Title: Ensemble Kalman Filter in a boundary layer 1D numerical model
1Ensemble Kalman Filter in a boundary layer 1D
numerical model
- Samuel Rémy and Thierry Bergot (Météo-France)
- Workshop on ensemble methods in meteorology and
oceanography, Paris, 15th-16th of May 2008
2Outline
- Description of the model
- Diagnosis of background error variance
- Results in a near-fog situation
- Ensemble Kalman Filter
- Hybrid assimilation scheme
- Results in a fog situation
- Conclusion and future work
3Description of COBEL-ISBA
- Main features of COBEL-ISBA (Météo-France,
LA-UPS) - Coupling of an atmospheric model (COBEL) and of a
surface-ground scheme (ISBA) - High vertical resolution (30 levels from 0.5m to
1360m, 20 under 200m) - 1DVar assimilation scheme with site-specific
observations - Detailed physical parameterizations for fog
modelling
References Bergot et al. (2005), Weather and
Forecasting
4Site-specific observation system
- COBEL-ISBA is in currently operational at the
Paris-CdG airport to help forecast fog events - Specific observation system consists of
- 30 meter tower temperature and humidity at
1,5,10 and 30m - Soil of temperature and water content measurement
- Shortwave and longwave radiative fluxes at 2 and
45m - Weather station 2m temperature and humidity,
visibility and ceiling - To complete the observations, temperature and
humidity profiles from the NWP ALADIN are used
5Initialization
- Two parts
- Assimilation scheme produces profiles of T and Q
- In case of clouds, the cloud init component
estimates the thickness of the cloud layer then
adjusts the Q profile to saturation within the
cloud - Assimilation/simulation every hour
- 8-hours simulations
6Current assimilation scheme
- Uses the local observations to give profiles of T
and Q with - Monovariate assimilation scheme
- Two parts for R
- Error variance of the observations no
covariance - Error variance of the ALADIN profiles non-zero
covariance - 1DVAR fixed values for B
- T variance 2 K²
- Q variance 0.5 (g/kg)²
- Correlation length 200m
7B diagnosis methods
- We used two methods
- Direct computation with an ensemble
-
-
- cross product method
- Gives variance over a long period of time, in
the observation space
References Desroziers et al., QJRMS, 2005
8Diagnosis ensemble
- Ensemble composed of the 8 previous simulations
- Important diurnal cycle
Spread of Q
Spread of T
1000m
200m
COBEL Levels
COBEL Levels
25m
Time (UTC)
Time (UTC)
9Background error variance-covariance
- B matrix for T (mean over the 2004-2005 winter)
estimate by the ensemble - Important variation linked with the development
of a mixed boundary layer during the day
3h
15h
1000m
200m
COBEL levels
COBEL levels
25m
COBEL levels
COBEL levels
10Ensemble Kalman Filter
- on the flow estimate of B seems more adequate
- Ensembles 8, 16, 32 and 64 members have been
tried - We choose 32 members
- Ensembles obtained by observation perturbation
- Perturbations follow a normal law with zero mean
and observation error variance - Different variance for real observations and the
ALADIN profiles used as observations - 0.1 K and 0.1 g/kg for real observations
- 2K and 0.5 g/kg for ALADIN profiles
- Perturbation on the other inputs of the model
- Geostrophic wind
- Soil temperature and humidity
- Advections
References Roquelaure and Bergot (2007), J.
of Applied Met. And Clim.
11Simulated observations
- To avoid model error better understanding of
the impact of the assimilation scheme on the
initial profiles and forecast - To have access to a truth
- To have access to observations not avalaible in
reality (ie liquid water content, top of cloud
cover, T and Q above 30m, ) - Better evalutation of the model
- Possibility of adding components to the local
observation system (sodar, ) - To be able to create observations for the
situations we wish to study - Observations are produced by adding a
perturbation on a reference run.
