The Average End Area Method is Not Generally Correct for Pond Volume Calculations

When calculating the volume of a pond using elevation contours, the U.S. Army Corps of Engineers H.E.C. software (H.E.C. 1 and HEC-HMS) uses the Conic Volume Method instead of the often-used Average End Area Method.  The Conic Volume Method is generally more correct and efficient, and can give significantly different results than the Average End Area Method.  Below are some examples:

Example 1: Square pond

An ideal square pond with a 100 x 100 top, a 60 x 60 bottom, and 10 depth (a truncated pyramid)

Average End Area Method

V=10/2*(10,000 + 3600)
= 68,000

Conic Volume Method

V=10/3*(10,000 + 3600 + sqrt(10,000*3600))
= 65,333

True Volume

Truncated pyramid formula is same as conic volume formula.  Average End Area overestimates the volume.

Example 2: Long pond

A long, narrow pond with a 1000 x 10 top, a 994 x 4 bottom, and 2 depth (a truncated pyramid)

Average End Area Method

V=2/2*(10,000 + 3976)
= 13,976

Conic Volume Method

V=2/3*(10,000 + 3976 + sqrt(10,000*3976))
= 13,521

True Volume

Once again, the truncated pyramid formula is same as conic volume formula.  Average End Area overestimates the volume again, though less severely.

Summary

The Average End Area Method always overestimates volume for an ideal shape, whether square or round.  The degree of overestimation is reduced when a pond is long and narrow, or when contour interval is reduced (additional data is collected/entered ).  For least effort (data collection and entry) and best results, use the Conic Volume Method every time.