  We formulate a nonlinear synergistic theory of coevolutionary systems,
disentangling and explaining dynamic complexity in terms of fundamental
processes for optimised data analysis and dynamic model design: Dynamic Source
Analysis (DSA). DSA provides a nonlinear dynamical basis for spatiotemporal
datasets or dynamical models, eliminating redundancies and expressing the
system in terms of the smallest number of fundamental processes and
interactions without loss of information. This optimises model design in
dynamical systems, expressing complex coevolution in simple synergistic terms,
yielding physically meaningful spatial and temporal structures. These are
extracted by spatiotemporal decomposition of nonlinearly interacting subspaces
via the novel concept of a Spatiotemporal Coevolution Manifold. Physical
consistency is ensured and mathematical ambiguities are avoided with
fundamental principles on energy minimisation and entropy production. The
relevance of DSA is illustrated by retrieving a non-redundant, synergistic set
of nonlinear geophysical processes exerting control over precipitation in space
and time over the Euro-Atlantic region. For that purpose, a nonlinear
spatiotemporal basis is extracted from geopotential data fields, yielding two
independent dynamic sources dominated respectively by meridional and zonal
circulation gradients. These sources are decomposed into spatial and temporal
structures corresponding to multiscale climate dynamics. The added value of
nonlinear predictability is brought out in the geospatial evaluation and
dynamic simulation of evolving precipitation distributions from the geophysical
controls, using DSA-driven model building and implementation. The simulated
precipitation is found to be in agreement with observational data, which they
not only describe but also dynamically link and attribute in synergistic terms
of the retrieved dynamic sources.
