Forestry, Faculty of
DSpace
UBCV
Kaluarachchi, Samadhee
Master of Science - MSc
University of British Columbia
Anthropogenic activities such as climate change and forest harvesting have amplified magnitudes and frequencies of a range of hydroclimatic extremes, with continued increases expected throughout the 21st Century. Extreme events have already caused deaths, adverse health impacts, infrastructure damage, lawsuits, and major economic losses worldwide, underscoring the urgent need for effective risk management. Reliable projections and effective solutions are essential for managing risk, and both depend on a sound understanding of hydroclimatic phenomena. This thesis synthesizes insights from across hydroclimatology literature to argue that a causal, stochastic approach is the most reliable framework for understanding extremes. Stochastic physics embeds physical understanding within probabilistic distributions, accounting for the phenomenon’s natural and anthropogenic controls. It allows for identification of change between a system’s natural and anthropogenically influenced states, especially large frequency changes which surpass those of magnitude. A review of changing hydroclimatic regimes, core stochastic physics principles, and finance literature on system fragility suggests that such large frequency changes under anthropogenic influence may stem, at least in part, from natural regimes which are inherently sensitive (or fragile) to disturbance. The strengths of a causal, stochastic approach are highlighted with a forest hydrology example, where the question of whether forests mitigate large floods remains a decades-long scientific controversy. The traditional deterministic approach uses regression analysis to compare floods between control (e.g., forested) and treatment (e.g., harvested) catchments to study the effects of changing forest cover. This approach evokes less relevant research questions, an improper hypothesis, and a non-causal experiment, indicating low rigour in its conclusions. In contrast, a causal, stochastic approach using probabilistic concepts to understand the flood response to changing forest cover evokes relevant research questions, falsifiable hypotheses, a controlled experiment, and sound physical insight. Its robust conclusion that forests can mitigate large floods thus informs harvesting practices which minimize increases in downstream floods and advance nature-based solutions for flood management. In this way, use of rigorous scientific methods best position hydroclimatology to motivate strong policy and support the design of innovative solutions in the Anthropocene.
UNDERSTANDING AND PREDICTING HYDROCLIMATIC EXTREMES IN THE ANTHROPOCENE: A CAUSAL, STOCHASTIC PHYSICS APPROACH by Samadhee Kaluarachchi B.Sc. (Hons), The University of British Columbia, 2023 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF SCIENCE in THE FACULTY OF GRADUATE AND POSTDOCTORAL STUDIES (Forestry) THE UNIVERSITY OF BRITISH COLUMBIA (Vancouver) October 2025 © Samadhee Kaluarachchi, 2025 ii The following individuals certify that they have read, and recommend to the Faculty of Graduate and Postdoctoral Studies for acceptance, the thesis entitled: Understanding and predicting hydroclimatic extremes in the Anthropocene: A causal, stochastic physics approach submitted by Samadhee Kaluarachchi in partial fulfilment of the requirements for the degree of Master of Science in Forestry Examining Committee: Dr. Younes Alila, Professor, Department of Forest Resources Management, UBC Supervisor Dr. Bianca Eskelson, Professor, Department of Forest Resources Management, UBC Supervisory Committee Member Dr. Scott McDougall, Associate Professor, Department of Earth, Ocean and Atmospheric Sciences, UBC Additional Examiner Additional Committee Members: Dr. Cindy Prescott, Professor Emerita, Department of Forest and Conservation Sciences, UBC Supervisory Committee Member iii Abstract Anthropogenic activities such as climate change and forest harvesting have amplified magnitudes and frequencies of a range of hydroclimatic extremes, with continued increases expected throughout the 21st Century. Extreme events have already caused deaths, adverse health impacts, infrastructure damage, lawsuits, and major economic losses worldwide, underscoring the urgent need for effective risk management. Reliable projections and effective solutions are essential for managing risk, and both depend on a sound understanding of hydroclimatic phenomena. This thesis synthesizes insights from across hydroclimatology literature to argue that a causal, stochastic approach is the most reliable framework for understanding extremes. Stochastic physics embeds physical understanding within probabilistic distributions, accounting for the phenomenon’s natural and anthropogenic controls. It allows for identification of change between a system’s natural and anthropogenically influenced states, especially large frequency changes which surpass those of magnitude. A review of changing hydroclimatic regimes, core stochastic physics principles, and finance literature on system fragility suggests that such large frequency changes under anthropogenic influence may stem, at least in part, from natural regimes which are inherently sensitive (or fragile) to disturbance. The strengths of a causal, stochastic approach are highlighted with a forest hydrology example, where the question of whether forests mitigate large floods remains a decades-long scientific controversy. The traditional deterministic approach uses regression analysis to compare floods between control (e.g., forested) and treatment (e.g., harvested) catchments to study the effects of changing forest cover. This approach evokes less relevant research questions, an improper hypothesis, and a non-causal experiment, indicating low rigour in its conclusions. In iv contrast, a causal, stochastic approach using probabilistic concepts to understand the flood response to changing forest cover evokes relevant research questions, falsifiable hypotheses, a controlled experiment, and sound physical insight. Its robust conclusion that forests can mitigate large floods thus informs harvesting practices which minimize increases in downstream floods and advance nature-based solutions for flood management. In this way, use of rigorous scientific methods best position hydroclimatology to motivate strong policy and support the design of innovative solutions in the Anthropocene. v Lay Summary Human activities such as climate change and logging make large events like floods, heatwaves, and wildfires much more common and severe, impacting peoples’ lives and livelihoods. For floods, adapting to these events or slowing their increase requires a good understanding of floods by using “causal” scientific methods which ask the right questions and identify causes of changing floods. For example, causal methods show that removing forest cover can make floods bigger and more common. While changes in size are usually emphasized, changes in flood frequency could be even larger. In fact, events becoming much more frequent under human influence may come from natural systems that are very sensitive, or react strongly, to change. This knowledge can be used to motivate effective policies, design industrial practices so that they have lesser impacts on floods, and support solutions that help make society more resilient to floods. vi Preface Under the supervision of Dr. Younes Alila and the guidance of my thesis committee, I completed all tasks related to the research in this thesis. This includes designing research questions, conducting the literature synthesis, drafting the original versions of the thesis and manuscripts, and making subsequent edits. Generative AI has not been used in this research and thesis. Each body chapter of the thesis is written as a manuscript that has been submitted to a journal with appropriate modifications. Chapter 2 of this thesis has been published as: Kaluarachchi, S., & Alila, Y. (2025). Managing extremes in the Anthropocene: a causal, stochastic physics approach. Frontiers in Environmental Science, 13, 1643416. https://doi.org/10.3389/FENVS.2025.1643416 Chapter 3 of this thesis, which is currently under review, is: Kaluarachchi, S., & Alila., Y. (2025). Why forests can mitigate floods of all sizes: Evaluating the scientific basis for forest-based flood mitigation. vii Table of Contents Abstract ......................................................................................................................................... iii Lay Summary .................................................................................................................................v Preface ........................................................................................................................................... vi Table of Contents ........................................................................................................................ vii List of Tables ..................................................................................................................................x List of Figures ............................................................................................................................. xiii List of Symbols ........................................................................................................................... xvi List of Abbreviations ................................................................................................................ xvii Acknowledgements .................................................................................................................... xix Dedication .....................................................................................................................................xx Chapter 1: Introduction ................................................................................................................1 1.1 Changing hydroclimatic realities in the 21st Century ..................................................... 1 1.2 A scientific stalemate and impaired decision-making: a motivating example ............... 2 1.3 Current methods in scientific and professional practice in hydrology ........................... 5 1.3.1 Determinism, reductionism, and the microscale: A misplaced focus? ................... 5 1.3.2 Frequency: The missed dimension.......................................................................... 7 1.3.3 The mathematical and statistical basis .................................................................. 11 1.4 Building a strong framework for understanding and predicting change....................... 12 1.4.1 The right investigation .......................................................................................... 12 1.4.2 Searching for insights from across disciplines ...................................................... 13 1.5 A scientifically rigorous approach for understanding and predicting change .............. 15 viii 1.5.1 Thesis objectives ................................................................................................... 15 1.5.2 Overview ............................................................................................................... 16 Chapter 2: Managing extremes in the Anthropocene: A causal, stochastic physics approach........................................................................................................................................................17 2.1 Introduction ................................................................................................................... 17 2.2 Methods......................................................................................................................... 24 2.3 The need for a causal, stochastic approach ................................................................... 27 2.3.1 Integrating physics into hydroclimatic risk prediction: a stochastic approach ..... 27 2.3.2 A brief overview of tail heaviness ........................................................................ 30 2.4 Environmental controls of the flood frequency curve’s upper tail ............................... 32 2.4.1 Overview ............................................................................................................... 32 2.4.2 Climatic controls of the upper tail ........................................................................ 34 2.4.3 Physiographic controls of the upper tail ............................................................... 37 2.5 Tail behaviour under change ......................................................................................... 42 2.5.1 Implications of tail behaviour: Magnitude-centric or frequency-centric? ............ 42 2.5.2 Anthropogenic controls of the flood frequency curve’s upper tail ....................... 44 2.6 Where do we go from here? .......................................................................................... 48 2.6.1 Guiding science and professional practice ............................................................ 48 2.6.2 Re-examining current understanding of tail behaviour ........................................ 51 2.6.3 Implications for risk assessments, planning, and decision-making ...................... 53 Chapter 3: Can forests mitigate floods of all sizes? Evaluating the foundations of a decades-long scientific controversy ...........................................................................................................57 3.1 Introduction ................................................................................................................... 57 ix 3.2 Methods......................................................................................................................... 64 3.3 Causally investigating effects of forest cover changes on floods ................................. 65 3.3.1 Causality is central to the science of extremes ..................................................... 65 3.3.2 What is the appropriate causal framework? .......................................................... 66 3.4 Evaluating two scientific approaches to the forest and floods disagreement ............... 71 3.4.1 Evaluating scientific merits and flaws .................................................................. 71 3.4.2 Critically assessing the deterministic approach .................................................... 72 3.4.3 Critically assessing the stochastic approach ......................................................... 78 3.5 Revisiting the role of forests in flood management ...................................................... 84 3.5.1 Revisiting the scientific disagreement .................................................................. 84 3.5.2 Policy implications................................................................................................ 88 Chapter 4: Conclusion .................................................................................................................90 4.1 Summary ....................................................................................................................... 90 4.2 Limitations .................................................................................................................... 93 4.3 Recommendations for future studies ............................................................................ 94 Bibliography .................................................................................................................................96 Appendices ..................................................................................................................................159 Appendix A ............................................................................................................................. 159 Appendix B ............................................................................................................................. 193 x List of Tables Table A.1 Synthesis of attribution science literature using the Scopus database that provide a direct quantification of change or frequency distributions relating event magnitudes to frequencies (see section 2.2). “RR” represents risk ratio, which is the probability of an event of a certain magnitude occurring under factual conditions (“current” unless otherwise stated) to that under counterfactual conditions (specified). “OBS” and “MOD” represent observations and models, respectively, and “GEV” represents the Generalized Extreme Value distribution (see section 2.2). Natural, anthropogenic, all forcings (natural and anthropogenic), greenhouse gases only, and aerosols only scenarios are represented by “NAT”, “ANT”, “ALL”, “GHGs”, and “AER”, respectively. ................................................................................................................... 159 Table A.2 Overview of flood frequency literature studying effects of climatic and physiographic controls on the variance, skewness, and/or tail behaviour, using the Scopus database to find appropriate studies and examining citations in papers which linked controls to their effects on variance, skewness, and/or tail behaviour (see section 2.2). CS and CV stand for coefficient of skewness and coefficient of variation, respectively. ................................................................... 176 Table B.1 Key conclusions of forest effects on peak flows are tabulated from studies using a deterministic data analysis procedure, using the Scopus database to search for deterministic studies on the effects of changing forest cover on floods (see section 3.2). For each study cited, location of the study, its hydroclimatic regime, range of catchment size(s) studied (or treatment watershed size if there is only one treatment watershed), record length, key conclusions regarding forest effects on peak flows, and whether convergence of regression lines is observed in key figures are listed whenever possible. Post-treatment record lengths are provided whenever listed, but overall record lengths (including pre- and post-treatment periods) are provided if post-xi treatment record length is not listed. Key conclusions discussing behaviour for larger events or convergence are bolded. Figure numbers correspond to figures in the cited work. ................... 193 Table B.2 Key conclusions of forest effects on peak flows are tabulated from studies using a stochastic data analysis, using the Scopus database to search for stochastic studies on the effects of changing forest cover on floods (see section 3.2). For each study cited, location of the study, its hydroclimatic regime, range of catchment size(s) studied (or treatment watershed size if there is only one treatment watershed), record length, key conclusions regarding forest effects on peak flows, and tail behaviour of Flood Frequency Curves (FFCs) are listed whenever possible (parallelism, convergence, and divergence are underlined). Post-treatment record lengths are provided whenever listed, but overall record lengths (including pre- and post-treatment periods) are provided if post-treatment record length is not listed. Key conclusions discussing behaviour for larger events are bolded. Figure numbers correspond to figures in the cited work. ............. 202 Table B.3 Key conclusions of forest effects on peak flows are tabulated from studies using both deterministic and stochastic analysis procedures, using the Scopus database to search for studies that applied both deterministic and stochastic procedures to study the effects of changing forest cover on floods (see section 3.2). Study location, hydroclimatic regime, range of catchment size(s) (or treatment watershed size if there is only one treatment watershed), record length, and key conclusions regarding forest effects on peak flows including descriptions of key supporting figures are listed whenever possible. Post-treatment record lengths are provided whenever listed, but overall record lengths (including pre- and post-treatment periods) are provided if post-treatment record length is not listed. Key conclusions discussing behaviour for larger events are bolded. Figure descriptions state whether regression of convergence lines are observed in deterministic figures or the behaviour of Flood Frequency Curve (FFC) tails in stochastic studies xii (parallelism, convergence, and divergence are underlined), with figure numbers corresponding to figures in the cited work. ............................................................................................................ 217 xiii List of Figures Figure 1.1 Illustration of a flood frequency curve (FFC) and probability density function (PDF) with “heavier” (purple) and “lighter” (blue) upper tails. The FFC relates event magnitudes to their frequencies (typically expressed as return periods). The PDF shows the probabilities of outcomes of different discharges. The PDF best illustrates how the heavier tail goes to zero slower than the lighter tail, thus the heavier tail lies above the lighter tail..................................... 8 Figure 2.1 Distribution of a hydroclimatic variable through time under stationary and nonstationary conditions. Floods under the threshold (grey dotted line) represent the population of common events while floods greater than the threshold represent extremes. In stationary panel A, the stationary distribution does not change in time. In nonstationary panel B, the blue curve suggests an earlier period with reduced anthropogenic activity, while the red curve suggests a later period with increased anthropogenic activity. The nonstationary distribution changes with time in location, shape, and scale (see section 2.3.2), all of which influence tail behaviour. Figure inspired in part by Salas & Obeysekera (2014). ........................................................................... 20 Figure 2.2 Sensitivity of lighter and heavier tails under nonstationarity. A nonstationary distribution is portrayed using “snapshots in time” at different stages across the modelled period, showing how magnitude–frequency relationships evolve with varying intensities of anthropogenic activity. This conceptual drawing shows example changes in magnitude (light green, dashed) and frequency (dark green, dashed) between an earlier “snapshot” with less anthropogenic activity (blue) and a later “snapshot” with greater anthropogenic activity (red) under lighter (A) and heavier (B) tails. The 100-year event undergoes a larger change in frequency under lighter tails (i.e., to a 5-year event) than under heavier tails (i.e., to a 50-year event)............................................................................................................................................. 23 xiv Figure 2.3 Controls of the upper tail of the flood frequency curve (FFC). Conceptual drawing of climatic, physiographic, and anthropogenic controls of the upper tail of the FFC. The three groups of controls influence both each other (larger red arrows) and the upper tail (smaller arrows). For anthropogenic controls, only those with sufficient literature assessing their impacts on the FFC tail are considered. ..................................................................................................... 34 Figure 2.4 Upward and downward shifts of a hydroclimatic distribution following a disturbance. The shift from a pre-disturbance (blue) to a post-disturbance (red) FFC are shown in the case of an upward shift (A) or downward shift (B) following anthropogenic influence. Example changes in magnitude (light purple, dashed) and frequency (dark purple, dashed) are shown for each scenario. While changes in variance can lead to convergence or divergence of tails, or the two tails may even superimpose on each other, these scenarios are not depicted here for simplicity. 46 Figure 3.1 Conceptual diagram showing major differences between the deterministic (left) and stochastic approaches (right) for the same property (middle) when studying impacts of forest cover changes on flood peaks. Although both utilize the Before-After, Control-Impact (BACI) experimental design, differences in ensuing data analysis are shown by highlighting how these approaches differ for various properties of the analysis procedure. ............................................. 72 Figure 3.2 Examples of typical deterministic regression and stochastic flood frequency curve (FFC) plots. While convergence is apparent on deterministic plots, tails may remain parallel, diverge (as shown), converge, or superimpose on stochastic plots. ............................................. 77 Figure 3.3 Conceptual changes of an increase in mean, variance, or both mean and variance to a hypothetical flood probability distribution. The grey dashed line represents a hypothetical threshold above which floods are considered large (such as the 10-year event), with increases in mean, variance, or both mean and variance increasing the number of large floods and record xv floods (i.e., floods which surpass all previously observed peak discharges in the instrumental record). While anthropogenic activity may also change the shape (skewness) of the distribution, it is not depicted here for simplicity. ............................................................................................ 81 Figure 3.4 Hypothetical changes to a FFC with a decrease in forest cover. Changes in magnitude (light blue arrow) and frequency (dark blue arrow) are shown under both lighter- and heavier-tailed flood regimes....................................................................................................................... 83 xvi List of Symbols 𝜇: location parameter 𝜎: scale parameter 𝜉: shape parameter xvii List of Abbreviations AER: aerosols only scenario ALL: all forcings scenario AMC: antecedent moisture condition ANT: anthropogenic forcings scenario BACI: Before-After, Control-Impact BC: British Columbia CV: coefficient of variation CS: coefficient of skewness ENSO: El Niño-Southern Oscillation EVT: Extreme Value Theory FFA: flood frequency analysis FFC: flood frequency curve GEV: Generalized Extreme Value GHGs: greenhouse gases scenario GRADEX: GRADient of EXtreme values LULC: land use and land cover MOD: models NAT: natural forcings scenario NBS: nature-based solutions NFM: natural flood management OBS: observations PDF: probability density function xviii RR: Risk Ratio USA: United States of America USD: United States dollars xix Acknowledgements I would like to express my deepest gratitude to my supervisor, Dr. Younes Alila, who first inspired my interest in hydrology and has since guided, supported, and encouraged me throughout my Master’s degree. He challenged me to question the norms and think critically, encouraging me to seek deeper understanding. I am also thankful for the members of my supervisory committee, Dr. Bianca Eskelson and Dr. Cindy Prescott, as well as Dr. Nicholas Coops for their valuable support and suggestions which greatly improved my work. I would also like to acknowledge the generous financial support provided by the Natural Sciences and Engineering Research Council of Canada, the Faculty of Forestry, the Gordon and Nora Bailey Fellowship in Sustainable Forestry, and the Mary and David Macaree Fellowship for this work. I am deeply appreciative of my lab and office members for all the ways in which they have supported and motivated me. In particular, I would like to thank Britany, Spencer, Sam, Sylvie, and Mark, whose conversations provided stress relief, helped give me a sense of community within the program, and helped me reflect more deeply on hydrology and its place in a broader societal context. Lastly, I am forever grateful to my family for their love and support. I particularly want to thank my parents for encouraging me to pursue my interests and for their unwavering support, and my sister for never failing to cheer me up, especially during long days of writing and deadlines. xx Dedication This thesis is dedicated to my family and friends, who support and inspire me. 1 Chapter 1: Introduction 1.1 Changing hydroclimatic realities in the 21st Century Hydroclimatic regimes are intensifying around the world, leading to unprecedented increases in frequencies and magnitudes of extreme events. They include both high and low extremes over a range of variables, including floods (Gillett et al., 2022; Hirabayashi et al., 2021; N. Singh & Chinnasamy, 2021), droughts (Luo et al., 2022; Zachariah et al., 2023), heatwaves (Ciavarella et al., 2021; White et al., 2023), wildfires (Barbero et al., 2020; Van Oldenborgh et al., 2021), and compound events (Treppiedi et al., 2024; Zscheischler et al., 2025), including “whiplash” events where one extreme is rapidly followed by its opposite extreme (e.g., heavy rain to drought) (Zscheischler et al., 2025). They have led to major socioeconomic impacts to peoples’ lives and livelihoods, spanning a broad range of economic sectors (Lee & Parfitt, 2022; Newman & Noy, 2023; White et al., 2023). Many of these changes in hydroclimatic regimes have been attributed to anthropogenic activity, with continued increases in extreme event magnitudes and frequencies expected throughout the century (e.g., Ciavarella et al., 2021; Gillett et al., 2022; Malinina & Gillett, 2024; Teufel et al., 2017). For instance, current and projected increases in flood magnitude and frequency have been attributed to both climate change (Gillett et al., 2022; Hirabayashi et al., 2021) and land use and land cover (LULC) changes such as urbanization (Prosdocimi et al., 2015) and forest harvesting (Johnson & Alila, 2023). Consequently, a rigorous, physically based understanding of hydroclimatic phenomena and their controls can help communities adapt to and mitigate the effects of extreme events. Implementing cost-effective solutions which meaningfully reduce risk requires reliable projections and a sound understanding of how natural controls and anthropogenic interventions attenuate or enhance extremes, all of which are highly relevant for flood management. 2 1.2 A scientific stalemate and impaired decision-making: a motivating example A key discipline where sound scientific understanding is needed to advance flood management is forest hydrology, which “has a sad history of being embroiled in controversies that never seem to get resolved” (Dunne, 1998, p. 795). For centuries, the question of whether deforestation increases flood risk and the role of forests in flood management remained a point of contention among foresters, engineers, conservationists, and the public. Knowledge gaps and methodological limitations, combined with “the diverging philosophical, esthetic, and financial interests of the various participants… [including] their fear of suffering great loss of biodiversity, esthetic values, natural resources, jobs, or revenue” (Dunne, 1998, p. 795) have fueled debate and unresolved science that persists today. This section outlines how the understanding of the role of forest cover in flood mitigation has evolved through time but remains unresolved, impairing flood management. The earliest views, dating back at least to 17th century European forestry, viewed forests as a “sponge” that temporarily stored event precipitation and prevented flood peaks then slowly released this water during drier periods, maintaining baseflow (Saberwal, 1998). Based on this logic that largely continued to prevail in the 18th and 19th centuries, perceived increases in flood peaks and droughts were linked to upstream deforestation (Saberwal, 1998). This motivated countries like France, Switzerland, and Germany to protect and restore forests in the 19th century (Rudel et al., 2020). For example, flood management efforts following Switzerland’s disastrous 1868 flood included both diking and reforestation in source areas (Jordan, 2007). In 20th century American forestry, however, foresters and engineers disagreed on the role of forests in flood mitigation. Gifford Pinchot of the United States Forest Service argued that forests regulate streamflow, preventing floods when there is enough forest cover in the 3 catchment and until saturation is reached, after which stormwater “runs into the streams almost as fast as it would over bare ground” (Pinchot, 1905, p. 69). The general understanding that forests mitigate floods was central to foresters’ support for the 1911 Weeks Act (Rudel et al., 2020; Saberwal, 1998). Perceiving upland agriculture in the Appalachian Mountains as the cause of downstream flooding, this Act established high-elevation national forests in the eastern United States to reduce flood risk (Rudel et al., 2020). This sparked industrial backlash as state control of lands restricted timber harvesting, and the Army Corps of Engineers also emphasized that there was no scientific backing that forests mitigate floods (Saberwal, 1998). This feud led to the beginning of forest hydrology research. The 1910 Wagon Wheel Gap experiment showed that forest removal increased runoff throughout the year, followed by a study in Emmenthal, Switzerland, showing higher water losses with greater tree cover (Bates & Henry, 1928; Cooper et al., 2021; Hoyt & Troxell, 1932). Both showed year-round increases in runoff, refuting the former “sponge” concept stating that forest harvesting amplifies peak flows and dry season droughts (Hoyt & Troxell, 1932). This benefited engineers, who received substantially more funding for building flood control infrastructure such as dams and levees than was allocated for the purchase of forest lands for flood control (Saberwal, 1998). Given pressure on the United States Forest Service to adopt more quantitative methods, many research stations were established in the 1950s to further examine the forests and floods relationship (Saberwal, 1998). Decades of continuing research from these experiments gave rise to today’s dominant scientific viewpoint, including that (1) forest cover removal increases flows throughout the year (Saberwal, 1998), and (2) mitigative effects of forest cover decrease with increasing flood size, with little or no impacts on large floods (Barnes et al., 2023; Bathurst et al., 2011, 2018, 2020; Cooper et al., 2021; Fahey & Payne, 2017; Moore & Scott, 2005; Peskett et 4 al., 2023; van Dijk et al., 2009; Xiao et al., 2022). Although the definition of “large” (and “extreme”) floods, or how rare an event must be to qualify as such, is “[a]n open question” (Sturdevant-Rees et al., 2001, p. 2161), many studies have found minimal or no impacts for events beyond the 5-year (e.g., the event that occurs, on average, once in five years) or 10-year event magnitude (e.g., Bathurst et al., 2011, 2020; Birkinshaw et al., 2011; Harr, 1986). Later, in the late 20th and 21st centuries, a wave of new studies utilizing a different method of data analysis directly opposed the earlier conclusions. Their conclusions that forest cover can mitigate small, medium, and large floods (Alila et al., 2009; Bradshaw et al., 2007; Duncan, 1995; Green & Alila, 2012; Hurkmans et al., 2009; Johnson & Alila, 2023; Lallemant et al., 2021; McEachran et al., 2021; Preti et al., 2011; Reynard et al., 2001; Siriwardena et al., 2006; Te Linde et al., 2010) thus amplified scientific disagreement on the role of forests in flood mitigation. Such differences in viewpoints throughout forest hydrology led Dunne (1998, p. 795) to make the following statement: “Forest hydrologists could be recruited to defend almost any side of a debate, because our confusion about the various processes and their interactions in forests and streams…has left much room for opinion and its attendant influences.” Thus, scientific disagreement may signal foundational gaps in understanding and possible limitations in methodology. Opposing scientific perspectives on whether forests can mitigate large floods (e.g., Barnes et al., 2023; CIFOR & FAO, 2005; Cooper et al., 2021; Lallemant et al., 2021) impair effective land use planning and flood mitigation strategies. This warrants a 5 closer examination of whether hydrology as currently practiced can deliver reliable understanding and projections to support effective flood management in the 21st Century. 