Assessing the Sustainability of Instream Flow Under Climate Change Considering Reservoir Operation in a Multi-Dam Watershed

Abstract

Sustaining instream flows is becoming increasingly critical due to the combined pressure of climate change and intensive reservoir operations in multi-dam watersheds. This study evaluates instream flow sustainability in the Seomjin River basin by integrating the SWAT and K-WEAP models with CMIP6-based climate scenarios. Two contrasting dam operation strategies—firm and deficit supply—were assessed over multiple temporal scales, including hydrological seasons and agricultural activity. Sustainability was quantified using the Sustainability Index (SI), which integrates reliability, resilience, and vulnerability. The probabilistic assessment revealed that the relative performance of the two strategies varied depending on the season and flow conditions. The firm supply generally exhibited higher sustainability under drought and low-demand periods, effectively reducing the probability of unsustainable outcomes. In contrast, the deficit supply often achieved higher sustainability under wet conditions or peak agricultural demand, although it was occasionally linked to extremely low SI values. These findings underscore the importance of season-specific, risk-informed dam operation planning over reliance on a single strategy and emphasize the need for flexible management frameworks capable of responding to diverse hydrological futures.

1. Introduction

While historically essential to human advancement, rapid water resource development in recent decades has cumulatively resulted in significant environmental degradation [1]. One notable consequence is the ongoing degradation of river ecosystems, which led to the introduction of the instream flow concept to mitigate such impacts [2,3]. The concept of instream flow was first implemented in the United States in the 1940s [4], and, subsequently, many countries adopted this concept to address aquatic ecosystem degradation due to excessive water utilization [5]. Due to limited data availability in the early stages, water allocation efforts primarily focused on determining the minimum flow requirements; however, research clarifying the relationships between flow and ecological responses has progressively supported effective water management strategies [6,7]. Adaptive management has since evolved to quantify ecological responses to hydrological variability and to promote optimized operations that consider environmental interactions [8,9].

The management of instream flow releases in multipurpose dam operations has become a major global concern in water resources planning [10]. Increasing dam construction has exacerbated negative impacts on river ecosystems, prompting extensive research into long-term flow changes and ecosystem interactions, thereby advancing scientific methodologies for instream flow management [2,11]. This recognition has emphasized the need for river ecosystem conservation and environmentally aligned water allocation [12]. However, growing water demands for food and energy security, coupled with hydrological uncertainties due to climate change, complicate policies centered on ecosystem conservation [6,13]. Despite growing awareness, biodiversity conservation and ecosystem restoration often remain lower priorities in water allocation policies [14]. South Korea has followed a similar pathway, defining instream flow as water preserved or released for maintaining aquatic ecosystem conditions [15]. Major multipurpose dam projects have incorporated instream flow management practices, advancing scientific research and management techniques. Over recent decades, various policies and regulations for instream flow calculation and assessment have continually evolved and been refined in South Korea [16].

Climate change is increasingly recognized as a significant challenge for instream flow management. Global warming has intensified hydrological uncertainty by altering precipitation and evapotranspiration patterns, thereby increasing river flow variability and complicating water resource management [17]. Recent studies project increased frequency and severity of floods and droughts under future climate scenarios, making the stable provision of instream flow for ecosystem maintenance more complex [18,19,20]. Furthermore, traditionally static and deterministic dam operation practices are shifting toward dynamic, adaptive management approaches to accommodate hydrological variability driven by climate change. Therefore, incorporating climate scenarios into instream flow assessments is crucial, and recent research has quantitatively analyzed changes in river flows using various climate scenarios integrated into hydrological models, such as the Soil and Water Assessment Tool (SWAT), and water balance models, like the Water Evaluation and Planning (WEAP) system [21]. These approaches are expected to offer essential insights into assessing long-term instream flow sustainability and formulating effective management strategies to mitigate climate change-related risks to river ecosystems.

This study aims to assess the long-term sustainability of instream flow in a multi-dam watershed under climate change. The assessment focuses on how different dam operation strategies affect instream flow and increase the hydrological uncertainty. To this end, a probabilistic approach was established using an integrated water balance modeling framework to examine scenario-based variations in sustainability, considering both climate-driven runoff conditions and seasonal patterns of water demand. The evaluation was carried out not only for the entire period but also for hydrologically meaningful divisions, as well as farming seasons. The analysis was believed to reveal the structural differences between operation strategies and support scenario-based interpretations of sustainability, inform climate-adaptive strategies for instream flow management, and indicate insights for adaptive, ecosystem-oriented water management under future climate conditions.

