Effects of Threshold Nonlinearities on the Transformation of Rainfall to Runoff to Floods in a Lake Dominated Catchment System

Transcription

1 Effects of Threshold Nonlinearities on the Transformation of Rainfall to Runoff to Floods in a Lake Dominated Catchment System DYAH INDRIANA KUSUMASTUTI B.Sc. (Hons), M.Sc. This thesis is submitted in fulfilment of the requirements of the degree Doctor of Philosophy of The University of Western Australia

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3 ABSTRACT Runoff generation behaviour and flooding in a lake dominated catchment are nonlinear, threshold-driven processes that result from the interactions between climate and various catchment characteristics. A complicating feature of the rainfall to runoff transformation, which may have implications for the flood frequency, is that the various surface and subsurface flow pathways are dynamic, heterogeneous and highly nonlinear, consisting of distinct thresholds. To understand the impact of threshold nonlinearities on the rainfall-runoff transformation in such catchments, a systematic examination was carried out to investigate runoff generation behaviour of the catchment itself, the overflow behaviour of a lake in combination with the catchment draining into it, as well as the lake organisation within a lake chain network. Three storage based thresholds were considered: the catchment field capacity storage governing catchment subsurface stormflow, total storage capacity governing catchment surface runoff, and lake storage capacity governing lake-overflow. The effects of these threshold-driven processes and their interactions on the flood frequency curve have been examined using simple conceptual rainfall-runoff models, which are driven by inputs generated by a stochastic rainfall model. Through these investigations, this thesis has provided valuable insights into the process controls of lake-overflow events and the associated flood frequency behaviour in lake dominated catchments. In particular, the relative roles of climate, soil depth, the soil s drainage capacity, as well as the relative geometry of the lake vis a vis the contributing catchment, in the determination of the dynamic characteristics of lake-overflow events and associated flood frequency behaviour have been highlighted. In addition, the importance of lake organization, as expressed in terms of the average ratio of catchment area to lake area and the spatial variability of this ratio from upstream to downstream, and their impact upon connectivity and flood frequency have also been explored. The outcomes of this study highlight the importance of thresholds governing flood frequency, and provide insights into the complex interactions between rainfall variability and the various threshold nonlinearities in the rainfall-runoff process, which are shown to have a significant impact on the resulting flood frequency curves. The improved understanding of these process controls will be useful in assisting the 1

4 management of the catchment-lake system in the study region, and in regions elsewhere. In particular, the outcome of this study can provide guidance towards the adoption of various management strategies for lake chain systems by illustrating the effects of potential flow interruption and retardation as ways to assist in flood prevention and mitigation, whether it is aimed at decreasing the frequency of occurrence of lake overflows, or merely decreasing the flow magnitude for a given return period. 2

5 ACKNOWLEDGEMENTS I am indebted to many people, including many not specially mentioned here, who have rendered their time, knowledge and assistance to me to accomplish this research. First and foremost, I would like to gratefully acknowledge the guidance, constructive criticism, enthusiastic encouragement and perseverance of my supervisors, Dr David Reynolds and Prof Murugesu Sivapalan. I gratefully acknowledge the support and valuable inputs from Dr Iain Struthers in the last nine months of my studies. Thanks to Tilo Masserbauer and Cameron Hennessy of the Department of Conservation and Land Management (CALM), Esperance, for providing valuable logistic support during my field work in Esperance. Special thanks to my friends and fellow students, Selva, Tara, and Kyongho, for all the assistance rendered in the field and through simulating discussions. My sincere gratitude is also extended to other individuals who have contributed to this thesis, including Drs Berwin Turlach and Kevin Murray of the Department of Mathematics and Statistics, UWA, Dr. Chris Spence of Environment Canada, Prof. Jeff McDonnell of Oregon State University and Dr. Krystina Haque of UWA Student Services. Thanks also must go to the many staff in the School of Environmental Systems Engineering and the Centre for Water Research for providing support and a stimulating work environment. I gratefully acknowledge the scholarship provided by Ausaid and a supplementary stipend from the Centre for Groundwater Studies. Special thanks to Ausaid Liaison officer Rhonda Haskell, Cathy Tang, and Chris Kerin for their support throughout my study. Thanks to the Australian Research Council and the Department of Conservation and Land Management for the Industry Linkage grant which contributed to the extensive field work. Thanks to the Indonesian Government and the University of Lampung for giving me the chance to study at the University of Western Australia. I would like to thank fellow postgraduate students within the School of Environmental Systems Engineering and the Centre for Water Research, who made the period of my study here an enjoyable and memorable experience. In particular, my office mates of 3

6 Room 1.14 over the years: Stan, Mike, Jos, and Ben. Thanks also to the Indonesian postgraduate students in UWA who have made my life in Perth more enjoyable. Finally, I would like to express my deep appreciation for the encouragement and support of my husband Joko and daughter Laras, for the many sacrifices they have made throughout my studies. Special thanks also go to my mother, my late father, brothers and sisters for their understanding, support and encouragement throughout my studies. 4

7 CONTENTS Abstract Acknowledgement Table of Contents List of Figures List of Tables Preface Chapter 1. Introduction Background Research Objectives Structure...20 Chapter 2. Threshold effects in catchment storm response and the occurrence and magnitude of flood events: implications for flood frequency Introduction Methodology Rainfall Model Rainfall-Runoff Models Results Schematic description of thresholds in catchment storm response Flood frequency for synoptic events Runoff Response of Synoptic and Cyclonic Events Analysis of flood frequency curves including cyclonic events Discussion and Conclusions...61 Chapter 3. Thresholds in the storm response of a catchment-lake system and the occurrence and magnitude of lake overflows: implications for flood frequency Introduction Methodology Rainfall model

8 3.2.2 Rainfall-runoff Model Results Illustrations of threshold filtering at event scale Cascading of variability through catchment-lake system: a population of events Sensitivity analysis - the impacts of climate and catchment properties on occurrence frequency of lake-overflows Insights into observed behaviour exploration of the impact of antecedent condition of lake storage Implications for flood frequency Discussion and conclusions Chapter 4. Thresholds in the storm response of a lake chain system and the occurrence and magnitude of lake overflows: implications for flood frequency Introduction Methodology Rainfall Model Rainfall-Runoff Model of Lake Chain System Results Illustration of threshold filtering Frequency of occurrence of lake-overflow events: threshold filtering Impact of lake organization on connectivity and flood frequency Artificial Interruption of Flow Connectivity Incorporation of Time delay in Stream Corridors Discussion and Conclusion Chapter 5. Summary, Implications and Recommendations Summary Implications Recommendations for further research

9 LIST OF FIGURES Figure 1.1 Location map of the Lake Warden Catchment (source: CALM Esperance)...19 Figure 2.1. The variability of individual storms in the rainfall time series for (a) η=0.5, (b) η=1.5 and (c) η= Figure 2.2 Bucket configurations for Models 1, 2, 3 and 4. The difference between Models 3 and 4 is the nonlinearity of Qss in Model 4 (Eq. 2.20)...36 Figure 2.3. Schematic representation of rainfall and corresponding runoff generated by Models 1, 2 and 3 (M1, M2, M3) using η= Figure 2.4 Comparison between runoff responses generated by Models 3 and 4 (M3 and M4) using S b =300mm and η= Figure 2.5 The impact of bucket capacity generated by Model 4 using η=0.5 and (a) S b =100 mm, (b) S b =150 mm, and (c) S b =200 mm Figure 2.6 The impact of within storm patterns generated by Model 4 using S b =150 mm and (a) η=0.5, (b) η=1.51, and (c) η= Figure 2.7 Flood frequency curves for the four models using (a) η=0.5, (b) η=1.5, and (c) η=3, and S b =150 mm...49 Figure 2.8 Flood frequency curves generated by Model 4 using η=0.5 and various S b...51 Figure 2.9 Storm event and the corresponding flow components generated by Model 4 using S b =150 mm and η=0.5 in one year time window for (a) rainfall, (b) surface runoff, (c) subsurface flow, (d) catchment storage...53 Figure 2.10 Flood frequency curves for (a) surface runoff and (b) subsurface flow generated by synoptic events only (Syn) and synoptic and cyclonic events (Cyc+Syn) using Model 4 with S b =150 mm and η= Figure 2.11 Flood frequency curves generated by (a) Model 1 and (b) Model 4 using synoptic events only (Syn) and synoptic and cyclonic events (Cyc+Syn) for S b =150 mm, η=0.5 and η= Figure 2.12 Flood frequency curves generated by Model 4 using η=0.5 and (a) S b =150 mm and (b) S b =300 mm by synoptic storm only (Syn) compared to cyclonic summer storm only (Cyc) Figure 3.1 The Lake Warden catchment

10 Figure 3.2 Runoff model for landscape (catchment and lake) utilising catchment and lake buckets...84 Figure 3.3 Schematic representation of the threshold filtering of storms by catchment and lake in the early winter time window; (a) storm events, (b) subsurface flow, (c) surface runoff, (d) lake overflow using ratio A C /A L =10, (e) lake overflow using ratio A C /A L = Figure 3.4 Schematic representation of the threshold filtering of storms by catchment and lake in the middle winter time window; (a) storm events, (b) subsurface flow, (c) surface flow, (d) lake overflow using ratio A C /A L =10, (e) lake overflow using ratio A C /A L = Figure 3.5 PDF for interstorm period of consecutive threshold-exceeding events for (a) all storm events, (b) sub-surface flow-generating storms, (c) surface flow-generating storms, and (d) lake overflowgenerating storms Figure 3.6 The effect of rainfall intensity on the frequency of lake overflow...94 Figure 3.7 The impact of climate represented by P/E calculated based on ((i p *t r )/(e p *t b )) on the frequency of lake overflow...96 Figure 3.8 The effect of subsurface flow concentration time, a, on the frequency of lake overflow...99 Figure 3.9 Probability of lake overflow as a function of (a) antecedent conditions of lake storage and catchment storage for A C /A L =10, and antecedent condition of lake storage and storm depth for (b) A C /A L =2, (c) A C /A L =10 and (d) A C /A L = Figure 3.10 Probability density function of antecedent conditions of lake storage for all storms and lake overflow triggering storms for (a) A C /A L =1, (b) A C /A L =10, and (c) A C /A L = Figure 3.11 The impact of A C /A L and P/E on the initiation point of antecedent condition of lake to overflow Figure 3.12 Flood frequency curve for various (a) ratios of A C /A L, (b) bucket capacity, (c) average rainfall intensity and (d) coefficient a Figure 3.13 FFC using synoptic storm (Syn) and cyclonic and synoptic storms (Cyc+Syn) for various (a) A C /A L ratios, (b) bucket capacity, (c) average rainfall intensity and (d) coef. a Figure 4.1 Upstream part of the Lake Warden catchment: chains of small lakes and connecting streams Figure 4.2 (a) Runoff model for a chain of lakes, (b) Schematic representation of a typical arrangement of lakes and catchments in series, where A C and A L represent catchment and lake areas respectively and 8

11 their numerical subscripts increase in the downstream direction. Note: total catchment area remains invariant for all spatial arrangements explored in this study Figure 4.3 Schematic representation of the threshold filtering of storms in a landscape with lake chain; (a) storm events, (b) catchment (surface runoff, Q se, and subsurface runoff, Q ss ), (c) chain lakes with A C1 /A L1 =1 and A C2 /A L2 =5, (d) chain lakes with A C1 /A L1 =100 and A C2 /A L2 =5 (overflow from upstream lake, Q l1, and overflow from downstream lake, Q l2 ) Figure 4.4 Frequency of lake overflow for Lake 1 and Lake 2 using A C1 /A L1 ratio varies from 1 to 100 (as shown in the axis), and A C2 /A L2 =10 (fixed) Figure 4.5 The flood frequency curves and connectivity for two serial lakes by fixing A C2 /A L2 =2 and vary the A C1 /A L1 =1, 2, and Figure 4.6 (a) Connectivity and (b) flood frequency curves of landscapes consisting of seven lakes connected serially using average A C /A L value of 2 with increasing A C /A L ratio in the downstream direction Figure 4.7 (a) Connectivity and (b) flood frequency curves of landscapes consisting of seven lakes connected serially using average A C /A L value of 10 with increasing A C /A L ratio in the downstream direction Figure 4.8 (a) Connectivity and (b) flood frequency curves of landscapes consisting of seven lakes connected serially using average A C /A L value of 2 with decreasing A C /A L ratio in the downstream direction Figure 4.9 (a) Connectivity and (b) flood frequency curves of landscapes consisting of seven lakes connected serially using average A C /A L value of 10 with decreasing A C /A L ratio in the downstream direction Figure 4.10 The flood frequency curve and connectivity as a result of artifical interruption of connectivity Figure 4.11 Schematic illustration of the impact of time delay upon flood response behaviour, where A is the relative area of individual units, e.g. A: indicates that all units comprise the same unit total (catchment plus lake) area; A: indicates that the area of the most upstream unit is 10 times that of the most downstream unit, etc

12 Figure 4.12 Effect of artificial flow retardation (and attenuation) on the flood frequency curves for different numbers of units and (a) the same area of units, (b) decreasing area of units, (c) increasing area of units, in the downstream direction

13 LIST OF TABLES Table 2.1 Rainfall Model parameters...34 Table 2.2 Rainfall-runoff model parameters...39 Table 2.3a The frequency of occurrence for surface runoff...55 Table 2.3b The frequency of occurrence for subsurface runoff...55 Table 3.1 Rainfall and runoff model parameters with normal value and range/list values used in sensitivity experiments...82 Table 4.1 Rainfall Model parameters

14 PREFACE The thesis is composed essentially of three paper manuscripts that have been submitted for publication in relevant international journals, and constitute Chapters 2 to 4 of the thesis. The only minor changes made to the submitted manuscripts were adjustment to equation and figure numbers to reflect chapter numbers. Chapter 1 provides a general introduction to the thesis as well as an outline of the material presented in Chapters 2 to 4, while Chapter 5 summarizes the main conclusions of the thesis and presents recommendations for further research arising from the outcome of this research. The details of the publications arising from this thesis are summarized below: Chapter 2 of the thesis was submitted for publication in Hydrology and Earth System Sciences journal, special issue Threshold and pattern dynamics: a new paradigm for predicting climate driven processes, as Threshold effects in catchment storm response and the occurrence and magnitude of flood events: implications for flood frequency by D.I. Kusumastuti, I. Struthers, M. Sivapalan and D. Reynolds. Chapter 3 of the thesis was submitted for publication in Water Resources Research journal as Thresholds in the storm response of a catchment-lake system and the occurrence and magnitude of lake overflows: implications for flood frequency by D.I. Kusumastuti, M. Sivapalan, I. Struthers, D. Reynolds, K. Murray and and. B.A. Turlach. Chapter 4 of the thesis was submitted for publication in Advances in Water Resources journal as Thresholds in the storm response of a lake chain system and the occurrence and magnitude of lake overflows: Implications for flood frequency by D.I. Kusumastuti, I. Struthers, M. Sivapalan and D. Reynolds. The thesis is wholly my own composition. Except where referenced, the material presented in this thesis is a synthesis of my own ideas and work undertaken by myself, though valuable contributions came from my supervisors 12

15 Dr. David Reynolds and Prof. Murugesu Sivapalan, and other co-authors of various papers, Dr. Iain Struthers, K. Murray and Dr. B.A. Turlach. The thesis or parts of it have not previously been accepted for any other degree in this or any other institution. 13

16 CHAPTER 1. INTRODUCTION 14

17 1.1 Background Runoff generation and flooding are nonlinear, threshold-driven processes that result from the interactions between climate and catchment characteristics. The transformation of the rainfall to runoff signal undergoes a concentrating action in the spatial domain (due to topography, soil layering and the river network), and a smoothing or filtering action in the time domain (due to the flow of water over and within the hillslopes) (Sivapalan et al., 2001). The filtering action in the time domain, which is the focus of this study, can be attributed to the multiplicity and heterogeneity of flow pathways that water takes in its movement to the catchment outlet (Robinson and Sivapalan, 1997; Jothityangkoon and Sivapalan, 2001). A complicating feature of the rainfall to runoff transformation in the time domain, which may have implications on the flood frequency, is that the various surface and subsurface flow pathways are dynamic, heterogeneous and highly nonlinear. Indeed, many of the rainfall-runoff processes are associated with threshold nonlinearities. Surface runoff generation, a fast process, is often conceptualized as a threshold process, reliant upon one of two important mechanisms; infiltration excess and saturation excess. Infiltration excess runoff occurs when the rainfall intensity exceeds an infiltration capacity threshold, whereas saturation excess overland flow is said to occur when the volume of rainfall inputs exceeds the remaining storage capacity of the soil. Similarly, subsurface stormflow can also be considered as a threshold process which occurs when soil moisture storage exceeds the conceptual field capacity storage threshold. Threshold nonlinearities introduce intermittency to the rainfall-runoff process. For example, the presence of surface water storage features, such as natural lakes and manmade reservoirs within or at the downstream end of catchments, causes intermittency to the catchment runoff response due to the effect of these stores attenuating or terminating runoff, and producing runoff via overflow only when the storage capacity of the water storage feature is exceeded. In addition to traditional effects of filtering at the event scale, e.g., attenuation, time delay, dispersion etc., in the presence of threshold nonlinearities, intermittency becomes an additional manifestation of associated nonlinear, threshold filtering (Struthers et al., 2007; Struthers and Sivapalan, 2007), a concept which is only meaningful with respect to a population of events. 15

