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Earth-surface Dynamics Modeling & Model Coupling A short course. James PM Syvitski & Eric WH Hutton, CSDMS, CU-Boulder With special thanks to Pat Wiberg, Carl Friedrichs, Courtney Harris, Chris Reed, Rocky Geyer, Alan Niedoroda, Rich Signell, Chris Sherwood. - PowerPoint PPT Presentation
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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)
Earth-surface Dynamic Modeling & Model Coupling, 2009
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
Earth-surface Dynamic Modeling & Model Coupling, 2009
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
Earth-surface Dynamic Modeling & Model Coupling, 2009
(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
Earth-surface Dynamic Modeling & Model Coupling, 2009
(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
Earth-surface Dynamic Modeling & Model Coupling, 2009
Wave orbitalvelocity
Top: Plumes & Wave Diffusion; Bottom: Plumes, Waves & Fluid Muds
Earth-surface Dynamic Modeling & Model Coupling, 2009
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
Earth-surface Dynamic Modeling & Model Coupling, 2009
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.
Earth-surface Dynamic Modeling & Model Coupling, 2009
SLICE DescriptionSLICE Description
tides
wind
waves
grid
Neidoroda & Reed
Earth-surface Dynamic Modeling & Model Coupling, 2009
SLICE Description
Neidoroda & Reed
Earth-surface Dynamic Modeling & Model Coupling, 2009
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
Earth-surface Dynamic Modeling & Model Coupling, 2009
Neidoroda & ReedEarth-surface Dynamic Modeling & Model Coupling, 2009
Neidoroda & Reed
Earth-surface Dynamic Modeling & Model Coupling, 2009
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
Earth-surface Dynamic Modeling & Model Coupling, 2009
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
Earth-surface Dynamic Modeling & Model Coupling, 2009
C. Sherwood, USGS
Earth-surface Dynamic Modeling & Model Coupling, 2009
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
Earth-surface Dynamic Modeling & Model Coupling, 2009
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
Earth-surface Dynamic Modeling & Model Coupling, 2009