The Development of Adaptation Pathways for the Long Term Planning of Urban Drainage Systems

Babovic, Filip1 & Mijic, Ana1

1Department of Civil and Environmental Engineering, Imperial College London

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AbstractCities must adapt their drainage systems to cope with the effects of land use and climate change on growing flood risk. However, the development of robust adaptation strategies remains a challenge due to the deep uncertainty surrounding future conditions. To address this problem, an Adaptation Tipping Points (ATP) approach was utilised to investigate the impacts of future rainfall with respect to increases in both depth and intensity on an urban drainage system. A set of Adaptation Pathways was generated to assess how the drainage system could be adapted using a range of infrastructure solutions. The most effective combination of adaptations to increase the system’s ATP was an increase in system storage followed by green infrastructure solutions to add additional capacity to the system. The methodology enabled no-regret adaptation by proposing a set of selected interventions that can be incrementally implemented to achieve maximal combined effect. The resulting pathways effectively communicate to decision makers how short-term solutions allow for long-term adaptation and sustainable development. The ATP approach proved to be an excellent tool for decision-making that provided a structured approach for the long-term planning of urban drainage systems.

1.0 IntroductionLondon’s population has grown significantly over the past 25 years with continued growth expected in the decades to come (Mayor of London 2016). London’s drainage system, originally built over 150 years ago, is currently operating in a vastly different hydrological environment than the one it was initially designed to serve. Growth in impermeable land cover has lead to increased volumes of runoff to be conveyed by the sewer system,. Independently of land use, climate change has augmented the storm flows that need to be managed. To maintain the required level of pluvial flood protection as defined by national regulations (British Standard Insitute 2013) existing drainage systems in the UK must be adapted. However, there is a high degree of ambiguity surrounding the land use and climate conditions that these potential adaptations may be exposed to (Hallegatte 2009). This greatly challenges the planning of infrastructure, as it is not known whether design choices made in the present will remain valid in the future. This means that a long term decision making related to environmental risk reduction occurs within a context of deep uncertainty (Hallegatte et al. 2012).

Situations of deep uncertainty are defined by an inability to reliably quantify the probability of events occurring, this may encapsulate both the direction and magnitude of change (Regos 2012). Deep uncertainty results in the presence of multiple valid plausible futures that must be considered (Hallegatte, Shah, Brown, et al., 2012). The resulting ambiguity poses serious challenges on how to choose appropriate models, identify and characterise sources of uncertainty, and rank potential policies (Kwakkel, Haasnoot & Walker, 2014). Traditionally, these shortcomings are overcome by increased data collection. However, under conditions of deep uncertainty this may not lead to improved predictive ability, as the past is of limited use as an indicator of the future (Milly et al. 2008). Deep uncertainty does not reflect complete ignorance about what may happen in the future; it is possible to identify plausible futures, but it is not possible to explore all possible uncertainties (Herman, Zeff, Reed, et al., 2014; Kwakkel & Pruyt, 2013) A thorough exploration of Decision Making under Deep Uncertainty (DMDU) can be found in Walker, Haasnoot & Kwakkel (2013), while (Babovic et al. (2018) explores DMDU in an urban drainage context.

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Within urban flooding, deep uncertainty arises through the interaction of multiple sources of uncertainty such as population growth, land use change and climate change (Babovic et al. 2018; Deng et al. 2013). Given the limited degree of confidence that can be attributed to projections of the future, it is critical that methodologies of planning account for these uncertainties as the “traditional optimum expected utility approach, at least in its most basic form, is insufficient to address decision challenges with the characteristics of climate change” (Groves & Lempert 2007 pp4). The expected utility approach uses a priori probability distributions to estimate the benefits and costs of a potential project.

Using London as a case study, this work represents the first known investigation of how a drainage system can be adapted to a combination of risk aggravators using the Adaptation Tipping Points method. These risk aggravators are increases in the design storm’s depth and its ratio of peak to mean rainfall intensity, known as peakedness. This study is also unique with regards to the large number of potential adaptation strategies investigated.

2.0 Cranbrook CatchmentThe analysis and modelling conducted in this study is based upon the Cranbrook catchment. The Cranbrook is located within the North East of London in the Borough of Redbridge as shown in Figure 1. The catchment has a drainage area of approximately 9 km2 and is predominately urban with the exception of a large park that contains two offline-lakes.

