Fast-Processing Modelling of Urban Pluvial Flooding: Kinematic Hierarchical Filling-and-Spilling Algorithm

Fast-Processing Modelling of Urban Pluvial Flooding: Kinematic Hierarchical Filling-and-Spilling Algorithm | 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 Fast-Processing Modelling of Urban Pluvial Flooding: Kinematic Hierarchical Filling-and-Spilling Algorithm Kay Khaing Kyaw, Luis Mediero, Stefano Bagli, Attilio Castellarin This is a preprint; it has not been peer reviewed by a journal. https://doi.org/ 10.21203/rs.3.rs-9492481/v1 This work is licensed under a CC BY 4.0 License Status: Posted Version 1 posted You are reading this latest preprint version Abstract Pluvial flood modelling plays a critical role in enhancing flood preparedness in urban areas, where such events pose significant risks to communities and infrastructure. Recent studies underscore the ongoing challenges in flood modelling, particularly the need to balance accuracy and computational efficiency. Existing models often fall into two categories: highly detailed but computationally intensive, or fast processing yet overly simplified, which compromises their ability to capture essential flow dynamics. In this study, we improve an existing and widely used simplified approach, i.e. the Hierarchical Filling-and-Spilling Algorithms (HSFAs). The original HSFA approach generally underpredicts the inundated areas and maximum water depths as it cannot inundate an urban depression above its spilling point, due to its hydrostatic assumptions. We incorporate a kinematic runoff travel time distribution within watersheds and weir equations at watersheds’ spilling points. Our proposed modifications enable a simplified yet physics-based representation of the depression filling above its spilling point, resulting in a more accurate overall flooded extent and water depths. The algorithm was tested on a case study in the Cottonwood Lake area, USA, where freely available input data facilitated code development and reproducibility. Additionally, it was applied to a real-world pluvial flooding event in Pamplona, Spain, for further evaluation. A comparison of the algorithm’s results with the outputs of 2D hydrodynamic models demonstrated a similar representation of flooding extents around depressions. Finally, we discuss the potentials and limitations of the enhanced algorithm and propose directions for future research to further improve pluvial flood modelling. Environmental Engineering Urban flooding Flood hazard hotspots Hierarchical Filling-and-Spilling Algorithms Hydrodynamic Modelling Simplified pluvial flood modelling Weir Equation Figures Figure 1 Figure 2 Figure 3 Figure 4 Figure 5 Figure 6 Figure 7 Figure 8 Figure 9 Figure 10 Figure 11 Figure 12 Figure 13 Figure 14 1.Introduction Urban flooding poses significant risks to lives and infrastructure, necessitating efficient modelling solutions for hazard assessment and disaster preparedness. Cities and towns around the world urgently require a unified approach to urban water management that accounts for the links between water, infrastructure, and land use, while maintaining a dependable supply through varied water sources 1 . Recent research has focused on developing rapid flood mapping techniques for large-scale urban areas. 2 proposed a cellular automata approach for fast 2D urban flood modelling, while 3 presented a GIS-based methodology for quick flood hazard assessment in data-scarce regions. Hybrid machine learning models for urban flooding prediction showed promising results while comparing with storm water management models 4 . 5 introduced Safer_RAIN, a DEM-based algorithm for pluvial flood mapping across extensive urban areas, demonstrating good agreement with 2D hydraulic models. These approaches offer alternatives to traditional, computationally intensive 2D models 6 , enabling faster flood characterization and risk analysis. The development of such rapid modelling techniques is crucial for improving urban flood management, particularly in the context of increasing flood frequency and severity due to climate change, ongoing urban development in flood-prone areas and in real-time flood forecasting. Flood modelling is an essential tool for understanding and forecasting flood events, which are crucial for effective flood risk management, urban development planning, and emergency response strategies. Most flood models are based on hydraulic simplifications, with one-dimensional (1D) models utilizing the Saint-Venant equations and two-dimensional (2D) models employing the Diffusion wave or shallow water equations (SWE) 7 , 8 . While 1D models are computationally efficient, they have limitations in capturing complex flow dynamics, such as overland flow and detailed inundation patterns, where lateral velocities can be predominant 9 . In contrast, 2D models, which solve the SWE, offer a more accurate representation of flow dynamics but require significantly higher computational resources 10 – 12 . Accurate 2D simulations depend mainly on high-resolution topographic and surface roughness data, which can be difficult to obtain or estimate, particularly in ungauged or data-scarce areas. Additionally, calibrating these models often involves time-consuming processes and extensive field data collection of past flood events, which is particularly challenging in urban settings or areas with complex terrain 13 , 14 . Fast processing DEM based inundation modelling algorithms have emerged as efficient alternatives to traditional 2D hydrodynamic models, addressing the need for rapid flood predictions. These algorithms leverage digital elevation models (DEMs) and simplified computational techniques to enhance performance while maintaining accuracy. Fast processing models, such as Safer_RAIN, can use Hierarchical Filling-and-Spilling Algorithms (HSFAs) to simulate pluvial flooding efficiently over large areas, significantly reducing computational costs. Machine learning methods have been developed to approximate flow characteristics, allowing for real-time predictions without extensive computational resources 15 . The choice of DEM resolution and computational mesh significantly influences modelling outcomes, with high horizontal resolution data (i.e. ~1m) leading to more reliable inundation predictions 16 . Fast processing algorithms can adapt to various terrains, making them suitable for diverse flooding scenarios, including urban and rural contexts 17 . While these fast-processing DEM based models offer significant advantages, traditional 2D hydrodynamic models still provide detailed insights into complex flow dynamics, which may be essential for certain applications. Balancing speed and accuracy remain a critical consideration in flood modelling. Identification and handling of depressions in grid DEMs is critical to accurate hydrological modelling and flow direction determination. Various algorithms have been developed, each employing different strategies and information sources, such as stream network data, to enhance computational efficiency and accuracy. Algorithms can either modify DEM elevations (e.g., smoothing filters, depression filling) or maintain original elevations while determining flow paths 18 . A new data structure (depression hierarchy) captures the complexity of depressions, allowing for selective filling or breaching, which aids in dynamic hydrological modelling 19 . 20 presents a level-set method for nested depressions in DEMs, which offers an efficient alternative to traditional depression filling methods and enhances hydrological modelling and terrain analysis. The LiDAR Python package implements this method, providing an interactive GUI for users 21 . Earlier work by 22 introduced a novel concept of spill elevation and least-cost search for optimal flow paths, significantly improving computational efficiency. 23 further enhanced depression filling and flat surface processing algorithms using priority and “first-in, first-out” (FIFO) queues, achieving better performance by reducing computational effort, as reflected in its time complexity. These advancements in DEM processing are particularly valuable for analysing high resolution LiDAR derived DEMs, which can capture actual surface depressions in urban and peri-urban areas 21 . These methods collectively contribute to more accurate hydrological analysis and watershed modelling. These concepts and tools are harnessed by Safer_RAIN 5 , a fast-processing algorithm designed to assess and map pluvial flooding in urban areas. This tool utilizes high resolution DEMs and can account for spatially distributed rainfall and infiltration processes through a pixel-based Green Ampt model, making it suitable for rapid assessments across extensive urban landscapes (see https://saferplaces.co/ ). Safer_RAIN expands the capabilities of existing HSFAs by allowing for the mapping of pluvial flooding associated with partial filling of depression systems. Safer_RAIN has been applied to various scenarios, including rural inundation modelling and urban flooding caused by drainage system outflows 24 . The algorithm has shown good agreement with 2D hydrodynamic model outputs and ground evidence 5 , 25 . A stochastic methodology using Safer_RAIN has been developed to generate high resolution pluvial flood hazard maps, addressing current limitations of the standard synthetic design storm approach 25 . However, HSFAs have some limitations such as lack of hydraulic backwater effect, which usually tends to underestimate flood extents, and single flow path constraints. In this study, we improve the current version of Safer_RAIN by incorporating a kinematic travel time distribution for runoff within depression watersheds, alongside the application of weir equations at their overflow points. These enhancements enable the algorithm to inundate a depression above its spilling point, similarly to what happens in the real world when upstream runoff volumes exceed the overall depression capacity. We test improved version of Safer_RAIN “Kinematic Safer_RAIN” in a case study in Cotton Wood Lake Area in USA and it is applied to a set of real flooding events in urban areas of Pamplona, Spain. The structure of the paper is organized as follows: Section2 introduces the main components of the current version of Safer_RAIN, details the conceptual framework of the Kinematic Safer_RAIN, including its newly added capability and the confusion matrices used to evaluate the performance of the models; Section 3 explains the location and data used in two case study areas; Section 4 provides the application of the proposed approach in test and real-world case study areas and also presented the results from the comparisons between Kinematic Safer_RAIN with 2D hydrodynamic models, followed by a discussion of the algorithm's overall performance; and Section 5 concludes the paper by summarizing the key findings. In addition, Appendix A1 includes a pseudo-code representation of the proposed algorithm. 2.Materials and Models 2.1 Main Elements of Safer_RAIN HSFAs identify areas prone to pluvial flooding based on nested surface depressions derived from high-resolution DEMs. Rainfall volume accumulates within these depressions, and once they reach their capacity, excess water spills over into downstream depressions situated at lower elevations. HSFAs relied on several simplifying assumptions: (i) flow direction is determined by the D8 algorithm, which assigns flow to the steepest downslope neighbour among the eight adjacent cells.; (ii) overland flow dynamics are neglected, with net rainfall volume assumed to accumulate within the nested depression system based on the capacity and hierarchical structure of the depressions; (iii) rainfall is assumed to be uniformly distributed across the area, and (iv) the terrain is considered entirely impermeable. Safer_RAIN relaxed assumptions (iii) and (iv) to account for more realistic conditions by allowing spatially variable rainfall and incorporating infiltration (e.g., via a pixel-based Green–Ampt model). Original Safer_RAIN consists of two main phases: (1) DEM preprocessing, and (2) depressions (hereafter referred to as “blue spots”) flooding. Phase (1) includes two steps (Fig. 1 ). The first step characterizes horizontal hydrological hierarchy, including (a) identifying all blue spots and their contributing watersheds using a DEM pit-filling algorithm, and (b) determining each blue spot’s pour point (spilling point). The term "pour point" refers to the same concept as "spilling point," representing the point from which excess water volume overflows. For consistency, we will use the term "pour point" throughout the remainder of this paper. The second step establishes a vertical hierarchical structure within each blue spot through a top-down level set method 20 . Phase (2) simulates the flooding of the identified blue spots under a given rainfall event. Using the depression hierarchy from Phase 1, the algorithm fills each blue spot from the bottom up (incrementally raising water level) until the net rainfall volume is allocated, akin to the method in 5 . Phase 1 is executed once to generate the depression hierarchy (geometry and connectivity of all blue spots), and this information is then used in Phase 2 to simulate specific flood events. Please refer to 5 for further details. The numerous tests to compare Safer_RAIN outputs with detailed 2D hydrodynamic models (see e.g., 5,24,25 ) highlighted the good overall accuracy of the simulation results. However, they also showed the tendency of the algorithm to underpredict the maximum inundated areas and water depths relative to detailed 2D hydrodynamic simulations considered as ground truth. In the original algorithm, once a blue spot’s volume to the pour point is filled, any additional runoff is immediately diverted downstream, so the water level never exceeds the pour point elevation. In reality, if the outflow is constrained (such as through a narrow spillway or conduit), water can rise higher than the spill elevation, causing a backwater effect that increases flood depth and extent. This process is not captured in the original HSFA, leading to underestimation of flooding. 2.2. Kinematic Safer_RAIN conceptualization To represent the temporal dynamics of runoff delivery to each blue spot, we extend Safer_RAIN with a kinematic component that transfers rainfall volumes through the contributing watershed with a travel-time distribution and applies a weir-based computation at the pour point to simulate ponding above the spill elevation. The enhanced version of Safer_RAIN, referred here to as “Kinematic Safer_RAIN”, is also structured into two phases. Phase (1) involves LiDAR DEM preprocessing. It includes the original Safer_RAIN preprocessing steps that identify blue spot boundaries. Kinematic Safer_RAIN adds the computation of the flow length (in meters) from each pixel to the nearest blue spot boundary (frontier), which represents the topographic boundary that separates the depression from adjacent terrain. Phase 2 comprises three sub-steps: (i) generation of event hydrographs; (ii) computation of additional flooding above pour points using the weir equation and (iii) recursive update of upstream-to-downstream volumes. Phase (2) maintains the original Safer_RAIN flooding process (Step 2A in Fig. 2 ) while introducing additional steps (Steps 2B, 2B(i), and 2B(ii) in Fig. 2 ). In Step 2B, rainfall volumes are transferred from the pixels where the rainfall drops to the blue spot boundary with a time distribution. A constant routing velocity (default 1 m s⁻¹) is assumed to approximate the average overland flow velocity within the watershed. This simplification neglects local slope and roughness variations but allows derivation of travel-time distributions from flow length rasters. Step 2B(ii) incorporates the recursive calculation of delays of water volumes that are spilled from a given upstream blue spot and flow into downstream blue spots. Finally, Step 2B(ii) uses the weir equation to compute the additional water depth above the spilling point elevation (∆h) that is required to spill a given water volume. This also accounts for the potential further filling of a given depression due to the time distributed runoff inflow. Throughout this paper, we use the term ‘backwater effect’ in a simplified sense, to denote ponding above the pour-point elevation caused by delayed runoff inflows, rather than a true hydraulic backwater computed from momentum equations. Figure 2 schematically illustrates the new processes introduced in Kinematic Safer_RAIN (time-distributed runoff transfer and additional filling above the pour point via a weir equation) superimposed on the original Safer_RAIN framework. The proposed algorithms in Kinematic Safer_RAIN are further detailed in the following sub sections. 2.2.1 Kinematic Safer_RAIN: LiDAR preprocessing Kinematic Safer_RAIN uses the original DEM preprocessing phase with the new addition of calculating the distance classes of each pixel within the watershed that contributes to a given blue spot to its boundary. The process begins by filling the blue spots as they are the lowest depression areas. Afterwards, a flow length raster is generated using the flow direction for each watershed, excluding the blue spots (Fig. 3 ). The flow length is then divided into distance classes for each pixel that reaches the boundary of the blue spots. Finally, the number of pixels in each distance class is counted to compute the volume and time distribution. 2.2.2 Kinematic Safer_RAIN: Flooding Phase In the original Safer_RAIN, the inundation extent is necessarily confined within the blue spot boundary. However, during real flood events, the flooded area can extend beyond this boundary (as illustrated by the dashed blue line in Step 2B of Fig. 2 ). Kinematic Safer_RAIN can simulate a larger extent of inundation in blue spots, accounting for potential backwater effects. Therefore, the flooding phase in Kinematic Safer_RAIN involves two key steps: (1) producing a simplified representation of the event hydrograph (Step 2Bi, in Fig. 2 ), and (2) applying the weir equation to estimate the additional water surface elevation above the pour point (Step 2Bii, in Fig. 2 ). 2.2.3 Event hydrograph After obtaining the distance classes from the flow length raster of each watershed and determining the pixel counts for each distance class, the runoff travel time from each pixel to the boundary of the blue spot area is calculated using a constant routing velocity V (e.g. V = 1 m/s), which is a fixed parameter of the approach. For each distance class dj (where j represents a specific class), the discharge contribution Qj(t) at time t is calculated by lagging the rainfall excess Rj(t) by its travel time tj. The travel time tj is given by the formula tj = dj / V, where dj is the distance for the class and V is routing velocity. This discretization travel time method is also used in the work of 26 , where the travel time for each channel cell is computed from the travel distance of the cell and the cell velocity. The initial travel time estimate is then updated by incorporating the blue spot delay time based on the inflow runoff volumes coming from upstream and rain inflow that drops directly in the blue spot, as a given blue spot cannot spill downstream through its pour point until it is filled. Following this, the rainfall depth corresponding to each travel time is calculated for each distance class. The final step involves calculating the discharge at each travel time (Eq. 1 ). The kinematic approach used to generate event hydrographs is also used by 27 for their Urban Morpho-climatic Instantaneous Unit Hydrograph. Their framework likewise accounts for the upstream contribution of flow and the intensity of excess rainfall in its travel time calculations. $$\:Q=\frac{R\times\:n\:\times\:A}{T}$$ 1 \(\:R\) = rainfall depth(m) \(\:n\) = number of pixels \(\:A\) = pixel area (m 2 ) \(\:T\) = travel time (sec) 2.2.4 Additional Flooding and Weir Formula In this step, we focus on the computation of the additional flooding extent above the pour point elevation for a given blue spot and rainfall event (panel 2.B(ii) in Fig. 2 ). First, the water volume required for filling a given blue spot is subtracted from the beginning of the kinematic hydrograph identified as described in the previous section. Second, referring to the resulting hydrograph, the time step associated with the maximum runoff inflow and peak inflow hydrograph itself (Q max ) is identified. Third, the overall inflow runoff volume reaching the blue spot up to Q max ’s timestep (i.e. upstream volume, V ups ) is computed. Fourth, the weir equation (Eq. 2 ) is used to calculate the water depth above the pour point (∆h) associated with an outflow equal to Q max , which is considered as an initial estimate of the maximum outflow spilled by the pour point. A weir width (B) (e.g 3m) and a discharge coefficient (µ) (e.g. 0.385) 28 , need to be selected as additional parameters of the approach. As a fifth step, the algorithm identifies from a LiDAR DEM analysis for the water volume stored in the blue spot that is associated with the additional flood elevation ∆h above the pour point (required volume; V req ). V req represents the required volume to raise the depression by ∆h and V ups is the upstream inflow volumes up to Q max . V req is compared with V ups . If V ups is larger than V req , we select this ∆h as ∆h max for the backwater effect. If V ups is insufficient, ∆h max is recalculated based on V ups . Once ∆h max is determined, the additional flooding associated with the additional water level above the pour point is calculated from the LiDAR DEM. The pour point elevation of each blue spot is already known, and the overall pour point elevation is computed by summing the ∆h max and the original pour point elevation. The new blue spot extent is then identified as the intersection of the DEM and the overall pour point elevation. $$\:{Q}_{max}=\mu\:.B.