MEASUREMENT OF THE CALIFORNIA COUNTER- CURRENT
By Keith Coddington
Thesi s C53025
NAVAL POSTGRADUATE SCHOOL
Monterey, California
THESIS
MEASUREMENT OF THE CALIFORNIA COUNTERCURRENT
by
Keith Coddington June 1979
Thesis Advisors:
J. B. Wickham S. P. Tucker
Approved for public release; distribution unlimited
I
T191027
G-BionS
n
UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS RACE (Whan Data Entaratf;
REPORT DOCUMENTATION PAGE
1 »e»o-.T NUMSC*
2. OOVT ACCESSION NO
READ INSTRUCTIONS BEFORE COMPLETING FORM
». RECIPIENT'S CATALOG Nuul[«
4. TITLE (and Subtitle)
Measurement of the California Counter current
S. TYRE OF REPORT ft RERlOO COVERED
Master's Thesis; June 1979
• ■ PERFORMING ORG. RERQRT NUM|[«
7. autmorc*;
S. CONTRACT OR GRANT NUMlCM^ij
Keith Coddington
• ■ RERFORMINO ORGANIZATION NAME AND ADDRESS
Naval Postgraduate School Monterey, California 93940
10. PROGRAM ELEMENT. PROJECT TASK AREA * WORK UNIT NUMBERS
11. CONTROLLING OFFICE NAME ANO ADDRESS
Naval Postgraduate School Monterey, California 93940
12. REPORT DATE
June 1979
t9. NUMBER OF RAGES
135
14. MONITORING AGENCY NAME * AOOR tiS(lt dltferont Irom Controlling Otllea)
IS. SECURITY CLASS, (ol thla report)
Unclassified
ISa. DECLASSIFICATION/ DOWNGRADING SCHEOULE
16. DISTRIBUTION STATEMENT (of thl» Report)
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17. DISTRIBUTION STATEMENT (ol tho mbetrmet entered In Bloek 20, II dllterent from Report)
IS. SUPPLEMENTARY NOTES
IS. KEY WORDS (Continue on rererae aide II neceeeary and Identity by Mock number)
California Countercurrent California Undercurrent Davidson Current California Current
20. ABSTRACT (Continue an revet ae alda It neeaeamry and Identity ay block number)
Direct measurements by moored current meters and indirect measurements from geostrophy are compared and discussed for a regior over the continental slope off central California during the Davidson Current period.
During that same period vertical temperature and salinity profiles were made at 23 stations on four separate cruises in the study area south of Monterey, California. These arrays of
DD ,5
(Page 1)
'ST,, 1473
EDITION OF 1 NOV 6S IS OBSOLETE
S/N 0102-014- 6»01 |
UNCLASSIFIED
SECURITY CLASSIFICATION OF THIS RAOB (When Deim Kmered)
UNCLASSIFIED
#20 - ABSTRACT - CONTINUED
moored current meters simultaneously recorded the flow of the current at specified levels.
The California Countercurrent was found to be present in the region of study during the entire observation period Its offshore position and extent, its intensity and its vertical location and extent varied in a way largely consistent with its reported behavior in other locations along the U.S. West Coast.
DD Form 1473
, 1 Jan 73 UNCLASSIFIED
S/N 0102-014-6601
$CCU*lTv eiAMl'lCATiOM O* TnU HOtr***- Dmia !«»•»••*)
Approved for public release; distribution unlimited
Measurement of the California Countercurrent
by
Keith ;Coddington Lieutenant, United States Coast Guard B.S., United States Coast Guard Academy, 1973
Submitted in partial fulfillment of the requirements for the degree of
MASTER OF SCIENCE IN OCEANOGRAPHY
from the
NAVAL POSTGRADUATE SCHOOL June 1979
ABSTRACT
Direct measurements by moored current meters and indirect measurements from geostrophy are compared and dis- cussed for a region over the continental slope off central California during the Davidson Current period.
During that same period vertical temperature and salinity profiles were made at 23 stations on four separate cruises in the study area south of Monterey, California. These arrays of moored current meters simultaneously recorded the flow of the current at specified levels.
The California Countercurrent was found to be present in the region of study during the entire observation period Its offshore position and extent, its intensity and its vertical location and extent varied in a way largely con- sistent with its reported behavior in other locations along the U.S. West Coast.
TABLE OF CONTENTS
I. INTRODUCTION 13
A. THE CALIFORNIA CURRENT SYSTEM 13
B. PREVIOUS STUDIES OF THE CALIFORNIA UNDERCURRENT I4
C. STATEMENT OF THE PROBLEM I9
II. AREA OF INVESTIGATION 24
III. SALINITY-TEMPERATURE-DEPTH OBSERVATIONS 27
A. INSTRUMENTATION AND DATA COLLECTION 27
B. RESULTS 28
C. DISCUSSION OF WATERMASS PROPERTIES AND GEOSTROPHY 29
IV. DIRECT CURRENT OBSERVATIONS 54
A. INSTRUMENTATION AND DATA COLLECTION 54
B. DISCUSSION OF DIRECT CURRENT MEASUREMENTS - 58
V. COMPARISON OF GEOSTROPHY WITH DIRECT
CURRENT MEASUREMENTS "70
VI. CONCLUSIONS 73
APPENDIX A: NOYFB PROGRAM 76
APPENDIX B: TEMPERATURE, SIGMA-T, SOUND SPEED,
AND SIGMA-T AND SALINITY SUPERIMPOSED
VERTICAL SECTIONS 99
BIBLIOGRAPHY 131
INITIAL DISTRIBUTION LIST 134
LIST OF TABLES
TABLES PAGE
I. Latitude, longitude and depth of stations — 26
II. Comparison of current meter and geo-
strophic current velocities on 27 November
1978 and 8 January 1979 75
LIST OF FIGURES
FIGURE PAGE
1. Temperature-salinity curves from selected stations (Sverdrup and Johnson, 1941) 21
2. Diagram showing T-S curves defining percentage southern water (Sverdrup and Johnson, 1941) 21
3. Mean dynamic topography of the sea surface reference 500 db during January off California
and Baja California (Hickey, 1978) 22
4. Mean dynamic topography of the 200 db surface reference 500 db during January off
California and Baja California (Hickey, 1978) -- 22
5. Temperature-salinity relationships for selected stations in California undercurrent (Wooster
and Jones, 1970) 23
6. Chart indicating area of investigation and stations ■ 25
7. Salinity (%, ) on a vertical section for the
Cape San Martin line on 27-28 November 1978 34
8. Salinity ( °/00 ) on a vertical section for the
Slate Rock line on 27-28 November 1978 35
9. Salinity (%<, ) on a vertical section for the
Cape San Martin line on 8-9 January 1979 36
10. Salinity (%<, ) on a vertical section for the
Slate Rock line on 8-9 January 1979 37
11. Salinity (%<, ) on a vertical section for the
Cape San Martin line on 22-23 January 1979 38
12. Salinity (%„ ) on a vertical section for the
Slate Rock line on 22-23 January 1979 39
13. Salinity ( %<, ) on a vertical section for the
Cape San Martin line on 21-22 February 1979 40
14. Salinity (%<> ) on a vertical section for the
Slate Rock line on 21-22 February 1979 41