2. Materials and Methods

2.1. Study Area

The Seomjin River basin, situated in southwestern South Korea, covers an area of approximately 4911.9 km². It is one of the nation’s five major river basins, with the Seomjin River originating from highland areas in the north and flowing southward into the sea. The main river stretches about 223.9 km in length. Its largest tributary, the Boseong River, rises in the southwest and merges with the Seomjin River in its lower reaches. The basin experiences an average annual precipitation of 1432.6 mm [22], with a distinct seasonal pattern, and approximately 60 to 70% of the total rainfall occurs during the wet season between June and September. In response to the increasing water demand, numerous dams have been constructed across the basin. These include multipurpose dams (e.g., Seomjin and Juam), municipal water supply dams (e.g., Dongbok and Sueo), the Donghwa Dam, which serves both agricultural and municipal needs, and the hydroelectric Boseong River Dam (Figure 1a).

Although these large-scale facilities have endowed the basin with significant water storage capacity, approximately 80% of the stored water is transferred to regions outside the basin. This extensive transfer is largely driven by high demand from surrounding regions and industrial complexes located in the lower Seomjin River basin. The concentration of major reservoirs in the upper basin, coupled with high downstream demand, makes reservoir operations a critical factor controlling downstream flow regimes. Releases from these reservoirs directly influence the instream flow and become a dominant source of flow variability within the basin. This dependency, especially during dry seasons or drought events, heightens the risk of conflicts among water users.

A total of 13 instream flow monitoring points have been officially designated by the government and are distributed primarily along the Seomjin River and its key tributaries (Figure 1b). Each point is assigned a minimum flow requirement based on low-flow statistics, ecological conditions, and water management criteria. With the exception of Point 1 (Unam-gyo), all monitoring locations are directly affected by dam releases. As such, the operation of upstream reservoirs plays a decisive role in meeting the designated minimum flow targets. These monitoring sites play a key role in observing changes in flow regimes induced by regulated releases and diversions, while also serving as indicators of the long-term sustainability and reliability of water supply in the basin.

The Seomjin River estuary supports the harvesting of corbicula (freshwater clams), a regional specialty. However, the expansion of the Daap intake station and increased water withdrawals have substantially reduced downstream flows, contributing to multiple cases of environmental degradation. Declining flow volumes have led to deteriorated water quality and increased salinity levels, resulting in reduced shellfish productivity and growing public complaints. Despite the basin’s extensive storage infrastructure, these developments underscore its high vulnerability to drought stress and highlight persistent challenges in ensuring balanced water allocation.

2.2. Model Setting

2.2.1. Hydrological Modeling

This study integrates the Soil and Water Assessment Tool (SWAT) with the Korea Water Evaluation and Planning (K-WEAP) model to assess the sustainability of instream flow at multiple demand sites under climate change scenarios. SWAT functions as the primary hydrological model, simulating natural runoff under climate scenarios. The K-WEAP model then uses this runoff to perform detailed water budget analyses under varying water supply management strategies.

SWAT is a physically based, semi-distributed watershed model developed by the United States Department of Agriculture, Agricultural Research Service (USDA-ARS), designed to represent essential hydrological processes such as surface runoff, evapotranspiration, infiltration, and groundwater flow at watershed scales [23]. These hydrological processes are governed by the following water balance equation:

$${SW}_t={SW}_0+\sum _{i=1}^t{(R}_{day}-Q_{surf}-W_{seep}-E_a-Q_{gw})$$

(1)

where SW_t represents the soil water content at the time (mm H₂O), SW₀ is the initial soil water content on the day (mm H₂O), R_day is the daily precipitation (mm H₂O), Q_surf denotes the daily surface runoff (mm H₂O), W_seep indicates the daily percolation to the vadose zone (mm H₂O), E_a signifies the daily evapotranspiration (mm H₂O), and Q_gw describes the daily groundwater return flow (mm H₂O). SWAT has been widely applied in hydrological studies to estimate unregulated runoff under diverse watershed and climate conditions [24,25,26]. This study utilizes SWAT to derive runoff estimates reflecting climate-induced hydrological variations.

The K-WEAP model, a modified version of WEAP, was co-developed by the Stockholm Environment Institute Boston Center and the Korea Institute of Construction Technology, specifically tailored to the hydrological and operational characteristics of South Korean watersheds [27]. As a conceptual tool, K-WEAP allows users to define and manipulate parameters such as water demands, allocation priorities, supply preferences, and ecological requirements, thereby facilitating the detailed analysis and optimization of regional water supply infrastructures. Numerous studies have applied K-WEAP to assess and enhance water resource management in various watersheds of South Korea [28,29].

