Diagnostic initialization generated extremely strong thermohaline sources sinks in south china sea
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Diagnostic Initialization Generated Extremely Strong Thermohaline Sources & Sinks in South China Sea . MAJ Ong Ah Chuan RSN, USW. SCOPE. Problems of the Diagnostic Initialization Proposed Research in this Thesis Environment of the South China Sea Experiment Design

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Diagnostic initialization generated extremely strong thermohaline sources sinks in south china sea
Diagnostic Initialization Generated Extremely Strong Thermohaline Sources & Sinks in South China Sea

MAJ Ong Ah Chuan

RSN, USW


Scope
SCOPE Thermohaline Sources & Sinks in South China Sea

  • Problems of the Diagnostic Initialization

  • Proposed Research in this Thesis

  • Environment of the South China Sea

  • Experiment Design

  • Sensitivity Study Result and Analysis

  • Conclusion


Numerical ocean modeling
NUMERICAL OCEAN MODELING Thermohaline Sources & Sinks in South China Sea

  • Ocean modeling - Need reliable data for specifying initial condition

  • Past observations - Contributed greatly to T & S fields

  • (Tc, Sc) obtained from NODC or GDEM as initial T & S fields

  • Initial Vc usually not available

  • Initialization of Vc important

  • To accurately predict ocean – need a reliable initialization 

N Equatorial Current

South China Sea

Model output


Problems of diagnostic initialization
PROBLEMS OF DIAGNOSTIC INITIALIZATION Thermohaline Sources & Sinks in South China Sea

  • Widely used model initialization - diagnostic mode

  • Integrates model from (Tc, Sc), zero Vc & holding (Tc, Sc) unchanged

  • After diagnostic run, a quasi-steady state & Vc is established  

  • (Tc, Sc, Vc) are treated as the initial conditions


Problems of diagnostic initialization1
PROBLEMS OF DIAGNOSTIC INITIALIZATION Thermohaline Sources & Sinks in South China Sea

  • Initial condition error can drastically affect the model

  • Diagnostic mode initialization extensively used - need to examine reliability  

  • Chu & Lan [2003, GRL] has pointed out the problems:

    • - Artificially adding extremely strong heat/salt sources or sinks


Problems of diagnostic initialization2
PROBLEMS OF DIAGNOSTIC INITIALIZATION Thermohaline Sources & Sinks in South China Sea

  • Horizontal momentum equation   – (1)

  • Temp & Salinity equations – (2) and (3)

----- (1)

------------------ (2)

------------------ (3)

  • (KM, KH) – Vertical eddy diffusivity

  • (Hv, HT, HS) – Horizontal diffusion & subgrid processes causing change (V, T, S )


Problems of diagnostic initialization3
PROBLEMS OF DIAGNOSTIC INITIALIZATION Thermohaline Sources & Sinks in South China Sea

------- (1)

------------------ (2)

------------------ (3)

  • Diagnostic initialization integrate (1)-(3):

  • with T and S unchanged


Problems of diagnostic initialization4

------------------ (5) Thermohaline Sources & Sinks in South China Sea

------------------ (6)

PROBLEMS OF DIAGNOSTIC INITIALIZATION

  • Analogous to adding heat & salt source/sink terms (FT, FS)

  • (2) & (3) becomes:

Keeping :

------------------ (7)

  • Combining (5), (6) & (7):


Problems of diagnostic initialization5

, Thermohaline Sources & Sinks in South China Sea

PROBLEMS OF DIAGNOSTIC INITIALIZATION

------------------- (8)

------------------- (9)

are artificially generated at each time step

  • Examine these source/sink terms

  • POM is implemented for the SCS


Princeton ocean model alan blumberg george mellor 1977
PRINCETON OCEAN MODEL Thermohaline Sources & Sinks in South China Sea (Alan Blumberg & George Mellor, 1977)

