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Airborne Laser Scanning (ALS) has implied a disruptive transformation of how data are gathered for forest management planning in Nordic countries. We show in this study that the accuracy of ALS pre...

Presence–absence sampling is an important method for monitoring state and change of both individual plant species and communities. With this method, only the presence or absence of the target species is recorded on plots and thus the method is straightforward to apply and less prone to surveyor judgement compared to other vegetation monitoring methods. However, in the basic setting, all plots must be equally large or otherwise it is unclear how data should be analysed. In this study, we propose and evaluate five different methods for estimating plant density based on presence–absence registrations from surveys with variable plot sizes. Using artificial plant population data as well as empirical data from the Swedish National Forest Inventory, we evaluated the performance of the proposed methods. The main analysis was conducted through sampling simulation in artificial populations, whereby bias and variance of density estimators for the different methods were quantified and compared. Both for state and change estimation of plant density, we found that the best method to handle variable plot size was to perform generalized least squares regression, using plot size as an independent variable. Methods where plots smaller than a certain threshold were excluded or their registrations recalculated were, however, almost as good. Using all registrations as if they were obtained from plots with the nominal plot size resulted in substantial bias. Our findings are important for plant population studies in a wide range of environmental monitoring programmes. In these programmes, plots are typically randomly laid out and may be located across boundaries between different land‐use or land‐cover classes, resulting in subplots of variable size. Such splitting of plots is common when large plots are used, for example, with the 100 m2 plots used in the Swedish National Forest Inventory. Our methods overcome problems to estimate plant density from presence–absence data observed in plots that vary in size.

Inventories of plant populations are fundamental in ecological research and monitoring, but such surveys are often prone to field assessment errors. Presence/absence (P/A) sampling may have advanta ...

Thin, hair-like lichens (Alectoria, Bryoria, Usnea) form conspicuous epiphyte communities across the boreal biome. These poikilohydric organisms provide important ecosystem functions and are useful indicators of global change. We analyse how environmental drivers influence changes in occurrence and length of these lichens on Norway spruce (Picea abies) over 10 years in managed forests in Sweden using data from >6000 trees. Alectoria and Usnea showed strong declines in southern-central regions, whereas Bryoria declined in northern regions. Overall, relative loss rates across the country ranged from 1.7% per year in Alectoria to 0.5% in Bryoria. These losses contrasted with increased length of Bryoria and Usnea in some regions. Occurrence trajectories (extinction, colonization, presence, absence) on remeasured trees correlated best with temperature, rain, nitrogen deposition, and stand age in multinomial logistic regression models. Our analysis strongly suggests that industrial forestry, in combination with nitrogen, is the main driver of lichen declines. Logging of forests with long continuity of tree cover, short rotation cycles, substrate limitation and low light in dense forests are harmful for lichens. Nitrogen deposition has decreased but is apparently still sufficiently high to prevent recovery. Warming correlated with occurrence trajectories of Alectoria and Bryoria, likely by altering hydration regimes and increasing respiration during autumn/winter. The large-scale lichen decline on an important host has cascading effects on biodiversity and function of boreal forest canopies. Forest management must apply a broad spectrum of methods, including uneven-aged continuous cover forestry and retention of large patches, to secure the ecosystem functions of these important canopy components under future climates. Our findings highlight interactions among drivers of lichen decline (forestry, nitrogen, climate), functional traits (dispersal, lichen colour, sensitivity to nitrogen, water storage), and population processes (extinction/colonization).

