Resource assessment exercises: introduction to response designs

Revision as of 16:06, 23 June 2014

This article is part of the Resource assessment exercises. See the category page for a (chronological) table of contents.

In the introduction we mentioned that in forest inventories we usually do not sample individual trees. In this section we will have a look at different response designs. These include fixed area, nested fixed area plots, and plots of variable size. For other types of observation units see, e.g. Gregoire & Valentine (2008)^[1], and Kleinn (2013) ^[2].

Our target parameter will be the basal area (BA) ha\(^{-1}\). The BA in square meters (m\(^{2}\)) of a single tree, i.e., the cross-section of a tree trunk, is defined as,

Here, the DBH is given in centimeters, and we, therefore, have to divide by 10,000. The BA ha\(^{-1}\) for the simulated forest is

trees$ba <- (pi * (trees$dbh/2)^2)/10000
sum(trees$ba)/50 # the area of the forest is 50 hectares

## [1] 28.66
    
tapply(trees$ba, trees$stratum, function(x) sum(x)/25) # per stratum
##     1     2 
## 13.95 43.36

What the function sum() does

the function sum(x) simply takes the sum of x. To get the sums of columns and rows use colSums() and rowSums(), respectively.

What the function tapply() does

The function tapply(x, group, function) applies a function to values in a group. In the last code example we looked at the variable ba of trees. The grouping variable is stratum. For all values ba in each group (i.e., stratum) we apply a function. The argument x in function(x) stands for the values in group $i$. The sum is taken for all the values in the group and then divided by 25. tapply(trees$dbh,trees$stratum, mean)

Related pages

• Previous page: Basic statistics additional exercises
• Next page: Fixed area plots

References

1. ↑ Gregoire, T.G., Valentine, H.T., 2008. Sampling Strategies for Natural Resources And The Environment, Applied Environmental Statistics. Chapman & Hall/CRC.
2. ↑ Kleinn, C., 2013. Lecture Notes for the Teaching Module Forest Inventory.