  • POM: time-dependent, primitive equation numerical model on a 3-D

  • Includes realistic topography & a free surface

  • Sigma coordinate model

s ranges from s = 0 at z = h to s = -1 at z = -H

  • Sigma coordinate - Dealing with significant topographical variability


Criteria for strength of source sink
CRITERIA FOR STRENGTH OF SOURCE/SINK Thermohaline Sources & Sinks in South China Sea

  • Chu & Lan [2003, GRL] had proposed criteria for strength of artificial source & sink

  • Based on SCS, maximum variability of T, S: 35oC & 15 ppt

  • Max rates of absolute change of T, S data:

  • These values are used as standard measures for ‘source/sink’

----- (10)


Criteria for strength of source sink1
CRITERIA FOR STRENGTH OF SOURCE/SINK Thermohaline Sources & Sinks in South China Sea

  • Twenty four times of (10) represents strong ‘source/sink’ :

----- (11)

  • Ten times of (11) represents extremely strong ‘source/sink’

------ (12)

  • (10), (11) & (12) to measure the heat/salt ‘source/sink’ terms generated


Areas of research in this thesis
AREAS OF RESEARCH IN THIS THESIS Thermohaline Sources & Sinks in South China Sea

  • Chu & Lan [2003] found the problem:

    • Generation of spurious heat/salt sources and sinks

    • Did not analyze uncertainty of initialized V to the uncertainty of horizontal eddy viscosity & duration of initialization

  • Thesis Demonstrate:

    • -Duration of diagnostic initialization needed to get initial V ?

    • - Uncertainty of C affect artificial heat & salt sources/sinks ?

    • - Uncertainty of C affect initial V from diagnostic initialization ?

    • - Uncertainty of V due to uncertain duration ?


Areas of research in this thesis1
AREAS OF RESEARCH IN THIS THESIS Thermohaline Sources & Sinks in South China Sea

  • Area of study: SCS

  • POM implemented for SCS to investigate physical outcome of diagnostic initialization

  • NODC annual mean (Tc, Sc)

  • SCS initialized diagnostically for 90 days (C = 0.05, 0.1, 0.2 & 0.3)

  • 60th Day V with C = 0.2 taken as reference


Environment of south china sea

SCS Area = 3.5 x 10 Thermohaline Sources & Sinks in South China Sea 6 km2

Sill depth:

2600 m

ENVIRONMENT OF SOUTH CHINA SEA

  • Largest marginal sea in Western Pacific Ocean

  • Large shelf regions & deep basins

  • Deepest water confined to a bowl-type trench

  • South of 5°N, depth drops to 100m


Environment of south china sea1
ENVIRONMENT OF SOUTH CHINA SEA Thermohaline Sources & Sinks in South China Sea

Climatological wind stress

  • Subjected to seasonal monsoon system

  • Summer: SW monsoon (0.1 N/m2 )

  • Winter: NE monsoon (0.3 N/m2)

  • Transitional periods - highly variable winds & currents

Jun

Dec


Environment of south china sea2

Kuroshio Thermohaline Sources & Sinks in South China Sea

Luzon Strait

Sill depth: 2600 m

South China

Sea

Jun

ENVIRONMENT OF SOUTH CHINA SEA

  • Circulation of intermediate to upper layers: local monsoon systems & Kuroshio

  • Kuroshio enters through southern side of channel, executes a tight, anticyclonic turn

  • Kuroshio excursion near Luzon Strait, anti-cyclonic rings detached


Environment of south china sea3

Winter

Summer

ENVIRONMENT OF SOUTH CHINA SEA


Scs model input into pom for diagnostic run
SCS MODEL INPUT INTO POM FOR DIAGNOSTIC RUN Thermohaline Sources & Sinks in South China Sea

  • 125 x 162 x 23 horizontally grid points with 23 s - levels

  • Model domain: 3.06°S to 25.07°N, & from 98.84°E to 121.16°E

  • Bottom topography: DBDB 5’ resolution

  • Horizontal diffusivities are modeled using Smagorinsky form (C = 0.05, 0.1, 0.2 and 0.3)

