Structural Causal Discovery and Predictive Sufficiency in High-Dimensional Dynamical Systems

Abstract

High-dimensional environmental systems contain variables that may be predictive, causally informative, physically coupled, or redundant, and these roles need not coincide. We study this distinction in precipitation dynamics using High-Resolution Rapid Refresh atmospheric fields and Multi-Radar Multi-Sensor precipitation observations over the Southwestern United States. We introduce a projection-based, variable-level formulation of entropic regression that identifies candidate causal parents without constructing a global nonlinear expansion library. Ten physical variables are selected sequentially by conditional-information forward selection using linear regression projections. A quadratic library is then formed only over those variables, followed by two sequential variable-block eliminations that produce an eight-variable local representation. Applied across 1227 precipitation-guided superpixels, the method recovers a compact and spatially recurrent causal structure. Under the same final cardinality, entropic regression yields a substantially more concentrated recurrence profile than transfer entropy and causation entropy. Six variables exceed a recurrence threshold of 0.25: land-surface moisture availability, composite reflectivity, geometric vertical velocity, wind speed, convective available potential energy, and maximum upward vertical velocity. Predictive models restricted to these variables achieve strong one-hour discrimination of precipitation occurrence, with an area under the receiver operating characteristic curve of 0.948, while pointwise intensity prediction remains more limited. The results provide a scalable variable-level procedure for high-dimensional causal discovery and show that recurrent causal relevance and predictive sufficiency are distinct properties of a reduced dynamical representation.