In this integrated modeling framework, SWAT delineates the watershed into standardized sub-basins, typically used as fundamental hydrological analysis units in Korea, providing daily runoff estimates for each sub-watershed. In contrast, K-WEAP operates on a five-day timestep to better represent water routing processes such as abstraction, consumption, and return flows, thereby minimizing potential errors associated with shorter intervals. The simulation period spans 90 years (2011–2100), with model calibration performed over the decade 2010–2019. Key input datasets, such as digital elevation models, soil types, and land use data, were sourced from national GIS databases. Data on water abstraction, return flows, and inter-basin transfers were obtained from government statistics and incorporated into the modeling framework.

2.2.2. Climate Change Scenario

CMIP6, developed by the Intergovernmental Panel on Climate Change (IPCC), offers a robust framework for analyzing a range of future climate conditions [30]. CMIP6 scenarios are structured around five distinct Shared Socioeconomic Pathways (SSPs): SSP1 (sustainability), SSP2 (middle of the road), SSP3 (regional rivalry), SSP4 (inequality), and SSP5 (fossil-fueled development). These pathways incorporate varying assumptions about demographic trends, economic growth, and greenhouse gas emissions, presenting distinct challenges for climate mitigation and adaptation. This study employs climate data from four CMIP6 scenarios—SSP1, SSP2, SSP3, and SSP5—to enhance predictive robustness and minimize uncertainties associated with reliance on a single climate projection. The meteorological inputs for SWAT include precipitation, maximum and minimum temperatures, relative humidity, wind speed, and solar radiation, as summarized in

Table 1. Climate models of CMIP6 applicable to the SWAT model.

Model	Institute
ACCESS-CM2	Commonwealth Scientific and Industrial Research Organization (Australia)
ACCESS-ESM1-5	Commonwealth Scientific and Industrial Research Organization (Australia)
CanESM5	Canadian Centre for Climate Modeling and Analysis (Canada)
CNRM-CM6-1	Centre National de Recherches Meteorologiques (France)
CNRM-ESM2-1	Centre National de Recherches Meteorologiques (France)
GFDL-ESM4	Geophysical Fluid Dynamics Laboratory (USA)
INM-CM4-8	Institute for Numerical Mathematics (Russia)
INM-CM5-0	Institute for Numerical Mathematics (Russia)
IPSL-CM6A-LR	Institute Pierre-Simon Laplace (France)
MIROC6	Japan Agency for Marine-Earth Science and Technology/Atmosphere and Ocean Research Institute/National Institute for Environmental Studies/RIKEN Center for Computational Science (Japan)
MPI-ESM1-2-HR	Max Planck Institute for Meteorology (Germany)
MPI-ESM1-2-LR	Max Planck Institute for Meteorology (Germany)
MRI-ESM2-0	Meteorological Research Institute (Japan)
NorESM2-LM	NorESM Climate modeling Consortium consisting of CICERO (Norway)
UKESM1-0-LL	Met Office Hadley Centre (UK)

.

To systematically identify extreme climatic conditions—particularly those that predispose watersheds to drought and water shortages—this study adopted the methodology developed by the Expert Team on Climate Change Detection and Indices (ETCCDIs), a joint initiative of the World Meteorological Organization (WMO) and the World Climate Research Program [31]. Extreme events, notably drought episodes, are fundamentally driven by variations in precipitation intensity and frequency [32]. Therefore, accurately projecting and assessing these extreme events is essential for understanding the underlying causes of water deficits. The ETCCDI framework includes 27 standardized indices, consisting of 11 precipitation-related and 16 temperature-related metrics (

Table 2. Precipitation indices of ETCCDI.

Index	Definition	Unit
RX1day	Monthly maximum 1-day precipitation	mm
RX5day	Monthly maximum consecutive 5-day precipitation	mm
SDII	Annual total precipitation divided by the number of wet days (PRCP ≥ 1.0 mm) in the year	mm/day
R10	Annual count of days when precipitation ≥ 10 mm	Days
R20	Annual count of days when precipitation ≥ 20 mm	Days
R25	Annual count of days when precipitation ≥ 25 mm	Days
CDD	Maximum number of consecutive days with RR < 1 mm	Days
CWD	Maximum number of consecutive days with RR ≥ 1 mm	Days
R95p	Annual total precipitation from days > 95th percentile	mm
R99p	Annual total precipitation from days > 99th percentile	mm
PRCPTOT	Annual total precipitation in wet days (RR ≥ 1 mm)	mm

). In this study, precipitation-based indices were applied to the target watershed to categorize and quantify dryness under each climate scenario.

