Nonlinear dynamics of River biogeomorphic feedbacks

Rivers are amongst the most dynamic ecosystems on earth. River ecosystems are highly disturbed environments, where riparian vegetation, water and sediments, are interconnected by positive and negative feedbacks, driven by a set of interactions. In the last two decades, it has been widely recognized that these eco-morphodynamic feedbacks play a crucial role in governing the equilibrium and dynamics of river ecosystem. However, the incomplete understanding and quantification of these feedbacks limit the comprehension of river behavior and the development of efficient predictive models. Thus, in this research, fundamental intrinsic feedbacks between riparian vegetation and hydro-morphodynamic disturbance are modeled, where the disturbance is generated by the vegetation itself. The aim is to investigate how these intrinsic feedbacks govern the equilibrium and dynamics of a simplified river ecosystem. To this end, numerical simulations were conducted using both a 0D model (non-spatial) and a 1D model (spatial) coupling hydro-morphodynamics with vegetation dynamics. The case study is a straight channel where vegetation can grow only in the central patch, while upstream and downstream there are bare soil regions. The system is perturbed periodically by a succession of floods of constant amplitude. Vegetation growth occurs in between of two consecutive floods, during low flood periods. Vegetation consists of two components, the above-ground biomass (canopy) and below-ground biomass (root depth). In both models, the canopy increases the roughness, reducing flow velocity. Variations in the flow field and the reduction of bottom shear stress modify sediment transport, leading to a greater imbalance between the vegetated and bare areas and thus, inducing erosion. Erosion increases the probability of vegetation uprooting, and when scour reaches root depth, uprooting occurs. The overall feedback loop is negative: higher vegetation biomass causes greater sediment flux imbalance and more erosion, ultimately resulting in less vegetation. However, root growth may inhibit the negative feedback loop, promoting positive feedbacks. Indeed, this interplay between hydro-morphodynamic disturbance (erosion) and the vegetation resistance (root depth), governs the predominance of either a positive or a negative feedback overall balance. Model results demonstrate that when the positive feedback overall balance prevails, the system always reaches a stable configuration. Furthermore, the system can exhibit hysteresis, meaning that, depending on the initial condition, it can achieve a stable configuration in two alternative states, the fully vegetated condition or bare soil. In the presence of the vegetated patch, the system can also exhibit a more complex multi-stable behavior, with infinite equilibria between the two alternative states. This also implies that spatial interactions smooth out critical transitions and tipping points, by facilitating smoother shifts that occur gradually through multiple smaller intermediate steps. Indeed, the resilience of the system, which is the ability of the system to still maintain its fundamental structure and functions after being subject to the ecological disturbance, increases due to spatial interactions. In contrast, when the negative feedback overall balance prevails, the system never reaches a steady state but exhibits dynamic oscillations. The oscillations can be either (i) periodic or (ii) aperiodic, strongly dependent on initial conditions, and with a positive Maximum Lyapunov Exponent, indicating chaotic behavior. The study also reveals that the route to chaos is a period-doubling bifurcation, and the calculation of time scale of predictability shows that the system is predictable only for a few growth-flood cycles. These results suggest that altering the ratio between hydro-morphodynamic disturbance and vegetation resistance, such as through anthropogenic pressure and climate change, may shift the system from a positive to a negative feedback overall balance. This shift could lead from a stable state to periodic oscillations or unpredictable chaotic behavior, limiting long-term predictions of river trajectories. Additionally, understanding how positive and negative eco-morphodynamic feedbacks govern river dynamics can contribute to develop efficient predictive models. Models are essential tools for implementing efficient river management and facilitate effective communication with stakeholders.