# A Risk-Based Approach for the Analysis of Flood Impact in Villahermosa (Tabasco, Mexico)

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Design Flows Calculation

^{2}. Table 3 shows the extrapolated 24-h annual maximum precipitation values (${h}_{p}$), excess precipitation (${P}_{e}$) and design flow values (${Q}_{d}$), calculated for different return periods, in each sub-basin.

#### 2.2. Hydraulic Simulations of Flood Scenarios

#### 2.3. Construction of Vulnerability Maps

- Starting from the coverage percentage of each indicator, their highest and lowest values, as well as the interval between them were recorded.
- This interval was divided between the number of categories according to which the vulnerability condition is determined (in this case five) and the value defining the extent of each vulnerability level was calculated.
- The extreme values of the vulnerability are constructed: Very High, or Very Low. In cases where the variable indicates a shortage of the population (for example the lack of drainage systems), the value encountered corresponds to a greater vulnerability. While, in cases where the variable indicates a satisfaction for the population (for example the level of education), the value found is equivalent to a lower vulnerability. To construct the intervals of the intermediate vulnerability conditions (ranges considered as Low, Medium and High), the procedure is as follows: one thousandth is added to the highest value of the immediately preceding vulnerability condition (0.001) and the result constitutes the lower limit of the vulnerability in construction. Subsequently, the interval is added to said value and thus the upper limit of this condition is obtained; this procedure is repeated to obtain the next range.
- Once the indicators have been classified, they are assigned a rating ranging from 1.00 (Very High Vulnerability) to 0.20 (Very Low Vulnerability).

#### 2.4. Calculation of Severity Indexes and Construction of Hazard Maps

#### 2.5. Construction of Risk Maps

## 3. Results

#### 3.1. Flood Maps

#### 3.2. Vulnerability Maps

#### 3.3. Hazard Maps

#### 3.4. Risk Maps and Potential Economic Damage

## 4. Discussion

## 5. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## References

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**Figure 2.**Map of the sub-basins that drain in Villahermosa. The location of the hydrometric and climatological stations, as well as the inlet points of each river used for the hydraulic simulations are shown.

**Figure 5.**Design hydrographs of the Carrizal and Viejo Mezcalapa sub-basins, corresponding to different return periods.

**Figure 6.**Design hydrographs of the Pichucalco and de la Sierra sub-basins, corresponding to different return periods.

**Figure 7.**Location map of the study area. The main land uses identified in the area are indicated (urban vegetation and residential land), as well as the inlet and outlet points to define the boundary hydraulic conditions.

**Figure 8.**Maximum water depth values, obtained from hydraulic simulations for the 10- and 50-year return periods.

**Figure 9.**Maximum water depth values, obtained from hydraulic simulations for the 100- and 500-year return periods.

**Figure 10.**Maximum water velocities, obtained from hydraulic simulations for (

**a**) 10-year return period and (

**b**) 500-year return period.

Carrizal | Viejo Mezcalapa | Pichucalco | de la Sierra | |
---|---|---|---|---|

Length of the channel (km) | 36.35 | 77.34 | 146.37 | 141.60 |

Average slope of the channel (%) | 0.02 | 0.06 | 1.45 | 1.67 |

Basin area (km${}^{2}$) | 99.8 | 470.9 | 1266.9 | 1003.8 |

Maximum elevation of the channel (m) | 17 | 60 | 2137 | 2373 |

Average elevation of the channel (m) | 13 | 35 | 1073 | 1191 |

Concentration time ${t}_{c}$ (h) | 28.03 | 32.84 | 15.75 | 14.54 |

Delay time ${t}_{r}$ (h) | 16.82 | 19.7 | 9.45 | 8.72 |

Peak time ${t}_{p}$ (h) | 22.11 | 25.43 | 13.42 | 12.53 |

Base time ${t}_{b}$ (h) | 59.04 | 67.9 | 35.82 | 33.47 |

**Table 2.**Fit standard errors calculated in the frequency analysis of precipitation data, for the Carrizal river sub-basin.

Distribution Function | Moments | Maximum Likelihood |
---|---|---|

Normal | 11.64 | 11.64 |

GEV | 7.64 | — |

Gumbel | 6.35 | 5.53 |

**Table 3.**Annual maximum precipitations (${h}_{p}$), excess precipitations (${P}_{e}$) and design flows (${Q}_{d}$) for every basin and 12 return periods from T = 2 years to T = 500 years.

