{"paper_id":"2054ea79-9750-4e53-8c18-48af2d39bc13","body_text":"Methodology for determining runoff coefficients based on rainfall depth and sensitivity analysis of influencing factors | Research Square window.SnipcartSettings = { analytics: { enabled: false } }; (function() { var accessVector = localStorage.getItem('access_vector') || ''; window.dataLayer = window.dataLayer || []; if (accessVector) { window.dataLayer.push({ user: { profile: { profileInfo: { snid: accessVector } } } }); } })(); (function(w,d,s,l,i){w[l]=w[l]||[];w[l].push({'gtm.start':new Date().getTime(),event:'gtm.js'});var f=d.getElementsByTagName(s)[0],j=d.createElement(s),dl=l!='dataLayer'?'&l='+l:'';j.async=true;j.src='https://www.googletagmanager.com/gtm.js?id='+i+dl;f.parentNode.insertBefore(j,f);})(window,document,'script','dataLayer','GTM-K279D39R'); Browse Preprints In Review Journals COVID-19 Preprints AJE Video Bytes Research Tools Research Promotion AJE Professional Editing AJE Rubriq About Preprint Platform In Review Editorial Policies Our Team Advisory Board Help Center Sign In Submit a Preprint Cite Share Download PDF Research Article Methodology for determining runoff coefficients based on rainfall depth and sensitivity analysis of influencing factors Hao Yu, Fei Han, Wei Zhang This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-7863234/v1 This work is licensed under a CC BY 4.0 License Status: Under Review Version 1 posted 6 You are reading this latest preprint version Abstract The roof runoff coefficient (RC) is a critical design parameter for roof rainwater harvesting systems (RRHS), traditionally derived from standard norms with limited accuracy. This study investigates the influencing factors and determination methodology of RC through simulated rainfall experiments and analysis of 116 actual rainfall events. Pearson correlation and response surface analysis identified rainfall intensity as the primary factor affecting RC, followed by roof slope, while roof material and area showed negligible impact. A linear regression model (RC = 0.86 − 0.48 × 0.94 H ) was developed to estimate RC based on rainfall depth ( H ), demonstrating high reliability with a Nash-Sutcliffe efficiency coefficient of 0.927. Experimental results revealed that higher rainfall intensity and steeper slopes significantly increase RC by reducing runoff generation and confluence time. Application of the model in RRHS design optimized storage volume by 50.79% compared to traditional methods, although it resulted in a moderate decrease in cumulative water supply and reliability. The study provides a data-driven approach for accurately determining RC, enhancing the efficiency and economic viability of rainwater resource utilization in urban water management. Roof runoff coefficient Rainwater resource utilization Response surface curve Linear regression model Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 1. Introduction Rapid urbanization has led to the expansion of impermeable surfaces, which has altered the natural hydrological cycle and caused frequent urban waterlogging (Damien et al. 2016 ; Fiaz et al. 2019 ). Meanwhile, water demand has surged due to population growth and pollution, exacerbating water scarcity (Burak et al. 2022 ). These challenges not only threaten global ecosystems but also compromise regional security and stability (Flora et al. 2023 ; Li and Cathy. 2017; Yanet al. 2012 ). In this context, utilizing urban rainwater has become an essential measure for alleviating floods and overcoming water shortages, making it a priority for contemporary urban development (Xu et al. 2023 ). To mitigate these challenges, many nations have promoted rainwater utilization strategies, among which Roof Rainwater Harvesting Systems (RRHS) have gained widespread acceptance (Shokri. 2023). Unlike traditional end-of-pipe drainage systems, RRHS is implemented directly at the catchment source. These systems function by collecting roof runoff during rainfall events and storing it for later use during dry periods. RRHS offer numerous advantages, including ease of access, minimal pollution, low maintenance costs and risks, and the avoidance of water rights disputes (Huang et al. 2015 ). Given the complexity and variability of rainfall, recent research has focused on optimizing RRHS design to maximize rainwater resource utilization, thereby improving both system efficiency and economic viability (Alberto and Carlo. 2012; Monzur et al. 2011 ; Zhang et al. 2024 ). Simulation-based water yield models have been developed to determine the most cost-effective combination of roof catchment area and storage tank capacity for ensuring a reliable water supply (Arash et al. 2024 ). Furthermore, actual rainfall data are utilized to evaluate RRHS performance and sustainability (Ashim et al. 2015 ; Cristina et al. 2023 ; Flora et al. 2023 ). Given its frequent mention in RRHS studies, the runoff coefficient (RC) is recognized as a critical design parameter. Given that roofs are predominantly impermeable, some researchers have equated the effective runoff depth from roof catchments directly to the rainfall depth (Ana et al. 2024 ; Mark et al. 2024 ). However, hydrological losses due to evaporation and minor infiltration do occur during rainfall events (Ramon et al. 2011 ). Therefore, the runoff coefficient (RC) is employed to calculate the effective runoff depth across various rainfall events, accounting for these losses (Ren et al. 2024 ). The Runoff Coefficient (RC) is defined as the ratio of the total runoff volume to the total rainfall depth over a specific period. Although RC has often been treated as a constant to reflect the influence of different catchment surfaces on effective runoff depth (Zhang et al. 2014 ), it can assume different constant values under varying circumstances (Anirban and Niranjali. 2010; Mun Jand Han. 2011; Olanike and Omotayo. 2010. ; Ren et al. 2023 ). In reality, RC fluctuates significantly depending on catchment characteristics and climatic conditions (Chow et al. 2018 ). For instance, typical values are approximately 0.9 for concrete/asphalt roofs, 0.95 for metal roofs, and 0.8–0.85 for rubble roofs. Scholars typically determine RC through the analysis of monitored rainfall and runoff events (Ronalton et al. 2022 ). Furthermore, RC is crucial for refining urban catchment hydrological models, thereby enhancing rainwater resource utilization efficiency (Stephen et al. 2020 ). A statistical summary of documented RC values is provided in Table 1 . Table 1 Statistical table of roof runoff coefficient RC Material Area (m 2 ) Slope (°) Location Preference 0.7 ~ 0.9 Pitch 12 0/2/5/7 University Tenaga Nasional (Malaysia) Chow et al. 2018 . 0.75 ~ 0.95 Concrete 8000/1200 0 University of Western Sydney (Australia) Monzur et al. 2011 . 0.8 - 350/550/750 - University of Catania (Italy) Alberto and Carlo. 2012. 0.7 Mental 1500 - University of Exeter (UK) Ward et al. 2010 . 0.58/0.75 Dry/Wet soil 1 - Beijing (China) Liu et al. 2020 . 0.83 ~ 0.85 Clay tiles 120 30 Barcelona (Spain) Ramon et al. 2011 . 0.92 Metal 40.6 0.9 ~ 0.92 Plastic 40.6 0.58 ~ 0.66 Gravel 56.6 0 Ljubljana (Slovenia) Mark et al. 2024 . 0.82 Mental 120 - Istanbul (Turkey) Burak et al. 2022 . 0.81 Concrete 120 0 Baise City (China) Mo et al. 2023 . 0.81 Mental 3 Parabolic Taiwan (China) Arash Ret al. 2024 . 0.84 Mental Inverted-V 0.83 Mental Saw Tooth In this paper, the variation of the RC within the roof catchment under different influencing factors was investigated through simulated rainfall experiments. By analyzing the sensitivity of the RC, the main influencing factors of the RC are determined. Combined with the actual rainfall data, a linear regression model is used to establish a method for determining the value of the roof RC. The aim is to improve the utilization efficiency of the RRHS and promote the development of rainwater utilization. 2. Materials and methods 2.1 Research location Located in North China and extending from 36°20′ to 36°44′N latitude and 114°03′ to 114°40′E longitude, the study area experiences a warm-temperate continental monsoon climate, with an average annual temperature of 13.5℃ and an average annual rainfall of 558.5 mm. The artificial rainfall simulation platform, covering an area of approximately 400 m 2 , consists of three main components: a rainfall system, an underlying surface system, and a water collection/storage system. This design was informed by a field survey of roofing materials in northern China, which identified asphalt and metal as the predominant types. Accordingly, the experimental roof module spans an area of 60 m 2 and features an adjustable slope ranging from 0° to 60°. The rainfall system can simulate rainfall intensities from 20 to 200 mm/h. Moreover, the spatial coverage of the rainfall system is adjustable, capable of accommodating a maximum experimental area of 200 m 2 . A schematic diagram of the overall platform is presented in Fig. 1 . 2.2 Experimental design The experiment was designed to investigate the individual effects of four key factors: roof material, catchment area, roof slope, and rainfall intensity (RI). The RC was the primary response variable, while the antecedent dry period was considered a controlled auxiliary variable. Runoff from the roof module was collected by a network of gutters and downpipes, which channeled the water into a polyethylene storage tank for volumetric measurement. To simulate typical field conditions, the experimental setup did not incorporate an initial rainfall diversion device, and the roof surfaces were not subjected to any special cleaning or maintenance routines. Based on an analysis of historical daily rainfall data, three rainfall intensities—20, 50, and 100 mm/h—were selected and configured for the simulation experiments. To monitor the actual RI during experiments, three SL-1 automatic tipping-bucket rain gauges were installed at representative locations: on the asphalt roof, the metal roof, and at ground level. Furthermore, roof runoff was monitored using automatic flow meters installed at the outlets of each roof module. Infiltration-excess and saturation-excess are widely recognized as the two primary mechanisms of runoff generation (Arash et al. 2024 ). To ensure that infiltration-excess runoff was the consistent dominant mechanism across all trials, each roof surface was pre-wetted until initial runoff was observed immediately before the formal experiment. Following pre-wetting, the system was allowed to drain and was then left undisturbed for a consistent antecedent dry period of 3 days to establish uniform initial conditions for every test. The experimental variables included two roofing materials (asphalt and metal) and three slope gradients (0°, 2°, and 5°). Each simulated rainfall event had a fixed duration of 30 minutes. A preliminary experiment was conducted to determine the optimal data collection interval by comparing the cumulative runoff depth recorded at 1-minute and 5-minute intervals. The 1-minute interval was found to capture the dynamics of runoff generation more effectively, as it revealed more pronounced trends in the cumulative runoff curve. Consequently, the 1-minute interval was adopted for all subsequent formal experiments. A summary of the specific experimental parameters is provided in Fig. 2 . 2.3 Data collection The deployment of telemetric rain gauges (SL-1, China) at the study sites was informed by an analysis of long-term (2015–2024) daily rainfall and temperature data obtained from the local meteorological department. Between 2022 and 2024, a total of 116 natural rainfall events were monitored. The characteristics of these events are summarized in Table 2 . Table 2 Rainfall event record sheet Year Annual rainfall depth/mm Number of monitored events 0 ~ 5mm 5 ~ 15mm 15 ~ 25mm 25 ~ 35mm 35 ~ 45mm > 45mm 2022 216.6 29 8 2 1 1 0 2023 1103.2 55 14 6 1 4 7 2024 544.5 43 7 6 1 4 2 Total 1864.3 127 29 14 3 9 9 Rainfall losses on roofs, leading to runoff retention, are primarily attributed to infiltration and evapotranspiration. These processes are particularly significant during the initial phase of a rainfall event. However, the widespread adoption of first-flush diversion strategies in RRHS to improve stormwater quality (Abbasi and Abbasi. 2011; Georgios and Vassilios. 