15. Dynamic topography of the 100/500 db surface
on 27-28 November 1978 42
FIGURE PAGE
16. Dynamic topography of the 200/500 db
surface on 27-28 November 1978 42
17. Dynamic topography of the 300/500 db
surface on 27-28 November 1978 42
18. Dynamic topography of the 100/500 db
surface on 8-9 January 1979 43
19. Dynamic topography of the 200/500 db
surface on 8-9 January 1979 43
20. Dynamic topography of the 30 0/500 db
surface on 8-9 January 1979 43
21. Dynamic topography of the 100/500 db
surface on 22-23 January 1979 44
22. Dynamic topography of the 20 0/500 db
surface on 22-23 January 1979 44
23. Dynamic topography of the 300/500 db
surface on 22-23 January 1979 44
24. Dynamic topography of the 100/500 db
surface on 21-22 February 1979 45
25. Dynamic topography of the 2 0 0/500 db
surface on 21-22 February 1979 45
26. Dynamic topography of the 300/500 db
surface on 21-22 February 1979 45
27. Vertical section of the normal component of geostrophic velocity for the Cape San Martin
line on 27-28 November 1978 46
28. Vertical section of the normal component of geostrophic velocity for the Slate Rock line
on 27-28 November 1978 47
29. Vertical section of the normal component of geostrophic velocity for the Cape San Martin
line on 8-9 January 1979 48
30. Vertical section of the normal component of geostrophic velocity for the Slate Rock line
on 8-9 January 1979 49
FIGURE PAGE
31. Vertical section of the normal component of geostrophic velocity for the Cape San Martin
line on 22-23 January 1979 50
32. Vertical section of the normal component of geostrophic velocity for the Slate Rock line
on 22-23 January 1979 51
33. Vertical section of the normal component of geostrophic velocity for the Cape San Martin
line on 21-22 February 1979 52
34. Vertical section of the normal component of geostrophic velocity for the Slate Rock line
on 21-22 February 1979 54
35. Array configuration 57
36. Progressive vector diagram for the current meter at station 2 at 220 meters depth from
25 July 1978 to 28 August 1978 63
37. Progressive vector diagram for the current meter at station 2 at 190 meters depth from
20 September 1978 to 27 November 1978 64
38. Progressive vector diagram for the current meter at station 2 at 100 meters depth from
27 November 1978 to 22 January 1979 65
39. Progressive vector diagram for the current meter at station 2 at 175 meters depth from
27 November 1978 to 22 January 1979 66
40. Progressive vector diagram for the current meter at station 2 at 300 meters depth from
27 November 1978 to 22 January 1979 67
41. Progressive vector diagram for the current meter at station 5 at 140 meters depth from
27 November 1978 to 22 January 1979 bb
42. Progressive vector diagram for the current meter at station 5 at 215 meters depth from
27 November 1978 to 22 January 1979 69
43. Temperature (°C) on a vertical section for
the Cape San Martin line on 27-28 November 1978 - 99
44. Temperature (°C) on a vertical section for the Slate Rock line on 27-28 November 1978 100
FIGURE PAGE
45. Temperature (°C) on a vertical section for the
Cape San Martin line on 8-9 January 1979 101
46. Temperature (°C) on a vertical section for the
Slate Rock line on 8-9 January 1979 i02
47. Temperature (°C) on a vertical section for the
Cape San Martin line on 22-23 January 1979 103
48. Temperature (°C) on a vertical section for the
Slate Rock line on 22-23 January 1979 104
49. Temperature (°C) on a vertical section for the
Cape San Martin line on 21-22 February 1979 105
50. Temperature (°C) on a vertical section for the
Slate Rock line on 21-22 February 1979 106
51. Sigma-t on a vertical section for the Cape
San Martin line on 27-28 November 1978 107
52. Sigma-t on a vertical section for the Slate
Rock line on 27-28 November 1978 108
53. Sigma-t on a vertical section for the Cape
San Martin line on 8-9 January 1979 109
54. Sigma-t on a vertical section for the Slate
Rock line on 8-9 January 1979 110
55. Sigma-t on a vertical section for the Cape
San Martin line on 22-23 January 1979 111
56. Sigma-t on a vertical section for the Slate
Rock line on 22-23 January 1979 112
57. Sigma-t on a vertical section for the Cape
San Martin line on 21-22 February 1979 113
58. Sigma-t on a vertical section for the Slate
Rock line on 21-22 February 1979 114
59. Sound speed (m/sec) on a vertical section for
the Cape San Martin line on 27-28 November 1978 - 115
60. Sound speed (m/sec) on a vertical section for
the Slate Rock line on 27-28 November 1978 116
61. Sound speed (m/sec) on a vertical section for
the Cape San Martin line on 8-9 January 1979 117
10
FIGURE PAGE
62. Sound speed (m/sec) on a vertical section for
the Slate Rock line on 8-9 January 1979 118
63. Sound speed (m/sec) on a vertical section for
the Cape San Martin line on 22-23 January 1979 -- 119
64. Sound speed (m/sec) on a vertical section for
the Slate Rock line on 22-23 January 1979 120
65. Sound speed (m/sec) on a vertical section for
the Cape San Martin line on 21-22 February 1979 - 121
66. Sound speed (m/sec) on a vertical section for
the Slate Rock line on 21-22 February 1979 122
67. Sigma-t and salinity ( %«, ) superimposed on a vertical section for the Cape San Martin line
on 27-28 November 1978 123
68. Sigma-t and salinity ( %<, ) superimposed on a vertical section for the Slate Rock line
on 27-28 November 1978 124
69. Sigma-t and salinity (%„ ) superimposed on a vertical section for the Cape San Martin line
on 8-9 January 1979 125
70. Sigma-t and salinity ( °/00 ) superimposed on a vertical section for the Slate Rock line on
8-9 January 1979 126
71. Sigma-t and salinity (%o ) superimposed on a vertical section for the Cape San Martin line
on 22-23 January 1979 127
72. Sigma-t and salinity ( %<> ) superimposed on a vertical section for the Slate Rock line on
22-23 January 1979 128
73. Sigma-t and salinity ( %<> ) superimposed on a vertical section for the Cape San Martin line
on 21-22 February 1979 129
74. Sigma-t and salinity ( %<, ) superimposed on a vertical section for the Slate Rock line
on 21-22 February 1979 130
11
ACKNOWLEDGMENT
The author would like to express his sincere apprecia- tion to his thesis advisors, Professor S.P. Tucker and Professor J.B. Wickham. Their knowledge and expertise in this project was only surpassed by their willingness to freely devote their time.
