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The utility of remotely sensed auxiliary data for increasing the precision of sample-based inventory estimates of population parameters is well-established. To this end, the model-assisted estimators with remotely sensed auxiliary data are particularly effective for use with continuous dependent variables. The model-assisted estimators take somewhat different forms, depending on the sampling design used to collect the data. The forms are well-documented for simple random sampling but considerably less so for variations of two-stage sampling designs. The objectives of the study were three-fold: (1) to derive the more commonly used Cochran (1977)-like notation for two-stage, model-assisted regression estimators for population means from the Särndal et al. (1992) estimators for population totals, (2) to assess the unbiasedness of the two-stage, model-assisted regression estimators of the population mean and the corresponding variance estimators of the estimate of the population mean, and (3) to compare the precision of estimates of the mean for different combinations of PSU size and first- and second-stage sample sizes. The conclusions were that the two-stage, model-assisted estimators of Särndal et al. (1992) could be much more simply expressed using the familiar Cochran notation and that neither the estimators of the mean nor the estimators of the variance of the estimate of the mean exhibited any indications of bias other than possibly for small sample sizes. For equal total sample sizes, standard errors were smaller for combinations of larger first-stage and smaller second-stage sample sizes and slightly smaller for a larger PSU size. • Särndal notation for regression estimators was converted to Cochran notation. • Precision for different PSU sizes and allocation of plots to stages were compared. • Estimators of means and variances were unbiased or nearly so. [ABSTRACT FROM AUTHOR]

Although estimating forest disturbance area is essential in the context of carbon cycle assessments and for strategic forest planning projects, official statistics are currently not available in several countries. Remotely sensed data are an efficient source of auxiliary information for meeting these needs, and multiple algorithms are commonly used worldwide for this purpose. However, both more accurate maps and precise area estimates are strongly required, especially in Mediterranean ecosystems, and scientific research in this topic area is anything but concluded. In this study, we present the new Three Indices Three Dimensions (3I3D) algorithm for the automated prediction of forest disturbances using statistical analyses of Sentinel-2 data. We tested 3I3D in Tuscany, Italy, for the year 2016, and we compared the results to those obtained using the Global Forest Change Map (GFC), LandTrendr (LT), and the Two Thresholds Method (TTM). The 3I3D map was the most accurate (omissions = 27%, commissions = 30%) followed by TTM (omissions = 35%, commissions = 39%), LT (omissions = 41%, commissions = 43%) and lastly GFC with slightly fewer omissions than LT (39%) but with many more commissions (69%). We also presented a probability sampling framework to estimate the forest harvested area using a model-assisted estimator that can be used at an operational level to produce large-scale statistics. 3I3D and TTM produced the smallest standard errors of the area estimates (8%) followed by LT (13%) and GFC (17%). [ABSTRACT FROM AUTHOR]

Assessing forest biodiversity, naturalness and old-growth status (B-N-OG) is crucial for supporting sustainable forest planning, yet comprehensive monitoring networks specifically designed for such purposes are lacking in many countries. National Forest Inventories (NFIs) are the official source of statistics on status and trends of forests. While initially designed for wood production assessment, NFI data may be pivotal for ecological forest monitoring, thanks to their robust sampling protocols—enabling statistical inference—and regular field campaigns that ensure continuous information updates. As a consequence, in this study we explore the potential of NFIs for estimating B-N-OG indexes, aiming to establish compatible, scientifically relevant, and cost-effective indicators using existing NFI data at a European level. Based on data from the 2005 Italian NFI collected from 6563 plots, 18 indicators were selected following previous experiences and then used to estimate B-N-OG aggregated indexes. Relationships between the 18 indicators and the three indexes were investigated, along with comparisons of their relationships relative to forest type categories, management types and protected versus non-protected areas. Results confirm that NFI data offer valuable insights into specific B-N-OG indexes, especially concerning forest structure and deadwood. Moreover, the indexes contribute to developing meaningful relationships across geographic regions, forest categories and types of management. However, limitations in NFI field protocols are evident, as they are not explicitly designed for certain indicators. The study suggests the potential for NFIs to evolve into accessible, harmonized European reference networks for B-N-OG assessment for better supporting sustainable forest management, planning and conservation decisions related to forest ecosystems. [ABSTRACT FROM AUTHOR]

National greenhouse gas inventories often use variations of the gain–loss approach whereby emissions are estimated as the products of estimates of areas of land-use change characterized as activity data and estimates of emissions per unit area characterized as emission factors. Although the term emissions is often intuitively understood to mean release of greenhouse gases from terrestrial sources to the atmosphere, in fact, emission factors can also be negative, meaning removal of the gases from the atmosphere to terrestrial sinks. For remote and inaccessible forests for which ground sampling is difficult if not impossible, emission factors may be based on map-based estimates of biomass or biomass change obtained from regional maps. For the special case of complete deforestation, the emission factor for the aboveground biomass pool is simply mean aboveground, live-tree, biomass per unit area prior to the deforestation. If biomass maps are used for these purposes, estimates must still comply with the first IPCC good practice guideline regarding accuracy relative to the true value and the second guideline regarding uncertainty. Accuracy assessment for a map-based estimate entails comparison of the estimate to a second estimate obtained using independent reference data. Assuming ground sampling is not feasible, a map of greater quality than the regional map may be considered as a source of reference data where greater quality connotes attributes such as finer resolution and/or greater accuracy. For a local, sub-regional study area in Minnesota in the USA, the accuracy of an estimate of mean aboveground, live-tree biomass per unit area (AGB, Mg/ha) obtained from a coarser resolution, regional, MODIS-based biomass map was assessed using reference data sampled from a finer resolution, local, airborne laser scanning (ALS)-based biomass map. The rationale for a local assessment of a regional map is that, although assessment of a regional map would be difficult for the entire extent of the map, it can likely be assessed for multiple local sub-regions in which case expected local regional accuracy for the entire map can perhaps be inferred. For this study, the local assessment was in the form of a test of the hypothesis that the local sub-regional estimate from the regional map did not deviate from the local true value. A hybrid approach to inference was used whereby design-based inferential techniques were used to estimate uncertainty due to sampling from the finer resolution map, and model-based inferential techniques were used to estimate uncertainty resulting from using the finer resolution map unit values which were subject to prediction error as reference data. The test revealed no statistically significant difference between the MODIS-based and ALS-based map estimates, thereby indicating that for the local sub-region, the regional, MODIS-based estimate complied with the first IPCC good practice guideline for accuracy. [ABSTRACT FROM AUTHOR]

Two approaches to greenhouse gas (GHG) inventories are common, namely the stock-change approach and the gain–loss approach. With the stock-change approach, mean annual emissions are estimated as the ratio of the difference in stock estimates at two points in time and the number of intervening years. The stock-change approach is fairly easy to implement for countries with well-established forest sampling programs. However, countries without established forest sampling programs more commonly use the gain–loss approach. With this approach, emissions are estimated as the product of the areas of classes of land use change, characterized as activity data, and the responses of carbon stocks for those classes, characterized as emission factors. Regardless of the approach, the Intergovernmental Panel on Climate Change (IPCC) good practice guidelines specify that GHG inventories produce neither over- nor under-estimates and reduce uncertainties to the degree possible. For a study area in southeastern Norway, the objectives of the study were to compare the stock-change and gain–loss approaches with respect to estimates of carbon emissions for the aboveground biomass pool and to illustrate statistically rigorous methods for complying with the two IPCC good practice guidelines for both approaches. The primary conclusions were that the two approaches produced comparable estimates of mean annual emissions, but that the stock-change approach produced considerably smaller estimates of uncertainty. [ABSTRACT FROM AUTHOR]