2012; Xie et al. 2023 ; Zhang et al. 2010 ) makes it particularly challenging to capture the initial portion of stormwater runoff. This challenge is most acute during the beginning of rainfall events or in the case of minor rainfall events with the depth of less than 5 mm. During each simulated rainfall event, the initiation of runoff at the outlet was automatically detected and recorded by a soil erosion monitor. This recorded timestamp was defined as the runoff generation time. To determine the flow concentration time, a red water-soluble tracer powder was applied at the point farthest from the outlet on the roof surface. The moment when the runoff at the outlet exhibited a distinct color change was recorded, signaling the completion of the runoff confluence process. The flow concentration time was calculated as the difference between the confluence completion time and the runoff generation time. Owing to the spatially uniform rainfall design, the total rainfall volume was calculated as the product of the rainfall intensity (RI) and the catchment area. The total runoff volume was determined by measuring the change in water level within the calibrated storage tank. 2.4 Data analysis The principal analytical methods employed in this study included the Pearson correlation analysis, linear regression modeling, response surface methodology (RSM), and the Nash-Sutcliffe efficiency coefficient (NSE). Experimental data on the runoff processes, including the runoff generation time, confluence time, and runoff volume, were systematically collected across a range of rainfall intensities and roof conditions. The average rainfall runoff coefficient (ARC) is accurately calculated using Eq. (1). ARC = 1000 V / HA (1) where V is the rainfall runoff volume (m 3 ), H is the total rainfall depth (mm), A is the catchment area (m 2 ). The formula for calculating the instantaneous rainfall runoff coefficient (IRC) is given in Eq. (2). IRC = H 1 / H 0 (2) where H 1 is the depth of runoff per unit time (mm), H 0 is the rainfall depth per unit time (mm). The mathematical description of the daily water balance model for RRHS is given by Eq. (3). S t = V t + S t −1 - D t (3) Where S t is the cumulative rainfall storage volume at RRHS on day t (m 3 ), V t is the rainwater runoff volume collected by RRHS on day t (m 3 ), S t −1 is the cumulative rainfall storage volume (m 3 ) at RRHS on day t -1, D t is the daily water supply volume of RRHS on day t (m 3 ). On day t , the free volume of RRHS is given by Eq. (4). V k = V R - S t −1 + D t (4) Where V k is the free volume of RRHS on day t (m 3 ), V R is the total volume of RRHS (m 3 ). Daily roof runoff volume as Eq. (5). V d = RC × HA × 10 − 3 (5) Where V d is the daily rainfall runoff volume (m 3 ). The method for calculating water supply reliability is shown in Eq. (6). R = D / N × 100 (6) Where R is the RRHS water supply reliability (%), D is the RRHS time to meet water demand (d), N is the RRHS water supply cycle (d). The relationship between the RC and each individual influencing factor was quantified using the Pearson correlation coefficient. The goodness-of-fit of these relationships was evaluated based on the dispersion of data points around the regression line, with a coefficient of determination ( R 2 ) greater than 0.95 considered indicative of a high-quality fit. RSM was employed to analyze the effects of interaction terms between various influencing factors on the runoff coefficient. The relative importance of the primary influencing factors was determined by the steepness of the gradient of the response surface. For cross-validation, the dataset was partitioned into two subsets based on data source: actual rainfall and simulated rainfall. A linear regression model was established to analyze the relationship between the RC and cumulative rainfall depth. Based on the observed trends in the regression coefficients, a novel method for estimating the roof RC is proposed. Finally, the predictive reliability of the proposed RC estimation method was validated using the Nash-Sutcliffe efficiency coefficient (NSE). 3. Results and discussion 3.1 Roof runoff generation and confluence Roof runoff generation and confluence collectively describe the process of rainfall accumulating on a roof surface to form runoff, a process governed by both catchment characteristics (material, slope) and climatic conditions (rainfall intensity). Through a series of simulated rainfall experiments, data including runoff generation time, confluence time, runoff depth, and rainfall depth were collected and analyzed for various rainfall events. The analysis revealed a consistent pattern in the runoff generation and confluence processes under varying conditions, as illustrated in Fig. 3 . The complete rooftop runoff hydrograph under specified conditions can be divided into four distinct phases: generation, confluence, stabilization, and recession (Fig. 3 ). A magnified view of the hydrograph shows that runoff initiation occurs at 0.97 minutes, as indicated by the red marker. The runoff generation phase is influenced by antecedent dry conditions and evapotranspiration. Consequently, runoff does not commence immediately after rainfall begins. As precipitation continues, the cumulative rainfall eventually surpasses the initial losses (infiltration and wetting). This threshold marks the commencement of runoff generation, after which water flows over the surface and converges into the drainage system. RI and roof slope are two critical factors influencing the runoff generation time under various conditions. The runoff generation time gradually decreases with increasing rainfall intensity and roof slope. Since the roof represents a typical impervious surface, the initial rainfall loss—primarily determined by antecedent dry conditions and evapotranspiration—can be considered a relatively fixed volume. The higher RI delivers a greater volume of rainfall per unit time. Consequently, as the cumulative rainfall volume increases, this fixed initial loss constitutes a diminishing proportion of the total rainfall. This decreasing proportion means the threshold for runoff generation is reached more rapidly, leading to a shorter generation time. Furthermore, a steeper roof slope accelerates the runoff generation rate by reducing surface retention and facilitating faster flow convergence. The confluence phase (0.97 to 6 min) describes the process wherein runoff generated across the roof surface converges towards the drainage outlets. The path length for runoff to travel to the outlet varies depending on its point of origin on the roof. Longer flow paths consequently require longer travel times. As rainfall continues, the instantaneous runoff rate increases progressively. The confluence phase is considered complete when runoff originating from the hydraulically most remote point on the roof reaches the outlet. During the confluence phase, the rate of runoff discharge exhibits a positive correlation with both the RI and the roof slope. A steeper roof slope accelerates the overland flow velocity. This increased velocity results in a higher volume of runoff reaching the drainage outlet per unit time. Therefore, the duration of the confluence phase is governed by the combined effects of RI and roof slope. Furthermore, the roof catchment area directly affects the confluence time, with larger areas requiring more time for runoff to fully converge. The runoff process transitions into the stabilization phase once flow from the hydraulically most remote point on the roof reaches the drainage outlet. During this phase, the instantaneous runoff depth approaches the instantaneous rainfall depth, exhibiting minor fluctuations around a stable equilibrium value. Factors such as surface evaporation cause losses, resulting in the instantaneous runoff depth being marginally lower than the instantaneous rainfall depth. Due to the designed constant-intensity rainfall pattern, the stabilization phase persists until the rainfall cessation. The duration of the stabilization phase is therefore determined by the time of confluence completion and the total rainfall duration. Consequently, factors influencing the confluence time (roof area, slope, rainfall intensity) indirectly govern the commencement and duration of the stabilization phase. Upon the conclusion of the designed rainfall event, the rainfall simulation system was switched off. This marks the beginning of the recession phase. Monitoring instruments indicated that a diminishing amount of residual runoff continued to be collected from the roof outlets. Since rainfall input had ceased, no new runoff was generated; the runoff observed during this phase represents the drainage of water that was temporarily stored or moving slowly across the roof surface. Given the impervious nature of the roof surfaces, the volume of water in this recession phase is limited. A rapid decrease in instantaneous runoff depth commences at the 30-minute mark, corresponding to the end of rainfall (Fig. 3 ). Comparative analysis of the recession curves under different conditions identified the roof slope as the dominant factor influencing the recession process. A steeper slope facilitates faster drainage of the stored water, leading to a shorter recession phase. Since RI is zero during this phase, it does not exert any influence. Throughout the rainfall event, a dynamic discrepancy existed between the instantaneous rainfall depth and the runoff depth (Fig. 3 ). Due to the challenges in directly monitoring roof runoff volume under natural rainfall conditions, the runoff coefficient (RC) provides a practical method for estimating the effective runoff depth from various rainfall events. Accurate estimation of this depth through RC analysis is crucial for optimizing the operational efficiency of Roof Rainwater Harvesting Systems (RRHS). 3.2 Runoff coefficient The RC is a crucial parameter in urban hydrology for assessing rainfall-runoff response and water yield (Ana et al. 2024 ). However, the hydrological behavior of roofs, as artificial catchments, is complex and influenced by diverse local factors, leading to significant spatial and temporal variability in the RC. This study aims to quantify the impacts of rainfall characteristics and roof surface properties on the RC during standardized rainfall events. To achieve this, we tracked runoff dynamics for four roof types under controlled conditions, calculating both the IRC and the ARC to assess discrepancies between rainfall input and runoff output. Despite varying conditions, the patterns of RC variation exhibited consistent trends across the different roof types, as summarized in Fig. 4 . For analytical purposes, two types of runoff coefficients were examined: the IIRC and the ARC. The IRC is defined as the ratio of instantaneous runoff volume to instantaneous rainfall volume per unit time. The ARC is calculated as the ratio of the total runoff volume to the total rainfall volume at the conclusion of a rainfall event (Fermando et al. 2020 ). Figure 4 demonstrates that the temporal variation of the IRC closely follows the pattern of instantaneous runoff depth. The IRC exhibits two distinct phases: a rapid rising phase and a subsequent stable phase. The rising phase coincides with the confluence phase of the runoff, during which the IRC increases rapidly with rainfall duration until reaching a peak. After peaking, the IRC transitions into a stable phase, where it fluctuates slightly around this peak value until rainfall cessation. This stable phase parallels the stabilization phase of the runoff hydrograph and is characterized by minor fluctuations around a steady value. In contrast to the dynamic, two-phase behavior of the IRC, the ARC remains constant for a given event, as clearly illustrated by the comparative data presented in Fig. 5 . Under identical rainfall intensity and slope conditions, both the IRC and ARC values remain consistent across asphalt roofs with different areas (Fig. 5 a). Specifically, the IRC values for Rf1#, Rf2#, and Rf3# were 0.928, 0.926, and 0.927, respectively, while the corresponding ARC values were 0.741, 0.746, and 0.747. The observed minor variations in coefficients, with errors of merely 0.11% (IRC) and 0.27% (ARC), are within the expected range of measurement uncertainty (Li et al. 2020 ). Therefore, it can be concluded that variations in roof area have no significant impact on either the IRC or the ARC. Furthermore, under these conditions, the rainfall duration required to reach the peak IRC value was also consistent across different roof areas. Similarly, for roofs Rf3# and Rf4# with identical surface areas but differing materials, their IRC values were 0.927 and 0.929 respectively, while their ARC values were 0.747 and 0.751 respectively (Fig. 5 b). The coefficient errors here were 0.1% and 0.27%, which are again within the accepted margin of error (Li et al. 2020 ). Analysis of the IRC revealed that the metal roof exhibited a shorter runoff generation time compared to the asphalt roof under identical experimental conditions. The peak IRC for the metal roof was attained at the 9-minute mark, whereas that for the asphalt roof was reached at the 10-minute mark. Furthermore, the IRC was consistently higher for the metal substrate than for the asphalt throughout the rising phase for any given rainfall duration. This difference is attributed to the lower surface roughness of the metal roof, which reduces its rainwater retention capacity and facilitates faster runoff flow. Consequently, a greater volume of runoff reaches the outlet on metal roofs within the same timeframe, resulting in a higher IRC. During the stabilization phase, both the IRC and ARC values converged and became very similar for both materials. This indicates that the influence of roofing material on the runoff coefficients is minimal during the stabilization phase. Therefore, it can be concluded that the primary influence of roofing material is on the rising phase of the IRC, and the degree of this influence is positively correlated with the surface roughness of the material. In contrast, the roofing material was found to have no significant effect on the ARC. This conclusion was further corroborated by data from actual rainfall events, which showed no significant impact of material on the RC. Holding rainfall characteristics and other factors constant, variations in roof slope were found to significantly influence both the IRC and the ARC. Data from roof Rf3# under scenarios M1, M4, and M7 (Fig. 5 c) were selected for analysis to isolate the effect of slope. For Rf3# at three distinct slopes, the IRC values were 0.912, 0.927, and 0.937, and the corresponding ARC values were 0.731, 0.747, and 0.756. The observed coefficient variations (1.4% for IRC, 1.2% for ARC) exceeded the typical margin of experimental error. This indicates that roof slope has a statistically significant impact on the runoff coefficient. With rainfall characteristics and other factors held constant, both the instantaneous runoff coefficient and the mean runoff coefficient increase with steeper slopes (Fig. 5 c). For a given rainfall duration, a steeper roof slope is associated with a higher IRC. An increased slope shortens the time to peak runoff and elevates the IRC. Analysis of the runoff generation and confluence times confirms that steeper slopes reduce the duration of both phases. Physically, a steeper slope enhances the gravitational potential energy of the runoff, which is converted into greater kinetic energy and thus higher flow velocity. Consequently, the volume of runoff discharged per unit time increases, resulting in a higher IRC on steeper slopes. Rainfall characteristics are a primary factor in the runoff simulation process, with RI exerting a particularly notable influence on roof runoff generation. The response of the runoff coefficient for roof Rf3# to varying RI (conditions M1, M2, M3) is illustrated in Fig. 5 d. For Rf3# under these conditions, the IRC values were 0.912, 0.950, and 0.979, respectively, representing a total increase of 3.7%. Similarly, the ARC values were 0.731, 0.783, and 0.833, representing a larger total increase of 6.5%. The substantial increases in both coefficients underscore the significant impact of rainfall intensity on the runoff coefficient. Both the IRC and ARC exhibit a strong positive correlation with increasing rainfall intensity. For a given duration, the IRC increases with rainfall intensity. Furthermore, a higher RI shortens the time required to reach the peak runoff rate. The positive correlation between the runoff coefficient and rainfall intensity is consistent with the dynamics of runoff volume accumulation. An increase in rainfall intensity reduces the time required for both runoff generation and confluence. Due to the impervious nature of roof surfaces, their water retention capacity is limited. A higher rainfall intensity delivers a greater volume of precipitation per unit time. This leads to a more rapid formation of runoff and a higher instantaneous runoff rate. Consequently, the runoff coefficient increases correspondingly with rainfall intensity. 