NASA's Global Ecosystem Dynamics Investigation (GEDI) mission offers data for temperate and pan-tropical estimates of aboveground forest biomass (AGB). The spaceborne, full-waveform LiDAR from GEDI provides sample footprints of canopy structure, expected to cover about 4% of the land area following two years of operation. Several options are available for estimating AGB at different geographical scales. Using GEDI sample data alone, gridded biomass predictions are based on hybrid inference which correctly propagates errors due to the modeling and accounts for sampling variability, but this method requires at least two GEDI tracks in the area of interest. However, there are significant gaps in GEDI coverage and in some areas of interest GEDI data may need to be combined with other wall-to-wall remotely sensed (RS) data, such as those from multispectral or SAR sensors. In these cases, we may employ hierarchical model-based (HMB) inference that correctly considers the additional model errors that result from relating GEDI data to the wall-to-wall data. Where predictions are possible from both hybrid and HMB inference the question arises which framework to choose, and under what circumstances? In this paper, we make progress towards answering these questions by comparing the performance of the two prediction frameworks under conditions relevant for the GEDI mission. Conventional model-based (MB) inference with wall-to-wall TanDEM-X data was applied as a baseline prediction framework, which does not involve GEDI data at all. An important feature of the study was the comparison of AGB predictors in terms of both standard deviation (SD: the square root of variance) and root mean square error (RMSE: the square root of mean square error – MSE). Since, in model-based inference, the true AGB in an area of interest is a random variable, comparisons of the performance of prediction frameworks should preferably be made in terms of their RMSEs. However, in practice only the SD can be estimated based on empirical survey data, and thus it is important also to study whether or not the difference between the two uncertainty measures is small or large under conditions relevant for the GEDI mission. Our main findings were that: (i) hybrid and HMB prediction typically resulted in smaller RMSEs than conventional MB prediction although the difference between the three frameworks in terms of SD often was small; (ii) in most cases the difference between hybrid and HMB inference was small in terms of both RMSE and SD; (iii) the RMSEs for all frameworks was substantially larger than the SDs in small study areas whereas the two uncertainty measures were similar in large study areas, and; (iv) spatial autocorrelation of model residual errors had a large effect on the RMSEs of AGB predictors, especially in small study areas. We conclude that hybrid inference is suitable in most GEDI applications for AGB assessment, due to its simplicity compared to HMB inference. However, where GEDI data are sparse HMB inference should be preferred.

Field inventoried data are often used as references (ground truth) in forest remote sensing studies. However, the reference values are affected by various kinds of errors, which tend to make the reported accuracies of the remote sensing-based predictions worse than they are. The more accurate the remote sensing techniques are becoming, the more pronounced this problem will be. This paper addresses the impact of uncertainties in field reference data due to measurement errors, model errors, and position errors when evaluating the accuracy of biomass predictions from airborne laser scanning at plot level. We present novel theoretical analysis methods that take the interactions of the error sources into account. Further, an error characterization model (ECM) is used to describe the error structure of the remote sensing-based predictions, and we show how the parameters of the ECM can be adjusted when field references contain errors. We also show how root mean square error (RMSE) estimates can be adjusted. Based on data from Scandinavian forests, we conclude that the field reference errors have an impact on the remote sensing-based predictions. By accounting for these errors the RMSE of the remote sensing-based predictions was reduced by 6–18%. The most influential sources of error in the field references were found to be the residual errors of the allometric biomass model and the field plot position errors. Together, these two sources accounted for 97% of the variance while measurement errors and biomass model parameter uncertainties were negligible in our study.

The boreal forest floor vegetation is critical for ecosystem functioning and an important part of forest biodiversity. Given the ongoing global change, knowledge on broad-scale changes in the composition and abundance of different plant species and species groups is hence important for both forest conservation and management. Here, we analyse permanent plot data from the National Forest Inventory (NFI) on changes in the vegetation over a 10-year period in four regions of Sweden. To limit the direct and relatively well-known effects of forest management and associated succession, we only included mature forest stands not influenced by forestry during the 10 years between inventories, and focused on vegetation change mainly related to other factors. Results show strong decrease among many species and species groups. This includes dominant species such as Vaccinimum myrtillus and Deschampsia flexuosa as well as several forest herbs. The only species increasing are some mosses in the southern regions. Our data do not allow for a causal interpretation of the observed patterns. However, the changes probably result from latent succession in combination with climate change and nitrogen deposition, and with time lags complicating the interpretation of their relative importance. Regardless of the cause, the observed changes are on a magnitude that suggest impacts on ecosystem functioning and hence highlight the need for more experimental work.

