WRC RESEARCH REPORT NO.
53
GREAT LAKES HYDROLOGY BY MONTHS, 1946-1965
Douglas M. A. J o n e s
I l l i n o i s S t a t e Water Survey
Urbana, I l l i n o i s 61801
and
Dale D. M e r e d i t h
Department of C i v i l E n g i n e e r i n g
U n i v e r s i t y of I l l i n o i s a t Urbana-Champaign
Urbana, I l l i n o i s 61801
F I N A L
R E P O R T
P r o j e c t No. B-035-ILL
The work upon which t h i s p u b l i c a t i o n i s b a s e d was s u p p o r t e d by f u n d s
p r o v i d e d by t h e U.S. ~ e ~ a r t m e noft t h e I n t e r i o r as a u t h o r i z e d u n d e r
t h e Water Resources R e s e a r c h Act of 1964, P.L. 88-379
Agreement No. 14-31-0001-3169
UNIVERSITY OF ILLINOIS
WATER RESOURCES CENTER
2535 Hydrosystems L a b o r a t o r y
Urbana, I l l i n o i s 61801
A p r i l 1972
ABSTRACT
GREAT LAKES HYDROLOGY BY MONTHS, 1946-1965
Monthly e s t i m a t e s of p r e c i p i t a t i o n on each l a k e , e v a p o r a t i o n from each
l a k e s u r f a c e , and runoff i n t o each l a k e from surrounding l a n d a r e a s
a r e developed f o r t h e Great Lakes f o r c a l e n d a r y e a r s 1946 through 1965.
Overlake p r e c i p i t a t i o n i s e s t i m a t e d by e x t r a p o l a t i o n of t h e l a n d
i s o h y e t a l p a t t e r n s m u l t i p l i e d by lake-land r a t i o s a s e s t a b l i s h e d from
i s l a n d - s h o r e s t a t i o n s . Evaporation by months i s c a l c u l a t e d u s i n g t h e
mass t r a n s f e r method. An i s o p l e t h mapping t e c h n i q u e i s used t o e s t i m a t e
t h e r u n o f f . The n e t b a s i n supply f o r a l a k e i s e q u a l t o t h e t o t a l runoff p l u s t h e p r e c i p i t a t i o n on t h e l a k e s u r f a c e minus t h e e v a p o r a t i o n
from t h e l a k e s u r f a c e . The monthly and annual n e t b a s i n s u p p l i e s f o r
each l a k e a r e determined from t h e e s t i m a t e d v a l u e s of r u n o f f , p r e c i p i t a t i o n , and e v a p o r a t i o n and a r e compared w i t h t h e monthly and annual n e t .
b a s i n s u p p l i e s a s r e p o r t e d by t h e U.S. Army Corps of Engineers. The
e s t i m a t e d 20 y e a r mean annual n e t b a s i n s u p p l y f o r a l l l a k e s i s about
6 p e r c e n t l e s s t h a n t h e v a l u e r e p o r t e d by t h e U.S. Army Corps of
Engineers.
Jones, Douglas M. A., and Meredith, Dale D .
GREAT LAKES HYDROLOGY BY MONTHS, 1946-1965
Research Report t o O f f i c e of Water Resources Research, Department of
I n t e r i o r , A p r i l 1972, Washington, D . C . , 59 p.
KNWORDS--Great ~ a k e s / h y d r o l o g i cb~dget/~reci~itation/evaporation/
runoff
TABLE O F CONTENTS
Page
Abstract
L i s t of T a b l e s
L i s t of F i g u r e s
INTRODUCTION
P R E C I P I T A T I O N ON THE LAKES
EVAPORATION FROM THE LAKE SURFACES
RUNOFF I N T O LAKES FROM SURROUNDING LAND AREAS
GROUNDWATER
NET B A S I N SUPPLY
N e t B a s i n Supply as a S u m of H y d r o l o g i c C o m p o n e n t s
N e t B a s i n Supply as a R e s i d u a l
D I S C U S S I O N O F RESULTS
SUMMARY AND CONCLUSIONS
REFERENCES
iii
LIST OF TAElLES
Table
Page
1.
Dimensions of t h e Great Lakes
2.
Monthly l a k e / l a n d p r e c i p i t a t i o n r a t i o s
3.
P r e c i p i t a t i o n on Lake S u p e r i o r
4.
P r e c i p i t a t i o n on Lake Michigan
5.
P r e c i p i t a t i o n on Lake Huron
6.
P r e c i p i t a t i o n on Lake S t . C l a i r
7.
P r e c i p i t a t i o n on Lake E r i e
8.
P r e c i p i t a t i o n on Lake O n t a r i o
9.
Seasonal average p r e c i p i t a t i o n on l a k e s f o r 1946
through 1965
Lake S u p e r i o r s u r f a c e w a t e r temperature
Lake Michigan s u r f a c e water temperature
Lake Huron s u r f a c e w a t e r temperature
Lake E r i e s u r f a c e water temperature
Lake Ontario s u r f a c e w a t e r temperature
S t a t i o n s from which d a t a were obtained t o c a l c u l a t e
evaporation
Evaporation from Lake S u p e r i o r
Evaporation from Lake Michigan
Evaporation from Lake Huron
Evaporation from Lake E r i e
Evaporation from Lake O n t a r i o
2
Amount of l a n d a r e a i n t h e Great Lakes Basin f o r which
streamflow r e c o r d s a r e a v a i l a b l e f o r t h e p e r i o d 1946
through 1965
Runoff i n t o Lake S u p e r i o r
Runoff i n t o Lake Michigan
Runoff i n t o Lake Huron
Runoff i n t o Lake S t . C l a i r
Runoff i n t o Lake E r i e
Runoff i n t o Lake Ontar,io
Net b a s i n supply f o r Lake S u p e r i o r
Net b a s i n supply f o r Lake Michigan-Huron
N e t b a s i n supply f o r Lake E r i e
Net b a s i n supply f o r Lake O n t a r i o
LIST OF FI(;URES
Figure
1.
Page
Great Lakes d r a i n a g e b a s i n showing d r a i n a g e a r e a f o r
each l a k e , t h e l o c a t i o n of p r e c i p i t a t i o n s t a t i o n s ,
and t h e l o c a t i o n of i s l a n d - s h o r e s t a t i o n s
3
2.
I s o h y e t s f o r J u l y , 1964
9
3.
Areas f o r which streamflow r e c o r d s a r e a v a i l a b l e f o r
p e r i o d 1946 through 1965
36
4.
Runoff i s o p l e t h s f o r J u l y , 1964
37
5.
Average n e t b a s i n s u p p l y f o r 1946 through 1965
53
INTRODUCTION
The G r e a t Lakes a r e t h e e a r t h ' s g r e a t e s t expanse of f r e s h
water.
The f i v e Great Lakes i n o r d e r of descending e l e v a t i o n a r e
S u p e r i o r , Michigan, Huron, E r i e , and O n t a r i o .
The d r a i n a g e a r e a of
2
t h i s system i s approximately 295,000 s q u a r e m i l e s (764,000 km ) .
The dimensions of t h e Great Lakes a r e g i v e n i n T a b l e 1 and a map of
t h e Great Lakes d r a i n a g e b a s i n i s shown i n F i g . 1.
From t h e c o n s e r v a t i o n of m a t t e r p r i n c i p l e , a w a t e r b a l a n c e
e q u a t i o n can b e w r i t t e n f o r each l a k e a s f o l l o w s
where AS i s t h e change i n amount of w a t e r s t o r e d i n t h e l a k e , p l u s
i f s u p p l i e s exceed removals, minus i f removals exceed s u p p l i e s ; P
i s t h e amount of p r e c i p i t a t i o n on l a k e ' s s u r f a c e ; R i s t h e amount of
r u n o f f i n t o t h e l a k e from t h e s u r r o u n d i n g l a n d a r e a ; E i s t h e amount
of e v a p o r a t i o n from t h e l a k e ' s s u r f a c e ; I i s t h e amount of i n f l o w
from t h e upstream l a k e ; 0 i s t h e amount of o u t f l o w from t h e l a k e
through i t s n a t u r a l o u t l e t ; D i s t h e amount of d i v e r s i o n , p l u s i f i n t o
l a k e , minus i f o u t of l a k e ; and G i s t h e amount of groundwater flow
entering o r leaving the lake.
A l l v a r i a b l e s a r e e x p r e s s e d i n t h e same
u n i t s and f o r t h e same p e r i o d of t i m e .
Obviously, any v a r i a b l e may b e
e q u a l t o z e r o f o r a l a k e where i t i s n o t p e r t i n e n t .
The T i d e s and Water L e v e l s S e c t i o n , Marine S c i e n c e s Branch,
Department of Energy, Mines and Resources, Canada and t h e Lake Survey
C e n t e r , N a t i o n a l Ocean Survey, United S t a t e s Department of Commerce
TABLE 1. Dimensions of t h e G r e a t Lakes.
Lake
~ e n g t h BreadEha
~
(mi)
(mi)
Area a
Water2Sar.
Draina e
(mi
(cfs)
>
Average
Discharge
1946-1965~
(cfs)
Max.
Deptpa
(ft)
Mean
Deptba
(ft)
78,000
1,333
487
923
276
750
195
Superior
350
160
31,820
80,000
Michigan
307
118
22,400
67,860
Huron
206
183
23,010
72,620
St. Clair
182,000
26
24
490
7,430
Detroit
186,000
Erie
241
57
9,930
32,490
Niagara
198,000
210
58
Ontario
193
53
7,520
34,800
S t .Lawrence
239,000
802
283
S t . Clair
a
b
C
21
Source:
U.S. Army E n g i n e e r D i v i s i o n , North C e n t r a l (1965a)
Source:
From d a t a s u p p l i e d by U.S. Department o f Commerce, Lake Survey
C e n t e r , ( P e r s o n a l Communication, 1972)
1 m i l e (mi) = 1 . 6 1 K i l o m e t e r s (km)
2
2
dl s q u a r e m i l e (mi ) = 2.59 s q u a r e k i l o m e t e r s (km )
e
3
1 c u b i c f o o t p e r s e c o n d ( c f s ) = 0.028 c u b i c meters p e r second (m / s e c )
£ 1 f o o t ( f t ) = 0.305 meters (m)
10
m a i n t a i n w a t e r l e v e l gages on t h e Great Lakes, r i v e r s which connect t h e
l a k e s , and channels i n which water i s d i v e r t e d i n t o o r o u t of t h e l a k e s .
The change i n amount of w a t e r s t o r e d i n a l a k e i s c a l c u l a t e d from t h e
a r e a of t h e l a k e and t h e measured change i n t h e e l e v a t i o n of t h e w a t e r
s u r f a c e over a p e r i o d of time.
The amount of i n f l o w from t h e upstream
l a k e , o u t f l o w from t h e l a k e through i t s n a t u r a l o u t l e t , and d i v e r s i o n s
i n t o and o u t of t h e l a k e a r e determined from t h e w a t e r l e v e l r e c o r d s
and r a t i n g curves which g i v e t h e r e l a t i o n s h i p between t h e amount of flow
p a s t a p o i n t and t h e s u r f a c e e l e v a t i o n of t h e w a t e r a t t h a t p o i n t .
