Recent advancements in remote sensing technology, specifically Light Detection and Ranging (LiDAR) sensors, provide data needed to quantify forest characteristics at a fine spatial resolution over large geographic domains. From an inferential standpoint, there is interest in prediction and interpolation of the often sparsely sampled and spatially misaligned LiDAR signals and forest variables. We propose a fully process-based Bayesian hierarchical model for forest variables and LiDAR signals. The process-based framework offers richness in inferential capabilities, e.g., inference on the entire underlying processes instead of estimates only at prespecified locations. Key challenges we obviate using a Nearest Neighbor Gaussian Process (NNGP) include misalignment between the forest variable observations and LiDAR signals and the high-dimensionality in the model emerging from LiDAR signals in conjunction with the large number of spatial locations.