Real-time Control of Stormwater Storages to Improve Performance of Urban Stormwater Systems

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Real-time Control of Stormwater Storages to Improve Performance of Urban Stormwater

Systems

Ruijie Liang

BEng (Civil & Environmental) Hons

Thesis submitted in fulfilment of the requirements for the degree of Doctor of Philosophy

The University of Adelaide

Faculty of Sciences, Engineering and Technology School of Architecture and Civil Engineering

Copyright

©

2023

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Abstract

The impact of urban flooding is increasing due to the effects of increasing urbanization and climate change. The use of storages is a relatively well- established approach to reduce peak flows and therefore reduce the need for costly upgrades to stormwater conveyance infrastructure. Recently, real-time control (RTC) has been considered as a means of increasing the performance of these storages.

Real-time control strategies can generally be grouped into two categories: 1) predictive control and 2) reactive control. For predictive control, control schemes are generally developed based on forecast temporal patterns of future rainfall events. They are tailored to specific events using optimization algorithms, thereby maximizing the peak flow reductions that can be achieved for particular events. However, this requires knowledge of rainfall forecast information, which makes it challenging to implement in practice. For reactive control, generic control rules that can be applied to any event are developed and optimized based on a range of 'design' rainfall events. These generic rules translate available information, such as storage levels, flow rates and rainfall information, into control strategies and thus require these inputs to be measured in real-time during storm events. However, the reactive RTC approach has the disadvantage of requiring calibration, making it difficult to apply control strategies that have been tuned to particular catchment conditions to other catchments with different physical or climatic properties.

In this thesis, one novel predictive RTC control approach that controls storages during storms and one novel reactive RTC approach that does not require calibration are introduced and tested for achieving urban stormwater management objectives, such as limiting peak flows to mitigate urban flooding and matching desired hydrographs for environmental purposes. The major research contributions are presented in five journal publications, with papers 1 and 2 introducing and testing the novel predictive RTC approach and papers 3 to 5 introducing and testing the novel reactive RTC approach.

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Paper 1 provides a comprehensive assessment of a proof-of-concept predictive RTC approach that controls storages during storm events based on the knowledge of the rainfall forecast information, thereby offsetting the timing of outflow peaks from different storages. The effectiveness of this approach is tested under a wide range of design rainfall conditions for three Australian cities with different climates. Results show that a generic relationship exists between the ratio of tank volume to runoff volume and percentage peak flow reduction, irrespective of location and storm characteristics, with a relative performance improvement on the order of 35 to 50% compared with storages that are not controlled.

In Paper 2, the proof-of-concept predictive RTC approach is extended to precinct scale, and a two-step approach to minimizing peak flows by firstly optimizing the layout of distributed storages and then optimizing their RTC strategies is introduced. The effectiveness of this approach is tested on a real catchment in Adelaide, South Australia. Results show that distributed storage with optimized layouts can achieve significantly higher peak flow reductions than more commonly used end-of-system storage. The addition of optimized RTC to distributed storages is able to achieve an additional 10% peak flow reduction.

In Paper 3, a novel 'calibration-free' reactive RTC approach is introduced at lot scale, which is able to maintain system outflows at or below specified target flows (e.g., existing system capacity). This approach is tested on a simple two- storage system for 750 design rainfall events from a range of climates, event durations, rainfall intensities and temporal patterns using a practically achievable control time step of 30 seconds. Results show that the TFC approach can achieve the desired target flows effectively, with 95% of the experiments having less than 10% errors in target flow.

In Paper 4, the 'calibration-free' reactive RTC approach in Paper 3 is extended so that it can achieve desired target hydrographs, not just maximum peak flows.

The effectiveness of this approach is demonstrated for three different 'future worlds' on a simple example catchment located in Darwin, Australia. Results show that the proposed approach is able to achieve target hydrographs

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effectively with less than 3.1% error for all experiments. This is despite the inflow hydrograph varying significantly as a result of land use and climate change.

In Paper 5, the 'calibration-free' reactive RTC approach in Paper 3 is extended from lot to precinct scale, enabling the real-time control of systems of storages to achieve the desired stormwater management objectives at locations of interest. This approach is tested on three case studies, each with different configurations and stormwater management objectives, and its performance is compared with that of five RTC approaches, including three best-performing advanced approaches from the literature. Results show that the proposed approach is the only one of the five control approaches analysed that has both the best overall performance and the highest level of practicality.

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Statement of Originality

I certify that this work contains no material which has been accepted for the award of any other degree or diploma in my name, in any university or other tertiary institution and, to the best of my knowledge and belief, contains no material previously published or written by another person, except where due reference has been made in the text. In addition, I certify that no part of this work will, in the future, be used in a submission in my name, for any other degree or diploma in any university or other tertiary institution without the prior approval of the University of Adelaide and where applicable, any partner institution responsible for the joint-award of this degree.

I acknowledge that copyright of published works contained within this thesis resides with the copyright holder(s) of those works.

Liang, R., Di Matteo, M., Maier, H.R. and Thyer, M.A., 2019. Real-time, smart rainwater storage systems: potential solution to mitigate urban flooding. Water, 11(12), p.2428.

Liang, R., Thyer, M.A., Maier, H.R., Dandy, G.C. and Di Matteo, M., 2021.

Optimizing the design and real-time operation of systems of distributed stormwater storages to reduce urban flooding at the catchment scale. Journal of Hydrology, 602, p.126787.

Liang, R., Maier, H.R., Thyer, M.A., Dandy, G.C., Tan, Y., Chhay, M., Sau, T.

and Lam, V., 2022. Calibration-free Approach to Reactive Real-time Control of Stormwater Storages. Journal of Hydrology, p.128559.

I also give permission for the digital version of my thesis to be made available on the web, via the University's digital research repository, the Library Search and also through web search engines, unless permission has been granted by the University to restrict access for a period of time.

Signed: …… …. Date: ………….... 06/02/2023

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Acknowledgements

First of all, I would like to thank my supervisors, Professor Holger Maier and Associate Professor Mark Thyer, for their supervision, support,

encouragement, and dedication during my PhD research. I would like to express my deepest gratitude to Professor Holger Maier for his guidance, enthusiasm and determination in developing my research skills. I am also deeply indebted to Associate Professor Mark Thyer for his encouragement, critical thinking and inspiration. I could not have undertaken this journey without the help of my supervisors.

