Analysis behaviors

In this document:
Analysis parameters
Tree Volume Calculator behavior
Dimension Analysis behavior
Tree Bole Volume calculator behavior
Tree Age behavior
Merchantable Timber Value behavior
Carbon Value behavior

Analysis behaviors are those whose only purpose is to prepare data for output. They do not change model state, such as growing trees or updating grid values. They assemble, calculate, or analyze data for the user.

Analysis parameters

Tree Volume Calculator

This behavior calculates the volume of tree trunks. It can be used to find both merchantable volume and total volume. Make sure to distinguish between this behavior and the other tree volume behavior.

How it works

Tree volume is estimated by dividing the trunk into segments, and calculating the volume of each segment. You control where the trunk starts and stops, and the length of segments used.

Trunks start at the value in the Height to Begin Calculating Trunk Volume, in cm parameter. To calculate merchantable volume, set this to the average stump height. To calculate total volume, set this to zero. Trunks end when their diameter inside the tree bark becomes smaller than the volume in the Minimum Trunk Diameter for Volume Calculations, in cm parameter. For merchantable volume, set this to the minimum usable diameter. For total volume, set this to zero.

Trunks are divided into segments for volume calculations. The length of these segments is set in the Trunk Segment Length for Volume Calculations, in m parameter. Setting this to a smaller value increases the accuracy of the calculations. Setting this to a larger value increases the speed at which the calculations are made. The total tree's volume is the sum of the volumes of each of the segments. Any segments whose beginning or ending diameter is less than the value in the Minimum Trunk Diameter for Volume Calculations, in cm parameter are not included in the volume total.

The volume of a tree trunk segment is found as follows:

V = ((A1 + A2) / 2) * l

where:

The cross-sectional area of a tree trunk at a particular point above the ground (such as at the beginning or end of a trunk segment) is calculated as:

A = π(d / 2)2

where A is the cross-sectional area, in square meters, and d is the diameter of the tree inside the bark at that height, in meters.

To find the diameter of the tree trunk inside the bark at a particular height above the ground, the taper equation is used. (This equation comes from Kozak (2004) Forest Chronicle 80: 507 - 515; it's the "2002 model"). The equation is:

Taper equation

where:

SORTIE-ND considers its DBH parameter to be diameter without bark. To find the diameter outside the bark, the equation is:

D = a1 + a2DBH + a3DBH2

where:

Important note. The math in this behavior is particularly susceptible to producing extreme numbers if the parameters are not chosen very carefully. These extreme numbers (incredibly large or small numbers) will crash SORTIE if they happen, and cannot be guarded against ahead of time. Be very careful when selecting parameters, and test your parameters to ensure they produce sensible results for a wide range of tree sizes. If you have problems with SORTIE crashing, try verifying that this behavior is the problem by removing it from the run and trying again. If you can verify that this behavior is the problem, carefully re-examine your parameters.

How to apply it

Apply this behavior to saplings, adults, or snags of any species, and enter parameters in the Parameter edit window. This behavior does not automatically create output. Once you have added this behavior to your run, the Detailed output setup window for trees will have a tree data member called "Tree Volume". Add this to your detailed output file to output volume in cubic meters. You can then view charts and graphs with the resulting volume data using data visualization on your detailed output file.

Dimension Analysis

This behavior calculates the biomass of trees based on DBH. This approach comes from Jenkins et al, 2004.

How it works

The paper above outlines 9 different biomass equations in Table 6, as follows:

IDEquation
1log10 biomass = a + b * (log10(dia c))
2ln biomass = a + b * dia + c * (ln(dia d))
3ln biomass = a + b * ln(dia) + c * (d + (e * ln(dia)))
4biomass = a + b * dia + c * (dia d)
5biomass = a + (b * dia) + c * (dia 2) + d * (dia 3)
6biomass = a * (exp(b + (c * ln(dia)) + (d * dia)))
7biomass = a + ((b * (dia c)) / ((dia c) + d))
8log100 biomass = a + (b * log10(dia))
9ln biomass = ln(a) + (b * ln(dia))

In all equations, dia is DBH. You choose the equation ID that you wish to use for each species.

