Academic journal article The Geographical Review

The Flatness of U.S. States

Academic journal article The Geographical Review

The Flatness of U.S. States

Article excerpt


Asked which U.S. state is the flattest, in a recent nationwide poll, 33 percent of respondents said Kansas and 23 percent said Florida (Kozak and others 2013). Kansans know well this popular notion that Kansas is exceptionally flat, yet any mildly alert observer can see that most of the state is rolling to quite hilly. Indeed, the Great Plains region as a whole is not as flat as most Americans think it ought to be.

What is the flattest state? Florida is the obvious answer, since its highest point is only 105 meters above sea level, but 77 percent of all respondents, including 62 percent of Florida residents, did not recognize its overwhelming flatness.

Which state is second and how do other famously flat states rank when measured geomorphometrically? Flow well does perception match reality? Landforms can now be measured rigorously over large areas and these questions can be tested empirically.

In the past century, at least three successful attempts have been made to map the physiography of U.S. terrain, and slope has been a key variable in each algorithm (Fenneman 1928, 1931, 1938; Hammond 1954; Sayre and others 2010). Areas of low slope are discernible in the final results, and some of the algorithms have been automated in recent years (Dikau 1989; Dikau and others 1991; Thelin and Pike 1991). The results are suitable for synoptic characterization of large areas at coarse scale, but they do not relate directly to personal perception of topographic landforms at fine scale.

We aimed for a specific measure of flatness that would mimic human perception in situ at close range. Our approach utilized only free and open source Geographic Information Systems (GIS) software, specifically GRASS GIS 6.4 (GRASS Development Team 2010) and Quantum GIS version 1.5 (QGIS Project 2013). Our definition of flatness utilizes a ray-tracing algorithm, r.horizon in GRASS (Neteler and others 2008; Huld and others 2013) performed along multiple directions and then combined to produce an index of flatness. Horizontally, the algorithm projects 16 radians from the center point of each 90-meter cell (1) at uniform intervals of 22.5 degrees of azimuth. Vertically, for each radian the algorithm constructs an angle of incidence between the earth tangent and the nearest intersection with a higher cell on the terrain. The ray continues outward to a distance of 5,310 meters with the output being the largest angle encountered along the ray. Determining the appropriate distance to extend the ray relies on a visibility-at-sea conceptual model of flatness. Using the appropriate equation from the Annapolis Book of Seamanship (Rousmaniere and Smith 1999), it was determined that an observer who is 1.83 meters tall, focusing solely on the horizon, can see a distance of 5,310 meters

Once all 16 rays were computed for each cell, they were classified into binary "flat or not-flat" categories. This again required some estimation to determine at what angle of incidence a flat landscape changes into a not-flat landscape. Based on personal experience with Great Plains landscapes, the authors determined that an angle of 0.32[degrees] was the appropriate end point for the classification. In practical terms, the visual effect is equivalent to observing a stand of trees 15 meters tall at 2,655 meters distance, or a 30-meter tree at 5,310 meters distance. (This example serves purely as an illustration related to ordinary human experience; trees do not count in our elevation figures.) This directional approach may seem odd from the viewer's perspective at any given cell, but it means, conversely, that any promontory (such as any cell more than 30 meters higher than its neighboring cells) exerts an influence over all cells occurring within 5,310 meters of it (Figure 1). This approach is not concerned with depressions (lower elevations) relative to the surrounding area--for example, small canyons or arroyos--because observers often ignore such depressions in perceiving "flatness" and, in many cases, cannot see them anyway. …

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