1. 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

2. Teleconnections: Context
Strong statistical relationship between ‘weather’ in different parts of the globe Information propagates through the atmosphere
La Nina anomalous SL pressure
Long-distance propagation of allogenic forcing (e.g. sea level change) through the transport system via erosion and deposition on geologic time scales

3. Road map: (1) Downstream (eustatic) forcing
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

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

5. (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

6. 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?

7. + hydrodynamics & stress closure
Morphodynamics:
Absorb subsidence:
Diffusive fluvial morphodynamics (Paola, 2000):
+ hydrodynamics & stress closure
Swenson & Muto (2006), Swenson (2005)
Shoreline BC:
Alluvial-basement transition BC:
Problem is not closed…

8. Closure (moving boundaries):
…need additional pair of equations to locate shoreline and alluvial-basement transition and close problem
Shoreline:
Alluvial-basement transition:

9. Scaling No imposed length scale… Elevation scale: Invent one:
Response time:
Non-dimensionalization:
Dimensionless numbers for morphodynamics
dRsl/dt ~ 1 mm/a
(late-Quaternary systems )

10. Three-phase evolution: Widespread aggradation  degradation
timelines
widespread
degradation
(offlap)
‘mixed’
widespread
aggradation
(onlap)
modified Wheeler diagram

11. What controls the duration of aggradation?
Focus on timing of offlap (toff): Gross measure of aggradational interval Good experimental observable
Scaling arguments:

12. Supporting flume experiments (Tetsuji Muto, Nagasaki University)
Theory and experiments similarly
‘sophisticated’
Require similarity in qso/(uf) & f/b
Scale issue: Sediment flux varies non-linearly with slope; resort to blatant empiricism
u = kqw
k ~ 3.6; a ~ 1.95
Gives non-linear morphodynamics

13. Representative experimental results

14. Sensitivity study: variations in qso/(uf)
Shoreline
Swenson & Muto (2006, Sedimentology)
Source of ‘noise’ = Stick-slip on the delta foreset

15. (1b) Downstream forcing Fluviodeltaic response to periodic eustatic forcing: Frequency dependence of teleconnection between shoreline and alluvial-basement transition

16. Perturbation theory with two moving boundaries…wiggle sea level
Imposed response
forcing
qs = steady
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):

17. Alluvial-basement
transition:
Shoreline:
Puff…

18. Teleconnections: fluviodeltaic systems as filters to eustasy
Why?  ‘Skin’ depth:
Swenson (2005, JGR)

19. Experimental ‘test’ (XES Facility, SAFL group, C. Paola, W. Kim)
Kim et al. (2006, JSR)

20. (2) Upstream forcing Shoreline response to fluctuations in sediment supply: Frequency dependence

21. More perturbation theory…wiggle upstream BC
forcing
response
Determine amplitude and phase of shoreline

22. Teleconnections: fluviodeltaic systems as filters to Dqs

23. (3) Mesoscale teleconnections between shallow-marine and fluvial systems Suppression of avulsion via increases in wave energy

24. Avulsion frequency: Quick overview
Avulsion frequency is dominant control on ‘mesoscale’ stratigraphic architecture…
Figure by Paul Heller
Avulsion appears to be driven by superelevation of channel…
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
Rivers are one part of a linked depositional system…
Previous studies ignore potential role of nearshore processes

25. 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 (t) or avulsion frequency (1 / t)
Lena (N > 100)
Today… force N =1; analyze t
Problem statement: To what extent does wave energy affect avulsion frequency?
Nile (N = 4)
Can the tail wag the dog?
Images courtesy of James Syvitski ( INSTAAR)

26. Basic hypothesis: Wave energy suppresses avulsion
Observation: Fluviodeltaic systems prograde as approximately self-similar waveforms (clinoforms)
Mechanism du jour = Wave energy & alongshore sand transport

27. Conceptual model: Idealized ‘highstand’ deltaic system
Basic assumptions:
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

28. Channel-belt (fluvial) morphodynamics:
‘Cheat’ and assume diffusive morphodynamics (Paola, 2000) works:
Shoreline condition:
Upstream condition:

29. Shoreface morphodynamics (map view):
Longshore transport on long timescales is poorly understood (Cooper & Pilkey, 2004)
Simplify and use generalized CERC relationship (Komar, 1988; CERC, 1984):
Diffusivity:
Channel-belt condition:
Far-field condition:

30. Coupling channel-belt & shoreface morphodynamics:
Longshore flux and wave extraction from channel-belt:
Channel-belt progradation:
Problem is closed mathematically

31. superelevation ~ channel depth
Avulsion criterion
Avulsion set-up:
superelevation ~ channel depth
(Mohrig et al., 2000)
Geometric argument:
Diffusion gives:

32. Time Shoreface / channel-belt evolution Solve and
Shoreface (map view)
Channel belt (cross section)
Time
Solve
and
subject to boundary & initial conditions…

33. Lazy approach…use simple scaling arguments
Supply over
‘lifespan’ (t)
Channel belt
progradation
Channel belt
aggradation
(superelevation)
Cuspate ‘wings’
(‘smearing’)
to = Avulsion time scale (zero-energy limit)
Solution:
= Dimensionless parameter grouping
that embodies interplay of river and waves

34. Relative importance of fluvial input and wave energy (x)
Expanding…
qwf = flood water flux
qsf = flood sediment flux
If = flood intermittency
Hb = storm breaker height
Is = storm intermittency

35. Analytical solution (approximate):
Sand budget (from before):
<<1 (generally)
General solution:
River-dominated limit:
Wave-dominated systems:
‘Smearing’ length >>
channel-belt width

36. Teleconnection: wave-driven suppression of avulsion
after Swenson (2005, GRL)

37. Conclusions
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?