Plot design

Forest Inventory lecturenotes

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Introduction

The response design defines what is being done once a sampling element is selected. In forest inventory, it makes sense to speak of “plot design” as we usually select sample plots or more general of “observation design”. There are 4 basic types of observation units:

1. individual objects, such as trees, stands, properties; on individual objects any attribute can be observed;
2. (dimensionless) points: a typical application are dot grids. Only limited categorical variables can be observed on dimensionless points, either dichotomous variables (for example forest/non-forest) or categorical variables with more than two classes, such as forest type.
3. (one-dimensional) lines: on a sample line it can be observed how many intersections there are with line features (roads, forest edge, …) or which portion of the sample line is in a particular forest type.
4. (two-dimensional) areas: such as fixed area plots. On the set of objects (trees) found on that area, attributes are being observed.

While all of these types of observation units are found in forest inventory, the sample plots are probably the most frequently used. In fact, all the basic plot types (fixed area plots, relascope plot, distance based plots) can be uniformly characterized as follows: the sampling design defines how sample points are being selected in the (forest) area of interest. Once a sample point is selected, the plot design defines how to select around that point the sample trees that are to be observed. For fixed area plots, some geometric shape is defined around the sample point and all trees within this shape are observed; in relascope sampling all those trees are taken as sample trees that appear wider than a defined opening angle with which the surrounding trees are aimed at; and in distance based plots a fixed number of k nearest trees is taken as sample trees in each sample point.

That is, the plot design implies defining how to select the sample trees to be measured around each sample point. It is important to recall the factors randomization and sample size: each randomization increments the sample size by 1. That is, when we select sample plots at random, then the number of sample plots is the sample size and not the number of trees that are measured on these plots!

Measurement procedures must be defined for all variables that are measured on the plot. When doing the measurements, care must be taken, that no tree is forgotten and that no tree is measured twice. It helps to mark the measured trees with chalk or other color, where it is recommendable to mark it such that it can be well seen from the center point (in circular plots). In strip plots this is usually not a problem as one proceeds on the central line step by step. Temporary plots and permanent plots can be distinguished. Temporary plots are visited once. Permanent plots are visited in regular intervals. Therefore, permanent plots need to be prepared such that they can be easily found on the next inventory and that future measurement can straightforwardly be taken.

Spatial autocorrelation

Figure 1 Typical shape of a spatial autocorrelation function. Here, however, the covariance is given. The correlation would look exactly the same, but with a y-axis re-scaled to the range of 0.0 to 1.0 (Kleinn 2007).

“Correlation” describes the relationship between two variables. Autocorrelation (“self-correlation”) describes the relationship between two observations of the same variable, taken at two different objects or times. “Spatial autocorrelation” is an autocorrelation where the pairs of objects are defined by the distance between them.

Spatial autocorrelation is an important concept that helps understanding many relevant features in forest inventory sampling. It is introduced here because it has also relevance for the design of the forest inventory observation units.

Spatial autocorrelation is present in all forests and has to do mainly with site factors and growth conditions that are highly correlated for trees that are close together and that are much lesser correlated for trees that are farther away from each other. The same holds also for sample plots: plots that are spatially close to each other tend to exhibit more similar values than those with a longer distance in between. Figure 1 gives an example; there, however, the covariance is given; as correlation is simply the standardized covariance, the shape of the function holds exactly also for the autocorrelation; for the autocorrelation the y-axis would need to be re-scaled to the range of 0.0 to 1.0. In that graph, the points mark measured covariances of various pairs of observations at the same distance. The line is then a smooth curve fitted to the observed values. The shape of the curve is typical: high correlation for observations that are close to each other (and an autocorrelation of 1.0 if the distance is 0, because then, the same object is observed twice), and constantly decreasing covariance (autocorrelation) with increasing distance. From a certain distance onwards a more or less steady level of no correlation is reached.

Relevance for plot design planning

First we state that we would like to design observation plots such that the within-plot variability is as high as possible. That means, per sample plot we wish to capture as much variability as possible. The reason is simple: the more variability we capture per plot the smaller will be the variability between the sample plots – and it is the variance between the plots that determines the error variance. High correlation means that by knowing one value we can fairly well predict the other value of the pair of observations. That means, if two variables are highly correlated, the added value of measuring the second variable is relatively low once the value of the first variable is known (because the value of the second variable can fairly well be predicted). And the same holds for autocorrelation: if the autocorrelation between the values of two objects is high then it is less beneficial (in terms of gain of information) to also measure the second object.

As a consequence of this consideration, from a statistical viewpoint of capturing as much information as possible per plot we wish to keep the autocorrelation between pairs of observed objects (trees or plots or …) low; and that means that we want to make the distances between the objects large.