1.3 Current methods in scientific and professional practice in hydrology 1.3.1 Determinism, reductionism, and the microscale: A misplaced focus? Many applications rely on deterministic analyses which “exclud[e] randomness in hydrological variables” (WMO, 2012, p. 373), running contrary to the inherently random (or “stochastic”) nature of these hydroclimatic variables (Pham & Alila, 2024; Swain et al., 2020). Flood generation depends on multiple factors such as rainfall and antecedent moisture condition (AMC) (and additionally snowpack accumulation and energy available for snowmelt in snow-influenced regions), each of which varies stochastically (Gillett et al., 2022; Green & Alila, 2012; Pham & Alila, 2024; Sturdevant-Rees et al., 2001). Imposing a deterministic framework onto inherently stochastic phenomena cannot adequately capture the core role of stochasticity in hydroclimatic event generation (Swain et al., 2020) or allow for resilient planning under uncertainty. A key example is in forest hydrology, where large spatiotemporal scales of floods (Robinson & Sivapalan, 1997) are reduced to single-event comparisons; event rainfall input is compared to catchment storage capacity at the time to predict the flood response following a change in forest cover (Xiao et al., 2022). However, single-event framing cannot capture how climatic, physiographic, and anthropogenic drivers interact across spatiotemporal scales to produce floods, hindering an understanding of floods as they occur in nature. Reductionist approaches also dominate hydrology, where isolated system components are studied with less attention paid to understanding how these components interact with each other to yield the overall system state or response. For example, isolating components of an energy balance under snowy forested and non-forested plots (e.g., Berris & Harr, 1987; Ellis et al., 6 2011) or stands (e.g., Winkler et al., 2005) could provide necessary insights to clarify the relationship between forest cover and snowmelt. However, a primary focus on reductionism at the expense of understanding the whole overlooks how large-scale characteristics (e.g., under differences in elevations and slopes) influence or modify these relationships and how interactions among other parts of the system can be equally or even more important for defining a system’s state or response (e.g., influence of other landscape elements on flood generation). This dominance of reductionist and deterministic approaches may result, at least in part, from the nature of the human brain, as humans tend to “respond to problems in relatively simplistic, reductionist, mechanical ways” (Rees, 2023a, p. 19, 2023b). Nevertheless, they may impair obtaining an understanding of the holistic hydrological system relevant for societal application. Similarly, many hydrological disciplines have historically focused on the microscale, such as the scale of a single tree, stand, plot, hillslope, or small headwater catchment (e.g., Harr & McCorison, 1979), but macroscale properties are critical for understanding floods (McDonnell et al., 2021; Rogger et al., 2017). This has led to difficulties in upscaling microscale understanding to macroscale phenomena (Beven, 2000; Eder et al., 2003; McDonnell et al., 2007; Sivapalan, 2003). The impact of this misplaced focus is highlighted by Dunne (1998, p. 796), who notes: “…a continuing separation between the interests of research hydrologists working on small scale problems in carefully selected, relatively simple environments and the needs of society for assessments…at a sufficiently large geographical scale to be useful for decision making.” 7 Thus, rather than attempting to fit nature into hydrology’s models (or even into its reductionist approaches), perhaps hydrology should aim to develop models that better capture reality at the appropriate spatiotemporal scales (Hirschboeck, 1999). The dominance of deterministic, reductionist, and microscale approaches may have led to challenges in causally understanding drivers of increasing flood frequencies and magnitudes. While there is widespread agreement that climatic and LULC changes simultaneously impact floods (B. Merz et al., 2012; Runge et al., 2019), there has been less success in causally disentangling relationships among these drivers and their effects (B. Merz et al., 2012). A lack of success may result from the dominance of methods which cannot capture the stochasticity inherent in flood extremes at spatiotemporal scales relevant to their generation, leading to difficulties in rigorous understanding and prediction. An example is in forest hydrology, where a lack of a causal understanding of the role of forest cover on flood mitigation (especially amidst other superimposing drivers) has led to unresolved science and intensified debate throughout scientific and policymaking arenas (Bradshaw et al., 2009; Penning et al., 2023). This calls for a paradigm shift (Alila et al., 2009) to rigorously and causally understand floods and their drivers, going beyond simply detecting hydrological change to rigorous attribution (B. Merz et al., 2012) at appropriate spatiotemporal scales. 1.3.2 Frequency: The missed dimension Much of hydrology is based upon Flood Frequency Analysis (FFA), which relates flood magnitudes to their frequencies (e.g., the magnitude of the 50-year or 100-year event) and plots these magnitude–frequency relations as Flood Frequency Curves (FFCs) (see Figure 1.1). For other hydroclimatic extremes such as high temperatures (e.g., Christidis & Stott, 2022) and wildfires (e.g., Kirchmeier-Young et al., 2019), similar frequency distributions also relate event 8 magnitudes to frequencies. The largest events are represented by the “upper tail” of the FFC (or frequency distribution), which may be “heavier” (e.g., their tails go to zero slower than the exponential distribution, such as tails of the lognormal, Fréchet, and Pareto distributions) or “lighter” (e.g., tails of the normal or exponential distributions) (see Figure 1.1) (El Adlouni et al., 2008; B. Merz et al., 2022; Taleb, 2019). Figure 1.1 Illustration of a flood frequency curve (FFC) and probability density function (PDF) with “heavier” (purple) and “lighter” (blue) upper tails. The FFC relates event magnitudes to their frequencies (typically expressed as return periods). The PDF shows the probabilities of outcomes of different discharges. The PDF best illustrates how the heavier tail goes to zero slower than the lighter tail, thus the heavier tail lies above the lighter tail. Rigorously capturing the stochasticity of hydroclimatic extremes calls for probability-based approaches (Swain et al., 2020) which, by definition, require both magnitude and frequency (e.g., Eslamian & Eslamian, 2023). Hydroclimatic extremes are also natural phenomena occurring with or without anthropogenic influence, but anthropogenic activity can make them more common (or sometimes rarer) (Allen, 2003; Fischer & Knutti, 2015; Otto, 9 2017). This means that frequency must be evoked alongside magnitude for rigorous, causal prediction of changing hydroclimatic phenomena. However, this fundamental importance of frequency in both understanding and predicting hydroclimatic phenomena (and its implications) is rarely acknowledged in hydrological literature, as outlined in this section. The tendency to overlook frequency is demonstrated by the prevalence of magnitude-centric approaches. Methods may examine magnitude only, such as in forest hydrology where the dominant approach compares the magnitude of a flood in a forested watershed to its corresponding magnitude in a harvested watershed (Barnes et al., 2023; Xiao et al., 2022), without the ability to evoke whether flood frequencies differ between the two watersheds. In methods such as FFA, magnitudes are related to their frequencies in the modelling procedure, but results are typically interpreted with a sole or primary focus on the magnitude (B. Merz et al., 2022). For example, engineering applications require infrastructure to be built to withstand flood magnitudes associated with a specified frequency, such as the 200-year flood in British Columbia (BC) (Engineers & Geoscientists BC, 2018). Although frequency is evoked (e.g., 200-year), the focus lies in identifying the corresponding magnitude and designing structures accordingly (e.g., Mishra et al., 2024; Quintero et al., 2018). Yet, frequencies of extremes display much larger changes than magnitudes under anthropogenic activity (Allen & Ingram, 2002). Failing to properly acknowledge frequency can prevent a thorough understanding of change. This can include overlooking the implications of changing frequencies, such as how increased frequencies of small, medium, and large floods change natural flow regimes. Changed flow regimes can then impact ecological systems (e.g., Poff et al., 1997), communities, and infrastructure. 10 Furthermore, FFA traditionally assumes stationarity of the hydrological variable (Engineers & Geoscientists BC, 2018), which implies that the probability distribution of that variable does not change with time (Koutsoyiannis & Montanari, 2015; WMO, 2012). Although stationary FFC continues to dominate today in both scientific (e.g., B. Merz et al., 2022 and citations therein) and professional practice (e.g., Engineers & Geoscientists BC, 2018), this runs contrary to observations that flood magnitudes and frequencies are changing in many parts around the world (especially in relation to extreme events), potentially rendering such estimates “invalid and increasingly unreliable” (Engineers & Geoscientists BC, 2018, p. 154). Instead, nonstationarities (i.e., where statistical properties of the distribution change in time (WMO, 2012)) may be accounted for by nonstationary FFA, which can indicate how magnitudes and their corresponding frequencies (indicated by return levels rather than return periods) evolve throughout the period of interest (Johnson & Alila, 2023). Therefore, assuming hydrological stationarity without appropriate rationale or investigating whether nonstationarities are present reflects an outdated approach (Milly et al., 2008) which must be replaced by nonstationary approaches whenever possible. In fact, a stationary and magnitude-centric focus risks obscuring, or potentially mischaracterizing, a system’s sensitivity to change, especially for large events. In hydrology, FFC upper tails are often assumed to be heavier tailed (B. Merz et al., 2022). In literature outside hydrology, heavier tails are considered “antifragile” to change as they suffer less from variability while lighter tails are fragile to, or suffer from, change (Taleb, 2012; Taleb & Douady, 2013). The implications of tail behaviour can be brought into hydroclimatology in the context of understanding a system’s sensitivity to disturbance. The dominance of heavier tails in hydrology (B. Merz et al., 2022; Zaerpour et al., 2024) which are “antifragile” to change (Taleb, 2012; 11 Taleb & Douady, 2013) appears inconsistent with documented realities; the recent large increases in frequencies of extremes following anthropogenic activity (e.g., Gillett et al., 2022; Johnson & Alila, 2023; Kuraś et al., 2012) may instead hint at an underlying fragility of flood regimes to disturbance. Mischaracterizing sensitive watersheds as resilient to change (i.e., lighter-tailed as heavier-tailed) can have dire consequences for communities (e.g., inundation), infrastructure (e.g., structural failure) (Flint et al., 2017; Wardhana & Hadipriono, 2003), and organisms adapted to a river’s natural flow regime (e.g., decrease in species abundance or diversity) (Bower et al., 2022; Poff et al., 1997) if flood regimes intensify and become more frequent beyond projections. Thus, there is a need to ensure that upper tails are reliably characterized to predict change and the system’s sensitivity under nonstationary conditions. 1.3.3 The mathematical and statistical basis Hydrology has long been criticized for its overreliance on mathematical and statistical formulations at the expense of physical understanding, which can increase the possibility of misconceptions (Hirschboeck, 1999; R. Merz & Blöschl, 2008). A key issue is in prediction, where extrapolating beyond the range of existing data without sound physical or empirical basis can be dangerous and misleading (Klemeš, 1986), especially given limited record lengths of most hydrological variables (B. Merz et al., 2022). Record lengths of a few decades or less (L. Hu et al., 2020) typically only capture small and medium events adequately, but statistical techniques are often used to make predictions concerning large events. This is demonstrated in studies examining the effects of forest harvesting on floods (Bathurst et al., 2011; Harr, 1986; Jones, 2000; Moore & Scott, 2005; Rothacher, 1973), where two regression lines are used to show pre- and post-harvesting fits between control and treatment watershed floods. Regression lines are extrapolated beyond small and medium events to predict the harvesting response to 12 large flood events. In hydrological disciplines relying on FFA, the “art of curve fitting” (Klemeš, 1993, p. 168), with its emphasis on selecting statistical distributions to match observations (e.g., Opere et al., 2006; Papalexiou & Koutsoyiannis, 2013), can inhibit efforts to obtain a sound physical understanding of extremes (R. Merz & Blöschl, 2008). While many distributions may fit available data, they can yield widely divergent predictions for larger events (Klemeš, 1986). Compared to errors arising in interpolation, “the dangers of extrapolation are much more subtle because its results may look plausible in the light of the analyst's expectations” (Klemeš, 1978, p. 181). Therefore, overreliance on statistical frameworks without sufficient physical reasoning may produce less reliable conclusions (although they may seem plausible), especially regarding extreme events under new or changing conditions. In this way, issues in prediction and extrapolation may persist not necessarily from a lack of data as “there is significantly more information in large-scale hydrological data sets than hydrologists have been able to translate into theory or models,” but rather from how it is integrated into existing models and frameworks (Nearing et al., 2021, p. 1). 1.4 Building a strong framework for understanding and predicting change 1.4.1 The right investigation With the need for hydrological methods which capture changing realities and directly support flood management, scientific investigations must be guided by the right questions and rigorous, causal experiments. The importance of the research question was emphasized by Leopold & Langbein (1963, p. 192), who stated that “[t]he vitality of a branch of science is a reflection of the magnitude or importance of the questions on which its students are applying their effort.” Only the right questions can advance society (Berkson, 1989) and directly help manage society’s water-related challenges. The value of testable, falsifiable hypotheses, 13 especially focused hypotheses to understand important phenomena (McKnight, 2017), has also been acknowledged both within and outside of hydrology (Kirchner, 1989; McKnight, 2017; Popper, 1935). Finally, experiments should aim to causally and rigorously answer research questions, using methods that allow hydrology to disentangle the effects of the driver(s) of interest amidst other superimposing drivers (Runge et al., 2019). As human activities alter the risks of a range of hydroclimatology extremes, understanding and predicting their changes spans many disciplines throughout hydroclimatology. Therefore, examining how different fields address analogous and overlapping questions can provide insights for developing a rigorous scientific approach to understand and predict extremes. 1.4.2 Searching for insights from across disciplines Many hydroclimatic disciplines investigate analogous or overlapping questions, each with its characteristic methods. For instance, one major topic in forest hydrology is understanding the influence of forest cover on mitigating floods. Traditional methods include regression analyses, which are non-causal and deterministic, and employ single-event reasoning (e.g., Xiao et al., 2022). Flood peaks derived from a control catchment are related to their corresponding peaks in a treatment (e.g., harvested) catchment to understand the effects of changing forest cover. Despite sample sizes spanning one or a few decades which only adequately capture small and medium events, these analyses are often extended to predict the flood response for large events (Bathurst et al., 2011; Beschta et al., 2000; Harr, 1986; Jones, 2000). Many branches in wider hydrology and climate science study how climate change or LULC changes influence floods and other hydroclimatic variables. Their approaches are 14 stochastic (i.e., use probabilistic concepts (WMO, 2012)), in line with the stochastic nature of hydroclimatic events (Klemeš, 1978; Stott et al., 2016; Swain et al., 2020). They construct scenarios with increased and decreased anthropogenic influence to investigate how event frequencies change for events of a given magnitude (or vice versa). Alternatively, hydrological studies may use two physical watersheds, where only one is subject to the disturbance under study (e.g., Alila et al., 2009). Using the Extreme Value Theory (EVT) statistical framework for extremes, hydroclimatic studies may compare frequency distributions relating event magnitudes to their frequencies for these different scenarios. These methods typically place a strong reliance on mathematical and statistical equations (B. Merz et al., 2012; Van Oldenborgh et al., 2022). In contrast, while the branch of “stochastic hydrology” uses probability concepts (Rubin, 2003; WMO, 2012) akin to general hydroclimatology, it centres physical knowledge into the analysis (Blöschl & Sivapalan, 1997; Eagleson, 1972; R. Merz & Blöschl, 2009). Although its history spans many decades, it has rarely been applied to the study of extreme events. These disciplines are interconnected not just by their analogous questions, but also in that they study interconnected parts of Earth’s hydroclimatic systems. Climatological and hydrological variables are heavily linked (e.g., climatic controls of flooding (B. Merz et al., 2022)) and have key commonalities such as their stochastic nature (Otto, 2017; Pham & Alila, 2024; Swain et al., 2020). Consequently, integrating insights from these disciplines and assessing the strengths and limitations of their deterministic or stochastic methods can help develop a rigorous scientific approach for studying hydroclimatic extremes. 15 1.5 A scientifically rigorous approach for understanding and predicting change 1.5.1 Thesis objectives This thesis advocates for rigorous methods that capture the nature of the system under study and key facets by which it is changing. It presents a holistic, big-picture framework for understanding and predicting extremes in the form of an “architect” work that questions several dominant methods and assumptions (Loeb, 2013). It examines both deterministic and stochastic scientific approaches used throughout hydroclimatology to determine which one allows for the most scientifically rigorous understanding and prediction of floods and other hydroclimatic extremes. This thesis is guided by the following overarching questions: 1. How should the physics of floods be understood scientifically? 2. Could observed dramatic increases in hydroclimatic extremes stem, at least in part, from an inherently sensitive, or fragile, regime? 3. How can a sound understanding of flood controls be used for overall flood management and to design flood mitigation strategies? This thesis formulates the following hypotheses: 1. A causal, stochastic approach best captures the relationships between floods and their drivers (both natural and anthropogenic). 2. Large increases in frequencies of hydroclimatic extremes may stem, at least in part, from a natural regime that is inherently sensitive, or fragile, to disturbances. 3. A strong understanding of flood controls informs sustainable land and resource planning which manages downstream flood risks and allows for developing flood mitigation solutions, especially those which draw from nature. 16 By examining these questions and hypotheses, this thesis argues that the study of floods and other hydroclimatic extremes requires a causal, stochastic approach which integrates understanding and prediction using a frequency-centric lens. 1.5.2 Overview This thesis is structured as follows: Chapter 2 outlines the causal, stochastic framework required for studying hydroclimatic extremes, namely floods. It emphasizes obtaining a sound, physically based understanding of floods to predict change, characterize watershed sensitivity to this change, and design appropriate flood mitigation strategies. Chapter 3 provides a tangible example of the need for this sound, causal understanding by examining a contentious flood management topic: the use of forests to mitigate large floods. Currently, opposing conclusions between deterministic and stochastic approaches have led to scientific controversy surrounding the forests and floods relationship. This chapter examines the suitability of each approach to answer whether forests can mitigate (large) floods, emphasizing that only the scientifically rigorous approach can support effective flood management. Finally, Chapter 4 summarizes the main conclusions of the thesis and provides recommendations for future studies. 17 Chapter 2: Managing extremes in the Anthropocene: A causal, stochastic physics approach 2.1 Introduction While hydroclimatic extremes such as heatwaves, wildfires, storms, floods, and droughts have long been a reality, recent decades have seen an unprecedented and alarming rise in their frequencies and severities worldwide (Chiang et al., 2021; Fischer & Knutti, 2015; S. Philip et al., 2019; J. Wang et al., 2021). In 2021 alone, British Columbia (BC), Canada, experienced an extreme heatwave causing 619 heat-related deaths (White et al., 2023), a severe wildfire destroying much of the municipality of Lytton (Parisien et al., 2023), and extensive flooding (Gillett et al., 2022), with disproportionate impacts on local and Indigenous communities and estimated costs up to 17 billion Canadian dollars (Parisien et al., 2023). Elsewhere, heatwaves have led to tens of thousands of deaths (Ballester et al., 2023), severe wildfires are projected to cost billions of United States dollars (USD) or equivalent in mortality effects alone (Borchers-Arriagada et al., 2024), and floods, storms, and droughts are projected to cost trillions of US dollars or equivalent in damages in seven major countries (GHD, 2022). While climate change, land use and cover (LULC) change, and other human activities all influence extremes, those attributable to climate change alone cost USD 143 billion per year globally (Newman & Noy, 2023). These events have motivated the rise of attribution science, which compares “factual” (real-world) conditions to those of a “counterfactual” world with minimal anthropogenic influence (i.e., natural or early industrial conditions), isolating the role of human disturbance on risks of extremes (Stott et al., 2016). They have led to startling conclusions, especially 18 concerning changes in frequency (Lloyd & Shepherd, 2020) (see Table A.1). In some cases, events that were nearly impossible or extremely rare under counterfactual conditions became less than 200- (or even 100-) year events. Despite uncertainties in quantification of these shifts and increased vulnerability to type 2 errors (false negatives) (Lloyd & Shepherd, 2020; S. P. Xie et al., 2015), the conclusions are clear: human activity has greatly altered risks of extremes, with trends expected to continue or accelerate (Fischer & Knutti, 2015; Seneviratne et al., 2014). Consequently, there is growing pressure to re-evaluate current adaptation and mitigation strategies for changing risks of hydroclimatic extremes, especially as other factors such as increased urbanization onto flood-prone areas (Rentschler et al., 2023) further increase vulnerability and exposure to risks. Since risk is often defined as a function of probability and event impact (Eslamian & Eslamian, 2023), both changes in probability and magnitude must be accurately quantified. In the case of floods, for instance, traditional engineering-based solutions such as dikes and bridges can fail from either hydrologic or geomorphic activity. Hydrological failures often occur during flow maxima or rare events, when a single flood event exceeds a structure’s design capacity, such as the 200-year event, which it is engineered to withstand (Flint et al., 2017). Geomorphic failures result from longer-term cumulative work associated with frequent flows, leading to failures at lower return periods (Flint et al., 2017; Wardhana & Hadipriono, 2003). While scour is often emphasized (Wardhana & Hadipriono, 2003), mobilization and accumulation of sediments additionally aggrade the channel, lowering its capacity to contain flood volumes (Hudson, 2021). Transport of sediment can also increase impact forces on flood infrastructure and encourage further scour, potentially leading to infrastructure failure (Vázquez-Tarrío et al., 2024). Therefore, assessing impacts of changing flood risk to older structures and designing new structures must use nonstationary frameworks 19 (i.e., accounts for statistical properties of the flood distribution changing in time; see Figure 2.1) to examine both changes in magnitude (i.e., exceedance of flood design capacity) and frequency (i.e., increased geomorphic activity). Even though design flood magnitudes can be increased, small changes in magnitude produce much larger changes in frequency (Allen & Ingram, 2002; Mearns et al., 1984) which often go unrecognized (Quintero et al., 2018). With a range of floods (i.e., medium and large) increasing in frequency, a magnitude-centric approach is ill-suited to capture these more frequent (i.e., sustained) higher flows and consequent increases in geomorphic activity. Furthermore, a change in hydrological regime, especially through changes in variability which greatly alter flood frequencies and magnitudes, can lead to changes in species abundance, richness, and diversity (Strickland et al., 2024), which are underestimated with a magnitude-centric focus on the design flood event. Only a frequency-centric approach emphasizes both sustained higher flows and its geomorphic and ecological implications for a holistic understanding of change. Moreover, engineering-based solutions require regular maintenance and upgrades (especially with rising flood risks) (Baldassarre et al., 2018), provide a false sense of security which encourages development in high-risk areas (Hudson, 2021; Jongman, 2018), and may treat only symptoms rather than address the root cause of the problem (Awah et al., 2024), thus they are increasingly deemed insufficient for managing risk (Kiesel et al., 2023). 20 Figure 2.1 Distribution of a hydroclimatic variable through time under stationary and nonstationary conditions. Floods under the threshold (grey dotted line) represent the population of common events while floods greater than the threshold represent extremes. In stationary panel A, the stationary distribution does not change in time. In nonstationary panel B, the blue curve suggests an earlier period with reduced anthropogenic activity, while the red curve suggests a later period with increased anthropogenic activity. The nonstationary distribution changes with time in location, shape, and scale (see section 2.3.2), all of which influence tail behaviour. Figure inspired in part by Salas & Obeysekera (2014). Due to the limitations of traditional engineering solutions, many calls instead focus on nature-based solutions (NBS) (Jongman, 2018), which temporarily store and gradually discharge stormwater, preventing sudden increases in fast runoff (Dadson et al., 2017). Sponge parks and retention basins have already been implemented in China and Europe (Chan et al., 2018; Leanza, 2022), and reforestation and afforestation programs show promise elsewhere to mitigate risk (Lallemant et al., 2021; Penny et al., 2023). While many emphasize their cost-effectiveness (Vicarelli et al., 2024) and benefits for flood loss avoidance (Atkins, 2015), NBS can be costly to install (Chan et al., 2018). Others have questioned effectiveness of NBS for larger floods (Dadson et al., 2017; Kay et al., 2019), suggesting that their suitability under changing risks must first be established prior to their widespread adoption for mitigating extremes. 21 Although science has advanced on the prediction front (i.e., attribution science), an accurate quantification of risk must be supported by the right physical understanding of the phenomenon. Due to the interconnected nature of drivers within Earth systems, time series of hydroclimatic variables such as streamflow are influenced by multiple simultaneous drivers (B. Merz et al., 2012; Runge et al., 2019), thus understanding of extremes must stem from the correct framework. Only a causal investigation can disentangle multiple influences and identify direct, causal relationships between both natural and anthropogenic drivers and extremes (Runge et al., 2019). In fact, the fields of causation (Pearl, 2009) and extreme value theory (EVT) (Chapman et al., 2023; Coles, 2001; El Adlouni et al., 2008) common to hydroclimatology have largely remained separate. Instead, the two fields must be bridged together to understand extremes and their causative factors (Chavez-Demoulin & Mhalla, 2024) through a stochastic physics approach (Klemeš, 1978; Pham & Alila, 2024). This approach uses probability to understand the system of interest (WMO, 2012), accounting for inherent stochasticity (randomness) in nature (Klemeš, 1978; Swain et al., 2020). It “tries to place the statistics in a physical framework” to understand physical controls of a given phenomenon (Dawdy & Gupta, 1997, p. 274) and is already well-established in many fields (Ayalew & Krajewski, 2017; Commenges, 2018; Eagleson, 1972; Lague, 2014; Loewer, 2020; McCuen & Smith, 2008; Palmer & Williams, 2008; Parascandola & Weed, 2001; Sudakov et al., 2022). However, despite numerous hydrology studies investigating climatic and catchment controls of extremes (Macdonald et al., 2022; B. Merz et al., 2022; Sivapalan et al., 2005), attention remains directed on predictions via fitting frequency distributions to time series (e.g., Opere et al., 2006) or understanding anthropogenic impacts using predominantly mathematical or statistical methods (e.g., Dhasmana et al., 2023). Instead, a stochastic physics approach integrating environmental 22 and anthropogenic controls of frequency distributions is urgently needed for more reliable quantification of risk, especially given nonstationarities and limited record lengths, and for design of NBS. The upper tail of frequency distributions represents the most extreme events, with the shape of this tail linked to a system’s sensitivity to change, especially in literature outside of hydroclimatology. “Lighter-tailed” systems are fragile, losing from environmental variations (or anthropogenic disturbances) while “heavier-tailed” systems are “antifragile,” gaining from variability (Taleb, 2012; Taleb & Douady, 2013). Although governing mechanisms of tail behaviour differ across hydroclimatic variables, Taleb's (2012) distinction between fragility and antifragility can be used to predict a hydroclimatic system’s sensitivity to disturbance. However, despite frequency distributions being ubiquitous throughout hydroclimatology, their tail behaviour and implications are often overlooked. Studies that examine tail behaviour within a stationary framework typically link high-magnitude events to heavier tails, suggesting that this tail behaviour is more consequential for producing more extreme events (B. Merz et al., 2022) although lighter tails suggest highly sensitive regimes following a disturbance (Taleb, 2012; Taleb & Douady, 2013); even under small changes in magnitude, “boundedness” of distributions (i.e., a lighter tail that appears to reach an upper limit) leads to large frequency changes following a disturbance (Fischer et al., 2023) (see Figure 2.2). Similarly, aggregation of flood-generating factors more easily yields heavier tails than maintains lighter tails (B. Merz et al., 2022), further emphasizing fragility of lighter tails. Consequently, these two tail behaviours have contrasting implications on a regime’s fragility and response to change. For example, whether the current 100-year event becomes a 5-year or 50-year event depends greatly on pre-disturbance 23 tail behaviour and its shift to the post-disturbance distribution. Therefore, to reliably quantify risk and support risk management, how should the physics of extremes be understood? Figure 2.2 Sensitivity of lighter and heavier tails under nonstationarity. A nonstationary distribution is portrayed using “snapshots in time” at different stages across the modelled period, showing how magnitude–frequency relationships evolve with varying intensities of anthropogenic activity. This conceptual drawing shows example changes in magnitude (light green, dashed) and frequency (dark green, dashed) between an earlier “snapshot” with less anthropogenic activity (blue) and a later “snapshot” with greater anthropogenic activity (red) under lighter (A) and heavier (B) tails. The 100-year event undergoes a larger change in frequency under lighter tails (i.e., to a 5-year event) than under heavier tails (i.e., to a 50-year event). Additionally, even though tails are an asymptotic property of the distribution, most studies assess tail behaviour in the pre-asymptote. For instance, in hydrology, sample sizes typically span only a few decades (L. Hu et al., 2020), but they are primarily used to model the upper tail including up to the 100- or 200-year event (B. Merz et al., 2022), exacerbating its likelihood of mischaracterization (Fisher & Tippett, 1928). Given these pre-asymptotic practices (e.g., use of pre-asymptotic samples to model the pre-asymptote or even asymptote), known sensitivity of lighter tails, and the global surge in extremes, another crucial question is raised: 24 can such dramatic frequency changes be a manifestation, at least in part, of a pre-disturbance distribution that is inherently milder than previously thought? This chapter thus investigates how hydroclimatic extremes should be studied and why some regimes may be more sensitive than others to change. Using floods as an illustrative example, it is guided by the following questions: 1. How should the physics of floods be understood scientifically? 