18 The rainfall to runoff transformation is highly nonlinear in a catchment having multiple surface water storages, such as chains of lakes. One of the defining features of intermittent surface pathway connections is the introduction of the concept of connectivity to the rainfall-runoff process. The flows in the drainage lines from the upstream to the downstream can be disjointed, partly connected or fully connected depending on the water balance in each lake. The effects of catchment thresholds have received little attention in derived flood frequency analyses. In addition, detailed studies of thresholds in lake systems are relatively rare worldwide, and relatively little is known about them. The few studies that are relevant to this issue relate to catchments containing small lakes in the Arctic environment in Canada, undertaken within a broad framework aimed at determining the effects of various threshold processes on runoff magnitude and timing (Woo et al., 1981; Spence and Woo, 2003; Spence and Woo, 2006). These studies have shown the high dependence of small high arctic lakes upon the upstream catchment areas as sources of water, rather than upon direct precipitation falling on the lakes. Spence (2000) indicated that the location of a lake (whether a lake is located in the upper, middle or lower part of the catchment) is very crucial in the determination of the dominant sources of streamflow reaching the lakes and also the catchment outlet. In addition to the relative location of the lakes within a catchment, contributing areas to the lakes also influence lake-overflow behaviour as well as the overall catchment response (Spence, 2000; FitzGibbon and Dunne, 1981). Similarly, lake size is also an important factor in determining the overall effect of lakes on the lake-overflow response. FitzGibbon and Dunne (1981) found that lakes are efficient in smoothing the hydrograph of incoming catchment runoff response only when they comprise more than 5% of the catchment area. A recent study of the hydrology of subarctic heterogeneous headwater basins in the Canadian Shield (Spence and Woo, 2006) showed that flows in a catchment can be disjointed during dry periods but may easily cascade from the upper to lower sections of a catchment under wet conditions, clearly a consequence of threshold filtering. All these issues prompted the development of this research, which has an overall objective to understand the impact of thresholds in rainfall-runoff transformation, the 16

19 occurrence and magnitude of runoff as well as the implications for flood frequency. To understand the rainfall-runoff transformation in such catchments, this study systematically examined the role of thresholds by utilizing a range of simple to complex models. The study firstly focused on threshold nonlinearities in a catchment (with no lakes) by investigating the role of storage field capacity and total storage capacity on runoff generation in a catchment. The understanding of these threshold effects were used to assist in the next stage of the study which was to investigate the role of lake storage threshold, which causes intermittency, in a catchment-lake system. The last part of this study brings together the understanding of thresholds in catchment and lake systems to investigate the impact of lake organization in lake chain systems (i.e. multiple lakes and associated catchments) on the runoff behaviour, where connectivity plays a significant role in lake-overflow generation. This study has been motivated by a lake-dominated catchment system, Lake Warden, located near Esperance in south-east Western Australia (Figure1.1), which recently has been the focus of a comprehensive investigation to understand and mitigate the processes that could potentially contribute to catastrophic flooding. Natural swamps and small lakes exist throughout the Lake Warden catchment, with chains of small lakes and streams particularly common in the upper catchment. In addition, the catchment is terminated by a wetlands system located downstream of the catchment, which consists of Lake Warden and a number of other similar sized lakes. The Lake Warden wetlands system is of international importance and is included in the Ramsar List (the Ramsar Convention is a list of wetlands of international importance formulated on the basis of ecological, botanical, zoological, limnological or hydrological criteria) (CALM, 1997). The catchment and the wetlands system experienced severe flood events in 1999 and 2000, when flow contributions from the catchment areas to the lakes resulting from rare summer cyclonic events exceeded the lake s storage capacity, causing overflows into the nearby town of Esperance. Prevention and/or mitigation of such catastrophic floods in the future require an improved understanding of the role of the various thresholds upon the hydrologic response of the lake dominated system to extreme storm events, and the impacts on the frequency and magnitude of extreme floods. Investigations into the impact of the large number of inland lakes upon the hydrology of the Lake Warden catchment system have been limited, primarily due to the lack of 17

20 long-term rainfall, lake level, and streamflow data. Primary hydrological data have been gathered since December 2003 as part of a larger research project, but there are some significant periods of missing data, making this dataset insufficient for conducting a detailed field-data based examination of threshold driven processes, which by their nature are highly intermittent. Given the lack of long time series data, this study is predominantly conceptual with the aim being to bring about an improvement in the understanding of the climate and landscape controls upon the runoff behaviour of a lake chain system. Such an examination is most readily achieved using the separate components of the work, i.e.: (1) to examine the runoff generation behaviour of the catchment itself, since catchments are (potentially) an important source of water to any given lake, (2) to examine the overflow behaviour of a lake in combination with the catchment draining into it, and (3) to examine how the organization of these lakes (and associated catchments) within a lake chain network impacts upon the outflow at the downstream end. The results from this study could then be used to design a long-term monitoring programme on the combined catchment-lake-wetland system, focusing on those key processes and process controls that are identified through this investigation. While the approach adopted in this study is general, climate conditions and catchment (and lake) characteristics typical of south-east Western Australia (where small and shallow lakes are numerous) have been used to parameterise the adopted conceptual models. 18

21 Figure 1.1 Location map of the Lake Warden Catchment (source: CALM Esperance) 19

22 1.2 Research Objectives 1. To gain insights into the roles of threshold nonlinearities on catchment storm response, their impact on the temporal frequency of occurrence and magnitude of the resulting flood peaks, and consequently on the flood frequency curve. The additional objective is to understand the dominant process controls of intermittent flood events caused by summer storm events associated with infrequent tropical cyclones, and their impact on flood frequency. 2. To investigate the effect of lake storage thresholds on the nonlinear filtering and transformations of the rainfall to runoff signals. In addition, the effects of climate, catchment and lake characteristics upon catchment runoff processes and the lake overflow generation are examined. 3. To investigate the effects of thresholds associated with a chain of lakes, their interactions with nonlinear rainfall-runoff processes, and the effects on flood frequency associated with lake-overflows and lake connectivity. 1.3 Structure This thesis is presented as a series of scientific papers that resulted from the study. Following this introduction of the research, three chapters containing the three scientific papers, which can be read either as a part of the whole thesis, or as separate entities. Each of these chapters includes an independent introduction, methods, results and discussion and conclusion sections. A general discussion and conclusions chapter closes the thesis. In Chapter 1, the background, objective and scope of the research are presented. In addition, this chapter provides the basic motivation for the study and outlines the fundamental research questions to be addressed in the thesis. In Chapter 2 Threshold effects in catchment storm response and the occurrence and magnitude of flood events: implications for flood frequency, the effects of selected catchment storage thresholds upon runoff behaviour, and specifically their impact upon 20

23 flood frequency are illustrated. The analysis is carried out with the use of a stochastic rainfall model, incorporating rainfall variability at intra-event, inter-event and seasonal timescales, as well as infrequent summer tropical cyclones, coupled with deterministic rainfall-runoff models that incorporate runoff generation by both saturation excess and subsurface stormflow mechanisms. This study underlines the importance of thresholds on flood frequency, and provides insights into the complex interactions between rainfall variability and threshold nonlinearities in the rainfall-runoff process, which are shown to have a significant impact on the resulting flood frequency curves. Changing runoff generation mechanisms (i.e. from subsurface flow to surface runoff) associated with a given threshold (i.e. saturation storage capacity) is shown to be manifested in the flood frequency curve as a break in slope. It is observed that the inclusion of infrequent summer storm events increases the temporal occurrence and magnitude of surface runoff events, in this way contributing to steeper flood frequency curves, and an additional break in the slope of the flood frequency curve. In Chapter 3 Thresholds in the storm response of a catchment-lake system and the occurrence and magnitude of lake overflow: Implications for flood frequency, the effect of catchment and lake thresholds upon the frequency and magnitude of lakeoverflows were examined. In addition to the two storage thresholds discussed in Chapter 2, lake storage capacity that governs the lake overflow is introduced here. The roles of these threshold-driven processes, and their interactions, on the frequency and magnitude of lake-overflow events have been examined using a conceptual rainfallrunoff model of the combined catchment-lake system, which is driven by inputs generated by a stochastic rainfall model. This study has provided valuable insights into the process controls on lake-overflow events and the associated flood frequency behaviour in lake dominated catchments. In particular, the relative roles of climate, soil depth, the soil s drainage capacity, as well as the location of the lake vis a vis the contributing catchment, as manifested in the ratio of catchment area to lake area, in the determination of the characteristics of lakeoverflow events and associated flood frequency behaviour, have been highlighted. The improved understanding of these process controls will be useful in assisting the 21

24 management of the combined catchment-lake system in the study region and in similar regions elsewhere. In particular, the results of this study can also provide guidance towards the monitoring of catchment-lake systems in ways that are more targeted towards those controls critical to the determination of the magnitude and frequency of lake-overflow events to assist in flood prevention and mitigation. In Chapter 4 Thresholds in the storm response of a chain of catchment-lake system and the occurrence and magnitude of lake overflow: Implications for connectivity and flood frequency, the effects of lake organisation upon lake overflow behaviour, and specifically their impact upon connectivity and flood frequency has been demonstrated. The analysis was carried out with the use of a stochastic rainfall model combined with three storage based thresholds: the catchment field capacity storage governing catchment subsurface stormflow, total storage capacity governing catchment surface runoff, and lake storage capacity governing lake-overflow from one lake to the next downstream lake. The improved understanding of the process controls on lake-overflow generation and the associated flood frequency behaviour will be useful in the management of the chains of lake system in the study region, and other similar regions. In particular, the results of this study can provide guidance towards improved flood management in catchment-lake systems by illustrating the use of flow interruption and flow retardation strategies to assist in flood prevention and mitigation. The final chapter presents an overall summary of the thesis and suggests some future work to improve the model development. 22

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26 CHAPTER 2. THRESHOLD EFFECTS IN CATCHMENT STORM RESPONSE AND THE OCCURRENCE AND MAGNITUDE OF FLOOD EVENTS: IMPLICATIONS FOR FLOOD FREQUENCY 24

27 ABSTRACT The aim of this paper is to illustrate the effects of selected catchment storage thresholds upon runoff behaviour, and specifically their impact upon flood frequency. The analysis is carried out with the use of a stochastic rainfall model, incorporating rainfall variability at intra-event, inter-event and seasonal timescales, as well as infrequent summer tropical cyclones, coupled with deterministic rainfall-runoff models that incorporate runoff generation by both saturation excess and subsurface stormflow mechanisms. Changing runoff generation mechanisms (i.e. from subsurface flow to surface runoff) associated with a given threshold (i.e. saturation storage capacity) are shown to be manifested in the flood frequency curve as a break in slope. It is observed that the inclusion of infrequent summer storm events increases the temporal frequency occurrence and magnitude of surface runoff events, in this way contributing to steeper flood frequency curves, and an additional break in the slope of the flood frequency curve. The results of this study highlight the importance of thresholds on flood frequency, and provide insights into the complex interactions between rainfall variability and threshold nonlinearities in the rainfall-runoff process, which are shown to have a significant impact on the resulting flood frequency curves. 25

28 2.1 Introduction The flood frequency curve, typically estimated from observed flood records and widely used in flood estimation practice, is the culmination of complex interactions between climatic inputs (rainfall intensities, evaporation demand) and those landscape properties that have a bearing on the rainfall to runoff to flood peak transformation, presented within a stochastic framework (Eagleson, 1972; Wood, 1976; Sivapalan et al., 1990; Sivapalan et al., 2005). For a given storm event, apart from its dependence on rainfall intensity and volume, the flood peak is a function of storm duration and the response time of the dominant flood producing process (Robinson et al., 1997a; Gupta and Waymire, 1998). However, time scales of subsurface flow and evapotranspiration, and longer time scales associated with rainfall, e.g., seasonality, are also important since together they determine the antecedent flow and soil moisture conditions in the catchment through the memory of previous, even distant, storm events via the catchment s water balance (Jothityangkoon et al., 2001). Rainfall intensity exhibits temporal variability at a range of timescales, such as withinstorm, between-storm, seasonal (annual), inter-annual and inter-decadal variabilities. Similarly, the catchment runoff response is associated with processes such as overland flow, subsurface flow and baseflow which also operate at a range of different time scales, associated with the various pathways that water takes to the catchment outlet and hence different travel distances and travel speeds. Thus the magnitudes of flood peaks and the shape of the flood frequency curve reflect, and are affected by, interactions between rainfall and runoff variabilities over the multiplicity of time scales (Robinson and Sivapalan, 1997b; Jothityangkoon et al., 2001). A number of previous studies (Robinson and Sivapalan, 1997b; Blöschl and Sivapalan, 1997; Sivapalan et al., 2005) have explicitly incorporated the effects of within-storm patterns of rainfall intensity on flood peaks within the context of derived flood frequency analysis. A linear rainfall-runoff model was used in the flood studies carried out by Robinson and Sivapalan (1997a,b) and Sivapalan et al. (2005), which showed that the inclusion of within-storm patterns contributed to a steepening of the flood frequency curves. This behaviour suggested that the nonlinearity of the interactions between temporal rainfall patterns and runoff processes may be significant, but such 26

29 behaviour was not investigated further. Within the framework of a linear rainfall-runoff model, Sivapalan et al. (2005) quantified the effects of within-storm patterns in terms of a correction factor, which was shown to be a function of the ratio of the mean storm duration to the mean residence time of the catchment. In general, runoff generation and flooding are nonlinear, threshold-driven processes. Saturation excess runoff occurs when the soil becomes saturated through the exceedance of an antecedent soil moisture deficit, and the ongoing rainfall rate exceeds the rate of ongoing subsurface flow and/or drainage. Even subsurface stormflow has been found to be a nonlinear, threshold driven process caused by the effects of subsurface heterogeneity (e.g., bedrock topography, preferred pathways etc.) (Spence and Woo, 2003). The role of threshold nonlinearities in surface and subsurface hydrology has become an intense area of research in recent years. For example, Blöschl and Sivapalan (1997) showed that the coefficient of variation (CV) of the flood frequency curve increased by a factor of 4 when nonlinearity is introduced into the rainfall-runoff relationship, effectively swamping the effects of the complex interactions of rainfall-runoff time scales mentioned previously. In more recent work, Fiorentino and Iacobellis (1999) have analysed the effect of runoff thresholds that underpin different generation mechanisms on the resulting flood frequency distributions. This study has been motivated by specific flooding problems in the downstream of the Lake Warden catchment, located near Esperance, Western Australia, where the presence within the catchment of a large number of finger lakes of various sizes introduces obvious thresholds to the rainfall-runoff transformation, which are suspected to have a significant impact on the triggering of floods and on the shape of the flood frequency curve (Kusumastuti et al., 2005; Spence and Woo, 2006). In two instances over the past decade, environmentally destructive flood events have occurred in this region from the combination of paired high volume rainfall events, where the devastating flooding occurred only during the second, significantly smaller magnitude rainfall event. Those specific flooding events in Esperance represent clear evidence of the role of catchment thresholds, which can be defined as those catchment features which variously impart a threshold effect on the rainfall-runoff transformation. 27

30 In spite of the practical importance of catchment thresholds, which is well recognized by engineering hydrologists involved in flood estimation (Chow et al., 1998; Institution of Engineers Australia, 1987), the effects of catchment thresholds have received little attention in derived flood frequency analysis. Owing to the lack of long time series data, this study is predominantly an exploratory one, carried out in a hypothetical catchment but utilizing typical climate and catchment parameters that are representative of the Lake Warden catchment near Esperance, Western Australia. The primary purpose of this study is a first order investigation into the effect of catchment storage thresholds, their interactions with nonlinear rainfall-runoff processes, and their combined impacts on flood frequency. With this in mind the model being used is a simple one, just sufficient to capture the main thresholds that impact on flood frequency the results need to be interpreted in this light. The specific role of threshold effects caused by the finger-lakes themselves, over and above the effects of catchment storage thresholds, is the subject of a subsequent investigation (Kusumastuti et al., 2005). A Monte Carlo simulation based derived flood frequency approach (Eagleson, 1972; Ott and Linsley, 1972) is adopted, utilizing a synthetic realization of rainfall time series combined with simple but nonlinear conceptual rainfall-runoff models. The overall scientific objective is to gain insights into the roles of threshold nonlinearities on catchment storm response, their impact on the temporal frequency of occurrence and magnitude of the resulting flood peaks, and consequently on the flood frequency curve. Given the specific occurrence of flooding events in the Lake Warden catchment during the occurrence of summer storms under dry conditions, an additional objective is to understand the dominant process controls of intermittent flood events during summer storm events associated with infrequent tropical cyclones, and their impact on flood frequency. The paper begins with descriptions of the stochastic rainfall model which was used to generate the synthetic rainfall time series and the four rainfall-runoff models used in the simulation of runoff time series. The rainfall-runoff models used vary systematically from a simple linear bucket without thresholds to a non-linear bucket with multiple storage thresholds. By comparing runoff generation behaviour for each model over a range of different climate and catchment parameterisations, the impact of thresholds upon the time series of runoff generation and flooding events and upon flood frequency could be examined. The implications of these results are then examined for flood 28

