# Uncertainty Analysis in Data-Scarce Urban Catchments

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Methodology

## 3. Study Area, Hydrological Model and Uncertainty Methods

#### 3.1. Study Area

^{2}was instrumented with seven automatic weather stations, each of which measured climatic parameters with a temporal resolution of 10 min.

#### 3.2. Hydrological Model

#### 3.3. Sensitivity Analysis

#### 3.4. Uncertainty Analysis Techniques

#### 3.4.1. GLUE Methodology

#### 3.4.2. AMALGAM Method

## 4. Results and Discussion

#### 4.1. Model-Data Comparison

#### 4.2. Sensitivity Analysis

#### 4.3. Uncertainty Analysis Techniques of Model Parameters

#### 4.4. ARIL Calculation

#### 4.5. Modelling of Storm Events with Optimal Parameters

#### 4.6. Model Validation

## 5. Conclusions

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## References

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**Figure 2.**(

**a**) Urban basin of Tuxtla Gutierrez, Mexico; Rainfall events; (

**b**) Event 1; (

**c**) Event 2; (

**d**) Event 3; and (

**e**) Event 4; and (

**f**) Hydrometric station 5 from 1 July 2011 to 31 October 2011.

**Figure 3.**Generated depth via the observed precipitation and initial hydrologic parameters compared with the observed depth: (

**a**) Event 1 and (

**b**) Event 2.

**Figure 4.**Sensitivity of the model parameters of urban drainage: (

**a**) maximum sensitivity and (

**b**) average sensitivity.

**Figure 9.**Depth levels of Sabinal River for (

**a**) Event 1 & C276 and (

**b**) Event 2 & C272, using parameter sets obtained by GLUE.

**Figure 10.**Depth levels of Sabinal River for (

**a**) Event 1 & C365 and (

**b**) Event 2 & C1501, using parameter sets obtained by AMALGAM.

**Figure 11.**Validation of the depth levels of the Sabinal River using the optimal parameter set, C365, obtained by the method AMALGAM for (

**a**) Event 3 and (

**b**) Event 4.

**Figure 12.**Validation of the depth levels of the Sabinal River using non-uniform distribution of Nimperv parameter, for (

**a**) Event 1 and (

**b**) Event 2.

**Figure 13.**Validation of the depth levels of the Sabinal River using non-uniform distribution of Nimperv parameter, for (

**a**) Event 3 and (

**b**) Event 4.

Parameter | Abbreviation | Minimum Value | Maximum Value | Initial Value |
---|---|---|---|---|

Manning coefficient n conduit | ManN | 0.01 | 0.03 | 0.065 |

Manning coefficient n impermeable surface | Nimperv | 0.001 | 0.2 | 0.01 |

Manning coefficient n permeable surface | Nperv | 0.01 | 0.2 | 0.1 |

Height depression storage on the impermeable area, $\mathrm{mm}$ | Simperv | 0 | 10 | 5 |

Height depression storage on the permeable area, $\mathrm{mm}$ | Sperv | 0 | 20 | 1.27 |

Percent impermeable area without storage in the depression, $\text{\%}$ | PctZero | 0 | 100 | 25 |

Maximum rate of infiltration, $\mathrm{mm}/\mathrm{h}$ | MaxRate | 1 | 200 | 11.7 |

Minimum rate of infiltration, $\mathrm{mm}/\mathrm{h}$ | MinRate | 1 | 25 | 5.6 |

Decay coefficient, $\mathrm{L}/\mathrm{h}$ | Decayk | 1 | 30 | 4 |

Event | Uncertainty Analysis Techniques | |||||
---|---|---|---|---|---|---|

GLUE | AMALGAM | |||||

Set | IAd | ARIL | Set | IAd | ARIL | |

1 | 276 | 0.8392 | 0.4153 | 365 | 0.8302 | 0.4394 |

2 | 272 | 0.7285 | 0.3110 | 1501 | 0.7249 | 0.3088 |

Optimal Parameter Set | Nimperv | Nperv | Simperv | Sperv | PctZero | MaxRate_fa | MinRate_fe | Decay_k |
---|---|---|---|---|---|---|---|---|

Event 1 C276 | 0.011 | 0.099 | 6.957 | 10.258 | 0.024 | 126.937 | 20.509 | 23.693 |

Event 2 C272 | 0.003 | 0.028 | 8.196 | 18.31 | 34.558 | 108.512 | 11.575 | 21.037 |

Optimal Parameter Set | Nimperv | Nperv | Simperv | Sperv | PctZero | MaxRate_fa | MinRate_fe | Decay_k |
---|---|---|---|---|---|---|---|---|

Event 1 C365 | 0.018 | 0.05 | 9.424 | 4.524 | 5.252 | 30.317 | 20.378 | 4.08 |

Event 2 C1501 | 0.005 | 0.071 | 6.268 | 19.482 | 63.102 | 164.592 | 21.237 | 18.568 |

Event | Before the Uncertainty Analysis | After the Uncertainty Analysis, GLUE | After the Uncertainty Analysis, AMALGAM | |||
---|---|---|---|---|---|---|

Average APE, % | Maximum APE, % | Average APE, % | Maximum APE, % | Average APE, % | Maximum APE, % | |

1 | 28.40 | 114.25 | 19.03 | 79.15 | 22.95 | 63.34 |

2 | 44.02 | 323.13 | 33.03 | 478.53 | 35.29 | 482.10 |

Event | Average APE, % | Maximum APE, % | APE between Peaks, % | IAd |
---|---|---|---|---|

3 | 14.46 | 72.28 | 42.53 and 2.69 | 0.9329 |

4 | 24.81 | 178.02 | 35.95 and 38.80 | 0.8624 |

Event | Average APE, % | Maximum APE, % | APE between Peaks, % |
---|---|---|---|

1 | 23.68 | 52.06 | 37.20 |

2 | 52.23 | 126.47 | 75.90 and 36.61 |

3 | 12.85 | 60.05 | 43.83 and 3.62 |

4 | 29.31 | 183.83 | 32.67 and 45.89 |

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**MDPI and ACS Style**

Ballinas-González, H.A.; Alcocer-Yamanaka, V.H.; Pedrozo-Acuña, A.
Uncertainty Analysis in Data-Scarce Urban Catchments. *Water* **2016**, *8*, 524.
https://doi.org/10.3390/w8110524

**AMA Style**

Ballinas-González HA, Alcocer-Yamanaka VH, Pedrozo-Acuña A.
Uncertainty Analysis in Data-Scarce Urban Catchments. *Water*. 2016; 8(11):524.
https://doi.org/10.3390/w8110524

**Chicago/Turabian Style**

Ballinas-González, Héctor A., Victor H. Alcocer-Yamanaka, and Adrián Pedrozo-Acuña.
2016. "Uncertainty Analysis in Data-Scarce Urban Catchments" *Water* 8, no. 11: 524.
https://doi.org/10.3390/w8110524