Double sampling for stratification in periodic inventories—Infinite population approach

Double sampling for stratification is a sampling design that is widely used for forest and other resource inventories in forest ecosystems. It is shown that this sampling design can be adapted to repeated inventories including estimators of net change, even for non-proportional allocation of second-phase units and periodically updated stratification. The method accounts for the transition of sampling units among strata. Moreover, it may outperform classical single phase designs if sample plots are appropriately allocated to strata with respect to predefined target variables, here: volume per ha of bigger trees of the main tree species. The latter requires a clear definition of predominant aims of the inventory and an appropriate optimization method. Access to inventory data of a state forest district from two occasions allowed for an optimization of the design based on the first occasion, which proved to be still advantageous on the following occasion. Estimators are developed under the infinite population approach, which is generally deemed more appropriate for forest inventories.     

Estimating the volume of forest growing stock using auxiliary information derived from relascope or ocular assessments

The aim of this study is to demonstrate the potential of integrating probabilistic sampling and estimation with the conventional technique referred to as forest inventory by compartments. The objective of this paper is to propose two strategies for the assessment of growing stock volume using two-phase sampling, namely: (i) relascope basal area estimation performed on first-phase sampling points followed by volume estimation performed on a sub-sample of points selected in the second phase; (ii) ocular evaluation of growing stock volume performed on first-phase sampling plots of fixed size followed by volume estimation performed on a sub-sample of plots selected in the second phase. The effectiveness of using the auxiliary information gathered in the first phase is assessed by comparing the double-expansion estimator of total volume which depends solely on the second-phase sample with the two-phase ratio estimator which instead calibrates the double-expansion estimator on the basis of first-phase information. Conservative estimators of sampling variances and confidence intervals are derived for both the estimators. As is usual in forest inventories, first-phase sampling is assumed to be performed on a systematic random grid while three different schemes are considered for drawing the second-phase sample: simple random sampling without replacement, stratified sampling and 3-P sampling. The performance of double-expansion and ratio estimators under the three schemes adopted in the second phase is empirically checked by means of a simulation study performed on a real compartment in a beech forest of Central Italy. Simulation results show that the use of auxiliary information generated in the first phase constitutes a very effective way of increasing the accuracy of volume estimation at the compartment level, with a moderate increase of fieldwork.     

A three-phase sampling procedure for continuous forest inventory with partial re-measurement and updating of terrestrial sample plots

For a current inventory using double sampling for stratification with a reduced second-phase sample size, compared with a previous inventory, we develop a three-phase sampling procedure that exploits plot data from the previous inventory or their updates based on a growth model to increase precision. The three-phase procedure combines double sampling for stratification with a two-phase regression estimator within strata. We consider sampling from an infinite population in the first phase. The combined estimator is tested in a case study using data from two consecutive inventories in four State Forest Districts in Lower Saxony, Germany. Data from a reduced number of sample plots from the second occasion are combined with (1) volumes from the first occasion or (2) growth simulations on the sample plots from the first occasion. The data from the previous inventory or their updates serve as the auxiliary variable for the regression estimator of the strata means of the target variable. This case study indicates a remarkable increase in precision and thereby an enormous cost-saving potential for reduced intermediate inventories in a periodic inventory design with both types of auxiliary variables.     

栽植密度对黄檗苗期生物量的影响

以黄檗3 a生幼树为材料,对不同栽植密度的生物量进行研究,结果表明:栽植当年和翌年秋季的成活率与保存率分别为92%和91%。不同株距树高、地径生长量均达到极显著差异(P0.01),树高、地径生长量从大到小顺序依次为株距0.5 m1 m0.3 m1.5 m;而不同行距对树高、地径生长量均无影响。采用一元生物量模型计算生物量,总生物量最大的种植密度为33 300株·hm~(-2)(株行距0.3 m×1.0 m),可产生干物质3 930.06 kg·hm~(-2);最小的为3 300株·hm~(-2)(株行距1.5 m×2.0 m),干物质仅为344.08 kg·hm~(-2)。     

