A. Monster adaptation: Aleatory uncertainty and the design flood concept

Although direct, systematic observations of precipitation and river flows have been made in some places since at least the 17th century (Deming, Reference Deming2021), it was the development of mathematical theory about the statistics of extremes that enabled a coherent, quantitative approach to flood risk analysis. In the United States, Dawdy et al. (Reference Dawdy, Griffis and Gupta2012)) reported that statistical analysis of flooding started with Fuller (Reference Fuller1914), who advocated that “study of their [floods] past frequency gives the best indication of what may be expected in the future” (although Robert Horton had applied probability analysis to plot flood data on logarithmic paper since 1896).

By the mid-20th century, the theoretical foundations for probabilistic analysis of flooding were growing stronger with pioneering work by Gumbel (Reference Gumbel1958) on extreme value theory, which included analysis of “the design flood,” amongst other applications in climatology, meteorology and hydrology.

Aided by extreme value theory, the concept of a statistical design flood effectively internalized aleatory uncertainty by simplifying the flood-protection decision problem to one of selecting an appropriate tail quantile of the flood distribution to reflect a chosen tolerance of risk. This internalization has proven to be a lasting and important form of monster adaptation, even though some did object to it, exemplified by T. Merriman’s statement in the 1926 Transactions of the American Society of Civil Engineers that flooding could not be “fairly treated by any method of probabilities” (Dawdy et al., Reference Dawdy, Griffis and Gupta2012), arguably a case of determinism leading to monster exorcism.

By the late 1960s and early 1970s, statistical analysis of river flow extremes was an established tool for hydrologists and engineers. Even so, hydrologists were aware of epistemic uncertainties, with the choice of statistical distribution being both an important practical question and a lively topic of research ever since (Benson, Reference Benson1968; Bobée et al., Reference Bobée, Cavadias, Ashkar, Bernier and Rasmussen1993; Vogel et al., Reference Vogel, McMahon and Francis1993a, Reference Vogel, Thomas and McMahon1993b; Kochanek et al., Reference Kochanek, Renard, Arnaud, Aubert, Lang, Cipriani and Sauquet2014). In a global meta-review by Diaconu et al. (Reference Diaconu, Costache and Popa2021)), 20% of 1,326 research papers about flood risk analysis methodology published between 1979 and 2020 concerned statistical analysis. Detailed guidance emerged for practical applications in which choices about statistical distributions and procedures for assessing data adequacy were considered (NERC, 1975; Institute of Hydrology, 1999; Ball et al., Reference Ball, Babister, Nathan, Weeks, Weinmann, Retallick and Testoni2019; England Jr et al., Reference England, Cohn, Faber, Stedinger, Thomas, Veilleux, Kiang and Mason2019). In Europe, Castellarin et al. (Reference Castellarin, Kohnova, Gaal, Fleig, Salinas, Toumazis, Kjeldsen and Macdonald2012) found that public agencies and institutions of six countries provide guidance about statistical distributions suitable for flood hydrology, while national statistical analyses of flood peaks exist in 12 of the 18 countries surveyed.

Deterministic models of flood hydrology have been used in estimating design floods since at least the development of unit hydrograph theory (Sherman, Reference Sherman1932; Clark, Reference Clark1945; Dooge, Reference Dooge1973). Eagleson (Reference Eagleson1972) showed how aleatory uncertainty about rainfall extremes, embedded in a statistical model, could be integrated analytically with a deterministic model of rainfall–runoff dynamics to derive a flood peak flow distribution. In our monster analogy, this physically motivated reasoning can be interpreted as an attempt to address epistemic uncertainty about the representation of complex hydrological processes that may have otherwise been ignored (monster denial). Subsequently, many combinations of stochastic weather models and deterministic hydrological system models have been proposed or applied to support flood risk analysis (Boughton and Droop, Reference Boughton and Droop2003; Lamb, Reference Lamb and Anderson2006). Primary motivations for the rainfall–runoff approaches were to incorporate knowledge about hydrological processes into design flood estimation (Lamb et al., Reference Lamb, Faulkner, Wass and Cameron2016), and to take advantage of both river flow data and precipitation measurements, which can be longer and spatially denser. Aleatory uncertainty in the rainfall or river flow data remained the dominant guise of the uncertainty monster, with the target remaining a design event.

