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.     

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.     

林地面积空间抽样方法研究

论文采用空间简单随机抽样、空间分层抽样和三明治空间抽样模型,利用两种布样方式,随机和分层布样。通过对总体样本量和空间相关性的估算,进行样本分配和空间分层,结果表明：三明治空间抽样模型的抽样精度最高,其次是空间分层抽样、简单随机抽样;布样时采用分层抽样方式,将地理区域上分布的对象依照相似的属性值划分到不同的区域里,可以明显提高抽样调查效率及估计精度。     

Estimating forest area at the year 1990 by two-phase sampling on historical remotely sensed imagery in Italy

Forest area in the year 1990 is a figure of great interest under the Kyoto Protocol. This note is devoted to a scientific exercise for the probabilistic ex post assessment of such a figure in Italy. Estimation was performed by two-phase point sampling, which made use of historical remotely sensed imagery. In the first phase, a sample of 12 089 points was selected according to an unaligned systematic sampling and the selected points were classified in land-use categories by Landsat 5 TM imagery. In the second phase, a sample of 3000 points was selected by stratified sampling in which the strata were determined by the satellite classification and the selected points were classified by aerial photos, assumed as ground truth. A two-phase estimate of land-use coverage partitioning the Italian territory was obtained together with a conservative estimate of the sampling variance-covariance. The procedure has proved to be of relatively easy implementation and objective repeatability.     

Adaptive cluster sampling for estimation of deforestation rates

National estimates of deforestation rates may be based on a survey. Precise estimation requires an efficient design. When deforestation rates are low (<1%) large sample sizes are required with traditional sampling designs to meet a precision target. This study explores the efficiency of adaptive cluster sampling (ACS) for this estimation problem. The efficiency is assessed by simulated ACS sampling from 18,200 × 200 km populations with 78–10,742 deforestation polygons (DFP) of different shape and size and average 10-year deforestation rates between 0.2% and 1.0%. Each population is composed of four million square 1 ha population units (PU) in a regular grid. Relative root mean square errors (RMSE) of ACS were, depending on sample size, 30–50% lower than comparable errors with simple random sampling (SRS) designs. ACS achieves this advantage by adaptively adding PUs to an initial SRS sample of size n. Realized ACS sample sizes were, on average, twice the nominal size (n). Three measures of ACS efficiency indicated that the costs of adaptively increasing the sample size are critical for the effectiveness of ACS. Population effects were manifest in all estimators. Estimates of the abundance, size, and shape of DFPs will allow a prediction of these effects. Populations dominated by a few large DFPs were clearly unsuited for ACS. The performance of ACS relative to that of SRS was similar across plot sizes of 1, 10, and 40 ha. The general conclusion of this study is that the lower RMSE of ACS remains attractive when the average cost of adaptively adding a PU to the initial sample is low relative to the average cost of sampling a PU at random.     

The assessment of tree row attributes by stratified two-stage sampling

Tree row inventories are of increasing interest because tree rows mitigate wind erosion and desertification, protect agricultural crops, enhance rural landscape quality, act as bio-corridors, carbon sinks, and a source for bio-energy. The main objective of tree row inventories is to estimate population parameters such as total tree numbers, total tree numbers by species, the mean stem diameter at breast height, the mean tree height and total wood volume. The estimation of these quantities may be straightforwardly carried out whenever aerial images are available in such a way that tree rows can be counted: in these cases, a two-stage cluster sampling may be performed in which the primary units sampled in the first stage are the tree rows in the study area while the secondary units sampled in the second stage are the trees within the selected rows. This paper proposes two sets of two-stage estimators for the interest parameters, based on the Horvitz–Thompson and ratio criteria, together with the corresponding estimators for their sampling variances. The use of stratification is also considered. The proposed procedure was applied to perform a tree row inventory in the Pontina plain (Central Italy): in this case, the tree rows were enumerated by means of ortho-corrected airborne images and stratification was carried out on the basis of the prevailing species and age classes. The inventory results are interesting from a forestry perspective as well as for checking the effectiveness of the procedure.     

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 national forest resources assessment for Costa Rica based on low intensity sampling

A goal of a National Forest Inventory (NFI) is the provision of information which is relevant and required for national level decision making and monitoring in forestry, but also for related sectors.

This paper presents and discusses a pilot study from Costa Rica where in 2000/2001 a low intensity sampling approach was used to generate national level forestry information. On a 15 km × 15 km grid air photo plots were interpreted for forest and land cover type. Readily available 1997 aerial photographs were used that were, however, only available for about 70% of the country: of the 228 grid points for the whole country only 159 could be aerial photo interpreted. Out of the 15 km × 15 km base grid of sample points, a 2 × 3 subset was selected for field assessment, resulting in a sample of 40 cluster plots, each comprising of four elongated rectangular sub-plots of 150 m × 20 m located on the perimeter of a square of 500 m side length.