{\varDelta\:h}_{max}.\sqrt{2g{\varDelta\:h}_{max}}$$ 2 \(\:{Q}_{max}\) = maximum discharge \(\:\mu\:\) = discharge coefficient \(\:B\) = weir width \(\:{\varDelta\:h}_{max}\) = Hydraulic Head \(\:g\) = acceleration due to gravity 2.2.5 Filtering Algorithm Rule Running the original Safer_RAIN algorithm in the flooding phase for a given rainfall event results in detailed data on the spilling volume for each blue spot. Some blue spots may be found to have a spilling volume of zero, indicating that those blue spots possess sufficient storage capacity to retain all the rainfall volume received during the storm event without overflowing. In addition to the spilling volume data, the algorithm also provides information on the upstream volume for each blue spot. This data reveals the hydrological connectivity between blue spots, showing that certain blue spots contribute water volumes to downstream blue spots. This upstream-downstream relationship is critical for identifying how water flows through the landscape and for analysing areas where hydrological interactions may lead to an additional flooding above the blue spot pour point. In Kinematic Safer_RAIN, we establish a rule to identify the blue spots with the potential to experience a backwater effect. According to the rule, blue spots with both zero spilling volume and zero upstream inflow volume are excluded from further analysis. Blue spots that meet these criteria neither overflow nor receive additional water from upstream sources, making them irrelevant for backwater effect calculations. By applying this rule, we focus only on the remaining blue spots that either spill water or receive contributions from upstream blue spots. These remaining blue spots are classified as potential blue spots for backwater effect analysis. 2.3 Matrices for evaluating the performance of models For a comparative analysis of flooding scenarios in terms of inundation extents, we adopted several evaluation metrics 29 as shown in Table 1 . Model performance was evaluated by comparing Kinematic Safer_RAIN simulations against a HEC-RAS benchmark. We classified pixels as: True Positives (TP), flooded in both models; False Positives (FP), flooded only in Safer_RAIN; True Negatives (TN), non-flooded in both models; and False Negatives (FN), flooded only in the HEC-RAS benchmark. From these, we derived several metrics ranging from 0 to 1: the True Positive Rate (TPR) or sensitivity; the False Negative Rate (FNR) or miss rate; the True Negative Rate (TNR) or specificity; the False Positive Rate (FPR) or fall-out; Area under the receiver-operating-characteristic curve(AUROC) is a probability that a flooded pixel is correctly distinguished; Accuracy Correlation Coefficient (ACC) for overall accuracy; and the Matthews Correlation Coefficient (MCC) as a balanced performance measure between the binary classifications in the simulations. Table 1 Confusion matrix for quantifying the performance of algorithm. HEC-RAS simulations Flooding Non-flooding Kinematic Safer_RAIN simulations Flooding True positives (TP) False positives (FP) Non-flooding False negatives (FN) True negatives (TN) True positive rate (TPR) = TP/(TP + FN) True negative rate (TNR) = TN/(FP + TN) Accuracy (ACC) = (TN + TP)/(TP + TN+FN + FP) False negative rate (FNR) = FN/(FN + TP) False positive rate (FPR) = FP/(FP + TN) Mathew’s correlation coefficient (MCC) = (TP.TN – FP. FN)/ SQRT((TP + FP) (TP + FN) (TN + FP) (TN + FN)) 3.Case studies This section evaluates Kinematic Safer_RAIN using two testbeds: a test case in Cotton Wood Lake Study Area, USA and a real event in Pamplona, Spain. Each subsection describes input data, parameter settings and comparisons with HEC-RAS 2D. 3.1 Cotton Wood Lake Study Area, USA The open access test bed for our first experiment is the Cottonwood Lake Study Area (CLSA), situated in Stutsman County, North Dakota (refer to Fig. 5a). The CLSA is one of three long-term wetland ecosystem monitoring sites established by the United States Geological Survey (USGS) within the Prairie Pothole Region of North America. This site has been an active research area over the past decades 20 , 30 . For this experiment, airborne LiDAR data with a 1-meter resolution was utilized for the CLSA (see Fig. 5b). The availability of high resolution freely accessible data made the CLSA an ideal choice for our test case study. By using a well-documented study area with open-source datasets ( https://github.com/opengeos/lidar ), we ensure that our methodology can be easily tested, replicated and validated by others. We used 100mm uniform rainfall event for the model simulations. With Safer_RAIN’s LiDAR DEM preprocessing, we got 22 blue spots with its related 22 watersheds, 22 pourpoints, 22 flow paths and 3 junctions (Fig. 5(c)). Figure 6 . (a) Location map of the Piepstem watershed in the Prairie Pothole Region of North Dokota (b) LiDAR DEM for the cotton wood lake area, (c) Safer_RAIN preprocessing result of CLSA based on LiDAR DEM. Figure 5. (a) Location map of the Piepstem watershed in the Prairie Pothole Region of North Dokota (b) LiDAR DEM for the cotton wood lake area, (c) Safer_RAIN preprocessing result of CLSA based on LiDAR DEM. 3.2 Pamplona, Spain Pamplona, the capital of the Navarre Region in northern Spain, is an important urban area known for its susceptibility to pluvial and fluvial flooding. The Pamplona metropolitan area covers 68.26 km² and is home to approximately 335,000 inhabitants. This population is distributed across several municipalities, including Barañáin, Burlada, Cendea de Olza, Cizur, Huarte, Orcoyen, Pamplona, Villava, and Zizur Mayor (see Fig. 6 ). For this study, we use a 2m resolution Digital Elevation Model (DEM) supplied by the Spanish National Geographic Institute (IGN). Pluvial flooding events in the region are primarily driven by intense rainfall, particularly during the summer months. Among the municipalities, Barañáin and Zizur Mayor have experienced the highest flood losses from pluvial floods, based on data provided by the Spanish "Consorcio de Compensación de Seguros (CCS)," an organization that compensates for damages caused by natural hazards in Spain, in the period 1996–2018. The largest pluvial flood event recorded in the Pamplona metropolitan area in that period occurred on 20 July 2010 25,31 . Two significant cloudbursts hit the study area on 20 July 2010 resulting in pluvial flooding. The first event took place between 6:30 PM and 7:20 PM, while the second event occurred later, starting at 9:10 PM and ending at 10:40 PM. For our analysis, we selected the second event for simulation as it is considered the largest in the period 1996–2020, contributing to total rainfall amount over 110 mm in 1 hour 40 mins. To investigate and model this event, we employed the Kinematic Safer_RAIN and compared its results with HEC-RAS RoG simulations. Precipitation data are received from multiple sources, including the SAIH real-time system of the River Ebro Basin Authority, the Spanish Meteorological Agency (AEMET), the regional government of Navarre, and the Universidad Pública de Navarra (UPN). To validate the flood hotspots identified in Barañáin and Zizur Mayor by the Kinematic Safer_RAIN, we cross-referenced the model outputs with reports from the “Diario de Navarra” (DN) newspaper. These reports provided real-world evidence of the most affected areas, supporting the accuracy and reliability of our findings. 4.Results and Discussions 4.1 Original vs. Kinematic Safer_RAIN in Cotton Wood Lake Study Area, USA We used a synthetic uniform rainfall of 100mm in 1 hr, with a pixel size of 1m since the LiDAR DEM data has a resolution of 1m. Following the filtering rule in this CLSA (see details in section 2.2.5 ), we identify 9 blue spots and their corresponding 9 watersheds as being subject to backwater effects. These blue spots were determined to either have spilling volumes or receive contributions from upstream sources, making them significant for further analysis. Therefore, these nine blue spots and their associated watersheds will be considered for calculating and evaluating the backwater effect, providing critical insights into the hydrological interactions and potential flooding impacts in these areas. In the first stage (the watershed routing stage), we compute the flow length raster for each watershed contributing area (excluding blue spots) to determine the distance classes for each pixel, representing the travel distance to the boundary of the blue spot (see Fig. 7 – flow length raster for watersheds). For each distance class, we calculate the pixel counts and the travel time using a constant routing velocity ( V = 1m/s). Using this information, we then calculate the discharge Q for each distance class using Eq. 1 . Additionally, the discharge contributed by the rainfall that drops directly on the blue spot is added to the watershed's discharge time series, as blue spots represent the lowest depressions, which are filled first during the rainfall event. Once we have the discharges, we cumulate Q over time. Using this cumulative discharge Q at the latest time step, we calculate the ∆h max for the backwater effect using the weir formula (see Eq. 2 ). To determine whether this calculated ∆h represents the backwater effect correctly, we compare the V req and Volume Upstream V ups . The detail calculation of these volumes is explained in section 2.2.4 . The results of this comparison, including the values for V ups , V req and ∆h max are presented in the following Table 2 . Table 2 (a) ∆h max after first comparison of V ups and V req before considering upstream blue spots contribution, (b) final ∆h max after comparison of V ups and V req after considering upstream blue spots contribution. Table 2 . (a) Table 2 . (b) Bspot_id V ups (m 3 ) V req (m 3 ) ∆h max (m) Bspot_id V ups (m 3 ) V req (m 3 ) ∆h max (m) 2 3989 1458 0.77 2 3989 1458 0.77 4 8928 6777 1.36 4 10190 7185 1.40 6 637 76 0.22 6 637 76 0.22 12 2694 440 0.60 12 2695 440 0.60 13 4522 1018 0.84 13 9882 2807 1.37 16 8903 4076 1.34 16 14910 6967 1.81 20 181 12 0.10 20 181 12 0.10 21 1041 159 0.31 21 1041 159 0.31 22 4096 1385 0.80 22 5807 2037 0.96 According to the upstream downstream relationship explained in detail in Section 2.2.5 (filtering algorithm rule), we have known that only four blue spots (4,13, 16 and 22) receive contributions from upstream blue spots. Based on the comparison as shown in Table 1 (b), we update new ∆h values for those blue spots. Using the water level elevation (pour point elevation + ∆h) and the watershed mask, we calculate the new extent of each blue spot. Additionally, the water depth in each blue spot is determined by subtracting the DEM elevation data for the watershed from the overall pour point elevation. The updated results are visually compared in Fig. 9 , which shows the difference between the Safer_RAIN original output and the Kinematic Safer_RAIN output. These comparisons provide insight into the impact of upstream contributions and updated ∆h values on the extent and depth of water in the back water affected blue spots. The water depth results shown in Fig. 9 are at the maximum water depth simulation result (100mm uniform rainfall in 1 hour event). The comparison between the Original Safer_RAIN and the Kinematic Safer_RAIN simulations, as shown in Fig. 8, reveals notable differences in the predicted flood extents and water depth distributions. In several blue spots, the Kinematic Safer_RAIN simulation produces a larger flooded extent compared to the Original Safer_RAIN. These differences are particularly evident in blue spots affected by backwater effects. This observation is further confirmed by the water depth differences illustrated in Fig. 8(c). In these backwater-affected blue spots, the Kinematic Safer_RAIN simulation predicts higher water depths within the original extent of the flooded area when compared to the original Safer_RAIN. Additionally, the Kinematic approach demonstrates a tendency to extend the flood coverage beyond the original boundaries, albeit with lower water depth values in these extended areas. These results indicate that the kinematic routing enables the model to reproduce extended ponding areas consistent with expected hydrological behaviour. 4.2 Kinematic Safer_RAIN vs. 2D hydrodynamic model in Cotton Wood Lake Study Area In the absence of observed data, we used a HEC-RAS 2D rain-on-grid simulation with the same uniform 100 mm h⁻¹ rainfall as benchmark. RoG modelling using HEC-RAS 2D has gained popularity for storm-event hazard assessment and pluvial flooding analysis. This approach integrates hydrological and hydrodynamic processes within a 2D model. HEC-RAS 2D with RoG has been applied to various scenarios, including urban areas and actual basins, demonstrating its potential for flood risk assessment 32 . Therefore, the HEC-RAS results are compared with the Kinematic Safer_RAIN simulation with a synthetic uniform rainfall of 100mm in 1 hour, as shown in Fig. 9 . When focusing on the blue spots considered for backwater effects (e.g., blue spots 12), we observed that the flooded area produced by Kinematic Safer_RAIN closely matches the results of the HEC-RAS simulation. A similar observation is made for blue spots 2, 4, and 6. In terms of water depth within the blue spots, the original Safer_RAIN simulation produces a maximum water depth of 1.87 m, which is significantly less than the maximum water depth of 3.77 m produced by the HEC-RAS simulation. However, the improved Kinematic Safer_RAIN generates a maximum water depth of 2.75 m, bringing it closer to the HEC-RAS results. In terms of computation efficiency, HEC-RAS required 2 hours, 38 minutes, and 4 seconds to simulate a 1-meter mesh size consisting of 1,721,122 pixels. In contrast, Kinematic Safer_RAIN completed the same simulation in just 1min and 16seconds on the same hardware (i.e., 12th Gen Intel(R) Core (TM) i7-12650H processor running at 2300 MHz with 10 cores). Despite these improvements, some limitations remain. Kinematic Safer_RAIN filters out small blue spots according to the threshold area selected by the user in the preprocessing phase, while HEC-RAS includes these in the simulation. Additionally, HEC-RAS is capable of identifying flooding along the flow paths between blue spots, which is an intrinsic limitation of HSFAs that will be a key target for future improvements. We identified that nine blue spots experience the so-called backwater effect out of the total of 22 modelled blue spots. To further characterize these results, we conducted detailed water depth distribution and flood extent analysis by examining the simulated maximum water depth raster files generated by Kinematic Safer_RAIN and HEC-RAS. The analysis is focused on the relevant areas only, which we identified using a 100m circular buffer enveloping each blue spot of interest and its pour point (see Fig. 9 ). Kinematic Safer_RAIN utilises the weir equation to compute the additional water depth above the pour point, denoted as ∆h, as detailed in section 2.2.4 . The weir width B is a critical parameter in this calculation, and we assessed its influence on flood modelling results through a sensitivity analysis. In particular, we tested a range of weir widths from 1m to 5m, analysing the resulting flood extent and comparing it to the flood extent derived from the HEC-RAS simulation. Among the tested parameters, we found that a weir width of 2.5m in most blue spots (see e.g. of blue spot 2 in Fig. 10 ) provides results that are closely aligned with the HEC-RAS simulation outcomes in terms of flooded area, demonstrating the suitability of this parameter across the study area. We conducted the water depth distribution in each backwater effected blue spots using maximum water depths simulated by Kinematic Safer_RAIN and HEC-RAS in tuning the weir width parameter. Diagrams in Fig. 11 illustrate the exceedance probability of specified water depth values across the computational domain. These exceedance probabilities represent the likelihood that a given water depth is exceeded and based on the dimensions of the computational mesh pixels, they can also be interpreted as the surface area flooded by water depths exceeding a certain threshold. In this analysis, only the pixels experiencing inundation (non-zero water depths) are included in the curve estimation. Any NA values or water depths equal to 0 m are excluded to ensure the analysis focuses strictly on areas with flooding. To aid in understanding the distribution of lower water depth values, the y-axis is displayed on a logarithmic scale. This allows for clearer visualization of both small and large water depths, which would otherwise be difficult to interpret on a linear scale. Additionally, the diagrams include a reference horizontal line at 0.05 m, which represents the water depth threshold used to differentiate between flooded and non-flooded pixels. This threshold ensures that only significant water depths are considered when analysing water depth distributions and exceedance probabilities. According to the graphs in Fig. 11 , the Kinematic Safer_RAIN simulations with a weir width of 2.5 m for most blue spots provide the best overall fit with the HEC-RAS simulation results. However, there are exceptions, such as blue spot 13, where the simulation with a weir width of 1.5 m aligns more closely with the HEC-RAS results. To maintain uniformity across the domain, a weir width of 2.5 m can be used as a standard parameter. This parameter is locally adaptable and depends on the specific topographic characteristics of the area. The difference arises because the Kinematic Safer_RAIN algorithm employs a hydrostatic approach to simulate flooding above the blue spot pour point. In contrast, the HEC-RAS model calculates maximum water depths using hydrodynamic modelling, which more accurately reproduces backwater effects in a strict hydraulic sense. Our goal is for Kinematic Safer_RAIN to produce results that approximate those of traditional hydrodynamic models while maintaining low computational demands. This locally adaptable weir width parameter will be retained for future analyses, particularly for the detection of LiDAR data. In addition to the water depth distribution analysis, we performed the flood extent analysis using the confusion matrices explained details in section 2.3 . A pixel is considered flooded if the simulated water depth exceeded a threshold of 5 cm. This chosen threshold agrees with the findings of 33 , who mentioned that the impact of flood depths below this level is generally minor and confined to areas with the lowest-lying topographies due to relatively uniform patterns of subsidence and local microtopographic variations at the local scale. Furthermore, applying this threshold ensures consistency in identifying inundated areas across both simulation models. According to the performance metrics in the table (results are from taking the weir width parameter as 1m), most blue spots demonstrate a high TPR (≥ 0.84), indicating that the Kinematic Safer_RAIN model effectively detects flooded areas, with low FNR (≤ 0.16), showing it rarely misses them. Similarly, the Kinematic Safer_RAIN model achieves high TNR (≥ 0.94) for most blue spots, meaning it is reliable at identifying