31 estimation practice and approaches to future monitoring aimed at prevention and amelioration of catastrophic floods that may occur in the study region. 2.2 Methodology Rainfall Model The study used the stochastic rainfall generation model of Sivandran (2002), which is an extension of the model of Robinson and Sivapalan (1997b). This model accounts for seasonal variability in the dominant storm type by considering separate synoptic components (year-round) and a cyclonic component in summer months. The synoptic component considers each year to consist of 12 months, with storm durations and interstorm periods estimated from observed rainfall data, while the summer cyclonic component assumes each year to consist of just 3 months, with a different set of storm durations and inter-storm periods reflecting the infrequent tropical cyclones. These two sequences are then superimposed, by concatenation, to obtain a complete rainfall time series. Synoptic rainfall model The model is capable of generating synthetic realizations of rainfall time series consisting of discrete rainfall events whose arrival times, durations, average rainfall intensity and within-storm intensity patterns are all random governed by specified probability density functions (pdf). Storm duration and inter-storm period are both considered to be exponentially-distributed, although with seasonally-varying mean values: fτ r fτ b 1 t = r ( tr δ ) exp t r > 0 (2.1) δ δ 1 t = b ( tb γ ) exp t b > 0 (2.2) γ γ where δ is the mean storm duration, and γ is the mean inter-storm period. These mean values are considered to vary deterministically with time of year according to the following sinusoids: 29

32 2π δ = δ r + α r cos ( τ τ r ) ω (2.3) 2π γ = γ b α b cos ( τ τ b ) ω (2.4) where δ r and γ b are the seasonally averaged storm duration and inter-storm period, respectively, τ r and τ b are seasonal phase shifts which are assumed to be equal, and α b are the amplitudes of the seasonal variations of t r and t b, respectively, τ is the time of year, and ω is the total number of time units in a year (i.e., ω = 8760 hours). α r The mean storm intensity i is a random variable stochastically dependent upon storm duration t r ; that is, i and t r follow the joint pdf, f ( i, t ), which is also seasonally I, T r δ r varying due to the variation of δ. Correlation between i and t r is expressed as: b1 [ i t ] a 2 b E = CV i t = a (2.5) r 1t r with the coefficient a 1 [ ] 2 r 2t r assumed to also vary seasonally in order to account for variability of rainfall generating mechanisms within the year: a 2π = a1 m + a1a cos ( τ τ ) ω 1 a (2.6) The power functions given in equation (5) provide relationships between t r and the first two moments of f I ( i tr follow the gamma distribution: f ( i t I r λ ) = ( λi) Γ( κ) ), the conditional distribution of i given tr, which is assumed to κ 1 exp( λi) (2.7) Both λ and κ are gamma distribution parameters and are functions of storm duration t r. These parameters can be expressed, in terms of t r and the coefficients of the conditional statistics: b2 r t κ = and a 2 b1 b2 tr λ = (2.8) a a 1 2 The mean storm intensity is further disaggregated to hourly intensity patterns (withinstorm pattern) using stochastically generated mass curves (Huff, 1967). The temporal pattern generated by the stochastic rainfall model is highly dependent upon the random variables w, which governs how the total depth of rainfall within the event is 30

33 disaggregated sequentially until the required temporal resolution of event rainfall is achieved. The random variables are drawn from a beta distribution that is given by: 1 η 1 η f w ( w) = w (1 w) (2.9) B( η η ) 1 2 The selection of η 1 and η 2 is significant, as it is the magnitude of these parameters that controls the patterns of variability of rainfall within the event around the median. For the purposes of this study it is assumed that η 1 =η 2 ; this results in a normalised mass curve which is symmetrical about w = 0.5. The higher the values for η, the more the values tend to be centred on w = 0.5. However if small values are used the resulting random variables drawn tend to be distributed at the extremes with w values approaching zero or one. The values of η used in this study are 0.5, 1.5, and 3. This choice of the η values is based on the analysis of within storm patterns of several years of storm data in the study region (Hipsey et al., 2002; Robinson et al., 1997b). Figure 1 presents typical rainfall hyetographs generated by the model for different values of η. The average intensity, and hence the total rainfall volume, is the same in all three cases. The simulated patterns demonstrate that lower η values produce highly variable, even intermittent rainfall patterns, whereas higher η values generate less variable rainfall, approaching almost uniform rainfall intensities. Cyclonic summer rainfall model A particular feature of rainfall that is crucial in the study region is the inclusion of the effects of large, infrequent but important tropical cyclones that tend to occur during the summer months of December, January and February. The town of Esperance experienced severe summer storms in January 1999 and again in February-March A total of 209 mm of rainfall was recorded in the January 1999 event, the heaviest rainfall event in the region since rainfall records began in 1889, and the resultant environmentally catastrophic flood was estimated to have a return period of around 200 years. The same modelling framework outlined for synoptic rainfall (Section 2.1.1) was used in the cyclonic summer rainfall model. Several alterations were made in order to account for the different characteristics of cyclonic events. The summer cyclonic storm 31

34 model generates a stochastic time series of 90 days duration representative of December, January and February, which was accomplished by setting parameter ω to 2160 hours (Equations 3, 4 and 6). An equal probability of occurrence was applied to each summer month. The seasonal component of the stochastic rainfall model was removed as tropical storm arrivals appeared to totally random showing little preference for any of the three summer months. Therefore the amplitude of seasonal variations of storm duration a 1a α r (Equation 3), inter-storm period α b (Equation 4) and mean intensity (Equation 6) were all set to zero. From the analysis of rainfall records in the region the temporal frequency of cyclonic rainfall events appeared to be, on average, once in 7 8 years, the inter-storm parameter γ b (Equation 4) was therefore set as 700 days or hours (i.e., roughly 8 times 90 days). Table 1 presents the rainfall model parameterisations both for synoptic and cyclonic storms, which is based upon observed rainfall records for the Esperance region. The setting and validation of the stochastic rainfall generation model is described by Robinson and Sivapalan (1997b). 32

35 8 (a) rainfall, mm/h time, hours 8 (b) rainfall, mm/h time, hours 8 (c) rainfall, mm/h time, hours Figure 2.1. The variability of individual storms in the rainfall time series for (a) η=0.5, (b) η=1.5 and (c) η=

36 Table 2.1 Rainfall Model parameters Value Parameter Equation Synoptic rainfall model δ r (3) 11 Cyclonic summer rainfall model 24 Units hours α r (3) hours γ b (4) hours α b (4) 69 0 hours τ r = τ b (3),(4) 0 0 month ω (3),(4) hours a 1 (6) a 1 m (6) a 1 a (6) b 1 (5) a 2 b 2 (5) (5)

37 2.2.2 Rainfall-Runoff Models Following Farmer et al. (2003), four models describing the most common hydrological processes in a catchment were utilized in this work, ranging from a simple linear bucket (Model 1) to a relatively more complex nonlinear bucket with thresholds (Model 4) as illustrated in Figure 2.2. Model 1 is a very simple conceptualisation of the hydrological processes within a catchment, which transforms the rainfall input into runoff simply as a function of precipitation, storage and evaporation. Potential evaporation data is obtained from measured pan evaporation from Esperance Meteorological Bureau. The range of measured annual potential evaporation values is between 1500 mm to 2000 mm. The runoff models developed in this paper used a fixed value of annual potential evaporation, equal to the mean annual potential evaporation of approximately 1700 mm. The governing equations for the processes represented in Model 1 are: ds dt = i( t) Ep( t) Q( t) (2.10) S( t) Q( t) = (2.11) t c where S is storage in mm, t is time in hours, Q is runoff in mm/h, and t c is the catchment response time (hours). Model 2 expands upon Model 1 by adding a field capacity threshold, S fc, such that flow will occur only if the storage exceeds this threshold. Field capacity is a commonly-used conceptual threshold, representing the water content below which capillary forces are larger than those of gravity, such that drainage and runoff are negligible. Model 2 has the same equation for describing storage change with time (equation 2.10) as Model 1, but uses a different equation for Q(t). ( S( t) S fc ) Q( t) = (2.12) t c where S fc is the field capacity threshold in mm. 35

38 P E p P E p P E bs E veg S Q S fc S Q S b S fc ss Q se Q ss Model 1 Model 2 Models 3 and 4 Figure 2.2 Bucket configurations for Models 1, 2, 3 and 4. The difference between Models 3 and 4 is the nonlinearity of Qss in Model 4 (Eq. 2.20). 36

39 Model 3 introduces a bucket capacity, S b (mm), such that runoff is now separated into two components: subsurface flow, Q ss (mm/h), when catchment storage exceeds the field capacity threshold; and saturation excess runoff or surface runoff (Q se, mm/h) when the bucket capacity is exceeded (Figure 2.2). In view of the climate and soils in this region, the main runoff generating mechanism is subsurface stormflow, whereas infiltration excess runoff and deep groundwater flow are rare phenomena. For that reason, these two runoff components are not included in the model. The governing equation for the processes represented in Model 3 is: ds dt = i( t) Q ( t) Q ( t) E ( t) E ( t) (2.13) ss se In order to account for the effects of heterogeneity of vegetation cover, total evaporation is divided into bare soil evaporation (E bs ) and transpiration (E veg ). The evaporation term in Model 3, E p (t) in mm, is separated into evaporation from vegetation or transpiration, E veg in mm and bare soil evaporation E bs in mm. Transpiration is a function of the percentage of vegetation covering the catchment, M, and potential evaporation, E p. The introduction of E bs and E veg to replace E p in Models 3 and 4 is to provide continuity with previous modeling studies (e.g., Farmer et al., 2003). The model structure presented here worked well for many catchments in this region. bs veg E = if S( t) (2.14) veg ME p S fc E veg = ME p S( t) S fc if S ( t) < S (2.15) fc Bare soil evaporation is a function of potential evaporation and the portion of the catchment covered by vegetation. E bs = E ( 1 M ) if S( t) (2.16) p S b E bs = E p S( t) ( 1 M ) if S ( t) < Sb (2.17) Sb Total runoff from the catchment is the summation of subsurface flow and surface runoff. Subsurface flow (Q ss ) is a linear function of storage above field capacity and concentration time t c. 37

40 > < < = b c fc b b fc c fc ss S t S t S S S t S S t S t S Q ) ( ) ( ) ( (2.18) Surface runoff (Q se ) occurs if the soil is fully saturated which occurs when the storage exceeds the bucket capacity (S b ). se S b t S Q = ) ( if (2.19) S b t S > ) ( The bucket capacity, S b, is assumed to be equal to S b = φ.d, where φ is the catchmentaverage soil porosity, and D is the catchment-average soil depth. Bucket capacity, S b, was calculated based on the estimated average depth of the upper layer of the duplex soils in the Lake Warden Catchment, multiplied by the porosity of the soil. The field capacity threshold S fc is the product of the catchment-average field capacity, f c, and D. Model 4 is similar to Model 3, but with a non-linear storage-discharge relationship for subsurface flow. The linear storage-discharge relationship (Eq. 2.18) with single parameter t c, is thus replaced with two parameters and b. The and b values used in this study are normally estimated through recession analysis carried out on the measured streamflow data. a a > < < = b b fc b b fc b fc ss S t S a S S S t S S a S t S Q ) ( ) ( ) ( 1 1 (2.20) Parameters of the rainfall-runoff models for Model 1 to Model 4 are described in Table

41 Table 2.2 Rainfall-runoff model parameters Normal value / Range / List Parameters Model 1 Model 2 Model 3 Model 4 Units Storage-discharge relationship t c hour a mm 0.5 h 0.5 b Soil properties S b , mm S fc , mm Vegetation M Rainfall model parameter : η 0.5, 1.5, 3 0.5, 1.5, 3 0.5, 1.5, 3 0.5, 1.5, 3-39

42 2.3 Results Schematic description of thresholds in catchment storm response To illustrate the impacts of threshold nonlinearities, we will first compare time series runoff response for each of Models 1 to 4 schematically. Figure 2.3a shows typical rainfall inputs and Figure 2.3b the corresponding runoff generated by Models 1 and 2. In Model 1 the catchment is conceptualized with infinite storage and no threshold, and as a result runoff magnitude is determined by the rainfall volume, evaporation and catchment s response time. The catchment storage capacity remains infinite in Model 2, but a field capacity threshold is introduced. As a consequence, rain must first bring soil moisture to a basic level of wetness, S fc, at which point excess water becomes available for runoff generation. Since subsurface flow is zero at field capacity, the reduction of storage to below field capacity is due to evaporative drying during the inter-storm period. Figure 2.3b shows that the field capacity threshold enhances the intermittency, with not all storms generating a runoff response. Model 3 gives the system a finite storage capacity which, if reached, is capable of generating saturation excess surface runoff. Figure 2.3c shows the storm events and corresponding runoff responses (subsurface flow, Qss, and surface runoff, Qse) generated by Model 3. Differing from the response time for subsurface runoff, surface runoff is assumed to be immediately transferred downstream (response time ~0 hrs). The occurrence of surface runoff is determined by the value of the bucket capacity. 40

43 50 (a) rainfall, mm/h time, hours 1.4 Q-M1 Q-M2 (b) runoff, mm/h time, hours (c) subsurface flow, mm/h 0.7 Qss-M3 Qse-M3 15 surface runoff, mm/h time, hours Figure 2.3. Schematic representation of rainfall and corresponding runoff generated by Models 1, 2 and 3 (M1, M2, M3) using η=

44 Model 4 assumes a non-linear storage-discharge function for subsurface flow. The difference between a linear and nonlinear storage-discharge relationship for subsurface flow can be seen by comparing Models 3 and 4 (Figure 2.4), where the two models show similar recession behaviour but different peak responses. During low flow, Model 3 produces a higher flood peak than Model 4. Conversely, during high flow, the flood peak produced by Model 3 is lower than that from Model 4. Previous work has examined the impact of the nonlinear storage-discharge relationship (Farmer et al., 2003) in Australian catchments similar to the Lake Warden scenario. Farmer et al. (2003) found an under prediction of the flow duration curve by using a linear parameter, and an improvement in the flow duration curve with the utilization of a nonlinear approach. 42

45 2 0 subsurface flow, mm/h Qss-M3 Qss-M4 rainfall rainfall, mm/h time, hours Figure 2.4 Comparison between runoff responses generated by Models 3 and 4 (M3 and M4) using S b =300mm and η=

46 Effects of bucket capacity Soil depth is an important controlling parameter in flood events given the fact that soil moisture storage excess is a direct contributor to flooding. To investigate the effect of soil depth on the runoff response, Model 4 with bucket capacities of 100 mm, 150 mm, and 200 mm are used to generate runoff responses (surface runoff and subsurface flow). Figures 2.5a, 2.5b, and 2.5c show that soil depth significantly impacts the frequency of occurrence of saturation excess surface runoff, i.e. deeper soils require more rainfall to fill, such that surface runoff is less likely to occur. Even when a deep soil generates saturation excess, the volume of saturation excess will be less than for shallower soils. Larger soil depths are also capable of generating higher rates of subsurface flow prior to becoming saturated, such that the contribution of subsurface flow to total runoff will be larger for deeper soils. 44

47 4 80 Qss (a) subsurface flow, mm/h Qse surface runoff, mm/h time, hours 4 80 Qss (b) subsurface flow, mm/h Qse surface runoff, mm/h time, hours 4 80 Qss (c) subsurface flow, mm/h Qse surface runoff, mm/h time, hours Figure 2.5 The impact of bucket capacity generated by Model 4 using η=0.5 and (a) S b =100 mm, (b) S b =150 mm, and (c) S b =200 mm. 45

48 Effect of within storm pattern To investigate the impact of the degree of within-storm variability of rainfall intensity upon flood frequency, rainfall time series with three different values of η were considered (η=0.5, 1.5 and 3). Figure 2.6 illustrates the impact of each η value upon subsurface flow and surface runoff. The figure shows that variation in η significantly impacts the magnitude of surface runoff, but has a negligible impact upon subsurface flow. The impact of within-storm variability, which represents variability at small timescales, is most significant for a fast-response mechanism, such as surface runoff. In contrast, mechanisms with a large response, such as subsurface flow, will attenuate the small timescale variability. The magnitude of surface flow is determined primarily by the rate of the rainfall and the within-storm rainfall pattern. For the shallow soils of the Lake Warden Catchment, where surface runoff occurs frequently, within-storm variability will therefore have a significant impact upon flood response. 46

49 4 Qss 50 (a) subsurface flow, mm/h 2 Qse 25 surface runoff, mm/h time, hours 4 50 (b) subsurface flow, mm/h 2 Qss Qse 25 surface runoff, mm/h time, hours 4 50 (c) subsurface flow, mm/h 2 Qss Qse 25 surface runoff, mm/h time, hours Figure 2.6 The impact of within storm patterns generated by Model 4 using S b =150 mm and (a) η=0.5, (b) η=1.51, and (c) η=3. 47

