ASSESSMENT OF THE INFLUENCE OF NONSTATIONARY CLIMATE ON EXTREME HYDROLOGY OF SOUTHWESTERN CANADA

A Thesis

Submitted to the Faculty of Graduate Studies and Research

For the Degree of

Special Case Doctor of Philosophy in Geography

University of Regina

By

Sunil Gurrapu

Regina, Saskatchewan

January 2020

Copyright 2020: S. Gurrapu

UNIVERSITY OF REGINA

FACULTY OF GRADUATE STUDIES AND RESEARCH

SUPERVISORY AND EXAMINING COMMITTEE

Sunil Gurrapu, candidate for the degree of Special Case Doctor of Philosophy in Geography, has presented a thesis titled, Assessment of the Influence of Nonstationary Climate on Extreme Hydrology in Southwestern Canada, in an oral examination held on November 7, 2019. The following committee members have found the thesis acceptable in form and content, and that the candidate demonstrated satisfactory knowledge of the subject material.

External Examiner: *Dr. Stephen Jacques Dery, University of Northern British Columbia

Co-Supervisor: Dr. David Sauchyn, Department of Geography & Environmental Studies

Co-Supervisor: *Dr. Kyle Hodder, Department of Geography & Environmental Studies

Committee Member: *Dr. Jeannine St. Jacques, Adjunct

Committee Member: Dr. Peng Wu, Environmental System Engineering

Committee Member: Dr. Ulrike Hardenbicker, Department of Geography & Environmental Studies

Chair of Defense: Dr. Fanhua Zeng, Faculty of Graduate Studies & Research

*Via ZOOM conferencing

ABSTRACT

The demand for water supplies across southwestern Canada has increased substantially over the past century with growing population and economic activities. At the same time, the region’s resilience to the impacts of hydrological extremes, floods and droughts is challenged by the increasing frequency of these extreme events. In addition, increased winter temperatures over the past century have led to declines in winter snowpack and caused earlier snowmelt, leading in some years to a substantial shortage of water during late summer and fall seasons. This calls for a better understanding of the flood and drought characteristics in addition to the information on water availability for effective water management and to design infrastructure resilient to such extreme conditions.

The objective of this thesis is to examine the spatial and temporal variability of available water in the naturally flowing watersheds of southwestern Canada and evaluate various regional hydroclimatic and large-scale climatic indices in representing the regional hydrology and hydrological extremes. To do so, I first examined the empirical relationships between historically observed streamflow in 24 naturally flowing watersheds across southwestern Canada and the associated watershed’s hydroclimate, represented by the watershed averaged Standardised Precipitation

Evapotranspiration Index (SPEI). The hydroclimate of all the selected watersheds is assumed to be represented by the second version of the NRCAN gridded climate dataset. These empirical relationships indicate that the water availability can be represented by the watershed averaged SPEI. I then developed SPEI-based principle component regression (PCR) equations and found them to be very efficient in representing the variability in historically observed monthly and annual streamflow.

These equations are simpler to build than calibrating a numerical hydrological model

S. Gurrapu, 2020 P a g e | ii and can be applied over large areas and many sub-basins with minimal data requirements to estimate streamflow.

I then analysed the annual peak flows in 119 naturally flowing watersheds and

8 regulated watersheds, but with naturalized streamflow datasets, across southwestern

Canada to examine the impact of the Pacific Decadal Oscillation (PDO) on annual flood risk. Using Spearman’s rank correlation ρ and permutation tests on quantile-quantile plots, I found that higher magnitude floods are more likely during the negative phase of the PDO than during the positive phase. In addition, the flood frequency analysis

(FFA) stratified according to PDO phase suggests that higher magnitude floods may also occur more frequently during the negative PDO phase than during the positive phase. These results question the validity of the stationarity assumption made in FFA and suggest that the knowledge of large-scale climate state should be considered prior to the design and construction of key infrastructure. The results indicate that the stationarity assumption is not tenable in the watersheds of southwestern Canada.

To demonstrate the invalidity of the stationarity assumption, I evaluated the variability in drought characteristics, i.e. severity, duration and frequency as applied to the City of Calgary, as a case study. The drought characteristics are defined by the historic (100 years of observed) and prehistoric (900 years of stochastically generated from tree-ring reconstructions of annual streamflow) weekly streamflow datasets. The results indicate that the severity and duration of hydrological drought with the same frequency is substantially larger and longer in the prehistoric period than that observed over the historical period. The results also indicate that varying lengths of data used in determining characteristics of extreme events produce varying results, which indicate that the stationarity assumption could be deceptive. Overall, the results demonstrate the implications of the non-stationary climate. in the analysis of hydrological extremes.

S. Gurrapu, 2020 P a g e | iii ACKNOWLEDGEMENTS

I would like to express my gratitude to everyone that supported and guided me in completing my research work and putting this thesis together. I owe a many thanks to my co-supervisors Dr. David J Sauchyn and Dr. Kyle R Hodder, for their constant support, patience and belief in me. I could not have completed this thesis without their guidance and continuous feedback. Their encouraging and supporting words have reassured me and helped me to work harder in completing the research work. I also would like to thank all of my committee members for their advice and encouragement in many meetings we have had. My rationale thinking has evolved over the past few years from all the critical suggestions and comments from the committee members, which has helped me in making relevant conclusions from my research work. A very special thanks to Dr. Jeannine St. Jacques for the encouragement she gave me in accomplishing all the objectives of my research work. Her encouraging words have always helped me boost up my confidence and inspired me to work harder in putting this thesis together. I sincerely appreciate her constant support and advice in correcting my English grammar and writing skills. This has helped me substantially in preparing the manuscripts and this thesis.

I also would like to acknowledge the constant support I received from my family and friends. Their encouragement has helped me to pursue and accomplish one of the major objectives of my career. Long conversations with my friends Solomon Yadessa

Kenno and Vikas Methre have helped me rebuild my confidence and work towards my goals. I can never forget the comforting words from all my other friends. A very special thanks to the God-given sister Dr. Meena Pole for her constant support every time I needed.

S. Gurrapu, 2020 P a g e | iv DEDICATION

I would like to dedicate this thesis to all the members of my family whose love and support over many years have laid foundation for the discipline and dedication necessary in completion of this work.

S. Gurrapu, 2020 P a g e | v TABLE OF CONTENTS

Page # ABSTRACT ii ACKNOWLEDGEMENTS iv DEDICATION v CHAPTER 1: Introduction and Literature Review 1.1. Overview 1 1.2. Objectives 5 CHAPTER 2 Abstract 7 Keywords 7 2.1. Introduction 8 2.2. Data and Study Region 10 2.3. Methods 12 2.4. Results 16 2.5. Discussion 21 2.6. Conclusions 24 2.7. Figures 25 2.8. Tables 34 Appendix 38 CHAPTER 3 Abstract 39 Key Terms 39 3.1. Introduction 40 3.2. Study Area and Data 42 3.3. Methods 44 3.4. Results and Discussion 47 3.5. Conclusion 53 3.6. Figures 55 3.7. Tables 64 Supplementary Figures 70

S. Gurrapu, 2020 P a g e | vi Supplementary Tables 74 Supplementary Text 88 CHAPTER 4 Abstract 97 Key Points 97 4.1. Introduction 98 4.2. Study Region and Data 100 4.3. Methods of Analysis 103 4.4. Results and Discussion 108 4.5. Conclusions 114 4.6. Figures 118 4.7. Tables 128 CHAPTER 5: Conclusions 5.1. Summary 130 5.2. Assessment of Regional Hydroclimate for Streamflow Prediction 130 5.3. Influence of Non-stationary climate on Hydrological Extremes 131 5.4. Reliability of Current Water Supply and Management Systems 132 BIBLIOGRAPHY 135 APPENDIX Statement of Co-Authorship 151

S. Gurrapu, 2020 P a g e | vii CHAPTER 1: Introduction and Literature Review

1.1. Overview

A growing population and economic activities across southwestern Canada have increased the demand for water supplies and at the same time increased the region’s vulnerability to extreme hydrological events, floods and droughts (e.g. Schindler &

Donahue, 2006; Horbulyk, 2014; Sauchyn et al., 2015; Hurlbert and Gupta, 2017).

Therefore, the planning and design of water resources (e.g. dams, canal systems) and transportation (e.g. roads, bridges) infrastructure for efficient distribution and management of the available water in this region requires a depth of knowledge on the magnitude, duration, and frequency of regional hydrological extremes, in addition to information on water availability.

The majority of the watersheds across southwestern Canada are snow- dominated; and winter snowpack is the primary reservoir of summer water supplies in this region, although in a few watersheds glaciers contribute in varying amounts (e.g.

Déry et al., 2009; Schnorbus et al., 2014). However, increased winter temperatures in this region over the past century have led to a reduced snowpack (e.g. Gan, 1998; Cayan et al., 2001; Mote et al., 2005; Rood et al., 2005; Mote, 2006; Pederson et al., 2011) and have caused earlier snowmelt in watersheds across the region (Burn, 1994;

Whitfield and Cannon, 2000; Barnett et al., 2005; Stewart et al., 2005; Sauchyn and

Kulshreshtha, 2008; Kang et al., 2016). Such a shift in the dominant flow season from the early summer to the late winter and early spring months could pose a serious risk to the amount of available water during summer and fall months when the water is most needed. There is increasing evidence that summer streamflow in these watersheds has declined over the past century (Yulianti and Burn, 1998; Schindler and Donahue, 2006;

Sauchyn and Kulshreshtha, 2008) and that the summer water supplies will decline

S. Gurrapu, 2020 P a g e | 1 during the 21st century (Cohen, 1991; Gan, 1998; Stewart et al., 2004; Lapp et al., 2009;

PaiMazumdar et al., 2013; St. Jacques et al., 2013, 2018; Islam et al., 2017). Therefore, understanding the spatial and temporal variability of available water, and the region’s vulnerability to hydrological extremes, is vital in decision-making to address management practices and policies for planned adaptation to the changing climate.

The spatial and temporal variability of available water supplies is predominantly defined by the region’s hydroclimate, i.e. the water balance and its response to various hydrological and meteorological processes. Therefore, the measured quantities of precipitation, evapotranspiration, storage, and streamflow are primary indicators of the volume of water available in a watershed and indices such as the self-calibrating Palmer

Drought Severity Index (scPDSI), Standardised Precipitation Index (SPI), Standardised

Precipitation Evapotranspiration Index (SPEI), derived by assimilating several such indicators provide a means to express water availability across a range of spatial and/or temporal scales (Mishra and Singh, 2010). A few studies from recent decades have observed that the variability of monthly and annual streamflow with varying hydroclimatic conditions can be represented by such regional hydroclimatic indices

(e.g. O’Brien and Stroich, 2005; Vicente-Serrano and Lopez-Moreno, 2005;

Abatzoglou et al., 2014). These empirical relationships between historical hydroclimate and water availability are capable of projecting streamflow (e.g. St. Jacques et al.,

2013).

Surface water availability and variability can also be modelled by various existing physically-based hydrological models (e.g. Leavesley, 1994; Lapp et al., 2009;

Gray and McCabe, 2010; Shepherd et al., 2010; Solander, 2010; Kienzle et al., 2012;

Devi et al., 2015). These models are based on the physical processes of the hydrological cycle, although several processes are typically parameterised to reduce the complexity

S. Gurrapu, 2020 P a g e | 2 of the model (Devi et al., 2015). The parameterization, calibration and validation of such models is cumbersome and requires much information concerning the physical characteristics of the watershed and historical climate data, which might only exist for short time periods that may not be representative of the full range of historical and future hydroclimate (Leavesley, 1994; Devi et al., 2015). The capability of these models in realistically representing historical water availability varies with the representation

(or parameterisation) of various physical processes in the models (Devi et al., 2015).

Regardless of such uncertainties in model building, the hydrological models are capable of projecting or predicting water availability, critical information for water management. Nonetheless, the effective management of available water requires efficient water distribution networks and other infrastructure such as storage structures resilient to hydrological extremes.

The effective design and management of water resources infrastructure requires a depth of knowledge of the frequency of extreme hydrological events, floods and droughts. Traditionally, these frequencies are derived from the analysis of historically observed extreme events, assuming that they are independent and identically distributed

(i.i.d.), and that the system fluctuates within a fixed envelope of variability, the concept of stationarity (Tallaksen et al., 2000; Milly et al., 2008). Although instrumental records provide some insights on the severity, duration and frequency of historically observed extremes, they fail to explain the extreme events that are outside the tails of the observed distribution. For example, the drought of 2001 and 2002 across much of the Canadian

Prairies was unprecedented during the historical period of 100 years (Wheaton et al.,

2008); and the 2013 flood across southern Alberta, one of the largest and costliest natural disasters in Canadian history, caused unprecedented damage to the local communities (Milrad et al., 2015; Pomeroy et al., 2016). Paleoclimate records for the

S. Gurrapu, 2020 P a g e | 3 region (e.g., Sauchyn et al., 2002, 2015) capture extreme events of greater severity and duration than the observed records do (e.g. Sauchyn & Skinner, 2001; Axelson et al.,

2009; Bonsal et al., 2013). Therefore, detailed knowledge of extreme hydrological events, i.e. their severity, duration and frequency, is vital in the optimal planning and design of reliable infrastructure and in planning appropriate adaptation strategies for effective drought management (e.g. Wilhite et al., 2000; Hayes et al., 2004; Spinoni et al., 2014).

The i.i.d. assumption made in traditional flood frequency analysis fails to account for the influence of the large-scale climate oscillations that significantly affect the regional hydroclimate, which are known to significantly influence the hydroclimate of Western Canada. Numerous studies have identified teleconnections between the hydroclimate of western Canada and ocean-atmosphere oscillations such as the Pacific

Decadal Oscillation (PDO) and the El Niño-Southern Oscillation (ENSO) (e.g.,

Shabbar and Khandekar, 1996; Shabbar et al., 1997; Bonsal and Lawford, 1999; Rood et al., 2005; Gobena and Gan, 2006; Bonsal and Shabbar, 2008; Whitfield et al., 2010;

St. Jacques et al., 2010, 2014; Lapp et al., 2013). Winters are typically cooler and wetter, with deeper snowpacks, and annual discharge greater during the negative (cold)

PDO phase and La Niña, whereas the positive (warm) PDO phase and El Niño produce generally warmer and drier winter months with thinner snowpacks and less annual discharge. These oscillations in the regional hydroclimate, and the associated wet and dry cycles, challenge the assumption of stationarity (e.g., Kwon et al., 2008; Stedinger and Griffis, 2008; 2011; Lόpez and Francѐs, 2013; Barros et al., 2014; Tan and Gan,

2015), in the analysis of hydrological extremes. Moreover, the influence of such low- frequency ocean-atmosphere oscillations on the magnitude and frequency of

S. Gurrapu, 2020 P a g e | 4 hydrological extreme events is least explored, with the exception of very few studies

(Woo & Thorne, 2003; Asong et al., 2018).

1.2. Objectives

The primary objective of this research was to evaluate the use of regional hydroclimatic and large-scale climate indices in representing the regional hydrology and hydrological extremes of southwestern Canada. This objective was achieved in several steps (study objectives), which are aggregated into three chapters. The study objectives are listed as below:

1. To evaluate and establish relationships between regional (watershed) hydroclimate

and its hydrological response, i.e. streamflow, in southwestern Canada.

2. To analyse instrumental and pre-instrumental streamflow records of watersheds

across southwestern Canada to determine the range of hydrological extremes.

3. To evaluate the influence of low-frequency atmosphere-ocean oscillations on the

magnitude and frequency of occurrence of hydrological extremes, floods and

droughts in western Canada.

4. To investigate the stationarity assumption commonly presumed in the frequency

analysis of hydrological extremes.

5. To appraise the reliability of current water supply and management systems given

the range of hydroclimatic variability and hydrological extremes.

This thesis primarily focuses on the hydrological extremes, floods and droughts, and their association with the regional hydroclimate and large-scale climate. The thesis provides insight and information for water managers and policy makers to reassess the assumptions made in the frequency analysis of extreme events for the planning and design of infrastructure resilient to hydrological extremes, and to redefine the threshold levels for effective allocation of the region’s available water. The study area primarily

S. Gurrapu, 2020 P a g e | 5 focuses on southwestern Canada, and predominantly near-pristine watersheds across southern Saskatchewan, Alberta and British Columbia. The hydroclimate of this region is significantly influenced by low-frequency large-scale climate oscillations and the variability in streamflow can be represented by indices that describe these oscillations

(e.g. St. Jacques et al., 2010; 2011, Sauchyn et al., 2012). Communities and local economies are vulnerable to the negative impacts of hydrological extremes, and a better understanding of the severity, variability, and frequency of such events supports optimal planning and design of reliable infrastructure and the planning of appropriate adaptation strategies for effective drought management.

This thesis is presented in a paper-style format. The introduction chapter provides an overview of the works presented in Chapters 2 – 4, and provides continuity between the chapters. A concluding Chapter 5 provides a synthesis of the results of the research documented in these chapters. All the references cited in each chapter are given in the bibliography chapter.

S. Gurrapu, 2020 P a g e | 6 CHAPTER 2

Assessment of the Standardized Precipitation Evapotranspiration Index (SPEI) for Streamflow Prediction in the Watersheds of Western Canada†

Sunil Gurrapu, Kyle R. Hodder, David J. Sauchyn, Jeannine-Marie St-Jacques

Abstract: Knowledge of the spatial and temporal distribution of water resources is vital to address management practices and policies for planned adaptation to a changing climate. The primary objective of this study is to examine the spatial and temporal variability of available water in the naturally flowing watersheds of southwestern Canada using regional hydroclimatic indices. To do so, we first examined the empirical relationships between historically observed streamflow in 24 naturally flowing watersheds across southwestern Canada and the associated watershed’s hydroclimate, represented by the watershed averaged Standardised Precipitation Evapotranspiration Index (SPEI). The hydroclimate of all the selected watersheds is assumed to be represented by the second version of the NRCAN gridded climate dataset. We then developed SPEI-based principle component regression (PCR) equations and found them to be very efficient in representing the variability in historically observed monthly and annual streamflow. Based on our analysis, we conclude that the SPEI is able to adequately simulate historical streamflow in the naturally-flowing watersheds, depending, however, on the hydrologic response of the watershed to the regional climate, i.e. the time-lag between the input (precipitation) to and output (streamflow) from the watershed. The SPEI-based PCR equations are simpler to build than calibrating a numerical hydrological model and can be applied over large areas and many sub-basins with minimal data requirements to estimate streamflow.

Keywords: Standardized Precipitation-Evapotranspiration Index (SPEI), Streamflow, Principal Component Analysis, Principal Component Regression, Watersheds of Western Canada, Potential Evapotranspiration.

† Manuscript Submitted to the Canadian Water Resources Journal (CWRJ) and is under review.

S. Gurrapu, 2020 P a g e | 7 2.1. Introduction

Variability in the magnitude of streamflow is related primarily to changes in the volume and timing of precipitation, and crucially to the phase of precipitation, i.e. whether snow or rain (Whitfield and Cannon, 2000; Bates et al., 2008). Temperature has a significant influence on both timing and magnitude of streamflow by determining the phase of precipitation and losses from evapotranspiration. Increased mean temperature with little or no change in precipitation has led to significant decrease in annual mean streamflow across southern Canada (Zhang et al., 2001). A majority of the watersheds in southern

Canada are snow-dominated and so increased winter temperatures lead to reduced snowpack (e.g. Gan, 1998; Mote et al., 2005; Mote, 2006; Pederson et al., 2011) and earlier snowmelt runoff (Burn, 1994; Whitfield and Cannon, 2000; Barnett et al., 2005;

Stewart et al., 2005; Sauchyn and Kulshreshtha, 2008). Summer streamflow in the watersheds of western Canada has declined over the past century (Yulianti and Burn,

1998; Schindler and Donahue, 2006; Sauchyn and Kulshreshtha, 2008) and summer water supplies of the 21st century are projected to be, on average, less than historical levels (Cohen, 1991; Gan, 1998; Stewart et al., 2004; Lapp et al., 2009; PaiMazumdar et al., 2013; St. Jacques et al., 2013, 2018).

Knowledge of the spatial and temporal distribution of water resources is important for decision making to address adaptive management practices and policies in a changing climate. Numerical models of the hydrological cycle are generally used to simulate streamflow. Although these models dynamically represent physical processes, model parameterization, calibration and validation are time consuming and require much information concerning the physical characteristics of the watershed and data on the regional climate and hydrology, which might span short time periods and not capture the full range of historical and future flows (Leavesley, 1994; Devi et al.,

S. Gurrapu, 2020 P a g e | 8 2015). Similarly, the use of conceptual (e.g. water-balance) models is limited by the availability of calibration datasets (Devi et al., 2015). On the other hand, statistical or regression models are more convenient and less time consuming because they depend primarily on empirical relations between historical climate and streamflow. Although the future validity of these empirical relationships is uncertain, these models provide reasonable estimates of near future streamflow (St. Jacques et al., 2013). In addition, such models can be applied over large areas and many sub-basins with minimal data requirements.

Measured quantities of precipitation, evapotranspiration, storage, and streamflow are primary determinants of water availability. Indices derived by assimilating several such variables provide a means to express water availability across a range of spatial and/or temporal scales (Mishra and Singh, 2010). Regional climate indices, such as the Standardized Precipitation Index (SPI, McKee et al., 1993) and the

Standardized Precipitation Evapotranspiration Index (SPEI, Vicente-Serrano et al.,

2010) are useful tools to monitor water availability in a watershed. O’Brien and Stroich

(2005) examined correlations between monthly streamflow in three watersheds across

Canada and concluded that streamflow in these watersheds can be represented by a regional climate index, the SPI at 3-, 6- and 9-month timescales. In another study,

Abatzoglou et al. (2014) reported that annual mean streamflow in a majority of snow- dominated watersheds across Idaho, USA, is best represented by spring (April – June)

SPEI at the 9-month timescale. These studies demonstrate that the standardized regional climate indices at longer timescales are good indicators of hydrological conditions in snow-dominated watersheds. Therefore, such indices are well suited to monitor water supplies in the watersheds of western Canada (O’Brien and Stroich, 2005) as the hydrologic regime of these watersheds is primarily nival. Because water availability in

S. Gurrapu, 2020 P a g e | 9 these watersheds is influenced by fluctuations in temperature, we chose to explore the use of the SPEI as a measure of water availability and its relation to monthly and annual streamflow. The SPEI is a simple water balance model accounting for the two major processes of the hydrological cycle, precipitation and evapotranspiration. In addition, the SPEI can be computed at several timescales to monitor the watershed’s water availability with respect to specific seasonal demands.

In this study, we examined the empirical relationships between historical streamflow and the associated regional climate, to test our hypothesis that the water availability in the watersheds of western Canada can be represented by the regional hydroclimatic indices. We first evaluated the associations between monthly (annual) mean streamflow and the corresponding watershed averaged regional climate index,

SPEI, at various temporal scales. Then, we used principal component regression (PCR) to formulate SPEI-based PCR equations and assess the SPEI as a predictor variable in simulating historical monthly and annual streamflow in the selected watersheds.

2.2. Data and Study Region

To evaluate the relationships between streamflow and the SPEI, we chose 24 streamflow gauging stations on naturally flowing rivers across British Columbia,

Alberta and Saskatchewan (Figure 2.1., Table 2.1.). Spatially, these gauges are distributed across six ecozones (Canadian Council of Ecological Areas, 2014, www.ccea.org/ecozones-downloads/), i.e. 12 gauges in the Montane Cordillera, six gauges in the Boreal Plains, two gauges each in the Pacific Maritime and Boreal

Cordillera, and one gauge each in Prairies and Boreal Shield Ecozones (Figure 2.1.).

These gauges were chosen based on the availability of long-term daily streamflow records; all gauges have ≥ 30 years of data between 1950 – 2010, whether continuous or discontinuous. These gauges are also part of the Reference Hydrometric Basin

S. Gurrapu, 2020 P a g e | 10 Network (RHBN; Harvey et al., 1999). Daily streamflow datasets were obtained from the Water Survey of Canada (WSC) database (Environment and Climate Change

Canada, HYDAT Database, https://www.canada.ca/en/environment-climate- change/services/water-overview/quantity/monitoring/survey/data-products- services/national-archive-hydat.html). To account for the missing data in these daily streamflow datasets, we used a similar approach practised in meteorological studies

(e.g. WMO, 2011; Anderson and Gough, 2017). For each gauge, monthly data were included only if there were at most 5 missing days (consecutive or random) in each month, and annual flow for any given year was included only if there were at most 10 missing days (consecutive or random) throughout the spring and early summer months

(March – June).

We generated gross watersheds for the selected gauges using mosaics of digital elevation models (DEM) at a spatial scale of 1:250,000 from the Canadian Digital

Elevation Data (CDED, http://ftp.geogratis.gc.ca/pub/nrcan_rncan/archive/elevation).

The grid spacing in the model is 3-arc seconds, or approximately 93 m (north-south) and between 65 and 35 m (east-west) after projection. We used the hydrology toolbox in ESRI ArcMap that accounts for the elevation of the surrounding terrain to generate the drainage that feeds into a specific gauge. In the majority of the watersheds, the rivers drain the melting snowpack in the western Cordillera. The effective drainage area of the selected watersheds ranges between 403 and 20,300 km2. Streamflow in these watersheds typically peaks during spring and early summer months from rapid snowmelt and rain-on-snow events (MacCulloch and Whitfield, 2012). The annual flows are for the water year starting October 1st and ending on September 30th of the following calendar year.

S. Gurrapu, 2020 P a g e | 11 We chose the second version of the Natural Resources Canada (NRCAN) gridded climate dataset to characterize climate within each watershed (NRCAN, 2018).

NRCAN, the Canadian Forest Service, and their partners developed this dataset from spatial splines using the ANUSPLIN interpolation algorithm (McKenney et al., 2011).

The grid covers most of southern Canada with a resolution of 100-arc seconds, or approximately 10 km after projection, and the data span the years 1950 through 2010.

The dataset contains a variety of climatic variables including monthly precipitation and monthly-averaged minimum and maximum temperature. It also contains the elevation, latitude and longitude of each grid point. The number of NRCAN grid nodes per watershed, representing its climate, ranges between 4 and 202 depending on the size of the watershed (Table 2.1.).

2.3. Methods

We assumed that the climate of each watershed is captured by the climate data at the

NRCAN grid nodes that lie within the watershed. We used the SPEI package (Begueria and Vicente-Serrano, 2013) in the R statistical language (R Core Team, 2015) and the

NRCAN data to compute the SPEI series for each grid node at various timescales: 1-,

3-, 6-, 9-, 12-, and 24-months (i.e. SPEI1, SPEI3, SPEI6, SPEI9, SPEI12, and SPEI24).

The timescale determines the months of climate data used to compute the SPEI. For example, the 12-month SPEI for December (SPEI12, Dec) includes monthly precipitation and mean temperature from January through December. The SPEI is computed based on the non-exceedance probability of precipitation (P) and potential evapotranspiration

(PET) differences (P-PET). The computation involves fitting the P-PET series with a suitable probability distribution and the fitted series are then transformed into the standardized values that define the SPEI (Vicente-Serrano et al., 2010). Precipitation data from various regions of Canada can be best fit by a two parameter log-logistic

S. Gurrapu, 2020 P a g e | 12 distribution (Shoukri et al., 1988), whereas the P-PET series require a three parameter distribution as it includes negative values. Vicente-Serrano et al. (2010) determined that the 3-parameter log-logistic distribution (LL3) modelled the P-PET series very well in various climate regions across the globe. Therefore, we fit our P-PET series with a LL3 distribution to compute the SPEI. We averaged the SPEI series of all the NRCAN grid nodes contained within a watershed to produce the watershed averaged SPEI (WSPEI).

The estimation of potential evapotranspiration (PET) is a crucial component for the computation of the SPEI. Although the Penman-Monteith (P-M) algorithm (Allen et al., 1998) is recommended for computing PET, the Thornthwaite method

(Thornthwaite, 1948) is generally adopted to overcome the insufficiency of data required for the P-M equations (e.g. Vicente-Serrano et al., 2010; Bonsal et al., 2017).

However, the Thornthwaite equation is predominantly based on temperature and is known to introduce bias into the estimated PET (e.g. Chen et al., 2005; Dai, 2011;

Hoerling et al., 2012; Sheffield et al., 2012). In addition to temperature, the magnitude of actual losses to evapotranspiration is a function of several other meteorological factors, including available moisture (Hoerling et al., 2012). Because the data requirements of the P-M equations are seldom fulfilled, several variants of the P-M formulation exist that are based on empirical relations with regional climate. One such form, the Climate Moisture Index (CMI) developed by Hogg (1997), pertains to western

Canada.

The CMI was developed based on the observation that forest evapotranspiration is typically more sensitive to vapour pressure deficit than to net radiation because of high aerodynamic conductance (Hogg, 1997). The majority of rivers analysed in this study originate and flow through forested regions of western Canada; only one watershed is confined to the semi-arid interior prairies. Moreover, we observed that

S. Gurrapu, 2020 P a g e | 13 watershed averaged SPEI computed from the Thornthwaite-based PET (WSPEIT) produced relatively drier events in wet periods and wetter events in dry periods when compared with the WSPEI computed using the CMI as an estimate of PET (WSPEICMI; results not shown). In addition, Hogg (1997) determined that the annual PET estimated using the CMI is nearly the same (within ± 10 mm per year) as the PET estimated using the original Penman-Monteith equations. In addition, Abatzoglou et al. (2014) demonstrated that the SPEI from the P-M based PET showed stronger correlations with streamflow in snowmelt dominated watersheds. We therefore chose to use the CMI of

Hogg (1997) to represent PET in all watersheds. This method derives vapour pressure deficit from mean, maximum and minimum daily air temperature, and the dew-point is assumed to equal the saturation vapour pressure at 2.5 ºC less than the minimum temperature (e.g. equation 3 in Hogg, 1997).

We examined the associations between the WSPEI, for each watershed at several timescales (1-, 3-, 6-, 9-, 12-, and 24-months), and the corresponding standardized monthly mean streamflow (Zflow). We used the rank-based Spearman’s correlation coefficient (ρ) to measure the strength of the correlations between Zflow and the WSPEI because it is robust and non-parametric, i.e. not influenced by the distributions of the climate and hydrologic data (Woo and Thorne, 2003; Wilks, 2006).

In this analysis, any Spearman’s correlation ρ with p-value ≤ 0.1 is deemed statistically significant. The WSPEI at the timescale showing the strongest statistically significant

Spearman correlation with Zflow is regarded as the best predictor variable (BPV) for the corresponding monthly streamflow. For example, if the June monthly streamflow shows a statistically significant correlation with the watershed averaged 6-month SPEI

(WSPEI6, June) of ρ = 0.5 and the watershed averaged 9-month SPEI (WSPEI9, June) shows a correlation of ρ = 0.8, we consider WSPEI9, June as the BPV predictor for June

S. Gurrapu, 2020 P a g e | 14 monthly streamflow. Similarly, we also analysed the associations between the WSPEI and standardized annual streamflow (Zflow, annual) using Spearman’s rank correlation coefficient (ρ) and extracted the BPVs for annual streamflow. We then used the simple linear regression to model relationships between annual streamflow (Zflow, annual) and the

2 associated BPV to derive an approximate measure of the shared variance (푅푎푑푗).

With some watersheds containing as many as 202 grid nodes (e.g. the Muskwa

River near Fort Nelson; WSC 10CD001), the simple spatially averaged WSPEI does not capture the extent of variability in Zflow (the predictand) in relation to climate (the predictor). Therefore, we used principal component analysis (PCA), a multivariate statistical procedure used to reduce the dimensionality of a dataset. PCA accounts for the cross correlations among grid nodes and establishes linearly uncorrelated principal components (PCs) that capture the maximum variance (Johnson and Wichern, 2007;

Westra et al., 2007). To model streamflow in each watershed, we adopted Principal

Component Regression (PCR; Jolliffe, 1982; Mason and Gunst, 1985; Jolliffe, 2002), whereby principal components derived from PCA were used as predictor variables in a multiple linear regression to simulate monthly and annual streamflow. Given n SPEI grid nodes within the watershed, n PCs were calculated. The optimal number of PCs to be used in linear regression is debatable (Sutter et al., 1992; Næs and Helland, 1993;

Hadi and Ling, 1995); we followed the generally accepted approach of using the PCs with the highest explained variance (Helsel and Hirsch, 2002; Johnson and Wichern,

2007), in this case, at least 95% (cumulative) of the PCA-explained variance. To generate PCs, we chose to use the individual grid node, within the watershed, SPEIs of the same timescale as that of the watershed’s BPV. Finally, to evaluate the performance of the PCR equations in simulating observed streamflow, we computed several error statistics including Mean Bias Error (MBE), Mean Absolute Error (MAE), Root Mean

S. Gurrapu, 2020 P a g e | 15 Square Error (RMSE), Mean Absolute Percentage Error (MAPE), and Root Mean

Square Percentage Error (RMSPE) (Willmott and Matsuura, 2005; Shcherbakov et al.,

2013; de Myttenaere et al., 2016). Formulae of these error statistics, as used in this study, are given in the Appendix.

2.4. Results

Figure 2.2. presents the statistically significant correlations between watershed averaged SPEI (WSPEI), at the timescales of 1-, 3-, 6-, 9-, 12-, and 24-months, and monthly mean streamflow (Zflow). The majority of the watersheds across southwestern

Canada have a nival regime, although a few are primarily or partly glacier-fed (e.g.

