Issue link: https://read.dmtmag.com/i/62129
Needed Restructuring Much of the earlier efforts in structuring a framework for quantitative map analysis focused on how analyti- cal operations work within the context of Focal, Local and Zonal classification by C. Dana Tomlin, or even my own Reclassify, Overlay, Distance and Neighbors classification scheme (see the top portion of Figure 2 and "Author's Note 3"). The bottom portion of Figure 2 outlines a restructuring of the basic spatial-analysis operations to align with traditional mathematical concepts and operations (see "Author's Note 4"). This provides a means for the STEM community to jump right into map analysis without learning a whole new lexicon or an alternative GIS-centric mindset. Recasting 'On the Fly' Figure 3 outlines the conceptual development of three of these operations. The top set of graphics identi- fies the Calculus Derivative as a measure of how a mathematical function changes as its input changes by assessing the slope along a curve in 2-D abstract space. In an equivalent manner, the Spatial Derivative creates a slope map depicting the rate of change of a continuous map variable in 3-D geographic space. Advanced Grid Math includes most of the buttons on a scientific calculator to include trigonometric functions. For example, calculating the "cosine of the slope values" along a terrain surface and then multiplying times the planimetric surface area of a grid cell to solve for the increased real-world surface area of the "inclined plane" at each grid location. The Calculus Integral is identified as the "area of a region under a curve," expressing a mathematical function. The Spatial Integral counterpart "summa- rizes map-surface values within specified geographic regions." The data summaries aren't limited to a total, but can be extended to most statistical metrics. By recasting GIS concepts and operations of map analysis within the general scientific language of math/statistics, we can more easily educate tomorrow's "movers and shakers" in other fields in "spatial reasoning"—to think of maps as "mapped data" and express the wealth of quantitative-analysis thinking they already understand on spatial variables. Innovation and creativity in spatial problem solving is being held hostage to a trivial mindset of maps as pictures and a nonspatial mathematics that presuppose mapped data can be collapsed into a single central-tendency value that ignores the spatial variability inherent in data. Simultaneously, the "build it (GIS) and they will come (and take our existing courses)" educational paradigm isn't working, as it requires potential users to become "GIS'perts" in complicated software systems. Mobility/GPS Special Issue Figure 2. Alternative frameworks are described for quantitative map analysis. GIS must take an active leadership role in leading the STEM community to the similarities/differences and advantages/disadvantages in the quantitative analysis of mapped data—there's little hope that the STEM folks will make the move on their own. Next month, I'll consider recasting spatial-statistics concepts and operations into a traditional statistics framework. Author's Notes: 1) See "A Multifaceted GIS Community," in Topic 27, "GIS Evolution and Future Trends," in the online book, Beyond Mapping III, at www.innovativegis.com. 2) Bruce Alberts in Science, Jan. 20, 2012, Vol. 335, No. 6066, page 263. 3) See "An Analytical Framework for GIS Modeling" at www.innovativegis.com/basis/ Papers/Other/GISmodelingFramework. 4) See "SpatialSTEM: Extending Traditional Mathematics and Statistics to Grid-based Map Analysis and Modeling" at www.innovativegis.com/basis/Papers/ Other/SpatialSTEM. Figure 3. A series of graphics show the conceptual extension of derivatives, trigonometric functions and integrals to mapped data and map-analysis operations. APRIL 2O12 / WWW . GEOPLA CE . COM 11