Relascope Sampling Research Articles

Monitoring spatial tree diversity indices using relascope sampling: Estimators, interactions and limitations

With ongoing climate change the monitoring of tree diversity has become very important for avoiding or at least decelerating the loss of biodiversity and for maintaining forest ecosystem resilience. As part of such monitoring, spatial indices of tree diversity which are calculated for individual trees often serve as surrogates for more direct measures of biodiversity. Mainly for its efficiency and ease of application, relascope sampling is a widespread method applied in forest inventory of many countries and thus has often been suggested as a data source for the monitoring of tree diversity. Since the interaction between sampling design and spatial diversity indices is not always clear to data analysts, we reviewed existing estimators and experimentally examined a new one, conducted extensive sampling simulations using different indices and estimators and additionally analysed the data from a large-scale forest inventory in Austria. We found that both forest structure and index algorithm greatly influence the sampling error. The largest source of sampling error was the index variance and contrary to our expectation not so much the bias due to spatial effects. For diversity indices related to distances, it has turned out to be best to apply estimators that include spatial edge correction methods. For all other indices an estimator performed better that included information on both the sample trees and their nearest neighbours, as it much reduced overall index variance. However, if possible the plus-sampling edge correction method should be applied.

Sampling theory inspires quantitative forest ecology: The story of the relascope kernel function

Understanding and modelling plant interactions is an important field in quantitative forest ecology. Many spatially explicit techniques have been devised for shedding light into these processes. One of these methods includes the application of kernel functions, which describe the decay with increasing distance of interaction effects of each plant of a given community on others. In forest inventory, a method referred to as relascope sampling is often applied to collect information on the state and change of tree resources: somewhat unexpectedly, the mathematical principles of this technique have been turned into measures of competition for use in ecological modelling. In this study, we combined methods from quantitative ecology and sampling theory by defining a parameter-parsimonious relascope kernel function, thus generalising the concept of individual-tree basal-area factors. By using both relative and absolute growth rates as response variables in the regression we compared the performance of the relascope kernel with an alternative, the exponential kernel function. Our results indicated that the relascope kernel can indeed be applied to both types of growth rates in individual-based models. Using individual-tree basal-area factors, it is even possible to anticipate the performance of the relascope kernel. In most cases the estimation efficiency was greater, when absolute growth rate was the response variable. The exponential kernel was more efficient than the relascope kernel, but at the expense of parameter parsimony and estimation robustness. Our study has shown that simple, parsimonious models, inspired by another field of natural sciences, such as the relascope kernel, can effectively encapsulate the interaction dynamics of forest ecosystems.

Two neighborhood-free plot designs for adaptive sampling of forests

Adaptive cluster sampling (ACS) has the potential of being superior for sampling rare and geographically clustered populations. However, setting up an efficient ACS design is challenging. In this study, two adaptive plot designs are proposed as alternatives: one for fixed-area plot sampling and the other for relascope sampling (also known as variable radius plot sampling). Neither includes a neighborhood search which makes them much easier to execute. They do, however, include a conditional plot expansion: at a sample point where a predefined condition is satisfied, sampling is extended to a predefined larger cluster-plot or a larger relascope plot. Design-unbiased estimators of population total and its variance are derived for each proposed design, and they are applied to ten artificial and one real tree position maps to estimate density (number of trees per ha) and basal area (the cross-sectional area of a tree stem at breast height) per hectare. The performances—in terms of relative standard error (SE%)—of the proposed designs and their non-adaptive alternatives are compared. The adaptive plot designs were superior for the clustered populations in all cases of equal sample sizes and in some cases of equal area of sample plots. However, the improvement depends on: (1) the plot size factor; (2) the critical value (the minimum number of trees triggering an expansion); (3) the subplot distance for the adapted cluster-plots, and (4) the spatial arrangement of the sampled population. For some spatial arrangements, the improvement is relatively small. The adaptive designs may be particularly attractive for sampling in rare and compactly clustered populations with critical value of 1, subplot distance equal to the diameter of initial circular plots, or plot size factor of 2.5 for an initial basal area factor of 2.

Critical length sampling: a method to estimate the volume of downed coarse woody debris

In this paper, critical length sampling for estimating the volume of downed coarse woody debris is presented. Using this method, the volume of downed wood in a stand can be estimated by summing the critical lengths of down logs included in a sample obtained using a relascope or wedge prism; typically, the instrument should be tilted 90° from its usual orientation in sampling live trees. The critical length of a downed tree is the length of the log section large enough in diameter to be counted from the selected sample point. A simulation study was conducted to compare critical length sampling with diameter relascope sampling and perpendicular distance sampling. For the population studied, diameter relascope sampling tended to have the smallest variance but exhibited a small design-bias. By combining critical length sampling with critical height sampling—a method previously described for estimating the volume of standing trees—the total volume of dead wood in a stand can be estimated using the same basic principle. One use of the combined method might be in rapid in-place inventories where a quick estimate of the volume of dead wood is needed for biodiversity management purposes. The combined critical length/height method provides a relatively simple means for obtaining such estimates.