Déry et al., 2009; Schnorbus et al., 2014). Because the precipitation (snowfall) received over the winter months eventually contributes to streamflow during spring-summer seasons in a nival watershed (Gray and Landine, 1988; MacCulloch and Whitfield,

2012), the 1-month WSPEI fails to explain the variability in streamflow as it is a measure of precipitation and evapotranspiration in that given month only. Thus, the majority of the correlations between WSPEI1 and monthly Zflow are either weak or statistically insignificant (Figure 2.2a.). Therefore, the 1-month WSPEI was not analysed further. Moreover, unlike the glacier-fed watersheds, streamflow in a nival watershed is little influenced by previous years’ climate unless heavy precipitation from previous years is stored in the watershed, either naturally (groundwater, snowpack, glaciers, lakes, wetlands, etc.) or by regulation. Since all the streams in this study are naturally flowing, we assumed that these watersheds are not strongly influenced by previous years’ climate. As a result, in the majority of the watersheds, the correlations of monthly streamflow with 24-month WSPEI are either weak or insignificant (Figure

2.2f.). However, the WSPEI at timescales longer than 12-months should relate to winter streamflow (i.e. baseflow), since there is little or no input of atmospheric water (e.g.

S. Gurrapu, 2020 P a g e | 16 Paznekas and Hayashi, 2016). Therefore, further results are presented for the spring, summer, and early fall (March to October) months alone.

As an illustration, Figure 2.3. shows the relationship between the hydrologic regime (monthly-averaged streamflow) of two watersheds, the Crowsnest River at

Frank (WSC 05AA008) and Illecillewaet River at Greeley (WSC 08ND013) and the climate observed in these watersheds. Although the hydrologic regime of these watersheds is comparable, with peak flow occurring in June, the precipitation patterns differ strikingly. The Crowsnest watershed receives high amounts of precipitation

(rainfall) during the spring and summer months (Figure 2.3a.), whereas the Illecillewaet watershed receives high amounts of precipitation (snowfall) in winter (Figure 2.3b.).

Despite the contrasting precipitation patterns and the highest demand for evapotranspiration (PET) during summer months, streamflow in these watersheds reaches its peak in June with contributions from rainfall, in addition to the major contribution from snowmelt. In both watersheds, June monthly streamflow (Zflow) shows a strong and significant correlation with the 6-month WSPEI (WSPEI6, June) for the Crowsnest River (Spearman’s ρ = 0.75, p-value = 0.01) and the Illecillewaet River

(Spearman’s ρ = 0.48, p-value = 0.01), i.e. the June monthly streamflow in these watersheds is influenced by the climate of the previous 6 months.

The uppermost plot in Figures 2.3a. and 2.3b. presents the WSPEI (timescale as indicated) with the highest statistically significant Spearman’s rank correlation to the monthly Zflow. In both watersheds, Spearman’s ρ is statistically significant and greater than 0.4 for all months, which indicates that the WSPEI at timescales of 3-, 6-, 9-, and

12-months are good indictors of monthly streamflow. We found comparable relationships in the other watersheds and Table 2.2. lists the BPVs of summer (June,

July and August) monthly streamflow for all watersheds. Figure 2.4. illustrates the

S. Gurrapu, 2020 P a g e | 17 spatial distribution of the BPVs for summer monthly streamflow (June through

August). Table 2.2. and Figure 2.4. indicate that the June and July monthly streamflow

(Zflow) is best modelled by the 6-, and 9-month WSPEI (18 watersheds), and the August monthly streamflow is best modelled by the 6-, 9-, and 12-month WSPEI (17 watersheds) in the majority of the watersheds. Overall, the 6-, 9-, and 12-month WSPEI are good indicators of summer monthly streamflow in at least 70% of the watersheds analysed.

For the principal component regression (PCR), the predicted variable was mean monthly streamflow and the predictors were the principal components (PCs) from a

2 PCA of the gridded SPEI data for each watershed. The adjusted R-squared (푅푎푑푗) of

2 these PCR equations is as large as 0.73 and the mean 푅푎푑푗 in all the watersheds is approximately 0.39. July monthly streamflow and the PCR equations based on the

BPVs listed in Table 2.2. share a minimum of 39% of the variance in 16 out of the 24 watersheds, i.e. a minimum of 39% of the variability in July streamflow can be explained by these BPVs. Figure 2.5. illustrates the spatial variability of the adjusted

R2 for summer (June-July-August) monthly streamflow, modelled using the PCR equations based on the BPVs listed in Table 2.2. We observe that the ability of PCR to represent summer monthly streamflow is relatively weak in the watersheds located in the Prairie and Pacific Maritime Ecozones. The prairie watersheds are primarily seasonal, activated by snowmelt (Gray and Landine, 1988; MacCulloch and Whitfield,

2012) and summer flow, if any, is produced by frontal rainfall and convective storms

(Gray and Landine, 1988; Burn et al., 2008; Buttle et al., 2012). Moreover, the hydrology of a Prairie watershed is complex because of depression storage (sloughs, wetlands, etc.), which may not contribute to surface runoff (e.g. Van der Kamp et al.,

2008; Shaw et al., 2013). Therefore, the amount of variance explained by the PCR

S. Gurrapu, 2020 P a g e | 18 equations for Iron Creek near Hardisty (WSC 05FB002) watershed declined from June

2 to August, with 푅푎푑푗 < 0.2 for August monthly streamflow (Figure 2.5.). Similarly, the

PCR equations fail to explain summer streamflow variability for watersheds in the

Pacific Maritime Ecozone (WSCs 08MG005 and 08CG001). This conforms to the earlier observed weak correlations between monthly streamflow and WSPEI in these watersheds (Figure 2.2.). These watersheds originate in the Coast Mountains and receive varying amounts of glacier melt (Ryder, 1987; Moore, 1992) and runoff from snowmelt. Hence the runoff from these watersheds is not just the contribution from that year’s precipitation alone. In addition, the hydrological regime of these watersheds is influenced by the autumn Pacific rain storms or Pineapple Express storms (Spry et al.,

2014; Sharma and Déry, 2019). In summary, the PCR equations based upon the SPEI

2 successfully represent summer monthly streamflow (mean 푅푎푑푗 ≈ 0.40) in the majority of the watersheds and fail in only a few.

Exploring the associations between the standardized annual streamflow (Zflow, annual) and the WSPEI at various timescales, we identified BPVs based on the highest statistically significant Spearman’s ρ (Table 2.3.). We observed that the annual streamflow in the majority of the watersheds (19 out of 24) is best represented by the

9- and 12-month WSPEI. Overall, we observed strong statistically significant correlations (Spearman’s ρ ≥ 0.5) in the majority of the watersheds. Figure 2.6. displays the spatial distribution of the best predictor variables for annual streamflow. Next, we used a simple linear regression to model the relationship between Zflow, annual and the

2 associated BPV to derive an approximate measure of shared variance (푅푎푑푗; Table 2.3.).

The majority of the watersheds (14 out of the 24) had more than 40% of the variability in annual streamflow captured by these BPVs (Table 2.3., Figure 2.6.). Therefore, for each watershed, we chose to use the individual grid node SPEIs of the same timescale

S. Gurrapu, 2020 P a g e | 19 as that of the watershed’s BPV as input for the PCR to model annual streamflow (Table

2.3.). Figure 2.7. compares the observed and PCR-modelled annual streamflow in four selected watersheds. The adjusted R2 indicates that the PCR equations captured nearly

40 - 80% of the variability in annual streamflow in 18 out of 24 watersheds, which is a decent improvement over the variability explained by the BPV-based SLR equations

(Table 2.3.).

Further exploring the spatial variability of the goodness-of-fit between annual streamflow and the PCR equations, we observed that the variability in annual streamflow in the majority of watersheds is well represented by the PCR equations

2 2 (mean 푅푎푑푗 = 0.46) (Table 2.3., Figure 2.8.). A minimum of 40% variability (푅푎푑푗 ≥

0.4) in annual streamflow is captured by the BPVs in 18 out of the 24 watersheds: 10 out of 12 in the Montane Cordillera, 5 out of 6 in the Boreal Plains, 1 out of 2 in the

Boreal Cordillera, and 1 in the Prairie Ecozones. Table 2.4. lists the error statistics for all the watersheds, showing the performance of the PCR equations in representing observed annual streamflow. The percentage errors, MAPE and RMSPE, in most watersheds is relatively less, which indicate that the PCR equations were able to represent annual streamflow efficiently in these watersheds (Table 2.4.). For example,

PCR captured variance in the Illecillewaet River watershed (WSC 08ND013) is nearly

2 80% (푅푎푑푗 = 0.80) and the percentage error is < 5% (Figure 2.9. and Table 2.4.).

Although the PCR equations failed in representing summer monthly streamflow in watersheds of Pacific Maritime ecozone (WSCs 08CG001 and 08MG005), the annual

2 streamflow is relatively well represented by the PCR equations (푅푎푑푗 > 0.3) with percentage errors less than 10% (Table 2.4.). However, the percentage errors between the observed and the simulated streamflow in the Iron Creek watershed (WSC

05FB002) indicate the inefficiency of the PCR equations in representing annual

S. Gurrapu, 2020 P a g e | 20 streamflow in this watershed, despite the PCR equations capturing 45% of the variance.

Based on the historical observations, the mean annual streamflow in this watershed is approximately 0.5 m3/s excluding one exceptionally high peak flow during the 1970s; the PCR equations fail to capture these low-magnitude flows and the exceptionally high peak flow (Figure 2.7d.). Therefore, except for the Prairie watershed, the PCR equations successfully model the annual streamflow in all other watersheds, with the averaged

2 푅푎푑푗 and average percentage error being 0.46 and 15% respectively.

2.5. Discussion

Dwindling winter snowpacks (e.g. Pederson et al., 2011) and the projected decline in summer water supplies (e.g. PaiMazumdar et al., 2013) across western Canada necessitate adaptive planning and management of available water resources. To do so, knowledge of the spatial and temporal distribution of water resources is imperative. To predict future water availability, conceptual or physics-based hydrological models are run using climate change projections (e.g. Lapp et al., 2009; Gray and McCabe, 2010;

Shepherd et al., 2010; Kienzle et al., 2012). However, the use of these models is made difficult by the lack of availability of calibration datasets, poor understanding of complex physical processes, and lack of information on the physical characteristics of watersheds (Devi et al., 2015). Regression equations like those in this manuscript offer an alternative approach since they are based on the empirical relationships between historical climate and streamflow. Future validity of these empirical relationships is uncertain in a changing hydroclimate, but these regression equations can provide reasonable estimates of near future streamflow. For example, St. Jacques et al. (2013) developed generalised least squares (GLS) regression equations based on the empirical relationships between streamflow and various low-frequency atmosphere-ocean

S. Gurrapu, 2020 P a g e | 21 oscillation indices to project 21st century streamflow in selected watersheds of southern

Alberta. The validity of these projections depends on the reliability of the chosen global climate model (GCM) in simulating low frequency atmosphere-ocean oscillations

(Lapp et al., 2012). Although the GCMs are capable of simulating these oscillations, their reliability is uncertain (e.g. Furtado et al., 2011; Zhang and Sun, 2014). GCMs are comparatively reliable in projecting climatic variables, such as temperature and precipitation (Mearns et al., 2012), although precipitation simulations could be improved (McMahon et al., 2015).

The use of climatic variables in quantifying moisture (water) availability has been explored by various researchers (e.g. McKee at al., 1993; Hayes et al., 1999;

Vicente-Serrano and Lopez-Moreno, 2005; Vicente-Serrano et al., 2012; Abatzoglou et al., 2014). These studies have established that multi-scalar climate indices are good indicators of the regional hydrological regimes. For example, O’Brien and Stroich

(2005) established statistical relationships between the regional climate index, the SPI, and monthly streamflow in three watersheds across Canada. To further evaluate the empirical relationships between regional climate and streamflow in watersheds of western Canada, we chose 24 naturally-flowing watersheds. We observed that monthly streamflow is significantly correlated to the SPEI in all the watersheds, although the strength of the relationships differed spatially. Our results from correlation analysis concur with research elsewhere in the world (e.g. Vicente-Serrano and Lopez-Moreno,

2005; Abatzoglou et al., 2014; Haslinger et al., 2014) that demonstrated the link between regional climate indices and river flows.

Using principal component regression (PCR), we modelled monthly streamflow in all 24 watersheds and found that the SPEI is a good predictor of monthly streamflow in the majority of watersheds. The ability of SPEI to represent streamflow depends on

S. Gurrapu, 2020 P a g e | 22 the hydrologic response to the regional climate, i.e. the time-lag between the input

(precipitation) to and output (streamflow) from the watershed. Therefore, the timescale of the SPEI capturing the variability of streamflow differs based on the regional hydrologic regime (O’Brien and Stroich, 2005; Vicente-Serrano and Lopez-Moreno,

2005; Abatzoglou et al., 2014; Haslinger et al., 2014). For example, whilst the variability in June monthly streamflow in Iron Creek watershed (WSC 05FB002) is

2 captured by the PCR equations (푅푎푑푗 > 0.4) based on the corresponding BPV (Figure

2.5.), the same is not true for the July and August monthly streamflow because Prairie streams are generally activated by melting snow and run almost dry throughout the summer months. On the other hand, in the Waskahigan River watershed (WSC

07GG001), a non-prairie watershed, the variability in summer monthly streamflow is

2 reasonably captured well (푅푎푑푗 > 0.4) by the PCR equations. This watershed is spread across the foothills of the Rockies with higher elevations and greater topographical relief, due to which the runoff from spring freshet and summer rainfall is relatively quicker and larger in volume (Wagner, 2010). Hence the BPV for June, July and August monthly streamflow in this watershed is 3-month SPEI, i.e. SPEI3, June, SPEI3, July, and

SPEI3, August, respectively. Our results augment the findings from earlier studies which demonstrate that the streamflow in a mountainous Mediterranean watershed is better captured by climatic conditions over a shorter timescale (e.g. Vicente-Serrano and

Lopez-Moreno, 2005) and the streamflow in a nival watershed is better captured by climatic conditions over a longer timescale (e.g. O’Brien and Stroich, 2005; Abatzoglou et al., 2014). We also observed that the variability in annual (October to September) streamflow in the majority of the watersheds is well captured by the respective PCR equations based on the BPVs (Table 2.3. and Figure 2.9.).

S. Gurrapu, 2020 P a g e | 23 2.6. Conclusion

Our results suggest that use of the regional climate index SPEI is a useful method for examining the variability of monthly and annual streamflow in the naturally flowing watersheds of western Canada. In this study, we analysed the empirical relationships between SPEI, computed at a range of timescales, and monthly streamflow in 24 watersheds. Based on the statistically significant relationships between streamflow and watershed averaged SPEI (WSPEI), we devised SPEI-based principal component regression equations. These equations are simpler to build than calibrating a numerical hydrological model and can be applied over large areas and many sub-basins with minimal data requirements to estimate watershed runoff. These models compliment the previously developed statistical models based on large-scale climate oscillations (e.g.

St. Jacques et al., 2013) and are capable of producing estimates of streamflow with minimal data requirements.

Data Availability

Observed streamflow data are publicly available at the WSC database: http://www.ec.gc.ca/rhc-wsc/default.asp?lang=En&n=9018B5EC-1. ANUSPLIN data are currently freely available on-line through Natural Resources Canada at https://cfs.nrcan.gc.ca/projects/3/3 (NRCAN, 2018; McKenney et al., 2011).

S. Gurrapu, 2020 P a g e | 24 2.7. Figures

Figure 2.1. Locations of the selected streamflow gauges on the naturally flowing rivers of western Canada from the Canadian Hydrometric Database (Water Survey of Canada; WSC). The gauges are numbered from west to east based on their longitude. Details of each watershed are listed in Table 2.1., using the same ID numbers as in this figure.

S. Gurrapu, 2020 P a g e | 25

Figure 2.2. Statistically significant Spearman correlations (ρ) between the standardised monthly streamflow and the associated watershed averaged SPEI

(WSPEI) at timescales (a) 1-month, WSPEI1, (b) 3-month, WSPEI3, (c) 6-months,

WSPEI6, (d) 9-months, WSPEI9, (e) 12-months, WSPEI12, and (f) 24-months,

WSPEI24. White blocks indicate a statistically not significant or weak correlation (Spearman’s ρ < 0.2).

S. Gurrapu, 2020 P a g e | 26

Figure 2.3. (i) Relationships (i.e. the strongest Spearman’s rank correlations) between the standardized monthly streamflow (Zflow) and the watershed averaged SPEI (WSPEI) at the timescales indicated, (ii) the mean monthly streamflow hydrograph, (iii) the temporal (monthly) distribution of mean monthly precipitation and (iv) PET for the (a) Crowsnest River at Frank, Alberta (WSC 05AA008) and (b) Illecillewaet River at Greeley, British Columbia (WSC 08ND013).

S. Gurrapu, 2020 P a g e | 27 Figure 2.4. Distributions of the WSPEI at timescales of 3-, 6-, 9-, and 12-months with the highest statistically significant Spearman’s rank correlations for (a) June, (b) July, and (c) August monthly streamflow. The specified WSPEI is considered the best predictor variable (BPV) of monthly streamflow in the respective watershed. NS indicates that the correlations are not statistically significant.

S. Gurrapu, 2020 P a g e | 28 Figure 2.5. Spatial variability of 2 푅푎푑푗, the amount of variance in (a) June, (b) July, and (c) August monthly streamflow captured by the PCR equations based on the best predictor variables (BPVs) listed in Table 2.2. and shown in Figure 2.4.

S. Gurrapu, 2020 P a g e | 29

Figure 2.6. The spatial distribution of the highest statistically significant Spearman’s rank correlations between annual (October – September) streamflow (Zflow, annual) and the best predictor variable (BPV) of the WSPEIs at the various time scales. The statistically significant Spearman’s correlation and the amount of variance captured by the BPV-based simple linear regression (SLR) equation (dashed red line) are presented at the bottom right corner of each of the four representative watersheds. Grey lines represent 1-to-1 lines.

S. Gurrapu, 2020 P a g e | 30

Figure 2.7. Observed annual (October to September) streamflow plotted against the PCR-modelled streamflow for (a) Stuart River near Fort St. James (WSC: 08JE001), (b) Muskwa River near Fort Nelson (WSC: 10CD001), (c) Oldman River near Waldron’s Corner (WSC: 05AA023) and (d) Iron Creek near Hardisty (WSC: 2 05FB002). The 푅푎푑푗 of the PCR-modelled streamflow is given on the bottom right corner of each plot. Also, given are the percentage errors between the observed and PCR-modelled streamflow.

S. Gurrapu, 2020 P a g e | 31

2 Figure 2.8. Spatial distribution of the 푅푎푑푗, the variance in annual (October – September) streamflow, as explained by the PCR equations. The numbers within the parentheses in the legend indicate the number of watersheds with the associated range 2 of 푅푎푑푗.

S. Gurrapu, 2020 P a g e | 32

Figure 2.9. Observed (blue solid line) and PCR-modelled (red dashed line) annual (October to September) streamflow for the Illecillewaet River at Greeley (WSC: 08ND013). The PCR-modelled streamflow is based on the timescale of the best 2 predictor variable (BPV) and the associated 푅푎푑푗 is given on the top right corner of the plot.

S. Gurrapu, 2020 P a g e | 33 2.8. Tables

Table 2.1. List of the 24 selected streamflow gauges from the Canadian Hydrometric Database (Water Survey of Canada - WSC), with their WSC code, location, and drainage area (km2). Also included are the number of nodes from the NRCAN gridded climate dataset encompassed within the corresponding watershed and the number of years of data used in the analysis. Effective No. of No. of WSC Drainage ID Gauge Name Latitude Longitude Grid Data Code Area Nodes (Years) (km2) 1 08CG001 Iskut River below Johnson 56.74 -131.67 9500 91 51 River 2 08CD001 Tuya River near Telegraph 58.07 -130.82 3550 40 48 Creek 3 08FB006 Atnarko River near the mouth 52.36 -126.01 2550 25 45 4 10BE004 Toad River above Nonda Creek 58.85 -125.38 2540 27 49 5 08JB002 Stellako River at Glenannan 54.01 -125.01 3600 42 61 6 08JE001 Stuart River near Fort St. James 54.42 -124.28 14200 140 61 7 08MG005 Lillooet River near Pemberton 50.34 -122.79 2100 24 61 8 10CB001 Sikanni Chief River near Fort 57.23 -122.69 2180 23 61 Nelson 9 10CD001 Muskwa River near Fort 58.79 -122.66 20300 202 61 Nelson 10 07FC003 Blueberry River below Aitken 56.68 -121.22 1770 18 46 Creek 11 07FB001 Pine River at East Pine 55.72 -121.21 12100 122 49 12 08LA001 Clearwater River near 51.65 -120.07 10300 102 61 Clearwater Station 13 08LD001 Adams River near Squilax 50.94 -119.65 3210 31 61 14 08ND013 Illecillewaet River at Greeley 51.01 -118.08 1150 11 47 15 07AA002 Athabasca River near Jasper 52.91 -118.06 3873 39 61 16 07GG001 Waskahigan River near the 54.75 -117.21 1040 12 42 mouth 17 08NB005 Columbia River at Donald 51.48 -117.18 9700 95 61 18 05DA009 North Saskatchewan River at 52.00 -116.47 1923 20 40 Whirlpool Point 19 05BB001 Bow River at Banff 51.17 -115.57 2210 22 61 20 05AA008 Crowsnest River at Frank 49.59 -114.41 403 4 61 21 05AA023 Oldman River near Waldron’s 49.81 -114.18 1446 16 59 Corner 22 07KE001 Birch River below Alice Creek 58.32 -113.07 9856 107 43 23 05FB002 Iron Creek near Hardisty 52.71 -111.31 815 36 46 24 06BD001 Haultain River above Norbert 56.24 -106.56 3680 39 44 River

S. Gurrapu, 2020 P a g e | 34 Table 2.2. List of the best predictor variables (BPV) of monthly streamflow, i.e., the WSPEI at a specified timescale with the strongest statistically significant (p-value ≤ 0.1) Spearman’s correlation (ρ) with the corresponding monthly streamflow. NS indicates that Spearman’s ρ is statistically not significant.

Monthly (Summer Season) Streamflow JUNE JULY AUGUST ID BPV ρ p-value BPV ρ p-value BPV ρ p-value

-3 -2 1 SPEI 12, Jun 0.44 1.4×10 SPEI 9, Jul 0.26 6.6×10 NS NS NS

-6 -9 -11 2 SPEI 9, Jun 0.64 1.3×10 SPEI 3, Jul 0.74 3.4×10 SPEI 3, Aug 0.80 1.2×10

-7 -5 -4 3 SPEI 9, Jun 0.69 1.1×10 SPEI 9, Jul 0.58 2.2×10 SPEI 12, Aug 0.49 4.8×10

-4 -5 -6 4 SPEI 9, Jun 0.49 3.1×10 SPEI 9, Jul 0.58 1.2×10 SPEI 3, Aug 0.59 6.2×10

-7 -7 -8 5 SPEI 9, Jun 0.61 2.0×10 SPEI 9, Jul 0.59 7.2×10 SPEI 12, Aug 0.63 8.7×10

-7 -9 -11 6 SPEI 9, Jun 0.62 1.1×10 SPEI 9, Jul 0.68 3.0×10 SPEI 12, Aug 0.74 1.7×10

-2 -4 7 SPEI 9,Jun 0.24 6.6×10 SPEI 9, Jul 0.46 2.3×10 NS NS NS

-6 -10 -13 8 SPEI 6, Jun 0.53 9.0×10 SPEI 6, Jul 0.70 3.4×10 SPEI 9, Aug 0.78 2.1×10

-7 -9 -9 9 SPEI 3, Jun 0.61 1.9×10 SPEI 6, Jul 0.67 3.5×10 SPEI 9, Aug 0.67 5.2×10

-6 -8 -6 10 SPEI 3, Jun 0.65 2.0×10 SPEI 6, Jul 0.74 1.2×10 SPEI 3, Aug 0.66 1.3×10

-10 -8 -11 11 SPEI 9, Jun 0.75 5.9×10 SPEI 9, Jul 0.70 1.8×10 SPEI 6, Aug 0.77 7.0×10

-4 -7 -9 12 SPEI 9, Jun 0.46 2.6×10 SPEI 9, Jul 0.60 3.7×10 SPEI 9, Aug 0.69 1.1×10

-4 -5 -9 13 SPEI 6, Jun 0.48 1.3×10 SPEI 9, Jul 0.53 2.2×10 SPEI 6, Aug 0.69 1.2×10

-4 -6 -5 14 SPEI 6, Jun 0.48 7.0×10 SPEI 9, Jul 0.64 1.0×10 SPEI 12, Aug 0.58 1.8×10

-3 -2 -4 15 SPEI 6, Jun 0.41 7.0×10 SPEI 9, Jul 0.38 1.3×10 SPEI 12, Aug 0.53 3.7×10

-8 -10 -12 16 SPEI 3, Jun 0.74 1.4×10 SPEI 3, Jul 0.80 1.8×10 SPEI 3, Aug 0.83 4.3×10

-3 -5 -5 17 SPEI 9, Jun 0.36 4.5×10 SPEI 9, Jul 0.52 1.8×10 SPEI 12, Aug 0.49 8.0×10

-2 18 NS NS NS NS NS NS SPEI 12, Aug 0.36 2.3×10

-3 -4 -5 19 SPEI 6, Jun 0.36 4.6×10 SPEI 9, Jul 0.45 2.7×10 SPEI 12, Aug 0.50 5.7×10

-12 -13 -13 20 SPEI 6, Jun 0.75 5.1×10 SPEI 9, Jul 0.77 7.2×10 SPEI 6, Aug 0.77 4.2×10

-15 -14 -14 21 SPEI 6, Jun 0.81 8.8×10 SPEI 3, Jul 0.80 3.4×10 SPEI 6, Aug 0.80 3.1×10

10-11 -10 -10 22 SPEI 6, Jun 0.80 5.6× SPEI 3, Jul 0.78 4.1×10 SPEI 3, Aug 0.78 6.2×10

-8 -11 -6 23 SPEI 6, Jun 0.72 1.5×10 SPEI 6, Jul 0.80 1.8×10 SPEI 12, Aug 0.62 3.4×10

-6 -7 -8 24 SPEI 12, Jun 0.66 1.5×10 SPEI 12, Jul 0.71 1.8×10 SPEI 9, Aug 0.75 12×10

S. Gurrapu, 2020 P a g e | 35 Table 2.3. List of the best predictor variables (BPV) of standardized annual 2 streamflow (Zflow, annual), the adjusted R s of the modelled annual streamflow using a simple linear regression (SLR) using the BPV and the Principal Component Regression (PCR) (see text for details). Also presented are the p-values from the significance test of the statistics.

ퟐ Spearman’s 푹풂풅풋 ID BPV p-value ρ SLR p-value PCR p-value -5 -5 -5 1 SPEI 3, Jan 0.55 5.02×10 0.30 3.53×10 0.31 9.76×10 -6 -7 -6 2 SPEI 9, Jun 0.66 1.20×10 0.46 2.50×10 0.45 2.00×10 -7 -8 -8 3 SPEI 6, Mar 0.70 1.45×10 0.49 9.66×10 0.52 3.72×10 -4 -5 -4 4 SPEI 9, Aug 0.47 7.28×10 0.27 9.32×10 0.29 2.26×10 -10 -10 -9 5 SPEI 9, Apr 0.70 7.30×10 0.49 3.62×10 0.48 3.63×10 -9 -10 -10 6 SPEI 12, Jun 0.69 1.13×10 0.48 5.20×10 0.56 1.36×10 -9 -6 -6 7 SPEI 6, Mar 0.69 1.40×10 0.33 1.48×10 0.35 2.12×10 -7 -8 -7 8 SPEI 12, Jul 0.66 1.17×10 0.43 7.36×10 0.43 3.50×10 -8 -8 -7 9 SPEI 12, Jul 0.67 6.04×10 0.44 6.32×10 0.47 2.36×10 -8 -7 -7 10 SPEI 12, Jul 0.71 8.35×10 0.45 3.25×10 0.45 5.83×10 -8 -7 -6 11 SPEI 9, Jul 0.71 4.38×10 0.43 4.46×10 0.42 2.75×10 -8 -9 -10 12 SPEI 9, Jun 0.65 1.75×10 0.45 3.17×10 0.54 3.18×10 -6 -7 -8 13 SPEI 12, Jul 0.58 2.19×10 0.37 2.77×10 0.46 6.03×10 -7 -8 -16 14 SPEI 9, Jun 0.68 1.56×10 0.50 1.64×10 0.80 3.89×10 -7 -7 -6 15 SPEI 6, Mar 0.71 3.15×10 0.49 3.13×10 0.49 1.73×10 -10 -9 -9 16 SPEI 12, Sep 0.80 2.16×10 0.57 3.83×10 0.57 5.98×10 -6 -7 -13 17 SPEI 9, Jun 0.54 6.80×10 0.37 1.42×10 0.65 2.81×10 -3 -3 -3 18 SPEI 6, Feb 0.50 1.20×10 0.24 1.03×10 0.23 1.24×10 -5 -6 -10 19 SPEI 9, Jun 0.51 3.17×10 0.30 4.36×10 0.54 3.66×10 -6 -5 -5 20 SPEI 9, Jun 0.55 6.46×10 0.27 1.61×10 0.27 1.61×10 -12 -14 -15 21 SPEI 9, Jul 0.76 3.03×10 0.64 4.35×10 0.70 2.32×10 -6 -6 -6 22 SPEI 12, Jun 0.65 2.79×10 0.40 3.82×10 0.40 4.84×10 -8 -7 -7 23 SPEI 12, Apr 0.70 4.93×10 0.45 2.06×10 0.45 2.52×10 -4 -4 -4 24 SPEI 12, Jul 0.54 2.30×10 0.29 1.85×10 0.29 1.87×10 Mean 0.64 0.41 0.46

S. Gurrapu, 2020 P a g e | 36 Table 2.4. Differences between the observed and PCR-modelled annual streamflow as measured by the error statistics (see appendix for full definitions).

MBE MAE MAPE RMSE RMSPE ID 푹ퟐ 풂풅풋 (m3/s) (m3/s) (%) (m3/s) (%) 1 0.31 6 × 10-14 35.86 7.81 46.55 10.14 2 0.45 -5 × 10-15 4.44 11.96 5.73 15.45 3 0.52 -1 × 10-14 4.21 14.97 5.55 19.73 4 0.29 2 × 10-15 3.75 8.79 4.65 10.90 5 0.48 5 × 10-15 3.87 18.69 4.98 24.02 6 0.56 4 × 10-14 13.32 10.03 16.49 12.42 7 0.35 2 × 10-14 8.96 7.20 12.43 9.99 8 0.43 2 × 10-15 3.10 12.12 4.02 15.71 9 0.47 6 × 10-14 26.43 12.39 31.46 14.74 10 0.45 2 × 10-16 1.38 26.54 1.75 33.65 11 0.42 -2 × 10-14 18.55 9.82 23.51 12.45 12 0.54 -2 × 10-14 15.63 6.98 19.19 8.56 13 0.46 -5 × 10-16 5.66 7.91 7.07 9.88 14 0.80 2 × 10-15 1.94 3.69 2.63 4.99 15 0.49 2 × 10-15 4.56 5.36 5.83 6.86 16 0.57 -1 × 10-16 0.90 19.62 1.19 25.96 17 0.65 -5 × 10-14 10.77 6.24 13.58 7.87 18 0.23 2 × 10-15 3.23 6.15 4.45 8.46 19 0.54 -5 × 10-15 2.77 7.16 3.40 8.80 20 0.27 4 × 10-16 1.07 20.58 1.42 27.30 21 0.70 -3 × 10-16 1.85 14.40 2.21 17.22 22 0.40 -2 × 10-15 11.50 29.82 14.42 37.39 23 0.45 0.02609 0.31 52.88 0.53 91.14 24 0.29 -1 × 10-14 3.16 17.29 3.75 20.51 Mean 0.46 3 × 10-15 7.8 14.202 9.866 19.043

S. Gurrapu, 2020 P a g e | 37 Appendix

Error statistics used to evaluate the PCR equations are listed below

푛 1 1. Mean Bias Error, MBE = ∑(푄 − 푄 ) 푛 푖, model 푖, obs 푖=1

푛 1 2. Mean Absolute Error, MAE = ∑|푄 − 푄 | 푛 푖, model 푖, obs 푖=1

푛 1 푄 − 푄 3. Mean Absolute Percentage Error, MAPE = ∑ | 푖, model 푖, obs| × 100 푛 푄mean, obs 푖=1

푛 1 2 4. Root Mean Square Error, RMSE = √ ∑(푄 − 푄 ) 푛 푖, model 푖, obs 푖=1

푛 1 푄 − 푄 2 5. Root Mean Square Percentage Error, RMSPE = √ ∑ ( 푖, model 푖, obs) × 100 푛 푄mean, obs 푖=1

Where,

푄푖, model = Modelled streamflow from PCR equations at time 푖

푄푖, obs = Observed streamflow at time 푖

푛 = Total number of streamflow data

푄mean, obs = Mean of the observed streamflow

S. Gurrapu, 2020 P a g e | 38 CHAPTER 3

The Influence of the Pacific Decadal Oscillation (PDO) on Annual Floods in the Rivers of Western Canada‡

Sunil Gurrapu, Jeannine-Marie St-Jacques, David J. Sauchyn, Kyle R. Hodder

Abstract: We analysed annual peak flow series from 127 naturally-flowing or naturalized streamflow gauges across western Canada to examine the impact of the Pacific Decadal Oscillation (PDO) on annual flood risk, which has been previously unexamined in detail. Using Spearman’s rank correlation ρ and permutation tests on quantile-quantile plots, we show that higher magnitude floods are more likely during the negative phase of the PDO than during the positive phase (shown at 38% of the stations by Spearman’s rank correlations and at 51% of the stations according to the permutation tests). Flood frequency analysis (FFA) stratified according to PDO phase suggests that higher magnitude floods may also occur more frequently during the negative PDO phase than during the positive phase. Our results hold throughout much of this region, with the upper Fraser River Basin, the Columbia River Basin and the North Saskatchewan River Basin particularly subject to this effect. Our results add to other researchers’ work questioning the wholesale validity of the key assumption in FFA that the annual peak flow series at a site is independently and identically distributed. Hence, knowledge of large-scale climate state should be considered prior to the design and construction of infrastructure.

