Northern Water Problems Institute (NWPI),

Strongly non-linear waves in lakes:generation, transformation and

meromixis (project INTAS–03-51-3728)

Northern Water Problems Institute (NWPI), Karelian Scientific Centre, Russian Academy of Sciences,

Petrozavodsk, Russia

Task 1. Data collection and analysis.

Further development

Source of data:

• field measurements in Bol’shoe Onego Bay, Lake Onega (July 2005)

• field measurements in the Bol’shoe Onego Bay (Osetrovskaya Bank), Lake Onega (May-September 1977)

• field measurements in Lizhemskaya Guba, Bol’shoe Onego Bay, Lake Onega (August-September 1987)

Red box: 1-5 – stations of field measurements in 2004-2005; 6 – RCM (1977), 7 – TR (1977)

Blue box: 1, 2, 4, 5 – TRs; 3 – RCM; 6 – АЦИТТ [ADCTM]; 7 – БПВ [LPCM] (АЦИТТ – Autonomic Digital Current & Temperature Meter; БПВ – Letter-Printing Current Meter)

Performing field work.

Win

d s

pe

ed

, m

·s-1

0

2

4

6

8

10

12

13.0

7.0

5

14.0

7.0

5

15.0

7.0

5

16.0

7.0

5

17.0

7.0

5

18.0

7.0

5

19.0

7.0

5

20.0

7.0

5

21.0

7.0

5

22.0

7.0

5

23.0

7.0

5

24.0

7.0

5

Win

d D

ire

ctio

n,

de

g

0

60

120

180

240

300

360

Wind speed and direction during the field campaign 2005

a

13.0

7.05

14.0

7.05

15.0

7.05

16.0

7.05

17.0

7.05

18.0

7.05

19.0

7.05

20.0

7.05

21.0

7.05

22.0

7.05

23.0

7.05

24.0

7.05

Te

mp

era

ture

, 0 C

4

6

8

10

12

14

16

18

20

22

24

1.5 m 3.5 m 5.5 m 7.5 m 9.5 m 11.5 m 13.5 m 15.5 m 17.5 m 19.5 m

b

13.0

7.05

14.0

7.05

15.0

7.05

16.0

7.05

17.0

7.05

18.0

7.05

19.0

7.05

20.0

7.05

21.0

7.05

22.0

7.05

23.0

7.05

24.0

7.05

De

pth

, m

0

5

10

15

20

Development of the water temperature in time at st. 2: 13 July 2005, 19:50 - 23 July 2005, 09:50 (a); depth of 14C isotherm location calculated from thermistor chain data for the same period (b).

a

13.0

7.05

14.0

7.05

15.0

7.05

16.0

7.05

17.0

7.05

18.0

7.05

19.0

7.05

20.0

7.05

21.0

7.05

22.0

7.05

23.0

7.05

24.0

7.05

Te

mp

era

ture

, 0 C

2

4

6

8

10

12

14

16

18

20

22

243.4 m 4.4 m 5.4 m 6.4 m 7.4 m 8.4 m 9.4 m 11.3 m 13.3 m 15.3 m 17.3 m 19.3 m 21.3 m 23.3 m 25.3 m 27.3 m 29.3 m 31.3 m

b

13.0

7.05

14.0

7.05

15.0

7.05

16.0

7.05

17.0

7.05

18.0

7.05

19.0

7.05

20.0

7.05

21.0

7.05

22.0

7.05

23.0

7.05

24.0

7.05

De

pth

, m

0

5

10

15

20

25

Development of the water temperature in time at st. 5: 13 July 2005, 22:20 - 23 July 2005, 09:20 (a); location of 12C isotherm calculated from thermistor chain data for the same period (b).

13.0

7.05

14.0

7.05

15.0

7.05

16.0

7.05

17.0

7.05

18.0

7.05

19.0

7.05

20.0

7.05

21.0

7.05

22.0

7.05

23.0

7.05

24.0

7.05

Dep

th, m

0

5

10

15

20

25

Development of the water temperature in time at st. 4: 14 July 2005, 09:00 - 23 July 2005, 09:00 (absciss axis shows a number of profiles, 96 of which correspond to one day) (a); location of 12C isotherm calculated from vertical profiling data for the same period (b).

