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A STATlSTlCAL ASSESSMENT OF THE RELATIONSHIP OF THE EL NIN0 I SOUTHERN OSCILLATION TU
GREAT LAKES WATER LEVELS
BY
KIMBERLY A. PESKAN
A Thesis Submitted to the Faculty of Graduate Studies and Research
through the Department of Geography in Partial fulfillrnent of the Requirements for
the Degree of Master of Arts at the University of Windsor
GEOGRAPHY DEPARTMENT UNIVERSITY OF WINDSOR
WINDSOR, ONTARIO CANADA N9B 3P4
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ABSTRACT
Water levels and basin data of the Laurentian Great Lakes were related to two major
meteorological indices. Historical fluctuations have lead to suggestions that GLWL fluctuations
are due to clirnate change and increased climatic variability of the local region. Related to
climate change, increased frequency and intensity of the El NinoISouthem Oscillation (ENSO)
phenomenon indicates that Lake Ievel fluctuation may be related. This thesis considers the
relationship between fluctuations of Great Lakes water levels and the El NinoISouthem
Oscillation using data collected h m 1950 to 1999. Water level data and net basin supply data
collected monthly over this time span for Lakes Superior, Michigan-Huron, Erie and Ontario. The
two major rneteorological indices used to study water levels and basin data are the Southem
Oscillation lndex (SOI) and the Multivariate ENSO lndex (MEI) which, were statistically modeled
using Box-Jenkins time series analysis. Time series analysis was used to determine how well
each model could predict the historical pattems in the time series. Additionally, this thesis
attempled to determine how well historical lake levels were described by the Multivariate ENS0
lndex (MEI), which is used to calculate ENSO parameters. Great Lakes net basin suppiy values
(comprising net over-lake precipitation, evaporation, and runoff) were used to detemine whether
the ENSO phenomenon could be attributed to similar variations. The final anaiysis involved
taking the information gained through tirne series analysis, and relating it to physical and
systematic aspects of the Great Lakes water system.
Great Lakes water levels could indeed be satisfactorily characterized by the changes in ENSO
events represented by the Multivariate ENSO Index. Using ME1 as the independent regressor to
water levd data, statistical results are indicative of a system-wide swino of fluctuation, in regard
to extreme weather patterns. It is apparent that ENSO events affect lake levels, despite the
many other factors present within the Great Lakes system. With the peculiar lagged forms of the
Multivariate ENSO lndex when regressed with Lake level data, it appears that there is a temporal
pattern present regarding ENSO events and Great Lakes Water Levels. Thus the present results
suggest that with the introduction of an ENSO event, Lake ievels are shifted most significantly
after 3.5 years, with the exception of Lake Superior, which experiences modifications after 4.5
years. With regard to Lake net basin supply data, it was determined that when regressed against
the Multivariate ENSO Index, a weak relationship between the iwo was apparent.
ACKNOWLEDGEMENTS
i would like to extend the most sincere gratitude to my advisors Dr. P.D. Lavalle and Dr. V.C. Lakhan. Their insight, support, and guidance were pivotal to its success. Their influence and assistance have been constant mainstays throughout rny graduate Hiwlc, as w d l as my entire undergraduate career. For ttiis, I am very appreciative. As well, thank you to Dr. J. Lovett-Doust for being a valuable and thoughtful extemal examiner. Thank you to all of rny friends and family for their continual support ttiroughout my university career.
TABLE OF CONTENTS
PAGE
Abstract Acknowledgements List of Figures List of Tables List of Abbnsviations
iii iv vii W ii ix
CHAPTER
1 .O INTRODUCTION ... ... ... ... ... ...... ..- ... ... ... ... ... ... ... ... ...... ...... .-.... ... ..-... ... ... ... ... ..- ... ..- ...- 1
2.0 REGION OF STUDY .............................. --. - - . . - . . . . ......... . . ......... . . .... 3
2.1 Physical Aspects 2.2 Great Lakes System Flow 2.21 Great Lakes Connecting Channels 2.3 Clirnafic Characteristics 2.31 Latitude and Situation 2.32 Atrnospheric Circulation Patterns 2.33 Impacts of the Great Lakes on Regional Climate 2.4 Resource Management Aspects
3.0 REVIEW OF THE UTERATURE ......... ... ...... ... ... ... .................. ... ... ... ... ... ............ ... .... 14
3.1 History of Great Lakes Water Levels 3.2 Aspects of Great Lakes Water Level Fluctuation 3.3 Factors lnfluencing Water Levels 3.31 Precipitation 3.32 Temperature 3.33 Evaporation 3.34 Runoff 3.35 Great Lakes Circulation 3.4 Net Basin Supply and Outflow 3.5 El Nino, La Nina, and the Southem Oscillation (ENSO) 3.51 The Southem Oscillation lndex (SOI) 3.52 The Multivariate ENSO lndex (ME])
4.0 CONCEPTUAL BASIS OF THE STUDY ..,.... -....- ..... -.. ............... ... ...... ...... ... ... ........... 30
5.0 METHODOLOGY .........~~~..~~.~~.~~-.~~......................... . ....................... 36
5.1 Data: Acquisition and Characteristics 5.2 Data Analysis 5.3 Aspects of Time Series Analysis 5.4 Modeling of the SOI and ME1
6.0 STAl'iSTlCAL RESULTS .... ... ... ... ... ... ..... ... ... ... ..... .. . . . . . . . . . 4 8
Statistical Results Assessmen t of Hypothesis #1 Assessrnent of Hypothesis #2 Assessment of Hypothesis #3 Assessment of Hypothesis #4
DISCUSSION ... ... .. . ... ... ... ... ... ... ...... ... ... ... ... ... ...... ... ... ... ... ... ... ... ... -.- ... ... ... ...... ... ..... 78
7.1 SOI and MEI Modeling 7.2 Hypothesis #l 7.3 Hypothesis #2 7.4 Hypothesis #3 7.5 Hypothesis ##4 7.6 System Responses 7.61 Lake Levet Modeling 7.62 Lake Levels and the Multivariate 7.63 Net Basin Supply
ENS0 Index
8.0 CONCLUSIONS ..............-... -...-............... .... ........ - ............................ 88
8.1 Suggestion for Further Studyïrheoretical Implication 90
REFERENCES.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92 APPENDIXI . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 APPENDIX I l . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 APPENDIX III . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 105 VlTA AUCTORIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 O8
LIST OF FIGURES
FIGURE PAGE
1. The Laurentian Great Lakes and Drainage Basin 2. Great Lakes: Surrounding Areas 3. Standardized Tirne Series Plots of the Great Lakes 1950 - 1999
3.1 Lake Superior 3.2 Lake Michigan-Huron 3.3 Lake Erie 3.4 Lake Ontario
4. The Southern Oscillation Index 1950 - 1999 5. The Mulüvariate ENSO lndex 1950 - 1999 6. A Pion Model 7. Box Jenkins Modeling Approach 8. The Muhafiate ENSO lndex A: ACF and B: PACF 9. Mulüvariate ENSO lndex ARMA (1,0,1) Model - Error 10. The Southern Oscillation lndex A: ACF and 0: PACF 1.1. Souîhern Oscillation lndex AR (Ill ,O) Model- Error 12. Lake Superior Water Level ACF 13. Lake Superior Water Level ARMA Model- &or 14. Lake Michigan-Huron Water Level ACF 15. Lake Michigan-Huron Water Level ARMA Model- Error 16. Lake Superior Water Level and the ME! Mode! ACF - Error 17. Lake Michigan-Huron Water Level and tfie ME1 Model ACF - Error 18. Lake Erie Water Level ACF 19. Lake Erie Water Level AR (1,0,0) Model ACF - B o r 20. Lake f i e Water Level and the ME1 Model ACF - Error 21. Lake Ontario Water Level ACF 22. Lake Ontario AR (2,0,0) Model - Error 23. Lake Ontario and îhe ME1 Model ACF- Error 24. Lake Superior Net Basin Supply ACF 25. Lake Supenor Net Basin Supply Modei ACF - Error 26. Lake Superior Net Basin Suppty and the ME1 Model ACF - Error 27. Lake Michigan-Huron Net Basin Suppiy ACF 28. Lake Michigan-Huron Net Basin Supply Model ACF - Error 29. Lake f i e Net Basin Suppfy ACF 30. lake Erie Net Basin Supply Model ACF - Emr 31. Lake Erie Net Basin Suppiy and oie ME1 Model ACF - Ermr 32. Lake Ontario Net Basin Suppfy ACF 33. Lake Ontario Net Basin Suppiy Model ACF - Eiror 34. Lake Ontario Net Basin Suppfy and the ME1 Model ACF - Emor
vii
LIST OF TABLES
PAGE
1. Phyçicai Characteristics of the Great Lakes 2. Charaderistics of the Great Lakes Connecting Channels 3. Drainage Basin Area to Water Surface Area Ratios 4. ME1 Model ARMA (1,0,1) Statistical Resub 5. SOI Model AR (1,l ,O) Statistical Resutts 6. Statistical Resuk 7. Lake Superior Water Levei Mdef Statistical Resuks 8. Lake Mchigan-Huron Water Levei Model Statistical Resuits 9. Lake Superior and the ME1 Model Statistical Results 10. Lake Michigan-Huron and the MEI Model Statistical Results 11. Lake- Erie Water Level Model Stafjstical Resutts 12. Lake Erie and the ME1 Modei Statistical Resuits 13. Lake Ontario Water Level Model Statistical Resub 14. Lake Ontario and ttie ME1 Model Statistical Resuits 15. Lake Superior Net Basin Supply Model Statisticai Resub 16. Lake Superior Net Basin Suppty and the ME1 Model Staûsticai Resutts 17. Lake Michigan-Huron Net Basin Supply Madel Statisticai Resub 18. Lake Erie Net Basin Supply Model Statistical Resub 19. Lake Erie Net Basin Supply and the ME1 Model Statistical Results 20. Lake Ontario Net Basin Suppiy Model Statistical Resutts 21. Lake Ontario Net Basin Suppiy and the ME1 Model Statistical Resuits
ACF
AIC
AR
ARMA
ARlMA
CDC
COADS
ENS0
GLWL
MA
MEI
MElQn
NBS
PACF
SBC
SOI
SST
LEWt
LMHWL
LOWL
LSWL
Autocorela tion Func bon
Akaike Infortnation Critefion
Auforegressive
Mixed Auforegressive Moving Average
Autoregresive lntegrated Moving Average
Ciimate Diagnostic &n@e
Comprehensjwe Ocean-Ahasphere Data Sef
El NindSouthern Oscillation
Great Lakes Water Levels
Moving Average
MuKivariate ENS0 Index
Denofes the lagged valuelquader (n) of the MEI in sfatisbcacal analysis.
Net Basin Suppiy
Partial Autoconelatbn Function
Schwartz Bayesian Critenon
Soufhern Oscillafion Index
Sea-Surface Tempera ture
Lake Ede Wa fer Level
Lake Michigan-Huron Water Level
Lake Onfario Water Level
Lake Supenor Water Level
1 .O INTRODUCTION
Water is one of the most vital and precious nahiral resources on earth. The long but often
dficun reléonship between humankind and the coastal environment has lead to both lacustrine and
tenestnal degradation, h i l e ttie value of water has continually increased. Since the coaçtal zone is
where land, water and air meet, cuastal components are exceedingk COmplex, and must be treated
accordingly. As a Resource Manager, 1 is wnsidered necessary that any ccastal environment be
thoroughiy studied, properly managed, and kept sustainable. Thus, the most important q~estions
needing answers are considered interdisciplinary in nature, and surpass the definition of the problem
and define the processes, which may rnagnify these problems over the long term.
The North American Great Lakes are a comrnon resource to a great rnany people, bordering
two nations. With increasing global environmental crises, the changes within a system such as the
Great Lakes should be regarded with much care and much caution. In particular, fake lever fluctuation,
whether past, present, or future, have become more sensitive to varÎous physicai factors in which it is
influenced. As a resutt, clirnatic influences are deemed most essential to Lake systern productivity.
With increased frequency and seven'ty of the El NinoISouthern Oscillation (ENSO), me various impacts
on Lake levels has become a paramount concern among researchers.
The Great Lakes-Si Lawrence River Basin is a huge, cornplex, interdependent systern which
has rnany varied, interacting components, most of which are exceedingly complex (Clamen, 1988). It is
one of the wrld's largest freshwater resources, as well as one of the most extensiveiy utilized.
Fluctuation of Great Lakes Water Levels (GLWL) affects dire* and indirectly, most of fhe 40 million
people that live m i n the boundaries of the watershed (Environment Canada, 1999). it is the deviation
of lake levelç to externes that cause profound impacts on the many uses the resource provides. As
such, a study and examination of historical Great Lake water levels may enhance knowledge of the
factors infiuencing the Ruchation. It will also promote necessary rernedial and preventative measures,
and detemine how this valuable and extensive resource will be affected by Mure climate change and
vaiability. The premise of this investigation is that sake levels will fluctuate in the future as aiey have in
the past (Sanderçon, 1993).
The historical fluctuation of lake levels may also be better underaod with respect ta factors
that influence hem. Consequenüy, these fluctuations have been of particula interest among
researchers. Numerous studies have investigated the historical fluctuation of GLWL, h i l e mmpting
to correlate thern vrioi some factor of cfimate variability. This vast and vatuable natural reçource is both
unique and rare and thus demands continued research and investigation. Numerous studies, indicate
the magnlde and significance of ail that the Great Lakes qstem provides.
The purpose of mis thesis is to investigate the statisti~al relationship between Great Lake
water levels, and certain meteorological features of clirnate change such as precipitation, evaporation,
ninoff, temperature and so on. The El NinoISouthern Oscillation (ENSO) phenornenon is mnsidered to
be the lagest factar invohring an inter-annual time-scaie, and clirnatic variability. This is the resutt of
global ocean-atmosphere interactions which resuk in global climate teleconnections (Ji et el., 1994).
Consequently, increased effects of global warming factors suggest a rehirn inuease in the severity and
frequency of ENSO events. The ENSO phenornena is believed to mate short-tm clirnatic changes
to the atrnosphere world-wide, creating atteratjons to factors such as rainfall, evaporatiùn, runoff and
ternperatures. These are the main areas of concern for water ievel fluctuations within the Great Lakes.
The niuo major indices used to measure ENSO are the Southem Oscillation lndex (SOI) and the
Mulüvariate ENSO lndex (MEI). These will be examined in this thesis, in relation to historical lake level
data, and net basin suppty values.
The practicality of this thesis is based on an irnproved understanding of Great Lake water level
fluctuabon and those factors believed to be responsible. Efforts to recognize and incorporate a global
phenornenon, such as ENSO should sîrengthen existing theohes due to its mub-faceted impacts on
physical and societal process. Hence, this research is directed toward ttie uçefulness of statistical fit,
and appücability of the ENSO indices to desaibe GLWL This thesis offers information faci l i ing
responsible decision-making, and the possibility of reliable forecasting tools, to better understanding for
coastal zone management of the Great Lakes region.
2.0 THE LAURENTIAN GREAT LAKES BASIN
2.1 Physical Aspects of the Great Lakes
The Great Lakes (see Figure 1 and Table 1) were fomed by a series of geologiwl Procews
approximately 11, 000 p a r s ago, upon retreat of the glaciers at the end of the ice age. They lie
between the latitudes of 40B01 and 50130' north and between the longitudes of approximably 7920'
and 93f1101 west Its basin is the largest freshwater systern in the wrld, containing approxirnatety 20%
of the world's supply, while occupying an area of 7'70 000 km2 (Craig and Kedand, 1998; minn et el.,
1997; Croley and Hunter, 1994; Sanderson, 1993).
The five major component are Lakes Superior, Hum, Michigan, O n t ~ o , and Erie; ail of which
rnake up a naturai series of storage reservoin linked by connecting channels and strab (Lee, 1993);
and are among the fifteen largest freshwater lakes in the world. Despite the mflad of çtatistics about
the vast volume of water mese lakes contain, the system is not a limiff e s supply of water, and is more
reactive to stressors than many would think. This bounty of water is being used at an unprecedented
rate, and mis will likeiy inwease with tinte.
The Great Lakes (see Figure 2) are bordered by the Canadian Province of Ontario, and eight
US sMes (New York, Pennsylvania, Ohio, Michigan, Indiana, Illinois, Wisconsin and Minnesota).
Donahue (1988) estimates that 20% of the entire U.S. population and 60% of the Canadian population
reside along the Great Lakes Basin. The Great Lakes ecosystern provides fish and wiMlife habitat,
climate control, reereationai opportunities, transportation routes, and water supply for drinking water,
im'gation, and industrial uses (Vigmostadl et d., 1988). As such, there is a large proporb'on of the
population of both couritries whose iivelihoods, heatth and quality of life are infiuenced by the resource.
2.2 The Great Lakes Systern Flows
The Great Lakes basin extends approximateiy 1300km from the western edge of Lake
Supwior to the Mess-Saunders Power Dam on the S t Lawrence river. Lake Superior is the largest,
deepest, coolest, and most-upstream lake in the system. It is approximately 563 km in length, has an
average depth of 147 m, and has a total area of approximateiy 209 800 km2 (GLERL. 1999). Its
watershed is approximatefy 127 700 square kilorneters which is considered srnaIl for a lake its site
(GLERL 1999). It is completeiy regulated, and has hm interbasin diversions of watar into the system.
These diversions coma frorn the Long Lac, and Ogoki Diversions.
Lake Superior has an average annual temperature of 4 O C, which makes winters wamer and
summers cooler (GLERL, 1999). ln winter, temperatures near Supenor can fall to about -35" C, Hihile
inland temperatures reach -43" C (GLERL, 1999). During most winters, Lake Superior is
TABLE 1
Physical Characteristics ûf The Great Lakes
Totals
Length (&j I
, (ml Maximum Depth (ml
Erie 1 73
Huron 176
Breadth (km) Average Depth
Where: Average depth and volume where rneasured at Low Water Datum Land Drainage Area for Lake Huron includes S t Mary's River Lake Erie includes the St Clair-Detoit system Lake Onbno inctudes the Niagara River Shoreline Length values includes islands
Ontario 74
Michigan 176 Elevation (ml
1
563 257 147
406
Voiume (km3) I
Area (km2) Total Area (km2) Shonline length (km 1 Retention Time (YB) OuUet
Shorefine lengm and Retention Tirne totals are greater than the sum of the shareline length for the lakes because they include the connecting channels (excluding the St Lawrence River).
Superior 183
388 92 19
494 190 85
4 920 57 800 118 000
Water Area (km2) 1 Land Drainage
Source: Great Lakes Environmental Research Laboratory (1 999).
31 1 85 86
332 245 59
282
12 100 82 100 127 700
209 800 4 385
191
St Mary's River
3 540 59 600 134 100
175 800 2 633
99
Straits of Mackinaw
244 !
484 25700 78 000
229
193 700 6 157
22
St Clair River
64
1640 18 960 64 030
22 684 244 160 521 830
1 03 700 1 402
2.6
Niagara River1 Welland Canal
82 900 1 146
6
St Lawrence River
765 900 17 017
FIGURE 1
The Laurentian Great Lakes and Drainage Basin
Source: Quinn (1992). Hydraulic Residence limes of the Great Lakes. Journal of Great Lakm Research; l8(l):Z-2
covered Mth ice approxirnately 40 to 90 percent (Beranek. 1999). O p n water is often found in the
centre of the lake due to icebreakage and strong winds. Evaporation is greatest during the monm of
December (Mason, 1998).
The flow pmceeds through various locks, d o m through St Mary's River into Lake Huron,
where it is joined by water flowing tom Lake Uchigan (Crnley, 1986). St Mary's River is sihted at
Lake Superiots southeast corner. It is a crooked 98 km channel of water sepaating Mcchigan's upper
peninsula from the province of Ontario (Beranek, 1999). The St Mary's Rapids are sibiated only 26 km
from the mouth of the river, and Lake Huron (Beranek, 1999).
Water flows from this point into Lakes Michigan and Huron, which are mmrnonly, considered a
single lake, due to h ydmiogic and hydraulic sirnilaribes (Canadian Hydrograp hic Service, 1 999;
Hartmann, 1990). The key to this is the deep and immense straitç of the Mackinaw river that ailows for
a close and interdependent relationship between the two lakes. According to Croley (1986), itç vast
surface area, (togemer- 117 400 km2) provides a 'buffer to flow changes leaving the lake.' Additionaliy,
because boa lakes have the same elevation (176 km), many researchers deem them systematicaliy
similar (GLERL, 1999).
Lake Michigan has the second diversion, where water is diverted at Chicago to the Mississippi
River Basin. The shape of Lake Michigan is long and narmw, (494 km by 190 km), and is considered a
naturai cui-de-sac, meaning that waier entering the lake circulates slowly, and remains for a long time
before 1 leaves me basin through the straits of Mackinaw (Farid et el., 1997). It is important to note
that oniy a relatively small amount of water flows out of the boffleneck at the strait between Michigan
and Huron. Lake Michigan therefore, has a long retention time (Beranek, 1999). Lake Huron serves as
a conveyor of water within the Great Lakes, as it carries water from the upper hNo takes, to the rest of
the systern. Incidentally, Bishop (1990) M e s that water levels of Lake Michigan-Huron have
substantialfy been influenced by various humaninduced actions at the outlets of Lake Huron and the
S t Clair River.
