Resilience of Specialized Transportation Systems for People with Disabilities Under Extreme Weather Conditions

Abstract

Climate change is increasing the frequency of extreme weather events, posing critical challenges for the resilience of specialized transportation services (STSs) that provide essential mobility for people with disabilities. In the South Korean context, heatwaves, cold spells, and heavy rainfall are particularly relevant because they directly affect health risks, trip demand, and operational reliability, making them central stressors for evaluating STS resilience in Busan. This study examines STS resilience in Busan, South Korea, focusing on three weather stressors: heatwaves, cold spells, and heavy rainfall. Large-scale operational data from the STSs of Busan were analyzed using the 4R (robustness, rapidity, redundancy, and resourcefulness) framework to classify daily service performance into distinct profiles. The analysis revealed that heatwaves coincided with reduced trip demand and shorter waiting times, yet this apparent stability reflected demand suppression rather than genuine robustness. Heavy rainfall produced the most severe disruptions, with longer and more variable waiting times that exacerbated inequities across users. Cold spells were associated with rapid recovery and the preservation of critical trips, although the small number of cases limits broader interpretation. These findings indicate that resilience in STSs is not uniform but event-specific, offering policy insights for strengthening operational stability and promoting equity in accessible transport.

1. Introduction

Urban transportation systems are increasingly recognized as complex adaptive systems whose performance depends not only on physical infrastructure but also on the dynamic interaction of operators, users, and external stressors [1,2,3]. This perspective emphasizes that urban transportation cannot be reduced to fixed infrastructure networks alone; instead, it emerges from continuous interactions between system components and the surrounding environment. Among the most pressing external stressors are extreme weather events, which are intensifying in frequency, duration, and severity under climate change [4,5]. These events destabilize the interaction between service provision and travel demand, producing cascading disruptions across infrastructure, operations, and user behavior. Extreme temperatures accelerate pavement deterioration, heavy rains impair corridor reliability, and snow or ice reduces road surface skid resistance [6,7,8]. At the same time, weather stressors alter behavioral responses such as reductions in trip-making, delayed departures, and modal shifts toward private modes [9]. Therefore, extreme weather functions as a systemic stress test for urban mobility, challenging not only the robustness of infrastructure but also the equity of access [10,11].

A growing body of empirical studies has examined how adverse weather conditions affect travel demand and transit operations. Findings consistently show reductions in trip frequency, altered departure timing, and decreased ridership during severe weather events [12,13]. Studies further document that fixed-route and demand-responsive transit systems experience efficiency losses and longer passenger wait times when exposed to adverse conditions [14,15]. Such findings highlight that weather impacts extend beyond infrastructure damage to include system-level performance and reliability. While these studies significantly advance knowledge on the interactions between climate change and transportation, they overwhelmingly focus on mainstream public transport, leaving the resilience of specialized mobility services largely unexamined. Addressing this gap requires closer attention to specialized transportation services (STSs), which are especially vulnerable to climate-related disruptions due to their operational and structural characteristics.

STSs, often delivered through reservation-based or demand-responsive models, serve as essential lifelines for people with mobility impairments, providing indispensable access to healthcare, education, and social participation. However, STS riders typically lack the flexibility to reschedule or substitute trips with active modes such as walking or cycling. STS users may include individuals with physical disabilities, elderly riders, and others whose mobility is constrained. Constraints including limited fleet sizes, narrower service coverage, and scheduling requirements amplify exposure to disruptions during climate stress, producing heightened risks of missed trips or extended delays [16]. Broader climate adaptation research further shows that people with disabilities face disproportionate risks under climate stress, underscoring the urgency of addressing accessibility in transportation planning [17]. These dynamics illustrate that service disruptions are not evenly distributed across populations, but instead systematically disadvantage vulnerable groups who rely most heavily on STS. In South Korea, these challenges are amplified by rapid population aging and a rising prevalence of disability, which have created increasing demand for assisted mobility services [18]. Moreover, Korean studies have highlighted that older adults face heightened risks during extreme heat and cold [19,20], while heavy rainfall and flooding regularly disrupt transport networks in coastal cities such as Busan [21,22]. These stressors are particularly relevant for STS users because they directly influence health risks, trip demand, and operational reliability. Extreme heat elevates the risk of health complications and suppresses trip-making [23,24], cold spells exacerbate vulnerabilities among older and disabled populations [19,20], and heavy rainfall creates congestion and corridor blockages that degrade service reliability [21,22].

In rapidly aging societies such as South Korea, where both the prevalence of disability and the demand for assisted mobility are rising, these challenges are especially pronounced. The resilience of STS thus emerges as a pressing policy concern that requires targeted empirical investigation.

