1. Global Statistics of Inertial Motions from Profiling Floats
ARGO Science Workshop
Tokyo, Japan
Global Statistics of Inertial Motions from Profiling Floats
November 14, 2003
Kuh Kim, Jong Jin Park, Brian A. King,
Howard Freeland and Stephen C. Riser

2. Example of Profiling Float Trajectory
North Pacific
ID : 21852
10km
2001
Oct. 7 ~ Nov. 6
~10days
~19 hours
Poster Presentation
An advanced method to estimate deep currents from Profiling Floats

3. Introduction
Inertial motion : producing mixing in the upper pycnocline [Gregg, 1984] and a prominent source of energy for deep ocean internal waves [Gill, 1982].
Inertial motion generates by local wind stress. (Pollard and Millard, 1970; Pollard, 1980; D’Asaro, 1985)
Seasonal variation of the energy flux from the wind based on Pollard-Millard Model (modified) and wind data (D’Asaro,1985)
Extract inertial amplitude from surface trajectory of Profiling Float

4. Surface Inertial Amplitude
Historical Measurements of Surface Inertial Amplitude
Author
Surface Inertial Amplitude
Instrument
Time (Location)
Hunkins (1967)
Typical : ~ 10cm/s
ice
Webster (1968)
10~80cm/s
CM at 7m
Oct.~Nov. (30N, 70W)
Pollard (1970)
Maximum : 49cm/s
CM at 10m
Oct. (39N, 70W)
Kundu (1976)
0 ~ 20cm/s
CM at 7.7m
Jul.~Aug. (45N, 124W)
Pollard (1980)
0 ~ 55cm/s
CM at 12m
Jul.~Aug. (39N, 70W)
Weller (1982)
0 ~ 20 cm/s (mean = 10cm/s) CM
Jul.~Sep.(60N, 12W)
Weller (1985)
Maximum : 40cm/s
FLIP
Apr. (31N, 124W )
Poulain (1990)
Typical : 10 ~ 20 cm/s
Drifter (15m)
Jan.~Feb. (5~10N, 105~100W)
Sep.~Oct. (5~7N, 143~135W)
Oct.~Dec. (4~7N, 145~140W)
Mar.~Apr. (2~5N, 109~106W)
Paduan (1993)
7~24 cm/s
FLIP, CMD
Oct.~Nov. (35N, 125W)
Thompson (1998)
5~40cm/s
Aug.~Dec. (~50N, 160W)
Saji (2000)
10-75cm/s
(15S~15N, Indian Ocean)
CM : Current meter, CMD : Current Meter Drifter
FLIP : Research Platform

5. Water Following Characteristics of Profiling Float36 35 39 38 37
Surface drifter trajectory
Profiling float
Surface trajectory
QuikSCAT
Wind vector (11/6 12:00)
Latitude (°N)
Latitude (°N)
Surface drifter trajectory
Profiling float
Surface trajectory
Quikscat
Wind vector (11/3 00:00)
Longitude (°W)
Longitude (°W)

6. Inertial Motion from Profiling Float : Method
m : cycle number
Weighted Function Fitting Method
(uL, vL) : Linear velocity
(xo, yo) : Reference position at time t1
(xi, yi) : Inertial origin
: 1000m for class 1, 350m for class 2, 150m for class 3 (Weight)

7. Error Estimation
Inertial amplitude errors in case of 6 fixes (left) and position error of 500m (right) which are estimated with a numerical error simulation.
Inertial Amplitude Error (cm/s)
Number of Fixes : 6
Inertial Amplitude Error (cm/s)
Position Error : 500m
Data Length
Local Inertial Period
(%)
(%)
Local Inertial Period
Data Length
The error in the inertial amplitude estimated from the fitting method is mostly dependent on accuracy of measured positions and total data length of a surface trajectory.

8. Global Statistics ~ 68% = 14.8 cm/s ~ 68% =15.1 cm/s
Surface drift time > 0.6 x Inertial Period
(# of data : 9969)
Surface drift time > 0.8 x Inertial Period
(# of data : 1713)
(# of data : 9969)
(# of data : 1713)
~ 68% = 14.8 cm/s
~ 68% =15.1 cm/s

9. Data
Positions in a cycle whose data length is
more than 68% of local inertial period
1997/08/01~2003/08/31
Purple (JMA) , Red (AOML) , Blue (Coriolis) ,Green (Meds) , Black, Gray, and Cyan (Authors)
Using temperature profiles from Profiling Floats and wind speed from Quikscat scatterometer.

10. Global Statistics (# of data : 9969) (# of data : 4096)

11. Statistics in the North Atlantic and the North Pacific
~68%
~68%
11.7
10.5
14.5
12.9
15.8
14.4
18.1

12. Seasonal Statistics in the North Atlantic & the North Pacific
North Atlantic (30~65N)
Summer (Jun.~Sep.)
Winter (Jan.~Apr.)
North Atlantic
North Atlantic
Summer (Jun.~Sep.)
Winter (Jan.~Apr.)
North Pacific (30~65N)
North Pacific
North Pacific

13. Meridional Distribution (Mid & High Latitude only)
Summary & Discussion
(Unit = cm/s)
Basin
Total
Meridional Distribution
Seasonal Variation
(Mid & High Latitude only)
Global
15.1
Low
(0 ~ 30N)
Mid
(30~45N)
High
(50~65N)
Summer
(Jun.~Sep.)
Winter
(Jan.~Apr.)
North Atlantic
Within 68%
13.1
10.5
14.4
12.9
15.5
12.3
North Pacific
16.3
11.7
18.1
14.5
17.7
14.7
Ratio
(Atlantic / Pacific)
0.80
0.90
0.89
0.86
0.84
Indian Ocean
8~51

14. MLD and Inertial Amplitude Relationship
North Pacific (30~45N)
Aug ~ Dec. 2002
Wind Speed = 4~8 m/sec
T(z)
Mixed Layer Depth (m) H
Inertial Amplitude (cm/s)
MLD from Profiling Floats at the same cycle
Wind Speed from QuikSCAT scatterometer

15. Seasonal and Meridional Variation of MLD and Wind Speed
Monthly Mean Mixed Layer Depth (from Profiling Floats)
North Atlantic (160E~160W)
North Pacific (60W~20W)
Monthly Mean Wind Speed (from QuikSCAT Scatterometer)
North Atlantic (160E~160W)
North Pacific (60W~20W)
55~65N
55~65N
35~45N
35~45N
15~25N
15~25N

16. Temporal Variation of Surface Inertial Amplitude
160W
140W
120W
100W
: Energy flux from the wind into the inertial motions
(D’Asaro, 1985)
North Pacific (50~65N)
Energy Flux( )

19. Temporal Variation of Surface Inertial Amplitude
North Pacific (30~45N)
: Energy flux from the wind into the inertial motions (D’Asaro, 1985)
North Pacific (30~45N)
North Pacific (50~65N)
Energy Flux( )