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Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji Muto, and Lincoln Pratson
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Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Dec 14, 2015

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Page 1: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Teleconnections in the Source-to-Sink System

John Swenson

Department of Geological SciencesUniversity of Minnesota Duluth

THANKS : Chris Paola, Tetsuji Muto, and Lincoln Pratson

Page 2: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Teleconnections: Context

La Nina anomalous SL pressure

Strong statistical relationship between ‘weather’ in different

parts of the globe

Information propagates through the atmosphere

Long-distance propagation of allogenic forcing (e.g. sea level change) through the transport system via erosion and deposition on geologic time scales

Page 3: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Road map:

(1) Downstream (eustatic) forcing

(1a) Response to steady Rsl fall

(1b) Response to periodic perturbations (filtering)

(2) Upstream forcing: Propagation of sediment-supply signals

(3) Wave energy and mesoscale suppression of fluvial aggradation

Page 4: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Talk = theory & experiments

Theory developed for geologic time scales, where forcing data are poorly constrained / non-existent

average over many ‘events’

implicitly involves the ‘upscaling’ problem

Teleconnections in S2S fundamentally involve coupling of environments

Cannot overemphasize the need to treat morphodynamics of the transport environments and the coupling of environments with equivalent levels of sophistication*

*Requires considerable simplification of transport relations…

A few important points (and a plea for forgiveness…)

Page 5: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

(1a) Downstream forcing

Fluviodeltaic response to steady sea-level fall

Classic teleconnection problem: How do alluvial rivers respond to sea level and what is the upstream (‘stratigraphic’) limit of sea-level change?

Sequence stratigraphy (e.g. Posamentier & Allen, 1999): Fall in relative sea level (Rsl) at shoreline = degradation & sequence-boundary development

Recent models & experiments (e.g. Cant, 1991; Leeder and Stewart, 1996; Van Heijst

and Postma, 2001): Rivers can remain aggradational during Rsl fall

Page 6: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Let’s analyze the response to a steady rate of fall…

Note: Rsl is falling everywhere

Investigate how allogenic forcing (sediment & water supply, fall rate) and basin geometry control aggradation?

Page 7: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Morphodynamics:

∂ ′ η ∂t

= υ∂2 ′ η

∂x2

′ η =η+σt

Problem is not closed…

Diffusive fluvial morphodynamics (Paola, 2000):

Shoreline BC:

Alluvial-basementtransition BC:

′ η s,t( ) = Rsl t( )

′ η r,t( ) = −φr

Rsl t( ) = Zsl t( ) + σt

Swenson & Muto (2006), Swenson (2005)

υ∝ qwo = Ifqwf

Absorb subsidence:

qs = −υ∂ ′ η

∂x

+hydrodynamics& stress closure

Page 8: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Closure (moving boundaries):

qs s,t( ) = −υ∂ ′ η

∂x s,t

=1

β− φ( )φs +Rsl( ) β

ds

dt+

dRsl

dt

⎝ ⎜

⎠ ⎟

qs r,t( ) = υ∂ ′ η

∂x r,t

= qso

…need additional pair of equations to locate shoreline and alluvial-basement transition and close problem

Shoreline:

Alluvial-basement transition:

Page 9: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

τ =1

υ

qso2

dRsl dt2

Scaling

dRsl/dt ~ 1 mm/a(late-Quaternary systems )

Non-dimensionalization:

ηH

= Fx

Λ,t

τ;qso

υφ,φ

β

⎝ ⎜

⎠ ⎟

Response time:

Invent one:

Dimensionless numbers for morphodynamics

Elevation scale:

Λ =qso

dRsl dt

H =qso

υ

qso

dRsl dt

qso υφ < 1

φ β <<1

No imposed length scale…

Page 10: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Three-phase evolution: Widespread aggradation degradation

widespread aggradation

(onlap)

widespreaddegradation

(offlap)

‘mixed’

timelines

modified Wheeler diagram

Page 11: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Focus on timing of offlap (toff):

Gross measure ofaggradational interval

Good experimental observable

Scaling arguments:

What controls the duration of aggradation?

toff τ = f φ β,qso υφ( )

Page 12: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

qs

qw

~ κ Sα ~ 3.6; ~ 1.95υ = qw

Supporting flume experiments (Tetsuji Muto, Nagasaki University)

Theory and experiments similarly‘sophisticated’

Require similarity in qso/(υ) & /β

Scale issue: Sediment flux varies non-linearly with slope; resort to blatant empiricism

∂ ′ η ∂t

= α κqw( )∂ ′ η

∂x

α−1

⋅∂2 ′ η

∂x2Gives non-linear morphodynamics

Page 13: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Representative experimental results