Background The increasing availability of remotely sensed data has recently challenged the traditional way of performing forest inventories, and induced an interest in model-based inference. Like traditional design-based inference, model-based inference allows for regional estimates of totals and means, but in addition for wall-to-wall mapping of forest characteristics. Recently Light Detection and Ranging (LiDAR)-based maps of forest attributes have been developed in many countries and been well received by users due to their accurate spatial representation of forest resources. However, the correspondence between such mapping and model-based inference is seldom appreciated. In this study we applied hierarchical model-based inference to produce aboveground biomass maps as well as maps of the corresponding prediction uncertainties with the same spatial resolution. Further, an estimator of mean biomass at regional level, and its uncertainty, was developed to demonstrate how mapping and regional level assessment can be combined within the framework of model-based inference. Results Through a new version of hierarchical model-based estimation, allowing models to be nonlinear, we accounted for uncertainties in both the individual tree-level biomass models and the models linking plot level biomass predictions with LiDAR metrics. In a 5005 km2 large study area in south-central Sweden the predicted aboveground biomass at the level of 18 m ×18 m map units was found to range between 9 and 447 Mg ·ha−1. The corresponding root mean square errors ranged between 10 and 162 Mg ·ha−1. For the entire study region, the mean aboveground biomass was 55 Mg ·ha−1 and the corresponding relative root mean square error 8%. At this level 75% of the mean square error was due to the uncertainty associated with tree-level models. Conclusions Through the proposed method it is possible to link mapping and estimation within the framework of model-based inference. Uncertainties in both tree-level biomass models and models linking plot level biomass with LiDAR data are accounted for, both for the uncertainty maps and the overall estimates. The development of hierarchical model-based inference to handle nonlinear models was an important prerequisite for the study.

Background Large area forest inventories often use regular grids (with a single random start) of sample locations to ensure a uniform sampling intensity across the space of the surveyed populations. A design-unbiased estimator of variance does not exist for this design. Oftentimes, a quasi-default estimator applicable to simple random sampling (SRS) is used, even if it carries with it the likely risk of overestimating the variance by a practically important margin. To better exploit the precision of systematic sampling we assess the performance of five estimators of variance, including the quasi default. In this study, simulated systematic sampling was applied to artificial populations with contrasting covariance structures and with or without linear trends. We compared the results obtained with the SRS, Matérn’s, successive difference replication, Ripley’s, and D’Orazio’s variance estimators. Results The variances obtained with the four alternatives to the SRS estimator of variance were strongly correlated, and in all study settings consistently closer to the target design variance than the estimator for SRS. The latter always produced the greatest overestimation. In populations with a near zero spatial autocorrelation, all estimators, performed equally, and delivered estimates close to the actual design variance. Conclusion Without a linear trend, the SDR and DOR estimators were best with variance estimates more narrowly distributed around the benchmark; yet in terms of the least average absolute deviation, Matérn’s estimator held a narrow lead. With a strong or moderate linear trend, Matérn’s estimator is choice. In large populations, and a low sampling intensity, the performance of the investigated estimators becomes more similar.

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

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 (m3/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.

Tree growth response to recent environmental changes is of key interest for forest ecology. This study addressed the following questions with respect to Norway spruce (Picea abies, L. Karst.) in Central Europe: Has tree growth accelerated during the last five decades? What are the main environmental drivers of the observed tree radial stem growth and how much variability can be explained by them? Using a nationwide dendrochronological sampling of Norway spruce in the Czech Republic (1246 trees, 266 plots), novel regional tree-ring width chronologies for 40(± 10)- and 60(± 10)-year old trees were assembled, averaged across three elevation zones (break points at 500 and 700 m). Correspondingly averaged drivers, including temperature, precipitation, nitrogen (N) deposition and ambient CO2 concentration, were used in a general linear model (GLM) to analyze the contribution of these in explaining tree ring width variability for the period from 1961 to 2013. Spruce tree radial stem growth responded strongly to the changing environment in Central Europe during the period, with a mean tree ring width increase of 24 and 32% for the 40- and 60-year old trees, respectively. The indicative General Linear Model analysis identified CO2, precipitation during the vegetation season, spring air temperature (March–May) and N-deposition as the significant covariates of growth, with the latter including interactions with elevation zones. The regression models explained 57% and 55% of the variability in the two tree ring width chronologies, respectively. Growth response to N-deposition showed the highest variability along the elevation gradient with growth stimulation/limitation at sites below/above 700 m. A strong sensitivity of stem growth to CO2 was also indicated, suggesting that the effect of rising ambient CO2 concentration (direct or indirect by increased water use efficiency) should be considered in analyses of long-term growth together with climatic factors and N-deposition.

