Using an idealized width-averaged process-based model, the role of a mud pool on the bed and time-varying river discharge on the trapping of fine sediment is systematically investigated. For this purpose, a dynamically and physically motivated description of erodibility is presented, which relates the amount of sediment on the bed to the suspended sediment concentration (SSC). We can distinguish between two states: in the availability-limited state, the SSC is limited by the amount of erodible sediment at the bed. Over time, under constant forcing conditions, the estuary evolves to morphodynamic equilibrium. In the erosion-limited state, there is an abundant amount of sediment at the bed so that sediment pickup occurs at the maximum possible rate. The SSC is then limited by the local hydrodynamic conditions. In this state, the estuary keeps importing sediment, forming an erodible bottom pool that grows in time. These two states can be used to explain the response of an estuary to changing river discharge. Under availability-limited conditions, periods of high river discharge push estuarine turbidity maxima (ETMs) downstream, while drier periods allow ETMs to move upstream. However, when the estuary is in an erosion-limited state during low river discharge, a bottom pool is formed. When the discharge then increases, it takes time to deplete this pool, so that an ETM located over a bottom pool moves with a significant time lag relative to changes in the river discharge. Good qualitative agreement is found between model results and observations in the Scheldt Estuary of surface SSC using a representative year of discharge conditions.@en

The well-known empirical relationship between the equilibrium cross-sectional area of tidal inlet entrances (A) and the tidal prism (P), first developed by O'Brien (1931), has been extensively reviewed. Our theoretical investigations indicate that a unique A-P relationship should only be expected for clusters of inlets that are phenomenological similar (i.e. fairly similar hydrodynamic and morphological conditions), and that the exponent q in the A-P relation should be larger than 1. However, relevant published data available to date do not clearly support this theoretical finding. A re-analysis of the available data sets by Stive et al. (2009) indicated that they may not be sufficiently reliable to verify our theoretical finding with regard to q>1 due to the violation of the condition of phenomenological similarity, and possibly also due to violating the initial definitions given by O'Brien (1931) in estimating the tidal prism. The resolution of this issue is important because slightly different values of q result in significantly variable values for the equilibrium cross-sectional area of the tidal entrance. This may have significant implications in determining the true stable equilibrium entrance cross-sectional area. Here we present a re-analysis of the available data with a focus on determining the phenomenological dependencies of the A-P relationship. The available A-P data from the US Pacific, Atlantic and Gulf coasts (Jarrett, 1976 and Powell, 2003) have been re-scrutinized and categorized following the above mentioned phenomenological similarity criteria, viz. similar tidal range, similar sediment size, similar littoral transport and similar hydraulic radius. All together, some 20 different categories were considered and A-P relationships were obtained for each category. Generally, high correlations were found between the stable inlet predicted by each A-P relationship and the corresponding data. However, only in a limited number of categories were they significantly better than the correlations for the complete datasets. Finally, we point out that only in a number of categories the q value associated with the A-P relationship exceeded unity as suggested by the theoretical derivations. In the majority of categories the q value associated with the A-P relationship does not exceed unity. This is truly disappointing, and we have no physical explanation for this and consider this issue unresolved.@en