3.3 Sensitivity analysis of the RC The varying degrees of influence exerted by roofing materials, slope gradients, and RI upon RC are clearly illustrated in Fig. 5 . To quantitatively identify the dominant factors, a systematic analysis was conducted. The study aimed to quantify the relative importance of each factor on the RC. First, the Pearson correlation coefficient was employed to assess the linear relationship between the RC and each individual factor. Subsequently, RSM was applied to identify the principal factors and their interactions affecting the RC. The results of the correlation analysis are presented in Fig. 6 . The horizontal axis represents the RC values for the 0° slope condition, while the vertical axis represents the corresponding RC values for the 2° and 5° slope conditions (Fig. 6 a). A linear regression analysis of the RC values across the three slopes indicates a strong linear relationship. This is supported by high coefficients of determination ( R 2 ) of 0.996 (for 0° vs. 2°) and 0.969 (for 0° vs. 5°). However, a discernible deviation is observed between the fitted regression lines and the lines of perfect agreement (1:1 lines) on the graph. The magnitude of this deviation increases with increasing slope. This pattern confirms that roof slope has a significant and systematic influence on the RC. The correlation between RC for roofs of different areas and materials is shown in Fig. 6 b. The horizontal axis represents the RC values for the reference roof (Rf3#), while the vertical axis represents the RC values for the other roofs (Rf1#, Rf2#, and Rf4#). Linear regression analysis of the RC values across the four roof types yielded Pearson correlation coefficients ( R 2 ) of 0.999, 0.999, and 0.996, indicating an exceptionally strong linear fit. Furthermore, the fitted regression lines lie very close to the line of perfect agreement (1:1 line). This indicates that the runoff coefficients for all four roof types can be considered equivalent under identical rainfall conditions. Therefore, it can be concluded that, under the conditions tested, roof area and material have a negligible effect on the runoff coefficient. The horizontal axis represents the RC values at 20 mm/h, while the vertical axis represents the corresponding values at 50 mm/h and 100 mm/h. The relationship between runoff coefficients obtained under different rainfall intensities is shown in Fig. 6 c. The relationship was analyzed using linear regression, which indicated a reasonable fit, with coefficients of determination ( R 2 ) of 0.961 and 0.854, respectively. The resulting regression lines show a clear deviation from the line of perfect agreement (1:1 line). Furthermore, the magnitude of this deviation increases with increasing rainfall intensity. These results demonstrate that rainfall intensity exerts a significant influence on the RC. The analysis confirms that both roof slope and rainfall intensity significantly influence the RC. To determine which factor is dominant, the interaction between them was analyzed using the RSM based on the experimental design illustrated in Fig. 7 . The response surface analysis presented in Fig. 7 demonstrates the effects of roof slope and RI on the RC. The maximum effect magnitudes were 0.78 for slope and 0.83 for RI, respectively. Since RI exerts a greater effect than slope, it is identified as the primary factor influencing the RC. 3.4 Modeling of roof coefficient values The hydrological response of roofs under natural rainfall events is influenced by a complex interplay of diverse roof characteristics and climatic factors. In the statistical analysis of daily rainfall data, rainfall depth serves as the primary quantitative metric. In the subsequent analysis, rainfall depth was set as the independent variable (horizontal coordinate), and the RC was treated as the dependent variable (vertical coordinate). Under simulated rainfall and actual rainfall conditions, the distribution of runoff coefficient values exhibits the same pattern (Fig. 8 ). The results indicate that the RC increases with rainfall depth, but the rate of this increase diminishes as the depth becomes larger. For rainfall depths exceeding 5 mm, the RC from simulated rainfall events is consistently higher than that from actual rainfall events. This discrepancy is attributed to the difference in rainfall intensity patterns: actual rainfall exhibits time-varying intensity, whereas simulated rainfall maintains a constant intensity. Furthermore, field observations indicated that natural rainfall events often commence with a high intensity that gradually decays over time. Consequently, during the initial phase of an event, the RC for actual rainfall can be slightly higher. However, as cumulative rainfall depth increases, the RC for simulated rainfall becomes progressively greater. This occurs because actual rainfall, with its typically decaying intensity, requires a longer duration to accumulate the same depth achieved under constant simulated intensity. Extended rainfall duration leads to greater volumetric losses (evaporation, infiltration). These increased losses result in a lower RC. Accounting for the variability in rainfall depth and its interaction with duration-dependent losses, the runoff coefficient is modeled by Eq. (7). RC = 0.86 − 0.48 × 0.94 H (7) where RC is the runoff coefficient, dimensionless, H is the rainfall depth (mm). The NSE was employed as the metric to evaluate the model's performance in simulating actual rainfall scenarios. An NSE value of 0.927 indicates a strong agreement between the modeled and observed runoff coefficients, demonstrating the model's reliability in predicting roof runoff under natural conditions. 3.5. Application of runoff coefficient estimation models In urban water resource management, the RC for impervious roofs is conventionally estimated within a range of 0.95 to 1.0, a value primarily derived from empirical studies of hard-surfaced areas (Lotte et al. 2020 ). However, as research advances and data accumulate, a growing body of literature suggests that these traditional estimation methods may lack the accuracy required to represent the actual runoff responses of diverse roof types under varying rainfall conditions. To quantify the performance improvement, a daily water balance model was implemented in Python (Section 2.4 ). This model compared system performance metrics—including cumulative water supply, full storage days, water supply reliability, spatial utilization rate, and operational efficiency—between the traditional fixed RC method and the proposed spectrum-based RC method. The comparison elucidates the enhancement achieved by the RC spectrum in RRHS performance. The simulation was configured for the year 2023, with a roof catchment area of 500 m 2 , a daily water supply demand of 1 m 3 /d, and an annual runoff capture efficiency target of 70%. The specific parameters and results are summarized in Table 3 . Table 3 Analysis of operating parameters of RRHS under different models Method Volume (m 3 ) Cumulative water supply volume (m 3 ) Maximum storage days (d) R (%) Space utilization rate (%) Operational Efficiency (%) 0.95 ~ 1 63 180.71 4 47.12 0.7 70.45 Model 31 148.71 6 38.08 1.3 70.55 The required storage capacity of the retention facility differed significantly between the two runoff coefficient determination methods. The design based on the runoff coefficient spectrum required a storage volume of 31 m 3 , whereas the traditional method necessitated a volume of 63 m 3 . This represents a reduction of 32 m 3 (50.79%) in required storage volume compared to the traditional design. In terms of system output, the cumulative water supply provided by the RRHS was 148.71 m 3 using the spectrum-based method, compared to 180.71 m 3 with the traditional method. However, the number of days the storage facility remained at full capacity increased from 4 days to 6 days under the spectrum-based design, a 50% increase. The water supply reliability was 38.08% for the spectrum-based method, lower than the 47.12% achieved by the traditional method. Analysis of spatial utilization efficiency revealed rates of 0.7% for the spectrum-based method versus 1.3% for the traditional method. Finally, the operational efficiencies of the RRHS were 70.45% and 70.55% for the spectrum-based and traditional methods, respectively. 4. Conclusion (1) Both runoff volume and runoff coefficient will increase with the rainfall calendar time. The change in runoff volume and runoff coefficient per unit of time after peaking tends to stabilize. (2) Rainfall intensity is the main factor affecting the runoff coefficient. This is because the higher the intensity, the higher the runoff coefficient. In addition, slope also has an effect on the runoff coefficient. Neither the roofing material nor the area affects the runoff coefficient. (3) Leveraging the established relationship between the runoff coefficient and rainfall depth, a model has been developed to calculate the runoff coefficient based on rainfall depth. This method not only diversifies the techniques for deriving runoff coefficients but also improves their accuracy. (4) Although average rainfall was employed in this study, the actual rainfall process is complex. Incorporating various rainfall peak patterns might better align the simulated rainfall effects with real-world conditions. Linearly simulating runoff coefficients influenced by individual factors aids in analyzing the effects of various factors on model parameters. Declarations CRediT authorship contribution statement Hao Yu : Data Curation, Investigation, Methodology, Writing - original draft. Fei Han : Conceptualization, Methodology, Supervision. Wei Zhang : Funding acquisition, Writing - review & editing. 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Cite Share Download PDF Status: Under Review Version 1 posted Editorial decision: Major revisions 22 Apr, 2026 Reviewers agreed at journal 16 Nov, 2025 Reviewers invited by journal 13 Nov, 2025 Editor invited by journal 06 Nov, 2025 Editor assigned by journal 16 Oct, 2025 First submitted to journal 15 Oct, 2025 You are reading this latest preprint version Research Square lets you share your work early, gain feedback from the community, and start making changes to your manuscript prior to peer review in a journal. As a division of Research Square Company, we’re committed to making research communication faster, fairer, and more useful. We do this by developing innovative software and high quality services for the global research community. Our growing team is made up of researchers and industry professionals working together to solve the most critical problems facing scientific publishing. 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platform\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"1.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/12a6876a2b3855a9c616edd3.png\"},{\"id\":96814182,\"identity\":\"dd35508e-da06-4fba-ac21-7a6a55fb8b19\",\"added_by\":\"auto\",\"created_at\":\"2025-11-26 10:47:25\",\"extension\":\"png\",\"order_by\":2,\"title\":\"Figure 2\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":123429,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eExperimental parameter.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"2.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/8953a34a9ae01d9a5289f57b.png\"},{\"id\":96814187,\"identity\":\"87bd5a78-a541-4e61-bfdc-1e25f3662778\",\"added_by\":\"auto\",\"created_at\":\"2025-11-26 10:47:25\",\"extension\":\"png\",\"order_by\":3,\"title\":\"Figure 3\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":183985,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eProcess of the rainfall and roof runoff.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"3.