non-flooded areas and minimizing false alarms (FPR ≤ 0.06). The AUROC values (≥ 0.78) across all blue spots highlight the algorithm's strong ability to distinguish between flooded and non-flooded areas. Notably, blue spots 6 and 16 stand out with the highest AUROC values (0.98 and 0.97, respectively), reflecting near-perfect classification performance. Additionally, ACC values are consistently high (≥ 0.78), showcasing the algorithm's strong overall accuracy in predicting flood and non-flood scenarios. However, MCC scores show variation, indicating differences in classification quality across blue spots. Blue spots 12 and 13 demonstrate excellent overall performance, combining high sensitivity, specificity, and low error rates, while blue spot 22 shows the weakest performance, likely due to a lower TNR (0.71) and higher FPR (0.29). In summary, blue spots 6, 12, and 13 stand out as the most reliable, with high sensitivity, specificity, AUROC, and MCC values. Aggregating these results provides a clear picture of the model's overall high performance. On average, TPR, TNR, AUROC, and ACC rates are 0.84, 0.94, 0.89, and 0.91, respectively, with corresponding FPR and FNR error rates of only 0.06 and 0.16. The average MCC is 0.81, which, despite localized variations, signifies a strong and reliable classification performance across the entire study area. The performance metrics for a weir width of 2.5m demonstrate notable improvements over the 1m weir width across several key indicators. The average TPR for the 2.5m weir width is 0.90, higher than the 0.84 observed for the 1m weir width. This indicates that the model with a 2.5m weir width is more effective at detecting flooded areas, reducing the likelihood of missed detections. For several blue spots, such as 12, 6, and 22, the TPR reaches near-perfect levels (≥ 0.98), showcasing the model's ability to identify almost all flooded areas. The average FNR with a 2.5m weir width is 0.10, significantly lower than the 0.16 for the 1m weir width. This reduction in missed detections further supports the improved sensitivity of the model when a wider weir width 2.5m is used. The average TNR for the 2.5m weir width is 0.96, slightly higher than the 0.94 for the 1m weir width. This improvement highlights the model's ability to accurately identify non-flooded areas, minimizing false alarms. Similarly, the FPR is reduced to 0.04 (compared to 0.06 for the 1m weir width), further enhancing the reliability of the model. The average AUROC value for the 2.5m weir width is 0.93, higher than the 0.89 for the 1m weir width. This underscores the model's improved ability to distinguish between flooded and non-flooded areas, indicating stronger overall classification performance. Notably, Blue Spots 12 and 6 have exceptional AUROC values of 0.99 and 0.96, respectively. The average ACC increases to 0.95 for the 2.5m weir width, compared to 0.91 for the 1m weir width. This improvement reflects the model's enhanced overall ability to correctly classify both flooded and non-flooded areas. Most blue spots, such as 12, 21, and 6, achieve ACC ≥ 0.97, showcasing consistently superior performance. The average MCC for the 2.5m weir width is 0.88, higher than the 0.81 for the 1m weir width. MCC is a holistic metric that accounts for both true and false positives and negatives. The improvement in MCC demonstrates that the classification quality is more balanced and reliable with the wider weir width. Blue Spots 12 and 6 reach near-perfect MCC values of 0.98 and 0.94, respectively. In summary, the weir width of 2.5m consistently outperforms the 1m weir width across all key performance metrics. This result aligns with the weir width sensitivity analysis conducted earlier, which also demonstrated that a weir width of 2.5m closely corresponds to the water depth distribution across several blue spots. Table 3 Comparing flooded area results in potentially flooded blue spots in Cotton Wood Lake Study area (weir width 1m). Blue spot TPR FNR TNR FPR AUROC ACC MCC 2 0.70 0.30 0.99 0.01 0.84 0.95 0.76 4 0.67 0.33 0.99 0.01 0.83 0.81 0.68 6 0.96 0.04 0.99 0.01 0.98 0.97 0.94 12 0.86 0.14 0.98 0.02 0.92 0.92 0.85 13 0.87 0.13 0.99 0.01 0.93 0.95 0.89 16 0.99 0.01 0.95 0.05 0.97 0.97 0.93 20 0.57 0.43 0.99 0.01 0.78 0.89 0.70 21 0.99 0.01 0.91 0.09 0.95 0.95 0.91 22 0.97 0.03 0.71 0.29 0.85 0.78 0.60 Average values 0.84 0.16 0.94 0.06 0.89 0.91 0.81 Table 4 Comparing flooded area results in potentially flooded blue spots in Cotton Wood Lake Study area (weir width 2.5m). Blue spot TPR FNR TNR FPR AUROC ACC MCC 2 0.89 0.11 0.99 0.01 0.94 0.98 0.91 4 0.87 0.13 0.94 0.06 0.91 0.91 0.82 6 0.99 0.01 0.92 0.08 0.96 0.97 0.94 12 0.98 0.02 0.99 0.01 0.99 0.99 0.98 13 0.82 0.18 0.99 0.01 0.91 0.89 0.79 16 0.85 0.15 0.99 0.01 0.93 0.97 0.90 20 0.78 0.22 0.99 0.01 0.89 0.97 0.87 21 0.89 0.11 0.99 0.01 0.94 0.99 0.93 22 0.98 0.02 0.85 0.15 0.92 0.90 0.81 Average values 0.90 0.10 0.96 0.04 0.93 0.95 0.88 4.3 Kinematic Safer_RAIN vs. 2D hydrodynamic model in Pamplona, Spain We used the same rainfall event and input data for both models, as detailed in Section 3.2 . After running the Kinematic Safer_RAIN in Barañáin, we determined that 11 blue spots needed to be calculated out of a total of 18 blue spots in the area. Similarly, in Zizur Mayor, 8 blue spots were identified for calculation out of a total of 13 blue spots. In Barañáin, the blue spot ID11 exhibited the highest ∆h, indicating it could be the most critical area for backwater effects, and followed by blue spots ID14, ID7, ID16, and ID12. In Zizur Mayor, the blue spot ID9 had the highest ∆h, followed by ID5, ID10, and ID11. We found that such blue spots with the highest ∆h are the flooding hotspots reported in the DN newspaper. We also carried out HEC-RAS simulations for both study areas. The results clearly show that the Kinematic Safer_RAIN simulations for the selected blue spots closely match the flooding extents generated by the HEC-RAS simulations. In contrast, the original Safer_RAIN simulations were unable to replicate larger flooding extends beyond the boundaries of the blue spots. Figures 12 and 13 show the comparison of simulation results of three models: Original Safer_RAIN, Kinematic Safer_RAIN and HEC-RAS in Barañáin and Zizur Mayor. In terms of computation efficiency, HEC-RAS required 53 mins 15 sec to simulate a 1 m mesh size consisting of 475,808 pixels for Barañáin and 2 hr 07 min 50 sec to simulate a 1 m mesh size consisting of 655,193 pixels. In contrast, Kinematic Safer_RAIN completed the same simulation for Barañáin in 26 sec and for Zizur Mayor in 28 sec on the same hardware (i.e, 12th Gen Intel(R) Core (TM) i7-12650H processor running at 2300 MHz with 10 cores). 4.4 Overall algorithm performance We conducted the performance evaluation of the Kinematic Safer_RAIN model by using the same metrics employed in the CLSA, as detailed in Section 2.3 . In the absence of real observed data, we used HEC-RAS simulations as the reference dataset to compare with Kinematic Safer_RAIN simulations. The results show that blue spot 11 in the Barañáin study area achieved the highest TPR, followed by blue Spots 12, 14, 7, and 16 (Table 5 ). Furthermore, Blue Spot 11 exhibited the best overall model performance, with the highest values for AUROC, Accuracy (ACC), and Matthews Correlation Coefficient (MCC), indicating its strong ability to discriminate between flood and non-flood areas and its reliability in flood prediction. Conversely, Blue Spot 16 demonstrated the weakest flood detection, with the lowest MCC, reflecting poorer model performance in this location. Notably, the superior performance at Blue Spot 11 corresponds with its real flooded area during the 20 July 2010 storm, as confirmed by newspaper images of the event. This alignment strengthens the validity of the Kinematic Safer_RAIN model for accurately identifying actual flood-prone areas. The same performance evaluation is done for Zizur Mayor area. We found that blue spot 9 has the highest TPR and followed by blue spot 10 and 11. Blue Spot 9 demonstrates the strongest performance overall, with the highest TPR (0.95), AUROC (0.92), ACC (0.90), and MCC (0.75), indicating its high reliability in both detecting floods and avoiding false alarms (Table 6 ). Blue Spot 10 and 11 have moderate TPR (0.56–0.63) and AUROC (0.72–0.76) but lower MCC (0.45–0.54), suggesting average flood detection ability with some misclassification. Overall, these findings highlight the variability in the model’s performance across different locations in both Barañáin and Zizur Mayor. While the results for Blue Spot 11 in Barañáin and Blue Spot 9 in Zizur Mayor demonstrate strong predictive capability, other blue Spots exhibit moderate performance, indicating areas where the model could be improved. According to the average comparison matrix values in Table 5 , the TPR value in our study is 0.64, aligning with the findings of the 25 .Their study compared the Original Safer_RAIN with the 2D hydrodynamic model IBER for Barañáin and Zizur Mayor under the same 2010 storm event, reporting a TPR of 0.505 in Barañáin, which is consistent with our averaged TPR of 0.64 (See Table 3 in 25 ). This suggests that Kinematic Safer_RAIN improves the TPR rate. Additionally, the ACC value in their study is 0.96, which is comparable to our result of 0.91. Furthermore, we achieved an improved MCC value of 0.70, compared to their reported MCC of 0.626. Similarly, the average TPR value in Zizur Mayor is 0.70, compared to 0.309 in the findings of 25 . The ACC and MCC values are comparable in both studies, averaging around 0.9 and 0.5, respectively. While 25 study focused on comparing the Original Safer_RAIN with the IBER model, our research evaluates the Kinematic Safer_RAIN against the HEC-RAS model. Although the two studies are not identical, they share a similar approach of comparing HSFAs with traditional hydrodynamic models. At the time of 25 study, only the Original Safer_RAIN was available. Since then, we tried to advance it, developing the Kinematic Safer_RAIN to achieve greater accuracy and efficiency. Table 5 Comparison of flooded area results from both HEC-RAS and Kinematic Safer_RAIN simulation results in the potentially flooded blue spots identified in Barañáin, Pamplona. Blue spot Rainfall Scenario TPR FNR TNR FPR AUROC ACC MCC 7 20 July 2010 0.51 0.49 0.99 0.01 0.76 0.90 0.67 11 20 July 2010 0.90 0.10 0.95 0.05 0.92 0.93 0.85 12 20 July 2010 0.74 0.26 0.98 0.02 0.86 0.94 0.77 14 20 July 2010 0.59 0.41 0.99 0.01 0.79 0.89 0.70 16 20 July 2010 0.46 0.54 0.97 0.03 0.71 0.91 0.50 Average 20 July 2010 0.64 0.36 0.98 0.02 0.81 0.91 0.70 Table 6 Comparison of flooded area results from both HEC-RAS and Kinematic Safer_RAIN simulation results in the potentially flooded blue spots identified in Zizur Mayor, Pamplona. Blue spot Rainfall Scenario TPR FNR TNR FPR AUROC ACC MCC 9 20 July 2010 0.95 0.05 0.88 0.12 0.92 0.90 0.75 10 20 July 2010 0.63 0.37 0.89 0.11 0.76 0.79 0.54 11 20 July 2010 0.56 0.44 0.88 0.12 0.72 0.81 0.45 Average 20 July 2010 0.71 0.29 0.89 0.12 0.80 0.83 0.58 We calculated the distribution of water depths using Kinematic Safer_RAIN simulations and compared them with HEC-RAS simulations. A similar comparison was performed for CLSA, with detailed explanations provided in Section 4.2 . Figure 14 illustrates the comparison of water depth distributions (in log scale) predicted by HEC-RAS and Kinematic Safer_RAIN for Blue Spot 11 in Barañáin and Blue Spot 9 in Zizur Mayor. These two blue spots are the most affected and prominent in the study area, as they exhibit the highest TPR among all blue spots. In addition, such real hotspots were validated by newspaper images. 25 also confirmed that Safer_RAIN correctly identifies the main depressions prone to flooding in pluvial flooding events while benchmarking with 2D hydrodynamic models. Similar to the sensitivity analysis of weir width in CLSA, the weir width for blue spots varies depending on their location. In Pamplona, we found that a weir width of 2.5 m in Kinematic Safer_RAIN aligns well with HEC-RAS simulations for the most affected blue spots. Therefore, a weir width of 2.5 m can also be used as a standard parameter for this study area. In general, HEC-RAS predicts deeper water depths, especially at lower exceedance probabilities, indicating its capability to model more severe flooding scenarios. The gap between HEC-RAS and Kinematic Safer_RAIN ‘s water depth distribution lines is because the Kinematic Safer_RAIN uses a hydrostatic approach to simulate the flooding above the blue spot’s pour point, while HEC-RAS model uses a hydrodynamic approach, which calculates the backwater effects in a hydraulic manner. Overall, based on the water depth distribution comparison graphs for both Barañáin and Zizur Mayor, the trends of both models are similar, showing higher water depths at lower exceedance probabilities and lower water depths at higher exceedance probabilities. These case studies confirm that Kinematic Safer_RAIN maintains high computational efficiency while substantially improving the accuracy of predicted flood extents and depths relative to traditional HSFAs; the next section summarizes overall findings and remaining limitations. 5.Conclusions This study introduced Kinematic Safer_RAIN, an enhanced Hierarchical Filling-and-Spilling Algorithm that incorporates runoff travel-time distribution and a weir-based formulation to better reproduce inundation above pour points in urban depressions. The original algorithm accounts for spatially distributed rainfall inputs and infiltration processes using a pixel-based Green-Ampt model. Building on the Safer_RAIN module of the SaferPlaces digital-twin platform ( https://saferplaces.co/ ), we improved the algorithm’s physical realism while preserving computational efficiency 5 . However, due to the nature of the HSFAs, it is limited to containing the flooded extent within the predefined boundaries of blue spots and cannot consider water elevations above their pour point elevations, as any excess flood volume is transferred downstream once a blue spot is fully filled. To address this limitation, we enhanced the HSFA algorithm by incorporating a Kinematic approach, improving its ability to model flood extent beyond blue spot boundaries. Kinematic Safer_RAIN models the travel time distribution of water within watersheds and incorporates the weir equation to describe inundations in which the water elevation can exceed the pour point elevation in some depressions. These enhancements are tested in the Cotton Wood Lake Study Area, a test case study selected due to the availability of freely accessible LiDAR DEM, allowing researchers to test the algorithm. We conducted HEC-RAS Rain-on-Grid (RoG) modelling in this area using uniform rainfall, treating HEC-RAS simulations as the reference, and comparing the results with Kinematic Safer_RAIN. The findings revealed that, in terms of flooding extent within the targeted blue spots, Kinematic Safer_RAIN produced results closely matching HEC-RAS. Across all blue spots. Kinematic Safer_RAIN achieved an average TPR (0.90), ACC (0.95) and MCC (0.88). In terms of water depth distribution, both models exhibit similar trends. After tuning the weir width parameter, the Kinematic Safer_RAIN simulations with a constant weir width of 2.5 m across all depressions provided the best overall match with HEC-RAS results, suggesting that a representative opening width of this magnitude is appropriate for typical urban depressions, though locally adjustable. Differences between Kinematic Safer_RAIN and HEC-RAS arise from their governing equations: the former assumes hydrostatic equilibrium and constant routing velocity, whereas the latter solves full shallow-water dynamics. Despite this simplification, the enhanced algorithm reproduces the spatial extent and depth distribution of floods with good fidelity. By adopting a locally adaptable weir width parameter, Kinematic Safer_RAIN achieved results close to 2D hydrodynamic models while maintaining computational efficiency. This adaptable parameter will be retained and applied in future analyses, particularly for processing LiDAR data. We tested the Kinematic Safer_RAIN algorithm in two real case study areas in Pamplona, Spain, during the heavy storm event of July 20, 2010. The blue spots expected to have greater flooding beyond their boundaries align with locations observed in newspaper images. Kinematic Safer_RAIN produced similar flood extents in these blue spots comparable to HEC-RAS simulations. Regarding water depth distribution graphs, both models showed similar trends, with higher water depths at lower exceedance probabilities and lower water depths at higher exceedance probabilities. Some blue spots in the Pamplona metropolitan area are identified as the most affected areas in the study, validated by high True Positive Rates (TPRs) and newspaper image evidence, confirming the reliability of Kinematic Safer_RAIN in identifying flood-prone depressions. A constant weir width of 2.5m in Kinematic Safer_RAIN also aligns well with HEC-RAS simulations for these areas, providing a practical parameter for consistent application across the Pamplona study area. Differences between the models arise from their simulation methods, with HEC-RAS using a 2Dhydrodynamic approach to account for backwater effects and Kinematic Safer_RAIN employing a hydrostatic approach with less computation time. In conclusion, the Kinematic Safer_RAIN algorithm demonstrates significant improvements over the original Safer_RAIN (HSFA), as it provides flood extents in blue spots that are much closer to those predicted by HEC-RAS. Additionally, the Kinematic Safer_RAIN outperforms HEC-RAS in computational efficiency, requiring less time for simulations on the same grid cell size and duration. In terms of water depth distribution, the algorithm produces results similar to HEC-RAS, with HEC-RAS focusing on higher, more concentrated depths, while Kinematic Safer_RAIN offers a broader and potentially more realistic distribution, though it may result in slightly higher depths in certain areas. As a hydrostatic nature of this algorithm, Kinematic Safer_RAIN retains the advantage of fast processing but has certain limitations, such as the absence of flooding along the flow path between blue spots. Future work will focus on addressing this limitation, which will be detailed in our next publication. These advances demonstrate that simplified, DEM-based algorithms can bridge the gap between empirical flood-mapping tools and full hydrodynamic models, offering a scalable approach for rapid urban-flood assessment under increasing climatic pressures. Declarations Funding This publication was produced while the author Kay Khaing Kyaw was attending the PhD programme PhD@DICAM at the University of Bologna, Cycle XXXVIII, with the support of a scholarship co-financed by the Ministerial Decree no. 352 of 9 April 2022, based on the NRRP—funded by the European Union—NextGenerationEU—Mission 4 “Education and Research”, Component 2 “From Research to Business”, Investment 3.3, and by the company GECOsistema—Geographic Environmental Consulting, Rimini (RN), Italy. This research was also partly funded by the projects LIFE21-IPC-IT-LIFE CLIMAX PO, CLIMate Adaptation for the PO river basin district (grant agreement number: 101069928; WP7; Task: 7.1) and DIRETED - DIsaster Resilience for Extreme ClimaTe Events providing interoperable Data, models, communication and governance- grant agreement ID: 101073978. Author Contributions Conceptualization, K.K.K., and A.C.; methodology, K.K.K. and A.C.; software, S.B. and K.K.K.; validation, S.B. and K.K.K.; formal analysis, S.B and K.K.K.; investigation, L.M ., S.B ., A.C. and K.K.K.; data curation,, L.M., S.B. and K.K.K., writing—original draft preparation, L.M., S.B., A.C. and K.K.K.; writing—review and editing, L.M., S.B., A.C. and K.K.K.; visualization K.K.K.; supervision, A.C.; project administration, S.B. and A.C.; funding acquisition, S.B. and A.C.. All authors have read and agreed to the published version of the manuscript. Acknowledgements The authors would like to acknowledge the Spanish Instituto Geográfico Nacional(IGN) for supplying the digital terrain model and land-cover data, and the Sistema Automático de Información Hidrologíca (SAIH) real-time system of the River Ebro Basin Authority, the Regional Government of Navarre and the Universidad Pública de Navarra (UPNA) for supplying the rainfall data used in the Spanish case studies. 