Description: This study used two different approaches to model diameter distributions on data from 201 field plots in a boreal conifer forest in south eastern Norway using airborne laser scanning. These two methods were a non-parametric most similar neighbour (MSN) approach and a parametric seemingly unrelated regression (SUR) approach to predict diameter percentiles, and their accuracies were compared by validation with an independent dataset. Based on calculated differences between predicted and observed number of stems on the entire validation dataset, we found that SUR gave unbiased results and that MSN slightly underestimated total number of stems. However, both methods overpredicted the number of stems per hectare in the range of 15.6–61.5 stems in the smallest diameter classes (between 4 and 12 cm). If the predicted diameter distributions were converted into basal area per hectare ( G ), both methods gave unbiased results. The average difference for G was 1.9 per cent of the observed value for the MSN approach. The corresponding number for the SUR model was 12.4 per cent. Neither of these differences were statistically significant ( P 〉 0.05). We concluded that the even though both methods overall yielded accurate results, the MSN approach was more reliable in terms of predicting the number of large trees.

Description: Estimation of wood volume and biomass is an important assignment of any National Forest Inventory. However, the estimation process is often expensive, laborious and sometimes imprecise because of small sample sizes relative to population variability. Remote sensing techniques are an option to assist in surveying large areas by providing data that can be related to the forest attribute of interest through mathematical models of relationships. Light Detection and Ranging (LiDAR) is a technology that can provide data that are closely related to forest wood volume and biomass. With these data, linear regression is often used to estimate forest attributes. If the relationship provides evidence of nonlinearity, a transformation in the variables can be considered. However, modern computation allows fitting nonlinear regression models without transformations of the variables. Nonlinear least squares (NLS) techniques also give more freedom to assure satisfaction of natural conditions such as non-negativity and/or lower and upper asymptotes. Like any estimation technique, NLS is subject to overfitting when using a large number of predictor variables. Because NLS is more computationally intensive than linear regression, stepwise selection techniques may require considerable programming effort. We compared three methods to select predictor variables for nonlinear models of relationships between forest attributes and LiDAR metrics, two of them based on genetic algorithms (GAs) and one based on random forest (RM). GAs were implemented to optimize a cost function that yields root mean square error or the Akaike Information Criterion (AIC), while RM was based on variable importance in decision trees. A model with the predictor variable most correlated with the response variable was also considered. We compared the results of overall estimation for two datasets using the model-assisted, generalized regression estimator and concluded that the combination of GAs and AIC was the most efficient and stable procedure for selection of variables. We attribute this result to the penalty that AIC applies to models with large numbers of variables, which leads to a more efficient model with a minimum loss of information.

Description: Airborne laser scanning data and corresponding field data were acquired from boreal forests in Norway and Sweden, coniferous and broadleaved forests in Germany and tropical pulpwood plantations in Brazil. Treetop positions were extracted using six different algorithms developed in Finland, Germany, Norway and Sweden, and the accuracy of tree detection and height estimation was assessed. Furthermore, the weaknesses and strengths of the methods under different types of forest were analyzed. The results showed that forest structure strongly affected the performance of all algorithms. Particularly, the success of tree detection was found to be dependent on tree density and clustering. The differences in performance between methods were more pronounced for tree detection than for height estimation. The algorithms showed a slightly better performance in the conditions for which they were developed, while some could be adapted by different parameterization according to training with local data. The results of this study may help guiding the choice of method under different forest types and may be of great value for future refinement of the single-tree detection algorithms.

Description: The method of predicting an unknown target probability distribution via a Gram–Charlier A-series expansion (GCAE) of a user-defined base probability function and cumulants of a known distribution of an auxiliary variable is demonstrated in two applications. Both applications concern predictions of the distribution of tree stem diameters with cumulants of airborne laser scanning (ALS) canopy heights and an index of canopy density as predictors. All predictions were generated in a leave-one-out cross-validation scheme, and statistical inference was based on 100 stochastic predictions of the tree sizes in 308 plots of 400 m 2 . The mean and variance of GCAE-predicted distributions were rarely significantly different from actual values, yet between 19 and 32% of the predicted GCAE distributions were significantly different from the actual distribution. The rejection rate with predictions generated from a simpler DECILE method was, on average, 2.5% lower. GCAE is still recommended due to its potential usefulness. Cumulants of ALS canopy heights are independent of plot area and effective for area-based least-squares predictions of forest inventory variables.

Description: Inferences for forest-related spatial problems can be enhanced using remote sensing-based maps constructed with nearest neighbours techniques. The non-parametric k -nearest neighbours ( k -NN) technique calculates predictions as linear combinations of observations for sample units that are nearest in a space of auxiliary variables to population units for which predictions are desired. Implementations of k -NN require four choices: a distance or similarity metric, the specific auxiliary variables to be used with the metric, the number of nearest neighbours, and a scheme for weighting the nearest neighbours. The study objective was to compare optimized k -NN configurations with respect to confidence intervals for airborne laser scanning-assisted estimates of mean volume or biomass per unit area for study areas in Norway, Italy, and the USA. Novel features of the study include a new neighbour weighting scheme, a statistically rigorous method for selecting feature variables, simultaneous optimization with respect to all four k -NN implementation choices and comparisons based on confidence intervals for population means. The primary conclusions were that optimization greatly increased the precision of estimates and that the results of optimization were similar for the k -NN configurations considered. Together, these two conclusions suggest that optimization itself is more important than the particular k -NN configuration that is optimized.

Description: Earth Observation data are uniquely positioned to estimate forest aboveground biomass density (AGBD) in accordance with the United Nations Framework Convention on Climate Change (UNFCCC) principles of 'transparency, accuracy, completeness, consistency and comparability'. However, the use of space-based AGBD maps for national-level reporting to the UNFCCC is nearly non-existent as of 2023, the end of the first global stocktake (GST). We conduct an evidence-based comparison of AGBD estimates from the NASA Global Ecosystem Dynamics Investigation and ESA Climate Change Initiative, describing differences between the products and National Forest Inventories (NFIs), and suggesting how science teams must align efforts to inform the next GST. Between the products, in the tropics, the largest differences in estimated AGBD are primarily in the Congolese lowlands and east/southeast Asia. Where NFI data were acquired (Peru, Mexico, Lao PDR and 30 regions of Spain), both products show strong correlation to NFI-estimated AGBD, with no systematic deviations. The AGBD-richest stratum of these, the Peruvian Amazon, is accurately estimated in both. These results are remarkably promising, and to support the operational use of AGB map products for policy reporting, we describe targeted ways to align products with Intergovernmental Panel on Climate Change (IPCC) guidelines. We recommend moving towards consistent statistical terminology, and aligning on a rigorous framework for uncertainty estimation, supported by the provision of open-science codes for large-area assessments that comprehensively report uncertainty. Further, we suggest the provision of objective and open-source guidance to integrate NFIs with multiple AGBD products, aiming to enhance the precision of national estimates. Finally, we describe and encourage the release of user-friendly product documentation, with tools that produce AGBD estimates directly applicable to the IPCC guideline methodologies. With these steps, space agencies can convey a comparable, reliable and consistent message on global biomass estimates to have actionable policy impact.