ensemble kalman filter in a boundary layer 1d numerical model

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

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

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

1DVar1DVar

ALADIN ALADIN

COBELCOBEL

ISBAISBA

+

+ALADINALADIN

ICForcings

Guess COBELReferences : Bergot et al. (2005), Weather and Forecasting

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

Initialization

Final Analysis (T,Q,Ql)1DVar/EnKF/Hybrid Cloud initGuess (T,Q)

Input

ObservationsALADIN

Radiative fluxes observations

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

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

][( bo-1TTba Hx - yR) HBHBH xx ++=

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

])[(1

1

1

TN

iN

ffi

ffi x)(xxxB −−

−= ∑

=

)()(2 aoTbo HxyHx y −−=oσ)()(2 baTbo HxHxHx y −−=bσ

References : Desroziers et al., QJRMS, 2005

Diagnosis ensemble Ensemble composed of the 8 previous simulations

Important diurnal cycle

t-1ht-2ht-3ht-4h t(…)

CO

BE

L L

evel

s

CO

BE

L L

evel

s

Time (UTC)Time (UTC)

Spread of QSpread of T

200m

25m

1000m

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

CO

BE

L le

vels

15h

CO

BE

L le

vels

COBEL levels COBEL levels

25m

200m

1000m

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.

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.

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 => 360 simulations for each situation

NEAR-FOG FOG

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

∑∑

−

−

=

i

i

i

iλ

λ

/?)(

/?)(

exp

expi-t

t

BB

CO

BE

L le

vels

COBEL levels COBEL levelsCOBEL levels

No filtering Spatial filtering Spatial & time filtering

Adaptative covariance inflation

References : Anderson, Tellus, 2007

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

Adaptative covariance inflation

References : Anderson, Tellus, 2007

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 4Day 3Day 2Day 1

Results for NEAR-FOG

Estimates of B for T and Q, mean over the 360 simulations

Smaller variances at 15h

Covariances relatively greater (vs variances) at 15h

3h

15h

T Q


CO

BE

L le

vels

CO

BE

L le

vels


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)

Init

Truth

T+1

Obs

Day 1, 14h Day 2, 3h


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

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 < 600m

And/or

– Ceiling < 60m

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

1DVAR

EnKF

Mean –34

Stdev 41

Mean 3

Stdev 18

Mean -17

Stdev 44

Mean 6

Stdev 25

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

3h

CO

BE

L le

vels

for

T

15h

CO

BE

L le

vels

for

T

COBEL levels for Q COBEL levels for Q

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



Important decrease at 3h as compared with EnKF

Smaller decrease at 15h

3h

15h

T Q


CO

BE

L le

vels

CO

BE

L le

vels



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


Frequency histograms for onset and burnoff of fog events

More standard deviation on the onset for HYBRID

HYBRID

EnKF

Mean –18

Stdev 53

Mean 5

Stdev 23

Mean -17

Stdev 44

Mean 6

Stdev 25

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

Results for FOG


As compared with NEAR-FOG– Smaller

covariances at 3h

– Larger T covariance at 15h

3h

15h

T Q


CO

BE

L le

vels

CO

BE

L le

vels

Results for FOG


Mean over the 360 simulations Degradation for EnKF as

compared with 1DVAR HYBRID (not shown) : reduced

degradation

T

Q

Fog forecasting for FOG

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

HYBRID

EnKF

1DVAR

Mean –6

Stdev 86

Mean –16

Stdev 70

Mean 4

Stdev 89

Mean -4

Stdev 63

Mean 8

Stdev 91

Mean -1

Stdev 67

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

EnKF HYBRID

Forecast timeForecast time

Hit rate

Pseudo FAR

Mean HR 0.83

Mean pFAR 0.12

Mean HR 0.83

Mean pFAR 0.14

Mean HR 0.83

Mean pFAR 0.14

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

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

EnKF HYBRID

Forecast timeForecast time

Hit rate

Pseudo FAR

Mean HR 0.62

Mean pFAR 0.5

Mean HR 0.6

Mean pFAR 0.46

Mean HR 0.6

Mean pFAR 0.48

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 :3h

CO

BE

L le

vels

for

T

15h

CO

BE

L le

vels

for

T

COBEL levels for Ql COBEL levels for Ql

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

ensemble kalman filter in a boundary layer 1d numerical model

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