The well-known empirical relationship between the equilibrium cross-sectional area of tidal inlet entrances (A) and the tidal prism (P), first developed by O'Brien (1931), has been extensively reviewed. Our theoretical investigations indicate that a unique A-P relationship should only be expected for clusters of inlets that are phenomenological similar (i.e. fairly similar hydrodynamic and morphological conditions), and that the exponent q in the A-P relation should be larger than 1. However, relevant published data available to date do not clearly support this theoretical finding. A re-analysis of the available data sets by Stive et al. (2009) indicated that they may not be sufficiently reliable to verify our theoretical finding with regard to q>1 due to the violation of the condition of phenomenological similarity, and possibly also due to violating the initial definitions given by O'Brien (1931) in estimating the tidal prism. The resolution of this issue is important because slightly different values of q result in significantly variable values for the equilibrium cross-sectional area of the tidal entrance. This may have significant implications in determining the true stable equilibrium entrance cross-sectional area. Here we present a re-analysis of the available data with a focus on determining the phenomenological dependencies of the A-P relationship. The available A-P data from the US Pacific, Atlantic and Gulf coasts (Jarrett, 1976 and Powell, 2003) have been re-scrutinized and categorized following the above mentioned phenomenological similarity criteria, viz. similar tidal range, similar sediment size, similar littoral transport and similar hydraulic radius. All together, some 20 different categories were considered and A-P relationships were obtained for each category. Generally, high correlations were found between the stable inlet predicted by each A-P relationship and the corresponding data. However, only in a limited number of categories were they significantly better than the correlations for the complete datasets. Finally, we point out that only in a number of categories the q value associated with the A-P relationship exceeded unity as suggested by the theoretical derivations. In the majority of categories the q value associated with the A-P relationship does not exceed unity. This is truly disappointing, and we have no physical explanation for this and consider this issue unresolved.@en

The iFlow modelling framework is a width-averaged model for the systematic analysis of the water motion and sediment transport processes in estuaries and tidal rivers. The distinctive solution method, a mathematical perturbation method, used in the model allows for identification of the effect of individual physical processes on the water motion and sediment transport and study of the sensitivity of these processes to model parameters. This distinction between processes provides a unique tool for interpreting and explaining hydrodynamic interactions and sediment trapping. iFlow also includes a large number of options to configure the model geometry and multiple choices of turbulence and salinity models. Additionally, the model contains auxiliary components, including one that facilitates easy and fast sensitivity studies. iFlow has a modular structure, which makes it easy to include, exclude or change individual model components, called modules. Depending on the required functionality for the application at hand, modules can be selected to construct anything from very simple quasi-linear models to rather complex models involving multiple non-linear interactions. This way, the model complexity can be adjusted to the application. Once the modules containing the required functionality are selected, the underlying model structure automatically ensures modules are called in the correct order. The model inserts iteration loops over groups of modules that are mutually dependent. iFlow also ensures a smooth coupling of modules using analytical and numerical solution methods. This way the model combines the speed and accuracy of analytical solutions with the versatility of numerical solution methods. In this paper we present the modular structure, solution method and two examples of the use of iFlow. In the examples we present two case studies, of the Yangtze and Scheldt rivers, demonstrating how iFlow facilitates the analysis of model results, the understanding of the underlying physics and the testing of parameter sensitivity. A comparison of the model results to measurements shows a good qualitative agreement. iFlow is written in Python and is available as open source code under the LGPL license.@en

Many estuaries are strongly modified by human interventions, including substantive channel deepening. In the Ems River Estuary (Germany and Netherlands), channel deepening between the 1960s and early 2000s coincided with an increase in the maximum near-bed suspended sediment concentration from moderate (∼1 kg/m 3 ) to high (>10 kg/m 3 ). In this study the observed transition in the suspended sediment concentration in the Ems is qualitatively reproduced by using an idealized width-averaged iFlow model. The model is used to reproduce observations from 1965 and 2005 by only changing the channel depth between the years. Model results show an increase in sediment concentrations from approximately 1–2 kg/m 3 to 20–30 kg/m 3 near the bed between 1965 and 2005 if the river discharge is below 70 m 3 /s, which holds approximately 60% of the time. Thereby, this study for the first time provides strong evidence for earlier published hypotheses that channel deepening was the main driver of the increased sediment concentrations in the Ems. The results are explained using two aspects: sediment transport (longitudinal processes) and local resuspension (vertical processes). The magnitude of the sediment import increased, because a combination of channel deepening and sediment-induced damping of turbulence increased the M 2 –M 4 tidal asymmetry. This effect is particularly strong, because the M 4 tide evolved to a state close to resonance. All imported sediment is kept in suspension when it is assumed that resuspension is sufficiently efficient, which depends on the value of the erosion parameter used and inclusion of hindered settling in the model. @en

