A curve fitting procedure to derive inter-annual phenologies from time series of noisy satellite NDVI data

Annual, inter-annual and long-term trends in time series derived from remote sensing can be used to distinguish between natural land cover variability and land cover change. However, the utility of using NDVI-derived phenology to detect change is often limited by poor quality data resulting from atmospheric and other effects. Here, we present a curve fitting methodology useful for time series of remotely sensed data that is minimally affected by atmospheric and sensor effects and requires neither spatial nor temporal averaging. A two-step technique is employed: first, a harmonic approach models the average annual phenology; second, a spline-based approach models inter-annual phenology. The principal attributes of the time series (e.g., amplitude, timing of onset of greenness, intrinsic smoothness or roughness) are captured while the effects of data drop-outs and gaps are minimized. A recursive, least squares approach captures the upper envelope of NDVI values by upweighting data values above an average annual curve. We test this methodology on several land cover types in the western U.S., and find that onset of greenness in an average year varied by less than 8 days within land cover types, indicating that the curve fit is consistent within similar systems. Between 1990 and 2002, temporal variability in onset of greenness was between 17 and 35 days depending on the land cover type, indicating that the inter-annual curve fit captures substantial inter-annual variability. Employing this curve fitting procedure enhances our ability to measure inter-annual phenology and could lead to better understanding of local and regional land cover trends.