Uncertainties and variabilityCelya Summer School ‘Atmospheric sound propagation’
14-06-2018
David EcotièreUMRAE
o A start with a few truisms (… but not always considered as such)
It is impossible to measure (or predict) EXACTLY a physical quantity (evenif you are Nobel prize in metrology)
A measurement result given without its associated uncertainty should make no sense
Several dB uncertainties are common in environmental acoustics (depending on the quantity observed)
Introduction
Celya Summer School – Uncertainties and variability 14/06/20182
I’m 1.6m tall I’m 1m tall Who is right ?
Both !
o Uncertainties : where are they come from?
Epistemic uncertainties : unknown (or bad known) parameters
Model limitations, measuring instrument uncertainties, methodologyuncertainty …
‘Natural’ variability of the observed quantity, sampling uncertainty
Introduction
Celya Summer School – Uncertainties and variability 14/06/20183
o Uncertainties : what is it ?
Measurement (or prediction) -> measurement (or prediction) error
Introduction
Celya Summer School – Uncertainties and variability 14/06/20184
Referencevalue
Measureresult
Measurand value
Systematic random
Error
o Uncertainties: what do I do with them? what do I need it for?
Uncertainty information = information on the quality of its measurement/calculation against a defined requirement
Comparison to a threshold
Introduction
Celya Summer School – Uncertainties and variability 14/06/20185
Threshold
dB
Estimation
Estimation
dB
dB
dB
I’m 1.6m tall I’m 1m tall
Who will you trust in ?
o Several kinds of uncertainties
Accuracy
• e.g. due to the instrument resolution
Dispersion
Systematic error (trueness)
Introduction
Celya Summer School – Uncertainties and variability 14/06/20186
-> Uncertainty is a combination of all of these
o Roadmap
Define precisely the quantity of interest
Investigate the measurement process to identify the possible causes of error (if possible)
Choose a method for estimating standard uncertainties :• Depending on the knowledge we have of the measurement process
• Depending on the possibility to model the process
• Depending on whether the measurement process can be repeated easily or not
Calculate the expanded uncertainty and a confidence interval
Methodology
Celya Summer School – Uncertainties and variability 14/06/20187
Methodology
Celya Summer School – Uncertainties and variability 14/06/20188
[Désenfant, Priel, A road map for uncertainty estimation approaches, 2006]
o Bias, expanded standard uncertainty, confidence interval
Result:
𝐿𝑐 = 𝐿𝑚𝑒𝑠 − 𝑏
in the x% confidence interval: [𝐿𝐶 − 𝑈min ;𝐿𝐶 + 𝑈max ]
Methodology
Celya Summer School – Uncertainties and variability 14/06/20189
k=2 : IC 95%
- b : bias (systematic error)- Umin et Umax : expanded standard uncertainty
-- u : standard uncertainty (standard deviation)
utu
utu
maxmax
minmin
Referencevalue
Measureresult
MeasurandvalueSystematic rand
omError
o GUM method (ISO/CEI Guide 98-3) – analytical approach(errors propagation law)
An analytical model is required:
• Estimations:
• Combined uncertainty:
• If influence quantities Xi are not correlated:
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201810
1
1
,
11
2
2
2 2N
i
xx
j
N
ij i
N
i
x
ijii x
f
x
f
x
fu
),...,,( 21 NXXXfY
N
i
x
iix
fu
1
2
2
2
),...,,( 21 Nxxxfy
o In France : new standard XP S 31-115 (GUM compliant)
o General process
a) identification of influence quantitiesb) bias induced by each influence quantityc) standard uncertainty induced by each influence quantityd) calculation of combined uncertainty and total biase) calculation of the expanded uncertainty and confidence intervalf) presentation of the measurement result and uncertainty
information
Celya Summer School – Uncertainties and variability 14/06/201811
Methods : GUM
o a) Main influence quantities
Instrumentation Implementation and environmentalconditions
- Microphone Directivity- Linearity of levels- Frequency weighting and frequency
linearity (A, C, Z)- Air temperature and humidity- Ambient air pressure- Field standard level- Wind screen- Power supply- Proper noise of the instrumentation- Time Weighting (F, S, I)
- Duration of measurement;- Post-treatment ;- Local weather conditions at the
microphone (wind, rain,...) ;- Electromagnetic fields outside the acoustic
measuring device
Celya Summer School – Uncertainties and variability 14/06/201812
Methods : GUM
o b) and c) bias and standard uncertainty of each influence quantity
Standard uncertainty estimated by standard deviation
o (d) total bias and combined uncertainty
Total Bias :
-> biases can compensate each other (and the total bias can be null)
Combined uncertainty (decorrelated quantities) : 𝑢𝐶 =
𝑖
𝑢𝑖2
𝑏 =
𝑖
𝑏𝑖
-> standard uncertainties do not compensate each other (the composed standard uncertainty cannot be zero)
Celya Summer School – Uncertainties and variability 14/06/201813
Methods : GUM
o e) Expanded uncertainty and confidence level
Expanded uncertainty
k=coverage factor (depend on the confidence level)
Confidence interval
𝑈 = 𝑘. 𝑢𝐶(𝑦
k=2 : IC 95%
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201814
o Values for standard uncertainties
Standard values (overestimation)
• Standard (ISO/CEI 61672 for ex.)