From a theoretical perspective, resilience in STS can be conceptualized within a systems-theoretical framework. Rather than conceiving resilience as the rapid return to an optimal steady state, it is more accurately described as the capacity of systems to absorb disturbances, adapt, and reorganize while retaining essential functions [2,25]. This conceptualization is particularly suitable for transportation systems, where services are expected to remain functional even when performance is degraded. Vulnerability complements this perspective by emphasizing the degree of exposure and sensitivity to harm in conjunction with adaptive capacity [26]. Research on social–ecological systems further demonstrates that resilience is multi-scalar and path-dependent, with disturbances at one level cascading through cross-scale feedback and panarchy dynamics [27,28]. Within transportation systems, such cascading effects imply that localized service disruptions can propagate into broader inequalities in accessibility, disproportionately affecting individuals who depend on specialized services for essential activities [29,30]. Hence, resilience failures in STSs can have much wider implications than system operators may initially anticipate, indicating the importance of evaluating resilience holistically rather than narrowly.

A widely adopted framework for operationalizing resilience is the 4R model, which encompasses robustness, rapidity, redundancy, and resourcefulness [31]. Robustness denotes the ability to withstand shocks without major performance loss, rapidity refers to the speed of recovery following disruption, redundancy captures the availability of alternative capacity to buffer against failure, and resourcefulness reflects the ability to mobilize resources to sustain critical functions [31]. This framework has been extensively applied to infrastructure resilience, including bridges, power grids, and emergency systems [32,33]. However, the application of the 4R framework to the operational dynamics of transportation services remains limited. Existing studies largely emphasize physical robustness, often focusing on how network connectivity withstands disruption [34]. Meanwhile, issues of service reliability and continuity for vulnerable user groups remain underexplored despite evidence that extreme weather exacerbates vulnerabilities in operational performance [15]. Extending the 4R model to STSs thus provides an opportunity to evaluate resilience at the service level while situating the analysis within a broader systems framework. This perspective moves resilience research beyond physical infrastructure and network connectivity toward user-centered performance metrics that reflect service continuity and accessibility under stress.

The objective of this study is to evaluate the resilience of STSs for mobility-impaired users under climate-induced stress. The focus is on the publicly operated “Duribal” program in Busan, South Korea, which provides paratransit services for people with disabilities. This study applies the 4R framework (i.e., robustness, rapidity, redundancy, and resourcefulness) to capture resilience through service-level dynamics. The analysis leverages a unique dataset of daily origin–destination (OD) records and passenger wait times linked with daily indicators of extreme weather events, including heatwaves, cold spells, and heavy rainfall. Robustness is assessed through the immediate impacts of extreme weather on trip volumes and wait times. Rapidity is measured through recovery trajectories, including half-life estimates, cumulative deviations, and disruption durations. Redundancy is examined through variability in wait times and the turnover of delay patterns across service zones. Resourcefulness is evaluated through service continuity and the extent to which critical trips are preserved under stress. By quantifying these four dimensions, this study provides a multidimensional profile of resilience for STSs in Busan. The contribution of this analysis lies not only in expanding the empirical evidence on specialized transportation resilience but also in demonstrating how systems theory and resilience frameworks can be applied to the operational performance of paratransit services. Also, the findings of this study may offer actionable insights for transportation planners and policymakers seeking to ensure equitable and sustainable mobility services for people with disabilities under conditions of climate stress.

2. Methods

2.1. Study Area and Data Sources

The empirical context of this study is Busan, the second-largest city in South Korea, with a population of approximately 3.3 million residents as of 2024 [35]. As the principal metropolitan center of the southeastern region, Busan is characterized by a complex urban geography in which coastal lowlands, steep hillsides, and river corridors coexist within the same urban fabric. This topographical heterogeneity poses structural challenges for transportation networks and makes accessibility particularly difficult for mobility-impaired people. Busan also has a humid subtropical climate with hot, humid summers and relatively mild winters. The city is frequently affected by extreme weather events such as summer heatwaves and heavy monsoon rainfall, while episodic cold surges during winter occasionally disrupt transportation operations. Demographically, Busan has one of the highest proportions of elderly residents among South Korean metropolitan areas, with more than one-fifth of its population aged 65 or older as of 2024 [35]. According to the Busan Metropolitan City Government [36], 174,256 persons with disabilities were registered in Busan as of December 2024, of whom 100,815 were aged 65 or older. These figures indicate the intersection of aging and disability in the study area. They justify the emphasis on accessibility for mobility-impaired users.

