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21/08/2014
1
Faculty of Geosciences
River and delta morphodynamics
Introduction MSc course Fluvial Systems GEO4-4436
Dr. Maarten G. Kleinhans
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C D
B A
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Fluvial systems
geomorphology
sedimentology / geology
engineering
… in one course
→ challenge is to communicate
You cannot truly cross the borders of your own culture
until you master the language of another
(Chaim Potok, Wanderings)
4
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Four scales
Flow, sediment transport and channel
morphodynamics (morphodynamic loop)
repetition of earlier courses!
River patterns
Bifurcations and avulsion
From source to sink and in between 5
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Four scales (1)
Flow, sediment transport and channel
morphodynamics (morphodynamic loop)
steady uniform flow and backwater effect
equilibrium sediment transport
exner equation
required initial / boundary conditions
effects of changing boundary conditions
and time scale
basics of numerical modelling
6
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The morphodynamic system
also needed:
source of flow and sediment
initial valley shape
vegetation?
where it all ends: downstream
7
flow
sediment
transport
morphology
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Four scales (2)
River patterns
floodplain formation
morphodynamic instability
bar patterns
river patterns
■ underlying physics (sketch)
■ necessary and sufficient boundary conditions
effect of changing boundary conditions
preservation, sedimentology
8
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Four scales (3)
Bifurcations and avulsion
physics of bifurcation stability
causes of avulsion
accommodation space
9
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Four scales (4)
From source to sink and in between
simple cases: mass conservation
sediment budgets and transfer
through valleys and multiple basins
reconstructing allogenic forcing
accommodation space
fluvial architecture
10
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What is the use of all this?
river engineering
river management
nature restoration
geological resources
sediments
water, oil
application to reconstruction
predict effects of global change
sustainable use of sinking/drowning deltas 11
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How do this course? approach
scales
logic
basic techniques
didactics
explicit clarification of terms
play: do yourself
discuss and provide constructive criticisms
reflection on different disciplinary approaches!
(it’s one world…) 12
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Cross-talk: main terminology
Morphodynamics: Quaternary Geology:
upstream boundary
conditions
climate
downstream boundary
conditions
base level, tides, waves
yet another term in the
sediment mass balance
tectonics / subsidence
wash load suspended load
bed + suspended bed
material load
bed load 13
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Course activities Lectures–tutorials
contribute! discussion, questions, calculations,
literature
Read many papers
Computer practicals
to get you started, finish reports at home
provides tools
for creative programming assignment
Delta project
turn one delta inside out:
explain/understand evolution
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Assessment The Matrix: matlab code: (1/3 grade)
5% for small exercises
18% for creative exercise
also presented in 5 min in ppt
The Delta Force: team project (1/3 grade)
turn delta inside out
presented in powerpoint + abstract
individual contributions indicated
The Final Frontier: exam (1/3 grade)
tests insight
STUDY the study guide!
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Literature and resources
Papers
Library, course website
Slides
Course website, make your own notes
Matlab
instructions
matlab help
Us, the lecturers
matlab code
geological and morphological data
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“This lecture: main questions and points”
main questions help you think
answer! your own summary = structure
Before lectures:
prepare! answer questions
about prescribed literature
17
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How to read literature?
title, abstract
figures + captions
what are you looking for?
write your own papers like this too
hints: http://www.lc.unsw.edu.au/olib.html
18
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Matlab programming
build up from simple exercises
build tools for data analyses (MSc thesis)
building a simple model helps to understand
existing complicated models
evaluation:
works? (does it run)
understandable? (comments)
does what it has to do? (RTFM)
http://plagiarism.org/?
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Your creative Matlab project
your own creative idea: anything fluvial
flow, particles, avalanches, avulsions..
see things as if for the first time
and ask the ‘stupid’ questions
analyse and plot (available) data
■ sediment transport / bedforms
■ experimental meandering
■ core data of Rhine-Meuse delta
model
■ 1D morphological model (as in Parker E-book)
■ meandering line or 2D cellular braiding
■ Connect other model code/output
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How conduct an investigation?
curiosity → question
hypothesis
method
results
evaluate hypothesis
tell the world
new questions
21/26
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How to make a ppt presentation?
structure
question, hypothesis, methods, results, discussion,
conclusion
kill your darlings
main message?
elevator pitch
figures not (much) words
yet keep core of creative idea!
