CSDMS 2014 annual meeting - Uncertainty and Sensitivity in Surface Dynamics Modeling

The FESD Delta Dynamics Modeling Collaboratory: A Progress Report

Rudy Slingerland

Penn State, United States
David Mohrig University of Texas at Austin United States
Douglas Edmonds Indiana University United States
Efi Foufoula-Georgiou University of Minnesota – Twin Cities United States
Wonsuck Kim University of Texas at Austin United States
Ehab Meselhe The Water Institute of the Gulf United States
Christopher Paola University of Minnesota – Twin Cities United States
Gary Parker University of Illinois at Urbana-Champaign United States
Paola Passalacqua University of Texas at Austin United States
James Syvitski University of Colorado, Boulder United States
Paul Venturelli University of Minnesota – Twin Cities United States
Alberto Canestrelli Pennsylvania State University United States
Fei Xing University of Colorado at Boulder United States
Ben Roth University of Louisiana at Lafayette United States
Ashok Khadaka University of Louisiana at Lafayette United States
Man Liang University of Texas at Austin United States
Corey Van Dyk University of Texas at Austin United States
Matt Czapiga University of Illinois United States
Enrica Viparelli University of South Carolina United States

The Delta Dynamics Collaboratory (DDC) is a four-year effort to develop an inter-disciplinary and multi-scale understanding of the interplay among and within the various sub-systems of deltas. It is funded through the National Science Foundation’s “Frontiers in Earth System Dynamics” (FESD) Program. The overall objective of the DDC is to develop tested, high-resolution, quantitative models incorporating morphodynamics, ecology, and stratigraphy to predict river delta dynamics over engineering to geologic time-scales. In this way we hope to specifically address questions of delta system dynamics, resilience, and sustainability. There are two laboratories in the DDC: a field laboratory for discovering process-interactions and testing model predictions (Wax Lake Delta, LA), and a virtual modeling laboratory. Here we report on the progress made to date in advancing models of delta processes and morphodynamic interactions.

The models consist of three types: 1) reduced complexity delta models (RCDM); 2) a 2- and 3D eco-geo-morpho-dynamic sediment transport delta model; and 3) vegetation and fish population ecological models. The RCDM are focused on large-scale interactions, and as such offer the opportunity to explore aspects of system dynamics that may be harder to pick out of the details of a high-resolution model. DeltaRCM is a “2.5-D” cellular delta formation model that computes a depth-averaged flow field and bed topography as the delta evolves in time. The model adopts a Lagrangian view of transport: water and sediment fluxes are treated as a large number of "parcels" that are routed scholastically through a lattice grid. The probability field for routing the parcels is updated through time and is determined by a set of rules abstracting the governing physics of fluid flow and sediment transport. Sediment parcels are treated as "leaking buckets" that lose sediment to the bed by deposition and gains sediment from the bed by erosion. In the current version of the model sediment parcels represent coarse and fine materials respectively ("sand" and "mud"), which have different rules for routing and conditions for deposition and entrainment. DeltaRCM is able to produce delta morphology at the level of selforganized channel behaviors such as bifurcations and avulsions. The model can also record stratigraphy in terms of grain-size or deposition age. Validation work on the flow routing component of the model (FlowRCM) shows that the model gives reasonable channel-to-channel and channel-to-floodplain flow partitioning but falls short in predicting fine scale hydrodynamic details at fine scales (e.g., sub-channel scale). A second RCDM (Kim et al. 2009) is being modified to include self-formed channels and separate channel and floodplain elevations, treat alluvial-bedrock and bedrock-alluvial transitions in low-slope sand-bed rivers, and exploit new channel geometry closure rules for self-formed alluvial sand-bed channels developed during the course of this study.

Along the lines of reduced complexity models, we have also developed a network-based modeling framework for understanding delta vulnerability to change. The deltaic system is mapped into a directed graph composed of a set of nodes (or vertices) and links (or edges) and represented by its connectivity or adjacency matrix. For flux routing a weighted adjacency matrix is used to reflect how fluxes are split downstream and to enforce mass balance. Using the proper tree representation, we show that operations on the adjacency matrix quantify several properties of interest, such as immediate or distant connectivity, distinct sub-networks, and downstream regions of influence from any point on the network. We use these representations to construct “vulnerability maps”, e.g., maps of delta locations where an imposed change in water and/or sediment fluxes would most drastically affect sediment and water delivery to the coastal zone outlets or to a specific region of the delta. Dam construction can be emulated by reducing water and sediment downstream by a given fraction, the location and operation of irrigation dykes can be varied, and different alternative management options can be evaluated in a simple yet spatially extensive framework.

