Transcript The South China Sea - Naval Postgraduate School

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
N Equatorial
Current
South
China
Sea
• To accurately predict ocean – need a
reliable initialization
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)
V
V
1

V
 V V  w
 k  fV  p  ( K M
)  HV
t
z

z
z
----- (1)
T
T 
T
  V T  w
 (KH
)  HT
t
z z
z
------------------ (2)
S
S 
S
 V S  w  ( K H
)  HS
t
z z
z
------------------ (3)
• (KM, KH) – Vertical eddy diffusivity
• (Hv, HT, HS) – Horizontal diffusion & subgrid processes causing change (V, T, S )
PROBLEMS OF DIAGNOSTIC INITIALIZATION
V
V
1

V
 V V  w
 k  fV  p  ( K M
)  HV
t
z

z
z
------- (1)
T
T 
T
  V T  w
 (KH
)  HT
t
z z
z
------------------ (2)
S
S 
S
 V S  w  ( K H
)  HS
t
z z
z
------------------ (3)
• Diagnostic initialization integrate (1)-(3):
T  TC , S  SC , V  0,
with T and S unchanged
at t  0
PROBLEMS OF DIAGNOSTIC INITIALIZATION
• Analogous to adding heat & salt source/sink terms (FT, FS)
• (2) & (3) becomes:
T
T 
T
  V T  w
 (KH
)  H T  FT
t
z z
z
------------------ (5)
S
S 
S
  V S  w

(KH
)  H S  FS
t
z z
z
------------------ (6)
Keeping :
T
 0,
t
S
0
t
• Combining (5), (6) & (7):
------------------ (7)
PROBLEMS OF DIAGNOSTIC INITIALIZATION
FT  V T  w
T

T

(KH
)  HT
z
z
z
------------------- (8)
FS  V S  w
S

S

(KH
)  HS
z z
z
------------------- (9)
FT , FS 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
x * = x, y * = y ,  =
z - *
,t =t
H +
 ranges from  = 0 at z =  to  = -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:
T 35C

 0.1C
,
day
t
yr
S 15 ppt

 0.04 ppt
day
t
yr
----- (10)
• These values are used as standard measures for ‘source/sink’
CRITERIA FOR STRENGTH OF SOURCE/SINK
• Twenty four times of (10) represents strong ‘source/sink’ :
T
t
 0.1C
Strong
hr
,
S
t
 0.04 ppt
Strong
hr
----- (11)
• Ten times of (11) represents extremely strong ‘source/sink’
T
t
 1C
Extremely
Strong
hr
,
S
t
 0.4 ppt
Extremely
Strong
hr
------ (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,
drops to 100m
depth
SCS Area =
3.5 x 106 km2
Sill depth:
2600 m
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
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
Kuroshio
Luzon Strait
Sill depth: 2600 m
South
China
Sea
Jun
ENVIRONMENT OF SOUTH CHINA SEA
• 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
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
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
HORIZONTAL DISTRIBUTION OF FT
Max Heat
Source =
2778 Wm-3
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
Max Heat
Sink = -3555
Wm-3
• Features
consistent for
different Cvalues
On day-60 with
C = 0.05
HORIZONTAL DISTRIBUTION OF FT
Max Heat
Source =
2787 Wm-3
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
Max Heat
Sink = 2385 Wm-3
On day-60 with
C = 0.1
HORIZONTAL DISTRIBUTION OF FT
Max Heat
Source =
2785 Wm-3
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
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
HORIZONTAL DISTRIBUTION OF FT
Max Heat
Source =
2778 Wm-3
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
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
HORIZONTAL DISTRIBUTION OF FS
Max Salinity
Source =
0.372 ppt hr-1
• Features
similar for
different Cvalues
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
Max Salinity
Sink = -0.198
ppt hr-1
On day-60 with
C = 0.05
HORIZONTAL DISTRIBUTION OF FS
Max Salinity
Source =
0.372 ppt hr-1
Max Value =
0.372
Min Value =
- 0.085
Unit: ppt/hr
Max Value =
0.079
Min Value =
- 0.198
Unit: ppt/hr
Max Salinity
Sink = -0.198
ppt hr-1
when C-value
increases, FS
weakens
Max Value =
0.018
Min Value =
- 0.066
Unit: ppt/hr
Max Value =
0.011
Min Value =
- 0.012
Unit: ppt/hr
On day-60 with
C = 0.1
HORIZONTAL DISTRIBUTION OF FS
Max Salinity
Source =
0.373 ppt hr-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
Max Salinity
Sink = -0.199
ppt hr-1
On day-60 with
C = 0.2
HORIZONTAL DISTRIBUTION OF FS
Max Salinity
Source =
0.378 ppt hr-1
Max Value =
0.378
Min Value =
- 0.075
Unit: ppt/hr
Max Value =
0.011
Min Value =
- 0.068
Unit: ppt/hr
Max Value =
0.055
Min Value =
- 0.200
Unit: ppt/hr
Max Value =
0.008
Min Value =
- 0.011
Unit: ppt/hr
Max Salinity
Sink = -0.200
ppt hr-1
when C-value
increases, FS
weakens
But above
criterion
On day-60 with
C = 0.3
RESULT OF SENSITIVITY STUDY
• Horizontal mean | FT | :
1 N j
M (|FT |)   |FT |
N j 1
----- (17)
• 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)
HORIZONTAL MEAN | FT |
• Mean |FT| increases
rapidly with time
• Oscillate around quasistationary 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 quasistationary 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 quasistationary 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 quasistationary 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 | :
1 N j
M (|FS |)   |FS |
N j 1
• 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 quasistationary 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 quasistationary 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 quasistationary 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
uncertainty of C ?
Diagnostically initialized V due to
• 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 setup 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
 U (i , j ,k )  U (i , j ,k )