Combining double sampling for stratification and cluster sampling to a three-level sampling design for continuous forest inventories

We extend the well-known double sampling for stratification sampling scheme by cluster subsampling to a three-level design and present corresponding estimators based on the infinite population approach in the first phase. After stratification of the sample points (phase I), a second-phase sample is drawn independently among the first-phase points within each stratum. On level III, clusters are formed of those phase II points and a sample of clusters is finally drawn without replacement. We used the forest planning units compartment and subdistrict as clusters and moreover formed clusters with a heuristic for the vehicle routing problem. The precision of the new estimator was compared to that achieved with classical double sampling for stratification in a case study. The results indicate that the expected increase in sampling errors caused by clustering cannot be compensated by the reduced inventory costs under the conditions given in the case study.     

Laser scanning of forest resources: the nordic experience

This article reviews the research and application of airborne laser scanning for forest inventory in Finland, Norway and Sweden. The first experiments with scanning lasers for forest inventory were conducted in 1991 using the FLASH system, a full-waveform experimental laser developed by the Swedish Defence Research Institute. In Finland at the same time, the HUTSCAT profiling radar provided experiences that inspired the following laser scanning research. Since 1995, data from commercially operated time-of-flight scanning lasers (e.g. TopEye, Optech ALTM and TopoSys) have been used. Especially in Norway, the main objective has been to develop methods that are directly suited for practical forest inventory at the stand level. Mean tree height, stand volume and basal area have been the most important forest mensurational parameters of interest. Laser data have been related to field training plot measurements using regression techniques, and these relationships have been used to predict corresponding properties in all forest stands in an area. Experiences from Finland, Norway and Sweden show that retrieval of stem volume and mean tree height on a stand level from laser scanner data performs as well as, or better than, photogrammetric methods, and better than other remote sensing methods. Laser scanning is, therefore, now beginning to be used operationally in large-area forest inventories. In Finland and Sweden, research has also been done into the identification of single trees and estimation of single-tree properties, such as tree position, tree height, crown width, stem diameter and tree species. In coniferous stands, up to 90% of the trees represented by stem volume have been correctly identified from canopy height models, and the tree height has been estimated with a root mean square error of around 0.6 m. It is significantly more difficult to identify suppressed trees than dominant trees. Spruce and pine have been discriminated on a single-tree level with 95% accuracy. The application of densely sampled laser scanner data to change detection, such as growth and cutting, has also been demonstrated.     

Inventory Procedures for Smallholder and Community Woodlots in the Philippines: Methods,Initial Findings and Insights

This paper details the processes and challenges involved in collecting inventory data from smallholder and community woodlots on Leyte Island, Philippines. Over the period from 2005 through to 2012, 253 woodlots at 170 sites were sampled as part of a large multidisciplinary project, resulting in a substantial timber inventory database. The inventory was undertaken to provide information for three separate but interrelated studies, namely (1) tree growth, performance and timber availability from private smallholder woodlots on Leyte Island; (2) tree growth and performance of mixed-species plantings of native species; and (3) the assessment of reforestation outcomes from various forms of reforestation. A common procedure for establishing plots within each site was developed and applied in each study, although the basis of site selection varied. A two-stage probability proportion to size sampling framework was developed to select smallholder woodlots for inclusion in the inventory. In contrast, community-based forestry woodlots were selected using stratified random sampling. Challenges encountered in undertaking the inventory were mostly associated with the need to consult widely before the commencement of the inventory and problems in identifying woodlots for inclusion. Most smallholder woodlots were only capable of producing merchantable volumes of less than 44 % of the site potential due to a lack of appropriate silviculture. There was a clear bimodal distribution of proportion that the woodlots comprised of the total smallholding area. This bimodality reflects two major motivations for smallholders to establish woodlots, namely timber production and to secure land tenure.     

