref name="Barnes2007" />
In 1958, the American Association of Geographer's annual meeting was held in Los Angeles, California.<ref name="Kostanick1958">Template:Cite journal</ref><ref name="AAG1958">Template:Cite journal</ref> At this meeting, Tobler arranged a tour of the computer facilities that SDC operated.<ref name="ToblerAutobiography" /><ref group=Note name=Note01/> Tobler stated this was his first experience with the AAG.<ref name="ToblerAutobiography" />
Pierce County planning commission
After the SDC, Tobler worked for two years for the Pierce County planning commission.<ref name="ToblerAutobiography" /><ref name="Monmonier2019" /> During this time, he worked to create land-use maps by manually shading with colored pencils.<ref name="ToblerAutobiography" /> He left this position after getting an NSF fellowship and returned to school to get his PhD.
University of Michigan
After earning his PhD in 1961, Tobler became an assistant professor at the University of Michigan.<ref name="Karan2000" /><ref name="Flowerdew2011"/><ref name="Michigan1">Template:Cite web</ref> While at the University of Michigan, Tobler was a member of the Michigan Inter-University Community of Mathematical Geographers (MICMOG), organized by fellow University of Washington geography PhD graduate William Bunge, which brought together faculty from both the University of Michigan and Michigan State University.<ref name="Karan2000" /><ref name="Bunge2001">Template:Cite journal</ref> These meetings sought to discuss topics related to quantitative geography, and organized joint seminars, which resulted in several discussion papers.<ref name="Karan2000" /><ref name="Golledge1979">Template:Cite journal</ref> At the MICMOG meetings, Tobler was given the nickname "Ptobler", as he was "the greatest cartographer since Ptolemy."<ref name="Bunge2001"/><ref name="Unwin2019" /> The MICMOG seminars and publications eventually led to the creation of the journal Geographical Analysis.<ref name="Karan2000" /> Tobler remained at the University of Michigan until 1977.<ref name="Michigan1"/>
University of California, Santa Barbara
In 1977, Tobler then moved to the University of California, Santa Barbara 1977, to be closer to the West Coast, where he grew up.<ref name="Karan2000" /><ref name="Flowerdew2011"/><ref>Template:Cite web</ref> Here, he continued his research in applying computers to cartography, flow, and other applications.<ref name="Karan2000" /> At UC Santa Barbara, he worked with geographers Reginald Golledge and Michael Frank Goodchild.<ref name="Flowerdew2011"/> Until his retirement, he held the positions of Professor of Geography and Professor of Statistics at the University of California, Santa Barbara.<ref name="AAG1" /> He was an active Professor Emeritus here until his death.<ref name="AAG1" />
Other organizations
Tobler was one of the principal investigators and a senior scientist in the National Science Foundation-sponsored National Center for Geographic Information and Analysis.<ref name="UCSantaBarbra2023">Template:Cite web</ref><ref name="AAG1" /> Tobler served on the National Research Council the Board on Earth Sciences.<ref name="Yang2018" /> He has been on the editorial board of several journals, including The American Cartographer, Journal of Regional Science, Geographical Analysis, and the International Journal of Geographical Information Systems. He was a charter member of the Urban and Regional Information Systems Association, a council member of the Regional Science Association, member and chairman of the Mathematical Social Science Board, and served as the United States delegate to the International Geographical Union Commission on Geographical Data Processing and Sensing.<ref name="Yang2018" /> Until his retirement, he was a member of the Royal Geographical Society of Great Britain.<ref name="Yang2018" />
Research and publications
While Tobler may have fewer publications than some contemporary geographers, his publications covered a broad range of topics and are considered of exceptional quality.<ref name="Unwin2019" /> His career in geography profoundly impacted the discipline, and he is perhaps the most influential geographer of the past century.<ref name="UCSantaBarbra2023"/> The Library of Congress maintains some of Tobler's early work in "The Waldo Tobler Collection" within the broader "Geographic Information Systems (GIS) & Geospatial Resources," and the UC Santa Barbra Library maintains a collection of his work in "The Waldo Tobler Academic Archives".<ref name="UCSantaBarbra2023" /><ref name="LibraryofCongress1">Template:Cite web</ref>
Cartography
