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A Unified Ontario Flood Method: Regional Flood Frequency Analysis of Ontario Streams Using Multiple
Regression
by
Kirti Sehgal
A thesis submitted in conformity with the requirements for the degree of Master of Applied Science
Department of Civil Engineering University of Toronto
© Copyright by Kirti Sehgal 2016
ii
A Unified Ontario Flood Method: Regional Flood Frequency
Analysis of Ontario streams using Multiple Regression
Kirti Sehgal
Master of Applied Science
Department of Civil Engineering
University of Toronto
2016
Abstract
The Ontario Ministry of Transportation (MTO) requires regional flood frequency equations to
determine peak flows of specific return periods, established using the data from gauged
locations, to design structures at the crossings of streams and rivers. This study intends to bridge
the gaps in the current estimation techniques used in Ontario and utilize the additional data to
improve its accuracy. Regional Flood Frequency Analysis (RFFA) of Ontario streams was
performed using multiple regression and the equations for the T-year flood quantile (2, 10, 25, 50
and 100 year) were developed. The results of the regression based Unified Ontario Flood Method
(UOFM) for the province reaffirms the conclusions of previous studies that peak discharge is
directly related to drainage area. Other factors such as the lake attenuation index, representative
of the area of lakes and wetlands, and climatological factors also contribute to the determination
of the peak discharge.
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Acknowledgments
Flood Frequency and statistics were strangers I never wanted to be friends with before
September 2014. A transfer to MASc brought along with it an opportunity to overcome my fears.
I owe the success of this work to Dr. Jennifer Drake. It wouldn’t have been possible without her
motivation and constant belief in me throughout the course of this project. Her countless
suggestions for my research and constructive feedback on my reports and thesis helped me to
achieve the results and the project could be completed in a short time span.
I would also like to thank the Ontario Ministry of Transportation, in particular Dr. Hani Fargaly,
for funding the project under its Highway Infrastructure Innovation and Funding Program
(HIIFP). Hani’s constant input of the user requirements and expectations were helpful in working
towards a simple solution for engineers and designers.
My achievement would not have been possible without the constant love and support of my
friends and family. The group lunch and coffee breaks became an important part of my day and
kept me going. Thanks to my friends Vivek, Balsher, Dikshant, Divyam and all others in GB415.
I would like to thank my brother Deepak for being there when I was tensed and encouraging me
to get back and fight it out. I am deeply indebted to my uncle and aunt, Dinesh and Sangeeta
Chhura for being my motivator and facilitator. They took such good care when I was new in
Canada and couldn’t support myself. My masters would not have been possible without their
support. This journey would have been difficult without my husband Pawan who took the
endless proofreading tasks I had for him and taught me the use of excel macros to speed up the
repetitive jobs. He loved me when I was impossible and this journey could have been longer, if
he was not there. I am grateful to my mother who has been my constant support and pillar of
strength. I credit her for the passionate woman I am today. I can never be grateful enough for
supporting my education even during the hard times. Last, but most importantly, Thank you
Papa for always being there. From where I see, you haven’t gone anywhere. Your love and
belief still inspires me to give my best without worrying about the results.
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Table of Contents
Acknowledgments .......................................................................................................................... iii
Table of Contents ........................................................................................................................... iv
List of Tables ................................................................................................................................ vii
List of Figures ................................................................................................................................ ix
Chapter 1 Introduction .................................................................................................................... 1
1.1 Background ......................................................................................................................... 1
1.2 Research Objectives ............................................................................................................ 2
1.3 Thesis Structure .................................................................................................................. 3
Chapter 2 Literature Review ........................................................................................................... 5
2.1 Background ......................................................................................................................... 5
2.2 Factors affecting Peak Flows .............................................................................................. 6
2.2.1 Physiography ........................................................................................................... 7
2.2.2 Climate .................................................................................................................... 9
2.3 Regional Analysis Procedures for Flood Frequency Studies ............................................ 10
2.4 Review of the Current Regional Flood Frequency Analysis (RFFA) Procedures ............ 11
2.4.1 RFFA Procedures for Ontario ............................................................................... 11
2.4.2 RFFA Procedures for Other Jurisdictions ............................................................. 15
2.5 Review of Available Data ................................................................................................. 18
2.5.1 Flow data ............................................................................................................... 18
2.5.2 Physiographic Data ............................................................................................... 22
2.5.3 Climatic Data ........................................................................................................ 23
2.6 Review of Statistical Analysis Methods ........................................................................... 23
2.6.1 Non-parametric testing .......................................................................................... 23
2.6.2 Station Frequency Analysis .................................................................................. 27
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2.6.3 Multiple Regression .............................................................................................. 30
2.7 Summary ........................................................................................................................... 32
Chapter 3 Methodology ................................................................................................................ 34
3.1 Data Collection ................................................................................................................. 34
3.2 Data Preparation and Screening ........................................................................................ 36
3.2.1 Estimating Annual Maximum Instantaneous (AMI) values for gaps in
historical records ................................................................................................... 36
3.2.2 Screening of HYDAT stations .............................................................................. 37
3.3 Data Analysis .................................................................................................................... 41
3.3.1 Non-parametric Testing ........................................................................................ 41
3.3.2 Station Frequency Analysis .................................................................................. 42
3.3.3 Multiple Regression Analysis ............................................................................... 44
3.4 Summary ........................................................................................................................... 46
Chapter 4 Results of Regional Flood Frequency Analysis ........................................................... 48
4.1 Unified Ontario Flood Method (UOFM) .......................................................................... 48
4.2 Illustration of Calculation Steps ........................................................................................ 50
4.3 Summary ........................................................................................................................... 52
Chapter 5 Verification and Evaluation ......................................................................................... 53
5.1 Verification of Regression Method: Application to Ontario ............................................ 53
5.2 Analysis of the UOFM for a Small Urban Watershed ...................................................... 56
5.3 Analysis of UOFM for Medium to Large Urban Watersheds .......................................... 57
5.4 Simulation for Peak Flow Estimation: Case of Urban Floods .......................................... 60
5.5 Comparison with Other RFFA Methods ........................................................................... 61
5.5.1 Comparison of UOFM and MIFM (South) ........................................................... 61
5.5.2 Comparison of UOFM and MIFM (Shield) .......................................................... 62
5.5.3 Comparison of UOFM and NOHM ...................................................................... 64
vi
5.6 Climate Change Considerations ........................................................................................ 65
5.7 Summary ........................................................................................................................... 65
Chapter 6 Conclusions and Recommendations ............................................................................. 67
6.1 Conclusions ....................................................................................................................... 67
6.2 Limitations and Recommendations for Future Studies ..................................................... 69
References ..................................................................................................................................... 71
Appendix A: Example of the Annual flow data for WSC ............................................................ 76
Appendix B: Summary of all HYDAT Stations ........................................................................... 79
Appendix C: Estimation of AMI flow data from AMAD flows ................................................... 90
Appendix D: Summary of results of Non Parametric Analysis .................................................... 92
Appendix E: Illustration of Station Frequency Analysis .............................................................. 99
Appendix F: Stepwise regression output from SPSS .................................................................. 102
Appendix G: Stations rejected from Multiple Regression Analysis ........................................... 143
Copyright Acknowledgement ..................................................................................................... 147
vii
List of Tables
Table 1: Function Classification and Design Flows (Source: Ontario Ministry of Transportation,
2008) ............................................................................................................................................... 6
Table 2: Relationship of Watershed Class with Class Coefficient (Joy & Whiteley, 1996) ........ 12
Table 3: Ratios to Flood Quantiles of Different Return Periods to the 25-year Quantile (Joy &
Whiteley, 1994) ............................................................................................................................. 13
Table 4: Summary of Previous Studies ......................................................................................... 16
Table 5: Example of Data from OFAT (Representative Station: 05PB018) ................................ 36
Table 6: Summary of the Difference in AIC ................................................................................ 43
Table 7: Correlation Matrix of Predictor Variables ...................................................................... 44
Table 8: Coefficients of the Regression Model and Output Summary ......................................... 48
Table 9: Range of Parameters used for Equation Development ................................................... 49
Table 10: Range of Quantile Estimates ........................................................................................ 50
Table 11: Verification Stations Parameters .................................................................................. 53
Table 12: Application of UOFM to Verification Stations ............................................................ 54
Table 13: Small Catchment Parameters ........................................................................................ 56
Table 14: Small Catchment Flood Quantiles ................................................................................ 56
Table 15: Medium to Large Urban Catchment Parameters .......................................................... 57
Table 16: Analysis Results for Medium to Large Urban Watersheds .......................................... 58
Table 17: Station Parameters for Comparison with MIFM (South) ............................................. 61
Table 18: Comparison of UOFM with MIFM (South) ................................................................. 62
viii
Table 19: Station Parameters for Comparison with MIFM (Shield) ............................................ 62
Table 20: Comparison of UOFM with MIFM (Shield) ................................................................ 63
Table 21: Station Parameters for Comparison with NOHM ......................................................... 64
Table 22: Comparison of UOFM with NOHM ............................................................................. 64
ix
List of Figures
Figure 1: Ecozones of Ontario (Source: Ecozone, 2012) ............................................................... 8
Figure 2: Isohyetal Map with Location of Environment Canada Weather Stations ..................... 10
Figure 3: Empirical Guidance Chart (Source: Watt et al. (1989)) ................................................ 18
Figure 4: Flow Data Comparison for a Typical Station (HYDAT station: 02HB021) ................. 20
Figure 5: Location of HYDAT Stations ........................................................................................ 35
Figure 6: Estimation of Missing Values of Instantaneous Peak (Sangal (1981)) ......................... 37
Figure 7: Location of Urban catchments ...................................................................................... 38
Figure 8: Delineation of an Urban Watershed with OFAT ........................................................... 38
Figure 9: Watershed Delineation Discrepancy in OFAT .............................................................. 40
Figure 10: Stations in the Hudson Plain ....................................................................................... 40
Figure 11: Stations Eliminated (non-compliant with nonparametric test hypotheses) ................. 42
Figure 12: Histogram for Q25 Quantile (dependent variable) ...................................................... 45
Figure 13: Regression Stations and Ontario Highways (Source: Highways, 2014) ..................... 46
Figure 14: Observed and Predicted Quantiles for Verification Stations ....................................... 55
Figure 15: Observed and Predicted Quantiles for Medium to Large Urban Watersheds ............. 59
1
Chapter 1 Introduction
1.1 Background
Flooding of streams and rivers have been a concern for designers and policy makers for a long
time. The destructive nature and randomness of floods has often led researchers and engineers to
develop prediction tools for large flood events. The history of flooding in Ontario encompasses
many notable events, the most severe of which was Hurricane Hazel in 1954. Flooding caused by
Hurricane Hazel took 81 lives (mostly in the City of Toronto) while simultaneously leaving
thousands of Ontario residents homeless (TRCA, 2014). Property damages associated with this
event have been approximated at $100 million, which is about $1 billion today (TRCA, 2014).
Another notable severe flooding event occurred in May 1974 in the Grand River watershed.
Approximately, $6.7 million was assessed by Leach (1974) as residential, industrial and
municipal losses. In June 2004 a storm event in the Grand River watershed deposited 200 mm of
rain in a very short span of time causing severe flooding and excessive erosion
(Hebb and Mortsch, 2007). In 2013 both Alberta and Ontario experienced dramatic flooding of
Downtown, Calgary and the Don Valley Parkway, Toronto. The damages for these flood events
have been estimated at more than $1.72 billion and 465 million in insured losses for Southern
Alberta and Toronto, respectively (Insurance Bureau of Canada, 2015) Thus, floods have
become important and their prediction is pivotal for design of structures on our water courses.
Design floods are the peak flood discharge (or flow rates) which are critical when assessing the
risk and safety of hydraulic structures (e.g. culverts and bridge crossings), both planned and
existing. The prediction of these peak flood values during design of a hydraulic structure at water
crossing requires historical flow records at that location. These values are typically obtained at
gauging stations built on streams and rivers. However, it is common to encounter situations
where the location of interest lacks the associated historical stream flow data. For a water rich
province like Ontario it is not possible to have gauges on all water courses and, even for
situations where the stream is gauged, the point of interest may not coincide with the location of
the gauge station. Thus, when sizing bridges and culverts, engineers regularly depend on regional
analysis to estimate flood quantiles. Regional flood frequency analysis (RFFA) is performed to
develop relationships between flow estimates and relevant physiographic and climatic
2
parameters of gauged streams in a hydrologically homogeneous region. These equations are
developed using the flow data available from the stream gauging stations. The resulting
relationships are used to predict flood quantiles at ungauged locations within the same region.
1.2 Research Objectives
Ontario currently uses a combination of different regional analysis methods for the design of
highway culvert and bridge crossings (Ontario Ministry of Transportation, 1997). Accepted
methods include the Modified Index Flood Method (MIFM) (Joy and Whiteley, 1996), the
Northern Ontario Hydrology Method (NOHM) (Watt, 1994) and the Rational Method. It was
observed that there are inconsistencies in the method which should be used based on the drainage
area of a watershed. For example, the MIFM cannot be applied for watersheds less than 25 km2.
The NOHM is applicable for drainage areas located in the Canadian Shield only and can only be
used for watersheds ranging from 1 km2-100 km
2. Also, both the MIFM (Shield) and the NOHM
can be used for drainage area ranging from 25 km2-100 km
2 in the Shield region of Ontario. Such
a situation creates the potential condition where none of the approved analysis methods are
suitable for an engineer’s design work (e.g. For a watershed of size approx. 13 km2 located in the
southern region of Ontario) or conversely, scenarios where multiple methods may be applied
(e.g. For a watershed of size 68 km2 located in the Shield region). During discussions with the
Ontario Ministry of Transportation (MTO), the requirements and analysis tools for the study
were finalized. The following points were identified as the limitations in the current RFFA
procedures that necessitated the need for this study.
1. Availability of approximately twenty years of additional stream flow data since the last
study of MIFM and NOHM completed in 1996 and 1994, respectively. The additional data,
when accounted for, will provide a better representation of the current watershed and stream
flow conditions.
2. Changes in catchment characteristics, which lead to gradual changes in the flow regime,
should be taken into consideration.
3. Inconsistency in area classification and the corresponding equation for prediction of flood
quantiles needs to be addressed.
3
4. Analysis procedures for urban watersheds, predominately required for the south, are non-
existent. A review of the available data to ascertain the feasibility of such a study was
requested to be performed.
Thus, the objective of the study is to develop a simple and easy to use set of equations for
regional flood frequency analysis (RFFA). This thesis discusses the analysis procedures
undertaken and presents the results of the RFFA for Ontario.
1.3 Thesis Structure
The thesis presents the development of a unified method for prediction of peak flows for Ontario
streams and consists of six chapters. The contents of each chapter are presented below:
Chapter 1– Introduction
This chapter provides the background for the current research; identifies the research objectives
and provides a description of the thesis structure.
Chapter 2– Literature Review
This chapter provides a detailed review of the physiography, climate and hydrologic data for
Ontario. It also presents a review of relevant statistical literature and recent RFFA studies. This
establishes the foundation for the methodology used for the thesis and outlines the rationale of all
the subsections in the methodology.
Chapter 3– Methodology
This chapter describes the research methodology undertaken and presents the results obtained at
intermediary steps during the analysis work. The results of each step are also presented in this
section because, for majority of the cases, the subsequent step is dependent on the result obtained
at the previous step. For example, station frequency analysis is performed for only those stations
which were accepted during the non-parametric testing.
Chapter 4– Results of Regional Flood Frequency Analysis
This chapter presents the results of step-wise regression analysis to develop the Unified Ontario
Flood Method (UOFM). It also presents the design table developed for computation of peak
4
flows for ungauged drainage basins for two regions of Ontario. The chapter highlights the
computation of the probable range for the predicted quantiles, established from the standard
errors of stepwise regression process, and illustrates an example calculation for UOFM.
Chapter 5– Verification and Evaluation
This chapter provides the results of the verification and evaluation of the UOFM equation for
predicting flood flows. A separate analysis was also performed to check the applicability of the
equations for urban watersheds. Finally, a comparison study was performed to check the
performance of the equations relative to the methods currently used in Ontario.
Chapter 6 – Conclusions and Recommendations
This chapter discusses the important conclusions of the thesis with respect to the research
objectives. Limitations of the current investigation and regression-based flood methods are
discussed. This may serve as the recommendations for additional research for improving the
peak flow estimates for Ontario.
5
Chapter 2 Literature Review
The following sections provide an overview of the relevant literature related to Regional Flood
Frequency Analysis (RFFA) and the methods adopted for the current investigation. It provides a
background highlighting the need of RFFA procedures and its relevance to the MTO. It
subsequently discusses the factors which affect peak flows for any drainage catchment. This
section also reviews the methods currently used for regional analysis and reviews recent
investigations in various provinces of Canada and the United States. Subsequently, this section
reviews the available data and procedures for the development of RFFA equations through
multiple regression analysis.
2.1 Background
Provincial Highway Directive B-237 sets forth the MTO Drainage Management Policy and
Practice (Ontario Ministry of Transportation, 2008) for the province of Ontario. Ministry of
Transportation and Communication (MTC) as was known previously, now MTO has been
publishing its drainage design manuals since 1979. It has undergone several revisions since its
original publication and outlines the existing policies and design methodologies adopted by
MTO to date. In 1989, the MTO Drainage Management Technical Guidelines was prepared
which outlines the MTO standards and was used in conjunction with the drainage manual. Since
1997, the MTO has issued a single Drainage Management Manual (DMM) to replace the two
previous manuals. DMM includes the standards of practice and design methodologies but did not
include the drainage management policies guiding the practices and design. In 2008 MTO
published its Highway Drainage Design Standards (HDDS). This document outlines the existing
drainage design standards for components of highway infrastructure that have been adopted by
MTO over the years. The HDDS focuses on the highway surface drainage, water crossings and
storm water management for different components of the highway infrastructure. The HDDS
provides recommendations for the return period of design flows to be considered for various
highway classifications based on its function. The return period for various highway
infrastructures is summarized in Table 1.
6
Table 1: Function Classification and Design Flows (Source: Ontario Ministry of
Transportation, 2008)
Functional Road
Classification
Return Period of Design Flows (Years)
Total Span (≤ 6 m) Total Span (> 6 m)
Freeway, Urban Arterial 50 100
Rural Arterial, Collector Road 25 50
Local Road 10 25
The MTO owns and operates approximately 2800 bridges across the province (Ontario Minstry
of Transportation, 2015). MTO requires peak flow estimates (flood quantiles) of various return
periods to size new hydraulic structures or for repair of existing structures. For design of these
structures, like brides and culverts, a return period is specified, for example T= 100 years for a
freeway bridge of more than 6 m span (Ontario Ministry of Transportation (2008),
Watt et al. (1989)). A return period of a flood may be defined as the average time between two
flood events of similar intensity. So, it may be expected that large flood events have large return
periods and vice-versa (Rao and Hamed, 2000). A T-year return period instantaneous flood has a
recurrence interval of T years or the annual probability of exceedance of p (=1/T). Thus, a 100
year flood has an annual exceedance probability of 1%. A flood quantile of T-year is the
magnitude of flood corresponding to the exceedance probability of p. Return period of the flood
to be considered for design purpose (design flood) is often decided based on the anticipated
design life of the structure in consideration among other factors such as highway class, annual
daily traffic (ADTs), importance of the structure, etc. (Watt et al. (1989), (Ontario Ministry of
Transportation, 1997)).
2.2 Factors affecting Peak Flows
The variation in climate, in combination with the physiographic parameters, produces unique
flood characteristics for different watersheds. The climate determines the flood generating
mechanism in a watershed, whereas physiography affects and distinguishes the response to the
climatic parameters. Thus, physiography and climate are both important factors which should be
considered while developing the regional flood frequency equations.
7
2.2.1 Physiography
Physiography is an important determinant of the flood response for a drainage basin. Drainage
characteristics such as area, land use, storage and slope influence the hydrologic response to
floods and vary significantly throughout the province (Moin and Shaw, 1985). One of the earliest
investigations for Southern Ontario by Karuks (1961) identified the dependence of peak flows in
a catchment on the drainage area, storage factor, slope and the stream density. Further
investigations by Moin and Shaw (1986) for the whole of Ontario found the following
physiographic parameters as important: drainage area, slope of the channel, area of lakes and
swamps and the shape factor (parameters mentioned in the order of importance). Analysis by
Joy and Whiteley (1996) and Watt (1994), MIFM and NOHM respectively, concluded drainage
area to be the most significant determinant of peak flows. Other significant factors included the
slope, area occupied by lakes and swamps and the curve number. In recent years, urban flooding
has also become a common and costly phenomenon throughout the province. The
imperviousness associated with the urban environment decreases its ability to absorb and allow
infiltration of rainfall. This change causes more peaked floods than an equivalent rural
environment.
Homogenous region classifications have the inherent assumption that watersheds within a region
exhibit similar hydrologic properties and behavior. The assimilation of information together from
gauged stations within a homogenous region provides a better estimate of the flood quantiles
when the information is transferred to ungauged points of interest during regional analysis. Thus,
delineation of homogeneous regions in a geographical area is an important step before
proceeding with regional flood frequency analysis. Various homogeneous region classifications
have been proposed for Ontario in previous studies based on different criterion (e.g. Moin and
Shaw (1985), Moin and Shaw (1986), Gingras et al. (1994)). The homogenous regions employed
in these flood regression studies are based on (1) flood characterestics (by computing of
regression residuals) up to and including the data till the 1980’s and/or 1990’s, (2) grouping the
regions based on homogeniety tests or (3) the peak flood generating mechanism. Since flood
characteristics may change over time a more general method of regional classification is
required. A classification by the National Ecological Framework identifies the ecozones in
Canada. This classification is based on dividing large geographical units with an ecosystem
perspective. These divisions, called ecozones, depict regions of broadly similar climatic and
8
geological characteristics (Wiken, 1995) and do not depend on the flood data for this
classification, unlike previous studies like Moin and Shaw (1986) and Gingras et al. (1994)).
Thus, it can also provide a common index for comparison of climate and related phenomenon
within Ontario across different research areas. According to the classification, Ontario is divided
into three ecozones shown in Figure 1. The three ecozones present in Ontario are the Hudson
Plains, Boreal Shield and Mixed Wood Plains.
Figure 1: Ecozones of Ontario (Source: Ecozone, 2012)
The Hudson Plain ecozone, located in Northern Ontario, has large portions of its land cover in
the form of wetlands. This is a result of poor drainage creating a high degree of water retention
throughout the region (Moin and Shaw, 1985). This ecozone has sedimentary bedrock which
gradually drains to the Hudson Bay and James Bay (Wiken, 1995). The Boreal Shield ecozone is
dominated by the Canadian Shield and forest vegetation. The Shield has a thin soil cover over
9
the rocks, resulting in rapid flows in the streams (Moin and Shaw, 1985). It is also characterized
by large natural storages in the form of lakes and wetlands which attenuate flows
(Moin and Shaw, 1985). The Mixed Wood Plains represent one of the most fertile and
productive ecozones of Canada and most of the urbanization has concentrated in this region
(Wiken, 1995). The soil in this region is well drained and has marshes which provide some
storage to runoff (Moin and Shaw, 1985).
2.2.2 Climate
The climatology across Ontario varies and so do the flood causing mechanisms. Flooding occurs
due to various climatic and hydrologic factors such as snowmelt, spring rainfall, thunderstorms,
hurricanes, ice jams and/or a combination of these factors (Gingras et al. (1994),
Moin and Shaw (1985)). Spring rainfall is the most common cause of flooding across the
province (Moin and Shaw, 1985). The recent floods due to spring rainfall in Peterborough in
June 2004 caused damages in millions of dollars (City of Peterborough , 2005). The 49th
parallel
storm in June 2002, also due to excessive precipitation (approximately 400 mm) caused severe
flooding in north-western Ontario and other parts of Canada and the United States. It caused
damages in excess of $31 million, impacted infrastructure and also affected the local First Nation
communities (Hebb and Mortsch, 2007). Thus, climate and specifically precipitation is a variable
factor throughout the province and its various forms determine the flood causing mechanism.
The isohyetal map presented in Figure 2 shows the variation of mean annual precipitation across
the province. This is based on the data from Climate Normals published by Environment Canada
for 151 weather stations across Ontario from 1981-2010. Average annual precipitation ranges
from less than 700 mm in the northwest part of the province to more than 1250 mm in the
“snowbelt” east of Lake Huron.
Previous studies (Karuks (1961); Moin and Shaw(1986)) have identified the precipitation over a
region as an important determinant of the observed stream flows. However, in the currently used
regional analysis methods, NOHM and MIFM, precipitation over a drainage catchment was
either not considered or found to be statistically insignificant during the investigation procedures
by Watt (1994) and Joy and Whiteley (1994). In contrast most American studies such as
Capesius and Stephens (2009), Waltemeyer (2008) and Landers and Wilson (1991) for the states
of Colarado, New Mexico and Mississippi, respectively, as well as studies for Maritime
10
provinces Newfoundland (Rollings, 1999) and New Brunswick (Aucoin et al. 2011) all consider
precipitation to be a crucial parameter for predicting peak flows.
Figure 2: Isohyetal Map with Location of Environment Canada Weather Stations
2.3 Regional Analysis Procedures for Flood Frequency Studies
Statistical analysis of long term stream flow records are considered the best source of
information to predict future events of a specific return period (Joy and Whiteley, 1996). Two
analysis procedures have historically been applied to regional flood frequency analysis in
Ontario: index flood method and the multiple regression method. Index flood method was
traditionally the most popular method of estimating peak flows and was used in most Canadian
provinces during the 1960s and 70s (Watt et al., 1989). This method involves developing a
relation between physiographic parameters with an ‘index flood’, usually the mean annual flood.
A frequency curve relates this index flood to any other T-years flood quantile. The index flood
method assumes a single shape or slope of this frequency curve within one region. This
11
assumption does not hold for situations where there are large storage effects (Watt et al., 1989)
which have an attenuation effect on peak flows. The second technique, called the multiple
regression involves developing a regression based relation between the peak flows of different
return periods or the mean annual flow and the physiographic and/or climate parameters using
various regression procedures. Multiple regression and its various procedures are discussed in
detail in Section 2.6.3.Watt et al. (1989) identified direct regression of quantiles of different
return periods as an improvement over index flood method. Regression based methods have a
limitation on their applicability and should only be applied to watersheds with basin
characteristics within the range of those used for the development of the regression equation
(Watt et al. 1989). Additionally, the data should represent natural flow conditions and the
equation should not be applied to watersheds with basin characteristics outside of the range of
parameters used to develop the equations. Regression based methods have also started to have
wider acceptability in various provinces of Canada and the United States. Watt et al. (1989)
mentions the studies based on direct regression of quantiles in the late 1980s. Other recent
examples include Waltemeyer (2008) for New Mexico, Capesius and Stephens (2009) and Vaill
(2000) for Colorado, Eash (2001) for Iowa; Rollings (1999) for Newfoundland,
Aucoin et al. (2011) for New Brunswick and Sandrock et al. (1992) for Saskatchewan. All of
these reports use a regression based approach for determination of flood quantiles.
2.4 Review of the Current Regional Flood Frequency Analysis (RFFA) Procedures
2.4.1 RFFA Procedures for Ontario
The MTO Drainage Management Manual (Ontario Ministry of Transportation, 1997) outlines the
procedures for regional flood frequency analysis allowed for the design of provincial highway
culverts and bridge crossings. Currently, the methods used in Ontario are the Modified Index
Flood Method (MIFM) and the Northern Ontario Hydrology Method (NOHM). A review of
these methods is presented below.
2.4.1.1 Modified Index Flood Method
The Modified Index Flood Method (MIFM), presented in Joy and Whiteley (1994) and
Joy and Whiteley (1996), is based on the basic form of the Index flood equation used for the
estimation of the mean annual flood. The procedure is modified for prediction of Q25 quantile
12
and its implementation is illustrated in the drainage management manual (Ontario Ministry of
Transportation, 1997). The MIFM requires estimates of the Curve Number (CN) to compute its
corresponding Base Class.