50 2.3.2 Flood frequency for synoptic events The two most commonly used partial series for flood analysis are the annual exceedance series and annual maxima series (Chow et al. 1988). Annual exceedance series considers data above a predetermined threshold as extreme, with an advantage of selecting every significant flood present within the data series. The annual exceedance series consists of the n largest flood peaks for a record of n-year duration. Annual maxima series, which is the most commonly used technique for flood frequency analysis in Australia (Pilgrim 1987), selects the largest flood peak for each year of the data series and is the approach used in this study. There is a risk associated with using annual maximum series where often significant floods with respect to the entire data may be omitted because of another large flood in the same year. However, the use of sufficiently long time series may reduce these effects significantly, and that approach has been adopted in this study (the use of 1000 years generated rainfall data). The flood frequency curves generated by all 4 Models incorporating the selected withinstorm patterns are presented in Figure 2.7. There is a significant difference in behaviour at low return periods as shown by the results generated by Models 1 and 2. In addition, the flood frequency curves for Model 2 remain slightly lower than those for Model 1, due to intermittent drying below field capacity. The impact of the storage capacity threshold upon the flood frequency is manifested as a break in slope, associated with a change in flow mechanism from subsurface flow to saturation excess surface runoff, as shown by the flood frequency curves for Models 3 and 4. For example, Figure 2.7a indicates that flood peaks associated with return periods of less than approximately 40 years are caused by subsurface flow only, whereas events with a larger return period have an additional surface runoff component. The flood frequency curves presented in Figure 7 for Models 3 and 4 indicate a shift in position, which is due to the nature of the deterministic rainfall-runoff model, particularly the differences in the storage-discharge relationships used for subsurface flow. 48

51 (a) flood peaks, mm/h M1 M2 M3 M return period, years (b) flood peaks, mm/h M1 M2 M3 M return period, years 1000 (c) flood peaks, mm/h M1 M2 M3 M return period, years Figure 2.7 Flood frequency curves for the four models using (a) η=0.5, (b) η=1.5, and (c) η=3, and S b =150 mm. 49

52 Within-storm patterns have an observable impact upon the flood frequency curves for Models 3 and 4 only at return periods after the break in slope, where surface runoff is contributing to the flood peak (Figures 2.7a, 2.7b, and 2.7c). Previous findings by Robinson and Sivapalan (1997b) and Sivapalan et al. (2005) for models without threshold nonlinearities established that higher degrees of within-storm variability lead to steeper flood frequency curves; the findings of this study clarify that such an impact is only important for the portion of the flood frequency curve associated with a fast runoff response mechanism, which is itself associated with the relative frequency of threshold exceedance. The flood peaks predicted with high within-storm variability (η=0.5) reach 139 mm/h for the 1000 year return period flood, significantly greater than the predicted flood peaks with medium (η=1.51) and low (η=3.0) variability. As discussed previously, the bucket capacity (which represents soil depth), influences the relative frequency of activation of surface runoff. Based on observed soil properties in several locations in the catchment, bucket capacities of 100 mm to 400 mm were utilized to study the sensitivity of flood frequency to soil depth (Figure 2.8). It is evident that the flood frequency curve for a bucket capacity of 100 mm has the earliest break compared to that for larger buckets (i.e. deeper soils). The inflection point in the response has moved from a return period of around 40 years to a return period of 500 years for a bucket capacity of 400 mm. With the decreasing frequency of surface runoff, the impact of within-storm variability upon flood frequency also decreases for deeper soils (results not shown here for reasons of brevity). 50

53 1000 flood peaks, mm/h Sb=100 Sb=150 Sb=200 Sb=300 Sb= return period, years Figure 2.8 Flood frequency curves generated by Model 4 using η=0.5 and various S b 51

54 2.3.3 Runoff Response of Synoptic and Cyclonic Events A schematic representation of one year of storm events containing both synoptic and cyclonic storms and their corresponding flow components generated using Model 4 is presented in Figure 2.9. A single summer cyclonic event occurs early in the year and synoptic events occur mostly between June and August (Figure 2.9a). Saturation excess surface runoff occurs just twice within the year; once by a cyclonic storm and once by a synoptic event in winter (Figure 2.9b). Subsurface flow responds to both cyclonic and synoptic events (Figure 2.9c) The catchment storage fluctuates throughout the year with dry antecedent condition prior to the summer event and relatively high antecedent conditions during winter (Figure 2.9d). The low antecedent condition of catchment storage during summer means that only a large-volume storm will be capable of triggering surface runoff, such as the presented summer event (Figure 2.9a) which has a depth of 230 mm over 4 days. On the other hand, due to high antecedent conditions of catchment storage during winter, smaller storm depths are capable of triggering surface runoff. 52

55 150 (a) rainfall, mm/h time, hours 60 (b) surface runoff, mm/h time, hours 2.6 (c) subsurface flow, mm/h time, hours 200 (d) storage, mm time, hours Figure 2.9 Storm event and the corresponding flow components generated by Model 4 using S b =150 mm and η=0.5 in one year time window for (a) rainfall, (b) surface runoff, (c) subsurface flow, (d) catchment storage 53

56 A detailed examination of the occurrence of surface runoff and subsurface flow generated by synoptic events only, cyclonic events only, and by the combination of both is presented in Tables 2.3a and 2.3b. The frequency of occurrence for surface runoff caused by synoptic storm events is relatively low (Table 2.3a). The frequency of occurrence for surface runoff including summer cyclonic events is only slightly larger. Consideration of cyclonic events independently shows that slightly over 40 percent of cyclonic storm events are able to generate surface runoff in the shallowest bucket (50 mm); even though, numerically, the number of cyclonic events is negligible relative to the number of synoptic storms, they are much more likely than synoptic storms to trigger surface runoff, and therefore have a large potential to impact flood frequency. As the bucket capacity increases, the frequencies of surface runoff, due to both cyclonic and synoptic events, decreases. For sufficiently deep soils (e.g. S b = 300 mm), surface runoff triggering may be a summer phenomenon only. The frequency of subsurface flow occurrence generated by synoptic events is relatively much higher (i.e. 70%; Table 2.3b). A larger soil depth slightly reduces the occurrence of subsurface flow, indicating threshold effects, as the field capacity threshold may increase with deeper soil depth. The frequency of occurrence of subsurface flow generated by cyclonic storm events only is more than 70% at the shallowest bucket capacity (S b =50 mm), but decreases considerably with deeper bucket capacity. The decrease of the frequency of subsurface flow occurrence due to the increase of field capacity threshold as the bucket capacity increases will increase the ability for evaporation to cause drying below field capacity. 54

57 Table 2.3a The frequency of occurrence for surface runoff f(q se ) S b Winter storm Winter & summer storms Summer storm Table 2.3b The frequency of occurrence for subsurface flow f(q ss ) S b Winter storm Winter & summer storms Summer storm

58 2.3.4 Analysis of flood frequency curves including cyclonic events An examination of the flood frequency of the individual flow components (i.e. subsurface flow and surface runoff) generated by Model 4 for synoptic events only, and for synoptic and cyclonic events combined, is presented in Figure The figure indicates that the addition of summer cyclonic storms significantly increases flood magnitudes, by more than an order of magnitude relative to the synoptic-only case. The inclusion of summer cyclonic events also increases the frequency of surface runoff, resulting in a break of slope at lower return periods in the flood frequency curve. The inclusion of cyclonic storms increases the frequency of surface runoff triggering directly, as suggested in Table 2.3a, as well as indirectly by increasing antecedent soil moisture leading up to the synoptic rainfall peak in winter. Interestingly, the flood frequency curve due to subsurface flow only is not significantly impacted by the inclusion of cyclonic events (Figure 2.10b), with the only difference being a slight decrease in the value of the return period at which the subsurface flow reaches its maximum value (i.e. the saturated value of subsurface flow, as given by equation 20 when S(t) > S b. 56

59 1000 (a) flood peaks, mm/h Qse (Cyc+Syn) Qse (Syn) return period, years 10 (b) flood peaks, mm/h 1 Qss (Cyc+Syn) Qss (Syn) return period, years Figure 2.10 Flood frequency curves for (a) surface runoff and (b) subsurface flow generated by synoptic events only (Syn) and synoptic and cyclonic events (Cyc+Syn) using Model 4 with S b =150 mm and η=

60 The flood frequency responses for the complete (cyclonic and synoptic) rainfall model and for the synoptic events only are shown for Model 1 (Figure 2.11a) and Model 4 (Figure 2.11b) for both low and high within-storm variability. For the linear model (Model 1) the magnitude of the 1000-year flood peak is approximately halved if cyclonic events are not incorporated. This is a direct result of the larger storm depth due to cyclonic event at high return period. The impact of within storm pattern variability is insignificant (Figure 2.11a) even at high return period of the flood frequency, as the runoff generated by Model 1 represents subsurface flow which has large concentration time. Figure 2.11b clearly shows that the inclusion of cyclonic storm events using high within storm variability (η=0.5) impact on an additional inflection point occurring at high return periods of the flood frequency response generated by Model 4. Given that the flood frequency curve for the low within-storm variability case does not exhibit this secondary inflection point, it suggests that the combination of large cyclonic storm depths combined with strong within-storm variability can lead to rare, extreme magnitude flood responses (Figure 2.11b). The flood frequency responses generated by Model 4 for the cyclonic events, and for the synoptic events independently, are presented in Figures 2.12a and 2.12b. In addition, the impact of bucket capacities on the flood frequency response for each event is examined. The flood frequency curves generated by synoptic events show the response on the impact of bucket capacity, such that the flood frequency curve for a bucket capacity of 150 mm has an early break compared to that using Sb = 300 mm. Figures 2.12a and 2.12b show that the flood frequency curves generated by summer cyclonic events curtail at return period of ~ 40 years, due to the requirement of a minimum storm volume which is required to overcome the field capacity and soil depth thresholds present due to the dry antecedent conditions prevalent in summer. 58

61 10 M1-η=0.5 (Cyc+Syn) M1-η=0.5 (Syn) (a) flood peaks, mm/h 1 M1-η=3 (Cyc+Syn) M1-η=3 (Syn) return period, years (b) flood peaks, mm/h M4-η=0.5 (Cyc+Syn) M4-η=0.5 (Syn) M4-η=3 (Cyc+Syn) M4-η=3 (Syn) return period, years Figure 2.11 Flood frequency curves generated by (a) Model 1 and (b) Model 4 using synoptic events only (Syn) and synoptic and cyclonic events (Cyc+Syn) for S b =150 mm, η=0.5 and η=3. 59

62 1000 Cyc (a) flood peaks, mm/h Syn return period, years 1000 Cyc (b) flood peaks, mm/h Syn return period, years Figure 2.12 Flood frequency curves generated by Model 4 using η=0.5 and (a) S b =150 mm and (b) S b =300 mm by synoptic storm only (Syn) compared to cyclonic summer storm only (Cyc). 60

63 2.4 Discussion and Conclusions The paper investigated the effect of catchment thresholds upon flood frequency. The catchment thresholds that were examined include field capacity storage and a total storage capacity. For the parameterisation of climate and landscape used in this study, which relate to a specific catchment in Western Australia, model results suggest that most storms trigger a subsurface flow response, with surface runoff due to saturation excess occurring relatively rarely. Analysis of the effect of thresholds has been performed systematically in this study, by utilizing a range of simple to complex models which add a single threshold at a time. Thresholds cause nonlinearity in the rainfall-runoff transformation, where runoff response is not only nonlinearly dependent on the magnitude of rainfall inputs but also on the catchment thresholds. The field capacity threshold requires the rainfall to bring soil moisture to a basic level of wetness, the point where excess water will enable subsurface flow generation. The role of field capacity is clearly demonstrated in the results produced by Model 2 (as compared to Model 1), with the lack of occurrence of runoff at low return periods (Figure 2.7, for Model 2) being due to the catchment storage falling below the field capacity threshold for the entire year as a result of low rainfall volume in those years relative to potential evaporation. For a given climate, the magnitude and frequency of occurrence of saturation excess, which is a thresholdactivated process, are both inversely related to the magnitude of the catchment storage capacity, S b ; as this capacity increases, both the magnitude and frequency of threshold exceedance will decrease. The derived flood frequency approach adopted in this work demonstrated the impact of thresholds, where the thresholds impart a significant change on the shape and magnitude of the flood frequency. A change in the dominant runoff generating mechanism associated with threshold exceedance is manifested as an inflection point in the flood frequency curve. The interactions between climatic inputs (rainfall intensities, evaporation demand, dryness index, seasonality and within storm pattern), landscape properties (soil depth, field capacity and concentration time) and soil moisture/antecedent condition (water balance), have been clearly demonstrated to control the rainfall to runoff response, and therefore impact the flood frequency curve. 61

64 This complex interaction, although somewhat intuitive when its components are considered in isolation, can result in system behaviours that are not normally considered in the modelling of rainfall to runoff transformations, nor in the design of engineered flood control systems. The study of the impact of summer cyclonic storm events on flood frequency was an additional aim of this work, given historical instances of summer flooding in the study catchment. The research indicated that summer storm characteristics and the interaction between winter rainfall and evaporation which affect the antecedent catchment conditions for summer storm events strongly impacts the occurrence and magnitude of the flood events. The difference of the catchment state between summer and winter storm events lies in the antecedent catchment wetness, where the antecedent condition is driven by seasonality of synoptic events and seasonality of evaporation. During winter months the rainfall rate exceeds the evaporation rate causing relatively wet antecedent conditions, and therefore small floods are frequent due to small to medium rainfall intensities. If large rainfall intensities occur during this period, the magnitude of the flood peak will be at the greatest. However, the largest rainfall intensities occur during summer months with relatively dry antecedent conditions, such that small floods are less frequent but a number of large floods have occurred. The flood frequency curves for synoptic (year-round) and cyclonic (summer-only) storm events show a continuous curve with the break demonstrating the change of mechanism and the largest flood peak at the highest return period is due to cyclonic summer events. The study has some implications for our understanding of other types of catchment threshold behaviour, such as the overflow behaviour of small lakes within the Lake Warden catchment. In general, the storages of the lakes tend to increase during winter and almost dry during summer months. However, the flow contribution to the lakes following large volume summer cyclonic events may exceed lake storage capacity, causing overflow into the town and the wetlands system which is located downstream of the catchment, as has occurred in recent years. This is a major concern to the management of Lake Warden catchment and surrounding wetlands system. The Lake Warden wetlands system is an important landmark and resting place to many migratory water birds and rare flora species, and the system is listed in the Ramsar List, (the Ramsar Convention is a list of wetlands of international importance formulated on the 62

65 basis of ecological, botanical, zoological, limnological or hydrological criteria) (CALM, 1997). The quantification of the runoff during these events will assist the catchment and wetlands management. However, the utilization of the method presented has its own limitations in that the results presented here only dealt with a hypothetical catchment and the model parameterisation is limited to the catchments which have similar climatic and catchment characteristics. Climatic and hydraulic data from the study catchment is also limited such that a validation of the model cannot be performed. Furthermore the rainfall-runoff model utilized in this study is simple and does not include a rate threshold, and the process that largely depends on the intensity of rainfall and related to infiltration excess runoff. Nevertheless, the model developed using long time series of synthetic rainfall data adapted to the catchment coupled with rainfall-runoff model including catchment thresholds can be used as a tool to predict and take precautionary measures to reduce the impact of the floods in the Lake Warden catchment. Overall the study has provided valuable insights into the process controls of flood frequency which can be achieved through utilization of the derived flood frequency method. A better understanding of the mechanisms that trigger runoff, their frequency of activation, and magnitude of runoff response will improve the management capabilities of the Lake Warden catchment and other similar catchments in the region. The results are valuable for understanding the occurrence of subsurface flow and surface runoff, which is essential to assist in the mitigation of the flood response of both synoptic winter and cyclonic summer storm events. Traditional statistical flood frequency analyses based on limited records of flood series do not recognize the underlying processes and change of dominant processes with increasing return period. In the presence of significant thresholds and climatic features such as infrequent summer flood events caused by tropical cyclones traditional techniques are fraught with considerable difficulties. Flood records that do not contain samples from these infrequent floods tend to over-estimate their return periods, whereas records that do contain samples from these summer floods tend to under-estimate their return periods, as in both cases the flood frequency analysis is dominated by the more common winter floods. Derived flood frequency analysis procedures such as the one 63

66 presented here can be extremely useful to assess the frequency of such extreme floods through a much more realistic assessment of the associated changes in process controls. They also focus attention on the conditions under which these extreme floods are caused, which enables managers and engineers to design monitoring schemes that can help predict or prevent such floods from ever occurring. 64

67 REFERENCES Blöschl, G. and Sivapalan, M Process controls on regional flood frequency: coefficient of variation and basin scale. Water Resour Res., 33(12): CALM (Department of Conservation and Land Management) Esperance Lakes Nature Reserves, Draft Management Plan for the National Parks and Nature Conservation Authority, Perth, Western Australia. Chow, V.T., D.R. Maidment, and L.W. Mays Applied Hydrology, McGraw-Hill, New York. Eagleson, P.S Dynamics of flood frequency, Water Resour. Res., 8(4), Fiorentino, M. and Iacobellis, V Non-linearity effects in the process of floods generation. Proc. EGS Plinius Conference on Mediterranean Storms, Maratea, Italy, October Farmer, D., Sivapalan, M. and Jothityangkoon, C Climate, soil, and vegetation controls upon the variability of water balance in temperate and semiarid landscapes: downward approach to water balance analysis. Water Resour Res, 39(2), 1035, doi: /2001 WR Gupta, V.K., Waymire E Scale variability and scale invariance in hydrological regionalization. pp , in: Scale Invariance and Scale Dependence in Hydrology, G. Sposito (Editor), New York: Cambridge University Press. Hipsey, M., Sivapalan, M. and Menabde, M.: The incorporation of risk in the design of engineered catchments for rural water supply in semi-arid Western Australia. Hydrol. Sci. J., 48(5), , Huff, F.A Time distribution of rainfall in heavy storms, Water Resour. Res., 3(4), Institution of Engineers Australia Australia Rainfall and Runoff Pilgrim, D. H. (Editor). The Institution of Engineers Australia, Barton, ACT. Jothityangkoon, C., and M. Sivapalan Temporal scales of rainfall-runoff processes and spatial scaling of flood peaks: Space-time connection through catchment water balance, Adv. In Water Resour., 24(9-10),

