Predictability of Japan / East Sea (JES) System to Uncertain Initial / Lateral Boundary Conditions...

Predictability Predictability of of

Japan / East Sea (JES) System Japan / East Sea (JES) System to to

Uncertain Initial / Lateral Uncertain Initial / Lateral Boundary Conditions Boundary Conditions

and and Surface Winds Surface Winds

Predictability Predictability of of

Japan / East Sea (JES) System Japan / East Sea (JES) System to to

Uncertain Initial / Lateral Uncertain Initial / Lateral Boundary Conditions Boundary Conditions

and and Surface Winds Surface Winds

LCDR. Chin-Lung Fang LCDR. Chin-Lung Fang LCDR. Chin-Lung Fang LCDR. Chin-Lung Fang

OutlineOutlineOutlineOutline

• IntroductionIntroduction

• Experimental designExperimental design

• Statistical analysis methods Statistical analysis methods

• ResultsResults

• ConclusionsConclusions

• IntroductionIntroduction

• Experimental designExperimental design

• Statistical analysis methods Statistical analysis methods

• ResultsResults

• ConclusionsConclusions

IntroductionIntroduction

• Three Three DifficultiesDifficulties

• JES JES Geography & Geography & bottom bottom topographytopography

• Princeton Princeton Ocean ModelOcean Model




Numerical ocean modelingNumerical ocean modelingNumerical ocean modelingNumerical ocean modeling

InitialInitial- and - and BoundaryBoundary-value problems-value problems

InitialInitial- and - and BoundaryBoundary-value problems-value problems

ThreeThree major difficulties major difficultiesThreeThree major difficulties major difficulties

Uncertainty Uncertainty

of the of the initial initial

velocity velocity conditioncondition


of the of the initial initial

velocity velocity conditioncondition


of the of the open open

boundary boundary conditioncondition


of the of the open open

boundary boundary conditioncondition

Uncertainty Uncertainty of the of the

atmospheric atmospheric

forcingforcing

Uncertainty Uncertainty of the of the

atmospheric atmospheric

forcingforcing

It is important for us to It is important for us to investigate investigate the response of a the response of a

ocean model to these ocean model to these uncertaintiesuncertainties. .

It is important for us to It is important for us to investigate investigate the response of a the response of a

ocean model to these ocean model to these uncertaintiesuncertainties. .



• JESJES Geography & Geography & bottom bottom topographytopography



• JESJES Geography & Geography & bottom bottom topographytopography


Tatar StraitTatar Strait (connects with the Okhotsk SeaOkhotsk Sea)

Tatar StraitTatar Strait (connects with the Okhotsk SeaOkhotsk Sea)

Soya StraitSoya Strait (connects with the Okhotsk SeaOkhotsk Sea)

Soya StraitSoya Strait (connects with the Okhotsk SeaOkhotsk Sea)

Tsugaru StraitTsugaru Strait (connects with the North North PacificPacific)

Tsugaru StraitTsugaru Strait (connects with the North North PacificPacific)

Korea/Tsushima Korea/Tsushima StraitStrait (connects with the North North PacificPacific)

Korea/Tsushima Korea/Tsushima StraitStrait (connects with the North North PacificPacific)

IntroductionIntroduction• Three Three

DifficultiesDifficulties• JES JES

Geography & Geography & bottom bottom topographytopography

• Princeton Princeton Ocean ModelOcean Model• General General

informationinformation• Surface & Surface &

lateral lateral boundary boundary forcingforcing

• Two step Two step initializationinitialization







POM : a time-dependent, primitive equation model rendered POM : a time-dependent, primitive equation model rendered on a three-dimensional grid that includes realistic on a three-dimensional grid that includes realistic topography and a free surface. topography and a free surface.

Z=0σ =0

σ =-1

2323 σσ levels levels

10’ (11~15 Km)10’ (11~15 Km)

10’ (18 Km)10’ (18 Km)

91 grid points91 grid points10

0 gr

id p

oin

ts10

0 gr

id p

oin

ts


• Wind stress at each time step is interpolated Wind stress at each time step is interpolated from monthly mean climatological wind stress from monthly mean climatological wind stress from COADS (1945-1989). from COADS (1945-1989).

