Periodic annual increment

Periodic annual increment (growth), or PAI for short, is the change in the size of a tree between the beginning and ending of a growth period, divided by the number of years that was designated as the growing period (Avery, 339). The graph of PAI increases rapidly and then quickly declines after cresting.

File:Sheet2 Chart 1.JPG

Equation

$PAI=(Y2-Y1)/(T2-T1)$

Where: Y is the yield (volume, height, DBH, etc.) at times 1 and 2 and T1 represents the year in which you start the growth period, and T2 is the end year.

Example: Say that the growth period is from age 5 to age 10, and the yield (height of the tree), is 14 feet at the begining of the period and 34 feet at the end.

Then: (34-14) / (10-5) = 4 feet/year

Uses

The maximum point on the curve of PAI is the same as the inflection point on a graph of yield versus time. The inflection point is the point corresponding to the fastest change in yield.

When mean annual increment (MAI) and periodic annual increment (PAI) are graphed together, the point in which they intersect is called the biological rotation age. The biological rotation age is the age in which a stand should be harvested to maximize long-term yield.

File:Sheet1 Chart 3.JPG

File:Sheet2 Chart 2.JPG

References

Avery, Thomas E., Harold E. Burkhart. Forest Measurements, fifth edition. New York, New York: McGraw-Hill, 2002.

Chapman, Herman H., Forest Mensuration, second edition. New York: John Wiley & Sons, Inc., 1921.

--Stabs79 (talk) 00:57, 28 March 2008 (UTC)Stephen DeFrancoStabs79 (talk) 00:57, 28 March 2008 (UTC)--