Randomized Branch Sampling Research Articles

Modelling branch surface area of Fagus sylvatica L.

ABSTRACT Allometric models describe properties of trees that are difficult to measure. Here, we provide a set of allometric models for estimating branch properties for European beech (Fagus sylvatica L.). Branches affect rainfall and snow interception, provide habitat for other organisms and contribute to the economic and aesthetic value of trees. Using randomized branch sampling (RBS) of 27 beech trees in Austria we developed models for branch surface area, branch number, branch base diameter and branch length, depending on stem diameter, tree height and crown ratio. For individual branches, branch diameter was the best predictor of branch surface area while including branch length or position along the stem did not improve the models. For the entire tree, stem diameter was the most important predictor. Branch surface area (and in consequence also branch volume) assessed by RBS was greater than the branch surface area estimated as a cylinder from measurements of branch length and branch base diameter. Since the branch allometry of beech differs considerably from a previous study on branches of Picea abies, we conclude that assumptions and models derived from other tree species can lead to considerable biased results in assessing the functions of tree branches.

Simple Allometry To Estimate The Aboveground Tree Biomass For Five Cool-Broadleaved Species Of Bhutan Himalaya

Million tons of carbon was found to be stored in the forest biomass with maximum storage capacity in the broadleaved trees. Developing tree biomass allometric equation being considered fundamental to determine the carbon sequestration potential of tree species. Thus, five broadleaved tree species of Quercus lamellosa, Beilschemidia sikkimensis, Castonopsis hystrix, Persea clerkania and Symplocos sumintia were destructively sampled using Randomized Branch Sampling technique (RBS) to develop allometry for aboveground biomass estimation in cool broadleaved forests in Bhutan. The total of 159 sample trees with minimum 32 trees from each species under different diameter class (5 cm < 90 cm), height class (4 m < 46 m) from four physiographic zones were sampled. The observed total aboveground dry biomass of the trees ranges from 4.12 < 5579.31 kg; 3.62 < 3464.51 kg; 5.99 < 3600.52; 8.89 < 3689.82 kg; kg and 7.08 < 2993.22 kg respectively for above five species. Linear regression was attributed to heteroskedasticity with un-equal distribution of the residual errors. While linearized regression with transformed variables exhibited the best fit line for biomass estimation. Significant prediction of aboveground tree biomass was observed with natural log base transformed linearized power function of DBH -tree height relationships (t (29) = 11.91, 1.63, p ≤ .001) R² = .98) followed by the transformed model of DBH as independent variable (t (30) = 34.31, p ≤ .001) R² = .97). Therefore, the study concluded that, linearized power function with antilog bias correction factor seemed better in predicting aboveground tree biomass of cool broadleaved species in Bhutan

Predicting the number of fruits and the seed biomass of Trichilia emetica (Vahl.) in the eastern coastal region of South Africa

Trichilia emetica is a coastal fruit tree species from sub-Saharan Africa that has a potential for commercial harvest for its edible and useful seed oils. However, the prediction of its fruit and seed yields is necessary to plan a profitable harvest. This study aims to calibrate allometric equations that predict the amount of fruits and the biomass of seeds of T. emetica. A total of 35 trees were selected based on seven classes of the diameter at breast height (DBH) in the Umkhanyakude district. The trees were measured during fruit maturation period. The measurements included the DBH, the canopy diameter, and the total height. Fruits were counted on each tree using randomized branch sampling technique. Twelve fruits were harvested per tree and were brought to the laboratory for the determination of biomass. Six allometric models were identified and fitted to the data using ordinary least squares method. The Akaike information criterion (AIC) was used to select the best-fit models. The results suggested that simple linear models, basing solely on DBH (in cm), were the best predictors of both the number of fruits on the trees (NF) and the fresh seed biomass (SB; in kg) of T. emetica. The exponential forms of the best-fit general models were: (1) NF = 375.364 × DBH1.009; and (2) SB = 1.858 × DBH1.009. The prediction tests of these models indicated that the errors were large when predicting the fruit number and the seed biomass of smaller trees (DBH ≤ 20 cm) and bigger trees (DBH ≥ 30 cm). For medium-size trees (20 cm < DBH < 30 cm), the error was small. On the other hand, tree size category models developed in this study improved statistically the accuracy of predictions. The findings recommend the use of the fitted tree size category equations.