A flexible stem taper and volume prediction method based on mixed-effects B-spline regression

Modelling stem taper and volume is crucial in many forest management and planning systems. Taper models are used for diameter prediction at any location along the stem of a sample tree. Furthermore, taper models are flexible means to provide information on the stem volume and assortment structure of a forest stand or other management units. Usually, taper functions are mean functions of multiple linear or nonlinear regression models with diameter at breast height and tree height as predictor variables. In large-scale inventories, an upper diameter is often considered as an additional predictor variable to improve the reliability of taper and volume predictions. Most studies on stem taper focus on accurately modelling the mean function; the error structure of the regression model is neglected or treated as secondary. We present a semi-parametric linear mixed model where the population mean diameter at an arbitrary stem location is a smooth function of relative height. Observed tree-individual diameter deviations from the population mean are assumed to be realizations of a smooth Gaussian process with the covariance depending on the sampled diameter locations. In addition to the smooth random deviation from the population average, we consider independent zero mean residual errors in order to describe the deviations of the observed diameter measurements from the tree-individual smooth stem taper. The smooth model components are approximated by cubic spline functions with a B-spline basis and a small number of knots. The B-spline coefficients of the population mean function are treated as fixed effects, whereas coefficients of the smooth tree-individual deviation are modelled as random effects with zero mean and a symmetric positive definite covariance matrix. The taper of a tree is predicted using an arbitrary number of diameter and corresponding height measurements at arbitrary positions along the stem to calibrate the tree-individual random deviation from the population mean estimated by the fixed effects. This allows a flexible application of the method in practice. Volume predictions are calculated as the integral over cross-sectional areas estimated from the calibrated taper curve. Approximate estimators for the mean squared errors of volume estimates are provided. If the tree height is estimated or measured with error, we use the “law of total expectation and variance” to derive approximate diameter and volume predictions with associated confidence and prediction intervals. All methods presented in this study are implemented in the R-package TapeR.     

全国营造林综合核查抽样精度计算方法探讨

对目前全国营造林综合核查抽样方法的特点进行了分析,提出可用一阶单元大小不等的两阶抽样或比估计方法计算各类核实率和合格率的抽样精度,并用实例对具体计算方法进行了说明,为今后综合核查结果的精度计算提供了理论依据。     

Comparison of estimators and feature selection procedures in forest inventory based on airborne laser scanning and digital aerial imagery

Digital maps of forest resources are a crucial factor in successful forestry applications. Since manual measurement of this data on large areas is infeasible, maps must be constructed using a sample field data set and a prediction model constructed from remote sensing materials, of which airborne laser scanning (ALS) data and aerial images are currently widely used in management planning inventories. ALS data is suitable for the prediction of variables related to the size and volume of trees, whereas optical imagery helps in improving distinction between tree species. We studied the prediction of forest attributes using field data from National Forest Inventory complemented with ad hoc field plots in combination with ALS and aerial imagery data in Aland province, Finland. We applied feature selection with genetic algorithm and greedy forward selection and compared multiple linear and nonlinear estimators. Maximally around 40 features from a total of 154 were required to achieve the best prediction performances. Tree height was predicted with normalized root mean squared error value of 0.1 and tree volume with a value around 0.25. Predicting the volumes of spruce and broadleaved trees was the most challenging due to small proportions of these tree species in the study area.     

