GeoWorld January 2012

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SpatialSTEM Has Deep Mathematical Roots BEYONDMAPPING R BY JOSEPH BERRY ecently my interest has been captured by a new arena and expression for the conten- tion that "maps are data," spatialSTEM (sSTEM for short), as a means for redirecting educa- tion in general and GIS education in par- ticular. I suspect GeoWorld readers have heard of STEM (Science, Technology, Engineering and Mathematics) and the educational crisis that puts U.S. students well behind many other nations in these quantitatively based disciplines. Although Googling around the globe makes for great homework in cultural geography, it doesn't advance quantita- tive proficiency, nor does it stimulate the spatial- reasoning skills needed for problem solving. A lot of folks, ranging from Fareed Zakaria of Time and CNN to Bill Gates to U.S. President Barack Obama, are looking for ways that the United States can recapture its leadership in the quantitative fields. That's the premise of spatialSTEM: "maps are numbers first, pictures later," and we do mathematical things to mapped data for insight and better understanding of spatial patterns and relationships within decision-making contexts. Joseph Berry is a principal in Berry & Associates, consultants in GIS technology. He can be reached via e-mail at 10 Structural Differences Figure 1 outlines the important com- ponents of map analysis and modeling within a mathematical structure that has been in play since the 1980s (see "Author's note," page 11). Of the three disciplines forming geotechnology (remote sensing, GIS and GPS), GIS is at the heart of converting mapped data into spatial information. There are two primary approaches for generating this information: mapping/geo-query and map analysis/modeling. The major differences between the two approaches lie in the structuring of mapped data and their intended use. Mapping and geo-query use a data structure akin to manual mapping in which discrete spatial objects (points, lines and polygons) form a collection GEO W ORLD /JANUAR Y 2O12 of independent, irregular features to characterize geographic space. For example, a water map might contain categories of spring (points), stream (lines) and lake (polygons), with the features scattered throughout a landscape. Map analysis and modeling procedures, however, operate on continuous map variables (i.e., map surfaces) composed of thousands of map values stored in georegistered matrices. Within this context, a water map no longer contains separate and distinct features, but is a collection of adjoining grid cells with a map value indicating the characteristic at each location (e.g., spring = 1, stream = 2 and lake = 3). Vectors and Rasters Figure 2 illustrates two broad types of digital maps, formally termed vector for storing discrete spatial objects and raster for storing continuous map sur- faces. In vector format, spatial data are stored as two linked data tables. A "spatial table" contains all the X,Y coordinates defining a set of spatial objects that are grouped by object-identification numbers. For example, the location of the forest polygon identified on the figure's left side is stored as ID#32, followed by an ordered series of X,Y coordinate pairs delineat- ing its border (connect the dots). In a similar manner, the ID#s and X,Y coordinates defining the other cover-type polygons are sequen- tially listed in the table. The ID#s link the spatial table (where) to a corresponding "attribute table" (what) containing information about each spatial object as a separate record. For example, polygon ID#31 is characterized as a mature 60-year-old Ponderosa Pine (PP) forest stand. Figure 1. A conceptual overview describes the SpatialSTEM framework. Imagery/LIDAR Special Issue

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