The p r e s e n t s t u d y was undertaken t o determine t h e magnitude of
t h e p r e c i p i t a t i o n on t h e l a k e , e v a p o r a t i o n from t h e l a k e s u r f a c e , and
runoff i n t o t h e l a k e from surrounding l a n d a r e a s f o r each of t h e Great
Lakes f o r each month of c a l e n d a r y e a r s 1946 through 1965.
PRECIPITATION ON THE LAKES
It has u s u a l l y been assumed t h a t t h e l a k e s u r f a c e s have r e c e i v e d
t h e same depth of p r e c i p i t a t i o n a s measured a t s i t e s a l o n g t h e l a k e s s h o r e s
(Brunk, 1962; Weiss and Kresge, 1962).
A f t e r a s t u d y of a v a i l a b l e r e c o r d s
of p r e c i p i t a t i o n and p r e c i p i t a t i o n t y p e s over t h e l a k e and t h e a d j a c e n t
l a n d a r e a s , Changnon (1968) r e p o r t e d t h a t t h e annual average p r e c i p i t a t i o n
over Lake Michigan i s 29.6 i n .
(75.2 cm) which i s 6 p e r c e n t less t h a n t h e
p r e c i p i t a t i o n over t h e l a n d p o r t i o n of t h e b a s i n .
He concluded t h a t t h e
l a k e s u p p r e s s e s summertime thundershowers by 20 p e r c e n t , b u t enhances w i n t e r
s n o w f a l l a l o n g t h e e a s t e r n s h o r e by 25 t o 100 p e r c e n t .
Although some of t h e
snow f a l l s on t h e l a k e s u r f a c e , most of t h e i n c r e a s e i s on t h e downwind
shores with the n e t r e s u l t t h a t t h e r e is a g r e a t e r decrease i n p r e c i p i t a t i o n
on t h e l a k e i n t h e warm months than t h e r e i s an i n c r e a s e i n t h e w i n t e r months.
These Lake Michigan p r e c i p i t a t i o n amounts a r e p r e s e n t e d a s s e a s o n a l and
a n n u a l averages.
Changnon's work i s extended h e r e t o a l l of t h e Great Lakes
f o r i n d i v i d u a l months f o r c a l e n d a r y e a r s 1946 through 1965.
The monthly p r e c i p i t a t i o n d a t a f o r 840 United S t a t e s r e p o r t i n g
s t a t i o n s i n and around t h e Great Lakes b a s i n were o b t a i n e d on punched c a r d s
o r magnetic t a p e from t h e N a t i o n a l C l i m a t i c C e n t e r , N a t i o n a l Oceanic and
Atmospheric A d m i n i s t r a t i o n .
The d a t a f o r 130 Canadian s t a t i o n s were o b t a i n e d
on magnetic t a p e from t h e M e t e o r o l o g i c a l S e r v i c e of Canada.
was n o t used.
Some of t h e d a t a
When two o r more s t a t i o n s were l o c a t e d c l o s e t o g e t h e r , u s u a l l y
w i t h i n t h e same c i t y , o n l y t h e d a t a f o r t h e s t a t i o n w i t h t h e l o n g e r r e c o r d
was used.
The l o c a t i o n s of t h e s t a t i o n s f o r which d a t a were used i n t h e
s t u d y a r e shown i n Fig. 1.
The monthly p r e c i p i t a t i o n d a t a was p l o t t e d o n t o a common b a s e map.
I s o h y e t s were i n t e r p o l a t e d from t h e s t a t i o n v a l u e s a t s p a c i n g s determined
by the range of values for each monthly chart. Usually, isohyets were
drawn at one-inch (2.54 cm) intervals with the 0.5-inch (1.27 cm) and zero
isohyets drawn where applicable.
Far more data points (stations) were
used in this study than have been used in any previous study. This is
reflected in the detail of the isohyets. The pattern of the isohyets over
the land determined the pattern of isohyets over the lakes near the shores,
but the pattern of isohyets over the lakes was determined by two methods.
Deep, large lakes gain and lose heat very slowly, the rate of heat exchange
with the atmosphere being a function of the configuration of the lake with
the prevailing winds, the intensity of the winds, the contrast in temperature between the lake and the overlying air mass, the amount of cloudiness,
and the contrast in vapor pressure between the lake surface and the overlying
air.
These factors cause the individual lakes in the Great Lakes system to
adjust to the climate of the surrounding land at varying rates in both time
and space.
Since the contrasts in temperature, atmospheric stability, and
moisture between the lakes and the surrounding land determine the difference
in precipitation between the lakes and the land, these factors have been
taken into account qualitatively in the drawing of the isohyets over the
lake surfaces. Quantitatively, ratios between observed monthly mean values
of precipitation at island and peninsular stations were established with
coastal stations and these ratios were then applied to values at other coastal
stations along the same side of the lake in order to obtain values representative of the rainfall to be expected further out over the lake surface.
This extrapolation procedure was only appropriate for Lakes Superior,
Michigan, and Erie because these lakes have islands or peninsulas with precipitation stations on them which can be paired with coastal stations in order
to determine the ratios. The ratios for the station pairs on each lake for
t h e i n d i v i d u a l months a r e shown i n Table 2.
s t a t i o n p a i r s a r e shown i n F i g . 1.
The geographic l o c a t i o n s of t h e
E x t r a p o l a t i o n of t h e r a t i o s was a p p l i e d
o n l y t o c o a s t a l s t a t i o n s which could be expected t o b e i n f l u e n c e d by t h e same
atmospheric flow c o n d i t i o n s which a f f e c t e d t h e s t a t i o n s which were used t o
establish the ratio.
Thus, t h e r a t i o e x t r a p o l a t i o n s were r e s t r i c t e d i n use
t o t h e l a k e f o r which they were c a l c u l a t e d and t o t h e same c o a s t from which
t h e r a t i o s were o b t a i n e d .
F i g . 1 has upon i t t h e p a i r s of c o a s t a l s t a t i o n s
and p o i n t s t o which e x t r a p o l a t i o n s of t h e p r e c i p i t a t i o n v a l u e s were made.
The i s o h y e t s a s drawn f o r J u l y , 1964, a r e shown i n F i g . 2.
The
a r e a s between t h e i s o h y e t s were planimetered and t h e average p r e c i p i t a t i o n .
was determined f o r each l a k e f o r each of t h e 240 months.
The r e s u l t s a r e
g i v e n i n T a b l e s 3 through 8 w i t h t h e 20-year average f o r each month, t h e
annual t o t a l s , and t h e annual average p r e c i p i t a t i o n over t h e 20-year p e r i o d .
During t h a t p e r i o d Lake S u p e r i o r had t h e l e a s t annual average p r e c i p i t a t i o n
w i t h 28.35 i n c h e s (72.01 cm) and Lake E r i e averaged t h e most w i t h 32.79
i n c h e s (83.29 cm).
i n Table 9.
The s e a s o n a l a v e r a g e p r e c i p i t a t i o n on each l a k e i s given
Here i t w i l l be noted t h a t t h e l a r g e s t s e a s o n a l amount a g a i n
o c c u r s on Lake E r i e i n t h e s p r i n g , b u t t h a t Lake S u p e r i o r has almost a s l a r g e
a n amount i n t h e summer.
T h i s i s an i l l u s t r a t i o n of t h e l a g i n t h e seasons
between t h e more n o r t h e r l y , deep l a k e and t h e more s o u t h e r l y , s h a l l o w l a k e .
The l o w e s t average s e a s o n a l amount f a l l s on Lakes Michigan i n t h e w i n t e r .
The
low w i n t e r p r e c i p i t a t i o n on Lake Michigan i s probably due t o t h e north-south
o r i e n t a t i o n of t h e major a x i s of t h i s narrow l a k e and t h e f a c t t h a t t h e prev a i l i n g winds i n t h e w i n t e r a r e from t h e west.
There i s no l a k e of major
s i z e upwind from Lake Michigan when t h e winds a r e o u t of t h e west and, t h u s ,
t h e r e i s no adequate m o i s t u r e supply f o r g e n e r a t i o n of o v e r l a k e p r e c i p i t a t i o n
i n the winter.
Monthly l a k e l l a n d p r e c i p i t a t i o n r a t i o s
TABLE 2.
Jan.
Feb
.
Mar.
Apr.
May
.
June
July
Aug.
Sept.
Oct.
Nov
Dec.
1.101
1.184
0.978
0.985
0.948
0.896
0.865
0.818
0.816
0.947
0.782
1.088
0.846
0.762
0.939
0.978
1.319
1.178
0.952
0.832
0.677
0.983
0.952
0.979
0.911
1.042
0.954
0.809
0.953
1.075
1.053
1.048
1.201
1.033
0.928
0.844
0.932
1.007
0.955
0.925
1.042
1.305
0.702
0.559
0.850
0.951
0.880
0.830
1.208
0.935
1.128
0.912
0.975
1.202
LAKE ERIE
P e l e e I s l a n d , Ontario/Harrow, O n t a r i o
1.120
0.840
0.958
1.129
1.168
G i b r a l t e r I s l a n d , Ohio/Sandusky, Ohio
0.851
0.833
0.838
0.882
0.910
LAKE MICHIGAN
North Manitou I s l a n d , Mich. / S u t t o n , Mich.
0.690
0.568
0.951
0.822
1.149
Beaver I s l a n d , Mich. /Petosky, Mich.
0.638
0.736
0.815
1.014
1.183
Washington I s l a n d , ~ i c h . / E s c a n a b a , Mich.
0.950
0,785
1.480
1.030
1.015
LAKE SUPERIOR
Madeline I s l a n d , Wisc. /Ashland, Wisc.
1.512
1.283
0.974
0.907
1.009
Eagle Harbor, Mich. /L 'Anse, Mich.
1.669
1.212
1.256
0.714
0.793
Mott I s l a n d , Mich. / P o r t A r t h u r , O n t a r i o
0.815
&
TABLE 3 .
MEAN
a
a
P r e c i p i t a t i o n on Lake S u p e r i o r ( i n c h e s )
Jan.
Feb.
Mar.
Apr.
May
June
July
1.66
1.30
1.57
2.12
3-08
3.09
2.88
1 inch ( i n . )
=
2.54 c e n t i m e t e r s (cm)
Aug.
3.07
Sept.
3.16
Oct.
2.00
Nov.
Dec.
Total
TABLE 4.
P r e c i p i t a t i o n on Lake Michigan ( i n c h e s a )
1
I
Jan.
a
Feb.
Mar.
Apr.
May
1 i n c h ( i n . ) = 2.54 c e n t i m e t e r s (cm)
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Total
TABLE 5 .
Jan.
Feb.
1946
3-35
2.43
MEAN
2.64
2.18
a
Mar.
P r e c i p i t a t i o n on Lake Huron ( i n c h e s a )
Apr.
May
June
July
Aug.
1.29
0.81
3-42
2.58
1.33
2-00
2.05
2.54
2.56
2.55
2.60
2.65
1 i n c h ( i n . ) = 2 . 5 4 c e n t i m e t e r s (cm)
Sept.
Oct.
Nov.
Dec.
Total
2-57
1.38
2.50
3-61
27-27
3.21
2-47
3.03
2-84
31.31
TABLE 6.
Jan.
Feb.
1946
1.35
2.20
MEAN
2.07
2.10
a
Mar.
P r e c i p i t a t i o n on Lake S t . C l a i r ( i n c h e s a )
Apr.
