atlantic oceanographic laboratory · gauges, values of the harmonic constituents m2, s2, n2, k1, 0...

LIBRARY,

FISHERIES RESEARCH BOARD OF CANADA,

DEPARTMEW -95PikreftY,MINES AND RESOURCES CH

MINISTERE DE L'ENERGIE DE MINES ET DES RESSOURCES DIRECTION DES SCIENCES DE LA MER

ATLANTIC OCEANOGRAPHIC LABORATORY Cr)

BEDFORD INSTITUTE

LABORATOIRE OCEANOGRAPHIQUE DE L'ATLANTIQU INSTITUT de BEDFORD

Dartmouth, Nova Scotia

Canada

TIDAL TRANSPORTS AND STREAMS

IN THE

ST. LAWRENCE RIVER AND ESTUARY

by

W. D. FORRESTER

REPORT B.I. 69-2

APRIL 1969

PROGRAMMED BY-

THE CANADIAN COMMITTEE OF OCEANOGRAPHY

ATLANTIC OCEANOGRAPHIC LABORATORY

BEDFORD INSTITUTE, DARTMOUTH, N.S. - CANADA

This is a technical report to our Headquarters which has received only limited circulation. On citing this report in a bibliography, the title should be followed by the words "UNPUBLISHED MANUSCRIPT", in accordance with accepted bibliographic custom.

TIDAL TRANSPORTS AND STREAMS

IN THE


by

W.D. Forrester

REPORT B.I. 69-2

April 1969

TIDAL TRANSPORTS AND STREAMS IN THE


INTRODUCTION

The principle of continuity makes it possible to calculate the

transport through any cross-section of a channel from a knowledge of

the changes in the surface elevation along the channel and the trans-

port through a single cross-section. This principle was used by

Forrester (1967) to calculate the average M2 tidal streams in a

cross-section of the St. Lawrence estuary near Pte. au Pere for

comparison with the value observed directly with current meters. The

good agreement obtained indicated that it would be valuable to calcu-

late similar information for other cross-sections and for other tidal

constituents in addition to M2 .

During the summer of 1967 the Tides and Water Levels Section

of the Department of Energy, Mines and Resources had in operation a

network of about 20 additional temporary tide gauges in the estuary

between Quebec and Pte. au Pere. The availability of this new tidal

data below Quebec to supplement that already available above Quebec

decided the author to prepare tidal transport and average tidal

stream information for various cross-sections between Lake St. Peter

and Pte. des Monte.

METHOD

For the purposes of this study tidal movements are considered

to be negligible above the head of Lake St. Peter, which provides the ,

boundary condition that tidal transports have zero amplitude at this

cross-section. To carry out the continuity calculations the river

and estuary were divided into 22 regions as delineated in fig. 1.

2

The surface area of each region at mean water level was scaled from

Canadian Hydrographic Service charts. The regions and also their

surface areas are referred to as Ai, i being the number of the

region. The area of the vertical cross-section at the downstream

end of each region was also determined from the charts. The cross-

sections and also their areas are referred to as ai. From the tide

gauges, values of the harmonic constituents M 2, S 2, N2, K1, 0 M4,

and MS4 of the vertical tide were assigned to each region; where

more than one tide gauge was taken to represent a region, a vector

average was employed. The symbols H i and g i (of M2 , etc.) are used

to denote the amplitude and phaselag respectively of the constituents

of the vertical tide in the ith region. Fig. 1 shows the regions and

cross-sections treated, along with the locations from which tide

gauge information was obtained. Where information from one tide

gauge was used in two regions this has been shown by arrows pointing

from the gauge to the two regions. The prefix "T" identifies the

temporary gauges placed in 1967. All tide gauge information came

from the Tides and Water Levels Section of the Department of Energy,

Mines and Resources in Ottawa.

The harmonic constituent of tidal volume above cross-section

an is denoted as having amplitude Vn and phaselag Gn (of M2 , etc.).

Thus, n

(Vn , Gn) =

E (HiAi, gi)

1=1

the summation being carried out vectorially.

The harmonic constituent of tidal volume transport through

cross-section an is the time derivative of (Vn

, Gn) and is denoted

(1)

3

as (Tn

, Jn). Thus,

(T n

, J n dt ) ■ — (V n , G n) = (w Vn , Gn - 90° ), (2)

where w is the angular frequency of the constituent (M 2 , etc.).