There are many different published parameters using the equation forms above, which use a range of different units. Thus, you specify what units dia (that is, DBH) is in, and what units of biomass the equation is expected to produce. The possible DBH units are millimeters (mm), centimeters (cm), and inches (in); the possible biomass units are grams (g), kilograms (kg), and pounds (lb). This behavior handles all unit conversions so that biomass is appropriately calculated. The final biomass values are reported in metric tons (Mg).

For those equations that calculate log10, log100, or ln biomass, some papers specify a correction factor to remove bias that may be introduced when biomass is calculated. If you wish, you may use such a correction factor. Set the value of the Dimension Analysis: Use Correction Factor? parameter to "true", then specify the appropriate correction factor in the Dimension Analysis Correction Factor parameter. This value is multiplied by the final biomass value.

How to apply it

Apply this behavior to saplings, adults, or snags of any species, and enter parameters in the Parameter edit window. This behavior does not automatically create output. Once you have added this behavior to your run, the Detailed output setup window for trees will have a tree data member called "Tree Biomass". Add this to your detailed output file to output biomass in metric tons (Mg). You can then view charts and graphs with the resulting volume data using data visualization on your detailed output file.

Tree Bole Volume Calculator

This behavior calculates merchantable tree volume. Make sure to distinguish between this behavior and the other tree volume behavior.

How it works

Tree volume is calculated as follows:

V = b0 + (b1 * DBH b2) + (b3 * DBH b4 * Height b5)

Where:

The bole length is the number of 16-foot logs the tree can provide, in feet (i.e. 3 logs = bole length of 48 feet). The base of the bole is the top of the cut stump; the top of the bole is the merchantable height. This behavior defines the merchantable height as the height at which the trunk diameter inside the bark tapers to 60% of DBH.

To determine at what bole length the merchantable height occurs, the behavior tries fitting in as many 16-foot logs as possible before the 60% taper occurs. The amount of taper at the top of the first 16-foot log is established by the form classes. A species's form class is the percentage of DBH to which the bole has tapered at the top of the first 16-foot log. This value is entered as the Bole Volume Form Class, 60% - 100% parameter.

Then the behavior determines how many more logs the tree contains. The amount of taper at the top of the first 16-foot log is subtracted from the DBH, to see how much taper is left before the 60% merchantable-height diameter is reached. There is no formula that establishes clearly how many logs will fit; the behavior uses a trial-and-error approach taken from Messavage and Girard, 1956. This paper includes the table below for upper-log taper for trees of various DBH and bole heights. The behavior uses this table to determine the maximum number of logs it can fit into the taper available.

Trees below 10 inches of DBH have no volume. Trees greater than 40 inches of DBH are treated like 40-inch trees.

DBH (in)2-log tree3-log tree4-log tree5-log tree6-log tree
2d log2d log3d log2d log3d log4th log2d log3d log4th log5th log2d log3d log4th log5th log6th log
101.41.21.4------------------------------------
121.61.31.51.11.41.9---------------------------
141.71.41.61.21.52---------------------------
161.91.51.71.21.62.1---------------------------
1821.61.81.31.72.2---------------------------
202.11.71.91.41.82.41.11.62.22.9---------------
222.21.821.422.51.11.72.32.9---------------
242.31.82.21.52.22.61.11.82.43.1---------------
262.41.92.31.52.32.71.11.92.53.2---------------
282.51.92.51.62.42.81.21.92.63.30.91.42.13.24.4
302.622.61.72.531.222.73.50.91.42.13.24.5
322.722.71.72.53.11.22.12.93.711.42.13.24.6
342.82.12.71.82.53.31.32.133.811.42.23.34.7
362.82.12.81.82.63.41.32.233.91.11.52.23.34.9
382.92.12.81.92.63.41.32.23.13.91.11.52.33.45.1
402.92.22.81.92.73.41.42.33.241.21.52.43.55.3

How to apply it

Apply this behavior to saplings, adults, or snags of any species, and enter parameters in the Parameter edit window. This behavior does not automatically create output. Once you have added this behavior to your run, the Detailed output setup window for trees will have a tree data member called "Tree Bole Volume". Add this to your detailed output file to output volume in cubic feet. You can then view charts and graphs with the resulting volume data using data visualization on your detailed output file.