Base class = −5.64 + 0.191 ∗ CN Equation (1)
The channel slope and storage are then used to compute the adjustments in the base class and the
adjusted watershed class is calculated.
𝑆𝑙𝑜𝑝𝑒 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 = 1.815 ∗ [{𝑆𝑊
0.004}
0.5
− 1] Equation (2)
𝑆𝑡𝑜𝑟𝑎𝑔𝑒 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡 = −0.1142 ∗ 𝑆𝐴 Equation (3)
where SW = the slope of the drainage basin (dimensionless); SA =Storage Area (%)
𝐴𝑑𝑗𝑢𝑠𝑡𝑒𝑑 𝑊𝑎𝑡𝑒𝑟𝑠ℎ𝑒𝑑 𝐶𝑙𝑎𝑠𝑠 = 𝐵𝑎𝑠𝑒 𝐶𝑙𝑎𝑠𝑠 + 𝐴𝑑𝑗𝑢𝑠𝑡𝑚𝑒𝑛𝑡𝑠 Equation (4)
A range has been established (Table 2) for the adjusted class and the associated class coefficient
and the final class coefficient is ascertained by interpolation.
Table 2: Relationship of Watershed Class with Class Coefficient (Joy & Whiteley, 1996)
Watershed Class Class Coefficient, C
1 0.15
2 0.22
3 0.31
4 0.44
5 0.63
6 0.90
7 1.29
8 1.84
9 2.62
10 3.74
11 5.34
12 7.63
13
The Modified Index Flood Method (MIFM) calculates the 25 year flood quantile from Equation
(5). The 2.33-year, 5-year, 10-year, 50-year and 100-year quantile are calculated from the
established ratios (Table 3).
𝑄25 = 𝐶25 ∗ 𝐴0.75 Equation (5)
where C is the class coefficeint and A is the total drainage area (km2).
Table 3: Ratios to Flood Quantiles of Different Return Periods to the 25-year Quantile (Joy
& Whiteley, 1994)
Basin Type Return Period (yrs)
2.33 5 10 25 50 100
Non Detentive type Southern
Basins 0.49 0.66 0.81 1.00 1.16 1.32
Shield and Detentive type
Southern Basins 0.57 0.71 0.84 1.00 1.13 1.27
North Shores of Lake Erie and
Ontario 0.41 0.62 0.79 1.00 1.16 1.32
The advantage of MIFM is its applicability to drainage areas in both the Shield type and
Southern drainage basins. It is however restricted in watershed size and cannot be used for
drainage areas less than 25 km2. The classification of basin types presented in Table 3 is used as
a design chart by MTO. However, the definitions of detentive and non-detentive basins are not
explicitly stated in Joy and Whiteley (1994), Joy and Whiteley (1996) and Ontario Ministry of
Transportation (1997), which creates a situation of uncertainty for engineers and designers. Also,
the computation of CN can also be challenging for rapidly urbanizing watersheds. The flow
predictions for these watersheds may not be close to the observed flows due to the urban flood
control measures within a drainage basin. An example in Joy and Whiteley (1996) predicted the
change in peak flow by approximately four times ( from 12 m3/s to 46 m
3/s) when the CN is
increased by 10 units (from 60 to 70) for a medium sized watershed (60 km2) located in Southern
Ontario. The sensitivity of flow prediction to CNs necessitates tools and methodologies for its
accurate estimation in a drainage basin. These are not yet available for the province of Ontario.
Thus, CN estimates depend on the judgement of the project engineer. The MIFM prediction for a
14
Shield type basin, however, does not require CN estimate and the watershed class is calculated
from the percentage of water detention. As per the procedures for MIFM (Shield), the calculation
of percentage of water detention considers the area of lakes and wetlands only if the total
drainage area is greater than 100 km2. It does not consider the area of lakes and wetlands for
smaller watersheds.
2.4.1.2 Northern Ontario Hydrology Method
The Northern Ontario Hydrology Method (NOHM) (Watt,1994) is a regression based estimation
of the mean annual annual flood from the distribution parameters (the mean, standard deviation
and skewness). These distribution parameters are related to the basin characteristics. A frequency
factor relation is used to determine the other quantiles of interest from the assumed regional
distribution (Watt, 1994). The calculation of peak flow is illustrated from Equation (6) to
Equation (12). A T-year maximum daily flow value is calculated from Equation (9). A peaking
factor (P) is calculated and applied which is based on the outlet point and if it is a lake outlet
Equation (11) is chosen. The peaking factor is used to compute the maximum instantaneous
peak from Equation (12).
𝑄𝑚 = 0.170 ∗ 𝐴1.06 ∗ (1 −
𝐴𝑑
𝐴)
2.07
Equation (6)
𝐶𝑣 = 0.502 ∗ (1 −
𝐴𝑑
𝐴)
1.85
Equation (7)
𝐶𝑆 = −2.52 + [3.73 ∗ (1 −
𝐴𝑑
𝐴) Equation (8)
If Cs is < 0.5 then its value is set as 0.5
where Qm is the mean annual flood (m3/s), Cv is the coefficient of variation, Cs is the coefficient
of skew, Ad is the area of lakes and swamps (km2) and A is the total drainage area (km
2).
𝑄𝑇 = 𝑄𝑚 (1 + 𝐾(𝑇,𝑔) ∗ 𝐶𝑣) Equation (9)
𝑃 = 1 + exp [−22 ∗ (𝐴𝑑
𝐴− 0.06)] Equation (10)
Or
15
𝑃 = 1 + 6 ∗ 𝐴−0.36 ∗ exp [−22 ∗𝐴𝑑
𝐴] Equation (11)
𝑄𝑝,𝑇 = 𝑃𝐹 ∗ 𝑄𝑇 Equation (12)
Where QT is the T-year maximum daily flow, K(T,g) is the frequency factor;
P is the peaking factor and Qp,T is the peak flow with a T year return period.
The advantage of NOHM is that it is developed specifically for the Shield region where large
storages affect the rainfall-runoff response (Ontario Ministry of Transportation, 1997). However,
this method is only applicable to watersheds with drainage areas between 1-100 km2. The small
dataset used for the study (11 hydrometric stations) limits the accuracy to a regression based
method to observed flows in a larger geographic region. At the same time, the verification study
was not extended to stations which were not a part of the analysis. Also, as discussed in Section
2.2.2, precipitation is an important parameter which varies across the province and was not
considered during the development of NOHM.
2.4.2 RFFA Procedures for Other Jurisdictions
Flood frequency relationships are required by designers and planners for reliable and accurate
prediction of flood discharge, cost effective planning and safe designs of structures located on
water courses. Various other studies have been conducted in other provinces across Canada and
the United States. Most of these studies utilize data from a station having a minimum of 10 years
of record length to predict peak flows of up to 100 years. Few Canadian studies have been
utilizing non parametric testing to assess the quality of data obtained from stream gauging
stations. However, none of the reviewed studies from the US consider non parametric screening
to analyze data quality. Table 4 provides an overview of the most recent studies from Canada
and the United Stated. All the studies presented in Table 4 conclude drainage area as the most
important parameter for determination of peak flows.
16
Table 4: Summary of Previous Studies
Province Reference
Min. no.
of record
years
No of
stations
used
Range of
Drainage
Area Used
Predictors considered Regulation
Non-
Parametric
Screening
Canadian Provinces
New
Brunswick
Aucoin et
al., 2011 11 56
3.89 km2 -
39,900 km2
Drainage area, mean annual
precipitation No No
Newfoundland Rollings,
1999 10 70
3.63 km2-
4,400 km2
Drainage area, amount & location of
natural storage, watershed slope,
watershed shape, soils, vegetation,
land use
No Yes
Saskatchewan Sandrock et
al., 1992 11 33
10 km2-
350 km2
Drainage area, drainage density,
slope, watershed relief and shape
factor
No No
United States
Iowa Eash, 2001 10 291 1.3 mi
2-
5452 mi2
Drainage area, main channel slope,
ratio of basin area within des moines
lobe landform region to the total
drainage area
No No
Colorado Capesius et
al., 2009
10
422
0.5 mi2-
5250 mi2
Drainage area, mean watershed
elevation, Mean watershed slope, %
drainage area above 7,500 feet
elevation, mean annual precipitation,
and 6-hour, 100-year precipitation.
No No
North
Carolina
Pope et al.,
2001 10 317
0.1 mi2-
8671 mi2
Drainage area, channel length,
channel slope, basin Slope, Shape No No
17
Province Reference
Min. no.
of record
years
No of
stations
used
Range of
Drainage
Area Used
Predictors considered Regulation
Non-
Parametric
Screening
New Mexico Waltemeyer,
2008 10 293
0.059 mi2-
12,7000 mi2
Drainage area, basin slope upstream,
basin elevation, maximum
precipitation intensity ( storm of 24-
hour & recurrence interval 100
years, mean annual precipitation
No No
Illinois Soong et al.,
2004 10 288
0.03 mi2-
9554 mi2
Drainage area,
main channel slope, average
permeability, % area of open water
& wetland, basin length, basin width,
main-channel length, & 2-day, 24-
hour rainfall depth
No No
18
2.5 Review of Available Data
2.5.1 Flow data
Flood series, depending on the record length and the purpose of the study can be using two
different approaches for flood frequency analysis: Peak over Threshold (POT) and Annual
Maximum Series (AMS). The AMS consists of a single maximum value (either the instantaneous
peak or the average daily value) recorded over a given year. It may be used if the data records
available for a stream gauging station have sufficient record length. Watt et al. (1989) argues that
the minimum number of record years considered for flood frequency studies should depend on
the intended extrapolation from the flow series. An empirical guidance chart is provided in Watt
et al. (1989), Chapter 5 Figure 5.3.
Figure 3: Empirical Guidance Chart (Source: Watt et al. (1989))
The chart (reproduced in Figure 3) illustrates that for short length of stream records and
prediction of large design floods, reliance on only station frequency analysis should not be
19
preferred. On reading the design chart it can also be inferred that while performing station
frequency analysis a record length of 10 years may be sufficient to predict a design flood of
approximately 50 years. However, to predict a 100 year design flood, the record length should be
approximately 25 years. Thus, it is important to use judgement for a balance between the
minimum acceptable record length, degree of extrapolation required and uncertainty in the
prediction of flood quantile.
The Annual Maximum series may sometimes lead to loss of information as only a single peak
flow of a given year is considered and the subsequent second or third peak of the same year are
ignored. These subsequent flows, ignored in AMS series, may be greater than the peak flows of
other years (Rao and Hamed, 1999). On the contrary, POT consists of all data / flow records
above a given threshold level that may be selected based on the number of available records and
the selected threshold. It is generally used when the record length is short. The inter event time
between POT events is also not equal. A minimum inter event time may be selected to ensure the
independence of the data series. Adamowski (2000) observed that the POT models are not useful
in the analysis of events which results from more than one flood causing mechanism like
combination of spring rainfall, snowmelt, thunderstorms etc. The condition of bimodal data may
not be new to the climatic conditions in Ontario where flooding may occur due to a combination
of different mechanisms (Moin and Shaw (1985), Gingras et al. (1994)). Thus, if sufficient data
is available, AMS series can be considered for analysis of streamflow data.
Water Survey of Canada (WSC) collects hydrometric data at its stream gauging stations across
Canada. Its central database, HYDAT, contains flow data such as daily and monthly mean flow,
water levels, sediment concentration, peak flow etc. WSC operates 2,500 gauging stations across
Canada. Achieved data of approximately 5,500 stations is also stored in HYDAT (Environment
Canada, 2011). Reference Hydrometric Basin Network (RHBN) is a subset of the national
network which is available for long term hydrological monitoring. These stations are a part of the
Global Climate Observing System (GCOS) and the long term flow records available from RHBN
stations maybe useful while dealing with pressing issues like climate change phenomenon.
The average flow recorded over a day, referred to as the average daily flow, and instantaneous
peak flows are reported at stream gauging stations throughout Ontario in the HYDAT database.
For a given stream gauge, an Annual Maximum Average Daily (AMAD) dataset reports the
20
maximum value of the average daily flows recorded for each year of the historical stream record.
A single maximum instantaneous flow value recorded over a year is also reported as the Annual
Maximum Instantaneous (AMI) flow. For RFFA, AMAD data series are generally used if AMI
data series are not available. If AMAD series is used for flood frequency studies it is
recommended to apply a peaking factor to the predicted T-year quantiles (Watt 1994). As evident
from Figure 4, which provides a comparison of AMI and AMAD values for a representative
station it is evident that the values of AMAD can vary considerably in relation to the AMI flow
data. It may be observed that AMI flow data provides a better representation of the peak flow
conditions in a drainage basin and should ideally be selected if sufficient records are available.
This view has also been supported by previous studies such as Sangal (1981).
Figure 4: Flow Data Comparison for a Typical Station (HYDAT station: 02HB021)
2.5.1.1 Estimating Peak Flow from Mean Daily Flow
Historically, numerous procedures such as the Fullers Method and Langbein’s Approach
(Moin and Shaw, 1985) have been used to predict instantaneous peak flows from average daily
flows when gaps in the stream record exist. Watt et al. (1989) suggest that the missing or
incomplete flow data may be ascribed to two reasons: broken series or incomplete records. When
a broken series is not related to the magnitude of the event, such data, with gaps, may be
combined and used as a single dataset. An incomplete record on the other hand is when an
extreme event has left the gauging station un-operational. Such missing events should be
21
estimated based on information by the recording agency. Application of estimation procedures is
particularly important when either the data series is not of adequate length or is not available in
the form to be utilized for peak flow estimation. Flow recordings and flood frequency studies up
until the early and mid-90s were mostly based on AMAD flow data as this was the only recorded
data available for a long time. With the advent of data recorders which can record values at 15
minute interval, currently there are a large number of stations with appreciable length of AMI
flow data. To extract information for early station years Sangal (1981) investigated the Fuller’s
and Langbein’s method and thereby developed a procedure which was specifically applied to
Ontario’s context.
1. Fuller’s Method is based on the data for 24 drainage basins from Eastern United States uptill
1914. He plotted the ratio of ((Qp- Qm)/ Qm) with the drainage area on a log-log scale and
derived a curve with the following relationship.
𝑄𝑝 = 𝑄𝑚( 1 + 1.5𝐴−0.3) Equation (13)
where Qp is the peak and Qm is the mean flow and A is the drainage area (km2).
Sangal (1981), after investigation, opined that this method represents a statistically poor
relationship with an R2 of 0.48 but it continues to be used due to a lack of alternative
approaches.
2. Langbiens Approach: This method uses the data of mean flows for three consecutive days
(Q1, Q2 (or Qm) and Q3; where the mean annual flow is the flow of the second day), the peak
flow (Qp) and the time for the peak. The ratio of the Qp and Qm are described as functions of
Qm/Q1 and Qm/Q2. Thus, for similar ratios of the flows for the three consecutive days,
Langbiens approach gives similar ratios for Qp and Qm. This method therefore neglects any
effect of the size of drainage catchment (Sangal, 1981; Moin and Shaw, 1985).
3. Sangal’s Method: Sangal (1981) has put forth a procedure, which is an extension of the
Langbiens concept, for determination of peak flows from average daily flows. This method
has been developed and successfully applied for Ontario’s context in previous flood frequency
studies by Moin and Shaw (1985) and MNR (2014). Sangal (1981)’s procedure for prediction
of missing AMI flow values also uses the average daily flow for three consecutive days (Q1,
22
Q2 and Q3). The second position (Q2) is occupied by the AMAD flow value of the year. A
parameter called the base factor K is also employed in the study by Sangal (1981) which is the
base of the assumed triangular hydrograph. Equation (14) depicts the general form of the
relation between the instantaneous peak flow and average daily flow for any year. For the
station years having both AMI and AMAD flow data, Equation (14) was employed to
estimate the base factor (K) for the year. For the current study, the average of the base factor
for all the years was adopted as the base factor for the station. The station base factor was
subsequently used in Equation (15) to predict the AMI values for any given year which had
the AMAD flow data available.
𝐾 = (4𝑄2 − 2𝑄1 − 2𝑄3)/(2𝑄𝑃 − 𝑄1 − 𝑄3) Equation (14)
QP′ = (Q1 + Q3)/2 + [2Q2 − Q1 − Q3]/K Equation (15)
Where, QP = peak flow (m3/s); QP' = predicted peak flow (m
3/s), Q1, Q2 and Q3= mean daily
flow (m3/s) for 3 consecutive days where Q2 represents the AMAD value of the year.
Sangal (1981) study yielded 79% of predicted peaks within ±20% of their actual values for
Ontario demonstrating that it as an effective method for predicting AMI flows. Sangal (1981)
provides the value of the parameter K for 387 watersheds in Ontario, which can be used during
estimating the peak flows for situations when the K value cannot be predicted. However, in the
current dataset of stream flow records most station years have both AMI and AMAD data. Thus,
it was possible to estimate K values for all individual watersheds used in this study instead of
using the K values provided in Sangal (1981).
2.5.2 Physiographic Data
Ontario’s physiographic data is accessible through the Ministry of Natural Resources and
Forestry (MNR)’s web-based Ontario Flow Assessment Tool (OFAT), the use of which is
increasing in the province of Ontario. OFAT can compute watershed boundaries and site specific
hydrologic information. OFAT 1 was released in 2002 as an add-on to GIS software (MNR,
2015). The current version 3 of OFAT is web based which utilizes the digital elevation models to
delineate the contributing drainage area at any point of interest. It also computes ten associated
physiographic characteristics along with the land cover information for and selected point of
23
interest. The land cover information from OFAT is extracted from the land cover maps of
Ontario which combines the compilation from Provincial Land Cover Database, Far North Land
Cover and the Southern Ontario Land Resource Information System. Additionally, OFAT III
runs various Hydrology models at ungauged points of interests to calculate stream flow at these
locations. A limitation of OFAT is that it assumes natural flow condition and any regulation in
flow are not considered. A review of the data from OFAT is provided in Table 5.
2.5.3 Climatic Data
Climatic factors like precipitation determine the flood causing mechanism in a catchment.
Environement Canada provides Climate Normals which summarize average climatic information
of a given weather station. Climate Normals are updated every 10 years to represent the climatic
conditions for the last 30 years. Precipitation information at its weather stations is provided
within the climate normal dataset. The mean annual precipitation is the total amount of rainfall
and snowfall over the year. However, the value of mean annual precipitation, as the predictor of
flood, is required at the point of interest, i.e. the stream gauging stations. Various interpolation
techniques can be employed to interpolate the mean annual precipitation at ungauged locations.
Empirical Bayesian Kriging (EBK) is a geo-statistical Interpolation method which helps to make
predictions at unknown locations using values at known locations. EBK takes into account the
errors introduced by the variance of difference between two locations (Environmental Systems
Research Institute, Inc. (ESRI), 2012). Thus, EBK has an inherent advantage over other
interpolation methods, like inverse distance weighing (IDW), which tend to underestimate the
standard errors of prediction. Interpolation techniques are generally used for preparation of
isohyetal maps for region. It has also been widely used in flood frequency analysis in the United
States to prepare skew maps in various provinces like Illinois and Iowa (Soong et al. (2004),
Eash (2001)).
2.6 Review of Statistical Analysis Methods
2.6.1 Non-parametric testing
The underlying assumptions associated with the time series for RFFA is that the dataset is
random, homogeneous, independent and stationary (Watt (1994), Rao and Hamed (2000)). Thus,
compliance with these conditions is a pre-requisite for any statistical analysis. Non-parametric
24
testing does not assume any underlying distribution and the evaluation are based on assigning
ranks to the dataset. These tests help in ensuring that a probabilistic model applies to the dataset
(Watt, 1994). The necessity of these tests has also been highlighted in Watt et al. (1989) and Rao
and Hamed (2000). The compliance with the aforementioned assumptions has also been tested in
previous studies like Watt (1994), Moin and Shaw (1985) and MNR (2014). The description of
these tests, given in Appendix A & B of Ottawa River Flood Mapping (1984) and Rollings
(1999), is reproduced in the subsequent sections. The hypotheses for all the tests are generally
accepted at either 1% or 5% significance level. Though Watt (1994) recommends these statistical
testing, rejection of the non-parametric hypothesis is not necessarily a strong evidence of
nonconformity with the statistical assumptions and, as such, rejected cases may require further
investigation. This could involve examining changes in the drainage basin for the beginning and
the end of the record period for urbanization, or changes in flow or storage.
2.6.1.1 Test for Independence
Independent events are those where the probability of occurrence of one of the event does not the
affect the probability of occurrence of the second event (Rollings, 1999). Thus, it tests the
significance of correlation coefficient between N-1 pairs of ith and (i+1)th event. The significance
of the correlation coefficient helps in establishing the independence of the data series
(Rollings, (1999), Ottawa River Flood Mapping (1984)). Pearson coefficient has an underlying
assumption of a normal sampling distribution. Thus, for flood frequency studies where a single
distribution cannot be ascribed to the dataset with certainty, a non-parametric form based on
ranking of dataset is used Ottawa River Flood Mapping (1984). Spearman rank order serial
correlation coefficient for independence, detailed in in Ottawa River Flood Mapping (1984) and
(Rollings, 1999) is used to test the assumption of independence for the dataset of each station.
The null hypothesis for the test is that the two series are independent. The process is illustrated
below:
The data series Q1, Q2, Q3………Qn-1 is represented in chronological order and xi denoting the
ranks of Qi. Similarly, Q2, Q3………Qn is represented in chronological order and yi denoting the
ranks of Qi.
The spearman rank order serial correlation coefficient is given as:
25
𝑆1 =1
2 ( ∑ 𝑥𝑖
2 + ∑ 𝑦𝑖2 − ∑ 𝑑𝑖
2) (∑ 𝑥𝑖2 ∑ 𝑦𝑖
2)−
12 Equation (16)
∑ 𝑥𝑖2 =
𝑚3 − 𝑚
12− ∑ 𝑇𝑥 Equation (17)
∑ 𝑦𝑖2 =
𝑚3 − 𝑚
12− ∑ 𝑇𝑦 Equation (18)
where di is difference in rank of xi and yi ; m=N-1and summation is taken for m pairs of xi and yi.
The moment of T adjusts for the tied ranks and is calculated as follows:
𝑇𝑥 =𝑟3 − 𝑟
12 Equation (19)
where r is the number of observations tied at a given rank. ∑ Tx 𝑎𝑛𝑑 ∑ Ty are then extended to
all the tied ranks.
For N less than 10, special tables are available for defining the region of rejection for S1 at given
significance level. When N is 10 or greater, then the function t is distributed like students t and a
one tail test is used to test the significance of the hypothesis.
𝑡 = 𝑆1 [𝑚 − 2
1 − 𝑠12]
1/2
Equation (20)
2.6.1.2 Test for Stationarity
The land use conditions of a watershed change with time thereby causing changes in flow data
series. If flow conditions are changing with time, a trend in the flow series may be observed.
Spearman rank order correlation coefficient is used to test the stationarity of the data set. The test
process from Ottawa River Flood Mapping (1984) is illustrated below. The null hypothesis for
the test states that the the there is no trend or serial correlation between the dataseries.
26
The data series Q1, Q2, Q3………Qn is represented in chronological order and yi denoting the
ranks of Qi . Similarly, 1, 2, ……N is represented in the sequential order and xi denoting the
ranks of Qi.
The spearman rank order correlation coefficient, illustrated in Ottawa River Flood
Mapping (1984), is computed as:
𝑟𝑠 =1
2 ( ∑ 𝑥𝑖
2 + ∑ 𝑦𝑖2 − ∑ 𝑑𝑖
2) (∑ 𝑥𝑖2 ∑ 𝑦𝑖
2)−
12 Equation (21)
where Equation (17) and Equation (18) are used to compute the value of ∑ 𝑥𝑖2 𝑎𝑛𝑑 ∑ 𝑦𝑖
2.
Here di is difference in rank of xi and yi; m=N; summation is taken for m pairs of xi and yi and
∑ 𝑇𝑥 = 0 and ∑ Ty is calculated as in Equation (19).
For N less than 10, special tables are available for defining the region of rejection for 𝑟𝑠 at given
significance level. When N is 10 or greater, then the function t is distributed like students t. The
null hypothesis states that there is no trend either upward or downward so a two tail test is used
to test the significance of the hypothesis.
𝑡 = 𝑟𝑠 [𝑁 − 2
1 − 𝑟𝑠2
]1/2
Equation (22)
2.6.1.3 Test for Homogeneity
Homogeneity tests take into consideration any abrupt changes in the drainage basin, like
construction of a reservoir etc., by analyzing two sub samples from the drainage basin (Rollings,
1999). Mann-Whitney split sample test is used to ascertain the homogeneity of the sample. The
condition of non-homogeneity may be possible in hydrology due to natural as well as
anthropogenic reasons (Ottawa River Flood Mapping, 1984). The procedures for the Mann-
Whitney test, highlighted below, help in identification of non-homogeneous flood series. The
null hypothesis of the Mann Whitney U-test is that the two samples are from the same population
(homogeneous).
The sample is split into two sub-samples and ranks are assigned. The Mann-Whitney U statistic
is computed. It is defined as the smaller value of U1 and U2.
27
𝑈1 = 𝑛1𝑛2 +𝑛1(𝑛1 + 1)
2− 𝑅1 Equation (23)
𝑈2 = 𝑛1𝑛2 − 𝑈1 Equation (24)
where n1(smaller sample) and n2 are the sample size ; R1 is the sum of ranks in n1.
The significance of U is ascertained by assessing the critical values and the associated regions of
rejection which have been tabulated and published. For large sample size, a normal variate z
(0,1) as Equation (25) and the associated regions of rejection at different significance levels are
analyzed.
𝑧 = 𝑈 −
𝑛1𝑛2
2
{[𝑛1𝑛2
𝑁(𝑁 − 1)] [(
𝑁3 − 𝑁12 ) − ∑ 𝑇]}
1/2 Equation (25)
2.6.1.4 Test for Randomness
Runs test, performed by calculating the runs below and above the median, is used to test the
randomness of the flow series for each station (Moin & Shaw, 1985). A run is a group of data
items which follow a sequence with similar adjacent elements. The runs test designates the data
into two different categories with values above and below the median (SPSS Statistics 21 Help,
2012). The number of ordered sequence of each group gives the runs in the sample. The null
hypothesis for runs test is that the sequence is random. The significance associated with the
number of runs helps decide the acceptance or rejection of the hypothesis (Mathworks, 2015).
2.6.2 Station Frequency Analysis
Station frequency analysis is performed for gauged locations in a hydrologically homogeneous
region and the value of the flood quantiles is determined. This process is performed by fitting
theoretical probability distribution curves to the dataset and the fitted distribution is used to
compute the quantile values associated with a particular exceedance probability. Several
theoretical probability distributions have been proposed for fitting annual maximum flow data
including Normal, Lognormal, 3-Parameter Lognormal, Gumbel, Pearson type 3, Log Pearson
28
type 3 and the Generalized Extreme Value (Watt et al., 1989). Historically, a 3-Parameter Log
normal distribution has been adopted for studies like Moin and Shaw (1985) and Joy and
Whiteley (1994) in the province of Ontario Similarly, Log-Pearson type 3 has been an accepted
probability distribution in the United States recommended by the Interagency Advisory
Committee on Water Data (1982). It has subsequently been adopted in all flood frequency
studies in the United States including those highlighted in Table 4 in Section 2.4.2. Similarly,
Generalized Extreme Value is the recommended probability distribution in the United Kingdom
(Chow and Watt, 1992). Chow and Watt (1992) argue that there may be more than one
distribution which fits the data. Thus, recommendation of a single distribution for a large
geographical region may not be desirable.
