lake Survey Center

DE.TI!OIT, MI CH.

NOA" 1M NOS lSC R 4

NOAA Technical Memorandum NOS LSC R 4 U. S. DEPARTMENT Of COIiIIURCE Hatiollal ~a"ic .1111 Atmosphedc ""minimilion Hatio/l.1 CIte." Surw.,

Lake Superior Beginning -of- Month Water Levels and Monthly Rates of Storage Changes

flbnoorJI91f L-_________________ -'

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U. S. DfP,\RTMF.NT UI' o.:l.NlI'RCI" Na t iona l Ocean i c Dr><! A. t"'~l'hcdc ;\dmi n i str"li on

)I' tiona l Oce .j." "" r vcr

YlJM T., ~h,'; ca I J.\enoranJ WI NO;; I.SC R -4

t.A)([; ::;Ul'lR lUk

and

MOHTHL Y RATeS or STORAGE CHANGES

F ra" ~ II. Qui n"

Ma l e..,'" J. TuoJd

Lake SUrvey Cen t er Li~logy Ulv i s i on

Fede r a l Bui hling Uetrvi t . Mi ch i gan

Fe bru ;l ry 1974

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•

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Ahstr ;l.ct .. IntroJuction lIethodol°Ii:Y·

CON1UITS

•

Basic and Computed Data. Re!a" I ts . • • . . •

• •

• •

Effe ct of Gage Network Size. Effect of Weighting Factors.

•

Gage Network Sele ction . . . Lake SUperior Beginning-of-Month Rates of Ch;l.nge in Storage

Levels.

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• • • •

Conclusions ... Acknowlerlgement~

References . . • •

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Table Table Table Table Table

Table

Tables Table Ta ble

Fi&Ur e Figures Figure

L 2 . ;. ,. ,. ,.

7-15.

". n.

L 2_6. ,.

TAlILES

Water Level Gages and Period of Record. • • Gage Networks and Weighting Factors .. . Effect of Network Size on Beginning-of-Iotonth Levels Annual M.ean Leve l Differences • . •• .. . Differences of Weighted and Average Beginning_of_M.onth Leve ls ••• ••••• • ••. . ..• • Gage Networks Us ed for Lake Superior Beginning-of-Month Levels. • . •• • •• •••••• . •.... Beginning-of-Month Wate r Leve ls for Individual Ga~es. Lake Superior Beginning-of-Month Leve ls Lake Superior Rates of Storage Changes. • •

FIGURES

Wate r Level GILge Location • • PolYgon Networks... ••• Plot Demonstrating the Trend of Sub s idence of Relative to Thunder SILy (Port Arthur)

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Duluth

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tAKE SlJPERIOII RI:GJNNINC.OF-MOIn'H WATER t~VELS AN O ~NrnLV RAn.S or S"nlRAGIO OIANGES

Frank H. Quinn and Malcolm J. Todd

Lake ~urvey Cent e r Nationa l Oo.:nn Survey, NOM

Detr oi t, Mi ch i Ean

AIISTRACT. This rcport de ~ (:tibes re5ul ts frOll II. ~ tudr of !.,ake Super i.or beginn i ng-of-_onth l e vels and rat ,," of ~ torage chang". _ These are l isted for the period 1900-1972 of suf fi cient quality for scientific and planning s tudies . Also it indicat es t hat the nuaber and di s tribution of ... ater l eve l gages i n the presently c~i 5tin i gage network a r e adequate for an accurate det ermination of begi nninR-of- mon th water l evel s.

I ~OOCTION

,

The ThieSSCTl po lygon pr ocedu", was U! ed to cOlIpute t he b"ginnin~­

of_month l ake l evel s . This i ~ t he te~hnique c~nly used by hydrol ogist s to abuin a weighted average (a l'epnsent ative hasin valu.:) of point source measur ement s of pr~cipitation within a basin. I t provid~s (l.

better overall repr esentative lake leve l th,m s t ra i ght aVerPling and. :ot the same t;~ s tandard.i ~~s a procedur e for computing these leve l s.

The heghlni n.,;-of-aonth lake l eVels ca.putcd are neeessn y for studin of: l ake hydr o lOilY. beach and shor e eros i(>n , Ilav t lation and hydr o- eloct r i c po.e r and lake r egulat lon. The mon t h ly rates of lake s torage ch~es whlch are CORputed fr~ the beginni n&-o( - DOn th l eve l s ar e utili~ ed i n water hudget s t udies , such as the deten.i netion of lake evaporation ra t eS and ne t groundwater i nflux into the l a~ os .

