Info-Gap robustness pathway method for transitioning of urban drainage systems under deep uncertainties

Recent endeavors in urban water management aim to avoid piped (so-called ‘gray’) infrastructure and the related rapid discharge of stormwater. By mimicking the natural hydrological cycle, so-called ‘green/blue’ concepts are expected to be more flexible and more robust when facing future changes like climate change and urbanization (De Vleeschauwer et al. 2014; Kirshen et al. 2014). From the technical point of view, a reduction of the peak flow and the runoff volume as well as the protection of the receiving waters is sought. Furthermore, socio-economic factors, like the creation of attractive living space in urban areas, the positive effects on the micro-climate and the sustainable management of water resources are of high interest (Bach et al. 2013). Such green/blue strategies can include the realization of an ecosystems-services-based approach (Van Bueren et al. 2011), with additional green spaces, green roofs, infiltration systems, wetlands or retention ponds, also known as ‘best management practices’, ‘sustainable urban drainage systems’, ‘water sensitive urban design’ or ‘low impact development’ (Fletcher et al. 2015). In the following the term LID is used in this context.

By bringing the nature into the city not only hydraulic and environmental benefits are observed, but also social preferences of a liveable and sustainable future city can be addressed. From a technical point of view, the implementation of decentral stormwater treatment measures within the existing or newly constructed systems is a gradual, rather than a single-stage process, and can follow different pathways (e.g. climate, population or policy scenarios). In literature this process is defined as system transition (Pahl-Wostl 2007; Brown et al. 2008). A helpful planning tool for engineers is a city's masterplan, which describes the temporal and spatial development of such system transitions and lays out a strategic direction, which can be used as an expected (‘baseline’) scenario for future system design.

However, future developments are highly uncertain and exact predictions are not possible. Uncertain urban developments, the raising challenges of climate change and uncertainties in forecasting require the investigation of different scenarios (Willems et al. 2012). Conventional studies focused on the analysis of a few individual scenarios, with the drawback that they are highly dependent on the quality of their assumption (Gersonius et al. 2012; Urich & Rauch 2014). With the Info-Gap (IG) decision theory variations from a baseline scenario (e.g. the design rain and expected land use) can be analyzed under deep uncertainty and allows for statements on weak points and robustness of the systems and the pursued strategy (Herman et al. 2015). Furthermore, in sustainable urban planning the topic of ‘system adaptation’ has gained a high significance, posing the question of how to cope best with the upcoming challenges of (disruptive) change, like urbanization or climate change. With the IG robust pathway method future adaptation measures can be directly estimated by determining the performance level through combination of uncertain parameters until achieving the desired system efficiency.

During transition processes from an existing system to a desired final stage, changes in the system's structure and function occur. Cities and their water infrastructure are changing over time (e.g. network growth) and lately sustainable decentralized water treatment measures (e.g. LID controls) are becoming more popular (Sitzenfrei et al. 2013). Usually, the design of water infrastructure systems corresponds to a single design stage, describing a baseline scenario at the end of an assumed life-cycle and using state-of-the-art guidelines. However, for engineers and primarily for the main stakeholders like responsible public (or private) bodies, users and citizens, an efficient and safe operation at all stages of a system transition is crucial. Previous studies mostly focused on the topics of network transitioning and phasing of construction, however with emphasis on water distribution systems (Sempewo 2012; Creaco et al. 2013). Here we combine the topics of phasing of construction and IG robustness analysis in the transition of urban drainage systems for the first time.

In this work we consider the dynamics of changing drainage systems by investigating discrete intermediate stages between the existing and final systems. Originally, the system is designed for final stage; however a re-design is considered at the intermediate stages in case a required performance is not fulfilled. Furthermore, the assessment of different planning alternatives (strategies) of future stormwater handling, comparing traditional approaches of gray infrastructure with new hybrid concepts including green/blue infrastructures, is addressed. Beyond the synthetic design rainfalls used for design purpose, real rain events are applied to investigate hydraulic, ecologic and economic performance indicators. In addition, the IG robustness analysis is applied to all stages of the system transition, aiming to support engineers and decision makers in planning and operating the systems. The investigations are based on a case study in Sweden where a huge city-scale transformation occurs during the upcoming decades. Major parts of the current town, including its entire infrastructure, have to be relocated and therefore this highly defined city relocation is well suited to present our methodology (Leonhardt et al. 2015).

For the system design a suitable level of spatial implementation of LID structures is to be pursued. It is assumed to start from a completely pipe-based system stage and transition to a desired future stage by integrating different LID structures. In this work, three strategies (planning alternatives) are systematically compared for this transitioning. Strategy 1 follows a traditional approach of solely underground piped infrastructure. In Strategy 2 and Strategy 3 LID structures are stepwise implemented at suitable and desired sites within the existing new city framework. In Strategy 2, possible central retention ponds are integrated in the (adapted) city landscape, whereas in Strategy 3 decentralized structures like infiltration trenches and bio-retention cells of smaller size are distributed over the catchment areas in such an adapted city landscape. Strategy 1 is investigated for the purpose of comparing the potential planning alternatives. The two objectives for the conduit and LID design for all strategies are (1) to avoid flooding for design rain events and (2) to maximize their utilized capacity at the same time.

PI_flooding considers the normalized flooding volume, while PI_flooding,n observes the number of flooded nodes (#N_flooding) with respect to the total number of nodes (#N). In both cases a performance value of one indicates the best performance and a desired system stage.

Finally, the normalized LID overflow volume (⁠⁠) and the discharge to the receiving water Q [m³/s] are determined to assess the ecological performances. In case an LID overflow occurs (r > 0), the water is not treated in the LIDs and has a negative effect on the downstream water quality.