The development of the Väisäla-Brent frequency in time at station 4, 14 July 2005, 09:00 - 23 July 2005, 09:00.

Rank 2 Eqn 6870 Chebyshev=>Std Polynomial Order 20r^2=0.94915981 DF Adj r^2=0.94877002 FitStdErr=0.8750996 Fstat=2557.7185

0 2e+05 4e+05 6e+05 8e+05Time index

0

2.5

5

7.5

10

12.5

15

17.5

20

De

pth

, m

0

2.5

5

7.5

10

12.5

15

17.5

20

De

pth

, m

Rank 2 Eqn 6870 Chebyshev=>Std Polynomial Order 20r^2=0.94915981 DF Adj r^2=0.94877002 FitStdErr=0.8750996 Fstat=2557.7185

0 2e+05 4e+05 6e+05 8e+05Time index

-3

-2

-1

0

1

2

3

Resid

uals

-3

-2

-1

0

1

2

3

Resid

uals

5090959999.9

9.425e-06

1.239e-05

1.5496e-05

1.8891e-05

2.2085e-05

2.3882e-05

2.6716e-05

3.0105e-05

3.2529e-05

3.5997e-05

4.2355e-05

0 1e-05 2e-05 3e-05 4e-05 5e-05Frequency, Hz

0

50

100

150

200

250

300

350

PS

D S

SA

, m

2 /H

z

0

50

100

150

200

250

300

350

Frequency, Hz Period, h PSD SSA

9,43E-06 29,5 187,14

1,24E-05 22,4 319,44

1,55E-05 17,9 346,95

1,89E-05 14,7 38,71

2,21E-05 12,6 92,99

2,39E-05 11,6 121,08

2,67E-05 10,4 25,23

3,01E-05 9,2 39,89

3,25E-05 8,5 20,99

3,60E-05 7,7 36,67

4,24E-05 6,6 19,30

PSD calculated for 14C DIL, st. 2: the Curve-Fit Graph (a), the residuals (b), and the Fourier spectrum (c). Horizontal lines mark five significance levels (50%, 90%, 95%, 99%, and 99.9%). The table presents corresponding periods.

Temporal evolution of the vertical thermal structure and currents at the Osetrovskaya Banka [shoal] during the period 27 May – 11 October 1977 (data from thermistor chain registrations). Depth of location 30 m.

