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On Localised Particle Filters for the Global Weather Prediction Model
ICONRoland Potthast and Anne Walter
and Andreas Rhodin
German Meteorological Service (DWD)
Data Assimilation Unit
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 2
Content
1. The ICON-Model and DA-System
2. Bayesian Filtering via Particle Filters
3. The Localised Adaptive Particle Filter (LAPF)
4. The Localised Markov Chain Particle Filter (LMCPF)
5. Numerical Testing
6. Summary
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[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 3
1. The ICON-Model
• Operational NWP model of DWD: ICON (ICOsahedral Nonhydrostatic)
• Two-way NEST over Europe (~6.5 km)
• Resolution: 13 km deterministic 40 km ensemble (40 member)
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[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 4
1. DA System at DWD
• Hybrid EnVar operational since January 20, 2016
• Following Hunt et al. (2007), (see also Schraff et al., 2016)
• EnVar-B-Matrix: 70% LETKF, 30% Climatology
•
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B-Matrix
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Global Model Verification Comparison
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Created: 28.02.2018
EnVarICON
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 6
• Our Particle Filters are based on the LETKF philosophy
Localisation: as LETKF in ensemble space
Adaptivity: tools for spread control
2. Bayesian Filtering via PF
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PRIOR
DATA
Posterior
AnalysisEnsemble
Able to handle with multi-modal distributions
Able to handle with Non-Gaussianity
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2. Bayesian Filtering via PF
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LETKF
Classical PF
DATA
PriorPosterior
DATA
Prior
Posterior
LAPF
DATA
Prior
Posterior
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 8
2. Bayesian Filtering via PF
• Employ Bayes formula to calculate new analysis distribution
is a normalization factor:
• To carry out the analysis step at time a posteriori weights are calculated
is chosen such that
•
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First Step: The Classical Particle Filter
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 9
2. Bayesian Filtering via PF
• Accumulated weights are defined:
where denotes the ensemble size
• Drawing , set and define transform matrix W for the particles by:
with , denotes the interval of values .
•
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Second Step: Classical Resampling
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 10
2. Bayesian Filtering via PF
• Based on the adaptive multiplicative inflation factor determined by the LETKF
• Weighting factor has been chosen, due to the small ensemble size ()
•
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Third Step: Spread Control
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 11
2. Bayesian Filtering via PF
• Pertubation factor is used to add spread to the system
where , , and , with if and if
•
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Third Step: Spread Control
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 12
• Weights W are modified by applying the pertubation factor
with normally distributed random numbers
•
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3. The LAPF
Fourth Step: Gaussian Resampling
An example for a W-Matrix after applying determined with the LAPF for 60°N/90°O ~500 hPa, 26.05.2016 0 UTC is shown. 10 particles are chosen
DATA
Prior
Posterior
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 13
4. The LMCPF
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LMCPFLAPFDATA
Prior
Posterior
LETKF
DATA
PriorPosterior
DATA
Prior
Posterior
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• Weights W are calculated by drawing from the posterior•
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Fourth Step: Gaussian Resampling
4. The LMCPF
with normally distributed random numbers, and calculated with Gaussian radial basis function (rbf) Approximation for prior density and observation error
DATA
Prior
Posterior
It is an explicit calculation of the Bayes posterior based on radial basis function approximation of the prior.