Waldo Tobler described himself as a "geographical cartographer", and his research interests reflect this.<ref name="Clarke2015">Template:Cite book</ref> He published the first paper on using computers for making maps, established the discipline of analytical cartography, and contributed to the literature around thematic maps.<ref name="Karan2000" /><ref name="AAGGISS1" /><ref name="Clarke2015"/> His early work, including his dissertation, involved map projections, which he continued to work on throughout his life.<ref name="Karan2000" /> Tobler's time working at SDC on the SAGE system influenced his development of both computer and analytical cartography, and it is possible much of his work was kept confidential for some time due to military applications.<ref name="Barnes2007"/><ref name="Tobler1976">Template:Cite journal</ref> Geographer Mark Monmonier described Tobler as "arguably the twentieth century's most innovative cartographer."<ref name="Memoir20176">Template:Cite book</ref>
Map projections
One of Tobler's largest interests, especially early in his career, was map projections, with much of his dissertation focusing on them.<ref name="Karan2000" /> He is the inventor of novel and unusual map projections, including the family of Tobler hyperelliptical projections and the first derivation of the partial differential equations for area cartograms.<ref name="Karan2000" /><ref name="Tobler1973a">Template:Cite journal</ref> He also invented a method for smooth two-dimensional mass-preserving areal data redistribution.
In 1972, Tobler translated and published Johann Heinrich Lambert's 1772 "Notes and comments on the Composition of Terrestrial and Celestial Maps."<ref name="Karan2000" /><ref name="Clarke1" /> Tobler served as the third author of a book by Qihe Yang and John P. Snyder titled "Map Projection Transformation: Principles and Applications." This book was based on substantial translations by first author Qihe Yang from his work originally published in Chinese, and Tobler stepped in to help revise and assemble the book after Snyder died.<ref name="Yang2000">Template:Cite book</ref>
Computer cartography
Using his time and experience on the SAGE system, Tobler built upon the concepts and published his work in academic journals.<ref name="Barnes2007"/> Computer cartography originates as a concept from a paper written by Waldo Tobler as a graduate student in 1959, titled "Automation and Cartography".<ref name="LibraryofCongress1" /><ref name="Clarke1990">Template:Cite book</ref><ref>Template:Cite journal</ref><ref name="ArchaeologyAward2014" /> This paper's concepts, such as the "Map in-Map out" system (MIMO), was extremely influential in early Geographic Information Systems.<ref name="ArchaeologyAward2014" /><ref name="DeMers2023">Template:Cite web</ref> Tobler's research in developing applications for computer cartography is described by Mark Monmonier as occupying "a pivotal place in map history".<ref name="Monmonier2019" />
Analytical cartography
Tobler's research emphasized mathematical modeling and graphic interpretations in geography through cartography. In 1976, he published a paper titled "Analytical Cartography", which pioneered the discipline of analytical cartography.<ref name="Clarke1990" /><ref name="Clarke2000">Template:Cite journal</ref><ref name="McMaster2018">Template:Cite journal</ref> Analytical cartography is the foundation for many of the developments in Geographic information systems, and shapes how spatial analysis and cartography are taught today.<ref name="Clarke1990" /><ref name="Clarke2000" /> Keith C. Clarke defined Analytical cartography as "the theoretical and mathematical background behind cartography and the rules cartographers employed in the mapping process."<ref name="Clarke1990" /><ref name="Clarke2000" /> Analytical cartography is described as the leading paradigm in cartography and is likely Tobler's most enduring contribution to the discipline.<ref name="AAGGISS1" /><ref name="Clarke2015"/><ref name="Mcmaster2002">Template:Cite journal</ref><ref name="McMaster2018" />
Animated mapping
Tobler was among the first to create a true animated map, using animation to show change over time, in his famous 1970 paper, "A Computer Movie Simulating Urban Growth in the Detroit Region."<ref name="Clarke2015" /><ref name="Flowerdew2011"/> While this paper is most often cited as the first time the first law of geography was invoked, the focus of the paper was on animation to show change over time, with the first law an "aside" to this.<ref name="Clarke2015" />
Choropleth
Tobler formally introduced the unclassified color scheme for choropleth maps in 1973.<ref name="Peterson1979">Template:Cite journal</ref><ref name="dobson1973">Template:Cite journal</ref><ref name="dobson1980">Template:Cite journal</ref> Tobler argued that these maps would increase data density, and avoided many of the issues with Data binning and Statistical classification. There has been significant debate around the best approach to solve this issue with choropleth maps, and most choropleth maps today continue to make use of class breaks.<ref name="dobson1973" /><ref name="Peterson1979"/><ref name="dobson1980" /><ref name="Slocum2015">Template:Cite book</ref> Other approaches to creating classes in choropleth maps include using the Jenks natural breaks optimization, quantile, or equal class intervals.<ref name="McMaster">Template:Cite journal</ref><ref name="CDC">Template:Cite web</ref><ref name="ESRI1">Template:Cite web</ref>
