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Diagnostic Initialization Generated Extremely Strong Thermohaline Sources & Sinks in South China Sea MAJ Ong Ah Chuan RSN, USW

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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 - PowerPoint PPT Presentation

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Page 1: MAJ Ong Ah Chuan RSN, USW

Diagnostic Initialization Generated Extremely Strong Thermohaline Sources & Sinks in South China Sea

MAJ Ong Ah ChuanRSN, USW

Page 2: 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

• Sensitivity Study Result and Analysis

• Conclusion

Page 3: MAJ Ong Ah Chuan RSN, USW

• (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 

NUMERICAL OCEAN MODELING

N Equatorial Current

South China Sea

• Ocean modeling - Need reliable data for specifying initial condition

• Past observations - Contributed greatly to T & S fields

Model output

Page 4: MAJ Ong Ah Chuan RSN, USW

PROBLEMS OF DIAGNOSTIC INITIALIZATION

• 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

Page 5: MAJ Ong Ah Chuan RSN, USW

PROBLEMS OF DIAGNOSTIC INITIALIZATION

• 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

Page 6: MAJ Ong Ah Chuan RSN, USW

PROBLEMS OF DIAGNOSTIC INITIALIZATION

• Horizontal momentum equation   – (1) • Temp & Salinity equations – (2) and (3)

1 ( )Mw f p Kt z z z

VV V VV V k V H

( )H TT T TT w K Ht z z z

V

( )H SS S SS w K Ht z z z

V

----- (1)

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

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

• (KM, KH) – Vertical eddy diffusivity

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

Page 7: MAJ Ong Ah Chuan RSN, USW

PROBLEMS OF DIAGNOSTIC INITIALIZATION

1 ( )Mw f p Kt z z z

VV V VV V k V H

( )H TT T TT w K Ht z z z

V

( )H SS S SS w K Ht z z z

V

------- (1)

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

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

• Diagnostic initialization integrate (1)-(3): with T and S unchanged

, , 0, at 0C CT T S S t V

Page 8: MAJ Ong Ah Chuan RSN, USW

• Analogous to adding heat & salt source/sink terms (FT, FS) • (2) & (3) becomes:

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

• Combining (5), (6) & (7):

0, 0T St t

Keeping :

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

( )H T TT T TT w K H Ft z z z

V ------------------ (5)

( )H S SS S SS w K H Ft z z z

V

PROBLEMS OF DIAGNOSTIC INITIALIZATION

Page 9: MAJ Ong Ah Chuan RSN, USW

( )T H TT TF T w K Hz z z

V

( )S H SS SF S w K Hz z z

V

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

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

are artificially generated at each time stepTF , SF

• Examine these source/sink terms

• POM is implemented for the SCS

PROBLEMS OF DIAGNOSTIC INITIALIZATION

Page 10: MAJ Ong Ah Chuan RSN, USW

PRINCETON OCEAN MODEL (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

* * *- = , = , = , = +

zx x y y t tH

• Sigma coordinate - Dealing with significant topographical variability

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

Page 11: MAJ Ong Ah Chuan RSN, USW

CRITERIA FOR STRENGTH OF SOURCE/SINK

• 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’

35 150.1 , 0.04T C S ppt pptCday dayt yr t yr

----- (10)

Page 12: MAJ Ong Ah Chuan RSN, USW

CRITERIA FOR STRENGTH OF SOURCE/SINK

0.1 , 0.04Strong Strong

T S pptChr hrt t

1 , 0.4Extremely ExtremelyStrong Strong

T S pptChr hrt t

• 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

Page 13: MAJ Ong Ah Chuan RSN, USW

AREAS OF RESEARCH IN THIS THESIS

• 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 ?

