Morphological predictor for mixed beds
Project Phase: Planning and Design
Purpose: Predict changes in bed level and composition resulting from deposition and erosion processes
Requirements: Basic modelling skills; knowledge on sediment transport; field data on bed composition
Relevant Software: Delft3D; also available as stand-alone tool
Changes in level and composition of the bed of surface water systems may affect both their economic and ecological functions. It is therefore often desirable to predict trends in bed level and composition due to human interventions or autonomous natural developments. This facilitates, for instance, a habitat assessment of future Building with Nature projects. A sand-mud bed composition module has been developed to predict of bed level and composition changes as computed from deposition and erosion of multiple sediment fractions. Depending on the mud fraction, the bed may behave cohesive or non-cohesive, resulting in different erosion behaviour. The bed module consists of multiple layers and may include mixing by bioturbation or bedform migration. The bed module is open-source and has been developed by Deltares. It is available both within Delft3D and as a stand-alone tool. For a quick assessment of potential bed level and bed composition changes due to human or natural changes of the environment, it can be run in 1D-mode. It is also applicable for a comprehensive 3D model study in the detailed design phase of a project. The intended users of the bed module are scientists or professionals with some affinity to sediment transport.
Building with Nature interest
The tool is applicable in the Planning and Design Phase of a BwN project, to analyse the effects of different strategies on morphology and bed composition. Projects that can benefit from the tool are those in which morphology and/or bed composition are expected to have a large impact on ecological or economic system functions. The tool is also beneficial for turbidity modelling, if sediment resuspension from the bed is an important source of turbidity.
The bed module is intended to be used in projects in which significant changes in bed level and bed composition are expected which cannot be quantified straightforwardly. It is a tool to compute bed composition and bed level changes due to erosion and deposition of multiple sediment fractions, which may range from gravel to clay. Depending on the mud fraction, the bed may behave cohesive or non-cohesive, each of which yields a different erosion behaviour. The bed module takes multiple bed layers into account and may include mixing by bioturbation or bedform migration . The output consists of the bed level and the vertical profile of the bed composition as a function of time in the nodal points of a horizontal numerical grid (or at a single position in 1D-mode). The output can be visualised or used as input for habitat assessment, for instance. As compared with existing bed modules (e.g. Sanford, 2008), the present one combines open-access with sophistication in numerical techniques and advanced process description of sand-mud interaction.
The tool consists of the following elements:
Bed module: the bookkeeping system for the bed, taking into account an arbitrary number of sediment fractions and bed layers. Layer thickness may be constant or varying with time. The uppermost layer and layers of constant thickness below it behave Lagrangian, i.e. they move in vertical direction along with the eroding or accreting water-bed interface. Lower layers of variable thickness behave Eulerian, i.e. they have a fixed vertical position and may disappear upon erosion or be split upon deposition. This hybrid approach combines the advantages of an active (mixing) layer concept at the interface with those of no numerical mixing deeper down. Physical mixing (e.g. by bioturbation) is described as a diffusion process, with a user-defined mixing coefficient and active depth below the water-bed interface. Consolidation remains to be included.
Erosion formulations: given the composition of the upper bed layer and the shear stress exerted on it by the water flow, an erosion flux is computed:
- Below the critical mud content, the bed is non-cohesive and mud is assumed to be eroded in proportion with sand; the presence of mud only influences the erosion velocity of sand via a change in the critical bottom shear stress. This means that the erosion flux of each sand fraction can be computed using a standard erosion formula (e.g. Van Rijn, 1993 and 2004) with a modified critical shear stress.
- Above the critical mud content the bed is cohesive and considered to be homogeneous, i.e. the properties of the sediment mixture determine the erosion behaviour instead of the properties of the individual sediment fractions. The erosion fluxes of mud and sand fractions are proportional to their percentage in the cohesive mixture. For pure mud, the standard Partheniades-Krone formulations apply, with a critical shear stress for erosion tau_e and an erosion parameter M. For a mud content p above the the critical value but below 100% there is a gradual transition between the non-cohesive regime and the all-mud regime. Both the critical shear stress and the erosion parameter are interpolated according to the Van Ledden et al. (2004) expressions extended for multiple sand and mud fractions. These formulations are described in detail in the Zhou et al. (2016) and Baart et al. (2017).