Key Terms: Western Canada, floods, independently and identically distributed assumption (i.i.d.) of flood frequency analysis, multi-decadal variability, Pacific Decadal Oscillation, Fraser River Basin, Columbia River Basin, North Saskatchewan River Basin, permutation test for quantile-quantile plots.

‡ Published in Journal of the American Water Resources Association (JAWRA). Citation: Gurrapu, S., J-M. St-Jacques, D. J. Sauchyn, and K. R. Hodder. 2016. The influence of the Pacific Decadal Oscillation on annual floods in the rivers of Western Canada. Journal of the American Water Resources Association 52(5): 1031 – 1045. DOI: 10.1111/1752-1688.12433.

S. Gurrapu, 2020 P a g e | 39 3.1. Introduction

Numerous studies have identified teleconnections between western Canadian hydroclimate and ocean-atmosphere oscillations such as the Pacific Decadal Oscillation

(PDO) and the El Niño-Southern Oscillation (ENSO) (e.g., Shabbar and Khandekar,

1996; Shabbar et al., 1997; Bonsal and Lawford, 1999; Rood et al., 2005; Gobena and

Gan, 2006; Bonsal and Shabbar, 2008; Whitfield et al., 2010; St. Jacques et al., 2010,

2014; Lapp et al., 2013). Winters are typically cooler and wetter, with deeper snowpacks, and annual discharge greater during the negative (cool) PDO phase and La

Niña, whereas the positive (warm) PDO phase and El Niño produce generally warmer and drier winter months with shallow snowpacks, and less annual discharge. However, despite these many studies of teleconnections and total annual discharge, there has not been as much work related to the magnitude and frequency of annual peak flows in the rivers of western Canada. The seminal work of Woo and Thorne (2003) showed that the high-frequency ENSO and the Pacific North American mode (PNA) have a significant influence on peak streamflow in western Canada, with peak flows being higher during La Niña events and when the PNA is in a negative state, and with peak flows being lower during El Niño events and when the PNA is in a positive state.

However, no researchers have examined the effect of the low-frequency PDO on annual peak flows in western Canada.

In western Canada, the Fraser, Columbia, North Saskatchewan, South

Saskatchewan and Peace-Athabasca Rivers arise in the mountains from snowpacks and flow through the provinces of British Columbia, Alberta and Saskatchewan. The region has experienced devastating floods, causing much economic damage and creating a demand for the construction of flood-resistant infrastructure that is also respectful of the natural environment. For example, the May 1948 Vanport flood on the Fraser and

S. Gurrapu, 2020 P a g e | 40 Columbia Rivers extended throughout southern British Columbia (including

Vancouver), Washington and Oregon and caused over $100 million in infrastructure and property damage and killed 51 people. Presently in western Canada, there is a debate over whether the proposed Northern Gateway Pipeline (from near Edmonton,

Alberta, through the upper Fraser River Valley, to a new marine terminal in Kitimat,

British Columbia, for the exportation of petroleum) can be safely constructed through a pristine natural environment and First Nations territories (http://gate waypanel.review-examen.gc.ca/clf-nsi/dcmnt/rcmndtnsrprt/rcmndtnsrprtvlm 2ppndx- eng.html). Regionally, there is a vast amount of infrastructure, including pipelines, already in place, possibly constructed according to unrealistic flood frequency scenarios.

Information concerning flood magnitude and frequency is vital in the optimal planning and design of reliable infrastructure. Flood frequency analysis (FFA) is widely used for effective planning and design of water resource and transportation infrastructure. A primary assumption in FFA is that the annual peak flow series at a site is independently and identically distributed (i.i.d.). This implies that the state of the relevant climate oscillations that are known to affect the regional hydroclimate can be ignored. However, research is questioning the validity of the i.i.d. assumption (e.g.,

Kwon et al., 2008; Stedinger and Griffis, 2008; 2011; Lόpez and Francѐs, 2013; Barros et al., 2014; Tan and Gan, 2015) and suggests that consequently, knowledge of large- scale climate state patterns should be considered when performing FFA.

In this study, we analysed the annual peak flows of the rivers of western Canada with the hypothesis that they are influenced by the PDO. Our study was motivated by the observation that the influence of low-frequency climate oscillations such as the

PDO upon annual flood risk across the region is not yet a key ingredient in the planning

S. Gurrapu, 2020 P a g e | 41 and design of regional infrastructure. It is the first to examine the impact of the PDO, which is known to be a major influence on annual mean streamflow (e.g., Mantua et al., 1997; Rood et al., 2005; Gobena and Gan, 2006; Wang et al., 2006; Fleming et al.,

2007; Fleming and Whitfield, 2010; Whitfield et al., 2010; St. Jacques et al., 2010;

2014), on peak flow in the region. The necessity of such a study is illustrated by annual hydrographs of regional rivers that show higher peak flow during the negative PDO phase and lower peak flow during the positive PDO phase. For example, the annual discharge and the annual peak flow in Crowsnest River at Frank (WSC 05AA008) in

1956, the year with the lowest negative PDO index over 1901-2013, were substantially higher than those in 1987, the year with the highest positive PDO index (Figure 3.1.).

3.2. Study Area and Data

To evaluate the influence of the PDO on annual peak streamflow in the rivers of western

Canada, we chose daily peak flow records from 119 naturally-flowing streamflow gauges (Figure 3.2., Supplemental Figure 3.S1., Table 3.1. and Supplemental Table

3.S1.) across British Columbia, Alberta and Saskatchewan. The datasets were obtained from the Water Survey Canada (WSC) database (Environment and Climate Change

Canada, HYDAT Database, http://www.ec.gc.ca/rhc- wsc/default.asp?lang=En&n=9018B5EC-1). These stations were chosen based on the availability of long-term daily streamflow records. All stations have at least 30 years of data, whether continuous or discontinuous. One hundred and ten of these stations were analysed earlier by Woo and Thorne (2003) for the influence of ENSO and the PNA on the peak flows. In addition, eight naturalized records (two naturally-flowing and six regulated) from the North Saskatchewan River Basin (NSRB), with weekly peak flows from Alberta Environment, were included in the analysis (http://esrd.alberta.ca/)

(Figure 3.2., Supplemental Figure 3.S1., Table 3.1. and Supplemental Table 3.S1.).

S. Gurrapu, 2020 P a g e | 42 These 8 stations were included for additional spatial coverage and to examine continuous long-term data from this economically important watershed. The earliest of the 127 records begins in 1905 and the majority end in 2013. The 127 records have an average length of 52 years. The gross drainage area of the selected river basins ranges from 155 km2 to 60,000 km2. The majority of these rivers originate from snowmelt in the western Cordillera (Supplemental Figure 3.S1.). Annual peak flow in these rivers typically occurs during the spring or early summer months from rapid snowmelt and precipitation as rain. The time series of annual peak flows at each station were extracted from the daily (weekly for the 8 NSRB records) averaged streamflow records for the water year starting October 1st and ending on September 30th of the following year. For each gauge, peak flow data for any given year was included only if there were at most

10 missing days throughout spring (March-June).

To analyse the influence of the PDO on annual peak streamflow, we used the

November to March monthly averaged PDO (Figure 3.3.) index from the Joint Institute for the Study of Atmosphere and Ocean (JISAO), University of Washington

(http://jisao.washington. edu/pdo/) (Mantua et al., 1997). The annual peak flow series at each station was stratified based on the negative (cold: 1890 – 1924, 1947 – 1976,

2009 – 2013) and positive (warm: 1925 – 1946, 1977 – 2008) phases of the PDO

(Mantua et al, 1997; Minobe, 1997).

To directly compare the results from the low-frequency PDO to those from the higher-frequency ENSO, we also analysed the influence of ENSO on peak streamflow.

The Southern Oscillation Index (SOI) was used to categorize ENSO events (Climatic

Research Unit, University of East Anglia, http://www.cru.uea.ac.uk/cru/data/soi/). We used the June to November averaged SOI, with the annual peak flows at the gauges stratified into El Niño (SOI ≤ -0.5), La Niña (SOI ≥ 0.5) or neutral-year (-0.5 < SOI <

S. Gurrapu, 2020 P a g e | 43 0.5) flows based on the previous year’s SOI (Table 3.2. and Supplemental Figure 3.S2.), because ENSO's impact on the Pacific Northwest is lagged by a year (Redmond and

Koch, 1991).

3.3. Methods

First, to explore whether the magnitude of annual peak flows are related to the large- scale climate oscillations, we computed the non-parametric Spearman’s rank correlation coefficient (ρ) to measure the strength of the correlation between the annual peak flows and the PDO index or SOI at each of the 127 gauges. Spearman’s coefficient was used because it is robust and is not affected by the distribution of the climate and hydrologic data (Woo and Thorne, 2003; Wilks, 2006). In this analysis, any rank correlation ρ with p-value ≤ 0.1 is considered significant. We used the full period of record throughout this study because it is the longest record lengths that enable detection of the impact of the low-frequency PDO.

To further explore if the peak flows stratified according to PDO phase came from the same population, we ranked the peak flow series of each phase of the PDO and created quantile-quantile (Q-Q) plots (Chambers et al., 1983; Helsel and Hirsch,

2002). For each of the 127 gauges, the ranked floods (quantiles) of the negative PDO phase (y-axis) were plotted against the ranked floods (quantiles) of the positive PDO phase (x-axis), (i.e., for an individual point (xi, yi) of the plot, xi is the peak flow of the th th i ranked flood in the positive PDO phase, and yi is the peak flow of the i ranked flood in the negative PDO phase). If the data length of peak flows is the same for both phases, the peak flows were directly plotted against each other. If the data sets are not of equal size, the quantiles were picked to correspond to the sorted values from the smaller data set and then quantiles for the larger data set were interpolated. The datasets can be assumed to be from the same population if the points fall along the 1:1 line. If the ratio

S. Gurrapu, 2020 P a g e | 44 th th ri = (yi / xi) of the i ranked floods is greater than 1, then the i ranked flood in the negative PDO phase is higher than that in the positive PDO phase. Values of ri less than

1 indicate that the ith ranked flood in the positive PDO phase is higher than that in the negative PDO phase. If the PDO phase has no effect on the magnitudes of the floods, the mean ratio R for a given gauge should be approximately 1. For each record, we tested the significance of R at the 0.1 level using a two-sided permutation test with

10,000 iterations (Supplemental Text 3.S1.) (Manly, 2007).

The impact of the PDO on peak flows also was investigated using flood frequency curves fitted to the annual peak flow series stratified according to PDO phases, and 90% confidence intervals were constructed (USGS, 1982) for all 127 records. If the 90% confidence intervals of the flood frequency curves separate, it cannot be assumed that the annual peak flow series is i.i.d. (Franks and Kuczera, 2002).

The Kolmogorov-Smirnov goodness-of-fit test was used to determine the probability distribution that best represents the annual peak flow series. EasyfitXL 5.5® was used to test six distributions: the Generalized Extreme Value (GEV), 2 & 3 Parameter

Lognormal (LN & LN3), Log-Pearson III (LP3) and 2 & 3 Parameter Log-Logistic (LL

& LL3). This analysis (Supplementary Table 3.S2.) showed that the peak flow series in this region are generally best represented by the LP3 distribution, which is also recommended by the United States Geological Survey (USGS) for defining flood series in the adjacent United States (USGS, 1982; Opere et al., 2006).

Next, to further evaluate if the magnitude of peak flows differ between phases of the PDO, we computed the ratio of the flood (fitted) quantiles in the negative phase to flood quantiles in the positive phase for selected return periods, 2, 5, 10, 25 and 50 years. If this ratio, termed the flood ratio (Franks and Kuczera, 2002; Micevski et al.,

2006), is greater than 1, it may be assumed that the higher magnitude peaks are more

S. Gurrapu, 2020 P a g e | 45 common in the negative PDO phase. In this analysis, we expect that peaks will be higher in the negative phase because it is known that total annual discharge is higher in this phase (Whitfield et al., 2010; St. Jacques et al., 2010, 2014). This was done for all the records that Spearman’s rank correlation coefficient ρ showed a significant relationship between the PDO and peak flows.

Flood quantiles estimated through flood frequency analysis, using the data from an individual gauge, can have limited predictive value, whereas a regional flood frequency analysis gives more stable and reliable flood quantiles (Lettenmaier et al.,

1987; Cunnane, 1988; Hosking and Wallis, 1997). Therefore, the regional index (RI) approach developed by Franks (2002) was applied to the North Saskatchewan River

Basin (NSRB) to explore its characteristics in further detail. We concentrated on this watershed because the naturalized streamflow datasets from Alberta Environment are available for two phases of the PDO, providing sufficient data for this modeling approach. Unfortunately, most of the gauges from the other watersheds do not have continuous and long enough records to perform regional frequency analysis. The log- normalized annual peak flow series from the 8 gauges (Equation 1), within the NSRB, were collapsed into a single regional index time series by averaging (Equation 2).

ln Q j x j  t 1 t n ln Q j  t t1 n

m j xt RIt   2 j1 m

j j Where xt and Qt are the normalized index and annual peak flow, respectively, at gauge j occurring in year t, n is the length of annual peak flow record at each selected gauge, RIt is the regional index for the year t, and m is the total number of gauges. The

S. Gurrapu, 2020 P a g e | 46 series of the regional indices was then stratified according to the PDO phases and the

LP3 distribution was used to construct the flood frequency curves.

3.4. Results and Discussion

The PDO has a definite impact on flood magnitudes in western Canada. Spearman’s rank correlation coefficient ρ shows that a significant relationship exists between the winter PDO index and peak flow magnitude for 38% of the gauges examined (48 out of the 127 records) (Figure 3.4A.). These gauges show a negative relationship between the winter PDO and flood magnitude, i.e., floods are higher during the negative PDO phase than during the positive PDO phase. There is a single exception where a positive relationship exists, the gauge 08FF001 (Kitimat River below Hirsch Creek). The gauges showing a significant negative relationship are concentrated in the Fraser River Basin, southern British Columbia, the mountain headwaters of the South and North

Saskatchewan River Basins and the Peace River Basin, with a few scattered gauges in central Saskatchewan. In particular, the western half of the proposed path of the

Northern Gateway Pipeline runs through the upper Fraser Valley, British Columbia, where the PDO phase has a clear impact on the peak flows as shown by Spearman’s ρ.

The positive relationship at coastal Kitimat is unsurprising because the relationship between the PDO and total winter precipitation becomes a positive one in central and northern coastal British Columbia and northeastern Saskatchewan (Supplemental

Figure 3.S3.). Throughout the rest of the study area, there is a negative relationship between the PDO and total winter precipitation. We also ran Spearman’s rank correlation coefficients for the fixed time period 1961-2010 and found almost identical results (results not shown). To the best of our knowledge, this study is the first to examine in detail the effect of the PDO on flood magnitudes in western Canada. Sharif and Burn (2009) examined the effect of the PDO on 62 Reference Hydrological Basin

S. Gurrapu, 2020 P a g e | 47 Network (RHBN) stations across all of Canada and found that 3 stations were affected by the positive phase of the PDO and 5 by the negative phase across the entire country.

Unfortunately, they give neither the location of these stations, nor the sign of the relationships.

Similar to the PDO, ENSO has a clear impact on these same flood magnitudes.

Spearman’s ρ shows that a significant positive relationship exists between the SOI and peak flow magnitude for 39% of the gauges examined (49 out of 127 records) (Figure

3.4B.). Thus floods are higher during La Niña events than during El Niño events. Again, the gauge 08FF001 (Kitimat River) is the exception with a negative relationship instead.

The geographic pattern is similar to that from the PDO, although not identical. Woo and Thorne (2003) examined 110 stations spread across British Columbia, Alberta and

Saskatchewan to analyse the effect of ENSO on annual peak flows for 1968-1998 and identified that 34% (37 out of 110) of the stations show statistically significant relations with the October – March averaged SOI. Our analysis shows a slightly stronger impact of ENSO on peak flows (i.e., a higher percentage of gauges) than that of Woo and

Thorne (2003) for two possible reasons: 1) we are analysing longer full period of record datasets and 2) although we both use the SOI, we are using different definitions of

ENSO events. We follow the definition of Redmond and Koch (1991) who examined the SOI to determine the definition of ENSO events that produced the strongest teleconnection pattern for the Pacific Northwest region. That the spatial pattern and sign of the PDO’s effect is so similar to that of ENSO is expected, given that it is thought that the PDO is not a primary mode of variability, but rather a function of multiple interacting climate processes, including ENSO, mid-latitude atmospheric influences on SSTs, and mid-latitude ocean circulation (e.g., the Kuroshio Current)

(Alexander, 2010). Consequently, El Niño events are more likely to occur during the

S. Gurrapu, 2020 P a g e | 48 positive PDO phase and La Niña events are more likely to occur during the negative

PDO phase (Kiem et al., 2003; St. Jacques et al., 2014).

The Q-Q plots also present evidence that PDO phase has a clear impact on peak flood magnitudes. Figure 3.5. shows the Q-Q plots for the 48 gauges that showed a significant relationship between the winter PDO index and annual peak flows according to Spearman’s ρ (Figure 3.4A.). These Q-Q plots confirm that it is unlikely that the annual peak flows are identically distributed regardless of the PDO phase since there are few gauges where the quantiles fall along the 1:1 line (Figure 3.5.). The Q-Q plots demonstrate that higher magnitude floods are typically more common during the negative PDO phase, since the flood quantiles largely appear above the 1:1 line. The permutation tests show that this is a significant result (p < 0.1) for 39 of the 48 records.

Again, the Kitimat River (08FF001) is the exception where the points fall significantly below the 1:1 line, i.e., higher magnitude floods are more common during the positive phase of the PDO. An additional 26 gauges that did not show a relationship between the PDO and peak flow according to Spearman’s ρ, do show a significant relationship according to the permutation tests on the Q-Q plots, giving a total of 51% (65 out of

127) of the gauges (Figure 3.6. and Supplemental Figure 3.S4.). The geographical pattern of these 65 gauges is broadly similar to that of the 48 gauges significant by

Spearman’s ρ, but it is denser and shows a much greater impact of the PDO in central and southern Alberta and Saskatchewan. The positive relationship between the PDO and flood magnitudes at the coastal Kitimat and Atlin Rivers in British Columbia are unsurprising because the relationship between the PDO and total winter precipitation becomes a positive one here (Supplemental Figure 3.S3.).

Similarly, flood frequency analysis presents further evidence that it is unlikely that the annual peak flows are i.i.d. regardless of the PDO phase, although it is more

S. Gurrapu, 2020 P a g e | 49 mixed. Some records, e.g., the North Saskatchewan River at Saunders (05DC002), show a complete separation of the confidence intervals of the flood frequency curves stratified by PDO phase (Figure 3.7A.). Other records showed only partial separation.

For example, Figures 3.7B and 7C show the stratified flood frequency curves for the still naturally-flowing headwaters of the Columbia River at Nicholson (08NA002) and

Donald (08NB005), British Columbia. They indicate that the annual peak flows in the negative PDO phase are not identical to those of the positive phase, since at Nicholson the confidence intervals separate at higher frequencies or lower return periods, and at

Donald the confidence intervals separate at lower frequencies or higher return periods.

Of the 48 records that showed the impact of the PDO on peak flows using Spearman’s

ρ, 8% showed clearly separated flood frequency curves and the confidence intervals,

29% showed separation at higher frequencies, 6% showed separation at lower frequencies, and 54% showed no separation (e.g., Figure 3.7D. – the Bow River at

Banff (05BB001)). Many of the records that showed no separation of the confidence intervals still showed more frequent higher magnitude floods during the negative PDO, e.g., the Oldman River at Waldron’s Corner (results not shown). Overall, FFA analysis was hampered by the shortness of peak flow record lengths in western Canada, (the records had an average length of 52 years) (Supplemental Table 3.S1.). As well, longer record lengths would improve the accuracy of the tails of the stratified flood frequency curves. The flood records were of relatively short length (an average of 58 years) in the upper Fraser River Valley (the location of the proposed Northern Gateway Pipeline), which precluded the use of the regional index approach and made FFA analysis at individual gauges problematic (Supplemental Table 3.S1.).

Even though only slightly less than half the records have stratified flood frequency curves with confidence intervals that show some separation, the following

S. Gurrapu, 2020 P a g e | 50 results still suggest that the impact of PDO phase on annual peak flows can be detected using FFA curves. Figure 3.8. shows the histogram of the flood ratios for the 48 gauges that show a significant relationship between the PDO index and annual peak flow according to Spearman’s ρ (Figure 3.4A.). If the annual floods in both PDO phases were i.i.d., ~50% of the gauges would have a flood ratio less than one (Micevski et al.,

2006). However, the flood ratios for the return period of 25 years is less than 1 for 21% of the gauges (Figure 3.8.). For the 50-year return period, 27% of the gauges have flood ratios less than 1, which again is much less than the 50% threshold (Figure 3.8.). The mean of the flood ratios at the 48 gauges is greater than 1.23 for all the return periods

(Table 3.3.). Although the flood ratios have a wide spread (as shown by their standard deviations) at shorter return periods, the results indicate strong differences in annual flood quantiles dependent on PDO phase, providing further evidence that the annual floods are not identically distributed.

Focusing on the economically important NSRB with its longer records spanning approximately two PDO cycles (an average length of 98 years) (Supplemental Table

3.S1.), a regional index (RI) was computed based on the annual peak flow data from the 8 NSRB gauges, and flood frequency curves were fit along with 90% confidence intervals to the stratified RI series (Figure 3.9.). These results show that the annual peak flows from the NSRB stratified according to PDO phase are not i.i.d. The flood frequency confidence intervals separate for return periods greater than 4 years, and the negative PDO phase produces significantly higher magnitude floods occurring at greater frequency compared to those in the positive phase.

We explored creating a similar regional index for the equally economically important South Saskatchewan River Basin (SSRB), Canada’s large portion of agricultural region, which is heavily dependent on SSRB surface flows for irrigation

S. Gurrapu, 2020 P a g e | 51 (Figure 3.4A.). This region is under such severe demand for surface water supplies that large portions of the SSRB have been closed to further allocation (Rood and

Vandersteen, 2010; Sauchyn et al., 2015). It was also severely impacted by the June

2013 southern Alberta floods, heightening interest in more accurate flood frequency curves. This flooding is the costliest natural disaster in Canadian history, estimated at more than $1.7 billion of insured damage (Calgary Sun, Insurance Bureau of Canada says $1.7 billion southern Alberta flood costliest disaster in Canadian history. Published on 23rd September, 2013, http://www.calgarysun.com/2013/09/23/-insurance-bureau- of-canada-says-17-billion-southern-alberta-flood-costliest-disaster-in-canadian- history). We concluded that there was neither a set of high-enough quality naturalized peak flow records, nor a large enough set of mixed naturally-flowing and regulated gauge records that were free enough of the effects of dam construction in this heavily humanly modified region. Unfortunately, many dams were constructed here at the same time as PDO phase changes, making it difficult to separate out the effects of the PDO phase versus that of dam construction for flood control.

There is accumulating worldwide evidence that flood magnitudes and frequencies are affected by the major climate oscillations such as the PDO and ENSO.

The effects of the PDO on floods in western Canada are similar to those observed in eastern Australia from the Inter-decadal Pacific Oscillation (IPO) (Franks, 2002; Franks and Kuczera, 2002; Kiem et al., 2003). Similar to the role of the PDO in western

Canada, the flood risk in eastern Australia is higher when the IPO is in a negative versus positive phase. The IPO is closely related to the PDO, if not its pan-Pacific manifestation (Folland et al., 1999; Franks, 2002; Kiem et al., 2003). Franks and

Kuczera (2002) and Kiem et al. (2003) also demonstrated that flood frequency in eastern Australia is impacted by ENSO. Ward et al. (2014) determined that La Niña

S. Gurrapu, 2020 P a g e | 52 events produce higher annual floods compared to El Niño events in the majority of the world's river basins. Andrews et al. (2004) determined that El Niño events produced higher annual floods along the California coast.

3.5. Conclusions

Knowledge of the magnitude and frequency of floods is necessary in the planning and design of infrastructure and adaptive water management policy. Results such as ours and Franks (2002), Franks and Kuczera (2002), Kiem et al. (2003), Andrews et al.

(2004) and Ward et al. (2014) highlight the potential inadequacy of widely used, traditional FFA with its primary assumption of i.i.d. peak annual flows. Kwon et al.

(2008), Stedinger and Griffis (2008, 2011), Lόpez and Francѐs (2013) and Barros et al.

(2014) argue that the i.i.d. assumption can no longer be considered valid. Therefore, knowledge of climate state with regard to teleconnection patterns should be considered before performing FFA. However, almost all FFA done in Canada invokes the i.i.d. assumption (e.g., Neill and Watt, 2001; Aucoin et al., 2011). Our results suggest that the i.i.d. assumption is not tenable in western Canada where the hydroclimatology is strongly influenced by the low-frequency PDO (Mantua et al., 1997; Rood et al., 2005;

Gobena and Gan, 2006; Wang et al., 2006; Fleming et al., 2007; Fleming and Whitfield,

2010; Whitfield et al., 2010; St. Jacques et al., 2010; 2014). In particular, the upper

Fraser River Basin (the pathway of the proposed Northern Gateway pipeline), the

Columbia River Basin, and the North Saskatchewan River Basin are sub-regions where the i.i.d. assumption seems dubious. Ignoring the multi-decadal variability of large- scale climate states here could lead to flood risk underestimation, and under-design and under-construction of key infrastructure. The extent of this problem remains to be explored; it is manifest in western Canada, California and eastern Australia (this study,

Franks, 2002; Franks and Kuczera, 2002; Kiem et al., 2003; Woo and Thorne, 2003;

S. Gurrapu, 2020 P a g e | 53 Andrews et al., 2004; Ward et al., 2014). Any region with a strong teleconnection with the PDO or IPO may be subject to flood risk underestimation arising in this fashion.

Furthermore, other regions with strong teleconnections to other atmosphere-ocean oscillations, e.g., the North Atlantic Oscillation or the Atlantic Multi-decadal

Oscillation, may also be at risk.

Data Availability

All data are publicly available at the WSC database: http://www.ec.gc.ca/rhc- wsc/default.asp?lang=En&n=9018B5EC-1.

Supporting Information

Additional supporting information may be found in the online version of this article.

This includes a detailed map of streamflow gauges with major rivers, ENSO variability, map of Spearman’s rank correlations (ρ) between annual peak flow & PDO, and the additional significant Q-Q plots. In addition, table of streamflow gauges with additional details, a table of best fits (distribution) to the annual peak flow data and a table of

Spearman’s rank correlation (ρ) are added. Also, an R-script is provided to perform permutation test on the Q-Q plots for significance.

S. Gurrapu, 2020 P a g e | 54 3.6. Figures

Figure 3.1. Response hydrographs of the Crowsnest River at Frank (WSC 05AA008) for 1956, the year with the most negative Pacific Decadal Oscillation (PDO) index (- 2.72; blue line), and for 1987, the year with the most positive PDO index (1.85; red line). The PDO index is averaged for November to March.

S. Gurrapu, 2020 P a g e | 55

Figure 3.2. Locations of the selected streamflow gauges on the rivers of western Canada from the Canadian Hydrometric Database (Water Survey of Canada; WSC). The gauges are numbered from west to east based on their longitude. Details of each station are listed in Table 3.1. and Supplemental Table 3.S1.

S. Gurrapu, 2020 P a g e | 56

Figure 3.3. Variability in the Pacific Decadal Oscillation (PDO) as represented by the November to March averaged PDO index for the period 1901 to 2013, together with the 5-year running mean (dark red line).

S. Gurrapu, 2020 P a g e | 57

Figure 3.4. (A) Geographical pattern of the significant Spearman’s rank correlation coefficients ρ between peak flows at the 127 gauges and the winter (November- March) Pacific Decadal Oscillation (PDO) index. (B) Geographical pattern of the significant Spearman’s rank correlation coefficients ρ between peak flows at the 127 gauges and the previous year’s June-November Southern Oscillation Index (SOI). Significant relationships are shown by large colored circles. NS denotes not significant. Significant correlations denote a negative relationship for the PDO unless denoted otherwise, and a positive relationship for the SOI unless denoted otherwise.

S. Gurrapu, 2020 P a g e | 58

Figure 3.5. Quantile-quantile (Q-Q) plots based on the annual peak flows (m3 s-1) stratified according to Pacific Decadal Oscillation (PDO) phase, for the 48 streamflow gauges in western Canada that Spearman’s rank correlation coefficient ρ shows a significant relationship between PDO phase and peak floods. Shown in blue are the 1:1 lines. WSC station codes are shown in the upper left hand corners, together with record length. Shown in the lower right hand corners are the significance levels of the permutation test. N.S. denotes not significant.

S. Gurrapu, 2020 P a g e | 59

Figure 3.6. Geographical pattern of the significant permutation tests on the quantile- quantile (Q-Q) plots exploring the relationship between peak flows at the 127 gauges and the winter (November-March) Pacific Decadal Oscillation (PDO) index. Significant relationships are shown by large colored circles. NS denotes not significant. Significant correlations denote a negative relationship unless denoted otherwise.

S. Gurrapu, 2020 P a g e | 60

Figure 3.7. Log-Pearson III (LP3) expected quantiles and their 90% confidence intervals (dashed lines) for the annual peak flows for selected rivers, stratified according to cool (1905-1924, 1947-1976, 2009-2013 and warm (1925-1946, 1977- 2008) phases of the Pacific Decadal Oscillation (PDO). (A) North Saskatchewan River at Saunders (05DC002), (B) Columbia River at Nicholson (08NA002), (C) Columbia River at Donald (08NB005) and (D) Bow River at Banff (05BB001).

S. Gurrapu, 2020 P a g e | 61

Figure 3.8. Histogram of flood ratios for return periods [RP] between 2 and 50 years for the 48 western Canadian rivers that show a significant relationship between the PDO index and annual peak flow according to Spearman’s rank correlation coefficient ρ (see Figure 3.4A.).