• Volume transports at open boundaries are Volume transports at open boundaries are specified from historical data. specified from historical data.













MonthMonth Feb.Feb. Apr.Apr. Jun.Jun. Aug.Aug. Oct.Oct. Dec.Dec.

Tatar strait (Tatar strait (inflowinflow)) 0.050.05 0.050.05 0.050.05 0.050.05 0.050.05 0.050.05

Soya strait (Soya strait (outflowoutflow)) -0.1-0.1 -0.1-0.1 -0.4-0.4 -0.6-0.6 -0.7-0.7 -0.4-0.4

Tsugaru strait Tsugaru strait ((outflowoutflow))

-0.25-0.25 -0.35-0.35 -0.85-0.85 -1.45-1.45 -1.55-1.55 -1.05-1.05

Tsushima strait Tsushima strait ((inflowinflow))

0.30.3 0.40.4 1.21.2 2.02.0 2.22.2 1.41.4

Unit: Sv, 1 Sv = 106 m3s-1

IntroductionIntroduction• Three Three

DifficultiesDifficulties• JES JES

Geography & Geography & bottom bottom topographytopography











•From zero velocity and Tc and Sc fields (Levitus).•Wind stress from COADS data & without flux forcing.

•From zero velocity and Tc and Sc fields (Levitus).•Wind stress from COADS data & without flux forcing.

JD-1 JD-360/JD-1 JD-360

The final states are taken as initial conditions for the second step

The final states are taken as initial conditions for the second step

JD-1 JD-360/JD-1 JD-180

I.C.I.C.

I.C.I.C.

F.S.F.S.

F.S. (VVJD180JD180,T,TJD180JD180,S,SJD180JD180)F.S. (VVJD180JD180,T,TJD180JD180,S,SJD180JD180)

The first step:The first step:

The second step:The second step:

•From the final states of the first step.•Wind stress from COADS data & with flux forcing.

•From the final states of the first step.•Wind stress from COADS data & with flux forcing.

The final states are taken as standard initial conditions (VV00,T,T00,S,S00) for the experiments.

The final states are taken as standard initial conditions (VV00,T,T00,S,S00) for the experiments.

Experimental DesignExperimental Design

Experiment Property

0 Control runControl run

1

Uncertain velocity initialization processesvelocity initialization processes2

3

4

5Uncertain wind stresswind stress

6

7Uncertain lateral boundary transportlateral boundary transport

8

9

Combination of uncertaintyCombination of uncertainty10

11


• Control RunControl Run• Uncertain Uncertain

Initial Initial ConditionsConditions

• Uncertain Uncertain Wind ForcingWind Forcing

• Uncertain Uncertain Lateral Lateral TransportTransport

• Combined Combined UncertaintyUncertainty






JD-180 JD-360

I.C.I.C.

•From the standard initial conditions (VV00 = V = VJD180JD180 , T , T00 = T = TJD180JD180 , S , S00 = S = SJD180JD180) .•Lateral transport from historical data and Wind stress from COADS data & with flux forcing.

•From the standard initial conditions (VV00 = V = VJD180JD180 , T , T00 = T = TJD180JD180 , S , S00 = S = SJD180JD180) .•Lateral transport from historical data and Wind stress from COADS data & with flux forcing.

The simulated temperature and salinity fields and circulation pattern are consistent with observational studies (Chu et al. 2003).

The simulated temperature and salinity fields and circulation pattern are consistent with observational studies (Chu et al. 2003).












Experiment Experiment Initial Initial

ConditionsConditionsWind ForcingWind Forcing

Lateral Lateral Boundary Boundary ConditionsConditions

1

V0 = 0 ,

T0 = TJD180,

S0 = SJD180

Same as Run-0 Same as Run-0

2 T0 = TJD180,

S0 = SJD180


3 T0 = TJD180,

S0 = SJD180


4 T0 = TJD180,

S0 = SJD180


( )0 90 ,Diag

DV V

( )0 60 ,Diag

DV V

( )0 30 ,Diag

DV V















55 Same as Run-0Same as Run-0

Adding Gaussian Adding Gaussian random noise with random noise with zero mean and zero mean and 0.5 0.5 m/sm/s noise intensity noise intensity

