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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

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.