  • No atmospheric forcing


Scs model input into pom for diagnostic run1
SCS MODEL INPUT INTO POM FOR DIAGNOSTIC RUN Thermohaline Sources & Sinks in South China Sea

  • Closed lateral boundaries

    • Free slip condition

    • Zero gradient condition for temp & salinity

  • No advective or diffusive heat, salt or velocity fluxes through boundaries

  • Open boundaries, radiative boundary condition with zero vol transport


Experiment design
EXPERIMENT DESIGN Thermohaline Sources & Sinks in South China Sea

  • Analyze impact of uncertainty of C to initialized V

  • 1 control run, 3 sensitivity runs of POM

  • Control run: C = 0.2, Sensitivity runs: C = 0.05, 0.1 & 0.3

  • Assess duration of initialization & impact on Vunder different C

  • - diagnostic model was integrated 90 days

  • - 60th day of model result used as reference

  • - RRMSD of V between day-60 & day-i (i = 60, 61,62…...90)

  • Investigate sensitivity of V to uncertainty of initialization period


Experiment design1
EXPERIMENT DESIGN Thermohaline Sources & Sinks in South China Sea

  • POM diagnostic mode integrated with 3 components of V = 0

  • Temp & salinity specified by interpolating annual mean data

  • FT & FS obtained at each time step

  • Horizontal distributions of FT & FS derived & compared to measures established earlier

  • Horizontal mean | FT | & | FS | to identify overall strength of heat & salt source/sink


Experiment design2
EXPERIMENT DESIGN Thermohaline Sources & Sinks in South China Sea

  • 30 days for mean model KE to reach quasi-steady state

Figure 7. Model Day: 90 days with C = 0.05

Figure 8. Model Day: 90 days with C = 0.1


Experiment design3
EXPERIMENT DESIGN Thermohaline Sources & Sinks in South China Sea

  • (FT, FS) generated on day-30, day-45, day-60 & day-90

  • Identify their magnitudes & sensitivity to the integration period

Figure 9. Model Day: 90 days with C = 0.2

Figure 10. Model Day: 90 days with C = 0.3


Result of sensitivity study
RESULT OF SENSITIVITY STUDY Thermohaline Sources & Sinks in South China Sea

  • Horizontal distribution of FT (°C hr-1)

  • - at 4 levels (surface, subsurface, mid-level, near bottom)