Tree Age

This behavior calculates tree age.

How it works

The age of a tree, in years, is kept in a tree data member called "Tree Age" and updated each timestep. If this behavior is after the establishment behaviors, new seedlings will have an age equal to one timestep on the timestep they are created.

Some trees can be created at the beginning of a run, either in a tree map or to provide a specified initial tree density. These trees are given an age of 10000, so they can be easily distinguished from trees created during a run. If a tree map is provided and the trees are specifically given an age in the map, that age is kept and they are not re-assigned an age of 10000.

This behavior may not be applied to snags, since they have a different age counter.

How to apply it

Apply this behavior to the trees for which you want to track age. You can then save the "Tree Age" data in a detailed output file for analysis.

Merchantable Timber Value

This behavior calculates the value of merchantable timber.

How it works

The value for each tree is calculated by finding out its volume in board feet, and multiplying that by the price for its species. The price is held in the Merchantable Timber Value Price / 1000 Board Feet parameter. The currency used doesn't matter. The tree's final value is placed in a tree data member called "Merchantable Value". The total value for each species is saved in a grid called Merchantable Timber Value. You can save these values in a detailed output file for analysis.

The volume of merchantable timber in a tree depends on its size and form class. These control how many 16-foot logs there are in a tree, and how many board feet of timber (assuming 0.25-inch thickness) those logs can create. The form class is entered in the Merchantable Timber Value Form Class parameter.

The behavior begins by finding out how many 16-foot logs the tree can provide in its bole. The base of the bole is the top of the cut stump; the top of the bole is the merchantable height. This behavior defines the merchantable height as the height at which the trunk diameter inside the bark tapers to 60% of DBH. The behavior tries fitting in as many 16-foot logs as possible before the 60% taper occurs. The amount of taper at the top of the first 16-foot log is established by the tree's form class. A species's form class is the percentage of DBH to which the bole has tapered at the top of the first 16-foot log.

Then the behavior determines how many more logs the tree contains. The amount of taper at the top of the first 16-foot log is subtracted from the DBH, to see how much taper is left before the 60% merchantable-height diameter is reached. There is no formula that establishes clearly how many logs will fit; the behavior uses a trial-and-error approach taken from Messavage and Girard, 1956. This paper includes the table below for upper-log taper for trees of various DBH and bole heights. The behavior uses this table to determine the maximum number of logs it can fit into the taper available.

Trees below 10 inches of DBH contain no merchantable timber and have a value of zero. Trees greater than 40 inches of DBH are treated like 40-inch trees.

Once the behavior figures out how many 16-foot logs a tree contains, it uses another set of tables, based on form class, to determine how many board-feet of timber the tree contains. These tables are also from Messavage and Girard, 1956, and are shown below.

Average upper-log taper (inches) in 16-foot logs
DBH (in)2-log tree3-log tree4-log tree5-log tree6-log tree
2d log2d log3d log2d log3d log4th log2d log3d log4th log5th log2d log3d log4th log5th log6th log
101.41.21.4------------------------------------
121.61.31.51.11.41.9---------------------------
141.71.41.61.21.52---------------------------
161.91.51.71.21.62.1---------------------------
1821.61.81.31.72.2---------------------------
202.11.71.91.41.82.41.11.62.22.9---------------
222.21.821.422.51.11.72.32.9---------------
242.31.82.21.52.22.61.11.82.43.1---------------
262.41.92.31.52.32.71.11.92.53.2---------------
282.51.92.51.62.42.81.21.92.63.30.91.42.13.24.4
302.622.61.72.531.222.73.50.91.42.13.24.5
322.722.71.72.53.11.22.12.93.711.42.13.24.6
342.82.12.71.82.53.31.32.133.811.42.23.34.7
362.82.12.81.82.63.41.32.233.91.11.52.23.34.9
382.92.12.81.92.63.41.32.23.13.91.11.52.33.45.1
402.92.22.81.92.73.41.42.33.241.21.52.43.55.3