Two novel components were integrated into the inventory: (1) the field plots were established on all lands, so that the tree resource was not only tallied inside forests but also on all other tree-bearing lands outside forests. (2) In addition to the biophysical information gathered on the traditional field plots, interviews were carried out with forest owners on the site of the field plots, in order to obtain data on the use of the forest resource.

Field work was carried out by 6 field crews and took altogether about 3 months. Results were generated from the field samples for the entire country. Aerial photo based area estimates were compared to the corresponding estimations from field sampling for the same area. According to the field sampling the forest cover for Costa Rica in 2001 is estimated to be 48.4% (simple standard error percent 9.3%). An estimated 8.2% of the total volume (dbh > 30 cm, all species) is outside forest.

This inventory took place with support from Food and Agriculture Organization (FAO) in the framework of FAO–Forest Resources Assessment's (FRA) Program Support to National Forest Assessments; it was carried out jointly by Sistema Nacional de Áreas de Conservación (SINAC), the Costa Rican authority responsible for forestry issues, and Centro Agronómico de Investigación y Enseñanza (CATIE), an international agricultural research center. Experiences of the study were subsequently used to implement similar inventories in three more countries (Guatemala, Cameroon, The Philippines).     

一种新的估计林分算术平均高抽样方法的验证与应用

本文用计算机模拟取样,探讨Yojiro Ueno提出的一种新的抽样方法应用于长白山落叶松人工林和柞树林的试验样地的有效性。应用不同次数的重复试验结果表明:1)随着样本容量的增加,不同重复的差异逐渐减小,当增加到一定程度,重复一次随机抽样即可有较好的稳定性和较低的抽样误差。2)平均相对误差[AKP-]和不同重复间变异系数CV曲线都随取样数目的增加而呈下降趋势,且上升波动程度也随之减小,渐平稳。当样本量大小达到某值之前 ,[AKP-]和CV相似文献   

Poisson sampling and some alternatives in timber sales sampling

Sampling schemes are studied for timber sales where every tree in the population has to be visited. A strong linear relationship is known to hold between the variable of interest, volume in m³ (y), and tree basal area times height (x) (in cm²m). Purposive sampling of trees over the X-range and stratified sampling with regression estimators are recommended as worthwhile alternatives to Poisson sampling for efficiency and for yielding consistently good results where the model between the dependent and independent variables is known to be reasonable. Two other designs, selecting the n trees with largest X-values and the trees with 20% smallest and 80% largest X-values, are shown to be high-risk procedures.     

Two new density estimators for distance sampling

Two new density estimators for k-tree distance sampling are proposed and their performance is assessed in simulated distance sampling from 22 stem maps representing a wide range of natural to semi-natural forest tree stands with random to irregular (clustered) spatial distribution of trees. The new estimators are model-based. The first (Orbit) computes density as the inverse of the average of the areas associated with each of the k-trees nearest to a sample location. The area of the k-th tree is obtained as a prediction from a linear regression model while the area of the first is obtained via a Poisson probability integral. The second (GamPoi) is based on the expected distribution of distance to the k nearest tree in a forest where the local distribution of trees is random but the stem density varies from sample location to sample location as a gamma distribution. In a comprehensive assessment with 17 promising reference estimators, a subset composed of Morisita’s, Persson’s, Byth’s, Kleinn’s, Orbit, and GamPoi was significantly better, in terms of relative root mean square error (RRMSE), than average. GamPoi emerged as the better estimator for sample sizes larger than or equal to 30. For smaller sample sizes, both Kleinn’s and Morisita’s appear attractive.     

Transect relascope sampling for assessing coarse woody debris: The case of a π/2 relascope angle

In transect relascope sampling, a wide‐angle relascope is used along survey lines for selecting a sample of objects that extend linearly in the plane, e.g. downed logs. The method is closely related to line intersect (intercept) sampling. In this article, a special case of the transect relascope technique is studied. Using a π/2 radian relascope angle, the method becomes invariant to the orientation of the line objects in the population. The reason is that the area of inclusion around objects, through which a survey line should pass for an object to be included, turns out to be circular. In analytical studies and Monte Carlo simulations, the cost‐efficiency of transect relascope and line intersect sampling is evaluated. It is found that transect relascope sampling is a competitive alternative to line intersect sampling in inventories of the total volume of coarse woody debris (in the form of downed logs) in forest compartments.     

Effect of cluster configuration and auxiliary variables on the efficiency of local pivotal method for national forest inventory

ABSTRACT

Planning a forest inventory comprises making decisions related to the sampling strategy: cluster configuration, sample size and sample allocation within the survey area. Cluster configuration includes deciding on the number of sample plots within the cluster and distances between them. Available resources set the limit for field work in terms of man-days. If the time consumption for measurements is known, the sample size can be determined under the constraint. In this study, we simulated the second phase of inventory sampling with fixed time resources by replicating sample selection with a spatially balanced sampling utilizing local pivotal method (LPM) for different cluster configurations to find the most efficient. As a result, the temporary cluster configuration was changed from 9 to 5-sample plot configuration in a pilot inventory. Further, the sample selection was performed with LPM having total growing stock volume and broadleaf volume proportion as auxiliary information. The pilot results were aligned with the time series in respect to forest area and total growing stock volume, but in tree species groups deviations were observed in growing stock volume. A more comprehensive optimization should include the travelling routes, the plot-to-plot distances and the plot design. In any case, the result is region specific.     