The gain-loss approach for greenhouse gas inventories requires estimates of areas of human activity and estimates of emissions per unit area for each activity. Stratified sampling and estimation have emerged as a popular and useful statistical approach for estimation of activity areas. With this approach, a map depicting classes of activity is used to stratify the area of interest. For each map class used as a stratum, map units are randomly selected and assessed with respect to an attribute such as forest/non-forest or forest land cover change. Ground observations are generally accepted as the most accurate source of information for these assessments but may be cost-prohibitive to acquire for remote and inaccessible forest regions. In lieu of ground observations, visual interpretations of remotely sensed data such as aerial imagery or satellite imagery are often used with the caveat that the interpretations must be of greater quality than the map data. An unresolved issue pertains to the effects of interpreter error on the bias and precision of the stratified estimators of activity areas. For a 7500-km 2 study area in north central Minnesota in the United States of America, combinations of forest inventory plot observations, visual interpretations of aerial imagery, and two forest/non-forest maps were used to assess the effects of interpreter error on stratified estimators of proportion forest and corresponding standard errors. The primary objectives related to estimating the bias and precision of the stratified estimators in the presence of interpreter errors, identifying factors and the levels of those factors that affect bias and precision, and facilitating planning to circumvent and/or mitigate the effects of bias. The primary results were that interpreter error induces bias into the stratified estimators of both land cover class proportion and its standard error. Bias increased with greater inequality in stratum weights, smaller map and interpreter accuracies, fewer interpreters and greater correlations among interpreters. Failure to account for interpreter error produced stratified standard errors that under-estimated actual standard errors by factors as great as 2.3. Greater number of interpreters mitigated the effects of interpreter error on proportion forest estimates, and a hybrid variance estimator accounted for the effects on standard errors. [ABSTRACT FROM AUTHOR]

Model-based inference is an alternative to probability-based inference for small areas or remote areas for which probability sampling is difficult. Model-based mean square error estimators incorporate three components: prediction covariance, residual variance, and residual covariance. The latter two components are often considered negligible, particularly for large areas, but no thresholds that justify ignoring them have been reported. The objectives of the study were threefold: ( i) to compare analytical and bootstrap estimators of model parameter covariances as the primary factors affecting prediction covariance; ( ii) to estimate the contribution of residual variance to overall variance; and ( iii) to estimate thresholds for residual spatial correlation that justify ignoring this component. Five datasets were used, three from Europe, one from Africa, and one from North America. The dependent variable was either forest volume or biomass and the independent variables were either Landsat satellite image bands or airborne laser scanning metrics. Three conclusions were noteworthy: ( i) analytical estimators of the model parameter covariances tended to be biased; ( ii) the effects of residual variance were mostly negligible; and ( iii) the effects of spatial correlation on residual covariance vary by multiple factors but decrease with increasing study area size. For study areas greater than 75 km2 in size, residual covariance could generally be ignored. [ABSTRACT FROM AUTHOR]

For remote sensing-assisted natural resource inventories, the effects of spatial resolution in the form of pixel size and the effects of subpixel information on estimates of population parameters were evaluated by comparing results obtained using Landsat 8 and RapidEye auxiliary imagery. The study area was in Burkina Faso, and the response variable of interest was firewood volume (m 3 /ha). A sample consisting of 160 field plots was selected from the population following a two-stage sampling design. Models were fit using weighted least squares; the population mean, μ , and the variance of the estimator of the population mean, V μ ̂ , were estimated using two inferential frameworks, model-based and model-assisted, and compared. For each framework, V μ ̂ was estimated both analytically and empirically. Empirical variances were estimated using bootstrapping that accounted for the two-stage sampling. The primary results were twofold. First, for the effects of spatial resolution and subpixel information, four conclusions are relevant: (1) finer spatial resolution imagery indeed contributed to greater precision for estimators of population parameter, but despite the finer spatial resolution of RapidEye, the increase was only marginal, on the order of 10% for model-based variance estimators and 36% for model-assisted variance estimators; (2) subpixel information on texture was marginally beneficial for inference of large area population parameters; (3) RapidEye did not offer enough of an improvement to justify its cost relative to the free Landsat 8 imagery; and (4) for a given plot size, candidate remote sensing auxiliary datasets are more cost-effective when their spatial resolutions are similar to the plot size than with much finer alternatives. Second, for the comparison between estimators, three conclusions are relevant: (1) sampling distribution for the model-based V ̂ μ ̂ was more concentrated and smaller on the order of 42% to 59% than that for the model-assisted V ̂ μ ̂ , suggesting superior consistency and efficiency of model-based inference to model-assisted inference; (2) bootstrapping is an effective alternative to analytical variance estimators; and (3) prediction accuracy expressed by RMSE is useful for screening candidate models to be used for population inferences. [ABSTRACT FROM AUTHOR]

National forest inventories routinely report estimates of parameters related to aboveground biomass (AGB), but sample sizes are often insufficient to satisfy precision guidelines and reporting requirements. Aerial photography, satellite imagery, and increasingly airborne laser scanning (ALS) data are all used as sources of auxiliary information to address this challenge. Combining inventory ground plot and ALS data requires that the data be co-registered to a common coordinate system. When measuring plots, inventory field crews typically obtain estimates of plot coordinates using global positioning system (GPS) receivers of varying degrees of accuracy. GPS-related errors in plot coordinates contribute to a sequence of adverse effects: (i) plot data are associated with erroneous ALS metrics, (ii) statistical models fit to such data may not adequately represent the true relationship between the plot data and the ALS metrics; and (iii) bias may be induced into model-assisted statistical estimators of population parameters. The primary objectives of the study focused on assessing the effects of GPS receiver inaccuracies on the estimated bias and precision of model-assisted estimators of mean AGB per unit area. The underlying motivation was to determine if the advantages of using ALS data as auxiliary information can be achieved apart from the substantial additional expense of purchasing GPS receivers with sub-meter accuracy. The analyses focused on comparing estimates based on three variations of plot coordinates obtained using field crew GPS receivers with maximum location errors on the order of 5–10 m to estimates based on plot coordinates obtained using survey grade GPS receivers with sub-meter accuracy. The study area was in north central Minnesota in the USA and is characterized by both upland and lowland forest areas interspersed with lakes and wetlands. The primary results were twofold. First, estimates of mean AGB per unit area based on plot coordinates obtained using the less accurate field crew GPS receivers varied little from estimates based on the much more accurate survey grade receivers. Second, standard errors were greater by as much as 20% when using field crew GPS receivers than when using survey grade GPS receivers. However, even though the ALS-assisted standard errors obtained using field crew GPS receivers were greater than when using survey grade receivers, they were still substantially smaller than satellite image-assisted standard errors. Thus, the operational conclusion is that avoiding the substantial additional cost of providing a survey grade GPS receiver for each of more than 100 field crews likely outweighs the adverse consequences of somewhat larger standard errors. [ABSTRACT FROM AUTHOR]

The term shelf-life is used to characterize the elapsed time beyond which a commodity loses its usefulness. The term is most often used with reference to foods and medicines, but herein it is used to characterize the elapsed time beyond which airborne laser scanning (ALS) data are no longer useful for enhancing inferences for forest inventory population parameters. National forest inventories (NFI) have a long history of using remotely sensed auxiliary information to enhance inferences. Although the combination of model-assisted estimators and ALS auxiliary data has been demonstrated to be particularly useful for this purpose, the expense associated with the acquisition of the ALS data has been an argument against their operational use. However, the longer the shelf-life of ALS data, the less the continuing acquisition costs and the greater the utility of the data. The objective of the study was to assess the shelf-life of ALS data for enhancing inferences in the form of confidence intervals for mean aboveground, live tree, stem biomass per unit area. Confidence intervals were constructed using both model-assisted estimators and post-stratified estimators, four measurements of mostly the same forest inventory plots at 5-year intervals over a 17-year period, and a single set of ALS data acquired near the end of the 17-year period. The study area in north central Minnesota in the USA was characterized by naturally regenerated, uneven-aged, mixed species stands on both lowland and upland sites. The primary conclusions were twofold. First, the shelf-life of ALS data when used with model-assisted estimators exceeded 10 years, and second, even for 12 years elapsed time between plot measurement and ALS data acquisition, the variance of the model-assisted estimator of the mean was smaller by a factor of at least 1.75 than the variance of the stratified estimator used by the national forest inventory. [ABSTRACT FROM AUTHOR]