Quality improvement of loblolly pine (Pinus taeda) plantation inventory GIS using Shuttle Radar Topography Mission (STRM) and the National Elevation Dataset (NED)

An essential element of timber inventory management involves organizing cruises to generate/update databases. Timely updates are crucial to maintaining any inventory. The availability of Shuttle Radar Topography Mission (STRM) and National Elevation Dataset (NED) have provided additional reference datasets to timber managers to independently conduct quality improvement of their inventories. The difference between SRTM and NED is known to be an effective measure of tree heights. With respect to 2612 loblolly pine (Pinus taeda) plantation stands (>15 ha) in western Louisiana and eastern Texas, the estimated tree height was correlated using plantation year in inventory GIS and the coefficient of determination R² was 0.694. Outliers from the trend line were identified and evaluated for potential stand's attribute error. Using historical satellite images, three stands were confirmed to have errors in plantation year. A solid procedure was developed through this experiment, which is applicable to large industrialized timberlands. This study demonstrates that SRTM and NED can present an effective and efficient solution for quality improvement of timber inventory GIS.     

Root length and nitrate under Sesbania sesban: Vertical and horizontal distribution and variability

Measurements of root and nutrient distributions in agroforestry systems have often been obtained from unreplicated plots. We, therefore, measured the vertical and horizontal distribution of root length and soil nitrate in replicated plots of sesbania [Sesbania sesban (L.) Merr.] to assess plot-to-plot variation and identify appropriate sampling schemes. Sampling was on profile walls exposed from pits at two on-farm sites (Ochinga and Muange) in Kenya. At Ochinga, soil was sampled at 27 0.15-m depth intervals and eight 0.15-m-wide locations perpendicular to 2.25-m-wide rows of 19-month-old sesbania. At Muange, sampling was 18 months after establishment of sesbania from seedlings with a 1 m by 1 m spacing. Soil was sampled at 17 0.15-m depth intervals and nine 0.15-m-wide sampling locations – one exactly below the tree and four each on opposite sides of the tree. Root length density generally decreased with distance from sesbania and with soil depth. Soil nitrate, however, followed different trends in the four replications at Ochinga and the three replications at Muange. At Ochinga, nitrate above 2.5-m depth clearly increased with distance from the tree in two replications but followed no distinct trend in another replication. At Muange, nitrate above 1.2-m depth decreased with distance from the tree in one replication, increased with distance from the tree in another replication and followed no clear trend in another replication. The suitability of various sampling schemes for measuring root length and nitrate was accessed from percent bias between measured values at sampling locations in the scheme and actual values for an entire transect of sampling locations. Bias associated with selection of sampling locations tended to be higher within the 2.25-m-wide sesbania rows than the 1 m by 1 m sesbania spacing. Soil sampling in systems with rows of young trees should be at several locations along a transect perpendicular to tree rows in order to minimize bias. This revised version was published online in June 2006 with corrections to the Cover Date. This revised version was published online in June 2006 with corrections to the Cover Date.     

Area-level analysis of forest inventory variables

Small-area estimation is a subject area of growing importance in forest inventories. Modelling the link between a study variable Y and auxiliary variables X—in pursuit of an improved accuracy in estimators—is typically done at the level of a sampling unit. However, for various reasons, it may only be possible to formulate a linking model at the level of an area of interest (AOI). Area-level models and their potential have rarely been explored in forestry. This study demonstrates, with data (Y = stem volume per ha) from four actual inventories aided by aerial laser scanner data (3 cases) or photogrammetric point clouds (1 case), application of three distinct models representing the currency of area-level modelling. The studied AOIs varied in size from forest management units to forest districts, and municipalities. The variance explained by X declined sharply with the average size of an AOI. In comparison with a direct estimate mean of Y in an AOI, all three models achieved practically important reduction in the relative root-mean-squared error of an AOI mean. In terms of the reduction in mean-squared errors, a model with a spatial location effect was overall most attractive. We recommend the pursuit of a spatial model component in area-level modelling as promising within the context of a forest inventory.     