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J Hydrol (Amst) 369:44–54 Gironás J, Niemann JD, Roesner LA, Rodriguez F, Andrieu H (2009) A morpho-climatic instantaneous unit hydrograph model for urban catchments based on the kinematic wave approximation. J Hydrol (Amst) 377:317–334 Chen Y, Fu Z, Chen Q, Cui Z (2018) Discharge Coefficient of Rectangular Short-Crested Weir with Varying Slope Coefficients. Water (Basel) 10:204 Jadhav AS (2020) A novel weighted TPR-TNR measure to assess performance of the classifiers. Expert Syst Appl 152:113391 Wu Q, Lane CR (2017) Delineating wetland catchments and modeling hydrologic connectivity using lidar data and aerial imagery. Hydrol Earth Syst Sci 21:3579–3595 Bianucci P, Fernández-Fidalgo J, Kyaw KK, Soriano E, Mediero L (2025) Evaluating Infiltration Methods for the Assessment of Flooding in Urban Areas. Water (Basel) 17:2773 Costabile P, Costanzo C, Ferraro D, Barca P, Is (2021) HEC-RAS 2D accurate enough for storm-event hazard assessment? Lessons learnt from a benchmarking study based on rain-on-grid modelling. J Hydrol (Amst) 603:126962 Yin J, Yu D, Yin Z, Liu M, He Q (2016) Evaluating the impact and risk of pluvial flash flood on intra-urban road network: A case study in the city center of Shanghai, China. J Hydrol (Amst) 537:138–145 Additional Declarations The authors declare no competing interests. Supplementary Files Appendix.docx Cite Share Download PDF Status: Posted Version 1 posted 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. Also discoverable on Platform About Our Team In Review Editorial Policies Advisory Board Help Center Resources Author Services Accessibility API Access RSS feed Manage Cookie Preferences © Research Square 2026 | ISSN 2693-5015 (online) Privacy Policy Terms of Service Do Not Sell My Personal Information {"props":{"pageProps":{"initialData":{"identity":"rs-9492481","acceptedTermsAndConditions":true,"allowDirectSubmit":true,"archivedVersions":[],"articleType":"Research Article","associatedPublications":[],"authors":[{"id":627543564,"identity":"6a3b1557-9d1e-4368-8c43-8fb2f1216b86","order_by":0,"name":"Kay Khaing Kyaw","email":"data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZAAAAAyAQMAAABI0h/eAAAABlBMVEX///8AAABVwtN+AAAACXBIWXMAAA7EAAAOxAGVKw4bAAABIElEQVRIiWNgGAWjYBACNgYGZiCVkACiGBuATH6QcEIBKVokQUSCAV6LoFoYoFoMDoCYeLTwsZ9ONvjZlpbH3857+OXMNrvEzedXJ354YMAgzy92ALvDeHI3J/a25RRLHOZLs9zYlpy47cbbzRJAhxnOnJ2Awy+5mw/wtlUkNhzmMTN82Macu+3G2Q0gLQkGt3Fo4X+7+eBfoJb5EC31uZtnnN38A68WidzNybxtOYkbDvMYP9zYdjh3A3/vNvy2SLzdbCxzLi1xI9AWxhnnjtfPuMG7zSLBQAKnX+T7czdLvilLTpx3/ozxx56yamP+/rObb/6osJHnl8auBQwY2aA2ghkSYJUSuJWDwR8wyfwBzOA/QED1KBgFo2AUjDQAAM+IaK3ZhY9IAAAAAElFTkSuQmCC","orcid":"https://orcid.org/0009-0009-8940-1161","institution":"University of Bologna","correspondingAuthor":true,"prefix":"","firstName":"Kay","middleName":"Khaing","lastName":"Kyaw","suffix":""},{"id":627543567,"identity":"84fb3750-e484-46f6-ab20-ee64964cd7c4","order_by":1,"name":"Luis Mediero","email":"","orcid":"https://orcid.org/0000-0002-9346-6592","institution":"Universidad Politécnica de Madrid","correspondingAuthor":false,"prefix":"","firstName":"Luis","middleName":"","lastName":"Mediero","suffix":""},{"id":627543569,"identity":"5ff8e293-90b8-4934-ae49-eb447c319d2d","order_by":2,"name":"Stefano Bagli","email":"","orcid":"","institution":"GECOsistema srl","correspondingAuthor":false,"prefix":"","firstName":"Stefano","middleName":"","lastName":"Bagli","suffix":""},{"id":627543571,"identity":"c85c2a06-3a44-4976-989d-045c46c68269","order_by":3,"name":"Attilio Castellarin","email":"","orcid":"https://orcid.org/0000-0002-6111-0612","institution":"University of Bologna","correspondingAuthor":false,"prefix":"","firstName":"Attilio","middleName":"","lastName":"Castellarin","suffix":""}],"badges":[],"createdAt":"2026-04-22 07:37:05","currentVersionCode":1,"declarations":{"humanSubjects":false,"vertebrateSubjects":false,"conflictsOfInterestStatement":false,"humanSubjectEthicalGuidelines":false,"humanSubjectConsent":false,"humanSubjectClinicalTrial":false,"humanSubjectCaseReport":false,"vertebrateSubjectEthicalGuidelines":false},"doi":"10.21203/rs.3.rs-9492481/v1","doiUrl":"https://doi.org/10.21203/rs.3.rs-9492481/v1","draftVersion":[],"editorialEvents":[],"editorialNote":"","failedWorkflow":false,"files":[{"id":107620347,"identity":"8edbc821-f45d-4148-a3e6-109685c0cd77","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":1,"title":"Figure 1","display":"","copyAsset":false,"role":"figure","size":115345,"visible":true,"origin":"","legend":"\u003cp\u003eOriginal Safer_RAIN components: Phase 1 (DEM preprocessing) and Phase 2 (Blue spots flooding) \u003csup\u003e5\u003c/sup\u003e.\u003c/p\u003e","description":"","filename":"1.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/881a46a1a5b8f207de0a1441.jpg"},{"id":107620352,"identity":"8940cb83-f09a-4b9e-9704-5478bba32af2","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":2,"title":"Figure 2","display":"","copyAsset":false,"role":"figure","size":207710,"visible":true,"origin":"","legend":"\u003cp\u003eConceptualization of Kinematic Safer_RAIN\u003c/p\u003e","description":"","filename":"2.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/a4a54259a83dab812f1532fb.jpg"},{"id":107620349,"identity":"be2460d3-1f4f-4d40-8c88-96218a9b743e","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":3,"title":"Figure 3","display":"","copyAsset":false,"role":"figure","size":65716,"visible":true,"origin":"","legend":"\u003cp\u003eExample of flow length raster for each watershed excluding blue spot.\u003c/p\u003e","description":"","filename":"3.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/65a5754fdf90bb37db120300.jpg"},{"id":107620350,"identity":"1bbb9eb3-24fc-4b1d-85b0-a49a0e6258d0","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":4,"title":"Figure 4","display":"","copyAsset":false,"role":"figure","size":150799,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Schematic representation of V\u003csub\u003eups\u003c/sub\u003e, V\u003csub\u003ereq\u003c/sub\u003e and \u0026nbsp;, (b) New additional flood extent of blue spots.\u003c/p\u003e","description":"","filename":"4.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/0841ee7648459b9a2780dcdf.jpg"},{"id":107706874,"identity":"7d5b1fb2-71ee-42fe-9d7d-7c816358f71e","added_by":"auto","created_at":"2026-04-24 09:18:58","extension":"jpg","order_by":5,"title":"Figure 5","display":"","copyAsset":false,"role":"figure","size":205768,"visible":true,"origin":"","legend":"\u003cp\u003e(a) Location map of the Piepstem watershed in the Prairie Pothole Region of North Dokota (b) LiDAR DEM for the cotton wood lake area, (c) Safer_RAIN preprocessing result of CLSA based on LiDAR DEM.\u003c/p\u003e","description":"","filename":"5.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/0cb7e994bcd9cab053be3019.jpg"},{"id":107705786,"identity":"b4799e96-1054-4ff3-b39c-3ec130de23e4","added_by":"auto","created_at":"2026-04-24 09:15:16","extension":"jpg","order_by":6,"title":"Figure 6","display":"","copyAsset":false,"role":"figure","size":213386,"visible":true,"origin":"","legend":"\u003cp\u003ePamplona Study area\u003c/p\u003e","description":"","filename":"6.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/8d7126bac37d73ad8a80f0d8.jpg"},{"id":107707252,"identity":"52b4bb73-86e9-41c9-a45b-7c4931a858c5","added_by":"auto","created_at":"2026-04-24 09:19:54","extension":"jpg","order_by":7,"title":"Figure 7","display":"","copyAsset":false,"role":"figure","size":98282,"visible":true,"origin":"","legend":"\u003cp\u003eExample of flow length rasters for Watershed ID 2,4 and 6.\u003c/p\u003e","description":"","filename":"7.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/debe9c70e3c0125d2f3fe386.jpg"},{"id":107620355,"identity":"1315b732-f9ae-41b8-be58-1abffec78cde","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":8,"title":"Figure 8","display":"","copyAsset":false,"role":"figure","size":232114,"visible":true,"origin":"","legend":"\u003cp\u003eUniform 100 mm rainfall event: (a) Water depth from Original Safer_RAIN simulation, (b) Water depth from Kinematic Safer_RAIN simulation and (c) Water Depth Raster differences (Kinematic – Original).\u003c/p\u003e","description":"","filename":"8.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/d43f347edd2f6a8634284714.jpg"},{"id":107620356,"identity":"ef2aed74-2741-4ccc-b136-ad40144282b0","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":9,"title":"Figure 9","display":"","copyAsset":false,"role":"figure","size":195655,"visible":true,"origin":"","legend":"\u003cp\u003eUniform 100mm rainfall event: (a) HEC-RAS simulation and (b) Kinematic Safer_RAIN simulation.\u003c/p\u003e","description":"","filename":"9.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/a2c8d1ca5b88c9720c8de39f.jpg"},{"id":107705807,"identity":"e204a32e-045e-4558-9704-8324a01ceb1b","added_by":"auto","created_at":"2026-04-24 09:15:21","extension":"jpg","order_by":10,"title":"Figure 10","display":"","copyAsset":false,"role":"figure","size":182381,"visible":true,"origin":"","legend":"\u003cp\u003eWeir Width Sensitivity analysis of blue spot 2.\u003c/p\u003e","description":"","filename":"10.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/989f2be3668501154646ba9a.jpg"},{"id":107620357,"identity":"2b8fe560-6a5b-4beb-bf1a-a53cf5d9ecb7","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":11,"title":"Figure 11","display":"","copyAsset":false,"role":"figure","size":231019,"visible":true,"origin":"","legend":"\u003cp\u003eWater depth distribution for (a) Blue spot 2, (b) Blue spot 12, (c) Blue spot 20 and (d) Blue spot 13, diagrams illustrate HECRAS output and Kinematic Safer_RAIN output corresponding to various weir widths.\u003c/p\u003e","description":"","filename":"11.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/111ce84646550d3d16f79eed.jpg"},{"id":107707303,"identity":"22ee15df-829e-4419-857a-1014c5eae032","added_by":"auto","created_at":"2026-04-24 09:20:02","extension":"jpg","order_by":12,"title":"Figure 12","display":"","copyAsset":false,"role":"figure","size":185424,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of modelling results from Original Safer_RAIN, Kinematic Safer_RAIN and HEC-RAS in Barañáin, Pamplona. Source: Newspaper images extracted from the Diario de Navarra.\u003c/p\u003e","description":"","filename":"12.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/6b5d58f8eb5ebbc1d4998b20.jpg"},{"id":107620358,"identity":"30a6c757-c858-4636-8e8f-0e574f8feb91","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":13,"title":"Figure 13","display":"","copyAsset":false,"role":"figure","size":201478,"visible":true,"origin":"","legend":"\u003cp\u003eComparison of modelling results from Original Safer_RAIN, Kinematic Safer_RAIN and HEC-RAS in Zizur Mayor,Pamplona. Source: Newspaper images extracted from the Diario de Navarra.\u003c/p\u003e","description":"","filename":"13.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/0feaa9c2d708161756b5850d.jpg"},{"id":107620360,"identity":"1a9fa5cb-b4f7-4cfb-b8b8-8ddeba0c6f64","added_by":"auto","created_at":"2026-04-23 09:36:25","extension":"jpg","order_by":14,"title":"Figure 14","display":"","copyAsset":false,"role":"figure","size":127515,"visible":true,"origin":"","legend":"\u003cp\u003eWater Depth Distributions in (a) Blue spot 11, Barañáin and (b) Blue spot 9 in Zizur Mayor, diagrams illustrate HEC-RAS output and Kinematic Safer_RAIN output corresponding to various weir widths.\u003c/p\u003e","description":"","filename":"14.jpg","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/8d70494781f96299913cb23b.jpg"},{"id":107709262,"identity":"c9193cf4-ef0a-424b-a391-d728afb4e766","added_by":"auto","created_at":"2026-04-24 09:35:13","extension":"pdf","order_by":0,"title":"","display":"","copyAsset":false,"role":"manuscript-pdf","size":2999556,"visible":true,"origin":"","legend":"","description":"","filename":"manuscript.pdf","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/0364e108-b359-41c4-bc48-90fb75c0b9c6.pdf"},{"id":107706051,"identity":"fa757f82-953f-4913-9a13-9dc370092341","added_by":"auto","created_at":"2026-04-24 09:17:14","extension":"docx","order_by":1,"title":"","display":"","copyAsset":false,"role":"supplement","size":318976,"visible":true,"origin":"","legend":"","description":"","filename":"Appendix.docx","url":"https://assets-eu.researchsquare.com/files/rs-9492481/v1/c438c2795478b6bebebe3ca6.docx"}],"financialInterests":"The authors declare no competing interests.","formattedTitle":"\u003cp\u003e\u003cstrong\u003eFast-Processing Modelling of Urban Pluvial Flooding: Kinematic Hierarchical Filling-and-Spilling Algorithm\u003c/strong\u003e\u003c/p\u003e","fulltext":[{"header":"1.Introduction","content":"\u003cp\u003eUrban flooding poses significant risks to lives and infrastructure, necessitating efficient modelling solutions for hazard assessment and disaster preparedness. Cities and towns around the world urgently require a unified approach to urban water management that accounts for the links between water, infrastructure, and land use, while maintaining a dependable supply through varied water sources\u003csup\u003e\u003cspan citationid=\"CR1\" class=\"CitationRef\"\u003e1\u003c/span\u003e\u003c/sup\u003e. Recent research has focused on developing rapid flood mapping techniques for large-scale urban areas. \u003csup\u003e2\u003c/sup\u003e proposed a cellular automata approach for fast 2D urban flood modelling, while \u003csup\u003e\u003cspan citationid=\"CR3\" class=\"CitationRef\"\u003e3\u003c/span\u003e\u003c/sup\u003e presented a GIS-based methodology for quick flood hazard assessment in data-scarce regions. Hybrid machine learning models for urban flooding prediction showed promising results while comparing with storm water management models \u003csup\u003e\u003cspan citationid=\"CR4\" class=\"CitationRef\"\u003e4\u003c/span\u003e\u003c/sup\u003e. \u003csup\u003e5\u003c/sup\u003e introduced Safer_RAIN, a DEM-based algorithm for pluvial flood mapping across extensive urban areas, demonstrating good agreement with 2D hydraulic models. These approaches offer alternatives to traditional, computationally intensive 2D models \u003csup\u003e\u003cspan citationid=\"CR6\" class=\"CitationRef\"\u003e6\u003c/span\u003e\u003c/sup\u003e, enabling faster flood characterization and risk analysis. The development of such rapid modelling techniques is crucial for improving urban flood management, particularly in the context of increasing flood frequency and severity due to climate change, ongoing urban development in flood-prone areas and in real-time flood forecasting.\u003c/p\u003e \u003cp\u003eFlood modelling is an essential tool for understanding and forecasting flood events, which are crucial for effective flood risk management, urban development planning, and emergency response strategies. Most flood models are based on hydraulic simplifications, with one-dimensional (1D) models utilizing the Saint-Venant equations and two-dimensional (2D) models employing the Diffusion wave or shallow water equations (SWE) \u003csup\u003e\u003cspan citationid=\"CR7\" class=\"CitationRef\"\u003e7\u003c/span\u003e,\u003cspan citationid=\"CR8\" class=\"CitationRef\"\u003e8\u003c/span\u003e\u003c/sup\u003e. While 1D models are computationally efficient, they have limitations in capturing complex flow dynamics, such as overland flow and detailed inundation patterns, where lateral velocities can be predominant \u003csup\u003e\u003cspan citationid=\"CR9\" class=\"CitationRef\"\u003e9\u003c/span\u003e\u003c/sup\u003e. In contrast, 2D models, which solve the SWE, offer a more accurate representation of flow dynamics but require significantly higher computational resources \u003csup\u003e\u003cspan additionalcitationids=\"CR11\" citationid=\"CR10\" class=\"CitationRef\"\u003e10\u003c/span\u003e\u0026ndash;\u003cspan citationid=\"CR12\" class=\"CitationRef\"\u003e12\u003c/span\u003e\u003c/sup\u003e. Accurate 2D simulations depend mainly on high-resolution topographic and surface roughness data, which can be difficult to obtain or estimate, particularly in ungauged or data-scarce areas. Additionally, calibrating these models often involves time-consuming processes and extensive field data collection of past flood events, which is particularly challenging in urban settings or areas with complex terrain \u003csup\u003e\u003cspan citationid=\"CR13\" class=\"CitationRef\"\u003e13\u003c/span\u003e,\u003cspan citationid=\"CR14\" class=\"CitationRef\"\u003e14\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e \u003cp\u003eFast processing DEM based inundation modelling algorithms have emerged as efficient alternatives to traditional 2D hydrodynamic models, addressing the need for rapid flood predictions. These algorithms leverage digital elevation models (DEMs) and simplified computational techniques to enhance performance while maintaining accuracy. Fast processing models, such as Safer_RAIN, can use Hierarchical Filling-and-Spilling Algorithms (HSFAs) to simulate pluvial flooding efficiently over large areas, significantly reducing computational costs. Machine learning methods have been developed to approximate flow characteristics, allowing for real-time predictions without extensive computational resources \u003csup\u003e\u003cspan citationid=\"CR15\" class=\"CitationRef\"\u003e15\u003c/span\u003e\u003c/sup\u003e. The choice of DEM resolution and computational mesh significantly influences modelling outcomes, with high horizontal resolution data (i.e. ~1m) leading to more reliable inundation predictions \u003csup\u003e\u003cspan citationid=\"CR16\" class=\"CitationRef\"\u003e16\u003c/span\u003e\u003c/sup\u003e. Fast processing algorithms can adapt to various terrains, making them suitable for diverse flooding scenarios, including urban and rural contexts \u003csup\u003e\u003cspan citationid=\"CR17\" class=\"CitationRef\"\u003e17\u003c/span\u003e\u003c/sup\u003e. While these fast-processing DEM based models offer significant advantages, traditional 2D hydrodynamic models still provide detailed insights into complex flow dynamics, which may be essential for certain applications. Balancing speed and accuracy remain a critical consideration in flood modelling.\u003c/p\u003e \u003cp\u003eIdentification and handling of depressions in grid DEMs is critical to accurate hydrological modelling and flow direction determination. Various algorithms have been developed, each employing different strategies and information sources, such as stream network data, to enhance computational efficiency and accuracy. Algorithms can either modify DEM elevations (e.g., smoothing filters, depression filling) or maintain original elevations while determining flow paths\u003csup\u003e\u003cspan citationid=\"CR18\" class=\"CitationRef\"\u003e18\u003c/span\u003e\u003c/sup\u003e. A new data structure (depression hierarchy) captures the complexity of depressions, allowing for selective filling or breaching, which aids in dynamic hydrological modelling \u003csup\u003e\u003cspan citationid=\"CR19\" class=\"CitationRef\"\u003e19\u003c/span\u003e\u003c/sup\u003e. \u003csup\u003e20\u003c/sup\u003e presents a level-set method for nested depressions in DEMs, which offers an efficient alternative to traditional depression filling methods and enhances hydrological modelling and terrain analysis. The LiDAR Python package implements this method, providing an interactive GUI for users \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Earlier work by \u003csup\u003e22\u003c/sup\u003e introduced a novel concept of spill elevation and least-cost search for optimal flow paths, significantly improving computational efficiency. \u003csup\u003e23\u003c/sup\u003e further enhanced depression filling and flat surface processing algorithms using priority and \u0026ldquo;first-in, first-out\u0026rdquo; (FIFO) queues, achieving better performance by reducing computational effort, as reflected in its time complexity. These advancements in DEM processing are particularly valuable for analysing high resolution LiDAR derived DEMs, which can capture actual surface depressions in urban and peri-urban areas \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. These methods collectively contribute to more accurate hydrological analysis and watershed modelling.