Post on 13-Jan-2016
ISPOL Ocean Turbulence Project
Miles McPhee
McPhee Research Co.
Naches WA USA
Objectives
Characterize exchanges at or near the ice/ocean interface, representative of the entire ISPOL floe.
Pertinent variables include:
• Turbulent stress
• Turbulent heat flux
• Turbulent salt (salinity) flux
• The ocean velocity profile, including an estimate of geostrophic flow
• Eddy exchange factors for momentum and scalar variables: eddy viscosity/eddy diffusivity
SonTek ADVOcean (5 Mhz)
SBE 03 thermometerSBE 07 microstructureconductivity meter
SBE 04 conductivity meter
SonTek Instrument Cluster
-20 -10 0 10 20
-40
-30
-20
-10
0
10
20
30
40
333 337
341
345
349
353
357
361
365
km East
km N
ort
h
(28 Nov 04)
(30 Dec 04) 67 30'S
68 S
55 W 55 30'W Two methods used for fitting ship GPS
positions to a differentiable function to obtain velocity:
(1) Polynomial fit: all 5-min position vectors in a 1-h time window centered at even half-hour intervals were converted to complex numbers and least-squares fitted to complex second-order polynomial. The derivative provides a continuous velocity record.
(2) Complex demodulation: fits all of the data over a 1-day time window to a position function including mean velocity and clockwise and anticlockwise oscillating components at the inertial and diurnal frequencies. Done every 90 minutes
335 340 345 350 355 360-0.2
-0.1
0
0.1
0.2
1.7 cm/s
V (north) ice velocity, Phase A
m s
-1
335 340 345 350 355 360
-0.2
-0.1
0
0.1
-1.5 cm/s
U (east) ice velocity, Phase A
Day of 2004 (335=30 Nov)
m s
-1
Polynomial fit
complex demod fit
361 362 363 364 365 366 367 368
-0.1
0
0.1
0.2
7.5 cm/s
V (north) ice velocity, Phase B
m s
-1
361 362 363 364 365 366 367 368
-0.1
0
0.1
0.2
0.3
1.5 cm/s
U (east) ice velocity, Phase B
Day of 2004 (367=1 Jan 2005)
m s
-1
Polynomial fit
complex demod fit
335 340 345 350 355 360
-10
-5
0
5
10
cm s
-1
Day of 2004
Eastward tidal components
335 340 345 350 355 360
-10
-5
0
5
10
cm s
-1
Northward tidal components
<VK1
>: 4.2 cm/s; <VM2
>: 2.6 cm/s
M2
K1
These are tidal components in the ice motion– they correspond to the ocean tidal current only if the ice drifts passively with the tide.
340 345 350 355 360 3650
2
4
6
8
10
12
Day of 2004
m s
-1
Ship Wind/Ice Speed Comparison
1.5%
Wind Speed
Mean ice speed*50
345 346 347 348 349 350 351 352-0.1
0
0.1
0.2Northward absolute velocity
345 346 347 348 349 350 351 352-0.2
-0.1
0
0.1
0.2
Day of 2004
Eastward absolute velocity
U20
Uice
V20
Vice
356.5 357 357.5 358 358.5 359 359.5 360 360.5-0.2
-0.1
0
0.1Northward absolute velocity
356.5 357 357.5 358 358.5 359 359.5 360 360.5-0.2
-0.1
0
0.1
Day of 2004
Eastward absolute velocity
U20
Uice
V20
Vice
Site A Deployment 1:
1 mast with 2 turbulence clusters nominally 6 and 10 m depth (4 and 8 m below the ice/ocean interface) with upward/downward looking RDI ADPs
From 336.75 to 343.75
Site A Deployment 2:
Same mast as Deployment 1, plus 2nd mast with 1 turbulence cluster at 4 m depth (2 m from interface) and 500 kHz Sontek ADP
From 345.00 to 353.375
Site A Deployment 3:
1 mast with 3 turbulence clusters nominally 4, 8, and 12 m depth (2, 4, 10 m below the ice/ocean interface) with upward/downward looking RDI ADPs, plus the Sontek ADP deployed separately in the same hydrohole.
From 354.75 to 360.25
Site B Deployment:
1 mast with 2 turbulence clusters nominally 2 and 4 m depth (1 and 2 m below the ice/ocean interface) with the Sontek ADP on the bottom of the mast.
From 362.625 to 367.50
337 338 339 340 341 342 343
4
6
8
10
12
x 10-3
Day of 2004
m s
-1
u*=1/2
345 346 347 348 349 350 351 352 353
2
4
6
8
10
x 10-3
Day of 2004
m s
-1
u*=1/2
4 m
6 m10 m
6 m
10 m
5.4
5.8
3.4
4.4
5.0
Site A-1
Site A-2
4/122
* )( wvwuu 15-minute realizations (covariance calculations) averaged for 3 hours.
