National Forest Inventories (NFIs) are becoming increasingly important worldwide in order to provide information about the multiple functions of forests, e.g. their provision of raw materials to industry, biodiversity and their capacity to store carbon for mitigating climate change. In several countries the history of NFIs is very long. For these countries a specific challenge is to keep the inventories up-to-date without sacrificing the advantages associated with long time series. At the turn of the 20th century European NFIs faced some major challenges. In this article we describe the history and the recent developments of the Swedish NFI as an example from which general observations are made and discussed. The Swedish NFI started in 1923 and has evolved from an inventory with a narrow focus on wood resources to an inventory today which aims to provide information about all major forest ecosystem services. It can be concluded that the traditional approaches of most European NFIs, e.g. to collect data through sample plot field inventories, has proved to be applicable even for a wide range of new information requirements. Specifically, detailed data about land use, trees, vegetation, and soils has found new important uses in connection with biodiversity assessments and the estimation of greenhouse gas emissions. Though time-consuming and difficult, making NFI information comparable across countries through harmonization appears to be a useful approach. The European National Forest Inventory Network (ENFIN) was formed in 2003 and has been successful in pan-European NFI harmonization.

Accurate estimation of aboveground forest biomass stocks is required to assess the impacts of land use changes such as deforestation and subsequent regrowth on concentrations of atmospheric CO₂. The Global Ecosystem Dynamics Investigation (GEDI) is a lidar mission launched by NASA to the International Space Station in 2018. GEDI was specifically designed to retrieve vegetation structure within a novel, theoretical sampling design that explicitly quantifies biomass and its uncertainty across a variety of spatial scales. In this paper we provide the estimates of pan-tropical and temperate biomass derived from two years of GEDI observations. We present estimates of mean biomass densities at 1 km resolution, as well as estimates aggregated to the national level for every country GEDI observes, and at the sub-national level for the United States. For all estimates we provide the standard error of the mean biomass. These data serve as a baseline for current biomass stocks and their future changes, and the mission’s integrated use of formal statistical inference points the way towards the possibility of a new generation of powerful monitoring tools from space.

Recent developments in remote sensing (RS) technology have made several sources of auxiliary data available to support forest inventories. Thus, a pertinent question is how different sources of RS data should be combined with field data to make inventories cost-efficient. Hierarchical model-based estimation has been proposed as a promising way of combining: (i) wall-to-wall optical data that are only weakly correlated with forest structure; (ii) a discontinuous sample of active RS data that are more strongly correlated with structure; and (iii) a sparse sample of field data. Model predictions based on the strongly correlated RS data source are used for estimating a model linking the target quantity with weakly correlated wall-to-wall RS data. Basing the inference on the latter model, uncertainties due to both modeling steps must be accounted for to obtain reliable variance estimates of estimated population parameters, such as totals or means. Here, we generalize previously existing estimators for hierarchical model-based estimation to cases with non-homogeneous error variance and cases with correlated errors, for example due to clustered sample data. This is an important generalization to take into account data from practical surveys. We apply the new estimation framework to case studies that mimic the data that will be available from the Global Ecosystem Dynamics Investigation (GEDI) mission and compare the proposed estimation framework with alternative methods. Aboveground biomass was the variable of interest, Landsat data were available wall-to-wall, and sample RS data were obtained from an airborne LiDAR campaign that produced simulated GEDI waveforms. The results show that generalized hierarchical model-based estimation has potential to yield more precise estimates than approaches utilizing only one source of RS data, such as conventional model-based and hybrid inferential approaches.

∙ Key message: The study presents novel model-based estimators for growing stock volume and its uncertainty estimation, combining a sparse sample of field plots, a sample of laser data, and wall-to-wall Landsat data. On the basis of our detailed simulation, we show that when the uncertainty of estimating mean growing stock volume on the basis of an intermediate ALS model is not accounted for, the estimated variance of the estimator can be biased by as much as a factor of three or more, depending on the sample size at the various stages of the design. ∙ Context: This study concerns model-based inference for estimating growing stock volume in large-area forest inventories, combining wall-to-wall Landsat data, a sample of laser data, and a sparse subsample of field data. ∙ Aims: We develop and evaluate novel estimators and variance estimators for the population mean volume, taking into account the uncertainty in two model steps. ∙ Methods: Estimators and variance estimators were derived for two main methodological approaches and evaluated through Monte Carlo simulation. The first approach is known as two-stage least squares regression, where Landsat data were used to predict laser predictor variables, thus emulating the use of wall-to-wall laser data. In the second approach laser data were used to predict field-recorded volumes, which were subsequently used as response variables in modeling the relationship between Landsat and field data. Results: ∙ The estimators and variance estimators are shown to be at least approximately unbiased. Under certain assumptions the two methods provide identical results with regard to estimators and similar results with regard to estimated variances. ∙ Conclusion: We show that ignoring the uncertainty due to one of the models leads to substantial underestimation of the variance, when two models are involved in the estimation procedure.

This discussion paper addresses (1) the challenge of concisely reporting uncertainties in forest remote sensing (RS) studies, primarily conducted at plot and stand level, and (2) the influence of reference data errors and how corrections for such errors can be made. Different common ways of reporting uncertainties are discussed, and a parametric error model is proposed as a core part of a comprehensive approach for reporting uncertainties (compared to, e.g., conventional reporting of root mean square error (RMSE)). The importance of handling reference data errors is currently increasing since estimates derived from RS data are becoming increasingly accurate; in extreme cases the accuracies of RS- and field-based estimates are of equal magnitude and there is a risk that reported RS accuracies are severely misjudged due to inclusion of errors from the field reference data. Novel methods for correcting for some types of reference data errors are proposed, both for the conventional RMSE uncertainty metric and for the case when a parametric error model is applied. The theoretical framework proposed in this paper is demonstrated using real data from a typical RS study where airborne laser scanning and synthetic aperture radar (SAR) data are applied for estimating biomass at the level of forest stands. With the proposed correction method, the RMSE for the RS-based estimates from laser scanning was reduced from 50.5 to 49.5 tons/ha when errors in the field references were properly accounted for. The RMSE for the estimates from SAR data was reduced from 28.5 to 26.1 tons/ha.