12Simulated observations
- Two 15-days situation were produced
- A situation with mostly clear skies and shallow
fogs at the end of the period, to study fog
formation and false alarm situations (NEAR-FOG) - A situation with frequent and thick fogs, to
study the cloud init and the dissipation of fog
(FOG) - Simulations every hours gt 360 simulations for
each situation
NEAR-FOG
FOG
13Covariance filtering
- Time filter
- Spatial filter Schur product with a correlation
length of 200m - B matrix for T, NEAR-FOG situation, mean over 360
simulations
COBEL levels
COBEL levels
COBEL levels
COBEL levels
No filtering
Spatial filtering
Spatial time filtering
14Adaptative covariance inflation
- Increase the spread of the ensemble, as a
function of - Distance between the mean of the ensemble and the
observation - Observation error variance
- Ensemble spread
- Applied sequentially for each observations
- This method works only with observations with
zero covariance (ie not with ALADIN profiles) - Applied separately for T and Q
References Anderson, Tellus, 2007
15Adaptative covariance inflation
- Inflation factor for T and Q
- Larger during the day
- Ensemble spread is generally smaller then
- Larger for T than for Q
- Smaller difference between the perturbation added
to produce the ensemble and the observation error
variance
Day 1
Day 2
Day 3
Day 4
Day 4
Day 3
Day 2
Day 1
References Anderson, Tellus, 2007
16Results for NEAR-FOG
Q
T
- Estimates of B for T and Q, mean over the 360
simulations - Smaller variances at 15h
- Covariances relatively greater (vs variances) at
15h
3h
COBEL levels
COBEL levels
COBEL levels
COBEL levels
15h
17Results for NEAR-FOG
- Initial profiles have less impact during the day,
when the atmosphere is neutral/slightly unstable - The mean of the perturbations have more impact
than the perturbations themselves (hence the
value of B diagnosed with the ensemble of 8
previous simulations)
Day 1, 14h
Day 2, 3h
Init
Truth
T1
Obs
18Results for NEAR-FOG
- Results on temperature and specific humidity
RMSE and bias, as compared with 1DVAR - Mean over the 360 simulations
- Better for T than for Q, especially for the bias
- Analyzed Q is worse than 1DVAR at 6am because a
single case cloud top was estimated much higher
than 1DVAR (and truth).
T
Q
19Fog forecasting for NEAR-FOG
- NEAR-FOG 42 half-hours of observed LVP
- Scores on LVP forecast against observation (ie
Hit Rate, False Alarm Rate) not very significant
not enough cases - Statistics on the onset and liftoff of fog events
- Airports want to know the beginning and end of
fog/low cloud events - At Paris-CdG, Low Visibility Procedures (LVP) if
- Visibility lt 600m
- And/or
- Ceiling lt 60m
20Fog forecasting for NEAR-FOG
- Frequency histograms for onset and lift-off of
fog events - Mean and Stdev computed without false alarms
- Much more standard deviation on onset than on
burnoff - False alarms less frequent with EnKF
- Onset less biased with EnKF
Mean 3 Stdev 18
Mean 34 Stdev 41
1DVAR
Mean -17 Stdev 44
Mean 6 Stdev 25
EnKF
21Multivariate EnKF
- Correlation matrix between T and Q, estimate from
the 8 previous simulations ensemble, mean over
the 2004-2005 winter - Not to be neglected, especially during the night
- Work in progress
22Hybrid scheme for NEAR-FOG
- Hybrid scheme the B matrixes used in the
ensemble are fixed - The B matrix used in the reference run is
computed with the ensemble, as for EnKF - Same ensemble as for EnKF (32 members)
- Same vertical and time filtering of covariances
- Same adaptative inflation algorithm
- Values of the inflation factor for T and Q are a
bit smaller
