# Calculating area of polygon considering relief in ArcGIS Desktop?

I work in a fire department and i'm mapping all the fires that occur in my area, creating polygons that represent burnt areas. my problem is that the values are not accurate... for instance, arcgis calculates one of the polygons as 51000 square meters when, in reality, I know that the real area is 60000 square meters. the issue is that the relief is not being considered for the measurement and I need to have the most accurate possible values.

is there any way to calculate an area considering the relief in arcgis 9.3?

• Do you have a DEM? If so, you should be able to calculate surface area within the polygons. However, I don't have the Spatial Analyst extension so I'm not sure if you can calculate it using that. You should be able to use open source software such as GRASS GIS to calculate surface area. Check out the r.surf.area tool.
– Fezter
Aug 8, 2012 at 6:38
• The average slope of your area would have to be 32 degrees in order to increase 5.1 HA to 6.0 HA. If this is the case, follow @Fezter's advice. If not, the problem likely lies with the coordinate system being used. You are using an equal-area projection, right? Aug 8, 2012 at 13:30
• @fetzer - yes, i've the corresponding DEM, but i can't find a way of making the correct mesure... i never worked with grass, so it's like chinese to me... Aug 14, 2012 at 0:14
• @whuber - system coordinates i use: Datum_73_Hayford_Gauss_IPCC Projection: Transverse_Mercator Aug 14, 2012 at 0:21

As mentioned in the comments, you should first make sure that you are using an equal area projection to avoid inaccurate area measure. Mercator (and Transverse Mercator) are NOT equal area (they are conformal), so that area will be distorted. With a Transverse mercator projection in its "domain" (close to its central meridian), the distortion is however limited and does not explain the size difference alone. Working with, e.g., Lambert Azimuthal Equal Area (EPSG 3035)*, would solve this first issue.

Now for the elevation, you can handle the relief using the following method :

• compute the slope of your DEM (in degree)
• create a new raster with map algebra (horizontal_pixel_area/cos(slope))
• use zonal statistics as a table to compute the sum of slope corrected pixel areas inside your polygon.

*I assume you work in Portugal, so I selected an European coordinate system.