James PM Syvitski & Eric WH Hutton, CSDMS, CU-Boulder

James PM Syvitski & Eric WH Hutton, CSDMS, CU-BoulderWith special thanks to Pat Wiberg, Carl Friedrichs, Courtney Harris,

Chris Reed, Rocky Geyer, Alan Niedoroda, Rich Signell, Chris Sherwood

Earth-surface Dynamics Modeling & Model Coupling A short course

Module 5: Shelf Sediment Transport

ref: Syvitski, J.P.M. et al., 2007. Prediction of margin stratigraphy. In: C.A. Nittrouer, et al. (Eds.) Continental-Margin Sedimentation: From Sediment Transport to Sequence Stratigraphy. IAS Spec. Publ. No. 37: 459-530.

Shelf diffusivity (3)Gravity-driven slope equilibrium

(4) Event-based models (7)Coastal Ocean Models (4)Summary (1)

Earth-surface Dynamic Modeling & Model Coupling, 2009

Shelf diffusivityLocal transport occurs if the probability of wave resuspension is exceeded at a particle’s water depth.

20 30 40 50 60 70 80 90100 120 1500

0.2

0.4

0.6

0.8

1

Water Depth (m)

Exc

ee

da

nce

Pro

ba

bili

ty

NDBC Buoy 46022, 1982-1998

ubs

>50 cm/s

ubs

>35 cm/s

ubs

>25 cm/s

ubs

>15 cm/s

Eel

40 50 60 70 80 90 1000

5000

10000

15000

20000

Depth (m)

across shelfalong shelf

Sed

imen

t di

ffus

ivity

(m

2/h

r)


Resuspension and Advection by Bottom Boundary Energy

Shelf diffusivity

∂h∂t

=∂∂x

k(t,x)∂h∂x

⎛

⎝ ⎜

⎞

⎠ ⎟

∂hi

∂t= ˜ k i

∂h∂t

• k(t,z) varies over time t (pdf of storms), and water depth z. Following Airy wave theory, k falls off exponentially with water depth. • ki is an index between 0 and 1 that reflects the ability

of grain size i to be resuspended and advected. • k(t,z) ≥ ki for sediment transport


Plumes Only

Plumes & Wave DiffusionEarth-surface Dynamic Modeling & Model Coupling, 2009

(a) If excess sediment enters BBL & Ri increases beyond Ricr, then turbulence is dampened, sediment is deposited, stratification is reduced and Ri returns to Ricr

(b) If excess sediment settles out of boundary layer, or bottom stress increases & Ri decreases beyond Ricr then turbulence intensifies. Sediment re-enters base of boundary layer. Stratification is increased in boundary layer and Ri returns to Ricr.

Sediment concentration Sediment concentration

Hei

ght a

bove

bed

Ri = Ricr Ri < Ricr

Ri > Ricr

Ri = Ricr

Gradient RichardsonNumber (Ri) =

density stratification

velocity shear

Shear instabilities occur for Ri < Ricr

“ “ suppressed for Ri > Ricr

(a) (b)

Gravity-driven slope equilibriumH

eigh

t abo

ve b

ed


(i) Momentum balance:

x-shelf gravity flowvelocity

= Bottom frictionDown-slopepressure gradient

x-shelfbed slope

depth-integratedbuoyancy anomaly

bottom dragcoefficient

wave-averaged,x-shelf component

of quadratic velocity

B = cd < | u | u > = cd Umax ugrav

total velocity = (Uw2 + vc

2 +ugrav

2)1/2

(ii) Maximum turbulent sediment load:

RichardsonNumber

Buoyancy

Shear= = Critical value

(c.f. Trowbridge & Kineke, JGR 1994)

z = 0

z = h

z

y

x

c'

Umax = (Uw + vc + ugrav)1/2

ugrav

vcUw

Gravity-driven slope equilibrium


(Wright et al., Mar.Geol. 2001)

Predicted bedelevation

Observed bedelevation

(Observations from Traykovski et al., CSR 2000)

Deposition Rate = − Ricr2

(1-P) cd g s ddx

(α Umax3)

Porosity (sed/water -1) Bed slope Richardson # Drag coeff.

P = 0.9 s = 1.6 = 0.004 Ricr = 0.25 cd = 0.003

Suspendedsediment

COMPARISON OF MODEL PREDICTIONS TO OBSERVED DEPOSITION

Application to 1996-97 Eel River Flood at 60-meter Site


Wave orbitalvelocity

Top: Plumes & Wave Diffusion; Bottom: Plumes, Waves & Fluid Muds


Event-based transport modelCalculate suspended sediment flux (by grain size) using a 1-D shelf sediment transport model at a cross-shelf grid of nodes of specified depth and sediment characteristics. For each event (set of wave & current conditions), the net flux is calculated at each node. The divergence of the flux gives the change in bed elevation.