Page 14: MAJ Ong Ah Chuan RSN, USW

AREAS OF RESEARCH IN THIS THESIS

• 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

Page 15: MAJ Ong Ah Chuan RSN, USW

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

SCS Area = 3.5 x 106 km2

Sill depth: 2600 m

Page 16: MAJ Ong Ah Chuan RSN, USW

ENVIRONMENT OF SOUTH CHINA SEA

• 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

Climatological wind stress

Jun Dec

Page 17: MAJ Ong Ah Chuan RSN, USW

ENVIRONMENT OF SOUTH CHINA SEA

Jun

South China

Sea

Luzon Strait Sill depth: 2600 m

Kuroshio

• 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

Page 18: MAJ Ong Ah Chuan RSN, USW

ENVIRONMENT OF SOUTH CHINA SEA

SummerWinter• North: Cold, saline. Annual variability of salinity small• South: Warmer & fresher• Summer: 25-29°C (> 16°N) 29-30°C (< 16°N)

• Winter: 20-25°C (> 16°N) 25-27.5°C (< 16°N)

Page 19: MAJ Ong Ah Chuan RSN, USW

SCS MODEL INPUT INTO POM FOR DIAGNOSTIC RUN

• 125 x 162 x 23 horizontally grid points with 23 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

Page 20: MAJ Ong Ah Chuan RSN, USW

SCS MODEL INPUT INTO POM FOR DIAGNOSTIC RUN

• 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

Page 21: MAJ Ong Ah Chuan RSN, USW

EXPERIMENT DESIGN

• 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 V under 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