Special appreciation is extended to the Captain, W.W. Reynolds, and crew of the R/V ACANIA. Their highly skilled seamanship provided for smooth array installation and retrieval. Appreciation is also extended to Mr. Tim Stanton for his assistance in translating the current meter tapes.
Finally, a devoted thanks to my wife, Michelle, for her patience and understanding during this time.
12
I. INTRODUCTION
A. THE CALIFORNIA CURRENT SYSTEM
In the past decade eastern boundary currents and coastal upwelling have come under considerable scrutiny. This is due in part to their influence on the fishing industry and various other economic enterprises. Examples of eastern boundary current systems are the California, the Peru, the Benguela and the Canary Current Systems.
One eastern boundary current system, the California Current system is made up of an equatorward surface flow which extends along the entire west coast of the United States and Baja California and a counterflow, poleward, sometimes beneath this, at others on the surface shoreward of it. The equatorward surface flow is fed by the North Pacific Current, i.e. the northern limb of the North Pacific Gyre, and is known as the California Current. The poleward flow may be submerged, when it is then termed the California Undercurrent, or, at certain times of the year it may appear at the sur- face, when it is called the Davidson Current.
Reid, Roden and Wyllie (1958) apply the term California Current to all southward flow in the North Pacific Gyre. It is common to define the boundary of the California Current at a distance 1000 kilometers from shore (Hickey, 1978). High velocities are generally not encountered in this cold water mass.
13
The California Undercurrent is a poleward flow of water, the temperature and salinity of which is slightly higher than that of the surrounding water and which is usually found shoreward of the southward flowing California Current. It is much narrower and has a maximum of northward flow at intermediate depth. It is uncertain whether the Davidson Current is superimposed on the California Undercurrent, suppressing the core to great depths, or whether the Davidson Current is actually the expression of the undercurrent at the surface (Hickey, 1978) .
The California Undercurrent is present year round and, with the onset of north-northwest winds and upwelling along California, it is found predominately below 200 meters. It is characterized by relatively high temperature, salinity and phosphate and low dissolved oxygen concentrations because of its southern origin. The undercurrent has been intensely studied off Oregon, Washington, and Southern California, but direct current measurements are lacking for the Central California region.
B. PREVIOUS STUDIES OF THE CALIFORNIA UNDERCURRENT
The California Undercurrent was first discussed by Sverdrup and Fleming (1941). During their cruises in 1937, they defined "northern water" on a T-S curve which showed an in- crease in salinity with decreasing temperature (Figure 1, curve C131) . The T-S curve for "southern water" showed salinity relatively constant as temperature decreased (Figure 1,
14
curves 5.3 and B III, 31). They constructed a chart, defining percentage of southern water for given T-S pairs (Figure 2) . Using these parameters they traced southern water as far north as Cape Mendocino. They also found that the southern water was close to the coast and was concen- trated in the northward flowing current. They also showed the existence of the northward flowing undercurrent by means of dynamic heights.
Reid, Roden, and Wyllie (1958) expanded on Sverdrup and Fleming (1941) and Sverdrup, et al . (1942). They concluded the evidence for the undercurrent was of two sorts: (1) The warm or more saline subsurface water of low oxygen content suggested southern origin; and (2) geostrophic flow at the 200 decibar surface with respect to both the 500 and 1000 decibar surfaces indicated a northward flowing current, 3 0- 60 miles in width near the coast north of 30 °N and somewhat wider to the south.
Direct measurements of the undercurrent was made by Reid (1962, 1963) and Reid and Schwartzlose (1962) using drogues. Their results indicated the existence of a northward flowing current at 200 meters depth off Monterey, California, and Baja California. During the winter they found that a northward flow existed at the surface.
As a part of a California Cooperative Oceanic Fisheries Investigation (CALCOFI) study Wyllie (1966) showed the exis- tence of a northward flowing undercurrent on the basis of dynamic topography. Wyllie 's charts of mean monthly dynamic
15
topography on the 200 decibar surface relative to 500 decibars provide the best description of the flow of the undercurrent in January south of Cape Mendocine (Figures 3 and 4 ) .
From Point Conception northward stronger subsurface flow was observed in winter than in summer. The weakest flow occured from March to May. Pavlova (1966) found that during the spring, when the undercurrent appears to be absent at the usual depth of about 200 meters, it may be present at depths exceeding 500 meters. Pavlova also con- cluded that the undercurrent actually reaches the surface during late fall and winter, when it is known as the Davidson Current. Wyllie's data supported these conclusions.
Wooster and Jones (1970) found that a characteristic of the undercurrent was a relatively high salinity bulge centered at sigma-t equal 26.54 (150 cl/t) on the T-S dia- gram (Figure 5) . They also gave some evidence for an inter- annual variation in the northward extent of a given isohaline. They pointed out that a coastal deepening of isotherms and isopycnals and rising of isohalines are characteristics of the poleward undercurrent.
In the last ten years the study of the undercurrent has been concentrated north of Cape Mendocino and to some extent in the vicinity of Monterey, California. Mooers, Collins and Smith (1976) in their study of upwelling off the Oregon coast found a northward flow along the continental slope between 300 and 1000 meters. They suggested that it may exist
16
at greater depths and may extend from the continental slope to perhaps 500 kilometers from shore. Their primary obser- vations were conducted during the same year and season as those of Wooster and Jones (1970). Mooers , et al, (1976) found that during July 1975, the near surface flow was predominately southward, and the near bottom flow alternated between northward and southward. In August and September 1965 and 1966 the near bottom flow was predominately north- ward.