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/b255aa77eb03ca5d4fb6aa63.png\"},{\"id\":96917421,\"identity\":\"587cbd80-e53d-4ebd-bc6f-8796852840db\",\"added_by\":\"auto\",\"created_at\":\"2025-11-27 14:09:43\",\"extension\":\"png\",\"order_by\":4,\"title\":\"Figure 4\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":188516,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eVariation of runoff coefficient.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"4.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/0c858a429e8d6c5af95524f6.png\"},{\"id\":96917854,\"identity\":\"ca578b77-07bc-48bc-87c5-fae5b9fe4390\",\"added_by\":\"auto\",\"created_at\":\"2025-11-27 14:10:38\",\"extension\":\"png\",\"order_by\":5,\"title\":\"Figure 5\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":381147,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eVariations in IRC and ARC under different influencing factors (a) areas, (b) materials, (c) slopes, (d) rainfall intensities.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"5.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/5160406df84c0fc4ed8b9c92.png\"},{\"id\":96917923,\"identity\":\"b3fd2693-0b2e-40d5-bc98-dc9955e97c48\",\"added_by\":\"auto\",\"created_at\":\"2025-11-27 14:10:45\",\"extension\":\"png\",\"order_by\":6,\"title\":\"Figure 6\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":243852,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eRelationship between runoff coefficients under the influence of different factors (a) slopes, (b) materials and areas, (c) rainfall intensities.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"6.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/ce2e006d8e0cfd6d91cc657d.png\"},{\"id\":96814190,\"identity\":\"b9ef7be8-6e37-4473-bd38-38f65bf7ba20\",\"added_by\":\"auto\",\"created_at\":\"2025-11-26 10:47:25\",\"extension\":\"png\",\"order_by\":7,\"title\":\"Figure 7\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":274360,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eResponse surface curve of influencing factors.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"7.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/04d2b81f29c49501d812786c.png\"},{\"id\":96917451,\"identity\":\"669a3e9f-64a7-48af-9f9e-46bef980befb\",\"added_by\":\"auto\",\"created_at\":\"2025-11-27 14:09:45\",\"extension\":\"png\",\"order_by\":8,\"title\":\"Figure 8\",\"display\":\"\",\"copyAsset\":false,\"role\":\"figure\",\"size\":135957,\"visible\":true,\"origin\":\"\",\"legend\":\"\\u003cp\\u003eRelationship between rainfall depth and runoff coefficient.\\u003c/p\\u003e\",\"description\":\"\",\"filename\":\"8.png\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/24e056b4e358b35c578cb269.png\"},{\"id\":96923011,\"identity\":\"4e43805a-4881-4c87-bc4a-2989b9e8faa0\",\"added_by\":\"auto\",\"created_at\":\"2025-11-27 14:20:33\",\"extension\":\"pdf\",\"order_by\":0,\"title\":\"\",\"display\":\"\",\"copyAsset\":false,\"role\":\"manuscript-pdf\",\"size\":2235978,\"visible\":true,\"origin\":\"\",\"legend\":\"\",\"description\":\"\",\"filename\":\"manuscript.pdf\",\"url\":\"https://assets-eu.researchsquare.com/files/rs-7863234/v1/08871f2b-1b2d-43a1-853c-cf90b10fabd1.pdf\"}],\"financialInterests\":\"\",\"formattedTitle\":\"Methodology for determining runoff coefficients based on rainfall depth and sensitivity analysis of influencing factors\",\"fulltext\":[{\"header\":\"1. Introduction\",\"content\":\"\\u003cp\\u003eRapid urbanization has led to the expansion of impermeable surfaces, which has altered the natural hydrological cycle and caused frequent urban waterlogging (Damien et al. \\u003cspan citationid=\\\"CR10\\\" class=\\\"CitationRef\\\"\\u003e2016\\u003c/span\\u003e; Fiaz et al. \\u003cspan citationid=\\\"CR13\\\" class=\\\"CitationRef\\\"\\u003e2019\\u003c/span\\u003e). Meanwhile, water demand has surged due to population growth and pollution, exacerbating water scarcity (Burak et al. \\u003cspan citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). These challenges not only threaten global ecosystems but also compromise regional security and stability (Flora et al. \\u003cspan citationid=\\\"CR14\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Li and Cathy. 2017; Yanet al. \\u003cspan citationid=\\\"CR36\\\" class=\\\"CitationRef\\\"\\u003e2012\\u003c/span\\u003e). In this context, utilizing urban rainwater has become an essential measure for alleviating floods and overcoming water shortages, making it a priority for contemporary urban development (Xu et al. \\u003cspan citationid=\\\"CR34\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e).\\u003c/p\\u003e\\u003cp\\u003eTo mitigate these challenges, many nations have promoted rainwater utilization strategies, among which Roof Rainwater Harvesting Systems (RRHS) have gained widespread acceptance (Shokri. 2023). Unlike traditional end-of-pipe drainage systems, RRHS is implemented directly at the catchment source. These systems function by collecting roof runoff during rainfall events and storing it for later use during dry periods. RRHS offer numerous advantages, including ease of access, minimal pollution, low maintenance costs and risks, and the avoidance of water rights disputes (Huang et al. \\u003cspan citationid=\\\"CR16\\\" class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e). Given the complexity and variability of rainfall, recent research has focused on optimizing RRHS design to maximize rainwater resource utilization, thereby improving both system efficiency and economic viability (Alberto and Carlo. 2012; Monzur et al. \\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e2011\\u003c/span\\u003e; Zhang et al. \\u003cspan citationid=\\\"CR37\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e). Simulation-based water yield models have been developed to determine the most cost-effective combination of roof catchment area and storage tank capacity for ensuring a reliable water supply (Arash et al. \\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e). Furthermore, actual rainfall data are utilized to evaluate RRHS performance and sustainability (Ashim et al. \\u003cspan citationid=\\\"CR5\\\" class=\\\"CitationRef\\\"\\u003e2015\\u003c/span\\u003e; Cristina et al. \\u003cspan citationid=\\\"CR9\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Flora et al. \\u003cspan citationid=\\\"CR14\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e). Given its frequent mention in RRHS studies, the runoff coefficient (RC) is recognized as a critical design parameter.\\u003c/p\\u003e\\u003cp\\u003eGiven that roofs are predominantly impermeable, some researchers have equated the effective runoff depth from roof catchments directly to the rainfall depth (Ana et al. \\u003cspan citationid=\\\"CR3\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e; Mark et al. \\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e). However, hydrological losses due to evaporation and minor infiltration do occur during rainfall events (Ramon et al. \\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e2011\\u003c/span\\u003e). Therefore, the runoff coefficient (RC) is employed to calculate the effective runoff depth across various rainfall events, accounting for these losses (Ren et al. \\u003cspan citationid=\\\"CR28\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e).\\u003c/p\\u003e\\u003cp\\u003eThe Runoff Coefficient (RC) is defined as the ratio of the total runoff volume to the total rainfall depth over a specific period. Although RC has often been treated as a constant to reflect the influence of different catchment surfaces on effective runoff depth (Zhang et al. \\u003cspan citationid=\\\"CR39\\\" class=\\\"CitationRef\\\"\\u003e2014\\u003c/span\\u003e), it can assume different constant values under varying circumstances (Anirban and Niranjali. 2010; Mun Jand Han. 2011; Olanike and Omotayo. 2010. ; Ren et al. \\u003cspan citationid=\\\"CR29\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e). In reality, RC fluctuates significantly depending on catchment characteristics and climatic conditions (Chow et al. \\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e). For instance, typical values are approximately 0.9 for concrete/asphalt roofs, 0.95 for metal roofs, and 0.8\\u0026ndash;0.85 for rubble roofs. Scholars typically determine RC through the analysis of monitored rainfall and runoff events (Ronalton et al. \\u003cspan citationid=\\\"CR26\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e). Furthermore, RC is crucial for refining urban catchment hydrological models, thereby enhancing rainwater resource utilization efficiency (Stephen et al. \\u003cspan citationid=\\\"CR31\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). A statistical summary of documented RC values is provided in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab1\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab1\\\" border=\\\"1\\\"\\u003e\\u003ccaption language=\\\"En\\\"\\u003e\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 1\\u003c/div\\u003e\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\u003cp\\u003eStatistical table of roof runoff coefficient\\u003c/p\\u003e\\u003c/div\\u003e\\u003c/caption\\u003e\\u003ccolgroup cols=\\\"6\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eRC\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMaterial\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003eArea (m\\u003csup\\u003e2\\u003c/sup\\u003e)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003eSlope (\\u0026deg;)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eLocation\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003ePreference\\u003c/p\\u003e\\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.7\\u0026thinsp;~\\u0026thinsp;0.9\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003ePitch\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e12\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e0/2/5/7\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eUniversity Tenaga Nasional (Malaysia)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eChow et al. \\u003cspan citationid=\\\"CR8\\\" class=\\\"CitationRef\\\"\\u003e2018\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.75\\u0026thinsp;~\\u0026thinsp;0.95\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eConcrete\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e8000/1200\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e0\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eUniversity of Western\\u003c/p\\u003e\\u003cp\\u003eSydney (Australia)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eMonzur et al. \\u003cspan citationid=\\\"CR21\\\" class=\\\"CitationRef\\\"\\u003e2011\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.8\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e-\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e350/550/750\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e-\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eUniversity of Catania (Italy)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eAlberto and Carlo. 2012.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.7\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMental\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1500\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e-\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eUniversity of Exeter (UK)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eWard et al. \\u003cspan citationid=\\\"CR33\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.58/0.75\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eDry/Wet soil\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e1\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e-\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eBeijing (China)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eLiu et al. \\u003cspan citationid=\\\"CR20\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.83\\u0026thinsp;~\\u0026thinsp;0.85\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eClay tiles\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e120\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003e30\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eBarcelona (Spain)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eRamon et al. \\u003cspan citationid=\\\"CR27\\\" class=\\\"CitationRef\\\"\\u003e2011\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.92\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMetal\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e40.6\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.9\\u0026thinsp;~\\u0026thinsp;0.92\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003ePlastic\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e40.6\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.58\\u0026thinsp;~\\u0026thinsp;0.66\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eGravel\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e56.6\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e0\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eLjubljana (Slovenia)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eMark et al. \\u003cspan citationid=\\\"CR22\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.82\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMental\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e120\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e-\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eIstanbul (Turkey)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eBurak et al. \\u003cspan citationid=\\\"CR7\\\" class=\\\"CitationRef\\\"\\u003e2022\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.81\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eConcrete\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e120\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e0\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003eBaise City (China)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eMo et al. \\u003cspan citationid=\\\"CR23\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.81\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMental\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c3\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003e3\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003eParabolic\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c5\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eTaiwan (China)\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c6\\\" morerows=\\\"2\\\" rowspan=\\\"3\\\"\\u003e\\u003cp\\u003eArash Ret al. \\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e.