Comparison of field sampling methods for assessing coarse woody debris and use of airborne laser scanning as auxiliary information

Coarse woody debris (CWD) has been recognized as one of the strongest indicators of forest biodiversity and its assessment has been emphasized in the development of new inventory methods. In this study, the most commonly referenced probability sampling methods were tested in a field area of 305.8 ha to gain comparative information on their performance and efficiency. Simple random sampling (SRS), systematic sampling and cluster sampling with fixed sized circular sample plots were tested, as well as strip sampling, transect relascope sampling and adaptive cluster sampling (ACS). Point relascope sampling and line intersect sampling were also tested for inventories of downed dead wood volumes. In addition, the amount of standing dead wood was assessed by means of traditional small angle relascope sampling. In general, the use of additional information in the inventory process has shown promising results. A new method for using data derived from airborne laser scanning (ALS) as a source of auxiliary information in the assessment of CWD volumes is presented, using probability proportional to size (PPS) sampling for the selection of the first-stage sample units in ACS (ACS PPS) and for the placement of fixed sized plots (PLOT PPS). The sampling methods were compared in terms of the cost-effectiveness. Point relascope sampling proved the most efficient sampling method for inventorying CWD volumes. PLOT PPS and ACS PPS were more efficient than the inventory of fixed sized plots (PLOT SRS) and ACS (ACS SRS) where sample units were selected with SRS. However, these methods could not achieve the same efficiency as relascope samplings. Nevertheless, the use of probability layers derived from ALS data gave promising results and offers new possibilities for inventorying CWD volumes more efficiently.

A relascope for measuring canopy cover

Angle count or relascope sampling has traditionally been used in forestry to estimate stand basal area. In this paper, we present an extension to the basal area relascope, the crown relascope, which differs from the normal relascope in that the relascope’s slot is very high and wide. We describe the theoretical basis of the instrument and present results from a field test in which a crown relascope with a basal area factor of 250 m2/ha (0.025) was used to estimate canopy cover of 73 sample plots in northern Finland. The crown relascope estimates had a root mean square difference of 9.3% and an average difference of –3.1% when compared with estimates obtained with the control method, line intersect sampling using the Cajanus tube. The results indicated that the crown relascope is a quick and fairly reliable instrument for canopy cover estimation, especially in relatively sparse forests where crown overlap is insignificant and visibility does not limit an efficient use of the instrument.

A new empirical approach for estimation in k-tree sampling

Point-to-tree distance techniques (also known as k-tree or fixed count sampling) are a practical field sampling method for forest inventories and ecological surveys, but statistical estimation remains a problem. Various approximation techniques have been proposed, partly on an empirical basis, partly under model assumptions about the underlying point processes. In this paper we present a brief history of k-tree sampling in forestry and introduce a new and simple empirical approximation method. This method builds on calculating the variable sample plot area from the distance not only to the k tree but averaging the distance to the k and to the ( k + 1) tree. Simulation studies were done on a tree map from the Miombo woodlands in northern Zambia and five artificially generated tree maps with different point patterns. In terms of bias, our techniques are superior to Prodan's approach; however, Eberhardt's estimator produces consistently the smallest bias for the studied clustered patterns, and is unbiased for random patterns. For the two uniform patterns studied, bias was smallest on average for our new estimators. A comparison with relascope sampling and fixed area sample plots sized to yield k trees per sample plot indicated that the k-tree sampling estimators studies produced higher standard errors for the estimation of basal area and number of stems than fixed area plots for the clustered and random maps. For the two uniform patterns, k-tree sampling with our mean-area estimator produces smallest errors, in particular for small values of k. It is concluded that it is mainly the simplicity of the method that makes point-to-tree distance sampling interesting for forest and ecological sampling, but its statistical performance remains somewhat uncertain.

Sperimentazione di procedure probabilistiche innovative per la cubatura della massa legnosa a fini assestamentali

The cost of management plan elaboration is one of the main factors hampering the operational implementation of forest management in Italy. Besides compartment descriptions, such a cost is mainly due to the quantitative assessment of stand dendrometrical attributes. The aim of this work is to test the integration of conventional forest mensuration techniques with probabilistic estimation procedures that in the last years have found ever wider implementation for inventorying small forest areas. Distinctively, the objective of this note is the comparative experimental testing of the following methods of timber volume assessment: two-phase relascope sampling; two-phase visual estimation. Under the examined conditions referred to Turkey oak and beech high stands in Central Italy, the latter method has provided hopeful results. The most accurate and precise options of two-phase visual estimation have allowed an average time saving around 40% with respect to the total tally, with an absolute bias around 4-5% with respect to the true value of compartment timber volume, and efficiency higher than the conventional one-phase systematic plot sampling.

