lagrangian statistics of three rafos floatspsguest/oc3570/cdrom/... · floats (nps #80 & #81)...
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Lagrangian Statistics of three RAFOS floats NPS #80, #81 and #82 in the California Undercurrent
LT Hsieh, Chung-Ping R.O.C Taiwan Navy
14 Sep 2006
2
LIST OF CONTENTS
TABLE OF FIGURES AND TABLES 3
1. INTRODUCTION 4
2. DATA AND ANALYSIS 5
2.1 Three RAFOS floats observations 5
2.2 Single Particle Dispersion 11
2.3 Two Particles Dispersion 13
2.4 Three Particles Dispersion 23
III. CONCLUSIONS 26
REFERENCES 28
3
LIST OF FIGURES AND TABLES
Figure 1. Temperature along NPS #80 trajectory. 6 Figure 2. Temperature and Pressure of NPS #80. 6 Figure 3. Velocity vector of NPS #80. 7 Figure 4. Temperature along NPS #81 trajectory. 8 Figure 5. Temperature and Pressure of NPS #81. 8 Figure 6. Velocity vector of NPS #81. 9 Figure 7. Temperature along NPS #82 trajectory. 10 Figure 8. Temperature and Pressure of NPS #81. 10 Figure 9. Velocity vector of NPS #81. 10 Figure 10. Velocity vs. Latitude in the CUC 11 Figure 11. Single particle dispersion Kuu and Kvv. 12 Figure 12. Pair 1(NPS #80 & #81) trajectories. 14 Figure 13. Separation and Square Separation of Pair 1. 15 Figure 14. Diffusivity of Pair 1. 15 Figure 15. The Comparison of alongshore and cross-shore component of pair 1. 16 Figure 16. Pair 2(NPS #80 & #82) trajectories. 17 Figure 17. Separation and Square Separation of Pair 2. 18 Figure 18. Diffusivity of Pair 2. 18 Figure 19. The Comparison of alongshore and cross-shore component of pair 2. 19 Figure 20. Pair 3(NPS #81 & #82) trajectories. 20 Figure 21. Separation and Square Separation of Pair 3. 21 Figure 22. Diffusivity of Pair 3. 21 Figure 23. The Comparison of alongshore and cross-shore component of pair 3. 22 Figure 24. Three particles trajectories and enclosed triangle area. 24 Figure 25. The triangle area growth of three RAFOS floats. 24 Figure 26. Base and Height of the triangle area. 25
Table 1. NPS #80 trajectory information. 5 Table 2. NPS #81 trajectory information. 7 Table 3. NPS #82 trajectory information. 9 Table 4. Single Particle Diffusivity result. 12 Table 5. Particle Pair Diffusivity result. 23
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1. INTRODUCTION
The California Undercurrent is a poleward flow adjacent to the continental slope
along the West coast of the United State. It transports warm, salty and low oxygen equatorial
water at the intermediate depth. The three RAFOS floats, NPS #80, #81 and #82 were
deployed between Jul 2000 and May 2002 above 400 dbar. After launch, they trapped in the
California Undercurrent (CUC) and moved along the coast, and then turn into the interior of
the Pacific Ocean at different time and trapped into the westward small scale cyclonic
California eddies (cuddy) close to the California Current (CU). After a period time, two
floats (NPS #80 & #81) resume the ploeward CUC movement, and then went back to the
interior again. When in the interior, the NPS #82 had two periods, one was in the larger
cyclonic eddy and the other one was in the smaller cyclonic eddy. The detail of these three
RAFOS floats will discuss in section 2.1.
The purpose of these RAFOS floats is using the Lagrangian measurement of the
trajectory of each float to determine the character of single float dispersion in the
undercurrent, the separation (distance) between two floats to determine the two particles
dispersion, and the triangle area of three RAFOS floats at the same time step to determine the
three particles dispersion.
In single particle dispersion, the comparison of alongshore and cross-shore velocity
diffusivity is the key to determine the dispersion. And the as expected that the alongshore
component dominated the total dispersion in the CUC (detailed in Sec 2.2). In two-particle
dispersion, the square separation is the main factor to find the correlation between the two
floats and compare to the Richardson growth regime (D2 ∝ t3). The results show that in pair 1
(#80 & #81) and pair 2 (#80 & #82), alongshore diffusivity dominated the total diffusivity.
But in Pair 3 (#81 R), each of alongshore and cross-shore diffusivity dominated the total
5
diffusivity in two different periods (detailed in 2.3). The triangle area growth of three
RAFOS floats is the main idea to the three particles dispersion. But, there still have no exact
equation to calculate the diffusivity (detailed in 2.4).