• Technical spec., publications
Specific value
• Estimated by the user
27/04/2018CFA 2018 - norme XP S 31-115-1 15
Methods : GUM
o Ex : from NF EN 61672-1 (sound level meter spec.) for class I
Influence quantity u (dB)Level linearity error 0.46Supply voltage 0.06Static air pressure 85 kPa à 108 kPa 0.23
65 kPa à 85 kPa 0.52Air temperature -10 à + 50°C 0.28
0 à + 40°C -Air humidity 20% à 90% 0.28Electromagnetic fields 0.57Calibrator 0.17Wind screen 63 Hz à 2 kHz 0.28
2 kHz à 8 kHz 0.46Time weighting F and S 0.06Leq measurement 0.06Rounding of the measurement 0.03Adjustment 0.01Measurement of C-weighted peak sound pressure levels
1.15
Celya Summer School – Uncertainties and variability 14/06/201816
Methods : GUM
o Ex : from NF EN 61672-1 (sound level meter spec.)
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
10 100 1000 10000
1/3 octave (Hz)
u (
dB
)
Classe 1
Classe 2
0.00
0.50
1.00
1.50
2.00
2.50
3.00
3.50
4.00
10 100 1000 10000
f (Hz)
u (
dB
)
30° - Classe 1
30° - Classe 2
90° - Classe 1
90° - Classe 2
150° - Classe 1
150° - Classe 2
Microphone directivity‘A’ frequency weighting
Celya Summer School – Uncertainties and variability 14/06/201817
Methods : GUM
o Wet wind screen [Ribeiro, Ecotière et al, 2014] [XP S 31-115]
Correction C j
(protections mouillées)
-0,8
-0,6
-0,4
-0,2
0
0,2
0,4
0,6
10 100 1000 10000 100000
Fréquence (Hz)
dB
Modèle 1
Modèle 2
Incertitude-type u Cj
(protections mouillées)
0
0,2
0,4
0,6
0,8
1
1,2
10 100 1000 10000 100000
Fréquence (Hz)
dB
Modèle 1
Modèle 2
Celya Summer School – Uncertainties and variability 14/06/201818
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201819
o Wind induced noise [Ecotière, Rumeau et al. 2012, 2018] [XP S 31-115]
Bias :
Standard uncertainty :
54 56 58 60 62 64
01
23
45
6
Biais
Lmes (dBA)
dB
A
54 56 58 60 62 64
01
23
4incertitude-type
Lmes (dBA)
dB
A
Ex : wind speed 5/m/s, microphone height 1.5m.
