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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]

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]

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]

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]

A framework for estimating aboveground forest carbon stock (AFCS) is required for measurement, reporting, and verification (MRV) systems under the United Nations Collaborative Program on Reducing Emissions from Deforestation and Forest Degradation (REDD) in Developing Countries. Recently, methods for estimating the spatial distribution of AFCS using remotely sensed datasets and multiple prediction techniques have been found to be useful, particularly given the prohibitive costs of acquiring the necessary sample sizes for sufficiently precise pure field-based estimation of this variable. The objective of the study was to assess and compare the capabilities of airborne laser scanning (ALS) data, L-band radar data and UltraCam images in combination with four commonly used prediction techniques for estimating mean AFCS per unit area: multiple linear regression (MLR) and the nonparametric k-Nearest Neighbors (k-NN), support vector regression (SVR), and random forest (RF) algorithms. Our study area was a part of Hyrcanian deciduous forests in two managed and unmanaged stands at Shast Kalateh forest. We used a systematic sample consisting of 308 circular field plots of 0.1 ha located at the intersections of a 150 × 200 m grid with a random starting point and remote sensing-derived metrics as auxiliary data. We used 67% of the sample plots for training purposes and the remaining 33% for validation. Also, we used the model-assisted estimators to statistically rigorously estimate mean AFCS per unit area and its standard error (SE). Among the remotely sensed datasets, considered singly, the ALS data with R2⁎ = 0.34, rRMSE = 47.42% and relative efficiency (RE) = 1.51 produced the greatest accuracy and precision for AFCS estimation. RE can be interpreted as the factor by which the sample size for the pure field-based estimator would have to be increased to obtain the same precision as for the model-assisted estimator using auxiliary data. Among the remotely sensed datasets considered in combination, the ALS and PALSAR dataset with R2⁎ = 0.41, rRMSE = 44.80% and RE = 1.70 produced the greatest prediction accuracy and precision and increased the proportion of variability explained relative to ALS and PALSAR separately by 7% and 36%, respectively. Contrary to our expectation, the combination of PALSAR and UltraCam data decreased the precision of AFCS estimates. All the remotely sensed datasets, singly and in combination, with the most accurate prediction techniques for each combination produced estimates of AFCS that were within the 95% confidence interval for the field-based estimate. • ALS produced greater accuracy than PALSAR and UltraCam for AFCS estimation. • ALS and PALSAR in combination produced the greatest accuracy for AFCS estimation. • Nonparametric k-NN, SVR and RF were more accurate than multiple linear regression. • Remote sensing-assisted 95% confidence intervals included the field-based estimate. [ABSTRACT FROM AUTHOR]

Data assimilation (DA) has a broad category of mathematical procedures for updating and calibrating existing predictions or parameter estimates using new observations. Typical DA procedures such as the Kalman filter require that the observations of a variable of interest used in a forecast of this variable to be collected just prior to the updating procedure and that they continue to be collected over time, a requirement that is not always practical for forest inventory problems. Distinct from the Kalman filter, the best linear unbiased predictor (BLUP) circumvents this time constraint, because it can calibrate the predicted values of a variable of interest using observations from other variables correlated with this variable of interest. Remote sensing played a major role in this study by providing the latter observations. The objective of this study was threefold: (1) to propose and illustrate a DA calibration procedure that incorporates simultaneous predictions and BLUP to improve prediction accuracy; (2) to expand this procedure in the framework of model-based inference; and (3) to compare the inferential properties before and after DA calibration for multiple scenarios. Four major conclusions are relevant. First, the prediction accuracies for all variables of interest were consistently increased by 10%–74% after implementing the DA procedure. Second, the DA procedure supported simultaneous inference, and the precision of the simultaneously estimated population means for the variables of interest were increased by 55%–76% after implementing this procedure. Third, the parametric bootstrap procedures used to estimate the inferential precisions for this complex estimation problem were effective and converged rapidly. In addition, this DA calibration procedure is universally applicable for DA calibrations using other data sources such as airborne or terrestrial laser scanning and spectral data, given that cross-model correlations exist. Overall, the proposed procedure demonstrated considerable potential for better serving forest inventory with respect to both simultaneous inference and inferential precision. • We proposed a remote sensing-assisted model-based calibration procedure. • This procedure incorporated data assimilation and simultaneous inference. • Multiple forest attributes were simultaneously predicted, calibrated and estimated. • Remote sensing played a major role to provide observations for the calibration. • Considerable improvements in efficiency and estimation precision greater than 55%. [ABSTRACT FROM AUTHOR]

