Direct physical damage over time t to an asset or infrastructure j caused by two concurrent impacts, as graphically represented in Fig. a can be calculated according to Eq. (). 2dj(t)[tS1,tREC1,2]=f1iftS1≤t<tRES1,2f1⋅Rj,1,2(t)iftRES1,2≤t<tREC1,2 with 3f1=fvj,1,2(h1,max,h2,max)

According to Eq. (), at any time t between the start of the first hazard event tS1 and the end of the response phase of the multi-hazard event tRES1,2, asset j experiences a level of damage equal to f1. After the response phase of the multi-hazard event concludes (i.e., for t≥tRES1,2), the asset begins to recover from the concurrent impacts according to the recovery function Rj,1,2(t), until t=tREC1,2.

Equation () represents the damage model used to quantify the effects of two concurrent hazards, referred to as the “concurrent damage model.” This model assesses the combined impact of both hazards on asset performance. In the literature, concurrent damages are typically evaluated using bivariate vulnerability or fragility functions. Accordingly, the model is expressed as fvj,1,2, where the resulting damage depends on the maximum intensity of each hazard event, h1,max and h2,max. classifies this approach as a “vector-valued fragility model.” Bivariate vulnerability functions have been applied in single-hazard scenarios, such as assessing flood damage considering both flow velocity and duration , and in multi-hazard contexts, such as hurricanes, where structural impacts are evaluated by combining the effects of coastal surges and wind forces . However, there are instances where concurrent damages are calculated using “state-dependent fragility models” , where the fragility of an asset to a secondary hazard is conditional on its damage state after the primary hazard. This approach is applied, for example, to assess the impacts of an earthquake-tsunami combination, where the fragility curve for the post-shock tsunami depends on the earthquake-induced damage .

Direct physical damage over time t to an asset or infrastructure j caused by two consecutive impacts is calculated according to Eq. (). 4dj(t)[tS1,tREC2]=f2iftS1≤t<tRES1f2⋅Rj,1(t)iftRES1≤t<tS2f3⋅[1-f2⋅Rj,1(tS2)]+f2⋅Rj,1(tS2)iftS2≤t<tRES2{f3⋅[1-f2⋅Rj,1(tS2)]+f2⋅Rj,1(tS2)}⋅Rj,2(t)iftRES2≤t<tREC2 with 5f2=fvj,1(h1,max)6f3=fvj,2|d(tS2)(h2,max)

According to Eq. (), at time tS1, due to the impact of the first hazard event, the asset j experiences a level of damage equal to f2. Equation () represents a single hazard damage model (e.g., a depth-damage curve for floods or a fragility curve for earthquakes), as a function of the maximum intensity of the hazard events h1,max. After the response phase of the first event is complete (that is, for t≥tRES1), the asset begins to recover from the impacts of a single danger according to the recovery function Rj,1(t). At time tS2, the asset is still recovering from the previous hazard event when it is impacted by a second event. The damage caused by this consecutive event is expressed as f3⋅[1-f2⋅Rj,1(tS2)]+f2⋅Rj,1(tS2). This expression accounts for the sum of the residual damage at time tS2, denoted by Rj,1(tS2), and the additional damage from the second event, which is calculated as the percentage damage caused by the second event, represented by f3, applied to the remaining undamaged portion of the asset, i.e., [1-f2⋅Rj,1(tS2)]. This approach prevents the double-counting of damage. After the response phase of the second event concludes (i.e., for t≥tRES2), the asset begins to recover from the consecutive impacts according to the recovery function Rj,2(t), until t=tREC2. This evolution of damage over time, as described in Eq. (), is graphically represented in Fig. b.

Equation () represents the damage model used to quantify the effects of two consecutive impacts, known as the “consecutive damage model”. This model is based on a “state-dependent fragility model” , denoted as fvj,2|d(tS2). It defines the fragility or vulnerability of an asset to a secondary hazard, conditional on the asset's residual damage state due to incomplete recovery. The resulting damage is a function of the maximum intensity of the second hazard h2,max and the residual damage to the asset calculated at tS2 according to the recovery function of the asset. State-dependent fragility models are relatively scarce in the literature and are mainly developed within the seismic field to assess the effects of a primary event followed by aftershocks on an already weakened asset . Another application in the seismic domain involves evaluating the worsening condition of assets, often bridges, due to factors like time and corrosion. In this scenario, the primary seismic event impacts an asset in a deteriorated state, resulting in increased damage .