Methods : GUM
𝑏𝑤𝑖𝑑 = 𝑎𝑏,1 +𝑎𝑏,2
𝐿𝑚𝑒𝑠 − 𝐿0
𝑢𝑤𝑖𝑛𝑑 = 𝑎𝑢,1 +𝑎𝑢,2
𝐿𝑚𝑒𝑠 − 𝐿0
2
+ 𝑢𝑤𝑖𝑛𝑑,𝑚𝑜𝑑2
o GUM method (ISO/CEI Guide 98-3) – stochastic approach(distributions propagation, Monte Carlo)
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201820
Y=f(x1,x2,x3)
x1
x2
x3
n samples
n calculations
Y
IC95%
Y
Ymin Ymax
YY Result :
within the 95% confidence interval =[Ymin, Ymax]
n samples
n samples
o An example of Monte Carlo application : uncertainties of windinduced noise in a screened microphone
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201821
o An example of Monte Carlo application : uncertainties of windinduced noise in a screened microphone
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201822
8,74)()(
/log7,26/log4,69 00,
CzF
lDVVL Aat
)./215.0log(20)(
,)/ln(/log20)(
),3/(
0
2
0
0
3/1
pVC
zzDzzF
DVf c
Input parameters :
Wind screen: zD ,,
HTzV ,,, 00Environment:
[van den Berg, 2006]
Bias and bias uncertainty estimation by Monte Carlo technique
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201823
Lsource
105 samples
80dB20dB
105 calculations for each wind class
V
Vi Vi+1
T0
-20oC 40oC
H
700W/m2-150W/m2
105 samples
105 samples
105 samples
10/10/1010log10 sourcewind LL
mesL
messource LLC
windL : van den Berg model
Monte Carlo method
[Ecotière,2012, 2018]
Methods : GUM
V=5 m/s
V=6 m/s
Celya Summer School – Uncertainties and variability 14/06/201824
Bias and bias uncertainty
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201825
negligible biasBig uncertainty[Ecotière,2012, 2018]
Bias and standard uncertainty for wind induced noise
Methods : GUM
Celya Summer School – Uncertainties and variability 14/06/201826
[Ecotière,2018]
𝑏𝑤𝑖𝑑 = 𝑎𝑏,1 +𝑎𝑏,2
𝐿𝑚𝑒𝑠 − 𝐿0
𝑢𝑤𝑖𝑛𝑑 = 𝑎𝑢,1 +𝑎𝑢,2
𝐿𝑚𝑒𝑠 − 𝐿0
2
+ 𝑢𝑤𝑖𝑛𝑑,𝑚𝑜𝑑2
o Interlaboratory approach (CEI Guide 98-3) – approach
Requires numerous experimental trials with several labs
Based on a statistical method of analysis of variance (ANOVA)
Allows the estimation of 2 uncertainties :
• Repeatability: 𝑢𝑟
• Reproducibility: 𝑢𝑅
• Final Uncertainty: u2 = ur2 + 𝑢𝑅
2
Possibility to calculate intermediate precision (repeat. per lab, per operator, etc.)
Methods : ISO 5725
Celya Summer School – Uncertainties and variability 14/06/201827
Methods : ISO 5725
1 2 3 4 5
Laboratories
Deviation / ref
Repeatability L1
Reproducibility
Repeatability L3
Ex of interlab. approach
o An example of ISO 5725 application : uncertainties of an in situ method for measuring ground acoustic impedance
A 2 mic. Method [Hess,1990] [Sabatier,1990] [Sabatier,1993][Guillaume,2015]
Methods : ISO 5725
Celya Summer School – Uncertainties and variability 14/06/201829
2
2
110log10
p
pL
HPMicrophone 1
Microphone 2
Rd1
Rd2
Rr1 Rr2Z
- Measurement of the spectrum transfer function between 2 points
- Estimation of the Z parameters by fitting calc/measured of ΔL
The round robin test : protocol
Methods : ISO 5725
Celya Summer School – Uncertainties and variability 14/06/201830
-5 laboratories, whith the same kind of exp. device-3 repetitions / point
-5 outdoor grounds-3 points / ground
S *
R *
dSR
S *
R *
dSR
S *
R *
dSR
Ground i
Point 1
5m mini 5m mini
Point 2 Point 3x 3 x 3 x 3
Lab j
[Ecotière, Glé et al 2015]
The round robin test : ground samples
Methods : ISO 5725
Celya Summer School – Uncertainties and variability 14/06/201831
Synthetic lawn
Natural lawn
Natural grass
Compacted ground
Non porous asphalt
Reprod. and repeat. vs ground type
Methods : ISO 5725
Celya Summer School – Uncertainties and variability 14/06/201832
Asphalt
Compacted
Lawn
Grass
Synth_lawn
10 50 100 500 5000 50000
Air flow resistivity
kNsm-4
Air flow resistivity (kNsm-4) Mean sR (reprod.) Sr (repeat.) sL (interlab.)
