Adjoint Estimation of the Forecast Impact of Observation Error - - PowerPoint PPT Presentation

Adjoint Estimation of the Forecast Impact

• f Observation Error Correlations

Derived from A Posteriori Covariance Diagnosis

DACIAN N. DAESCU Portland State University, Portland, OR ROLF H. LANGLAND NRL Marine Meteorology Division, Monterey, CA 6th WMO Symposium on Data Assimilation – 2013

Outline

NRL NAVDAS-AR/NAVGEM T319L50 resolution 4D-VAR, 6-hour window Time period: 2012 10/15-11/01, all UTC Adjoint-DAS forecast error sensitivity (Daescu&Langland 2013) error covariance sensitivity a priori guidance & forecast impact estimates A posteriori error covariance diagnosis (Desroziers et al. 2001+) Radiance σ2

• estimates
• bs error

correlations spatial interchannel Merging information is necessary feasible SYNERGISTIC APPROACH TO ERROR COVARIANCE TUNING

Error Covariance Diagnosis: xa = xb + K[y − h(xb)]

• R

= E

• do

a(do b)T

= R

• HBHT + R

−1 HBtHT + Rt

• H

BHT = E

• da

b(do b)T

= HBHT HBHT + R −1 HBtHT + Rt

• Innovation error covariance consistency valid for any (R, B)

H BHT + R = HBtHT + Rt Error covariance estimates valid if and only if H BHT = HBtHT ⇔ R = Rt ⇔ HK = HKt What is the analysis impact/benefit of the ( R, B) iteration? H K = H BHT H BHT + R −1 = HBHT HBHT + R −1 = HK      Hxa = H xa H = I ⇒ xa = xa

Adjoint-DAS Forecast Error Sensitivity e

• xa(xb, B, y, R)
• Which DAS components contribute most to forecast uncertainties?

Identify high-impact error covariance parameters Provide the steepest descent directions −∇Re, −∇Be

e(xa

a

x ) R B K Σ

b

C

• Σ
• C

b

MT y

b

x

A priori guidance to the gain in the forecast skill of ( ˜ R, ˜ B) e[xa( ˜ R, ˜ B)] − e[xa(R, B)]

• gain

≈ ∂e ∂R, δR

• p×p

+ ∂e ∂B, δB

• n×n

The optimal corrections δR⋆, δB⋆ not provided

Forecast (R, B)-sensitivity: xa = xb + K[y − h(xb)]

Daescu and Langland (2013)

• HBHT + R
• z

= y − h(xb) (solver) xa = xb + BHTz (post − multiplication) Observation sensitivity Background sensitivity† ∂e ∂y = KT ∂e ∂xa ∂e ∂xb = ∂e ∂xa − HT ∂e ∂y Forecast R-sensitivity Forecast B-sensitivity ∂e ∂R = − ∂e ∂yzT ∂e ∂B = ∂e ∂xb

• HTz

T δR-impact estimation δB-impact estimation δe ≈ − (δR z)T ∂e ∂y δe ≈

• δB HTz

T ∂e ∂xb

A posteriori σo-estimates: (˜

σo

i )2 =

1 nobsi [y − h(xa)]T

i [y − h(xb)]i

AMSU-A IASI - 51 channels The estimates ˜ σo are much lower than the assigned σo In consensus with estimates at other NWP centers Will forecasts benefit from a ˜ σo-specification?

Forecast error σ2

• -weight sensitivity guidance: (so

i)σ2

• 24-hr moist total energy error norm, e(xa) = xa

f − xa v2 E

AMSU-A IASI Guidance to maximize the forecast impact of σo-tuning

Reduce assigned σo for AMSU-A channels 5-8 Inflate assigned σo for most IASI channels (error correlations !?)

OSE validation of σo-tuning impact: AMSUA, IASI, AIRS

self-validation: e(EXP) - e(CTL) radiosonde T: EXP/CTL mean Jo(xb

EXP ) − Jo(xb CT L)

EXP1: AMSUA Ch 5-8 ˜ σo = 1

2σo

EXP2: IASI ˜ σo = 2σo EXP3:

AMSUA Ch 5-8 ˜ σo = 1

2σo

IASI, AIRS ˜ σo = 2σo

IASI spatial error correlations

R(r) = E

• [y − h(xa)]i
• y − h(xb)
• j
• For each channel assume

C(ǫo

i , ǫo j) = φ(dist{yi, yj})

d1 < dist(yi, yj) < d2 25Km separation bin

A priori forecast error R-impact estimation: IASI

A priori ˜ σ2

• - and

R-impact estimation: IASI

IASI inter-channel error correlations diagnosis/impact

• R(i, j) = E
• [y − h(xa)]ch#i [y − h(xb)]ch#j
• error correlation estimates

forecast error impact A priori forecast impact assessment of the error correlations ˜ R covariance model: e( ˜ R) − e(R) ≈ ∂e ∂R, δR

Summary & Research Prospects

Design of improved error covariance models

A posteriori error covariance consistency diagnosis/estimates Adjoint-DAS sensitivity & a priori guidance to covariance tuning impact Merging information is both necessary and feasible

Future research & adjoint-DAS applications

Adaptive B-optimization, hybrid ensemble/4D-Var Model error covariance Q-diagnosis/sensitivity/impact

There is a need for improved validation procedures

Forecast error metric e, verification state xv selection

Summary & Research Prospects

Design of improved error covariance models

A posteriori error covariance consistency diagnosis/estimates Adjoint-DAS sensitivity & a priori guidance to covariance tuning impact Merging information is both necessary and feasible

Future research & adjoint-DAS applications

Adaptive B-optimization, hybrid ensemble/4D-Var Model error covariance Q-diagnosis/sensitivity/impact

There is a need for improved validation procedures

Forecast error metric e, verification state xv selection

Thank you!

Thank you!