0

2

4

6

8

10

12

14

16

18

20

22

24

26

09

.07

.19

77

00

:00

10

.07

.19

77

00

:00

11

.07

.19

77

00

:00

12

.07

.19

77

00

:00

13

.07

.19

77

00

:00

14

.07

.19

77

00

:00

15

.07

.19

77

00

:00

16

.07

.19

77

00

:00

17

.07

.19

77

00

:00

18

.07

.19

77

00

:00

19

.07

.19

77

00

:00

20

.07

.19

77

00

:00

21

.07

.19

77

00

:00

22

.07

.19

77

00

:00

23

.07

.19

77

00

:00

24

.07

.19

77

00

:00

25

.07

.19

77

00

:00

26

.07

.19

77

00

:00

27

.07

.19

77

00

:00

28

.07

.19

77

00

:00

29

.07

.19

77

00

:00

30

.07

.19

77

00

:00

Dep

th, m

15

16

17

18

19

20

21

22

23

19

.07

.19

77

00

:00

19

.07

.19

77

06

:00

19

.07

.19

77

12

:00

19

.07

.19

77

18

:00

20

.07

.19

77

00

:00

20

.07

.19

77

06

:00

Dep

th, m

Izo_11,5Detrend Data

0 20000 40000 60000 80000Time index

17

18

19

20

21

22

23

17

18

19

20

21

22

23

Izo_11,5Fourier Frequency Spectrum

50

90

95

99

99.9

3.5484e-05

9.7472e-05 0.00018197 0.00020506

0 0.0002 0.0004 0.0006 0.0008Frequency

0

5

10

15

20

25

PS

D S

SA

0

5

10

15

20

25

Frequency, Hz

PSD SSA Period, h

3,55E-05 24,4 7,8

9,75E-05 1,5 2,8

0,000182 1,4 1,5

0,000205 1,0 1,4

Izo_11,5Rank 3 Eqn 6820 Chebyshev Polynomial Order 20

r^2=0.93126573 DF Adj r^2=0.91882246 FitStdErr=0.28249478 Fstat=79.260384

0 20000 40000 60000 80000X

17

18

19

20

21

22

17

18

19

20

21

22

-0.5

0

0.5

Res

idua

ls [5

2]

-0.5

0

0.5

Res

idua

ls [5

2]Residuals

Fourier Frequency Spectrum

50

90

95

99

9.432e-05

0.00012523

0.0001816

0.00020517

0.00026528

0.0005811

0 0.0002 0.0004 0.0006 0.0008Frequency

0

0.25

0.5

0.75

1

1.25

1.5

PS

D S

SA

0

0.25

0.5

0.75

1

1.25

1.5

Frequency, Hz PSD SSA Period, h

9,43E-05 0,5 2,9

0,000125 0,8 2,2

0,000182 1,3 1,5

0,000205 1,0 1,4

0,000265 0,5 1,0

0,000581 0,5 0,5

0

2

4

6

8

10

12

14

16

18

20

22

24

26

09

.07

.19

77

00

:00

10

.07

.19

77

00

:00

11

.07

.19

77

00

:00

12

.07

.19

77

00

:00

13

.07

.19

77

00

:00

14

.07

.19

77

00

:00

15

.07

.19

77

00

:00

16

.07

.19

77

00

:00

17

.07

.19

77

00

:00

18

.07

.19

77

00

:00

19

.07

.19

77

00

:00

20

.07

.19

77

00

:00

21

.07

.19

77

00

:00

22

.07

.19

77

00

:00

23

.07

.19

77

00

:00

24

.07

.19

77

00

:00

25

.07

.19

77

00

:00

26

.07

.19

77

00

:00

27

.07

.19

77

00

:00

28

.07

.19

77

00

:00

29

.07

.19

77

00

:00

30

.07

.19

77

00

:00

Dep

th, m

18,5

19,0

19,5

20,0

20,5

21,0

21,5

22,0

20

.07

.19

77

00

:00

20

.07

.19

77

06

:00

20

.07

.19

77

12

:00

20

.07

.19

77

18

:00

21

.07

.19

77

00

:00

21

.07

.19

77

06

:00

Dep

th, m

Izo_11,5Detrend Data

0 20000 40000 60000 80000 1e+05Time index

18.5

19

19.5

20

20.5

21

21.5

22

18.5

19

19.5

20

20.5

21

21.5

22

Izo_11,5Fourier Frequency Spectrum

50

90

95

99

99.9

2.1633e-05

6.2746e-05

9.2459e-05

0.00014277

0 0.0002 0.0004 0.0006 0.0008Frequency

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

PS

D S

SA

0

0.5

1

1.5

2

2.5

3

3.5

4

4.5

5

Frequency, Hz

PSD SSA

Period, h

2,16E-05 4,7 12,8

6,27E-05 2,0 4,4

9,25E-05 0,5 3,0

0,000143 1,1 1,9

Izo_11,5Rank 3 Eqn 6820 Chebyshev Polynomial Order 20


0 20000 40000 60000 80000 1e+05X

18.5

19

19.5

20

20.5

21

21.5

18.5

19

19.5

20

20.5

21

21.5

-0.5

0

0.5

Res

idua

ls [5

3]