∂ηi

∂t=−

1cb

∂∂x

Dcx

∂ci

∂x+

∂∂y

Dcy

∂ci

∂y

⎛

⎝ ⎜ ⎜

⎞

⎠ ⎟ ⎟

∂F∂t

=−1

cbLa

∂qi

∂x

⎛

⎝ ⎜

⎞

⎠ ⎟ − Fei

∂η∂t

+σ⎛

⎝ ⎜

⎞

⎠ ⎟

∂η∂t

=∂ηi

∂ti=1

N

∑

qxi =−Dcx

∂ci

∂xqyi =−Dcy

∂ci

∂y


4 6 8 10 12 14 160

0.5

1

Silt

fra

ctio

n

4 6 8 10 12 14 160

0.5

1

San

d fr

actio

n

Cross-shelf distance (km)

4 6 8 10 12 14 16-5

0

5

Bed

ele

vatio

n (c

m)

<45m45-63m63-125 m125-500 m

Example of 5 repetitions of a transport event on Eel Margin.


SLICE DescriptionSLICE Description

tides

wind

waves

grid

Neidoroda & Reed


SLICE Description

Neidoroda & Reed


Distance (m)0 5000 10000 15000 20000

-120

-100

-80

-60

-40

-20

0

Distance (m)1000 2000 3000 4000

-40

-30

-20

Distance (m)0 5000 10000 15000 20000

-120

-100

-80

-60

-40

-20

0

Distance (m)0 5000 10000 15000 20000

-120

-100

-80

-60

-40

-20

0

0 4000 8000 12000 16000Distance Offshore (m)

-0.2

-0.1

0

0.1

0.2

Heigth

(m)

Mudflow Deposit

Mudflow Profile

SLICE Density FlowsNeidoroda & Reed


Neidoroda & ReedEarth-surface Dynamic Modeling & Model Coupling, 2009

Neidoroda & Reed


Average Sediment and Currents.

Sept, 2002 – May, 2003

Global Met. Model (NOGAPS)(coupled ocean-atm model)

toRegional Met. Model (COAMPS)

(coupled ocean-atm model)to

Wave Model (SWAN)for

Sediment Resuspension (ROMS)

Global Ocean Model (NOGAPS)

(coupled ocean-atm model)to

Regional Ocean Model (ROMS)

(coupled ocean-atm model)for

Regional Circulation and Current Shear

Regional Hydrological Model (HydroTrend)

(atm-landsurface model)to

Regional Ocean Model (ROMS)for

Sediment Supply, Buoyancy, Sediment Plumes

C.Harris, VIMS

C.Harris, VIMS

Nested Modeling


Circulation and Sediment-Transport Modeling

• ROMS: Regional Ocean Modeling System — RANS for heat & momentum fluxes

• 3-8 km grid, 21 vertical “S” levels• Initialized with ship data• Zero-gradient b.c. near Otronto, seven tidal components• LAMI forcing every 3 hours, SWAN waves, Po River discharge• k- turbulence model, Styles & Glenn wave-current boundary layer• Resuspension & transport of single grain size, ws = 0.1 mm/s, c =0.08Pa

Winds; Wave height

Bottom currents;Sus. Seds.

Salinity;Depth-mean

currents


C. Sherwood, USGS


VIMS-NCOM 3D Transport Model

NCOM Vertical Grid

Inputs: sediment

sources, sizes, critical shear

stress, settling velocity.

Calculates: flux,

concentration, erosion /

deposition.

Sea Floor Grid

2 km Sediment Model

Currents, Bed Shear


Conclusions:Conclusions:Shelf diffusivityAdvantages: uses daily pdf of regional ocean energy, simple and robust; compatible with landscape evolution modelsDisadvantages: depends wave energy pdf -- how variable is diffusion in response to decadal and longer term variability?

Gravity-driven slope equilibriumAdvantages: uses daily pdf of local total velocity, simple and robust; can be tested against field dataDisadvantages: Needs pdf for wave energy and sediment discharge from rivers, to calculate Richardson numberEvent-based Approach Advantages: uses wave, current, and sediment information available for a site, preserving all correlations, can be tested against field dataDisadvantages: time scales short, data needs intensive for long-term simulations, inshore boundary condition difficult to specifyCoastal Ocean ModelAdvantages: Can get it right if all terms are included & appropriate resolution is used.Disadvantage: Computationally intensive: data needs intensive


James PM Syvitski & Eric WH Hutton, CSDMS, CU-Boulder

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