# 4. Observations units and their characteristics

Following the sampling design, objects are select for observation. Each selected object constitutes**one**independent observation for the estimation of mean, variance and variance of the mean.

The ¿objects¿ selected for observation in NFAs are usually of one of the following types

- Individual elements (e.g. tree)

- points: dimensionless observation units,
- lines: one-dimensional observation units, and
- areas, fixed or variable: two-dimensional observation units.

## 4.1 Individual elements

In the context of NFAs the selection of individual elements as observation units is not a major issue. It is mainly done (1) when not all tree variables are to be observed on all individual trees within a plot, for example tree height. Then, sub-sampling of those individual trees can be done to carry out those measurements. However, a common way to handle this selection is also to determine those trees in a non-sampling manner, for example defining that the five trees closest to the plot centre are to be measured for height.Another example for the selection and observation of individual elements is when interviews are made; then, individual ¿elements¿ are selected for observation (such as forest owners, forest users, ¿). For more details visit Who does the NFA ask?).

## 4.2 Points (dimensionless observation units)

Sample points are commonly used to estimate the area of condition classes, in remote sensing imagery and also in the field, where the centre of a plot is a sample point, in which values of categorical variables are observed: either of binary variables (such as forest/non-forest, burned/not-burned) or of a categorical variable with more than two classes (such as forest type, soil type, ownership).## 4.3 Lines (one-dimensional observation units)

Lines are one-dimensional observation units, without width (in contrast, narrow strips, sometimes erroneously also referred to as lines, do have a width and are of the ¿area¿ type, treated in the following paragraph). Line sampling can be applied in remote sensing imagery and also in the field. A common application in NFAs is, when cluster plots are used, that the line connecting the sub-plots of the cluster plot is used as observation unit, as well.On dimensionless lines, only a limited set of types of observations can be made:

- Whether an element is intersected or not. Lines are then used as a tool to select individual elements from the population. One could, for example, lay out a sample line and make measurements an all those understorey shrubs that intersect with it. This, however, is not a common application in NFAs.
- Number of intersections of a sample line with one-dimensional features in the forest or landscape, such as roads, rivers, alleys, forest border. The number of intersections allows making an estimation of the total length of these features. The underlying technique is called ¿line intersect sampling¿.
- Proportion of the sample line length that comes to lie in a particular condition class. With these observations we estimate areas and area proportions. The underlying technique is called ¿line intercept sampling¿.

## 4.4 Areas, fixed or variable (two-dimensional observation units)

Sample plots are probably the most important observation units in forest inventory in general, and also in NFAs. A variety of plot types is in use. They have all in common that for one single selection step of the sampling procedure a*set*of trees comes into the sample. On a plot, we usually observe plot-related variables (such as forest type, topographic variables, soil variables), and tree variables.

It should be clearly understood, that also for the tree variables, the

*entire plot*is the observation unit, and each plot delivers

*one*independent observation for estimation (i.e. the plot mean or the plot total).

### 4.4.1 Fixed area plots

Fixed area plots are probably the most frequently applied, and for many situations the most practical, efficient and easiest to process plot design option. As soon as the plot position is found, plot and tree related measurements are taken. Tree measurements are taken for all those trees that are defined as sample trees and plot measurements are taken at the defined locations within the plot area. The most common shapes are circular, rectangular and square plots. There is no standard plot size. For orientation, in temperate and boreal regions, sizes of 500m^{²}and also 1000

^{²}are common; in the tropics, usually larger area strip plots are employed, for example of 20m x 250m.

### 4.4.2 Subdividing a plot into sub-plots

It is inefficient to work with one single plot area for all tree dimensions. This is particularly true in natural forests, where we would find very many small trees and only few bigger trees on a given area. Therefore, we would use different sample areas for different tree dimension classes. Then, we have plots of different sizes, where the whole plots are referred to as plot, the smaller ones as sub-plots. For practical reasons, these sub-plots are usually arranged in such a way that they are contained in the plot area. We call these nested plots.Nested plots can be designed for any plot shape, also combining different plot shapes. In the tropics, for practical reasons, the sub-plots for larger trees are frequently strip plots, and smaller circular plots are used for observation of the regeneration.

A question may arise if sub plots for regeneration measurement, may be placed completely or partly outside the ¿main¿ plot. There is no objection from a methodological point of view. However, it might complicate data recording in rare cases, when the sub-plot section that lies outside falls into another forest type. One should record the additional type as well. Do not place regeneration plots on the center of a circular plot or directly on the central track of a strip plot, as there is a high chance the field crew may trample down or damage the regeneration plants.