B. Monster assimilation: Recognition of epistemic uncertainties in flood hydrology

The introduction of process-based modeling to derive design flows was at first motivated by a desire to reduce uncertainty by applying deterministic understanding of processes to add information in deriving a design flood. Yet opening the door to physical processes inevitably exposes the decision analysis to complexities of the real world, where it is difficult to find simple adaptations to uncertainty monsters. In flood management, and across other natural hazards, there has been an increasing focus on the epistemic uncertainties, which are not well-determined by historical observations (Beven et al., Reference Beven, Almeida, Aspinall, Bates, Blazkova, Borgomeo, Freer, Goda, Hall, Phillips, Simpson, Smith, Stephenson, Wagener, Watson and Wilkins2018). Where the uncertainties can be expressed in terms of input factors or choices made in applying a model, then sensitivity analysis is a powerful tool to structure and quantify a wide range of sources of uncertainty (Pianosi et al., Reference Pianosi, Beven, Freer, Hall, Rougier, Stephenson and Wagener2016; Gupta and Razavi, Reference Gupta and Razavi2018; Wagener and Pianosi, Reference Wagener and Pianosi2019; Pianosi et al., Reference Pianosi, Sarrazin and Wagener2020).

Quantification is difficult, or may be impossible, for deep epistemic uncertainties (Stein and Stein, Reference Stein and Stein2013), so the uncertainty monster appears in guises that are not amenable to monster adaptation. Instead, we try to assimilate those monsters to avoid the pathological states of embracement, exorcism, denial or anesthesia. Environmental or socioeconomic change is often the dominant uncertainty for long-term FRM planning. A typical paradigm for assimilating such deep uncertainty monsters is to use scenario-based analysis (Hallegatte et al., Reference Hallegatte, Shah, Lempert, Brown and Gill2012), an approach formalized for national FRM investment planning in England by the Environment Agency (2021b). Future projections of risk are needed for scenario-based decision analysis, but growing evidence of historical changes in flooding (Blöschl et al., Reference Blöschl, Hall, Viglione, Rui, Parajka, Merz, Lun, Arheimer, Aronica, Bilibashi, Boháč, Bonacci, Borga, Čanjevac, Castellarin, Chirico, Claps, Frolova, Ganora, Gorbachova, Gül, Hannaford, Harrigan, Kireeva, Kiss, Kjeldsen, Kohnová, Koskela, Ledvinka, Macdonald, Mavrova-Guirguinova, Mediero, Merz, Molnar, Montanari, Murphy, Osuch, Ovcharuk, Radevski, Salinas, Sauquet, Šraj, Szolgay, Volpi, Wilson, Zaimi and Živković2019; Environment Agency, 2020; Hannaford et al., Reference Hannaford, Mastrantonas, Vesuviano and Turner2021; Slater et al., Reference Slater, Villarini, Archfield, Faulkner, Lamb, Khouakhi and Yin2021) has also challenged the assumption of stationarity that has been inherent in most statistical flood models. Practical guidance on the incorporation of nonstationary extreme value analysis is now appearing for flood analysts (US Army Corps of Engineers, 2018; Ryberg et al., Reference Ryberg, Kolars, Kiang and Carr2020; Environment Agency, 2021a), enabling uncertainty relating to the choice of an appropriate baseline to be quantified within a decision analysis.

