Subfilter-scale turbulence modeling for large-eddy simulation of the

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					Source inversion for dispersion in urban
 environments using CFD and Bayesian
   inference with stochastic sampling




               Tina Katopodes Chow
            University of California, Berkeley

         Branko Kosović and Stevens Chan
         Lawrence Livermore National Laboratory
Goal: source inversion in a complex domain

• Given a highly
  complex domain, with
  buildings of various
  shapes and sizes,
  and concentration
  measurements at a
  few locations, is it
  possible to find the
  source of a
  contaminant plume?

                         Wind
Urban dispersion
• Computational fluid
  dynamics
• Turbulence modeling
• Adaptive mesh
  refinement tools
• Immersed boundary
  methods
• Source inversion

                        Staten Island, NY oil barge explosion 2003
Overview

•   Motivation, background
•   Source inversion methodology
•   Prototype building example
•   Oklahoma City - Joint URBAN 2003
Event reconstruction: What happened?

                                     What?
                                     When?
                                    Where?
                                   How much?



        Observations                                     Emergency
                            Event Reconstruction
      (visual, sensors)                                   Response

 Uncertainty due to unknown sources and meteorology
 Atmospheric releases can spread fast and affect large populations
 Who needs to know?

     Emergency response teams, public health officials, poison centers,
       hospitals, media
NARAC @ LLNL
• National Atmospheric
  Release Advisory Center
• Modeling and emergency
  response for chemical,
  biological, nuclear releases
• Support DOE and DoD sites,
  and other federal/state/local
  agencies
• 24/7 on-call
NARAC emergency response
• Three Mile Island Nuclear Power Plant,
  Harrisburg, PA - 1979
• Chernobyl Nuclear Power Plant, USSR,1986
• Persian Gulf - Kuwait oil fires, 1991
• Staten Island, NY - Petroleum Fire, 2003
• New Orleans, LA - Industrial fires due to
  Hurricane Katrina, 2005
• Graniteville, SC - Chlorine railcar spill, 2005
• Phoenix, AZ - Explosion at rocket fuels plant,
  2006
• Salt Lake City, UT - Hydrochloric acid plant
  accident, 2006                                     https://narac.llnl.gov/
• Shepherdsville, KY - Railcar fire and interstate
  closure, 2007
Operational requirements for event reconstruction


• Quantitative and probabilistic estimates
• Optimal solutions
• Problem complexity (time-dependence, high-
  dimensionality, multi-scale phenomena, stochasticity due
  to natural atmospheric variability, disparate data types)
• Dynamic uncertainty estimates as additional data
  become available
• Robustness and performance constraints for operational
  use
• Design tools for sensitivity and sensor network studies
Event reconstruction framework:
Bayesian inference and stochastic sampling
                 STOCHASTIC SAMPLING
                OF UNKNOWN PARAMETERS                       METEOROLOGY
                  Informed prior and improved
                      proposal distribution
                                                        DISPERSION MODELS
                 Markov Chain Monte Carlo
                                                         Global and
                   Sequential Monte Carlo             regional models:
                                                                         Urban models:
                                                                          (empirical puff,
                Hybrid and multi-resolution methods     (2D, 3D, puff,
                                                                              CFD)
                                                           particle)
  Rejected
configuration                                              Model predictions
                BAYESIAN COMPARISON
                      (Bayes Theorem)
                P(M | D) = P(D | M) P(M) / P(D)
                                                            OBSERVED DATA
     Accepted configuration

                                                        ERROR QUANTIFICATION
                  Update likelihood until
                convergence to a posterior
                       distribution
Meteorological complexity
Meteorological complexity




        Tracy, CA – tire fire, 1998
Urban geometries




                   San Francisco, CA
Urban geometries




               Manhattan Island
Urban geometries




                   Plume can travel perpendicular to
                   mean wind
 FEM3MP CFD Model
• Primary urban dispersion modeling
  code used at NARAC
• 3D Finite-Element based Navier-
  Stokes solver
   – Structured grids with Quad
     Elements
   – RANS, LES turbulence models
• Validation
   – Joint Urban 2003 in Oklahoma City
   – Urban 2000 in Salt Lake City
   – Wind tunnel experiments
Overview

•   Motivation, background
•   Source inversion methodology
•   Prototype building example
•   Oklahoma City - Joint URBAN 2003
CFD source inversion prototype:
flow around a cube building
CFD source inversion prototype:
flow around a cube building
•   3D building-resolving FEM3MP Reynolds Averaged Navier-Stokes code
•   Presence of building causes asymmetric plume
•   Bayesian inference with stochastic sampling




              Source
                                      Sensors
                        Building
Markov Chain Monte Carlo for source inversion
Markov Chain Monte Carlo for source inversion
Markov Chain Monte Carlo for source inversion
Markov Chain Monte Carlo for source inversion
Markov chains converge on source
MCMC algorithm – Metropolis-Hastings
• Generate x, y, q from prior distributions
   – E.g. 0.000001 < q < 1.0, uniform
   – Each variable tested separately against
     prior
       • Poor comparisons do not always fail – use
         coin flip
• Forward dispersion calculations using
  proposed state
• Compare predicted results with
  observed concentration data
   – If better than previous state, ‘accept’
   – If worse than previous state, ‘coin flip’
Markov chains converge on source
Probability distribution of source location




