Transcript Deterministic and stochastic modeling of the end-to-end interdisciplinary system,
Deterministic and stochastic modeling of the end-to-end interdisciplinary system, and its errors and uncertainties
P.F.J. Lermusiaux April 9, 2003 1. END-TO-END SYSTEMS AND COUPLED MODELS 2. UNCERTAINTIES IN END-TO-END COMPONENTS
– SOURCES, FORWARD TRANSFERS, BACKWARD TRANSFERS
3. RESEARCH SUBJECTS FOR END-2-END UNCERTAINTY MODELING
– TOPICS AND DIRECTIONS – ILLUSTRATIVE QUESTIONS AND CHALLENGES Harvard University P.F.J. Lermusiaux
Harvard University
AD: Acoustical Data MD: Meteorological Data PD: Physical Data GD: Geological Data ND: Noise Data SD: Sonar Data PMD: Physical Model Data BMD: Bottom Model Data NMD: Noise Model Data APMD: Acous. Prop. Model Data SMD: Sonar Model Data TMD: Target Model Data
P.F.J. Lermusiaux
Coupled (Dynamical) Models and Outputs
PHYSICAL MODELS
•Non-hydrostatic models (PDE,
x,y,z,t)
•Primitive-Eqn. models (PDE, •Feature models
x,y,z,t
) •Quasi-geostrophic models, shallow-water •Objective maps, balance eqn. (thermal-wind)
BOTTOM MODELS
•Hamilton model, Sediment flux models (G&G), etc •Statistical/stochastic models fit-to-data
OUTPUTS
•Wave-speed, density and attenuation coefficients
OUTPUTS
•
T, S
, velocity fields and parameters,
C
•Dynamical balances field
ACOUS. PROP. MODELS
•Parabolic-Eqn. models (
x,y,z,t/f
) •(Coupled)-Normal-Mode parabolic-eqn. (
x,z,f
) •Wave number eqn. models (
x,z,f
: OASIS) •Ray-tracing models (CASS)
OUTPUTS
•Full-field TL (pressure
p,
phase ) •Modal decomposition of •Processed series: arrival strut., travel times, etc.
•CW / Broadband TL
p
field
NOISE MODELS
•Wenz diagram, empirical models/rule of thumbs
OUTPUTS
•
f
-dependent ambient noise (
f,x,y,z,t
): due to sea surface, shipping, biologics
SONAR SYS. MODELS AND SIGNAL PROCES.
•Sonar equations (
f,t
) •Detection, localization, classification and tracking models and their inversions
OUTPUTS
•SNR, SIR, SE, FOM •Beamforming, spectral analyses outputs (time/frequency domains)
REVERBERATION MODELS (active)
•Surface, volume and bottom scattering models
OUTPUTS:
scattering strengths
TARGET MODELS
•Measured/Empirical
OUTPUTS:
SL, TS for active
DEFINITION AND REPRESENTATION OF UNCERTAINTY
•
x
= estimate of some quantity (measured, predicted, calculated) •
x
t
= actual value (unknown true nature) •
e
=
x - x
t
(unknown error) Uncertainty in
x
is a representation of the error estimate
e
e.g. probability distribution function of
e
• Variability in
x
vs.
