NorgePro: A spreadsheet program for the management of allaged, mixed-species Norwegian forest stands
Espen Halvorsen1, Joseph Buongiorno2, Ole-Martin Bollandsås1
1
Department of Ecology and Natural Resource Management, Norwegian University of Life Sciences, Ås,
Norway.
2
Department of Forest and Wildlife Ecology, University of Wisconsin, Madison, USA.
1
Abstract
NorgePro is a spreadsheet program for Microsoft Excel to simulate the growth and management of allaged forests stands of Norwegian spruce (Picea Abies), Scots pine (Pinus Sylvestris), birch (Betula spp.)
and other hardwood trees in Norway. Its built-in growth models were calibrated on data from 7241 field
plots in Norway. Stands are described by the number of trees per unit area in each of 13 species specific
size classes.
NorgePro allows managers to predict stand development by 5 year periods and for many
decades from a specific initial state. Users can choose cutting regimes by specifying the interval between
harvests (cutting cycle) and a target distribution of trees remaining after harvest. Tabulated and graphic
results show diameter distributions, basal areas, volumes, income, net present values, biomass, carbon
sequestration and indices of stand diversity by species and size.
This manual documents the program installation and activation, and provides suggestions for
working with Excel. It offers an example comparing two different management regimes.
Keywords: Uneven-aged Management, Economics, Ecology, NorgePro, Simulation, Software, Growth
model, Diversity.
2
Contents
Introduction .................................................................................................................................................. 4
What is NorgePro? .................................................................................................................................... 4
Why simulate this type of stand? ............................................................................................................. 4
How does NorgePro Work? ...................................................................................................................... 5
What is in this manual?............................................................................................................................. 5
Getting Started.............................................................................................................................................. 5
System Requirements ............................................................................................................................... 5
Installing NorgePro: .................................................................................................................................. 6
Using NorgePro ............................................................................................................................................. 6
NorgePro Input ......................................................................................................................................... 6
Saving and retrieving data ........................................................................................................................ 7
Running Simulations ................................................................................................................................. 7
Simulation output ..................................................................................................................................... 8
Products worksheet .............................................................................................................................. 9
Basal area worksheet .......................................................................................................................... 10
Diversity worksheet ............................................................................................................................ 11
Volume by grade worksheet ............................................................................................................... 12
Trees per ha worksheet ...................................................................................................................... 13
Biomass and carbon worksheet .......................................................................................................... 14
Species BA ........................................................................................................................................... 15
Class BA chart ...................................................................................................................................... 16
Diversity chart ..................................................................................................................................... 17
Volume chart....................................................................................................................................... 18
Biomass chart ...................................................................................................................................... 19
Carbon chart ....................................................................................................................................... 20
Acknowledgements..................................................................................................................................... 20
Literature cited............................................................................................................................................ 21
Glossary ....................................................................................................................................................... 22
Appendix 1: Example comparing two management regimes: .................................................................... 23
Appendix 2: Equations ............................................................................................................................... 26
Appendix 3: Definition of Diversity of Tree Species and Size ..................................................................... 33
3
Introduction
NorgePro is a program intended to help forest managers predict the effects of management, or lack
thereof, on stand growth, productivity, income, wood quality, diversity of species, and diversity of tree
size, in Norwegian forests.
The NorgePro user’s manual documents background, instruction, and additional suggestions for using
the NorgePro program. The manual explains how to install NorgePro on your computer and provides a
description of the input data, as well as instructions for loading and saving these data, running
simulations, and saving the results.
The manual gives examples of applications in simulating management regimes. If you are new to
NorgePro, it will be useful to run these examples while reading the manual. Appendixes cover the
growth equations, volume equations and log grade equations of NorgePro.
What is NorgePro?
NorgePro is a spreadsheet program that simulates the development of all-aged mixed species
Norwegian spruce (Picea Abies) forest stands in Norway. With this program various management
regimes can be considered, and their outcomes can be quickly predicted in terms of stand structure,
species composition, economic returns, diversity indices, biomass and CO2 equivalence.
