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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]

Abstract Data uncertainty due to spatial gaps and heterogeneity is a fundamental problem in conservation and environmental planning. Thus, investigation of issues related to data uncertainty contributes to more efficient conservation plans. We evaluated the uncertainty of data related to forest diversity descriptors using a diffusion-based cartogram approach that visually displays how data information change in function with respect to degree of uncertainty. We used ground vegetation data for 3093 plots collected as part of the BioSoil project through the ICP Forests Level I network and stored in the LI-BioDiv database. For each plot, we assigned an uncertainty value based on the survey season and the mean monthly temperature for the survey period. The density-equalizing map or cartogram highlights that data collected in Spain, the United Kingdom and the German federal states of Berlin and Brandenburg have smaller values of species richness corresponding to larger values of uncertainty. We found that an awareness of the negative relationship between the survey period and species richness can lead to improved data handling and analysis. We demonstrated that cartograms are efficient tools for evaluating and managing uncertainty and can strengthen the results of data analysis by providing alternative perspectives and interpretations of spatial phenomena. Highlights • The assessment of data uncertainty is a crucial issue in vegetation science and is needed to avoid biased ecological inference • Density-equalizing maps are an increasingly used way to represent different aspects of spatial variation of several variables • We provide a solution to handle and compare data which contain uncertainty by a diffusion-based method • The cartograms show a geographic relationship between attributes and to highlight the effect of uncertainty on data pattern • Once highlighted data limitation, we provide a way for understanding how different survey may influence data analysis and statistical inference [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]

National forest inventories have a long history of using remotely sensed auxiliary information to enhance estimation of forest parameters. For this purpose, aerial photography and satellite spectral data have been shown to be effective as sources of information in support of stratified estimators. These spectral-based stratifications are much more effective for reducing variances for forest area-related parameters than for parameters related to continuous attributes such as volume and biomass. For variables related to the latter attributes, stratified estimators using airborne laser scanning auxiliary data are much more effective, but are less effective than model-assisted estimators using the same auxiliary data. For inventory applications, however, stratified estimators using the same stratification for all response variables are naturally multivariate, whereas model-assisted estimators are not. A consequence is that multiple, univariate applications of model-assisted estimators cannot ensure compatibility among estimates of inventory parameters related to variables such as forest area, growing stock volume, and tree density. The objectives of the study were twofold: (1) to optimize a multivariate, k-NN approach for simultaneously predicting multiple forest inventory variables; and (2) to compare multivariate model-assisted generalized regression estimators using optimized k-NN predictions to post-stratified estimators with respect to inferences in the form of confidence intervals for multiple forest inventory parameters. The analyses included use of airborne laser scanning data as auxiliary information and the multivariate k-NN technique for prediction in support of the model-assisted estimators. The study area was in north central Minnesota in the USA and is characterized by both lowland and upland forest types interspersed with wetlands and lakes. The first primary result was that the optimized k-NN technique in combination with a model-assisted estimator produced compatible multivariate estimates of population means for six inventory parameters. Second, variances for the multivariate model-assisted estimators were smaller by 23%–35% than variances for a post-stratified estimator. These results warrant serious consideration of this approach for operational implementation by national forest inventories. [ABSTRACT FROM AUTHOR]

International organizations increasingly require estimates of forest parameters to monitor the state of and changes in forest resources, the sustainability of forest practices and the role of forests in the carbon cycle. Most countries rely on data from their national forest inventories (NFI) to produce these estimates. However, because NFI survey years may not match the required reporting years, techniques for updating NFI-based estimates are necessary. The main aim was to develop an unbiased method to update NFI estimates of mean growing stock volume (m 3 /ha) using models to predict annual plot-level volume change, and to estimate the associated uncertainties. Because the final large area volume estimates were based on plot-level model predictions rather than field observations, hybrid inference was necessary to accommodate both model prediction uncertainty and sampling variation. Specific objectives were to compare modelling approaches, to assess the utility of Landsat data for increasing model prediction accuracy, to select the most accurate method, and to compare model-based and design-based uncertainty components. For four monospecific forest types, data from the 2nd and 3rd Spanish NFI surveys together with site variables and Landsat images were used to construct models to predict NFI information for the year of the 4th NFI survey. Data from the 3rd and 4th surveys were used to assess the accuracy of the model predictions at both plot-level and large area spatial scales. The most accurate method used a set of three models: one to predict the probability of volume removals, one to predict the amount of removed volume, and one to predict gross annual volume. Incorporation of Landsat-based variables in the models increased prediction accuracy. Differences between large area estimates based on plot-level field observations for the 4th NFI survey and estimates based on the model predictions were minimal for all four forest types. Further, the standard errors of the estimates based on the model predictions were only slightly greater than standard errors based on the field observations. Thus, model predictions of plot-level growing stock volume based on field and satellite image data as auxiliary information can be used to update large area NFI estimates for reporting years for which spectral data are available but field observations are not. Finally, variances of means are under-estimated unless hybrid inferential methods are used to incorporate both model prediction uncertainty and sampling variation. For the two forest types for which the two sources of uncertainty were of the same order of magnitude, the under-estimation was non-negligible. [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]