These lakes discharge thmugh the S t Clair River, to shallow Lake S t Clair, and then through
the btroi t River system into Lake Erie. Lake St Clair has a surface area of 692 square kilornekes.
and has an average natural depth of approximately 6.5m (Beranek, 1999). The drop in elevation
betuwen the lakes, through their outlets, and Lake Erie is appmximateiy 2Sm, which creates a
'backwater effecf among the Lakes (Beranek, 1999; Canadian Hydmgraphic Service, 1999; Hartmann,
1990; Cmley 1986). The waterway behwaen Lake Humn and Lake Erie is about 145 km long, and with
the re lae ly small elevation difference, another seerningiy large bottleneck o a u n m i n the overall
qstem (Beranek, 1999). This may mean that the potential amount of water that could flow *in the
system is quite large. However, the relatively srnall and narrow waterways between these lakes cause
fewer and slower movement over a longer period of time. Levels of the lakes on both sidas of the
systern usually result in corresponding levels of the S t Clair River, Lake St Clair, and the Detroit River
(Bishop, 1990; Canadian Hydrographie Service, 1999).
Source:
FIGURE 2
The Great Lakes: Surrounding Areas
Environment Canada and US EPA. In: Great Lakes Information Network (2001). Http://www.great-lakes.net/lakes/
In hm, 95% of Lake Erie's total inflow cornes via the Detroit River water from al1 of the "upper
Lakes" in the system (Environment Canada and US EPA, 1995). HosteUer (1995) states mat Lake Erie
is especially influenced by the magnitude and phase of hydrological variations such as precipitation,
evaporation and runoff. Because of its srnail size and shallow depth, it is quite vuinerable to lake level
fluctuation. Frorn Lake Erie, the water flows oirough its natural outiet, the Niagara River and Welland
Diversion into Lake Ontario. The Welland Diversion bypasses Niagara Falls and is used for navigation
and hydroelectric power. There are no major deviations in lake levels to upstream lakes due to water
flowing thmugh Niagara Falls. The difference in elevation between Lake Erie and Lake Ontario is
approxirnately 99rn (Canadian Hydrographic SeMce, 1999).
Lake Ontario is the lowes? of the Great Lakes (74m in elevation) and its water Rows mrough
the S t Lawrence River into the Gulf of S t Lawrence and continues toward the ocean, over 19ûOkm
away. The differenca in elevation between Lake Ontario and the S t Lawrence River is about 1.7m
(Canadian Hydrographic Service, 1999). Lake Ontario is regulated whereby its outflows are conîrolled
by the MossSaunders Power Dam located between Massena, New York and Cornwall, Ontario
(Croley, 1986). Its canals do not serve as regulation, but a means for navigation thmugh the
bottlenecked channel. Lake Ontario is said to be strongly influenced by rneteorological events, Mile
water circulation is highly variable, being influenced by wind s i res on surface waters, and hydraulic
flows h m discharging tributaries (Flint and Stevens, 1989). Flint and Stevens (1989) çMe that of al1
the Great Lakes, Lake Ontario has the largest ratio of watershed land area to lake surface area,
suggesting a much larger relative drainage basin than the other lakes.
2.21 Great Lakes Connecting Channels
The connecting channels of the Great Lakes are S t Mary's River, the S t Clair River, Lake S t
Clair, the Detroit River, the Niagara River, and the S t Lawrence River. These make up the system in
which water flows from one lake to another (see Table 2). Considering the sizes of the lakes, these
connecting channels are mnsidered quite small (Mason, 1998). They are extremely important in water
level management, as well as the most heavity used areas within the basin.
TABLE 2
Characteristics of the Great Lakes Connecting Channels
1 ST.MARY'S 1 ST. CLAIR 1 DETROIT 1 NIAGARA 1 ST.
Source: Mason (1998). Lake by Lake. State of the Great Lakes Repwt Environment Canada.
LENGTH (KM)
ELEVATION DROP (M)
MEAN ANNUAL DISCHARGE
RIVER 121
6.7
2 100
63
1.5
5 097
41
1 .O
5 210
58
99.3
5 692
MWRENCE 150
1.6
7 739
St M w s River drain's Lake Superior into Lake Huron, with a 6.7 metre drop in elevation
between the W. According to Maçon (1998). the river has several tributanes, however the w a h
entering from these are onfy a small fraction of the water drainage h m Lake Superior. The S. Clair
River drains Lake Huron into Lake St Clair. Its natural depth is actualiy quite shallow, howver it has
been dredged extensively to meet t r ansp~ r t~on needs. Here as well, the main water cornes h m Lake
H u m than any other source. This river is characterized with a noncornplex shoreline, fast airrent,
and substantial M c i a i depth (Mason, 1998). The Detroit m e r conne& Lake St Clair 1i, Lake Erie.
Mason (1 998) cites th& 95% of the total river fiow wmes h m the upper Mes. In addition, the Niagara
River drains Lake Erie into Lake Ontario and drops in elevaüon by alrnost 100 mefres along its course.
Like the others, the large majonty of water within the river cornes rnainiy h m the lake itseL Finaliy, the
St Lawrence River is the o ~ q e t of the Great Lakes systern. It drains Lake Ontario to oie Gulf of St
Lawrence on a course that extends 870 kilometers to the ocean.
2.3 Climatic Characteristics and their Controls
There is no question that climate change, and aspects of regional climate have the potential to
affect the water levels of the Great Lakes. This w u l d invoîve rnany factors, aîfhough dimatic variables
such as precipitation, evaporation, and runoff patterns, are of particulair importance (Hartmann, 1990).
Overall, the clirnate of Southem Ontario varies irnmenseiy especially due to the effects of the Great
Lakes. Brown et al., (1980) states that the meteorological affect of the lakes is most pronounced along
the shoreline, where the climate diîTers considerabfy from that in the uplands. Eichenlaub (1979) and
Lee (1993) state at least four major conîrofs that exert a marked influence over the clima?e of the Great
Lakes area. These are 1) latitude; 2) air masses and atmospheric disturbances; 3) the continentality of
the region (related to its position within the interior of North Arnerica); and 4) the modifying marine
effects resulting frorn the presence of the Great Lakes. The following will describe these details as wll
as other pertinent cornponents of climatic characteristics.
Controlling factors of climate indicate the effects of related components affecting the levels of
the Great Lakes. Day-today weatber is variable because much of the basin is located wi'thin the paths
of several major storm lracks. Additionally, the climate of the Great Lake Basin rnay be simpb
characterized by a mix of conf nental and maritime climates (Eichenlaub, 1979). These factors induce
the components affecting water levels. Factors such as precipitation, temperature, evaporation,
hospheric circulation patterns, lake circulation, and x, on. Therefore, the unique climatic
characteristic of the region under study must be presented in a desaiptive and precise manner. The
following will desaibe Great Lakes clirnatic characteristics, h i l e later chapten will specifcaliy focus on
resutting factors that d i r e influence water levels.
2.31 Latitude and Situation
According to Eichenlaub (1979) latitude is the dominant confrol mnceming climate, insuring
that large differences in çolar radiation will occur seasonally. This means that there is a marked
contrast in energy received during the winter and sumrner rnonths. These factors are essentially
detemined by the energy from the Sun. The mid-latitude location effects seasonal and temperhre
variation, due to solar energy being fhree to four fmes greater in early surnrner than in earfy winter
(Lee, 1993). The exact situation of the basin allows for a mix of air maççes, stom kacks, variation in
the prominence of four distinct seasons, and afmospheric circulation (Brown et al., 1980). These effed
the hydrologie cycle, seasonal variation, while cornprising the main clirnaüc traits of the region.
Sihiation of the region is an important factor in explaining and desaibing specific climate
characteristics of the Great Lakes Region. For example, winter periods in most portions of the basin
are quite cold and precipitous. The la& of relief or other barrien allow Arctic air masses, canying
extremeiy cold air masses to easily flow into the region. Lee (1993) states that the temperature rnay
reach as low as QOC. During winter seasons, the sustained cool temperature allow the build up of
snow and ice over the lakes, and such storage of snow and ice on land and lake is responsible for
lowr lake levels during such periods.
2.32 Atrnospheric Circulation Patterns
Weather systems, stomi tracks and air masses cantinuousiy move aaoss the Great Lakes
region. These systems bring wih them periods of heat, cold, rain or snow, sunshine or clouds. Brown
et al. (1980) states that the strength and predominance of atmospheric patterns and various source-
regions of air ttiat allow for the variations in weather paüerns and hence, the distinct properb'es of Great
Lakes regional clirnate. The dominant air masses of the region are those originating from the Arcüc,
the northem oceans and the topics, al1 of wtiich Mng distincüve types of weather (Brown et al., 1980).
Stons develop along 'weaiher fronts', or along the zone between two types of air masses.
Other factors responsible for the clirnate in the basin invofve the large-scale general circulation
of the atmosphere. The wntroiüng factors of this are the polar jet stream and the semigermanent
high-pressure systern located in the subtropical Atlantic (Lee, 1993). The pola jet Stream is
responsible for lowpressure storms that are mnducive to precipitation. The subtropical high-pressure
systern is rnost intense during the sumrner, and Mngs with it large arnounts of moisture from the Guif of
Mexico and the Atlantic Ocean. These may be considered the main sources of moisbire/precipitation
poducing systems for this area. These systems aiso account for the high frequency of w a m and
humid days during the wmmer season especially over the southem poitions of the basin (Lm, 1993).
Lee (1993) alço contends that these systems are predominant and resun in a VerY large range of
variability concerning day-to-day weather.
ENSO events may be defined as the combination of m a n waming and the reversal of
surface air pressure, at opposite ends of the tropical Pacifie Ocean, usually occur imubneousfy
(Ahrens, 1991). During ENSO events, air circulation at 5km high in tbe atmosphere is aftared during El
Nino and La Nina events. Dunng El Nino winters, the jet Stream over the North Pacifc is likely to split
on its approach to North Arnerica. Shabbar (1999) uintends thai a weaker branch wouM be dberted
northward into the Northwest Territories h i l e the lower subtropical branch (whose mean position is
over the Pacific northwestern region of Canada) would be shiffed several degrees latitude southwest
The southern Canadian region lies in behnieen the two jets and receives rnilder, and drier than normal,
winters (Shabbar, 1999). Shabbar et a/., (1997) and Shabbar and Khandekar (1996) have found that
temperature and precipitation patterns over Canada respond to ENSO events which induce
atrnospheric agitation.
Peixoto and Oort (1992) found a very sîrong correlation between Sea Surface Temperatures
(SST) anomalies in the eastem equatorial Pacific and ttiat of the atrnospheric temperature over the
Northem Hernisphere. The correlation found is said to rnost skong *en the aîmospheric temperature
lags the ocean temperature by four months (~0.82). lt was concluded that 'since conelaüons witti the
mean Southem Hemisphere temperatures are very high, it is cIear ttiat a large part of the observed
variability in the global atmosphere must be connecied with ENSO events." Sirnilar to that of Daly
(1999), Peixoto and Oort found that atmospheric temperatures lag the SOI by approxirnateiy 8.5
months.
Meadows et el. (1997) related phenornena of high lake levels wïth signficant changes in the
nature of the Great Lakes basin cyclones. Support for tfiis finding is providsd by an apparent inter-
decadal clirnate change reflected in a marked shift in track lines of extra tropical cyclones passing over
the Great Lakes. This is paralleled by a deaeaçe in lake levels and wave anergies during different
peiods. Rohli et al. (1999), indicated important factors that define how local atmospheric anomalies
affect the Great Lakes Basin. These are believed to affect local temperature regimes, as well as
precipitaiion patterns.
2.33 Impact of Great Lakes on Regional Clirnate
The Great Lakes have a significant effect on their own regional climate. Amrdingty, such
knowledge allows for the ability to conventionally determine and devise a standard th& mu ld allow
researdiers to compare and base al1 other climatic difierences or changes against Brown et d. (1 980)
stated for example that heat provided by energy from the sun is transporteci to and from ttie e e a t
Lakes by the wind, and plays a dominant role in shaping the ciimate of Souhem Ontafio. For example.
the temperature difference between the large water bodies and the landmases, especially during
different seasons, allow for atterations in climatic characteristics. The slow response of water
temperature to seasonal changes in solar input has a significant effect on air temperatures at locations
along the shoreline, strikingly dfierent from places located away from the shore. In addition, Lee
(1993) demonstrated that prevailing winds dunng the winter cause locations near the southeastein
shores to be wanner han those at the same latitudes, h i l e those in the surnrner near norttieastem
shores have cooler temperabres.
The tem 'lake effect" is a well-known climatic influence of the Great Lake region (Scott and
Huff, 1996). Scott and Huff state that lake effects are most nofceable in precipitation and temperature,
and Vary with season, time of day, and lake sire. As well, the lakes act as a large source of moisture to
the lower abnosphere, allowing for changes h precipitation, temperature, and evaporation that would
not normally exist without the presence of such a large lake system. The lake effect shows how Lake
Superior has the gnatest influence 'where up to 100% more precipitation falls downwind of the lake in
winter cornpared to aa t expected without its presence.' Furthemore, in summer, ail lakes cause a
10% to 20% downwind decrease in precipitation. Temperature aspects of the basin are akered in a
manner where mean minimum temperatures are higher during al1 seasons; M i l e producing a reduction
in mean maximum temperatures during the spring and summer seasons (Scott and Huff, 1996).
The resub of Scott and Huff (1996) suggest that lake-induced changes include cfoud cover,
which is greatest during the winter, and greatest immediatety downwind of Lakes Superior and
Michigan. During the summer, Lakes Huron and Michigan are said to induce a reduction of cloud cover
by approximately 10%. Cloud cover rnay reduce the arnount of sunshine, and indirecüy, heat, by as
much as 50% of the total possible (Eichenlaub, 1979). In winter, this is reduced by as much as 75%
(Brown et el., 1980). As such, the apparent lake effect on the surrounding area of the basin is a
significant climatic effector, as well as a factor that influences lake levels
2.4 Resource Management Aspects
The inclusion of resource management aspects in any study concerning the Great Lakes is
essantial. considering its present and projected uses. The Great Lakes system is complex and requires
meticulous research, regulation, and policy, for maintenance and protedion. It must be addresçed mat
the presence of several competing uses, often means having different ideas, plans, and goals for the
future uses of the Great Lakes. Since a scenario such as mis is usually acwrnpanied by degradation
of the resaurce, fastidious resource management, must be adapted. Although at present, there are
several organizationç attempting to keep the integnty of the syçtern at an acceptable level, it is
becoming an increasingly arduous task.
Therefore, in the course of comprehensive water planning, problems are identifid, data are
wllected and anaiyzed, and projections are made. This provides a basis for integrating al1 of the
functional wmponents of comprehensive water management (Enger and Smith. 1993). The existing
management strategies attempt to deal with the bemendous demand for use of the resource, while
aüernpting to devise forecasting tools so mat reliable long-tem goals can be contnved, and eventually
met Over tirne, the Great Lake basin has seen approaches that comprise and are based on, net basin
supplies, lake levels, and connecting channel fiows ihat have been expeiienced over the first 75 years
of this century (Hartmann, 1990). Projects include shore protection siructures, hydropower production
facilities and navigation locks, al1 of which have thair own various impacts, both known and uncertain.
3.0 REVlEW OF THE LITERATURE
Researchen from various disciplines have long sought to detemine the major causative
factors of lake level fluctuation in the Great Lakes Basin. It has been suggeçted mat fluctuation, at
either a maximum or minimum, is a consequence to some degree or another, of local climate vxiabbility
among many othw components. Recent clirnate variability studies have focused on ENSO, thus
developing indices to rate the severity and intensdy of separate events over tirne. The %uthem
Oscillation lndex (SOI) and the Mulovariate ENSO lndex (MEI) have been used in various independent
&dies (Shabbar and Khandekar, 1996; Shabbar et ai., 1997; Assel, 1998; Wobr and Timlin, 1993
and 1998), Mi le no one study has yet to resohre whether a particular index is more suitable. The
following review includes past and recent research cornpleted Meoretically and ernpirically, hom the
field, to oie laboratory.
3.1 History of Great Lakes Water Level (GLWL)
Water levels of the Great Lakes have historically fluctuated due to a variety of components.
Many studies have attempted to define various factors mat are responsible for influencing lake levels.
The practicality of such studies, especialfy those wncemed with coastal and water policy management
remains to be focused on extreme water level situations (Hartmann, 1990). Quinn (1999) has stated
that there is great need for reliable lake level event frequency distributions because it is 'a critical
wrnponent of any wmprehensive strategy for coping with lake level fluctuations.' This becornes
increasingiy apparent when exberne fluctuation in lake levels occur more persistently than they have
ever in history.
Great Lakes water levels have been continuousty recorded since approxirnateiy 1860, with
some of these records going back to about 1800 by sporadic and individual records. Bishop (1990)
determined mat histoncal records show that variation of lake levels did not fluctuate with any great
significance. Likewise, Quinn et al. (1997) contended that despite the great concem and attention
received by lake level variation, water levels change relatively slow due to 'large lake surface areas and
constrictecl ouüet channels, which integrate short-tem climate fluctuations.' The recent fluctuation data
are indicative of more recurrent and severe exberne levels. Figure 3 illustrates the standardized time
&es plots for the Great Lakes (1950-1999). Such research has led others to examine ttie cause of
lake level fluctuation, and the grounds of its inaeased pen-odicity and rigor. It is suggested thaclimate
change, global wamiing, and human alteration of the environment is the root and the generator of this
phenornenon (Bruce, 1984; Hadmann, 1990; Sanderson, 1993; Croley, et al. 1996; Craig and Kertland,
1997; Assel, 1998; Quinn, 1998).
It has been detemined Bat overall historical variabili in annual lake leveis is about 1.8m
h i l e seasonal vwability is appmximakly 2 W c m (Hamann, 1990; Quinn et al. 1997; Angel, 1995).
Ahough these values do not seem significant, many uses are dependent on water levets remaining at
sameiiutiat constant levels, and have become quite sensitive ta even the smallest changes. This
suggests that iake levei sensitivity is inueasing which may create potential coastal haz;irds. Croley
(1986) has found through extensive and detailed m a c h that precipitation and lake-levels a e indeed
conelated, and precipitation leads water levels by appmximately one year. Therefore, may
assumed mat shifts in precipitation patterns wÎll lead lu corresponding shifts in lake leveis. m e r
factors considered will detemine the extent to which lake levelç will fluctuate. Figure 3 illustrates T h e
Series Graphs of the Great Lakes (1950-1999).
Since the 1960's, it was considered that there have been comparatively high lake levels in
place. This has been said to be atbibuted to a particular different climate regirne from e d e r times
which has been portrayed with persistently high precipitation (Quinn et e1.,1997; H m a n n , 1988; and
Croley, 1986). Specifically, lake levels are said to be high in the 19501s, record bws in the eariy
1960 '~~ with a consistently high precipitation regime h m the iate 1960's until oie pfesent time. This
period is characterized by rapid and e&eme shifb in lake levels. For example, record low lake levels
in 1964 w r e directly replaced with high levels merely nine years later in 1973 (Croley, 1986). In facf
1973 levels were so high that through ihe intervening pend, record highs were set yet again on Lakes
Suparior, Michigan-Huron, and En-e. Hadmann (1988); Croley (1986), and Quinn (1986) idenw mis
high precipitation pattern since about 1970.
Changnon and Changnon (1996) daim that sudden clirnate condition changes are responsible
for the maked precipitation changes during the 1960 '~~ 1970 '~~ and 1980's (see also Harbnann, 1988;
Croley, 1986; and Quinn, 1988). This is related to the extrernely wet conditions expdenced throughout
the 1970-1994 period. Bishop (1990) identifies highs beginning in 1985 through to 1986. Lee and
Noorkbakhsh (1 9%) studied GLWL forecasting during the years between 1982 and 1988.
It was found that, at the beginning of this period, the lakes w e more or Iess at their average
long-terni levels. Someti me before 1985, the lakes experienced a steady rise and by 1985 and 1986,
the lakes hit record highs. Harbnann (1988) M e s that this period was chaacterized mth a O.Sm
increase in long-terni mean monthiy lake levels. In facf al1 lakes hit rnonthly record levels for at kast
one year except for Lake Ontario, wtiich has different hydrological conditions on the basin, as wll as
regulation of its ouüiow (Lee and Noorkbakhsh, 1992). Abniptly by the end of
FIGURE 3
Standardized Time Series Plots of the Great Lakes 1950 - 1999
Figure 3.1 Lake Superior
Figure 3.2 Lake Michigan-Huron
YEAR
WATER LEVEL ?, LI -. I 0 .A h) W
WATER LEVEL 3 L . Q h ) W
1986 and me beginning of 1987, low precipitation resuîted in steadi)y deaeasing lake l8vels- BY me
end of 1987, the lakes were for the most part below their long-terni average levels.