May
June
July
2.10
0.45
4.10
5.70
0.90
2.51
2.99
2.70
3.01
2.28
1 i n c h ( i n . ) = 2.54 c e n t i m e t e r s (cm)
Aug.
Sept.
Oct.
Nov.
Dec.
Total
3.85
1.15
2.50
1.20
3.10
28.60
3.09
2.34
2.35
2.12
2.22
29.79
TABLE 7.
Jan.
Feb.
1946
1.14
1.08
1957
2.75
1958
1.81
1959
4.29
1960
2.78
1961
0.55
1962
2.93
1963
1.22
1964
2.08
1965
4.31
MEAN
2.73
a
1 inch (in.)
=
Mar.
2.51
P r e c i p i t a t i o n on Lake E r i e ( i n c h e s a )
Apr.
May
June
July
0.90
5.23
4034
2049
2.54 c e n t i m e t e r s (cm)
Aug.
1.99
Sept.
1.47
Oct.
Nov.
Dec.
Total
3.31
2.29
2.52
29.27
I
i
TABLE 8.
i
i
1946
Jan.
Feb.
1.71
2.26
Mar.
1.03
Precipitation on Lake Ontario (inchesa )
Apr.
May
June
July
1.18
3.33
2.44
1.91
1958
1959
1960
1961
1962
1963
1964
1965
MEAN
a
1 inch (in.) = 2.54 centimeters (cm)
Aug.
2.03
Sept.
2.36
Oct.
Nov.
Dec.
Total
3.81
2.70
3.37
28.13
TABLE 9.
Seasonal average p r e c i p i t a t i o n
on l a k e s f o r 1946 t h r o u g h 1965 ( i n c h e s a ) .
Winter
Spring
Summer
Fall
Lake S u p e r i o r
4.80
6.77
9.04
7.74
Lake Huron
7.66
7.15
7.80
8.70
Lake E r i e
6.92
9.17
8.92
7.78
Lake O n t a r i o
7.45
7.84
7.51
7.83
Lake Michigan
4.73
7.98
8.66
7.82
a
1 i n c h ( i n . ) = 2.54 c e n t i m e t e r s (cm)
EVAPORATION FROM THE LAKE SURFACES
S e v e r a l methods have been proposed f o r c a l c u l a t i n g t h e monthly
e v a p o r a t i o n from t h e Great Lakes w a t e r s u r f a c e s .
The energy budget
method h a s been found t o be a n e f f e c t i v e method f o r d e t e r m i n i n g evaporat i o n (Rodgers and Anderson, 1961).
The u s e of t h i s method r e q u i r e s d a t a
such a s amounts of s o l a r r a d i a t i o n , a l b e d o , and c l o u d i n e s s , which a r e
n o t a v a i l a b l e f o r a l l t h e l a k e s f o r t h e c a l e n d a r y e a r s 1946 through 1965.
The r e s u l t s of t h e s t u d y of l a k e e v a p o r a t i o n performed on
e t a l . , 1954) h a s been a d a p t e d f o r u s e on l a r g e r
Lake Hefner (Harbeck, -l a k e s (Harbeck, 1962).
Yu and B r u t s a e r t (1969) used t h e m a s s - t r a n s f e r
e q u a t i o n proposed by Harbeck (1962) t o c a l c u l a t e t h e e v a p o r a t i o n from
Lake O n t a r i o .
The e q u a t i o n h a s t h e form:
i n which E i s t h e e v a p o r a t i o n i n i n c h e s p e r day, A i s t h e a r e a i n a c r e s ,
u 2 i s t h e wind v e l o c i t y i n m i l e s p e r hour 2 m e t e r s above t h e s u r f a c e , e
W
i s t h e s a t u r a t i o n vapor p r e s s u r e a t t h e t e m p e r a t u r e of t h e w a t e r s u r f a c e
i n mb, and e
a
i s t h e vapor p r e s s u r e of t h e ambient a i r .
They used a n
a v e r a g e wind v e l o c i t y o b t a i n e d a t Toronto which was reduced t o t h e 2
meter l e v e l by u s i n g t h e one-seventh power law.
wind a t 8 m e t e r s h e i g h t o b t a i n e d a t Toronto.
They used a n average
The l a k e s u r f a c e temper-
a t u r e s were e s t i m a t e d from a r e g r e s s i o n e q u a t i o n developed f o r s u r f a c e
w a t e r t e m p e r a t u r e a s a f u n c t i o n of t h e mean monthly a i r t e m p e r a t u r e .
The a i r vapor p r e s s u r e s were o b t a i n e d by m u l t i p l y i n g t h e s a t u r a t i o n
vapor p r e s s u r e by t h e average r e l a t i v e humidity a t Toronto o r R o c h e s t e r ,
whichever was t h e lower.
The area-dependent c o e f f i c i e n t assumes a c i r c u l a r l a k e such t h a t
wind d i r e c t i o n i s unimportant i n determing t h e l e n g t h of overwater f e t c h .
Obviously, t h e Great Lakes w i t h t h e average winds from a w e s t e r l y d i r e c t i o n and Lakes S u p e r i o r , E . r i e , and O n t a r i o w i t h t h e i r major a x i s o r i e n t e d
east-west,
and Lakes Michigan and Huron w i t h t h e i r major a x i s o r i e n t e d
north-south,
w i l l n o t b e i n f l u e n c e d a s much by t h e s u r f a c e a r e a of t h e
i n d i v i d u a l l a k e s a s they w i l l by t h e overwater f e t c h d u r i n g a p a r t i c u l a r
evaporation period.
It seems q u i t e l i k e l y t h a t t h e ' o a s i s ' e f f e c t f o r
which t h e a r e a c o e f f i c i e n t i s designed t o account becomes n e g l i g i b l e
w i t h l a k e s a s l a r g e a s t h e Great Lakes.
The a i r s t r e a m i n p a s s i n g o v e r
t h e exposed w a t e r s u r f a c e should r e a c h a s t a t e of e q u i l i b r i u m w i t h t h e
w a t e r underneath a f t e r some d i s t a n c e of t r a v e l even though t h i s e q u i l i b rium would n o t b e t h e t o t a l wet-bulb s a t u r a t i o n a t t h e s u r f a c e w a t e r
t e m p e r a t u r e (Morton, 1967).
Richards and I r b e (1969) have a d a p t e d t h e Lake Hefner e q u a t i o n
t o t h e p e c u l i a r c o n d i t i o n s of t h e Great Lakes:
i n which e
s
i s t h e s a t u r a t i o n vapor p r e s s u r e a t s u r f a c e w a t e r t e m p e r a t u r e
i n i n c h e s of mercury, e
ad
i s t h e vapor p r e s s u r e of t h e a i r over l a n d , H
i s a monthly humidity r a t i o determined from h i s t o r i c a l r e c o r d s , V i s t h e
wind v e l o c i t y i n m i l e s p e r day a t 8 m e t e r s , and R i s t h e monthly wind r a t i o
a s determined from t h e work of Lemire (1961) and Richards and F o r t i n (1962).
T h i s e q u a t i o n d i f f e r e s from t h a t of Yu and B r u t s a e r t i n t h a t t h e r e i s no
a r e a c o e f f i c i e n t , b u t t h e r e a r e c o r r e c t i o n s ( r a t i o s ) a p p l i e d t o t h e wind
speed and a i r vapor p r e s s u r e which, on t h e a v e r a g e , e f f e c t i v e l y i n c r e a s e
the coefficient.
The r a t i o s a p p l i e d by Richards and I r b e t e n d t o a d j u s t
t h e b a s i c Lake Hefner e q u a t i o n i n t h e same d i r e c t i o n a s t h e a r e a c o e f f i -
c i e n t a p p l i e d by Yu and B r u t s a e r t .
Over t h e 16-year p e r i o d from 1950
t h r o u g h 1965 t h e two methods r e s u l t e d i n t h e Yu and B r u t s a e r t e q u a t i o n
a v e r a g i n g a p p r o x i m a t e l y 5 p e r c e n t more e v a p o r a t i o n a n n u a l l y t h a n t h e
R i c h a r d s and I r b e e q u a t i o n .
S i n c e t h e R i c h a r d s and I r b e e q u a t i o n i n -
d i r e c t l y a c c o u n t s f o r t h e s i z e of t h e i n d i v i d u a l l a k e s t h r o u g h r a t i o s
w i t h what seems t o u s as a more r e a l i s t i c method, t h e R i c h a r d s and
I r b e e q u a t i o n h a s been used t o c a l c u l a t e t h e e v a p o r a t i o n from Lakes
S u p e r i o r , Michigan, Huron, E r i e and O n t a r i o f o r t h e p e r i o d s 1946
t h r o u g h 1958, 1946 t h r o u g h 1965, 1946 t h r o u g h 1958, 1946 t h r o u g h 1949,
and 1946 t h r o u g h 1949 r e s p e c t i v e l y .
The s u r f a c e w a t e r t e m p e r a t u r e s u s e d i n computing t h e evapo r a t i o n from Lake Michigan w e r e d e t e r m i n e d from t h e r e c o r d s of i n t a k e
t e m p e r a t u r e s a t t h e Muskegon H e i g h t s , Michigan, w a t e r p l a n t .
i n t a k e i s a p p r o x i m a t e l y 40 f e e t (12.2 m) b e n e a t h t h e s u r f a c e .
This
The
most l i k e l y s u r f a c e t e m p e r a t u r e was d e t e r m i n e d by a m o d i f i c a t i o n o f a
t e c h n i q u e due t o R i c h a r d s and Rodgers (1964).
A g r a p h of t h e march
o f r e c o r d e d w a t e r t e m p e r a t u r e s w i t h t i m e was p l o t t e d .
For t h e p a r t
o f t h e y e a r when t h e t e m p e r a t u r e s w e r e above t h e t e m p e r a t u r e a t which
w a t e r i s a t i t s maximum d e n s i t y a n e n v e l o p e c u r v e of maximum temperat u r e was drawn.
S i m i l a r l y , f o r t h e p a r t of t h e y e a r when t h e temper-
a t u r e s were below t h e t e m p e r a t u r e a t which w a t e r i s a t i t s maximum
d e n s i t y a n e v e l o p e c u r v e o f minimum t e m p e r a t u r e s was drawn.
The
combined c u r v e i s assumed t o i n d i c a t e t h e t r e n d of t h e s u r f a c e w a t e r
temperature f o r t h e year.
Muskegon H e i g h t s i s i n t h e s o u t h e r n b a s i n
of Lake Michigan and s h o u l d n o t b e e x p e c t e d t o r e p r e s e n t t h e t o t a l
s u r f a c e area o f t h e l a k e .
The Muskegon H e i g h t s t e m p e r a t u r e s w e r e av-
e r a g e d and t h e d i f f e r e n c e between t h e a v e r a g e t e m p e r a t u r e
t h e r e and
M i l l a r ' s (1952) a v e r a g e t e m p e r a t u r e f o r t h e e n t i r e l a k e w a s n o t e d by months.
M i l l a r ' s a v e r a g e monthly t e m p e r a t u r e s w e r e t h e n a l t e r e d by t h e d i f f e r e n c e
between t h e a v e r a g e monthly and a c t u a l monthly v a l u e s a t Muskegon H e i g h t s .
