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.     

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.     

Small area estimations of proportion of forest and timber volume combining Lidar data and stereo aerial images with terrestrial data

Abstract

Methods for small area estimations were compared for estimating the proportion of forest and growing stock volume of temperate mixed forests within a district of a member state (canton) in Switzerland. The estimators combine terrestrial data with remotely sensed auxiliary data. By using different model types, different sources of auxiliary data and different methods of processing the auxiliary data, the increase in estimation precision was tested. Using the canopy height derived from remote sensing data, the growing stock volume and the proportion of forest were estimated. The regression models used for the small area estimation provided a coefficient of determination of up to 68% for the timber volume. The proportion of plots correctly classified into forest and non-forest plots ranged between 0.9 and 0.98. Models calibrated over forest area only resulted in a maximal coefficient of determination of 37%. Even though these coefficients indicate a moderate model quality, the use of remote sensing data clearly improved the estimation precision of both the proportion of forest and the growing stock volume. Generally, Lidar data led to slightly higher estimates compared to data from aerial photography. It was possible to reduce the variance of the estimated proportion of forest to nearly one tenth compared with the variance based on the terrestrial measurements alone. Similarly, the variance of the growing stock volume could be reduced to one fourth as compared with the variance based solely on the terrestrial measurements.     

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.     

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.     

Small area estimation of forest attributes in the Norwegian National Forest Inventory

The Norwegian National Forest Inventory (NNFI) provides estimates of forest parameters on national and regional scales by means of a systematic network of permanent sample plots. One of the biggest challenges for the NNFI is the interest in forest attribute information for small sub-populations such as municipalities or protected areas. Frequently, too few sampled observations are available for such small areas to allow estimates with acceptable precision. However, if an auxiliary variable exists that is correlated with the variable of interest, small area estimation (SAE) techniques may provide means to improve the precision of estimates. The study aimed at estimating the mean above-ground forest biomass for small areas with high precision and accuracy, using SAE techniques. For this purpose, the simple random sampling (SRS) estimator, the generalized regression (GREG) estimator, and the unit-level empirical best linear unbiased prediction (EBLUP) estimator were compared. Mean canopy height obtained from a photogrammetric canopy height model (CHM) was the auxiliary variable available for every population element. The small areas were 14 municipalities within a 2,184 km² study area for which an estimate of the mean forest biomass was sought. The municipalities were between 31 and 527 km² and contained 1–35 NNFI sample plots located within forest. The mean canopy height obtained from the CHM was found to have a strong linear correlation with forest biomass. Both the SRS estimator and the GREG estimator result in unstable estimates if they are based on too few observations. Although this is not the case for the EBLUP estimator, the estimators were only compared for municipalities with more than five sample plots. The SRS resulted in the highest standard errors in all municipalities. Whereas the GREG and EBLUP standard errors were similar for small areas with many sample plots, the EBLUP standard error was usually smaller than the GREG standard error. The difference between the EBLUP and GREG standard error increased with a decreasing number of sample plots within the small area. The EBLUP estimates of mean forest biomass within the municipalities ranged between 95.01 and 153.76 Mg ha^?1, with standard errors between 8.20 and 12.84 Mg ha^?1.     

In search of a variance estimator for systematic sampling

Seven variance estimators to be used under systematic sampling are evaluated in a simulation study with 270 artificial spatial populations with different levels and structure of autocorrelation. In settings without an auxiliary variable a proposed new spatial resampling estimator RHO is recommended. In setting with an auxiliary variable, an estimator based on post-stratification (PST), and one with a correction for spatial autocorrelation (DOR), generated estimates with less bias than the SRS estimator in the majority of studied settings. Only in populations with either a near zero autocorrelation at the interval of sampling, or a very strong correlation between the target and the auxiliary variable did the otherwise conservative SRS estimator perform as well as the alternatives.     

Sampling strategies for estimating forest cover from remote sensing-based two-stage inventories