NorgePro is the latest of a series of similar programs developed for various species types in North
America: SouthPro (Schulte et al., 1998), WestPro (Ralston et al., 2003), NorthPro (Liang et al. 2004a),
CalPro (Liang et al. 2004b), WestProPlus (Liang et al. 2006).
Why simulate this type of stand?
Even-aged forest management emphasizing timber production has been the dominating management
regime in Norway for 50–60 years. However, in the past few years more attention has been given to
uneven-aged forest management with selective cuttings.
This increased interest is partly due to possible higher profits in timber production, but also to expected
benefits for the biodiversity of the forest ecosystem and to better recreational values of the forest
landscape. Although even-aged management regimes are expected to remain important in future, the
options for alternative silvicultural treatments will increase in number and diversity (Lexerød & Eid,
2005).
4
How does NorgePro Work?
NorgePro predictions are based on a multi-species, site- and density-dependent matrix growth model
for Norway (Bollandsås et al. 2008). The data used to estimate the model parameters came from 7241
permanent field plots of the Norwegian national forest inventory, measured at least twice between
1994 and 2005. The sample design, a 3 × 3 km grid, gave a representative sample of the Norwegian
forest area. The northernmost county (Finnmark, above 70ºN latitude) which has few forests was
excluded.
The model equations of NorgePro predict growth, mortality, and the rate of ingrowth (recruitment) for
Spruce, Pine, Birch and other Hardwoods as functions of stand basal area, site index, and individual tree
size (See appendix 2).
What is in this manual?
The next section explains how to install NorgePro on your computer. This is followed by a description of
the data input, saving and loading the data, running simulations, and saving the results. Next, two
examples of applications are given. The manual assumes familiarity with the basics of Microsoft Excel.
Getting Started
System Requirements
You must have the following hardware and software to operate NorgePro:



Computer with at least 128 megabytes of random access memory (RAM)
Windows® 95 or newer
Microsoft Excel 5.0 or newer
5
Installing NorgePro:
To install NorgePro download the xls-file to a known location.
To remove NorgePro, close NorgePro, select the file NorgePro and delete it
Using NorgePro
NorgePro Input
In the input data worksheet (figure 1) you enter the initial state of the stand you want to simulate. The
state is defined by the number of trees per ha by species and size category. The target state, defined in
the same way as the stand state, is the required state after each harvest.
The target stand state should be consistent with uneven-aged management principles, whereby
substantial tree cover is left at all times.
After entering the input data, you immediately get a few summary statistics on the input data
worksheet (Figure 1). On the right of the input data worksheet is a summary of the basal area and
volume per ha of the initial and target state. Below the input data you get the total number of trees by
species and diameter classes for the initial and target state.
At the bottom left of the sheet you are required to put in the year of the first harvest, length of the
cutting cycle, simulation length, re-entry cost, interest rate (for the NPV calculations), site index, county,
altitude and latitude of the simulated stand. See the glossary for the definition of terms. The year of
first harvest, cutting cycle, and simulation length must be multiples of 5 years, the time unit used by the
growth model.
At bottom middle you enter stumpage prices, by species and timber quality.
At bottom right there are two buttons. Pressing “Examples” gives you the choice of three different
management regimes.
Example 1 cuts all the trees except those suggested by the Living Forest standard (Living Forest, 2009),
with a common initial distribution for an uneven aged stand, and a cutting cycle of 60 years.
Example 2 simulates a diameter limit cut, where all trees over 35 cm d.b.h. are cut, with a different
starting stand than in example 1. The cutting cycle here is 5 years.
Example 3 gives another diameter limit cut, where all trees over 20 cm d.b.h. are cut. The starting stand
is the same as example 2, but the cutting cycle is 15 years.
6
Figure 1: Input data worksheet.
Saving and retrieving data
After completing the Input Data worksheet, you can save this worksheet for later use. You should save
your work frequently to avoid losing data. It is advisable to save the work in a particular folder with a
descriptive name to facilitate locating the file in the future.
