Mining time-lagged relationships in spatio-temporal climate data

Time series data in climate are often characterized by a delayed relationship between two variables, for example precipitation and temperature anomalies occurring at a place might also occur at another place after some time. These lagged relations generally signify the time lag between the cause and the effect or the spread of a common cause and are important to study and understand as they can aid in prediction. Identifying lagged relationships in climate data is challenging due to the various complex dependencies present in the data like spatial and temporal auto-correlation, seasonality, trends and long distance teleconnections. In this paper, we present a general framework for finding all pairs of lagged positive and negative relations that can exist in a given spatio-temporal dataset. We use a graph based approach based upon the concept of shared reciprocal nearest neighbor to generate cluster pairs of locations sharing similar or opposing behavior for every time lag. Our framework can be generalized to extract multivariate lagged relationships across different variables thus can be used to understand the lagged response of one variable on another. We show the utility of our approach by extracting some of the known delayed relationships like the Madden Julian Oscillation (MJO) and the Pacific North American (PNA) pattern at different lags using the sea level pressure dataset provided by the NCEP/NCAR. Our approach can be broadly applied to other problems in spatio-temporal domain to extract lagged relationships.