Carbon accounting is at the heart of efforts to mitigate the effects of climate change. One approach for estimating population parameters for live tree stem carbon entails three primary steps: (1) construction of an individual tree, allometric carbon model, (2) application of the model to tree-level data for a probability sample of plots, and (3) use of a probability-based (design-based) estimator of mean carbon per unit area for a population of interest. Compliance with the IPCC good practice guidance requires satisfaction of two criteria, one related to minimizing bias and one related to minimizing uncertainty. For this carbon estimation procedure, the portion of uncertainty attributed to the variance of the probability-based estimator of the population mean using the plot-level predictions is usually correctly estimated, but the portion attributed to the variance of the allometric model estimator is usually ignored. The result is that the total variance of the population mean estimator cannot be asserted to comply with the IPCC good practice criteria because not only is it not minimized, it is not even correctly estimated. Within the framework of what is coming to be characterized as hybrid inference, model-based inferential methods were used to estimate the variance of the tree-level allometric model estimator which was then propagated through to the variance of the probability-based estimator of mean carbon per unit area. This combined estimator, consisting of a model-based estimator used to predict a variable for a probability sample of a population followed by a probability-estimator of the population total or mean using the sample predictions, is characterized as a hybrid estimator. For this study, two probability-based estimators of the mean were considered, simple random sampling estimators and model-assisted regression estimators that used airborne laser scanning (ALS) data as auxiliary information. The variance of the allometric model estimator incorporated variances of distributions of diameter and height measurement errors, covariances of model parameter estimators, model residual variance, and variances of distributions of wood densities and carbon content proportions. The novel features of the study included the hybrid inferential framework, consideration of six sources of uncertainty including the variances of distributions of wood densities and carbon content proportions, use of ALS data with model-assisted regression estimators of the population mean, and use of confidence intervals for the population mean as the basis for comparisons rather than intermediate products such as model prediction accuracy. The primary conclusions were that the variance of the allometric model estimator was negligible or marginally negligible relative to the variance of the probability estimator when using species-specific allometric models and simple random sampling estimators, but non-negligible when using species-specific models and model-assisted regression estimators and when using a non-specific model with either estimator. [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]

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]

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]

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]

For most national forest inventories, the variables of primary interest to users are forest area and growing stock volume. The precision of estimates of parameters related to these variables can be increased using remotely sensed auxiliary variables, often in combination with stratified estimators. However, acquisition and processing of large amounts of remotely sensed data can be costly and laborious, and stratified estimation requires construction of strata and satisfaction of within-stratum sample size constraints. An alternative to both challenges is to use an existing remote sensing-based, spatial product with the model-assisted estimators. The latter estimators use continuous auxiliary information directly rather than their aggregation into strata and are not subject to such severe sample size constraints. The objective of the study was to compare estimates of mean proportion forest area and mean growing stock volume per unit area obtained using both stratified and model assisted estimators with a remote sensing-based percent tree canopy cover map as auxiliary information. For a study area in Minnesota, USA, the primary conclusion was that estimates obtained with both sets of estimators were acceptably precise, but that the model-assisted estimators were easier to implement and facilitated aggregation of estimates from smaller sub-areas to estimates for larger 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]

• We tested the effectiveness of several weighting procedures in allometric models. • Some weighting procedures were more effective for accommodating heteroscedasticity. • Heteroscedasticity caused moderate differences in estimates over large forest areas. • Omitting height as predictor of biomass resulted in large differences of estimates. • Model prediction uncertainty had a substantial contribution to total uncertainty. Allometric models are commonly used to predict forest biomass. These models typically take nonlinear power-law forms that predict individual tree aboveground biomass (AGB) as functions of diameter at breast height (D) and/or tree height (H). Because the residual variance is in most cases heteroscedastic, accommodating the heteroscedasticity (i.e., heterogeneity of variance) becomes necessary when estimating model parameters. We tested several weighting procedures and a logarithmic transformation for nonlinear allometric biomass models. We further evaluated the effectiveness of these procedures with emphasis on how they affected estimates of mean AGB per hectare and their standard errors for large forest areas. Our results revealed that some weighting procedures were more effective for accommodating heteroscedasticity than others and that effectiveness was greater for single predictor models but less for models based on both D and H. Failing to effectively accommodate heteroscedasticity produced small to moderate differences in the estimates of mean AGB per hectare and their standard errors. However, these differences were greater between model forms (models based on D and H versus models based on D only), regardless of the weighting approach. Similar consequences were observed with respect to whether model prediction uncertainty was or was not included when estimating mean AGB per hectare and standard errors. When including model prediction uncertainty, the standard errors of the estimated means increased substantially, by 44–59%. Therefore, to avoid possible negative consequences on large-area biomass estimation, we recommend: (i) testing the effectiveness of a weighting procedure when accommodating heteroscedasticity in allometric biomass models, (ii) incorporating model prediction uncertainty in the total uncertainty estimate and (iii) including H as an additional predictor variable in allometric biomass models. [ABSTRACT FROM AUTHOR]