  • - with 4 different C-values

  • Show extremely strong heat sources/sinks

  • Unphysical sources/sinks have various scales and strengths

  • Reveal small- to meso-scale patterns


H orizontal distribution of f t

Max Value = 2.331 Thermohaline Sources & Sinks in South China Sea

Min Value = - 0.987

Unit: C/hr

Max Value = 1.872

Min Value = - 2.983

Unit: C/hr

Max Value = 1.682

Min Value = - 0.591

Unit: C/hr

Max Value = 0.374

Min Value = - 0.367

Unit: C/hr

HORIZONTAL DISTRIBUTION OF FT

  • Max Heat Source = 2778 Wm-3

  • Features consistent for different C-values

Max Heat Sink = -3555 Wm-3

On day-60 with

C = 0.05


H orizontal distribution of f t1

Max Value = 2.338 Thermohaline Sources & Sinks in South China Sea

Min Value = - 0.595

Unit: C/hr

Max Value = 1.724

Min Value = - 2.001

Unit: C/hr

Max Value = 1.627

Min Value = - 0.595

Unit: C/hr

Max Value = 0.314

Min Value = - 0.364

Unit: C/hr

HORIZONTAL DISTRIBUTION OF FT

Max Heat Source = 2787 Wm-3

Max Heat Sink = -2385 Wm-3

On day-60 with

C = 0.1


H orizontal distribution of f t2

Max Value = 2.337 Thermohaline Sources & Sinks in South China Sea

Min Value = - 0.348

Unit: C/hr

Max Value = 1.332

Min Value = - 1.016

Unit: C/hr

Max Value = 1.632

Min Value = - 0.602

Unit: C/hr

Max Value = 0.287

Min Value = - 0.369

Unit: C/hr

HORIZONTAL DISTRIBUTION OF FT

Max Heat Source = 2785 Wm-3

Max Heat Sink = -1211 Wm-3

  • C-value increases, FT weakens

  • Still above extremely strong heat source criterion

On day-60 with

C = 0.2


H orizontal distribution of f t3

Max Value = 2.331 Thermohaline Sources & Sinks in South China Sea

Min Value = - 0.346

Unit: C/hr

Max Value = 1.013

Min Value = - 0.908

Unit: C/hr

Max Value = 1.661

Min Value = - 0.607

Unit: C/hr

Max Value = 0.277

Min Value = - 0.363

Unit: C/hr

HORIZONTAL DISTRIBUTION OF FT

Max Heat Source = 2778 Wm-3

Max Heat Sink = -1082 Wm-3

  • large C cause unrealistically strong diffusion in ocean model

On day-60 with

C = 0.3


Result of sensitivity study1
RESULT OF SENSITIVITY STUDY Thermohaline Sources & Sinks in South China Sea

  • Horizontal distribution of FS (ppt hr-1)

  • - at 4 levels (surface, subsurface, mid-level, near bottom)

  • - with 4 different C-values

  • Show strong salinity sources/sinks

  • Unphysical sources/sinks have various scales and strengths

  • Reveal small- to meso-scale patterns


H orizontal distribution of f s

Max Value = 0.372 Thermohaline Sources & Sinks in South China Sea

Min Value = - 0.115

Unit: ppt/hr

Max Value = 0.134

Min Value = - 0.198

Unit: ppt/hr

Max Value = 0.019

Min Value = - 0.067

Unit: ppt/hr

Max Value = 0.014

Min Value = - 0.016

Unit: ppt/hr

HORIZONTAL DISTRIBUTION OF FS

  • Max Salinity Source = 0.372 ppt hr-1

  • Features similar for different C-values

Max Salinity Sink = -0.198 ppt hr-1

On day-60 with

C = 0.05


H orizontal distribution of f s1

when Thermohaline Sources & Sinks in South China Sea C-value increases, FS weakens

Max Value = 0.372

Min Value = - 0.085

Unit: ppt/hr

Max Value = 0.079

Min Value = - 0.198

Unit: ppt/hr

Max Value = 0.018

Min Value = - 0.066

Unit: ppt/hr

Max Value = 0.011

Min Value = - 0.012

Unit: ppt/hr

HORIZONTAL DISTRIBUTION OF FS

Max Salinity Source = 0.372 ppt hr-1

Max Salinity Sink = -0.198 ppt hr-1

On day-60 with

C = 0.1


H orizontal distribution of f s2

Max Value = 0.373 Thermohaline Sources & Sinks in South China Sea

Min Value = - 0.075

Unit: ppt/hr

Max Value = 0.065

Min Value = - 0.199

Unit: ppt/hr

Max Value = 0.013

Min Value = - 0.067

Unit: ppt/hr

Max Value = 0.009

Min Value = - 0.011

Unit: ppt/hr

HORIZONTAL DISTRIBUTION OF FS

Max Salinity Source = 0.373 ppt hr-1

Max Salinity Sink = -0.199 ppt hr-1

On day-60 with

C = 0.2


H orizontal distribution of f s3

Max Salinity Sink = -0.200 ppt hr Thermohaline Sources & Sinks in South China Sea -1

when C-value increases, FS weakens

But above criterion

Max Value = 0.378

Min Value = - 0.075

Unit: ppt/hr

Max Value = 0.055

Min Value = - 0.200

Unit: ppt/hr

On day-60 with

C = 0.3

Max Value = 0.011

Min Value = - 0.068

Unit: ppt/hr

Max Value = 0.008

Min Value = - 0.011

Unit: ppt/hr

HORIZONTAL DISTRIBUTION OF FS

Max Salinity Source = 0.378 ppt hr-1


Result of sensitivity study2
RESULT OF SENSITIVITY STUDY Thermohaline Sources & Sinks in South China Sea