A multiple regression analysis revealed t h a t the surface water
t e m p e r a t u r e s f o r Lakes E r i e and O n t a r i o a r e a f u n c t i o n of t h e a v e r a g e a i r
t e m p e r a t u r e s of t h e p r e s e n t and two p r e c e d i n g months.
The s u r f a c e w a t e r
t e m p e r a t u r e s r e p o r t e d by R i c h a r d s and I r b e were used i n t h e a n a l y s i s .
The
same r e l a t i o n s h i p was found t o b e a p p l i c a b l e f o r Lakes S u p e r i o r and Huron
e x c e p t f o r t h e months of J a n u a r y t h r o u g h May f o r S u p e r i o r and J a n u a r y and
F e b r u a r y f o r Huron.
The s u r f a c e w a t e r t e m p e r a t u r e s f o r Lakes S u p e r i o r and
Huron i n J a n u a r y and F e b r u a r y w e r e found t o b e a f u n c t i o n of t h e a i r temp e r a t u r e s f o r t h e same months.
The l a c k of y e a r - t o - y e a r
v a r i a t i o n of
s u r f a c e t e m p e r a t u r e s o n Lake S u p e r i o r from March t h r o u g h May d i c t a t e d t h e
u s e o f mean monthly s u r f a c e t e m p e r a t u r e s f o r t h o s e months.
The e s t i m a t e d
s u r f a c e w a t e r t e m p e r a t u r e s a r e l i s t e d i n T a b l e s 10 t h r o u g h 1 4 .
The s t a t i o n s whose wind, r e l a t i v e h u m i d i t y , and t e m p e r a t u r e
r e c o r d s w e r e used t o c a l c u l a t e t h e e v a p o r a t i o n from t h e i n d i v i d u a l l a k e s
a r e l i s t e d i n Table 15.
T a b l e s 1 6 t h r o u g h 20 c o n t a i n t h e c a l c u l a t e d
amounts of e v a p o r a t i o n from each of t h e f i v e l a k e s f o r t h e months of t h e
p e r i o d - 1 9 4 6 t h r o u g h 1965 f o r which R i c h a r d s and I r b e d i d n o t r e p o r t evaporation values.
TABLE 10.
Lake S u p e r i o r s u r f a c e w a t e r t e m p e r a t u r e a ('Fb)
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept.
1946
35.8
32.8
32.0
33.0
35.0
38.8
43.9
55.3
1947
35.7
32.7
32eO
33.0
35.0
37.2
44.7
1948
34e9
31.9
32.0
33.0
35.0
38.5
1949
35.7
32.7
32.0
33.0
35.0
1950
35.2
32.2
32.0
33.0
1951
35.5
32.5
32.0
1952
35.6
32.6
1953
35.8
1954
1955
a
Oct.
Nov.
Dec.
53.9
47.2
41.8
39.0
62.7
55.8
49.9
43.8
39.4
44.4
57.2
58.4
49.1
43.9
39.3
39.0
43.3
5409
54.5
48.6
42.8
3903
35.0
3404
43.2
51.4
52.7
45.8
42.7
38.8
33.0
34.0
40.0
46.9
54.1
51.1
45.4
41.6
38.5
32.0
33.0
35.0
40.0
44.2
52.8
54.9
46.4
42.1
38.5
32.8
32.0
33.0
35.0
37.7
43.9
57.5
56.1
49.2
43.4
39.6
35.1
32.1
32.0
33.0
35.0
34.7
41.6
53.9
53.6
47.4
42.7
38.8
35.6
32.6
32.0
33.0
35.0
40.0
45.4
59.1
56.7
50.1
43.0
38.7
Values f o r J a n u a r g 1959, through December, 1965, a r e i n R i c h a r d s and I r b e (1969).
TABLE 11.
1946
a
Lake Michigan s u r f a c e w a t e r t e m p e r a t u r e (OF )
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
32.2
32.4
34.9
43.3
49.9
56.9
64.3
66.2
66.4
62.6
54.6
43.0
TABLE 1 2 .
1946
/
1
b
Lake Huron s u r f a c e w a t e r t e m p e r a t u r e a (OF )
Jan.
Feb.
Mar.
Apr.
May
June
July
38-8
34.9
34-4
37-0
39.3
46-5
59-5
Aug.
Sept.
Oct.
Nov.
Dec.
65.1
63.4
55.9
47.6
42-4
a V a l u e s f o r J a n u a r y , 1959, t h r o u g h December, 1965, a r e i n R i c h a r d s and I r b e (1969).
TABLE 13.
Jan.
a
Feb.
Mar.
Apr.
Lake E r i e s u r f a c e w a t e r t e m p e r a t u r e a
May
June
July
Aug.
Sept.
(OF
b)
Oct.
Nov.
V a l u e s f o r J a n u a r y , 1 9 5 0 , t h r o u g h December, 1965, a r e i n R i c h a r d s and I r b e ( 1 9 6 9 ) .
Dec.
I
TABLE 14.
J
1
Jan.
Feb.
Mar.
b
Lake O n t a r i o s u r f a c e w a t e r temperaturea (OF )
Apr.
May
June
July
Aug.
Sept.
Oct.
Nov.
l
a
I
Values f o r January, 1950, through December, 1965, a r e i n Richards and I r b e (1969).
b
OC
= 519 (OF -32)
Dec.
TABLE 1 5 ,
S t a t i o n s from which d a t a were
obtained t o c a l c u l a t e evaporation.
Lake S u p e r i o r
Duluth, Minn.
Grand Marais, Minn.
Marquette, Mich.
Houghton, Mich.
W h i t e f i s h P o i n t , Mich.
S a u l t S t e . Marie, Mich.
White R i v e r , Ont.
S c h r e i b e r , Ont
.
F o r t William, Ont.
P o r t A r t h u r , Ont.
Caribou I s l a n d , Ont
Munsing, Mich.
Lake Michipan
Chicago, Ill.
Es canaba, Mich
.
.
Green Bay, W i s c
Milwaukee, Wisc.
Muskegon, Mich.
South Bend, Ind.
Gore Bay, Ont.
Wiarton, Ont.
Sudbury, Ont.
Muskoka, Ont.
C e n t r a l i a , Ont.
Sandusky, Ohio
E r i e , Pa.
B u f f a l o , N. Y .
Long P o i n t , Ont.
Lake Huron
S a u l t S t e . Marie, Mich.
Alpena, Mich.
D e t r o i t , Mich.
Lake E r i e
D e t r o i t , Mich.
Toledo, Ohio
Cleveland, Ohio
Lake O n t a r i o
Rochester, N. Y .
Syracuse, N. Y .
.
Oswego, N. Y
Trenton, Ont.
Toronto, Ont.
.
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SE'O
9 L 0 1 - 9L'O
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12'0
€0'0€0'0
65'0
69'0
51'015'0
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€9'0
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E8'0
Z1'Z
'79'Z
86'1
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€5'1
6'7.1
91'E
11'2
68'0
ZO'Z
65'2
EZ'E
98'1
15'1
'79'1
08'1
ZL'Z
58'1
9 1 'E
L'7
"7
61'E
85'47
18'E
ZE'
z
9E'E
Z6'E
86' E
L8' Z
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50'E
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9E'Z
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TABLE 17.
1946
Jan.
.
2.59
2.75
0.57
2.23
2.14
MEAN
3.40
2.55
2-02
0.81
0.71
.
-
Feb.
Mar.
Apr.
a
E v a p o r a t i o n f o r Lake Michigan ( i n c h e s )
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Total
----.-
0.12
-0.20
0.06
-0.03
3.66
5.68
4.93
6.64
5.91
37.28
3.67
6.07
4.11
5.37
4.59
33.07
/
a
1 i n c h ( i n . ) = 2 . 5 4 c e n t i m e t e r s (cm)
1
1
TABLE 18.
Jan.
Feb.
Mar.
Apr.
May
1.31
1.26-0.34
1946
4.46
3.65
0.02
MEAN
4.57
3.13
1.83
a
E v a p o r a t i o n from Lake Huron a ( i n c h e s b )
-0.59
-0.25
June
-0.87
July
Aug.
Sept.
Oct.
Nov.
Dec.
0.17
3.17
4.32
4.44
5.15
5.32
32.93
-0.14
1.80
3.63
4.11
4.45
4.74
26.40
Values f o r J a n u a r y , 1959, t h r o u g h December, 1965, a r e from R i c h a r d s and I r b e (1969).
1 inch (in.)
= 2.54 c e n t i m e t e r s (cm)
Total
( 6 9 6 ~ )s ~ a 3 a m ~ 3 u aSP'Z
3
= ('LIT)Y
~ U T1
'(6961) aqxI pue spxsq3yx moxj ale ' ~ 9 6 1'~aqma3aaq 2 n o ~ q 3 ' 0 ~ 6 1'Lxenuer 203 sanTeA
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66'9
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10'9
81'5
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L9'ZE
8h'f
L9'E
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81'5
88'5
Ef"7
L9'47f
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Zf'S
L8'E
Z1'8E
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09'1
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'71'1
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Lf'O-
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11'08L'U
6f-0
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55'1
LY'O
EO'O
80'1
'70'1-
'7'7.2
59'0
98'1
61'E
65'2
9
e
NVjW
5961
'7961
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1961
'70'E
16'Z
f f ' E
61'0
EL' Z18'00 0 ' E85.Z-
EO'O
98'1ff'16E'O11'0
'7L.1-
90'1-
U6'O
'71.1
91.E
L9' 1
15 'Z
15'2
fE'O
LZ' 1
60' 1
59'0
f'7.U
6U'Z
L6 ' 0
UZ'E
s a q 3 u ~ )e a ~ ~
aye?
3 m o ~ 3u o ~ 3 e ~ o d e ~-61
3 3?gv~,
(9
TABLE 20.
Jan.
Feb.
Mar.
Apr.
E v a p o r a t i o n from Lake O n t a r i o a ( i n c h e s b )
May
July
Aug.
0.48
5.40
4.64
Sept.
Oct.
Nov.
Dec.
Total
6.61
4.04
3.50
4.33
35.34
1962
4.67
3.07
0.92
-1.19
1963
4.44
3070
1.18
-0.08
0.37
0.50
0.84
1.94
4.69
2.72
2.27
4.14
26.71
1964
4.22
3.39
1.83
-0.15
0.22
0.51
1.43
3.72
4.77
4.37
3.75
3.29
31.35
1965
5.02
3.44
1.71
-0.03
0.15
1.61
2.73
2.01
5.36
3.21
2.42
27.07
MEAN
3.87
2.73
1.63-0.60
0.22
1.97
3.30
4.41
3.39
3.46
3.45
28.16
a
b
-1.13
June
-0.56
0.31
V a l u e s f o r J a n u a r y , 1950, t h r o u g h December, 1965, a r e from R i c h a r d s and I r b e (1969).
1 inch (in.)
=
2.54 c e n t i m e t e r s (cm)
RUNOFF INTO LAKES FROM SURROUNDING LAND AREAS
S e v e r a l i n v e s t i g a t o r s have a t t e m p t e d t o d e t e r m i n e t h e amount
of r u n o f f which e n t e r s t h e G r e a t Lakes from t h e s u r r o u n d i n g l a n d a r e a s .
Brunk (1964) s t u d i e d t h e 1940-1959 a v e r a g e monthly d i s t r i b u t i o n of t h e
e v a p o t r a n s p i r a t i o n , s t r e a m f l o w , and p r e c i p i t a t i o n on t h e l a k e f o r Lakes
E r i e and O n t a r i o .