2.2.3. Dam Operation Scenario

From a water supply perspective, dam and reservoir operations can be broadly classified into two main strategies: firm supply and deficit supply. The firm supply strategy involves releasing a predetermined, constant volume of water—known as the planned supply—regardless of downstream water demand or shortage conditions. This method prioritizes delivering the planned release volume, with no additional discharge unless the reservoir exceeds the full supply level, in which case excess water is released via the spillway. Under this approach, downstream hydrological conditions are not explicitly considered in the operational logic.

In contrast, the deficit supply strategy is demand-responsive, focusing on actual downstream water needs and shortages. When the natural river flow is insufficient to meet water demand, the dam compensates by releasing additional volumes equivalent to the observed deficit. It does not follow a fixed release schedule but responds dynamically to real-time deficits and available storage. Water is continuously released as long as the dam has sufficient capacity to address downstream shortfalls. Although this strategy aims to minimize downstream shortages through maximum releases, its idealized nature often faces real-world constraints—physical, institutional, or environmental.

In South Korea, the current national water resources plan adopts the deficit supply strategy as an operational assumption. This approach is intended to reflect the maximum theoretical capacity of the existing water supply system to meet future water demands. However, the deficit supply represents an idealized form of dam operation and, in practice, is rarely implemented in its pure form. In practice, most infrastructure operates under firm supply principles or hybrid models that combine both strategies depending on situational demands. Recognizing this, incorporating both firm and deficit supply scenarios into long-term planning enables a more realistic assessment of future water shortages. Such a dual-scenario approach enables planners to identify the full range of possible deficits under varying hydrological and operational conditions. This approach strengthens water resources planning by enabling proactive risk assessments and the development of adaptive strategies for addressing future supply-demand imbalances.

2.3. Sustainability Index

Three key indices commonly used to evaluate water security—reliability, resilience, and vulnerability (RRV)—were first introduced by Hashimoto et al. [33]. Reliability (R_el) measures the likelihood of a system meeting water demand and is calculated as the ratio of satisfactory periods to the total number of periods. Resilience (R_es) assesses the system’s recovery capability after a failure, representing the probability of returning from an unsatisfactory to a satisfactory condition. Vulnerability (V_ul) quantifies the severity of system failure by evaluating the volume of unmet demand. The three indicators are calculated as follows:

$$R_{el}=1-{\displaystyle \frac{\sum _{j=1}^{M}d\left(j\right)}{T}}$$

(2)

$$R_{es}=\{{{\displaystyle \frac{1}{M}}\sum _{j=1}^{M}d\left(j\right)\}}^{-1}$$

(3)

$$V_{ul}={\displaystyle \frac{1}{M}}\sum _{j=1}^{M}v\left(j\right), V_{ul.d}={\displaystyle \frac{\frac{1}{M}\sum _{j=1}^{M}v\left(j\right)}{Annual demand}}$$

(4)

where M is the total number of water deficit events, T is the number of time intervals, d(j) is the duration of the water deficit event j (days), and v(j) is the severity of the jth water deficit event (Mm³).

While each of these performance metrics offers standalone insight, they can also be integrated into a composite indicator for holistic evaluation. Loucks [34] introduced the Sustainability Index (SI) to quantitatively assess water system sustainability and facilitate comparisons among management strategies. This index has since been widely applied to assess the sustainability of both demand sites and supply sources. The SI can be calculated using the following equation:

$$SI={[R_{es}\times R_{es}\times \left(1-V_{ul.d}\right)]}^{1/3}$$

(5)

Each component of the SI is dimensionless and ranges from 0 to 1; accordingly, the SI also lies within the [0, 1] interval. If any of the component metrics equals zero, the SI becomes zero, indicating complete unsustainability. Unlike reliability and resilience, vulnerability represents an inverse relationship with system stability. To ensure conceptual consistency with reliability and resilience, vulnerability is transformed as 1 − V_ul.d. In this study, equal weighting was assigned to each component, assuming uniform importance among the three indicators in the SI formulation.

Sandoval-Solis et al. [35] proposed a group-level SI to assess the sustainability of an entire water system, shifting focus from individual demand sites to system-wide performance. This approach involves aggregating the sustainability indices of individual demand sites using a weighted average that reflects the relative water demand of each site. The group SI can be calculated using the following expression:

$$W_i={\displaystyle \frac{Water deman{d}_i}{Water deman{d}_k}}$$

$${SI}_k=\sum _{i=1\in k}^{i=j\in k}{W}_i\times S{I}_i$$

(6)

where $W_i$ is the relative weight of demand site i within group k, $S{I}_i$ is the sustainability index of site i, and ${SI}_k$ is the group-level sustainability index, calculated as the weighted average of the individual indices.

