24

3.3  Harmonic  Analysis:  Elevations
The  results  of  the  harmonic  analysis  of  the  water  level  records  are  listed  in  Table  6.  Figure  9  shows
how  the  semi-diurnal  M 2  and  S 2  amplitudes  H  and  phases  G  vary  from  west  to  east  along  the  NORA  section. ­
  Data  from  the  “Class  A  Network  Dataring  Gauge”  at  the  port  of  Wick  (58°  26.5’  N,  3°  05.1’  E)  are  included ­
  in  Table  6  and  Fig.  9  for  comparison  purposes  (Shaw  [1992a,b]).  Harmonic  synthesis  calculations
by  means  of  the  constituents  of  Table  6  indicate  that  the  tide,  as  well  as  the  tidal  stream,  is  delayed  by  about
0.5  hours  between  2°  W  and  2°  E.  The  synthesis  shows  a  mean  time  lag  of  about  1.5  hours  between  the
MOVENS  and  the  NORA  data.  Amplitudes  and  phases  of  the  Q b  0 1?  K b  N 2 ,  M 2  and  S 2  tidal  constituents
can  be  compared  with  the  model  results  given  by  Schwiderski  [1979-1981]  (see  Table  7).  Generally,
the  NORA  amplitudes  agree  well  with  Schwiderski’s  results.  Most  phase  angles  agree  within  a  few  degrees,
but  there  are  some  positions  with  considerable  differences,  e.  g.  S 2  at  N1.  With  the  exception  of  the  N 2  constituent ­
  at  M9,  the  MOVENS  amplitudes  are  definitely  larger  than  the  model  results.  Some  of  the  MOVENS
phase  angles  agree  well,  other  differ  up  to  126°.  The  possible  reasons  for  the  differing  phase  angles  are  the
limited  length  of  our  time  series  (about  1  month)  and  the  method  used  by  Schwiderski  to  model  ocean  tides.
The  M 2  phase  along  the  NORA  section  agrees  better  with  Davis’s  results  [1981].  As  in  many  papers ­
  by  other  authors,  however,  Davis  investigated  only  the  M 2  tide.  Other  harmonic  constituents  cannot
therefore  be  compared.

Table  6

Amplitudes  H  and  phase  angles  G  of  17  tidal  constituents  calculated  from  tide  gauge  time  series  of
the  NORA-  and  MOVENS  section

Constituent ­


WICK*'
H  G

N1
H  G

N2
H  G

N3
H  G

N4
H  G

N5
H  G

M8
H  G

M9
H  G

cm

O

cm

O

cm

o

cm

O

cm

O

cm

O

cm

O

cm

O

Qt

3.2

343

2.5

338

2.2

340

1.4

342

1.5

4

1.7

0

3.5

287

5.1

214

o,

11.7

25

10.0

26

7.9

33

6.0

40

5.5

41

4.6

40

11.1

14

8.9

90

M,

-

-

1.0

293

1.1

298

0.5

278

1.0

310

1.2

315

3.9

255

15.6

168

K,

10.8

175

10.6

189

8.8

191

7.0

194

5.7

200

4.6

203

7.6

149

13.1

233

J,

0.8

240

0.9

210

1.1

196

0.5

192

0.6

232

0.7

214

1.4

194

2.0

153

MNS,

-

-

0.2

39

1.2

30

0.8

1

0.5

331

0.2

355

4.5

246

8.5

0

M2

-

-

1.0

331

0.6

96

1.1

334

1.4

325

1.1

309

3.9

45

5.5

88

N,

20.3

303

14.1

286

11.3

299

9.7

302

8.1

302

7.0

301

14.5

258

4.2

171

M,

101.7

322

79,4

314

64.2

318

51.3

328

42.4

329

34,9

326

57.9

295

50.9

295

L,

-

-

3.4

346

2.9

356

1.9

348

1.6

343

1.7

329

6.0

273

8.0

94

S,

35.0

0

28.0

7

23,0

11

19.7

20

16.9

19

14.2

17

31.9

316

32.6

320

MSN,

-

-

1.6

259

1.9

281

0.9

297

0.6

286

1.1

277

5.0

80

7.2

62

2SM,

-

-

2.2

182

1.2

168

1.1

190

0,6

151

0.3

193

2.7

282

7.5

114

M 4

3.6

317

2.8

267

4.3

281

1.6

286

1.4

265

1.3

265

1.3

295

1.7

69

MS 4

2.0

51

0.8

2

2.0

348

1.2

21

1.0

8

0.7

25

1.9

280

1.7

85

M 6

0.6

227

1.2

179

1.0

197

0.7

249

0.5

308

0.7

22

0.3

202

0.7

93

2MS 6

-

-

1.0

237

1.1

272

0.8

302

0.6

326

0.3

80

0.4

277

1.3

355

F

0.17

0.19

0.19

0.18

0.19

0.19

0.21

0.26

f=(K l  +  0,)/(M 2  +  S 2 )

*'  data  from  Shaw  [  1992]