~------

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i

NOTICE

The NOAA Environmental Research Laboratories do not

approve. recommend, or endorse any proprietary product or

proprietary material mentioned in tbis publication. No

reference shall be made to the NOAA Environmental Research

Laboratories. or to this publication furnished by the NOAA

Environmental Research Laboratories. in any advertising or

sales promotion which would indicate or imply that the NOAA

Environaental Research Laboratories approve, recommend, or

endorse any proprietary product or proprietary material

mentioned herein. or which has as its purpose an intent to

cause directly or indirectly the advertised product to be

used or purchased because of this NOAA Environmental Research

Laboratories publication.

11
Foreword

This report presents the results of an analysis of water current recordings collected in Lake Huron during 1966 by the Federal Water Pollution

Control Administration. Most of the curreat data were collected during the

interval of May through September 1966 and are therefore representative of

the sl1llllller heating and density stratified season of Lake Huron. This is a

contribution to the International Joint Cow-ission Upper Lakes Reference

Study and was supported through an Interagency Agreemeat by the Environmental

Protection Agenc.y, Region V.

iii

1

J

I

I

t

I
CONTENTS

ABSTRACT

1. INTRODUCTION

2. DATA ANALYSIS

3. CIRCULATION PATTERNS

4. FLOWS AT DEPTHS BELOW 10 m

5. EFFECTS OF THERMAL STRUCTURE

6. OSCILLATORY CURRENTS

7. SlJHIfARY AND CONCLUSIONS

8. REFERENCES

v

Pa.ge

1

1

3

4

20

25

25

37

39
1.

2a.

2b.

3a.

3b.

4a.

4b.

Sa.

5b.

6a.

6b.

7a.

7b.

8a.

8b.

9a.

9b.

lOa.

lOb.

lla.

llb.

lIe.

lld.

12.

FIGURES

Location map for 1966 FWPCA current-meter moorings in

Lake Buran.

Half-month average current vectors at 10 m and 30 m for

1-14 May 1966.

Ha1f-month average current vectors at 15 In and 22 m for

1-14 May 196tl11'

Half-month average current vectors at 10 III and 30 III for

15-31 May 1966.

Half-month average current vectors at 15 III and 22 m for

15-31 May 1966.

Half-month average current vectors at 10 III and 30 m for

1-14 June 1966.

Half-month average current vectors at 15 III and 22 III for

1-14 June 1966.

Half-lllOnth average current vectors at 10 III and 30 m for

15-30 June 1966.

Half-month average current vectors at 15 m and 22 m for

15-30 .June 1966.

Half-month average current vectors at 10 m and 30 m for

1-14 .July 1966.

Half-month average current vectors at 15 m and 22 m for

1-14 July 1966.

Half-month average current vectors at 10 m and 30 m for

15-31 .July 1966.

Half-month average current vectors at 15 III and 22 m for

15-31 .July 1966.

Half-month average current vectors at 10 m and 30 m for

1-14 August 1966.

Ha1f-month average current vectors at 15 m and 22 m for

1-14 August 1966.

Half-month average current vectors at 10 m and 30 m for

15-31 August 1966.

Hal£-month average current vectors at 15 II and 22 m for

15-31 August 1966.

Half-month average current vectors at 10 II and 30 m for

1-14 September 1966.

Half-month average current vectors at 15 II and 22 m for

1-14 September 1966.

Temperature profiles (bathythermograph) from R/V Shenehon

taken near mooring 27.

Temperature profiles from near mooring 18.

Temperature profiles from near mooring 16.

Temperature profiles from near mooring 13.

Schematic representation of data subsets for spectrull

computation.

vi

Page

2

5

6

7

8

9

10

11

12

14

15

16

17

18

19

21

22

23

24

26

26

26

26

27

"----------
+=0

•

t

FIGURES (continued) ,

I

f

Page I

13a. Power spectra of north (heavy Une) and east (Ught line)

hourly velocity components at station 13, depth 10 m, for

1-16 July 1966. 29

Db. Rotational spectra of clockwise (heavy line) and counterclockwise (light line) hourly velocity components at station

13, depth 10 m, for 1-16 July 1966. 30

l4a. Power spectra of north (heavy line) and east (light line)

hourly velocity components at station 13, depth 10 m, for

17 July-3 August 1966. 31

l4b. Rotational spectra of clockwise (heavy line) and counterclockwise (light line) hOurly velocity components at station

13, depth 10 m, for 17 July-3 August 1966. 32

l5a. Rotational spectra of clockwise (heavy line) and counterclockwise (light line) 2-hourly averaged velocity components

at station 17, depth 10 m, 9 July-13 September 1966. 33

l5b. Rotational spectra of clockwise (heavy line) and counterclockwise (light line) 2-hourly averaged velocity components

at station 17, depth 30 m, 9 July-13 September 1966. 34

16a. Power spectra of north (heavy Une) and east (light line)

hourly velocity components at station 35, depth 16 _, for

16 June-20 July 1966. 35

16b. Rotational spectra of clockwise (heavy line) and counterclockwise (light line) hourly velocity components at station

35, depth 16 m, for 16 June-20 July 1966. 36

17. Power spectra of north (heavy line) and east (light line)

2-hourly averaged velocity components at station 32 (Straits

of Mackinac), depth 10 m, 15 July-16 September 1966. 38

vii
MEASUREMENTS OF CURRENT FLOW DURING SUMMER IN LAKE HURON

Peter W. Sloss snd James H. Saylor

Reanalyses of the data from the 1966 Great Lakes-Illinois River

Basin Project (GLIRBP) of the (then) Federal Water Pollution Control

Administration (FWPCA) reveal some of the large-scale, persistent

summertime circulation patterns in Lake Huron. The greatest density

of data from the original 45 current meter moorings covers June

through August 1966, when some 21 stations returned synopticallysignificant data from meters at depths of 10 and 15 m. From this

somewhat sparse sample, it is deduced that at lG-m depth a counterclockwise circulation dominates the northern 2/3 of the lake. The

shallower southern portion shows a more complex pattern, with generally southward flow along the shorelines on both sides and a

"return flow northward near the centerline of the southern basin.