Initi al consideration was given to the 1950- 1970 t i .e base, since it conta ins a suffici en t number of wat er Jevel gages to .nl l yze the e f fec t o ( t he gage ne twor k size on the beginning-of _~nth l eve l s de ter-ination. Th is pe ri od is 11. 110 s i lnifican t as i t i n~ l udes t he OIOdern TeCON high late l evels of 19!.2 as .. el l 35 t he record l ows o f 19 64.

Results of t he initia l s tudy r evoal ed that the Th t e5sen polygon procedure was adequate and shoul d be used in quantify ing the data

, for t he year s pr i or to 1950 , i.e. , for the 1900- 1949 period. Further, i t showed t hat t il e pr es C"RUy e1i sthe gage network i s ad"'l""'te for upda ting futu re data. Therefore, til ls study has qu,mtified beginni n&­of- lIIQnth l e Vel s a nd catcs of lal<e $torage aU.nlt"s for the period 19<1O-1972, as presented i n the r esults s ec tion.

MEn klOOLOGY

The beeinnilli - of-lKlnth wat er levols were c~puted usinl! <II water lcv~l 1:11l0 network i oc<lted an the periphery of the lake . Ideally, t h=s e l ovols shoul d represent t he i ns tantaneous l evel ~ at the beginning of t he .anth, . Practicall y. however , r epr esentative i ns tantaneous t rue w.t e r levels are di fficult, if not i ~poss ib le . to ~aSure because of the ef fe c t u ( s ho rt terw fJuc tu.1t i ons i n wind ~ p"'ed a ..... di r ection and " hanges i n ~ara.et r i c pressure over very s-al l t l~e per iods. These fluctuation~ could cause conSi derable error in c~utin, a true i ns tant aneous l eve l for the lake . The error i5 lessened by 5Fecl fying that t he begi nni n, _ of _AQnth leve l for each iaie sha l l be ~ual t o the average of t he dai l y ~an ~ate r level s of t he firs t day of the ~nth and the las t day of the pr~ViOlJ5 MOnth.

The computational procedure was s e~ forth by Quinn (1971) and cons ists of applying weighting fac t ors t o each water l evel gage in t ho network . The wei ght i ng factors were co-vutcd fr~ Thiessen polygon netwOfks dr awn fro- the various watef level gage ne tworks. Th i s i s expressed . athellatically as

Where

" ""

LO is the wei gh t ed Lake Superior beti nni ng-of-lIOnth water l eve l .

L -L 1 n are the b eginniD2 _of_~nth l evels at the variou~ gage

, -, I ,

hx:ations,

are t he Thiessen polygon w"i&hti ng f ,,~tors for gage l ~cations 1 to n,

n i ~ the nu-ber ~f Water level gates 1D the network.

=

•

1

8.\S IC A.~ COKPlITED DATA

The b~ic dat~ used consis t of daily mean vater l evels for t he fir s t and '.,t days of the mo"ths f or each oyerating water level Rage . The I:u ~e s used in the ~tudy tO llether Wi th t he i r period of recor d i s Il lven in Tab l e I ; l ocations arc ~hown i n Fi gure 1. The beiinninll- of-.onth wat er level s wore computed for "aeh gase 8! ,jescribed and are tabul a t ed On Tab l es 7-\5. Occasional MI ~, tng gaie data were interpol ated from c:t! sti ng ga lj!es.

T~ l e 1. Wat er Level Gage~ and Pertod of Record

f o i n t Iroquois Marquette Ontonagon lAlluth Two Harbors GrlUld Marai S Thunder Bay (!'ort Arthur ) Mi dlipicoten lIatbo:­Rossport

P~iod o f Rocol'd (dai l y...., ans)

19 30-Date 1891-D. t .. 19S9_Date lilliS-Data 1941 -Dat., 1966-D ... t ..

1!H2-Date InS_lJa te 1967 - 0 Il.t e

I n thl! i nit i a l ana l y!<is f h e di ££er ent gage .... t works WeTe deve loped for t he 1950- 1970 period [0 dete~ine the opti~ ne£work ~ ile as we ll a~ t o quantify a data set Cor thi s period. To Obt~in a quant i fied da t a s e t for the period 1900- 19. 9, an additional four different l age networks were establis hed. The 'i'hin sen potYIOM 5h""n i n Figures 2_6 ~re dr..,n a nd we i aht1ng f actors cocputed faT each gage in t he various netwarks . These networ ks wi th their COYTRspondina aages and weighting fac t ors ar e a1ven in Tab le 2 .