For example, in JBA Consulting (2022) (Section 6), a decision analyst’s choice between adopting a stationary or nonstationary model for river flow extremes was framed as an epistemic uncertainty in the design of an idealized flood management scheme. The implications were investigated by assessing the sensitivity of the scheme design to this choice between models, using a method outlined in Figure 2, adapted from Rehan (Reference Rehan2016) and Rehan and Hall (Reference Rehan and Hall2016). Context was provided by basing the idealized case on a real flood management scheme, and adding a comparison with a second source of epistemic uncertainty, represented by contamination of the gauged flow data with hydrometric measurement errors that were introduced artificially for the purposes of the experiment. The three possible inputs are plotted in Figure 3. The models adopted for the flood peaks were generalized logistic distributions, which are widely used in U.K. flood hydrology. Sensitivity of the design with respect to these input choices was studied by simulating an FRM economic appraisal to minimize the total present value cost with respect to the design height of the scheme’s flood defense. Monte Carlo simulation (MCS) was used to account for sampling uncertainty about the flood peak distribution for comparison with the epistemic uncertainties.

Figure 2. Schematic of flood risk management (FRM) decision simulation by JBA Consulting (2022). Economic relationships for the scheme costs and flood damages are combined with models for the extreme value distribution of peak river flows and the hydraulic model outputs relating flows and flood depths. The choice between a stationary or a nonstationary flood peak model is represented as an epistemic uncertainty, as is the effect of artificially introducing errors to the gauged flows. Parameters of the peak flow model are sampled randomly in a Monte Carlo simulation to allow the epistemic uncertainties to be compared with aleatory uncertainty related to the sampling of the gauged flows.

Figure 3. Inputs to the flood risk management (FRM) decision simulation shown in Figure 2 as epistemic uncertainties. The curves are generalized logistic distributions, which are adopted as extreme value models for the peak flows. The choices available to the analyst are a stationary model fitted to gauged peak flows, a stationary model fitted after errors were added to the gauged flow data, and a nonstationary model fitted to gauged flows (evaluated for 2016, taken to be the year of the decision analysis).

Results of the simulation in Figure 4 show that the adoption of a nonstationary model for the flood peak distribution would make a substantial difference to the idealized scheme design. This impact was larger than the effect of the second counterfactual case, in which errors were added to the peak flow data as a confounding uncertainty, and distinguishable from the sampling uncertainty as indicated by the interquartile range obtained by MCS.

Figure 4. Results of the flood risk management (FRM) decision simulation outlined in Figure 2, showing the economically optimum defense height, with uncertainties estimated by drawing 1,000 samples from the covariance matrices of generalized logistic distribution parameters fitted to the peak river flows. Panels show the results for different combinations of input factors. Comparison of panels (a) and (b) reveals epistemic uncertainty about the choice between a stationary and nonstationary model for the peak flows. Panel (c) simulates the effect of adding data errors to the stationary model for comparison. Plotted using R v4.2.0 boxplot function with default options: shaded boxes represent interquartile range (IQR), interior thick line is median, interior dot is mean, open circles are outliers and whiskers extend to a maximum of 1.5xIQR beyond the box (see function documentation for further details and Krzywinski and Altman, Reference Krzywinski and Altman2014 for interpretation).

Statistical models applied routinely in U.K. flood management practice have usually been predicated on stationarity assumptions. However, recent guidance (Environment Agency, 2021a) describes situations in which a nonstationary model may be preferred to inform the planning and economic appraisal of FRM schemes. The guidance requires analysts to apply judgment after taking account of different analytical approaches, which raises a need for the type of epistemic uncertainty assimilation that is illustrated in the case study.

