National Center for Earth-surface Dynamics Contribution from the
National Center for Earth-surface Dynamics for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006 DELTA-SCALE NUMERICAL
MODELING: A TOOL FOR DECISIONMAKING IN THE REHABILITATION OF THE
MISSISSIPPI DELTA Adapted from a lecture given by Gary Parker,
University of Illinois on behalf of the National Center for
Earth-surface Dynamics (NCED) at the ASCE World Environmental and
Water Resources Congress, May 25, 2006. The Mississippi Delta is
sinking into the Gulf of Mexico. Slide 2 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 THE PROBLEMS OF THE MISSISSIPPI DELTA AND THE RISK
TO NEW ORLEANS WERE WELL-KNOWN LONG BEFORE HURRICANE KATRINA
Scientific American, October, 2001 Slide 3 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 THE MISSISSIPPI DELTA FALLS WITHIN THE CLASS OF
FANS AND FAN-DELTAS The Okavango Inland Fan, Botswana. From NASA
The Nile Delta, Egypt. From NASA Slide 4 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 THE FAN-DELTA AT THE MOUTH OF THE YELLOW RIVER IS
A GOOD ILLUSTRATION Mouth of the Yellow River. From NASA. Slide 5
National Center for Earth-surface Dynamics Contribution from the
National Center for Earth-surface Dynamics for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006 THE PROCESSES Channel
aggradation and progradation overbank sediment deposition as
channel aggrades delta extension as channel head progrades channel
migration or avulsion to shorter path to sea The processes that
build fans and fan-deltas are: Slide 6 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 THE ENTIRE NORTH CHINA PLAIN IS AN ALLUVIAL FAN
Over thousands of years of historical time the Yellow River has
repeatedly shifted between courses north and south of the Shandong
peninsula. Present delta Shandong peninsula Slide 7 National Center
for Earth-surface Dynamics Contribution from the National Center
for Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 WHAT HAPPENS WHEN HUMANS INTERFERE WITH THIS
PROCESS BY BUILDING DIKES AND PREVENTING AVULSIONS? Adapted from Hu
Yisan and Xu Fuling (1989) One reach of the Yellow River is perched
10 m above the surrounding North China Plain Slide 8 National
Center for Earth-surface Dynamics Contribution from the National
Center for Earth-surface Dynamics for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006 THE KUSATSU RIVER FORMS A
FAN-DELTA ON LAKE BIWA, JAPAN WHICH IS DENSELY POPULATED It has not
been allowed to avulse since the 10 th Century. Slide 9 National
Center for Earth-surface Dynamics Contribution from the National
Center for Earth-surface Dynamics for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006 OVER GEOMORPHIC TIME THE
MISSISSIPPI RIVER HAS REPEATEDLY AVULSED TO FORM NEW LOBES Slide 10
National Center for Earth-surface Dynamics Contribution from the
National Center for Earth-surface Dynamics for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006 Under natural conditions, this
subsidence is balanced by overbank deposition of sediment and
avulsion into low areas. Mississippi River and levees downstream of
New Orleans. Subsiding fan-delta surface behind levees south of New
Orleans. LIKE MANY LARGE DELTAS, THE MISSISSIPPI DELTA SUBSIDES BY
COMPACTION UNDER ITS OWN WEIGHT Slide 11 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 THE RIVER IS DIKED ALONG ITS ENTIRE LENGTH AND IS
NOT ALLOWED TO AVULSE Sediment is either stored in-channel or
funneled out to sea. Slide 12 National Center for Earth-surface
Dynamics Contribution from the National Center for Earth-surface
Dynamics for the Short Course Environmental Fluid Mechanics:
Theory, Experiments and Applications Karlsruhe, Germany, June
12-23, 2006 SO THE RIVER BED GETS HIGHER AND HIGHER E.G. AT THE OLD
RIVER CONTROL STRUCTURE, Slide 13 National Center for Earth-surface
Dynamics Contribution from the National Center for Earth-surface
Dynamics for the Short Course Environmental Fluid Mechanics:
Theory, Experiments and Applications Karlsruhe, Germany, June
12-23, 2006 THE RIVER MOUTH EXTENDS FARTHER AND FARTHER INTO THE
GULF OF MEXICO, Slide 14 National Center for Earth-surface Dynamics
Contribution from the National Center for Earth-surface Dynamics
for the Short Course Environmental Fluid Mechanics: Theory,
Experiments and Applications Karlsruhe, Germany, June 12-23, 2006
AND THE REST OF THE DELTA SUBSIDES UNDER COMPACTION, WITH NO
REPLACEMENT SEDIMENT, CAUSING THE SHORELINE TO ADVANCE At this
rate, New Orleans will be exposed to the open sea by 2090.
