Coupled 4D-variational physical and biological data assimilation in - - PowerPoint PPT Presentation

Coupled 4D-variational physical and biological data assimilation in the California Current System

Hajoon Song1, Christ Edwards2, Andy Moore2 and Jerome Fiechter2 Sixth Symposium on Data Assimilation

2013.10.09 1 2 funding from

Physics Ecosystem

Advection Diffusion Temperature

Coupled ecosystem model

Introduction ●◦◦◦◦

Physics Ecosystem

Observations

• Oschlies and Garçon (1998)
• Miller et al. (2000)
• Berline et al. (2007)
• Fiechter et al. (2011)

Coupled ecosystem model

Introduction ●●◦◦◦

Physics Ecosystem

Observations

• Garcia-Gorriz et al. (2003)
• Natvik and Evensen (2003)
• Hoteit et al. (2003)
• Ciavatta et al. (2011)
• Rousseaux and Gregg (2012)
• Ford et al. (2012)

Well summarized in Gregg (2008)

Coupled ecosystem model

Introduction ●●●◦◦

Physics Ecosystem

Observations Observations

• Anderson et al. (2000)
• Ourmieres et al. (2009)
• Shulman et al. (2013)

Coupled ecosystem model

Introduction ●●●●◦

Physics Ecosystem

Observations Observations

Coupled ecosystem model

Introduction ●●●●●

PDA BDA CDA Physical variables

56% 13% 57%

Biological variables

7% 43% 49%

Quick Summary

RMSE reduction in twin experiment 13%

J(δz0) = 1 2δzT

0 B−1δz0 + 1

2

No

X

i=1

(di − OiHiMi,0Xδz0)T R−1

i

(di − OiHiMi,0Xδz0)

The cost function of the incremental 4D-Var

Coupled 4D-Var ●◦◦◦◦◦

J(δz0) = 1 2δzT

0 B−1δz0 + 1

2

No

X

i=1

(di − OiHiMi,0Xδz0)T R−1

i

(di − OiHiMi,0Xδz0)

1δz0

Surface chlorophyll, SeaWiFS

Unwanted

Concentration (mg g-3)

Sea surface temperature, AVHRR

Temperature (℃)

5 10 15 20 25

• 5

5 10 15

 −

• δz0 =

 δxphy δxbio

• =

 xphy − xb,phy xbio − xb,bio

• Coupled 4D-Var ●●◦◦◦◦

J(δz0) = 1 2δzT

0 B−1δz0 + 1

2

No

X

i=1

(di − OiHiMi,0Xδz0)T R−1

i

(di − OiHiMi,0Xδz0)

1δz0

ln(Surface chlorophyll), SeaWiFS Sea surface temperature, AVHRR

Temperature (℃)

5 10 15 20 25

Concentration (mg g-3)

• 5
• 4
• 3
• 2
• 1

1 2 3 4 5



• δz0 =

 δxphy δ ln xbio

• =

 xphy − xb,phy ln xbio − ln xb,bio

• 
• − OiH

i,0Xδ

Coupled 4D-Var ●●●◦◦◦

based on Fletcher and Zupanski (2006, 2007), Fletcher (2010) and Song et al. (2012)

J(δz0) = 1 2δzT

0 B−1δz0 + 1

2

No

X

i=1

(di − OiHiMi,0Xδz0)T R−1

i

(di − OiHiMi,0Xδz0) zT

0 B−1δ

(di )T R−1

i

di =  yphy − xo

b,phy

ln ybio − ln xo

b,bio

• i

B = Bphy Bln(bio)

• Ri =

Rphy Rln(bio)

• i

Coupled 4D-Var ●●●●◦◦

based on Fletcher and Zupanski (2006)

J(δz0) = 1 2δzT

0 B−1δz0 + 1

2

No

X

i=1

(di − OiHiMi,0Xδz0)T R−1

i

(di − OiHiMi,0Xδz0) − OiH

i,0Xδ

Oi = 1 (Xo

b,bio)−1

• i

X = 1 X−1

b,bio

• Coupled 4D-Var ●●●●●◦

Diagonal matrices!