I would like to thank Dr Michael Di Matteo from Kellogg Brown & Root (KBR) Pty Ltd for his generous support and technical assistance, which extensively impacted and inspired my PhD research. I am also grateful to Emeritus Professor Graeme Dandy for his constant motivation and scientific insights into my research.

I am grateful to the University of Adelaide for sponsoring my scholarship.

Many thanks to all my friends, without you I would have graduated much earlier. However, I never regret it. The joyful time spent with all of you is a worthless treasure in my life.

Lastly, I would be remiss in not mentioning my family, especially my parents (Wen Xu and Wanyong Liang). Their love and trust have kept my spirits and motivation high during my PhD journey. I would also like to thank my loving partner, coffee (especially flat white), who is the only reason I survived sleepy morning and late night.

.

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List of Tables

Table 1.1 Classification of papers by topics addressed ... 8

Table 2.1 Configuration of case study system. ... 21

Table 2.2 Summary of experiment configurations. ... 23

Table 2.3 Design Rainfall Intensity (mm/hr) for the 1% AEP event. ... 23

Table 4.1 System characteristics for the case study ... 90

Table 4.2 Experimental configurations ... 91

Table 5.1 Experimental Configurations ... 109

Table 5.2 Case Study System Characteristics ... 109

Table 5.3 Summary of Changes in Inflow Hydrographs ... 114

Table 6.1 Case Study Characteristics ... 133

Table 6.2 Summary of Metrics ... 135

Table 6.3 Performance of TFCS Approach ... 138

Table 6.4 Summary results of TFCS versus Benchmark RTC Approaches (RL: Reinforcement Learning, MPC: Model Predictive Control, PC: Predictive Control) ... 144

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List of Figures

Figure 1.1 Research gaps, objectives and contributions ... 7 Figure 2.1 Schematic of an example two-tank system operated using the real- time, smart systems approach ... 16 Figure 2.2 Conceptual illustration of performances of (1) “benchmark

approach” (i.e., tanks emptied prior to the arrival of the storm, but not

controlled during the storm) and (2) “real-time smart systems approach” (i.e., tanks emptied prior to the arrival of the storm, and controlled as a system during the storm so as to minimize peak system outflow). ... 18 Figure 2.3 Details of the simulation-optimization approach used to identify tank outflow control strategies that minimize system peak outflows. ... 20 Figure 2.4 Performance of real-time, smart tank systems versus benchmark tanks for the three locations (Adelaide, Melbourne and Sydney), two tank sizes (2×2 m³ and 2×10 m³), and five AEPs (50%, 10%, 5%, 2% and 1%) considered. For the sake of clarity, only results for the shortest (30 min) and longest (24 h) durations considered are shown, with results for the full set of durations considered shown in Figure 2.5 and Appendix A. ... 26 Figure 2.5 Percentage peak flow reduction of benchmark tanks and real-time, smart tank systems for a range of durations and AEPs with 2 x 2 m³ tanks for Adelaide. ... 28 Figure 2.6 Relationship between the ratio of tank to runoff volume and peak flow reduction for all computational experiments (i.e. for all locations, AEPs, rainfall durations and tank sizes considered) for benchmark tanks (blue circles and dashed line) and real-time, smart tank systems (orange circles and dashed line). The green solid line represents the additional peak flow reduction that can be achieved by using real-time, smart tank systems control based on the difference between the two trendlines fitted to the data sets. The trendlines were developed by trial and error and visual inspection for data where x < 0.9 (Trendline – Real-time, smart tank systems: y = 2×ln(x)+90 (r² = 0.7953) and Trendline –Benchmark tanks: y = 70x⁴ -20 x³+10 x²+10x (r² = 0.8327)).

Results for tank to runoff volume ratios in excess of 1.0 are not shown, as they all result in peak flow reductions of 100%. ... 30

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Figure 2.7 Typical operation rules for (2) 2 m³ real-time, smart tank systems compared to (1) 2 m³ benchmark tanks (Adelaide, 24h duration, 1%AEP). .. 32 Figure 2.8 Typical operation rules for real-time, smart tank systems approach for systems where the ratio of tank:runoff volume is less than 0.15 (Sydney, 24h duration, 1% AEP). ... 35 Figure 3.1 Outline of the proposed two-step approach to reducing peak flows in urban catchments ... 46 Figure 3.2 Conceptual comparison between performances of (a) ‘No Storage’

Scenario, (b) Distributed Storage with optimised layout and (c) Distributed storage with optimised layout and control ... 48 Figure 3.3 Simulation-Optimisation Process for Identifying the Optimised System Layout ... 51 Figure 3.4 Simulation-Optimisation Process for Identifying the Optimal RTC Strategy for the Optimised System Layout ... 54 Figure 3.5 Case study Information. Including location (GoogleMap 2020), catchment map with sub-catchments (5m counter lines) and eight potential storage locations ... 55 Figure 3.6 Experiment configurations for all three experiments in this study (Note: AEP = Annual Exceedance Probability) ... 56 Figure 3.7 Evaluation of peak flow reduction for end-of-system storage (Experiment 1). ... 61 Figure 3.8 System peak flows and peak flow percentage reduction of three options including end-of-system storage (Experiment 1), distributed storage (Experiment 2), and distributed storage with real-time smart control

(Experiment 3), 25min duration, 10% AEP and all peak flow reductions are averaged over ten storm patterns and compared to the ‘No Storage’ scenario.

The red line shows the difference in storage by adding RTC to Distrib.

Storage for a 39% peak flow reduction. ... 63 Figure 3.9 Performance comparison of ‘No Storage’ scenario and two typical storage volumes with optimised layouts (200 m³ and 800 m³,Experiment 2) and control (200 m³,Experiment 3) for flow at the system outfall for a typical rainfall event (storm pattern 4) ... 65 Figure 3.10 Optimised layouts for two typical storage volumes (200m³ and 800m³) ... 66

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Figure 3.11 Flood hydrographs at multiple internal catchment Locations for typical cases: 1). ‘No Storage’ scenario and two typical storage volumes with optimised layouts (200 m³ and 800 m³,Experiment 2) for a typical rainfall

event (storm pattern 4) ... 70

Figure 3.12 Flood hydrographs at multiple internal catchment Locations for 200m³ distributed storage with and without RTC and the optimised control strategy for a typical rainfall event (storm pattern 4) ... 72