\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.84\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMental\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003eInverted-V\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.83\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eMental\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003eSaw Tooth\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003c/tbody\\u003e\\u003c/colgroup\\u003e\\u003c/table\\u003e\\u003c/div\\u003e\\u003c/p\\u003e\\u003cp\\u003eIn this paper, the variation of the RC within the roof catchment under different influencing factors was investigated through simulated rainfall experiments. By analyzing the sensitivity of the RC, the main influencing factors of the RC are determined. Combined with the actual rainfall data, a linear regression model is used to establish a method for determining the value of the roof RC. The aim is to improve the utilization efficiency of the RRHS and promote the development of rainwater utilization.\\u003c/p\\u003e\"},{\"header\":\"2. Materials and methods\",\"content\":\"\\u003cdiv id=\\\"Sec3\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e2.1 Research location\\u003c/h2\\u003e\\u003cp\\u003eLocated in North China and extending from 36\\u0026deg;20\\u0026prime; to 36\\u0026deg;44\\u0026prime;N latitude and 114\\u0026deg;03\\u0026prime; to 114\\u0026deg;40\\u0026prime;E longitude, the study area experiences a warm-temperate continental monsoon climate, with an average annual temperature of 13.5℃ and an average annual rainfall of 558.5 mm.\\u003c/p\\u003e\\u003cp\\u003eThe artificial rainfall simulation platform, covering an area of approximately 400 m\\u003csup\\u003e2\\u003c/sup\\u003e, consists of three main components: a rainfall system, an underlying surface system, and a water collection/storage system. This design was informed by a field survey of roofing materials in northern China, which identified asphalt and metal as the predominant types. Accordingly, the experimental roof module spans an area of 60 m\\u003csup\\u003e2\\u003c/sup\\u003e and features an adjustable slope ranging from 0\\u0026deg; to 60\\u0026deg;. The rainfall system can simulate rainfall intensities from 20 to 200 mm/h. Moreover, the spatial coverage of the rainfall system is adjustable, capable of accommodating a maximum experimental area of 200 m\\u003csup\\u003e2\\u003c/sup\\u003e. A schematic diagram of the overall platform is presented in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig9\\\" class=\\\"InternalRef\\\"\\u003e1\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec4\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e2.2 Experimental design\\u003c/h2\\u003e\\u003cp\\u003eThe experiment was designed to investigate the individual effects of four key factors: roof material, catchment area, roof slope, and rainfall intensity (RI). The RC was the primary response variable, while the antecedent dry period was considered a controlled auxiliary variable. Runoff from the roof module was collected by a network of gutters and downpipes, which channeled the water into a polyethylene storage tank for volumetric measurement. To simulate typical field conditions, the experimental setup did not incorporate an initial rainfall diversion device, and the roof surfaces were not subjected to any special cleaning or maintenance routines.\\u003c/p\\u003e\\u003cp\\u003eBased on an analysis of historical daily rainfall data, three rainfall intensities\\u0026mdash;20, 50, and 100 mm/h\\u0026mdash;were selected and configured for the simulation experiments. To monitor the actual RI during experiments, three SL-1 automatic tipping-bucket rain gauges were installed at representative locations: on the asphalt roof, the metal roof, and at ground level. Furthermore, roof runoff was monitored using automatic flow meters installed at the outlets of each roof module.\\u003c/p\\u003e\\u003cp\\u003eInfiltration-excess and saturation-excess are widely recognized as the two primary mechanisms of runoff generation (Arash et al. \\u003cspan citationid=\\\"CR4\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e). To ensure that infiltration-excess runoff was the consistent dominant mechanism across all trials, each roof surface was pre-wetted until initial runoff was observed immediately before the formal experiment. Following pre-wetting, the system was allowed to drain and was then left undisturbed for a consistent antecedent dry period of 3 days to establish uniform initial conditions for every test.\\u003c/p\\u003e\\u003cp\\u003eThe experimental variables included two roofing materials (asphalt and metal) and three slope gradients (0\\u0026deg;, 2\\u0026deg;, and 5\\u0026deg;). Each simulated rainfall event had a fixed duration of 30 minutes. A preliminary experiment was conducted to determine the optimal data collection interval by comparing the cumulative runoff depth recorded at 1-minute and 5-minute intervals. The 1-minute interval was found to capture the dynamics of runoff generation more effectively, as it revealed more pronounced trends in the cumulative runoff curve. Consequently, the 1-minute interval was adopted for all subsequent formal experiments. A summary of the specific experimental parameters is provided in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig10\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec5\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e2.3 Data collection\\u003c/h2\\u003e\\u003cp\\u003eThe deployment of telemetric rain gauges (SL-1, China) at the study sites was informed by an analysis of long-term (2015\\u0026ndash;2024) daily rainfall and temperature data obtained from the local meteorological department. Between 2022 and 2024, a total of 116 natural rainfall events were monitored. The characteristics of these events are summarized in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab2\\\" class=\\\"InternalRef\\\"\\u003e2\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab2\\\" border=\\\"1\\\"\\u003e\\u003ccaption language=\\\"En\\\"\\u003e\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 2\\u003c/div\\u003e\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\u003cp\\u003eRainfall event record sheet\\u003c/p\\u003e\\u003c/div\\u003e\\u003c/caption\\u003e\\u003ccolgroup cols=\\\"8\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c7\\\" colnum=\\\"7\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c8\\\" colnum=\\\"8\\\"\\u003e\\u003c/div\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\" morerows=\\\"1\\\" rowspan=\\\"2\\\"\\u003e\\u003cp\\u003eYear\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\" morerows=\\\"1\\\" rowspan=\\\"2\\\"\\u003e\\u003cp\\u003eAnnual rainfall depth/mm\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colspan=\\\"6\\\" nameend=\\\"c8\\\" namest=\\\"c3\\\"\\u003e\\u003cp\\u003eNumber of monitored events\\u003c/p\\u003e\\u003c/th\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e0\\u0026thinsp;~\\u0026thinsp;5mm\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e5\\u0026thinsp;~\\u0026thinsp;15mm\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e15\\u0026thinsp;~\\u0026thinsp;25mm\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003e25\\u0026thinsp;~\\u0026thinsp;35mm\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c7\\\"\\u003e\\u003cp\\u003e35\\u0026thinsp;~\\u0026thinsp;45mm\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c8\\\"\\u003e\\u003cp\\u003e\\u0026gt;\\u0026thinsp;45mm\\u003c/p\\u003e\\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2022\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e216.6\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e29\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e8\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e2\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003e1\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c7\\\"\\u003e\\u003cp\\u003e1\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c8\\\"\\u003e\\u003cp\\u003e0\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2023\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e1103.2\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e55\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e14\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e6\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003e1\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c7\\\"\\u003e\\u003cp\\u003e4\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c8\\\"\\u003e\\u003cp\\u003e7\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e2024\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e544.5\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e43\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e7\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e6\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003e1\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c7\\\"\\u003e\\u003cp\\u003e4\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c8\\\"\\u003e\\u003cp\\u003e2\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eTotal\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e1864.3\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e127\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e29\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e14\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003e3\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c7\\\"\\u003e\\u003cp\\u003e9\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c8\\\"\\u003e\\u003cp\\u003e9\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003c/tbody\\u003e\\u003c/colgroup\\u003e\\u003c/table\\u003e\\u003c/div\\u003e\\u003c/p\\u003e\\u003cp\\u003eRainfall losses on roofs, leading to runoff retention, are primarily attributed to infiltration and evapotranspiration. These processes are particularly significant during the initial phase of a rainfall event. However, the widespread adoption of first-flush diversion strategies in RRHS to improve stormwater quality (Abbasi and Abbasi. 2011; Georgios and Vassilios. 2012; Xie et al. \\u003cspan citationid=\\\"CR35\\\" class=\\\"CitationRef\\\"\\u003e2023\\u003c/span\\u003e; Zhang et al. \\u003cspan citationid=\\\"CR38\\\" class=\\\"CitationRef\\\"\\u003e2010\\u003c/span\\u003e) makes it particularly challenging to capture the initial portion of stormwater runoff. This challenge is most acute during the beginning of rainfall events or in the case of minor rainfall events with the depth of less than 5 mm.\\u003c/p\\u003e\\u003cp\\u003eDuring each simulated rainfall event, the initiation of runoff at the outlet was automatically detected and recorded by a soil erosion monitor. This recorded timestamp was defined as the runoff generation time. To determine the flow concentration time, a red water-soluble tracer powder was applied at the point farthest from the outlet on the roof surface. The moment when the runoff at the outlet exhibited a distinct color change was recorded, signaling the completion of the runoff confluence process. The flow concentration time was calculated as the difference between the confluence completion time and the runoff generation time. Owing to the spatially uniform rainfall design, the total rainfall volume was calculated as the product of the rainfall intensity (RI) and the catchment area. The total runoff volume was determined by measuring the change in water level within the calibrated storage tank.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec6\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e2.4 Data analysis\\u003c/h2\\u003e\\u003cp\\u003eThe principal analytical methods employed in this study included the Pearson correlation analysis, linear regression modeling, response surface methodology (RSM), and the Nash-Sutcliffe efficiency coefficient (NSE). Experimental data on the runoff processes, including the runoff generation time, confluence time, and runoff volume, were systematically collected across a range of rainfall intensities and roof conditions. The average rainfall runoff coefficient (ARC) is accurately calculated using Eq.\\u0026nbsp;(1).\\u003c/p\\u003e\\u003cp\\u003eARC\\u0026thinsp;=\\u0026thinsp;1000\\u003cem\\u003eV\\u003c/em\\u003e/\\u003cem\\u003eHA\\u003c/em\\u003e (1)\\u003c/p\\u003e\\u003cp\\u003ewhere \\u003cem\\u003eV\\u003c/em\\u003e is the rainfall runoff volume (m\\u003csup\\u003e3\\u003c/sup\\u003e), \\u003cem\\u003eH\\u003c/em\\u003e is the total rainfall depth (mm), \\u003cem\\u003eA\\u003c/em\\u003e is the catchment area (m\\u003csup\\u003e2\\u003c/sup\\u003e).\\u003c/p\\u003e\\u003cp\\u003eThe formula for calculating the instantaneous rainfall runoff coefficient (IRC) is given in Eq.\\u0026nbsp;(2).\\u003c/p\\u003e\\u003cp\\u003eIRC\\u0026thinsp;=\\u0026thinsp;\\u003cem\\u003eH\\u003c/em\\u003e\\u003csub\\u003e1\\u003c/sub\\u003e/\\u003cem\\u003eH\\u003c/em\\u003e\\u003csub\\u003e0\\u003c/sub\\u003e (2)\\u003c/p\\u003e\\u003cp\\u003ewhere \\u003cem\\u003eH\\u003c/em\\u003e\\u003csub\\u003e1\\u003c/sub\\u003e is the depth of runoff per unit time (mm), \\u003cem\\u003eH\\u003c/em\\u003e\\u003csub\\u003e0\\u003c/sub\\u003e is the rainfall depth per unit time (mm).