Angle-count sampling method for estimating forest stand volume – a practical approach

Point sampling, which is also known as angle-count sampling (ACS), can be considered an efficient way of estimating the basal area and volume of forest stands. It is possible to use it in forest management: providing more accurate estimates (precision <10%) of site and stand characteristics needed for management planning. 20 black locust (Robinina pseudoacacia L.) stands were selected at final cutting age to determine the regeneration criteria based on their total volume. It was verified that at P=5% there was no difference between the main volume values of stands indicated in the relevant forest plans as well as calculated by the ACS method.

Angle count sampling reliability as ground truth for area-based LiDAR applications in forest inventories

LiDAR-based techniques to estimate forest variables at the stand level require accurate calibration through ground truth data. One purpose of this study was to verify whether angle count samples can be used as suitable ground truth to calibrate LiDAR-based models for timber volume estimation. Volume data were acquired on the ground for 79 plots in the Latemar forest (province of Bolzano, Italian Alps). A simple linear regression model, using the sum of all of the tree canopy heights in the plot as the explanatory variable, was adopted. As angle count samples have no fixed area, three different methods to approximate their size were compared. The angle count sample area can be properly approximated by visual assessment of the tree size classes and by callipering the largest tree in the plot. The results show that angle count sampling can be an efficient solution to calibrate LiDAR-based models: they produced fair estimates at the plot level (relative root mean square error (RMSE), 26.6%) that were better than fixed-radius plot estimates with full callipering (RMSE, 29.7%). Estimate uncertainty at increasingly large forest stand areas was also calculated by means of a simulation procedure. It showed that low uncertainty (standard error of estimate = approximately 2%) could be reached at a forest compartment level (19 ha on average).

Relascope sampling for crown ratio estimation

In this study, we apply vertical angle count sampling to estimate the crown ratio of trees in unthinned forest stands. The rationale is to be able to quickly assess the relative crown size of forest stands to support thinning decisions by simply counting trees. We provide estimators and discuss their precision based on pilot studies in Scots pine (Pinus sylvestris L.) plantations in northern Sweden. A separate study was conducted to investigate the amount of measurement errors, i.e., how many trees are wrongly selected or overlooked when using the method. Sampling errors for estimating crown ratio were found to be remarkably low, partly due to high correlation between crown length and tree height and partly due to low variability in the study sites. Measurement errors were in the range of what is commonly obtained with horizontal angle count sampling for basal area estimation.

Correcting the nondetection bias of angle count sampling

The well-known angle count sampling (ACS) has proved to be an efficient sampling technique and has been applied in forest inventories for many decades. However, ACS assumes total visibility of objects; any violation of this assumption leads to a nondetection bias. We present a novel approach, in which the theory of distance sampling is adapted to traditional ACS to correct for the nondetection bias. Two new estimators were developed based on expanding design-based inclusion probabilities by model-based estimates of the detection probabilities. The new estimators were evaluated in a simulation study as well as in a real forest inventory. It is shown that the nondetection bias of the traditional estimator is up to −52.5%, whereas the new estimators are approximately unbiased.

New and composite point sampling estimates

A new estimator for basal area is introduced that is based on the concepts of angle count and angle summation sampling. Using the ratio of the angle count basal area factor and the angle summation (borderline) factor, it is possible to estimate stand volume without measuring the diameters and distances of the trees included in the sample. Employing simulation of repeated sampling in a 40 ha forest of known population parameters, it is demonstrated that the new sampling methodology is unbiased and weakly correlated with conventional angle count sampling. Hence, considerable gains in efficiency are made by combining the two sampling methods with composite estimators. Two applications are explored with the new composite point sampling estimates, including the use of the big basal area factor sampling method and critical height sampling using a Max and Burkhart taper formulation.

Stratified space angle-count sampling for an estimation of stand volume

Stratified space angle-count sampling is a newly proposed method for estimating stand volume. This new method includes the theory and all the premises of space point sampling, as well as the following: (i) all trees taper, (ii) the box-like sampling space imagined in space point sampling is divided into several strata with the same vertical distances, (iii) the diameter of expanded tree stems in each stratum is represented at the middle of the vertical distance in each stratum. Stand volume is calculated using the following equation: V (m3/ha)=kH/Z Σ[Formula: see text] λi, where V is volume (m3/ha), k is basal area factor (m2/ha), H is the maximum tree height in the stand, Z is the number of strata in the sampling space, N is the number of trees in the stand, and λi is an indicator variable that takes the value 1 or 0, depending on whether the tree stem is in the sample or not. Since this method does not require a measurement or an estimation of a critical height, it could be an easy method for estimating stand volume.