ASSESSMENT OF CHANGES IN PRECIPITATION
INTENSITIES IN ONTARIO
A Thesis
Presented to
The Faculty of Graduate Studies
of
The University of Guelph
by
BRANISLAVA VASIUEVIC
In partial fulfilment of requirements
for the degree of
Master of Science
December, 2007
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While these forms may be included Bien que ces formulaires in the document page count, aient inclus dans la pagination, their removal does not represent il n'y aura aucun contenu manquant. any loss of content from the thesis. Canada ABSTRACT
Branislava Vasiljevic Advisor:
University of Guelph, 2007 Dr. Edward A. McBean
The intensities of short-duration rainfalls are fundamental inputs to design of stormwater management infrastructure for urban areas. Such infrastructure, are designed, in part, to control urban flooding and require specification of storms for specific recurrence intervals. However, implicit in design tasks of stormwater infrastructure is the need for the infrastructure to function for many decades. Given that there is widespread evidence that climate change is likely occurring, there is extensive interest in whether the frequencies of urban storms are changing and hence, whether urban infrastructure designs need to be changed in response to the global climate change reality.
To examine whether the recurrence intervals of severe storms are changing, historical records for thirteen locations distributed throughout Ontario are evaluated. The results of the analyses of the historical records for rainfall intensity/recurrence interval/duration are provided for each of these locations, and demonstrate there is evidence that rainfall intensities are, indeed, changing in Ontario. ACKNOWLEDGEMENTS
I would like to acknowledge the many people who have supported me during my master's studies.
I would first like to thank my Mentor, Dr Edward A. McBean, for his financial and moral support. While working with such an exceptional expert is one of the greatest honors I have had, it is his personal qualities that make me so proud to be his student. Many thanks for his brilliant ideas and extraordinary experience, which he shares so freely, his exceptional level of guidance throughout my research, and for two excellent courses. I would also like to express my gratitude to Professor McBean for the opportunity to be a part of a great multicultural community at the School of Engineering
I would also like to acknowledge Dr Ramesh P. Rudra, for his participation on my advisory committee and financial support of this project
I highly appreciate Dr Andrea Bradford, for an excellent course, and
Professor Emeritus Dr Trevor Dickinson for useful advices.
Special thanks to Goran Vrakela and Branko Jovanovic for their help and advice on software development; Laura Wagner and Brian Verspagen, from Conestoga-Rovers & Associates, for contributions regarding existing infrastructure analyses; and Joan Klaassen and Heather Auld, from
Meteorological Service of Canada, for providing useful comments despite busy schedules.
i I would like to thank my colleagues and dear friends at the School of
Engineering: Ana, Cuit, Fernando Chantelle, Joel, Maryam, Mijin and Ash, for their great emotional support and empathy. Also, many thanks to my family and friends, for just being there.
Last but not least, I would like to thank my husband for his encouragement, support, and patience during the past two years.
Finally, this thesis is dedicated to my parents, Ljubinka and Blagoje
Matic, for their tremendous and unconditional love and support during their lives.
ii TABLE OF CONTENTS
ACKNOWLEDGEMENTS i TABLE OF CONTENTS iii LIST OF TABLES v LIST OF FIGURES v CHAPTER 1 INTRODUCTION 1 1.1 RESEARCH MOTIVATION 1 1.2 OBJECTIVES 5 1.3. SCOPE OF THE THESIS 6 CHAPTER 2 LITERATURE REVIEW 8 2.1 METHODOLOGIES AND REVIEW OF CLIMATE CHANGE STUDIES 8 2.1.1 Methodologies Used in Previous Climate Change Studies 8 2.1.2 Preceding Climate Change Studies Review 11 2.2 LOCAL POINT RAINFALL DATA FREQUENCY ANALYSES 24 2.2.1 Probability Distributions 24 2.2.2 Recurrence Interval and Frequency Factor 27 2.2.3. IDF curves 29 2.3 TREND TEST 31 2.3.1 Linear regression 31 2.3.2 Mann- Kendall non - parametric test 32 CHAPTER 3 THEORETICAL BASE AND METHODOLOGY 33 3.1. DATA RANKING 33 3.1.1 The Annual Maxima 33 3.1.1 The Partial Duration Series 34 3.2 IDF CURVES 35 3.2.1 Extreme Value I distribution 36 3.2.2 Frequency Analyses 37 3.3 INTENSITY EQUATION COEFFICIENTS 38 3.3.1 The Log-Linear Regression 38 3.3.2 The Method of Least Squares 39 3.4 TREND DETECTION 40
iii 3.4.1 Linear Regression 40 3.4.2 Mann - Kendall Trend Test 40 3.5 CONFIDENCE INTERVAL AND FREQUENCY 42 CHAPTER 4 MODEL DEVELOPMENT AND RESULTS 45 4.1 INTRODUCTION 45 4.2 DATA AVAILABLE 46 4.3 LOCAL POINT IDF CURVES ANALYSES 49 4.3.1 Application of Model to IDF curves Temporal Change Analyses 53 4.3.2 Model Application to Seasonal Analyses in IDF curves 58 4.4 MODEL APPLICATION TO THE CASE STUDY AREA: WATERLOO STATION 66 4.4.1 IDF Curves Analyses ... 67 4.4.2 Intensity Equation Temporal Analyses 72 4.4.3 Evaluation of Existing Hydrological Model 75 4.5. RECURRENCE INTERVALS CONFIDENCE LIMITS 77 4.6 TREND ANALYSES FOR THE NUMBER OF DRY DAYS AND THE AMOUNT OF RAINFALL 85 CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 88 5.1 CONCLUSIONS 88 5.2 RECOMMENDATIONS FOR FUTURE WORK 90 REFERENCES 92 APPENDIX A: Tables 98 APPENDIX B: Computer Programs 119 APPENDIX C: Confidence Intervals Calculations Example for 18 Samples at Waterloo Station 122
IV LIST OF TABLES
Table 4.2 Annual missing data summary 48 Table 4.5 Trend Analyses Results for Seasonal Changes in IDF Curves for Twelve Stations Across Ontario 66 Table 4.6.1 IDF Curves Table 4.6.1 IDF Curves Evaluation for 2 Year Event Evaluation for 5 Year Event at Waterloo station at Waterloo station...68 Table 4.7 IDF Comparison between Different Periods of Observation for 2 and 5 Year Events at Waterloo Station 70 Table 4.8 IDF Curves Constants Comparison at Waterloo 73 Station for two Period of Observation with Existing IDF curves 73 Table 4.9 Stormwater Sewer Pipe Size Analyses Based on Various Scenarios in Terms of Heavy Rainfall Intensity for 5 Year Event at Waterloo/Kitchener location 76 Table 4.10 Summarized Results for Confidence Limits Calculations at Waterloo Station for Different Sample Size and Periods of Observation .83 Table4.11 Summarized Results for Mann-Kendall Trend Tests for 5% Level of Significance at 13 Locations in Ontario 86 Table 4.1 Meteorological stations used for analyses; Data are provided by Environment Canada; 98 Table 4.3.1 DELHI IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1962-1978 and 1979-1995 99 Table 4.3.2 PORT COLBORNE IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1962-1978 and 1979-1995 99 Table 4.3.3 PRESTON IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1970-1984 and 1985-1996.. 100 Table 4.3.4 SARNIA IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1970-1984 and 1985-2003 100 Table 4.3.5 WATERLOO IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1970-1984 and 1985-2003 101 Table 4.3.6 BOWMANVILLE IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1966 -1984 and 1985-2001 101 Table 4.3.7 BURKETON IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1969 -1984 and 1985-2001 102 Table 4.3.8 KINGSTON IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1960-1981 and 1982-2003 102 Table 4.3.9 ORILLIA IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1965-1978 and 1979-1992 103
v Table 4.3.10 OSHAWA IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1969-1984 and 1985-2003 103 Table 4.3.11 CHALK RIVER IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1962-1978 and 1979-1995 104 Table 4.3.12 SUDBURY IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1971-1984 and 1985-1996 104 Table 4.3.13 TIMMINS IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1969-1984 and 1985- 1999 105 Table 4.3.14 Summarized IDF Curves Average Annual Changes in Percentage for 5 Year Recurrence Interval 105 Table 4.4.1 DELHI Seasonal Percentage Change in IDF Curves 106 for Time Series: 1962 - 1978 and 1979 - 1995 106 Table 4.4.2 PORT COLBORNE Seasonal Percentage Change in IDF Curves for Time Series: 1962 - 1978 and 1979 - 1995 107 Table 4.4.3 PRESTON Seasonal Percentage Change in IDF Curves for Time Series: 1970 - 1984 and 1985 - 1996 108 Table 4.4.4 SARNIA Seasonal Percentage Change in IDF Curves for Time Series 1970-1984 and 1985 - 2003 109 Table 4.4.5 WATERLOO Seasonal Percentage Change in IDF Curves for Time Series: 1970- 1984 and 1985 - 2003 110 Table 4.4.6 BOWMANVILLE Seasonal Percentage Change in IDF Curves for Time Series 1966 -1984 and 1985 - 2001 Ill Table 4.4.7 BURKETON Seasonal Percentage Change in IDF Curves for Time Series: 1969 - 1984 and 1985 - 2001 112 Table 4.4.8 KINGSTON Seasonal Percentage Change in IDF Curves for Time Series 1960 - 1981 and 1982 - 2003 113 Table 4.4.9 ORILLIA Seasonal Percentage Change in IDF Curves for Time Series 1965 - 1978 and 1979 - 1992 114 Table 4.4.10 OSHAWA Seasonal Percentage Change in IDF Curves for Time Series 1969 - 1984 and 1985 - 2003 115 Table 4.4.11 CHALK RIVER Seasonal Percentage Change in IDF Curves for Time Series: 1962 - 1978 and 1979 - 1995 116 Table 4.4.12 SUDBURY Seasonal Percentage Change in IDF Curves 117 for Time Series 1971 - 1984 and 1985 - 1996 117 Table 4.4.13 TIMMINS Seasonal Percentage Change in IDF Curves for Time Series 1969 - 1984 and 1985 - 1999 118
vi LIST OF FIGURES
Figure 2.1 Schematic view of the components of the global climate system 11 Figure 3.1 Observed heavy rainfall data arranged in the order of magnitude for annual maxima and partial-duration series 35 Figure 4.1 Map of the Stations in Ontario 46 Figure 4.3 Flow Chart for IDF curves Temporal Assessment 52 Figure 4.5.1 Temporal Percentage Change in IDF Curves for 5 year Recurrence Interval: Storm of 30 minutes duration 57 Figure 4.5.2 Temporal Percentage Change in IDF Curves for 5 year Recurrence Interval: Storm of 60 hr duration 58 Figure 4.5.3 Temporal Percentage Change in IDF Curves for 5 year Recurrence Interval: Storm of 2 hr duration 59 Figure 4.5.3 Temporal Percentage Change in IDF Curves for 5 year Recurrence Interval: Storm of 6 hr duration 59 Figure 4.6.1 Temporal Seasonal IDF Changes at Port Colborne Station Compared with Temporal Changes in Full IDF curves for Time Series: 1962 - 1978 and 1979 - 1995 61 Figure 4.6.2 Temporal Seasonal IDF Changes at Oshawa Station Compared with Temporal Changes in Full IDF curves for Time Series: 1969 - 1984 and 1985 - 2003 63 Figure 4.6.1 Temporal Seasonal IDF Changes Sudbury Station Compared with Temporal Changes in Full IDF curves for Time Series: 1971 - 1984 and 1985 - 2003 65 Figure 4.7 IDF Curves Comparison for Waterloo Station and 5 Year Event ..69 Figure 4.8 Graphical Demonstration of Change in Rainfall Frequency for 2 Year Event at Waterloo Station 71 Figure 4.8 Best-fit Curve Graphical Evaluation at Waterloo Station for 5 year Event, and period of observation 1985-2003 74 Figure 4.9 Recurrence Intervals Confidence Region Graphical Estimation for Period of Observation from 1970 to 2003 at Waterloo Station for 1 hr duration and 33 Samples 80 Figure 4.10 Recurrence Intervals Confidence Region Graphical Estimation for Period of Observation from 1970 to 1984 at Waterloo Station for 1 hour duration and 15 Samples 81 Figure 4.11 Recurrence Intervals Confidence Region Graphical Estimation for Period of Observation from 1985 to 2003 at Waterloo Station for 1 hour duration and 18 Samples 82
VII Figure 4.2 Microsoft Access Query for Percentage of Missing Data Calculations for Element 127(i.e. 15 minutes duration) at all Stations 119 Figure 4.4 Interface of Computer Program Developed in Microsoft Access for IDF Analyses with Attached Output Table 120 Figure 4.5 Interface of Computer Program Developed in Microsoft Access for Seasonal IDF Analyses with Attached Output Table 121
viii CHAPTER 1 INTRODUCTION
1.1 RESEARCH MOTIVATION
Naturally occurring greenhouse gases such as nitrous oxides, water vapor, carbon dioxide, ozone and methane have a critical function for Earth's temperature - controlling system. The role they provide is responsible for
maintaining the temperature of the Earth as 20°C to 30°C warmer than it would be without this natural greenhouse blanket. However, anthropogenic activities are changing the concentrations of these constituents within the atmosphere. One of the most reliable sources of information on climate change and its causes, the Intergovernmental Panel on Climate Change
(IPCC), endorse in their reports that the observed increase in anthropogenic contributions in greenhouse gas concentrations has witnessed increased temperatures since the mid 20th century. Additionally, the global concentration of carbon dioxide in 2005 has reached 379 parts per million
(ppm) from the pre-industrial level of 280 ppm,(IPPC, WGI Fourth
Assessment Report, 2007) and hence there has been increasing concern that the concentrations of greenhouse gases are influencing surface air temperature. Further, according to IPCC, carbon dioxide levels above 500 ppm are considered to pose a "dangerous" level of interference with the climate system, with an increase in global temperature affecting the hydrological cycle (Houghton et al., 1996) and influencing water resources
(Brent and Yu, 1999).
1 In the review of the world's scientific literature on climate change, the
IPCC states that "more intense precipitation events" are becoming very likely
over many areas. The climate and water- related variables may be driven by
influences of greenhouse gases. Thus, a continuing trend of greater
precipitation and more frequent intense rain events is "very likely", as the
IPCC has phrased it (Bruce et al., 2005), and precipitation over many mid to
high latitude land areas in the Northern Hemisphere has become more and
more intense (IPCC, 2001).
The latest IPCC report proposes that since the IPCC Third Assessment,
confidence that some extreme weather events will become more frequent,
more intense, and more common through the 21st century has increased. In
addition, as indicated by IPCC table SMP-2 in their fourth report (2007), there is a high likelihood of a number of phenomena. The likelihood of
occurrence in this report is indicated as very probable (e.g. 90-99 %
probability of occurrence) for heavy precipitation events and heat waves with
increased frequency over most land areas.
Consequently, the hydrologic cycle is likely to intensify due to
increases in greenhouse gases concentration in the atmosphere and temperature, respectively. Furthermore, changes in hydrological regime that do occur as a result of changes in both precipitation and evapotranspiraton are not expected to be equally distributed during the year (Burn et al.,
2002).
2 Although different water resources infrastructure systems are designed for various levels of service, the most important meteorological variable for decision - making and design procedures is precipitation. Even a small shift in precipitation intensity and frequency might generate substantial adverse effects for water resources infrastructure. Unfortunately, the expected changes in climate regime could result in our current water resources design approach being rendered inappropriate to maintain the desired level of service and protection (Bruce et al., 1999).
Diverse studies have investigated consequences of climate change effects in Canada, and worldwide. Zwiers et al. (1998) identified that one-day heavy rainfall frequency could appear with halved recurrence intervals.
Groisman et al. (1999) analyzed mean summer daily precipitation data from
93 stations within Canada and showed that an increase in mean summer precipitation by 5% is followed by 20 % increase in the probability of summer daily rainfall data above the specified threshold (i.e., 25.4mm ) with no change in number of days with rain. Hence, based on the statistical model developed by Groisman et al. (1999) to evaluate changes in the probability of heavy daily precipitation, the frequency of heavy rainfall exceeding the threshold value has increased four times in mean precipitation for Canada.
Precipitation daily totals data from 489 stations across Canada were analyzed for the observation period from 1900 to 1998 by Zhang et al. (2000) where they indicated that the annual total precipitation has changed from -10% to
35 % for different seasons and regions across the country. Precipitation events greater than the 66th percentile (i.e. unusual wet conditions) have
3 increased during the period of observation. Besides, atypical dry conditions
(e.g. precipitation less than 34 the % percentile) have been decreased.
In the study by Adamowski et al. (2003), annual maxima data for stations across Ontario were used to analyze the trend in rainfall data. The significance of the trend was evaluated by the Mann - Kendall trend test for single sites. Trends were detected for locations across Ontario and short duration storms (e.g. from 5 minutes to 1 hour). This study indicates that different trends and propensities are present for different regions across
Ontario as characterized by observed data.