simple language
practice 22
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Delta project
Choice from some well-documented deltas
unravel causes and evolution:
mechanisms
■ avulsion / mouth bar formation
■ subsidence, peat
boundary conditions
■ wash load
■ base level rise
how representative for other deltas
■ in record
■ wave/tide/fluvial dominated 23
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Present delta project
As in scientific conference:
On the basis of sound research
(not armwaving, not guessing)
2 page referenced abstract with figures
(densely written because scientists are busy)
Brief presentation
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Twisting the lion’s tail
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Physics and stamp collecting however complicated a system,
it must adhere to the laws of physics
e.g. mass conservation
Physics lead to fantastic patterns
mechanisms as explanations
typical cases/classes as helpful tools
Boundary / initial conditions
also cause patterns
e.g. climate, setting such as North Sea basin
forcings as explanations
type locations as helpful tools in reconstruction 26
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Mechanistic explanation (Machamer, Darden, Craver,
Philosophy of Science 2000)
reduce a phenomenon
to the workings of the underlying mechanisms
examples:
role of egg in pancakes
why can we preserve food
by salting or cooling?
key to researchable question:
unpeel your question! 27/26
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Logic
abduction
laws / generalisations major premises
mechanisms
causes / minor premises /
initial and boundary conditions (the world as it was)
effects / consequent
outcome (the world as it is now)
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Scales and explanatory elements explanation:
scale:
mechanisms generalisations causes
1.
river channel,
river reach
flow, sediment
transport
constitutive
(empirical)
relations
required
boundary
conditions
2.
river pattern,
channel belt
bar formation,
floodplain
formation
channel pattern
diagrams
necessary
conditions incl.
hinterland
3.
fluvial plain, river
displacement
bifurcation stability avulsion cycles boundary
conditions,
climate, base
level
4.
valley, delta
subsidence, peat
formation
Wave/tide/fluvial
dominated delta
shapes
Climate, tectonics
29
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Now what?
Collect + study indicated literature
quick repetition flow, sed tr and morph
learn matlab
new material,
new combinations of approaches
first matlab project, then delta project
professional scientific discourse
scientific presentations
exam: insight, combination, case? 30
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1
Faculty of Geosciences
River and delta morphodynamics
Flow, sediment transport
and morphological change MSc course Fluvial Systems GEO4-4436
Dr. Maarten G. Kleinhans
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This lecture: main questions and points
quick review of basic concepts
and equations for
flow
sediment transport
morphology
What are physical concepts behind the
equations?
Sediment transport is nonlinear function of
flow force
so what? 2
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Position of this lecture in the course
Flow, sediment transport and channel
morphodynamics
River patterns
Bifurcations and avulsion
From source to sink and in between
3
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Cross-talk: main terminology
Morphodynamics: Quaternary Geology:
upstream boundary
conditions
climate
downstream boundary
conditions
base level
yet another term in the
sediment mass balance
tectonics / subsidence
wash load suspended load
bed + suspended bed
material load
bed load 4
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5
flow
sediment
transport
morphology
The morphodynamic system
• Fluid mechanics
• Hydraulic roughness
• Bedforms
• Sediment transport
• Hydraulic geometry
• Bars, bends, islands
• Overbank
sedimentation
• Channel patterns
• vegetation
Some essential review of knowledge:
Remember 3rd years course?
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1. Flow: essential fluid mechanics
Steady uniform flow (normal flow) steady
1. Flow strength parameters
2. Turbulent flow uniform
Steady nonuniform flow
3. Sub- and supercritical flow
4. Backwater effect
0
t
u
0
x
u
0
x
u
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Big Questions about Flow
How do we describe flow strength?
Why would flow be nonuniform?
What determines flow resistance?
How account for complications of turbulence?
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Flow strength parameters
u = flow velocity (averaged over depth h)
Q = flow discharge:Q = uhW = uA
τ = flow shear stress: τ = ρghS
S = gradient, ρ = fluid density (1000kg/m3)
ω = stream power: ω = τu
many different symbols in use!
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Subcritical Supercritical
9/32
• slow
• downstream control
• Fr<1
• fast
• no downstr. control
• Fr>1
gh
uFr ghc Rivers?
