Survey of Evolutionary and Probabilistic Approaches for Source Term Estimation!

Transcription

1 Survey of Evolutionary and Probabilistic Approaches for Source Term Estimation! Branko Kosović" " George Young, Kerrie J. Schmehl, Dustin Truesdell (PSU), Sue Ellen Haupt, Andrew Annunzio, Luna Rodriguez (NCAR), Roger D. Aines, Rich D. Belles, Kathleen M. Dyer, William G. Hanley, Gardar Johannesson, Shawn C. Larsen, Art A. Mirin, John J. Nitao, Gayle A. Sugiyama, Phil J. Vogt (LLNL), Fotini K. Chow (Univ. California at Berkeley) Julie K. Lundquist (Univ. Colorado), Luca Delle Monache (NCAR) NATIONAL CENTER FOR ATMOSPHERIC RESEARCH!

2 Outline! Common components of source term estimation (STE)! Probabilistic approach using Bayesian inference Example: Algeciras accidental release! Optimization using Genetic Algorithms Example: Redoubt volcano release! Summary

3 Source Term Estimation Problem Requirements for STE methodology:! Effective (quantitative & accurate)! Efficient (within time constraints)! Flexible (adaptable, multiple data types)! Robust (operational use)! Quantifies uncertainty (probabilistic) wind

4 Source Term Estimation Process Input Data Sensor Data Met Data (Measurements, NWP) Initial Source Parameter Estimates (Guesses/Samples from Prior) Transport and Dispersion Analytic, Eulerian, Lagrangian Forward Backtrajectory Adjoint Metric Cost Function Likelihood Function Updated Parameter Estimate Variational Approach Optimization/Minimization Stochastic Sampling Convergence

5 Source Term Estimation Process Input Data Sensor Data Met Data (Measurements, NWP) Initial Source Parameter Estimates (Guesses/Samples from Prior) Transport and Dispersion Analytic, Eulerian, Lagrangian Forward Backtrajectory Adjoint Metric Cost Function Likelihood Function Updated Parameter Estimate Variational Approach Optimization/Minimization Stochastic Sampling Convergence

6 Source Term Estimation Process Input Data Sensor Data Met Data (Measurements, NWP) Initial Source Parameter Estimates (Guesses/Samples form Prior) Transport and Dispersion Analytic, Eulerian, Lagrangian Forward Backtrajectory Adjoint Metric Cost Function Likelihood Function Updated Parameter Estimate Variational Approach Optimization/Minimization Stochastic Sampling Convergence

7 Source Term Estimation Process Input Data Sensor Data Met Data (Measurements, NWP) Initial Source Parameter Estimates (Guesses/Samples from Prior) Transport and Dispersion Analytic, Eulerian, Lagrangian Forward Backtrajectory Adjoint Metric Cost Function Likelihood Function Updated Parameter Estimate Variational Approach Optimization/Minimization Stochastic Sampling Convergence

8 Source Term Estimation Process Input Data: Sensor Data Met Data (Measurements, NWP) Initial Source Parameter Estimates (Guesses/Samples from Prior) Transport and Dispersion Analytic, Eulerian, Lagrangian Forward Backtrajectory Adjoint Metric Cost Function Likelihood Function Updated Parameter Estimate Variational Approach Optimization/Minimization (with or without gradients) Stochastic Sampling Convergence

9 Source Term Estimation Process Input Data: Sensor Data Met Data (Measurements, NWP) Initial Source Parameter Estimates (Guesses/Samples from Prior) Transport and Dispersion Analytic, Eulerian, Lagrangian Forward Backtrajectory Adjoint Metric Cost Function Likelihood Function Updated Parameter Estimate Variational Approach Optimization/Minimization (with or without gradients) Stochastic Sampling Convergence Single Set of Parameters Probability Distribution

10 Source Term Estimation Input Data: Sensor Data Met Data (Measurements, NWP) Initial Source Parameter Estimates (Guesses/Samples from Prior) PROBABILISTIC APPROACH USING BAYESIAN INFERENCE WITH STOCHASTIC SAMPLING Transport and Dispersion Analytic, Eulerian, Lagrangian Forward Backtrajectory Adjoint Metric Cost Function Likelihood Function Updated Parameter Estimate Variational Approach Optimization/Minimization (with or without gradients) Stochastic Sampling Convergence Single Set of Parameters Probability Distribution