Fluff layer: a fluff layer concept is implemented to improve the description of fine sediment transport. The fluff layer only contains mud fractions and no sand. It is an intermediate state for mud between water column and bed. Mud in the fluff layer is stationary (unlike suspended sediment), but is very easily resuspended due to its low critical shear stress for erosion. Mud that becomes part of the bed is more resistant to erosion.
Consolidation module: In addition, a consolidation module has been developed, using existing consolidation theory, which is suitable for long-term morphodynamic simulations - we refer to the DECON model (Dynamic Equilibrium CONsolidation). This model is applicable for muddy systems, with small fractions of sand, where sedimentation rates are smaller than consolidation rates. Thus, the model assumes quasi-equilibrium of the consolidating bed. It is derived from the full consolidation (Gibson) equation and is implemented in a mixed Lagrangian-Eulerean bed model guaranteeing stable and non-negative solutions, while numeric diffusion remains small. Erosion and deposition of sand and mud is accounted for, whereas internal mixing (e.g. bioturbation) is modeled through diffusion. Parameter settings for the new consolidation model (hydraulic conductivity, consolidation coefficient and strength) can be obtained from consolidation experiments in the laboratory. The model reproduces one-dimensional consolidation experiments and the qualitative behavior of erosion and deposition in a tidal flume. Next, the DECON model has been applied to more natural conditions, simulating the fine sediment dynamics on a schematised mud flat and in a schematised tidal basin under tide and wave forcing. The computational results of the mudflat simulations compare well with simulations with the full Gibson equation. For the tidal basin simulations, DECON predicts the expected landward tidal transport of fine sediment during tide-dominated conditions while withstanding erosion during more energetic wave-dominated periods. Computational times in the morphodynamic simulations of the tidal basin example increased by a factor five for simulations without waves, and a factor two when waves are included. Applying a complete consolidation model would be prohibitive. The DECON model therefore serves as a useful tool to simulate fine sediment dynamics in complex wave- and tide-dominated conditions, as well as the effects of seasonal variations (for more detailed information refer to Winterwerp et al., 2018).
How to Use
The intended users of the sand-mud-bed module are scientists and professionals with affinity to sediment transport. The bed module can be used in a simple 1-D mode with a small number of sediment fractions and bed layers. It can also be used in a more advanced 3-D model with many fractions and layers. The best choice depends on the questions to be answered, the complexity of the system, the quality of available field data and the modeller’s experience.
The bed module is open-source and has been developed by Deltares. It can be applied in three different ways:
- The sand-mud module is available as part of the Delft3D open source software environment (see repository; registration - free of charge - required). In this way it can be used together with all other features within this environment, for instance in comprehensive 3-D model studies in the detailed design phase of a project; to be able to use the module in this setting, the Delft3D software environment should be installed at the user’s computer system;
- For a quick assessment of potential bed level and bed composition changes due to human or natural changes to the environment, it can be run in 1-D mode as a stand-alone Matlab library;
- The plain Fortran code code of the module is available as well; this requires Fortran programming skills and a Fortran compiler and enables incorporation of the sand-mud bed module in any (open source) software environment.
Phased plan process
- The first step in applying the bed module is to define the prevailing hydrodynamic forcing (currents + waves). The forcing can be computed with a hydrodynamic and wave model such as Delft3D and SWAN, or can be supplied by the user based on analytical expressions (in 1-D mode).
- The second step is to define sediment boundary conditions (supply) and sediment properties such as settling velocity and erosion properties for multiple fractions. Generally some calibration is required to reproduce the observed spatial and vertical distribution of bed composition. In 1-D mode, the boundary condition is the sediment concentration in the water column.