Huyer and Smith (1976) and Halpern, Smith and Reed (1978) used direct measurements of current on the slope and shelf to describe the seasonal developments of the undercurrent off the coast of Oregon. Huyer and Smith's (.1976) data suggest that the northward flow is present at depths greater than 400 meters in the spring but increases in speed and vertical extent as the season progresses. That the undercurrent was found at the shelf edge by summer is consistent with Pavlova's (1966) findings for northern California. Halpern, Smith, and Reed*s (1978) current meter results support those of Huyer and Smith (1976) . The data of both these studies suggest that the shelf and slope undercurrents were portions of the same flow.
Eddies are frequently observed off the coast of Vancouver Island, B.C. Mysak (1977) in conjunction with his study of the undercurrent suggests that the eddies are produced by baroclinic instability of the California Undercurrent. For the undercurrent he found a northward flow along the
17
continental slope but a southward flow farther offshore. Thus, off Vancouver Island the northward flowing California Undercurrent is essentially confined to the continental slope. The main core of the current at that latitude occurs around 300 meters.
Off Monterey, California, the undercurrent has been studied by Molnar (1972), Hughes (1975), Greer (1975), and Wickham (1975) . Wickham (1975) used drogues and a continu- ous measuring salinity-temperature-depth profiler (STD) . For August three main results were found in conjunction with the undercurrent: (1) At both 50 meters and 200 meters geo- strophy and drogues both indicate that there is a narrow band of poleward flowing water near the shelf edge; (2) both drogues and geostrophy also indicate that there is a com- plex flow father west which seems to split the poleward flow into two branches; and (3) there is a broader poleward flow still farther west which is centered at 40-50 kilometers from the shelf edge.
An analytical model by McCreary (1977) indicated that, due to local wind forcing, the pycnocline tilts alongshore to balance the meridional component of the wind and results in an alongshore flow. This disturbance is not confined to the coast but propagates offshore and northward as a Kelvin- Rossby wave carrying along with it both the pycnocline deformation and the alongshore flow.
Hickey (1978) has examined most of the data to date. She found that the northward subsurface flow is generally
18
found off the west coast of North America over the contin- ental slope. The flow on the 200 decibar surface is most continuous alongshore and strongest (south of Point Concep- tion only) in summer and early fall. It is weakest and least continuous in the spring. North of Point Conception, the flow on the 200 decibar surface is stronger during winter than during summer and fall. She found that the depth of the high-speed core varied seasonally and that the flow appeared to have a jet-like structure, both vertically and horizontally and appeared to extend to the bottom over the slope. This is in agreement with McCreary (1977) who called this jet-like flow, quasi-geostrophic . In support of Wooster and Jones (1970), Hickey (1978) found that the salinity and temperature at the core of the undercurrent generally decreased from about 34.6%,, and 9.5°C off Baja California to about 33.9%, and 7°C off Vancouver Island.
The flow from the surface to a depth of about 500 meters is confined to the continental slope, but the overall width of the region of northward flow has not been firmly established The relationship between the undercurrent jet that occurs over the upper slope and the slower broader flow that occurs deeper in the water column farther offshore is uncertain.
C. STATEMENT OF THE PROBLEM
The presence of southern water can be inferred from iso- halines, isotherms, and isopleths of sound speed; and the geostrophic current can be inferred from isopycnals. The
19
current can also be found through direct measurements by means of current meters. Wickham (1975) noted that a com- parison of geostrophic observations with direct measurements of current would test the utility of geostrophy to describe flow in areas of complexity, such as off Monterey, California
The initial objective of this study was to collect data by both means. This involved setting up stations where salinity, temperature and depth measurements could be taken and moored current meter arrays could be maintained. The thesis addresses the problems associated with the assembly and maintenance of the moored current arrays, the collection of salinity, temperature and depth data, and the analysis and interpretation of the direct and indirect current observations .
20
33 9 |
340 |
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343 |
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Figure 1. Temperature-salinity curves selected stations (Sverdrup and Johnson, 1941) .
Figure 2. Diagram showing T-S curves defining percentage southern water (Sverdrup and Johnson, 1941.
21
x: |
|
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22
SALINITY,*..
Figure 5. Temperature-salinity relationships for selected stations in California under- current (Wooster and Jones, 1970)
23
II. AREA OF INVESTIGATION
The area of investigation is south of Monterey, Cali- fornia, as shown in Figure 6. Two lines of stations were established. The station locations and water depths are listed in Table I.
One of the reasons for positioning the stations on this part of the California coast is the relative simplicity of the bathymetric features. The depth contours run approxi- mately parallel to the coast, and the shelf break is close to the coast. Another, but crucial, reason for using this part of the California coast is that it is less heavily fished than the areas immediately to the north and to the south. The current meter arrays are entirely subsurface with no surface markers. The presence of fishing activity increases the possibility of array damage or loss which we have tried to minimize through our selection of the study area.
24
Figure 6. Chart indicating area of investigation and stations. Depth contours in fathoms.
25
TABLE I |
|||
STATION |
LATITUDE |
LONGITUDE |
DEPTH (METERS) |
1 |
35-53.0 |
121-29.8 |
100 |
2 |
35-52.5 |
121-32.3 |
357 |
3 |
35-52.1 |
121-34.7 |
520 |
4 |
35-51.6 |
121-37.4 |
668 |
5 |
35-51.1 |
121-39.9 |
759 |
6 |
35-50.7 |
121-42.4 |
833 |
7 |
35-50.2 |
121-45.0 |
915 |
8 |
35-49.7 |
121-47.6 |
988 |
9 |
35-49.2 |
121-50.1 |
1061 |
10 |
35-48.7 |
121-52.7 |
1150 |
11 |
35-48.3 |
121-55.4 |
1182 |
12 |
35-47.8 |
121-57.7 |
1044 |
13 |
35-49.5 |
121-56.1 |
1274 |
14 |
35-51.1 |
121-54.6 |
1183 |
15 |
35-52.7 |
121-53.0 |
1146 |
16 |
35-54.3 |
121-51.3 |
1089 |
17 |
35-55.9 |
121-49.9 |
1080 |
18 |
35-57.6 |
121-48.3 |
1098 |
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121-47.8 |
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20 |
36-00.9 |
121-45.2 |
842 |
21 |
36-02.5 |
121-43.5 |
732 |
22 |
36-04.3 |
121-42.0 |
560 |
23 |
36-05.9 |
121-40.2 |
350 |
26
III. SALINITY-TEMPERATURE-DEPTH OBSERVATIONS
A. INSTRUMENTATION AND DATA COLLECTION
Watermass data was collected on four separate cruises of the R/V ACANIA, the oceanographic vessel of the Naval Postgraduate School. The cruises were on 27-28 November 1978, 8-9 January 1979, 22-23 January 1979, and 21-22 February 1979. During each cruise all 23 stations were occupied. Sampling of watermass properties was done where possible to 500 meters, the reference level used by CALCOFI (Wyllie, 1966) .
