ensemble calibration for uncertainty estimation · 2012. 4. 18. · conclusion • ensemble...
TRANSCRIPT
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Ensemble Calibration forUncertainty Estimation
Damien Garaud 1,2
Vivien Mallet 2,1
CEREA1, INRIA2
27 October 2009
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Introduction to Air Quality
∂ci∂t
= −div(Vci) + div(ρK∇ci
ρ
)+ χi(c, t) + Si − Pi
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Air Quality Forecast
-10 -5 0 5 10 15 20
35
40
45
50
55
41
53
65
78
90
102
115
127
139
Ozone map (µg m−3)
May Jun Jul Aug20
40
60
80
100
120
140
160
Concentration
SimulationObservation
Ozone daily peak concentration
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Uncertainty Sources
Input Data
• Emission data• Meteorological fields
Physical Parameterizations
• Chemical mechanism• Vertical diffusion coefficient
Numerical Approximations
• Time step• Vertical resolution• Schemes
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Ensemble Approach
Different alternatives
• Kz : T&M or Louis• Chemical mechanism: RACM
ou RADM2• Numerical approximations: ∆t ,
Nz, . . .• Perturbations: winds,
emissions, boundaryconditions. . .
Large dispersion
0 5 10 15 20Hour
40
60
80
100
120
140
Concentration
Ozone daily profiles from 101members (µg m−3)
∂ci∂t
= −div(Vci) + div(ρK∇ci
ρ
)+ χi(c, t) + Si − Pi
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Uncertainty Estimation
• Concentration: random vector — a normal distribution for instanceN (µ,Σ)
• Measure example: standard deviation (Σ)
Why is it important?
• Confidence in forecasts• Risk prediction ([O3] ≥ 240 µg m−3)• Economic and health issues• Data assimilation (matrix B)
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Uncertainty Example
-10 -5 0 5 10 15 20
42
44
46
48
50
52
54
56
1.5 4.5 7.5 10.5 13.5 16.5 19.5 22.5 25.5 28.5
Standard deviation (µg m−3)
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Strategy
1 List all possible alternatives and so available models (150 billion)
2 Sample possible model space efficiently in order to obtain asmaller space (100 models)
3 Select according to an objective criterion (30–50 models)
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Ensemble Assessment
Rank Histogram
0 5 10 15Member
0
500
1000
1500
2000
2500
3000
3500
Num
ber
of
obse
rvati
ons
Brier Score
Assessment for a given event.c ≥ 240µg m−3
BS = 1N∑N
i=1(pi − oi)2 .
pi : probability for the date i .
oi : observed probability for thedate i .
The best Brier Score is 0.
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Objective Criterion and Method
Rank Histogram Variance
S ⊆ E
Cost function:
J(S) =NS∑i=0
(bi − b̂S)2
minS⊆E
J(S)
Genetic Algorithm
1 Population {S1,S2, . . . ,SK}
2 Assessment and selection{Si/J(Si) ≤ δ}
3 Crossover (Sa,Sb)→ (Sc ,Sd )
4 Mutation Si → S ′i
5 New population of Ksubensembles
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Rank Histograms
0 20 40 60 80 100Member
0.0
0.5
1.0
1.5
2.0
2.5
Num
ber
of
obse
rvati
ons
1e4
limitobservation
Large ensemble
0 2 4 6 8 10 12 14Member
0
1
2
3
4
5
6
Num
ber
of
obse
rvati
ons
1e4
limitobservation
Random subensemble
0 2 4 6 8 10 12 14Member
0.0
0.5
1.0
1.5
2.0
2.5
3.0
Num
ber
of
obse
rvati
ons
1e4
limitobservation
Calibrated subensemble
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Uncertainty Maps
Large ensemble Random subensemble Calibrated subensemble
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Time series
0 10 20 30 40 50Week
16
18
20
22
24
26
28
30
Sta
ndard
Devia
tion
LargeRandomCalibrated
Weekly standard deviation (µg m−3)
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Conclusion
• Ensemble calibration to estimate uncertainty
• D.Garaud and V.Mallet. Automatic generation of a largeensemble for air quality forecasting using the Polyphemussystem. Geoscientific Model Development Discussion, 2,889-933, 2009
• Comparison with other ensembles
• Other pollutants (aerosols, NO, . . . )
• Risk prediction