The corresponding harmonic constituent of the average tidal

stream through cross-section an is obtained by dividing the tidal

volume transport by the cross-sectional area, so

(vn , Jn — ) = (Tn, J n). an

(3 )

Values of the average river diicharge volume through the

various cross-sections and the corresponding average river current

are also given for comparison with the tidal volume transports and

tidal streams. The discharge values came from a variety of sources

and are only approximate. The actual river discharge is subject to

considerable variation through changes in run-off and water level

control conditions.

Farquharson (1966) describes a current meter survey in

cross-section a22 near Pte. des Monts in 1963, and Forrester (1967)

describes a current meter survey in cross-section a21 near

Pte. au Pere in 1965. For comparison with the continuity calcula-

tions, weighted averages of the tidal constituents were formed from

the eleven current meters of Forrester in a21 and from the ten

current meters of Farquharson in a22. The weighting was done on

the basis of the depth of the meters, and the same weights were used

for each of the tidal constituents (M 2 , etc.).

RESULTS

Table I lists the surface areas of the regions, the areas of

their downstream cross-sections, the distance along the channel from

-4-

Quebec to the downstream cross-section, the river volume discharge,

and the average river current through the cross-section.

Table IIa lists the M2 harmonic constituent of the vertical

tide for each region and the tidal volume transport and mean tidal

stream through each downstream cross-section. The average M 2 tidal

stream through cross-sections a21 and a22 as obtained from the

current meters is also shown in Table Ha. Tables IIb to IIg contain

the same information for the harmonic constituents S2' N2, K1 , 0

1' M4,

and MS4 respectively. All phaselags refer to Eastern Standard Time

(EST). Inflowing tidal streams have positive sign.

DISCUSSION

Comparison in Tables IIa to IIg of the average tidal streams

in cross-sections a21 and a22 obtained by the continuity calculation

and by direct current measurement shows remarkably good agreement:

the greatest disagreement is 0.02 m/sec., which occurs for the M2

constituent. The agreement, however, would probably be worse in

sections above Quebec because of the greater effect of the sloping

banks in the narrow cross-sections, for which no allowance was made

in the continuity calculations. Insufficient current meter obser-

vations are available above Quebec, however, to permit such a

comparison. The calculated values of the constituents M 4 and MS4

above Quebec should be regarded as particularly suspect.

The tidal volume transport as a function of distance from

Quebec varies much more smoothly than does the mean tidal stream.

For this reason, interpolation to cross-sections intermediate to

those treated in the tables should be done only on the tidal volume

transport as a function of distance from Quebec: to obtain the

- 5 -

corresponding mean tidal stream, the appropriate cross-sectional

area should be measured from a chart and divided into the interpolated

tidal volume transport.

The current or tidal stream calculated for a particular

cross-section is the average over the entire cross-section, and as

such tells nothing of possible variations from top to bottom or

from shore to shore; direct current measurement is still required

to supply this information. The calculated averages for the large

cross-sections below Ile d'Orleans, are, however, more accurate

than could be obtained by direct current measurement with the limited

quantity and reliability of equipment at present available.

ACKNOWLEDGEMENTS

The author wishes to acknowledge the assistance of

Mr. G.C. Dohler and the staff of the Tides and Water levels Section

of the Department of Energy, Mines and Resources in Ottawa in

providing the tidal height information and some of the cross-

sectional area information used in this study. It is also wished

to thank Dr. C.D. Maunsell and Mr. R.C. Melanson of the Bedford

Institute for reading and commenting on the manuscript for this

report.

REFERENCES

Farquharson, W.I., 1966: St. Lawrence estuary current surveys. Bedford Institute Oceanography, Dartmouth, N.S., Can. Unpubl. man. rep. 66-6.

Forrester, W.D., 1967:

Currents and geostrophic currents in the St. Lawrence estuary, Bedford Institute Oceanography, Dartmouth, N.S., Can. Unpubl. man. rep. 67-5.

70.103,

• TIDES A1■0 WATER LEVELS GAUGING SITE (T• temporary gouge.1967)

Ai • Oh region of • Coscahnan cross-wilco of im regko

Fig. 1. Regions and cross-sections of St. Lawrence River and estuary, showing tide gauge locations.