Large-scale surveys, such as national forest inventories and vegetation monitoring programs, usually have complex sampling designs that include geographical stratification and units organized in clusters. When models are developed using data from such programs, a key question is whether or not to utilize design information when analyzing the relationship between a response variable and a set of covariates. Standard statistical regression methods often fail to account for complex sampling designs, which may lead to severely biased estimators of model coefficients. Furthermore, ignoring that data are spatially correlated within clusters may underestimate the standard errors of regression coefficient estimates, with a risk for drawing wrong conclusions. We first review general approaches that account for complex sampling designs, e.g. methods using probability weighting, and stress the need to explore the effects of the sampling design when applying logistic regression models. We then use Monte Carlo simulation to compare the performance of the standard logistic regression model with two approaches to model correlated binary responses, i.e. cluster-specific and population-averaged logistic regression models. As an example, we analyze the occurrence of epiphytic hair lichens in the genus Bryoria; an indicator of forest ecosystem integrity. Based on data from the National Forest Inventory (NFI) for the period 1993–2014 we generated a data set on hair lichen occurrence on >100,000 Picea abies trees distributed throughout Sweden. The NFI data included ten covariates representing forest structure and climate variables potentially affecting lichen occurrence. Our analyses show the importance of taking complex sampling designs and correlated binary responses into account in logistic regression modeling to avoid the risk of obtaining notably biased parameter estimators and standard errors, and erroneous interpretations about factors affecting e.g. hair lichen occurrence. We recommend comparisons of unweighted and weighted logistic regression analyses as an essential step in development of models based on data from large-scale surveys.

This study presents an approach for predicting stand-level forest attributes utilizing mobile laser scanning data collected as a nonprobability sample. Firstly, recordings of stem density were made at point locations every 10th metre along a subjectively chosen mobile laser scanning track in a forest stand. Secondly, kriging was applied to predict stem density values for the centre point of all grid cells in a 5 m x 5 m lattice across the stand. Thirdly, due to nondetectability issues, a correction term was computed based on distance sampling theory. Lastly, the mean stem density at stand level was predicted as the mean of the point-level predictions multiplied with the correction factor, and the corresponding variance was estimated. Many factors contribute to the uncertainty of the stand-level prediction; in the variance estimator, we accounted for the uncertainties due to kriging prediction and due to estimating a detectability model from the laser scanning data. The results from our new approach were found to correspond fairly well to estimates obtained using field measurements from an independent set of 54 circular sample plots. The predicted number of stems in the stand based on the proposed methodology was 1366 with a 12.9% relative standard error. The corresponding estimate based on the field plots was 1677 with a 7.5% relative standard error.

Previous studies have utilized ground plots, airborne lidar scanning or profiling data, and space lidar profiling data to estimate biomass across large regions, but these studies have failed to take into account the variance components associated with multiple models because the proper variance equations were not available. Previous large-domain studies estimated the variances of their biomass density estimates as the sum of the GLAS sampling variability plus the model variability associated with the models that predict airborne lidar estimates of biomass density (Y) as a function of satellite lidar measurements (X). This approach ignores the additional variability associated with the predictive models used to estimate ground biomass density as a function of airborne lidar measurements. This paper addresses that shortcoming. Analytic variance expressions are provided that include sampling variability and model variability in situations where multiple models are employed to generate estimates of biomass. As an example, the forest biomass of the continental US is estimated, by forest stratum within state, using a space lidar system (ICESat/GLAS). An airborne laser system (ALS) is used as an intermediary to tie the GLAS measurements of forest height to a small subset of US Forest Service (USFS) ground plots by flying the ALS over the ground plots and, independently, over individual GLAS footprints. Two sets of models are employed to relate satellite measurements to the ground plots. The first set of equations relates USFS ground plot estimates of total aboveground dry biomass density (Y 1 ) to spatially coincident ALS forest canopy measurements (X 1 ). The second set of models predicts those ALS canopy height measurements (X 1 ) used in the first set of models to GLAS waveform measurements (X 2 ). The following important conclusions are noted. (1) The variability associated with estimation of the plot-ALS model coefficients is significant and should be included in the overall estimate of biomass density variance. In the continental US, the total variance of mean forest biomass density (98.06 t/ha) increases by a factor of 3.6 ×, i.e., from 1.91 to 6.94 t 2 /ha 2 , when plot-ALS model variance is included in the calculation of total variance. (2) State-level results are more variable, but on average, the percent model variance at the state level, i.e., (model variance / total variance) ∗ 100, increases from 16% to 59% when plot-ALS model variance is included. (3) The overall model variance is driven in large part by the number of plots overflown by the ALS and the number of GLAS pulses overflown by the ALS. Given a choice of improving precision by either increasing the number of plot-ALS observations or increasing ALS-GLAS observations, there is no obvious benefit to selecting one over the other. However, typically the number of ground plots overflown is the limiting factor. (4) If heteroskedasticity is evident in either the ground-air or air-satellite models, it can modeled using weighted regression techniques and incorporated into these model variance formulas in straightforward fashion. The results are unambiguous; in a hybrid three-phase sampling framework, both the ground-air and air-satellite model variance components are significant and should be taken into account.