Several studies and reports explored climate change impact on
Canadian drainage infrastructure (Watt et al., 2003; Coulibaly et al., 2005) among others. Despite the fact that different methodologies were used in existing infrastructure studies, all of them generate judgment that in the future, we can expect drainage infrastructure systems failure to perform as designed, if climate change influence in rainfall intensity is overlooked.
Moreover, the potential risk of failure of drainage systems might
increase vulnerability of Canada's other water resources infrastructure systems, and have adverse consequences on water quality, human health, environment, and the economy.
All of these studies indicate that rainfall statistics are changing and intensities of heavy rainfall events are, overall, on the rise. While important, the previous studies have not demonstrated whether the intensity-duration- frequency curves for the fundamental inputs to urban infrastructure design
4 should be changed, and by which magnitude. Urban infrastructure is
intended to function for many decades and hence design scenarios need to
reflect the projected rainfall intensities in order to maintain the level of
desired operational capacity.
Additionally, current trend analyses in extreme rainfall events are
based on annual maxima series while the second or third highest values
within one year are neglected. With increasing rainfall intensities due to
climate change, disregarding the second or third value within a particular year of observation may make water resources infrastructure more sensitive,
especially those designed based on short duration rainfall. Hence, there is
merit in considering use of the partial duration series.
1.2 OBJECTIVES
The main goal of this research is to examine trends in extreme rainfall and to improve understanding of the vulnerability of Ontario water resources
infrastructure due to climate change consequences. To accomplish this objective, the following methodologies are employed:
• Review selection of criteria and techniques to be applied for IDF
curve analyses.
• Single site IDF curves temporal evaluation in partial duration
series data for locations across Ontario for different record
lengths, and rainfall durations.
5 • Comparison of existing IDF curves and those estimated by
partial duration series for a case study area and analyses of
existing water resources infrastructures under the different
circumstances.
• Temporal trend analyses in partial duration series for different
seasons in the Province of Ontario.
• Examine trend detection in number of dry days and amount of
rain for rainfall stations within different regions within Ontario
and selected duration of rain by the linear regression tests and
the Mann - Kendall test.
• Evaluate heavy rainfall frequency confidence intervals for
selected case study area and duration of rain.
1.3. SCOPE OF THE THESIS
This thesis consists of five chapters. The first chapter is a general introduction to climate change and its consequences on rainfall, accompanied by research motivation and objectives. The second chapter contains a literature review for local point rainfall data frequency analyses and climate change studies/Chapter three contains the theoretical basis and different methodologies used in heavy rainfall and trend detection studies. The adopted methodology, model development, and application for 14 stations in
Ontario, including a case study for Waterloo, and confidence intervals for
6 rainfall frequency, are provided in chapter 4. Chapter five contains research conclusions and recommendations for future work. CHAPTER 2 LITERATURE REVIEW
2.1 METHODOLOGIES AND REVIEW OF CLIMATE CHANGE STUDIES
Climate change refers to a statistically significant variation in either the mean state of the climate or in its variability, persisting for an extended
period (typically one decade or longer), and it may be due to natural processes, or to continuous anthropogenic change in land use, or in the composition of atmosphere (IPCC, 2001).
During the past few decades, increases in the concentrations of the greenhouse gases accompanied with increases in global temperature have arisen as a major scientific issue worldwide. While the IPCC First Assessment
Report was published in 1990, the potential sensitivity of Earth's climate to the concentrations of greenhouse gases had been evaluated more than a century ago by different scientists (e.g., Mariotte, 1681; Benedict de
Saussure, 1760; Fourier, 1824; Tyndal, 1861). In 1895, Arrhenius described what is now known as the greenhouse effect in which a 40% increase or decrease in the C02 might provoke the glacial advances and retreats
(Fleming, 1998). One century later, it would be confirmed that the initial studies predicted climate change phenomenon very well (IPCC, 2007).
2.1.1 Methodologies Used in Previous Climate Change Studies
The climate system is complex in its nature; thus any change in one variable (e.g. changes in greenhouse gases concentration) could precede a change of other variables within this system (e.g. temperature). 8 To deal with climate change complexity, scientists worldwide have used various methodologies to examine diverse meteorological variables, to evaluate their effects on different sectors (e.g. water resources, human health, etc.), and to predict future climate change scenarios to provide governments, local authorities, and public with vital information to mitigate possible climate change impacts.
Diverse methodologies have been used in recent studies to minimize uncertainties related to climate change at the global, regional, and local levels. Namely, General Circulation Models (GCMs) and various statistical analyses (e.g. Gamma distribution, Generalized Extreme Value I distribution, various methodologies for trend detection, etc) have been employed.
The former were mainly used in prediction of future climate scenarios based on meteorological data archives, while the latter were applied by scientists in the evaluation of empirical data time series for different meteorological and hydrologic variables (Karl et al., 1995; Groisman et al.,
1999; Zhang et al., 2000; Burn an Elnur, 2002; among others)
Although the recent GCM spatial scales are more suitable at regional and global levels than at the local, watershed scale, there is general agreement that climate has changed, and that those changes may affect the frequency of climate extremes and hydrologic variables. Based on current bodies of knowledge, it is likely that the origins of these changes are anthropogenic more than natural during the last century (IPPC, 2007).
9 Broad agreement in the international scientific community exists that global climate change will alter the frequency and magnitude of hydrologic extremes due to higher air temperatures and, as a result, the enhanced hydrological cycle will then likely produce extremes different from those historically observed (Cunderlik and Simonovic, 2005).
Furthermore, due to linkages between water resources infrastructure systems, it is likely that any change in the frequency of extremes will result in increasing vulnerability of Canada's infrastructure systems and the value for improving the resiliency of those systems is accelerating (McBean, personal communication, 2006).
Constituents of the global climate system components, their interactions and processes, accompanied with some features which may be changed (e.g. hydrological cycle) due to climate change are presented schematically in Figure 2.1.
10 Cryosphere: Sea Ice, Ice Sheets, Glaciers
Changes in the Ocean: Changes Won the Land Surface: Circulation, Sea Level, Biogeochemistry Orography, Land Use, Vegetation, Ecosystems
2.1.2 Preceding Climate Change Studies Review
Prior to the 1990s, a major focus in climate change studies was on the global scale, while more attention to regional and local climate change consequences has developed afterwards. The study by Nemec and Schaake
(1982), in which they analyzed effects of precipitation and temperature changes on river flows and reservoir operations for several catchments in
North America was innovative in this respect (Burlando and Rosso, 2002).
Since then, research interest in climate change effects, on both local and global level has, increased.
A comprehensive literature review of the climate change is provided in the IPCC reports. In their Third Assessment Report (2001) they revealed that
11 in the mid and high latitudes of the northern hemisphere, heavy precipitation extremes have increased, accompanied with increases in precipitation totals.
Additionally, in some regions (such as eastern Asia) where downward trends
have been detected in total precipitation, extreme rainfall events have increased.
Possible changes in summer heavy rainfall probability in eight countries was subject of a study by Groisman etal. (1999). Subsets of century-long daily precipitation data for 113 stations in Australia, 93 stations in Canada, 13 for Norway, and 134 in the United States, whereas for China
(198 stations), Mexico (202 stations), Poland (10 stations), the former Soviet
Union (223 stations) and additional 226, 8, and 53 daily record for Australia,
Norway, and the United States of America, respectively with shorter time series (e.g. 40-60 years) were evaluated in their analyses ( refer to
Groisman et al., 1999).
Heavy rainfall events in these analyses are accepted as values above the thresholds of 25.4 mm for northern hemisphere, and 50.8 mm in mid -latitude countries and Australia, respectively. The modified gamma distribution statistical model was used in the analyses with the assumption that the frequency of daily precipitation events has a binary distribution and the amount of rain during this event, a gamma distribution, results in the three parameter distribution: shape, scale, and probability of daily precipitation. Lastly, 5 % increases in the mean daily precipitation were applied to observed data, since increases in this variable in all of the
12 evaluated countries (except China) has been found to be at least 5 % (IPCC,
1996; among others).
For southern Canada, Norway, Poland, and the former Soviet Union,
increases in heavy precipitation have been 20 %, and their contribution to
summer precipitation totals differ from region to region. In Canada,
Kazakhstan, Norway, and Russia, this contribution is less than 5 %, and less than 10% for Belarus, Poland, and the Ukraine. Nevertheless, those events above a threshold of 24 mm in Canada, northern Norway, and Russia contribute up to 30 % in the increase in mean daily precipitation, and more than 40% in Belarus, Poland, southern Norway, and the Ukraine.
Moreover, in the eastern United States of America, a 5 % rise in daily
precipitation is causing an increase in the likelihood of rainfall above threshold (i.e. 50.8 mm) by almost 20 %, which is compatible with studies of
Karl et al. (1995), and Karl and Knight (1998) in the United States.
Furthermore, in the Mississippi watershed, heavy rainfall events contribute
up to an increase of 50 % in mean summer precipitation (Groisman et al.,
1999).
In Australia and China, heavy rainfall events above the threshold of
50.8 mm have increased from 10 - 20 %. This increase is less noticeable in coastal and inland areas in China with higher precipitation rates, and the contribution to summer totals vary from more than 50 % over eastern China up to 70 % over the tropical parts of southern China except in the Sinkiang
Province, i.e. northwestern part of China and Tibetan Plateau that are too
13 arid, and there is no heavy precipitation during the summer season
(Groisman et al., 1999).
In Mexico, increases of 10-20 % in mean precipitation during the 20 th century are indicated by IPCC (1998). Increases in mean summer precipitation by 5% generated increases in heavy rainfall probability from 20
-30 %, with contribution of those events in mean summer precipitation more than 70 % over the tropical regions of Mexico, except for arid regions.
On the whole, Groisman et al. (1999) substantiated that an increase in mean summer precipitation by 5 %, with no change in the number of days with precipitation, generate increases in probability of heavy rainfall events by about 20%, which is four times the increase in mean daily precipitation.
A study by Kiely et al. (1999) investigated climate change impacts in
Ireland. They evaluated 34 to 50 years of observed data for hourly precipitation and partial -duration series (PDS) of extreme events for different durations, i.e. 1-24 hours at eight sites, and daily streamflow data at four rivers with the same length of record. Precipitation statistics were compared for two periods of observation, namely pre -1975 and post -1975 records for different time series: annual, biannual, quarterly, and monthly
(e.g. March and October).
In general, there was a change point in the mid-1970s (after Kiely at al., 1990), in precipitation and streamflow observations, with prevalent increasing trends in both precipitation and streamflow data in the latter period (after 1975). For the annual and monthly time series, for streamflow
14 data, there was an increasing trend for all stations, with different levels of significance, e.g. from 0.72 to 0.99 for the River Boyne at Slane in October, excluding October at one site for the River Erne at Belturbet, represented a significant decreasing trend (i.e.0.98) was detected. Differences were observed in precipitation data in annually and monthly data series. For the former, downward trends with different levels of significance (e.g. 0.52-0.88) were detected at five sites, specifically, at Dublin, Cork, Shannon, Rosslare, and Birr stations, while an upward trend manifested level of significance from
0.95 to 0.99. In the latter time series (i.e. monthly), increasing trend was observed for all stations and both in March and October with different significance level ranging from 0.68 to 0.99.
Statistics of extreme events have also changed, based on the study by
Kiely et al. (1999). Kiely et al. compared PDS for full observation interval with time series after mid-1970s (i.e. 1975). For 24 hour duration, and 30 years recurrence interval, increasing in precipitation depth is 25%, which indicates that the 10 year curve for time series after 1975 become the 30 year curve for the full period of observation. Additionally, of the order of
magnitude of twenty PDS for eight different durations and full time series there are approximately twice as many high values in the post-1975 period
(Kiely et al., 1999).
