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Numerical Sediment Transport Modeling


Project Title: Numerical Sediment Transport Modeling
Mendenhall Fellow: John C. Warner
Duty Station: Woods Hole, Massachusetts
Start Date: September 9, 2001
Education: Ph.D. (2000), Civil and Environmental Engineering, University of California, Davis
Research Advisors: Brad Butman, (508) 457-2212, bbutman@usgs.gov; Chris Sherwood, (508) 457-2269, csherwood@usgs.gov
  John C. Warner
Dr. John Warner is currently a research scientist with the Coastal and Marine Geology Team of the USGS in Wood Hole, Mass.

Project Summary:

Introduction
The ability to predict the fate and transport of sediment in coastal oceans and estuarine environments is important because sediments may contain adhered contaminants, have implications for navigation, fishing, recreation, waste disposal, and affect habitats of endangered species. The physical processes that contribute to the transport of sediments are complex and the ability to simulate these processes is best approached with numerical models. These models can offer a means to evaluate the impacts of natural and anthropogenic influences on sediment transport. However, there are few publicly available models that contain full-featured algorithms and are fully tested and widely established. There exists a need to develop a sediment transport model that is community based, freely available, well tested, widely accepted, and applicable to a variety of coastal settings.

Project Goals
This research sought to (1) develop and implement numerical code with algorithms for transport of suspended sediment and algorithms to simulate turbulent mixing, (2) promote the Community Sediment Transport Model, (3) develop specific numerical application test cases to compare and check the performance of hydrodynamic and sediment transport models, and (4) apply the sediment transport model to a regional study.

Project Achievements
My USGS Mendenhall Post-doctoral experience started at Woods Hole, MA, in September 2001 and has been tremendously rewarding. The excellent environment for oceanographic studies (which includes the USGS, the Woods Hole Oceanographic Institution, and the Marine Biological Laboratory) and my personal ambition to develop a public tool has provided me a fundamentally advantageous experience. The main effort of my research for these last two years has been focused towards the Community Sediment Transport Modeling Project. I have spent most of this time developing and writing new Fortran code subroutines, attending meetings to promote the model development, attend conferences to demonstrate the performance of the model, and writing of peer reviewed publications that describe the methods and results of the subroutines. Initially my efforts focused on writing subroutines to model suspended sediment transport processes. As this progressed, we identified the need to include a recently published state of the art turbulence closure method. The turbulence closure is responsible for determining the amounts of mixing for momentum, heat, salinity, and suspended sediment. This lead to the coding of a second subroutine for the "Generic Length Scale" turbulence closure algorithm (discussed below).

Both the sediment transport and turbulence closure algorithms are part of a larger hydrodynamic oceanographic circulation model. The oceanographic model we chose to incorporate these subroutines was the three-dimensional ocean circulation model called ROMS (Regional Ocean Model System). ROMS is a free-surface, hydrostatic, primitive equation ocean model that uses stretched, terrain-following coordinates in the vertical and orthogonal curvilinear coordinates in the horizontal. ROMS includes advanced, high-order advection algorithms and is efficient on both single processors and multi-threaded computer architectures. It is a modern, full-featured ocean model and is freely available to the public (http://marine.rutgers.edu/po/index.php). The sediment transport and turbulence closure routines have been tested by myself and other research collaborators. The model is now being used in regional studies such as the Hudson River Estuary and Massachusetts Bay.

Specific accomplishments:
(1) Develop and implement numerical code.
I developed and coded two substantial algorithms that have been adopted by the ROMS model. The first algorithm is for the transport of suspended sediment. Three processes are modeled: 1) suspended sediment transport in the water column, which includes advection, diffusion, and vertical settling, 2) temporal evolution of a bottom sediment layer, and 3) fluxes across the sediment-water interface (erosion and deposition). Sediment suspended in the water column is transported, like other conservative tracers (e.g., temperature and salinity), by solving the advection-diffusion equation with two additional terms added for 1) vertical settling and 2) sources or sinks related to erosion or deposition, as follows:

Equation 1. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov   (1)


where C is the volume concentration of suspended sediment, t is time, Ui (i =1, 2) are the x and y directional velocities, K is the diffusivity tensor, ws is the vertical settling velocity (positive upwards), and sources/sinks are parameterized interactions with the bed. The model solves each term independently, in the sequence: vertical settling, source/sink, horizontal advection, vertical advection, vertical diffusion, and finally horizontal diffusion. Separation of these calculations has practical advantages because it allows 1) reuse of the routines for advection and diffusion of water-column tracers, 2) use of high-order numerical schemes for vertical settling, and 3) formulation of the flux conditions to ensure conservation of sediment in both bottom sediments and the water column.

