Stand Volume and Growth:
Getting the Numbers

2. Using the numbers

Volume projections Your completed Volume Computation Form (Figure 4) includes all the information you need to determine past, present, and future stand volumes and the volume growth rate of your trees. Upon completion of the volume projections for your stand, you’ll have information that is essential to making well-informed decisions regarding the management of your woodland property. To obtain your volume projections, you need to perform some basic calculations and follow a few simple steps.

Step 1: calculate beginning average stand diameter To calculate the average stand diameter at the beginning of the 5-year growth period, merely double the average radial growth figure recorded on your Volume Computation Form (remember, we need diameter growth, so we double the radial growth figure). Subtract this number from your current average stand diameter to obtain the size of your trees at the beginning of the 5-year growth period.

Beginning average stand diameter = average stand diameter – (2 x average radial growth)

Step 2: calculate beginning average basal area per tree Now we’ll determine the basal area per tree at the beginning of the growth period. We do this by converting from diameter in inches to basal area in square feet by using the following formula:

Beginning average basal area per tree = (Average diameter at beginning of growth period)² x .005454

Step 3: calculate growth projection factor You’re ready to estimate how fast your stand is growing by calculating a growth projection factor (GPF). To compute the growth projection factor, you simply divide the current average basal area per tree from your Volume Computation Form by the average basal area per tree at the beginning of the growth period that you calculated in the previous step.

Growth projection factor = current average basal area per tree average basal area per tree at the beginning of the growth period.

Step 4: calculate future volume per acre Now you can project the future volume per acre by multiplying the current volume from your Volume Computation Form by the growth projection factor. This method assumes that current stand volume growth will continue at the same rate as the previous 5-year growth period. Its accuracy will depend on how consistently your stand is growing. For most young stands (less than 50 years), this estimate may be on the conservative side – that is, it may be slightly less than the growth that actually will occur. As the stand ages beyond 50 years, the trees will tend to slow down in their rate of growth.

Future volume of stand = Current volume x GPF

THIS SECTION GOES ALONGSIDE THE VOLUME PROJECTIONS Projecting volumes

Beginning average stand diameter For the stand, the beginning average stand diameter is: 13.002 (average stand diameter) - 2 x 0.60 (average radial growth) = 11.80 inches (5 years ago)

Beginning average basal area/tree You’ve determined the beginning average stand diameter to be 11.80 inches. The average basal area per tree at the beginning of the growth period will be: (11.80)² x .005454 = .759 ft.²

Growth projection factor Inserting the average basal areas into the GPF formula gives the growth projection factor. Once you have determined this number, you can look to the future. GPF equals: .922 = 1.215 .759

Future volumes Multiplying current stand volumes by the GPF shows us the stand in 5 years should have a volume of approximately 29,039 board feet (23,900 x 1.215), or 6955 ft.³ (5724 x 1.215).

Calculating Mean Annual Increment MAI is calculated for the life of the stand. Dividing the current total volume per acre by stand age gives: 23,900 = 478 board feet per acre per year 50

Periodic Annual Increment You want to calculate the PAI for the next 5 years. To do this, subtract the current total volume per acre of the stand by the future volume (remember future volume was determined by using the growth projection factor). 29,039 - 23,900 = 1,028 board feet per acre per year for the next 5 years 5 (years) PAI exceeds MAI, suggesting the stand is not biologically mature and should be allowed to continue growing. (although it may need thinning?)

Step 5: calculate mean annual increment Another useful stand number you can derive is the mean annual increment (MAI) of volume growth. This represents the average volume growth per acre per year over the total life of the stand. You have already generated the numbers necessary to determine MAI. It is calculated by dividing the total current volume per acre for the stand by the stand age.

Mean Annual Increment = total current volume per acre stand age

You can calculate the cubic-foot MAI for any stand age, but you can’t calculate board-foot MAI until the trees in a stand have reached a minimum merchantable size. Think of MAI as the long-term average or track record of the stand’s growth.

Step 6: calculate periodic annual increment The average annual volume growth of a timber stand measured over a specific time period is termed periodic annual increment (PAI). This figure is useful because volume growth per acre can vary substantially as the stand ages. The PAI of either board-foot or cubic-foot volumes can be calculated for any time period, but 5 or 10 year periods are most common. Calculate PAI by dividing the total volume per acre for the stand by the chosen time period (in years).

Periodic annual increment = total volume per acre at end of time period – total volume per acre at beginning of time period Given time period (years)

PAI can be used to measure previous growth or determine future growth projections. Core samples enable you to take measurements back from the present and your calculated growth projection factor enables you to determine a future periodic annual increment. This enables you to determine how your stand is growing by taking a “snapshot” over time.

Hypothetical ideal harvest time Foresters have a long tradition of analyzing timber stand growth. The pattern of growth for even-aged stands tends to be similar for all tree species (see Figure 4).

From analyses and long experience, foresters have derived the general rule that when PAI falls below MAI, the timber stand is “mature” – that is, it has passed its peak of wood growth production in the biological sense. Thus, the stand might be harvested if growth rate is the overriding factor in the harvest decision

The point where the PAI line crosses the MAI line also is the highest value for MAI. This point, therefore, is referred to as culmination of MAI. The stand will continue to add volume after this point, but at a slower rate than before. Thus, by comparing estimates of PAI and MAI, we can test whether our stands are biologically mature. Thinning stands can boost the growth of residual trees and delay the culmination of MAI.

Often, there are overriding factors such as cash flow or market cycles that dictate a timber harvest before or after culmination of MAI. By combining this biological information with financial analysis, you can tailor your management decisions to your own situation and objectives.