Non porous Asphalt 19 609 15 070 13 065 7 510
Compacted ground 3 519 567 512 245
Natural lawn 1 154 248 217 119
Grass 277 34 34 6
Synthetic lawn 51 7 5 5
Uncertainties on sound levels estimation
Methods : ISO 5725
Celya Summer School – Uncertainties and variability 14/06/201833
hs=0.05 m hs=1 m hs=3 m hs=10 m
σ =3 519 1,7 dB 2,1 dB 1,2 dB 1 dB
σ = 1 154 2,1 dB 2,3 dB 1,6 dB 1 dB
σ = 277 2,6 dB 2,9 dB 2,2 dB 1 dB
Maximum type-uncertainty of SPL 1/3rd octave band (under reproducibility conditions)
example for hr=2m, d=1:200m and f=100:5000 Hz
Standard uncertainty (1/3rd oct bands) <3 dB
Uncertainties on sound levels estimation
Methods : ISO 5725
Celya Summer School – Uncertainties and variability 14/06/201834
Maximum type-uncertainty of SPL 1/3rd octave band (under repeatability conditions)
example for hr=2m, d=1:200m and f=100:5000 Hz
hs=0.05 m hs=1 m hs=3 m hs=10 m
σ =3 519 0,7 1 0,6 0,6
σ = 1 154 1 1,2 0,8 0,6
σ = 277 1,2 1,3 1,3 0,6
Standard uncertainty (1/3rd oct bands) <1,3 dB
Journée SFA/GABE – Lyon – 13/10/2014
Incertitude élargie (k=2)
Incertitude composée
Linéarité de niveau
Tension d''alimentation
Pression statique
Température
Humidité
Calibreur
Ecran anti-vent
Filtre A
Directivité (30°) Classe 1
Classe 2
Incertitudes - NF CEI 61672-1
dB
0.0 0.5 1.0 1.5 2.0 2.5 3.0
Sound level meter : minimum ± 2dB (class I)± 3dB (class II)
Celya Summer School – Uncertainties and variability 14/06/201835
About sound level measurement uncertainties
Ex of vertical sound speed gradient measurement
• Influence of method : sonic vs mast
• Influence of the devices : sonic vs sonic
• Influence of the height meas.
Celya Summer School – Uncertainties and variability 14/06/201836
Uncertainties due to meas. processes
Ex of vertical sound speed gradient measurement
• Influence of devices
Celya Summer School – Uncertainties and variability 14/06/201837
Uncertainties due to meas. processes
Uncertainties on sound level estimation due to uncertainties on vertical sound speed gradient measurement
Celya Summer School – Uncertainties and variability 14/06/201838
Uncertainties due to meas. processes
How my measurement result is representative ?
‘Natural’ variability
• Source emission variability
• Meteorological variability
• Ground properties variability
• ...
• Spatial and temporal variability
Sampling uncertainty
Celya Summer School – Uncertainties and variability 14/06/201839
Variability
Variability due to meteo
Celya Summer School – Uncertainties and variability 14/06/201840
LAeq(15min)
30
35
40
45
50
55
60
65
70
13/06/2005
00:00
14/06/2005
00:00
15/06/2005
00:00
16/06/2005
00:00
17/06/2005
00:00
18/06/2005
00:00
19/06/2005
00:00
20/06/2005
00:00
21/06/2005
00:00
22/06/2005
00:00
23/06/2005
00:00
dB
(A)
d=50m
d=100m
d=200m15dB(A)
50m 100m 200m0m
2m
Lannemezan 2005 (Junker et al, 2006)
)( cfLAeq z
Step 1
Acoustic model (PE)
[Gauvreau, JASA, 2002]
[Lihoreau et al., JASA, 2006]
Site data(geometry, ground …)
+ celerity gradients
LAeq(1h) over x years
Statistical analysis
Step 2
Micrometeo model(Choisnel model based on Monin-Obukhov theory)[Brunet et al., LRSP, 1996]
Meteo data measured hourly over x years
Hourly celerity gradient over x
yearswzzz VTTgc )(
Celya Summer School – Uncertainties and variability 14/06/201841
Noise variability due to meteo
o Estimation of variability due to meteo : LTS method[Zouboff, 2000][Ecotière 2008]
2
4
6
8
10
12
14
16
%
0 5 10 15 20
45
50
55
60
65
70
Mean
Mean +/- 1 st. dev.