- The third step is to adapt the hydrodynamic forcing to the future situation (either computed by a hydrodynamic model or defined by the user) and to define changes in sediment supply if necessary.
- The fourth and last step is to compute changes in bed level and bed composition in the new situation, with the corresponding changes in hydrodynamic forcing or sediment supply.
To apply the bed module successfully, some local information on hydrodynamic forcing, sediment composition and sediment properties is required. Although the tool is simple to use, especially in its 1-D mode, we recommend users to acquire a basic understanding of the implemented formulations prior to practical application. This is important for the interpretations of the results. Start simple and gradually extend the model’s complexity (number of sediment fractions and layers) as far as necessary. Be aware of the time scale of bed composition and/or bed level changes compared with the simulation time scale.
On 29 June 2012, an international workshop was organised in Delft to disseminate the knowledge on and promote the use of the bed module within the communities of Building with Nature, NCK (Netherlands Centre for Coastal Research) and PACE (a German-Dutch science project on the fine sediment dynamics in the Wadden Sea).
Example output in 1-D mode for a constant deposition
flux between t=0 and t=100 with changing composition
(san fraction between 0 and 1). After t=100, deposition
stops, but the upper half of the bed gradually becomes
homogeneous because of mixing.
Computed mud fraction in the top bed layer in the Dutch Wadden Sea.
The tool was developed and tested within the framework of the first project. Apart from idealised 1-D tests (top figure), it has been applied to fine sediment transport models of the Dutch coastal zone and the Wadden Sea. Maps of computed bed compositions have been used as input to habitat evaluations (lower figure). After proper calibration, observed gradients in bed composition can be reproduced. Quantitative results from studies on biota-mud interactions are planned to be included in the bed module. The development of the Wadden Sea model will continue in the framework of the PACE (NWO GeoRisk) project.
These applications have demonstrated the need for sufficient field data on the actual bed composition in the systems considered. Without such data, the bed module application lacks validation and the predicted response to changes in forcing or sediment supply remains uncertain. So a proper field survey of a potential project site is essential. Although present experience with the sand-mud bed module is limited to shallow shelf seas and intertidal areas, it can also be applied in different environments such as rivers, lakes and deep seas.
- Braat, L., van Kessel, T., Leuven, J.R. and Kleinhans, M.G., 2017. Effects of mud supply on large-scale estuary morphology and development over centuries to millennia. Earth Surface Dynamics, 5(4), p.617.
- PACE project
- Sanford, L.P., 2008. Modeling a dynamically varying mixed sediment bed with erosion, deposition, bioturbation, consolidation, and armoring. Computers & Geosciences34: pp. 1263-1283
- Van der Hout, C.M., Gerkema, T., Nauw, J.J. and Ridderinkhof, H., 2015. Observations of a narrow zone of high suspended particulate matter (SPM) concentrations along the Dutch coast. Continental Shelf Research, 95, pp.27-38.
- Van Kessel et al. 2012. Bed module for sand-mud mixtures in framework of BwN project NTW 1.3 mud dynamics. Deltares Report no. 1200327, Delft, The Netherlands
- Van Ledden, M., van Kesteren, W.G.M. and Winterwerp, J.C. 2004. A conceptual framework for the erosion behaviour of sand-mud mixtures. Cont. Shelf Res.24, pp. 1--11
- Van Rijn, L.C., 1993. Principles of sediment transport. Aqua publications. ISBN 90-800356-2-9
- Winterwerp, J.C. et al., 2018 An efficient consolidation model for morphodynamic simulations in low SPM-environments. Accepted for publication in J. Hydr. Eng.
- Zhou, Z., van der Wegen, M., Jagers, B. and Coco, G., 2016. Modelling the role of self-weight consolidation on the morphodynamics of accretional mudflats. Environmental Modelling & Software, 76, pp.167-181.
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