Exam 4                                                 FR 3218/5218                                 Semester II, 2006

 

If it is not clear what a question is asking, request clarification from the instructor. Misreading a question is not grounds for partial credit. To receive partial credit for a calculation problem, formulas and intermediate calculations must be legibly shown. A good strategy would be to go through and answer/set up as much of each question as you can and then go back to fill in details.

 

The number preceding the question number is the point value of that particular question. Total points = 94.

 

(8) 1. Draw the prototypical (e.g. what you’d expect to see for tree total height) sigmoid-shaped cumulative growth curve on the axes below labeled a. and the corresponding instantaneous growth curve on the axes below labeled b. Be sure the correspondence between the inflection point of your curve in a. and the peak (maximum) of your curve in b. is clear in your drawings.

b.
 
 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


(6) 2. Given an equation for cumulative growth (what you drew in 1a.), describe how you would use the calculus to find the age at which instantaneous growth is a maximum. Just give me the steps.

 

 

 

 

 

 

 

(6) 3. What field forestry measurement tool/technique allows a forester to most easily observe/reconstruct past tree DBH growth? Tree height growth?

a.       DBH –

 

b.      Height –

 

 

(6) 4. Production is defined to be S + I + O where:

            S = survivor growth

            I = ingrowth

            O = outgrowth (cut)

 

A CFI plot was measured on two occasions, ten years (growth seasons) apart. Live trees exceeding 4.5-inches DBH were measured at each occasion. Volume per acre at the first measurement was found to be 1500 ft3/acre. Volume per acre at the second measurement was found to be 2000 ft3/acre. No trees on the plot were cut during the growth period but mortality amounted to 100 ft3/acre. Compute production for the CFI plot.

 

 

 

 

(6) 5. How do the location (minimum or mean), spread (variability), and shape of the DBH distribution of an even-aged stand typically change as the stand ages?

            location –

 

 

 

            spread –

 

 

 

            shape –

 

 

 

(6) 6. Maintenance of a static (constant) DBH distribution through time is central to managing all-aged forest stands. Draw what a typical all-aged DBH distribution looks like and explain why a form different than what is found in even-aged stands is a necessity.

 

 

 

 

 

 

 


Why is this shape (versus that we find in even-aged stands) a necessity for the continued viability of an all-aged stands?

 

 

 

(10) 7. Given the number of trees in each DBH class, the 15-year DBH increments (inches), and the mortality percents below, predict the future stand table in 15 years using stand table projection. Assume no stand ingrowth or cutting.

 

DBH

DBH Increment

Mortality Percent

Current Trees Per Acre

6

0.8

15

80

8

1.4

10

60

10

1.8

5

40

12

2.2

0

10

 

 

 

 

 

 

 

 

 

 

 

 

 

(6) 8. Differentiate between how competition is assessed in a distance-dependent and a distance-independent individual tree growth model.

 

 

 

 

 

 

 

 

Which type of model (distance-dependent or distance-independent) is TWIGS?

 

 

(4) 9. Why is it necessary to average multiple runs of an individual tree growth model if a stochastic approach is used when applying tree mortality probabilities?

 

 

 

 

(6) 10. In your homework assignment with TWIGS, you set projection interval to 1 year, growth cycle to 5 years, and number of cycles to 2. What do these mean?

            projection interval = 1 year:

 

            growth cycle = 5 years:

 

            number of cycles = 2:

 

(4) 11. Age, site quality, and density are important determinants of stand dynamics in even-aged stands. Which of these factors is/are not accounted for in normal or empirical yield tables?

 

 

(6) 12. Schlaegel, in his study of aspen stands in Minnesota, found annual basal area growth (DG) to be well-predicted by:

 

           

 

where G = basal area (square feet per acre) and ln is natural (base e) logarithm. Given a stand volume equation for aspen of:

 

           

 

where H is height of dominant/co-dominant trees, estimate stand volume at age 40 years for an aspen stand that at age 38 years has 100 square feet per acre of basal area growing on land assessed to be site index 70 feet. Site index curves for aspen in Minnesota are attached.

 

 

 

 

 

 

(6) 13. A red pine plantation is predicted to have 400 trees per acre at age 40 years (it is currently 30 years old). The predicted DBH distribution at age 40 years is approximated by the probability distribution function:

           

which looks like

From this I estimate there will be 24 trees per acre in the 6-inch DBH class (5.5 – 6.5 inches) at age 40 years.

 

a.       How did I find trees per acre in the 6-inch DBH class at 40 years given the information provided? Be explicit.

 

 

 

b.      Provide an estimate of basal area per acre in the 6-inch DBH class for the plantation at 40 years.

 

 

 

c.       What other information must I possess to estimate volume per acre in the 6-inch DBH class at 40 years? Remember this is a red pine plantation.

 

 

 

(6) 14. In the question on the final homework where you used the PCWTHIN DBH-distribution model you were to evaluate different thinning strategies.

a.       How was the amount of thinning specified?

 

 

 

b.      What were you trying to maximize by applying (or not applying) different thinning strategies for your stand?

 

 

 

 

(4) 15. The PnET-II and 3-PG models both include environmental modifiers. Describe what those modifiers are meant to do and list the modifiers for each model.

 

 

 

 

(4) 16. Identify three main properties of “big-leaf” ecosystem process models and list the four main processing steps in such a model (e.g. PnET-II or 3-PG).

a.       Three main properties

 

 

 

 

b.      Four main processing steps

 

 

 

 

 

 

FROM PREVIOUS EXAM (12 points total)

 

(6) 1. A total of 20, 16-inch DBH sugar maple trees were tallied on 12, 20BAF variable-radius plots. The total volume of the 20 trees was determined to be 3700 board feet. Provide the stand table (only) entry for 16-inch DBH sugar maple.

 

 

 

 

 

 

(6) 2. The Reineke stand density boundary line for species X is given by (also see attached chart):

 

           

 

Currently species X is planted at 400 stems per acre. The existing initial thinning prescription for species X in you company management guide is to thin to 90 square feet per acre when the stand reaches 140 square feet per acre.

            a. What percent of maximum stocking will such stands be at when the first thin is initiated based on the company management guide?

 

 

 

 

 

The new company vice president suggests that the current company management guide prescription involves waiting too long for the first thin. He suggests the first thin should occur when the stand reaches 50% of maximum stocking.

            b. Based on the vice president’s prescription, what will basal area per acre be when the first thin is initiated (again, 400 stems per acre planted)?

 

 

 

 

 

 

“Equation sheet”