2.4. Temporal Resolution

Relying solely on annual mean SI values in assessing long-term instream flow sustainability can obscure important hydrological and demand-driven dynamics. This approach risks distorting the system performance by masking inter-annual variability and seasonal clustering of flow deficits or surpluses. Consequently, evaluations based solely on annual averages may underestimate significant hydrological risks. To overcome these limitations, this study employed a multi-temporal resolution framework that incorporates intra-annual variations in hydrology and demand.

Firstly, the simulation period was divided into two hydrological seasons: dry and wet. The wet period, from June to September, corresponds to Korea’s monsoon season, characterized by substantial increases in precipitation and runoff [36]. In contrast, the dry period spans January to May and October to December, when limited precipitation and inflows may constrain instream flow maintenance. Secondly, the analysis accounted for seasonal water demand by distinguishing between the farming busy season and the off-season. The busy season, from May to October, coincides with peak agricultural water demand, potentially intensifying competition with instream flow requirements [37]. The off-season, from November to April, is marked by lower agricultural demand, allowing for more flexible water resource operations. This seasonal and demand-based stratification captures intra-annual imbalances in flow availability and related operational risks, which are often overlooked in annual-scale assessments.

3. Results and Discussion

3.1. Model Preparation

The framework for water balance modeling builds on the approach of Kim et al. [38], where the SWAT and K-WEAP models were calibrated to simulate water supply dynamics in the Seomjin River basin. The calibration was conducted using daily streamflow data from monitoring stations unaffected by dam operations. The SWAT model was used to estimate natural flow conditions, and its outputs were post-processed into a format compatible with K-WEAP input requirements. These process data were then provided as inflow time series to the K-WEAP model. The K-WEAP calibration involved optimizing the operational parameters, including flow routing and allocation ratios. The results demonstrated strong applicability for runoff simulation. Visual comparisons of observed and simulated streamflow confirmed that the model reproduced hydrological patterns. The calibration results of the integrated hydrological model are described in detail in the previous study.

Climate change scenarios were selected following the methodology of Kim et al. [38]. Out of 60 scenarios (15 GCMs × 4 SSPs), those consistently showing low precipitation across the indices—namely INM-CM4-8 SSP5, INM-CM4-8 SSP2, and MIROC6 SSP3—were selected as the representative dry scenarios. To support a balanced probabilistic assessment, additional scenarios reflecting moderate and wet conditions were selected. These included CNRM-ESM2-1 SSP3, MPI-ESM1-2-HR SSP5, and MRI-ESM2-0 SSP3 as the moderate scenarios and CanESM5 SSP1, SSP3, and SSP5 as the wet scenarios. Climate data from the nine selected scenarios were applied to the calibrated SWAT-KWEAP model to simulate long-term inflow dynamics. This enabled the evaluation of instream flow sustainability under diverse future climate conditions.

3.2. Group-Level Evaluation of Sustainability Index

Annual SI values from individual instream flow sites were aggregated into a group-level indicator, reflecting the overall sustainability within the Seomjin River basin. A boxplot analysis was used to evaluate the collective behavior of the basin’s flow management system under different strategies (Figure 2). The analysis focused on statistical metrics such as the first (Q1) and third (Q3) quartiles, minimum values (Min), and outlier minimums (O_min). The outliers were defined based on the interquartile range (IQR), with lower and upper bounds set at Q1 − 1.5 × IQR and Q3 + 1.5 × IQR, respectively.

Over the entire period, both strategies exhibited high sustainability, with comparable Q1 values (firm: 0.9276; deficit: 0.9280). However, the firm supply showed a higher outlier minimum (0.6134) compared to the deficit supply (0.4397), indicating stronger performance in reducing extremely low SI occurrences. This implies that firm supply can provide greater lower-bound stability, which is not evident from average performance alone.

During the wet period, the third quartile values were slightly higher under the deficit supply scenario (firm supply: 0.9774; deficit supply: 0.9786). Nonetheless, both Min (0.8847) and O_min (0.7099) under firm supply were higher than those under deficit supply (Min = 0.8792, O_min = 0.6080), reinforcing that the firm supply provides more consistent stability even during high-flow seasons. In contrast, the dry period revealed more pronounced differences. While the frequency of extreme values increased under the firm supply, the deficit supply showed significantly lower minimum (0.8643) and outlier minimum values (0.4240), indicating heightened hydrological risk under the deficit supply strategy. This highlights the trade-offs of each strategy under water-scarce conditions, where firm operation may generate more outliers but avoids extremely low values, whereas deficit operation may amplify risk during droughts.