For Canada, Stone et al. (2000) evaluated precipitation data for 69 stations scattered across the country with different lengths of records from
34 - 102 years. Three different intensity classes (p): light, intermediate, and heavy were assessed based on threshold value for each station for yearly and
15 seasonal time series which were joined together to produce five regional data sets. Precipitation intensity classes were assessed based on following criteria: light intensity class {(0.6 {(2 Heavy precipitation events increased in May, Jun, and July in southwestern Canada, while downward trends were found statistically significant at 5 % in the intermediate and light events classes, for the former during the spring season, and for the latter in winter seasons, respectively. In the northwestern region, increases in frequency of heavy events were detected in the winter and spring seasons, while a downward trend was observed for light events. Intermediate events have become more frequent in December, January and February (Stone et al., 2000). Decreasing frequency of light precipitation events during the winter season was observed in southeastern region, were accompanied by increases in the intermediate and heavy events in summer and fall. In the Arctic region of Canada, light events (as they are defined in this study) trends remained stable, intermediate and heavy events generally increased for all seasons, excluding the summer season (Stone et al., 2000). 16 Precipitation and temperature trend analyses for Canada were additionally reported in Zhang et al. (2000). They evaluated data from the 210 stations to detect trends in temperature and data from 489 stations daily precipitation were used for precipitation analyses, with record lengths from 1900 to 1998. Due to lack of data prior to the 1950s in the high Arctic, two different time series were used in the analyses: in Canada as a whole, trends were estimated based on shorter time series and for southern Canada, longer time series were used, 48 and 98 years respectively. Evaluations of trend detection were performed for six elements (e.g. minimum temperature, precipitation totals, maximum temperatures, etc). These were supplemented by precipitation and temperature analyses for abnormal and extreme climate conditions. The former, i.e. abnormal conditions, were characterized in this study as a threshold below 34 % or above 66% for these meteorological variables in their relevant time series, while the latter were defined similar to those by Jones et al. (1999) among the others, namely, precipitation or temperature lesser than 10 % or higher than 90%. Across Canada, temperature has increased by 0.3°C, with strong pattern of cooling in the northeast (1.5 °C), while warming was detected in the southwest (e.g.l.5°C -2°C). Furthermore, the areas in the southern regions affected by abnormally low temperatures decreased since 1960, while little trend has been detected for abnormally high temperatures. Canada has become less cold as reported in Zhang et al. (2000). Annual precipitation totals increased in general by 5-35 % during the second half of 20th century, in some regions downward trends were observed 17 during the winter season, in contrast upward trends were observed in all seasons with most significant increasing detected in the Arctic region (Zhang et al.,2000). Observed changes in the abnormal weather conditions were different for the first and second half of the century in southern Canada where areas affected by wet conditions increased by 27.3 % and dry conditions decreased by 23.4% on an annual basis, while on a seasonal basis the highest change had been detected during the winter season, 25.6 % decreasing and 21.4 % increasing for dry and wet conditions, respectively. Although in general, results for extreme climate conditions were comparable with abnormal weather conditions, there is a difference for precipitation in summer season, i.e. 1.4 % and 5.2% increasing in extremely dry and wet climate conditions, respectively (Zhang et al., 2000). The fact that temperatures in summer and areas affected by extremely dry and wet conditions demonstrated an upward trend may be an indicator of a reinforced hydrologic cycle (Zhang et al., 2000). Brunetti et al. (2000) examined trends in precipitation intensities in Northern Italy for five stations and different length of records: Genoa (1833- 1998), Milan (1858-1998), Mantova (1868-1997), Bologna (1879-1998) and Ferrara (1879-1996). For each station, a gamma distribution was fit to daily data for each month, following with yearly and seasonal calculations of for precipitation, number of rainy days (e.g. precipitation equal or greater than 1 mm ), amount of rain per day, and proportion of daily precipitation (DP) 18 failing in five different precipitation class intervals:0-2.5 mm, 2.5-12.5mm, 12.5-25 mm, 25-50 mm, and DP values greater than 50 mm. Examination of the trend in data series was performed by using the Mann - Kendall test. The above results indicate a downward trend, both on seasonal and annual bases in number of rainy days and total precipitation, higher significant negative trend was detected for the former than latter variable, with confidence interval > 99 % on a yearly basis (Brunetti et al.,2000). In contrast, an upward trend was detected in precipitation intensity, which results in increases in proportion for higher daily precipitation class intervals, e.g. equal or greater than 25 mm, and decreases in the proportion of lower intervals, respectively. Additionally, the Mann-Kendall test application provided evidence that the trend predominantly has occurred in the last 60-80 years in Northern Italy. In the report presented by Kije Sipi Ltd (2001), the possible change in level of service for existing drainage systems due to climate change were evaluated for the Ottawa region. Two hydrologic models were used in this study: Rational Method and Hydrograph model SWMHYMO. Existing IDF curve intensities were increased from 5 to 20 %, based on literature review, and temperatures were increased 2-4 °C to evaluate the hydrologic consequences. Different scenarios with change or no change in impervious, CN number, runoff coefficient, different increasing in both precipitation (from 5% to 20 % in increments of 5 %) and temperature were applied in models for urban and rural areas. 19 Peak flows calculated by both methods increased consistently more than rainfall intensities for all recurrence intervals with ratio from 1.1:1 to 1.35:1, for the Rational Method and SWMHYMHO, respectively. Additionally, increases in pipe size were predicted to differ 2 % - 5 % for 5 % increasing in intensity of rainfall up to 8% - 15 % for 20 % increased rainfall intensity (Kije Sipi Ltd., 2001), In summary, based on Kije Sipi Ltd (2001) with 5 % increasing in rainfall intensity, drainage systems designed based on 5 year return period could safely convey 4 year design storm, and for an increase in rainfall by 20 % level of service could be lessen by two, i.e. 5 year design could be reduced to approximately 2.5 year. Moreover, 10 year design storm by 20 % increasing in rainfall intensity will have 4 year level of service. However, this is very generalized statement and would need to be evaluated in specific circumstances. Burn and Elnur (2002) evaluated trends in 18 different hydrologic variables ,e.g. annual mean flow, annual maximum and minimum flows, monthly mean flow for each month and station, maximum daily flow date, date of start and end of ice conditions , and number of ice days, for network of 248 Canadian catchments, and record lengths at of least 20 years. Furthermore, correlations between selected hydrologic and meteorological variables were evaluated for several locations. Strong increasing trends were observed in the monthly mean flows in March and April. On the contrary, the monthly mean flows displayed strong 20 decreasing trends in June and October, with strong spatial variability across Canada. In the Great Lakes St.- Lawrence region, an increasing trend in monthly flows were observed in January, October, and November, accompanied with increases in annual flow, while in the Pacific climate region, the annual flow decreased as well as the monthly flows from May to October, except the monthly flow in April (Burn and Elnur,2002). For all selected locations similar trend directions were observed in the hydrologic variables and the meteorological variables used in this set of analyses. The monthly flow for August was strongly positively correlated with the August precipitation in the Atlantic area for the Torrent River, namely, significant at the 1% level. Moreover, in both variables increasing trends were observed in the late 1960s, followed by decreasing trends for both since then. Significance levels for the August flow were 10 %, while the precipitation decreasing trend was observed to be weak and it is not significant at the 10% level. Aronica et al. (2002), analyzed changes in extreme rainfall for the urbanized area of Palermo, Italy. Observed annual maxima data from eight stations, and length of record 70 years with fixed duration (1, 3, 3, 12, 24 hours) were fitted by Gumbel distribution for external and internal areas for 10 year recurrence interval. Aronica et al. (2002) based this work on two different approaches. The first approach evaluated only data for the last 20 years of observation, while 21 the second approach estimated data based on all historical observations, for both external (less urbanized) and internal, i.e. urbanized area . Analyses of total annual precipitation found decreasing trend, which is more regular for rural rather than urban areas. Moreover, decreasing trend has been observed for 10 year recurrence interval in annual maxima series either by the first or the second approach applied in this study, for both external and internal areas, with higher variability and more significant trend in the internal areas. In the study by Adamowski et al. (2003), annual maxima (AM) time series for 15 locations across Canada were evaluated to detect the trends for short duration rainfall (5,10,15,30 minute, and 1 hour). Gumbel distribution was used to fit AM data, conducted with estimation of direction, magnitude, and significance of trend, and change in frequency for different durations due to trends in observed data. Except for Burketon (5 and 10 minute duration), Port Colborne, i.e. 10 minute, and Delhi for 5 minute duration, trend rates for the rest of stations and all durations of rain evaluated by Adamowski et al. (2003), are positive, with average rate of 0.07, 0.09, 0.14, 0.20,and 0.21 for durations of 5,10, 30 minute and 1 hour, respectively. Additionally, a total of 22 tests were found to be significant; specifically 12 tests at 5 %, and 10 tests at 10 % significant level, for increasing trends, with the highest value for duration of 10 minute at Orillia station. Furthermore, with increasing in return period IDF compared values 22 with and without trends lessened. The highest increasing observed for storm durations 15 and 30 minutes, 15.55 and 33%, respectively. Climate change effects on future drainage infrastructure design standards in Ontario were evaluated in study by Coulibaly and Shi (2005). Data sets for AM series and maximum daily precipitation for two regions Grand River region, and Kenora and Rainy River region, each of them consists of four stations in this study, were evaluated to detect the trends in both precipitation (Mann - Kendall test) and IDF curves in two time series, namely, 1961-1980 and 1981-2000 for different recurrence intervals. Furthermore, downscaled Canadian Global Circulation Model (CGCM2) was used to predict possible future climate patterns based on detected trends in observed data. They then assumed these changes would occur to predict the change in change in pipe diameter with future climate projections using the Rational Method for two areas. Upward trends were observed on precipitation data for seven locations, of which six are insignificant (p= 0.1-0.68) and one is significant, except for Glen Allan station where no significant downward trend was detected. It appears from study by Coulibaly and Shi (2005),that rainfall intensity increased in latter time series for all return periods and all locations, except for one location, with variations for various recurrence intervals and locations, e.g. at Woodstock station (Grand River region), increasing in 24 hr intensity in latter period is 19.6% for 2 year recurrence interval and 59.7% 23 for 100 year recurrence interval, while downward trends were detected at Glen Allen station, -1% for 2 year recurrence interval and -14% percents for 100 year recurrence interval. Furthermore, it was observed that current 10 year drainage system will be able to convey only a 5 year storm by 2050s. Based on this study (Coulibaly and Shi ,2005), in Southern Ontario there will be significant changes in the design discharge and related pipe diameter in the future, for the 10 recurrence interval observed change in 2050, and 2080 pipe diameter should be increased by 10% and 16 %, respectively. 2.2 LOCAL POINT RAINFALL DATA FREQUENCY ANALYSES 2.2.1 Probability Distributions Statistical analyses of rainfall data are of great interest for both single site and regional analyses since this variable is one of the most important inputs for different planning and design purposes in water resources. The first step in this analysis is to select a theoretical probability distribution that is appropriate to exemplify data of interest. Although many well - defined probability distributions are used to evaluate and explain rainfall phenomena, it be understood that any theoretical distribution is only a description which approaches natural processes and it is not an exact description of them (Viessman et al., 1977). Hydrologic variables are assumed to come from continuous random processes and hence theoretically, almost all existing continuous frequency 24 distributions may be applied in frequency analyses to fit historical time series. However, based on experience, only a limited number of probability distributions are applied successfully to empirical data, i.e. Gaussian (normal), lognormal, Gamma ( with two parameters, and Pearson III type), and simple and double exponential distribution (Yevjevich, 1971). The World Meteorological Organization (1981) indicated that the most widely used probability distribution in extreme rainfall analyses is Gumbel, also known as Extreme Value I (EV I)or Fisher-Tippet type I distribution. This is a two parameter (a and |3) distribution with constant skewness and kurtosis coefficients, 1.11396 and 4.5,. respectively. Parameters a and B are scale and location parameters, and a function of the mean and standard deviation. This distribution has been questioned and reviewed since it was presented. Barricelli (1943) and Brooks and Carruthers (1953) discovered that for rainfall data, this distribution underestimates maximum rainfall data for long recurrence intervals (Chow et al., 1964). An objection was made by Yevjevich (1971) since the application of this distribution to positive -valued variables which cannot be less than zero is not applicable and that the lower part of distribution losses its practical importance. In the study by Uppala (1978) different extreme value distributions were evaluated. It had been detected that rainfall data in western Finland are best fitted with extreme value II (EV II) distribution, while for the eastern part of Finland Extreme Value III distribution was the best choice. 25 In Ontario, Pilon et al. (1991) reported that the rainfall data were best fitted by the General Extreme Value Distribution where parameters are based on duration of storm and mean annual precipitation. Wilks (1993) analyzed eight three-parameter distributions both for annual maxima and partial-duration series data for fourteen stations in the northeastern and southeastern United States, with different lengths of records, e.g. from 38 to 90 years, respectively. Based on this study, the Gumbel distribution underestimated rainfall with lower frequency of occurrence, e.g. the 50 and 100 year events in each data series. Furthermore, in annual maxima series, the right tail of distribution was best indicated by the beta-k distribution, while for partial duration series the best distribution was found to be the beta-P distribution. Analogous results were reported by Keim and Faiers (2000) for the western Texas region, and the study by Koutsoyiannis and Baloutsos (2000) for Greece. In the latter study it was reported that EV I distribution underestimated large recurrence intervals by 1:2 when it was compared with GEV distribution, while for shorter records and recurrence intervals, the Gumbel distribution was found to be appropriate to fit the observed data. Subsequent to selection of the probability distribution is the task of parameter estimation. Several methodologies were found to be appropriate in this procedure, namely graphical estimation method, method of moments, maximum likelihood, and least-squares estimation method. 26 The method of moments had been recommended to be used in extreme rainfall data analyses by Gumbel, while some other authors found out that there might be some questions about that methodology for variables that are more or less skewed (Yevjevich, 1971; Matalas and Wallis; 1973, among others) reported that Maximum Likelihood procedure should be used in parameter estimation. Despite the fact that the above- mentioned comments have raised questions about the Gumbel distribution accuracy and its application in extreme rainfall analyses, this methodology is still the most popular among the scientific and engineering communities worldwide. 