The statistical framework of data assimilation provides methods for utilizing new data for obtaining up-to-date forest data: existing forest data are forecasted and combined with each new remote sensing data set. This new paradigm for updating forest database, well known from other fields of study, will provide a framework for utilizing all available remote sensing data in proportion to their quality to improve prediction. It also solves the problem that not all remote sensing data sets provide information for the entire area of interest, since areas with no remote sensing data can be forecasted until new remote sensing data become available. In this study, extended Kalman filtering was used for assimilating data from 19 TanDEM-X InSAR images on 137 sample plots, each of 10-meter radius at a test site in southern Sweden over a period of 4 years. At almost all time points data assimilation resulted in predictions closer to the reference value than predictions based on data from that single time poi...

Forest resource assessments utilizing remotely sensed auxiliary data are becoming increasingly important due to their ability to provide precise estimates of forest parameters at low cost. In presenting results from such surveys, it is important to provide not only estimates of the target parameters, but also their confidence intervals, which provide the range of values wherein the true value is located with a certain level of confidence. If such an interval is narrow the point estimates from the survey can be considered very reliable. In estimating the confidence interval the variance of an estimator must first be estimated. Unbiasedness, i.e. that an estimator on average coincides with the true value, is an important property also for variance estimators. Another important property is that the variance estimator itself has low variance, not least in cases when the variance estimates obtained with the estimator may not be strictly positive. One such important case is when two-stage designs are used to first allocate sample clusters in the form of strips from which auxiliary data, such as metrics derived from airborne laser scanning, are obtained; field data are then derived from sample plots beneath each sample strip in a second stage. In this article we compare two variance estimators for such surveys. The first estimator is a standard estimator suggested in reference textbooks on model-assisted sampling. The second estimator is proposed by the authors, and utilizes the auxiliary data to a larger extent. Through Monte Carlo simulation we show that both variance estimators are approximately unbiased, but that the new estimator is more stable (i.e., has lower empirical variance) and provides empirical confidence interval coverage rates that coincide more closely with the nominal coverage rates.

Specially designed forest damage inventories, directed to areas with potential or suspected damage, are performed in many countries. In this study, we evaluate a new approach for damage inventories in which auxiliary data are used for the sample selection with the recently introduced local pivotal sampling design. With this design, a sample that is well spread in the space of the auxiliary variables is obtained. We applied Monte Carlo sampling simulation to evaluate whether this sampling design leads to more precise estimates compared with commonly applied baseline methods. The evaluations were performed using different damage scenarios and different simulated relationships between the auxiliary data and the actual damages. The local pivotal method was found to be more efficient than simple random sampling in all scenarios, and depending on the allocation of the sample and the properties of the auxiliary data, it sometimes outperformed two-phase sampling for stratification. Thus, the local pivotal method may be a valuable tool to cost-efficiently assess the magnitude of forest damage once outbreaks have been detected in a forest region.

