Post-traitement statistique des prévisions d'ensemble à Météo-France - Meteo France
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Post-traitement statistique des prévisions d’ensemble à Météo-France
Maxime Taillardat
maxime.taillardat@meteo.fr
12 mars 2019
Motivation of post-processing ensemble forecasts
Run: 2012−10−26 Lead time: 12 h
Rank of the observed temperature: 18
Météo-France’s forecast
35-members global observed
ensemble system −10 0 10 20 30
(PEARP), 10 km Temperature (°C)
resolution over France.
Observations and
forecasts of 2-m
temperature (T2m) at
Lyon-Bron for the run
of 1800UTC (different
lead times)
Maxime Taillardat 1/16
Motivation of post-processing ensemble forecasts
Météo-France’s
35-members global
ensemble system
(PEARP), 10 km
resolution over France.
Observations and
forecasts of 2-m
temperature (T2m) at
Lyon-Bron for the run
of 1800UTC (different ◮ Need of a simultaneous correction of bias and
lead times) dispersion
◮ Whatever the quality of the raw ensemble,
post-processing improves forecast attributes
(Hemri, 2014)
Maxime Taillardat 1/16
The state of the art
◮ Existing methods: Analogs, Perfect Prog., Rank-based matching,
CDF-matching, Member dressing, Bayesian Model Averaging, SAMOS...
◮ A review of techniques: Gneiting, 2014
The most (famous // widely-used // efficient) post-processing method :
◮ Ensemble model output statistics (EMOS) (Gneiting, 2005) also
called Non-homogeneous Regression (NR)
◮ fitting parameters linearly on predictors on some training period:
X
N
f (y |x1 , . . . , xN ) = N (µ = a0 + ai xi , σ2 = b + cs2 )
i=1
y response variable, x1 , . . . , xN ensemble member values or any other
predictor, s2 ensemble variance
Maxime Taillardat 2/16
Benefits of non-parametric post-processing
No assumptions on the weather variable you deal with
◮ Raw ensemble (not EMOS
post-processed) :
Non-parametric
Maxime Taillardat 3/16
Benefits of non-parametric post-processing
No assumptions on the weather variable you deal with
◮ Raw ensemble (not EMOS
post-processed) :
◮ EMOS post-processing :
Non-parametric
Maxime Taillardat 3/16
Benefits of non-parametric post-processing
No assumptions on the weather variable you deal with
◮ Raw ensemble (not EMOS
post-processed) :
◮ EMOS post-processing :
Non-parametric
◮ Post-processing possible results :
Maxime Taillardat 3/16
Benefits of non-parametric post-processing
No assumptions on the weather variable you deal with
◮ Raw ensemble (not EMOS
post-processed) :
◮ EMOS post-processing :
Non-parametric
◮ Post-processing possible results :
Maxime Taillardat 3/16Best-of post-processing possible outputs
(initialization: 18 UTC)
Maxime Taillardat 4/16From binary regression trees to QRF
◮ Example: CART algorithm (Breiman, 1984)
Taillardat, Maxime, Olivier Mestre, Michaël Zamo, and Philippe Naveau.
"Calibrated ensemble forecasts using quantile regression forests and
ensemble model output statistics." Monthly Weather Review 144, no. 6
(2016): 2375-2393.
Maxime Taillardat 5/16How to verify/evaluate ensemble forecasts ?
◮ Differ from deterministic forecasts
◮ A "point" (eg. for one day) verification is a nonsense
◮ It has to be statistical
Several attributes sought
◮ Reliability
◮ Accordance between forecasted probabilities and observed frequencies of
an event and/or exchangeability between observations and ensemble
members
◮ Resolution/Discrimination
◮ Ability to differ from a climatological forecast
◮ Sharpness
◮ Getting the least dispersed forecast
"the paradigm of maximizing the sharpness of the predictive distributions
subject to calibration"(Gneiting et al. 2006)
Maxime Taillardat 6/16How to verify/evaluate ensemble forecasts ?