68 Jothityangkoon, C., and Sivapalan, M.: Towards estimation of extreme floods: examination of the roles of runoff process changes and floodplain flows, J. Hydrol.. 281: , Kusumastuti, DI, Reynolds D, Sivapalan M Impact of the presence of a network of interconnected lakes within a catchment on flood frequency. Paper presented at the Seventh IAHS Scientific Assembly, Foz do Iguacu, Brazil, April 3-9, Ott, R.F., and R.K. Linsley Streamflow frequency using stochastically generated hourly rainfall, in International Symposium on Uncertainties in Hydrologic and Water Resources Systems, Vol. 1, pp , Univ. of Ariz., Tucson. Robinson, J. S., and M. Sivapalan. 1997a. An investigation into the physical causes of scaling and heterogeneity of regional flood frequency. Water Resour. Res., 33(5), Robinson, J. S., and M. Sivapalan. 1997b. Temporal scales and hydrological regimes: Implications for flood frequency scaling. Water Resour. Res., 33(12), Sivandran, G Effect of Rising Water Tables and Climate Change on Annual and Monthly Flood Frequencies. B. Eng. Thesis, Centre for Water Res., Univ. of West. Aus., Crawley, Australia. Short, R A conceptual hydrogeological model for the Lake Warden recovery catchments Esperance, Western Australia. Resource Management Technical Report 200. Sivapalan, M., E.F. Wood, and K. Beven On hydrologic similarity: 3. A dimensionless flood frequency model using a generalized geomorphologic unit hydrograph and partial area runoff generation, Water Resour. Res., 26(1), Sivapalan, M., G. Blöschl, R. Merz and D. Gutknecht Linking flood frequency to long-term water balance: Incorporating the effects of seasonality. Water Resour. Res., 41, W06012, doi: /2004WR Spence, C. and Woo, M.-K Hydrology of subarctic Canadian shield: soil filled valleys. J. Hydrol., 273: Spence, C. and Woo, M.-K Hydrology of subarctic Canadian Shield: heterogeneous headwater basins. J. Hydrol.. 317,

69 Wood, E.F An analysis of the effects of parameter uncertainty in deterministic hydrologic models, Water Resour. Res., 12(5),

70 CHAPTER 3. THRESHOLDS IN THE STORM RESPONSE OF A CATCHMENT-LAKE SYSTEM AND THE OCCURRENCE AND MAGNITUDE OF LAKE OVERFLOWS: IMPLICATIONS FOR FLOOD FREQUENCY 68

71 ABSTRACT This study examined the effect of catchment and lake thresholds upon the frequency and magnitude of lake-overflows, and their implications for the magnitude and shape of the resulting flood frequency curve. Three storage based thresholds were considered: the catchment field capacity storage governing catchment subsurface stormflow, total storage capacity governing catchment surface runoff, and lake storage capacity governing lake-overflow. The roles of these threshold-driven processes, and their interactions, on the frequency and magnitude of lake-overflow events have been examined using a conceptual rainfall-runoff model of the combined catchment-lake system, which is driven by inputs generated by a stochastic rainfall model. This purely model-based study has provided valuable insights into the process controls on lakeoverflow events and the associated flood frequency behaviour in lake dominated catchments. In particular, the relative roles of climate, soil depth, the soil s drainage capacity, as well as the relative geometry of the lake vis a vis the contributing catchment, as manifested in the ratio of catchment area to lake area, in the determination of the characteristics of lake-overflow events and associated flood frequency behaviour, have been highlighted. The improved understanding of these process controls will be useful in assisting the management of the combined catchmentlake system in the study region, and in regions elsewhere. In particular, the results of this study can also provide guidance towards the monitoring of catchment-lake systems in ways that are more targeted towards those controls that are critical to the determination of the magnitude and frequency of lake-overflow events to assist in flood prevention and mitigation. 69

72 3.1 Introduction The hydrological variabilities resulting from interactions between precipitation fields and the land surface undergo, firstly, a concentrating action in the spatial domain (due to topography, soil layering and the river network), and a smoothing or filtering action in the time domain (due to the flow of water over and within the hillslopes) (Sivapalan et al., 2001). The filtering action in the time domain, which is the focus of this study, can be attributed to the multiplicity and heterogeneity of flow pathways, covering a broad range of timescales, which water takes in its movement to the catchment outlet (Robinson and Sivapalan, 1997; Jothityangkoon and Sivapalan, 2001). One of the complicating features of the rainfall to runoff transformation in the time domain, which may have implications for the magnitudes and frequency of floods and droughts, is that the various surface and subsurface flow pathways are dynamic, heterogeneous and highly nonlinear. Indeed, many of the rainfall-runoff processes are associated with threshold nonlinearities. Surface runoff generation, a fast process, is often conceptualized as a threshold process, reliant upon two important mechanisms; infiltration excess and saturation excess. Infiltration excess runoff occurs when the rainfall intensity exceeds an infiltration capacity threshold, whereas saturation excess overland flow is said to occur when the volume of rainfall inputs exceeds a soil moisture storage capacity threshold. Similarly, subsurface stormflow can also be deemed as a threshold process which occurs when soil moisture storage exceeds the field capacity storage threshold. One of the defining features of threshold nonlinearities is the introduction of intermittency to the rainfall-runoff process. For example, the presence of surface water storage features, such as natural lakes and man-made reservoirs within or at the downstream end of catchments, introduces intermittency to the catchment runoff response due to the effect of these stores attenuating or quite often terminating runoff, and producing runoff outflows only at times when a specified lake storage capacity is exceeded. In addition to traditional effects of filtering at the event scale, e.g., attenuation, time delay, dispersion etc., in the presence of threshold nonlinearities, intermittency becomes an additional manifestation of associated nonlinear, threshold filtering (Struthers et al., 2007a; Struthers et al., 2007b; Struthers and Sivapalan, 2007), a concept which is only meaningful with respect to a population 70

73 of events. Termination can thus be seen as a specific type of filtering, which acts to reduce the frequency of runoff generation occurrences in a population of storm events. Intermittency, as measured through the frequency of occurrences of threshold driven processes, is governed by interactions between the strength of climatic inputs, be it rainfall intensity or event rainfall depth, and the antecedent moisture state, be it soil moisture storage, or infiltration capacity. At a broader level, the antecedent condition will be the end result of the balance between precipitation, evaporation and runoff, which is in turn governed by interactions between climate, soil and vegetation. Antecedent conditions will be critical and controlling during times or in situations when the magnitude of the antecedent saturation deficit is of the same order of magnitude as the storm volume (Struthers et al., 2007a; Struthers et al., 2007b). On the other hand, the threshold filtering is strongest when the event rainfall volume is low and the antecedent storage thresholds are high. In this case much of the rainfall is utilized to first satisfy the antecedent saturation deficit and it is only when the deficit is exceeded that runoff will be generated; the magnitudes of flood peaks that do result are reduced as result of the need to satisfy the initial saturation or infiltration capacity deficit. Indeed, one often finds that it is only during extreme storm events that the threshold storage deficit, or for that matter infiltration capacity deficit, is greatly exceeded by the rainfall volume, or rainfall intensity, leading to high flood peak values. However, under circumstances where the exceedance of a storage or intensity threshold leads to rapid storm response, e.g., surface runoff or overland flow, then the magnitudes of the resulting flood peaks can be significantly affected by not just the event rainfall volume, but also the within-storm intensity patterns (Kusumastuti et al., 2007). The present study is designed to examine the effects of surface water storage features such as lakes, on the transformation of the rainfall to runoff signal in a combined catchment-lake system. This study has been motivated by a lake-dominated catchment system, Lake Warden, located near Esperance in south-east Western Australia, which recently has been the focus of a comprehensive investigation to understand and mitigate the processes that potentially could contribute to catastrophic flooding. Natural swamps and small lakes exist throughout the Lake Warden catchment, with chains of small lakes and streams particularly common in the upper catchment. In addition, the catchment is terminated by a wetlands system located downstream of the catchment, which consists 71

74 of Lake Warden and a number of other similar sized lakes (Figure 3.1). The Lake Warden wetlands system is of international importance and is included in the Ramsar List (the Ramsar Convention is a list of wetlands of international importance formulated on the basis of ecological, botanical, zoological, limnological or hydrological criteria) (CALM, 1997). The catchment and the wetlands system have experienced severe, even catastrophic, flood events in 1999 and 2000 when flow contributions from the catchment areas to the lakes resulting from otherwise rare summer cyclonic events exceeded the lake s storage capacity, causing overflows into the nearby town of Esperance. Prevention and/or mitigation of such catastrophic floods in the future require an improved understanding of the role of the various thresholds in the hydrologic response of the combined catchment-lake system to extreme storm events, and their combined impacts on the frequency and magnitude of extreme floods. 72

75 Figure 3.1 The Lake Warden catchment 73

76 Detailed studies of combined catchment-lake systems are relatively rare worldwide, and relatively little is known about them. The few studies that are relevant to this issue appear to be limited to those in respect of catchments containing small lakes in the Arctic and Subarctic Canadian Shield environment of Canada, generally undertaken within a broad framework aimed at determining the effects of various threshold processes on runoff magnitude and timing (Woo et al., 1981; Mielko and Woo, 2006; Spence and Woo, 2003; Spence and Woo, 2006). These studies have so far shown the high dependence of small high arctic lakes upon the upstream catchment areas as sources of water, rather than upon direct precipitation falling on the lakes, because not much precipitation falls on these lakes due to the generally dry climate. Spence (2000) has indicated that the location of a lake (i.e., whether a lake is located in the upper, middle or lower part of the overall catchment) is very crucial in the determination of the dominant sources of streamflow reaching the lakes and also the catchment outlet. For example, in the Canadian Shield landscape during snowmelt events, it was found that all runoff from upland or source areas (except runoff immediately adjacent to large rivers) had to travel through headwater lakes before it reaches higher-order streams (Spence, 2000). As a consequence, much of the snowmelt runoff from the upland areas almost never reached the outlet of the catchment-lake system, especially when there existed high antecedent storage deficits in the lakes prior to the onset of snowmelt. In addition to the relative location of the lakes within a catchment, contributing areas to the lakes also influence lake-overflow behaviour as well as the overall catchment response (Spence, 2000; FitzGibbon and Dunne, 1981). Similarly, lake size is also an important factor in determining the overall effect of lakes on the lake-overflow response. For example, lakes have been found to be efficient in smoothing the hydrographs of incoming catchment runoff responses only when they comprised more than 5% of the catchment area (FitzGibbon and Dunne, 1981; Mielko and Woo, 2006). A recent study of the hydrology of subarctic heterogeneous headwater basins in the Canadian Shield (Spence and Woo, 2006) showed that flows in a catchment can be disjointed during dry periods but may easily cascade from the upper to lower sections of a catchment under wet conditions, clearly a consequence of the kind of threshold filtering, the subject matter of this paper. 74

77 Investigations into the impact of the large number of inland lakes upon the hydrology of Lake Warden catchment system have been limited, primarily due to the lack of longterm rainfall, lake level, and streamflow data. Primary hydrological data has been gathered since December 2003 as part of a larger research project, but this short dataset is insufficient for conducting a detailed field-data based examination of threshold driven processes, which by their nature are highly intermittent. Given the lack of long time series data, this study is predominantly conceptual, with the aim being an improvement in the understanding of the interactions between climate properties and catchment and lake characteristics, and their combined impacts on runoff behaviour, with a specific emphasis on understanding how the presence of lakes alters the overall rainfall-runoff behaviour. The results from this study could then be used to design a long-term monitoring programme on the combined catchment-lake-wetland system, focusing on those key processes and process controls that could be identified through this rather theoretical investigation. While the approach adopted in this study is general enough, climate conditions and catchment (and lake) characteristics typical of south-east Western Australia (where small and shallow lakes are numerous) will be used to parameterise the adopted conceptual models. The primary aim of this study is the investigation of the effect of lake storage thresholds, their interactions with nonlinear (including threshold) rainfallrunoff processes, and their combined effects on flood frequency, including specifically the flood frequency associated with lake-overflows. The specific aims of this study are to investigate (1) the effects of thresholds on the nonlinear filtering and related transformations of the rainfall to runoff signals, (2) the effects of catchment and lake characteristics, such as soil depths and catchment residence time, and the ratio of catchment area to lake area, upon catchment runoff processes and the lake-overflow process, all of which are deemed as threshold processes, and (3) the characteristics of the subsets of all rainfall events which trigger lake-overflow events, to give us insights into the nature of threshold filtering that might be possible in the combined system. 75

78 3.2 Methodology Rainfall model The rainfall signal used in this study is generated with a stochastic rainfall generation model developed by Sivandran (2002), which is an extension of the model developed previously by Robinson and Sivapalan (1997). The rainfall model includes seasonal variability in the dominant storm types characteristic of the study region through considering separate synoptic components (year-round), which contribute about twothirds of the annual rainfall, and as well as rain bearing depressions from ex-tropical cyclones and local thunderstorms which occur from December to March. The synoptic component applies to the entire 12 month period of a year, with stochastic properties of storm duration, inter-storm period and rainfall intensity that can be estimated from observed rainfall data, while the summer cyclonic component assumes each year to consist of just 3 summer months, with a different set of properties of storm duration, inter-storm period and intensity that reflect infrequent summer tropical cyclones. Some simulations presented in this study use the synoptic rainfall model alone, while some other simulations also include cyclonic storm. To include tropical cyclonic storms in the rainfall time series, the two generated sequences (synoptic and cyclonic) are superimposed by concatenation. Synoptic rainfall model The model is capable of incorporating any combination of storm, within-storm, between-storm and seasonal variabilities of rainfall intensities. The storm occurrence is defined using probability distributions of storm duration and inter-storm period, whose parameters are assumed to be independent of each other but vary seasonally. Storm duration and inter-storm period are assumed to be distributed according to the following exponential probability density functions (PDF), with seasonally varying parameters: fτ r fτ b 1 t = r ( tr δ ) exp (3.1) δ δ 1 t = b ( tb γ ) exp (3.2) γ γ 76

79 where δ is mean storm duration, and γ is mean inter-storm period. It is assumed that δ and γ are assumed to vary sinusoidally with time of year τ as follows: 2π δ = δ r + α r cos ( τ τ r ) (3.3) ωh 2π γ = γ b + α b cos ( τ τ b ) (3.4) ωh where δ r and γ b are the seasonally averaged storm duration and inter-storm period, respectively, τ r and τ b are seasonal phase shifts which are assumed to be equal, and α b are the amplitudes of the seasonal variations of t r and t b, τ describes the time of year, and ω h is the total number of time units in a year (i.e., ω h = 8760 hours). α r Mean storm intensity i is a random variable stochastically dependent upon storm duration t r ; that is, i and t r follow the joint PDF, f ( i, t ), which is also seasonally I, T r δ r varying due to the variation of δ with time of year τ. The dependence between i and t r is expressed as: b1 2 b2 E [ i t ] = a [ i t ] a r 1t r CV = (3.5) r 2t r with the coefficient a 1 being assumed to also vary seasonally, as follows: a 2π = a1 m + a1a cos ( τ τ ) ω 1 a (3.6) The power functions presented in equation (5) provide relationships between tr and the first two moments of f ( i tr follow the gamma distribution. I ), the conditional PDF of i given tr, which is assumed to The mean storm intensity satisfying the above properties is further disaggregated to hourly intensity patterns (within-storm patterns) using stochastically generated mass curves (Huff, 1967), using the methodology presented by Robinson and Sivapalan (1997). In this way, the rainfall model is able to generate rainfall sequences at scales ranging from a fraction of an hour to many hundred years incorporating both withinevent, event, inter-event and seasonal variabilities. 77

80 Cyclonic summer rainfall model A particular feature of the rainfall model that is crucial for the study region is the inclusion of the effects of large, infrequent but important tropical cyclones that tend to occur during the summer months of December, January and February. A modelling framework similar to the one outlined for synoptic rainfall was used to generate cyclonic summer rainfall events. Several alterations were made in order to account for the different characteristics of cyclonic events. The summer cyclonic storm model generates a stochastic time series of 90 days period each year representative of December, January and February, which was accomplished by setting the parameter ω to 2160 hours (Equations 3.3, 3.4 and 3.6). The seasonal (intra-annual) component of the stochastic rainfall model was removed as tropical storm arrivals appeared to be totally random showing little preference for any of the three summer months. Therefore, the amplitude of seasonal variations of storm duration α r (Equation 3.3), inter-storm period α b (Equation 3.4) and mean intensity (Equation 3.6) were all set to zero. From the analysis of rainfall records in the region the temporal frequency of cyclonic rainfall events appeared to be, on average, once in 7 8 years, and therefore the interstorm parameter days). a 1a γ b (Equation 3.4) was set to hours (i.e., roughly 8 times 90 Table 3.1 presents the rainfall model parameterisations for both synoptic and cyclonic storms, which are based upon observed rainfall records for the Esperance region in Western Australia. The setting and validation of the stochastic rainfall generation model is described by Robinson and Sivapalan (1997) Rainfall-runoff Model The notional study region, closely resembling Esperance in Western Australia, has a Mediterranean climate with cool, wet winters and hot, dry summers, resulting in a qualitatively dry catchment with low annual rainfall and high potential evaporation, with seasonal rainfall variability completely out of phase with that of potential evaporation. The rainfall-runoff model utilized in this study is based on work of Manabe (1969) and Milly (1994), in which the catchment is represented using buckets 78