When probability samples are not available, the model-based framework may be the only option for constructing inferences in the form of prediction intervals for population means. Further, for machine learning and some non-parametric and nonlinear regression prediction techniques, resampling methods such as the bootstrap may be the only option for obtaining the standard errors necessary for constructing those prediction intervals. All bootstrap approaches entail repeatedly sampling from the original sample, estimating the parameter of interest for each replication, and estimating the standard error of the estimate of the parameter as the standard deviation of the bootstrap estimates over replications. The objective of the study was to develop a procedure for terminating resampling such that the resulting number of replications assures, at least in probability, that the estimate of the standard error stabilizes to the standard error corresponding to one million replications. The analyses used a variety of datasets: five forest inventory datasets with either volume or aboveground biomass as the dependent variable and metrics from either airborne laser scanning or Landsat as independent variables, three from Europe, one from Southwest Asia, and one from Africa; and two forest/non-forest versus Landsat datasets, one from Minnesota and one from Wisconsin, both in the USA. The primary contribution of the study was development and demonstration of a procedure that specifies criteria for terminating resampling that assure in probability that the bootstrap estimate of the standard error stabilizes to the estimate obtained with one million replications. • Proposes and demonstrates criteria for terminating bootstrap resampling. • Assures in probability that the bootstrap standard error stabilizes. • Minimizes the uncertainty of a bootstrap standard error-based prediction interval. • Results are demonstrated for seven international forest inventory datasets. [ABSTRACT FROM AUTHOR]

Forest structural diversity plays a major role for forest management, conservation and restoration and is recognized as a fundamental aspect of forest biodiversity. The assessment, maintenance and restoration of a diversified forest structure have become major foci in the effort to preserve forest ecosystems from loss of biological diversity. However, the assessment of forest biodiversity is difficult because it involves multiple components and is characterized using multiple variables. The objective of the study was to develop a methodological approach for predicting, mapping, and constructing a statistical inference for a multiple-variable index of forest structural diversity. The method included three key components: (i) use of the k-Nearest Neighbors (k-NN) technique, field plot data, and airborne laser scanning metrics to predict multiple forest structural diversity variables simultaneously, (ii) incorporation of multiple diversity variable predictions into a single index, and (iii) construction of a statistically rigorous inference for the population mean of the index. Three structural diversity variables were selected to illustrate the method: growing stock volume and the standard deviations of tree diameter at breast-height and tree height. Optimization of the k-NN technique produced mean relative deviations less in absolute value than 0.04 for predictions for each of the three structural diversity variables, R 2 values between 0.50 and 0.66 which were in the range of values reported in the literature, and a confidence interval for the population mean of the index whose half-width was approximately 5% of the mean. Finally, the spatial pattern depicted in the resulting map of forest structural diversity for the study area contributed to validating the proposed method. [ABSTRACT FROM AUTHOR]

Almost all relevant data in forestry databases arise from either field measurement or model prediction. In either case, these values have some amount of uncertainty that is often overlooked when doing analyses. In this study, the uncertainty associated with both measured and predicted data was quantified for upper-stem diameter at 5.27 m. This uncertainty was propagated through a tree taper model into predictions of individual-tree volume. The effects of uncertainty on individual-tree volume predictions and population estimates of total volume were assessed. Generally, when little or no systematic measurement deviation was present, less uncertainty was associated with field-measured diameters compared to model predictions. However, diameters predicted from a model were preferred when systematic deviations in field measurement exceeded approximately 0.2 cm. Comparisons of results obtained from an alternative taper model showed that more precise estimates of population totals might be obtained without upper-stem diameter information. Upper-stem diameter information increases the prediction accuracy of individual-tree volume, and thus, models using this information may be preferable in applications such as timber sales containing high-value trees. Due to the various factors that influence measurement and modeling uncertainty, foresters are encouraged to make similar evaluations in the context of their specific activities. [ABSTRACT FROM AUTHOR]

The relatively small sampling intensities used by national forest inventories are often insufficient to produce the desired precision for estimates of population parameters unless the estimation process is augmented with auxiliary information, usually in the form of remotely sensed data. The k-Nearest Neighbors (k-NN) technique is a non-parametric, multivariate approach to prediction that has emerged as particularly popular for use with forest inventory and remotely sensed data and has been shown to contribute substantially to increasing precision. k-NN predictions are calculated as linear combinations of observations for sample units that are nearest in a space of auxiliary variables to the population unit for which a prediction is desired. Implementation of a nearest neighbors algorithm requires four choices: (i) a distance metric, (ii) specific auxiliary variables to be used with the distance metric, (iii) the number of nearest neighbors, and a (iv) scheme for weighting the nearest neighbors. Regardless of the choices for a distance metric and weighting scheme, emerging evidence suggests that optimization of the technique, including selection of an optimal subset of auxiliary variables, greatly enhances prediction. However, optimization can be computationally intensive and time-consuming. A promising approach that is gaining favor is based on genetic algorithms, a technique that uses search heuristics that mimic natural selection to solve optimization problems. The objective of the study was to compare optimized k-NN configurations with respect to inferences for mean volume per unit area using airborne laser scanning variables as auxiliary information. For two study areas, one in Norway and one in Minnesota, USA, the analyses focused on optimizing k-NN configurations that used the weighted Euclidean and canonical correlation distance metrics and two neighbor weighting schemes. Novel features of the study include introduction of a neighbor weighting scheme that has not previously been used for forestry applications, simultaneous optimization of all four k-NN choices, and basing comparisons on confidence intervals, rather than intermediate products such as prediction accuracies. Two conclusions were primary: (1) optimized selection of feature variables produced greater precision than using all feature variables, and (2) computational intensity necessary to optimize the weighted Euclidean metric was considerably greater than for the canonical correlation analysis metric. Specific findings were that optimization produced pseudo-R 2 as large as 0.87 for the Norwegian dataset and as large as 0.89 for the Minnesota dataset. For the optimized canonical correlation distance metric, widths of approximate 95% confidence intervals as proportions of the estimated means were as small as 0.13 for the Norwegian dataset and as small as 0.15 for the Minnesota dataset. [ABSTRACT FROM AUTHOR]

Remotely sensed data have been widely used in recent years for mapping and estimating biomass. However, the characterization of the uncertainty of mapped or estimated biomass in previous studies was either based on ad-hoc approaches (e.g., using model fitting statistics such root mean square errors derived from purposive samples) or mostly limited to the analysis of mean biomass for the whole study area. This study proposed a novel uncertainty analysis method that can characterize biomass uncertainty across multiple spatial scales and multiple spatial resolutions. The uncertainty analysis method built on model-based inference and can propagate errors from trees to field plots, individual pixels, and small areas or large regions that consist of multiple pixels (up to all pixels within a study area). We developed and tested this method over northern Minnesota forest areas of approximately 69,508 km 2 via a unique combination of several datasets for biomass mapping and estimation: wall-to-wall airborne lidar data, national forest inventory (NFI) plots, and destructive measurements of tree aboveground biomass (AGB). We found that the pixel-level AGB prediction error is dominated by lidar-based AGB model residual errors when the spatial resolution is near 380 m or finer and by model parameter estimate errors when the spatial resolution is coarser. We also found that the relative error of AGB predicted from lidar can be reduced to approximately 11% (or mean 5.1 Mg/ha; max 43.6 Mg/ha) at one-hectare scale (or at 100 m spatial resolution) over our study area. Because our uncertainty analysis method uses model-based inference and does not require probability samples of field plots, our methodology has potential applications worldwide, especially over tropics and developing countries where NFI systems are not well-established. [ABSTRACT FROM AUTHOR]

