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I have a slope dataset. I have a polygon shapefile with territory within the extent of the slope map. I have to calculate the real surface area of this shapefile using the zonal statistics as table tool, which I have done and selected the Statistic Type "All" for results. Having these results, how do I know what the raster cell in square meter if for this extent? (ArcInfo 10.1)

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Typically you can look at the Layer Properties (by right-clicking the layer in the table of contents) and go to the "Source" tab and it should show you "Cell Size (X, Y) in the list of properties and values.

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The general properties (cell size, coverage extent, geographic projections, datums, units, etc) of raster datasets can be viewed in numerous ways with ESRI products. In ArcMap, you can right-click on the raster and select 'Properties'. Under the 'Source' tab, you will see a dialog window with the many properties of your raster that you can use to determine the cell size (with appropriate units). In ArcCatalog, the process is essentially identical, however the properties dialog window will be in a slightly different format.

This of course, is contingent upon your raster dataset being properly referenced before it was loaded into your project. If any of this raster information is missing, you will need to refer back to the original data source and examine any metadata that is available.

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The surface area cannot be computed solely from the sum of slopes.

(Think about what would happen for a perfectly horizontal surface: the sum of the slopes would be zero regardless of the surface's extent.)

The area of each raster cell, which is a rectangle, is the product of the two cell sides--assuming you are using an equal area projection. (If you are not using an equal area projection, first reproject the slope raster into an equal area projection and start from there.) Trigonometry teaches us that the factor by which its area is increased in constantly sloping terrain is the secant of the slope. Compute the secant in one of several ways depending on how the slope is expressed:

  • When the slope is expressed in degrees, the secant is the reciprocal of the cosine of the slope. (Make sure you express the slope in the units expected of your cosine function: degrees or radians.)

  • When the slope is expressed as a tangent, its secant is given by the formula

    secant = sqrt(1 + tangent^2)
    
  • When the slope is expressed as a percent, convert that to a tangent by first dividing by 100 and then apply the preceding formula.

After this preliminary calculation, the zonal sum of the secants of the slope, when multiplied by the area of any individual cell, gives the total area within each zone.

To guard against serious errors, display both the slope map and the secant map: they should look qualitatively similar, with secants near 1 corresponding to slopes near 0. No secant should be less than 1 (which is geometrically obvious: tilting the land cannot decrease its area compared to that of a horizontal patch). Except in extremely mountainous areas or near cliffs, most of the secants will be substantially less than 2.

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