2.2.2 Recurrence Interval and Frequency Factor The most important information from the perspective of frequency analyses used in hydrology is to provide design values as input for different water resources design and decision- making procedures. Although different probability distributions might be used to fit the observed data (e.g. two, three parameter distributions) the most important information concerns the recurrence interval or exceedance probability of events design value. Although the use of the latter has been recommended by American Society of Civil Engineers (ASCE, 1996a), to avoid misunderstanding that for example, 10 years rainfall is equaled or exceeded once in every 10 years, in this thesis the term recurrence interval is used. The following methodologies can be applicable in estimation of frequency for selected distributions: • Frequency Histogram 27 • Probability Plots • Frequency Factor Frequency Histogram is a graphics exhibition of data set frequencies in which the spell of possible values is divided in subintervals, known as class intervals. For the finite or small simple sizes which are common in hydrologic analyses, frequency histograms are not practically applicable, since it is impossible to determine the shape of distribution for smaller sample sizes (Kendall, 1966) and different hydrometeorological questions cannot be answered with data grouped in class intervals (Yevjevich,1971). The second procedure employs different plotting position formulas. The first step is to rank data for n observations, where a rank (m) of 1 is applied to the largest value to calculate the plotting position P. The second step is frequency analyses of data by plotting the magnitude versus a cumulative distribution function (McBean and Rovers, 1998). Different probability papers are used for visual assessment of data (e.g. normal, lognormal, Gumbel, etc). The recurrence interval (R) of m - ranked observations is commonly estimated by Weibull (1938) plotting formula for n number of samples. Although the Weibull plotting position formula is generally used for graphical estimation of frequency and magnitude in extreme events analyses and it had been advocated by many scientists and engineers e.g. Gumbel (1954), Yevjevich (1971) among others, during the last decades questions about its usage have arisen. Different scientists (Gringorten, 1963; Cunnane, 1978; Harter, 1984) among others reviewed and discussed different plotting position formulas for the general extreme value distribution (GEV) and its 28 special case Gumbel or Extreme Value I distribution (EV I). In the study by Guo (1990), four plotting formulae for GEV were assessed: Weibull (1938), Cunnane (1978), Arnell et al. (1986), and In-na and Nguyen (1989). The results of this study illustrated that Cunnane formula, which is based on Gringotern's formula (1963) is the least biased for GEV distribution with respect of predictive ability, while the Arnell et al. (1986) formula performed with less accuracy than Weibull formula, and had the largest absolute deviation and root mean square errors than other three formulas. The third methodology used in frequency analyses is application of frequency factor Kt proposed by Chow (1951). Design value is estimated by: Xt=x + KtS (2.1) Where Xtis designed value for recurrence interval of interest, xis mean, S is standard deviation, and Kt is frequency factor which varies with sample size and recurrence interval and its values are available for various sample sizes and recurrence intervals in the form of tables. 2.2.3. IDF curves The most common and widely applied formula used to express heavy rainfall intensity-duration -frequency relationship (IDF) in mathematical form is Sherman's (1931) formula: I(t)=7ir^ (mm/hr) (2.2) 29 In the above formula, I (t) represent maximum rainfall magnitude for different rainfall durations (e.g. 5, 10, 30 minute, 1, 2, 3 hr, etc), and a, b, and c are fitting coefficients that vary with frequency and location. For given rainfall intensity and duration, their values might be obtained by log-linear transformation or the method of least squares. In Canada, IDF curves are readily available countrywide, and are usually provided by Environment Canada and local municipalities, or from the Rainfall Atlas for Canada. Commonly, the annual maxima extreme rainfall data are fitted with the Gumbel (EV I) distribution for observation period. By reason of their importance, the IDF curves maps have been developed in different countries, e.g. in the United States of America (Hersfield, 1961; Miller et al., 1973; among the others), India (UNESCO, 1974), the United Kingdom (National Environmental Research Council, 1975), Sri Lanka (Baghirathan and Shaw, 1978), Namibia (Pitman, 1980), Australia (Canterford et al., 1987), etc. Since IDF curves are used as input to various water resources design methodologies, their mathematical form (equation 2.2) has been reviewed by scientists worldwide. Bell (1969) proposed Generalized Rainfall -Duration- Frequency Relationship, Chen (1983) established a new rainfall -duration frequency formula in which the maximum rainfall rate in one hour has been used as a rescale factor. In recent decades, various authors used different IDF curve equations in rainfall analyses. Cassas et al. (2004) applied the formula proposed by 30 Chen (1983) to analyze rainfall data in Barcelona, Spain, while formula presented by Koutsoyiannis et al. (1998) had been used in studies by Koutsoyiannis and Baloutsos (2000) for IDF curves study in Athens Greece and by Mohymont et al. (2004) for both local, and regional IDF curves analyses in Central Africa. Although some new formulas had been proposed for IDF curves, in this thesis, Equation 2.2 is used since it is the mostly used worldwide, including Canada. 2.3 TREND TEST Detection of trends in hydrometeorological variables is very important in climate change studies. Although various authors had used data with different record length, sometimes it is very difficult to detect significant trends in either longer or shorter time series. Two main groups of trend detection test are available, namely parametric and nonparametric tests. 2.3.1 Linear regression Although linear regression is one of the most common trend tests, it requires some assumptions e.g. data are normally distributed, independent, linear related, which is not likely for hydrologic data in general, linear regression is not a powerful tool to be used in their evaluation and trend detection. However, this trend test can be considered for the first estimation of trend in data series, in a correlation assessment between two variables 31 e.g. daily flow and precipitation. In some situations complex distributions can be transformed to be normally distributed (EPA, 2006). 2.3.2 Mann- Kendall non - parametric test There are many practical applications where the assumption of normality cannot be met. For that reason, statisticians had developed alternative techniques which have become known as non-parametric tests (Miller and Freund, 1985). Mann -Kendall test had been used in various studies e.g. Brunetti et al. (2000) applied this test in rainfall data analyses, Burn and Elnur (2002) used this test for regional hydrologic trend analyses in Canada, Adamowski and Bougadis (2003) applied it in extreme rainfall trend detection study,etc. This test was used by Mann in (1945) and afterwards the test statistic distribution was derived by Kendall (1975). Mann - Kendall test can be applied to either nonlinear or linear trends for different significance levels. Test application and calculations have been well described by Sneyers (1990) and EPA (2006). 32 CHAPTER 3 THEORETICAL BASE AND METHODOLOGY Water resources infrastructures will be exposed to a range of hydrometeorological variable due to climate change. To understand the potential changes, it is necessary to establish the specifics associated with the precipitation patterns. This chapter describes aspects of alternative methodologies and statistical analyses used in heavy rainfall evaluation in Ontario, Canada. The primary methodology applied in this research to assess possible change in observed heavy rainfall data involves evaluation of the temporal intensity-duration-frequency (IDF) curves. The analyses include confidence intervals and trend detection analyses, respectively. 3.1. DATA RANKING Two approaches for raw data ranking are commonly applied in local heavy rainfall analyses, as overviewed in following section of this chapter, namely, the annual maxima (AM) and partial-duration series (PDS). 3.1.1 The Annual Maxima In Canada, IDF curves are generally calculated based on annual maxima series. The annual maxima series include only the highest values for each year, while the second or the third highest values within one year are neglected in any further rainfall analyses based on this ranking methodology. 33 3.1.1 The Partial Duration Series Partial-duration series incorporate the highest values for the period of observation regardless of the year in which they occurred. With this ranking approach, all observed data are arranged in the order of decreasing magnitude, and the length of record is equal to number of samples, e.g. for 30 years of record number of partial-duration series to be used in analyses will be 30. These series are also referred to as either the annual exceedances (Chow, 1953) or the peaks over specified threshold (Madsen et al., 1997). As a demonstrative example, both the AM and annual exceedances PDS, rainfall data were ranked for Waterloo station (and for storm duration of 30 minutes) and depicted graphically in Figure 3.1. It is evident from Figure 3.1 that the PDS events exceed the annual maxima. The difference between the annual maxima and partial-duration series argues for the use of the partial-duration series in derivation of the IDF curves, an approach which will be used herein. Since there are two commonly used approaches in PDS derivation from measured data, in this study annual exceedances will be used. Hence, hereafter PDS is related to annual exceedances. 34 Waterloo - 30 minutes duration for observation period 1970-2003 45 40 35 j • Partial Duration Series 30-| D Annual Maxima Magnitiude 25 (mm) 20 15 10 5 r-"t—'i-"*r 1 3 5 7 9 11 13 15 17 19 21 23 25 27 29 31 33 Rank of Values Figure 3.1 Observed heavy rainfall data arranged in the order of magnitude for annual maxima and partial-duration series. 3.2 IDF CURVES For short-term intensive rainfalls, and inputs to design of infrastructure systems, the most accepted statistics are in the form of IDF curves which incorporate information on the intensity of the precipitation, duration of the event, and frequency (recurrence interval or return period). Commonly, extreme values are fitted with Gumbel distribution, succeeded by frequency analyses, as it is described in the next subsections of this chapter. 35 3.2.1 Extreme Value I distribution The main goal of extreme value statistical theory is to analyze observed events and to establish frequency of specific magnitudes (Gumbel, 1958), such as flood, rainfall, etc. In a study by Fisher and Tippett (1928), the cumulative distribution function for extreme values was defined as: F(x) = exp{- exp[oc(x - p)]} (3.1) F(x) represents the cumulative distribution function of extreme value x, and parameters a and p are scale and location parameters, respectively. The probability distribution is estimated by: f(x) = [- a(x - p)e"a(x-P) J (3.2) The two parameters, a and p, are related to the mean and standard deviation of data by: x = p + ^ (3.3) a where 7 = 0.5772 or Euler's constant, then Equation (3.3) becomes: _ Q 0.5772 X = P + (3.4) a The standard deviation of data is computed by following: aV6 a Commonly, a and p are estimated by the method of moments proposed by Fisher and Tippett (Chow, 1953) as follows: 36 P = x-0.450S (3.6) 1.282 ,, ,. a = —-— (3.7) In hydrology, the double exponential function, (3.1), was first applied by Gumbel (1941) in flood analyses. This is a two parameter distribution with constant skewness and kurtosis coefficients, 1.11396 and 4.5, respectively, and data used in analyses are assumed to be independent. 3.2.2 Frequency Analyses The most commonly used methodologies in extreme values frequency analyses are plotting position formulas and frequency factors (Kt). Gumbel (1958) and Yevjevich (1972) determined that the Weibull plotting position formula best satisfied extreme value distribution plotting position, which is given as: R = il±i (3.8) m In the above formula R is occurrence interval, m is rank of the data, and n is the total number of extreme values used in frequency analyses. The frequency factor (Kt) for Gumbel distribution is calculated by: Kt =- —fo.5772 + lnln-^l (3.9) it ^ T-1J Formula (3.9) was defined by Chow (1951), where 0.5772 is Euler's constant, and T is recurrence interval, respectively. Although, values for 37 frequency factors are readily available for different numbers of sample, and recurrence intervals, in this thesis Equation (3.9) was used for frequency factor calculations. Thus, design values or the realization of x for different rainfall durations and recurrence intervals are estimated by following equations: XpQs = XpQs +KfSpDs (3.10) XAM = XAM + Kt^AM (311) In the above equations, namely 3.10 and 3.11, X PDs represents design values for partial-duration series, and XAM is value for annual maxima respectively. 3.3 INTENSITY EQUATION COEFFICIENTS 3.3.1 The Log-Linear Regression IDF curves are represented in mathematical form as: Im= (3.12) (b + t)c I is rainfall intensity (mm/hr) for different durations, t is duration of rainfall (min), and a, b, and c are constants that vary with recurrence interval and location. For the period of observation, these coefficients are estimated by logarithmic linear transformation of Equation (3.12), as it was described in MTO Drainage Management Manual (1997). Hence, the Equation (3.13) represents the log-linear form of Equation (3.12): 38 log(I) = log(a) - c * log(td + b) (3.13) This equation has the form of straight line, where the coefficient 'a' represents the intercept of that line, Ab' is the value which must be solved by trial, and xc' is the slope of the best fit line for the log I (abscissa), versus log (td +b), plotted on x axis, respectively. For the first assumption for coefficient b, values for coefficients a and c were determined by linear regression analyses. The procedure of trial was repeated until the correlation coefficients closest to -1 were determined. Correlation coefficients were calculated as: Cov(X,Y) = i Z (Xj -x)(Yj -y) (3.14) nj=i 3.3.2 The Method of Least Squares For the n pairs of observations (xi; yi), if the regression of y on x is assumed to be linear, the equation of the line which represents the best fit for data has to be determined. If y is predicted by: y = a + bx (3.15) where a and b are constants, then ei is the error in predicting value of y corresponding to the given Xi (Miller and Freund, 1985): er=Yi-y (3.16) To determine a and b with errors as small as possible, and to find the equation of the line that best fits the paired data, either observed or 39 independent versus dependent data, the method of least squares which minimizes the errors is given as : l[yi-(a + bX|)] (3.17) i=l Since the Equation (3.13) is a straight- line equation, it was be solved by the last squares method, followed by trials for the coefficient 'b' in Equation (3.13), and correlation coefficients computations Equation (3.14), respectively. 3.4 TREND DETECTION 3.4.1 Linear Regression The statistical analyses were applied in this thesis in the general form for linear regression, Equation (3.15), for estimation of IDF curves coefficients as it was described in the previous section, and in trend detection as a first approximation for dry days and amount of rain time series for all observed data, respectively. 3.4.2 Mann - Kendall Trend Test This non-parametric rank- based test was applied in trend estimation on the annual time series. This test is distribution free, and the significance of the trend was calculated for various levels of significance. For each year of observation, pairwise differences were computed as: 40 + Xj>Xj 0 Xj=Xj sign(Xj-Xi) (3.18) < Xj where x3 is rank of data i= 1,.., n-1; Xi is data rank for j= i+l,..,n, and n is the number of years in observed time series. S statistics are the difference between positive and negative signs as calculated as: n-1 n / N S= I Z sign(xj-Xi) (3.19) i=l j=i+l If S is a large negative value, there is evidence of downward trend in the data, while a large positive S value indicates upward trend in the observed data. For sample size 10 or more, a normal approximation to the Mann-Kendall procedure was used for calculation of the test statistic (Z0): S ± sign(S) Z0 = (3.20) if S >1 sign (S) =1, while for S<1 sign (S) = -1. In the case where S = 0 the test statistics (Z0) is 0. A positive value of Z0 indicates an increasing trend, while negative Z0 suggests a decreasing trend. Standard deviation V(S) was computed as: 41 V(S) = * n(n - l)(2n + 5) - £ t^ - l)(2t, + 5) (3.21a) 18 j=1 in which g is the number of tied groups, and t3 is the number of points in the jth group. V(S) = ^ [n(n - l)(2n + 5)] (3.21b) When ties do not exist in data set, Equation (3.21b) is applied for standard deviation computation. For different level of significance table for normal distribution was used to find the critical value Zi-a, for significance level (a), and p-value (corresponding tail probability for Z value). The subsequent sets of analyses were completed to evaluate the test statistic (Z0): if | z0|> Zi-c, then the hypothesis of no trend was rejected, i.e. trend is present in observed data at significance level a, and (3.22) if p -value < a, the null hypothesis of no trend was rejected (3.23) 3.5 CONFIDENCE INTERVAL AND FREQUENCY Statistical confidence limits characterize an interval that there is a specified degree of probability (1- a) that the variable such as rainfall, flood, etc, will be subsumed into the confidence intervals (McBean and Rovers, 1998). In a mathematical form, the probability that the confidence intervals 42 (the upper and the lower) subsume a specified population parameter (e.g. mean, variance, etc) is estimated by: Pr{x(|) In the above equation, {(1- a) 100} %, is the degree of confidence for the upper (x(u)) and the lower (x(i)) confidence intervals, respectively. The joint confidence intervals for mean and standard deviation in rainfall time series were estimated by the graphical method described by Yevjevich (1972) that generates subsets of following statistical analyses: • Rainfall data for particular duration were plotted by Weibull plotting position formula, namely Equation (3.8). • Straight - line fit was obtained by lognormal transformation of data • Upper and lower straight line limits were acquired by using the points for the upper and the lower confidence limits for sample mean (x) , and standard deviation (S): — tS — — tS Xn - —^- < Xn < Xn + —^ (3.24) Vn Vn Sn-t*(Sn/V2N)£Sn<;Sn+t*(Sn/^/2N) (3.25) In the above formulas, the t distribution values for standard normal variable was used, e.g. for 90 % confidence level, and sample size (N) greater than 30 t value is 1.645. The right fragments of above formulas, 43 namely (3.24) and (3.25), exemplify the lower confidence limits(x(i)and Sn (i)), while the left fragments exemplify the upper confidence limits (x(u)and Sn (U)), respectively. 