The source/sink term (net flux into the water column) is calculated as the sum of depositional flux (downward advection through the bottom of the lowest grid cell by settling) and erosional flux. Erosional flux is parameterized as


Equation 2. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov   (2)
when τ > τe

where Es is the surface erosion mass flux (kg m-2s-1), E0 is a user-defined bed erodibility constant (kg m-2s-1), is the porosity (volume of voids/total volume) of the top bed layer, τce is the critical shear stress for erosion, and β is the bed shear stress determined by the hydrodynamic routines. The erosional flux is limited by availability in the bottom sediment layer, which consists of a single layer with a specified initial thickness and sediment composition. These sediment transport capabilities are suitable for analyses of temporal and spatial evolution of sediment transport in many situations.

The second algorithm was to simulate turbulence mixing of mass and momentum. This algorithm is a two-equation turbulence model - one equation for turbulence kinetic energy and a second equation for a generic turbulence length scale quantity. The generic length scale quantity is designed so that the two-equation model can represent many popular existing turbulence closures, including the k-kl (Mellor-Yamada Level 2.5), k-ε , and k-ω schemes. Additionally, the two-equation model can be used to develop new turbulence closure methods. The incorporation of this algorithm in ROMS allows for an unprecedented range of existing and new turbulence closure selections in a single 3D oceanographic model. This approach allows inter-comparison and evaluation of many turbulence models in an otherwise identical numerical environment. This also allows evaluation of the effect of different turbulence models on other processes, such as suspended-sediment distribution or ecological processes.

The Generic Length Scale (GLS) approach (Umlauf and Burchard, 2003) is a two-equation model that takes advantage of the similarities in other two equation formulations. The first equation in the GLS model is the standard equation for transport of k, but the second equation is for a generic parameter that is used to establish the turbulence length scale. The first equation is

Equation 3. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov (3)

where is the turbulence Schmidt number for k. P and B represent production by shear and buoyancy as:

Equation 4. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov (4)

Equation 5. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov (5)

where N is the buoyancy frequency. Dissipation is modeled according to

Equation 6. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov (6)

where is the stability coefficient based on experimental data for unstratified channel flow with a log-layer solution. Parameter is a generic parameter defined by establishing the coefficients of p, m, and n and solved in the second transport equation for the GLS model as

Equation 7. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov (7)

where c1 and c2 are coefficients selected to be consistent with von Kármán's constant and with experimental observations for decaying homogeneous, isotropic turbulence. The parameter is the turbulence Schmidt number for and

Equation 8. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov (8)

Equation 9. For a more detailed explanation, contact John Warner at jcwarner@usgs.gov (9)

The reader is referred to Warner, et al. (2005) for a more detailed description, full explanation of equations, and complete reference list for both the sediment transport and turbulence closure algorithms.

(2) Promote the Community Sediment Transport Model.
I have assisted to promote the concept and exposure of a community sediment transport model. I attended many open meetings to discuss the development of a model, the needs of potential users, model platforms, structure, etc. Meetings attended include the Ocean Sciences Conference in Honolulu (Feb. 2002), a special Community Modeling Conference in Williamsburg, VA (Oct. 2002), presentations at the USGS Center for Coastal Geology at St. Petersburg, FL (Sept. 2002), and presentations at a Chesapeake Bay Modeling seminar at the USGS headquarters in Reston, VA (April 2002) and in Annapolis, MD (June 2002).

(3) Develop specific cases to test hydrodynamic and sediment transport models.
We developed specific idealized cases to test both the suspended sediment and turbulence closure subroutines. The test cases can be used to verify the performance of a subroutine or to compare results from different models. Most numerical modeling applications are very complex and it can be difficult to assess the performance of the code. The cases were designed to be simple so that modelers can easily test their routines, as well as test advancements to the model. The four test cases were (a) straight channel with homogenous steady flow to test continuity and sediment transport in an idealized river, (b) straight channel with tidal forcing and stratified flow to compare turbulence closures and test sediment transport in an idealized estuary, (c) wind induced surface mixing to test turbulence closures, (d) rectangular lake to test sediment transport, wave bottom boundary layer studies, and eventually multiple grain size transport. The test cases are presented in detail at http://woodshole.er.usgs.gov/project-pages/sediment-transport/Test_Cases.htm.

