A new non-destructive method for the estimation of annual height increment in standing trees

Abstract

Measurement of tree growth is needed in many scientific and production sectors, especially in forestry for wood and biomass production. The assessment of annual height increment in standing living trees, under ambient field conditions, is challenging or even impossible. This study develops a new simple non-destructive method for the estimation of annual height increment in standing trees, based on sampling two increment cores for each targeted tree.,. Τhe method combines the tree annual ring-analysis and trigonometry. The extracted data by the method application can be widely used in many forest disciplines, such as forest ecology, silviculture, and forest management.

• •Annual height increment in standing trees is a valuable parameter needed in biology, ecology, and forestry.
• •Measurement of annual height increment in standing trees is a very difficult tusk.
• •This study develops a new non-destructive and simple method for the estimation of annual height increment in standing trees.

Graphical abstract

Specifications table

Subject area:	Agricultural and Biological Sciences
More specific subject area:	Forestry
Name of your method:	Non-destructive method for the estimation of tree annual height increment
Name and reference of original method:	NA
Resource availability:	NA

Introduction

The growth of forest tree is an ecological parameter that accounts for important responses of trees to environmental changes and is therefore an indicator of forest condition [1]. Tree growth in the field is a complicated biological process that greatly differs between the tree species. It mainly depends on site quality, and the endogenous species rate, which is different for each tree species [2], and it varies annually with climate fluctuations. Measuring forest tree growth could help estimate carbon sequestration and thereby mitigate climate change [3]. Thus, tree growth over time is a key parameter for forest science e.g. forest ecology, growth ecology, silviculture (site quality assessment, planning treatments etc.), assessing and predicting wood volume, biomass and carbon sequestration and forest management [4].

The tree growth estimation is commonly based on data of tree diameter and height, two variables that can be easily measured, unlike annual height growth data of standing trees which are difficult to acquire. Although the diameter annual increment can be accurately measured by the tree annual ring-analysis, the annual height increment in standing trees in ambient field conditions is challenging or even impossible.

Tree height increment is defined as the rate of change in tree height over a specified period of time [4]. Tree height annual or periodical increment is of great importance for stand volume growth estimations, forest management planning, and evaluating silvicultural options, as well as for urban silviculture in terms of ecosystem services and practical reasons [5], [6]. Especially during the last years, when data on biomass and carbon accumulation in forest stands are greatly needed under the climate changes demands.

In forestry science and practice, only two basic methods exist for assessing tree height (H) increment data: (i) felled tree measurements and, (ii) repeated height measurements on standing trees in the field annually [7]. The first option, which is based on stem analysis method of the felled trees, is the most accurate method, but it is a destructive method, and a quite time-consuming and expensive method [7]. This method concerns a total tree volume reconstruction, including estimation of tree dimensions during the whole life of the felled tree by stem analysis. Complete stem analysis break down and then reconstructs the past tree growth using annual increments in height anddiameter [8]. Height curves are reconstructed based on the cross section data. Then, annual height values are interpolated from cross section data using an algorithm, usually that of Carmean [9], which is the most accurate method for height curve reconstruction [10], [11], [12]. The interpolation provides an estimation of the actual height at each cross section age, since the cross section height in itself does not often include the full measurement of the last growth height. Then, height at each age is estimated by Carmean algorithm.

However, some efforts were made for the estimation of tree annual height increment in standing trees, based on the measurement of tree diameter, and afterwards correlating the height increment with the rate of diameter increment between the referred periods [13], [14], [15], [16], [17]. These methods are generally not widely accepted.

This study develops a new simple non-destructive method for the reliable estimation of height annual increment in standing trees, in the field. Τhe method combines the tree annual ring-analysis from two increment cores taken for each targeted tree, and the trigonometry.

Methods

The estimation of the annual height increment of a standing tree is performed us follows:

We take two increment cores from the targeted tree with a Pressler's increment borer or similar equipments; one in the height of 0.5 m above ground and the second at a height of 2.0 m above ground. Both increment cores are taken from the same aspect of the tree (Fig. 1).

Fig. 1.

Tree stem simulation showing the sampling two increment cores at two different tree heights. Red line shows the tree radius at 0.5 m (R_0.5), Blue line shows the tree radius at 2.0 m (R₂). Ht = current tree Height, Ht-1= tree Height at one year before, etc.

Each of the two increment cores are then analyzed under a stereomicroscope or an image analysis system (e.g. WinDEDRO). Such equipment is usually available in forestry scientific laboratories. From these two increment cores, starting from the external point of the core towards the tree pith, the tree-ring number and widths are then determined. Tree rings are dated for both cores, and tree radius corresponding to the same year (e.g. last year, the year before, etc.) at the two sampling height points are paired.