Shea (Vitellaria paradoxa Gaertn C. F.) fruit yield assessment and management by farm households in the Atacora district of Benin.

Vitellaria paradoxa (Gaertn C. F.), or shea tree, remains one of the most valuable trees for farmers in the Atacora district of northern Benin, where rural communities depend on shea products for both food and income. To optimize productivity and management of shea agroforestry systems, or "parklands," accurate and up-to-date data are needed. For this purpose, we monitored120 fruiting shea trees for two years under three land-use scenarios and different soil groups in Atacora, coupled with a farm household survey to elicit information on decision making and management practices. To examine the local pattern of shea tree productivity and relationships between morphological factors and yields, we used a randomized branch sampling method and applied a regression analysis to build a shea yield model based on dendrometric, soil and land-use variables. We also compared potential shea yields based on farm household socio-economic characteristics and management practices derived from the survey data. Soil and land-use variables were the most important determinants of shea fruit yield. In terms of land use, shea trees growing on farmland plots exhibited the highest yields (i.e., fruit quantity and mass) while trees growing on Lixisols performed better than those of the other soil group. Contrary to our expectations, dendrometric parameters had weak relationships with fruit yield regardless of land-use and soil group. There is an inter-annual variability in fruit yield in both soil groups and land-use type. In addition to observed inter-annual yield variability, there was a high degree of variability in production among individual shea trees. Furthermore, household socioeconomic characteristics such as road accessibility, landholding size, and gross annual income influence shea fruit yield. The use of fallow areas is an important land management practice in the study area that influences both conservation and shea yield.

Estimating biomass and carbon for Gilbertiodendron dewevrei (De Wild) Leonard, a dominant canopy tree of African tropical Rainforest: Implications for policies on carbon sequestration

Estimates of global carbon stocks in standing forests are subject to uncertainty because of regional and tree species differences that are usually ignored in global allometric equations. The absence of appropriate site-specific and individual tree allometric equations has led to broad use of pan moist tropical equations, which use has raised questions on the accuracy of the resulting predictions of standing biomass. Here we develop site-specific individual tree allometric equations for estimating biomass of Gilbertiodendron dewevrei, a canopy tree that dominates extensive areas of forest in the Congo basin region. We applied both antithetic and randomized branch sampling to sample for total aboveground biomass components. We evaluated a series of regression models (linear and non-linear) for predicting total aboveground biomass asa function of commonly measured variables including diameter, basal area and total height of 43 sample trees for Ituri and Yoko forests in the Democratic Republic of Congo. We found the best model for total aboveground biomass to be a linear, 3-knot cubic spline model that used only basal area asa predictor with the lowest AIC and BIC of 602 and 610 respectively. The incorporation of height in biomass equations did not significantly improve model performance, while models with diameter alone or in combination with height perform poorly. Our results show that models using only basal area are sufficient to accurately estimate biomass for Gilbertiodendron dewevrei and carbon stock, which is an important outcome given that height measurements are usually difficult to acquire. We also demonstrate that general models used can significantly overestimate amounts of carbon for Gilbertiodendron dewevrei as compared to the site and species-specific regression model that we have developed.

Modelling the economically viable wood in the crown of European beech trees

Long-term forest development programs in Germany aim on an increase of close-to-nature broadleaf forest stands. This means that the economic importance of European beech is expected to increase. The economic potential of a tree basically consists of the stem as well as the economically viable wood volume in the crown. Due to the high morphological variability of European beech crowns, taper models are often not satisfactory for predicting the economically viable wood volume arising from crowns. Prediction models with a higher precision are recently still lacking. Aim of this study is thus the development of prediction model for the economically viable crown wood volume of European beech trees.We determined the distribution of the wood volume in the crown over the branch diameters using the multistage ‘randomized branch sampling’ method (RBS). The tree-specific wood volume distribution on the branch diameters were used to cluster all sampled trees into 3 groups. Additionally, we developed a method able to distinguish between economically viable and unviable crown branches. Basing on the RBS measurements as well as revenues and processing costs, we modeled the economically viable wood volume from the crown for each tree. To calculate the wood volume under bark, we parameterized a bark thickness function from disk samples of the trees.We showed that the European beech crowns could be clustered into 3 groups differing in their wood volume distribution. The economically viable wood volume in the crown significantly depended on this grouping parameter as well as diameter at breast height (DBH). By contrast, the total amount of wood in the crown only depended on DBH. The differing viable wood volumes in the crowns were thus explained by different wood distributions and not by differing total crown wood volume. To make the results applicable in practice forestry, the modelling results were used to develop a regression formula able to predict the economically viable wood volume in the crown depending on the DBH and the crown type. As the crown type can also be predicted via measurable tree covariates, the regression model of the viable wood volume in the crown can be used as a support tool for the management of European beech stands. Sensitivity analysis quantifies how harvest revenues and costs translate into different viable tree volume.