The focus within this context is the “Duribal” program, a paratransit service publicly operated by the Busan Metropolitan City Government. Duribal is designed to ensure mobility for individuals with disabilities who face substantial barriers in accessing conventional public transportation. The service is reservation-based and demand-responsive, requiring advance booking through phone or mobile application, and operates with a limited fleet of sedans and vans equipped with accessibility features. Because of the small fleet size and constrained resources, service disruptions often result in extended delays or missed trips.

The operational data used in this study consist of comprehensive service records obtained from the Busan Infrastructure Corporation, the agency responsible for Duribal operations. These records include daily OD trip data covering all rides provided through the service. Each trip record used in this study contains information on the reservation request time, boarding time, and alighting time. A key performance metric is passenger wait time, defined as the elapsed time between reservation confirmation and vehicle arrival for boarding. Because wait time directly reflects service quality and responsiveness, it is employed as a central variable for assessing resilience. The dataset covers a period of 15 months, from March 2024 to May 2025.

Alongside service records, this study incorporates meteorological data obtained from the Korea Meteorological Administration (KMA). For each calendar day in the study period, extreme weather events were identified according to the official classification criteria. A heatwave is defined as when at least one of the following conditions is met: the daily maximum apparent temperature of 33 °C or higher is expected to persist for two or more consecutive days, or a rapid increase or prolonged period of apparent temperature is expected to cause significant damage. A cold spell is defined between October and April when at least one of the following conditions is met: the morning minimum temperature drops by at least 10 °C from the previous day to 3 °C or lower and is at least 3 °C below the seasonal average, the morning minimum temperature of −12 °C or lower is expected to persist for two or more consecutive days, or a rapid temperature drop is expected to cause significant damage. Heavy rainfall is defined as when either a three-hour accumulated precipitation of 60 mm or more is expected or a twelve-hour accumulated precipitation of 110 mm or more is expected. Based on these thresholds, three binary indicators were constructed for each day: Heatwave, Cold Spell, and Heavy Rainfall. Each indicator takes the value 1 when the relevant condition is satisfied and 0 otherwise.

The operational and meteorological data are merged by date to create a unified daily dataset. Each observation day in the dataset is represented by service performance indicators derived from individual trip records. The first indicator is total trip volume, measured as the count of completed trips provided by the Duribal service on that day. The second indicator is average passenger wait time, calculated as the arithmetic mean of the elapsed time between reservation confirmation and vehicle boarding across all trips served on that day. In addition to the mean, the standard deviation of daily wait times is also considered to capture variability in service responsiveness. These daily indicators are then matched with the corresponding extreme weather event for the same calendar date, resulting in a dataset that aligns operational outcomes with external climatic stressors.

2.2. Resilience Framework and Operationalization

The resilience of STS can be understood as the capacity to absorb external disturbances, adapt to disruptions, and sustain critical functions during stress. This study operationalizes resilience by applying the 4R framework, which emphasizes robustness, rapidity, redundancy, and resourcefulness as key performance dimensions [31,33]. In the context of STS such as Duribal, the framework offers a structured means to quantify resilience in terms of service delivery rather than physical network performance. Each dimension is translated into measurable indicators derived from daily trip records and extreme weather events, allowing resilience to be systematically evaluated under conditions of heatwaves, cold spells, and heavy rainfall.

Robustness is conceptualized as the immediate capacity of the system to withstand stress without significant performance loss. In this study, robustness is measured by the percentage change in service indicators on event days compared with baseline values. Here, baseline performance is defined using all days without extreme weather events, from which the average daily wait time ${\overline{w}}_0$ and average daily trip volume ${\overline{v}}_0$ are calculated. For each event day $t$, robustness is then expressed as

$$\Delta W_t=\left({\displaystyle \frac{{\overline{w}}_t}{{\overline{w}}_0}}-1\right)\times 100, \Delta V_t=\left({\displaystyle \frac{v_t}{{\overline{v}}_0}}-1\right)\times 100,$$

(1)

where ${\overline{w}}_t$ is the mean wait time on day $t$ and $v_t$ is the number of completed trips on day $t$. The values $\Delta W_t$ and $\Delta V_t$ capture the percentage deviation of the service outcome from normal conditions. That is, a positive value of $\Delta W_t$ indicates longer wait times compared with normal conditions, while a negative value of $\Delta V_t$ indicates a reduction in service volume. Robustness is a widely adopted measure in resilience research because it provides an immediate signal of service deterioration or preservation when exposed to external shocks [31]. In the context of STS for people with disabilities, robustness is particularly meaningful since users have limited substitution options. Accordingly, this study reports both $\Delta W_t$ and $\Delta V_t$ in the main analysis, in order to reflect changes in user-facing service quality as well as system throughput under extreme weather conditions.

