analysis and prediction of a noisy nonlinear ocean

Analysis and Prediction of a Noisy Nonlinear OceanAnalysis and Prediction of a Noisy Nonlinear Ocean

With:L. Ehret, M. Maltrud, J. McClean, and

G. Vernieres

With:L. Ehret, M. Maltrud, J. McClean, and

G. Vernieres

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

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

Modeling and AnalysisModeling and Analysis

The Dynamical Systems Approach

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.

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.

Example: The KuroshioExample: 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

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

Fine Resolution ModelFine Resolution Model

1/10o North Pacific model

Courtesy J. McClean & M. Maltrud

1/10o North Pacific model

Courtesy J. McClean & M. Maltrud QuickTime™ and a

decompressorare needed to see this picture.

Model-Data ComparisonModel-Data Comparison

Model-Data ComparisonModel-Data Comparison

2-Level QG Model2-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

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

Typical steady states of the KuroshioTypical steady states of the Kuroshio(adapted from Kawabe, 1995)

Typical steady states of the KuroshioTypical steady states of the Kuroshio(adapted from Kawabe, 1995)

nNLM: nearshore non largemeander

ssh [cm] and geostrophic velocities [m/s] (AVISO merged TOPEX/POSEIDON products)

Typical steady states of the KuroshioTypical steady states of the Kuroshio(adapted from Kawabe, 1995)

oNLM: offshore non largemeander

Typical steady states of the KuroshioTypical steady states of the Kuroshio(adapted from Kawabe, 1995)

tLM: typical largemeander

ssh [cm] and geostrophic velocities [m/s] (AVISO merged TOPEX/POSEIDON products)

tLM

nNLM

nNLMLM

Contours of ssh

tLM

nNLM

nNLMLM

Contours of ssh

Unstable

tLM

nNLM

nNLMLM

Contours of ssh

Stable

Qualitative comparison with satellite data

Qualitative comparison with satellite data

~4.0 km/day

Qualitative comparison with satellite data

~4.0 km/day

~4.0 km/day

Qualitative comparison with satellite data

~ 800 km

Qualitative comparison with satellite data

~ 800 km

~ 800 km

3 data points forthe assimilation!

Data / Forward model

We want to assimilate ssh data that spans the last transition from the nNLM to the tLM state

QuickTime™ and a decompressor

are needed to see this picture.

SummarySummary

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

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