sai ravela massachusetts institute of technology j. marshall, a. wong, s. stransky, c. hill...
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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
Planet-in-a-bottleRavela, Marshall , Wong, Stransky , 07
OBS
MODEL
DA
Z
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
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.
Marshall et al., 1997
Domain 120x 23 x 15 (z){45-8 }x 15cm
1. Cylindrical coordinates.2. Nonuniform discretization of the
vertical 3. Random temperature IC4. Static temperature BC5. Noslip boundaries6. Heat-flux controlled with anisotropic
thermal diffusivity
Estimate what?
Estimation from model and data
1.State Estimation:1.NWP type
applications, but also reanalysis
2.Filtering & Smoothing
2. Parameter Estimation: 1. Forecasting &
Climate
3. State and Parameter Estimation1. The real problem.
General Approach: Ensemble-based, multiscale methods.
Schedule
Producing state estimates
Ravela, Marshall, Hill, Wong and Stransky, 07
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?
Approach
Ravela, Marshall, Hill, Wong and Stransky, 07
P(T ): Thermal BC
Perturbations 4
P(X0|T): IC Perturbation 1
P(Xt|Xt-1): Snapshots in time
10
E>e0?
P(Yt|Xt) P(Xt|Xt-1): Ensemble
update
P(Yt|Xt) P(Xt|Xt-1): Deterministic
update
BC+IC
Deterministic update:5 – 2D updates5 – (Elliptic) temperatureNx * Ny – 1D problems
Snapshots capture flow-dependent uncertainty (Sirovich)
EnKF revisited
The analysis ensemble is a (weakly) nonlinear combinationof 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
With thanks toK. Emanuel, D. McLaughlin and W. T. Freeman
Thunderstorms Hurricanes
Solitons
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.
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 standardAssumption; Forecasts are unbiased
Bend, then blend
Improved control of solution
Flexible Application
StudentsRyan Abernathy:
Scott Stransky
Classroom
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
Bend, then Blend
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
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.
Other applications
Magnetometry Alignment (Shell)
Example-based Super-resolved Fluids
Super-resolution
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.