Fischetti (2001), Scientific American Slide 15 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 The Mississippi Delta rapidly subsides by
compaction under its own weight. Under natural conditions this
subsidence is balanced by overbank deposition of sediment abetted
by channel avulsion. The mud that would construct the floodplain is
held behind levees and delivered out to sea. Meanwhile the sand
deposits on the channel between the levees as it elongates. As a
result, the levees and the prevention of avulsion is causing the
shoreline to advance, not in geomorphic time, but in engineering
time. THE PROBLEM IN A NUTSHELL Slide 16 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 THE MISSISSIPPI DELTA PROJECT OF THE NATIONAL
CENTER FOR EARTH-SURFACE DYNAMICS (NCED) NCED has been developing
large-scale morphodynamic models to evaluate the rehabilitation of
the Mississippi Delta. Slide 17 National Center for Earth-surface
Dynamics Contribution from the National Center for Earth-surface
Dynamics for the Short Course Environmental Fluid Mechanics:
Theory, Experiments and Applications Karlsruhe, Germany, June
12-23, 2006 HURRICANE KATRINA HIGHLIGHTED THE NEED FOR THE
MISSISSIPPI DELTA PROJECT which is being conducted as as a joint
effort between NCEDs Stream Restoration and Subsurface Architecture
programs Slide 18 National Center for Earth-surface Dynamics
Contribution from the National Center for Earth-surface Dynamics
for the Short Course Environmental Fluid Mechanics: Theory,
Experiments and Applications Karlsruhe, Germany, June 12-23, 2006
THE MISSISSIPPI DELTA/NEW ORLEANS PROBLEM IS OFTEN THOUGHT OF AS A
HURRICANE/STORM-SURGE PROBLEM There is no hope of alleviating the
storm surge problem without building land. This house is not in
standing water because of storm surge! The root of the problem,
however is the disappearance of delta land as sediment that would
replenish the sinking delta is instead channeled by dikes straight
out to the Gulf of Mexico. Slide 19 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 CAN WE BUILD LAND BY MEANS OF A PARTIAL DIVERSION
(CONTROLLED AVULSION) OF THE MISSISSIPPI RIVER? HERE? OR HERE?
Slide 20 National Center for Earth-surface Dynamics Contribution
from the National Center for Earth-surface Dynamics for the Short
Course Environmental Fluid Mechanics: Theory, Experiments and
Applications Karlsruhe, Germany, June 12-23, 2006 PROOF OF CONCEPT:
THE WAX LAKE DELTA During the Great Flood of 1973, the Mississippi
River nearly avulsed into the Atchafalaya River and part of the
Atchafalaya River avulsed into a drainage channel (Wax Lake Outlet)
to form the Wax Lake Delta Slide 21 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 THE WAX LAKE DELTA HAS BEEN BUILDING NEW LAND
SINCE 1973 The Atchafalaya River has been receiving 30 ~ 60% of the
sediment of the Mississippi River, and the Wax Lake Delta has been
receiving about half of the sediment of the Atchafalaya River.
Slide 22 National Center for Earth-surface Dynamics Contribution
from the National Center for Earth-surface Dynamics for the Short
Course Environmental Fluid Mechanics: Theory, Experiments and
Applications Karlsruhe, Germany, June 12-23, 2006 CAN WE CAPTURE
THIS LAND BUILDING IN A NUMERICAL MODEL? Cooperating researchers at
Louisiana State Univ. (Roberts, Twilley), Univ. of Louisiana
Lafayette (Meselhe), Univ. of New Orleans (McCorquodale) and Tulane
Univ. (Allison). NCED researchers at the Univ. of Minnesota (Paola)
and the Massachusetts Institute of Technology (Mohrig), and A first
model has been developed by NCED at the Univ. of Illinois, in
cooperation with Slide 23 National Center for Earth-surface
Dynamics Contribution from the National Center for Earth-surface
Dynamics for the Short Course Environmental Fluid Mechanics:
Theory, Experiments and Applications Karlsruhe, Germany, June
12-23, 2006 ELEMENTS INCLUDED IN THE MODEL Deposition of mud
Channel-floodplain co- evolution Self-channelization Flood
hydrology Deposition of sand Sea level rise Delta progradation
Subsidence Slide 24 National Center for Earth-surface Dynamics
Contribution from the National Center for Earth-surface Dynamics
for the Short Course Environmental Fluid Mechanics: Theory,
Experiments and Applications Karlsruhe, Germany, June 12-23, 2006
THE GEOMETRY Fluvial reach x v = downvalley coordinate on fluvial
reach L f = reach length B fc = channel bankfull width on fluvial
reach B f = floodplain width on fluvial reach Fan-delta reach r f =
downfan radial coordinate r u = value of r f at upstream end of fan
reach r d = r d (t) = value of r f at downstream end of fan-delta
reach = fan-delta angle B d = r = fan-delta width B dc = width of
channel (or amalgamated channels) on fan-delta reach Slide 25
National Center for Earth-surface Dynamics Contribution from the
National Center for Earth-surface Dynamics for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006 SOME ASSUMPTIONS Sand deposits
in both the channel and the floodplain, but mud deposits only in
the floodplain, For each volume unit of sand deposited in the
channel-floodplain complex units of mud are deposited in the
channel-floodplain complex. The channel(s) migrates or avulses
across the floodplain (width B f ) or fan-delta (width B c = r) to
fill all the available space. The channel is meandering and has
sinuosity f on the fluvial reach and d on the fan-delta reach.
