Evaluating Adaptation Pathways in a Complex Multi‐Risk System

Disaster Risk Management (DRM) is complex due to interacting climate risks from interacting hazards and sectors. We develop a synthetic multi‐risk test case to explore the effects of these interactions on decision‐making under deep uncertainty. The test case accounts for changes in hazard impacts and occurrence frequency due to interactions between floods and droughts. Interactions between the shipping, housing and agricultural sectors are considered as well. We use this test case to explore the utility of the Dynamic Adaptive Policy Pathways for Multi‐Risk (DAPP‐MR) framework. DAPP‐MR has been introduced to assess DRM policies' effectiveness under deep uncertainties and to develop integrated adaptive strategies considering interactions across hazards, sectors and time. With the test case, we show that the stage‐wise approach of DAPP‐MR, which gradually increases the complexity of the analysis, can facilitate the evaluation process. Earlier stages of the analysis can be used to establish the direct cause‐effect relations, later stages allow us to identify whether additional interacting factors have a significant effect on the direct cause‐effect relations. As a result, decision‐makers can gain insights into dependencies and their relevance for developing short‐to long‐term strategies under deep uncertainty. We show that multi‐risk interactions can lead to non‐linear effects that influence the outcome of the policy analysis, for example, the indirect influence of a decision in one sector on another. Future work could investigate further improving the operationalization of this staged approach as well as extending the set of uncertainties, dynamics and decision‐rules accounted for in the multi‐risk test case.


Introduction
Research on climate adaptation and disaster risk management (DRM) has traditionally examined risks associated with either flooding or drought in isolation (Rashid & Wahl, 2022).Yet, there is a growing understanding that droughts and floods can intersect, especially when they overlap spatially or temporally (Claassen et al., 2023;Gill & Malamud, 2014;Zscheischler et al., 2020).Thus a multi-risk approach that accounts for interactions across hazards and sectors is necessary (Simpson et al., 2021;United Nations Office for Disaster Risk Reduction, 2017;Zschau, 2017).Multiple studies have indicated that these so-called multi-hazard interactions differ from the sum of their individual effects (de Ruiter et al., 2020;Rashid & Wahl, 2022).Moreover, risk reduction efforts targeting one specific hazard can inadvertently exacerbate risks associated with another or have other trade-offs when considering multiple objectives.A striking example of multi-hazard interaction occurred in California between 2012 and 2016 when a prolonged drought had significant direct and indirect impacts across various sectors (Lund et al., 2018).This drought was subsequently followed by heavy rainfall, leading to dike breaches and severe flooding in February 2017 (Wang et al., 2020).In the semi-arid regions of Iran, efforts to deal with droughts resulted in over-extraction of groundwater, subsequently inducing sinkholes and land subsidence, clearly exemplifying DRM strategies with strong trade-off effects (Loghmani Khouzani et al., 2022).To identify effective DRM measures, it is crucial to consider interactions between multiple hazards, multi-dimensional vulnerability and implemented risk reduction measures (de Ruiter & van Loon, 2022;Simpson et al., 2021;Stolte et al., 2022).
Additionally, DRM measures, such as the installation of dike systems or the use of groundwater for irrigation, are intended to serve their purpose for multiple years or even decades.Over these timescales, evolving socioeconomic systems and the uncertainties of climate change influence the frequency and intensity of compounding and consecutive events (IPCC, 2022;McEvoy et al., 2021;Reed et al., 2022), as well as exposure and vulnerability, ultimately determining the service lifetime of these measures (Haasnoot et al., 2013).
At this point in time, most DRM practice often fall short of encapsulating these multifaceted dynamics (Arribas et al., 2022;Hochrainer-Stigler et al., 2023;Poljansek et al., 2021;Ward et al., 2022).Schlumberger et al. (2022) sought to bridge this gap by tailoring the Dynamic Adaptive Policy Pathways framework (DAPP) (DAPP, Haasnoot et al., 2013) for multi-risk systems.The primary purpose of the DAPP approach is to support the design of an adaptive plan consisting of robust and flexible short-term actions and potential long-term options to further adapt depending on how the future unfolds.The method explores alternative sequences of measures (pathways) under a wide range of uncertain future scenarios.DAPP has been previously applied for flood or drought risk management (Haasnoot et al., 2014;Lawrence & Haasnoot, 2017;Totin et al., 2021;Vizinho et al., 2021).By adopting a long-term planning perspective, DAPP can help decision-makers avoid maladaptation and lock-in situations in dynamic systems (Werners et al., 2021).However, the original DAPP approach does not address multi-risk dynamics.In contrast, the tailored version, called DAPP-MR (DAPP for Multi-Risk), accounts for interactions across sectors and hazards and respective path-dependence (Hanger-Kopp et al., 2022;Thaler et al., 2023), fostering the formulation and assessment of comprehensive DRM strategies in multi-risk settings.
So far, no use cases are available that provide evidence regarding the utility of DAPP-MR.In this study, we address this gap by applying DAPP-MR to develop and evaluate pathways in a synthetic multi-risk test case.We employ a model-based approach to investigate how multi-hazard and multi-sectoral interactions affect the flexibility and robustness of DRM strategies.Exploring the implications of interactions in complex systems for DRM decision-making, this paper provides insights into the benefits and limitations of the DAPP-MR approach.As a multi-risk test case, we build on the existing "Waas" test case, based on a river stretch in the Netherlands, adding interaction effects of floods and droughts as well as their impacts on different sectors.
The remainder of the paper is structured as follows: Section 2 presents the multi-risk test case.Section 3 elaborates on the methodology of applying DAPP-MR to the test case to develop and evaluate pathways.Section 4 presents the results of the modeling experiment.Section 5 discusses these results and Section 6 provides a summary and outlook for future work.