This latter pattern may decay later in the summer, but the data

become too patchy for definite analysis. The data set from l5-m

depth indicates similar circulations. Spectral analysis of currents

at individual stations reveals a strong inertial rotation of the

current vector at open-lake sites. Only the data from the Straits

of Mackinac lack the inertial components and are dominated by the

lunar semidiurnal tide and the seiches of Lake Michigan.

1. INTRODUCTlOli

Currents in Lake Huron were described in an early study by Harrington

(1895) in which drift bottles were the measuring devices. More recently,

Ayers et al. (1956) combined drift bottle paths with temperatures and the

resulting dynamic height data to determine large-scale flow patterns at three

times during the summer of 1954. Neither study used continuous current measurements to determine the degree of persistence or the variability of the

reported currents.

In 1966, under the auspices of the Federal Water Pollution Control

Administration (FWPCA) and its Great Lakes-Illinois River Basin project

(GLIRBP), some 40 current-meter moorings were placed in Lake Huron for varying intervals of time from April through September. Seven moorings also were

deployed through the previous winter at locations near the Michigan shore.

Usable data were returned from stations I, 4, and 9, but were too sparse for

any interpretation of winter currents. Details of typical moorings and

meters can be found in the report entitled "Lake Michigan Currents"

(FWPCA, 1967). The Lake Huron station network 18 shown in fig. 1.

Of the summer moorings, a maximum of 25 produced Simultaneous, usable data

representing flow at the same depth (10 m) for the interval mid-June through

July 1966. By the middle of August, the number of functioning instruments at
21 22

- - 4'!/

•

11-

,.-

43

GlIRBP Hat"rif,vi." 51 1eI Moorings 20-

1966 4

--37 -18 45- ;J

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or or

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Figu:t'e 1. Location map loY' 1966 FWPCA CW'l'ent-mete2' m001'ings in Lake

1ha'on. Stations 1 and 4-9 W6Y'6 deptoyed for winter 19G5-G6; the.

remainder "'ere set late ApriZ through Septembe2' 1966.

2
10-m depth was down to 13. At other depths. the maxilllum number of simultaneous usable records was 12 at JO-m depth during the second half of June. The

entire available data set from all moorings consists of 187 data files on

magnetic tape. There are, however, timing and data-quality problema evident

on many of the files. The exact percentage of "good" data rl!turned depends

on the user's quality criteria and patience--some 30 of the original data

films from the current meters were recently reprocessed by Geodyne, Inc •• to

correct serious timing discrepancies in eases where the number of observations was not in agreement with the indicated start and stop dates and the

interval between observations. Absolute timing, for purposes of correlation

between different meters. remains a serious problem with lllUch of the data the

authors have seen from Geodyne "Type G" _tera.

The majority of the current data wu recorded at 3O-adn intervals, although some records were timed at 20-, 10-. or 5-min spacing. and data from

station 16 include several periods of about a week's durstion each. during

which data were taken at 1-lll1n spacing. The purpose of these intensive observations is not known.

2. DATA ANALYSIS

The velocity time series generated by the current meters were analyzed

in two ways: block averages over various time periods. and spectrua analysis.

Spectrum analysis of lake current data (Verber. 1966; Malone, 1968) has shown

a strong component of rotary motion at the local inertial frequency in openlake areas during the season of stratification. The GLIRBP Lake Huron data

show this behavior at stations as close as 5 km frOlll the shore.

The presence of a st.rong inertial component in the current fluct.uations

suggests that short-tem net flows can best be computed on the basis of

vector-averaged currents from an integral number of inertial periods. Inertial periods in Lake Huron range from 17.6 hours at the south end of the lake

(latitude 43°N) to 16.7 hours at the north end (latitude 46°N). For data

taken every 30 min, this north-south variation represents a difference of two

data points per inertial period; thus. the same averaging interval does not

apply to every station.

For convenience. the averaging interval could be chosen to be one inertial period rounded back to the nearest data point. lor data spaced at 30-lll1n

intervals, application of thia averaging scheme results in a maxilllum deviation

from a complete inertial cycle of about 10· of rotation. Closer data spacing

reduces the deviation at some stations to less than I percent of a cycle. For

example, spectra of currents at stati0!1 13 in the southern arm of Lake Huron

indicate that in July more than 1/3 of the total kinetic energy in long-period

motions was contained in a band of frequencies spanning 1/16 to 1/18 cycles

per hour. Mare details of spectrum cOlllputationa are presented later in this

paper.