              Actual source
          Peak of distribution
Release rate histogram



                Actual release rate
Convergence rates
       Composite plume for 90% confidence intervals




                                                HIGH




                                                LOW

p(c)
                                         p(c)
            90%                                    90%

            c     clow                          chigh    c
Stochastic sampling inversion algorithm

• Methodology is robust
  – Always gives a probabilistic answer
  – Bayesian comparison – Metropolis-Hastings sampler
  – Invert for location (x,y,z) and release rate (q)
• Can handle:
  –   Unsteady flows
  –   Unsteady releases
  –   Chemistry
  –   Complex geometries
Overview

•   Motivation, background
•   Source inversion methodology
•   Prototype building example
•   Oklahoma City - Joint URBAN 2003
Source inversion for Oklahoma City

• FEM3MP – 3D building-
  resolving forward model
• Joint URBAN 2003 SF6
  releases (IOP3, IOP9)
• Steady log profile inflow,
  southerly winds at
  uz=50m=6.5 m/s
• Winds steady after ~10
  min, used to drive
  dispersion simulations
FEM3MP configuration
Computational domain
 Domain size (m): 600 x 650 x 250, 1000 x 3000 x 350
 Grid points: 132 x 146 x 30 (~0.5M) , 201 x 303 x 45 (~2.75M)

Simulated experiments:                     IOP 3           IOP 9
 Wind speeds (at 50 m):                        6.5          7.2
 Wind directions (degrees):                   185          180
 Atmospheric stability:                       neutral      neutral
 Source rate of SF6 (g/s):                     5.0          2.0




                                                     Explicitly resolved buildings
Complex flow for inversion

• Plume splitting,
  corner eddies
• Max building height
  120m
• Sheltering, updrafts
• Model error,
  assumptions

                         Velocity vectors and horizontal
                             wind speed contours
IOP3 – Wind comparison

                Model

                DPG PWIDS Data




       Source
Computational shortcuts

• Typical inversion requires 20,000 forward runs – too
  expensive!

• Green’s function approach
   – Store runs for unit source at each point in the domain and
     rescale with sampled source strength
   – Then reconstruction only needs ~2 minutes
• 2560 sources, 128 forward runs required
   – 20 sources/run using steady wind flow
   – Each forward run uses 32 processors
   – Checkerboard grid to cover larger area
• Total CPU hours = 13,056
   – 12+ hours on 1024 2.4 GHz Xeon processors
   – (or 17 days on 32 processors)
Markov chains quickly focus on source region




                                         Sensors ( )

         Actual source




        Wind        Markov chain paths
Probability distribution of source location




                         Actual source
                         location




  Possible source
  locations
Release rate histogram




           Actual release rate
Convergence rates
Forward model predictions




Predictions from actual   Predictions from inverted
   source location            source location
High-resolution predictions




                    High-resolution
                                      Chan 2005
Modeled vs. predicted concentrations
   Composite plume for 90% confidence intervals




                                                 HIGH




                                                 LOW


p(c)
                                      p(c)
         90%                                    90%

         c     clow                          chigh    c
IOP9 – nighttime release
IOP9 – nighttime release
Probability distribution of source location
Conditional probability distribution
Convergence rates
Synthetic data inversion
Synthetic sensor data generated from a forward simulation at the actual source
location.
Event Reconstruction - Computational framework will support
multiple stochastic algorithms, models, and platforms
                                               MODEL DRIVER
STOCHASTIC
                                                     Job Distributor
   TOOLS

                     Input Handler        Input Handler        Input Handler            Input Handler

   MCMC
                     2D Puff Model      3D Particle Model    Urban Puff Model         Urban CFD Model
    SMC
  HYBRID
 MULTI-RES.                                                                     ...
Informed prior and
proposal sampling     Output Handler       Output Handler      Output Handler           Output Handler
  with nonlinear
    optimization
                                                   Model Handler


                     PC          workstation

 SYSTEM
HARDWARE                                                    Massively parallel system
Summary and future applications

• Successfully inverted source location and release rate
   – Prototype isolated building
   – Complex urban flow (Oklahoma City)

• Post-emergency forensic analysis tool
   – Robust methodology, can have unsteady flows and releases
• Emergency response tool
   – With grid nesting
   – With advance planning
      • Could use database of wind/source scenarios
      • Reconstruction takes only a couple of minutes
• Optimal sensor network design
Sensor network design
Sensor network design
Acknowledgments

•   Funded by LDRD project number
    04-ERD-037
•   Livermore Computing center
•   This work was performed under
    the auspices of the U.S.
    Department of Energy by the
    University of California, Lawrence
    Livermore National Laboratory
    under Contract W-7405-Eng-48.


    Reference:
    Chow, F.K., Kosovic, B., and S.T. Chan. 2008. Source inversion for
    contaminant plume dispersion in urban environments using building-resolving
    simulations. Journal of Applied Meteorology and Climatology 47(6), 1553-
    1572.