Forest Management Review
April 24th
Final May 1 Time 10:00am – 12:00pm
Topics
Models: Predicting Forest Outcomes and Conditions:
Lectures March 11, 13 and 18. Chapter 5 from Davis.
Timber Harvest Schedules (The classics. Regulated
forests, even age, uneven age systems) Chapter 10 from
Davis, and the hand outs provided.
Financial planning. Lectures from March 27 – April 3.
Chapters 6 and 7 from Davis.
Multi-temporal and spatial scale aspects in Management
April 8th lecture. Kohm and Franklin Chapter 14,
Gustafson, and Gustafson and Crow papers.
Fuel and Wildfire Management. National Fire Plan.
Kohm and Franklin chapter 12
Management of spatially distributed resources. Hand outs
on GIS . Queen and Blinn article, and The chapter from
Maguire, Goodchild and Rhind “Geographic Information
Systems” Loomis Chapter 5.
Models: Predicting Forest Outcomes and Conditions:
Lectures March 11, 13 and 18. Chapter 5 from Davis.
Whole Stand Models
Density-Free Models
Variable Density Models
Diameter Class Models
Empirical stand table projections
Diameter class growth models
Individual Tree Models
Distance Dependent Models
Distance Independent Models
Buckman (1962): Red Pine Minnesota. First study in
USA that directly predicted growth from stand
variables
Density is explicitly considered in model: Basal area,
but could be number of trees, or volume per acre or
other measure.
Different growth at different ages, but the same growth
at different basal area for same age.
Y = 1.6 + .041066BA – 0.00016303BA2 - 0.076958A +
0.0002274141A2 + 0.06441S
Y = Periodic Net annual basal area increment
BA = basal area in square feet per acre
A = Age in year
S = Site index
Volume growth tables developed by combining
1) basal area growth equation
2) a height growth table
3) stand volume equation
V = ƒ (K, BA, H)
Diameter Class Models:
Separately simulate growth in each dbh class
Growth = inventoried # of stemsdbh X average tree dbh
Tree growth is projected on a diameter class basis & then
aggregated to the stand level
Stand Growth = ∑ (Volumes of all dbh classes)
Two General Forms
o Actual radial increment data
o Generalized growth functions
Ni, t + 1 = Nit + Ii – Ui – Mi - Ci
Notation:
Ni, t + 1 Number of trees in dbh class I at time t + 1
(the next survey period)
Nit = Number of trees in dbh class I at time t (first
survey period)
Ii = number entering dbh class from smaller classes
Ui = number growing into larger classes
Mi = mortality
Ci = harvested
A. Individual Tree Models
Crown Competition Index: measure of how well a tree
competes and captures light, nutrition, and growing space
relative to other trees in the stand.
Used as a basis for determining life or death of the tree in
the stand simulation
If it lives: diameter growth, height, and crown size is
simulated.
 Distance-dependent: measured or mapped tree to tree
distances
 Distance-independent: only subject tree is considered
aggregated stand characteristics are used.
Major difference between stand and individual tree
models:
1. Individual tree models consider competitive
environment
2. Stand models aggregate individual tree data into stand
info before operating the growth model. Individual tree
models do this after the model grows each tree.
--------------------------------------------------------------------Timber Harvest Schedules (The classics. Regulated
forests, even age, uneven age systems) Chapter 10 from
Davis, and the hand outs provided.
Classical Timber Harvest Scheduling
How many acres and how much volume can be cut?
Area Control: Regulated forests can be achieved on 1
rotation but with short term harvest sacrifice
Volume control: Stable harvest can be achieved in near
future but at the sacrifice of not achieving a regulated
forest after the 1st rotation.
Importance of Site Quality
SI 80
SI 100
SI 90
SI 70
SI 80
SI 60
SI 50
Since site quality differs, productivity differs. In the evenaged forest the regulated forest A/R are harvested since
growth = harvest.
Because the productivity of the whole forest varies the
basic model doesn’t work.
Now harvest areas of equal productivity rather than equal
area. Adjusting harvested volume by site quality provides
the management alternative. Cut more from lower
productivity sites, and less higher site index sites.
Calculation of LTSY
Determine rotation age for each site class,
Calculate the MAI for each site class at the selected
rotation
LTYS is equal to the sum over site classes of the MAI for
the site class
LTSY = ∑ [ MAI R X As ]
Site Class
1
2
3
Acres
4200
5600
3500
Rotation
35
45
50
Yield at Rotation
41
46
48
LTSY = 4200(41/35) + 5600(46/45) + 3500(48/50)
LTSY =14,004 cords / year
Financial Analysis
Future Value Equation: Vn = Vo(1 + i)(1 + i) … (1 + i)
Present Value Equation: Vn = Vo(1 + i) n
Earnings Rate Equation:
Solve for i in terms of Vn, Vo and N
Vn = Vo (1 + i) n
Vo (1 + i) n = Vn
(1 + i) n = Vn / Vo
(1 + i) n = Vn / Vo
i = √ Vn / Vo – 1 where the root is nth root
Present Value of a perpetual periodic series
Vo = p / (1+i)t + p /(1+i)2t + p /(1+i) 3t … + p / (1+i)∞
Vo = p / (1 + i) t - 1
Uneven-aged Management based on harvesting species by
dbh class, rather than age.
Need a decision tool to help make choice for electing to
harvest individual trees at different periods of time.
Duerr (1956) developed a financial maturity guide
1. Determine guiding rate of return
2. calculate the current stumpage value
3. Est. the stumpage value of the tree at various
potential harvest ages
4. Compare highest values increase in terms of a
compound annual rate of value increase with the
guiding rate of return.
Find the compound rate of values increases
SVo = current stumpage value
SVn = value at the end of the nth planning period
i = compound interestrate
solve for i SVo(1+i)n = SVn
(1 + i) n = SVn / SVo or 1 + i = n√ SVn / SVo
32.31 / 22.17 = 1.048 interest is .048 or 4.8%
compare interest against the guiding rate of 4% and elect
to allow tree to grow.
Rotation Decisions
1.
2.
3.
4.
What kind of silvicultural treatments are necessary
When will they be accomplished
What intensity
when will the harvest occur
Bare ground in Douglas fir region
Estimate 50 year SI of 105
How long should the stand be allowed to grow?
Growth and yield simulator
Simulate the growth for SI 105 returns maximum average
growth at 80 years. MAI = 146ft3 / year
Price to initiate the stand
Site preparation $120.00 /ac
Planting
$100.00 /ac
Annual mgt cost $ 3.00/ac
Guiding rate of 4%
NPV1 = VRPR / (1+i)R - T[(1+i) R -1] / i(1+i) R-G
VR = cubic ft vol/ac harvested at R(rotation age)
VR = price cubic ft harvested at R
T = annual management cost
G = regeneration costs
i = guiding interest rate / year
R = rotation age in years
8212 x .75
NPV1
3[(1 + .04)60 – 1]
= -------------- - -------------------- - 220 = $298
(1+.04)60
.04(1+.04)60