◮ Differ from deterministic forecasts
◮ A "point" (eg. for one day) verification is a nonsense
◮ It has to be statistical
Several attributes sought
◮ Reliability
◮ Accordance between forecasted probabilities and observed frequencies of
an event and/or exchangeability between observations and ensemble
members
◮ Resolution/Discrimination
◮ Ability to differ from a climatological forecast
◮ Sharpness
◮ Getting the least dispersed forecast
"maximizing the value of the predictive distributions subject to good overall
performance"
Maxime Taillardat 6/16"Here comes the rain again..."
Production constraints
◮ Relatively shallow datasets ( 1 up to 3 years)
◮ Costly reforecasts
Possible alternatives
◮ Data-shifting: Work with anomalies (obs −→ obs − ensemble mean)
◮ Data-pooling: Regionalization/Neighborhood
◮ Data-boosting: Work with several observations/distribution
Maxime Taillardat 7/16"Here comes the rain again..."
Example: post-processing RR6 (6-h rainfall)
◮ This variable is (by far !) the most difficult to calibrate whatever the
method, a really hard nut to crack for statisticians
◮ A lot of zeros, a lot of "extremes"
What we have tested
For EMOS:
◮ Try different distributions "tailored" for extremes (Gamma, GEV...)
◮ Try different sets of predictors
For QRF:
◮ Improve QRF for "quantiles": Gradient Forests (GF) (Athey et al., 2017)
◮ Extrapolation in distributions tails: semi-parametric approach
Maxime Taillardat 8/16A semi-parametric approach
Goal: Be skillful for extremes without degrading overall performance
Use QRF/GF outputs to fit a distribution which would:
◮ Model jointly low, moderate and heavy rainfall
◮ Be flexible
◮ Use of an Extended GP distribution (EGP3) (Papastathopoulos and
Tawn, 2013 ; Naveau et al., 2016 ; Tencaliec’s PhD 2018)
Maxime Taillardat 9/16A semi-parametric approach
Goal: Be skillful for extremes without degrading overall performance
What we expect:
◮ QRF/GF possible output
Maxime Taillardat 9/16A semi-parametric approach
Goal: Be skillful for extremes without degrading overall performance
What we expect:
◮ QRF/GF possible output ◮ After "EGP TAIL"
Maxime Taillardat 9/16Results on RR6
Raw ensemble Analogs Analogs_C Analogs_COR
0.20
0.20
0.20
0.20
JPZ test : 0 % JPZ test : 85 % JPZ test : 100 % JPZ test : 99 %
0.15
0.15
0.15
0.15
0.10
0.10
0.10
0.10
0.05
0.05
0.05
0.05
0.00
0.00
0.00
0.00
1 3 5 7 9 11
Analogs_VSF EMOS CSG EMOS EGP EMOS GEV
0.20
0.20
0.20
0.20
JPZ test : 98 % JPZ test : 89 % JPZ test : 11 % JPZ test : 98 %
0.15
0.15
0.15
0.15
0.10
0.10
0.10
0.10
0.05
0.05
0.05
0.05
0.00
0.00
0.00
0.00
QRF QRF EGP TAIL GF GF EGP TAIL
0.20
0.20
0.20
0.20
JPZ test : 100 % JPZ test : 91 % JPZ test : 98 % JPZ test : 63 %
0.15
0.15
0.15
0.15
0.10
0.10
0.10
0.10
0.05
0.05
0.05
0.05
0.00
0.00
0.00
0.00
Maxime Taillardat 10/16ROC curves
◮ Value: Focus on the upper left corner
◮ Taillardat, Maxime, Anne-Laure Fougères, Philippe Naveau, and Olivier
Mestre. "Forest-based and semi-parametric methods for the
postprocessing of rainfall ensemble forecasting" Accepted in Weather
and Forecasting (2019). HAL preprint . ArXiv preprint
1711.10937
Maxime Taillardat 11/16ROC curves
◮ Value: Focus on the upper left corner
◮ Taillardat, Maxime, Anne-Laure Fougères, Philippe Naveau, and Olivier
Mestre. "Forest-based and semi-parametric methods for the