Figure 4.1 The conceptual approach of the proposed TFC ... 86

Figure 4.2 Conceptual performance of the proposed TFC approach ... 87

Figure 4.3 Framework for implementing the proposed TFC approach ... 89

Figure 4.4 Performance of the proposed TFC approach for a wide range of design rainfall events. Coloured box and whisker plots represent range of target flows, with scale on left y-axis and grey box and whisker plots represent range of target flow errors, with scale on right y-axis. Box represents the upper and lower quartiles of the range, while whiskers represent 90% limits of this range ... 94

Figure 4.5 Impact and operation of TFC approach for two typical rainfall patterns: 1) Example 1 (Simple) (Sydney: 1% AEP, 30 min duration, Temporal Pattern 9) and 2) Example 2 (Complex) (Sydney: 50% AEP, 24 hr duration, Temporal Pattern 7) for 2kL storage ... 97

Figure 5.1 Conceptual Approach and Simulation Framework of the THC Approach ... 107

Figure 5.2 Performance of the THC Approach to Achieve Target Hydrographs for Three Worlds (a. Current World, b. Future World 2050 and c. Future World 2090) ... 113

Figure 5.3 Control Schemes of the THC Approach to Achieve a Target Hydrograph for Three Worlds (Current World, Future World 2050 and Future World 2090) ... 114

Figure 6.1 Conceptual approach to controlling outflows at each storage to meet desired target storage outflows used in the TFC and TFCS approaches, where the orifice equation is used to determine the orifice opening required at time step t to achieve the desired target outflow at that time step for each individual storage in the system. ... 125

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Figure 6.2 Illustration of the relationship between outflows at individual storages and flows at the location of interest for (a) a single storage (a) and systems of storages with different configurations (i.e., systems of storages in parallel (b) and systems of storages in series (c)) ... 126 Figure 6.3 Examples of Required Linear Equations (Equations 6.3, 6.7 and 6.8) for (a) Example Storage in Parallel System, (b) Example Storages in Series System and (c) Example Storage in Mixed System (Storages in Parallel and in Series) ... 130 Figure 6.4 Implementation of the TFCS Approach ... 131 Figure 6.5 Storage Network Topology and Sizes for the Selected Case

Studies: (a) Gamma, (b) Astlingen and (c) Delta – M ... 134 Figure 6.6 Comparison between the TFCS approach and ‘No Control’

scenario for the combined storage system of Case Study 2 for an example 8 hr rainfall period (10/5/2000 19:00 - 11/5/2000 3:00). Storage 5 is not shown as it is not controlled. ... 141 Figure 6.7 Mapping of the relationship between performance and practicality for five RTC control approaches considered and ‘No Control’ benchmark scenario ... 146

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Chapter 1 Introduction

Urbanization, densification and climate change are likely to increase urban flooding and stress on current stormwater systems (Locatelli et al., 2017, Van der Bruggen et al., 2010, Pandey et al., 2003). This is because the extent of impervious areas is likely to increase due to the impact of urbanization and densification (Li et al., 2017), leading to higher runoff volumes and peak runoffs (Burns et al., 2012). In addition, climate change is likely to result in an increase in extreme rainfall events (Sharma et al., 2018), leading to a further increase in peak runoff (Wasko and Sharma, 2015). Therefore, the capacity of current stormwater systems is unlikely to be able to accommodate these projected increases in future peak runoffs and potentially expensive infrastructure upgrades will be required.

Recently, real-time control (RTC) has been considered an effective way to deal with increasing peak runoffs (Campisano et al., 2017, Shishegar et al., 2018) and thus reduce the stress on stormwater systems (Kerkez et al., 2016). RTC can not only help with urban flood mitigation (Bilodeau et al., 2018, Mullapudi et al., 2018, Chang et al., 2014) but also provides opportunities to achieve co- benefits, including the provision of non-potable stormwater (Xu et al., 2018, Xu et al., 2020, Campisano et al., 2017), water quality improvement (Muschalla et al., 2014, Sharior et al., 2019, Shen et al., 2020) and the ability to meet the requirements of an ecological and environmental flow regime (Xu et al., 2018, Xu et al., 2020). For example, by detaining stormwater in the storage for a particular length of time, downstream water quality can be improved (Sharior et al., 2019), especially by integrating storages with bioretention systems (Shen et al., 2020).

Based on required information, real-time control strategies can generally be grouped into two categories: 1) predictive control and 2) reactive control (Lund et al., 2018).

For predictive control, the most straightforward approach to real-time control is to empty the storage before a predicted rainfall event in order to utilize the available storage capacity as retention storage (Xu et al., 2018, Campisano et

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al., 2017, Schubert et al., 2017). However, the ability of this control strategy to reduce peak flows deteriorates rapidly when the total runoff volume of the rainfall event exceeds the system storage volume. When the storage is full, it loses the ability to reduce runoff peaks. To deal with this limitation, the author of this thesis contributed to a proof-of-concept approach introduced in Di Matteo et al. (2019a) prior the commencement of his PhD candidature (see appendix D), which controls the outflow from systems of storages in real time during a storm event so as to minimize system peak flow rate based on knowledge of future rainfall patterns. This approach is tailored to specific events using optimization algorithms, thereby maximizing the peak flow reductions that can be achieved for particular events (Di Matteo et al., 2019a).

However, Di Matteo et al. (2019a) only considered a single return period, a single rainfall duration and a single location (Adelaide, South Australia). While this provides a proof-of-concept of the approach, it does not provide a comprehensive assessment of the effectiveness of the approach under the range of conditions likely to be experienced for different urban catchments.

Consequently, there is a need to test this approach under a wider range of conditions. In addition, Di Matteo et al. (2019a) only considered a simple two- tank system that is applicable at the lot scale (a small parcel of land with 1 or 2 buildings, see Ball et al., 2019). Consequently, there is also a need to expand and test the approach at the precinct scale (hundreds of parcels of land each with at least one building, see Ball et al., 2019).

For reactive control, generic control rules that can be applied to any event are generally developed and optimized based on a range of 'design' rainfall events (Li, 2020, Meneses et al., 2018, Sharior et al., 2019). These generic rules translate available information, such as storage levels, flow rates and rainfall information into control strategies and thus require these inputs to be measured in real-time during storm events (Chang et al., 2014). Reactive control can be either static (Muschalla et al., 2014, Sadler et al., 2020) or dynamic by using approaches such as reinforcement learning (Mullapudi et al., 2020a).

