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## Computer Simulation of Critical Height Sampling

Johnson, Alan Lawrence

Johnson, Alan Lawrence

##### Abstract

In order to better understand the work presented in this study, it is necessary to understand several topics from mensuration and forest sampling. First, the problem of concern is improvement of the variance associated with the estimation of forest growth from remeasurement of permanently established locations in a forested area. When sample trees at these locations are chosen by an angle gauge the locations are often called permanent points. To simulate this on a computer data are required which give the position of each tree (using a Cartesian coordinate system) relative to every other tree and the entire border of the forest stand. Data of this type are known as mapped stand data. The data consist of the Diameter at Breast Height (DBH), (the diameter of the tree at a standardized height of 4.5 feet above the ground) and the total height of the tree at each specified age. Second, two different sampling systems are compared in order to determine which one estimates growth with the least variance. The first method is known as Horizontal Point Sampling and shall also be written as HPS. It is a system of forest sampling that selects trees by using an angle whose vertex is centered at a point in the forest. The second method is called Critical Height Sampling and shall also be called CHS. Two characteristics of each system will be examined. The first, the volume estimator, refers to the estimate of forest volume obtained with the use of each sampling system. The second, the growth estimator, refers to the estimate of forest growth obtained with the use of each sampling system. Third, two common topics in mensuration will be mentioned. In this study K is a constant which, when multiplied by the square of the Diameter at Breast Height (DBH) of a tree, gives the cross sectional area of the tree at Breast Height (4.5 feet above the ground) in square feet. This is called the Basal Area (BA) of the tree. Basal Area (BA) can also be expressed in terms of an entire stand (on a square feet per acre basis). Similarly, there is a constant K associated with metric units which when multiplied by the square of the DBH in centimeters (cm) yields Basal Area in square meters. In the metric system, the Breast Height is 1 .3 meters (m) above the ground and Basal Area (BA) is in square meters (for a single tree) or square meters per hectare (for an entire stand). The Basal Area.Factor (BAF) is the number of square feet of Basal Area per acre that is represented by each and every sample tree selected� by an angle gauge in horizontal point sampling or critical height sampling. In HPS and CHS, the BAF is the same for each tree tallied. Finally, each sample tree will be classified into one of five different categories. The categories represent the different types of individual tree growth encountered in growth estimation through horizontal point sampling. The categories and their definitions are from Martin (1982). 1) Ingrowth trees are below the minimum dbh and "in" at the first measurement but grow enough to exceed the minimum dbh at the second measurement. 2) Survivor trees are above the minimum dbh and "in" at both measurements. 3) Mortality trees are above the minimum dbh and "in" at the first measurement but die prior to the second measurement. 4) Ongrowth trees are below the minimum dbh and "out" at the first measurement but are above the minimum dbh and "in" at the second measurement. 5) Nongrowth Trees are above the minimum dbh and "out" at the first measurement but are "in" at the second measurement.

##### Date

1988-12-01