As a non-Annex 1 Party to the United Nations Framework Convention on Climate Change (UNFCCC), Tanzania has committed to submit the results of the measurement, reporting, and verification of greenhouse gas (GHG) emissions reductions and removals by sinks under the Biennial Update Reports of national GHG inventory and mitigation actions. Thus, implementation of a robust and cost-efficient carbon accounting system is one of the prerequisites for receiving financial benefits under the REDD + mechanism. For estimation targeting large areas (i.e., country, region, and sub-regional), remote sensing techniques like airborne laser scanning (ALS) enable precise and timely estimation of biomass stocks and biomass changes. The main objective of the study was to compare alternative sampling strategies using ALS for estimating aboveground biomass (AGB) changes in miombo woodlands that would be suitable components of the National Forestry Resources Monitoring and Assessment (NAFORMA) program of Tanzania and of the Biennial Update Reports under UNFCCC. NAFORMA is the national forest inventory of Tanzania. The study area of 15,867 km2 was located in the administrative district of Liwale, south-eastern Tanzania and dominated by miombo woodlands. A longitudinal survey was carried out during two temporally consistent field and ALS data acquisition campaigns in 2012 and 2014. The field data were collected on permanent plots of the NAFORMA program. ALS measurements were acquired along 32 parallel strips spaced 5 km apart and covering approximately 25% of the study area. Estimation methods (1) solely based on the ground inventory data provided by NAFORMA and (2) by incorporating field observations and auxiliary variables derived from ALS data were pursued for assessing AGB change as the difference between estimated AGB in 2012 and 2014, together with the uncertainties related to sampling variability. The AGB estimates varied from 58.48 to 59.55 Mg ha− 1 in 2012 and between 58.20 and 59.29 Mg ha− 1 in 2014. The sampling variability (in terms of standard errors) was between 1.37 and 4.79 Mg ha− 1 in 2012, and 1.77 and 5.03 Mg ha− 1 in 2014. The mean AGB change varied from 0.11 to 0.35 Mg ha− 1 with standard errors of 0.31 to 0.85 Mg ha− 1. Compared to direct estimation based on field data only, the efficiency gain under ALS-assisted (design-based, model-assisted) estimation was 5–22%, and approximately 66% when using ALS data in a model-dependent estimation. The results provide statistically significant evidence of change in AGB over the 2-yr period spanned by the study only under model-dependent estimation at 50% confidence level, illustrating the great challenges of change estimation over such short time periods as requested for UNFCCC reporting.

Sweden aims to increase the proportion of renewable energy sources, ultimately to be able to phase out fossil fuels. To achieve this, new energy sources need to be explored. In this multi-disciplin ...

NASA’s Global Ecosystem Dynamics Investigation (GEDI) mission will collect waveform lidar data at a dense sample of ∼25 m footprints along ground tracks paralleling the orbit of the International Space Station (ISS). GEDI’s primary science deliverable will be a 1 km grid of estimated mean aboveground biomass density (Mg ha−1), covering the latitudes overflown by ISS (51.6 °S to 51.6 °N). One option for using the sample of waveforms contained within an individual grid cell to produce an estimate for that cell is hybrid inference, which explicitly incorporates both sampling design and model parameter covariance into estimates of variance around the population mean. We explored statistical properties of hybrid estimators applied in the context of GEDI, using simulations calibrated with lidar and field data from six diverse sites across the United States. We found hybrid estimators of mean biomass to be unbiased and the corresponding estimators of variance appeared to be asymptotically unbiased, with under-estimation of variance by approximately 20% when data from only two clusters (footprint tracks) were available. In our study areas, sampling error contributed more to overall estimates of variance than variability due to the model, and it was the design-based component of the variance that was the source of the variance estimator bias at small sample sizes. These results highlight the importance of maximizing GEDI’s sample size in making precise biomass estimates. Given a set of assumptions discussed here, hybrid inference provides a viable framework for estimating biomass at the scale of a 1 km grid cell while formally accounting for both variability due to the model and sampling error.