Point source (300m,300°) - LAeq(1h) - July
Hours of the day (h)
LA
eq(1
h)
(dB
(A),
arb
. re
f.)
Point source (300m,300°)
LAeq(1h) - July.
>20 dB(A)
>8 dB(A)
Daily fluctuations of LAeq(1h) – seasonal influence
2
4
6
8
10
12
14
16
%
0 5 10 15 20
45
50
55
60
65
70
Mean
Mean +/- 1 st. dev.
Point source (300m,300°) - LAeq(1h) - Jan.
Hours of the day (h)
LA
eq(1
h)
(dB
(A),
arb
. re
f.)
>13 dB(A)>6 dB(A)
Point source (300m,300°)
LAeq(1h) - Jan.
Celya Summer School – Uncertainties and variability 14/06/201842
Noise variability due to meteo
[Ecotière 2008]
Noise variability due to meteo
5
10
15
20
%
Jan. Apr July Oct Dec
50
55
60
65
Mean
Mean +/- 1 st. dev.
Point source (300m,300°) - LAeq(6h22h)
Month
LA
eq(6
h22h)
(dB
(A),
arb
. re
f.)
>10 dB(A)>4 dB(A)
Point source (300m,300°) - LAeq(6h22h)
5
10
15
20
%
Jan. Apr July Oct Dec
50
55
60
65
Mean
Mean +/- 1 st. dev.
Point source (300m,300°) - LAeq(22h6h)
Month
LA
eq(2
2h6h)
(dB
(A),
arb
. re
f.)
>10 dB(A)>1 dB(A)
Point source (300m,300°) - LAeq(22h6h)
[Ecotière 2008]
Celya Summer School – Uncertainties and variability 14/06/201843
Seasonal fluctuations of LAeq(day/night)
North
Receiver
2m
0m
0.05m
Di
Si
Application for a road source
Site : Avrillé (49) - meteo data : 1960 to 1990 (>250 000 samples LAeq(1h))
Flat ground, Model of impedance Miky ( =300 kNms-4 )
Road source - Road noise spectrum
Celya Summer School – Uncertainties and variability 14/06/201844
Noise variability due to meteo
Noise variability due to meteo
Error of estimation of the LAeq(day/night) – Road source (150m, 0°)
0 50 100 150 200 250 300 350
02
46
81
0
Error of estimation of LAeq(6h22h) - Road(150m,0°)
Duration of observation (day)
Err
or
(dB
(A))
12
34
56
78
9
Mean
Range
Error of estimation of LAeq(6h22h)
0 50 100 150 200 250 300 350
05
10
15
Error of estimation of LAeq(22h6h) - Road(150m,0°)
Duration of observation (day)
Err
or
(dB
(A))
13
57
91
11
41
7
Mean
Range
Error of estimation of LAeq(22h6h)
Celya Summer School – Uncertainties and variability 14/06/201845
Noise variability due to meteo
Error of estimation of the LAeq(day/night) – Road source (150m, 0°)
Celya Summer School – Uncertainties and variability 14/06/201846
- Summer : error>2 dB(A)
- Winter : error>1 dB(A)
0 5 10 15 20 25
02
46
81
0
Error on estimation of LAeq(6h22h) - Road(150m,0°)
Duration of estimation (day)
Err
or
(dB
(A))
12
34
56
78
91
0
Jan.
Apr
July
Oct.