2. Could dramatic increases in frequencies of flood extremes stem, at least in part, from a natural flood frequency curve (FFC) which is more lighter-tailed than widely assumed? 3. How can a frequency-centric perspective and a sound understanding of flood controls be used for flood management? Section 2.2. will discuss the methods used to conduct this literature synthesis, after which section 2.3 discusses the need for a causal, stochastic physics approach for understanding risk, and hence the upper tail of the frequency distribution. The following sections discuss the environmental (2.4) and anthropogenic (2.5.2) controls of the upper tail of the FFC, including implications of tail behaviour under change (2.5.1). Finally, section 2.6 re-examines a key assumption of upper tails in hydrology, provides suggestions to guide scientific and professional practice, and discusses implications for flood management. 2.2 Methods This chapter consists of a literature review which brings together key insights from hydroclimatology and beyond to advance understanding and prediction of extremes, as well as to provide suggestions to guide future research. The Scopus database was used in November 2023 to search for literature that directly investigated how anthropogenic climate change or LULC changes alter likelihoods of hydroclimatic extremes. The keywords “attribution”, “flood”, 25 “drought”, “wildfire”, “heat”, “temperature”, “compound”, “climate change”, “urbanization”, “forest”, and “harvest” were used, with appropriate search terms abbreviated with (*) and connected through the Boolean operators “AND” or “OR” as necessary. Titles and abstracts were screened for relevance, then full texts of appropriate papers were examined for final suitability. Only studies with a direct quantification of change or frequency distributions relating event magnitudes to frequencies were retained. Direct quantifications of change include: • The risk ratio (i.e., the probability of an event of a certain magnitude occurring under factual conditions to that under counterfactual conditions) (e.g., Stott et al., 2004), • The fraction of attributable risk (i.e., 1 −1𝑟𝑖𝑠𝑘 𝑟𝑎𝑡𝑖𝑜 which suggests how many event occurrences could be attributable to human activity) (e.g., Fischer & Knutti, 2015), and • A change in frequency expressed in years or X-fold changes (e.g., Johnson & Alila, 2023). These quantifications are the most common methods of reporting change in these studies. This process yielded 112 studies for consideration (see Table A.1). The variable or event which inspired the analysis, geographic location, and changes in frequency were tabulated. These studies were used to summarize trends in hydroclimatic extremes, anthropogenic controls of floods, general behaviours of statistical “tails” representing extreme events, and to examine any possible linkages between tail behaviour and system sensitivity to change. High-profile methods-oriented studies and those outlining socioeconomic impacts throughout hydroclimatology were not formally analyzed, but were incorporated for context and additional insights. These additions shed light on the field’s key methodological principles and insights such as the linkages between magnitude and frequency, the EVT framework, and effects of changing mean and variance on extreme events. 26 To provide a physically based understanding of floods, this chapter also synthesizes hydrology papers investigating climatic, physiographic, and anthropogenic controls of variance, skewness, and the flood frequency distribution (FFC) relating flood magnitudes to frequencies. Keywords such as “flood frequency”, “variance”, “skew”, “light” and “heavy” were combined with those of controls, including “climate”, “snow”, “rain”, “arid”, “humid”, “seasonality”, “mixture”, “ENSO”, “PDO”, “oscillation”, “physiography”, “slope”, “aspect”, “topography”, “elevation”, “size”, “area”, “shape”, “storage”, “soil”, “permeability”, “forest”, “storage”, and “reservoir” to search for appropriate papers on the Scopus database in September 2023. Multiple searches were conducted, varying the controls keywords to search for 3-5 controls at a time, again using (*) and the Boolean operators “AND” or “OR” as necessary. The titles and abstracts were screened for relevance, then full texts of appropriate papers were examined for final suitability. However, as many studies examine several of these controls but these controls may not appear in the title or abstract, capturing relevant studies was challenging. Therefore, citations in papers which linked controls to their effects on the variance, skewness, or FFC were also further examined and included. These methods provided a total of 48 studies (see Table A.2). Relevant conclusions were tabulated, including geographic locations, control(s) examined, and the influence(s) of stated control(s) on the variance, skewness, and/or FFC. General conclusions from these studies are discussed, noting any inconsistencies amongst these studies. Finally, additional insights from the modern science of causation, quantum physics, and other sciences are included (but not formally analyzed) to highlight similarities between hydroclimatology and other sciences. Insights from finance and climate science literature are also brought in to suggest novel connections between statistical distributions representing hydroclimatic systems and their sensitivity to change. 27 2.3 The need for a causal, stochastic approach 2.3.1 Integrating physics into hydroclimatic risk prediction: a stochastic approach A rigorous quantification of risk requires a causal framework due to the entangled nature of drivers within Earth systems (Runge et al., 2019; Swain et al., 2020). Multiple drivers may superimpose on a time series (e.g., concurrent climate and LULC changes on flood peaks) (Johnson & Alila, 2023), making trend detection difficult when conventional statistical tests are applied to raw data (Runge et al., 2019), especially under limited record lengths (Yue et al., 2002). Similarly, correlational analyses can yield ambiguous and misleading results under multiple superimposing drivers while causal methods can isolate effects of a disturbance, identify cause and effect relationships, and separate the direct from the indirect (Martínez-Sánchez et al., 2024; Runge et al., 2019). This principle was articulated by Klemeš (1978, p. 297), who emphasized that, “…knowledge is not identical with the sum of empirical facts and their descriptions by empirical laws, but arises through an ability of the human mind to discover causal relationships between these empirical laws, i.e., its ability to understand nature.” He further articulated that this means progressing beyond mere observations and descriptions of phenomena to the “discovery of their underlying causal structure” (Klemeš, 1978, p. 285). In the science of extremes, a causal investigation of risk requires a probability-based approach accounting for the “multiple and chancy” nature (Karhausen, 2000, p. 59) of hydroclimatic phenomena (Pham & Alila, 2024). It uses probability to understand physics (Rubin, 2003; WMO, 2012) and anchors physical understanding in the framework of frequency distributions (Dawdy et al., 2012; R. Merz & Blöschl, 2008). This stochastic (or quantum) approach accounts for both stochasticity (randomness) and complexity (from multiple causes) of 28 nature (Parascandola & Weed, 2001; Strevens, 2014), which are characteristics of flood generation (Klemeš, 1978; Pham & Alila, 2024; Rubin, 2003) and climatic extremes (Swain et al., 2020). Thus, a probability-based definition has been identified as highly suitable for causation because it accounts for the indeterministic (i.e., chancy) nature of the phenomenon of interest, the infinitely many combinations of conditions, processes, and events that may have led to it, incorporation of other unknown causes, and even the lack of knowledge to predict the phenomenon perfectly (Karhausen, 2000; Parascandola & Weed, 2001; Strevens, 2014). While such approaches, namely the EVT, are common in the science of extremes (Brunner et al., 2021; Stott et al., 2016), incorporation of physical knowledge required for a deeper, causal understanding is often overlooked when modelling and interpreting frequency distributions (R. Merz & Blöschl, 2008). Mathematical or statistical formulations may provide insights, but they are insufficient by themselves to provide physical explanations (Hirschboeck, 1999). As Klemeš (1986, p. 184) stated, “…no hydrologic, climatic, geologic, or other physical conditions are invoked in the analysis. The floods are stripped of all hydrologic context down to bleached skeletons of numbers giving their peak flows and these numbers are then subjected to the most rigorous treatments…, apparently in an unshakeable belief that the amount of this rigour determines the degree of hydrologic relevance of the results.” Despite being articulated by Klemeš several decades ago, this reliance on mathematical and statistical procedures persists and is criticized today (Dawdy et al., 2012; R. Merz & Blöschl, 2008). Similarly, hydrology is in dire need of a move away from simply detecting trends to a focus on attribution (i.e., identifying causes), which “is addressed, if at all, rather sloppily” (B. Merz et al., 2012, p. 1385). Thus, many have advocated for a move away from a “statistics only 29 approach” (Dawdy & Gupta, 1997, p. 274) to one which centres physical understanding (Dawdy et al., 2012; R. Merz & Blöschl, 2008). Stochastic hydrology boasts a 50-year history of understanding environmental controls of frequency distributions (Blöschl & Sivapalan, 1997; Eagleson, 1972) and skewness (McCuen & Hromadka, 1988; R. Merz & Blöschl, 2009), but to the best of our knowledge its connection to causality and causal inference has seldom been discussed (except by Klemeš (1978)) and incorporation of this knowledge into flood frequency analysis (FFA) is often neglected. In fact, while “most hydrologists would agree on the importance of hydrological reasoning in flood frequency estimation, most publications in the hydrological literature have focused on solving the estimation problem,” (R. Merz & Blöschl, 2008, p. 2) leading hydrology astray from its original aim of understanding and predicting probabilities of extremes (Klemeš, 1993). Thus, FFA must incorporate physical knowledge for more reliable predictions (Klemeš, 1986; R. Merz & Blöschl, 2008), especially given nonstationarities and limited record lengths (Dawdy et al., 2012). Similarly, in the wider attribution science literature, despite large changes in frequencies noted under anthropogenic activity (see Table A.1), environmental controls of frequency distributions are typically overlooked. The authors are not aware of studies linking tail heaviness of hydrometeorological variables (outside of floods) to their environmental controls, in line with Van Oldenborgh et al. (2022, p. 4) who stated that they are “not aware of a rigorous derivation of the origin of the upper bound” for temperature extremes. To address these gaps, a stochastic physics approach can be used to integrate physical understanding into the prediction of hydroclimatic extremes. Frequency distributions integrate interactions across space and time at the holistic macroscale (e.g., at the watershed scale for 30 floods) (Robinson & Sivapalan, 1997). Hence, identifying the distribution’s physical (environmental and anthropogenic) controls, how its tail behaviour and environmental controls influence its sensitivity to disturbances, and what physical characteristics may have led to an observed post-disturbance shift (or lack of shift) all provide physically meaningful information crucial for managing risk. While pre- and post-disturbance shifts are typically evaluated using a stochastic framework (i.e., quantile to quantile comparison), many interpretations of this change ironically utilize a deterministic (i.e., event to event) reasoning which more easily lends itself to conceptual fallacies, such as in forest hydrology (Alila et al., 2009; Pham & Alila, 2024), urban hydrology (e.g., Bian et al., 2020; Hettiarachchi et al., 2019), and reservoir analysis (e.g., Maheshwari et al., 1995). Consistent with the stochastic framework, this chapter will thus advocate for a causal, stochastic interpretation assessing how classes of events (i.e., flood quantiles) including small, medium, large, and apocalyptic events are changing. 2.3.2 A brief overview of tail heaviness As this chapter primarily serves as a guide to understanding and predicting extremes with particular attention to tail heaviness, a quick mathematical definition of lighter and heavier tails is first provided. The Extreme Value Theory (EVT) commonly used throughout hydroclimatology states that distributions converge asymptotically on one of the Gumbel, Fréchet, or Weibull families in their upper limit (Coles, 2001). Within this framework, the Generalized Extreme Value (GEV) distribution is most often used for annual maximum series data, with its cumulative distribution function as follows: 𝐺(𝑧) = exp {− [1 + 𝜉 (𝑧−𝜇𝜎)]−1𝜉}, defined where 1 + 𝜉 (𝑧−𝜇𝜎) > 0, 31 and where −∞ < 𝜇 < ∞, 𝜎 > 0, and −∞ < 𝜉 < ∞. Its location (𝜇), scale (𝜎), and shape (𝜉) parameters represent its centre, spread, and tail behaviour, respectively, with the upper-bounded Weibull distribution characterized by 𝜉 < 0, Gumbel by 𝜉 = 0, and Fréchet by 𝜉 > 0 (Coles, 2001). The Fréchet distribution is heavy-tailed with a polynomial decay at the upper tail, while the Gumbel is light-tailed with an exponential decay (El Adlouni et al., 2008; Merz et al., 2022). Similarly, the Generalized Pareto Distribution may be used for Peak-over-Threshold series, with its shape parameter 𝜉 also dictating tail behaviour (i.e., heavy-tailed if 𝜉 > 0, upper-bounded if 𝜉 < 0) (Coles, 2001). For an in-depth statistical discussion of heavier- and lighter- tailed distributions and generation of heavier tails, the reader is referred to El Adlouni et al. (2008) and Merz et al. (2022). EVT is an asymptotic theory and corresponding identification of tail behaviour requires a focus on the asymptote. Although the pre-asymptote is often considered more applicable for hydrological practice (Merz et al., 2022), a slow rate of convergence in the Gumbel distribution for instance can produce a heavier pre-asymptotic tail, while it is asymptotically within the Gumbel domain of attraction (Fisher & Tippett, 1928). Any mischaracterization of tail behaviour impairs the assessment of sensitivity of extremes to disturbances and hence, understanding of system fragility, leading Taleb (2009) to emphasize the danger in utilizing asymptotic theories outside of “idealized” (i.e., asymptotic) conditions. Thus, in conjunction with existing asymptotic theories, an asymptotic focus utilizing appropriate sample sizes is key. While shape parameters are most commonly used to identify tail behaviour, skewness is also commonly examined (Klemeš, 1978; McCuen & Smith, 2008). A skewed distribution does not necessarily suggest heavier tails, but skewness is directly linked to shape parameters in the GEV distribution for instance (Merz et al., 2022). Similarly, variance is incorporated within 32 mathematical equations of skewness (Chattamvelli & Shanmugam, 2023). Thus, linkages between shape parameters, skewness, and variability suggest similarities in their underlying physical controls, though to different extents. Additionally, mean and variance can be utilized to understand change in a post-disturbance frequency curve relative to its pre-disturbance curve. While changes in mean vastly influence frequencies of extremes (Mearns et al., 1984) by shifting the frequency distribution, changes in variability can be much more influential (Katz, 1993; Katz & Brown, 1992) as they lighten or steepen the distribution tail; increased variability increases steepness (i.e., “divergence” of the two curves) and decreased variability decreases steepness (i.e., “convergence”) (Beckers et al., 2002; Green & Alila, 2012; Pham & Alila, 2024). In this way, shape parameters most directly determine tail behaviour, but variance and skewness may be additionally evoked to understand physical controls of tail behaviour. 2.4 Environmental controls of the flood frequency curve’s upper tail 2.4.1 Overview A causal, physically based understanding of extremes requires consideration of natural and anthropogenic controls of frequency distributions. Establishing how natural controls yield the undisturbed state can help to infer a system’s inherent sensitivity and offer a baseline for understanding change, with subsequent quantification of anthropogenic influence allowing for prediction of risks and designing of cost-effective solutions. Examining physical controls of the FFC and its tail behaviour requires a holistic, macroscale approach, as highlighted by Robinson & Sivapalan (1997, p. 2981): “The flood frequency curve represents one of the most comprehensive and compact descriptions of a catchment's storm response. It is the culmination of interactions, across both time and space, between climatic inputs, that is, rainfall influxes and evaporative 33 effluxes (radiant energy), and properties of the catchment's landscape, for example, topography, soils, and vegetation.” Understanding and predicting flood extremes thus requires viewing interactions among climatic, physiographic, and anthropogenic controls holistically (see Figure 2.3), as any combination may amplify or attenuate streamflow response (Green & Alila, 2012; Johnson & Alila, 2023). Use of limited sample sizes also dominates hydrology, leading to difficulties in determining higher order moments (Klemeš, 1970) and tail behaviours (Bernardara et al., 2008; Merz et al., 2022). Thus, this thesis uses the terms “lighter” and “heavier” to showcase the “direction of influence” of each control without a direct association with formally defined “light” and “heavy” tails, respectively. The remainder of section 2.4 presents key influences of environmental controls highlighted throughout stochastic hydrology literature (see Table A.2). 34 Figure 2.3 Controls of the upper tail of the flood frequency curve (FFC). Conceptual drawing of climatic, physiographic, and anthropogenic controls of the upper tail of the FFC. The three groups of controls influence both each other (larger red arrows) and the upper tail (smaller arrows). For anthropogenic controls, only those with sufficient literature assessing their impacts on the FFC tail are considered. 2.4.2 Climatic controls of the upper tail Snow- or glacier- dominated regions exhibit decreased variability and lighter tails relative to rain environments (R. Merz & Blöschl, 2003, 2009; Pitlick, 1994). In these regions, higher baseflow conditions suggest greater diversion of runoff from quicker surface or near-subsurface routes (which typically contribute to flood peaks) towards slower subsurface pathways (Guo et al., 2014). These slower pathways act as a filtering mechanism, attenuating variability and increasing uniformity of flood peaks throughout the year (Blöschl & Sivapalan, 1997; Guo et al., 2014; R. Merz & Blöschl, 2009). A poorly draining catchment with low baseflow conditions would instead allow multiple precipitation events to interact and amplify flood response, increasing nonlinearity and tail heaviness (Blöschl & Sivapalan, 1997; Guo et al., 2014; 35 Robinson & Sivapalan, 1997). Additionally, limitations in daytime energy available for snowmelt constrain tail behaviour, producing lighter, upper-bounded tails in snow environments (R. Merz & Blöschl, 2003; G. Yu et al., 2022). In contrast, rain environments are unlikely to display upper bounds in the pre-asymptote (R. Merz & Blöschl, 2003; G. Yu et al., 2022). Whether this behaviour prevails in the asymptotic tail is likely watershed-size dependent and requires further investigation. Extremes can result from storms bringing strong convergence of water vapour, including high intensity (i.e., convective) or long-duration (i.e., frontal) storms (B. Merz et al., 2021; L. Yang et al., 2017). Higher rain fractions and convective activity increase tail heaviness for both precipitation (Araujo et al., 2023) and floods (Pitlick, 1994), thus yielding heavier FFCs even relative to areas with mixed rain and snow contributions (R. Merz & Blöschl, 2003). In a similar fashion, arid or semi-arid regions exhibit smaller runoff coefficients, higher variability, and heavier tails than humid regions. In arid catchments, floods typically result from high-intensity storms with limited spatial extent, with their decreased regularity increasing inter-annual variability in flood generation (Farquharson et al., 1992). With some years experiencing no floods or only minor floods, occasional extremes lead to higher coefficients of variation (CV) and skewness (CS) (R. Merz & Blöschl, 2009). Runoff coefficients also tend to be small (i.e., under dry conditions) but increase significantly during extreme events (R. Merz & Blöschl, 2009). Thus, in semi-arid regions where a few storm events generate much of the annual precipitation and/or where rainfall dominates flood generation, tail heaviness is increased (Beckers et al., 2002; Pitlick, 1994). Wetter catchments see lower CVs and CSs due to greater consistency of runoff coefficients and flood-producing events (R. Merz & Blöschl, 2009). These humid and/or snow-dominated catchments and those experiencing frontal storms are likely to 36 experience longer periods of precipitation, increased subsurface flow, and lighter FFCs (Pitlick, 1994). Additionally, when flood seasonality is present, the largest floods occur when high rainfall intensities and runoff coefficients (i.e., from wetter catchments) coincide, or are “in phase” (Sivapalan et al., 2005). When wetter seasons coincide with lower rainfall intensities, a lighter tail is produced (Sivapalan et al., 2005). Drier seasons coinciding with higher rainfall intensities would instead produce fewer small floods but with occasional larger events, increasing tail heaviness (Sivapalan et al., 2005). Any differences in flood generation mechanisms can produce a break in the FFC separating upper tail extremes from common events (Alila & Mtiraoui, 2002) through an inflection point (i.e., a change in slope) (Miniussi et al., 2023) or a sudden step change (Rogger et al., 2012). Breaks can be associated with a shift from subsurface to fast surface runoff or an increase in contributing area (see section 2.4.3) (Rogger et al., 2012), differences in storm types (e.g., synoptic to larger cyclonic storms) (Kusumastuti et al., 2007), and/or influences of natural variability (e.g., El Niño-Southern Oscillation (ENSO) conditions and monsoonal events) (Alila & Mtiraoui, 2002). While breaks in the FFC are typically linked to heavier tails (Kusumastuti et al., 2007; Macdonald et al., 2024), use of homogeneous distributions common to FFA (i.e., those assuming events are all identically distributed and consist of only one population or flood generation mechanism) under two or more flood populations may yield a poor fit at the upper tail, particularly under extreme outliers (Alila & Mtiraoui, 2002). Use of mixed distributions can improve characterization of upper tails under heterogeneities, underscoring the need for large sample sizes and knowledge of flood-generating processes (Alila & Mtiraoui, 2002). 37 Finally, both climatic and physiographic drivers influence the FFC, but climatic controls conveniently dominate at sufficiently high return periods. The GRADEX (GRADient of EXtreme values) concept assumes that flood volumes mimic the exponential tail of rainfall volumes after exceedance of watershed storage capacity (Naghettini et al., 2012). The FFC is shifted down relative to the rainfall curve such that flood volumes are consistently lower than rainfall volumes for the same return period (Naghettini et al., 2012). Other studies also suggest that flood skewness or tail behaviour more closely echo rainfall skew (McCuen & Smith, 2008) or tail behaviour (Macdonald et al., 2024) (respectively) after catchment saturation, with higher saturation thresholds indicating larger ratios of watershed storage to catchment wetness (Macdonald et al., 2024). Therefore, while both physiography and runoff generation modulate the FFC, exceedance of storage thresholds leads to a dominance of climatic influences on the most extreme floods (Macdonald et al., 2024), hence imposing the asymptotic behaviour of upper tails. 2.4.3 Physiographic controls of the upper tail Catchment physiography strongly modulates flood response to meteorological controls through its topography (i.e., slope, aspect, and elevation distributions), catchment shape and size, soil and bedrock characteristics, floodplain storage, and the presence of lakes, ponds and wetlands (see Table A.2). These physiographic characteristics shape the FFC’s upper tail primarily through their influence on watershed storage. Many controls such as subsurface characteristics and the presence of lakes, ponds, wetlands, and floodplains directly influence the availability of above- (i.e., as a snowpack) and below-ground storage of snow, snowmelt, and rainwater. Others such as heterogeneity in elevation, slope, and aspect influence the relative timing and efficiency with which stored precipitation is delivered as runoff to the channel 38 network (i.e., synchronization or desynchronization of runoff), influencing variability and tail heaviness. Increased storage capacity decreases variability and delays occurrence of “kinks” or “step changes” (i.e., breaks) in the FFC to larger return periods (Macdonald et al., 2024; Rogger et al., 2012). Step changes can occur when catchment storage thresholds are exceeded, generating faster surface runoff through saturation excess (Rogger et al., 2012). Storage capacity can be increased through deeper soils and permeable geology, both of which promote infiltration, increase baseflow, and support deeper flowpaths (M. Chen et al., 2021; Kusumastuti et al., 2007). Additionally, when water-retaining features such as lakes, wetlands, and ponds are present, their retention capacity must be filled (Blöschl & Sivapalan, 1997) before water can be “spilled” to other down-gradient storages and conveyed to streams (i.e., the “fill-and-spill” mechanism) (McDonnell et al., 2021). This reduces quick flow and variability (Johnson & Alila, 2023) and can drive skewness towards negative values (Klemeš, 1970; McCuen & Smith, 2008). Even catchments containing wide, active floodplains can yield lighter tails (Archer, 1981); for floods above bankfull stage, overbank storage of floodwaters can produce lighter tails relative to floodwaters contained within the channel (Archer, 1981). Thus, increasing catchment storage capacity and its spatial heterogeneity can yield lighter tails and step changes which are less prominent or occur only at the highest return periods (Rogger et al., 2012). When storage capacity is low and spatially uniform, threshold exceedances can yield notable step changes at earlier return periods (Rogger et al., 2012), heavier tails (Macdonald et al., 2024), and a greater influence of climatic controls (Macdonald et al., 2024). Additionally, nonlinear expansion of runoff generating areas increases synchronous delivery of flow to the drainage network. Areas generating runoff are typically small for 39 common floods, but larger floods involve simultaneous activation of large contributing areas, leading to changes in runoff generating mechanisms (e.g., from saturation excess to infiltration excess) (Sivapalan et al., 1990) and/or nonlinearity in runoff generation (Rogger et al., 2012). Resulting synchronous delivery of runoff can yield step changes in the FFC (Rogger et al., 2012). However, in a British study, a similar nonlinear growth was noted only in dry catchments (Archer, 1981). Increased soil moisture conditions in wetter upland catchments led to an initial increase in steepness (Archer, 1981). When the contributing area consisted of most or nearly all of the catchment, flood tails mainly depended on rainfall growth rates, leading to step changes with lighter tails (Archer, 1981). Together, these studies demonstrate that the dynamic nature of runoff contributing areas and stream networks (Prancevic & Kirchner, 2019) may yield nonlinearities which influence tail behaviour. Tail behaviours are also controlled by catchment area. Smaller catchments are more likely to experience greater storm coverage and catchment saturation (R. Merz & Blöschl, 2009; Sivapalan et al., 1990; L. Yang et al., 2017). High-intensity, short-duration storms with limited spatial extent (e.g., convective storms) typically form their upper tails (R. Merz & Blöschl, 2009; L. Yang et al., 2017). Increased spatial uniformity in storage capacity is also likely, promoting simultaneous activation of larger source areas and notable step changes (Rogger et al., 2012). In larger catchments, long-duration storms with greater spatial extent are required to first fill up retention capacity before flood generation can occur (Blöschl & Sivapalan, 1997; R. Merz & Blöschl, 2009; L. Yang et al., 2017). Their heterogeneous storage capacity is also likely to prevent synchronized saturation over large areas, yielding less notable step changes (Rogger et al., 2012). Increased importance of flood routing and baseflow conditions further attenuate the catchment’s response to rainfall variability (Blöschl & Sivapalan, 1997; H. J. Wang et al., 2023), 40 especially with asynchronous delivery of flow (Beckers et al., 2002). These differences suggest tendencies towards lighter tails and lower skew and variability in larger catchments (L. Yang et al., 2019). While some studies did not find a dependence of tail behaviour on catchment area (Smith et al., 2018), other climatic and physiographic factors varying with catchment size (Benson, 1962) may obscure this relationship, underscoring the need for a holistic evaluation of controls and their interactions. Other controls such as heterogeneity in elevations and slope-aspects influence energy, storage, and efficiency at which stored precipitation is delivered to the stream network. Topographical heterogeneities influence patterns of radiation input (i.e., higher on south-facing slopes in the northern hemisphere), soil moisture (i.e., higher on north-facing or shaded slopes in the northern hemisphere), and snowpack accumulation, determining above- and below-ground storage in both rain and snow environments (Duncan, 1995; Q. Liu et al., 2024; Moreno et al., 2016). These heterogeneities also influence synchronization or desynchronization of runoff (Hendrick et al., 1971), and thus of variability and tail heaviness. North-facing aspects (in the northern hemisphere) experience increased natural shading, limited shortwave irradiance, and limited evaporation rates relative to south-facing aspects, inducing differences in snowmelt timing (in snow environments) and runoff generation (in rain and snow environments) (Duncan, 1995; Ellis et al., 2011; Green & Alila, 2012; Moreno et al., 2016). Increased aspect heterogeneity may thus promote asynchronous, “time-staggered” snowmelt and floods while minimal heterogeneity may promote synchronized melt and floods (Green & Alila, 2012; Hendrick et al., 1971). Similarly, gradual snowmelt from lower to higher elevations can desynchronize runoff while subdued terrain synchronizes melt, increasing variability and tail heaviness (Green & Alila, 2012; Hendrick et al., 1971; Johnson & Alila, 2023). While more 41 research is required (particularly in rain environments), low elevation and/or less heterogeneous catchments may experience heavier tails due to increased rainfall contributions or synchronized runoff. Conversely, high elevation and/or heterogenous catchments may display lighter tails due to a greater influence of snowmelt or asynchronous runoff. Similarly, synchronization of runoff can increase variability and tail heaviness in circular catchments while elongated catchments desynchronize runoff (Ayalew & Krajewski, 2017). Even though H. J. Wang et al. (2023) found that flood tail heaviness increased most readily with spatial rainfall variability for elongated catchments, these catchments displayed greater symmetry in runoff routing distances, ultimately synchronizing flows. In circular and less elongated catchments, asymmetric routing led to asynchronous delivery of flow and increased buffer capacity, preventing increases in tail heaviness (H. J. Wang et al., 2023). Therefore, these studies all underscore the role of catchment shape in synchronizing or desynchronizing runoff. Together, these watershed characteristics combine with climatic controls to influence tail behaviour. For example, integrating climatic and physiographic attributes into a single index led to catchments with “erratic regimes” (i.e., a lower ratio of flood-producing rainfall events to mean watershed recession rate) displaying increased variability, step changes, and steeper FFCs, contrasting “persistent regimes” with decreased variability and lighter tails (Basso et al., 2016). In this way, a holistic, physical understanding of tail behaviour requires assessing interactions among climatic and physiographic controls, with emphasis on climatic controls for the largest floods in catchments with little storage capacity. Incorporating this physical knowledge supports a rigorous, stochastic interpretation of the upper tail, relates environmental characteristics to a system’s sensitivity or response to disturbances, and aids in the design of nature-based solutions. 