Constrained Functional Regression of National Forest Inventory Data Over Time Using Remote Sensing Observations

The USDA Forest Service uses satellite imagery, along with a sample of national forest inventory field plots, to monitor and predict changes in forest conditions over time throughout the United States. We specifically focus on a 230,400 ha region in north-central Wisconsin between 2003 and 2012. The auxiliary data from the satellite imagery of this region are relatively dense in space and time, and can be used to learn how forest conditions changed over that decade. However, these records have a significant proportion of missing values due to weather conditions and system failures that we fill in first using a spatiotemporal model. Subsequently, we use the complete imagery as functional predictors in a two-component mixture model to capture the spatial variation in yearly average live tree basal area, an attribute of interest measured on field plots. We further modify the regression equation to accommodate a biophysical constraint on how plot-level live tree basal area can change from one year to the next. Findings from our analysis, represented with a series of maps, match known spatial patterns across the landscape. Supplementary materials for this article, including a standardized description of the materials available for reproducing the work, are available as an online supplement.