3 2 Aspects of Water Level Fluctuation
In direct response to numerous and varied physical processes, water levels on Re Great
Lakes modulate on a wide range of time scafes (Lee, 1993). The physical proceses mentioned above
include net basin supplies, inflowç, oufflow, and hydrologic variations. It is stated that variations ocwr
over a very large time sale, of monas in response to seasonal variations in supplies. In addition,
diversity of temporal episodes may ocair over several years in response to long- tm climaüc or
atmospheric variation.
Watw level fluctuations occur annually, seasonally, and over short-tem periods. Annual levels
of each lake rnay be superjmposed within seasonal cycles. Variations rnay be understood as each lake
undergoes annual cycles, as a resuft of a variety of climatic factors, M i le seasonal fluctuations occur
with magnitudes depending on water supply and the local hydrologic cycle (Hartmann, 1990; Quinn,
1988; Croley, 1986). M e m e ieveis, or record highs or lows of the Great Lakes, are the resutt of
rnainly annual fluctuations, witti a variability range of approximately 1.8m (Hartmann, 1990). Seasonal
fluctuation in water levels may be logically defined as being at a minimum during winter pen'ods (due to
increased autumn and earty winter evaporation from lake surfaces). As a result, spring and summer
levels are usually inueased due to increased snowmelt, spring precipitation and deaeased
evaporation; reaching a maximum in June (Croley, 1986).
Short-term precipitation patterns or variations invotve storm surges and water set-up levels.
This describes the build up of water on one side of a particular lake due to severe storms, high winds,
and air pressure jurnps due to the unique aspects of storm tracks and air masses that frequent the
region (Quinn, 1988). Storm events cause a temporary redistribution of water in the lakes, as well as
waves mat aeate a short-term oscillation in the water surface (Lee, 1993). Short-ten fluctuations are
considered transitory and fleeting, and will not be included in this research problem. It must be noted
however that ttiese short-term fluctuations are significant because they describe the active area in
which the Great Lakes are located. Here, cyclone passage due to the convergence of the weçterly and
s ~ u t h ~ s t e d y stom tracks are most active in late fall and eariy winter (Angel, 1995).
3.3 Factors lnfluencing Water Levels
The significance of studying the factors that influence GLWLs is critical considenng the local
climatic characteristics of the Great Lake basin, which are described in detail below. Hartmann (1988)
puts mis into perspective by staüng mat vaiations in GLWL are linked closely to the regional cl imh,
and thus forecasts of lake levels are no beüer than îhe weather forecasts on which they are based.
Hence, it is irnperative to strictly examine the facton involved in water level fluctuation. Assel (1999)
confimis the notions of many others when he states that this region needs a rnanner in which to better
define the linkages between regional and global climate, and to analyze the potential effects of ENS0
events on Great Lakes rnonthly air temperature and precipitaoon, ice Cover and water leveb As well,
Sousounis (1998) states mat studies of water level fluctuation have show that the Great Lakes can
respcnd relativeiy quickiy to periods of varied but exlreme precipitation, water supply and temperatura
conditions. The following will describe these facton as well as those that are related to the distinct
study area.
3.31 Precipitation
Precipitation is indeed a major componen! of Great Lake water inflow. Over-lake precipitation
is especially significant since over one-third of the Great Lakes basin (total land and water) area is lake
surface (Canadian Hydrographie Service, 1999). Variations in hydrology Ne deemed effeded by
conf nental and regional shifîs in atmospheric circulation that may penist for several years (Hostetler,
1996). Thus, it is believed that lakes fluctuate in size from 'sbmderived' inaeases in water inputs.
Sanderson (1993) assertç that in order for GLWL to rernain relativeiy constant the renewable portion
rnust be re-supplied by nature. Thus, this renewable portion of the systern rnust corne in the f om of
precipitation (rain and snow). Precipitation may be considered here as rain and snow, minus oie
evaporation from lake surface, plus the run off from the land areas of îhe basin. This represents
approximateiy 75cm on the surface of the Great Lakes annualîy (Sanderson, 1993).
Croley (1986) states that other variables affecting infiow, besides precipitation, include infiow
from upstream lakes, and diversions into the Lake. However, it is cleariy sMed and accepted, mat it is
precipitation that causes the major long-terni variations in lake levels, and is the dominant and most
important fom of basin inflow. Again, Croley (1986) states mat precipitation and lake levels are
correlated, with precipitation leading lake levels by approxirnateiy one year. This points to a positive
and interrelated relationship that the Great Lakes and precipitation have between each other. This may
be because the lakes are an excellent source of atmospheric rnoishire, while being able to add or take
away, significant arnounts of heat fmrn air masses which crosses them. Brown et al. (1980) M e that,
consequenüy, areas to the lee of the lakes experience more precipitation, as well as other factors such
as clouds and moderate temperatures.
Shabbar et al. (1997) asserts that there is a significant relationship that exists between
precipitation and the Southem Oscillation phenomenon. Both composite and correlation analyses
indicate that regionç of Southern Canada, including the Great Lakes region, a e influenced by oie
Southern Oscillation, via precipitaüon pattern variations. Shabba et al (1997) indic* an ongoing
pattern of 'negativelpositive precipitaijon patterns in these regions are cornmon and indicative of this
phenomenon during the Crst winter foliowing the onset of El NinoILa Nina events'. Shabbar et al (1997)
suggest that the melat ions are so significant that it rnay be possible to cwrelate SOI values with
observed precipitation patterns (over Southern Canada) thus, developing longrange forecasting
techniques. This rnay be based on Canadian precipitation patterns and the occurrence and evolution
of various phases of the Southem Oscillation.
3.32 Temperature
Air temperature affects lake level fluctuations in general since higher temperatures cause
plants to use more water, resulong in higher evapo-transpiration r a s , causing higher net rates of
evaporation h m the ground surface (Croley, 1986). This resub in less runoff for the same amount of
precipitation han would occur during a low ternperature period, when mere is l e s evaporation and
transpiration.
The impact of ENSO on Canadian surface temperature is believed to be most strong during
the winter season, disappearing by spring months. Shabbar and Khandekar (1996) have documented
the two phases of ENSO (El NinolLa Nina) concerning the surface and lower tropospheric fields over
Canada. Their study clearly shows that with the onset of an El Nino event, the cmesponding,
signficant positive surface temperature anomalies spread eastward from the west coast of Canada to
the Labrador mast from the late fall to early spring (November through May). Atrnospheric circulation
conceming this region results in a transition where accompanying temperatures in the lower
troposphere Vary. This tends to concentrate around the North American dornain, and more specifically,
the Great Lakes region dun'ng El Nino events. This resultç in a converse phenornenon where
significant negative surface temperature anomalies spread southeastward from the Yukon that extends
into the upper Great Lakes region by the winter season following the onset of La Nina epiçodes.
Assel (1999) analysed seasonal temperature and precipitation records for El Nino, La Nina,
and non-ENS0 years for the tirne span of 1900-1990. The anaiysis showed that 'seasonai average
temperabres are significantly cooler in Me spring (La Nina onset year), surnmer, and fall (El Nino onset
year), and late fall to winter (following the La Nina onset).' This corresponded to the additional findings
that suggest that seasonal average temperatures are warmer for the late winter to eaiy spring following
the El Nino onset year. This is related to the seasonal average precipitation, which is significantly less
from mid fall through winter following Me onset of El Nino.
3.33 Evaporation
Evaporation from the Great Lakes represents a major bss to lake leveis and must be
considered an important factor. Evaporation is significant in the detemination of lake levels because it
has been found mat levels are usually higher when evaporafion rates are low, and vice-versa.
Evaporation is at its highest when the differences between air and water temperdre are greatest This
is due to being dependent on solar radiation, temperature differences betwwn air m a s and waters and
on humidity and wind (Canadian Hydrographic Service, 1999). Thus evapcraüon from the lake surface
is lower in winter and reaches a maximum in early fall. According to Croley (1986), there is an invane
relationship between evaporation and lake levels. Here, it is sMed that as evaporation rates inaease,
lake levels tend to decrease. Croley (1986) sîudied such factors and determined that the highest lake
levels occur in early wmmer when evaporation rates are low, and when snow and ice mek In addition,
there is a positive correlatjon between evaporaüon and temperature.
Evaporation rates for any of the Great Lakes varies in timing and magnitude. For example,
Sousounis (1998) states mat Lake Erie peaks in evaporation during October, h i l e Lake Superior
peaks in Decernber. In relation, a shallow, warm lake, such as Lake H e , experiences more
evaporation than a deeper, colder lake, such as Lake Superior. The Canadian Hydrographic Service
(1999) uincluded that on average, the Great Lakes, annual evaporation is almost equivalent to average
annual precipitation. This describes a sirong relationship between evaporation, precipitation, and
temperature that allows for the extreme IeveIs the Great Lakes experience.
3.34 Runoff
Anoher factor that is invoived in the detemination of lake levels is the runoff of water from
land, which fiows into the lake. It is considered quite significant because it involves the region's
hydmlogical cycle, while cornprising a weighty part of the water supply. Correspondingly, ninoff from
the land areas peak in eariy spring and is at its minimum in the auturnn (Sanderson, 1993).
Approximatety 10 to 150 km of land surface around the lakeshores is contributed to lake mnoff oirough
a series of cornplex rivers and streams (Canadian Hydrographic Setvice, 1999).
Runoff is most notable baàn-wide during spring when snowmett occun, nonnally during late
&h mrough eariy June (Croley and Hunter, 1994). Net supplies of water are greatest in late spring
due to meMng, Hile they are at their lowest during eariy fall. Thus it rnay be stated that ninoff is a
factor of seasonaiity, where annual precipitation is raîher more constant, but has seasonal features. It
must be noted however, that ninoff is usualiy direcüy nlated to precipitation and temperature. Runoff is
ofbn tabuiated as precipitation rates per year, h i l e temperature affects the iength of time snow and
ice remain on lake and land masses.
3.35 Great Lakes Circulation
Accwding to Beletsky et al., (1 999), wind stress and surface heat powers long-tm circulafion
or patterns in the Great Lakes. This is considerd quite cornplex given the interplay between these twD
factors as well as underlying lake bathyrnetry. The results M e that M i l e some features of lake
circulation appear stable, others tend to demonstrate significant interannual variabilW. Belebky et d.,
(1999) have deduced that summer circulation patterns are more cornplex than winter pWems due to
the presance of 'baroclinic effects' in summer circulation, despite the fact that i n t e r circulation currents
are much stronger than that of surnrner circulation currents. Winter circulation is stated to be powered
by winddriven forces. Densitydriven forces are negligible in winter because at mis tirne, lakes lack
significant surface heat
Beletsky et al., (1 999). also concluded that circulation patterns show a tendency to be cyclonic
in the larger Lakes (Lake Huron, Lake Superior, and Lake Michigan), especially in winter. Larger lakes
are characterized by larger surface areas, and stronger lake-atmosphere temperature gradients
(Beletsky et d, 1999; Ullman et. al., 1998). These factors are suggested to indicate the signlficance of
'lake-induced mesoscale vorücity in the wind field' (Beletsky, et al., 1999). In summer, the circulation in
Lake OnPano is sdmewhat cyclonic most likely due to densitydriven currents. This is similar to qclonic
circulation in the larger Lakes (Michigan, Superior, and Huron) in the sumrnc:. The other smaIle: lake,
Lake f i e , was anticyclonic in the surnrner, which is attributed to wind. Lake Erie acd CGwo exhibit
'two-gyre' circuiation patterns in winter, which are stated to be most Iikely due to somewhat uniforrn
wind fields (Beletsky et al., 1999).
A seiche is a free oscillation of water in a closed or semi-closed basin. It is frequently found in
bays, lakes, and in alrnost any distinct basin of average size (Environment Canada, 1999). Seiches are
usually induced by meteorofogicaf disturbances uvhereby the water surges back and fortfi. They are
important Men studying lake level fluctuation because they represent short-tenn lake level changes.
The physical aspects of each lake determine how they are affected by, or conducive to seiche sire,
intensity, and fraquency. The distinctive oscillation usually damps out by friction over a penod of a few
hours depending on the energy of the parücular seiche. Lake Superior has very infrequent and weak
seiches. Accwding to Environment Canada (1999), seiches in this lake are typicalty l e s than 0.3m1
sdwm conditions may inaease this to 0.6m. Seiche formation in Lakes Huron and Michigan is
greatest ai fhe exbernifies of the lakes. Bays are typicalty effected with the most intensity due to strong
e a m winds found flowing acmss Georgian Bay. Lake Erie has very pronounced seiche &vity
because it is very shallow, and aligned with prevailing wind directions. Therefore, the perimeters of the
lakes are subject to the greatest water level fluctuation. During stwm conditions, the fluctuation has
been found to be approximately 5rn (Environment Canada, 1999). Finally, Lake Ontano has very M e
seiche actjvity because of its small area, deep waters, and symmeMcal shape.
3.4 Net Basin Supply and Outflow
Net Basin Supply (NBS) is defined as direct rainfall plus runoff and net gmundwater inflow, l e s
lake evaporation associated with a lake basin (Boland, 1989). This not onfy includes ovw-lake
dynamics, but also those that occur within the drainage systems as well. As a resuk lransient &anges
in NBS lead to changes seen in lake levels. Understanding the impacts of climate change on Great
Lakes water resources includes those invoived with its NBS. Sousounis (1998) stated concems about
exireme changes in NBS due to clirnate change, and sMed that decreases for example, would result
frorn Iower land based runoff (tom higher evapotranspiration and lake evaporation) dunng fall and eady
winter. This is illustated in the following simple equation:
NBS=P+R-E
Where: NBS denotes Net Basin Supply; P denotes precipibtion; R denotes runofi and E denotes
evaporation (Quinn and Guerra, 1986).
Tbe report by Sousounis (1998) outlined the importance of regional clirnate, especialiy weather
exiremes and inter annual variability. Exberne lows w u l d resuft in louer lake levels, M i le oie
reduction in NBS would result in lower water levels as wll. This is especially true when taking into
consideration, the substantiaf variation in the hydrological cycle over each lake. Quinn and Guerra
(1986) stated that the principal variables in Great Lake basin water suppiy are precipitation, ~ n o f f and
evaporation. Water suppiy is added to tfirough precipitation, and lost #rough evaporation, outfiows and
consurnptive uses.
Lake outffows also Vary as a function of lake levels. This means that the lakes on average rise in
the spring due to runoff, and recede in late sumrner and early fall as runoff usually deueases
(Sousounis, 1998). This seaçonal variation is the resuR of melng ice and snow in the spdng, which
causes additional water into the systern. As well, inaeased temperature and evaporation resutt in
lower oufflows since water levels are usualfy loww during this period. It must be noted however, that
vanation in lake levels are in part due to the gradua1 variation in lake outRows. This means mat not al1
water entering the lake is irnmediately pushed through the systern. There is an element of time
involved which cause the fluctuation in lake levels. it is sMed mat the length of time required for
noticeable changes in lake levels (and outflows) mainly depend on the intensity or sbength of the
wather, such as precipitation, and on assuciated temperahrres.
TABLE 3
Ratios of Drainage Basin Area To Water Surface Area
LAKE SUPERIOR LAKE MICHIGAN-HURON
Source: Environment Canada and the US Environmental Protection Agemy (1995). ln: The Great
1.6 2.1
LAKE ERIE LAKE ONTARIO
Lakes Information Network. ~ttp:f/www..areat-lakes.netnakei.
3.4 3.0 -
0th- factors taken into consideration are drainage basin area, or catchment area (see Table 3 for
drainage basin ratios for the lakes). This detemines the potential amount of water a Iake rnay receive
through land ninoff. The larger drainage basin, the greater the potential suppîy of land ninoff. As wll,
another major factor is water flow from upstream lakes to downsbeam lakes. According to Farid et al.
(1989), Lakes Superior and Michigan are not affected by mis. However due to its orientation, Lake
Huron receks 1.2 times as much water h m Lakes Superior and Michigan than it receives frorn
precipitation and ninoff. The çame study &tes that Lake Erie receives 3.6 tirnes as much water h m
the upsbearn lakes Mile, Ontario, receives approximately 3.8 times as much. On the sarne note, Farid
et al. (11997) continues with the importance of outflows which, are stated to be on average, higher than
Iake infiows. With Bis, it is put forward that in Lake Huron, its outfiow into the S t Clair River is about
1.4 times as high as inflow frorn Lakes Michigan and SupeBor.
3.5 El Nino, La Nina, and the Çouthem Oscillation (ENSO)
Philander (1990) states that the coordinated El NinoISoothem Oscillaüon phenomenon (ENSO) is
the strongest source of natural vaiabiliiy in the global climate system. El Nino was first called to
attention in 1871 by Dr. Luis Carranza of Lima, who described a counter cunent flow moving north to
south between the ports of Paita and Pacasrnayo in P m (Philander, 1990). This is evident akng h e
west coast of South America, where the cool P m current sweeps northward, and souü~eriy winds
promote upwlling of mld, nutrient-rich water that gives rise to an abundanœ in local marine
populations (Ahrens, 1991). Thus, this natural p a t h does not mate very many local distuhames
and no gkbal disturbances. However, near the end of each calenda year, a w m . nuirient-pwr
moves southward replacing the cold, nutrientdch surface water. Nomalk this wming persists onw a
few weeks to a month or more, aRer which weather patterns retum to nomal (Ahrens, lgB1).
A major El Nino event ocairs when this waming lasts for many months to a year, wih a more
extensive wming pattam taking place. These are reported to occur in approximata intewals d 3 tD 7
yean (Daly, 1999; Ahrens, 1991; Philander, 1990). This fact may change with increased clirnate
change, which is suggested to inaease the seventy and frequency of ENSO events. This may posçibb
expiain why El NinoISouthem Oscillation events are not prominent in past records. Sinœ the beginning
of the data set used (1950-1999), there have been various shng to moderate ENSO events. These
are 1951, 1953, 195758, 1963, 1965-66, 1969, 1972-73, 198283, 1986-87, 199l-92,1994, and 1997-
98 (Canadian Hydrograhic SeMce, 1999; W o h and dmiin, 1993; WoLr and TimCn, 1998, A w l ,
1998; Trenberth, 1990). The seven stongest ENSO eventç (according to the standard SOI) during this
tirne period are as followç, 1957-58, 196546, 1972-73, 198283, 198687, 1991-92, and 1997-98
(CDC, 1999).
El NinolSouthern Oscillation (ENSO) considers botti the oceanic and the mospheric changes
in the Pacific Ocean region. More specifcally, SouoiM Oscillation rnay be desaibed as a 'see saw' in
abnospheric rnass invoiving exchanges of air between eastern and western hernispheres (Rohli et al.,
1999; Kane, 1997; Bunkers and Miller, 1996, and Glantz et el., 1 991; Trenberth, 1990). Consequentfy,
because of its characteristic inter-annual variaüons in wather and clirnate, it is considered a reliable
indicator of prominent anomalies. As well, it is no longer considered merely a regional phenornenon,
but one that is appreciated as global, affecting many regions of the world, witfi various implications.
Research cornpleted on how ENSO affects various regions of the globe include Daly (1999);
Assel (1998); Kane (1 997); Bunkers and Miller, (1996); Guetter and Goergakakos (1995); Glantz et al.,
1991; Trenberth (1990) and Wotter (1987). This suggests that investigation of the processes of global
ciirnate systems and variability, dl1 allow more preciçe research conceming inter-annual tirne-sales.
Daty (1999) and Peixoto and Oort (1992) both have found through similar research that atmospheric
anomalies, both positive and negaüve, are correlated to the global temperature of the lower
Wposphere. In addition, there was found a strong correlation betwwn SST anomalies and
mosphenk temperature. 00th shidies clah that ENSO events are overwhelmingiy responsible for the
observed variability in global temperature, atmospheric cirwbtion, and SSTs.
As one invedgates the significance of Great Lake levels, the dynamics of the atrnasphere
must be considered to fulty understand the essential processes invohmd in ENSO. The most broad
impact on circulation vaiability and associated climatic anomalies wwldwide is the abnosphdc
response to the oceanic El Nino phenornenon, the Souîhern OsciIboon. Rohli et al. (1999) stated that
air masses of both Ardc and tropical source regions exeit dominance over aie Great Lakes basin
during various monhs, but for any given month of the year the degree of influence of both air m a s
types varies interanually. As a resuft it is stated that regional-scale circulation pat$ms are the most
dired cause of the degree of influence of air masses. Variables stated to be effected are considered to
be surface componentç, because it is aûnospheric circulation that forms the main link beîwwn regional
changes in wind, temperature, precipitation, and other clirnatic variables (Trenberth, 1990).
The Indices
Research conceming ENSO has developed a number of rneasures that &mpt to moniior the
phenomenon using nurnerous variables. In order to s ~ v e for a better manner to understand and
represent the ENSO phenomenon, the present research aitically examines tw general indices, to
observe how well they predict the natural system of coastal phenomenon.