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10 Bodewes & Leuven (2012), based on dataset Kleinhans
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Backwater effect subcritical flow: downstream roughness affects
upstream flow (e.g. dams, vegetation)
upstream distance over which water depth is
affected: adaptation length
h
S,i
BW : 63% adaptation
S
hBW
3%63
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Turbulence
Self-generated resistance of flow (at boundaries)
Reynolds number
laminar < 500
turbulent > 2000
uDuh Re,Re
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Effect of turbulence
13
vertical flow velocity gradient: logaritmic profile
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Flow velocity over depth
z
u
dz
du
* )(ucity shear velowith 10
*
ms
0.40-0.38 Kármán von ofconstant
0
*
0*
**
ln
ln0for
ln:givesofnIntegratio
z
zuu
zu
cu
czu
uz
u
dz
du
z
z
z
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How to deal with turbulence? Turbulence is very complicated and far from solved
use semi-empirical equations
Note: [m/s]/([m/s2][m][m/m])0.5 dimensional
homogeneity
hW
WhR
gRS
u
ff
gRSu
empirical
2
88
Darcy-Weisbach law
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Friction I
friction scales with R and roughness length ks
Semi-empirical formula
90509065
1010
35.2,1,1
086.1log74.52.12log74.58
DtoupDDDk
k
R
k
R
f
s
ss
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Friction II
Use the log-profile to get the friction law
ss
ss
szz
k
RCandRS
k
Ru
e
xxandgRSu
k
Ru
ek
Ruu
zkande
Rzatuugiven
z
zuu
12log18
12log18
log
logln*
14.12ln
*33ln
*
33ln*
1010
10
10
0
0
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Roughness
hydraulic roughness + obstruction = flow resistance
form friction + skin friction = total friction
Bedforms grains
Vegetation
Engineering structures
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Vegetation
well-submerged vegetation
submerged veg with through-flow
through-flowed vegetation
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Steady uniform flow shear:
τ = ρgRS and
Turbulence is accounted for by:
Note: [C]=[m/s]/([m][m/m])0.5 = [m0.5/s]
Thus not dimensionally correct
uRSC 2
C
ug
sk
RC
12log18 10
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2. Sediment transport
Water flow results in sediment transport!
1. Sediments
2. Bedload sediment transport
3. Suspended sediment transport
4. Washload
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Sediments For example plot grain size against rel. cum. freq.:
Ways to measure: sieving, settling tube, lasers
Best method depends on application
Sample Grain Size Distribution (with Extrapolation)
0
10
20
30
40
50
60
70
80
90
100
0.001 0.01 0.1 1 10
Grain Size mm
Perc
en
t F
iner
D50 = 0.286 mm
D90 = 0.700 mm Dx is size such that x percent
of the sample is finer than Dx
Characteristics of sediment: Examples:
D50 = median size
D90 ~ roughness height
Mean and Standard deviation
Skewness/Kurtosis
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Sediment transport
Flow energy, τ = τ’+τ’’
dissipated by bedforms sediment transport
We use: ks’ – grain related roughness (skin friction)
C’ – grain related Chezy
τ’ – grain related shear stress
θ’ – grain related shields number
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The beginning of motion
Shields’ (1936) curve
*
50
:
''
u
note
gDs
Du**Re
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Bedload transport qb = c ∙ δ (c=celerity, δ=layer thickness)
c depends on u* ~ τ1/2
δ is related to τ
So: qb = f(τ3/2)
Include treshold for motion: qb = f(τ’-τc)3/2
Make dimensionless: φb = f(θ’-θc)3/2
φ = dimensionless transport rate
θ’ = dimensionless shear stress (skin friction)
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Bedload transport
Many (semi) empirical forms:
calibrated for limited sets of conditions
MPM
Parker Van Rijn
Ribberink
general form
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Bedload transport Plot sediment transport against shields:
sediment transport is more nonlinear
near beginning of motion
Up to power 16
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Suspended sediment transport Bagnold (1966)
Van Rijn (1984)
depends on sediment characteristics
and flow shear stress to the power of 1.5
total load predictor:
Engelund and Hansen (1967)
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Washload transport (Almost) no exchange between bed and
suspended sediment
Limited by the amount of upstream supply
29/4
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Nonlinear
qb = f(u3) Why? Remember τ = …
Nonlinearity of sediment transport
Now: Why do rivers exist at all?
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Big Questions about Bedforms
How do we know which bedform is stable?
When are bedforms in equillibrium? Are they
in nature?
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Bedforms
Sediment transport bedforms
organised sediment transport and bedform
friction
1. Bedform types
2. Bedform stability
3. Bedform dynamics
Kleinhans (2002)
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Bedforms
30 m
Dunes
Ripples on top of dunes
phenomenon at boundary between two materials
with different physical properties in transport
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Dunes in Parana river
34/41
Best (2005)
Parsons
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Bedforms and bed states
subcritical flow (Fr<0.8)
lower stage plane bed (no motion)
current ripples
current dunes
upper stage plane bed (sheet flow)
supercritical flow (Fr>1)
upper flow regime plane bed
standing waves
antidunes: migrate against the flow
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Dunes and Antidunes
36/41
1gh
uFr
1Fr
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Bedform stability (Van den Berg & van Gelder, 1993)
Emperical Diagram
)('
)(3'
'
12log18'
1''
90
90
31
250*
50
2
2
gravelDk
sandDk
k
hC
gDD
DsC
u
s
s
s
s
Temp
20
10.40 6
upper flow plane bed
because Fr>1!!
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Bedform stability Lines are not hard tresholds,
but gradual transitions
Physically based diagram
Bedforms depend
on flow and sediment
transport rate+mode
Note: bedforms are
often in disequilibrium
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Rivers during bankfull conditions
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Dune tracking
Migration of dunes = sediment transport
Can be measured by dune tracking:
Deviation from a triangle!