Error of estimation of LAeq(6h22h)
Noise variability due to meteo
Error of estimation of the LAeq(day/night) – Road source (150m, 0°)
Celya Summer School – Uncertainties and variability 14/06/201847
6h22h =50% =90%
50j 1.5 dB(A) 2.7 dB(A)
100j 1.2 dB(A) 2.4 dB(A)
22h6h =50% =90%
50j 1.5 dB(A) 2.5 dB(A)
100j 1 dB(A) 1.8 dB(A)
Maximum error - confidence level
and duration of observation
0 50 100 150 200 250 300 350
02
46
81
01
2
Error of the estimation of LAeq
Duration of observation (day)
Err
or
(dB
(A))
50%
90%
LAeq(6h22h)
LAeq(22h6h)
Noise variability due to meteo
Confidence level - LAeq(day/night) – Road source (150m, 0°)
Celya Summer School – Uncertainties and variability 14/06/201848
Level confidence as a function of
the duration of observation (max
error = 1 dB(A))
0 50 100 150 200 250 300 350
20
40
60
80
10
0
Confidence levels for a max. error of 1dB(A)
Duration of observation (day)
Co
nfid
en
ce
le
ve
l (%
)
LAeq(6h22h)
LAeq(22h6h)
Minimum number of days to have an error < 1 dB(A) with a confidence level of 50% :
- LAeq(6h22h) : 150 days
- LAeq(22h6h) : 60 days
10/02/2017Séminaire scientifique 49
o Spatial and temporal ground variability
[Junker et al, 2006][Baume 2006]
Spatial variability
Temporal variability
Noise variability due to the ground
Celya Summer School – Uncertainties and variability 14/06/201850
Noise variability due to the ground
o Temporal ground variability
[Junker et al, 2006][Baume 2006]
Celya Summer School – Uncertainties and variability 14/06/201851
o Spatial ground variability
Noise variability due to the ground
50
100
150
200
250
300
350
05/0
6/0
5 0
0:0
0
09/0
6/0
5 0
0:0
0
13/0
6/0
5 0
0:0
0
17/0
6/0
5 0
0:0
0
21/0
6/0
5 0
0:0
0
25/0
6/0
5 0
0:0
0
29/0
6/0
5 0
0:0
0
03/0
7/0
5 0
0:0
0
07/0
7/0
5 0
0:0
0
11/0
7/0
5 0
0:0
0
15/0
7/0
5 0
0:0
0
19/0
7/0
5 0
0:0
0
23/0
7/0
5 0
0:0
0
27/0
7/0
5 0
0:0
0
31/0
7/0
5 0
0:0
0
04/0
8/0
5 0
0:0
0
08/0
8/0
5 0
0:0
0
12/0
8/0
5 0
0:0
0
16/0
8/0
5 0
0:0
0
20/0
8/0
5 0
0:0
0
24/0
8/0
5 0
0:0
0
28/0
8/0
5 0
0:0
0
01/0
9/0
5 0
0:0
0Date/heure
Sig
ma
(k
Ns
m-4
)
I3-10 Suivi temporel (EDF)
I3-10 Suivi spatial (LCPC)
I1-25 Suivi spatial (LCPC)
I1-75 Suivi spatial (LCPC)
I1-125 Suivi spatial (LCPC)
I1-175 Suivi spatial (LCPC)
I2-25 Suivi spatial (LCPC)
I2-75 Suivi spatial (LCPC)
I2-125 Suivi spatial (LCPC)
I2-175 Suivi spatial (LCPC)
I2-225 Suivi spatial (LCPC)
I3-25 Suivi spatial (LCPC)
I3-75 Suivi spatial (LCPC)
I3-125 Suivi spatial (LCPC)
[Junker et al, 2006][Baume 2006]
Celya Summer School – Uncertainties and variability 14/06/201852
Noise variability due to ground
o Spatial ground variability
[Junker et al, 2006][Baume 2006]
o Uncertainties: what do I do with them?
Comparison to a threshold
Celya Summer School – Uncertainties and variability 14/06/201853
Threshold
dB
Estimation
Estimation
dB
dB
dB
Conclusion
and/or
Lower uncertainty
Lower confidence level
IC 95%, 75% …
X+kucX-kuc X
The real world is uncertain, uncertainties will always exist and you can’tdo without it
Uncertainties of several dB are common in environmental acoustics
Confidence level : uncertainties are a tool for risk management
Celya Summer School – Uncertainties and variability 14/06/201854
Conclusions
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55Celya Summer School – Uncertainties and variability 14/06/2018
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