A data assimilation system by using DMI

ocean model BSHcmod

Jiang Zhu, Ye Liu, Shiyu Zhuang, Jun She, Per

Institute of Atmospheric Physics

Chinese Academy of Sciences

YEOS Annual meeting and Workshop on Yellow Sea Operational Oceanography24-25 April 2008, Copenhagen, Denmark

Outlines

• Motivations

• Bathymetry-following covariance : A recursive filter approach

• Some test results

• Conclusions and next steps

Motivations

• The North-Baltic Sea and the Yellow Sea are both shallow seas;

• The North-Baltic Sea is more observed than the Yellow Sea and provides a test bed for a data assimilation system of shallow coastal/shelf seas;

• BSHcmod for North-Baltic Sea has a SST data assimilation system and does not have a profile data assimilation system yet;

• We first develop a profile data assimilation system for BSHcmod in North-Baltic Sea.

0 5 1 0 1 5 2 0 2 5 3 0

L o n g i t u d e

5 0

5 5

6 0

6 5

D M U o b s e r v a t i o n

B S H o b s e r v a t i o n

I C E S o b s e r v a t i o n

0 5 1 0 1 5 2 0 2 5 3 0

L o n g i t u d e

5 0

5 5

6 0

6 5

D M U o b s e r v a t i o n

B S H o b s e r v a t i o n

I C E S o b s e r v a t i o n

The spatial distribution of T/S profiles observation used in the experiments in 2005

0

10

20

30

40

50

60

The

Numb

er o

f TS

Pro

file

s

The daily total number of profiles in 2005.

Bathymetry-following covariance : A recursive filter approach

Basic formulism: solving a minimization of the following cost function

Though theoretically equivalent, the variational approach is used instead of Optimal Interpolation (OI) scheme for easy handling of

• additional penalty terms added to the cost function;

• imposing inequality constraints to avoid density reversal.

Considering the narrow channels and complex coastal lines, the inhomogeneous, anisotropic background error covariance is necessary to propagate information.

A Bathymetry-following covariance is used in the infinitesimal differential form:

22

2 2

1 ( )exp

2

T

br f

dy dy df

L L

B

Analysis incremental from a single observation

IsotropicAnisotropic

An recursive filter using the aspect tensor A defined by

12 2

( ) ( )T

r f

f f

L L

I

A

can be constructed after determination of the two length scales.

6 6.5 7 7.5 8 8.5 9 9.5 105

6

7

8

9

10

11

12

13

14

Error field correlation length (m)

Ho

rizo

nta

l co

rre

latio

n le

ng

th

0.28

0.3

0.32

0.34

0.36

0.38

0.4

0.42

0.44

RMSE of Temperature is shown as function of the two length scales Lf and Lr using all observed profiles in 26 Apr. 2005.

(9 grid points, 9.5m)

Some test results

The assimilation system is setup at the two model grid area : coarse grid area and fine grid area.

However, here only implementting the coarse grid area assimilation and only presentatting some coarse assimilation results.

We assimilated the T/S profiles into the cmod every day at 12:00 for a 20-day period (Jan 16 2005 to 3 Feb 2005. )

0

5

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1-13

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1-31 2-2

2-4

The

Numb

er o

f T/

S Pr

ofile

s

The daily total number of profiles in experiment period.

The impact of the assimilation scheme to forcasting effect can be vertified by

• all the observation data before assimilation and

• the withheld BSH profiles (the yellow points)

Obs

Ana

For

Locations of profiles in the experiment.

0 5 1 0 1 5 2 0 2 5 3 0

5 0

5 5

6 0

6 5

1-15 1-17 1-19 1-21 1-23 1-25 1-27 1-29 1-31 2-2 2-4 0.3

0.4

0.5

0.6

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0.9

1

1.1

Time (day)

RM

SE

( o

C )

with assimilationwithout assimilation

The overall RMSEs for T verified daily just before the assimilation.

1-16 1-18 1-20 1-22 1-24 1-26 1-28 1-30 2-1 2-20.2

0.4

0.6

0.8

1

1.2

Time (day)

RM

SE

(p

su)

with assimilation without assimilation

The overall RMSEs for S verified daily just before the assimilation.

Little impact could be due to the large S observation error setup (0.5psu).

