Source Term Estimation for Hazardous Releases

Transcription

1 Source Term Estimation for Hazardous Releases Fukushima Workshop NCAR, 22 nd 23 rd February 2012 Dstl/DOC61790 Dr. Gareth Brown

2 Presentation Outline Dstl s approach to Source Term Estimation Recent developments Spatially and temporally gridded urban met object Processing of deposition measurements Toy example Application to Fukushima

3 Source Term Estimation Monte Carlo Bayesian Data Fusion (MCBDF) MCBDF provides a set of likely source terms for calculating probabilistic hazards Accounts for uncertainty in source, meteorology, sensor performance & human reporting P. Robins, V. Rapley, N. Green, Realtime Sequential Inference of Static Ministry Parameters of Defence with Expensive Likelihood Calculations (2009)

4 Bayes Theorem p( θ y) p( yθ) p( θ) Posterior probability density of hypothesis θ given the data y Likelihood probability density of the data y conditional on the hypotheses θ Prior probability density of θ based on prior knowledge Iterative update of belief in a hypothesis Likelihood calculation particularly costly Necessary to run dispersion model for sensor data Sensor likelihood function complex

5 MCBDF: Bayesian data fusion MCBDF uses Bayesian inference over a sample set of hypothesized source-terms and Met. variables θ 1 = * x * y L 0 Source term Met ( xytmdau,,,,,,, u,,ln z, DP, ) ( ) Model The dimensionality of problem depends on its complexity Complex source terms Gridded meteorology in time and space Urban dispersion

6 Physics Modelling Dispersion is a turbulent process θ ( x, t, t ) 1 Impossible to model accurately Use ensemble puff dispersion models SPRINT model optimised for STE Implements SCIPUFF closure relations 2 2 ccc, dispersion 2 p χχχ, 2 χd χd, χ d

7 MCBDF: Example Prior

8 Sensor Likelihood Calculations When CB sensor measurements are passed to MCBDF the likelihood is calculated as ( 2) ( ) ( 2 µσ µσ ) py, = pyc pc, dc y Sensor measurement 0 measurement concentration density density µ Mean mass-concentration from dispersion simulation 2 σ Mass concentration variance from dispersion simulation c Unobserved ground-truth concentration

9 MCBDF: Upon Receipt of a Detection

10 Estimating the Posterior Distribution ( θ y) ( θ) ( θ) p p y p i Calculated as the product of the individual likelihoods and the prior Posterior estimated by sampling lots of hypotheses MCBDF uses Differential Evolution Markov Chain (DEMC) Monte Carlo to generate new hypotheses i

11 Calculating Hazard Areas The Hazard Calculator obtains the probability of exceeding a specified threshold dosage A weighted sum of these gridded probabilities is used to define the probable hazard area Release location Sensor network Red: ground truth; green: predicted

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13 Recent Developments MCBDF initially developed for rapid warning of chemical attacks based on input from sensor networks Short effective duration approximates to spatially and temporally invariant meteorology However STE for Bio and Rad releases in major cities requires Fast dispersion models accounting for urban areas Much longer temporal windows Efficient methods to compute long duration dosage / deposition Spatially varying meteorology for large scale dispersion

14 Meteorological Inference Urban capability Gridded urban meteorological model defined Wind flow components gridded in 2D space and time Surface properties gridded in 2D space Atmospheric stability gridded in time extra dimensions in parameter space MCMC techniques still efficient if converged Much more difficult to achieve convergence f Sykes et al, SCIPUFF Tech Doc ( zh,, α ) = exp α 1 c c c c Canopy height z h c Canopy flow parameter

15 Toy Problem Example Single, short duration release Single isotope Quantitative deposition measurements Spatially gridded, but temporally invariant meteorology No transport due to rain run-off before measurements taken

16 Deposition data Likelihood model for quantitative measurement of deposited material Assume local detection only, alpha, beta, not longrange gamma Uncertainty per measurement, not fixed Time taken to collect Poisson count statistics Energy spectrum uncertainty on which isotope is being measured Naturally occurring background (with uncertainty) subtracted Simple, normally distributed measurement error model Lower limit and saturation can be input