He concluded t h a t topography and a b s o r p t i v e c a p a c i t y
of s o i l s are p r o b a b l y r e s p o n s i b l e f o r t h e wide v a r i a t i o n s i n t h e p e r c e n t a g e of monthly p r e c i p i t a t i o n which f l o w s i n t o t h e l a k e s as streamf l o w from t h e v a r i o u s r i v e r b a s i n s .
A map of mean a n n u a l r u n o f f i n t h e G r e a t Lakes b a s i n f o r t h e
p e r i o d 1931 t h r o u g h 1960 was developed by Browzin (1966).
Pentland
(1968) p r e s e n t e d maps of a v e r a g e monthly and a n n u a l r u n o f f f o r t h e
G r e a t Lakes b a s i n f o r t h e b a s e p e r i o d 1935 t h r o u g h 1964.
Sanderson (1966) used t h e T h o r n t h w a i t e w a t e r b a l a n c e techn i q u e t o e s t i m a t e monthly p o i n t r u n o f f a t 1 3 3 c l i m a t i c s t a t i o n s i n
t h e Lake E r i e b a s i n f o r t h e p e r i o d October, 1958, t h r o u g h September,
1963.
An i s o p l e t h mapping t e c h n i q u e was t h e n used t o estimate t o t a l
monthly r u n o f f i n t o t h e l a k e .
The T h o r n t h w a i t e w a t e r b a l a n c e t e c h -
n i q u e was a l s o used f o r e s t i m a t i n g p o i n t r u n o f f a t 8 1 c l i m a t i c s t a t i o n s
i n and n e a r t h e Lake O n t a r i o b a s i n (Sanderson, 1 9 7 1 ) .
These r u n o f f
v a l u e s were t h e n used t o p r e p a r e a map of a n n u a l a v e r a g e r u n o f f a s w e l l
as maps of p l u s and minus two s t a n d a r d d e r v i a t i o n s of a n n u a l a v e r a g e
runoff
.
Witherspoon (1970) developed a h y d r o l o g i c model based on t h e
w a t e r and energy b a l a n c e s f o r t h e Lake O n t a r i o l o c a l d r a i n a g e b a s i n
which i n c l u d e d t h e e n t i r e l a n d a r e a of t h e b a s i n .
Using a h y p o t h e s i s
which p r o v i d e d e s t i m a t e s of t h e a c t u a l r e g i o n a l e v a p o r a t i o n , r e g i o n a l
m o i s t u r e v a l u e s were o b t a i n e d which, when r o u t e d , s i m u l a t e t h e measured
monthly o u t f l o w s from t h e l a n d a r e a .
The p e r i o d O c t o b e r , 1935, t h r o u g h
September, 1964, was s i m u l a t e d and computed r u n o f f was compared t o
11
measured" r u n o f f .
The "measured" r u n o f f was d e t e r m i n e d by e x t r a p o l a t i n g
t h e r u n o f f d i s t r f b u t i o n from gaged r e p r e s e n t a t i v e b a s i n s t o ungaged a r e a s
on a monthly b a s i s .
The r u n o f f v a l u e s d e s i r e d f o r t h i s s t u d y are t h e t o t a l r u n o f f
i n t o e a c h l a k e from s u r r o u n d i n g l a n d a r e a s f o r e a c h month of c a l e n d a r
y e a r s 1946 t h r o u g h 1965.
T h e r e i s a p p r o x i m a t e l y 200,000 s q . m i l e s
2
(518,000 km ) of l a n d a r e a i n t h e G r e a t Lakes b a s i n of which a p p r o x i m a t e l y
2
114,000 s q . m i l e s (295,300 km ) a r e i n t h e U n i t e d S t a t e s and 86,000 s q .
2
m i l e s (222,700 km ) a r e i n Canada.
F o r t h e p e r i o d 1946 t h r o u g h 1965
a p p r o x i m a t e l y 59 p e r c e n t of t h e a r e a i n t h e U n i t e d S t a t e s was gaged and
a p p r o x i m a t e l y 30 p e r c e n t of t h e a r e a i n Canada was gaged.
I n addition,
an a d d i t i o n a l 1 0 p e r c e n t of t h e a r e a i n t h e U n i t e d S t a t e s was gaged f o r
p a r t o f t h e p e r i o d and a b o u t 32 p e r c e n t of t h e a r e a i n Canada was gaged
f o r p a r t of t h e period.
A summary of t h e amount of l a n d a r e a f o r which
streamflow r e c o r d s a r e a v a i l a b l e is presented i n Table 2 1 f o r each l a k e .
A map of t h e G r e a t Lakes b a s i n was p r e p a r e d f o r e a c h month
of t h e p e r i o d 1946 through 1965 w i t h t h e amount of r u n o f f from each
gaged a r e a d u r i n g t h e month p l o t t e d a t t h e c e n t r o i d of t h e gaged a r e a
i n u n i t s of c f s / s q . m i .
p r e p a r i n g t h e maps:
A t o t a l of 309 s t a t i o n r e c o r d s w e r e u s e d i n
96 complete r e c o r d s t a t i o n s i n t h e b a s i n , 4 1
p a r t i a l r e c o r d s t a t i o n s i n t h e b a s i n , and 67 complete r e c o r d s t a t i o n s
o u t s i d e of t h e b a s i n f o r t h e U n i t e d S t a t e s ; and 28 complete r e c o r d
TABLE 21.
Lake
Total
Land
Basin
Area
(mi
>
Amount of l a n d a r e a i n t h e G r e a t Lakes b a s i n
f o r which s t r e a m f l o w r e c o r d s a r e a v a i l a b l e
f o r t h e p e r i o d 1946 t h r o u g h 1 9 6 5 ~ .
Canada
Area
completeb p a r t i a l C
2 d
(mi21d (mi )
(mi )
Superior
48,180
Michigan
45,460
Huron
49,610
34,180
11,976
6,940
4,164
Erie
22,560
Ontario
S t . Clair
United S t a t e s
30,980
6,845
11,318
Area
>
(mi 2 d
1
P e r c e n t of
Sub-basin gaged
completeb p a t i a l C
2 d
2 d
(mi)
(mi 1
1
completeb p a r t i a l C
I
j
1
17,200
6,751
2,084
28.2
27.8
45,460
27,867
5,616
61.3
12.4
11,692
15,430
7,559
1,875
39.4
27.3
519
1,371
2,776
1,394
395
27.6
25.4
4,715
1,360
1,406
17,845
12,755
929
62.6
10.4
1
27,280
11,950
4,850
1,859
15,330
10,608
471
56.7
8.5
200,030
85,989
25,550
27,646
114,041
66,934
11,370
46.2
19.5
1
J
1
1
Total
1
a
Complied from S u r f a c e Water D a t a f o r O n t a r i o , I n l a n d Waters Branch, Department o f Energy,
Mines and R e s o u r c e s , Canada, and Water Supply P a p e r s , G e o l o g i c a l Survey, U.S. Department
of I n t e r i o r , f o r y e a r s 1946 t h r o u g h 1965.
b ~ r e af o r which r e c o r d s a r e a v a i l a b l e f o r t h e complete p e r i o d 1946 t h r o u g h 1965.
C
Area f o r which r e c o r d s a r e o n l y a v a i l a b l e f o r p a r t of t h e p e r i o d 1946 t h r o u g h 1965.
2
2
dl s q u a r e m i l e ( m i ) = 2.59 s q u a r e k i l o m e t e r s (km )
.
.
1
.
s t a t i o n s i n t h e b a s i n , 6 1 p a r t i a l r e c o r d s t a t i o n s i n t h e b a s i n , and
1 6 complete r e c o r d s t a t i o n s o u t s i d e of t h e b a s i n f o r Canada.
Fig. 3
shows t h e a r e a s f o r which streamflow r e c o r d s were used i n t h i s s t u d y
Runoff i s o p l e t h s were t h e n i n t e r p o l a t e d from t h e p l o t t e d
v a l u e s a t s p a c i n g s determined from t h e range of v a l u e s f o r each map.
The e x t r a p o l a t i o n of t h e i s o p l e t h s o v e r t h e ungaged a r e a s was made
a f t e r t a k i n g i n t o c o n s i d e r a t i o n t h e d i s t r i b u t i o n of p r e c i p i t a t i o n a s
i n d i c a t e d by t h e p r e c i p i t a t i o n map f o r t h a t month.
The r u n o f f
i s o p l e t h s f o r J u l y , 1964, a r e p r e s e n t e d i n F i g . 4.
The amount of
r u n o f f from t h e ungaged a r e a s was then o b t a i n e d by p l a n i m e t e r i n g t h e
a r e a s between t h e i s o p l e t h s .
The t o t a l r u n o f f i s t h e sum of t h e run-
o f f from t h e ungaged a r e a s and t h e r u n o f f from t h e gaged a r e a s .
amount of r u n o f f i n t o each l a k e i n u n i t s of c f s / s q . m i .
The
of s u r r o u n d i n g
l a n d a r e a f o r each month of t h e p e r i o d 1946 through 1965 i s p r e s e n t e d
i n T a b l e s 22 through 27.
TI
n
C r
C H
0
>
2
w
3
an
a m
P W
m m
z +
m
zr-TI
011
0
-
P m
m w
H
1
0
0
00
m-rl
n
w
- m
an
m o
u l w
0
0
m o
n -rl
-w
a m
m n
w
ulo
0
TABLE 22.
Jan.
Feb.
Runoff i n t o Lake S u p e r i o r ( c f s / s q . m i
Mar.
Apr.
May
June
July
a
Aug.
of s u r r o u n d i n g l a n d a r e a )
Sept.
Oct.
Nov.
Dec.
Ave
.
TABLE 23.
Jan.
Feb.
1946
1.11
0.77
MEAN
0.71
0.70
Runoff i n t o Lake Michigan (cf.s/sq.mia of s u r r o u n d i n g l a n d a r e a )
Apr.
May
June
July
Aug.
Sept.
Oct.
Nov.
Dec.
Ave.
1.83
0.90
0.70
0.80
0.61
0.43
0.44
0.42
0.62
Om59
Om77
1.07
1.50
1.14
0.75
0.60
0.49
0.52
0.59
0.67
0.67
0.78
Mar.
88'0
E6'0
00'1
L8'0
1
LO'1
9
8E-1
1
0
'79'0
'76'0
90'1
1
2
LL'O
28'0
06'0
+6'0
' 7 1
0
5
E9'0
99'0
+9'0
1'71
OE'1
88'0
'7L'O
66'0
0
8'7'0
05'0
0'7'0
2'7'0
85'0
6L'O
5 2 1
0
58'0
56'0
'aAV
1
8E01
69'0
88'0
ZE'1
9E'O
29'0
86'1
1
'=aa
OL'O
1
0
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.' ~ O N
+9'0
80'1
19'0
LZ'O
0
OL'O
55'0
96'0
0'7'0
59'0
89'0
OE'O
00'2
5E'O
0
62'1
6E'O
ZE'O
LE'O
---
'330
0
08'0
L'7'O
OE'O
LZ'O
99'0
0
25'0
62'0
£5'0
29'0
EZ'O
0
LE'O
05'0
9'7'0
' 7 0
81'0
EE'O
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2+'0
05'0
82'0
OE'O
92'0
£5'0
09'0
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92'0
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0'7'0
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e
19'0
1E'O
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1E'O
1L'O
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1'7.0
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5
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82'0
29'0
'79'0
09'0
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' 7 0
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0
Ic:~nr
98'0
6'7 ' 0
'7'7 ' 0
09'0
69'2
'76'1
1E'Z
9
96'1
2
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9'7'1
1
5
58'0
L5'1
09'1
65 ' 0
18'1
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d1'E
O f'1
LE'O
58'0
85'0
LZ'I
bg'0
05'0
01'2
00'1
EE'1
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GROUNDWATER
There i s some d i s c h a r g e from groundwater i n t o l a k e s a l o n g t h e
s h o r e s and t h e r e may b e seepage l o s s e s from t h e l a k e s t o deep a q u i f e r s .