Page 22: MAJ Ong Ah Chuan RSN, USW

EXPERIMENT DESIGN

• 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

Page 23: MAJ Ong Ah Chuan RSN, USW

EXPERIMENT DESIGN

• 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

Page 24: MAJ Ong Ah Chuan RSN, USW

EXPERIMENT DESIGN

• (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

Page 25: MAJ Ong Ah Chuan RSN, USW

• 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

RESULT OF SENSITIVITY STUDY

Page 26: MAJ Ong Ah Chuan RSN, USW

Max Heat Sink = -3555 Wm-3

HORIZONTAL DISTRIBUTION OF FT

Max Value = 2.331Min Value = - 0.987Unit: C/hr

Max Value = 1.872Min Value = - 2.983Unit: C/hr

Max Value = 1.682Min Value = - 0.591Unit: C/hr

Max Value = 0.374Min Value = - 0.367Unit: C/hr

On day-60 with C = 0.05

Max Heat Source = 2778 Wm-3

• Features consistent for different C-values

Page 27: MAJ Ong Ah Chuan RSN, USW

Max Heat Sink = -2385 Wm-3

HORIZONTAL DISTRIBUTION OF FT

On day-60 with C = 0.1

Max Value = 2.338Min Value = - 0.595Unit: C/hr

Max Value = 1.724Min Value = - 2.001Unit: C/hr

Max Value = 1.627Min Value = - 0.595Unit: C/hr

Max Value = 0.314Min Value = - 0.364Unit: C/hr

Max Heat Source = 2787 Wm-3

Page 28: MAJ Ong Ah Chuan RSN, USW

Max Heat Sink = -1211 Wm-3

HORIZONTAL DISTRIBUTION OF FT

On day-60 with C = 0.2

Max Value = 2.337Min Value = - 0.348Unit: C/hr

Max Value = 1.332Min Value = - 1.016Unit: C/hr

Max Value = 1.632Min Value = - 0.602Unit: C/hr

Max Value = 0.287Min Value = - 0.369Unit: C/hr

Max Heat Source = 2785 Wm-3

• C-value increases, FT weakens

• Still above extremely strong heat source criterion

Page 29: MAJ Ong Ah Chuan RSN, USW

Max Heat Sink = -1082 Wm-3

HORIZONTAL DISTRIBUTION OF FT

On day-60 with C = 0.3

Max Heat Source = 2778 Wm-3

Max Value = 2.331Min Value = - 0.346Unit: C/hr

Max Value = 1.013Min Value = - 0.908Unit: C/hr

Max Value = 1.661Min Value = - 0.607Unit: C/hr

Max Value = 0.277Min Value = - 0.363Unit: C/hr

• large C cause unrealistically strong diffusion in ocean model

Page 30: MAJ Ong Ah Chuan RSN, USW

• 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

RESULT OF SENSITIVITY STUDY

Page 31: MAJ Ong Ah Chuan RSN, USW

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

Max Value = 0.372Min Value = - 0.115Unit: ppt/hr

Max Value = 0.134Min Value = - 0.198Unit: ppt/hr

Max Value = 0.019Min Value = - 0.067Unit: ppt/hr

Max Value = 0.014 Min Value = - 0.016Unit: ppt/hr

On day-60 with C = 0.05

Page 32: MAJ Ong Ah Chuan RSN, USW

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

Max Value = 0.372Min Value = - 0.085Unit: ppt/hr

Max Value = 0.079Min Value = - 0.198Unit: ppt/hr

Max Value = 0.018Min Value = - 0.066Unit: ppt/hr

Max Value = 0.011Min Value = - 0.012Unit: ppt/hr

when C-value increases, FS weakens

Page 33: MAJ Ong Ah Chuan RSN, USW

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

Max Value = 0.373Min Value = - 0.075Unit: ppt/hr

Max Value = 0.065Min Value = - 0.199Unit: ppt/hr

Max Value = 0.013Min Value = - 0.067Unit: ppt/hr

Max Value = 0.009Min Value = - 0.011Unit: ppt/hr

Page 34: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL DISTRIBUTION OF FS

Max Salinity Source = 0.378 ppt hr-1

Max Salinity Sink = -0.200 ppt hr-1

On day-60 with C = 0.3

Max Value = 0.378Min Value = - 0.075Unit: ppt/hr

Max Value = 0.055Min Value = - 0.200Unit: ppt/hr

Max Value = 0.011Min Value = - 0.068Unit: ppt/hr

Max Value = 0.008Min Value = - 0.011Unit: ppt/hr

when C-value increases, FS weakens But above criterion

Page 35: MAJ Ong Ah Chuan RSN, USW

• 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)

RESULT OF SENSITIVITY STUDY

1

1M (| |) | | N

jT

jTF F

N

----- (17)

Page 36: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL MEAN | FT |

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

• Mean |FT| increases rapidly with time

• Oscillate around quasi-stationary value

• Large - Mean |FT| based on horizontal average

Page 37: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL MEAN | FT |

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

• Mean |FT| increases rapidly with time

• Oscillate around quasi-stationary value

• Similar features observed at other C-values

Page 38: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL MEAN | FT |

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

• Mean |FT| increases rapidly with time

• Oscillate around quasi-stationary value

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

Page 39: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL MEAN | FT |

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

• Mean |FT| increases rapidly with time

• Oscillate around quasi-stationary value

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

Page 40: MAJ Ong Ah Chuan RSN, USW

DEPTH PROFILE OF MEAN | FT |

Figure 25. Depth Profile with C = 0.05

• Max mean |FT| at subsurface

• Min at mid-level

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

Page 41: MAJ Ong Ah Chuan RSN, USW

DEPTH PROFILE OF MEAN | FT |

Figure 26. Depth Profile with C = 0.1

• Max mean |FT| at subsurface

• Min at surface

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

Page 42: MAJ Ong Ah Chuan RSN, USW

DEPTH PROFILE OF MEAN | FT |

Figure 27. Depth Profile with C = 0.2

• Max near bottom

• Higher value indicates a greater heat sources & sinks problem

• Min at surface

Page 43: MAJ Ong Ah Chuan RSN, USW

DEPTH PROFILE OF MEAN | FT |

Figure 28. Depth Profile with C = 0.3

• Max at bottom

• Higher value indicates a greater heat sources & sinks problem • Min at surface

Page 44: MAJ Ong Ah Chuan RSN, USW

• 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)

