Representation of Near-Bed Sediment Gravity Flows within the Regional Ocean Modeling System (ROMS)

1. MOTIVATION: Sediment-induced stratification very close to the bed (bottom 10-20 cm) creates strong limits to resuspension. This vertical scale, however, is well below the resolution of most 3-D ocean models. Sediment concentrations from field data (o) and estimated by high-resolution (vertical scale ~mm) 1-D model. When the model neglected stratification in bottom 10 cm, it overestimated vertical mixing and sediment concentrations. Much of this stratification occurs at the top of the wave boundary layer. Additionally, high-concentration layers create near-bed gravity flows. Figure from Traykovski, et al. (2007) Current Sediment Exchange Cd Udiff2 Figure modified from Traykovski, et al. (2007). GOAL: Account for stratification near the bed by using an additional grid cell for the wave boundary layer. Estimates of (A) sediment deposition, (B) transport in the wave boundary layer, and (C) transport in dilute suspension during a time (D) following peak discharge during (E) high waves. Nearly all cross-shelf flux occurs in the wave boundary layer gravity flow. APPROACH: Across-shelf Model of Near-bed Turbid Layer: Modify for inclusion into three-dimensional model TEST CASE NEGLECTING GRAVITY FLOW: (A) Beginning sediment deposit thickness (m) and (B) that at the end of 2.5 days. Waves preferentially erode material from the shoreward edge. Sediment is carried southward in suspension. (C) Net erosion (blue) and deposition (yellow) estimated over 2.5 days. ROMS Test Case: continental shelf geometrically similar to west coast, US. (A) (B) (C) Muddy River (D) Transient inner shelf deposit Gravity flow (E) (B) 200 m 70 km (A) Final mid-shelf deposit 20 km • Add wave boundary layer beneath s-grid of ROMS, following Harris et al. (2004): • Sediment exchanged between wbl and both the bed and overlying water. • Exchange with sea-bed=(Cwbl – Cref) ws • Exchange with overlying water depends on Richardson number. • Velocity in wbl depends on a Chezy balance between buoyancy anomaly of suspension and frictional drag. • Simple continental shelf geometry with a freshwater source. • Currents (~XXX m/s) forced at open boundary. • Waves (Hsig = 3m, T = 15 sec) • Initial sediment bed has a 10 cm thick layer of mud (tcr = 0.1 Pa, ws = 0.1 mm s-1) Estimated near-bed suspended sediment concentrations (g/L). Values highest over available sediment and in shallow water where wave shear stresses are high. u(1), v(1) u(1), v(1) uwbl, vwbl Representation of Near-Bed Sediment Gravity Flows within the Regional Ocean Modeling System (ROMS) Courtney K. Harris and Aaron J. Bever Virginia Institute of Marine Science Gloucester Point, Virginia USA ABSTRACT: Within the past decade, data from several continental shelf and deltaic environments has shown near-bed sediment gravity flows to be an important component of across-shelf sediment transport. Both observational and theoretical work has concluded that stratification at the top of the wave-boundary layer can trap sediment within this thin layer (~10 cm thick), creating fluid muds whose density anomaly is sufficient to cause downslope transport. This transport process, however, can not be represented within standard vertical grids (z-, s-, or sigma-coordinate) used within ocean models because the thickness of the wave boundary layer typically increases as water depth decreases, and because it is usually too thin to be resolved. Additionally, standard wave-current interaction modules used within ocean models do not resolve velocities and turbulence at the vertical resolution of the wave boundary layer. These considerations motivated previous work within ECOM-SED (Estuarine and Coastal Ocean Model – SEDiment) to represent near-bed sediment gravity flows using a separate grid cell underneath of the model’s sigma-grid (Harris et al., 2004; 2005). A similar component is being implemented within the Regional Ocean Modeling System (ROMS) and being tested using an idealized continental