GeoWorld August 2012

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Altering Our Spatial Perspective through Dynamic Windows BEYONDMAPPING T BY JOSEPH BERRY he use of "roving windows" to summarize ter- rain configuration is well established. The po- sition and relative magnitude of surrounding values at a location on an elevation surface have long been used to calculate localized terrain steepness/slope and orientation/aspect. A search radius and geometric shape of the window are specified, then surface values within the window are retrieved, a summary technique applied (e.g., slope, aspect, average, coefficient of variation, etc.) and the resulting summary value assigned to the center cell. The roving window is systematically moved throughout the surface to create a map of the desired surface summary. Elevation Warps The top portion of Figure 1 illustrates the plani- metric configuration of three locations of a circular fixed window with a radius of 10 grid spaces. When superimposed onto the surface, the shape is warped to conform to the relative elevation values occurring within the window. Note that the first location is mod- erately sloped toward the south, the second location is steeply sloped toward the west, and the third loca- tion is fairly flat with no discernible orientation. What your eye detects is easily summarized by mathematical algorithms, with the resultant values for all the surface locations creating continuous maps of landform character, such as surface roughness, tilted area and convexity/ concavity as well as slope and aspect (see "Author's Note 1," page 11). A "weighted window" is a variant on Joseph Berry is a principal in Berry & Associates, consultants in GIS technology. He can be reached via e-mail at 10 the simple fixed window that involves preferential weighting of nearby data values. For example, inverse distance-weighted interpolation uses a fixed shape/size of a roving window to identify data samples that are weight- averaged to favor nearer sample values more than distant ones. GEO W ORLD / AUGUST 2O12 Alternatively, a user-specified weighting kernel can be specified as a decay function (see "Author's Note 2") or any other weighting preference, such as assigning more importance to easterly conditions to account for strong and dry Santa Ana winds when modeling wildfire threat in southern California. It's common sense that these easterly conditions are more influential than a simple or distance-weighted average in all directions. "Dynamic windows" use the same basic process- ing flow, but don't use a fixed reach or consistent geometric shape in defining a roving window. Rather, the size and shape are dependent on the conditions at each map location and vary as the window is moved over a map surface. Dynamic Considerations For example, Figure 2 depicts a roving window based on uphill, downhill and across-slope move- ments from the center location. A lot of spatial processes respond differently to these basic land- form conditions. For example, uphill conditions can contribute surface runoff to the center cell, downhill locations can receive flows from the center cell, and sedi- ment movement at the across-slope locations is independent of the center cell. Wildfire movement, however, is most rapid uphill, particularly in steep terrain, due to preheating of forest fuels. Hence, downhill conditions are more important in modeling threat at a location than either the across or uphill surrounding conditions. Another dynamic consideration is effective distance (see "Author's Note 3"). For example, a window's geographic reach and direction can be a function of intervening conditions, such as the relative habitat preference when considering the surroundings in a wildlife model. The window will expand and con- tract depending on neighboring conditions, forming Figure 1. Fixed windows form circles in planimetric space, but they become warped when fitted to a 3-D surface.

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