Sampling And Statistics

Estimations of total values from plot sample data

Basics

Assume we have sampled n plots in a stand (called treatment unit in Heureka), and that all trees have been measured in each plot. The stand has area A and we want to estimate some variable Y, such as total volume. We are also interested in Y per area unit, denoted as Y_ha, which is computed as:

        (1a)

where
estimated value in plot i, and
inventoried area of plot i, in our case given in ha units

We then compute the estimated value of Y by simply multiplying with A (assuming that A is known):

Adaption to prognosis model

In a prognosis, growth is computed for each plot separately, one period at a time (although treatments may be coordinated between plots). A prognosis model often includes some variables that describe the density of the tree cover. For example, total basal area and stem density are common variables in growth functions, expressed as basal area per ha (m²)/ha) and number of trees per ha (trees/ha). Therefore, it is practical to keep all density variables at the plot level to a per ha-value. We can rewrite equation (1a) above to

         (1b)
where
= the variable value per area unit, and
= the plot weight

Estimation of plot values from tree measurements

The variable is computed from the m number of trees registered on the plot:

where
y_ij = value (tree volume or tree biomass),
p_ij = tree weight, or expansion factor, for the number of trees the tree record represents per area unit. For example, if the plot area is 0.0314159 ha (given a plot radius of 10 m and hence a plotarea of 314.159 m² = 0.0314159 ha) then the tree weight is 1/0.0314159 = 31.831)

Estimation of the variance within a stand

The following formula is valid also when sample plots have unequal size.