Longer-term averages of vector velocities are not as sensitive to

inertial currents. T!!! above example of station 13 had a mean flow at lO-m

depth of about 1 em s over a 16-day period. while the standard deviations

3
• -1 of the current components were on the order of 8 CIIl s At the latitude of

station 13 the local inertial period is 17.3 hours, 80 the 16-day averaging

period represents 22.15 inertial cycles. The weight of the "extra" 0.15

cycle, spread over >:he whole interval, does not affect the long-term mean

current significantly as it represents less than 1 percent of the total time.

3. CIRCULATION PATTERNS

The greate..t density of data was obtained from the 10-m level, with BlOre

than 20 stations operating from mid-June through July. The surface-layer

circulation is ass~to follow a pattern similar to the 10-m currents in

summer. The thermocline was below 10 m after early July. Fig. 2-10 depict

the surface-layer circulation meaaured over l4-16-day intervals from 1 May

through 14 September. Larger circles represent operating current meters;

the average current vectors are represented by line segments originating at

the mooring locations and extending in the direction of flow with a length

proportional to the speed of flow. Map fig. (2, 3, 4, 5, 6, 7, 8, 9, and 10)

mark.ed !. show 16- and 36-m currents; figures marked b show 15- and 22-m

currents..

The first group of data for 16-m currents represents 1-14 May 1966,

shown in fig. 2a. Data were returned only frOlD meters in the southern end

of the lake and show evidence of a possible counterclockwise circulation.

Strong shears are evident between 10 and 30 m. Currents at intermediate

levels (fig. 2b) show similar patterns. The lake was thermally homogeneous

for the period of these maps.

A slightly larger data sample was returned for the second half of May

(fig. 3a), but the measured flow looks extr_ly disorganized, in spite of

several frontal passages early in the period. Data from the northern part of

the lake show another possible small counterclockwise gyre west of stations

26-28, visible also in fig. 3b.

Fig. 4a-b show flows for 1-14 June. The flow northward from station 26

toward station 28 continued at all depths. There is evidence of the reestablishment of the gyre in the southern lake, but data are spsue. The lake Willi

still homogeneous through this period.

Fig. 5a-b, representing the second half of June, show a somewhat disorganized pattern of flow. There is an apparent counterclockwise circulation

occupying the middle 1/3 of the lake, flowing southward past Harrisville and

returning northward on the Ontario side. Local weather patterns for this

period were dominated by high-pressure or west!!ly to southwesterly winds.

Net current speeds averaged around 2 to 3 cm s over the lake, being stronger

in coastal areas than in the open lake.

During the period 1-14 July there were some four frontal passages over

Lake Huron. Meteorological conditions were determined from summary maps for

each day (American Meteorological Society, 1966), and wind recorders at

moorings 11, 16, 28, 29, and 32. Stronger and 1llOre frequent winds from the

4

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Figure 2a, HaZf-nu:mt;h average C!Ul'l'm1t vectOl'6 at 10 m and SO m fOX'

1-14 May 1966,

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FiguN 2b. HaZf-month average cu:z".l"ent 'lIeato:rll at 15 m and 22 m for

1-14 Mau 1966.

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Figlaoe Sa. Ha~f-month average I.lla'1'IiJnt veotors at 10m and SO m foX'

15-31 May 1966.

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Fifru:r'e 5b. HaZf-month ave:rage auzTent veeto1'8 at IS m and 22 m for

15-$1 May 1966.

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Figure 4a. Batf-month ave:I'aiJe C'Ul'l'ent vectors at 10 m and 30 m for

1-14 June 1966.

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Figu;re. 4b. Ha~f-mOl'lth average CU2'%'6'IIt vectops at 15 m and 22 m fop

1-14 June 1966.

10
Figure Sa. Ha~f-month average ~t vectoZ'8 at 10

m and 30m fop

15-30 June 1966.

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Figure 5b. Hatf-month (l/)erage CUPl'ent vect01'8 at 15 m and 22 m fop

15-30 June 1966.

12
northwest quadrant apparently strengthened the southward flow along the western shore as shown in fig. 6a-b. The gyre in the central part of the lake,

between latitudes 44· and 45·, was less well d~1ined than in, the previous half

month. There was,.t net inflow of some 10 em s from Lake Michigan and an

outflow of 8 cm s into Georgian Bay; both of these appear to be responses

to the prevailing winds. It should be noted, however, that the direction of

surface flow in both the Straits of Mackinac and the channel into Georgian

Bay does not prevail to the bottoms of the channels and, in fact, may be

nearly balanced by opposing currents at great depth (E. B. Bennett. personnel

communication, 1975).

The second half of July saw three major frontal passages which continued

the pattern of prevailing westerly to northwesterly winds. Wind records from

the moorings equipped with functioning anemometers showed evidence of the

frontal activity. The average winds at stations 16 and 32 tended to be westerly, but the winds recorded at stations 11 and 29 had a more north-south

bias. It should be noted that for the interval 15-31 July some 30 percent of

the expected wind data points from station 11 were missing or of unusable

quality. Station 29 winds were dominantly from the northwest.

