**1. Introduction**

Flood has become an annual disaster that is probably the most destructive, boundless, and causes significant losses in many countries [1]. This inundation phenomenon usually inundates areas which are normally dry, and causes significant losses physically, socially, and environmentally [2].

Lima Puluh Kota Regency is a regency in West Sumatera Province Indonesia that is located in sub-catchment Batang Sinamar River Basin, and is part of the upstream of Indragiri catchment area with a total area about 1330.65 km2. This regency is located on the hillside of the Sago Mountain that has experienced floods from Batang Sinamar River Basin every year in the last decade, from 2010 to 2019. The annual floods cause significant losses in agriculture and public facilities; therefore, a flood prediction model is needed to evaluate this phenomenon.

Hydrodynamic and hydrological models are widely applied to represent flood assessment. Hydrological models such as HEC-HMS, SWAT, and MIKE 11 are usually applied to reproduce the precipitation-runoff process. Hydrodynamic models such as MIKE 21, HECRAS, and DELFT 2D can simulate flow along rivers and floodplains [3,4]. The selection

**Citation:** Arlis, A.P.; Farid, M.; Wahid, A.N.; Suryadi, Y.; Kuntoro, A.A. Prediction of Flooding Area in Batang Sinamar River Basin Based on Design Return Period Simulation by Using Rainfall Runoff Inundation Model. *Environ. Sci. Proc.* **2023**, *25*, 91. https://doi.org/10.3390/ ECWS-7-14320

Academic Editor: Athanasios Loukas

Published: 3 April 2023

**Copyright:** © 2023 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/).

of the model is onthepurposeofthemodel andavailabilityoftime,funds,

and data. Availability and quality of hydrometeorological data are the main problems in developing countries. The lack of long-term hydro-meteorological observation data and river's topography affects the result of the hydraulic and hydrological model. However, over the last decades, a large number of satellites have been developed by international agencies. Even though the qualities and resolution of these data are not as detailed and accurate as observation data, they provide sufficient results for this phenomenon [5,6].

Common model practitioners run their flood model in two different models, one for hydrological process for the input in the upstream boundary condition, and another for hydrodynamics for the flood inundation. These methods are quite difficult to identify in larger basins if many floods happen. Therefore, the Rainfall-Runoff-Inundation (RRI) model was developed with fully two-dimensional distributed rainfall-runoff inundation [7]. This model is widely applied in flood risk mapping [8,9] and flood damage assessment and managemen<sup>t</sup> [10–12].

In this paper, the flood inundation model using the Rainfall-Runoff-Inundation model is presented. The model is calibrated with a 2019 flood event and simulated with 10- and 25-years' time return to see the performance and the maximum inundation area.

### **2. Methods and Materials**

### *2.1. Rainfall-Runoff-Inundation Model*

considered

The Rainfall-Runoff-Inundation model is a two-dimensional-based model that can simulate rainfall runoff and inundation processes simultaneously [7,13,14]. This model is able to simulate the water that flows on slopes using 2D diffusion wave equations, and the discharge in rivers using 1D diffusion wave equations. For more realistic results from rainfall-runoff simulation processes, this model also takes consideration of lateral subsurface flow, vertical infiltration, and surface flow. The infiltration process is calculated using the Green-Ampt method [13] with parameters including saturated hydraulic conductivity (K) [mm/hour], soil surface porosity (*φ*), suction head (Sf) [mm], and depth of saturated soil (d) [mm]. The river geometry parameter that is the input of the model can be obtained using Equations (1) and (2) as a function of catchment area *A* [km2]. The river geometry is considered as a rectangle with *W* [m] as the width of the river and *D* [m] as the depth of the river.

$$\mathcal{W} = \mathbb{C}\_w A^{S\_w} \tag{1}$$

$$D = \mathbb{C}\_d A^{\mathbb{S}\_d} \tag{2}$$

### *2.2. Target Flood Event*

Batang Sinamar River Basin is a sub-catchment of Indragiri River's catchment area. The area of Batang Sinamar River Basin catchment is 1330.65 km2. This river is used to irrigate 7766 Ha agriculture areas. It is on average 1246 m at the upstream and 486 m at the downstream above mean sea level.

In December 2019, there uncommon flood events happened at two adjacent times. The rainfall high is within the average, but the volume increased because of the length of the rain event. It affected six districts and damaged residents, public facilities, and agriculture. Besides the flood event in 2019, the model is performed for the flood event in 2013.

