The accompanying maps were produced in conjunction with a larger study of spatial interaction. They are extracted here because they have as a common theme the movement of commodities

Tobler, W.

International Institute for Applied Systems Analysis (IIASA)

Commodity FieldsTobler, W.IIASA Working PaperWP-75-026March 1975 Tobler, W. (1975) Commodity Fields. IIASA Working Paper. WP-75-026 Copyright © 1975 by the author(s). http://pure.iiasa.ac.at/402/ Working Papers on work of the International Institute for Applied Systems Analysis receive only limited review. Views or opinions expressed herein do not necessarily represent those of the Institute, its National Member Organizations, or other organizations supporting the work. All rights reserved. Permission to make digital or hard copies of all or part of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage. All copies must bear this notice and the full citation on the first page. For other purposes, to republish, to post on servers or to redistribute to lists, permission must be sought by contacting repository@iiasa.ac.at COMMODITY FIELDSW. ToblerMarch 1975Working Papers are not intended fordistribution outside of IIASA, andare solely for discussion and ｩ ｮ ｦ ｯ ｲ ｾmation purposes. The views expressedare those of the author, and do notnecessarily reflect those of IIASA.RM-77-2LINKING NATIONAL MODELS OF FOOD AND AGRICULTURE:An IntroductionM.A. KeyzerJanuary 1977Research Memoranda are interim reports on research being con-ducted by the International Institt;te for Applied Systems Analysis,and as such receive only limited scientifk review. Views or opin-ions contained herein do not necessarily represent those of theInstitute or of the National Member Organizations supporting theInstitute.COMMODITY FIELDSThe accompanying maps were produced in conjunctionwith a larger study of spatial interaction.* They are ex-tracted here because they have as a common theme the move-ment of commodities. The larger study treats of more generalclasses of geographical interaction, specifies in greaterdetail the theoretical justification for the particulartechnique used, and develops additional consequences there-from. It is asserted that the method of representationemployed provides a particularly felicitous and dramaticsummary of the asymmetry of large geographical exchanges.A table of county to county trade in the united States wouldcontain in excess of 9 x 106 numbers, for example, and thisis an incomprehensible amount of data. A flow field, onthe other hand, showing and summarizing these data asa set of vectors seems more tractable. The reader knowledge-able in commodity studies is invited to comment on thedegree to which the maps do in fact accord with insightsobtained from alternatve modes of study and analysis. Thechoice of the particular commodities represented here wasmade on the basis that a person with general knowledge ofthe economic geography of the united States has a prioriexpectations in each case. The livestock flow pattern mayalso, for example, be compared with that given in G. Judge,J. Havlicek, and R. Rizek, "A Spatial Analysis of the u.S.Livestock Economy" (pp. 261-273 of G. Judge, and T. Takayama,Studies in Economic Planning Over Space and Time, New York,Elsevier, 1973), or, inter alia, E. Ullman, AmericanCommodity Flow, Seattle, University of Washington Press,1957.The data in each case consist of square (48 x 48),asymmetric, tables in which are indicated the dollar value*National Science Foundation Grant GS-34070X, "GeographicalPatterns of Interaction", the University of Michigan,Department of Geography, 1972-1974.- 2 -(M .. ) of goods moving from region i to region j. The data1)are all taken from J.M. Rodgers, State Estimates of Inter-regional Commodity Trade 1963 (Lexington--Heath Books,New York; 1971) as supplied on magnetic tape by theDepartment of Transportation. In addition the coordinates(x,y) of a point within each region are required, and,for display purposes, the coordinates of an outline of thearea. The following calculation is then performed.1 m M .. - M .. 1 [(X j x. ) , (Y. Yi)]-+ 1) J1 - -V. = L 0 0 1 )1 n-l M .. + M .. e:r-:-j=l 1) )1 1)jtiwhere2d ..1) = (X. - X.) 2 + (Y. _ y.) 2 0) 1 J 1-+The vector V." is1plotted at the map location (XiY i ), after an arbitraryscaling appropriate to the particular map. It appears tobe a dimensionless number, the relative net exchange. Theinterpretation is thus not quite as simple as would be thecase for a vector field based on the net flows. The fieldseems to show the directional tendancy toward trade ratherbetter than would the absolute amount of flow. "If, at anypoint on the map, a commodity were thrown into the air,it would tend to fall in the direction indicated by theexchange field". The patterns are more easily studiedwhen the irregular scattter of vectors is interpolated toa regular lattice, and interpolated vector fields are thusalso shown for each commodity. This has the advantage ofreducing the somewhat arbitrary placement of vectors withineach state, but also the compensating disadvantage ofyielding values outside of the U.S. borders, where thereｾ ｲ ･ no observations.w. 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Commodity Fields

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