Currents at 10 m for 15-31 July (fig. 7a) reflected the dominance of

northwesterly flow, with a strengthening of t~i southward flow along the

Michigan shore, with mean speeds up to 8 cm s . The gyre in the central

region of the lake retained its identity, but flows in the Saginaw Bay mouth

and the southern basin of the lake remained complex. Flow in the Straits of

Mackinac appeared to angle across the channel, but lo!~-term averaging of

flows which oscillated with amplitudes up to 100 cm s , alternately eastward

and westward, confused the picture. The meter at mooring 32 (Straits of

Mackinac) at 22-m depth (fig. 7b) gave mostly north-south readings, although

no equipment malfunction or data processing errors were reported; compass

failure or misalignment is assumed to be the cause of these anomalous direction readings at 22 m. In the southern basin, flow at 15 m shows a strong

gyre.

The weather maps for 2, 8, and 14 August show low-pressure centers

crossing the Lake Huron region. Wind records at station 29 show wind directions rotating through two complete circles during the first half of the

month. Unfortunately, the current meters at stations 26 and 27 had ceased

functioning. Winds at station 16 prevailed westerly and southwesterly, while

winds at station 11 were largely from the south until a deepening storm over

Quebec pulled winds around to the north on 12 August. The lack of northerly

wind components at station 16 gives cause for suspicion that the data from

that meter are not entirely reliable.

Current patterns determined from the 13 meters still operating during the

first half of August show the effects of the more southerly wind flow (fig.

8a-b). In the southern basin, flow was northward along both shores, as was

the flow out of Saginaw Bay. Evidence of the gyre in mid-lake remained,

indicated principally by vectors at stations 17, 20, and 21.

13
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Figure 6a. HaZ!-month ave1'afle ma'1"ent VIilCltO%'S at 10 m and so m fo%' 1-14

.ru1.y 1966. Note revsl'sa1. betl.leen 10 m and 30 m leveZs at station 26.

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1-14 July 1966.

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15-31 JuLy 1966. Note that 30 m /LOb) at 8tati0n8 15 and 16 run8

opPo8ite apparent 10 m j'U:M.

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lli-31 JuZy 1966.

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1-14 August 1968.

18

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Fig'uPe 8b. Ha~f-month avemge euITtmt vectors at 16 m and 22 m for

1-14 August 1966.

19
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, Flows for 15-31 August remained similar to those for the first half of

the month. Fig. 9a-b show the same large mid-lake gyre and persistent northward flow at stations 26-28 appearing in fig. lOa-b for 1-14 September. These

flow patterns seem to define the circulation throughout the stratified season.

Thus, the general summertime circulation of surface water in Lake Huron

appears to consist of a large counterclockwise gyre, which-occupies most of

the lake north of latitude 44·N, and more complex and transient flows in the

southern arm and around Saginsw Bay. Circulation patterns determined from the

GLIRBP data have some of the characteristics described in the study by Ayers

et al. (1956), and although the lake's response to meteorological inputs

created significant~fferences,such features as the persistent southward

current along the Michigan shore at latitude 45°N and a southward (along

shore) flow at the south end of the lake are cOllllllOn to both sets of observations.

Also confirming the May through August current patterns revealed by tbe

moored current meters are numerous dynamic height computations made for this

interval from Lake Buron temperature data collected since 1960 by tbe Great

Lakes Institute of the University of Toronto and by the Canada Centre for

Inland Waters. These data invariably show a pool of colder water centered

over the deep basin in the northeastern part of Lake Huron with warmer, less

dense water along both the United States and Canadian coasts. Dynamic height

computations therefore indicate a large counterclockwise circulation about

the colder core, essentially of the same dimensions as the current meters

reveal. Current speeds determined by the two methods are of the same order of

magnitude. Therefore, bathymetry of the lake basin plays an importane role in

shaping the circulation pattern during the summer heating interval we have

examined •

4. FLOWS AT DEPTHS BlI:LOIl 10 m

Flows at 15-m depth [map fig. (2, 3, 4, 5, 6, 7, 8, 9, and 10) marked bl

generally seemed to follow the shallower layer, but the density of observations

was not great enough to define circulations. Particularly problematical was

a lack of simultaneous. reliable data for IIlOre than one depth at any mooring.

Phase relationships between inertial oscillations above and below the thermocline, as reporeed by Malone (1968). are difficult to determine from the

CLIRBP Lake Huron data. Only 6 moorings provided data at botb 10- and l5-m

depths in July, and only 11 moorings gave any usable 15-111 datil at all. Missing data are attributable to instrument failures and possible inadequacies in

the automated data-reduction hardware and processing methods (Mehr. 1965 and

1970). Data were also taken at 22-, 30-, 60-, 90-, and 120-m depths, where

applicable, but the sample sizes from these levels were smaller than even the

15-.. set. Half-monthly flows could be computed at a maximum of 12 moorings

for 30-m dePth, and only for the second half of June were that many available.

Existing 30-m daea showed flows similar to surface currents in the southern basin and a persistent current northeastward and antieyclonically curved

from station 26 toward station 28. There were insufficient data to determine

the continuations up or downstream of this region, but the prevailing winds

20
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•

•

•

--l+------..-~+_--

·1

.' ~.

I' 0 .riJ

•

•

4

30m@.......

10m••--

,,'

Figu:re 9a. Hatf-month average CUl'I'ent vectors at 10 m and 30 m for

15-31 Auguat 1966.

21

••_~ > __ e._~ .e__ e••.
'0' 82·

\,

\

\

•

l

.' i

.{

.1'

•

I

•

•

•

•

•

..

'f) •

•

'0'

em ....'

22m ..

18

........_. J(1L.OMnt~~

.. = • .. .. .. .. .. .,' ~-~ ~~ATUTf MilES

.. = • .. .. ..