  • Horizontal mean | FT | :

  • Identify overall strength of heat source/sink

  • Figure 21 to 24: temporal evolution at 4 levels:

    • Near surface ( = –0.0125)

    • Subsurface ( = –0.15)

    • Mid-level ( = –0.5)

    • Near bottom ( = –0.95)

----- (17)


H orizontal mean f t
H Thermohaline Sources & Sinks in South China Sea ORIZONTAL MEAN | FT |

  • Mean |FT| increases rapidly with time

  • Oscillate around quasi-stationary value

  • Large - Mean |FT| based on horizontal average

Figure 21. Temporal evolution at 4 different levels with C = 0.05


H orizontal mean f t1
H Thermohaline Sources & Sinks in South China Sea ORIZONTAL MEAN | FT |

  • Mean |FT| increases rapidly with time

  • Oscillate around quasi-stationary value

  • Similar features observed at other C-values

Figure 22. Temporal evolution at 4 different levels with C = 0.1


H orizontal mean f t2
H Thermohaline Sources & Sinks in South China Sea ORIZONTAL MEAN | FT |

  • Mean |FT| increases rapidly with time

  • Oscillate around quasi-stationary value

  • Strength mean |FT| decreases across corresponding level when C increases

Figure 23. Temporal evolution at 4 different levels with C = 0.2


H orizontal mean f t3
H Thermohaline Sources & Sinks in South China Sea ORIZONTAL MEAN | FT |

  • Mean |FT| increases rapidly with time

  • Oscillate around quasi-stationary value

  • Strength mean |FT| decreases across corresponding level when C increases

Figure 24. Temporal evolution at 4 different levels with C = 0.3


Depth profile of mean f t
DEPTH PROFILE OF Thermohaline Sources & Sinks in South China Sea MEAN | FT |

  • Max mean |FT| at subsurface

  • Min at mid-level

  • Different C values, max & min mean |FT| occurred at different levels

Figure 25. Depth Profile with C = 0.05


Depth profile of mean f t1
DEPTH PROFILE OF Thermohaline Sources & Sinks in South China Sea MEAN | FT |

  • Max mean |FT| at subsurface

  • Min at surface

  • Different C values, max & min mean |FT| occurred at different levels

Figure 26. Depth Profile with C = 0.1


Depth profile of mean f t2
DEPTH PROFILE OF Thermohaline Sources & Sinks in South China Sea MEAN | FT |

  • Max near bottom

  • Higher value indicates a greater heat sources & sinks problem

  • Min at surface

Figure 27. Depth Profile with C = 0.2


Depth profile of mean f t3
DEPTH PROFILE OF Thermohaline Sources & Sinks in South China Sea MEAN | FT |

  • Max at bottom

  • Higher value indicates a greater heat sources & sinks problem

  • Min at surface

Figure 28. Depth Profile with C = 0.3


Result of sensitivity study3
RESULT OF SENSITIVITY STUDY Thermohaline Sources & Sinks in South China Sea

  • Horizontal mean | FS | :

  • Identify overall strength of salt source/sink

  • Figure 29 to 32: temporal evolution at 4 levels:

    • Near surface ( = –0.0125)

    • Subsurface ( = –0.15)

    • Mid-level ( = –0.5)

    • Near bottom ( = –0.95)


H orizontal mean f s
H Thermohaline Sources & Sinks in South China Sea ORIZONTAL MEAN | FS |