Reactive control overcomes the limitation of predictive control of requiring knowledge of the temporal pattern of future rainfall events by only requiring information that can be measured easily during the rainfall event itself.

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However, it has the disadvantage of requiring calibration. Thus, the performance of reactive control strategies can be impacted significantly by the calibration process, as well as the data used for calibration. For example, calibration data are generally catchment-specific, making it difficult to apply control strategies that have been tuned to particular catchment conditions to catchments with different physical or climatic properties without a significant reduction in performance (Schmitt et al., 2020). In addition, as control strategies are generally static (Muschalla et al., 2014, Sadler et al., 2020), if underlying rainfall-runoff processes are altered in response to climate change, strategies calibrated on historical data are likely to perform poorly and would need to be recalibrated in order to deal with future rainfalls or to be adapted using approaches such as reinforcement learning (Mullapudi et al., 2020a).

Consequently, while existing reactive control approaches have demonstrated the potential of using real-time control for urban flood mitigation, they rely on calibration to site-specific data and are, therefore, not generally applicable across a wide range of catchments and climates. Consequently, the practicality and applicability of reactive RTC could be increased by developing a

“calibration-free” reactive RTC approach.

1.1 Research Objectives

This research aims to introduce and assess novel real-time control (RTC) approaches to utilizing storage capacity for improving performance of stormwater management that address the research needs related to both predictive and reactive RTC outlined above.

Objective 1 of this thesis is to address the shortcomings of the predictive RTC approaches that are not controlled during storm and the proof-of-concept approach as outlined above, including:

Objective 1.1: To assess the effectiveness of the proof-of-concept predictive RTC approach under a wider range of conditions, including a range of return periods, storm durations and storage sizes for locations with different climates at the lot scale. (Journal Paper 1)

Objective 1.2: To extend the proof-of-concept predictive RTC approach so that it is applicable at the precinct scale. This involves a two-step

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process, including first optimising the volumes and locations of distributed storages and then optimising the predictive RTC of each of these storages for a given rainfall event. (Journal Paper 2)

Objective 2 of this thesis is to overcome the requirement of existing reactive control approaches to be calibrated to case-study specific conditions, including:

Objective 2.1: To introduce a 'calibration free' reactive RTC control approach for limiting peak flows that can be applied to a wide range of catchments and under changing conditions in real-time without knowledge of future rainfall events at the lot scale. (Journal Paper 3) Objective 2.2: To extend the 'calibration free' reactive RTC control approach in Objective 2.1 so that it can achieve desired target hydrographs, not just limiting peak flows, at the lot scale. (Journal Paper 4)

Objective 2.3: To extend the 'calibration free' reactive RTC control approach in Objective 2.1 so that it is applicable to systems of storages at the precinct scale that are controlled to achieve desired flow target(s) at downstream locations(s) of interest, rather than just a single storage.

(Journal Paper 5)

1.2 Thesis Overview

This thesis consists of seven chapters, with the main contributions provided in Chapters 2 to 6, which are presented in the form of five journal papers (see Figure 1.1 and Table 1.1). Chapter 2 has been published in Water, and Chapter 3 and Chapter 4 have been published in the Journal of Hydrology.

Chapter 2 (Journal Paper 1, Published) assesses the effectiveness of the proof- of-concept predictive RTC approach of Di Matteo et al. (2019a) at lot scale under climatic conditions from three major Australian cities (Adelaide, Melbourne, and Sydney) for a wide range of storm durations (30 min to 24 h) and frequencies (50% to 1% AEP) (Objective 1.1).

Chapter 3 (Journal Paper 2, Published) extends the predictive RTC approach in Chapter 2 so that it is applicable at the precinct scale by introducing a two-

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step approach to minimising peak flow that first optimises the volumes and locations of distributed storages and then optimises the predictive RTC for a given rainfall event (Objective 1.2) The effectiveness of this approach (including the relative impact of each of its two steps) is tested on a real catchment in Adelaide, South Australia, and compared with that of the more commonly used end-of-system storage.

Chapter 4 (Journal Paper 3, Published) introduces a 'calibration free' reactive RTC approach for limiting peak flows that is applicable at the lot scale (Objective 2.1). Given its calibration free nature, the approach can be applied to a wide range of catchments and under changing conditions in real-time without knowledge of future rainfall events. The utility of this approach is assessed by using a hypothetical case study at the lot scale under climatic conditions from three major Australian cities (Adelaide, Melbourne, and Sydney) for a wide range of storm durations (30 min to 24 h) and frequencies (50% to 1% AEP).

Chapter 5 extends the 'calibration-free' reactive RTC approach in Chapter 4 so that it can achieve desired target hydrographs, not just maximum peak flows (Objective 2.2), which is tested on a hypothetical case study at the lot scale under climatic conditions from Darwin, Northern Territory.

Chapter 6 extends the 'calibration-free' reactive RTC approach in Chapter 4 so that it is applicable to systems of storages at the precinct scale that are controlled to achieve desired flow target(s) at downstream locations(s) of interest, rather than just a single storage (Objective 2.3). The effectiveness of this approach is then tested on three precinct scale case studies from literature, each with different configurations and stormwater management objectives.

The research gaps, objectives and contributions are shown in Figure 1.1, and the classification of the papers by the different topics addressed is presented in Table 1.1. Although the manuscripts have been reformatted in accordance with University guidelines and sections renumbered for inclusion within this thesis, the material within these papers is otherwise presented herein as published.

Copies of the first three papers "as published" are provided in Appendices E, F and G.

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Conclusions of the research within this thesis are provided in Chapter 7, which summarises: 1) the research contributions and 2) directions for future research

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Figure 1.1 Research gaps, objectives and contributions

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Table 1.1 Classification of papers by topics addressed Category Sub-category Paper

0*

Paper 1

Paper 2

Paper 3

Paper 4

Paper 5 Type of Control Predictive

Control

X X X X

Reactive Control

X X X

Case Study Scale Lot Scale X X X X

Precinct Scale X X

Case Study Extent

Extensive X X X X

Medium X

Limited X Stormwater

Management Objectives

Limiting Peak Flows

X X X X X

Achieve Desired Target

Hydrographs

X

*The author of this thesis contributed to Di Matteo et al. (2019a) prior to the commencement of his PhD candidature, and a copy of this paper is provided in Appendix D

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Chapter 2 Real-Time, Smart Rainwater Storage Systems: Potential Solution to

Mitigate Urban Flooding (Journal Paper 1,

Published)

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Abstract

Urban water systems are being stressed due to the effects of urbanization and climate change. Although household rainwater tanks are primarily used for water supply purposes, they also have the potential to provide flood benefits.