C  0.2
 C
j 1 i 1 
My Mx
RRMSDV (k , C ) 
 U
2
(i , j ,k )
C  0.2
  V

(i, j ,k ) 2
C  0.2

 W (i , j ,k )  W (i , j ,k ) 2 

C  0.2
 C

j 1 i 1 
My Mx
RRMSDW (k , C ) 

2
j ,k )

 VC( i,0.2

(i, j ,k )
C
2
My Mx
j 1 i 1
  V
 W
My Mx
j 1 i 1
(i , j ,k )
C  0.2

2
----------- (17)
----------- (18)
RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE
HORIZONTAL VELOCITY (RRMSDV)
• RRMSDV(k,C) increases
with time rapidly
• Oscillate around quasistationary value between
0.6 & 0.8
Day of diagnostic run.  = -0.0125
Day of diagnostic run.  = -0.15
Day of diagnostic run.  = -0.5
Day of diagnostic run.  = -0.95
• 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 (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
RRMSDV
RRMSDV
RRMSDV
RRMSDV
• Decreases with depth
from mid-level to bottom
Figure 42. RRMSDV(k, 0.05)
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)
Day of diagnostic run.  = -0.0125
Day of diagnostic run.  = -0.15
Day of diagnostic run.  = -0.5
Day of diagnostic run.  = -0.95
• 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 (RRMSDW)
• Vertical profile of
RRMSDW(k, C) decreases
from surface to bottom
• Decreased rate of
decrease of RRMSDW(k, C)
RRMSDW
RRMSDW
RRMSDW
RRMSDW
Figure 44. RRMSDW(k, 0.05)
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
Day of diagnostic run.  = -0.0125
Day of diagnostic run.  = -0.15
Day of diagnostic run.  = -0.5
Day of diagnostic run.  = -0.95
Figure 45. RRMSDV(k, 0.1)
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)
Day of diagnostic run.  = -0.0125
Day of diagnostic run.  = -0.15
Day of diagnostic run.  = -0.5
Day of diagnostic run.  = -0.95
• 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 (RRMSDW)
• RRMSDW(k, C) decreases
when C-value increases
• RRMSDW(k, C=0.1 &
C=0.05) > 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
Figure 47. RRMSDW(k, 0.1)
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
Day of diagnostic run.  = -0.0125
Day of diagnostic run.  = -0.15
Day of diagnostic run.  = -0.5
Day of diagnostic run.  = -0.95
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
 U
Mz 1 My Mx
RRMSDV (t ) 
k  2 j 1 i 1
 U
Mz 1 My Mx
k  2 j 1 i 1
2
(i , j ,k )
day  60
(i , j ,k )
day t
  V
2
(i , j ,k )
day  60


2
(i , j ,k )

 Vday
 60


2
 (i , j ,k )
(i , j ,k )

 Wday t  Wday 60
k  2 j 1 i 1 
Mz 1 My Mx
RRMSDW (t ) 
  V
(i , j ,k )
 U day
 60
(i , j ,k )
day t
 W
Mz 1 My Mx
k  2 j 1 i 1
(i , j ,k )
day  60


2



----------- (17)
----------- (18)
2
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 day70
C = 0.2
• C increases, RRMSDV(t)
decreases
Figure 49. RRMSDV(t)
C = 0.3
RELATIVE ROOT MEAN SQUARE DIFFERENCE OF THE
VERTICAL VELOCITY ( RRMSDW(t) )
C =0.05
C = 0.1
• RRMSDW(t) fluctuates
irregularly
• Increases with time
rapidly
• Both RRMSDV(t) and
RRMSDW(t) fluctuate
irregularly with time
C = 0.2
Figure 50. RRMSDW(t)
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
T
T 
T
  V T  w
 (KH
)  H T  FT
t
z z
z
------------------ (5)
S
S 
S
  V S  w

(KH
)  H S  FS
t
z z
z
------------------ (6)
• Extremely strong & spatially non-uniform initial
heating/cooling rates are introduced into ocean models
SMAGORINSKY FORMULA
AM  C xy
Where
1
T
V   V 
2
1
T
2
2
2
V   V    u / x    v / x  u / y    v / y  


2
C is the horizontal viscosity parameter
1
2
CRITERIA FOR STRENGTH OF SOURCE/SINK
• Standard measures for ‘source/sink’
T 35C

 0.1C
,
day
t
yr
S 15 ppt

 0.04 ppt
day
t
yr
----- (10)
• Strong ‘source/sink’
T
t
 0.1C
Strong
hr
,
S
t
 0.04 ppt
Strong
----- (11)
hr
• Extremely strong ‘source/sink’
T
t
 1C
Extremely
Strong
hr
,
S
t
 0.4 ppt
Extremely
Strong
hr
------ (12)