MAJ Ong Ah Chuan RSN, USW
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Transcript of MAJ Ong Ah Chuan RSN, USW
Diagnostic Initialization Generated Extremely Strong Thermohaline Sources & Sinks in South China Sea
MAJ Ong Ah ChuanRSN, 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
• (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
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 ( )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 )
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
• 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
( )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
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
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)
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
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
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
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
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
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)
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
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 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
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
• 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
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
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
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
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
• 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
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
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
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
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
• 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)
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
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
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
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
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
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
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
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
• 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
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
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
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
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
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
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
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
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
• 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
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
• 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
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
UNCERTAINTY OF DIAGNOSTICALLY INITIALIZED V
• Near bottom of SCS, anti-cyclonic eddy-like structure more pronounced when C is small
• 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)
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
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
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
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
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
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
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
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
• 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
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
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
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
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
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
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’