Resource assessment exercises: fixed area plots
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| − | Suppose a forest inventory has been conducted in the simulated 50 hectare forest. In total <math>n=50</math> fixed area sample plots with a radius of <math>r=15.45</math> meters have been randomly placed in the forest (see Figure '''A'''). The area covered by a single plot is 0.08 hectares. If parts of the plot | + | Suppose a forest inventory has been conducted in the simulated 50 hectare forest. In total <math>n=50</math> fixed area sample plots with a radius of <math>r=15.45</math> meters have been randomly placed in the forest (see Figure '''A'''). The area covered by a single plot is 0.08 hectares. If parts of the plot lay outside the forest area, this part was mirrored back (see Kleinn (2013)<ref name=Kleinn13>Kleinn, C., 2013. ''Lecture Notes for the Teaching Module Forest Inventory.''</ref> and this [[Fixed area plots at the stand boundary|article]] for details). For all trees with a DBH <math>\geq</math> 5 cm the DBH (cm), height (m) and tree species was recorded. Furthermore the azimuth (1–360<math>^\circ</math>) and distance (m) of each tree to the plot center on which the tree was found was measured. |
| − | + | ||
[[image:Resource_assessment_specshares.png|thumb|center|500px|'''Figure A:''' Pie chart of the species shares in the population (left) and in the sample (right).]] | [[image:Resource_assessment_specshares.png|thumb|center|500px|'''Figure A:''' Pie chart of the species shares in the population (left) and in the sample (right).]] | ||
| − | The “forest inventory” was conducted in . The resulting dataset (as well as all other data we need in subsequent sections) is stored in the file <code>MES.RData</code>. We load the data into the workspace. | + | The “forest inventory” was conducted in [[:wikipedia:R_(programming_language)|R]]. The resulting dataset (as well as all other data we need in subsequent sections) is stored in the file <code>MES.RData</code>. We load the data into the workspace. |
| − | < | + | <pre> |
| + | load("./data/MES.RData") # Don't forget to adjust the path! | ||
| + | str(fixed.area) # Data for the fixed area plots | ||
| − | + | ## 'data.frame': 2158 obs. of 9 variables: | |
## $ plotID : num 1 1 1 1 1 1 1 1 1 1 ... | ## $ plotID : num 1 1 1 1 1 1 1 1 1 1 ... | ||
## $ plot.x : num 620753 620753 620753 620753 620753 ... | ## $ plot.x : num 620753 620753 620753 620753 620753 ... | ||
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## $ ab : num 0.1056 0.1292 0.152 0.1421 0.0831 ... | ## $ ab : num 0.1056 0.1292 0.152 0.1421 0.0831 ... | ||
## $ azimuth : num 101.1 235.7 63.3 309.4 280 ... | ## $ azimuth : num 101.1 235.7 63.3 309.4 280 ... | ||
| − | ## $ distance: num 12.22 12.75 8.05 9.52 13.98 ...</pre> | + | ## $ distance: num 12.22 12.75 8.05 9.52 13.98 ... |
| + | </pre> | ||
| + | |||
The variable <code>plotID</code> indicates on which plot the tree was found. How many trees are there on each of the 50 plots? | The variable <code>plotID</code> indicates on which plot the tree was found. How many trees are there on each of the 50 plots? | ||
| − | < | + | <pre> |
| + | n.trees <- table(fixed.area$plotID) | ||
| − | + | ## | |
## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 | ||
## 47 63 92 46 42 66 52 66 49 74 79 52 48 40 30 56 67 51 59 60 45 44 49 76 35 33 | ## 47 63 92 46 42 66 52 66 49 74 79 52 48 40 30 56 67 51 59 60 45 44 49 76 35 33 | ||
## 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | ## 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 | ||
| − | ## 25 37 29 36 31 39 54 20 24 27 21 25 38 32 37 31 39 16 20 36 29 33 21 37</pre> | + | ## 25 37 29 36 31 39 54 20 24 27 21 25 38 32 37 31 39 16 20 36 29 33 21 37 |
| + | </pre> | ||
| + | |||
| + | {{info|message=What the function <code>table()</code> does|text=The function <code>table(x)</code> provides the counts of unique values in a vector. E.g.,<code>table(fixed.area$stratum)</code> would give us the number of trees sampled in each stratum.}} | ||
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Suppose we would like to estimate the number of stems ha<math>^{-1}</math> in the forest. Since each plot covers an area of 0.08 hectares we need to compute the so-called plot expansion factor in order to be able to estimate the stems per hectare. If we have a radius of <math>r=15.45</math> the area covered by one plot is 750 m<math>^2</math>. | Suppose we would like to estimate the number of stems ha<math>^{-1}</math> in the forest. Since each plot covers an area of 0.08 hectares we need to compute the so-called plot expansion factor in order to be able to estimate the stems per hectare. If we have a radius of <math>r=15.45</math> the area covered by one plot is 750 m<math>^2</math>. | ||
Revision as of 19:26, 8 July 2014
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This section is still under construction! This article was last modified on 07/8/2014. If you have comments please use the Discussion page or contribute to the article! |
Suppose a forest inventory has been conducted in the simulated 50 hectare forest. In total \(n=50\) fixed area sample plots with a radius of \(r=15.45\) meters have been randomly placed in the forest (see Figure A). The area covered by a single plot is 0.08 hectares. If parts of the plot lay outside the forest area, this part was mirrored back (see Kleinn (2013)[1] and this article for details). For all trees with a DBH \(\geq\) 5 cm the DBH (cm), height (m) and tree species was recorded. Furthermore the azimuth (1–360\(^\circ\)) and distance (m) of each tree to the plot center on which the tree was found was measured.
