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

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


NUMERICAL OCEAN MODELING

  • 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

  • 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 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


PROBLEMS OF DIAGNOSTIC INITIALIZATION

  • 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 INITIALIZATION

------- (1)

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

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

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

  • with T and S unchanged


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

------------------ (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 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)

  • 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

  • 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/SINK

  • 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

  • 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 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


SCS Area = 3.5 x 106 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 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


Kuroshio

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


  • 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)

Winter

Summer

ENVIRONMENT OF SOUTH CHINA SEA


SCS MODEL INPUT INTO POM FOR DIAGNOSTIC RUN

  • 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 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


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 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 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


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


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


RESULT OF SENSITIVITY STUDY

  • 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


Max Value = 2.331

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


Max Value = 2.338

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


Max Value = 2.337

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


Max Value = 2.331

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 STUDY

  • 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


Max Value = 0.372

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


when 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


Max Value = 0.373

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


Max Salinity Sink = -0.200 ppt hr-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 STUDY

  • 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)


HORIZONTAL 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


HORIZONTAL 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


HORIZONTAL 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


HORIZONTAL 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 | 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 | 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 | 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 | 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 STUDY

  • 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)


HORIZONTAL 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


HORIZONTAL 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


HORIZONTAL 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


HORIZONTAL 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 | 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 | 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 | 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 | 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 STUDY

  • 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

  • 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 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 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 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 STUDY

  • 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)


Day of diagnostic run.  = -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)


RRMSDV

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)


Day of diagnostic run.  = -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)


RRMSDW

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)


Day of diagnostic run.  = -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)


Day of diagnostic run.  = -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)


Day of diagnostic run.  = -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)


Day of diagnostic run.  = -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 Vc 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) )

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)


C =0.05

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

  • 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


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

------------------ (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

  • C is the horizontal viscosity parameter

Where


CRITERIA FOR STRENGTH OF SOURCE/SINK

  • Standard measures for ‘source/sink’

----- (10)

  • Strong ‘source/sink’

----- (11)

  • Extremely strong ‘source/sink’

------ (12)


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