For each cruise the primary instrument, a Bis set Berman Model 9006 STD , was used for delineating the vertical dis- tributions of temperature and salinity. Nansen bottles and reversing thermometers provided independent measurements to check the calibration of the STD. Expendible bathythermo- graph (XBT) drops and surface temperature observations were made also at each station.
The analog recorder usually used with the Model 9006 STD was replaced on these cruises. The three separated signal frequencies were sent through a Hewlett-Packard Model 57307A VHF Switch with a 20 milisecond settling time to a Hewlett- Packard Model 5328A Universal Counter. The resulting binary coded decimal output was then read into the random access memory of a Hewlett-Packard 98 31A desktop computer. After each complete profile the data was transferred to magnetic
27
tape. Profiles were recorded for both the descent and ascent of the STD.
Spikes in the salinity trace are known to be caused by a poorly matched time constant between the conductivity sensor and the platinum resistance thermometer used in the STD to correct the conductivity measurements to salinity. Salinity spikes were eliminated by comparison of descent and ascent profiles and XBT profiles. This was done by hand during examination of the profiles.
B. RESULTS
The results for each cruise are shown as vertical sec- tions for both the Cape San Martin line and the Slate Rock line. Vertical sections are drawn for: salinity, tempera- ture, sigma-t, sound speed, geostrophic currents, and sigma- t and salinity together. The dynamic topography of the 100 db, 200 db, and 300 db surfaces relative to 500 decibars is also given for the four separate cruises.
Salinity and temperature sections were contoured using data stored on the magnetic tapes from the HP 9831A computer after the salinity spikes had been removed. Sigma-t, geo- strophic shear, and dynamic heights were calculated using the library computer program HYDRO, available at the Naval Postgraduate School for the IBM 3 60 computer. Sound speed was calculated using Wilson's equations (Wilson, 1960), available in the same program.
From the calculation of geostrophic shear mean values for four station intervals were found. This was done to
28
reduce the non-geostrophic contributions to the calculations which are inversely proportional to the distance over which geostrophic shear is averaged. Thus, resolution is diminished in order to give a more accurate picture of the larger scale circulation features.
Dynamic heights were smoothed in a similar manner. Values were averaged over three station heights. For sta- tion 12 the mean value was found using stations 11, 12, and 13. For the coastal stations 1 and 23 only two stations were used in the averaging, i.e., stations 1 and 2 and stations 22 and 23. For the coastal stations with less than 500 meters of water the stations were treated as if the depth were 500 meters and dynamic topographies were extrapolated from the first station seaward with such depth.
There are no results for stations 21, 22, and 23 during the cruise of 21-22 February 1979, as these stations were lost due to failure of the data recording equipment. On the same cruise there were four stations at five nautical mile intervals added to the west of station 12. This allowed computation of geostrophic shear out to station 12.
C. DISCUSSION OF WATERMASS PROPERTIES AND GEOSTROPHY
The presence of souther water is indicated by the dis- tributions in two cross-sections of salinity, temperature, sigma-t, and sound speed on the series of four cruises. The current structure for the same series is deduced from geo- strophic current sections and from dynamic topography at
29
three different levels, both currents and topographies being referred to 500 decibars. Direct current measurements are discussed later in Section IV.
Water with relatively high southern watermass properties is present below the pycnocline on the first cruise on 27-28 November 1978. This is particularly evident on the salinity sections, Figures 7 and 8. Both show a bulge of high salinity water below 200 meters, on Figure 7 for example between sta- tions 3 and 10. The associated temperature and sound speed sections (Appendix B) also indicate the presence of southern water in this region. On this cruise the southern water characteristics appear below 200 meters and from about 4 kilometers to 38 kilometers offshore over the continental slope.
Geostrophy, Figures 27 and 28, indicates northward flow in the upper layers with a surface maximum of 25 to 30 cm/sec. The current appears to have two branches with weaker south- ward flow between them. Wickham (1975) found similar indi- cations of branched flow farther offshore for his August data in the latitude of Monterey, and these were confirmed by drogue drifts. This branched northward flow is further shown at each of the three levels of contoured dynamic topography (100, 200, and 300 decibars, Figures 15, 16, and 17). Some southward flow appears at all three levels from stations 15 to 18. This is a small-scale feature and might not be real since small scales are not well resolved by geostrophy.
30
Comparison will be made in Section V between geostrophic and direct current measurements.
The cruise of 8-9 January 1979 also showed southern water; but, as Figures 9 and 10 show, the bulge of high salinity occurs farther west. The associated temperature and sound speed sections (Appendix B) also show this west- ward displacement of the southern water. Below 200 meters this southern water is found 15 kilometers farther offshore than on the last cruise. Although Pavlova (1966) and Hickey (1978) indicated the countercurrent moves offshore in the spring, our observations were made during the winter season. McCreary's (1977) view of the current's variations as mani- festations of baroclinic Kelvin-like waves is consistent with this offshore movement.
Geostrophy in the cross-sections for 8-9 January 1979 (Figures 29 and 30) also shows the northward flow farther offshore. There is still a maximum at the surface, but with an increase in velocity to 70 cm/sec normal to the Cape San Martin line and 35 cm/sec normal to the Slate Rock line. There is an indication that this may be the shoreward branch of the northward flow found during the first cruise, as southward flow appears on the offshore edge of both sections. Dynamic topography (Figures 18, 19, and 20) shows this same pattern. At the 100 db level (Figure 18) the flow is intense and northward between stations 3 and 9. To the west of station 9 the flow intensity drops off sharply and southward flow appears between stations 13 and 15. To the east of
31
station 3 the dynamic topography is generally flat with northward flow indicated. At the 2 00 db level (Figure 19) the flow is weaker but is still northward between stations 3 and 9. Southward flow is now more evident between stations 13 and 15. At the 300 db level (Figure 20) the flow is southward with only a trace of northward flow between sta- tions 15 and 17.