Horizontal Line Sampling for Riparian Forests without Land Area Estimation

Abstract Sampling forests in riparian areas presents unique difficulties that can be addressed by judicious application of line sampling. Land areas associated with riparian forests often have highly irregular boundaries, making accurate area determination difficult. Therefore, estimators for total amounts of forest attributes that do not depend on land area are desirable. Such estimators can be obtained by using horizontal line sampling from sample lines that are located at random intervals along a straight baseline and which extend entirely through the riparian area of interest. Horizontal line sampling selects sample trees that subtend an angle whose vertex is located on a length of line. This is conceptually similar to Ståhl's transect relascope sampling (Ståhl, G. 1998. Transect relascope sampling—A method for the quantification of course woody debris. For. Sci. 44:58–63), which estimates total amounts of coarse woody debris from lines established at fixed intervals. Use of a control variate or importance sampling based on predicted line length (where available) is suggested as a variance reduction technique. An unbiased estimator for sampling at intervals along the line is suggested. Monte Carlo integration estimates of riparian land area are proposed for estimation of per-unit area quantities. These estimators could be applied to any forested area but appear to be most well suited to long, relatively narrow riparian areas.

Critical point relascope sampling for unbiased volume estimation of downed coarse woody debris

Critical point relascope sampling is developed and shown to be design-unbiased for the estimation of log volume when used with point relascope sampling for downed coarse woody debris. The method is closely related to critical height sampling for standing trees when trees are first sampled with a wedge prism. Three alternative protocols for determining the critical sampling points on a log are presented and simulations are employed to suggest the most efficient protocol to use in practice.

Comparing line-intersect, fixed-area, and point relascope sampling for dead and downed coarse woody material in a managed northern hardwood forest

We present the results of a timed field trial comparing the bias characteristics and relative sampling efficiency of line-intersect, fixed-area, and point relascope sampling for downed coarse woody material. Seven stands in a managed northern hardwood forest in New Hampshire were inventoried. Significant differences were found among estimates in some stands, indicating a potential for difference in bias in field implementation of the methods. In terms of relative sampling efficiency, results for each method varied among stand. However, point relascope sampling had comparable or better time efficiency than the other methods in most stands.

Prism sweeps for coarse woody debris

A new method for sampling coarse woody debris (CWD) is presented, based on relascope sampling of CWD midpoint diameter. In this method, CWD is included in a sample if the angle subtended by the midpoint diameter viewed from plot center is greater than the critical relascope angle. The method is therefore referred to as diameter relascope sampling (DRS). Other methods for sampling CWD are reviewed and compared with DRS using sampling simulations and statistical power calculations. These are fixed area sampling, line intercept sampling, and point rela scope sampling. DRS is shown to be have greater statistical power per unit sampling effort than other methods when CWD diameter and length are linearly or allometrically related, but results can vary with the diameter-length relationship employed. The relative benefits of different methods for sampling CWD are discussed.

A Field Test of Point Relascope Sampling of down Coarse Woody Material in Managed Stands in the Acadian Forest

We field tested a new method for sampling down coarse woody material (CWM) using an angle gauge and compared it with the more traditional line intersect sampling (LIS) method. Permanent sample locations in stands managed with different silvicultural treatments within the Penobscot Experimental Forest (Maine, USA) were used as the sampling locations. Point relascope sampling (PRS) with three different angles spanning the practical range of angles for such stands was used along with 40 m of LIS sample per sample point. Compared to LIS, the three angles resulted in similar number of pieces and volume of CWM from stands with different histories of repeated partial harvests. In terms of sampling efficiency, PRS was up to 4 times more efficient than LIS. These results, while limited to only one forest type and a relatively small sample, are the first published results available on the field performance of PRS.

Correction for Slope in Point and Transect Relascope Sampling of Downed Coarse Woody Debris

Abstract In this article, the effect of sloping terrain on estimates in point and transect relascope sampling (PRS and TRS, respectively) is studied. With these inventory methods, a wide angle relascope is used either from sample points (PRS) or along survey lines (TRS). Characteristics associated with line-shaped objects on the ground are assessed, e.g., the length or volume of downed logs. In their basic forms, the methods only work in flat terrain, and thus bias is incurred under sloping conditions. Two different possibilities to correct for bias due to slope are presented. The first one involves using a slightly modified relascope device and making a measurement of the angle of inclination of each sampled object. The second involves applying correction factors based on the steepness of the terrain in the area surveyed. However, it is shown that moderate slopes cause only limited bias and in such cases there is little need to adjust the measurement procedures or apply correction factors. For. Sci. 48(1):85–92.