Figure 1. Map of Cranbrook Catchment (Simões et al. 2015).

The main watercourse running through the catchment is 5.75 km long; its 5.7 km reach is culverted and part of a separated drainage system that discharges into a tributary of the River Thames.

The catchment has a population of approximately 41,000 inhabitants resulting in a population density of 4,500 people per km2. The Cranbrook catchment is projected to experience a 15%

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increase in population by the year 2040 (GLA Intelligence Unit 2014). It is highly probable that this population growth will result in urban creep.

The Cranbrook catchment’s land surface is 52% impervious; as such it has a rapid response to rainfall. Surface runoff generally flows and ponds along the natural drainage pathways, most of which have been covered by impervious surfaces. Partly due to this, the Cranbrook catchment has experienced flooding in the past; with at least two major flood events having occurred since the turn of the century (London Borough of Redbridge 2011).

2.1 British Drainage RegulationsThe Cranbrook’s drainage system must conform to British Standard EN 752:2008, the United Kingdom’s national regulatory framework that lays out the requirements for drainage systems. The standard requires that the frequency of surcharge of manholes within urban areas be limited to once in every thirty years (British Standard Insitute 2013).

Beyond national standards, within the London region there is a complex tapestry of governmental and environmental management bodies that produce guidance on how to manage flood risk (Ashley et al. 2010). These include the Mayor’s Office, the Local Authority, and the Environment Agency. Together, these agencies have produced at least twenty sets of guidance that influence how London’s flood risk should be managed. This greatly complicates the choice and design of potential drainage adaptations.

2.2 Climate ChangeThere is evidence to suggest that climate change has begun to affect precipitation patterns within the UK (Jenkins et al. 2009). However, there is a high degree of heterogeneity in the direction and magnitude of change. Broadly speaking, rainfall depths have decreased in the summer and the South-East of Britain; while increases have been observed in the winter and North of Britain (Jenkins et al. 2009).

It should be recognised that the effects of climate change on precipitation vary across temporal scales. There is evidence to suggest that while aggregate precipitation depths will decrease over the summer, the precipitation that will occur will be concentrated in fewer and stronger summer showers (Kendon et al. 2014). A great deal of investigation has been performed on projecting precipitation change at temporally coarse resolutions of one month or longer. However, drainage design is ideally conducted utilising sub-daily precipitation information. This is a domain of climate change research where projections are scarce; however, there are indications that individual rainfall events will increase in intensity although it is not clear to what degree (Chan et al. 2014).

3.0 Adaptation Tipping Points MethodologyAdaptation Tipping Points (ATP) is a methodology of adaptation planning in which a system is modelled and then exposed to increasingly large stresses in order to identify when the system will no longer be able to operate to a desired level of reliability (Kwadijk et al. 2010). These levels of operation are typically defined through the use of national standards; however, any reliability criterion chosen by a decision-maker could be used. Adaptation Pathways builds upon the ATP method by modelling a system adaptation once the reliability metric is breached. The ATP methodology is then repeated on the adapted system resulting in a series of Adaptive Pathways that can deliver a given level of system reliability across a planning horizon. A generic ATP methodology is outlined in Figure 2Error: Reference sourcenot found.

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Figure 2. ATP Methodology (Adapted from Gersonius, Nasruddin, Ashley, et al., 2012)

The method exposes systemic vulnerabilities that potential adaptations can address. This is known as an effect-based method as the focus is on system performance under potential change as opposed to projections of the future (Gersonius et al. 2014). The ATP method allows for decisions to be made despite these uncertainties as the choice and exploration of potential futures is independent of forecasts (Babovic et al. 2017). The ATP approach allows for the implementation of low-regret adaptation as it addresses the most urgent effects of change, while while at the same time Adaptation Pathways structuringordering solutions such that they are viable elements of potential future adaptation strategies.

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4.0 Methodology and DataThe generic ATP methodology explained in Section 3.0 was modified to application for the urban flooding case study through the following procedure.

Step 1: Identification of drivers of changeThe drivers of change investigated were increases in the depth and peakedness of the design storm. Peakedness, defined as the ratio of peak rainfall intensity to mean rainfall intensity describes the temporal distribution of precipitation across the duration of the storm. Currently, the pluvial flood defence infrastructure in Cranbrook consists of drains, gullies, and culverts.

