*2.1. Overview*

Two procedures are used in the selection of monitoring nodes for cooperative operation of drainage facilities. The first step identifies the node where overflow first occurs, and the second identifies nodes where the maximum overflow occurs. Each procedure is described below.

The first flooding node is determined using rainfall probability, as proposed by Huff [14], with selection of an appropriate quartile for the study basin. The Huff formula distributes rainfall in a selected quartile once the event duration is selected. The Storm Water Management Model (SWMM) is run with uniform rainfall depths, starting at 1 mm and increasing by 1 mm until flooding occurs. The node where the first flooding occurs is designated as one of the monitoring nodes. We continue to

review the first flooding node as rainfall duration changes. We also identify the maximum flooding node using the Huff distribution.

There are four quartiles in the Huff distribution. Equations (1)–(4) are different from other regions because these are the ones available in Seoul (Korea Precipitation Frequency Data Server, www.k-idf.re.kr) [15]. The quartiles in the Huff distribution represent the peak values in the rainfall data. The appropriate quartile is selected for the study area from among the four quartiles of the Huff distribution, each of which has a different timing of peak rainfall. For example, the maximum value of the first quartile is located between 0% and 25% of the total rainfall duration. The maximum values of the second, third, and fourth quartiles are then located between 25% and 50%, 50% and 75%, and 75% and 100% of the total rainfall duration.

When an appropriate Huff quartile is selected for the basin, synthetic precipitation occurs according to frequency and duration times. Rainfall-runoff simulation depends on rainfall probability. The node with the highest flood volume is selected as the second monitoring node. In the study area of Seoul, the first, second, third and fourth Huff quartiles are determined using Equations (1)–(4), respectively.

$$y = 29.289 \text{x}^6 - 95.64 \text{x}^5 + 119.7 \text{x}^4 - 70.768 \text{x}^3 + 18.176 \text{x}^2 + 0.2426 \text{x} - 0.0007 \tag{1}$$

$$y = -38.505x^6 + 118.93x^5 - 132.67x^4 + 60.815x^3 + 8.3001x^2 + 0.7296x + 0.0005\tag{2}$$

$$y = 37.835x^6 - 106.21x^5 + 105.18x^4 - 44.549x^3 + 9.1084x^2 - 0.3603x + 0.0005\tag{3}$$

$$y = -25.498 \mathbf{x}^6 + 63.75 \mathbf{\tilde{x}}^5 - 57.196 \mathbf{x}^4 + 22.882 \mathbf{x}^3 - 3.437 \mathbf{\tilde{x}}^2 + 0.4955 \mathbf{x} - 0.0002 \tag{4}$$

where *y* indicates the accumulated rainfall ratio and *x* indicates the accumulated time ratio. The time ratio *x* is cumulative time divided by total rainfall duration. The rainfall ratio *y* is cumulative rainfall at time ratio *x* divided by total rainfall. The third quartile of the Huff distribution is selected to review the first and maximum flooding nodes in the target basin. Yoon et al. (2013) suggested that the third quartile in the Huff distribution is appropriate for South Korea [16]. Figure 1 describes the complete process for obtaining rainfall data using the Huff distribution.


**Figure 1.** Process for obtaining rainfall data using the Huff distribution.

Using the process in Figure 1, each rainfall event can be obtained using the Huff distribution. If the total rainfall amount is 100 mm and the duration is 90 min in the third quartile, we can obtain rainfall data using the Huff distribution and use it as input data for the rainfall-runoff model. The total rainfall amount is set to 11 mm, in 1 mm increasing intervals, if there is no flooding after simulation of the rainfall-runoff model. This process is repeated until there is flooding in one node. We call this node the first flooding node.

SWMM, developed by the United States Environmental Protection Agency (US-EPA) in 1971, was used to simulate the rainfall-runoff process and to investigate the first and maximum flooding nodes. SWMM has been developed to simulate the flow volume and water quality within urban drainage systems. SWMM can be used for planning, analysis, and design related to stormwater runoff, combined/sanitary sewers, and other drainage systems in urban areas. Furthermore, it can be used in rural area simulations. It is a comprehensive model that can be used to simulate runoff volume caused by rainfall events and runoff of pollutants in surface and sewer pipes, to trace runoff volume in sewer distribution networks, and to calculate retained volume [17]. Users can select either steady-flow routing, kinematic wave routing, or dynamic wave routing as flow routing options in SWMM.

We analyze the flooding that is contingent on CR operation on the basis of monitoring node levels. When the level at the monitoring node indicates possible flooding of sewer conduits, the backwater effect caused by high CR water level is minimized by operation of drainage pumps in order to reduce the burden on sewer conduits. Thus, flooding is reduced through early operation of pump station drainage pumps to minimize CR levels.

We applied the method of Lee et al. to DR operation analysis based on monitoring node levels [18]. One of the weaknesses of urban detention reservoirs is a vulnerability to continuous rainfall. To counter this, we secure additional space in the DR by operating drainage pumps if the sewer conduit levels, identified by the monitoring node, are low. However, if the level of the DR is higher than the limit (discharge level), discharge in the DR is initiated whilst current drainage facility operations are performed.