-0.5

0

0.5

Res

idua

ls [5

3]Residuals

Fourier Frequency Spectrum with tapering window

50

90

95

99

99.9

8.875e-05

0.00014256

0.00019435

0.000243 0.00034703

0 0.0002 0.0004 0.0006 0.0008Frequency

0

0.25

0.5

0.75

1

1.25

1.5

PS

D S

SA

0

0.25

0.5

0.75

1

1.25

1.5

PS

D S

SA

Frequency, Hz PSD SSA Period, h

8,88E-05 0,2 3,1

0,000143 1,3 1,9

0,000194 0,3 1,4

0,000243 0,2 1,1

0,000347 0,3 0,8

August-September 1987: Development of water temperature in Lizhemskaya Guba, Bol’shoe Onego Bay, Lake Onega

7 m

Cur

rent

vel

ocity

, cm

·s-1

-500

-400

-300

-200

-100

0

100

200

300

400

500

17 m

Cur

rent

vel

ocity

, cm

·s-1

-500

-400

-300

-200

-100

0

100

200

300

400

500

22 m

Cur

rent

vel

ocity

, cm

·s-1

-500

-400

-300

-200

-100

0

100

200

300

400

500

20.0

8.8

7

21.0

8.8

7

22.0

8.8

7

23.0

8.8

7

24.0

8.8

7

25.0

8.8

7

26.0

8.8

7

27.0

8.8

7

28.0

8.8

7

29.0

8.8

7

30.0

8.8

7

31.0

8.8

7

01.0

9.8

7

02.0

9.8

7

03.0

9.8

7

04.0

9.8

7

05.0

9.8

7

06.0

9.8

7

07.0

9.8

7

08.0

9.8

7

09.0

9.8

7

10.0

9.8

7

11.0

9.8

7

12.0

9.8

7

13.0

9.8

7

The water temperature development at Station 2, depth 58 m.

7 m (19.08.1987 18:50 - 13.09.1987 09:20)

Distance E, m

-40000 -20000 0 20000 40000 60000

Dis

tanc

e N

, m

-40000

-20000

0

20000

40000

60000

17 m (19.08.1987 18:40 - 13.09.1987 08:30)

Distance E, m

-60000 -40000 -20000 0 20000 40000

Dis

tanc

e N

, m

-40000

-20000

0

20000

40000

60000

22 m (19.08.1987 18:50 - 13.09.1987 08:40)

Distance E, m

-40000 -20000 0 20000 40000 60000

Dis

tanc

e N

, m

-40000

-20000

0

20000

40000

60000

St. 1

St. 2

28.0

8.87

29.0

8.87

30.0

8.87

31.0

8.87

01.0

9.87

02.0

9.87

03.0

9.87

04.0

9.87

05.0

9.87

06.0

9.87

Dep

th, m

0

5

10

15

20

25

30

35

40

station 1 station 2

Depth of 11.85°C location at stations 1 and 2.

st1_11,85Rank 3 Eqn 6820 Chebyshev Polynomial Order 20


0 50000 1e+05 1.5e+05 2e+05 2.5e+05X

5

10

15

20

5

10

15

20

-2

-1

0

1

2

Resid

uals

[128

]

-2

-1

0

1

2

Resid

uals

[128

]Residuals

Fourier Frequency Spectrum (Chebyshev data tapeirng window)

50

909599

99.9

3.3632e-05

9.4737e-05

0.00012424

0 0.0001 0.0002 0.0003 0.0004 0.0005Frequency

0

10

20

30

40

50

60

PS

D S

SA

0

10

20

30

40

50

60

PS

D S

SA

Frequency, Hz

PSD SSA

Period, h

3,36E-05 54,5 8,3

9,47E-05 4,9 2,9

0,000124 6,9 2,2

St. 1, depth of 11.85°C isotherm location, 28.08.1987, 20:55 – 31.08.1987, 16:35



0 50000 1e+05 1.5e+05 2e+05 2.5e+05X

10

15

20

25

30

35

10

15

20

25

30

35

-1.5

-0.5

0.5

1.5

2.5

Res

idua

ls [1

77]

-1.5

-0.5

0.5

1.5

2.5

Res

idua

ls [1

77]