- 7 -

Table I

Distance (21.) along chan- Downstream nel from

(Al) Cross- Quebec to Surface Section end

Region Area Area downstream

(km2) (km2) (km)

River Mean Discharge River Volume Current

(106m3/sec) (m/sec)

Al 347 0.017 -142 0.0076 0.45 A2 14 0.017 -134 0.0076 0.45 A3 27 0.013 -119 0.0079 0.61

A4 48 0.019 -1p3 0.0079 0.42

AS 31 0.013 - 90 0.0081 0.62

A6 24 0.010 - 81 0.0081 0.81

A7 24 0.014 - 68 0.0084 0.60 A8 52 0.028 - 47 0.0084 0.30 A9 96 0.022 12 0.0087 0.39

A10 110 0.056 + 25 0.0087 0.16

All 106 0.110 + 37 0.0087 0.08 Al2 416 0.200 + 63 0.0087 0.04 A13 392 0.25 + 81 0.0090 0.04 A14 392 0.32 + 98 0.0090 0.03 A15 316 0.57 +117 0.0090 0.02

A16 683 0.77 +154 0.0093 0.012

A17 313 0.68 +170 0.0093 0.014

A18 742 1.04 +190 0.0102 0.010

A19 769 4.28 +220 0.0108 0.003 A20 1278 5.28 +258 0.0113 0.002 A21 1501 8.59 +290 0.0119 0.001

A22 5804 11.58 +402 0.0125 0.001

- 8 -

Table Ha

Tidal constituent M2 (EST)

Region

Mean Vertical Tide

(m)

Tidal Volume Transport

(106m3/sec

Mean Tidal Stream (Calculated)

(m/sec)

Mean Tidal Stream (Observed)

(m/sec)

Al (0.03, 085 ° ) (.0013, 355 ° ) (0.08, 355 ° )

A2 (0.07, 018 ° ) (.0014, 350 ° ) (0.08, 350 ° )

A3 (0.08, 355 ° ) (.0015, 338 ° ) (0.12, 338 ° )

A4 (0.26, 326 ° ) (.0020, 280 ° ) (0.11, 280° )

A5 (0.35, 314 ° ) (.0032, 257 ° ) (0.25, 257 ° )

A6 (0.71, 283 ° ) (.0047, 230 ° ) (0.49, 230 ° )

A7 (0.86, 275 ° ) (.0071, 213 ° ) (0.52, 213 ° )

A8 (1.46, 245 ° ) (.0156, 178 ° ) (0.55, 178 ° )

A9 (1.54, 226 ° ) (.0340, 154 ° ) (1.55, 154 ° )

A10 (1.83, 174 ° ) (.0512, 123 ° ) (0.91, 123 ° )

All (2.00, 162 ° ) (.0739, 104 ° ) (0.67, 104 ° )

Al2 (1.98, 150 ° ) (.1765, 077 ° ) (0.88, 077 ° )

Al3 (1.93, 137 ° ) (.2736, 066 ° ) (1.10, 066 ° )

Al4 (1.86, 125 ° ) (.3655, 058 ° ) (1.16, 058 ° )

Al5 (1.81, 108 ° ) (.4306, 051 ° ) (0.75, 051 ° )

Al6 (1.68, 092 ° ) (.5507, 038 ° ) (0.71, 038 ° )

All (1.58, 084 ° ) (.6028, 033 ° ) (0.89, 033 ° )

A18 (1.56, 074 ° ) (.7197, 023 ° ) (0.69, 023 ° )

Al9 (1.45, 062 ° ) (.8261, 015 ° ) (0.19, 015 ° )

A20 (1.35, 055 ° ) (.9994, 004 ° ) (0.19, 004 ° )

A21 (1.32, 054 ° ) (1.226, 356 ° ) (0.14, 356 ° ) (0.12, 353 ° ) A22 (1.16, 048 ° ) (2.056, 339 ° ) (0.18, 339 ° ) (0.16, 341°)

- 9 -

Table IIb

Tidal constituent S 2 (EST)

Mean Vertical

Region Tide



Mean Tidal Stream (observed)

(m) (106m

3/sec) (m/sec)

(m/sec)

Al (0.01, 112 ° ) (.0005, 022 ° ) (0.03, 022 ° )

A2 (0.02, 052 ° ) (.0005, 018 ° ) (0.03, 018 ° )

A3 (0.02, 027 ° ) (.0005, 007 ° ) (0.04, 007 ° )

A4 (0.06, 003 ° ) (.0007, 324 ° Y (0.04, 324 ° )

A5 (0.08, 356 ° ) (.0009, 304 ° ) (0.07, 304 ° )

A6 (0.14, 329 ° ) (.0012, 282 ° ) (0.12, 282 ° )

A7 (0.18, 318 ° ) (.0017, 264 ° ) (0.12, 264 ° )