RESULT OF SENSITIVITY STUDY

1

1M (| |) | | N

jS

jSF F

N

Page 45: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL MEAN | FS |

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

• Mean |FS| increases rapidly with time

• Peak value of 0.0137 ppt hr-1

• Oscillate around quasi-stationary value

Page 46: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL MEAN | FS |

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

• Mean |FS| increases rapidly with time

• Peak value of 0.0127 ppt hr-1

• Oscillate around quasi-stationary value

Page 47: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL MEAN | FS |

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

• Mean |FS| increases rapidly with time

• Peak value of 0.0124 ppt hr-1

• Oscillate around quasi-stationary value

Page 48: MAJ Ong Ah Chuan RSN, USW

HORIZONTAL MEAN | FS |

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

• Peak value of 0.0121 ppt hr-1

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

Page 49: MAJ Ong Ah Chuan RSN, USW

DEPTH PROFILE OF MEAN | FS |

Figure 33. Depth Profile with C = 0.05

• 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

Page 50: MAJ Ong Ah Chuan RSN, USW

DEPTH PROFILE OF MEAN | FS |

Figure 34. Depth Profile with C = 0.1

• Max value at surface

• Oscillates with decreasing value as depth increases

• Min occurred at bottom

• Similar pattern for other C-values

Page 51: MAJ Ong Ah Chuan RSN, USW

DEPTH PROFILE OF MEAN | FS |

Figure 35. Depth Profile with C = 0.2

• Max value at surface

• Oscillates with decreasing value as depth increases

• Min occurred at bottom

Page 52: MAJ Ong Ah Chuan RSN, USW

DEPTH PROFILE OF MEAN | FS |

Figure 36. Depth Profile with C = 0.3

• Greater salting rate at surface

• Strength decreases across corresponding level when C-value increases

Page 53: MAJ Ong Ah Chuan RSN, USW

• 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)

RESULT OF SENSITIVITY STUDY

Page 54: MAJ Ong Ah Chuan RSN, USW

UNCERTAINTY OF DIAGNOSTICALLY INITIALIZED 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

Page 55: MAJ Ong Ah Chuan RSN, USW

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

• 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 V

Page 56: MAJ Ong Ah Chuan RSN, USW

Day-60 with C = 0.2

UNCERTAINTY OF DIAGNOSTICALLY INITIALIZED V

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

Page 57: MAJ Ong Ah Chuan RSN, USW

Day-60 with C = 0.3

UNCERTAINTY OF DIAGNOSTICALLY INITIALIZED V

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

Page 58: MAJ Ong Ah Chuan RSN, USW

• 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

RESULT OF SENSITIVITY STUDY

2 2( , , ) ( , , ) ( , , ) ( , , )0.2 0.2

1 1

22( , , ) ( , , )

0.2 0.21 1

( , )

y x

y x

M Mi j k i j k i j k i j k

C C C Cj i

M Mi j k i j k

C Cj i

U U V VRRMSDV k C

U V

2( , , ) ( , , )0.2

1 1

2( , , )

0.21 1

( , )

y x

y x

M Mi j k i j k

C Cj i

M Mi j k

Cj i

W WRRMSDW k C

W

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

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

Page 59: MAJ Ong Ah Chuan RSN, USW

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

Figure 41. RRMSDV(k, 0.05)

• 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)

Day of diagnostic run. = -0.5 Day of diagnostic run. = -0.95

Day of diagnostic run. = -0.0125 Day of diagnostic run. = -0.15

Page 60: MAJ Ong Ah Chuan RSN, USW

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

Figure 42. RRMSDV(k, 0.05)

• 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

RRMSDV RRMSDV

RRMSDV RRMSDV

Page 61: MAJ Ong Ah Chuan RSN, USW

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

Figure 43. RRMSDW(k, 0.05)

• 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

Day of diagnostic run. = -0.5 Day of diagnostic run. = -0.95

Day of diagnostic run. = -0.0125 Day of diagnostic run. = -0.15

Page 62: MAJ Ong Ah Chuan RSN, USW

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

Figure 44. RRMSDW(k, 0.05)