Uncertainties in above ground tree biomass estimation

Models of above-ground tree biomass have been widely used to estimate forest biomass using national forest inventory data.However,many sources of uncertainty affect above-ground biomass estimation and are challenging to assess.In this study,the uncertainties associated with the measurement error in independent variables(diameter at breast height,tree height),residual variability,variances of the parameter estimates,and the sampling variability of national inventory data are estimated for five above-ground biomass models.The results show sampling variability is the most significant source of uncertainty.The measurement error and residual variability have negligible effects on forests above-ground biomass estimations.Thus,a reduction in the uncertainty of the sampling variability has the greatest potential to decrease the overall uncertainty.The power model containing only the diameter at breast height has the smallest uncertainty.The findings of this study provide suggestions to achieve a trade-off between accuracy and cost for above-ground biomass estimation using field work.     

Stem mapping and estimating standing volume from stereoscopic hemispherical images

Sustainable forest management requires knowledge of forest structure and dynamics as well as an estimation of growing stock. The forest inventory provides the data for estimating stand variables. The measurement device MU2005-01738, patented by the Center for Forest Research (INIA-CIFOR), provides stereoscopic hemispherical images which can allow the 3D restoration of the stand around the sampling point. The aim of this study is to develop a methodology for forest stand mapping as well as tree diameter and height measurement along with volume estimation from the stereoscopic hemispherical images provided by the MU2005-01738. Using the MU2005-01738, Eucalyptus globulus Labill. plantations were sampled. Distance, diameter, height and volume were derived from the stereoscopic hemispherical images of 30 trees located at distances ranging from 0 to 15 m from the device. These variables were then compared with field measurements and the estimation errors analyzed. The (root-mean-squared error) RMSE was 0.23 m (8.95 %) for tree position and 1.51 cm (10.43 %) for diameter at breast height measurement at distances of less than 8 m. In the case of stem height and individual tree volume estimation, the RMSE was 2.59 m (23.05 %) and 0.025 m³ (17.94 %), respectively. The analysis of measurement errors indicated that the measurement precision decreases beyond 8 m from the device as well as for directions close to the baseline (the line between the optical centers of the two images), whereas the precision was highest for directions near to the line which is perpendicular to the base line. Future research should focus on improving measurement accuracy and possible applications in the field of forestry of the techniques presented in this study.     

Picea abies sapwood width: Variations within and between trees

Abstract

This study focused on the amount of sapwood and its variation by means of computed tomographic (CT) imaging. Twenty-four trees were selected from four Norway spruce [Picea abies (L.) Karst.] stands in north-eastern France, varying in age, density and fertility. In each stand, sampled trees represented the dominant, co-dominant and suppressed strata. The heartwood/sapwood boundary was detected from the CT images, and the heartwood and sapwood amount and their variations were then evaluated. At the within-tree level sapwood width was relatively constant along the tree stem above the butt swelling and below the living crown. The between-tree sapwood width variations were partially explained by the total cross-sectional area of living branches. This result opens up the possibility of investigating within-tree allometric relationships. Sapwood width was found to be highly correlated with tree slendemess (tree height/breast height diameter) and with the relative height of the crown. This suggests that sapwood width could be readily predicted from conventional forest inventory measurements. The number of sapwood rings within the stem was largely dependent on cambial age, and could be determined dynamically using the concept of mean lifetime of sapwood rings.     

Using pre-classification to improve the accuracy of species-specific forest attribute estimates from airborne laser scanner data and aerial images

The aim of this study was to examine whether pre-classification (stratification) of training data according to main tree species and stand development stage could improve the accuracy of species-specific forest attribute estimates compared to estimates without stratification using k-nearest neighbors (k-NN) imputations. The study included training data of 509 training plots and 80 validation plots from a conifer forest area in southeastern Norway. The results showed that stratification carried out by interpretation of aerial images did not improve the accuracy of the species-specific estimates due to stratification errors. The training data can of course be correctly stratified using field observations, but in the application phase the stratification entirely relies on auxiliary information with complete coverage over the entire area of interest which cannot be corrected. We therefore tried to improve the stratification using canopy height information from airborne laser scanning to discriminate between young and mature stands. The results showed that this approach slightly improved the accuracy of the k-NN predictions, especially for the main tree species (2.6% for spruce volume). Furthermore, if metrics from aerial images were used to discriminate between pine and spruce dominance in the mature plots, the accuracy of volume of pine was improved by 73.2% in pine-dominated stands while for spruce an adverse effect of 12.6% was observed.     

