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

Sixth Symposium on Data Assimilation Coupled 4D-variational physical and biological data assimilation in the California Current System Hajoon Song 1 , Christ Edwards 2 , Andy Moore 2 and Jerome Fiechter 2 2013.10.09 funding from 1 2

Coupled ecosystem model Physics Advection Diffusion Ecosystem Temperature Introduction ●◦◦◦◦

Coupled ecosystem model Observations • Oschlies and Garçon (1998) • Miller et al. (2000) Physics • Berline et al. (2007) • Fiechter et al. (2011) Ecosystem Introduction ●●◦◦◦

Coupled ecosystem model • Garcia-Gorriz et al. (2003) • Natvik and Evensen (2003) • Hoteit et al. (2003) Physics • Ciavatta et al. (2011) • Rousseaux and Gregg (2012) • Ford et al. (2012) Well summarized in Gregg (2008) Observations Ecosystem Introduction ●●●◦◦

Coupled ecosystem model Observations • Anderson et al. (2000) • Ourmieres et al. (2009) Physics • Shulman et al. (2013) Observations Ecosystem Introduction ●●●●◦

Coupled ecosystem model Observations Physics Observations Ecosystem Introduction ●●●●●

Quick Summary RMSE reduction in twin experiment PDA BDA CDA Physical 13% 56% 13% 57% variables Biological 7% 43% 49% variables

N o 1 0 B − 1 δ z 0 + 1 ( d i − O i H i M i, 0 X δ z 0 ) T R − 1 X 2 δ z T J ( δ z 0 ) = ( d i − O i H i M i, 0 X δ z 0 ) i 2 i =1 The cost function of the incremental 4D-Var Coupled 4D-Var ●◦◦◦◦◦

N o 1 0 B − 1 δ z 0 + 1 ( d i − O i H i M i, 0 X δ z 0 ) T R − 1  � X 2 δ z T 1 δ z 0 J ( δ z 0 ) = ( d i − O i H i M i, 0 X δ z 0 ) i 2 i =1 −  �  � δ x phy x phy − x b,phy δ z 0 = = δ x bio x bio − x b,bio 0 0 0 Sea surface temperature, AVHRR Surface chlorophyll, SeaWiFS Unwanted 5 -5 0 5 10 15 10 15 20 25 Temperature ( ℃ ) Concentration (mg g -3 ) Coupled 4D-Var ●●◦◦◦◦

N o 1 0 B − 1 δ z 0 + 1 ( d i − O i H i M i, 0 X δ z 0 ) T R − 1  � X 2 δ z T 1 δ z 0 J ( δ z 0 ) = ( d i − O i H i M i, 0 X δ z 0 ) i, 0 X δ − O i H i 2 i =1 based on  �  � Fletcher and Zupanski δ x phy x phy − x b,phy δ z 0 = = (2006, 2007), δ ln x bio ln x bio − ln x b,bio Fletcher (2010) 0 0 and Song et al. (2012)  � Sea surface temperature, AVHRR ln(Surface chlorophyll), SeaWiFS 5 -5 -4 -3 -2 -1 0 1 2 3 4 5 10 15 20 25 Temperature ( ℃ ) Concentration (mg g -3 ) Coupled 4D-Var ●●●◦◦◦

N o 1 0 B − 1 δ z 0 + 1 ( d i − O i H i M i, 0 X δ z 0 ) T R − 1 ) T R − 1 X 2 δ z T z T 0 B − 1 δ J ( δ z 0 ) = ( d i − O i H i M i, 0 X δ z 0 ) ( d i i i 2 i =1  y phy − x o �  B phy �  R phy � 0 0 b,phy d i = B = R i = ln y bio − ln x o 0 B ln ( bio ) 0 R ln ( bio ) b,bio i i based on Fletcher and Zupanski (2006) Coupled 4D-Var ●●●●◦◦

N o 1 0 B − 1 δ z 0 + 1 ( d i − O i H i M i, 0 X δ z 0 ) T R − 1 X 2 δ z T J ( δ z 0 ) = ( d i − O i H i M i, 0 X δ z 0 ) i, 0 X δ − O i H i 2 i =1  1 � 0  1 � 0 X = O i = X − 1 0 b,bio ) − 1 ( X o 0 0 b,bio i Diagonal matrices! Coupled 4D-Var ●●●●●◦