A similar pattern was observed for the farming seasons. During the busy season, when water demand intensifies, the deficit supply exhibited lower minimum and outlier minimum values, indicating greater instability in maintaining flow conditions. While the differences were less notable in the off-season, the firm supply still exhibited higher minimum values and a more stable distribution. These findings highlight the importance of lower-tail stability, which cannot be captured by mean or median SI values alone. In particular, the lower tails of the distributions expose the system vulnerabilities under extreme conditions. The firm strategy’s capacity to mitigate tail-end risks is clearly illustrated, reinforcing its relative robustness. This analysis highlights the importance of considering both distributional structure and tail sensitivity, especially when combined with probabilistic approaches aimed at informing resilience-based water resource planning.

3.3. Probabilistic Approach to Evaluate the Sustainability Index

3.3.1. Probability Distribution Fitting

To assess how water deficit events affect instream flow reliability, this study analyzed SI across different dam operation strategies and temporal conditions. Specifically, empirical cumulative distribution functions (CDFs) were compared with five theoretical probability distributions: Gamma, Log-Normal, Generalized Extreme Value (GEV), Exponential, and Chi-square. This allowed for a quantitative understanding of the probabilistic structure of deficit events and identification of best-fit distributions for future risk and extreme value analyses.

As shown in Figure 3, the empirical and fitted CDFs matched closely in the mid-range of the SI values. However, more pronounced discrepancies were observed in the lower (<0.8) and upper (>0.98) extremes. These intervals are particularly important for water shortage risk evaluation, indicating that distribution selection is highly sensitive in these tails.

The seasonal analysis showed that the dry period and the busy farming season had a higher likelihood of extreme water deficiency events, with the greatest differences in the distributional fit occurring during these times. The GEV distribution effectively captured tail behavior, highlighting its suitability for extreme value-based risk assessments. By contrast, during the wet and off-seasons, differences among the fitted distributions were relatively minor, suggesting that multiple distributions may be equally applicable under stable hydrological conditions.

These results indicate that the probabilistic nature of deficit events varies considerably with the season and operational strategy [39]. This highlights the need to integrate distribution-based approaches into policy evaluation and risk-informed planning to support more precise decision-making. Selecting appropriate distributions that accurately capture the frequency and magnitude of extremes is essential for developing resilience-based designs that ensure the long-term sustainability of instream flow.

3.3.2. Evaluation of Deficit Events

A probabilistic comparison between the two dam operation strategies was performed by analyzing differences in their probability density functions (PDFs) across predefined SI intervals. The analysis is based on two inflection points (I1 and I2), which are marked as vertical lines in the figure and derived from the zero-crossing points of the PDF difference curve. These points divide the SI domain into three distinct ranges that represent different sustainability ranges.

—

S1 (SI < I1): low sustainability with high vulnerability to instream flow deficits.

—

S2 (I1 ≤ SI < I2): main occurrence zone where the system performance is most evident.

—

S3 (SI ≥ I2): high sustainability and long-term system reliability.

Figure 4 displays the PDF-based comparison between two dam operation strategies for the total period. In the S1 range (SI < 0.918), the firm supply exhibited a higher probability (+0.015), indicating more frequent occurrences of low-sustainability events. This implies that lower sustainability conditions occurred more frequently under the firm supply. In the S2 range (0.918 ≤ SI < 0.986), the deficit supply outperformed the firm supply with a higher probability density (−0.017), reflecting better performance under typical conditions. In the S3 range (SI ≥ 0.986), the firm supply had a slight advantage (+0.001), suggesting stronger performance under highly stable conditions.

These results suggest that the firm supply is more prone to generating low-sustainability events, exposing vulnerability in meeting instream flow demands. Although infrequent, such events pose substantial risks to ecological continuity and long-term ecosystem health [40]. In contrast, the deficit supply strategy demonstrated relatively stable performance within the high-probability range and produced more favorable sustainability outcomes over the entire simulation period. However, this general trend differs from the boxplot results (Figure 3), which revealed occasional extremely low SI values under the deficit supply. These rare events typically reflect severe water deficits that arise when storage usage is maximized under high-confidence operational targets. These rare events, due to their low frequency, may not be fully reflected in PDF-based evaluations. Therefore, potential risks under the deficit strategy require interpretation beyond PDF-based statistics.

In summary, the full-period analysis confirms the firm supply’s weakness in low-sustainability ranges and the deficit supply’s superior performance under typical conditions. These results underscore the importance of adopting a risk-informed evaluation framework that considers the entire distribution structure.

Seasonal analysis under varying hydrological conditions revealed clear differences in the SI distribution characteristics between the firm and deficit supply strategies. By separating the climate time series into wet and dry periods and analyzing PDF differences across three SI intervals (S1–S3), scenario-specific patterns were identified (Figure 5).

