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Figure 2. Proximity rings extending into urban areas are calculated and used to incrementally “step” the flame-length information into the urban area. The Ring of Ooze Figure 2 shows the first step in extending wildfire con- ditions into an urban area. A proximity map from the urban edge is created and then divided into a series of rings. In this example, a 180-meter overall reach into the urban no-data area uses three two-cell rings. A roving four-cell window is used to average the neighboring flame lengths for each location within the first ring, and these data are added to the original data. The result “oozes” the flame lengths a little bit into the urban area. In turn, the second ring’s average is computed and added to the original first-ring data to extend the flame length data a little bit more. The process is repeated for the third ring to “ooze” the original data the full 180 meters (six cells) into the urban area (see Figure 3). Master Strokes It’s important to note that this procedure isn’t estimat- ing flame lengths at each urban location, but is a “first cut” at extending average flame-length information into the urban fringe based on the nearby wildfire-behavior conditions. Coupling this information with a response function implies greater loss of property where the nearby flame lengths are greater. Locations in red identify generally high neighboring flame lengths, while green identifies generally low locations. What’s novel in this procedure is the iterative use of nested rings to propagate the information; “oozing” the data into the urban area instead of one large “gulp.” If a single large roving window (e.g., a 10-cell radius) were used for the full 180-meter reach, inconsistencies would arise. The large window Figure 3. The original smoothed flame-length information is added to the first ring’s data and then sequentially to second- and third-ring data for a final result that extends the flame-length information into the urban area. JUL Y 2O11 / WWW . GEOPLA CE . COM 11 produces far too much smoothing at the urban outer edge and has too little information at the inner edge, as most of the window will contain no data. The ability to “iteratively ooze” information into an area step-by-step keeps the data bites small and localized, similar to the brush strokes of an artist. Author’s Note: For more discussion of roving-window concepts, see the online book, Beyond Modeling III, Topic 26, “Assessing Spatially Defined Neighborhoods,” at www.innovativegis.com/ Basis/MapAnalysis/Default.htm.