N o 1 0 B − 1 δ z 0 + 1 ( d i − O i H i M i, 0 X δ z 0 ) T R − 1 X 2 δ z T J ( δ z 0 ) = ( d i − O i H i M i, 0 X δ z 0 ) H i M i, 0 X i 2 i =1 Tangent linear model N o o ∂ J X X M T B − 1 δ z 0 − X T M T 0 ,i H T i O T i R − 1 = ( d i − O i H i M i, 0 X δ z 0 ) . 0 ,i H i ∂δ z 0 i =1 =1 Adjoint model Tangent linear and Adjoint model bridge information between two components Coupled 4D-Var ●●●●●●

Test. Year 2000 Year 2000 ●◦◦◦◦◦ Test

California Current System h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png; Year 2000 ●●◦◦◦◦ Test

h face es s, em c- m Annual mean tal ln (Chlorophyll), tz, 1987; SeaWiFS t Kudela et al. (2009) - n, tal s, Nutrient-rich water California Current System h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png; Year 2000 ●●●◦◦◦ Test

Annual mean ln (Chlorophyll), ROMS-NPZD, Free Schematic of the ecosystem model. Figure 3. Banas et al. (2009) ROMS-NPZD model Simulation on year 2000 h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png; Year 2000 ●●●●◦◦ Test

Spatial averaged chlorophyll RMSE 4 CDA 3.5 Free 3 Misfit (mg m − 3 ) 2.5 Annual mean 2 ln (Chlorophyll), 1.5 ROMS-NPZD, DA 1 0.5 0 50 100 150 200 250 300 350 Day of year 41% reduction Observations ROMS-NPZD model Satellite data (sea level, T, Chl) Data assimilation on year 2000 and in situ T, S h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png; Year 2000 ●●●●●◦ Test

RMS error with respect to independent observations Free PDA CDA CalCOFI stations T ( ℃ ) 1.04 0.76 0.70 S (psu) 0.15 0.07 0.08 Chl ( 𝜈 g/l) 0.40 0.71 0.32 Nutrient 3.02 2.94 2.81 ( 𝜈 mol/l) h"p://cce.lternet.edu/aboutus/media5gallery/ mediaDB/graphics/cce_currents.png; Year 2000 ●●●●●● Test

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

Physical)Obs.) Physical)IC) We can improve the estimation of Advec6on)&) ocean current using chlorophyll observations. Diffusion) Physical<Biological)Coupled)model) Biological)Obs.) Thank you! Summary ●●

Summary ●●●

Assimilating physical observations P D N Z u v T � 1.25 1.25 C C o o : PDA : PDA r r r r 0.5 e 0.5 e l l : BDA : BDA a a t t i i 0.6 0.6 : CDA : CDA o o n n 1 1 C C 1 1 o o 0.7 0.7 e e f f f f Standard deviation Standard deviation i i c c 0.8 0.8 i i e e 0.75 0.75 n n t t 0.9 0.9 0.5 0.5 0.5 0.5 0.95 0.95 0.25 0.25 0.99 0.99 0 0 0 0 Ref. Ref. Biological variables Physical variables Test 2. ●●●●◦◦

Assimilating biological observations P D N Z u v T � 1.25 1.25 C C o o : PDA : PDA r r r r 0.5 e 0.5 e l l : BDA : BDA a a t t i i 0.6 0.6 : CDA : CDA o o n n 1 1 C C 1 1 o o 0.7 0.7 e e f f f f Standard deviation Standard deviation i i c c 0.8 0.8 i i e e 0.75 0.75 n n t t 0.9 0.9 0.5 0.5 0.5 0.5 0.95 0.95 0.25 0.25 0.99 0.99 0 0 0 0 Ref. Ref. Biological variables Physical variables Test 2. ●●●●●◦

Assimilating physical and observations P D N Z u v T � 1.25 1.25 C C o o : PDA : PDA r r r r 0.5 e 0.5 e l l : BDA : BDA a a t t i i 0.6 0.6 : CDA : CDA o o n n 1 1 C C 1 1 o o 0.7 0.7 e e f f f f Standard deviation Standard deviation i i c c 0.8 0.8 i i e e 0.75 0.75 n n t t 0.9 0.9 0.5 0.5 0.5 0.5 0.95 0.95 0.25 0.25 0.99 0.99 0 0 0 0 Ref. Ref. Biological variables Physical variables Test 2. ●●●●●●