postprocessing of rainfall ensemble forecasting" Accepted in Weather
and Forecasting (2019). HAL preprint . ArXiv preprint
1711.10937
Maxime Taillardat 11/16ROC curves
◮ Value: Focus on the upper left corner
◮ Taillardat, Maxime, Anne-Laure Fougères, Philippe Naveau, and Olivier
Mestre. "Forest-based and semi-parametric methods for the
postprocessing of rainfall ensemble forecasting" Accepted in Weather
and Forecasting (2019). HAL preprint . ArXiv preprint
1711.10937
Maxime Taillardat 11/16ROC curves
◮ Value: Focus on the upper left corner
◮ Taillardat, Maxime, Anne-Laure Fougères, Philippe Naveau, and Olivier
Mestre. "Forest-based and semi-parametric methods for the
postprocessing of rainfall ensemble forecasting" Accepted in Weather
and Forecasting (2019). HAL preprint . ArXiv preprint
1711.10937
Maxime Taillardat 11/16Post-processing strategy for hourly rainfall
◮ Work on 3 watersheds in Brittany (global size : 720 km2 )
◮ Météo-France’s LAM-EPS PEAROME (12 members, grid scale : 2.5
km), base time : 21UTC, lead times from 1 to 45 hours
◮ Use of hourly calibrated (over rain gauges) radar precipitation
observations ANTILOPE (grid scale : 1 km)
◮ Data spans from 12/2015 to 03/2016 and from 05/2016 to 06/2016
◮ Predictors : statistics on the hourly rainfall ensemble, and on surface
humidity and temperature
Ensemble Copula Coupling (ECC) (Schefzik et al., 2013)
◮ Restores physical consistency between grid points and time steps
For each time step, each watershed :
ECC
Result of calibration : 1 distribution for the watershed −−→ 12 members for
each grid point
Maxime Taillardat 12/16ECC + post-processing visualization Maxime Taillardat 13/16
Future architecture
◮ Data pooling + Data boosting
Raw PEAROME 12 mem 2.5 km
Raw PEAROME* 300 mem 10 km
(vs. 81 ANTILOPE obs)
Post-P of PEAROME* on H.C.A 10km
300 PEAROME* quantiles 10 km
ANTILOPE grid 1.25km
PEAROME grid 2.5km
PEARP grid 10km
HOMOGENEITY CALIBRATION AREA 10km Calib PEAROME 12 mem 2.5 km
Maxime Taillardat 14/16The after sales service...
Ensemble forecasting requires met. skill (as deterministic) +
◮ understanding of probabilities
◮ notions in game theory
◮ communication of uncertainty
Maxime Taillardat 15/16The after sales service...
Ensemble forecasting requires met. skill (as deterministic) +
◮ understanding of probabilities
◮ notions in game theory
◮ communication of uncertainty
One must provide statistical//vizualisation tools
Roebber diagram RR24 > 150mm
10 5 3 2 1.5 1.3
1.0
1
0.9
0.8
0.8
0.8
0.7
Probability of Detection
0.6
0.6
0.5 0.5
0.4
0.4
0.3 0.3
0.2
0.2
0.1
0.0
0.0 0.2 0.4 0.6 0.8 1.0
Success Ratio
Maxime Taillardat 15/16Other references
Gneiting, T., A. E. Raftery, A. H. Westveld III, and T. Goldman, 2005:
Calibrated probabilistic forecasting using ensemble model output statistics
and minimum crps estimation. Monthly Weather Review, 133 (5),
1098–1118.
Schefzik, R., T. L. Thorarinsdottir, T. Gneiting, and Coauthors, 2013:
Uncertainty quantification in complex simulation models using ensemble
copula coupling. Statistical Science, 28 (4), 616–640.
Whan, K., and M. Schmeits, 2018: Comparing area-probability forecasts of
(extreme) local precipitation using parametric and machine learning
statistical post-processing methods. Monthly Weather Review, (2018).
Maxime Taillardat 16/16You can also read
