A Statistical Framework for Near-Real Time Detection of Beetle Infestation in Pine Forests Using MODIS Data

Abstract

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 near-real-time detection of beetle infestation in North American pine forests using high temporal resolution and coarse spatial resolution MODIS (eight-day 500-m) satellite data. We show that the parameter sequence of a stationary vegetation index time series, which is derived by fitting an underlying triply modulated cosine model over a sliding window using nonlinear least squares, resembles a martingale sequence. The advantage of such properties of the parameter sequence is that standard martingale central limit theorem and well-known Gaussian distribution statistics can be effectively used to detect any nonstationarity 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 a well-documented procedure of $z$ -value selection from the table of Gaussian distribution, depending upon the percentage of the distribution considered as outlier. The proposed framework is tested on different vegetation index data sets derived from MODIS eight-day 500-m image time series of beetle infestations in North America. The results show that the proposed framework can detect nonstationarities in the vegetation index time series accurately and performs the best on red–green index.