81 with a finite storage capacity estimated from spatially averaged soil depth and porosity. In recent years the bucket model has been extensively used to model the water balance of diverse catchments, including in this region (Jothityangkoon et al., 2001, Atkinson et al., 2002; Atkinson et al., 2003; Farmer et al., 2003). In this study, the landscape is represented in terms of a single catchment bucket connected in series to a lake bucket, with the outflow from the lake constituting the runoff response of the overall catchment-lake (landscape) system. Herein, the term landscape is used to refer collectively to the catchment-lake combination. Catchment water balance The catchment bucket model is nonlinear, containing both field capacity and bucket capacity thresholds. The field capacity threshold S fc is calculated from the product of the catchment-average field capacity, f c, and the catchment-average soil depth, D. The bucket capacity, S b, is assumed to be equal to S b = φ.d, where φ is the catchmentaverage soil porosity. The area under consideration consists of three dominant soil types, i.e. deep duplex ( m), deep sand (up to 1.2 m) and shallow duplex (less than 0.3 m), covering more than 75 percent of the catchment (Short et al., 2000). Based on the available soil depth data, the bucket capacity used for the majority of this study is 150 mm, representing a shallow soil depth that would be highly responsive to storm inputs. Potential evaporation is obtained from measured pan evaporation data from the Esperance Meteorological Bureau, with an annual pan evaporation of approximately 1700 mm, from which a typical, mean intra-annual (within-year) variation of potential evaporation is constructed for the catchment as a whole. The water balance equation for the catchment bucket is: ds dt = i( t) Q ( t) Q ( t) E ( t) E ( t) (3.7) se ss bs where S(t) is storage (mm), t is time (hours), Q is surface runoff (mm/h), Q is subsurface flow (mm/h), E is bare soil evaporation (mm) and E is transpiration (mm). bs veg se veg ss 79

82 Transpiration is a function of the fraction of vegetation covering the catchment, M, potential evaporation, E p, and storage at field capacity (S fc ). E veg ME p = S( t) ME p S fc S( t) S fc S( t) < S fc (3.8) Bare soil evaporation is a function of potential evaporation and the fraction of the catchment which is not vegetated, i.e. (1-M). E bs E = E p p (1 M ) S( t) (1 M ) Sb S( t) S S( t) < S b b (3.9) Subsurface flow occurs when the soil moisture storage in the bucket exceeds the field capacity threshold and is therefore a function of the dynamic storage, S(t). The nonlinear storage-discharge relationship for subsurface flow is represented by two coefficients a and b. The b value used in this study, 0.5, is a reasonable value for arid and semi-arid catchments of south-west Western Australia (Wittenberg and Sivapalan, 1999). Parameter a is usually derived from the analysis of recession curves of the observed discharge hydrographs (Atkinson et al., 2003; Jothityangkoon and Sivapalan, 2001). Q ss = S( t) S a S b S a fc fc 1 b 1 b S fc < S( t) < S S( t) > S b b (3.10) Surface runoff (Q se ) occurs when the soil is fully saturated, which occurs when the soil moisture storage S(t) exceeds the bucket capacity. Q = S( t) if S ( t) > (3.11) se S b S b Surface runoff is assumed to reach the catchment outlet instantaneously, i.e., there is no river network routing included in this study; estimated flood peaks would therefore be expected to be slight over-estimates. 80

83 Lake water balance Inputs to the lake bucket are direct rainfall and runoff from the contributing catchment area (i.e. the catchment bucket), and losses are due to evaporation and lake overflow. The lake bucket has only one threshold, i.e. the lake storage capacity, which for this study is assumed to vary from 1000 mm to 5000 mm. The lake storage capacity used for the majority of this study is 1500 mm, representing a shallow lake depth which is common to the study area. The water balance equation for the lake bucket is given by: dsl dt AC = i( t) + Qin ( t) 0.7E p ( t) Qsel ( t) (3.12) A L where S l is lake storage, A C and A L are catchment and lake area respectively, Q in is inflow from the contributing area ( Q ( t) = Q ( t) Q ( t) ), and Q sel is outflow from the in ss + se lake. Q sel ( t) = S ( t) S if S ( t) > (3.13) l bl l S bl A schematic of the combined rainfall-runoff model, including both the catchment and lake compartments, is presented in Figure 3.2. Lake evaporation is commonly considered to occur at 0.7 times the rate of potential evaporation (Penman, 1948), which has been validated in the study region by Marimuthu et al. (2005) through observational and modelling investigations. A sensitivity analysis has been performed to examine the impact of climate and landscape properties on the magnitude and timing of lake overflows, as reported later in this paper. The ranges of parameter values for all parameters used in the rest of this study, including in the sensitivity analyses, are summarised in Table

84 Table 3.1 Rainfall and runoff model parameters with normal value and range/list values used in sensitivity experiments Parameter Equation Normal value Range/List Units Rainfall model parameters δ r α r Winter Summer storm storm (3) hours (3) hours γ b (4) hours α b (4) 69 0 hours τ r = τ b (3),(4) 0 0 month ω a 1 a 1 m a 1 a b 1 a 2 (3),(4) hours (6) (6) (6) (-300) - (5) (5) b 2 (5) η 1.5 Storage discharge relationship a (12) (mm 0.5 h 0.5 ) b (12) 0.5 Soil properties S b (11),(12),(13) mm S fc (10),(11),(12) mm 82

85 Vegetation M (10),(11) 0.1 Lake storage capacity S bl (15) 1500 mm Catchment area to lake area ratio A C /A L (14) Annual potential evaporation , 856, 1284, 1712 mm 83

86 P E bs E veg P E p S b Q ss S Q se S bl Q l S fc Catchment bucket S l Lake bucket Figure 3.2 Runoff model for landscape (catchment and lake) utilising catchment and lake buckets 84

87 3.3 Results Illustrations of threshold filtering at event scale Thresholds are ubiquitous in land surface hydrology. In the case of catchment storm response, both subsurface stormflow and saturation excess surface runoff are threshold processes, and occur when the addition of storm event depth to the antecedent moisture storage exceeds, respectively, the storage capacity at field capacity and the soil moisture storage capacity. In the case of the catchment-lake system, the runoff from the catchment itself becomes an input to the lake, in addition to the direct rainfall, and when the inputs from the catchment and from direct rainfall, in combination, exceed the antecedent storage deficit in the lake, this results in lake-outflow, thus making it also a threshold process. Two different illustrations of threshold filtering associated with the partitioning of rainfall into various types of runoff in a catchment-lake system are presented in Figures 3.3 and 3.4 for a small number of consecutive storm events, to provide insight into the kinds of transformations that might be occurring in the catchment at event scale and the interactions between catchment and lake. The figures represent two different time periods for the same simulation behaviour, representing early winter (Figure 3.3) and mid-winter (Figure 3.4) time windows to illustrate the effect of different antecedent conditions on the extent of threshold filtering that would be expected. For the sake of this analysis, we characterize the degree of threshold filtering in terms of the number of threshold exceeding storms, i.e. those storms that can generate various threshold driven processes, such as subsurface runoff, surface runoff and lake-overflow, compared the number of all incoming storms. In the first example, for the storm events presented in Figure 3.3, the number of subsurface flow triggering storm events is the same as the number of storm events. On the other hand, in this case, the rainfall volume is not sufficient to trigger surface runoff for any of the events. To quantify the amount of runoff from the catchment to the lake, a ratio of catchment area to lake area (A C /A L ) is used in the water balance computations (equation 3.12). Figures 3.3d and 3.3e present the lake-overflows generated using A C /A L =10 and A C /A L =2, respectively. It can be seen that the number of lake-overflow occurrences for A C /A L =10 is higher than that for A C /A L =2, meaning that a smaller ratio of A C /A L increases intermittency. 85

88 For the storm events presented in Figure 3.4, once again the number of subsurface flow events is the same as the number of storm events. However, in this case, surface runoff is generated during some events, but the occurrence is still rare. The difference between Figures 3.3 and 3.4 is noticeable on the frequency of lake overflows for A C /A L = 2 compared to A C /A L = 10. At small A C /A L the lake receives less runoff input from the catchment, so that it needs a longer time to fill up the lake storage capacity compared to the time needed with a larger A C /A L. Therefore, in the early winter the lake overflow at A C /A L = 2 (Figure 3.3e) starts later than that at A C /A L = 10 (Figure 3.3d). In mid-winter wetter antecedent condition of lake storages for both A C /A L = 2 and 10 allow the subsequent storms to trigger lake overflow (Figures 3.4d and 3.4e). Despite the similar response in terms of the occurrences of lake-overflows in mid-winter, the magnitudes of lake-overflows are different due to the different interactions between catchment and lake. For A C /A L =10, the magnitude of lake-overflow is highly influenced by runoff from the catchment. The contribution of surface runoff increases the corresponding magnitude of lake-overflows (Figure 3.4d). Conversely, for A C /A L =2, the magnitude of lake-overflow is governed by direct rainfall. High storm rainfall intensity and volume are manifested in a higher peak lake-overflow, whereas surface runoff from the catchment has a smaller influence on the peak of lake-overflows. Figures 3.3 and 3.4 also show that the shapes of the runoff hydrographs are different for the different runoff processes. The larger response time for subsurface stormflow results in hydrographs that rise and fall slowly (Figures 3.3b and 3.4b). On the other hand, surface runoff is a fast-response process, and as a result, the surface runoff response is manifested in rapidly rising and falling hydrographs (Figures 3.3c and 3.4c). The hydrographs of lake-overflow exhibit a rapid rise due to the simplified nature of our model, which does not include attenuation towards the outlet. The lake-overflow hydrograph recedes more slowly than the hydrographs for catchment surface runoff (Figures 3.3d and 3.4d); as long as the volume of catchment runoff contribution (mostly due to subsurface stormflow) exceeds lake evaporation, lake-overflow will be continuous once triggered. 86

89 10 (a) rainfall, mm/h time, hours (b) subsurface runoff, mm/h time, hours (c) surface runoff, mm/h time, hours (d) lake overflow, mm/h 4 2 A C /A L = time, hours 4 A C /A L =2 (e) lake overflow, mm/h time, hours Figure 3.3 Schematic representation of the threshold filtering of storms by catchment and lake in the early winter time window; (a) storm events, (b) subsurface flow, (c) surface runoff, (d) lake overflow using ratio A C /A L =10, (e) lake overflow using ratio A C /A L =2. 87

90 24 (a) rainfall, mm/h time, hours 8 (b) subsurface flow, mm/h time, hours 8 (c) surface runoff, mm/h time, hours (d) (e) lake overflow, mm/h lake overflow, mm/h 8 A C /A L = time, hours 8 A C /A L = time, hours Figure 3.4 Schematic representation of the threshold filtering of storms by catchment and lake in the middle winter time window; (a) storm events, (b) subsurface flow, (c) surface flow, (d) lake overflow using ratio A C /A L =10, (e) lake overflow using ratio A C /A L =2. 88

91 3.3.2 Cascading of variability through catchment-lake system: a population of events An examination of the properties of threshold-exceeding storms was conducted for each threshold process (subsurface flow, surface runoff, and lake-overflow) to understand the filtering and transformation of the rainfall signal in a combined catchment-lake system, now for a population of events. As a part of this process, the occurrence frequency of threshold-exceeding storms for each threshold process was analysed. Simulations of 2000 years in length were conducted with the model, and probability distribution functions (PDFs) of the properties of threshold-exceeding storms were constructed, to understand how the properties of these subsets relate to the full distribution of storm properties, as described by equations (3.1) to (3.6). As illustrated in Figures 3.3 and 3.4 the total number of incoming storm events will be filtered down to a smaller number of storm events triggering subsurface flow, surface runoff and lake-overflows, respectively. The resulting PDFs of threshold exceeding storm events are shown in Figure 3.5 for simulations using A C /A L =10. The parent distribution of inter-storm periods for the rainfall time series is the exponential distribution (Figure 3.5a). The PDF of inter-event period between threshold-exceeding events is considered as the period between consecutive threshold-exceeding events. The PDF of inter-storm periods for events triggering subsurface flow is found to be bimodal (Figure 3.5b), although the second peak is weak. The dominant inter-storm period is in the range hours, which means that subsurface flow is usually generated by consecutive, or near-consecutive, storm events, pointing to clustering. During winter the catchment storage is usually above the field capacity storage, therefore subsurface flow is generated continuously. The second (weak) peak occurs at around 4000 hours, which corresponds to one half of a year, which roughly relates to the period between subsurface flow cessation following the end of winter and the resumption of subsurface flow once the soil is wetted up to field capacity by the first rains of the subsequent winter. Note that this bimodality is the result of pronounced wet and dry seasons. The PDF of the inter-storm period for surface runoff-triggering storms is exponential in shape (Figure 3.5c), where the most common occurrence of surface runoff (governed by the median value of the PDF) is about hours or less. This suggests that surface 89

92 runoff events may occur only once a year or once in two years, indicating that surface runoff occurrence is rare. The PDF of the inter-storm period of lake-overflow triggering events is multi-modal. The most common or dominant period between lake-overflow triggering events is in the range hours (Figure 3.5d), reflecting the fact that, once lake storage capacity is exceeded, the high antecedent condition of lake storage increases the likelihood of subsequent storms also exceeding lake storage capacity, leading to clustering. The other (weak) peaks of the PDF occur around 6000 hours, and around hours. This indicates that for the A C /A L values considered here, the lake usually overflows every year. The first peak relates to the inter-storm period itself, where consecutive storm events in winter trigger lake-overflows, the second peak relates to seasonality in lake storage, while the third peak relates to inter-annual variability in rainfall, indicating that lake-overflow may not be triggered at all in drier than average years. 90

93 0,0084 0,0063 (a) p(t b ) 0,0042 0, hours 0,008 (b) p(tbqss) 8, E-03 6, E-03 4, E-03 p(tbqss) 0, ,4E hours 2,E-03 0,E hour Qss) p(tb 7,0E-06 0,0E hours 5,E-05 (c) p(tbqse) 4,E-05 3,E-05 2,E-05 1,E-05 0,E hours 91

94 1,E-02 p(t b Q l ) 5,E-03 0,E+00 0, hours 2,E-05 (d) p(tbql) 0,006 0, hours p(t b Q l ) p(t b Q l ) 1,E-05 0,E+00 3,E-07 2,E hours 0,E hours Figure 3.5 PDF for interstorm period of consecutive threshold-exceeding events for (a) all storm events, (b) sub-surface flow-generating storms, (c) surface flow-generating storms, and (d) lake overflow-generating storms. 92

95 3.3.3 Sensitivity analysis - the impacts of climate and catchment properties on occurrence frequency of lake-overflows Having highlighted in previous sections the nature of the transformations involved in threshold filtering, we next look at the roles of climate, catchment and lake characteristics, and their interactions, on the frequency of occurrence of lake-overflow events. The ratio of contributing catchment area to lake area significantly impacts the one-dimensional rate of inflow into the lake, and therefore the incidence of lakeoverflow. Figures 3.6 to 3.9 show the relative per-storm frequency of lake-overflow for a range of sensitivity experiments involving systematic alteration of both climate and landscape parameter values, as detailed in Table 3.1. The frequency of lake-overflow events is quantified by the ratio of the number of lake-overflow triggering storms to the total number of storms. Figure 3.6 presents the frequency of lake-overflows as generated using four different values of the rainfall intensity parameter, a 1m = 0.4, 0.6, 0.8 and 1.6 mm/h (Equation 3.6) over a range of values of A C /A L : note that a 1m governs the magnitude of the average intensity of storms. For a 1 m<0.8mm/h, lake overflow does not occur for A C /A L <0.1. Further increases in a lm to 1.6mm/h results in higher per-storm frequency of lake overflow for smaller A C /A L. Considering that small values of A C /A L mean that lakeoverflow can only occur through direct rainfall falling in the lake, this suggests that lake-overflow due to direct rainfall into the lake (i.e. with negligible input from catchment runoff) requires, for the particular lake size considered here, a certain minimum value of a lm between mm/h. As the value of A C /A L increases, catchment contribution supplements direct rainfall, and overflow triggering will commence at progressively lower values of a 1m, dependent increasingly upon the properties of the catchment as well as the size of the lake. 93

96 frequency of lake overflow 1 a1m=0.4 a 0.8 a1m=0.6 a a1m=0.8 a 0.6 a1m=1.6 a A C /A L Figure 3.6 The effect of rainfall intensity on the frequency of lake overflow 94

