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Yale University School of Forestry & Environmental Studies FES519B - Methods of Ecosystem Analysis 1998 |
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What's below
On this page, you'll find the following information about the Sassafras
allometry project
at Totoket Mountain:
Allometry is useful because it allows the total biomass of a forest or stand to be estimated, without having to cut down all the trees, take them back to the lab, dry the pieces in an oven, and then weigh all the pieces. Part of our study at Totoket Mountain was to estimate the biomass of the entire forest: click here to jump to that page.
To calculate the total biomass of our Sassafras trees, we had to calculate
By combining our estimates of bole and branch weights, we calculated the total above-ground biomass of each tree. We then estimated another regression, this one relating tree diameter to total above ground biomass.
When we calculated our regression equations, we used a log-log transformation on the data. Rather than make total above ground biomass a function of dbh, we made log10 (total above ground biomass) a function of log10 (dbh). The relationship between the transformed variables is a linear one: we can calculate this regression line much more easily than if we dealt with untransformed data. Another effect that the log transformation has is that it can make large absolute differences appear relatively small: for example, although the difference between 600 kg and 1000 kg is 400 kg, log(600) = 2.78, log (1000) = 3, and the difference of the logs, 0.22, is less than 8%!
We arrived at the following equations:
Bole biomass:
log10 (bole
biomass, g) = 2.3904 * log10 (dbh, cm) + 1.8632
Individual branch weight:
log10 (branch
dry weight, g) = 2.807 * log10 (branch diameter, cm) + 1.4418
Total branch weight:
log10 (total
branch biomass, g) = 2.5533 * log10 (dbh, cm) + .9020
Total above-ground biomass
log10 (bole
+ branch biomass, g) = 2.3836 * log10 (dbh, cm) + 1.9566
As described above, we cut down four sassafras trees on the east slope
at Totoket Mountain, North Branford, CT for analysis. Basic data
for these four trees are given below.
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Tree 1
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Tree 2
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Tree 3
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Tree 4
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| Total height, m |
9.1
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16.4
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14.7
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17.2
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| Tree age (at base), years |
73.0
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77.0
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77.0
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| Avg. annual radial increment, mm, last 5 years |
2.0
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0.6
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0.9
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| DBH, cm |
5.0
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23.4
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11.8
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16.7
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| Diameter at base, cm |
6.4
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28.1
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13.9
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21.1
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| Crown width, widest, m |
2.0
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6.3
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3.7
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2.6
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| Crown width, narrowest, m |
1.5
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5.9
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3.5
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2.0
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| Height to lowest live branch, m |
6.8
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7.2
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8.0
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7.0
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| Estimated bole dry weight, OD kg |
4.7
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137.3
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27.5
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71.2
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| Estimated total branch dry weight, OD kg
(live + dead) |
0.6
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32.0
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3.2
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5.6
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| Weight dead branches, OD kg |
0.3
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4.9
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1.2
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2.2
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| Estimated biomass, OD kg
(above ground, no leaves) |
5.4
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169.3
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30.7
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76.7
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| Average bark thickness, cm |
2.1
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1.1
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1.5
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| Bark water content (g H20 / g OD) |
31%
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26%
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30%
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| Wood water content (g H20 / g OD) |
59%
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39%
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45%
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| Bark density, g / cc |
0.26
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0.30
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0.24
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| Wood density, g/cc |
0.42
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0.41
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0.41
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| Total bark weight in bole, OD kg |
19.4
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4.7
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10.1
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| Total wood weight in bole, OD kg |
117.0
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22.8
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61.1
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We estimated height-age curves for Trees 2, 3, and 4 by aging the cookies taken at 1 m intervals. In some cases, rot inside the bole prevented an accurate measurement, because rings could not be counted all the way back to age 1. Best-fit curves (third order polynomial equations) suggest that, in the case of Trees 2 and 3, some sort of release has occurred during the last 20 or so years.
Tree 2
Tree
3
Tree 4
We also used data collected by previous years' FES 519b classes. This and more can be found in our downloadable data workbook.
The bole of a tree can be considered as any of a number of three-dimensional solids. Usually, the bole volume is estimated as if it were a cone, a paraboloid, or a neolid (a solid that flares at the base). We found that sassafras is pretty much cone-shaped, as the following graph illustrates.
The graph below is the same as the graph above, except that the log-log
transformation has not been carried out. Observe that the best-fit
line is no longer linear. Also, note that even though it fits the
data very well, the biomass predicted by the equation is rarely exactly
what we measured in the lab (the deviation between measured and calculated
biomass is greater than 20% for some of the larger diameter trees)!
We measured the average radial
growth over the last five years (1996-1992: the 1997 ring was usually impossible
to read due to the bark having been removed) for each tree from each cookie
(1 m height increments along the bole). Tree 2 appears to have put
on more radial growth high in the bole than low in the bole; for Trees
3 and 4, the radial growth changes little with height.
By taking the average annual radial growth, multiplying this
by five, doubling that (to get the diameter change over the last five years),
and then subtracting this value from the measured dbh, we estimated the
tree's diameter in 1993. We then put this value into our biomass
equation, and approximated the tree's biomass in 1993. The trees
appear to have grown by 25-30% over the last five years, as the following
table shows.
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1998 Biomass
(from lab, kg)
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1993 dbh
(cm)
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1998 dbh
(cm)
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1993 Biomass
(from eq., kg)
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1998 Biomass
(from eq., kg)
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% Change
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| Tree 2 |
169.3
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21.4
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23.4
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110.5
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136.8
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+24%
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| Tree 3 |
30.7
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10.6
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11.8
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20.6
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26.6
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+29%
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| Tree 4 |
76.7
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14.9
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16.7
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46.5
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61.1
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+31%
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If you want to use our data
and see our calculations, you can download the Microsoft Excel workbook.
Click here to download.
| Sassafras allometry brought
to you by
Jocelyn Forbush Andrew Richardson Yale School of Forestry & Environmental Studies With thanks to
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