\\u003c/p\\u003e\\u003cp\\u003eThe mathematical description of the daily water balance model for RRHS is given by Eq.\\u0026nbsp;(3).\\u003c/p\\u003e\\u003cp\\u003e\\u003cem\\u003eS\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u003c/sub\\u003e=\\u003cem\\u003eV\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u003c/sub\\u003e+\\u003cem\\u003eS\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u0026minus;1\\u003c/sub\\u003e-\\u003cem\\u003eD\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u003c/sub\\u003e (3)\\u003c/p\\u003e\\u003cp\\u003eWhere \\u003cem\\u003eS\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u003c/sub\\u003e is the cumulative rainfall storage volume at RRHS on day \\u003cem\\u003et\\u003c/em\\u003e (m\\u003csup\\u003e3\\u003c/sup\\u003e), \\u003cem\\u003eV\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u003c/sub\\u003e is the rainwater runoff volume collected by RRHS on day t (m\\u003csup\\u003e3\\u003c/sup\\u003e), \\u003cem\\u003eS\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u0026minus;1\\u003c/sub\\u003e is the cumulative rainfall storage volume (m\\u003csup\\u003e3\\u003c/sup\\u003e) at RRHS on day \\u003cem\\u003et\\u003c/em\\u003e-1, \\u003cem\\u003eD\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u003c/sub\\u003e is the daily water supply volume of RRHS on day \\u003cem\\u003et\\u003c/em\\u003e (m\\u003csup\\u003e3\\u003c/sup\\u003e).\\u003c/p\\u003e\\u003cp\\u003eOn day \\u003cem\\u003et\\u003c/em\\u003e, the free volume of RRHS is given by Eq.\\u0026nbsp;(4).\\u003c/p\\u003e\\u003cp\\u003e\\u003cem\\u003eV\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003ek\\u003c/em\\u003e\\u003c/sub\\u003e=\\u003cem\\u003eV\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eR\\u003c/em\\u003e\\u003c/sub\\u003e-\\u003cem\\u003eS\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u0026minus;1\\u003c/sub\\u003e+\\u003cem\\u003eD\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003et\\u003c/em\\u003e\\u003c/sub\\u003e (4)\\u003c/p\\u003e\\u003cp\\u003eWhere \\u003cem\\u003eV\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003ek\\u003c/em\\u003e\\u003c/sub\\u003e is the free volume of RRHS on day \\u003cem\\u003et\\u003c/em\\u003e (m\\u003csup\\u003e3\\u003c/sup\\u003e), \\u003cem\\u003eV\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003eR\\u003c/em\\u003e\\u003c/sub\\u003e is the total volume of RRHS (m\\u003csup\\u003e3\\u003c/sup\\u003e).\\u003c/p\\u003e\\u003cp\\u003eDaily roof runoff volume as Eq.\\u0026nbsp;(5).\\u003c/p\\u003e\\u003cp\\u003e\\u003cem\\u003eV\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003ed\\u003c/em\\u003e\\u003c/sub\\u003e=\\u003cem\\u003eRC\\u003c/em\\u003e \\u0026times; \\u003cem\\u003eHA\\u003c/em\\u003e \\u0026times; 10\\u003csup\\u003e\\u0026minus;\\u0026thinsp;3\\u003c/sup\\u003e (5)\\u003c/p\\u003e\\u003cp\\u003eWhere \\u003cem\\u003eV\\u003c/em\\u003e\\u003csub\\u003e\\u003cem\\u003ed\\u003c/em\\u003e\\u003c/sub\\u003e is the daily rainfall runoff volume (m\\u003csup\\u003e3\\u003c/sup\\u003e).\\u003c/p\\u003e\\u003cp\\u003eThe method for calculating water supply reliability is shown in Eq.\\u0026nbsp;(6).\\u003c/p\\u003e\\u003cp\\u003e\\u003cem\\u003eR\\u003c/em\\u003e\\u0026thinsp;=\\u0026thinsp;\\u003cem\\u003eD\\u003c/em\\u003e/\\u003cem\\u003eN\\u003c/em\\u003e \\u0026times; 100 (6)\\u003c/p\\u003e\\u003cp\\u003eWhere \\u003cem\\u003eR\\u003c/em\\u003e is the RRHS water supply reliability (%), \\u003cem\\u003eD\\u003c/em\\u003e is the RRHS time to meet water demand (d), \\u003cem\\u003eN\\u003c/em\\u003e is the RRHS water supply cycle (d).\\u003c/p\\u003e\\u003cp\\u003eThe relationship between the RC and each individual influencing factor was quantified using the Pearson correlation coefficient. The goodness-of-fit of these relationships was evaluated based on the dispersion of data points around the regression line, with a coefficient of determination (\\u003cem\\u003eR\\u003c/em\\u003e\\u003csup\\u003e2\\u003c/sup\\u003e) greater than 0.95 considered indicative of a high-quality fit. RSM was employed to analyze the effects of interaction terms between various influencing factors on the runoff coefficient. The relative importance of the primary influencing factors was determined by the steepness of the gradient of the response surface. For cross-validation, the dataset was partitioned into two subsets based on data source: actual rainfall and simulated rainfall. A linear regression model was established to analyze the relationship between the RC and cumulative rainfall depth. Based on the observed trends in the regression coefficients, a novel method for estimating the roof RC is proposed. Finally, the predictive reliability of the proposed RC estimation method was validated using the Nash-Sutcliffe efficiency coefficient (NSE).\\u003c/p\\u003e\\u003c/div\\u003e\"},{\"header\":\"3. Results and discussion\",\"content\":\"\\u003cdiv id=\\\"Sec8\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e3.1 Roof runoff generation and confluence\\u003c/h2\\u003e\\u003cp\\u003eRoof runoff generation and confluence collectively describe the process of rainfall accumulating on a roof surface to form runoff, a process governed by both catchment characteristics (material, slope) and climatic conditions (rainfall intensity). Through a series of simulated rainfall experiments, data including runoff generation time, confluence time, runoff depth, and rainfall depth were collected and analyzed for various rainfall events. The analysis revealed a consistent pattern in the runoff generation and confluence processes under varying conditions, as illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig11\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eThe complete rooftop runoff hydrograph under specified conditions can be divided into four distinct phases: generation, confluence, stabilization, and recession (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig11\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e). A magnified view of the hydrograph shows that runoff initiation occurs at 0.97 minutes, as indicated by the red marker. The runoff generation phase is influenced by antecedent dry conditions and evapotranspiration. Consequently, runoff does not commence immediately after rainfall begins. As precipitation continues, the cumulative rainfall eventually surpasses the initial losses (infiltration and wetting). This threshold marks the commencement of runoff generation, after which water flows over the surface and converges into the drainage system.\\u003c/p\\u003e\\u003cp\\u003eRI and roof slope are two critical factors influencing the runoff generation time under various conditions. The runoff generation time gradually decreases with increasing rainfall intensity and roof slope. Since the roof represents a typical impervious surface, the initial rainfall loss\\u0026mdash;primarily determined by antecedent dry conditions and evapotranspiration\\u0026mdash;can be considered a relatively fixed volume. The higher RI delivers a greater volume of rainfall per unit time. Consequently, as the cumulative rainfall volume increases, this fixed initial loss constitutes a diminishing proportion of the total rainfall. This decreasing proportion means the threshold for runoff generation is reached more rapidly, leading to a shorter generation time. Furthermore, a steeper roof slope accelerates the runoff generation rate by reducing surface retention and facilitating faster flow convergence.\\u003c/p\\u003e\\u003cp\\u003eThe confluence phase (0.97 to 6 min) describes the process wherein runoff generated across the roof surface converges towards the drainage outlets. The path length for runoff to travel to the outlet varies depending on its point of origin on the roof. Longer flow paths consequently require longer travel times. As rainfall continues, the instantaneous runoff rate increases progressively. The confluence phase is considered complete when runoff originating from the hydraulically most remote point on the roof reaches the outlet.\\u003c/p\\u003e\\u003cp\\u003eDuring the confluence phase, the rate of runoff discharge exhibits a positive correlation with both the RI and the roof slope. A steeper roof slope accelerates the overland flow velocity. This increased velocity results in a higher volume of runoff reaching the drainage outlet per unit time. Therefore, the duration of the confluence phase is governed by the combined effects of RI and roof slope. Furthermore, the roof catchment area directly affects the confluence time, with larger areas requiring more time for runoff to fully converge.\\u003c/p\\u003e\\u003cp\\u003eThe runoff process transitions into the stabilization phase once flow from the hydraulically most remote point on the roof reaches the drainage outlet. During this phase, the instantaneous runoff depth approaches the instantaneous rainfall depth, exhibiting minor fluctuations around a stable equilibrium value. Factors such as surface evaporation cause losses, resulting in the instantaneous runoff depth being marginally lower than the instantaneous rainfall depth. Due to the designed constant-intensity rainfall pattern, the stabilization phase persists until the rainfall cessation. The duration of the stabilization phase is therefore determined by the time of confluence completion and the total rainfall duration. Consequently, factors influencing the confluence time (roof area, slope, rainfall intensity) indirectly govern the commencement and duration of the stabilization phase.\\u003c/p\\u003e\\u003cp\\u003eUpon the conclusion of the designed rainfall event, the rainfall simulation system was switched off. This marks the beginning of the recession phase. Monitoring instruments indicated that a diminishing amount of residual runoff continued to be collected from the roof outlets. Since rainfall input had ceased, no new runoff was generated; the runoff observed during this phase represents the drainage of water that was temporarily stored or moving slowly across the roof surface. Given the impervious nature of the roof surfaces, the volume of water in this recession phase is limited. A rapid decrease in instantaneous runoff depth commences at the 30-minute mark, corresponding to the end of rainfall (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig11\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e). Comparative analysis of the recession curves under different conditions identified the roof slope as the dominant factor influencing the recession process. A steeper slope facilitates faster drainage of the stored water, leading to a shorter recession phase. Since RI is zero during this phase, it does not exert any influence.\\u003c/p\\u003e\\u003cp\\u003eThroughout the rainfall event, a dynamic discrepancy existed between the instantaneous rainfall depth and the runoff depth (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig11\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e). Due to the challenges in directly monitoring roof runoff volume under natural rainfall conditions, the runoff coefficient (RC) provides a practical method for estimating the effective runoff depth from various rainfall events. Accurate estimation of this depth through RC analysis is crucial for optimizing the operational efficiency of Roof Rainwater Harvesting Systems (RRHS).\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec9\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e3.2 Runoff coefficient\\u003c/h2\\u003e\\u003cp\\u003eThe RC is a crucial parameter in urban hydrology for assessing rainfall-runoff response and water yield (Ana et al. \\u003cspan citationid=\\\"CR3\\\" class=\\\"CitationRef\\\"\\u003e2024\\u003c/span\\u003e). However, the hydrological behavior of roofs, as artificial catchments, is complex and influenced by diverse local factors, leading to significant spatial and temporal variability in the RC. This study aims to quantify the impacts of rainfall characteristics and roof surface properties on the RC during standardized rainfall events. To achieve this, we tracked runoff dynamics for four roof types under controlled conditions, calculating both the IRC and the ARC to assess discrepancies between rainfall input and runoff output. Despite varying conditions, the patterns of RC variation exhibited consistent trends across the different roof types, as summarized in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig12\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eFor analytical purposes, two types of runoff coefficients were examined: the IIRC and the ARC. The IRC is defined as the ratio of instantaneous runoff volume to instantaneous rainfall volume per unit time. The ARC is calculated as the ratio of the total runoff volume to the total rainfall volume at the conclusion of a rainfall event (Fermando et al. \\u003cspan citationid=\\\"CR12\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). Figure\\u0026nbsp;\\u003cspan refid=\\\"Fig12\\\" class=\\\"InternalRef\\\"\\u003e4\\u003c/span\\u003e demonstrates that the temporal variation of the IRC closely follows the pattern of instantaneous runoff depth. The IRC exhibits two distinct phases: a rapid rising phase and a subsequent stable phase. The rising phase coincides with the confluence phase of the runoff, during which the IRC increases rapidly with rainfall duration until reaching a peak. After peaking, the IRC transitions into a stable phase, where it fluctuates slightly around this peak value until rainfall cessation. This stable phase parallels the stabilization phase of the runoff hydrograph and is characterized by minor fluctuations around a steady value. In contrast to the dynamic, two-phase behavior of the IRC, the ARC remains constant for a given event, as clearly illustrated by the comparative data presented in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eUnder identical rainfall intensity and slope conditions, both the IRC and ARC values remain consistent across asphalt roofs with different areas (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003ea). Specifically, the IRC values for Rf1#, Rf2#, and Rf3# were 0.928, 0.926, and 0.927, respectively, while the corresponding ARC values were 0.741, 0.746, and 0.747. The observed minor variations in coefficients, with errors of merely 0.11% (IRC) and 0.27% (ARC), are within the expected range of measurement uncertainty (Li et al. \\u003cspan citationid=\\\"CR18\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). Therefore, it can be concluded that variations in roof area have no significant impact on either the IRC or the ARC. Furthermore, under these conditions, the rainfall duration required to reach the peak IRC value was also consistent across different roof areas. Similarly, for roofs Rf3# and Rf4# with identical surface areas but differing materials, their IRC values were 0.927 and 0.929 respectively, while their ARC values were 0.747 and 0.751 respectively (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003eb). The coefficient errors here were 0.1% and 0.27%, which are again within the accepted margin of error (Li et al. \\u003cspan citationid=\\\"CR18\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e).