However, this potential is limited for long-duration storms, as they become ineffective once their capacity is exceeded. This limitation can be overcome by controlling tanks as systems during rainfall events, as this can offset the timing of outflow peaks from different tanks. In this paper, the effectiveness of such systems is tested for two tank sizes under a wide range of design rainfall conditions for three Australian cities with different climates. Results show that a generic relationship exists between the ratio of tank:runoff volume and percentage peak flow reduction, irrespective of location and storm characteristics. Smart tank systems are able to reduce peak system outflows by between 35 and 85% for corresponding ranges in tank:runoff volumes of 0.15 to 0.8. This corresponds to a relative performance improvement on the order of 35 to 50% compared with smart tanks that are not operated in real-time.

These results highlight the potential for using household rainwater tanks for mitigating urban flooding, even for extreme events.

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2.1 Introduction

Urban water supply systems are experiencing unprecedented changes due to population growth (Hoekstra et al., 2018), increased urbanization (Van der Bruggen et al., 2010), and climate change (Pandey et al., 2003). Population growth and increased urbanization lead to an increase in demand for water resources (McDonald et al., 2014), while climate change is more likely to reduce the amount of water that is available to meet this demand (Vorosmarty et al., 2000). These are creating a number of challenges for current urban water systems, as well as the design of and planning for future systems.

Household rainwater tanks have been shown to be an effective means of assisting with addressing this problem, as they have the ability to supplement existing water supplies by using a water resource that would otherwise not be utilized. For example, Coombes and Barry (Coombes and Barry, 2008) reported that household rainwater tanks can significantly increase the resilience of water supply systems under natural variations and future climate change. Similarly, Newman et al. (2014) and Burns et al. (2015a) suggested that tank water usage can lead to a reduction in mains water use, which will help existing water supply systems to meet required demand. Paton et al. (2014a), Paton et al. (2014b), Beh et al. (2015) and Beh et al. (2017) found that additional supplies from household rainwater tanks, along with those from other sources, such as stormwater harvesting and desalinated water, can form part of optimal integrated strategies for increasing regional water supply security for cities.

In addition to increasing water supply security, household rainwater tanks have a number of other benefits, such as improving the water quality of receiving waters (Ahiablame et al., 2013, Xu et al., 2018) and reducing peak flows for short-duration storm events (Campisano and Modica, 2015, Coombes and Barry, 2008, Gilroy and McCuen, 2009, Schubert et al., 2017, Lund et al., 2019).

The ability of household rainwater tanks to reduce peak flows is of particular interest, as not only water supply systems, but also stormwater systems, are likely to be adversely affected by increased urbanization and climate change.

Increased urbanization is often associated with urban infill and densification,

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which will increase the percentage of impervious area, and hence result in increased runoff (Burns et al., 2012). In addition, climate change is likely to cause more extreme rainfall events (Wasko and Sharma, 2015), placing further pressure on existing stormwater systems.

However, the capacity of rainwater tanks to reduce discharge rates from connected roofs is generally not fully utilized in practice, as they are commonly not empty during storm events (Pezzaniti et al., 2003). This limitation can be overcome with the aid of smart technologies, which enable rainwater tanks to be emptied based on knowledge of impending rainfall events, thereby maximizing available retention storage (Xu et al., 2018, Oberascher et al., 2019, Behzadian et al., 2018, Campisano et al., 2017). For example, South East Water (Melbourne, Australia) use controlled outlets to empty rainwater tanks before a forecasted storm event, which can maximize retention capacity to reduce peak flows (Burns et al., 2015b, Lee, 2019). However, smart rainwater tanks operated by simply emptying tanks prior to a storm event, so that they essentially behave like a retention tank during a storm event, can be limited in their ability to reduce peak flows for storm events that have large volumes of runoff (Vaes and Berlamont, 2001, Schubert et al., 2017). Consequently, while tanks that are emptied prior to the arrival of storm events with the aid of smart technologies are able to deal with nuisance flooding, they are generally unable to prevent the upgrade of existing stormwater systems to cope with storms associated with the increased runoff resulting from the impacts of urbanization and climate change (Schubert et al., 2017).

In order to address this shortcoming, Di Matteo et al. (2019a) introduced an approach for controlling the outflow from systems of rainwater tanks in real time during a storm event so as to minimize system peak flow rate based on knowledge of future rainfall patterns. They showed that by using a real-time systems control strategy during the storm, this approach is able to reduce peak flows by up to 48% under conditions that result in large runoff volumes (i.e., 1 in 100 year rainfall event of 24 h duration), compared with no reduction in peak flow when tanks are emptied prior to the rainfall event, but not operated as systems during the rainfall event.

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However, Di Matteo et al. (2019a) only considered a single return period, a single rainfall duration and a single location (Adelaide, South Australia). While this provides a proof-of-concept of the approach, it does not provide a comprehensive assessment of the effectiveness of the approach under the range of conditions likely to be experienced for different urban catchments.

Consequently, the objective of this paper is to compare the effectiveness of tanks that are emptied prior to the arrival of a storm and then operated as systems in real time during storm events and tanks that are emptied prior to the arrival of storms, but not controlled during storm events, under a range of return periods, storm durations and tank sizes for locations with different climates.

The remainder of this paper is organized as follows. The methodology used to perform the assessment of the effectiveness of the real-time smart systems approach under different conditions is given in Section 2.2, followed by details of the case study and experimental methods to which this approach is applied in Section 2.3. An outline and discussion of the case study results are given in Section 2.4 and a summary and conclusions are provided in Section 2.5.

2.2 Real-time Smart Systems Conceptual Approach and Implementation

2.2.1

Conceptual Approach

By controlling smart rainwater tanks as systems during storm events, the timing of the peak flows from the sub-catchments contributing to each tank can be shifted, which will lead to a reduction in the peak discharge rate of the system as a whole. In order to illustrate this concept, a typical two-storage smart rainwater tank system is used (Figure 2.1). In this system, each tank is fed from roof runoff via a system of gutters and downpipes and the outflow from the tanks feeds into a drainage system (simplified as a freely draining stormwater pipe in the schematic in Figure 2.1). Both tanks are emptied prior to the arrival of a storm and the outflow from each tank is controlled independently throughout the storm event via remote-controlled, actuated orifices so as to minimize the total system outflow based on information on the temporal distribution of the incoming rainfall.