With this non-probabilistic method, perturbations of a given estimate (baseline scenario) are investigated and routed to the limit of system functioning and failure by reaching the so-called ‘critical reward level’ (see Figure 2(b)). This method is called the IG robustness pathway method and has the benefit of searching the robustness level â until each scenario reaches the critical reward level (Roach et al. 2016). Here, the robustness level â is defined as the normalized area that delimits sufficient system performances over different system stages (see Figure 2(c)). In general, the criteria for efficient system performances that define the critical reward levels can be any indicators and thresholds chosen by the user. The results allow for a comparison between planning alternatives (strategies), but also quantify possible adaptation strategies by determining the trade-off between the unknown factors that ensure the same performance within the same system stage (Kleidorfer et al. 2014).

In this study, variations of the surface imperviousness and future rainfall depths are used as the uncertain variables U1 and U2, respectively. The main motivation for varying the rainfall depth (changing of the design rain) is the future climate change, but it can also present a change in future design guidelines. On the other hand, a changing surface imperviousness (modelled as deviation of the baseline scenario) may originate from different developments of population, policy making or city planning. Changing the surface imperviousness is only a simple but easily applicable approach to consider city development and could be related to the changing of population densities or land use. Factors like vulnerability to flooding, available funding for infrastructure or the price of land are not considered in this analysis.

The contrasting performance criteria that define the critical reward levels are chosen with user-defined thresholds of the flooding performance PI_flooding (Formula (1)) and the utilization of the network capacity η_C (Formula (3)). While the former indicator represents a safety requirement to prevent damage caused by pluvial flooding, the latter factor can be seen as an economic indicator that prescribes a minimum utilization of the installed system capacity, assuming that higher capacities are more cost-intensive. For each system variation both performance values are determined based on Storm Water Management Model version 5.1 (SWMM5.1) simulations. With this method the robustness level can be determined for each stage of the system transition.

The Swedish design guideline defines the protection of the ecology of the receiving water by limiting the maximum outflow Q_max to 15 l/(s*ha). This value corresponds to the natural runoff for a 10-year event. The design rainfall event for the stormwater system corresponds to a 15-min block rain with a return period of 10 years (SWWA 2016).

Altogether, 15 possible future stormwater models (five time points and three strategies) were created and iteratively designed with the hydrodynamic software SWMM5.1 (Rossman 2010), by following the baseline scenario that defines the expected impervious area. The system design was based on Austrian and Swedish state-of-the-art requirements (ÖWAV 2009; SWWA 2016). First the fully constructed final stage system (year 2100) was designed. In addition, intermediate state models (years 2018, 2023, 2033 and 2050) were created on the basis of the masterplan and assessed with the performance indicator PI_flooding. In case the performance was insufficient (PI_flooding < 1) at these states, the conduit diameters were increased and assigned to the subsequent state models.

Beyond the simple hypothetical rainfalls used for design purpose, various performances of the drainage systems were investigated with real rain events recorded for this case study (IRF 2016). This allowed for the consideration of the local climate, a verification of the system design and a prediction of the system operation (Seo et al. 2015), in particular the interaction of piped network and temporal storage structures (e.g. LIDs).

In this work a multi-stage robustness analysis with IG decision theory to assess the drainage system behavior under deep uncertainty over time was shown for the first time. In this analysis perturbations of a given pathway (baseline scenario) were made at five network stages (time points) and then iteratively routed to the critical reward level, where defined performance criteria fulfilled the minimum requirements. Furthermore, it was shown how a masterplan of a phased city transformation was realized step by step with the focus on the design of different planning alternatives. The iterative multi-stage design of the new stormwater system was well suited when planning the expansion of the stormwater system (e.g. city growth) and ensured sufficient performances at every time point. The obtained IG-robustness models allowed for the determination of two-dimensional uncertainty regions, where future pathways will be satisfactory in terms of the predefined minimum required system performances. The ‘expected’ pathway of the baseline scenario was within the efficient performance region in all cases, which proves an appropriate system design during the phased network growth.

One limitation of the presented work is that the uncertain space was abstracted by two-dimensionality. This simplified approach could be extended to a high-dimensional parameter space comprising a redefinition of the robustness levels (efficient volumes). A possible third parameter with regard to green/blue infrastructure implementation could be the integration of additional surface storage (LIDs) to reach the desired performance levels. In this case the presented ecological indicators would represent useful performance criteria. A more efficient sampling method when applying this method for a high-dimensional parameter space should be considered. Furthermore, the assessment of the robust area considers all parameter combinations with the same probability, regardless of the ‘distance’ to the ‘most likely’ baseline scenario. In a further study a weighting of the efficient area could be investigated, for example with a normal distributed probability of the events around the baseline scenario. For further investigations or the application to other case studies, the sensitivity of different performance indicators and their thresholds (critical performance levels) should be addressed.

Future work will also emphasize the integration of different future pathways in the IG robustness models. By taking into account political, socio-economic, climate, population and wildcard scenarios, the city development and its influence on the system robustness will be considered in a broader context. This could, for example, include ‘adoption-curves’ of additional green/blue infrastructure implementation. Furthermore, this study builds the basis for a cost-benefit analysis of the different planning alternatives also taking into account the multiple benefits of green/blue infrastructures for future city developments.

The JPI Urban Europe project ‘Green/Blue Infrastructure for Sustainable, Attractive Cities’ is jointly funded by FFG – Austrian Research Promotion Agency (project 839743), The Netherlands Organization for Scientific Research (NWO), the Swedish Research Council Formas and the Swedish Government Agency for Innovation (VINNOVA).