RESULTS

Effe~ t of Gage Net work Si~e

This analys i s was based on the ~3ta for the 195D- 1970 peri od. The cf fec t of the gage network ~ i :e was i nves tiaated by coapari na beil nning­Of _MOn t h l aie levc l s co-put ed by various sized ne£works dur i n, correSponding tiac per i ods. The s tati st i cill parameters us"",, i n the ana lys i s were the _~ tandard deviation about zer o, tile _an , and the llaJl:i _ of t he differences in begi nni nlt · of-...... th l eve ls between t wo di f fe rent s i zed ne tworks . Addit iona l da t a points wer e added t o tho 1966- 1970 period ~o makc i t s t a t i s t lcli lly co-patabl e with the ot her per i ods . These addit ional po i nts cons i St ed of mid-and_~nthly leve l '

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~ ..-put"d usi nl/ t he ":De proo;edur e as the b",g i " ni nl/ - of_OInn th l enh . TIle re,ul ts are pr e"entetl i n Table 3.

Table 3. Effect of ,.., twori<. she on beglnning-of-I'lonth levels

Period ~o. 0; N ~twor~5 Callpared ).l ean Std. M:l.X .

Mon t hs Dev (l) """ 0 ) 0," l') ( ft ) (ft) (ft J

19$ 1- I 'HO ,W , Ita,e "' • ,age .00 .01 _ .OS 1960- 1970 on 6 ,a,e "

, ga!:e .00 .01 . . ro 1966-19 70 ""

, galle "' , ,;I,e .", . 01 - .02

1967- 19 70 '" , ,age "' , gage .01 .01 • . 06

( I ) Dev = Devi a tion be twe en ~~Tesponding he~inning_o f_~onth l eve ls.

The fiTs t thr~e co .. par isons presented in Table 3 indi cate that no IIddi tiona} accuracy was obt" i nl!'d hy i ncroasing the network 5 i Ie above SeVe n gages. However, the last cO!1IJlari s on i1l<iic"ted ,. r eve r sa l of thi~ t rend .

Thl!re ar~ two primary r elsons for t hi s oecurrence. The fi r s t i s that the Ross port gage, the 9th g',e o[ the ne twort , is . t a 5tra t e. i c location , a~ r e f l ected hy I ts po l ygon which covers nearl y 20 per cent of the toUi l u e area . n ,us i ts we1ghtin, f actor i s second oll ly t o that of t he Harquc"tte e:llle. The $8COnd is that the d ata aea s ur«len ts f~ the Rossport gage are s i gnificant l y di f f ereDt fro. the oajorlty of the g"ees ar ound t he l ake as show n in T;>b le 4.

Although the analysis indi cates additional study is neces sary ~oncerning the Ros~port g'ee, the differ ences be tween the 8 and 9 gage Ilfltwort results are generally with i n the accuracy of thl! ,age KlCuurelilents . Fo r this reason the fi nal results presented in t ht.. paper are those obtained us i n, thn 9 - ga 8" network,

Effect of Wl! lihting Fac tors

( ""'Paris on" were ,,150 drawn between the b C i:innjn~-of_lWnth levels COIOp:.ot<l<l uung I.h" Th i essen weightino: £dcters and thos" co.lpu t e..! by ass i a ni roi " qUIll "'e i gil t s to eadl lIaae in the nc two" _ Thh cODparlson was developed t o s~ow the d ifference be twee n the proposed pnx:edure. Th~ess~'n ;.olyton "ei &llt i 1l.l: ... n<l t !le aoSt .;.cmoonly u~ed procedure. st raight a veraging. The TL'SuJ U aY e givcn i n TaU. ~,

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Tab le 5_ ll lffenn~c s of we ighted a nd u.VCl'aaC beinnina- of -TIOntll lcvd~

""bor\( Sia No. " ,.M Std. ~!1lX • ",., ~nth5 "" ( ' ) "" (1 ) PO' (I j

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T~ le S , h~s t hat the r e is a , i :ni f t cant diffcrence in the t~o procedures fo r Lake Superior. The la rge OIa~i.WI difh-renees are attributed to wind Jet-up and seiche!. n ,ese difference, indi cste that the selection of weighting fact01'5 hL! a large e ffect upon the lake level computation~ dUl'l na periods of wind s tres s and se iches .