44'r,-------i--..,....L.---=-~~;>,.....-----____jc_-+---_j ...

!15-31AUGUST ee, A1_ "f--~--+-_.~-4--':::=e..-_+~_._--~----+---~~ 15ml'.__

Figu:r.'e 9b, BaZf-month average aurrerrt veatora at 1ii m and 22 m for

15-31 AU(lUllt 1966.

22
• GoOerMlh

" '

1

•

•••••o(!)

•

o

•

8J'

•

o

(to 0

10

IS

"'rl--------+--r~'-~

1

I

11-14 SEPTEMBER 116

"1 ::::....... ·~r-- em·.'"

H 6 l

o • •

IUI.OM(f(RS ::.....Joool...I;i;i

1O(lft/-loQ'tOeo

st'TUfE WILES h.-~_ 1'·"

:lO 0 10 ..0:

I _

k .'

Figure lOa, IiaZ!-month aveNge ourroent vectora at 10 m and 30 m

fop 1-14 September 1966,

23

------------~---- --_ .._--
•

•

.1'

•

,

• •

•

•

•

10

"---, i

"-~.

I,

I

15ml••--

I

r-f"~~~~~7"'::-;::-;:::I-;:::>7·~~ -ci~~f.£l ;o;;...~~.,.

I 22m(jl.......

i em·s-' ifB sA

I

• 44.~- -,i--;t"-'-----;::""'..<.+T.s,;?,:-- -~----.t---+--"--~.....

•

I

i

I

f,,-~

*"

Figure lOb. Balf-month aPeraue <1U1'l'ent vectors at 1:; m and 22 m fop

1-14 September 1966.

24
would have favored upwelling inshore of station 26. There are two explanations

for this flow. There is a topographic ridge in the lake bottom which extends

northeastward from the Michigan shore east of Calcite (at approximately 83.SoW

longitude) toward, and including, the Duck Islands at longitude near 83.0oW.

Also, the dynamic height computations from the Canada Ce?tre for Inland Waters

and others referred to earlier in this paper show a persistent cold core which

lies west of the line of moorings 26-28 and may control the flow in that

region.

5. EFFECTS OF THERMAL STRUCTURE

Fig. 11 a-d show temperature profiles taken by the U.S. Lake Survey

Center's R/V Shenehon as part of a separate study. the profiles show

stratification started in early June, with the thermocline passing lo-m depth

early in July, but remaining shallower than 30 m through August. The locations at which the profiles were taken were: lla, near mooring 27; lIb,

near mooring 18; llc, near mooring 16; and lId, near mooring 13.

Examination of even these few, selected profiles reveals some reason

for the behavior of the current vectors. Fig. lId, from the southern basin,

shows that the warm surface layer did not penetrate to the lQ-m depth until

after July 5. The lo-m currenta at station 13 consisted mostly of inertial

oscillations until mid-July, at which time a definite directional current

began to develop. By early August, the surface layer was thicker than 15 m,

and the mean flow at station 13 strongly directional, although the inertial

component remained. (Spectrum analysis of station 13 currents is presented

in the next section.) Similarly, the directional flow at stations 17 and 21

strengthened as the epilimnion deepened. Flow in the upper hypolimnion,

represented by the 3o-m vectors, sometimes opposed the surface flow, as at

moorings 26 in all of July and at mooring 20 in the first half of July. Other

thermal effects have been described earlier in this paper.

6. OSCILLATORY CURRENTS

Spectrum computations in this study were done by applying the fast

Fourier transform (FFT) algorithm to time series formed from the cartesian

velocity components along the east~est and north-south directions. Following the method of Gonella (1972), rotary spectra also were computed. A

multispectral averaging technique was employed, rather than prefiltering and

sub-sampling as was done by Malone (1968). In the present study, spectra

were computed for several overlapping subsets of the total data series; then

the spectra were ensemble-averaged and smoothed by Hanning to produce a

single spectrum representative of the entire data series. The alignment of

overlapping data is ahown schematically in fig. 12. Each subset was linearly

detrended and cosine-tapered at the ends before transforming.

The resulting spectrum admittedly is biased in favor of the middle portion of the data series, which is included in more than one subseries, but by

varying the amount of overlap, it is possible to cover almost the entire

original data series in spite of the FFT constraint which requires a number

of data points equal to a power of 2. Sufficient resolution may be obtained

25
: r

\

\

I

I

I

I

/

-"

,,/

/ ,-

/

" ,,/

,,;,....'"

,

/

I

I

I

I

,

*r ""","

i';-'

,

Figure 11a. 'l'eJfl[>6Ntu1'e profilea tbathytherrJwgraphJ from

P../V Shenehon taken neal' mooring 27. The thermocUne passed

10 m in ea::zo'ty Ju'ty 1986 and had not l'eachsd 30 m by lrt

date shoum. Ma:t:imum tempe:rature gradient is 1.0oC m- •

Figure llb. Tempemture p'Y'OfUes frat! Mar mooring 18.

Thermoct.ine touchsd 30..", depth fil'Bt at end of ~'tYllis

pe:riod. Ma:1:imum tempe:rature gradient is O. lOC m- •

Figure 110. Tempemtul'e profiles from neal' mooring 18.

Tlpi1..tmnion included 10..", depth firollt at end of ~'tYlli8

period. Ma:z:ilrIum temperature groadient is 1.8°C m- •

Figla>e l1d. 'l'empe:ratu'l'e p'Y'Ofitea frat! neal'mooring 13.