Step 2: Identification of reliability criterionThe standards for pluvial flood defence defined within British Standard EN 752:2008 state that the frequency of manhole flooding should not occur more frequently than once every 30-years.

Step 3: Assessing the system’s ATP

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The ‘current’ design storm, i.e. the thirty year return period summer storm with no climate change factors applied was selected following guidance from Part Four of the Flood Estimation Handbook (Houghton-Carr 1999). The resulting storm profile is shown in Figure3. The rainfall depths are associated with each fifteen-minute period.

Figure 3. Storm profile for a 30-year return period storm in Cranbrook.

A variety of urban flood models can be utilised to simulate the effects of potential precipitation events. In this study, four models were tested, which incorporated a range of simplifications of physical processes; as a result, there was a wide range of model run times, as shown in Table 1.

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Table 1. Flood models investigated and their associated run times.

Model Run Time1D-1D Simplified 1.5 Seconds1D-1D 40 Seconds1D-2D Semi-Distributed 2.5 Minutes1D-2D Fully Distributed 5 Minutes

These models were originally created and calibrated as part of the RainGain Project (Simões et al. 2015; Ochoa-Rodriguez et al. 2015). Based upon the run times and the degree to which physical processes were replicated, the catchment was modelled using a 1D-2D fully distributed Infoworks ICM 6.5 model. Within this model, the sewer system was modelled one-dimensionally and the ground surface two-dimensionally using a triangular mesh. This mesh was generated from a Digital Terrain Model (DTM) and was composed of 267,724 triangles. Estimations of model uncertainty with respect to flows can be found within Pina et al. (2016).

The design storm was then modified such that the effects of potential changes could be explored. The design storm’s depth was modified by applying climate change factors at 5% intervals ranging from 0% to 50%, this resulted in 11 potential increases in depths. Additionally, the temporal distribution of precipitation was modified. Following guidance from the Flood Estimation Handbook, urban drainage systems are designed using a summer storm (Butler & Davies 2010). This results in a symmetrical storm with peakedness of approximately 3.0. The peakedness is dictated through two shape parameters: alpha and beta. These parameters were modified to generate storms that had peakednesses in the range of 3.0 to 6.0 in increments of 0.3. Modifying peakedness has the effect of increasing maximum intensity while keeping rainfall depth constant. The effects of increases in depth and peakedness can be seen in Figure 4, where the current design storm, the design storm modified to have a peakedness of 6.0, and the design storm with a 50% increase in depth are shown. The range and extent to which drivers were explored was chosen based upon a balance of computational cost to conduct all the simulations and a desire to sufficiently explore the realm of future possibilities.

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Figure 4. Effects of modifications to design storm.

The 11 increases in depth and 11 peakedness profiles resulted in 121 potential future rainfall scenarios. These were simulated within Infoworks to identify under which combination of increases in depth and peakedness the current drainage system in Cranbrook would fail to offer sufficient protection to a thirty-year return period storm.

Step 3a: Conversion of ATP to forecastsIn order to convert the ATP to an estimate of when they may occur, projections of how individual storms events may change were used. Projections of how individual rainfall events’ depths may change due to climate change were generated by the Environment Agency (2016). These data were utilised to derive continuous projections for event level precipitation increases, as shown in Figure 5. Three potential projections are shown, which represent the 90%, 50%, and 10% probability levels-denoted as high, central, and low scenarios. These forecasts were then used to derive estimates of when ATP may be reached.

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Figure 5. Potential increase in rare storm events over time.

Step 4: Identification of Adaptation OptionsIn the UK, a range of planning documents provide guidance on pluvial flood solutions that are being actively considered by local governments. These documents recommend various options that could act as potential adaptations to ATP being reached. In this study, the options were identified after consulting the documents listed in Table 2.

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Table 2. Planning Documents Consulted for Potential Drainage Adaptations.

