Different approaches to modeling inner-shelf ‘Sorted Bedform’ behaviors under variable forcing

1. 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

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

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

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

5. Wave/ripple/current interaction

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

7. 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

9. Initial Results reversing current, plan view

10. 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? 0 0 suspended sediment velocity ripple-prediction schemes

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

13. Results current 20 cm/s, asymm. reversals

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

15. 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? 0 0 suspended sediment velocity ripple-prediction schemes

16. 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

17. Theoretical Contexts • Chaos theory -> complexity from simple interactions

18. 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)

19. 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?

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

21. 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)

22. 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)

23. 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’

24. 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’

25. 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.

26. 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

27. 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

28. Numerical Model—Expl. Num. Reductionism • 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

30. 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

31. 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)

32. 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