42 2.5 Tail behaviour under change 2.5.1 Implications of tail behaviour: Magnitude-centric or frequency-centric? Perhaps the most critical implication of tail behaviour is its sensitivity to disturbance, which shapes how society perceives, adapts to, and mitigates risk. A well-established concept in climate change science is that a small increase in magnitude yields a larger, disproportionate increase in frequency, especially for extremes (Allen & Ingram, 2002; Mearns et al., 1984). Changes in frequency can therefore be much more impactful than changes in magnitude and the former are often the foundation of attribution science (Lloyd & Shepherd, 2020) (see Table A.1). While concepts of lighter tail fragility and heavier tail antifragility originate in finance literature (Taleb, 2012; Taleb & Douady, 2013), their application to hydroclimatology suggest that highly sensitive lighter tails may experience large changes in event frequencies under nonstationarity (Fischer et al., 2023; Johnson & Alila, 2023) (see Figure 2.2). Hence, a magnitude-centric approach and improper use of heavier tails for lighter-tailed distributions can underestimate change and diminish the perceived efficacy of NBS for managing flood risk, especially for extremes. Yet, much of hydrological reasoning remains magnitude-centric and stationary, particularly when evaluating tail behaviour. These studies (e.g., B. Merz et al., 2022) often compare the sharp rise in magnitude of heavier tails (per rise in return period) to the slower increase in magnitude of lighter tails, utilizing a stationary framework rather than assessing change between pre- and post-disturbance curves under nonstationarity. As high-magnitude events seemingly correspond to lower return periods, extremes are said to be more likely, arise unexpectedly, and be more difficult to predict under heavier tails (B. Merz et al., 2022; H. J. Wang et al., 2023). However, given known nonstationarities and large frequency changes, it is 43 worth re-thinking whether a magnitude-centric, stationary quantification of risk suffices in the 21st Century. Could a frequency-centred, nonstationary analysis better highlight sensitivity to change and support resilient adaptation? A similar debate concerns NBS. While initial installation may be costly (Chan et al., 2018), NBS are generally deemed cost-effective (Vicarelli et al., 2024) and can yield high annual savings in flood loss prevention (Atkins, 2015), bolstering the global push for NBS (Faivre et al., 2017; Leanza, 2022). However, NBS are also accompanied by magnitude-centric skepticism regarding their effectiveness against large floods (i.e., when flood magnitudes exceed watershed storage capacity) (Dadson et al., 2017; Kay et al., 2019; Kiesel et al., 2023; Lallemant et al., 2021). Yet, NBS continues to gain traction worldwide; China has pioneered the “Sponge City Program” (Chan et al., 2018) while Europe’s NBS-friendly policies and initiatives, particularly in the Netherlands and Denmark, have led to afforestation, stripping of pavement, and installations such as “sponge parks” and retention basins (Faivre et al., 2017; Jongman, 2018; Leanza, 2022). While the efficacy of NBS for mitigating smaller floods is well-acknowledged (Kay et al., 2019; Lallemant et al., 2021), the key question remains: are they truly inadequate for preventing large floods or have misunderstandings and misguided assumptions in the science of extremes prevented society from benefitting from the value of NBS for mitigating against large events? While concerns surrounding reliable quantification of risks and cost-effective adaptation strategies remain unsolved and require further research, particularly on the efficacy of NBS for flood extremes, existing literature on anthropogenic controls of the FFC may offer a starting point. 44 2.5.2 Anthropogenic controls of the flood frequency curve’s upper tail Many studies assessing anthropogenic impacts focus on climate change, forest cover changes, urbanization, and dam or reservoir construction, with conventional wisdom leading many to suggest decreasing influences of such activities on the largest floods (Barnes et al., 2023; Brath et al., 2006; Maheshwari et al., 1995). In fact, the human and scientific tendency for event-by-event reasoning suggests that when flood magnitudes exhaust available storage capacity, forest cover and dams/reservoirs have little or no influence on floods (Dadson et al., 2017; Maheshwari et al., 1995). Similarly, urbanization (or even the role of catchment moisture in urbanized landscapes) is typically perceived to have little influence on the largest floods (Bian et al., 2020; Brath et al., 2006; Hettiarachchi et al., 2019). However, the stochastic (probabilistic) framework assesses differences between pre-disturbance (i.e., with little or no anthropogenic influence) and post-disturbance (i.e., under anthropogenic change) curves, allowing for detection and attribution of changing risk (Gillett et al., 2022; Johnson & Alila, 2023; Prosdocimi et al., 2015). The corresponding stochastic interpretation emphasized by this subsection instead highlights how climatic and LULC changes alter flood magnitudes and (most notably) frequencies using flood quantiles. Forests intercept both rainfall and snowfall, enhancing interception moisture loss and decreasing snow accumulation underneath the canopy, in addition to drawing up soil moisture through their roots (Alila et al., 2009; Duncan, 1995). By reducing moisture available for runoff (equivalent to increasing available watershed storage) and decreasing flood peaks (Alila et al., 2009; Duncan, 1995), the forested FFC is typically shifted “down” relative to one without forest cover (or typically shifted “up” under deforestation) (see Figure 2.4) (Duncan, 1995; McEachran et al., 2021; Reynard et al., 2001; Te Linde et al., 2010). However, this effect, as explained 45 earlier, could be exacerbated, reduced, or sometimes reversed depending on physiographical characteristics (e.g., Pham et al., 2025). For example, deforestation in watersheds with little environmental (e.g., aspect and elevational) heterogeneity can amplify changes in net radiation and stored precipitation, thus synchronizing snowmelt and runoff, increasing variability, and leading to divergence of the two FFCs (see section 2.4.3) (Green & Alila, 2012; Pham & Alila, 2024). Overall, a consistent upward (downward) shift under deforestation (forest cover), even at the upper tail, suggests increased (decreased) magnitudes and frequencies in both rain and snow environments (Duncan, 1995; Johnson & Alila, 2023). In fact, lack of a clear threshold event size beyond which forest cover has no influence on floods supports the hypothesis that effects of forest cover (or deforestation) remain notable for extreme events (Birkinshaw et al., 2011; Duncan, 1995; Green & Alila, 2012; Reynard et al., 2001; Te Linde et al., 2010), though more research is needed utilizing a stochastic framework. Even though large floods may occur with and without forest cover, forest cover significantly decreases flood frequencies as a whole (Barnes et al., 2023). Thus, contrary to perceptions that NBS involving afforestation or reforestation are ineffective for the largest floods (Dadson et al., 2017), a stochastic interpretation suggests that forest cover interacts with physiography to greatly influence flood frequencies and magnitudes, even of the most extreme events. 46 Figure 2.4 Upward and downward shifts of a hydroclimatic distribution following a disturbance. The shift from a pre-disturbance (blue) to a post-disturbance (red) FFC are shown in the case of an upward shift (A) or downward shift (B) following anthropogenic influence. Example changes in magnitude (light purple, dashed) and frequency (dark purple, dashed) are shown for each scenario. While changes in variance can lead to convergence or divergence of tails, or the two tails may even superimpose on each other, these scenarios are not depicted here for simplicity. Presence of dams and reservoirs increases catchment storage capacity and attenuation of flows, delaying catchment saturation to higher return periods. After exceedance of storage capacity, the reservoir-containing tail resembles the no-reservoir tail but shifted “downwards” such that the two tails are parallel (Ayalew et al., 2015; Fleischmann et al., 2019; Xiong et al., 2020). Their vertical difference represents water storage within reservoirs (Fleischmann et al., 2019). Even though individual flood magnitudes may exceed storage capacity (Xiong et al., 2019), added capacity through dams and reservoirs stores more runoff, decreasing overall frequencies and magnitudes as evidenced by upper tail “parallelism” (Fleischmann et al., 2019). Thus, contrary to common perceptions (Maheshwari et al., 1995), dams, reservoirs, and similar 47 NBS can shift the FFC tail “downwards”, decreasing flood frequencies and magnitudes for both common and extreme events. Urbanization increases impervious cover of the watershed, decreases infiltration of precipitation into the subsurface, and promotes fast runoff, shifting the FFC “upwards” relative to its pre- (or reduced-) urbanization curve (Brath et al., 2006; Prosdocimi et al., 2015; Reynard et al., 2001). Shifting of the FFC, generally without convergence of the two tails, increases flood magnitudes and frequencies across all return periods (Brath et al., 2006). Finally, climate change-induced shifts in the FFC depend highly on region-specific climatic trends. Many have highlighted increased flood risk through an “upward” shift of the FFC, with large changes in frequency (Ross et al., 2021; Schaller et al., 2016). This is often linked to a higher water-holding capacity of a warmer atmosphere and precipitation increases (Schaller et al., 2016) surpassing any increase in evapotranspiration (Ross et al., 2021), increasing overall flood risk (Gillett et al., 2022). Other regions, however, may see decreased flood risk (i.e., FFC shifted “down”) (Dhasmana et al., 2023) or unclear trends. In some areas, opposing influences of greenhouse gases and sulfate aerosols on precipitation extremes have led to unclear trends, but future reductions in sulfate aerosols are expected to increase flood frequencies and magnitudes (S. Philip et al., 2019). Similarly, snow-influenced regions may see increased rainfall levels counterbalanced by decreased snowpack accumulation and spring snow cover, leading to little (or unclear) change between the two FFCs (Teufel et al., 2019). Together, these studies underscore the importance of considering local and regional climatic trends when assessing flood risk. Overall, urbanization, deforestation, and climate change can increase flood risk (or potentially decrease risk depending on climatic trends) while forest cover and added storage 48 capacity decrease risk through a “downward” shift in the tail. Akin to GRADEX, this vertical difference reflects added storage capacity through dams or reservoirs or loss of moisture under the forest canopy, both of which allow for greater storage of precipitation and attenuation of floods. Perhaps similar NBS can shift the tail “down”, helping decrease flood risk (i.e., frequencies and magnitudes) under otherwise-increasing risks by anthropogenic activities and impacts such as urbanization and climate change (Hettiarachchi et al., 2019; Te Linde et al., 2010), presenting promising future research directions. If extremes exist such that NBS have negligible influence on floods, only a stochastic approach to both modelling and interpretation can provide a rigorous answer. 2.6 Where do we go from here? 2.6.1 Guiding science and professional practice Knowledge of tail behaviour is typically generated using limited, pre-asymptotic record lengths under a stationary framework, hindering proper understanding of controls of floods and reliable prediction of associated risks, which increases the likelihood of upper tail mischaracterization. Although several distributions may appear to fit data well under limited record lengths, large differences in their tail behaviours greatly impact prediction of extremes (Alila & Mtiraoui, 2002; Klemeš, 1986). Even one or a few extremes plotting above (or below) the curve fitting the body of the sample unduly affects tail characteristics (i.e., heavier versus lighter), particularly under pre-asymptotic conditions (Bernardara et al., 2008; R. Merz & Blöschl, 2009). While these problems are well recognized, the use of sample sizes generally under 50 years persists in hydrology (L. Hu et al., 2020), as longer records are generally not available. Given the urgent need for reliable prediction of large floods for flood management, 49 scientific and professional practice must aim for a rigorous, asymptotic characterization of the upper tail. Limited sample sizes can be extended using stochastic or deterministic simulations, supplementing observational records. By mimicking statistical characteristics of observations, stochastic simulations produce longer time series and generate larger numbers of extremes for study (Brunner et al., 2021). Similarly, despite vulnerability to many data-related, structural, and parameter uncertainties (Renard et al., 2010), deterministic models can utilize climatic and streamflow inputs to simulate longer time series (Brunner et al., 2021; Stott et al., 2016), complementing observed records. For instance, the inability of climate models to resolve processes finer than their grid resolution can cause “models to drift compared with reality” (Palmer & Williams, 2008, p. 2423). This has prompted calls to shift away from relying solely on ensemble means and statistics to the integration of models, observational records, and physical understanding (Stott et al., 2016; S. P. Xie et al., 2015). Similarly, perhaps the real need in hydrological sciences is not necessarily that of more data (Nearing et al., 2021) but rather incorporation of hydrological reasoning (Dawdy et al., 2012; R. Merz & Blöschl, 2008) using the correct causal (stochastic) framework for a deeper understanding of tail behaviour, especially for modelling asymptotic upper tails. Concepts such as GRADEX (where “hydrological reasoning is part of a formal method” (R. Merz & Blöschl, 2008, p. 10)) can be used to allow for physically based modelling and making of attribution statements, especially under limited record lengths. In hydrology, other methods can also be used to supplement records, identify trends, and generate FFCs. Derived FFCs simulate streamflow using a statistical rainfall model, a deterministic rainfall-runoff model, and a mathematical model depicting the transformation of rainfall to peak flows (Kusumastuti et al., 2007; Sivapalan et al., 2005). For ungauged 50 watersheds and those with insufficient record lengths, gauges at nearby watersheds can be used to increase effective record length through regional FFA (Schaefer, 1990). Regional FFA allows for substitution of spatial randomness with that of time, yielding an effective record length greater than that of any one station used in the regional FFA (Avance et al., 2021; Schaefer, 1990). Another approach consists of a meta-analysis of available streamflow records to identify trends due to anthropogenic disturbances (N. K. Singh & Basu, 2022). Moreover, paleoflood hydrology uses geological evidence to estimate magnitudes and frequencies of past floods while historical flood hydrology considers observations before systematic records began (Benito & O’Connor, 2013; Blöschl et al., 2020). As both are associated with large uncertainties, they are typically combined to increase reliability and help constrain upper tails (Benito & O’Connor, 2013; Blöschl et al., 2020). Additionally, while FFA traditionally used in science and professional practice assumes stationarity, recognition that past trends are no longer representative of the future (B. Merz et al., 2021; Milly et al., 2008) has led to nonstationary analyses and attribution science methods gaining momentum in hydrology (McEachran et al., 2021). Despite increased uncertainties (F. Lu et al., 2020), nonstationary FFA can incorporate climatic and land use-related covariates, allowing for detection of relevant drivers and improved modelling of observed time series (M. Chen et al., 2021; Xiong et al., 2020). While the shape parameter is often assumed constant due to difficulties and high uncertainties at the tail (Salas & Obeysekera, 2014), more rigour in modelling can allow for a proper understanding of how anthropogenic controls alter the FFC and flood risk (Hani et al., 2025; Ouarda & Charron, 2019). Additionally, current use of nonstationary methods focuses on trend detection with attribution “treated as an appendix to detection studies” and supported mainly through qualitative reasoning (B. Merz et al., 2012, p. 51 1382). Instead, nonstationary frequency analysis can be used to make more robust attribution statements which quantify cause and effect relationships (Johnson & Alila, 2023; Prosdocimi et al., 2015). Furthermore, as conventional FFA assumes a homogeneous population of floods, forcing such assumptions onto records containing multiple populations increases potential for mischaracterization of upper tails, thus mixed distributions may be more suitable alternatives (Alila & Mtiraoui, 2002; G. Yu et al., 2022). Additionally, with climate and LULC changes exerting greater influences on current and recent past events relative to those in the distant past, could this present another source of mixture in the FFC, increasing likelihood of tail mischaracterization? This possibility may warrant careful investigation in both scientific and professional practice. While we are unaware of any hydrologist disputing the fact that the past no longer represents current and future conditions, fitting a stationary, homogeneous FFC to the flood record (e.g., BGC Engineering Inc., 2022) conflates extremes of the distant past with those of the recent past, highlighting a large discrepancy between established knowledge and scientific practice. By addressing the above challenges, hydroclimatological sciences and professional practice obtain a deeper understanding of upper tails and produce more reliable projections under changing conditions. 2.6.2 Re-examining current understanding of tail behaviour Flood frequency literature has predominantly yielded heavier tails (B. Merz et al., 2022), although some have long called for a closer examination of the assumption of such heavy-tailed behaviour (Smith, 1987). This assumption emanates from a body of literature in which limited sample sizes are available and stationary approaches are used to fit statistical distributions. When 52 extreme events occur within a short observational period (B. Merz et al., 2022), heavier tails may, at least in part, reflect artifacts of short sample sizes and stationary approaches. With nonstationarity leading to once-rare extremes now becoming much more probable and heavier tails influenced largely by one or a few extremes under short observational periods, are the heavier tails we observe, in fact, truly heavy or are once-rare extremes from lighter-tailed distributions now becoming the norm? In fact, the “antifragile” (Taleb, 2012; Taleb & Douady, 2013) nature of commonly assumed heavy tails in floods appears seemingly at odds with large observed increases in frequencies under anthropogenic change (see Table A.1). For example, watersheds in many regions around BC (Loukas et al., 2000; Waylen & Woo, 1983), especially snow-dominated and wetter regions, are considered to have comparatively lighter tails than arid areas (Beckers et al., 2002) or areas with greater rainfall influence (Zaerpour et al., 2024). In the recent past, BC has also seen large changes in extreme event frequencies under anthropogenic activities, such as 7-fold (Kuraś et al., 2012) or 10-fold increases (Johnson & Alila, 2023) following forest harvesting or 2- to 4-fold increases under climate change (Gillett et al., 2022) in the 100-year event. These large frequency changes which accompany even small changes in magnitude (Allen & Ingram, 2002) have been noted to be significant under lighter tails in hydrology (Johnson & Alila, 2023) and especially climatology (Fischer et al., 2023; Van Oldenborgh et al., 2022), in line with the known “fragility” of lighter tails elsewhere (Taleb, 2012; Taleb & Douady, 2013). Could the large increases in flood frequencies under anthropogenic change thus hint at an underlying sensitivity of natural systems to change? As much of hydrological research has been dominated by limited sample sizes and stationary frameworks, obtaining a proper answer requires further investigation using 53 nonstationary, asymptotic approaches. In the absence of stochastic reasoning, however, neither a reliance on statistical theory nor a sole focus on fitting distributions can rigorously support or refute such hypotheses due to challenges with record lengths and nonstationarity. Causal, stochastic physics must be incorporated to overcome these challenges for more reliable, physically based modelling. While using heavier-tailed distributions to prevent underestimation of maxima may seem appealing (Moccia et al., 2021), it impedes obtaining a reliable understanding of the upper tail and, hence, its risks under change. A stationary, magnitude-centric approach misses potentially large increases in frequency, as lighter tails can yield alarming reductions in return periods under nonstationarity. Therefore, a reliable quantification of upper tails is key for flood prediction and management. 2.6.3 Implications for risk assessments, planning, and decision-making Decision-making, policy implementation, and land use and management planning must be preceded by assessments of how projected or proposed anthropogenic activities will alter hydroclimatic risks. These assessments should aim to predict the combined influences of all relevant anthropogenic drivers (James et al., 2019) which may exert an influence on the extreme(s) of interest over the relevant spatiotemporal scales. For example, for floods, projections should aim to identify the combined effects of climate change and LULC changes such as forest harvesting, land conversion, and urbanization. Effects on both magnitudes and frequencies should be examined, as well as any other important attributes such as duration and inundated area (Guido et al., 2023; Poff et al., 1997). While much of the discourse regarding extreme event attribution currently focuses on climate change (see Table A.1), a sole focus on climate change may misrepresent change, fail to identify other key drivers, and divert attention away from LULC practices which could help mitigate these risks (Lahsen & Ribot, 2022). To 54 account for simultaneous climatic and LULC changes, models can be used to simulate different scenarios (Reynard et al., 2001) and techniques such as nonstationary FFA can be used on both observations and modelled data for flood projection (Johnson & Alila, 2023). Quantifying extreme event magnitudes and frequencies should be based on causal stochastic reasoning, along with the use of appropriate sample sizes and consideration of nonstationarity. This reasoning supports quantitative estimates by allowing for more reliable projections given a catchment’s climatic and physiographic properties, especially where record lengths are limited. An example where addressing the multiple root causes of flooding may show promise for effective flood management is BC. Flood management in BC has traditionally relied upon engineering-based solutions which appear ill-suited to the realities of the 21st Century. For example, a dike assessment in its Lower Mainland region (which contains the largest population in the province) found that 69% of dikes were classified as Poor to Fair and only 13% as Fair to Good, although none fully met the province’s standards due to increasing flood risks since dike reconstruction (Fraser Basin Council, 2016). This highlights both serious shortcomings in the current engineering-based approach and an opportunity to implement longer-term solutions addressing root causes of increased flood risk. Climate change typically receives the spotlight in influential technical (BGC Engineering Inc., 2022; Fraser Basin Council, 2016) and governmental (Government of British Columbia, 2024) reports with little or no attention to other LULC causes of flooding, despite documented causal linkages of the latter and often substantial impacts (e.g., Green & Alila, 2012; Johnson & Alila, 2023). A shift towards more effective LULC management which targets underlying drivers of flood risk increases could thus present a more resilient path forward. 55 In any assessments of change or proposed flood management strategies, how changing magnitudes and frequencies for small, medium, and large events will impact key values should then be considered holistically. Magnitudes may be important in legal contexts to estimate the fraction of losses attributable to defendants (Callahan & Mankin, 2025) or in engineering and construction purposes (Flint et al., 2017; Hudson, 2021) where design flood magnitudes may be updated accordingly through nonstationary approaches. However, frequency changes may be more compelling from other impacts perspectives. In engineering applications, flood infrastructure should account not just for increased magnitudes and frequencies of extremes, but also the geomorphic consequences of small and medium flows increasing in frequency, such as increased scour and aggradation (Wardhana & Hadipriono, 2003; Wolman & Miller, 1960). A changed hydrological regime from sustained increases in small and medium flows may also change river geomorphology and its associated habitats (Poff et al., 1997; Wolman & Miller, 1960). This can make conditions less suitable for both aquatic and riparian species which are dependent on a river’s natural flow regime (Bower et al., 2022; Poff et al., 1997), highlighting the need to identify and support vulnerable species. Assessments of changing magnitudes and frequencies further provide a starting point for identifying vulnerability and exposure (James et al., 2019; Young et al., 2019), such as upland harvesting leading to larger inundated areas downstream. With even small increases in magnitude, large changes in flood frequencies which were once highly unlikely may be especially impactful for property owners. Frequency can also be more impactful for communicating change, especially through attribution-style statements (Brunner et al., 2021); while smaller increases in m3/s of floods may be challenging to conceptualize, communicating larger increases in frequency through a change in return periods 56 or x-fold increases may be easier to understand and more meaningful to the public (Swain et al., 2020). For resource management, lighter-tailed watersheds may indicate the need for careful resource extraction and a greater need for mitigation of downstream flood risks. This can motivate more effective LULC policies which decrease vulnerability and exposure downstream, such as preventing new development in projected high-risk areas. Resource extraction or harvesting activities can be conducted in ways that desynchronize floods (e.g., sizes and locations of harvested areas supporting gradual, staggered snowmelt to mitigate increases in large floods) and leave key areas intact for flood control (e.g., landscapes which act as natural flood buffers). Downstream interventions such as retention basins can also increase storage capacity and mitigate flood risk (Chan et al., 2018; Leanza, 2022). Although management practices and interventions may not prevent floods (Barnes et al., 2023), stochastic reasoning suggests that even a small reduction in flood magnitude may greatly reduce the frequency of a flood extreme (e.g., 20-year to 70-year event), which may constitute a meaningful decrease in flood risk for communities and the public. In this way, this chapter emphasizes that a proper understanding of the physics in a causal, stochastic framework allows for reliable prediction of risks and the design of appropriate solutions for adaptation and mitigation. In the words of Good (2007, p. 407), “We are controlled by nature, but by discovering causes we can recover some of the control.” 