2. DATA AND ANALYSIS
2.1 Three RAFOS floats observations.
The three RAFOS floats NPS #80, #81 and #82 launched on Jul 2000. The
deployment period of NPS #81 was longer than the other two floats. Each float movement
can be divided into two main period, CUC and interior period.
2.1.1 NPS #80
After launch on Jul 2000, NPS #80 was entrained in the CUC and moving ploeward
in first 30 days and then move into the interior. After 294 days, it resumed to the CUC and
then moved into the interior again (Table 1,Figure 1).
Table 1. NPS #80 trajectory information Launch Surface
Date φ °N λ °W Depth,m Date φ °N λ °W Sample/day26/07/00 36.63 122.48 2541 23/09/01 35.63 125.13 2
Pressure (dbar) and Temperature °C Mission Day Planned Actual Planned Actual
275 ---
348±53.4 7.31±0.4 425 425
Alongshore (CUC) Interior 1-30
295-340 31-294 341-425
6
From figure 1, the four periods of the float movement can be easily noticed. At the
first period, the temperature in the CUC was warmer than other periods due to the poleward,
warm and salty equator water. The temperature all over the period was 7.31 ± 0.4 °C and the
pressure was around 348 ± 53.4 dbar(figure 2). The direction of the movement in the CUC
was about 30° northwest, and resulted in the positive alongshore velocity component and
negative cross-shore velocity component (Figure 3).
(a)
(b)
Figure 1. Temperature along the trajectory of NPS 80.
Figure 2. (a) Temperature (green dot) and Pressure (blue dot) vs. Time. (b) Temperature vs. Pressure of NPS 80. The temperature was about 6 to 8 °C and pressure was 300 to 400 dbar.
7
(a)
(b)
2.1.2 NPS #81
NPS #81 also entrained in CUC for 24 days after the launch and then entered into the
interior. After 168 days, it resumed to the CUC and then trapped in the interior again. This
float traveled the widest area (36 °N to 45 °N) and survived longer than the other two floats
(Table2, Figure 4). The temperature was around 7 to 8 °C and the pressure was about 300
dbar (Figure 5). Again, the northwest movement resulted in the positive alongshore velocity
and negative cross-shore velocity component (Figure 6).
Table 2. NPS #81 trajectory information Launch Surface
Date φ °N λ °W Depth,m Date φ °N λ °W Sample/day26/07/00 36.46 122.8 3031 22/05/02 39.67 126.91 1
Pressure (dbar) and Temperature °C Mission Day Planned Actual Planned Actual
275 ---
275.8±53.7 7.54±0.2 666 666
Alongshore (CUC) Interior 1-24
169-289 25-168 190-665
Figure 3. (a) Total, alongshore and cross-shore velocities in the CUC period 1(1-24 days). (b) Total, alongshore and cross-shore velocities in the CUC period (169-289 days) of NPS 80. The total velocity was moving in northwest direction in the CUC and had a result of negative cross-shore velocity and positive velocity.
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(a)
(b)
Figure 4. Temperature along the trajectory of NPS 81.
Figure 5. (a) Temperature (green dot) and Pressure (blue dot) vs. Time. (b) Temperature vs. Pressure of NPS 81. The temperature was about 7 to 8 °C and pressure was 200 to 400 dbar.
9
(a)
(b)
2.1.3 NPS #82
This float entrained in the CUC for first 88 days and then entered into the interior. In
the interior period, the float first trapped in the larger small-scale cyclonic eddy (California
Current eddy-cuddy) and then trapped into a smaller westward cuddy and made a series of
three cyclonic circles (Table 3, Figure 7).
Table 3. NPS #82 trajectory information Launch Surface
Date φ °N λ °W Depth,m Date φ °N λ °W Sample/day26/07/00 36.55 122.62 3034 24/09/01 42.02 130.13 2
Pressure (dbar) and Temperature °C Mission Day Planned Actual Planned Actual
275 ---
215.5±22.6 7.61±0.25 425 425
Alongshore (CUC) Interior 1-88 89-425
The temperature of whole period was between 7.61 ± 0.25 °C and the pressure was
215.5 ± 22.6 dbar (Figure 8). The northwest movement also resulted in the positive
alongshore velocity and negative cross-shore velocity (Figure 9).
