Linear and weakly nonlinear analyses on morphological instabilities

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An integrated methodology for the riparian vegetation modelling

We propose a methodology to calibrate a stochastic model for riparian vegetation dynamics that is based on real data. The methodology integrates various tools that are often used individually in fluvial investigations and it is here applied to the case of the Cinca river (Spain), aiming to explore how its riparian vegetation responds to changing climate conditions

Calibration of a stochastic model for riparian vegetation dynamics from LiDAR acquisitions

The distribution of phreatophyte riparian vegetation can be described by a stochastic model for vegetation growth. According to this, vegetation dynamics are influenced by the topography of the riparian transect and the randomness of hydrological fluctuations, acting as a dichotomous Markov noise. Also, the response of vegetation to this forcing, i.e. its rate of growth and decay, depends of its intrinsic biological features, which are represented in the model by specific input parameters. Although most of these parameters has already been set and literature values provided for the most common tree species in riparian environments, the one representing the vegetation decay still needs to be properly calibrated. To this purpose, a segment of Cinca River (Spain) is here modelled, aiming to obtain a calibration of the decay rate of riparian vegetation in temperate climate. The choice of the study river was done according to the availability of hydrological and LiDAR data. The processing of LiDAR raw data allowed to define the digital terrain model of the study area, providing the geometrical input data of the model. Moreover, LiDAR acquisitions returned a measure of vegetation height and its spatial density, thus leading to the estimation of riparian above-ground biomass, which represents the model output. As the decay rate was the sole unknown parameter for the modelling of the study river, its calibration was possible. Furthermore, as LiDAR provided a highly detailed geometry, the outcome of calibration was not a single value of decay rate for the entire riparian corridor, but a set of values for increasing altitude bands, thus allowing the investigation of its relation with topographic positio

The Carbon-Capture Efficiency of Natural Water Alkalinization: Implications For Enhanced weathering

Enhanced weathering (EW) is a promising negative-emission technology that artificially accelerates the dissolution of natural minerals, promotes biomass growth, and alleviates the acidification of soils and natural waters. EW aims to increase the alkalinity of natural waters (alkalinization) to promote a transfer of CO2 from the atmosphere to the water. Here we provide a quantification of the alkalinization carbon-capture efficiency (ACE) as a function of the water chemistry. ACE can be used for any alkaline mineral in various natural waters. We show that ACE strongly depends on the water pH, with a sharp transition from minimum to maximum in a narrow interval of pH values. We also quantify ACE in three compartments of the land-to-ocean aquatic continuum: the world topsoils, the lakes of an acid-sensitive area, and the global surface ocean. The results reveal that the efficiency of terrestrial EW varies markedly, from 0 to 100 %, with a significant trade-off in acidic conditions between carbon-capture efficiency and enhanced chemical dissolution. The efficiency is more stable in the ocean, with a typical value of around 80 % and a latitudinal pattern driven by differences in seawater temperature and salinity. Our results point to the importance of an integrated hydrological and biogeochemical theory to assess the fate of the weathering products across the aquatic continuum from land to ocean

Finite Amplitude of Free Alternate Bars With Suspended Load

River bars are macroscale sediment patterns, whose main geometrical features (wavelength and amplitude) depend on the mutual interactions between hydrodynamics and sediment transport. River bars develop as an instability of the plane bed to an infinitesimal perturbation, which grows in time to eventually reach a finite amplitude. We here determine, with reference to both bed and suspended loads, a closed form for the finite amplitude, through the nonlinear Center Manifold Projection technique. Results show that suspension plays a destabilizing role in bar instability, affecting both the bar wavelength (linear analysis) and the bar amplitude (weakly nonlinear analysis). This proves the importance of considering suspended load for practical purposes. The outcomes of the model are satisfactorily compared with field observations

Nonlinear and subharmonic stability analysis in film-driven morphological patterns

The interaction of a gravity-driven water film with an evolving solid substrate (calcite or ice) results in the formation of fascinating wavy patterns similar both in caves and in ice-falls. Due to their remarkable similarity, we adopt a unified approach in the study of pattern formation of longitudinally oriented organ-pipe-like structures, called flutings. Since the morphogenesis of cave patterns can evolve for millennia, they have an additional value as silent repositories of past climates. Fluting formation is studied with the aid of gradient expansion and center manifold projection. In particular, through gradient expansion, a Benney-type equation accounting for the movable boundary is obtained. The coupling with a wall evolution equation provides a morphodynamic model for fluting formation, explored through linear and nonlinear analyses. In this way, closed relationships for the selected wave number and for the finite amplitude are achieved. However, as finite-amplitude monochromatic waves may be destabilized by nonlinear interactions with other modes, we verify, through center manifold projection, the stability of the fundamental to subharmonic disturbances. Conclusively, we perform numerical simulations of the fully nonlinear equations to validate the theory results

Parametric transitions between bare and vegetated states in water-driven patterns

Conditions for vegetation spreading and pattern formation are mathematically framed through an analysis encompassing three fundamental processes: flow stochasticity, vegetation dynamics, and sediment transport. Flow unsteadiness is included through Poisson stochastic processes whereby vegetation dynamics appears as a secondary instability, which is addressed by Floquet theory. Results show that the model captures the physical conditions heralding the transition between bare and vegetated fluvial states where the nonlinear formation and growth of finite alternate bars are accounted for by Center Manifold Projection. This paves the way to understand changes in biogeomorphological styles induced by man in the Anthropocene and of natural origin since the Paleozoic (Devonian plant hypothesis)

Stochastic ice stream dynamics

Ice streams are narrow corridors of fast-flowing ice that constitute the arterial drainage network of ice sheets. Therefore, changes in ice stream flow are key to understanding paleoclimate, sea level changes, and rapid disintegration of ice sheets during deglaciation. The dynamics of ice flow are tightly coupled to the climate system through atmospheric temperature and snow recharge, which are known exhibit stochastic variability. Here we focus on the interplay between stochastic climate forcing and ice stream temporal dynamics. Our work demonstrates that realistic climate fluctuations are able to (i) induce the coexistence of dynamic behaviors that would be incompatible in a purely deterministic system and (ii) drive ice stream flow away from the regime expected in a steady climate. We conclude that environmental noise appears to be crucial to interpreting the past behavior of ice sheets, as well as to predicting their future evolution