Slide 1

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 2

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 3

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 4

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 5

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 6

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 7

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 8

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 9

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 10

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 11

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 12

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 13

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 14

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 15

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 16

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 17

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 18

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 19

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 20

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 21

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 22

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 23

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 24

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 25

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 26

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 27

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 28

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 29

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 30

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.


Slide 31

“PLANET IN A BOTTLE”
A REALTIME
OBSERVATORY
FOR
LABORATORY
SIMULATION
OF
PLANETARY
CIRCULATION

Sai Ravela
Massachusetts Institute of
Technology
J. Marshall, A. Wong, S. Stransky,
C. Hill
Collaborators: B. Kuszmaul and
C. Leiserson

Geophysical Fluids in the Laboratory

Inference from models and data is
fundamental to the earth sciences

Laboratory analogs systems
can be extremely useful

Ravela, Marshall , Wong, Stransky , 07

Planet-in-a-bottle

OBS

Z
DA

MODEL

Velocity Observations
• Velocity

measurements
using correlationbased optic-flow
• 1sec per 1Kx1K
image using two
processors.
• Resolution,
sampling and
noise cause
measurement
uncertainty
• Climalotological
temperature BC in
the numerical
model

Marshall et al., 1997

Numerical
Simulation

MIT-GCM (mitgcm.org): incompressible
boussinesq fluid in non-hydrostatic mode
with a vector-invariant formulation

• Thermally-driven System (via EOS)
• Hydrostatic mode Arakawa C-Grid
• Momentum Equations: Adams-Bashforth-2
• Traceer Equations: Upwind-biased DST with
Sweby Flux limiter
• Elliptic Equaiton: Conjugate Gradients
• Vertical Transport implicit.

Domain
1.
2.
3.
4.
5.
6.

Cylindrical coordinates.
Nonuniform discretization of the vertical
Random temperature IC
Static temperature BC
Noslip boundaries
Heat-flux controlled with anisotropic thermal
diffusivity

120x 23 x 15 (z)
{45-8 }x 15cm

Estimation from model and data
Estimate what?
1. State Estimation:
1. NWP type applications,
but also reanalysis
2. Filtering & Smoothing
2. Parameter Estimation:
1. Forecasting & Climate

3. State and Parameter
Estimation
1. The real problem.
General Approach:

Ensemble-based, multiscale methods.

Schedule

Producing state estimates
Ensemble-methods
 Reduced-rank Uncertainty

Key questions
 Where does the ensemble come
from?

 Statistical sampling


How many ensemble members are
necessary?



What about the computational cost
of ensemble propagation?



Does the forecast uncertainty contain
truth in it?
 What happens when it is not?



What about spurious longrange
correlations in reduced rank
representations?

 Tolerance to nonlinearity
 Model is fully nonlinear

 Dimensionality
 Square-root representation

via the ensemble

 Variety of approximte

filters and smoothers

Ravela, Marshall, Hill, Wong and Stransky, 07

Approach
Snapshots capture
flow-dependent
uncertainty
(Sirovich)

BC+IC

Deterministic update:
5 – 2D updates
5 – (Elliptic) temperature
Nx * Ny – 1D problems

P(Yt|Xt) P(Xt|Xt-1):
Deterministic update

P(X0|T): IC
Perturbation

1

P(T ): Thermal BC
Perturbations 4

P(Xt|Xt-1): Snapshots
in time
10
E>e0
?

P(Yt|Xt) P(Xt|Xt-1):
Ensemble update

Ravela, Marshall, Hill, Wong and Stransky, 07

EnKF revisited
The analysis ensemble is a
(weakly) nonlinear
combination
of the forecast ensemble.

This form greatly facilitates
interpretation of smoothing

Evensen 03, 04

Ravela and McLaughlin, 2007

Ravela and McLaughlin, 2007

Next Steps


Lagrangian Surface
Observations : Multi-Particle
Tracking
 Volumetric temperature
measurements.


Simultaneous state and
parameter estimation.
 Targeting using FTLE &
Effective diffusivity
measures.


Semi-lagrangian schemes for
increased model timesteps.



MicroRobotic Dye-release
platforms.

Ravela et al. 2003, 2004, 2005, 2006, 2007

THE AMPLITUDEPOSITION FORMULATION
OF DATA ASSIMILATION
With thanks to
K. Emanuel, D. McLaughlin and W. T. Freeman

Many reasons for
position error
There are many sources of position error: Flow and
timing errors, Boundary and Initial Conditions,
Parameterizations of physics, sub-grid processes,
Numerical integration…Correcting them is very
difficult.

Thunderstorms

Solitons

Hurricanes

Amplitude
assimilation of
position errors
is nonsense!

3DVAR

EnKF

Distorted analyses are optimal, by definition. They are also
inappropriate, leading to poor estimates at best, and blowing
the model up, at worst.

Key Observations
 Why do position errors occur?
 Flow & timing errors, discretization and numerical

schemes, initial & boundary conditions…most prominently
seen in meso-scale problems: storms, fronts, etc.

 What is the effect of position errors?
 Forecast error covariance is weaker, the estimator is both

biased, and will not achieve the cramer-rao bound.

 When are they important?
 They are important when observations are uncertain and

sparse

Joint Position Amplitude Formulation
Question the standard
Assumption; Forecasts
are unbiased

Bend, then blend

Improved control of solution

Flexible Application


Data Assimilation
 Hurricanes , Fronts & Storms
In Geosciences
 Reservoir Modeling
 Alignment a better metric
for structures
 Super-resolution simulations
 texture (lithology) synthesis

Students

Ryan Abernathy:
Scott Stransky


Flow & Velocimetry
 Robust winds from GOES

Classroom


Fluid Tracking
 Under failure of brightness
constancy

Bend,
then Blend
 Cambridge 1-step

(Bend and Blend)

 Variational solution to

jointly solves for diplas and
amplitudes
 Expensive

 Cambridge 2-step

(Bend, then blend)
 Approximate solution
 Preprocessor to 3DVAR

or EnKF
 Inexpensive

Key Observations
 Why is “morphing” a bad idea
 Kills amplitude spread.

 Why is two-step a good idea
 Approximate solution to the joint inference

problem.
 Efficient O(nlog n), or O(n) with FMM

 What resources are available?
 Papers, code, consulting, joint prototyping etc.

Adaptation to multivariate
fields

Ravela & Chatdarong, 06

Velocimetry, for Rainfall Modeling
Aligned time sequences of cloud fields are used to
produce velocity fields for advecting model
storms.
Velocimetry derived this way is more robust than
existing GOES-based wind products.

Other applications

Magnetometry Alignment (Shell)

Super-resolution
Example-based
Super-resolved Fluids

Ravela and Freeman 06

Next Steps
 Fluid Velocimetry: GOES & Laboratory, release

product.

 Incorporate Field Alignment in Bottle project DA.
 Learning the amplitude-position partition function.
 The joint amplitude-position Kalman filter.
 Large-scale experiments.