Background: Remote sensing-based inventories are essential in estimating forest cover in tropical and subtropical countries, where ground inventories cannot be performed periodically at a large scale owing to high costs and forest inaccessibility(e.g. REDD projects) and are mandatory for constructing historical records that can be used as forest cover baselines. Given the conditions of such inventories, the survey area is partitioned into a grid of imagery segments of pre-fixed size where the proportion of forest cover can be measured within segments using a combination of unsupervised(automated or semi-automated) classification of satellite imagery and manual(i.e. visual on-screen)enhancements. Because visual on-screen operations are time expensive procedures, manual classification can be performed only for a sample of imagery segments selected at a first stage, while forest cover within each selected segment is estimated at a second stage from a sample of pixels selected within the segment. Because forest cover data arising from unsupervised satellite imagery classification may be freely available(e.g. Landsat imagery)over the entire survey area(wall-to-wall data) and are likely to be good proxies of manually classified cover data(sample data), they can be adopted as suitable auxiliary information.Methods: The question is how to choose the sample areas where manual classification is carried out. We have investigated the efficiency of one-per-stratum stratified sampling for selecting segments and pixels, where to carry out manual classification and to determine the efficiency of the difference estimator for exploiting auxiliary information at the estimation level. The performance of this strategy is compared with simple random sampling without replacement.Results: Our results were obtained theoretically from three artificial populations constructed from the Landsat classification(forest/non forest) available at pixel level for a study area located in central Italy, assuming three levels of error rates of the unsupervised classification of satellite imagery. The exploitation of map data as auxiliary information in the difference estimator proves to be highly effective with respect to the Horvitz-Thompson estimator,in which no auxiliary information is exploited. The use of one-per-stratum stratified sampling provides relevant improvement with respect to the use of simple random sampling without replacement.Conclusions: The use of one-per-stratum stratified sampling with many imagery segments selected at the first stage and few pixels within at the second stage- jointly with a difference estimator- proves to be a suitable strategy to estimate forest cover by remote sensing-based inventories.     

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.     

基于遥感分层技术的平南县森林蓄积抽样调查方法研究

采用遥感数据辅助分层可解决分层抽样在大范围森林资源调查中分层面积不准确的缺点.以ALOS数据为基础,将平南县的森林资源分为A层（有林地、疏林地层）和B层（其它地类层）.在各层内机械预布设样地,比较预布样地缓冲区（角规控制检尺所能绕测到的最大范围）的SAVI值、DNN IR值及对明显地物的目视解译,确定各样地缓冲区的地类,A层样地数有578个,B层有978个.根据分层抽样各层所需样本数,在确定好地类的样地中,随机抽取各层所需样本数并调查其蓄积量.结果表明,抽样的估计精度为91.5%,全县森林蓄积量为5 900 186.7 m3.     

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%.     

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.     

应用航天遥感资料估测森林蓄积量的一个新方法

本研究是用陆地卫星 TM图象和多元分析方法直接估测森林蓄积量的一次新尝试。其自变量选择了定性和定量因子,所选定性因子是色彩、树种组;定量因子是波段密度值及其比值,较大限度地发挥了遥感资料的潜力。此方法辅以少量地面样地,对有林地蓄积估测精度可达80％以上。是一个简便、易行、经济的方法。     

Integration of remote sensing-based bioenergy inventory data and optimal bucking for stand-level decision making

This paper tests the reliability of a biomass prediction procedure which combines aerial data collection, biometric models and optimisation for forest management planning. Tree stock information is obtained by predicting species-specific diameter and height distributions by a combination of field sampling, ALS data and aerial photographs. The subsequent steps in the chain are (1) assignment of the plots to forestry operation classes by means of remote sensing-based tree stock estimates, (2) estimation of the biomass components removed by simulating forestry operations, and (3) estimation of forest owners’ income flow from optimised bucking of the species-specific diameter distributions. The error effects caused by these steps are analysed, and the applicability of remote sensing–based data collection for biomass inventories and planning is assessed. The approach used for assigning the plots to operation classes resulted in moderate accuracies (75%). The reliability estimates indicated quite poor performance when predicting the biomass components removed in forest treatments, with RMSEs of 33.0–69.4% in the case of final cutting and 76.9–228.0% in the case of thinning. The relative RMSEs of the above-ground biomass estimates of the standing stock were about 19%. The relative bias for the biomasses removed was 10.0–88.6% and that for the standing stock biomasses 0.0%. When optimising bucking, the bucked assortments were larger and the incomes enhanced with this estimation method relative to the reference. This explains why the estimation of forest owner’s incomes in the energy wood thinning simulations led to suboptimal decisions and income losses.     

基于RS、GIS 的呈贡县总体活立木蓄积量分层抽样控制方法

在传统的森林资源调查中,总体活立木蓄积量抽样控制法所需的样地数多,需耗费大量的人力物力.利用SPOT 5卫星数据,基于RS和GIS将呈贡县森林资源先分为A层(有疏林地层)和B层(其它地类),在各层内机械抽样初步确定样本数为1 816个,再根据样地SAVI值和DNNIR值确定各层最终样本数为424个.可极大地减少外业工作量.     

Hierarchical model-based inference for forest inventory utilizing three sources of information

? Key message

The study presents novel model-based estimators for growing stock volume and its uncertainty estimation, combining a sparse sample of field plots, a sample of laser data, and wall-to-wall Landsat data. On the basis of our detailed simulation, we show that when the uncertainty of estimating mean growing stock volume on the basis of an intermediate ALS model is not accounted for, the estimated variance of the estimator can be biased by as much as a factor of three or more, depending on the sample size at the various stages of the design.

? Context

This study concerns model-based inference for estimating growing stock volume in large-area forest inventories, combining wall-to-wall Landsat data, a sample of laser data, and a sparse subsample of field data.