To investigate the internal mechanics of the proposed formulation under consecutive multi-hazard dynamics, a model behaviour analysis is conducted via a structured parameter influence assessment. The objective is to examine how the mechanisms embedded in Eq. () generate additional cumulative damage relative to the independent baseline configuration. Therefore, the analysis isolates the endogenous amplification effects arising from the interaction between residual damage, recovery progression, and state-dependent vulnerability.

The investigation focuses on consecutive interactions because their cumulative effects emerge over time as each hazard occurs sequentially. In consecutive events, residual damage and evolving vulnerability modify the response to subsequent loading, producing additional loss amplification through the damage-state update term in Eq. () and the state-dependent vulnerability function in Eq. (). In contrast, concurrent impacts are captured directly by the bivariate damage function in Eq. (), which defines the combined effect of simultaneous hazards at a single time step. Since concurrent effects are already structurally integrated into the formulation, the analysis concentrates on consecutive interactions to isolate and quantify the unique mechanisms driving cumulative damage across sequential events.

Three parameters are examined, consistent with the conceptual drivers identified by and : i.

the inter-event time interval (Δt);

Figure  reports additional cumulative loss as a function of Δt under three alternative recovery trajectories: exponential, linear, and logistic. These functional forms, commonly adopted in resilience modelling , represent distinct temporal distributions of restoration capacity and therefore different persistence patterns of residual damage.

When the second event occurs during the early recovery phase, cumulative damage substantially exceeds the independent baseline. As Δt increases, additional cumulative loss decreases and asymptotically converges toward independent behaviour. However, both the rate and magnitude of convergence are governed by the functional form of Rj,1(t). Under exponential recovery, rapid early restoration reduces residual damage quickly, limiting amplification. Linear recovery produces intermediate behaviour. Logistic recovery, characterised by delayed early restoration and accelerated later recovery, prolongs vulnerability persistence and sustains elevated amplification over a wider Δt range.

These results show that recovery trajectory assumptions are structurally influential within Eq. (). The assumed recovery trajectory directly determines how long residual damage persists and, therefore, how likely the second event is to interact with a weakened system. Assuming instantaneous or implicitly complete recovery collapses this mechanism and systematically biases cumulative loss toward additive behaviour.

The second test isolates the contribution of state-dependent vulnerability (Eq. ). The vulnerability function of the second event is progressively shifted (+10 %, +20 %, +30 %) to represent increasing fragility due to incomplete recovery. Although state-dependent fragility formulations have been explored primarily in seismic contexts , they are rarely embedded within a general multi-hazard quantitative structure.

Figure  shows that state-dependent vulnerability modification generates convex, non-linear amplification of cumulative damage. Even moderate fragility shifts (+10 %) produce measurable increases in additional loss, while larger shifts (+30 %) substantially increase both median outcomes and upper-tail behaviour. Crucially, amplification does not arise solely from residual damage magnitude, but from the alteration of the fragility profile itself. Through Eq. (), incomplete recovery modifies the system's response function, changing the probability structure of damage exceedance. In this sense, consecutive multi-hazard interaction is not merely additive accumulation but a structural reconfiguration of vulnerability between events. The recovery trajectory should not be interpreted as an abstract modelling parameter. Empirical evidence shows that recovery dynamics reflect governance effectiveness, institutional capacity, infrastructure robustness, and socioeconomic conditions . At the macro scale, such dimensions can be synthesised through composite recovery capacity indicators, such as the Recovery Gap Index (RGI) . Lower recovery capacity implies prolonged vulnerability persistence, increasing the likelihood that subsequent hazards interact with residual damage and trigger multiplicative effects.

Overall, the parameter influence analysis shows that cumulative loss in consecutive multi-hazard scenarios depends primarily on three factors: the time interval between events, the speed and shape of recovery, and possible modifications of vulnerability due to residual damage. When the second event occurs after substantial recovery has taken place, total damage remains close to the sum of the two independent events. In contrast, when recovery is incomplete and vulnerability is increased, the second event acts on a weakened system, producing higher cumulative losses than those obtained under independent modelling assumptions. The proposed formulation makes these mechanisms explicit by linking inter-event timing, recovery progression, and vulnerability modification within a single damage function. Rather than assuming that assets fully recover between events, the model allows vulnerability to evolve over time and directly influence subsequent damage estimates. In Sect. , this modelling framework is applied to the Puerto Rico disaster sequence, where incomplete recovery and evolving fragility conditions significantly influenced cumulative impacts.