Agency Document

Borough of Redbridge

Strategic Flood Risk Assessment (London Borough of Redbridge 2016)Local Development Framework (London Borough of Redbridge 2008)Local Flood Risk Management Strategy (London Borough of Redbridge 2015)Surface Water Management Plan (London Borough of Redbridge 2011)

Mayor's Office

Sustainable Planning Guidelines-Sustainable Design and Construction (Greater London Authority 2014b)London Plan (Mayor of London 2016)Mayor’s Water Strategy (Mayor of London 2011)The Mayor’s Climate Change Adaptation Strategy (Moss et al. 2012)

Environment Agency Regional Flood Risk Appraisal (Greater London Authority 2014a)

National Government

National Planning Policy Framework (Department for Communities and Local Government 2012)Flood Risk Regulation (Great Britain 2009)Flood and Water Management Act (Great Britain 2010)

The subset of options that was chosen includes converting 25% of roofs to green roofs, converting 50% of roofs to green roofs, converting 20% of streets to porous pavements, converting 40% streets to porous pavement, deepening a large lake by 0.5m, deepening the lake by 1m and increasing the diameter of the trunk sewer by ten per cent. However, once the combinations of potential adaptations were considered, the number of strategies increased from 7 to 53. These 53 strategies were stress-tested against the 121 storms derived previously in order to identify their behaviour in response to potential change. Spatially distributed solutions such as green roofs and porous pavements were distributed across the catchment uniformly by modifying the porosity of different land-use types.

Upon the completion of every model run, the maximum flood extent caused by each precipitation event was exported as GIS layers. Surface water depths greater than 15 cm were considered to be floodwaters, following guidance from the London Borough of Redbridge (2016) & HM Government (2010). Within a GIS environment, the surface water flood extent was laid over the manholes to identify the proportion of manholes surcharged. This procedure was repeated for all 53 adaptation strategies across the 121 potential future storms. This resulted in a data set that specified the number of manholes flooded for any potential combination of increase in design storm depth and peakedness under any adaptation strategy. When more than 2% of the manholes were surcharged, the drainage system was considered to exhibit failure implying that the ATP had been reached.

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5.0 Results and DiscussionThe reliability criterion for the Cranbrook’s drainage system is assumed to be breached when 2% of manholes are flooded, which is equivalent to 154 manholes flooding. In order to identify an adaptation strategy’s ATP the exact increase in depth that resulted in 154 manholes flooding was found. This was achieved by linearly interpolating between the number of manholes flooded for the climate change factor that resulted in more than 154 manholes flooding; and the number of manholes flooded for the climate change factor below it. For example, when simulating the conversion of 25% of roofs to green roofs, an increase of storm depth of 25% resulted in 140 manholes being flooded, which was an acceptable level of system performance. When the system was further stressed by an additional 5% increase (total of 30% increase in the design storm’s depth), a failure of the system was reached when a total of 159 manholes flooded. By linearly interpolating between the numbers of manholes flooded below and above the system failure criterion, the exact ATP for a proposed adaptation option was found, which in the case of green roof 25% conversion corresponded to a 29% increase in depth. This analysis was repeated for all 53 strategies, and it was found that the majority of adaptation options resulted in a small increase in ATP, usually in the range of 2-3%.

Generation Of PathwaysTo generate the pathways, individual adaptation options were ranked by their ability to increase the ATP of the drainage system. Additionally, the strategies that had the highest ATP were identified. This resulted in an exercise to find a logical combination of adaptation strategies that resulted in pathways from the individual options that represent the simplest adaptations, to the adaptation strategies with the highest ATP. Pathways were chosen such that only one adaptation option could be implemented at a time. In instances where similar adaptation strategies had the same ATP, the cheaper strategy was chosen.

The results of the methodology are usually presented as a set of adaptation pathways (Figure 6), which are interpreted by reading the figure from left to right. The x-axis represents the driver of change, starting with the baseline value (0% in the case of Cranbrook) to the largest explored increase (in our case 45%). The current situation is identified as a performance of the system without any adaptation option, and that path is followed until the system reaches the failure criterion. This point represents the current system’s ATP. Decision makers can then choose to adopt one of the strategies that are connected to the current strategy (four possible options in Figure 6). Adaptations can then be added in sequence to cover the full range of potential futures explored.

Solutions Identified for Increases in Storm DepthThe Adaptation Pathways for storms with peakedness of 3.0 are displayed in Figure 6. When combining all adaptation strategies considered, the largest possible increase in the drainage system’s ATP was an adaptation capacity to 44% increase in storm precipitation depth. For such a high level of flood protection to be delivered solutions that addressed both surface water infiltration and pipe network capacity were required.