The Multi-Risk Test Case
The multi-risk test case, called Waas-MR, builds on the existing synthetic "Waas" case, as described by Haasnoot et al. (2012), which has previously been used to test water management strategies under long-term climate change scenarios (Haasnoot et al., 2012;Jafino et al., 2019;Kwakkel et al., 2015;Manocha & Babovic, 2016).We have modified the Waas test case to include dependencies across the considered sectors (shipping, agriculture, urban housing), DRM measures (see Section 2.1) and multiple hazards (see Section 2.2).The modeling framework for the test case is introduced in Section 2.3.In the test case, sectors seek to identify sequences of DRM measures (referred to as "DRM pathways") to keep future risks at bay.All sectors face vulnerabilities to future floods and/or droughts exacerbated in intensity and frequency by climate change.
We conceptualized the test case using the Drivers-Pressure-State-Impact-Response (DPSIR) framework (Smeets & Weterings, 1999) as shown in Figure 1.We define Drivers as external causes (e.g., climate change, food price development,…) that underlie change of a system away or toward certain targets; Pressures as the direct consequence that force the change; State as the system's condition and dynamics; Impact as observable changes in the system conditions and dynamics cause by the pressures; and Response as the societal decisions to adapt to the changes or address pressure or impacts (Ness et al., 2010;Zare et al., 2019).

Multiple Sectors and Their Dependencies
Most interactions between sectors occur through the interplay of different sectoral DRM measures.For instance, flood damages experienced by the urban sector may vary depending on whether the agricultural sector implements measures that reduce crop vulnerability or measures that reduce exposure, such as heightening dikes.Additionally, one direct dependency between the agricultural and the urban sector is taken into account: residents purchase local crops (which are slightly more expensive than imported ones) only if they have not experienced flood impacts in the past year.A flood event makes residents acutely aware of their financial risks, leading them to adjust their lifestyle by reducing expenses.As a consequence, the agricultural sector sees a decrease in local sales compared to undisturbed conditions for a year following a flood, resulting in reduced revenue.Although this specific behavior is not extensively discussed in literature, the significant financial burden of home repairs and related financial concerns about future flood events are well-documented (Aerts et al., 2018;Twiddy et al., 2022).
These and additional unique vulnerabilities and dependencies of each sector and their available DRM measures are summarized in Table 1 in the Waas-MR test case.In the Waas region, each sector aims to effectively manage climate risks by implementing sequences of DRM measures (referred to as "DRM pathways") over 100 years.Some of these measures are influenced by specific multi-hazard or multi-sector interactions (see Table S1 to S8 in Supporting Information S1).The goal of each sector is to maximize risk reduction while minimizing implementation and maintenance costs over this period.Risk reduction is measured by the extent of experienced drought/flood-related damages: structural damages in the urban sector due to flooding, increased transport costs in the shipping sector due to droughts and in the agricultural sector, structural damages (due to flooding) and crop losses (due to flooding or drought impacts).Consequently, the urban and shipping sectors have two DRM objectives, while the agricultural sector has three.