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Figure 2.1 Schematic of an example two-tank system operated using the real- time, smart systems approach

A conceptual representation of how the use of the real-time, smart systems approach is able to reduce peak flows is given in Figure 2.2. In this figure, the behaviour of the real-time smart systems approach is compared with that of a benchmark approach, as part of which the tanks are drained prior to the arrival of the storm, as is the case with the real-time, smart systems approach, but where the orifices remain closed during the rainfall event so that the tanks behave as retention tanks during the storm. As can be seen, when the benchmark approach is used (Figure 2.2(1)), both tanks are starting to fill from the beginning of the storm. Once the tanks are full, but rainfall continues, both tanks overflow, and the system operates as though there is no storage from that point onwards. As a result, the peak flows from the two sub-catchments are coincident, resulting in a relatively large outflow from the system as whole.

In contrast, when the real-time, smart systems approach is used, the outlet of one of the tanks remains open at the beginning of the rainfall event. As a result, the peak outflows from the two tanks do not occur at the same time, but are distributed over a longer time period, reducing the peak outflow from the system as a whole (Figure 2.2(2)). By offsetting the outflows from the two tanks, both the stormwater system and the available storages are being utilized

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more effectively. With regard to the stormwater system, the real-time, smart systems approach enables the system to be used throughout the duration of the entire rainfall event, rather than being idle for part of the rainfall event while the tanks are being filled and then receiving a high load once both tanks spill.

With regard to the storages, the real-time, smart systems approach enables the available storage to be used at different times, ensuring empty storage is available throughout the rainfall event and enabling the outflow hydrographs from the two sub-catchments to be staggered.

With the help of real-time control, numerous control strategies can be used to reduce the system peak flow rate. Which strategy is optimal is a function of several complex, interacting factors, such as rainfall pattern, time of concentration, tank capacity etc. Despite this complexity, the principle illustrated above underpins most of these strategies. However, which strategies maximize peak system outflow needs to be determined for particular systems and storm events using advanced optimization techniques. Details of the formulation of the above optimization problem are given in the following sub- section.

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Figure 2.2 Conceptual illustration of performances of (1) “benchmark approach” (i.e., tanks emptied prior to the arrival of the storm, but not controlled during the storm) and (2) “real-time smart systems approach” (i.e.,

tanks emptied prior to the arrival of the storm, and controlled as a system during the storm so as to minimize peak system outflow).

2.2.2 Formulation of Optimization Problem

As mentioned above, as part of the real-time, smart systems approach, the outlets of systems of tanks can be operated independently during a rainfall event. Given the large number of choices associated with when to open and close each of the tank outlets, and by how much, as well as the variability in rainfall events, it is challenging to identify control schemes that maximize flood peak reduction. Consequently, the optimal control strategies for each tank are identified using a formal optimization approach, based on knowledge of the

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hyetograph of an incoming rainfall event. It should be noted that these hyetographs are assumed to be known as part of the experiments conducted in this study, as was the case in Di Matteo et al. (2019a), thereby providing a theoretical upper bound on the effectiveness of the real-time control of systems of smart tanks for reducing peak system outflows.

In order to enable the peaks of the hydrographs from different roofs to be offset, the outflow from each tank is adjusted by changing the timing and degree of opening of the orifices. Consequently, the decision variables of the formal optimization problem are the percentage opening of the orifice for each tank, ranging from 0% (fully closed) to 100% (fully open), for each control time step during a rainfall event. The number of control time steps and the control horizon depend on the storm duration and number of time steps desired. For this optimization problem, the decision variables for the ith control strategy are given as:

𝐷𝑉_𝑖 = [𝑂_𝑇=1^𝑡=0, 𝑂_𝑇=1^𝑡=1, … , 𝑂_𝑇=1^𝑡=𝑁, … , 𝑂_𝑇=𝑆^𝑡=0, 𝑂_𝑇=𝑆^𝑡=1, … , 𝑂_𝑇=𝑆^𝑡=𝑁] (2.1) where, 𝑂_𝑇^𝑡 is the orifice opening fraction for the tth control time step for a control horizon with N time steps, and for tanks T = 1, 2, … S, where S is the number of tanks being controlled in the system.

The optimization objective is to identify the control scheme(s) that minimize(s) the peak flow rate leaving the system. The objective function of the formal optimization problem is given by:

𝑀𝐼𝑁𝐼𝑀𝐼𝑍𝐸{max (𝑄_{𝑠𝑦𝑠𝑡𝑒𝑚})} (2.2)

where, max(Qsystem) is the peak flow rate measured at the system outlet.

2.2.3 Optimization Process

In order to solve the optimization problem outlined in Section 2.2.2, a simulation-optimization approach is used (Maier et al., 2014, Maier et al., 2019) (Figure 2.3). An evolutionary algorithm (Maier et al., 2014) is used to select values of the decision variables (i.e., the combination of the degree of opening of the orifices of each tank at each time step) so as to minimize the peak flow rate of the system (see Section 2.2.2). A stormwater simulation model is then used to evaluate the peak flow rate at the system outlet for the selected values

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of decision variables. Based on the relative success of the selected decision variable values in reducing system peak flow rates, these values will be adjusted using the operators of the evolutionary algorithm (i.e., selection, cross-over, mutation) so as to further reduce peak flows. This process of selecting a particular control strategy with the aid of the evolutionary algorithm, evaluating the effectiveness of this strategy using a simulation model, adjusting the control strategy based on the relative success of the previous strategies using the evolutionary algorithm etc. is repeated hundreds or thousands of times until certain stopping criteria have been met, such as completing a fixed number of iterations or until there has been no reduction in peak flows for a certain number of iterations (Maier et al., 2019).

Figure 2.3 Details of the simulation-optimization approach used to identify tank outflow control strategies that minimize system peak outflows.

2.3 Case Study and Experimental Methods

2.3.1 System Configuration

The effectiveness of the real-time, smart systems approach is tested for a theoretical residential two-allotment catchment adapted from Di Matteo et al.