Monte Carlo approaches to sampling forested tracts with lines or points

Several line- and point-based sampling methods can be employed to estimate the aggregate dimensions of trees standing on a forested tract or pieces of coarse woody debris lying on the forest floor. Line methods include line intersect sampling, horizontal line sampling, and transect relascope sampling; point methods include variable- and fixed-radius plot sampling, and point relascope sampling. We demonstrate that the line methods can be interpreted as applications of importance sampling and that point methods can be interpreted as two-stage applications of importance sampling and crude Monte Carlo. Interestingly, each of the line methods also can be implemented as a point method. Operationally, the two stages of a point method effectively reduce to a single stage. Estimators of target parameters are derived from the Monte Carlo approach for all six methods. Two new methods of estimating cross-sectional areas of slanted or tilted log-shaped objects are suggested for use in line intersect sampling. Boundary problems also are discussed.

Two-phase approaches to point and transect relascope sampling of downed logs

Point relascope sampling and transect relascope sampling were recently proposed as methods for the inventory of downed coarse woody debris. By only counting logs with a relascope device, the total length squared (with point relascope sampling) or the total length (with transect relascope sampling) of downed logs in an area can be estimated. For estimates of other variables, such as volume, additional measurements on the sampled logs are required. In this article, two-phase approaches to the methods are presented that makes use of the estimates from fast counts of logs as auxiliary data. The presented approaches serve two purposes: (i) to improve the efficiency of the methods and (ii) to avoid the bias that is likely to occur if careful checks of whether or not doubtful logs should be counted are neglected. Each two-phase design was compared with a single-phase design in terms of the standard error obtained for a given inventory cost. The two-phase designs decreased the standard errors with ca. 17–18% for points and 10–15% for lines. Including subjective judgements as additional auxiliary variables further decreased the standard errors in the line case but not in the point case. In the former case, the improvement in comparison with the single-phase design was 17–23%.

Point Relascope Sampling: A New Way to Assess Downed Coarse Woody Debris

Abstract This article presents a practical review of one of two recently developed methods for sampling downed coarse woody debris in forest stands. The method discussed here, point relascope sampling, is closely related to the familiar horizontal point sampling and this relationship is demonstrated throughout. Formulas, worked examples, and guidelines for the field implementation of the technique are presented.

Two-phase approaches to point and transect relascope sampling of downed logs

Point relascope sampling and transect relascope sampling were recently proposed as methods for the inventory of downed coarse woody debris. By only counting logs with a relascope device, the total length squared (with point relascope sampling) or the total length (with transect relascope sampling) of downed logs in an area can be estimated. For estimates of other variables, such as volume, additional measurements on the sampled logs are required. In this article, two-phase approaches to the methods are presented that makes use of the estimates from fast counts of logs as auxiliary data. The presented approaches serve two purposes: (i) to improve the efficiency of the methods and (ii) to avoid the bias that is likely to occur if careful checks of whether or not doubtful logs should be counted are neglected. Each two-phase design was compared with a single-phase design in terms of the standard error obtained for a given inventory cost. The two-phase designs decreased the standard errors with ca. 17–18% for points and 10–15% for lines. Including subjective judgements as additional auxiliary variables further decreased the standard errors in the line case but not in the point case. In the former case, the improvement in comparison with the single-phase design was 17–23%.

Point relascope sampling of downed coarse woody debris

This paper presents a method based on angle-gauge sampling useful for inventorying downed coarse woody materialin forest stands. The method is closely related to transect relascope sampling, except that sample points are used rather than line transects. Theestimators for the total and per unit area are given along with theestimators of their variances. Methods for handling both borderline material and boundaryoverlap situations are also presented.

On the Field Performance of Transect Relascope Sampling for Assessing Downed Coarse Woody Debris

Transect relascope sampling is a recently proposed method for making efficient inventories of coarse woody debris on the ground. However, before the method can be recommended, its performance in the field requires investigation. This paper presents the results of a field study in which 11 surveyors tested the method in two coniferous stands in northern Sweden. The average bias introduced by the surveyors was moderate under normal sighting conditions, but underestimation was substantial when combining a small relascope angle with poor sighting conditions. In all cases, the differences between the systematic errors of individual surveyors were substantial. The conclusion is that transect relascope sampling is not an appropriate method when the demand for unbiased estimates is high, e.g. in connection with long-term monitoring, but that the method can be useful as a first phase in double sampling or in ocular-based inventories aimed at identifying biologically valuable areas.