Rapidity refers to the speed at which a system returns toward its baseline state after disruption. Extending previous research [25,31], this study defines rapidity as the half-life, namely the number of days required for a disrupted indicator to recover halfway to its baseline. For an event occurring on day $t_0$, let $m_t$ denote the performance metric of interest, either average wait time or trip volume. Rapidity is calculated as

$$\tau =\mathrm{m}\mathrm{i}\mathrm{n}\left\{h\ge 1:\left|m_{t0+h}-m_0\right|\le {\displaystyle \frac{\left|m_{t0}-m_0\right|}{2}}\right\},$$

(2)

where $m_0$ is the baseline value. The half-life $\tau$ summarizes how quickly the system reduces performance deviations by half. Thus, this formulation treats recovery trajectories as a function of time until stabilization [33].

A fixed 30-day observation window is applied for half-life measurement. If the threshold in Equation (2) is not met within 30 days after $t0$, $\tau$ is treated as right-censored and is omitted from distributional summaries while being noted in the text. This convention prevents a small number of non-recovering cases from unduly inflating summary statistics.

In addition to the half-life, this study also employs the area under the curve (AUC) to capture the cumulative magnitude of deviation from baseline performance. In this approach, resilience loss is measured by the area between the baseline functionality and the observed recovery trajectory. Subsequent studies have applied AUC to diverse infrastructure and service systems, including transportation and telecommunication networks, as a measure of cumulative performance loss under disruption [37,38]. Formally, AUC is calculated as

$$\mathrm{A}\mathrm{U}\mathrm{C}=\sum _{d=0}^{14}\left|{\displaystyle \frac{{\overline{w}}_{t0+d}-{\overline{w}}_0}{{\overline{w}}_0}}\times 100\right|,$$

(3)

where ${\overline{w}}_{t0+d}$ is the mean wait time on day $t0+d$ and ${\overline{w}}_0$ is the baseline mean wait time, and the summation extends across a 14-day horizon following the event. The observation horizon is set to 14 days after each event, consistent with prior studies that emphasize the importance of short-term recovery trajectories in transportation and infrastructure systems [31,39]. A larger AUC indicates a greater cumulative deterioration in system performance, providing a comprehensive measure that complements the point estimate offered by the half-life.

In this study, AUC is computed for the wait-time series only, using absolute percentage deviations from baseline so that overshoots above and below baseline contribute symmetrically to cumulative loss. Recovery trajectories are additionally summarized by the median and interquartile range (IQR) across events of the same type to visualize typical paths and dispersion.

Redundancy describes the ability of the system to provide alternative capacity or buffer against disruptions. In traditional infrastructure resilience research, redundancy often refers to spare physical capacity or redundant network connections [32]. In the case of Duribal, where fleet resources are limited and service is demand-responsive, redundancy is proxied by the variability of passenger wait times across individual trips. For each day $t$, redundancy is measured as

$${\sigma }_t^2={\displaystyle \frac{1}{n_t-1}}\sum _{i=1}^{n_t}{\left(w_{it}-{\overline{w}}_t\right)}^2,$$

(4)

where $w_{it}$ is the wait time of trip $i$ on day $t$, ${\overline{w}}_t$ is the mean wait time on that day, and $n_t$ is the number of completed trips. A higher variance ${\sigma }_t^2$ indicates greater dispersion in user experience, suggesting that the system lacks the buffering capacity to maintain consistent service across users. Although this is an indirect proxy, it reflects operational vulnerability that would otherwise remain hidden in mean-based indicators. To mitigate undue influence from extreme day-level outliers, ${\sigma }_t^2$ is capped at the 99th percentile prior to visualization and descriptive summaries. This threshold balances the removal of undue influence from extreme outliers while retaining the vast majority of daily variation. All inference remains descriptive and nonparametric.