We also evaluate cooperative operation of CR and DR based on monitoring node levels. Discharge released in order to secure additional space in the DR is transported to the CR at the basin outlet through the drainage system. Backwater effects of the CR are reduced by early discharge of reserved water. The ultimate goal of cooperative operation is to reduce inundation in urban areas. This is achieved through efficient sharing of flood discharge by linking the operation of drainage facilities, such as upstream detention reservoirs in drainage areas, with other drainage facilities, such as downstream pump stations. In addition, we develop a resilience index to quantify the ability of the system to mitigate inundation (i.e., system failure), and then quantitatively compare current and new operational approaches of drainage facilities. Resilience of drainage systems can be calculated on the basis of patterns from flooding to recovery. Figure 2 summarizes the cooperative operation approach used in our study.

**Figure 2.** Flowchart for cooperative operation of urban drainage systems.

### *2.2. Components of Urban Drainage Systems in Korea*

The pump stations that are currently installed and operational in Korea are divided into two types; those with and without CR. Pump stations without CR are usually installed in small basins that have low maximum inflow, and pump stations with CR are installed in large basins with high maximum inflow. In addition, gate pump stations have recently been introduced, but these are largely limited to basins without CR. The structure of a typical pump station with CR is shown in Figure 3.

**Figure 3.** Structure of a typical pump station with a centralized reservoir.

For each CR in pump stations, a High Water Level (HWL) and a Low Water Level (LWL) are defined. The initial and total operating levels for drainage pumps are determined between the LWL and the HWL (Figure 3). The LWL is above the base of the CR and the initial operating level is higher than the LWL in order to prevent cavitation of drainage pumps, which may occur when there is no CR inflow.

The DR is located in the midstream and upstream; it is connected to sewer conduits or rivers, and is designed to reduce peak discharge (Figure 4). There are two types of DR, online and offline. An online DR is generally larger and is effective in continuous storms. However, due to its large capacity, it is difficult to install in urban areas. An offline DR is generally smaller, and is not so effective in continuous storms, but its small capacity makes it easy to install in urban areas.

**Figure 4.** Structure of a typical decentralized reservoir.

Operation of the offline DR is controlled by inlet and outlet components. The height of the inlet weir directly affects DR operation and its capacity to retain runoff. However, once weir height is determined, there is no way to control inflow volume. With consideration of current design standards (only inflow which goes over the weir at a fixed height can be delivered), it is impossible to control inflow volume during operation. Thus, it is important to focus on controlling outflow volume in order to secure additional space within the DR. Using outflow control, the DR retains rainfall until the rainfall event ends, and then initiates runoff within a designed exclusion time or until the limit for drainage is reached. However, this operation has some disadvantages. As detention or drainage is performed without consideration of the condition of the sewer conduits, it is vulnerable to flooding. In addition, if it continues to rain, the DR retains the first peak inflow and is then full so cannot store additional inflow. To compensate for this, runoff is regulated according to the condition of the sewer distribution network in order to secure space for the first peak inflow as well as additional inflow.

### *2.3. Operation of Urban Drainage Facilities*

Pump stations operate drainage pumps based on the level of the CR. The initial operating level of drainage pumps is set by taking into account cavitation and flood volume. When rainfall occurs, drainage pumps are activated if the CR reaches the initial operating level. After that, the operating level is determined by considering the capacity, number of drainage pumps, CR area, and effective depth. As the CR is operated on a fixed level basis, without considering sewer conduit conditions, it is not effective for reducing inundation.

For operation of the CR proposed in this study, we select monitoring nodes representative of the sewer distribution network (Figure 5). An early operation of drainage pumps at the pump station is determined by water levels at the monitoring nodes in order to maintain the minimum level required to prevent cavitation. Like the CR, the DR is operated independently of other urban drainage facilities. Offline DRs are installed within drainage systems in urban areas and drain only in two cases: first, when the level of the DR reaches full capacity (the limit level), discharge starts by operating drainage pumps; and second, when rainfall is deemed to have ended, runoff is initiated. However, as discussed in Section 2.2, the system has some disadvantages. It is not straightforward to determine whether rainfall has ended. Moreover, when the discharge is released, the condition of the sewer conduits is not considered.

**Figure 5.** New operation method for a pump station with a centralized reservoir.

As explained above, current CR and DR operations run independently of each other and of the sewer conduits, and are not effective in reducing urban flooding or adapting during a heavy rainfall event. Cooperative operation of the facilities, involving connecting the DR to the sewer conduits and to the CR, is essential in order to address urban flooding. In order to operate them as one system, the condition of the sewer conduits is examined in real time on the basis of levels at the monitoring nodes (Figure 6).