44 CHAPTER 4 MODEL DEVELOPMENT AND RESULTS 4.1 INTRODUCTION Implicit in the design of stormwater management infrastructure is the need for the infrastructure to function for many decades. Given that there is widespread evidence that climate change is likely occurring, there is need for review of urban design storms to determine if, indeed, design storms are changing in response to the global climate change reality. To examine the potential that the recurrence intervals of severe storms are changing, historical records for fourteen tipping bucket gauges distributed within Ontario, Canada, are examined. The results of the analysis of the historical records for rainfall intensity/duration/frequency (IDF curves) and durations of 2, 6 and 12 hours and short-duration rainfalls, e.g. one hour and finer time steps are provided for each of these stations accompanied by the trend examination in the number of dry days and amount of rain annual datasets. Additionally, this chapter includes for Waterloo station: i. The change in recurrence intervals of different events, followed by determination of IDF equations ( Equation (3.12)); ii. An evaluation of existing hydrologic model application for Waterloo; iii. Confidence limits of recurrence intervals are discussed in the subsequent sections of this chapter, specifically, section 4.5. 45 4.2 DATA AVAILABLE Environment Canada has provided data which have been analyzed in this research. The data base consists of 967 745 measured heavy rainfall data for different storm durations, from 5 minutes to 24 hours duration, and 14 locations distributed across the province of Ontario, within different regions, namely, northern, central, and southern Ontario, Figure 4.1. Figure 4.1 Map of the Stations in Ontario Measured data set has been imported from Microsoft Excel to Microsoft Access as Microsoft Excel is found to be unsuitable for large datasets (Goran Vrakela, personal communication, 2006). Three subsets of analyses were completed to evaluate amount of missing data in historical observation datasets, namely evaluation of the number of years with records at each site, the number of missing years for 46 each station and for a given period of observation, and assessment of the missing data within each year of record, for the fourteen available stations within Ontario. In general, all stations have observation records equal or longer than 30 years, with the exception of Preston station that has 26 years of record, and Orillia station which has 28 years of records. Additionally, for all locations, rainfall historical records are available from mid -1960s or later (e.g. either the late 1960s or early 1970s) to mid -1990's or later (e.g. up to 2003), while missing data for entire years exist for Moosonee (10 years), and one year for Waterloo and Timmins, respectively. Geographical characteristics, periods of observation, and lengths of record employed for each station as used in the study are listed in Table 4.1(Appendix A). The count of missing data per year was calculated as a percentage of the missing data (e.g. denoted as "-999" in observed data set) within each year of observation out of total number of observations per year. Figure 4.2 (Appendix B) illustrates Microsoft Access query used for these analyses. Table 4.2 summarizes results of the missing data analyses with definition of percentage classes (pc), and average of missing data for all stations with historical records, respectively. 47 Table 4.2 Annual missing data summary Number of Percentage Class -pc Station years with Average (0/0) name missing (%) data 10 On average, missing data percentiles were found to be from 2.62 % at Sudbury station to 10.82 % at Timmins station. The highest value for percentage class > 10 % of missing data was detected at Timmins station; namely, 37.93 % of years with missing data (29 years in total) had more than 10% of missing observations in their records , while the highest value for percentage class smaller than 5 % was detected at Sudbury station, specifically, for 32 years with missing observations, only 12.50 % of years had more than 5 % and less then 10% of missing data out of total number of records, while for the remaining years (i.e. 87.50%) the percentage of missing data is smaller than 5%. Furthermore, at six stations, only one year has more than 20% of missing data; Burketon has 30.5 % in 1994, for Chalk River 30.26% was identified in 1994, Kingston has 26.8 % in 1960, 26.8 % was observed for 48 Moosonee in 1967, at Oshawa station 22.4% was detected in 1974, and Port Colburne has 39.98 % of the missing data in 1982. Only for one station, more than one year with amount of the missing data greater than 20 % were detected, namely, Timmins, that has 36.96 % in 1980, 21.31% in 1992, and 21.31% of the missing data in 1987. In general, throughout the entire data set there is no uniform pattern of missing data, neither within the year of observation or region in Ontario. Hence, it was concluded that amount of missing data will not affect the accuracy of analyses, and all stations were selected to be included in analyses, except Moosonee, since there are 10 years of missing data at that station. Thus, the further heavy rainfall evaluation and additional analyses will be applied at 13 locations across the province of Ontario. 4.3 LOCAL POINT IDF CURVES ANALYSES Until now, the trends in rainfall events within Canada have been mainly quantified in Annual Maxima Series or, total precipitation series, either for daily or sub-daily observed data. Despite the fact that numerous studies have analyzed trends in rainfall time series, in recent decades there is still controversy and uncertainty concerning intensities for design scenarios. In this research, the temporal variations in heavy rainfall historical records at the local scale are examined in partial duration series for two time periods at each station. There are two primary reasons for selecting partial duration series as opposed to annual maxima series in this study. 49 Consideration of both AM and PDS should be applied in the hydrologic data assessment (Chow, 1953); secondly, it was presumed that temporal changes in IDF curves would be better described by partial duration than annual maxima series, since the exceedance frequency is relevant to design of urban infrastructure. As mentioned in the previous chapter, the Gumbel distribution is generally applied to fit the observed data for different extreme variable studies. Thus, for 13 locations across the province of Ontario measured sub- daily (i.e. 1,2,6, and 12 hours) and sub-hourly heavy rainfall data were fitted by the Gumbel distribution, and distribution parameters (3 and a are estimated by the method of moments, Equations (3.6) and (3.7), respectively. The frequency factor, Equation (3.9) was calculated for all durations, and commonly- used recurrence intervals at all stations. Finally, IDF curves were calculated for two time series, for the periods 'before' and 'after' the year 1984 at most locations, and compared at each location. The procedure employed in selection of the years to be included two periods of observation in the study is described below. For most stations, with the record of observations started in the late 1960s (i.e. Timmins, 1969) or earlyl970s (i.e. Sarnia, 1971), two time series for the IDF curves temporal analyses are specified as the period of observation prior to 1984, and period of observation post - 1984, since the Rainfall Atlas for Canada was published in 1985, and number of years in each 50 time periods is approximately one-half of the records length. The record lengths were segmented into two pieces, with approximately 15 years within the time series for each station. At the stations with rainfall records ranging from either early 1960s or mid-1960s to either mid - 1990s or early 2000s, lengths of observation were segmented into two equal time series with a variety of number of years within them, and the last year in earlier period of observation and the first year for more recent period , specifically, at Orillia and Chalk River stations the last year is in former is 1978 and 1979 for the latter; while for Kingston and Port Colborne the year 1982 was selected as the last year for earlier period of measurements, and 1983 is the first year for more recent period of observation. The procedure for described above has been employed for both annual and seasonal temporal variability tests. The flow chart that summarizes the methodology applied for the single site, heavy rainfall, analyses is schematically presented in Figure 4.3: 51 Observed Heavy Rainfalls Data Ranking Data Ranking Annual Maxima PDS IDF Computation IDF Computation ' ' i ' Temporal Trend Estimation Figure 4.3 Flow Chart for IDF curves Temporal Assessment Figure 4.4 (Appendix B), exhibits the program interface developed in Microsoft Access for IDF analyses, while Microsoft Excel was used for the temporal trend estimate. Although the IDF curves based on either annual maxima or partial duration series can be calculated by this program, partial duration series were used for the temporal difference assessment in rainfall time series. The rainfall statistics as derived from two segments are compared to examine whether there is evidence of change over time. 52 4.3.1 Application of Model to IDF curves Temporal Change Analyses Since the accuracy of the IDF curves depends on the length of timeframe for which calculations are performed, and for most locations temporal variations are based on a 15 year period, on average, discussion of results are divided into two groups for this set of analyses in terms of accuracy, e.g. 2, 5, and 10 year recurrence intervals and 25, 50, and 100 year recurrence intervals, respectively. It is noted that estimates of 2, 5, and 10 year events from a fifteen year record are relatively good, whereas for the less frequent events, greater uncertainty exists with any estimates. The uncertainty of the recurrence intervals estimates is discussed in section 4.5. The summarized results of the extreme point rainfall intensities temporal change assessment are presented separately, for each region in this section, succeeded by exhaustive results for five year recurrence interval, all stations and various durations, namely, 30 minutes, 60 minutes, 2 hours, and 12 hours, that are summarized in Figures 4.5.1 to 4.5.4. Furthermore, the Tables 4.3.1 to 4.3.13 (Appendix A) detailed change in rainfall intensity magnitude for each station, duration, and recurrence interval. Since the different number of years were used in temporal IDF curves evaluation, as a result of difference in record length at locations across Ontario, the average annual change in rainfall intensity, for all stations, 5 year storm, and duration ranging from 5 minute to 2 hr, are summarized in Table 4.3.14 53 It is noteworthy to mention that in the following sections, decreasing trend (i.e., sign '-' in tables which summarized temporal changes in IDF curves) is specified as negative difference in percentage between two time series employed in temporal changes in IDF curves analyses, e.g., before and after 1984, while the increasing trend stands for positive difference in percentage between time series, or more specifically, the increasing trend means that the magnitude of measured heavy rainfall is higher after the year 1984. The sign '0' in tables mean there is no change in rainfall intensity over time. Temporal change in IDF curves for 2, 5 and 10 year recurrence intervals On the whole, for all stations, the highest identified decreasing trend is at the Oshawa station, while the highest increasing trend corresponds to 10 year recurrence interval and 5 minute duration at Sarnia station. • South Ontario The substantial majority of the findings indicate the intensities of rainfall are increasing over time for the 2 ,5 , and 10 year event. The highest increasing trend is detected at Sarnia station, 65 % change in magnitude, for 10 year recurrence interval and 5 minute rainfall duration, while the highest decreasing trend in the southern part of Ontario is observed for Port Colborne - 19 %, for 10 year recurrence interval and 12 hours. 54 • Central Ontario The most interesting results are that most of the analyses showed increased intensities over time for 2, 5, and 10 year recurrence intervals. Within four stations with observations after the 1995, the highest decreasing trend is observed at Oshawa station, -28 % for 12 hours duration and 10 year recurrence interval. The highest increasing trend, 46 % is detected for Burketon, 10 year recurrence interval and 6 hour event. At the Orillia station, the lowest trend is detected for 10 minute and 10 year recurrence interval, i.e. 10 % while the highest trend is for 6 hour, and 10 year recurrence interval, namely, 40 %. • North Ontario The highest downward trends are identified at Sudbury and Chalk River stations for 10 year recurrence interval , and 2 and 12 hour rainfall duration, (i.e. -7 % and - 7%), respectively. In contrast, the highest upward trend is at Timmins station 64 %, for duration of 30 minute and 10 year recurrence interval. Temporal change in IDF curves for 25, SO and 100 year recurrence intervals For all stations regardless of the region, duration and return period, the highest downward trend is at Oshawa station -39 % for the 100 year recurrence interval and 12 hours, while the highest upward value is detected for 100 year recurrence interval and 30 minutes duration at Timmins station, 105 %. 55 • South Ontario The highest downward trend is identified at the Port Colborne station, 100 year recurrence interval and duration of 12 hours, i.e. -21 %, while the highest detected upward trend is at Sarnia station 96 %, for 10 minute rainfall duration and 100 year recurrence interval. • Central Ontario For this region the highest decreasing trend is detected for the Oshawa station - 40 %, for 100 year recurrence interval and 12 hour duration, while the highest increasing trend is detected for Bowmanville, 64 % change in intensity, for 100 year recurrence interval and 12 hours duration. • North Ontario Of the three locations in this region of the Province of Ontario, namely, Chalk River, Sudbury, and Timmins the highest decreasing trend in IDF curves has been found at Sudbury station , i.e. -11 % for 12 hour duration and 100 year recurrence interval. The highest increasing trend of rainfall, 101 %, is detected at Timmins for 100 year recurrence interval and 30 minute duration. The above - discussed results indicate that both increasing and decreasing trends are present in the historical dataset regardless of record length, location, storm duration, recurrence interval, and the annual percentage of missing data. The highest temporal changes, either increasing or decreasing in rainfall magnitude, are observed for less frequent events, 56 e.g. 100 year recurrence interval. Generally, at most stations, there are more upward than downward trends in observed data, for different recurrence intervals and storm durations. Furthermore, for short-duration events, namely, one hour or shorter, that are more frequent, e.g. five year, at most locations, the highest detected change in rainfall magnitude, is for durations between 15 and 60 minutes. Maps were created presenting the temporal changes in rainfall intensities for 5 year recurrence interval, various durations, and all stations with data available across the Province of Ontario, Figures 4.5.1 - 4.5.4. South Ontario ) Delhi 33% k Port Cotoome 2% I Preston 37 % m Sarnla 46% n Waterloo 34% Figure 4.5.1 Percentage Figure 4.5.2 Percentage Change in Temporal Change in Temporal IDF Curves for 5 year IDF Curves for 5 year Recurrence Interval: Recurrence Interval: Storm of 30 minutes duration Storm of 60 minutes duration 57 /North Ontario /North Ontario / a Chalk River -6% X aChelkRIverOto / c Sudbury 11 % : X e Sudbury 0 * X d TimmWs 26 % X dnmmhi»17% I Central Ontario ! : 1 Central Ontario \ « Bowmarywtlie 29% I m Bowmanwiile 3t% \ fSurketonl8% 1 f Burketon 38 % \ 9 Kingston-B% If Kingston-1% I hOrilla37% dii \ hOr«a24% Yi Oshawa 18* VI Oshaiwa 16% «• mW\^/""y '"'" *9^M/~5 : South Ontario South Ontario JD*thI3% jDelhIM* '*lji§P: ; k Port Colbome -12% :.. kPortColbome 1% lPrest»n3W •Welt^ ; 1 Preston: 211!. : mSamlaW* ' :::*»• m Sarnla 30% . mp n Waterloo 15% n Waterloo 30% Figure 4.5.3 Percentage Figure 4.5.4 Percentage Change in Temporal Change in Temporal IDF Curves for 5 year IDF Curves for 5 year Recurrence Interval: Recurrence Interval: Storm of 2 hr duration Storm of 6 hr duration 4.3.2 Model Application to Seasonal Analyses in IDF curves The period of three decades, on average, with various rainfall events durations were investigated for the seasonal patterns of IDF curves temporal changes at thirteen locations across Ontario, Canada. Moosonee station is not included due to the 10 years of missing data. There is interest in seasonality of the IDF curves to determine if there is greater significance within the individual seasons. The methods outlined in the preceding section, Figure 4.3, for temporal IDF curves analyses were applied for seasonal analyses; for spring (i.e. March-May), summer (i.e. July - August), and fall (i.e. September - November) seasons, excepting the 58 winter season (i.e. December- February) as the prevalent form of precipitation during this period is snowfall. Seasons are denoted by the initials of months within them (e.g., SON for September - November, or fall season) and Figure 4.5 (Appendix B), exhibits the program interface developed for the seasonal analyses. Considering the annual level, most of the stations have had generally increasing intensities for all durations and recurrence intervals. However, high seasonal fluctuations were detected, decreasing by - 64% in the summer season, and reaching the point of + 126 % for the fall season, at Oshawa station for 100 year recurrence interval. Due to the large number of seasonal analyses 144 (i.e., 3 seasons * 6 recurrence intervals * 8 durations) for each station, the overall results for seasonal IDF alterations are presented separately for the three regions in Ontario. Detailed seasonal outcomes are exhibited in Tables 4.4.1- 4.4.13 (Appendix A). • South Ontario In general, the seasonal trends in rainfall magnitude demonstrate significant shifts, regardless of durations, seasons and recurrence intervals at all stations in this region. The total number of upward trends is 546, while 164 downward trends are detected. Additionally, most of the negative trend values were identified at Port Colborne station (i.e. 77 %) in spite of the season. 