17 Sample Points 88 points 20km exclusion zone shown Release point known No met data

18 Hazard Plot First measurement above background Close to source Huge met uncertainty

19 Hazard Plot First 3 rings of data Less uncertainty close to source

20 Hazard Plot 4 rings of data

21 Hazard Plot 6 rings of data

22 Hazard Plot All data More time for convergence

23 Problems to solve for Fukushima Parameters to infer: Mass released in each hour over the last year Gridded meteorology for each hour over the last year 10km spatial resolution Modelling: Gamma sensors pick up spatially averaged dose Function of range needs integrating 1/r 2, attenuation through air, scatter build up factors Longer range second order closure dispersion model needed SCIPUFF Other? Further transport of deposited material due to water run-off

24 Backup

25 The Concentration Sensor Likelihood Model Critical to the performance of MCBDF is an accurate probabilistic description of the detector s response 2 σ e L L ( 2, σ ) e Φ Lc y= L ( ) ( 2 p yc = φ yc, σ ) e L< y< L ( 2 1 Φ Lc, σ ) = e y L Measurement error variance Sensor saturation point Sensor limit of detection normal distribution CDF

26 Deposition modelling Improved physics improves consistency of sensor data likelihood modelling More accurate source term estimation in presence of deposition Amount of deposition inferred from data and/or uncertainty correctly passed to hazard calculations 17 February 2012

27 Deposition data Likelihood model for detection of deposited material already in place Biological hazards Similar to a probit model Extended to include: Probability of false alarm Probability of false negative Integrate out unobserved true amount of deposited material 17 February 2012

28 Prelim. deposition results (simulated met. constant) Collectors + Identifiers (dosage) + Survey ID (deposition) 20km 10km 10km 5km 1 detection, 8 nulls 17 February 2012

29 Burn In and Convergence Initial hypotheses may be far from the peak of the posterior But rapid answers are required Data continually changing the posterior limited time for new sample weights to make the old ones insignificant Limited time for samples to spread out and capture true uncertainty Detection of non-convergence delays message processing Re-weight Re-sample 17 February 2012

30 Hazard Calculation Probit slope model S used to indicate uncertainty in appropriate value for χ d 50 1 S 1 log 2 2 ( χd ) = + erf 10 p Hazard χd χ d 50 (, 2 ) (, 2 ) ( ) p Hazard χ χ = p χ χ χ p Hazard χ dχ d d d d d d d 0 Average over 1000 release/met samples from posterior. 17 February 2012

31 Deposition data likelihood (clipped normal) 2 ( χd, σe ) 2 (, ) 2 ( χd σe ) Φ L y = L p( y χd) = φ y χd σe L< y< L 1 Φ L, y = L 2 2 ( χ, ) unclipped (, d χ d µ N σn) ( L χd, σ ) e ( 0 µ N, σn) δ ( χd) φ( χ d µ N, σ ) Φ Φ + N dχd y = L p( y µ N, σn) = φ( y χd, σ e ) ( 0 µ N, σn) δ ( χd) φ( χ d µ N, σn) Φ + dχd L< y< L ( 1 ( L χd, σ e )) ( 0 µ N, σn) δ ( χd) φ( χ d µ N, σn) Φ Φ + dχd y = L 0 L Φ( L 0, σ e ) Φ ( 0 µ N, σ N) + k( y) 1 ( 0 µ ( y), σ ( y) ) Φ dy y = L p( y µ N, σn) = φ( y 0, σ e ) Φ ( 0 µ N, σ N) + k( y) 1 Φ ( 0 µ ( y), σ ( y) ) L< y< L Φ( L 0, σ e ) Φ ( 0 µ N, σ N) + k( y) 1 Φ ( 0 µ ( y), σ ( y) ) dy y = L L 2 2 ( x, ) ( x, ) φ µσ φ µ σ σ σσ = 2 2 σ1 + σ2 2 µ 1 µ 2 µ σ = + σ σ 2 k ( x, 2 ) ( x, 2 ) k ( x, 2 ) φ µ σ φ µ σ φ µ σ σ = σσ e π µ 1 µ 2 µ σ1 σ2 σ Romberg (closed and semi-infinite) numerical integration 17 February 2012