Randomized branch sampling to estimatefruit production in Pecan trees cv. ‘Barton’

ABSTRACT: Sampling techniques to quantify the production of fruits are still very scarce and create a gap in crop development research. This study was conducted in a rural property in the county of Cachoeira do Sul - RS to estimate the efficiency of randomized branch sampling (RBS) in quantifying the production of pecan fruit at three different ages (5,7 and 10 years). Two selection techniques were tested: the probability proportional to the diameter (PPD) and the uniform probability (UP) techniques, which were performed on nine trees, three from each age and randomly chosen. The RBS underestimated fruit production for all ages, and its main drawback was the high sampling error (125.17% - PPD and 111.04% - UP). The UP was regarded as more efficient than the PPD, though both techniques estimated similar production and similar experimental errors. In conclusion, we reported that branch sampling was inaccurate for this case study, requiring new studies to produce estimates with smaller sampling error.

Seed production, seed dispersal and seedling establishment of two afromontane tree species in and around a church forest: implications for forest restoration

Seed production, seed dispersal and seedling establishment are relevant life phases of plants. Understanding these processes and their patterns is essential to recognize vegetation dynamics and to apply it to forest restoration. For Olea europaea and Schefflera abyssinica, fecundity was estimated using randomized branch sampling. Seed dispersal and seedling establishment were monitored using spatially explicit seed traps and plots. Dispersal functions were calibrated applying inverse modeling. O. europaea produced more seeds and had longer dispersal distances compared to S. abyssinica. Correlations between observed and predicted number of recruits were statistically significant. Seedlings of the two species showed different niche requirements. The studied species were recruitment-limited due to low dispersal activity or lack of suitable microsites. Restoration relying on natural regeneration should overcome these limitations by increasing disperser visitation and reducing biotic and abiotic stresses.

Generalized and synthetic regression estimators for randomized branch sampling

In felled-tree studies, ratio and regression estimators are commonly used to convert more readily measured branch characteristics to dry crown mass estimates. In some cases, data from multiple trees are pooled to form these estimates. This research evaluates the utility of both tactics in the estimation of crown biomass following randomized branch sampling (RBS). Synthetic generalized regression (GREG) estimators are developed, and their properties examined against standard estimators. It is shown that synthetic GREG estimators with zero or low design-bias can be obtained, and that the variance of a design-unbiased class of GREG estimators can be unbiasedly estimated. Simulated sampling from 20 censused crowns of two Rocky Mountain species indicated that improvements in accuracy can be obtained through GREG estimation following RBS. Simulations also showed that synthetic GREG estimators that pool data from multiple trees can stabilize coefficients of multivariate regression models to provide improved accuracy over direct GREG estimators. However, for the univariate regression models that proved most adept for the censused crowns, direct GREG estimation provided the lowest average root mean squared error (RMSE) for RBS. Simulations also showed that model-based branch aggregation estimators have generally low RMSE but can be heavily design-biased. For the crown forms studied, use of branch auxiliary information at both the design and estimation stages through RBS and GREG estimation appears to be more efficient than using the information only at the estimation stage following simple or stratified random sampling.

Branch aggregation and crown allometry condition the precision of randomized branch sampling estimators of conifer crown mass

Characterizations of conifer crown biomass are important for assessing forest fuel loadings, bioenergy supplies, carbon stocks, and growth and yield. There is considerable variation in conifer crown mass, but to guide sampling programs, there is little quantitative information available concerning its structure or extent. This research examines several randomized branch sampling (RBS) strategies adapted for excurrent crown forms, as well as the impact of allometric relationships on their precision. The RBS strategies differ in terms of how primary branches (those attached directly to the bole) are aggregated into selection nodes and are evaluated using destructively sampled Douglas-fir (Pseudotsuga menziesii (Mirb.) Franco) and western larch (Larix occidentalis Nutt.) trees. Strong linear relationships between branch mass and basal area improve the precision of RBS relative to simple random sampling. Yet because the sample trees exhibited area-increasing branching patterns, the RBS strategies could not achieve the same precision as two-pass probability proportional-to-size methods. For the same reason, aggregation of branches improved the precision of RBS. For practical reasons, we recommend aggregating branches by 1 m intervals along the stem. This strategy brought the relative standard errors for crown mass below 20% with sample sizes of four to eight branches, with smaller sample sizes yielding this result for more slender trees. We also report results on the variability of branch area and mass, as well as results that recommend against the practice of allocating equal numbers of sample branches to crown strata of equal length.

