A Spatial Mixture Model for Spaceborne Lidar Observations Over Mixed Forest and Non-forest Land Types

The Global Ecosystem Dynamics Investigation (GEDI) is a spaceborne lidar instrument that collects near-global measurements of forest structure. While expansive in scope, GEDI samples are spatially sparse and cover a small fraction of the land surface. Converting the sparse samples into spatially complete predictive maps is of practical importance for a number of ecological studies. A complicating factor is that GEDI collects measurements over forested and non-forested land alike, with no automatic labeling of the land type. Such classification is important, as it categorically influences the probability distribution of the spatial process and the ecological interpretation of the observations/predictions. We propose and implement a spatial mixture model, separating the observations and the greater spatial domain into two latent classes. The latent classes are governed by a Bernoulli spatial process, with spatial effects driven by a Gaussian process. Within each class, the process is governed by a separate spatial model, describing the unique probabilistic attributes. Model predictions take the form of scalar predictions of the GEDI observables as well as discrete labeling of the class membership. Inference is conducted through a Bayesian paradigm, yielding rich quantification of prediction and uncertainty through posterior predictive distributions. We demonstrate the method using GEDI data over Wollemi National Park, Australia, using optical data from Landsat 8 as model covariates. When compared to a single spatial model, the mixture model achieves much higher posterior predictive densities on the true value. When compared to a random forest model, a common algorithmic approach in the remote sensing community, the random forest achieves better absolute prediction accuracy for prediction locations far from observed training data locations, but at the expense of location-specific assessments of uncertainty. The unsupervised binary classifications of the mixture model appear broadly ecologically interpretable as forest and non-forest when compared to optical imagery, but further comparison to ground-truth data is required.