As an example, the estuary test case is used to both compare solutions from different turbulence closures and to test the transport of suspended sediment. Figure (1) shows the model domain. Values of all the parameters are provided on the web site, but the relevant dimensions are a length of 100 km and a depth that varies from 10 m at the (left) oceanic end to 5 m at the (right) riverine end. Tidal, fresh water, and slat flux boundary conditions allow the development of an oscillatory estuarine flow in the domain.

Model domain for the estuary test case.   Figure 1. Model domain for the estuary test case.

The model was initialized with a linearly varying longitudinal salinity field that ranged from 30 at the oceanic end to 0 at the riverine end. Simulations were the calculated for 20 tidal cycles (10 days), after which time a quasi-steady state had been reached. Figure 2 shows the resulting salinity fields for 4 different closure methods near the end of 20 tidal cycles. The 4 different closures are: MY25, Generic Length Scale (GLS) as KKL, GLS as KE, and GLS as KW88. The MY25 closure is computed based on a classical scheme of Mellor/Yamada (1982), and the GLS closures are computed with the method of Umlauf and Burchard (2003, Jrnl. Mar. Res.). The main difference is in the length scale limitations. For the MY25 method, the length scale is only limited in the calculation of the stability functions, whereas for the GLS method the length scale is limited in the production, wall proximity function, and the stability functions. The MY25 closure does not develop a well defined surface mixed layer as with the closures computed with the GLS method. This is most likely due to the length scale limitation and the buoyancy parameter.

Salinity distribution after 9.9 days for the estuary simulations.   Figure 2. Salinity distribution after 9.9 days for the estuary simulations.

Suspended sediment results (figure 3) are very dependent on the bottom stresses and vertical mixing processes. For these simulations, a thin layer of sediment was placed on the bed at time = 10 days. Sediment parameters were selected to allow rapid erosion. Upstream riverine flow will transport the sediment downstream and the estuarine circulation creates a turbidity maximum at the limit of salt intrusion. Figure 3 shows the results of the suspended sediment at day 19.9375. For the MY25 closure, the salt limit is near x = 35 km, while for the KE and KW simulations, a near bottom turbidity maximum is located near x = 50 km. For the KKL simulation, the turbidity maximum is further upstream, near x = 60 km.

Suspended   Figure 3. Suspended sediment concentration distribution after 9.9 days for the estuary simulations.

These results identified variations among the different turbulence closure schemes and identify the capabilities of the ROMS model to be able to simulate suspended sediment transport and parameterize several different turbulence closure methods. It is beyond the scope of this summary to discuss the intricacies of the results, but the reader is referred to Warner et al., (2005) for a full in depth discussion.

(4) Apply a sediment transport model to a regional study.
I have applied the ROMS model to several regional study applications. These include modeling of Suisun Bay, a northern sub-embayment of San Francisco Bay, to describe a the interaction between a shallow bay and an adjacent deep tidal channel. Observational data had identified a strange physical process of a sudden increase in flood tide velocity after very low tides. Numerical modeling helped to identify and qualify this process, caused by increased frictional effects in shallow water. This research concluded an effort originally started while I worked with the USGS WRD in Sacramento, and is discussed in detail in Warner, Schoellhamer, Ruhl, and Burau (2004).

Another application of the model is to the Hudson River Estuary. I am working closely with oceanographers at the Woods Hole Oceanographic Institution to conduct numerical modeling experiments of the Hudson River from New York Harbor northward 200 km to a dam near Albany. This research is to study the physical processes that control salt flux and sediment transport in an estuary. This site was chosen because there are many high quality observational data sets in this section of the river and many leading scientists continue to work in the region. This research is presented in Warner, Geyer, and Lerczak (in press).

A third application is to Massachusetts Bay, a 100x50 km subembayment on the northeastern shelf of the US with maximum depth on the order of 100 m. Observational and numerical studies are being conducted to predict the transport and fate of fine-grained sediments introduced to Massachusetts` coastal waters. We emphasize sediments because most contaminants introduced to the ocean are adsorbed by and transported with suspended sediments. After complicated cycles of deposition, resuspension, and biological and chemical interactions, contaminants on particles may be eventually buried in bottom sediments, which become the ultimate contaminant sink.