Tlpiltmnion roeached 10 m in mid-Ju'ty 1986. Ma:1:imum tempe:ratu1'e gNdient is 2. 8°C m-1•

26
with a transform of length 256 points, which results in 129 spectral estimates

from :/oero frequency to the Nyquist frequency; this is analogous to a "conventional" Fourier transform using 128 lags. For example, 32 days of hourly

data give a total set of 768 observations that may be subdivided into 3 contiguous, independent subsets of length 256 and 2 more subsL~s of length 256

which are centered over the 2 connecting points between the other 3 sets. The

overlaid sets will pick up details of the signal that may have been suppressed

by the tapering at the ends of the independent sets.

QSob:'::':'in=N;'/=5:.=:;.;::.:,=:;;.=~._

Figure 12. Sc1u<matic representation of

data subsets for spectrum computation.

Each subset must coneist of an i.nteger

polller of 2 points. For the case

shor.m, a subset of 25/1 points would

aLZow C()7)e1'age of a totaL of 1,280

points (not an integer polllel' of 2).

OVSl''Lap shoLm is 50 percent.

Statistical degrees of freedom (v) are calculated on the basis of the

number of independent data points. by the formulae

v • (2N - N/4M)/(N/2M)

or v • 41'1 - 1/2.

(la)

(lb)

where N is the number of points in the total data set and 1'1 is the number of

transformed subsets. Note that the degrees of freedom do not depend on the

size of the transformed subsets. but only on their number. The dependence of

v on the ratio of the size of a subset to the total sample, which would be

controlled by the number of lags used, is eliminated here sinee the FFT is

analogous to a lagged-product method using all the allowable lags. The FFT

yields spectral estimates at n/2 + 1 nonnegative frequencies for a sample of

size n.

Rotary components of the velocity vector are computed following Gonella

(1972), according to

PCW(f) • [PA(f) - Qxy(f)112

PCCW(f) - [PA(f) + Qxy(f)1/2,

(2a)

(2b)

-

Where P and P are the clockwise and counterclockwise components of the

phasor ~pre8en~~ion of the velocity at frequency f, PA is the average scalar

power at f, and Qxy is the quadrature spectrum evaluatea at f. While the

rotary componenta-~ and P could be computed from any pair of scalar series they obViously ~ve phy~sl meaning primarily for velocity components

slong perpendicular axes at a aingle site. The rotary components are conven27
tan 2~ • 2Sxr'(Sxx - Syy), (3)

iently invariant with respect to orientation of the coordinate axes. Alignment of the major axis is detemined (Canella, 1972) by

Fig. 13a-b and~a-b show cartesian-component and rotary spectra for

currents at 10_ depth at mooring 13 for the periods 1-16 July and 17 July2 August. The raw data for each spectr\lll consist of 168 consecutive half-hour

readings of current velocity. To increase low-frequency resolution, the

data were first averaged in 4'" to give 2-hourly velocities, lowering the

Nyquist frequency from 1.0 to 0.25 cycle per hour. The resulting data

set, reduced in length to 192 2-hourly values, was then transfomed in 3

overlapping subsets of length 12~; each subset began at the 33rd point of

the previous set for 75 percent overlap. From fig. II, it appears that

the meter in this example was in the thet1llOcline for at least part of the

1-16 July interval, during which there was a strong spectral component at

the local inertial frequency with a clockwise rotation of the velocity

vector at all frequencies up to 20 percent lower and 80 percent higher.

The energy of motions with periods of 16 to 18 hours was almost 60 percent

greater than the energy of all motions with periods longer than 50 hours.

For the interval 17 July-3 August, energy in the inertial range (16-18 hours)

exceeded the energy 10 long-period motions by 25 percent. The relative drop

is attributable to thickening of the epilimnion and the consequent greater

involvement of water at the 1O-m level 10 IIIl!teorological scale IIIOtions; total

energy had increased more than threefold. For the entire observation period,

motions in the inertial range were nearly circular. There is no ready explanation for the additional energy peak in fig. l4a-b at 8.8 hours: Lake

Huron haa no free oscillations at that period and the spectral methods used

here do not produce such strong side lobes. It is possible that inertia1-

period waves on the thermocline were large enough to place the meter alternately in the epilimnion and hypolimnion.

S is the

t*l autowhere, for any frequency, the angle' is clockwise from north,cospectrum between east and north motions, and Svv and Syy are

spectra of the east and north components, respectfvely.

,

Fig. 15a-b show rotary spectra for station 11 for the period 9 July13 September at depths of 10 and 30 II, respectively. While both records

contained strong inertial components, attempts to correlate motions at the

2 depths were unsuccessful. In the light of other studies which showed coherence and expected phase reversals across the thermocline CHalone, 1968),

it is evident that the data from station 11 were subject to the timing

discrepancies which seem to pervade the GLIRBP data. These data were also

averaged over 2-hour intervals, but longer data sets were used, with 5 subsets of length 256 and 50 percent overlap.

Fig. l6a-h are a component and rotary spectra for station 35 at 16-.

depth, probably in the hypolimnion for the analyzed period of 16 June-20 July.

Data were averaged over I-hour intervals and transfomed as 5 sets of length

256 with 50 percent overlap. The mooring W8.$ approximately 5 Jan from shore

in a total water depth of 26 m, yet the inertial lIlOtiona are quite strong.

