Data Assimilation- O01. FSO & EFSO Shunji Kotsuki
Environmental Prediction Science Laboratory
Center for Environmental Remote Sensing (CEReS), Chiba University(shunji.kotsuki@chiba-u.jp)
with many thanks to Mrs. T. Saito and K. Fujimura

Observation Diagnosis
Observation Space Analysis‣ Innovation statistics‣ Degrees of freedom to signals
Forecast Sensitivity
Forecast Sensitivity to Observation (FSO)
DA(iteration)

Adjoint

Ensembleiterative

Langland and Baker (2004)

Buehner et al. (2018)

deterministic

N/A

Kalnay et al. (2012)

Forecast Sensitivity to R (FSR)

DA(iteration)

Adjoint

Ensemble

Adjoint

Daescu (2008)

N/A

Ensemble

N/A

Hotta et al. (2017)Forecast Sensitivity
to Observation (FSO)FSO: Forecast Sensitivity to Obs
model space

analysis time

verification time

truth state(unknown)
reference-60ttime (hr)FSO: Forecast Sensitivity to Obs
model space

analysis time

verification time

truth state(unknown)
reference-60ttime (hr)FSO: Forecast Sensitivity to Obs
model space

analysis time

verification time

truth state(unknown)
reference-60ttime (hr)FSO: Forecast Sensitivity to Obs
model space

analysis time

verification time

truth state(unknown)
reference-6

The difference b/w

0andttime (hr)depends only on the obs DA’ed at t=0.

FCST Error Reduction
Error Reduction w.r.t. Obs: square norms(e.g. L2 for L63/L96, dry/moist energy norm for NWP)FCST Sensitivity to Obs (FSO)××

too large memoryneeds adjoint (linererror
growthapprox.

|

||

|

|

i.e., impact of ith obs is&,)Ensemble FSO||i.e., impact of ith obs isensemble approx.

,Experiments
w/ Lorenz96
Kotsuki, S., Greybush, S., and Miyoshi, T. (2017):
Can we optimize the assimilation order in the serial ensemble Kalman filter?
A study with the Lorenz-96 model.
Mon. Wea. Rev., 145, 4977-4995. doi: 10.1175/MWR-D-17-0094.1

Experimental Setting‣ Serial EnSRF (Whitaker and Hamill 2001)‣Ensemble size : 8‣# of observations : 40
‣Adaptive multiplicative inflation (Miyoshi 2011)‣ Assimilation order

1. Randomly-determined
2. From better to worse obs based on EFSO
cf. Kotsuki et al. (2017, MWR)

DebugA case w/ serial EnSRF
ー RMSE--- SPRD

Seeing a DA
degraded bydetrimental obs.
Improved bybeneficial obs.
Improved bybeneficial obs.
degraded bydetrimental obs.

FG－: random orderAN－: EFSO better  worse obs.

Ave of 1460 cases
ー RMSE--- SPRD

FG－: random orderAN－: EFSO better  worse obs.
－: EFSO worse  better obs.

Replication by students
Fujimura

Saito

Experiments
w/ NICAM-LETKF
Kotsuki, S.*, Kurosawa, K., and Miyoshi, T. (2019):
On the Properties of Ensemble Forecast Sensitivity to Observations.
Q. J. R. Meteorol. Soc., 145, 1897-1914. doi: 10.1002/qj.3534

Reference & Norms
model space

analysis time

verification time

truth state(unknown)
reference-6t0

Moist Total Energy for Error Normtime (hr)Verified against subsequent Anl.,or Anl from other center

Normalized Obs. Departure for Error Norm

Verified against future obs

Ensemble FSO
Moist Total Energy for Error Norm (Otaet al. 2013)

obs-minus-FG

AN ptb FCST ptb
in obs space

Normalized Obs. Departure for Error Norm (Sommer and Weissmann 2016)

obs-minus-FG

AN ptb FCST ptb
in obs spaceEFSO with NICAM-LETKF

Estimated Impacts by EFSO

● Beneficial observation● Detrimental observation

2014/07/11/00UTC; vs. ERA interim

FCST MTE Error Reduction
vs. NICAM-LETKF

Positive Impact(improving 6-hr FCST)

vs. ERA Interim■ME : Moist Energy■PE : Potential Energy■KE : Kinetic Energy

Monthly average in July 2014; FT 06hr

FCST NOD Error Reduction-1.15x10-3-32.6x10-3-1.11x10-3-0.02x10-3

Each type of observations mainly contributes
to the improvement of the observed variable.
Monthly average in July 2014; FT 12hr

Detection of detrimental
AMSU-A radiances
Impacts of AMSU-A on upper atmos. (~350hPa, vs. ERA)EFSO Estimates

detrimental 

w/wo AMSU-A

detrimental 

We can evaluate impacts of AMSU-A by EFSO
without expensive w/wo OSE experiments

On Beneficial &Detrimental Obs

FCST Error Reduction (2014071100UTC)

vs. ERAvs.
NICAM-LETKF

Fraction of Beneficial Obs
Ref.

Subseq. AN

ERA Interim

AMSU-AFT 06hr58.8 %

55.4 %

53.1 %FT 12hr

56.1 %

54.2 %

53.2 %FSO may overestimate observational impact
with subsequent analyses for verification reference.
 It is good to use an independent anl for referenceImpacts in Time (vs. ERA Interim)
detrimental

AIRCFTVADWND PROFLR

MTE (J/kg)

GSMaP

FT: 24 hr

Impacts in Space (vs. ERA Interim)
MTE (J/kg)

Bad

Good

統計的に予報を改悪する観測を除くと良くなるのか?（課題）A Case ofHeavy Rain in July 2018

Kotsuki, S.*, Terasaki, K., Kanemaru, K., Satoh, M., Kubota, T. and Miyoshi, T. (2019):
Predictability of Record-Breaking Rainfall in Japan in July 2018:
SOLA, 15A, 1-7. doi: 10.2151/sola.15A-001

NICAM-LETKF Ens. FCSTs
24-hr Accumulated Precip

JMA’s Obs
Forecast Lead Time (FT)
& Initialized DateNICAM-LETKF Ens. FCSTs

shifting initialized time

NICAM-LETKF Ens. FCSTs

NICAM-LETKF Ens. FCSTs

Obs Impacts

Obs at 07/03 12UTC

Ave 4/01~4/07

Heavy② RainUsual①① Large impacts than usual  rapid error growth② Impacts on moist field is bigger■ME : Moist Energy■PE : Potential Energy■KE : Kinetic Energy(水蒸気の改善)(気温・気圧の改善)(風向風速の改善)

Radiosondes’ Impacts
Obs at 07/03 12UTC■ME : Moist Energy■PE : Potential Energy■KE : Kinetic Energy●: beneficial radiosondes●: detrimental radiosondes(水蒸気の改善)(気温・気圧の改善)(風向風速の改善)

Thank you for your attention!
Presented by Shunji Kotsuki(shunji.kotsuki@chiba-u.jp)
Further information is available athttps://kotsuki-lab.com/