57 Chapter 3: Can forests mitigate floods of all sizes? Evaluating the foundations of a decades-long scientific controversy 3.1 Introduction Increasing flood frequencies and magnitudes worldwide (e.g., Bian et al., 2020; Gillett et al., 2022; Hirabayashi et al., 2021; Schaller et al., 2016) are causing the loss of human and non-human lives, damaging infrastructure, provoking lawsuits, and disrupting key sectors such as transportation and agriculture (Lee & Parfitt, 2022; Mortimer & Visser, 2004; Newman & Noy, 2023). This has led to intensified debate over underlying drivers of flood extremes and who should be held accountable. In both scientific (see Table A.1) (e.g., Dhasmana et al., 2023; Gillett et al., 2022; Hirabayashi et al., 2021; Teufel et al., 2019) and policy-making arenas (Government of British Columbia, 2024; Lahsen & Ribot, 2022), anthropogenic climate change is often considered the main driver of large flood events. While land use and land cover (LULC) drivers such as urbanization (e.g., Prosdocimi et al., 2015) and forest harvesting (e.g., Johnson & Alila, 2023) play notable roles in altering flood magnitudes and frequencies, these drivers typically receive less attention. Yet, appropriate LULC management can notably decrease flood magnitudes and frequencies and their socioeconomic impacts (e.g., Lallemant et al., 2021), which is all the more needed under increasing climate-related risks (see Table A.1). Therefore, the roles of both climate and LULC changes in increasing flood magnitudes and frequencies, and how effective LULC management may be used to mitigate these increases, must be examined through scientific methods which clearly attribute changing flood regimes to their drivers. Solutions for flood mitigation are increasingly drawing from nature. Terms such as nature-based solutions (NBS) (Duarte et al., 2024; Manes et al., 2024) and natural flood 58 management (NFM) (Lane, 2017) advocate for holistic flood mitigation, while providing multiple socioeconomic benefits and ecosystems services (Creed et al., 2019; Dadson et al., 2017; Ferrario et al., 2024; Grafton et al., 2024; Harvey et al., 2024; Lallemant et al., 2021; Vicarelli et al., 2024; Yao, 2024; K. Yu et al., 2025). They generally aim to increase catchment storage capacity and temporarily store precipitation, reducing peak discharge (Penning et al., 2023; Pérez-Corredor et al., 2024). Many of these interventions include the maintenance of or increase in forest cover, stemming from the understanding that forested areas evaporate and transpire precipitation back into the atmosphere, increase infiltration into soils, and recharge groundwater which maintains dry season baseflow (Hurkmans et al., 2009; I. L. Martins & Lyra, 2022; Penning et al., 2023). Consequently, NBS have already been implemented, or are on their way to implementation, in many countries around the world (Chan et al., 2018, 2024; Faivre et al., 2017, 2018; Frantzeskaki & McPhearson, 2022; Jongman, 2018; Leanza, 2022). Despite increasing public support for NBS, forest hydrology remains divided on the effectiveness of forest cover on flood mitigation, especially for large events (i.e., larger than the 10-year event) (Buttle, 2011; Calder et al., 2007; CPAWS Southern Alberta, 2020; Environment Agency, 2018; Fahey & Payne, 2017; Stratford et al., 2017). This divide originates from decades of studies that investigate how a change in forest cover, typically through harvesting of a treatment catchment, alters downstream floods (Alila et al., 2009; e.g., Bathurst et al., 2011). These studies adopt the Before-After, Control-Impact (BACI) approach, where two neighboring watersheds of similar physical and climatic characteristics are first monitored before any disturbance and their streamflow are calibrated through linear regression (e.g., Bathurst et al., 2018, 2020). The treatment watershed is then disturbed (e.g., harvested) while the control remains undisturbed (e.g., Bathurst et al., 2018, 2020). Observed streamflow peaks in the control 59 watershed are used to calculate peaks had the treatment not occurred (e.g., Bathurst et al., 2018, 2020). These estimated peaks are compared with those of the harvested watershed (e.g., Bathurst et al., 2018, 2020). Ensuing conclusions about the effects of forest cover on floods (or lack thereof) have thus informed scientific perspectives on the use of forest-based solutions for mitigating large floods. Most of forest hydrology remains skeptic of the mitigative effects of forest cover on larger floods (e.g., Bathurst et al., 2011; Dadson et al., 2017; Xiao et al., 2022), shaped largely by conclusions from the deterministic scientific approach which dominate forest hydrology. When analyzing results from the BACI design, deterministic studies define the effects of forest cover on flood magnitude as the difference in magnitude of an event when the control and treatment watersheds are subject to the same storm or snowmelt event. These studies conclude that forest cover mitigates small and medium floods but cannot mitigate large events, as effects of forest cover decrease with increasing flood size (see Tables B.1 and B.3). Many deterministic studies even suggest an event size beyond which forest removal has little or no effect on floods, which can be as short as the flood event with a recurrence interval of 2 years (MacDonald & Stednick, 2003; Thomas & Megahan, 1998) but is typically on the order of 5 to 10 years (Bathurst et al., 2011, 2020; Birkinshaw et al., 2011; Harr, 1986). Deterministic studies have been conducted around the world, including in the Americas (Bathurst et al., 2011; Harr, 1986; Moore & Scott, 2005), Europe (e.g., Bathurst et al., 2018, 2020), Asia (e.g., Guillemette et al., 2005 and citations therein), and Oceania (e.g., Bathurst et al., 2020; Guillemette et al., 2005 and citations therein). They span rain-dominated (Bathurst et al., 2011), rain-on-snow (Harr et al., 1979, 1982; Rothacher, 1973; Thomas & Megahan, 1998), and snow-dominated (Moore & Scott, 2005; Troendle & Olsen, 1994; Van Haveren, 1988) environments in small (Harr et al., 1979; 60 Harr & McCorison, 1979) to large (Moore & Scott, 2005) catchments, with some studies suggesting forests have little influence on large catchments in general (e.g., Thomas & Megahan, 1998). In this way, the deterministic approach has been applied over many hydroclimatic regimes and catchment sizes. The limited ability of forests to mitigate large floods is thus regarded as the dominant conclusion in forest hydrology (Bathurst et al., 2011; Cooper et al., 2021; DeWalle, 2003; van Dijk et al., 2009; Xiao et al., 2022) which is echoed in forest hydrology textbooks (e.g., Brooks et al., 2012; Chang, 2012) and fuels skepticism that forests can be incorporated into NBS to mitigate large floods (Bathurst et al., 2011; Dadson et al., 2017; DeWalle, 2003; Kaimowitz, 2005; Kay et al., 2019; Xiao et al., 2022). Skepticism that forests can mitigate large floods is also found in influential policy papers (e.g., Environment Agency, 2018; Kaimowitz, 2005; Stratford et al., 2017). Some of these policy papers suggest that the idea of forests mitigating (large) floods are manufactured by the media and conservationists with little scientific backing (Calder et al., 2007; Calder & Aylward, 2006; CIFOR & FAO, 2005; Hamilton, 1990), possibly as a “red herring” to oppose development projects entailing logging (DeWalle, 2003). As the idea that forests mitigate large floods is “far more widespread in public opinion than in scientific circles” (Xiao et al., 2022, p. 7), this suggests a disconnect between scientific and public perceptions (Calder & Aylward, 2006; CIFOR & FAO, 2005; DeWalle, 2003; Mortimer & Visser, 2004; Xiao et al., 2022) and between scientific perception and policy (Bhattarai & Conway, 2021). Scientific results from a less dominant approach both within and outside of forest hydrology challenge the dominant scientific conclusion that forests have little effects on large floods. These stochastic studies draw on probability concepts which capture the stochastic nature of floods (Klemeš, 1978; Pham & Alila, 2024; WMO, 2012). When analyzing results from the 61 BACI experiment, stochastic studies instead define effects of changing forest cover on flood magnitude as the difference in magnitude of peak flows between the two watersheds which are of the same frequency. Stochastic studies investigate how a change in forest cover changes flood frequencies for a given flood magnitude, or vice versa. Stochastic results indicate that forest cover has the potential to mitigate small, medium, and large floods (see Tables B.2 and B.3), even when deterministic methods applied to the same data suggest otherwise (see Table B.3). Stochastic studies have been conducted in rain-dominated (Birkinshaw et al., 2011; Lallemant et al., 2021; Pham et al., 2025; Preti et al., 2011), mixed (Hurkmans et al., 2009), and snow-dominated (Green & Alila, 2012; Kuraś et al., 2012; Schnorbus & Alila, 2004, 2013) catchments, and from small (Pham et al., 2025) to large (Huang et al., 2018; Hurkmans et al., 2009; Lallemant et al., 2021; Reynard et al., 2001; Te Linde et al., 2010) catchments, emphasizing conclusions that directly oppose deterministic predictions and lending support to the use of forests for flood mitigation. Interestingly, persisting scientific controversy and skepticism has not prevented the promotion or implementation of NBS including forests, either acknowledging this disagreement (Bradshaw et al., 2009; Creed et al., 2019; Penning et al., 2023) or not (Faivre et al., 2017, 2018; Mansourian et al., 2009; K. Yu et al., 2025). Proponents of NBS have retained the intuitive claim that forests mitigate flood events. Could this claim “contain more truth than has been acknowledged by the scientific community” (Bruijnzeel, 2005, p. 1825), particularly by forest hydrology? This scientific controversy may speak to three issues. There is (1) difficulty in predicting future changes in flood regimes, especially for adaptation and design of solutions. Prediction requires sound understanding of floods and their drivers, leading to (2) difficulty in causally 62 teasing out effects of changing forest cover on floods, especially amidst other superimposing anthropogenic drivers such as climate change, urbanization, and other LULC changes. Finally, (3) there is difficulty in communicating the role of forests on floods to lawmakers and the public. As summarized by Hewlett (1982, p. 546), “[H]ydrologists have understandably been confused by the difficulties inherent in describing the nature and frequency of floods to laymen, who are apt to have little patience with probability statements....But among ourselves we must drop back to rigorous language in order to discuss and trade information about land-use causes and flood effects.” Addressing these three difficulties, and thus the scientific controversy, requires a critical assessment of each framework’s (i.e., stochastic and deterministic) strengths and limitations. While some argue that both approaches can co-exist (Bathurst, 2014; Birkinshaw, 2014; Lewis et al., 2010), policymakers cannot enact effective solutions with contradictory scientific advice (i.e., forests do and do not mitigate large floods). Science must thus present clear guidance as to whether forests play a role in flood mitigation. A rigorous scientific framework with suitable research questions (Leopold & Langbein, 1963), falsifiable hypotheses (Kirchner, 1989; Popper, 1935), and controlled experiments is the foundation for understanding, predicting, and communicating change. Only by capturing the nature of flood generation and the causal relationships between floods and their drivers (e.g., changes in forest cover) in a changing climate (K. Yu et al., 2025) can hydrology resolve the scientific controversy and support flood management. Thus, forest hydrology must evaluate which conclusion(s) stem from a rigorous scientific approach based on the suitability of the deterministic and stochastic frameworks to answer whether forests can mitigate floods. 63 To ensure that reliable science guides LULC policies and flood management, this chapter advocates for a scientifically rigorous forest hydrology approach. It is guided by the following questions: 1. To causally study changes in flood regimes and their drivers, what key aspects of flood generation must be accounted for in scientific studies? 2. What is the suitability of the underlying research questions, hypotheses, and experimental procedures of the deterministic and stochastic approaches to causally answer the question of whether forests mitigate large floods? 3. What is the effect of the presence, or absence, or forest cover on large floods? This chapter first discusses the methods used to conduct the literature synthesis (section 3.2). Incorporating insights from the philosophy of science, climatology, and wider hydrology, section 3.3 then emphasizes that a causal approach is needed to disentangle how different anthropogenic activities are changing floods. Section 3.4 examines the suitability of the research question, hypothesis, and experimental design of both deterministic and stochastic frameworks to answer whether forests can mitigate floods. Building on this critical evaluation, Section 3.5 reframes the dispute, highlighting which conclusion(s) are scientifically rigorous and can thus inform policymaking and solution design. If science is to meaningfully inform flood policy and management, it must adhere to the highest standards of causal reasoning and testability. This is perhaps best stated by Platt (1964): “Whether it is hand-waving or number-waving or equation-waving, a theory is not a theory unless it can be disproved. That is, unless it can be falsified by some possible experimental outcome… A failure to agree for 30 years [or many decades in the forests and floods disagreement] is public advertisement of a failure to disprove.” 64 3.2 Methods This chapter presents a literature review drawing primarily from literature within forest hydrology and throughout wider hydroclimatology. It aims to rigorously understand the relationship between forest cover and flood mitigation and to provide suggestions to guide future research. First, it synthesizes literature examining the effects of changing forest cover on flood peaks using one of two primary methods of data analysis (deterministic and stochastic). The keywords “forest”, “harvest”, “flood”, “peak”, and “hydrology” were used, with (*) and the Boolean operators “AND” or “OR” as necessary, to search for relevant studies in the Scopus database in January and July 2025. Titles and abstracts were first examined for relevance, then full texts were examined if deemed relevant. Studies which investigated other hydrological variables (e.g., water yield) without any connection to peak flows were discarded. Only papers which linked forest cover, or change in forest cover, to flood peaks were retained. 23 studies using only the deterministic approach, 17 studies using only the stochastic approach, and 9 studies using both the deterministic and stochastic approaches were synthesized. Their location(s), catchment size(s), hydroclimatic regime(s), record length(s), and key conclusions were tabulated. Dominant conclusions from each approach are discussed. These studies, along with literature discussing deterministic and stochastic research methods, were further examined for their typical research questions, hypotheses, and analysis procedures. Strengths and limitations of each approach are discussed by incorporating insights from wider hydrology and climate science, including: • The nature of flood generation, and of hydroclimatic extremes in general • Stochasticity as an inherent property of nature • Causally understanding anthropogenic impacts on hydroclimatic variables 65 3.3 Causally investigating effects of forest cover changes on floods 3.3.1 Causality is central to the science of extremes Whether forest cover—rather than climate change or other LULC changes alone—is a main driver of downstream flooding has received much attention in ongoing debates. Policy reports criticize the public and media for oversimplifying “overlapping influences” of anthropogenic activities when discussing whether forests mitigate floods (CIFOR & FAO, 2005, p. 3). The same, if not higher, standards must also apply to science: has its dominant understanding emerged from a rigorous framework which causally isolates the effects of forest cover changes on floods? In Earth systems science, multiple superimposing drivers act on the variable or system’s response of interest, convoluting cause-and-effect relationships (Runge et al., 2019; Su et al., 2023). This is particularly pronounced in observed time series (e.g., streamflow records), where only a causal inference approach can distinguish cause-and-effect relationships amidst other drivers influencing the time series (Johnson & Alila, 2023; Runge et al., 2019; Su et al., 2023). Combined with their profound societal impact, the rarity (and consequent sampling errors) of flood extremes makes causal attribution not just important but necessary for reliable scientific insight. Identifying changes in forest cover (as opposed to climatic or other LULC changes) as a cause of downstream flooding thus requires causally isolating the effects of forest cover changes on floods. Identifying the extent to which anthropogenic activities causally modify hydroclimatic events, especially extremes, must be a shared pursuit across forest hydrology, wider hydrology, and climate science. Similar to how increased flood events prompted forest hydrologists to investigate their drivers, increasing frequencies and intensities of hydroclimatic extremes 66 (including floods) inspired climate science’s specialized branch of attribution science (Stott et al., 2016). Attribution science attempts to causally link (or attribute) anthropogenic climate change to shifts in hydroclimatic regimes (see Table A.1), helping motivate effective policies and hold greenhouse gas emitters accountable (Allen, 2003). These studies may investigate how human activity has increased likelihoods and magnitudes for a single type of event (e.g., Stott et al., 2004) or for the entire distribution of the variable from small to large events (i.e., general attribution) (e.g., Kirchmeier-Young et al., 2017). While attribution science originated from climate science, its ability to causally identify drivers of changing flood regimes has broadened its application beyond climate change (Gillett et al., 2022; Hirabayashi et al., 2021; S. Philip et al., 2019; N. Singh & Chinnasamy, 2021) to LULC changes such as urbanization (Bian et al., 2020; Prosdocimi et al., 2015) and forest removal (Johnson & Alila, 2023). In fact, attribution is at the core of forest hydrology’s current dilemma; whether anthropogenic changes in forest cover have altered downstream flood regimes, especially for extreme events, is a question of attribution. With many blaming logging operations for perceived increases in flooding (Bathurst, 2014) and the need to implement effective NBS, the role of forest cover (or removal) on flooding must be causally attributed. This raises a critical question: what is the appropriate scientific framework in forest hydrology to causally attribute (and predict) changing flood regimes? 3.3.2 What is the appropriate causal framework? A strong scientific framework must capture key characteristics of the system under study. In the case of floods, this involves capturing its multiple flood-generation factors, each of which are stochastic (i.e., random) and dynamically interact with each other. 67 Floods are fundamentally natural phenomena which occur with or without climatic and LULC changes and are thus governed naturally by multiple controls. Rainfall input, snowpack accumulation, antecedent catchment wetness, and energy available for snowmelt are all climatic controls driving floods (Gillett et al., 2022; Green & Alila, 2012; Pham & Alila, 2024; Sharma et al., 2018; Sivapalan et al., 2005; Sturdevant-Rees et al., 2001). Physiographical controls modulate climatic influences by modifying both above-ground (e.g., a snowpack) and below-ground (e.g., within soils) storage of water, synchronizing or desynchronizing snowmelt throughout the watershed, and influencing the efficiency with which runoff is delivered to the channel network, as described in section 2.4.3. For example, deeper and permeable soils, larger catchment area, and the presence of water-retaining features such as lakes, wetlands, and ponds all increase available storage capacity, promote deeper flowpaths, and attenuate runoff and hence flood peaks (Archer, 1981; Blöschl & Sivapalan, 1997; M. Chen et al., 2021; Kusumastuti et al., 2007; R. Merz & Blöschl, 2009; L. Yang et al., 2017). Homogeneity or heterogeneity in slope-aspect, elevation, and other environmental characteristics also helps synchronize or desynchronize (respectively) timings at which stored water is delivered to the channel network, influencing runoff and hence flood peaks (Duncan, 1995; Ellis et al., 2011; Q. Liu et al., 2024; Moreno et al., 2016). This is strongly demonstrated in snow environments, where gradual, “time-staggered” snowmelt from lower to higher elevations and from south-facing to north-facing aspects (in the northern hemisphere) can desynchronize melt, “dampening” flows (Ellis et al., 2011; Green & Alila, 2012; Johnson & Alila, 2023). These multiple natural controls vary randomly (i.e., stochastically) in space and time. As climatic controls vary stochastically (e.g., spatial and temporal variation in precipitation and energy), the role that physiography plays in influencing the hydrological response also becomes 68 stochastic. For instance, catchment storage in water-retaining features such as lakes, wetlands, floodplains, and soils coinciding with a precipitation or snowmelt event is the legacy of past stochastic weather conditions and wetness states, thereby making catchment state stochastic (Robinson & Sivapalan, 1997). Similarly, source areas and stream networks expand and contract as a response to precipitation inputs, thus they also vary stochastically in both space and time (Dunne, 1983; Prancevic & Kirchner, 2019; Rogger et al., 2012). In this way, flood generation is shaped by the stochastic nature of floods, including stochastic spatiotemporal variability in their controls. Many key flood-generation processes (e.g., hydrological connectivity) are also best encapsulated at the macroscale (McDonnell et al., 2021; Rogger et al., 2017), thus spatiotemporal variability must be incorporated through causal, stochastic methods at appropriate scales in both space and time. Furthermore, these stochastic climatic and physiographic controls interact with each other dynamically through space and time. This means that controls cannot be hierarchically organized by importance because any combination of them may amplify or attenuate streamflow (Green & Alila, 2012; Johnson & Alila, 2023; Pham et al., 2025) and can lead to nonlinearities in flood generation (Rogger et al., 2012). For example, in snow environments, annual flood peaks are a product of any combination of snow accumulation and snowmelt rates (in addition to other controls), thus any one factor may not always dominate flood generation (Alila et al., 2009). In this way, if science is to understand and predict floods, it must capture the multiple, stochastic, and dynamically interacting nature of its drivers. This understanding is not unique to hydrology; first originating from quantum mechanics, understanding stochasticity as an inherent property of the system rather than a mere consequence of lack of knowledge is now widespread across the sciences (Klemeš, 1978). Stochastic 69 hydrology captures the stochastic nature of floods (Eagleson, 1972; Yevjevich, 1974) and centres physical understanding into experimental design and interpretation to support scientifically sound analysis (Dawdy et al., 2012; Eagleson, 1972; Klemeš, 1978; R. Merz & Blöschl, 2008; Nearing et al., 2021), although its connection to causal inference has rarely been discussed in hydrology literature (with the exception of Klemeš (1978)). In quantum mechanics, this recognition has shifted the focus away from deterministic predictions of single measurements to probabilistically predicting outcomes based on the entire set of measurements (Albert, 2000; Ballentine, 1970; Loewer, 2015, 2020). This shift in quantum mechanics contributed to a broader rethinking of causality and an interest in stochastic approaches across scientific disciplines, including stochastic hydrology (Klemeš, 1978). Stochastic approaches have thus become central to stochastic hydrology (Dawdy et al., 2012; Eagleson, 1972; Yevjevich, 1974), attribution science (Allen, 2003; Otto, 2017; S. Philip et al., 2020; Swain et al., 2020), and other sciences (e.g., Lague, 2014), where they are identified to account for the “multiple” and “chancy” (i.e., stochastic) nature of phenomena (Karhausen, 2000, p. 59) and be highly suitable for causal studies (Commenges, 2018; Loewer, 2015, 2020; Monod, 1972; Parascandola & Weed, 2001; Sudakov et al., 2022). In hydrology, the multiple, stochastic, and dynamically interacting nature of flood controls suggests that an event of a given magnitude can be stochastically generated by many combinations of drivers. For events of the same magnitude (e.g., when stored water nears watershed storage capacity), combinations of controls leading to these events will differ. This is a long-understood concept in attribution science; any one event can never occur the same way again with its unique combination of ingredients, conditions, and processes leading up to it (Otto, 2017; S. Philip et al., 2020), but events of the same magnitude may reoccur with different 70 combinations of drivers. Prediction thus requires shifting away from a deterministic focus on singular events to a stochastic focus on classes of events (i.e., quantiles) to assess whether event magnitudes are changing (Otto, 2017). Furthermore, as magnitude and frequency are “two sides of the same analytical coin” (Swain et al., 2020, p. 525), any event of a given magnitude occurs with its corresponding frequency. Event classes thus represent the various stochastic combinations in which events of a given magnitude and frequency are generated. In fact, both magnitude and frequency must be evoked to understand how anthropogenic activity influences flood quantiles. Although high-magnitude events may still occur by chance without human-mediated changes (Otto, 2017), human activities change their likelihoods of occurrence (Allen, 2003; Otto, 2017). Equivalently, rare events (e.g., 100-year event) may change in magnitude due to anthropogenic activity. For instance, attribution science acknowledges that rising temperatures modify factors required for high-magnitude events to occur (Fischer & Knutti, 2015). This makes overall conditions more favourable for extremes and such events thus become more probable (Fischer & Knutti, 2015). By evoking both magnitude and frequency, these studies compare the likelihood of an extreme event class occurring under today’s “factual” conditions (i.e., with anthropogenic influence) to its likelihood under “counterfactual” conditions (i.e., with minimal anthropogenic influence), or assesses how the entire distribution of a variable (i.e., multiple classes) changes under factual conditions relative to counterfactual conditions (Otto, 2017; Swain et al., 2020). In this way, magnitude and frequency are inseparable; both must be evoked to understand if high-magnitude events are increasing in frequency, or if low-frequency events are increasing in magnitude, with frequency required to reveal highly sensitive hydrological regimes (as suggested in Chapter 2). 71 3.4 Evaluating two scientific approaches to the forest and floods disagreement 3.4.1 Evaluating scientific merits and flaws While only the stochastic framework captures the multiple, stochastic, and dynamically interacting nature of flood drivers and allows for making causal claims, critically assessing both deterministic and stochastic approaches can allow a deeper understanding of their scientific rigor. By scrutinizing their research questions, hypothesis strength, and experimental details (see Figure 3.1), this section assesses the suitability of each approach to answer whether forests can mitigate (large) floods. Additionally, many studies assess the role of forest cover on peak flows through harvesting. Although associated operations like road construction and soil compaction may influence flood peaks, this chapter focuses on tree-related effects of forest cover change, such as changes in interception, evapotranspiration, and shading. 72 Figure 3.1 Conceptual diagram showing major differences between the deterministic (left) and stochastic approaches (right) for the same property (middle) when studying impacts of forest cover changes on flood peaks. Although both utilize the Before-After, Control-Impact (BACI) experimental design, differences in ensuing data analysis are shown by highlighting how these approaches differ for various properties of the analysis procedure. 3.4.2 Critically assessing the deterministic approach Forest hydrology dominantly uses a deterministic approach, with its research question asking, “How does the presence or absence of forest cover alter flood magnitudes for a given rain- or snow-generated event?” (Bathurst, 2014). In the data analysis procedure following the BACI experimental setup, observed streamflow peaks in the control watershed are used to identify corresponding peaks in the treatment watershed by the same rainfall or snowmelt event, 73 leading to event-wise chronological pairing between the two catchments (e.g., Alila et al., 2009; Bathurst et al., 2018, 2020). Comparing each observed treatment peak to the expected value derived from the corresponding control peak and calibration equation (i.e., streamflow peak had the disturbance not occurred), any difference in these values represents the treatment effect (e.g., Alila et al., 2009; Bathurst et al., 2018, 2020). The rest of section 3.4.2 examines the strength of the underlying research question, hypothesis, and experimental details of this approach. Firstly, the deterministic research question is upheld by a perceived need to answer the general question, “Would that flood have occurred, or would it have been as big, if the forest cover had not been lost?” (Bathurst, 2014, p. 2756). Although this question is claimed to be relevant to communities impacted by large floods and answerable only through deterministic methods (Bathurst, 2014; Birkinshaw, 2014), this same type of question is considered “ill-posed” outside of forest hydrology (Stott et al., 2004). It is scientifically invalid to deterministically ask whether a given event would have occurred, or by how much it has been exacerbated, due to anthropogenic activity (James et al., 2019) as large events may occur naturally by chance. Additionally, as extremes result from multiple stochastic drivers which interact dynamically with each other, understanding human influence may only be framed stochastically (Pham & Alila, 2024; Swain et al., 2020). This concept is fundamental to climate and attribution science (Allen, 2003; Fischer & Knutti, 2015; Stott et al., 2004; Swain et al., 2020). In their landmark study of the 2003 European heatwave, Stott et al. (2004, p. 610) make the following statement, “It is an ill-posed question whether the 2003 heatwave was caused, in a simple deterministic sense, by a modification of the external influences on climate—for example, increasing concentrations of greenhouse gases in the atmosphere—because almost any such weather event might have occurred by chance in an unmodified climate.” 74 Other prominent climatologists have echoed this statement, including that “no single weather event exclusively results from anthropogenic influence in a deterministic sense” (Fischer & Knutti, 2015, p. 563) and that science “will never be able to say, at any confidence level, that human influence has contributed x% to an actual weather event” (Allen, 2003, p. 892). In addition to attribution science’s explicit remarks, such questions are hardly asked in wider hydrology. With its broader discipline (i.e., hydrology) and sister disciplines (i.e., climate science, attribution science) denouncing the use of such guiding questions to investigate highly analogous topics, forest hydrology’s adherence to them is increasingly scientifically untenable. Furthermore, the research question is tied to an uncontrolled experiment that does not isolate the role of forest cover changes on floods. To understand whether forests can mitigate floods, a causal link must be established by isolating the effects of forest cover changes on floods. However, deterministically fixing by one factor fails to account for other factors also recognized to influence flood generation (Alila et al., 2009; Alila & Green, 2014b, 2014a; Green & Alila, 2012; Sturdevant-Rees et al., 2001). For instance, by only accounting for storm size, a ceteris paribus conclusion is reached: when all other flood-generation factors are held constant, increasing storm size increases flood magnitudes (Pham & Alila, 2024). However, this does not explain how forest removal influences the whole of these factors and their interactions, which define the flood response. In rain environments, antecedent catchment wetness also controls flood generation, therefore floods are not a function of rainfall alone. In snow environments, both snowpack accumulation and energy available for snowmelt additionally control floods and can be altered by forest removal (Ellis et al., 2011; Green & Alila, 2012; Johnson & Alila, 2023). Yet, chronological event-wise pairing does not account for how combinations of these multiple flood-generation factors differ for all flood events. By accounting for only one “slice” of flood-75 generation processes at a time, the ceteris paribus approach does not capture how all factors, each of which varies stochastically, interact to yield flood events and how the whole of these interactions is influenced by human activity. Given the presence of unaccounted factors (e.g., antecedent moisture), the effects of changing forest cover on floods are not isolated, and the causal link is not established. Without isolating this relationship, magnitude conclusions regarding the role of forest cover on floods are rendered incorrect. It also disregards frequency, which often displays much larger changes than magnitude (Allen & Ingram, 2002). Therefore, the deterministic approach is not relevant to answer whether forests can mitigate floods because the latter assumes that all drivers outside of changing forest cover are effectively controlled. The ill-posed research question and non-causal experiment are also associated with a self-fulfilling hypothesis, contradicting philosophy of science principles. While a false hypothesis can narrow down possibilities, untestable theories are “empty” and “misleading” (Kirchner, 1989, p. 226). In the latter, “confirmation of the hypothesis does not restrict the sphere of possibilities because the set of excluded data (data that would have been inconsistent with the hypothesis) is empty”. Thus, theories become “doomed to inevitable and inconsequential success” (Kirchner, 1989, p. 226). The idea that forest cover has minimal impact on large flood magnitudes (Bathurst et al., 2011), with some studies reporting a threshold event size beyond which forests have no effect on flood mitigation (e.g., Birkinshaw et al., 2011; L. H. MacDonald & Stednick, 2003; Thomas & Megahan, 1998), illustrates a self-fulfilling hypothesis. Many deterministic studies, especially those which examine effects on larger floods, show convergence (or apparent convergence) of control and treatment regression lines for the largest event(s) (see Figure 3.2 and Tables B.1 and B.3). This expected convergence is also incorporated into conceptual figures outlining conclusions of deterministic forest hydrology research in published literature (Bathurst 76 et al., 2011, 2020). Physically, the convergence of regression lines suggests that a decrease in forest cover primarily increases small and medium-sized floods, with little impact on large events following catchment saturation (Bathurst et al., 2011, 2020; Birkinshaw et al., 2011; Harr, 1986; MacDonald & Stednick, 2003; Thomas & Megahan, 1998). When a large storm coincides with wet conditions or greatly overwhelms storage capacity, the flood magnitude in the forested catchment must be similar to that in the logged catchment due to little influence of any storage capacity differences on this single event (Birkinshaw et al., 2011; Chang, 2012; Xiao et al., 2022; Zhao et al., 2024). This must lead to convergence at this peak flow value. In fact, given typical record lengths of a few decades or less (Harr et al., 1979, 1982; Moore & Scott, 2005; Van Haveren, 1988), which only allow adequate sampling of small and medium events, it was this deterministic, single-event logic that was often extrapolated to large events (e.g., Bathurst et al., 2011). While this logic originated in the rain environment (e.g., Bathurst et al., 2011), it has now been extended to other hydrological regimes such as snow environments (MacDonald & Stednick, 2003) and rain-on-snow environments (Bathurst et al., 2011; Jones, 2000; Perry et al., 2016) and continues to be taught in forest hydrology textbooks (Brooks et al., 2012; Chang, 2012). 