Forest Productivity Council Policy

DEFINITION AND ESTIMATION OF TOP HEIGHT FOR SITE INDEX

1.0 Introduction

1.1 Scope

Top height has been widely used for a variety of purposes and defined in various ways. This makes it difficult to determine how it could be measured in a consistent fashion and when it is appropriate to use in estimating site index through traditional height and age routes (either site index equations or growth intercept functions). In this report, we provide a definition and selection criteria for top height trees that are appropriate for individuals building or using site index tools. We recognize that the height of various components of a stand (perhaps by layer and/or by species) provides important information to various users of forest data and advocate that these height measurements be maintained. However, we recommend that the term "top height" be reserved for heights of those trees that are suitable for use in estimating site index.

This report includes a summary of previous definitions of top height along with the key issues and arguments involved in developing a top height definition. It then presents four possible options for a top height definition and concludes with TAC’s recommendation to the Forest Productivity Council (FPC) on the best option.

1.2 Objective

The objective of this report is to provide the Forest Productivity Council with the necessary technical and business information to make a decision on the definition of top height.

1.3 Problem Statement

In order to ensure compatibility across uses, it is necessary to have one set of standards for defining top height. Any definition developed must:

• have a clear purpose, i.e., to estimate site index;
• state where top height should be used and where it should not be used;
• lead to procedures that are repeatable, robust, simple, unambiguous, and technically defensible; and
• have minimal impacts on the current business.

1.4 Technical and Historical Perspective

Stand Height is an attribute of forest stands. It is commonly used for estimation of site index as a regressor for predicting standing volume and as a driver for growth models. The technical definition of stand height varies widely in different jurisdictions around the world but most definitions involve some subset of the largest trees in the stand. The definitions vary in the number of dominant and codominant trees they include, and in the constraints on their spatial distribution. We use stand height here as a generic term to describe the average height of some subset of the dominant and codominant trees.

The definition of stand height used in B.C. has changed over time. A summary of definitions is provided in Table 1. Before the mid-1980s, the Ministry standard was Dominant-Codominant Height. This was the mean height of dominants and codominants, with the restriction that two codominants should be selected for every dominant chosen. The actual selection of the trees was subjective and left to the judgment of the person taking the measurements.

Concerns about the subjectivity of dominant-codominant height led to the adoption of Top Height in 1985. The origins of top height can be traced back to the definition provided by the British Forestry Commission (Hamilton 1975), which apparently was influenced by IUFRO recommendations made in the early 1960s (Rennolls 1978). Top Height is not defined consistently everywhere, but nearly all definitions involve the same stand fraction (i.e., largest 100 trees per ha) and most select the trees based on girth rather than height. In B.C. it was defined as "the mean height of the trees corresponding to the 100 trees per hectare of largest diameter", and is denoted here as TH85. TH85 was used in the document "Site Index Estimates by Site Series for Coniferous Tree Species in B.C.", published by the Site Productivity Working Group in 1997.

In time, it became clear that there were some problems with this definition.

1. The effect of plot size had been ignored. The selection of a fixed number of trees from the available trees in a plot produces a quantile estimator, which is not scaleable. That is, although the largest 4 in a 0.04 plot and the largest 10 in a 0.10 plot all represent the equivalent of 100 per hectare, the statistics based on trees selected in this manner are not compatible estimators. Fixing the plot size in the definition would ensure compatibility. The estimated magnitude of the ‘plot-size effect’ is illustrated in Figure 1.
2. The distinction between the sampling procedure and definition needed to be clarified.
3. The definition of suitable trees (i.e., those most likely to be expressing the site potential) needed to be incorporated.

In 1992, a subcommittee of the Technical Advisory Committee (TAC) to the FPC recommended that top height be based on the largest diameter "suitable" tree on a 0.01 ha plot. A number of factors would be considered when determining the suitability of a tree including species, crown class and no evidence of damage. The subcommittee also addressed the distinction between the sampling procedure and the definition. They recommended that "true" top height be defined as the average of the heights measured on a random sample of non-empty 0.01 ha plots, rather than the average height of the 100 largest diameter trees on a hectare. No recommendation was made regarding the number of 0.01 ha plots that should be used in a stand (polygon) or in a permanent sample plot. This definition is referred to as Top Height 1992 (TH92).

Figure 1. Notional¹ effects of plot size on top height estimate relative to 1 tree in a 0.01 ha plot

In 1994, Nigh & Soderberg recommended a modified version of TH85, which was endorsed by the Chief Forester as a standard for the Ministry of Forests. The Nigh-Soderberg definition, referred to as Top Height 1994 (TH94), differed from TH85 in that it specified that site trees all be of one species. Like the TH85 definition, it allowed for plots of different sizes to be established. However, they proposed that the plot sizes be enlarged (as compared to the proportional one tree per 0.01 ha) for 1, 2 or 3 tree plots to reduce bias. This recommendation was based on work done by Fries (1974) and Matern (1976).

Meanwhile, the Vegetation Inventory Working Group, which was designing the new inventory, recommended a top height definition very similar to the one suggested by TAC in 1992 (TH92). The Vegetation Resources Inventory (VRI) External Review Panel endorsed this definition in 1995, with some minor modifications (see Table 1). We refer to it as TH95.

In 1996, Resources Inventory Branch established another top height committee to review the top height definition again. They recommended the following definition: "For a given canopy layer in a stand, top height is defined as the expected value of the height of the four largest suitable trees by species, on circular plots 0.04 ha in area." We refer to this definition as Top Height 1997 (TH97).

Table 1. Definitions of stand height used in British Columbia

1.5 Current Status of Stand Height Usage

Figure 2 depicts the notional estimated relative magnitudes of the stand height statistics in current use (largely based on theoretical considerations).

The Forest Productivity and Decision Support (FPDS) Section of Research Branch uses TH85 when summarizing the data from permanent research plots. The TASS/TIPSY models are calibrated against those statistics. Since the TH85 definition does not specify a plot size, its relative magnitude depends on the size of the plots to which it is applied. Nearly all the research plots are 0.05 ha and larger.

The temporary inventory samples that underpin VDYP have dominant-codominant height as the measure of stand height. The relative magnitude of dominant-codominant height is unknown but analysis of plots that have both dominant-codominant height and TH85 suggests that dominant-codominant height is about 7% lower than TH85.

The stand height found on inventory polygon labels is the height determined by photo interpreters (photo height). The relative magnitude of photo height is believed by many to be close to dominant-codominant height, but this assertion has not been tested.

Silviculture surveys in young stands feature plots of 0.005 ha. Top heights based on the largest trees in these plots are probably close, but theoretically lower, than the top heights derived from 0.01 ha plots.

Figure 2. Notional relative magnitudes of different stand height definitions

Previous page   |   Next page

Last updated: 01/13/99