Same as Run-0Same as Run-0

66 Same as Run-0Same as Run-0


Same as Run-0Same as Run-0














Lateral Boundary Lateral Boundary ConditionsConditions

77 Same as Run-0Same as Run-0 Same as Run-0Same as Run-0

Adding Gaussian Adding Gaussian random noise with random noise with the zero mean and the zero mean and

noise intensity being noise intensity being 5%5% of the transport of the transport

(control run)(control run)

88 Same as Run-0Same as Run-0 Same as Run-0Same as Run-0
















conditionsconditionsWind forcingWind forcing

Lateral Boundary Lateral Boundary ConditionsConditions

9 T0 = TJD180,S0 = SJD180

Adding Gaussian random noise with 1.0 m/s

noise intensity

Same as Run-0

10 T0=TJD180,S0=SJD180

Same as Run-0

Adding Gaussian random noise with noise intensity being 10% of the transport (control run)

11T0=TJD180,S0=SJD180

Adding Gaussian random noise with 1.0 m/s

noise intensity

Adding Gaussian random noise with noise intensity being 10% of the transport (control run)

( )0 30 ,Diag

DV V

( )0 30 ,Diag

DV V

( )0 30 ,Diag

DV V

Statistical Analysis MethodsStatistical Analysis Methods

Model Error :Model Error :Model Error :Model Error :

Root Mean Root Mean Square Error Square Error (RMSE) :(RMSE) :

Root Mean Root Mean Square Error Square Error (RMSE) :(RMSE) :

Relative Root Relative Root Mean Square Mean Square Error (RRMSE) :Error (RRMSE) :

Relative Root Relative Root Mean Square Mean Square Error (RRMSE) :Error (RRMSE) :

2 2

1 1

1( , ) ( , , , ) ( , , , )

y x

u v

M M

i j i j

j i

RMSE z t x y z t x y z tMy Mx

2 2

1 1

1( , ) ( , , , ) ( , , , )

y x

u v

M M

i j i j

j i

RMSE z t x y z t x y z tMy Mx

( , , , ) ( , , , ) ( , , , )c ex y z t x y z t x y z t ( , , , ) ( , , , ) ( , , , )c ex y z t x y z t x y z t

2 2

1 1

2 2

1 1

( , , , ) ( , , , )

( , )

( , , , ) ( , , , )

y x

u v

y x

u v

M M

i j i j

j i

M M

c i j c i j

j i

x y z t x y z t

RRMSE z t

x y z t x y z t

2 2

1 1

2 2

1 1

( , , , ) ( , , , )

( , )

( , , , ) ( , , , )

y x

u v

y x

u v

M M

i j i j

j i

M M

c i j c i j

j i

x y z t x y z t

RRMSE z t

x y z t x y z t

Model Errors Due To Initial Conditions


• Model Error Model Error DistributionDistribution• Horizontal

distribution• Histogram

• Relative Relative Root Mean Root Mean Square Error Square Error (RRMSE)(RRMSE)




The 5The 5thth Day Day The 180The 180thth Day Day


ConditionsConditions

1

V0 = 0 ,

T0 = TJD180,

S0 = SJD180

2 T0 = TJD180,

S0 = SJD180

3 T0 = TJD180,

S0 = SJD180

4 T0 = TJD180,

S0 = SJD180

( )0 90 ,Diag

DV V

( )0 60 ,Diag

DV V

( )0 30 ,Diag

DV V

Model error is decreasing with time.


Difference among each run is < 0.3< 0.3 cm/s


Difference among the four runs is not significant.






• Model Error Model Error DistributionDistribution

• Relative Relative Root Mean Root Mean Square Error Square Error (RRMSE)(RRMSE)• Vertical

Variation• Temporal

Evolution




Evolution

75% 75% In Run 1In Run 1


The 5The 5thth Day Day



50%50%

20%20%

Effects to the horizontal velocity prediction are quite significant.


No obvious difference among these four runs.

No obvious difference among these four runs.

The 180The 180thth Day Day

Model Errors Due To Wind Forcing








Experiment Experiment Wind ForcingWind Forcing

55


66


Model error is increasing with time.


Larger model error in Run 6.