Resourcefulness emphasizes the extent to which the system mobilizes its limited capacity to preserve essential services during disruptions [31,33]. At the level of STS, this concept can be operationalized as throughput preservation and the protection of critical trips. For each event day $t$, two measures are defined:

$${\rho }_t={\displaystyle \frac{v_t}{{\overline{v}}_0}}\times 100, {\kappa }_t={\displaystyle \frac{1}{n_t}}\sum _{i=1}^{n_t}I\left(w_{it}\le 30\right),$$

(5)

where ${\rho }_t$ is the percentage of baseline trip volume maintained and ${\kappa }_t$ is the proportion of trips with wait times of 30 min or less. The 30 min threshold is consistent with ADA paratransit service guidelines, where delays exceeding this level are generally considered unacceptable [40]. The function $I\left(·\right)$ denotes the indicator function, which equals 1 if the condition inside the parentheses is satisfied and 0 otherwise. These measures reflect the continuity of service provision and the preservation of timely access, respectively. Since users of STS often rely on the service for medical appointments and daily necessities, maintaining short wait times for a critical subset of trips can be interpreted as an expression of resourcefulness under constrained conditions. In reporting, ${\kappa }_t$ is computed as a proportion in $[0, 1]$ and displayed as a percentage in figures for readability, while ${\rho }_t$ is already expressed as a percentage of baseline.

All four resilience dimensions are computed separately for heatwaves, cold spells, and heavy rainfall. The indicators are calculated directly from observed daily outcomes without imposing parametric models, ensuring that results are transparent and reproducible. While robustness and rapidity capture the immediate and temporal responses of the system, redundancy and resourcefulness provide insights into variability and continuity under stress. All analyses were conducted using R (version 4.5.0) with publicly available statistical packages [41].

3. Results

During the 15-month observation period, 63 extreme weather events were recorded, including 46 heatwaves, 3 cold spells, and 14 heavy rainfall episodes. Because cold spells occurred only three times, their results are reported descriptively in the text rather than included in the comparative analyses.

Across all 458 observation days, the STS system completed a total of 473,330 trips, which corresponds to an average of approximately 1033 trips per day.

Table 1. Descriptive statistics of daily STS operations (March 2024–May 2025).

Event Type	Days	Mean Daily Trips	SD Daily Trips	Mean Wait Time (min)	SD Wait Time (min)	Mean Critical Share (≤30 min)
Normal	396	1039	304	40.2	9.66	0.434
Heatwaves	46	1009	304	39.4	8.84	0.447
Heavy rainfall	14	977	316	41.0	11.10	0.422
Cold spell	3	914	238	33.1	5.26	0.550

Note: Event types are not mutually exclusive. A single day may be classified under more than one event type.

summarizes descriptive statistics for daily trips, waiting times, and the share of critical trips during the observation period. The mean passenger waiting time of 40.1 min, while around 44% of trips were completed within 30 min.

Each event was linked with daily operational outcomes of the STS system in Busan, producing resilience indicators for robustness, rapidity, redundancy, and resourcefulness. The following subsections present results for each dimension. Robustness is assessed using deviations in passenger wait times, rapidity is summarized through recovery half-life and cumulative deviation, redundancy is represented by the dispersion of individual wait times, and resourcefulness is described by throughput preservation and the share of critical trips.

3.1. Robustness of STS Under Extreme Weather Events

The robustness analysis revealed distinct patterns of system response across extreme weather types. Figure 1 shows the changes in passenger volume (Δ$V$), while Figure 2 presents the corresponding changes in passenger waiting time (Δ$W$).

During heatwaves (n = 46), passenger demand declined slightly, with an average change in Δ$V$ of −2.91% and a 95% confidence interval (CI) of [−11.36, 5.53]. Passenger waiting times also decreased, with an average Δ$W$ of −2.03% (95% CI: [−8.39, 4.32]). This pattern suggests that reductions in travel demand during hot weather may have eased operational pressure, resulting in shorter waiting times despite the adverse conditions.

Cold spells (n = 3) were associated with lower demand and shorter waiting times, with average Δ$V=-12.10\%$ and Δ$W=-17.66\%$. These values indicate that reduced demand during cold weather may have relieved operational load. However, because only three events were observed, these results are descriptive only and should not be interpreted as statistically robust.

Heavy rainfall events (n = 14) produced a different pattern from heatwaves and cold spells. Passenger demand declined on average by −6.03% (95% CI: [−21.95, 9.89]), while waiting times increased, with an average Δ$W$ of +2.10% (95% CI: [−12.42, 16.61]). This divergence suggests that rainfall disrupted service operations to the extent that reduced demand did not translate into shorter waits. In contrast to heatwaves and cold spells, where lower demand was accompanied by shorter waiting times, heavy rainfall imposed additional operational challenges that lengthened passenger delays despite fewer trips being served.

3.2. Rapidity of Recovery Following Disruption

The analysis of rapidity focused on how quickly service performance recovered following extreme weather events. Figure 3 presents the distribution of half-life values calculated only for events with recovery observed within 30 days. Outliers above this threshold were right-censored and excluded from visualization to focus on short-term recovery dynamics.