The model-assisted difference and regression estimators are increasingly used with forest inventory and remotely sensed data to increase the precision of estimates of inventory parameters. Although these estimators date back at least 50 years and appear in multiple current sampling textbooks, the associated terminology is inconsistently defined, even among the prominent authorities. Further, two of the most prominent statistical sampling textbooks, Cochran (1977) and Särndal et al. (1992), use considerably different notation. The study focused on three objectives: (1) to formulate consistent and operationally useful definitions via a synthesis of the literature, (2) to construct a bridge between the more complex Särndal et al. (1992) notation and the more commonly used Cochran (1977) notation, and (3) to assess sample size, model form and g-weight effects on the unbiasedness of the regression estimators of both the population mean and the variance of its estimate. The data analyses entailed Monte Carlo simulations using an artificial population constructed using inventory and airborne laser scanning data and both across- and within-dataset analyses for 11 inventory datasets representing six countries on four continents. The analyses focused on assessing the unbiasedness of the regression estimators of both the mean and variance, the role of the g-weights on the unbiasedness of the variance estimator, and differences for linear versus nonlinear models. Key terminological distinctions were that the generalized estimators accommodate unequal probability sampling and that the difference estimator of the mean is unbiased whereas the regression estimator of the mean is only asymptotically unbiased, meaning it only approaches unbiasedness as the sample size increases. The key analytical conclusions were threefold: (1) the regression variance estimator was confirmed as asymptotically unbiased, (2) the form of the regression variance estimator that incorporated the g-weights was more accurate, and (3) the regression variance estimator was more accurate for linear models than for nonlinear models. • Operational definitions were synthesized from the literature. • The regression and difference estimators were distinguished. • The regression and generalized regression estimators were distinguished. • The role of the g-weights was described and demonstrated. • The variance estimator was more accurate for linear models than for nonlinear models. [ABSTRACT FROM AUTHOR]

Statistically rigorous inferences in the form of confidence intervals for map-based estimates require model-based inferential methods. Model-based mean square errors (MSE) incorporate estimates of both residual variability and sampling variability, of which the latter includes population unit variance estimates and pairwise population unit covariance estimates. Bootstrapping, which can be used with any prediction technique, provides a means of estimating the required variances and covariances. The objectives of the study were to to demonstrate a method for estimating the sampling variability, Var ̂ sam μ ̂ , that can be used with all prediction techniques, to develop an efficient method that map makers can use to disseminate metadata that facilitates calculation of Var ̂ sam μ ̂ for arbitrary subregions of maps, and to estimate the individual contributions of sampling variability and residual variability to the overall standard error of the prediction of the population mean. The primary results were fourfold: (i) map makers must provide metadata that facilitate estimation of population unit variances and covariances for arbitrary map subregions, (ii) bootstrapping was demonstrated as an effective means of estimating the variances and covariances, (iii) the very large matrix of pairwise population unit covariances can be aggregated into a much smaller matrix that can be readily communicated by map makers to map users, and (iv) MSEs that include only estimates of residual variability and/or estimates of population unit variances, but not estimates of the pairwise population unit covariances, grossly under-estimate the actual MSEs. • Inferences constructed directly from maps require model-based methods. • The effects of sampling variability dominate the effects of residual variability. • Bootstrap approaches were used to estimate map unit, pairwise, sampling covariances. • Efficient methods that map-makers can use to communicate covariances were developed. [ABSTRACT FROM AUTHOR]

For a study area in the Brazilian state of Santa Catarina, the utilities of local and global forest maps in combination with poststratified and model-assisted estimators for increasing the precision of estimates of forest area were compared. Auxiliary information was in the form of local maps, the recent Global Forest Change map, and combinations of these maps. The poststratified estimators produced estimates of greater precision than the model-assisted regression estimators for maps of categorical variables, but the model assisted estimators produced estimates of greater precision for maps of continuous variables. The Global Forest Change map was the least accurate of all the maps, but it produced estimates of forest area that were similar to those for the other maps and that were more precise than if the map had not been used. Thus, the Global Forest Change map may be an attractive option if local maps are not available or cannot be constructed. The primary contributions of the study are two-fold. First, this is one of the first case studies that rigorously assess the utility of global maps for national estimation. After accumulation of a few more such studies, broader generalizations should be forthcoming. Second, a statistical basis is provided for the previously unexplained greater precision for poststratified estimators than for model-assisted estimators. [ABSTRACT FROM AUTHOR]

We report on the operational use of remotely sensed data by national forest inventory (NFI) programmes in 45 countries representing approximately 65% of the world's forest area. The analysis is based on responses to a questionnaire prepared under the auspices of COST Action FP1001 “Improving Data and Information on the Potential Supply of Wood Resources: A European Approach from Multisource National Forest Inventories (USEWOOD)”. Responses were received from NFI remote sensing experts from both European and non-European countries. Three major conclusions were drawn from the study: (1) remote sensing now plays an essential role in many NFI programmes and provides data that can be used to enhance estimates for the most meaningful and commonly reported forest resource parameters; (2) a wide spectrum of remote sensing methods are currently used by NFI teams; and (3) although substantial effort and attention has been focused on the use of aerial photography and spaceborne sensor data for mapping and enhancing estimation, integration of uncertainly estimation requires additional attention. The operational use of remotely sensed data by NFI programmes is illustrated for three case studies: a case study for Switzerland focuses on digital aerial photography, a case study for Finland focuses on spaceborne sensor data for small area estimation, and a case study for the USA focuses on spaceborne sensor data for increasing the precision of large area estimates. Although use of remotely sensed data by NFI programmes may remain region-specific and some approaches are not readily transferable, generally applicable good practice guidelines were formulated on the basis of the questionnaire responses and the case studies. These guidelines are intended to promote better use of limited financial resources and to increase the accuracy and precision of NFI estimates. [ABSTRACT FROM AUTHOR]

Among the forestry-related applications for which airborne laser scanning (ALS) data have been shown to be beneficial, forest inventory has been investigated as much if not more than other applications. Metrics extracted from ALS data for spatial units such as plots and grid cells are typically of two forms: echo-based metrics derived directly from the three-dimensional distribution of the point cloud data and metrics derived from a canopy height model (CHM). For both cases, a large number of metrics can be calculated and used to construct parametric and non-parametric models to predict forest variables. We compared model-assisted estimates of total forest aboveground biomass (AGB) obtained using echo-based and CHM-based height metrics with two prediction methods: (i) a parametric linear model, and (ii) the non-parametric k-Nearest Neighbors (k-NN) technique. Model-assisted (MA) estimators were used with sample data obtained using a two-phase, tessellation stratified sampling (TSS) framework to estimate population parameters. The study was conducted in Molise Region in central Italy. For the four combinations of metrics and prediction techniques, estimates of total biomass were similar, in the range 1.96–2.1 million t, with standard error estimates that were also similar, in the range 0.20–0.21 t. Thus, the CHM-based metrics produced AGB estimates that were similar to and as accurate as those for the echo-based metrics, regardless of whether the parametric or the non-parametric prediction method was used. Additionally, the proposed MA estimator was more accurate than the estimator that did not use auxiliary data. [ABSTRACT FROM AUTHOR]

Due to the availability of good and reasonably priced auxiliary data, the use of model-based regression-synthetic estimators for small area estimation is popular in operational settings. Examples are forest management inventories, where a linking model is used in combination with airborne laser scanning data to estimate stand-level forest parameters where no or too few observations are collected within the stand. This paper focuses on different approaches to estimating the variances of those estimates. We compared a variance estimator which is based on the estimation of superpopulation parameters with variance estimators which are based on predictions of finite population values. One of the latter variance estimators considered the spatial autocorrelation of the residuals whereas the other one did not. The estimators were applied using timber volume on stand level as the variable of interest and photogrammetric image matching data as auxiliary information. Norwegian National Forest Inventory (NFI) data were used for model calibration and independent data clustered within stands were used for validation. The empirical coverage proportion (ECP) of confidence intervals (CIs) of the variance estimators which are based on predictions of finite population values was considerably higher than the ECP of the CI of the variance estimator which is based on the estimation of superpopulation parameters. The ECP further increased when considering the spatial autocorrelation of the residuals. The study also explores the link between confidence intervals that are based on variance estimates as well as the well-known confidence and prediction intervals of regression models. [ABSTRACT FROM AUTHOR]