ResidualsFourier Frequency Spectrum (Chebyshev data tapeirng window)

50

9095

99

99.9

3.8741e-05

6.4692e-05

9.1599e-05

0.00017587

0 0.0001 0.0002 0.0003 0.0004 0.0005Frequency

0

5

10

15

20

25

30

35

40

45

PS

D S

SA

0

5

10

15

20

25

30

35

40

45

PS

D S

SA

Frequency, Hz

PSD SSA

Period, h

3,87E-05 43,2 7,2

6,47E-05 13,9 4,3

9,16E-05 8,3 3,0

0,000176 3,2 1,6




0 1e+05 2e+05 3e+05 4e+05X

10

12.5

15

17.5

20

22.5

10

12.5

15

17.5

20

22.5

-2

0

2

Resid

uals

[142

]

-2

0

2

Resid

uals

[142

]Residuals

Fourier Frequency Spectrum (Chebyshev data tapeirng window)

50909599

99.9

2.146e-05

3.1365e-05

4.2728e-05

5.4242e-05

0 0.0001 0.0002 0.0003 0.0004 0.0005Frequency

0

25

50

75

100

125

150

PS

D S

SA

0

25

50

75

100

125

150

PS

D S

SA

Frequency, Hz

PSD SSA

Period, h

2,15E-05 130,5 12,9

3,14E-05 48,6 8,9

4,27E-05 74,8 6,5

5,42E-05 18,3 5,1

0,000117 8,5 2,4


11,85 gradRank 3 Eqn 6820 Chebyshev Polynomial Order 20


0 1e+05 2e+05 3e+05 4e+05X

5

10

15

20

25

30

35

5

10

15

20

25

30

35

-2

0

2

4

Res

idua

ls [1

04]

-2

0

2

4

Res

idua

ls [1

04]

ResidialFourier Frequency Spectrum (Chebyshev data tapering window)

50

9095

99

99.9

3.3295e-05

3.9081e-05

4.9086e-05

7.9725e-05

0 0.0001 0.0002 0.0003 0.0004 0.0005Frequency

0

50

100

150

200

250

PS

D S

SA

0

50

100

150

200

250

PS

D S

SA

Frequency, Hz

PSD SSA

Period, h

3,34E-05 240,7 8,3

4,92E-05 57,5 5,6

7,95E-05 16,1 3,5

0,000181 10,2 1,5


29/08/1987 08:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4029/08/1987 09:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

29/08/1987 10:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4029/08/1987 11:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

29/08/1987 12:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4029/08/1987 13:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

29/08/1987 14:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4029/08/1987 15:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

Evolution of the vertical temperature profile at St. 2 during the 29 –

30.08.1987 period.

30/08/1987 16:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4030/08/1987 17:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

30/08/1987 18:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4030/08/1987 19:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

30/08/1987 20:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

3008/1987 22:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4030/08/1987 23:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

30/08/1987 21:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

01/09/1987 00:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4001/09/1987 01:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

01/09/1987 02:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4001/09/1987 03:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

01/09/1987 04:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4001/09/1987 05:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

01/09/1987 06:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

4001/09/1987 07:00

Temperature, 0C

5 6 7 8 9 10 11 12 13 14

Dep

th, m

0

5

10

15

20

25

30

35

40

The development of the Väisäla-Brent frequency in time at stations 1, 2, and 4 during the 28.08 – 05.09.1987 period.

Preliminary conclusionsPreliminary conclusions

• The development of non-linear internal waves may eventually invoke vertical mixing within the lake thermocline (data 2004data 2004);

• This is not a synoptical event (data 1997data 1997);• The wave activity may lead to the complete mixing of a

water column mostly in late summer when the stratification becomes weaker (data 1977 – indirectly & data 1977 – indirectly & 19871987);

• [not for eyes of Brussels] The selection of the measurement sites/s is very important issue (data 1977data 1977)

Thanks for your attention!

Documents

Northern Water Problems Institute (NWPI),