\u003c/p\u003e \u003cp\u003eThese concepts and tools are harnessed by Safer_RAIN \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e, a fast-processing algorithm designed to assess and map pluvial flooding in urban areas. This tool utilizes high resolution DEMs and can account for spatially distributed rainfall and infiltration processes through a pixel-based Green Ampt model, making it suitable for rapid assessments across extensive urban landscapes (see \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://saferplaces.co/\u003c/span\u003e\u003cspan address=\"https://saferplaces.co/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e). Safer_RAIN expands the capabilities of existing HSFAs by allowing for the mapping of pluvial flooding associated with partial filling of depression systems. Safer_RAIN has been applied to various scenarios, including rural inundation modelling and urban flooding caused by drainage system outflows \u003csup\u003e\u003cspan citationid=\"CR24\" class=\"CitationRef\"\u003e24\u003c/span\u003e\u003c/sup\u003e. The algorithm has shown good agreement with 2D hydrodynamic model outputs and ground evidence \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e,\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. A stochastic methodology using Safer_RAIN has been developed to generate high resolution pluvial flood hazard maps, addressing current limitations of the standard synthetic design storm approach \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e. However, HSFAs have some limitations such as lack of hydraulic backwater effect, which usually tends to underestimate flood extents, and single flow path constraints. In this study, we improve the current version of Safer_RAIN by incorporating a kinematic travel time distribution for runoff within depression watersheds, alongside the application of weir equations at their overflow points. These enhancements enable the algorithm to inundate a depression above its spilling point, similarly to what happens in the real world when upstream runoff volumes exceed the overall depression capacity. We test improved version of Safer_RAIN \u0026ldquo;Kinematic Safer_RAIN\u0026rdquo; in a case study in Cotton Wood Lake Area in USA and it is applied to a set of real flooding events in urban areas of Pamplona, Spain.\u003c/p\u003e \u003cp\u003eThe structure of the paper is organized as follows: Section2 introduces the main components of the current version of Safer_RAIN, details the conceptual framework of the Kinematic Safer_RAIN, including its newly added capability and the confusion matrices used to evaluate the performance of the models; Section \u003cspan refid=\"Sec11\" class=\"InternalRef\"\u003e3\u003c/span\u003e explains the location and data used in two case study areas; Section \u003cspan refid=\"Sec14\" class=\"InternalRef\"\u003e4\u003c/span\u003e provides the application of the proposed approach in test and real-world case study areas and also presented the results from the comparisons between Kinematic Safer_RAIN with 2D hydrodynamic models, followed by a discussion of the algorithm's overall performance; and Section \u003cspan refid=\"Sec19\" class=\"InternalRef\"\u003e5\u003c/span\u003e concludes the paper by summarizing the key findings. In addition, Appendix A1 includes a pseudo-code representation of the proposed algorithm.\u003c/p\u003e"},{"header":"2.Materials and Models","content":"\u003cdiv id=\"Sec3\" class=\"Section2\"\u003e \u003ch2\u003e2.1 Main Elements of Safer_RAIN\u003c/h2\u003e \u003cp\u003eHSFAs identify areas prone to pluvial flooding based on nested surface depressions derived from high-resolution DEMs. Rainfall volume accumulates within these depressions, and once they reach their capacity, excess water spills over into downstream depressions situated at lower elevations. HSFAs relied on several simplifying assumptions: (i) flow direction is determined by the D8 algorithm, which assigns flow to the steepest downslope neighbour among the eight adjacent cells.; (ii) overland flow dynamics are neglected, with net rainfall volume assumed to accumulate within the nested depression system based on the capacity and hierarchical structure of the depressions; (iii) rainfall is assumed to be uniformly distributed across the area, and (iv) the terrain is considered entirely impermeable. Safer_RAIN relaxed assumptions (iii) and (iv) to account for more realistic conditions by allowing spatially variable rainfall and incorporating infiltration (e.g., via a pixel-based Green\u0026ndash;Ampt model). Original Safer_RAIN consists of two main phases: (1) DEM preprocessing, and (2) depressions (hereafter referred to as \u0026ldquo;blue spots\u0026rdquo;) flooding. Phase (1) includes two steps (Fig.\u0026nbsp;\u003cspan refid=\"Fig1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The first step characterizes horizontal hydrological hierarchy, including (a) identifying all blue spots and their contributing watersheds using a DEM pit-filling algorithm, and (b) determining each blue spot\u0026rsquo;s pour point (spilling point). The term \"pour point\" refers to the same concept as \"spilling point,\" representing the point from which excess water volume overflows. For consistency, we will use the term \"pour point\" throughout the remainder of this paper. The second step establishes a vertical hierarchical structure within each blue spot through a top-down level set method \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e\u003c/sup\u003e. Phase (2) simulates the flooding of the identified blue spots under a given rainfall event. Using the depression hierarchy from Phase 1, the algorithm fills each blue spot from the bottom up (incrementally raising water level) until the net rainfall volume is allocated, akin to the method in\u003csup\u003e5\u003c/sup\u003e. Phase 1 is executed once to generate the depression hierarchy (geometry and connectivity of all blue spots), and this information is then used in Phase 2 to simulate specific flood events. Please refer to\u003csup\u003e5\u003c/sup\u003e for further details.\u003c/p\u003e \u003cp\u003eThe numerous tests to compare Safer_RAIN outputs with detailed 2D hydrodynamic models (see e.g., \u003csup\u003e5,24,25\u003c/sup\u003e) highlighted the good overall accuracy of the simulation results. However, they also showed the tendency of the algorithm to underpredict the maximum inundated areas and water depths relative to detailed 2D hydrodynamic simulations considered as ground truth. In the original algorithm, once a blue spot\u0026rsquo;s volume to the pour point is filled, any additional runoff is immediately diverted downstream, so the water level never exceeds the pour point elevation. In reality, if the outflow is constrained (such as through a narrow spillway or conduit), water can rise higher than the spill elevation, causing a backwater effect that increases flood depth and extent. This process is not captured in the original HSFA, leading to underestimation of flooding.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec4\" class=\"Section2\"\u003e \u003ch2\u003e2.2. Kinematic Safer_RAIN conceptualization\u003c/h2\u003e \u003cp\u003eTo represent the temporal dynamics of runoff delivery to each blue spot, we extend Safer_RAIN with a kinematic component that transfers rainfall volumes through the contributing watershed with a travel-time distribution and applies a weir-based computation at the pour point to simulate ponding above the spill elevation. The enhanced version of Safer_RAIN, referred here to as \u0026ldquo;Kinematic Safer_RAIN\u0026rdquo;, is also structured into two phases. Phase (1) involves LiDAR DEM preprocessing. It includes the original Safer_RAIN preprocessing steps that identify blue spot boundaries. Kinematic Safer_RAIN adds the computation of the flow length (in meters) from each pixel to the nearest blue spot boundary (frontier), which represents the topographic boundary that separates the depression from adjacent terrain. Phase 2 comprises three sub-steps: (i) generation of event hydrographs; (ii) computation of additional flooding above pour points using the weir equation and (iii) recursive update of upstream-to-downstream volumes.\u003c/p\u003e \u003cp\u003ePhase (2) maintains the original Safer_RAIN flooding process (Step 2A in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) while introducing additional steps (Steps 2B, 2B(i), and 2B(ii) in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). In Step 2B, rainfall volumes are transferred from the pixels where the rainfall drops to the blue spot boundary with a time distribution. A constant routing velocity (default 1 m s⁻\u0026sup1;) is assumed to approximate the average overland flow velocity within the watershed. This simplification neglects local slope and roughness variations but allows derivation of travel-time distributions from flow length rasters. Step 2B(ii) incorporates the recursive calculation of delays of water volumes that are spilled from a given upstream blue spot and flow into downstream blue spots. Finally, Step 2B(ii) uses the weir equation to compute the additional water depth above the spilling point elevation (∆h) that is required to spill a given water volume. This also accounts for the potential further filling of a given depression due to the time distributed runoff inflow. Throughout this paper, we use the term \u0026lsquo;backwater effect\u0026rsquo; in a simplified sense, to denote ponding above the pour-point elevation caused by delayed runoff inflows, rather than a true hydraulic backwater computed from momentum equations. Figure\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e schematically illustrates the new processes introduced in Kinematic Safer_RAIN (time-distributed runoff transfer and additional filling above the pour point via a weir equation) superimposed on the original Safer_RAIN framework. The proposed algorithms in Kinematic Safer_RAIN are further detailed in the following sub sections.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cdiv id=\"Sec5\" class=\"Section3\"\u003e \u003ch2\u003e2.2.1 Kinematic Safer_RAIN: LiDAR preprocessing\u003c/h2\u003e \u003cp\u003eKinematic Safer_RAIN uses the original DEM preprocessing phase with the new addition of calculating the distance classes of each pixel within the watershed that contributes to a given blue spot to its boundary. The process begins by filling the blue spots as they are the lowest depression areas. Afterwards, a flow length raster is generated using the flow direction for each watershed, excluding the blue spots (Fig.\u0026nbsp;\u003cspan refid=\"Fig3\" class=\"InternalRef\"\u003e3\u003c/span\u003e). The flow length is then divided into distance classes for each pixel that reaches the boundary of the blue spots. Finally, the number of pixels in each distance class is counted to compute the volume and time distribution.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec6\" class=\"Section3\"\u003e \u003ch2\u003e2.2.2 Kinematic Safer_RAIN: Flooding Phase\u003c/h2\u003e \u003cp\u003eIn the original Safer_RAIN, the inundation extent is necessarily confined within the blue spot boundary. However, during real flood events, the flooded area can extend beyond this boundary (as illustrated by the dashed blue line in Step 2B of Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). Kinematic Safer_RAIN can simulate a larger extent of inundation in blue spots, accounting for potential backwater effects. Therefore, the flooding phase in Kinematic Safer_RAIN involves two key steps: (1) producing a simplified representation of the event hydrograph (Step 2Bi, in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e), and (2) applying the weir equation to estimate the additional water surface elevation above the pour point (Step 2Bii, in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec7\" class=\"Section3\"\u003e \u003ch2\u003e2.2.3 Event hydrograph\u003c/h2\u003e \u003cp\u003eAfter obtaining the distance classes from the flow length raster of each watershed and determining the pixel counts for each distance class, the runoff travel time from each pixel to the boundary of the blue spot area is calculated using a constant routing velocity \u003cem\u003eV\u003c/em\u003e (e.g. \u003cem\u003eV\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1 m/s), which is a fixed parameter of the approach. For each distance class dj (where j represents a specific class), the discharge contribution Qj(t) at time t is calculated by lagging the rainfall excess Rj(t) by its travel time tj. The travel time tj is given by the formula tj\u0026thinsp;=\u0026thinsp;dj / V, where dj is the distance for the class and V is routing velocity. This discretization travel time method is also used in the work of \u003csup\u003e26\u003c/sup\u003e, where the travel time for each channel cell is computed from the travel distance of the cell and the cell velocity. The initial travel time estimate is then updated by incorporating the blue spot delay time based on the inflow runoff volumes coming from upstream and rain inflow that drops directly in the blue spot, as a given blue spot cannot spill downstream through its pour point until it is filled. Following this, the rainfall depth corresponding to each travel time is calculated for each distance class. The final step involves calculating the discharge at each travel time (Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e). The kinematic approach used to generate event hydrographs is also used by \u003csup\u003e27\u003c/sup\u003e for their Urban Morpho-climatic Instantaneous Unit Hydrograph. Their framework likewise accounts for the upstream contribution of flow and the intensity of excess rainfall in its travel time calculations.\u003cdiv id=\"Equ1\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ1\" name=\"EquationSource\"\u003e\n$$\\:Q=\\frac{R\\times\\:n\\:\\times\\:A}{T}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e1\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:R\\)\u003c/span\u003e \u003c/span\u003e = rainfall depth(m)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:n\\)\u003c/span\u003e \u003c/span\u003e = number of pixels\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:A\\)\u003c/span\u003e \u003c/span\u003e = pixel area (m\u003csup\u003e2\u003c/sup\u003e)\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:T\\)\u003c/span\u003e \u003c/span\u003e = travel time (sec)\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec8\" class=\"Section3\"\u003e \u003ch2\u003e2.2.4 Additional Flooding and Weir Formula\u003c/h2\u003e \u003cp\u003eIn this step, we focus on the computation of the additional flooding extent above the pour point elevation for a given blue spot and rainfall event (panel 2.B(ii) in Fig.\u0026nbsp;\u003cspan refid=\"Fig2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). First, the water volume required for filling a given blue spot is subtracted from the beginning of the kinematic hydrograph identified as described in the previous section. Second, referring to the resulting hydrograph, the time step associated with the maximum runoff inflow and peak inflow hydrograph itself (Q\u003csub\u003emax\u003c/sub\u003e) is identified. Third, the overall inflow runoff volume reaching the blue spot up to Q\u003csub\u003emax\u003c/sub\u003e\u0026rsquo;s timestep (i.e. upstream volume, V\u003csub\u003eups\u003c/sub\u003e) is computed. Fourth, the weir equation (Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e) is used to calculate the water depth above the pour point (∆h) associated with an outflow equal to Q\u003csub\u003emax\u003c/sub\u003e, which is considered as an initial estimate of the maximum outflow spilled by the pour point. A weir width (B) (e.g 3m) and a discharge coefficient (\u0026micro;) (e.g. 0.385) \u003csup\u003e\u003cspan citationid=\"CR28\" class=\"CitationRef\"\u003e28\u003c/span\u003e\u003c/sup\u003e, need to be selected as additional parameters of the approach. As a fifth step, the algorithm identifies from a LiDAR DEM analysis for the water volume stored in the blue spot that is associated with the additional flood elevation ∆h above the pour point (required volume; V\u003csub\u003ereq\u003c/sub\u003e). V\u003csub\u003ereq\u003c/sub\u003e represents the required volume to raise the depression by ∆h and V\u003csub\u003eups\u003c/sub\u003e is the upstream inflow volumes up to Q\u003csub\u003emax\u003c/sub\u003e. V\u003csub\u003ereq\u003c/sub\u003e is compared with V\u003csub\u003eups\u003c/sub\u003e. If V\u003csub\u003eups\u003c/sub\u003e is larger than V\u003csub\u003ereq\u003c/sub\u003e, we select this ∆h as ∆h\u003csub\u003emax\u003c/sub\u003e for the backwater effect. If V\u003csub\u003eups\u003c/sub\u003e is insufficient, ∆h\u003csub\u003emax\u003c/sub\u003e is recalculated based on V\u003csub\u003eups\u003c/sub\u003e. Once ∆h\u003csub\u003emax\u003c/sub\u003e is determined, the additional flooding associated with the additional water level above the pour point is calculated from the LiDAR DEM. The pour point elevation of each blue spot is already known, and the overall pour point elevation is computed by summing the ∆h\u003csub\u003emax\u003c/sub\u003e and the original pour point elevation. The new blue spot extent is then identified as the intersection of the DEM and the overall pour point elevation.\u003cdiv id=\"Equ2\" class=\"Equation\"\u003e\u003cdiv format=\"TEX\" class=\"mathdisplay\" id=\"FileID_Equ2\" name=\"EquationSource\"\u003e\n$$\\:{Q}_{max}=\\mu\\:.B.{\\varDelta\\:h}_{max}.\\sqrt{2g{\\varDelta\\:h}_{max}}$$\u003c/div\u003e\u003cdiv class=\"EquationNumber\"\u003e2\u003c/div\u003e\u003c/div\u003e\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"BlockQuote\"\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{Q}_{max}\\)\u003c/span\u003e \u003c/span\u003e = maximum discharge\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:\\mu\\:\\)\u003c/span\u003e \u003c/span\u003e= discharge coefficient\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:B\\)\u003c/span\u003e \u003c/span\u003e = weir width\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:{\\varDelta\\:h}_{max}\\)\u003c/span\u003e \u003c/span\u003e= Hydraulic Head\u003c/p\u003e \u003cp\u003e \u003cspan class=\"InlineEquation\"\u003e \u003cspan class=\"mathinline\"\u003e\\(\\:g\\)\u003c/span\u003e \u003c/span\u003e = acceleration due to gravity\u003c/p\u003e \u003c/div\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec9\" class=\"Section3\"\u003e \u003ch2\u003e2.2.5 Filtering Algorithm Rule\u003c/h2\u003e \u003cp\u003eRunning the original Safer_RAIN algorithm in the flooding phase for a given rainfall event results in detailed data on the spilling volume for each blue spot. Some blue spots may be found to have a spilling volume of zero, indicating that those blue spots possess sufficient storage capacity to retain all the rainfall volume received during the storm event without overflowing. In addition to the spilling volume data, the algorithm also provides information on the upstream volume for each blue spot. This data reveals the hydrological connectivity between blue spots, showing that certain blue spots contribute water volumes to downstream blue spots. This upstream-downstream relationship is critical for identifying how water flows through the landscape and for analysing areas where hydrological interactions may lead to an additional flooding above the blue spot pour point. In Kinematic Safer_RAIN, we establish a rule to identify the blue spots with the potential to experience a backwater effect. According to the rule, blue spots with both zero spilling volume and zero upstream inflow volume are excluded from further analysis. Blue spots that meet these criteria neither overflow nor receive additional water from upstream sources, making them irrelevant for backwater effect calculations. By applying this rule, we focus only on the remaining blue spots that either spill water or receive contributions from upstream blue spots. These remaining blue spots are classified as potential blue spots for backwater effect analysis.\u003c/p\u003e \u003c/div\u003e \u003c/div\u003e \u003cdiv id=\"Sec10\" class=\"Section2\"\u003e \u003ch2\u003e2.3 Matrices for evaluating the performance of models\u003c/h2\u003e \u003cp\u003eFor a comparative analysis of flooding scenarios in terms of inundation extents, we adopted several evaluation metrics \u003csup\u003e\u003cspan citationid=\"CR29\" class=\"CitationRef\"\u003e29\u003c/span\u003e\u003c/sup\u003e as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Model performance was evaluated by comparing Kinematic Safer_RAIN simulations against a HEC-RAS benchmark. We classified pixels as: True Positives (TP), flooded in both models; False Positives (FP), flooded only in Safer_RAIN; True Negatives (TN), non-flooded in both models; and False Negatives (FN), flooded only in the HEC-RAS benchmark. From these, we derived several metrics ranging from 0 to 1: the True Positive Rate (TPR) or sensitivity; the False Negative Rate (FNR) or miss rate; the True Negative Rate (TNR) or specificity; the False Positive Rate (FPR) or fall-out; Area under the receiver-operating-characteristic curve(AUROC) is a probability that a flooded pixel is correctly distinguished; Accuracy Correlation Coefficient (ACC) for overall accuracy; and the Matthews Correlation Coefficient (MCC) as a balanced performance measure between the binary classifications in the simulations.