Chow and Watt (1992) recommend the Akaike Information Criterion (AIC) to select the best
probability distribution amongst a set of candidate distributions. AIC gives a model selection
criterion based on the combination of model fit, determined by the log likelihood term in
Equation (26), and the number of parameters (k) of the model determined by the second term in
Equation (26). A combination of these two terms would result in a unique value. According to
the Akaike model selection procedure the model with a minimum AIC value best describes the
sample data set and should be selected. So, choosing a distribution with more number of
parameters is not held by this selection criterion because there is an additional uncertainty
associated with parameter estimation, which increases as the number of parameters increase. The
improved fit and the number of parameters should compensate each other thereby resulting in a
minimum AIC value, as can be observed from Equation (26). Goodness-of-fit tests such as the
Kolmogorov-Smirnov or Chi-Square tests could not be adopted as these methods have a
tendency to select a distribution with more number of parameters, which essentially means a
better fit. However, the uncertainty inherent with these additional parameters is not reflected
during distribution selection by goodness-of-fit tests. This situation ultimately creates a false-
sense of certainty and confidence when applied to real-life design applications. AIC has also
been previously applied to the context of Northern Ontario in the study by Watt (1994) which
resulted in minimizing the relative standard errors of the RFFA equations when compared to the
results obtained by previous studies. Thus, considering all the above mentioned factors
distribution selection using AIC was identified as the best approach that can also be extended to
the current study.
29
AIC = −2 log(𝐿) + 2k Equation (26)
Burnham and Anderson (2004) identified a limitation in existing model selection literature when
AIC value is used for small sample sizes (defined by n/k < 40; where n is the sample size and k
is the number of parameters). Using Equation (26) researchers have concluded that for small
sample sizes AIC sometimes over fits the data (Burnham and Anderson, 2004). Overfitting
implies that the statistical model has random errors and the model is not a true representation of
the underlying condition. For finite and small sample sizes a second order criterion as proposed
by Burnham and Anderson (2004). The data series generally available for flood frequency
studies are relatively small so a second order criterion, like in Equation (27) is applied.
AIC = −2 log(𝐿) + 2k + 2𝑘(𝑘 + 1)
𝑛 − 𝑘 − 1 Equation (27)
Where k = number of parameters; L = maximized value of the likelihood function; n = sample
size.
For large sample sizes Equation (27) converges to Equation (26). However, for the purpose of
the current study, Equation (27) is used to estimate the AIC for each candidate distribution.
Statistical software’s can be used to estimate the value of the likelihood function and also the
associated station flood quantiles (2 year, 10 year, 25 year, 50 year and 100 year). These
software’s use different fitting methods like the method of moments, method of maximum
likelihood, L-moments etc. A distribution fitting software, Easyfit, with its excel add-in, utilizes
the least computationally intensive method for estimation of underlying distribution and the
distribution parameters. The methods used for parameter estimation for the different candidate
distributions are available in its software documentation. A comparison study for two
representative stations was also carried out in ‘R project’, an open source programming language
for statistical computation, which presented identical results of AIC values.
Alberta Transportation (2001) argues that the selection of an appropriate probability distribution
is more important than the differences caused by various fitting methods (like method of
moments, method of maximum likelihood, for example) for prediction of flood quantiles.
30
Chow and Watt (1992) recommended the used of AIC as a distribution selection criterion.
However, it may also be observed from Table 3 of Chow and Watt (1992) that for the 42 stations
used in the study, the difference in the AIC for the best and second best distribution is very
small. For instances when the difference in AIC values is small, Burnham and Anderson (2004)
recommends a range of difference in AIC values between the model with the lowest AIC and
other candidate distribution models when a particular model cannot be accepted with certainty.
For such models, Burnham and Anderson (2004) recommended calculation of Akaike weights as
in Equation (28) and averaging of the estimates from each candidate model based on these
weights.
𝑤𝑖 =exp (−
∆𝑖
2 )
∑ exp (−∆𝑟
2 )𝑁
𝑟=1
∆𝑖 = AIC𝑖 – AIC𝑚𝑖𝑛 Equation (28)
where i = the model in consideration; wi represents the model weight;
N = the total number of models in consideration for calculation of weights;
AICmin = AIC value of the best fit distribution.
Thus, appropriate weights may be applied to the quantile estimates of the candidate distributions
to compute the station quantiles.
2.6.3 Multiple Regression
The use of multiple regression procedures to develop prediction models for peak flood flows has
increased in the last few decades due to the increased availability of statistical packages (like
SPSS, SAS) capable of processing large datasets. Statistical packages broadly use three
regression procedures which are adopted based on the research goals. These procedures have
different types of controls for entry of a variable in the regression equation. For example the
simultaneous entry (forced entry) procedure is used mainly for exploratory purposes
(Field, 2009). This method gives the control of variable selection to the researcher and may be
used when a given theoretical model is under consideration. Thus, it allows assessment of impact
of each independent variable (Field, 2009). On the other hand, stepwise regression procedure
gives this control of variable selection to the computer which, based on standard algorithms,
31
chooses the independent variables. It maximizes the coefficient of determination (R2) and
minimizes the number of predictors at the same time (Field, 2009). Thus, all independent
variables may not be a part of the final regression equation and the most significant variables are
chosen. The third procedure, called hierarchical regression, is generally used for testing
theoretical models of a researcher. The variable entry order is decided by the researcher and is
based on a theoretical justification (Field, 2009).
During the stepwise regression process, a variable is added and is retained at a particular
significance level (generally 5-percent significance for regression analysis). This variable may be
removed when a variable added in a subsequent step has higher significance (Field, 2009).
Stepwise linear regression procedures in SPSS also help in identifying multi-collinearity through
its collinearity diagnostics (Field, 2009). During regression analysis, the results of the
collinearity diagnostics are adopted by SPSS and the corresponding variable demonstrating
multi-collinearity is automatically dropped.
The stepwise regression procedure identifies a relation between the dependent variable (i.e. the
T-year quantile in the current study) and the predictor variables (i.e. climate and physiographic
parameters).The variables that are required for regression analysis with respect to flood
frequency studies can be classified as follows:
1. Response variables: Response variables are those which are measured and are also called the
dependent variables. Thus, the flood quantiles in flood frequency studies may be treated as
the response variables. Each of the variables should be separately tested with all the
predictor variables.
2. Predictor variables: Predictor variables are the independent variables used for development
of a regression equation with the dependent variables. These variables affect the response.
The physiographic and climatic variables in flood frequency studies may be considered as
the predictor variables.
2.6.3.1 Assumptions in Multiple Regression
Predictor variables used in a RFFA study should not be correlated with other predictor variables.
A condition when the predictor variables are related to each other is also referred as multi-
collinearity, which can be identified from the values of correlation coefficients. Parameters that
32
are highly correlated have the correlation coefficient close to 1 or -1 in their correlation matrix.
The highly correlated parameters need to be removed from the study unless there is an
appropriate rationale against the removal of variables. RFFA studies (Joy and Whiteley (1996),
Watt (1994), Karuks (1961)) have concluded that drainage area is the most important parameter
for determining peak flow. Thus, predictor variables correlated with the drainage area would
essentially convey the same information about peak flow and thus cannot be treated as its
independent determinant (Watt,1994). Previous studies on flood frequency analysis
(Watt (1994); Rollings (1999)) have also highlighted the importance of the effect of lakes in
decreasing the peak flows and a factor to represent this effect was adopted.
Another important assumption of multiple regression is the condition of normality for both the
response and predictor variables. It is essential to ascertain this assumption before proceeding
with the regression analysis. The assumption for normality can be tested by confirming if the
ratio of skewness and standard error (S.E.) is less than 1.96 or by visual examination of the
histograms before and after transformation. Generally, the annual maximum flow data is highly
right skewed (Chin, 2013). Thus, to perform a regression analysis the data is commonly log
transformed. Log transformations to base 10 have previously been applied to regression analysis
(GREHYS, 1996; Grover et al., 2002; Moin and Shaw, 1986). Logarithmic transformations,
when applied on all the dependent variables and predictor variables, help to linearize the
assumed power equation and to achieve equal variance (normality) required for linear regression.
Thus, a general form of the power function, Equation (29), is assumed which on log-
transformation took the form Equation (30), to be used as the linear regression model.
𝑄 = 𝐾𝑅 ∗ 𝐴𝑎 ∗ 𝐵𝑏 ∗ 𝐶𝑐 …. Equation (29)
𝑙𝑜𝑔𝑄 = 𝑙𝑜𝑔𝐾𝑅 + 𝑎 ∗ 𝑙𝑜𝑔𝐴 + 𝑏 ∗ 𝑙𝑜𝑔𝐵 + 𝑐 ∗ 𝑙𝑜𝑔𝐶 …. Equation (30)
where Q represents the dependent variable; A, B and C represent independent variables; KR, a, b
and c are constants.
2.7 Summary
The detailed review of the hydrology aspects of flood frequency analysis was conducted in the
above chapter with emphasis on the physiography and climate of Ontario. The chapter reviewed
33
statistical methods and the recent RFFA studies. Drainage area is the most important contributing
factor when predicting peak flows and urbanization causes changes the flow regime in
catchments. The climate in general and more specifically precipitation is the important flood
causing mechanism. Non parametric screening to assess independence, stationarity, randomness
and homogeneity of flow data has not been investigated in most of the studies from the United
States. But few Canadian studies have adopted non-parametric testing to assess the quality of
streamflow data. This is important considering the temporal changes in drainage catchments and
verifying the statistical assumptions before applying statistical methods. Different statistical
methods have been identified in this section and the availability of statistical packages has
caused a shift towards regression based RFFA equations. The chapter establishes the foundation
for the methodology used in Chapter 3.
34
Chapter 3 Methodology
The subsequent sections outline the thesis methodology. The study area for the project, i.e. the
province of Ontario, is divided into ecozones. Flow data were obtained for the gauged stations
across the province. The physiographic parameters were obtained from the Ontario Flow
Assessment Tool (OFAT) III and the precipitation data were obtained from Environment Canada
weather stations. Subsequently, a regression based regional flood frequency analysis is
performed.
3.1 Data Collection
Historical stream flow data were obtained from Environment Canada’s archived Hydrometric
Data Portal. The data from the gauging stations, referred to as HYDAT stations, is collected by
Water Survey of Canada (WSC). Amongst these stations, 17 stations were selected from the
Reference Hydrometric Basin Network (RHBN). Inclusion of these stations was prioritized
because they are likely to remain active in the future and are available for long term monitoring.
For a given HYDAT station the Hydrometric Data Portal provides AMI flow, AMAD flow and
overall average daily flow for all operational years. The overall average daily flow data were
used while synthesizing AMI flow data following procedures outlined by Sangal (1981) when
there were gaps in the historical records. While compiling hydrometric data from WSC a
station’s latitude, longitude and the gross drainage area of the gauge stations was also collected.
Historical stream flow datasets were downloaded for all 271 HYDAT stations in Ontario that
have been operating for over 15 years (Figure 5). Flow data collected by WSC up to and
including December 31st, 2014 were considered for this analysis. All of the 271 stations represent
natural flow conditions and regulated stations were excluded in this study. Regulation affects the
natural flow data and stream flow series, if used, are not reflective of the true hydrologic
conditions of the catchment. It was noted that the actual station record length available was
occasionally shorter than the stations operational length (15 years selected as the threshold). In
all cases the AMI series were shorter than AMAD series. An example of the annual maximum
series for a representative station is provided in Appendix A. The complete dataset for 271
stations used for the analysis (AMAD, AMI and the daily flows) is not reproduced in the thesis
35
and is available from the Hydrometric data portal of WSC. A summary of the record data for all
HYDAT stations used in this study is provided in Appendix B.
Figure 5: Location of HYDAT Stations
Physiographic data (i.e. watershed characteristic and land cover) associated with each HYDAT
station were obtained from the Ministry of Natural Resources and Forestry (MNR)’s web-based
Ontario Flow Assessment Tool (OFAT) III utilizing latitude and longitude information collected
from the WSC portal. An example of the data obtained from OFAT is provided in Table 5.
Mean annual precipitation data was collected from the Climate Normals published by
Environment Canada for all 151 weather stations across Ontario from 1981-2010. An isohyetal
map was prepared in ARCMap 10.2 using the Empirical Bayesian Kriging (EBK). The isohyet
36
map is shown previously in Figure 2 and was used to determine the interpolated precipitation
values at the individual HYDAT stations.
Table 5: Example of Data from OFAT (Representative Station: 05PB018)
Parameter OFAT representation Value
Station ID 05PB018
Area (km2) Area Km 345.95
Shape Factor ShapFactr 34.61
Mean Elevation (m) MeanElevM 449.7
Maximum Elevation (m) MaxElevM 521.9
Mean Slope (%) MeanSlpPc 5.068
Length of the Main Channel (km) LeOMChKm 109.432
Maximum Channel Elevation (m) MaxChElvM 505.58
Minimum Channel Elevation (m) MinChElvM 400.93
Channel slope (m/km) ChSlp_M_Km 0.96
Channel Slope (%) ChSlp_Pcnt 0.096
Total Area of Water storage (km2) WatrAreaKm 72.07
Area of lakes and open water (km2) OpWAreaKm 54.89
Area of Wetlands (sqkm) WetlAreaKm 17.18
3.2 Data Preparation and Screening
3.2.1 Estimating Annual Maximum Instantaneous (AMI) values for gaps in historical records
Sangal (1981)’s procedure, outlined in Section 2.5.1.1, was used to estimate the gaps in the
historical AMI flow series. Appendix B summarizes the number of years that required AMI
values to be estimated. The procedure used for prediction of K is illustrated in the form of a
flowchart in Figure 6. The estimation of AMI values for a representative station is tabulated in
Appendix C. The procedure was repeated to predict the AMI data for all the station years for the
271 stations selected for the study. After prediction of AMI flow values HYDAT stations with
more than 15 years of data were retained for further analysis.
37
Figure 6: Estimation of Missing Values of Instantaneous Peak (Sangal (1981))
3.2.2 Screening of HYDAT stations
The land cover information extracted from OFAT was used to identify and exclude HYDAT
stations that contained more than 20% impervious cover. The value of 20% was determined as
suitable based on various studies, such as Center for Watershed Protection (2003), which suggest
that the hydrology of watersheds within the range of 10-25% impervious cover are impacted by
urbanization. These watersheds exhibit significant differences with respect to both quality and
quantity of runoff. Ten such stations were subsequently separated from the current analysis.
Eight of these ten stations were located in the Mixed Wood region in southern Ontario. Figure 7
shows the location of the urban watersheds in Ontario. Figure 8 shows an urban watershed
delineated by OFAT.
38
Figure 7: Location of Urban catchments
Figure 8: Delineation of an Urban Watershed with OFAT
02GH011
39
Additionally, information regarding seven stations could not be extracted as OFAT did not
recognize the latitude and longitude reported by WSC as valid points on the stream. The lack of
basin parameters required for the study necessitated the removal of these stations.
A limitation that was identified during data extraction was that OFAT only includes digital
elevation data that is within the provincial boundaries of Ontario. Parts of a watershed extending
outside of the province are not reported by OFAT. Thus, discrepancies were observed in the
drainage area reported by WSC and obtained through delineation by OFAT, for example, WSC
station 05PC018 (latitude: 48.6344, longitude:-93.9133), shown in Figure 9. OFAT delineates
the boundary through lakes and streams along the Ontario provincial boundary excluding the
contributing watershed area within the adjacent State of Minnesota. This led to gross mismatch
in the areas reported by OFAT and WSC for stations with cross-border watersheds.
For a few other stations, which were not along the provincial border, the root cause of
discrepancies between reported OFAT and WSC drainage areas could not be identified.
Discrepancies with respect to WSC data and observed data have also been highlighted in Joy and
Whiteley (1994). The stations with differences greater than 15% in reported watershed area from
WSC and delineated by OFAT were excluded from analysis. The uncertainty in ascertaining the
correct area and the associated data (e.g. channel length, slope, area of lakes and reservoirs)
forced the removal of these stations. Forty-one such stations were identified and removed.
Two stations with drainage areas less than 1 km2 were removed from the Boreal Shield ecozone
as the station quantiles (calculated in the Section 3.3.2) and the area occupied by lakes and
wetlands for these stations were approximately zero. For the current dataset, there were stations
with very large drainage area (largest drainage area = 13,559.5 km2). These stations had a
drainage area that was more than 5 times the mean of the drainage areas used in this study and
were identified as outliers. Thus, five more stations in the Boreal Shield with extremely large
drainage areas (> 5000 km2) were removed.
The Hudson Plain ecozone is a very remote region of Ontario and MTO does not currently
operate any provincial highways this far north. Only three HYDAT stations remained in this
ecozone after the initial data screening (shown in Figure 10) which was insufficient to support
regression analysis. Hence, subsequent analysis presented was limited to two regions: the Boreal
Shield and the Mixed Wood Plains.
40
Figure 9: Watershed Delineation Discrepancy in OFAT
Figure 10: Stations in the Hudson Plain
Drainage area
Provincial boundary
Drainage boundary
HYDAT station (05PC018)
41
3.3 Data Analysis
New RFFA equations for Ontario were developed following data screening. The analysis
procedure can be understood in three stages as detailed in Chapter 2. Here, each stage depends
on the result obtained at the previous stage.
1. Non parametric testing
2. Station frequency analysis
3. Multiple regression of quantiles
3.3.1 Non-parametric Testing
The first step in development of RFFA equations was to check conformity of stream flow data
for each HYDAT station with basic statistical assumptions (highlighted in Chapter 2). This
statistical analysis was completed using the package SPSS Statistics 22. Only station data found
to be independent, stationary, homogeneous and random were subsequently considered for
station frequency analysis. Completed statistical tests included:
1. Spearman rank order serial correlation coefficient for independence
2. Spearman rank order correlation coefficient for stationarity
3. Mann-Whitney split sample test for homogeneity
4. Runs test for general randomness
The hypotheses for all statistical tests were accepted at 5% significance level. The summary of
the results of non-parametric tests is provided is Appendix D. For the sake of completeness,
Appendix D includes the urban watersheds and also the stations rejected in previous steps.
Fourteen stations in the Boreal Shield Region and twenty-nine stations in the Mixed Wood Plains
were eliminated due to non-compliance with the hypotheses of non-parametric tests. A map of
the stations, non-compliant with the statistical assumptions, is presented in Figure 11.
42
Figure 11: Stations Eliminated (non-compliant with nonparametric test hypotheses)
3.3.2 Station Frequency Analysis
Station frequency analysis was performed for the HYDAT stations meet statistical assumption
necessary for multiple regression at 5% significance level. One hundred and fifty stations (rural
watersheds) were retained for analysis at this stage after the previous screening steps. Different
probability distributions have been recommended for flood frequency studies in studies including
Watt (1994), Watt et al. (1989), Chow and Watt (1992), Rao and Hamed (2000), Cunnane
(1989). Seven theoretical probability distributions were tested during station frequency analysis:
1. Normal
2. Lognormal
3. 3-Parameter Lognormal
4. Gumbel
5. Pearson type 3
43
6. Log Pearson type 3
7. Generalized Extreme Value
Akaike Information Criterion (AIC) was used for selection of the best probability distribution
amongst the set of candidate distributions. The model with a minimum AIC value best describes
the sample data set and should be selected. Equation (27) outlined in Section 2.6.2, with the
second order correction for finite datasets was used to compute the AIC value. The analysis was
performed using the excel add-in of the distribution fitting software, Easyfit. The initial results
obtained after AIC analysis indicated a small difference between the AIC values for the 1st and
2nd
best fit distribution. Table 6 summarizes the results for the HYDAT data from Ontario.
Table 6: Summary of the Difference in AIC
Difference in AIC value
(between 1st and 2
nd best distribution)
No. of stations
0-2 126
2-7 20
>7 4
Total 150
The intervals for Table 6 were selected based on recommendations from
Burnham and Anderson (2004). Akaike weights, as in Equation (28) (discussed in Section 2.6.2),
were applied to the computed station quantiles as discussed below. Weighing is considered for
three best distributions (w1, w2 and w3) for each station and the weights are applied to
respective quantile estimates to get the station quantiles.
Thus, based on Equation (28), w1 +w2 +w3 =1
For the five return periods selected for the study (Q2, Q10, Q25, Q50 and Q100) the station
quantile is estimated as below
𝑄𝑇 = 𝑤1 ∗ 𝑄𝑇1 + 𝑤2 ∗ 𝑄𝑇2 + 𝑤3 ∗ 𝑄𝑇3 Equation (31)
where, QT1, QT2 and QT3 = T year quantile estimate for the three best candidate distributions
44
An example of the calculations for station frequency analysis, i.e. computation of AIC, AIC
weights and the station flood quantiles is shown in Appendix E.
3.3.3 Multiple Regression Analysis
Multiple Regression analysis was chosen for the development of regional equations for Ontario.
A correlation study (Table 7) was performed to check the degree of correlation between predictor
variables. Analysis of the correlation matrix in Table 7 shows that the parameters like the length
of the main channel is strongly correlated with total drainage area (correlation coefficient of
0.83). Thus, it was removed as an independent predictor variable. The area of lakes and wetlands
was also highly correlated with the drainage area (correlation coefficient = 0.98). As highlighted
in Chapter 2, it was essential to include the area of lakes and wetlands because these water
bodies have an attenuation effect on peak flood flows. For the current investigation, several
transformations were tested and the transformation for the variable representing the area of lakes
and wetlands which was weakly correlated with drainage area (correlation coefficient =0.1) was
adopted as the Lake Attenuation Index (Equation (32) ). Thus, this was used as an independent
predictor variable representing lake storage and its attenuation effect on peak flows.
𝐿𝑎𝑘𝑒 𝐴𝑡𝑡𝑒𝑛𝑎𝑡𝑖𝑜𝑛 𝑖𝑛𝑑𝑒𝑥(𝐿𝐼) = 1 +𝑊𝐴
𝐴 Equation (32)
Table 7: Correlation Matrix of Predictor Variables
A SF L WA P
SF -0.009 - - - -
L 0.838 0.371 -
-
WA 0.921 -0.073 0.687 - -
P -0.347 0.015 -0.321 -0.327 -
CS -0.182 -0.381 -0.369 -0.127 -0.139
Where
A = Total drainage area (km2),
SF = Shape Factor = Length x Length/Area (dimensionless),
L = Length of the Main Channel (km),
WA = Area of lakes and Wetlands (km2),
P = Mean Annual Precipitation (mm),
CS = Channel slope (dimensionless).
45
Further analysis of the histograms of the independent and dependent variables lead to the
interference that the dataset was highly right skewed. An example for Q25 quantile (dependent
variable) for the 118 stations used in the analysis is shown in Figure 12. As outlined in Section
2.6.3 and Equation (30) the response and predictor variables were log transformed and multiple
regression was subsequently performed.
Figure 12: Histogram for Q25 Quantile (dependent variable)
Variable transformations were performed as outlined in Chapter 2 and stepwise regression was
subsequently performed. The output of the stepwise regression process for the log transformed
variables is enclosed in Appendix F and results are summarized in the subsequent chapter.
Regression analysis was carried out for forty-three stations in the Boreal Shield Region and
seventy-five stations in the Mixed Wood Plains Region. The 118 stations used for flood
frequency analysis, along with the location of Ontario Highways, are shown in Figure 13. The
stations not included in regression analysis, along with the reason for rejection, have been
summarized in Appendix G.
46
Figure 13: Regression Stations and Ontario Highways (Source: Highways, 2014)
3.4 Summary
This chapter presents the methodology undertaken for the development of new regional flood
frequency equations for the province of Ontario. All the data available up to and including Dec
2014 for Ontario, i.e. 271 HYDAT stations were selected. After extension of the data series
through established methods, like Sangal (1981), pre-screening was performed where a minimum
record length for each station was set to be 15 years. Non-parametric testing was performed for
HYDAT stations to verify compliance to statistical assumptions. 41 stations demonstrated non-
compliance and were not a part of the subsequent steps, i.e. station frequency analysis and
multiple regression. Station Frequency Analysis helped to calculate the dependent variables, that
is, the T-year Flood Quantile. Ten HYDAT stations were identified as urban watersheds which
had to be subsequently removed from the analysis due to lack of additional data (w.r.t the
47
urbanization pattern, initial land cover information at the start of the flow series, etc.). Issues
were identified during watershed delineation using OFAT where the location of HYDAT stations
from WSC was not recognized in OFAT. There were instances where the watersheds were
limited to the provincial boundary and its contributing parts in neighboring provinces are not
considered. This caused removal of such station as the data was not reliable. A correlation study
between predictors helped to identify variables which showed correlation with the drainage area.
Area of lakes and wetlands was transformed before including in the regression analysis.
Subsequently, multiple regression was performed for development of regional flood frequency
equation for Ontario. The results, referred as the Unified Ontario Flood Method, are presented in
Chapter 4.
48
Chapter 4 Results of Regional Flood Frequency Analysis
The subsequent chapter presents the results of the regression analysis and the development of the
Unified Ontario Flood Method (UOFM). Computational procedures for the UOFM are presented.
A Design table (Table 8) in conjunction with Figure 1 and Figure 2, can be used by engineers to
compute the T-year flood Quantile. Table 10 is used for the prediction of the range (i.e. the upper
and lower limit) of the T-year flood Quantile.
4.1 Unified Ontario Flood Method (UOFM)
The result of multiple regression is represented as the power equation of the form Equation (33).
The coefficients for Equation (33) are provided in Table 8, which is the design table for the
application of the UOFM. Table 9 provides the summary of descriptive statistics and the range of
independent predictor variables for each region.
𝐐𝑼𝑶𝑭𝑴 = 𝐊𝑹 ∗ 𝐀𝒂 ∗ 𝐋𝐈𝒃 ∗ 𝐏𝒄 Equation (33)
Where QUOFM = annual flood with a T year return period (m3/s) from the regression analysis
A = drainage area (km2)
LI = lake attenuation index (dimensionless)
P = mean annual precipitation (mm)
KR = 10x (x = value of constant obtained from the output of stepwise regression)
a,b,c = exponents (obtained from the output of regression)
Table 8: Coefficients of the Regression Model and Output Summary
T x a b c Adjusted R2
Standard error
(SE) (log units)
Boreal Shield
2 -10.870 0.839 -4.633 3.583 0.965 0.159
10 -8.583 0.795 -4.522 2.917 0.954 0.174
25 -7.834 0.779 -4.510 2.703 0.947 0.183
50 -7.371 0.769 -4.520 2.572 0.942 0.189
100 -6.967 0.759 -4.541 2.457 0.937 0.195
49
T x a b c Adjusted R2
Standard error
(SE) (log units)
Mixed Wood Plains
2 -5.483 0.756 -3.061 1.837 0.824 0.147
10 -4.139 0.734 -3.780 1.491 0.790 0.165
25 -3.680 0.728 -4.017 1.372 0.769 0.177
50 -3.397 0.724 -4.162 1.299 0.752 0.186
100 -3.151 0.721 -4.287 1.236 0.736 0.195
Table 9: Range of Parameters used for Equation Development
Range of parameters used to establish the equations
Minimum Maximum Mean Median Standard deviation
Boreal Shield (No. of stations=43)
Area (km2) 1.80 4416.77 908.36 404.53 1189.88
Water Area (km2) 0.168 892.81 143.24 52.00 205.93
Precipitation (mm) 705 1056 866 848 101
Mixed Wood Plains (No. of stations=75)
Area (km2) 13.16 1230.39 243.00 163.91 241.97
Water Area (km2) 0.02 104.33 18.30 12.56 20.29
Precipitation (mm) 813 1219 965 962 94
The standard error of the estimate obtained from the output of the regression analysis is in log
units. Transformation from log units is undertaken to establish the probable range of flood
quantiles (Table 10) following log over addition/subtraction relations (Moin and Shaw, 1985).
These lower and upper limits are applied to the estimated value from Equation (33).