32 Deposition data likelihood (clipped gamma) 2 ( χd, σe ) 2 (, ) 2 ( χd σe ) Φ L y = L p( y χd) = φ y χd σe L< y< L 1 Φ L, y = L 2 * ( χ, ) (,, d χ d sk λ) Romberg (closed and semi-infinite) numerical integration χd + λ * k 1 exp 2 χd λ s + Φ ( L χd, σ ) e + (1 γδχ ) ( ) * d dχd y = L s s ( k ) 0 Γ χd λ + * k 1 exp 2 2 χd λ s + p( y µ N, σn) = φ( y χd, σ e ) (1 γδχ ) ( ) + * d dχd L< y< L s s ( k ) 0 Γ χd + λ * k 1 exp 2 χd + λ s ( 1 Φ( L χd, σe )) + (1 γδχ ) ( ) * d dχd y = L s 0 sγ( k ) χd + λ * k 1 exp 2 2 χd λ s + Φ( L 0, σe )( 1 γ) + Φ( L χd 0, σ ) e dc y = L * ( ) 0 s sγ k χd λ + * k 1 exp χd λ s + p ( y µ N, σn) = φ( y 0, σe )( 1 γ) φ( y χd, σ + e ) dc L < y < L * s s ( k ) 0 Γ χd + λ k 2 2 ( 1 Φ( L 0, σe ))( 1 γ) + ( 1 Φ( L χd 0, σe )) * 1 exp χd λ s + dc x = L * s sγ( k ) 0 17 February 2012

33 Urban meteorology Displacement height Canopy blending Mean wind vector Shifted wind vector z ( h, α ) = 0.7 hf( α ) d c c c c c ( α ) 2 c Fc( αc) = 1 exp α c u ' ( xyzt,,, ) = gxyz (,, ) u( xyzt,,, ) ' ' fsl ( z, z0, L) ux(, xyzt,,) = u* x(, xyt,) k ' ' fsl ( z, z0, L) uy(, xyzt,,) = u* y(, xyt,) k u(, xyzt,,) = 0 ' z ( hc < zs + zd) and ( z < hc) h ( c s d) c zd if or h z + z z zd if ( hc < zs + zd) and ( hc z < zs + zd) (,, ) = zs if ( hc < zs + zd) and ( z zs + zd) ' z xyz Surface layer profile Canopy layer profile Blending function z z fsl ( zz, 0, L) = ln + 1 Ψm( ) z0 L z fc( zh, c, αc) = exp αc 1 hc gxyz (,, ) = F( α ) f( zh,, α ) + (1 F( α )) c c c c c c c fsl (, zz0, L) f ( h, z, L) sl c 0 17 February 2012

34 Wind vector spatial derivatives Calculated by chain rule, e.g.: gxyz (,, ) αc gxyz (,, ) hc + αc xi hc xi if z < h gxyz (,, ) gxyz (,, ) gxyz (,, ) z = + + xi z0 xi z xi if z h 0 hc < zs + z z0 d hc zs + zd gxyz (,, ) = x i gxyz (,, ) αc gxyz (,, ) hc + α x h x c i c i gxyz (,, ) z gxyz (,, ) z < s + z0 xi z xi c c if z z z gxyz (,, s + zd) αc gxyz (,, s + zd) hc + αc xi hc xi gxyz (,, s + zd) z0 + if z zs + zd z0 xi gxyz (,, s + zd) zd αc zd h c + + z αc xi hc xi d 17 February 2012

35 Hypotheses Temporal gridding Spatial gridding θ 1 ( ) ( d) x y L ( ) ( c) ( αc) = 1 2 * * 0 Source-term Meteorology ( l, l, t, m,ln d,ln v, a, u, u,,ln z,ln h,ln, DP ) Model Location Time Mass Duration Deposition velocity Agent Friction velocity components Reciprocal Monin Obukhov length Surface roughness Canopy Height Canopy Flow Dispersion model Dispersion model output PDF Floating point values used to index discrete values 17 February 2012

36 Accuracy Compared to ATP45 Concentration sensor network Meteorology sensor Shear LIDAR SODAR Multiple anenometers Probability of hazard effect Ground Truth Inferred 17 February 2012

37 Uncertainty Compared to ATP45 Single prompt alarm Forecast meteorology Probability of hazard effect Ground Truth Inferred 17 February 2012

38 Processing dynamic sensor data MCBDF performs sourceterm estimation in realtime A time window is maintained - typically 30 minutes into the past for chem, 2 days for bio On receipt of new data, old hypotheses and old data will become obsolete and are removed as they exit the current time window Total likelihood housekeeping Remaining hypothesis weights are modified by the likelihood of new data 17 February 2012

39 Exam Question Source term means to an end How much material is in the soil Can the land be used for habitation or farming. 17 February 2012

40 Summary Deposition survey data as a data source appears effective Modelling/inference extensions required 17 February 2012