S. Gurrapu, 2020 P a g e | 62

Figure 3.9. Log-Pearson III (LP3) flood frequency curves and their 90% confidence intervals (dashed lines) for the regional index of the annual peak flow series from the 8 North Saskatchewan River Basin (NSRB) rivers stratified according to the negative (1912-1925, 1947-1976, 2009-2013) and positive (1926-1946, 1977-2008) phases of the Pacific Decadal Oscillation (PDO)

S. Gurrapu, 2020 P a g e | 63 3.7. Tables

Table 3.1. List of the 127 selected streamflow gauges from the Canadian Hydrometric Database (Water Survey of Canada - WSC), with their WSC code, drainage area (km2) and location. Full details of these gauge records are in Supplemental Table 3.S1. Please Note: AB – Alberta, BC – British Columbia, and SK - Saskatchewan Drainage WSC ID Gauge Name Province Area Latitude Longitude Code (km2) 1 09AA006 Atlin River near Atlin BC 6860 59.595 -133.814 2 09AE003 Swift River near Swift River BC 3390 59.931 -131.768 3 08CG001 Iskut River below Johnson River BC 9500 56.739 -131.674 4 08CE001 Stikine River at Telegraph Creek BC 29000 57.901 -131.154 5 08CD001 Tuya River near Telegraph Creek BC 3550 58.072 -130.824 6 08CC001 Klappan River near Telegraph BC 3550 57.900 -129.704 Creek 7 10AC004 Blue River near the mouth BC 1700 59.758 -129.128 8 08DB001 Nass River above Shumal Creek BC 18400 55.264 -129.086 9 08FF001 Kitimat River below Hirsch Creek BC 1990 54.049 -128.690 10 08EF001 Skeena River at Usk BC 42300 54.631 -128.432 11 08EF005 Zymoetz River above O.K. Creek BC 2850 54.483 -128.331 12 08EB004 Kispiox River near Hazelton BC 1880 55.434 -127.714 13 08ED002 Morice River near Houston BC 1900 54.118 -127.424 14 08FA002 Wannock River at outlet of BC 3900 51.679 -127.179 Owikeno Lake 15 10BC001 Coal River at the mouth BC 9190 59.691 -126.951 16 08EE004 Bulkley River at Quick BC 7340 54.618 -126.899 17 08EC013 Babine River at outlet of BC 6760 55.425 -126.703 Nolkitkwa Lake 18 08FB007 Bella Coola River above Burnt BC 3720 52.422 -126.158 Bridge Creek 19 08FB006 Atnarko River near the mouth BC 2550 52.361 -126.006 20 08FC003 Dean River below Tanswanket BC 3720 52.890 -125.771 Creek 21 07EA002 Kwadacha River near Ware BC 2410 57.450 -125.638 22 10BE004 Toad River above Nonda Creek BC 2540 58.855 -125.383 23 08JB002 Stellako River at Glenannan BC 3600 54.008 -125.009

S. Gurrapu, 2020 P a g e | 64 24 08GD004 Homathko River near Fort Fraser BC 5680 50.990 -124.918 25 08JB003 Nautley River near Fort Fraser BC 6030 54.085 -124.599 26 08JE001 Stuart River near Fort St. James BC 14200 54.418 -124.275 27 08MA001 Chilko River near Redstone BC 6880 52.070 -123.537 28 07EE007 Parsnip River above Misinchinka BC 4930 55.078 -122.905 River 29 08KG001 West Road River near Cinema BC 12400 53.311 -122.888 30 08MG005 Lillooet River near Pemberton BC 2100 50.336 -122.799 31 10CB001 Sikanni Chief River near Fort BC 2180 57.234 -122.694 Nelson 32 08KC001 Salmon River near Prince George BC 4230 54.096 -122.678 33 10CD001 Muskwa River near Fort Nelson BC 20300 58.788 -122.659 34 08MB005 Chilcotin River below Big Creek BC 19200 51.849 -122.653 35 08KE016 Baker Creek at Quesnel BC 1550 52.973 -122.520 36 08KE009 Cottonwood River near Cinema BC 1910 53.155 -122.476 37 08KH006 Quesnel River near Quesnel BC 11500 52.844 -122.224 38 08MH001 Chilliwack River at Vedder BC 1230 49.097 -121.963 Crossing 39 08MG013 Harrison River near Harrison Hot BC 7890 49.311 -121.802 Springs 40 08KB003 McGregor River at Lower Canyon BC 4780 54.231 -121.669 41 07FC003 Blueberry River below Aitken BC 1770 56.677 -121.221 Creek 42 07FB001 Pine River at East Pine BC 12100 55.718 -121.212 43 08LG008 Spius Creek near Canford BC 775 50.135 -121.030 44 07FC001 Beatton River near Fort St. John BC 15600 56.280 -120.700 45 07FD001 Kiskatinaw River near Farmington BC 3630 55.957 -120.563 46 08NL007 Similkameen River at Princeton BC 1810 49.460 -120.502 47 08LA001 Clearwater River near Clearwater BC 10300 51.649 -120.066 Station 48 08NL004 Ashnola River near Keremeos BC 1050 49.209 -119.990 49 08LB047 North Thompson River at Birch BC 4490 51.603 -119.915 Island 50 08LE031 South Thompson River at Chase BC 15800 50.765 -119.740 51 07FD009 Clear River near Bear Canyon AB 2878.6 56.308 -119.681 52 08LD001 Adams River near Squilax BC 3210 50.938 -119.654

S. Gurrapu, 2020 P a g e | 65 53 07GD001 Beaverlodge River near AB 1610 55.189 -119.437 Beaverlodge 54 08KA007 Fraser River at Red Pass BC 1710 52.986 -119.007 55 07GE001 Wapiti River near Grande Prairie AB 11300 55.071 -118.803 56 08NN002 Granby River at Grand Forks BC 2060 49.044 -118.439 57 07GF001 Simonette River near Goodwin AB 2037.6 55.140 -118.182 58 08ND013 Illecillewaet River at Greeley BC 1150 51.014 -118.083 59 07AA002 Athabasca River near Jasper AB 3872.7 52.910 -118.059 60 07HA005 Whitemud River near Dixonville AB 2019.8 56.511 -117.661 61 07GJ001 Smoky River at Watino AB 50300 55.715 -117.623 62 07HC001 Notikewin River at Manning AB 4678.8 56.920 -117.618 63 08NJ013 Slocan River near Crescent Valley BC 3330 49.461 -117.564 64 08NE074 Salmo River near Salmo BC 1240 49.047 -117.294 65 07GG001 Waskahigan River near the mouth AB 1040 54.752 -117.206 66 07GG002 Little Smoky River at Little AB 3007.1 54.740 -117.180 Smoky 67 08NB005 Columbia River at Donald BC 9700 51.483 -117.179 68 07GG003 Iosegun River near Little Smoky AB 1950 54.745 -117.152 69 07HA003 Heart River near Nampa AB 1968.1 56.056 -117.130 70 08NH119 Duncan River below B.B. Creek BC 1310 50.638 -117.047 71 08NA002 Columbia River at Nicholson BC 6660 51.244 -116.913 72 05DA006 North Saskatchewan River at AB 1290 51.967 -116.725 Saskatchewan Crossing 73 07AF002 McLeod River above Embarras AB 2561.6 53.470 -116.632 River 74 07BF002 West Prairie River near High AB 1151.8 55.448 -116.493 Prairie 75 05DA009 North Saskatchewan River at AB 1923.2 52.001 -116.471 Whirlpool point 76 07BF001 East Prairie River near Enilda AB 1466.6 55.418 -116.340 77 05DC010 North Saskatchewan River Below AB 3890 52.310 -116.323 Bighorn Plant 78 07AH003 Sakwatamau River near AB 1145.1 54.201 -115.779 Whitecourt 79 05DC002 North Saskatchewam River at AB 5160 52.453 -115.756 Saunders

S. Gurrapu, 2020 P a g e | 66 80 05BB001 Bow River at Banff AB 2209.6 51.172 -115.572 81 05DC006 Ram River near the mouth AB 1853.6 52.368 -115.422 82 07BJ001 Swan River near Kinuso AB 1900.4 55.316 -115.417 83 07BB002 Pembina River near Entwistle AB 4401.6 53.604 -115.005 84 05DC001 North Saskatchewan River near AB 11006.8 52.377 -114.941 Rocky Mountain House 85 07AH001 Freeman River near Fort AB 1661.7 54.365 -114.905 Assiniboine 86 08NK016 Elk River near Natal BC 1840 49.866 -114.868 87 05BJ004 Elbow River at Bragg Creek AB 790.8 50.949 -114.571 88 05AA008 Crowsnest River at Frank AB 402.7 49.597 -114.411 89 07BK005 Saulteaux River near Spurfield AB 2595.6 55.157 -114.239 90 07BK007 Driftwood River near the mouth AB 2100.4 55.255 -114.231 91 05AA023 Oldman River near Waldron’s AB 1446.1 49.814 -114.183 Corner 92 05AA022 Castle River near Beaver Mines AB 820.7 49.489 -114.144 93 05CB001 Little Red Deer River near the AB 2578.3 52.028 -114.140 mouth 94 05CC001 Blindman River near Blackfalds AB 1795.9 52.354 -113.795 95 05DF910a North Saskatchewan River at AB NA 53.363 -113.732 Devon 96 05FA001 Battle River near Ponoka AB 1821.5 52.663 -113.581 97 05DF001 North Saskatchewan River at AB 28096 53.537 -113.486 Edmonton 98 05EA001 Sturgeon River near Fort AB 3247.1 53.838 -113.282 Saskatchewan 99 05AE005 Rolph Creek near Kimball AB 222.4 49.125 -113.143 100 07KE001 Birch River below Alice Creek AB 9856.4 58.325 -113.065 101 11AA032 North Fork Milk River above St. Montana 157.6 48.964 -113.062 Mary Canal 102 05CE002 Kneehills Creek near Drumheller AB 2428.6 51.469 -112.978 103 07CA005 Pine Creek near Grassland AB 1456.4 54.820 -112.778 104 06AA002 Amisk River at Highway No. 36 AB 2495.9 54.475 -112.014 105 05FB002 Iron Creek near Hardisty AB 3500.3 52.708 -111.310 106 06AB001 Sand River near the mouth AB 4910.9 54.467 -111.188

S. Gurrapu, 2020 P a g e | 67 107 05AF010 Manyberries Creek at Brodin’s AB 338 49.358 -110.725 Farm 108 06AD006 Beaver River at Cold Lake AB 14504.6 54.355 -110.217 Reserve 109 05EF001 North Saskatchewan River near SK 57153.4 53.523 -109.618 Deep Creek 110 05EF004 Monnery River near Paradise Hill SK 875 53.541 -109.527 111 06BA002 Dillon River below Dillon Lake SK 2330 55.710 -109.386 112 05EF005 Big Gully Creek near Maidstone SK 1620 53.244 -109.296 113 06AF005 Waterhen River near Goodsoil SK 7760 54.446 -109.223 114 07MB001 MacFarlane River at outlet of SK 9120 58.967 -108.175 Davy Lake 115 06BD001 Haultain River above Norbert SK 3680 56.244 -106.561 River 116 05GF001 Shell Brook near Shellbrook SK 2560 53.253 -106.386 117 05GF002 Sturgeon River near Prince Albert SK 5100 53.213 -105.885 118 11AE008 Poplar River at International Montana 928 48.991 -105.696 Boundary 119 05GG010 Garden River near Henribourg SK 903 53.394 -105.611 120 05JJ009 Saline Creek near Nokomis SK 950 51.416 -105.103 121 06DA004 Geiki River below Wheeler River SK 7730 57.589 -104.203 122 05KB003 Carrot River near Armley SK 4400 53.136 -104.021 123 05KF001 Ballantyne River above SK 1870 54.561 -103.942 Ballantyne Bay 124 05JM010 Ekapo Creek near Marieval SK 1100 50.530 -102.710 125 05MC001 Assiniboine River at Sturgis SK 1930 51.940 -102.547 126 05LC001 Red Deer River near Erwood SK 11000 52.859 -102.195 127 05LE008 Swan River near Norquay SK 1920 51.998 -102.074 a Not a WSC Gauge

S. Gurrapu, 2020 P a g e | 68 Table 3.2. List of El Niño (SOI ≤ -0.5) and La Niña (SOI ≥ 0.5) events during 1900 - 2013 as identified by the June to November averaged Southern Oscillation Index (SOI).

El Niño events La Niña events 1911, 1912, 1913, 1914, 1918, 1919, 1910, 1915, 1916, 1917, 1921, 1924,

1923, 1925, 1932, 1939, 1940, 1941, 1938, 1947, 1950, 1955, 1956, 1964,

1946, 1951, 1953, 1957, 1963, 1965, 1970, 1971, 1973, 1974, 1975, 1988,

1969, 1972, 1976, 1977, 1982, 1987, 1996, 1998, 2000, 2008, 2010, 2011

1991, 1992, 1993, 1994, 1997, 2002,

2004, 2006

Table 3.3. Means and standard deviations of the flood ratios (ratios of the fitted flood quantiles in the negative and positive PDO phases) for selected return periods at the 48 gauges in western Canada that show a significant relationship between the PDO index and annual peak flow according to Spearman’s rank correlation coefficient ρ (see Figure 3.4A.). Return Period [RP] Flood Ratio [FR] (years) Mean Standard Deviation 2 1.52 1.18 5 1.33 0.64 10 1.27 0.56 25 1.24 0.58 50 1.23 0.63

S. Gurrapu, 2020 P a g e | 69 Supplementary Figures

Figure 3.S1. Detailed map of the region used in this study showing the major rivers (Tables 3.1. and 3.S1.).

S. Gurrapu, 2020 P a g e | 70

Figure 3.S2. Variability in the El Niño-Southern Oscillation (ENSO) as defined by the June-November averaged Southern Oscillation Index (SOI) for the period 1901 to 2013.

S. Gurrapu, 2020 P a g e | 71

Figure 3.S3. Correlation plot between winter (November–March) averaged Pacific Decadal Oscillation (PDO) and concurrent precipitation for 1950–2005. Correlations are between the winter PDO indices and the 0.5° by 0.5° gridded (1950– 2005) precipitation data from the Canadian Forest Service Climate Dataset (McKenney et al., 2006). Figure courtesy of Dr. Suzan Lapp.

S. Gurrapu, 2020 P a g e | 72

Figure 3.S4. Quantile-quantile (Q-Q) plots based on the annual peak flows (m3 s-1) stratified according to the phases of Pacific Decadal Oscillation (PDO), for the additional 26 streamflow gauges in western Canada that Spearman’s rank correlation coefficient ρ did not show a significant relationship between PDO phase and peak floods. Shown in blue are the 1:1 lines. WSC station codes are shown in the upper left hand corners, together with record length. Shown in the lower right hand corners are the significance levels of the permutation test.

S. Gurrapu, 2020 P a g e | 73 Supplementary Tables

Table 3.S1. Detailed list of the 127 selected streamflow gauges from the Canadian Hydrometric Database (Water Survey Canada – WSC), with their WSC Code, name, location, gross drainage area, status of the river, start and end year of the period analysed, and available length of data. The table also shows the approximate day (Julian day) of peak flow in a year, estimated by averaging the peaks from annual streamflow hydrographs of the available data. The table also indicates if the gauge is part of the Canadian Reference Hydrometric Basin Network (RHBN). The streamflow gauges are ordered and numbered based on their longitudinal position moving from west to east. Please Note: AB – Alberta, BC – British Columbia, and SK – Saskatchewan. Gross Data Avg. Peak WSC Start Last ID Gauge Name Province Lat Lon Drainage Status Length Day (Julian RHBN Code Year Year (km2) (years) Day) 1 09AA006 Atlin River near Atlin BC 59.6 -133.81 6860 Natural 1951 2013 60 238 Yes 2 09AE003 Swift River near Swift River BC 59.93 -131.77 3390 Natural 1958 2013 52 163 Yes 3 08CG001 Iskut River below Johnson River BC 56.74 -131.67 9500 Natural 1962 2012 50 192 Yes 4 08CE001 Stikine River at Telegraph Creek BC 57.9 -131.15 29000 Natural 1958 2013 53 163 No 5 08CD001 Tuya River near Telegraph Creek BC 58.07 -130.82 3550 Natural 1965 2011 45 151 Yes 6 08CC001 Klappan River near Telegraph Creek BC 57.9 -129.7 3550 Natural 1965 1995 31 168 No 7 10AC004 Blue River near the mouth BC 59.76 -129.13 1700 Natural 1965 1995 31 163 No 8 08DB001 Nass River above Shumal Creek BC 55.26 -129.09 18400 Natural 1930 2013 63 159 No 9 08FF001 Kitimat River below Hirsch Creek BC 54.05 -128.69 1990 Natural 1965 2012 47 153 No 10 08EF001 Skeena River at Usk BC 54.63 -128.43 42300 Natural 1929 2011 77 162 No 11 08EF005 Zymoetz River above O.K. Creek BC 54.48 -128.33 2850 Natural 1964 2013 50 154 No 12 08EB004 Kispiox River near Hazelton BC 55.43 -127.71 1880 Natural 1965 2012 47 154 No 13 08ED002 Morice River near Houston BC 54.12 -127.42 1900 Natural 1962 2012 51 170 No 14 08FA002 Wannock River at outlet of Owikeno BC 51.68 -127.18 3900 Natural 1928 2012 57 195 No Lake

S. Gurrapu, 2020 P a g e | 74 15 10BC001 Coal River at the mouth BC 59.69 -126.95 9190 Natural 1962 1994 32 152 No 16 08EE004 Bulkley River at Quick BC 54.62 -126.9 7340 Natural 1931 2012 67 156 No 17 08EC013 Babine River at outlet of Nolkitkwa BC 55.43 -126.7 6760 Natural 1973 2012 40 164 No Lake 18 08FB007 Bella Coola River above Burnt BC 52.42 -126.16 3720 Natural 1966 2009 43 208 No Bridge Creek 19 08FB006 Atnarko River near the mouth BC 52.36 -126.01 2550 Natural 1966 2010 43 155 Yes 20 08FC003 Dean River below Tanswanket BC 52.89 -125.77 3720 Natural 1973 2013 41 153 No Creek 21 07EA002 Kwadacha River near Ware BC 57.45 -125.64 2410 Natural 1962 1998 33 167 No 22 10BE004 Toad River above Nonda Creek BC 58.86 -125.38 2540 Natural 1962 2013 51 171 Yes 23 08JB002 Stellako River at Glenannan BC 54.01 -125.01 3600 Natural 1930 2013 64 161 Yes 24 08GD004 Homathko River near Fort Fraser BC 50.99 -124.92 5680 Natural 1958 2012 50 208 No 25 08JB003 Nautley River near Fort Fraser BC 54.09 -124.6 6030 Natural 1952 2013 60 149 No 26 08JE001 Stuart River near Fort St. James BC 54.42 -124.28 14200 Natural 1931 2012 79 184 Yes 27 08MA001 Chilko River near Redstone BC 52.07 -123.54 6880 Natural 1930 2013 70 208 No 28 07EE007 Parsnip River above Misinchinka BC 55.08 -122.91 4930 Natural 1968 2013 45 153 No River 29 08KG001 West Road River near Cinema BC 53.31 -122.89 12400 Natural 1971 2011 41 130 No 30 08MG005 Lillooet River near Pemberton BC 50.34 -122.8 2100 Natural 1915 2012 90 194 Yes Sikanni Chief River near Fort 31 10CB001 BC 57.23 -122.69 2180 Natural 1946 2012 59 166 Yes Nelson 32 08KC001 Salmon River near Prince George BC 54.1 -122.68 4230 Natural 1954 2007 51 124 No 33 10CD001 Muskwa River near Fort Nelson BC 58.79 -122.66 20300 Natural 1945 2010 58 198 Yes 34 08MB005 Chilcotin River below Big Creek BC 51.85 -122.65 19200 Natural 1971 2012 42 210 No 35 08KE016 Baker Creek at Quesnel BC 52.97 -122.52 1550 Natural 1964 2012 48 127 No 36 08KE009 Cottonwood River near Cinema BC 53.16 -122.48 1910 Natural 1955 1998 38 135 No 37 08KH006 Quesnel River near Quesnel BC 52.84 -122.22 11500 Natural 1942 2012 67 167 No 38 08MH001 Chilliwack River at Vedder Crossing BC 49.1 -121.96 1230 Natural 1912 2011 75 156 No

S. Gurrapu, 2020 P a g e | 75 39 08MG013 Harrison River near Harrison Hot BC 49.31 -121.8 7890 Natural 1952 2011 60 176 No Springs 40 08KB003 McGregor River at Lower Canyon BC 54.23 -121.67 4780 Natural 1961 2013 53 157 No 41 07FC003 Blueberry River below Aitken Creek BC 56.68 -121.22 1770 Natural 1965 2011 45 123 Yes 42 07FB001 Pine River at East Pine BC 55.72 -121.21 12100 Natural 1965 2012 48 153 Yes 43 08LG008 Spius Creek near Canford BC 50.14 -121.03 775 Natural 1915 2008 41 149 No 44 07FC001 Beatton River near Fort St. John BC 56.28 -120.7 15600 Natural 1963 2011 46 125 No 45 07FD001 Kiskatinaw River near Farmington BC 55.96 -120.56 3630 Natural 1946 2013 52 127 No 46 08NL007 Similkameen River at Princeton BC 49.46 -120.5 1810 Natural 1917 2013 72 154 Yes 47 08LA001 Clearwater River near Clearwater BC 51.65 -120.07 10300 Natural 1915 2011 71 165 Yes Station 48 08NL004 Ashnola River near Keremeos BC 49.21 -119.99 1050 Natural 1915 2011 67 154 No 49 08LB047 North Thompson River at Birch BC 51.6 -119.92 4490 Natural 1961 2011 51 155 No Island 50 08LE031 South Thompson River at Chase BC 50.77 -119.74 15800 Natural 1914 2013 87 171 No 51 07FD009 Clear River near Bear Canyon AB 56.31 -119.68 2878.6 Natural 1972 2011 39 116 No 52 08LD001 Adams River near Squilax BC 50.94 -119.65 3210 Natural 1912 2011 89 168 Yes 53 07GD001 Beaverlodge River near Beaverlodge AB 55.19 -119.44 1610 Natural 1969 2013 45 117 No 54 08KA007 Fraser River at Red Pass BC 52.99 -119.01 1710 Natural 1956 2013 58 171 No 55 07GE001 Wapiti River near Grande Prairie AB 55.07 -118.8 11300 Natural 1961 2011 51 165 No 56 08NN002 Granby River at Grand Forks BC 49.04 -118.44 2060 Natural 1915 2011 50 146 No 57 07GF001 Simonette River near Goodwin AB 55.14 -118.18 5037.6 Natural 1970 2011 42 215 No 58 08ND013 Illecillewaet River at Greeley BC 51.01 -118.08 1150 Natural 1964 2013 50 169 Yes 59 07AA002 Athabasca River near Jasper AB 52.91 -118.06 3872.7 Natural 1914 2011 58 195 Yes 60 07HA005 Whitemud River near Dixonville AB 56.51 -117.66 2019.8 Natural 1972 2013 42 127 No 61 07GJ001 Smoky River at Watino AB 55.72 -117.62 50300 Natural 1916 2013 64 165 No 62 07HC001 Notikewin River at Manning AB 56.92 -117.62 4678.8 Natural 1962 2011 49 127 No 63 08NJ013 Slocan River near Crescent Valley BC 49.46 -117.56 3330 Natural 1925 2013 89 158 No 64 08NE074 Salmo River near Salmo BC 49.05 -117.29 1240 Natural 1950 2012 63 145 No

S. Gurrapu, 2020 P a g e | 76 65 07GG001 Waskahigan River near the mouth AB 54.75 -117.21 1040 Natural 1969 2012 44 126 Yes 66 07GG002 Little Smoky River at Little Smoky AB 54.74 -117.18 3009.1 Natural 1968 2013 46 194 No 67 08NB005 Columbia River at Donald BC 51.48 -117.18 9700 Natural 1945 2013 69 176 Yes 68 07GG003 Iosegun River near Little Smoky AB 54.75 -117.15 1950 Natural 1970 2013 44 120 No 69 07HA003 Heart River near Nampa AB 56.06 -117.13 1968.1 Natural 1964 2011 48 107 No 70 08NH119 Duncan River below B.B. Creek BC 50.64 -117.05 1310 Natural 1964 2013 50 169 No 71 08NA002 Columbia River at Nicholson BC 51.24 -116.91 6660 Natural 1905 2013 96 178 No 72 05DA006 North Saskatchewan River at AB 51.97 -116.73 1290 Naturalised 1913 2010 98 196 No Saskatchewan Crossing 73 07AF002 McLeod River above Embarras AB 53.47 -116.63 2561.6 Natural 1955 2012 58 157 No River 74 07BF002 West Prairie River near High Prairie AB 55.45 -116.49 1151.8 Natural 1928 2011 54 116 No 75 05DA009 North Saskatchewan River at AB 52 -116.47 1923.2 Naturalised 1913 2010 98 196 Yes Whirlpool point 76 07BF001 East Prairie River near Enilda AB 55.42 -116.34 1466.6 Natural 1928 2011 54 116 No 77 05DC010 North Saskatchewan River Below AB 52.31 -116.32 3890 Naturalised 1913 2010 98 196 No Bighorn Plant 78 07AH003 Sakwatamau River near Whitecourt AB 54.2 -115.78 1145.1 Natural 1973 2013 41 126 No 79 05DC002 North Saskatchewam River at AB 52.45 -115.76 5160 Naturalised 1913 2010 98 196 No Saunders 80 05BB001 Bow River at Banff AB 51.17 -115.57 2209.6 Natural 1911 2012 102 169 Yes 81 05DC006 Ram River near the mouth AB 52.37 -115.42 1853.6 Natural 1970 2012 43 169 No 82 07BJ001 Swan River near Kinuso AB 55.32 -115.42 1900.4 Natural 1962 2011 49 190 No 83 07BB002 Pembina River near Entwistle AB 53.6 -115.01 4401.6 Natural 1915 2011 65 193 No 84 05DC001 North Saskatchewan River near AB 52.38 -114.94 11006.8 Naturalised 1913 2010 98 178 No Rocky Mountain House 85 07AH001 Freeman River near Fort Assiniboine AB 54.37 -114.91 1661.7 Natural 1966 2012 47 190 No 86 08NK016 Elk River near Natal BC 49.87 -114.87 1840 Natural 1951 2013 62 158 No 87 05BJ004 Elbow River at Bragg Creek AB 50.95 -114.57 790.8 Natural 1952 2011 60 158 No

S. Gurrapu, 2020 P a g e | 77 88 05AA008 Crowsnest River at Frank AB 49.6 -114.41 402.7 Natural 1911 2010 69 147 Yes 89 07BK005 Saulteaux River near Spurfield AB 55.16 -114.24 2595.6 Natural 1970 2011 42 195 No 90 07BK007 Driftwood River near the mouth AB 55.26 -114.23 2100.4 Natural 1969 2011 43 181 No 91 05AA023 Oldman River near Waldron’s AB 49.81 -114.18 1446.1 Natural 1950 2008 59 158 Yes Corner 92 05AA022 Castle River near Beaver Mines AB 49.49 -114.14 820.7 Natural 1946 2011 65 158 No 93 05CB001 Little Red Deer River near the mouth AB 52.03 -114.14 2578.3 Natural 1961 2013 53 171 No 94 05CC001 Blindman River near Blackfalds AB 52.35 -113.8 1795.9 Natural 1917 2012 56 104 No 95 05DF910a North Saskatchewan River at Devon AB 53.36 -113.73 NA Naturalised 1913 2010 98 179 No 96 05FA001 Battle River near Ponoka AB 52.66 -113.58 1821.5 Natural 1915 2013 61 106 No 97 05DF001 North Saskatchewan River at AB 53.54 -113.49 28096 Naturalised 1913 2010 98 179 No Edmonton 98 05EA001 Sturgeon River near Fort AB 53.83 -113.28 3247.1 Natural 1915 2011 85 116 No Saskatchewan 99 05AE005 Rolph Creek near Kimball AB 49.13 -113.14 222.4 Natural 1936 2011 76 160 No 100 07KE001 Birch River below Alice Creek AB 58.33 -113.07 9856.4 Natural 1968 2011 44 129 Yes 101 11AA032 North Fork Milk River above St. Montana 48.96 -113.06 157.6 Natural 1942 2011 32 112 No Mary Canal 102 05CE002 Kneehills Creek near Drumheller AB 51.47 -112.98 2428.6 Natural 1922 2012 62 49 No 103 07CA005 Pine Creek near Grassland AB 54.82 -112.78 1456.4 Natural 1967 2011 44 111 No 104 06AA002 Amisk River at Highway No. 36 AB 54.48 -112.01 2495.9 Natural 1972 2012 40 116 No 105 05FB002 Iron Creek near Hardisty AB 52.71 -111.31 3500.3 Natural 1965 2012 48 112 Yes 106 06AB001 Sand River near the mouth AB 54.47 -111.19 4910.9 Natural 1969 2011 43 185 No 107 05AF010 Manyberries Creek at Brodin’s Farm AB 49.36 -110.73 338 Natural 1913 2010 91 104 No 108 06AD006 Beaver River at Cold Lake Reserve AB 54.36 -110.22 14504.6 Natural 1956 2013 58 116 No 109 05EF001 North Saskatchewan River near SK 53.52 -109.62 57153.4 Naturalised 1913 2010 98 181 No Deep Creek 110 05EF004 Monnery River near Paradise Hill SK 53.54 -109.53 875 Natural 1968 2013 34 110 No 111 06BA002 Dillon River below Dillon Lake SK 55.71 -109.39 2330 Natural 1973 2013 40 132 No 112 05EF005 Big Gully Creek near Maidstone SK 53.24 -109.3 1620 Natural 1971 2013 31 111 No

S. Gurrapu, 2020 P a g e | 78 113 06AF005 Waterhen River near Goodsoil SK 54.45 -109.22 7760 Natural 1968 2012 33 182 No 114 07MB001 MacFarlane River at outlet of Davy SK 58.97 -108.18 9120 Natural 1968 2013 46 139 No Lake 115 06BD001 Haultain River above Norbert River SK 56.24 -106.56 3680 Natural 1969 2013 44 131 Yes 116 05GF001 Shell Brook near Shellbrook SK 53.25 -106.39 2560 Natural 1966 2013 34 111 No 117 05GF002 Sturgeon River near Prince Albert SK 53.21 -105.89 5100 Natural 1967 2013 35 114 No 118 11AE008 Poplar River at International Montana 48.99 -105.7 928 Natural 1933 2010 78 50 No Boundary 119 05GG010 Garden River near Henribourg SK 53.39 -105.61 903 Natural 1967 2013 36 113 No 120 05JJ009 Saline Creek near Nokomis SK 51.42 -105.1 950 Natural 1973 2013 41 110 No 121 06DA004 Geiki River below Wheeler River SK 57.59 -104.2 7730 Natural 1967 2013 47 132 Yes 122 05KB003 Carrot River near Armley SK 53.14 -104.02 4400 Natural 1956 2013 46 115 No 123 05KF001 Ballantyne River above Ballantyne SK 54.56 -103.94 1870 Natural 1967 2013 31 193 No Bay 124 05JM010 Ekapo Creek near Marieval SK 50.53 -102.71 1100 Natural 1969 2013 45 112 No 125 05MC001 Assiniboine River at Sturgis SK 51.94 -102.55 1930 Natural 1957 2013 56 115 No 126 05LC001 Red Deer River near Erwood SK 52.86 -102.2 11000 Natural 1957 2013 56 112 No 127 05LE008 Swan River near Norquay SK 52 -102.07 1920 Natural 1966 2012 35 125 No a Not a WSC Gauge

S. Gurrapu, 2020 P a g e | 79 Table 3.S2. Goodness-of-fit of the period of record length peak flows by the six distributions for the 127 gauges. The six distributions are the Generalized Extreme Value (GEV), 2 & 3 Parameter Lognormal (LN & LN3), Log-Pearson III (LP3) and 2 & 3 Parameter Log-Logistic (LL & LL3). GOF1, GOF2, and GOF3 denotes the Goodness-of-fit to the distributions based on the first, second and third lowest Kolmogorov-Smirnov (K-S) statistic, respectively. Bold denotes no significant difference between the peak flows and the distribution at the 0.05 level according to the K-S test. An asterisk (*) denotes no significant difference between the peak flows and the distribution at the 0.05 level according to a χ2 (chi-squared) test. The hash (#) sign denotes that the shown distribution is either not a good fit or no fit is possible.