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

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

RRMSDW RRMSDW

RRMSDW RRMSDW

Page 63: MAJ Ong Ah Chuan RSN, USW

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

Figure 45. RRMSDV(k, 0.1)

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

• Max RRMSDV(k,C=0.1) > 0.5

Day of diagnostic run. = -0.5 Day of diagnostic run. = -0.95

Day of diagnostic run. = -0.0125 Day of diagnostic run. = -0.15

Page 64: MAJ Ong Ah Chuan RSN, USW

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

Figure 46. RRMSDV(k, 0.3)

• 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

Day of diagnostic run. = -0.5 Day of diagnostic run. = -0.95

Day of diagnostic run. = -0.0125 Day of diagnostic run. = -0.15

Page 65: MAJ Ong Ah Chuan RSN, USW

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

Figure 47. RRMSDW(k, 0.1)

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

• RRMSDW(k, C=0.1 & C=0.05) > 1

Day of diagnostic run. = -0.5 Day of diagnostic run. = -0.95

Day of diagnostic run. = -0.0125 Day of diagnostic run. = -0.15

Page 66: MAJ Ong Ah Chuan RSN, USW

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

Figure 48. RRMSDW(k, 0.3)

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

• RRMSDW(k, C=0.3) > 0.6

Day of diagnostic run. = -0.5 Day of diagnostic run. = -0.95

Day of diagnostic run. = -0.0125 Day of diagnostic run. = -0.15

Page 67: MAJ Ong Ah Chuan RSN, USW

• How long diagnostic integration is needed?

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

• 60th day selected to compute RRMSDV & RRMSDW

UNCERTAINTY OF Vc DUE TO UNCERNTAIN LENGTH OF DIAGNOSTIC INTEGRATION

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

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

1

1

2 2( , , ) ( , , ) ( , , ) ( , , )60 60

2 1 1

22( , , ) ( , , )

60 602 1 1

( )

yz x

yz x

MM Mi j k i j k i j k i j k

day t day day t dayk j i

MM Mi j k i j k

day dayk j i

U U V VRRMSDV t

U V

1

1

2( , , ) ( , , )

602 1 1

2( , , )

602 1 1

( )

yz x

yz x

MM Mi j k i j k

day t dayk j i

MM Mi j k

dayk j i

W WRRMSDW t

W

t = 60, 61, 62 ….90

Page 68: MAJ Ong Ah Chuan RSN, USW

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

Figure 49. RRMSDV(t)

• RRMSDV(t) fluctuates irregularly

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

• C increases, RRMSDV(t) decreases

C = 0.2

C = 0.1C =0.05

C = 0.3

Page 69: MAJ Ong Ah Chuan RSN, USW

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

Figure 50. RRMSDW(t)

• RRMSDW(t) fluctuates irregularly

• Increases with time rapidly

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

C = 0.2

C = 0.1C =0.05

C = 0.3

Page 70: MAJ Ong Ah Chuan RSN, USW

CONCLUSION

• 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

Page 71: MAJ Ong Ah Chuan RSN, USW

CONCLUSION

• Uncertainty of C-value affect Vc significantly

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

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

( )H T TT T TT w K H Ft z z z

V ------------------ (5)

( )H S SS S SS w K H Ft z z z

V

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

Page 72: MAJ Ong Ah Chuan RSN, USW

SMAGORINSKY FORMULA

C is the horizontal viscosity parameter

12

TMA C x y V V

1

2 2 2 21 / / / /2

TV V u x v x u y v y Where

Page 73: MAJ Ong Ah Chuan RSN, USW

CRITERIA FOR STRENGTH OF SOURCE/SINK

0.1 , 0.04Strong Strong

T S pptChr hrt t

1 , 0.4Extremely ExtremelyStrong Strong

T S pptChr hrt t

• Strong ‘source/sink’

----- (11)

• Extremely strong ‘source/sink’

------ (12)

35 150.1 , 0.04T C S ppt pptCday dayt yr t yr

----- (10)

• Standard measures for ‘source/sink’