Estimating Flood Inundation in Urban Areas Using a Scenario Generation Method and Inundation Graphs

Abstract

As the frequency and intensity of natural and social disasters increase due to climate change, damage caused by disasters affects urban areas and facilities. Of those disasters, inundation occurs in urban areas due to rising water surface elevation because of concentrated rainfall from storm surges or urban drainage system failures. For this research, a scenario generation method for estimating flood inundation was developed to analyze the flood effects on urban areas to prepare for disasters and minimize damage. A scenario generation method using various distribution functions and return periods was developed and applied to create input values for the flow model for inundation analysis. By simulating multiple scenarios using a two-dimensional flow model and storing its results into a graph-form database called an inundation graph, it is possible to assess the probability and potential impact of different flood events quickly, which could be later used for disaster response and prevention. The flood risk and flood vulnerability of each section of the urban area could be evaluated based on the input data from the scenarios and the results of the flood analysis.

1. Introduction

Urban areas and infrastructure are impacted by natural and social disasters and the frequency and severity of natural and social catastrophes are rising due to climate change. Urban areas experience inundation from these disasters due to elevated water levels caused by concentrated rainfall from storm surges or by rural storm sewer drainage failures. These inundation events cause human casualties and high property damage in densely populated urban areas. This is a phenomenon that is taking place globally across all continents and is becoming a worldwide issue [1]. Also, there is a greater chance of flooding and increased damage as a result of land use change and urbanization.

In previous attempts to mitigate damage from inundation, conventionally large-sized structures were constructed near potential inundation areas based on former measured flooding data. Later, the focus shifted to using other solutions such as the installation of green infrastructure or monitoring systems for measures against floods [2]. However, these other solutions had limitations in mitigating extreme flood situations, so understanding and analyzing past and potential extreme floods still remain an important part of flood mitigation. Recently, analysis of extreme floods was done via the development and application of computer models to simulate the flood size, water depth, duration, flow velocity, and damages that occur in these events in order to identify and study the effects of the inundation in urban areas [3,4]. The amount of study on flood inundation models and related issues has increased significantly over the past three decades due to the fact that floods account for a sizable portion of natural catastrophes that are reported worldwide [5].

Flood inundation models have recently been used in combination with an approach and strategy for the mitigation and prevention of flood disasters based on risk assessment studies. As a result, research on the risk and effects of flood damage has grown in recent years [6,7]. Also, flood scenarios were utilized for flood vulnerability analysis in order to control flood risk and mitigate disasters [8,9]. Risk assessment studies usually include an estimation of how vulnerable flood-prone areas are, or the potential loss and damage from flood events of varying magnitudes [10,11]. Combined with hydrological models and hydrodynamic river models, the application of flood modeling has been extended to modeling that aims to formulate risk mitigation strategies from these flood events [12]. For flood risk mitigation planning, flooding scenarios with respect to future conditions were continuously applied for flood damage evaluation [13,14,15].

In reference to flood modeling, this study dealt with scenario creation and its application using similar methods used by the hydraulic performance graph for data accumulation. The hydraulic performance graph is a method that calculates the drainage level curve for all possible flow conditions in a section of an arbitrary number of channels and displays them in a graph [16]. In this method, the relationship between the downstream water level and upstream water level for all possible flow conditions in each channel section is shown on a single graph, and all possible downstream water level ranges are included. The governing equation of the flow calculation in this method was originally derived from the one-dimensional energy equation. After using the topographical data, the slope, roughness coefficient, and length of the channel as the input, the area and radius of the section are calculated first, and then the water depth, uniform flow depth, and drainage level of the channel are estimated. This method has been shown to be useful in creating structural or non-structural flood defense measures [17]. To depict the stage-discharge relations for open channel flows, the hydraulic performance graph was later modified to build a theoretical water level-flow connection [18]. Additionally, a volumetric performance graph (VPG) was developed based on the earlier results and was compared with actual experimental data [19], and in later research it was also used for application in complex river networks [20].

Following the previous research related to flood scenarios used for vulnerability analysis and the hydraulic performance graph, a new scenario generation algorithm tool for estimating flood inundation was developed to analyze the flood effects on urban areas to prepare for disasters and minimize damage. This algorithm generates synthetic or hypothetical flood events that may occur in a given area, based on measured precipitation data from former events and other relevant information such as terrain and topography. By generating multiple scenarios using a two-dimensional flow model and storing its results in a graph-form database called an inundation graph, it is possible to assess the probability and potential impact of different flood events quickly. This can improve decision-making regarding flood protection measures. Additionally, in the event of an emergency involving flash floods, the user can quickly and conveniently estimate the inundation water level using the stored database instead of utilizing a two-dimensional flow model during the event.