ID WSC Code Gauge Name GOF1 GOF2 GOF3 1 09AA006 Atlin River near Atlin LL3 LN3 LP3 2 09AE003 Swift River near Swift River LL3 LN3 LL 3 08CG001 Iskut River below Johnson River LL3 GEV LP3 # 4 08CE001 Stikine River at Telegraph Creek LL3 * GEV LN * 5 08CD001 Tuya River near Telegraph Creek LL3 GEV LL 6 08CC001 Klappan River near Telegraph Creek GEV LP3 LN 7 10AC004 Blue River near the mouth GEV LL * LL3 * 8 08DB001 Nass River above Shumal Creek LL LN3 * GEV * 9 08FF001 Kitimat River below Hirsch Creek LN GEV LL3 10 08EF001 Skeena River at Usk LN GEV LL3 11 08EF005 Zymoetz River above O.K. Creek LN3 LL3 GEV 12 08EB004 Kispiox River near Hazelton LL3 GEV LP3 13 08ED002 Morice River near Houston LN3 LL3 GEV * 14 08FA002 Wannock River at outlet of Owikeno Lake LN3 GEV LL3 15 10BC001 Coal River at the mouth LL LN GEV 16 08EE004 Bulkley River at Quick GEV * LN3 LP3 * 17 08EC013 Babine River at outlet of Nolkitkwa Lake GEV LL3 LN3 18 08FB007 Bella Coola River above Burnt Bridge Creek LN3 * GEV LP3 19 08FB006 Atnarko River near the mouth GEV LN LP3 20 08FC003 Dean River below Tanswanket Creek LN GEV LP3 21 07EA002 Kwadacha River near Ware GEV LN3 * LL3 22 10BE004 Toad River above Nonda Creek LL3 GEV LL 23 08JB002 Stellako River at Glenannan GEV * LP3 * LL 24 08GD004 Homathko River near Fort Fraser LL3 GEV LN3 25 08JB003 Nautley River near Fort Fraser LL GEV LL3 26 08JE001 Stuart River near Fort St. James GEV LP3 LN3 27 08MA001 Chilko River near Redstone LL3 GEV LL 28 07EE007 Parsnip River above Misinchinka River LL3 LN3 LN 29 08KG001 West Road River near Cinema LL LL3 LN3 30 08MG005 Lillooet River near Pemberton LL3 LN3 GEV 31 10CB001 Sikanni Chief River near Fort Nelson LN3 GEV LL

S. Gurrapu, 2020 P a g e | 80 32 08KC001 Salmon River near Prince George LN3 GEV LL3 33 10CD001 Muskwa River near Fort Nelson GEV LL3 LN3 34 08MB005 Chilcotin River below Big Creek LL3 LN LL 35 08KE016 Baker Creek at Quesnel LP3 GEV LL3 36 08KE009 Cottonwood River near Cinema LN3 * LL3 LP3 * 37 08KH006 Quesnel River near Quesnel GEV * LP3 LN3 38 08MH001 Chilliwack River at Vedder Crossing LN3 * GEV * LP3 39 08MG013 Harrison River near Harrison Hot Springs GEV * LP3 * LL 40 08KB003 McGregor River at Lower Canyon LL3 GEV LN3 41 07FC003 Blueberry River below Aitken Creek LP3 LN LN3 42 07FB001 Pine River at East Pine LN3 GEV LL3 * 43 08LG008 Spius Creek near Canford LP3 GEV LN 44 07FC001 Beatton River near Fort St. John LL3 GEV * LN3 * 45 07FD001 Kiskatinaw River near Farmington LP3 LN3 LN 46 08NL007 Similkameen River at Princeton LP3 GEV LN3 * 47 08LA001 Clearwater River near Clearwater Station GEV * LN * LP3 48 08NL004 Ashnola River near Keremeos LP3 * LL3 * LN * 49 08LB047 North Thompson River at Birch Island GEV LP3 LN3 50 08LE031 South Thompson River at Chase LN GEV LP3 51 07FD009 Clear River near Bear Canyon LP3 LN * LN3 * 52 08LD001 Adams River near Squilax LN GEV LP3 53 07GD001 Beaverlodge River near Beaverlodge GEV LL3 LP3 54 08KA007 Fraser River at Red Pass LN3 GEV LL3 * 55 07GE001 Wapiti River near Grande Prairie LN3 LL3 * LP3 * 56 08NN002 Granby River at Grand Forks GEV LN3 LP3 57 07GF001 Simonette River near Goodwin LL GEV LN 58 08ND013 Illecillewaet River at Greeley LL3 GEV LN3 59 07AA002 Athabasca River near Jasper LL3 LN3 GEV 60 07HA005 Whitemud River near Dixonville GEV * LL3 LN3 61 07GJ001 Smoky River at Watino LP3 GEV LN3 62 07HC001 Notikewin River at Manning LN3 LL3 * GEV 63 08NJ013 Slocan River near Crescent Valley LL LL3 GEV 64 08NE074 Salmo River near Salmo LL3 LL * GEV 65 07GG001 Waskahigan River near the mouth LP3 GEV LN 66 07GG002 Little Smoky River at Little Smoky LL3 LN3 * LP3 * 67 08NB005 Columbia River at Donald LL LN * LL3 68 07GG003 Iosegun River near Little Smoky LP3 GEV LN3 69 07HA003 Heart River near Nampa LP3 * LL3 GEV 70 08NH119 Duncan River below B.B. Creek GEV LN3 LP3 71 08NA002 Columbia River at Nicholson GEV LP3 LN 72 05DA006 North Saskatchewan River at Saskatchewan Crossing LL3 LL GEV 73 07AF002 McLeod River above Embarras River LP3 GEV LL3 74 07BF002 West Prairie River near High Prairie LP3 GEV LN3 75 05DA009 North Saskatchewan River at Whirlpool point LL3 LL LN 76 07BF001 East Prairie River near Enilda GEV LP3 LL3 77 05DC010 North Saskatchewan River Below Bighorn Plant LL3 LL * LN3

S. Gurrapu, 2020 P a g e | 81 78 07AH003 Sakwatamau River near Whitecourt LN3 * LL3 * LP3 * 79 05DC002 North Saskatchewam River at Saunders LL3 LL LN3 80 05BB001 Bow River at Banff LN3 GEV * LP3 * 81 05DC006 Ram River near the mouth LN3 * LL3 LP3 82 07BJ001 Swan River near Kinuso GEV LP3 LN 83 07BB002 Pembina River near Entwistle LN3 LL3 LP3 84 05DC001 North Saskatchewan River near Rocky Mountain LN GEV LN3 House 85 07AH001 Freeman River near Fort Assiniboine GEV LN LP3 86 08NK016 Elk River near Natal LN3 GEV LP3 87 05BJ004 Elbow River at Bragg Creek LL3 LN3 LP3 88 05AA008 Crowsnest River at Frank LP3 LN GEV 89 07BK005 Saulteaux River near Spurfield LL3 GEV LN3 90 07BK007 Driftwood River near the mouth GEV LN3 LL3 * 91 05AA023 Oldman River near Waldron’s Corner LN3 LL3 LP3 92 05AA022 Castle River near Beaver Mines GEV LL3 LP3 # 93 05CB001 Little Red Deer River near the mouth LP3 LL3 LN 94 05CC001 Blindman River near Blackfalds LN3 LP3 GEV 95 05DF910a North Saskatchewan River at Devon LN3 GEV LP3 96 05FA001 Battle River near Ponoka LP3 GEV LL3 97 05DF001 North Saskatchewan River at Edmonton LN3 GEV LP3 98 05EA001 Sturgeon River near Fort Saskatchewan GEV * LL3 * LP3 * 99 05AE005 Rolph Creek near Kimball GEV LP3 LL3 100 07KE001 Birch River below Alice Creek GEV LP3 LN3 101 11AA032 North Fork Milk River above St. Mary Canal LN LP3 GEV 102 05CE002 Kneehills Creek near Drumheller LP3 * LL3 LN3 103 07CA005 Pine Creek near Grassland GEV LP3 LL3 # 104 06AA002 Amisk River at Highway No. 36 LL3 LP3 * LN3 105 05FB002 Iron Creek near Hardisty LP3 GEV LN 106 06AB001 Sand River near the mouth LL3 GEV LN 107 05AF010 Manyberries Creek at Brodin’s Farm LP3 GEV LL3 # 108 06AD006 Beaver River at Cold Lake Reserve LL GEV LP3 109 05EF001 North Saskatchewan River near Deep Creek LN3 GEV LL3 110 05EF004 Monnery River near Paradise Hill LP3 LN3 LL3 111 06BA002 Dillon River below Dillon Lake GEV LP3 * LN3 112 05EF005 Big Gully Creek near Maidstone LP3 LL3 GEV 113 06AF005 Waterhen River near Goodsoil LL3 * LN3 GEV 114 07MB001 MacFarlane River at outlet of Davy Lake LN LL3 LL 115 06BD001 Haultain River above Norbert River LL3 * LN3 * LP3 116 05GF001 Shell Brook near Shellbrook LL3 LN3 LP3 117 05GF002 Sturgeon River near Prince Albert LL LP3 LL3 118 11AE008 Poplar River at International Boundary LL3 LN3 LL 119 05GG010 Garden River near Henribourg LP3 LL3 GEV 120 05JJ009 Saline Creek near Nokomis LL3 * LN3 * LP3 121 06DA004 Geiki River below Wheeler River LP3 LL GEV 122 05KB003 Carrot River near Armley LL3 LN3 GEV

S. Gurrapu, 2020 P a g e | 82 123 05KF001 Ballantyne River above Ballantyne Bay LL3 LL LN3 124 05JM010 Ekapo Creek near Marieval LP3 LL3 GEV 125 05MC001 Assiniboine River at Sturgis LL3 LN3 GEV 126 05LC001 Red Deer River near Erwood GEV LL3 LP3 127 05LE008 Swan River near Norquay LL3 LN3 GEV a Not a WSC Gauge

S. Gurrapu, 2020 P a g e | 83 Table 3.S3. Correlations between annual peak streamflow and the Pacific Decadal Oscillation (PDO) as measured by Spearman’s rank correlation (ρ). Level of significance for the statistically significant correlations are as shown.

Level Correlation WSC Record p of ID Gauge Name (Spearman’s Code Length value Signifi- ρ) cance 1 09AA006 Atlin River near Atlin 60 -0.021 0.873 - 2 09AE003 Swift River near Swift River 52 -0.224 0.111 - 3 08CG001 Iskut River below Johnson River 50 -0.093 0.522 - 4 08CE001 Stikine River at Telegraph Creek 53 -0.126 0.367 - 5 08CD001 Tuya River near Telegraph Creek 45 -0.224 0.138 - 6 08CC001 Klappan River near Telegraph Creek 31 -0.157 0.398 - 7 10AC004 Blue River near the mouth 31 0.067 0.720 - 8 08DB001 Nass River above Shumal Creek 63 -0.165 0.196 - 9 08FF001 Kitimat River below Hirsch Creek 47 0.436 0.002 0.01 10 08EF001 Skeena River at Usk 77 -0.244 0.032 0.05 11 08EF005 Zymoetz River above O.K. Creek 50 0.029 0.843 - 12 08EB004 Kispiox River near Hazelton 47 -0.190 0.200 - 13 08ED002 Morice River near Houston 51 -0.334 0.018 0.05 14 08FA002 Wannock River at outlet of Owikeno 57 -0.074 0.585 - Lake 15 10BC001 Coal River at the mouth 32 -0.228 0.209 - 16 08EE004 Bulkley River at Quick 67 -0.321 0.008 0.01 17 08EC013 Babine River at outlet of Nolkitkwa 40 -0.307 0.054 0.1 Lake 18 08FB007 Bella Coola River above Burnt Bridge 43 -0.181 0.245 - Creek 19 08FB006 Atnarko River near the mouth 43 -0.395 0.009 0.01 20 08FC003 Dean River below Tanswanket Creek 41 -0.294 0.062 0.1 21 07EA002 Kwadacha River near Ware 33 0.240 0.179 - 22 10BE004 Toad River above Nonda Creek 51 0.063 0.659 - 23 08JB002 Stellako River at Glenannan 64 -0.376 0.002 0.01 24 08GD004 Homathko River near Fort Fraser 50 0.028 0.847 - 25 08JB003 Nautley River near Fort Fraser 60 -0.375 0.003 0.01 26 08JE001 Stuart River near Fort St. James 79 -0.270 0.016 0.05 27 08MA001 Chilko River near Redstone 70 -0.114 0.346 - 28 07EE007 Parsnip River above Misinchinka River 45 -0.150 0.325 - 29 08KG001 West Road River near Cinema 41 -0.569 0.0001 0.01 30 08MG005 Lillooet River near Pemberton 90 -0.047 0.657 - 31 10CB001 Sikanni Chief River near Fort Nelson 59 -0.017 0.899 - 32 08KC001 Salmon River near Prince George 51 -0.346 0.013 0.05 33 10CD001 Muskwa River near Fort Nelson 58 0.157 0.238 - 34 08MB005 Chilcotin River below Big Creek 42 -0.169 0.284 - 35 08KE016 Baker Creek at Quesnel 48 -0.595 0.000 0.01

S. Gurrapu, 2020 P a g e | 84 36 08KE009 Cottonwood River near Cinema 38 -0.345 0.034 0.05 37 08KH006 Quesnel River near Quesnel 67 -0.255 0.037 0.05 38 08MH001 Chilliwack River at Vedder Crossing 75 -0.061 0.604 - 39 08MG013 Harrison River near Harrison Hot 60 -0.147 0.262 - Springs 40 08KB003 McGregor River at Lower Canyon 53 -0.192 0.168 - 41 07FC003 Blueberry River below Aitken Creek 45 0.153 0.316 - 42 07FB001 Pine River at East Pine 48 -0.256 0.079 0.1 43 08LG008 Spius Creek near Canford 41 -0.331 0.034 0.05 44 07FC001 Beatton River near Fort St. John 46 0.049 0.748 - 45 07FD001 Kiskatinaw River near Farmington 52 -0.041 0.774 - 46 08NL007 Similkameen River at Princeton 72 -0.253 0.032 0.05 47 08LA001 Clearwater River near Clearwater 71 -0.145 0.229 - Station 48 08NL004 Ashnola River near Keremeos 67 -0.238 0.053 0.1 49 08LB047 North Thompson River at Birch Island 51 -0.088 0.538 - 50 08LE031 South Thompson River at Chase 87 -0.343 0.001 0.01 51 07FD009 Clear River near Bear Canyon 39 -0.130 0.431 - 52 08LD001 Adams River near Squilax 89 -0.289 0.006 0.01 53 07GD001 Beaverlodge River near Beaverlodge 45 -0.256 0.090 0.1 54 08KA007 Fraser River at Red Pass 58 -0.294 0.025 0.05 55 07GE001 Wapiti River near Grande Prairie 51 -0.341 0.014 0.05 56 08NN002 Granby River at Grand Forks 50 -0.034 0.813 - 57 07GF001 Simonette River near Goodwin 42 -0.118 0.458 - 58 08ND013 Illecillewaet River at Greeley 50 -0.236 0.099 0.1 59 07AA002 Athabasca River near Jasper 58 -0.296 0.024 0.05 60 07HA005 Whitemud River near Dixonville 42 -0.014 0.928 - 61 07GJ001 Smoky River at Watino 64 -0.253 0.043 0.05 62 07HC001 Notikewin River at Manning 49 -0.096 0.511 - 63 08NJ013 Slocan River near Crescent Valley 89 -0.258 0.015 0.05 64 08NE074 Salmo River near Salmo 63 -0.135 0.293 - 65 07GG001 Waskahigan River near the mouth 44 -0.153 0.320 - 66 07GG002 Little Smoky River at Little Smoky 46 -0.115 0.446 - 67 08NB005 Columbia River at Donald 69 -0.349 0.003 0.01 68 07GG003 Iosegun River near Little Smoky 44 -0.279 0.067 0.1 69 07HA003 Heart River near Nampa 48 -0.081 0.582 - 70 08NH119 Duncan River below B.B. Creek 50 -0.013 0.930 - 71 08NA002 Columbia River at Nicholson 96 -0.435 0.000 0.01 72 05DA006 North Saskatchewan River at 98 -0.290 0.004 0.01 Saskatchewan Crossing 73 07AF002 McLeod River above Embarras River 58 -0.067 0.615 - 74 07BF002 West Prairie River near High Prairie 54 -0.128 0.356 - 75 05DA009 North Saskatchewan River at Whirlpool 98 -0.290 0.004 0.01 point 76 07BF001 East Prairie River near Enilda 54 -0.014 0.921 - 77 05DC010 North Saskatchewan River Below 98 -0.316 0.002 0.01 Bighorn Plant 78 07AH003 Sakwatamau River near Whitecourt 41 -0.073 0.649 -

S. Gurrapu, 2020 P a g e | 85 79 05DC002 North Saskatchewam River at Saunders 98 -0.347 0.000 0.01 80 05BB001 Bow River at Banff 102 -0.240 0.015 0.05 81 05DC006 Ram River near the mouth 43 -0.124 0.427 - 82 07BJ001 Swan River near Kinuso 49 0.087 0.551 - 83 07BB002 Pembina River near Entwistle 65 -0.138 0.273 - 84 05DC001 North Saskatchewan River near Rocky 98 -0.248 0.014 0.05 Mountain House 85 07AH001 Freeman River near Fort Assiniboine 47 -0.163 0.274 - 86 08NK016 Elk River near Natal 62 -0.242 0.058 0.1 87 05BJ004 Elbow River at Bragg Creek 60 -0.127 0.333 - 88 05AA008 Crowsnest River at Frank 69 -0.411 0.000 0.01 89 07BK005 Saulteaux River near Spurfield 42 -0.150 0.342 - 90 07BK007 Driftwood River near the mouth 43 0.075 0.633 - 91 05AA023 Oldman River near Waldron’s Corner 59 -0.308 0.018 0.05 92 05AA022 Castle River near Beaver Mines 65 -0.253 0.042 0.05 93 05CB001 Little Red Deer River near the mouth 53 -0.167 0.231 - 94 05CC001 Blindman River near Blackfalds 56 -0.096 0.481 - 95 05DF910 a North Saskatchewan River at Devon 98 -0.162 0.111 - 96 05FA001 Battle River near Ponoka 61 -0.007 0.959 - 97 05DF001 North Saskatchewan River at Edmonton 98 -0.158 0.121 - 98 05EA001 Sturgeon River near Fort Saskatchewan 85 -0.061 0.582 - 99 05AE005 Rolph Creek near Kimball 76 -0.235 0.041 0.05 100 07KE001 Birch River below Alice Creek 44 -0.104 0.502 - 101 11AA032 North Fork Milk River above St. Mary 32 -0.111 0.547 - Canal 102 05CE002 Kneehills Creek near Drumheller 62 -0.173 0.180 - 103 07CA005 Pine Creek near Grassland 44 -0.081 0.601 - 104 06AA002 Amisk River at Highway No. 36 40 0.050 0.761 - 105 05FB002 Iron Creek near Hardisty 48 -0.004 0.980 - 106 06AB001 Sand River near the mouth 43 -0.077 0.624 - 107 05AF010 Manyberries Creek at Brodin’s Farm 91 0.072 0.497 - 108 06AD006 Beaver River at Cold Lake Reserve 58 -0.146 0.274 - 109 05EF001 North Saskatchewan River near Deep 98 -0.177 0.081 0.1 Creek 110 05EF004 Monnery River near Paradise Hill 34 -0.121 0.494 - 111 06BA002 Dillon River below Dillon Lake 40 0.023 0.889 - 112 05EF005 Big Gully Creek near Maidstone 31 -0.332 0.068 0.1 113 06AF005 Waterhen River near Goodsoil 33 -0.186 0.300 - 114 07MB001 MacFarlane River at outlet of Davy 46 0.175 0.243 - Lake 115 06BD001 Haultain River above Norbert River 44 -0.028 0.853 - 116 05GF001 Shell Brook near Shellbrook 34 -0.182 0.302 - 117 05GF002 Sturgeon River near Prince Albert 35 -0.155 0.374 - 118 11AE008 Poplar River at International Boundary 78 -0.121 0.290 - 119 05GG010 Garden River near Henribourg 36 -0.122 0.477 - 120 05JJ009 Saline Creek near Nokomis 41 -0.131 0.415 - 121 06DA004 Geiki River below Wheeler River 47 0.164 0.271 -

S. Gurrapu, 2020 P a g e | 86 122 05KB003 Carrot River near Armley 46 -0.249 0.096 0.1 123 05KF001 Ballantyne River above Ballantyne Bay 31 0.030 0.873 - 124 05JM010 Ekapo Creek near Marieval 45 -0.303 0.043 0.05 125 05MC001 Assiniboine River at Sturgis 56 -0.229 0.090 0.1 126 05LC001 Red Deer River near Erwood 56 -0.238 0.077 0.1 127 05LE008 Swan River near Norquay 35 -0.030 0.862 - a Not a WSC Gauge

S. Gurrapu, 2020 P a g e | 87 Supplementary Text

Text 3.S1. R script for the permutation test on the quantile-quantile (Q-Q) plots. #******************************************************************************** ********** # THIS CODE IS TO TEST THE SIGNIFICANCE OF QUANTILE-QUANTILE (Q-Q) PLOTS USING PERMUTATION TEST # AND DRAW Q-Q PLOTS FOR ALL THE GAUGING STATIONS # # FOLLOWING FUNCTIONS SHOULD BE RUN FIRST (Function scripts are at the end of this script) # - func_significance: TO COMPUTE SIGNIFICANCE # - func_stat: TO COMPUTE STATISTIC OF INTEREST # - func_resamples: TO RESAMPLE THE DATASET AND RECOMPUTE THE STATISTICS # # TEST STATISTIC USED IN THE PERMUTATION TEST IS THE MEAN OF THE RATIOS OF QUANTILES FROM THE # NEGATIVE AND POSITIVE PDO PHASES (Mean Quantile Ratio) # # FIRST, TEST STATISTIC IS COMPUTED WITH THE ORIGINAL DATASET. # # PEAK FLOW DATA IS THEN PERMUTED TO OBTAIN 10,000 RESAMPLES (Resampling without replacement) AND # THE TEST STATISTIC IS RECOMPUTED FOR ALL THE 10,000 RESAMPLES. NUMBER OF TIMES THE # RESAMPLED STATISTIC IS LARGER OR SMALLER THAN THE ORIGINAL STATISTIC IS COUNTED AND THE # PERCENTAGE IS COMPUTED. THIS PERCENTAGE IS LATER USED TO IDENTIFY THE LEVEL OF SIGNIFICANCE # # WHEN THE ORIGINAL TEST STATISTIC IS HIGHER THAN 0 # IF THE PERMUTED STATISTIC IS LESS THAN THE ORIGINAL STATISTIC MORE THAN 90 PERCENT OF THE # TIME, HIGHER MAGNITUDE FLOWS ARE SIGNIFICANTLY HIGHER IN NEGATIVE PDO PHASE, STATISTICALLY # SIGNIFICANT AT 0.1 SIGNIFICANCE LEVEL # # WHEN THE ORIGINAL TEST STATISTIC IS LESS THAN 0 # IF THE PERMUTED STATISTIC IS HIGHER THAN THE ORIGINAL STATISTIC MORE THAN 90 PERCENT OF # THE TIME, HIGHER MAGNITUDE FLOWS ARE SIGNIFICANTLY HIGHER IN POSITIVE PDO PHASE, # STATISTICALLY SIGNIFICANT AT 0.1 SIGNIFICANCE LEVEL # # PHASES OF PDO ARE DEFINED AS PUBLISHED BY EARLIER RESEARCHERS # - Cool Phase: 1890 - 1925; 1947 - 1976; 2009 - 2013 # - Warm Phase: 1926 - 1946; 1977 - 2008 # # PEAK FLOW DATASET SHOULD BE ORGANISED IN TWO COLUMNS, NAMELY # Year Peak_Flow # # LIST OF STATION ARE READ FROM A CSV FILE WHICH IS ORGANISED IN SEVERAL COLUMNS, NAMELY

S. Gurrapu, 2020 P a g e | 88 # Stn_ID Stn_Name Latitude Longitude Data_Type # (WSC Code) (Observed or Naturalised) # # THE ANALYSIS WAS DONE ON THE DATA UNTIL 2013. ANY DATA AFTER 2013 IS IGNORED #******************************************************************************** ********** # REMOVE ALL THE EARLIER DEFINED VARIABLE DATA, EXCEPT FOR THE FUNCTIONS rm(list = setdiff(ls(), lsf.str()))

# READ ALL THE REQUIRED LIBRARIES library(Hmisc)

# DEFINE THE NAME OF THE RIVER/TRIBUTARY/REGION OF INTEREST project_name = 'SW_Canada'

# PRINT A DEFAULT MESSAGE ONTO THE SCREEN print('***** Permutation test for Quantile-Quantile (Q-Q) plots is running *****')

# DEFINE DEFAULT NAMES OF INFILES OR OUTFILES, IF KNOWN stn_file = paste('stn_list_',project_name,'.csv',sep='')

# DEFINE PATHS TO THE PROJECT AND INPUT DATA FOLDERS project_path = paste('C:/1. Research/Data Exploratory Analysis/Q- Q_Plots/',project_name,'/',sep='')

data1_path = paste('C:/1. Research/Data/Streamflow/1. Water Year Peak Flows/',sep='')

data2_path = paste('C:/1. Research/Data/Streamflow/Naturalised Flows/1. Water Year Peak Flows/',sep='')

# DEFINE PATH TO THE FOLDER WITH THE LIST OF GAUGING STATIONS stn_path = paste('C:/1. Research/Data/Streamflow/Station_Lists/',sep='')

# READ IN THE LIST OF GAUGING STATIONS AND COUNT THE NUMBER OF GAUGES stn_list = read.csv(paste(stn_path,stn_file,sep=''),header=T) n_stns = length(stn_list[,1])

# DEFINE THE PHASES OF PDO AS DEFINED BY EARLIER RESEARCHERS neg_phase = c(1890:1924,1947:1976,2009:2013) pos_phase = c(1925:1946,1977:2008)

# INITIATE A PLOT AND DEFINE NAME plot_name = paste('Q-Q Plots_Water Year_Peaks_vs_PDO_phases_%02d.png',sep='') plot_path = paste(project_path,plot_name,sep='') png(plot_path,width=1500,height=1000,bg="transparent")

# DEFINE PLOT PARAMETERS par(mfrow=c(4,6),omi=c(0.05,0.2,0.05,0.2)+1.5,mar=c(2.5,2,0,0)+0.1,pty='s')

# INITIATE A DATA FRAME TO STORE OUTPUT FROM PERMUTATION TEST output = data.frame()

S. Gurrapu, 2020 P a g e | 89 # DEFINE APPROPRIATE PATH TO STORE OUTPUT FROM PERMUTATION TEST out_path = paste(project_path,'Significance test on Q-Q plots.csv',sep='')

# INITIATE REQUIRED POINTERS AND COUNTERS i_stn = 0 plot_cnt = 0

# WHILE LOOP TO READ IN ANNUAL PEAK FLOW DATA, PERFORM PERMUTATION TESTS, AND DRAW Q-Q PLOTS # AT EACH STATION while (i_stn < n_stns) { i_stn = i_stn+1

# EXTRACT THE REQUIRED STATION DATA stn_details = stn_list[i_stn,] stn_ID = as.character(stn_details$Stn_ID) data_type = as.character(stn_details$Data_Type) stn_lat = as.numeric(stn_details$Latitude) stn_lon = as.numeric(stn_details$Longitude)

# DEFINE NAME OF THE INPUT DATASET BASED ON THE DATA TYPE (Observed or Naturalised) if (data_type == 'Observed') { flow_infile = paste(data1_path,stn_ID,' peak flow series.csv',sep='') } else if (data_type == 'Naturalised') { flow_infile = paste(data2_path,stn_ID,'_Nat_peak flow series.csv',sep='') }

# CHECK IF THE FILE EXISTS. IF YES CONTINUE, ELSE PRINT ERROR MESSAGE AND SKIP TO THE NEXT STATION file_status = file.exists(flow_infile)

if (file_status == 'FALSE') { print (paste('Input dataset for the station ',stn_ID, ' is missing',sep='')) output[i_stn,'Stn_ID'] = stn_ID output[i_stn,'Significance'] = 'NS' next }

# READ THE PEAK FLOW DATA flow_data = read.csv(flow_infile,header=T)

# REMOVE ANY UNAVAILABLE OR MISSING DATA flow_data = flow_data[complete.cases(flow_data[,'Peak_Flow']),c('Year','Peak_Flow')]

# ANALYSE DATA PRIOR TO 2013 ALONE, ANY DATA AFTER 2013 IS IGNORED flow_data = flow_data[flow_data$Year <= 2013,]

# COUNT THE NUMBER OF DATA n_years = length(flow_data$Peak_Flow)

# DIVIDE THE FLOOD DATA BASED ON THE PDO PHASES neg_flood = flow_data[flow_data$Year %in% neg_phase,'Peak_Flow']

S. Gurrapu, 2020 P a g e | 90 pos_flood = flow_data[flow_data$Year %in% pos_phase,'Peak_Flow']

# EXTRACT THE MAGNITUDE OF MAXIMUM FLOOD max_flood = max(pos_flood,neg_flood) # IF THE LENGTH OF STRATIFIED DATA IS LESS THAN 5 IN EITHER OF THE PHASES, PRINT ERROR MESSAGE # AND SKIP TO THE NEXT STATION if (length(neg_flood) < 5 || length(pos_flood) < 5) { print (paste("Data length in either of the phases is less than 5 for the station ",stn_ID,sep='')) output[i_stn,'Stn_ID'] = stn_ID output[i_stn,'Significance'] = 'NS' next }

# COMPUTE STATISTICS AND EVALUATE THE SIGNIFICANCE OF Q-Q PLOTS USING PERMUTATIONS TESTS # BASED ON THE EARLIER DEFINED STATISTIC, 'stat_1' OR 'stat_2' percentages = func_significance(flow_data,neg_flood,pos_flood,neg_phase,pos_phase)

# PERCENTAGE OF TIMES THE RESAMPLED DATA IS LESSER OR GREATER THAN THE ORIGINAL STATISTIC percent_A = percentages[1] percent_B = percentages[2]

# IF THE PERCENTAGE IS HIGHER THAN 90%, ASSOCIATE THE RESPECTIVE PDO PHASE TO THE PEAK FLOWS if (percent_A >= 90) { peak_phase = 'Negative' } else if (percent_B >= 90) { peak_phase = 'Positive' } else { peak_phase = 'NA' }

# EXTRACT THE SIGNIFICANCE LEVEL BASED ON THE PERCENTAGE OF TIMES THE RESAMPLED STATISTIC IS # ABOVE OR BELOW THE ORIGINAL STATISTIC if (percent_A >= 90 & percent_A < 95 || percent_B >= 90 & percent_B < 95) { significance = 0.1 } else if (percent_A >= 95 & percent_A < 99 || percent_B >= 95 & percent_B < 99) { significance = 0.05 } else if (percent_A >= 99 || percent_B >= 99) { significance = 0.01 } else { significance = 'NS' }

# ENTER ALL THE REQUIRED INFORMATION INTO THE DATA FRAME INITIATED EARLIER ALONG WITH THE # OUTPUT FROM PERMUTATION TESTS output[i_stn,'Stn_ID'] = stn_ID output[i_stn,'Latitude'] = stn_lat

S. Gurrapu, 2020 P a g e | 91 output[i_stn,'Longitude'] = stn_lon output[i_stn,'Sample_Stat'] = percentages[3] # STAT_ORIGINAL output[i_stn,'Percent_A'] = percent_A output[i_stn,'Percent_B'] = percent_B output[i_stn,'Peak_Phase'] = peak_phase output[i_stn,'Significance'] = significance

#**************************** # START PLOTTING THE Q-Q PLOTS #**************************** # COUNT THE PLOTS plot_cnt = plot_cnt+1

# DRAW Q-Q PLOTS TO THE WATER YEAR FLOODS STRATIFIED AS PER PDO quantiles = qqplot(x=pos_flood,y=neg_flood,xlim=c(0,max_flood),xlab=NA,ylab=NA,axes=F,col=’red’, ylim=c(0,max_flood),pch=19,cex=1.5) box()

# DEFINE LEGENDS AND PLACE THEM ON Q-Q PLOTS AS REQUIRED leg_1 = c(stn_ID,paste(n_years,' yrs',sep=''))

if (significance != 'NS') { leg_2 = paste('Significant at ',significance,sep='') } else { leg_2 = significance }

legend('topleft',legend=leg_1,bty='n',cex=2,text.font=2,y.intersp=1.25) legend('bottomright',legend=leg_2,bty='n',col=ifelse(peak_phase == 'Negative','Blue','Red'),cex=1.5, text.font=2)

# USE MAXIMUM FLOOD MAGNITUDE TO DEFINE THE AXES LABELS x = round(max_flood/5) axes_lab = c(0,x,(2*x),(3*x),(4*x),(5*x))

# ADD ADDITIONAL LINES AS REQUIRED FOR EASY UNDERSTANDING abline(0,1,col='blue',lwd=2)

abline(h=axes_lab[1],lty=2,col='grey') abline(h=axes_lab[2],lty=2,col='grey') abline(h=axes_lab[3],lty=2,col='grey') abline(h=axes_lab[4],lty=2,col='grey') abline(h=axes_lab[5],lty=2,col='grey') abline(h=axes_lab[6],lty=2,col='grey')

abline(v=axes_lab[1],lty=2,col='grey') abline(v=axes_lab[2],lty=2,col='grey') abline(v=axes_lab[3],lty=2,col='grey') abline(v=axes_lab[4],lty=2,col='grey') abline(v=axes_lab[5],lty=2,col='grey')

S. Gurrapu, 2020 P a g e | 92 abline(v=axes_lab[6],lty=2,col='grey')

# WRITE LABELS FOR BOTH THE AXES (X & Y) axis(1,at=axes_lab,axes_lab,cex.axis=1.9,line=-0.35,lwd=0) axis(2,at=axes_lab,axes_lab,cex.axis=1.9,line=-0.35,lwd=0)

# ADD APPROPRIATE AXES (X & Y) TITLES if (plot_cnt%%24 == 0 || (plot_cnt-1)%%24 == 0) { # 24 BECAUSE, 24 PLOTS ARE IN EACH PAGE mtext(side=1,expression('Peak Flows' ~ (m^{3} ~ s^{-1}) ~ 'in Positive PDO Phase'),cex=2.5,font=2,line=4, outer=T) mtext(side=2,expression('Peak Flows' ~ (m^{3} ~ s^{-1}) ~ 'in Negative PDO Phase'),cex=2.5,font=2,line=2, outer=T) } }

# TURN OFF THE GRAPHICS graphics.off()

# SAVE THE OUTPUT FROM PERMUTATION TEST write.csv(output,out_path,row.names=F)

# PRINT A DEFAULT MESSAGE ONTO THE SCREEN AT THE END OF THE CODE print('***** Completed plotting Q-Q plots and computing their significance *****')

# COMPLETED COMPUTING SIGNIFICANCE OF Q-Q PLOTS USING PERMUTATION TEST AND PLOTTING THEM

#******************************************************************************** ********** # THIS FUNCTION IS REQUIRED FOR PERMUTATION TEST ON Q-Q PLOTS # # THIS FUNCTION MEASURES THE PERCENTAGE OF TIMES THE RESAMPLED TEST STATISTIC IS LOWER OR # LARGER THAN THE ORIGINAL TEST STATISTIC. FUNCTIONS ('func_stat' & 'func_resamples') ARE CALLED # WITHIN THIS FUNCTION # # LEGEND: # population: ANNUAL PEAK FLOW DATASET # sample_neg & sample_pos: SAMPLES FROM NEGATIVE & POSITIVE PDO PHASES RESPECTIVELY # neg_phase & pos_phase: NEGATIVE AND POSITIVE PHASES OF PDO RESPECTIVELY # stat: TEST STATISTIC (MEAN OF THE RATIOS OF QUANTILES FROM NEGATIVE AND POSITIVE PDO PHASES) # count_A & count_B = NUMBER OF TIMES THE RESAMPLED TEST STATISTIC IS SMALLER OR LARGER THAN # THE ORIGINAL STATISTIC #******************************************************************************** ********** func_significance = function(population,sample_neg,sample_pos,neg_phase,pos_phase) {

S. Gurrapu, 2020 P a g e | 93 # CALL FUNCTION 'func_stat' TO COMPUTE THE STATISTICS OF THE ORIGINAL DATA stat_original = func_stat(sample_neg,sample_pos)

# CALL FUNCTION 'func_resamples' TO EXTRACT A RESAMPLE AND COMPUTE TEST STATISTIC stat_resample = func_resamples(population,neg_phase,pos_phase)

# INITIATE REQUIRED COUNTERS AND POINTERS count_A = 0 count_B = 0 i_ptr = 0

# WHILE LOOP TO COUNT THE NUMBER OF TIMES THE RESAMPLED TEST STATISITIC IS SMALLER OR LARGER # THAN THE ORIGININAL STATISTIC while (i_ptr < 10000) { i_ptr = i_ptr+1

if (stat_resample < stat_original) { count_A = count_A+1 } else if (stat_resample > stat_original) { count_B = count_B+1 } }

# COMPUTE PERCENTAGE OF TIMES THE RESAMPLED STATISTIC IS AT LEAST 50 % percent_A = (count_A/10000)*100 percent_B = (count_B/10000)*100

# RETURN THE PERCENTAGES AND ORIGINAL STATISTIC, TO BE USED IN THE MAIN CODE return (c(percent_A,percent_B,stat_original)) }

# END OF THE FUNCTION "func_significance"

#******************************************************************************** ********** # THIS FUNCTION IS REQUIRED FOR PERMUTATION TEST ON Q-Q PLOTS # # THIS FUNCTION COMPUTES THE TEST STATISTIC USING THE DATA SAMPLES PROVIDED. # # LEGEND: # sample_neg & sample_pos: SAMPLES FROM NEGATIVE & POSITIVE PDO PHASES RESPECTIVELY # neg_Quantiles & pos_Quantiles: QUANTILES OF THE SAMPLES FROM NEGATIVE AND POSITIVE PDO PHASES # stat: TEST STATISTIC (MEAN OF THE RATIOS OF QUANTILES FROM NEGATIVE AND POSITIVE PDO PHASES #******************************************************************************** ** func_stat = function(sample_neg,sample_pos) {

# COMPUTE QUANTILES OF SAMPLES PROVIDED quantiles = qqplot(x=sample_pos,y=sample_neg,plot.it=F)

S. Gurrapu, 2020 P a g e | 94

# EXTRACT QUANTILES OF NEGATIVE AND POSITIVE PDO PHASES COMPUTED USING FUNCTION ‘qqplot’. # IN THE Q-Q PLOT, X-AXIS REPRESENTS POSITIVE PHASE AND Y-AXIS REPRESENTS NEGATIVE PHASE neg_Quantiles = quantiles$y pos_Quantiles = quantiles$x

# COMPUTE AND RETURN THE TEST STATISTIC stat = mean(neg_Quantiles/pos_Quantiles)

return(stat)

}

# END OF THE FUNCTION 'func_stat' #******************************************************************************** ********** # THIS FUNCTION IS REQUIRED FOR PERMUTATION TEST ON Q-Q PLOTS # # THIS FUNCTIONS PERMUTES THE ORIGINAL PEAK FLOW SERIES. THE OERMUTED DATASET IS NOW STRATIFIED # BASED ON THE PHASES OF PDO AND THE STATISTIC IS COMPUTED BY CALLING THE FUNCTION ‘func_stat’ # # LEGEND: # population: ANNUAL PEAK FLOW DATASET # neg_phase & pos_phase: NEGATIVE AND POSITIVE PHASES OF PDO RESPECTIVELY # data_resample: PERMUTED (Randomised) SAMPLE OF THE ORIGINAL DATASET (population) #******************************************************************************** ********** func_resamples = function(population,neg_phase,pos_phase) {

# EXTRACT THE PEAK FLOWS SERIES flood_data = population$Peak_Flow

# INITIATE A MATRIX TO STORE TEST STATISTIC OF EACH SAMPLE stat_perms = data.frame()

# INITIATE REQUIRED COUNTERS AND POINTERS i_ptr = 0

# WHILE LOOP TO PERMUTE THE ORIGINAL DATASET 10,000 TIMES AND COMPUTE TEST STATISTIC while (i_ptr < 10000){ i_ptr = i_ptr+1

# PERMUTE THE DATASET AND EXTRACT A RESAMPLE WITHOUT REPLACEMENT data_resample = sample(flood_data,replace=F)

# REPLACE THE ORIGINAL PEAK FLOW SERIES IN THE DATASET WITH THE RESAMPLE population$Peak_Flow = data_resample

S. Gurrapu, 2020 P a g e | 95

# STRATIFY THE PERMUTED DATASET BASED ON THE NEGATIVE AND POSITIVE PHASES OF PDO sample_neg = population[population$Year %in% neg_phase,'Peak_Flow'] sample_pos = population[population$Year %in% pos_phase,'Peak_Flow']

# CALL FUNCTION 'func_stat' TO COMPUTE STATISTICS FOR EACH RESAMPLE sample_stat = func_stat(sample_neg,sample_pos)

# ENTER THE COMPUTED STATISTICS INTO A TABLE stat_perms[i_ptr,'Stat'] = sample_stat }

# SPIT OUT THE TABLE OF RESAMPLED STATISTICS return(stat_perms) }

# END OF THE FUNCTION 'func_resamples'

S. Gurrapu, 2020 P a g e | 96 1 CHAPTER 4

2 Assessment of Historic versus Prehistoric Hydrological Drought Risk

3 using Weekly River Flows since 1110 AD§

4 Sunil Gurrapu, David J. Sauchyn, Kyle R. Hodder

5 Abstract: Planning and management of water resources infrastructure requires a 6 depth of knowledge on the frequency of extreme hydrological events, floods and 7 droughts. Infrastructure design is traditionally based upon historically observed 8 extreme events assuming they are independent and identically distributed and 9 stationary, that is, fluctuate within a fixed envelope of variability. Information on 10 historical hydroclimate provides limited range of hydrological extremes, which 11 rarely includes long-term worst droughts. In this paper, we demonstrate the 12 application of a paleo-environmental dataset, 900 years of weekly streamflow, 13 stochastically derived from a tree-ring reconstruction of annual streamflow. Our case 14 study analyzes the long-term characteristics, i.e. severity, duration and frequency, of 15 hydrological drought at Calgary, Canada. Our results indicate that the severity and 16 duration of hydrological drought with the same recurrence interval is substantially 17 larger and longer than those observed during the historical period. Historic and 18 prehistoric drought severity-duration-frequency (SDF) relationships established in 19 this study demonstrate the implications of non-stationary climate in the analysis of 20 extreme droughts. Therefore, projected droughts of the 21st century may not exceed 21 the drought severity found in the prehistoric record to the same extent that they 22 exceed historical droughts in the instrumental record. This study also emphasizes 23 the importance of paleohydrology in comprehending the region’s drought 24 characteristics.