The 2017 landfall of Hurricane Maria provides a real configuration of concurrent multi-hazard interaction, in which wind and flood hazards overlapped spatially and temporally across Puerto Rico. In this setting, damage amplification arises from the simultaneous action of multiple stressors acting on the same asset during the emergency phase, as formalised in Eq. ().

Within the proposed damage model, compound hurricane damage is represented through a multi-parameter vulnerability formulation fvj,1,2(h1,max,h2,max) that accounts for the joint influence of peak wind intensity and flood depth under overlapping conditions. In practice, the concurrent formulation integrates standard Hazus wind fragility curves and flood depth-damage functions within the unified structure of Eq. (). Hazus does not provide an explicit bivariate fragility surface for combined wind–flood loading. Instead, wind- and flood-induced damages are evaluated consistently using the respective Hazus vulnerability components, while their interaction is represented through the concurrent damage operator, which accounts for their temporal and spatial superposition. This approach ensures methodological consistency with the standard Hazus framework while preserving the multi-hazard interaction logic embedded in the proposed formulation.

Vulnerability functions are derived from the FEMA Hazus-MH methodology . Wind fragility curves are parametrized according to structural typology, construction material, roof anchorage, number of storeys, and code compliance level. Flood damage is represented through depth-damage functions calibrated for different occupancy classes. From a physical standpoint, wind and flood mechanisms are structurally interdependent. High wind speeds induce roof uplift, envelope breach, and cladding failure, increasing structural susceptibility to water ingress. Subsequent or simultaneous inundation accelerates the deterioration of load-bearing and non-structural components. Post-event assessments indicate that buildings exposed to overlapping wind and flood loading experienced repair costs 30 %–40 % higher than buildings exposed to a single hazard . Field observations further show that flood depths exceeding 1.5 m resulted in near-complete failure of unreinforced masonry structures, particularly where prior wind damage had reduced lateral resistance.

The modelled compound loss for Hurricane Maria is approximately USD 90 billion, consistent with official economic assessments . The agreement with reported losses does not result from post-event parameter fitting, but from the direct application of observed hazard intensities and standardised Hazus vulnerability functions within the concurrent formulation. In this phase of the Puerto Rico sequence, vulnerability parameters are not modified between hazards; amplification derives from hazard superposition under overlapping conditions rather than from recovery-mediated fragility evolution. The subsequent seismic sequence, in contrast, introduces a fundamentally different mechanism, where damage persistence and state-dependent vulnerability shifts govern cumulative impacts.

The earthquake sequence that began in late 2019 and culminated in the magnitude 6.4 event on 7 January 2020 struck Puerto Rico at a time when many regions were still in the process of recovering from Hurricane Maria. This temporal overlap between the recovery phase and the occurrence of a new hazard event represents a critical scenario within multi-hazard damage assessment, where pre-existing damage and delayed reconstruction substantially influence the vulnerability landscape.

To spatially contextualise this interaction, Fig.  integrates three key spatial data sets: the track of Hurricane Maria (September 2017), the distribution of buildings still damaged as of November 2018 (based on Hazus post-event assessments), and the contours of the peak ground acceleration (PGA) from the January 2020 earthquake. The post-hurricane assessment identified nearly 138 000 buildings in Puerto Rico that had not yet been fully repaired more than a year after the hurricane.

As illustrated in Fig. , many of the damaged buildings were concentrated in coastal and southern municipalities, including regions such as Ponce and Guayanilla, which later experienced the highest levels of ground shaking during the earthquake (PGA > 0.5 g). These areas faced dual exposure, first to high winds and flooding from Hurricane Maria and later to seismic loading from the 2020 event. Residual structural weaknesses, whether due to incomplete reconstruction or substandard repairs, likely increased the risk of damage and collapse.

To model the seismic impacts on the buildings still damaged by the hurricane, a consecutive damage model (Sect. ) is applied. Standard fragility curves provided by FEMA are transformed into state-dependent curves to properly account for residual damage. The approach introduces parametric adjustments to account for pre-existing damage conditions. Specifically, the median values of both structural and non-structural fragility curves are shifted according to hypothetical levels of residual damage. Given the absence of building-level recovery data, a homogeneous distribution of residual damage is assumed throughout the building portfolio.