97 Rainfall intensity and the ratio of A C /A L are important factors governing the frequency of lake-overflow occurrence. Large A C /A L corresponds to large runoff inputs from the catchment. Small A C /A L corresponds to dominance of direct rainfall in the lake, with the rainfall intensity having a direct influence on the occurrence of lake-overflows. A similar (but opposite) result was obtained for the effect of evaporation (result not shown), which points to the importance of the rainfall-evaporation deficit in governing the frequency of occurrence of lake-overflows. To elucidate the competitive influences of rainfall and evaporation, Figure 3.7 presents the per-storm frequency of lake-overflow estimated as a function of A C /A L and an event-scale climate index, it e t P = r (3.14) E p b In a very wet climate, one would expect that all storms will generate lake-overflow and in a very dry climate none of the storms will generate lake-overflow. This is indeed what was obtained by means of model simulations, with the frequency of occurrence of lake-overflow increasing as the climate moves from very dry to very wet, as shown in Figure 3.7. In particular, the relationship between the frequency of lake-overflow triggering and the ratio P/E appears to take the form of a logistic function (Struthers et al., 2007; Struthers et al., 2007b; Struthers and Sivapalan, 2007). However, we also find that not only the climate, but also the ratio of A C /A L impacts on the frequency of lakeoverflow. With increasing values of the ratio A C /A L the curves shift towards drier climates, meaning that lake-overflows can be triggered even in drier climates; small values of A C /A L require relatively wetter climates to initiate triggering of lakeoverflows. 95

98 1 frequency of lake overflow P/E AAc/Al=0.001 C L AAc/Al=0.01 C L AAc/Al=0.1 C L AAc/Al=1 C L AAc/Al=100 C L AAc/Al=10000 C L Figure 3.7 The impact of climate represented by P/E calculated based on ((i p *t r )/(e p *t b )) on the frequency of lake overflow 96

99 Figure 3.8 presents the frequency of lake-overflow as a function of the residence time coefficient a (see equation 3.10) for the case where the exponent b takes on the value of 0.5. Note that a higher value of the parameter a corresponds to a slower responding catchment, and may be associated with flatter slopes, longer drainage lines, or soils with lower hydraulic conductivity. Several values of the coefficient a, ranging from 10.0 to mm 0.5 hour 0.5 were applied in these simulations. The subsurface flow parameter a is found to have a significant effect on the frequency of lake-overflow. In all cases presented, the frequency of lake-overflows is at its highest at low a values, decreasing with increasing a values, before stabilizing at a lower value at high values of a. The shape of the resulting relationship is governed by the dominant runoff mechanism occurring in the catchment. In a catchment with small value of coefficient a (e.g. a =10) subsurface stormflow occurs frequently with a significantly higher magnitude of the peak, compared to that with a large a value (as can be seen from Equation 3.10). At the same time, surface runoff occurs much less often than subsurface stormflow. The contribution of subsurface stormflow alone will be sufficient to generate lake-overflow while the frequency of occurrence of lake-overflow will be higher for a larger ratio of AC/A L (Figure 3.8a). Therefore for a smaller a value, subsurface stormflow (in addition to direct rainfall) is the main contributor to the triggering of lake-overflows. The frequency of lake-overflow occurrence is highest at small a values because the magnitude of subsurface flow is then the largest (Figures 3.8a, 3.8b and 3.8c). As a increases, subsurface flow becomes smaller in magnitude but more persistent. Consequently, soil moisture storage at any point in time will be greater than that for small a values, such that the incidence of surface runoff is increased. Although the perevent frequency of saturation excess surface runoff remains small relative to the frequency of subsurface flow, it will have a much larger magnitude than subsurface flow at high values of a. The contribution of a single surface runoff event upon triggering lake-overflow will therefore be disproportionately larger than that for a single subsurface runoff event. Surface runoff becomes the dominant mechanism that contributes to the lake and generates lake-overflow, with the occurrence becoming more frequent at a larger ratio of AC/A L (Figure 3.8a). Comparing the frequency of lake- 97

100 overflow occurrence at large and small values of a, it shows that the frequency of lakeoverflow is the lowest for large a value, as the occurrence of surface runoff is the least frequent compared to subsurface flow occurrence (Figures 3.8a, 3.8b and 3.8c). In addition to the ratio of A C /A L, the model s bucket capacity, which represents soil depth, is another important landscape characteristic that impacts upon the frequency of occurrence of lake-overflow. Three different values of S b and the ratio A C /A L =10 were used in the simulations. The impact of bucket capacity upon lake-overflow is most apparent at values of a > 1000, where the frequency of lake-overflows is highest when the bucket capacity is small. It is clear that large values of a and small values of Sb both act to maximise the frequency of saturation excess occurrence, indicating that the increased frequency of lake-overflow is directly related to the increased frequency of surface runoff from the catchment. For lower values of a, subsurface stormflow is the dominant input to the lake and contributor to the generation of lake-overflow, regardless of the size of the bucket capacity. The impact of a1m upon the relationship between a and the per-event frequency of lakeoverflow is presented in Figure 3.8c. The results show that, for a given value of a, the larger the rainfall intensity the higher the frequency of lake overflow. A similar explanation can be given for the shape of the curve; high frequency of lake-overflows for small values of a coefficient and low frequency for large values of a coefficient are again the result of the dominant runoff mechanism. 98

101 1 (a) frequency of lake overflow AAc/Al=2 C L AAc/Al=5 C L AAc/Al=10 C L AAc/Al=100 C L subsurface flow concentration time coef, a 1 (b) frequency of lake overflow Sb=30 Sb=100 Sb=300 subsurface flow concentration time coef, a 1 (c) frequency of lake overflow a1m=0.2 a1m=0.4 a1m=1.6 subsurface flow concentration time coef, a Figure 3.8 The effect of subsurface flow concentration time, a, on the frequency of lake overflow 99

102 3.3.4 Insights into observed behaviour exploration of the impact of antecedent condition of lake storage In this section we present additional results of internal system behaviour to elucidate the behaviour and sensitivity results presented in the previous section. In particular, we focus on the role of antecedent lake storage in governing the frequency of occurrence of lake-overflow events. Figure 3.9a presents estimates of the probability of per-event lake overflow triggering associated with various combinations of antecedent catchment storage and antecedent lake storage. Darker pixels represent a higher probability that any given random storm occurring with these antecedent conditions will trigger lakeoverflow. In summer, lake and catchment storages tend to be lower due to longer interstorm periods (and higher evaporation rates) combined with shorter storm durations. Following summer and with the onset of winter, catchment storage values increase in response to larger storm volumes relative to evaporative losses, while lake storage increases as it receives lateral inflow from the catchment and through direct rainfall in excess of evaporation (transect A). Once it reaches the storage capacity, the lake storage will remain close to the threshold so long as the lake continues to receive inputs from direct rainfall and runoff. Following winter, as summer approaches, and as inputs decrease relative to evaporation, catchment and lake storages will start to decrease (transect B). Results presented in Figure 3.9a show that the probability of lake-overflow is higher when the antecedent conditions of lake storage and catchment storage are high, which is as expected. Figure 3.9b shows the interaction between storm depth and antecedent lake storage on the triggering of lake-overflow. The transect C roughly represents a cut-off, indicating that the magnitude of the storm depth necessary to trigger lake overflow increases as the magnitude of the antecedent storage deficit increases. Comparing the results for A C /A L = 2, 10 and 100 (Figures 3.9b, 3.9c and 3.9d respectively), as the contribution from the catchment becomes more dominant, the slope of the transect increases, signifying that the catchment runoff response even during small storms is most often sufficient to satisfy the antecedent lake storage deficit. Figures 3.10a, 3.10b and 3.10c show the PDFs of the antecedent lake storage prior to storm events (all events) versus the antecedent condition that leads to lake-overflow. Higher probability at lower antecedent lake storage for A C /A L =1 suggests that mostly 100

103 the antecedent lake storage is very low. The distribution changes for A C /A L =10 and A C /A L =100, with lower probability at low antecedent condition of lake storage and higher probability near the lake storage capacity. The PDF of antecedent lake storage near lake storage capacity is higher for the higher ratio of A C /A L. The frequency distribution of antecedent moisture shifts to higher values as A C /A L increases primarily because of the increased contribution of continuous subsurface stormflow from the catchment. The PDFs of the antecedent lake storage that leads to lake overflow for A C /A L =1 (Figure 3.10a) appear flat and are equal to near zero values for lake storages less than 1400 mm, and show a sharp (Dirac delta-function type) increase between 1400 mm and 1500 mm (the lake storage capacity in this case). The main difference between the PDFs of the antecedent lake storage prior to lake-overflow triggering storms is in the lowest antecedent condition that leads to lake-overflow, which we will define as the initiation point. The smaller the ratio of A C /A L the higher the initiation point for lakeoverflow triggering storms (Figure 3.10a). The lowest antecedent conditions are 1434mm, 670mm, and 418mm for A C /A L equal 1, 10 and 100, respectively (Figures 3.10a, 3.10b and 3.10c). This demonstrates that for small A C /A L values (e.g., A C /A L =1) the antecedent condition of lake storage needs to be sufficiently high in order for the storms to trigger lake-overflow. 101

104 A B C (a) (b) C C (c) (d) Figure 3.9 Probability of lake overflow as a function of (a) antecedent conditions of lake storage and catchment storage for A C /A L =10, and antecedent condition of lake storage and storm depth for (b) A C /A L =2, (c) A C /A L =10 and (d) A C /A L =

105 0.012 All storm Ac/Al=1 A C L =1 Trigger overflow Ac/Al=1 A C L = (a) pdf antecedent condition of lake storage, mm All storms Ac/Al=10A C L Trigger overflow Ac/Al=10 A C L =10 (b) pdf antecedent condition of lake storage, mm All storm Storms AAc/Al=100 C L Trigger overflow Ac/Al=100 A C L (c) pdf antecedent condition of lake storage, mm Figure 3.10 Probability density function of antecedent conditions of lake storage for all storms and lake overflow triggering storms for (a) A C /A L =1, (b) A C /A L =10, and (c) A C /A L =

106 The initiation point that was defined and illustrated through Figure 3.10 only used one climate scenario. Further examination of the impact of climate on the initiation point of antecedent lake storage prior to lake-overflow occurrence is presented in Figure For A C /A L values less than 0.1, the initiation point for lake-overflow triggering storms is high, e.g. above 900 mm. When the lake is dominant, direct rainfall is the main contributor to the lake, and therefore, antecedent lake storage has to be sufficiently high so that the storm volume can be expected to exceed the resulting lake storage deficit. For A C /A L >0.1, the initiation point starts to decrease. In this case, the lake is not only receiving water from direct rainfall, but also runoff from the catchment. However, above some critical value of A C /A L, e.g., A C /A L = , the magnitude of the initiation point of antecedent lake storage begins to increase once again, especially for wetter climates. The increase of antecedent lake storage is due to the large amount of runoff produced within its contributing catchment, which is capable of maintaining high values of lake storage, i.e., the higher the value of A C /A L (the more runoff from the contributing catchment) the higher is the lake storage. The inflection point for wetter climates (i.e. high P/E) occurs at a smaller value of A C /A L than for drier climates, suggesting that for wetter climates the catchment is beginning to dominate at smaller value of A C /A L (contributing runoff from the catchment is larger than direct rainfall on the lake). 104

107 initiation point of antecedent lake storage of lake overflow P/E=0.11 P/E=0.22 P/E=0.33 P/E=0.55 P/E=2.75 A C /A L Figure 3.11 The impact of A C /A L and P/E on the initiation point of antecedent condition of lake to overflow 105

108 3.3.5 Implications for flood frequency As illustrated in the schematic description of the lake response (Figures 3.3 and 3.4), the climate and landscape characteristics impact not only the frequency of lake-overflow events but also the magnitude of the resulting runoff and peak response. Figures 3.12 and 3.13 present the results of an examination of process controls upon both the frequency and magnitude of runoff response expressed in terms of the flood frequency curve. Figure 3.12a is the flood frequency curve showing the impact of the ratio of A C /A L for S b =150 mm. Note that the total area of the landscape, A C + A L, is the same for all simulations reported here. It can be seen that when A C /A L =1.5 the flood frequency shows truncation below a return period of about 50 years, which is due to the absence of lake overflow in some years, where direct rainfall is insufficient to generate lake-overflow. For A C /A L =2, runoff from the catchment in addition to direct rainfall will increase the flood peaks and the occurrence of lake-overflow, with the truncation only happening below a return period of about 5 years. The change in the shape of the flood frequency curve is noticeable when A C /A L approaches 10, becoming continuous, but showing a break associated with change of catchment runoff generation mechanism. When the catchment becomes more dominant, the flood frequency curve of lakeoverflow reflects the shape of the catchment flood frequency curve, including the break associated with the change of runoff generation mechanism from subsurface flow to surface runoff. As the ratio of A C /A L increases further, the catchment becomes more dominant and the impact of direct rainfall becomes minimal and the effect of surface runoff is greatest. This can be observed in the flood frequency curves associated with A C /A L values in the range The impact of the catchment bucket capacity upon flood frequency is shown in Figure 3.12b. The simulation uses A C /A L =10, implying a catchment dominant landscape. As the catchment storage capacity increases, the relative frequency of saturation excess surface runoff production by the catchment will decrease, such that the break in the flood frequency curve associated with the transition from subsurface flow to surface runoff dominated flood peaks will occur at higher return periods (Figure 3.12b). The impact of rainfall intensity upon flood frequency is presented in Figure 3.12c. As the average storm intensity increases, the annual flood peak is increasingly associated 106

109 with surface runoff generation by the catchment, such that the break in the flood frequency curve occurs at progressively smaller return periods; for the a 1m =1.6 mm/h, all annual flood peaks result from catchment surface runoff. The impact of the subsurface runoff parameter a upon flood frequency is presented in Figure 3.12d. For A C /A L =10, the flood frequency of lake overflow resembles the flood frequency of the catchment response. For a =10, subsurface flow occurs frequently with significantly high magnitudes of the peak, such that the flood frequency curve for a =10 is dominated by subsurface flow. As a increases, the magnitude of subsurface flow peaks decreases, while the frequency of surface runoff increases. As with increased average rainfall intensity, increased values of a result in the break in the flood frequency curve, associated with the transition from subsurface runoff-dominated flood peaks to surface runoff-dominated flood peaks, occurring at progressively lower return periods. The flood frequency curves generated using cyclonic (summer) and synoptic (winter) storms compared to synoptic (winter) storms only are shown in Figure It is seen that the inclusion of cyclonic storms increases the frequency of surface runoff occurrence, resulting in a break of slope at lower return periods of the flood frequency curve for A C /A L =1000, which is the case where the catchment is dominant. Where the lake is dominant (e.g., A C /A L =1.5), the inclusion of cyclonic storms reduces the instances of year-long flow cessation, and increases the magnitude of flood peaks associated with a given return period (Figure 3.13a). Besides increasing the frequency of occurrence of flooding, the addition of cyclonic storms increases the magnitude of the flood peaks in both catchment dominant and lake dominant systems. Moreover, the effects of the inclusion of cyclonic storms on the flood frequency, i.e. increasing the magnitude of the flood peaks and their frequency of occurrence, are more noticeable for smaller soil depths (Figure 3.13b), higher average rainfall intensities (Figure 3.13c), and smaller subsurface flow parameter a (Figure 3.13d). All of these results are consistent with the results of the sensitivity analyses presented in Figures 3.6, 3.7 and

110 1000 (a) flood peaks, mm/h AAc/Al=1.5 C L AAc/Al=2 C L AAc/Al=10 C L AAc/Al=1000 C L return period, years 1000 (b) flood peaks, mm/h Sb=100 Sb=150 Sb=200 Sb= return period, years 1000 (c) flood peaks, mm/h a1a=0.4 a 1m =0.4 a1a=0.8 a 1m a1a=1.6a 1m return period, years 1000 (d) flood peaks, mm/h a a=10 a a=50 a a=100 a a= return perid, years Figure 3.12 Flood frequency curve for various (a) ratios of A C /A L, (b) bucket capacity, (c) average rainfall intensity and (d) coefficient a 108

111 (a) flood peaks, mm/h AAc/Al=1.5 C L (Cyc+Syn) AAc/Al=1000 C L (Cyc+Syn) AAc/Al=1.5 C L (Syn) AAc/Al=1000 C L (Syn) return period, years (b) flood peaks, mm/h Sb=100 (Cyc+Syn) Sb=500 (Cyc+Syn) Sb=100 (Syn) Sb=500 (Syn) return period, years 1000 (c) flood peaks, mm/h aa1m=0.4 (Cyc+Syn) aa1m=0.8 (Cyc+Syn) aa1m=0.4 (Syn) (Syn) aa1m=0.8 (Syn) return perid, years 1000 (d) flood peaks, mm/h 10 a=50 a (Cyc+Syn) a=1000 a (Cyc+Syn) a=50 a (Syn) a=1000 a (Syn) return period, years Figure 3.13 FFC using synoptic storm (Syn) and cyclonic and synoptic storms (Cyc+Syn) for various (a) A C /A L ratios, (b) bucket capacity, (c) average rainfall intensity and (d) coef. a 109