Upper limit (UL):
UL = log (𝑄𝑈𝑂𝐹𝑀) + SE = log (𝑄𝑈𝑂𝐹𝑀 × 10𝑆𝐸) Equation (34)
Lower limit (LL):
LL = log (𝑄𝑈𝑂𝐹𝑀) − SE = log (𝑄𝑈𝑂𝐹𝑀 ÷ 10𝑆𝐸) Equation (35)
50
Where 𝑄𝑈𝑂𝐹𝑀 is the result obtained from regression and SE is the standard error of regression in
log units. Thus, the probable range for the QUOFM can thus be established by the relative standard
error:
Relative upper limit (RUL):
RUL: 𝑄𝑈𝑂𝐹𝑀 𝑋 10𝑆𝐸 − 𝑄𝑈𝑂𝐹𝑀
𝑄𝑈𝑂𝐹𝑀= 10𝑆𝐸 − 1 Equation (36)
Relative lower limit (RLL):
RLL: 𝑄𝑈𝑂𝐹𝑀 −
𝑄𝑈𝑂𝐹𝑀
10𝑆𝐸
𝑄𝑈𝑂𝐹𝑀= 1 −
1
10𝑆𝐸 Equation (37)
Table 10: Range of Quantile Estimates
T Standard error
(log units)
Range of Quantiles
Lower limit Upper limit
Boreal Shield
2 0.159 -31% 44%
10 0.174 -33% 49%
25 0.183 -34% 52%
50 0.189 -35% 55%
100 0.195 -36% 57%
Mixed Wood Plains
2 0.147 -29% 40%
10 0.165 -32% 46%
25 0.177 -33% 50%
50 0.186 -35% 53%
100 0.195 -36% 57%
4.2 Illustration of Calculation Steps
The procedure for calculation of flood quantiles by the Unified Ontario Flood Method (UOFM)
is presented in the following steps. This procedure can be applied to any ungauged stream
location within the two ecozones in Ontario. Ungauged locations which are a part of a regulated
51
stream should be analyzed on a catchment level, and not using UOFM, as the flow conditions
downstream of a regulation will not follow a naturalized flow regime. The following example for
HYDAT station 02AE001 illustrates the steps to obtain the flood quantiles by UOFM. This
station, in the Boreal Shield region, is not a part of the regression study. The procedure, as
outlined should be used to predict the T year quantiles at the location of interest.
HYDAT Station: 02AE001
Step 1: Obtain the latitude and longitude of the ungauged location
Latitude: 48°55'33" N; Longitude: 87°41'24" W
Step 2: Identify the region in which the drainage basin is located from the ecozone map of
Ontario (Figure 1)
Step 3: Obtain the physiographic parameters required in the regression equations from OFAT:
Drainage Area: 605.47 km2
Area of Lakes and wetlands: 54.15 km2
Step 4: Obtain the mean annual precipitation for the station from the IsoHyetal map shown in
Figure 2.
Mean Annual Precipitation: 827 mm
Step 5: Using Equation (33) and respective coefficients from Table 8 the regression T year
flood Quantiles, QUOFM, are calculated (summarized below). Use the coefficients of the region
where the station is located based the ecozone identified in Step 2.
Step 6: The standard errors of the regression equation were used to establish the lower and upper
limit of the prediction. The range (lower and upper limit) is provided in Table 10. These
percentages are applied to the quantile estimates from Step 5. The final values for T-year
quantile and the lower and upper limit are summarized below.
52
Return Period (years) 2 10 25 50 100
QUOFM (m3/s) 56 94 113 127 139
Lower limit of QUOFM (m3/s) 39 63 74 82 89
Upper limit of QUOFM(m3/s) 80 140 172 197 219
4.3 Summary
The result of the Regional Flood frequency Analysis for Ontario is outlined in Chapter 4, Section
4.1. Section 4.2 presents the methodology for designers for the application of Unified Ontario
Flood Method (UOFM). UOFM aims to provide designers with a tool to predict the T-year flood
quantile for drainage basins where the location of interest lacks stream flow data. The presented
equation and design table (Table 8) are anticipated to be adopted by MTO and replace the MIFM
and NOHM for prediction of design flows at streams and river crossings. The subsequent chapter
discusses the verification and comparison study for the UOFM.
53
Chapter 5 Verification and Evaluation
The verification and evaluation of the UOFM was undertaken and the results of the verification
analysis are illustrated in Section 5.1. As MTO may frequently encounter small sized watersheds
(less than the lower limit for the UOFM), a check was performed for a small urban watershed
(Section 5.2). Additional analysis was undertaken to validate the performance of the equation for
medium to large urbanized watersheds (Section 5.3). Subsequently, a comparison of UOFM with
other existing RFFA methods in Ontario was performed.
5.1 Verification of Regression Method: Application to Ontario
For verification of the UOFM, eight stations (Table 11) were tested. Stations 1-3 were not a part
of the regression study, and hence can be considered as better indicators of the accuracy of the
regression method. These stations were not a part of HYDAT dataset from WSC till 2014. Due
to lack of additional data all the other stations were selected from the dataset in Appendix B. The
mean annual precipitation for each station was extracted from the isohyetal map of Ontario
(Figure 2). The comparison between the observed quantiles (QT) and predicted quantiles (QUOFM)
are presented in Table 12 and in Figure 14 (bars indicating probable range for UOFM quantiles).
Table 11: Verification Stations Parameters
S.No. Station
ID Latitude/ Longitude
Region*
Drainage Area (km
2)
Lakes & Wetlands (km
2)
Precipitation (mm)
1 02HL003 44°32'22" N/ 77°22'10" W
BS 424.10 50.39 921
2 02AC002 48°54'15" N/ 88°22'36" W
BS 2599.09 256.09 820
3 02AE001 48°55'33" N/ 87°41'24" W
BS 605.47 54.15 827
4 02BF004 46°30'57" N/ 84°27'54" W
BS 49.75 3.34 923
5 05QD017 49°41'56" N/ 93°42'50" W
BS 2.42 0.01 707
6 02FF007 43°33'4" N/ 81°35'22" W
MWP 462.02 4.90 1071
7 02GA043 43°21'52" N/ 80°37'57" W
MWP 13.16 1.03 962
8 02HK008 44°20'17" N/ 77°28'37" W
MWP 89.29 25.86 923
*BS= Boreal Shield; MWP= Mixed Wood Plains
54
Table 12: Application of UOFM to Verification Stations
Return Period (years) 2 10 25 50 100
02H
L003
QT (m3/s) 32 62 78 89 100
QUOFM (m3/s) 54 86 101 113 123
Lower limit of QUOFM (m3/s) 37 57 67 73 78
Upper limit of QUOFM (m3/s) 77 128 154 175 193
02A
C002
QT (m3/s) 103 180 220 249 278
QUOFM (m3/s) 177 281 331 368 398
Lower limit of QUOFM (m3/s) 123 188 217 238 254
Upper limit of QUOFM (m3/s) 255 419 504 569 623
02A
E001 QT (m
3/s) 73 119 132 149 161
QUOFM (m3/s) 56 94 113 127 139
Lower limit of QUOFM (m3/s) 39 63 74 82 89
Upper limit of QUOFM(m3/s) 80 140 172 197 219
02B
F004 QT (m
3/s) 15 26 31 35 39
QUOFM (m3/s) 11 19 24 27 30
Lower limit of QUOFM (m3/s) 8 13 16 18 19
Upper limit of QUOFM (m3/s) 16 29 36 42 47
05Q
D017
QT (m3/s) 0.08 0.23 0.32 0.39 0.46
QUOFM (m3/s) 0.45 1.06 1.44 1.76 2.07
Lower limit of QUOFM (m3/s) 0.31 0.71 0.94 1.13 1.32
Upper limit of QUOFM (m3/s) 0.65 1.58 2.2 2.71 3.25
02F
F007 QT (m
3/s) 150 268 328 373 419
QUOFM (m3/s) 121 208 250 281 313
Lower limit of QUOFM (m3/s) 86 142 167 183 200
Upper limit of QUOFM (m3/s) 170 303 376 432 490
02G
A043
QT (m3/s) 3 4 5 6 6
QUOFM (m3/s) 6 10 12 14 16
Lower limit of QUOFM (m3/s) 4 7 8 9 10
Upper limit of QUOFM (m3/s) 8 15 19 22 25
02H
K008 QT (m
3/s) 7 11 13 14 16
QUOFM (m3/s) 13 20 23 26 28
Lower limit of QUOFM (m3/s) 9 14 15 17 18
Upper limit of QUOFM (m3/s) 18 29 35 39 44
Overestimated UOFM quantiles relative to observed quantiles (QT )
55
Figure 14: Observed and Predicted Quantiles for Verification Stations
0
50
100
150
200
250
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02HL003)
QUOFM QT
0
200
400
600
800
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02AC002)
QUOFM QT
0
50
100
150
200
250
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02AE001)
QUOFM QT
0
10
20
30
40
50
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02BF004)
QUOFM QT
0
1
2
3
4
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 05QD017)
QUOFM QT
0
200
400
600
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02FF007)
QUOFM QT
0
10
20
30
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02GA043)
QUOFM QT
0
10
20
30
40
50
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02HK008)
QUOFM QT
56
For three of the verification stations the observed flood flows (QT) are not within the probable
range established by the upper and lower limit of the regression relation (shown as bars above
and below QUOFM in Figure 14). Two of these stations (05QD017 and 02GA043) have very small
drainage areas (2.62 km2 and 13.16 km
2, respectively) and therefore it is not surprising that
prediction errors are more significant. Station 02KH008 has a medium sized catchment
(89.29 km2) but observed flood quantiles still fall outside of probable range. In all three cases the
UOFM method overestimated the size of the flood. This produces conservative flood estimates
that will likely be larger than observed flood flows.
5.2 Analysis of the UOFM for a Small Urban Watershed
The UOFM equations are developed for rural catchments and the range of parameters used for
development of equation is outlined in Table 9. However, during subsequent discussions with
MTO it was felt necessary to test the performance of UOFM for small urban catchments,
particularly in the Mixed Wood plains ecozone. Only a single station was identified in the Mixed
Wood plains with an urban watershed that also conformed to the statistical assumptions tested
through nonparametric testing. The parameters and results for this station are highlighted in
Table 13 and Table 14 below. It should be noted UOFM was not developed using the data for
urban catchments. Thus, caution and professional judgement must be considered if applying this
method to an urban setting.
Table 13: Small Catchment Parameters
S.
No.
Station
ID
Latitude/
Longitude Region
*
Drainage
Area (km2)
Lakes &
Wetlands (km2)
Precipitation
(mm)
1 02HB021 43°13'52" N/
79°58'25" W MWP 8.12 0.16 937
*BS= Boreal Shield; MWP= Mixed Wood Plains
Table 14: Small Catchment Flood Quantiles
Return Period(years) 2 10 25 50 100
02H
B021
QT (m3/s) 2 4 6 7 8
QUOFM (m3/s) 4 8 11 12 14
Lower limit of QUOFM (m3/s) 3 6 7 8 9
Upper limit of QUOFM (m3/s) 6 12 16 19 22
Overestimated UOFM quantiles relative to observed quantiles (QT )
57
Similar to the verification stations the UOFM produced flood predictions are moderately larger
than observed flood flows. It may be noted that the urban water cycle and urban flow regime can
be drastically different from its pre-development state. Caution and judgement must be exercised
if applying the UOFM to urban catchments. Recommendations for urban flood modelling are
discussed further in Section 5.4.
5.3 Analysis of UOFM for Medium to Large Urban Watersheds
Urbanization poses a challenge of increase in peak flows. The complex interplay of various
components in the urban environment and lack of adequate data for urban Ontario makes it
difficult to perform frequency analysis as for the rural watersheds. However, with changes in
land use such watersheds are frequently encountered by MTO. Thus, it would be imperative to
evaluate the performance of the UOFM equations for medium to large sized urban watersheds.
The urban watersheds tested are summarized in Table 15. The imperviousness (obtained from the
OFAT land cover information) for these watersheds varies from 23% for station 2 below to about
86% for Station 7. It may be noted that the equations are not developed using the data for urban
catchments and so adequate caution must be applied while using them for urban catchments.
Table 15: Medium to Large Urban Catchment Parameters
S.No. Station
ID
Latitude/
Longitude Region
*
Drainage
Area (km2)
Lakes &
Wetlands (km2)
Precipitation
(mm)
1 02DD014 46°18'42" N/
79°26'54" W BS 35.55 3.45 1025
2 02GE005 42°56'2" N/
81°21'4" W MWP 149.83 4.78 1001
3 02HC030 43°36'6" N/
79°33'22" W MWP 216.42 3.50 812
4 02EC009 44°5'41" N/
79°29'22" W MWP 174.73 9.65 855
5 02CF012 46°25'38" N/
81°5'54" W BS 205.28 33.32 898
6 02GH011 42°18'35" N/
82°55'42" W MWP 55.11 0.47 923
7 02HC033 43°38'50" N/
79°31'10" W MWP 68.93 0.56 817
8 02HA023 43°12'1" N/
79°49'13" W MWP 25.73 0.02 899
*BS= Boreal Shield; MWP= Mixed Wood Plains
58
Table 16: Analysis Results for Medium to Large Urban Watersheds
Return Period (years) 2 10 25 50 100
02D
D014 QT (m
3/s) 9 15 18 20 22
QUOFM (m3/s) 11 18 21 24 27
Lower limit of QUOFM (m3/s) 7 12 14 16 17
Upper limit of QUOFM (m3/s) 16 27 33 37 42
02G
E005
QT (m3/s) 31 53 65 74 83
QUOFM (m3/s) 43 76 93 105 117
Lower limit of QUOFM (m3/s) 31 52 62 68 75
Upper limit of QUOFM (m3/s) 60 111 139 161 183
02H
C030
QT (m3/s) 87 136 162 180 199
QUOFM (m3/s) 40 77 96 111 126
Lower limit of QUOFM (m3/s) 29 53 64 72 80
Upper limit of QUOFM(m3/s) 57 113 145 170 197
02E
C009
QT (m3/s) 30 54 67 77 87
QUOFM (m3/s) 34 62 76 87 98
Lower limit of QUOFM (m3/s) 24 42 51 57 62
Upper limit of QUOFM (m3/s) 47 90 115 133 153
02C
F012 QT (m
3/s) 24 36 41 45 49
QUOFM (m3/s) 22 38 45 51 56
Lower limit of QUOFM (m3/s) 16 25 30 33 36
Upper limit of QUOFM (m3/s) 32 56 69 79 88
02G
H011 QT (m
3/s) 28 41 44 47 49
QUOFM (m3/s) 19 35 44 50 57
Lower limit of QUOFM (m3/s) 13 24 29 33 36
Upper limit of QUOFM (m3/s) 26 51 66 77 89
02H
C033
QT (m3/s) 34 56 67 75 83
QUOFM (m3/s) 18 35 44 50 57
Lower limit of QUOFM (m3/s) 13 24 29 33 37
Upper limit of QUOFM (m3/s) 25 51 66 77 90
02H
A023
QT (m3/s) 19 25 27 28 29
QUOFM (m3/s) 10 20 25 29 33
Lower limit of QUOFM (m3/s) 7 14 17 19 21
Upper limit of QUOFM (m3/s) 14 29 38 44 51
Overestimated UOFM quantiles relative to observed quantiles (QT )
59
Figure 15: Observed and Predicted Quantiles for Medium to Large Urban Watersheds
0
10
20
30
40
50
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02DD014)
QUOFM QT
0
50
100
150
200
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02GE005)
QUOFM QT
0
50
100
150
200
250
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02HC030)
QUOFM QT
0
50
100
150
200
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02EC009)
QUOFM QT
0
20
40
60
80
100
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02CF012)
QUOFM QT
0
20
40
60
80
100
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02GH011)
QUOFM QT
0
20
40
60
80
100
0 20 40 60 80 100Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02HC033)
QUOFM QT
0
20
40
60
0 20 40 60 80 100
Flo
od
Qu
an
tile
(m
3/s
)
Return period, T (years)
Flood Quantiles (Station: 02HA023)
QUOFM QT
60
The result of the limited analysis shown graphically in Figure 15 and presented in Table 16 does
not conclusively reflect the performance of the UOFM on medium to large urban watersheds.
Three of the eight watersheds of varied drainage area were over predicted by the UOFM. For
many of the cases, the UOFM under predicted the flood quantiles compared to the observed
values. Thus, appropriate caution and engineering judgement should be applied if using the
UOFM for urban drainage basins.
5.4 Simulation for Peak Flow Estimation: Case of Urban Floods
Evaluation of flood frequency characteristics of urban drainage basins was not possible due to
the limited availability of stream flow data. In situations when the data was available, the record
length was not suitable. Urbanization significantly alters the hydrological cycle by increasing the
volume and speed of runoff. Thus, the runoff characteristics of such a developed state are very
different from its pre development state. Another important feature of urban floods, pointed out
by Watt et al. (1989), is the behavior of urban flood control measures. These features affect the
‘urban response’ to basic hydrologic events. Thus, urban runoff models require detailed analysis
of the urban drainage basin, its connection with the basins flood control infrastructure and
changes in the hydrologic cycle which have resulted because of urbanization-particularly the
effect of abstractions, rainfall and runoff characteristics of the basin.
Simulation based approach also depends on the availability of relevant hydrologic and basin
parameters of the basin. It may be selected depending on the objective of the project and level of
precision required (which is high in case of urban projects due to its effect on life and property).
These involve detailed mathematical simulation of rainfall-runoff models in either 1-D or 2-D
environment. They are helpful in understanding the interaction between rainfall and flooding.
Models like rational method and unit hydrograph are generally used for simpler applications
whereas SWMM, which has a good applicability for detailed analysis, can be used for complex
problems like design of systems and prediction of peak flows (Watt et al. (1989)). Currently,
flood mapping techniques also integrate runoff models with GIS technology and produce
inundation maps which are necessary for planning in an urban environment. Additionally, there
are only few studies which deal with the condition of a surcharged pipe network and flooding on
the catchment surface together (Mark et al. 2004). This condition is a common occurrence in
urban environments which also needs detailed investigation.
61
In view of the limited availability of flow data (10 HYDAT stations) and incomplete land cover
information for the starting year of the flow series for the available stations, it was difficult to
assess the stationarity of the HYDAT stations. The lack of information about the urban flood
control measures in the catchments and the complex interaction among various elements in an
urban hydrologic cycle, the enormous cost on life and property in an urban environment
necessitates a detailed analysis on a catchment level for urban drainage basins. In view of the
above consideration, the feasibility of a study for regional flood frequency analysis for urban
catchments could not be established. All urban flood frequency analysis should be done
separately for each drainage basin taking into account all the mentioned considerations along
with the climate and physiography of the basin.
5.5 Comparison with Other RFFA Methods
The results of the regression based UOFM are compared with the flood estimates derived from
currently accepted practices including the MIFM and NOHM. The calculations for MIFM
(Southern and Shield Region) and NOHM are performed as prescribed in Ontario Ministry of
Transportation (1997).
5.5.1 Comparison of UOFM and MIFM (South)
Two stations are selected for comparison of UOFM with MIFM for Southern Region (Table 17).
As shown in Table 18 both the UOFM and MIFM under predicted flood quantiles. The two
methods produce comparable results however for the two stations tested herein; the UOFM
provided a better estimate of the observed floods.
Table 17: Station Parameters for Comparison with MIFM (South)
S.No. Station
ID
Latitude/
Longitude Region
*
Drainage
Area (km2)
Lakes &
Wetlands
(km2)
Precipitation
(mm)
Slope
(%)
1 02GB009 43°5'57" N/
80°29'19" W MWP 89.34 8.52 951 0.15
2 02MB006 44°31'30" N/
75°48'19" W MWP 107.25 24.64 980 0.141
*BS= Boreal Shield; MWP= Mixed Wood Plains
62
Table 18: Comparison of UOFM with MIFM (South)
Station
ID
Return
Period
(yrs)
QT QMIFM QUOFM
Lower limit
of QUOFM
(m3/s)
Upper limit
of QUOFM
(m3/s)
Error
MIFM
(%)
Error
UOFM
(%)
02G
B009
2 35 - 22 16 31 - -38
2.33 - 17 - - - - -
10 61 28 38 26 56 -54 -37
25 71 34 47 31 70 -52 -35
50 79 40 52 34 80 -50 -34
100 86 45 59 37 92 -48 -32
02M
B006
2 26 - 19 13 26 - -27
2.33 - 7 - - - - -
10 38 12 30 20 43 -68 -22
25 44 15 35 23 52 -66 -21
50 48 18 38 25 59 -64 -21
100 53 20 42 27 66 -62 -20
5.5.2 Comparison of UOFM and MIFM (Shield)
Four stations are selected for comparison of UOFM with the MIFM for the Shield region (Table
19). MIFM (Shield) and UOFM flood estimates are presented in Table 20. As an engineer, under
prediction of flows is undesirable and may lead to more frequent flooding events than
anticipated. For the limited comparison, in some instances both UOFM and MIFM under predict
flood quantiles. However, the UOFM captures the observed flood within the established range of
the probable lower and upper limit. Additionally, errors associated with the UOFM were
noticeably smaller than the MIFM (Shield) errors.
Table 19: Station Parameters for Comparison with MIFM (Shield)
S.No. Station
ID
Latitude/
Longitude Region
*
Drainage
Area
(km2)
Lakes
(km2)
Wetlands
(km2)
Precipitation
(mm)
1 02KF017 44°58'6" N/
76°57'58" W BS 151.45 11.86 7.76 880
2 02DD015 45°56'57" N/
79°36'24" W BS 101.45 6.25 6.13 1045
3 02CA002 46°15'48" N/
79°23'42" W BS 108.09 5.47 6.68 999
4 02DD013 46°33'46" N/
84°16'54" W BS 68.27 2.07 10.11 1014
*BS= Boreal Shield; MWP= Mixed Wood Plains
63
Table 20: Comparison of UOFM with MIFM (Shield)
Station
ID
Return
Period
(yrs)
QT QMIFM QUOFM
Lower limit
of QUOFM
(m3/s)
Upper limit
of QUOFM
(m3/s)
Error
MIFM
(%)
Error
UOFM
(%)
02K
F017
2 13 - 18 13 27 - 42
2.33 - 17 - - - - -
10 22 25 32 21 47 14 45
25 26 30 38 25 59 13 47
50 29 33 44 28 67 14 48
100 33 38 48 31 75 15 47
02D
D015
2 16 - 25 17 36 - 54
2.33 - 14 - - - - -
10 25 21 39 26 59 -16 60
25 28 24 46 30 70 -14 62
50 31 28 51 33 80 -12 64
100 34 31 56 36 88 -9 63
02C
A002
2 28 - 23 16 34 - -18
2.33 - 16 - - - - -
10 49 23 38 25 56 -53 -23
25 60 27 45 29 68 -54 -26
50 68 31 50 32 77 -55 -27
100 77 35 55 35 86 -55 -29
02D
D013
2 13 - 13 9 19 - 0
2.33 - 8 - - - - -
10 20 12 21 14 31 -39 6
25 23 14 25 16 38 -38 8
50 26 16 28 18 43 -37 10
100 28 18 31 20 48 -35 10
64
5.5.3 Comparison of UOFM and NOHM
Four stations which are a part of the UOFM study are selected for comparison of UOFM with the
NOHM (Table 21). UOFM and NOHM flood values are summarized in Table 22. In general, for
the tested stations the NOHM produced slightly lower flood quantile values relative to the
UOFM. Overall the UOFM performs better and the station estimates are within the probable
range of the quantile estimates for the selected watersheds.
Table 21: Station Parameters for Comparison with NOHM
S.No. Station
ID
Latitude/
Longitude Region
*
Drainage
Area (km2)
Lakes &
Wetlands (km2)
Precipitation
(mm)
1 02DD013 46°15'48" N/
79°23'42" W BS 68.27 12.18 1014
2 02BF006 47°03'1" N/
84°24'46" W BS 8.00 1.24 947
3 02BF004 46°30'57" N/
84°27'54" W BS 49.75 4.26 923
4 02BF007 47°2'41" N/
84°24'36" W BS 4.99 0.62 947
*BS= Boreal Shield; MWP= Mixed Wood Plains
Table 22: Comparison of UOFM with NOHM
Station
ID
Return
Period
(yrs)
QT QNOHM QUOFM
Lower limit
of QUOFM
(m3/s)
Upper limit
of QUOFM
(m3/s)
Error
NOHM
(%)
Error
UOFM
(%)
02D
D013
2 13 10 13 9 19 -22 0
10 20 15 21 14 31 -22 6
25 23 18 25 16 38 -24 8
50 26 19 28 18 43 -26 10
100 28 20 31 20 48 -28 10
02B
F00
6
2 2 1 2 1 3 -37 -7
10 3 2 3 2 5 -42 4
25 4 2 4 3 7 -45 8
50 4 2 5 3 8 -47 11
100 5 3 6 4 9 -49 13
65
Station
ID
Return
Period
(yrs)
QT QNOHM QUOFM
Lower limit
of QUOFM
(m3/s)
Upper limit
of QUOFM
(m3/s)
Error
NOHM
(%)
Error
UOFM
(%) 02B
F004
2 15 11 11 8 16 -28 -27
10 26 18 19 13 29 -29 -25
25 31 22 24 16 36 -31 -24
50 35 24 27 18 42 -32 -23
100 39 26 30 19 47 -34 -23
02B
F007
2 2 1 1 1 2 -42 -12
10 3 1 3 2 4 -47 -5
25 3 2 3 2 5 -51 -4
50 4 2 4 3 6 -54 -4
100 5 2 4 3 7 -57 -5
5.6 Climate Change Considerations
Researchers often associate changes in flood risk as a possible effect of climate change, but there
are very few studies to substantiate the hypothesis of any increase in peak flows due to the
changing climate (IPCC, 2001). In order to complete regression analysis HYDAT stations were
tested for independence, stationarity, homogeneity, and general randomness. Stations which
failed any one of these statistical tests were excluded from the station frequency analysis and
multiple linear regression analysis. As a result the UOFM presented herein inherently assumes
stationary conditions. The future impacts of climate change on Ontario hydrology remain
uncertain. Isolating climatic (i.e. climate change) and anthropogenic (e.g. urbanization, evolving
SWM infrastructure) causes of changes in stream flow regimes is highly contentious. Moreover,
global climate models cannot accurately predict localized changes in peak flow scenarios and
any short duration change may not necessarily translate to long term ‘climate change’.
Nonetheless, the assumption of continuous changes in climate cannot be relinquished. It is
however a gradual phenomenon, which needs published local evidence to be able to extend it to
the probability-based flood frequency studies.
5.7 Summary
The chapter above presents the results of the verification and evaluation of UOFM to ascertain its
applicability to Ontario watersheds. The smallest drainage area of the watershed analyzed in the
66
Mixed Woods region was 13.16 km2. The range for the Mixed Wood ecozones could not be
lowered further due to lack of HYDAT stations that fit the station selection criterions. Thus,
using the regression equation for watersheds below this range is not advisable. However, such
watersheds may be frequently encountered by MTO; hence a check was performed for a small
urban watershed with area less than 13.16 km2 (Section 5.2). UOFM was also tested medium to
large urbanized watersheds. A comparison study was conducted to examine the performance of
the equations relative to the peak flow prediction methods currently used in Ontario. The
comparisons of UOFM estimates with observed values (Section 5.1 and Section 5.5) produced
instances of both over prediction in few cases while under prediction in other cases. Such a
situation establishes that the regression model may be free from bias and the model can be
suitably applied. The chapter also discussed the case of urban floods and the implications of
climate change on flow regimes.
67
Chapter 6 Conclusions and Recommendations
This thesis presents the development of new regional flood frequency equations for the province
to Ontario, referred to as the Unified Ontario Flood Method (UOFM). Regional equations have
design applications in predicting the peak flows necessary for planning structures on water
courses. Thus, there is a need to keep them updated with the current flow regimes. The sections
below present the most significant conclusions and recommendations from the current study.
6.1 Conclusions
The broad objective of the study was the development of Regional Flood Frequency Analysis
(RFFA) procedures for the province of Ontario. Based on the analysis of currently used methods,
like MIFM and NOHM, some drawbacks were identified and highlighted in Section 1.2. These
drawbacks led to the need of the current study. The important conclusions with respect to these
considerations are discussed.
1. Availability of approximately twenty years of additional stream flow data since the last
study of MIFM and NOHM completed in 1996 and 1994, respectively. The additional
data, when accounted for, will provide a better representation of the current watershed
and stream flow conditions.