2. Methodology

2.1. Model for Application

The model used for this research is the HDM-2D model, which is an unsteady two-dimensional depth-averaged flow model using the Petrov–Galerkin stabilization approach. The model uses the depth-averaged mass and momentum equations, as shown in Equations (1) and (2) [21,22].

$$\frac{\partial h}{\partial t}+h\frac{\partial u_j}{\partial x_j}+u_j\frac{\partial h}{\partial x_j}=0$$

(1)

$$\frac{\partial u_i}{\partial t}+u_j\frac{\partial u_i}{\partial x_j}=-g\frac{\partial (H+h)}{\partial x_i}+\frac{\partial }{\partial x_j}\left({\nu }_T\frac{\partial u_i}{\partial x_j}\right)-g{n}^2\frac{u_i\sqrt{u_j{u}_j}}{h^{4/3}}$$

(2)

where $t$ is time; $u_1,u_2$ are the vertically averaged velocity components corresponding to the $x$, $y$ directions, respectively; $g$ is the acceleration of gravity; $H$ is bottom elevation and $h$ is flow depth, $n$ is Manning’s roughness coefficient, and ${\nu }_T$ is kinematic eddy viscosity. The above-shown equations are written using the indicial notation and the Einstein summation convention for repeated indices. Through solving equations that use principles of mass and momentum conservation, the model utilizes boundary conditions of discharge and water surface elevation to calculate the water velocity and depth outputs for the constructed grids. This enables the model to estimate hydraulic parameters within complex topographical settings. The model has shown accuracy in modeling and its assessments in later research, with continuous validation and practical implementation showing a mass conservation error of less than 0.7% [23]. Also, it was applied to the confluence of the primary and tributary channels [24] and was employed for application with a pollutant dispersion model [25]. Furthermore, the model was applied to a dam break problem and showed the ability to simulate subcritical and supercritical transition, with some limitations showing discrepancies immediately after the break [26,27]. Also, some inaccurate performance was observed at the joint area of the main and tributary channel when applied to a confluent channel due to the three-dimensional flow structure in the joint area [21]. Recent applications have been associated with inland flooding and river inundation, using a wet/dry handling technique using a flux-blocking scheme also known as the thin film method [28,29,30]. Therefore, this model was applied to this study for scenario application due to its capabilities.

2.2. Scenario Generation and Application

The proposed scenario generation method is presented in Figure 1. First, this scenario generation includes the estimation of rainfall based on high return periods using widely used theoretical statistical distributions known as the Gumbel distribution and Generalized Extreme Value (GEV) distribution. The second part involves flood inundation modeling using the introduced two-dimensional flow model. For the rainfall estimation, the method utilizes return periods of up to 500 years based on the regional rainfall data that were collected using local hydrologic data from the Flood Control Offices. Since there is limited data availability for extreme precipitation, the precipitation data for extreme floods were recreated using the two distributions. Considering methods used by former research on flood scenario generation, the amount of runoff that can occur from extreme rainfall for each scenario was calculated taking into account the recent high rainfall. After examining the maximum rainfall data by year of the rainfall station in the target area, these data were used as sample data to estimate the variables of the Gumbel and GEV distribution, which can be used for rainfall calculation frequency [31,32]. Equation (3) is the CDF for the Gumbel distribution, and the parameters $\alpha$ and $\xi$ can be estimated using Equations (4) and (5) [33].

$$F_X(x)=\exp \left[-\exp \left(-\frac{x-\xi }{\alpha }\right)\right]$$

(3)

$${\mu }_X=\xi +0.5772\alpha$$

(4)

$${\sigma }_X^2=\frac{{\pi }^2}{6}{\alpha }^2\approx 1.645{\alpha }^2$$

(5)

where ${\mu }_X$ is the sample mean and ${\sigma }_X^2$ is the sample variance. Equation (6) is the CDF for the GEV distribution, and the GEV parameters were computed using the L-Moments method [34]. The parameters $\alpha$, $\xi$, and $\kappa$ can be estimated with Equations (7) and (8).