Page 14: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Sensitivity study: variations in qso/(υ)

Shoreline

Source of ‘noise’ = Stick-slip on the delta foreset

Swenson & Muto (2006, Sedimentology)

Page 15: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

(1b) Downstream forcing

Fluviodeltaic response to periodic eustatic forcing: Frequency dependence of teleconnection between shoreline and alluvial-basement transition

Page 16: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Perturbation theory with two moving boundaries…wiggle sea level

Zsl = −iεeiωt€

s = so + iεαei ωt+ψ( )

r = ro + iεβei ωt+φ( )

η=ηo − iεη1ei ωt+θ( )

forcing

Imposed response

Operate on ‘imposed’ response with governing PDE and BCs

Determine amplitude and phase of shoreline and alluvial-basement transition

Gives frequency dependence (‘filtering’)

Note change in basin response time (diffusive timescale):

qs = steady

Λ

τb = Λ2 υ

Page 17: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

eiψ = em

c1 + ic2

c3

βeiφ =eb

1− eb

c4 + ic5

H2

c1 = 1+1

1− so*

T

4πτb

em 1− so*2

( ) +1[ ] Re G[ ] + Im G[ ]( ) + em

T

2πτb

1+ so*( )1− so*( )

G2

c2 =1

1− so*

T

4πτb

em 1− so*2

( ) −1[ ] Re G[ ] − Im G[ ]( )

c3 = 1+ 2em 1+ so*( )T

4πτb

Re G[ ] + Im G[ ]( ) + em2 T

2πτb

1+ so*( )2

G2

c4 = Re H[ ] ⋅ 1+ so*2 −1( )em

c1

c3

⎣ ⎢

⎦ ⎥+ Im H[ ] ⋅ so*

2 −1( )em

c2

c3

c5 = Re H[ ] ⋅ so*2 −1( )em

c2

c3

− Im H[ ] ⋅ 1+ so*2 −1( )em

c1

c3

⎣ ⎢

⎦ ⎥

G = tanhπT

τb

1+ i( ) ⋅so*

⎣ ⎢

⎦ ⎥=

sinh so* πT τb( ) + i ⋅sin so* πT τb( )

cosh so* πT τb( ) + cos so* πT τb( )€

H = coshπT

τb

1+ i( ) ⋅so*

⎣ ⎢

⎦ ⎥= cos so*

πT

τb

⎝ ⎜

⎠ ⎟cosh so*

πT

τb

⎝ ⎜

⎠ ⎟+ i ⋅sin so*

πT

τb

⎝ ⎜

⎠ ⎟sinh so*

πT

τb

⎝ ⎜

⎠ ⎟

Shoreline:Alluvial-basementtransition:

Puff…

Page 18: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Teleconnections: fluviodeltaic systems as filters to eustasy

Swenson (2005, JGR)

Why? ‘Skin’ depth:

λ = υT

λ* = T τb

Page 19: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Experimental ‘test’ (XES Facility, SAFL group, C. Paola, W. Kim)

Kim et al. (2006, JSR)

Page 20: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

(2) Upstream forcing

Shoreline response to fluctuations in sediment supply:Frequency dependence

Page 21: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

qs = qso − iεeiωt

s = so − iεαei ωt+ψ( )

forcing

response

Determine amplitude and phase of shoreline

More perturbation theory…wiggle upstream BC

η=ηo − iεη1ei ωt+θ( )

Page 22: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Teleconnections: fluviodeltaic systems as filters to qs

Page 23: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

(3) Mesoscale teleconnections between shallow-marine and fluvial systems

Suppression of avulsion via increases in wave energy

Page 24: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Avulsion frequency is dominant control on ‘mesoscale’ stratigraphic architecture…

Avulsion frequency: Quick overview

Previous studies ignore potential role of nearshore processes

Figure by Paul Heller

Avulsion appears to be driven by superelevation of channel…

Rivers are one part of a linked depositional system…

Avulsion frequency = F(sedimentation rate)

Past studies (field, experimental, theoretical) have focused on this relationship, using sediment supply, subsidence, or changes in relative sea level as proxies for sedimentation rate

Page 25: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Deltaic (distributary) systems: The larger problem…

Deltaic systems have two fundamental degrees of freedom:

(1) Adjust number of channels (N)

(2) Adjust channel residence time (τ) or avulsion frequency (1 / τ)

Nile (N = 4)

Lena(N > 100)

Images courtesy of James Syvitski ( INSTAAR)

Problem statement:

To what extent does wave energy affect avulsion frequency?

Can the tail wag the dog?