### *2.3. Data Used and Preparation*

The general workflow of this study is shown in Figure 1, and the required input data gathered for this study include high daily rainfall in Suliki and Tanjung Pati Station for ten years, and Batang Sinamar Water Surface Elevation Station by Water Resources Agency of West Sumatera, digital elevation model (dem) by DEMNAS Indonesia (you can access it here: DEMNAS (indonesia.go.id)), and land use and soil type by Indonesia Geospatial Agency as shown in Figure 2. The surface raster is processed to obtain the flow characteristic raster data of the area as shown in Figure 3. The river's geometry, which are scarce data, is digitally measured using satellite images and dem shown in Figure 4. Digital measurements are applied in several cross sections along the river to obtain geometry coefficients *Cw, Sw, Cd*, and Sd with the result values of 1.8931, 0.3772, 0.162, and 0.4772, respectively. Rainfall data are processed using the polygon Thiessen method to obtain high rainfall design with 10- and 25-years as shown in Figure 5.

### *2.4. Performance Assessment*

The RRI model input parameter is sensitive especially for the roughness and infiltration, which need a calibration for approach real events [14]. The model is compared and calibrated with real discharge observation data. Furthermore, the performance of the model is evaluated using Nash–Sutcliffe Efficiency (NSE) [15] and its correlation value is checked with the following equation.

$$NSE = 1 - \frac{\sum\_{1}^{n} \left(Q\_{t}^{\text{obs}} - Q\_{t}^{\text{sim}}\right)^{2}}{\sum\_{1}^{n} \left(Q\_{t}^{\text{obs}} - \overline{Q^{\text{obs}}}\right)^{2}} \tag{3}$$

$$R = \frac{n\sum\_{1}^{n} Q\_{t}^{obs} Q\_{t}^{sim} - \sum\_{1}^{n} Q\_{t}^{obs} \Sigma\_{1}^{n} Q\_{t}^{sim}}{\sqrt{n\sum\_{1}^{n} Q\_{t}^{obs} - n\sum\_{1}^{n} \left(Q\_{t}^{obs}\right)^{2}} \sqrt{n\sum\_{1}^{n} Q\_{t}^{sim^{2}} - n\sum\_{1}^{n} \left(Q\_{t}^{sim}\right)^{2}}} \tag{4}$$

where *Qobs t* is observed discharge at time *t*, *Qsimt* is simulated discharge value at time *t*, and *n* is number of available discharge value.

**Figure 1.** Workframe of the study.

**Figure 2.** General information of the study area: (**a**) focus area elevation map; (**b**) land use classification map; (**c**) Soil type map.

**Figure 3.** Topographic information as input RRI Model: (**a**) dem; (**b**) flow direction raster; (**c**) flow accumulation raster; (**d**) Thiessen polygon area; (**e**) roughness coefficient.

**Figure 4.** River geometry input for model RRI: (**a**) cross-section checking using dem; (**b**) river width checking using satellite images (source: Google Earth).

**Figure 5.** (**a**) Annual rainfall data, (**b**) river geometry parameter analysis, (**c**) rainfall distribution in time recurrence.

### **3. Result and Discussion**

The RRI model is applied to simulate two scenarios in the Batang Sinamar River Basin in two scenarios; the first scenario is the flood event on 20 December 2019 and the second is 3 March 2017 as shown in Figure 6. The results of the model were calibrated with flow observation station data and the NSE and correlation value were checked. The simulation for the first scenario used rainfall for 17 days from 9 to 26 December 2019, with the peak on 20 December 2019. Meanwhile the second was simulated for 31 days from 8 February to 10 March 2017. Based on observed and simulated result, the highest discharges of the hydrograph on 20 December are 222.20 m3/s and 224.65 m3/s, respectively, and on 3 March are 257.50 m3/s and 190.48 m3/s, respectively. The model provides satisfactory results with the NSE and correlation value for the first scenario as 0.768 and 0.908, respectively, and for the second scenario, 0.531 and 0.828, respectively.

**Figure 6.** The hydrograph results of Rainfall-Runoff-Inundation modelling compared with daily observation discharge data (**a**) flood scenario 9 to 26 December 2019; (**b**) flood scenario 8 February to 10 March 2017.

The evaluation of flood inundation used 10-year and 25-year design rainfall. These threshold rainfalls are used in the Indonesia standard flood modelling. The result provides

**Figure 7.** Simulation result for time return design rainfall: (**a**) 10-year return; (**b**) 25-year return.