355 355.5 356 356.5 357 357.5 358 358.5 359 359.5 360
2
4
6
8
10
x 10-3
Day of 2004
m s
-1
u*=1/2
363 363.5 364 364.5 365 365.5 366 366.5 367 367.5
4
6
8
10
12
14x 10
-3
Day of 2004
m s
-1
u*=1/2
2 m
4 m
4 m
8 m12 m
3.9
4.6
5.4
7.3
Site A-3
Site B
337 338 339 340 341 342 343
-20
-10
0
Day of 2004
W m
-2
Hf=c
p<w'T'>
337 338 339 340 341 342 343
0.04
0.06
0.08
Day of 2004
K
T=T-Tf(S)
6 m
6 m
10 m
-4.3
-3.9
0.041
Site A-1
Site A-2
345 346 347 348 349 350 351 352 353-40
-20
0
Day of 2004
W m
-2
Hf=c
p<w'T'>
345 346 347 348 349 350 351 352 353
0.04
0.06
0.08
0.1
Day of 2004
K
T=T-Tf(S)
6 m
10 m
4 m
6 m
10 m
+1.6
-4.2
-1.7
0.064
355 355.5 356 356.5 357 357.5 358 358.5 359 359.5 360
-60
-40
-20
0
Day of 2004
W m
-2
Hf=c
p<w'T'>
355 355.5 356 356.5 357 357.5 358 358.5 359 359.5 360
0.06
0.08
0.1
Day of 2004
K
T=T-Tf(S)
8 m
12 m
4 m
8 m
12 m
-1.8-2.1-3.2
0.0620.061
Site A-3
363 363.5 364 364.5 365 365.5 366 366.5 367 367.5
0
5
10
Day of 2004
W m
-2
Hf=c
p<w'T'>
363 363.5 364 364.5 365 365.5 366 366.5 367 367.5
0.05
0.055
0.06
0.065
Day of 2004
K
T=T-Tf(S)
2 m
4 m
2 m
4 m
2.6
4.6
0.0550.055
Site B
337 338 339 340 341 342 343
-2
0
2
4
x 10-6
Day of 2004
psu
m s
-1<w'S'> from std C
6 m
7.6x10-7
Site A-1
Site A-2
345 346 347 348 349 350 351 352 353
-2
0
2
4
6
x 10-6
Day of 2004
psu
m s
-1
<w'S'> from std C
345 346 347 348 349 350 351 352 353
-2
-1
0
1
x 10-6
Day of 2004
psu
m s
-1
<w'S'> from C
4 m
6 m
10 m
0.2x10-7
10.7x10-7
0.8x10-7
Site A-3
355 355.5 356 356.5 357 357.5 358 358.5 359 359.5 360-5
0
5
10
x 10-6
Day of 2004
psu
m s
-1
<w'S'> from std C
355 355.5 356 356.5 357 357.5 358 358.5 359 359.5 360
0
1
2
3
4
x 10-6
Day of 2004
psu
m s
-1
<w'S'> from C
4 m
8 m
12 m
6.9x10-7
8.8x10-7
4.8x10-7
Site B
363 363.5 364 364.5 365 365.5 366 366.5 367 367.5
-3
-2
-1
0
1x 10
-6
Day of 2004
psu
m s
-1
<w'S'> from std C
2 m
4 m-12.8x10-7
-9.6x10-7
0.15 m s-1
337 338 339 340 341 342 343 344
336 337 338 339 340 341 342 343 344 345-40
-20
0
20
Day of 2004
W m
-2
Hf=c
p<w'T'>
336 337 338 339 340 341 342 343 344 3450
5
10
15
mm
s-1
u*=1/2
4 m
4 m
8 m
10
cm s
-1
VTIC1
500 m
10 cm s-1
Vice
VTIC1
PS
3-h average centered at 336.75
10
cm s
-1
VTIC1
10 cm s-1
500 m
PS
VTIC1
Vice
3-h average centered at 343.75
Relative current, TIC 1
0.15 m s-1
337 338 339 340 341 342 343 344
336 337 338 339 340 341 342 343 344 345-40
-20
0
20
Day of 2004
W m
-2
Hf=c
p<w'T'>
336 337 338 339 340 341 342 343 344 3450
5
10
15
mm
s-1
u*=1/2
4 m
4 m
8 m
Relative current, TIC 1
10
cm s
-1
VTIC1
3-h average centered at 339.75PS