Today… force N =1; analyze τ

Page 26: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Basic hypothesis: Wave energy suppresses avulsion

Mechanism du jour = Wave energy & alongshore sand transport

Observation: Fluviodeltaic systems prograde as approximately self-similar waveforms (clinoforms)

Page 27: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Conceptual model: Idealized ‘highstand’ deltaic system

Steady sand / water supply & wave climate

Sand channel belt & shoreface

Channel belt = fixed width

Shoreface = fixed geometry

Mud floodplain and pro-delta

No tides, subsidence, or sea-level change

Basic assumptions:

Page 28: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Channel-belt (fluvial) morphodynamics:

‘Cheat’ and assume diffusive morphodynamics (Paola, 2000) works:

qs = −υ∂η

∂x

Upstream condition:

∂η∂t

= υ∂2η

∂x2

∂η∂x x=0

= −qso

υ€

η scb,t( ) = 0Shoreline condition:

qso = Ifqsf

Page 29: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Shoreface morphodynamics (map view):

Simplify and use generalized CERC relationship (Komar, 1988; CERC, 1984):

qls = −κ∂s

∂y

Channel-belt condition:

∂s

∂t= κ

∂2s

∂y2

limy→±∞ s y,t( ) = 0Far-field condition:€

∝ IsHb( )5 2

Diffusivity:

Longshore transport on long timescales is poorly understood (Cooper & Pilkey, 2004)

s 0,t( ) = scb t( )

Page 30: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Coupling channel-belt & shoreface morphodynamics:

Problem is closed mathematically

Channel-belt progradation:

−∂s

∂yy=0

⎝ ⎜ ⎜

⎠ ⎟ ⎟D =

1

2qswW

Longshore flux and wave extraction from channel-belt:

−υ∂η∂x x=scb t( )

− qsw = Ddscb

dt

Page 31: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Avulsion criterion

Avulsion set-up:superelevation ~ channel depth

he = αh

0.6 < α < 1.1

Geometric argument:

scrit ~ h So

Diffusion gives:

So ~ qso υ

h∝1 So

(Mohrig et al., 2000)

Page 32: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Shoreface (map view) Channel belt (cross section)

Shoreface / channel-belt evolution

∂s

∂t= κ

∂2s

∂y2

∂η∂t

= υ∂2η

∂x2Solve and subject to boundary & initial conditions…

Tim

e

Page 33: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

qsoW( )τ ~h

So

WD +1

2

h

So

hW +h

So

2κ ⋅ τ

Solution:

Lazy approach…use simple scaling arguments

Supply over‘lifespan’ (τ)

Channel beltprogradation

Channel beltaggradation

(superelevation)

Cuspate ‘wings’(‘smearing’)

ττo

= f ξ( )τo = Avulsion time scale (zero-energy limit)

= Dimensionless parameter groupingthat embodies interplay of river and waves

Page 34: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Relative importance of fluvial input and wave energy ()

=1

Wqso

π

2Dhκυ

∝qwf

If1 2qsf

3 2 ⋅ IsHb( )5 4

qwf = flood water flux

qsf = flood sediment flux

If = flood intermittency

Hb = storm breaker height

Is = storm intermittency

Expanding…

→ 0

Page 35: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Analytical solution (approximate):

ττo

2⋅ 1+ 1+

4

ξ2

⎣ ⎢

⎦ ⎥

ττo

→ 1

ττo

~ ξ2€

→ 0

>>1

General solution:

River-dominated limit:

Wave-dominated systems:

‘Smearing’ length >> channel-belt width

qsoτ ~h

So

D 1+1

2

h

D+

π 2( )κ ⋅ τ

W

⎣ ⎢ ⎢

⎦ ⎥ ⎥

Sand budget (from before):

<<1 (generally)

Page 36: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Teleconnection: wave-driven suppression of avulsion

after Swenson (2005, GRL)

Page 37: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.

Morphodynamic models hint at long-term teleconnections in the S2S system:

Alluvial aggradation during Rsl fall can be long lived

Eustasy can affect the entire alluvial system

Fluviodeltaic systems behave as low-pass filters to both upstream and downstream forcing

Wave energy can effectively suppress avulsion on appropriate spatiotemporal scales

How do we test predictions in natural systems?

Conclusions

∝qwf

If1 2qsf

3 2 ⋅ IsHb( )5 4

τb =1

υ

qso2

dRsl dt2

λ* = T τb ~ 1

τ τo ~ ξ2

Page 38: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.
Page 39: Teleconnections in the Source-to-Sink System John Swenson Department of Geological Sciences University of Minnesota Duluth THANKS : Chris Paola, Tetsuji.