![Page 1: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/1.jpg)
“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
![Page 2: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/2.jpg)
Geophysical Fluids in the Laboratory
Inference from models and data is fundamental to the earth sciences
Laboratory analogs systems can be extremely useful
![Page 3: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/3.jpg)
Planet-in-a-bottleRavela, Marshall , Wong, Stransky , 07
OBS
MODEL
DA
Z
![Page 4: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/4.jpg)
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
![Page 5: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/5.jpg)
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
![Page 6: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/6.jpg)
Domain 120x 23 x 15 (z)
{45-8 }x 15cm1. Cylindrical coordinates.
2. Nonuniform discretization of the vertical
3. Random temperature IC4. Static temperature BC5. Noslip boundaries6. Heat-flux controlled with anisotropic
thermal diffusivity
![Page 7: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/7.jpg)
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.
![Page 8: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/8.jpg)
Schedule
![Page 9: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/9.jpg)
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?
![Page 10: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/10.jpg)
![Page 11: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/11.jpg)
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
updateP(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)
![Page 12: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/12.jpg)
EnKF revisitedThe analysis ensemble is a (weakly) nonlinear combinationof the forecast ensemble.
This form greatly facilitates interpretation of smoothing Evensen 03, 04
![Page 13: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/13.jpg)
Ravela and McLaughlin, 2007
![Page 14: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/14.jpg)
Ravela and McLaughlin, 2007
![Page 15: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/15.jpg)
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.
![Page 16: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/16.jpg)
THE AMPLITUDE-POSITION FORMULATION OF DATA ASSIMILATION
Ravela et al. 2003, 2004, 2005, 2006, 2007
With thanks toK. Emanuel, D. McLaughlin and W. T. Freeman
![Page 17: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/17.jpg)
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.
![Page 18: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/18.jpg)
Amplitude assimilation of position errors is nonsense!
3DVAR
![Page 19: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/19.jpg)
EnKF
Distorted analyses are optimal, by definition. They are also inappropriate, leading to poor estimates at best, and blowing the model up, at worst.
![Page 20: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/20.jpg)
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
![Page 21: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/21.jpg)
Joint Position Amplitude FormulationQuestion the standardAssumption; Forecasts are unbiased
![Page 22: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/22.jpg)
Bend, then blend
![Page 23: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/23.jpg)
Improved control of solution
![Page 24: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/24.jpg)
![Page 25: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/25.jpg)
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
![Page 26: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/26.jpg)
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.
![Page 27: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/27.jpg)
Adaptation to multivariate fields
![Page 28: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/28.jpg)
Velocimetry, for Rainfall ModelingRavela & 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.
![Page 29: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/29.jpg)
Other applications
Magnetometry Alignment (Shell)
![Page 30: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/30.jpg)
Example-based Super-resolved Fluids
Super-resolution
Ravela and Freeman 06
![Page 31: Sai Ravela Massachusetts Institute of Technology](https://reader036.vdocuments.mx/reader036/viewer/2022062302/5681649b550346895dd676e2/html5/thumbnails/31.jpg)
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.