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We formulate a nonlinear synergistic theory of coevolutionary systems,disentangling and explaining dynamic complexity in terms of fundamentalprocesses for optimised data analysis and dynamic model design: Dynamic SourceAnalysis (DSA). DSA provides a nonlinear dynamical basis for spatiotemporaldatasets or dynamical models, eliminating redundancies and expressing thesystem in terms of the smallest number of fundamental processes andinteractions without loss of information. This optimises model design indynamical systems, expressing complex coevolution in simple synergistic terms,yielding physically meaningful spatial and temporal structures. These areextracted by spatiotemporal decomposition of nonlinearly interacting subspacesvia the novel concept of a Spatiotemporal Coevolution Manifold. Physicalconsistency is ensured and mathematical ambiguities are avoided withfundamental principles on energy minimisation and entropy production. Therelevance of DSA is illustrated by retrieving a non-redundant, synergistic setof nonlinear geophysical processes exerting control over precipitation in spaceand time over the Euro-Atlantic region. For that purpose, a nonlinearspatiotemporal basis is extracted from geopotential data fields, yielding twoindependent dynamic sources dominated respectively by meridional and zonalcirculation gradients. These sources are decomposed into spatial and temporalstructures corresponding to multiscale climate dynamics. The added value ofnonlinear predictability is brought out in the geospatial evaluation anddynamic simulation of evolving precipitation distributions from the geophysicalcontrols, using DSA-driven model building and implementation. The simulatedprecipitation is found to be in agreement with observational data, which theynot only describe but also dynamically link and attribute in synergistic termsof the retrieved dynamic sources.

Synergistic Dynamic Theory of Complex Coevolutionary Systems: Disentangling Nonlinear Spatiotemporal Controls on Precipitation