To run several simulations (e.g., to examine the effects of changing some of the parameters), you may
find it efficient to work with previously saved input data. You retrieve the data by opening the stored
worksheet as you would any other excel-file.
Running Simulations
After completing the Input Data worksheet or retrieving a previously saved one, you are ready to run a
simulation. Clicking on the “start” button gives you the option to start the simulation immediately or to
change the settings. The settings allow you to select what parts of the trees should be included in the
biomass and carbon sequestration calculations. By default all parts of the trees are included.
Each NorgePro simulation produces the following worksheets and charts which show the development
of various stand and harvest data over time:







Products worksheet: The physical output and financial return from the harvests.
Basal Area worksheet: The basal area by species and timber size.
Diversity worksheet: Shannon’s indices of species and size diversity, and Gini index of size
diversity.
Volume by grade worksheet: The volume in stock by log grade.
Trees per ha worksheet: The number of trees by species and diameter.
Biomass and carbon worksheet: The biomass and CO2 equivalents of standing stock by species.
Species BA chart: The stand basal area by species.
7





Class BA chart: The stand basal area by timber class.
Diversity chart: Shannon’s indices of species and size diversity, and Gini index of size diversity.
Volume chart: The volume in stock by log grade.
Biomass chart: The biomass by tree species.
Carbon chart: The stored CO2 equivalents.
All the data in the output worksheets are protected and you cannot change them. To see how the
results change with different assumptions, change the Input Data worksheet and rerun the simulation.
Upon running a simulation, NorgePro will replace any old tables and charts with new ones. For this
reason, you should save the workbook with a separate name after each simulation if you want to keep
it. To run a series of simulations, load the input data for the first management regime, run the
simulation, save your outcome, and proceed to load and run the second management regime. You can
then compare the economic return, various ecological criteria, and wood quality for different regimes.
To that end, comparative charts and tables can be built with Excel from the NorgePro output
worksheets.
Simulation output
The following results are for the simulation with initial condition and management specified by the input
data in Figure 1 which correspond to the Example 2 stored in the program. This example applies a d.b.h
limit cut of 20 cm to all species of trees, every 25 years.
8
Products worksheet
In the left part of the products worksheet (Figure 2) you will find the data for each year of harvest, the
total basal area cut, the volume harvested by log grade, the gross income, the NPV of the current
harvest, the total (cumulative) NPV of all harvests, and the initial stock value.
The right part of the products worksheet shows the average annual cut and the average stock in terms
of basal area and volume by log grade. It also displays the average species diversity and size diversity
over the whole simulation period.
The results show that with these particular starting parameters and a 25-year cutting cycle, the average
yield over 200 years would be 5,8 m3/ha/yr, for a NPV of 131581 NOK/ha. This is the return from the
land and the initial trees, under this management.
Figure 2: Products worksheet, showing production and economics of a 20 cm d.b.h. limit management regime, with a 25 year
cutting cycle.
9
Basal area worksheet
The Basal area worksheet (Figure 3) shows for each simulated year, the total stand basal area, the stand
basal area by tree species, by log grade (Prime, Second, Pulpwood), and basal area for three timber size
categories: small timber for trees from 50 to 250 mm in diameter at breast height (d.b.h.), medium
timber from 250 to 350 mm d.b.h., and large timber from 350 mm d.b.h. and larger. Underlined
numbers show the year of harvest and the basal areas just after harvest. The row marked “average”
shows the average basal area over the whole simulation period.
Figure 3: Basal area worksheet for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
10
Diversity worksheet
The diversity worksheet (Figure 4) shows Shannon equitability indices (that is Shannon indices relative to
their maximum theoretical value) for species and size diversity. The Gini index of size diversity is also
reported for each simulated period. The indices are defined in Appendix 3. The underlined data show
the year of harvest and the values of the diversity indices just after harvest. The average of the diversity
indices over all periods is in the first row.