59 On the contrary, for Waterloo station only 7 negative values are detected, mostly for short durations (i.e. 5 and 10 minute), and the spring season (MAM), as opposed to 137 positive trend values. At three other stations within southern Ontario, the numbers of negative seasonal trends are 29, 27, and 29, ranging from -1% to - 47%, at Preston (i.e. the fall season), Delhi (i.e. the spring season) and Sarnia station (i.e. the fall season), in given order. In contrast, the number of increased intensities detected at Sarnia, Preston, and Delhi locations are 112, 114, and 116, respectively. The most notable feature is an increasing trend in the summer (DA) in seasonal rainfall magnitude at Sarnia station (i.e. 110 %, for 100 year event and 10 minute duration), while the most prevalent decreasing trend is present at Preston station, explicitly - 47 %, for 6 hours duration and 100 year event. Finally, for Preston and Sarnia, rainfall magnitudes decrease in trend existing in SON season that is opposite to observed changes for Delhi and Waterloo stations where downward trends were noticed for MAM season and at Port Colborne (Figure 4.6.1) station for all seasons. 60 Port Colbome station seasonal intensity magnitude changes: 5 Year Event -A—MAM -•--DA -•—SON -*—Annual 15 *•. 10 y \ "> • •« » s\i/ '• x*"> /'•A ^ x—• / • Change / (°/o) -5 \j / -10 xi/ \i/ * y A\ -15 '• -20 10 15 30 60 120 360 720 Duration (min) Figure 4.6.1 Temporal Seasonal IDF Changes at Port Colborne Station Compared with Temporal Changes in Full IDF curves for Time Series: 1962 - 1978 and 1979 - 1995 As presented in the Figure 4.6.1, there is a decreased intensity for short duration storms; while for the fall season there is decreased intensity for both short duration and longer duration storms. For the storms which occur during the summer, increased intensities are detected, except for durations longer then 6 hours. • Central Ontario Of the four locations in this region, the largest overall seasonal difference is detected for Kingston, where decreasing trends are observed for 61 all durations and frequencies during the fall season. Explicitly, there are 84 negative trends ranging from -2% to -56% mainly in the fall and spring seasons. In contrast, 59 increasing trends are observed at this location, primarily for the summer season. Completely different trends are observed at Bowmanville station where the negative trends (i.e. 9) are noticed during the spring for 2 and 6 hours duration. Overall, the highest number of increased intensity (i.e. 135 in total), is observed during the same season (i.e. spring), for short -duration rainfall events and all frequencies, while for longer duration events (i.e. 2, 6 12 hours) the maximum seasonal changes are discovered in summer season. An interesting seasonal shift has been noticed at Burketon station. While the highest increasing trends are observed during the fall for more frequent events (i.e. 2- 10 year), the peak seasonal changes for less frequent events are noticed in the spring season. In contrast, there are five downward trends for 2 year recurrence interval detected mostly for short- duration rainfalls, both in spring and summer. In summary for this station the numbers of increasing and decreasing trends are 136 and 8, respectively. Significant irregularities in seasonal rainfall magnitude changes are discovered at Oshawa station for all frequencies, and durations in spring and summer. Out of the total number of trends, 50 are decreasing, while 94 are increasing. Regardless of the recurrence intervals and durations, the highest increases in rainfall intensities were detected during the fall season and 5 year event. 62 Oshawa station seasonal intensity magnitude changes: 5Year Event -k— MAM -•-••-• HA -•—SON —*— Annual 100 80 • —•— 60 40 V -'HllNs;[^rrJ T 20 Change (%) * »„ 0 ••-• -^"^ *. -20 ^^A-"""'^ •r * rf\ -40 '• -60 10 15 30 60 120 360 720 Duration (min) Figure 4.6.2 Temporal Seasonal IDF Changes at Oshawa Station Compared with Temporal Changes in Full IDF curves for Time Series: 1969 - 1984 and 1985 - 2003 • North Ontario For this region the most remarkable feature is an upward trend in the fall seasonal rainfall magnitude at Sudbury station (e.g.,126 %, for 100 year event and 12 hours duration), while the most prevalent decreasing trend is present at Timmins station (- 42 %, for 12 hours duration and 100 year event). In general, at the Chalk River station, for all recurrence intervals and short - duration storms, the maximum increasing seasonal changes in 63 rainfall intensities are evident in the spring season, as opposed to the fall season in which the majority of the decreasing trends are discovered. Completely different trends are observed for longer durations (i.e. 2 and 6 hours) and all frequencies where the peak negative values are in the summer season, while the highest upward trends fluctuate with frequency and duration, namely, for 25 year event the peak increasing trends for 2 and 12 hours are observed in the fall and the spring season, respectively. The largest seasonal dissimilarities are at the Sudbury station between MAM and SON seasons. In the spring season, major negative trends were detected (except for the 2 year event) while completely different trends were noticed for the fall period. In summary, the number of negative trends is 53, and 97 positive trends were observed for this location and all seasons. Figure 4.6.3 exhibits the results for seasonal analyses for Sudbury station, and 5 year event. Finally, atTimmins station the number of upward and downward trends is 79 and 62. The majority of increasing trends are observed in the fall season. On the contrary, the highest increasing trends are discovered during the summer in all frequencies and durations, except for the 2 and 5 year events where for longer durations (i.e. 6 and 12 hours) the highest upward trends are detected in spring. 64 Figure 4.6.1 Temporal Seasonal IDF Changes Sudbury Station Compared with Temporal Changes in Full IDF curves for Time Series: 1971 - 1984 and 1985 - 2003 Table 4.5 summarizes the results for each seasonal trend analyses at each station, for all frequencies, and durations. In the table below sign n+" represents the increasing in rainfall intensity as opposite to sign "-" that symbolizes the decreasing trend, while sign "0" indicate that there is no trend. 65 Table 4.5 Trend Analyses Results for Seasonal Changes in IDF Curves for Twelve Stations Across Ontario Region Total number of tests Period of Record In Station name Observation Length Ontario ii i H "0" ll_ll Delhi 1962-1995 34 116 1 27 Port Col borne 1964-2000 37 61 6 77 South Preston 1970-1996 26 114 1 29 Ontario Sarnia 1970-2003 34 112 3 29 Waterloo 1970-2003 33 137 0 7 Bowmanville 1966-2001 36 135 0 9 Burketon 1969-2001 33 136 0 8 Central Kingston 1960-2003 44 59 1 84 Ontario Orillia 1965- 1992 28 49 0 95 Oshawa 1969-2003 34 94 0 50 Chalk River 1962-1995 34 110 0 34 North Sudbury 1971-2002 32 87 4 53 Ontario Timmins 1969-1999 30 79 3 62 4.4 MODEL APPLICATION TO THE CASE STUDY AREA: WATERLOO STATION There are two main reasons to select Waterloo location as a case study of potential focus for this research. In the first place, this is a typical well - developed urban municipality in the southern part of Ontario, the most populated region in Canada. In the second place, hydrologic model is available for existing stormwater infrastructure; thus, there is an opportunity to evaluate the adequacy of the current level of service provided by the drainage system based on temporal IDF curves analyses of observed data. 66 4.4.1 IDF Curves Analyses Although the temporal changes in heavy rainfall intensities, discussed in the preceding section, do not have the consistent pattern for various stations, seasons, durations, and frequencies, the results are in agreement with other climate change studies which acknowledged that heavy rainfall statistics are changing. Due to fact that the information regarding rainfall intensity and frequency is used extensively as the source for stormwater management systems designs, it is of particular interest to examine whether the IDF curves should be changed, and if so, by which magnitude. The minor drainage systems are usually designed based on recurrence intervals from 2 to 10 years, with reference to either local authority or conservation authority requirements for pre - and post - development conditions for particular watershed. Rainfall intensities for both annual maxima and partial-duration series derived from raw data and full period of observation, namely from 1970- 2003, are compared at Waterloo station. The results are presented in Table 4.6.1 and Table 4.6.2 for the 2 year and 5 year events, respectively. 67 Table 4.6.1 IDF Curves Table 4.6.1 IDF Curves Evaluation for 2 Year Event Evaluation for 5 Year Event at Waterloo station at Waterloo station I(mm/hr) I(mm/hr) Partial Annual Partial Annual Duration Maxima Duration Maxima Series Series Duratio n (min ) Duratio n (min ) 1970-2003 1970-2003 1970-2003 1970-2003 5 128.6 99.9 5 145.3 133.5 10 90.1 70.7 10 103.8 94.9 15 73.4 58.3 15 85.4 78.1 30 48.9 38.4 30 60.7 54.9 60 29.5 23.5 60 40.1 36.5 120 17.5 14.1 120 23.7 21.7 360 7.1 6.1 360 9.5 8.9 720 4.0 3.4 720 5.1 4.8 The IDF curves resulting from partial-duration series have exceeded those developed from annual maxima data, both for the 2 and 5 year recurrence intervals that are consistent with results exhibited in Figure 3.1 for 30 minutes duration at Waterloo station. Furthermore, the differences between two data sets are more noticeable for rainfall extremes with high temporal resolutions (e.g. one hour or shorter) which is of particular interest for urban drainage infrastructure systems. Since the Region of Waterloo and Area Municipal Design Guidelines were revised in January 2007, the existing IDF curve from this guideline is compared with IDF curves calculated from partial- duration series and two period of observation, prior to and after the year 1984, for Waterloo station. The results are presented in Figure 4.7. 68 While the existing IDF curve for Waterloo station and IDF curve calculated for events prior to 1984 are the same for 5 year event, the differences are detected between the existing IDF curve and IDF curve based on partial -duration series and period of observation after the year 1984. Hence, the IDF curves generated from heavy rainfall events in the latter period of observation (1985 - 2003) exceed the magnitude of the existing Waterloo IDF curves which are used frequently for various water resources projects. IDF arves Waterloo 5 year reorrence interval 160 • Existing Waterloo Curve 140 - • PDS (70 - 84) 120 - • PDS (85-03) \# 100 - oU " I (mm/hr) \ 4 • ou " ^v^< • 40 20- U n (D 30 60 90 120 Diration (rrin) Figure 4.7 IDF Curves Comparison for Waterloo Station and 5 Year Event 69 Although the temporal changes in annual IDF curves ranging from 11% to 37 % were identified at Waterloo station for 2 year recurrence interval based on the analyses in the subsection 4.3.1 in this chapter (Table 4.3.5), it is not apparent how these variation might influence heavy rainfall frequency, e.g., has the intensity of rainfall increased during the latter decades. Thus, IDF curves generated from partial duration series are compared for two different periods of observation, namely, before and after the year 1984, in terms of recurrence intervals for the 2 year and 5 year events at Waterloo station. The results are introduced in Table 4.7 and exhibited graphically in Figure 4.8. Table 4.7 IDF Comparison between Different Periods of Observation for 2 and 5 Year Events at Waterloo Station I(mm/hr) I(mm/hr) I(mm/hr) Duration mm PDS PDS PDS 2 YR 2 YR 5 YR 1970-1984 1985-2003 1970-1984 5 121.4 136.5 135.3 10 80.4 99.5 94.0 15 66.1 81.5 72.9 30 43.8 55.7 51.5 60 25.3 34.6 33.0 120 15.8 19.8 20.8 360 6.8 7.6 8.9 720 3.8 4.3 4.9 70 Waterloo station 150 125 -•-5YR (1970-1984) • 2YR (1985-2003) A 2 YR (1970-1984) 100 I(nmVhr) 75 50 25 0 0 30 60 90 120 Duration(rrin) Figure 4.8 Graphical Demonstration of Change in Rainfall Frequency for 2 Year Event at Waterloo Station The differences in storm magnitude ranging from 9.3 mm/hr to 19.1 mm/hr were noticed for the 2 year events and two time series (Table 4.7). Hence, based on these analyses, the findings indicate that storm intensities are increased from (1970 -1984) to (1985 - 2003). For storm durations ranging from 5 to 30 minutes for the five year storm for the period (1970 - 1984) and for the two year storm (1985 - 2003), respectively, are very similar. 71 Both tabulated (i.e. Table 4.7) and graphically (Figure 4.8), the IDF curves for two time periods have demonstrated that in the recent decades what used to be the 5 year event (1970 - 1984) becomes now approximately the 2 year event for the period (1985 -2003). Thus, for different durations at Waterloo station, extreme events recurrence intervals are changing on observed heavy rainfall data (i.e. what was the 5 year storm intensity is now the 2 year storm intensity). 4.4.2 Intensity Equation Temporal Analyses Commonly, IDF curves are represented in mathematical form, Equation (3.12): These equations are readily available, for various recurrence intervals and durations in Canada and worldwide. Coefficients are derived based on computed intensities and frequencies, by the methodology explained in Chapter 3, subsections 3.3.1 and 3.3.2, respectively. Due to their extensive application in different water resources models, it is important to evaluate possible changes in IDF coefficients as a result of detected temporal changes in heavy rainfall frequency at Waterloo station. In these analyses, IDF equation constants (Equation (3.12)) were calculated for computed intensities based on observed data, 2 and 5 year events, and two periods of observation, specifically, prior to 1984 and after the year 1984. 72 The results are presented in Table 4.8, together with existing Waterloo IDF curve coefficients (source: Region of Waterloo design guidelines and supplemental specifications for municipal services, 2007). It is evident from Table 4.8 that changes in rainfall intensity generate different values for constants a, b, and c. The most significant difference is detected for the constants a (e.g. for 2 year event values are 852 and 1420, for period prior to 1984 and succeeding years, respectively), while the coefficients c are almost the same for all four examined storms (i.e. 2 and 5 year events, and two period of observations for these intensities). Table 4.8 IDF Curves Constants Comparison at Waterloo Station for two Period of Observation with Existing IDF curves Recurrence Interval Data Used 2 Year 5 year Municipality of Waterloo j 582 r 1395 Design 0756 0 839 Guideline (td + 4.6) ~(td+12.7) - 1970 -1984 j 852 j 1580 PDS 0 807 0 857 "(td+6.4) - (td + 14.4) ' 1985-2003 j_ 1420 2375 PDS (td + 9.8)0,881 (td+16.4)0'917 Actually, the rainfall intensity equation (Equation (3.12)) represents the best-fit curve for the data. Thus, the graphical evaluation of the procedure applied in intensity equation calculations for Waterloo station, 5 73 year recurrence interval, and period of observation after the year 1984 is displayed in the Figure 4.9. As presented in Figure 4.9, both heavy rainfall intensities derived from data and rainfall intensity equation (Table 4.8), are plotted against durations ranging from 5 minutes to 2 hours. It is apparent from the Figure 4.9 that the observed data at Waterloo station are described well by IDF curve in mathematical form, and can be used for the analyses in subsequent section of this chapter. Waterloo - 5 year reccurence interval 180 160 1 • Raw data (1985 -2003) 140 120 100 I (mm/hr) •V 80 60 40 20 0 0 30 60 90 120 Duration (min) Figure 4.8 Best-fit Curve Graphical Evaluation at Waterloo Station for 5 year Event, and period of observation 1985-2003 74 4.4.3 Evaluation of Existing Hydrological Model The possible adverse effects due to heavy rainfall magnitude and frequency temporal changes on existing facilities are of particular interest since the IDF curves are frequently applied in various water resources models and design principles. Hence, as a part of this study, additional analyses were undertaken relating to the existing storm sewer pipes and different scenarios with respect to rainfall intensity, and the 5 year event. As presented in the Table 4.9, four different scenarios are considered for pipe size calculations. The scenarios are as follows: • I is existing scenario, i.e. based on the City of Kitchener IDF curves; • II is scenario based on existing curves for City of Waterloo; • Scenarios III and IV are based on IDF curves coefficients estimated by the procedure explained in the previous subsection of this chapter (i.e., Table 4.4.2) for Waterloo station, for periods of observation (1970 -1984), and for (1985 -2003), respectively; The rational method was used for peak flow calculations and pipe size evaluation. The criteria used for area and runoff coefficients are the same under all four circumstances considered for stormwater sewer pipe assessment, while the intensities vary from scenario to scenario. 