Synergistic Dynamic Theory of Complex Coevolutionary Systems:   Disentangling Nonlinear Spatiotemporal Controls on Precipitation
  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. 
Rui A. P. Perdig\~ao, Carlos A. L. Pires, Julia Hall
math.DS physics.ao-ph