Averaging over many bends, the relation between down-channel
coordinate x and down-valley coordinate x v in the fluvial reach is
given as Where r is down-channel coordinate on the fan-delta, the
corresponding relation for the fan-delta reach is Slide 26 National
Center for Earth-surface Dynamics Contribution from the National
Center for Earth-surface Dynamics for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006 SOME ASSUMPTIONS (contd.) The
bulk porosity of the deposit in the channel-floodplain complex of
the fluvial reach is pf. The corresponding value for the fan-delta
is pd. The mean elevation of the bed of the channel-floodplain
complex of the fluvial reach is f ; the corresponding value for the
fan-delta reach is d. Well below the surface channel-floodplain
complex is a basement with elevation bf in the fluvial reach and
elevation bd in the fan-delta reach. These basements are subsiding
under compaction at the respective fluvial and fan-delta rates f
and d, where xvxv ff bf ff Slide 27 National Center for
Earth-surface Dynamics Contribution from the National Center for
Earth-surface Dynamics for the Short Course Environmental Fluid
Mechanics: Theory, Experiments and Applications Karlsruhe, Germany,
June 12-23, 2006 EXNER EQUATION OF SEDIMENT CONTINUITY: FLUVIAL
REACH The volume flood transport rates sand and mud during floods
load in m 3 /s are denoted as Q s and Q m, respectively. Flood
intermittency is I f so that e.g. I f Q s = mean annual volume sand
load. Sand and mud are transported down the channel(s). Only sand
deposits in the channel; sand and mud deposit across the entire
channel-floodplain complex. Reduce with to get Slide 28 National
Center for Earth-surface Dynamics Contribution from the National
Center for Earth-surface Dynamics for the Short Course
Environmental Fluid Mechanics: Theory, Experiments and Applications
Karlsruhe, Germany, June 12-23, 2006 EXNER EQUATION OF SEDIMENT
CONSERVATION: FLUVIAL REACH AND FAN-DELTA REACHES Fluvial reach:
sediment is transported in the channel but deposited over the
entire floodplain width to model long-term floodplain deposition,
channel migration and avulsion. Where the subscript f denotes
fluvial reach: Fan-delta reach: sediment is transported in the
channel, or an amalgamation of more than one active channels, but
deposited over the entire width B d = r f of an axially symmetric
fan-delta to model long-term floodplain deposition, channel
migration and avulsion. The analogous form of sediment
conservation, for which the subscript d denotes fan-delta reach,
is: Slide 29 National Center for Earth-surface Dynamics
Contribution from the National Center for Earth-surface Dynamics
for the Short Course Environmental Fluid Mechanics: Theory,
Experiments and Applications Karlsruhe, Germany, June 12-23, 2006
CLOSURE FOR SELF-FORMED CHANNEL GEOMETRY Channel geometry is
described using bankfull parameters. A Chezy resistance relation
with constant Cz = C f -1/2 ) is applied to gradually varied flow.
Where U bf denotes flow velocity at bankfull flow, the bed shear
stress is given as (slide 34 of lecture on hydraulics) The sand in
the streambed is characterized with a single grain size D. A
constant channel-forming Shields number is assumed; recalling Q bf
= U bf B bf H bf, where from slide 25 of the lecture on hydraulic
geometry form * ~ 2.16. The sand transport relation is that of
Engelund and Hansen (1967); reducing the relation of slide 11 of
the lecture on hydraulics with Q s = B bf q t = sand load at
bankfull flow, Slide 30 National Center for Earth-surface Dynamics
Contribution from the National Center for Earth-surface Dynamics
for the Short Course Environmental Fluid Mechanics: Theory,
Experiments and Applications Karlsruhe, Germany, June 12-23, 2006
IS THE ASSUMPTION OF CONSTANT CHANNEL-FORMING SHIELDS NUMBER
REASONABLE? The diagram below is from the lecture on bankfull
hydraulic geometry Slide 31 National Center for Earth-surface
Dynamics Contribution from the National Center for Earth-surface
Dynamics for the Short Course Environmental Fluid Mechanics:
Theory, Experiments and Applications Karlsruhe, Germany, June
12-23, 2006 BACKWATER AT BANKFULL FLOW IN A SELF-FORMED CHANNEL The
full backwater equation is (slides 34 and 25 of the lecture on
hydraulics) A constant channel-forming Shields number form *
implies a bankfull velocity U bf that is constant in the downstream
direction: The backwater equation applied to bankfull flow thus
reduces to Where Fr bf = bankfull Froude number. In low-slope
sand-bed streams, Fr bf 2 is usually < 0.1, and can be
neglected, yielding Slide 32 National Center for Earth-surface
Dynamics Contribution from the National Center for Earth-surface
Dynamics for the Short Course Environmental Fluid Mechanics:
Theory, Experiments and Applications Karlsruhe, Germany, June
12-23, 2006 ARE THE ASSUMPTIONS OF CONSTANT BANKFULL FLOW VELOCITY
AND Fr bf 2