Figure 6. (a) Total, alongshore and cross-shore velocities in the CUC period 1(1-24 days). (b) Total, alongshore and cross-shore velocities in the CUC period (169-889 days) of NPS 81. The total velocity was moving in northwest direction in the CUC and had a result of negative cross-shore velocity and positive velocity.
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(a)
(b)
Figure 7. Temperature along the trajectory of NPS 82.
Figure 8. (a) Temperature (green dot) and Pressure (blue dot) vs. Time. (b) Temperature vs. Pressure of NPS 82. The temperature was about 7 to 9 °C and pressure was 150 to 300 dbar.
Figure 9. Total, alongshore and cross-shore velocities in the CUC period (1-88 days) of NPS 82. The total velocity was moving in northwest direction in the CUC and had a result of negative cross-shore velocity and positive velocity.
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2.1.4 Velocity vs. Latitude
In figure 10, the RAFOS caught in the CUC had larger speed around Pt. Reyes. And
at the Cape Mendocino and Pt. Reyes, the floats entered or exited the CUC, it means around
here have lager upwelling and result in divergence of the water. Then the float was forced to
enter the interior and resume in the CUC while smaller upwelling effect.
When these three floats trapped in the CUC, the northwest motion affected the
characteristics of any single float, two floats and even three or more floats dispersion. So, the
alongshore component domination can be expected.
2.2 Single Particle Dispersion
In order to have a clear picture of alongshore and cross-shore component, the
conversion to the Cartesian coordinate and rotating about 30 ° was applied. The Largranian
correlation Rij(τ) is defined as [Taylor, 1921; Batchelor, 1952; Moffat, 1983; Collins et al,
Figure 10. Velocity vs. Latitude in the CUC. NPS80-1(blue solid line), NPS 80-2(blue dashed line). NPS 81-1(red solid line). NPS 81-2(red dashed line). NPS 82(green solid line)
12
2004] and the diffusivity tensor is determined as :
The single particle diffusivity of all the RAFOS floats caught in the CUC had the
same result, the alongshore diffusivity (Kuu) was larger than the cross-shore diffusivity (Kvv).
This result proves that in the CUC, the cross-shore and alongshore diffusivity both exist and
affect the RAFOS float dispersion but the alongshore is the dominant of the total diffusivity
(Figure 11, Table 4).
Table 4. Single particle Diffusivity result
Diffusivity ×107 , cm2/s RAFOS NO. CUC Period (days) Kvv (alongshore) Kuu (cross shore) 1-30 0.8 0.4 NPS #80 295-340 0.045 0.028 1-24 2.4 0.5 NPS #81 169-189 0.62 0.1
NPS #82 1-88 0.65 0.3
(a)
(b)
r2i j = V0
2Ri j (τ ) = Vi (x0 , t)Vj (x0 , t + τ ) = limT→∞
1
TVi (x0 , t)Vj (x0 , t + τ )dt
t0
t0 +τ
∫ ..............................(1)
Ki j = r2i jdτ
0
∞
∫ = V02 Ri j (τ )
0
∞
∫ dτ ..................................................................................................(2)
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(c)
(d)
(e)
2.3 Two Particles Dispersion
In two particles dispersion, the distance (separation) between two RAFOS floats —
pair 1(NPS #80 & #81), pair 2 (NPS #80 & #82) and pair 3 (NPS #81 & #82) — is main
factor to determine the dispersion. Here, the diffusivity can be expressed as [Davis. 1985;
Garfield and Collins et al, 1998]:
α ij =1
4
d
dtSi 'Sj ' =
1
4
d
dt
1
NSi 'S j '∑
.....................................................................................(3)
2.3.1 Pair 1 (NPS #80 & #81)
a. Total Separation
The NPS #80 and #81 had initial separation of 33.3km. After launch, the two float
moving in the CUC and correlated, and then uncorrelated and moving independently (figure
Figure 11. Alongshore diffusivity Kvv (red line) and cross-shore diffusivity Kuu (blue line) of (a) NPS 80-1. (b) NPS 80-2. (c) NPS 81-1. (d) NPS 81-2. (e) NPS 82.
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12). They moved toward (separation decreased) in first 3.25 days and then moved away
(separation increased) until 19.25 days. After 19.25 days, the separation decreased and
increased randomly (figure 13 a). It indicated the two floats were moving independently and
not correlated after 19.25 days. The diffusivity was determined only during 3.25 and 19.25
days.