Climate and human pressures can influence the evolution of estuarine sediment dynamics concurrently, but the understanding and quantification of their cause–effect relationships are still challenging due to the occurrence of complex hydro-morpho-sedimentary feedbacks. The Garonne Tidal River (GTR, upper Gironde Estuary, France) is a clear example of a system stressed by both anthropogenic and climate change, as it has been subject to decreasing river discharges, natural morphological changes, and gravel extraction. To understand the relative effect of each hydrological and geomorphological pressure on the turbidity maximum zone (TMZ), the sediment dynamics in the GTR over the last six decades was evaluated using the width-averaged idealized iFlow model. Model results show a gradual increase in tidal amplitude and currents over the decades that has led to the upstream shift of the landward sediment-transport capacity components (external M4 tide, spatial settling lag, and tidal return flow). The upstream displacement of the TMZ between the 1950s and the 2010s was estimated to be at least 19 km, of which about three fourth was induced by geomorphological changes and one fourth by hydrological changes. Concerning the geomorphological changes, the natural evolution of the lower Gironde morphology was the main pressure inducing the displacement of the TMZ in the GTR. Anthropogenic and natural changes in morphology and bed roughness in the GTR itself also contributed to this evolution. The natural geomorphological changes were, in turn, probably promoted by the evolution of sediment dynamics, so this study reveals the closed circle that governs the intensification of the TMZ.@en

Climate and human pressures can influence the evolution of estuarine sediment dynamics concurrently, but the understanding and quantification of their cause–effect relationships are still challenging due to the occurrence of complex hydro-morpho-sedimentary feedbacks. The Garonne Tidal River (GTR, upper Gironde Estuary, France) is a clear example of a system stressed by both anthropogenic and climate change, as it has been subject to decreasing river discharges, natural morphological changes, and gravel extraction. To understand the relative effect of each hydrological and geomorphological pressure on the turbidity maximum zone (TMZ), the sediment dynamics in the GTR over the last six decades was evaluated using the width-averaged idealized iFlow model. Model results show a gradual increase in tidal amplitude and currents over the decades that has led to the upstream shift of the landward sediment-transport capacity components (external M4 tide, spatial settling lag, and tidal return flow). The upstream displacement of the TMZ between the 1950s and the 2010s was estimated to be at least 19 km, of which about three fourth was induced by geomorphological changes and one fourth by hydrological changes. Concerning the geomorphological changes, the natural evolution of the lower Gironde morphology was the main pressure inducing the displacement of the TMZ in the GTR. Anthropogenic and natural changes in morphology and bed roughness in the GTR itself also contributed to this evolution. The natural geomorphological changes were, in turn, probably promoted by the evolution of sediment dynamics, so this study reveals the closed circle that governs the intensification of the TMZ.@en

Climate and human pressures can influence the evolution of estuarine sediment dynamics concurrently, but the understanding and quantification of their cause–effect relationships are still challenging due to the occurrence of complex hydro-morpho-sedimentary feedbacks. The Garonne Tidal River (GTR, upper Gironde Estuary, France) is a clear example of a system stressed by both anthropogenic and climate change, as it has been subject to decreasing river discharges, natural morphological changes, and gravel extraction. To understand the relative effect of each hydrological and geomorphological pressure on the turbidity maximum zone (TMZ), the sediment dynamics in the GTR over the last six decades was evaluated using the width-averaged idealized iFlow model. Model results show a gradual increase in tidal amplitude and currents over the decades that has led to the upstream shift of the landward sediment-transport capacity components (external M4 tide, spatial settling lag, and tidal return flow). The upstream displacement of the TMZ between the 1950s and the 2010s was estimated to be at least 19 km, of which about three fourth was induced by geomorphological changes and one fourth by hydrological changes. Concerning the geomorphological changes, the natural evolution of the lower Gironde morphology was the main pressure inducing the displacement of the TMZ in the GTR. Anthropogenic and natural changes in morphology and bed roughness in the GTR itself also contributed to this evolution. The natural geomorphological changes were, in turn, probably promoted by the evolution of sediment dynamics, so this study reveals the closed circle that governs the intensification of the TMZ.@en