The current open-source state of the art in 3D delta morphodynamic modeling is Delft3DFLOW Version developed by Deltares, an independent, Dutch-based research institute for matters relating to water, soil and the subsurface ( We are using Delft3D 6.0 to test various hypotheses concerning the emergent behaviors of deltas subject to various sediment fluxes, basin depths, and base level variations, and to investigate the specific morphodynamics and sediment retention of Wax Lake Delta. Predictions of sand and mud transport through the various distributaries compare well with data collected by the FESD Wax Lake Team and indicate that total sediment load is rarely split equally at bifurcations, in accordance with earlier predictions. These and other studies have shown that improvements to Delft3D are needed to solve the following problems: 1) morphodynamic simulations of deltas are in part, an artifact of the underlying orthogonal grid structure; 2) the ecogeomorphic interactions are primitive; 3) the algorithm for eroding channel banks is ad hoc; and 4) simulations are restricted by computational inefficiencies. We are attempting to address these problems in collaboration with Deltares scientists. A mass-conservative, staggered, three-dimensional immersed boundary, shallow water Delft3D+ model is under development for flow on complex geometries. It allows channels to evolve independent of the underlying grid, and allows cohesive channel banks to erode laterally according to user-specified bank-erosion rules. The method consists of hybrid cut- ghost-cells: ghost cells are used for the momentum equations in order to prescribe the correct boundary condition at the immersed boundary, while cut-cells are used in the continuity equation to conserve mass. Results show that the resulting scheme is robust, does not suffer any time step limitation for small cut cells and conserves fluid mass up to machine precision. Comparisons with analytical solutions and reference numerical solutions on curvilinear grids confirm the quality of the method.

To improve ecogeomorphic interactions, we have created a sub-grid vegetation-flow interaction module for Delft3D and Delft3D+ based upon the Baptist et al. (2005) equations. Baptist’s formulation is based on the theory that vegetation can be modeled as rigid cylinders, which influences the momentum calculation and turbulence structure. Vegetation is characterized by plant height, density, stem diameter, and drag coefficient in the model. The vertical flow velocity profile is divided into a constant zone of flow velocity inside the vegetated part and a logarithmic velocity profile above for submerged vegetation. Results show that in deltaic freshwater marshes, adding vegetation increases the fraction of sediment deposited inside the marsh but the vegetative roughness also forces more water into the channels, leading to more erosion in the channels and also more water by-passing the marsh surface. Thus under certain conditions, adding vegetation to freshwater marshes can reduce net deposition rates. In addition to the above-ground effects of plants, the role of roots in binding sediment is being modeled in a separate vegetation-root routine through increasing critical shear stress for erosion. When combined flow-wave shear stress is larger than a rooted-soil critical value, aggregate or block erosion occurs. The model is tested against cumulative sediment erosion and deposition on Wax Lake Delta during Hurricane Rita in 2005. The simulation shows that roots significantly change the sedimentation-erosion pattern at the marsh area by protecting the vegetated marshes from erosion.

A fish dynamics model explores the co-evolution of fish populations, vegetation, and delta morphology. The model simulates the individuals of five fish species on a spatial grid of bathymetry, water levels, vegetated habitat, and basal prey. An existing version of this model uses historical water levels, together with fixed bathymetric maps, to determine water depths on each cell and its vegetation type. Model simulations follow each individual of each species through the processes of growth, reproduction, mortality, and movement. Individuals compete for space and invertebrate prey, and individuals of predatory species consume other model individuals. The sum over individuals for a species yields abundances, and the combination of abundance and growth yields productivity. We use the model to identify strong relationships between morphodynamic features (such as mouth bar hypsometry) and predicted total and species-specific fish productivity.

As these models reach maturity in the next two years they will be incorporated into the CSDMS architecture and framework. All models will be open source and made freely available via the CSDMS Repository. If you have a specific immediate request please email

Please acknowledge the original contributors when you are using this material. If there are any copyright issues, please let us know ( and we will respond as soon as possible.

Of interest for:
  • Coastal Working Group
  • Marine Working Group
  • Human Dimensions Focus Research Group
  • Ecosystem Dynamics Focus Research Group