**Figure 6.** New operation method for a decentralized reservoir.

### *2.4. Cooperative Operation of Urban Drainage Facilities*

For the cooperative operation of urban drainage facilities, a cooperative operation of both the main and the sub pump station is performed. When the capacity of the main pump station is not sufficient to drain the outlet, the sub pump station is added. When natural drainage is carried out, the sewer is directed to the main pump station with a large CR. When drainage is forced using drainage pumps, flooding is mitigated by considering the capacity of each pump station (pump capacity + CR capacity). Such cooperative pump station functions are available when pump stations are connected with a DR through sewer conduits. Cooperative operation with a DR installed in the basin is not considered in this type of cooperative operation between pump stations.

For the cooperative operation of urban drainage facilities proposed in this study, the water level at monitoring nodes is selected on the basis of the early operating level of the CR and the pump stop level of the DR. When sewer conduit levels are elevated and reach the early operating level of the CR, pumps are operated and rainwater is rapidly drained. When the level reaches the pump stop level of the DR, drainage pumps are stopped to remove the burden on sewer conduits.

In this section, we describe three characteristics of cooperative operations between CR and DR in detail. These are: additional space in the DR; reduction of the backwater effect by CR; and flood mitigation of the DR/sewer conduits/CR. First, we can secure additional space in the DR by drainage, based on monitoring node levels. Moreover, we reduce the risk of floods caused by CR backwater effects by performing early drainage in pump stations based on monitoring node levels. In addition, controlling flow delivery based on performance of the DR, sewer conduits, and CR provides efficient flood-mitigation for the entire urban drainage network. As low water levels are maintained due

to rapid drainage of urban drainage facilities, including pump stations and detention reservoirs, the CR and DR can be equipped with sufficient capacity to prevent floods caused by continuous rainfall (Figure 7). Cooperative operation is more effective for flood mitigation than both current and new drainage facility operations because of the detention effectiveness of DR, the rapid drainage effectiveness of CR, and the cooperation effectiveness of the monitoring nodes.

**Figure 7.** Cooperative operation of a centralized and a decentralized reservoir.

### *2.5. Resilience Index for Urban Drainage Systems*

Many indicators have been proposed for quantifying the ability for urban drainage systems to mitigate flooding [19–21]. For example, House et al. (1993) suggested an index for receiving water impacts and making better judgments regarding the acceptable performance of CSO (Combined Sewer Overflows). Cembrano et al. (2004) used a performance index for reducing flooding and discharge pollution in containing gates and detention tanks of urban drainage systems. Mitchell (2005) proposed an urban catchment wetness index (UCWI) for mapping hazards related to non-point pollution in urban drainage system.

There are few studies applying the concept of a resilience index for the evaluation of urban drainage systems. Mugume et al. (2014) is the only study to propose a resilience index according to flood depth in urban drainage systems [12]. The resilience index for urban drainage systems evaluates their ability to recover from floods, and flood (failure)–restoration–recovery is considered as one process.

The resilience of urban drainage systems can be defined as the ability to prepare for, recover, and restore after facility malfunction and flooding (failure). For example, failure is defined as the occurrence of flooding in urban areas due to malfunctions of equipment, such as sudden power outages in pump stations and remote control system shut-down of water gates in pump stations. Figure 8 conceptually defines the resilience of a system as a function of failure depth and recovery time.

**Figure 8.** Conceptual illustration of resilience.

*Water* **2016**, *8*, 469

Resilience is calculated using the performance evaluation function, which is based on the variables of flood volume per minute, accumulated rainfall for a certain time until the present, and basin area. Values of the performance evaluation function range from 0 to 1. When there is no flooding in urban drainage facilities, the value is 1. Equation (5) gives the performance evaluation function *<sup>u</sup>*(*T*)*i* at the *i*th minute (arbitrary time).

$$
\mu(T)\_i = \max\left(0, \quad 1 - \frac{F\_i}{R\_d \times A\_u}\right) \tag{R\_d = \sum\_{i=t\_c}^i R\_i} \tag{5}
$$

where *Fi* is flood volume (m3), *tc* is time of concentration (min), *Rd* is accumulated rainfall during current time (*t*) and i − *t*c (10−<sup>3</sup> m = mm), and *Au* is the basin unit area (10−<sup>8</sup> m<sup>2</sup> = 0.01 km2). High values of the performance evaluation function mean that the urban drainage system has a high ability to recover after flooding (failure) or minor system failure, and low values indicate a low ability to recover. The resilience of the entire urban drainage system is calculated as shown in Equation (6).

$$R\_s = \frac{1}{T\_n} \int\_{T\_0}^{T\_n} u(T)dT\tag{6}$$

where *Rs* is resilience of the entire system, *T*0 is the start time and *Tn* is the end time. In this study, we calculate and compare resilience of the current urban drainage system with the DR system and the cooperative system, including pump stations and detention reservoirs. For validation with experimental/measured in-situ data, measurement of the flooding area and flooding depth by aerial photography is essential. Nowadays, drones are employed for this; however, there are several associated problems such as high costs and inaccuracy of measured data.

### **3. Applications and Results**