Multi-Hazard Interactions and Impacts
Three types of multi-hazard interactions are incorporated in this test case (see Text S1 to S4 in Supporting Information S1 for further details): 1. Co-occurring or preceding droughts can amplify flood damages in the agricultural sector.This amplification occurs due to increased exposure and vulnerability from low soil infiltration capacities, prolonging crop inundation.This waterlogging exacerbates stress on crops already suffering from other water-related extremes (Bin Rahman & Zhang, 2022;Kaur et al., 2017;Lombardi & Davis, 2023;Luo et al., 2008;Rivero et al., 2022).2. Preceding droughts can also increase the probability of floods.This happens as drought affects the stability of dikes through reduced soil moisture, leading to changes in soil structure and weight (Bezuijen et al., 2005;Bottema et al., 2021;van Vliet et al., 2017).3. Consecutive flood events can influence the uptake of DRM in the residential sector.Immediately after a flood, risk perceptions are heightened, leading to increased DRM investments to protect buildings.However, a few years post-flood, risk perceptions decrease, resulting in reduced DRM activities (Barendrecht et al., 2019;Collenteur et al., 2015;de Ruiter et al., 2020;Köhler et al., 2023).

The Modeling Framework for Waas-MR
Figure 2 presents a simplified representation of the integrated assessment meta-model (IAMM, Giupponi et al., 2013;Saeki, 1998) for the Waas-MR test case.The Waas-MR IAMM simulates various parameters at a

Methodology
We test the DAPP-MR analytical framework for the development and evaluation of potential pathways using the multi-risk Waas-MR test case.Figure 3 (left) presents the steps of DAPP-MR.It follows the same steps as the original DAPP (Haasnoot et al., 2013) to (a) define the decision boundaries defining sectors of interest and relevant uncertainties, (b) identify sources of vulnerability subject to these uncertainties and (c) identify possible DRM measures that can mitigate these vulnerabilities enabling users to 4) ultimately develop and evaluate robust and flexible pathways, comprised of sequences of measures over the planning horizon.Building beyond DAPP, DAPP-MR follows three stages of analysis (first stage: siloed, no interactions across hazards or sectors; second stage: multi-hazard, interactions across hazards; third stage: multi-risk, interactions across hazards and sectors) and includes interactions across hazards and sectors step-by-step.The first three steps of DAPP-MR were used to develop the multi-risk test case as presented in Section 2. Guiding questions as provided in the Supplemental Material of Schlumberger et al. (2022) were used.
In this study, we focus on step 4 of DAPP-MR, as visualized in Figure 3 (right).To illustrate, we describe the development and evaluation of flood risk management pathways for the agricultural sector.Stage 1 represents "siloed single hazard/single sector."In stage 2, "multi-hazard," we develop flood risk management pathways tailored to flood-drought interactions and the simultaneous presence of drought risk management measures.In stage 3, "multi-risk," we consider all multi-risk interactions, thus identifying flood risk management pathways that address both flood-drought interactions and the effects of management measures from other sectors on floods and droughts.We conduct three activities in each stage: (a) select measures from a list to identify potential pathways, (b) stress-test these pathways using the Waas-MR model and (c) evaluate the pathways using robustness and interactions indicators.Consequently, a set of promising pathways is identified for each stage.
To identify these promising pathways, per stage st, we are searching for the pathways p * st within the set of all pathways P st that minimize the evaluation function F p .In practical terms, we are looking for the pathways that yield the lowest DRM cost ( f cost ), highest crop loss reduction ( f CLR ) and highest structural damage reduction ( f SDR ) at the end of the planning horizon of 100 years and across multiple uncertainties.For the agricultural sector A and its associated flood DRM F, the evaluation function can thus be formalized as follows: with Earth's Future 10.1029/2023EF004288 SCHLUMBERGER ET AL.
where f i is defined as a robustness indicator assessing a pathway's performance by means of the set of all outcomes Y i (p) for objective i for a given pathway p over all uncertainty realizations t, with better performance corresponding to higher risk reduction effects and lower costs.
The outcome y i (p, t) for a given objective i, pathway and uncertainty realization is furthermore determined by a set of decision rules D and the state of the system σ It is important to note that σ is defined differently depending on the stage of analysis.In stage 1, the system state is influenced by the agricultural sector and the flood DRM measures (A,F).In stage 2, it is also influenced by the drought DRM measures of the same sector (A,D) and in stage 3 also by all sectors and the respective hazards (Urban, Flooding and Shipping Drought): Other pathways evaluation studies with many options have used multi-objective optimization algorithms to solve similar evaluation problems (e.g., Gold et al., 2022;Kwakkel et al., 2015Kwakkel et al., , 2016)).In this study, only a limited number of pathways options need to be assessed (see Section 3.2).Thus, the evaluation problem will be addressed by means of visualizations.
In addition, we analyze the interaction between pathways using an interdependency parameter IA in stages 2 and 3.This parameter evaluates how the risk reduction effect of pathway a for one sector changes when another sector b implements either pathway c compared to when sector b does not implement any measures (b = 0).Values less than 1 indicate trade-offs, while values greater than 1 indicate synergistic effects.The interdependency parameter is calculated as follows: Here, f i,a|b is the robustness indicator for objective i of pathway a given the implementation of pathway b.

