Download - Source Reconstruction
Source Reconstruction
CRTI-02-0093RD Project Review MeetingCanadian Meteorological CentreAugust 22-23, 2006
Component 6: Inverse Source Determination and Bayesian Inference
urbanBLSurbanAEU
Bayesian inference for inverse source
determination
Adaptive sampling strategy
PSTP Component 6
• Localization of leakage of toxic gases and other pollutants (regulatory application)
• Terrorist incidents – localization of unknown source following event detection by network of CBR sensors (“electronic noses”) as quickly as possible
• Comprehensive Nuclear Test Ban Treaty (CTBT) – “sniffing” out clandestine nuclear tests (133Xe network of electronic noses)
Putative release event(s) Observations from sensors(electronic noses)
Source characteristics• emission rate• spatial location• on/off times• number of sources
Source reconstruction
Motivation for Source Reconstruction
Bayesian Inference: Foundations
)(),|()(
GDfIDPf NN
ForwardMap: G
Source-receptorrelationship
Modelerror
Inputerror
―
Stochasticuncertainty
Observationerror
CpCo
Noise:
BayesianInference
Prior
Likelihood
Posterior • input uncertainty (meteorology)• model errors• stochastic uncertainty• observation error
Noise:
Posterior distribution for source parameters: ),|()|(),|( IDPIPIDP
Estimate
Bayes’ rule
(Probabilisticdata fitting)
inference prior likelihood×
Application of Bayesian Inference for Inverse Source Determination
),,( ,)()()(),( ssssebs zyxxTtHTtHxxQtxS
)h (kg rate Emission
(h) time off Source
(h) time on Source
(m) Altitude
E) (deg Longitude
N) (deg Latitude
1- :
:
:
:
:
:
Q
T
T
z
y
x
e
b
s
s
s
),,,,,( QTTzyx ebsss
Assumed source distribution:
Source parameter vector
Infer source parameter vector using Bayes theorem:
likelihoodprior inference
),|()|()|(
),|()|(),|(
IDPIPIDP
IDPIPIDP
where
need to specify likelihood and prior to define posterior PDF for source parameters
Source-Receptor Relationship
),( ss txS
Unspecified source
Knownreceptor
),( txh
iu
),(),|,(),( ** txhtxtxGtxC ssss
),(
),(),(),(
*
*
SC
txStxCdtxdtxC ssssss
,
,0 ; ,0
0
0
**
*
**
*
to normal outward is and nB
xz
CxCnu
n
CK
hx
CK
xCu
xt
C
H
H
iii
i
Problem: Determine the concentration at fixed receptor location, for an arbitrary unspecified source distribution
0
H
),(),( txhtxdtCxd
Duality relation
),(),(),( * QChCtxC
Eulerian
Receptor oriented approach
urbanAEU
Design of Backward Lagrangian Stochastic Model
– Constraints imposed by the duality relation between the forward and backward transition PDFs on the coefficients of LS models:
Principal Result:The duality between the forward and backward transition PDFs imply that the backward drift and diffusion coefficients are related to the forward drift and diffusion coefficients as follows (converse is also true):
j
E
Ei
EijjE
ii
ijij
u
p
ptxCtuxa
pButxup
tuxatuxa
txC
1),(),,(
),;(
2),,(),,( )2(
),( )1(
0
2/10
),,;,,,(),;(),,;,,,(),;( 000000000 tuxtuxptxuptuxtuxptxup LELE
(Source-oriented approach) (Receptor-oriented approach)
urbanBLS-1
Examples of Source Reconstruction
• Joint Urban 2003 (JU2003)– Real cityscape (highly disturbed flow)
• European Tracer Experiment (ETEX)– Non-stationary, inhomogeneous flow over
complex terrain– Long-range dispersion on continental scales
Joint Urban 2003
Dual Concentration Field C*
*logC
Detector # 515(1-km sampling arc)
[C] = pptv[Q] = kg s-1
log C*
),( * SCC
urbanAEU
Example 1: (4 detectors)
N
Actual source location:
(xs , zs) = (3.2506,1.5537)
– estimated source location at one standard deviation:
093.0642.1
,0.6108.3
est
est
s
s
zss
xss
zz
xx
74
Detector
Source
Distributed drag force representation
0 1 2 3 4 50
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Q (g s-1)
P(
Q |
D,I)
/ P0
0 1 2 3 4 5 60
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
xs
P(
x s | D
,I)/ P
0
Example 1: (4 detectors)
0 0.5 1 1.5 2 2.5 30
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
zs
P(
z s | D
,I)/ P
0
Actual xs :
3.2506
Actual zs :
1.5537
Actual Q :2.00 g s-1
– estimated source parameters at one standard deviation:
1
est
est
est
s g 41.054.1
,093.0642.1
,0.6108.3
Q
zss
xss
zz
xx
s
s
European Tracer Experiment
Inverse Source Determination for ETEX
• Concentration data extracted only from 10 sampling sites out of a total of 168 sampling sites