77 Figure 3.2 Examples of typical deterministic regression and stochastic flood frequency curve (FFC) plots. While convergence is apparent on deterministic plots, tails may remain parallel, diverge (as shown), converge, or superimpose on stochastic plots. Yet, even when both watersheds show similar magnitudes for one large flood event defined by the same rainfall/snowmelt event, there may be other events which are small or medium in the control (and thus are not considered in the analysis) but are large in the treatment catchment due to influences of other flood generation factors. For example, a small or medium snowmelt event in the forested control catchment may exclude a control–treatment pair, but the corresponding treatment event could be large due to a significant increase in energy available for snowmelt after decreased forest cover (Alila et al., 2009). Chronological single-event pairing cannot account for such cases. This implies that large events could be more frequent when assessing the entire distribution of flood events rather than a subset of control–treatment peaks. Linkage of frequency to magnitude (Swain et al., 2020) further suggests that magnitudes change. This directly contrasts deterministic studies, where regression lines must converge for physically meaningful reasons. 78 Furthermore, deterministic studies paradoxically introduce quantile frequencies (i.e., 5-year flood event, 10-year flood event) when discussing “no effect” thresholds (e.g., Bathurst et al., 2020; Birkinshaw et al., 2011; Jones, 2000; Thomas & Megahan, 1998). Such patterns may hint at an underlying recognition that understanding flood response requires integrating magnitude and frequency, and of the key role of frequency in planning and policymaking. For these reasons, the deterministic hypothesis can be misleading, preventing a sound understanding of changing flood regimes. In short, the deterministic approach is motivated by an unanswerable question, leading to a non-relevant and non-causal approach and a self-fulfilling hypothesis. By failing to causally isolate the effects of changing forest cover on floods, its magnitude conclusions are rendered incorrect and changing frequencies are ignored. 3.4.3 Critically assessing the stochastic approach The stochastic approach (e.g., Alila et al., 2009; Duncan, 1995; Green & Alila, 2012; Johnson & Alila, 2023; McEachran et al., 2021) accounts for the multiple, stochastic, and dynamically interacting nature of flood drivers. It can ask either of two types of probability-based research questions (i.e., single-event or general causation) (Swain et al., 2020): (1) For an event of a certain magnitude (frequency), how has a change in forest cover influenced its frequency (magnitude)? (2) How have flood magnitudes and frequencies for small, medium, and large floods changed due to a change in forest cover? By utilizing magnitude–frequency classes, both questions account for the many combinations by which events of the same magnitude or frequency are generated. 79 Following this research question, the resulting experimental design is controlled, isolating effects of changing forest cover on floods and establishing the causal link. It uses the same BACI design as in the deterministic approach, but differences lie in how the control and treatment data are analyzed (Johnson & Alila, 2023; Pham & Alila, 2024). Rather than attempting to match control and treatment floods based on the same rainfall or snowmelt event, the highest peaks are selected in each of the control and treatment watersheds, and then they are paired by equal frequency. These peaks are used to build a pre-disturbance flood frequency curve (FFC) representing forested conditions (or less anthropogenic influence) and a post-disturbance FFC representing forest removal (or more anthropogenic influence). These curves can be compared to estimate differences in flood magnitudes and frequencies following a disturbance (Alila et al., 2009; Barnes et al., 2023; Bathurst et al., 2018, 2020; Birkinshaw et al., 2011, 2014; Duncan, 1995; Green & Alila, 2012; Hurkmans et al., 2009; Johnson & Alila, 2023; Kuraś et al., 2012; Lallemant et al., 2021; McEachran et al., 2021; Pham et al., 2025; Reynard et al., 2001; Schnorbus & Alila, 2004, 2013; Te Linde et al., 2010). As FFCs represent magnitude–frequency classes, they account for the multiple, stochastic, and dynamically interacting nature of flood generation, and therefore all the combinations in which floods can be generated. This approach is no longer ceteris paribus; it isolates effects of forest cover changes on floods, answering the ultimate question of interest, “How does the presence or absence of forest cover influence downstream flood magnitudes and frequencies?”. Furthermore, when comparing more forested and less forested FFCs, “upper tails” representing extremes may remain parallel (e.g., forest removal increases or sometimes decreases flood magnitude and frequencies, with effects remaining steady) (Hurkmans et al., 2009; Lallemant et al., 2021; Te Linde et al., 2010), diverge (e.g., increasing effects of forest removal 80 for larger events) (Kuraś et al., 2012; Pham et al., 2025; Reynard et al., 2001; Schnorbus & Alila, 2004, 2013), converge (i.e., decreasing effects of forest removal for larger events) (Green & Alila, 2012) or sometimes superimpose on each other (i.e., no effects), as illustrated in Figure 3.2 and suggested by Tables B.2 and B.3. As all of these are real possibilities (see later discussion in this section), the hypothesis that forest cover can decrease both magnitudes and frequencies for large flood events is falsifiable. Incorporating sound physical insight is also central to stochastic hydrology, allowing for scientifically rigorous predictions that better reflect hydrologic reality. Both climate and physiography (as described in section 2.4) control the “natural” FFC, with climatic controls prevailing over physiographic controls after storage capacity is overwhelmed (Macdonald et al., 2024; McCuen & Smith, 2008; Naghettini et al., 2012). These natural characteristics control the shape of the FFC, leading to a lighter or heavier tail (Taleb, 2012; Taleb & Douady, 2013) which has important implications for understanding watershed sensitivity and flood management, as suggested by section 2.6.3. Anthropogenic activity such as forest removal or climate change then acts upon these influences, shifting the natural FFC to its post-disturbance position. These changes in the FFC reflect how mean, variance, and skewness of flood populations change (see Figure 3.3); while changes in the mean influence frequencies of extremes (Mearns et al., 1984; Wigley, 2009), changes in variability can be much more consequential (Katz, 1993; Katz & Brown, 1992), leading to divergence (i.e., increased variability) or convergence (i.e., decreased variability) of the FFCs (Beckers et al., 2002; Green & Alila, 2012; Pham & Alila, 2024). By tying these changes to physical causes, stochastic hydrology supports a physically based understanding of change. 81 Figure 3.3 Conceptual changes of an increase in mean, variance, or both mean and variance to a hypothetical flood probability distribution. The grey dashed line represents a hypothetical threshold above which floods are considered large (such as the 10-year event), with increases in mean, variance, or both mean and variance increasing the number of large floods and record floods (i.e., floods which surpass all previously observed peak discharges in the instrumental record). While anthropogenic activity may also change the shape (skewness) of the distribution, it is not depicted here for simplicity. In forest hydrology, forest removal suggests an “upward” shift of the FFC relative to the forested FFC (see Figure 3.4), with divergence, parallelism, or convergence (or in some cases, little or reversed effects) at the tails, as suggested by Tables B.2 and B.3 (Alila et al., 2009; Barnes et al., 2023; Bathurst et al., 2018, 2020; Birkinshaw et al., 2011, 2014; Duncan, 1995; Green & Alila, 2012; Hurkmans et al., 2009; Johnson & Alila, 2023; Kuraś et al., 2012; Lallemant et al., 2021; McEachran et al., 2021; Pham et al., 2025; Reynard et al., 2001; 82 Schnorbus & Alila, 2004, 2013; Te Linde et al., 2010), all depending on climatic and catchment scale features. Increased evapotranspiration and moisture loss under forest cover (Duncan, 1995) may decrease catchment water storage. This translates to an increase in available storage capacity, which allows greater attenuation of runoff. Conversely, wetter soils under less forested conditions may reduce available storage capacity and consequently decrease potential for attenuating runoff, favouring more frequent and higher magnitude floods (Duncan, 1995; Pham & Alila, 2024). In snow environments, greater snow accumulation and increased energy input into the snowpack additionally increase moisture availability for flood generation and cause faster snowmelt (Green & Alila, 2012). However, it is catchment scale characteristics such as cut rates, spatial locations of cutblocks, and physiographical variations that govern how these smaller-scale processes translate to overall flood responses and effects on the FFC. As suggested by Tables B.2 and B.3 and shown in Figure 3.2, the less forested FFC is typically lifted “up” with parallelism (Birkinshaw et al., 2011; Hurkmans et al., 2009; Lallemant et al., 2021; Te Linde et al., 2010), divergence (Kuraś et al., 2012; Pham et al., 2025; Reynard et al., 2001; Schnorbus & Alila, 2004, 2013), or convergence (Green & Alila, 2012) of the tails, or in some cases there is little difference (or even a “downward” shift (Pham et al., 2025)), again all of which depend on climatic and catchment scale properties. For instance, increased synchronization (i.e., low diversity in slope-aspects and elevations which promotes simultaneous melt) may lead to similar timings at which flows reach the outlet, suggesting larger effects on large flood events (i.e., divergence) (Green & Alila, 2012; Johnson & Alila, 2023; Pham & Alila, 2024). On the contrary, greater diversity in slope-aspects and elevations may support staggered conveyance of flows to the outlet, dampening effects on large events and leading to convergence (Green & Alila, 2012; Johnson & Alila, 2023; Pham & Alila, 2024). In this way, stochastic 83 hydrology advocates for a causal and physically meaningful understanding of why FFCs generally shift “up” (“down”) following a decrease (an increase) in forest cover and why effects may increase or decrease for extreme events. This stochastic understanding of the role of forests in increasing storage capacity is consistent with the general hydrological understanding that any increase in storage capacity must increase attenuation of runoff, even for 100- and 1000-year events (Fleischmann et al., 2019; Liew et al., 2021; Svoboda, 1991). Figure 3.4 Hypothetical changes to a FFC with a decrease in forest cover. Changes in magnitude (light blue arrow) and frequency (dark blue arrow) are shown under both lighter- and heavier-tailed flood regimes. This stochastic interpretation is fundamentally different from the deterministic, single-event interpretation. The latter focuses on a single event; when a precipitation event exceeds available storage capacity, forest cover has little impact on the flood event. The stochastic interpretation integrates space and time (Robinson & Sivapalan, 1997), focusing on effects of forest cover to classes of events in the FFC rather than any individual event. For instance, as more water can be stored from precipitation or snowmelt events (along with smaller snowpacks and slowed melt rates in snow environments (Green & Alila, 2012)) under forested conditions, 84 overall conditions are less favourable for large floods. Even though large floods can still occur (Barnes et al., 2023), their magnitudes and (especially) frequencies are overall reduced. In fact, even small changes in magnitude lead to disproportionately large changes in frequency (see Figure 3.4) (Allen & Ingram, 2002). These larger frequency changes are the basis and emphasis of attribution science (Lloyd & Shepherd, 2020) and they are only revealed through a stochastic approach. While the deterministic framework fails to capture these largest changes, a stochastic approach highlights the natural sensitivity of flood regimes to change. In conclusion, the physically based stochastic approach is supported by valid research questions, a falsifiable hypothesis, and a controlled experiment. Its results are clear: forest cover can attenuate floods of all sizes (see Table B.2 and B.3) (Hurkmans et al., 2009; Kuraś et al., 2012; Lallemant et al., 2021; Pham et al., 2025; Preti et al., 2011; Reynard et al., 2001; Schnorbus & Alila, 2004, 2013; Te Linde et al., 2010), even when deterministic methods suggest there is no influence of forest cover on the largest floods (see Table B.3) (Birkinshaw et al., 2011; Green & Alila, 2012). 3.5 Revisiting the role of forests in flood management 3.5.1 Revisiting the scientific disagreement With scientific merit of each approach established, their findings can now be analyzed to determine whether forests hold potential for flood mitigation. Scientific skepticism towards forest-based NBS stems from the deterministic understanding that forests mitigate small and medium floods but have little impact following catchment saturation (Barnes et al., 2023; Dadson et al., 2017; Kay et al., 2019), which has made its way into influential policy documents (Calder & Aylward, 2006; CIFOR & FAO, 2005). However, its non-relevant research question, self-fulfilling hypothesis, and uncontrolled experimental design indicate low scientific rigour in 85 its conclusions. In contrast, the stochastic approach suggests that forest cover can mitigate small, medium, and large floods (Bradshaw et al., 2007; Green & Alila, 2012; Hurkmans et al., 2009; Kuraś et al., 2012; Lallemant et al., 2021; Pham et al., 2025; Preti et al., 2011; Reynard et al., 2001; Schnorbus & Alila, 2004, 2013; Te Linde et al., 2010). It uses valid and effective research questions, a falsifiable hypothesis, and a controlled experimental design to yield scientifically rigorous conclusions. Consequently, this approach is considered valid within forest hydrology (e.g., Alila & Green, 2014b; McEachran et al., 2021) even by proponents of deterministic approaches (e.g., Bathurst, 2014; Birkinshaw, 2014), wider hydrology (e.g., Ayalew et al., 2015; Brath et al., 2006; Brunner et al., 2021), and climatology and attribution science (e.g., Barbero et al., 2020; Christidis & Stott, 2022) to investigate anthropogenic impacts on floods (e.g., Gillett et al., 2022; Johnson & Alila, 2023) and other extremes (e.g., Barbero et al., 2020; Christidis et al., 2023; Du et al., 2021; Kirchmeier-Young et al., 2017). In the forests and floods controversy, this stark asymmetry in scientific rigour and contradictory conclusions suggests that the less rigorous approach must be replaced by the scientific rigorous approach. In other words, there appears to be greater truth to arguments brought up by proponents of forest-based NBS than previously given credit for by forest hydrology (Bruijnzeel, 2005), especially on the role of forests in mitigating large floods. While proponents of deterministic approaches suggest that both approaches can co-exist (Bathurst, 2014; Birkinshaw, 2014), science cannot simultaneously maintain two contradictory sets of conclusions (i.e., increasing forest cover both mitigates and does not mitigate large floods). Here, the stochastic framework known to establish cause and effect in multiple disciplines must be upheld over a flawed alternative. Furthermore, attempts to maintain both approaches often fall back on the misconception that frequency changes are independent of 86 magnitude changes, allowing event frequencies to increase while magnitudes do not after a decrease in forest cover (Barnes et al., 2023; Bathurst, 2014; Dadson et al., 2017). However, magnitude and frequency are two sides of the same coin (Swain et al., 2020), thus a change in frequency is always accompanied by a change in magnitude, and vice versa. For instance, if flood frequencies increase following forest removal, from a 100-year event to a 25-year event, the flood magnitude corresponding to the former 100-year event now occurs more often. Consequently, the magnitude corresponding to the new 100-year event is larger. Thus, an increase in frequency necessitates an increase in magnitude (and vice versa). Even though large floods still occur under forested conditions, additional storage capacity can greatly reduce frequencies, and therefore flood magnitudes. In this way, stochastic conclusions are incommensurable with deterministic conclusions. In the words of Kuhn (1970, p. 103), “the normal-scientific tradition that emerges from a scientific revolution is not only incompatible but often actually incommensurable with that which has gone before” (Kuhn, 1962, p. 103). Thus, stochastic frequency conclusions and deterministic magnitude conclusions cannot both co-exist; accepting stochastic frequency conclusions necessitates accepting stochastic magnitude conclusions. This may lead to the question of whether both approaches could co-exist if they produce the same answer. However, contradictory conclusions between the two bodies of literature demonstrate that they rarely produce the same answers (Birkinshaw et al., 2011; Green & Alila, 2012; Pham & Alila, 2024). Furthermore, convergence of deterministic regression lines does not equate to the convergence of FFCs. In the former, convergence must occur due to the self-fulfilling nature of the hypothesis, thus use of this approach does not exclude the possibility that forest cover mitigates large floods. In contrast, FFCs between the control and treatment scenarios 87 may diverge, remain parallel, or sometimes converge or superimpose (depending on hydroclimatic regime, physiography, cutblock location, and cut rate, to name a few)—all of which are possibilities. Even where the use of deterministic approaches (rarely) lead to answers typical of a stochastic approach (e.g., S. Liu et al., 2025), these results differ from those obtained through a stochastic framework where probability is central to the analysis, as only the latter is causal. As society enters unchartered territories in the Anthropocene, only a sound, causal understanding can guide flood projections and appropriate adaptation. This means that regardless of how answers compare, science must ensure it is “getting the right answers for the right reasons” (Kirchner, 2006) for effective flood management. Thus, effects of harvesting, deforestation, and afforestation/reforestation, especially for extreme events in a changing climate, should be examined stochastically with a frequency-centric lens. Causal attribution methods, including models and nonstationary frameworks (Brunner et al., 2021; Johnson & Alila, 2023; Runge et al., 2019), can separate influences of climate and LULC changes. As typical record lengths are insufficient for capturing large events (Bernardara et al., 2008; R. Merz & Blöschl, 2009), sufficiently large sample sizes can be simulated to complement observational records (Brunner et al., 2021; Stott et al., 2016). By integrating hydrological reasoning (R. Merz & Blöschl, 2008; Nearing et al., 2021) and physically based interpretation of change (e.g., Johnson & Alila, 2023), studies can be carried out in various hydroclimatic regimes and physiographies and under differing vegetation (e.g., density, deciduous versus coniferous) and harvesting characteristics (e.g., clearcut versus selective logging, cut rate, cutblock location) to support sustainable industry and effective NBS. For instance, the GRADEX (GRADient of EXtreme values) concept suggests that flood tails parallel those of rainfall after watershed storage capacity is exceeded, with the vertical difference 88 between rainfall and flood tails representing storage of precipitation in the catchment (R. Merz & Blöschl, 2008; Naghettini et al., 2012; Pham & Alila, 2024). From this logic, decreased storage capacity following forest removal must lead to an earlier return period at which flood tails mimic that of rainfall (i.e., flood tail is shifted “up” relative to the forested tail), with the vertical difference between forested and less forested FFC representing differences in catchment storage capacity. In this way, even where sample sizes are limited, methods such as GRADEX can be used to help predict the behaviour of extremes following a change in forest cover with appropriate stochastic reasoning (R. Merz & Blöschl, 2008). Finally, integrating tail behaviour of the natural (or forested) FFC and its controls can reveal watershed sensitivity to change, especially with a frequency-centric perspective (Fischer et al., 2023; Taleb, 2012; Taleb & Douady, 2013). Watersheds with lighter-tailed FFCs under natural (or forested) conditions may see the largest changes following forest removal, especially in their frequencies (see Figure 3.4). Linking physical characteristics to tail sensitivity helps identify which watersheds may be most sensitive to change, inform sustainable harvesting (i.e., in ways that desynchronize snowmelt in snow environments), and design NBS to manage downstream risks. 3.5.2 Policy implications Causal, probabilistic results can motivate effective policies, land use planning, industry practices, and flood management. While attribution studies of the role of climate change on floods has received much attention in scientific and policy-making arenas (Lahsen & Ribot, 2022; Raju et al., 2022), they typically do not examine other drivers (James et al., 2019; Young et al., 2019) or the vulnerability and exposure of populations to risks (James et al., 2019; Lusk, 2017). However, LULC drivers such as deforestation, agriculture, or urbanization have real impacts on the hydrological cycle (James et al., 2019; Young et al., 2019) and they can be 89 managed on a local or national scale to reduce flood risks. Hydrology can fill this important knowledge gap by causally attributing effects of various LULC covers on floods, especially amidst ongoing climate change (e.g., Johnson & Alila, 2023). This provides a sound understanding of changing flood regimes and informs exposure (i.e., upstream harvesting exposes downstream communities to flood) and vulnerability, all of which can help motivate adaptation and foster resiliency (James et al., 2019; Lusk, 2017). In these studies, while magnitude should absolutely be evoked and considered, larger frequency changes could be highly impactful for planning and decision making (Swain et al., 2020). For example, while a meager increase in magnitude can seem inconsequential to the public and policy makers, a former 100-year event now becoming a 25-year event may be much more compelling, motivating action. Furthermore, large increases in frequencies of flows can be detrimental for ecology (Strickland et al., 2024) and increase potential for geomorphic failures (Flint et al., 2017; Hudson, 2021; Wardhana & Hadipriono, 2003). These impacts may be missed with a focus only on magnitude, thus both frequency and magnitude must be considered. Furthermore, causally understanding changes in floods and their controls support reliable predictions of future flood risks and design of cost-effective flood management strategies. For instance, watershed storage capacity may be increased upstream by increasing forest cover, which can prevent flood risk increases downstream. Implications of forest cover and greater storage capacity can also be used to design downstream flood management strategies such as urban forests, green spaces in cities, and detention basins (e.g., Chan et al., 2018; Faivre et al., 2017; Lallemant et al., 2021; Leanza, 2022; Yu et al., 2025). In this way, adaptation and policy decisions all hinge on a sound, causal understanding of flood risk and its multiple drivers. 90 Chapter 4: Conclusion 4.1 Summary As magnitudes and frequencies of hydroclimatic extremes change around the world (Hirabayashi et al., 2021; Seneviratne et al., 2014; Slater et al., 2021), many subnational (e.g., Government of British Columbia, 2024), national (e.g., Chan et al., 2018), and multinational (Faivre et al., 2017) governments are grappling with how to adapt to changing realities in the 21st Century. For floods and other extremes, resilient adaptation requires reliable projections of change and the design of appropriate solutions, both of which rest on a strong understanding of the phenomena and their drivers. While hydroclimatic extremes are interconnected and share key commonalities (e.g., Pham & Alila, 2024; Swain et al., 2020), methods of understanding and predicting these phenomena vary among disciplines, with many traditional methods failing to capture changing realities and their drivers. This has led to apparent inconsistencies between scientific understanding and observed realities, such as the dominance of antifragile (Taleb, 2012) heavy tails (B. Merz et al., 2022) in hydrology despite evidence that flood regimes could be highly sensitive to change (e.g., Gillett et al., 2022; Johnson & Alila, 2023). Even when investigating analogous or overlapping questions, stark asymmetries in scientific rigour of different methods have produced contrasting conclusions, such as those concerning the mitigating effects of forest cover on floods. This thesis sought to bring together the strengths and key insights of various hydroclimatic disciplines to devise a common, robust framework for understanding and predicting extremes, using floods as an illustrative example. This thesis was guided by the following hypotheses: 91 1. A causal, stochastic approach best captures the relationships between floods and their drivers (both natural and anthropogenic). 2. Large increases in frequencies of hydroclimatic extremes may stem, at least in part, from a natural regime that is inherently sensitive, or fragile, to disturbances. 3. A strong understanding of flood controls informs sustainable land and resource planning which manages downstream flood risks and allows for developing flood mitigation solutions, especially those which draw from nature. The key conclusions of this thesis are summarized as follows: 1. Only a causal inference approach can disentangle the effects of different drivers superimposing on a time series (Runge et al., 2019). Literature throughout hydroclimatology emphasize the stochastic nature of hydroclimatic extremes, which imposes a causal, stochastic approach for understanding and predicting hydroclimatic extremes (Pham & Alila, 2024; Swain et al., 2020). This is illustrated with an example from forest hydrology, where stochastic approaches account for the nature of flood generation and incorporate valid research questions, falsifiable hypotheses, and a controlled experiment. Incorporation of sound physical knowledge emphasizes a physically based understanding of change and increases reliability in predictions, especially under limited record lengths. 2. Attribution science shows evidence of disproportionately large increases in extreme event frequencies under anthropogenic activity (see Table A.1) compared to changes in magnitude (Allen & Ingram, 2002). Hydrology (Johnson & Alila, 2023) and climatology (Gessner et al., 2023; Van Oldenborgh et al., 2022) literature suggest that these large frequency changes may be associated with lighter tails, in line with the “fragile” 92 characterization of lighter tails outside hydroclimatology (Taleb, 2012; Taleb & Douady, 2013). Increased frequencies of extremes may thus stem, at least in part, from lighter-tailed, highly sensitive (or fragile) regimes, although more focused research is needed. This conclusion also suggests that the common characterization of floods as heavy-tailed (B. Merz et al., 2022), which is based on literature using limited sample sizes and stationary approaches, should be re-examined using appropriate sample sizes and by accounting for nonstationarity. 3. An example from forest hydrology is used to show that causal, stochastic knowledge, especially of flood controls, supports effective flood management. Stochastic forest hydrology conclusions demonstrate that forests have potential to mitigate small, medium, and large floods. This suggests that forests can be integrated into flood management, in stark contrast to traditional forest hydrology understanding. In both forest and wider hydrology, understanding flood controls can be used to design resource extraction activities in ways that minimize effects on flood regimes and to design flood mitigation solutions. In this way, this thesis provides a blueprint for robustly understanding and predicting hydroclimatological extremes. It shows why a causal, physically based understanding is needed (Johnson & Alila, 2023; Runge et al., 2019) which focuses on the stochastic, spatiotemporal whole rather than maintain deterministic and reductionist approaches. While challenges persist in modelling extreme events, they cannot deter hydroclimatology from rigorously estimating upper tails due to the severe socioeconomic consequences that may result from possible mischaracterization. Thus, this thesis provides suggestions to improve current understanding of 93 system change and sensitivity, helping bridge the gap between acknowledged hydroclimatic realities and common scientific and professional practices. 4.2 Limitations Most attribution science work has focused on climatic changes to heatwaves, wildfires, and precipitation, with comparatively fewer studies examining floods (and especially their LULC drivers) (see Table A.1). Although this limited the availability of flood studies for analysis, published literature suggests that flood regimes are experiencing major changes from climatic and LULC drivers in many regions throughout the world (e.g., Gillett et al., 2022; Hirabayashi et al., 2021; Johnson & Alila, 2023; Pham et al., 2025; Prosdocimi et al., 2015; Singh & Chinnasamy, 2021; Slater et al., 2021; Sweet et al., 2016; Teufel et al., 2017), emphasizing the need for further flood research. Similarly, availability of instrumented experimental watersheds (e.g., for paired watershed studies) has a strong influence on the geographic location of forest hydrology studies. For example, H.J. Andrews Experimental Watershed in Oregon is a common study site for paired watershed studies (Alila et al., 2009; Bathurst et al., 2020; Beschta et al., 2000; Harr, 1986; Harr et al., 1982; Harr & McCorison, 1979; Rothacher, 1973), which may provide insights for similar rain-on-snow environments in the Pacific Northwest but may be less applicable to other hydroclimatic regimes. Many studies are also conducted in small headwater catchments (Harr & McCorison, 1979). Additionally, fewer forest hydrology studies use stochastic approaches, with many of these studies conducted in snow regimes. Therefore, this thesis aimed to bring in available research from diverse hydroclimatic regimes, locations, and catchment sizes whenever possible, but it emphasized these knowledge gaps and provided appropriate suggestions for future research recognizing these limitations. 94 Finally, a key limitation is that many hydrological studies utilize limited sample sizes and a stationary framework which may mischaracterize the upper tail. This thesis thus examined the direction of influence (i.e., towards lighter or heavier tails) rather than definitively discussing “light” or “heavy” tails while relying upon stochastic physical reasoning. The limitations of these practices are also highlighted throughout this thesis to motivate more rigorous modelling in future studies. 4.3 Recommendations for future studies Rather than simple identification of nonstationarity, there is a need to progress beyond trend detection towards rigorous attribution (B. Merz et al., 2012). This is especially relevant in hydrology where attribution work is less prominent, despite its ability to provide causal understanding of why and how floods are changing. Attribution studies should assess the effects of climatic and LULC changes including forest harvesting, urbanization, and land conversion by modelling various scenarios (Reynard et al., 2001) and conducting nonstationary frequency analysis (Johnson & Alila, 2023). Expanding such analyses to regions where flood attribution studies are few, or even where they are becoming less common (Slater et al., 2021), would improve understanding of flood dynamics in less-studied regions. Additionally, while compound event attribution is advancing in hydroclimatology, most work to date has examined anthropogenic impacts to compound heatwaves and droughts (Luo et al., 2022; Zachariah et al., 2023). Hydrological studies of compound events involving floods (Zscheischler et al., 2025) can help fill this knowledge gap. Further research using a causal, stochastic approach is needed to evaluate sustainable resource harvesting or extraction practices, and to inform or test the efficacy of NBS. For forest hydrology, this includes investigating how forest cover or harvesting affects floods across 95 different hydroclimatic regimes (especially rain, rain-on-snow, and glacial) and under different harvesting approaches to inform logging operations which mitigate downstream flood risk increases. In locations where long-term paired watershed data are available, datasets previously analyzed through deterministic methods can be analyzed stochastically to generate new causal insights. Current heavy geographical inequalities in stochastic literature can be rectified through a focus on understudied hydroclimatic regimes, physiographies, and locations, especially by analyzing paired watershed data in regions that have historically received less attention. In less instrumented regions, techniques such as regional FFA (Schaefer, 1990) and modelling of different scenarios can provide valuable insights. As opposed to a primary focus on small headwater catchments, a greater focus on larger watersheds or watersheds where changing flood regimes could threaten communities or important resources could deliver highly relevant knowledge. Studies which explicitly examine reforestation and afforestation efforts, especially their potential to offset projected effects of climate change or urbanization, could be particularly valuable. Whenever possible, including the impacts of associated practices such as ditching to increase water drainage (Bathurst et al., 2018) can provide further insights relevant for reforestation and afforestation efforts. Finally, assessing how individual or combined NBS measures such as forest cover and retention basins mitigate floods can help inform future flood management, especially as governments increasingly promote NBS (e.g., Government of British Columbia, 2024). By examining effects of various LULC management practices on floods with rigorous, causal approaches, science can help develop strategies which meaningfully reduce flood risk and are practical for local, regional, and national governments. 