J(δz0) = 1 2δzT

0 B−1δz0 + 1

2

No

X

i=1

(di − OiHiMi,0Xδz0)T R−1

i

(di − OiHiMi,0Xδz0) HiMi,0X

Tangent linear model

∂J ∂δz0 = B−1δz0 − XT

No

X

i=1

MT

0,iHT i OT i R−1 i

(di − OiHiMi,0Xδz0) .

• X

=1

MT

0,iH

Adjoint model

Coupled 4D-Var ●●●●●●

Tangent linear and Adjoint model bridge information between two components

• Test. Year 2000

Test Year 2000 ●◦◦◦◦◦

h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png;

California Current System

Test Year 2000 ●●◦◦◦◦

h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png;

Annual mean ln(Chlorophyll), SeaWiFS

h face es s, em c- m tal tz, 1987; t

• n,

tal s,

Kudela et al. (2009)

Nutrient-rich water

California Current System

Test Year 2000 ●●●◦◦◦

h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png;

Figure 3. Schematic of the ecosystem model.

Banas et al. (2009) Annual mean ln(Chlorophyll), ROMS-NPZD, Free

ROMS-NPZD model Simulation on year 2000

Test Year 2000 ●●●●◦◦

h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png;

50 100 150 200 250 300 350 0.5 1 1.5 2 2.5 3 3.5 4

Misfit (mg m−3) Day of year Spatial averaged chlorophyll RMSE CDA Free

Annual mean ln(Chlorophyll), ROMS-NPZD, DA

ROMS-NPZD model Data assimilation on year 2000

Test Year 2000 ●●●●●◦

Observations Satellite data (sea level, T, Chl) and in situ T, S

41% reduction

h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png;

Free PDA CDA T (℃) 1.04 0.76 0.70 S (psu) 0.15 0.07 0.08 Chl (𝜈g/l) 0.40 0.71 0.32 Nutrient (𝜈 mol/l) 3.02 2.94 2.81

RMS error with respect to independent observations

Test Year 2000 ●●●●●●

CalCOFI stations

Physical)Obs.) Biological)Obs.) Physical)IC) Advec6on)&) Diffusion) Physical<Biological)Coupled)model)

Summary ●◦

Physical)Obs.) Biological)Obs.) Physical)IC) Advec6on)&) Diffusion) Physical<Biological)Coupled)model)

We can improve the estimation of

• cean current using chlorophyll observations.

Summary ●●

Thank you!

Summary ●●●

0.5 1 0.25 0.5 0.75 1 1.25 0.5 0.6 0.7 0.8 0.9 0.95 0.99 Standard deviation C

• r

r e l a t i

• n

C

• e

f f i c i e n t

Ref.

u v T

• : CDA

: BDA : PDA 0.5 1 0.25 0.5 0.75 1 1.25 0.5 0.6 0.7 0.8 0.9 0.95 0.99 Standard deviation C

• r

r e l a t i

• n

C

• e

f f i c i e n t

Ref.

P D N Z : CDA : BDA : PDA

Physical variables Biological variables

Assimilating physical observations

Test 2. ●●●●◦◦

0.5 1 0.25 0.5 0.75 1 1.25 0.5 0.6 0.7 0.8 0.9 0.95 0.99 Standard deviation C

• r

r e l a t i

• n

C

• e

f f i c i e n t

Ref.

P D N Z : CDA : BDA : PDA 0.5 1 0.25 0.5 0.75 1 1.25 0.5 0.6 0.7 0.8 0.9 0.95 0.99 Standard deviation C

• r

r e l a t i

• n

C

• e

f f i c i e n t

Ref.

u v T

• : CDA

: BDA : PDA

Physical variables Biological variables

Assimilating biological observations

Test 2. ●●●●●◦

0.5 1 0.25 0.5 0.75 1 1.25 0.5 0.6 0.7 0.8 0.9 0.95 0.99 Standard deviation C

• r

r e l a t i

• n

C

• e

f f i c i e n t

Ref.

P D N Z : CDA : BDA : PDA 0.5 1 0.25 0.5 0.75 1 1.25 0.5 0.6 0.7 0.8 0.9 0.95 0.99 Standard deviation C

• r

r e l a t i

• n

C

• e

f f i c i e n t

Ref.

u v T

• : CDA

: BDA : PDA

Physical variables Biological variables

Assimilating physical and observations

Test 2. ●●●●●●