Keck Institute for Space Studies Postdoctoral Fellowship Final ...
Postdoctoral Final Report
Transcript of Postdoctoral Final Report
Puerto Rico
SW coast and shelf
Location of the shelf and offshelf ADCP.
Figure 1b
Offshelf
shelfbreakshelf
IMF sifting of u (tk , z) z=30 m, k = 1,2,3…K ; CE(100,5)Figure 2
270 275 280 285 290 295 300 305 310 315-10
0
10
F1
270 275 280 285 290 295 300 305 310 315-10
0
10
F2
270 275 280 285 290 295 300 305 310 315-10
0
10
F3
270 275 280 285 290 295 300 305 310 315-10
0
10
F4
270 275 280 285 290 295 300 305 310 315-10
0
10
F5
270 275 280 285 290 295 300 305 310 315-40
-20
0
20
Year day (2000)
cm/s
Original signal: u ( t , z ), Z = 30 m
Figure 3
270 275 280 285 290 295 300 305 310 315-15
-10
-5
0
5
10
15
Year day (2000)
Spe
ed (
cm/s
)
First IMF of u(t), F1, and its envelope, a(t); Z=30 m
Generate matrix F from original dataFigure 4
=
),(),(),(),(
),(),(),(),(
),(),(),(),(
),(),(),(),(
321
3332313
2322212
1312111
MKKKK
M
M
M
ztXztXztXztX
ztXztXztXztX
ztXztXztXztX
ztXztXztXztX
LMMMM
L
L
L
XOriginal Data
Time Series
L Intrinsic Mode Functions (IMF)
F1(tk,z1)F2(tk,z1)F3(tk,z1)...FL(tk,z1)
EMD
Matrix F containsL IMFs for each depth.
),(),(),(),(
),(),(),(),(),(),(),(),(
),(),(),(),(
321
3332313
2322212
1312111
MKLMLMLML
MKMMM
MKMMM
MKMMM
ztFztFztFztF
ztFztFztFztFztFztFztFztF
ztFztFztFztF
LMMMM
L
L
L
),(),(),(),(
),(),(),(),(
),(),(),(),(
),(),(),(),(
3333231
33333323313
32332322312
31331321311
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
KLLLL
K
K
K
LMMMM
L
L
L
),(),(),(),(
),(),(),(),(
),(),(),(),(
),(),(),(),(
2232221
23233223213
22232222212
21231221211
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
KLLLL
K
K
K
LMMMM
L
L
L
Repeat the analysison each time series.
zm
),(),(),(),(
),(),(),(),(
),(),(),(),(
),(),(),(),(
1131211
13133123113
12132122112
11131121111
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
KLLLL
K
K
K
LMMMM
L
L
L
l
tk
Decomposition of the 3D matrix F into a series of 2D matrices Fl slicing it at a particular component l where l=1, 2, 3…L
=
),(),(),(),(
),(),(),(),(
),(),(),(),(),(),(),(),(
321
3332313
2322212
1312111
MKLKLKLKL
MLLLL
MLLLL
MLLLL
ztFztFztFztF
ztFztFztFztF
ztFztFztFztFztFztFztFztF
LMMMM
L
L
L
LF
=
),(),(),(),(
),(),(),(),(
),(),(),(),(
),(),(),(),(
3332313
33333233133
23323223123
13313213113
MKKKK
M
M
M
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
LMMMM
L
L
L
3F
=
),(),(),(),(
),(),(),(),(
),(),(),(),(
),(),(),(),(
2322212
32332232132
22322222122
12312212112
MKKKK
M
M
M
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
ztFztFztFztF
LMMMM
L
L
L
2F
=
),(),(),(),(
),(),(),(),(
),(),(),(),(),(),(),(),(
1312111
31331231131
21321221121
11311211111
MKKKK
M
M
M
ztFztFztFztF
ztFztFztFztF
ztFztFztFztFztFztFztFztF
LMMMM
L
L
L
1F
IMF C
ompo
nent
l
Depth zm
Tim
e t k
Amplitude of IMF component L for time tk (k=1) and depth level zm (m=1)
Dimension of F= K x M x LDimension of Fl= K x M
Figure 5
EOF decomposition of the 2D matrices F1, F2, F3… FL and their rearrangement to generate the 3D matrix Fn (n=1,2,3…M).