A8 (0.29, 294 ° ) (.0033, 230° ) (0.12, 230 ° )

A9 (0.34, 278 ° ) (.0076, 205 ° ) (0.35, 205 ° )

A10 (0.44, 221 ° ) (.0117, 169 ° ) (0.21, 169 ° )

All (0.48, 213 ° ) (.0177, 152 ° ) (0.16, 152 ° )

Al2 (0.49, 197 ° ) (.0442, 123 ° ) (0.22, 123° )

A13 (0.53, 182 ° ) (.0715, 111 ° ) (0.29, 111 ° )

A14 (0.50, 162 ° ) (.0954, 100 ° ) (0.30, 100° )

A15 (0.48, 142 ° ) (.1117, 091 ° ) (0.20, 091 ° )

A16 (0.52, 129 ° ) (.1486, 076 ° ) (0.19, 076 ° )

A17 (0.48, 122 ° ) (.1652, 070° ) (0.24, 070° )

A18 (0.50, 113 ° ) (.2059, 059 ° ) (0.20, 059 ° )

A19 (0.47, 101 ° ) (.2437, 050 ° ) (0.06, 050° )

A20 (0.43, 094 ° ) (.3053, 039 ° ) (0.06, 039 ° )

A21 (0.42, 095 ° ) (.3850, 031 ° ) (0.04, 031 ° ) (0.03, 023 ° )

A22 (0.34, 083 ° ) (.6368, 015 ° ) (0.06, 015 ° ) (0.06, 022°)

- 10 -

Table IIc

Tidal constituent N 2 (EST)

Mean Mean Mean Tidal Tidal Tidal Vertical Volume Stream Stream

Region Tide Transport (Calculated) (Observed)

(106m

3/sec) (m/sec) (m/sec)

Al (0.01, 045 ° ) (.0003, 315 ° ) (0.02, 315 ° )

A2 (0.01, 353 ° ) (.0003, 312 ° ) (0.02, 312 ° )

A3 (0.02, 328 ° ) (.0003, 302 ° ) (0.02, 302 ° )

A4 (0.04, 309 ° ) (.0005, 264 ° )' (0.03, 264 ° )

A5 (0.06, 307 ° ) (.0006, 248 ° ) (0.05, 248 ° )

A6 (0.10, 266 ° ) (.0008, 226 ° ) (0.08, 226 ° )

A7 (0.12, 246 ° ) (.0010, 205 ° ) (0.07, 205 ° )

A8 (0.19, 225 ° ) (.0019, 164 ° ) (0.07, 164 ° )

A9 (0.33, 188 ° ) (.0055, 117 ° ) (0.25, 117 ° )

A10 (0.28, 155 ° ) (.0088, 094 ° ) (0.16, 094 ° )

All (0.30, 142 ° ) (.0124, 081 ° ) (0.11, 081 ° )

Al2 (0.36, 125 ° ) (.0308, 052 ° ) (0.15, 052 ° )

A13 (0.37, 114 ° ) (.0497, 041 ° ) (0.20, 041 ° )

A14 (0.33, 099 ° ) (.0654, 033 ° ) (0.21, 033 ° )

Al5 (0.35, 082 ° ) (.0776, 025 ° ) (0.14, 025 ° )

A16 (0.30, 064 ° ) (.0977, 012 ° ) (0.13, 012 ° )

A17 (0.31, 056 ° ) (.1073, 007 ° ) (0.16, 007 ° )

A18 (0.31, 049 ° ) (.1309, 357 ° ) (0.13, 357 ° )

Al9 (0.30, 038 ° ) (.1535, 348 ° ) (0.04, 348 ° )

A20 (0.27, 031 ° ) (.1887, 337 ° ) (0.04, 337 ° )

A21 (0.25, 031° ) (.2323, 330° ) (0.03, 330° ) (0.03, 330° )

A22 (0.24, 030° ) (.4129, 316 ° ) (0.04, 316 ° ) (0.04, 318°)

(m)

- 11 -

Table IId

Tidal constituent K1 (EST)

Region

Mean Vertical Tide

(m)


(106m

3/sec)


(m/sec)


(m/sec)

Al (0.02, 090 ° ) (.0004, 000 ° ) (.02 , 000° )

A2 (0.02, 052 ° ) (.0004, 358 ° ) (.02 , 358 ° )

A3 (0.03, 034 ° ) (.0004, 352 ° ) (.03 , 352 ° )

