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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: 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

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**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

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**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…

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**(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

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**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?

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**+ 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…

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**Closure (moving boundaries):**

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

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**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 )

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**Three-phase evolution: Widespread aggradation degradation**

timelines widespread degradation (offlap) ‘mixed’ widespread aggradation (onlap) modified Wheeler diagram

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**What controls the duration of aggradation?**

Focus on timing of offlap (toff): Gross measure of aggradational interval Good experimental observable Scaling arguments:

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**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

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**Representative experimental results**

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**Sensitivity study: variations in qso/(uf)**

Shoreline Swenson & Muto (2006, Sedimentology) Source of ‘noise’ = Stick-slip on the delta foreset

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

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**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):

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Alluvial-basement transition: Shoreline: Puff…

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**Teleconnections: fluviodeltaic systems as filters to eustasy**

Why? ‘Skin’ depth: Swenson (2005, JGR)

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

Kim et al. (2006, JSR)

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

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**More perturbation theory…wiggle upstream BC**

forcing response Determine amplitude and phase of shoreline

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**Teleconnections: fluviodeltaic systems as filters to Dqs**

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

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**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

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**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)

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**Basic hypothesis: Wave energy suppresses avulsion**

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

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**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

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**Channel-belt (fluvial) morphodynamics:**

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

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**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:

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**Coupling channel-belt & shoreface morphodynamics:**

Longshore flux and wave extraction from channel-belt: Channel-belt progradation: Problem is closed mathematically

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**superelevation ~ channel depth**

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

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**Time Shoreface / channel-belt evolution Solve and**

Shoreface (map view) Channel belt (cross section) Time Solve and subject to boundary & initial conditions…

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**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

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**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

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**Analytical solution (approximate):**

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

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**Teleconnection: wave-driven suppression of avulsion**

after Swenson (2005, GRL)

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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?

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