25 Key Points: 26 1. Prehistoric drought characteristics differed from those occurred over the past 27 century. 28 2. The assumption of stationary climate in determining the frequency of severe 29 droughts is irrational.

§ Manuscript submitted to the Water Resources Management (WRM) Journal and is under review.

S. Gurrapu, 2020 P a g e | 97 4.1. Introduction

Droughts are among the most precarious natural disasters in Canada by virtue of their severity, duration and areal extent (Bonsal et al., 2011). They are characterized by a deficiency in precipitation over a specific region for a specific period of time (Mishra

& Singh, 2010). Although drought is regarded as a meteorological phenomenon, an appropriate definition of drought depends on the response of an environmental system to persistent moisture deficiency (Mishra & Singh, 2010). Prolonged shortfall in precipitation (meteorological drought) would first impact the surface and groundwater storage in a watershed, which in turn affects the magnitude of the streamflow and results in a hydrological drought. Hydrological drought is defined as a significant decrease in the availability of water in all its forms, appearing in the land phase of the hydrological cycle (Nalbantis & Tsakiris, 2009). Among all the processes in the land phase of the hydrological cycle, streamflow is the key component in describing hydrological drought because it is the aggregate of runoff and baseflow received from the surface and subsurface storage, respectively (Tsakiris et al., 2013). Thus, the method of flow thresholds is a relevant and widely adopted approach to the analyses of hydrological drought characteristics using available streamflow datasets (e.g. Kjeldsen et al., 2000;

Tigkas et al., 2012; Watts et al., 2012; Sung & Chung, 2014). A drought is said to occur if the streamflow is below a pre-defined threshold, which is generally considered to be a percentile of a flow duration curve (e.g. Watts et al., 2012; Sung & Chung, 2014).

Knowledge of severity, duration and frequency of droughts is vital to assess the impacts and to plan appropriate adaptation strategies for effective drought management

(Wilhite et al., 2000; Hayes et al., 2004; Spinoni et al., 2014). Decision-making in drought planning and management is based primarily on knowledge gained from the analysis of quantifiable droughts of the 20th century (e.g. Gan, 2000; CDMP, 2011).

S. Gurrapu, 2020 P a g e | 98 Although instrumental records provide some insights on the severity, duration and frequency of historically observed droughts, they fail to explain the extreme events that are outside the tails of the observational distribution. For example, droughts of 2001 and 2002 across much of the Canadian Prairies were unprecedented for the historical period of 100 years (Wheaton et al., 2008); however, paleoclimate records for the region (e.g., Sauchyn et al., 2002, 2015) capture droughts of greater severity and duration than the observed (e.g. Sauchyn & Skinner, 2001; Bonsal et al., 2013). These studies in dendroclimatology tend to be limited to summer droughts (seasonal or July monthly), reproduced based on the correlations between tree-ring chronologies and historical droughts, quantified by Palmer Drought Severity Index (PDSI) and

Standardized Precipitation Index (SPI). A better understanding of variability in prehistoric droughts at higher resolution would help inform preparation for adaptation to anticipated severe droughts of the 21st century (e.g. Sauchyn et al., 2010;

PaiMazumdar et al., 2012). In this context, using methodologies of paleoclimatology and stochastic hydrology, Sauchyn and Ilich (2017) reproduced 900 years of weekly streamflow at various locations in the Saskatchewan River watershed. Taking advantage of research on the region’s paleo-hydroclimate, we analysed the records of proxy streamflow for the past millennium reconstructed using tree-rings (Sauchyn &

Ilich, 2017), with a focus on establishing the drought severity-duration-frequency

(SDF) relationships of the historic and prehistoric droughts.

We also evaluated the influence of Pacific Decadal Oscillation (PDO) on the frequency and severity of drought over the historic and prehistoric periods. The significant influence of the PDO, and other low-frequency atmosphere-ocean oscillations, on the hydroclimate of the Canadian Prairies is well established (e.g.

Gobena & Gan, 2006; Bonsal & Shabbar, 2008; St. Jacques et al., 2010, 2014; Lapp et

S. Gurrapu, 2020 P a g e | 99 al., 2013; Gurrapu et al., 2016). Although these studies acknowledge that the negative phase of the PDO produces wet years, and positive phase is associated with relatively dry years, these inferences were made solely based on the historically observed climate.

Moreover, the influence of low frequency oscillations on drought severity is the topic of relatively few studies, with the exception of recent research by Asong et al. (2018) who demonstrated that the periodicities in drought variability are associated with the El

Niño-Southern Oscillation (ENSO) and Pacific North American (PNA) teleconnections.

In this paper, we demonstrate the application of proxy streamflow records of the past millennium (≈ 900 years) to better understand the variability in drought characteristics, i.e. severity, duration and frequency applied to the city of Calgary,

Canada as a case study. To do so, we analysed the historic and prehistoric droughts of the region and established severity-duration-frequency (SDF) relationships to compare and contrast time series of hydrological drought. Our first objective was to analyse the gauge and proxy streamflow records of the study river basin, the combined watershed of the Bow and Elbow Rivers at Calgary, to determine the range of hydrological drought. The second objective was to evaluate the reliability of current water supply and management systems given the range of hydroclimatic variability and extremes, implicitly contained in this unique dataset of 900 years of weekly flows. Our last objective was to evaluate the influence of low frequency PDO on the severity of hydrological droughts.

4.2. Study Region and Data

The city of Calgary is located in southwestern Alberta in the eastern foothills of the

Canadian Rockies. The major sources of water supply to the city are the Bow and Elbow

Rivers (Figure 4.1.), which mainly rely on the winter snowpack in the Rockies and

S. Gurrapu, 2020 P a g e | 100 rainfall during summer months (CDMP, 2011). Recent studies have shown declines in the winter snowpack over the Canadian Rockies (e.g. Rood et al., 2005; Mote, 2006;

Pederson et al., 2011). In contrast, the water demand is rising with increasing population and expanding economic activities in and around the city (Schindler & Donahue, 2006).

Moreover, climate models project increased frequency and severity of droughts over the region (e.g. Sauchyn et al., 2010; PaiMazumdar et al., 2012).

To compare and evaluate the historic and prehistoric hydrological droughts in these watersheds, we chose streamflow datasets from two gauging stations located in and around the city, Bow River at Calgary (05BH004) and Elbow River below

Glenmore Dam (05BJ001). Several flow regulating structures are in operation on these rivers for domestic/industrial water supply, hydroelectric power generation, etc.

(AMEC, 2009; CDMP, 2011). Therefore, to avoid the effects of human interventions on otherwise naturally flowing rivers, we used the naturalized records of instrumental streamflow produced by Alberta Environment (http://esrd.alberta.ca/). They generated these datasets using the project depletion method (i.e. measured flows are adjusted to account for the effects of storage and diversions). In this study, naturalized weekly records represent the instrumental or historical streamflow. Furthermore, we used the weekly streamflow of the past millennium to analyse the prehistoric droughts in these watersheds. This dataset is approximately 900 years long, each year containing 52 weeks of flow data generated using the methods described in Sauchyn and Ilich (2017).

To obtain a streamflow dataset for the combined watershed (Figure 4.1.) of the

Bow and Elbow rivers, we took the algebraic sum of weekly streamflow in both rivers for a common period (Instrumental: 1912 – 2009; Paleo: 1111 – 2010). To facilitate identification of the combined watershed, we called it the ‘study watershed’ and named it ‘05BHBJ0 ' using the similar convention followed by Water Survey of Canada (WSC)

S. Gurrapu, 2020 P a g e | 101 in naming its streamflow gauging stations, “05B” represents the Bow River basin, “BH” and “BJ” represents Upper Bow and Elbow sub-basins respectively and “0” represents the number of the common outlet, albeit imaginary, of these sub-basins. The timeseries of weekly streamflow in the study watershed (05BHBJ0) represents the total flow available for the city of Calgary. Any week with streamflow below a pre-defined threshold suggests the beginning of a longer duration drought, however defining a threshold is crucial. So, to determine drought episodes and for effective drought management, the City of Calgary developed five critical flow rate triggers, also termed drought response triggers, for each of the six seasons defined in the drought management plan (Table 4.1.). We used these triggers in addition to several other thresholds from flow duration curves (discussed later) to determine the severity, duration and frequency of paleo and instrumental droughts.

The timescale of the streamflow datasets is weekly whereas the seasons defined by the City of Calgary are in number of days (Table 4.1.). Therefore, using a simple conversion we defined seasons as number of weeks for ease of analysis. Referring to the first and last days of a season defined in CDMP (2011), the first season S1 starts

th with the first week W1 and if the last day of a season Si is the 4 or later day in a week

Wj, we consider the week Wj to be part of the season Si. But if the last day of season Si

rd is 3 or earlier day of the week Wj, we considered Wj to be part of the next season, Si+1.

Using these definitions of seasons, we were able to extract seasonal flow datasets, all weekly flows in a season from each year, for further analysis.

To evaluate the influence of the PDO on prehistorical (proxy) droughts, we used the PDO index reconstructed by MacDonald and Case (2005). They produced this annual index using hydrologically sensitive tree-ring chronologies from California,

USA and Alberta, Canada. This dataset was obtained from the repository of World Data

S. Gurrapu, 2020 P a g e | 102 Center for Paleoclimatology, Boulder

(ftp://ftp.ncdc.noaa.gov/pub/data/paleo/treering/reconstructions/ pdo- macdonald2005.txt). Figure 4.2. shows variability in the reconstructed PDO index over the past millennium (1004 years; 993 – 1196 AD). Although several reconstructions of the PDO exist (e.g. Biondi et al., 2001; D’Arrigio et al., 2001; Shen et al., 2006), we chose to use MacDonald and Case (2005) because it covers the entire length of the reconstructed streamflow dataset (≈ 890 years) and is based in part on tree-ring data from our region. Paleo droughts are stratified into positive (PDO ≥ 0.5), negative (PDO

≤ -0.5) or neutral (-0.5 < PDO < 0.5) events based on the annual PDO index. We assumed that the drought severity is least influenced by the PDO during neutral years

(-0.5 < PDO < 0.5). Similarly, to analyse the influence of PDO on the historical droughts, we used November to March monthly averaged PDO index derived from sea surface temperature observations by the Joint Institute for the Study of Atmosphere and

Ocean (JISAO), University of Washington (http://jisao.washington.edu/pdo/) (Mantua et al., 1997). The droughts are stratified based on the negative (cold: 1890-1924, 1947-

1976, 2009-2013) and positive (warm: 1925-1946, 1977-2008) phases of PDO (Mantua et al., 1997; Minobe, 1997).

4.3. Methods of Analysis

Sauchyn and Ilich (2017) describe the methods used to generate 900 years of weekly streamflow datasets. To create these unique datasets, they combined the methodologies of paleohydrology, the variability of water levels over centuries and millennia (Meko

& Woodhouse, 2010, 2011; Meko et al., 2012), and stochastic hydrology, the use of statistical methods to generate randomized hydrological time series that closely represent natural hydrologic processes (Ilich & Despotovic, 2008; Ilich, 2014). They used the tree-ring chronologies from several locations in the headwaters of the Bow and

S. Gurrapu, 2020 P a g e | 103 Elbow Rivers to first construct the paleohydrology (annual streamflow) of these watersheds and then stochastically downscaled them to produce 900 years of weekly streamflow datasets. To do so, they developed a new algorithm for generating stochastic time series of weekly flows constrained by the statistical properties of both the weekly historical recorded flow and annual proxy flow estimates, and also by the necessary condition that weekly flows correlate between the end of one year and start of the next.

The weekly flows thus produced introduces hydrologic variability, and sequences of wet and dry years, not evident in the short historic flow record (Sauchyn and Ilich,

2017).

We used the threshold level approach, introduced by Yevjevich (1967) to evaluate the characteristics of hydrological droughts in the study watershed. In this method, several threshold levels are defined below which the flow is considered to be in deficit, i.e. low flow (Kjeldsen et al., 2000; Sung & Chung, 2014; Rivera et al., 2017).

Kjeldsen et al. (2000) suggest that the threshold levels in a perennial river can range between the 50th and 90th percentiles of the flow duration curve (FDC), where the FDC relates the magnitude of flow to the percentage of time it is equaled or exceeded and summarizes the flow information (Searcy, 1959; Vogel & Fennessey, 1994). We chose to evaluate the drought characteristics using four threshold levels (also referred to as

th th th th truncation levels), i.e. 50 (Q50), 70 (Q70), 75 (Q75), and 90 (Q90) percentiles of the

FDC. A week with a flow magnitude below Q70 is either an isolated drought event (flow deficit) or contributing to a longer duration drought. Therefore, to establish threshold levels, we first constructed seasonal FDCs based on the weekly flows for each season for the entire period of record. Threshold levels can also be defined in two ways based on the time resolution of the data analysed, fixed or variable (Sung & Chung, 2014).

The threshold is considered fixed when a constant value is used for a definite period

S. Gurrapu, 2020 P a g e | 104 (season or year) and it is variable when the value changes over the course of a year based on the timescale specified, i.e. daily, weekly or monthly (Hisdal & Tallaksen,

2003). We developed 24 fixed threshold levels (4 each from 6 seasonal FDCs) and 208 variable threshold levels (4 each from 52 weekly FDCs). All the threshold levels (fixed or variable) were established based on the FDCs of historical streamflow records. We also explored the use of first level (Level 1) drought response triggers suggested in

CDMP (2011), as one of the threshold levels (Table 4.1.).

To define the severity of drought, we first computed the flow deficit, i.e. the difference between the actual flow and the flow threshold (fixed or variable). Then, we took the ratio of this difference to the standard deviation (SD) of the dataset used for constructing the corresponding FDC (fixed or variable). This standardized deficit is termed the low flow index (LFI). It is a non-dimensional number used to identify individual flow deficit or surplus events; a week with negative index (LFI < 0) indicates flow deficit or a hydrologic drought and a week with positive index (LFI ≥ 0) indicates flow surplus or adequate streamflow. The LFI defined either by the fixed or variable thresholds can be computed using equations (1) and (2).

푄푖− 푄푃,푗 퐿퐹퐼푓푖푥푒푑 = (1) 푄푆퐷,푗

푄푖− 푄푃,푖 퐿퐹퐼푣푎푟푖푎푏푙푒 = (2) 푄푆퐷,푖

Where,

th  Qi – i weekly flow th th  QP,j – P percentile of j seasonal FDC (Historical)

th th  QP,i – P percentile of i weekly FDC (Historical)

th  QSD,j – Standard deviation of weekly flow series of j season for the entire period of record th  QSD,i – Standard deviation of i weekly flow series for the entire period of record

S. Gurrapu, 2020 P a g e | 105 We categorized the hydrological droughts based on their severity (LFI), using the drought classification derived by other indices such as the standardized precipitation index (SPI, McKee et al., 1993), standardized precipitation evapotranspiration index

(SPEI, Vicente-Serrano et al., 2010) and streamflow drought index (SDI, Nalbantis &

Tsakiris, 2009), (Table 4.2.).

We defined the duration of a hydrologic drought by the number of consecutive weeks with negative index (LFI < 0) as illustrated in Figure 4.3. However, if a weak positive index (0 ≤ LFI ≤ 0.5) is preceded by a 12-week or longer duration drought and is succeeded by a negative index (LFI < 0), then we assumed that the weak positive LFI contributes to a longer duration drought. Thus the first drought event in Figure 4.3. (A1 to A3) is a 3-week duration drought, the second event (B1 to B15) is a 15-week drought

th with a weak surplus event in the 14 week and the last event (C1) is an isolated 1-week drought. Although the severity of an isolated drought is defined by the magnitude of the LFI, the severity of a longer duration drought was represented by the average of the severities (LFI) of all individual events. For example, the average of the individual events A1, A2 and A3 quantifies the severity of a 3-week duration drought and similarly the average of individual events B1 to B15 quantify the severity (inclusive of a weak surplus event B14) of a 15-week duration drought, whereas the severity of an isolated drought C1 is defined by the LFI.

Severity-duration-frequency (SDF) curves provide crucial information on the frequency and duration of severe droughts (Dalezios, 2000; Todisco et al., 2013; Sung

& Chung, 2014). To construct these curves, we first computed the low flow indices

(LFI) using equations (1) and (2) for the fixed and variable thresholds respectively and categorically separated droughts, LFI < 0. We then extracted droughts with the specified duration, i.e. 1-, 2-, 4-, 6-, … 48-, 50-, 52-weeks, from both gauge and proxy

S. Gurrapu, 2020 P a g e | 106 streamflow records, as described above. In addition, we assumed that a single longer duration drought consists of several shorter duration events, for example, the first drought in Figure 4.3., consists of three 1-week droughts (A1, A2, A3), two 2-week droughts (A1A2, A2A3) and one 3-week (A1A2A3) drought. The severity of a > 1-week duration drought is quantified by taking the average of the severity of all individual events within the period of drought of specified duration.

The frequency of droughts was identified by fitting a suitable probability distribution to the extracted droughts of specified duration. To determine the suitable distribution that best represents the distribution of droughts over the period of record, we used Kolmogorov-Smirnov goodness-of-fit test. We used Easyfit Professional version 5.6 to test the suitability of five distributions: the Generalized Extreme Value

(GEV), 3 Parameter Lognormal (LN), 3 Parameter Log-Logistic (LL3), Gumbel

Minimum (GMin), and 3 Parameter Weibull (W3). This analysis showed that the distribution of droughts is best represented by the GEV distribution, a special case of which is one of the generally recommended distributions for frequency analysis of low flows in Canada, the W3 distribution (e.g. Stedinger et al., 1993). Therefore, the GEV distribution was fitted to the dataset of drought severity and the distribution parameters were estimated using the method of L-moments. We used the ‘lmom’ package

(Hosking, 2017) in the R statistical language (R Core Team, 2015) to estimate the distribution parameters and fit the data to the GEV distribution. Then, we extracted the quantiles of drought severity from the fitted curve at several return periods, e.g. 500-,

300-, 200-, 100-, 50-, and 10-years. We repeated this to fit the droughts of other durations to the GEV distribution and extract quantiles of drought severity with the above-mentioned frequency. We then constructed SDF curves for both gauge and paleo datasets.

S. Gurrapu, 2020 P a g e | 107 The other major aspect of this analysis was to examine the influence of the PDO on drought severity. First, we categorized the individual droughts (LFI< 0) according to the positive and negative phases of the PDO using annual indices of the PDO reconstructed by MacDonald and Case (2005) for the prehistoric period and November to March monthly averaged PDO index by Mantua et al. (1997) for the historic period.

Then, we adopted the method of creating quantile-quantile (Q-Q) plots to determine if the LFI series of both phases of the PDO came from the same population. This method was earlier described and was successfully adopted by Gurrapu et al. (2016) to identify the influence of the PDO on annual peak flows in the watersheds of western Canada.

We constructed Q-Q plots by plotting the ranked droughts (quantiles) of the negative

PDO phase (y-axis) against the ranked droughts (quantiles) of the positive PDO phase

th (x-axis). For an individual point (xi, yi), xi is the LFI of the i ranked drought in the

th positive PDO phase, and yi is the LFI of the i ranked drought in the negative PDO phase. The LFI series from both phases of the PDO can be assumed to be from the same

th population if the points fall along the 1:1 line. If the quantile ratio ri = (yi/xi) of the i ranked drought is < 1, then the ith ranked drought in the positive PDO phase is more severe than that in the negative PDO phase. Similarly, values of ri > 1 indicate that the ith ranked drought in the negative PDO phase is more severe than that in the positive phase. If the PDO has no influence on the drought severity (LFI), then the mean of the quantile ratios (R) should be approximately 1. We tested the significance of R at the 0.1 level using a two-sided permutation test with 10,000 iterations (Manly, 2007).

4.4. Results and Discussion

The historical (instrumental) records of hydroclimate rarely include the long-term worst droughts and the knowledge of prehistorical (pre-instrumental) hydroclimate can assist in understanding the region’s vulnerability to extreme droughts. To illustrate the

S. Gurrapu, 2020 P a g e | 108 importance of prehistorical hydroclimate, we assessed the historic and prehistoric drought characteristics based on the instrumental and proxy records of streamflow from the study watershed, 05BHBJ0. Figures 4.4a. and 4.4b. are the annual hydrographs for the instrumental and proxy records of weekly streamflow. Figure 4.4. also shows the six seasons (S1 to S6) and the corresponding first level (Level 1) drought response triggers defined in CDMP (2011), Table 4.1. While the black curves represent the averaged streamflow hydrographs, dotted blue and red curves are obtained by mapping the highest and lowest weekly flows, and represents the maximum and minimum hydrographs, respectively. Although the average hydrographs of both periods match, the extreme (maximum and minimum) hydrographs are distinctively different with prehistoric hydrographs showing extremely high and low flows. There were several instances of flow being lower than the drought response trigger within the seasons of high water demand, i.e. S3, S4, and S5 (summer and early fall), Figure 4.4a. The seasonal drought response triggers, Table 4.1., were defined based on the analysis of historical records of streamflow (CDMP, 2011) and the minimum hydrograph from

Figure 4.4a. demonstrates the importance of updating the drought response triggers.

To further examine the low flows in detail, we constructed seasonal flow duration curves (FDC) using all the weekly streamflow records within a season for the entire period of record. Figure 4.5. presents the lower half, exceedance probabilities larger than 50%, of the seasonal FDCs. FDCs for both gauge and proxy datasets were plotted together to enable comparison of the flow characteristics. Historical flow (blue dots) with 100% exceedance probability was as low as low as 5 m3/s, indicating the perennial nature of the river. This low magnitude flow occurred during seasons 1 and

6, which includes winter months when the majority of the watershed is frozen with least precipitation as rainfall. Figure 4.5. also presents the level 1 drought response trigger

S. Gurrapu, 2020 P a g e | 109 (red dotted line) for each season and the corresponding historical low flow (blue dashed line). It is apparent from Figure 4.5. that the seasonal historical low flows of seasons 1,

2, and 6 were lower than the corresponding drought response triggers, Figures 4.5a,

4.5b, and 4.5f. In winter to early spring, a critical period of water supply from the regional snowpack, the drought response triggers were generally conservative, i.e. within the range of historically observed streamflow. The margin between the water supply and demand is minimal during these seasons and hence the demand management, i.e. reduced per capita demand, is adopted for drought preparedness

(CDMP, 2011).

The historically observed low flow of seasons 3, 4, and 5, were higher than the corresponding seasonal drought response triggers, Figures 4.5c, 4.5d, and 4.5e. These seasons, summer and early fall, are periods of high water demand (Akuoko-Asibey et al., 1993), which necessitates the appropriate management of available water resources.

The study watershed responds quickly in translating melting snow and rainfall into streamflow because of steep headwater catchments and minimal storage as ground or surface waters. Thus water management during the periods of high demand is critical in times of hydrological drought, i.e. deficit flow compared to a seasonal drought response trigger. In response to a hydrological drought, the water allocation to different sectors is as indicated in Table 4.1. Although the drought response developed by the

City of Calgary seemed reasonable and relevant to the historical FDC (blue dots), the prehistorical FDC (red dots) reveals much lower magnitude flows during the high demand seasons, i.e. seasons 3, 4, and 5. Therefore, to evaluate the characteristics of drought in this watershed, we analysed and evaluated the flows that occurred at least

50% of the time, i.e. low flows, in both gauge and proxy streamflow datasets from the study watershed.

S. Gurrapu, 2020 P a g e | 110 We used four threshold levels, i.e. Q50, Q70, Q75, and Q90 derived from the FDCs to evaluate the hydrological drought characteristics in the study watershed. The threshold levels were either fixed or variable over the course of a year. The fixed thresholds were derived from the FDC for the weekly flows in a season for the entire record period and the variable thresholds were derived from the FDC for the specified week’s flow for the entire period of record. Figure 4.6. illustrates the range and distribution of fixed and variable thresholds corresponding to the (a) Q50, (b) Q70, (c)

Q75, and (d) Q90 threshold levels and the seasonal averaged values of these thresholds are presented in Table 4.3. The variable thresholds (blue dots) were larger than the fixed thresholds (red lines) because the variable threshold captures the variability of weekly flows in a season (Figure 4.6. and Table 4.3.). For example, the seasonal averaged fixed

3 threshold corresponding to Q70 was 84 m /s whereas the corresponding variable threshold was 93 m3/s. Moreover, the thresholds were larger during summer (season 3), a period of mountain snowmelt runoff and rainfall.

Drought severity was measured using the low flow indices (LFI) based on the pre-defined threshold levels. Figures 4.7a. and 4.7b. depict the sensitivity of LFI in identifying the prehistoric droughts based on various fixed and variable threshold levels, respectively. Indices 1, 2, 3, and 4 correspond to the low flows identified using the threshold levels Q50, Q70, Q75 and Q90, respectively and index 5 corresponds to the low flows identified using the level 1 drought response trigger, which is a fixed threshold for a season. Index 5 for variable threshold was computed assuming that the weekly flow threshold is fixed at the level 1 drought response trigger of that season.

th Index 1 is based on the Q50 threshold level, which is the 50 percentile or quantile of the 50% exceedance probability from FDC. Since the 50th percentile denotes the median of the dataset, the number of weeks with flow surplus (LFI > 0) and flow deficit (LFI

S. Gurrapu, 2020 P a g e | 111 < 0) should approximately be equal although the intensities differ. It is apparent from

Figures 4.7a. and 4.7b. that Index 1 is distributed equally on either side of the y = 0 line, irrespective of the severity. The drought severity measured using a fixed threshold appears to be invariable (i.e. ≈ constant) because the flow variability within a season was averaged (Figure 4.7a).

The indices based on the fixed thresholds fail to capture the seasonal variability and the severity of an event is compromised (Figure 4.7a), whereas those based on the variable thresholds capture the associated variability (Figure 4.7b), highlighting the region’s earlier identified prehistoric severe and longer drought episodes, i.e. 1300’s,

1480 – 1500, 1550 – 1575, 1620 – 1655, etc. (e.g. Bonsal et al., 2013; Sauchyn & Ilich,

2017). For example, fixed threshold based indices 3 and 4 classified these droughts as mild to moderate (-1.5 < LFI ≤ 0) whereas the variable threshold based Indices 3 and 4 classified them as severe to extreme (LFI ≤ -1.5). Kjeldsen et al. (2000) suggest that the variable threshold will reflect the expected flow in a river and therefore gives more realistic drought patterns than a fixed threshold. Therefore, we chose to use variable threshold levels to measure drought severity for further analysis of drought characteristics. Moreover, Figures 4.4. and 4.5. reveal the perennial nature of the studied rivers and henceforth, we measured the drought severity using the threshold level Q75, which is within the range of generally recommended threshold levels, i.e. Q70 to Q90, for perennial rivers (Kjeldsen et al., 2000; Sung & Chung, 2014).

Frequency curves of prehistoric and historic droughts were constructed by fitting the droughts severities (LFI < 0) to a GEV distribution. We observed that these curves were not much different for shorter duration droughts, i.e. 1- and 2-week (results not shown), but were substantially different for longer duration (≥ 3-weeks) droughts.

Figure 4.8. shows the frequencies of a 12-week (≈ 3 months) drought from the historic

S. Gurrapu, 2020 P a g e | 112 and prehistoric periods. These curves indicate that the frequency of droughts with similar severity was much higher than what was observed over the past century. For example, based on the historically observed droughts, a 12-week drought AH (severity

≈ -0.85) has a frequency of 10 years (Figure 4.8b.), whereas prehistoric 12-week droughts (APH) had a frequency of 3-4 years, Figure 4.8a. Similarly, the prehistoric drought frequency curve implies that a 100-year historical drought (BH) had a chance of occurring every 8 years (BPH). Moreover, the majority of the historical droughts were mild to moderate (i.e. -1.25 < LFI ≤ 0), whereas the droughts over the past millennium were more severe (LFI ≤ -1.5).

To summarize drought frequency, we developed severity-duration-frequency

(SDF) curves for both historic and prehistoric periods. In Figure 4.9., the SDF curves for the study watershed 05BHBJ0, drought severity (LFI) is based on Q75 threshold level or 75th percentile of the FDC. It is apparent from these figures that the prehistoric droughts of any specified duration are more severe than the historic droughts. For example, historically observed 12-week duration drought (AH) with a 100-year return period is moderate (LFI ≈ -1.1), whereas its prehistoric counterpart (APH) is a severe drought (LFI ≈ -1.6). Otherwise, a 100-year 12-week duration severe drought, APH (LFI

≈ -1.6) of the prehistoric period has no counterpart in the historic period. These curves demonstrate that the occurrence of severe and longer duration droughts are not uncommon in this region.

Lastly, we analysed the influence of the PDO on drought severity in the watershed. The Q-Q plot, Figure 4.10., presents evidence that the severity of hydrological droughts (LFI < 0) is influenced by the phase of the PDO. Figure 4.10. shows the Q-Q plots for the prehistorical and historical droughts quantified by the low flow indices (LFI) based on the variable threshold defined by the 75th percentile of the

S. Gurrapu, 2020 P a g e | 113 corresponding FDCs. Prehistorical droughts are stratified into PDO phases using the annual indices reconstructed by MacDonald and Case (2005), whereas the historical

(gauge) droughts are stratified according to the previously identified phases of PDO

(e.g. Mantua et al., 1997; Minobe, 1997). The Q-Q plots demonstrate that severe droughts are typically more common in the positive phase of the PDO, since the quantiles of drought severity largely appear below the 1:1 line. The permutation tests show that this is a significant result (p < 0.1) in both prehistoric and historic periods.

