GeoWorld October 2012

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To Boldly Go Where No Map Has Gone Before BEYONDMAPPING S BY JOSEPH BERRY Of course, this resolution is far too coarse for everal previous "Beyond Mapping" columns described a mathematical framework (dare I say a "map-ematical" framework?) for quantitative analysis of mapped data (see "Author's Notes," page 11). Recall that spatial analysis operations investigate the "contextual" relation- ships within and among maps, such as variable-width buffers that account for intervening conditions. Spatial statis- tics operations, however, examine the "numerical" relationships, such as map clustering, to uncover inherent geo- graphic patterns in data. The cornerstone of these capabilities lies in the grid-based nature of the data that treats geographic space as continuous map surfaces composed of thousands of cells, with each containing data values that identify the characteristics/conditions occurring at each location. This simple matrix structure provides a detailed account of the unique spatial distribution of each map variable, and a geo-registered stack of map layers provides the foothold to quantitatively explore their spatial patterns and relationships. Pair them Up The most fundamental and ubiquitous grid form is the latitude/longitude (lat/ lon) coordinate system that enables every location on Earth to be specified by a pair of numbers. The upper portion of Figure 1 depicts a 2.50° lat/lon grid Joseph Berry is a principal in Berry & Associates, consultants in GIS technology. He can be reached via e-mail at 10 forming a matrix of 73 rows by 144 col- umns = 10,512 cells in total, with each cell having an area of about 18,735 square miles. The figure's lower portion shows that the data could be stored in Microsoft Excel, with each spreadsheet cell directly corresponding to a geographic grid cell. In turn, additional map layers could be stored as separate spreadsheet pages to form a map stack for analysis. GEO W ORLD / O CT O BE R 2O12 Figure 1. Latitude and longitude coordinates provide a universal framework for parsing Earth's surface into a standardized set of grid cells. most map-analysis applications, but it doesn't have to be. Using the standard single-precision floating-point storage of lat/lon coordinates expressed in decimal degrees, the precision tightens to less than half a foot anywhere in the world (365,214 feet/degree * 0.000001 = 0.365214 feet * 12 = 4.38257 inches or 0.11132 meters). However, current grid-based technology limits the practical resolution to about one meter (e.g., IKONOS satellite images) to 10 meters (e.g., Google Earth), due to the massive amounts of data storage required. For example, to store a 10-meter grid for the state of Colorado, it would take more than 2.5 billion grid cells (26,960 square kilometers = 269,601,000,000 square miles / 100 square meters per cell = 2,696,010,000 cells). To store Earth's entire surface (148,300,000 square kilometers = 148,000,000,000,000 square miles / 100 square meters per cell = 1,483,000,000,000), it would take nearly 1.5 trillion cells. At first, these storage loads seem outrageous, but with distributed cloud computing, the massive grid can be "easily" broken into manageable mouthfuls. Users select an area of interest, and data for that area are downloaded and stitched together. For example, Google Earth responds to users' screen interactions to near-instantaneously download millions of pixels, allowing them to pan/zoom and turn on/off map layers that are just a drop in the bucket of the trillions of pixels and grid data available in the cloud.

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