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Hierarchical model-based inference for forest inventory utilizing three sources of information
- Saarela, Svetlana, Holm, Sören, Grafström, Anton, Schnell, Sebastian, Næsset, Erik, Gregoire, Timothy G., Nelson, Ross F., Ståhl, Göran
- Annals of forest science 2016 v.73 no.4 pp. 895-910
- Landsat, Monte Carlo method, forest inventory, models, uncertainty, variance
- ∙ 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.