Cartograms
Tobler's interest in cartograms stemmed from his interest in map projections.<ref name="Karan2000" /><ref name="Clarke1" /><ref name="Dorling2018">Template:Cite journal</ref> A chapter of his dissertation was developed for their creation, later adapted and published in the Geographical Review.<ref name="Karan2000" /><ref name="Tobler2004b">Template:Cite journal</ref> Tobler was among the first to use computers to create cartogram maps, with the rubber sheet method being the first method he proposed for their creation.<ref name="Dorling2018" /> This method uses rubbersheeting to transform the map coordinates based on the values of interest.<ref name="Dorling2018" /> He later proposed the "Pseudo-Cartogram" method, which approximates the pycnomirastic solution.<ref name="Tobler1986">Template:Cite journal</ref> Tobler's methods for creating cartograms are still employed, however they have some practical problems in implementation that can sometimes ruin topology.<ref name="Gastner2004">Template:Cite journal</ref> Tobler's methods serve as the basis for many other methods to create them.<ref name="Karan2000" />
Flow maps
Template:Main Tobler was also concerned with representing flow (due to its involvement with movement as a mechanism of geographic change), and considered them critical to understanding geography.<ref name="Karan2000" /> Combining this interest in movement with his knowledge of cartography, Tobler worked on incorporating flow maps to the problem.<ref name="Rey2020">Template:Cite journal</ref> While crude, the result of this research was that Tobler was the first to develop a software approach to creating flow maps in 1987.<ref name="GISTBoK" /><ref name="Rey2020"/><ref name="Koylu2023">Template:Cite journal</ref> The first demonstration of this technology by Tobler involved mapping the flow of money through the US Federal Reserve to the various US states.<ref name="Rey2020" /> In 2003, Tobler released a freeware, Microsoft Windows-based version of his flow representation software Flow Mapper.<ref name="Kim2012">Template:Cite journal</ref> Tobler's flow mapper software, and similar programs, continue to be built upon and applied to new topics.<ref name="Rey2020"/><ref name="Koylu2023"/>
Spatial interpolation and isorhythmic mapping
Spatial interpolation, which involves estimating values for a spatial surface from sample locations, is a major research focus and application in spatial analysis.<ref name="Murray2020">Template:Cite journal</ref> Tobler published several studies on different approaches to spatial interpolation, including an extension of bilinear weighted interpolation and other models.<ref name="Murray2020" />
Tobler's pycnophylactic approach to interpolation had early applications to interpolation of surfaces used in isarithmic mapping on computers.<ref name="Slocum2015" /> Tobler's approach was more straightforward then other methods of the time, and is more appropriate for samples collected at enumeration units like census tracts.<ref name="Slocum2015"/>
Spatial Resolution
According to Tobler, a dictionary definition of resolution is "the capability of making distinguishable the individual parts of an object". In terms of digital raster data, which consists of pixels, spatial resolution (also referred to as ground sample distance GSD) refers to the size of one pixel on the ground.<ref name="Tobler1987">Template:Cite journal</ref>
With regard to spatial resolution Tobler has formulated the following rule of thumb: "The usefulness of a GIS is constrained by its spatial resolution. The size of the smallest detectable feature is twice that of the resolution. The rule is: divide the denominator of the map scale by 1,000 to get the detectable size in meters. The resolution is one half of this amount."<ref name="Tobler1987"/>
The spatial precision of a database is expressed by a distance and a scale, which are mathematically related by this rule of thumb about the relation between map scale and image resolution. This rule is derived from the equivalent of 0.5 mm on a map, the smallest physical mark that a cartographer can make:
- Map Scale = Raster resolution (in meters) * 2 * 1,000
or
- Raster resolution (in meters) = Map Scale /(2 * 1,000)
By example, if the image resolution is 5m only the map scale should not be larger than 1:10,000. If you want to work at a scale of 1:2,000 the image resolution should be at least 1m.