\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\u003eConfusion matrix for quantifying the performance of algorithm.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"5\"\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 \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colspan=\"4\" nameend=\"c5\" namest=\"c2\"\u003e \u003cp\u003eHEC-RAS simulations\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFlooding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eNon-flooding\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\" morerows=\"3\" rowspan=\"4\"\u003e \u003cp\u003e\u003cb\u003eKinematic Safer_RAIN simulations\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eFlooding\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTrue positives (TP)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFalse positives (FP)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e\u003cb\u003eNon-flooding\u003c/b\u003e\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFalse negatives (FN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTrue negatives (TN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTrue positive rate \u003c/p\u003e \u003cp\u003e(TPR)\u0026thinsp;=\u0026thinsp;TP/(TP\u0026thinsp;+\u0026thinsp;FN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTrue negative rate\u003c/p\u003e \u003cp\u003e(TNR)\u0026thinsp;=\u0026thinsp;TN/(FP\u0026thinsp;+\u0026thinsp;TN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eAccuracy (ACC) = (TN\u0026thinsp;+\u0026thinsp;TP)/(TP\u0026thinsp;+\u0026thinsp;TN+FN\u0026thinsp;+\u0026thinsp;FP)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFalse negative rate\u003c/p\u003e \u003cp\u003e(FNR)\u0026thinsp;=\u0026thinsp;FN/(FN\u0026thinsp;+\u0026thinsp;TP)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFalse positive rate\u003c/p\u003e \u003cp\u003e(FPR)\u0026thinsp;=\u0026thinsp;FP/(FP\u0026thinsp;+\u0026thinsp;TN)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e \u003cp\u003eMathew\u0026rsquo;s correlation coefficient\u003c/p\u003e \u003cp\u003e(MCC) = (TP.TN \u0026ndash; FP. FN)/\u003c/p\u003e \u003cp\u003eSQRT((TP\u0026thinsp;+\u0026thinsp;FP) (TP\u0026thinsp;+\u0026thinsp;FN) (TN\u0026thinsp;+\u0026thinsp;FP) (TN\u0026thinsp;+\u0026thinsp;FN))\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"3.Case studies","content":"\u003cp\u003eThis section evaluates Kinematic Safer_RAIN using two testbeds: a test case in Cotton Wood Lake Study Area, USA and a real event in Pamplona, Spain. Each subsection describes input data, parameter settings and comparisons with HEC-RAS 2D.\u003c/p\u003e \u003cdiv id=\"Sec12\" class=\"Section2\"\u003e \u003ch2\u003e3.1 Cotton Wood Lake Study Area, USA\u003c/h2\u003e \u003cp\u003eThe open access test bed for our first experiment is the Cottonwood Lake Study Area (CLSA), situated in Stutsman County, North Dakota (refer to Fig.\u0026nbsp;5a). The CLSA is one of three long-term wetland ecosystem monitoring sites established by the United States Geological Survey (USGS) within the Prairie Pothole Region of North America. This site has been an active research area over the past decades \u003csup\u003e\u003cspan citationid=\"CR20\" class=\"CitationRef\"\u003e20\u003c/span\u003e,\u003cspan citationid=\"CR30\" class=\"CitationRef\"\u003e30\u003c/span\u003e\u003c/sup\u003e. For this experiment, airborne LiDAR data with a 1-meter resolution was utilized for the CLSA (see Fig.\u0026nbsp;5b). The availability of high resolution freely accessible data made the CLSA an ideal choice for our test case study. By using a well-documented study area with open-source datasets (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/opengeos/lidar\u003c/span\u003e\u003cspan address=\"https://github.com/opengeos/lidar\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), we ensure that our methodology can be easily tested, replicated and validated by others. We used 100mm uniform rainfall event for the model simulations. With Safer_RAIN\u0026rsquo;s LiDAR DEM preprocessing, we got 22 blue spots with its related 22 watersheds, 22 pourpoints, 22 flow paths and 3 junctions (Fig.\u0026nbsp;5(c)).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eFigure \u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e. (a) Location map of the Piepstem watershed in the Prairie Pothole Region of North Dokota (b) LiDAR DEM for the cotton wood lake area, (c) Safer_RAIN preprocessing result of CLSA based on LiDAR DEM.\u003c/p\u003e \u003cp\u003eFigure 5. (a) Location map of the Piepstem watershed in the Prairie Pothole Region of North Dokota (b) LiDAR DEM for the cotton wood lake area, (c) Safer_RAIN preprocessing result of CLSA based on LiDAR DEM.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec13\" class=\"Section2\"\u003e \u003ch2\u003e3.2 Pamplona, Spain\u003c/h2\u003e \u003cp\u003ePamplona, the capital of the Navarre Region in northern Spain, is an important urban area known for its susceptibility to pluvial and fluvial flooding. The Pamplona metropolitan area covers 68.26 km\u0026sup2; and is home to approximately 335,000 inhabitants. This population is distributed across several municipalities, including Bara\u0026ntilde;\u0026aacute;in, Burlada, Cendea de Olza, Cizur, Huarte, Orcoyen, Pamplona, Villava, and Zizur Mayor (see Fig.\u0026nbsp;\u003cspan refid=\"Fig5\" class=\"InternalRef\"\u003e6\u003c/span\u003e). For this study, we use a 2m resolution Digital Elevation Model (DEM) supplied by the Spanish National Geographic Institute (IGN).\u003c/p\u003e \u003cp\u003ePluvial flooding events in the region are primarily driven by intense rainfall, particularly during the summer months. Among the municipalities, Bara\u0026ntilde;\u0026aacute;in and Zizur Mayor have experienced the highest flood losses from pluvial floods, based on data provided by the Spanish \"Consorcio de Compensaci\u0026oacute;n de Seguros (CCS),\" an organization that compensates for damages caused by natural hazards in Spain, in the period 1996\u0026ndash;2018. The largest pluvial flood event recorded in the Pamplona metropolitan area in that period occurred on 20 July 2010 \u003csup\u003e25,31\u003c/sup\u003e. Two significant cloudbursts hit the study area on 20 July 2010 resulting in pluvial flooding. The first event took place between 6:30 PM and 7:20 PM, while the second event occurred later, starting at 9:10 PM and ending at 10:40 PM. For our analysis, we selected the second event for simulation as it is considered the largest in the period 1996\u0026ndash;2020, contributing to total rainfall amount over 110 mm in 1 hour 40 mins.\u003c/p\u003e \u003cp\u003eTo investigate and model this event, we employed the Kinematic Safer_RAIN and compared its results with HEC-RAS RoG simulations. Precipitation data are received from multiple sources, including the SAIH real-time system of the River Ebro Basin Authority, the Spanish Meteorological Agency (AEMET), the regional government of Navarre, and the Universidad P\u0026uacute;blica de Navarra (UPN). To validate the flood hotspots identified in Bara\u0026ntilde;\u0026aacute;in and Zizur Mayor by the Kinematic Safer_RAIN, we cross-referenced the model outputs with reports from the \u0026ldquo;Diario de Navarra\u0026rdquo; (DN) newspaper. These reports provided real-world evidence of the most affected areas, supporting the accuracy and reliability of our findings.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"4.Results and Discussions","content":"\u003cdiv id=\"Sec15\" class=\"Section2\"\u003e \u003ch2\u003e4.1 Original vs. Kinematic Safer_RAIN in Cotton Wood Lake Study Area, USA\u003c/h2\u003e \u003cp\u003eWe used a synthetic uniform rainfall of 100mm in 1 hr, with a pixel size of 1m since the LiDAR DEM data has a resolution of 1m. Following the filtering rule in this CLSA (see details in section \u003cspan refid=\"Sec9\" class=\"InternalRef\"\u003e2.2.5\u003c/span\u003e), we identify 9 blue spots and their corresponding 9 watersheds as being subject to backwater effects. These blue spots were determined to either have spilling volumes or receive contributions from upstream sources, making them significant for further analysis. Therefore, these nine blue spots and their associated watersheds will be considered for calculating and evaluating the backwater effect, providing critical insights into the hydrological interactions and potential flooding impacts in these areas.\u003c/p\u003e \u003cp\u003eIn the first stage (the watershed routing stage), we compute the flow length raster for each watershed contributing area (excluding blue spots) to determine the distance classes for each pixel, representing the travel distance to the boundary of the blue spot (see Fig.\u0026nbsp;\u003cspan refid=\"Fig6\" class=\"InternalRef\"\u003e7\u003c/span\u003e \u0026ndash; flow length raster for watersheds). For each distance class, we calculate the pixel counts and the travel time using a constant routing velocity (\u003cem\u003eV\u003c/em\u003e\u0026thinsp;=\u0026thinsp;1m/s). Using this information, we then calculate the discharge Q for each distance class using Eq.\u0026nbsp;\u003cspan refid=\"Equ1\" class=\"InternalRef\"\u003e1\u003c/span\u003e. Additionally, the discharge contributed by the rainfall that drops directly on the blue spot is added to the watershed's discharge time series, as blue spots represent the lowest depressions, which are filled first during the rainfall event. Once we have the discharges, we cumulate Q over time. Using this cumulative discharge Q at the latest time step, we calculate the ∆h\u003csub\u003emax\u003c/sub\u003e for the backwater effect using the weir formula (see Eq.\u0026nbsp;\u003cspan refid=\"Equ2\" class=\"InternalRef\"\u003e2\u003c/span\u003e). To determine whether this calculated ∆h represents the backwater effect correctly, we compare the V\u003csub\u003ereq\u003c/sub\u003e and Volume Upstream V\u003csub\u003eups\u003c/sub\u003e. The detail calculation of these volumes is explained in section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e2.2.4\u003c/span\u003e. The results of this comparison, including the values for V\u003csub\u003eups\u003c/sub\u003e, V\u003csub\u003ereq\u003c/sub\u003e and ∆h\u003csub\u003emax\u003c/sub\u003e are presented in the following Table\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e.\u003c/p\u003e \u003cp\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\u003e(a) ∆h\u003csub\u003emax\u003c/sub\u003e after first comparison of V\u003csub\u003eups\u003c/sub\u003e and V\u003csub\u003ereq\u003c/sub\u003e before considering upstream blue spots contribution, (b) final ∆h\u003csub\u003emax\u003c/sub\u003e after comparison of V\u003csub\u003eups\u003c/sub\u003e and V\u003csub\u003ereq\u003c/sub\u003e after considering upstream blue spots contribution.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\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 \u003cdiv align=\"left\" class=\"colspec\" colname=\"c7\" colnum=\"7\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c8\" colnum=\"8\"\u003e\u003c/div\u003e \u003cdiv align=\"left\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c4\" namest=\"c1\"\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. (a)\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/th\u003e \u003cth align=\"left\" colspan=\"4\" nameend=\"c9\" namest=\"c6\"\u003e \u003cp\u003eTable\u0026nbsp;\u003cspan refid=\"Tab2\" class=\"InternalRef\"\u003e2\u003c/span\u003e. (b)\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBspot_id\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003eV\u003csub\u003eups\u003c/sub\u003e(m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003eV\u003csub\u003ereq\u003c/sub\u003e(m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e∆h\u003csub\u003emax\u003c/sub\u003e(m)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003eBspot_id\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003eV\u003csub\u003eups\u003c/sub\u003e(m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003eV\u003csub\u003ereq\u003c/sub\u003e(m\u003csup\u003e3\u003c/sup\u003e)\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e∆h\u003csub\u003emax\u003c/sub\u003e(m)\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e3989\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1458\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e3989\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e1458\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8928\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e6777\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e10190\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e7185\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.40\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e637\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e637\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e2694\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e440\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e2695\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e440\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4522\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1018\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e9882\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2807\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.37\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e8903\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e4076\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e1.34\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e14910\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e6967\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e1.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e181\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\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e181\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e1041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e1041\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e159\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.31\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e4096\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c3\"\u003e \u003cp\u003e1385\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c4\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c5\"\u003e\u0026nbsp;\u003c/td\u003e \u003ctd align=\"left\" colname=\"c6\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c7\"\u003e \u003cp\u003e5807\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c8\"\u003e \u003cp\u003e2037\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c9\"\u003e \u003cp\u003e0.96\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\u003eAccording to the upstream downstream relationship explained in detail in Section \u003cspan refid=\"Sec9\" class=\"InternalRef\"\u003e2.2.5\u003c/span\u003e (filtering algorithm rule), we have known that only four blue spots (4,13, 16 and 22) receive contributions from upstream blue spots. Based on the comparison as shown in Table\u0026nbsp;\u003cspan refid=\"Tab1\" class=\"InternalRef\"\u003e1\u003c/span\u003e(b), we update new ∆h values for those blue spots. Using the water level elevation (pour point elevation + ∆h) and the watershed mask, we calculate the new extent of each blue spot. Additionally, the water depth in each blue spot is determined by subtracting the DEM elevation data for the watershed from the overall pour point elevation. The updated results are visually compared in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e9\u003c/span\u003e, which shows the difference between the Safer_RAIN original output and the Kinematic Safer_RAIN output. These comparisons provide insight into the impact of upstream contributions and updated ∆h values on the extent and depth of water in the back water affected blue spots. The water depth results shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e9\u003c/span\u003e are at the maximum water depth simulation result (100mm uniform rainfall in 1 hour event).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eThe comparison between the Original Safer_RAIN and the Kinematic Safer_RAIN simulations, as shown in Fig.\u0026nbsp;8, reveals notable differences in the predicted flood extents and water depth distributions. In several blue spots, the Kinematic Safer_RAIN simulation produces a larger flooded extent compared to the Original Safer_RAIN. These differences are particularly evident in blue spots affected by backwater effects. This observation is further confirmed by the water depth differences illustrated in Fig.\u0026nbsp;8(c). In these backwater-affected blue spots, the Kinematic Safer_RAIN simulation predicts higher water depths within the original extent of the flooded area when compared to the original Safer_RAIN. Additionally, the Kinematic approach demonstrates a tendency to extend the flood coverage beyond the original boundaries, albeit with lower water depth values in these extended areas. These results indicate that the kinematic routing enables the model to reproduce extended ponding areas consistent with expected hydrological behaviour.\u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec16\" class=\"Section2\"\u003e \u003ch2\u003e4.2 Kinematic Safer_RAIN vs. 2D hydrodynamic model in Cotton Wood Lake Study Area\u003c/h2\u003e \u003cp\u003eIn the absence of observed data, we used a HEC-RAS 2D rain-on-grid simulation with the same uniform 100 mm h⁻\u0026sup1; rainfall as benchmark. RoG modelling using HEC-RAS 2D has gained popularity for storm-event hazard assessment and pluvial flooding analysis. This approach integrates hydrological and hydrodynamic processes within a 2D model. HEC-RAS 2D with RoG has been applied to various scenarios, including urban areas and actual basins, demonstrating its potential for flood risk assessment \u003csup\u003e\u003cspan citationid=\"CR32\" class=\"CitationRef\"\u003e32\u003c/span\u003e\u003c/sup\u003e. Therefore, the HEC-RAS results are compared with the Kinematic Safer_RAIN simulation with a synthetic uniform rainfall of 100mm in 1 hour, as shown in Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e9\u003c/span\u003e. When focusing on the blue spots considered for backwater effects (e.g., blue spots 12), we observed that the flooded area produced by Kinematic Safer_RAIN closely matches the results of the HEC-RAS simulation. A similar observation is made for blue spots 2, 4, and 6. In terms of water depth within the blue spots, the original Safer_RAIN simulation produces a maximum water depth of 1.87 m, which is significantly less than the maximum water depth of 3.77 m produced by the HEC-RAS simulation. However, the improved Kinematic Safer_RAIN generates a maximum water depth of 2.75 m, bringing it closer to the HEC-RAS results.\u003c/p\u003e \u003cp\u003eIn terms of computation efficiency, HEC-RAS required 2 hours, 38 minutes, and 4 seconds to simulate a 1-meter mesh size consisting of 1,721,122 pixels. In contrast, Kinematic Safer_RAIN completed the same simulation in just 1min and 16seconds on the same hardware (i.e., 12th Gen Intel(R) Core (TM) i7-12650H processor running at 2300 MHz with 10 cores). Despite these improvements, some limitations remain. Kinematic Safer_RAIN filters out small blue spots according to the threshold area selected by the user in the preprocessing phase, while HEC-RAS includes these in the simulation. Additionally, HEC-RAS is capable of identifying flooding along the flow paths between blue spots, which is an intrinsic limitation of HSFAs that will be a key target for future improvements.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe identified that nine blue spots experience the so-called backwater effect out of the total of 22 modelled blue spots. To further characterize these results, we conducted detailed water depth distribution and flood extent analysis by examining the simulated maximum water depth raster files generated by Kinematic Safer_RAIN and HEC-RAS. The analysis is focused on the relevant areas only, which we identified using a 100m circular buffer enveloping each blue spot of interest and its pour point (see Fig.\u0026nbsp;\u003cspan refid=\"Fig7\" class=\"InternalRef\"\u003e9\u003c/span\u003e).