$$F_X(x)=\exp \left[-{\left(1-\frac{\kappa (x-\xi )}{\alpha }\right)}^{1/\kappa }\right]$$

(6)

$${\mu }_X=\xi +\left(\frac{\alpha }{\kappa }\right)\left[1-\mathsf{\Gamma }(1+\kappa )\right]$$

(7)

$${\sigma }_X^2={\left(\frac{\alpha }{\kappa }\right)}^2\left[\mathsf{\Gamma }(1+2\kappa )-{\{\mathsf{\Gamma }(1+2\kappa )\}}^2\right]$$

(8)

Using the estimated variables, the Gumbel and GEV distribution suitable for the rainfall data from the rainfall observation station was constructed, and the rainfall in the designated return period for each scenario was calculated by calculating the inverse function of the cumulative probability of the Gumbel and GEV distribution. Then, using the rainfall from the return periods, the empirical rational flow formula for discharge was utilized to estimate the discharge in the target area. Then the discharge values were used as the scenario boundary conditions for the introduced two-dimensional model. This calculation of inundation elevation through simulation would be based on various scenario-based model boundary condition changes to conduct multiple versions of simulating scenarios. The database storage of results was undertaken using the results of the two-dimensional flow model, so for the upstream water depth or the target point of interest, additional two-dimensional flow modeling would be less necessary since modeling was pre-conducted.

3. Application Results

The field target area of study is the Gampo Sewage Treatment Plant, which is located near Gyeongju City as the first sewage treatment plant built as a pilot project for sewerage advancement. There is a small river to the north of the sewage treatment plant, so areas where flooding may occur in the event of flooding are analyzed. The buildings and areas that would be later used for the inundation graph creation are depicted in Figure 2.

The runoff of the target area corresponding to the calculated rainfall was estimated using an empirical rational formula. Then, the scenario generation method was applied to create input values and boundary conditions for the flow model for inundation analysis. Flood risk and flood vulnerability of each urban area were evaluated based on the input data from the scenarios and the results of the flood analysis. For this field target area, the scenario generation used return periods of 50, 100, 200, and 500 years, based on the regional rainfall data that was collected using local hydrologic data from the Flood Control Offices. After collecting the maximum rainfall data by year of the rainfall station in the target area up to 57 years, these data were used as sample data to estimate the variables for the theoretical distributions, which was used for rainfall estimation for higher return periods up to 500 years. The Gumbel and GEV distribution suitable for the rainfall data of the observation station was constructed, and the rainfall in the designated return period for each scenario was calculated. The distribution functions for the measured precipitation for the target area, for time scales of 9 h of rainfall, were compared with the observed rainfall using the Weibull plotting position in Figure 3.

The comparison with observed data showed the mean absolute percentage error was 13.3% and 4.8% for the Gumbel and GEV distribution. Also, the coefficients of determination from the two distribution functions were 0.79 and 0.88 for the Gumbel and GEV distribution. The results show that both Gumbel and GEV distributions are appropriate for modeling, but the GEV had better accuracy. Next, the flow-time distribution using Huff’s third-quartile classification of rainfall intensity profiles was also created. Finally, the rational method for runoff [35] was utilized to estimate the flow rate in the target area shown in Figure 4.

The discharge boundary conditions for the two-dimensional flow model for inundation analysis used the time-discharge values from the estimated flow rate. For the river overflow conditions for the water surface elevation, the conventional power function equation $Q=C{(h-h_0)}^m$ were applied to the ungauged small river which was located in the north part of the target area shown in Figure 5, using similar C values from stage-discharge equations developed in a nearby city since actual measured stage data at the river in the model was not available. Then for the flow model, a triangular mesh was constructed using topographical data from the site, which consisted of 6684 elements and 3558 nodes shown in Figure 5.

Using the flow rates from the return period scenarios, the two-dimensional flow simulation was conducted through several cases of scenarios. The results of the estimated depth were then stored in the inundation graph. Originally, the results of running the two-dimensional flow model in various cases would have looked similar to those in Figure 6, which depicts all the scenarios with 50–200-year flood frequency based on the theoretical functions of Gumbel and GEV. Although this is the typical result for two-dimensional simulation, the target area of interest may be located in a specific area of the constructed mesh.

