FORS230: Introduction to Fire Management Exercise 1: How Much Potential Energy i
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Question
FORS230: Introduction to Fire Management
Exercise 1: How Much Potential Energy is in a Forest?
Before you put pen to paper, please read this assignment in its entirety.
We have talked in class about combustion energy of cellulose. Recall that the heat of combustion of cellulose is -17.84MJ/kg (MegaJoules – million joules). That is ~4 million calories, which seems like a lot of potential energy for one kilogram of fuel. So how much potential energy is stored in a whole forest full of cellulose?
One way to investigate this question is to estimate the mass (biomass) of individual trees in area and sum them. Equations have been developed through the destructive sampling of trees in order to relate easily measured attributes such as diameter at breast height (dbh) with hard-to-measure characteristics such as biomass. One such equation is as follows, for ponderosa pine.
TTb = e (b0 + b1 x ln dbh)
Where:
TTb = Total Tree aboveground biomass (kg)
dbh = diameter at breast height (cm)
b0 = -2.5356 (intercept term)
b1 = 2.4349 (allometric scaling term)
ln = natural log of a number
e = base of the natural logarithm (2.718281828…)
By applying this equation to a tree list from a plot or set of plots, it becomes possible to estimate total biomass for individual pine trees, and then to sum this list of estimates to produce a per plot total tree biomass prediction. The dimensions of the plot can then be used to scale the estimate to a per hectare basis.
Once the biomass per hectare is estimated, it is possible to convert to total energy by using the value expressed in the first paragraph above (from lecture: -17.84MJ/kg).
Because not all biomass will be consumed in a fire (e.g., the live boles (trunks) of trees), it is also useful to estimate biomass for the parts of the trees that might burn in a crown fire. It is possible to do this on a per tree basis using the result from the equation above with the results from the equations below.
Crownb = TTb * (1-SWR-SBR)
Where:
Crownb = Total Crown Biomass (kg)
TTb = Total Tree aboveground biomass (kg)
SWR = Stem Wood Ratio (SWR) = Exp ( - 0.3737 - 1.8055/dbh)
SBR = Stem Bark Ratio (SBR) = Exp( - 2.098 - 1.1432/dbh)
Once again, you can sum crown biomass by stem for the plot, scale the estimate to a per hectare basis, and convert to total energy.
Your assignment is to use the equations above to estimate the energy of combustion of a ponderosa pine forest from the plot data below for all above ground biomass (TTb) and for only the part of the biomass that would likely burn in a crown fire (Crown Biomass (Crownb)). You should express these estimates on a per hectare basis using the fact that the plot below is 0.101 hectares in size. You can set up the equations any way you like with any tools you choose. Probably the easiest thing to do is to set up an excel spreadsheet and do all of the calculations at once in different columns. Notes: Pay attention to order of operations. In excel, you can represent e using EXP(1).
1. First use the TTb allometric equation to solve for the total biomass of each tree in the plot. Then use the SWR and SBR equations to solve for bark stem and bark ratios. Finally, use the Crownb equation to solve for crown biomass for each stem.
2. Sum the total and crown biomass estimates separately by adding the estimates for each tree and convert the estimates to a per hectare basis by dividing the estimate by the plot size. Finally convert the per hectare estimates of Total and Crown Biomass to combustion energy (MJ/kg) using the value expressed above.
3. What proportion of total potential energy in the forest might be expected to be released in a crown fire?
SHOW YOUR WORK.