\u003c/p\u003e \u003cp\u003eKinematic Safer_RAIN utilises the weir equation to compute the additional water depth above the pour point, denoted as ∆h, as detailed in section \u003cspan refid=\"Sec8\" class=\"InternalRef\"\u003e2.2.4\u003c/span\u003e. The weir width B is a critical parameter in this calculation, and we assessed its influence on flood modelling results through a sensitivity analysis. In particular, we tested a range of weir widths from 1m to 5m, analysing the resulting flood extent and comparing it to the flood extent derived from the HEC-RAS simulation. Among the tested parameters, we found that a weir width of 2.5m in most blue spots (see e.g. of blue spot 2 in Fig.\u0026nbsp;\u003cspan refid=\"Fig8\" class=\"InternalRef\"\u003e10\u003c/span\u003e) provides results that are closely aligned with the HEC-RAS simulation outcomes in terms of flooded area, demonstrating the suitability of this parameter across the study area.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eWe conducted the water depth distribution in each backwater effected blue spots using maximum water depths simulated by Kinematic Safer_RAIN and HEC-RAS in tuning the weir width parameter. Diagrams in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e11\u003c/span\u003e illustrate the exceedance probability of specified water depth values across the computational domain. These exceedance probabilities represent the likelihood that a given water depth is exceeded and based on the dimensions of the computational mesh pixels, they can also be interpreted as the surface area flooded by water depths exceeding a certain threshold. In this analysis, only the pixels experiencing inundation (non-zero water depths) are included in the curve estimation. Any NA values or water depths equal to 0 m are excluded to ensure the analysis focuses strictly on areas with flooding. To aid in understanding the distribution of lower water depth values, the y-axis is displayed on a logarithmic scale. This allows for clearer visualization of both small and large water depths, which would otherwise be difficult to interpret on a linear scale. Additionally, the diagrams include a reference horizontal line at 0.05 m, which represents the water depth threshold used to differentiate between flooded and non-flooded pixels. This threshold ensures that only significant water depths are considered when analysing water depth distributions and exceedance probabilities.\u003c/p\u003e \u003cp\u003eAccording to the graphs in Fig.\u0026nbsp;\u003cspan refid=\"Fig9\" class=\"InternalRef\"\u003e11\u003c/span\u003e, the Kinematic Safer_RAIN simulations with a weir width of 2.5 m for most blue spots provide the best overall fit with the HEC-RAS simulation results. However, there are exceptions, such as blue spot 13, where the simulation with a weir width of 1.5 m aligns more closely with the HEC-RAS results. To maintain uniformity across the domain, a weir width of 2.5 m can be used as a standard parameter. This parameter is locally adaptable and depends on the specific topographic characteristics of the area. The difference arises because the Kinematic Safer_RAIN algorithm employs a hydrostatic approach to simulate flooding above the blue spot pour point. In contrast, the HEC-RAS model calculates maximum water depths using hydrodynamic modelling, which more accurately reproduces backwater effects in a strict hydraulic sense. Our goal is for Kinematic Safer_RAIN to produce results that approximate those of traditional hydrodynamic models while maintaining low computational demands. This locally adaptable weir width parameter will be retained for future analyses, particularly for the detection of LiDAR data.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003eIn addition to the water depth distribution analysis, we performed the flood extent analysis using the confusion matrices explained details in section \u003cspan refid=\"Sec10\" class=\"InternalRef\"\u003e2.3\u003c/span\u003e. A pixel is considered flooded if the simulated water depth exceeded a threshold of 5 cm. This chosen threshold agrees with the findings of \u003csup\u003e33\u003c/sup\u003e, who mentioned that the impact of flood depths below this level is generally minor and confined to areas with the lowest-lying topographies due to relatively uniform patterns of subsidence and local microtopographic variations at the local scale. Furthermore, applying this threshold ensures consistency in identifying inundated areas across both simulation models.\u003c/p\u003e \u003cp\u003eAccording to the performance metrics in the table (results are from taking the weir width parameter as 1m), most blue spots demonstrate a high TPR (\u0026ge;\u0026thinsp;0.84), indicating that the Kinematic Safer_RAIN model effectively detects flooded areas, with low FNR (\u0026le;\u0026thinsp;0.16), showing it rarely misses them. Similarly, the Kinematic Safer_RAIN model achieves high TNR (\u0026ge;\u0026thinsp;0.94) for most blue spots, meaning it is reliable at identifying non-flooded areas and minimizing false alarms (FPR\u0026thinsp;\u0026le;\u0026thinsp;0.06). The AUROC values (\u0026ge;\u0026thinsp;0.78) across all blue spots highlight the algorithm's strong ability to distinguish between flooded and non-flooded areas. Notably, blue spots 6 and 16 stand out with the highest AUROC values (0.98 and 0.97, respectively), reflecting near-perfect classification performance. Additionally, ACC values are consistently high (\u0026ge;\u0026thinsp;0.78), showcasing the algorithm's strong overall accuracy in predicting flood and non-flood scenarios. However, MCC scores show variation, indicating differences in classification quality across blue spots. Blue spots 12 and 13 demonstrate excellent overall performance, combining high sensitivity, specificity, and low error rates, while blue spot 22 shows the weakest performance, likely due to a lower TNR (0.71) and higher FPR (0.29). In summary, blue spots 6, 12, and 13 stand out as the most reliable, with high sensitivity, specificity, AUROC, and MCC values. Aggregating these results provides a clear picture of the model's overall high performance. On average, TPR, TNR, AUROC, and ACC rates are 0.84, 0.94, 0.89, and 0.91, respectively, with corresponding FPR and FNR error rates of only 0.06 and 0.16. The average MCC is 0.81, which, despite localized variations, signifies a strong and reliable classification performance across the entire study area.\u003c/p\u003e \u003cp\u003eThe performance metrics for a weir width of 2.5m demonstrate notable improvements over the 1m weir width across several key indicators. The average TPR for the 2.5m weir width is 0.90, higher than the 0.84 observed for the 1m weir width. This indicates that the model with a 2.5m weir width is more effective at detecting flooded areas, reducing the likelihood of missed detections. For several blue spots, such as 12, 6, and 22, the TPR reaches near-perfect levels (\u0026ge;\u0026thinsp;0.98), showcasing the model's ability to identify almost all flooded areas. The average FNR with a 2.5m weir width is 0.10, significantly lower than the 0.16 for the 1m weir width. This reduction in missed detections further supports the improved sensitivity of the model when a wider weir width 2.5m is used. The average TNR for the 2.5m weir width is 0.96, slightly higher than the 0.94 for the 1m weir width. This improvement highlights the model's ability to accurately identify non-flooded areas, minimizing false alarms. Similarly, the FPR is reduced to 0.04 (compared to 0.06 for the 1m weir width), further enhancing the reliability of the model. The average AUROC value for the 2.5m weir width is 0.93, higher than the 0.89 for the 1m weir width. This underscores the model's improved ability to distinguish between flooded and non-flooded areas, indicating stronger overall classification performance. Notably, Blue Spots 12 and 6 have exceptional AUROC values of 0.99 and 0.96, respectively. The average ACC increases to 0.95 for the 2.5m weir width, compared to 0.91 for the 1m weir width. This improvement reflects the model's enhanced overall ability to correctly classify both flooded and non-flooded areas. Most blue spots, such as 12, 21, and 6, achieve ACC\u0026thinsp;\u0026ge;\u0026thinsp;0.97, showcasing consistently superior performance. The average MCC for the 2.5m weir width is 0.88, higher than the 0.81 for the 1m weir width. MCC is a holistic metric that accounts for both true and false positives and negatives. The improvement in MCC demonstrates that the classification quality is more balanced and reliable with the wider weir width. Blue Spots 12 and 6 reach near-perfect MCC values of 0.98 and 0.94, respectively. In summary, the weir width of 2.5m consistently outperforms the 1m weir width across all key performance metrics. This result aligns with the weir width sensitivity analysis conducted earlier, which also demonstrated that a weir width of 2.5m closely corresponds to the water depth distribution across several blue spots.\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\u003eComparing flooded area results in potentially flooded blue spots in Cotton Wood Lake Study area (weir width 1m).\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\"\u003e \u003cp\u003eBlue spot\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTPR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFPR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAUROC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eACC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMCC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.30\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.76\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.33\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.68\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.57\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.43\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.09\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.60\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage values\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.84\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.81\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\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab4\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 4\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparing flooded area results in potentially flooded blue spots in Cotton Wood Lake Study area (weir width 2.5m).\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\"\u003e \u003cp\u003eBlue spot\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eTPR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eFNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eTNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eFPR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eAUROC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eACC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eMCC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e2\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e4\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.06\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e6\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.08\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e13\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.82\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.18\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e20\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.78\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.87\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e21\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e22\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.15\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage values\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c2\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.96\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.04\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003c/tbody\u003e \u003c/colgroup\u003e \u003c/table\u003e\u003c/div\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec17\" class=\"Section2\"\u003e \u003ch2\u003e4.3 Kinematic Safer_RAIN vs. 2D hydrodynamic model in Pamplona, Spain\u003c/h2\u003e \u003cp\u003eWe used the same rainfall event and input data for both models, as detailed in Section \u003cspan refid=\"Sec13\" class=\"InternalRef\"\u003e3.2\u003c/span\u003e. After running the Kinematic Safer_RAIN in Bara\u0026ntilde;\u0026aacute;in, we determined that 11 blue spots needed to be calculated out of a total of 18 blue spots in the area. Similarly, in Zizur Mayor, 8 blue spots were identified for calculation out of a total of 13 blue spots. In Bara\u0026ntilde;\u0026aacute;in, the blue spot ID11 exhibited the highest ∆h, indicating it could be the most critical area for backwater effects, and followed by blue spots ID14, ID7, ID16, and ID12. In Zizur Mayor, the blue spot ID9 had the highest ∆h, followed by ID5, ID10, and ID11. We found that such blue spots with the highest ∆h are the flooding hotspots reported in the DN newspaper.\u003c/p\u003e \u003cp\u003eWe also carried out HEC-RAS simulations for both study areas. The results clearly show that the Kinematic Safer_RAIN simulations for the selected blue spots closely match the flooding extents generated by the HEC-RAS simulations. In contrast, the original Safer_RAIN simulations were unable to replicate larger flooding extends beyond the boundaries of the blue spots. Figures\u0026nbsp;\u003cspan refid=\"Fig10\" class=\"InternalRef\"\u003e12\u003c/span\u003e and \u003cspan refid=\"Fig11\" class=\"InternalRef\"\u003e13\u003c/span\u003e show the comparison of simulation results of three models: Original Safer_RAIN, Kinematic Safer_RAIN and HEC-RAS in Bara\u0026ntilde;\u0026aacute;in and Zizur Mayor. In terms of computation efficiency, HEC-RAS required 53 mins 15 sec to simulate a 1 m mesh size consisting of 475,808 pixels for Bara\u0026ntilde;\u0026aacute;in and 2 hr 07 min 50 sec to simulate a 1 m mesh size consisting of 655,193 pixels. In contrast, Kinematic Safer_RAIN completed the same simulation for Bara\u0026ntilde;\u0026aacute;in in 26 sec and for Zizur Mayor in 28 sec on the same hardware (i.e, 12th Gen Intel(R) Core (TM) i7-12650H processor running at 2300 MHz with 10 cores).\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e \u003cdiv id=\"Sec18\" class=\"Section2\"\u003e \u003ch2\u003e4.4 Overall algorithm performance\u003c/h2\u003e \u003cp\u003eWe conducted the performance evaluation of the Kinematic Safer_RAIN model by using the same metrics employed in the CLSA, as detailed in Section \u003cspan refid=\"Sec10\" class=\"InternalRef\"\u003e2.3\u003c/span\u003e. In the absence of real observed data, we used HEC-RAS simulations as the reference dataset to compare with Kinematic Safer_RAIN simulations. The results show that blue spot 11 in the Bara\u0026ntilde;\u0026aacute;in study area achieved the highest TPR, followed by blue Spots 12, 14, 7, and 16 (Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e). Furthermore, Blue Spot 11 exhibited the best overall model performance, with the highest values for AUROC, Accuracy (ACC), and Matthews Correlation Coefficient (MCC), indicating its strong ability to discriminate between flood and non-flood areas and its reliability in flood prediction. Conversely, Blue Spot 16 demonstrated the weakest flood detection, with the lowest MCC, reflecting poorer model performance in this location. Notably, the superior performance at Blue Spot 11 corresponds with its real flooded area during the 20 July 2010 storm, as confirmed by newspaper images of the event. This alignment strengthens the validity of the Kinematic Safer_RAIN model for accurately identifying actual flood-prone areas.\u003c/p\u003e \u003cp\u003eThe same performance evaluation is done for Zizur Mayor area. We found that blue spot 9 has the highest TPR and followed by blue spot 10 and 11. Blue Spot 9 demonstrates the strongest performance overall, with the highest TPR (0.95), AUROC (0.92), ACC (0.90), and MCC (0.75), indicating its high reliability in both detecting floods and avoiding false alarms (Table\u0026nbsp;\u003cspan refid=\"Tab6\" class=\"InternalRef\"\u003e6\u003c/span\u003e). Blue Spot 10 and 11 have moderate TPR (0.56\u0026ndash;0.63) and AUROC (0.72\u0026ndash;0.76) but lower MCC (0.45\u0026ndash;0.54), suggesting average flood detection ability with some misclassification. Overall, these findings highlight the variability in the model\u0026rsquo;s performance across different locations in both Bara\u0026ntilde;\u0026aacute;in and Zizur Mayor. While the results for Blue Spot 11 in Bara\u0026ntilde;\u0026aacute;in and Blue Spot 9 in Zizur Mayor demonstrate strong predictive capability, other blue Spots exhibit moderate performance, indicating areas where the model could be improved.\u003c/p\u003e \u003cp\u003eAccording to the average comparison matrix values in Table\u0026nbsp;\u003cspan refid=\"Tab5\" class=\"InternalRef\"\u003e5\u003c/span\u003e, the TPR value in our study is 0.64, aligning with the findings of the \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.Their study compared the Original Safer_RAIN with the 2D hydrodynamic model IBER for Bara\u0026ntilde;\u0026aacute;in and Zizur Mayor under the same 2010 storm event, reporting a TPR of 0.505 in Bara\u0026ntilde;\u0026aacute;in, which is consistent with our averaged TPR of 0.64 (See Table\u0026nbsp;\u003cspan refid=\"Tab3\" class=\"InternalRef\"\u003e3\u003c/span\u003e in \u003csup\u003e25\u003c/sup\u003e). This suggests that Kinematic Safer_RAIN improves the TPR rate. Additionally, the ACC value in their study is 0.96, which is comparable to our result of 0.91. Furthermore, we achieved an improved MCC value of 0.70, compared to their reported MCC of 0.626. Similarly, the average TPR value in Zizur Mayor is 0.70, compared to 0.309 in the findings of \u003csup\u003e25\u003c/sup\u003e. The ACC and MCC values are comparable in both studies, averaging around 0.9 and 0.5, respectively. While \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e study focused on comparing the Original Safer_RAIN with the IBER model, our research evaluates the Kinematic Safer_RAIN against the HEC-RAS model. Although the two studies are not identical, they share a similar approach of comparing HSFAs with traditional hydrodynamic models. At the time of \u003csup\u003e25\u003c/sup\u003e study, only the Original Safer_RAIN was available. Since then, we tried to advance it, developing the Kinematic Safer_RAIN to achieve greater accuracy and efficiency.\u003c/p\u003e \u003cp\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab5\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 5\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of flooded area results from both HEC-RAS and Kinematic Safer_RAIN simulation results in the potentially flooded blue spots identified in Bara\u0026ntilde;\u0026aacute;in, Pamplona.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\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=\"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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBlue spot\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRainfall Scenario\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTPR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFPR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAUROC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eACC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMCC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e7\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.51\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.49\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.67\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.93\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.85\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.74\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.26\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.86\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.94\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.77\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e14\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.59\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.41\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.99\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.01\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.70\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e16\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.46\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.97\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.03\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.50\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.64\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.36\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.98\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.02\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.91\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.70\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\u003e \u003cdiv class=\"gridtable\"\u003e\u003ctable float=\"Yes\" id=\"Tab6\" border=\"1\"\u003e \u003ccaption language=\"En\"\u003e \u003cdiv class=\"CaptionNumber\"\u003eTable 6\u003c/div\u003e \u003cdiv class=\"CaptionContent\"\u003e \u003cp\u003eComparison of flooded area results from both HEC-RAS and Kinematic Safer_RAIN simulation results in the potentially flooded blue spots identified in Zizur Mayor, Pamplona.