Median half-life values were short for both major event types: 3.0 days [Q1 = 2.0, Q3 = 6.3] for heatwaves and 2.0 days [Q1 = 1.0, Q3 = 4.0] for heavy rainfall. During heatwaves, the median half-life was 3 days, indicating that disruptions in waiting times typically diminished within a few days, though the wider dispersion suggests that some episodes required longer recovery. Heavy rainfall events showed a slightly shorter median half-life but with considerably larger variability, implying delayed recovery in a subset of cases. Descriptively, the three cold spell events exhibited half-life values of 1–2 days, suggesting very short-lived disruptions, but the small number of cases prevents further interpretation.

Cumulative impacts were assessed through the 14-day AUC of absolute deviations from baseline, as shown in Figure 4. The AUC measures the magnitude of instability by summing absolute deviations from baseline performance.

Heatwaves produced a mean AUC of approximately 255, while heavy rainfall yielded a larger average of about 285. This pattern indicates that although recovery was somewhat slower for heatwaves, the cumulative instability burden was greater under rainfall, reflecting larger fluctuations during the recovery period. Cold spells displayed average AUC values near 290, consistent with their initial shocks despite rapid recovery.

Figure 5 illustrates median recovery trajectories and IQRs of wait-time deviations over the 14-day horizon. Heatwaves produced relatively stable trajectories, with deviations generally within ±5–10% of baseline, although fluctuations persisted for several days. Heavy rainfall generated the strongest and most irregular disruptions, with initial increases of +15–20% and wide oscillations throughout the recovery period. The three cold spell events often exhibited sharp initial drops in waiting time, reaching as low as −20% compared with baseline.

These results highlight that although recovery generally occurred within a short timeframe, the cumulative disruption burden varied across event types. Heatwaves were characterized by moderate but persistent disturbances, whereas heavy rainfall produced the most severe and irregular instability, making it the most disruptive condition for maintaining stable service performance. Cold spells, in contrast, showed brief and sharp shocks.

3.3. Redundancy Through Variability in Wait Time Experience

Figure 6 presents the distribution of daily wait-time variance for heatwaves and heavy rainfall, capped at the 99th percentile to mitigate the influence of outliers. This indicator reflects the degree of consistency in user experiences, where higher variance denotes greater disparities in passenger waiting times.

During heatwaves, the median variance was 508.5 (IQR: 406.3–619.0). This level indicates that although the system generally maintained functionality, passenger experiences diverged considerably, with some riders facing substantial delays while others experienced minimal disruption. The results suggest that heatwaves generate uneven service delivery, amplifying heterogeneity in user outcomes.

Heavy rainfall exhibited the highest degree of inconsistency, with a median variance of 554.3 (IQR: 398.0–623.7). This result indicates that heavy rainfall events not only suppressed trip volumes but also created large disparities in waiting times, with some passengers experiencing significant delays while others were served much more promptly. Such variability underscores the operational instability of the system during heavy rainfall, reflecting the most pronounced loss of redundancy among the three event types.

The three cold spell events were associated with lower variance, with a median of 386.4 (IQR: 315.7–443.1).

Therefore, the redundancy analysis indicates that heatwaves and heavy rainfall both increased inequality in service delivery, with heavy rainfall standing out as the most destabilizing condition in terms of user-level variability. Cold spells, by contrast, appeared to produce relatively uniform impacts, though the evidence is too limited to draw firm conclusions.

3.4. Resourcefulness in Preserving Critical Service

Resourcefulness was evaluated in terms of two complementary measures: overall service sustainment (${\rho }_t$), defined as the proportion of baseline trip volume maintained during events, and critical trip preservation (${\kappa }_t$), defined as the share of trips served within 30 min of request. Figure 7 and Figure 8 summarize these indicators for heatwaves and heavy rainfall.

During heatwaves, service sustainment remained near baseline levels, with an average ${\rho }_t$ of 97.1% (95% CI: 88.6–105.5). Heavy rainfall events showed a similar pattern, with an average ${\rho }_t$ of 94.0% (95% CI: 78.1–109.9). These results indicate that overall throughput was largely preserved even under adverse weather conditions.

The preservation of critical trips exhibited a distinct pattern. The median ${\kappa }_t$ during heatwaves was 0.41 (IQR: 0.32–0.61), reflecting relatively stable performance near baseline. Heavy rainfall produced wider fluctuations, with ${\kappa }_t$ values ranging from below 0.30 to above 0.60, suggesting that timely access for critical trips was less consistently maintained under conditions of intense precipitation.

The three cold spell events showed lower sustainment, with an average ${\rho }_t$ of 87.9% and wide uncertainty intervals, but a relatively high ${\kappa }_t$ of about 0.54.

