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In many applications, estimates are required for small sub-populations with so few (or no) sample plots that direct estimators that do not utilize auxiliary variables (e.g. remotely sensed data) are not applicable or result in low precision. This problem is overcome in small area estimation (SAE) by linking the variable of interest to auxiliary variables using a model. Two types of models can be distinguished based on the scale on which they operate: i) Unit-level models are applied in the well-known area-based approach (ABA) and are commonly used in forest inventories supported by ne-resolution 3D remote sensing data such as airborne laser scanning (ALS) or digital aerial photogrammetry (AP); ii) Area-level models, where the response is a direct estimate based on a sample within the domain and the explanatory variables are aggregated auxiliary variables, are less frequently applied. Estimators associated with these two model types can make use of sample plots within domains if available and reduce to so-called synthetic estimators in domains where no sample plots are available. We used both model types and their associated model-based estimators in the same study area with AP data as auxiliary variables. Heteroscedasticity, i.e. for continuous dependent variables typically an increasing dispersion of residuals with increasing predictions, is often observed in models linking eld-and remotely sensed data. This violates the model assumption that the distribution of the residual errors is constant. Complying with model assumptions is required for model-based methods to result in reliable estimates. Addressing heteroscedasticity in models had considerable impacts on standard errors. When complying

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Background The Norwegian forest resource map (SR16) maps forest attributes by combining national forest inventory (NFI), airborne laser scanning (ALS) and other remotely sensed data. While the ALS data were acquired over a time interval of 10 years using various sensors and settings, the NFI data are continuously collected. Aims of this study were to analyze the effects of stratification on models linking remotely sensed and field data, and assess the accuracy overall and at the ALS project level. Materials and methods The model dataset consisted of 9203 NFI field plots and data from 367 ALS projects, covering 17 Mha and 2/3 of the productive forest in Norway. Mixed-effects regression models were used to account for differences among ALS projects. Two types of stratification were used to fit models: 1) stratification by the three main tree species groups spruce, pine and deciduous resulted in species-specific models that can utilize a satellite-based species map for improving predictions, and 2) stratification by species and maturity class resulted in stratum-specific models that can be used in forest management inventories where each stand regularly is visually stratified accordingly. Stratified models were compared to general models that were fit without stratifying the data. Results The species-specific models had relative root-mean-squared errors (RMSEs) of 35%, 34%, 31%, and 12% for volume, aboveground biomass, basal area, and Lorey’s height, respectively. These RMSEs were 2–7 percentage points (pp) smaller than those of general models. When validating using predicted species, RMSEs were 0–4 pp. smaller than those of general models. Models stratified by main species and maturity class further improved RMSEs compared to species-specific models by up to 1.8 pp. Using mixed-effects models over ordinary least squares models resulted in a decrease of RMSE for timber volume of 1.0–3.9 pp., depending on the main tree species. RMSEs for timber volume ranged between 19%–59% among individual ALS projects. Conclusions The stratification by tree species considerably improved models of forest structural variables. A further stratification by maturity class improved these models only moderately. The accuracy of the models utilized in SR16 were within the range reported from other ALS-based forest inventories, but local variations are apparent.

Nation-wide Sentinel-2 mosaics were used with National Forest Inventory (NFI) plot data for modelling and subsequent mapping of spruce-, pine- and deciduous-dominated forest in Norway at a 16m×16m resolution. The accuracies of the best model ranged between 74% for spruce and 87% for deciduous forest. An overall accuracy of 90% was found on stand level using independent data from more than 42,000 stands. Errors mostly resulting from a forest mask reduced the model accuracies by approximately 10%. The produced map was subsequently used to generate model-assisted (MA) and post stratified (PS) estimates of species-specific forest area. At the national level, efficiencies of the estimates increased by 20% to 50% for MA and up to 90% for PS. Greater minimum numbers of observations constrained the use of PS. For MA estimates of municipalities, efficiencies improved by up to a factor of 8 but were sometimes also less than 1. PS estimates were always equally as or more precise than direct and MA estimates but were applicable in fewer municipalities. The tree species prediction map is part of the Norwegian forest resource map and is used, among others, to improve maps of other variables of interest such as timber volume and biomass.

Image-based point clouds obtained using aerial photogrammetry share many characteristics with point clouds obtained by airborne laser scanning (ALS). Two approaches have been used to predict forest parameters from ALS: the area-based approach (ABA) and the individual tree crown (ITC) approach. In this article, we apply the semi-ITC approach, a variety of the ITC approach, on an image-based point cloud to predict forest parameters and compare the performance to the ABA. Norwegian National Forest Inventory sample plots on a site in southeastern Norway were used as the reference data. Tree crown objects were delineated using a watershed segmentation algorithm, and explanatory variables were calculated for each tree crown segment. A multivariate kNN model for timber volume, stem density, basal area and quadratic mean diameter with the semi-ITC approach produced RMSEs of 30%, 46%, 25%, 26%, respectively. The corresponding measures for the ABA were 30%, 51%, 26%, 35%, respectively. Univariate kNN models resulted in timber volume RMSEs of 25% for the semi-ITC approach and 22% for the ABA. A non-linear logistic regression model with the ABA produced an RMSE of 23%. Both approaches predicted timber volume with comparable precision and accuracy at the plot level. The multivariate kNN model was slightly more precise with the semi-ITC approach, while biases were larger.

This study aimed at estimating total forest above-ground net change (ΔAGB; Mt) over five years (2014-2019) based on model-assisted estimation utilizing freely available satellite imagery. The study was conducted for a boreal forest area (approx. 1.4 Mill hectares) in Norway where bitemporal national forest inventory (NFI), Sentinel-2, and Landsat data were available. Biomass change was modelled based on a direct approach. The precision of estimates using only the NFI data in a basic expansion estimator were compared to four different alternative model-assisted estimates using 1) Sentinel-2 or Landsat data, and 2) using bi-or uni-temporal remotely sensed data. We found that the use of remotely sensed data improved the precision of the purely field-based estimates by a factor of up to three. The most precise estimates were found for the model-assisted estimation using bi-temporal Sentinel-2 (standard error; SE= 1.7 Mt). However, the decrease in precision when using Landsat data was small (SE= 1.92 Mt). In addition, we found that ΔAGB could be precisely estimated also when remotely sensed data were available only at the end of the monitoring period. We conclude that satellite optical data can considerably improve ΔAGB estimates, even in those cases where repeated and coincident NFI data are available. The free availability, global coverage, frequent update, and long-term time horizon make data from programs such as Sentinel-2 and Landsat a valuable data source for a consistent and durable monitoring of forest carbon dynamics.

The effectiveness of generating virtual transects on unmanned aerial vehicle-derived orthomosaics was evaluated in estimating the extent of soil disturbance by severity class. Combinations of 4 transect lengths (5-50 m) and five sampling intensities (1-20 transects per ha) were used in assessing traffic intensity and the severity of soil disturbance on six post-harvest, cut-to-length (CTL) clearfell sites. In total, 15% of the 33 ha studied showed some trace of vehicle traffic. Of this, 63% of was categorized as light (no visible surface disturbance). Traffic intensity varied from 787 to 1256 m ha −1 , with a weighted mean of 956 m ha −1 , approximately twice the geometrical minimum achievable with CTL technology under perfect conditions. An overall weighted mean of 4.7% of the total site area was compromised by severe rutting. A high sampling intensity, increasing with decreasing incidence of soil disturbance, is required if mean estimation error is to be kept below 20%. The paper presents a methodology that can be generally applied in forest management or in similar land-use evaluations.