Figure 6
2D F1
F2
F3
FL
EOF R2(zi,zj)
EOF R1(zi,zj)
EOF R3(zi,zj)
EOF RL(zi,zj)
F31 F3
2 F33 F3
M
F11 F1
2 F13 F1
M
F21 F2
2 F23 F2
M
FL1 FL
2 FL3 FL
M
Reconstruct F1 along each EOF mode
F1 F2 F3 FM3D
88.36%
2.43%
4.28%
7.45%
11.72%
13.34%
49.14%
Explained Variance
2nd ApproachAl
n
93.52%
2.34%
2.63%
6.48%
10.29%
15.87%
55.91%
Explained Variance
1st ApproachFl
n
First IMFl=1
6
Subtotal
5
4
3
2
1
Mode numbern
Table 1
n
n
λλ
Σ n
n
λλ
Σ
Year Day (2000)
Freq
uenc
y (C
PD
)
Hilbert Spectrum
275 280 285 290 295 300 305 310
0.5
1
1.5
2
2.5
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Year Day (2000)
Freq
uenc
y (C
PD
)
Hilbert Spectrum
275 280 285 290 295 300 305 310
0.5
1
1.5
2
2.5
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Year Day (2000)
Freq
uenc
y (C
PD
)
Hilbert Spectrum
275 280 285 290 295 300 305 310
0.5
1
1.5
2
2.5
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Year Day (2000)
Freq
uenc
y (C
PD
)
Hilbert Spectrum
275 280 285 290 295 300 305 310
0.5
1
1.5
2
2.5
3
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
A
B
C
D
),),(( 3011 kk ttH lω
),),(( 3021 kk ttH lω
),),(( 3031 kk ttH lω
),),(( 301 kk ttH lω( ) 2
1
CPDcm/s
Figure 7
270 275 280 285 290 295 300 305 31010
12
14
16
18
20
22
24
26
28
30
32Barotropic currents range and lunar phases
Year day (2000)
Ran
ge (
cm/s
)
1.6 2.4 0.0 1.74 1.22 -0.81- 4 , 6 - 4- new moon
4 first Qt.
, full moon
6 last Qt.
Figure 8
Table 2
A11
2.74
3.83
2.25
Time lag between barotropic neap
tides and baroclinic
spring tides (days)
3.05
2.43
0.23
Time lagbetween
barotropicand baroclinic
spring tides (days)
FQ
LQ
FQ
Moon PhaseFQ=first quarter
LQ=last quarter
NM
FM
NM
Moon PhaseNM=new moon
FM=full moon
2.29311.6-0.45308.86309.31
4.37298.70.54294.87294.33
2.64282.10.39279.85279.46
Total time lagbetween phase andbaroclinic spring
tides (days)
BaroclinicTides
(spring)
Age ofBarotropicneap tides
BarotropicTides
(neap)
PhaseYD
2000
2.24303.57-0.81300.52301.33
3.65291.021.22288.59287.37
1.97273.81.74273.57271.83
Total time lagbetween phase andbaroclinic spring
tides (days)
BaroclinicTides
(spring)
Age ofBarotropic
spring tides
BarotropicTides
(spring)
PhaseYD
2000
Year Day (2000)
Dep
th (
m)
EOF 3
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
-4
-3
-2
-1
0
1
2
3
4
Year Day (2000)
Dep
th (
m)
EOF 2
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
-10
-8
-6
-4
-2
0
2
4
6
8
10
Year Day (2000)
Dep
th (
m)
F11
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
-10
-5
0
5
10
Year Day (2000)
Dep
th (
m)
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
-10
-5
0
5
10
F12
F13
F1: u
A
B
C
D
Figure 9
F11
cm/s
cm/s
cm/s
cm/s
Figure 10
cm/s
dept
h (m
)
F11
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
275 280 285 290 295 300 305 3100
5
10
15
20
25
30
year day (2000)
rang
e (c
m/s
)
Range of barotropic U at ADCP3
-10
-5
0
5
10
cm/s
cm/s
cm/s
cm/s
Year Day (2002)
Dep
th (
m)
EOF 3
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
-6
-4
-2
0