The available datasets until Dec 2014 was utilized for the development of the UOFM. The total
number of station analyzed in the province was increased to 271 stations (from 46 in MIFM and
11 in NOHM). As outlined in Section 5.5, the UOFM has shown to provide improved prediction
than the currently used methods, the MIFM and NOHM. UOFM minimized the errors with
respect to the observed station quantiles in comparison to MIFM and NOHM. The range of flood
quantiles, i.e. the upper and lower limit of UOFM, provides additional flexibility to engineers
and designers based on the catchment conditions under consideration. The results of the
verification study tend to provide conservative estimates of peak flows in drainage catchments.
Such a situation may be desirable for engineers and designers given the uncertainty of future
conditions both in terms of extreme weather and increasing urbanization. Overall comparison of
observed values of during the verification and comparison study showed both over prediction by
UOFM in some cases whereas under prediction in other cases. This leads to the conclusion of
68
less bias in the regression model. It is not advisable to use the UOFM prediction for drainage
area outside the size range used for its development. At the same time, UOFM may not perform
for urbanized catchments and regulated streams.
2. Changes in catchment characteristics, which lead to gradual changes in the flow
regime, should be taken into consideration.
The catchments characteristics are gradually changing in the province, especially in southern
Ontario which is characterized as the Mixed Wood Plain Ecozone. Changes in catchment
characteristics lead to gradual changes in the flow regime. This needs to be taken into
consideration during the development of RFFA procedures. Thus, the RFFA equations should be
updated every 10 years (Vaill, 2000) and the proposed UOFM should also be updated in due
course.
3. Inconsistency in area classification and the corresponding equation for prediction of
flood quantiles needs to be addressed.
The adoption of one method, i.e. the UOFM will remove the inconsistencies in the area
classification. This is especially relevant for the Shield region where there was uncertainty in the
equation to be used for drainage areas greater than 25 km2, when both the MIFM (Shield) and
NOHM can be applied. It can also be observed from Table 20 and Table 22 for HYDAT station
02DD013, which is tested with both MIFM and NOHM, the flood estimates obtained are slightly
different on comparison of both the methods. Thus, UOFM removes the uncertainty in the
method to be applied for drainage areas in the Shield region.
4. Analysis procedures for urban watersheds, predominately required for the south, are
non-existent. A review of the available data to ascertain the feasibility of such a study
was requested to be performed.
This thesis analyzed the data available for urban catchments. Only 10 urban catchments could be
identified for the whole province (Figure 7). A flood frequency study with 10 catchments was
not practical. Addition data was also provided by the Credit valley conservation (CVC) authority.
The maximum record length of the CVC stream gauging stations was approximately 7 years.
69
Thus, in the current scenario, flood frequency analysis for urban Ontario was not considered
feasible. There is a need to start long term monitoring of stream flows in urban catchments.
6.2 Limitations and Recommendations for Future Studies
The objective of the study was to develop a simple and easy to use set of equations for regional
flood frequency analysis (RFFA). Ontario does not have a preset procedure for development of
RFFA equations. Such a situation may be of advantage to a researcher, where she is not fixed in
her ideas and has the freedom to explore. At the same time, not having a defined procedure is a
challenge, because this forces the researcher to difficult decisions based on the copious, and
sometimes conflicting, recommendations available worldwide for development of RFFA
equations. With the variation in climate and physiography, across Canada in general and Ontario
in particular, the lack of defined RFFA procedures presented to opportunity to break with
tradition and use individually selected distributions to fit station data (Section 3.3.2) instead of
imposing a single probabilistic distributions (e.g. Log-Pearson type 3 as has been specified for
the United States or 3-Parameter Lognormal which is widely accepted in Ontario) to all gauge
stations. Implementing more analytically rigorous and computationally complex RFFA
procedures improved the predictive performance of the UOFM. The used of more HYDAT
stations than previous studies helped to minimize the standard errors of regression. Thus, it is
highly recommended that long term stream flow monitoring is crucial and more such stations,
like the RHBN stations should be added in the province.
There is a need for a tool, such as the Consolidated Frequency Analysis Tool from Ministry of
Natural Resources and Forestry (previously available for Ontario but is no longer supported), for
station frequency analysis and computation of station quantiles. RFFA should be conducted at
least every 10 years (Vaill, 2000) to account for changes in the catchment and the flow regimes
and the current UOFM should be subsequently updated. A tool, specifically designed for Flood
Frequency Analysis, will provide an ease when revising the UOFM, instead of using various
statistical software for different computational tasks.
With rapid changes in watershed characteristics it is imperative to acknowledge the variations
which the regression model would bring to flood estimates. Only 10 HYDAT stations from the
271 stations were classified as predominately urban stations (more than 20% of impervious
cover) based on the current land cover data obtained from OFAT. The land cover details for
70
these stations at the beginning of their respective flow series were not available to ascertain if the
land cover changed drastically with time. Thus, it is recommended to study the urban floods for
each watershed separately rather than on a regional basis. The considerations and simulation
techniques identified in Section 5.4 may be applied here.
Over the course of this study many limitations of RFFA were encountered. Analysis work is also,
ultimately limited by scope, resources and time. Future investigators may wish to compare the
flood frequency values using regression residuals technique (used in studies like Moin and Shaw
(1985)) to classify homogeneous regions. Comparison of the results obtained from the ecozone
classification may either cause a reclassification of these homogenous regions or provide
legitimacy to the current classification which is based on the ecosystem perspective. At the same
time, ecozones extend to neighboring provinces such as Quebec and Manitoba. Stream flow data
from these regions may be considered if reliable sources of physiographic characteristic can be
obtained. The inclusion of additional data may improve the robustness of the equations.
A challenge during the course of the current investigation was a reliable method for distribution
selection. AIC values led to objective decision making during distribution selection. But, small
difference in AIC values between different candidate distributions posed a challenge of selecting
one distribution over the other. A study considering a distribution selection approach based on
analysis of the skew of the data and the log transformed series as recommended in Alberta
Transportation (2001) may provide more insight into distribution selection. At the same time, it
was also concuded during the course of the current investigation that no ‘one’ distribution can be
universally applied to a province like Ontario with wide variation in climate and physiography.
Finally, additional research needs to address ‘climate change’ scenarios which were not
considered during the course of current investigation. This issue categorically warrants further
investigation. The rejection of approximately 41 stations due to non-compliance with
assumptions of independence, stationarity, homogeneity and randomness indicate the need to
consider changes in the climate and flow regimes. Planned infrastructure and urban growth
should be adaptable to future climate scenarios. Further examining the HYDAT stations for
which the hypothesis of the non-parametric tests was rejected may involve investigating parts of
the data series for conformity with the hypothesis of the non-parametric tests. This may
subsequently alter the number of stations available for regression analysis.
71
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76
Appendix A: Example of the Annual flow data for WSC
Representative station: 02AD010
Annual Maximum Instantaneous Flow:
ID Year TIMEZ
ONE HH:MM MM--DD MAX
02AD010 1971
02AD010 1972
02AD010 1973 EST 1:34 04--26 52.4
02AD010 1974 EST 22:26 05--24 52.1
02AD010 1975 EST 2:03 06--21 56.1
02AD010 1976 EST 5:47 04--24 59.5
02AD010 1977 EST 22:05 04--25 73.3
02AD010 1978 EST 5:45 06--05 39.1
02AD010 1979 EST 4:36 05--15 48.2
02AD010 1980 EST 23:57 05--01 52.4
02AD010 1981 EST 11:36 04--19 24.3
02AD010 1982
02AD010 1983 EST 18:52 05--06 37.7
02AD010 1984 EST 8:04 05--01 47.9
02AD010 1985 EST 19:04 09--28 60.1
02AD010 1986 EST 7:11 05--02 50.2
02AD010 1987 EST 18:18 04--20 21.1
02AD010 1988 EST 23:22 05--06 37.5
02AD010 1989 EST 20:13 05--09 66.5
02AD010 1990 EST 9:19 05--01 66.3
02AD010 1991 EST 16:04 05--04 38
02AD010 1992
02AD010 1993 EST 11:24 05--09 35.3
02AD010 1994 EST 0:36 06--25 36.2
02AD010 1995
02AD010 1996 EST 7:45 05--22 151
02AD010 1997 EST 20:30 05--02 56.9
02AD010 1998 EST 2:00 10--24 43.5
02AD010 1999 EST 23:00 04--24 36
02AD010 2000 EST 16:00 05--12 35.8
02AD010 2001 EST 23:00 05--03 68
02AD010 2002 EST 20:00 04--23 38.2
02AD010 2003 EST 22:00 04--28 39.1
02AD010 2004 EST 21:00 11--02 36
02AD010 2005 EST 9:00 04--20 37.2
77
ID Year TIMEZ
ONE HH:MM MM--DD MAX
02AD010 2006 EST 2:00 04--22 60.3
02AD010 2007 EST 2:50 06--03 41.1
02AD010 2008 EST 13:15 04--29 61.2
02AD010 2009 EST 4:40 05--04 47.8
02AD010 2010 EST 9:00 10--01 13.7
02AD010 2011 EST 9:35 05--05 47.8
02AD010 2012 EST 5:15 06--02 55.1
02AD010 2013 EST 21:25 05--12 52.6
Annual Maximum Average Daily Flow:
ID Year MM--DD MAX
02AD010 1971
02AD010 1972 05--05 56.1
02AD010 1973 04--25 52.1
02AD010 1974 05--24 52.1
02AD010 1975 06--21 55.5
02AD010 1976 04--23 59.2
02AD010 1977 04--25 72.5
02AD010 1978 06--05 38.5
02AD010 1979 05--15 48.1
02AD010 1980 05--01 52.3
02AD010 1981 04--19 24.2
02AD010 1982 05--05 54.4
02AD010 1983 05--06 37.4
02AD010 1984 05--01 47.7
02AD010 1985 09--28 59.8
02AD010 1986 05--02 50.1
02AD010 1987 04--20 21.1
02AD010 1988 05--07 37.3
02AD010 1989 05--09 65.9
02AD010 1990 05--01 65.9
02AD010 1991 05--04 38
02AD010 1992 05--15 123
02AD010 1993 05--09 35.2
02AD010 1994 06--24 36
02AD010 1995 10--07 40
02AD010 1996 05--22 150
02AD010 1997 05--02 56.4
02AD010 1998 10--24 43
02AD010 1999 04--25 35.9
78
ID Year MM--DD MAX
02AD010 2000 05--12 35.6
02AD010 2001 05--04 67.5
02AD010 2002 05--16 37.9
02AD010 2003 04--29 38.9
02AD010 2004 11--03 35.9
02AD010 2005 04--17 36.8
02AD010 2006 04--22 60.2
02AD010 2007 06--03 40.9
02AD010 2008 04--29 60.8
02AD010 2009 05--04 47.5
02AD010 2010 10--01 13.7
02AD010 2011 05--05 47.6
02AD010 2012 06--02 54.5
02AD010 2013 05--12 52.1
79
Appendix B: Summary of all HYDAT Stations
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
1 02HB021 ANCASTER CREEK AT
ANCASTER 28 22 22 0 22
2 04DB001 ASHEWEIG RIVER AT
STRAIGHT LAKE 48 34 41 7 41
3 05PB018 ATIKOKAN RIVER AT
ATIKOKAN 35 22 30 8 30
4 04FB001
ATTAWAPISKAT RIVER
BELOW ATTAWAPISKAT
LAKE
48 18 29 11 29
5 04FC001 ATTAWAPISKAT RIVER
BELOW MUKETEI RIVER 45 23 39 16 39
6 02CB003 AUBINADONG RIVER ABOVE
SESABIC CREEK 34 29 32 3 32
7 05PA012 BASSWOOD RIVER NEAR
WINTON 87 59 83 24 83
8 02BF001 BATCHAWANA RIVER NEAR
BATCHAWANA 47 43 46 3 46
9 02FF007 BAYFIELD RIVER NEAR
VARNA 48 42 45 3 45
10 02LB008 BEAR BROOK NEAR
BOURGET 65 15 49 35 50
11 02GG004 BEAR CREEK ABOVE
WILKESPORT 21 18 20 2 20
12 02GG009 BEAR CREEK BELOW
BRIGDEN 33 28 31 3 31
13 02GG006 BEAR CREEK NEAR PETROLIA 48 43 47 4 47
14 02FC017 BEATTY SAUGEEN RIVER
NEAR HOLSTEIN 29 15 16 1 16
15 02EC011 BEAVERTON RIVER NEAR
BEAVERTON 48 23 33 10 33
16 05RC001 BERENS RIVER ABOVE
BERENS LAKE 33 23 23 0 23
17 02BF004 BIG CARP RIVER NEAR SAULT
STE. MARIE 35 27 32 5 32
18 02GC011 BIG CREEK NEAR KELVIN 51 22 23 1 23
19 02GC010 BIG OTTER CREEK AT
TILLSONBURG 54 47 49 2 49
20 02BB002 BLACK RIVER NEAR
MARATHON 24 21 23 2 23
21 02EC002 BLACK RIVER NEAR
WASHAGO 99 36 98 62 98
22 02AD010 BLACKWATER RIVER AT
BEARDMORE 43 38 42 4 42
23 02JC008 BLANCHE RIVER ABOVE
ENGLEHART 45 38 41 4 42
24 02HE001 BLOOMFIELD CREEK AT 24 22 23 1 23
80
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
BLOOMFIELD
25 02CG003 BLUE JAY CREEK NEAR
TEHKUMMAH 29 19 21 2 21
26 02FE014 BLYTH BROOK BELOW
BLYTH 30 21 21 0 21
27 02HF004 BOB CREEK NEAR MINDEN 18 13 16 3 16
28 02HD006 BOWMANVILLE CREEK AT
BOWMANVILLE 54 22 41 19 41
29 02FE010 BOYLE DRAIN NEAR
ATWOOD 47 20 22 2 22
30 02ED102 BOYNE RIVER AT EARL
ROWE PARK 47 26 32 6 32
31 04GB005 BRIGHTSAND RIVER AT
MOBERLEY 46 23 24 1 24
32 02HB022 BRONTE CREEK AT CARLISLE 25 23 24 1 24
33 02KF017 BUCKSHOT CREEK NEAR
PLEVNA 21 15 13 0 15
34 02MB010 BUELLS CREEK AT
BROCKVILLE 25 19 16 2 21
35 02GA036 CANAGAGIGUE CREEK NEAR
FLORADALE 15 12 14 2 14
36 02GH003 CANARD RIVER NEAR
LUKERVILLE 38 30 36 7 37
37 02KF011 CARP RIVER NEAR KINBURN 43 29 41 12 41
38 02FC011 CARRICK CREEK NEAR
CARLSRUHE 61 39 50 11 50
39 02LB006 CASTOR RIVER AT RUSSELL 66 22 57 35 57
40 04GA002 CAT RIVER BELOW
WESLEYAN LAKE 44 37 39 2 39
41 02GC030 CATFISH CREEK AT AYLMER 27 19 23 4 23
42 02GC018 CATFISH CREEK NEAR
SPARTA 50 42 49 7 49
43 05QE008 CEDAR RIVER BELOW
WABASKANG LAKE 44 40 43 3 43
44 02DD014 CHIPPEWA CREEK AT NORTH
BAY 40 37 39 2 39
45 02HK007 COLD CREEK AT ORLAND 33 28 31 3 31
46 02HC023 COLD CREEK NEAR BOLTON 52 37 40 3 40
47 02ED007 COLDWATER RIVER AT
COLDWATER 48 41 45 4 45
48 02HM005 COLLINS CREEK NEAR
KINGSTON 45 32 43 11 43
49 02DD015 COMMANDA CREEK NEAR
COMMANDA 40 29 36 7 36
50 02GA017 CONESTOGO RIVER AT
DRAYTON 23 19 22 3 22
51 02DB007 CONISTON CREEK ABOVE
WANAPITEI RIVER 34 25 32 7 32
52 02DB004 CONISTON CREEK NEAR 15 0 8 0 0
81
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
CONISTON
53 02AB021 CURRENT RIVER AT
STEPSTONE 25 21 22 1 22
54 02GE005 DINGMAN CREEK BELOW
LAMBETH 49 18 40 22 40
55 02GC031 DODD CREEK BELOW
PAYNES MILLS 27 23 25 2 25
56 02DD008 DUCHESNAY RIVER NEAR
NORTH BAY 27 13 26 13 26
57 02HC019 DUFFINS CREEK ABOVE
PICKERING 54 37 46 9 46
58 02HC049 DUFFINS CREEK AT AJAX 25 22 23 1 23
59 02LB012
EAST BRANCH SCOTCH
RIVER NEAR ST. ISIDORE DE
PRESCOTT
25 8 20 14 22
60 02GA035 EAST CANAGAGIGUE CREEK
NEAR FLORADALE 15 12 14 2 14
61 02HC032 EAST HUMBER RIVER AT
KING CREEK 49 34 37 3 37
62 02HC009 EAST HUMBER RIVER NEAR
PINE GROVE 61 42 58 16 58
63 02HB004 EAST SIXTEEN MILE CREEK
NEAR OMAGH 58 43 56 13 56
64 04EA001 EKWAN RIVER BELOW
NORTH WASHAGAMI RIVER 47 15 28 13 28
65 05QA002 ENGLISH RIVER AT
UMFREVILLE 93 34 91 57 91
66 05QA001 ENGLISH RIVER NEAR SIOUX
LOOKOUT 61 14 60 46 60
67 02HC030 ETOBICOKE CREEK BELOW
QUEEN ELIZABETH HIGHWAY 48 42 47 5 47
68 02HC002 ETOBICOKE CREEK NEAR
SUMMERVILLE 18 3 15 12 15
69 02GB007 FAIRCHILD CREEK NEAR
BRANTFORD 50 33 48 15 48
70 04CE002 FAWN RIVER BELOW BIG
TROUT LAKE 26 19 23 4 23
71 02GD010 FISH CREEK NEAR PROSPECT
HILL 69 34 55 21 55
72 02HD012 GANARASKA RIVER ABOVE
DALE 38 26 35 10 36
73 02HD002 GANARASKA RIVER NEAR
DALE 26 14 25 11 25
74 02BF002 GOULAIS RIVER NEAR
SEARCHMONT 47 43 46 3 46
75 02KF015 GRAHAM CREEK AT NEPEAN 27 15 11 0 15
76 02GA041 GRAND RIVER NEAR
DUNDALK 30 15 22 8 23
77 02HB012 GRINDSTONE CREEK NEAR 49 39 47 8 47
82
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
ALDERSHOT
78 04KA002 HALFWAY CREEK AT
MOOSONEE 22 12 20 8 20
79 02HD013 HARMONY CREEK AT
OSHAWA 34 28 30 3 31
80 02HC013 HIGHLAND CREEK NEAR
WEST HILL 58 35 45 11 46
81 02ED017 HOG CREEK NEAR VICTORIA
HARBOUR 26 17 22 5 22
82 02EC009 HOLLAND RIVER AT
HOLLAND LANDING 49 41 48 7 48
83 02HC025 HUMBER RIVER AT ELDER
MILLS 52 35 45 10 45
84 02HC047 HUMBER RIVER NEAR
PALGRAVE 33 17 22 5 22
85 02GA045 HUNSBURGER CREEK NEAR
HAYSVILLE 16 1 1 0 1
86 02GA046 HUNSBURGER CREEK NEAR
SCHINDELSTEDDLE 16 1 1 0 1
87 02GA043 HUNSBURGER CREEK NEAR
WILMOT CENTRE 21 19 20 1 20
88 02KC014 INDIAN RIVER NEAR
PEMBROKE 17 8 16 8 16
89 02HJ001 JACKSON CREEK AT
PETERBOROUGH 52 38 48 11 49
90 02LA007 JOCK RIVER NEAR
RICHMOND 45 31 43 12 43
91 02CF012 JUNCTION CREEK BELOW
KELLEY LAKE 37 30 35 5 35
92 04JA002 KABINAKAGAMI RIVER AT
HIGHWAY NO. 11 38 19 36 17 36
93 04FA002 KAWINOGANS RIVER NEAR
PICKLE CROW 48 26 28 2 28
94 02GB009 KENNY CREEK NEAR
BURFORD 31 18 28 10 28
95 02GC029 KETTLE CREEK ABOVE ST.
THOMAS 29 26 28 2 28
96 02GC002 KETTLE CREEK AT ST.
THOMAS 69 44 47 3 47
97 04KA001 KWATABOAHEGAN RIVER
NEAR THE MOUTH 46 26 41 15 41
98 05PC016 LA VALLEE RIVER NEAR
DEVLIN 27 12 5 0 12
99 02DD013 LA VASE RIVER AT NORTH
BAY 40 38 38 0 38
100 05PD014 LAKE 114 OUTLET NEAR
KENORA 24 17 5 3 20
101 05QD017 LAKE 223 OUTLET NEAR
KENORA 21 14 6 2 16
83
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
102 05QD018 LAKE 224 OUTLET NEAR
KENORA 21 14 6 3 17
103 05QD019 LAKE 225 OUTLET NEAR
KENORA 18 15 3 0 15
104 05QD015 LAKE 226 OUTLET NEAR
KENORA 23 17 5 1 18
105 05QD008 LAKE 227 OUTLET NEAR
KENORA 27 18 7 3 21
106 05PD023 LAKE 239 OUTLET NEAR
KENORA 26 20 23 3 23
107 05PD024 LAKE 239, LOWER EAST
INLET, NEAR KENORA 21 12 6 2 14
108 05PD015 LAKE 240 OUTLET NEAR
KENORA 27 20 24 4 24
109 05PD019 LAKE 303 OUTLET NEAR
KENORA 26 21 7 1 22
110 05PD017 LAKE 470 OUTLET NEAR
KENORA 27 19 25 6 25
111 04JF001 LITTLE CURRENT RIVER AT
PERCY LAKE 46 31 32 1 32
112 02HC029 LITTLE DON RIVER AT DON
MILLS 33 25 31 6 31
113 02HC004 LITTLE DON RIVER NEAR
LANSING 21 2 18 16 18
114 02DD020 LITTLE FRENCH RIVER AT
OKIKENDAWT ISLAND 32 0 18 0 0
115 02BA003 LITTLE PIC RIVER NEAR
COLDWELL 42 34 39 5 39
116 02GH011 LITTLE RIVER AT WINDSOR 31 23 25 2 25
117 02HC028 LITTLE ROUGE CREEK NEAR
LOCUST HILL 51 38 48 11 49
118 05QE012 LONG-LEGGED RIVER BELOW
LONG-LEGGED LAKE 34 33 34 1 34
119 02FD002 LUCKNOW RIVER AT
LUCKNOW 35 25 25 0 25
120 02MB006 LYN CREEK NEAR LYN 44 23 34 11 34
121 02HC018 LYNDE CREEK NEAR WHITBY 54 33 47 14 47
122 02MA001 LYNDHURST CREEK AT
LYNDHURST 43 15 15 1 16
123 02ED015 MAD RIVER AT AVENING 26 19 23 4 23
124 02BD003 MAGPIE RIVER NEAR
MICHIPICOTEN 52 34 43 16 50
125 02FE011 MAITLAND RIVER NEAR
HARRISTON 33 24 25 1 25
126 02HG001 MARIPOSA BROOK NEAR
LITTLE BRITAIN 32 15 22 7 22
127 04LK001 MATTAWISHKWIA RIVER AT
HEARST 28 15 16 1 16
128 02GE007 MCGREGOR CREEK NEAR 37 27 29 2 29
84
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
CHATHAM
129 02AB019 MCVICAR CREEK AT
THUNDER BAY 29 21 23 2 23
130 02FE013 MIDDLE MAITLAND RIVER
ABOVE ETHEL 31 24 24 1 25
131 02FE008 MIDDLE MAITLAND RIVER
NEAR BELGRAVE 47 38 40 2 40
132 02GD004 MIDDLE THAMES RIVER AT
THAMESFORD 76 59 68 9 68
133 02HC033 MIMICO CREEK AT
ISLINGTON 48 45 47 2 47
134 04LJ001 MISSINAIBI RIVER AT
MATTICE 94 51 94 43 94
135 04LM001 MISSINAIBI RIVER BELOW
WABOOSE RIVER 42 28 39 11 39
136 02KF016 MISSISSIPPI RIVER BELOW
MARBLE LAKE 26 26 26 0 26
137 02HL005 MOIRA RIVER NEAR DELORO 49 43 47 5 48
138 02BE001
MONTREAL RIVER AT
ALGOMA CENTRAL AND
HUDSON BAY RAILWAY
21 0 7 0 0
139 02GA042 MOOREFIELD CREEK NEAR
ROTHSAY 25 5 4 0 5
140 02KC015 MUSKRAT RIVER NEAR
PEMBROKE 45 9 14 5 14
141 04GF001 MUSWABIK RIVER AT
OUTLET OF MUSWABIK LAKE 26 11 16 5 16
142 04JC002 NAGAGAMI RIVER AT
HIGHWAY NO. 11 64 41 61 20 61
143 05PA006 NAMAKAN RIVER AT OUTLET
OF LAC LA CROIX 93 51 91 40 91
144 02AB008 NEEBING RIVER NEAR
THUNDER BAY 60 40 55 16 56
145 02GA038 NITH RIVER ABOVE
NITHBURG 42 38 41 3 41
146 02GA018 NITH RIVER AT NEW
HAMBURG 63 53 59 7 60
147 02GA010 NITH RIVER NEAR CANNING 100 51 71 21 72
148 02BF005 NORBERG CREEK (SITE A)
ABOVE BATCHAWANA RIVER 34 30 31 1 31
149 02BF006 NORBERG CREEK (SITE B) AT
OUTLET OF TURKEY LAKE 35 31 32 1 32
150 02BF007
NORBERG CREEK (SITE C) AT
OUTLET OF LITTLE TURKEY
LAKE
33 31 29 0 31
151 02BF008 NORBERG CREEK (SITE D)
BELOW WISHART LAKE 34 29 32 3 32
152 02BF009 NORBERG CREEK (SITE E)
BELOW BATCHAWANA LAKE 33 27 30 3 30
85
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
153 02BF012
NORBERG CREEK (SITE F) AT
OUTLET OF BATCHAWANA
LAKE
32 29 30 1 30
154 02LB017
NORTH BRANCH SOUTH
NATION RIVER NEAR
HECKSTON
37 11 20 9 20
155 02AB014 NORTH CURRENT RIVER
NEAR THUNDER BAY 42 24 31 7 31
156 04MF001 NORTH FRENCH RIVER NEAR
THE MOUTH 47 31 46 15 46
157 02EA010
NORTH MAGNETAWAN
RIVER ABOVE PICKEREL
LAKE
45 40 44 4 44
158 02EA005 NORTH MAGNETAWAN
RIVER NEAR BURKS FALLS 99 45 98 53 98
159 02ED024 NORTH RIVER AT THE FALLS 26 22 24 2 24
160 05PD022 NORTHWEST TRIBUTARY TO
LAKE 239 NEAR KENORA 26 18 6 2 20
161 02ED026 NOTTAWASAGA RIVER AT
HOCKLEY 25 19 22 3 22
162 02ED101 NOTTAWASAGA RIVER NEAR
ALLISTON 47 20 25 5 25
163 02ED003 NOTTAWASAGA RIVER NEAR
BAXTER 67 38 61 23 61
164 02GF001 O.A.C. FARM GAUGE NO. 2
NEAR MERLIN 17 3 4 1 4
165 02GA032 O.A.C. FARM GAUGE NO. 5 AT
GUELPH 19 15 17 2 17
166 04GB004 OGOKI RIVER ABOVE
WHITECLAY LAKE 43 39 40 1 40
167 02HD008 OSHAWA CREEK AT OSHAWA 55 40 53 13 53
168 02HA024 OSWEGO CREEK AT
CANBORO 26 16 17 2 18
169 04FA001 OTOSKWIN RIVER BELOW
BADESDAWA LAKE 48 27 34 7 34
170 04JD005 PAGWACHUAN RIVER AT
HIGHWAY NO. 11 45 36 44 8 44
171 02FF008 PARKHILL CREEK ABOVE
PARKHILL RESERVOIR 41 35 39 4 39
172 02FF003 PARKHILL CREEK NEAR
PARKHILL 15 43 53 6 49
173 04GA003
PASHKOKOGAN RIVER AT
OUTLET OF PASHKOKOGAN
LAKE
46 6 7 1 7
174 02LB022 PAYNE RIVER NEAR
BERWICK 38 24 30 6 30
175 02EC018 PEFFERLAW BROOK NEAR
UDORA 27 16 25 9 25
176 02EC103 PEFFERLAW BROOK NEAR
UDORA 18 12 15 3 15
86
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
177 02KA004 PERCH LAKE INLET NO. 1
NEAR CHALK RIVER 22 20 20 0 20
178 02KA005 PERCH LAKE INLET NO. 2
NEAR CHALK RIVER 22 19 19 0 19
179 02KA006 PERCH LAKE INLET NO. 3
NEAR CHALK RIVER 21 18 20 2 20
180 02KA007 PERCH LAKE INLET NO. 4
NEAR CHALK RIVER 21 18 20 2 20
181 02KA008 PERCH LAKE INLET NO. 5
NEAR CHALK RIVER 16 15 16 1 16
182 02KA003 PERCH LAKE OUTLET NEAR
CHALK RIVER 30 28 27 0 28
183 02BB003 PIC RIVER NEAR MARATHON 44 34 43 9 43
184 02AA001 PIGEON RIVER AT MIDDLE
FALLS 79 47 75 28 75
185 05OD032 PINE CREEK NEAR PINE
CREEK 26 20 25 5 25
186 02FD001 PINE RIVER AT LURGAN 40 25 31 6 31
187 02ED014 PINE RIVER NEAR EVERETT 47 32 41 9 41
188 04FA003 PINEIMUTA RIVER AT EYES
LAKE 48 32 42 10 42
189 05PC011 PINEWOOD RIVER NEAR
PINEWOOD 47 31 6 1 32
190 05PB015 PIPESTONE RIVER ABOVE
RAINY LAKE 36 12 15 3 15
191 04DA001 PIPESTONE RIVER AT KARL
LAKE 48 39 42 3 42
192 04MD004 PORCUPINE RIVER AT HOYLE 37 19 24 5 24
193 02BC005 PUKASKWA RIVER AT
PUKASKWA NATIONAL PARK 17 6 8 2 8
194 05PC018 RAINY RIVER AT MANITOU
RAPIDS 83 65 82 17 82
195 02MC027 RAISIN RIVER AT BLACK
RIVER 28 10 8 0 10
196 02MC001 RAISIN RIVER NEAR
WILLIAMSTOWN 54 32 49 17 49
197 02HK008 RAWDON CREEK NEAR WEST
HUNTINGDON 32 22 27 5 27
198 02HA023 REDHILL CREEK AT ALBION
FALLS 15 14 15 1 15
199 02HA014 REDHILL CREEK AT
HAMILTON 37 27 29 2 29
200 02MC026 RIVIERE BEAUDETTE NEAR
GLEN NEVIS 31 21 26 5 26
201 02MC028 RIVIERE DELISLE NEAR
ALEXANDRIA 29 16 21 5 21
202 02FC004 ROCKY SAUGEEN RIVER
NEAR TRAVERSTON 26 0 25 0 0
203 02CA002 ROOT RIVER AT SAULT STE. 43 41 43 0 41
87
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
MARIE
204 05OD030 ROSEAU RIVER NEAR
CARIBOU 81 45 78 34 79
205 04CA003 ROSEBERRY RIVER ABOVE
ROSEBERRY LAKES 47 30 35 5 35
206 02GH002 RUSCOM RIVER NEAR
RUSCOM STATION 43 37 39 3 40
207 04CD002 SACHIGO RIVER BELOW
OUTLET OF SACHIGO LAKE 23 18 20 2 20
208 02FA004 SAUBLE RIVER AT
ALLENFORD 27 16 19 3 19
209 02FC016 SAUGEEN RIVER ABOVE
DURHAM 38 24 28 5 29
210 02GA037 SCHNEIDER CREEK AT
KITCHENER 22 20 20 0 20
211 02EC010 SCHOMBERG RIVER NEAR
SCHOMBERG 48 33 41 9 42
212 04CC001 SEVERN RIVER AT
LIMESTONE RAPIDS 25 5 22 17 22
213 04CA004 SEVERN RIVER AT OUTLET
OF DEER LAKE 47 14 20 6 20
214 04CA002 SEVERN RIVER AT OUTLET
OF MUSKRAT DAM LAKE 49 27 34 7 34
215 04DC002
SHAMATTAWA RIVER AT
OUTLET OF SHAMATTAWA
LAKE
48 28 38 10 38
216 04JC003 SHEKAK RIVER AT HIGHWAY
NO. 11 38 22 37 15 37
217 02GA044 SILVER SPRING CREEK NEAR
WILMOT CENTRE 16 1 1 0 1
218 02HL004 SKOOTAMATTA RIVER NEAR
ACTINOLITE 59 48 56 8 56
219 02HD007 SOPER CREEK AT
BOWMANVILLE 29 13 24 11 24
220 02LB031
SOUTH BRANCH SOUTH
NATION RIVER NEAR
WINCHESTER SPRINGS
16 3 3 0 3
221 02LB020 SOUTH CASTOR RIVER AT
KENMORE 36 18 26 9 27
222 02FE009 SOUTH MAITLAND RIVER AT
SUMMERHILL 47 42 45 3 45
223 02LB007 SOUTH NATION RIVER AT
SPENCERVILLE 66 44 61 17 61
224 02FF004 SOUTH PARKHILL CREEK
NEAR PARKHILL 59 43 47 4 47
225 02MC030 SOUTH RAISIN RIVER NEAR
CORNWALL 28 9 7 1 10
226 02HB023 SPENCER CREEK AT
HIGHWAY NO. 5 27 25 26 1 26
227 05OD031 SPRAGUE CREEK NEAR 54 49 51 2 51
88
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
SPRAGUE
228 02BA002 STEEL RIVER NEAR TERRACE
BAY 25 22 24 2 24
229 02FA002 STOKES RIVER NEAR
FERNDALE 38 22 37 15 37
230 02HA022 STONEY CREEK AT STONEY
CREEK 25 16 17 1 17
231 02GH001 STURGEON CREEK NEAR
LEAMINGTON 22 15 18 4 19
232 05QA004 STURGEON RIVER AT
MCDOUGALL MILLS 53 44 51 7 51
233 05QE009 STURGEON RIVER AT
OUTLET OF SALVESEN LAKE 54 47 52 5 52
234 02DC012 STURGEON RIVER AT UPPER
GOOSE FALLS 28 28 28 0 28
235 05PC010 STURGEON RIVER NEAR
BARWICK 35 4 0 0 4
236 02GG003 SYDENHAM RIVER AT
FLORENCE 30 28 29 1 29
237 02GG005 SYDENHAM RIVER AT
STRATHROY 48 36 36 1 37
238 02GG002 SYDENHAM RIVER NEAR
ALVINSTON 67 43 65 22 65
239 02GG007 SYDENHAM RIVER NEAR
DRESDEN 18 15 18 3 18
240 02FB007 SYDENHAM RIVER NEAR
OWEN SOUND 99 42 77 35 77
241 02GD021 THAMES RIVER AT INNERKIP 36 32 35 3 35
242 02GD006 THAMES RIVER NEAR
INGERSOLL 20 2 10 8 10
243 02BF013 TRIBUTARY TO NORBERG
CREEK AT TURKEY LAKE 25 8 22 14 22
244 02GD019 TROUT CREEK NEAR
FAIRVIEW 48 39 40 1 40
245 02GD009 TROUT CREEK NEAR ST.