Similar uncertainties arise in the context of land use change. This is both a historical issue, in terms of its influence on observed flood data, and an uncertainty in evaluating future flood management actions that involve nature-based solutions (NBS, also called working with natural processes, and including NFM). With rapidly growing interest worldwide in the potential of NBS to deliver multiple co-benefits (Iacob et al., Reference Iacob, Rowan, Brown and Ellis2014; Seddon et al., Reference Seddon, Chausson, Berry, Cécile, Smith and Turner2020), uncertainties about the effects of land management changes on flooding have received considerable attention (Dadson et al., Reference Dadson, Hall, Murgatroyd, Acreman, Bates, Beven, Heathwaite, Holden, Holman, Lane, O’Connell, Penning-Rowsell, Reynard, Sear, Thorne and Wilby2017; Lane, Reference Lane2017; Möller, Reference Möller2019; Ellis et al., Reference Ellis, Anderson and Brazier2021). Some modeling studies have attempted to capture uncertainties about land use changes through conditional probabilistic approaches to the inference of shifts in the parameters of deterministic models (Hankin et al., Reference Hankin, Trevor, Chappell, Beven, Smith, Kretzschmar and Lamb2021; Beven et al., Reference Beven, Page, Hankin, Smith, Kretzschmar, Mindham and Chappell2022), although there may be residual risks associated with some systems of NBS (Hankin et al., Reference Hankin, Hewitt, Sander, Danieli, Formetta, Kamilova, Kretzschmar, Kiradjiev, Wong, Pegler and Lamb2020). Controversy about the effectiveness of NBS for FRM (Ellis et al., Reference Ellis, Anderson and Brazier2021) can also be rooted in uncertainties, a form of monster embracement such as that documented by Turnhout et al. (Reference Turnhout, Hisschemöller and Eijsackers2008) in two controversies regarding cockle fisheries and gas mining in the Wadden Sea (an estuarine area with high ecological potential), where scientific uncertainties were exploited by competing stakeholders to undermine each other’s claims.

When confronted with deep uncertainties and knowledge controversies, one strategy that may help to navigate a path from pathological monster coping strategies toward assimilation is expert elicitation. Structured, performance-weighted elicitation has been shown in many applications to add decision- or policy-relevant information (Colson and Cooke, Reference Colson and Cooke2018). Good elicitation practice requires skill, resources and care; it is not a low-cost alternative to research or analysis (Morgan, Reference Morgan2014), and can surface meta-uncertainties related to cognitive biases (Morgan, Reference Morgan2014) or methodological choices (Clemen, Reference Clemen2008). By conditioning expert judgments against calibration questions (for which uncertainty ranges are known objectively) and pooling multiple expert views, it is possible to obtain probabilistic statements from an elicitation (Aspinall and Cooke, Reference Aspinall, Cooke, Rougier, Hill and Sparks2013). In the case of scour damage to bridges caused by river flooding, Lamb et al. (Reference Lamb, Aspinall, Odbert and Wagener2017) demonstrated an elicitation approach to deriving scour failure probabilities (similar to the uncertain failure probabilities in our case study in Section 5C) by applying the method of Cooke (Reference Cooke1991).

C. Monster assimilation and adaptation: Fluvial flood-mitigation case study

We introduce a mock or hypothetical flood-mitigation study on pluvial or surface flooding in a local neighborhood to highlight decision-making challenges in FRM. The study fits in the middle of the monster-metaphor schematic of Figure 1, as it is of intermediate complexity but some uncertainties are difficult to quantify. It is inspired by an actual case. The study will employ a graphical cost-effectiveness tool, see Bokhove et al. (Reference Bokhove, Kelmanson, Kent, Piton and Tacnet2019) and Bokhove (Reference Bokhove2021), which has successfully engaged decision-makers in France and Slovenia (see Piton et al., Reference Piton, Dupire, Arnaud, Mas, Marchal, Moncoulon, Curt and Tacnet2018a, Reference Piton, Pagano, Basile, Cokan and Lesjak2018b; Bokhove et al., Reference Bokhove, Hicks, Kent and Kelmanson2021; Bokhove et al., Reference Bokhove, Kelmanson, Piton and Tacnet2024). First, fluvial flooding of the neighborhood can be caused by the adjacent river and the outflow of the stream or brook “High Beck” into that river is closed off at higher river levels. Newly built flood walls aim to protect against fluvial events with return periods of $ 1:200\mathrm{yrs} $ . Second, High Beck has caused intermittent pluvial or surface flooding for decades, regarding beck-flooding events with return periods of $ 1:10\mathrm{yrs} $ or higher. To avoid increased surface flooding when the beck cannot flow into the river, a pump with a maximum rate of Q_T = 0.245 m³/s has been installed. Hence, without further interventions, the intermittent surface-flooding events remain. The stream or beck has a length of circa 2,000 m with a drop of circa 100 m. Upstream of the outflow into the river, the beck passes under a canal in a nearly horizontal 200 m-long culvert passing under playing fields to the river, which culvert floods the neighborhood in extreme beck events. The relevant canal segment has a large size of 7.5 km × 10 m × 1.5 km with several overflow weirs to the river.