(2019a), as illustrated in Figure 2.1. Details of the configuration of the case study system are given in Table 2.1. The catchment consists of two 200 m² roofs, each of which is fully connected to a rainwater tank. The outlets of the rainwater

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tanks are directly connected to the stormwater pipe, which is assumed to discharge freely. It is assumed that there is no initial loss for the storm event, which enables the volumes of runoff from various storms to be directly compared. The tank height is set as 2 meters to represent typical above-ground rainwater tanks. As mentioned previously, the orifice opening percentages are the decision variables and are therefore determined with the aid of a genetic algorithm as part of the optimization process. This simple system was selected to enable the impact of the control rules on the ability to reduce system peak flows to be isolated and to enable the results to be applicable to other catchments with different roof sizes.

Table 2.1 Configuration of case study system.

Design Parameter Value

Orifice opening percentage (%) Variable

Tank height (m) 2

Roof catchment size (m2) 200

Percentage of roof connected to tank (%) 100

Initial loss (mm) 0

Number of roofs 2

Number of tanks 2

2.3.2 Implementation of Simulation-Optimization Approach

The simulation-optimization approach (Section 2.2.3) was implemented by linking two existing software packages in the Python language: DEAP and PySWMM. DEAP (Distributed Evolutionary Algorithms in Python) (Fortin et al., 2012a) is an evolutionary computation framework developed for solving real-world problems by applying evolutionary algorithms to simulation modules. DEAP is used to select the decision variable values i.e., the degree and timing of the opening of the tank outlets (see Sections 2.2.2 and 2.2.3). The NSGA-II genetic algorithm was chosen in the DEAP package, as its variants have already been used successfully for the optimization of urban stormwater systems (Di Matteo et al., 2019a, Paseka et al., 2018, Di Matteo et al., 2017).

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For each optimization run, a population size of 500 was used and the optimization process was continued for 1000 generations to ensure the convergence of the optimization process (Di Matteo et al., 2019a). All optimization runs were repeated three times from different random starting positions in the decision variable space due to the stochastic nature of genetic algorithms.

The stormwater simulation model used to evaluate the peak flow performance of the controlled tank systems was EPA SWMM (v5.1.012) developed in the United States. SWMM is a widely used dynamic rainfall-runoff-subsurface runoff model that enables the flows from the outlets of rainwater tanks to be controlled. This is achieved with the aid of PySWMM (v0.5.1), which is a software package written in Python that enables these controls to be implemented. As mentioned above, in this case these control schemes are selected by the genetic algorithm implemented in the DEAP package, thereby operationalizing the approach illustrated in Figure 2.3

2.3.3 Computational Experiments

In order to test the effectiveness of the real-time, smart systems approach, a number of computational experiments were conducted for storm events with different annual exceedance probabilities (AEPs), which correspond to the percentage of a particular storm event being exceeded in any one year, durations and storm patterns in three Australian capital cities (Adelaide, Melbourne and Sydney), as summarized in Table 2.2. These cities were chosen as their different climates produce different extreme rainfall intensity (see Table 2.3 for examples of the design rainfall intensity for the 1% AEP). As summarized in Li et al. (2016), Adelaide’s Mediterranean climate with wet winters and hot dry summers, has the lowest rainfall intensity of all three cities (see Table 2.3).

Melbourne’s moderate oceanic climate produces severe events in spring and summer due to thunderstorms, resulting in higher rainfall intensity than in Adelaide. Sydney’s temperate climate produces the highest rainfall intensity of all three cities, with the extreme rainfall produced in summer, by convective processes.

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Table 2.2 Summary of experiment configurations.

Parameter Value

Location in Australia

Adelaide, South Australia Melbourne, Victoria Sydney, New South Wales Storm frequency (%

AEP) 50, 10, 5, 2, 1

Storm duration 30 min, 1hr, 6hr, 12hr, 24hr Storm pattern ten burst patterns

Tank size (𝑚³) 2, 10

Orifice opening

percentage (%) 0% (Fully closed), 10%, … 90%, 100% (Fully open)

Orifice diameter 20mm

Control update time step 5 min for 30 mins, 1hr storms 1 hr for 6hr, 12hr, 24hr storms

As the real-time, smart systems approach is optimized for a particular storm event, its performance can be quite sensitive to the characteristics of the rainfall events it is responding to. Consequently, experiments were repeated for five annual exceedance probabilities, including 1%, 2%, 5%, 10% and 50%, as well as five different durations, including 30min, 60min, 360min (6hr), 720min (12hr) and 1440min (24hr). These were selected as they represent typical ranges of AEPs and critical durations that might be of interest for sub-catchment scale urban drainage infrastructure.

Table 2.3 Design Rainfall Intensity (mm/hr) for the 1% AEP event.

Duration 30 min 1 hour 6 hour 12 hour 24 hour

Adelaide 67.4 43.5 12.3 7.2 4.1

Melbourne 78.3 48.6 13.5 8.54 5.46

Sydney 118 76.7 26 18 12.5

Storm temporal patterns can have a significant impact on design peak flow estimates. If only a single storm temporal pattern was used it could introduce significant biases in the estimate of the design flow (Ball et al., 2019).

Consequently, in order to obtain unbiased estimates of peak design flow for the robust evaluation of the effectiveness of the real-time smart systems approach, the approach recommended by Australian Rainfall and Runoff 2019 (ARR2019) (Ball et al., 2019) is adopted. As part of this approach, design peak flows for a

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given duration and AEP are estimated by taking the average peak flow from ten different storm temporal patterns, instead of using a single storm temporal pattern. These temporal patterns are selected based on the recommendations provided by ARR2019 (Ball et al., 2019). Consequently, for the remainder of this paper, the term “peak flow” for a given duration and AEP refers to the design peak flow estimated from the average of the 10 storm temporal patterns.

All computational experiments were repeated for two tank sizes, including 2 m³ and 10 m³. A 2 m³ tank is considered to be a reasonably popular size for a rainwater tank in Australia, while a 10 m³ rainwater tank was selected as a reasonable upper limit to a publicly acceptable size for residential allotments in an urban infill area.

For the real-time smart system approach, eleven different degrees of opening were considered for each tank outlet, consisting of orifice openings corresponding to 0% (fully closed), 10%, 20%, …, 100% (fully open) open, for an orifice diameter of 20mm. These openings were implemented for two different control time steps, depending on storm duration. As can be seen from Table 2.2, a 5-minute control time step was used for storms of 30 and 60 minute duration, whereas a 1 hour time step was used for storms of 6, 12 and 24 hour duration. This was done to strike an appropriate balance between search space size and the ability to identify the control strategy that minimizes system peak outflow.