3.51 The Southern Oscillation lndex (SOI)
Sir Gilbert Walker first described the Southern Oscillation, and devised an index that eventually
becarne known as the Southern Oscillation Index. According to Kyle (1999) the rnanner in wtiich to
fom the SOI, requires the annual cycle of pressure at each station and rernoving by foming anomalies,
or differences, from the long-tem monthiy averages. Monttity values are then nonnalized by the
appropriate rnonthly standard deviations, then the difference Tahiti minus those fram Darwin, Austratia
is taken. Research cornpleted using or studying the Southern Oscillation lndex include: Troup (1965);
Wotter and Tirnlin (1998); Kane (1997); Bunkers and Miller (1996); Shabbar and Khandekar (1996);
Guetter and Georgakakos, (1995); and Wang (1995). These studies attempted carrelation anaiysis
between the SOI and climate patterns are related phenornena.
Kyle (1999) states that the Southem Oscillation involves a negative correlation between
pressure over lndonesia and pressure over the southeastem Pacific. When the souihem oscillation is
coupled with wming of the ocean off western South America, a resuiüng El NinolSouoiern Oscillation
event can effect weather patterns across the globe. The Southem Oscillation lndex (SOI) is defined as
the difference between sea level pressures at Tahiti and D m h , Australia (Glane et el., 1991; Daty,
1999). The difference behwean the two can be used to generate an 'index' number, indicaëng w m
and wld events with sustained low negative values and high positive values respectively. This index is
commonly used due to its efficiency and reliability conceming the defining and understanding of the
kng-terni variability and influence of this oceanic and atmospheric phenornenon. Figure 4 showç graph
of the Southem Oscillation lndex from 1950-1999.
FIGURE 4
The Southern Oscillation lndex 1950 - 1999
Standardized Values (Z Scores)
Source: Jones (1 999).
3.52 The Multivariate ENSO lndex (MEI)
The Muiüvariate ENS0 lndex (MEI) is a method used to monitor and study the coupled
oceanic-atmospheric character of ENSO, by basing its values on the principal variables observed over
the tropical Pacific (Woiter, 1999a). Woiter (1 9994 defined ME1 as a weighted average of the 6 major
feabrres that approximate ENSO characteristics. These van'ables a e sea-level pressure, sea surface
temperature (SST), surface air temperature, ttie east-wst and nortfi-south cornponents of aie surface
wind, and total amount of cloudiness. The values for oie parameters are colkted over the tropical
Pacific. Figure 5 illustrates the ME1 index calculated dunng the years 1950 - 1999. These values are in standard score format to serve as a dimensionles aitenon &en undergoing anatyçis. The ME1
values are a resutt of principle component anatysis, which derive the standard scores out of a huge
variable bank.
The MuJtivariate ENSO lndex attempts to approxirnate the wuplad oceanic-mosphdc
character of ENSO through the incorporation of six variables mentioned above. The region comprises
the entire tropical Pacific basin. It is believed mat becauçe the variables are in lage scak pattern
fons, rather than point measurements, the variables can be used in relation to each oiher to obtain a
more cornprehensive measure of ENSO related interactions (Wotter, 1999b). Research using the ME1
include Wolter (1999a and b); Assel (1998); Wotter and Timlin (1998); and W o k (1987). These
comprise reçearch conceming the feasibility of the index, and how wll they relate to climatic
phenornena of the Great Lakes. More specificaliy, ttiese studies related cfimate phenornena to the
Muttivariate ENSO Index.
FIGURE 5
The Multivanate ENSO lndex 1950 - 1 999
Standardized Values (2 Scores)
YEAR
Source: Wolter (1 999a).
Woher (1999a) considers it a superior index desaibing ENSO events because it is said to be
less vulnerable to occasional gfitches in the monthty update cycles due to the efficiency of variable
description. This is cuupled with the incorporation of several ENS0 variables (stated above) which are
said to make this index more descriptive, therefore more reliable and efficient This is stated in
reference to the general monitoring of the ENSO phenornenon, whereas orner ENSO indices might
serve as wll, depending on the nature of the research being employed.
4.0 CONCEPTUAL BASIS OF THE STUDY
An a prion rnodel is a provisional mental construct used to
world under study, while dernonslrating meaningful aspects of theocy.
portray sorne aspect of the real
In order to define a pmblem, it is
1
required to fashion a manner in which to invesügate the theoretical background, previous research
accomplished, Mi le atternpting to resolve and determine possible explandons to the present querY.
Figure 6 illusbates the a prion rnodel developed for this thesis which is based on the rmrded historical
data (1950-1999) of Great Lakes water levels, and previous inveStigatJ0ns plus a çMisücal mode1
inmrporating temporal and spatial behaviour.
A cornmon group of factors has been identified through the inquiries of many ottiers that have
accomplished successful and rneaningful research conceming lake level and climate variabilii.
However, a scientific investigation to obtain a deeper anamcal understanding of the precise
rnechanisrns affecting lake level externes rernains to be uncovered. As such, researchers continue
meir quest for higher levels of expianation. Previous work has indicated that there exisis a mutütude of
various cornponents that are in some degree or another, factors affecting Great Lakes water levels
(Assel, 1998; Quinn, 1998; Gabriel ef al., 1997; Meadow et ai., 1997; Lee, 1993; Sanderson, 1993;
Bishop, 1990; Hartmann, 1990; Croley, 1986; Quinn and Guerra, 1986; Bruce, 1984).
Arnongst these and rnany others, it is suggeçted that clirnate vaiabilrty is the dominant
elernent explaining fluctuation, and thus, will be the focus of this thesis. Examination and review of the
pertinent literature suggests mat clirnatic variability has been augmented by El NinolSouthem
Oscillaüon events, Mi le owing sorne responsibility to signficant fluctuations in GLWL The relation
between Great Lakes Water Levels and the El Nino 1 Southem Oscillation have been examined by
many researchers in the past and have discovered positive correlations (Assel, 1999; Assel, 1998;
Quinn, 1998; Croiey et al., 1996; Hostetler, 1996; Stakhiv, 1996; H m a n n , 1990). Thus, the essence
of mis thesis lies in the determination of how El Nino 1 SouthernOscillation events affect Great Fakes
Water Levels through further examination of two indices that porbay it The indices examined are the
smthern Oscillation lndex and the MuNivariate f NSO Index.
m e a prior rnodel that wiII be employed for the purpose of this investigation suggests that a
masonable explanation should be found conming the ENSO indices, and how they conel- with
shoe-terrn water level fluctuation in each of the five Great Lakes. A systernatk response &dy will also
be explored. More specifically, both the Southem Oscillation lndex and the Muthariate ENSO lndex
FIGURE 6
A Priori Model
Great Lakes Ciirnate i
f
Changes in Storage s
' El Nin01
Southern Oscillation
Great Lakes Water Levels
B
Storm TracksrAir Masses/ Atmosphenc Circulation Patterns
Source: Author, 2000.
represent different aspects of ENSO mechanisms and thus, rnay describe Great Lake water levels in
distinct fashions. Kite (1989, 1991) siated mat climat~elated time series should, through statistical
anaiysis, have valid physical explanations for the cornponents utilized. It is the purpose of this thesis to
detmine better understanding of GLWL fluctuation with the index that desaibes lake levels wilh the
utmost fit, applicability, and usefulness.
In surnrnary it is found:
The quest for reliable information concerning GLWL fluctuation is a uiorttruihile endeavor, and should be exarnined so that efficient indiators and prediction tools can be developed.
ENSO events rnay be statistically correlateci to GLWL fluctuation, although a l mechanisms and aspects involved are not cornpletely understood.
Factors affected by ENSO, and in tum effect GLWL are those such as airlstom tracks, ahosphek circulation, precipitation, temperature, evaporation, and mnoff.
The ME1 and the SOI are two of the rnost cornmon ENSO indicators and rnay be most useful in determining a relationship between ENSO and GLWL.
The situation and systern of the Great Lakes to local air masses and storm tracks rnay reveal different temporal and spatial behaviour, thus using different statistical rneans to poiûay them.
T h e series anabsis rnay provide description and explanation of GLWL fluctuation and the extent if any, that ENSO rnay be involved. if possible, one of the indicators rnay sewe the study most efficiently, and better explain the connection between ENSO and GLWL.
Hypotheses
In essence, boa phases of ENSO affect clirnate and its variabili, and thus, We related
components of local Great Lakes basin climatic characteristics Meteorological facbrs such as
precipitation, evaporation, temperature, general atmospheric circulation and sa on, are in some way
altered frorn their normal range of variability in a rnanner mat is hindered or enhanced. In other words,
there is a resufüng change in the inflow and outflow rates within the basin. Hence these components
are suggested by many reçearchers to be responsible for the exireme fluctuations of Great Lakes water
levels.
Aithough the Great Lakes behave and react as a systern, each will react to
abnosphericlclimate vari-ability distinctly. It is not suffident b render al1 lakes b one specfic tirne series
model, since each 1 1 1 behave according to various factors such as size, depth. orientation, local
climate phenomena, and so on. This includes of course, We effects received from the ottier lakes. The
foliowing hypotheses are loosely based on the assumption that lake level fluctuation is fundon of a
collective system, as well as what characterizes the individual lake. Appendix III defines the statistical
terminology.
Thus, it is hypothesized:
Hypothesis #l
Lake Superior, being the westemmost lake, of$n receives the dne& part of climate patterns
(Croley et d, 1995; and Quinn et al., 1997). Lakes Michigan-Hwon are &abd perpendiailar to the
stom iracks, thus are less expoçed, and are therefore more sensiüve to short terni memory shocks in
the first year and l e s sensitive b the second d e r autoregressive tefm. statistically, this means th&
instead of a long rnemory process being preçent, the affects of the second shodc are muted to a
rnoving average process. This means that Lakes S u p ~ o r and Uchigan-Huron (through water level
fluctuation) will encounter responses to ENSO induced clirnate changes, ahough the response wifl be
eveniually damped out over a finite period of time. This is what characterires the nature of an ARMA
(1 ,O, 1) process.
Thus, it is hypothesized that Lakes Superior and Michigan-Huron will exhibit a response to
ENSO in thai the effect of the lag 2 random shock exposure to îhe passage of waîher systems is
dampened. This may be due to their large sizes and orientation. mus it is hypothesized that an ARMA
(1 ,O, 1) process rnay be present in the systems characterizhg Lake Supior and Michigan-Huron. The
ARMA (1,0,1) process is represented by the following equaüon.
Where Yt denotes the forecasting function, @ denotes the AR (Autoregressive Model), 8 denotes the
MA (Moving Average Modei) and € denotes the error (Chatfield, 1985).
Hypothesis #2
Since Lake Erie's long axis is oriented in a northeast-southeast direction (oblique), and due to
its relatively small size and shallow nature, neither an ARMA or AR(2) proces rnay describe the data.
As well, the effects of the random shock (or ENSO induced climate changes) at lag 1-2 rnay be darnped
out or absent (Lavalle et al., 1999). It is hypoîhesized then that mis should yield a simple AR(1) model.
Yt = @1 Yt-i * €
As above, Yi denotes the forecasting function, @ denotes the AR (Autoregresive Model), and
6 denotes the error. Here, the (or longer response tô the shock) may be conçidered non-
signifkant This rnay be due io its constricted outlet It is constrained by the Welland Canal, Niagara
Falls etc. at a 30 degree angle. Lavalle et al., (1999) found that Lake Erie rnodeling contained first-
order autoregression with semester data (semi-annual), thus suggesting that with quaterly data, the
resutis should be similar.
Hypothesis #3
Since Lake Ontario has L long axis oriented in an eastwest diredon, it should be peal ly
prone to the effectç weather systems. This would lengthen its exposure to ENSO induced climate
changes and therefore approxirnate an AR (2) rnodel. The effects of ENSO induced clirnate changes
would be sbangiy fett due to its small size and deep nature which makes it capable of thermal heat
storage, effecting evaporaticn rates (Quinn et ai., 1997). This rneans that the lake level fluctuation will
be affected significanüy in the sense of a prolonged time interval. Therefore, it is hypothesized that
Lake Ontario water levei behaviour may be characterized by a second order AR (2) process according
to the equation:
Where Yi denotes the forecasting function, @ denotes the AR (Auto Regressive Model), and €
denotes oie error, and on the condition, that the data is not seasonalized (Troup 1965; Chatfield, 1985).
All data has already been deseasonalized in the standardization process. An AR (2) rnodel will exhibit
a 'rnernory' in the sense ihat each value is correlated with al1 ihe preceding values. Thus, each shock
or disturbance to the system will have a dirninishing effect on al1 the subsequent timeperiods. An AR
(2) rnodel deabes a pseudooscillatory process generated by long-term memory random shocks ai
lag 1 and lag 2.
Hypothesis #4
Since ME1 is an indicator of the ENSO phenornena, whicti affects climaüc variables basin-
Mde, Lake NBS shouM be a function of ENSO events. Since wabr levels change slow due to the
large lake surface areas and consiricted outlet channels, (Habnann, 1988; Quinn et el., 1997; Mason,
1998) they combine short-term climate fluctuations. Thus it is hypothesized that Lake NBS shouid
approxirnate a mode1 wfiere a random shock associated with ENSO at lag t-2 may be absent, or
dampened. Thus, Lake NBS models should approxirnate a weak AR(1) mode!.
One wuld exped to find a weak AR mode! with iower lags since the ENSO phenornena muid
generate changes in local climate variability for each of the Mes. As wll, this hypottiesized weak
relatjonship with the ME1 may be due to me fact that ME1 may be rnereiy a trigger, dissipahg by the
Cme the effects reach this region. Thus, each shock or disturbance to the system will have a
dirnhishing effect on ail ensuing time periods. This should be present in the NBS data for al1 lakes, and
melate with the findings conming ENSO and watr levels.
5.0 METHODOLOGY
The following will define the variables under investigation, and ootline how they will be employed.
5.1 Data: Acquisition and Characteristics
The monmfy Great Lake water level data used in this thesis have been provided by
Environment Canadz (1999). These data are comprised of rnonthly values be-n the pars of 1950
to 1939. Earlier data exists for botti the Southern Osciliation Index and Great Lakes Water Levels, but
precise and reliable Mulovariate ENSO lndex data is not available prior to 1950. For wnsistency, the
base year was set at 1950, allowing for a sirong 50-year inquiry.
The Muftivariate ENSO lndex values were bken frorn Klaus Wobr (1999bj through the
NOAA-CIRES Climate Diagnostic Center. The Mulovariate ENSO lndex values are bimonthly
(DedJan .... Nov/Dec), and span the years of 1950 - 1999. All values have aiready been nonnalized for
each season so that there is an average of zero and a standard deviation of one (Wohr, 1999a). It is
computed rnonthly, based on two preceding calendar months. Negative ME1 values indicate cooling, or
La Nina events. Correspondingly, positive MEI values indicate wanning, or El Nino events.
Values of the Southern Oscillation lndex (SOI) w r e taken from the Climatic Research Unit
(Jones, 1999). For the purpose of this thesis, SOI may be defined as the seslevel air pressure
difference between statjons at Tahiti and Darwin, Australia divided by standard deviation of these
differences. This SOI formulation follows that of Troup (1965). The rnonthiy data have been
standardized to remove different units of rneasurernent among the variables. Net Basin Suppty (NBS)
data (rnonthfy approximations of precipitation plus runoff minus evaporation for each lake) were
provided by Rob Caldwell (2000) of the Deparîment of Fisheries and Oceans at Environment Canada.
The data used w re monthly values for the years spanning 1950 to 1999. NBS data involve total water
values cornprishg of precipitation, ninoff, and net ground water infiow, minus evaporation. Although
NBS is not invohred in the hypotheses, it was used to provide a foundation in wbich to base the
changes in lake levels. Net Basin Supply data for each lake were exarnined and used as a regressor
against the ENSO indices to detemine whether the statistics found among the same lakes were
comparable, thus providing more supportive resutts.
5.2 Data Analysis
The original monthty values were cbrnpiled into quarters, comprising thremontfi intervals,
specifically: December to February; March to May; June to Augusf and September to Novernber.
QuaterM data m e generated because an ENSO event is appmxirnately 4 to 8 months bng, and
monthly data is thought to disperse or rnask any real affects of ENS0 factors (Lavalle ef al., 1999). An
ENSO event usualiy consists of a long sequence whose cumulative effect acts as a random shock mat
alters weather patterns (Lavalle et d., 1999). Therefore, in order to view the effects of ENS0 induced-
climaüc triggers on lake levels, quarterly data will be used to best provide a snapshot of hiçtoncal
fluctuation.
To compare the sequential dynamics of GLWL wifh both the SOI and the ME], the data were
standardized to remove the effects of the different units of measurement in the variable set, as MAI as
seasonal effects of the Great Lakes variables (Lavalie et el., 1999). In order to convert each variable
in$ a dimensionless criterion, the data were transformeci into standard scores (z) using the following
formula:
z = X - p / a
Here, X is a variate score, p is the data mean, and (J is the standard deviation (Lavalle et d., 1999).
The initial step taken to analyze the data was to create correlograms, or autoconelation
funcüon (ACF) and parüal autocorrelation funtion (PACF) diagrams to examine initial observations
against time. This includes studying important features such as trend, seasonality, discontinuities, and
outliers. Each data set was identified with a partiwlar (AR), andlor (MA), process.
Afier examining lake leve! time series ploh, it was deterrnined that the data sets should be
split This rneans that in most cases Me series are characterized with an abrupt change in trend frorn
one varying range of values, which differ from the preceding values. This was executed with the SPSS
statistical software, which modeled the data, and served to prepare the variables for statistical anabsis.
Therefore, case number 91 or year 1972 (second quarter) was chosen because it seems to intervene at
a peak El NinoISouthern Oscillation event, and separates two distinct averages found within al1 of the
series.
This allowed for the acceptance of BoxJenkins properües which define an approach to time
series analysis. These properties are outlined in Chatfield (1985) and concern the following in the data
senes k i n g used;
a) There should be no systematic change, or trend in mean.
b) There should be no systernatic change in variance.
c) There should be no deterministic periodic variations.
d) The autoconelation function is dependent on the lag interval and not the starthg position of the series.
In order to ensure sound staüstical resutts, the foliowing steps wwe taken to anaiyze the data,
and test the hypotheses. Once the ACF and PACF cwrelograms m e consbucted and examined, the
data were ft to either an autoregresive rnodel, moving averages rnodel, w a combination of the M.
SPSS statistical software was used to fit the models. The residuals Worn the fitted rnodels were tested
for serial autocomlation on the correiograrns. This estimation and diagnosis of the most acceptable
model was cornpleted to detemine the rnodels' goodnes~f-fit
The hypotheses were fumer examined by ushg the ME1 as an independent regressw to more
fully understand the effectç of ENS0 induced changes and the corresponding responçes 60 lake level
fluctuation. These resub and discussion are included with each hypothesis. Once this was complete,
the data sets w e analyzed using Ime senes anaiysis. This was done by constwcting models based
on the processes identifieci during the previous stage (SPSS, 1994).
The Muftivariate ENSO Index was found to be the best descriptor according to îhe resub of
the model fiitong ( s e Figures 8-1 1, and Tables 4 and 5) and was used as the regressor to each lake's
NBS, data and the lake level data, to determine how well the index fit the ofher models. The statistical
significance and sirength of various parameters were idenüfïed as well during this stage of data
anaiysis. Estimation and diagnosis of Me most acceptable and efficient models have been completed
through examination of residuals. The parameters that are said b affect d e r Ievels include
precipitation, evaporation, ninoff and temperature. These are said ta be modified by the presence of
an ENSO event Lake level data and lake Net Basin Suppfy data were examined for statistical
significance using the best fit between the SOI and the ME!, to detemine any correlation between
atmospheric changes induced by the ENSO influence. This is presented below.
5.3 Aspects of Time Series Analysis
Tirne series anaiysis is used because it is mainly mncerned with decomposing a series into a
tend. Trends may be defined in many ways including seasonai effects, cyclic changes and other
Ïrregular fiuctuations (Chatfield, 1985). Therefore, udthin the Great Lakes study region, one may
suspect to end trends due to a variety of conditions including dmatic change, stochastic processes,
and extreme variability. Therefore, Ime series analysis may be used as a manner of estirnating the
probabiîi of obseMng enhanced forms of predicted and recorded lake levels (Kite, 1991). Kite (1991)
contands hat the trend component of a time series is generaliy associated with changes in the
drudure of the tirne series caused by cumulatike natural or rnanmade phenornena.
In order b examine the pmposed statisiical awrelation arnongst lake levels, the
Autoregressive lnbgrated Moving Average (AR1 MA) rnodeling procedure was used. AR1 MA models
ae, in meory, the most general class of models fw forecasting a time series. vrhich may be
stationarized by transformations such as differencing and logging (Chatfieid, 1985). More spdcally,
lags of the forecast errors are calied 'moving average' ternis, and a tims series which
FIGURE 7
AND PACF'S
MODIFY MODEL
FORECAST
Source: Arsham (2000). TÏme Seiies and Forecasting Techniques. Hüp9hvw.ubmail.tlbalt.edu
39
needs to be diRerenced to be made stat ionq is said to be an integrated version of a smonary series.
