# A Novel Hybrid Approach Based on Cellular Automata and a Digital Elevation Model for Rapid Flood Assessment

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

^{2}with a 1 m resolution [39].

## 2. Hybrid Inundation Model

#### 2.1. Cellular Automata 4-Direction (CA-4D) Model

_{NH}(m

^{3}/s) denotes the flow rates from the central cell to the NH, M is the total number of cells in the NH, WS

_{0}(m) is the water level in the central cell, WS

_{NH}(m) is the water level of the NH analyzed, n is the Manning roughness coefficient (m

^{−1/3}s), dx is the grid size (m), h

_{NH}(m) represents the depth at which water can flow between the central cell and NH cells, and Z

_{0}and Z

_{NH}are ground elevations (m) for central and neighboring cells.

_{lim}is the minimum time step set by the users, and α is a coefficient used to maintain simulation stability for most flow conditions. The parameter α is included because the stable time step is often less than that indicated by the CFL condition. Instead of finding the most stable time step value by using a complex equation, in which the time step decreases quadratically as the cell size decreases, α is introduced to reduce the time computation complexity. V

_{max}is the maximum of the wave celerity c and water velocity V

_{i}to the surrounding cells. The stable time step in the zero-inertia model is required to ensure that oscillation chequerboard does not occur and destroy the results. Unlike the equation proposed by [15], which sometimes returns a very small dt to ensure stability, the CFL stability criterion allows some flexibility. For emergency purposes, where time is essential, a higher value of α could be chosen to obtain a larger time step. Of course, oscillation likely occurs as a result. However, if the oscillation does not destroy the whole solution, it could be treated as data noise. Furthermore, when time is not an issue, α could be set lower to produce more stable results.

^{2}) is the area of the cell, ${Q}_{NH}$ (m

^{3}/s) is the outflow from the central cell to the NH cell, ${V}_{in}$ (m

^{3}) is the lateral input volume of water into the central cell (e.g., precipitation, drainage overflow, or discharge from the upstream area), and ${V}_{out}$ (m

^{3}) is an outflow volume of water from the central cell (e.g., outflow to the downstream catchment or lateral outflow). However, under certain conditions, more water leaves the central cell than is available. The water is distributed to the NH cells proportionally according to the water flux rates. Equations (8) and (9) are used to update the water depth for the extreme condition:

#### 2.2. DEM Based on the Flat-Water Assumption (D-Flat) Model

## 3. Details of Case Studies

#### 3.1. Three UK EA Benchmark Test Cases

#### 3.2. A Historical Flood Event

## 4. Results and Discussion

#### 4.1. Three UK EA Benchmark Test Cases

^{−1/3}s was applied to the whole domain. The scenario was simulated until the time reached 5 h with 6 specified points (see Figure 8a). Figure 9 shows the water level versus time at points 1, 3, 5, and 6. The results obtained from CA-4D and the HIM are in very good agreement with those from TUFLOW and LISFLOOD-FP, with no significant discrepancy. This means that the CA-4D model and HIM show good performance in modeling wave propagation. The HIM successfully predicted 97.7% of the inundated area predicted by CA-4D, and only 0.39% of the area was overpredicted by the HIM. The RMSE value was only 0.0035 m, which is almost negligible.

^{2}with an average slope of 4.3%, and the ground elevation ranges from 21 m to 37.6 m. The provided DEM, see Figure 13, is a 0.5 m resolution DEM (no vegetation or buildings) created from LiDAR data. The model is expected to simulate flood routing using a 2 m resolution DEM. Two Manning values are used: 0.02 for road and pavement and 0.05 elsewhere. All boundaries of the domain are closed, and the initial condition is a dry bed.

#### 4.2. Coastal Areas of Chiayi County

^{2}. A rainfall event of 550 mm over 30 h was applied to the whole domain, and the temporal distribution is shown in Figure 16. The drainage system was not included since this is not yet implemented in the HIM. However, this is reasonable in this case since the drainage system was reported as having failed due to a high tide. The full simulation time was 36 h. To examine the effect of the DEM ratio, two scenarios that used different DEM ratios were simulated. Two coarse DEMs with resolutions of 25 and 40 m, obtained from averaging the 5 m DEM, were used as an input for the CA-4D model, and within this study, these are called the C25 m and C40 m scenarios, respectively. The D-Flat model interpolated the outputs from CA-4D into 5 m resolution results.

#### 4.3. Model Efficiency

## 5. Conclusions

## Author Contributions

## Funding

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 2.**Pseudocode for calculating velocity by using the Numpy function library. Python functions are shown in blue, and comments are shown in green.

**Figure 3.**IZ illustration. The block of cells on the left (

**a**) represents the coarse grid used by the CA-4D model. Each coarse grid cell acts as an IZ for the finer grid (

**b**) used by the D-Flat model.

**Figure 4.**Pseudocode for distributing the water volume within the coarse grid cells to the finer grid cells. The IZ parameter refers to the ground elevation within the IZ.