11 Source Term Estimation Input Data: Sensor Data Met Data (Measurements, NWP) Initial Source, Met Data Estimates (Guesses/Samples from Prior) OPTIMIZATION APPROACH USING GENETIC ALGORITHM Transport and Dispersion Analytic, Eulerian, Lagrangian Forward Backtrajectory Adjoint Metric Cost Function Likelihood Function Updated Parameter Estimate Variational Approach Optimization/Minimization (with or without gradients) Stochastic Sampling Convergence Single Set of Parameters Probability Distribution

12 Outline! Common components of source term estimation (STE)! Probabilistic approach using Bayesian inference Example: Algeciras accidental release! Optimization using Genetic Algorithms Redoubt volcano release! Summary

13 Models and Observations are Coupled Through Bayesian Inference STOCHASTIC SAMPLING OF UNKNOWN PARAMETERS Informed prior and improved proposal distribution Markov Chain Monte Carlo Sequential Monte Carlo METEOROLOGY DISPERSION MODELS Urban models: (empirical puff, CFD) Rejected configuration Hybrid and multi-resolution methods BAYESIAN COMPARISON (Bayes Theorem) P(θ d) = P(d θ) P(θ) / P(d) Accepted configuration Update likelihood until convergence to a posterior distribution Global, regional models: (2D, 3D, puff, particle) (Model predictions) OBSERVED DATA ERROR QUANTIFICATION Dynamic Data-Driven Event Reconstruction for Atmospheric Releases, UCRL-TR

14 Algeciras Accidental Release! 30

15 Simulation Set-up and Assumptions! Surface point source! Time and duration of the release ( UTC, May 30, 1998)! Sampling box (next slide)! 11 stations for 17 observations (9 on 06/02/ on 06/03/1998)! Zero concentrations not used

16 Prediction of Source Location Using Three Markov Chains! ~3600 km ~1800 km

17 Probability Contours for Source Location Using Three Markov Chains!

18 Location and Release Rate Probability Densities

19 Plume Prediction! After Several Hours 1200 UTC)! 30

20 Prediction plume after 1 day 31

21 Prediction plume after 2 days June 1

22 Prediction plume after 3 day 2

23 Prediction plume after 5 day 4

24 Prediction plume after 6 day 5

25 Outline! Common components of source term estimation (STE)! Probabilistic approach using Bayesian inference Example: Algeciras accidental release! Optimization using Genetic Algorithms Redoubt volcano release! Summary

26 Genetic Algorithm Initial Random Population of Chromosomes Q, u, θ Dispersion Model New Variables Iterate No Evaluate Cost Function Low Cost Mate Mutate High Cost Discard cost function = TS TS s= 1 [ O C ] s 2 TS [ O ] [ C ] s s= 1 s= 1 s s Convergence? Yes Final Variables

27 Redoubt Volcano Eruption March 23, 2009 Eruption The Alaska Volcano Observatory (AVO) observed eleven major explosive events during the first week, and a total of 19 events over the 14 day explosive eruptive period in March and early April. Coordinates: N W Elevation: 3108 meters (10,197 ft.) Volcano Type: Stratovolcano

28 Eruption Timeline Sunday March 22 Monday March 23 First Eruption Begins Fifth Eruption Ends!!!!!!!!!!10PM!!!!!!!11PM!!!!!!!12AM!!!!!!!1AM!!!!!!!!!!2AM!!!!!!!!!3AM!!!!!!!!!4AM!!!!!!!!!5AM!!!!!!!!!6AM!!!!!!!!!7AM! First 4 PM Second Sounding Satellite Pass

29 Satellite Data GOES-11 satellite provided data for use with the GA

30 Single Uniform Release Results Ten Runs Wind direction ( ) Wind speed (m s-1) Emission Rate (kg s-1) Cost Function Value Run x Run x Run x Run x Run x Run x Run x Run x Population 64 Generations 200 Mutation Rate 20% Run x Run x Mean x STD x Selection 50%

31 Single Uniform Release: GA Initialized Best Solution Emission Rate Total Mass Emitted Wind Direction Wind Speed 8.0x10 4 kg/s 2.6x10 9 kg m/s

32 Summary How to achieve effectiveness and efficiency while dealing with complexity and uncertainty? Both algorithms are effective but require significant computational expense. Bayesian approach: Provides probabilistic solution Flexible framework Delle Monache et al. Bayesian Inference and Markov Chain Monte Carlo Sampling to Reconstruct a Contaminant Source on a Continental Scale, J. Appl. Meteor. and Climatol., 47, Genetic Algorithm approach: Efficient exploration of parameter space Single best solution, but also probabilistic Schmehl et al. A Genetic Algorithm Variational Approach to Data Assimilation and Application to Volcanic Emissions, accepted for publication in Atmospheric Environment.