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Planet in a bottleA 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
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Geophysical Fluids in the Laboratory
Inference from models and data is fundamental to
the earth sciences
Laboratory analogs systems can be extremely
useful
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Planet-in-a-bottle
Ravela, Marshall , Wong, Stransky , 07
OBS
Z
DA
MODEL
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Velocity Observations

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

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Numerical Simulation
Marshall et al., 1997
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.

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Domain

• x 23 x 15 (z)
• 45-8 x 15cm

1. Cylindrical coordinates.
2. Nonuniform discretization of the vertical
3. Random temperature IC
4. Static temperature BC
5. Noslip boundaries
6. Heat-flux controlled with anisotropic thermal
   diffusivity

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Estimation from model and data

• Estimate what?

1. State Estimation
2. NWP type applications, but also reanalysis
3. Filtering Smoothing
4. Parameter Estimation
5. Forecasting Climate
6. State and Parameter Estimation
7. The real problem.

General Approach Ensemble-based,
multiscale methods.
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Schedule
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Producing state estimates

• Ensemble-methods
• Reduced-rank Uncertainty
• Statistical sampling
• Tolerance to nonlinearity
• Model is fully nonlinear
• Dimensionality
• Square-root representation via the ensemble
• Variety of approximte filters and smoothers

• Key questions
• Where does the ensemble come from?
• 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?

Ravela, Marshall, Hill, Wong and Stransky, 07
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Approach
Snapshots capture flow-dependent uncertainty
(Sirovich)
BCIC
P(T ) Thermal BC Perturbations 4
P(X0T) IC Perturbation 1
Deterministic update 5 2D updates 5
(Elliptic) temperature Nx Ny 1D problems
P(XtXt-1) Snapshots in time
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Egte0?
P(YtXt) P(XtXt-1) Ensemble update
P(YtXt) P(XtXt-1) Deterministic update
Ravela, Marshall, Hill, Wong and Stransky, 07
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EnKF revisited
The analysis ensemble is a (weakly) nonlinear
combinationof the forecast ensemble.
This form greatly facilitates interpretation of
smoothing
Evensen 03, 04
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Ravela and McLaughlin, 2007
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Ravela and McLaughlin, 2007
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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.

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The Amplitude-Position Formulation of Data
Assimilation
Ravela et al. 2003, 2004, 2005, 2006, 2007
With thanks to K. Emanuel, D. McLaughlin and W.
T. Freeman
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Many reasons for position error
Solitons
There are many sources of position error Flow
and timing errors, Boundary and Initial
Conditions, Parameterizations of physics,
sub-grid processes, Numerical integrationCorrecti
ng them is very difficult.
Hurricanes
Thunderstorms
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Amplitude assimilation of position errors is
nonsense!
3DVAR
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EnKF
Distorted analyses are optimal, by definition.
They are also inappropriate, leading to poor
estimates at best, and blowing the model up, at
worst.
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Key Observations

• Why do position errors occur?
• Flow timing errors, discretization and
  numerical schemes, initial boundary
  conditionsmost 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

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Joint Position Amplitude Formulation
Question the standard Assumption Forecasts are
unbiased
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Bend, then blend
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Improved control of solution
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Flexible Application
Bend, then Blend

• Data Assimilation
• Hurricanes , Fronts Storms
• In Geosciences
• Reservoir Modeling
• Alignment a better metric for structures
• Super-resolution simulations
• texture (lithology) synthesis
• Flow Velocimetry
• Robust winds from GOES
• Fluid Tracking
• Under failure of brightness constancy

• 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

• Students
• Ryan Abernathy
• Scott Stransky
• Classroom

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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.

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Adaptation to multivariate fields
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Velocimetry, for Rainfall Modeling
Ravela Chatdarong, 06
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.
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Other applications
Magnetometry Alignment (Shell)
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Super-resolution
Example-based Super-resolved Fluids

Ravela and Freeman 06
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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.