The Set of Decision-Rules D
We assume a sector implements up to four measures across the 100-year horizon, with a minimum 10-year interval between each measure of a given pathway.These measures influence the physical processes in the model and reduce hazard impacts following implementation.A sector implements new measures when an Adaptation Tipping Point (ATP) is surpassed (Kwadijk et al., 2010).For flood risk management, the agricultural sector implements a new measure if losses within a year (sum of crop and structural damages) exceed EUR 30 million or if the expected annual losses in a 15-year moving period surpass EUR 7 million (see Table S13 in Supporting Information S1 for all ATP definitions for the different sectors and hazards).The Waas-MR IAMM applies these decision-rules at the end of each year to determine whether to implement the next measure from a potential pathway.An example is shown in Figure S5 in Supporting Information S1.

The Sets of Pathways P st
DRM measures for each sector and hazard are used to create potential pathways, utilizing a storyline approach (Shepherd et al., 2018).We identify various potential pathways that either (a) initially rely on costly, structural Earth's Future 10.1029/2023EF004288 SCHLUMBERGER ET AL.
measures, followed by smaller additional measures, (b) interchangeably implement large, structural measures and smaller ones or (c) begin with smaller, less expensive options, adding more costly measures later in the planning horizon.As a result, 9 to 15 potential pathways are identified for each sector to manage a specific hazard risk.
For illustration, Figure 4 lists all potential DRM pathways for the agricultural sector to address flood risk (see Tables S9 to S12 in Supporting Information S1 a complete overview of all pathways per sector and hazard).In stage 1, 9 potential flood risk pathways were identified, with additional pathways emerging in multi-hazard or multi-risk system conceptualizations.For instance, flood risk pathway 9 includes the measure "Dike maintenance," reducing the probability of drought-induced dike failures.Similarly, flood risk pathways 12 to 14 incorporate the multi-risk measure "Local support scheme," addressing the indirect effects of flood damages on crop revenues.
Although DAPP-MR suggests that potential pathways tested in one stage can be refined to a set of promising pathways for the next stage, we identify promising pathways for each stage without eliminating them from further analysis.This approach allows for the consideration of the potential drawbacks of removing pathways during the analysis, as it might result in overlooking better-performing pathways that account for a wider range of interactions.

The Set of Uncertainty Realizations T st
An ensemble of 10 realizations for the relevant inputs as shown in Figure 2 was generated with the KNMI weather generator (Brandsma & Buishand, 1997) for the current climate and two future climate scenarios: a "low to moderate climate change scenario" (+2°C in 2100) and a "high climate change scenario" (+4°C in 2100), both developed by KNMI (Haasnoot et al., 2015;van den Hurk et al., 2007).Other uncertainties, such as land use and transport volume changes, are not considered in this analysis.Details regarding the type of multi-hazard events covered in this data -set are shown in Figures S6 to S9 in Supporting Information S1.The set of uncertainty realizations is stage dependent.In stage 1, pathways are stress-tested for 10 ensemble realizations of each climate scenario.In stages 2 and 3, other sector-hazard pathways can affect pathway performance (through the state of the system σ, see function 5).For instance, the urban sector's DRM decisions can impact the agricultural sector's DRM decisions in stage 3.To consider shifting implementation timing, synergies and trade-offs between pathway combinations are treated as an additional uncertainty source in stages 2 and 3, increasing the number of uncertainty realizations.For example, in stage 2, the agricultural sector identified 12 flood risk and 11 drought risk pathways.Testing the interaction effects between these pathways requires stresstesting each drought risk pathway under climate ensemble realizations for all combinations with the 12 flood risk pathways, totaling 360 model runs.Similarly, each flood risk pathway undergoes 330 model runs.In stage 3, with multi-sector pathway combinations, we consider sector-hazard pathway quartets (e.g.agriculture flood pathway option 1, agriculture drought pathway option 3, urban flood pathway option 10, shipping drought pathway option 3) accounting for all sector-hazard pathways.