A 40 day numerical simulation of tidal circulation and suspended-sediment transport was conducted in Massachusetts Bay using the 3D numerical model Regional Ocean Modeling System (ROMS). Figure 4 shows the numerical grid consisting of an 68×68 grid cell pattern and extending 20 cells in the vertical. To predict the local wave field and bottom orbital velocities, another numerical model called Simulating Waves Nearshore (SWAN) model was used. Three simulations were performed to compare (1) circulation resulting only from tides, (2) circulation resulting from tides enhanced with a typical surface wind stress, and (3) circulation from tides plus a storm event. The storm event was a wave field from a northwest storm (October 1996) that had 11 second 6 m offshore swell and a wind speed of 15 m/s.

Site location and numerical grid 
        for model simulations of tidal currents and sediment transport in Massachusetts 
        Bay. Color bar denotes depth   Figure 4. Site location and numerical grid for model simulations of tidal currents and sediment transport in Massachusetts Bay. Color bar denotes depth (m).

Results demonstrate that tidal currents alone only account for a weak component in the total sediment flux in Massachusetts Bay. Simulations that include tidal currents plus a surface wind stress and enhanced wave bottom orbital velocities demonstrate greatly increased near bottom resuspensions and increased fluxes of sediment. Figure 5 shows one frame from an animated sequence of model results from case 3. The panels show magnitude of bottom velocity, bottom stress due to the combined affects of waves and currents, suspended sediment concentration, and change in bed thickness due to the resuspension or deposition of sediment. Results suggest transport of sediment along the coast south towards Cape Cod Bay. Erosion occurs along the top of Stellwagen Bank and the deposition of sediment is predicted in Stellwagen Basin. The results qualitatively agree with observational data. Further study is needed to increase the predictive capabilities of the model. These results are discussed in Warner, Butman, and Alexander (in prep).

Frame from animation sequence showing 
        model results of Massachusetts Bay. Panel show magnitude of bottom velocity, 
        bottom stress due to waves and currents, sediment concentration, and change 
        in bed thickness.   Figure 5. Frame from animation sequence showing model results of Massachusetts Bay. Panel show magnitude of bottom velocity, bottom stress due to waves and currents, sediment concentration, and change in bed thickness.

References Cited
Warner, J.C., Sherwood, C., Arango, H., and Signell, R. (2005). “Performance of Four Turbulence Closure Models Implemented Using a Generic Length Scale Method.” Ocean Modeling, v. 8/1-2, p. 81-113.

Warner, J.C., Schoellhamer, D.H., Ruhl, C.A., and Burau, J.R. (2004). “Floodtide pulses after low tides in shallow subembayments adjacent to deep channels.” Estuarine, Coastal, and Shelf Science, 60, p. 213-228.

Ganju, N., Schoellhamer, D.H., Warner, J.C., Barad, M.F., Schladow, G. (2004). “Tidal oscillation of sediment between a river and a bay.” Estuarine, Coastal, and Shelf Science, 60, p.81-90.

Warner, J.C., Geyer, W.R., and Lerczak. J.A. (in press) "Numerical modeling of an estuary: a comprehensive skill assessment." Journal of Geophysical Research – Oceans.

Warner, J.C., Butman, B., and Alexander, P. (in preparation) "Storm driven sediment transport in Massachusetts Bay."


Original Project Description: Prediction of the transport and fate sediment in coastal environments is important because sediment may contain adhered contaminants, have implications for navigation, fishing, recreation, waste disposal, and affect habitats of endangered species. The physical processes that transport sediment are complex, and simulation of these processes is best approached with numerical models. Models offer a means to evaluate the impacts of both natural and anthropogenic influences on sediment transport. However, there are few publicly available models that contain full-featured algorithms and are fully tested and widely established. There is a need for a model that is community based (freely available), widely accepted, and applicable to various coastal settings. John's research seeks to (1) assist in the development of a Community Sediment Transport Model; (2) develop specific cases and test hydrodynamic and sediment transport models; and (3) apply sediment transport models in regional studies.

One oceanographic model that John is working with is the Regional Ocean Modeling System (ROMS). ROMS is a free-surface, hydrostatic, primitive equation ocean model that uses stretched, terrain-following coordinates in the vertical and orthogonal curvilinear coordinates in the horizontal. A more complete description of the model may be found at http://marine.rutgers.edu/po/index.html. John is in the process of coding sediment-transport routines and multiple turbulence closure algorithms for this model. These routines will be tested and then applied to regional studies in the Hudson River, Massachusetts Bay, and possibly elsewhere. Model advances made during these efforts will contribute to the community modeling effort.

Publications:


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