MARYS 69 38 50 13 51
246 05QC003 TROUTLAKE RIVER ABOVE
BIG FALLS 43 42 43 1 43
247 02GH004 TURKEY CREEK AT WINDSOR 30 29 29 0 29
248 05PB014 TURTLE RIVER NEAR MINE
CENTRE 100 47 95 48 95
249 02HA020 TWENTY MILE CREEK ABOVE
SMITHVILLE 27 22 26 4 26
250 02HA006 TWENTY MILE CREEK AT
BALLS FALLS 57 43 57 14 57
251 02GC021 VENISON CREEK NEAR
WALSINGHAM 48 35 35 0 35
252 02CF011 VERMILION RIVER NEAR VAL
CARON 44 23 30 7 30
89
S. No. HYDAT
Station ID Station Name
No. of years
Years of
operation
Annual
maximum
Instantaneous
(AMI)
Annual
Maximum
average
daily
(AMAD)
No of
predicted
AMI
values
Total
AMI
years
253 02DD012 VEUVE RIVER NEAR VERNER 41 23 26 3 26
254 02GD020 WAUBUNO CREEK NEAR
DORCHESTER 36 30 33 3 33
255 02HM009
WEST BRANCH LITTLE
CATARAQUI CREEK AT
KINGSTON
25 18 14 0 18
256 02LB018
WEST BRANCH SCOTCH
RIVER NEAR ST. ISIDORE DE
PRESCOTT
35 10 15 8 18
257 02HC038 WEST DUFFINS CREEK
ABOVE GREEN RIVER 40 17 20 4 21
258 02HC031 WEST HUMBER RIVER AT
HIGHWAY NO. 7 49 36 43 7 43
259 02AB017 WHITEFISH RIVER AT
NOLALU 34 30 33 3 33
260 02BA005 WHITESAND RIVER ABOVE
SCHREIBER AT MINOVA MINE 24 22 22 0 22
261 02CF007 WHITSON RIVER AT
CHELMSFORD 54 45 52 7 52
262 02CF008 WHITSON RIVER AT VAL
CARON 54 35 38 3 38
263 02ED009 WILLOW CREEK ABOVE
LITTLE LAKE 23 21 22 1 22
264 02ED010 WILLOW CREEK AT
MIDHURST 26 26 26 0 26
265 02HD009 WILMOT CREEK NEAR
NEWCASTLE 49 37 43 6 43
266 02HM004 WILTON CREEK NEAR
NAPANEE 49 32 46 15 47
267 04CB001 WINDIGO RIVER ABOVE
MUSKRAT DAM LAKE 47 30 33 3 33
268 04DC001
WINISK RIVER BELOW
ASHEWEIG RIVER
TRIBUTARY
48 18 40 22 40
269 02AC001 WOLF RIVER AT HIGHWAY
NO. 17 43 38 39 1 39
270 02GD013 WYE CREEK NEAR
THORNDALE 39 16 19 4 20
271 02KD002 YORK RIVER NEAR
BANCROFT 99 34 85 51 85
90
Appendix C: Estimation of AMI flow data from AMAD flows
Illustration of the Sangal (1981)’s procedure for a representative station: 02BF002
02BF002
Year
Annual maximum
Instantaneous
(AMI)
Annual Maximum
Average daily
(AMAD) AMI/AMAD Base
factor, K
Date Flow
(m3/s)
Date Flow
(m3/s)
1968
269.95 04--15 238
1969 06--27 337.00 06--27 211 1.60 1.11
1970 06--01 187.00 06--01 182 1.03 1.86
1971 04--21 132.00 04--21 129 1.02 1.69
1972 05--03 180.00 05--03 176 1.02 1.54
1973 04--21 173.00 04--22 153 1.13 1.12
1974 04--30 169.00 04--29 161 1.05 0.97
1975 05--01 235.00 05--01 208 1.13 1.39
1976
254.35 04--19 235
1977
242.18 04--19 224
1978 05--13 114.00 05--13 109 1.05 1.59
1979 04--26 370.00 04--26 353 1.05 1.67
1980 04--10 120.00 04--10 106 1.13 0.90
1981 04--05 222.00 04--05 200 1.11 1.25
1982 05--02 194.00 05--02 182 1.07 0.98
1983 05--03 117.00 05--03 113 1.04 1.52
1984 04--16 135.00 04--16 130 1.04 1.56
1985 04--25 342.00 04--25 321 1.07 1.19
1986 04--20 121.00 04--20 117 1.03 1.41
1987 04--12 52.30 04--12 51.1 1.02 1.45
1988 04--07 203.00 04--07 194 1.05 1.44
1989 04--28 154.00 04--28 146 1.05 1.18
1990 04--26 173.00 04--26 163 1.06 1.09
1991 04--08 139.00 04--08 134 1.04 1.75
1992 04--22 188.00 04--22 179 1.05 1.67
1993 05--04 157.00 05--05 142 1.11 0.78
1994 04--27 214.00 04--27 196 1.09 1.45
1995 10--21 99.40 10--21 86.7 1.15 1.39
1996 05--19 172.00 05--20 165 1.04 1.10
1997 04--29 142.00 04--29 136 1.04 0.40
1998 04--01 171.00 04--01 159 1.08 0.70
91
02BF002
Year
Annual maximum
Instantaneous
(AMI)
Annual Maximum
Average daily
(AMAD) AMI/AMAD Base
factor, K
Date Flow
(m3/s)
Date Flow
(m3/s)
1999 04--08 169.00 04--08 162 1.04 1.39
2000 03--27 74.40 03--27 73.6 1.01 1.53
2001 10--14 199.00 10--15 157 1.27 0.59
2002 04--18 278.00 04--18 256 1.09 0.93
2003 04--21 186.00 04--21 179 1.04 1.69
2004 04--19 172.00 04--19 163 1.06 1.64
2005 04--11 88.00 04--11 85.9 1.02 1.28
2006 04--14 111.00 04--14 108 1.03 0.67
2007 10--06 75.60 10--20 63.2 1.20 1.20
2008 04--22 244.00 04--23 236 1.03 1.20
2009 04--25 128.00 04--25 123 1.04 1.57
2010 09--24 216.00 09--24 148 1.46 1.05
2011 04--28 115.00 04--28 109 1.06 1.58
2012 03--20 164.00 03--20 158 1.04 1.11
2013 11--18 271.00 05--03 248 1.09 0.67
r= 1.6 K= 1.26
Predicted Value
92
Appendix D: Summary of results of Non Parametric Analysis
Note:
= Test accepted at 5% significance = Test rejected at 5% significance
Station
Number
Station
ID Stationarity Homogeneity Randomness Independence
1 02HB021
2 04DB001
3 05PB018
4 04FB001
5 04FC001
6 02CB003
7 05PA012
8 02BF001
9 02FF007
10 02LB008
11 02GG004
12 02GG009
13 02GG006
14 02FC017
15 02EC011
16 05RC001
17 02BF004
18 02GC011
19 02GC010
20 02BB002
21 02EC002
22 02AD010
23 02JC008
24 02HE001
25 02CG003
26 02FE014
27 02HF004
28 02HD006
29 02FE010
30 02ED102
31 04GB005
32 02HB022
33 02KF017
34 02MB010
93
Station
Number
Station
ID Stationarity Homogeneity Randomness Independence
35 02GA036
36 02GH003
37 02KF011
38 02FC011
39 02LB006
40 04GA002
41 02GC030
42 02GC018
43 05QE008
44 02DD014
45 02HK007
46 02HC023
47 02ED007
48 02HM005
49 02DD015
50 02GA017
51 02DB007
52 02DB004
53 02AB021
54 02GE005
55 02GC031
56 02DD008
57 02HC019
58 02HC049
59 02LB012
60 02GA035
61 02HC032
62 02HC009
63 02HB004
64 04EA001
65 05QA002
66 05QA001
67 02HC030
68 02HC002
69 02GB007
70 04CE002
71 02GD010
72 02HD012
73 02HD002
74 02BF002
94
Station
Number
Station
ID Stationarity Homogeneity Randomness Independence
75 02KF015
76 02GA041
77 02HB012
78 04KA002
79 02HD013
80 02HC013
81 02ED017
82 02EC009
83 02HC025
84 02HC047
85 02GA045
86 02GA046
87 02GA043
88 02KC014
89 02HJ001
90 02LA007
91 02CF012
92 04JA002
93 04FA002
94 02GB009
95 02GC029
96 02GC002
97 04KA001
98 05PC016
99 02DD013
100 05PD014
101 05QD017
102 05QD018
103 05QD019
104 05QD015
105 05QD008
106 05PD023
107 05PD024
108 05PD015
109 05PD019
110 05PD017
111 04JF001
112 02HC029
113 02HC004
114 02DD020
95
Station
Number
Station
ID Stationarity Homogeneity Randomness Independence
115 02BA003
116 02GH011
117 02HC028
118 05QE012
119 02FD002
120 02MB006
121 02HC018
122 02MA001
123 02ED015
124 02BD003
125 02FE011
126 02HG001
127 04LK001
128 02GE007
129 02AB019
130 02FE013
131 02FE008
132 02GD004
133 02HC033
134 04LJ001
135 04LM001
136 02KF016
137 02HL005
138 02BE001
139 02GA042
140 02KC015
141 04GF001
142 04JC002
143 05PA006
144 02AB008
145 02GA038
146 02GA018
147 02GA010
148 02BF005
149 02BF006
150 02BF007
151 02BF008
152 02BF009
153 02BF012
154 02LB017
96
Station
Number
Station
ID Stationarity Homogeneity Randomness Independence
155 02AB014
156 04MF001
157 02EA010
158 02EA005
159 02ED024
160 05PD022
161 02ED026
162 02ED101
163 02ED003
164 02GF001
165 02GA032
166 04GB004
167 02HD008
168 02HA024
169 04FA001
170 04JD005
171 02FF008
172 02FF003
173 04GA003
174 02LB022
175 02EC018
176 02EC103
177 02KA004
178 02KA005
179 02KA006
180 02KA007
181 02KA008
182 02KA003
183 02BB003
184 02AA001
185 05OD032
186 02FD001
187 02ED014
188 04FA003
189 05PC011
190 05PB015
191 04DA001
192 04MD004
193 02BC005
194 05PC018
97
Station
Number
Station
ID Stationarity Homogeneity Randomness Independence
195 02MC027
196 02MC001
197 02HK008
198 02HA023
199 02HA014
200 02MC026
201 02MC028
202 02FC004
203 02CA002
204 05OD030
205 04CA003
206 02GH002
207 04CD002
208 02FA004
209 02FC016
210 02GA037
211 02EC010
212 04CC001
213 04CA004
214 04CA002
215 04DC002
216 04JC003
217 02GA044
218 02HL004
219 02HD007
220 02LB031
221 02LB020
222 02FE009
223 02LB007
224 02FF004
225 02MC030
226 02HB023
227 05OD031
228 02BA002
229 02FA002
230 02HA022
231 02GH001
232 05QA004
233 05QE009
234 02DC012
98
Station
Number
Station
ID Stationarity Homogeneity Randomness Independence
235 05PC010
236 02GG003
237 02GG005
238 02GG002
239 02GG007
240 02FB007
241 02GD021
242 02GD006
243 02BF013
244 02GD019
245 02GD009
246 05QC003
247 02GH004
248 05PB014
249 02HA020
250 02HA006
251 02GC021
252 02CF011
253 02DD012
254 02GD020
255 02HM009
256 02LB018
257 02HC038
258 02HC031
259 02AB017
260 02BA005
261 02CF007
262 02CF008
263 02ED009
264 02ED010
265 02HD009
266 02HM004
267 04CB001
268 04DC001
269 02AC001
270 02GD013
271 02KD002
99
Appendix E: Illustration of Station Frequency Analysis
Calculation of AIC:
Representative station: 02FE009 (station no 222 from the summary list in Appendix B)
Station
Name222
Min AIC 462.508 Normal Lognormal Gumbel / EV1Gamma3 /
Pearson III3PLN LP3 GEV
Distribut
ion
Gumbel /
EV1
Normal(43.636;
105.22)
Lognormal(0.40929
; 4.5746)
GumbelMax(34.023;
85.584)
Gamma(5.0275;
18.943; 9.9885)
Lognormal(0.33243;
4.7769; -20.294)
LogPearson3(61.4
; -0.05282; 7.818)
GenExtreme(0.09754;
30.778; 84.191)
Q2 98.054 parameter 1 43.636 0.40929 34.023 5.0275 0.33243 61.4 0.09754
Q10 162.148 parameter 2 105.22 4.5746 85.584 18.943 4.7769 -0.05282 30.778
Q25 194.408 parameter 3 9.9885 -20.294 7.818 84.191
Q50 218.340 k 2 2 2 3 3 3 3
Q100 242.095 AIC 470.82 463.31 462.51 465.42 465.09 465.28 466.28
SIG(LL) -233.267 -229.511 -229.111 -229.416 -229.254 -229.349 -229.849
Data
Count45
loglik
(normal)loglik (lognormal) loglik (gumbel)
loglik
(gamma3)loglik (3PLN) loglik (LP3) loglik (GEV)
1968 202.0 -7.154 -6.940 -6.981 -6.969 -7.001 -6.946 -7.035
1969 93.7 -4.730 -4.569 -4.553 -4.595 -4.561 -4.592 -4.498
1970 99.1 -4.705 -4.623 -4.596 -4.629 -4.600 -4.629 -4.569
1971 62.9 -5.165 -4.727 -4.808 -4.817 -4.811 -4.809 -4.687
1972 81.3 -4.845 -4.517 -4.535 -4.587 -4.549 -4.577 -4.422
1973 71.4 -4.995 -4.574 -4.627 -4.666 -4.638 -4.655 -4.490
1974 87.5 -4.777 -4.529 -4.529 -4.578 -4.540 -4.572 -4.443
1975 179.0 -6.124 -6.334 -6.337 -6.269 -6.326 -6.272 -6.451
1976 128.0 -4.831 -5.107 -5.061 -5.023 -5.040 -5.039 -5.153
1977 158.3 -5.435 -5.807 -5.783 -5.703 -5.757 -5.719 -5.916
1978 98.8 -4.706 -4.620 -4.594 -4.627 -4.598 -4.627 -4.565
1979 89.5 -4.760 -4.539 -4.533 -4.581 -4.544 -4.576 -4.457
1980 90.9 -4.749 -4.548 -4.539 -4.585 -4.548 -4.580 -4.470
1981 181.0 -6.203 -6.386 -6.392 -6.327 -6.383 -6.329 -6.502
1982 152.0 -5.269 -5.652 -5.621 -5.544 -5.594 -5.562 -5.753
1983 41.1 -5.774 -5.942 -5.916 -5.805 -5.903 -5.824 -6.280
1984 97.7 -4.710 -4.608 -4.584 -4.619 -4.588 -4.618 -4.549
1985 115.0 -4.720 -4.857 -4.813 -4.807 -4.802 -4.817 -4.860
1986 105.0 -4.695 -4.698 -4.663 -4.682 -4.661 -4.686 -4.665
1987 72.0 -4.985 -4.567 -4.618 -4.658 -4.630 -4.647 -4.481
1988 75.5 -4.927 -4.537 -4.576 -4.622 -4.588 -4.611 -4.444
1989 35.0 -5.990 -6.682 -6.463 -6.362 -6.473 -6.385 -7.203
1990 85.1 -4.801 -4.520 -4.527 -4.578 -4.540 -4.570 -4.430
1991 80.9 -4.850 -4.517 -4.537 -4.588 -4.550 -4.579 -4.422
1992 93.7 -4.730 -4.569 -4.553 -4.595 -4.561 -4.592 -4.498
1993 93.7 -4.730 -4.569 -4.553 -4.595 -4.561 -4.592 -4.498
1994 70.7 -5.008 -4.583 -4.639 -4.676 -4.649 -4.665 -4.501
1995 81.1 -4.848 -4.517 -4.536 -4.587 -4.549 -4.578 -4.422
1996 137.0 -4.960 -5.302 -5.259 -5.202 -5.234 -5.220 -5.373
1997 228.0 -8.653 -7.636 -7.728 -7.830 -7.795 -7.761 -7.674
1999 70.1 -5.019 -4.590 -4.648 -4.683 -4.658 -4.673 -4.510
2000 103.0 -4.696 -4.671 -4.638 -4.662 -4.639 -4.665 -4.631
2001 102.4 -4.697 -4.664 -4.632 -4.657 -4.633 -4.659 -4.621
2002 79.9 -4.863 -4.519 -4.542 -4.593 -4.555 -4.583 -4.423
2003 85.4 -4.798 -4.521 -4.527 -4.578 -4.539 -4.570 -4.431
2004 140.0 -5.012 -5.369 -5.328 -5.267 -5.302 -5.285 -5.448
2005 114.0 -4.715 -4.840 -4.796 -4.793 -4.786 -4.802 -4.839
2006 86.6 -4.786 -4.525 -4.527 -4.578 -4.539 -4.571 -4.437
2007 75.8 -4.922 -4.535 -4.573 -4.619 -4.585 -4.609 -4.442
2008 197.0 -6.907 -6.808 -6.840 -6.811 -6.851 -6.795 -6.910
2009 164.0 -5.602 -5.949 -5.932 -5.851 -5.909 -5.865 -6.063
2010 71.4 -4.995 -4.574 -4.627 -4.666 -4.638 -4.655 -4.490
2011 115.0 -4.720 -4.857 -4.813 -4.807 -4.802 -4.817 -4.860
2012 34.5 -6.008 -6.756 -6.514 -6.417 -6.527 -6.439 -7.292
2013 109.0 -4.699 -4.758 -4.718 -4.727 -4.713 -4.733 -4.739
Parameters
3
1
2
3
4 3
2
100
Illustration of the sections (marked in red above):
Section 1: Illustrates the data for the station.
Section 2: Presents the log likelihood calculation for the station data. The top row presents the summation of the log likelihood for each of
the distributions.
Section 3: Provides the parameters of each of the distribution as obtained from easy fit and the AIC value.
Section 4: Provides the summary of the best fit distribution and the associated quantiles.
Normal Lognormal Gumbel / EV1Gamma3 /
Pearson III3PLN LP3 GEV
Normal(43.636;
105.22)
Lognormal(0.40929
; 4.5746)
GumbelMax(34.023;
85.584)
Gamma(5.0275;
18.943; 9.9885)
Lognormal(0.33243;
4.7769; -20.294)
LogPearson3(61.4
; -0.05282; 7.818)
GenExtreme(0.09754;
30.778; 84.191)
parameter 1 43.636 0.40929 34.023 5.0275 0.33243 61.4 0.09754
parameter 2 105.22 4.5746 85.584 18.943 4.7769 -0.05282 30.778
parameter 3 9.9885 -20.294 7.818 84.191
k 2 2 2 3 3 3 3
AIC 470.82 463.31 462.51 465.42 465.09 465.28 466.28
SIG(LL) -233.267 -229.511 -229.111 -229.416 -229.254 -229.349 -229.849
Parameters
101
AIC values for all candidate distributions:
Below is the summary of the AIC value of all the candidate distributions and the difference of the candidate distribution with the model
with lowest AIC.
Calculation of AIC weights and the station flood quantiles:
Min AIC 462.51 463.31 465.09 465.28 465.42 466.28 470.82
Delta AIC 0.00 0.80 2.59 2.78 2.91 3.78 8.31
Distribution Gumbel / EV1 Lognormal 3PLN LP3 Gamma3 / Pearson III GEV Normal
STATI
ON #AIC
Delta
AIC
exp(-
deltaA
IC/2)
Q2 Q10 Q25 Q50 Q100 AICDelta
AIC
exp(-
deltaA
IC/2)
Q2 Q10 Q25 Q50 Q100 AICDelta
AIC
exp(-
deltaA
IC/2)
Q2 Q10 Q25 Q50 Q100 W1 W2 W3 Q2 Q10 Q25 Q50 Q100
222 462.51 0 1 98.05 162.15 194.41 218.34 242.09 463.31 0.8 0.67 96.99 163.88 198.57 224.79 251.33 465.09 2.59 0.27 98.44 161.51 192.19 214.72 237.01 0.51 0.34 0.14 97.74 162.65 195.53 220.05 244.56
Gumbel / EV1 Lognormal 3PLN AIC weights Station flood quantiles
102
Appendix F: Stepwise regression output from SPSS
Regression Results
(Note:
1. Only the final output is shown in the part.
2. SI1 in the regression output denotes the transformation of lake attenuation index
3. The output below is the results after the log transformation was applied on the variables.)
Region = Boreal Shield
Descriptive Statisticsa
Mean Std. Deviation N
logQ100 1.7734 .77999 43
logAreaKm 2.3566 .99527 43
logMAP 2.9348 .05119 43
logSI1 .0575 .02563 43
logShapFactr 1.1180 .25951 43
logChSlpDmls -2.5392 .57989 43
a. Region = Boreal Shield
Correlationsa
logQ100 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ100 1.000 .938 .140 -.069 .724 -.815
logAreaKm .938 1.000 -.069 .134 .710 -.941
logMAP .140 -.069 1.000 -.309 .200 .224
logSI1 -.069 .134 -.309 1.000 -.053 -.311
logShapFactr .724 .710 .200 -.053 1.000 -.683
logChSlpDmls -.815 -.941 .224 -.311 -.683 1.000
Sig. (1-
tailed)
logQ100 . .000 .185 .330 .000 .000
logAreaKm .000 . .330 .195 .000 .000
logMAP .185 .330 . .022 .100 .074
logSI1 .330 .195 .022 . .369 .021
logShapFactr .000 .000 .100 .369 . .000
logChSlpDmls .000 .000 .074 .021 .000 .