Is randomized branch sampling suitable to assess wood volume of temperate broadleaved old-growth forests?

Old-growth forests are characterized by the presence of large and very large trees. The estimation of their wood volume and biomass is essential in order to monitor the ecological processes in these stands and their contribution to carbon cycle. However, conventional wood volume estimation techniques based on mensuration of stem diameter at breast height and tree height is most often unfeasible for large and very large trees in old-growth forests because volume models or tables are usually elaborated from trees of smaller size grown up in regularly managed forest stands. Random Branch Sampling (RBS) is often proposed as a possible estimation alternative under such conditions. Starting from the ground level some of the parts of the main trunk and of the branches are sampled and measured to estimate the overall wood volume (or other biophysical variables). The application of RBS in old-growth forests, where tree cutting is usually forbidden or very difficult, requires that the crown of the tree can physically be reached to measure the sampled parts. We argue that under such conditions it is usually preferable to fully measure all the components of the tree crown because RBS estimates are not precise if based on only one sampling path and that, on the other hand, measuring the main trunk and all the branches by tree-climbing consumes the same time as replicating several RBS paths on the same tree. To demonstrate our hypothesis we selected 16 large beech trees located in the old-growth forest of Mount Cimini in Central Italy. Using a modern tree-climbing approach the main trunk and all the branches were measured and recorded in the field. The database was used to simulate RBS paths. Real values from volume census were contrasted with estimates based on RBS. On the whole, RBS estimates based on one single path prove to be highly imprecise. Even for trees characterized by a rather regular form, at least three RBS paths should be repeated on the same tree to maintain the relative standard error under or near 15%. This paper introduces the problem and describes the experimental test. The results are discussed under the perspective of standardized application of the proposed methodology.

Equations for estimating aboveground biomass of cadaghi (Corymbia torelliana) trees in farm windbreaks

Agroforestry systems have received global attention lately as a strategy for carbon mitigation but still are one of the least studied systems. This study was conducted in south Florida to develop biomass equations for windbreak grown cadaghi (Corymbia torelliana) trees and to estimate biomass in various aged windbreaks. Trees were selected for destructive sampling based on diameter at breast height (DBH) distribution from five windbreaks. Crown biomass was estimated using randomized branch sampling (RBS) and trunk biomass by taking disks every 1.5 m along the stem. Separate nonlinear equations were developed for crown, trunk and whole tree biomass estimation using DBH and height as predictors. Results indicated that DBH alone was sufficient to predict aboveground biomass, but including height in the models gave better results. Average oven-dry whole tree biomass ranged between 6 and 935 kg for 2- and 20-year-old windbreaks. Oven-dry whole tree biomass per100 m windbreak length in the same windbreaks ranged between 166 and 26,605 kg. Because fast-growing cadaghi is efficient and can produce significantly more biomass in a short period versus other windbreak species, landowners can expect higher returns from biomass or carbon trade over a shorter period, where available, to offset the cost of land occupied by the windbreaks.

Two-stage sampling to estimate individual tree biomass

The accurate estimation of tree biomass is crucial for the efficient management of forest resources. In this study, we used a subsampling method for unbiased estimates of above-ground tree biomass. The method consists of 2 stages: the first stage consists of randomized branch sampling (RBS) and the second stage uses importance sampling (IS). RBS is used to select a path from the butt of an object branch to a terminal segment. IS is used for selecting a disk that produces unbiased estimates of the fresh biomass of tree. In this study, the subsampling method was tested on 14 black pine sample trees (Pinus nigra Arnold subsp. pallasiana (Lamb.) Holmboe) in order to estimate the trees' biomass quickly and easily. The results showed a wide range of sampling error per tree, ranging from 2.51% to 22.63%. However, the sampling error for the total biomass of the 14 trees tested was only 2.65%. The proposed 2-stage sampling method generally performed better for the bole biomass than the branch biomass. These results indicated that the proposed 2-stage sampling method is effective and might overcome many of the identified constraints in biomass estimation. It is a viable alternative to the current methods used in Turkey.