Return Period (Years) | ${\mathit{h}}_{\mathit{p}}$ (mm) | ${\mathit{P}}_{\mathit{e}}$ (mm) | ${\mathit{Q}}_{\mathit{d}}$ (mm${}^{3}$/s) | |
---|---|---|---|---|

T = 2 | 54.103 | 20.001 | 18.773 | |

T = 5 | 71.369 | 32.960 | 30.937 | |

T = 10 | 82.801 | 42.199 | 39.608 | |

T = 20 | 93.766 | 51.409 | 48.253 | |

T = 50 | 107.959 | 63.713 | 59.801 | |

Carrizal | T = 100 | 118.595 | 73.153 | 68.662 |

T = 200 | 129.192 | 82.707 | 77.629 | |

T = 500 | 143.173 | 95.494 | 89.631 | |

T = 2 | 61.206 | 14.879 | 57.302 | |

T = 5 | 78.054 | 25.195 | 97.028 | |

T = 10 | 87.932 | 31.896 | 122.833 | |

T = 20 | 96.552 | 38.053 | 146.547 | |

T = 50 | 106.588 | 45.528 | 175.331 | |

Mezcalapa | T = 100 | 113.359 | 50.730 | 195.365 |

T = 200 | 119.527 | 55.567 | 213.992 | |

T = 500 | 126.866 | 61.430 | 236.574 | |

T = 2 | 83.650 | 34.631 | 680.256 | |

T = 5 | 102.136 | 48.995 | 962.419 | |

T = 10 | 111.808 | 56.872 | 1117.151 | |

T = 20 | 119.793 | 63.524 | 1247.813 | |

T = 50 | 128.778 | 71.146 | 1397.537 | |

Pichucalco | T = 100 | 134.766 | 76.298 | 1498.733 |

T = 200 | 140.246 | 81.057 | 1592.209 | |

T = 500 | 146.887 | 86.875 | 1706.507 | |

T = 2 | 81.066 | 32.759 | 545.696 | |

T = 5 | 104.237 | 50.747 | 845.346 | |

T = 10 | 121.449 | 64.985 | 1082.517 | |

T = 20 | 140.805 | 81.618 | 1359.589 | |

T = 50 | 172.741 | 110.066 | 1833.487 | |

de la Sierra | T = 100 | 201.961 | 136.852 | 2279.684 |

T = 200 | 233.265 | 166.094 | 2766.799 | |

T = 500 | 275.222 | 205.898 | 3429.851 |

**Table 4.**Optimal values of cell size, roughness and simulation times, adopted to simulate flood scenarios.

Land Use | Roughness | Cell Size (m) | |
---|---|---|---|

Residential | 0.8 | 50 | |

Urban vegetation | 0.08 | 200 | |

Water bodies | 0.02 | 100 | |

River | 0.035 | 15/25 | |

Total simulation time | 259,200 (s)/72 (h) | ||

Time step (s) | 2700 |

Category | Indicators |
---|---|

Health | Proportion of doctors per 1000 inhabitants |

Infant mortality rate | |

Percentage of population that does not rely on public health services | |

Education | Illiteracy rate |

Average level of education | |

Housing | Percentage of homes without piped water |

Percentage of houses without drainage | |

Housing deficit | |

Percentage of houses with adobe floors | |

Employment and income | Percentage of the Economically Active Population (EAP) that receives less than two minimum wages |

Dependency ratio (% of dependent population, in relation to the EAP) | |

Population | Population density (inhabitants per km${}^{2}$) |

Percentage of indigenous-speaking population | |

Percentage of population living in towns with fewer than 2500 inhabitants |

**Table 6.**Values of the indicators calculated for the categories Population, Education, Health, Employment, Housing.

District | Population | Education | Health | Employment | Housing |
---|---|---|---|---|---|

1 | 0.40 | 0.30 | 0.80 | 0.40 | 0.40 |

2 | 0.47 | 0.30 | 0.80 | 0.50 | 0.33 |

3 | 0.47 | 0.30 | 0.80 | 0.40 | 0.33 |

4 | 0.40 | 0.40 | 0.80 | 0.40 | 0.30 |

5 | 0.60 | 0.30 | 0.40 | 0.40 | 0.33 |

**Table 7.**Social vulnerability indexes (SVI) calculated for the five geostatistical districts of Villahermosa.

District | Average of the Indicators | SVI |
---|---|---|

1 | 0.46 | Low |

2 | 0.48 | Low |

3 | 0.46 | Low |

4 | 0.46 | Low |

5 | 0.61 | Very Low |

Hazard | Color | V = Velocity Threshold (m/s) | Y = Water Depth Threshold (m) |
---|---|---|---|