These results highlight distinct trade-offs in system resourcefulness under different types of stress. Heatwaves preserved both throughput and critical trips at stable levels. Heavy rainfall, on the other hand, showed relatively high throughput sustainment but limited consistency in preserving timely access, revealing a vulnerability in maintaining equitable service quality during episodes of intense precipitation.

4. Discussion

This study examined the resilience of STS for people with disabilities in Busan under extreme weather events, focusing on heatwaves, cold spells, and heavy rainfall. The results revealed that different types of weather stressors produced distinct operational and equity-related disadvantages, which have direct implications for how such systems can be made more resilient in the future.

Heatwaves produced a pattern of reduced trip demand alongside shorter passenger wait times. On the surface, this outcome may suggest that service performance is preserved or even improved under high-temperature conditions. However, such improvements are largely the by-product of reduced user demand rather than operational robustness. In other words, the system appeared more efficient because fewer passengers were traveling, not because the service itself adapted effectively to heat-related stress. This reliance on suppressed demand reflects a fragile form of resilience, since climate stress does not reduce the need for essential mobility. Travel demand is known to decline during periods of extreme heat, but such behavioral adjustments cannot be interpreted as evidence of systemic robustness [9]. Moreover, the long-term resilience of transportation cannot rest on demand suppression alone, as structural measures are required to ensure continuity of critical mobility [4]. Users who are able to cancel or postpone trips may avoid excessive waiting times, but those with urgent needs, such as medical purposes, cannot exercise the same flexibility. To strengthen resilience during heatwaves, the emphasis should therefore be on operational stability. Guaranteeing vehicle availability during peak heat periods, modifying driver schedules to reduce fatigue risks, and monitoring vehicle performance to prevent heat-related breakdowns are strategies that can sustain service reliability when demand suppression alone would otherwise mask underlying vulnerabilities.

Heavy rainfall presented the most destabilizing set of conditions, producing reduced demand but increased wait times. Moreover, it generated the highest variability in passenger experience, indicating that users were affected in highly unequal ways depending on location and trip urgency. This divergence indicates that operational disruptions, such as congestion, flooded roadways, and extended trip durations, overwhelmed any relief generated by lower demand. Importantly, rainfall was associated with the greatest variation in service reliability among STS riders, with some passengers facing disproportionately long delays while others were served much more promptly depending on residence location. Such patterns highlight that rainfall not only diminishes average performance but also creates inequities within the STS user population. These results reinforce arguments that accessibility justice requires attention not just to mean outcomes but also to the distribution of mobility opportunities [29,30]. For a service that primarily serves people with disabilities and limited mobility, these disparities are particularly concerning. Policy responses must therefore prioritize rainfall resilience as a central challenge. Measures may include pre-positioning vehicles in high-demand or flood-prone areas, expanding coordination with emergency transport resources, and developing adaptive scheduling algorithms that reroute vehicles dynamically when corridors are impaired. Such operational adaptations are consistent with broader climate adaptation strategies that emphasize proactive contingency planning for extreme precipitation events [4,42]. Incorporating rainfall-specific contingency plans into resilience frameworks would help buffer the disruptive and inequitable impacts.

Cold spells were rare during the observation period, with only three events recorded. These episodes showed declines in trip volume and shorter wait times, but the limited number of cases prevents drawing meaningful insights about their resilience profile. At most, the results suggest that cold spells did not generate prolonged disruptions, yet the evidence is too limited to support broader interpretation or policy implications.

The differentiated effects observed across heatwaves, cold spells, and heavy rainfall highlight that resilience in STS cannot be treated as a uniform property but instead depends on the mechanisms through which stressors interact with demand and operations. Heatwaves reduce travel demand, which masks underlying fragility and calls for maintaining operational stability despite apparent improvements. Heavy rainfall directly disrupts transport corridors, leading to instability and inequities that require proactive rerouting, vehicle pre-positioning, and monitoring of user-level disparities. Cold spells, while too rare in this dataset to support firm conclusions, suggest that prioritization of essential trips can emerge under constrained capacity. The overarching lesson is that resilience planning should be tailored to the type of stressor: sustaining supply during heat, managing instability and inequality during rainfall, and treating rare cold events as tests of prioritization protocols. This differentiated framing moves beyond simply ranking weather events by severity and instead links each stressor to distinct resilience strategies that can guide operators and policymakers. For example, the results can generate profiles and their practical implications, as illustrated in

Table 2. Resilience profiles of specialized transportation service under extreme weather.