Laws of Geography
In a 1970 paper in the journal Economic Geography where he discussed creating a computer movie of Detroit, Tobler stated, "I invoke the first law of geography: everything is related to everything else, but near things are more related than distant things".<ref name="Waters2017">Template:Cite book</ref><ref name="Tobler1970">Tobler W. R. (1970) "A Computer Movie Simulating Urban Growth in the Detroit Region", Economic Geography, 46(Supplement): 234–240</ref> This text following the colon in his statement, which was not the main focus of the paper, is now known as "Tobler's First Law of Geography", and is probably what Tobler is most famous for.<ref name="Sui2004">Template:Cite journal</ref><ref name="Barnes2004">Template:Cite journal</ref><ref name="Phillips2004">Template:Cite journal</ref><ref name="Goodchild1">Template:Cite journal</ref> The first law of geography is widely cited and is relevant today, particularly within the sub-discipline of geographic information science.<ref name="Goodchild2022">Template:Cite journal</ref><ref name="Westlund2013">Template:Cite journal</ref><ref name=Hecht1>Template:Cite book</ref><ref name="ref3">Template:Cite journal</ref> The Geographic Information Science and Technology Body of Knowledge "Model Curricula" in particular emphasizes the importance of the first law in the section on "Metrical relationships: distance and direction."<ref name="GISTBoK">Template:Cite book</ref> It is considered the theoretical basis of many statistics in spatial analysis, including those involved in cluster analysis and spatial autocorrelation (such as Moran's I).<ref name="Goodchild1986">Template:Cite book</ref><ref name="Anselin2020">Template:Cite journal</ref><ref name="Miller2004">Template:Cite journal</ref><ref name="Klippel2011">Template:Cite journal</ref> Spatial autocorrelation, and Tobler's 1970 paper, are considered central to modern approaches in technical geography.<ref name="Haidu2016">Template:Cite journal</ref> Tobler's first law is included in the children's book "ABCs of Geography" under the letter "T" for "Tobler".<ref name="Ferrie2022">Template:Cite book</ref><ref name="Puttick2023">Template:Cite journal</ref>
In a 1999 paper titled "Linear pycnophylactic reallocation comment on a paper by D. Martin," Tobler stated "Philosophically, the phenomenon external to an area of interest affects what goes on in the inside; a sufficiently common occurrence as to warrant being called the second law of geography."<ref name="Tobler1999">Template:Cite journal</ref> In his 2004 paper "On the First law of Geography: A reply", he discussed this concept again.<ref name="Tobler2004">Template:Cite journal</ref><ref name="McClain2023">Template:Cite book</ref><ref name="Thompson2024">Template:Cite web</ref> This has come to be known as Tobler's second law of geography.<ref name="McClain2023"/><ref name="Thompson2024"/> In Tobler's 2004 paper, he discussed other potential candidates for laws of geography, including one proposed by Giuseppe Arbia, R. Benedetti, and G. Espa in a 1996 paper that stated "Everything is related to everything else, but things observed at a coarse spatial resolution are more related than things observed at a finer resolution."<ref name="Tobler2004" /><ref name="ref1">Template:Cite journal</ref> This has come to be known as Arbia's law of geography.<ref name="Otto1">Template:Cite journal</ref>
The laws of geography, particularly Tobler's first law of geography, have been debated heavily in literature, with their status as scientific laws questioned, changes and amendments proposed, exceptions noted, and corresponding defenses by proponents of the laws.<ref name="Goodchild1" /><ref name="Walker1">Template:Cite journal</ref><ref name="Zhu">Template:Cite journal</ref><ref name="Manning2023">Template:Cite journal</ref><ref name="Zheng2023">Template:Cite journal</ref> Tobler weighed in on this debate surrounding his law, and others, in a 2004 article titled "On the First law of Geography: A reply".<ref name="Tobler2004" />
The Global Demography Project