  • Mean |FS| increases rapidly with time

  • Peak value of 0.0137 ppt hr-1

  • Oscillate around quasi-stationary value

Figure 29. Temporal evolution at 4 different levels with C = 0.05


H orizontal mean f s1
H Thermohaline Sources & Sinks in South China Sea ORIZONTAL MEAN | FS |

  • Mean |FS| increases rapidly with time

  • Peak value of 0.0127 ppt hr-1

  • Oscillate around quasi-stationary value

Figure 30. Temporal evolution at 4 different levels with C = 0.1


H orizontal mean f s2
H Thermohaline Sources & Sinks in South China Sea ORIZONTAL MEAN | FS |

  • Mean |FS| increases rapidly with time

  • Peak value of 0.0124 ppt hr-1

  • Oscillate around quasi-stationary value

Figure 31. Temporal evolution at 4 different levels with C = 0.2


H orizontal mean f s3
H Thermohaline Sources & Sinks in South China Sea ORIZONTAL MEAN | FS |

  • Peak value of 0.0121 ppt hr-1

  • Strength of Mean |FS| decreases across corresponding level when C increases

Figure 32. Temporal evolution at 4 different levels with C = 0.3


Depth profile of mean f s
DEPTH PROFILE OF Thermohaline Sources & Sinks in South China Sea MEAN | FS |

  • Mean |FS| - max value at surface

  • Oscillates with decreasing value as depth increases

  • Higher value indicates a greater salt sources & sinks problem

  • Min occurred at bottom

Figure 33. Depth Profile with C = 0.05


Depth profile of mean f s1
DEPTH PROFILE OF Thermohaline Sources & Sinks in South China Sea MEAN | FS |

  • Max value at surface

  • Oscillates with decreasing value as depth increases

  • Min occurred at bottom

  • Similar pattern for other C-values

Figure 34. Depth Profile with C = 0.1


Depth profile of mean f s2
DEPTH PROFILE OF Thermohaline Sources & Sinks in South China Sea MEAN | FS |

  • Max value at surface

  • Oscillates with decreasing value as depth increases

  • Min occurred at bottom

Figure 35. Depth Profile with C = 0.2


Depth profile of mean f s3
DEPTH PROFILE OF Thermohaline Sources & Sinks in South China Sea MEAN | FS |

  • Greater salting rate at surface

  • Strength decreases across corresponding level when C-value increases

Figure 36. Depth Profile with C = 0.3


Result of sensitivity study4
RESULT OF SENSITIVITY STUDY Thermohaline Sources & Sinks in South China Sea

  • Uncertainty of Diagnostically initialized V due to uncertainty of C ?

  • V on 60th day for 4 levels for each of 4 C-values are plotted in Figures 37 to 40 for illustrations

    • Near surface ( = –0.0125)

    • Subsurface ( = –0.15)

    • Mid-level ( = –0.5)

    • Near bottom ( = –0.95)


Uncertainty of diagnostically initialized v
UNCERTAINTY OF DIAGNOSTICALLY INITIALIZED Thermohaline Sources & Sinks in South China Sea V

  • Surface & subsurface circulation heads southward in an anti-cyclonic pattern

  • Large uncertainty in these V , RRMSDV > 60%

  • Anti-cyclonic circulation contained within SCS

  • Consistent with model set-up of 0 volume transport

Day-60 with C = 0.05


Uncertainty of diagnostically initialized v1
UNCERTAINTY OF DIAGNOSTICALLY INITIALIZED Thermohaline Sources & Sinks in South China Sea V

  • Another anti-cyclonic eddy-like structure centered at (14N, 117E)

  • Near bottom of SCS, this anti-cyclonic eddy-like structure is more pronounced when C is small

Day-60 with C = 0.1


Uncertainty of diagnostically initialized v2
UNCERTAINTY OF DIAGNOSTICALLY INITIALIZED Thermohaline Sources & Sinks in South China Sea V