\\u003c/p\\u003e\\u003cp\\u003eAnalysis of the IRC revealed that the metal roof exhibited a shorter runoff generation time compared to the asphalt roof under identical experimental conditions. The peak IRC for the metal roof was attained at the 9-minute mark, whereas that for the asphalt roof was reached at the 10-minute mark. Furthermore, the IRC was consistently higher for the metal substrate than for the asphalt throughout the rising phase for any given rainfall duration. This difference is attributed to the lower surface roughness of the metal roof, which reduces its rainwater retention capacity and facilitates faster runoff flow. Consequently, a greater volume of runoff reaches the outlet on metal roofs within the same timeframe, resulting in a higher IRC. During the stabilization phase, both the IRC and ARC values converged and became very similar for both materials. This indicates that the influence of roofing material on the runoff coefficients is minimal during the stabilization phase. Therefore, it can be concluded that the primary influence of roofing material is on the rising phase of the IRC, and the degree of this influence is positively correlated with the surface roughness of the material. In contrast, the roofing material was found to have no significant effect on the ARC. This conclusion was further corroborated by data from actual rainfall events, which showed no significant impact of material on the RC.\\u003c/p\\u003e\\u003cp\\u003eHolding rainfall characteristics and other factors constant, variations in roof slope were found to significantly influence both the IRC and the ARC. Data from roof Rf3# under scenarios M1, M4, and M7 (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003ec) were selected for analysis to isolate the effect of slope. For Rf3# at three distinct slopes, the IRC values were 0.912, 0.927, and 0.937, and the corresponding ARC values were 0.731, 0.747, and 0.756. The observed coefficient variations (1.4% for IRC, 1.2% for ARC) exceeded the typical margin of experimental error. This indicates that roof slope has a statistically significant impact on the runoff coefficient.\\u003c/p\\u003e\\u003cp\\u003eWith rainfall characteristics and other factors held constant, both the instantaneous runoff coefficient and the mean runoff coefficient increase with steeper slopes (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003ec). For a given rainfall duration, a steeper roof slope is associated with a higher IRC. An increased slope shortens the time to peak runoff and elevates the IRC. Analysis of the runoff generation and confluence times confirms that steeper slopes reduce the duration of both phases. Physically, a steeper slope enhances the gravitational potential energy of the runoff, which is converted into greater kinetic energy and thus higher flow velocity. Consequently, the volume of runoff discharged per unit time increases, resulting in a higher IRC on steeper slopes.\\u003c/p\\u003e\\u003cp\\u003eRainfall characteristics are a primary factor in the runoff simulation process, with RI exerting a particularly notable influence on roof runoff generation. The response of the runoff coefficient for roof Rf3# to varying RI (conditions M1, M2, M3) is illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003ed. For Rf3# under these conditions, the IRC values were 0.912, 0.950, and 0.979, respectively, representing a total increase of 3.7%. Similarly, the ARC values were 0.731, 0.783, and 0.833, representing a larger total increase of 6.5%. The substantial increases in both coefficients underscore the significant impact of rainfall intensity on the runoff coefficient. Both the IRC and ARC exhibit a strong positive correlation with increasing rainfall intensity. For a given duration, the IRC increases with rainfall intensity. Furthermore, a higher RI shortens the time required to reach the peak runoff rate.\\u003c/p\\u003e\\u003cp\\u003eThe positive correlation between the runoff coefficient and rainfall intensity is consistent with the dynamics of runoff volume accumulation. An increase in rainfall intensity reduces the time required for both runoff generation and confluence. Due to the impervious nature of roof surfaces, their water retention capacity is limited. A higher rainfall intensity delivers a greater volume of precipitation per unit time. This leads to a more rapid formation of runoff and a higher instantaneous runoff rate. Consequently, the runoff coefficient increases correspondingly with rainfall intensity.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec10\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e3.3 Sensitivity analysis of the RC\\u003c/h2\\u003e\\u003cp\\u003eThe varying degrees of influence exerted by roofing materials, slope gradients, and RI upon RC are clearly illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig13\\\" class=\\\"InternalRef\\\"\\u003e5\\u003c/span\\u003e. To quantitatively identify the dominant factors, a systematic analysis was conducted. The study aimed to quantify the relative importance of each factor on the RC. First, the Pearson correlation coefficient was employed to assess the linear relationship between the RC and each individual factor. Subsequently, RSM was applied to identify the principal factors and their interactions affecting the RC. The results of the correlation analysis are presented in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eThe horizontal axis represents the RC values for the 0\\u0026deg; slope condition, while the vertical axis represents the corresponding RC values for the 2\\u0026deg; and 5\\u0026deg; slope conditions (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003ea). A linear regression analysis of the RC values across the three slopes indicates a strong linear relationship. This is supported by high coefficients of determination (\\u003cem\\u003eR\\u003c/em\\u003e\\u003csup\\u003e2\\u003c/sup\\u003e) of 0.996 (for 0\\u0026deg; vs. 2\\u0026deg;) and 0.969 (for 0\\u0026deg; vs. 5\\u0026deg;). However, a discernible deviation is observed between the fitted regression lines and the lines of perfect agreement (1:1 lines) on the graph. The magnitude of this deviation increases with increasing slope. This pattern confirms that roof slope has a significant and systematic influence on the RC.\\u003c/p\\u003e\\u003cp\\u003eThe correlation between RC for roofs of different areas and materials is shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003eb. The horizontal axis represents the RC values for the reference roof (Rf3#), while the vertical axis represents the RC values for the other roofs (Rf1#, Rf2#, and Rf4#). Linear regression analysis of the RC values across the four roof types yielded Pearson correlation coefficients (\\u003cem\\u003eR\\u003c/em\\u003e\\u003csup\\u003e2\\u003c/sup\\u003e) of 0.999, 0.999, and 0.996, indicating an exceptionally strong linear fit. Furthermore, the fitted regression lines lie very close to the line of perfect agreement (1:1 line). This indicates that the runoff coefficients for all four roof types can be considered equivalent under identical rainfall conditions. Therefore, it can be concluded that, under the conditions tested, roof area and material have a negligible effect on the runoff coefficient.\\u003c/p\\u003e\\u003cp\\u003eThe horizontal axis represents the RC values at 20 mm/h, while the vertical axis represents the corresponding values at 50 mm/h and 100 mm/h. The relationship between runoff coefficients obtained under different rainfall intensities is shown in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig14\\\" class=\\\"InternalRef\\\"\\u003e6\\u003c/span\\u003ec. The relationship was analyzed using linear regression, which indicated a reasonable fit, with coefficients of determination (\\u003cem\\u003eR\\u003c/em\\u003e\\u003csup\\u003e2\\u003c/sup\\u003e) of 0.961 and 0.854, respectively. The resulting regression lines show a clear deviation from the line of perfect agreement (1:1 line). Furthermore, the magnitude of this deviation increases with increasing rainfall intensity. These results demonstrate that rainfall intensity exerts a significant influence on the RC.\\u003c/p\\u003e\\u003cp\\u003eThe analysis confirms that both roof slope and rainfall intensity significantly influence the RC. To determine which factor is dominant, the interaction between them was analyzed using the RSM based on the experimental design illustrated in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig15\\\" class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e. The response surface analysis presented in Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig15\\\" class=\\\"InternalRef\\\"\\u003e7\\u003c/span\\u003e demonstrates the effects of roof slope and RI on the RC. The maximum effect magnitudes were 0.78 for slope and 0.83 for RI, respectively. Since RI exerts a greater effect than slope, it is identified as the primary factor influencing the RC.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec11\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e3.4 Modeling of roof coefficient values\\u003c/h2\\u003e\\u003cp\\u003eThe hydrological response of roofs under natural rainfall events is influenced by a complex interplay of diverse roof characteristics and climatic factors. In the statistical analysis of daily rainfall data, rainfall depth serves as the primary quantitative metric. In the subsequent analysis, rainfall depth was set as the independent variable (horizontal coordinate), and the RC was treated as the dependent variable (vertical coordinate). Under simulated rainfall and actual rainfall conditions, the distribution of runoff coefficient values exhibits the same pattern (Fig.\\u0026nbsp;\\u003cspan refid=\\\"Fig16\\\" class=\\\"InternalRef\\\"\\u003e8\\u003c/span\\u003e). The results indicate that the RC increases with rainfall depth, but the rate of this increase diminishes as the depth becomes larger.\\u003c/p\\u003e\\u003cp\\u003e\\u003c/p\\u003e\\u003cp\\u003eFor rainfall depths exceeding 5 mm, the RC from simulated rainfall events is consistently higher than that from actual rainfall events. This discrepancy is attributed to the difference in rainfall intensity patterns: actual rainfall exhibits time-varying intensity, whereas simulated rainfall maintains a constant intensity. Furthermore, field observations indicated that natural rainfall events often commence with a high intensity that gradually decays over time. Consequently, during the initial phase of an event, the RC for actual rainfall can be slightly higher. However, as cumulative rainfall depth increases, the RC for simulated rainfall becomes progressively greater. This occurs because actual rainfall, with its typically decaying intensity, requires a longer duration to accumulate the same depth achieved under constant simulated intensity. Extended rainfall duration leads to greater volumetric losses (evaporation, infiltration). These increased losses result in a lower RC. Accounting for the variability in rainfall depth and its interaction with duration-dependent losses, the runoff coefficient is modeled by Eq.\\u0026nbsp;(7).\\u003c/p\\u003e\\u003cp\\u003eRC\\u0026thinsp;=\\u0026thinsp;0.86\\u0026thinsp;\\u0026minus;\\u0026thinsp;0.48 \\u0026times; 0.94\\u003csup\\u003e\\u003cem\\u003eH\\u003c/em\\u003e\\u003c/sup\\u003e (7)\\u003c/p\\u003e\\u003cp\\u003ewhere RC is the runoff coefficient, dimensionless, \\u003cem\\u003eH\\u003c/em\\u003e is the rainfall depth (mm).\\u003c/p\\u003e\\u003cp\\u003eThe NSE was employed as the metric to evaluate the model's performance in simulating actual rainfall scenarios. An NSE value of 0.927 indicates a strong agreement between the modeled and observed runoff coefficients, demonstrating the model's reliability in predicting roof runoff under natural conditions.