Figure 4: Diversity worksheet, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
11
Volume by grade worksheet
The volume by grade worksheet (Figure 5) shows the volume in stock by log grade (prime, second, and
pulpwood). The log grade equations used by NorgePro appear in appendix 2. The underlined numbers
represent the year of harvest and the volume per hectare just after harvest. The first row shows the
average volume over the whole simulation period.
Figure 5: Volume by grade worksheet, for a 20 cm d.b.h. limit management regime, with a25 year cutting cycle.
12
Trees per ha worksheet
This worksheet (Figure 6) shows the number of trees per hectare, by species and diameter class for each
year of the simulation. Scrolling to the right reveals the tree distribution of the other species, the size
distribution for all species, and the total number of trees of all species and sizes in each period. The
underlined numbers are the year of harvest and the number of trees per hectare after the harvest.
Figure 6: Trees per ha worksheet, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
13
Biomass and carbon worksheet
This worksheet (Figure 7) shows the biomass and CO2 equivalents stored in the stand of trees, in total
and by species. CO2 equivalents are the mass of CO2 that would result from the carbon stored in the
trees. The output is the summed mass of the tree parts selected in the settings menu at the start the
simulation (by default every part of the tree is accounted for). The biomass and CO2 equations are in
appendix 2. The underlined numbers represent the year of harvest and the biomass and CO2 stored in
the remaining stock just after harvest. The top row gives the averages over the entire simulation period.
Figure 7: Biomass and carbon worksheet, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
14
Species BA
This chart (Figure 8) shows the development of basal area by species throughout the simulation period.
The sharp decreases in total basal area are due to the periodic harvests. This particular example
suggests that in both the long and short run we would not get much pine with this management, but we
would sustain all the other species.
Figure 8: Stand basal area by species chart, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
15
Class BA chart
This chart (Figure 9) shows the evolution of the stand basal area by timber quality; prime sawtimber,
second sawtimber, and pulpwood. This particular example suggests that, the total basal area would
increase over the period from 50 to 200 years, but there would be a reduction in timber quality as the
basal area of prime and second sawtimber would decrease relative to the basal area of pulpwood.
Figure 9: Stand basal area by timber class chart, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
16
Diversity chart
The diversity chart (Figure 10) displays the evolution of Shannon’s indices and of the Gini index over
time. In this particular example there would be an improvement in species diversity over the simulation
period as the index value increases. The size diversity would decrease sharply after each harvest but
remain fairly constant on average.
Figure 10: Diversity chart, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
17
Volume chart
The volume chart (Figure 11) shows the development of volume in stock by log grade throughout the
simulation period. As in the basal area charts this shows how the stand grows, but the volume chart
might be more interesting from a harvesting point of view. This example confirms a decrease in timber
quality as the volume of pulpwood increases over time while the volume of prime and second
sawtimber decreases.
Figure 11: Stand volume by log grade chart, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
18
Biomass chart
This chart (Figure 12) shows the stand biomass, in tons, in total and by species, given the settings
selected at the start of the simulation. This particular example suggests that the management being
investigated would lead, after the first harvest, to an increase in the total biomass due mostly to
hardwoods, while the biomass of spruce would decline.
Figure 12: Biomass by species chart, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
19
Carbon chart
This chart (Figure 13) shows the carbon sequestered in the stand, in metric tons of CO2 equivalents per
hectare, by tree species. The data depend in part on the settings selected at the start of the simulation.
The CO2 equivalents are directly proportional to the biomass (see appendix 2). This particular example
shows that although the CO2 equivalent stored in spruce would decrease, the total CO2 equivalent would
increase due to a larger amount being stored in hardwoods.
Figure 13: Carbon sequestration chart, for a 20 cm d.b.h. limit management regime, with a 25 year cutting cycle.
Acknowledgements
The research leading to this paper was supported in parts by the Department of Ecology and Natural
Resource Management, Norwegian University of life sciences, the Research Council of Norway and by
the Department of Forest and Wildlife Ecology, University of Wisconsin-Madison. We thank Jingjing
Liang for making available to us the source code of the NorthPro and WestProPlus programs, and Terje
Gobakken and Ole Hofstad for their advice and collaboration. Any error in NorgePro remains our sole
responsibility.