In the absence of spatially explicit residual damage data, a predefined range of vulnerability modifications (5 %–30 %) was considered. This range provides an exploratory basis for investigating how different levels of residual vulnerability influence cumulative damage estimates. An empirical calibration against reported losses from the Puerto Rico case study identified a 15 % vulnerability modification as the value most consistent with the observed losses. This value falls within the proposed range, which is intended for future ex ante applications to account for a broader spectrum of plausible residual damage conditions. The lower bound of 5 % captures a limited but non-negligible residual effect, while the upper bound of 30 % allows more substantial effects to be explored. Although the modifications were applied uniformly, their impact is particularly pronounced in areas with high PGA values, where even small increases in vulnerability result in disproportionately large increases in expected losses.

Figure  illustrates the conceptual effect of residual damage on fragility curves. As residual damage increases, the curves change to the left, reflecting a greater susceptibility to damage at lower levels of seismic demand.

Simulated damage probabilities are translated into direct economic losses using the Hazus-MH damage-to-loss methodology. For each building class and damage state, Hazus defines empirically derived loss ratios representing expected repair costs as a percentage of total replacement value. These ratios are based on historical US claims data and post-disaster reconstruction evidence, and differentiate between structural and non-structural components. In this study, replacement values are taken directly from the FEMA building inventory for Puerto Rico, ensuring internal consistency between exposure, vulnerability, and economic conversion assumptions. Total portfolio loss is obtained by multiplying damage state exceedance probabilities by the corresponding loss ratios and aggregating across building typologies.

Based on the vulnerability modification range defined above, structural and non-structural fragility medians were progressively shifted, representing increasing levels of residual vulnerability. For each modification level, seismic damage was recomputed and converted into economic loss, allowing systematic evaluation of how cumulative impacts vary under different recovery assumptions. The results show that total loss increases more than proportionally as fragility medians are shifted toward lower capacity. Even modest modifications produce noticeable increases in simulated loss, while larger shifts lead to disproportionately higher damage estimates. The complete numerical matrix of results is reported in Appendix , while Fig.  illustrates how total loss varies across structural and non-structural modification levels.

Official damage estimates for the 2019–2020 seismic sequence amount to approximately USD 1 700 000 in 2020 prices . All monetary values reported in this section are expressed in 2020 USD, so that simulated losses are directly comparable with the official estimate. When the earthquake is modelled as an independent single-hazard event – thus assuming full recovery of building vulnerability after Hurricane Maria – the simulated loss equals USD 1 205 525. This configuration underestimates the official figure by approximately 29 %. The discrepancy indicates that assuming complete restoration of structural capacity before the earthquake is not consistent with the observed loss pattern. When state-dependent vulnerability is introduced by shifting the median of both structural and non-structural fragility curves by 15 %, the simulated total loss increases to USD 1 742 296, closely matching the official estimate. This modification represents a plausible level of residual vulnerability at the time of the seismic sequence and falls within the systematic range explored (5 %–30 %).

The difference between the two modelling configurations directly reflects the mechanism described in Eq. (). In the independent configuration, the recovery function implies full restoration before the second event, and the earthquake acts on an undamaged system. In the state-dependent configuration, residual damage from the hurricane shifts the fragility curves toward lower capacity, increasing damage probabilities under the observed PGA levels. The improved agreement with reported losses does not result from ex-post parameter fitting, but from the structural effect of incorporating incomplete recovery within the vulnerability formulation. The 15 % modification lies within the predefined exploration range and represents one plausible residual capacity scenario rather than a calibrated value. The Puerto Rico application illustrates, within the explored modelling framework, that accounting for residual damage persistence improves the representation of cumulative impacts in consecutive multi-hazard sequences, as neglecting recovery processes may lead to lower damage estimates.

The quantitative methodology presented for multi-hazard damage dynamics and its forensic application in Puerto Rico is subject to assumptions and limitations that define the scope of validity of the results.

