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Predictability of

Japan / East Sea (JES) System to

Uncertain Initial / Lateral Boundary Conditions

and 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. ChinLCDR. Chin--Lung Fang Lung Fang

OutlineOutlineOutline

• Introduction• Experimental design• Statistical analysis methods • Results• Conclusions

•• IntroductionIntroduction•• Experimental designExperimental design•• Statistical analysis methods Statistical analysis methods •• ResultsResults•• ConclusionsConclusions

IntroductionIntroduction

• Three Difficulties

• JES Geography & bottom topography

• Princeton Ocean Model

•• Three Three DifficultiesDifficulties

•• JES JES Geography & Geography & bottom bottom topographytopography

•• Princeton Princeton Ocean ModelOcean Model

Numerical ocean modelingNumerical ocean modelingNumerical ocean modeling

Initial- and Boundary-value problems

InitialInitial-- and and BoundaryBoundary--value problemsvalue problems

Three major difficultiesThreeThree major difficultiesmajor difficulties

Uncertainty of the initial

velocity condition

Uncertainty Uncertainty of the of the initial initial

velocity velocity conditioncondition

Uncertainty of the open

boundary condition

Uncertainty Uncertainty of the of the open open

boundary boundary conditioncondition

Uncertainty of the

atmospheric forcing

Uncertainty Uncertainty of the of the

atmospheric atmospheric forcingforcing

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

these uncertainties.

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

these uncertaintiesthese uncertainties. .

IntroductionIntroduction


• JESGeography & bottom topography

• Princeton Ocean Model


•• JESJESGeography & Geography & bottom bottom topographytopography

•• Princeton Princeton Ocean ModelOcean Model

Tatar Strait (connects with the Okhotsk Sea)

Tatar StraitTatar Strait (connects with the OkhotskOkhotsk SeaSea)

Soya Strait (connects with the Okhotsk Sea)

Soya StraitSoya Strait (connects with the OkhotskOkhotsk SeaSea)

Tsugaru Strait(connects with the North Pacific)

TsugaruTsugaru StraitStrait(connects with the North North PacificPacific)

Korea/Tsushima Strait (connects with the North Pacific)

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

IntroductionIntroduction• Three

Difficulties• JES

Geography & bottom topography

• Princeton Ocean Model• General

information• Surface &

lateral boundary forcing

• Two step initialization



•• Princeton Princeton Ocean ModelOcean Model•• General General

informationinformation•• Surface & Surface &

lateral lateral boundary boundary forcingforcing

•• Two step Two step initializationinitialization

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

Z=0σ =0

σ =-1

2323σσ levelslevels

1010’’ (11~15 Km)(11~15 Km)

1010’’ (18 Km)(18 Km)

91 grid points91 grid points10

0 gr

id p

oint

s10

0 gr

id p

oint

s

IntroductionIntroduction•• 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 (1945from COADS (1945--1989). 1989).

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


• JES Geography & bottom topography











1.41.42.22.22.02.01.21.20.40.40.30.3Tsushima strait Tsushima strait ((inflowinflow))

--1.051.05--1.551.55--1.451.45--0.850.85--0.350.35--0.250.25TsugaruTsugaru strait strait ((outflowoutflow))

--0.40.4--0.70.7--0.60.6--0.40.4--0.10.1--0.10.1Soya strait (Soya strait (outflowoutflow))

0.050.050.050.050.050.050.050.050.050.050.050.05Tatar strait (Tatar strait (inflowinflow))

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

Unit: Sv, 1 Sv = 106 m3s-1

IntroductionIntroduction• Three

Difficulties• JES

Geography & bottom topography











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

•From zero velocity and Tcand 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. (VJD180,TJD180,SJD180)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 (V0,T0,S0) for the experiments.

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

Experimental DesignExperimental Design

11

10 Combination of uncertaintyCombination of uncertainty

9

8Uncertain lateral boundary transportlateral boundary transport

7

6Uncertain wind stresswind stress

5

4

3

2Uncertain velocity initialization processesvelocity initialization processes

1

Control runControl run0

PropertyExperiment


• Control Run• Uncertain

Initial Conditions

• Uncertain Wind Forcing

• Uncertain Lateral Transport

• Combined Uncertainty

•• 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(V0 = VJD180 , T0 = TJD180 , S0 = SJD180) .•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).



Initial Conditions









Same as Run-0Same as Run-0T0 = TJD180,S0 = SJD180

4


3


2

Same as Run-0Same as Run-0V0 = 0 ,T0 = TJD180,S0 = SJD180

1

Lateral Lateral Boundary Boundary ConditionsConditions

Wind ForcingWind ForcingInitial Initial ConditionsConditionsExperiment Experiment

( )0 90 ,

DiagD=V V

( )0 60 ,

DiagD=V V

( )0 30 ,

DiagD=V V



Initial Conditions









Same as RunSame as Run--00

Adding Gaussian Adding Gaussian random noise with random noise with zero mean and zero mean and 1.0 1.0 m/sm/s noise intensitynoise intensity






Wind ForcingWind ForcingInitial Initial ConditionsConditionsExperiment Experiment



Initial Conditions









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

noise intensity being noise intensity being 10%10% of the transport of the transport

(control run)(control run)

Same as RunSame as Run--00Same as RunSame as Run--0088




Same as RunSame as Run--00Same as RunSame as Run--0077

Lateral Boundary Lateral Boundary ConditionsConditionsWind ForcingWind Forcing

Initial Initial ConditionsConditionsExperiment Experiment



Initial Conditions









T0=TJD180,S0=SJD180

T0=TJD180,S0=SJD180

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

Adding Gaussian random noise with 1.0 m/s

noise intensity

11

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

Same as Run-010

Same as Run-0

Adding Gaussian random noise with 1.0 m/s

noise intensity

T0 = TJD180,S0 = SJD180

9

Lateral Boundary Lateral Boundary ConditionsConditionsWind forcingWind forcing

Initial Initial conditionsconditionsExperiment Experiment

( )0 30 ,

DiagD=V V

( )0 30 ,

DiagD=V V

( )0 30 ,

DiagD=V V

Statistical Analysis MethodsStatistical Analysis Methods

Model Error :Model Error :Model Error :

