calculate areas

June 12 2009 | 0 comments
Categories: Map Data

I am calculating the areas of polygons representing a world land cover distribution. The polygons are derived from satellite images interpretation and are distributed within the north-south tropical zone. All the polygons are shapefiles projected in lat long WGS84.

In areas where polygons extends mainly north-south I have projected the shapefiles into the relevant UTM zone and have applied the “calculate areas” script from Spatial Statistics Tools, Utilities. For areas with continental dimension and distribution east-west I have instead used the Albers-Equal Area projection.

I have experienced that by converting the same shapefile into different equal-area projections (for example Albers Equal Area, Mollweide, Lambert Azimuthal Equal-Area) the values of the areas are not the same even if the above projections are all considered "equal area" and the shapefile is the same but just projected into the relevant equal-area projection. I believe this is due to the different parameters and formulas from which the above projections are built?
As I am requested to explain in some details the procedure applied for areas calculation, I will be grateful to receive from you some feedback and/or references regarding the best approach and general criteria to follow for the choice of the right projection when an area calculation is needed and some details on the "calculate areas" script.

Many thanks for your help

### Mapping Center Answer:

The Calculate Areas tool calculates the area of a polygon based on the straight-line distance between vertices. The Project Tool projects the polygon vertices only. Therefore, when you project the dataset, the distance between polygon vertices can vary significantly from one projection to the next. Just as you suspected, the difference in area values is a result of the different projection parameters of your selected projections.

One way to reduce the difference between the calculated values between projections is to densify the polygon features before you project them. The ArcGIS Desktop Discussion Conference has a thread on this topic.

Sinusoidal, Cylindrical Equal Area and Bonne projections produce the most consistent results for the polygon area calculations. All are world equal area projections. You could use one of these projections or average the calculated values from the three projections. The table below shows the calculated areas (in square meters) for the World Ecological Zones (Holdridge Life Zones 1990) in the Sinusoidal, Cylindrical Equal Area and Bonne projections.

Keep in mind that the calculated areas will only be "accurate" relative to some specified parameter(s). Error can be introduced anywhere along the way and can be related to:

• Projecting the data
• The interpretation and derivation of the polygons from satellite imagery
• The spatial resolution of the original satellite imagery
• Human error
• And more...

To learn more about accuracy and maps, check out "Chapter 10: Map Accuracy and Uncertainty" in the Map Use: Reading and Analysis book that ESRI Press released earlier this year.