\u003c/p\u003e \u003c/div\u003e \u003c/caption\u003e \u003ccolgroup cols=\"9\"\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=\"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 \u003cdiv align=\"char\" char=\".\" class=\"colspec\" colname=\"c9\" colnum=\"9\"\u003e\u003c/div\u003e \u003cthead\u003e \u003ctr\u003e \u003cth align=\"left\" colname=\"c1\"\u003e \u003cp\u003eBlue spot\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c2\"\u003e \u003cp\u003eRainfall Scenario\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c3\"\u003e \u003cp\u003eTPR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c4\"\u003e \u003cp\u003eFNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c5\"\u003e \u003cp\u003eTNR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c6\"\u003e \u003cp\u003eFPR\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c7\"\u003e \u003cp\u003eAUROC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c8\"\u003e \u003cp\u003eACC\u003c/p\u003e \u003c/th\u003e \u003cth align=\"left\" colname=\"c9\"\u003e \u003cp\u003eMCC\u003c/p\u003e \u003c/th\u003e \u003c/tr\u003e \u003c/thead\u003e \u003ctbody\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e9\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.95\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.05\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.92\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.90\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.75\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e10\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.63\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.37\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.76\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.79\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.54\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003e11\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.56\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.44\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.88\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.72\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.81\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.45\u003c/p\u003e \u003c/td\u003e \u003c/tr\u003e \u003ctr\u003e \u003ctd align=\"left\" colname=\"c1\"\u003e \u003cp\u003eAverage\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"left\" colname=\"c2\"\u003e \u003cp\u003e20 July 2010\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c3\"\u003e \u003cp\u003e0.71\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c4\"\u003e \u003cp\u003e0.29\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c5\"\u003e \u003cp\u003e0.89\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c6\"\u003e \u003cp\u003e0.12\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c7\"\u003e \u003cp\u003e0.80\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c8\"\u003e \u003cp\u003e0.83\u003c/p\u003e \u003c/td\u003e \u003ctd align=\"char\" char=\".\" colname=\"c9\"\u003e \u003cp\u003e0.58\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\u003eWe calculated the distribution of water depths using Kinematic Safer_RAIN simulations and compared them with HEC-RAS simulations. A similar comparison was performed for CLSA, with detailed explanations provided in Section \u003cspan refid=\"Sec16\" class=\"InternalRef\"\u003e4.2\u003c/span\u003e. Figure\u0026nbsp;\u003cspan refid=\"Fig12\" class=\"InternalRef\"\u003e14\u003c/span\u003e illustrates the comparison of water depth distributions (in log scale) predicted by HEC-RAS and Kinematic Safer_RAIN for Blue Spot 11 in Bara\u0026ntilde;\u0026aacute;in and Blue Spot 9 in Zizur Mayor. These two blue spots are the most affected and prominent in the study area, as they exhibit the highest TPR among all blue spots. In addition, such real hotspots were validated by newspaper images. \u003csup\u003e25\u003c/sup\u003e also confirmed that Safer_RAIN correctly identifies the main depressions prone to flooding in pluvial flooding events while benchmarking with 2D hydrodynamic models. Similar to the sensitivity analysis of weir width in CLSA, the weir width for blue spots varies depending on their location. In Pamplona, we found that a weir width of 2.5 m in Kinematic Safer_RAIN aligns well with HEC-RAS simulations for the most affected blue spots. Therefore, a weir width of 2.5 m can also be used as a standard parameter for this study area. In general, HEC-RAS predicts deeper water depths, especially at lower exceedance probabilities, indicating its capability to model more severe flooding scenarios. The gap between HEC-RAS and Kinematic Safer_RAIN \u0026lsquo;s water depth distribution lines is because the Kinematic Safer_RAIN uses a hydrostatic approach to simulate the flooding above the blue spot\u0026rsquo;s pour point, while HEC-RAS model uses a hydrodynamic approach, which calculates the backwater effects in a hydraulic manner. Overall, based on the water depth distribution comparison graphs for both Bara\u0026ntilde;\u0026aacute;in and Zizur Mayor, the trends of both models are similar, showing higher water depths at lower exceedance probabilities and lower water depths at higher exceedance probabilities. These case studies confirm that Kinematic Safer_RAIN maintains high computational efficiency while substantially improving the accuracy of predicted flood extents and depths relative to traditional HSFAs; the next section summarizes overall findings and remaining limitations.\u003c/p\u003e \u003cp\u003e \u003c/p\u003e \u003c/div\u003e"},{"header":"5.Conclusions","content":"\u003cp\u003eThis study introduced Kinematic Safer_RAIN, an enhanced Hierarchical Filling-and-Spilling Algorithm that incorporates runoff travel-time distribution and a weir-based formulation to better reproduce inundation above pour points in urban depressions. The original algorithm accounts for spatially distributed rainfall inputs and infiltration processes using a pixel-based Green-Ampt model. Building on the Safer_RAIN module of the SaferPlaces digital-twin platform (\u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://saferplaces.co/\u003c/span\u003e\u003cspan address=\"https://saferplaces.co/\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e), we improved the algorithm\u0026rsquo;s physical realism while preserving computational efficiency \u003csup\u003e\u003cspan citationid=\"CR5\" class=\"CitationRef\"\u003e5\u003c/span\u003e\u003c/sup\u003e. However, due to the nature of the HSFAs, it is limited to containing the flooded extent within the predefined boundaries of blue spots and cannot consider water elevations above their pour point elevations, as any excess flood volume is transferred downstream once a blue spot is fully filled. To address this limitation, we enhanced the HSFA algorithm by incorporating a Kinematic approach, improving its ability to model flood extent beyond blue spot boundaries.\u003c/p\u003e \u003cp\u003eKinematic Safer_RAIN models the travel time distribution of water within watersheds and incorporates the weir equation to describe inundations in which the water elevation can exceed the pour point elevation in some depressions. These enhancements are tested in the Cotton Wood Lake Study Area, a test case study selected due to the availability of freely accessible LiDAR DEM, allowing researchers to test the algorithm. We conducted HEC-RAS Rain-on-Grid (RoG) modelling in this area using uniform rainfall, treating HEC-RAS simulations as the reference, and comparing the results with Kinematic Safer_RAIN. The findings revealed that, in terms of flooding extent within the targeted blue spots, Kinematic Safer_RAIN produced results closely matching HEC-RAS. Across all blue spots. Kinematic Safer_RAIN achieved an average TPR (0.90), ACC (0.95) and MCC (0.88). In terms of water depth distribution, both models exhibit similar trends. After tuning the weir width parameter, the Kinematic Safer_RAIN simulations with a constant weir width of 2.5 m across all depressions provided the best overall match with HEC-RAS results, suggesting that a representative opening width of this magnitude is appropriate for typical urban depressions, though locally adjustable. Differences between Kinematic Safer_RAIN and HEC-RAS arise from their governing equations: the former assumes hydrostatic equilibrium and constant routing velocity, whereas the latter solves full shallow-water dynamics. Despite this simplification, the enhanced algorithm reproduces the spatial extent and depth distribution of floods with good fidelity. By adopting a locally adaptable weir width parameter, Kinematic Safer_RAIN achieved results close to 2D hydrodynamic models while maintaining computational efficiency. This adaptable parameter will be retained and applied in future analyses, particularly for processing LiDAR data.\u003c/p\u003e \u003cp\u003eWe tested the Kinematic Safer_RAIN algorithm in two real case study areas in Pamplona, Spain, during the heavy storm event of July 20, 2010. The blue spots expected to have greater flooding beyond their boundaries align with locations observed in newspaper images. Kinematic Safer_RAIN produced similar flood extents in these blue spots comparable to HEC-RAS simulations. Regarding water depth distribution graphs, both models showed similar trends, with higher water depths at lower exceedance probabilities and lower water depths at higher exceedance probabilities. Some blue spots in the Pamplona metropolitan area are identified as the most affected areas in the study, validated by high True Positive Rates (TPRs) and newspaper image evidence, confirming the reliability of Kinematic Safer_RAIN in identifying flood-prone depressions. A constant weir width of 2.5m in Kinematic Safer_RAIN also aligns well with HEC-RAS simulations for these areas, providing a practical parameter for consistent application across the Pamplona study area. Differences between the models arise from their simulation methods, with HEC-RAS using a 2Dhydrodynamic approach to account for backwater effects and Kinematic Safer_RAIN employing a hydrostatic approach with less computation time.\u003c/p\u003e \u003cp\u003eIn conclusion, the Kinematic Safer_RAIN algorithm demonstrates significant improvements over the original Safer_RAIN (HSFA), as it provides flood extents in blue spots that are much closer to those predicted by HEC-RAS. Additionally, the Kinematic Safer_RAIN outperforms HEC-RAS in computational efficiency, requiring less time for simulations on the same grid cell size and duration. In terms of water depth distribution, the algorithm produces results similar to HEC-RAS, with HEC-RAS focusing on higher, more concentrated depths, while Kinematic Safer_RAIN offers a broader and potentially more realistic distribution, though it may result in slightly higher depths in certain areas. As a hydrostatic nature of this algorithm, Kinematic Safer_RAIN retains the advantage of fast processing but has certain limitations, such as the absence of flooding along the flow path between blue spots. Future work will focus on addressing this limitation, which will be detailed in our next publication. These advances demonstrate that simplified, DEM-based algorithms can bridge the gap between empirical flood-mapping tools and full hydrodynamic models, offering a scalable approach for rapid urban-flood assessment under increasing climatic pressures.\u003c/p\u003e"},{"header":"Declarations","content":"\u003ch2\u003eFunding\u003c/h2\u003e \u003cp\u003eThis publication was produced while the author Kay Khaing Kyaw was attending the PhD programme PhD@DICAM at the University of Bologna, Cycle XXXVIII, with the support of a scholarship co-financed by the Ministerial Decree no. 352 of 9 April 2022, based on the NRRP\u0026mdash;funded by the European Union\u0026mdash;NextGenerationEU\u0026mdash;Mission 4 \u0026ldquo;Education and Research\u0026rdquo;, Component 2 \u0026ldquo;From Research to Business\u0026rdquo;, Investment 3.3, and by the company GECOsistema\u0026mdash;Geographic Environmental Consulting, Rimini (RN), Italy. This research was also partly funded by the projects LIFE21-IPC-IT-LIFE CLIMAX PO, CLIMate Adaptation for the PO river basin district (grant agreement number: 101069928; WP7; Task: 7.1) and DIRETED - DIsaster Resilience for Extreme ClimaTe Events providing interoperable Data, models, communication and governance- grant agreement ID: 101073978.\u003c/p\u003e\u003ch2\u003eAuthor Contributions\u003c/h2\u003e \u003cp\u003eConceptualization, K.K.K., and A.C.; methodology, K.K.K. and A.C.; software, S.B. and K.K.K.; validation, S.B. and K.K.K.; formal analysis, S.B and K.K.K.; investigation, L.M ., S.B ., A.C. and K.K.K.; data curation,, L.M., S.B. and K.K.K., writing\u0026mdash;original draft preparation, L.M., S.B., A.C. and K.K.K.; writing\u0026mdash;review and editing, L.M., S.B., A.C. and K.K.K.; visualization K.K.K.; supervision, A.C.; project administration, S.B. and A.C.; funding acquisition, S.B. and A.C.. All authors have read and agreed to the published version of the manuscript.\u003c/p\u003e\u003ch2\u003eAcknowledgements\u003c/h2\u003e \u003cp\u003eThe authors would like to acknowledge the Spanish Instituto Geogr\u0026aacute;fico Nacional(IGN) for supplying the digital terrain model and land-cover data, and the Sistema Autom\u0026aacute;tico de Informaci\u0026oacute;n Hidrolog\u0026iacute;ca (SAIH) real-time system of the River Ebro Basin Authority, the Regional Government of Navarre and the Universidad P\u0026uacute;blica de Navarra (UPNA) for supplying the rainfall data used in the Spanish case studies. The rainfall inputs come from \u003csup\u003e25\u003c/sup\u003e, as Peio Oria was the paper co-author that developed the rainfall fields we are using.\u003c/p\u003e\u003ch2\u003eData Availability\u003c/h2\u003e \u003cp\u003eLiDAR DEM is publicly accessible using the lidar python package, which can be found in the link: \u003cspan class=\"ExternalRef\"\u003e\u003cspan class=\"RefSource\"\u003ehttps://github.com/opengeos/lidar\u003c/span\u003e\u003cspan address=\"https://github.com/opengeos/lidar\" targettype=\"URL\" class=\"RefTarget\"\u003e\u003c/span\u003e\u003c/span\u003e \u003csup\u003e\u003cspan citationid=\"CR21\" class=\"CitationRef\"\u003e21\u003c/span\u003e\u003c/sup\u003e. Rainfall fields that we used in Pamplona case study area are obtained from previously published work \u003csup\u003e\u003cspan citationid=\"CR25\" class=\"CitationRef\"\u003e25\u003c/span\u003e\u003c/sup\u003e.\u003c/p\u003e"},{"header":"References","content":"\u003col\u003e\u003cli\u003e\u003cspan\u003eNlend B et al (2025) Building resilient urban water systems: emerging opportunities for solving long-lasting challenges. Hydrol Sci J 70:2003\u0026ndash;2015\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eGhimire B et al (2013) Formulation of a fast 2D urban pluvial flood model using a cellular automata approach. J Hydroinformatics 15:676\u0026ndash;686\u003c/span\u003e\u003c/li\u003e \u003cli\u003e\u003cspan\u003eZhou Q et al (2021) A GIS-Based Hydrological Modeling Approach for Rapid Urban Flood Hazard Assessment. 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J Hydrol (Amst) 537:138\u0026ndash;145\u003c/span\u003e\u003c/li\u003e\u003c/ol\u003e"}],"fulltextSource":"","fullText":"","funders":[],"hasAdminPriorityOnWorkflow":false,"hasManuscriptDocX":true,"hasOptedInToPreprint":true,"hasPassedJournalQc":"","hasAnyPriority":true,"hideJournal":true,"highlight":"","institution":"","isAcceptedByJournal":false,"isAuthorSuppliedPdf":false,"isDeskRejected":"","isHiddenFromSearch":false,"isInQc":false,"isInWorkflow":false,"isPdf":false,"isPdfUpToDate":true,"isWithdrawnOrRetracted":false,"journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true},"keywords":"Urban flooding, Flood hazard hotspots, Hierarchical Filling-and-Spilling Algorithms, Hydrodynamic Modelling, Simplified pluvial flood modelling, Weir Equation","lastPublishedDoi":"10.21203/rs.3.rs-9492481/v1","lastPublishedDoiUrl":"https://doi.org/10.21203/rs.3.rs-9492481/v1","license":{"name":"CC BY 4.0","url":"https://creativecommons.org/licenses/by/4.0/"},"manuscriptAbstract":"\u003cp\u003ePluvial flood modelling plays a critical role in enhancing flood preparedness in urban areas, where such events pose significant risks to communities and infrastructure. Recent studies underscore the ongoing challenges in flood modelling, particularly the need to balance accuracy and computational efficiency. Existing models often fall into two categories: highly detailed but computationally intensive, or fast processing yet overly simplified, which compromises their ability to capture essential flow dynamics. In this study, we improve an existing and widely used simplified approach, i.e. the Hierarchical Filling-and-Spilling Algorithms (HSFAs). The original HSFA approach generally underpredicts the inundated areas and maximum water depths as it cannot inundate an urban depression above its spilling point, due to its hydrostatic assumptions. We incorporate a kinematic runoff travel time distribution within watersheds and weir equations at watersheds\u0026rsquo; spilling points. Our proposed modifications enable a simplified yet physics-based representation of the depression filling above its spilling point, resulting in a more accurate overall flooded extent and water depths. The algorithm was tested on a case study in the Cottonwood Lake area, USA, where freely available input data facilitated code development and reproducibility. Additionally, it was applied to a real-world pluvial flooding event in Pamplona, Spain, for further evaluation. A comparison of the algorithm\u0026rsquo;s results with the outputs of 2D hydrodynamic models demonstrated a similar representation of flooding extents around depressions. Finally, we discuss the potentials and limitations of the enhanced algorithm and propose directions for future research to further improve pluvial flood modelling.\u003c/p\u003e","manuscriptTitle":"Fast-Processing Modelling of Urban Pluvial Flooding: Kinematic Hierarchical Filling-and-Spilling Algorithm","msid":"","msnumber":"","nonDraftVersions":[{"code":1,"date":"2026-04-23 09:36:19","doi":"10.21203/rs.3.rs-9492481/v1","editorialEvents":[{"type":"communityComments","content":0}],"status":"published","journal":{"display":true,"email":"[email protected]","identity":"researchsquare","isNatureJournal":false,"hasQc":true,"allowDirectSubmit":true,"externalIdentity":"","sideBox":"","snPcode":"","submissionUrl":"/submission","title":"Research Square","twitterHandle":"researchsquare","acdcEnabled":true,"dfaEnabled":false,"editorialSystem":"","reportingPortfolio":"","inReviewEnabled":false,"inReviewRevisionsEnabled":true}}],"origin":"","ownerIdentity":"b9c61f8f-bd0d-4559-8de0-2b216cb342a4","owner":[],"postedDate":"April 23rd, 2026","published":true,"recentEditorialEvents":[],"rejectedJournal":[],"revision":"","amendment":"","status":"posted","subjectAreas":[{"id":66789533,"name":"Environmental Engineering"}],"tags":[],"updatedAt":"2026-04-23T09:36:20+00:00","versionOfRecord":[],"versionCreatedAt":"2026-04-23 09:36:19","video":"","vorDoi":"","vorDoiUrl":"","workflowStages":[]},"version":"v1","identity":"rs-9492481","journalConfig":"researchsquare"},"__N_SSP":true},"page":"/article/[identity]/[[...version]]","query":{"redirect":"/article/rs-9492481","identity":"rs-9492481","version":["v1"]},"buildId":"XKTyCvWXoU3ODBz1xrDgd","isFallback":false,"isExperimentalCompile":false,"dynamicIds":[84888],"gssp":true,"scriptLoader":[]}