The cruise on 22-23 January 1979 shows reductions in southern water characteristics. All indicators, i.e., isopleths of salinity, temperature, sigma-t, and sound speed, are nearly parallel with only small horizontal gradi- ents. Note that the 34.20 °/00 isohaline which in November lay in places higher in the water column than 200 meters is now at a depth of 300 meters, except within a few kilometers of the slope. This may indicate that southern water has moved seaward or deeper beyond the range of observations.
Geostrophy shows slight westward propagation of the northward flow (Figures 31 and 32, also, 21, 22, and 23). The flow appears slower, 20 cm/sec, and more diffuse. At the 200 db level (Figure 22) southward flow now exists shoreward of station 4. At the 300 db level (Figure 23) the flow has become more diffuse and the southern flow is now shoreward of stations 5 and 20.
The observations for the cruise of 21-22 February 1979 indicate an increase in salinity below 200 meters (Figures 13 and 14), the 34.20 °/QO isohaline having risen to a depth of 250 meters over most of both sections. The dynamic topography
32
(Figures 24 , 25, and 26) now indicates a northward flow at stations 2 and 3 at the 200 db and 300 db levels. The geostrophic sections do not show this since the station averaging interval used in their construction does not permit calculations shoreward of station 4. This flow at the eastern stations and below 200 meters may be the start of the undercurrent.
An immediate observation must be made: The regions with indications of southern water and the regions where north- ward flow is indicated by geostrophy do not exactly coin- cide. For all the cruises considered, geostrophy shows a northward surface flow, in some instances with flow as great as 70 cm/sec, even though the watermass characteris- tics in some regions are not southern. This is not too surprising, since near the boundaries between watermasses, eddies and entrainment of anomalous water is common. The observed variations in salinity and velocity may also have alternative explanations. Passing eddies or meanders in the countercurrent might give results similar to those just discussed.
In the following section the currents inferred from geo- strophy are compared to those measured directly by moored current meter arrays along the Cape San Martin line.
33
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53
IV. DIRECT CURRENT OBSERVATIONS
A. INSTRUMENTATION AND DATA COLLECTION
Data collection was begun with the first array installed on 25 July 1978. This array contained one meter. The array was placed in 371 meters of water at approximately the position of station 2 (Figure 6) and remained in the water for one month. The second array was also placed near sta- tion 2 in 354 meters of water on 20 September 1978. The array contained one meter and remained in the water for two months. The meters from both the first and second array were placed at approximately 200 meters depth. Two larger arrays were installed on 27 November 1978. They contained three meters each and were installed in water of 353 meters depth near station 2 and 777 meters depth near station 5. The meters were situated at depths of 100, 175, and 300 meters. Both arrays remained in place until 22 January 1979.
Organization of each array was done by means of the NOYFB computer program. The original program was written by Donald Moller of the Woods Hole Oceanographic Institution in Fortran II for the Hewlett-Packard 2100 series. The pro- gram has been rewritten in Fortran IV for compatibility with the IBM 360 computer and is given in Appendix A. Through the use of on line terminals the program gives the operator a description of the mooring and its performance from an
54
operational point of view. Given environmental data and mooring components, the program presents the operator with mooring behavior information for evaluation of collected data as well as array design modifications. Step by step instructions for program operation are displayed to the user with the sequence determined by his selection of options. Standard mooring component characteristics (buoyancy, cross- sectional areas, elastic properties, etc.) are written into the program. These components are those used by Woods Hole Oceanographic Institution. Components which are non-standard with respect to the program are added during initialization or may be changed by an option.
The current meter used in these arrays is the Aanderaa Recording Current Meter Model 4 (RCM4). It is a self-contained instrument for recording speed, direction, and temperature of ocean currents with conductivity and pressure options. The RCM4 has a depth capability of 2000 meters. The RCM4 uses a rotor type current speed sensor, a magnetic compass, and a thermistor. An electro-mechanical encoder (analog to digital converter) samples and converts the measurements to binary digital signals which are then recorded on 1/4- inch magnetic tape. A sampling interval of 10 minutes was chosen for our meters. Input parameters for the RCM4 into the NOYFB program are: W(I) = -64.66 (buoyancy per meter length) and A (I) = +0.065 (area of component in square meters per meter length) .
55
The array is arranged as in Figure 3 5 with no surface markers in order to keep all array elements out of the region of strong surface wave action. An acoustic release is used for retrieval of the arrays. It is an AMF Acoustic Release/Pinger Model 242, which is activated acoustically and also has a reply pinger used for interrogation and, if necessary, as a locating beacon.
Buoyancy for the array is provided by Benthos glass spheres. The glass spheres are 17-inches in diameter, housed in plastic hard hats and are capable to a depth of 6700 meters. They provide 55 pounds of buoyancy each and are connected together in pairs with 3/8-inch galvanized chain.
The wire finally used was 5/32-inch, 7x7 stainless steel wire, breaking strength about 2400 pounds, and stainless Nicopress fillings around plastic thimbles. Although the initial arrays used 1/4-inch galvanized wire with copper Nicopress fittings for terminations- Zinc anodes were attached to all Nicopress fittings, following a technique developed at Oregon State University (OSU) . After one month of immersion the zincs on some of the wire fittings had almost totally disappeared. It was feared that a longer use would have led to corrosion of the copper Nicopress fittings and possibly to the loss of the array. It was then decided to use stainless steel wire. Again, following the technique developed at OSU, plastic 1/2-inch thimbles are used at all eye terminations. Galvanized anchor shackles with stainless steel cotterpins were used as connectors for
56
m
2 Benthos 17" Olass Spheres
-Aanderaa RCM-4 Current Meter
-5/32" SS Wire
2 Benthos 17" Glass Spheres
)-Aanderaa RCM-4
Current Meter 5/32" SS Wire
6 Benthos 17" Glass Spheres
AMF Model 2^2 Acoustic Release
15 Meters of 5/32" SS Wire ■3/8" Chain, 3 Meters
■Anchors, 2 or more RR wheels
Figure 35. Array configuration
57
the various components. Zincs are maintained on the meters and release as a protection against their corrosion. Input parameters for the wire into the NOYFB program are: W(I) = -0.1225 (weight of component in pounds per meter length), A(I) = +0.00397 (diameter in meters), RBS(I) = +2400.0 (rated breaking strength in pounds), and AW (I) = +0.065 (cross sectional metal area of wire in square inches) .