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Figure 6. Adaptation Pathways for constant peakedness of 3.0.

Augmenting the trunk sewer’s capacity by increasing its diameter would result in a 2% increase in the drainage system’s ATP; however, there were no logical paths from this option to adaptation strategies with higher ATP. This strategy therefore leads to lock-in and a limited ability to improve the drainage system into the future. Both options of increasing the lake’s retention volume by deepening were shown to have sizable impacts on the drainage system’s ATP. Porous pavements are shown to be ineffective at adding drainage capacity as a stand-alone adaptation. However, they were effective as adaptations once the drainage system’s ATP had been increased by increasing the lake depth.

Based on Figure 6, in order to develop an adaptation strategy that delivers the largest possible increase in ATP, in the short-term, local decision makers should choose to convert either a quarter of roofs to green roofs or to deepen the lake by one meter. These options offer a logical progression to more robust drainage strategies. As the design storm’s depth is increased, the combination of solutions able to deliver reliable service converges to a combination of green roofs and lake deepening.

Based on the pathways developed, it is hypothesised that there are two elements of pluvial flood protection that define the efficacy of a particular adaptation option when the adaptation is assumed to be implemented only when the system reaches the failure in the performance. These are system capacity, defined as the amount of runoff able to be conveyed by the drainage system and secondly, the rate at which runoff is managed at the land surface. The initial efficacy of increasing the size of the trunk sewer and increasing lake retention volume in comparison to implementing Sustainable Drainage systems (SuDs) options indicates that a lack of capacity within the current drainage system needs to be addressed first to alleviate the immediate causes of flooding This implies that initially surface flooding is due to pipes surcharging and a lack of conveyance capacity within the drainage system. These two factors also reflect why SuDs are more effective as a second stage adaptation. After lack of drainage capacity is addressed, the primary source of flooding is an inability to remove runoff from the

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surface. These two factors also reflect why the total ATP of an adaptation strategy is not simply the sum of the strategy component’s ATP. Finally, the results showed that when directly compared with the solutions that significantly increase the storage capacity, SuDs cannot match their performance. Rather than used as an adaptation option, SuDs could be adapted as a lever for delaying the decision on the large-scale infrastructure solutions until we have a better knowledge on the future state of the world, and other drivers of the system such as land use planning, housing standards and human behaviour.

Timing of AdaptationsPotential increases in depth were converted to estimates of when they may occur based on the projections shown in Figure 5. This resulted in three different timelines. Depending on which scenario is used to convert the ATPs to a timeline there can be large differences in the timing of the implementation of the options. For example, the current drainage system’s ATP could be reached in the year 2060, 2090, or beyond 2100 depending upon which scenario is used. This uncertainty may be reduced through improved understanding of how climate change will affect individual storm events.

This high degree of variability in the potential timelines suggests that rainfall monitoring is needed within the catchment in order to identify the rate at which changes in precipitation are occurring. This is similar to recommendations by my Reeder & Ranger (2011) for the Thames Esturary 2100 plan. Doing so will ensure that decision makers are not caught unaware of the hydrological trends present within their catchment. Although discerning a climate change signal for either depth or peakedness will prove to be a challenge due to the variation between storms and the difficulty of separating the effects of increases in total precipitation depth and changes in the temporal distribution of precipitation.

5.1 Adaptation Pathways for Increases in Storm PeakednessIncreases in the peakedness of the storm reflect the effect of multiple possible processes that could increase flood risk. Peakedness’ ability to increase flood risk greatly depends on if it is coupled with an associated increase in a storm’s precipitation depth. For storms with increases in depth of 10% or less the model results showed that flood risk was not affected even by extreme increases in peakedness. This indicates that the current system will offer sufficient protection from flooding if runoff volumes remain constant, even if they are more concentrated. This is likely to be the case if changing precipitation patterns result in shorter and more intense storms.

Storms with a 35% or higher increase in total depth resulted in flooding for almost all adaptation strategies, regardless of how peaked the storms were. This is observed in Figure 6, where the majority of strategies were unable to prevent flooding for storms with high increases in depth but no increase in peakedness. In between these two extremes there exists a range where there is heterogeneity in the efficacy of potential adaptation strategies. Therefore, peakedness only plays a role in the effectiveness of adaptation strategies if the design storm’s depth is also increased by 15-30%. Such an increase in runoff volume, and concentration of runoff most accurately reflects the potential impact of land use change. Figure 7 shows the Adaptation Pathways for increases in peakedness for a fixed increase in design storm depth of 15%.