For purposes of greenhouse gas emissions (GHG) accounting, estimation of deforestation area in tropical countries often relies on satellite remote sensing in the absence of National Forest Inventories (NFI). Gabon has recently launched a National Climate Action Plan with the intent of establishing a National Forest Monitoring System that meets the Intergovernmental Panel on Climate Change (IPCC) 2006 guidelines for the Agriculture, Forestry and Other Land Use (AFOLU) sector. The assessment of areas of forest cover and forest cover change is essential to estimate activity data, defined as areas of various categories of land use change by the IPCC guidelines. An appropriately designed probability sample can be used to estimate forest cover and net change and their associated uncertainties and express them in the form of confidence intervals at selected probability thresholds as required in the IPCC 2006 guidelines and for reporting to the United Nations Framework Convention on Climate Change (UNFCCC). However, wall-to-wall mapping is often required to provide a comprehensive assessment of forest resources and as input to land use plans for management purposes, but wall-to-wall approaches are more expensive than a sample based approach based on visual interpretation and require specialized equipment and staff. The recent release of the University of Maryland (UMD) Global Forest Change (GFC) map products could be an alternative for tropical countries wishing to develop their own wall-to-wall forest map products but without the resources to do so. Therefore, the aim of this study is to assess the feasibility of replacing national wall-to-wall forest maps with forest maps obtained from the UMD GFC initiative. A model assisted regression (MAR) estimator was applied using the combination of reference data obtained from a probability sample and forest cover and forest cover change maps either (i) produced nationally or (ii) obtained from the UMD GFC data. The resulting activity data are potentially more accurate than the SRS estimate and provide an assessment of the precision of the estimate which is not available from map accuracy indices alone. Results obtained for 2000 and 2010 for both the national and UMD GFC datasets confirm the high level of forest cover in Gabon, more than 23.5 million ha representing approximately 88.5% of the country. Although the UMD GFC dataset provides a reliable means of producing area statistics at national level combined with appropriate sample reference data, thus offering an alternative to nationally produced datasets (i) the classification errors associated with the Global dataset have non-negligible effects on both the estimate and the precision which supports the more general statement that map data should not be used alone to produce area estimates, and (ii) the maps obtained from the UMD GFC dataset require specific calibration of the tree cover percentage representing a non-negligible effort requiring specialized staff and equipment. Guidelines on how to use and further improve UMD GFC maps for national reporting are suggested. However, this additional effort would still most likely be less than the production of national based maps. [ABSTRACT FROM AUTHOR]

Among the wide array of terrestrial habitats, forest and wooded lands are the richest from both biological and genetic points of view because of their inherent structural and compositional complexity and diversity. Although species composition is an important biodiversity feature, forest structure may be even more relevant for biodiversity assessments because a diversified structure is likely to have more niches, which in turn, host more species and contribute to a more efficient use of available resources. Structure plays a major role as a diversity indicator for management purposes where maps of forest structural diversity are of great utility when planning conservation strategies. Airborne laser scanning (ALS) data have been demonstrated to be a reliable and valid source of information for describing the three-dimensional structure of forests. Using ALS metrics as predictor variables, we developed regression models for predicting indices of forest structural diversity for a study area in Molise, Italy. The study had two primary objectives: (i) to estimate indices of structural diversity for the entire study area, and (ii) to construct maps depicting the spatial pattern of the structural diversity indices. Our results demonstrate the utility of simple linear models using ALS data for improving areal estimates of mean structural diversity, and the resulting maps capture the patterns of structural diversity in the study area. [ABSTRACT FROM AUTHOR]

Emerging satellite radar and lidar platforms are being developed to produce gridded aboveground biomass (AGB) predictions that are poised to expand our understanding of global carbon stocks and changes. However, the spatial resolution of AGB map products from these platforms is often larger than the available field plot data underpinning model calibration and validation efforts. Intermediate-resolution/extent remotely sensed data, like airborne lidar, can serve as a bridge between small plots and map resolution, but methods are needed to estimate and propagate uncertainties with multiple layers of data. Here, we introduce a workflow to estimate the pixel-level mean and variance in AGB maps by propagating uncertainty from a lidar-based model using small plots, taking into account prediction uncertainty, residual uncertainty, and residual spatial autocorrelation. We apply this workflow to estimate AGB uncertainty at a 100 m map resolution (1 ha pixels) using 0.04 ha field plots from 11 sites across four ecoregions. We compare uncertainty estimates using site-specific models, ecoregion-specific models, and a general model using all sites. The estimated AGB uncertainty for 1 ha pixels increased with mean AGB, reaching 7.8–33.3 Mg ha−1 for site-specific models (one standard deviation), 11.1–28.2 Mg ha−1 for ecoregion-specific models, and 21.1–22.1 Mg ha−1 for the general model for pixels in the AGB range of 80–100 Mg ha−1. Only 3 of 11 site-specific models had a total uncertainty of <15 Mg ha−1 in this biomass range, suitable for the calibration or validation of AGB map products. Using two additional sites with larger field plots, we show that lidar-based models calibrated with larger field plots can substantially reduce 1 ha pixel AGB uncertainty for the same range from 18.2 Mg ha−1 using 0.04 ha plots to 10.9 Mg ha−1 using 0.25 ha plots and 10.1 Mg ha−1 using 1 ha plots. We conclude that the estimated AGB uncertainty from models estimated from small field plots may be unacceptably large, and we recommend coordinated efforts to measure larger field plots as reference data for the calibration or validation of satellite-based map products at landscape scales (≥0.25 ha). [ABSTRACT FROM AUTHOR]

Remote sensing-based change estimation typically takes two forms. Indirect estimation entails constructing models of the relationship between the response variable of interest and remotely sensed auxiliary variables at two times and then estimating change as the differences in the model predictions for the two times. Direct estimation entails constructing models of change directly using observations of change in the response and the remotely sensed auxiliary variables for two dates. The direct method is generally preferred, although few statistically rigorous comparisons have been reported. This study focused on statistically rigorous, indirect and direct estimation of biomass change using forest inventory and airborne laser scanning (ALS) data for a Norwegian study area. Three sets of statistical estimators were used: simple random sampling estimators, indirect model-assisted regression estimators, and direct model-assisted regression estimators. In addition, three modeling approaches were used to support the direct model-assisted estimators. The study produced four relevant findings. First, use of the ALS auxiliary information greatly increased the precision of change estimates, regardless of whether indirect or direct methods were used. Second, contrary to previously reported results, the indirect method produced greater precision for the study area mean than the traditional direct method. Third, the direct method that used models whose predictor variables were selected in pairs but with separate coefficient estimates and models whose predictor variables were selected without regard to pairing produced the greatest precision. Finally, greater emphasis should be placed on the effects of model extrapolations for values of independent variables in the population that are beyond the range of the variables in the sample. [ABSTRACT FROM AUTHOR]

Nearest neighbors techniques calculate predictions as linear combinations of observations for a selected number of population units in a sample that are most similar, or nearest, in a space of auxiliary variables to the population unit requiring the prediction. Nearest neighbors techniques have been shown to be particularly effective when used with forest inventory and remotely sensed data. Recent attention has focused on developing an underlying foundation consisting of diagnostic tools, inferential extensions, and techniques for optimization. For a study area in Norway, forest inventory and airborne laser scanning data were used with the k-Nearest Neighbors technique to estimate mean aboveground biomass per unit area. Optimization entailed reduction of the dimension of feature space, deletion of influential outliers, and selection of optimal weights for the weighted Euclidean distance metric. These optimization steps increased the proportion of variability explained in the reference set by as much as 20%, reduced confidence interval widths by as much as 35%, and produced standard errors that were as small as 3% of the estimate of the mean. [ABSTRACT FROM AUTHOR]

Forest inventory estimates of tree volume for large areas are typically calculated by adding the model predictions of volumes for individual trees at the plot level, calculating the mean over plots, and expressing the result on a per unit area basis. The uncertainty in the model predictions is generally ignored, with the result that the precision of the large-area volume estimate is optimistic. The primary study objective was to assess the performance of a Monte Carlo based approach for estimating model prediction error that had been developed for boreal and temperate forest applications when used for a subtropical forest application. Monte Carlo simulation approaches were used because of the complexities associated with multiple sources of uncertainty, the nonlinear nature of the models, and heteroskedasticity. A related objective was to estimate the effects of model prediction uncertainty due to residual and parameter uncertainty on the large-area volume estimates for the Brazilian state of Santa Catarina. The primary conclusions were fourfold. First, the methodological approach worked well. Second, the effects of model residual and parameter uncertainty on large-area estimates of mean volume per unit area were negligible for the models and calibration datasets used for the study. Third, for the models currently in use in Santa Catarina, the effects of model residual and parameter uncertainty may be ignored when calculating large-area estimates of mean volume per unit area. Fourth, differences were negligible between estimates of the mean and standard error obtained using a single, nonspecific volume model and estimates obtained using both forest-type models and species-specific/species-group models. [ABSTRACT FROM AUTHOR]

