A Variance Partitioning Multi-level Model for Forest Inventory Data with a Fixed Plot Design

Forest inventories are often carried out with a particular design, consisting of a multi-level structure of observation plots spread over a larger domain and a fixed plot design of exact observation locations within these plots. Consequently, the resulting data are collected intensively within plots of equal size but with much less intensity at larger spatial scales. The resulting data are likely to be spatially correlated both within and between plots, with spatial effects extending over two different areas. However, a Gaussian process model with a standard covariance structure is generally unable to capture dependence at both fine and coarse scales of variation as well as for their interaction. In this paper, we develop a computationally feasible multi-level spatial model that accounts for dependence at multiple scales. We use a data-driven approach to determine the weight of each spatial process in the model to partition the variability of the measurements. We use simulated and German small tree inventory data to evaluate the model's performance.Supplementary material to this paper is provided online.