Different approaches to modeling inner-shelf ‘Sorted Bedform’ behaviors under variable forcing A. Brad Murray Nicholas School of the Environment and Earth Sciences; Center for Nonlinear and Complex Systems, Duke University Giovanni Coco, Malcolm Green National Institute for Water and Atmospheric Research, NZ Rob Thieler US Geological Survey, Coastal and Marine Geology Program, Woods Hole I The phenomenon - description - hypothesized mechanism II Contrasting modeling approaches, new results III Numerical modeling strategies

One example of sorted bedforms, Wrightsville Beach, NC, USA Side-scan sonar over bathymetry; light = coarse sediment

Morphology and stratigraphy (cross –sections from diver observations, bathymetric mapping, and vibracores, Wrightsville Beach, NC, USA)

Enlarged sidescan-sonar imagery Diver photo Coarse bed -> large wave-generated ripples, roughness

Wave/ripple/current interaction

Feedback, then bedform-like organization? Numerical model to explore hypothesis

Numerical Model: Exploratory Version Separate transport of coarse, fine sed. Saturated sediment flux, profile height, both linear f(bed composition); proxy for ripple size Lumps ripple growth, effects on sed., current profiles

Initial Results reversing current, plan view

Model: Explicit Numerical Reductionism Explicit treatments of: Ripple dimensions (Styles & Glenn 2002, others) Vertical profiles of: - suspended sediment (exponential, or Rouse), - current velocity (logarithmic) Reproduce main results? suspended sediment velocity ripple-prediction schemes 0 0

Results Waves: H=3m, T=10s; reversing current, 40 cm/s; depth 20 m

Results current 20 cm/s, asymm. reversals

Results current 20 cm/s, random then const. direction

Model: Explicit Numerical Reductionism Explicit treatments of: Ripple dimensions (Styles & Glenn 2002, others) Vertical profiles of: - suspended sediment (exponential, or Rouse), - current velocity (logarithmic) Reproduce main results? Numerically reliable results? suspended sediment velocity ripple-prediction schemes 0 0

Numerical Modeling Strategies Range of scales, interacting processes ‘Explicit Numerical Reductionism’ –Base models on smallest, fastest scales practical –Parameterize only when unavoidable e.g. eddy viscosity –i.e. ‘bottom up’ ‘Top Down,’ ‘Synthesist,’ ‘hierarchical’ –Treat only pertinent effects of smaller, faster scales –Explicitly treat interactions on commensurate scales –Embrace separation of scales

Theoretical Contexts Chaos theory -> complexity from simple interactions

Theoretical Contexts Chaos theory -> complexity from simple interactions Emergent phenomena –New variables; collective behavior of << smaller scale (e.g. water waves: pressure, density, surface elevs.) –Not directly predictable from constituent parts (e.g. molecular collisions)

Theoretical Contexts Chaos theory -> complexity from simple interactions Emergent phenomena –New variables; collective behavior of << smaller scale (e.g. water waves: pressure, density, surface elevs.) –Not directly predictable from constituent parts (e.g. molecular collisions) –Influences down through scales as well as up; slaving of much smaller scales –Emergent interactions cause large-scale behaviors -> better for explanation—and prediction?

Numerical Modeling Strategies Parameterization always involved w/fluid, sediment –e.g. eddy viscosity –rheology –bulk sediment transport Often based on lab experiments

Numerical Modeling Strategies Parameterization always involved w/fluid, sediment –e.g. eddy viscosity –rheology –bulk sediment transport Often based on lab experiments For top-down model, appropriate parameterization may not be available -> need to invent (observation, theory, experience)

Numerical Modeling Strategies Parameterization always involved w/fluid, sediment –e.g. eddy viscosity –rheology –bulk sediment transport Often based on lab experiments For top-down model, appropriate parameterization may not be available -> need to invent (observation, theory, experience) Less tested, refined: ‘rules’ Likely not quantitatively accurate (initially)

Numerical Modeling Strategies Simplified parameterizations and explanation: To max. clarity, leave out many processes, Represent those included in simplified ways -> key aspects of essential interactions Detail, accuracy less important than illuminating key feedbacks: ‘exploratory model’

Numerical Modeling Strategies Simplified parameterizations and explanation: To max. clarity, leave out many processes, Represent those included in simplified ways -> key aspects of essential interactions Detail, accuracy less important than illuminating key feedbacks: ‘exploratory model’ vs. ‘simulation model’

Numerical Modeling Strategies Simplified parameterizations and explanation: To max. clarity, leave out many processes, Represent those included in simplified ways -> key aspects of essential interactions Detail, accuracy less important than illuminating key feedbacks: ‘exploratory model’ tend to be top-down vs. ‘simulation model’ tend to be E. N. R.

Numerical Modeling Strategies Model Scales and Prediction: Is Expl. Num. Reductionism best route to prediction? (of behaviors, not particular occurrences; forcing, sensitive dependence, model imperfections…) Inherent danger: wrong emergent behavior Basing model on emergent interactions safer strategy

Numerical Modeling Strategies Model Scales and Prediction: Is Expl. Num. Reductionism best route to prediction? (of behaviors, not particular occurrences; forcing, sensitive dependence, model imperfections…) Inherent danger: wrong emergent behavior Basing model on emergent interactions safer strategy e.g. sorted bedforms

Problems with Expl. Num. Reductionism attempt: Different formalisms give very different results e.g. reference height for sed. profile suspended sediment velocity ripple-prediction schemes Numerical Model—Expl. Num. Reductionism

Problems with Expl. Num. Reductionism attempt: Different schemes give very different results e.g. reference height for sed. Profile Observed interaction—ripple size, flux incr. w/gr. sz.— did not necessarily emerge! suspended sediment velocity ripple-prediction schemes Numerical Model—Expl. Num. Reductionism

Numerical Modeling Strategies To improve numerical reliability, two options: –Improve small-scale parameterizations (all) –Empirically based, larger-scale parameterizations Latter more efficient, surer bet Especially landscape-scale with biology (& humans)

Numerical Modeling Strategies To improve numerical reliability, two options: –Improve small-scale parameterizations (all) –Empirically based, larger-scale parameterizations Latter more efficient, surer bet Especially landscape-scale with biology (& humans) Expl. Num. Reductionism, Top-Down: end members Most effective strategy depends: –available parameterizations –complexity of system (multi-scales) For many pressing issues, should focus on new, larger-scale parameterizations