However, t h e s e have u s u a l l y been ignored o r assumed t o be v e r y s m a l l o r
compensating.
Groundwater d i s c h a r g e s i n t o Lake Michigan from t h e g e n e r a l
a r e a e a s t of t h e M i s s i s s i p p i - G r e a t Lakes d i v i d e .
The d i s c h a r g e i s mainly
by t h e b a s e flow of streams t h a t e n t e r t h e l a k e and by bank seepage and
underflow a l o n g t h e l a k e s h o r e .
S i n c e an impermeable g l a c i a l till under-
l i e s much of t h e s h o r e a r e a , a v a l u e f o r bank seepage and underflow a s
3
low a s 800 c f s (22.4 m / s e c ) f o r 3500 m i l e s (5635 km) of s h o r e may b e
r e a s o n a b l e under p r e v a i l i n g c o n d i t i o n s (Bergstrom and Hanson, 1962).
H a e f e l i (1970) concluded t h a t t h e c o n f i g u r a t i o n of t h e w a t e r
t a b l e between Lake Simcoe and Lake O n t a r i o corresponds g e n e r a l l y w i t h
t h e topography.
P i e z o m e t r i c , hydrogeochemical and mathematical a n a l y s i s
demonstrated t h e non-existence of major seepage from Lake Simcoe i n t o
t h e Lake O n t a r i o b a s i n .
The groundwater d i v i d e c o n i n c i d e s approximately
w i t h t h e b a s i n boundary i n t h e q u a n t e r a r y d e p o s i t s a s w e l l a s i n t h e
d i f f e r e n t u n d e r l y i n g bedrock formations.
Hence, groundwater was considered t o be n e g l i g i b l e i n t h i s
study.
NET BASIN SUPPLY
The p r e c i p i t a t i o n , e v a p o r a t i o n , r u n o f f , and groundwater t e r m s
i n Eq. 1 a r e u s u a l l y combined i n t o a s i n g l e t e r m which i s c a l l e d t h e n e t
b a s i n s u p p l y , NBS, t o t h e l a k e .
The w a t e r b a l a n c e e q u a t i o n c a n t h e n b e
written
The v a l u e of t h e n e t b a s i n s u p p l y t e r m i n Eq. 4 can b e d e t e r m i n e d as t h e
sum of t h e p r e c i p i t a t i o n , e v a p o r a t i o n , r u n o f f , and groundwater c o n t r i b u t i o n s t o t h e l a k e , o r i t can b e d e t e r m i n e d as t h e r e s i d u a l a f t e r t h e v a l u e
of t h e o t h e r t e r m s i n Eq. 4 h a v e been d e t e r m i n e d .
N e t B a s i n Supply as a Sum of H y d r o l o g i c Components
S i n c e t h e groundwater c o n t r i b u t i o n i s assumed t o b e n e g l i g i b l e ,
t h e n e t b a s i n s u p p l y t o e a c h l a k e c a n b e computed as
The n e t b a s i n s u p p l y v a l u e s , which are o b t a i n e d when t h e p r e c i p i t a t i o n ,
e v a p o r a t i o n , and r u n o f f amounts are s t a t e d i n u n i t s of c f s and s u b s t i t u t e d
i n t o Eq. 5 , are l i s t e d i n T a b l e s 2 8 t h r o u g h 31.
The n e t b a s i n s u p p l y f o r
Lake Michigan and Lake Huron i s r e p o r t e d as though t h e s e l a k e s w e r e a
s i n g l e lake.
These l a k e s are c o n s i d e r e d as one l a k e b e c a u s e t h e boundary
between them i s d i f f i c u l t t o e s t a b l i s h and t h e f l o w from Lake Michigan
t o Lake Huron c a n n o t b e a c c u r a t e l y d e t e r m i n e d .
Therefore, t h e n e t basin
s u p p l y v a l u e s a v a i l a b l e f o r comparison a r e f o r t h e combined l a k e s .
TABLE 28.
1946
1947
b
J-Mc
C-F
Net b a s i n s u p p l y f o r Lake S u p e r i o r (1000 c f s a )
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
S e p t . Oct.
5
2
-15
17
99
77
111
118
139
113
221
147
164
123
109
7R
80
73
Nov.
Dec.
Ave.
82
79
11
45
-39
-19
81
71
J-M
C-E
-60
-16
-23
-2
8
33
147
149
227
234
310
223
188
141
111
95
60
59
33
25
7
-12
-46
-35
80
1948
J-M
C-E
-47
-39
-42
-17
29
65
221
176
108
147
144
91
222
101
110
91
25
22
-6
5
59
30
-19
2
67
56
1949
J-M
C-E
-24
-11
-27
-7
13
28
108
124
190
15R
248
175
310
162
94
68
35
42
65
54
-17
2
-59
-17
79
65
lQ50
J-M
C-E
-10
2
-1
11
22
61
112
201
294
266
254
248
264
179
156
126
70
98
65
88
18
44
-18
-9
103
110
1951
J-M
C-E
-28
-21
33
57
63
118
213
204
218
199
254
175
179
144
173
129
166
143
112
89
-20
35
-16
7
113
107
1952
J-M
C-E
-12
3
-14
3
40
53
183
130
155
15P
258
182
308
193
198
142
59
6
-38
-52
-1
-7
0
-14
95
67
1953
J-M
C-E
-24
-10
9
22
50
68
122
144
235
224
285
249
266
172
149
106
43
44
6
-5
14
-8
-26
-6
95
84
1954
J-M
C-E
-26
-23
34
3
11
51
205
202
242
261
242
178
152
110
101
55
94
45
39
29
-25
-8
-28
-38
87
72
1955
J-M
C-E
-26
-34
-18
11
25
76
187
143
155
149
175
115
245
112
138
90
27
47
56
57
-26
29
-55
-9
74
66
1956
J-M
C-E
-22
-18
-40
-19
-25
26
84
108
158
147
214
167
210
141
143
87
51
32
5
8
-10
-2
-38
-27
61
55
1957
J-M
C-E
-77
-26
-16
19
16
57
148
135
114
154
196
157
186
123
44
65
77
36
-9
17
23
7
-44
-13
55
61
1958
J-M
C-E
-14
-9
-61
8
28
29
157 237
135
1 5 2 1 3 7 1 1 4
70
82
24
36
-7
-46
1 8 - 2 0
59
60
1959
J-M
C-E
-77
-20
-63
-17
22
34
87
120
245
184
204
158
218
121
260
151
150
138
76
69
-83
1
-22
-22
86
77
1960
J-M
C-E
-44
2
-38
-14
-25
25
225
195
254
233
173
155
201
98
138
75
79
44
17
24
-2
11
-87
-20
75
69
1961
J-M
C-E
-76
-19
35
60
110
134
151
148
158
111
191
77
107
66
137
67
35
43
-8
22
-48
-8
66
60
1962
J-M
C-E
-84
-26
-25
-22
15
29
89
129
219
170
142
127
162
87
161
100
90
76
22
-9
-45
-26
-73
-22
57
52
1963
J-M - 1 0 0
C-E
-30
-80
7
7
75
153
133
105
155
249
153
205
111
127
63
64
38
52
20
-48
7
-82
-33
55
58
1964
J-M
C-E
-42
-27
-40
-2
-9
29
188
178
290
228
203
162
210
130
157
118
139
98
61
52
14
30
-19
10
97
84
1965
J-M
C-E
-68
9
-42
-4
10
47
137
141
270
190
166
161
194
138
183
114
166
113
49
90
4
60
-8
38
89
92
MEAN
MEAN
J-M
C-E
-43
-15
-24
3
22
52
146
147
192
181
213
164
216
130
140
97
84
65
37
36
-7
14
-39
-13
79
72
-4
14
95
79
6 8 1 0 5
75
3
a 1 c f s = 0.028 m / s e c
J-M d e n o t e s v a l u e s computed by Jones and Meredith
C-E denotes v a l u e s r e p o r t e d by Corps of Engineers (U.S. Army Engineer D i v i s i o n , 1 9 6 5 ~ )
except v a l u e s f o r September, 1964, through December, 1965, which were computed a s
described i n text.
TABLE 29.
N e t b a s i n s u p p l y f o r Lake Michigan-Huron (1000 c f s a )
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept. Oct.
Nov.
Uec.
Ave.
13
45
-37
67
68
170
451.
350
404
370
280
314
234
160
64
61
-23
43
-26
-7
-35
- 1
-23
-12
115
129
-24
39
79
84
1947
J-M
C-E
1948
J-M
C-E
-54
-22
12
79
249
253
335
334
218
221
206
141
107
106
-30
9
-87
-8s
-90
-77
104
17
1949
J-M
C-E
33
h l
79
132
110
159
199
225
13s
181
249
180
180
116
23-157
-28
-64
-16
-43
-78
-53
37
53
67
76
1950
J-M
C-E
106
149
64
134
177
215
327
310
234
238
209
201
182
161
9
84
-23
26
18
-14
-73
72
13
72
99
133
1951
J-M
C-F
40
Rh
77
167
167
291
491
367
240
769
197
212
261
177
127
95
8
92
184
110
75
1lQ
65
106
161
177
1952
J-M
C-E
107
132
56
154
150
225
381
302
229
714
226
217
337
212
101
93
-74
-72
-278
-110
44
47
78
115
121
J-M
C-E
64
63
104
126
217
217
751
281
307
737
245
714
199
150
47-136
37
-47
-69
-66
1954
J-M
C-E
-43
-4
115
I06
94
216
377
283
19R
795
383
253
173
137
60
54
55
131
227
156
1956
J-M
C-E
-51
-2
9
49
75
145
719
254
794
777
222
242
222
176
99
83
-59
-15
-15
-74
-A3
J-M
C-F
-74
-15
20
51
64
178
777
204
237
736
268
260
230
167
56
44
5
-
0
70
1
1958
J-M
C-E
-1
85
-64
50
69
hR
109
107
24
104
123
123
124
119
-47
64
3
0
1959
J-M
C-E
-47
-4
7
64
110
216
356
300
790
748
126
162
170
98
146
89
1960
J-M
C-E
79
157
34
76
31
125
452
37R
463
427
259
786
218
196
J-M
C-E
-55
-39
26
85
170
156
187
ivn
111
187
205
157
1967
J-M
C-E
-76
17
5
87
117
181
166
745
763
716
1963
J-M
C-E
-54
-1
-84
48
122
165
22s
253
J-M
C-E
-24
-18
-53
35
57
63
1965
J-M
C-E
-48
77
85
107
MFAN
MFAN
J-M
C-E
4
46
25
93
1953
1957
1961
1964
9
-9
97
Yh
-.?A
hO
136
147
-111
14
77
100
r,?
