# Optimization of plot design

## 5.1 Fixed area plots

What holds for sampling design optimization is also true for plot design: optimization is usually done for one principal variable, for convenience frequently growing stock. In NFAs, however, many variables are observed, and there are more than one variable that are simultaneously important. It is therefore frequently advisable to make a formal optimization along a key variable (usually volume) and make then a pragmatic decision in which also general experiences from other NFAs come in.What we want to achieve in a sampling exercise is highest precision at given cost (or lowest cost for defined precision). The response design contributes to that target through attempting to capture as much information as possible in each single observation unit.

It is obvious that, for a given sample size, larger plots yield more precise results, because more information is collected (at a higher price, of course). However, for a fixed size, 1000m

*²*, say, we may vary the plot shape which may also have a significant effect on precision.

Overall, the objective is to define the plot design - within the limits of practical and budget feasibility - in such a way that the variability within the plot is maximum, covering as many as possible different conditions. (This is completely different from designed experiments, where we want to have the conditions in an experimental plot as homogeneous as possible). High variability within the plot means that the differences between the plot values of a sample are smaller which leads in turn to a smaller standard error.

With respect to plot shape, given the same plot area, the conclusion from a statistical viewpoint is that,

- - elongated rectangular plots (strip plots) are better than compact shapes like circle or square,
- - cluster plots with spatially disjoint sub-plots are better than single plots.

Of course, there are also practical aspects to be considered. In cluster plots the field crews spend much time walking and in strip plots the number of boundary trees that need to be carefully checked is much higher than in circular plots of the same area.

Also, visibility in the stand is an issue: if visibility is bad, strips are preferable because to both sides of the central track observations are made only at relatively short distances. If visibility is good, circles allow a much faster measurement progress.

It would be valid (though uncommon) to combine in one and the same survey plots of the same areas but of different shapes. It needs, however, to be stressed that the plot shape must then not determined in the field only, adjusting, for example, to the terrain conditions encountered.

It has been empirically found that a number about 15-20 trees per plot is a good value for the definition of plot size. It his helpful to have an idea of the diameter distribution (for example from earlier inventories) so that, for different dbh-classes, the sizes of plot and sub-plots can be determined.

## 5.2 Cluster plot optimization

For practical reasons, cluster plots are employed in most NFAs, mainly for practical reasons: as transport is commonly expensive, one wishes to capture as much information at a specific location as possible. One could establish a single large plot; however, that is highly inefficient. Therefore, the plot area is subdivided, and cluster plots of spatially disjoint sub-plots established. The entire cluster is the plot which yields one single independent observation for estimation. The spatially disjoint areas constituting the cluster are__sub__-plots of this cluster plot

^{1}. When optimizing a cluster plot design a number of criteria are to be taken into account and practical and statistical aspects to be balanced. The following needs to be decided upon, where there is a trade-off between some of them:

*Cluster size = number of sub-plots.*

Geometric spatial arrangement of subplots:subplots arranged on a square tract, on a half square = L-shape, on a line, triangle, cross,...

Geometric spatial arrangement of subplots:

*Spatial distance between subplots*: the farther the subplots are from each other the statistically more efficient is the plot design, but the more time is used up by walking from one sub-plot to the other.

*Type of subplots and size of subplots.*The same considerations made for single plots hold.

^{1}It is important to be aware of the definition used in each specific situation, since it vary in different contexts. For example, in the work of national forest assessment group at FAO, the term "plot" is used for what we call "sub-plot" in this chapter. If one is not aware of this frequent occurring inconsistency, confusion can easily arise.