A4 (0.06, 359 ° ) (.0005, 327 ° ) (.03 , 327 ° )

A5 (0.08, 353 ° ) (.0006, 311 ° ) (.05 , 311 ° )

A6 (0.12, 330° ) (.0007, 294 ° ) (.07 , 294 ° )

A7 (0.14, 329 ° ) (.0009, 281 ° ) (.07 , 281 ° )

A8 (0.19, 302 ° ) (.0013, 251 ° ) (.05 , 251 ° )

A9 (0.19, 288 ° ) (.0024, 224 ° ) (.11 , 224 ° )

A10 (0.23, 263 ° ) (.0038, 202 ° ) (.07 , 202 ° )

All (0.24, 253 ° ) (.0054, 189 ° ) (.05 , 189 ° )

Al2 (0.24, 246 ° ) (.0121, 170°) (.06 , 170 ° )

Al3 (0.23, 240 ° ) (.0185, 163 ° ) (.07 , 163 ° )

Al4 (0.25, 232 ° ) (.0254, 157 ° ) (.08 , 157 ° )

A15 (0.25, 222°) (.0308, 153 ° ) (.05 , 153 ° )

A16 (0.24, 215 ° ) (.0419, 145 ° ) (.05 , 145 ° )

A17 (0.24, 213 ° ) (.0471, 142 ° ) (.07 , 142 ° )

A18 (0.25, 209 ° ) (.0596, 137 ° ) (.06 , 137 ° )

A19 (0.24, 205 ° ) (.0721, 133 ° ) (.017, 133 ° ) A20 (0.23, 200° ) (.0919, 128 ° ) (.017, 128 ° )

A21 (0.23, 201 ° ) (.1157, 124 ° ) (.014, 124 ° ) (.013, 150 ° )

A22 (0.23, 201 ° ) (.2111, 118 ° ) (.018, 118 ° ) (.015, 120°)

- 12 -

Table He

Tidal constituent 01 (EST)

Region

Mean Vertical Tide

(m)


(106m

3/sec)


(m/sec)


(m/sec)

Al (0.02, 052 ° ) (.0004, 322 ° ) (.02 , 322 ° )

A2 (0.03, 020 ° ) (.0004, 320 ° ) (.02 , 320 ° ) A3 (0.03, 005 ° ) (.0005, 316 ° ) (.04 , 316 ° ) A4 (0.07, 336 ° ) (.0006, 296 ° ). (.03 , 296 ° )

A5 (0.09, 330 ° ) (.0007, 284 ° ) (.05 , 284 ° )

A6 (0.13, 312 ° ) (.0008, 271 ° ) (.08 , 271 ° )

A7 (0.14, 306°) (.0010, 260 ° ) (.07 , 260 ° )

A8 (0.18, 286 ° ) (.0014, 236 ° ) (.05 , 236 ° )

A9 (0.20, 271 ° ) (.0024, 209 ° ) (.11 , 209 ° ) A10 (0.22, 244 ° ) (.0036, 187 ° ) (.06 , 187 ° ) All (0.24, 235 ° ) (.0050, 174 ° ) (.05 , 174 ° ) Al2 (0.24, 232 ° ) (.0113, 156 ° ) (.06 , 156 ° )

Al3 (0.24, 221°) (.0172, 147 ° ) (.07 , 147 ° )

Al4 (0.25, 214 ° ) (.0234, 141 ° ) (.07 , 141 ° ) A15 (0.24, 204 ° ) (.0281, 136° ) (.05 , 136 ° )

A16 (0.24, 197 ° ) (.0381, 128 ° ) (.05 , 128 ° )

A17 (0.23, 195 ° ) (.0427, 125 ° ) (.06 , 125 ° )

A18 (0.24, 192 ° ) (.0541, 120 ° ) (.05 , 120° )

A19 (0.23, 187 ° ) (.0651, 116 ° ) (.015, 116 ° )

A20 (0.22, 182°) (.0829, 111 ° ) (.016, 111 ° )

A21 (0.23, 183 ° ) (.1047, 107 ° ) (.012, 107 ° ) (.010, 107 ° ) A22 (0.21, 183 ° ) (.1858, 101 ° ) (.016, 101 ° ) (.015, 115°)

- 13 -

Table IIf

Tidal constituent M4

(EST)

Region

Mean Vertical Tide

(m)


(106m

3/sec)


(m/sec)


(m/sec)

Al (0.01, 039 ° ) (.0006, 309 ° ) (.04 , 309 ° )