The Global Demography Project was conducted by the National Center for Geographic Information and Analysis to map the human population in a series of 5 by 5 minute, or roughly one-kilometer, grids for most of the Earth.<ref name="Clarke2015" /><ref name="Dobson2000">Template:Cite journal</ref> While this project had serious limitations, largely due to data limitations, it was the finest scale population set produced to that point. The project was later supported by the Columbia University's Center for International Earth Science Information Network.<ref name="Clarke2015" />
Tobler's hiking function
Tobler was an avid hiker, and combined this with his interest in flow and movement to generate "Tobler's hiking function", also known as "Tobler's walking rule".<ref name="Dorling2018" /><ref name="Goodchild2020">Template:Cite journal</ref><ref name="Higgins2021">Template:Cite journal</ref> In this research, Tobler used himself as a subject, and published the results in a 1993 paper.<ref name="Goodchild2020" /> With this function, he sought to model and predict an average hiker's walking speed on various slopes.<ref name="Goodchild2020"/> Researchers have suggested this function has various real-world applications, including for self-driving cars, route decisions, and wayfinding apps.<ref name="Goodchild2020"/>
Archeological modeling
While at UC Santa Barbra in 1971, Tobler published models to predict the location of archaeological sites.<ref name="Flowerdew2011"/><ref name="Wilford1982">Template:Cite book</ref> Using the frequency of locations being noted in Cuneiform tablets discussing commercial transactions, he estimated the distance between the towns in Babylonia using a reverse gravity model.<ref name="Flowerdew2011"/><ref name="Wilford1982"/> Many of these predictions were for unknown locations and were proven accurate for at least three known towns; however, more excavation is needed to confirm the remainder of his predictions.<ref name="Flowerdew2011"/><ref name="Wilford1982"/> These ideas serve as the basis for numerous similar computer simulations to model ancient human migration, such as the settlement of Polynesia.<ref name="Wilford1982"/>
Awards and honors
The University of Zurich, Switzerland, awarded him an honorary doctorate in 1988.<ref name="Karan2000" /><ref name="UCGIS1">Template:Cite web</ref>
The Austrian Academy of Sciences created the Waldo Tobler Awards, which include the Waldo Tobler GIScience Prize and the Young Researcher Award in Geographic Information Science, to recognize Tobler's contributions to geographic research.<ref name="UCSantaBarbra2023" /><ref name="ÖAW3">Template:Cite web</ref> The awards seek to "encourage scientific advancement in the disciplines of Geoinformatics and/or Geographic Information Science."<ref name="ÖAW1" /> The Waldo Tobler GIScience Prize is issued to individuals who have "exhibited outstanding and sustained contributions to the discipline worthy of inspiring young scientists in Geoinformatics or Geographic Information Science, and has accomplished significant advances in these fields."<ref name="ÖAW1">Template:Cite web</ref> It has since been issued to David Mark (2016), Thomas Poiker (2017), Helena Mitasova (2018), Michael Batty (2019), Luc Anselin (2022), and Sara Irina Fabrikant (2023).<ref name="ÖAW2">Template:Cite web</ref> The Young Researcher Award in Geographic Information Science is awarded to "individuals, typically under the age of 35, acknowledging publications enhancing the body of Geoinformatics or GIScience literature."<ref name="ÖAW4">Template:Cite web</ref> It has since been issued to Filip Biljecki (2015), Xingjian Liu (2016), Song Gao (2016), Chen Min (2017), Pablo Cabrera Barona (2017), Auriol Degbelo (2018), Wei Luo (2018), Franz-Benjamin Mocnik (2019), Yingjie Hu (2019), Laura Knoth (2020),Yuhao Kang (2023 ), and Weiming Huang (2022).<ref name="ÖAW2" />