The boreal tree line is in many places expected to advance upwards into the mountains due to climate change. This study aimed to develop a general method for estimation of vegetation height change in general, and change in tree height more specifically, for small geographical domains utilizing bi-temporal airborne laser scanner (ALS) data. The domains subject to estimation may subsequently be used to monitor vegetation and tree height change with detailed temporal and geographical resolutions. A method was developed with particular focus on statistically rigorous estimators of uncertainty for change estimates. The method employed model-dependent statistical inference. The method was demonstrated in a 12 ha study site in a boreal–alpine tree line in southeastern Norway, in which 316 trees were measured on the ground in 2006 and 2012 and ALS data were acquired in two temporally coincident campaigns. The trees ranged from 0.11 m to 5.20 m in height. Average growth in height was 0.19 m. Regression models were used to predict and estimate change. By following the area-based approach, predictions were produced for every individual 2 m2 population element that tessellated the study area. Two demonstrations of the method are provided in which separate height change estimates were calculated for domains of size 1.5 ha or greater. Differences in height change estimates among such small domains illustrate how change patterns may vary over the landscape. Model-dependent mean square error estimates for the height change estimators that accounted for (1) model parameter uncertainty, (2) residual variance, and (3) residual covariance are provided. Findings suggested that the two latter sources of uncertainty could be ignored in the uncertainty analysis. The proposed estimators are likely to work well for estimation of differences in height change along a gradient of small monitoring units, like the 1.5 ha cells used for demonstration purposes, and thus may potentially be used to monitor tree line migration over time. [ABSTRACT FROM AUTHOR]

The effects of field plot configurations on the uncertainties of plot-level forest resource estimates were analyzed using airborne laser scanner data, aerial photographs and field measurements. The aim was to select a field sample plot configuration that can be used for both large area and management inventories. Error estimates were evaluated at the plot level using six different training plot configurations. Additionally, separate plots with two different sizes were used for evaluation. Stem volume and five other forest resource characteristics were considered. The field measurement costs of the different plot configurations were also studied. RMSEs and mean deviations for airborne laser scanning ALS-assisted estimates were practically the same for the fixed radius plot, the two concentric plots and the angle count plot with a basal area factor ofq= 1 for all three evaluation plot sizes. Angle count plots with basal area factors ofq= 1.5 and 2 increased the RMSEs. For the former plot configurations, the RMSEs for the ALS-assisted estimates could be attributed to inaccuracy in the predicted relationships between the field data and ALS data, not to the training plot configuration. Tree measurements and costs can, therefore, be reduced from those of the Finnish management inventories without increasing RMSEs. [ABSTRACT FROM PUBLISHER]

The conservation of biological diversity is recognized as a fundamental component of sustainable development, and forests contribute greatly to its preservation. Structural complexity increases the potential biological diversity of a forest by creating multiple niches that can host a wide variety of species. To facilitate greater understanding of the contributions of forest structure to forest biological diversity, we modeled relationships between 14 forest structure variables and airborne laser scanning (ALS) data for two Italian study areas representing two common Mediterranean forests, conifer plantations and coppice oaks subjected to irregular intervals of unplanned and non-standard silvicultural interventions. The objectives were twofold: (i) to compare model prediction accuracies when using two types of ALS metrics, echo-based metrics and canopy height model (CHM)-based metrics, and (ii) to construct inferences in the form of confidence intervals for large area structural complexity parameters. Our results showed that the effects of the two study areas on accuracies were greater than the effects of the two types of ALS metrics. In particular, accuracies were less for the more complex study area in terms of species composition and forest structure. However, accuracies achieved using the echo-based metrics were only slightly greater than when using the CHM-based metrics, thus demonstrating that both options yield reliable and comparable results. Accuracies were greatest for dominant height (Hd) (R 2 = 0.91; RMSE% = 8.2%) and mean height weighted by basal area (R 2 = 0.83; RMSE% = 10.5%) when using the echo-based metrics, 99th percentile of the echo height distribution and interquantile distance. For the forested area, the generalized regression (GREG) estimate of mean Hd was similar to the simple random sampling (SRS) estimate, 15.5 m for GREG and 16.2 m SRS. Further, the GREG estimator with standard error of 0.10 m was considerable more precise than the SRS estimator with standard error of 0.69 m. [ABSTRACT FROM AUTHOR]