1-16 1-18 1-20 1-22 1-24 1-26 1-28 1-30 2-1 2-30.2

0.3

0.4

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1

Time (day)

RM

SE

(

o C )

Without assimilationWith assimilation

The RMSEs for T at 9m verified daily just before the assimilation.

The RMSEs for S at 9m verified daily just before the assimilation.

1-16 1-18 1-20 1-22 1-24 1-26 1-28 1-30 2-1 2-20.2

0.4

0.6

0.8

1

1.2

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Time (day)

RM

SE

(p

su)

with assimilationwithout assimilation

4.083W 0 3E 6E 9E 12E 15E 18E 21E 24E 27E 30E48.55N

50N

52N

54N

56N

58N

60N

62N

64N

66N

Longitude (o)

La

titu

de

(o )

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1The temperature analysis increment at 4m depth, on Feb. 3 2005.

4.083W 0 3E 6E 9E 12E 15E 18E 21E 24E 27E 30E48.55N

50N

52N

54N

56N

58N

60N

62N

64N

66N

Longitude ( o )

La

titu

de

( o )

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

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0.5

The salinity analysis increment at 4m depth, on Feb. 3 2005.

4.083W 0 3E 6E 9E 12E 15E 18E 21E 24E 27E 30E48.55N

50N

52N

54N

56N

58N

60N

62N

64N

66N

Longitude ( o )

La

titu

de

( o )

-1

-0.8

-0.6

-0.4

-0.2

0

0.2The temperature analysis increment at 15m depth, on Feb. 3 2005.

4.083W 0 3E 6E 9E 12E 15E 18E 21E 24E 27E 30E48.55N

50N

52N

54N

56N

58N

60N

62N

64N

66N

Longitude ( o )

La

titu

de

( o )

-0.5

-0.4

-0.3

-0.2

-0.1

0

0.1

0.2

0.3

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0.5The salinity analysis increment at 15m depth, on Feb. 3 2005.

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Time (day)

Dep

th (m

)

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Time (day)

Dep

th (m

)

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1-16 1-18 1-20 1-22 1-24 1-26 1-28 1-30 2-1 2-2

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Time (day)

De

pth

(m

)

5.6

5.8

6

6.2

6.4

6.6

6.8

7

7.2

Obs

Simu Assi

Verified using independent profiles: Temperature

0 5 1 0 1 5 2 0 2 5 3 0

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6 5

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Time (day)

Dep

th(m

)

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3.5

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Time (day)

Dep

th(m

)

3.2

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4.8

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Time (day)

detp

h (m

)

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Obs

Simu Assi

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S at 6m

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20

Time (day)

Sa

linity

(p

su)

observationwith assi.(Lf=9,Lr=10without assi.with assi (Lf=9,Lr=13)

S at 6m

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5 0

5 5

6 0

6 5

0 5 1 0 1 5 2 0 2 5 3 0

L o n g i t u d e

5 0

5 5

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6 5

Latit

ude

0 1-17 1-19 1-21 1-23 1-25 1-27 1-29 1-31 2-2 2-431

31.5

32

32.5

33

33.5

34

34.5

35

Time (day)S

alin

ity (

psu

)

Observationwithout assimilationwith assimilation

S at 6m

0 1-17 1-19 1-21 1-23 1-25 1-27 1-29 1-31 2-2 2-432.5

33

33.5

34

34.5

35

Time (day)

Sa

linity

(p

su)

Observationwithout assimilationwith assimilation

S at 30m

1-15 1-17 1-19 1-21 1-23 1-25 1-27 1-29 1-31 2-2 2-45.2

5.4

5.6

5.8

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6.2

6.4

6.6

6.8

7

7.2

Time (day)

Te

mp

era

ture

(o C )

observation without assimilationwith assimilation

T at 30m

T at 13m T at 29m

Assimilation minus Simulation on Feb. 3, 2005

Conclusions and next steps

• Assimilation of profiles can improve the temperature and salinity forecasts in the North-Baltic Sea, especially the cold, fresh water mass in the Danish strait is more realistic;

• More parameter-tuning in the assimilation system;

• Perform one-year long experiment and verification;

• Installation in DMI;

• SST assimilation or water level assimilation.

END

Thanks