The American Association of Geographers Geographic Information Science and Systems Specialty Group (AAG GISS) and the publication Transactions in GIS hosts an annual session at the AAG conference titled "The Waldo Tobler Distinguished Lecture in GIScience."<ref name="AAGGISS1">Template:Cite web</ref><ref name="AAGGISS2">Template:Cite web</ref> This session honors the legacy of Waldo Tobler by featuring a leading researcher in GIScience.<ref name="AAGGISS1" /> The selected speakers are given the Tobler Lecture Award.<ref name="AAGGISS1" />
Mark Monmonier noted that Tobler "is one of a small handful of then-living persons accorded one of the 52 biographical entries in the twentieth-century volume of the History of Cartography."<ref name="Monmonier2019" />
Other awards and honors Tobler received throughout his life include:
- Member of the National Academy of Sciences of the United States
- Honorary Fellow, American Geographical Society (1965)<ref name="AGS1960s">Template:Cite web</ref>
- Osborn Maitland Miller Medal, American Geographical Society 1989<ref name="AGS1960s"/><ref name=honorslist>"The Cullum Geographical Medal" Template:Webarchive. American Geographical Society. Retrieved June 17, 2010.</ref>
- Meritorious Contributor Medallion, Association of American Geographers, 1971<ref name="AAG2">Template:Cite web</ref>
- Andrew McNally Award, 1986<ref name="UCSantaBarbra2023" />
- ESRI Lifetime Achievement Award, 1999.<ref name="UCSantaBarbra2023" /><ref name="ArcNews1999">Template:Cite web</ref>
- AAG Microcomputer Specialty Award, 1993.<ref name="UCSantaBarbra2023" />
- UCGIS Honorary Fellow, 2012<ref name="UCGIS1" />
- Archaeological Institute of America Pomerance Award for Scientific Contributions to Archaeology, 2014<ref name="ArchaeologyAward2014">Template:Cite journal</ref>
- GIS Hall of Fame Inductee, URISA (Urban and Regional Information Systems Association), 2016.<ref name="URISA1">Template:Cite web</ref>
Memorials
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Rachel Tobler (Waldo Tobler's widow) and the Geography department at UC Santa Barbra established the "Waldo Tobler Memorial Lecture Fund" in honor of Waldo Tobler.<ref name="UCSantaBarbra2023" /><ref name="GivingUCSB">Template:Cite web</ref> The fund helps "to support open lectures in the fields of demography, mapping and cartography, and geographic information science." Rachel Tobler donated Waldo Tobler's collection of papers and research materials to the UCSB Library, which now hosts them as "The Waldo Tobler Academic Archives".<ref name="UCSantaBarbra2023" /> On March 6, 2018, UCSB lowered their flag to honor Tobler after his death.<ref name="Yang2018" />
The journal Geographical Analysis dedicated a special issue titled "In honor of Waldo Tobler", edited by Alan T. Murray and Keith C. Clarke, which contained several articles discussing his research, including discussions and overviews of Tobler's contributions to the journal.<ref name="Murray2020" /><ref name="Murray2020b">Template:Cite journal</ref> The journal Cartography and Geographic Information Science honored Tobler with both an obituary authored by Keith C. Clarke and a graphic composite on the cover featuring themes of his work.<ref name="Clarke1" /><ref name="Cole">Template:Cite journal</ref> Two of the International Cartographic Association journals, (The Cartographic Journal, and the International Journal of Cartography), as well as the journals Imago Mundi, Transactions in GIS, and Annals of GIS honored Tobler with obituary articles.<ref name="Dorling2018" /><ref name="McMaster2018" /><ref name="Monmonier2019">Template:Cite journal</ref> The American Association of Geographers published a memorial for him on their website.<ref name="AAG1" /><ref name="Unwin2019" /><ref name="João2018">Template:Cite journal</ref>
See also
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Notes
References
External links
- Pages with broken file links
- Members of the United States National Academy of Sciences
- American geographers
- Swiss geographers
- 1930 births
- 2018 deaths
- University of California, Santa Barbara faculty
- University of Michigan faculty
- Human geographers
- University of Washington alumni
- American cartographers
- Geographic information scientists
- Scientists from Portland, Oregon