The council is exploring flood-mitigation measures against the surface flooding, as follows:

Measures B2 and FP3 offer insufficient protection in separation against the design flood but five permissible scenarios: C1, B2+FP3, B2+C1, FP3+C1 and B2+FP3+C1, do offer protection against 150 years return-period beck floods modeled using intense 3 h rainfall events. Except when C1 is fully used, scenarios with outflow into the river do require prolonged pumping of beck flood waters over the flood-defense wall into the river, for up to 10 h.

The following monster risks emerge:

Costs $ {q}_1,{q}_2,{q}_3 $ are known. Probabilities $ {p}_1,{p}_2,{p}_3 $ and costs $ {q}_{p_1},{q}_{p_2},{q}_{p_3} $ over the entire 25 years write-off period were unknown a priori but have been estimated through expert elicitation, a scientific consensus methodology (Aspinall and Cooke, Reference Aspinall, Cooke, Rougier, Hill and Sparks2013).

For a design-flood event with a $ 1:50\mathrm{yrs} $ return period or an annual event probability of $ 2\% $ the beck’s flood hydrograph is shown in Figure 5. Flooding occurs for discharges above the threshold $ {Q}_T $ . The flood-excess-volume (FEV) responsible for the flood damage is then the time-integrated discharge excess $ Q\left(\mathrm{t}\right)-{Q}_T $ over time $ t $ , with the event starting at $ t={t}_0 $ and ending at $ t={t}_0+T $ :

(1) $$ FEV={\int}_{t_0}^{t_0+T}\left(Q(t)-{Q}_T\right)\;\mathrm{d}t\approx 9600{\mathrm{m}}^3\approx 98\mathrm{m}\hskip0.24em \times 98\mathrm{m} \times 1\mathrm{m}, $$

reexpressed as a (dynamic) square lake of 1 m depth. This High-Beck FEV-lake is large, given the size of the neighborhood. Displaying FEV as a 1 m-deep lake therefore adds a sense of size to a flooding event, with 1 m being (half) a human-size scale.

Figure 5. Hydrograph of a simulated 150 years return-period design flood-event of High Beck, displaying discharge $ Q(t) $ versus time $ t $ with $ 5\% $ error bars indicated as dotted lines. The integrated discharge above the flooding threshold $ {Q}_T=0.245{\mathrm{m}}^3/\mathrm{s} $ constitutes the flood-excess volume, here $ FEV\approx 9600{\mathrm{m}}^3 $ , causing the flood damage.

Base costs $ {q}_1,{q}_2,{q}_3 $ concern basic construction, occurring with probability one. Monster failure or poorly quantified costs concern costs $ {p}_1{q}_{p_1},{p}_2{q}_{p_2},{p}_3{q}_{p_3} $ with the probabilities including adverse monstrous climate-change effects. Each option leads to overall costs, assuming the probabilities to be independent, as follows:

(2a) $$ C(anal),C1:\hskip0.72em {q}_1+{p}_1{q}_{p_1}, $$

(2b) $$ B(und)+ FP3,B2+ FP3:\hskip0.96em {q}_2+{q}_3+{p}_2{q}_{p_2}+{p}_3{q}_{p_3}, $$

(2c) $$ F(lood)P\left( lain\ storage\right)+C1, FP3+C1:\hskip0.72em {q}_3+{q}_1+{p}_3{q}_{p_3}+{p}_1{q}_{p_1}, $$

(2d) $$ B2+C1:\hskip0.72em {q}_2+{q}_1+{p}_2{q}_{p_2}+{p}_1{q}_{p_1}, $$

(2e) $$ B2+ FP3+C1:\hskip0.72em {q}_2+{q}_3+{q}_1+{p}_2{q}_{p_2}+{p}_3{q}_{p_3}+{p}_1{q}_{p_1}. $$