Then, the differences between the tree radiuses at the two sampling heights are computed for each year, e.g. AB for the last year t, A_IB₁ for the year before t-1, etc. (Fig. 1). Afterwards, by considering the triangle created by the distance between the two sampling points of the tree stem (1.5 m) as one vertical side (distance BC in Fig. 1) of the orthogonal triangle ABC and the difference between the paired tree radiuses (corresponding to the same year) as the second horizontal side of the triangle (distance AB for the current tree height), we computed the angle ∠A of the triangle, using the formula:

• Tangent ∠A = opposite side of a triangle/ adjacent side of a triangle,

• which in our case corresponds to: Tangent $\angle$Α = 1.5/ (R_0.5t - R₂t)

Based on the last equation, we compute the angle ∠A. Then, based on the size of the angle ∠A we can compute the total tree height, as the opposite side of the triangle formed by the total dimensions of the tree, named total height as vertical side (Ht in the Fig. 1), and total tree radius at 0.50 m (R_0.5) as horizontal side, which is the height point we made the sampling of the oldest core. Thus, the total tree height is computed as follows:

• Total tree height (Ht) = (Total tree radius at the point 0.5m * Tangent ∠A) + 0.5,

• i.e. Ht = (R_0.5 *Tangent ∠A) + 0.5

The same procedure is followed for the next annual ring pairs, corresponding to the previous years, towards the interior (pith) of the increment cores, computing the angles at year t_-1, t_-2 …. t_-n. Tree height estimation at each year is estimated with the same way, as follows:

• Tree height of the year t-1 (Ht-1) = (Tree radius at the year t-1 * Tangent A1 at the year t-1) + 0.5,

• i.e. Ht-1 = (R₂ *Tangent ∠A1) + 0.5,

Accordingly, tree height of the year t-2 (Ht-2) = (Tree radius at year t-2 * Tangent A2 at the year t-2) + 0.5.

Thus, following this procedure for each paired of annual rings (last year, the previous year etc.), we reconstruct the whole tree development during its life.

For avoiding any fault in the first step of the procedure (i.e. estimation of total tree height), we simultaneously measure the total tree height by a common tree hypsometer, and we check if any correction (- or +) is required, in the current method, in relation to the real total tree height.

The two sampling points at tree heights of 0.5 m and 2.0 m from the ground, were chosen because at these two heights the core sampling is feasible for a human from the ground. However, this distance (1.5 m) can be modified if other sampling conditions are feasible. In that case, the equation that gives the value for Tangent ∠A takes the form:

• Tangent ∠A = X / (R _t-1 - R _t-2),

where X is the distance (in m) between the two sampling points at year t-1 and t-2, and R _t-1, R _t-2 are tree radiuses form the two sampling points respectively.

Limitations of the method

This method assumes that the tree diameter's reduction rate with height is relatively uniform throughout the tree life span. This is probably not always true; however, the fact that the proposed method uses data from two height points of the tree in a distance of 1.5m that represents a period that it usually takes 3 to 10 years for the tree to grow, it removes the great part of any uncertainty. Field testing for the method validation would help to provide additional evidence of the accuracy and reliability of the method.

Conclusion

The method suggested in this paper for the assessment of annual height increment in standing trees under ambient field conditions without destruction of the measured tree, is expected to work well. It has the great advantage that is a non-destructive method, it is simple in application and of very low labor cost. It is a reliable method sine it is based on trigonometry rules, and it does not based only on one diameter measurement, as the method proposed by Meixner [15], but it considers the diameter increment at a part of the tree (stem distance 1.5 m), and to a period of the tree life, that it usually takes 3 to 10 years for the tree to grow at this stem distance, depending on how fast-growing the species is. This new method provides similar data as those provide by the complete stem analysis method for total tree growth reconstruction, which is a very time consuming and destructive. The data provided by current method application are extremely useful in forest science for the application of any silvicultural treatment., understanding crucial biological processes needed in forest ecology and management. Annual variation in tree biomass growth (height and diameter) is often the most dynamic component of the terrestrial carbon cycle and should be quantified in order to predict the response/contribution of forests to climate change.

Ethics statements

All authors declare that this work complies with ethical guidelines set by MethodsX.

CRediT authorship contribution statement

Petros Ganatsas: Conceptualization, Writing – original draft, Supervision. Lydia Petaloudi: Conceptualization, Methodology, Visualization, Software. Marianthi Tsakaldimi: Writing – review & editing, Validation.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Data availability

• No data was used for the research described in the article.