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.     

Effects of auxiliary data source and inventory unit size on the efficiency of sample-based coarse woody debris inventory

The efficiency of a sample-based inventory can be greatly improved if lower cost information on the study area is utilized. It has been observed that the use of airborne laser scanning (ALS) data in the design phase may improve the efficiency of dead wood (coarse woody debris, CWD) volume inventory notably, i.e. a smaller standard error of the mean is observed with the same inventory costs. In the present case, several auxiliary data sources were employed in the design phase by using ‘probability proportional to size’ sampling to select the sample units to be inventoried in the field. It was observed that a combination of ALS data with either aerial photographs or stand-register data can improve the sampling efficiency even more than the use of ALS as a single data source. Since these additional data sources are often gathered for the inventory of living trees, their use does not incur extra expenses for CWD assessment. Thus, the use of these data separately or together with ALS data can greatly improve the cost-efficiency of a CWD volume inventory. It was also observed that the size of the sample units has a slight effect on the sampling efficiency. Even though the improvement in the sampling efficiency was usually greater with larger sample unit sizes, the CWD volume inventory was most efficient with moderate grid cell sizes.     

Smart increment borer: a portable device for automated sampling of tree-ring cores

Manual sampling of large number of cores is an arduous task, especially when core diameter is large. We developed an automated tree-ring sampling device, the “smart increment borer”, to increase the sample throughput and minimize the need for muscular exertion. The lightweight, portable device employs a battery-powered electric wrench and the complete system to drive the boring operation weighs less than 10 kg. It is capable of taking both 5- and 12-mm diameter cores of more than 80-cm length. Compared to equipment used in previously published articles, this device enables more rapid sampling and demonstrates a superior torque output/total weight ratio. The device is also capable of facilitating the starting operation of a 12-mm increment borer. It facilitates a variety of effective sampling solutions for dendrochronology/climatology and wood anatomy/quality research.     

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.     

Design-unbiased point-to-object sampling on lines,with applications to areal sampling

Sampling methods that depend on the distance between a sample point and a fixed number of objects, such as trees or downed logs, have often been proposed in the forestry and ecology literature. However, such methods have been biased when objects are not distributed with complete spatial randomness, have required difficult field procedures (such as measuring the position of out-of-sample objects), or both. Here a new approach based on measurement of the distance to objects along sample lines is proposed. The approach does not require measuring the position of out-of-sample objects, and its design-unbiased estimators require only simple arithmetic. Furthermore, because many useful sampling procedures can be related back to sampling on a line, the new method leads quickly to sampling procedures applicable when objects are distributed in a two-dimensional region. These include, among others, fixed-count approaches to line intersect sampling, a new approach to variable-area transect sampling, and a density-adapted variable sector sampling method.     

Point transect sampling of deadwood: a comparison with well-established sampling techniques for the estimation of volume and carbon storage in managed forests

In managed forests, the occurrence of deadwood (DW) can be regarded as a stochastically rare event with strong clumping and high local variability (Meyer in Forstwissenschaftliches Centralblatt 118:167–180, 1999). Traditional sampling techniques, such as Fixed Area Sampling, Angle Count Sampling and Line Intersect Sampling, do not regard this fact and may be inefficient for surveys of DW, because of limited search areas. A sampling technique that should remedy this shortcoming is Point Transect Sampling (Buckland et?al. in Introduction to distance sampling: estimating abundance of biological populations. Oxford University Press, Oxford, 2001; Advanced distance sampling: estimating abundance of biological populations. Oxford University Press, Oxford, 2004), where as a matter of principle, all objects that are sighted from a fixed location are counted. We compare Point Transect Sampling with the other well-established sampling approaches for the estimation of volume, necromass and carbon storage in terms of precision and sampling effort. It is shown that Point Transect Sampling is the superior method for sampling standing DW regarding efficiency, whereas for sampling downed DW, it is clearly outperformed by Line Intersect Sampling.     

Spatial variability and optimal sampling strategy of soil respiration

Soil respiration is the second largest flux of carbon between terrestrial ecosystems and the atmosphere and is affecting climate sensitivity and vulnerability of the terrestrial carbon stock. Monitoring soil carbon dioxide efflux is a complex task, due to the high spatial and temporal variability of the fluxes. For this reason, more than 30 sampling points are required to attain reliable estimates of ecosystem soil respiration. However, the number of sampled points is often limited by labour, time and budget constraints. Stratified sampling is an alternative to random sampling as a method to reduce the number of sampling points when an effective proxy variable is available for the definition of the strata.