The five flood-mitigation scenarios each mitigate the entire FEV responsible for flood damage of the simulated $ 1:50\mathrm{yrs} $ event, which is the designated design flood. Each scenario can be graphed as a square lake viewed from above with each option $ (C1,B2, FP3 $ ) portioning the square lake, cf. Figure 6, with costs per option overlaid. Any option involving the canal $ (C1 $ ) can include additional storage against higher return-period or monster events beyond the target FEV emerging from the design flood, thus assimilating some monster events. Hitherto, the graphical cost-effectiveness tool has been used to inform decision-makers to make the available scenarios transparent, but no process has been developed to rationally and quantifiably choose between them. How do we value the monsters and fairies involved, in a just and science-based decision-making process, and choose the best one among these flood-mitigation scenarios?

Figure 6. Square-lake cost-effectiveness graphs of five flood-mitigation scenarios to prevent High Beck surface flooding for the $ 1:50\mathrm{yr} $ design flood. These involve possible combinations of storage into canal ( $ C1 $ , purple), upstream bunds ( $ B2 $ , red) and/or downstream flood-plain storage ( $ FP3 $ , green). Base costs $ {q}_1,{q}_2,{q}_3 $ plus costs with uncertainty $ {p}_1{q}_{p_1},{p}_2{q}_{p_2},{p}_3{q}_{p_3} $ have been superimposed using the double-sided arrows. Each square lake with a lateral depth of 1 m (out of the page) and side lengths of 98 m represents the FEV ( $ FEV\approx 9600{\mathrm{m}}^3\approx 98\mathrm{m}\times 98\mathrm{m}\times 1\mathrm{m} $ ) to be reduced to zero by the combinations of mitigation measures. The canal measure $ C1 $ can provide extra mitigation (as indicated) by diverting less flood water to the downstream fields, thus reducing $ FP3 $ , and some to the canal $ C1 $ . In those partial cases, uncertain costs may be lower. Diverting flood waters into the canal does not affect the upstream measure $ B2 $ .

Note that in the square graphs presented here, we have left out the uncertainties in the FEV and the flood-mitigation-measure volumes (the rectangular areas in the graphs). The latter (mitigation) uncertainties can be represented to some extent by using the vertical axis as uncertainty axis, from least to most uncertainty, leading to triangular and quadrilateral instead of rectangular shapes, cf. Bokhove et al. (Reference Bokhove, Kelmanson, Kent, Piton and Tacnet2019) and Bokhove (Reference Bokhove2021).

The above is an example of how the strategies of monster assimilation and monster adaptation can be. The decision problem has been made structured and complexity has been reduced to an unavoidable minimum level. Yet a final step has to be made: decision-makers need to be informed in a comprehensible way, to support what decisions are deemed “good.” Otherwise, new monsters of uncertainty can grow. The question is also what characteristics define “good,” that is, decisions need to be rational, cost-effective/efficient, have minimum regret and maximum political support and so forth. Furthermore, decision-makers should be supported in Bayesian decision-making, which implies that uncertainties are explicitly incorporated in the decision-making process (Morgan and Henrion, Reference Morgan and Henrion1990).

The importance of what could characterize and qualify a “good decision” in FRM can be illustrated by considering what can cause suboptimal decisions. Addressing only one dimension of flood-mitigation problems, albeit rationally, may adversely affect other aspects in that the chosen solution taken:

1. (a) may lead to new problems (e.g., loss of ecological functions) (Auerswald et al., Reference Auerswald, Moyle, Seibert and Geist2019);

2. (b) has unintended long-term consequences (e.g., a dependence on higher flood-defense walls to contain river levels for 1-in-200 years protection in a narrow channel could lead to a false sense of security, especially as return periods reduce due to climate change, causing future overtopping or breaches) (Kates et al., Reference Kates, Colten, Laska and Leatherman2006; Di Baldassarre et al., Reference Di Baldassarre, Kooy, Kemerink and Brandimarte2013a, Reference Di Baldassarre, Viglione, Carr, Linda Kuil and Blöschl2013b; Gohari et al., Reference Gohari, Eslamian, Mirchi, Abedi-Koupaei, Bavani and Madani2013); and,

3. (c) has an uneven distribution of costs and benefits when other sectors and social groups are taken into account (e.g., if optimism bias about the extrapolation of NFM benefits were to cause reduced investment in other, more predictable, flood risk mitigations for vulnerable communities) (Savelli et al., Reference Savelli, Rusca, Cloke and Di Baldassarre2021).