For remote and inaccessible forest regions, lack of sufficient or possibly any sample data inhibits estimation and construction of confidence intervals for population parameters using familiar probability- or design-based inferential methods. Although maps based on remotely sensed data may provide information on the distribution of resources, map-based estimates are subject to classification and prediction error, and map accuracy measures do not directly inform the uncertainty of the estimates. Model-based inference does not require probability samples and when used with synthetic estimation can circumvent small or no-sample difficulties associated with probability-based inference. The study focused on estimating proportion forest area using Landsat data for a study area in Minnesota, USA, and aboveground biomass using airborne laser scanning data for a study area in Hedmark County, Norway. For both study areas, model-based inference was used to estimate the components necessary for constructing confidence intervals for population means for non-sampled areas. The estimates were compared to simple random sampling, model-assisted, and model-based estimates that would have been obtained if the areas had been sampled. All estimates were within two simple random sampling standard errors of each other, thereby illustrating the utility of model-based inference for non-sampled areas. [ABSTRACT FROM AUTHOR]

Multiple remote sensing-based approaches to estimating gross afforestation, gross deforestation, and net deforestation are possible. However, many of these approaches have severe data requirements in the form of long time series of remotely sensed data and/or large numbers of observations of land cover change to train classifiers and assess the accuracy of classifications. In particular, when rates of change are small and equal probability sampling is used, observations of change may be scarce. For these situations, post-classification approaches may be the only viable alternative. The study focused on model-assisted and model-based approaches to inference for post-classification estimation of gross afforestation, gross deforestation, and net deforestation using Landsat imagery as auxiliary data. Emphasis was placed on estimation of variances to support construction of statistical confidence intervals for estimates. Both analytical and bootstrap approaches to variance estimation were used. For a study area in Minnesota, USA, estimates of net deforestation were not statistically significantly different from zero. [ABSTRACT FROM AUTHOR]

Forest cover maps were produced for the Gabonese Agency for Space Studies and Observations (AGEOS) for 1990, 2000 and 2010 for an area of approximately 102,000 km 2 corresponding to 38% of the total area of Gabon and representative of the range of human pressure on forest resources. The maps were constructed using a combination of a semi-automated classification procedure and manual enhancements to ensure the greatest possible accuracy. A two-stage area frame sampling approach was adopted to collect reference data for assessing the accuracy of the forest cover maps and to estimate proportion forest cover and net proportion deforestation. A total of 251 2 × 2 km segments or primary sample units (PSUs) were visually interpreted by a team of photo-interpreters independently from the map production team to produce a reference dataset representing about 1% of the study area. Paired observations were extracted from the forest cover map and the reference data for a random selection of 50 secondary sample units (SSUs) in the form of pixels within each PSU. Overall map accuracies were greater than 95%. PSU and SSU outputs were used to estimate proportion forest cover and net proportion deforestation using both direct expansion and model-assisted regression (MAR) estimators. All proportion forest cover estimates were similar, but the variances of the MAR estimates were smaller than variances for the direct expansion estimates by factors as great as 50. In addition, SSU-level estimates had standard errors slightly greater than those of PSU-level estimates, but the differences were small, particularly when auxiliary variables were obtained from forest cover maps. Therefore, a two-stage sampling approach was justified for collecting a reliable forest cover reference dataset for estimating proportion forest cover area and net proportion deforestation. Finally, despite large overall map accuracies, net proportion deforestation estimates obtained from the maps alone can be misleading as indicated by the finding that the MAR estimates, which included adjustment for bias estimates, were twice the non-adjusted map estimates for the periods 1990–2000 and 1990–2010. The results confirmed the expected generally small level of net deforestation for Gabon. However, loss of forest cover appears to have almost stopped in the last 10 years. One explanation could be the creation of national parks and the implementation of forest concession management plans from 2000 onward, but this should be further explored. [ABSTRACT FROM AUTHOR]

ABSTRACT The long-accepted conclusion that wolf density is regulated by nutrition was recently challenged, and the conclusion was reached that, at greater levels of prey biomass, social factors such as intraspecific strife and territoriality tend to regulate wolf density. We reanalyzed the data used in that study for 2 reasons: 1) we disputed the use of 2 data points, and 2) because of recognized heteroscedasticity, we used weighted-regression analysis instead of the unweighted regressions used in the original study. We concluded that the data do not support the hypothesis that wolf densities are regulated by social factors. Published 2014. This article is a U.S. Government work and is in the public domain in the USA. [ABSTRACT FROM AUTHOR]

Afforestation processes, natural and anthropogenic, involve the conversion of other land uses to forest, and they represent one of the most important land use transformations, influencing numerous ecosystem services. Although remotely sensed data are commonly used to monitor forest disturbance, only a few reported studies have used these data to monitor afforestation. The objectives of this study were two fold: (1) to develop and illustrate a method that exploits the 1985–2019 Landsat time series for predicting afforestation areas at 30 m resolution at the national scale, and (2) to estimate afforestation areas statistically rigorously within Italian administrative regions and land elevation classes. We used a Landsat best-available-pixel time series (1985–2019) to calculate a set of temporal predictors that, together with the random forests prediction technique, facilitated construction of a map of afforested areas in Italy. Then, the map was used to guide selection of an estimation sample dataset which, after a complex photointerpretation phase, was used to estimate afforestation areas and associated confidence intervals. The classification approach achieved an accuracy of 87%. At the national level, the afforestation area between 1985 and 2019 covered 2.8 ± 0.2 million ha, corresponding to a potential C-sequestration of 200 million t. The administrative region with the largest afforested area was Sardinia, with 260,670 ± 58,522 ha, while the smallest area of 28,644 ± 12,114 ha was in Valle d'Aosta. Considering elevation classes of 200 m, the greatest afforestation area was between 400 and 600 m above sea level, where it was 549,497 ± 84,979 ha. Our results help to understand the afforestation process in Italy between 1985 and 2019 in relation to geographical location and altitude, and they could be the basis of further studies on the species composition of afforestation areas and land management conditions. [ABSTRACT FROM AUTHOR]

Forests contribute substantially to maintaining the global greenhouse gas balance, primarily because among the five economic sectors identified by the United Nations Framework Convention on Climate Change, only the forestry sector has the potential to remove greenhouse gas emissions from the atmosphere. In this context, development of national forest carbon accounting systems, particularly in countries with tropical forests, has emerged as an international priority. Because these systems are often developed as components of or in parallel with national forest inventories, a brief review of statistical issues related to the development of forest ground sampling designs is provided. This overview addresses not only the primary issues of plot configurations and sampling designs, but also to a lesser extent the emerging roles of remote sensing and uncertainty assessment. Basic inventory principles are illustrated for two case studies, the national forest inventory of Brazil with special emphasis on the state of Santa Catarina, and an inventory for Tanzania. [ABSTRACT FROM AUTHOR]

Abstract: Estimation of large area forest attributes, such as area of forest cover, from remote sensing-based maps is challenging because of image processing, logistical, and data acquisition constraints. In addition, techniques for estimating and compensating for misclassification and estimating uncertainty are often unfamiliar. Forest area for the state of Santa Catarina in southern Brazil was estimated from each of four satellite image-based land cover maps, and an independent estimate was obtained using observations of forest/non-forest for more than 1000 points assessed as part of the Santa Catarina Forest and Floristic Inventory. The latter data were also used as an accuracy assessment sample for evaluating the four maps. The map analyses consisted of identifying classification errors, constructing error matrices, calculating associated accuracy measures, estimating bias, and constructing 95% confidence intervals for proportion forest estimates using a model-assisted regression estimator. Overall accuracies for the maps ranged from 0.876 to 0.929. The standard errors of the estimates were all smaller than the standard error of the simple random sampling estimate by factors ranging from approximately1.23 to approximately 1.69. The model-assisted regression estimator lends itself to easy implementation for adjusting for estimated classification bias and for constructing confidence intervals. [Copyright &y& Elsevier]