VTIC1
Vice
10 cm s-1
500 m
0.15 m s-1
337 338 339 340 341 342 343 344
336 337 338 339 340 341 342 343 344 345-40
-20
0
20
Day of 2004
W m
-2
Hf=c
p<w'T'>
336 337 338 339 340 341 342 343 344 3450
5
10
15
mm
s-1
u*=1/2
4 m
4 m
8 m
Relative current, TIC 1
10
cm s
-1
VTIC1
3-h average centered at 340.375
PS
VTIC1
Vice
10 cm s-1
500 m
0.10 m s-1
345 346 347 348 349 350 351 352 353
344 345 346 347 348 349 350 351 352 353 354
-40
-20
0
20
Day of 2004
W m
-2
Hf=c
p<w'T'>
344 345 346 347 348 349 350 351 352 353 3540
5
10
15
mm
s-1
u*=1/2
1 m
4 m8 m
1 m
4 m
8 m
10
cm s
-1
VTIC2
500 m
10 cm s-1
Vice
VTIC2
PS
3-h average centered at 346.875
Relative current, TIC 2
354 355 356 357 358 359 360 361
-60
-40
-20
0
Day of 2004
W m
-2
Hf=c
p<w'T'>
354 355 356 357 358 359 360 3610
5
10
15
mm
s-1
u*=1/2
2 m
6 m10 m
2 m
6 m
10 m
0.10 m s-1
355 356 357 358 359 360
10
cm s
-1
VTIC1
3-h average centered at 356.875
Vice
VTIC1
PS
500 m
10 cm s-1
Relative current, TIC 2
354 355 356 357 358 359 360 361
-60
-40
-20
0
Day of 2004
W m
-2
Hf=c
p<w'T'>
354 355 356 357 358 359 360 3610
5
10
15
mm
s-1
u*=1/2
2 m
6 m10 m
2 m
6 m
10 m
0.10 m s-1
355 356 357 358 359 360
10
cm s
-1
VTIC1
10 cm s-1
500 m
PS
VTIC1
Vice
3-h average centered at 359.50
Relative current, TIC 2
0.10 m s-1
362 363 364 365 366 367
361 362 363 364 365 366 367 368-10
0
10
20
Day of 2004
W m
-2
Hf=c
p<w'T'>
361 362 363 364 365 366 367 3680
5
10
15
mm
s-1
u*=1/2
1 m
3 m
1 m
3 m
10
cm s
-1
VTIC1
3-h average centered at 363.75
Vice
VTIC1
PS
400 m
10 cm s-1
Relative current, TIC 2
Day 363.50
Cluster u* U/u*
1 0.0085 4.5 2 0.0135 4.1
0.10 m s-1
362 363 364 365 366 367
361 362 363 364 365 366 367 368-10
0
10
20
Day of 2004
W m
-2
Hf=c
p<w'T'>
361 362 363 364 365 366 367 3680
5
10
15
mm
s-1
u*=1/2
1 m
3 m
1 m
3 m
10
cm s
-1
VTIC1
10 cm s-1
400 m
PS
VTIC1
Vice
3-h average centered at 365.25
Relative current, TIC 2
Day 365.25
Cluster u* U/u*
1 0.0048 17.9 2 0.0059 16.6
2 4-9
-8
-7
-6
-5
-4
-3
-2
-1
z0=0.3 cm
z0=4.0 cm
Distance from ice, m
log
(z0),
z0 i
n m
Site A, 345.750 to 360.250
1 3-9
-8
-7
-6
-5
-4
-3
-2
-1
z0=0.1 cm
z0=12.4 cm
Distance from ice, m
log
(z0),
z0 i
n m
Site B, 362.625 to 367.500Green circles: law of the wall, median value of log (z0) shown with error bars indicating 95% confidence interval for the median based on quartile limits.
Red squares: mixing length method, which includes as a measured parameter the length scale inversely proportional to the wavenumber at the peak of
the area-preserving w spectrum.