(;ajl:" Network Selection

Due to t he li"'itcd no.rOer o f aagn ~vailable, their distri but i on around the I~e and t he aonstant 'hi f tinr of L~e aege, f o r ~e 1900-1949 period, thi~ period cou ld not he a fforded t he s~e ana lys is as the 19SO_ }\'70 po r iod. Altt.ou2h all o£ tile ga2es lIere fourtd t o.> be shifting, SoGe were lI or se than others. The OU l ",t ll ga~c appears t o lIave undergone the greate~ t ~hange and has dellonstrate<l a dennite trend OVer the yea., ;lS evidenced by Fi gure 7. The 1I0~ t s table "f the iaies in the very early period " 01.5 )I&rqllet~e.

1

II. the 3el .. .::t1o" o f t ile gaie ncb/(}n;S careful attention was paid to t he d i s tribution around the 13k... For i ns tance, on l y ~rquet te .. as used [o r th" 1900- 19 14 period ber-'1US" of OUluth' ~ great aaount of s ubs idencoo and i r~ rel ati ve l ocati on. i.e. , i t did not r epresent I ba lanced condit ion. In Ins when Th ' '"!!'' r Bay (Port A.rtllUr) rrconls becPle ani bble tbe two-ia~e ne t llor\ wa~ developed, since Th"'nUer Hay (Po r t Arthur) appeared to be relat Lvely H able and its locat ion ac rOS5 the ll'ke ! r~ 'taxqllette cn:&tc .:i It s .... ewhat balanced condition. In I g]8 t he Duluth and Michipi cote1l. .l:aiO.cs ",ere added ~ 1""'lt Qneoo.:~ly, creating K balanced J_gage netwQrk. Gaga ne tworks for t he period 1931-1912 lI~re for.ed by adding addition. 1 , aie5 as th~y bec~e .v~ilable.

• l.ak e Sllrerior Beginning - c,f -~ron tiL I..~ve I •

l1L~ be"im""f:-of-,"onth T."I·~ Superior \,,"<,10 an' !"·",~nted in T"bl~ I~. They were <computed ,,,'ng th., ~ua;e n.]t",nr);,~ ~ivn' j •• Ta~l" 6.

T"ble 6. Gail e n et"orl~ u~e,1 f01" Lake <;uperior 'J e gil\nin ~ -of- .. ont" len']!

Pe ria;!

19f1O-191.\ 1915_1917 1915-J'nr 1931-19,\1 1942-1S44 1945-11)",:, 19~1-195fl

19(,0.1965 1966

1967-19n

No. cf (;"-!;~' in Se twork

, , , 5 (1\) , , .'

-----------,;',TE: CAj is liS cd to distin;:uish bet ... ""n t.wc ,Iifter"nt S-~,,~e netk'ol'ks.

Pefer to [-iguyes 3 anJ ~.

Rate of Storage Changes

The ~nthly storage changes were computed by multiplying the difference between two eon5ecutiv~ beginning-or-month levols by the area of Lake Superior, 31,700 square miles. The changes were then converted into monthly rates by dividing by the number of seconds in each month. These rates are ~iven in thousands of cubic feet per second (TCFSj in Table 17. The accuracy of the rates expressed in TCFS compare with that of the beginnin~-of-month levels fran which they were derived.

CONCLUSIONS

This study shows that the present gage network is adequate for both scientific and planning studies and that little additional accuracy was gained by increasing the network si~e above seven gages. However, the additional ~ages may be nece5sary for studies rela.tin~ to lake dynamics. It further indicates that additional investigation is desirable to clarify the Rossport ga~e discrepancy.

The method of computation, i.e., weighted or averaged. was found to have a larger effect on the beginning-of-month levels than the number of gages in the network. Therefore, the weighting factors shOUld be carefully selected using the Thiessen polygon procedure.

Based On this 3tudy it i s recommended that the beginning-of-~nth levels and rates of storage changes presented in Tables 16 and 11 be used for scientific studies of Lake Superior and that these data be updated on a yearly basi. using the Thiessen polygon procedure.

ACKNOIIIL£(X;EMENTS

This "tudy was performed under the general guidance of L. Bajorunas, Chief, LilllIl010gy Division, Lake Survey Cent. er, NOAA. The assistance of R. N. Kelley in data reduction and report assemblage is gratefully acknowledged.

REFERENCES

Quinn, F. ll. 1971. Quantitative Mathematical Mod e ls for Great Lakes Research. Ph. D. Dissertation, University of Michigan, Ann Arbor, Mich.

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