A System Dynamic Theory of Forest-Climate Coevolution

<jats:p>Forests are active components of the climate system rather than passive reservoirs embedded in an externally prescribed atmosphere. Through exchanges of radiation, momentum, heat, water and trace constituents they modify boundary-layer structure, cloud formation, precipitation, atmospheric moisture transport and regional circulation; those atmospheric changes in turn regulate forest function, resilience and spatial organization. This monograph develops a system-dynamic theory of this forest-climate coevolution, from thermodynamic and hydrological foundations to nonlinear, nonlocal, geometric and statistical-field-theoretic descriptions of coupled hydroclimatic organization. The theory begins from conservation laws and physically interpretable closures for surface energy partitioning, evapotranspiration, moist-air thermodynamics, hydrostatic and pressure adjustment, atmospheric moisture budgets, momentum convergence and precipitation. This foundation distinguishes local thermodynamic effects from dynamically generated circulation and provides a common framework in which passive moisture recycling, conventional coupled land-atmosphere dynamics and proposed condensation-induced mechanisms can be formulated as competing, falsifiable closures rather than conflated explanations. A two-column diagnostic theory then links pressure contrast, low-level inflow, moisture import and precipitation while keeping source effects, circulation effects and condensation-related hypotheses explicitly separable. These mechanisms are next embedded in nonlinear dynamical systems for the coupled evolution of pressure, moisture transport, moist-convective state, precipitation and forest function. Analytic stability theory identifies multistability, saddle-node loss of resilience, delayed oscillatory instability, slow-fast transitions, stochastic switching and front-mediated collapse and recovery. Spatial extension leads to directed and nonlocal source-receptor dynamics, non-normal amplification, anisotropic propagation, convective and absolute instability, caustics, direct-adjoint sensitivity and direction-dependent nonlinear fronts. The resulting theory treats forest influence not only as a perturbation of local fluxes but also as a perturbation of the atmospheric pathways through which hydroclimatic disturbances propagate. A central methodological step is therefore to promote atmospheric connectivity itself from a prescribed kernel to a dynamical object. Moisture transport is represented as a state-dependent resolvent of an atmospheric generator, so that vegetation modifies both moisture sources and the operator through which those sources communicate across space. This produces adaptive non-self-adjoint dynamics, exceptional points, topology-dependent memory, mode conversion and a rigorous decomposition of rainfall change into source modification, transport-operator modification and their nonlinear interaction. The framework is subsequently formulated geometrically through evolving positive-definite transport metrics, directed moisture kernels and polar transport order on a coupled state manifold. This yields intrinsic measures of structural hysteresis, geometric holonomy, symmetry breaking, covariant stability, curvature-defect coupling and ray focusing, and distinguishes state change, operator change and communication-geometry change as different levels of forest-climate reorganization. At long wavelengths the coupled theory is reduced to stochastic response functionals and renormalization-group descriptions. Structural orientation, hydroclimatic amplitude and their nonreciprocal interaction generate nonequilibrium multicritical dynamics. Differential atmospheric propagation selects a resonant Fourier wedge, which changes the effective phase-space dimension and gives an upper critical physical dimension for the quartic convective theory. Genuine two-loop calculations show that the wedge geometry produces topology-dependent corrections that cannot be recovered by a naive dimensional substitution. The resulting response, stiffness and noise residues close a convective nonequilibrium renormalization group and preserve a physical nonreciprocal fixed point with strong dynamic scaling, complex relevant exponents and exceptional-point structure. The communication geometry is finally allowed to evolve and itself become critical. Uniform positive wedge coefficients and constant communication metrics form redundant fixed orbits, whereas spatially varying geometry induces local renormalization, a connection and curvature on the bundle of scaling fields, and generally non-unitary geometric holonomy. When a geometric restoring mode softens, two distinct endpoint theories emerge: a symmetry-protected quartic geometry-critical theory with upper critical dimension 3, and a generic cubic geometry-to-mass theory with upper critical dimension 5. This establishes precise criteria for when changing atmospheric geometry is an irrelevant kinematic modulation, a relevant perturbation of criticality, or an independent critical degree of freedom. The formal development is translated back into thermodynamic, hydrological, operator-level and geometry-level diagnostics; observational and modelling experiments are proposed to distinguish source changes from circulation reorganization and structural criticality; and consequences are examined for forest resilience, restoration, moisture recycling and water-limited Mediterranean hydroclimates. The resulting framework treats forest-climate interaction not as a single feedback but as a hierarchy of coevolving states, operators and geometries. Its methodological contribution is therefore twofold: it provides a falsifiable biogeophysical theory of forest-climate coevolution and, independently, a mathematical physics of adaptive nonequilibrium systems in which the interaction operator and the geometry on which it acts become dynamical variables in their own right.</jats:p>