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.