The logarithm plot of the square separation (figure 13 b) showed that, between 3.25 to
5.75 days the square separations was exponential growth (stretching) and then applied the
least square method to find the square separation growth rate with time (S2 /t β), here the
growth rate β = 2.25. If the two floats were perfectly dispersed, the exponent relation with
time (S2 / tβ) will match the Richardson regime (S2 /t3) and closed together as a straight
horizontal line.
Figure 12. NPS 80 (red line) and NPS 81 (blue line) trajectories. The two floats had initial separation 33.3km.
15
(a)
(b)
The maximum total diffusivity of pair 1 is 6 × 10 7 from 5.75 to 12.75 days. And after
12.75 days the diffusivity decreased, then it could not be determine as dispersion. The total
dispersion was start from 5.75 to 12.75 days (figure 14).
(a)
(b)
b. Alongshore and cross-shore Separation
The alongshore and cross-shore separation, square separation and diffusivity were
showed in figure 15. In pair 1, the cross-shore component almost had no effect to the total
dispersion, and the alongshore component had almost the same result with the total
Figure 13. (a) Separation (b) Square Separation of pair 1(NPS 80 & 81). In (b) the red dot indicates the exponential growth, the purple line is the least square trend of the square separation. And at the right below corner is the plot of compensated Evolution of Square separation compare to the Richardson growth regime (S2 / t3).
Figure 14. (a) Diffusivity (red dot) vs. time (b) Diffusivity (red dot) vs. Separation of pair1 (NPS 80 & 81). The blue line is the least square trend of the diffusivity.
16
dispersion. So the alongshore diffusivity component dominated the total diffusivity in the
Pair 1.
(a)
(b)
(c)
Figure 15. The left side is the cross-shore component, and the right side is the alongshore component of pair 1(NPS 80 & 81). (a) Separation (b) Square separation and (c) Diffusivity.
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2.3.2 Pair 2 (NPS #80 & #82)
a. Total Separation
The NPS #80 and #82 had initial separation of 26.7 km. After launch, the two float
moved in the CUC and correlated to each other, and then they uncorrelated and moved
independently (figure 16). They moved away (separation increased) from each other for
50.25 days after launch. After then the separation decreased and increased randomly (figure
17 a). It indicated the two floats were moving independently and not correlated after 50.25
days. The diffusivity was determined only during 1 to 4.75 and 24.25 to 50.25 days.
The logarithm plot of the square separation (figure 17 b) showed that, between day1
to 4.75 the square separation was exponential growth (stretching) and square separation
growth rate between day 24.25 to 50.25 with β = 5.5. It was larger than the Richardson
regime (S2 /t3) and the Compensated evolution of square separation lined together. The
maximum total diffusivity of pair 2 was 10 × 10 7 from day 24.25 to 50.25 (figure 18).
Figure 16. NPS 80 (red line) and NPS 82 (green line) trajectories. The two floats had initial separation 26.7 km.
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(a)
(b)
(a)
(b)
b. Alongshore and cross-shore Separation
The alongshore and cross-shore separation, square separation and diffusivity were
showed in figure 19. In pair 2, the cross-shore component also almost had no effect to the
total dispersion, and the alongshore component dominated the total dispersion.
Figure 18. (a) Diffusivity (red dot) vs. time (b) Diffusivity (red dot) vs. Separation of pair 2 (NPS 80 & 82). The blue line is the least square trend of the diffusivity.
Figure 17. (a) Separation (b) Square Separation of pair 2(NPS 80 & 82). In (b) the red dot indicates the exponential growth, the purple line is the least square trend of the square separation. And at the right below corner is the plot of compensated Evolution of Square separation compare to the Richardson growth regime (S2 / t3).
19
(a)
(a)
(b)
(c)
2.3.3 Pair 3 (NPS #81 & #82)
a. Total Separation
The NPS #81 and #82 had initial separation of 38.5 km. After launch, the two floats
correlated and moved along the CUC, and then turned into the interior. When trapped in the
cyclonic cuddies, they flowed uncorrelated and independently (figure 20). From the track, it
Figure 19. The left side is the cross-shore component, and the right side is the alongshore component of pair 2(NPS 80 & 82). (a) Separation (b) Square separation and (c) Diffusivity.
20
can be seen clearly that at the beginning, the two floats move together to the north
(alongshore) with velocity of NPS #82 faster then the NPS #81, and then they turned into the
interior together. So we can expect that, when moved north in the CUC, the alongshore
component dominated and when leaving the CUC turning into the interior, the cross-shore
component dominated. They moved toward in first 3.75 days and then away from each other
till 64.25 days. After 64.25 days, the separation decreased and increased randomly (figure 21
a). It indicated the two floats were moving independently and not correlated after 64.25days.