Morgan and Henrion (Reference Morgan and Henrion1990) comprehensively discuss decision-taking criteria in their Section 3.4. In a nutshell, which does insufficient justice to their writing: they distinguish utility-based, rights-based, technology-based and hybrid criteria. In particular, maximization of a multi-attribute utility function would address the points above. Various relevant aspects are then brought together in one utility function, without assigning monetary values to relevant aspects. While that sounds simple, an apparent drawback can be that the as-such defined function often becomes complex and difficult to understand for the decision-makers. Transparency thereon and on the general decision-process can be achieved by defining the relevant decision-criteria and associated functionality at the beginning of the process with all relevant actors, including communication experts, in order to clearly define and accept the chosen criteria. Moreover, also in FRM, it is important to make the decision-process adaptive such that it can be revisited in the future, when new technology, observational data and information become available. Most organizations might find it difficult to adopt such adaptivity, but it should be adopted as long as the process is primarily geared to focus on improved decision-making and not on assigning blame for taking past wrong or suboptimal decisions. Finally, Morgan and Henrion (Reference Morgan and Henrion1990) discuss an “approved process” as decision criterion and declare that to be a widely used approach, in which a decision is considered acceptable when a specified set of procedures is followed. They point out that the language of decision analysis is inappropriate for such a social as opposed to analysis-based process.

A graphical cost-effectiveness tool was exemplified through a hypothetical study with five flood-mitigation scenarios. Each scenario had base construction costs and potentially additional costs associated with failures of uncertain nature, and some scenarios had a co-benefit. An outstanding question is how to construct a decision-tree in order to make the best decision under such uncertainties. While the square-lake cost-effectiveness graphics has proven to be beneficial to decision-makers, see Piton et al. (Reference Piton, Dupire, Arnaud, Mas, Marchal, Moncoulon, Curt and Tacnet2018a) and Piton et al. (Reference Piton, Pagano, Basile, Cokan and Lesjak2018b), a pressing question is how to visualize and explain decision-trees such these can be understood and applied by decision-makers.

This case study falls in the middle of our schematic of FRM-challenges displayed in Figure 1, as it is of intermediate complexity with estimates of the uncertainties involved. Intuitively, it seems obvious that the optimal scenario must include the canal-storage option since the canal offers extra buffer capacity beyond the target flood-excess volume FEV. However, when it turns out that the canal option becomes (nearly) impossible, it shifts the study to the right side of the schematic where FRM is poorly-structured: for example, when a combined-sewer overflow (CSO) pollutes the beck during intermediate rainfall and a short extra CSO-pipe along part of the beck and debris filter could prevent pollution flowing into the canal and lower pollution flow into the river, the issue can become that the public council is only responsible to deal with flooding, that the nonprofit “Trust” only maintains the canal and its ecological value, that private business “The Shire” is only responsible for the sewer system and that there is no legislation to enforce effective collaboration to solve the integral water-sewer management challenge described. A case of monster anesthesia?

The decision-making bodies on FRM can have highly different levels of expertise. In the Netherlands, for example, (fluvial and pluvial) FRM is channeled to a large extent through so-called waterboards or “Waterschappen,” which boards contain elected people who are exclusively focusing on decisions in water management. Perhaps in contrast, in the UK, FRM decisions span a range of organizations with differing responsibilities (Finlay and Bolton, Reference Finlay and Bolton2022), sometimes working independently, but often in partnership, and involving people with range of expertise and interests. Consequently, equipping decision-making bodies with adequate (visualization) tools to be engaged in a meaningful way with FRM will be a different task depending on the situation.