20
Literature cited
Blingsmo, K.R. and A. Veidahl.1992. Functions for gross price of standing spruce and pine trees,
Rapport fra Skogforsk 8 (1992), p. 23. (Norwegian)
Bollandsås. O.M., J. Buongiorno, and T. Gobakken. 2008. Predicting the growth of stands of
trees of mixed species and size: A matrix model for Norway. Scand. J. Forest Research
23:167-178.
Lexerød, N.L. and T. Eid, 2005. An evaluation of different diameter diversity indices based on
criteria related to forest management planning. Forest ecology and management. 222:1728.
Liang, J., J. Buongiorno, A. Kolbe, and B. Schulte, 2004a. NorthPro: A spreadsheet program for
the management of uneven-aged northern hardwood stands. Department of Forest Ecology
and Management, University of Wisconsin, Madison. 35p.
http://fwe.wisc.edu/facstaff/Buongiorno/
Liang, J., J. Buongiorno, and R.A. Monserud, 2004b. CalPro: A spreadsheet program for the
management of California mixed-conifer stands. USDA Forest Service, Pacific Northwest
Research Station, Gen. Tech. Rep. PNW-GTR-619. 32p.
http://fwe.wisc.edu/facstaff/Buongiorno/
Liang, J., J. Buongiorno, and R.A. Monserud, 2006. WestProPlus: A stochastic spreadsheet
program for the management of all-aged Douglas-fir-Hemlock forests in the Pacific
Northwest. USDA Forest Service, Pacific Northwest Research Station, Gen. Tech. Rep. PNWGTR-674. 42p. http://fwe.wisc.edu/facstaff/Buongiorno/
Living Forest, 2009.
http://www.levendeskog.no/levendeskog/vedlegg/levende_skog_standard_engelsk_18.06.
2007_11.43.18.pdf
Marklund, L. G, 1988. Biomass functions for pine, spruce and birch in Sweden. Department of
forest Survey, Report 45. Swedish University of Agricultural Sciences. Umeå. (In Swedish)
Nagoda, L, 1982. Chemical structure and properties of wood. Lecture notes. Departement of
wood Technology, Agric. Uni. of Norway, /I,S-NL7H1 xxp. (In Norwegian.)
Norsk Virkesmåling. 2009, http://www.tommermaling.no/tm-malereg-sag.asp
Petersson, H. and G. Ståhl, 2006. Functions for below-ground biomass of Pinus sylvestris, Picea
abies, Betula pendula and Betula pubescens in Sweden. Scandinavian Journal of Forest
Research 21:84–93.
Schulte, B., J. Buongiorno, C.R. Lin, and K. Skog, 1998. SouthPro a computer program for
managing uneven-aged loblolly pine stands. USDA Forest Service, Forest Products
Laboratory, Gen. Tech. Rep. FPL-GTR-112. 47p. http://fwe.wisc.edu/facstaff/Buongiorno/
Ralston, R., J. Buongiorno, B. Schulte, and J. Fried, 2003. WestPro: A computer program for
simulating uneven-aged Douglas-fir stand growth and yield in the Pacific Northwest. USDA
Forest Service, Pacific Northwest Research Station, Gen. Tech. Rep. PNW-GTR-574. 25p.
http://fwe.wisc.edu/facstaff/Buongiorno/
21
Glossary
Cutting Cycle ― The number of years between successive harvests.
Diameter class ― One of thirteen 50 mm diameter at breast height categories used by NorgePro to
classify trees by size. Diameter classes range from 75 to 675 mm, with each class denoted by its
midpoint. Diameter class 75 is for trees with diameters between 50 mm and 100 mm. The 675 mm
class is for all trees 650 mm in diameter and larger.
Initial stand state ― The number of live trees per ha, by species and size, at the start of a simulation.
Net present value (NPV) ― The net revenue discounted to the present.
Re-entry costs ― Costs per hectare associated with each harvest that are not reflected in the stumpage
prices. These may include, for example, the added expense of marking the stand for single-tree
selection.