112 3.4 Discussion and conclusions This exclusively modelling study has examined the combined effects of catchment and lake thresholds upon the frequency and magnitude of lake-overflow events, and explored the underlying process controls. A most dominant and readily identifiable control is antecedent storage in the lake, or more specifically the lake storage deficit. The storage deficit is likely to be small in wetter climates, i.e. in regions with high P/E values, as opposed to in drier climates. In this sense, the climate not only affects the water balance dynamics of the lake water storage, but also the water balance dynamics of the contributing catchment; in fact, the catchment and lake are likely to act synergistically. In this respect, the study has also highlighted the importance of seasonality: this is evident from the PDF of the inter-storm periods of lake-overflow triggering events which exhibits multiple modes, with the estimated multi-modality of arising from the inter-storm period of rainfall events within the year, seasonality (i.e., time between two consecutive rainy seasons), and inter-annual variability. Given the climatically determined antecedent lake storage deficit, the next major control on the magnitude and frequency of lake-overflow events, was shown to be the magnitude of storm depths, and their adequacy to replenish and exceed the lake storage deficit. When A C /A L is small, then direct rainfall on the lake is the dominant external input. However, their probability of triggering will be enhanced if A C /A L is larger, since then there is increased chance for the lake storage deficit to be replenished and exceeded by a combination of direct rainfall on the lake and runoff contributions from the upstream catchment area. In other words, when A C /A L is large, lake-overflows can be triggered even at larger antecedent lake storage deficits or lower storm depths or both. This clearly points to the importance of A C /A L as a critical parameter governing the frequency and magnitude of lake-overflow events. Now, with respect to the catchment contributions during the storm events discussed above, our simulation results have shown that fast draining catchments, i.e., those with smaller a parameter, enhance the triggering of lake-overflow events due to the fact that the drainage is rapid and thus there is the opportunity for the rapid subsurface stormflow to combine with direct rainfall to exceed the antecedent lake storage deficit and overcome the reducing influence of evaporation during the inter-storm period. Slow draining catchments, i.e., those with large a values, will not release subsurface runoff 110

113 fast enough to replenish the lake storage deficit before the evaporative effects take hold. The main qualification to this statement is the case where slowly draining catchments tend to raise the catchment soil moisture storage high enough to the point when rapid surface runoff could be generated. This situation arises especially when the catchment s total soil moisture storage capacity, associated with the total soil depth, is low enough to encourage saturation excess surface runoff generation. The derived flood frequency approach adopted in this work has demonstrated the impact of thresholds, i.e. catchment and lake storage thresholds, upon the magnitude and shape of the flood frequency curve. The shape of flood frequency curve captures the dominant lake-overflow generating mechanism. When the dominant lake overflow generating mechanism is catchment runoff, the shape of flood frequency curve of lakeoverflows resembles the shape of the catchment flood frequency curve, including the presence of a break point that relates to a change of runoff generation mechanism from subsurface stormflow to surface runoff. On the other hand, when the dominant lake overflow generating mechanism is direct rainfall falling on the lake, the shape of lakeoverflow flood frequency curve exhibits a persistent truncation below a critical return period, which is associated with the frequency of flow termination for the given climate in question. The main effect of the inclusion of summer cyclonic events is to increase both the magnitude and frequency of lake-overflow events, and to reduce the critical return period for flow termination. This study has provided valuable insights into the relative roles of climate, soil depth, the soil s drainage capacity as well as the relative geometry of the lake vis a vis the contributing catchment, as manifested in the ratio of catchment area to lake area. The improved understanding of these process controls will be useful in assisting the management of the combined catchment-lake system for the Lake Warden system and other systems in the same region and regions elsewhere, for example, catchments containing small lakes in the Arctic environment in Canada. The results of this study can also provide guidance towards the monitoring of catchment-lake systems in ways more targeted towards those features found to be critical to the determination of the magnitude and frequency of lake-overflow events on the basis of broad climatic information and the relevant landscape and lake characteristics. 111

114 However, it should be noted that the results of this study are based on a conceptual, first-order investigation carried out using hypothetical information, and need to be confirmed by detailed field monitoring in actual places, the data from which will assist in the development of much more improved and detailed models. It is through the combination of long-term field monitoring and targeted short-term measurements, combined with much improved models, that the hazard that may occur in such catchment-lake systems can be analysed and necessary steps taken to prevent them from catastrophic flooding. 112

115 REFERENCES Atkinson, S.E., Woods, R.A. and Sivapalan, M Climate and landscape controls on water balance model complexity over changing timescales. Water Resour. Res., 38(12), Atkinson, S.E., Sivapalan, M., Woods, R.A. and Viney, N.R Dominant physical controls on hourly flow predictions and the role of spatial variability: Mahurangi catchment, New Zealand. Adv. in Water Resour., 26, CALM (Department of Conservation and Land Management) Esperance Lakes Nature Reserves, Draft Management Plan for the National Parks and Nature Conservation Authority, Perth, Western Australia. Farmer, D., Sivapalan, M. and Jothityangkoon, C Climate, soil, and vegetation controls upon the variability of water balance in temperate and semiarid landscapes: downward approach to water balance analysis. Water Resour Res., 39(2), 1035, doi: /2001 WR Fitzgibbon J, Dunne T Land surface and lake storage during snowmelt runoff in a subarctic drainage system. Arctic and Alpine Research 13: Huff, F.A Time distribution of rainfall in heavy storms, Water Resour. Res., 3(4), Jothityangkoon, C., Sivapalan, M. and Farmer, D.L Process controls of water balance variability in a large semi-arid catchment: downward approach to hydrological model development. J. Hydrol., 254, Jothityangkoon, C. and Sivapalan, M Temporal scales of rainfall-runoff processes and spatial scaling of flood peaks: space-time connection through catchment water balance. Adv. in Water Resour., 24, Kusumastuti, D.I., Struthers, I., Sivapalan, M. and Reynolds, D.A Threshold effects in catchment storm response and the occurrence and magnitude of flood events: Implications for flood frequency. Submitted to Hydrol. and Earth Syst. Sci.. Manabe, S., Climate and the ocean circulation, 1, Atmospheric circulation and the hydrology of the Earth s surface, Mon. Weather. Rev., 97(11), ,

116 Marimuthu, S., Reynolds, D.A. and La Salle, C.L.G A field study of hydraulic, geochemical and stable isotope relationships in a coastal wetlands system. J. Hydrol., 315(1-4), Mielko C and Woo MK Snowmelt runoff processes in a headwater lake and its catchment, subarctic Canadian Shield. Hydrological Processes 20: Milly, P. C., Climate, soil water storage, and the average annual water balance, Water Resour. Res., 30(7), , Penman, H. L Natural evaporation from open water, bare soil and grass. Proc. Roy. Soc. London, Series A, A193, Robinson, J. and Sivapalan, M Temporal scales and hydrological regimes: implications for flood frequency scaling. Water Resour. Res., 33(12), Short, R., Salama, R., Pullock, D., Hatton, T., Bond, W., Paydar, Z., Cresswell, H., Gilfedder, M., More, A., Simpson, R., Salmon, R., Stefanski, A., Probert, M., Huth, N., Gaydon, D. and Keating, B., Assessment of salinity management options for Lake Warden catchments, Esperance, WA: Groundwater and crop water balance. National Land and Water Resources Audit. Theme 2 Dryland Salinity, Project 3 Catchment Groundwater Modelling and Water Balance. CSIRO Land and Water, Technical Report 20/00. Sivandran, G Effect of Rising Water Tables and Climate Change on Annual and Monthly Flood Frequencies. B. Eng. Thesis, Centre for Water Res., Univ. of West. Aus., Crawley, Australia. Sivapalan, M., Kumar, P. and Harris, D Preface: Nonlinear propagation of multiscale dynamics through hydrologic subsystems. Adv. in Water Resour., 24, Spence, C The effect of storage on runoff from a headwater subarctic shield basin. Arctic, 53(3), Spence, C. and Woo, M.-K Hydrology of subarctic Canadian shield: soil-filled valleys. J. Hydrol., 279, Spence, C. and Woo, M.-K Hydrology of subarctic Canadian Shield: heterogeneous headwater basins. J. Hydrol., 317,

117 Struthers, I. and Sivapalan, M Conceptual investigation of process controls upon flood frequency: role of thresholds. Hydrol. & Earth Syst. Sci. (in press). Struthers, I., Sivapalan, M. and Hinz, C. 2007a. Conceptual examination of climate-soil controls upon rainfall partitioning in an open-fractured soil. I. Single storm response. Adv. in Water Resour., 30(3), Struthers, I., Hinz, C. and Sivapalan, M. 2007b. Conceptual examination of the influence of climate upon water balance of an open-fractured soil. II. Long term response to a population of storms. Adv. in Water Resour., 30(3), Wittenberg, H. and Sivapalan, M Watershed groundwater balance estimation using streamflow recession analysis and baseflow separation. J. Hydrol., 219(1-2), Woo, M.-K., Heron, R. and Steer, P Catchment hydrology of a High Arctic Lake. Cold Regions Science and Technology, 5(1),

118 116

119 CHAPTER 4. THRESHOLDS IN THE STORM RESPONSE OF A LAKE CHAIN SYSTEM AND THE OCCURRENCE AND MAGNITUDE OF LAKE OVERFLOWS: IMPLICATIONS FOR FLOOD FREQUENCY 117

120 ABSTRACT The aim of this paper is to illustrate the effects of spatial organisation of lake chains and associated storage thresholds upon lake-overflow behaviour, and specifically their impact upon large scale flow connectivity and the flood frequency of lake overflows. The analysis was carried out with the use of a multiple bucket model of the lake chain system, consisting of a network of both lakes and associated catchment areas, which explicitly incorporates within it three storage thresholds: a catchment field capacity threshold that governs catchment subsurface stormflow, a total storage capacity threshold that governs catchment surface runoff, and a lake storage capacity threshold that determines lake-overflow. The model is driven by rainfall inputs generated by a stochastic rainfall model that is able to capture rainfall variability at a wide range of time scales. This essentially model-based study is used to gain insights into the process controls of lake-overflow generation, and in particular, to explore the crucial role of factors relating to lake organisation, such as the average catchment area to lake area (A C /A L ) ratio and the distribution of A C /A L with distance in the downstream direction (increasing or decreasing), and their combined effects on flood frequency of lake overflows. Improved understanding of these process controls will be useful towards land and water management of lake dominated catchments in the study region, as well as in other similar landscapes. In particular, the results of this study can provide guidance towards improved management of floods in lake dominated catchments by illustrating the use of flow interruption and retardation strategies to assist in flood prevention and/or mitigation. The flow interruption and retardation strategies must of course reflect the objective whether they are aimed at decreasing the frequency of occurrence of lake-overflows, or at merely decreasing the magnitude of lake-overflows associated with a specified return period. 118

121 4.1 Introduction The importance of landscape heterogeneity and the dynamic connectivity of the resulting complex flow pathways is increasingly recognized in hydrology (Spence and Woo, 2006; Western et al., 2001; Sidle et al., 2000; Beven and Freer, 2001). Many spatial fields exhibit and lead to flow connectivity features that have an important influence on overall hydrologic behaviour. Examples include high-conductivity preferred flow paths in aquifers (Western et al., 2001) and saturated source areas in drainage lines (Spence and Woo, 2006). The flow behaviour in lake chains, which is the focus of this study, is another example of dynamic connectivity in a spatial field. A landscape which is described here as the entire catchment that contains a lake chain system, can be viewed as consisting of a number of distinct hydrological elements, such as subcatchments, lakes and stream corridors etc. These landscape elements perform one or more functions, e.g., storing, contributing and transmitting water, to varying degrees at various times. Each of these elements can be expected to exhibit similar behaviour or functionality within its class (e.g., subcatchments), and dissimilar behaviour between elements in different classes (e.g., subcatchments and lakes). The water balance behaviour of each element contains one component that derives from its interaction with the atmosphere (precipitation and evaporation), and another that involves interactions with neighbouring, including upstream, elements of a different class. An important consideration in respect of these hydrological responses is the role of thresholds caused by soil heterogeneity, topography and landscape organisation. Topography is important because it governs the spatial organization of the elements at the larger scale and controls the inputs from adjacent elements, and from within each element. Spatial heterogeneity of topography and soils contributes to differences in storage capacity of the various elements. The functional status of each of the elements mentioned above, storing, contributing, transmitting etc., is determined by its water balance status relative to the thresholds that control each of these functions. The heterogeneity combined with landscape organization can cause spatial variations in the runoff response of the various elements such that flows in the landscape can be disjointed or can continuously cascade from the upstream to downstream elements, depending on the water balance status of each element. In view of the finite number of (even if large) distinct classes in the landscape, the response of the overall system and 119

122 its functionality, e.g., storing or transmitting, is therefore governed equally by the responses of the individual elements and by the nature of interactions between them. The resulting connectivity, or a lack of it, is therefore a dynamic and emergent landscape feature which is a crucial determinant of the overall catchment response. Studies about landscapes that contain chains of lake systems are few, the relevant data is quite patchy, and therefore relatively little is known about them. So far, relevant studies have been limited to those that investigated landscapes containing small lakes in the Arctic environment in Canada, undertaken within a broad framework aimed at determining the effects of various threshold processes on runoff magnitude and timing (Woo et al., 1981; Spence and Woo, 2003; Spence and Woo, 2006). These studies have so far shown the high dependence of the small high arctic lakes upon the contributing catchment areas as the sources of inputs, rather than upon direct precipitation falling on the lakes themselves. Spence (2000) has indicated that the location of the lakes in the landscape (whether they are located in the upper, middle or lower part of the catchment) is very crucial in the determination of the dominant sources of streamflow to the lakes and the catchment outlet, as well as their magnitude and timing. In addition, all runoff from upland areas have to travel through headwater lakes before it reaches higher-order streams (Spence, 2000), so much so that some of them never reach the outlet due to the high antecedent storage deficit of the lakes. In a previous but related theoretical study, Kusumastuti et al. (2007a) found that the ratio of catchment area to lake area (A C /A L ) to be significant in a single catchmentsingle lake system. If the area of the contributing catchment is negligible relative to the size/capacity of the lake, lake-overflow is triggered purely by direct rainfall into the lake. Consequently, lake-overflow is relatively rare, only occurring when rainfall is sufficiently intense and continuous. As A C /A L increases, however, the increased influence of catchment processes and catchment outflows results in the increased number of lake-overflow events due to the now significant contributions of catchment runoff in relation to direct rainfall into the lake. Where the size of the catchment is large relative to the lake, then the runoff behaviour of the catchment itself will be the primary determinant of lake overflow behaviour; in the case of multiple runoff mechanisms from the catchment (eg. subsurface and surface runoff mechanisms), this can result in 120

123 significant differences in the magnitude of lake overflow flooding events depending upon the dominant runoff mechanisms within the catchment. This study has been motivated by a lake-dominated catchment system, Lake Warden, located near Esperance in south-east Western Australia, which has recently been the focus of investigations aimed at understanding and mitigating the processes that potentially could contribute to catastrophic flooding. As mentioned, it follows previous studies that explore the effects of thresholds on flood frequency and landscape connectivity (Kusumastuti et al., 2007a,b). Natural swamps and small lakes exist throughout the Lake Warden catchment, with chains of small lakes and connecting streams particularly common in the upper catchment (Figure 4.1). The catchment is terminated by a wetlands system located downstream of the catchment, which consists of Lake Warden and a number of other similar sized lakes. The Lake Warden wetlands system is of international importance and is included in the Ramsar List, on the basis of its ecological, botanical, zoological, limnological or hydrological significance (CALM, 1997). The catchment and the wetlands system have experienced severe, even catastrophic, flood events in 1999 and 2000, as a result of rare summer cyclonic events when flow contributions from the catchment area (which include a large number of tiny finger-lakes) exceeded the storage capacity of Lake Warden and adjacent large lakes causing overflows into the nearby town of Esperance. Prevention and/or mitigation of such catastrophic floods in the future require an improved understanding of the role of the various thresholds in the hydrologic response to extreme storm events, including especially the role of hydrologic connectivity in lake dominated catchments, and their combined impacts on the frequency and magnitude of extreme floods. Investigations into the impact of lake chains upon the hydrology in the Lake Warden catchment system have been limited, mainly due to the lack of long-term rainfall, lake level, and streamflow records. Given the lack of long time series data, the present study utilizes a conceptual approach with the aim being to generate a detailed understanding of the impact of lake chains on overall runoff behaviour, with a particular emphasis on understanding how lake organization impacts the overall rainfall-runoff behaviour. The results from this study could then be used to provide guidance towards both targeted observational programme and improved management strategies for landscapes that 121

124 contain lake chain systems, focusing on key processes and process interactions that are identified through this theoretical investigation. In spite of its hypothetical approach, this study uses climate conditions and landscape characteristics typical of south-east Western Australia to parameterize the adopted conceptual models. The primary aim of this study is to investigate the hydrological behaviour of lake chains, their interactions with nonlinear (including threshold) rainfallrunoff processes, and their combined effects on the flood frequency associated with lake-overflows and lake connectivity. The specific aims of this study are to investigate (1) the effects of lake organization (by limiting it to lakes in series only), which includes the ratio of average catchment area to lake area (A C /A L ), the spatial distribution of the A C /A L ratio for each unit and the number of lake chains, upon flow connectivity and the flood frequency of lake overflows, and (2) the effect of time delays in the stream corridors on the magnitude and frequency of lake overflows, in order to give insights into the dynamics of lake overflows that might be possible in a landscape consisting of lake chains. 122

125 Figure 4.1 Upstream part of the Lake Warden catchment: chains of small lakes and connecting streams 123