In the wet period (Figure 5a), characterized by abundant precipitation and flow availability, both strategies showed SI distributions skewed toward higher values. However, the internal structure of the distributions varied. In the S1 range (SI < 0.911), the deficit supply showed a slightly higher probability (–0.015), suggesting occasional low-sustainability events even under favorable inflow. In the S2 range (0.911–0.978), the firm supply had a clear advantage (+0.039), indicating stronger performance in the main sustainability range. In the S3 range (SI ≥ 0.978), the deficit supply performed better (–0.027), reaching near-optimal sustainability under favorable conditions. In the dry period (Figure 5b), with limited inflows and greater difficulty in maintaining instream flows, the contrast between strategies became more pronounced. In the S1 range (SI < 0.913), the firm supply showed higher probability (+0.022), reflecting increased vulnerability to low-sustainability outcomes. Conversely, the S2 range (0.913–0.982) clearly dominated (–0.029), indicating more reliable performance under typical dry conditions. In the S3 range (SI ≥ 0.982), the firm had a slight advantage (+0.007), suggesting stability under rare high-SI conditions even during dry periods.

Both strategies demonstrated high overall sustainability during the wet season. The firm supply showed stronger stability in the main performance range (S2), whereas the deficit supply had better outcomes in the high-sustainability tail (S3). During the dry season, however, the firm supply was more prone to low SI events, suggesting that its fixed release approach may be less adaptive under hydrological stress.

To incorporate the seasonal characteristics of agricultural water demand, a probabilistic analysis of instream flow sustainability was conducted by dividing the year into the farming busy season and off-season. The probability density functions of the SI were compared between the firm and deficit supply strategies, revealing distinct differences in distribution across the three SI intervals for each period (Figure 6).

During the high-demand season (Figure 6a), the S1 range (SI < 0.909) showed a slightly higher probability under the deficit supply strategy (−0.013), indicating a marginal increase in the likelihood of low-sustainability events. In contrast, the firm supply demonstrated a higher density in the S2 range (0.909–0.977) with a difference of +0.035, reflecting a more stable flow maintenance. For the S3 range (SI ≥ 0.977), the deficit supply exhibited a higher probability (−0.023), achieving high SI outcomes under favorable conditions.

A contrasting pattern emerged during the off-season, where agricultural water demand is substantially reduced (Figure 6b). In the S1 interval (SI < 0.908), the firm supply recorded a notably higher occurrence probability (+0.027), implying that this strategy may struggle to maintain sustainability under low-demand conditions, potentially due to operational rigidity and reduced responsiveness to inflow fluctuations. Meanwhile, the deficit supply outperformed in the S2 range (–0.042), showing greater adaptability to stable flow maintenance. A minor advantage for the firm supply was observed in the S3 zone (+0.015).

These findings highlight the seasonal sensitivity of dam operation strategies. The firm supply showed stability in the main occurrence range during high-demand periods but became more vulnerable in the off-season, likely due to its fixed-release structure. The deficit supply maintained a more balanced distribution across seasons, effectively mitigating low SI risk and enhancing high SI potential. Nevertheless, under wet conditions, the low SI risk associated with the deficit supply strategy illustrates the potential ecological risks that may arise when water resources are utilized without constraint during high-demand periods. Overall, aligning dam operation strategies with seasonal agricultural demand is essential [41]. Firm supply may offer predictability, but its limitations emerge under hydrological or demand variability. The adaptive nature of the deficit supply strategy enables more flexible and resilient control, especially in off-peak periods, supporting long-term instream flow sustainability under climate uncertainty. However, its responsiveness to real-time deficits may lead to over-extraction during favorable conditions, potentially increasing ecological risks or reducing long-term reliability, particularly when inflows are overestimated or extreme droughts occur [42].

A visual comparison using 90% confidence intervals—including the lower boundary mode and upper boundary mode—was conducted to examine differences in SI distribution between the firm and deficit supply strategies (Figure 7 and

Table 3. SI value of confidence interval components under firm and deficit supplies across different temporal resolutions.

Category		Deficit			Firm
		Lower Boundary	Mode	Upper Boundary	Lower Boundary	Mode	Upper Boundary
Hydrological Stage	Dry	0.898	0.975	0.994	0.874	0.970	0.992
	Wet	0.892	0.983	0.995	0.899	0.979	0.994
Farming season	Off	0.884	0.969	0.992	0.873	0.971	0.992
	Busy	0.892	0.979	0.994	0.898	0.975	0.994

). While all scenarios exhibited mode values above 0.95, indicating generally favorable sustainability, differences in distributional spread and lower boundaries highlighted contrasting operational characteristics.

