Sai Ravela Massachusetts Institute of Technology J. Marshall, A. Wong, S. Stransky, C. Hill...

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.