Cohesive Sediment Algorithms in ROMSand Sediment Test Cases

Chris Sherwood1, Larry Sanford2, John Warner1

Bénédicte Ferré1, Courtney Harris3, Rich Signell1, and Alan Blumberg4

• Motivation• Non-cohesive formulation• Biodiffusive mixing• Cohesive sediment• Future work

1US Geological Survey2Univ. of Maryland3Univ. of Virginia4Stevens Institute

ROMS/TOMS WorkshopAlcalá de Henares, Nov. 6, 2006Funded by US EPA and USGS

Palos Verdes Shelf near Los Angeles

Contoured region:1993 Inventory >500 g/cm2 p,p’-DDE

• Spatial distribution Spatial distribution of DDE reflects of DDE reflects dominant transport dominant transport pathwaypathway

• 9 million m9 million m33 of of effluent affected effluent affected sediment sediment within 40 kmwithin 40 km22

• DDTDDTmaxmax 250 ppm 250 ppm PCBPCBmaxmax 20 ppm 20 ppm

• MassMassDDTDDT = 120 MT = 120 MTMassMassPCBPCB = 12 MT = 12 MT

• 70% of DDE is on 70% of DDE is on the shelf (the shelf ( 100 m) 100 m)

Lee et al., 2002

Palos Verdes Deposit- Two cohesive mud layers- DDE in lower layer- No sediment supply- Erosion of SE edge?

Porosity (from resistivity and water content)

at six sites in Feb 04

Stevens, Lewis, and Wheatcroft, 2004

Higher porosity =easier to erode (?)

Will the cohesive mud erode?Will the cohesive mud erode?

Sediment in ROMSSediment in ROMS• Non-cohesive sediment (sand and silt)Non-cohesive sediment (sand and silt)

– Bed response determined by particle characteristicsBed response determined by particle characteristics– Armoring caused by differential erosionArmoring caused by differential erosion

• Cohesive sediment (mud)Cohesive sediment (mud)– Bed response determined by bulk characteristicsBed response determined by bulk characteristics– Armoring caused by compaction (and biogeochemistry)Armoring caused by compaction (and biogeochemistry)

Sediment Variables

• Sediment class variables dimension(NST)– Median size, particle density, settling velocity, critical shear stress

• Bottom variables dimension(NX,NY,MBOTP)– Average grain size, critical shear stress, ripple geometry, hydraulic

roughness, parameters to specify “reference” critical shear stress and biodiffusion profiles, cohesive time scale

• Bed variables dimension(NX,NY,Nbed,MBEDP)– Thickness, volume solids fraction of each class, porosity, age, critical

shear stress, biodiffusivity

• Bed mass dimension (NX,NY,NBed,NST) • Bed fraction dimension (NX,NY,NBed,NST)

NST = # non-cohesive + # cohesive sediment typesMBOTP = # of bottom parameters

MBEDP = # of bed parametersNbed = # of bed layers

Sediment Transport Components

Suspended sediment transport

when tb > tce

Erosion formulation

Deposition formulation

s

CSink w

z

0 1 b ce

ce

Source E

*sf

sfs gD

3/ 2

*8 0.047sf

3sblq gD

non-dimensional shear stress

non-dimensional sediment flux

bed load transport rate, kg m-1s-1

Bed load transport: Meyer-Peter Muller

1,2 3

/iH V

i i

C U C C CK K Sources Sinks

t x x x x

Bed Model

Active layer thickness (Harris and Wiberg, 1997)

1 50( ) 6a sf cz k D

Sand – Armoring

Massachusetts BaySorting of Initially Uniform Sediments

Seafloor sediment distribution

Modeled Observed

Warner, J.C., Butman, B., and Dalyander, P.S. (submitted) "Storm-driven sediment transport in Massachusetts Bay"

Biodiffusive Mixing

• Implicit solution of diffusion equation

• Mixing profile Db(z) defined by five parameters

• Typical values in top ~5-8 cm of the bed are 10 cm2/y (O 10-7 m2 s-1)

b

C CD

t z z

Zero below some depth (~30 cm)

Exponential decrease

Constant (in surfacelayer (< 5 cm)

Sand - Biodiffusion

Cohesive Sediment Algorithm

• Key bed property is critical shear stress τcr

• τcr = F(depth, porosity, grain size, biology…)

• Assume τcr = F(mass depth) only

• So bulk density ρb is important

• Assume ρb = F(depth) only

• Assumes bed properties tend toward reference profiles• Determine reference profiles empirically• When system is perturbed (erosion or deposition), nudge

back toward reference profiles with appropriate time scale

Erosion Chamber Data

Photos and data: P. Wiberg, UVa

ln( ME ) = -0.34 + 2.00 ln( τ )

100 g/m3

Erosion• Initial τcref curve (red)

• Application of bed stress τb = 2 Pa

• Material with τcr < 2 Pa erodes

• Remaining material has higher τcr (black)

• τcr gradually relaxes to new, deeper τcr_ref

Deposition

ρb kg m-3

Sequence of Bed Operations

1. Erode / deposit to top layer2. New layer? Add to top; combine bottom3. [ Mix w/ mass conservation ]4. Determine active layer thickness5. Ensure top layer >= active layer6. Split / combine bottom layers7. Calc. bulk layer properties8. [ Relax bulk density toward reference profile]

9. [ Relax τc profile toward reference profile ]

Geostatistical Simulations of Erodibility

• Monte Carlo estimates of the slope term in the critical erosion profile• How does spatial variability affect sediment-transport calculations?

Chris Murray, Pacific Northwest National Lab

Next Steps

• Get the bugs out• Combine cohesive and non-cohesive calculations• Investigate sensitivity to time scale• Apply to Palos Verdes• Long term: try to characterize reference curves from bed

properties