FR 3218/5218 Spring 2008

Due April 18, 2008

This assignment covers site index equations, application of a stand density index chart, and application of a stocking chart. You will need to use the blank charts handed out in class as part of your answers to questions 2. and 3.

It is important that you show your work. Credit cannot be given if answers are not accompanied by intermediate calculations that demonstrate how you arrived at the final solution. The TA will use the intermediate calculations to determine the level of partial credit to be granted for wrong answers. If you turn in a printout of a spreadsheet be sure to include the formulas you used to calculate all intermediate and final estimates (see Excel insert in the solution set for Assignment 1).

1. The following equation was developed based on a sample of dominant trees from a range of white spruce stands:

ln H = 4.1 - 22.6 (1/A)

where ln = natural logarithm, H = height of dominants (feet) and A is total stand age (years).

1. Obtain a base age 50 anamorphic site index __equation__ for white spruce (as described in your text, pages 315-316).

2. Three dominant trees were measured in a 40 year old white spruce plantation. Their total heights were 55, 60, and 58 feet. What is the estimated site index for the plantation?
3. How tall would you estimate the dominant white spruce in the plantation in b. to be at age 55 years?
4. The site index conversion equation for white spruce to aspen is: SI(white spruce) = -15.1 + 1.14 * SI(aspen) (both base age 50 years). If aspen were growing on the site of the white spruce plantation in b., how tall would dominant aspen be at age 50 years?
5. Given the observed variability in height, how many trees should have been sampled to obtain a standard error for average height of 2.0%?
   

2. Using the information below find the thinning schedule for a red pine plantation on site index 60 (feet at base age 50) land planted at 700 stems per acre where: 1) the upper stocking limit is 63% of maximum, 2) the lower stocking limit is 36% of maximum, and 3) final harvest will occur when average stand diameter reaches 12.0 inches. The thinnings will be row thinnings. For each thinning and the final harvest find: stems per acre, basal area per acre, cubic foot volume per acre, and age at time of (start of) thinning (and final harvest). Also find stems per acre and basal area per acre after thinning (residual stand). The equations you'll need are:

• log N = 4.3 - 1.6 log D (stand density boundary line)

• H = S (1.96 - 2.18 exp(-.0164 A)) (site index curves)
• V = .0022 D^2 H N
• D = 17.2 V^.25 N^-.46

where log = base 10 logarithm, exp = inverse natural logarithm, N = stems per acre, N^-.46 means raise N to the -.46 power (etc.), D = quadratic mean DBH, H = height of dominants/codominants, S = site index (base age 50), A = age, and V = cubic foot volume per acre.

Calculations should be carried out with the equations (not the chart).

Is this a reasonable rotation age for red pine? Provide evidence for your answer. Are the time intervals between stand entries reasonable (practically speaking)?

Illustrate (only) the thinning schedule on the chart, including drawing the lower and upper stocking limits.

Note: Here you start with a trees planted value and "proceed upward and to the left": just opposite of what we did in class.

3. For the oak stand we used in class to illustrate application of a stocking chart, the TSI cut removed 25 square feet of the 40 square feet of unacceptable growing stock (UGS). The forester in charge decides to let the stand grow 18 years after the TSI cut and then thin basal area back to 95 square feet. Assuming the UGS basal area grows at a rate of 2.5% per year while the acceptable growing stock (AGS) basal area grows at a rate of 4.0% per year and there is no mortality:

1. what will stocking percent be in 18 years, before thinning

2. what will stocking percent be in 18 years, after thinning
3. how much of the basal area removed will be UGS
4. how much of the basal area removed will be AGS

Illustrate the further development of the stand on the stocking chart.