The BoxJenkins approach was used because it portrays Univariate ARMA analysis by evaludng time
s&es data by ex&acting the predictable movements from the data set Figure 7 illustates the steps
taken in time senes analysis, which are describecl in BoxJenkins pmcedures. This is the most efficient
method because it identifies which fitters are rnost appropriate for the series being analyed (Chatfieid,
1985).
Chatfield (1985) identifies three linear fitten used in mis rnethod and are the autoregresive.
the integrafion, and the moving average filter. In an autoregressive process, each value in a series is a
linear function of the preceding value or values. The order of the autoregresive process indicates how
many preceding values are used. fn a rnoving average process, the each value is detennined by the
average of the curent disturbance and one or more previous disturbances. The integrated terni in time
series analysis may indicate differencing to smooth the data, or to make it sbtionary.
Tirne series is best ernployed in such research because it posseçses the distinguished feature
of taking into account that successive observations are usual!y not independent (Chatfield, 1985).
Therefore, the anaiysis takes into account the time order of observations. If it is found mat the time
series can be predicted exacüy frorn usicg past obsenrations, the series may be stated as detemiinistic.
However, very few series confom to this, especially those that represent natural phenornenon and
naturaf variability. Consequenüy, the time series will be stated as stochastic if the future is oniy partly
deterrnined by past observations. The collection of GLWL data, and its correlation witti ENSO indices,
cannot realisticaliy, be completefy explained, Hltiich rneans that future values will have a probability
distrÏbution wtiich is conditioned by o knowiedge of past values (Chatfield, 1985).
5.4 Modeling of the Soüthem Oscillation lndex and the Multivariate ENSO lndex
In order to determine the extent of the effects of ENSO on Great Lakes Water Levels, an index
rnust be selected, which is believed to represent the nature of ENSO (temporal behaviour) optimally.
This thesis modeled both the Southen Oscillation lndex and the MufivaRate ENSO Index and found
that the laüer would serve this thesis more efficienuy due to the statistical results (see Figures 8 to 11 ;
and Tables 5 and 6 atthe end of this section).
Since the Muhivariate ENSO lndex uses more information to charactenze El NinoiSo~rthern
Oscillation (ENSO) events than the Southem Oscillation lndex (SOI), it should be more useful in
correlaüng the fiow variables describing Great Lakes hydrology with El NinoISoutfiem Oscillation
influences. The modeling was designed to isolate eeiter the SOI or fie MEI, by examination of
statisücal resutts indicaüng the most parsimonious model, and then using this to approxirnata Great
Lakes Water Levels and net basin supply values. When atbmpting to mode1 the SOI and ME1 time
series, it was found fhat a simple model could not fit either. By simple, we expect the time series to
have as few parameters as possible and a large number of degrees of * d o m among al1 models mat
fit the data (Chatfield, 1985). Crotîcorrelation anabsis suggested that the difficulty may be due to an
apparent interval in lag tirne. Atthough many modals appeared to be sMMcaib s ign i f~n t the
autocorrelation function indicated otherwise, with clear autocarrelation arnong the residuals. As a
resuk, it was tested whether lagged forms of the two indices wuld fair better outcornes. The resuits for
the rnodeling of the SOI and the ME1 are located at the end of this section.
The SOI was found to be best fifted by an ARlMA (1,1,0) process, with SOI lagged at 3 and 5.
The firstader autoregression model is charactenzed by differencing because the index reffects the
cumulative rnontfily effec? of the factors Bat Wgger it The integrated concept of ttiis model
characterizes an AR model of a differenced series. When modeled, the ME1 was lagged at 2 and 3,
with an ARMA (1,0,1) process. As in rnany natural phenornena, there is a random or stochastic
elernent, which defines much of the behaviour seen in the Ma indices. The lagged values, rnay indicate
the random and oscillatory nature of the factors triggering the various rnonthfy values of SOI and MEI.
As such, the rnodel represents a manner of tirne delay wiolin the series, resuhng in cycles within the
cycle.
The SOI rnodel was significant at a level of 0.05, wim al1 T-ratios significant The R value of
0.68 indicates a strong relatjonship Hnth approxirnately 46% of the van'ation in the SOI explained by the
lagged values of itseif. All Box-Ljung s ~ s t i c s were insignificant at 0.05, h i l e no rneaningful
autowrrelation existed among the residuals. This is supported by the Durbin Watson statistic of 1.758
( s e Figures 10, 11, and Table 5 for statistical resub).
As with the SOI, the ME1 model was ftt to a sufficient model. It was found that an ARMA
(1,0,1) with lagged values of ME1 at 2 and 3, served to fit the series. The model was significant at a
level of 0.05, with al1 T-ratios significant The R value of 0.86 indicates a strong reldonship wioi
approxirnately 74% of îhe variation in the MEI explained by the lagged values of itseif. The Box-Ljung
statistics were insignificant at 0.05, A i l e no meaningful autowrrelation existed arnong the residuals.
This is supported by the Durbin Watson statistic of 1.981 (see Figures 8, 9, and Table 4 for statistical
resuk).
The ME1 was chosen due to the variety of staüstical results such as a higher R value which, is
statistically sîronger, as well as the higher R Square value (74%, as opposed to 46%). In addlon,
residual variance and standard error values were al1 significantly l owr in the rnodel that approximated
the ME1 time series (see Table 4). Residual autocorrelations on the ACF plot were signifcantly higher,
conceming the Box-Ljung statistic (see Figure 9). This is concurred with one of the residual lags of me
$01 rnodel being slightly autocorrelated (ahough still statistically significant), vrhereas this is absent in
that of the ME1 model. AIC and SBC indicators w r e substantially lower, h i l e ail T-Ratios were
subsîantialfy higher than that of the SOI model. Therefore, although both models were not ideally
simple, it is still acceptable to embrace the ME1 data set, as the senes to be used for the examination of
lake Level fluctuation, and net basin supplies of the Great Lakes.
For our purposes, the lagging of the indices rnay represent important aspects of histoncal
patterns within the data set For instance, because the lag can represent the curnulatjve affect of
ENSO, and one Iag is equal to three months, then the lag aspect of both SOI and MEI, rnay be due to
pivotal periods within the time sefies. Not al1 values within the time senes are those that are associated
witb ENSO events. The lag values may represent Mgger periods, where both SOI and ME1 must be
lagged at particular intenrals to thoroughly portray the characteristics of each data set For example,
the ME1 was lagged at the 2rd and 3rd quarks, highlighting possible forcing mechanisms thmughout
the months of Apnl, May and June. The SOI was lagged at the 3" and 5" quarters, suggesting that
spnng and aie following winter periods are most meaningful. The ARMA nature of the ME1 suggests
disturbances wittiin the series rnay be characterized with a mernory, and one where the
disturbances are darnped out, and ceases to exkt The AR (1) nature of the SOI model rnay depict a
resilience of the disturbances, one where mernory continues to exist
Due to oie nature of both of the index models, semester series (semi-annual data) of both the
SOI and ME1 wre run to determine whether simple models were available, and ifthey corroborated the
findings using quarterly data. The semester series did indeed allow for more simple measures of fitüng
models for both the SOI and MEI. As well, the ME1 was found to have the superior model fit, showing
sûong staüstical resuits (see Appendix 1). The ME1 series was fit to an AR rnodel (2,0,0), with
sbtisb'cally sound resub, and an R value of -681, R Square of .463, and no significant autocorrelation
among the residuals. The SOI series was fit to an AR modef (1,0,0), Moi an R value of .4W, and an R
Square value of .241. All statistical results associated with the model were significant as well. The ME!
mode1 validated preferred results in the R value, R Square value, Durbin Watson statistic, oie AIC, and
residual variances. The ACF of the modeled series fawed the ME1 rnodel due to higher Box-ÿung
statistics. See Appendix 1 for the statistical resub for the semester data.
In addition, the series of both SOI and ME1 w r e converteci to yeariy averages to determine
whether a model couid be fi Ath more sirnplicity. Both series fit an MA rnodel with the SOI having to
be differenced. Quick examination of the resutts displayed that the parçimonious mode1 was ttiat which
was îït to the MEI. Autoregressive models did not fit either series probably due to the fact that they
w m averages. This means that the moving average characteristic is one that merely moothes
fluctuations and distortions in the data, while providing a meaningful representation of underiying bends
and cycles. In this case, each value in the series is a weighted average of the rnost recent random
disturbance. Here, a random disturbance affects the systern for a finite number of periods (the moving
average order), and then ceases to affect it (SPSS lnc., 1988).
It rnay be accepted that a satisfactory ENS0 index rnay be confidentty taken Zo use wioi the
lake Level data and net basin suppiy, b determine the theoreticai questions pased. This in no way
deems the SOI unacceptable, but merety excludes it for the purpose of sirnplicdy and precision related
to this thesis. Therefore, the ME1 was used in what follows, to determine whether there is a relation
between it, and Great Lakes water levels, and net basin supplies.
VGURE 8
A. THE ME1 AUTOCORRELATiON FUNCIION
Confidence Lirnits -
Lag Nurnber
B: THE ME1 PARTIAL AUTOCORRELATION FUNCTION
Confidence LirnÏts -
Lag Number
TABLE 4
MU ARMA MODEL (1,0,1) $tatistical Results
FINAL PAFIAMETERS: ANALYSiS OF VARIANCE: Number of residuals 187 DF ADJ.SUM OF SQ. RESIDUAL VARIANCE Stanctard emr .47463494 RESIDUAS 183 41 -826 0225 Log likelihood -1 25.31 903 AIC 258.63806 SBC 271 -56249
VARIABLES IN THE MODEL:
0 SEB T-RATIO APPROX. PROB.
MODEL SUMMARY CORREiATION BEMIEEN DEPENDENT VARIABLE AND MODEL FIT
R .861 R SQUARE .741 DURBIN WATSON 1.981 SIG -00
ME1 AUTOCORRELATION FUNCTION ARMA (1,0,1) RESIDUALS
Lag Number
RGURE 10
A: THE SOI AUTOCORRELATiON NNCïïON
Lag Number
6: THE SOI PARIAL AUT OCORRELATION NNCTiON
Confidence Limits -
Lag Number
SOI AR (1,l.O) MODEL Statidcal Resuits
FINAL PARAMETERS: ANALYSIS OF VARiANCE: Number of residuals 1 û4 DF SUM OF SQUARES RESIDUAL VARiANCE Stanctard ermr -721 7031 7 RESlDUALS 181 94.31 1 0.521 Log li keii hood -1 99.60888 AIC 405.21 776 SBC 414.S257
VARIABLES IN M E MODEL: B SE0 T-RATIO APPROX. PROB.
MODEL SUMMARY CORRELATlON BETWEEN DEPENDENT VARIABLE AND MODEL FIT
R -681 RSQUARE 0.464 DURBINWATSON 1.758 DF 183 SIG .O0
THE SOI AUTOCORRELATiON FUNCTiON AR MODEL (1,1,0) RESIDUALS
Lag Number
6.0 STATISTICAL RESULTS
6.1 W s t i c a l Resuits
Correlograms of the autoconelation functions linking lag intervals and autocorrelation values
were pmduced. These were studied to help to determine possible processes for mode1 fi'üing. Once
rnodeling was accomplished, it was found that Lake Superior characterized an ARMA process (see
Figure 12); Lake Michigan-Huron characterized an ARMA process (see Figure 14); Lake Erie displayed
an AR process (see Figure 18); Lake Ontario displayed an AR pmcess (see FigurePl); and both ME1
and SOI displayed an AR process (see Figure 8 and 10, respediveely). W h these resub, the next step
was to run and evaluate various models using the initial obsenrations. These are evaluated below.
See Table 6 for a display of the statistical results and Appendix III for Statistical Definiiions.
TABLE 6
Statistical Results and Fitted Models
NBS Model
ARMA (1,0,1) ME1 laged
Michigan-Huron
ME1 Model
ARMA (1,O.l) ME1 lagged
Lake
Supenor
Erie
No mode1 fit applicable.
Mode1
ARMA (1,0,1) ( by 18 quarters
ARMA (1 ,O, 1) / ARMA (1,0,1) ME1 lagged
6.2 Assessment of Hypothesis #1
by16 qyarters
AR (1,0,0) quarters AR (1,0,0) ME1 lagged at 3 quartes
i f by14 quarters
The first hypothesis states that Lakes Superior and Michigan-Huron rnay exhibit a response to
ENS0 in mat the effect of the lag 2 random shock exposure to the passage of weather systems is
dampened. Therefore, it is not expected that the effects of ENS0 induced climatic changes should not
On tario
alter they systams of Lake Superior and Michigan-Huron for a lengthy tirne interval. This means bat a
pseudocycle is thought to exist where a disturbance to the system will exist within a parücula time
by 14 quarters AR (1,0,0) ME1 lagged
i n m a l without creating iasting affects within the system. A pseudocycle suggests mat in al1 likelihood,
a cornpiete cycle does not exist in this case, Re climatic factws being affected by ENSO change h m
AR (1,0,0) ME1 lagged by 8
AR (2,0,0)
their nom due to atmospheric alterations (to precipitation, evaporation, runoff and temperature) and
aeate a resutting change in lake levels. The ARMA process suggestç #at ENSO meabes random
shock(s) which occur in the same lag intervat.
AR (2,0,0) ME1 lagged by14 quarters
Thus, it was tested that an ARMA (1,0,1) proces wuld be sufficient to mode1 the Lakes
Superior and Mchigan-Huron in regard to how they fluctuate with climatic v&abiüty such as ENSO
eventç. It was suggested that thoçs Great Lakes with their long axes oriented in a narth-souh direction
(Michigan-Huron) may exhibit a different response to ENSO induced effects. Co~e~ondingly, Lake
Superior being me westem-most lake and the large* wuld also exhibit ARMA chaacteristics. It was
hypothesized mat an ARMA (I,O,l) process was invohred due to the fact that Lakes Michigan and
Huron are situaed perpendicular to çtwm tracks and a e therefore more sensitive to short rnemory
shocks in the fast year and l e s sensitive to the second order autoregressive term. It was pmposed
that M e a d of a second long rnernory proces k ing presenf the effects of the second shock were
muted to an MA process due to the shortened exposure to stom îracks.
Lake Superior was found to be influenced by an autoregressive process given the resuk of
the autocorrelation function (ACF) correlogram (see Figure 12) which, decayed exponentially. This
supports the process fit with Lake Michigan-Huron water levels as well. Next, Lake Superior water
levels (LSWL) w r e fit to an ARMA (1,0,1) model (see Figures 12, 13, and Table 7). The
autocorrelation function of the residuals illusirates no significant autocorrelations. The probabilities
associated with the Box-Ljung Q statistics are al1 well over the .O5 signifïcance level, indicaüng no
autocoirelation among the residuals. The rnodel signifcance parameter was .O0 for both the AR and
MA terms respetively.
Lake Michigan-Huron water levek were parsirnoniously fit to an ARMA (1,0,1) (see Figures 14,
15, and Table 8). The ACF plot indicated no signifïcant autocorrelation among the residuals, witti the
BOX-Ljung staüstics al1 well above the 0.05 level. The B coefficients were statistically significant at an
alpha of 0.05, and the approxirnate probability at 0.00, respectively.
Since both Lakes Superior and Michigan-Huron exhibited an ARMA process, boai were tested
against the independent regresçw ME1 to determine how well a rnodel could be f i t When Lake
Superior water levels were regressed wim ME1 (lag 1814.5 years), an ARMA (1,0,1) model best fit the
series, in a significant and sirong manner (see Figure 16 and Table 9). The autoregressive parameter
is 0.82, hile the moving average parameter is 4.37. The MElQ18 coefficient is approximately 4.16
the approxirnate probabiiities were 0.00, 0.00, and 0.10 respecüvely, at an alpha of 0.05. The R value
of 0.89 denotes a strong relationship, h i l e the R Squae value suggests thai appmximately 81 % of the
variance of LSWL, over tirne, is accounted for by the model. The residuals on the wrrelograms
showed no signs of aut4cOirelafon. as illustrated by the non-signifcant Box-Ljung staüstics (see Figure
16).
When Lake Michigan-Humn was regressed using ME1 as the independent regressor, it was
found thai there existed a sirong and significant relationship was obsrved hem hl applied to
ARMA processes (see Figure 17 and Table IO) . Wth ME1 regressed 14 quarten (3.5 years), the AR
coefficient was 0.95. the MA coefficient was 4.42, the lagged fomi of ME1 value was set at 0.6. All T-
ratio values were significant at a level of 0.05. The R value of 0.95 denotes a dong rel~unship, Mile
the R Square indicated that 95% of the variation in the rnodel was accounted for. The plot of the
residuals (see Figure 17) show no significant autocomlation, and al1 of the Box-Ljung values are
insignificant at a levef of 0.05.
The weak AR(1) component suggests that each shock or disturbance to the system has a
dirninishing effect on al1 subsequent time periods (SPSS Inc., 1988). The MA(1) process within the
systern has a dampening effect whereby the shock depicted is abnipt and has a short memory. Since
both Lakes Superior and Michigan-Huron rnost efficientfy fi an ARMA rnodel. king both slmng and
staüstjcal!y significant the hypothesis rnay be accepted. Therefore, the two uppennost, and largest
lakes are typified with abrupt shocks without any meaningful long-term memory being present
Assessrnent of Hypothesis #2
In regard to Lake Erie, it was proposed mat since its long axis is orienteci in an norttieast-
wutheast direction. and due to its relativeîy mal1 size and shallow nature, neither an ARMA nor AR(2)
proces may describe the data, and the effects of the randorn shock at Y 1.2 rnay be damped out or
absent Thus, it was hypothesized that an AR(1) model rnay sufficiently describe the underlying
processes. It was found that Lake Erie did indeed exhibit a first-order autoregressive model (see
Figures 18, 19, and Table 11). The correlograrn in Figure 18 illusîrates me nature of an auttregressive
process, which requires the interdependence of lags, on the previous values. This is show through
the decay of iags over time. Figure 19 and Table 1 1 refer to the staüstical resutts generated wih the
ME1 as the independent regressor.
The autoregressive pararneter (B) of 0.94 is significant at an alpha of 0.05, and an
approximate pmbabilii of 0.00, respectively (see Table 11). Because this value is quite n e a to the
value of 1.0 (limit of stationanty), it may be stated that the differences between lake levels from one
observation to the next should be distributed as white noise or stochastic factors (SPSS Inc., 1994).
The autococrelation fundion illustrates ttiat the residuals have no significant autoconelaiion and appear
to be randornîy distributeda The Box-Ljung Q staüstics are al1 well above the 0.05 bvel.
flGURE 12
A. M E SUPERlOR WATER L M L AUTOCORRELATiON NNCTlON
Confidence tirnits -
Lag Nurnber
TABLE 7
LAKE SUPERlOR WATER LEMLS ARMA MODEL (1,0,1)
FINAL PARAMETERS: ANALYSIS OF VARIANCE:
Number of residuals 196 Sbnctardemr .449940 Log likelihood -121 -21078 AIC 246 -42 1 56 SBC 252.97779
DF Adj. S m of Squares Resiâual Variance
Resiciuals 194 39.53 .2019
VARIABLES IN THE MODEL:
8 SEB T-RATIO APPROX. PRO%.
k M E SUPEWOR WATER LEML ARMA MODEL (1,0,1) AUTOCORRELATiON NNCllON ERROR
Lag Number
B: LAKE SUPERJOR WATER LEVEL ARMA MODEL (1,0,1) PARTIAL AUTOCORRELATION FUNCllON ERROR
Confidence Limits
Lag Number
FIGURE 14 LAKE MICHIGAN-HURON WATER L E E L AUTOCORRELATiON NNCTlON
Confidence tirnits -
Lag Nurnber
TABLE 8
LAKE MICHIGAN-HURON ARMA MODEL (1,0,1)
FINAL PARAMETERS: ANALYSIS OF VARIANCE:
N m b of residuals 196 Standard emx .BI 70597 Log likelihood -37.349 13 AIC 78.69826 SBC 85.254489
DF Adj. S m of Squares Residual Variance
Residuals 194 16.799 .O851
VARIABLES IN THE MODEL:
B SEB TRATlO APPROX. PROB.
A: LAKE MICHIGM4URON W A E R L E E L ARMA MODEL (I,O,l) AUTOCORRELATION FUNCTiON ERROR
Confidence Limits -
coef f ic ient
Lag Number
B: LAKE MICHIGAN-HURON W A E R LEVEL ARMA MODEL (1,OJ) PARRAL AUTOCORRELATiON FUNCTION ERROR
Lag Number
54
TABLE 9
LAKE SUPERlOR WATER LWEL AND THE ME1 MODEL VARIABLE: LAKE SUPERlOR WATER LNELS) ARMA MODEL (1 ,O, 1) REGRESSOR: ME1 AT M G 18 (MEIQ18)
FINAL PARAMETERS: Number of residuals 105 Standard emr -44295 Log likelihood -1 17.2782 AIC 24û .55641 SBC 250.37541
ANALYSIS OF VARIANCE: DF Adj. S m of Squares Residual Variance
VARIABLES IN THE MODEL: B ÇEB 1-RATIO APPROX. PROB.