Abstract: Estimates of growing stock volume are reported by the national forest inventories (NFI) of most countries and may serve as the basis for aboveground biomass and carbon estimates as required by an increasing number of international agreements. The probability-based (design-based) statistical estimators traditionally used by NFIs to calculate estimates are generally unbiased and entail only limited computational complexity. However, these estimators often do not produce sufficiently precise estimates for areas with small sample sizes. Model-based estimators may overcome this disadvantage, but they also may be biased and estimation of variances may be computationally intensive. For a minor region within Hedmark County, Norway, the study objective was to compare estimates of mean forest growing stock volume per unit area obtained using probability- and model-based estimators. Three of the estimators rely to varying degrees on maps that were constructed using a nonlinear logistic regression model, forest inventory data, and lidar data. For model-based estimators, methods for evaluating quality of fit of the models and reducing the computational intensity were also investigated. Three conclusions were drawn: the logistic regression model exhibited no serious lack of fit to the data; estimators enhanced using maps produced greater precision than estimates based on only the plot observations; and third, model-based synthetic estimators benefit from sample sizes for larger areas when applied to smaller subsets of the larger areas. [Copyright &y& Elsevier]

Abstract: National forest inventories report estimates of parameters related to forest area and growing stock volume for geographic areas ranging in size from municipalities to entire countries. Landsat imagery has been shown to be a source of auxiliary information that can be used with stratified estimation to increase the precision of estimates, although the increase is greater for estimates of forest area than for estimates of growing stock volume. The objective of the study was to assess the utility of lidar-based stratifications for increasing the precision of mean proportion forest area and mean growing stock volume per unit area. Stratifications based on nonlinear logistic regression model predictions of volume obtained from lidar data reduced variances of mean growing stock volume estimates by factors as great as 3.2 and variances of mean proportion forest area estimates by factors as great as 1.5. [Copyright &y& Elsevier]

Abstract: Statistical inference requires expression of an estimate in probabilistic terms, usually in the form of a confidence interval. An approach to constructing confidence intervals for remote sensing-based estimates of net deforestation is illustrated. The approach is based on post-classification methods using two independent forest/non-forest classifications because sufficient numbers of observations of forest/non-forest change were not available for direct classification. Further, the approach uses a model-assisted estimator with information from a traditional error matrix for the forest/non-forest classifications to compensate for bias as the result of classification errors and to estimate variances. Classifications were obtained using a logistic regression model, forest inventory data, and two dates of Landsat imagery, although the approach to inference can be used with multiple classification approaches. For the study area in northeastern Minnesota, USA, overall pixel-level accuracies for the year 2002 and 2007 forest/non-forest classifications were 0.85–0.88, and estimates of proportion net deforestation for the 2002–2007 interval were less in absolute value than 0.015. However, standard errors for the remote sensing-based estimates of net deforestation were on the order of 0.02–0.04, meaning that the estimates were not statistically significantly different from zero. Particular attention is directed to the potentially severe sample size and classification accuracy requirements necessary for estimates of net deforestation to be detected as statistically significantly different from zero. [Copyright &y& Elsevier]

Abstract: Nearest neighbors techniques have been shown to be useful for estimating forest attributes, particularly when used with forest inventory and satellite image data. Published reports of positive results have been truly international in scope. However, for these techniques to be more useful, they must be able to contribute to scientific inference which, for sample-based methods, requires estimates of uncertainty in the form of variances or standard errors. Several parametric approaches to estimating uncertainty for nearest neighbors techniques have been proposed, but they are complex and computationally intensive. For this study, two resampling estimators, the bootstrap and the jackknife, were investigated and compared to a parametric estimator for estimating uncertainty using the k-Nearest Neighbors (k-NN) technique with forest inventory and Landsat data from Finland, Italy, and the USA. The technical objectives of the study were threefold: (1) to evaluate the assumptions underlying a parametric approach to estimating k-NN variances; (2) to assess the utility of the bootstrap and jackknife methods with respect to the quality of variance estimates, ease of implementation, and computational intensity; and (3) to investigate adaptation of resampling methods to accommodate cluster sampling. The general conclusions were that support was provided for the assumptions underlying the parametric approach, the parametric and resampling estimators produced comparable variance estimates, care must be taken to ensure that bootstrap resampling mimics the original sampling, and the bootstrap procedure is a viable approach to variance estimation for nearest neighbor techniques that use very small numbers of neighbors to calculate predictions. [Copyright &y& Elsevier]

Abstract: The scientific method has been characterized as having two distinct components, Discovery and Justification. Discovery emphasizes ideas and creativity, focuses on conceiving hypotheses and constructing models, and is generally regarded as lacking a formal logic. Justification begins with the hypotheses and models and ends with a valid scientific inference. Unlike Discovery, Justification has a formal logic whose rules must be rigorously followed to produce valid scientific inferences. In particular, when inferences are based on sample data, the rules of the logic of Justification require assessments of bias and precision. Thus, satellite image-based maps that lack such assessments for parameters of populations depicted by the maps may be of little utility for scientific inference; essentially, they may be just pretty pictures. Probability- and model-based approaches are explained, illustrated, and compared for producing inferences for population parameters using a map depicting three land cover classes: non-forest, coniferous forest, and deciduous forest. The maps were constructed using forest inventory data and Landsat imagery. Although a multinomial logistic regression model was used to classify the imagery, the methods for assessing bias and precision can be used with any classification method. For probability-based approaches, the difference estimator was used, and for model-based inference, a bootstrap approach was used. [ABSTRACT FROM AUTHOR]

Abstract: Satellite image-based maps of forest attributes are of considerable interest and are used for multiple purposes such as international reporting by countries that have no national forest inventory and small area estimation for all countries. Construction of the maps typically entails, in part, rectifying the satellite images to a geographic coordinate system, observing ground plots whose coordinates are obtained from Global Positioning System (GPS) receivers that are calibrated to the same geographic coordinate system, and then matching ground plots to image pixels containing the centers of the ground plots. Errors in rectification and GPS coordinates cause observations of ground attributes to be associated with spectral values of incorrect pixels which, in turn, introduces classification errors into the resulting maps. The most important finding of the study is that for common magnitudes of rectification and GPS errors, as many as half the ground plots may be assigned to incorrect pixels. The effects on areal estimates obtained by aggregating class predictions for individual pixels are deviation of the estimates from their true values, erroneous confidence intervals, and incorrect inferences. Results are reported in detail for both probability-based (design-based) and model-based approaches to inference for proportion forest area using maps constructed from Landsat imagery, forest inventory plot observations and a logistic regression model. [Copyright &y& Elsevier]

Abstract: Estimates of forest area are among the most common and useful information provided by national forest inventories. The estimates are used for local and national purposes and for reporting to international agreements such as the Montréal Process, the Ministerial Conference on the Protection of Forests in Europe, and the Kyoto Protocol. The estimates are usually based on sample plot data and are calculated using probability-based estimators. These estimators are familiar, generally unbiased, and entail only limited computational complexity, but they do not produce the maps that users are increasingly requesting, and they generally do not produce sufficiently precise estimates for small areas. Model-based estimators overcome these disadvantages, but they may be biased and estimation of variances may be computationally intensive. The study objective was to compare probability- and model-based estimators of mean proportion forest using maps based on a logistic regression model, forest inventory data, and Landsat imagery. For model-based estimators, methods for evaluating bias and reducing the computational intensity were also investigated. Four conclusions were drawn: the logistic regression model exhibited no serious lack of fit to the data; all the estimators produced comparable estimates for mean proportion forest, except for small areas; probability-based inferences enhanced using maps produced increased precision; and the computational intensity associated with estimating variances for model-based estimators can be greatly reduced with no detrimental effects. [Copyright &y& Elsevier]

New model-based estimators of the uncertainty of pixel-level and areal k-nearest neighbour (k nn) predictions of attribute Y from remotely-sensed ancillary data X are presented. Non-parametric functions predict Y from scalar ‘Single Index Model’ transformations of X . Variance functions generated estimates of the variance of Y. Three case studies, with data from the Forest Inventory and Analysis program of the U.S. Forest Service, the Finnish National Forest Inventory, and Landsat ETM+ ancillary data, demonstrate applications of the proposed estimators. Nearly unbiased k nn predictions of three forest attributes were obtained. Estimates of mean square error indicate that k nn is an attractive technique for integrating remotely-sensed and ground data for the provision of forest attribute maps and areal predictions. [Copyright &y& Elsevier]