Sawtimber ― Trees suitable for the production of saw logs. NorgePro recognizes two classes of
sawtimber trees:
(1) Prime sawtimber (as defined by Norsk Virkesmåling, 2009)
(2) Second sawtimber (as defined by Norsk Virkesmåling, 2009)
Site index ― The average height of the 100 per hectare largest trees according to diameter at age 40
years.
Size diversity ― The diversity of tree diameter classes as measured by the Shannon index and the Gini
index. With thirteen diameter classes, size diversity reaches its maximum value of 1 when the basal
area is distributed evenly among the diameter classes.
Species diversity ― The diversity of species groups as measured by the Shannon index. With four
species classes, species diversity reaches its maximum value of 1 when the basal area is distributed
evenly among the species groups.
Species ― The four tree species.
Spruce (Picea abies)
Pine (Pinus sylvestris)
Birch (Betula spp.)
Other Hardwood – Hardwoods other than Birch.
Stumpage prices ― Prices paid to a landowner for standing timber.
Target stand state ― The desired number of live trees per hectare in each species group and diameter
class after a harvest. NorgePro assumes that all and only the trees exceeding the target number are
harvested.
22
Appendix 1: Example comparing two management regimes:
Here we will compare two different diameter limit cuts, on the same stand. The first is a 30 cm diameter
limit cut, with cutting interval 5 years (the first cut at 5 years), a 2% interest rate, and a site index of 17.
The second has the same parameters except for a 20 cm diameter limit cut with a harvest interval of 15
years.
Figure 14: 30 cm limit cut & 5 year cutting interval
23
Figure 15: 20 cm limit cut & 15 year cutting interval
24
Figure 16: Comparison of two different management regimes
The charts in Figure 16 were built from the results in the Products worksheet and the biomass and
carbon worksheet of NorgePro. The 30 cm diameter-limit cut gave the overall best results except for in
tree species diversity where the difference is negligible. It seems that in the 20 cm cut the harvests
come before the trees reach the maximum volume growth. This accounts for the results we see here.
The trees don’t manage to reach the same size in 15 years from 20 cm d.b.h. as they do in 5 years from
30 cm d.b.h.
25
Appendix 2: Equations
The following variables are used in the equations:
Variable
a1-a8
ALT
amv#
LAT
m
Description
Parameters
Altitude of stand (m)
Share of pulpwood within harvest volume when the price ratio of pulpwood
price to sawtimber second price is # (%)
Total basal area of standing stock (m2/ha)
Basal area of trees of diameter larger than D (m2/ha)
Individual tree diameter (mm)
Mean diameter of N trees of total basal area BA
Height (m)
Probability that a tree stays alive and grows into the next diameter class in 5
years
Latitude of stand (0)
Mortality rate (1/ 5 year)
N
n(D)
p
Total number of trees per ha
Trees per ha in diameter class D
Recruitment probability (1/5year)
PBA
r
Proportion of a species within total basal area (%)
Conditional recruitment (trees/year)
R
Recruitment (trees/year)
SI
W
Width
Site index (H40, in meter)
Weight of biomass (t/ha)
Span of diameter classes (50 mm)
BA
BAL(D)
D
Dg(BA,N)
h
Id5
26
The following table shows the main characteristics of the 7,241 plots used to estimate the following
equation parameters (Bollandsås et al. 2008):
Variable
Site index, SI (m)
Stand age (yr)
Basal Area, BA (m2/ha)
Growth seasons (yr)
Latitude, LATa
Recruitment rate (ha-1yr-5)
Mortality rate (ha.1yr-5)
Mean
11.0
86.7
18.4
5.0
61.9
62.6
51.7
Min
6.0
20.0
0.1
4.0
58.0
0.0
0
Max
26.0
344
79.5
6.0
70.0
1520
1560
SD
4.0
35.6
10.3
0.5
3.0
104
98.5
Probability that a tree stays alive and changes diameter class in 5 years:
Tree
species
Spruce
Pine
Birch
Other
Hardwood
a1
17,8393
25,5426
11,8084
a2
0,04762
0,02509
0
a3
-0,0001159
- 0,0000566
0,00009616
2,20413
0,0631
- 0,0000832
Parameter
a4
a5
0
- 0,34116
0
- 0,21622
0,00000009585
0
0
0
a6
0,90604
0,69814
0,5185
a7
- 0,02414
- 0,12318
- 0,15176
a8
- 0,26781
- 0,33626
- 0,16052
0,35904
- 0,17678
0
BAL is the basal area of trees of diameter larger than D (m2/ha), obtained by summing the basal
area of trees larger than, and including diameter D (regardless of species).
