Spontaneous self-organization is ubiquitous in systems far from thermodynamic
equilibrium. While organized structures that emerge dominate transport
properties, universal representations that identify and describe these key
objects remain elusive. Here, we introduce a theoretically-grounded framework
for describing emergent organization that, via data-driven algorithms, is
constructive in practice. Its building blocks are spacetime lightcones that
embody how information propagates across a system through local interactions.
We show that predictive equivalence classes of lightcones -- local causal
states -- capture organized behaviors and coherent structures in complex
spatiotemporal systems. Employing an unsupervised physics-informed machine
learning algorithm and a high-performance computing implementation, we
demonstrate automatically discovering coherent structures in two real world
domain science problems. We show that local causal states identify vortices and
track their power-law decay behavior in two-dimensional fluid turbulence. We
then show how to detect and track familiar extreme weather events -- hurricanes
and atmospheric rivers -- and discover other novel coherent structures
associated with precipitation extremes in high-resolution climate data at the
grid-cell level