ecmwf training course 2005 slide 1 forecast sensitivity to observation carla cardinali

ECMWFTraining Course 2005 slide 1

Forecast sensitivity to Observation

Carla Cardinali


Outline Part 2: Forecast Sensitivity

Forecast Sensitivity to Observation

Sensitivity gradient

A-TReC campaigns

Comparing Observation Analysis Influence and Observation Forecast

Impact

Results and Conclusion


Forecast Sensitivity to Observation

Jy

J is measures the forecast error: its gradient respect the observation vector y gives the forecast error sensitivity respect

observations used in the initial condition for model forecast

J ax

ax

ythe sensitivity respect the initial condition xa

Analysis sensitivity with respect the observation


Define Forecast Sensitivity

1 1 1 1( )T Ta

x

K R H B H R Hy

1 1 1 1( )T

a

J J

R H B H R H

y x

1

a

J J

R HA

y x

J Ja

a

x

y y x


Change of Variable

1" ( )T T J I LH R HL

( )b x x Lχ

1 1 1

1 1 1 1 1

1

1 1( ) ( ) ( ) ( ) ( )

2 2

1 1( ) ( ) ( )( ) ( ) ( )

2 2

1 1( ) ( ) ( ) ( )

2 2

1 1( ) ( ) ( )

2 2

T T

T T T

T

T

J b b

b b

b b

J

x x x B x x Hx y R Hx y

x x L L x x HLχ y R HLχ y

xL x L xL x L HLχ y R HLχ y

χ χ HLχ y R HLχ y χ

TB LL

1( ) ( )

T T TJ

χ χ L H HLχ y R


Computation

1 1 1 1( )T

a

J J

R H B H R H

y x

1 1 1 11 1 12 2 2 2( )T

a

J J

R HB I B H R HB B

y x1 1

1 1 12 2( )T T

a

J J

R HB I LH R HL B

y x

z

1( ") az J z

11 2

2 aLz J B z 11 1 2

2

JL

R H B zy

Linear system to solve

za


Forecast Sensitivity to Observations

aJx

aJ J ay y xx

Tangent Linear Model ResolutionT95 L60

Jy

TJ J ay xK


Sensitivity Gradients

Sensitivearea

Verificationarea

T1

100*TE at t=0 100*KE at t=0

TE at t=T1

KE at t=T1

500 hPa Temperature Sensitivity Gradients aJx


aJx

Jy

Fc Sensitivity to Aircraft Temperature 500 hPa


Fc Sensitivity to Surface Pressure


Observation Campaign 5 Dec 18 UTC---Verification 7 Dec 12 UTC

AtreC 13% MSLP Relative Fc Improvement 9% Total Energy

Targeting = Verification Region Lat(30,50)-Lon(-85,-60)