75 Different abbreviations used in the second and third columns in Table 4.9 are various junctions within the stormwater pipe network, e.g., MH is manhole; CB is catch basin, and so on. Table 4.9 Stormwater Sewer Pipe Size Analyses Based on Various Scenarios in Terms of Heavy Rainfall Intensity for 5 Year Event at Waterloo/Kitchener location Note: * four different scenarios used in pipe sizing It is noted from Table 4.9, that 3 pipes out of 13 are underestimated based on this analyses, i.e., the highlighted rows, or almost one quarter of al evaluated pipes are changed. That means, in regard to peak flow, that capacities of 25 % of existing sewers will be exceeded in the future, as a result of storms intensity alterations. As presented in Table 4.9, at seven locations, within the existing stormwater network, no change in pipe size had been detected under the four different scenarios, while at two locations, explicitly, from MH4 to 76 CBMH5, and from CBMH12 to DCBMH13 the pipe sizes are the same for the existing Kitchener IDF curves and those estimated from the observed data and period of observation (1985 - 2003). Hence, the change in rainfall magnitudes might increase stormwater infrastructure vulnerability by 25 %, and have both environmental and economical adverse effects, among the others, based on these analyses. 4.5. RECURRENCE INTERVALS CONFIDENCE LIMITS The confidence limits can be calculated for any hydrologic curve that is applied in various models and design principles. Additionally, the information about confidence intervals are very useful for risk assessment and designs in water resources, i.e., whether the confidence interval will generate the higher risk, and vice versa. Basically, any hydrologic probability curve should not be drawn without a confidence region (Yevjevich, 1972). In this study, joint confidence limits for two statistical distribution parameters (i.e., mean and standard deviation), were calculated to present an approximate graphical estimate of the heavy rainfall frequencies for 1 hour duration at Waterloo. Due to fact that the assumption for the confidence region evaluation is that data are normally distributed, the first step in these analyses was the lognormal transformation of the observed data. Equations (3.24) and (3.25) were employed in confidence interval computations for mean and standard deviation, respectively. The only difference in computations is applied values 77 fort, 1.761, 1.740, and 1.645, for 15, 18, and 33 samples, respectively, for 90 % confidence limits. Since the two periods of observation were used in temporal evaluation of heavy rainfall intensities and intensity equations, confidence intervals are estimated for data (1970 -1984) and (1985 -2003), where 15 and 18 samples were used in analyses, respectively, while for full period of observation (1970 -2003) 33 samples were used. For the graphical estimation of the confidence regions the data are plotted on lognormal probability paper in the following way: the observed data (Line 1) are plotted by Weibull plotting Formula (3.8); the next step is drawing the frequency curve (Line 2) through the values (xn+2Sn) and (xn-2Sn) at 0.0228 and 0.09772 exceedance probability, in given order; the mean and standard deviation are estimated graphically by drawing the vertical lines from the exceedance probability points at 84.13 % and 15.83% to the frequency curve , and then moving horizontally to the abscissa to get the Sn values; as a final point, four confidence region lines (i.e., Lines from 3 to 6) are designed as: • Line (3) is obtained by using the upper limits of xn and Sn; • Line (4) is obtained by using the upper limits of xn and lower limit of Sn; • Line (5) is obtained by using the lower limits of xn and Sn; 78 • Line (6) is obtained by using the lower limit of xn and the upper limit of Sn; As presented in Figure 4.9 for 33 samples, and Figures 4.10 and 4.11 for 15 and 18 samples, and period of observation from 1970 to 1984 and from 1985 to 2003, the rainfall intensity (mm/hr) are plotted on the abscissa of the log - normal probability paper, against the exceedance percentage and recurrence intervals (years), the horizontal axis on the bottom of the lognormal probability paper and the axis along the top of the probability paper, respectively. Table 4.10 summarized the computation results and the detailed calculations for graphical estimation of confidence regions are presented in Appendix C. 79 Recurrence Interval (yr) 5 4 2 1.3 1.01 L. r \s 90 84.13 75 50 25 15.87 10 Exceedance Percentage Figure 4.9 Recurrence Intervals Confidence Region Graphical Estimation for Period of Observation from 1970 to 2003 at Waterloo Station for 1 hr duration and 33 Samples 80 Recurrence Interval (yr) 100 43.86 10 6,3 5 4 2 1.33 1.11 1.01 60.00 50,00 40.00 C 33.01 £ E £25,82 20,18 15.00F 99 97,72 90 84,13 75 50 25 15,87 10 Exceedance Percentage Figure 4.10 Recurrence Intervals Confidence Region Graphical Estimation for Period of Observation from 1970 to 1984 at Waterloo Station for 1 hour duration and 15 Samples 81 Recurrence Interval (yr) 100 43,8 10 6.3 5 4 2 1,33 1.11 1,01 Exceedance Percentage Figure 4.11 Recurrence Intervals Confidence Region Graphical Estimation for Period of Observation from 1985 to 2003 at Waterloo Station for 1 hour duration and 18 Samples 82 Table 4.10 Summarized Results for Confidence Limits Calculations at Waterloo Station for Different Sample Size and Periods of Observation Period of Sample Xn Sn Size to/ 2 Xn Sn ,) Observation (l) Xn(u) ( Sn(u) 1970 - 2003 33 1.4711 0.1319 1.645 1.4333 1.5088 0.1052 0.1586 1970 - 1984 15 1.4121 0.1066 1.761 1.3636 1.4605 0.0723 0.1408 1985 - 2003 18 1.5153 0.1401 1.740 1.4578 1.5728 0.0995 0.1808 It is apparent, and as would be expected from the Figures 4.9, 4.10, and 4.11, that the confidence region is narrower for sample size 33 then those confidence regions where 15 and 18 samples were used in confidence intervals estimation. As an example, 6.3 year event in Figure 4.9 is 40.9 mm/hr if the rainfall intensity is estimated from frequency curve, with corresponding exceedance probability 15.87 (%) or 84.13 (%) non-exceedance probability, and within the confidence limits from 34.45 mm/hr to 46.49 mm/hr. For the same event, namely 6.3 year recurrence interval and period of observation from 1970-1984 (i.e., Figure 4.10), the rainfall magnitude is 30.01 mm/hr within the confidence limits ranging from 27.28 mm/hr to 39.94 mm/hr. The rainfall intensity with the same frequency (i.e., 6.3 year) and period of observation from 1985 - 2003 (Figure 4.11) is 45.20 mm/hr within the confidence intervals from 36.08 mm/hr to 56.70 mm/hr. Hence, for larger sample size (i.e., 33) uncertainty related to graphical estimation of rainfall intensity is smaller than those regarding smaller sample 83 sizes. Thus, the risk related to either underestimation or an overestimation event frequency is higher for the smaller sample size. The lowest uncertainties with the respect of recurrence intervals confidence limits graphical assessment are for the 2 year event, and all periods of observation employed in these analyses, full period of observation (i.e., 33 samples), and periods (1970-1984) and (1985 - 2003), specifically, from 27.12 mm/hr to 32.26 mm/hr, from 23.10 mm/hr to 28.88 mm/hr, and from 28.96 mm/hr to 37.39 mm/hr, respectively. The rainfall magnitudes estimated from frequency curves in Figures 4.9, 4.10, and 4.11 are 29.58 mm/hr, 25.82 mm/hr, and 32.73 mm/hr, for 2 year recurrence interval, in given order. It is noteworthy that rainfall intensities estimated mathematically for the 2 year event are 29.5 mm/hr for 1 hour duration and period ranging from 1970 to 2003 (refer to Table 4.6.1), and 25.3 mm/hr and 34.6 mm/hr, for period of observation prior to year 1984 and after the year 1984 (refer to table 4.7), in given order. In summary, since the values estimated mathematically are almost the same as those from frequency curves; the graphical estimations of rainfall intensity are acceptable with regards to accuracy. 84 4.6 TREND ANALYSES FOR THE NUMBER OF DRY DAYS AND THE AMOUNT OF RAINFALL The results presented in the above sections of this chapter indicate existing temporal trends in heavy rainfall intensities, both increasing and decreasing, for annual and seasonal analyses at all stations used in study. It has been suggested in some of the preceding climate change studies, that increasing in rainfall intensity occurred with no change in number of days with rain Groisman et al. (1999), or decreasing in number of rainy days and total precipitation in Northern Italy (Brunetti et al., 2000). Similar analyses were applied for observed data set at 13 stations across Ontario. Specifically, the trend evaluations for annual number of dry days and amount of rainfall were accomplished by Mann - Kendall trend test. S statistics was computed by Equation (3.19). For dry day's trend tests Equations (3.20) and (3.21a) were applied in analyses, while for amount of rainfall trend assessments the Equation (3.20) and was applied for Z0 calculations and Equation (3.21b) was used to compute V(S) since there are no tied values in this data set. It is noteworthy to mention that annual number of dry days is calculated as percentage of data with record 0 within the total number of days with records for each year. The annual amount of rain was calculated as a summarized rainfall amount for all durations at particular station. The Null hypothesis was evaluated as: H0: There is no trend in observed data for S =0; 85 Ha: There is an increasing trend for S>0, or decreasing trend for S<0; Hb: An increasing or decreasing trend is significant at 5 % level if IZ0I > Zi-a. The results for both Mann - Kendall test trend analyses (i.e. number of dry days and rainfall amount) are exhibited in Table 4.11. Table4.11 Summarized Results for Mann-Kendall Trend Tests for 5% Level of Significance at 13 Locations in Ontario Station Name Z0 (Dry Days) Z0(Amount of Rain) Bowmanville -0.187 1.049 Burketon 2.278 0.449 Chalk River -0.865 0.252 Delhi -0.200 2.164 Kingston 0.625 -2.438 Orillia 1.153 -0.672 Oshawa 0.220 -0.119 Port Colborne 1.264 -2.747 Preston -0.102 1.102 Sarnia 0.000 -1.275 Sudbury -2.953 -0.730 Timmins 2.205 -1.998 Waterloo 1.386 -1.023 In Table 4.11 bold numbers symbolize that trend is statistically significant at 95% level, namely IZ0I > 1.96. Only for Timmins station the significant trends were detected for analysis of both dry days and amount of rain. For all stations H0was rejected, since there are trends in observed data. Only at Sarnia station, S is 0 for number of dry days test, thus the null hypothesis was accepted. 86 Since there are either upward or downward trends for 25 tests (except for dry days test at Sarnia station), Ha were accepted for those trend detection tests. Finally, Hb with 5% level of significance were rejected for 19 tests, and accepted for 7 tests. In summary, at 7 stations increasing in number of days with no rain were observed, with 2 statistically significant trends, namely, 2.278 and 2.205, for Burketon and Timmins, in given order. At 5 stations there are decreasing trends for number of dry days, with statistically significant test at Sudbury station (i.e. -2.953). For the annual amount of rain there are 8 downward trends of which 3 are statistically significant at 5% level, namely, -1.998 at Timmins station, - 2.747 at Port Colbome station, and -2.438 for Kinston. At 4 stations upward trend test were identified, but only one test is significant at 5 % level (i.e. for Delhi). There is no homogeneous trend prototype which can be applied in any region within the province of Ontario based on these analyses. Moreover, at Timmins station which is located in northern Ontario the statistically significant trends were detected similar to those in central part of province for number of dry days, while for annual amount of rain the trend observed at Timmins is similar with trends observed in south and central Ontario, at Port Colborne and Kingston, respectively. 87 CHAPTER 5 CONCLUSIONS AND RECOMMENDATIONS 5.1 CONCLUSIONS • Based on single site temporal IDF curve assessment derived from the annual exceedance series at 13 stations across Ontario, the consistency of the findings indicate that heavy rainfall intensities are changing for all durations and recurrence intervals evaluated in this research. • The same conclusions are apparent for seasonal IDF curves, regarding temporal analyses for all stations, durations, and frequencies used in the analyses. The seasonal changes in IDF curves might increase erosion during the spring and fall, when the vegetative cover is not so substantial. Further more, during the spring flooding might be more severe due to snow melting and lower soil infiltration capacities combined with more intense storms. • With respect to changes in rainfall intensity over time, there is no uniform pattern which can be applied in to regions within the Province of Ontario. However, the findings are the function of data available for this research. • There are more increasing trends than decreasing trends detected in the evaluation of temporal IDF curves for both annual and seasonal rainfall analyses. 88 • Results based on analyses applied in this study, relate only to single site rainfall data at specific locations evaluated in this research for Ontario conditions. • Changes in rainfall intensity at Waterloo station indicated that the 5 year event in the period of observation from 1970 tol984 has now become the 2 year event for period of observation ranging from 1985 to 2003. • Evaluation of IDF curves coefficients for two non-overlapping periods of observation showed that changes in heavy rainfall intensities have influenced design storms at Waterloo station for 2 and 5 year recurrence intervals. • The design of stormwater sewers using IDF curves for two periods of observation, using the rational method, indicated that five out of twelve pipes are changed in size due to increases in storm intensities at Waterloo station. • Instead of considering just change in pipe size as a mitigation option to increase in heavy rainfall, a broader view of response for stormwater management might be more appropriate, e.g. to improve infiltration, rain water harvesting, etc. • The joint confidence intervals for the mean and standard deviation in rainfall time series, estimated by the graphical method, confirmed there is correlation between uncertainty and 89 less frequent events with respect to sample size used in analyses. • The trend evaluations of the number of dry days and the amount of rain at all stations have demonstrated there to be presence of trend in both variables. However, no simple trend explanation appears feasible for either individual stations or regions across Ontario. • A variety of analyses applied in this research have indicated the significant variability in the heavy rainfall intensities, number of dry days, and amount of heavy rainfall. Hence, the results are consonant with most of preceding climate change studies. • Although yet-to-be-designed drainage systems could be sized to accommodate increases in runoff, existing systems will face a reduction in their intended level of service as the precipitation intensities increase. 5.2 RECOMMENDATIONS FOR FUTURE WORK • The further evaluation of possible effects of changes in rainfall intensities on the existing water resources infrastructure and IDF curves for more locations across Canada and Ontario, is recommended, to better understand the linkage between identified variability and infrastructure vulnerability. 90 • Datasets with lengths of more than 30 years might decrease uncertainties associated with less frequent events and hence employing these in similar analyses to those undertaken herein, would have great value. • There is value for more cooperation among universities, and the Meteorological Service of Canada to better understand possible effects of climate change in Canada, and to evaluate the vulnerabilities of water resources infrastructure and the short and long-term risks of systems potential failures due to changes in rainfall intensities. • The designing of important critical structures should incorporate adequate safety factors to mitigate impacts of climate changes. 91 REFERENCES Adamowski,K., Bougadis,J., Pessy,G.G., (2003) Influence of Trend on Short Duration Design Storms, University of Ottawa, unpublished, 15 pp. American Society of Civil Engineers (1996 a). 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Canadian Meteorological and Oceanographic Society. 