Figure 7 shows the induction graph for the target area of interest A from the buildings that were originally shown in Figure 2. Although Figure 6 is also suitable for inundation analysis, the inundation graph in Figure 7 can provide valuable information quickly to decision-makers related to water management administration who may not be familiar with flow models, especially in rural areas or local government. The estimated depth values to a certain area of interest can be shown more clearly based on flood frequency quantitively. This could be essential in some situations where it could be challenging for regional water management employees to perform the simulation on their own if they are not familiar with flow models. Since there may be issues, particularly in remote regional government areas where there might not be enough qualified researchers monitoring the target areas, an inundation graph created in this study would be beneficial in decision and policy-making.

Figure 8 is an inundation graph using the results of the unsteady flow simulation for the target area of interest A. Instead of using the maximum values from the estimated flowrate for the return period scenarios in Figure 4, it used the time–discharge values for the input boundary condition for the unsteady flow simulation. The results show the time–depth graph for each of the scenarios, using both distribution functions and various return periods. This graph could also serve as a tool to provide valuable information to decision-makers.

4. Discussion

Another possible way to apply this developed scenario method is by targeting the simulation results to specific areas in the site shown in Figure 9. This would be necessary if the target region included structures of interest; the sewage plant’s settling pond, reactor, and chamber were among the buildings that made up the application’s present target site. The various flood scenarios can demonstrate each urban building’s vulnerability and be used for additional assessment. The graph also shows the difference in results when using different distribution functions up to 11 percent of estimated depth, which depicts the importance of using various scenarios for extreme events such as the return period of 500 years. Later, these results could lead to Intensity–Duration–Frequency (IDF) curve creation and further analysis of the difference between the extreme value distributions using other theoretical distributions such as Log-Pearson III.

In the analysis of the developed scenario generation method, a flood hazard rating index was used to show what scenario results would be considered dangerous to individuals [36,37]. The index is shown below:

$$HR(i)=h(i)\times \left\{v(i)+0.5\right\}$$

(9)

where HR is the flood hazard rating index at point i, $h(i)$ is the water depth at point i, and $v(i)$ is the velocity magnitude of the water at point i. The utilized application flow model is a depth-averaged model, and the flow velocity is two-dimensional so there is a vector for the x-direction and y-direction. The velocity magnitude will then be the square root of the sum of the squares of velocities in the x and y directions. The result of the hazard rating is shown in Figure 10, with the scenario return period for the y-axis and time used in Figure 8 for the unsteady simulation as the x-axis. The time used is the same time for the unsteady simulation that is depicted in Figure 8 in a scenario, which uses input from the estimated flow rate in Figure 4. As water depths are calculated during the time span, the flow velocity is also calculated and used in creating the hazard matrix. If the HR is less than 0.75, floodwater would cause minimal damage to individuals; if it is more than 2.5, there is a high risk of damage [36,37]. The safety in flood situations would be calculated using these thresholds of 2.5 and 0.75 for classification. The results were shown in a matrix form for each building, to find the values of the flood hazard rating index for scenarios easily. The created matrix is shown below with application from the scenarios. Buildings A and B which are the settling pond and reactors showed high flood hazard rating values in certain scenarios, while building C showed low values, which would be considered relatively safe.

In regard to the hazard rating matrix, the formulation of a flood danger matrix and the corresponding hazard rating are generally based on expert judgment and customized to a particular case study such as this research. Various classifications of flooding hazards exist, and there is a lack of standardization on an international scale. Standardizing the assessment of flooding hazards is another issue on this topic, so this research decided to continue selecting a previous version which is simple and physically grounded based on water depth and velocity.

Overall, the main points of this paper are the following:

• This study created a scenario generation algorithm based on return periods and extreme value distributions using a two-dimensional flood model with the inundation method storing database according to various flood scenarios;
• This study provides a tool that could analyze the potential impact of different flood events using a pre-stored inundation database;
• The advantage of the method developed in this study is that by using the stored database, the user can secure speed and convenience in calculating the estimated water level without using a time-costly two-dimensional flow model in case of flash floods.

The inundation graphs for various flow conditions according to flood frequency are prepared and displayed so they can be easily utilized by composing the result of water level calculation in the form of several graphs according to the flow rate. In order to use an arbitrary return period or starting point water level that has not been pre-calculated and stored in the inundation graph database, an additional application process using interpolation or an index matrix would be helpful.