2.3.4 Performance Assessment

In order to assess the effectiveness of the real time, smart systems approach, its performance was compared to that of the benchmark approach, as defined in Section 2.2.1. For both these approaches, the tanks were assumed to be empty prior to the start of the rainfall event. As mentioned previously, the key difference between the two approaches is that for the benchmark approach, tank outflows are not controlled during the rainfall event, with the orifice remaining closed, whereas for the real-time, smart systems approach, the orifice opening/closing of each tank is optimized independently during the rainfall event so as to maximize system peak flow reduction, as explained in Section 2.2.

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To evaluate the performance of both of these approaches, a baseline scenario with no tanks was chosen as a basis of comparison. Therefore, the peak flow rate reduction for the i^th experiment configuration and j^th storm event is given by:

System peak flow reduction = (1 − max (𝑄_𝑀𝑎𝑥^𝑖,𝑗 )

max (𝑄_𝑀𝑎𝑥^{𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒,𝑗})) × 100(%) (2.3) where, max(𝑄_𝑀𝑎𝑥^𝑖,𝑗 ) is the peak flow of one specific trial, and max (𝑄_𝑀𝑎𝑥^{𝑏𝑎𝑠𝑒𝑙𝑖𝑛𝑒,𝑗}) is the peak flow from the case without a tank (“No tank”).

2.4 Results and Discussion

2.4.1 Performance of Real-Time, Smart System Approach

The results for the two-tank case study considered show that the real-time, smart systems approach can be highly effective in reducing peak flows in urban stormwater systems, with minimum peak flow reductions of ~30% under even the most severe rainfall conditions considered, provided the temporal variation of the incoming rainfall event is known (dashed orange lines, Figure 2.4). For Adelaide and Melbourne, this level of performance can be achieved using a 2 m³ tank (dashed orange lines, Figures 2.4a and 2.4c, respectively), whereas for Sydney, this requires a 10 m³ tank (dashed orange line, Figure 2.4f), as a result of the higher intensity rainfall, and hence higher runoff volumes, experienced in this city. For less severe events, such as those with an AEP of 10%, use of the real-time, smart systems approach is able to achieve even greater minimum peak flow reductions of around 60% (dashed orange lines, Figures 2.4b, 2.4d and 2.4f).

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Figure 2.4 Performance of real-time, smart tank systems versus benchmark tanks for the three locations (Adelaide, Melbourne and Sydney), two tank sizes (2×2 m³ and 2×10 m³), and five AEPs (50%, 10%, 5%, 2% and 1%) considered. For the sake of clarity, only results for the shortest (30 min) and longest (24 h) durations considered are shown, with results for the full set of

durations considered shown in Figure 2.5 and Appendix A.

The results in Figure 2.4 also show that long-duration events (24 h – solid orange lines) are more critical than short duration events (30 minutes – dashed orange lines) in terms of the ability of household rainwater tanks to reduce flood peaks, with the peak flow reductions obtained for the shorter duration events

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generally on the order of 20% and 40% greater than those obtained for the corresponding longer duration event for the 2 m³ (Figures 2.4a, 2.4c and 2.4e) and 10 m³ (Figures 2.4b, 2.4d and 2.4f) tanks, respectively. This trend in the decreasing effectiveness of household rainwater tanks in reducing flood peaks for longer duration events is confirmed by the results obtained for the intermediate durations (see Figure 2.5 for results for Adelaide for 2 m³ tanks and Appendix A for similar results for other locations and tanks sizes) and is agreement with the findings and assumptions in previous studies (Schubert et al., 2017, Di Matteo et al., 2019a). It should be noted that although shorter duration events generally result in larger peak flows for catchments without tanks, this is generally not the case once tanks have been added. This is because the runoff volume produced by shorter duration events can generally be fully contained within the tanks. In contrast, while the intensity of long-duration events is less, the runoff volume produced is larger, often exceeding the capacity of the tanks. As a result, for catchments with tanks, and downstream detention infrastructure operating near capacity, attenuation of runoff for longer duration events can be important, as these events produce potentially significant peak flows leaving the catchment (post-tank, as can be seen from Appendix B).

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Figure 2.5 Percentage peak flow reduction of benchmark tanks and real-time, smart tank systems for a range of durations and AEPs with 2 x 2 m³ tanks for

Adelaide.

In general, the performance of the real-time, smart systems approach (orange lines) is noticeably better than that of the benchmark approach (blue lines) for the same rainfall duration (e.g., either dashed or solid lines) (Figures 2.4 and 2.5, Appendix A). As can be seen in Figure 2.4, Exceptions are:

(i) When the available tank storage exceeds the total rainfall volume, as is the case for the short-duration rainfall events for the 10 m³tanks for Adelaide (Figure 2.4b), Melbourne (Figure 2.4d) and AEPs of 50, 10 and 5% for Sydney (Figure 2.4e), where both approaches result in 100% peak flow reduction (i.e.

the solid orange and blue lines are both at 100%), as all of the runoff is able to be retained in the tanks.

(ii) When the available tank storage is only slightly less than the total rainfall volume, in which case the benchmark storage still performs well, as is the case for an AEP of 50% for the long duration events for the 10 m³ tank for Adelaide (Figure 2.4b)

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and Melbourne (Figure 2.4d) (i.e. the dashed orange and blue lines are close together).

(iii)When long duration, extreme events at locations with higher rainfall intensity such as Sydney, are combined with smaller tank volumes (Figure 2.4e, dashed orange and blue lines), suggesting that the capacity of the tanks is insufficient to mitigate the large volume of runoff generated, even with the real-time, smart systems approach.

The above results suggest that the performance of both benchmark tanks and real-time, smart tank systems is affected by the volume of runoff generated by a rainfall event, which is a function of location, AEP and rainfall duration, as well as available tank volume. Consequently, in order to enable the above results to be generalized, the ratio of tank volume to total runoff is plotted against peak flow percentage reduction for all computational experiments conducted (Figure 2.6). As can be seen, the performance of benchmark tanks deteriorates rapidly once the tank volume to runoff ratio drops below 1.0, to the point where (blue circles and dashed line, Figure 2.6):

(i) below ratios of 0.8, peak flow reduction generally drops to below 30%;

(ii) below ratios of 0.6, peak flow reduction generally drops to below 20%;

(iii)below ratios of 0.3, peak flow reduction generally drops to below 10%;

and

(iv) below ratios of 0.15, peak flow reduction is generally 0%.

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Figure 2.6 Relationship between the ratio of tank to runoff volume