Uncertainty in
x
• Uncertainties in general have structures, in time and in space
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•
MAIN SOURCES OF UNCERTAINTIES IN END-TO-END COMPONENTS
Physical model uncertainties
–
Bathymetry
– Initial conditions – BCs: surface atmospheric, coastal-estuary and open-boundary fluxes – Parameterized processes: sub-grid-scales, turbulence closures, un-resolved processes • e.g. tides and internal tides, internal waves and solitons, microstructure and turbulence – Numerical errors: steep topographies/pressure gradient, non-convergence •
Bottom/geoacoustic model uncertainties
– Model structures themselves: parameterizations, variability vs. uncertainty – Measured or empirically-fit model parameters – BCs (bathymetry, bottom roughness) and initial conditions (for flux models) – 3-D effects, non-linearities – Numerical errors: e.g. geological layer discretizations, interpolations Harvard University P.F.J. Lermusiaux
Uncertainties in bathymetry (from data differences and statistical model) Smith and Sandwell NOAA soundings combined with Smith and Sandwell
(overlaid with GOM bathymetry) (predicted topography based on gravity anomaly not well compensated for regions with thick sediments) Harvard University P.F.J. Lermusiaux
Uncertainties in atmospheric forcings (from buoy-data/3d-model differences)
Harvard University
Baugmarter and Anderson, JGR (1996)
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Harvard University
Three-Hourly Atmospheric Forcings:
Adjusted Eta-29 model, 21 July 1996, 2pm EST
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Uncertainties in un-resolved processes: Stochastic forcing model of sub-grid-scale internal tides Hovmoller diagram Sample effects of sub-grid-scale internal tides: difference between non-forced and forced model
MAIN SOURCES OF UNCERTAINTIES IN END-TO-END COMPONENTS (Continued)
•
Acoustical model uncertainties
–
Sound-speed field (c)
– Bathymetry,
bottom geoacoustic attributes
– BCs: Bottom roughness, sea-surface state – Scattering (volume, bottom, surface) – 3-D effects, non-linear wave effects (non-Helmholz) – Numerical errors: e.g.
c
-interpolation, normal-mode at short range – Computation of
broadband TL
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Harvard University P.F.J. Lermusiaux
Harvard University P.F.J. Lermusiaux
MAIN SOURCES OF UNCERTAINTIES IN END-TO-END COMPONENTS (Continued)
• • • •
Sonar system model and signal processing uncertainties
– Terms in equation: SL, TL, N, AG, DT – Sonar equations themselves: 3D effects, non-independences, multiplicative noise – Beamformer posterior uncertainties, Beamformer equations themselves
Noise model uncertainties
– Ambiant noise: frequencies, directions, amplitudes, types (manmade, natural) – Measured or empirically-fit model parameters (Wenz, 1962)
Target model uncertainties
– Source level, target strength (measured or empirically-fit model parameters)
Reverberation model uncertainties (active)
– Scattering models themselves: parameterizations (bottom scattering, bubbles, etc) – Measured or empirically-fit model parameters Harvard University P.F.J. Lermusiaux
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METHOLOGIES FOR UNCERTAINTY MODELING
•
Representations
– Random numbers – Statistical moments – Bayesian, Bayesian hierarchical, Maximum entropy methods (Erickson and Smith,1988) – Error subspace (EOFs, Polynomial Chaos, ESSE, etc) – Fuzzy uncertainties (Klir and Wierman, 1999) – Belief functions (Dempster, 1990) •
Evolutions/propagations/forward transfers
– Deterministic/Stochastic calculus (e.g. Jazwinski, 1970) – Statistics (pdf convolutions, etc) – Information theory (Cover, 1991) – Deterministic differentials (outputs wrt inputs) •
Inversion methods/backward transfers
– Adjoint methods, Generalized inverse, Smoothing methods (KS, ESSE) Harvard University P.F.J. Lermusiaux
RESEARCH SUBJECTS FOR END-2-END UNCERTAINTY MODELING
Current and anticipated research organized in major subjects:
• • • • •
Modeling Approaches and Methodologies End-to-End Scales and Nonlinearities Error Estimation, Error Models and Error Reductions Sensitivities, Prioritizations and Idealized Uncertainty Modeling Uncertainty Complex Systems and Fleet Operations
Table provided for each subject: • List of research topics and directions (left column) • Series of illustrative research questions and challenges (right column, not intended to be comprehensive)
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Modeling Approaches and Methodologies Research Topics and Directions End-2-end models
end-2-end models to be done
Illustrative Questions and Challenges
• What are essential review references on models of the end-2-end components?
• Separate components ok, advanced coupling starting, uncertainty modeling limited situations: for bottom models, uncertainty close to variability - for parts of sonar models, dynamical models are pdfs: amplitudes, shapes of pdfs are then uncertainties careful transfer is essential!
• Is the limit in uncertainty modeling:
x = x(r,t) +
x
(r,t) +
(r,t) ?
