Shape selection in Landsat time series: a tool for monitoring forest dynamics

We present a new methodology for fitting nonparametric shape-restricted regression splines to time series of Landsat imagery for the purpose of modeling, mapping, and monitoring annual forest disturbance dynamics over nearly three decades. For each pixel and spectral band or index of choice in temporal Landsat data, our method delivers a smoothed rendition of the trajectory constrained to behave in an ecologically sensible manner, reflecting one of seven possible 'shapes'. It also provides parameters summarizing the patterns of each change including year of onset, duration, magnitude, and pre- and postchange rates of growth or recovery. Through a case study featuring fire, harvest, and bark beetle outbreak, we illustrate how resultant fitted values and parameters can be fed into empirical models to map disturbance causal agent and tree canopy cover changes coincident with disturbance events through time. We provide our code in the r package ShapeSelectForest on the Comprehensive R Archival Network and describe our computational approaches for running the method over large geographic areas. We also discuss how this methodology is currently being used for forest disturbance and attribute mapping across the conterminous United States.