A2 (0.02, 301 ° ) (.0006, 301 ° ) (.04 , 301 ° )

A3 (0.03, 254 ° ) (.0004, 277 ° ) (.03 , 277 ° )

A4 (0.09, 217 ° ) (.0008, 142 ° ) (.04 , 142 ° )

A5 (0.10, 196 ° ) (.0016, 124 ° ) (.12 , 124 ° )

A6 (0.21, 124 ° ) (.0022, 083 ° ) (.23 , 083 ° )

A7 (0.24, 113 ° ) (.0033, 057 ° ) (.24 , 057 ° )

A8 (0.33, 043 ° ) (.0051, 352 ° ) (.18 , 352 ° )

A9 (0.22, 009 ° ) (.0089, 312 ° ) (.40 , 312 ° )

A10 (0.27, 273 ° ) (.0073, 253 ° ) (.13 , 253 ° )

All (0.27, 256 ° ) (.0113, 207 ° ) (.10 , 207 ° )

Alt (0.15, 239 ° ) (.0256, 171 ° ) (.13 , 171 ° )

Al3 (0.05, 173 ° ) (.0264, 159 ° ) (.11 , 159 ° )

Al4 (0.05, 068 ° ) (.0207, 159 ° ) (.07 , 159 ° )

A15 (0.09, 046 ° ) (.0138, 172 ° ) (.02 , 172 ° )

A16 (0.08, 060° ) (.0060, 269 ° ) (.008, 269° )

A17 (0.06, 077 ° ) (.0087, 304 ° ) (.013, 304 ° )

Al8 (0.05, 123 ° ) (.0135, 353 ° ) (.013, 353 ° )

A19 (0.03, 113 ° ) (.0195, 003 ° ) (.005, 003 ° )

A20 (0.03, 064 ° ) (.0285, 353 ° ) (.005, 353 ° )

A21 (0.03, 085 ° ) (.0401, 354 ° ) (.005, 354 ° ) (.007, 021 ° )

A22 (0.01, 081 ° ) (.0550, 353 ° ) (.005, 353 ° ) (.008, 332°)

- 14 -

Table IIg

Tidal constituent MS4

(EST)

Region

Mean Vertical Tide

(m)


(106m3/sec)


(m/sec)


(m/sec)

Al (.003, 072 ° ) (.0003, 342 ° ) (.02 , 342 ° )

A2 (0.01, 000 ° ) (.0003, 336 ° ) (.02 , 336 ° )

A3 (0.02, 300° ) (.0003, 314 ° ) (.02 , 314°)

A4 (0.04, 268 ° ) (.0004, 205 ° ) (.02 , 205 ° )

A5 (0.04, 251 ° ) (.0007, 184°) (.05 , 184 ° )

A6 (0.07, 182 ° ) (.0009, 148°) (.09 , 148 ° )

A7 (0.09, 160°) (.0012, 116 ° ) (.09 , 116°)

A8 (0.12, 105 ° ) (.0019, 052 ° ) (.07 , 152 ° )

A9 (0.11, 073 ° ) (.0042, 008 ° ) (.19 , 008 ° )

A10 (0.13, 324 ° ) (.0033, 301 ° ) (.06 , 301 ° )

All (0.13, 318 ° ) (.0059, 260 ° ) (.05 , 260 ° )

Al2 (0.07, 295 ° ) (.0127, 227 ° ) (.06 , 227 ° )

A13 (0.03, 237 ° ) (.0139, 212°) (.06 , 212 ° )

A14 (0.02, 109 ° ) (.0115, 214 ° ) (.04 , 214 ° )

A15 (0.04, 086 ° ) (.0088, 230 ° ) (.02 , 230° )

Al6 (0.04, 100 ° ) (.0057, 284 ° ) (.007, 284 ° )

Al7 (0.02, 120 ° ) (.0055, 303 ° ) (.008, 303 ° )

A18 (0.02, 187 ° ) (.0027, 344 ° ) (.003, 344 ° )

A19 (0.02, 186 ° ) (.0034, 049 ° ) (.001, 049 ° )

A20 (0.01, 137 ° ) (.0056, 048 ° ) (.001, 048°)

A21 (0.01, 162 ° ) (.0094, 058 ° ) (.001, 058 ° ) (.003, 079 ° )

A22 (.003, 251 ° ) (.0096, 089 ° ) (.001, 089 ° ) (.001, 005°)

atlantic oceanographic laboratory · gauges, values of the harmonic constituents m2, s2, n2, k1, 0...

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