Focus on sudden-onset hazards. The multi-hazard damage formulation proposed in this study primarily targets sudden-onset hazards, characterised by short-duration events such as hurricanes and earthquakes, where the event phase is brief compared to the subsequent response and recovery phases. This assumption is particularly relevant for the Puerto Rico case study, where Hurricane Maria and the 2019–2020 earthquake sequence are treated as discrete events with well-defined temporal boundaries. However, this focus excludes slow-onset hazards such as droughts, sea-level rise, or subsidence, which evolve over extended periods and may blur the distinctions between the event, response, and recovery phases . Although this limitation does not diminish the applicability of the framework to sudden-onset events, it underscores the need for ad-hoc modelling approaches for long-duration slow-onset hazards.

Direct physical impacts only. The quantitative implementation focuses exclusively on direct physical damage to the built environment and does not capture indirect effects such as business interruptions, supply chain disruptions, or social impacts. In Puerto Rico, the prolonged loss of electricity and water after Hurricane Maria led to widespread socioeconomic challenges, including health crises, migration, and economic decline in key sectors such as agriculture and tourism . These indirect effects, while significant, fall outside the scope of the presented quantitative investigation.

Assumptions about the recovery process. In the Python code, and as a consequence, in the model behaviour analysis presented, the recovery process is modelled as a series of linear or exponential functions representing slow, medium, or fast recovery speeds. This approximation facilitates analysis but oversimplifies the inherently non-linear nature of recovery, which is influenced by a multitude of factors. In Puerto Rico, for example, bureaucratic inefficiencies, delayed federal funding, and inequitable distribution of resources significantly delayed recovery efforts in certain regions . Moreover, the proposed multi-hazard damage formulation assumes uniform recovery rates across structural and non-structural components, which may not reflect reality. Non-structural elements, such as utilities and interior finishes, often recover faster than structural systems, leading to mismatches in the actual recovery trajectory .

Simplification of temporal dynamics. In the proposed multi-hazard damage formulation, it is assumed that physical integrity is lost immediately at the onset of the event, and no further degradation occurs during the response phase. While this assumption is practical for mathematical modelling, it does not capture cases where damage continues to accumulate after the hazard peaks, such as when flooding persists or secondary hazards occur. In addition, physical integrity is assumed to remain constant during the response phase, despite minor fluctuations that may occur due to emergency repairs or further deterioration. Although these simplifications do not introduce significant bias, they limit the ability to model more complex temporal dynamics observed in real-world scenarios.

Generalized spatial resolution. The forensic analysis in Puerto Rico adopts a portfolio-based approach, grouping buildings into categories based on general characteristics such as structural type, construction material, and occupancy use. While this approach is suitable for regional-scale assessments, it does not capture localised variations in vulnerability or hazard exposure. Topography, proximity to fault lines, and floodplain dynamics are known to shape the spatial distribution of damage , and these factors are expected to have influenced the pattern observed in Puerto Rico. These localised effects were approximated rather than explicitly modelled, potentially reducing the precision of damage estimates.

Economic impact modelling limitations. The economic losses in the Puerto Rico case study were estimated using standard unit repair costs, downtime estimates, and sector-specific multipliers. Although these methods provide a useful approximation, they do not account for broader macroeconomic effects, such as long-term population decline, loss of workforce productivity, or disruptions in international trade. For example, the loss of agricultural infrastructure during Hurricane Maria had cascading effects on food security and export revenues, which are not explicitly captured in this study .

Uncertainty in state-dependent fragility curves. Adjustment of fragility curves to reflect residual damage is based on proportional modifications to the median curve values. Although this method effectively accounts for cumulative damage, it assumes uniform vulnerability changes across all buildings within a category. In reality, building-specific factors such as construction quality, maintenance history, and localised damage patterns may lead to significant variability in vulnerability . This limitation highlights the need for more granular data to refine the state-dependent fragility model.

In conclusion, while the proposed approach provides a reproducible analytical template that supports systematic exploration of multi-hazard damage interactions and facilitates forensic analyses, its assumptions and limitations must be carefully considered, specifically when interpreting the results of the Puerto Rico case study. Addressing these limitations in future developments, such as incorporating more sophisticated recovery models, indirect impacts, and higher spatial resolution, will improve the accuracy and applicability of the approach, allowing more comprehensive assessments of compound and consecutive multi-hazard impact scenarios.

Building on the current limitations of the proposed methodology, several promising avenues for improvement can be identified. These advances would not only improve the accuracy and applicability of the approach but also broaden its potential for integration into various fields of disaster risk reduction and management. Key directions for future developments are discussed below.