The diffusivity was determined only during 3.75 to 13.75 and 20.25 to 60.25 days.
Figure 20. NPS 81 (blue line) and NPS 82 (green line) trajectories. The two floats had initial separation 38.5 km.
21
(a)
(a)
The logarithm of the square separation (figure 21 b) showed that, the first period the
square separation had a growth rate of β=2.5 and the diffusivity α ~5×107, and then the
second period β = 3.7 and the diffusivity α ~15×107 (figure 22).
(a)
(b)
b. Alongshore and cross-shore Separation
The alongshore and cross-shore separation, square separation and diffusivity were
showed in figure 23. In pair 3, the alongshore component dominated the total diffusivity and
during the second period the cross-shore component dominated with larger diffusivity. This
result matched from the expectation from trajectories plot.
Figure 22. (a) Diffusivity (red dot) vs. time (b) Diffusivity (red dot) vs. Separation of pair 3 (NPS 81 & 82). The blue line is the least square trend of the diffusivity.
Figure 21. (a) Separation (b) Square Separation of pair 3(NPS 81 & 82). In (b) the red dot indicates the exponential growth, the purple line is the least square trend of the square separation. And at the right below corner is the plot of compensated Evolution of Square separation compare to the Richardson growth regime (S2 / t3).
22
(a)
(b)
(c)
The pair of any two of the RAFOS floats can be correlated only a short period of time
after launch. During this period, the floats usually still trapped in the CUC and then the
alongshore diffusivity component dominated the total diffusivity can be expected (table 5). If
the two floats move to the interior at the same time, then the cross-shore diffusivity became
the dominant but it didn’t happen quite often based on 3 floats statistics (not enough floats).
Figure 23. The left side is the cross-shore component, and the right side is the alongshore component of pair 3(NPS 81 & 82). (a) Separation (b) Square separation and (c) Diffusivity.
23
Table 5. Particle-Pair Diffusivity result
RAFOS Pair Diffusivity ×107 , cm2/s Power Exponent D2 ~ tβ
Total 5.9 2.3 Alongshore 6 1.9 NPS 80 & 81 Cross shore --- ---
Total 10 5.3 Alongshore 10 5.2 NPS 80 & 82 Cross shore --- ---
Total 4.5 15 2.3 3.7 Alongshore 4 --- 5.1 --- NPS 81 & 82 Cross shore --- 14 --- 4
2.4 Three Particles Dispersion
The three RAFOS data launched at the same time but with different record time.
After interpolation the time with six hours interval, they can be compared to each other and
determined the dispersion relation. The two particles dispersion was widely used in many
scientific papers but the three particles dispersion was not. The concept of the three particles
came from the two particles separation but the triangle area of three floats (figure 24).
The triangle area of these three RAFOS floats steadily increased within 60 days, then
it increased and decreased randomly. The dispersion relation needs to take the increasing
triangle area into account, so the only period can be determined as the three particles
diffusivity was the first 60 days (figure 25 a). And the triangle area can be calculated as
expressed:
∆area = s(s − a)(s − b)(s − c)...................................................................................(4)
s =1
2(a + b + c)............................................................................................................(5)
24
(a)
(b)
Because of no exact equation or coefficient can be applied to the triangle area growth
rate, the size of the triangle can be one way to determine how fast the area grew.
The size of a triangle was defined as [J.H. LaCasce and Carter Ohlmann, 2003].
R2 =1
3a2 + b2 + c2( ).....................................................................................................(6)
Figure 24. The three RAFOS floats trajectories (red line—NPS 80, blue line—NPS 81, green line—NPS 82) and the area (black enclosed lines) in 60 days
Figure 25 (a) The Triangle area of Three RAFOS floats increasing period. (b) Size of triangle (Root mean Square).
25
In figure 25 b, we can see the size of the triangle area increase with time of R~ t 5.5 in
the first 15 days, stayed the same size during 15 to 30 days and then increased with time of
R~ t9 till 60 days. It showed that the second period growth rate was larger than the first
period. There is another way to describe how big the size from the base—the longest leg of a
triangle and the height (figure 26 a). With the Aspect Ratio,base divided by the height, the
triangle area growth rate with time can also be determined. In figure 26 b, the first period, the
AR increased with time of AR~ t 0.28, and decreased in the second period of AR~ t -0.07. This
indicated that the base increased more than the height during first period, and meant there
were two of these three floats far away kept moved away from each other. Otherwise, during
the second period, the height increased more than base (height < base) and indicated that
there were two of three floats moved toward to each other.