27
Probability that a tree dies in 5 years:
Parameter
Tree species
Spruce
Pine
Birch
Other Hardwoods
a1
a2
a3
a4
-2,4916
-1,8079
-2,1876
-1,5512
-0,02
-0,0267
-0,0157
-0,0111
0,000032
0,000033
0,000027
0,000014
0,0308
0,055
0,0295
0,0159
Recruitment:
The recruitment is the number of trees that enter the smallest diameter class (50-100 mm) in a 5 year
interval:
R=p*r
where p is the probability that some trees of a particular species will appear in the smallest diameter
class during a 5 year interval, and r is the expected number of recruits, conditional on recruitment being
positive. The probability of positive recruitment is given by:
Species
Parameter
a2
-0,0175
-0,0616
-0,037
-0,029
a1
-2,2905
-3,5519
-0,9038
-3,4379
Spruce
Pine
Birch
Other Hardwoods
a3
0,019
0,0313
0,0159
0,1232
The conditional number of recruits (number of recruits/ha/year if there is recruitment) is predicted by:
Parameter
Species
Spruce
Pine
Birch
Other Hardwoods
a1
43.1419
5.62913
64.9428
31.4383
a2
-0.15665
-0.3233
-0.16102
-0.16945
a3
0.36812
0.40089
0.14293
0.44216
A4
0.05097
0.42026
0.1042
0.19348
Tree volume (dm3):
Tree species
With/
Diameter
a0
a1
a2
a3
Parameter
a4
a5
a6
a7
28
a8
without
Bark
Limits
[cm]
Spruce
With
Pine
With
D 10
10<D 13
13<D
D 12
12<D
Birch
Other
Hardwoods
With
With
0,52
-31,57
10,14
2,912
8,6524
-1,2541
-1,2541
0
0
0
0
0,07684
0,12739
0,12739
0,02403
0
0,0124
0,03999
0,03157
0,03166
0,03166
0,01463
0,0016
0,03117
-0,00109
0
0,000975
0,000975
-0,10983
0,0186
-0,36381
0
0
-0,01226
-0,01226
0,15195
0,63
0,28578
0
0
0
0
0
-2,34
0
0
0
0
0
0
3,2
0
0
0
0
0
Tree height (m):
Tree species
Spruce
Pine
Birch
Other
Hardwood
a1
-37,5651
-123,6
-16,3469
a2
-0,6693
-1,0175
-0,564
Parameter
a3
a4
17141,5
0,2491
17124,6
0,4604
1605,5
0,4606
a5
-1,0428
-1,328
-0,6737
a6
-0,0149
0
-0,0224
-14,8331
-0,5207
131104
-1,6993
0
0,3723
Log grade:
Share of different log grades are calculated using the functions of Blingsmo and Veidahl (Blingsmo and
Veidahl 1992).
amv# is the per-thousand share of pulpwood within harvest volume when the price second timber is #
percent more than the price of pulpwood.