Volume (board feet) by number of usable 16 foot logs
Form Class 78:
DBH (inches)1 log2 logs3 logs4 logs5 logs6 logs
10365973---------
11467696---------
125692120137------
1367112147168------
1478132174200------
1592156208242------
16106180241285------
17121206278330------
18136233314374------
19154264358427------
20171296401480542---
21191332450542616---
22211368500603691---
23231404552663714---
24251441605723782---
25275484665800865---
262995287258771,021---
273235727889521,111---
283476168501,0271,2011,358
293756679201,1121,3081,488
304037189911,1981,4151,619
314327721,0701,2991,5261,754
324628261,1491,4001,6371,888
334928801,2261,4951,7502,026
345219341,3041,5901,8642,163
355559981,3941,7022,0002,312
365891,0631,4851,8142,1352,461
376221,1241,5781,9262,2722,616
386561,1861,6702,0382,4102,771
396941,2581,7692,1662,5522,937
407311,3291,8682,2942,6933,103

Form Class 79:
DBH (inches)1 log2 logs3 logs4 logs5 logs6 logs
10386177---------
114878100---------
125896124141------
1370117153176------
1482138182211------
1595160214252------
16108183246292------
17124212286340------
18140240325388------
19158272370442------
20176305414496561---
21196342464558636---
22216378514621710---
23238418571687792---
24260458628753875---
25282499685826960---
263055407428991,046---
273315888109801,144---
283576358771,0611,2421,404
293856869481,1481,3501,537
304137371,0201,2351,4581,670
314447921,1001,3381,5721,808
324748481,1811,4401,6851,945
335069071,2651,5441,8082,094
345389661,3491,6471,9322,244
355701,0261,4351,7542,0002,384
366021,0871,5211,8602,1892,525
376381,1541,6201,9802,3382,694
386741,2201,7202,1012,4882,862
397121,2921,8222,2322,6323,031
407501,3651,9232,3622,7753,200

Form Class 80:
DBH (inches)1 log2 logs3 logs4 logs5 logs6 logs
10396380---------
114980104---------
125998127146------
1371120156181------
1483141186216------
1598166221260------
16112190256305------
17128219296354------
18144248336402------
19162281382457------
20181314427512580---
21201350478575656---
22221387528638732---
23244428586706816---
24266469644773899---
25290514706852992---
263155587679311,086---
273416068361,0141,185---
283676549041,0961,2841,453
293967069771,1841,3941,588
304247581,0501,2721,5031,723
314548141,1321,3761,6181,862
324858701,2131,4801,7332,001
335189301,2981,5861,8582,152
345509891,3831,6911,9842,304
355851,0551,4771,8062,1242,458
366201,1211,5711,9222,2642,612
376561,1881,6722,0442,4162,783
386931,2561,7722,1672,5682,954
397321,3301,8742,3002,7143,127
407701,4031,9772,4322,8603,300