96 Bibliography Albert, D. Z. (2000). Time and chance. Harvard University Press. https://doi.org/10.1093/mind/fzi113 Alila, Y., & Green, K. C. (2014a). Reply to comment by Bathurst on “a paradigm shift in understanding and quantifying the effects of forest harvesting on floods in snow environments.” Water Resources Research, 50(3). https://doi.org/10.1002/2013WR014334 Alila, Y., & Green, K. C. (2014b). 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Nature Reviews Earth and Environment, 6(4), 240–242. https://doi.org/10.1038/s43017-025-00657-y 159 Appendices Appendix A Table A.1 Synthesis of attribution science literature using the Scopus database that provide a direct quantification of change or frequency distributions relating event magnitudes to frequencies (see section 2.2). “RR” represents risk ratio, which is the probability of an event of a certain magnitude occurring under factual conditions (“current” unless otherwise stated) to that under counterfactual conditions (specified). “OBS” and “MOD” represent observations and models, respectively, and “GEV” represents the Generalized Extreme Value distribution (see section 2.2). Natural, anthropogenic, all forcings (natural and anthropogenic), greenhouse gases only, and aerosols only scenarios are represented by “NAT”, “ANT”, “ALL”, “GHGs”, and “AER”, respectively. Study reference Motivating variable or event Location Changes in frequency (Barbero et al., 2020) 2003 wildfire season France 500-year (NAT) to 10-year. (Bellprat et al., 2016) 2015 February cold temperatures Eastern North America None significant / not clear. (Bergaoui et al., 2015) 2013/14 winter drought Southern Levant Increased. (Bian et al., 2020) 1986-2013 flooding Qinhuai River, China Increased in urbanization period. (Cadiou et al., 2023) 2022 February-March "rain bomb" precipitation Australia None significant / not clear. (Y. Chen et al., 2019) 2017 July temperatures Central eastern China 47.7-year (NAT) to 4.9-year. (Christiansen et al., 2018) 2009/10 cold winter Europe RR = 9.8 relative to NAT. 160 Study reference Motivating variable or event Location Changes in frequency (Christidis & Stott, 2022) Seasonal precipitation, high & low Europe: Mediterranean & Northern High precipitation, Mediterranean Europe: 2-fold decrease relative to NAT. Mediterranean Europe: Less frequent high precipitation, more frequent low precipitation relative to NAT. Northern Europe: More frequent high precipitation, less frequent low precipitation relative to NAT. (Ciavarella et al., 2021) 2020 January-June temperatures Siberia Virtually impossible (1900) to 130-year. RR = 500 (or 60 000 by 2050), since early 1900s. (De Abreu et al., 2019) 2017 May-June heavy precipitation Uruguay River Basin, South America 285-year (NAT) to 61-year (1986). RR = 5 relative to NAT. (de Souza et al., 2024) 2020 March precipitation Baixada Santista, Brazil 60-day event: 21-year (NAT) to 12-year. RR = 1.74 relative to NAT. 3-day event: 5-year (NAT) to 3-year. RR = 1.46 relative to NAT. Joint: 26-year (NAT) to 21-year. RR = 1.25 relative to NAT. (Dhasmana et al., 2023) 2018 August extreme precipitation & flooding Kerala, India Precipitation: 88-year (NAT) to 373-year. RR = 0.31–0.82 (P) relative to NAT. Flooding: 29-year (NAT) to 35-year. RR = 0.55–0.8 relative to NAT. (Du et al., 2020) 2017/18 winter consecutive dry days Beijing, China RR = 1.29 or 2.09 relative to NAT. 161 Study reference Motivating variable or event Location Changes in frequency (Du et al., 2021) 2019 wildfire season Yunnan & southern Sichuan, Southwest China RR = 7.21 or 17.39 relative to NAT. (Du et al., 2022) 2020 summer dry – wet contrast Heavy precipitation: Yangtze River Basin Extreme temperature & drought: southern coastal China Dry-wet contrast: RR = 3.12–3.51 relative to NAT. (Eden et al., 2016) 2013 September heavy precipitation Boulder, Colorado, US Increased for 1-day event. (Eden et al., 2018) 2014 July heavy precipitation Netherlands RR = 4 (OBS) since pre-industrial, with smaller change from MOD. (Fučkar et al., 2020) 2018 February heavy precipitation Mozambique, Zimbabwe, & Zambia 37% less likely relative to 1901, but with high uncertainty. (Gessner et al., 2023) 1993 December extreme precipitation Central Europe None significant / not clear. (Gillett et al., 2022) 2021 November extreme precipitation & flooding British Columbia (BC), Canada Precipitation: RR = 1.45 since 1850–1900. 2–4 by 2100. Flooding, 100-year event: RR = 2.2–4.3 since 1950–1969. (Hannart et al., 2015) 2013 December heatwave (temperature) Argentina 75 years (NAT) to 15 years. RR = 5 relative to NAT. 162 Study reference Motivating variable or event Location Changes in frequency (Hauser et al., 2016) 2010 temperatures Western Russia 1998 event: 80-year (1960s) to 25-year (2000s). RR = 3 since 1960s. RRs for 2010 event: 6 (low soil moisture), 3 (climate change), & 13 (combined). (Haustein et al., 2016) 2013/14 winter heavy precipitation & warm temperatures England T: 14-year (NAT) to 3-year, with RR >4 relative to NAT. P: 100-year (NAT) to 60- or 70-year. (Hirabayashi et al., 2021) 2010-2013 flooding Global ANT activity affected 64% (14/22) of floods studied. (Z. Hu et al., 2021) 2018/19 winter heavy precipitation Yangtze River, China ~19% decrease in rainfall amounts due to ANT since 1961/62. No change in the number of excessive rainy days. (T. Hu et al., 2023) 2021 Sept heavy precipitation Northern China 1-day (GEV): 21-year (NAT) to 13-year (GHGs) or 100-year (AER). RR = 1.7 (GHGs) or 0.2 (AER). GEV, 5-day: RR = 1.3 (GHGs), 0.2 (AER), or 1.6 (combined). (Johnson & Alila, 2023) Flooding due to harvesting Deadman River & Joe Ross Creek, Interior BC, Canada 7-year to 2- (Joe Ross) or 3- (Deadman) year. 20-year to 4- (Joe Ross) or 5- (Deadman) year. 50-year to 7- (Joe Ross) or 8- (Deadman) year. RR: 2 (for 7-year), 4 (for 20-year), 6 (for 50-year), 10 (for 100-year). 163 Study reference Motivating variable or event Location Changes in frequency (Jong et al., 2023) Fall precipitation Northeast US >150 mm/day event: RR = 6 by 2100 relative to early 2000s. 180 mm/day: 270-year (1961–1990) to 95-year (1991–2020). 200 mm/day: 330-year (now) to 170-year (2050) or 58-year (2100). (Kay et al., 2011) 2000 fall & winter flooding England Mostly increased. (Kew et al., 2019) 2017 summer temperatures Southern Europe 3000-year (1950) to 20-year. RR = 140 since 1950, or conservative estimate of 3. (King et al., 2015) 2014 warm temperatures Central England 2006-like: 121-year (NAT) to 5-year. 2014-like: 2500-year (≥350-year) in 1914 to 25-year. RR: ≥13 (MOD), ≥22 (OBS). (King et al., 2016) 2015 July-October high temperatures & drought Indonesia Temperature: changes attributable to anthropogenic change. Drought: ≥37% more likely relative to NAT. (Kirchmeier-Young et al., 2019) 2017 extreme wildfire season BC, Canada Since 1961–1970: RR >20 (temperature), 2–4 (fire indices), 7–11 (burned area). (Krikken et al., 2021) 2018 severe wildfire season Sweden MOD: RR = 1.1 relative to pre-industrial (non-significant), ~2 with 2⁰C warming (significant). OBS: non-significant reduced likelihood. 164 Study reference Motivating variable or event Location Changes in frequency (Kumari et al., 2019) 2013 June extreme precipitation & streamflow Uttarakhand, India Precipitation: 100-year (now) to 39-year (1.5⁰C warmer world) or 23-year (2⁰C warmer). RR = 2.7 (1.5⁰C warmer) or 4.8 (2⁰C warmer) compared to NAT. Streamflow: 80% increase expected in a 1.5⁰C warmer world compared to now. (Li et al., 2021) 2019 March-July prolonged precipitation Southern China 4-year (NAT) to 9-year event, or 7-year (NAT) to 16-year (MOD dependent). RR = 0.43 or 0.38 relative to NAT. (Li et al., 2023) 2020 summer precipitation Yangtze River & Yellow River-Hai River Basin, China RR = 0.41 or 0.53 (1.12 or 0.77) for monthly Yangtze River (Yellow River-Hai River) relative to NAT. RR = 1.15 or 1.13 (1.41 or 1.02) for 1-day Yangtze River (Yellow River-Hai River). (Liang et al., 2024) 2022 July-August high temperatures Yangtze River Basin, China RR = 7 relative to NAT. (Z. Liu et al., 2022) 2020 summer wildfire season Siberia 8/13 hotspots: RR = 1.1–1.8 relative to 1880. 5 hotspots: small decreases. (Z. Liu et al., 2023) 2021 April wildfire Cape Town, South Africa RR = 1.2–4.1 (or 1.9 weighted) relative to 1880. (C. Lu et al., 2021) 2019 May-June very low precipitation (drought) Southwestern China RR = 1.4 or 6 (MOD dependent) relative to NAT. 165 Study reference Motivating variable or event Location Changes in frequency (Luo et al., 2022) 2019 spring & summer combined high temperatures & drought Southwestern China Temperature: 1000-year (1961) to 58-year (2020). RR = 2.7 relative to NAT. Drought: 58-year (1961) to 9-year (2020). RR = 1.5 relative to NAT. Temperature & drought: RR = 1.6 in the last 30 years. (Luu et al., 2018) Extreme precipitation Cévennes Mountains, France RR = 2.5 (3.1) for 100-year (1000-year) event since 1971–2000. (Luu et al., 2021) 2020 October precipitation Central Vietnam None significant / not clear. (Ma et al., 2020) 2019 June-July temperatures Western central Europe 1981–2014: 3004-year (NAT) to 128-year. RR = 23 relative to NAT. 1950–2014: 2339-year (NAT) to 331-year. RR = 7 relative to NAT. Expected: 1.8–7.2 in 2020–2100 depending on emissions scenarios. 166 Study reference Motivating variable or event Location Changes in frequency (Malinina & Gillett, 2024) 2021 June temperatures Pacific Northwest (Canada & USA) Return periods – 1850–1900, 2011–2030, 2081–2100: BC, 1-day: very high, 7668-year, 41-year. BC, 3-day: very high, 9814-year, 41-year. BC, 7-day: very high, 948-year, 13-year. Alberta, 1-day: 2322-year, 98-year, 6.2-year. Alberta, 3-day: 4056-year, 138-year, 7.0-year. Alberta, 7-day: 1119-year, 46-year, 3.4-year. Washington, 1-day: very high, 208-year, 12-year. Washington, 3-day: very high, 157-year, 10-year. Washington, 7-day: 3357-year, 35-year, 3.7-year. RR – (2011–2030)/(1850–1900), (2081–2100)/(1850–1900), (2081–2100)/(2011–2030): BC: very high, very high, 189 (1-day) or 226 (3-day) or 71 (7-day) Alberta, 1-day: 24, 374, 16. Alberta, 3-day: 30, 597, 20. Alberta, 7-day: 25, 325, 13. Washington, 1-day: very high, very high, 17. Washington, 3-day: 39, very high, 15. Washington, 7-day: 96, 914, 9.5. (E. S. P. R. Martins et al., 2018) 2012-16 drought Northeastern Brazil None significant / not clear. 167 Study reference Motivating variable or event Location Changes in frequency (Massey et al., 2012) 1960s to 2000s warm November & cold December temperatures Central England Warm November: 1250-year (1960s) to 20-year (2000s). RR = 62 since 1960s. Cold December: 139-year (1960s) to 278-year (2000s). Halving of risk since 1960s. (Mera et al., 2015) June-August temperatures Central Valley, California, USA 100-year (1960s) to 50-year (2000s), though smaller difference after bias correction. (Miao et al., 2016) 2015 July temperatures Northwest China RR = 3 relative to NAT. (Min et al., 2020) 2018 summer temperatures South Korea RR = 4.7 (or 10 considering duration) relative to NAT. (Mote et al., 2016) 2011-15 snow drought Washington, Oregon, & California, USA Greater increases in frequency and anthropogenic contributions to snow drought for Washington & Oregon than California. (Nanding et al., 2020) 2019 July extreme precipitation Yangtze River, China 2-day event: 30% relative to NAT. 14-day event: 20% decrease relative to NAT. (Nanditha et al., 2020) 2010 April-May temperatures India Most regions: 50-year (now) to 10-year (with 2⁰C warming) or 5-year (with 3⁰C warming). Arid: 500-year (now) to 9-year (2⁰C warming) or 3-year (3⁰C warming). RR ≥20 (with 2⁰C warming) or RR ≥100 (with 3⁰C warming) relative to now. Cold: 500-year (now) to 50-year (2⁰C warming) or 10-year (3⁰C warming). Cold, temperate, monsoon, & Savannah regions: RR ≥7 (with 2⁰C warming) or ≥20 (with 3⁰C warming) relative to now. 168 Study reference Motivating variable or event Location Changes in frequency (Nanditha et al., 2020) 2022 March-April temperatures India & Pakistan RR = 41 relative to NAT. RR = 2.2–2.5 with 1.5⁰C or 8-9 with 2⁰C of warming. (Otto et al., 2012) 2010 extreme temperatures Western Russia 99-year (1960s) to 33-year (2000s). RR = 3 relative to 1960s. (Otto et al., 2013) Low precipitation African rainforests None significant / not clear. (Otto, Boyd, et al., 2015) July minimum temperatures East Africa 2000–2010: RR = 6- or 7- year (NAT) to <1- year. 2005: 40-year (NAT) to <1-year. (Otto, Coelho, et al., 2015) 2014/15 drought Southeast Brazil None significant / not clear. (Otto, Rosier, et al., 2015) Heavy summer (July) precipitation England & Wales July: 100-year (NAT) to 35-year event (2000s). 100-year (1960s) to 50-year. Jun & Aug: Less clear. (Otto et al., 2018) 2015 December storm Desmond precipitation Northern England & southern Scotland 100-year event: RR = 1.3–1.9 (OBS) or 1.05–1.8 (MOD) relative to NAT. (S. Philip, Kew, van Oldenborgh, Otto, et al., 2018) 2015 drought Ethiopia None significant / not clear. (S. Philip, Kew, van Oldenborgh, Aalbers, et al., 2018) 2016 May-June heavy precipitation Seine & Loire basins, France RR = 1.9 (Loire) & 2.2 (Seine) since 1880. 169 Study reference Motivating variable or event Location Changes in frequency (S. Y. Philip et al., 2018) 2015 June high temperatures Washington, Oregon & California, USA RR = 2 (Washington), 10 (Oregon), 7 (California) since 1900. RR = 2.2 (Washington & California) & 3.4 (Oregon) relative to NAT. (S. Philip et al., 2019) 2017 August extreme precipitation & flooding Bangladesh For 2⁰C of warming, RR = 1.7 (precipitation) & 1.5 (flooding) since pre-industrial. (S. Philip et al., 2022) 2021 June temperatures Portland, Seattle, & New Westminster (Canada & USA) Virtually impossible (1850–1900) to 1000-year (now) to 5- or 10-year (2⁰C warming). RR = 150 since 1850–1990. (Prosdocimi et al., 2015) Flooding from urbanization Northern England Increased. (Qian et al., 2022) 2020 mid-August heavy precipitation Southwestern China RR = 2.4 relative to NAT. (Qian et al., 2023) 2020 compound heatwave & precipitation China SSP5-8.5: RR = 10 (2050) or 14 (2090) relative to 2001-2020. SSP1-1.9: RR = 7 (2050 & 2090). (Ren et al., 2020) 2018 summer 30-day temperatures Northeast China 30-day event: 500-year (NAT) to 60-year. 2nd most extreme year: RR = 57 relative to NAT. (Rimi et al., 2019) 2017 March-April pre-monsoon precipitation Northeast Bangladesh RR = 2 relative to NAT in 1986-2015 period. (Rivera et al., 2023) 2022 December temperatures Southern South America 20-year (currently) to 5-year (2⁰C of warming). RR = 60 relative to NAT. 170 Study reference Motivating variable or event Location Changes in frequency (Rosier et al., 2015) 2014 July heavy precipitation Northland New Zealand 350-year (NAT) to 200-year event. (Ross et al., 2021) 2019 water year extreme streamflow Susquehanna River, Pennsylvania, USA RR = 1.55 relative to NAT. (Rupp et al., 2012) 2011 drought (using low precipitation) & temperatures Texas, USA Low precipitation: 100-year (1964) to 25-year (2008). Temperature: 100-year (1964) to 5- or 6- year (2008). (Rupp et al., 2015) 2011 summer temperatures, precipitation, & drought Texas, USA Temperature: 100-year (NAT) to 10-year. RR = 10 relative to NAT. Precipitation & soil moisture: None significant / not clear. (Schaller et al., 2014) 2013 May-June heavy precipitation Upper Danube & Elbe, Central Europe None significant / not clear. (Schaller et al., 2016) 2014 January precipitation & flooding Thames River, England Precipitation: increased. Flooding: increase in 30-day streamflow, and some increase in daily peak flows. Flooding, 100-year event: risk of 4-day or 30-day peak flows increased by 4% or 21%, respectively. (N. Singh & Chinnasamy, 2021) Flooding Periyar River, Kerala, India RR = 20-, 40-, & 50-year (stationary) to 16-, 28-, & 39-year, respectively. 171 Study reference Motivating variable or event Location Changes in frequency (Sippel & Otto, 2014) 2012 temperatures & drought Southeast Europe July, temperature: >100-year (1960s) event an order of magnitude more frequent. July, 5-day mean temperature: 1-2 times per 100 years (1960s) to <10-year. Jun & Aug temperature: less prominent change. Drought: more frequent. (Sippel et al., 2015) 2013/14 winter min temperatures & maximum precipitation Northwest Russia & Iberian Peninsula Temperature: Warming at both tails of min T distribution. Precipitation: Increased in some parts of Europe. (Sippel et al., 2016) 2015 summer temperatures Europe RR = 10 (OBS) or 1.1–2.9 (MOD) relative to NAT. (Sparrow et al., 2018) 2017 July temperatures Central eastern China "Unequalled" (NAT) to 50-year in one MOD. RR = 4.8 in another. (Sun & Miao, 2018) 2016 June-July heavy precipitation Yangtze-Huai, China RR = 1.5 relative to NAT, 1.5–4 by El Nino, 10 due to ANT influences & El Nino. (Sweet et al., 2016) 2015 September tidal flooding Miami, USA 39-year (1994) to 6-year event (now) to 0.6-year by 2030 (RCP 2.6, 4.5, 8.2). With further 0.2 m increase, >10 times a year. (Tang et al., 2022) 2020 June-July heavy precipitation Yangtze River, China 31-year (NAT) to 55-year. RR = 0.56 relative to NAT. (Teufel et al., 2017) 2013 June extreme precipitation & flooding Southern Alberta, Canada Precipitation: 60-year (current) to 20-year (2070–2100, RCP 4.5 & 8.5). Flooding: None significant / not clear. 172 Study reference Motivating variable or event Location Changes in frequency (Teufel et al., 2019) 2017 April-May extreme precipitation & flooding Ottawa River Basin, Canada Precipitation: RR = 2–3 relative to NAT. Flooding: None significant / not clear. (Tozer et al., 2020) 2018 May extreme precipitation Hobart, Tasmania None significant / not clear. (Tradowsky et al., 2023) 2021 July heavy precipitation Western Europe RR = 1.2–9 compared to a 1.2⁰C cooler climate. (Uhe et al., 2018) 2016-17 low precipitation drought Kenya None significant / not clear. (Vasconcelos Junior et al., 2024) 2022 May precipitation Eastern Northeast Brazil No quantification possible, but "far outside range of the previous observed records." (Van Der Wiel et al., 2017) 2016 extreme precipitation Louisiana, USA 100-year to 70-year. RR = 1.4. (Van Oldenborgh et al., 2016) 2015 December heavy precipitation Chennai, India None significant / not clear. (Van Oldenborgh et al., 2018) 2017 August Hurricane Harvey precipitation Texas, USA RR = 3 relative to early industrial times. (Van Oldenborgh et al., 2021) 2019-20 bushfires Australia >800-year (1900) to 31-year with one metric. RR ≥2 in temperature since early 1900s. RR = 8 with 2⁰C warming relative to 1900. 173 Study reference Motivating variable or event Location Changes in frequency (Van Oldenborgh et al., 2022) 2019 July temperatures De Bilt, Netherlands Virtually impossible or ≥15 000-year (1900) to 30-year. (Vautard et al., 2015) 2014 fall high precipitation Cévennes Mountains, France RR = 3 since 1950. (S. Wang et al., 2021) 2019 March-June temperatures & drought Yunnan, China Temperature: RR = 2.4 relative to NAT. Drought (low rainfall): RR = 1.18 relative to NAT. Temperature & drought: 43% increase in last 30 years due to ANT activity. (L. Wang et al., 2023) 2021 July extreme precipitation Central & eastern China MOD dependent; >10000-year (1961) to 256-year (2021) OR 76-year (1961) to 212-year (2021). (Z. Wang et al., 2023) 1931, 1954, 1998, & 2020 heavy precipitation Yangtze River Valley, China 1931: RR = 0.77 (mean), 0.95 (maximum 1 day), 2.13 (maximum 5 day) relative to NAT. 1954: RR = 0.66 (mean), 0.65 (maximum 1 day), 1.00 (maximum 5 day) relative to NAT. 1998: RR = 0.66 (mean), 1.08 (maximum 1 day), 0.75 (maximum 5 day) relative to NAT. 2020: RR = 1.72 (mean), 1.33 (maximum 1 day), 1.25 (maximum 5 day) relative to NAT. (Wehner et al., 2018) 20th-21st century hot temperatures & heatwaves Global For a representative mid-latitude land cell: 20-year (NAT) to 2.5-year. RR = 8. 174 Study reference Motivating variable or event Location Changes in frequency (Wilcox et al., 2018) 2012 wet & dry conditions: precipitation, temperature, & drought Northern (wet) & southern (dry) Europe Temperature: 30 (90) since 1960 (1901). Precipitation & Drought: None significant / not clear. (Wolter et al., 2015) 2013/14 unusually cold winter temperatures Upper Midwest, USA 1880s: 10-year (General Pareto Distribution), 14-year (Gaussian), or 10-year (simulations). 2014: 1000-year (General Pareto Distribution), 200-year (Gaussian), or very unlikely/>300-year (simulations). 20- to 100-fold less likely now relative to 1880s. (J. Xie, 2022) 2021 February unusually warm temperatures North China 5000-year (NAT) to 500-year. RR = 4–20 relative to NAT. (X. Yang & Huang, 2023) Flooding, temperature, & precipitation 50 catchments in Norway Temperature & precipitation: Increased in >80% (T) or 40% (P) of catchments. Flooding: Earlier spring floods in 40% of catchments. (H. Yu et al., 2022) 2020 April cold temperatures Northeast China 7-year (NAT) to 40-year. (Yuan et al., 2018) 2016 June-July heavy precipitation Yangtze River, China 72-year (NAT) to 45-year. 175 Study reference Motivating variable or event Location Changes in frequency (Zachariah et al., 2023) 2015 high summer temperatures & drought Marathwada, India Temperature: 108-year (pre-1985) to 16-year (post-1985). 55-year (NAT) to 4-year. RR = 11 compared to NAT. Drought: 16-year (pre-1985) to 15-year (post-1985). Temperature & drought: 262-year (NAT) to 38-year (current) to 15-year (1.5⁰C world) to 12-year (2⁰C world). RR = 7 (now), 2.6 (1.5⁰C world), 2.8 (2⁰C world). (Zeder & Fischer, 2023) 2021 June temperatures Pacific Northwest, Canada & USA 200-year (2021) to 5-year (2060). (L. Zhang et al., 2020) 2018 April-May drought South China RR = 17 relative to NAT, or never occur in NAT (MOD dependent). (W. Zhang et al., 2020) 2018 June-July heavy precipitation Central western China RR = 0.53 (28-day) or 1.48 (1-day) relative to NAT. (Zhou et al., 2018) 2016 July extreme precipitation Wuhan, China 272-year (1961) to 28-year. (Zhou et al., 2019) 2017 July temperatures Yangtze River Delta, China Urban heat island effect: RR = 2.5. (Zhou et al., 2020) 2018 July-August hot temperatures Northeast China 80-year (rural) to 60-year (urban). (Zou et al., 2021) 2018 July-August extreme precipitation Hami City, Xinjiang, China Increased. 176 Table A.2 Overview of flood frequency literature studying effects of climatic and physiographic controls on the variance, skewness, and/or tail behaviour, using the Scopus database to find appropriate studies and examining citations in papers which linked controls to their effects on variance, skewness, and/or tail behaviour (see section 2.2). CS and CV stand for coefficient of skewness and coefficient of variation, respectively. Study reference Control examined Location or region (or based on) Main findings (Alila & Mtiraoui, 2002) Mixtures & heterogeneities Gila River Basin, Arizona, USA Frontal storms and El Niño-Southern Oscillation (ENSO) events make up the upper tail. Monsoonal events and both ENSO and non-ENSO events make up the lower tail. (Archer, 1981) Floodplain & nonlinearity Britain Floodplain: When wide, active floodplains are present, floods may be attenuated through overbank storage, leading to a lower growth curve (i.e., a lighter distribution). Nonlinearity: Dry catchments require soil saturation to generate runoff. Contributing area is small and grows slowly at first, but grows faster under a greater precipitation intensity and soil moisture conditions. This produces a break in the curve with a heavier tail. Wet upland catchments initially have lower catchment wetness deficits and see a faster growth rate. When most or all of the catchment is generating surface runoff, rainfall rates determine flood growth rates. This leads to a break in the curve with a lighter tail. 177 Study reference Control examined Location or region (or based on) Main findings (Ayalew & Krajewski, 2017) Catchment shape Iowa River Basin, Iowa, USA Floods are higher across all return periods in the circular catchment (curve shifted "up") relative to the elongated catchment. Divergence at the tail suggests higher steepness of the circular catchment's FFC. (Basso et al., 2015) Nonlinearity Italy, Switzerland, & USA Nonlinearities in catchment response (storage-discharge relationships) lead to heavy tails. (Basso et al., 2016) Nonlinearity Central & eastern USA Persistent regimes (i.e., greater ratio of flow-producing event frequencies to mean recession rate) show concave FFCs. Erratic regimes are more variable and show step changes and convex FFCs. (Basso et al., 2023) Nonlinearity Germany & USA Flood divides separating common and extreme floods originate from a hydrograph recession exponent and CV of daily flows. The recession exponent captures how runoff is conveyed to the outlet, accounting for spatial organization of the drainage network and how it changes through time. CV of daily flows represents interarrival periods between flow-producing storms divided by catchment response time, capturing likelihood of precipitation falling on dry or wet basins. 178 Study reference Control examined Location or region (or based on) Main findings (Basso et al., 2023) Rain vs snow, humid vs arid, & catchment area BC, Canada Catchment area: Increased area decreases CV. Climatic and physiographic features more strongly control floods in small headwater catchments, as precipitation and snowmelt are quickly transformed into runoff. Channel transport helps decrease variability in larger catchments, with contributing smaller basins delivering flow asynchronously. Increased area also decreases peak flow ratios (i.e., 100-year to 2-year events), and thus tail heaviness. Rain vs snow: Higher CV for rain-dominated regions compared to snow-dominated regions. Humid vs arid: Higher CV for semi-arid regions compared to wetter regions. Rain vs snow & humid vs arid: Peak flow ratios are lowest in wet, snowmelt-dominated regions (Columbia-southern Rockies). Ratios are modest in wet areas with rain, snow, or mixed regimes (Coast). Ratios are largest in semi-arid regions with spring snowmelt and rain-on-snow (Fraser-Thompson). Increasing CV leads to heavier tails. 179 Study reference Control examined Location or region (or based on) Main findings (Bernardara et al., 2008) Rain vs snow Rhone-Mediterranean, France Stronger tendency towards heavier tails (power law behaviour) in Mediterranean regimes, followed by oceanic regimes. Heavy tails were less prevalent in snow-dominated regimes. (Blöschl & Sivapalan, 1997) Catchment area & nonlinearity Austria Nonlinearity: Thresholds increase CV. Thresholds in runoff coefficients lead to "kinks" in the FFC and steepens the curve. Catchment area: Increased area decreases CV through increased travel times within the channel and presence of baseflow. Larger baseflow contributions decrease CV. Kinks in the FFC appear at higher return periods with increasing size of the catchment due to decreased rainfall intensities across larger spatial areas. 180 Study reference Control examined Location or region (or based on) Main findings (Breinl et al., 2021) Humid vs arid, catchment size, topography & geology Austria Humid vs arid: FFCs are steeper than rainfall curves, especially in drier catchments, although not in glaciated catchments. Wetter catchments have similar steepness in the rainfall and flood curves due to orographically-enhanced precipitation, frequent soil saturation, and higher event runoff coefficients. Catchment size: Increased area decreases variability. Topography: Increased variability in steeper catchments relative to flatter terrain. Geology: Pervious geology reduces variability. (M. Chen et al., 2021) Precipitation & geology United Kingdom Nonstationary distributions utilizing rainfall-related covariates provided the best fits. Areas that were better modelled by annual rainfall covariates had moderate-to-high permeability bedrock, allowing for greater infiltration of water, deep percolation, and higher baseflow contributions. Areas that were better modelled by maximum daily rainfall covariates had lower permeability bedrock, increasing susceptibility to high-intensity rainfall events. 181 Study reference Control examined Location or region (or based on) Main findings (Farquharson et al., 1992) Rain vs snow Northwestern Africa, Iran, Jordan, Saudi Arabia, Botswana, & South Africa Snowmelt driven floods (i.e., in Iran) and those with increased groundwater contributions (i.e., Jordan) were less steep and skewed. All other curves were steeper and more skewed. (Gioia et al., 2012) Storage N/A CS is highest when infiltration rate at saturation is medium-high and storage capacity is moderate, as both are high enough to be influential but not high enough to be too rare. Skewness is lower when only one factor is relevant. (Guo et al., 2014) Humid vs arid & baseflow Contiguous USA Humid vs arid: Increasing aridity increases CV due to generally drier conditions but greater nonlinearity in floods. Baseflow: Higher baseflow conditions increase subsurface contributions to flow, decreasing CV. Low baseflow conditions suggest greater nonlinearity due to poor drainage and greater retention of soil moisture, increasing steepness of the FFC. (Gurrapu et al., 2016) Natural variability Western Canada The negative (cold) phase of the Pacific Decadal Oscillation sees cooler and wetter winters, deeper snow accumulation, greater flood magnitudes, and higher FFCs (upward shift) relative to the positive phase in most of the area. 182 Study reference Control examined Location or region (or based on) Main findings (Klemeš, 1970) Storage N/A Even if precipitation is positively skewed, annual runoff may display negative skewness if the watershed has a large storage capacity through features such as lakes, snow and glacial cover, and underground storage. Storage capacity must be large enough to contain high levels of precipitation without allowing for large amounts of runoff. (Kusumastuti et al., 2007) Mixtures, soil depth & nonlinearity Lake Warden catchment, Australia Nonlinearity: Thresholds are linked to changes in runoff generation mechanisms (such as a change from predominantly subsurface to surface flow), and manifest as a break in the FFC. Mixture: During the winter, wetter soils allow for frequent smaller floods and some larger floods (if large rainfall intensities occur). During the summer, dry antecedent conditions coincide with cyclonic events, leading to less frequent small floods but more large floods. Inclusion of these summer cyclonic events led to higher flood magnitudes and earlier breaks in the FFC than if only year-round synoptic events were included. Soil depth: Deeper soils delay the appearance of this break in the FFC and reduce influences of within-storm variability. 183 Study reference Control examined Location or region (or based on) Main findings (Loukas et al., 2000) Rain vs snow Southern BC, Canada The Gumbel distribution was suitable for both watersheds, one with rainfall and rain-on-snow contributions (Upper Campbell) and the other with snowmelt, rain, and glacial contributions (Illecillewaet). (Macdonald et al., 2022) Rain vs snow & catchment area Austria & Germany Rain vs snow: Lighter tails for catchments with predominantly winter or snow-related floods. Heavier tails for catchments with predominantly summer or rain-generated floods. Catchment area: Lighter tails with increasing size of catchment (Macdonald et al., 2024) Storage & nonlinearity Central Europe Threshold return periods where flood tails mirror that of precipitation varied among catchments (from under 2 years to over 6000 years) but were typically between 100-500 years in their simulations. Runoff generation modulates flood peaks before this point. Return period of this threshold increases with a larger ratio of watershed threshold to mean annual precipitation (or catchment wetness). Thresholds produce step changes, which lead to higher shape parameters. (McCuen & Hromadka, 1988) Storage & precipitation USA Storage: Increasing watershed storage decreases flood skew. Precipitation: The upper limit of flood skew is controlled by rainfall skew. 184 Study reference Control examined Location or region (or based on) Main findings (McCuen & Smith, 2008) Storage & precipitation Maryland & Delaware, USA Storage: Flood skew decreases relative to rainfall skew with increasing storage capacity. When storage capacity is overwhelmed, it does not exert as strong an influence on flood skew. Precipitation: When watershed storage capacity is exhausted, flood skew more closely echoes rainfall skew. (Meigh et al., 1997) Humid vs arid & catchment area Tropical & subtropical countries Humid vs arid: Arid regions typically have lower average floods (1-year or 2-year event) but show steeper tails due to high inter-annual variability. Humid regions have larger average floods but show lighter (flatter) tails due to lower inter-annual variability. Catchment area: Large, humid catchments showed some of the lightest tails. (R. Merz & Blöschl, 2003) Rain vs snow & catchment area Austria Rain vs snow: CV is smaller for snowmelt floods due to upper limits of snowmelt. Their runoff coefficients are not small but see less of an increase with larger storm events. CV is larger for rain-dominated catchments. FFCs consisting of rain events were steeper than those with greater influence of rain-on-snow events. Catchment area: A decrease in CV with increasing area for most flood types, except for flash floods. 