For Birch and other hardwood, all volume is assumed to be pulpwood or firewood of same price
Tree
species
Spruce
Target
Amv20
Amv40
Amv60
a1
5049,107
5617,452
5411,076
a2
2,7023
2,7434
2,4982
Parameter
a3
a4
- 312,1785
3,1614
- 511,8791
3,0036
- 570,0585
2,4086
a5
- 770,3153
- 696,8697
- 581,6202
a6
- 0,006371
- 0,004664
- 0,003287
29
0
0
0
0
0
0,004214
0,004214
Pine
Amv40
Amv60
Amv80
Amv100
3990,422
4617,2
4856,922
5639,345
2,2512
2,3103
2,2456
2,6042
- 572,8183
- 596,1895
- 572,5128
- 680,7972
0,5559
1,386
1,9912
2,4537
- 228,8474
- 360,357
- 452,153
- 525,9713
- 0,002428
- 0,002613
- 0,002739
- 0,002645
30
Tree biomass (ton):
Most of the biomass is calculated using Marklund’s equations (Marklund 1988). The equations for other
hardwoods are as the same as for birch.
Tree
species
Spruce
Pine
Birch
Part
Dead branches
Living branches
Leaves and needles
Bark
Bole
Stump
Large roots
Dead branches
Living branches
Leaves and needles
Bark
Bole
Stump
Large roots
Dead branches
Living branches
Leaves and needles
Bark
Bole
Stump
Large roots
a1
-4,6351
-1,2063
-1,8551
-3,402
-2,3032
-3,3645
-6,3851
-5,8926
-2,5413
-3,4781
-3,2765
-2,6864
-3,9657
-6,3413
-6,6237
-3,3633
a2
3.6518
10.9708
9.7809
8.3089
7.2309
10.6686
13.3703
7.127
13.3955
12.1095
7.2482
7.6066
11.0481
13.2902
11.2872
10.2806
-4,0778
-3,3045
-3,9657
8.3019
8.1184
11.0481
Parameter
a3
a4
18
0.0493
13
- 0.0124
12
0
15
0.0147
14
0.0355
17
8
10
- 0.0465
10
7
0.0413
16
14
0.02
15
9
30
- 0.3081
10
Bole*0,011/0,52
14
11
15
Bole*0,042/0,52
a5
1.0129
- 0.4923
- 0.4873
0.2295
0.703
1.106
- 1.1955
- 1.565
0.4487
0.8658
2.6821
0.7433
0.9783
The biomass of small roots is calculated, with the following Petersson and Ståhl’s (Petersson and Ståhl,
2006) formula for underground biomass (including stump) and subtracting Marklund’s biomass for
stump and large roots. This is because Marklund’s functions for biomass tend to underestimate
underground biomass, because of the excavation of the smaller roots. Petersson and Ståhl made new
functions to remedy this.
31
Parameter
Tree species
Spruce
Pine
Birch
a1
0,36266
0,35449
0,32308
a2
6,1708
3,44275
4,58761
a3
225
113
138
a4
10,01111
11,06537
10,44035
CO2 sequestration (ton):
The amount of C02 sequestered is estimated from the biomass as: W*0.5 x 44/12.
This assumes that the carbon content is half of the biomass (Nagoda, 1982), while 44/12 is the mass of a
C02 molecule relative to a carbon atom.
Dominant Height:
32
Appendix 3: Definition of Diversity of Tree Species and Size
NorgePro uses Shannon’s index to measure the stand diversity in terms of tree species (how well trees
are distributed across the species: Spruce, Pine, Birch and other hardwoods) and size classes. NorgePro
measures the presence of trees in a species or sizes class by their basal area, which gives more weight to
larger trees.
The tree species diversity is defined in NorgePro as:
Where yi is the basal area of trees of species j per hectare, and y is the total stand basal area. In
NorgePro, m=4 tree species (shade-tolerant, mid-tolerant, shade-intolerant). The tree species diversity
reaches a maximum value 1, when basal area is equally distributed in all three species groups and a
minimum value of 0 when all trees are in the same species group.
Similarly, tree size diversity is:
Where, again, yj is the basal area of trees in diameter class j per acre. In NorgePro, n=13 diameter
classes. The tree size diversity reaches a maximum 1 when basal area is equally distributed in all
diameter classes and a minimum of 0 when all trees are in the same diameter class.
33
NorgePro also uses the Gini index of size diversity. It is based on the number of trees by size call, yi, to
give equal importance to small trees. n is the total number of trees per ha.
34