Calibration in practice:
cqb 21
60.055.0 withcqb
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Dunamics
Dune length
increases during and
after flood:
Dune height shows
hysteresis during
a flood:
0.0
0.9
1.8
0 7000 14000Discharge (m^3/s)
du
neh
eig
ht
(m)
flood 1982 flood 1988 flood 1995 flood 1997
1982
1988
1995
1997
0
30
60
0 7000 14000Discharge (m^3/s)
wavele
ng
th (
m)
flood 1982 flood 1988 flood 1995 flood 1997
1997
1982
19
95
1988
Wilbers 2004
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Prediction of duneheight Different Equilibrium predictors: f (h,τ,D), e.g.
Relaxation with adaptation time scale
Note: Bedforms are often NOT in equilibrium!
3.0
50
/
//
5.0
3.0
50
5.2-
Twith 3.7
25111.0
h
D
hh
Teh
D
h
cr
cr
T
van Rijn (1984) Julien & Klaassen (1995)
0.5 /
1 , 11 vR eqtimeT t T
t t t te
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Bedforms?
equilibrium form determined by
particle size (Bonnefille number)
mobility (Shields number)
flow regime (Froude number)
in nature often not in equilibrium
→ relaxed adaptation
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Morphodynamics
uniform steady sediment transport
→ no change!
needs gradient in sediment transport to change
morphology
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Modelling: big Questions
How are flow, sed transp and mass
conservation combined to model
morphodynamics?
How do rivers respond to changing boundary
conditions?
What are models (not) good at?
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Sediment continuity / mass conservation
Storage = Flux in – Flux out
This is the Exner equation Used in modeling/to predict changes in morphology
= porosity
= bed level
qb= transport rate
t = time
x = location transport gradient (out-in)
x
q
x
b
outb,inb,
-t
storaget
p
p
1
1
bed level change
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Equilibrium? discharge
and sediment feeder
sediment bed
water depth
h0
slope i
grain flow thickness
hg
When IN = OUT YES!!
So when the slope
remains exactly the same
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flow
sediment
transport
morphology
Model the morphodynamic system
• Introduction
• Hydraulic roughness and
• bedforms
• Sediment transport
• Hydraulic geometry
• Bars, bends, islands
• Overbank sedimentation
• Channel patterns
• vegetation
First 1D modelling,
then 3D modelling
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1D modelling
1. Equations needed
2. Input values needed
3. Model
4. Case study: terrace crossing
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Input values
h S
Q,W
ks
Qb,s D50, D90, bed porosity: λ
Specification of flow:
Specification of sediment transport:
S
→ u(x), h(x)
→ S(x), (x)
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Information propagation
Q, H, z
51
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Numerics
step by step
direction of influence
water level in upstream direction
sediment in downstream direction
boundaries
see Parker e-book chapter 20
AgDegBW
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53
Morphological change
General rate of change:
1. Exner: /t~qb/x
2. So after sudden change, gradient (and thus qb/x) is large
3. Therefore morph change fast
4. But then gradient decreases and morph change less fast
5. (t) = equil +/- e-t
6. Exponential decrease or increase with representative T:
time
parameter
~63 % of change accomplished at T
T
Think about gradients!
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Case study
Netherlands, river Rhine
Holocene sea level rise
reduced supply of upstream sediment
Result:
In the downstream part: sedimentation (layercake)
In the upstream part: incision (formation terraces)
In between: terrace crossing
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Simple model result elucidates
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Compare with reality
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57 Spitsbergen, Svalbard, see http://blog.geo.uu.nl
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Modelling philosophy (1)
models not good at details in reality
must be specified in initial/boundary conditions
given uncertainty in both initial conditions and laws:
models cannot be verified (Oreskes et al. 1994)
so, models rarely predict well without calibration
■ how much of ‘physics-based’ explanation in calibration?
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Process, noise or boundary condition?
tim
e s
ca
le o
f p
he
no
me
no
n
minute
1 cm 1 m million km 1000 km 1 km
billion
years
1000
years
year
million
years
turbulence
earthquake
plate tectonics, mantle convection
ocean circulation
El Nino and La Nina
glacials and interglacials
storm events: river meandering, coastal erosion
ripples, dunes
coastal dunefields
river terrace forming
delta formation
formation of solar system
meteorite impact
length scale of phenomenon
boundary
condition
noise
noise
forcing
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Modelling philosophy (2)
models good at trends and behaviour!
comprehend results of complicated set of equations
manipulation: sensitivity to parameters
run scenarios for certain changes
mediate between theory (laws of physics) and nature
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Application
build a simple model in matlab
use (your own) model for delta project
understand modellers in practice
approach and value
uncertainties
■ initial and boundary conditions
■ numerics