42h

TargetIN/NOTargetIN %AMDAR 2.5SONDE 5.5

1011

1014

1014

1017

10231026

An 5 Dec 18 UTC


N

J

y

1

NN

J

y

Observations Contribution to Forecast

0

0.00002

0.00004

0.00006

0.00008

0.0001

0.00012

0.00014

0.00016

0.00018

0.0002

airep u airep v airep t temp u temp v temp t temp q

Target NoTarget

Total Contribution

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6


Target NoTarget

Mean Contribution


1 1 a

N NN N

HxJ

y y

a

N N

HxJ

y y

Forecast and Analysis Sensitivity to Targeted Observations

0

100

200300

400

500

600700

800

900


Fc Sens An Sens

0

0.2

0.4

0.6

0.8

1

1.2

1.4


Mean Fc Sens Mean An Sens


200-300 hPa Targeted Aircraft Temperature Forecast Error

( )aJ y y HxJy Jy


Aircraft Observation U-Comp 200-300 hPa

30°N 30°N

60°N60°N

90°W

90°W 60°W

60°Wek4d airep_u Level:300

-0.8E-05

-0.5E-05

-0.1E-05

-0.8E-06

-0.5E-06

-0.3E-06

-0.1E-06

-0.8E-07

-0.3E-07

0.1E-07

0.3E-07

0.8E-07

0.1E-06

0.3E-06

0.5E-06

0.8E-06

0.1E-05

0.5E-05

0.8E-05

0.4

30°N 30°N

60°N60°N

90°W

90°W 60°W

60°WAn Sens Airep u-comp300-200 Hpa

0

0.2

0.4

0.6

0.8

1

Forecast Impact

Observation Influence in Analysis

Background Influence = 1-Observation Influence


TEMP Observation Temperature 850-1000 hPa

30°N 30°N

60°N60°N

90°W

90°W 60°W

60°Wek4d temp_t Level:900

-0.8E-05

-0.5E-05

-0.1E-05

-0.8E-06

-0.5E-06

-0.3E-06

-0.1E-06

-0.8E-07

-0.3E-07

0.1E-07

0.3E-07

0.8E-07

0.1E-06

0.3E-06

0.5E-06

0.8E-06

0.1E-05

0.5E-05

0.8E-05

0.2

30°N 30°N

60°N60°N

90°W

90°W 60°W

60°Wej4b temp_t Level:900

0

0.2

0.4

0.6

0.8

1

Forecast Impact

Observation Influence in Analysis

Background Influence = 1-Observation Influence


Total Forecast Error 5 Dec 2003

TargetIN/NOTargetIN 8%

ATreC 2003120518

-4.E-05

-3.E-05

-2.E-05

-1.E-05

0.E+00

1.E-05

2.E-05

Airep

Temp

Satob

Pilot

SynopDrib

uSca

tG

oes

AMSU-A

AMSU-B

AIRS

HIR

S

SSM/I

TargetIN

TargetOUT

NoTarget IN

NoTargetOUT


Observation Campaign 8 Dec 18 UTC---Verification 11 Dec 00 UTC

TargetIN/NOTargetIN %AMDAR 2.6SONDE 0.9

AtreC -71% MSLP Relative Fc Degradation -7% Total Energy

Targeting Lat(30,60)-Lon(-70,-15)Verification Lat(45,65)-Lon(-15,+10)

54h


200-300 hPa Targeted Aircraft U Forecast Error

( )aJ y y Hx Jy


Total Forecast Error 8 Dec 2003

TargetIN/NOTargetIN 3.5%

-3.E-05

-2.E-05

-1.E-05

0.E+00

1.E-05

2.E-05

3.E-05

Airep

Temp

Satob

Pilot

SynopDrib

uSca

tG

oes

AMSU-A

AMSU-B

AIRS

HIR

S

SSM/I

TargetIN

TargetOUT

NoTargetIN

NoTargetOUT


Conclusions

Forecast sensitivity to observations has been computed for the campaigns showing an impact (ATreC-Cntr)/Cntr ≥ ± 10%

13 cases out of 38: 9 positive and 4 negative

Two campaigns have been shown

5 Dec at 18 UTC - Targeted observations improved the forecast of a cyclone moving along the east coast of North America for which severe weather impact was forecast

8 Dec at 18 UTC – Targeted observations deployed to clarify the models uncertainties for the remnants of the east cost storm, degraded the forecast over Northern Europe – UK

However, differences in forecast impact between ATreC and Cntr come also from the continuous assimilation cycling that provides different model trajectories

Forecast Impact computed for the cancelled campaigns gives on average ±10% in term of RMSE in the verification area


END


Singular vectors brief definition

Singular vectors was one of technique used in AtreC-TOST campaign to find sensitivity areas where releasing additional observations

Singular vectors (SVs) define perturbations with fastest growth during a finite time interval (optimization time interval). They are defined by:

The model characteristics: TL95L60, dry, with simplified physics

The norm used to measure growth: localized total energy

The optimization time interval: 42-54 hours

Diagnostic Singular vectors have been computed to investigate the observation impact in the forecast

time

Sensitivearea

Verificationarea


Linear combination of 10 Diagnostic SVs

valid at observation time

AtreC observation time forecast step T1

localized total energymaximum in verification area

eigenvalues decompositionforecast error step T1

proj. fc error onto SVsBack to the observation time

Sensitivearea

Verificationarea

T1

ecmwf training course 2005 slide 1 forecast sensitivity to observation carla cardinali

Documents

observation slide

forecast sensitivity

hpa slide

utc slide

contribution slide

h slide

zaza slide

conclusion slide