**2. Materials and Methods**

Figure 1 shows the process of effectiveness assessment of flood mitigation used in this study. After the study area was selected, the hydrological data (such as rainfall, water level, and discharge) and physiographic data (such as drainage system, flood mitigation structure, land use, and digital elevation model) were collected for the chosen area. Then, computational cells were built based on the data collected, and historical rainfall events were used for the calibration and verification of the PHD model. The calibrated and verified PHD model was then used to simulate the max inundation depth and area for various NbS cases. Finally, the NbS case most suitable for the case area was chosen according to the results of the simulation and the consensus of residents and stakeholders.

**Figure 1.** The flow chart of assessment effectiveness of flood mitigation.

#### *2.1. Study Area*

This study selected Nangang River in central Taiwan for the NbS flood and disaster mitigation case area. Nangang River is a tributary of the Wu River upstream, and it is the fourth-largest river in Taiwan. The length of the mainstream of Nangang River is about 37 km, with a basin area of about 438 km<sup>2</sup> and a population of about 130,000. The surrounding area of the basin is mainly used for agriculture. The largest tributary upstream of Nangang River is Mei River, with a drainage area of 136 km<sup>2</sup> and accounting for about 1/3 of the area of the Nangang River [18]. After the two rivers converge, they enter the mainstream of Wu River, where most of the basin topography decreases with the elevation from east to west as shown in Figure 2.

**Figure 2.** The elevation of Nangang River catchment.

Nangang River's main channel is narrow, and several major floods occurred in the past due to insufficient protection standards. A heavy rain event washed out a bridge in 2017, and another bridge was broken by heavy rain in 2018. Although new levees have been built, the local people believe that the addition of cement structures has impacted the overall landscape and the increasingly scarce wetland ecology. The local stakeholders hope the river can be protected in a natural way.

#### *2.2. Flood Mitigation Case Based on Nature-Based Solutions*

The considerations of NbS in disaster mitigation includes three aspects: water, people, and nature. Based on this, possible stakeholders in the Nangang River case include the competent authority, local residents, and related non-governmental organizations. To consolidate the consensus of local residents and relevant stakeholders on river governance and environmental construction, the 3rd River Management Office conducted a total of three interviews in March, July, and September 2020. In the first interview, residents mentioned that the channel capacity is too small and often results in flooding after heavy rain. They suggested that the 3rd River Management Office expropriate the land instead of building new levees to achieve the objective of ecological resource protection and flood mitigation. In the second interview, residents and stakeholders mentioned that they want to know the flood mitigation effectiveness of each flood mitigation plan for comparison. They also called for promenades to be built or local tree species to be planted along with the planned flood mitigation facilities to satisfy protection standards and enrich the landscape simultaneously. In the third interview, residents and stakeholders mentioned that discontinuous levees and wildlife corridors could be set up to increase permeability

and reduce the impact on the ecological environment and the landscape. They suggested that the competent authority should propose feasible environmental solutions based on the local cultural background, environmental construction, and public expectations. Based on the interview results, this research conducted a site survey and proposed five cases, as shown in Table 1.


**Table 1.** Description of the 5 Nangang River NbS cases.

#### *2.3. The Flood Mitigation Assessment Model*

To understand the impact of the above cases on the Nangang River, numerical models are used to simulate and compare the changes in surface runoff of each case. As surface runoff is related to the temporal and spatial distribution of rainfall and surface water, when performing rainfall runoff simulation, the hydrological and physiographic conditions in the case area should be considered. This study adopts the Physiographic Drainage-inundation (PHD) model, which is widely used in Taiwan to simulate rainfall runoff. The PHD model can be used for flooding vulnerability assessment [19], detention pond operation optimization [20], and the assessment of the impact of extreme weather under climate change [21]. Its governing equation is shown as follows [22]:

$$As\_i \frac{dh\_i}{dt} = Pe\_i + \sum\_k Q\_{i,k} (h\_{i\prime} h\_k) \tag{1}$$

where *Asi* is the area of the *i* cell; *Qi*,*<sup>k</sup>* denotes the discharge from the *k* cell into its neighboring *i* cell. Discharge is positive when flowing into the *i* cell and negative when flowing out of the *i* cell; *hi* and *hk* represent the water levels of the *i* and *k* cells at time *t* respectively; and *Pei* expresses the effective rainfall volume per unit time in the *i* cell, which is equal to the effective rainfall per unit time in the *i* cell multiplied by its area *Asi*.

Total effective rainfall *P* can be calculate by the SCS-CN method; the equation can be writen as [23]:

$$P' = \frac{\left(P - I\_a\right)^2}{\left(P - I\_a\right) + S} \tag{2}$$

$$S = \frac{25400 - 254CN}{CN} \tag{3}$$

*P* is the total rainfall; *Ia* is the initial abstraction, including depression storage, intercepting, and evapotranspiration; and *CN* is the dimensionless curve number that is determined by soil type, type of vegetation cover, land use, hydrologic condition, antecedent moisture condition, and climate of the watershed [23]. In this study, *Ia* = 0.2*S* and *CN* is between 25 and 98.

The flow discharge between adjacent cells in the model can be divided into the river flow type, the weir flow type, and the pumping station type.

#### 2.3.1. River Flow Type

If there are no flow obstacles in the exchange of water between two adjacent cells, it is regarded as an overland flow, where the Manning formula can be used to calculate the water flow through the boundary of the two cells. From *i* cell, the flow from *k* cell to *i* cell is:

$$Q\_{i,k} = \frac{h\_k - h\_i}{|h\_k - h\_i|} \cdot \Phi(\overline{h\_{i,k}}) \cdot \sqrt{|h\_k - h\_i|} \text{ for } \frac{\partial Q\_{i,k}}{\partial h\_i} \le 0 \tag{4}$$

$$Q\_{i,k} = \Phi(h\_k) \cdot \sqrt{|h\_k - h\_i|} \text{ for } \frac{\partial Q\_{i,k}}{\partial h\_i} > 0 \tag{5}$$

where *hi*,*<sup>k</sup>* is the water level at the boundary of *i* and *k* cells.

$$
\overline{h\_{i,k}} = h\_k + (1 - a)h\_{i\prime} \; 0 \le a \le 1 \tag{6}
$$

and Φ(*h*):

$$\Phi(h) = \frac{A(h)R(h)^{2/3}}{n\sqrt{\Delta x}}\tag{7}$$

where Δ*x* is the distance between the center of the *i* and *k* cells; *n* is the Manning roughness coefficient of overland flow between the two neighboring cells; and *A*, *R* the hydraulic area and radius at the border between the two neighboring cells, respectively. When *hk* > *hi* and *hi* is decreasing, we can assume that *α* = 1 in Equation (4), to negate the influence of *hi* and calculate the water flow from the *k* cell to *i* cell with Equation (3).