Evolution




Evolution










28%28%

11%11%

Run 5Run 5

Run 6Run 6

Model Errors Due To Open Boundary Conditions








Experiment Experiment Lateral Boundary Lateral Boundary

ConditionsConditions

77




88













Evolution




Evolution







28% 28% In Run 8In Run 823% 23%

In Run 8In Run 8


17%17%

34%34%

Run 7Run 7 Run 8Run 8

Model Errors Due To Combined UncertaintyModel Errors Due To

Combined Uncertainty• Model Error Model Error

DistributionDistribution• Horizontal






ExperiExperiment ment

Initial Initial conditionsconditions

Wind Wind forcingforcing


9 T0 = TJD180,S0 = SJD180

with 1.0 m/s noise intensity

Same as Run-0

10 T0=TJD180,S0=SJD180

Same as Run-0

with noise intensity being 10% of the transport

11T0=TJD180,S0=SJD180

with 1.0 m/s noise intensity

with noise intensity being 10% of the transport

( )0 30 ,Diag

DV V

( )0 30 ,Diag

DV V

( )0 30 ,Diag

DV V







DistributionDistribution• Horizontal












DistributionDistribution• Relative Relative

Root Mean Root Mean Square Error Square Error (RRMSE)(RRMSE)• Vertical


Evolution




Evolution






78% 78% In Run 11In Run 11

78% 78% In Run 11In Run 11

73% 73% In Run 11In Run 11

73% 73% In Run 11In Run 11

55%55%

30%30%

Run 9Run 9

Run 10Run 10Run 11Run 11

ConclusionsConclusionsFor uncertainFor uncertain velocity initial conditionsvelocity initial conditions : :

• The model errors The model errors decreases decreases with time. with time.

• The model errors with and without The model errors with and without diagnostic initializationdiagnostic initialization are quite are quite comparable and significantcomparable and significant. .

• The The magnitude of model errorsmagnitude of model errors is is less dependentless dependent on the on the diagnostic initialization perioddiagnostic initialization period no matter it is no matter it is 30 day,60 day 30 day,60 day or 90 dayor 90 day. .

•

ExperimentExperiment

Vertically Vertically averaged averaged RRMSERRMSE

Max. RRMSEMax. RRMSE

Min.Min. Max.Max. 55thth Day Day 180180thth Day Day

For uncertainFor uncertain velocity initial velocity initial

conditionsconditions20%20% 50%50%

70%70% near the near the surfacesurface

25%25% near the near the surfacesurface

ConclusionsConclusionsFor uncertainFor uncertain wind forcingwind forcing : :

• The The model errormodel error increases with increases with timetime and and noise intensitynoise intensity. .

•





ForFor 0.5 m/s0.5 m/s noise intensitynoise intensity

8%8% 19%19%35%35% near the near the

surfacesurface50%50% near the near the

surfacesurface

For For 1.0 m/s1.0 m/s noise intensitynoise intensity

11%11% 28%28%60%60% near the near the

surfacesurface80%80% near the near the

surfacesurface

ConclusionsConclusionsFor uncertainFor uncertain lateral boundary transportlateral boundary transport : :

• The The model errormodel error increases with increases with timetime and and noise intensitynoise intensity. .

•





ForFor noise noise intensity as intensity as 5% 5%

ofof transporttransport9%9% 20%20%

14%14% near the near the bottombottom


ForFor noise noise intensity as intensity as 10% 10%

ofof transporttransport17%17% 34%34%



ConclusionsConclusionsFor For combined uncertainty :combined uncertainty :

•

ExperimentExperimentVertically Vertically

averaged RRMSEaveraged RRMSEMax. RRMSEMax. RRMSE


For uncertainFor uncertain initial initial conditioncondition andand wind wind

forcingforcing20%20% 52%52%

70%70% near near the the surfacesurface


For uncertainFor uncertain initial initial conditioncondition andand lateral lateral

boundary transportboundary transport 27%27% 50%50%

65%65% near near the the bottombottom

35%35% near near the the bottombottom

For uncertainFor uncertain initial initial conditioncondition, , wind wind

forcingforcing andand lateral lateral

boundary transportboundary transport

30%30% 55%55%73%73% near near the the surfacesurface


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Question ?Question ?

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Predictability of Japan / East Sea (JES) System to Uncertain Initial / Lateral Boundary Conditions...

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