Form Class 81:
DBH (inches)1 log2 logs3 logs4 logs5 logs6 logs
10406582---------
115082106---------
1260100130150------
1372122160186------
1485144190221------
15100170228268------
16115197265316------
17132226306366------
18148256346415------
19166290392471------
20185323439527598---
21206360492592676---
22227398544656754---
23250439602724838---
24272480659791923---
252985287268771,024---
263245757939631,124---
273516248631,0471,226---
283786749331,1311,3271,502
294067261,0061,2201,4381,640
304357791,0801,3101,5491,777
314668361,1621,4161,6661,918
324978921,2451,5221,7842,059
335309531,3321,6281,9102,214
345631,0141,4191,7342,0372,368
356001,0841,5181,8592,1882,534
366371,1541,6181,9842,3382,700
376741,2231,7212,1092,4942,874
387121,2921,8242,2342,6493,049
397511,3661,9282,3682,7963,224
407901,4412,0322,5022,9443,399

Form Class 84:
DBH (inches)1 log2 logs3 logs4 logs5 logs6 logs
10437191---------
115491118---------
1266111145168------
1380135178208------
1493159212248------
15108185249295------
16123211286342------
17142244332398------
18160277377453------
19180314428524------
20200351479576657---
21223392537649744---
22246434595722830---
23271480660798925---
242965257248731,020---
253225727909581,118---
263476198551,0421,217---
273766739321,1361,331---
284067271,0101,2301,4451,636
294387861,0921,3301,5691,790
304708441,1731,4291,6931,943
315049071,2651,5461,8232,101
325389701,3571,6641,9532,259
335741,0371,4531,7822,0962,431
346111,1041,5491,9012,2402,603
356471,1731,6482,0232,3872,766
366831,2421,7462,1452,5342,929
377241,3181,8592,2842,7063,123
387651,3931,9722,4222,8773,317
398081,4762,0882,5703,0423,512
408511,5582,2032,7193,2083,706

Form Class 85:
DBH (inches)1 log2 logs3 logs4 logs5 logs6 logs
10457494---------
115694122---------
1268114150173------
1382138184214------
1495163217254------
15111191257304------
16127219297355------
17146252342412------
18164285388468------
19184322440531------
20205360492594678---
21228402550667765---
22251444609740852---
23276490675818950---
243025377418951,047---
253305888129861,153---
263576388821,0761,259---
273876939611,1721,374---
284177451,0401,2671,4901,689
294488071,1221,3681,6161,844
304818661,2051,4691,7411,999
315169301,2981,5881,8742,160
325509931,3911,7062,0062,321
335871,0611,4881,8272,1502,495
346241,1291,5861,9482,2942,669
356631,2041,6922,0802,4542,846
367021,2781,7972,2122,6143,022
377441,3551,9122,3522,7883,219
387851,4322,0272,4932,9623,416
398281,5152,1442,6443,1303,614
408721,5982,2602,7953,2983,813

How to apply it

Apply this behavior to saplings, adults, or snags of any species, and enter parameters in the Parameter edit window. This behavior does not automatically create output. Once you have added this behavior to your run, the Detailed output setup window for trees will have a tree data member called "Merchantable Value". Add this to your detailed output file to output volume in cubic feet. You can also use the Detailed output grid setup window to save the data members in the Merchantable Timber Value grid, which contains the total value for each species. You can then view the contents of this grid as a table using SORTIE's data visualization system.

Carbon Value

This behavior calculates the amount of carbon per species and its value.

How it works

This behavior relies on the Dimension Analysis behavior to calculate each tree's biomass in metric tons. It then multiplies this value by the Carbon Value - Carbon Amount of Biomass (0-100%) parameter to find each tree's amount of carbon in metric tons. This behavior finds the total amount of carbon in each species, and then multiplies it by the Carbon Value - Price Per Metric Ton Carbon to find each species' carbon value.

Both the amount of carbon, in metric tons, for each species and the value of that carbon are saved in a grid called Carbon Value. You can save these values in a detailed output file for analysis.

How to apply it

Apply this behavior to saplings, adults, or snags of any species. These trees must also use the Dimension Analysis behavior. This behavior does not automatically create output. Once you have added this behavior to your run, the Detailed output grid setup window will list the Carbon Value grid. You can then view the contents of this grid as a table using SORTIE's data visualization system.


Last updated: 16-Mar-2006 06:37 AM