Ensemble Kalman Filter in a boundary layer 1D numerical model

1
Ensemble 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

2
Outline

• 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

3
Description 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
4
Site-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

5
Initialization

• 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

6
Current 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

7
B 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
8
Diagnosis 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)
9
Background 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
10
Ensemble 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.
11
Simulated 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.

12
Simulated 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
13
Covariance 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
14
Adaptative 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
15
Adaptative 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
16
Results 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
17
Results 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
18
Results 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
19
Fog 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

20
Fog 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
21
Multivariate 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

22
Hybrid 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

23
Hybrid 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
24
Hybrid 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
25
Hybrid 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
26
Conclusion 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

27
Results 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
28
Results 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
29
Fog 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
30
Fog 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
31
Conclusion 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

32
EnKF 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
33
Future 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
34
Future 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