For consideration, some limitations exist in the fact that the modeling performance to the target area for application should have been evaluated with actual observed data at the site. Due to the recent typhoon in 2020, nearby areas that were 1 km away from the site experienced flood damage from the sudden and large typhoon. Nevertheless, the target area did not have an official water gauge site to measure the increased water elevation or have areas where the inundation was measured for the incident. With actual measured stage values, a stage-discharge equation would have been applied to the boundary condition, which is the typical method for river modeling. However, since this area was an ungauged site, values in which ranges were expected had to be applied to the model. Other methods using discharge estimation and rating curve development at ungauged river sites could require additional routing methods such as the Muskingum stage hydrograph routing method [38]. Using the conventional power function equation $Q=C{(h-h_0)}^m$ where $C,$ $h_0,$ and $m$ are constants would be another option if some data were available [39]. The constant $m$ in some cases is known to be near 2 [39], but estimating the $C$ without actual data proved to be difficult. Stage-discharge equations developed in a nearby city had C values of near 1100, which was used in the model. Using nearby streams with similar characteristics would originally require regionalization methods which involve utilizing information from gauged sites to ungauged sites based on similarities in physical and climate characteristics [40]. The nearby city watershed had similar climate and channel materials, and the channel geometric characteristics had similarities in bottom width. Although some aspects of regionalization were conducted, there still remains the fact that actual measured data directly from the site were not used, which leads to uncertainty in flood simulation results and a limitation for this study.

Another point for discussion is the uncertainty of using theoretical statistical distributions for extreme floods. Figure 3 shows an underestimation of rainfall depth compared to the largest recorded rainfall, which is the return year of 58, but this type of discrepancy is also shown in previous research [41]. This could be reasonable, but the fact remains that high return periods have uncertainty in estimation and must be considered in using theoretical statistical distributions. Since extreme events are by definition rare, it is difficult to reliably estimate extreme quantiles from the site data, which frequently comes from limited record lengths. Regional frequency analysis could be conducted to deal with this problem, but this was out of the scope of this research.

Finally, instead of using an empirical equation for the flow rate estimation based on rainfall, an additional rainfall–runoff model would produce more accurate results. The utilization of a runoff model and the routing method was out of scope for this study, but it could be considered for future research.

5. Conclusions

Urban areas and infrastructure are impacted by disaster damage when the frequency and severity of natural catastrophes rise due to climate change. Among these catastrophes, inundation occurs in urban areas as a result of increasing water surface height caused by storm surge-induced concentrated rainfall or drainage failures. In order to prepare for disasters and lessen damage, a scenario generation method for calculating flood inundation was developed for this research. Scenario generation methods can be important for flood inundation analysis because they help simulate various flood scenarios, which can provide quick critical information for emergency management and flood risk assessment.

A scenario generation method was developed and applied to create input values and boundary conditions for the flow model for inundation analysis. By simulating multiple scenarios using a two-dimensional flow model and storing its results in a graph-form database called an inundation graph, it is possible to assess the probability and potential impact of different flood events quickly, which could be later used for disaster prevention. Flood risk and flood vulnerability of each section of the urban area could be evaluated based on the input data from the scenarios and the results of the flood analysis. By using two widely used extreme value distributions of Gumbel and GEV, the rainfall data near the site were analyzed for the estimation of rainfall frequencies, which were later used as an input for the rational flow formula for runoff. The time–discharge values from the runoff in several return periods were used as discharge boundary conditions for multiple scenarios. Then by using the generated scenarios, multiple runs of the two-dimensional model were conducted to create the inundation graph. In the analysis of the developed scenario generation method, a flood hazard rating index was also created to show what flood scenarios would be considered dangerous to individuals in certain areas.

A limitation to this study is the fact that the research was based on an ungauged site. Also, there are limitations to the model since this is a two-dimensional model, and there could be some inaccuracy when depicting areas that require 3D modeling, such as the joint area of the main and tributary channel when applied to a confluent channel, due to the three-dimensional flow structure in the joint area. Furthermore, the model showed some limitations when applied to a former dam break problem, showing some discrepancy immediately after the break which has three-dimensional characteristics.

The results of this research and its scenario generation algorithm showed that they could be used as a useful tool for accurate flood inundation analysis, providing valuable insights into the potential impact of different flood events and informing flood risk management. This method in this study could be a valuable tool and guide, providing risk and safety information quickly to decision-makers related to water management administration who may not be familiar with flow models, especially in rural areas or local government.