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, NZRob Thieler

US Geological Survey, Coastal and Marine Geology Program, Woods Hole

I The phenomenon- description- hypothesized mechanism

II Contrasting modeling approaches, new resultsIII Numerical modeling strategies

One example of sorted bedforms, Wrightsville Beach, NC, USASide-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?

suspendedsediment

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?suspendedsediment

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

suspendedsediment

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!

suspendedsediment

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