97 APPENDIX A: Tables Table 4.1 Meteorological stations used for analyses; Data are provided by Environment Canada; Remarks:* Missing Data (1994-2000); ** Length of record is less than 3 decades; *** Missing data for year 2001; ****Missing data for year 1998 Region Length In Station Latitude Longitude Period of of Station name Ontario ID N W Observation Record (years) Delhi 6131982 42°52' 80°33' 1962-1995 34 Port 6136606 42085' 79015' 1964-2000 37 South Colborne Ontario Preston 6146714 43023' 80°21' 1970-1996 26** Sarnia 6127514 43°00' 82019' 1970-2003 34 Waterloo 6149387 43°27' 80023' 1970-2003 33*** Bowmanville 6150830 43055' 78040' 1966-2001 36 Burketon 6151042 44002' 78048' 1969-2001 33 Central Kingston 6104175 44014' 76029' 1960-2003 44 Ontario Orillia 6115820 44037' 79025' 1965-1992 28** Oshawa 6155878 43°52' 78°50' 1969-2003 34 Chalk River 6106400 45059' 77026' 1962-1995 34 North Moosonee 6075425 51016' 80O39' 1967-2003 37* Ontario Sudbury 6068150 46037' 80048' 1971-2002 32 Timmins 6076572 48028' 81016' 1969-1999 30**** 98 Table 4.3.1 DELHI IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1962-1978 and 1979-1995 c E 2YR 5 YR 10 YR 25 YR 50 YR 100 YR C ,0 +5 Change Change Change Change Change Change m (%) (°/o) (0/0) (%) (%) (0/0) 3 o 5 2 -3 -5 -7 -9 -10 10 14 14 14 14 14 13 15 18 18 18 18 18 18 30 23 33 40 46 50 54 60 22 26 27 29 30 31 120 13 15 16 17 18 19 360 -1 3 4 6 7 8 720 8 17 22 26 28 30 Table 4.3.2 PORT COLBORNE IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1962-1978 and 1979-1995 c "i 2YR 5 YR 10 YR 25 YR 50 YR 100 YR C Change Change Change Change Change Change o (0/0) (0/0) (o/o) (O/o) (O/o) (o/o) n L. 3 5 Q -6 -1 10 5 7 8 10 -3 0 11 3 5 5 15 -2 5 10 12 15 17 30 2 2 12 2 2 2 60 1 11 10 23 26 29 120 -6 1 12 9 11 14 360 -5 -12 18 -18 -19 -20 720 -3 -12 19 -19 -21 -22 Table 4.3.3 PRESTON IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1970-1984 and 1985-1996 C I 2YR 5 YR 10 YR 25 YR 50 YR 100 YR c o Change Change Change Change Change Change m (%) (0/0) (0/0) (°/o) (0/0) (%) 3 Q 5 14 11 10 8 7 7 10 17 24 27 31 33 36 15 22 38 47 58 64 70 30 27 37 43 49 53 56 60 30 28 27 26 25 24 120 29 21 17 13 11 9 360 7 3 1 -1 -2 -3 720 10 5 3 1 0 -1 Table 4.3.4 SARNIA IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1970-1984 and 1985-2003 c 1 2 YR 5 YR 10 YR 25 YR 50 YR 100 YR C Change Change Change Change Change Change o (0/o) (°/o) (0/0) (O/O) (0/0) (o/o) re u 3 5 Q 13 49 65 80 89 96 10 9 46 63 79 88 96 15 11 45 61 76 85 92 30 19 46 59 72 80 86 60 21 42 52 62 68 73 120 17 30 36 42 46 49 360 15 17 18 20 20 21 720 16 22 26 29 31 33 100 Table 4.3.5 WATERLOO IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1970-1984 and 1985-2003 C 1 2YR 5 YR 10 YR 25 YR 50 YR 100 YR C o Change Change Change Change Change Change •w (O/O) 10 (%) (%) (%) (%) (%) l_ 3 Q 5 12 15 16 17 18 19 10 24 18 16 13 11 9 15 23 30 33 37 40 42 30 27 34 37 40 43 44 60 37 41 43 45 46 47 120 25 30 32 34 35 36 360 12 15 16 18 19 19 720 11 13 14 14 15 15 Table 4.3.6 BOWMANVILLE IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1966 -1984 and 1985-2001 c 1 2YR 5YR 10 YR 25 YR 50 YR 100 YR c o Change Change Change Change Change Change +3 (%) (°/o) (%) (%) (O/O) (%) ra 3 5 a 15 18 19 20 21 22 10 18 22 23 25 26 27 15 19 20 21 22 23 23 30 25 22 21 20 19 19 60 25 19 16 13 12 10 120 25 29 30 32 33 34 360 22 32 38 44 48 51 720 23 37 45 53 59 64 Table 4.3.7 BURKETON IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1969-1984 and 1985-2001 c E 2YR 5 YR 10 YR 25 YR 50 YR 100 YR c o "*3 Change Change Change Change Change Change n (°/o) (°/o) (%) (o/o) (%) 3 Q 5 12 3 -1 -14 -14 -15 10 1 11 17 9 18 22 15 8 24 33 23 35 42 30 18 28 33 23 32 36 60 22 29 33 22 29 32 120 23 38 46 32 44 50 360 23 18 16 2 4 4 720 21 13 9 -5 -4 -5 Table 4.3.8 KINGSTON IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1960-1981 and 1982-2003 c 1 2YR 5 YR 10 YR 25 YR 50 YR 100 YR C o Change Change Change Change Change Change (0 (%) (%) (O/o) (o/o) (%) (%) L. 3 Q 5 5 15 20 25 28 31 10 9 16 20 24 27 30 15 4 13 18 24 27 31 30 7 15 19 23 26 28 60 8 12 14 16 18 19 120 -4 -1 0 2 3 4 360 -5 -8 -10 -11 -12 -13 720 -5 -7 -9 -10 -10 -11 102 Table 4.3.9 ORILLIA IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1965-1978 and 1979-1992 c "i 2YR 5 YR 10 YR 25 YR 50 YR 100 YR c 0 Change Change Change Change Change Change 4J re (0/0) (°/o) (%) (%) (°/o) (%) i_ 3 Q 5 25 21 19 17 16 15 10 19 13 10 6 5 3 15 20 17 16 14 13 13 30 24 18 15 13 11 10 60 25 15 11 7 5 3 120 29 24 21 19 18 17 360 30 37 41 44 46 48 720 26 33 36 39 41 43 Table 4.3.10 OSHAWA IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1969-1984 and 1985-2003 c i 2YR 5YR 10 YR 25 YR 50 YR 100 YR C Change Change Change Change Change Change o re (0/0) (%) (O/o) (%) (°/o) (O/o) i. 3 Q 5 13 21 25 29 31 34 10 14 23 28 33 36 39 15 11 18 22 26 28 30 30 15 13 12 11 11 10 60 18 8 4 0 -3 -4 120 23 16 12 9 7 5 360 18 18 17 17 17 17 720 3 -21 -28 -34 -37 -40 103 Table 4.3.11 CHALK RIVER IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1962-1978 and 1979-1995 c i 2 YR 5YR 10 YR 25 YR 50 YR 100 YR c Change Change Change Change Change Change 0 +3 (%) (°/o) (0/0) (0/0) (0/0) re i_ 3 5 Q 8 4 2 1 0 -1 10 17 16 16 15 15 15 15 10 8 7 6 5 5 30 6 8 8 9 10 10 60 3 10 13 17 18 20 120 -4 -6 -7 -8 -9 -9 360 4 0 -1 -3 -3 -4 720 12 12 13 13 13 13 Table 4.3.12 SUDBURY IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1971-1984 and 1985-1996 c £ 2YR 5 YR 10 YR 25 YR 50 YR 100 YR C o Change Change Change Change Change Change re (0/0) (%) (0/0) (°/o) (O/O) (%) i_ 3 Q 5 6 10 11 13 14 14 10 7 7 7 7 7 7 15 19 18 17 17 16 16 30 31 25 22 19 18 17 60 31 18 13 8 5 3 120 18 11 8 5 3 2 360 7 0 -3 -6 -8 -10 720 -1 -5 -7 -9 -10 -11 104 Table 4.3.13 TIMMINS IDF Curves Temporal Trend Analyses Changes in IDF Curves for Time Series: 1969-1984 and 1985 - 1999 c E 2YR 5 YR 10 YR 25 YR 50 YR 100 YR c 0 33 Change Change Change Change Change Change a (%) (0/0) (O/o) (°/o) (O/O) (%) u 3 a 5 ' 19 48 37 41 45 48 10 21 57 45 51 55 59 15 24 65 54 62 68 74 30 15 70 63 78 90 101 60 3 38 28 34 39 44 120 3 26 12 12 14 15 360 -7 17 7 9 11 13 720 0 35 24 29 33 37 Table 4.3.14 Summarized IDF Curves Average Annual Changes in Percentage for 5 Year Recurrence Interval Number Duration Station of name Years 5 min 10 min 15min 30min lhr 2hr Delhi 17 -0.168 0.822 1.054 1.969 1.507 0.883 Port Col borne 18 -0.046 0.011 0.264 0.100 0.629 0.064 Preston 12 0.921 1.994 3.175 3.104 2.309 1.742 Sarnia 17 3.284 3.079 3.020 3.086 2.768 2.014 Waterloo 18 0.812 1.023 1.655 1.873 2.296 1.656 Bowmanville 16 1.094 1.348 1.271 1.394 1.190 1.799 Burketon 16 0.185 0.698 1.510 1.735 1.813 2.403 Kingston 22 0.670 0.729 0.601 0.662 0.537 -0.053 Orillia 12 1.745 1.054 1.427 1.514 1.266 1.980 Oshawa 18 1.143 1.285 1.019 0.719 0.445 0.863 Chalk River 17 0.243 0.941 0.462 0.448 0.595 -0.375 Sudbury 17 0.572 0.389 1.058 1.444 1.053 0.645 Timmins 16 3.025 3.560 4.042 4.392 2.404 1.595 105 Table 4.4.1 DELHI Seasonal Percentage Change in IDF Curves for Time Series: 1962 - 1978 and 1979 - 1995 2YR 5 YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 3 4 3 -21 -2 8 -29 -5 10 10 -2 18 9 -9 16 11 -16 16 12 15 4 21 11 -3 19 12 -10 17 12 30 10 26 4 7 35 3 5 40 3 60 -5 28 9 -5 29 2 -6 29 -2 120 -2 14 10 11 15 9 17 16 8 360 4 0 1 7 -1 10 8 -1 14 720 0 2 -3 10 10 17 14 14 27 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 -36 -7 12 -39 -9 13 -42 -11 14 10 -20 15 12 -22 15 13 -23 14 13 15 -14 16 13 -16 15 13 -17 14 13 30 4 46 3 3 49 3 2 52 3 60 -6 29 -5 -6 29 -7 -7 29 -8 120 23 17 7 27 17 7 31 18 6 360 10 -1 18 11 -1 21 11 -1 23 720 18 17 37 21 19 44 23 20 50 106 Table 4.4.2 PORT COLBORNE Seasonal Percentage Change in IDF Curves for Time Series: 1962 -1978 and 1979 - 1995 2YR 5YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 -16 2 -16 -13 5 -15 -12 7 -15 10 -17 -1 -13 -15 -3 -3 -14 -4 1 15 -13 -3 -9 -7 2 -1 -4 4 3 30 -6 -1 1 4 0 4 9 1 5 60 -4 -4 2 5 13 -4 11 22 -7 120 -2 -4 1 0 8 -12 0 14 -17 360 0 -7 0 -1 -8 -10 -1 -9 -15 720 -1 -9 2 5 -16 -2 8 -19 -4 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 -10 9 -14 -10 10 -14 -9 11 -14 10 -13 -5 6 -13 -6 8 -12 -6 11 15 -2 6 7 0 7 9 2 8 11 30 15 2 6 18 2 7 21 3 8 60 16 30 -9 20 35 -10 23 40 -11 120 1 20 -22 1 24 -24 2 27 -26 360 -1 -9 -19 -2 -10 -21 -2 -10 -22 720 11 -21 -5 13 -22 -6 15 -23 -7 107 Table 4.4.3 PRESTON Seasonal Percentage Change in IDF Curves for Time Series: 1970 - 1984 and 1985 - 1996 2YR 5 YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 26 15 3 30 12 -10 32 10 -15 10 15 18 10 25 23 0 29 26 -4 15 17 23 5 28 38 -3 33 46 -7 30 25 26 2 30 38 4 33 44 5 60 18 23 -5 44 22 12 56 22 20 120 11 23 -8 36 15 5 47 12 12 360 2 8 -6 20 3 -5 30 1 -4 720 9 15 -10 22 11 -12 28 10 -13 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON T , 5 34 8 -20 35 7 -22 36 6 -24 b 10 32 29 -8 35 31 -11 36 33 -12 1 e 15 37 55 -10 40 60 -12 42 65 -14 < 30 35 51 6 37 55 6 38 58 6 4 • 60 67 22 29 74 21 34 80 21 38 4 120 59 8 19 65 6 23 71 5 26 4 H 360 41 -1 -4 48 -3 -4 54 -4 -47 S 720 35 8 -14 39 7 -15 42 7 70 108 Table 4.4.4 SARNIA Seasonal Percentage Change in IDF Curves for Time Series 1970-1984 and 1985 - 2003 2YR 5YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 36 15 26 51 53 10 59 69 5 10 44 8 24 53 51 6 57 71 0 15 30 14 28 29 50 13 28 67 7 30 24 25 38 17 56 10 14 71 1 60 6 25 38 6 53 6 6 66 -4 120 -6 23 29 1 45 -5 4 56 -16 360 -3 19 20 -1 25 1 1 27 -7 720 -3 21 17 1 25 15 4 27 14 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 68 83 0 73 91 -3 77 98 -5 10 90 -5 64 -7 -9 T 62 101 67 110 / a 15 28 83 3 27 92 0 27 100 -1 3 11 86 -6 9 95 -10 8 103 -13 if ° e 60 6 80 -13 6 89 -17 6 96 -21 120 8 67 -25 10 74 -30 12 80 -33 4 360 2 30 -13 3 31 -17 4 33 -20 4 720 6 29 13 7 30 12 9 31 12 109 Table 4.4.5 WATERLOO Seasonal Percentage Change in IDF Curves for Time Series: 1970 - 1984 and 1985 - 2003 2YR 5YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 19 14 32 4 16 48 -2 17 57 10 22 29 40 4 22 40 -3 18 40 15 27 25 34 17 31 33 13 34 32 30 24 28 39 18 35 32 15 38 28 60 17 37 25 16 41 22 16 44 20 120 15 23 17 14 29 19 14 32 20 360 5 12 13 7 15 13 8 16 12 720 6 12 4 10 14 6 12 15 6 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 -7 18 65 -11 19 71 -13 19 75 10 -10 14 40 -14 12 40 -17 10 40 15 9 37 32 7 40 32 5 42 31 30 13 41 24 12 43 22 11 44 20 60 15 45 19 15 47 18 15 47 17 120 14 34 21 14 35 22 13 36 22 360 9 17 12 10 18 12 11 18 12 720 14 15 7 15 16 7 16 16 8 110 Table 4.4.6 BOWMANVILLE Seasonal Percentage Change in IDF Curves for Time Series 1966 -1984 and 1985 - 2001 2YR 5 YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 25 6 31 46 11 30 56 14 29 10 27 12 43 49 15 38 61 17 36 15 28 12 46 56 18 35 71 21 31 30 35 14 53 55 17 47 65 18 45 60 21 25 44 37 21 32 45 19 27 120 15 23 31 13 27 31 12 30 31 360 11 19 18 2 31 25 -2 38 28 720 1 12 24 -3 24 40 -5 31 48 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 66 16 29 72 18 28 77 19 28 10 73 18 35 81 20 34 88 21 33 15 88 24 28 98 25 26 108 27 25 30 76 20 43 83 20 41 89 21 40 60 54 17 23 60 16 20 66 15 18 120 10 32 31 10 33 30 9 35 30 360 -6 45 32 -8 49 34 -10 52 36 720 -7 37 57 -8 41 62 -9 44 67 Table 4.4.7 BURKETON Seasonal Percentage Change in IDF Curves for Time Series: 1969 - 1984 and 1985 - 2001 2 YR 5 YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 10 7 43 38 11 35 51 -3 31 10 -4 -2 26 7 25 16 12 17 12 15 -7 4 27 7 39 26 13 29 25 30 9 10 28 24 39 44 31 30 51 60 19 12 28 34 41 52 41 31 64 120 20 16 27 23 57 41 24 43 48 360 15 22 29 22 34 27 26 17 26 720 -1 17 30 1 26 32 2 9 33 25 YR 50 YR 100 YR Duration Cha nge (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 64 -6 29 72 -8 27 79 -9 26 10 17 24 8 19 29 6 21 33 5 15 19 39 24 23 45 24 26 51 24 30 37 38 58 41 44 62 44 48 66 60 48 39 77 52 43 85 55 48 92 120 26 53 55 26 59 59 27 65 63 360 30 15 25 33 15 25 35 14 24 720 3 7 34 3 5 34 4 4 35 112 Table 4.4.8 KINGSTON Seasonal Percentage Change in IDF Curves for Time Series 1960 - 1981 and 1982 - 2003 2YR 5YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 27 11 -16 12 25 -18 7 33 -19 10 16 14 -20 2 22 -16 -4 26 -14 15 11 12 -22 -4 19 -21 -9 22 -21 30 4 16 -25 -13 22 -22 -19 24 -20 60 -8 18 -16 -29 18 -7 -36 18 -2 120 -19 18 -22 -37 13 -21 -44 11 -21 360 -15 18 -13 -27 15 -16 -33 13 -18 720 -14 20 -16 -19 15 -15 -21 13 -15 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 2 41 -20 0 46 -20 -2 50 -21 10 -8 31 -13 -11 33 -12 -13 36 -11 15 -14 26 -20 -17 28 -20 -19 30 -19 30 -25 28 -19 -28 29 -18 -30 31 -17 60 -43 18 2 -46 18 5 -49 18 7 120 -50 9 -21 -54 8 -21 -56 7 . -21 360 -37 12 -20 -40 11 -21 -42 10 -21 720 -23 10 -14 -24 9 -14 -25 7 -14 113 Table 4.4.9 ORILLIA Seasonal Percentage Change in IDF Curves for Time Series 1965 - 1978 and 1979 - 1992 2YR 5 YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 20 20 31 56 18 41 74 17 47 10 18 18 28 45 13 32 58 10 33 15 8 19 26 25 17 29 33 16 30 30 13 20 25 12 17 41 11 16 50 60 6 20 18 -3 14 40 -6 11 53 120 5 18 13 5 21 26 4 22 33 360 15 21 10 5 31 36 0 35 49 720 23 19 8 10 28 31 4 31 43 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 91 16 47 102 16 55 111 15 58 10 71 7 33 79 6 37 86 5 38 15 40 15 30 44 15 32 48 14 33 30 10 14 50 10 14 66 10 13 72 60 -10 9 53 -12 8 76 -13 7 85 120 4 23 33 4 24 44 4 25 48 360 -4 39 49 -7 42 72 -9 44 79 720 -1 35 43 -5 37 65 -7 39 72 114 Table 4.4.10 OSHAWA Seasonal Percentage Change in IDF Curves for Time Series 1969 - 1984 and 1985 - 2003 2YR 5YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 26 9 34 18 19 45 15 24 51 10 30 12 19 15 23 27 10 29 31 15 17 12 20 1 20 25 -5 24 27 30 18 16 30 -2 13 39 -9 11 42 60 11 16 41 -5 2 60 -11 -4 69 120 -2 22 39 -14 2 60 -20 -6 71 360 -2 10 34 -5 2 57 -7 -2 68 720 -3 -10 30 -8 -41 65 -11 -51 83 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 13 29 57 12 32 61 12 35 64 10 6 35 35 4 39 38 4 42 40 15 -10 29 30 -12 31 31 -12 34 32 30 -15 10 46 -18 9 48 -18 8 50 60 -17 -9 78 -21 -12 84 -21 -15 89 120 -25 -14 81 -28 -18 87 -28 -21 92 360 -9 -6 80 -9 -8 87 -9 -10 93 720 -13 -58 103 -15 -61 115 -15 -64 126 Table 4.4.11 CHALK RIVER Seasonal Percentage Change in IDF Curves for Time Series: 1962 - 1978 and 1979 - 1995 2YR 5YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 10 14 -20 7 6 -23 6 3 -24 10 19 20 -15 16 17 -15 14 15 -15 15 19 13 -12 18 8 -12 18 6 -12 30 18 4 -5 32 7 2 38 8 5 60 20 2 1 32 10 10 38 13 15 120 25 -7 18 27 -8 37 28 -9 46 360 40 -2 28 38 -4 33 36 -5 35 720 42 2 22 49 8 23 52 10 24 25 YR 50 YR 100 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 5 0 -25 4 -2 -25 4 -3 -26 10 13 14 -15 13 13 -15 12 12 -15 15 17 5 -11 17 3 -11 17 2 -11 30 44 10 8 47 11 9 50 11 11 60 43 17 19 46 19 22 49 20 25 120 29 -10 57 30 -10 64 30 -10 70 360 35 -5 37 35 -5 38 34 -6 40 720 55 12 24 57 13 24 59 14 24 116 Table 4.4.12 SUDBURY Seasonal Percentage Change in IDF Curves for Time Series 1971 -1984 and 1985 - 1996 2 YR 5 YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 6 -4 31 -12 -2 71 -19 -1 91 10 12 -6 43 -3 -7 75 -9 -7 89 15 12 3 43 -8 6 80 -15 7 98 30 5 15 28 -14 16 73 -21 16 96 60 10 23 13 -5 12 42 -12 7 57 120 11 14 4 -2 3 22 -7 -2 31 360 1 9 5 5 -3 9 7 -8 10 720 0 4 2 11 -8 4 17 -13 5 25 YR 50 YR 100 YR Duration Cha nge (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 -25 0 112 -28 0 124 -30 1 135 10 -14 -7 103 -17 -8 111 -20 -8 118 15 -22 8 116 -26 8 127 -28 9 136 30 -28 17 121 -31 17 137 -34 17 151 60 -17 3 72 -21 1 81 -23 0 89 120 -12 -6 39 -15 -8 43 -18 -10 47 360 9 -13 12 10 -16 13 11 -18 14 720 22 -18 6 25 -21 6 28 -23 7 117 Table 4.4.13 TIMMINS Seasonal Percentage Change in IDF Curves for Time Series 1969 -1984 and 1985 - 1999 2YR 5 YR 10 YR Duration Change (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 -16 26 -31 -29 35 -21 -33 40 -16 10 -7 29 -32 -11 40 -17 -13 44 -10 15 -3 31 -29 -3 48 -15 -3 57 -9 30 -1 18 -26 6 45 -15 9 61 -11 60 0 5 -25 5 20 -20 8 27 -17 120 4 7 -15 6 12 -18 6 15 -19 360 10 2 -17 8 7 -28 6 9 -32 720 15 8 -21 16 19 -30 17 24 -34 25 YR 50 YR 100 YR Duration Cha nge (%) Change (%) Change (%) (min) MAM JJA SON MAM JJA SON MAM JJA SON 5 -36 45 -12 -37 47 -10 -39 50 -8 10 -14 49 -3 -15 52 0 -15 54 4 15 -3 66 -4 -3 71 0 -3 76 2 30 11 77 -6 13 87 -3 14 97 -1 60 10 35 -14 11 40 -13 12 44 -11 120 7 17 -20 7 19 -21 7 20 -21 360 5 11 -36 4 13 -38 4 14 -40 720 18 29 -38 18 32 -40 19 34 -42 118 APPENDIX B: Computer Programs iB^Jirosv^ -&isa5"^" ^.L">^i^^l^/i3ll J^lfejt^/j3W|^^ # File Edit View Insert Query lools Window Help i' Hti § £• ! -£'©£' ® SELECT a.StationName AS StatfonName, a.Year, a.MissingDatal??, b.TotaDatal27, (100* a.MissingDatal27 [ b.TotalDabal27) A5 [% MissingDatal27]; FROM [SELECT Tablel.StationName as [StationNamelTablei .Year as [Year], COUNT(*) A5 {Missln^)ataL27] FROMTablel WHERE Tablel.Element=127 AND Tablel.Rain*-999 GROUP BY Table 1 .Stah'onNamej Table ]. AS a INNER JOIN [SELECT Tablet .StationName as{StationNamel Tablel.Year as [Year], COUNT(*> A5 FROMTablel WHERE Tablel.Element = 127 GROUPBY tablel.StatioriName, Tablel.Year ; ]. AS b ON (a.StationName - b.StationName) AND (a.Year = b.Year) ORDER BY a.StationName, a.Year; Figure 4.2 Microsoft Access Query for Percentage of Missing Data Calculations for Element 127(i.e. 15 minutes duration) at all Stations 119 Hie Eci: v*v j>zr. -r'.-rit B.eojrte lools Window Help :: ja •-•"";* •'4iW '«wu^ •>-••' •* "a- Ea>> [y she- Mean &S.D. table Base Ma Mean &S.D. Max Part Duration Bi Record- Hi ijryjizr^i^SEffl! sHhm3 Element Mean StDevOfRam | Beta Alpha Gumbel 125 11.55333333333333 3.79188356260856 9.84698573016 2.95653161377' 19.3035533918361 12B ~ 16.78 i01586055855395~*"R5228627487 3.91086647750*" 27.0319031688871! 127^2049333333333333 5.84385717370528 17.8635976052 4.55645543834 32.4375764354392 128* 2547333333333333 6.25967441721403 226564798456 4.88066814310- 382674641200431 1 | 129 28.50666666666667 6.6956773546890? 25.4936118571 5.22061963345. 42.1919426206242 130 32.90666666666667 8.52169220843126 0719051728726 6.64436341491 r~" 50.3241292009689' 131 4^60666666666667 " " 12"4944254236306"35.984175226d ¥.74190350280 " B7.1439B735U«| 132 4699333333333333 9 9145251789387* 42 5317970028 7.73035528202* 67.2576032254924! 161, 614.5333333333333 117.889698245355" 561.482969123 91.9185977219 855 487753200447| Rf cord: H< 6 • M N- of 9 Figure 4.4 Interface of Computer Program Developed in Microsoft: Access for IDF Analyses with Attached Output Table 120 Microsoft Access File Edit View Insert Format Records Iools Window Help H$ # ;• - v *15i ^1 : *4 - ••>• E4- 0 TOP Station Name year From YearTflr Max Part Duration 122 Kingston ^Mjl982 J2003 Month From: Month To: Mean &S.D. table Base Max Return Period: 10 F y Mean &S.D. Max Part Duration Mean &S.D. Max Part Duration Seasonal qryMeanMaxPartDurationSeasonal: Select Qu. « 1 y Figure 4.5 Interface of Computer Program Developed in Microsoft Access for Seasonal IDF Analyses with Attached Output Table 121 APPENDIX C: Confidence Intervals Calculations Example for 18 Samples at Waterloo Station xn= 1.515 or it is log 32.73 mm/hr; Sn = (log 45.20 - log 23.71)/2 = 0.1401; For 90 percent confidence level and 18 samples t value is 1.740, the lower and upper confidence limits are 1.4578 and 1.5728 for xn, and 0.0995 and 0.1808 for Sn. The four straight lines are obtained as: Line 3 was constructed by using the points: 1.5728 and 1.7536 (1.5728 + 0.1808), at 50% and 84.13 % exceedence percentage; Line 4 was drawn thought the points 1.572 and 1.4732 (1.572 - 0.0995), at 50% and 15.87% exceedence percentage; Line 5 was constructed by using the points: 1.4578 and 1.5573 (1.4578 + 0.0995), at 50% and 84.13 % exceedence percentage; Line 6 was drawn thought the points 1.4578 and 1.2769 (1.4578 - 0.1808), at 50% and 15.87% exceedence percentage; 122