3
91
ion
-56
-30
-61
-45
-111
-73
9
51
-38
84
87
74
38
he
103
107
10Y
175
75
99
20
11
-15
-23
189
134
14
102
76
74
-a&
179
161
127
91
22
69
-71
25
37
-54
-86
-59
-76
-76
55
70
238
190
175
147
15.3
11s
40
55
-54
-1.6
-60 -105
- 1
-4n
-127
-50
40
71
237
191
190
717
80
132
138
07
52
52
94
17
-65
-39
-51
70
59
79
171
327
310
285
736
127
164
87
105
114
86
233
82
-31
09
78
70
1.15
93
116
133
170
178
289
264
237
736
206
193
173
134
45
55
-21
9
-11
-2
-15
7
-15
31
86
104
cz
-3A
-43
70
87
1.7
-75
7 5 -ill
I.
0
18
-6
-40
-5
-30
in
~ I Q
128
144
SH
93
55
-
a 1 cfs
J-M
= 0.028
3
m /sec
d e n o t e s v a l u e s computed by Jones and Meredith
C-E d e n o t e s v a l u e s r e o o r t e d by Corps of E n g i n e e r s (U.S. A m y Engineer D i v i s i o n , 1965c)
e x c e p t v a l u e s f o r September, 1964, through December, 1965, which were computed a s
described i n t e x t .
TABLE 30.
N e t b a s i n supply f o r Lake E r i e (1000 c f s a )
Jan.
Feb.
Mar.
Apr.
May
June
July
Aug.
Sept. Oct.
Nov.
Dec.
Ave.
C-E
7
-1
4
56
80
80
5
4
31
60
43
65
4
-1
-31
-50
-35
-3
-25
-37
-23
-7
0
-2
5
13
1947
J-M
C-E
61
40
-6
7
46
63
134
13R
79
105
62
78
20
7
18
4
-22
-30
-10
-34
1 - 5 7
11
62
30
35
1948
J-M
C-E
6
-21
35
54
114
105
78
67
49
7R
26
32
11
-5
-16
-1
-34
-39
-38
-22
9
10
10
14
21
22
1949
J-M
C-E
74
30
62
82
44
70
44
28
21
43
-0
18
9
6
-21
-42
-30
-16
-17
-20
-27
-2
23
35
15
19
1950
J-M
C-E
134
151
71
43
86
132
100
117
19
21
3
33
24
15
-12
-7
3
-21
11
15
41
53
40
46
1951
J-M
C-E
63
54
79
74
97
94
89
Ah
34
50
18
29
10
1
-30
-24
-30
-44
-13
-12
-6
-3
36
53
29
30
1952
J-M
C-E
105
103
50
68
7R
74
A7
81
23
48
-10
11
-6
-20
-19
-27
-80
-91
-12
12
12
14
1R
21
1953
J-M
C-E
39
27
16
30
64
55
40
45
54
63
8
10
-18
-21
-42
-43
-38
-48
-22
-10
1954
J-M
C-E
16
20
57
75
74
92
122
112
-9
3
7
17
-17
-22
-23
-11
-34
-37
65
50
-9
4
17
17
22
26
1955
J-M
C-E
26
35
41
34
91
92
$4
6R
1
16
-13
-7
8
-12
17
-R
-33
-34
6
-13
-6
-4
2
15
19
15
1957
J-M
C-E
20
28
41
63
33
24
146
123
27
48
39
40
37
28
-27
-29
-6
-14
-34
-34
-10
-7
47
49
26
26
1958
J-M
C-E
4
16
-9
9
35
-10
57
43
-2
2
16
43
38
43
-35
-26
-6
-76
-15
18
7
8
1959
J-M
C-E
55
75
71
90
67
87
93
82
53
59
-10
10
7
0
-5
-12
-15
-24
8
-13
0.
-11
47
71
31
34
1960
J-M
C-E
54
46
39
45
17
40
100
70
49
61
22
51
2
8
-4
0
-29
-39
-55
-72
-27
-15
-26
-28
12
14
1961
J-M
C-E
-13
8
45
36
65
75
132
135
11
37
24
35
23
24
13
0
-4
-19
-34
-47
-16
-5
-10
-25
19
21
1962
J-M
C-E
19
41
19
36
59
62
33
17
4
11
10
17
1
-20
-3
-15
-33
-30
-19
-32
-11
5
-0
-6
6
7
1963
J-M
C-E
-17
3
93
1.01
47
6R
-4
12
-2
1
3
-13
-25
-27
-48
-48
-36
-24
-23
-19
-18
-41
-4
-1
1964
J-M
C-E
18
23
-2
0
81
91
107
81
14
16
-5
8
-0
-8
5
-2
-46
-43
-43
-37
-34
-29
-3
22
8
10
1965
J-M
C-E
38
14
43
A4
61
67
69
47
28
33
6
-3
1
-7
1
-12
-7
-32
-25
-30
-7
-18
36
40
20
15
MEAN
MEAN
J-M
C-E
36
34
35
48
69
75
82
75
2R
43
13
26
10
2
-6
-13
-24
-29
-22
-26
-15
-11
11
19
18
20
1946
J-ME
-15
-19
-6
-21
1
-3
2
-4
2
-7
-1
-6
-11
-18
8
7
3
a 1 c f s = 0.028 m / s e c
J-M denotes values computed by Jones and Meredith
C-E denotes values reported by Corps of Engineers (U.S. Army Engineer Division, 1 9 6 5 ~ )
except values f o r September, 1964, through December, 1965, which were computed as
described i n t e x t .
TABLE 31.
b
Net b a s i n s u p p l y f o r Lake O n t a r i o (1000 c f s a )
Jan.
Feb.
Mar.
22
32
19
40
75
RP
1946
J-M
C-E
1947
J-M
C-E
47
66
21
41
64
74
1948
J-M
C-E
-1
15
25
42
1949
J-M
C-E
40
54
1950
J-M
C-E
1951
Apr.
May
Aug.
41
49
35
38
5
12
1
0
130
144
10R
109
109
112
61
59
102
112
RR
R7
64
71
35
41
52
59
42
52
69
73
21
33
63
82
27
42
43
68
87
114
J-M
C-E
46
53
61
69
97
103
1952
J-M
C-E
51
63
48
48
1953
J-M
C-E
26
33
1954
J-M
C-E
1955
Sept. Oct.
Dec.
Ave.
12
23
11
17
15
22
27
29
14
10
3
-5
12
-5
-1
7
12
10
48
57
17
21
4
2
-11
-13
6
2
34
75
12
3
31
34
6
20
-11
-27
-15
-9
9
1
7
-2
35
39
19
27
36
37
31
36
27
24
22
16
-12
-7
19
17
19
35
31
47
33
43
150
142
45
4R
37
45
34
44
3
1
0
4
8
0
21
77
40
40
45
48
70
78
102
101
48
67
18
27
11
14
-4
0
-4
-1
-22
-21
71
9
?8
77
30
34
20
29
67
R0
51
51
82
93
26
30
1
17
-1
4
-3
-3
-3
-13
1
-1
13
18
24
9
16
73
80
hh
77
114
111
44
60
35
42
-9
3
7
5
-1
12
39
33
34
33
40
76
37
41
J-M
C-E
71
35
26
77
104
106
109
101
35
37
47
19
-0
7
13
17
-71
-11
64
68
17
17
17
36
6
jh
J-M
C-F
9
21
31
29
70
77
131
178
89
104
37
36
9
23
8
21
2
o
3
-7
2
-3
37
78
35
39
1957
J-M
C-f
25
29
39
37
49
57
79
64
48
45
44
46
27
22
1.7
7
-10
-72
7
10
46
34
29
26
1958
J-M
C-F
13
12
14
20
53
53
A9
76
30
38
32
36
29
17
15
3
28
77
14
-2
8
16
5
12
27
25
1959
J-M
C-E
31
31
32
43
65
73
133
I30
40
56
19
26
18
25
1
-1
-16
-12
22
13
%R
21
71
68
147
39
1960
J-M
C-E
34
37
56
61
28
34
174
157
95
t37
46
52
9
10
4
-14
1 - 2 1
0
-11
15
-6
-8
3h
-16
37
J-M
C-E
-3
-6
35
38
65
67
107
R?
67
61
63
51
33
72
19
1
4
-17
17
Lt.
17
-0
J-M
C-F
13
16
I R
26
57
56
87
P4
47
30
19
18
-8
8
1
16
-4
3
11
10
15
18
11
9
25
1963
J-M
C- F
-3
1
-2
5
63
44
97
95
53
h l
14
1R
13
13
70
1R
-15
-1.4
-9
-11
33
70
10
1
23
24
1964
J-M
C-F
19
22
h
15
77
79
84
R3
43
51
18
24
14
17
11
7
-71
-19
-13
-15
-3
4
13
17
21
24
1965
J-M
C-E
R
17
53
55
41
49
R7
79
37
36
22
26
12
10
17
17
19
4
5
18
40
47
40
40
31
37
MEAN
MFAN
J-M
C-E
24
31
33
40
65
72
100
96
53
59
35
37
15
19
6
5
-3
-3
9
3
It
15
74
73
31
33
1961
19h?
a 1 c f s = 0.028
,
R
-13
-15
-
Nov.
4
h
1956
2 6
25
June July
3
4
28
45
tj
77
m3 / s e c
J-M d e n o t e s v a l u e s computed by J o n e s and M e r e d i t h
C-E d e n o t e s v a l u e s r e p o r t e d by Corps of E n g i n e e r s (U.S. Army E n g i n e e r D i v i s i o n , 1 9 6 5 ~ )
e x c e p t v a l u e s f o r September, 1964, t h r o u g h December, 1965, which were computed a s
described i n text.
Net Basin Supply a s a R e s i d u a l
Equation 4 can be r e w r i t t e n such t h a t
NBS = A S
- I+OTD
(6)
The v a l u e of t h e change i n s t o r a g e term i s c a l c u l a t e d from t h e a r e a of t h e
l a k e and t h e measured change i n t h e l e v e l of t h e l a k e o v e r t h e p e r i o d of
time.
The v a l u e of t h e i n f l o w , o u t f l o w , and d i v e r s i o n terms a r e determined
from s t r e a m gaging r e c o r d s and flow r a t i n g c u r v e s .
The Corps of Engineers
(U.S. Army Engineer D i v i s i o n , 1965c) used Eq. 6 t o d e t e r m i n e t h e n e t b a s i n
s u p p l y v a l u e s f o r t h e p e r i o d J a n u a r y , 1900, through August, 1964, f o r a l l
of t h e l a k e s .
The v a l u e s f o r J a n u a r y , 1946, through August, 1964, a r e
l i s t e d i n T a b l e s 28 through 31.
The end-of-period
s t a g e s used by t h e Corps of Engineers (U.S.
Army Engineering D i v i s i o n , 1965c) t o compute t h e amount o f change i n s t o r a g e f o r each month f o r Lakes S u p e r i o r and Michigan-Huron were d e r i v e d by
a v e r a g i n g t h e monthly mean l a k e s t a g e s f o r two c o n s e c u t i v e months.
The
d a i l y mean w a t e r l e v e l a t a l a k e l e v e l gage i s o b t a i n e d by a v e r a g i n g t h e
24 i n s t a n t a n e o u s h o u r l y r e a d i n g s of t h e day.