N logQ100 43 43 43 43 43 43
logAreaKm 43 43 43 43 43 43
logMAP 43 43 43 43 43 43
logSI1 43 43 43 43 43 43
logShapFactr 43 43 43 43 43 43
logChSlpDmls 43 43 43 43 43 43
103
a. Region = Boreal Shield
Variables Entered/Removeda,b
Model Variables Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
2 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
3 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
a. Region = Boreal Shield
b. Dependent Variable: logQ100
Model Summarya,e
Model R R Square Adjusted R Square
Std. Error of the
Estimate Durbin-Watson
1 .938b .879 .876 .27430
2 .960c .922 .918 .22380
3 .970d .941 .937 .19587 2.287
a. Region = Boreal Shield
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logMAP
d. Predictors: (Constant), logAreaKm, logMAP, logSI1
e. Dependent Variable: logQ100
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 22.467 1 22.467 298.612 .000c
Residual 3.085 41 .075
Total 25.552 42
2 Regression 23.548 2 11.774 235.070 .000d
Residual 2.004 40 .050
Total 25.552 42
3 Regression 24.056 3 8.019 209.004 .000e
Residual 1.496 39 .038
Total 25.552 42
a. Region = Boreal Shield
b. Dependent Variable: logQ100
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logMAP
e. Predictors: (Constant), logAreaKm, logMAP, logSI1
Coefficientsa,b
104
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) .042 .109 .383 .704
logAreaKm .735 .043 .938 17.280 .000 .938 .938 .938 1.000 1.000
2 (Constant) -9.206 1.992 -4.621 .000
logAreaKm .746 .035 .952 21.450 .000 .938 .959 .950 .995 1.005
logMAP 3.142 .676 .206 4.646 .000 .140 .592 .206 .995 1.005
3 (Constant) -6.967 1.849 -3.767 .001
logAreaKm .759 .031 .969 24.767 .000 .938 .970 .960 .981 1.019
logMAP 2.457 .621 .161 3.956 .000 .140 .535 .153 .904 1.107
logSI1 -4.541 1.249 -.149 -3.636 .001 -.069 -.503 -.141 .892 1.121
a. Region = Boreal Shield
b. Dependent Variable: logQ100
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .206c 4.646 .000 .592 .995 1.005 .995
logSI1 -.198c -4.341 .000 -.566 .982 1.018 .982
logShapFactr .118c 1.551 .129 .238 .495 2.019 .495
logChSlpDmls .593c 4.473 .000 .577 .114 8.741 .114
2 logSI1 -.149d -3.636 .001 -.503 .892 1.121 .892
logShapFactr .016d .234 .816 .037 .433 2.310 .433
logChSlpDmls .394d 2.891 .006 .420 .089 11.229 .089
3 logShapFactr -.009e -.156 .877 -.025 .427 2.342 .427
logChSlpDmls .215e 1.469 .150 .232 .068 14.727 .068
a. Region = Boreal Shield
b. Dependent Variable: logQ100
c. Predictors in the Model: (Constant), logAreaKm
d. Predictors in the Model: (Constant), logAreaKm, logMAP
e. Predictors in the Model: (Constant), logAreaKm, logMAP, logSI1
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logMAP logSI1
1 1 1.923 1.000 .04 .04
2 .077 4.992 .96 .96
2 1 2.897 1.000 .00 .02 .00
2 .103 5.310 .00 .98 .00
105
3 .000 140.226 1.00 .01 1.00
3 1 3.770 1.000 .00 .01 .00 .01
2 .135 5.275 .00 .42 .00 .64
3 .094 6.334 .00 .57 .00 .25
4 .000 168.762 1.00 .00 1.00 .10
a. Region = Boreal Shield
b. Dependent Variable: logQ100
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value -.1068 2.8216 1.7734 .75681 43
Residual -.46754 .43090 .00000 .18875 43
Std. Predicted Value -2.484 1.385 .000 1.000 43
Std. Residual -2.387 2.200 .000 .964 43
a. Region = Boreal Shield
b. Dependent Variable: logQ100
Charts
106
Region = Mixed WoodPlains
Descriptive Statisticsa
Mean Std. Deviation N
logQ100 1.9853 .38037 75
logAreaKm 2.2409 .34956 75
logMAP 2.9826 .04197 75
logSI1 .0390 .03444 75
logShapFactr 1.1352 .20216 75
logChSlpDmls -2.6722 .32149 75
a. Region = Mixed WoodPlains
Correlationsa
logQ100 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ100 1.000 .770 .137 -.560 .194 -.407
logAreaKm .770 1.000 .025 -.268 .340 -.532
logMAP .137 .025 1.000 .041 -.111 -.380
logSI1 -.560 -.268 .041 1.000 -.042 -.008
logShapFactr .194 .340 -.111 -.042 1.000 -.388
logChSlpDmls -.407 -.532 -.380 -.008 -.388 1.000
Sig. (1-tailed) logQ100 . .000 .120 .000 .048 .000
logAreaKm .000 . .414 .010 .001 .000
logMAP .120 .414 . .363 .172 .000
107
logSI1 .000 .010 .363 . .360 .472
logShapFactr .048 .001 .172 .360 . .000
logChSlpDmls .000 .000 .000 .472 .000 .
N logQ100 75 75 75 75 75 75
logAreaKm 75 75 75 75 75 75
logMAP 75 75 75 75 75 75
logSI1 75 75 75 75 75 75
logShapFactr 75 75 75 75 75 75
logChSlpDmls 75 75 75 75 75 75
a. Region = Mixed WoodPlains
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter <=
.050, Probability-of-F-to-remove >= .100).
2 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter <=
.050, Probability-of-F-to-remove >= .100).
3 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter <=
.050, Probability-of-F-to-remove >= .100).
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ100
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .770b .593 .587 .24432
2 .853c .728 .720 .20116
3 .864d .746 .736 .19554 1.625
a. Region = Mixed WoodPlains
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logSI1
d. Predictors: (Constant), logAreaKm, logSI1, logMAP
e. Dependent Variable: logQ100
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 6.349 1 6.349 106.359 .000c
Residual 4.357 73 .060
Total 10.706 74
2 Regression 7.793 2 3.896 96.292 .000d
Residual 2.913 72 .040
Total 10.706 74
108
3 Regression 7.991 3 2.664 69.667 .000e
Residual 2.715 71 .038
Total 10.706 74
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ100
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logSI1
e. Predictors: (Constant), logAreaKm, logSI1, logMAP
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) .108 .184 .584 .561
logAreaKm .838 .081 .770 10.313 .000 .770 .770 .770 1.000 1.000
2 (Constant) .520 .167 3.122 .003
logAreaKm .727 .069 .668 10.469 .000 .770 .777 .644 .928 1.077
logSI1 -4.210 .705 -.381 -5.974 .000 -.560 -.576 -.367 .928 1.077
3 (Constant) -3.151 1.619 -1.946 .056
logAreaKm .721 .068 .663 10.676 .000 .770 .785 .638 .927 1.079
logSI1 -4.287 .686 -.388 -6.251 .000 -.560 -.596 -.374 .926 1.080
logMAP 1.236 .542 .136 2.279 .026 .137 .261 .136 .997 1.003
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ100
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .118c 1.594 .115 .185 .999 1.001 .999
logSI1 -.381c -5.974 .000 -.576 .928 1.077 .928
logShapFactr -.077c -.968 .337 -.113 .885 1.130 .885
logChSlpDmls .004c .046 .964 .005 .717 1.395 .717
2 logMAP .136d 2.279 .026 .261 .997 1.003 .926
logShapFactr -.056d -.853 .397 -.101 .882 1.134 .820
logChSlpDmls -.079d -1.068 .289 -.126 .692 1.445 .643
3 logShapFactr -.038e -.585 .561 -.070 .867 1.153 .815
logChSlpDmls -.010e -.125 .901 -.015 .563 1.776 .563
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ100
c. Predictors in the Model: (Constant), logAreaKm
d. Predictors in the Model: (Constant), logAreaKm, logSI1
109
e. Predictors in the Model: (Constant), logAreaKm, logSI1, logMAP
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logSI1 logMAP
1 1 1.988 1.000 .01 .01
2 .012 12.985 .99 .99
2 1 2.643 1.000 .00 .00 .04
2 .346 2.762 .01 .01 .83
3 .010 15.984 .99 .99 .13
3 1 3.612 1.000 .00 .00 .02 .00
2 .373 3.110 .00 .01 .87 .00
3 .014 16.053 .00 .99 .11 .00
4 9.755E-5 192.433 1.00 .00 .00 1.00
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ100
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value 1.1997 2.6951 1.9853 .32862 75
Residual -.39632 .41307 .00000 .19154 75
Std. Predicted Value -2.391 2.160 .000 1.000 75
Std. Residual -2.027 2.112 .000 .980 75
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ100
Charts
110
Region = Boreal Shield
Descriptive Statisticsa
Mean Std. Deviation N
logQ50 1.7272 .78809 43
logAreaKm 2.3566 .99527 43
logMAP 2.9348 .05119 43
logSI1 .0575 .02563 43
logShapFactr 1.1180 .25951 43
logChSlpDmls -2.5392 .57989 43
a. Region = Boreal Shield
Correlationsa
logQ50 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ50 1.000 .939 .145 -.068 .727 -.816
logAreaKm .939 1.000 -.069 .134 .710 -.941
logMAP .145 -.069 1.000 -.309 .200 .224
logSI1 -.068 .134 -.309 1.000 -.053 -.311
logShapFactr .727 .710 .200 -.053 1.000 -.683
logChSlpDmls -.816 -.941 .224 -.311 -.683 1.000
Sig. (1-tailed) logQ50 . .000 .176 .332 .000 .000
logAreaKm .000 . .330 .195 .000 .000
logMAP .176 .330 . .022 .100 .074
111
logSI1 .332 .195 .022 . .369 .021
logShapFactr .000 .000 .100 .369 . .000
logChSlpDmls .000 .000 .074 .021 .000 .
N logQ50 43 43 43 43 43 43
logAreaKm 43 43 43 43 43 43
logMAP 43 43 43 43 43 43
logSI1 43 43 43 43 43 43
logShapFactr 43 43 43 43 43 43
logChSlpDmls 43 43 43 43 43 43
a. Region = Boreal Shield
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
2 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
3 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
a. Region = Boreal Shield
b. Dependent Variable: logQ50
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .939b .882 .880 .27345
2 .963c .927 .923 .21834
3 .973d .946 .942 .18977 2.273
a. Region = Boreal Shield
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logMAP
d. Predictors: (Constant), logAreaKm, logMAP, logSI1
e. Dependent Variable: logQ50
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 23.020 1 23.020 307.849 .000c
Residual 3.066 41 .075
Total 26.086 42
2 Regression 24.179 2 12.089 253.589 .000d
Residual 1.907 40 .048
Total 26.086 42
112
3 Regression 24.681 3 8.227 228.447 .000e
Residual 1.405 39 .036
Total 26.086 42
a. Region = Boreal Shield
b. Dependent Variable: logQ50
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logMAP
e. Predictors: (Constant), logAreaKm, logMAP, logSI1
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) -.026 .108 -.238 .813
logAreaKm .744 .042 .939 17.546 .000 .939 .939 .939 1.000 1.000
2 (Constant) -9.600 1.944 -4.939 .000
logAreaKm .755 .034 .954 22.263 .000 .939 .962 .952 .995 1.005
logMAP 3.253 .660 .211 4.930 .000 .145 .615 .211 .995 1.005
3 (Constant) -7.371 1.792 -4.114 .000
logAreaKm .769 .030 .971 25.877 .000 .939 .972 .961 .981 1.019
logMAP 2.572 .602 .167 4.273 .000 .145 .565 .159 .904 1.107
logSI1 -4.520 1.210 -.147 -3.735 .001 -.068 -.513 -.139 .892 1.121
a. Region = Boreal Shield
b. Dependent Variable: logQ50
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .211c 4.930 .000 .615 .995 1.005 .995
logSI1 -.198c -4.412 .000 -.572 .982 1.018 .982
logShapFactr .120c 1.608 .116 .246 .495 2.019 .495
logChSlpDmls .592c 4.545 .000 .584 .114 8.741 .114
2 logSI1 -.147d -3.735 .001 -.513 .892 1.121 .892
logShapFactr .016d .241 .811 .038 .433 2.310 .433
logChSlpDmls .383d 2.913 .006 .423 .089 11.229 .089
3 logShapFactr -.009e -.158 .876 -.026 .427 2.342 .427
logChSlpDmls .205e 1.459 .153 .230 .068 14.727 .068
a. Region = Boreal Shield
b. Dependent Variable: logQ50
c. Predictors in the Model: (Constant), logAreaKm
d. Predictors in the Model: (Constant), logAreaKm, logMAP
113
e. Predictors in the Model: (Constant), logAreaKm, logMAP, logSI1
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logMAP logSI1
1 1 1.923 1.000 .04 .04
2 .077 4.992 .96 .96
2 1 2.897 1.000 .00 .02 .00
2 .103 5.310 .00 .98 .00
3 .000 140.226 1.00 .01 1.00
3 1 3.770 1.000 .00 .01 .00 .01
2 .135 5.275 .00 .42 .00 .64
3 .094 6.334 .00 .57 .00 .25
4 .000 168.762 1.00 .00 1.00 .10
a. Region = Boreal Shield
b. Dependent Variable: logQ50
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value -.1801 2.7869 1.7272 .76658 43
Residual -.46136 .42615 .00000 .18287 43
Std. Predicted Value -2.488 1.382 .000 1.000 43
Std. Residual -2.431 2.246 .000 .964 43
a. Region = Boreal Shield
b. Dependent Variable: logQ50
Charts
114
Region = Mixed WoodPlains
Descriptive Statisticsa
Mean Std. Deviation N
logQ50 1.9393 .37473 75
logAreaKm 2.2409 .34956 75
logMAP 2.9826 .04197 75
logSI1 .0390 .03444 75
logShapFactr 1.1352 .20216 75
logChSlpDmls -2.6722 .32149 75
a. Region = Mixed WoodPlains
Correlationsa
logQ50 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ50 1.000 .782 .147 -.557 .195 -.422
logAreaKm .782 1.000 .025 -.268 .340 -.532
logMAP .147 .025 1.000 .041 -.111 -.380
logSI1 -.557 -.268 .041 1.000 -.042 -.008
logShapFactr .195 .340 -.111 -.042 1.000 -.388
logChSlpDmls -.422 -.532 -.380 -.008 -.388 1.000
Sig. (1-tailed) logQ50 . .000 .104 .000 .047 .000
115
logAreaKm .000 . .414 .010 .001 .000
logMAP .104 .414 . .363 .172 .000
logSI1 .000 .010 .363 . .360 .472
logShapFactr .047 .001 .172 .360 . .000
logChSlpDmls .000 .000 .000 .472 .000 .
N logQ50 75 75 75 75 75 75
logAreaKm 75 75 75 75 75 75
logMAP 75 75 75 75 75 75
logSI1 75 75 75 75 75 75
logShapFactr 75 75 75 75 75 75
logChSlpDmls 75 75 75 75 75 75
a. Region = Mixed WoodPlains
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
2 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
3 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ50
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .782b .611 .606 .23535
2 .861c .741 .734 .19319
3 .873d .763 .752 .18643 1.640
a. Region = Mixed WoodPlains
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logSI1
d. Predictors: (Constant), logAreaKm, logSI1, logMAP
e. Dependent Variable: logQ50
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 6.347 1 6.347 114.592 .000c
Residual 4.044 73 .055
Total 10.391 74
2 Regression 7.704 2 3.852 103.212 .000d
116
Residual 2.687 72 .037
Total 10.391 74
3 Regression 7.923 3 2.641 75.991 .000e
Residual 2.468 71 .035
Total 10.391 74
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ50
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logSI1
e. Predictors: (Constant), logAreaKm, logSI1, logMAP
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) .062 .177 .348 .729
logAreaKm .838 .078 .782 10.705 .000 .782 .782 .782 1.000 1.000
2 (Constant) .462 .160 2.885 .005
logAreaKm .730 .067 .681 10.951 .000 .782 .790 .656 .928 1.077
logSI1 -4.080 .677 -.375 -6.029 .000 -.557 -.579 -.361 .928 1.077
3 (Constant) -3.397 1.544 -2.201 .031
logAreaKm .724 .064 .675 11.245 .000 .782 .800 .650 .927 1.079
logSI1 -4.162 .654 -.382 -6.364 .000 -.557 -.603 -.368 .926 1.080
logMAP 1.299 .517 .146 2.513 .014 .147 .286 .145 .997 1.003
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ50
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .127c 1.767 .081 .204 .999 1.001 .999
logSI1 -.375c -6.029 .000 -.579 .928 1.077 .928
logShapFactr -.080c -1.026 .308 -.120 .885 1.130 .885
logChSlpDmls -.009c -.101 .920 -.012 .717 1.395 .717
2 logMAP .146d 2.513 .014 .286 .997 1.003 .926
logShapFactr -.059d -.924 .359 -.109 .882 1.134 .820
logChSlpDmls -.091d -1.265 .210 -.148 .692 1.445 .643
3 logShapFactr -.040e -.634 .528 -.076 .867 1.153 .815
logChSlpDmls -.019e -.243 .809 -.029 .563 1.776 .563
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ50
117
c. Predictors in the Model: (Constant), logAreaKm
d. Predictors in the Model: (Constant), logAreaKm, logSI1
e. Predictors in the Model: (Constant), logAreaKm, logSI1, logMAP
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logSI1 logMAP
1 1 1.988 1.000 .01 .01
2 .012 12.985 .99 .99
2 1 2.643 1.000 .00 .00 .04
2 .346 2.762 .01 .01 .83
3 .010 15.984 .99 .99 .13
3 1 3.612 1.000 .00 .00 .02 .00
2 .373 3.110 .00 .01 .87 .00
3 .014 16.053 .00 .99 .11 .00
4 9.755E-5 192.433 1.00 .00 .00 1.00
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ50
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value 1.1497 2.6462 1.9393 .32722 75
Residual -.39162 .40029 .00000 .18261 75
Std. Predicted Value -2.413 2.160 .000 1.000 75
Std. Residual -2.101 2.147 .000 .980 75
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ50
Charts
118
Region = Boreal Shield
Descriptive Statisticsa
Mean Std. Deviation N
logQ25 1.6751 .79747 43
logAreaKm 2.3566 .99527 43
logMAP 2.9348 .05119 43
logSI1 .0575 .02563 43
logShapFactr 1.1180 .25951 43
logChSlpDmls -2.5392 .57989 43
a. Region = Boreal Shield
Correlationsa
logQ25 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ25 1.000 .941 .151 -.068 .730 -.818
logAreaKm .941 1.000 -.069 .134 .710 -.941
logMAP .151 -.069 1.000 -.309 .200 .224
logSI1 -.068 .134 -.309 1.000 -.053 -.311
logShapFactr .730 .710 .200 -.053 1.000 -.683
logChSlpDmls -.818 -.941 .224 -.311 -.683 1.000
Sig. (1-tailed) logQ25 . .000 .167 .332 .000 .000
logAreaKm .000 . .330 .195 .000 .000
119
logMAP .167 .330 . .022 .100 .074
logSI1 .332 .195 .022 . .369 .021
logShapFactr .000 .000 .100 .369 . .000
logChSlpDmls .000 .000 .074 .021 .000 .
N logQ25 43 43 43 43 43 43
logAreaKm 43 43 43 43 43 43
logMAP 43 43 43 43 43 43
logSI1 43 43 43 43 43 43
logShapFactr 43 43 43 43 43 43
logChSlpDmls 43 43 43 43 43 43
a. Region = Boreal Shield
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
2 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
3 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
a. Region = Boreal Shield
b. Dependent Variable: logQ25
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .941b .885 .882 .27349
2 .965c .932 .929 .21293
3 .975d .951 .947 .18351 2.257
a. Region = Boreal Shield
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logMAP
d. Predictors: (Constant), logAreaKm, logMAP, logSI1
e. Dependent Variable: logQ25
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 23.643 1 23.643 316.097 .000c
Residual 3.067 41 .075
Total 26.710 42
2 Regression 24.897 2 12.448 274.569 .000d
Residual 1.814 40 .045
120
Total 26.710 42
3 Regression 25.397 3 8.466 251.396 .000e
Residual 1.313 39 .034
Total 26.710 42
a. Region = Boreal Shield
b. Dependent Variable: logQ25
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logMAP
e. Predictors: (Constant), logAreaKm, logMAP, logSI1
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) -.101 .108 -.937 .354
logAreaKm .754 .042 .941 17.779 .000 .941 .941 .941 1.000 1.000
2 (Constant) -10.057 1.896 -5.306 .000
logAreaKm .766 .033 .956 23.145 .000 .941 .965 .954 .995 1.005
logMAP 3.383 .643 .217 5.258 .000 .151 .639 .217 .995 1.005
3 (Constant) -7.834 1.733 -4.521 .000
logAreaKm .779 .029 .972 27.124 .000 .941 .975 .963 .981 1.019
logMAP 2.703 .582 .173 4.645 .000 .151 .597 .165 .904 1.107
logSI1 -4.510 1.170 -.145 -3.854 .000 -.068 -.525 -.137 .892 1.121
a. Region = Boreal Shield
b. Dependent Variable: logQ25
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .217c 5.258 .000 .639 .995 1.005 .995
logSI1 -.198c -4.488 .000 -.579 .982 1.018 .982
logShapFactr .123c 1.677 .101 .256 .495 2.019 .495
logChSlpDmls .591c 4.620 .000 .590 .114 8.741 .114
2 logSI1 -.145d -3.854 .000 -.525 .892 1.121 .892
logShapFactr .016d .258 .798 .041 .433 2.310 .433
logChSlpDmls .372d 2.940 .005 .426 .089 11.229 .089
3 logShapFactr -.008e -.149 .882 -.024 .427 2.342 .427
logChSlpDmls .195e 1.448 .156 .229 .068 14.727 .068
a. Region = Boreal Shield
b. Dependent Variable: logQ25
c. Predictors in the Model: (Constant), logAreaKm
121
d. Predictors in the Model: (Constant), logAreaKm, logMAP
e. Predictors in the Model: (Constant), logAreaKm, logMAP, logSI1
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logMAP logSI1
1 1 1.923 1.000 .04 .04
2 .077 4.992 .96 .96
2 1 2.897 1.000 .00 .02 .00
2 .103 5.310 .00 .98 .00
3 .000 140.226 1.00 .01 1.00
3 1 3.770 1.000 .00 .01 .00 .01
2 .135 5.275 .00 .42 .00 .64
3 .094 6.334 .00 .57 .00 .25
4 .000 168.762 1.00 .00 1.00 .10
a. Region = Boreal Shield
b. Dependent Variable: logQ25
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value -.2636 2.7478 1.6751 .77761 43
Residual -.45474 .42091 .00000 .17683 43
Std. Predicted Value -2.493 1.379 .000 1.000 43
Std. Residual -2.478 2.294 .000 .964 43
a. Region = Boreal Shield
b. Dependent Variable: logQ25
Charts
122
Region = Mixed WoodPlains
Descriptive Statisticsa
Mean Std. Deviation N
logQ25 1.8874 .36920 75
logAreaKm 2.2409 .34956 75
logMAP 2.9826 .04197 75
logSI1 .0390 .03444 75
logShapFactr 1.1352 .20216 75
logChSlpDmls -2.6722 .32149 75
a. Region = Mixed WoodPlains
Correlationsa
logQ25 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ25 1.000 .793 .158 -.553 .196 -.439
logAreaKm .793 1.000 .025 -.268 .340 -.532
logMAP .158 .025 1.000 .041 -.111 -.380
logSI1 -.553 -.268 .041 1.000 -.042 -.008
logShapFactr .196 .340 -.111 -.042 1.000 -.388
logChSlpDmls -.439 -.532 -.380 -.008 -.388 1.000
Sig. (1-tailed) logQ25 . .000 .088 .000 .046 .000
123
logAreaKm .000 . .414 .010 .001 .000
logMAP .088 .414 . .363 .172 .000
logSI1 .000 .010 .363 . .360 .472
logShapFactr .046 .001 .172 .360 . .000
logChSlpDmls .000 .000 .000 .472 .000 .
N logQ25 75 75 75 75 75 75
logAreaKm 75 75 75 75 75 75
logMAP 75 75 75 75 75 75
logSI1 75 75 75 75 75 75
logShapFactr 75 75 75 75 75 75
logChSlpDmls 75 75 75 75 75 75
a. Region = Mixed WoodPlains
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
2 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
3 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ25
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .793b .629 .624 .22635
2 .868c .754 .747 .18563
3 .882d .778 .769 .17747 1.659
a. Region = Mixed WoodPlains
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logSI1
d. Predictors: (Constant), logAreaKm, logSI1, logMAP
e. Dependent Variable: logQ25
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 6.347 1 6.347 123.889 .000c
Residual 3.740 73 .051
Total 10.087 74
2 Regression 7.606 2 3.803 110.362 .000d
124
Residual 2.481 72 .034
Total 10.087 74
3 Regression 7.851 3 2.617 83.084 .000e
Residual 2.236 71 .031
Total 10.087 74
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ25
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logSI1
e. Predictors: (Constant), logAreaKm, logSI1, logMAP
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) .010 .171 .058 .954
logAreaKm .838 .075 .793 11.131 .000 .793 .793 .793 1.000 1.000
2 (Constant) .395 .154 2.570 .012
logAreaKm .734 .064 .695 11.458 .000 .793 .804 .670 .928 1.077
logSI1 -3.930 .650 -.367 -6.044 .000 -.553 -.580 -.353 .928 1.077
3 (Constant) -3.680 1.469 -2.505 .015
logAreaKm .728 .061 .689 11.871 .000 .793 .815 .663 .927 1.079
logSI1 -4.017 .622 -.375 -6.453 .000 -.553 -.608 -.361 .926 1.080
logMAP 1.372 .492 .156 2.788 .007 .158 .314 .156 .997 1.003
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ25
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .138c 1.975 .052 .227 .999 1.001 .999
logSI1 -.367c -6.044 .000 -.580 .928 1.077 .928
logShapFactr -.083c -1.094 .278 -.128 .885 1.130 .885
logChSlpDmls -.023c -.275 .784 -.032 .717 1.395 .717
2 logMAP .156d 2.788 .007 .314 .997 1.003 .926
logShapFactr -.063d -1.007 .317 -.119 .882 1.134 .820
logChSlpDmls -.104d -1.492 .140 -.174 .692 1.445 .643
3 logShapFactr -.042e -.694 .490 -.083 .867 1.153 .815
logChSlpDmls -.028e -.379 .706 -.045 .563 1.776 .563
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ25
125
c. Predictors in the Model: (Constant), logAreaKm
d. Predictors in the Model: (Constant), logAreaKm, logSI1
e. Predictors in the Model: (Constant), logAreaKm, logSI1, logMAP
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logSI1 logMAP
1 1 1.988 1.000 .01 .01
2 .012 12.985 .99 .99
2 1 2.643 1.000 .00 .00 .04
2 .346 2.762 .01 .01 .83
3 .010 15.984 .99 .99 .13
3 1 3.612 1.000 .00 .00 .02 .00
2 .373 3.110 .00 .01 .87 .00
3 .014 16.053 .00 .99 .11 .00
4 9.755E-5 192.433 1.00 .00 .00 1.00
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ25
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value 1.0931 2.5910 1.8874 .32572 75
Residual -.38583 .38775 .00000 .17384 75
Std. Predicted Value -2.439 2.160 .000 1.000 75
Std. Residual -2.174 2.185 .000 .980 75
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ25
Charts
126
Region = Boreal Shield
Descriptive Statisticsa
Mean Std. Deviation N
logQ10 1.5928 .81277 43
logAreaKm 2.3566 .99527 43
logMAP 2.9348 .05119 43
logSI1 .0575 .02563 43
logShapFactr 1.1180 .25951 43
logChSlpDmls -2.5392 .57989 43
a. Region = Boreal Shield
Correlationsa
logQ10 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ10 1.000 .942 .160 -.069 .734 -.819
logAreaKm .942 1.000 -.069 .134 .710 -.941
logMAP .160 -.069 1.000 -.309 .200 .224
logSI1 -.069 .134 -.309 1.000 -.053 -.311
logShapFactr .734 .710 .200 -.053 1.000 -.683
logChSlpDmls -.819 -.941 .224 -.311 -.683 1.000
Sig. (1-tailed) logQ10 . .000 .152 .331 .000 .000
logAreaKm .000 . .330 .195 .000 .000
127
logMAP .152 .330 . .022 .100 .074
logSI1 .331 .195 .022 . .369 .021
logShapFactr .000 .000 .100 .369 . .000
logChSlpDmls .000 .000 .074 .021 .000 .