28

• $
Period. hours '''Or -'!L 8+'

1

_ 4

-... )-1

!

1

--2

.§'

-3

Figure 13a. P<MeJ' spectra of north (heavy Line) and east Hight tine}

hoW'ty ve'tocity components at station 13. depth 10 m. for 1-16 Juty

1966. Onty the firet hatf of the aomputed epeatrum illt shotJn; no

significant peaks appeared in lines 85-128. Note that most spectra

shotJn in this paper aPe truncated in this manner; e:x:ceptions aPe

noted. Spectral. density (pOlVer) scate ie l-ogarithmic.

29

j

- ,,( it. _$1 .OJ "as AU
0

:

;

-...

;t: I -1

Q

Ii

-.,

&

Ul i-2

...I

-3

•

l' Period, hours

8 4

-4+0--+----10.......--+---2-+0---+---3+0---1----4+-0--.......- .... 50---+---'-+0,.---+

Spectral Line Number

FifJUN 13D. Rotational. spectN of cZockhlise (heavy Une) and countercZockwe night Une} hourly veZoc:i.ty components at station 13, depth 10 m,

for 1-1/5 Jul.y 1966. The inertial. band contains 100 times as much energy

in cl.ockhliee motions as in countercl.ockhliee.

30
,all

!

I

- -2 .3

-3

16

Period, hours

8 ..

-4+----_+_--+--+--_+_--+--+----1---+--+---+---+--+--4

o w

Spectral Line Number

FiguN 14a. P0b)8r spectra of north (heavy 'LiM) and east (7,ight l.ine)

hou:Pl.y ve1.ocity COll'lpOMnts at station 13. depth 10 m. for 17 Ju1.y-J August

1966. P0b)8r in inertial. range has doubl.ed. as has 1.<mg-period power.

31
.. Period, hours

16 ,

-3

1

10

-...

! -1 ..

Q

I

';-2

o

...

FigUZ'e 14b. Rotationat spectra of oz.oc1<J.liBe (MtWy tine) and aounterel.ock-

...n.se (tight Une) houPty vez.ocity components at i1tation 13, depth 10 m,

for 1'1 July-3 August 1966. Inc:rease in po!Jer in counterel.oc1<J.liBe motion

at inertial period may indiaate devel.opment of linear motion added to

rotary current.

32

.ao
1'"

o

e

1- -2 !

32

Period. hours

1~

-4±--........--::':--.;-----,:':'""--t---=':::---+----:+:----t----:J;:-----;:I;:--+ o m

Spectral Line Number

Figul"e 1lia. Rotational. spectro of c1.oc1a.lise (heavy Une) and countel"clock-

/Jise (Ught Une) 2-hou1'1.y averoged ve1.oaity components at station 17,

depth 10 m, 9 July-liS Sqptember 1966. The spectrum is again truncated

at the midpoint, but the ho1"iaonta1. sca1.e now covers haLf the interoaL

of the previous fig. liSa-b, 14a-b.

33

______~_~__•• d __ ._•• _
.4'-1--_+_--+---+----<_-_--+---+--_+_-__+--0---_-..,.....--1- o ro

Spectral Line Humber

.,. -

-3

32

Period, hours

111 8

Figure 1Sh. Rotational. spect:m of Cl.oChn-SB (heavy l.ine) and counte:ml.ocktnse rUght line) ll-hourl.y alJeraged vel.ocit;y components at station 17,

depth 30 m, 9 Jul.II-13 September 1966. The inertial. peak is neal'l.y the

same strength aD at 10 III (tnthin 15 pel'Oent). but spl'ead betuleen clock.

tnse and counte:rel.ocktnse is larger.

34
-

!

--2

J

-3

HI

Period, Iloul'll

8 ..

-.Io.j.-----<,o--+---:2'="o------;3:':o-:---........-.7.o:----~50;;----.8I;;;O:-----t

Spectral Line Number

Figure 16a. P(Jl;)Gr spectra of north (heavy tine) and east night tine)

hourt.y vet.ocity components at stati-on 36. depth 16 m. for 16 .June-20 .July

1966. The east veloaity peak at 8. 6 hours (tine 39) C01."1'8sponds to the

first free oscUlation period for Lake Huron; the vet.ocity vector is

actually biased nearly perpendicular to .hare. according to equati-on (3),

35

~_e_-... .--,. uu

- _ IE >
Period, hours

1...;.. 1:;6:..- -'8~--------------- 4

-4i+---+--_+_--..-.--..---+----+--_+_---I---+---...---+--_---+ o ro

Spectral Line Number

-3

•

Figwoe 16b. RotationaZ speotl'a. of oZOOMse (heavy line) and oountel'oZook-

.nee (light line) houpZy veZocity components at stati.<m 35, depth 16 m,

fol.' 16 June-20 JuZy 1966. Neal' equaUty of cZoOMse and countel'cZockmae eomponente at line 39 implies Zinea:t' motion as deacl'ibed in the text.

>.