Although the mild droughts (LFI ≥ -1) are equally likely to occur in either of the PDO phases, moderate to extreme droughts (LFI < -1) are more likely to occur in the positive phase of PDO, Figure 4.10.

4.5. Conclusions

Planning and management of water resources infrastructure requires a depth of knowledge on the frequency of extreme hydrological events, floods and droughts.

Traditionally, these frequencies are derived from the analysis of historically observed extreme events assuming they are independent and identically distributed (i.i.d) and the system fluctuates within a fixed envelope of variability (Tallaksen et al., 2000; Milly et al., 2008). However, the validity of these assumptions has been questioned (e.g. Kwon et al., 2008; Stedinger & Griffis, 2008; Lopez & Frances, 2013; Barros et al., 2014;

Gurrapu et al., 2016).

The drought management plan for the city of Calgary proposed several drought response triggers, specified levels of streamflow, with the assumption of stationary climate. Streamflow below these triggers is considered deficit flow and appropriate drought response action is taken for effective water management (Steinemann &

Cavalcanti, 2006; CDMP, 2011). We analysed the instrumental and pre-instrumental streamflow records of the Bow and Elbow River basins to compare and contrast the

S. Gurrapu, 2020 P a g e | 114 drought characteristics of historic and prehistoric periods. We found that there were several pre-instrumental droughts of significantly greater severity and/or duration than the instrumental droughts of record in the 1930s-40s, late 1970s, 1980s and early 2000s,

(Figure 4.7b). We also found evidence for the teleconnection between the Pacific

Decadal Oscillation, a recurring pattern of ocean-atmosphere climatic variability, and drought severity, with a greater tendency for severe to extreme droughts in the positive phase of the PDO. Results from this study augment the earlier findings that the droughts of the 20th century were relatively mild compared to the pre-instrumental period (e.g.

Sauchyn & Skinner, 2001; Sauchyn et al., 2002; Axelson et al., 2009; Bonsal et al.,

2013; Sauchyn et al., 2015) by providing more information on the region’s exposure to severe drought. The results also demonstrate the implications of non-stationary climate in the analysis of extreme droughts and the study emphasizes the importance of paleohydrology in comprehending the region’s drought characteristics.

Despite considerable drought research in western Canada in recent decades, the focus of the majority of these studies was droughts observed over the last century (e.g.

Dey, 1982; Akinremi et al., 1996; Nkemdirim & Weber, 1999; Bonsal & Reiger, 2007;

Wheaton et al., 2008; Sun et al., 2012). With advances in paleo-environmental research, regional hydroclimate can be reconstructed for the past millennium and beyond using chronologies of tree-rings, lake sediments, etc. (e.g. Desloges et al., 1994; Sauchyn et al., 2002, 2015; Case & MacDonald, 2003; Hodder et al., 2007; St. George et al., 2009;

Cook et al., 2010). The value of paleo-environmental research lies in its extended view of hydroclimatic variability, with extremes in climate and water variables that are outside the tails of the observational distribution (Oldfield & Alverson, 2003).The novel contribution of this study is the use of weekly estimates of river flows for the past 900 years, which enabled an analysis of the drought frequency, severity and duration for

S. Gurrapu, 2020 P a g e | 115 both historic (1910-2015) and pre-historic (1110-1910) periods. Our analysis of weekly river flows for the Bow and Elbow rivers indicates that the potential severity of drought at Calgary (Alberta) has been underestimated. Furthermore, the more severe and prolonged droughts evident in the paleo-climate record very likely may reoccur but in a warmer climate.

The results of this study will inform drought management by enabling water managers to redefine the threshold levels for effective allocation of the region’s available water resources. The methodology developed here was applied to the city of

Calgary to inform drought planning and management options for the coming 20 to 50 years. It is transferable to other municipalities and river basins, with application to drought mitigation, reservoir operation, design of hydraulic structures, analysing performance of rural water management systems, assessing climate change impacts, predicting flow in ungauged watersheds, and long-term watershed protection plans.

There are policy implications for water protection, water conveyance and storage, and drought preparedness and mitigation strategies. The most relevant potential strategic impacts relate to adaptation to climate change: adjustments to design codes and standards, management practice and policy in response to recent and anticipated climate changes.

Acknowledgments

The research described in this paper was funded by Alberta Innovates – Energy and

Environmental Solutions, the City of Calgary and EPCOR Water Canada. This work was completed in close collaboration with our project partners. For their support and cooperation, we thank Margaret Beeston (Leader, Resource Planning and Policy, Water

Resources, The City of Calgary), Lily Ma (Team Lead, Resource Analysis, Strategic

S. Gurrapu, 2020 P a g e | 116 Services, Water Resources, The City of Calgary) and Dr. Lyndon Gyurek (Senior

Manager, Environment, EPCOR Water Canada).

S. Gurrapu, 2020 P a g e | 117 4.6. Figures

Figure 4.1. Drainage areas of the Bow (WSC: 05BH004) and Elbow (WSC: 05BJ001) River watersheds. Circles with dots represent the streamflow gauging stations operated by Water Survey Canada (WSC) and the triangle represent the city of Calgary which depends on both the watersheds as principal sources of water. Asterisks (*) represents the locations from where the tree-rings were collected to do the streamflow reconstructions.

S. Gurrapu, 2020 P a g e | 118

Figure 4.2. Variability of millennial Pacific Decadal Oscillation reconstructed by MacDonald and Case (2005) using tree-ring chronologies. Red bars represent positive years (PDO ≥ 0.5), blue bars represent negative years (PDO ≤ -0.5) and grey bars represents neutral years (-0.5 < PDO < 0.5).

S. Gurrapu, 2020 P a g e | 119

Figure 4.3 Definition sketch of drought duration. A, B and C in the sketch represent drought events, whereas the subscripts represent individual drought event.

S. Gurrapu, 2020 P a g e | 120

Figure 4.4. Annual streamflow hydrographs for the (a) prehistoric and (b) historic periods in the study watershed 05BHBJ0 Rivers. Solid blue lines represent the seasonal (S1 to S6) Level 1 drought response triggers defined in CDMP (2011).

S. Gurrapu, 2020 P a g e | 121

Figure 4.5. Frequency distribution of seasonal low flows, i.e. flows equaled or exceeded at least 50% of the time, derived from the seasonal flow duration curves (FDCs) constructed for the study watershed 05BHBJ0. Prehistoric low flows are represented by red dots and the historical low flows by the blue dots. Also shown are the historically observed low flow (blue dashed line) and the level 1 drought response triggers (red dotted lines) defined in CDMP (2011).

S. Gurrapu, 2020 P a g e | 122

Figure 4.6. Comparison of fixed (red lines) and variable (blue dots) threshold levels

(a) Q50, (b) Q70, (c) Q75, and (d) Q90.

S. Gurrapu, 2020 P a g e | 123

Figure 4.7. Sensitivity of prehistoric droughts to several (a) Fixed and (b) Variable flow thresholds defined from the corresponding seasonal and weekly flow durations curves of the watershed 05BHBJ0. Indices 1 to 4 are based on the thresholds from FDCs and index 5 is based on the Level 1 drought response trigger as defined in CDMP (2011). Grey bands represent the historical droughts of the region identified by Chipanshi et al. (2006), Bonsal & Regier (2007) and Wheaton et al. (2008).

S. Gurrapu, 2020 P a g e | 124

Figure 4.8. Frequency of 12-week duration droughts in the study watershed 05BHBJ0 for the (a) prehistoric and (b) historic periods. Drought severity is based on the variable threshold defined by the 75th percentile of weekly FDCs (Index 3).

S. Gurrapu, 2020 P a g e | 125

Figure 4.9. Drought Severity-Duration-Frequency (SDF) curves for the (a) Prehistoric and (b) Historic periods for the study watershed 05BHBJ0. Drought severity (LFI) is based on the variable threshold defined by the 75thpercentile of weekly FDCs.

S. Gurrapu, 2020 P a g e | 126

Figure 4.10. Quantile-Quantile (Q-Q) plots of (a) Prehistoric and (b) Historic periods based on the drought severity (LFI< 0) in the study watershed 05BHBJ0, stratified according to the phases of the Pacific Decadal Oscillation (PDO). Drought Severity is based on the variable threshold defined by the 75th percentiles of the historical FDCs. Shown in the lower right hand corner are the significance levels of the permutations test.

S. Gurrapu, 2020 P a g e | 127 4.7. Tables

Table 4.1. Flow rate triggers for the study watershed 05BHBJ0 (Figure 4.1.) proposed by the City of Calgary for implementations of restrictions and water management actions (Ref. Table 7 in “City of Calgary Drought Management Plan”; CDMP, 2011). FLOW RATE TRIGGER (m3/sec) Level 1 Level 2 Level 3 Level 4 Level 5 No impending IFN and IFN and WID storage; supply Irrigation water PERIOD demand cannot IFN not met, is 1.25 times demand (WID) City demand be met with WID demand plus met; City cannot be met City demand compromised instream flow demand restricted needs (IFN) restricted Season 1 18.1 16.6 15.1 5.1 4.3 (Jan 1 – May 1) Season 2 44.0 40.4 36.7 26.7 4.7 (May 1 – Jun 1) Season 3 69.9 64.1 58.2 28.2 4.7 (Jun 1 – Aug 20) Season 4 58.8 53.9 79.0 19.0 4.7 (Aug 20 – Sep 1) Season 5 47.6 43.7 39.7 29.7 4.7 (Sep 1 – Oct 1) Season 6 18.1 16.6 15.1 5.1 4.5 (Oct 1 – Dec 31)

S. Gurrapu, 2020 P a g e | 128 Table 4.2. Classification of droughts based on their severity. The LFI represents the number of standard deviations from the pre-defined thresholds.

Criterion Description LFI ≥ 0 No drought or flow excess 0 > LFI ≥ -1 Mild drought -1 > LFI ≥ -1.5 Moderate drought -1.5 > LFI ≥ -2 Severe drought LFI < -2 Extreme drought

Table 4.3. Seasonal average of the fixed and variables thresholds at specified percentiles of the flow duration curves.

3 Threshold Level (m /sec)

Q50 Q70 Q75 Q90

Season Fixed Variable Fixed Variable Fixed Variable Fixed Variable 1 31.08 31.75 26.99 28.02 25.96 26.96 21.95 22.51 2 108.32 123.51 73.39 99.86 65.30 95.51 51.20 75.40 3 221.58 234.61 178.57 194.46 165.37 184.89 135.14 154.14 4 122.38 122.18 107.39 108.18 104.62 105.33 95.22 93.16 5 93.81 94.31 83.90 84.92 81.84 83.10 71.81 73.89 6 46.12 47.85 36.72 42.59 34.67 41.12 27.14 34.65

S. Gurrapu, 2020 P a g e | 129 CHAPTER 5: Conclusions

5.1. Summary

Shrinking winter snowpacks (e.g. Pederson et al., 2011), shifts in peak flow season (e.g.

Stewart et al., 2005), and the projected decline in summer water supplies (e.g.

PaiMazumdar et al., 2013) across southwestern Canada necessitate adaptive planning and management of available water resources. The hydroclimate of this region is resilient to the impacts of hydrological extremes and a better understanding of their characteristics is vital in optimal planning and design of reliable infrastructure and the planning and implementation of appropriate adaptation strategies for effective drought management. This thesis addressed these issues by achieving a better understanding of the region’s hydrology and the characteristics of hydrological extremes affecting the watersheds of southwestern Canada. The primary objective of this thesis is to evaluate the use of regional hydroclimatic indices in representing watershed hydrology and assess the influence of various low-frequency large-scale climate oscillations on the region’s hydrological extremes. This chapter summarises the major findings of this thesis.

5.2. Assessment of Regional Hydroclimate for Streamflow Prediction

The use of indices of regional hydroclimate to represent available water in the naturally flowing watersheds of southwestern Canada was explored first; detailed analysis and results are presented in Chapter 2 of this thesis. The results indicate that the regional climate index, Standardised Precipitation Evapotranspiration Index (SPEI), is a good predictor of monthly and annual streamflow in these watersheds. However, its ability to represent streamflow depends on the watershed’s hydrologic response to the regional climate, i.e. the time lag between the input (precipitation) and output (streamflow) from

S. Gurrapu, 2020 P a g e | 130 the watershed. In addition, in case of a glacial or nival watershed, the residence time of the precipitated water (snow or rain) within a watershed influences the ability of SPEI in representing streamflow from a watershed. Therefore, the timescale of the SPEI capturing the variability of streamflow differed with the regional hydrologic regime. In addition, the results augment the findings from earlier studies which demonstrate that the streamflow in a pluvial and mountainous watershed is better captured by climatic conditions over a shorter timescale (e.g. Vicente-Serrano and Lopez-Moreno, 2005) and streamflow in a nival and glacial watershed is better captured by climatic conditions over a longer timescale (e.g. O’Brien and Stroich, 2005; Abatzoglou et al., 2014;

Haslinger et al., 2014). Finally, SPEI-based principal component regression equations were devised to model monthly and annual streamflow in 24 naturally flowing watersheds distributed across southwestern Canada. These equations are simpler to build than dynamical models and can be applied over large areas and many sub-basins with minimal data requirements to estimate watershed runoff. These models complement earlier developed statistical models based on large-scale climate oscillations (e.g. St. Jacques et al., 2013) and are capable of producing estimates of streamflow with minimal data requirements. These estimates provide vital information on water availability, although the efficient distribution and management of these resources requires adequate infrastructure designed to withstand changing hydroclimatic conditions.

5.3. Influence of Non-Stationary Climate on Hydrological Extremes

Infrastructure planning and design requires a depth of knowledge on the magnitude and frequency of floods and droughts, which is conventionally derived from the analysis of historically observed extreme events assuming a stationary hydroclimatic system, i.e. the system fluctuates within a fixed envelope of variability (Tallaksen et al., 2000; Milly

S. Gurrapu, 2020 P a g e | 131 et al., 2008). Previous studies have assessed this assumption of stationarity by evaluating the influence of non-stationary climate on the magnitude and frequency of hydrological extreme events. Several studies demonstrated that the hydroclimate of western Canada is strongly influenced by the low-frequency atmosphere-ocean oscillations originating over the equatorial Pacific Ocean (e.g. Mantua et al., 1997;

Rood et al., 2005; Gobena and Gan, 2006; Wang et al., 2006; Fleming et al., 2007;

Fleming and Whitfield, 2010; Whitfield et al., 2010; St. Jacques et al., 2010; 2014).

However, almost all flood frequency analyses (FFA) done in Canada invokes the stationary assumption, i.e. historical floods are independent and identically distributed

(i.i.d.) (e.g. Neill and Watt, 2001; Aucoin et al., 2011). The results of this thesis presented in Chapter 3 indicate that the i.i.d. assumption is not tenable in the watersheds of western Canada and the knowledge of climate with regard to teleconnection patterns should be considered before performing FFA. In particular, the upper Fraser River

Basin, the Columbia River Basin, and the North Saskatchewan River Basin are sub- regions where the i.i.d. assumption seems dubious. Therefore, ignoring the multi- decadal variability of large-scale climate states could lead to flood risk underestimation, and under-design and under-construction of key infrastructure.

5.4. Reliability of Current Water Supply and Management System

In a site-specific study detailed in Chapter 4, the influence of assuming stationary drought characteristics was evaluated by analysing nearly 100 years of historically observed, and approximately 1000 years of proxy, streamflow data. The results suggest that the pre-instrumental (proxy) droughts were longer and more severe than those that occurred over the instrumental period, i.e. the drought episodes of the 1930s-40s, late

1970s, 1980s, and early 2000s. These results augment the earlier findings that the droughts of the 20th century were relatively mild compared to the pre-instrumental

S. Gurrapu, 2020 P a g e | 132 period (e.g. Sauchyn & Skinner, 2001; Sauchyn et al., 2002; Axelson et al., 2009;

Bonsal et al., 2013; Sauchyn et al., 2015) by providing more information on the region’s exposure to severe drought. The results also provide evidence for the teleconnection between the PDO and drought severity, with a greater tendency for severe-to-extreme droughts in the positive phase of the PDO. These results also demonstrate the implications of non-stationary climate in the analysis of extreme droughts. The analysis of weekly river flows for the Bow River and Elbow River indicates that the potential severity of drought at Calgary (Alberta) has been underestimated and hence the drought response triggers proposed in the Drought Management Plan (CDMP, 2011) appear inadequate. Furthermore, the severe and prolonged droughts evident in the pre- instrumental period will very likely recur but in a warmer climate. The results of this study will enable water managers to redefine the threshold levels for effective drought management and allocation of the region’s available water resources.

The results from this thesis provide substantial evidence that runoff from a watershed (i.e. streamflow) can be represented by the regional hydroclimate and the characteristics of hydrological extreme events are significantly influenced by a non- stationary climate. The results also demonstrate the concerns / issues arising from the assumption of stationary climate in determining the characteristics of hydrological extremes, which were widely questioned earlier (e.g. Kwon et al., 2008; Stedinger &

Griffis, 2008; 2011; Lόpez & Francѐs, 2013; Barros et al., 2014). The results of this thesis will inform, (a) water management with information on water availability in a watershed, (b) water engineers providing precautions to be considered in efficient design of infrastructure resilient to hydrological extreme events, and (c) decision and policy makers for the design / redesign management plans for effective drought management. In principle, the most relevant potential strategic impacts relate to

S. Gurrapu, 2020 P a g e | 133 adaptation to hydroclimatic change, i.e. adjustments to design codes and standards, management practice and policy in response to recent and anticipated hydroclimate changes.

S. Gurrapu, 2020 P a g e | 134 BIBLIOGRAPHY

Abatzoglou, J. T., R. Barbero, J. W. Wolf, and Z. A. Holden. 2014. Tracking interannual streamflow variability with drought indices in the U.S. Pacific Northwest. Journal of Hydrometeorology 15(5): 1900 – 1912. DOI: 10.1175/JHM-D-13-0167.1.

Akinremi, O. O., S. M. McGinn, and A. G. Barr. 1996. Evaluation of the Palmer Drought Index on the Canadian prairies. Journal of Climate 9(5): 897 – 905. DOI: 10.1175/1520-0442(1996)009<0897:EOTPDI>2.0.CO;2.

Akuoko-Asibey, A., L. C. Nkemdirim, and D. L. Draper. 1993. The impacts of climatic variables on seasonal water consumption in Calgary, Alberta. Canadian Water Resources Journal 18(2): 107 – 116. DOI: 10.4296/cwrj1802107.

Alexander, M. A. 2010. Extratropical air-sea interaction, SST variability and the Pacific Decadal Oscillation (PDO). In Climate Dynamics: Why does Climate Vary? (eds.) D. Sun and F. Bryan. AGU Monograph # 189, Washington D. C., 123 – 148.

Allen, R. G., L. S. Pereira, D. Raes, and M. Smith. 1998. Crop evapotranspiration: Guidelines for computing crop water requirements. FAO Irrigation and Drainage Paper No. 56. Food and Agricultural Organisation of the United Nations, Rome, Italy. 333 pp. ISBN 92-5-104219-5.

AMEC. 2009. South Saskatchewan River Basin in Alberta: Water Supply Study. Alberta Agriculture and Rural Development. Lethbridge, Alberta.

Anderson, C. I., and W. A. Gough. 2017. Accounting for missing data in monthly temperature series: Testing rule-of-thumb omission of months with missing values. International Journal of Climatology 38: 4990 – 5002. DOI: 10.1002/joc.5801.

Andrews, E. D., R. C. Antweiler, P. J. Neiman, and F.M. Ralph. 2004. Influence of ENSO on flood frequency along the California Coast. Journal of Climate 17(2): 337 – 348. DOI: 10.1175/1520-0442(2004)017%3C0337:IOEOFF%3E2.0.CO;2.

Asong, Z. E., H. S. Wheater, B. Bonsal, S. Razavi, and A. Kurkute. 2018. Historical drought patterns over Canada and their teleconnections with large-scale climate signals. Hydrology and Earth System Sciences 22(6): 3105 – 3124. https:10.5194/hess-22- 3105-2018.

Aucoin, F., D. Caissie, N. El-Jabi, and N. Turkkan. 2011. Flood Frequency Analysis for New Brunswick Rivers. Canadian Technical Report of Fisheries and Aquatic Sciences 2920, 77p. ISSN: 0706-6457.

Axelson, J. N., D. J. Sauchyn, and J. Barichivich. 2009. New reconstructions of streamflow variability in the South Saskatchewan River Basin from a network of tree ring chronologies, Alberta, Canada. Water Resources Research 45(9): 1 – 10. DOI: 10.1029/2008WR007639.

S. Gurrapu, 2020 P a g e | 135 Barnett, T. P., J. C. Adam, and D. P. Lettenmaier. 2005. Potential impacts of a warming climate on water availability in snow-dominated regions. Nature 438: 303 – 309. DOI: 10.1038/nature04141.

Barros, A. P., Y. Duan, J. Brun, and M. A. Medina. 2014. Flood non-stationarity in the SE and mid-Atlantic regions of the United States. Journal of Hydrologic Engineering 19(10): 05014014. DOI: 10.1061/(ASCE)HE.1943-5584.0000955.

Bates, B., Z. W. Kundzewicz, S. Wu, and J. Palutikof, eds. 2008. Climate Change and Water. Technical Paper of the Intergovernmental Panel on Climate Change. IPCC Secretariat, Geneva: 210 pp.

Beguería, S., and S. M. Vicente-Serrano. 2017. SPEI: Calculation of the Standardized Precipitation-Evapotranspiration Index. R package version 1.7. http://cran.r- project.org/web/packages/SPEI/SPEI.pdf.

Biondi, F., A. Gershunov, and D. R. Cayan. 2001. North Pacific decadal climate variability since 1661. Journal of Climate 14(1): 5 – 10 DOI: 10.1175/1520- 0442(2001)014<0005:NPDCVS>2.0.CO;2.

Bonsal, B. R., and R. G. Lawford. 1999. Teleconnections between El Niño and La Niña events and summer extended dry spells on the Canadian Prairies. International Journal of Climatology 19(13): 1445 – 1458. DOI: 10.1002/(SICI)1097- 0088(19991115)19:13<1445::AID-JOC431>3.0.CO;2-7.

Bonsal, B. R., C. Cuell, E. Wheaton, D. J. Sauchyn, and E. Barrow. 2017. An assessment of historical and projected future hydro-climatic variability and extremes over southern watersheds in the Canadian Prairies. International Journal of Climatology 37(10): 3934 – 3948. DOI: 10.1002/joc.4967.

Bonsal, B. R., E. E. Wheaton, A. C. Chipanshi, C. Lin, D. J. Sauchyn, and L. Wen. 2011. Drought research in Canada: a review. Atmosphere-Ocean 49(4): 303 – 319. DOI: 10.1080/07055900.2011.555103.

Bonsal, B. R., R. Aider, P. Gachon, and S. Lapp. 2013. An assessment of Canadian Prairie drought: Past, present, and future. Climate Dynamics 41(2): 501 – 516. DOI: 10.1007/s00382-012-1422-0.

Bonsal, B., and A. Shabbar. 2008. Impacts of large-scale circulation variability on low streamflows over Canada: A review. Canadian Water Resources Journal 33(2): 137 – 154. DOI: 10.4296/cwrj3302137.

Bonsal, B., and M. Regier. 2007. Historical comparison of the 2001/2002 drought in the Canadian Prairies. Climate Research 33(3): 229 – 242. DOI: 10.3354/cr033229.

Burn, D. H. 1994. Hydrologic effects of climatic change in west-central Canada. Journal of Hydrology 160(1-4): 53 – 70. DOI: 10.1016/0022-1694(94)90033-7.

S. Gurrapu, 2020 P a g e | 136 Burn, D. H., L. Fan, and G. Bell. 2008. Identification and quantification of streamflow trends on the Canadian Prairies. Hydrological Sciences Journal 53(3): 538 – 549. DOI: 10.1623/hysj.53.3.538.

Buttle, J. M., S. Boon, D. L. Peters, C. Spence, H. J. van Meerveld, and P. H. Whitfield. 2012. An overview of temporary stream hydrology in Canada. Canadian Water Resources Journal 37(4): 279 – 310. DOI: 10.4296/cwrj2011-903.

Case, R. A., and G. M. MacDonald. 2003. Tree ring reconstructions of streamflow for three Canadian Prairie rivers. Journal of American Water Resources 39(3): 703 – 716. DOI: 10.1111/j.1752-1688.2003.tb03686.x.

Cayan, D. R., S. A. Kammerdiener, M. D. Dettinger, J. M. Caprio, and D. H. Peterson. 2001. Changes in the onset of spring in the western United States. Bulletin of American Meteorological Society 82(3): 399 – 415. DOI: 10.1175/1520- 0477(2001)082<0399:CITOOS>2.3.CO;2.

CDMP. 2011. City of Calgary: Drought Management Plan. Report by Strategic Services, Water Resources, City of Calgary. 53 pp.

Chambers, J. M., W. S. Cleveland, B. Kleiner, and P. A. Tukey. 1983. Graphical methods for data analysis (Statistics). Chapman and Hall/CRC Publishers, Belmont. ISBN-13: 978-0871504135.

Chen, D., G. Gao, C-Y. Xu, J. Guo, and G. Ren. 2005. Comparison of the Thornthwaite method and pan data with the standard Penman-Monteith estimates of reference evapotranspiration in China. Climate Research 28(2): 123 – 132. DOI: 10.3354/cr028123.

Chipanshi, A. C., K. M. Findlater, T. Hadwen, and E. G. O’Brien. 2006. Analysis of consecutive droughts on the Canadian Prairies. Climate Research 30(3): 175 – 187. DOI: 10.3354/cr030175.

Cohen, S. J. 1991. Possible impacts of climatic warming scenarios on water resources in the Saskatchewan River sub-basin, Canada. Climatic Change 19(3): 291 – 317. DOI: 10.1007/BF00140168.

Cook, E. R., R. Seager, R. R. Heim Jr., R. S. Vose, C. Herweijer, and C. Woodhouse. 2010. Mega droughts in North America: placing IPCC projections of hydroclimatic change in a long-term paleoclimate context. Journal of Quaternary Science 25(1): 48 – 61. DOI: 10.1002/jqs.1303.

Cunnane, C. 1988. Methods and merits of regional flood frequency analysis. Journal of Hydrology 100(1-3): 269-290. DOI: 10.1016/0022-1694(88)90188-6.

D’Arrigo, R., R. Villalba, and G. Wiles. 2001. Tree-ring estimates of Pacific decadal climate variability. Climate Dynamics 18(3-4): 219 – 224. DOI: 10.1007/s003820100177.

S. Gurrapu, 2020 P a g e | 137 Dai, A. 2011. Characteristics and trends in various forms of the Palmer Drought Severity Index during 1900 – 2008. Journal of Geophysical Research 116(D12): D12115. DOI: 10.1029/2010JD015541.

Dalezios, N. R., A. Loukas, L. Vasiliades, and E. Liakopoulos. 2000. Severity-duration- frequency analysis of droughts and wet periods in Greece. Hydrological Sciences Journal 45(5): 751 – 769. DOI: 10.1080/02626660009492375. de Myttenaere, A., B. Golden, B. Le Grand, and F. Rossi. 2016. Mean absolute percentage error for regression models. Neurocomputing 192: 38 – 48. DOI: 10.1016/j.neucom.2015.12.114.

Déry, S. J., K. Stahl, R. D. Moore, P. H. Whitfield, B. Menounos, and J. E. Burford. 2009. Detection of runoff timing changes in pluvial, nival, and glacial rivers of western Canada. Water Resources Research 45(4): W04426. DOI: 10.1029/2008WR006975.

Desloges, J. R., and R. Gilbert. 1994. Sediment source and hydroclimatic inferences from glacial lake sediments: the postglacial sedimentary record of Lillooet Lake, British Columbia. Journal of Hydrology 159(1-4): 375 – 393. DOI: 10.1016/0022- 1694(94)90268-2.

Devi, G. K., B. P. Ganasri, and G. S. Dwarakish. 2015. A review on hydrological models. Aquatic Procedia 4: 1001 – 1007. DOI: 10.1016/j.aqpro.2015.02.126.

Dey, B. 1982. Nature and possible causes of droughts on the Canadian Prairies – case studies. Journal of Climatology 2: 233 – 249. DOI: 10.1002/joc.3370020303.

Fleming, S. W. and P. H. Whitfield. 2010. Exploratory spatiotemporal mapping of ENSO and PDO surface meteorological signals in British Columbia, Yukon, and southeast Alaska. Atmosphere-Ocean 48(2): 122 – 131. DOI: 10.3137/AO1107.2010.

Fleming, S. W., P. H. Whitfield, R. D. Moore, and E. J. Quilty. 2007. Regime- dependent streamflow sensitivities to Pacific climate modes across the Georgia-Puget transboundary ecoregion. Hydrological Processes 21(24): 3264 – 3287. DOI: 10.1002/hyp.6544.

Folland, C. K., D. E. Parker, A. W. Colman, and R. Washington. 1999. Large scale modes of ocean surface temperature since the late nineteenth century, In: Beyond El Niño: Decadal and Interdecadal Climate Variability, A. Navarra (Editor), Springer- Verlag Berlin Heidelberg, pp. 73-102. DOI: 10.1007/978-3-642-58369-8.

Franks, S. W., and G. Kuczera. 2002. Flood frequency analysis: evidence and implications of secular climate variability, New South Wales. Water Resources Research 38(5): 20.1-20.7. DOI: 10.1029/2001WR000232.

Franks, S.W. 2002. Identification of a change in climate state using regional flood data. Hydrology and Earth System Sciences 6(1): 11-16. DOI: 10.5194/hess-6-11-2002.

S. Gurrapu, 2020 P a g e | 138 Furtado, J. C., E. Di Lorenzo, N. Schneider, and N. A. Bond. 2011. North Pacific decadal variability and climate change in the IPCC AR4 models. Journal of Climate 24(12): 3049 – 3067. DOI: 10.1175/2010JCLI3584.1.

Gan, T. Y. 1998. Hydroclimatic trends and possible climatic warming in the Canadian Prairies. Water Resources Research 34(11): 3009 – 3015. DOI: 10.1029/98WR01265.

Gan, T. Y. 2000. Reducing vulnerability of water resources of Canadian Prairies to potential droughts and possible climatic warming. Water Resources Management 14(2): 111 – 135. DOI: 10.1023/A:1008195827031.

Gobena, A. K., and T. Y. Gan. 2006. Low-frequency variability in southwestern Canadian streamflow: Links with large-scale climate. International Journal of Climatology 26(13): 1843 – 1869. DOI: 10.1002/joc.1336.

Gray, D. M., and P. G. Landine. 1988. An energy-budget snowmelt model for the Canadian Prairies. Canadian Journal of Earth Sciences 25(8): 1292 – 1303. DOI: 10.1139/e88-124.

Gray, S. T., and G. J. McCabe. 2010. A combined water balance and tree ring approach to understanding the potential hydrologic effects of climate change in the central Rocky Mountain region. Water Resources Research 46(5): W05513. DOI: 10.1029/2008WR007650.

Gurrapu, S., J-M. St-Jacques, D. J. Sauchyn, and K. R. Hodder. 2016. The influence of the Pacific Decadal Oscillation on annual floods in the rivers of Western Canada. Journal of the American Water Resources Association 52(5): 1031 – 1045. DOI: 10.1111/1752-1688.12433.

Hadi, A. S., and R. F. Ling. 1998. Some cautionary notes on the use of Principal Components Regression. The American Statistician 52(1): 15 – 19. DOI: 10.2307/2685559.

Harvey, K. D., P. J. Pilon, and T. R. Yuzyk. 1999. Canada’s reference hydrometric basin network (RHBN). Proceedings of the CWRA 52nd Annual Conference on ‘Partnerships in Water Resource Management’. Canadian Water Resources Association, Nova Scotia. 55 – 70.

Haslinger, K., D. Koffler, W. Schöner, and G. Laaha. 2014. Exploring the link between meteorological drought and streamflow: effects of climate-catchment interaction. Water Resources Research 50(3): 2468 – 2487. DOI: 10.1002/2013WR015051.

Hayes, M. J., M. D. Svoboda, D. A. Wilhite, and O. V. Vanyarkho. 1999. Monitoring the 1996 drought using the Standardized Precipitation Index. Bulletin of the American Meteorological Society 80(3): 429 – 438. DOI: 10.1175/1520- 0477(1999)080<0429:MTDUTS>2.0.CO;2.

Hayes, M. J., O. V. Wilhelmi, and C. L. Knutson. 2004. Reducing drought risk: bridging theory and practice. Natural Hazards Review 5(2): 106 – 113. DOI: 10.1061/(ASCE)1527-6988(2004)5:2(106).

S. Gurrapu, 2020 P a g e | 139 Helsel, D. R., and R. M. Hirsch. 2002. Chapter A3 – Statistical methods in water resources. In Book 4 – Hydrologic Analysis and Interpretation. Techniques of Water- Resources Investigations Reports, United States Geological Survey (USGS), 524p. available from http://pubs.usgs.gov/twri/twri4a3/.

Hisdal, H., and L. M. Tallaksen. 2003. Estimation of regional meteorological and hydrological drought characteristics: A case study for Denmark. Journal of Hydrology 281(3): 230 – 247. DOI: 10.1016/S0022-1694(03)00233-6.

Hodder, K. R., R. Gilbert, and J. R. Desloges. 2007. Glaciolacustrine varved sediment as an alpine hydroclimatic proxy. Journal of Paleolimnology 38(3): 365 – 394. DOI: 10.1007/s10933-006-9083-9.

