A statistical framework for near-real time detection of beetle infestation in pine forests using MODIS data

Beetle infestations have caused significant damage to the pine forest in North America. Early detection of beetle infestation in near-real time is crucial, in order to take appropriate steps to control the damage. In this letter, we consider nearreal time detection of beetle infestation in North American pine forests using high temporal resolution, coarse spatial resolution MODerate resolution Imaging Spectroradiometer (MODIS 8- days 500m) remotely sensed data. We show that the parameter sequence of a stationary vegetation index time-series, derived by fitting an underlying triply modulated cosine model over a sliding window using Nonlinear Least Squares (NLS), resembles a martingale sequence. The advantage of such properties of the parameter sequence is that standard martingale central limit (MCLT) theorem and well-known Gaussian distribution statistics can be used effectively to detect any non-stationarity in the vegetation index time-series with high accuracy. The proposed method exploits these properties of the parameter time-series , and hence does not require threshold tuning. The threshold is selected based on well-documented procedure of z-value selection from table of Gaussian distribution, depending upon the percentage of the distribution considered as outlier. The proposed framework is tested on different vegetation index datasets derived from MODIS 8-days 500 m image time-series of beetle infestations of North America (Colorado and British Columbia). The results show that the proposed framework can detect non-stationarities in the vegetation index time-series accurately, and performs the best on Red Green Index (RGI).