Highlights: [•] Comparison of approaches to compensate for nonresponse in the FIA program. [•] Nonresponse on private forest land varied by state: WI (3.4%), MN (6.1%), MI (10.4%). [•] More than 91% of nonresponse was due to denied access on private forest land. [•] Estimates from 20 of the 24 approaches were within one standard error of the baseline estimate. [•] Ignoring missing observations was the optimal approach across the study region. [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 become extremely popular, particularly for use with forest inventory data. With these techniques, a population unit prediction is calculated as a linear combination of observations for a selected number of population units in a sample that are most similar, or nearest, in a space of ancillary variables to the population unit requiring the prediction. Nearest neighbors techniques are appealing for multiple reasons: they can be used with categorical response variables for which the objective is classification and with continuous response variables for which the objective is prediction; they can be used for both univariate and multivariate prediction; they are non-parametric in the sense that no assumptions regarding the distributions of response or predictor variables are necessary; they are synthetic in the sense that they can readily use information external to the geographic area for which an estimate is sought; they are useful for map construction, small area estimation, and inference; and they can be used with a wide variety of data sets. Recent advances and emerging issues in nearest neighbors techniques are reviewed for four topic areas: (1) distance metrics, (2) optimization, (3) diagnostic tools, and (4) inference. The focus of the study is estimation of mean forest stem volume per unit area for small areas using a combination of forest inventory observations and Landsat Thematic Mapper (TM) imagery. However, the concepts and techniques are generally applicable for all nearest neighbors problems. [Copyright &y& Elsevier]

Abstract: Forest ecosystems are the largest terrestrial carbon sink on earth and their management has been recognized as a relatively cost-effective strategy for offsetting greenhouse gas emissions. Forest carbon stocks in the U.S. are estimated using data from the USDA Forest Service, Forest Inventory and Analysis (FIA) program. In an attempt to balance accuracy with consistency, the FIA program recently developed the component ratio method which utilizes regional volume models to replace the existing set of generalized allometric regression models used to estimate biomass and carbon stocks. This study describes the impact of the transition from the generalized allometric regression models to the component ratio method on the National Greenhouse Gas Inventory estimates by comparing estimates of carbon stocks from both approaches by common tree species and varying spatial scales (e.g., tree to national scale). Results for the 20 most abundant tree species in the 48 conterminous states of the U.S. suggest there is a significant difference in estimates of carbon stocks at the plot and national scales for the two estimation approaches. The component ratio method decreased estimates of national carbon stocks by an average of 16% for the species in the study. The observed reductions in carbon estimates can be attributed to incorporation of tree height as a predictor variable into species-specific volume models used to estimate tree biomass and carbon stocks. While the transition from the generalized allometric regression models to the component ratio method is procedural in nature, it may have important implications for national and global forest carbon sink estimates and the perception of the role forests play in mitigating the effects of atmospheric carbon dioxide. By combining regional accuracy with a nationally consistent approach, the component ratio method reflects a critical first step in aligning estimates of forest carbon stocks in the U.S.’s National Greenhouse Gas Inventory with estimates of tree volume in the FIA database. [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: Statistically-designed inventories and biodiversity monitoring programs are gaining relevance for biological conservation and natural resources management. Mandated periodic surveys provide unique opportunities to identify and satisfy natural resources management information needs. However, this is not an end in itself but rather is the beginning of a process that should lead to sound decision-making in biodiversity conservation. Forest inventories are currently evolving towards multipurpose resource surveys and are broadening their scope in several directions: (i) expansion of the target population to include non-traditional attributes such as trees outside the forest and urban forests; (ii) forest carbon pools and carbon sequestration estimation; (iii) assessment of forest health; and (iv) inclusion of additional variables such as biodiversity attributes that are not directly related to timber assessment and wood harvesting. There is an on-going debate regarding the role of forest inventories in biodiversity assessment and monitoring. This paper presents a review on the topic that aims at providing updated knowledge on the current contribution of forest inventories to the assessment and monitoring of forest biodiversity conditions on a large scale. Specific objectives are fourfold: (i) to highlight the types of forest biodiversity indicators that can be estimated from data collected in the framework of standard forest inventories and the implications of different sampling methods on the estimation of the indicators; (ii) to outline current possibilities for harmonized estimation of biodiversity indicators in Europe from National Forest Inventory data; (iii) to show the added value for forest biodiversity monitoring of framing biodiversity indicators into ecologically meaningful forest type units; and (iv) to examine the potential of forest inventory sample data for estimating landscape biodiversity metrics. [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]