### tidal_current_introduction

```NRCEST

Current Profilers
 Multi-layers (Three
or ten Layers)
2
Data Acquisition
Velocity : knot(0.51m/s)
Azimuth: the current flows to that direction
wind or wave comes from that direction
3
NRCEST

Data analysis methods in physical oceangraphy:
Emery and Thomson (1998) p.325-327

5

6

7

Wiegel (2005) :風吹流(wind driven current)、波浪

(uE (ti ), uN (ti ))

1975; Preisendorfer , 1988)

 n

  2(u E (ti )  u E )(u N (ti )  u N ) 
1

 p  tan1  n i 1
n

2
2
2 
(
u
(
t
)

u
)
(
u
(
t
)

u
)
 E i


R
N i
N
i 1
 i 1

8

9

1.重心法(centroid of scatter plot)；
2.最小力矩法(minimum inertia
3.最大方向分布(maximum
probability density of directional
distribution)。
10

Kmeans分群法

1 n j
(u E , u N )  (  uE (ti ),
n i 1
j
j
1 n j
uN (ti )) ,

n i 1

11
j  1,2

，且每群之重心可

12

13

14

15

61
233
64
231
65
224

56
242
59
239
58
234

55
241
56
239
57
236

58
238
57
239
61
239

345
273
58
189
67
183

6
243
38
210
38
211

15
243
32
228
38
223

41
221
34
226
39
219

，相差約2-3度，兩

16
Harmonic Analysis for tidal current
M


V(t )  u  U i cos(i t   i )  i v  Vi cos(i t   i )
i 1
i 1


M
 Vector (two-dimensional variables)
 E&N or (L&N) components
 Harmonic Analysis for Ui and Vi
17
Rotary component spectra
 Emery and Thomson (1998) p.427-431)
18
Rotary component spectra
19
Rotary component spectra
20
Rotary component spectra
21
Rotary component spectra
22
Rotary component spectra
Major axis
Minor axis


LM  A  A

Lm  A  A

Tilting angle   (   )
1
2
Flatness

Lm
e 1
LM
23

Evaluation
RMSE
1 N
2
 y(ti )  Y (ti )

N i1
RMSE 
R2(determination of coefficient)
N
R2  1 
  y(t )  Y (t )
2
i 1
N
i
i
  y(t )  y 
2
i
i 1
24
Main components of tides and tidal current
Taipei Harbor
M2
S2
50
50
+
0
-25
-50
-50
+
25
un(cm/s)
un(cm/s)
25
0
-25
-25
0
25
-50
-50
50
-25
N2
50
50
+
-
25
un(cm/s)
25
un(cm/s)
25
K1
50
0
-25
-50
-50
0
0
-25
-25
0
25
ue(cm/s)
50
25
-50
-50
-25
0
25
ue(cm/s)
50
Main compinents of tides and tidal current
KaoHsiung Harbor
K1
M2
50
50
-
0
-25
-50
-50
-
25
un(cm/s)
un(cm/s)
25
0
-25
-25
0
25
-50
-50
50
-25
O1
50
50
-
-
25
un(cm/s)
25
un(cm/s)
25
S2
50
0
-25
-50
-50
0
0
-25
-25
0
25
ue(cm/s)
-50
-50
50
26
-25
0
25
ue(cm/s)
50
Astronomical tides
20
1
15
0.95
10
0.9
5
0.85
0
TP
TC
AP
KH
HL
SA
KL
R2
RMSE(cm)
tide
0.8
Numerically simulated tides for Taipei and Anping harbor
27
U-component of tidal current
1
20
0.8
15
0.6
10
0.4
5
0.2
R2
RMSE(cm/s)
U-component
25
0
TP
TC
AP
KH
28
HL
SA
KL
0
V-component of tidal current
1
20
0.8
15
0.6
10
0.4
5
0.2
R2
RMSE(cm/s)
V-Component
25
0
TP
TC
AP
29
KH
HL
SA
KL
0
Main components of tides and tidal current
St.
TP
TC
AP
KH
HL
SA
KL
T&C
1
2
3
4
5
6
7
8
9
10
Tide
M2
K1
O1
S2
N2
P1
K2
Q1
Ssa
ν2
Cur.
M2
S2
N2
K1
K2
Sa
M4
Msf
O1
ν2
Tide
M2
S2
N2
K1
O1
K2
Sa
L2
ν2
μ2
Cur.
Sa
Ssa
M2
K1
Mm
Msf
O1
S2
Mf
P1
Tide
M2
K1
O1
S2
P1
N2
Q1
Ssa
K2
Sa
Cur.
M2
S2
Sa
K1
N2
S1
O1
ψ1
Ssa
K2
Tide
K1
M2
O1
Sa
S2
Ssa
P1
N2
Q1
K2
Cur.
K1
M2
O1
S2
Sa
P1
ψ1
N2
S1
Ssa
Tide
M2
S2
Sa
K1
O1
N2
K2
P1
Ssa
Q1
Cur.
M2
S1
Sa
K1
S2
M4
Ms4
K2
ν2
O1
Tide
M2
K1
O1
S2
Sa
N2
P1
K2
Q1
μ2
Cur.
M2
Sa
S2
K1
O1
S1
K2
M4
Msf
N2
Tide
M2
K1
O1
Sa
P1
N2
S2
Q1
μ2
K2
Cur.
M2
S2
N2
Sa
μ2
M4
Ssa
Op2
L2
Mks2
30
Main components of tides
tide-W
100
TP
TC
AP
KH
80
Ramp
60
40
20
0
0
2
4
6
No
31
8
10
Main components of tides and tidal current
current-W
100
80
Ramp
60
40
20
0
0
2
4
6
No
32
8
10
Main components of tides and tidal current
tilt-W
90
60
o
( )
30
0
-30
-60
-90
0
2
4
6
No
33
8
10
Main components of tides and tidal current
flat-W
1
0.8
e
0.6
0.4
0.2
0
0
2
4
6
No
34
8
10
Main components of tides and tidal current
tide-E
100
HL
SA
KL
80
Ramp
60
40
20
0
0
2
4
6
No
35
8
10
Main components of tidal current
current-E
100
80
Ramp
60
40
20
0
0
2
4
6
No
36
8
10
Main components of tidal current
tilt-E
90
60
o
( )
30
0
-30
-60
-90
0
2
4
6
No
37
8
10
Main components of tidal current
flat-E
1
0.8
e
0.6
0.4
0.2
0
0
2
4
6
No
38
8
10
```