The “forest inventory” was conducted in R. The resulting dataset (as well as all other data we need in subsequent sections) is stored in the file MES.RData. We load the data into the workspace.
load("./data/MES.RData") # Don't forget to adjust the path!
str(fixed.area) # Data for the fixed area plots
## 'data.frame': 2158 obs. of 9 variables:
## $ plotID : num 1 1 1 1 1 1 1 1 1 1 ...
## $ plot.x : num 620753 620753 620753 620753 620753 ...
## $ plot.y : num 5886461 5886461 5886461 5886461 5886461 ...
## $ species : num 1 1 1 1 1 1 1 1 1 1 ...
## $ dbh : num 21 23 26 26 21 13 25 22 26 21 ...
## $ height : num 11.86 12.06 11.08 10.36 9.36 ...
## $ ab : num 0.1056 0.1292 0.152 0.1421 0.0831 ...
## $ azimuth : num 101.1 235.7 63.3 309.4 280 ...
## $ distance: num 12.22 12.75 8.05 9.52 13.98 ...
The variable plotID indicates on which plot the tree was found. How many trees are there on each of the 50 plots?
n.trees <- table(fixed.area$plotID) ## ## 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 ## 47 63 92 46 42 66 52 66 49 74 79 52 48 40 30 56 67 51 59 60 45 44 49 76 35 33 ## 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 ## 25 37 29 36 31 39 54 20 24 27 21 25 38 32 37 31 39 16 20 36 29 33 21 37
What the function table()does- The function
table(x)provides the counts of unique values in a vector. E.g.,table(fixed.area$stratum)would give us the number of trees sampled in each stratum.
Suppose we would like to estimate the number of stems ha\(^{-1}\) in the forest. Since each plot covers an area of 0.08 hectares we need to compute the so-called plot expansion factor in order to be able to estimate the stems per hectare. If we have a radius of \(r=15.45\) the area covered by one plot is 750 m\(^2\).
## [1] 13.33
When we multiply the number of trees of each plot with the expansion factor we obtain the number of trees per hectare and plot.
## ## 1 2 3 4 5 6 7 8 9 10 ## 626.7 840.0 1226.7 613.3 560.0 880.0 693.3 880.0 653.3 986.7
The mean of stems.ha.i provides a population estimate of the stems per hectare.
## [1] 575.5
How good is our estimate (see Subsection [sub:se])?
## [1] 50
## [1] 32.43
# relative SE in %
## [1] 5.636
## [1] 510.3
## [1] 640.6
We know the truth.
## [1] 600
Next, we estimate the BA ha\(^{-1}\). Firstly, we need to calculate the BA (m\(^2\)) for each tree. Secondly, the total BA is calculated for each plot. Thirdly, the results are multiplied with the expansion factor. Finally, the BA ha\(^{-1}\) is estimated for the forest.
## [1] 33.17
We estimate the relative standard error in percent:
## [1] 10.29
Thus, we expect the BA ha\(^{-1}\) to be 33.17 \(\pm\) 6.86 m\(^2\). The parametric BA ha\(^{-1}\) is,
## [1] 28.66
Finally, we estimate the proportion of beech trees in the forest.
## [1] 0.6429
There is one plot (plotID 5) without any beech tree. One way to solve the problem would be use the levels argument of the factor() function.
## [1] 0.6429
The estimated standard error is
## [1] 0.06845
Figure [fig:pie] shows to pie charts of the proportion of beech trees in the population (left) and the sample (right).
[fig:pie]
Exercises
- Load the file
exercises.RDatainto the workspace. The file contains adata.framenamedfixed.area.Exthat holds data from a forest inventory using fixed area sample plots. The size of the plot is 750 m\(^2\). - Calculate the expansion factor for a plot.
- How large is \(n\) (
plotIDgives the plot number for each tree)? - Estimate the BA ha\(^{-1}\) and the number of stems per hectare. Provide an estimate of the standard error and construct confidence intervals for \(\alpha=0.10\).
Related articles
References
- ↑ Kleinn, C., 2013. Lecture Notes for the Teaching Module Forest Inventory.