  • Near bottom of SCS, anti-cyclonic eddy-like structure more pronounced when C is small

Day-60 with C = 0.2


Uncertainty of diagnostically initialized v3
UNCERTAINTY OF DIAGNOSTICALLY INITIALIZED Thermohaline Sources & Sinks in South China Sea V

  • Near bottom of SCS, anti-cyclonic eddy-like structure more pronounced when C is small

Day-60 with C = 0.3


Result of sensitivity study5
RESULT OF SENSITIVITY STUDY Thermohaline Sources & Sinks in South China Sea

  • Uncertainty of C-value affect V derived from the diagnostic initiation process ?

  • 4 different C-values (0.05, 0.1, 0.2 and 0.3) were used

----------- (17)

----------- (18)


Relative root mean square difference of the horizontal velocity rrmsdv

Day of diagnostic run. Thermohaline Sources & Sinks in South China Sea  = -0.0125

Day of diagnostic run.  = -0.15

Day of diagnostic run.  = -0.5

Day of diagnostic run.  = -0.95

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE HORIZONTAL VELOCITY (RRMSDV)

  • RRMSDV(k,C) increases with time rapidly

  • Oscillate around quasi-stationary value between 0.6 & 0.8

  • Largest value is between C = 0.05 & C = 0.2 (control run)

Figure 41. RRMSDV(k, 0.05)


Relative root mean square difference of the horizontal velocity rrmsdv1

RRMSDV Thermohaline Sources & Sinks in South China Sea

RRMSDV

RRMSDV

RRMSDV

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE HORIZONTAL VELOCITY (RRMSDV)

  • Vertical profile of RRMSDV(k, C) has a max at mid-level for different cases of C-values

  • Indicates strong variation of V in mid-level of SCS

  • Decreases with depth from mid-level to bottom

Figure 42. RRMSDV(k, 0.05)


Relative root mean square difference of the vertical velocity rrmsdw

Day of diagnostic run. Thermohaline Sources & Sinks in South China Sea  = -0.0125

Day of diagnostic run.  = -0.15

Day of diagnostic run.  = -0.5

Day of diagnostic run.  = -0.95

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE VERTICAL VELOCITY (RRMSDW)

  • RRMSDW(k,C) increases with time rapidly

  • Largest value is between C = 0.05 & C = 0.2 (control run)

  • RRMSDW(k,C) is much larger than RRMSDV(k,C)

  • Smaller magnitude & larger uncertainty of W

Figure 43. RRMSDW(k, 0.05)


Relative root mean square difference of the vertical velocity rrmsdw1

RRMSDW Thermohaline Sources & Sinks in South China Sea

RRMSDW

RRMSDW

RRMSDW

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE VERTICAL VELOCITY (RRMSDW)

  • Vertical profile of RRMSDW(k, C) decreases from surface to bottom

  • Decreased rate of decrease of RRMSDW(k, C)

Figure 44. RRMSDW(k, 0.05)


Relative root mean square difference of the horizontal velocity rrmsdv2

Day of diagnostic run. Thermohaline Sources & Sinks in South China Sea  = -0.0125

Day of diagnostic run.  = -0.15

Day of diagnostic run.  = -0.5

Day of diagnostic run.  = -0.95

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE HORIZONTAL VELOCITY (RRMSDV)

  • RRMSDV(k, C) decreases when C-value increases

  • Max RRMSDV(k,C=0.1) > 0.5

Figure 45. RRMSDV(k, 0.1)


Relative root mean square difference of the horizontal velocity rrmsdv3

Day of diagnostic run. Thermohaline Sources & Sinks in South China Sea  = -0.0125

Day of diagnostic run.  = -0.15

Day of diagnostic run.  = -0.5

Day of diagnostic run.  = -0.95

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE HORIZONTAL VELOCITY (RRMSDV)