Biometric assessment of aboveground carbon pools and fluxes in three European forests by Randomized Branch Sampling

Accurate measurements of carbon pools and fluxes and of the related uncertainties are required to support the estimation of regional and continental carbon budgets. For this purpose a rigorous statistical method, known as Randomized Branching Sampling (RBS), has been applied for the direct assessment of carbon pools, fluxes (Net Primary Productivity) and plant surface areas in three forests. RBS is an unequal probability selection scheme that is design unbiased and efficient. Through its theory and design, RBS provides an unbiased estimate of uncertainties both at single tree and ecosystem scales. RBS designed samplings proved to be less time-consuming than traditional ones by lowering the number of sample branches needed to achieve the target precision levels and by getting rid of fresh weight measurements in the field. RBS estimates of C pools were compared and discussed to traditional estimates achieved by allometric functions fitted using the power equation Y=β·Xα revealing good agreement; differences between the RBS and allometric approaches were higher in older or more structured forests. Optimal scaling exponents for foliage, branch and stem components, for pool, flux and surface parameters in European beech, Scots pine and Norway spruce stands were estimated by analysis of the precision of target aggregate estimators. In all stands, the scaling exponent for the stand-scale estimates proved to be lower than the scaling exponent estimated from the allometric fitting and than analytically derived exponents. This discrepancy could lead, should the latter scaling exponents be used, to over-estimate C pools in forests.

Leaf area of beech (Fagus sylvatica L.) from different stands in eastern Austria studied by randomized branch sampling

Few tree size/leaf area correlations have been produced for hardwoods, where the extrapolation from individual branches to the whole tree is less straightforward than in conifers with more regular branching patterns. We used randomized branch sampling to estimate leaf area of European beech (Fagus sylvatica L.) trees of different stands, ages and areas in Austria. Cross-sectional areas (CSA) predicted 87–92% of leaf area variation, the best predictor being the sum of branch CSA. Leaf area was somewhat better correlated with CSA at breast height than at the base of the crown, and using sapwood instead of total CSA made little difference. While there was no effect of growth area, a stepwise regression model showed that dominant trees in pole-stage had, for unclear reasons, significantly higher leaf area/CSA relationships. A comparison with regressions produced from smaller beech trees in other parts of Europe suggests that the leaf area/basal area regression is generally valid for beech in central Europe.

Biomass equations for forest regrowth in the eastern Amazon using randomized branch sampling

Forest regrowth occupies an extensive and increasing area in the Amazon basin, but accurate assessment of the impact of regrowth on carbon and nutrient cycles has been hampered by a paucity of available allometric equations. We develop pooled and species-specific equations for total aboveground biomass for a study site in the eastern Amazon that had been abandoned for 15 years. Field work was conducted using randomized branch sampling, a rapid technique that has seen little use in tropical forests. High consistency of sample paths in randomized branch sampling, as measured by the standard error of individual paths (14%), suggests the method may provide substantial efficiencies when compared to traditional procedures. The best fitting equations in this study used the traditional form Y=a×DBHb, where Y is biomass, DBH is diameter at breast height, and a and b are both species-specific parameters. Species-specific equations of the form Y=a(BA×H), where Y is biomass, BA is tree basal area, H is tree height, and a is a species-specific parameter, fit almost as well. Comparison with previously published equations indicated errors from -33% to +29% would have occurred using off-site relationships. We also present equations for stemwood, twigs, and foliage as biomass components.

Improving RBS estimates - effects of the auxiliary variable, stratification of the crown, and deletion of segments on the precision of estimates