Very High | Red | V > 2 | Y > 2 |

High | Orange | V ≤ 2 | 1 < Y ≤ 2 |

Medium | Yellow | V ≤ 2 | 0.8 ≤ Y ≤ 1 |

Low | Blue | V ≤ 2 | 0.3 ≤ Y ≤ 0.8 |

Very Low | Green | V ≤ 2 | Y ≤ 0.3 |

Risk Index | Color | Risk Level |
---|---|---|

0.67 < ${I}_{Rj}$ < 1 | Red | High |

0.33 < ${I}_{Rj}$ < 0.67 | Yellow | Medium |

0 < ${I}_{Rj}$ < 0.33 | Green | Low |

Potential Damage | Equation ^{1} |
---|---|

Very high | $DDHmax=247.63\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+668.44$ |

$DDHmin=141.36\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+382.45$ | |

$DDHmp=156.92\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+424.33$ | |

High | $DDHmax=289.63\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+801.56$ |

$DDHmin=228.58\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+637.93$ | |

$DDHmp=280.51\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+777.60$ | |

Medium—one-story house | $DDHmax=709.63\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+1976.04$ |

$DDHmin=544.93\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+1546.60$ | |

$DDHmp=685.51\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+1913.15$ | |

Medium—two-story house | $DDHmax=549.55\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+1345.57$ |

$DDHmin=405.03\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+965.27$ | |

$DDHmp=528.39\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+1289.88$ | |

Low—one-story house | $DDHmax=877.28\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+2479.23$ |

$DDHmin=797.24\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+2233.19$ | |

$DDHmp=865.56\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+2443.20$ | |

Low—two-story house | $DDHmax=666.15\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+1632.94$ |

$DDHmin=595.33\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+1409.03$ | |

$DDHmp=605.70\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+1441.82$ | |

Very low—one-story house | $DDHmax=1521.80\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+4051.63$ |

$DDHmin=1210.14\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+3321.20$ | |

$DDHmp=1255.78\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+3428.17$ | |

Very low—two-story house | $DDHmax=1230.35\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+2850.34$ |

$DDHmin=939.78\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+2221.33$ | |

$DDHmp=1187.79\phantom{\rule{3.33333pt}{0ex}}Ln\left(h\right)+2758.22$ |

^{1}$DDHmax$: Maximum damage cost in urban area; $DDHmin$: Minimum damage cost in urban area; $DDHmp$: Probable cost in urban area; h: Depth of water flow on the surface. The economic damage is estimated in minimum wage units.

**Table 11.**Characteristics of the Villahermosa flood-affected area relative to a 10-year return period and expected annual potential damage.

Inhabitants | Housing Units | Floodable Area (km${}^{2}$) | People with Minimum Wages | Economic Value of Exposed Assets (MXN) | Risk Index | Risk Classification | |
---|---|---|---|---|---|---|---|

Villahermosa | 33,819 | 9717 | 13.86 | 1,239,027 | 257,023,699 | 0.632 | Medium |

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**MDPI and ACS Style**

Ceragene, M.; Bonasia, R.; Cea, L.; Cuevas-Cancino, M.d.l.O.
A Risk-Based Approach for the Analysis of Flood Impact in Villahermosa (Tabasco, Mexico). *Water* **2023**, *15*, 3969.
https://doi.org/10.3390/w15223969

**AMA Style**

Ceragene M, Bonasia R, Cea L, Cuevas-Cancino MdlO.
A Risk-Based Approach for the Analysis of Flood Impact in Villahermosa (Tabasco, Mexico). *Water*. 2023; 15(22):3969.
https://doi.org/10.3390/w15223969

**Chicago/Turabian Style**

Ceragene, Mackendy, Rosanna Bonasia, Luis Cea, and Maria de la O Cuevas-Cancino.
2023. "A Risk-Based Approach for the Analysis of Flood Impact in Villahermosa (Tabasco, Mexico)" *Water* 15, no. 22: 3969.
https://doi.org/10.3390/w15223969