Microbial community diversity in a 21-year-old temperate alley cropping system

Soil physical and chemical properties in the crop alleys and tree rows in alley cropping systems vary greatly due to differences in litter quality and microclimate under trees compared to the alleys. Variations in soil properties influence microbial diversity and function, and thus, in alley cropping systems, bacterial diversity could be different between soils in tree rows and crop alleys. The objective of this study was to compare and contrast soil bacterial diversity in the crop alleys and tree rows in a 21-year-old alley cropping system in Northeast Missouri, USA. Soil samples were taken in three parallel transects to a depth of 10 cm in the tree row and at the middle of the alley in a silver maple (Acer saccharinum) alley cropping system with a companion maize (Zea mays)—soybean (Glycine max) rotation. Soil bulk density, C and N concentrations were similar between the different transects while minor differences were observed between crop alleys and tree rows. No significant difference in bacterial diversity was observed between the tree rows and alley soil based the denaturing gradient gel electrophoresis profiles, band richness (19.6 and 22.8 for tree row and alley, respectively) and Shannon–Weiner diversity (2.958 and 3.099 for tree row and alley, respectively). Identification of bacterial genera revealed dominance of gram +ve as well as gram ?ve bacteria in both soil types. Ordination plot revealed no clustering effect based on location (transect) or on the cropping system in the different samples. Bacterial diversity in crop alleys most likely was influenced not only by the maize-soybean rotation, but also by the tree rows contributing both above and belowground litter for the past 21 years.     

Statistical analysis of ratio estimators and their estimators of variances when the auxiliary variate is measured with error

Forest inventory relies heavily on sampling strategies. Ratio estimators use information of an auxiliary variable (x) to improve the estimation of a parameter of a target variable (y). We evaluated the effect of measurement error (ME) in the auxiliary variate on the statistical performance of three ratio estimators of the target parameter total τ _y . The analyzed estimators are: the ratio-of-means, mean-of-ratios, and an unbiased ratio estimator. Monte Carlo simulations were conducted over a population of more than 14,000 loblolly pine (Pinus taeda L.) trees, using tree volume (v) and diameter at breast height (d) as the target and auxiliary variables, respectively. In each simulation three different sample sizes were randomly selected. Based on the simulations, the effect of different types (systematic and random) and levels (low to high) of MEs in x on the bias, variance, and mean square error of three ratio estimators was assessed. We also assessed the estimators of the variance of the ratio estimators. The ratio-of-means estimator had the smallest root mean square error. The mean-of-ratios estimator was found quite biased (20%). When the MEs are random, neither the accuracy (i.e. bias) of any of the ratio estimators is greatly affected by type and level of ME nor its precision (i.e. variance). Positive systematic MEs decrease the bias but increase the variance of all the ratio estimators. Only the variance estimator of the ratio-of-means estimator is biased, being especially large for the smallest sample size, and larger for negative MEs, mainly if they are systematic.     

Estimators of Tree Species Richness: An Assessment for Central and Eastern Canada

Abstract

A total of 11 sample-based estimators of tree species richness (S) are evaluated in terms of accuracy and precision in a Monte Carlo simulated simple random sampling from 39,779 forest inventory plots with 7.8 million trees belonging to 85 species. The plots represent a 108 million hectare forested region in central and eastern Canada. Sample sizes varied from 50 to 800. A weighted index combining estimates of accuracy and precision identified Chao's first estimator (CHAO1) as overall best with an estimator based on the assumption of a gamma mixed Poisson distribution of species occurrence as a close runner-up. The observed sample species richness was almost always the most negatively biased estimate. A sample size of 400-700 conventional fixed area forest inventory plots are needed to produce results with bias <20%.