(a)
(b)
All these determinations of three particles dispersion from the triangle area growth
are only an idea. The exact equation and coefficient need more RAFOS floats experiments
and the statistics to prove it. Now, the only way to see the three particles dispersion is to see
how the triangle area’s size and aspect ratio increase with time.
Figure 26 (a) Base (blue line) and height (red line). (b) Aspect ratio (Base / height).
26
3. Conclusion
NPS #80, #81 and #82 launched at the same time and correlated between each other
only few days after the launch, usually still trapped in the California undercurrent.
When in the warm, salty poleward CUC, we can expect the alongshore component
will affect the characteristics of either single or two particles dispersion. From the data
analysis, the result showed both the cross-shore and alongshore diffusivity component
contributed to the total diffusivity, but when in the CUC, the alongshore diffusivity was
always larger than the cross-shore diffusivity due to the northwest motion along the coast.
In two particles dispersion, the alongshore diffusivity domination was still expected
due to the short period of time of correlation with any of these two floats. In pair 1 and pair 2,
the result met the expectation as alongshore domination. In pair 3, when in the CUC, the
alongshore diffusivity still dominated the total diffusivity, but when they turned in the
interior at the same time, the westward motion caused the larger cross-shore diffusivity and
dominated the total diffusivity during this time. But it only happened when the two float
moved westward at the same time.
The triangle area growth rate of three RAFOS floats is the idea to determine the three
particles dispersion. The size (root mean square of three legs) and the Aspect ration (base
divided by the height) can be applied to determine how the area grew with time. There still
have no exact coefficient and equation to calculated the relation. But with more and more
deployment of RAFOS floats and the data analysis to get the statistics, the three particles
dispersion can be determined more correctly and precisely.
27
Acknowledgement
Without the help from professor Collins and Margolin, Tetynan, I can’t learn the
particles dispersion idea and methods to analysis the RAFOS data and of course can’t finish
the this important project. I thank them for devoting their time and patiently explaining all
the detail.
I also want to thank all the people who devoted all their effort on deploying the
RAFOS floats and processed the data. With the existence data information, I don’t need to
worry about I can’t get the desire data from the cruise. So I could learned more things, such
as how to cast the CTD and Rawinsonde, how to get the synoptic measurement of the ocean
data and how to read the atmosphere but not only on what I eager to get.
I also thank professor Guest and the assistant during the cruise to let me learn the
basic meteorology concept and how to be an operational researcher. And thanks for all the
crews on the RV. Pt Sur to let me have safe and sound trip in the San Francisco Bay and
California coast.
The last I want to thank are all the classmates in our class. With your effort doing the
wonderful and excellent presentation, and the team work during the cruise ,I can easily learn
new ideas from you without a pain.
28
REFERENCES
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Newell Garfield, Curtis A. Collins, Robert G. Paquette, and Everett Carter (1996), Lagrangian Exploration of California Undercurrent, 1992-95, Journal of Physical Oceanography, Vol 29, pages 562-583.
Newell Garfield, Mathew E. Maltrud, Curtis A. Collins, Thomas A. Rago, Robert. Paquette (2001), Lagrangian flow in the California Undercurrent, an observation and model comparison, Journal of Marine Systems, Vol 29, pages 201-220.
Russ E. Davis (1985), Drifter Observations of Coastal Surface Current During CODE: The Method and Descriptive View, Journal of Geophysical Research, Vol 90, No C3, Pages 4741-4755.
Russ E. Davis (1985), Drifter Observations of Coastal Surface Current During CODE: The Statistics and Dynamical View, Journal of Geophysical Research, Vol 90, No C3, Pages 4756-4772.
Curtis A. Collins, Leonid M. Ivanov, Oleg V. Melnichenko, and Newell Garfield (2004), California Undercurrent variability and eddy transport estimated from RAFOS float observations, Journal of Geophysical Research, Vol 190, C05028, Pages 1-19.
J.H. LaCase and Carter Ohlmann (2003), Relative dispersion at the surface of the Gulf of Mexico, Journal of Marine Research, Vol 61, No. 3 Pages 285-312.
H.J. Freeland, P.B. Rhines and T. Rossby (1975), Statistics observations of the trajectories of neutrally buoyant floats in the North Atlantic, Journal of Marine Research, Pages 383-404.
J.H. LaCase and A. Bower (2000), Relative dispersion in the subsurface North Atlantic, Journal of Marine Research, Vol 58, Pages 863-894.