• Etc Harvard University P.F.J. Lermusiaux
Modeling Approaches and Methodologies (continued) Research Topics and Directions Illustrative Questions and Challenges Uncertainty representation/transfer methods
• Deterministic, statistic and stochastic models • Representations for efficient computations: sub-optimal reduction of uncertainty space to be optimal (error subspace) idealized and realistic situations • What methods of representing and transferring uncertainties are in use today?
• What methods are most promising? • Different methods for different purposes?
• How should methods be evaluated?
• What about methods that utilize the structure of end-2-end PDEs?
• Etc
Lessons from other fields
• Information theory, fuzzy statistics • Atmospheric/weather forecasting • What are useful uncertainty representations?
• What can be learned: methods, systems?
• Etc Harvard University P.F.J. Lermusiaux
End-to-End Scales and Nonlinearities Research Topics and Directions Illustrative Questions and Challenges Multiple scales and multivariate
scales, in 3D/2D models • Measurement models linking multi resolution data to relevant coupled models • Research, real-time, operational, crisis response
Nonlinear effects
• Multiplicative noise and stochastic calculus • Impacts of nonlinearities on forward and backward/inverse uncertainty transfers and data assimilation • Predictive capabilities and ultimate predictability limits for e-2-e systems • How to best combine relocatable 2D acoustic models with 3D ocean models?
• How efficiently utilize internal wave data, bottom data, in 3D?
• Etc • How nonlinear is the wave equation wrt its parameters? • Should this affect uncertainty modeling?
• What are and how to estimate the predictability limits of sonar systems dynamics?
• Etc Harvard University P.F.J. Lermusiaux
Error Estimation, Error Models and Error Reductions Research Topics and Directions Error models
• Stochastic, deterministic, adaptive (for both • Structural errors and parameter errors • Error models for unresolved processes, forcing and boundary condition errors, environmental noise • Measurement models and data geological, acoustical and sonar) data bases
Illustrative Questions and Challenges
• How to quantitatively prioritize uncertainties?
• How to differentiate between structural and parameter errors in such complex systems?
• How to estimate accurate stochastic forcings?
• How to account for and model interdisciplinary measurement errors?
• Etc
Efficient error reductions
• Data assimilation methods: Control, estimation, inverse and optimization • Why should uncertainty representations and uncertainty reduction criterion be compatible?
• Model state, model parameters and model structures estimations • End-2-end adaptive sampling and model improvements Harvard University P.F.J. Lermusiaux
Sensitivities, Prioritizations and Idealized Uncertainty Modeling Research Topics and Directions Illustrative Questions and Challenges Sensitivity studies
system components (e.g. bathymetry) • Impact of different or variable uncertainties (amplitude, pdf shape, types) on same components? On end-2-end system?
Idealized end-2-end models and systems
• Applied math and theoretical research for representing, characterizing, capturing and reducing (end-to-end) uncertainty for scientific and Naval purposes • Truncation issues and divergence • How different are the impacts of environmental uncertainties on target detection, localization, classification and tracking?
• Is the broadband TL more sensitive to volume than bottom uncertainties?
• Etc • What are the effects of simplifying assumptions?
• What is a parsimonious parameterization in a range dependent environment • Etc Harvard University P.F.J. Lermusiaux
Uncertainty Complex Systems and Fleet Operations Research Topics and Directions Illustrative Questions and Challenges Computations, technologies and systems
• Generic versus regional systems • Visualization of uncertainties (and uncertainties in visualization) • Information technology, scientific distributed computing
Fleet applications/operational systems
• Automated systems for uncertainty predictions, skill evaluations • Efficient research-to-operation and operation-to-research transitions/feedbacks • Research, real-time, operational, crisis response • Typical scenarios and rules of thumb • How to couple end-2-end components for efficient computing?
• How to benefit from Fleet experiences?
• How to downscale scientific descriptions to useful operational uncertainties?
• Can uncertainty models lead to improved and more efficient TDA, tactical advantage?
• How to usefully estimate accuracies/errors of an operational system?
• Should operator overload uncertainties be modeled?
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