Various studies have identified a strong relation between the hydrodynamic forces and the equilibrium profile for intertidal flats. A thorough understanding of the interplay between the hydrodynamic forces and the morphology, however, concerns more than the equilibrium state alone. We study the basic processes and feedback mechanisms underlying the long-term behavior of the intertidal system, restricting ourselves to unvegetated intertidal flats that are controlled by cross-shore tidal currents and wind waves and applying a 1-D cross-shore morphodynamic model. The results indicate that by an adjustment of the profile slope and shape, an initial imbalance between deposition and erosion is minimized within a few decades. What follows is a state of long-term seaward progradation or landward retreat of the intertidal flat, in which the cross-shore profile shape is largely maintained and the imbalance between deposition and erosion is not further reduced. These long-term trends can be explained by positive feedbacks from the morphology onto the hydrodynamic forces over the flat: initial accretion (erosion) decreases (increases) the shear stresses over the flat, which induces further accretion (erosion). This implies that a static equilibrium state cannot exist; the flat either builds out or retreats. The modeled behavior is in accordance with observations in the Yangtze Estuary. To treat these unbalanced systems with a one-dimensional numerical model, we propose a moving (Lagrangian) framework in which a stable cross-sectional shape and progradation speed can be derived for growing tidal flats, as a function of the wave climate and the sediment concentration in deeper water.

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We apply a 2‐D horizontal process‐based model (Delft3D) to study the feedback mechanisms that control the long‐term evolution of a fringing intertidal flat in the Western Scheldt Estuary. The hydrodynamic model is validated using a comparison with measurements on the intertidal flat and the sediment transport module is calibrated against long‐term morphology data. First, the processes that lead to net sediment exchange between channel and flat are studied. Then, long‐term simulations are performed and the dependency of sediment fluxes on the tidal flat bathymetry, and the corresponding morphodynamic feedback mechanisms are explained. In the long run, relatively stable states can be approached, which are shown to be typical for wave‐dominated fringing mudflats. The system behavior can be explained by the typical feedback mechanisms between the intertidal bathymetry and the hydrodynamic forces on the flat. In the subtidal domain, the impact of small (5–10 cm) wind waves increases with a rising elevation due to decreasing water depths. In the intertidal domain, the wave impact increases with increasing cross‐sectional slope due to wave shoaling. These relationships result in negative (stabilizing) morphodynamic feedback loops. The tidal current velocities and tide‐induced bed shear stresses, on the other hand, are largely determined by the typical horizontal geometry. A stabilizing feedback loop fails, so that there is no trend toward an equilibrium state in the absence of wind waves.

We use the results of a one‐dimensional morphodynamic model and the basis of the “Lagrangian equilibrium state” (Maan et al., 2015, https://doi.org/10.1002/2014JF003311) to derive a quantitative relationship between the progradation speed of tidal flats and the suspended sediment concentration in their adjacent waters and show that the speed increases more than linearly with the concentration. We also show that horizontally prograding flats rise vertically with sea level rise at the expense of their horizontal speed via a linear relationship. If accretion rates are insufficient to keep up with sea level rise, however, the intertidal flat submerges and retreats landward at the same time. We apply the obtained relationships to the Yangtze Estuary to estimate the critical sediment concentration level below which a shift from progradation to retreat can be expected.

Abstract. Plant roots are highly adaptable, but their adaptability is not included in crop and land surface models. They rely on a simplified representation of root growth, which is independent of soil moisture availability. Data of subsurface processes and interactions, needed for model setup and validation, are scarce. Here we investigated soil-moisture-driven root growth. To this end, we installed subsurface drip lines and small soil moisture sensors (0.2 L measurement volume) inside rhizoboxes (length × width × height of 45 × 7.5 × 45 cm). The development of the vertical soil moisture and root growth profiles is tracked with a high spatial and temporal resolution. The results confirm that root growth is predominantly driven by vertical soil moisture distribution, while influencing soil moisture at the same time. Besides support for the functional relationship between the soil moisture and the root density growth rate, the experiments also suggest that the extension of the maximum rooting depth will stop if the soil moisture at the root tip drops below a threshold value. We show that even a parsimonious one-dimensional water balance model, driven by the water input flux (irrigation), can be convincingly improved by implementing root growth driven by soil moisture availability.