**Figure 5.**(

**a**) EAT2 domain with contour lines every 0.05 m (

**b**) Inflow from the northwest point (x, y = 0 m, 2000 m).

**Figure 6.**Temporal variation in the water level for EAT2 at points 1, 2, 3, and 4; comparison among the CA-4D, HIM, TUFLOW, and LISFLOOD-FP models. (

**a**) simulated water level at point 1; (

**b**) simulated water level at point 2; (

**c**) simulated water level at point 3; (

**d**) simulated water level at point 4.

**Figure 7.**EAT2: predicted water depth at 48 h by (

**a**) the CA-4D model with 20 m resolution and (

**b**) the HIM.

**Figure 8.**(

**a**) EAT4 domain with 6 outpoints taken from Néelz and Pender [38] (

**b**) Inflow hydrograph at the central-west point (x, y = 0 m, 1000 m).

**Figure 9.**Temporal variation in water level for EAT4 at points 1, 3, 5, and 6; comparison among the CA-4D, HIM, TUFLOW, and LISFLOOD-FP models; (

**a**) simulated water level at point 1; (

**b**) simulated water level at point 3; (

**c**) simulated water level at point 5; (

**d**) simulated water level at point 6.

**Figure 14.**Temporal variation in water level for EAT8A at points 1, 2, 3, and 6; comparison among the CA-4D, HIM, TUFLOW, and LISFLOOD-FP models; (

**a**) simulated water level at point 1; (

**b**) simulated water level at point 2; (

**c**) simulated water level at point 3; (

**d**) simulated water level at point 6.

**Figure 15.**Flood extents produced by the HIM (left column) and CA-4D (right column) at t = 1800 s (first row) and t = 18,000 s (second row); (

**a**) the result of HIM at t = 1800 s; (

**b**) the result of CA-4D at t = 1800 s; (

**c**) the result of HIM at t = 18,000 s; (

**d**) the result of CA-4D at t = 18,000 s.

**Figure 17.**Maximum flood extent of the (

**a**) Chiayi County DEM and observation points (red dots), (

**b**) C25 m and (

**c**) C40 m.

Parameter/Test Case | EAT2 | EAT4 | EAT8A | |||
---|---|---|---|---|---|---|

CA-4D | HIM | CA-4D | HIM | CA-4D | HIM | |

Input Grid Resolution | 20 m | 100 m | 5 m | 20 m | 2 m | 10 m |

Output Grid Resolution | 20 m | 20 m | 5 m | 5 m | 2 m | 2 m |

Event Duration | 48 h | 48 h | 5 h | 5 h | 5 h | 5 h |

Output Frequency | 300 s | 300 s | 20 s | 20 s | 20 s | 20 s |

α | 0.0125 | 0.5 | 0.02 | 0.2 | 0.0015 | 0.025 |

∆t_{lim} | 1 s | 1 s | 1 s | 1 s | 1 s | 1 s |

Inc_Constant | - | 0.001 m | - | 0.001 m | - | 0.001 m |

Total Number of Cells | 10,000 | 80,000 | 97,000 |

Observation | C25m | C40m | TUFLOW | |
---|---|---|---|---|

Point 1 | 0.775 m | 0.572 m | 0.570 m | 0.513 m |

Point 2 | 1.100 m | 0.459 m | 0.426 m | 0.506 m |

Point 3 | 0.000 m | 0.000 m | 0.000 m | 0.030 m |

RMSE (m) | 0.388 m | 0.407 m | 0.375 m |

Model | Multiprocessing | Computation Time (min) | ||||
---|---|---|---|---|---|---|

UK EA Test Cases | Historical Event | |||||

EAT2 | EAT4 | EAT8A | C25m | C40m | ||

CA-4D | No | 136 | 580 | 21,160 | - | - |

HIM | No | 4.5 | 16.5 | 18.8 | 450 | 71 |

TUFLOW | Yes -GPU | 0.27 * | 0.42 * | 1.5 * | 480 | |

LISFLOOD-FP * | Yes | 0.12 * | 0.35 * | 4.5 * | - |

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**MDPI and ACS Style**

Wijaya, O.T.; Yang, T.-H.
A Novel Hybrid Approach Based on Cellular Automata and a Digital Elevation Model for Rapid Flood Assessment. *Water* **2021**, *13*, 1311.
https://doi.org/10.3390/w13091311

**AMA Style**

Wijaya OT, Yang T-H.
A Novel Hybrid Approach Based on Cellular Automata and a Digital Elevation Model for Rapid Flood Assessment. *Water*. 2021; 13(9):1311.
https://doi.org/10.3390/w13091311

**Chicago/Turabian Style**

Wijaya, Obaja Triputera, and Tsun-Hua Yang.
2021. "A Novel Hybrid Approach Based on Cellular Automata and a Digital Elevation Model for Rapid Flood Assessment" *Water* 13, no. 9: 1311.
https://doi.org/10.3390/w13091311