shelf / river plume test case. EXAMPLES USING GRAVITY FLOW MODEL WITHIN ECOM-SED: EEL RIVER SHELF, California: Model that included wave boundary layer flows delivered flood material to the mid-shelf, where it was observed to accumulate. When model neglected wave boundary layer flows, sediment deposits on the mid-shelf were much thinner (mm) than observed (~10cm). WAIAPU RIVER SHELF, NZ: The Waiapu River is a small, mountainous river near the East Cape of the North Island, NZ. It delivers about 35 million metric tons of sediment per year. Recent efforts by Kniskern (2007) included numerical modeling of flood dispersal for this river, as well as extensive sediment coring to map flood accumulation. (A) (D) (C) (B) Panels (A) and (B) show model estimates of flood sediment deposition that neglected wave boundary layer gravity flows. (A) used a low settling velocity (0.1 mm/s), compared to (B) (1.0 mm/s). Neither correctly estimated the location and size of the observed flood deposit (shown in panel C). Panel (D) shows model estimates that did include a wave boundary layer gravity flow. It was able to produce a mid-shelf mud deposit of a similar thickness to that observed. Cross-shelf sediment flux is dominated by transport in the wave boundary layer. (A) Mid-shelf mud deposit estimated by numerical model that resulted from cross-shelf transport via wave supported gravity flows. (B) Accumulation rates based on 210-Pb (~100 year half-life) indicates that sediment accumulates on the mid-shelf, not the inner shelf. (Figures modified from Harris et al. 2005) CONVENTIONAL SEDIMENT MODEL (Figures courtesy of T. Kniskern, UCSC/USGS, based on Kniskern, 2007) REVISED SEDIMENT MODEL concentration in layer is t(…,1,ised) • WHAT’S NEXT? • Debug code to fix problems with advection scheme and net erosion / deposition • Finish model testing by analyzing the test-case for conservation of mass, etc. • Write the new variables to NetCDF history and restart files. • Apply model code to a realistic model grid (Waipaoa River Shelf, New Zealand). concentration in layer is t(…,1,ised) TEST CASE INCLUDING GRAVITY FLOW: • STATUS: • Model has been coded into ROMS’ sediment.F using “if defined WBLGRAV_HTG”. • New variables added (CsedW, Uwbl, Vwbl) • New code compiles and runs  • Water column calculations seem reasonable. • Suspended sediment concentrations are in a reasonable range. • Velocity of wave boundary layer seems too high. • Seems to be a problem with stability of the advection scheme. • Causing CsedW < 0, which then causes Uwbl < 0. • Adjustments of sediment bed needs debugging. Hz(1) FC ero_flux: (Munk-Anderson stratification) FC Hz(1) ero_flux (Partheniades) dwbl FCW erow_flux Sediment Bed CsedW REFERENCES: Harris, C.K., P. Traykovski and W.R. Geyer, 2004. Including a near-bed turbid layer in a three dimensional sediment transport model with application to the Eel River shelf, northern California. In: M.L. Spaulding (Editor), Estuarine and Coastal Modeling. American Society of Civil Engineers, Monterey, CA, pp. 784-803. Harris, C.K., P. Traykovski and W.R. Geyer, 2005. Flood dispersal and deposition by near-bed gravitational sediment flows and oceanographic transport: A numerical modeling study of the Eel River shelf, northern California. Journal of Geophysical Research, 110(C09025): doi: 10.1029 / 2004JCO02727. Kniskern, T.A. 2007. Shelf sediment dispersal mechanisms and deposition on the Waiapu River shelf, New Zealand.Ph.D. Dissertation, Virginia Institute of Marine Science, College of William and Mary. Gloucester Point, VA USA. Traykovski, P., P.L. Wiberg and W.R. Geyer. 2007. Observations and modeling of wave-supported sediment gravity flows on the Po prodelta and comparison to prior observations from the Eel shelf. Continental Shelf Research, 27: 375 – 399. ACKNOWLEDGEMENTS: This project is funded by ONR Coastal Geosciences Program, Award N00014-07-1-0312. J.Paul Rinehimer (VIMS) helped with setting up the ROMS test case. Sediment Bed 2007 ROMS / TOMS User Workshop. October 2 - 4, 2007, Los Angeles, CA.