185 Study reference Control examined Location or region (or based on) Main findings (R. Merz & Blöschl, 2009) Rain vs snow & humid vs arid Austria Rain vs snow: Smaller CV for catchments with greater glacial or snow influence. Catchments with year-round rain-generated events see higher CVs, as rainfall may coincide with dry or wet catchments. Humid vs arid: Smaller CV and CS for wetter catchments, which have consistently high runoff coefficients. Drier catchments typically have lower runoff coefficients, but occasional large floods lead to much larger increases in runoff coefficients, greater interannual variability, and higher CS. A lighter tail in the wetter Bregenzer Ache catchment compared to the drier Altschlaining catchment. (Metzger et al., 2020) Humid vs arid Israel & US Heavier tails in arid/semi-arid regions compared to non-arid, Mediterranean regions (i.e., those experiencing similar patterns in precipitation, but greater yearly amounts). (Morrison & Smith, 2002) Catchment area Central Appalachian Mountains, USA No dependency of tail heaviness with catchment area. However, floods were most influenced by thunderstorms in smaller watersheds while extratropical cyclones were more influential in larger watersheds. (Mushtaq et al., 2023) Mixture Germany Upper tails may consist of flood-generation processes different than those leading to common floods, leading to "flood divides" separating common and extreme floods, and heavier tails. 186 Study reference Control examined Location or region (or based on) Main findings (Opere et al., 2006) Humid vs arid Nile Equatorial Basins Lighter (normal and Gumbel) tails provided the best fit for most stations in this semi-humid environment. (Pitlick, 1994) Rain vs snow & humid vs arid Cordilleran Rocky Mountains, USA Rain vs snow: Snowmelt-driven floods had the smallest tail ratios (100-year event to mean annual event) and relatively flat FFCs, with larger ratios for catchments with frontal storms. Humid vs arid: Flood variability is highly influenced by precipitation variability. Semi-arid regions see more of their annual precipitation made up of a few single storm events. Humid regions see longer periods of precipitation with runoff moving as slower subsurface flow, reducing variability. The largest tail ratios were in semi-arid catchments with intense thunderstorms. 187 Study reference Control examined Location or region (or based on) Main findings (Rogger et al., 2012) Nonlinearity & catchment area Austria Nonlinearity: Step changes appear when a threshold storage capacity is surpassed, where even small increases in rainfall lead to much larger increases in contributing source area and surface runoff. When storage capacity is rather uniform in space, thresholds can be quite prominent due to synchronous activation of many areas generating surface runoff. Watersheds with low storage capacity will see step changes at earlier return periods. Catchment area: Storage capacity is likely to be more uniform in space in smaller catchments, suggesting prominent thresholds. (Rogger et al., 2013) Nonlinearity N/A Step changes were less prominent with increasing temporal variability in antecedent soil moisture and were more prominent with an increase in the variably saturated region. Return period of the step change roughly corresponded to that of rainfall volumes needed to overwhelm storage capacity. (Sivapalan et al., 1990) Catchment area & nonlinearity N/A Catchment area: Increased catchment area led to a lighter tail, as the catchment was less likely to be covered by homogeneous rainfall patterns. Nonlinearity: A break in the FFC may result from a shift from saturation excess overland flow at low return periods to mostly infiltration excess overland flow at high return periods. 188 Study reference Control examined Location or region (or based on) Main findings (Sivapalan et al., 2005) Seasonality Austria The largest floods occur when high rainfall intensities and runoff coefficients (i.e., from wetter catchments) coincide, or are “in phase”, and decrease when do not coincide, or are “out of phase”. In seasons with greater catchment wetness and smaller rainfall intensities, smaller but more frequent floods may yield a gentler FFC. Where dry seasons coincide with larger rainfall intensities, fewer smaller floods with occasional larger floods may yield a heavier tail. (Smith et al., 2011) Mixtures Eastern USA While both tropical cyclones and extratropical systems lead to flooding in the eastern US, tropical cyclones more strongly influence the upper tail. (Smith et al., 2018) Humid vs arid, mixtures, & catchment area USA Humid vs arid: Upper tail ratios (ratio of 100-year to 10-year event) in arid and semi-arid regions were somewhat higher than those in humid regions. Mixtures: While snowmelt-driven floods and floods from winter/spring storms more commonly resulted in annual flood peaks, record floods consisted of those from thunderstorms and tropical cyclones. Catchment area: No dependency of shape parameters on catchment area. 189 Study reference Control examined Location or region (or based on) Main findings (Struthers & Sivapalan, 2007) Storage & nonlinearity N/A When storage capacity is finite, exceedance of this threshold leads to a change from subsurface flow to surface runoff, which manifests as a break in the FFC. Before this point, flood peaks see a greater influence of subsurface flow. After this point, the FFC is more similar to that of precipitation. Lower storage capacity leads to a break at earlier return periods. Including seasonality in models decreased chances of no flow years and increased chances of saturation, increasing flood magnitudes and producing an earlier break in the FFC. (Thorarinsdottir et al., 2018) Rain vs snow, catchment shape, catchment area, & lakes Norway Rain vs snow: The shape parameter was influenced by proportion of rainfall. Areas with greater snowmelt influence display negative shape parameters and upper bounds. Catchment area: The shape parameter was influenced by catchment area to a lesser extent. Catchment shape: Elongated catchments saw less variability. Lakes: Effective lake cover influenced scale parameter and reduced variation in floods. 190 Study reference Control examined Location or region (or based on) Main findings (Villarini et al., 2011) Mixture & catchment area Midwest USA Mixtures: Many of the largest floods consisted of summertime convective storms and removing these storms decreased tail heaviness. Mixtures of flood generating mechanisms lead to heavier tails. Catchment area: Shape parameter decreased with increasing area. (Villarini et al., 2012) Catchment area Austria Shape parameter showed a weak decrease with increasing area. (H. J. Wang et al., 2023) Catchment shape & area Germany Catchment shape: Rainfall spatial variability increased heaviness of the FFC, although more circular (or less elongated) catchments were more resilient. When a threshold of rainfall variability was reached, elongated catchments saw greater increases in FFC heaviness. For elongated catchments, their more symmetric routing distances and reduced buffering capacity led to streamflow more easily propagating heavier tails with increased rainfall variability. Circular catchments were found to have more asymmetric runoff routing distances, leading to asynchronous delivery of flow and greater buffering capacity. Catchment area: Larger catchments were also more resilient. 191 Study reference Control examined Location or region (or based on) Main findings (Waylen & Woo, 1983) Rain vs snow Southwestern BC, Canada Gradual snowmelt from lower to higher elevations decrease variability of spring snowmelt-driven floods. Floods generated by winter rain-on-snow events show greater variability due to influences of the storm’s spatial extent, precipitation levels, and snowpack accumulation. (L. Yang et al., 2017) Mixtures Arizona, USA The upper tail consists mainly of thunderstorms from North American monsoon events, producing heavier tails. Winter events yield more frequent, smaller-magnitude floods. (L. Yang et al., 2019) Mixtures & catchment area China Mixture: In China, floods may be generated by a mixture of tropical cyclones, extratropical systems, and monsoons. In Northern China, landfalling tropical cyclones occur less often than in Southern China, but they lead to record floods and positive shape parameters. In Southern China, monsoonal precipitation makes up the upper tail, producing both positive and negative shape parameters. Catchment area: Shape parameter showed a weak decrease with increasing area. (L. Yang et al., 2021) Humid vs arid China Larger upper tail ratios (flood peak divided by 10-year flood) are found on the windward sides of mountainous regions with mean annual rainfall of 550 mm. This suggests that semi-arid regions experienced more floods with larger upper tail ratios than arid and humid areas. 192 Study reference Control examined Location or region (or based on) Main findings (G. Yu et al., 2021) Mixtures Colorado Front Range (USA) Heavy rain and rain-on-snow events more strongly influence the upper tail. Antecedent soil moisture and snowmelt most strongly influence more frequent peak discharge events. Flood peaks are limited by daytime energy availability and energy gains from warm rain falling onto the snowpack. (G. Yu et al., 2022) Rain vs snow & mixtures Western US Rain vs snow: Positive shape parameters were more common for areas experiencing rain-driven floods. Negative shape parameters with upper bounds were more common in areas with snowmelt floods. Mixtures: Most extreme floods result from rainfall, as snowmelt-driven floods are limited by energy available for snowmelt. (Zaerpour et al., 2024) Rain vs snow Global Snow-dominated streams have the smallest shape parameters while intermittent streams have the highest. Mixed rain and snow influences lead to heavier tails than snowmelt alone. In North America, cold climates including central BC mountain forests have a melt regime with negative shape parameters while Appalachian and Prairie regions have positive shape parameters. 193 Appendix B Table B.3 Key conclusions of forest effects on peak flows are tabulated from studies using a deterministic data analysis procedure, using the Scopus database to search for deterministic studies on the effects of changing forest cover on floods (see section 3.2). For each study cited, location of the study, its hydroclimatic regime, range of catchment size(s) studied (or treatment watershed size if there is only one treatment watershed), record length, key conclusions regarding forest effects on peak flows, and whether convergence of regression lines is observed in key figures are listed whenever possible. Post-treatment record lengths are provided whenever listed, but overall record lengths (including pre- and post-treatment periods) are provided if post-treatment record length is not listed. Key conclusions discussing behaviour for larger events or convergence are bolded. Figure numbers correspond to figures in the cited work. Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Bathurst et al., 2011) Costa Rica, Ecuador, Chile, Argentina Catchment-dependent; rain, rain-on-snow 0.6–1545 2–28 Decreasing influences with increasing rainfall magnitude after harvesting. Convergence occurs around 5–10 years. No absolute convergence visible in Figure 4A, but relative convergence is suggested for larger events. Convergence in Figure 4B. 194 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Beschta et al., 2000) Cascade Mountains, Oregon, USA Rain-on-snow 0.6–640 28–56 (few observations above the >5-year event) Smaller watersheds: Peak flows increased after harvesting, with little effects on larger events (i.e., 5-year event). Larger watersheds: Less significant, with a decrease in peak flows following harvesting. Approximate convergence on Figures 1C and 2D for events beyond the 5-year flood. (Burton, 1997) Dry Fork Basin, Utah, USA Mainly snow 1.34 (treatment) 20 (post-treatment) Peak flows increased following harvesting. No convergence visible (Figure 3). 195 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Cheng, 1989) Camp Creek, British Columbia, Canada Snow 33.9 (treatment) 6 (post-treatment) Annual peak flows increased after harvesting. No figures. (Goodbrand et al., 2022) Tri-Creeks Experimental Watershed, Alberta, Canada Rain & snow 15.2–28.3 5–6 (post-treatment) Regression analysis did not detect change in daily or annual runoff after harvesting. No figures. (Harr et al., 1979) Coyote Creek Experimental Watersheds, Oregon, USA Rain & snow 0.49–0.69 5 (post-treatment) Peak flows increased after harvesting, including the 9-year event. No convergence visible (Figure 8). (Harr & McCorison, 1979) H.J. Andrews Experimental Forest, Oregon, USA Rain & snow (includes rain-on-snow) 0.085–0.10 1 (post-treatment) (13 events) Harvesting decreased peak flows (snow events) or no effects were found (rain events). Little change in Figure 1. No convergence visible in Figure 2. 196 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Harr, 1980) Bull Run Municipal Watershed, Oregon, USA Rain, rain-on-snow, & snow 0.59–2.53 Unclear; logging finished in 1972, suggesting a maximum of 6 PT years. No significant effects on peak flows following harvesting. No convergence visible (Figures 12–13). (Harr et al., 1982) H.J. Andrews Experimental Forest, Oregon, USA Rain-on-snow 0.13–0.21 5 (post-treatment) No change in peak flow size following logging. Little change (Figure 7). (Harr, 1986) H.J. Andrews Experimental Forest, Oregon, USA Rain-on-snow 0.085–0.96 18 (post-treatment) Logging increased rain-on-snow events (3- to 8-year events in one watershed), with moderate-sized peaks increasing the most. Convergence (Figure 1). 197 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Hewlett & Helvey, 1970) Coweeta Hydrologic Laboratory, North Carolina, USA Rain 0.44–0.49 4 (post-treatment) Some increase in peak flows following harvesting. No figures. (Hornbeck et al., 1970) Central New England, USA Rain & snow 0.16 3 (post-treatment) Growing season high flows increased following harvesting. No figures. (Jones & Grant, 1996) Cascade Mountains, Oregon, USA Rain & rain-on-snow 0.6–600 22–25 (post-treatment) for small catchments; progressive harvesting for large catchments Clear cutting and road construction increased peak discharges for both small and large events. No figures. 198 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Jones, 2000) Cascade Mountains, Oregon, USA Rain & rain-on-snow 0.1–2.53 10–34 (post-treatment) Decreasing effects of harvesting for >1-year rain-on-snow events. Most significant increases in peak flows were for small events. No figures. (Moore & Scott, 2005) Camp Creek, British Columbia, Canada Snow 33.9 (treatment) 18 (post-treatment) Harvesting increased peak flows for smaller events, not larger events (not statistically significant). No figures. (Rothacher, 1973) H.J. Andrews Experimental Forest, Oregon, USA Rain-on-snow 0.96 (treatment) 5 (post-treatment) Average peak flows increased after harvesting, but little effect on larger events. Convergence (Figure 3). 199 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Thomas & Megahan, 1998) Cascade Mountains, Oregon, USA Rain & rain-on-snow 0.6–600 23 (post-treatment) Small watersheds: Increases in peak flows were greatest for small events, with little effects for ≥2-year floods. Large watersheds: No effects or inconclusive results. Convergence or approximate convergence for Figures 1A, 1C–D, and 2A. No convergence visible on Figures 1B and 2B–E. (Troendle & King, 1985) Fraser Experimental Forest, Colorado, USA Snow 2.89 (treatment) 28 (post-treatment) Peak discharge increased following harvesting, with less relative increase or a decrease in peak flows of the largest events. No figures. The largest events (i.e., 1957, 1965, 1971, 1983) saw less relative increase or a decrease in peak flows in Table 2. 200 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Troendle & King, 1987) Fraser Experimental Forest, Colorado, USA Snow 0.41–0.78 0–6 (post-treatment) Peak flows increased (clearcut catchment) or saw no increase (partial cut & main catchments). No figures. (Troendle et al., 2001) Coon Creek, Wyoming, USA Snow 16.7 (treatment) 5 (post-treatment) No significant increase in annual peak flows following harvesting. No figures. (Van Haveren, 1988) Wagon Wheel Gap, Colorado, USA Snow 0.81 (treatment) 7 (post-treatment) Average maximum daily flows increased. No figures. (Walsh et al., 2020) Brooman State Forest, Australia Rain 0.013–0.048 2.5 (post-treatment) Harvesting increased peak flows. No convergence visible (Figure 8). 201 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: convergence (Xiao et al., 2022) United Kingdom and Ireland Rain 0.08–3.9 66 station-years, but appears to be 4–11 post-treatment years No significant increase in larger peak flows following disturbance. Only small, frequent peak flows (below the mean annual flood) saw increases. Little change in Figures 3 and 4A. Convergence in Figures 4B–C. 202 Table B.4 Key conclusions of forest effects on peak flows are tabulated from studies using a stochastic data analysis, using the Scopus database to search for stochastic studies on the effects of changing forest cover on floods (see section 3.2). For each study cited, location of the study, its hydroclimatic regime, range of catchment size(s) studied (or treatment watershed size if there is only one treatment watershed), record length, key conclusions regarding forest effects on peak flows, and tail behaviour of Flood Frequency Curves (FFCs) are listed whenever possible (parallelism, convergence, and divergence are underlined). Post-treatment record lengths are provided whenever listed, but overall record lengths (including pre- and post-treatment periods) are provided if post-treatment record length is not listed. Key conclusions discussing behaviour for larger events are bolded. Figure numbers correspond to figures in the cited work. Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Bradshaw et al., 2007) 56 developing countries Rain Country areas 11 Flood frequencies and durations decreased with greater natural forest cover (and increased with nonnatural forest cover). A 10% loss in natural forest cover increased flood frequencies from 4–28%. No figures 203 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Duncan, 1995) Brightwater, New Zealand Rain 0.04–0.077 20–23 years (≤4 post-treatment) Flood peaks from pine catchments were notably lower than those of pasture catchments. Following harvesting, annual runoff was greater than expected from forested conditions. Pines curve is shifted down relative to the pasture curve with parallelism at the upper tail, including for the 50-year event (Figure 5). (Gabriels et al., 2022) Maarkebeek, Flanders, Belgium Rain 48 45 Afforestation reduced the relative flood risk by 57%. No figures 204 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Huang et al., 2018) Upper Honganjian Watershed, China Rain 981 46 Significant negative correlation between forest area and flood frequency. For 20- to 1000-year events in the flood season, forest and urban land cover showed greater importance than rainfall, farmland, and grassland on the number of flood events. No figures 205 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Hurkmans et al., 2009) Rhine Basin, western Europe Rain & snow Tributaries range from 4118–27088 10 (model calibration & validation) Forested scenarios consistently produce the lowest flood peaks, including for large events (i.e., 15-year). Forest curve is shifted down relative to the current, climate scenarios, and grass curves with divergence at the upper tail, including for the 15-year event in Figure 7 Lahn subbasin. Forest curve is shifted down relative to all other curves except grass curve with parallelism at the upper tail, including for the 15-year event in Figure 7 Rhine basin. 206 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Johnson & Alila, 2023) Interior British Columbia, Canada Snow 99–1011 28–40 Increased frequencies following harvesting, with larger changes for more extreme events. 7-year, 20-year, 50-year, and 100-year events increased in frequency by 2, 4, 6, or 10 times (respectively). Harvested curve is shifted up relative to the no disturbance curve with parallelism at the upper tail, including for the 100-year event (Figure 6). 207 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Kuraś et al., 2012) 241 Creek, British Columbia, Canada Snow 4.74 4 years of records to generate 100 years of flow, then 10 000 runs of Monte Carlo simulations For 50% harvesting, peak flow magnitudes increased for 10- to 100-year events. Frequencies increased 5–6.7 times for the 100-year event and 1.7–2 times for the 10-year event, suggesting larger changes to larger floods. Harvested curve is shifted up relative to the control curves with divergence at the upper tail, including for the 100-year event (Figure 5). 208 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Lallemant et al., 2021) Chindwin River Basin, Myanmar Rain 113 800 Observations were extended using Markov Chain Monte Carlo Peak flow volume increased following deforestation for all return periods (including the 500-year event). Continued deforestation curve is shifted up relative to the forest protection curve with approximate parallelism at the upper tail, including for the 500-year event (Figure S5). 209 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Liao et al., 2024) Baoli River Watershed, Pingtung, Taiwan Rain 97.7 Unclear / Not stated The 10- and 20-year events saw flood probabilities decreasing to 4.8% and 27%, respectively, using off-line flood detention (i.e., classified as mixed forest) compared to an engineering approach. This suggests increasing changes in frequencies for larger events. No figures 210 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (McEachran et al., 2023) St. Louis River Basin, Minnesota, USA Glacial 56–8880 4–33 years Flood peak responses were inconsistent. While climate variability and physiography played a greater role, effects of forest disturbance are suggested to be apparent even in large catchments. No figures 211 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Pham et al., 2025) Coweeta Hydrologic Laboratory, North Carolina, USA Rain 0.12–0.16 44 (post-treatment) The north-facing watershed saw increases in magnitude and frequency following harvesting, with increasing effects for larger events (i.e., 70-year event). The south-facing watershed saw little change. Post-harvesting curve is shifted up relative to the expected curve (i.e., without harvesting) with divergence at the upper tail, including for the 70-year event (Figure 3A). Post-harvesting curve is shifted down relative to the expected curve, including for the 68-year event (Figure 3B). 212 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Preti et al., 2011) South to Central Italy Rain <100 to >5000 Unclear / Not stated Disregarding effects of 30% forest cover can lead to a return period of 7 rather than the correct 20 years (i.e., 3x increase in frequency). Although they suggest that relative effects of forest cover decrease with increasing catchment size, effects are still notable for large floods (i.e., 20-year unforested event). Failing to account for forest cover can lead to incorrect predictions. No figures 213 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Reynard et al., 2001) Thames & Severn Catchments, United Kingdom Rain 9895 & 9948 30-year baseline series, which are perturbed to create different scenarios 50% forest cover reduces flood peaks relative to the greenhouse gases only experiment in 2050, with impacts evident for the 50-year event. Increased forest curve is shifted down relative to climate change only, best guess land use change, and increased urbanization curves with divergence at the upper tail, including for the 50-year event (Figure 5). 214 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Schnorbus & Alila, 2004) Redfish Creek, British Columbia, Canada Snow 26 29 years, used to generate a 100-year time series Harvesting overall increased flood magnitudes for a range of return periods, including the 100-year event for the 7-day event (inconclusive results for hourly and daily events). Harvested curve is shifted up relative to the control curve with parallelism to slight divergence at the upper tail, including for the 100-year event (Figure 9). 215 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Schnorbus & Alila, 2013) Upper Penticton Creek, British Columbia, Canada Snow 4.7 100 years of streamflow were simulated and compared to 18 years of observations Hourly peak discharge magnitudes increased for all events with a return period of 2 years or greater. Frequencies increased following harvesting, with larger changes for increasing size of flood, including for the 100-year event. Post-harvest curves are shifted up relative to the control curve with divergence at the upper tail, including for the 100-year event (Figure 6). 216 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions Figures: FFC tails (Te Linde et al., 2010) Rhine Basin, northwestern Europe Rain & snow 185 000 10 000 years simulated Under changing climate conditions, 96% forest cover decreases peak flows, even for the 500-year event, relative to a climate change only scenario. Climate change with increased forest cover curve is shifted down relative to the climate change only curve with parallelism at the upper tail, including for the 1250-year event (Figure 8). 217 Table B.5 Key conclusions of forest effects on peak flows are tabulated from studies using both deterministic and stochastic analysis procedures, using the Scopus database to search for studies that applied both deterministic and stochastic procedures to study the effects of changing forest cover on floods (see section 3.2). Study location, hydroclimatic regime, range of catchment size(s) (or treatment watershed size if there is only one treatment watershed), record length, and key conclusions regarding forest effects on peak flows including descriptions of key supporting figures are listed whenever possible. Post-treatment record lengths are provided whenever listed, but overall record lengths (including pre- and post-treatment periods) are provided if post-treatment record length is not listed. Key conclusions discussing behaviour for larger events are bolded. Figure descriptions state whether regression of convergence lines are observed in deterministic figures or the behaviour of Flood Frequency Curve (FFC) tails in stochastic studies (parallelism, convergence, and divergence are underlined), with figure numbers corresponding to figures in the cited work. Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (Alila et al., 2009) Fool Creek, Colorado, USA H.J. Andrews Experimental Forest, Oregon USA Catchment-dependent; snow, rain-on-snow 1–2.9 23–48 Fast decrease in treatment effects with increasing event size. Convergence (Figure 3A). Increased magnitudes and frequencies after harvest, sometimes with greater effects on larger floods (i.e., 10- to 40-year events). Post-harvest curve is shifted up, with effects persisting up to the 100-year event (Figures 3D and 4–7). Despite converging trends, a “no-effect threshold” is not reached. 218 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (Barnes et al., 2023) Irthing Catchment & headwaters, England Rain 335 (headwaters are 1–10) ≤6 years 600 simulated years for stochastic analysis Decreased relative impacts of 100% forest cover relative to 100% grassland cover for the largest events. Convergence (Figure 6). Largest magnitude changes are for 15- to 35-year events, but effects persist for larger events. Frequencies remain large or increase. Forested curve is shifted up relative to the grass curve with some converging trends (Figure 7 Flothers and Irthing) or parallelism (Figure 7 Coalburn and Throssburn) at the tails, including for the 10-year event. For the simulated graph (Figure 8), forested curve is shifted up relative to the grass curve with paralellism at the tails, including for the 100-year event. 219 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (Bathurst et al., 2018) Northern England, United Kingdom Rain 1.4–6.9 3 (post-treatment) The forested catchment shows higher peak discharges than the grassland catchment. Convergence (Figure 8). Flood peaks were more frequent in the forested catchment Coalburn due to forest ditching. Not enough data to provide conclusions on larger floods. Forested Coalburn curve is shifted down compared to the grass Flothers curve with parallelism at the upper tail, including for the 8-year event (Figure 7). 220 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (Bathurst et al., 2020) Wark Forest, United Kingdom Glendhu, New Zealand H. J. Andrews Experimen-tal Forest, Oregon, USA La Reina, Chile Primarily rain, but includes snowmelt & rain-on-snow 0.34–3.1 Varies; 7–22 years For small and moderate events, removing forest cover increases flood peaks or has no effect (peaks decrease for Wark Forest). Convergence in Figure 5B and 5D. Little effect in Figure 5A. No convergence in Figure 5E. No convergence in Figures 5C and 5D (although slight converging trends are visible in 5C). Forested catchments had lower magnitudes than grassland or logged catchments (inverse for Wark Forest). Grassland GH1 curve is shifted up compared to the forested GH2 catchment with effects persisting at the upper tail, up to the 10-year event (Figure 6). Note: While convergence is suggested, it is based on the largest point(s) which are highly influenced by sampling variability (see section 2.6.1). Any change in behaviour at these highest point(s) should be interpreted with caution. Therefore, this table only considers general trends in large events. 221 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (Birkinshaw et al., 2011) La Reina, Chile Rain 0.35 1000 simulated years Convergence for large events (Figure 4). Relative change between logged (higher discharge) and forested (lower discharge) decreases with increasing return period but absolute differences persist. Logged curve is shifted up relative to the forested curve with parallelism at the upper tail, including the >1000-year event (Figure 8). 222 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (Birkinshaw et al., 2014) Coalburn catchment, England, United Kingdom Snow influence 1.5 19 (post-treatment) The taller trees scenario yielded lower discharge than the smaller trees scenario, but this effect decreased for larger events. No convergence (Figure 11). The 5-year, 10-year, and 20-year events in the scenario with taller trees are 3.2-year, 6.5-year, and 13-year events in the scenario with smaller trees, respectively. Even as the tails seem to be converging, frequency changes are about 50% for these larger events. Tall trees curve (Scenario 2) is shifted down relative to the small trees curve (Scenario 1) with converging trends at the upper tail (although convergence does not occur) (Figure 12). Effects persist beyond the 25-year event. 223 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (Fahey & Payne, 2017) Otago, New Zealand Mainly rain 2.16–3.10 23 (post-treatment; post-canopy closure period) Decreased reduction in flood peaks with forest cover for large events. No figures The forested catchment GH2 has lower flood magnitudes than the grassland GH1 catchment. While they state that relative effects decrease for larger return periods (i.e., 100-year event), absolute magnitude changes persist. No figures. 224 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (Green & Alila, 2012) Fool Creek, Colorado, USA Okanagan Valley, British Columbia, Canada Snow 3–37 19–99 (post-treatment) Decreasing effects for larger floods, with some floods even reduced following harvesting. Convergence in Figure 3B. No convergence visible in Figures 3A and 3C–D. Increased frequencies of all floods, including large (i.e., 50-year) floods. No thresholds at which there was no effect were observed. Harvested curve is shifted up relative to the pre-harvesting curve generally with parallelism (or slight converging trends) at the upper tails (Figure 2). Effects persist at the upper tail, including up to the 50-year event. 225 Study reference Location Hydro-climatic regime Catchment size (km2) Record length (Years) Conclusions & figures: deterministic Conclusions & figures: stochastic (McEachran et al., 2021) Marcell Experimental Forest, Minnesota, USA Rain & snow 0.089–0.53 36–46 (post-treatment) No significant changes to annual maximum flows following harvesting. Little change in Figure 3A. No convergence in Figure 3B. Increased annual maximum flows, including up to the 50-year event in one catchment. Effects increased with increasing size of event. Post-harvest curve is shifted up compared to the expected (i.e., without harvest) curve with divergence at the upper tails, including for the 50-year event (Figure 6A and 7A).
Thesis/Dissertation
eng
Forestry
Vancouver : University of British Columbia Library
Attribution-NonCommercial-NoDerivatives 4.0 International
Graduate
Alila, Younes, 1962-
Understanding and predicting hydroclimatic extremes in the Anthropocene : a causal, stochastic physics approach
Text