:t:

.,i -1

Q

36
describing an ellipse oriented with major axis toward 38' west of north,

or parallel to shore. Also present in the east-west component (approximately

30' from perpendicular to shore) was a spectral peak at the period of the

first Lake Huron seiche, 6.5 hours. Alignment of this motion was directed

toward 35' east of north. Superimposed on the broad inertial peak was a

motion that was coherent between the north-south and east-west components

(at greater than 95 percent significance) at the lunar semidiurnal tidal

frequency. The spectrum contained more energy in the north-south (30' from

parallel to shore) component, and the phase between the components of about

50' (north leading east) implies an elliptical motion with major axis inclined to be nearly parallel to shore along an angle of 36' west of north.

The Straits of Mackinac are discussed in detail elsewhere (Saylor and

Sloss, 1976, in press), but one spectrum from mooring 32 data is included

here (fig. 17) to show a strongly directional flow dominated by meteorological scale (about 3-day) motions and a strong energy spike at the lunar semidiurnal tide. The lake seiches were poorly delineated in the record shown

here, although the first seiche of Lake Michigan may be present with a period

of approximately 8.9 hours (cf. Rockwell, 1966). Long-period motions had the

most energy at periods ranging from 64-85 hours (cf. Powers and Ayers, 1960).

7. SUMMARY AND CONCLUSIONS

The summertime surface circulation of Lake Huron is dominated by a

counterclockwise gyre which occupies most of the northern 2/3 of the lake.

There is a smaller counterclockwise gyre in the northwestern end of the lake,

at least partially constrained by bottom topography. The southern basin displays more complex patterns dependent on weather. A topographic ridge, separating the southern basin from the deeper main basin, is followed by the southern boundary of the main gyre. Stndies of the thermal structure of Lake Huron

have shown temperature patterns which suggest similar circulations. The

surface circulation was not always well indicated by current meters at lO-m

depth, since the thermocline remained shallower than 30 m for the entire

season and appeared near 10 m until mid-July, e.g., parts of the southern

lake, where upwelling prevailed along the west shore, showed hypolimnion

motions at 10 m through mid-July.

Thermal stratification allowed the development of strong inertial

oscillations and rotary currents in most of the lake. Inertial motions were

most clearly defined where thermal stratification was sharpest and in such

cases accounted for much of the total water movement. At some stations

there were indications of possible tidal and seiche-driven currents, but

only at the Straits of Mackinac were such motions clearly detectable. Correlations of oscillatory currents at various locations were apparently not

possible due to inherent uncertainties in absolute timing of the GLIRBP data.

37
2

•

40 eo eo 100 120

Spectral Line Numbel'

20

Period, hours

3IOt 1f-6 ...;8i-- 4......

-1

Figure 17. POIJe1' spectI'a of north (heavy line) and east (tight line)

2-hourty veZocity components at station 32 (straits of Mackinac). depth

10 m, 15 J'uty-16 september 1966. 2'he strong spectI'at peak at tine 41

is the tunar 8emidiurnat tide, and the broad peak at tines 55-60 represents the first free seiche of In.ke Michigan. 2'he hatf of the spectt'W11 from 8- to 4-hour periods 81u:M8 no significant peake, although

the 8econd In.ke Michigan aeiche may appear around line lOS. (Plot not

truncated. )

38
8. REFERENCES

American Meteorological Society (A.M.S.), 1966, Daily weather maps. Weatherwise. 19, 179-181, 218-224.

Ayers, J. C., D. V. Anderson, D. C. Chandler, and G. H. Lauff, 1956, Currents

and water masses in Lake Huron. TechniooZ Paper No.1. Great Lakes

Research DiVision. University of Michigan, Ann Arbor, Michigan. No

pagination.

Federal Water Pollution Control Administration. 1967, Lake Michigan currents.

Federal Water Pollution Control Administration, U.S. Department of the

Interior. Great Lakes Region, Chicago, Illinois. No pagination.

Ganella, J., 1972, A rotary-component method for analysing meteorological and

oceanographic time series. Deep Sea Research. 19, 833-846.

Harrington. M. w., 1895, Surface currents of the Great Lakes, as deduced

from the movements of bottle papers during the seasons of 1992. 1893,

and 1894. BuHetin B (revised). U.S. Weather Bureau. 14 pp.

Malone, F. D., 1968. An analysis of current measurements in Lake Michigan.

Jow:onaZ of GeophysicaZ Research. 22, 7065-7081.

Mehr, E•• 1965, Computer processing of lake data 1963-1964. Report No.

TR-85-9. Geophysical Sciences Laboratory, Department of Meteorology

and Oceanography, New York University, Bronx, New York. 45 pp.

Mehr. E., 1970. Computer processing of lake data, 1970. Project Report for

Contract DI-14-12-6. Federal Water Pollution Control Administration,

U.S. Department of the Interior, Region 5, 14 pp.

Powers, C. F., and J. C. Ayers, 1960, Water transport studies in the Straits

of Mackinac region of Lake Huron. LimnoZogy and Oceanography. 15, 81-85.

Rockwell, D. C., 1966, Theoretical free oscillations of the Great Lakes.

TechnicaZ Report No. 20. Department of the Geophysical Sciences, University of Chicago, Chicago, Illinois. 87 pp.

Saylor, J. H•• and P. W. Sloss. 1976. Water volume transport and oscillatory

current flow in the Straits of Mackinac. Jow:onaL of PhysicaZ OCeanography. 6, in press.

Verber, J. L., 1966. Inertial currents in the Great Lakes. PubZication

No. 15. Great Lakes Research Division, University of Michigan, Ann Arbor,

Michigan. 375-379.

39
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$!

I

,;

.!

'C .,

1

I

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