2
4
6
Year Day (2002)
Dep
th (
m)
EOF 2
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
-4
-3
-2
-1
0
1
2
3
4
Year Day (2002)
Dep
th (
m)
EOF 1
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
-10
-8
-6
-4
-2
0
2
4
6
8
10
Year Day (2000)
Dep
th (
m)
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
0
2
4
6
8
10
12
A11
A12
A13
A1: u
A
B
C
D
Figure 11
Figure 12
dept
h (m
)
A11
275 280 285 290 295 300 305 310
-60
-50
-40
-30
-20
-10
275 280 285 290 295 300 305 3100
5
10
15
20
25
30
year day (2000)
rang
e (c
m/s
)
Range of barotropic U at ADCP3
-10
-5
0
5
10cm/s
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.60
1
2
3
4
5
6PDF estimate of envelope frequency
frequency (CPD)
0.135 CPD
-0.1 0 0.1 0.2 0.3 0.4 0.5 0.60
1
2
3
4
5
6PDF estimate of envelope frequency
frequency (CPD)
0.0706 CPD
Year Day (2000)
Freq
uenc
y (C
PD
)
Hilbert Spectrum: First four IMF's of the envelope A1(tk, 30 m)
275 280 285 290 295 300 305 3100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0
0.2
0.4
0.6
0.8
1
1.2
1.4
Year Day (2000)
Freq
uenc
y (C
PD
)
Hilbert Spectrum: all IMF's of the envelope A1(tk, 30 m)
275 280 285 290 295 300 305 3100
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.5
0
0.5
1
1.5
A
B
C
D
Figure 13
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide, F1 ADCP2
280 285 290 295 300 305
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
2
4
6
8
10
12
J/m3
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide, F1 ADCP1
280 285 290 295 300 305
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
2
4
6
8
10
12
14
16
18
20
22
J/m3
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide, F1 ADCP3
280 285 290 295 300 305
-110
-100
-90
-80
-70
-60
-50
-40
-30
-20
-10
1
2
3
4
5
6
7
8
9
J/m3
Figure 14
2.3 d
2.4 d
1.45 d1.4 d
A
B
C
275 280 285 290 295 300 305 310-40
-20
0
20
40original signal for depth level 30.5m
spee
d cm
/s
275 280 285 290 295 300 305 310-10
0
10
SD bandpass filtered signal
275 280 285 290 295 300 305 310-10
0
10
F1 signal from EMD analysis
275 280 285 290 295 300 305 310-10
0
10
D3 signal from Wavelet analysis
YD (2000)
Figure 15
KE of the baroclinic tide on YD 279-284 2000FFT vs. EMD
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide (SD bandpass filter)
279 279.5 280 280.5 281 281.5 282 282.5 283 283.5 284-30
-28
-26
-24
-22
-20
-18
-16
-14
-12
-10
0.5
1
1.5
2
2.5
3
3.5
J/m3
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide, F1 ADCP3
279 279.5 280 280.5 281 281.5 282 282.5 283 283.5 284-30
-28
-26
-24
-22
-20
-18
-16
-14
-12
-10
1
2
3
4
5
6
7
8
9
J/m3
A B
Figure 16
KE of the internal tide on YD 279-284 2000Wavelet vs. EMD
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide, F1 ADCP3
279 279.5 280 280.5 281 281.5 282 282.5 283 283.5 284-30
-28
-26
-24
-22
-20
-18
-16
-14
-12
-10
1
2
3
4
5
6
7
8
9
J/m3
A B
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide (Wavelets: db2; detail 3)
279 279.5 280 280.5 281 281.5 282 282.5 283 283.5 284-30
-28
-26
