A structure-preserving model for the dynamics of estuarine ecosystems and its application in western Patagonia fjords

Abstract

The Patagonian fjords of southern Chile are one of the largest and least-studied estuarine regions in the world. Its water bodies display a wide range in hydrodynamic and biogeochemical behavior, a function of diverse morphology/bathymetry and range of inputs from continental runoff. Numerical models, which are an essential tool in understanding the potential impacts of human or climate-driven perturbations on complex ecosystems, have not been applied in this zone. We present a novel model for simulating ecological processes in data-sparse marine water bodies, as a trade-off between model complexity and parsimony, based on a two-layer description of the water column. The upper layer represents the euphotic zone, where a NPZD model (Nutrients/Phytoplankton/Zooplankton/Detritus) is used to simulate the dynamics of a mass-conserving pelagic food web. Intense wind driven water column mixing, inducing an upward flux of nutrients that boosts high rates of primary production, is described by a time-dependent Gaussian pulse. Mass losses due to detritus sinking are also included. The ecosystem dynamics are represented by an externally forced, non-autonomous system of ordinary differential equations, characterized by strictly positive trajectories. This system is no longer mass-conserving. Therefore a structure-preserving time integrator, based on a splitting composition technique, was customized for solving the system’s equations. It is cast as a three-step algorithm and provides an exact estimation of biomass fluxes. In the first step, a modified Patankar–Runge–Kutta scheme (Burchard et al., 2003) is used to solve the unforced NPZD system. The second and third steps consider the effects of nutrient pulse and sinking detritus. Finally, genetic algorithms are used for model calibration, with the proposed model applied to previous published observations on an unusual winter bloom of dinoflagellates in an Austral fjord (Montero et al., 2017). Optimal parameters characterizing the biomass fluxes during the bloom were determined, as well as the time scales and mass/volume associated with primary production. To the best of the authors’ knowledge, this is the first attempt to model biogeochemical processes in the fjords of this region.