N logQ10 43 43 43 43 43 43
logAreaKm 43 43 43 43 43 43
logMAP 43 43 43 43 43 43
logSI1 43 43 43 43 43 43
logShapFactr 43 43 43 43 43 43
logChSlpDmls 43 43 43 43 43 43
a. Region = Boreal Shield
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter <=
.050, Probability-of-F-to-remove >= .100).
2 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter <=
.050, Probability-of-F-to-remove >= .100).
3 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter <=
.050, Probability-of-F-to-remove >= .100).
a. Region = Boreal Shield
b. Dependent Variable: logQ10
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .942b .888 .885 .27563
2 .969c .939 .936 .20594
3 .978d .957 .954 .17493 2.232
a. Region = Boreal Shield
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logMAP
d. Predictors: (Constant), logAreaKm, logMAP, logSI1
e. Dependent Variable: logQ10
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 24.630 1 24.630 324.195 .000c
Residual 3.115 41 .076
Total 27.745 42
2 Regression 26.049 2 13.024 307.105 .000d
Residual 1.696 40 .042
128
Total 27.745 42
3 Regression 26.552 3 8.851 289.223 .000e
Residual 1.193 39 .031
Total 27.745 42
a. Region = Boreal Shield
b. Dependent Variable: logQ10
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logMAP
e. Predictors: (Constant), logAreaKm, logMAP, logSI1
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) -.221 .109 -2.021 .050
logAreaKm .769 .043 .942 18.005 .000 .942 .942 .942 1.000 1.000
2 (Constant) -10.813 1.833 -5.898 .000
logAreaKm .782 .032 .958 24.442 .000 .942 .968 .956 .995 1.005
logMAP 3.599 .622 .227 5.783 .000 .160 .675 .226 .995 1.005
3 (Constant) -8.583 1.652 -5.197 .000
logAreaKm .795 .027 .974 29.052 .000 .942 .978 .965 .981 1.019
logMAP 2.917 .555 .184 5.259 .000 .160 .644 .175 .904 1.107
logSI1 -4.522 1.115 -.143 -4.054 .000 -.069 -.545 -.135 .892 1.121
a. Region = Boreal Shield
b. Dependent Variable: logQ10
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .227c 5.783 .000 .675 .995 1.005 .995
logSI1 -.199c -4.592 .000 -.588 .982 1.018 .982
logShapFactr .130c 1.794 .080 .273 .495 2.019 .495
logChSlpDmls .593c 4.722 .000 .598 .114 8.741 .114
2 logSI1 -.143d -4.054 .000 -.545 .892 1.121 .892
logShapFactr .018d .305 .762 .049 .433 2.310 .433
logChSlpDmls .357d 2.983 .005 .431 .089 11.229 .089
3 logShapFactr -.006e -.112 .911 -.018 .427 2.342 .427
logChSlpDmls .180e 1.432 .160 .226 .068 14.727 .068
a. Region = Boreal Shield
b. Dependent Variable: logQ10
c. Predictors in the Model: (Constant), logAreaKm
129
d. Predictors in the Model: (Constant), logAreaKm, logMAP
e. Predictors in the Model: (Constant), logAreaKm, logMAP, logSI1
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logMAP logSI1
1 1 1.923 1.000 .04 .04
2 .077 4.992 .96 .96
2 1 2.897 1.000 .00 .02 .00
2 .103 5.310 .00 .98 .00
3 .000 140.226 1.00 .01 1.00
3 1 3.770 1.000 .00 .01 .00 .01
2 .135 5.275 .00 .42 .00 .64
3 .094 6.334 .00 .57 .00 .25
4 .000 168.762 1.00 .00 1.00 .10
a. Region = Boreal Shield
b. Dependent Variable: logQ10
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value -.3970 2.6864 1.5928 .79510 43
Residual -.44448 .41232 .00000 .16857 43
Std. Predicted Value -2.503 1.375 .000 1.000 43
Std. Residual -2.541 2.357 .000 .964 43
a. Region = Boreal Shield
b. Dependent Variable: logQ10
Charts
130
Region = Mixed WoodPlains
Descriptive Statisticsa
Mean Std. Deviation N
logQ10 1.8054 .36207 75
logAreaKm 2.2409 .34956 75
logMAP 2.9826 .04197 75
logSI1 .0390 .03444 75
logShapFactr 1.1352 .20216 75
logChSlpDmls -2.6722 .32149 75
a. Region = Mixed WoodPlains
Correlationsa
logQ10 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ10 1.000 .809 .176 -.542 .197 -.464
logAreaKm .809 1.000 .025 -.268 .340 -.532
logMAP .176 .025 1.000 .041 -.111 -.380
logSI1 -.542 -.268 .041 1.000 -.042 -.008
logShapFactr .197 .340 -.111 -.042 1.000 -.388
logChSlpDmls -.464 -.532 -.380 -.008 -.388 1.000
Sig. (1-tailed) logQ10 . .000 .065 .000 .045 .000
131
logAreaKm .000 . .414 .010 .001 .000
logMAP .065 .414 . .363 .172 .000
logSI1 .000 .010 .363 . .360 .472
logShapFactr .045 .001 .172 .360 . .000
logChSlpDmls .000 .000 .000 .472 .000 .
N logQ10 75 75 75 75 75 75
logAreaKm 75 75 75 75 75 75
logMAP 75 75 75 75 75 75
logSI1 75 75 75 75 75 75
logShapFactr 75 75 75 75 75 75
logChSlpDmls 75 75 75 75 75 75
a. Region = Mixed WoodPlains
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
2 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
3 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ10
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .809b .655 .650 .21424
2 .877c .769 .762 .17651
3 .894d .799 .790 .16590 1.691
a. Region = Mixed WoodPlains
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logSI1
d. Predictors: (Constant), logAreaKm, logSI1, logMAP
e. Dependent Variable: logQ10
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 6.350 1 6.350 138.357 .000c
Residual 3.351 73 .046
Total 9.701 74
2 Regression 7.458 2 3.729 119.690 .000d
132
Residual 2.243 72 .031
Total 9.701 74
3 Regression 7.747 3 2.582 93.819 .000e
Residual 1.954 71 .028
Total 9.701 74
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ10
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logSI1
e. Predictors: (Constant), logAreaKm, logSI1, logMAP
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) -.073 .162 -.449 .655
logAreaKm .838 .071 .809 11.763 .000 .809 .809 .809 1.000 1.000
2 (Constant) .289 .146 1.976 .052
logAreaKm .741 .061 .715 12.160 .000 .809 .820 .689 .928 1.077
logSI1 -3.687 .618 -.351 -5.962 .000 -.542 -.575 -.338 .928 1.077
3 (Constant) -4.139 1.374 -3.013 .004
logAreaKm .734 .057 .708 12.805 .000 .809 .835 .682 .927 1.079
logSI1 -3.780 .582 -.360 -6.496 .000 -.542 -.611 -.346 .926 1.080
logMAP 1.491 .460 .173 3.240 .002 .176 .359 .173 .997 1.003
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ10
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .156c 2.330 .023 .265 .999 1.001 .999
logSI1 -.351c -5.962 .000 -.575 .928 1.077 .928
logShapFactr -.088c -1.205 .232 -.141 .885 1.130 .885
logChSlpDmls -.046c -.569 .571 -.067 .717 1.395 .717
2 logMAP .173d 3.240 .002 .359 .997 1.003 .926
logShapFactr -.069d -1.140 .258 -.134 .882 1.134 .820
logChSlpDmls -.124d -1.859 .067 -.215 .692 1.445 .643
3 logShapFactr -.046e -.794 .430 -.094 .867 1.153 .815
logChSlpDmls -.043e -.602 .549 -.072 .563 1.776 .563
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ10
133
c. Predictors in the Model: (Constant), logAreaKm
d. Predictors in the Model: (Constant), logAreaKm, logSI1
e. Predictors in the Model: (Constant), logAreaKm, logSI1, logMAP
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logSI1 logMAP
1 1 1.988 1.000 .01 .01
2 .012 12.985 .99 .99
2 1 2.643 1.000 .00 .00 .04
2 .346 2.762 .01 .01 .83
3 .010 15.984 .99 .99 .13
3 1 3.612 1.000 .00 .00 .02 .00
2 .373 3.110 .00 .01 .87 .00
3 .014 16.053 .00 .99 .11 .00
4 9.755E-5 192.433 1.00 .00 .00 1.00
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ10
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value 1.0032 2.5038 1.8054 .32355 75
Residual -.37517 .36837 .00000 .16250 75
Std. Predicted Value -2.479 2.159 .000 1.000 75
Std. Residual -2.261 2.220 .000 .980 75
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ10
Charts
134
Region = Boreal Shield
Descriptive Statisticsa
Mean Std. Deviation N
logQ2 1.3572 .85698 43
logAreaKm 2.3566 .99527 43
logMAP 2.9348 .05119 43
logSI1 .0575 .02563 43
logShapFactr 1.1180 .25951 43
logChSlpDmls -2.5392 .57989 43
a. Region = Boreal Shield
Correlationsa
logQ2 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ2 1.000 .941 .189 -.074 .745 -.815
logAreaKm .941 1.000 -.069 .134 .710 -.941
logMAP .189 -.069 1.000 -.309 .200 .224
logSI1 -.074 .134 -.309 1.000 -.053 -.311
logShapFactr .745 .710 .200 -.053 1.000 -.683
logChSlpDmls -.815 -.941 .224 -.311 -.683 1.000
Sig. (1-tailed) logQ2 . .000 .112 .319 .000 .000
135
logAreaKm .000 . .330 .195 .000 .000
logMAP .112 .330 . .022 .100 .074
logSI1 .319 .195 .022 . .369 .021
logShapFactr .000 .000 .100 .369 . .000
logChSlpDmls .000 .000 .074 .021 .000 .
N logQ2 43 43 43 43 43 43
logAreaKm 43 43 43 43 43 43
logMAP 43 43 43 43 43 43
logSI1 43 43 43 43 43 43
logShapFactr 43 43 43 43 43 43
logChSlpDmls 43 43 43 43 43 43
a. Region = Boreal Shield
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
2 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
3 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
a. Region = Boreal Shield
b. Dependent Variable: logQ2
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .941b .886 .883 .29347
2 .975c .951 .948 .19513
3 .984d .968 .965 .15973 2.167
a. Region = Boreal Shield
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logMAP
d. Predictors: (Constant), logAreaKm, logMAP, logSI1
e. Dependent Variable: logQ2
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 27.314 1 27.314 317.156 .000c
Residual 3.531 41 .086
Total 30.845 42
2 Regression 29.322 2 14.661 385.063 .000d
136
Residual 1.523 40 .038
Total 30.845 42
3 Regression 29.850 3 9.950 390.009 .000e
Residual .995 39 .026
Total 30.845 42
a. Region = Boreal Shield
b. Dependent Variable: logQ2
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logMAP
e. Predictors: (Constant), logAreaKm, logMAP, logSI1
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) -.552 .116 -4.753 .000
logAreaKm .810 .045 .941 17.809 .000 .941 .941 .941 1.000 1.000
2 (Constant) -13.155 1.737 -7.573 .000
logAreaKm .826 .030 .959 27.223 .000 .941 .974 .956 .995 1.005
logMAP 4.282 .590 .256 7.262 .000 .189 .754 .255 .995 1.005
3 (Constant) -10.870 1.508 -7.208 .000
logAreaKm .839 .025 .974 33.561 .000 .941 .983 .965 .981 1.019
logMAP 3.583 .507 .214 7.075 .000 .189 .750 .203 .904 1.107
logSI1 -4.633 1.018 -.139 -4.549 .000 -.074 -.589 -.131 .892 1.121
a. Region = Boreal Shield
b. Dependent Variable: logQ2
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .256c 7.262 .000 .754 .995 1.005 .995
logSI1 -.204c -4.708 .000 -.597 .982 1.018 .982
logShapFactr .153c 2.129 .039 .319 .495 2.019 .495
logChSlpDmls .613c 4.905 .000 .613 .114 8.741 .114
2 logSI1 -.139d -4.549 .000 -.589 .892 1.121 .892
logShapFactr .028d .527 .601 .084 .433 2.310 .433
logChSlpDmls .331d 3.103 .004 .445 .089 11.229 .089
3 logShapFactr .005e .115 .909 .019 .427 2.342 .427
logChSlpDmls .154e 1.416 .165 .224 .068 14.727 .068
a. Region = Boreal Shield
b. Dependent Variable: logQ2
137
c. Predictors in the Model: (Constant), logAreaKm
d. Predictors in the Model: (Constant), logAreaKm, logMAP
e. Predictors in the Model: (Constant), logAreaKm, logMAP, logSI1
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logMAP logSI1
1 1 1.923 1.000 .04 .04
2 .077 4.992 .96 .96
2 1 2.897 1.000 .00 .02 .00
2 .103 5.310 .00 .98 .00
3 .000 140.226 1.00 .01 1.00
3 1 3.770 1.000 .00 .01 .00 .01
2 .135 5.275 .00 .42 .00 .64
3 .094 6.334 .00 .57 .00 .25
4 .000 168.762 1.00 .00 1.00 .10
a. Region = Boreal Shield
b. Dependent Variable: logQ2
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value -.7794 2.5082 1.3572 .84304 43
Residual -.40212 .37227 .00000 .15392 43
Std. Predicted Value -2.534 1.365 .000 1.000 43
Std. Residual -2.518 2.331 .000 .964 43
a. Region = Boreal Shield
b. Dependent Variable: logQ2
Charts
138
Region = Mixed WoodPlains
Descriptive Statisticsa
Mean Std. Deviation N
logQ2 1.5694 .35051 75
logAreaKm 2.2409 .34956 75
logMAP 2.9826 .04197 75
logSI1 .0390 .03444 75
logShapFactr 1.1352 .20216 75
logChSlpDmls -2.6722 .32149 75
a. Region = Mixed WoodPlains
Correlationsa
logQ2 logAreaKm logMAP logSI1 logShapFactr logChSlpDmls
Pearson
Correlation
logQ2 1.000 .840 .227 -.494 .196 -.530
logAreaKm .840 1.000 .025 -.268 .340 -.532
logMAP .227 .025 1.000 .041 -.111 -.380
logSI1 -.494 -.268 .041 1.000 -.042 -.008
logShapFactr .196 .340 -.111 -.042 1.000 -.388
logChSlpDmls -.530 -.532 -.380 -.008 -.388 1.000
Sig. (1-tailed) logQ2 . .000 .025 .000 .046 .000
139
logAreaKm .000 . .414 .010 .001 .000
logMAP .025 .414 . .363 .172 .000
logSI1 .000 .010 .363 . .360 .472
logShapFactr .046 .001 .172 .360 . .000
logChSlpDmls .000 .000 .000 .472 .000 .
N logQ2 75 75 75 75 75 75
logAreaKm 75 75 75 75 75 75
logMAP 75 75 75 75 75 75
logSI1 75 75 75 75 75 75
logShapFactr 75 75 75 75 75 75
logChSlpDmls 75 75 75 75 75 75
a. Region = Mixed WoodPlains
Variables Entered/Removeda,b
Model
Variables
Entered
Variables
Removed Method
1 logAreaKm .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
2 logSI1 .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
3 logMAP .
Stepwise (Criteria: Probability-of-F-to-enter
<= .050, Probability-of-F-to-remove >= .100).
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ2
Model Summarya,e
Model R R Square
Adjusted R
Square
Std. Error of the
Estimate Durbin-Watson
1 .840b .705 .701 .19163
2 .885c .783 .777 .16555
3 .912d .831 .824 .14704 1.763
a. Region = Mixed WoodPlains
b. Predictors: (Constant), logAreaKm
c. Predictors: (Constant), logAreaKm, logSI1
d. Predictors: (Constant), logAreaKm, logSI1, logMAP
e. Dependent Variable: logQ2
ANOVAa,b
Model Sum of Squares df Mean Square F Sig.
1 Regression 6.411 1 6.411 174.573 .000c
Residual 2.681 73 .037
Total 9.091 74
2 Regression 7.118 2 3.559 129.848 .000d
140
Residual 1.973 72 .027
Total 9.091 74
3 Regression 7.556 3 2.519 116.505 .000e
Residual 1.535 71 .022
Total 9.091 74
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ2
c. Predictors: (Constant), logAreaKm
d. Predictors: (Constant), logAreaKm, logSI1
e. Predictors: (Constant), logAreaKm, logSI1, logMAP
Coefficientsa,b
Model
Unstandardized
Coefficients
Standardized
Coefficients
t Sig.
Correlations
Collinearity
Statistics
B
Std.
Error Beta
Zero-
order Partial Part Tolerance VIF
1 (Constant) -.317 .145 -2.196 .031
logAreaKm .842 .064 .840 13.213 .000 .840 .840 .840 1.000 1.000
2 (Constant) -.028 .137 -.207 .836
logAreaKm .764 .057 .762 13.375 .000 .840 .844 .734 .928 1.077
logSI1 -2.946 .580 -.289 -5.080 .000 -.494 -.514 -.279 .928 1.077
3 (Constant) -5.483 1.217 -4.504 .000
logAreaKm .756 .051 .754 14.879 .000 .840 .870 .726 .927 1.079
logSI1 -3.061 .516 -.301 -5.936 .000 -.494 -.576 -.289 .926 1.080
logMAP 1.837 .408 .220 4.503 .000 .227 .471 .220 .997 1.003
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ2
Excluded Variablesa,b
Model Beta In t Sig.
Partial
Correlation
Collinearity Statistics
Tolerance VIF
Minimum
Tolerance
1 logMAP .206c 3.469 .001 .378 .999 1.001 .999
logSI1 -.289c -5.080 .000 -.514 .928 1.077 .928
logShapFactr -.100c -1.499 .138 -.174 .885 1.130 .885
logChSlpDmls -.116c -1.561 .123 -.181 .717 1.395 .717
2 logMAP .220d 4.503 .000 .471 .997 1.003 .926
logShapFactr -.085d -1.460 .149 -.171 .882 1.134 .820
logChSlpDmls -.183d -2.917 .005 -.327 .692 1.445 .643
3 logShapFactr -.055e -1.055 .295 -.125 .867 1.153 .815
logChSlpDmls -.085e -1.316 .193 -.155 .563 1.776 .563
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ2
141
c. Predictors in the Model: (Constant), logAreaKm
d. Predictors in the Model: (Constant), logAreaKm, logSI1
e. Predictors in the Model: (Constant), logAreaKm, logSI1, logMAP
Collinearity Diagnosticsa,b
Model Dimension Eigenvalue
Condition
Index
Variance Proportions
(Constant) logAreaKm logSI1 logMAP
1 1 1.988 1.000 .01 .01
2 .012 12.985 .99 .99
2 1 2.643 1.000 .00 .00 .04
2 .346 2.762 .01 .01 .83
3 .010 15.984 .99 .99 .13
3 1 3.612 1.000 .00 .00 .02 .00
2 .373 3.110 .00 .01 .87 .00
3 .014 16.053 .00 .99 .11 .00
4 9.755E-5 192.433 1.00 .00 .00 1.00
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ2
Residuals Statisticsa,b
Minimum Maximum Mean Std. Deviation N
Predicted Value .7393 2.2555 1.5694 .31955 75
Residual -.33889 .31825 .00000 .14402 75
Std. Predicted Value -2.598 2.147 .000 1.000 75
Std. Residual -2.305 2.164 .000 .980 75
a. Region = Mixed WoodPlains
b. Dependent Variable: logQ2
Charts
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143
Appendix G: Stations rejected from Multiple Regression Analysis
S. No. Station ID Reason for rejection
1 02HB021 Urban station
2 04DB001 Rejection due to lack of OFAT data
3 04FB001 Rejection due to non parametric test
4 04FC001 Rejection due to lack of OFAT data
5 05PA012 Rejection due to lack of OFAT data
6 02GG009 Rejection due to lack of OFAT data
7 02EC011 Rejection due to non parametric test
8 02BB002 Rejection during fitting
9 02JC008 Rejection due to non parametric test
10 02HE001 Rejection due to non parametric test
11 02CG003 rejection due to area mismatch
12 02HF004 rejection due to area mismatch
13 02MB010 rejection due to area mismatch
14 02GA036 Rejection due to data<15yrs
15 02GH003 rejection due to area mismatch
16 02KF011 Rejection due to non parametric test
17 04GA002 Rejection due to non parametric test
18 05QE008 Rejection due to non parametric test
19 02DD014 Urban station
20 02ED007 Rejection due to non parametric test
21 02HM005 Rejection due to non parametric test
22 02GA017 Rejection during fitting
23 02DB007 rejection due to area mismatch
24 02DB004 Rejection due to data<15yrs
25 02GE005 Urban station
26 02GA035 Rejection due to data<15yrs
27 04EA001 Rejection due to lack of OFAT data
28 05QA002 rejection due to area mismatch
29 02HC030 Urban station
30 02HC002 Rejection due to non parametric test
31 04CE002 Rejection due to lack of OFAT data
32 02GD010 Rejection due to non parametric test
33 02HD002 Rejection due to non parametric test
34 02KF015 rejection due to area mismatch
35 04KA002 Rejection due to lack of OFAT data
144
S. No. Station ID Reason for rejection
36 02HD013 Rejection due to non parametric test
37 02HC013 Rejection due to non parametric test
38 02EC009 Urban station
39 02GA045 Rejection due to data<15yrs
40 02GA046 Rejection due to data<15yrs
41 02HJ001 Rejection due to non parametric test
42 02LA007 Rejection due to non parametric test
43 02CF012 Urban station
44 04KA001 reject-Hudson Plain
45 05PC016 Rejection due to data<15yrs
46 05QD018 Rejection due to non parametric test
47 05QD019 rejection due to area mismatch
48 05QD015 Rejection due to lack of OFAT data
49 05QD008 Rejection due to lack of OFAT data
50 05PD024 Rejection due to data<15yrs
51 05PD015 Rejection due to non parametric test
52 02HC029 Rejection due to non parametric test
53 02HC004 Rejection due to non parametric test
54 02DD020 Rejection due to data<15yrs
55 02GH011 Urban station
56 05QE012 Rejection due to non parametric test
57 02FD002 rejection due to area mismatch
58 02MA001 Rejection due to non parametric test
59 02AB019 Rejection due to non parametric test
60 02HC033 Urban station
61 04LJ001 Rejection due to lack of OFAT data
62 04LM001 Rejection due to lack of OFAT data
63 02BE001 Rejection due to data<15yrs
64 02GA042 Rejection due to data<15yrs
65 02KC015 Rejection due to data<15yrs
66 04GF001 Rejection due to lack of OFAT data
67 05PA006 rejection due to area mismatch
68 02GA018 Rejection due to non parametric test
69 02GA010 Rejection due to non parametric test
70 02BF012 rejection due to area mismatch
71 04MF001 reject-Hudson Plain
72 02EA005 rejection due to area mismatch
145
S. No. Station ID Reason for rejection
73 05PD022 Rejection due to lack of OFAT data
74 02ED101 Rejection during fitting
75 02GF001 Rejection due to data<15yrs
76 02GA032 Rejection due to lack of OFAT data
77 04GB004 Rejection due to lack of OFAT data
78 02HD008 Rejection due to non parametric test
79 02HA024 Rejection due to non parametric test
80 04JD005 Rejection during fitting
81 02FF003 rejection due to area mismatch
82 04GA003 Rejection due to data<15yrs
83 02EC018 Rejection during fitting
84 02KA004 Rejection due to lack of OFAT data
85 02KA005 Rejection due to non parametric test
86 02KA006 Rejection due to lack of OFAT data
87 02KA007 Rejection due to lack of OFAT data
88 02KA008 Rejection due to lack of OFAT data
89 02KA003 rejection due to area mismatch
90 02AA001 rejection due to area mismatch
91 05OD032 Rejection due to lack of OFAT data
92 02ED014 Rejection due to non parametric test
93 04FA003 Rejection due to lack of OFAT data
94 05PB015 rejection due to area mismatch
95 04DA001 rejection due to area mismatch
96 04MD004 Rejection during fitting
97 02BC005 Rejection due to data<15yrs
98 05PC018 rejection due to area mismatch
99 02MC027 Rejection due to data<15yrs
100 02MC001 rejection due to area mismatch
101 02HA023 Urban station
102 02HA014 Rejection due to non parametric test
103 02MC028 Rejection due to data<15yrs
104 02FC004 Rejection due to data<15yrs
105 05OD030 Rejection due to lack of OFAT data
106 02GH002 Rejection due to non parametric test
107 04CD002 Rejection due to non parametric test
108 02FC016 Rejection during fitting
109 02GA037 rejection due to area mismatch
146
S. No. Station ID Reason for rejection
110 02EC010 rejection due to area mismatch
111 04CC001 reject-Hudson Plain
112 04CA004 Rejection due to lack of OFAT data
113 04CA002 Rejection due to lack of OFAT data
114 04DC002 Rejection due to non parametric test
115 02GA044 Rejection due to data<15yrs
116 02HL004 Rejection due to non parametric test
117 02LB031 Rejection due to data<15yrs
118 02LB007 Rejection due to non parametric test
119 02MC030 Rejection due to data<15yrs
120 05OD031 Rejection due to lack of OFAT data
121 02FA002 rejection due to area mismatch
122 02HA022 rejection due to area mismatch
123 02GH001 Rejection due to non parametric test
124 02DC012 rejection due to area mismatch
125 05PC010 Rejection due to data<15yrs
126 02FB007 Rejection during fitting
127 02GD006 Rejection due to data<15yrs
128 02BF013 rejection due to area mismatch
129 02GD019 rejection due to area mismatch
130 02GD009 Rejection due to non parametric test
131 05QC003 Rejection due to non parametric test
132 02GH004 rejection due to area mismatch
133 05PB014 Rejection due to lack of OFAT data
134 02GC021 rejection due to area mismatch
135 02DD012 rejection due to area mismatch
136 02GD020 Rejection due to non parametric test
137 02HM009 rejection due to area mismatch
138 02HC038 rejection due to area mismatch
139 02BA005 rejection due to area mismatch
140 02CF007 Rejection due to non parametric test
141 02ED010 Rejection due to non parametric test
142 02HM004 Rejection due to non parametric test
143 04DC001 Rejection due to lack of OFAT data
144 02AC001 Rejection during fitting
145 02GD013 Rejection due to non parametric test
146 02KD002 Rejection due to non parametric test
147
Copyright Acknowledgement
This project was supported by the Ontario Ministry of Transportation (MTO) under its Highway
Infrastructure Innovation and Funding Program (HIIFP). The author has also produced a project
report for MTO. The contents of the thesis and results would find similarity with the final project
report submitted to MTO in December 2015. A publication based on this thesis is also currently
in progress.