Terminology is some times a tricky issue when working with sub-plots, particularly when clusters of sub-plots are employed (see also the later section in this subject paper Optimization of plot design). Then, from the point of view of the estimation design, each entire cluster delivers one independent observation and is therefore ¿the plot¿. The spatially disjoint sample areas are sub-plots of this cluster plot. However, if then each sub-plot is again subdivided into smaller sample areas one needs to find a clear terminology how to name them. Sub-sub-plot would probably not be a good idea. It may be preferable to use specific names such as ¿regeneration sub-plot¿ or ¿seedlings sub-plot¿.

The most important point in this terminology question is that it becomes clear right from the terminology what is to be considered 'the plot' for the statistical estimation. Otherwise the correct sample size (i.e. the number of cluster plots in the case of cluster sampling) is easily confused with the number of sub-plots - leading to an erroneously high sample size and an erroneously low estimated standard error.

### 4.4.3 Variable area plots = Relascope-plots = Bitterlich plots = horizontal point sampling

If the idea of different plot sizes for different dbh classes is extended such that each and every dbh gets its specific circular plot we come to a plot design which is known under a number of names: variable area plots, relascope plots, or Bitterlich plots (after the Austrian inventor of the method Walter Bitterlich). A sample point is selected and then all trees are included into the sample that appear - observed from that very sample point - wider than a defined angle. That means that the strictly size-proportional selection of sample trees is done indirectly, by establishing that particular view angle.By simple

*counting*the sample trees basal area per hectare can be estimated unbiasedly. If interest is in number of trees per hectare etc. the dbh of all sample trees must also be measured.

Different measurement devices have been developed to carry out relascope samples. A simple stick with a small plate at the end works as well as the thumb on the extended arm. In some regions, wedge prisms are used. The relascope offers many more additional functions.

Some variations of relascope plots have been developed but have not reached much practical relevance for NFAs so far (strip relascope sampling, vertical point sampling).

### 4.4.4 Point to object, object to object plots

Mainly known from ecological applications and lesser from NFAs are plots in which either a point or an object is selected and then all trees up to the*n*-th closest tree are observed. The number of trees per plot is then constant; but the plot size varies, defined by the distance to the

*n*-th tree which is the radius of that particular circular plot. It is a very practical and rapid method in the field; however, unbiased estimations are possible only if the spatial arrangement of the trees is random. As this is usually not the case in forests, systematic errors are to be expected, particularly if the tree spatial distribution is clustered.

## 4.5 Boundary trees, border plots and slope correction

**Boundary trees**

With fixed area plots there is always the possibility that it is not clear whether a tree is actually in the plot or not. It is time consuming to verify that, and we wish to keep the number of trees to be controlled low. Circular plots are optimal in that sense, as the circle has for a given area a minimum perimeter and therefore minimum number of boundary trees. Rectangular plots are worse, obviously, because, for the same area their perimeters are much longer.

In this context, there must be a clear definition which trees enter and which not. Usually the virtual center-axis of the stem defines it: is it in the plot area, then the tree is in. That means that a highly oblique tree the center of which is in will be counted even though the projection of its dbh may be outside the plot boundary. Or, the other way: an oblique tree that hangs over the plot is not counted if its center is outside.

**Border plots**

Border plots are those which are partly in the target condition class (e.g. forest type) of interest, partly not. They are an issue of concern, when the study refers exclusively to the target condition class (e.g. forest). If the inventory extends to all vegetation and land use classes (landscape type of tree inventory) border plots will occur more sparsely and only at the border of the inventory region.

Sample plots are established if their defined reference point (the center for circular or square plots or the starting point for rectangular plots) falls into the target condition class (e.g. forest). If a sampling point falls outside, a plot will not be established although part of it might be in forest.

Several options are discussed in the literature how to deal with border plots. The mirage method is accepted to be practical and unbiased: the section of the plot which falls outside forest is mirrored back into the forest and trees in that mirrored-back section are included twice in the sample.

The some times discussed options of leaving out the border plots or shifting them until they come completely to lie in forest will produce systematic errors of unknown magnitude and should not be applied.

**Slope correction**

If a plot is defined to have 1000m

^{²}then this area refers to the map plane like all area values used in forestry. Also on slopes, we must use horizontal distances: either we hold the distance tape strictly horizontal when measuring a distance (or use an instrument that measures the horizontal distance automatically), or we must employ a so-called slope correction that guarantees the area which we measure in the field will give the defined plot area when projected to the horizontal. The actual area measured on the slope is the larger the bigger the slope angle is. For circular plots, one calculates what the area of the ellipse would be if we projected the circle from the map plane onto the slope; then the radius of the area-equivalent circle is determined and used for the field plot. The fact that we then took the correctly adjusted area but not the elliptical shape, does not produce any problems.

Slope corrections need to be applied to all types of lines and area observation units. Some measurement devices do automatically correct for slope, such as the relascope for variable plot sampling.

Slope correction factors should be in every forest inventory field manual.