Better understanding and modelling recovery dynamics. The dynamics of the recovery process are central to the assessment of residual damage and the interactions between consecutive hazard impacts. Specifically, the timing of the response phase (tRES) determines whether the hazard impacts are classified as concurrent or consecutive, while the timing and shape of the recovery phase (tREC and Rj(t)) significantly influence the residual damage for subsequent events. The response phase, while critical for civil protection and disaster preparedness, has received limited attention in the scientific literature, often being conflated with the recovery phase. However, its proper evaluation is essential to improve disaster safety plans and understand its cascading effects on recovery . More attention has been paid to recovery dynamics, particularly in the context of seismic resilience. Recovery dynamics are highly variable, often following linear, exponential, or logistic patterns depending on socio-economic, political, and governance factors. The pioneering work of Miles and Chang introduced one of the first models of recovery behaviour after an earthquake, proposing recovery trajectories of the community . Based on this, developed an advanced method for the quantification of resilience by integrating recovery and preparedness metrics. Recent studies have highlighted the importance of recovery models in post-disaster decision-making , underscoring the need for reliable recovery functions. However, challenges remain in quantifying recovery due to the complexity of the influencing factors, including governance, technology, economic conditions, and social cohesion. Emerging methodologies, such as Agent-Based Models (ABMs), offer promising avenues to simulate recovery processes by integrating interactions between individuals, institutions, and resources. These models complement traditional approaches like community surveys and questionnaires, which are invaluable for understanding local recovery dynamics and identifying barriers to resilience .

Providing more reliable multi-hazard damage models. Improving multi-hazard damage models is essential for capturing the cumulative effects of consecutive hazards. Future research should focus on integrating damage-state-dependent functions that dynamically modify vulnerability and fragility curves based on residual damage from prior events. For example, scenarios involving hurricanes followed by earthquakes, as demonstrated in the Puerto Rico case study, require models capable of adapting to changes in structural and non-structural vulnerabilities caused by sequential impacts.

Evaluating dynamic exposure over time. In the current implementation, exposure is assumed to remain constant and is not explicitly modelled within the framework. However, exposure is inherently dynamic, evolving over time due to maintenance, retrofitting, and functional changes in assets. Hazard impacts can reduce exposure through physical damage, but exposure may increase following recovery processes or new construction. Future developments should aim to model these variations over time, capturing the cyclical nature of exposure changes in response to hazards and human interventions .

Incorporating indirect impacts through functionality modelling. The presented approach currently focuses on direct physical damage but does not explicitly address indirect impacts, such as loss of functionality, economic disruption, or cascading failures in interconnected systems. Future iterations could incorporate functionality as a key metric, using physical integrity as a proxy to estimate functionality . This approach would enable assessments of broader systemic impacts, including business interruptions and supply chain disruptions.

Adapting the formulation to slow-onset hazard dynamics. The multi-hazard damage assessment formulation is tailored to sudden-onset hazard dynamics, where event durations are short relative to the response and recovery phases. However, slow-onset hazards such as droughts, coastal erosion, and subsidence require a fundamentally different modelling approach. Extending the framework to account for these dynamics would improve its applicability to a wider range of hazard scenarios .

Advancing the model toward predictive multi-hazard applications. While the present approach demonstrates its value in forensic reconstruction and model behaviour analysis, its extension toward predictive multi-hazard risk assessment represents a crucial direction for future research. At present, vulnerability transitions and recovery trajectories are parameterised using stylised assumptions that are suitable for exploratory analysis but may not be sufficiently robust for forward-looking risk forecasting. To enable predictive applications, future developments should focus on: (i) empirical calibration of state-dependent fragility transitions across hazard combinations, (ii) development of transferable parameter sets that can be applied in data-scarce regions, and (iii) integration with probabilistic hazard occurrence models to simulate realistic multi-hazard event sequences. In particular, coupling the current damage accumulation formulation with stochastic event generation models would allow simulation of long-term compound risk under different climate or seismic scenarios. Such integration would transform the model from a post-event analytical tool into a prospective decision-support instrument capable of evaluating mitigation strategies and recovery policy alternatives under uncertainty. However, achieving this transition requires a stronger empirical foundation. Without these developments, predictive outputs may remain highly sensitive to modelling assumptions, limiting their reliability for operational risk management.