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Figure 7. Adpatation Pathways for Increasing Peakedness and an increase in depth of 15%

A reasonably high level of adaptation to increases in peakedness can be achieved by utilising a variety of pathways. For example, increasing the lake’s depth by one meter is the simplest adaptation that offers the greatest possible increase in the drainage system’s ATP. Alternatively, increasing the lake’s depth by half a meter would represent a more incremental adaptation while keeping two potential future pathways open. Increasing the trunk drain’s diameter also represents a viable adaptation which would allow for further adaptations in the future if the catchment’s flood risk becomes increasingly severe.

As there are no known projections of how peakedness may change, it is not possible to derive estimates of when these ATP may be reached. This impedes planning by hampering decision maker’s ability to assess how likely potential changes are and how far in advance adaptation options need to be implemented.

Comparison of Adaptation Pathways for Peakedness and Depth The Adaptation Pathways for increases in rainfall depth result in a relatively clear strategy on how to adapt the system well into the future due to the convergence of the pathways on a solution that utilises lake deepening and green roofs. In comparison, the pathways for increases in peakedness do not converge to a best solution and there is a wider choice of adaptations.

There is a range of differences and similarities between the two sets of adaptation pathways. Within the Adaptation Pathways for peakedness, increasing the diameter of the trunk drain does not result in lock-in and allows for the development of increasingly robust flood defences. This runs counter to the pathways for increases in depth (Figure 6) where long terms solutions to address flood risk do not include augmenting sewer systems. Increasing the lake depth is effective at addressing both increases in depth and peakedness; this is especially true if the lake’s depth were increased by one meter. Porous pavements are not shown to be particularly effective at addressing flooding on their own, however, they are shown to be effective complements to other solutions. In particular, they are effective at augmenting the ATP after other adaptations have been put in place. Lastly, there is a great deal of heterogeneity in the performance and timing of green roofs.

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The difference in the adaptation pathways has profound effects on the management of urban storm water. Increases in the storm peakedness results in faster and flashier responses to precipitation; as such, it can be seen as a proxy for land use change, and in particular urban creep. Therefore, the solutions identified as being particularly effective at coping with increases in peakedness are well suited to protect against increased runoff from urbanisation. Solutions effective at addressing increases in depth are likely to be effective at addressing both climate change and urbanisation. However, the efficacy of a given solution is largely dependent upon any previous adaptations that are influencing the drainage system.

5.2 Comparison to Predict–then-Act MethodIn order to assess the advantages and disadvantages of an ATP analysis a predict-then-act analysis was conducted and the results compared to one another. The lifespan of an adaption to the drainage system was assumed to be 50 years. The projections for increases in precipitation (Figure 5) show that in 50 years there will be a 28% increase in precipitation depth for the design storm under the high scenario. Based on this, the design storm was modified to reflect this increase in depth and simulated within Infoworks ICM. This storm resulted in excessive flooding. Under this increase in depth the enlarging of the trunk sewer offers the simplest solution to address the gap in flood protection.

Such a predict-then-act analysis requires only a minor computational expense; the run time for the model was approximately seven7 minutes long. However, the predict-then-act method is based upon a high level of confidence in the prediction. If the projection used underestimates the increase in depth by a small margin, the system would exhibit failure.

Within an ATP framework antecedent adaptations are chosen to act as a route to subsequent developments. The choice of adaptation is made in such a way so as to avoid lock-in. The predict-then-act method has a well-defined end date, and little thought is given to longer term planning for more intense rainfall. Upon comparing the solutions suggested by the predict-then-act analysis against the full set of Adaptation Pathways in Figure 6 there are clear differences. In the full set of pathways increasing the size of the trunk sewer is not identified as a suitable adaptation. This is because the modification of the sewers result in a lock-in, which indicates that it is not an element of adaptation strategies that deliver higher levels of protection. This stark difference shows how the broader exploration of futures in an ATP analysis prioritises solutions that can act as components of a larger adaptation strategy.