During the wet period, both the firm and deficit supply exhibited similar upper bounds and mode values, with the deficit supply showing a slightly higher mode. However, the firm supply maintained a higher lower boundary, suggesting greater effectiveness in preventing the occurrence of low-sustainability conditions even under abundant inflow. In contrast, the dry period revealed a notably higher lower boundary under the deficit supply, indicating stronger resilience against extremely low sustainability during drought or limited inflow conditions.

Comparable trends were observed in the farming season analysis. In the busy season, both strategies demonstrated similar modal values and upper bounds, reflecting comparable performance in the moderate-to-high SI range. Nevertheless, the deficit supply exhibited a lower boundary, implying increased vulnerability to low sustainability during peak demand periods. During the off-season, the firm supply showed a slightly lower boundary, suggesting a potential mismatch between the fixed supply releases and the actual inflow conditions when the demand is relatively low.

These results align with the PDF-based analysis, reaffirming that the firm supply is effective in minimizing risks in the low-sustainability range but may lack flexibility during favorable hydrological conditions. In contrast, the deficit supply performs well on average and adapts effectively to varying conditions, though it may still exhibit structural weaknesses during demand surges or hydrological instability.

4. Summary and Conclusions

This study conducted a quantitative assessment of instream flow sustainability in the Seomjin River basin under climate change scenarios based on two distinct dam operation strategies: firm and deficit supply. The analysis utilized the SI and was stratified across multiple temporal resolutions, including the entire simulation period, hydrological stages, and agricultural activity periods. A comprehensive comparison framework was applied—comprising boxplot interpretation, PDF-based comparison, and confidence interval evaluation—to interpret the structural differences between the scenarios from multiple perspectives.

In the boxplot interpretation, the firm supply consistently demonstrated superior lower-bound stability by maintaining higher minimum and outlier minimum values. This pattern was evident across all temporal scenarios. During wet and off-seasons, the firm strategy maintained a more stable distribution, while during dry and busy seasons—when hydrological stress and water demand increase—the deficit strategy exhibited lower minima and greater variability, indicating higher vulnerability. Although firm supply generated more frequent outliers in some cases, it effectively prevented extremely low sustainability outcomes. These findings emphasize that mean or median values alone are insufficient to evaluate the system’s resilience and highlight the critical importance of examining distribution tails when assessing operational robustness under climate-driven uncertainty.

The PDF-based comparison provided a detailed assessment by quantifying differences in the occurrence probabilities of SI values under varying temporal conditions. During periods characterized by constrained inflow or reduced demand—such as the dry season and the off-season—the firm supply strategy exhibited a higher probability of low SI outcomes, which indicates that fixed-release operations may lack the adaptive capacity needed to respond to variable hydrological conditions, thereby increasing the risk of insufficient instream flow. Conversely, under conditions of elevated water demand or increased inflow—such as the wet season and the busy farming season—the deficit supply strategy showed a greater frequency of low SI events. This suggests a potential trade-off in flexible operations, where prioritizing adaptive responses under high stress may inadvertently reduce sustainability in certain scenarios.

The final component of the analysis involved a comparison of 90% confidence intervals, including the lower boundary, mode, and upper boundary of the SI distributions. The result visually clarified the extent and concentration of each strategy’s performance. During the dry season and off-season, the firm supply maintained a higher lower boundary, suggesting stronger control over the minimum sustainability threshold. Meanwhile, the deficit supply strategy demonstrated higher modal or upper boundary values during the wet season and the busy farming season, indicating superior performance under certain favorable or high-demand conditions. However, in some cases, the firm supply strategy presented lower bounds even during periods of reduced demand, suggesting a structural limitation in maintaining the instream flow under specific conditions.

Collectively, the results indicate that the two dam operation strategies exhibit complementary strengths and weaknesses, with neither consistently outperforming the other under all conditions. Average SI values alone are insufficient for assessing operational effectiveness. A meaningful evaluation should incorporate extremes, the shape of the full distribution, and exposure to scenario-specific risks. Aggregating outcomes over the entire period may obscure seasonally distinct performance patterns, especially in regions with pronounced hydrological variability. Seasonally disaggregated analyses, therefore, provide a clearer view of how each strategy responds to shifting climatic and demand conditions. The selection of operational strategies should adopt a risk-informed, distribution-based perspective that reflects seasonal dynamics and variable water needs. Future research should explore adaptive strategies that optimize trade-offs across seasons and incorporate evolving climate and demand projections to enhance long-term sustainability.