? Aims

We develop and evaluate novel estimators and variance estimators for the population mean volume, taking into account the uncertainty in two model steps.

? Methods

Estimators and variance estimators were derived for two main methodological approaches and evaluated through Monte Carlo simulation. The first approach is known as two-stage least squares regression, where Landsat data were used to predict laser predictor variables, thus emulating the use of wall-to-wall laser data. In the second approach laser data were used to predict field-recorded volumes, which were subsequently used as response variables in modeling the relationship between Landsat and field data.

Results

? The estimators and variance estimators are shown to be at least approximately unbiased. Under certain assumptions the two methods provide identical results with regard to estimators and similar results with regard to estimated variances.

? Conclusion

We show that ignoring the uncertainty due to one of the models leads to substantial underestimation of the variance, when two models are involved in the estimation procedure.

     

基于ALOS数据的巨尾桉蓄积量遥感估测——以广西平南县为例

蓄积量是森林资源监测的一项重要指标,蓄积量遥感估测一直是林业遥感研究的重要内容。本文采用ALOS数据为遥感信息源,以广西自治区平南县优势树种巨尾桉为研究对象,分析选取影响巨尾按蓄积量估测主要的遥感信息和地理信息因子,结合郁闭度实地调查因子,建立了巨尾桉蓄积量估测模型,模型精度达91．18％。     

Species richness estimation from probabilities of observing new species

A new species richness estimator applicable to probability sampling with fixed-area (a) plots in a finite-area (A) population is presented and tested in simulated sampling from three stem-mapped forest compartments, and from six large collections of forest inventory data. The estimator of richness is the average number of species per plot times the sum—over the N = A/n plots in a population—of the probability (p _m ) of observing a new species in the mth plot (m = 1,…, N). A Cauchy distribution function is used to capture trends in p _m . The parameters of the Cauchy distribution were estimated by optimizing a weighted maximum likelihood function. In comparison to five presumed best alternative estimators, the new estimator was ‘average’ with respect to bias, but best in terms of average root mean squared error. Taking the average of the estimates of richness produced by the five alternate and the new estimator would, generally, keep bias below 15 %. With relatively large sample sizes, the bias is moderately small (<10 %).     

Estimation of aboveground tree carbon stock using SPOT-HRG data (a case study: Darabkola forests)

Forests are among the most important carbon sinks on earth. However, their complex structure and vast areas preclude accurate estimation of forest carbon stocks. Data sets from forest monitoring using advanced satellite imagery are now used in international policy agreements. Data sets enable tracking of emissions of CO₂ into the atmosphere caused by deforestation and other types of land-use changes. The aim of this study is to determine the capability of SPOT-HRG Satellite data to estimate aboveground carbon stock in a district of Darabkola research and training forest, Iran. Preprocessing to eliminate or reduce geometric error and atmospheric error were performed on the images. Using cluster sampling, 165 sample plots were taken. Of 165 plots, 81 were in natural habitats, and 84 were in forest plantations. Following the collection of ground data, biomass and carbon stocks were quantified for the sample plots on a per hectare basis. Nonparametric regression models such as support vector regression were used for modeling purposes with different kernels including linear, sigmoid, polynomial, and radial basis function. The results showed that a third-degree polynomial was the best model for the entire studied areas having an root mean square error, bias and accuracy, respectively, of 38.41, 5.31, and 62.2; 42.77, 16.58, and 57.3% for the best polynomial for natural forest; and 44.71, 2.31, and 64.3% for afforestation. Overall, these results indicate that SPOT-HRG satellite data and support vector machines are useful for estimating aboveground carbon stock.     

Quantitative study of poplar plantations in three Iranian provinces

Fast growing poplar species enjoy a highly favored position in Iran＇s forest product industries. Howeve~ information on poplar plantations, such as areas, growing stock and harvest volumes, are largely obtained by now scientific means and poorly executed methods. A few studies have been conducted to obtain data on the capacit,. of poplar plantations, their extent, existing growing stock, distribution and species choice in three provinces, i.e. Western Azerbaijan, Kurdistan and Hamedan, with relatively well developed management systems. We opted for cluster method, a standard sampling method for conducting similar investigations, consisting of two phases. In the firs phase we collected library information and conducted half-open interviews with villagers. In the second phase fiel~ measurements in the villages of these three provinces were carried out. Information from field measurements on growin! stock, cultivated areas, dominant species were used to estimate volumes by way of volume and weight tables. Result~ obtained from the present study indicate that the average annual volume of timber harvested in the three province~ was 697,723 m~, with an average sampling error of 22.7 per cent. This annual volume of poplar timber harvested fron the three provinces was estimated to amount to about 25 per cent of overall harvest; at that rate, the overall annu~ utilization potential of poplar plantations will be 10 million m3, which constitutes a reliable resource of raw timber for us~ in wood and paper industries.