When wildfire acreage is reported, does anyone know if local terrain is taken into consideration, or is the reported acreage the area as viewed on a map? I ask because the two figures are different. A square unit of area on a 30° slope would appear to be .866 square units on a map, whereas a square unit of area on a map would actually be 1.155 units of area on the slope (assuming I've done the math correctly, which I think I have). I'm guessing it's just the area as viewed on a map, because figuring out the average terrain would be pretty difficult, though not impossible.

  • $\begingroup$ Follow up question: land boundaries near active faults... $\endgroup$ – mankoff Jul 27 '15 at 18:09

The same issue arises when land is bought and sold. The area used is the flat area from a plan. Slope is not considered because it would require at lot of data because the rate of change of topography and slopes is never uniform. Also the calculations to determine the true area can be convoluted if the change in topography is complex.

  • $\begingroup$ I was not aware of that, @Fred. I always thought if you had an acre of land on an even 30° slope, you actually had an acre of land. So what you're saying is if you had an acre of land on an even 30° slope, you actually have .866 acres, right? Or to put it another way, whatever acreage you own, it is as viewed on a map. It actually make sense. $\endgroup$ – BillDOe Jul 24 '15 at 0:32
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    $\begingroup$ @BillOer: Land sales have a history. Despite us having the means to more easily determine true land area using computers, such methods were not available centuries ago. Land was sold from horizontal plans. It's easier to measure things using a rule from a horizontal plan. For the sake of consistency land areas still use the old methods of determining area. $\endgroup$ – Fred Jul 24 '15 at 0:42
  • $\begingroup$ Concerning 1 acre on a 30° slope you actually have more land. Draw a right angle triangle. The base is 1 acre & the slope is 1/(cos 30°) which is 1.15. So you end up with 15% more land $\endgroup$ – Fred Jul 24 '15 at 0:44
  • $\begingroup$ Fred, you're right. I was looking at the wrong set of numbers on my hastily sketched triangle. $\endgroup$ – BillDOe Jul 24 '15 at 0:50
  • $\begingroup$ If you were to try to consider surface area of the land rather than the acreage as described in the answer, then it would be dependent on the resolution of your DEM and would get rather fractal as you consider smaller and smaller features. $\endgroup$ – haresfur Jul 24 '15 at 2:42

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