Remotely sensed data from airborne laser scanning (ALS) and interferometric synthetic aperture radar (InSAR) can greatly improve the precision of estimates of forest resource parameters such as mean biomass and biomass change per unit area. Field plots are typically used to construct models that relate the variable of interest to explanatory variables derived from the remotely sensed data. The models may then be used in combination with the field plots to provide estimates for a geographical area of interest with corresponding estimates of precision using model-assisted estimators. Previous studies have shown that field plot sizes found suitable for pure field surveys may be sub-optimal for use in combination with remotely sensed data. Plot boundary effects, co-registration problems, and misalignment problems favor larger plots because the relative impact of these effects on the models of relationships may decline by increasing plot size. In a case study in a small boreal forest area in southeastern Norway (852.6 ha) a probability sample of 145 field plots was measured twice over an 11 year period (1998/1999 and 2010). For each plot, field measurements were recorded for two plot sizes (200 m 2 and 300/400 m 2 ). Corresponding multitemporal ALS (1999 and 2010) and InSAR data (2000 and 2011) were also available. Biomass for each of the two measurement dates as well as biomass change were modeled for all plot sizes separately using explanatory variables from the ALS and InSAR data, respectively. Biomass change was estimated using model-assisted estimators. Separate estimates were obtained for different methods for estimation of change, like the indirect method (difference between predictions of biomass for each of the two measurement dates) and the direct method (direct prediction of change). Relative efficiency (RE) was calculated by dividing the variance obtained for a pure field-based change estimate by the variance of a corresponding estimate using the model-assisted approach. For ALS, the RE values ranged between 7.5 and 15.0, indicating that approximately 7.5–15.0 as many field plots would be required for a pure field-based estimate to provide the same precision as an ALS-assisted estimate. For InSAR, RE ranged between 1.8 and 2.5. The direct estimation method showed greater REs than the indirect method for both remote sensing technologies. There was clearly a trend of improved RE of the model-assisted estimates by increasing plot size. For ALS and the direct estimation method RE increased from 9.8 for 200 m 2 plots to 15.0 for 400 m 2 plots. Similar trends of increasing RE with plot size were observed for InSAR. ALS showed on average 3.2–6.0 times greater RE values than InSAR. Because remote sensing can contribute to improved precision of estimates, sample plot size is a prominent design issue in future sample surveys which should be considered with due attention to the great benefits that can be achieved when using remote sensing if the plot size reflects the specific challenges arising from use of remote sensing in the estimation. That is especially the case in the tropics where field resources may be scarce and inaccessibility and poor infrastructure hamper field work. [ABSTRACT FROM AUTHOR]

The need for timely, spatially, and thematically accurate information regarding forests is increasing because of the key role of forests in the global carbon balance and sustainable social, economic, ecological, and cultural development. While an increasing number of countries in the world already are conducting statistically sound forest inventories, a few for 100 years, inventories in other countries are still lacking, which makes the global information about forest statistics inaccurate. This implies that remote sensing-based approaches are vulnerable to misclassification and inaccurate estimation of forest parameters and changes, such as the recognition of temporarily unstocked forest areas, forest degradation, and species composition, as well as in strictly following the globally adopted definitions. [Extracted from the article]