Results
This section presents the analysis of flood risk pathways for the agricultural sector and explores their potential relationships with other sector-hazard pathways across the different stages of the analysis.The focus of the pathways analysis lies on their performance (changes), but changes in relation to pathway timings are discussed exemplary.The performance evaluation results for the other sector-hazard pathways is available in Figures S6 to S13 in Supporting Information S1.

Identifying Promising Pathways Under Stage 1
Figure 5 displays the performance values across various evaluation criteria for different climate scenarios.The top row represents the baseline damages and costs if no measures were implemented.In the subsequent rows, the colors and values in each cell indicate the relative change in evaluation criteria compared to the baseline.Additionally, we include the expected number of implemented measures as supplementary information.The analysis reveals that costs generally correlate with the expense of flood risk measures and the number of implemented measures.Scenarios projecting more severe climate change show increased damages for the baseline (top row) but also greater risk reduction effects, a higher number of implemented measures and consequently, increased costs.When contrasting the costs against reduction gains, it is evident that the cost of all potential pathways exceeds the damage reduction in the current climate scenario.This suggests that the existing flood risk management system would suffice over the planning horizon if the climate remained unchanged.However, under scenarios of future climate change, certain pathways emerge as cost-efficient.
Pathways 6, 7, and 8, which begin with the measure "Dike elevation increase" followed by either introducing "Flood-resilient crops" or "Ditch system," appear promising for both medium and high climate change scenarios.Meanwhile, pathways 2 and 5 emerge as promising in a high climate change scenario.Pathways 1, 3, and 4 also show potential in terms of damage reduction and costs but they lead to significantly higher crop losses over the 100-year horizon.Pathways implementing "Ditch system" reduce the agricultural land available for crop cultivation, thereby increasing crop losses.The sooner this measure is implemented, the more pronounced its cumulative effect at the end of the planning horizon.Notably, for flood risk pathways 3 and 4, the total incomes are significantly lower than the baseline, while the damage reduction is relatively minor.This suggests that the risk reduction effects of these pathways are overshadowed by the trade-offs of the implemented measures.

Identifying Promising Pathways Under Stage 2
Figure 6 illustrates the performance of pathways, now factoring in multi-hazard interactions (left four columns) and their influence on drought-risk relevant evaluation criteria (right three columns).In addition to the nine stage 1 pathways, three multi-hazard conscious flood risk pathways (numbers 9, 10, and 11) are stress-tested.These pathways include dike maintenance to reduce drought-induced dike failures.It is notable that the baseline structural damage only marginally increases compared to stage 1, suggesting that drought-flood interactions marginally increase flood risk.However, crop losses significantly increase in stage 2, largely due to the combined impact of droughts and drought measures, including increased flood vulnerability from drought exposure and direct drought crop losses.Fewer measures are implemented in stage 2 pathways compared to stage 1, yet they exhibit higher damage reduction effects.This is attributed to the earlier implementation of flood risk measures due to vulnerabilities caused by drought risk measures or multi-hazard interactions, leading to enhanced long-term risk reduction.Consequently, this reduces the number of ATP conditions met, hence decreasing the number of implemented measures.
In stage 2, crop losses related to "Ditch system" in flood risk pathways 3 and 4 are less pronounced."Ditch system" positively affects groundwater recharge, improving water availability for crops, which, along with the increased number of flood events, results in less distinct trade-offs of the Ditch system.
Promising pathways from stage 1, such as 6, 7, and 8, remain promising in stage 2, as do pathways 2 and 5. Pathways 1, 3, and 4 also become promising under high climate change scenarios.However, the multi-hazard conscious pathways 9 to 11 are too costly (costs exceed the damage reduction effect) due to the early implementation of the "Dike maintenance" measure.
Interestingly, multi-hazard effects broaden the solution space for promising pathways, indicating that different strategies (initial heavy, costly structural measures vs. initial smaller, cheaper measures) become viable.A closer look reveals that in stage 2, pathway 6 ("Small dike elevation increase," then "flood-resilient crops") outperforms others, whereas in stage 1, pathway 7 ("large dike elevation increase," then "flood-resilient crop") was most promising.Thus, more flexible initial measures appear more attractive in stage 2.
The right section of Figure 6 shows the influence of flood risk pathways on drought risk objectives.Here, green cells indicate average synergistic interaction effects of the flood risk pathways across all drought risk pathways, while red cells hint at broad trade-off interactions.These interactions mostly affect the number of implemented measures but can also modify damages without altering the measure count.
Figure 7 shows how different drought risk pathways influence flood damage of given flood risk pathways and vice versa.It is apparent that interactions are not uniform across all combinations.For example, the "Ditch system's" trade-off is evident across all drought risk pathways (flood pathways 1, 3, 4, and 9).The trade-off is strongest when no drought DRM measures are implemented.It is also interesting to note that drought pathways 1, 2, 3, 8, and 9 seem to have significant synergistic effects in a 2°C scenario.This suggests that interaction effects are not automatically scaling with increasing hazard intensity.
The analysis in Figure 8 confirms the hypothesis regarding the earlier implementation of additional flood risk measures influenced by the presence of drought risk pathways.The stacked bar diagram in Figure 8 contrasts the timing of implemented measures in pathway 6 with and without drought pathway interactions.It is evident that for about a third of all realizations, the presence of a drought risk pathway leads to an earlier implementation of the first measure, resulting in long-term benefits from increased accumulated flood risk reduction.The observed patterns are heterogeneous and realization-specific, highlighting the complex interplay of hazard event timing, previous impacts and DRM measure efficacy.