Weather Condition	Robustness	Rapidity	Redundancy	Resourcefulness
Heatwaves	Apparent stability from lower demand	Not critical	Low system buffer	Essential trips exposed
Cold spells	Reduced overall service	Fast recovery	Critical trips preserved	Prioritization evident
Heavy rainfall	Service disrupted despite lower demand	Unstable recovery	High variability	Limited adaptive response

.

Building on these differentiated resilience profiles, targeted strategies can be outlined for Busan by linking operational vulnerabilities to established climate risks. During heatwaves, maintaining full fleet availability remains crucial, since suppressed travel demand often conceals rather than eliminates mobility needs. Evidence from Korea demonstrates that heat extremes significantly increase mortality among older adults and individuals with underlying health conditions [19]. In a city where population aging is pronounced, STS should therefore consider heat-adaptive workforce scheduling, enhanced cooling provisions for drivers, and systematic monitoring of vehicle systems prone to heat-related failures. Heavy rainfall presents a distinct set of challenges. Previous analyses have identified low-lying districts in Busan, particularly around the Suyeong and Oncheon rivers, as highly vulnerable to inundation [43]. More recent work indicates the necessity of integrated flood management, emphasizing anticipatory measures such as early-warning systems and pre-disaster operational planning [44]. For STS, this suggests the value of pre-positioning vehicles in areas with lower exposure, deploying real-time rerouting protocols to bypass waterlogged corridors, and monitoring service disparities across zones. Detecting uneven distributions of waiting times can provide early signals of inequity, prompting corrective allocation of resources to neighborhoods experiencing disproportionate delays. Cold spells, while infrequent, still pose non-negligible risks. National evidence shows that short-lived but intense cold extremes continue to generate elevated mortality [19]. In such episodes, the STS system of Busan would benefit from explicit prioritization rules embedded in the reservation platform, ensuring that health-related and essential daily-living trips receive precedence whenever capacity becomes constrained. These strategies align empirical resilience patterns with the broader policy context in Busan. Evaluations of Korean metropolitan adaptation policies reveal that the city has often lagged in translating planned measures into implementation, especially in domains related to health and disaster management [45]. Against the backdrop of intensifying climate hazards, rapid population aging, and a high prevalence of disability, the integration of resilience-oriented operational protocols into specialized transportation services is no longer optional but necessary for sustaining equitable mobility.

5. Conclusions

This study has demonstrated that the resilience of STSs for people with disabilities cannot be captured by aggregate indicators alone but must be assessed in terms of how systems perform under differentiated climatic stressors. By examining service responses to extreme weather, the analysis revealed that resilience is not a uniform attribute of STS systems but a context-dependent quality shaped by the type of disruption and its equity implications. Rather than focusing solely on continuity of operations, resilience must be understood as the capacity to sustain essential mobility for vulnerable users when conditions are most adverse.

Conceptually, this study seeks to contribute to resilience research by applying the 4R framework to STSs and illustrating how robustness, rapidity, redundancy, and resourcefulness manifest differently under distinct climatic stressors. This study also draws on a large-scale operational dataset from STS systems in Busan to provide insights into how extreme weather can influence both service continuity and equity of access. From a practical perspective, this study suggests several event-specific strategies that could strengthen the resilience of STSs, including operational stability for heatwaves, formal prioritization of critical trips during cold spells, and contingency planning for heavy rainfall. These findings shed light on the importance of embedding a resilience perspective more explicitly into transportation planning and social policy for vulnerable populations.

Nonetheless, several limitations should be acknowledged. First, the analysis covered only a 15-month observation window, which restricts the ability to capture long-term climatic variability or rare but high-impact events. Cold spell events were also rare during the study period, which limits the robustness of statistical inference and requires that the reported results for cold spells be interpreted as descriptive rather than conclusive. In addition, the analysis focused on a single metropolitan area, so the findings may not be generalizable to other institutional or climatic contexts. Finally, the study relied on service operation data and did not incorporate user perspectives, which are critical for assessing perceived accessibility and equity. Future research should address these limitations by conducting comparative studies across multiple cities, incorporating additional types of extreme weather events, and employing survey or qualitative methods to capture user experiences. Scenario-based simulations could also be used to evaluate the effectiveness of alternative resilience strategies under projected climate conditions.

Resilience planning for transportation systems for people with disabilities should not be approached as a matter of average service continuity but as the ability to sustain essential mobility for vulnerable populations under differentiated risks. As extreme weather becomes a recurring feature of urban environments, ensuring the resilience of STSs is not only a technical requirement but also a question of transport justice. Integrating the differentiated resilience strategies identified in this study into climate adaptation policies and accessibility frameworks will be essential for securing sustainable and inclusive mobility.