Extreme anomaly event detection in biosphere using linear regression and a spatiotemporal MRF model

Detecting abnormal events within time series is crucial for analyzing and understanding the dynamics of the system in many research areas. In this paper, we propose a methodology to detect these anomalies in multivariate environmental data. Five biosphere variables from a preliminary version of the Earth System Data Cube have been used in this study: Gross Primary Productivity, Latent Energy, Net Ecosystem Exchange, Sensible Heat and Terrestrial Ecosystem Respiration. To tackle the spatiotemporal dependencies of the biosphere variables, the proposed methodology after preprocessing the data is divided into two steps: a feature extraction step applied to each time series in the grid independently, followed by a spatiotemporal event detection step applied to the obtained novelty scores over the entire study area. The first step is based on the assumption that the time series of each variable can be represented by an autoregressive moving average (ARMA) process, and the anomalies are those time instances that are not well represented by the estimated ARMA model. The Mahalanobis distance of the ARMA models’ multivariate residuals is used as a novelty score. In the second step, the obtained novelty scores of the entire study are treated as time series of images. Markov random fields (MRFs) provide an effective and theoretically well-established methodology for integrating spatiotemporal dependency into the classification of image time series. In this study, the classification of the novelty score images into three classes, intense anomaly, possible anomaly, and normal, is performed using unsupervised K-means clustering followed by multi-temporal MRF segmentation applied recursively on the images of each consecutive $$L \ge $$ L ≥ 1 time steps. The proposed methodology was applied to an area covering Europe and Africa. Experimental results and validation based on known historic events show that the method is able to detect historic events and also provides a useful tool to define sensitive regions.