MODEL SUMMARY CORRELAilON BETWEEN DEPENDENT VARIABLE AND MODEL FIT
R ,899 RSQUARE 308 DURBlN WATSON 2.027 DF 180 SIG .O0
LAKE SUPERIOR WATER LEML AND MEIQ18 ARMA MODEL (1,0,1) AUTOCORRELATION FUNCTION ERROR
Lag Number
LAKE MICHIGAH-HURON WATER LEVEL AND THE ME1 MODEL VARIABLE: LAKE MICHIGAN-HURON WATER LEVEL ARMA MODEL (1,0,1) REGRESSOR: ME1 AT U G 14
FINAL PARAMETERS: P l W of residuals 182 Siancimi enor .20989547 Log likelihood 25.765128 AIC 4.530255 SEC 35.91 8235
ANALYSlS OF VARIANCE: DF Adj. S m of Sqicares Resibl Variance
VARMELES IN THE MODEL: B SEB T-RATIO APPROX. PROB.
AR1 .95299769 .O21 93005 43.456255 .ûû MAI -.42101140 .O6945568 -6.061584 .O0 MEIQ14 .O6045971 .02960W 2.042112 .O4
MOEL SUMMARY CORRELATION BEMCEEN DEPENDENT VARIABLE AND MODEL FIT
R 0.974 RSQUARE .95 DURBlN WATSON 1.797 DF 181 SIG .ûO
LAKE MICHIGAN-HURON WATER LEMI AND MEIQ 14 ARMA MODEL (1.0.1) AUTOCORRELATiON FUNCTlON ERROR
LL O < -7.0 l m -
Lag Number
Tharefore, it may be sMed that the Box-Ljung staüsüc for the ACF is not statistimlly significant at any
hg. This suggests that the Lake Erie rnodeling is a fi fstwder auboregr-e pcess. ConSWJenW,
the initial shock or ~ g g d n g effects of ENSO has a dirninistiing effect on the wbsequent üme &es.
Higherarder autoregressive parameters and the ARMA a>uki not suffiaenw deAbe fie
model.
Using ME! Lake Erie was found to exhibit a firstader autwegressive proœss with ME1 at lag
14. This waç determined through cross-co~elaüon, as well as nurnerous modehg attempts. This
model was the most parsimonious, with an AR coeffcient of 0.94, and the MEIQ14 (3.5 yeas)
coefficient being 0.13. The approximate probabilities were 0.00 at a significance level of 0.05. The T-
ratios m e al1 above the aitical levels (see Table 12). The R value of 0.95 representç a e n g
relationship, while the R Square value of 0.89 indicates oiat approximately 90% of the variance in the
mudel is accounted for by the ME!. The ACF pbt for this mode1 shows mat the residual series are dl
well over the value of 0.05, and there sems to be no autocorrelation present (see Figure 20). The
result of this model indicates that with ME1 lagged by 14 (3.5 years), the series is desaibed most
efficiently. Fluctuations in Lake Erie water levels are characterized Hntti an initial shock or disturbance,
that is after an approximate time period of 3.5 years, the relationship between Lake €rie water ievels
and the effects of ENSO becorne significant It is important to note that there exists 'feedback' or
rnemory within the series, which can be expreçsed as an autoregressiive function of theprevious value
of the series, and a randarn disturbance. Accwdingty, the hypothesis stating that Lake Erie would
approxirnate a firçt-order autoregressive process (AR 1) rnay be accepted.
6.3 Assessment of Hypothesis #3
It was hypothesized that since Lake Ontario has its long axis orientecl in an east-west direction,
it should be prone parücularty to the effects of the passage of wather systems. This wu ld lengthen
exposure to ENSO induced climate changes and appmxirnate a secondader autoregressive rnodel.
The AR(2) statistical sumrnary indicated that mis rnodel was best frt to Lake Ontatio with an AR(2)
coefficient of -0.25 (see Table 13). The fintader coefficient is 0.94. The choiœ of the secondorder
a W e g r e W e rnodel was chosen because the AIC values m e h s t uiioi mis model, and !he Box-
Ljung and probabilii values of the residuals were highest The T-ratio values are signifcant at a value
of 4 - 5 3 , with an approximate probability of 0.00 at a significanœ level of 0.05. With îhis, the
hypooiesis that Lake Ontario may be characterized by a secondder autoregresive pmcess rnay be
accepteci (see Figures 22.23, and Table 14).
FIGURE 18
LAKE ERlE WATER LEVEL AUTOCORRELAïïOIH FUNCliON
Lag Number
Confidence Limits -
TABLE 11
LAKE ERlE WATER LEVEL AR MODEL (1,0,0)
FINAL PARAMETERS: ANALYSiS OF VARIANCE:
Number of residuak 196 Standard en# 33431217 Log likdihood 43.921 837 AIC 129.84367 SBC 133.12179
DF Adj. Surn of Squares Residual Variance
Residuals 195 22.032 -1 12
VARIABLES !N THE MODEL:
0 SE0 T-RATIO APPROX. PROB.
A: LAKE ERlE WATER LEEL; AR MODEL (1,0,0) AUTOCORRELAlïON FüNCTiON ERROR
Lag Number
6: LAKE ERiE WATER LEML AR MODEL (1,0,6) PARTiAL AUTOCORRELAiiON NNCTiON ERROR
Lag Number
TABLE 12
LAKE ERlE WATER LEVEL AND THE ME1 MODEL VARIABLE: LAKE ERlE WATER LEVEL AR MODEL (1,0,0) REGRESSOR: ME! AT LAG14 (MEIQ14)
FINAL PARAMETERS: Number of residuals 182 Standard emx 32752223 Log likelihood -55.178441 AIC 114.3!388 SBC 120.7649
ANALYSIS OF VARIANCE: DF Adj. S m of Sguares Residual Variance
VARIABLES IN THE MODEL: B SEB T M T I O WPROX. PROB.
MODEL SUMMARY CORREMTiON BETWEEN DEPENDENT VARIABLE AND MODEL FIT
R .95 R SQUARE .89 DURBlN WATSON 1.81 DF 181 SIG .00
RGURE 20
LAKE ERJE WATER LEVEL AND MEiQ14 AR MODEL (1,0,0) AUTOCORRELATION FUNCflON ERROR
o., f i f i
Confidence tirnits -
Lag Number
Fumer, with ME1 lagged 14 quarters, and used as an independent regressor against Lake
Ontario water levels. a significant and dong relationship was shown to exist The awregressive
coefficients were significant at an approxirnate probabili of 0.00, 0.00 and 0.05 reçpedveb ( ~ e
Table 14). The R value was strong at 0.73. A i l e the R Square value indicated mat the model
amunted for approxirnately 53% of the explained variation in Lake Ontario water levels. The residuals
generated from this model showed no signs of aubcorrelation, with non-significant Box-Ljung statisücal
values (see Figure 23). Lake Ontano rnay be charactenzed by an AR (2) process because it is prone to
the effects of weather systems at a greater rate than the other lakes. Here, the shocks to the systam
would be fek frorn the first two lags, rnaintaining memory throughout the series. Consequently, since
Lake 0ntan.o water levels adequatety fit a secondorder autoregressive proces, the hypothesis rnay be
accepted due to the statistically significant resutts.
Assessrnent of Hypothesis #4
Net basin supply data for each lake were tested in order to gain a more complete view of lake
level fluctuation in the midst of an ENS0 event Examination of the results showed that for each Lake
NBS time series, the effects of the random shock to the system are being fek well after the incipient
ûigger. As seen on the model resutts, and the correlograms of the residuals, there are no significant
autocorrelations, and all values associated with the Box-Ljung Q staüstics are wll above the 0.05
value. This suggests a weak firstarder autoregressive process exists within each of the Lakes net
basin supplies. Furthemore, ail T-ratio values w e significanüy larger than the criticai value of
approximately 1.658, with the approximate probabilities at no larger than 0.01. See statistical resutts at
the end of this section. Once the net basin suppiy van'ables were appropriately modeled, the variables
w r e tested w iü~ the ME1 index to determine a temporaI fit The resutts show that onîy Lakes Erie and
Ontario approximate an AR (1) rnodel, wtiile Lake Superior fit an ARMA (1,0,1) and Michigan-Huron
failed to meet the requirements that fit any rnodel, attogether. The resuits are described in detail below.
Lake Superior Net Basin Supply and ME1
The relationship between the ME1 (the independent regressor) and Lake Superior net basin
suppu was found to fit an ARMA (1,0,1) rnodel wim a lagged MEI value of 16. This represents the
best-fit rnodel, amough statisticalty weak. Al! coefficients and parameters are statisticalty significant at
an approximate probability of 0.00 iespectivety. As wll, the Tratios for each variable wre acceptable.
The firstader autoregressive coefficient of 0.89 suggests a aong
FIGURE 21
LAKE ONTARIO AUTOCORREiATlON NNCTlON
Confidence tirnits
Lag Number
TABLE 13
LAKE ONTARIO WATER LEVEL AR(2) MODEL
FINAL PARAMETERS: ANALYSIS OF VARIANCE:
Number of residuals 196 Standard emx .63419093 Log likelihood -1 88.33228 AIC 380.66456 SBC 380.22079
DF Aa. Sum of Squares Residual Variance
Residuals 194 78.412 .a21
VARIA8LES IN THE MODEL:
0 SEB T-RATIO APPROX. PROB.
A: LAKE OKïARIO WATER M L AR (2) MODEL (2,0,0) AUTOCORRELATON RJNCTION ERROR
Lag Number
B: LAKE ONTARlO WATER L E E L AR (2) MODEL (2,0,0) PARTlAL AUTOCORRELATION FUNCTION ERROR
Confidence Limits -
Confidence Limits -
k g Number
TABLE 14
LAKE ONTARlQ WATER LEVEL AND THE MU MODEL VARIABLE: LAKE ONTARIO WATER LEVEL AR(2) MODEL (2,0,0) REGRESSOR: ME1 AT MG1 4 (MEIQI 4)
FINAL PARAMETERS: Number of residuals 182 Standard error . 6 S l O8 Log likelihaad -174.66131 AIC 355.32261 SBC 364.93463
ANALYSIS OF VARIANCE: DF Adj. Sun of Squares Residuai Variance
VARIABLES IN THE MODEL: B SEB T-RATIO APPROX. PROB.
MODEL SUMMARY CORREIATION BETWEEN THE DEPENDENT VARIABLE AND MODEL FIT
R -728 R SQUARE 529 DURBlN WATSON 1.894 DF 181 SIG .O0
FIGURE 33
LAKE ONTARIO W A E R L E M L AND MEIQl4 AR2 MODEL (&O$) AUTOCORRELATlON FUNCTION ERROR
Lag Nurnber
process existç between Lake Superior NBS and the MEI. The moving average parameter is 0-81
indicating points in the series where Lake NBS values fluctuate ai random intervals in a more abnipt
and bnef manner. This is reinforced with the observation that on@ 6% of the variations within the series
amuntable wittiin the model (R Square parameter). The R value cf 0.26 indicates a weak relationship
at a significance value of -00. This may be indicative of the size of the lake and its corresponding
drainage basin. The net basin suppiy for Lake Superior may act on random intewais rather than
anticipated cycles. The Iagged MEI value of 16 suggests a four-year, weak relationship exists between
Lake Superior NBS and MEI. Thus, the relationship is weak, although statisiically significant (sse
Figures 24 and 25; Tables 15 and 16); characterized by both long memory and short random shocks
(or damped oscillations). The plots of the residuals indicate a signikant resutt with al1 Box-Ljung
values being weli over the 0.05 levei, and characterized wih no significant autocorreiations (see
Figures 24 and 25; Tables 15 and 16).
Lake Michigan-Huron Net Basin Supply and ME1
The modeling of Lake Michigan-Huron NBS with ME1 as the independent regressor resulted in
a amplete inability to parsirnoniousty fit the variables. It was found thai despite initial success, either
the residuals m e autocorrelated or the statistical results wwe in no manner significant or acceptable.
Possible explanations for a is will be discussed in the following chapter.
Lake Erie Net Basin Supply and ME1
When Lake Erie NBS data was put into an AR model witti lagged values of ME! as an
independent regreçxir, an AR (1,0,0) process wim 8 lags (2 years), was found to produced significant,
although weak resub (see Tables 18 and 19). The autoregresive coefficient is 0.172, at an
approximate probability of 0.01 at an alpha of 0.05. The T-ratio staüstic were both at acceptable
values. The plot of the models errors indicate no autocorrelation arnong the residuals, Mich are
indicative of the insignificant Box-Ljung statistics. The model is considered waak wim an R value of
0.232, which was expected, while appmxirnately 5% of the variation in Lake Erie Net Basin Suppb was
accounted for W i n the rnodel (see Figures 30 and 31).
Lake Ontario Net Basin Suppty and ME1
Lake Ontario NBS modeled with ME1 as the independent regreçsw, resulted in a significant but
weak relationship as wll (see Figures 32 and 33; Tables 20 and 21)). The best-fit model was mat of a
firstorder autoregressive process with ME1 lagged at the third quarter (0.75 year i lag beginning:
Çeptember). W& an autoreggresive coefficient of 0.25, at alpha 0.05, the appximate probability
was about 0.01. There were no significant autocorrelation among the residuals, and al1 Box-Qung
values were non-signlcant at values well above the 0.05 level. The R value of 0.324 indicates a wedc
relationship, with approximately 10% of the variation of Lake Erie NBS being accounted for by the
rnodel.
In conclusion, it was found that ectdi lake level time series fit a w a k AR rnodel (1,0,0).
However, when fitted to rnodels associated with the ME1 as the independent regressor, it was found
that only Lakes Ontario and Erie fit the firstorder autoregressive model. Lake Superior fit an ARMA
(1,0,1) rnodel; while Lake Michigan-Huron could not parsimoniously fit a mode1 with MEI. Thus,
although the original correlograms of Lake NBS indicate a frst-order autoregresive pmcess, they do
not follow this pattern associated with the ME1 representing ENSO events. The hypothesis stating mat
Lake NBS should approximate an autoregressive model Mere a random shock associated with ENSO
at lag t-1 must be rejected. Of course, this is with the exception of the srnaller and southem lakes
min the systern (Erie and Ontario).
FIGURE 24
LAKE SUPERJOR NET BRSIN SUPPLY AUTOCORRELATION FUNCION
Lag Nurnber
1.0?
-5 a
0.0 9 I - P- m - *
-5
IL
- -
- Confidence tirnits -
œ ~ a f i c i e n t 1 3 5 7 9 11 13 15
2 4 6 8 10 12 14 16
TABLE 15
LAKE SUPERlOR NET BASIN SUPPLY AR MODEL (1,0,0)
N m k of residuals 196 Standard erra .97267946 Log likelihood -272.1 9328 AIC 546.39256 SBC 549.67067
ANALYSIS OF VARIANCE:
DF Adj. S m o f Squares ResiduaIVariance
Reskhis 195 184.51 .946
VARIABLES IN THE MODEL:
B SEB T-RATIO APPROX. PROB.
LAKE SUPERlOR NET BASlN SUPPLY AR MODEL (1,0,0) AUTOCORRELATION NNCTION ERROR
Confidence tirnits
Lag Number
TABLE 16
LAKE SUPERIOR NET BASIN SUPPLY AND THE ME1 MODEL VARIABLE: LAKE SUPERIOR NBS MODEL ARMA (1 ,O, 1) REGRESSOR ME1 AT LAG 16 (MEIQIG)
f INAL PARAMETERS: Nwnber of residuals 174 Standard errer .94020902 Log likelihood -234.70778 AIC 475.415% SEC 484.89272
M Y S I S OF VARIANCE: DF Adj.SurnofSquares ResidLtalVariance
VARIABLES IN THE MODEL: B SEB T-RATIO APPROX. PROB.
MODEL SUMMARY CORRELATION BETWEEN DEPENDEKT VARIABLE AND MODEL FIT
R .251 R SQUARE 0.06 DURBlN WATSON 1 -91 3 DF 173 SIG .O0
FIGURE 26
LAKE SUPERIOR NBS AND MEIQ 16 ARMA MODEL(1,0,1) AUTOCORRELATION FUNCTION ERROR
Lag Number
1 .O
.5 i
0.0
-.5 i
IL O q -1.0,
-
-- - I I
I
- Confidence Mi -
- - c o e f f i c i e n t 1 3 5 7 9 11 13 15
2 4 6 8 10 12 14 16
FiGURE 27
LAKE MICHIGAN-HURON NE7 BASIN SUPPLY AUTOCORRELATION FUNCTION
Confidence Limits -
coefficient
h g Number
TABLE 17
LAKE MICHIGAN-HURON NET BASIN SUPPLY AR MODEL (1,0,0)
FINAL PARAMETERS: ANALYSIS OF VARIANCE:
Number of rm-duals 1% OF Adj. Sum of Squares Residual VarWnce Stancfard emr .99l 52322 Log fikelihood -275.97148 Residuals 195 1 19 1.763 -983 AIC 553.94296 SBC 557.221 08
VARIABLES IN THE MODEL-
0 SEB T-RATIO APPROX. PROB.
AR1 23420199 .O6992198 3.3494761 -00
LAKE MICHIGAN-HURON NBS AR MODEL (1,0,0) AUTOCORRELATION FUNCTlON ERROR
Confidence tirnits -
coefficient
Lag Number
FIGURE 29
LAKE ERlE NET BASIN SUPPLY AUPOCORRELATlON FUNCTiON
coef f ic ient
Confidence Limits -
Lag Number
TABLE 18
LAKE ERIE NET BASIN SUPPLY AR MODEL (1,0,0)
FINAL PARAMETERS:
Nomber of residuais 196 Standard erm 1 .O034472 Log likelihood -278.30303 AIC 558.60505 SBC 561 .a841 7
ANALYSIS OF VARIANCE:
OF Adj. Sum of Squares f?e&d Variaria
Residwis 195 196.380 1-1 006
VARABLES IN THE MODEL:
B SEB T-RATIO APPROX. PROB.
LAKE ERiE NBS AR MODEL (1,0,0) AUTOCORRELATiON FUNCTlON ERROR
Lag Number
TABLE 19
LAKE ERiE NET BASIN SUPPLY AND THE ME1 MODEL VARIABLE: LAKE ERfE NBS MODEL AR (1,0,0) REGRESSOR: ME1 AT LAG 8 (MEIQ8)
FlNAi PARAMRERS: Number of residuak 188 Standard ermr -97672904 Log likelihood -261 -34862 AIC 526.69724 SBC 533.17012
ANALYSIS OF VARIANCE: DF Adj. Sumof Squafes ResiBialVaBance
VARIAELES IN THE MODEL B SEB T-RATIO APPROX. PROB.
MODU SUMMARY CORRELATION BETWEEN DEPENDENT VARIABLE AND MODEL FIT
R .232 R SQUARE .O54 DURBIN WATSON 1.993 RF 187 SIG .ûû
FIGURE 31
LAKE ERIE NBS AND MEIQ8 AR MODEL (1,0,0) AUTOCORRELATION N N C T i O N ERROR
Lag Number
FIGURE 32
LAKE ONTARIO NBS AUTOCORRELATION NNCTlON
Confidence tirnits -
c o e f f i c i e n t
Lag Number
TABLE 20
LAKE ONTARlO NET BASIN SUPPLY AR (1) MODEL (1,0,0)
FINAL PARAMETERS:
Nwiber of msiduais 196 Standard e m 92436368 Log likelihood -266.01483 AIC 534.02965 SBC 537.3776
ANALYSIS OF VARIANCE:
OF Adj. Sun of Squares Res&ai Variance
R a i s 195 173238 -8880
VARIABLES IN THE MODEL-
8 SEB T-RATIO APPROX. PROB.
M E ONTARIO N8S AR (1) MODEL (1,0,0) AUTOCORRELATION FUNCTlON ERROR
2 4 6 8 10 12 14 16
Lag Number
TABLE 21
LAKE ONTARO NET BASIN SUPPLY AND THE ME5 MODEL VARIABLE: LAKE ONTARIO NBS MODEL AR (1 -0.0) REGRESSOR: MEI AT LAG3 (MElQ3)
FINAL PARAMETERS: Nmber of residuals 193 Shdademw .92840272 Log likelihood -258.5491 5 AIC 521 -09829 SBC 527 -62637
ANALYSIS OF VAXIANCE: DF Adj. S m o f Squares Residual Variance
VARIABLES IN THE MODEL 0 SEB T-FiATIO APPROX, PROB.