Centers of posterior RBFs Shape of posterior RBFs
5. Numerical Testing
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Experimental set-up
• Full ensemble: 40 members
• Reduced resolution: - 26km deterministic- 52km ensembles
• Period: 01.05.2016 – 31.05.2016
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5. Numerical Testing
T [K] at 03.05.2016 15 UTC ~1000 hPa
5. Numerical TestingAssimilation Cycle
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 1806.03.2018
5. Numerical Testing - LAPF
RMSE
LETKFLAPF
RMSE
p-le
vel [
hPa]
Global RMSE for obs-fg statistics (Radiosondes vs. Model)Period: 08.05.2016 – 31.05.2016
Relative humidityTemperature
~14%~15%
~14%
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 1906.03.2018
5. Numerical Testing - LMCPF
RMSE
LETKFLMCPF
RMSE
p-le
vel [
hPa]
Global RMSE for obs-fg statistics (Radiosondes vs. Model)Period: 08.05.2016 – 22.05.2016
Relative humidityTemperature
~11%~12%
~11%
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 2006.03.2018
5. Numerical Testing
RMSE
LAPFLMCPF
RMSE
p-le
vel [
hPa]
Global RMSE for obs-fg statistics (Radiosondes vs. Model)Period: 08.05.2016 – 22.05.2016
Relative humidityTemperature
~7%
~7%
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 2106.03.2018
5. Numerical Testing
RMSE
LAPFLMCPF
RMSE
Cha
nnel
num
ber
Global RMSE for obs-fg statistics Period: 08.05.2016 – 22.05.2016
Bending Angles (GPSRO) (IASI)
~7%
~10%H
eigh
t [m
]
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 22
5. Numerical Testing
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mean
min
max
LETKFLAPFLMCPF
Global spread of T [K] ~ 500 hPa
01.05.2017
06.05.2017
12.05.2017
18.05.2017
25.05.2017
01.05.201706.05.2017
12.05.2017
31.05.2017
25.05.2017
31.05.2017
01.05.2017
06.05.2017
12.05.201718.05.2017
25.05.2017
31.05.2017
18.05.2017
5. Numerical TestingForecast Cycle
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 2406.03.2018
5. Numerical Testing - LAPF
Global verification of different lead times against RadiosondesPeriod: 02.05.2016 – 24.05.2016
LETKF LAPF
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 25
6. Summary
• LAPF and LMCPF implemented in an operational NWP system
• Both Particle Filters are able to provide reasonable atmospheric analysis in a large-scale environment and are running stably over a period of one month
• The LMCPF outperforms the LAPF but not yet the LETKF, but both Particle Filters nearly reach the results of the operational LETKF
Both Particle Filters are showing promising results; further tuning is in progress.
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[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 26
References• Gerald Desroziers and Serguei Ivanov. “Diagnosis and adaptive tuning of
observation-error parameters in a variational assimilation”. Quarterly Journal of the Royal Meteorological Society, 2001
• Brian Hunt, Eric Kostelich and Istvan Szunyogh. “Efficient data assimilation for spatiotemporal chaos: A local ensemble transform Kalman filter”. Physica D: Nonlinear Phenomena, 2007
• Gen Nakamura and Roland Potthast. “Inverse Modeling”. IOP Publishing, 2015
• Roland Potthast, Anne Walter and Andreas Rhodin. “A Localised Adaptive Particle Filter (LAPF) within an operational NWP Framework”. submitted to MWR
• Sebastian Reich and Colin Cotter. “Probabilistic Forecasting and Bayesian Data Assimilation”. Cambridge University Press, 2015
• Christoph Schraff, Hjendrick Reich, Andreas Rhodin, Annika Schomburh, Klaus Stehphan, Africa Periáñez and Roland Potthast. “Kilometre-scale ensemble data assimilation for the cosmo model (kenda)”. Quarterly Journal of the Royal Meteorological Society, 2016
• Peter Jan van Leeuwen, Yuan Cheng and Sebastian Reich. “Nonlinear Data Assimilation”. Frontiers in Applied Dynamical Systems: Reviews and Tutorials. Springer, 2015
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Thanks for the attention!
Appendix
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Appendix
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Global histogram of number of particles with weight31.05.2016 21 UTC ~1000 hPa
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 30
Appendix
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31.05.2016 21 UTC ~ 100 hPa
31.05.2016 21 UTC ~ 500 hPa
31.05.2016 21 UTC ~1000 hPa
Global histograms of number of particles with weight
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 31
Appendix
06.03.2018
Global verification of different lead times
against Radiosondes
Period: 02.05.2016 – 24.05.2016
LETKF LAPF
[email protected] Localised Particle Filters for the Global Weather Prediction Model ICON 32
Appendix
06.03.2018
Global verification of different lead times
against Radiosondes
Period: 02.05.2016 – 24.05.2016
LETKF LAPF