Randomized Branch Sampling (RBS) is a multistage sampling procedure using natural branching in order to select samples for the estimation of tree characteristics. The existing variants of the RBS method use unequal selection probabilities based on an appropriate auxiliary variable, and selection with or without replacement. In the present study, the effects of the choice of the auxiliary variable, of the deletion of segments, and of the stratification of the tree crown on the sampling error were analyzed. In the analysis, trees of three species with complete crown data were used: Norway spruce (&lt;i&gt;Picea abies&lt;/i&gt; [L.] Karst.), European mountain ash (&lt;i\&gt;Sorbus aucuparia&lt;/i&gt; L.) and Monterey pine (&lt;i&gt;Pinus radiata&lt;/i&gt; D. Don). The results clearly indicate that the choice of the auxiliary variable affects both the precision of the estimate and the distribution of the samples within the crown. The smallest variances were achieved with the diameter of the segments to the power of 2.0 (Norway spruce) up to 2.55 (European mountain ash) as an auxiliary variable. Deletion of great sized segments yielded higher precision in almost all cases. Stratification of the crown was not generally successful in terms of a reduction of sampling errors. Only in combination with deletion of stem segments, a clear improvement in the precision of the estimate could be observed, depending on species, tree, target variable, and definition and number of strata on the tree. For the trees divided into two strata, the decrease in the coefficient of variation of the estimate lies between 10% (European mountain ash) and 80% (old pine) compared with that for unstratified trees. For three strata, the decrease varied between 50% (European mountain ash) and 85% (old pine).

The tree crown distribution of hemlock woolly adelgid, Adelges tsugae (Hem., Adelgidae) from randomized branch sampling

Abstract: An exotic insect, the hemlock woolly adelgid, Adelges tsugae Annand (Hem., Adelgidae), is spreading through eastern North America, killing hemlock trees [Tsuga canadensis (L.) Carrière], and thereby impoverishing ecosystems. Adelges tsugae, like many alien invasive insects, is difficult to monitor or sample in the forest. Monitoring of A. tsugae has been hampered by lack of information about its distribution within tree crowns. In order to assist future monitoring and biocontrol of A. tsugae, this study investigates the crown distribution of A. tsugae by sampling from the entire height of mature hemlock trees in a forest with an established infestation. In addition to A. tsugae, sampling includes scale insects, which are another group of important pests on hemlock trees. This study demonstrates the utility of a randomized branch sampling (RBS) plan for monitoring both invasive insects as well as native insects that are difficult to sample. Results from the RBS show that in trees with high populations of A. tsugae, branches from the lower crown have slightly higher densities of A. tsugae than upper crown branches. In trees with low A. tsugae populations, the upper crown may have higher A. tsugae densities than the lower crown. North pointing branches also have higher densities of A. tsugae than branches pointing in other cardinal directions. Future sampling efforts for A. tsugae can take advantage of higher densities in certain portions of the crown to increase accuracy.

Comparison of randomized branch sampling with and without replacement at the first stage

Randomized Branch Sampling (RBS) is a multistage sampling procedure using natural branching in order to select samples for the estimation of tree characteristics. Usually, sampling units are selected with unequal probabilities. Conventional RBS uses sampling with replacement (SWR) for repeated sampling on the first stage, and the sample size equals 1 on all subsequent stages, thus resulting in n so-called sample paths. When the sampling fraction is large multiple selections of first stage units are likely. Sampling without replacement (SWOR) at the first stage is an alternative that is expected to increase efficiency of the procedure. In this case, the second stage sample size m must be larger than 1 to enable unbiased variance estimation. In the present study, a theoretical and an empirical comparison of the conventional RBS and the SWOR variant was accomplished. Requiring a certain precision of the RBS estimation, the conventional RBS method is mostly more time-consuming than the variant with SWOR at the first stage. Only if m = 1 is chosen as second stage sample size for the SWOR RBS, this is often more time-consuming. In those cases, conventional RBS is up to 5% cheaper. In general, the larger m is, the more expensive is conventional RBS compared with the variant with swor at the first stage. The smaller the ratio of the variance between the primary units to the total variance of the estimate, the larger is the advantage of the SWOR variant. Generally, it can be shown that the gain of efficiency by SWOR is larger in case of weak correlations between auxiliary and target variable.

Multistage point relascope and randomized branch sampling for downed coarse woody debris estimation

New sampling methods have recently been introduced that allow estimation of downed coarse woody debris using an angle gauge, or relascope. The theory behind these methods is based on sampling straight pieces of downed coarse woody debris. When pieces deviate from this ideal situation, auxillary methods must be employed. We describe a two-stage procedure where the relascope is used to select pieces of downed coarse woody debris in the first stage. If the pieces so chosen on the first stage have multiple branches and detailed estimates are required for the entire piece, then a second stage sample is advocated using the randomized branch technique. Both techniques are reviewed and an example is given examining possible surrogate variables for the second stage.