Analysis and Prediction of a Noisy Nonlinear Ocean

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Analysis and Prediction of a Noisy Nonlinear Ocean

• With
• L. Ehret, M. Maltrud, J. McClean, and G. Vernieres

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Modeling and Analysis

• Ocean models predict the evolution of the ocean
  from approximate initial conditions according to
  incompletely resolved dynamics forced by
  approximate inputs.
• We treat noise according to the formalism of
  random processes.
• Data assimilation is our best hope for resolving
  physical questions in terms of models and data
• Most data assimilation schemes are based on
  linearized theory

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The Dynamical Systems Approach

• Linear systems are characterized by their steady
  solutions and stability characteristics...
• But the ocean is nonlinear, and nonlinear systems
  may have multiple stable solutions
• Stable solutions may not be steady
• Stability characteristics tell you about
  essential local behavior.

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Example The Kuroshio

• The Kuroshio exhibits multiple states. Is it
• A system with multiple equilibria?
• A complex nonlinear oscillator?
• Both? Neither?
• Many plausible models give output that resembles
  the observations.
• We show results from a QG model and a 1/10 degree
  PE model (J. McClean, M. Maltrud)
• Use a variational method to assimilate satellite
  data (G. Vernieres)
• Dynamical systems techniques and data
  assimilation will help us decide among models

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Fine Resolution Model

• 1/10o North Pacific model
• Courtesy J. McClean M. Maltrud

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Model-Data Comparison
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Model-Data Comparison
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2-Level QG Model

• 2-layer QG model on curvilinear grid
• Assimilate SSH data at one point at three times
• Strong constraint adjust initial condition only
• First guess contains a transition
• Use representer method

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Typical steady states of the Kuroshio
(adapted from Kawabe, 1995)
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Typical steady states of the Kuroshio
(adapted from Kawabe, 1995)
nNLM nearshore non large meander
ssh cm and geostrophic velocities m/s (AVISO
merged TOPEX/POSEIDON products)
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Typical steady states of the Kuroshio
(adapted from Kawabe, 1995)
oNLM offshore non large meander
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Typical steady states of the Kuroshio
(adapted from Kawabe, 1995)
tLM typical large meander
ssh cm and geostrophic velocities m/s (AVISO
merged TOPEX/POSEIDON products)
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Contours of ssh
nNLM
LM
nNLM
tLM
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Contours of ssh
nNLM
LM
Unstable
nNLM
tLM
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Contours of ssh
nNLM
LM
Stable
nNLM
tLM
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Qualitative comparison with satellite data
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Qualitative comparison with satellite data
4.0 km/day
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Qualitative comparison with satellite data
4.0 km/day
4.0 km/day
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Qualitative comparison with satellite data
800 km
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Qualitative comparison with satellite data
800 km
800 km
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3 data points for the assimilation!
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Data / Forward model
We want to assimilate ssh data that spans the
last transition from the nNLM to the tLM state
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Summary

• Model nonlinear systems can behave as real world
  noisy nonlinear systems
• Simplified systems share enough with detailed
  models, and both resemble observations
  sufficiently to make comparisons useful
• Consequences of applying linearized techniques to
  intrinsically nonlinear systems are yet to be
  explored