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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 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

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Road map: (1) Downstream (eustatic) forcing (1a) Response to steady R sl 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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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…)

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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 (R sl ) 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 R sl fall

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Let’s analyze the response to a steady rate of fall… Note: R sl is falling everywhere Investigate how allogenic forcing (sediment & water supply, fall rate) and basin geometry control aggradation?

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

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

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

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

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~ 3.6; ~ 1.95 = q w Supporting flume experiments (Tetsuji Muto, Nagasaki University) Theory and experiments similarly ‘sophisticated’ Require similarity in q so /( ) & / Scale issue: Sediment flux varies non-linearly with slope; resort to blatant empiricism Gives non-linear morphodynamics

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Representative experimental results

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

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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 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): q s = steady

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Shoreline: Alluvial-basement transition: Puff…

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

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

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Teleconnections: fluviodeltaic systems as filters to q s

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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 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

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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 ( ) or avulsion frequency (1 / ) 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

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

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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:

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

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

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

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

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Shoreface (map view) Channel belt (cross section) Shoreface / channel-belt evolution Solveandsubject to boundary & initial conditions… Time

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Solution: Lazy approach…use simple scaling arguments Supply over ‘lifespan’ ( ) Channel belt progradation Channel belt aggradation (superelevation) Cuspate ‘wings’ (‘smearing’) o = Avulsion time scale (zero-energy limit) = Dimensionless parameter grouping that embodies interplay of river and waves

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Relative importance of fluvial input and wave energy ( ) q wf = flood water flux q sf = flood sediment flux I f = flood intermittency H b = storm breaker height I s = storm intermittency Expanding…

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

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

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Morphodynamic models hint at long-term teleconnections in the S2S system: Alluvial aggradation during R sl 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

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