\\u003c/p\\u003e\\u003c/div\\u003e\\u003cdiv id=\\\"Sec12\\\" class=\\\"Section2\\\"\\u003e\\u003ch2\\u003e3.5. Application of runoff coefficient estimation models\\u003c/h2\\u003e\\u003cp\\u003eIn urban water resource management, the RC for impervious roofs is conventionally estimated within a range of 0.95 to 1.0, a value primarily derived from empirical studies of hard-surfaced areas (Lotte et al. \\u003cspan citationid=\\\"CR17\\\" class=\\\"CitationRef\\\"\\u003e2020\\u003c/span\\u003e). However, as research advances and data accumulate, a growing body of literature suggests that these traditional estimation methods may lack the accuracy required to represent the actual runoff responses of diverse roof types under varying rainfall conditions. To quantify the performance improvement, a daily water balance model was implemented in Python (Section \\u003cspan refid=\\\"Sec6\\\" class=\\\"InternalRef\\\"\\u003e2.4\\u003c/span\\u003e). This model compared system performance metrics\\u0026mdash;including cumulative water supply, full storage days, water supply reliability, spatial utilization rate, and operational efficiency\\u0026mdash;between the traditional fixed RC method and the proposed spectrum-based RC method. The comparison elucidates the enhancement achieved by the RC spectrum in RRHS performance. The simulation was configured for the year 2023, with a roof catchment area of 500 m\\u003csup\\u003e2\\u003c/sup\\u003e, a daily water supply demand of 1 m\\u003csup\\u003e3\\u003c/sup\\u003e/d, and an annual runoff capture efficiency target of 70%. The specific parameters and results are summarized in Table\\u0026nbsp;\\u003cspan refid=\\\"Tab3\\\" class=\\\"InternalRef\\\"\\u003e3\\u003c/span\\u003e.\\u003c/p\\u003e\\u003cp\\u003e\\u003cdiv class=\\\"gridtable\\\"\\u003e\\u003ctable float=\\\"Yes\\\" id=\\\"Tab3\\\" border=\\\"1\\\"\\u003e\\u003ccaption language=\\\"En\\\"\\u003e\\u003cdiv class=\\\"CaptionNumber\\\"\\u003eTable 3\\u003c/div\\u003e\\u003cdiv class=\\\"CaptionContent\\\"\\u003e\\u003cp\\u003eAnalysis of operating parameters of RRHS under different models\\u003c/p\\u003e\\u003c/div\\u003e\\u003c/caption\\u003e\\u003ccolgroup cols=\\\"7\\\"\\u003e\\u003cdiv align=\\\"left\\\" class=\\\"colspec\\\" colname=\\\"c1\\\" colnum=\\\"1\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c2\\\" colnum=\\\"2\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c3\\\" colnum=\\\"3\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c4\\\" colnum=\\\"4\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c5\\\" colnum=\\\"5\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c6\\\" colnum=\\\"6\\\"\\u003e\\u003c/div\\u003e\\u003cdiv align=\\\"char\\\" char=\\\".\\\" class=\\\"colspec\\\" colname=\\\"c7\\\" colnum=\\\"7\\\"\\u003e\\u003c/div\\u003e\\u003cthead\\u003e\\u003ctr\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eMethod\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003eVolume\\u003c/p\\u003e\\u003cp\\u003e(m\\u003csup\\u003e3\\u003c/sup\\u003e)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003eCumulative water supply volume (m\\u003csup\\u003e3\\u003c/sup\\u003e)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003eMaximum storage days (d)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e\\u003cem\\u003eR\\u003c/em\\u003e (%)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003eSpace utilization rate (%)\\u003c/p\\u003e\\u003c/th\\u003e\\u003cth align=\\\"left\\\" colname=\\\"c7\\\"\\u003e\\u003cp\\u003eOperational Efficiency (%)\\u003c/p\\u003e\\u003c/th\\u003e\\u003c/tr\\u003e\\u003c/thead\\u003e\\u003ctbody\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003e0.95\\u0026thinsp;~\\u0026thinsp;1\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e63\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e180.71\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e4\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e47.12\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003e0.7\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c7\\\"\\u003e\\u003cp\\u003e70.45\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003ctr\\u003e\\u003ctd align=\\\"left\\\" colname=\\\"c1\\\"\\u003e\\u003cp\\u003eModel\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c2\\\"\\u003e\\u003cp\\u003e31\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c3\\\"\\u003e\\u003cp\\u003e148.71\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c4\\\"\\u003e\\u003cp\\u003e6\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c5\\\"\\u003e\\u003cp\\u003e38.08\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c6\\\"\\u003e\\u003cp\\u003e1.3\\u003c/p\\u003e\\u003c/td\\u003e\\u003ctd align=\\\"char\\\" char=\\\".\\\" colname=\\\"c7\\\"\\u003e\\u003cp\\u003e70.55\\u003c/p\\u003e\\u003c/td\\u003e\\u003c/tr\\u003e\\u003c/tbody\\u003e\\u003c/colgroup\\u003e\\u003c/table\\u003e\\u003c/div\\u003e\\u003c/p\\u003e\\u003cp\\u003eThe required storage capacity of the retention facility differed significantly between the two runoff coefficient determination methods. The design based on the runoff coefficient spectrum required a storage volume of 31 m\\u003csup\\u003e3\\u003c/sup\\u003e, whereas the traditional method necessitated a volume of 63 m\\u003csup\\u003e3\\u003c/sup\\u003e. This represents a reduction of 32 m\\u003csup\\u003e3\\u003c/sup\\u003e (50.79%) in required storage volume compared to the traditional design. In terms of system output, the cumulative water supply provided by the RRHS was 148.71 m\\u003csup\\u003e3\\u003c/sup\\u003e using the spectrum-based method, compared to 180.71 m\\u003csup\\u003e3\\u003c/sup\\u003e with the traditional method. However, the number of days the storage facility remained at full capacity increased from 4 days to 6 days under the spectrum-based design, a 50% increase. The water supply reliability was 38.08% for the spectrum-based method, lower than the 47.12% achieved by the traditional method. Analysis of spatial utilization efficiency revealed rates of 0.7% for the spectrum-based method versus 1.3% for the traditional method. Finally, the operational efficiencies of the RRHS were 70.45% and 70.55% for the spectrum-based and traditional methods, respectively.\\u003c/p\\u003e\\u003c/div\\u003e\"},{\"header\":\"4. Conclusion\",\"content\":\"\\u003cp\\u003e(1) Both runoff volume and runoff coefficient will increase with the rainfall calendar time. The change in runoff volume and runoff coefficient per unit of time after peaking tends to stabilize.\\u003c/p\\u003e\\n\\u003cp\\u003e(2) Rainfall intensity is the main factor affecting the runoff coefficient. This is because the higher the intensity, the higher the runoff coefficient. In addition, slope also has an effect on the runoff coefficient. Neither the roofing material nor the area affects the runoff coefficient.\\u003c/p\\u003e\\n\\u003cp\\u003e(3) Leveraging the established relationship between the runoff coefficient and rainfall depth, a model has been developed to calculate the runoff coefficient based on rainfall depth. This method not only diversifies the techniques for deriving runoff coefficients but also improves their accuracy.\\u003c/p\\u003e\\n\\u003cp\\u003e(4) Although average rainfall was employed in this study, the actual rainfall process is complex. Incorporating various rainfall peak patterns might better align the simulated rainfall effects with real-world conditions. Linearly simulating runoff coefficients influenced by individual factors aids in analyzing the effects of various factors on model parameters.\\u003c/p\\u003e\"},{\"header\":\"Declarations\",\"content\":\"\\u003cp\\u003e\\u003cstrong\\u003eCRediT authorship contribution statement\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eHao Yu\\u003c/strong\\u003e: Data Curation, Investigation, Methodology, Writing - original draft. \\u003cstrong\\u003eFei Han\\u003c/strong\\u003e: Conceptualization, Methodology, Supervision. \\u003cstrong\\u003eWei Zhang\\u003c/strong\\u003e: Funding acquisition, Writing - review \\u0026amp; editing.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eDeclaration of Competing Interest\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors declare no competing financial interest.\\u003c/p\\u003e\\n\\u003cp\\u003e\\u003cstrong\\u003eAcknowledgements\\u003c/strong\\u003e\\u003c/p\\u003e\\n\\u003cp\\u003eThe authors thank the National Natural Science Foundation of China [grant number 52379008] for funding this study.\\u003c/p\\u003e\"},{\"header\":\"References\",\"content\":\"\\u003col\\u003e\\n\\u003cli\\u003eAlberto C, Carlo M. 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Journal of Southeast University (English Edition). 30(2), 220-224. http://doi.org/10.3969/j.issn.1003-7985.2014.02.015.\\u003c/li\\u003e\\n\\u003c/ol\\u003e\"}],\"fulltextSource\":\"\",\"fullText\":\"\",\"funders\":[],\"hasAdminPriorityOnWorkflow\":false,\"hasManuscriptDocX\":true,\"hasOptedInToPreprint\":true,\"hasPassedJournalQc\":\"\",\"hasAnyPriority\":false,\"hideJournal\":false,\"highlight\":\"\",\"institution\":\"\",\"isAcceptedByJournal\":true,\"isAuthorSuppliedPdf\":false,\"isDeskRejected\":\"\",\"isHiddenFromSearch\":false,\"isInQc\":false,\"isInWorkflow\":false,\"isPdf\":false,\"isPdfUpToDate\":true,\"isWithdrawnOrRetracted\":false,\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"water-resources-management\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"warm\",\"sideBox\":\"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)\",\"snPcode\":\"11269\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11269/3\",\"title\":\"Water Resources Management\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false},\"keywords\":\"Roof runoff coefficient, Rainwater resource utilization, Response surface curve, Linear regression model\",\"lastPublishedDoi\":\"10.21203/rs.3.rs-7863234/v1\",\"lastPublishedDoiUrl\":\"https://doi.org/10.21203/rs.3.rs-7863234/v1\",\"license\":{\"name\":\"CC BY 4.0\",\"url\":\"https://creativecommons.org/licenses/by/4.0/\"},\"manuscriptAbstract\":\"\\u003cp\\u003eThe roof runoff coefficient (RC) is a critical design parameter for roof rainwater harvesting systems (RRHS), traditionally derived from standard norms with limited accuracy. This study investigates the influencing factors and determination methodology of RC through simulated rainfall experiments and analysis of 116 actual rainfall events. Pearson correlation and response surface analysis identified rainfall intensity as the primary factor affecting RC, followed by roof slope, while roof material and area showed negligible impact. A linear regression model (RC\\u0026thinsp;=\\u0026thinsp;0.86\\u0026thinsp;\\u0026minus;\\u0026thinsp;0.48 \\u0026times; 0.94\\u003csup\\u003e\\u003cem\\u003eH\\u003c/em\\u003e\\u003c/sup\\u003e) was developed to estimate RC based on rainfall depth (\\u003cem\\u003eH\\u003c/em\\u003e), demonstrating high reliability with a Nash-Sutcliffe efficiency coefficient of 0.927. Experimental results revealed that higher rainfall intensity and steeper slopes significantly increase RC by reducing runoff generation and confluence time. Application of the model in RRHS design optimized storage volume by 50.79% compared to traditional methods, although it resulted in a moderate decrease in cumulative water supply and reliability. The study provides a data-driven approach for accurately determining RC, enhancing the efficiency and economic viability of rainwater resource utilization in urban water management.\\u003c/p\\u003e\",\"manuscriptTitle\":\"Methodology for determining runoff coefficients based on rainfall depth and sensitivity analysis of influencing factors\",\"msid\":\"\",\"msnumber\":\"\",\"nonDraftVersions\":[{\"code\":1,\"date\":\"2025-11-26 10:47:20\",\"doi\":\"10.21203/rs.3.rs-7863234/v1\",\"editorialEvents\":[{\"type\":\"communityComments\",\"content\":0},{\"type\":\"decision\",\"content\":\"Major revisions\",\"date\":\"2026-04-22T10:52:44+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"reviewerAgreed\",\"content\":\"\",\"date\":\"2025-11-17T02:24:07+00:00\",\"index\":0,\"fulltext\":\"\"},{\"type\":\"reviewersInvited\",\"content\":\"\",\"date\":\"2025-11-13T12:07:19+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorInvited\",\"content\":\"Water Resources Management\",\"date\":\"2025-11-06T11:35:35+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"editorAssigned\",\"content\":\"\",\"date\":\"2025-10-16T06:45:48+00:00\",\"index\":\"\",\"fulltext\":\"\"},{\"type\":\"submitted\",\"content\":\"Water Resources Management\",\"date\":\"2025-10-16T02:02:00+00:00\",\"index\":\"\",\"fulltext\":\"\"}],\"status\":\"published\",\"journal\":{\"display\":true,\"email\":\"info@researchsquare.com\",\"identity\":\"water-resources-management\",\"isNatureJournal\":false,\"hasQc\":true,\"allowDirectSubmit\":false,\"externalIdentity\":\"warm\",\"sideBox\":\"Learn more about [Water Resources Management](https://www.springer.com/journal/11269)\",\"snPcode\":\"11269\",\"submissionUrl\":\"https://submission.nature.com/new-submission/11269/3\",\"title\":\"Water Resources Management\",\"twitterHandle\":\"\",\"acdcEnabled\":true,\"dfaEnabled\":true,\"editorialSystem\":\"em\",\"reportingPortfolio\":\"Springer Hybrid\",\"inReviewEnabled\":true,\"inReviewRevisionsEnabled\":false}}],\"origin\":\"\",\"ownerIdentity\":\"1db1decf-af13-4950-8cd2-c649e4477ba1\",\"owner\":[],\"postedDate\":\"November 26th, 2025\",\"published\":true,\"recentEditorialEvents\":[],\"rejectedJournal\":[],\"revision\":\"\",\"amendment\":\"\",\"status\":\"under-review\",\"subjectAreas\":[],\"tags\":[],\"updatedAt\":\"2026-05-19T09:07:08+00:00\",\"versionOfRecord\":[],\"versionCreatedAt\":\"2025-11-26 10:47:20\",\"video\":\"\",\"vorDoi\":\"\",\"vorDoiUrl\":\"\",\"workflowStages\":[]},\"version\":\"v1\",\"identity\":\"rs-7863234\",\"journalConfig\":\"researchsquare\"},\"__N_SSP\":true},\"page\":\"/article/[identity]/[[...version]]\",\"query\":{\"redirect\":\"/article/rs-7863234\",\"identity\":\"rs-7863234\",\"version\":[\"v1\"]},\"buildId\":\"8U1c8b4HqxoKbykW_rLl7\",\"isFallback\":false,\"isExperimentalCompile\":false,\"dynamicIds\":[84888],\"gssp\":true,\"scriptLoader\":[]}","source_license":"CC-BY-4.0","license_restricted":false}