23Hybrid scheme for NEAR-FOG
Q
T
- Estimates of B for T and Q, mean over the 360
simulations - Important decrease at 3h as compared with EnKF
- Smaller decrease at 15h
3h
COBEL levels
COBEL levels
COBEL levels
COBEL levels
15h
24Hybrid scheme for NEAR-FOG
- Results on temperature and specific humidity
RMSE and bias, as compared with 1DVAR - Mean over the 360 simulations
- A little bit better than EnKF for temperature
- RMSE as a function of forecast time
- Bias
- Not much change for specific humidity
- Small improvement for RMSE as a function of
forecast time
T
Q
25Hybrid scheme for NEAR-FOG
- Frequency histograms for onset and burnoff of fog
events - More standard deviation on the onset for HYBRID
Mean 5 Stdev 23
Mean 18 Stdev 53
HYBRID
Mean -17 Stdev 44
Mean 6 Stdev 25
EnKF
26Conclusion for NEAR-FOG
- Diurnal for B with EnKF and HYBRID more
realistic - EnKF and HYBRID better than 1DVAR after 3-4 hours
of forecast time - Hybrid is a slightly better than EnKF for RMSE
and bias - EnKF improves the biais for the onset of fog
- For the burnoff, the NEAR-FOG case is not
adequate shallow fogs dissipate very quickly
after sunrise - The burnoff will be studied with the FOG case
27Results for FOG
Q
T
- Estimates of B for T and Q, mean over the 360
simulations - As compared with NEAR-FOG
- Smaller covariances at 3h
- Larger T covariance at 15h
3h
COBEL levels
COBEL levels
COBEL levels
COBEL levels
15h
28Results for FOG
- Results on temperature and specific humidity
RMSE and bias, as compared with 1DVAR - Mean over the 360 simulations
- Degradation for EnKF as compared with 1DVAR
- HYBRID (not shown) reduced degradation
T
Q
29Fog forecasting for FOG
Mean 16 Stdev 70
Mean 6 Stdev 86
- Frequency histograms for onset and burnoff of fog
events - Onset same as NEAR-FOG, EnKF and HYBRID
forecast onset time later - Burnoff negative bias is reduced with EnKF and
HYBRID
1DVAR
Mean 4 Stdev 89
Mean -4 Stdev 63
EnKF
Mean 8 Stdev 91
Mean -1 Stdev 67
HYBRID
30Fog forecasting for FOG
- Hit Rate and pseudo False Alarm Ratio for LVP
events (half-hour forecasted vs observed) over
the 360 simulations - Function of forecast time
- HR differences mainly during the first 4 hours
of simulation - pFAR differences mainly during the last 3 hours
of simulation
1DVAR
Mean HR 0.83 Mean pFAR 0.12
Hit rate
Pseudo FAR
Forecast time
Forecast time
Mean HR 0.83 Mean pFAR 0.14
Mean HR 0.83 Mean pFAR 0.14
EnKF
HYBRID
31Conclusion for FOG
- Degradation of analyzed and forecasted RMSE and
bias, probably due to cloud init - Small improvement for the forecast of the burnoff
time of fog events - Not much change for HR and pFAR
- Need to improve EnKF and HYBRID in the presence
of liquid water
32EnKF with real observations
- Hit Rate and pseudo False Alarm Ratio for LVP
events (half-hour forecasted vs observed) over
the winter 2004-2005 (2200 simulations - EnKF is an interesting alternative to 1DVAR
1DVAR
Hit rate
Pseudo FAR
Mean HR 0.62 Mean pFAR 0.5
Forecast time
Forecast time
Mean HR 0.6 Mean pFAR 0.46
Mean HR 0.6 Mean pFAR 0.48
EnKF
HYBRID
33Future work
- Multivariate (T,Q) EnKF
- Problem in the presence of liquid water (FOG
case) - Take in account the influence of liquid water on
T and Q - Estimate of covariance between T and Ql, mean
over winter 2004-2005
15h
3h
COBEL levels for T
COBEL levels for T
COBEL levels for Ql
COBEL levels for Ql
34Future work
- Run EnKF and HYBRID with a different local
observation system - 10m mast (instead of 30m)
- No mast
- No radiative fluxes observations
- No soil temperature and water content observation
- Addition of a sodar
- Continue work on real cases