Nearest neighbors techniques have been shown to be useful for predicting multiple forest attributes from forest inventory and Landsat satellite image data. However, in regions lacking good digital land cover information, nearest neighbors selected to predict continuous variables such as tree volume must be selected without regard to relevant categorical variables such as forest/non-forest. The result is that non-zero volume predictions may be obtained for pixels predicted to be non-forest, and volume predictions for pixels predicted to be forest may be erroneously small due to non-forest nearest neighbors. For users who wish to circumvent this discrepancy, a two-step algorithm is proposed in which the class of a relevant categorical variable such as land cover is predicted in the first step, and continuous variables such as volume are predicted in the second step subject to the constraint that all nearest neighbors must come from the predicted class of the categorical variable. Nearest neighbors, multinomial logistic regression, and discriminant analysis techniques were investigated for use in the first step. The results were generally similar for the three techniques, although the multinomial logistic regression technique was slightly superior. The k-Nearest Neighbors technique was used in the second step because many continuous forest inventory variables do not satisfy the distributional assumptions necessary for parametric multivariate techniques. The results for six 15-km×15-km areas of interest in northern Minnesota, USA, indicate that areal estimates of tree volume, basal area, and density obtained from pixel predictions are comparable to plot-based estimates and estimates by conifer and deciduous classes are also comparable to plot-based estimates. When a mixed conifer/deciduous class was included, predictions for the mixed and deciduous class were confused. [Copyright &y& Elsevier]

Nearest neighbors techniques are non-parametric approaches to multivariate prediction that are useful for predicting both continuous and categorical forest attribute variables. Although some assumptions underlying nearest neighbor techniques are common to other prediction techniques such as regression, other assumptions are unique to nearest neighbor techniques. Graphical diagnostic tools are proposed to evaluate the assumptions and to address issues of bias, homoscedasticity, influential observations, outliers, and extrapolations. The tools are illustrated using results obtained from applying the k-Nearest Neighbors technique with Landsat imagery and forest inventory ground observations. [Copyright &y& Elsevier]

Abstract: Strategic forest inventory programs produce forest resource estimates for large areas such as states and provinces using data collected for a large number of variables on a relatively sparse array of field plots. Management inventories produce stand-level estimates to guide management decisions using data obtained with sampling intensities much greater than for strategic inventories. The costs associated with these greater sampling intensities have motivated investigations of alternatives to traditional sample-based management inventories. This study focused on a relatively inexpensive alternative to management inventories that uses strategic forest inventory plot data, Landsat Thematic Mapper (TM) satellite imagery, and the k-Nearest Neighbors (k-NN) technique. The approach entailed constructing stem density and basal area per unit area maps from which stand-level means were estimated as averages of k-NN pixel predictions. The study included investigations of the benefits of selecting optimal combinations of k-NN feature space variables derived from the TM imagery and the benefits of modifying the k-NN technique to eliminate spurious nearest neighbors. For both the stem density and basal area per unit area training data, the selection of optimal feature space covariates produced less than 1.5% improvement in root mean square error relative to using all covariates. The k-NN modification improved the sum of mean squared deviations for stand-level stem density and basal area per unit area estimates by 7–20% depending on the k-NN feature space covariates. For the best combination of feature space covariates, estimates of stand-level means were within confidence intervals for validation estimates for 11 of 12 stands for stem density and for 10 of 12 stands for basal area per unit area. [Copyright &y& Elsevier]

In this study, we explore the utility of data structures that facilitate efficient nearest neighbor searches for application in multi-source forest attribute prediction. Our trials suggest that the kd-tree in combination with exact search algorithms can greatly reduce nearest neighbor search time. Further, given our trial data, we found that enormous gain in search time efficiency, afforded by approximate nearest neighbor search algorithms, does not result in compromised kNN prediction. We conclude that by using the kd-tree, or similar data structure, and efficient exact or approximate search algorithms, the kNN method, and variants, are useful tools for mapping large geographic areas at a fine spatial resolution. [Copyright &y& Elsevier]

Forest structural diversity was estimated for an ecological province in the north-central region of the United States of America using data for nearly 350 000 trees observed on >12 000 forest inventory plots. Each plot was 672 m2 in area, and the sampling intensity was approximately 1 plot/2400 ha. Two indices were used for each of two commonly and accurately measured inventory variables: species count and the Shannon index for tree species and standard deviation and the Shannon index for tree diameter. The primary results of the study were fourfold: (i) ranges of spatial correlation for diversity indices were small, on the order of 5–10 km, (ii) high proportions of provincewide diversity were realized for circular areas with radii as small as 15 km, (iii) diversity for both species and diameter exhibited strong northwest to southeast spatial patterns, and (iv) plot-level α diameter diversity was highly correlated with mean plot-level tree diameter. La diversité structurale de la forêt a été estimée dans une province écologique du centre-nord des tats-Unis d’Amérique en utilisant les données de près de 350 000 arbres étudiés dans plus de 12 000 placettes d’inventaire forestier. Chaque placette couvrait une superficie de 672 m2 et l’intensité d’échantillonnage était approximativement d’une placette par 2 400 ha. Deux indices ont été utilisés pour chacune des deux variables d’inventaire communément et précisément mesurées : le nombre d’espèces et l’indice de Shannon pour l’espèce d’arbre, et l’écart-type et l’indice de Shannon pour le diamètre des arbres. Quatre résultats importants peuvent être tirés de cette étude : (i) l’étendue de la corrélation spatiale des indices de diversité était faible, de l’ordre de 5 à 10 km, (ii) une proportion élevée de la diversité à l’échelle de la province a été calculée dans des surfaces circulaires dont le rayon est aussi petit que 15 km, (iii) la diversité en espèces et en diamètres avait une structure spatiale nettement définie du nord-ouest vers le sud-est et (iv) la diversité en diamètres α à l’échelle de la placette était fortement corrélée avec le diamètre moyen des arbres à l’échelle de la placette. [ABSTRACT FROM AUTHOR]

The k-Nearest Neighbor (k-NN) technique has become extremely popular for a variety of forest inventory mapping and estimation applications. Much of this popularity may be attributed to the non-parametric, multivariate features of the technique, its intuitiveness, and its ease of use. When used with satellite imagery and forest inventory plot data, the technique has been shown to produce useful estimates of many forest attributes including forest/non-forest, volume, and basal area. However, variance estimators for quantifying the uncertainty of means or sums of k-NN pixel-level predictions for areas of interest (AOI) consisting of multiple pixels have not been reported. The primary objectives of the study were to derive variance estimators for AOI estimates obtained from k-NN predictions and to compare precision estimates resulting from different approaches to k-NN prediction and different interpretations of those predictions. The approaches were illustrated by estimating proportion forest area, tree volume per unit area, tree basal area per unit area, and tree density per unit area for 10-km AOIs. Estimates obtained using k-NN approaches and traditional inventory approaches were compared and found to be similar. Further, variance estimates based on different interpretations of k-NN predictions were similar. The results facilitate small area estimation and simultaneous and consistent mapping and estimation of multiple forest attributes. [Copyright &y& Elsevier]

National forest inventory programs are tasked to produce timely and accurate estimates for a wide range of forest resource variables for a variety of users and applications. Time, cost, and precision constraints cause these programs to seek technological innovations that contribute to measurement and estimation efficiencies and that facilitate the production and distribution of an increasing array of inventory data, estimates, and derived products. Many of the recent innovations have involved remotely sensed data and related statistical estimation techniques. Current applications of remote sensing in support of national forest inventories are reviewed for three areas: (1) observation or measurement, meaning using remotely sensed data in lieu of field observations or measurements; (2) estimation, meaning calculation of traditional inventory areal estimates such as forest area or volume per unit area; and (3) mapping. Future applications focus on two areas: augmenting field measurements with remotely sensed data obtained from lidar sensors and Internet accessible map-based estimation. [Copyright &y& Elsevier]