-24
-22
-20
-18
-16
-14
-12
-10
2
4
6
8
10
12
14
16
18
J/m3
Figure 17
80 85 90 95 100 105 110 115 120 1251.8
2
2.2
2.4
2.6
2.8
year day (2002)
rang
e(cm
/s)
Range of barotropic U at the offshelf ADCP
Figure 19
Year Day (2002)
Dep
th (
m)
F13 u
80 85 90 95 100 105 110 115 120 125-450
-400
-350
-300
-250
-200
-150
-100
-50
-5
-4
-3
-2
-1
0
1
2
3
4
5
Year Day (2002)
Dep
th (
m)
F12 u
80 85 90 95 100 105 110 115 120 125-450
-400
-350
-300
-250
-200
-150
-100
-50
-4
-3
-2
-1
0
1
2
3
4cm/s cm/s
cm/s cm/s
A
B
C
D
Figure 21
6.39 %4.56 %6
66.022 %5.66 %
6.47 %
9.17 %
9.79 %
11.94 %
16.60 %
Explained Variance
2nd ApproachAl
n
78.47 %3.82 %
5.99 %
9.08 %
11.51 %
16.25 %
27.26 %
Explained Variance
1st ApproachFl
n
First IMFl=1
7
Subtotal
5
4
3
2
1
Mode numbern
Table 3
n
n
λλ
Σ n
n
λλ
Σ
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide, F1
80 85 90 95 100 105 110 115 120 125-450
-400
-350
-300
-250
-200
-150
-100
-50
0
2
4
6
8
10
12J/m3
Year Day (2000)D
epth
(m
)80 85 90 95 100 105 110 115 120 125
-450
-400
-350
-300
-250
-200
-150
-100
-50
0
1
2
3
4
5
6
7
8
9Potential Energy of the internal tide, F1
J/m3
A B
Figure 24
Year day 2002 Year day 2002
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the diurnal internal tide
80 85 90 95 100 105 110 115 120 125-450
-400
-350
-300
-250
-200
-150
-100
-50
1
2
3
4
5
6
7
8
9
10
J/m3
Year Day (2000)D
epth
(m
)
Potencial Energy of the diurnal internal tide
80 85 90 95 100 105 110 115 120 125-450
-400
-350
-300
-250
-200
-150
-100
-50
1
2
3
4
5
6
7
8
A B
Figure 25
Year day 2002 Year day 2002
Year Day (2000)D
epth
(m
)
Kinetic Energy of the diurnal internal tide,F2, offshelf
80 85 90 95 100 105 110 115 120 125-75
-70
-65
-60
-55
-50
-45
-40
-35
-30
-25
0
1
2
3
4
5
6
7
8
9
10
11J/m3
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide, F1, offshelf
80 85 90 95 100 105 110 115 120 125-75
-70
-65
-60
-55
-50
-45
-40
-35
-30
-25
0
1
2
3
4
5
6
7
8
9
10
11J/m3
A B
Figure 26
Year day 2002Year day 2002
A B
Figure 28
79.5417 81.6267 83.7117 85.7967 87.8817 89.9667 92.0517 94.1367
F1, u, shelf
5
6
7
8
9
1011
12
1314
Year day 2002
79.5417 81.6267 83.7117 85.7967 87.8817 89.9667 92.0517 94.1367
F1, v, shelf
Year day 2002
A B
Figure 29de
pth
(m)
80 82 84 86 88 90 92 94
-20
-15
-10
-5
-10
-8
-6
-4
-2
0
2
4
6
8
10F1: u shelf cm/sF1: u, shelf
Year day 2002de
pth
(m)
80 82 84 86 88 90 92 94
-20
-15
-10
-5
-6
-4
-2
0
2
4
6F1 shelf
cm/sF1: v, shelf
Year day 2002
A B
Figure 30
Year Day (2000)
Dep
th (
m)
Kinetic Energy of the internal tide, F1 shelf
80 82 84 86 88 90 92 94
-22
-20
-18
-16
-14
-12
-10
-8
-6
0.5
1
1.5
2
2.5
3
3.5
J/m3
Year day 2002Year Day (2000)
Dep
th (
m)
80 82 84 86 88 90 92 94
-22
-20
-18
-16
-14
-12
-10
-8
-6
0.5
1
1.5
2
2.5
3Potencial Energy of the internal tide, F1 shelf
J/m3
Year day 2002
80 85 90 95 100 105 110 115 120 125
-0.15
-0.1
-0.05
0
0.05
0.1
0.15
0.2
Tidal Height at Magueyes Island, La Parguera, Puerto Rico
Year day 2002
Wat
er L
evel
hei
ght (
m)
Figure 31