Difference between revisions of "Sampling And Statistics"
| Line 3: | Line 3: | ||
==Estimations of total values from plot sample data== | ==Estimations of total values from plot sample data== | ||
===Basics=== | ===Basics=== | ||
| − | Assume we have sampled ''n'' plots in a treatment unit | + | Assume we have sampled ''n'' [[Definition:Sample plot|plots]] in a stand (called [[Definition:Treatment unit|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<sub>ha</sub>'', which is computed as: <br> |
<math>\hat{Y}_{ha}} = \frac{\sum_{i=1}^n{\hat{y}_i}}{\sum_{i=1}^n{a_i}}</math> (1a) | <math>\hat{Y}_{ha}} = \frac{\sum_{i=1}^n{\hat{y}_i}}{\sum_{i=1}^n{a_i}}</math> (1a) | ||
| Line 32: | Line 32: | ||
===Using sample trees for calibration=== | ===Using sample trees for calibration=== | ||
| − | + | ==Estimation of average values, such as mean diameter and mean height== | |
Revision as of 10:04, 31 August 2008
About sampling forest data
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 Yha, 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 (similar to inclusion probability)
Estimation of plot values from tree measurements
The variable is computed from the m number of trees registered on the plot:
where
yij = value (tree volume or tree biomass),
pij = tree weight, or expansion factor (cf. inclusion probability), for the number of trees the tre record represent a a per ha-basis. 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)
Using sample trees for calibration
Estimation of average values, such as mean diameter and mean height
Estimation of the variance within a stand
The following formula is valid also when sample plots have unequal size.