The monthly mean w a t e r l e v e l
i s t h e a v e r a g e of t h e d a i l y means f o r t h e month (U.S. Army Engineer Divi-
s i o n , 1965b).
A d i f f e r e n t method was used t o determined t h e end-of-period
s t a g e s f o r Lakes E r i e and O n t a r i o .
The mean of t h e Cleveland gage f o r two
days p r i o r and two days f o l l o w i n g t h e end of t h e month was used f o r t h e
end-of-period
l e v e l f o r Lake E r i e (U.S. Army Engineer D i v i s i o n , 1 9 6 5 ~ ) .
The end-of-period
l e v e l f o r Lake O n t a r i o was determined by s u p e r i m p o s i t i o n
of t h e d a i l y mean s t a g e s r e c o r d e d a t f o u r gages on t h e l a k e (U.S. Army Engineer Division, 1 9 6 5 ~ ) .
W
e t h e n used Eq. 6 t o c a l c u l a t e t h e n e t b a s i n s u p p l y v a l u e s f o r
September, 1964, through December, 1965.
T a b l e s 28 through 31.
These v a l u e s a r e a l s o l i s t e d i n
The i n f l o w , o u t f l o w , d i v e r s i o n , and s t a g e d a t a were
s u p p l i e d by t h e Lake Survey C e n t e r ( p e r s o n a l communication, 1971).
end-of-period
The
l e v e l s used t o compute t h e amount of change i n s t o r a g e f o r
each month were computed a s t h e a v e r a g e of t h e monthly mean w a t e r l e v e l f o r
two c o n s e c u t i v e months a t t h e gage a t P o i n t I r o q u o i s , Michigan, f o r Lake
S u p e r i o r and a t t h e gage a t Harbor Beach, Michigan, f o r Lakes MichiganHuron.
The end-of-period
l e v e l s f o r Lake E r i e were determined by t h e same
procedure a s used by t h e Corps of Engineers.
above.
The procedure i s d e s c r i b e d
The mean of t h e Oswego, New York, gage r e a d i n g f o r two days p r i o r
and two days f o l l o w i n g t h e end of t h e month was used a s t h e end-of-period
l e v e l t o compute t h e amount of change i n s t o r a g e f o r each month f o r Lake
Ontario.
DISCUSSION OF RESULTS
The average n e t b a s i n s u p p l y v a l u e s computed f o r t h i s s t u d y a r e
compared i n Fig. 5 w i t h t h e average of t h e n e t b a s i n supply amounts r e p o r t e d
by t h e Corps of Engineers f o r t h e p e r i o d 1946 through 1965.
The 20 y e a r
mean n e t b a s i n supply computed i n t h i s s t u d y f o r Lake S u p e r i o r i s approximately 9 p e r c e n t g r e a t e r t h a n t h e average of t h e v a l u e s r e p o r t e d by t h e
Corps of Engineers.
The 20 y e a r mean n e t b a s i n supply v a l u e s computed i n
t h i s s t u d y f o r Lakes Michigan-Huron,
E r i e , and O n t a r i o a r e r e s p e c t i v e l y
approximately 17, 10, and 6 p e r c e n t l e s s t h a n t h e average of t h e v a l u e s
r e p o r t e d by t h e Corps of Engineers.
The 20 y e a r t o t a l n e t b a s i n supply
f o r a l l l a k e s i s o n l y about 6% p e r c e n t l e s s than t h a t r e p o r t e d by t h e
Corps of Engineers.
There i s a c l o s e r agreement between t h e monthly n e t b a s i n s u p p l y
v a l u e s computed i n t h i s s t u d y and t h o s e r e p o r t e d by t h e Corps of Engineers
f o r Lakes E r i e and O n t a r i o than t h e r e i s f o r Lakes S u p e r i o r and MichiganHuron.
We b e l i e v e t h a t p a r t of t h e d i f f e r e n c e between t h e monthly v a l u e s
computed i n t h i s s t u d y and t h e v a l u e s r e p o r t e d by t h e Corps of Engineers
f o r Lakes S u p e r i o r and Michigan-Huron i s due t o t h e method of d e t e r m i n i n g
t h e end-of-period
l e v e l s f o r computing t h e monthly amount of change i n
storage i n the lake.
The end-of-period
l e v e l s f o r Lakes S u p e r i o r and
Michigan-Huron were determined by averaging t h e mean w a t e r l e v e l s f o r
two c o n s e c u t i v e months.
I n c o n t r a s t t h e end-of-period
l e v e l s f o r Lakes
O n t a r i o and E r i e were determined from d a t a f o r only one o r f o u r days n e a r
t h e end of t h e month.
The b e s t agreement i s f o r Lake O n t a r i o f o r which
d a t a from s e v e r a l gages f o r t h e l a s t day of t h e month a r e used t o determine t h e end-of-period
level.
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Waters of t h e G r e a t Lakes a r e u t i l i z e d a l o n g t h e l a k e s h o r e s and
i n t h e l a n d d r a i n a g e a r e a f o r many p u r p o s e s .
Any consumptive u s e i n t h e
l a n d d r a i n a g e a r e a would have t h e e f f e c t o f r e d u c i n g t h e amount of w a t e r
which would o c c u r a s s u r f a c e r u n o f f i n t o t h e l a k e .
The consumptive u s e of
w a t e r i n t h e Ohio p o r t i o n o f l a n d a r e a t r i b u t a r y t o Lake E r i e h a s been
e s t i m a t e d t o b e about 2 p e r c e n t of t h e s u r f a c e r u n o f f f o r t h i s a r e a (U.S.
Army E n g i n e e r D i v i s i o n , 1965b).
T h i s amounts t o o n l y a b o u t 220 c f s
3
(6.2 m / s e c ) which would have a n i n s i g n i f i c a n t e f f e c t on t h e . n e t b a s i n
3
s u p p l y v a l u e s which a r e computed i n u n i t s of 1000 c f s (28 m / s e c ) .
One f a c t o r which h a s n o t been c o n s i d e r e d i s t h e e f f e c t of t h e r m a l
e x p a n s i o n of w a t e r on t h e l a k e l e v e l s .
D e r e c k i (1964) e s t i m a t e d t h a t t h e r e
would b e a n e x p a n s i o n o r c o n t r a c t i o n of a b o u t 1 cm of d e p t h on a l a k e f o r a
6 " i~n c r e a s e o r d e c r e a s e i n t h e w a t e r t e m p e r a t u r e .
Monthly t e m p e r a t u r e
changes of t h i s magnitude o c c u r on each l a k e d u r i n g t h e l a t e s p r i n g o r
e a r l y summer and f a l l of each y e a r .
The c o n s i d e r a t i o n of t h e r m a l e x p a n s i o n
would change t h e v a l u e s of t h e AS term i n Eq. 6 and would have t h e e f f e c t
of r e d u c i n g t h e n e t b a s i n s u p p l y v a l u e s r e p o r t e d by t h e Corps of E n g i n e e r s
f o r t h e months when t h e t e m p e r a t u r e i s i n c r e a s i n g and i n c r e a s i n g t h e n e t
b a s i n s u p p l y v a l u e s when t h e t e m p e r a t u r e i s d e c r e a s i n g .
The change i n t h e
n e t b a s i n s u p p l y v a l u e s due t o 1 cm change i n l a k e l e v e l i s 11,000 c f s
3
(308 m / s e c ) ,
3
3
16,000 c f s (448 m / s e c ) , 3,500 c f s (98 m / s e c ) , and 2,650 c f s
3
( 7 4 m / s e c ) r e s p e c t i v e l y f o r Lakes S u p e r i o r , Michigan-Huron,. E r i e , and
Ontario.
These changes a r e s i g n i f i c a n t and would have t h e e f f e c t of
b r i n g i n g t h e monthly n e t b a s i n s u p p l y v a l u e s computed f o r t h i s s t u d y and
t h o s e r e p o r t e d by t h e Corps of E n g i n e e r s i n t o c l o s e r agreement f o r Lakes
E r i e and O n t a r i o .
However, i t would i n c r e a s e t h e d i s c r e p a n c y between t h e
monthly v a l u e s f o r Lakes S u p e r i o r and Michigan-Huron.
The y e a r l y a v e r a g e
would n o t change, though, because t h e n e t t e m p e r a t u r e change on a y e a r l y
b a s i s is i n s i g n i f i c a n t .
SUMMARY AND CONCLUSIONS
The amount of p r e c i p i t a t i o n , e v a p o r a t i o n , and r u n o f f i n t o t h e l a k e
from t h e s u r r o u n d i n g l a n d a r e a s h a s been d e t e r m i n e d f o r e a c h of t h e G r e a t
Lakes f o r e a c h month o f c a l e n d a r y e a r s 1946 t h r o u g h 1965.
Even though
Lake S t . C l a i r i s n o t u s u a l l y c o n s i d e r e d a s one of t h e G r e a t L a k e s , t h e
amounts of p r e c i p i t a t i o n on i t and t h e r u n o f f i n t o i t f o r e a c h month of 1946
t h r o u g h 1965 a r e a l s o p r e s e n t e d .
The n e t b a s i n s u p p l y v a l u e s computed f o r t h i s s t u d y a r e r e l a t i v e l y
c l o s e t o t h e v a l u e s r e p o r t e d by t h e Corps of E n g i n e e r s .
The monthly p r e c i p -
i t a t i o n , e v a p o r a t i o n , and r u n o f f v a l u e s p r o v i d e u s w i t h a r a t h e r complete
set of d a t a w i t h which t o b e g i n t o d e v e l o p h y d r o l o g i c models o f t h e l a k e s .
The groundwater c o n t r i b u t i o n t o t h e n e t b a s i n s u p p l y v a l u e s was
assumed t o b e i n s i g n i f i c a n t .
Not much i s known a b o u t t h e groundwater con-
t r i b u t i o n t o t h e l a k e s and t h i s s u b j e c t s h o u l d r e c e i v e f u r t h e r s t u d y .
The e f f e c t of t h e r m a l e x p a n s i o n on l a k e l e v e l s might a l s o b e
f u r t h e r s t u d i e d t o d e t e r m i n e i f t h e n e t b a s i n s u p p l i e s r e p o r t e d by t h e
Corps of E n g i n e e r s s h o u l d b e changed t o a c c o u n t f o r t h i s phenomenon.
F i n a l l y and p r o b a b l y most i m p o r t a n t we f e e l t h a t t h e amount of changes i n
l a k e volumes s h o u l d a l l b e computed u s i n g a c o n s i s t e n t method f o r d e t e r mining t h e end-of-period
lake levels.
I f t h e e f f e c t s of t h e r m a l e x p a n s i o n
and a c o n s i s t e n t method f o r d e t e r m i n i n g t h e end-of-period
lake levels are
u s e d t o d e t e r m i n e t h e amount of change i n s t o r a g e i n t h e l a k e , t h e monthly
n e t b a s i n s u p p l y v a l u e s a s computed i n t h i s s t u d y m i g h t b e a d j u s t e d t o
t h o s e d e t e r m i n e d from Eq. 6 by a d j u s t i n g t h e monthly e v a p o r a t i o n v a l u e s
s i n c e t h e s e a r e f e l t t o b e t h e l e a s t r e l i a b l e of t h e computed v a l u e s .
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