Plot 4. 2015 Lubrecht Resource Inventory (0.101 hectares)
TREE ID
Species
DBH(cm)
1780
PP
13.7
1781
PP
7.5
1782
PP
14.3
1783
PP
6.2
1784
PP
13.2
1785
PP
19.6
1786
PP
12.4
1787
PP
14.3
1788
PP
16.4
1789
PP
7.9
1790
PP
14.3
1791
PP
14.1
1792
PP
20.4
1793
PP
6.3
1794
PP
16.7
1795
PP
14.1
1796
PP
17.4
1797
PP
10.5
1798
PP
18.7
1799
PP
6.5
1800
PP
5.1
TREE ID
Species
DBH(cm)
1780
PP
13.7
1781
PP
7.5
1782
PP
14.3
1783
PP
6.2
1784
PP
13.2
1785
PP
19.6
1786
PP
12.4
1787
PP
14.3
1788
PP
16.4
1789
PP
7.9
1790
PP
14.3
1791
PP
14.1
1792
PP
20.4
1793
PP
6.3
1794
PP
16.7
1795
PP
14.1
1796
PP
17.4
1797
PP
10.5
1798
PP
18.7
1799
PP
6.5
1800
PP
5.1
Explanation / Answer
Answer:
Heat combustion of cellulose = -17.84 MJ/kg (mega joules – million joules)
I Joule = 0.000239 Kilocalorie
Therefore -17.84 MJ per kg = 4263Kilocalorie = 4263000 calorie = 4.263 million calorie (~4 million calorie) for 1 kg fuel
The equation to determine biomass of individual tree (for species ponderosa pine) from tree features is:
TTb = e(b0 + b1 x ln dbh) = e(-2.5356 + 2.4349 x ln dbh)
SWR = e(-0.3737 - 1.8055/dbh)
SBR = e(-2.098 -1.1432/dbh)
Crownb = TTb * (1-SWR-SBR)
From the equation, the biomass of the individual trees was calculated and then biomass of all the trees was added to determine the total biomass of entire plot.
Size of the plot = 0.101 hectare
Total biomass per plot (0.101 hectare) = 1014.40 kg
Therefore total biomass per hectare (TTb per hectare) = 1014.40/0.101 = 10043.57 kg
Total Crown biomass per plot (0.101 hectare) = 279.468 kg
Therefore total Crown biomass per hectare (Crownb per hectare) = 279.468/0.101 = 2767.011 kg
To determine the combustion energy:
Heat combustion of cellulose = -17.84 MJ/kg
TTb per hectare = 10043.57 kg
Therefore heat combustion of total tree above ground ttb for 1 hectare = -17.84*10043.57 =
-179177.2663 MJ
Crownb per hectare = 2767.011 kg
Therefore heat combustion of Crown biomass for 1 hectare = -17.84*2767.011 =
-179177.2663 MJ = -49363.47 MJ
3. Out of total combustion energy from total tree above ground only a certain proportion is involved in crown fire corresponding to the crown biomass.
Therefore, Proportion of energy relased in a crown fire =
(-49363.47*100)/(-179177.2663) = 27.55% or 0.2755
REE ID Species DBH(cm) TTb (Biomass) kg SWR SBR Crownb (kg) 1780 PP 13.7 46.41 0.6032 0.1129 13.176 1781 PP 7.5 10.70 0.5409 0.1054 3.785 1782 PP 14.3 51.51 0.6066 0.1133 14.433 1783 PP 6.2 6.73 0.5143 0.1020 2.583 1784 PP 13.2 42.39 0.6002 0.1125 12.178 1785 PP 19.6 111.00 0.6276 0.1157 28.485 1786 PP 12.4 36.41 0.5949 0.1119 10.673 1787 PP 14.3 51.51 0.6066 0.1133 14.433 1788 PP 16.4 71.92 0.6164 0.1144 19.354 1789 PP 7.9 12.15 0.5476 0.1062 4.206 1790 PP 14.3 51.51 0.6066 0.1133 14.433 1791 PP 14.1 49.78 0.6055 0.1131 14.007 1792 PP 20.4 122.35 0.6299 0.1160 31.089 1793 PP 6.3 7.00 0.5167 0.1023 2.667 1794 PP 16.7 75.16 0.6177 0.1146 20.125 1795 PP 14.1 49.78 0.6055 0.1131 14.007 1796 PP 17.4 83.06 0.6204 0.1149 21.991 1797 PP 10.5 24.28 0.5795 0.1100 7.540 1798 PP 18.7 98.99 0.6248 0.1154 25.712 1799 PP 6.5 7.55 0.5213 0.1029 2.839 1800 PP 5.1 4.18 0.4830 0.0981 1.753 Total Biomass kg 1014.40 Total Crownb kg 279.468Related Questions
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