• Only 35 concentration time samples out of the total available 5,040 concentration samples were utilized for inversion (0.69% utilization of available data)
Degrees Longitude
De
gre
es
La
titu
de
Sampling sites:
F02: Alencon [2]
F19: Paris Orly [4]F21: Rennes [2]D10: Essen [4]
D13: Offenbach [5]
D19: Hof [3]
D34: Nurburg [7]
D44: Trier-Petrisberg [4]
D45: Wasserkuppe [3] CR04: Temelin [1]Map adapted from Platt et al. (2004)
Meteorological Data for ETEX
• Global Environmental Multiscale (GEM) model was executed in regional configuration with core resolution of 0.14° over Europe
• GEM produced a series of 3 and 6 h forecasts over the period of time corresponding to ETEX releases
• Initial data for GEM came from CMC Global data assimilation system
• Series of forecasts was used to “drive” backward LS particle model (MLPD-0) for calculation of C* (viz., GEM model outputs were used as “smart interpolator” of meteorological fields in space and time)
• C* fields were computed on a polar stereographic 229 229 grid over Europe (including UK) with a 15 km mesh length
Example 1: Results
E01.104.2
,N 8.07.47
est
est
s
s
yss
xss
yy
xx
Actual source location:
E0083.2
N, 48.058
s
s
y
x
– estimate of source location at one standard deviation
Example 1: Results
h 2.59.13
,h 79.070.0
est
est
e
b
Tee
Tbb
TT
TT
Actual source on/off times:
h 0.13
h, 0.1
e
b
T
T
– estimate of source on/off times at one standard deviation
Example 1: Results
Actual source on/off times:
h 0.13
h, 0.1
e
b
T
T
Normalized Posterior PDFs of source on/off times
HPD interval (or, credible interval)(97.5% probability content)
h )0.20,25.0(
h, )5.2,0.0(
e
b
T
T
Source on
Source off (lower,upper)
Example 1: Results
1est h kg 2.722.6 QQQ
Actual source strength:1h kg 728.28 Q
Normalized Posterior PDF of source strength Q
– estimate of source strength at one standard deviation
HPD interval (or, credible interval)(97.5% probability content)
-1h kg )5.28,0.17(Q
(lower,upper)
Conclusions
• Bayesian inference applied successfully to source reconstruction in complex environments involving highly disturbed wind fields (meteorological complexity)
• Methodology allows optimal estimates of source parameters along with their reliabilities, fully accounting for model and data uncertainty
• Future effort will extend methodology to more complex source configurations– Multiple sources– Area/volume sources– Moving sources
Generate a comprehensive tracer, meteorological and sensor dataset suitable for testing of current and future Sensor Data Fusion algorithms.
• Provide an abundance of tracer sensors and met instruments rather than an “optimal” placement. Sparser data sets can be had by ignoring unwanted measurements.
• Provide a variety of source types, strengths and locations. Include simultaneous emissions from different locations.
Objective:
FUsing Sensor Information from Observing Networks (FUSION) Field Trial 2007 (FFT 07)
• Multiple and extended sources• High resolution (spatial and temporal) concentration sampling
– Limited vertical sampling– Potential 4-D sampling
• DPG DIAL and FTIR • Aerospace FTIR
• High resolution (spatial and temporal) meteorological measurements– Including vertical measurements (towers and profilers)
• Regular sampler grid• Dense sensor spacing for data denial studies
Combine a Unique and Synergistic Set of Instrumentation in a Single Test Series that includes
Approach
1 km
1 km
2 km
20 PWIDs to display real-time winds on the test bed
25 3D sonics for high temporal (10 Hz) resolution wind data close to high resolution samplers.
100 dPID propylene samplers in 1 km square grid for high temporal resolution (1 Hz) of propylene concentration data.
Propylene release areas
32 meter towers with sonics and other sensors at five levels (2, 4, 8, 16 and 32m).
Other Possible Instrumentation (locations TBD): DPG SAMS sites, DPG 924-MHz radar wind profiler and mini-sodars, DPG FM/CW boundary layer radar, Net SW/LW radiometers, DPG tethersonde, Aerospace FTIR, MIRAN detectors.
23 UK UVICS on the down-wind perimeter with high sensitivity (10 ppb) and temporal resolution (1-10 Hz) in the region of lowest expected concentration.
Details of the Proposed FUSION Test-bed