5.3 DiscussionA major assumption of the study is that the local council has sufficient funds to implement and maintain the adaptation pathways proposed. The economic cost and benefits of these solutions are critical in decision-making but have not been addressed within this study. The assessment of the costs and benefits will be affected by the uncertainty surrounding the pathways, however, methods such as real options may be effective at addressing this shortcoming (de Neufville & Scholtes 2011; Buurman & Babovic 2016). The addition of financial considerations at the start of the analysis may make certain adaptations financially unfeasible and may reduce the number of simulations to be run.

The Flood Estimation Handbook methodology used to derive the design storms assumes that the temporal distribution of precipitation across a design event is symmetrical such as in Figure 3. In reality, rainfall events do not exhibit these properties. A design storm that replicates physical storm behaviour would more accurately reflect real-world risk. Furthermore, the design storm assumes that the rainfall incident upon the catchment is

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spatially uniform; this is likely to be a minor issue given the case study’s size. However, if this study’s methodology were applied on a larger case study, it may be of interest to utilise spatially heterogeneous precipitation in order to investigate how this affects adaptive capacity.

The Cranbrook catchment is likely to experience development and urban creep, which will result in an increase in impermeable areas and will affect the runoff characteristics of the catchment. Increasing peakedness accounts for this change to some degree, however, the explicit modelling of land use change would result in a more through exploration of the space of future possibilities and improve decision maker’s ability to plan for potential increases in pluvial flood risk. Such an analysis would, however, further increase the computational cost of conducting such an analysis.

Many of the potential improvements to the analysis such as reducing the time step, increasing the spatial resolution, increasing the number of strategies to be evaluated, or increasing the number of potential risks to be investigated will increase computational loads. Individually, each model run requires a relatively short amount of time to complete, however, when aggregated across all the strategies and futures to be explored, the resulting computational time can take many days or weeks. The Infoworks model was run on a desktop computer using an Intel Xeon E5 CPU with 16 GB RAM and a NVIDIA Quadro k620 GPU. The 6,534 simulations run required the computer to run twenty-four hours a day for several weeks. This computational expense is likely to be a large impediment to future studies that attempt to marry DMDU and urban drainage.

The computational load could be reduced in a number of ways. Firstly, more computationally efficient models could be developed; alternatively, existing software could be used to run simpler, less physically based models. This follows the advice from Haasnoot et al. (2013) to utilise “simple but fast” models. Lastly, the sampling rate from which futures are explored could be reduced. The aforementioned solutions result in a reduction in the fidelity of the analysis by utilising less physically based models or by exploring fewer potential futures. An especially powerful improvement to future DMDU analysis for urban drainage would be to leverage the power of cloud and high performance computing. Current iterations of Infoworks and other flood modelling software have made progress towards utilising parallel computing and graphical-processing units. If this software could be migrated to perform on high-performance computers it would be possible to run a thorough DMDU analysis without increasing run time or reducing the degree to which physical processes are replicated within the models.

Finally, the method can be improved by assessing the relative benefits of adaptation options. An economic assessment of the potential pathways by taking into account both direct (water storage) and wider (ecosystem services) benefits would better inform decision makers on the feasibility of potential adaptations.

6.0 ConclusionThe use of Adaptation Tipping Points to generate Adaptation Pathways allows for the development of an incremental and evolutionary strategy to adapt urban drainage systems to potential change. These pathways allow for decisions to be made regarding adaptations even in situations characterised by a deep uncertainty. This is achieved by identifying a sequence of short-term solutions that act as elements of long-term strategies. The use of Adaptation

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Pathways also effectively communicates the limits of various adaptations that can be implemented and the variety of pathways that exist. In addition, they communicate the relative effectiveness of potential solutions to future changes, and in particular how the effect of adaption strategies is not necessarily the sum of its parts and how certain short-term solutions allow for further adaptation while others lead to a lock-in (Markolf et al. 2018). The practical usage of the pathways is constrained by the ambiguity surrounding the forecasts of potential changes and the resulting uncertainty when ATP may be reached. This uncertainty is best managed by monitoring precipitation trends within the analysed catchment. Finally, the full applicability of the ATP approach for urban drainage systems will be supported by the inclusion of an economic assessment that takes into account the ecosystem services and institutional long-term planning policies.

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