Identifying Promising Pathways Under Stage 3
Figure 9 assesses the pathways in a complex environment encompassing multi-hazard and multi-sector interactions.A total of 15 potential flood risk pathways are stress-tested in stage 3 using the model.
There is a notable decline in flood damages from stage 2 to stage 3, alongside a slight decrease in crop losses.This trend indicates that flood risk strategies have a decreasing effect on the crop damage in the agricultural sector.The presence of DRM measures from other sectors contributes to these changes, with urban flood risk pathways particularly playing a synergistic role, enhancing protection levels and reducing the agricultural sector's need for additional flood risk measures.However, no flood risk pathway emerges as particularly promising when considering damage reduction against costs in the context of these multi-sectoral interactions.
Figure 9 also explores the interaction effects of flood risk pathways on drought risk objectives.The influence of flood risk DRM decisions on drought risk in the agricultural sector is less pronounced, with fewer distinct pairwise interactions as shown in Figure 10.The analysis highlights synergistic effects, particularly in urban flood risk objectives, with pathways 5, 6, 7, and 8 significantly reducing urban flood damages and costs.These pathways, which involve "Dike elevation increase" early on, show strong synergies with certain urban flood risk pathways that start with smaller DRM measures.
Interestingly, while flood risk pathways 5, 6, 7, and 8 consistently reduce shipping sector damages, no specific pathway pair interactions are evident.This suggests indirect influences via urban flood risk pathways, particularly through measures like "Room for the River."Implementing "Dike elevation increase" as part of the agricultural flood risk delays certain urban flood DRM measures, including the "Room for the River," thereby deferring its trade-off effects on the shipping sector.This indirect impact of agricultural flood pathways through urban flood risk pathways on shipping drought pathways is considered in Figure 9 but not in Figure 10, highlighting the complexity of these multi-sectoral interactions.

Discussion and Recommendations
In this discussion, we first reflect upon the results of the analysis to summarize learnings about the implications of multi-hazard and multi-sector interactions on the potential pathways and their performance.We then reflect on the multi-risk test case and its limitations and conclude with reflections on the utility of DAPP-MR and some broader learnings.

Implications of Interactions for Short-to Longterm Strategies
The results of this test case underscore the significance of the interplay between hazards, risks and measures in determining the timing and nature of measure implementations.It is clear from the analysis that multi-hazard and multi-sector interactions significantly influence pathway viability.Traditional, siloed risk assessments suggest that pathways starting with "Dike elevation increase" followed by smaller measures (pathways 6, 7, and 8) are promising for a range of climate change scenarios.However, when accounting for droughts, drought risk strategies and other sectors, additional viable alternatives emerge that alter best performance assessments.Interestingly, under multi-sector considerations, none of these pathways remain viable due to the disproportionate costs relative to risk reduction effects, despite showing synergistic effects with urban flood risk management.Medium flexible pathways scalable with external climate scenarios are promising for the agricultural sector alone, however, more robust and less flexible pathways become attractive under a multi-sectoral perspective.This casespecific finding suggests the need for further investigation into the dynamics of specific measure interaction effects.
Pair-wise pathway interactions provide further insights, revealing that short-term trade-offs in DRM measures increasing the vulnerability or exposure can yield long-term benefits.We also observed that measure-measure can have indirect effects across sectors.For example, agricultural flood risk measures directly Earth's Future 10.1029/2023EF004288 influenced urban flood impacts, subsequently affecting the shipping sector's choices.This highlights the need for an integrated perspective beyond direct impact chains to understand broader interests and preferences regarding specific pathway alternatives.