Hoerling, M. P., J. K. Eischeid, X.-W. Quan, H. F. Diaz, R. S. Webb, R. M. Dole, and D. R. Easterling. 2012. Is a transition to semipermanent drought conditions imminent in the US Great Plains? Journal of Climate 25(24): 8380 – 8386. DOI: 10.1175/JCLI- D-12-00449.1.

Hogg, E. H. 1997. Temporal scaling of moisture and the forest-grassland boundary in western Canada. Agricultural and Forest Meteorology 84(1-2): 115 – 122. DOI: 10.1016/S0168-1923(96)02380-5.

Horbulyk, T. 2014. Resilience of river basin governance institutions in the Saskatchewan River Basin of western Canada. In Federal Rivers: Managing water in Multi-Layered Political Systems, (eds.) Garrick, D., G. R. M. Anderson, D. Connell, and J. Pittock. Edward Elgar Publishing Limited, UK, pp 90 – 104.

Hosking, J. R. M. 2017. L-Moments. R package version 2.6. http://CRAN.R- project.org/ package=lmom.

Hosking, J. R. M., and J. R. Wallis. 1997. Regional frequency analysis. Cambridge University Press, Cambridge, United Kingdom. ISBN-13: 978-0-521-01940-8.

Hurlbert, M., and J. Gupta. 2017. The adaptive capacity of institutions in Canada, Argentina, and Chile to droughts and floods. Regional Environmental Change 17(3): 865 – 877. DOI: 10.1007/s10113-016-1078-0.

Ilich, N. 2014. An effective three-step algorithm for multi-site generation of stochastic weekly hydrologic time series. Hydrological Sciences Journal 59(1): 85 – 98. DOI: 10.1080/02626667.2013.822643.

Ilich, N., and J. Despotovic. 2008. A simple method for effective multisite generation of stochastic hydrologic time series. Journal of Stochastic Environmental Research and Risk Assessment 22(2): 265 – 279. DOI: 10.1007/s00477-007-0113-6.

Islam, S., S. J. Déry, and A. T. Werner. 2017. Future climate change impacts on snow and water resources of the Fraser River Basin, British Columbia. Journal of Hydrometeorology 18(2): 473 – 496. DOI: 10.1175/JHM-D-16-0012.1.

S. Gurrapu, 2020 P a g e | 140 Johnson, R. A., and D. W. Wichern. 2007. Applied Multivariate Statistical Analysis, sixth edition. Pearson Prentice-Hall, Pearson Education, Inc., Upper Saddle River, New Jersey, 773 pp.

Jolliffe, I. T. 1982. A note on the use of principal components in regression. Journal of the Royal Statistical Society: Series C (Applied Statistics) 31(3): 300 – 303. DOI: 10.2307/2348005.

Jolliffe, I. T. 2002. Principal Component Analysis, second edition. Springer Series in Statistics. Springer-Verlag, New York. 518 pp. DOI: 10.1002/9781118445112.stat06472.

Kang, D. H., H. Gao, X. Shi, S. Islam, and S. J. Déry. 2016. Impacts of a rapidly declining mountain snowpack on streamflow timing in Canada’s Fraser River Basin. Scientific Reports 6, 19299. DOI: 10.1038/srep19299.

Kiem, A. S., S. W. Franks, and G. Kuczera. 2003. Multi-decadal variability of flood risk. Geophysical Research Letters 30(2): 1035. DOI: 10.1029/2002GL015992.

Kienzle, S. W., M. W. Nemeth, J. M. Byrne, and R. J. MacDonald. 2012. Simulating the hydrological impacts of climate change in the upper North Saskatchewan River basin, Alberta, Canada. Journal of Hydrology 412-413: 76 – 89. DOI: 10.1016/j.jhydrol.2011.01.058.

Kjeldsen, T. R., A. Lundorf, and D. Rosbjerg. 2000. Use of two component exponential distribution in partial duration modelling of hydrological droughts in Zimbabwean rivers, Hydrological Sciences Journal 45(2): 285 – 298. DOI: 10.1080/02626660009492325.

Kwon, H-H., C. Brown, and U. Lall. 2008. Climate informed flood frequency analysis and prediction in Montana using hierarchical Bayesian modelling. Geophysical Research Letters 35(5): L05404. DOI: 10.1029/2007GL032220.

Lapp, S. L., J.-M. St. Jacques, E. M. Barrow, and D. J. Sauchyn. 2012. GCM projections for the Pacific Decadal Oscillation under greenhouse forcing for the early 21st century. International Journal of Climatology 32(9): 1423 – 1442. DOI: 10.1002/joc.2364.

Lapp, S. L., J-M. St. Jacques, D. J. Sauchyn, and J. R. Vanstone. 2013. Forcing of hydroclimatic variability in the northwestern Great Plains since AD 1406. Quaternary International 310(15): 47 – 61. DOI: 10.1016/j.quaint.2012.09.011.

Lapp, S., D. J. Sauchyn, and B. Toth. 2009. Constructing scenarios of future climate and water supply for the SSRB: use of limitations for vulnerability assessment. Prairie Forum 34(1): 153 – 180.

Leavesley, G. H. 1994. Modeling the effects of climate change on water resources – a review. Climatic Change 28(1): 159 – 177. DOI: 10.1007/BF01094105.

S. Gurrapu, 2020 P a g e | 141 Lettenmaier, D. P., J. R. Wallis, and E. F. Wood. 1987. Effect of heterogeneity on flood frequency estimation. Water Resources Research 23(2): 313-323. DOI: 10.1029/WR023i002p00313.

Lόpez, J., and F. Francѐs. 2013. Non-stationary flood frequency analysis in continental Spanish rivers, using climate and reservoir indices as external covariates. Hydrology and Earth System Sciences 17(8): 3189 – 3203. DOI: 10.5194/hess-17-3189-2013.

MacCulloch, G., and P. H. H. Whitfield. 2012. Towards a stream classification system for the Canadian Prairie provinces. Canadian Water Resources Journal 37(4): 311 - 332. DOI: 10.4296/cwrj2011-905.

MacDonald, G., and R. A. Case. 2005. Variations in the Pacific Decadal Oscillation over the past millennium. Geophysical Research Letters 32(8): L08703. DOI: 10.1029/2005GL022478.

Manly, B. F. J. 2007. Randomization, Bootstrap and Monte Carlo Methods in Biology, 3rd edition Chapman and Hall, London.

Mantua, N. J., S. R. Hare, Y. Zhang, J. M. Wallace, and R. C. Francis. 1997. A Pacific interdecadal climate oscillation with impacts on salmon production. Bulletin of the American Meteorological Society 78(6): 1069 – 1079. DOI: 10.1175/1520- 0477(1997)078<1069:APICOW>2.0.CO;2.

Mason, R. L., and R. F. Gunst. 1985. Selecting principal components in regression. Statistics & Probability Letters 3(6): 299 – 301. DOI: 10.1016/0167-7152(85)90059-8.

McKee, T. B., N. J. Doesken, and J. Kleist. 1993. The relationship of drought frequency and duration to time scales. Proceedings of the Eighth Conference on Applied Climatology, 17 – 22 January 1993 Anaheim, California. Boston: American Meteorological Society, 179 – 184. Available from http://ccc.atmos.colostate.edu/relationshipofdroughtfrequency.pdf.

McKenney, D. W., M. F. Hutchinson, P. Papadopol, K. Lawrence, J. Pedlar, K. Campbell, E. Milewska, R. Hopkinson, D. Price, and T. Owen. 2011. Customized spatial climate models for North America. Bulletin of American Meteorological Society 92(12): 1611 – 1622. DOI: 10.1175/2011BAMS3132.1.

McMahon, T. A., M. C. Peel, and D. J. Karoly. 2015. Assessment of precipitation and temperature data from CMIP3 global climate models for hydrologic simulation. Hydrology and Earth System Sciences 19(1): 361 – 377. DOI: 10.5194/hess-19-361- 2015.

Mearns, L. O., R. Arritt, S. Biner, M. S. Bukovsky, S. McGinnis, S. Sain, D. Caya, J. Correia Jr., D. Flory, W. Gutowski, E. S. Takle, R. Jones, R. Leung, W. Moufouma- Okia, L. McDaniel, A. M. B. Nunes, Y. Qian, J. Roads, L. Sloan, and M. Snyder. 2012. The North American regional climate change assessment program: Overview of phase I results. Bulletin of the American Meteorological Society 93(9): 1337 – 1362. DOI: 10.1175/BAMS-D-11-00223.1.

S. Gurrapu, 2020 P a g e | 142 Meko, D. M., and C. A. Woodhouse. 2010. Application of streamflow reconstruction to water resources management. In Dendroclimatology, Developments in Paleoenvironmental Research book series, eds. M. K. Hughes, T. W. Swetnam, and H. F. Diaz (Vol. 11, pp. 231 – 261). DOI: 10.1007/978-1-4020-5725-0_8.

Meko, D. M., and C. A. Woodhouse. 2011. Dendroclimatology, Dendrohydrology, and Water Resources Management, In: Tree Rings and Climate, eds. H. F. Diaz, and M. K. Hughes. Kluwer/Springer.

Meko, D. M., C. A. Woodhouse, and K. Morino. 2012. Dendrochronology and links to streamflow. Journal of Hydrology 412-413: 200 – 2 9. DOI: 10.1016.j.hydrol.2010.11.041.

Micevski, T., S. W. Franks, and G. Kuczera. 2006. Multidecadal variability in coastal eastern Australian flood data. Journal of Hydrology 327(1-2): 219-225. DOI: 10.1016/j.jhydrol.2005.11.017.

Milly, P. C. D., J. Betancourt, M. Falkenmark, R. M. Hirsch, Z. W. Kundzewicz, D. P. Lettenmaier, and R. J. Stouffer. 2008. Stationarity is dead: Whither water management? Science, 319(5863): 573 – 574. DOI: 10.1126/science.1151915.

Milrad, S. M., J. R. Gyakum, and E. H. Atallah. 2015. A meteorological analysis of the 2013 Alberta flood: Antecedent large-scale flow pattern and synoptic-dynamic characteristics. Monthly Weather Review 143(7): 2817 – 2841. DOI: 10.1175/MWR- D-14-00236.1.

Minobe, S. 1997. A 50-70 year climatic oscillation over the North Pacific and North America. Geophysical Research Letters 24(6): 683 – 686. DOI: 10.1029/97GL00504.

Mishra, A. K., and V. P. Singh. 2010. A review of drought concepts. Journal of Hydrology 391(1-2): 202 – 216. DOI: 10.1016/j.jhydrol.2010.07.012.

Moore, R. D. 1992. The influence of glacial cover on the variability of annual runoff, Coast Mountains, British Columbia, Canada. Canadian Water Resources Journal 17(2): 101 – 109. DOI: 10.4296/cwrj1702101.

Mote, P. W. 2006. Climate-driven variability and trends in mountain snowpack in western North America. Journal of Climate 19(23): 6209 – 6220. DOI: 10.1175/JCLI3971.1.

Mote, P. W., A. F. Hamlet, M. P. Clark, and D. P. Lettenmaier. 2005. Declining mountain snowpack in western North America. Bulletin of American Meteorological Society 86(1): 39 – 49. DOI: 10.1175/BAMS-86-1-39.

Næs, T., and I. S. Helland. 1993. Relevant components in regression. Scandinavian Journal of Statistics 20(3): 239 – 250.

Nalabantis, I., and G. Tsakiris. 2009. Assessment of hydrological drought revisited. Water Resources Management 23(5): 881 – 897. DOI: 10.1007/s11269-008-9305-1.

S. Gurrapu, 2020 P a g e | 143 Neill, C. R., and W. E. Watt. 2001. Report on Six Case Studies of Flood Frequency Analyses. Transportation and Civil Engineering Division, Alberta Transportation. 66 pp. accessible from http://www.transportation.alberta.ca/Content/doctype30/Production/ffasixcase.pdf.

Nkemdirim, L., and L. Weber. 1999. Comparison between the droughts of the 1930s and the 1980s in the Southern Prairies of Canada. Journal of Climate 12(8): 2434 – 2450. DOI: 10.1175/1520-0442(1990)012<2434:CBTDOT>2.0.CO;2.

NRCAN. 2018. ANUSPLIN data, available at: https://cfs.nrcan.gc.ca/projects/3/3, last access: 5th July 2018.

O’Brien, E. G., and J. Stroich. 2005. Concept of defining drought in Canada: an evaluation of drought indicators for application in the agricultural landscapes of Canada. National Land and Water Information Service (NLWIS), Agriculture and Agri-Food Canada (AAFC). 118 pp.

Oldfield, F., and K. Alverson. 2003. The Societal Relevance of Paleoenvironmental Research. In Paleoclimate, Global Change, and the Future, eds. K. Alverson, R. S. Bradley, and T. F. Pedersen. Springer, Berlin. pp 1-10.

Opere, A. O., S. Mkhandi, and P. Willems. 2006. At-site flood frequency analysis for the Nile equatorial basins. Physics and Chemistry of the Earth 31(15-16): 919-927. DOI: 10.1016/j.pce.2006.08.018.

PaiMazumdar, D., L. Sushama, R. Laprise, M. N. Khalid, and D. J. Sauchyn. 2013. Canadian RCM projected changes to short- and long-term drought characteristics over the Canadian Prairies. International Journal of Climatology 33(6): 1409 – 1423. DOI: 10.1002/joc.3521.

Paznekas, A., and M. Hayashi. 2016. Groundwater contribution to winter streamflow in the Canadian Rockies. Canadian Water Resources Journal 41(4): 484 – 499. DOI: 10.1080/07011784.2015.1060870.

Pederson, G. T., S. T. Gray, C. A. Woodhouse, J. L. Betancourt, D. B. Fagre, J. S. Littell, E. Watson, B. H. Luckman, and L. J. Graumlich. 2011. The unusual nature of recent snowpack declines in the North American Cordillera. Science 333(6040): 332 – 335. DOI: 10.1126/science.1201570.

Pomeroy, J. W., R. E. Stewart, and P. H. Whitfield. 2016. The 2013 flood event in the South Saskatchewan and Elk River basins: Causes, assessment and damages. Canadian Water Resources Journal 41(1-2): 105 – 117. DOI: 10.1080/07011784.2015.1089190.

R Core Team. 2018. R: A language and environment for statistical computing. R Foundation for Statistical Computing, Vienna, Austria. URL https://www.R- project.org/.

Redmond, K. T., and R. W. Koch. 1991. Surface climate and streamflow variability in the Western United States and their relationship to large-scale circulation indices. Water Resources Research 27(9): 2381-2399. DOI: 10.1029/91WR00690.

S. Gurrapu, 2020 P a g e | 144 Rivera, J. A., D. C. Araneo, and O. C. Penalba. 2017. Threshold level approach for streamflow drought analysis in the Central Andes of Argentina: a climatological assessment. Hydrological Sciences Journal 62(12): 1949 – 1964. DOI: 10.1080/02626667.2017.1367095.

Rood, S. B., and J. W. Vandersteen. 2010. Relaxing the principle of prior approximation: stored water and sharing the shortage in Alberta, Canada. Water Resources Management 24(8): 1605 – 1620, DOI: 10.1007/s11269-009-9516-0.

Rood, S. B., G. M. Samuelson, J. K. Weber, and K. A. Wywrot. 2005. Twentieth- century decline in streamflows from the hydrographic apex of North America. Journal of Hydrology 306(1-4): 215 – 233. DOI: 10.1016/j.jhydrol.2004.09.010.

Ryder, J. M. 1987. Neoglacial history of the Stikine-Iskut area, northern Coast Mountains, British Columbia. Canadian Journal of Earth Sciences 24(7): 1294 – 1301. DOI: 10.1139/e87-125.

Sauchyn, D. J., and W. R. Skinner. 2001. A proxy record of drought severity for the southwestern Canadian Plains. Canadian Water Resources Journal 26(2): 253 – 272. DOI: 10.4296/cwrj2602253.

Sauchyn, D. J., E. M. Barrow, R. F. Hopkinson, and P. R. Leavitt. 2002. Aridity on the Canadian Plains. Géographie Physique et Quaternaire 56(2-3): 247-259. DOI: 10.7202/009109ar.

Sauchyn, D. J., H. Diaz, and S. Kulshreshta. 2010. The New Normal: The Canadian Prairies in a Changing Climate. Canadian Plains Research Center (CPRC) Press. University of Regina, Regina, SK. 379 pp.

Sauchyn, D. J., J-M. St-Jacques, and B. H. Luckman. 2015. Long-term reliability of the Athabasca River (Alberta, Canada) as water source for oil sands mining. Proceedings of the National Academy of Sciences of the United States of America 112(41): 12621 – 16626. DOI: 10.1073/pnas.1509726112.

Sauchyn, D., and N. Ilich. 2017. Nine hundred years of weekly streamflow: stochastic downscaling of ensemble tree-ring reconstructions. Water Resources Research 53(11): 9266 – 9283. DOI: 10.1002/2017WR021585.

Sauchyn, D., and S. Kulshreshtha. 2008. Chapter 7: Prairies. in From Impacts to Adaptation: Canada in a Changing Climate 2007, eds. D.S. Lemmen, F. J. Warren, J. Lacroix, and E. Bush. Government of Canada, Ottawa: p. 275 – 328.

Sauchyn, D., J. Vanstone, J-M. St. Jacques, and R. Sauchyn. 2015. Dendrohydrology in Canada’s western interior and applications to water resources management. Journal of Hydrology 529 (2): 548 – 558. DOI: 10.1016/j.jhydrol.2014.11.049.

Sauchyn. D. J., J-M. St. Jacques, E. Barrow, M. W. Nemeth, R. J. MacDonald, A. M. S. Sheer, and D. P. Sheer. 2015. Adaptive water resource planning in the South Saskatchewan River Basin: use of scenarios of hydroclimatic variability and extremes.

S. Gurrapu, 2020 P a g e | 145 Journal of the American Water Resources Association 1-19. DOI: 10.1111/1752- 1688.12378.

Schindler, D. W., and W. F. Donahue. 2006. An impending water crisis in Canada’s western Prairie Provinces. Proceedings of the National Academy of Sciences of the United States of America 103(19): 7210 – 7216. DOI: 10.1073/pnas.0601568103.

Schnorbus, M., A. Werner, and K. Bennett. 2014. Impacts of climate change in three hydrologic regimes in British Columbia, Canada. Hydrological Processes 28(3): 1170 – 1189. DOI: 10.1002/hyp.9661.

Searcy, J. K. 1959. Flow-Duration Curves. In Manual of Hydrology: Part 2. Low-Flow Techniques. Geological Survey Water-Supply Paper 1542-A. United States Government Printing Office, Washington.

Shabbar, A., and M. Khandekar. 1996. The impact of El Niño-Southern Oscillation on the temperature field over Canada. Atmosphere-Ocean 34(2): 401 – 416. DOI: 10.1080/07055900.1996.9649570.

Shabbar, A., B. Bonsal, and M. Khandekar. 1997. Canadian precipitation patterns associated with the Southern Oscillation. Journal of Climate 10(12): 3016 – 3027. DOI: 10.1175/1520-0442(1997)010<3016:CPPAWT>2.0.CO;2.

Sharif, M., and D. Burn. 2009. Detection of linkages between extreme flow measures and climate indices. International Journal of Civil, Environmental, Structural, Construction and Architectural Engineering 3(12): 495-500. DOI: scholar.waset.org/1999.3/6613.

Sharma, A. R., and S. J Déry. 2019. Variability and trends in landfalling atmospheric rivers along the Pacific Coast of northwestern North America. International Journal of Climatology 39: DOI: 10.1002/joc.6227.

Shaw, D. A., A. Pietroniro, and L. W. Martz. 2013. Topographic analysis for the prairie pothole region of Western Canada. Hydrological Processes 27(22): 3105 – 3114. DOI: 10.1002/hyp.9409.

Shcherbakov, M., A. Brebels, N. L. Shcherbakova, A. Tyukov, T. A. Janovsky, and V. A. Kamaev. (2013). A survey of forecast error measures. World Applied Sciences Journal 24(24): 171 – 176. DOI: 10.5829/idosi.wasj.2013.24.itimes.80032.

Sheffield, J., E. F. Wood, and M. L. Roderick. 2012. Little change in global drought over the past 60 years. Nature 491(7424): 435 – 438. DOI: 10.1038/nature11575.

Shen, C., W. C. Wang, W. Gong, and Z. Hao. 2006. A Pacific Decadal Oscillation record since 1470 AD reconstructed from proxy data of summer rainfall over eastern China. Geophysical Research Letters 33(3): L03702. DOI: 10.1029/2005GL024804.

Shepherd, A., K. M. Gill, and S. B. Rood. 2010. Climate change and future flows of Rocky Mountain Rivers: converging forecasts from empirical trend projection and

S. Gurrapu, 2020 P a g e | 146 down-scaled global circulation modelling. Hydrological Processes 24(26): 3864 – 3877. DOI: 10.1002/hyp.7818.

Shoukri, M. M., I. U. H. Mian, and D. S. Tracy. 1988. Sampling properties of estimators of the log-logistic distribution with application to Canadian precipitation data. The Canadian Journal of Statistics 16(3): 223 – 236. DOI: 10.2307/3314729.

Solander, K., L. Saito, and F. Biondi. 2010. Streamflow simulation using a water- balance model with annually resolved inputs. Journal of Hydrology 387(1-2): 46 – 53. DOI: 10.1016/j.jhydrol.2010.03.028.

Spinoni, J., G. Naumann, H. Carrao, P. Barbosa, and J. Vogt. 2014. World drought frequency, duration, and severity for 1951 – 2010. International Journal of Climatology 34(8): 2792 – 2804. DOI: 10.1002/joc.3875.

Spry, C. M., K. E. Kohfed, D. Allen, D. Dunkley, and K. Lertzman. 2014. Characterizing pineapple express storms in the lower mainland of British Columbia, Canada. Canadian Water Resources Journal 39(3): 302 – 323. DOI: 10.1080/07011784.2014.942574.

St. George, S., D. M. Meko, M. P. Girardin, G. M. MacDonald, E. Nielsen, G. T. Pederson, D. J. Sauchyn, J. C. Tardif, and E. Watson. 2009. The tree-ring record of drought on the Canadian Prairies. Journal of Climate 22(3): 689 – 710. DOI: 10.1175/2008JCLI2441.1.

St. Jacques, J-M., D. J. Sauchyn, and Y. Zhao. 2010. Northern Rocky Mountain streamflow records: global warming trends, human impacts or natural variability? Geophysical Research Letters 37(6): L06407. DOI: 10.1029/2009GL042045.

St. Jacques, J-M., S. L. Lapp, Y. Zhao, E. M. Barrow, and D. J. Sauchyn. 2013. Twenty- first century central Rocky Mountain river discharge scenarios under greenhouse forcing. Quaternary International 310: 34 – 46. DOI: 10.1016/j.quaint.2012.06.023.

St. Jacques, J-M., Y. A. Huang, Y. Zhao, S. L. Lapp, and D. J. Sauchyn. 2014. Detection and attribution of variability and trends in streamflow records from the Canadian Prairie Provinces. Canadian Water Resources Journal 39(3): 270 – 284. DOI: 10.1080/07011784.2014.942575.

St. Jacques, J-M., Y. Andreichuk, D. J. Sauchyn, and E. Barrow. 2018. Projecting Canadian Prairie runoff for 2041– 2070 with North American Regional Climate Change Assessment Program (NARCCAP) data. Journal of the American Water Resources Association 54(3): 660 – 675. DOI: 10.1111/1752-1688.12642.

Stedinger, J. R., and V W. Griffis. 2008. Flood frequency analysis in the United States: time to update. Journal of Hydrologic Engineering 13(4): 199 – 204. DOI: 10.1061/(ASCE)1084-0699(2008)13:4(199).

Stedinger, J. R., and V. W. Griffis. 2011. Getting from here to where? Flood frequency and climate. Journal of the American Water Resources Association 47(3): 506 – 513. DOI: 10.1111/j.1752-1688.2011.00545.x.

S. Gurrapu, 2020 P a g e | 147 Stedinger, J. R., E. Vogel, and Fufoula-Georgiou. 1993. Frequency analysis of extreme events. In: Handbook of Hydrology, eds. D. R. Maidment. McGraw Hill, 66 pp.

Steinemann, A. C., and L. F. N. Cavalcanti. 2006. Developing multiple indicators and triggers for drought plans. Journal of Water Resources Planning and Management 132(3): 164 – 174. DOI: 10.1061/(ASCE)0733-9496(2006)132:3(164).

Stewart, I. T., D. R. Cayan, and M. D. Dettinger. 2004. Changes in snowmelt runoff timing in western North America under a ‘Business as usual’ climate change scenario. Climatic Change 62(1-3): 217 – 232. DOI: 10.1023/B:CLIM.0000013702.22656.e8.

Stewart, I. T., D. R. Cayan, and M. D. Dettinger. 2005. Changes toward earlier streamflow timing across western North America. Journal of Climate 18(8): 1136 – 1155. DOI: 10.1175/JCLI3321.1.

Sun, L., S. W. Mitchell, and A. Davidson. 2012. Multiple drought indices for agricultural drought risk assessment on the Canadian prairies. International Journal of Climatology 32(11): 1628 – 1639. DOI: 10.1002/joc.2385.

Sung, J. H., and E. S. Chung. 2014. Development of streamflow drought severity- duration frequency curves using the threshold level method. Hydrology and Earth System Sciences 18: 3341 – 3351. DOI: 10.5194/hess-18-3341-2014.

Sutter, J. M., J. H. Kalivas, and P. M. Lang. 1992. Which principal components to utilize for principal component regression. Journal of Chemometrics 6(4): 217 – 225. DOI: 10.1002/cem.1180060406.

Tallaksen, L. M., H. Madsen, and H. Hisdal. 2000. Frequency Analysis. In Drought and Drought Mitigation in Europe, eds. Jürgen Vogt, and Francesca Somma. Springer Netherlands. pp 103 – 117. DOI: 10.1007/978-94-015-9472-1_8.

Tan, X., and T. Y. Gan. 2015. Nonstationary analysis of annual maximum streamflow of Canada. Journal of Climate 28(5): 1788 – 1805. DOI: 10.1175/JCLI-D-14-00538.1.

Thornthwaite, C. W. 1948. An approach toward a rational classification of climate. Geographical Review 38(1): 55 – 94. DOI: 10.2307/210739.

Tigkas, D., H. Vangelis, and G. Tsakiris. 2012. Drought and climate change impact on streamflow in small watersheds. Science of the Total Environment 440: 33 – 41. DOI: 10.1016/j.scitotenv.2012.08.035.

Todisco, F., F. Mannocchi, and L. Vergni. 2013. Severity-duration-frequency curves in the mitigation of drought impact: An agricultural case study. Natural Hazards 65(3): 1863 – 1881. DOI: 10.1007/s11069-012-0446-4.

Tsakiris, G., I. Nalbantis, H. Vangelis, B. Verbeiren, M. Huysmans, B. Tychon, L. Jacquemin, P. De Becker, and O. Batelaan. 2013. A system-based paradigm of drought analysis for operational management. Water Resources Management 27(15): 5281 – 5297. DOI: 10.1007/s11269-013-0471-4.

S. Gurrapu, 2020 P a g e | 148 USGS. 1982. Guidelines for Determining Flood Flow Frequency. Bulletin 17B of the Hydrology Subcommittee, United States Geological Survey (USGS). http://water.usgs. gov/osw/bulletin17b/dl_flow.pdf. van der Kamp, G., D. Keir, and M. S. Evans. 2008. Long-term water level changes in closed-basin lakes of the Canadian Prairies. Canadian Water Resources Journal 33(1): 23 – 38. DOI: 10.4296/cwrj3301023.

Vicente-Serrano, S. M., and J. I. Lopez-Moreno. 2005. Hydrological response to different time scales of climatological drought: an evaluation of the standardised precipitation index in a mountainous Mediterranean basin. Hydrology and Earth System Sciences 9(5): 523 – 533. DOI: 10.5194/hess-9-523-2005.

Vicente-Serrano, S. M., S. Begueria, and J. I. Lopez-Moreno. 2010. A multi-scalar drought index sensitive to global warming: The Standardised Precipitation Evapotranspiration Index. Journal of Climate 23(7): 1696 – 1718. DOI: 10.1175/2009JCLI2909.1.

Vicente-Serrano, S. M., S. Beguería, J. Lorenzo-Lacruz, J. J. Camarero, J. I. López- Moreno, C. Azorin-Molina, J. Revuelto, E. Morán-Tejeda, and A. Sanchez-Lorenzo. 2012. Performance of drought indices for ecological, agricultural and hydrological applications. Earth Interactions 16(10): 1 – 27. DOI: 10.1175/2012EI000434.1.

Vogel, R. M., and N. M. Fennessey. 1994. Flow Duration Curves I: new interpretation and confidence intervals. Journal of Water Resources Planning and Management 120(4): 485 – 508. DOI: 10.1061/(ASCE)0733-9496(1994)120:4(485).

Wagner, M. 2010. Technical data report on Hydrology: Enbridge Northern Gateway Project. AMEC Earth & Environmental, a division of AMEC Americas Limited. 82 pp. Available from: https://www.ceaa- acee.gc.ca/050/documents_staticpost/cearref_21799/2427/ Hydrology.pdf

Wang, J. Y., P. H. Whitfield, and A. J. Cannon. 2006. Influence of Pacific climate patterns on low-flows in British Columbia and Yukon, Canada. Canadian Water Resources Journal 31(1): 25 – 40. DOI: 10.4296/cwrj3101025.

Ward, P. J., S. Eisner, M. Flörke, M. D. Dettinger, and M. Kummu. 2014. Annual flood sensitivities to El Niño-Southern Oscillation at the global scale. Hydrology and Earth System Sciences 18: 47-66. DOI: 10.5194/hess-18-47-2014.

Watts, G., B. von Christierson, J. Hannaford, and K. Lonsdale. 2012. Testing the resilience of water supply to long droughts. Journal of Hydrology 414-415: 255 – 267. DOI: 10.1016/j.hydrol.2011.10.038.

Westra, S., C. Brown, U. Lall, and A. Sharma. 2007. Modeling multivariable hydrological series: Principal component analysis or independent component analysis? Water Resources Research 43(6): W06429. DOI: 10.1029/2006WR005617.

S. Gurrapu, 2020 P a g e | 149 Wheaton, E., S. Kulshreshtha, V. Wittrock, and G. Koshida. 2008. Dry times: hard lessons from the Canadian drought of 2001 and 2002. The Canadian Geographer 52(2): 241 – 262. DOI: 10.1111/j.1541-0064.2008.00211.x.

Whitfield, P. H., and A. J. Cannon. 2000. Recent variations in climate and hydrology in Canada. Canadian Water Resources Journal 25(1): 19 – 65. DOI: 10.4296/cwrj2501019.

Whitfield, P. H., R. D. Moore, S. W. Fleming, and A. Zawadzki. 2010. Pacific Decadal Oscillation and hydroclimatology of western Canada – review and prospects. Canadian Water Resources Journal 35(1): 1 – 28. DOI: 10.4296/cwrj3501001.

Wilhite, D. A., M. J. Hayes, C. Knutson, and K. H. Smith. 2000. Planning for drought: Moving from crisis to risk management. Journal of American Water Resources Association 36(4): 697 – 710. DOI: 10.1111/j.1752-1688.2000.tb04299.x.

Wilks, D. S. 2006. Statistical Methods in the Atmospheric Sciences. Second edition. Elsevier Academic Press, Burlington, United States of America, ISBN 13: 978-0-12- 751966-1.

Willmott, C. J., and K. Matsuura. 2005. Advantages of the mean absolute error (MAE) over the root mean square error (RMSE) in assessing average model performance. Climate Research 30(1): 79 – 82. DOI: 10.3354/cr030079.

WMO, World Meteorological Organization. 2011. Guide to climatological practices (WMO-No. 100), Geneva. 117 pp.

Woo, M., and R. Thorne. 2003. Comment on ‘Detection of hydrologic trends and variability, by Burn, D H, and Hag Elnur, M A, 2002. Journal of Hydrology 255, 107 – 122’. Journal of Hydrology 277: 150 – 160. DOI: 10.1016/S0022-1694(03)00079-9.

Yevjevich, V. 1967. An objective approach to definition and investigation of continental hydrologic droughts. Fort Collins, CO: Colorado State University.

Yulianti, J. S., and D. H. Burn. 1998. Investigating links between climatic warming and low streamflow in the Prairies region of Canada. Canadian Water Resources Journal 23(1): 45 – 60. DOI: 10.4296/cwrj2301045.

Zhang, T., and D.-Z. Sun. 2014. ENSO asymmetry in CMIP5 models. Journal of Climate 27(11): 4070 – 4093. DOI: 10.1175/JCLI-D-13-00454.1.

Zhang, X., K. D. Harvey, W. D. Hogg, and T. R. Yuzyk. 2001. Trends in Canadian streamflow. Water Resources Research 37(4): 987 – 998. DOI: 10.1029/2000WR900357.

S. Gurrapu, 2020 P a g e | 150 APPENDIX

Statement of Co-Authorship

I was the lead author for all the chapters of this thesis, along with various co-authors.

The third chapter in this thesis was published in an international journal and chapters 2 and 4 are under revision for publication. Chapter 2 was co-authored by Dr. Kyle R.

Hodder, Dr. David J. Sauchyn, and Dr. Jeannine-Marie St. Jacques and has been submitted to the Canadian Water Resources Journal (CWRJ) for publication and is under review. Chapter 3 was co-authored by Dr. Jeannine-Marie St. Jacques, Dr. David

J. Sauchyn and Dr. Kyle R. Hodder and was published in the Journal of American Water

Resources Association (JAWRA). Chapter 4 was co-authored by Dr. David J. Sauchyn and Dr. Kyle R. Hodder and is submitted to the Water Resources Management (WRM) journal for publication and is under review.

S. Gurrapu, 2020 P a g e | 151