MODEL SUY MARY CORRELATTlON BETWEEN INDEPENDENT VARIABLE AND MODEL FIT
R -324 RSQUARE -105 DURBIN WATSON 1.983 DF 192 SIG .O0
LAKE ONTARIO NBS AND MElQ3 AR MODEL (1,0,0) AUTOCORRELATION FUNCîïON ERROR
Confidence LVnits -
Lag Number
7.0 DISCUSSION
In evaluating processas that are important in influendng the dynamics of a lage and mmpkx
systern such as the Great Lakes, reseafchers typicalîy look at temporal averages. These fme s c a k
can be viewed as 'snap shots" of the system being studied, and may reveal important, but kansienf
responses by the entire system (Flint and Stevens, 1989). Causai mechanisms should be the basis for
research questions addressing the level of certainty needed to undentand pmcesîes in the Great
Lakes. These approaches may help to make predictions about the Mure which, can then be used to
formulate policy for successful environmental management
7.1 SOI and ME1 Modeling
The modeling of the SOI and ME1 heiped to detemine th& the Mulovariate ENSO index would
serve the study in an efficient manner. As previously stated, the aüempt to mode! the SOI and the MEI
was somewhat cornplex. The difficulty in modeüng these variables rnay be due ta the factttiame data
were divided into quarters. Because each quarter contains 3 months, and the characteristic length of
an ENSO event is approximately 4 to 8 months in duration, the lagging of the variables may be a
response to the sensitivity of the data sets to the initiation of ENSO at the monîh of May. If ENSO
events progress during îhe month of May, the time series may require lagging in order to efficientfy
represent this. This rnay be interpreted through the iag values of 3 and 5; and 2 and 3; for the SOI and
the MEI respectivefy. The ARMA nature of the time series found within this thesis rnay be indicative of
the lagging of MEI, and the stochastic nature of the factors it represents, and measured M i n it
The use of quarteriy data rnay not be the most efficient rnanner in uihich to compare the two
indices, if there were to be a method that allows one to do so. It did however allow the indices to be
measured in the same manner as al1 of the other variables studied. allowing fw wnsistency in the
analysis. The unpredictability of atrnospheric factors is offen dficult to rneasure with precision and
accuracy making the representative indices hem çornewtiat cryptic. This is evident within the models
generated to characterize ENSO events. Despite the complexity however, it is still satiçfactary to
accept tfie rnodefs produced and use hem witfi confidence.
7.2 Hypothesis # 1
The two uppermost and largest lakes (Superiw and Michigan-Huron) mve charactsrized by
ARMA (1,O.l) modek, rnost likely due the individual characteristic of each lake. This is in addition to
the orientation of the lakes to air masses, bringing precipitation, variation in air temperare, and its
resulong effects on evaporation rates. The ARMA (1,O.l) aspect of Lake Sumer water levels (LSWL)
and Lake Michigan-Huron water levels (LMHWL) is one where the swial behaviour of the time A e s
wggests that disturbances associated with lake levels are cyclic, and shorter in duration man th& of an
AR (2) process. Specifically, a pure AR rnodel or a pure MA mode1 muid be inappropfiate, to describe
the data. and thus the most parsimonious step wuld be to mi% the models.
The sheer sire and position of Lake Superior rnay causa many to fhink mat a was the
precunor to proceeding iake level fluctuations throughout the systern. However, it seerns that due b
its massive size, and depth, and westerly orientaüon, the effects of a phenomenon such as ENSO is
fett, afthough not at a suspected impact According to the results of the statistical anabsis with ME1 as
the independent regresçor, the optimum effect of ENSO is not fully realized for 18 lagslquabers. This
means that after 4.5 years, Lake Superior rnay reffect the nature and intensrty of a parücular ENSO
event It may be the size of the lake cornparecl to its relatively srnall drainage basin, which plays a mle
in the dampened outcorne of Lake Superior water levels (LSWL).
Likewise, k i n g at the head of the Great Lakes system and wiolout a major source of water
infiow by rivers or Wbutaries; Lake Superior water levels are most affected by infiow via its catchment
basin. and precipitation. Precipitation however, is deemed quite important because of the mere size of
its surface area. Hence the Iarger the lake surface area, the greater arnount of precipitation it is able to
catch. As well, Hartmann (1989) states that during particular months, evaporation rates may be more
important in effecting lake levels due to the surface area. This is rnost sign8cant during the month of
December, when aie lake temperature and air temperature is rnost different, creating the greatest rates
of evaporation.
Therefore, to considerably change lake levels at a rapid rate, one would require an externe
ENS0 event, persisting over a spart of at least a few years. Thus, the resulüng trançfonaüons on lake
levels wuld be one with an initial shock persisting for approximateiy 3-6 months (an ENSO event), and
quickly dissipating thereafter. The 3 8 month nature of the shock persistence is due to the ARMA
(1,0,1) characteristic cf the model, where both AR and MA oniy require one tem. The damped
oscillhry nature of the shock is reffective of the ARMA process where a pure cycle is not likely to
occur. This means that Lake Superior water levels exhibit responses to the iriggering effects of MEI,
mat are pseudoqcüc, where a ma l ! reversal in the response occurs, helping to dampen the proces.
Lake Michigan-Huron water levels also exhibit an ARMA (1,0,1) process, which suggestç that
m e n the lakes are considered to act as one, there is the nature of mernov uii8iin Itie system.
Howver, after the shock is presented, its effects last for a finite priai of tirne. It is suggested mat
because mey are situated perpendicular to stwm !racks, mey are less likely to feel Ihe full effectç of
ENSO events As well, Lake Michigan-Huron has onty a siighüy iarger drainage basin to & surface
m a ratio (2.1), îhan Lake Superior (GLERL, 1999). Therefwe, the effects uimulating on its catchment
basin will be somewhat dirninished since the land draining into the lakes is comparatively mall.
Additionally, the size and depth of the lakes add to the damping of irnrnediate aftereffects, due tD the
ability to absorb w& as storage. This may be, due to the fact hat Lake Mictiigan retins water for a
very long time, and is conçidered a natural cuidesac (Beranek, 1999). Beranek believes Lake Huron
to be the major conveyor of water lrorn the upper $ the rest of the s~stem.
Thus oie model urith ME1 as the independent regressor was found sbtisticalb significant at a iag of
14, or 3.5 years. Here, the nature of lake level fluctuation within Lake Michigan-Huron is one h e r e the
effectç of ENSO are most considerably enmuntered in a tirne domain that is synonymous with %xt bookm events. The moçt likety explanation rnaybe simpiy that the consequenceç of ciimatic change are
not realized in Lake Michigan-Huron for a longer period of time because of its size and depth,
orientation to stom tracks, and relatively small catchment basin. Indeed, the lag time may be
someuuhat shorter since water is fiowing frorn Lake Superior into Lake Michigan-Huron. Fatid et al.,
(1997) affirm that lake oufflows and inflows a e more significant to water volume than that of
precipitation and evaporation.
Therefore, it rnay be çtated that the responses to ENSO events are al% cyclic in nature, but onty
within a s~ecific period of tirne. The time series representing Lake Michigan-Huron suggests ttiat the
size and depth of the lake would allow substantial responses to take place, and refiect an
autoregressive explanation. Here, the responses or disturbances dwindle as time passes.
Consequently, the orientation of the lakes may r e m the moving-average nature of the model, allowing
intemediate aftereffects to remain in the systern for a fnite number of periods, and then ceasing to
affect it Hence, the time series is one where the response to ENSO events are evident, and
characteristic of Lake Michigan-Huron attributes.
The slow rnouing fluctuations of Lake Michigan-Huron is affmed in Hartmann (1988) which states
mat with simulation of lake Ievels, a a d y shows that even if Lake Superior outRows and net basin
supplies to the lakes wwe above its long-tami average, exireme conditions would have 10 persist for 2
consecutive years to raise the levels of Lake Michigan-Huron by even 0.5m. As such, one rnay
conclude that there is a slow process within oie systern, especially between Lakes Superior and Lake
Mchigan-Huron. This explains quite well the lager lags (ctiarscterized by M e s Superior and
Michigan-Huron), or the ti me it takes to most substantially induce changes in lake levek.
It is intsresting to note however, mat Meadow et d.. (1997) assert mat a nwthward shift of the
prefmed cyckne kack aaoss Lake Michigan exists. Therefwe, wim the assumption mat most intense
precipitation is 10- on the southeastem side of an exlra tropical cyclone system, the northward shfi
wuld king precipitation into the Iake and its adjacent drainage basin. It is believed that the combining
of me tw lakes takes away frorn unique chaactensüa, despb cornmon sirnilaities. Wmi wa$r
quickly flowing fiom Lake Supenor into Lake Huron, the stonng nature of Lake Mchigan maY cause
damping of inte readons to clirnatic events sudi as ENSO. This rnaY furfier explain the ARMA nature
of lake level fluctuations to MEI.
7.3 Hypothesis # 2
The su-ss of me statistical resuits suggest th& Lake Erie water level f l w h t h s are mfied
by memwy within the series, in relation to a disturbance or shock. The AR (1) mode1 exhibits a
parsimonious lit, with statisticalty confident resuits. As suggested by Kite (1992), the Orienta(i0n of the
lower lakes (Lakes Erie and Ontario) would generate an autoregresive process, or one vrim a rnemory
since the bulk of the water flowing into the lake is generated by the upper and bm~ght via the
Detroit River.
The acceptance of this hypothesis is supported by the various physical fadon configure
Lake Erie. This means that the small and shaliow nature of the lake allows for less storage capacity,
making extrerne changes in precipitation and infiow, fett for a long period of tirne. Hartmann (1988)
affirms this by siating that evaporation losses for Lake Erie can be quite extreme due to heat storage.
Consequently, evaporation losses should be at îheir greatsst during the month of October. Being along
the p m s of storm tracks and air masses allows it to receive the effects of precipitation, while its
position and shallow nature aliow for increasad heat storage. Therefore, evaporation rates are quite
high, illustrating anoîher causal factor associated with lake level change.
The examination of Lake Ene water levels and the MEI, has depicted a relationship where lake
levels are most significanüy effected aftw a lag of 14 or 3.5 years. One rnay expect a shorter lag
penod, due to the above physical factors; however, Lake Erie rnay be useful in rnimicking the actions of
ENS0 events. This rnay also be due to the fact that Lake Erie receives 3.6 tirnes the arnount of water
from the upper lakes via infiow than it does frorn precipitation and mnoff (Farid et el., 1997). Quinn and
Guerra (1986) have also found that improvements can be made to forecast Lake Erie total water
supplies by paying speciai attention to its net basin supplies, and the supply of water it receives fmrn
the upper lakes. They found that net basin supply values were useful indicatDn of future lake level
fluctuation.
Thefef~e, the effects of ENSO induced climat8 changes rnay require me 3.5 yesrs to
accumulate above and beyond the water it receives frorn the upper lakes. As vrith al1 of the Iakes, the
biggering affects mat cause lake-levels to flucbiate rnay have existed before it was fek within the
systern, but took a whiie longer to be realized. As a result, Lake Erie water level data, depicts a tirne
sefies vhere there is a decaying effect of the disturbance over fme, ail the H i l e penisting m i n the
s y a m . Wmout the size and cornplexities of the upper lakes, Lake Erie may exphence the affects of
ENSO eventç, with distinct rnernory rnost significantiy after 3.5 yean. This may also be reffecove of the
results found for Lake Michigan-Huron, h m wihich it receives a l q e amount of inflow. Thmfore. %
appean as though a systernaüc relationship exists bebween the lakes, wnceming the responçes to
ENSO.
7.4 Hypothesis # 3
Wth the acceptana of mis hypolheçis, Lake Ontario water levels may be sMad to be
characterized wiüi a lengthened exposure tn ENSO induced clirnate changes and sustain mese
influences within its system for a knger period of tirne. This is characteristic of an AR (2) pmcess
which was generated through statistical anaiysis.
The AR(2) nature of the tirne series data suggests that the introduction of a disturbance into
the systern is present for a slightly longer period of tirne, dwindling as it progresses. Lake Ontario water
ievels wiII then manifest according to the pdcular disturbance, with its greatest affect occumng &ter
3.5 years. The mernory or resonance of the disturbance will reside for at least 6 months after the initial
shock. The relationship betweeo ENSO events and lake level fluctuation appesn to be valid and quite
significant, Mile consistent wioi oie resutts found with the other lakes. It does however, possess
unique characteristics wtiich are responsible for the statistical resuk. These are describeci below.
Of all the Great Lakes, Lake Ontario has the Iargest ratio of watarshed land rtrea to lake
surface area which indicates a much larger relative draining basin than the other lakes (Flint and
Stevens, 1989; Farid et el., 1997). This allows for a quicker response to climatic factors that produce
precipitation and runoff over a larger ratio of land to surface water. This also corresponds to its
orientation, uutiich allows it b encounter the full effect of residing weattter patterns and air masses.
Despite ifs smaller water surface area, its large drainage basin and orientation to weaoier patterns
allows it to experience a full range of weather phenornena, thus the conesponding influences. This is
confirmed in Flint and Stevens (1989) that &tes Bat Lake Ontario is drongiy influenced by
rneteorological events.
As wll, Lake Ontario receives 3.8 tirnes as rnuch volume of water as inflow from the upper
lakes than it does via prscipitation and runoff (FarÏd et el., 1997). Its greatest infiow is from the Niagara
river, Mile ifs dominant oMow is focused into ttie St Lawrence River. Much of what Lake Ontario
receives as infiow leaves the lake as outffow. This illustrates the dynamic and fast-paced environment
in which water fluctuation behaves within this pab'cula systern. However, due to the deep nature of
the lake (average 86rn), storage capacity inaeases, causing a slight ability to stabilize initiai climatic
changes. This may explain why it requires 3.5 yeas to optirnally influence Lake Ontaio wabr levels.
However, once an exîrerne disturbance persists, the shock within the system rernains knger than any
of the other lakes. This is consistent with Lakes Michigan-Huron and Erie, suggesting a temporal
pattern m i n the system. -
7.5 Hypothesis # 4
~t is thought th& NBS should mimic GLWL hrough ti me due to its inIrinsic kinship with climatic
factors, however the staüstical relationships generated w e weak. One may indeed p o s b l a
essentialty, NBÇ rates are conirolled by storm tracks, which influence many local wather and cümaüc
conditions. Yet, these values are representative of discrete point measurements, over the individual
lake. Therefore, Lake NBS will be dependent on random averqes of air temperahm, predpmon,
mnoff values, and evaporation. The weak, albeit significant relationships can be the result of
inamrate and imprecise data colleclion, and the sheer magnitude of stochastic elaments within
atmospheric and clirnatic patterns. Because NBS values are based on averages (since it is impossible
to measure al1 clirnatic rates), it seems logical that the staüstica! analysis pertaining to it and fake levels
are weak.
In addition, WB know that the hydrologic cycle varies substantially by lake (Lee, 1993), vuhich
suggests that conformity would be an unrealistic expectation. These, variations result in distinct and
differing factors in the values of net basin supplies. Quinn et el. (1997) affims ttiis Mi le citing that
such deviations from each other are typical. For example, in Lake Erie 51% of the water in the cycle
leaves the lake through evaporation. On the other hand, 26% of the water added to Lake Ontan'o by
the hydrologic cycle leaves in that manner (Quinn et a/., 1997).
Aside, these interpretations may also lend in the explanation of not being able to fit a model to
Lake Michigan-Huron NBS with MEI as the independent regressor. The area in which net basin suppty
data is collected is quite large and combines iwo separate systerns. Discrete point data collection
cannot represent ail of the unique and characteristic factors of bath iakes, and then expect to exemplify
them by averaging the data. Proper representation of both lakes is not preçent, and thus biased results
may have been produced. This seems rnost logical since one would expect even the slightest
significant relationship due to cornmon factors M i n both of the variables.
Lakes Erie and Ontario NBS data sets adequately fit an AR (1) model, Mile wioi ME1 as the
independent regressor, the data also fit an AR (1) mode1 with ME1 lagged at 8, and 3 respectively. The
Lake Erie NBS tirne lag of 2 years may be explained by an inaeased sensiibii to NBS factors, that are
spread over a larger relative catchment basin. This of course is coupled with upper lake infbws and
the propensrty of residing weaiher patterns. The even sh- lag period associabd with Me Ontan'o
NBS, 0.75 yearç, may be the resutt of the same factors asociated with Lake Erie NBS, hile the
statistical resuîts tend to exceed those of the others. The AR process associated these madels
indicates the hypotheçized effect of random shocks, whereby feedback remains in the system after the
associateci disturbance.
ln reference to Lake Superior NBS, it was found that a weak AR (1) rnodel couid not
adequatety d-be the time series, while an ARMA (1,0,1) model could. The ARMA (1 ,O,1) process
may be a partMarty proficient model conceming how Lake Superior funcüons with perhrbaüons. The
slowr response to ENSO (conceming the lag value of 4 yem) rnirrors the physical properties of the
lake, where the enormity, and lack of a major inflow of water, allows for a slow but most definiteiy,
positive relationship. Here, ENSO a& as a random shock, which lriggers darnped oscillations of
change W i n the system. This means that the cycle of ENSO events are creating a change in me
NBS rates, although aïe effects are feit for a finite pdod of time, being eventualiy darnped out
Therefore, NBS time series are affected by ENSO events as indicated by the MEI, and reflect
the stochasüc elements of the variables that make up tbe data set Compared to that of GLWL the lag
tirnes are reduced, Mi le the statistical resub are not as confident or convincing. It is assumed tbat the
changes is NBS associated wiih the changes in MEI, are weak, and cannot açsuredfy explain more
suitably, how aie effects of ENSO effect the Great Lakes. The foundaüon to this lies in the fact of weak
statistical resuits and the vague nature of boa vaiables. It is difficuit to determine the aftereffects of
ENS0 when NBS values are most absiract and indeteninate. Consequentty, it is deemed that for the
purposes of this thesis, the use of NBS values were not overly helpful in supporb'ng the resutts of
change of Great Lake water levels.
7.6 SYSTEM RESPONSES
7.61 Lake Level Modeling
One may açsume that due to itç large size and position within the system, Lake Superior would set
the stage for the lowr lakes in regard to response rnechanisms to lake level exlrernes. This
apparentty, is not xi. Faid et al. (1997) confimis this by stdng that not al1 effects of water level
Ruduaiion will be diredy proporüoned to those of Lake Superior. The differences in preUpitation
patterns, air ternperatures, related evaporation rates, runoff, drainage basin aea, and lake inflow, and
ouüiow rates al1 exercise distinct patterns on the individual lake. In relation to lakdevel modeüng, the
system may be cuncluded to be one where the larger lakes (Superior and Michigan-Huron) expdence
shorter responses to disturbances, due to their sire, depth and relatively srnaller drainage basins.
Meanwhile, the smaller and lower iakes (Ontario and Erie) experienca longer distuhance mernory with
shorter periods of eqtiilibriurn after an initial shock.
Lake Superior and Lake Michigan-Huron encounter darnped oscillations, or a pseudocyciic
process, where lake level fluctuations are present, but wilhout significant memory or immediate
outcomes. The ARMA process representing past lake fluctuation suggests mat there are sbong
autoregresive processes present in the systems, mile there are points in the series where lake level
fluctuation disintegrates on a more curt basis. Lake Erie was modeled with an AR (1) process, where
there is a definite mernory m i n its systern, as it receives randorn disturbances. Lake Erie water level
fluctuations rnay behave in this manner due to its orientation to starm îracks, its small and shallow
nature, thus making it more susceptible to the effects of exireme meteorological events. Greater water
infiow h m the upper lakes also adds to the disorder within itç systern. This makes the agitation felt at
a longer rate than both Lakes Superior and Michigan-Huron. Lake Ontario receives water from the
upper Mes, and Lake Erie, Mi le the AR (2) aspect of the modeling, suggests that the fluctuations are
characterird with long mernory, or feedback as well. Here, disturbances 10 the systern will generate a
long memory, whereby lake level fiuctuations are influenced by shocks that omrred in the distant past
This makes it more sensitive to climatic anomalies such as ENSO, more so than what is encountered in
the upper fakes.
As a whole, the system rnodeled here rnay be approxirnated to one where thwe is inaeasing
sens- and longevij, to the effects of variables, iriggering changes and fluctuation in lake levels.
This is appmximated by the ARMA processes of Lake SupMor and Lake Michigan-Huron, and the AR
processes of Lakes Erie and Ontario, AR (1) and AR (2) respectiveîy. Aloiough various clirnatological
fachxs are distinct to each lake, the overall effect increases lhroughout the system. This is defined by
the size and orientation of each lake, the inflow of water to îhe system, as well as the rao of drainage
basin area to the site of the lake surface area. As a resutt, Ihe system cba* i h h k s an inmase of
lake level fluctuation by way of susceptibilii and duration of s h a s to me SY-m.
7.62 Lake Levels and the Multivariate ENSO Index
In regard to iakelevel fluctuation and ENSO, it was found that with ME1 as the independent
regressar, îhe modeis generated for each lake resernbled t h o ~ of fie original models. Wi ME1 acting
as the iriggering rnechanisrn, the lag tirne in the Cme secies re~esents me M o d of tirne M'ween the
change in the ME1 (ENSOinducing values), and its dronge~t or m s t ggnifi~ant effect on kvei
fluctuation. Therefore, Lake Superior water levels are designated a lag of 4.5 years, hi le Lake
Michigan-Huron, Lake Erie, and Lake Ontario water levels are characterized with a 3.5 year lag. Quhn
(1992) states that Lakes Erie and Ontario (due to #eir low ratio of volume to ouolow) He affected by
normal clirnatic vdaljons of less than 20 y e m in duraüon. M e m e lakdavel conditions over the
period of 2 to 8 years can also significantly affect the residence fime of Lake Erie and Ontario. This
affect is by way of an inaease (or decrease) of water fiowing thmugh the lakes. Further, mis is
confirrned by Farid et ai. (1997) which asserCs that the l o w lakes receive a greater percentage of
inflow, and will be more sensitive to random shocks to oieir system.