Reliable statistical inference is central to forest ecology and management, much of which seeks to estimate population parameters for forest attributes and ecological indicators for biodiversity, functions and services in forest ecosystems. Many populations in nature such as plants or animals are characterized by aggregation of tendencies, introducing a big challenge to sampling. Regardless, a biased or imprecise inference would mislead analysis, hence the conclusion and policymaking. Systematic adaptive cluster sampling (SACS) is design-unbiased and particularly efficient for inventorying spatially clustered populations. However, (1) oversampling is common for nonrare variables, making SACS a difficult choice for inventorying common forest attributes or ecological indicators; (2) a SACS sample is not completely specified until the field campaign is completed, making advance budgeting and logistics difficult; (3) even for rare variables, uncertainty regarding the final sample still persists; and (4) a SACS sample may be variable-specific as its formation can be adapted to a particular attribute or indicator, thus risking imbalance or non-representativeness for other jointly observed variables. Consequently, to solve these challenges, we aim to develop a generalized SACS (GSACS) with respect to the design and estimators, and to illustrate its connections with systematic sampling (SS) as has been widely employed by national forest inventories and ecological observation networks around the world. In addition to theoretical derivations, empirical sampling distributions were validated and compared for GSACS and SS using sampling simulations that incorporated a comprehensive set of forest populations exhibiting different spatial patterns. Five conclusions are relevant: (1) in contrast to SACS, GSACS explicitly supports inventorying forest attributes and ecological indicators that are nonrare, and solved SACS problems of oversampling, uncertain sample form, and sample imbalance for alternative attributes or indicators; (2) we demonstrated that SS is a special case of GSACS; (3) even with fewer sample plots, GSACS gives estimates identical to SS; (4) GSACS outperforms SS with respect to inventorying clustered populations and for making domain-specific estimates; and (5) the precision in design-based inference is negatively correlated with the prevalence of a spatial pattern, the range of spatial autocorrelation, and the sample plot size, in a descending order.

We examined the effect of individual environmental factors on the current spruce tree growth assessed from a repeated country-level statistical landscape (incl. forest) survey in the Czech Republic. An extensive set of variables related to tree size, competition, site characteristics including soil texture, chemistry, N deposition and climate was tested within a random-effect model to explain growth in the conditions of dominantly managed forest ecosystems. The current spruce basal area increment was assessed from two consecutive landscape surveys conducted in 2008/2009 and six years later in 2014/2015. Tree size, age and competition within forest stands were found to be the dominant explanatory variables, whereas the expression of site characteristics, environmental and climatic drives was weaker. The significant site variables affecting growth included soil C/N ratio and soil exchangeable acidity (pH KCl; positive response) reflecting soil chemistry, long-term N-deposition (averaged since 1975) in combination with soil texture (clay content) and Standardized Precipitation Index (SPI), a drought index expressing moisture conditions. Sensitivity of growth to N-deposition was positive, although weak. SPI was positively related to and significant in explaining tree growth when expressed for the growth season. Except SPI, no significant relation of growth was determined to altitude-related variables (temperature, growth season length). We identified the current spruce growth optimum at elevations about 800ma.s.l. or higher in the conditions of the country. This suggests that at lower elevations, limitation by a more pronounced water deficit dominates, whereas direct temperature limitation may concern the less frequent higher elevations. The mixed linear model of spruce tree growth explained 55 and 65% of the variability with fixed and random effects included, respectively, and provided new insights on the current spruce tree growth and factors affecting it within the environmental gradients of the country.

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.

For many decades remotely sensed data have been used as a source of auxiliary information when conducting regional or national surveys of forest resources. In the past decade, airborne scanning LiDAR (Light Detection and Ranging) has emerged as a promising tool for sample surveys aimed at improving estimation of above-ground forest biomass. This technology is now employed routinely in forest management inventories of some Nordic countries, and there is eager anticipation for its application to assess changes in standing biomass in vast tropical regions of the globe in concert with the UN REDD program to limit C emissions. In the rapidly expanding literature on LiDAR-assisted biomass estimation the assessment of the uncertainty of estimation varies widely, ranging from statistically rigorous to ad hoc. In many instances, too, there appears to be no recognition of different bases of statistical inference which bear importantly on uncertainty estimation. Statistically rigorous assessment of uncertainty for four large LiDAR-assisted surveys is expounded.