Regarding the Multi-Risk Test Case
While our test case is grounded in literature, it does not entirely reflect real-world dynamics or offers robust insights.Previous research indicates that limiting ensemble realizations could impact the sensitivity and outcomes of the system (Kwakkel et al., 2015).Despite testing various climate scenarios, future studies should consider broader uncertainties (Srikrishnan et al., 2022) and apply a global sensitivity analysis.This would improve model confidence and highlight the significance of certain tipping point definitions (Gao et al., 2016;Pianosi et al., 2016).Particularly concerning socio-economic uncertainties, this study had a narrow focus, overlooking factors like population growth in the area or interaction effects such as the "levee effect" (Di Baldassarre et al., 2015).
Our method, assessing pathway performances using simple, quantitative criteria, requires a more comprehensive evaluation, incorporating qualitative metrics to realistically reflect current and future needs (Bosomworth et al., 2017;Siders & Pierce, 2021).The independent, impact-based ATP decision rules oversimplify the integrated understanding sectors might have of their dynamics.Consequently, identified synergies and trade-offs in the model might not have real-world relevance.For example, prioritizing early implementation of droughtresilient crops because of the short-term trade-off leading to increased flood impacts and forcing the earlier implementation of new flood risk measures for the sake of long-term benefits seems counterintuitive.Current practice tends to focus more on the current needs of the farmers, while the pathways analysis and chosen performance evaluation of robustness indicators total benefits across the entire planning horizon more (Jafino et al., 2019).A bottom-up approach such as ours also overlooks top-down considerations, suggesting that future DAPP-MR applications should include government-led performance targets alongside individual sector objectives.

Regarding the Utility of DAPP-MR
Despite these limitations, the study demonstrates DAPP-MR's utility for decision-makers and policy analysts.Following a systematic staged approach allows for a step-by-step analysis of cause-effect relations, identifying recurring patterns and unique multi-process influences.Interestingly, pathways that performed well in less complex dynamics tended to remain viable even under increased complexity.
From the stylized case study we can learn that the DAPP-MR approach has been instrumental in revealing how DRM strategy performance is influenced by the complex interplay of measure implementations, timing and the dynamics of a multi-risk system (Hochrainer-Stigler et al., 2023;Simpson et al., 2021).As such the approach facilitates understanding of the trade-offs and synergies of sectoral DRM pathways and highlights the conditions under which these dependencies significantly affect decision-making.Some interactions such as those related to "Flood-resilient crops" were predictable, while others like sector trade-offs prompting adaptive responses appeared counterintuitive.
Increasing complexity can diminish the attractiveness of certain pathways, suggesting that eliminating less promising options early may overlook viable alternatives.Our study challenges the notion that a staged approach can reduce computational burden (Schlumberger et al., 2022).Future applications of DAPP-MR could include a pre-assessment step to limit the number of pathway combinations requiring stress-testing, focusing on those with distinct trade-off or synergistic effects, as indicated in Figures 9 and 10.

Conclusions
This study aimed to test and explore the DAPP-MR framework for developing multi-risk pathways, focusing on understanding the impact of interactions and dependencies on DRM pathways.We expanded the Waas test case, a region prone to both floods and droughts, to encompass diverse multi-hazard and multi-sector DRM measure interactions.Employing a three-stage DAPP-MR approach allowed us to incrementally increase the complexity of our evaluations.
Earth's Future 10.1029/2023EF004288 Our findings highlight the effectiveness of the staged approach of DAPP-MR in delineating cause-effect relationships within multi-risk systems.This approach facilitated the identification of clear pathway plans for varying levels of complexity.Interestingly, our results revealed that multi-risk interactions can have significant implications for long-term strategies, even in cases where direct links between sectors are not immediately apparent.We observed indirect effects through second-order measure interactions, where an agricultural flood measure influenced an urban flood measure, which in turn affected shipping drought measure decisions.Despite the increasing complexity in each stage of analysis, the relative performance of pathways remained remarkably consistent.
While our study primarily relied on a model-based quantitative evaluation, future research could further operationalize additional elements of the DAPP-MR framework or extend the existing multi-risk case study to include additional dynamics or uncertainties.Subsequent studies might explore the framework's applicability in various multi-risk contexts, such as spatially diverse pathways and heterogeneous sector pathways or in more realistic decision-making environments.A notable limitation in our study was the lack of direct incorporation of participatory or user-centered tools.These tools could be instrumental in effectively communicating pathway alternatives, elucidating trade-offs and highlighting synergies.Future research could focus on identifying a set of visualization tools that assist policy analysts in comprehending cause-effect chains, decision implications and the effects of trade-offs and synergies across different times and spaces.