Below each release is a 15-meter section of wire, 3- meter section of 3/8 inch chain and the weights. Weight is provided by scrap railroad wheels which have a weight of about 600 pounds per wheel in water. Two wheels are used for the shallow arrays and three for the deeper arrays.
Placement of arrays was done from the R/V ACANIA by the method of stringing the array out behind the ship, upper-most components first, and dropping the anchor last. As an added precaution a 7-foot cargo parachute was attached to the anchors to slow their rate of descent.
B. DISCUSSION OF DIRECT CURRENT MEASUREMENTS
All data obtained with the current meters was converted to speed and direction using Aanderaa calibration constants and consolidated on a single IBM compatible tape.
Current speed and direction were used to construct pro- gressive vector diagrams. Vertical and horizontal scales are equal in these diagrams. The vertical axis is zero degrees, magnetic north. The coast in the study area is aligned approximately in a 305° magnetic direction.
58
The current at station 2 during the period 25 July to 28 August 1978 is depicted by the progressive vector diagram shown in Figure 36. This meter was at 220 meters depth. During its operation the average overall current was 336° magnetic at 7.6 cm/sec. With respect to the alignment of the coast this shows a slight onshore component.
The semidiurnal components in the currents are visible upon close examination (the crosses on the diagram appear at two-day intervals) . Two reversals of current which last four-days each can be seen at the top of the figure.
The second meter was installed in September (Figure 37) at the same location, station 2, but at a depth of 190 meters It was in operation from 20 September to 27 November 1978. For this period the progressive vector diagram is shown in Figure 37, and the crosses are located at three-day intervals The mean flow was 318° magnetic at 2.9 cm/sec. During the middle of the observation period numerous reversals of flow appear. These oscillations suggest that the meter was near a frontal zone and that its position alternated between sides of that zone, perhaps as a meander or eddy in the counter- current moved through the station's position. The mean flow over the seventy days is dominated by the countercurrent flowing nearly parallel to the coast.
Figures 38 through 42 are progressive vector diagrams for the arrays in operation from 27 November 1978 to 22 January 1979 on moorings at stations 2 and 5. The crosses
59
in all these figures are at three-day intervals. Semi- diurnal components are again visible.
Figures 38, 39, and 40 are for the array at station 2. The upper meter was at 100 meters depth (Figure 38). The mean flow at this level was toward 337° magnetic at 12.8 cm/sec, a moderately strong onshore and northward flow. On the 8th of January the flow changes from northward to south- ward for three days. The next meter was at 17 5 meters depth (Figure 39) . The mean flow was toward 321° magnetic at 3.2 cm/sec. This small mean value is deceiving; it results from a period of mainly southward flow during the first nine days and oscillations during the last part of the period. The speed during the middle of the period was at a maximum of 25 cm/sec during a three-day period. Thus, although the oscillations result in a small value for the local time- averaged flow, weakening of the countercurrent is not necessarily implied. The oscillations may simply imply a spatially fluc- tuating front in the region.
The bottom meter on this array was at 300 meters (Figure 40) . The mean flow at this level was towards 151° magnetic at 1.8 cm/sec. During most of the period the flow appears weak and fluctuating. The oscillations are mainly in two directions, northward and southward parallel to the coast. The meter appears to be astride the front separating the countercurrent and the southward flow. As the countercurrent meanders the meter moves from one flow to the other. In summary the current is moderately strong and northward at
60
the surface and weak at mid-depth with the exception of the strong northward flow during the middle of the period. The oscillations during the first and last days and at the lower meter indicate a moving shear zone between the countercurrent and the southward flow.
Figures 41 and 42 are for the array installed at station 5 and operating in the interval 27 November 1978 through 22 January 1979. The upper meter was at 140 meters depth (Figure 41). The mean flow was toward 319° magnetic at 12.3 cm/sec. As can be seen, the flow is almost exclusively northward, parallel to the coast, during the entire period. The excep- tion is a three-day interval at the start with southward flow.
At 215 meters (Figure 42) the mean flow was toward 308° magnetic at 6.3 cm/sec. This reduction of the mean from the upper meter is largely due to the southward flows during the first nine days and an eight-day period beginning about 1 January. During these reversals the flow maintains its new direction and intensity without multiple oscillations. The sharp, clear change in flow indicates reversal from counter- current to southward flow with no lingering of the front in the region of the meter. This pattern is similar to that at station 2 with a weakening of flow with depth and the appearance of southward flow at the deeper meters.
In summary the mean flow at the surface during the period of 27 November 1978 through 22 January 1979 is north- ward with an onshore component and a surface maximum of speed. At mid-depth the current has maintained its direction
61
with reduced speed. At the deeper meters the flow is variable in direction and speed, indications of a frontal region separating northward and southward flow.
62
METER 2759
200 150 100
KILOMETERS (WEST)
a: o
z
CO
cr
UJ
Figure 36. Progressive vector diagram for the current meter at 220 meters depth at station 2 from 25 July 1978 to 28 August 1978. Crosses are positioned at 2 day intervals. Vertical axis indicates Magnetic North.
63
..§
-I
METER 2670 1 1-
100
60 40
KILOMETERS (WEST)
Figure 37. Progressive vector diagram for the current meter at 190 meters depth at station 2 from 20 September 1978 to 27 November 1978. Crosses are positioned at 3 day intervals. Vertical axis indicates Magnetic North.
64
o
■8
400 300 200 100
KILOMETERS (WEST)
Figure 38. Progressive vector diagram for the current meter at 100 meters depth at station 2 from 27 November 1978 to 22 January 1979. Crosses are positioned at 3 day intervals. Vertical axis indicates Magnetic North.
65
METER 1965
100
80 60 40
KILOMETERS (WEST)
Figure 39. Progressive vector diagram for the current meter at 175 meters depth at station 2 from 27 November 1978 to 22 January 1979. Crosses are positioned at 3 day intervals. Vertical axis indicates Magnetic North.
66
KILOMETERS (EAST)
100
— i —
150
— i —
200
— i —
250
— i —
METER 1624
Figure 40. Progressive vector diagram for the current meter at 300 meters depth at station 2 from 27 November 1978 to 22 January 1979. Crosses are positioned at 3 day intervals. Vertical axis indicates Magnetic North.
67
400 300 200 100
KILOMETERS (WEST)
Figure 41. Progressive vector diagram for the current meter at 14 0 meters depth at station 5 from 27 November 1978 to 22 January 1979. Crosses are positioned at 3 day intervals. Vertical axis indicates Magnetic North.