Lake Michigan-Huron, Lake Erie, and Lake 0nM.o rnay contain the sarne lagged ME1 value
because of the possible cornplements between Lakes Michigan and Huron. Aithough b k e Erie and
Lake Ontario water level fluctuations are designated witti a kng mernory, Lake Michigan-Humn rnay
realize ENSO inducing effects at a similar lag, but with a l e s distinct mernwy and consequence to the
disturbances. This is illustrated in the ARMA nature of its rnodel. As well, Lake Superior with its large
sire and deep waters rnay be able to darnpen any exireme effects of ENSO inducing climate variances,
or simpiy, not fuliy actualize the effects for approxirnateiy 4.5 years.
It is suggested that perhaps the water levels of Lake Michigan rnay be closer to the modeling of
Lake Superior due to b small catchment basin, 'cu1desac" nahire, and perpendicular orientation.
Lake Huron as sMed previousiy, acts as the conveyor of water h m Lake Superior to the lower lakes,
and rnay resemble the models of the lower lakes. Lake Huron has a larger catchment basin, and thus,
receives the lion's share of Lake Superiots outfiow, and rnay be mwe susceptibk tD dianges in
clirnaüc factors. Consequentty, despite hydraulic simildes, water level fluctuations of the two lakes
may stiRe long-term patterns, aeating a balancing of important chaactensti'cç. This rnay explain why
such a lage lake rnay share sirnilar lagged ME1 values as Lake Erie and Lake Ontao.
The ME1 as the independent regressor to lake-level fiuchiations is indicme of a çystem wide
swing of Ructuaîion, in regard to exVerne weaîher patterns. We rnay state that M S O definiteiy affects
water level. alhough there are many factors at play m i n the Great Lakes. The ability to stabilize
dishbancas into the system may be purely characteristic of the individual lake, and may be cumulative
over time, as the disturbance perçists. With the peailia lagged foms, it rnay be implied that there is a
temporal p&m present regarding ENSO eventç and GLWL Therefore, with the results generated
h m this research, it rnay be implied that wiîh the introduction of an ENSO event, GLWL are shiffed
most significantly af$r 3.5 yearç, with the exception of Lake Superior, which experienas modificaüons
afbr 4.5 years.
7.63 Net Basin Supply
The modeling of Great Lakes net basin supply values illusirate some interesting sy&m
response indicators. Like the previous models produced conceming Lake level flu&&'on, there
seems to be an inaease in sensitivity to various factors as you go down the lake system. This
examination muid not be fully acquired however, because Lake Michigan-Huron could not fit a model
with NBS. Wth Lake NBS as the independent regreçsor, Lake Supefior required 16 lags, Lake Erie
required 8 lags, and Lake Ontario required 3 lags. Thus, there seems to be a deaease in lag tirne, or
in other wwds, a decreaçe in the time in takes for a padicular ENSO event to significantly effect the
lakes, as it progresses within the systern. Even without the modeüng of Lake Michigan-Huron, mere
seems to be the same trend apparent, with NBS. This is qui$ logical since net basin supplies should
rnimic the hydmlogic properties of each lake. This is comparable to the system conclusions found
conceming the MEI, an indicator of ENSO events. Overall, the resutts generated were wak, although
statistically significant This attests to the large outfiow rates for most of the lakes cornpared to that
received by ninoff and precipitation.
The models generated might be explained by the study wrnpleted by Hostetler (1 990) which
çMes th& under transient clirnatic conditions, there is an assumption mat climatic variables and lake
levels change together for basins where the surface area of the iake is large cornpared with the total
catchment area. Here, the migratory short memory shocks may be a resuit of changes dire* related
to net basin suppiy. Quinn et al. (1997) has found using flood climate scenarios, that Lakes Michigan-
Huron, and Lake Erie experience the greatest impacts conceming NBS variables. This is reinforced
with t h -ment that although Lake Supefior averages were d isp lad accordingly. the changes m e
wnsiderably less than the lower lakes. Cmley et al., (1995) states that m i n the realrn of transposed
climates, it is ahmys Lake Superior that receives the driest m o n . The kwer lakes on the orner hand,
may realize the resonant transformations to their syçtems due to a slight inaease in sensitiv'i. As
mil, it is thought that sensitivity, no matter the migin of the shock, inaeases within the system because
the kwer lakes receive a greater percentage of inhw (Faid et el., 1997). Of course, Lake Sumer and Mchigan-Huron are effeded by this due to the Iack of major infiows. Thwefore, the affects
conceming net basin supplies rnay follow the same logic. The difference rernains in the lack of required
descriptive data to represent Lake NBS.
8.0 CONCLUSIONS
A a s t i c a l assessrnent between the Southern Oscillation Index and the Multivan'ate ENSO
lndex detemiined that the sufficienüy m e s the examination of Great Lakes water level fluctuation,
and net basin supply rates. Time series anaiysis was nin on the variables to determine p&monious
models of the variables thernseives, and those cornpleted with ME1 as the independent regresmr.
Histwical paüerns were exarnined to determine if insight into the sys$rn coukl be generated, and
whether significant relationships existed between lake level phenornena and speafic cfimaüc variables.
The final analysis invohred taking the information gained thmugh time series analysis, and relang L to
physicai aspects of the system under study.
In generai] the acting systern comprishg the Great Lakes is one where individual cornpanents
(the lakes), behave in a rnanner characteristic of the climatic, physical, and geographic feahires it
possesses. However, there are also systematic influences responsible for lake performance and
activity, uihich generate an inûinsic relationship. This is realized in the anaiyses perfonned within mis
research project In sumrnation, the following was found.
1. For the purposes of this thesis, the ME1 was believed to be the more suitable and useful, indicator
of ENSO events. The data series made into quarteriy periods needed quite cornplex models,
atthough a prefemed model was süll evident With semester data of both indices, the ME1 was
deemed more applicable as wll.
2. Lakes Superior and Michigan-Huron both exhibited mixed rnodel characteristics, whereas the
existence of short and long-temi mernory resided in ihe series. Random shocks ta the systern a e
designated by a pseudocyclic nature, whereas the effect of ENSO events are feît m i n oie
systern for a finite time-period. Staüstical analysis revealed strong relafionships behwen water
levels and the ME!. The size and orientation of ttrese lakes rnake for wn@asted models, which
indicate a damping affect to the influences of ENSO events. Lake Superior was regressed against
ME1 lagged at 18, while Lake Michigan-Huron was lagged against ME1 at 14.
3. Lake Erie water ievels were found to exhibe an AR (1) model, and with ME1 as the independent
regressor the best-fit model was that of an AR (1) with the ME1 lagged at 14. This suggests Bat
the variables associated vcim an ENSO event will be most signitïcantly nggered after
approximately 3 'Xyears. This is best explained by Quinn (1 992) which states that e m m e ldte
level conditions over the period of 2 to 8 y e n will increase the arnount of waber Rowing thmugh
the lake, Mile also affecting residence ümes of both Lake Erie and Ontario. The çhâllow nahire of
Lake Ene makes it vulnerable to ENSO events, especially conceming evaporation rates due to the
lack of heat storage capacity.
Lake Ontario water levels fit an AR (2) model wi(h the independent r q r e a r , MEI, lagged at 14 as
weîf. Akhougn possassing a reiativety srnail water surface area, Lake Ontario has great depth and
a comparatively large catchment basin. Together these allow for sensiüvity M i n the ti me a e s , :p which is illudrated through the AR (2) aspect of the data. Th8 resonanca of an DJSO event
rernains within the system longer than the orner Lakes, h i l e requin'ng 3'4ears 1D optimall~ affect
Lake Ontario water levels.
Generalfy, Great Lakes net basin supplies were found to have weak, aithough signCcant
relationships with the MEI. One may postulate that essentially, NBS values are closely linked to
prevailing weather systems, especially those oiat persist for a long period of Cme. As such, Lake
NBS values camy weak relationships with the ME1 due to simple stochastic processes. Essenti ally,
precipitation, evaporation, and runoff rates are random processes, and thus, almost impossible to
predict due to the nature of these factors. If Lake Michigan-Huron could have been modeled it may
have been seen that the lags required to fuliy effect the lake data decreased as the systern
progressed. The resutts of this thesis point to that conclusion although it is not appropriate to
finalize.
Systematicaffy, it was found that as a whole, the general rnodels aeated here rnay be
approxirnated to one where there is increasing sensitivity and longevity to the effects of variables,
kggwing changes and fluctuation in lake levels. This is approximated by the ARMA processes of
Lake Superior and Lake Michigan-Huron, and the AR processes of Lakes Erie and Ontario, AR (1)
and AR (2) respectivety.
Using ME1 as the independent regressor to water level data, it is indicalive of a system wide swing
of fluctuation, in regard to extreme weather patterns. We may sMe that ENSO events definiteiy
affect water level, despite the rnany other factws preçent within the Great Lakes. W h the peculiar
lagged foms, it may be implied that mere is a temporal pattern present regarding ENSO events
and GLWL Therefore, with the resuits generated fmm this reseadi, it may be impüed that with
the inlroduction of an ENSO event, GLWL a e shif$d rnost signicantty at$r 3.5 yean, with the
exception of Lake Superior, which experiences modifications after 4.5 years.
Using ME1 as the independent regresuK against Lake NBSl data, it was found mat signilicant
relaonships existed although its weak nature suggests mat ENSO events (reprecented through
ME1 values) influence these levels, whiie the randorn nature of both NBS and developing
abnosphMc conditions, make model creation sornewhat troubiesome. A temporal systemac
pattern could not be identified wittiout rnodeiing Lake Michigan-Huron net basin supply values. It
could be prewpposad that if there were a systernab'c frend present, it would follow that af the other
im identified above.
8.1 Suggestions For Fumer StudyKheoretical Implications
The question remains, how long does t take the ENSO to trigger the criücal factors long
enough to maka lake levels deviate fmrn their long t m averages. It is important to pay closer
ai$nti on to the lagging of the ME1 t m , because it rneans that it takes n lags to effect obsenred
changes in lake levels. However, we cannct at this point say Men the factors mat influence lake kvels,
(pre~ipit~on, evaporation, temperature, run off) begin to atter tD substantially affect them.
Furthemore, since clirnate change is not linear, with rapid and large changes in averages and in
variability occumng in the recent past, it is often difficutt to put clirnate change and its effect on the
Great Lakes into perspective (Quinn, 1998).
Furthemore, it is stated that the natural cornplexity of the Great Lakes, has features which
rnake it diflïcult to handle anaiyûcaliy. Flint and Stevens (1989) defined these wmplexities below.
1) The components or subsysterns are connected in a selected manner. Not everything is closeiy tied to everything else.
2) The impact of ecological events is not uniform. Different areas react in different ways.
3) Drarnatic changes in behaviour are naturai to rnany ecosysterns, such as lake syçtems, and rnany of these are beyond man's rneans to predict
4) Variability, not consistency is the characteristic of such systems, that enable them to adjust and therefore persist
For these reasons, it is betieved that the data concerning Lake Michigan-Huron should be
separated and not lumped togettier so that they are considered one lake. Aithough they are mnnected
by the deep siraits of the Mackinaw, Lake Michigan and Huron behave differentiy and should be Veated
so, especialiy when shidying syçtem dynamics. It is hypothesized mat Lake Huron and Michigan ofbn
damp out the dynarnics of each other, rnisçing important aspects of the individual lake.
Therefore, to further research the dynamics of the Great Lakes Basin, it is suggested that
increased study on system anabsis be accomplished. This shoufd include inaeased study on the
climatological factors that influence lake levels (precipitation, temperature, evaporation, and mnoff)
outside of the net basin suppiy, for each lake. This wukl allow for valuable knowledge on how the
individual lake is effected on a local basis by ENSO events. There is growing evidence that the
changing composition of the atmosphere is beginning to influence spwf~c components of the
hydrologie cycle. Notwioistanding, it is not yet possible to differentiate such effects from the natural
variability of Great Lakes water levels. It would be interesting to see how clirnataiogical facbws efFect
each lake, and how this is incurporated into the system dynamics. T h e is a large 'assurnption" of
observed lake levels by not specifying e x a m what the climate changes are, that are taking place other
than those that are quite general.
Finaliy, the concepts, staüstical analyses, and sumrnations depided here may be applied to
the vast collection of research being completed conceming the changing fates of the Great Lakes.
Pefhaps a more elegant model muid be developed that could efficienüy desaibe the exact forces
uiwking within the individual lake, and those that culminate W i n the entire system. As exploration into
ENS0 events increase, precise examination rnay be perfomed to delineate the mechanims invohred
in lake level fluctuation. Subsequenüy, the natural, dynarnic, and sensitive system comprising the
wastal environment may benefït frorn information gained ihrough further research, and a more
cooperative balance between nature and human.
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APPENDICES
APPENDIX I
SEMESTER SERIES RESULTS
THE ME! AND SOI
MODEL: THE ME1 AUTOCORRELATION FUNCTION SEMESTER DATA
Lag Number
1.0 1
.5 4
0.0
THE MEI PARTIAL AUTOCORRELATlON FUNCTlON
-.5 1
LI O a -1.0
Lag Number
1 3 5 7 9 11 13 15
2 4 6 8 10 12 14 16
, - - -
- Confidence Lirnits -
œ~beffiaent
MU AR MODEL (2,0,0) SEMESTER DATA
FINAL PARAMETERS: ANALYSlS OF VARIANCE:
NiPnber of residuals 98 DF ADJ.SUM OF SQ. RESIDUAL VARLANCE Standard erra .61299û44 RESIDUALS 96 3.3320 .3757 Log likelihaod -90.439313 AIC 184,87863 SBC 190.04856
VARIABLES IN THE MODEL:
B SEB T-RATIO APPROX. PROB.
MODEL SUMMARY CORRELATION BETWEEN DEPENDENT VARiABLE AND MODEL FIT
R 681 R SQUARE -463 DUREIN WATSON 2.014 DF 97 SIG .O0
THE MEi AUTOCORRELATlON FLJNCTiON AR MODEL (&O$)
Lag Number
MODEL THE SOI AUTOCORREIATION FUNCTION SEMESTER DATA
Lag Number
THE SOI PARRAL AUTOCORRELATION FUNCION
Lag Number
SOI AR MODEL (I,O,O) SEMESTER DATA
FINAL PARAMETERS: ANALYSIS OF VARIANCE:
NiLmberofreslreSldwk 98 DF ADJ-SUM OF SQ. RESIDUAL VARIANCE Sbndad emx -71 152845 RESIDUALS 97 49268 .SI63 Log Iikeiihood -105.36043 AIC 212.72086 SBC 21 5.3582
VARIABLES IN THE MODEL:
0 SEB TRATIO NPROX. PROB.
MODEL SUMMARY CORRELATf ON BElWEEN DEPENDENT VARlABLE AND MODEL FIT
R A91 R SQUARE .241 DURBIN WATSON 1.74 DF 97 SIG -00
THE SOI AUTOCORRELAllON FUNCTlON AR MODEL (l,O,O) SEMESTER DATA
Confidence Lirniîs I -
Lag Number
GREAT LAKES DIVERSIONS INFORMATlON AND DATA
IMPACT OF EXJSTING DIVERSIONS ON LAKE LEVELS
1 DIVERSION 1 AMOUNT ] SUPERlOR ( MICH-HUR 1 ONTARlO
Source: Croley (1986)
LAC CHICAGO WELLAND COMBJNED
Also in Croley (1986) is the consideration of diversion effects, which are deemed srnail in
cornparison witti the 1.5 foot seasonal cycle and the 6ft range of annual variations (values also statd
in Croley 1986). In addition, the ma I l diversion effects coupled with the long system response time,
are stated to make diversion plans unsuitabie for Great Lakes regulation of lake levels. The slow
response time to man-induced changes wuld not produce changes responsive to natural fluctuations.
3200 9400
- 0.07 - 0.06 + 0.07
- 0.21 - 0.18 - 0.02
- 0.14 - 0.44 - 0.33
- 0.10 O + 0.08
APPENDJX III
STAllSTlCAL DEFINITIONS
Autocorrelation Function (ACF)
Is often in the fom of a bar chart of the coefficients of correlation between a time series and the lags itseff. These should already be differenced. By looking at the ACF plot, you should be able to idenûfy the numbers of AR andior MA terms needed. Autocorrelation is an indication of wbether past behaviour of a variable affects its present value (SPSS, 1994).
Akaike Information Critarion (AIC ) Schwartz Bayesian Criterion (SBC)
Measures how well the mode1 fits the series taking into acmunt the fact that a more elahrate d e l is expected to fit better. Choose between different models for a given series. The model with the lowest AIC or SBC is best (SPSS ,1994).
Box-Jen kins Methodology
The basic idea behind self-projecting time series forecasting madels is to find a mathematical fomufa that wiIl approxirnately generate the historical patterns in a time series.
8ox-Jen kins Forecasting Method
The univariate version of ais rnethodoiogy is a self-projecting tirne series forecasting method. The underfying goal is to find an appropriate formula SI that the residuals are as maIl as possible, and exhibit no pattern. The mode1 building process involves 4 steps: Repeated as necessary, to end up with a specific formula that replicates the patterns in the series as closely as possible and al= produces accurate forecasts (Chatfield, 19%; Arsharn, 2000).
Is also based on statistical concepts and principles and are able to d e i a wide range of tirne series behaviour. It has a large cias of mdels to choose from and a systernatic approach for identifying the correct modei form. These are both statistical tests for venfying the mode1 validity and statistical masures of forecast uncertainty. In mntrast, traditional forecasting rnodels offer a limited number of models relative to the cornplex behaviour of many time series with little in the way of guidelines and statisticai tests for venfying the vaiidity of the selected rnodel (Chatfield, 1985; Arsharn, 2000).
bx-Ljung Q Statistic
Are probability values assocjated with the correlation amng the residuals of the mrnpoçed model. ldealiy once M 10 a correlogram, oie Box-Ljung Statisk should be over the value of 0.05 (the signficance levd) (SPSS, 1994).
Lag versions of the variable are often used in regular models. This allows varying amounts of recent history to be brought into the forecaçtlagging independent variables is often necessary to be able to predict the fuhire. To predict what wiil happen in pend t based on mat happened up to period t-1 ( m a m , 2000).
A transition that bnngs past values of a series into the current case. The case prior to the wrrent case is a lag of one. T w casas prior to the current case is a fag of W... (SPSS, 1994)).
Lag T i m
IS the difFmnce in time units of a series value and previous âeries values. In h'me series analysis, the lag typically represents the period of tirne between the change in the independent or predidor (exogenous) variable and its strongest (most signifcant) effect on the dependent or predicted (endogenous) variable (Arsharn, 2000).
A time series is said to be govemed by a first order autoregressive process if aiment values of the time series can be expressed as a linear funcüon of the previous value of the series and a random shock. The AR procsss is characterized with mernory or feedback and oierefore, the systern cm generate intemal dynamics (Chaffield, 1985).
The 2 rneans that you have 2 autoregressive terms. Therefore, the curent values of the üme series c m be expressed as a linear function of the iwo previous values of the series and a randorn shodc (Chaffield, 1 985).
THE AR Parameter
The AR parameter describes the effect of unit change in zt-1 on zt, and which needs to be estimated. The random shocks, also known as errors or white noise in the series are assumed to be normally distributecl wiü~ m a n = 0, cunstant covariance's and independent of zt-1 (Chaffield, 1985).
Moving Average Process (MA)
Moving average processes are simple mathematical processes. The moving average process is merely a moving, fixed interval dverage of a time series data used to smooth fiuctuanons and distortions in the data and provide a more rneaningful representation of underlying trends and cycles. An MA process is one wtiereby future data values are expressed as a linear combination of past errors. These processes have known inbinsic cycles (Chaffield, 1 985.)
A t-1 repreçenl random shocks of one or more prior points of the senes. Shocks are asstdmed to corne from cornmon (normal) distributions with common location and scale. Random shocks are propagated to future values of the series (non-linear). The events or disturbances will not only have an irnrnediate effect but also affect 'level' indicators to a lesser extent in several subsequant tirne-periods (Chaffietd, 1985).
Autoregressive Moving Average(ARMA) Process
Is a multiplicative rnodel which includes one or more nonseasonal pararneters with one or more seasonal pararneters. 80th long and short-term mernory resides within the mode!. The MA depicts abrupt, short-ten rnernory, where îhe disturbance effects the system for a finite period (fie order of the MA), and stops effecting it The order of the MA specifies how many previous disturbances are averaged into the new values. The AR disturbance dwindles as time passes (Chatfield, 1985).
NAME: Kimberfy Anne Peskan
PLACE OF BIRTH: Windsor, Ontario, Canada
YEAR OF BIRTH: 1972
EDUCATION: Catholic Central High School, Windsor, Ontario 1986-1 991
University of Windsor, Windsor, Ontario 1992-1 997 B.A. Geograph y (Environmental Resource Management)
University of Windsor, Windsor, Ontario 1998-200 1 M.A. Geography (Environmental Resource Management)