30 m10 m
North
Current measured relativeto ice, 3-h average centeredat day 365.25
V/V30
1+0i
V10
/V30
= 0.77-0.17i
=12.3
(10-30)
=14.6
Data, 345.000 to 367.750
Treat velocity vectors as complex numbers: V=u+iv
0 0.05 0.1 0.15 0.2-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
m s-1
m s
-1
GPS Ice Velocity, 3h average @ day 362.875
Vice
0 0.05 0.1 0.15 0.2-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18Day 362.875
m s-1
m s
-1
V20
(relative)
-1.85 -1.84 -1.83 -1.82
-35
-30
-25
-20
-15
-10
-5
C
m
Temperature, Day 362.875
34.32 34.33 34.34 34.35 34.36-40
-35
-30
-25
-20
-15
-10
-5
0
psu
Salinity
0 0.01 0.02 0.03-40
-35
-30
-25
-20
-15
-10
-5
0
m2s-1
Eddy viscosity/diffusivity
Km
Kh
-0.05 0 0.05 0.1 0.15-40
-35
-30
-25
-20
-15
-10
-5
0
m s-1
Model velocity (relative to Vgeo
)
u (east)
v (north)
1 2 3 4
x 10-3
-32
-30
-28
-26
m2s-1
Eddy viscosity/diffusivity
Km
Kh
-0.05 0 0.05 0.1 0.15-40
-30
-20
-10
0
m s-1
Model velocity (relative to Vgeo
)
u (east)
v (north)
0 0.01 0.02 0.03-40
-35
-30
-25
-20
-15
-10
-5
0
m2s-1
Eddy viscosity/diffusivity
Km
Kh
-0.05 0 0.05 0.1 0.15-40
-35
-30
-25
-20
-15
-10
-5
0
m s-1
Model velocity (relative to Vgeo
)
u (east)
v (north)
0 0.05 0.1 0.15 0.2-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18
m s-1
m s
-1
z0= 50.0 mm, u
*0=13.23 mm s-1
Model velocity, T/S structure @ day 362.875
Ekman spiral
0 0.05 0.1 0.15 0.2-0.02
0
0.02
0.04
0.06
0.08
0.1
0.12
0.14
0.16
0.18Model velocity, based on T/S structure @ day 362.875
m s-1
m s
-1
z0= 50.0 mm, u
*0=13.23 mm s-1
V20
(abs)
Vgeo
(10-30)
=6.1
Model with z0 = 1 mm
(10-30)
=14.6
Data, 361.875 to 367.750
(10-30)
=15.0
Model with z0 = 50 mm
(10-30)
=17.5
Model with z0 = 120 mmFor each 3-h segment of data, run the steady
model forced to agree with the current at 20 m, using the interpolated T/S structure in the upper ocean, adjusted to agree with upper cluster values. For each sample, calculate the nondimensional profile (with respect to the 30 m level) and compare the model average with measured.
2 4-9
-8
-7
-6
-5
-4
-3
-2
-1
z0=0.3 cm
z0=4.0 cm
Distance from ice, m
log
(z0),
z0 i
n m
Site A, 345.750 to 360.250
1 3-9
-8
-7
-6
-5
-4
-3
-2
-1
z0=0.1 cm
z0=12.4 cm
Distance from ice, m
log
(z0),
z0 i
n m
Site B, 362.625 to 367.500Green circles: law of the wall, median value of log (z0) shown with error bars indicating 95% confidence interval for the median based on quartile limits.
Red squares: mixing length method, which includes as a measured parameter the length scale inversely proportional to the wavenumber at the peak of
the area-preserving w spectrum.
335 340 345 350 355 360 365 3700
0.005
0.01
0.015
0.02
8.1 mm/sm s
-1
Day of 2004
Model u*0
= 01/2
335 340 345 350 355 360 365 3700
10
20
30
40
16.0 W m-2
W m
-2
Day of 2004
Model Hf=c
p<w'T'>
0
335 340 345 350 355 360 365 3700
1
2
3
4x 10
-6
1.6e-006
psu
-m s
-1
Day of 2004
Model <w'S'>0
335 340 345 350 355 360 365 3700
1
2
x 10-8
1.2e-008W k
g-1
Day of 2004
Model <w'S'>0
335 340 345 350 355 360 365 3700
0.005
0.01
0.015
58 cm2 s-1m2 s
-1
Day of 2004
Model Km
@ 2 m from ice
335 340 345 350 355 360 365 3700
0.02
0.04
115 cm2 s-1
m2 s
-1
Day of 2004
Model maximum Km
335 340 345 350 355 360 365 370
-0.2
-0.1
0
0.1
0.2
1.1 cm s-1
m s
-1
Day of 2004
Model vg (North pos)
335 340 345 350 355 360 365 370
-0.2
-0.1
0
0.1
0.2
-1.0 cm s-1
m s
-1
Day of 2004
Model ug (East pos)
Summary
The ocean turbulence data were characterized by much temporal variability and undersurface heterogeneity. For the purpose of estimating exchange properties for the entire floe, a relatively simple, steady state upper ocean model was applied to each 3-h average, for a range of roughness values. The modeled angular shear between 10 and 30 m was compared with observations, and from this, z0 = 0.05 m emerged as a representative value.
The model then provides interface values for the friction velocity, heat flux, salt flux. It additionally estimates eddy viscosity/diffusivity, and velocity through the boundary layer, along with estimates of the undisturbed geostrophic velocity.