  • RRMSDV(k, C) decreases when C-value increases

  • RRMSDV(k,C =0.3) > 0.35

  • Larger C-value lead to smaller RRMSDV(k, C)

  • Excessively large C cause unrealistically strong diffusion in ocean model

Figure 46. RRMSDV(k, 0.3)


Relative root mean square difference of the vertical velocity rrmsdw2

Day of diagnostic run. Thermohaline Sources & Sinks in South China Sea  = -0.0125

Day of diagnostic run.  = -0.15

Day of diagnostic run.  = -0.5

Day of diagnostic run.  = -0.95

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE VERTICAL VELOCITY (RRMSDW)

  • RRMSDW(k, C) decreases when C-value increases

  • RRMSDW(k, C=0.1 & C=0.05) > 1

Figure 47. RRMSDW(k, 0.1)


Relative root mean square difference of the vertical velocity rrmsdw3

Day of diagnostic run. Thermohaline Sources & Sinks in South China Sea  = -0.0125

Day of diagnostic run.  = -0.15

Day of diagnostic run.  = -0.5

Day of diagnostic run.  = -0.95

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE VERTICAL VELOCITY (RRMSDW)

  • RRMSDW(k, C) decreases when C-value increases

  • RRMSDW(k, C=0.3) > 0.6

Figure 48. RRMSDW(k, 0.3)


Uncertainty of v c due to uncerntain length of diagnostic integration
UNCERTAINTY OF V Thermohaline Sources & Sinks in South China Sea c DUE TO UNCERNTAIN LENGTH OF DIAGNOSTIC INTEGRATION

  • How long diagnostic integration is needed?

  • 30 days of diagnostic run, quasi-steady state is achieved

  • 60th day selected to compute RRMSDV & RRMSDW

----------- (17)

----------- (18)

t = 60, 61, 62 ….90


Relative root mean square difference of the horizontal velocity rrmsdv t
RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE HORIZONTAL VELOCITY ( RRMSDV(t) )

C =0.05

C= 0.1

  • RRMSDV(t) fluctuates irregularly

  • Increases with time rapidly from day-60 to day-70

  • Cincreases, RRMSDV(t) decreases

C=0.3

C= 0.2

Figure 49. RRMSDV(t)


Relative root mean square difference of the vertical velocity rrmsdw t

C =0.05 VELOCITY ( RRMSDV(t) )

C= 0.1

C=0.3

C= 0.2

RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE VERTICAL VELOCITY ( RRMSDW(t) )

  • RRMSDW(t) fluctuates irregularly

  • Increases with time rapidly

  • Both RRMSDV(t) and RRMSDW(t) fluctuate irregularly with time

Figure 50. RRMSDW(t)


Conclusion
CONCLUSION VELOCITY ( RRMSDV(t) )

  • Strong thermohaline source/sink terms generated for C = 0.05, 0.1, 0.2 & 0.3

  • Horizontal distributions of thermohaline source/sink terms show extremely strong sources/sinks

  • C increases, sources/sinks decrease in magnitude, but still above the criteria

  • Larger C lead to smaller spurious sources & sinks


Conclusion1

------------------ (5) VELOCITY ( RRMSDV(t) )

------------------ (6)

CONCLUSION

  • Uncertainty of C-value affect Vc significantly

  • Uncertainty of diagnostic integration period affects drastically the uncertainty in initialized Vc

  • Extremely strong & spatially non-uniform initial heating/cooling rates are introduced into ocean models


Smagorinsky formula
SMAGORINSKY FORMULA VELOCITY ( RRMSDV(t) )

  • C is the horizontal viscosity parameter

Where


Criteria for strength of source sink2
CRITERIA FOR STRENGTH OF SOURCE/SINK VELOCITY ( RRMSDV(t) )

  • Standard measures for ‘source/sink’

----- (10)

  • Strong ‘source/sink’

----- (11)

  • Extremely strong ‘source/sink’

------ (12)


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