Root Mean Square Error (RMSE) :

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

Relative Root Mean Square 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

ψ ψ= =

= ∆ + ∆ × ∑∑

( , , , ) ( , , , ) ( , , , )c ex y z t x y z t x y z tψ ψ ψ∆ = −

2 2

1 1

2 2

1 1

( , , , ) ( , , , )( , )

( , , , ) ( , , , )

y x

u v

y x

u v

M M

i j i jj i

M M

c i j c i jj i

x y z t x y z tRRMSE z t

x y z t x y z t

ψ ψ

ψ ψ

= =

= =

∆ +∆ =

+

∑∑

∑∑

Model Errors Due To Initial Conditions


• Model Error Distribution• Horizontal

distribution• Histogram

• Relative Root Mean Square Error (RRMSE)

•• Model Error Model Error DistributionDistribution• Horizontal


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

The 5The 5thth DayDay The 180The 180thth DayDay

T0 = TJD180,S0 = SJD180

4

T0 = TJD180,S0 = SJD180

3

T0 = TJD180,S0 = SJD180

2

V0 = 0 ,T0 = TJD180,S0 = SJD180

1

Initial Initial ConditionsConditionsExperiment Experiment

( )0 90 ,

DiagD=V V

( )0 60 ,

DiagD=V V

( )0 30 ,

DiagD=V V

Model error is decreasing with time.


Difference among each run is < 0.3 cm/s

Difference among each run is < 0.3< 0.3 cm/sDifference among the

four runs is not significant.

Difference among the four runs is not significant.

Difference among each run is < 0.15 cm/s

Difference among each run is < 0.15< 0.15 cm/s













Difference among each run is < 0.2cm/s

Difference among each run is < 0.2< 0.2cm/s

Difference among each run is < 0.1cm/s

Difference among each run is < 0.1< 0.1cm/s



• Model Error Distribution

• Relative Root Mean Square Error (RRMSE)• Vertical

Variation• Temporal

Evolution

•• Model Error Model Error DistributionDistribution

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


Evolution

75% In Run 1

75% 75% In Run 1In Run 1

The 5The 5thth DayDay

26% In Run 2


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 DayDay

Model Errors Due To Wind Forcing









66


55

Wind ForcingWind ForcingExperiment Experiment

Model error is increasing with time.


Larger model error in Run 6.







Evolution




Evolution






58% In Run 6


76% In Run 6


28%28%

11%11%

Run 5Run 5

Run 6Run 6

Model Errors Due To Open Boundary Conditions











88




77

Lateral Boundary Lateral Boundary ConditionsConditionsExperiment Experiment










Evolution




Evolution






28% In Run 8

28% 28% In Run 8In Run 823%

In 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







T0=TJD180,S0=SJD180

T0=TJD180,S0=SJD180

with noise intensity being 10%of the transport

with 1.0 m/s noise intensity

11

with noise intensity being 10%of the transport

Same as Run-010

Same as Run-0

with 1.0 m/s noise intensity

T0 = TJD180,S0 = SJD180

9


Wind Wind forcingforcing

Initial Initial conditionsconditions

ExperExperiment iment

( )0 30 ,

DiagD=V V

( )0 30 ,

DiagD=V V

( )0 30 ,

DiagD=V V









Evolution




Evolution






78% In Run 11

78% 78% In Run 11In Run 11

73% In 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. .

••

25%25% near the near the surfacesurface

70%70% near the near the surfacesurface50%50%20%20%

For uncertainFor uncertainvelocity initial velocity initial

conditionsconditions

180180thth DayDay55thth DayDayMax.Max.Min.Min.

Max. RRMSEMax. RRMSEVertically Vertically averaged averaged RRMSERRMSEExperimentExperiment

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/snoise intensitynoise intensity



For For 1.0 m/s1.0 m/snoise intensitynoise intensity



ConclusionsConclusionsFor uncertainFor uncertain lateral boundary transportlateral boundary transport ::

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

18%18% near the near the bottombottom

14%14% near the near the bottombottom20%20%9%9%

ForFor noise noise intensity as intensity as 5% 5%

ofof transporttransport

28%28% near the near the bottombottom

24%24% near the near the bottombottom34%34%17%17%

ForFor noise noise intensity as intensity as 10% 10%

ofof transporttransport



ConclusionsConclusionsFor For combined uncertainty :combined uncertainty :

••

35%35% near near the the bottombottom

65%65% near near the the bottombottom50%50%27%27%

For uncertainFor uncertain initial initial conditioncondition andand lateral lateral boundary transportboundary transport

77%77% near near the the surfacesurface

70%70% near near the the surfacesurface52%52%20%20%

For uncertainFor uncertain initial initial conditioncondition andand wind wind

forcingforcing

78%78% near near the the surfacesurface

73%73% near near the the surfacesurface55%55%30%30%

For uncertainFor uncertain initial initial conditioncondition, , wind wind

forcingforcing andand lateral lateral boundary transportboundary transport


Max. RRMSEMax. RRMSEVertically Vertically averaged RRMSEaveraged RRMSEExperimentExperiment

????

Question ?Question ?

Thank you !!Thank you !!

Predictability of Japan / East Sea (JES) System to Uncertain Initial / Lateral Boundary Conditions and Surface WindsOutlineThank you !!

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