Characterizing Causality In Spatio-temporal Environmental Systems

Abstract:

Significant advances have been made understanding causal dependencies in multi-variate system using information flow among the variables. These have been largely used for point observations where temporal symmetry breaking underpins the causal characterization, that is, the future cannot case the past. Such symmetry breaking is not present when we consider spatio-temporal systems, such as causal structure can be with reference to both space and time. For example, if measurements of solute concentrations are made at two locations along a stream, the variability of a variable at the downstream location can be affected by the interaction with other variables at the location while at the same time the upstream observations may also provide valuable causal insights. In this study we propose a framework for the information flow in space and time for the spatio-temporal dynamics using high frequency observations. This framework is based on Shannon’s entropy of joint space-time probability distribution function of interacting variables. The mathematical framework and example applications will be presented.