68
METER 1625 -i 1-
250
200 150 100
KILOMETERS (WEST)
Figure 42. Progressive vector diagram for the current meter at 215 meters depth at station 5 from 27 November 1978 to 22 January 1979. Crosses are positioned at 3 day intervals. Vertical axis indicates Magnetic North.
fi9
V. COMPARISON OF GEOSTRQPHY WITH DIRECT CURRENT MEASUREMENTS
The two methods of inferring currents, indirect (geo- strophy) and direct (current metering) coincided on 27 November 1978 and 8 January 1979. There were vertical profiling for watermass properties on the Cape San Martin line and simultaneous direct measurements at stations 2 and 5 of that line.
The mean velocity from the current meters was found for a 24-hour period bracketing the time during which watermass
properties were sampled. This was accomplished by computing:
$,.. $(t+12) -£(t-12) . ± . ..
V(t) = —jt — ■ where R is the position vector at
the given time taken from a list of the values used to pro- duce the progressive vector diagram. This 24-hour averaging was done so as to smooth the high frequency non-geostrophic contributions to the flow while retaining larger scales. It must be expected that this averaging process does not smooth out all non-geostrophic components. Those which remain con- tribute to differences between the direct (current meter) and indirect (geostrophic) velocity measurements.
The mean metered velocities at stations 2 and 5 on both 27 November 1978 and 8 January 1979 are compared to those velocities found by geostrophy in Table II.
As seen in Table II, on 27 November 1978 at station 2, there is general agreement on the direct and indirect measure- ment of velocities at 100 and 175 meters. At 300 meters the
70
methods of measurement indicate opposite flow directions. Dynamic topography indicates the region to be fairly flat with adjacent northward flow. The current meter shows a moderate southward flow of 10 cm/sec. This bottom meter is the meter which showed obvious non-geostrophic components, frequent oscillations between northward and southward flow. On the same data at station 5, the table shows strong agree- ment between the two methods of measurement. Geostrophy indicates a slightly stronger flow and the current meters show more of an onshore flow.
On 8 January 1979 at station 2, there is poor correlation of the current from the two measurement methods. Geostrophy indicates the region, at mid and lower depths, to be fairly flat with weak flow. Direction can only be inferred from that at station 4 (Figures 19 and 20) . At the 100 meter level the current meter shows an onshore southward flow while geostrophy indicates northward flow parallel to the coast. At station 5 one can see reasonable agreement between the two methods of measurement (Table II) . Current meters show uniform speed with depth and geostrophy indicates weakening of the flow with depth.
In summary there is general agreement between the two methods of measurement. It must be remembered that geo- strophic calculations for station 2 were based on extrapo- lations and to that extent are uncertain. Further, the averaging of the current over 24 hours does not remove all non-geostrophic components, especially in the periods of
71
strong fluctuations. The geostrophic current, as expected, is a more useful estimate of the flow in this variable regime during the relatively quiet (i.e., steady) flow periods.
72
VI. CONCLUSIONS
In summarizing the current and watermass variations, the time interval between cruises is used for an initial breakdown. Currents are described by geos trophy at the time of each cruise and by current meter measurements during the intervals. Watermass properties are known only at cruise times.
From 27 November 1978 to 8 January 1979, near the level of 100 meters, there is an increased halocline slope down- ward toward the coast and an intense northward flow spreading westward. This spreading flow also occurs at 200 and 300 meters. Below 300 meters, southward flow develops. A salinity maximum at 300 meters occurs near the center of the station lines in November and at the western edge in early January.
From 8 January 1979 to 22 January 1979 the halocline levels off and becomes less intense. At 100 meters the northward flow has weakened and at 200 meters remains un- changed. From 300 to 500 meters there is a reduction in salinity due to horizontal advection, vice vertical, of low salinity water. There is also reduced southward flow below 300 meters during this interval.
These results by indirect measurements are consistent with direct (current meters) methods. At 100 meters north- ward flow spreads westward from 27 November 197 8 to 22
73
January 1979. At about 1 January this flow shows an increased westward component, i.e. it crosses contours into deeper water. Vertical extent of the northward flow also increases during this period. Southward flow is present at mid-depth until 6 December when it turns northward at both stations 2 and 5. At 300 meters, a frontal region separating northward and southward flow, the flow is south- ward until early December when much oscillating dominates the rest of the period.
Indications are that the flow is branched and northward at the surface, consistent with Wickham's (1975) findings farther north. Presence of a surface maximum, Davidson Current, during the winter is almost universally consistent with the observations of other investigators. Westward propagation of the flow tends to support McCreary's (1977) model.
From 22 January 1979 to 21 February 1979 there is an increase in salinity at all levels. The northward jet shows further westward movement.
Measurement of the currents is still in progress. A 3- meter array was installed farther west at station 7 and in April 1979 was increased to a 4-meter array. Arrays are also being maintained at stations 2 and 5. Along with cur- rent meter measurements, simultaneous measurements of watermass properties are made at regular intervals.
74
TABLE II
COMPARISON OF CURRENT METER AND GEOSTROPHIC CURRENT VELOCITIES ON 27 NOVEMBER 1978 AND 8 JANUARY 197 9
Current Meters |
Geostrophy |
|||||
Date |
Station |
Depth (meters) |
6(1) V(l) direction (cm/sec) (ref . Mag N) |
6(2) V(3) direction (cm/ sec) (ref. Mag N) |
||
27 November |
2 |
100 175 300 |
331° 352° 112° |
16.2 2.9 10.0 |
310° 305° 335° |
strong moderate weak |
27 November |
5 |
140 215 |
337° 339° |
9.5 4.7 |
310° 305° |
15.1 9.1 |
8 January |
2 |
100 175 300 |
076° 249° 332° |
4.8 6.8 38.3 |
310° variable variable |
strong weak weak |
8 January |
5 |
140 215 |
300° 240° |
16.6 16.9 |
310° 285° |
25.1 weak |
NOTES
(1)
(2) (3)
8 and V (current Meters) found using
$(t+12) -R(t-12)
24
where
R is the position vector at the given time taken from a list of values used to produce the progressive vector diagram.
8 (geostrophy) found from dynamic topographies.
V
V (geostrophy) V =
n
cos
where V is the normal component of
velocity from geostrophic cross sections and from the normal.
is the angle
75
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131
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132
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