Figure 1 .
Figure 1.Conceptualization of the Waas-MR test case using DPSIR.Dashed lines represent cross-sectoral dependencies.

Figure 2 .
Figure 2. Simplified representation of the Waas-MR integrated assessment meta-model inputs, processes, decisions, and outputs.See Figure S1 to S3 in Supporting Information S1 for a detailed conceptualization of the impact modules.Processes or parameters affected by multi-hazard interactions or the implementation of Disaster Risk Management measures are highlighted.

Figure 3 .
Figure 3. Left: The Dynamic Adaptive Policy Pathways for Multi-Risk (DAPP-MR) framework of steps and stages to develop pathways in multi-risk systems, as proposed by Schlumberger et al. (2022).This study focuses on the development and evaluation of pathways (step 4 highlighted green box).Right: Operationalization of step 4 of DAPP-MR to develop and evaluate Disaster Risk Management pathways, starting with single hazard pathways for each sector (stage 1), progressing to multihazard pathways for each sector (stage 2) and culminating in pathways designed for multi-risk systems (stage 3).

Figure 4 .
Figure 4. List of all potential pathways per stage for the agricultural sector to manage flood risk.Measures are implemented sequentially.Each Disaster Risk Management pathway comprises a maximum of four measures across the planning horizon, implemented as the future unfolds and pre-specified conditions are reached.Interaction effects are categorized as interacting with drought processes (yellow), with general changes to the system (pink) and with multi-sector processes (green).Icons in this figure are used under a CC BY 3.0 license (refer to the Acknowledgments for further information).

Figure 5 .
Figure 5. Stage 1 robustness indicators for evaluation criteria (x-axis) for different flood risk pathways (y-axis) of the agricultural sector.Preferred pathways are indicated by limited orange and red cells along the x-axis across different climate scenarios (current climate, low/medium climate change, high climate change).The color coding is based on normalized values across climate scenarios and evaluation criteria of similar units to identify the best (green) and worst (red) performance values.Icons in this figure are used under a CC BY 3.0 license.

Figure 6 .
Figure 6.Stage 2 robustness indicators for flood risk objectives (left) and drought risk objectives (right) for different flood risk pathways.Color coding is similar to Figure 5. Robustness values from stage 1 are shown in brackets.For potential pathways that were not tested in stage 1 no values ( ) are provided.Icons in this figure are used under a CC BY 3.0 license.

Figure 7 .
Figure 7. Bi-directional heatmap exploring interaction effects for flood risk and drought risk pathway pairs on crop damage (top triangles) and flood damages (bottom triangles) under different climate scenarios for stage 2. Interaction effect factors are calculated by normalizing the given loss value for a specific pathway pair against the flood damages value for a flood risk pathway in the absence of drought risk measures.Values greater than 1 suggest synergistic effects, while values less than 1 suggest negative interactions.

Figure 8 .
Figure 8.Comparison of the timing of new measure implementations in flood risk management pathway 6 and the duration of their sufficiency across different realizations with and without interaction effects from drought risk pathway 3. The color-coded stacked bars represent different measures in pathway 6, illustrating changes in implementation timing and duration across the model runs.

Figure 9 .
Figure 9. Stage 3 robustness indicators for flood risk objectives (top left), drought risk objectives (top right), urban flood Disaster Risk Management (DRM) objectives (bottom left) and shipping drought DRM objectives (bottom right) for different flood risk pathways.Color coding is consistent with Figures 5 and 6.Robustness values from stage 2 are shown in brackets.For potential pathways that were not tested in stage 2 no values ( ) are provided.Icons in this figure are used under a CC BY 3.0 license.

Figure 10 .
Figure 10.Bi-directional heatmap exploring interaction effects for flood risk pathways with drought risk pathways (top row), urban flood risk pathways (middle row) and shipping drought pathways (bottom row) across different climate scenarios (left: current climate; center: 2°C; right: 4°C) for stage 3.The interaction effect factor is calculated as explained for Figure 7.

Table 1
Overview of Sector Vulnerabilities, and List of Available Disaster Risk Management Measures SCHLUMBERGER ET AL.