# Modelling Runoff from Permeable Pavements: A Link to the Curve Number Method

^{1}

^{2}

^{3}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Experimental Design

^{2}. However, three types of catchment were defined to check the effect of the catchment shape: narrow, squared, and wide catchments. As the defined area was 100 m

^{2}, shape defining widths were 1 m for the narrow shape, 10 m for the squared shape, and 100 m for the wide shape.

#### 2.2. Curve Number Method

#### 2.3. Storm Water Management Model

#### 2.4. Model Setup

#### 2.5. Hydrograph Performance and Calibration

## 3. Results and Discussion

#### 3.1. Relation for CN and Pavement Permeability

#### 3.1.1. General Analysis

#### 3.1.2. Influence of Selected Variables

#### 3.1.3. Performance of the Equivalent Hydrographs

#### 3.2. Test Case with Continuous Event

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Abbreviations

CN | Curve Number |

DE | Differential Evolution |

GA | Green–Ampt |

IDF | Intensity–Duration–Frequency |

LID | Low Impact Development |

NSE | Nash–Sutcliffe Efficiency |

PA | Permeable Asphalt |

PC | Permeable Concrete |

PIP | Permeable Interlocking Pavers |

PP | Permeable Pavement |

SCS | Soil Conservation Service |

SUDS | Sustainable Urban Drainage Systems |

SWMM | Storm Water Management Model |

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**Figure 4.**Pavement permeability values for fitted hydrographs in each selected CN and considered regression curves, with different colours for each proposed interval.

**Figure 5.**Pavement permeability values for fitted hydrographs with different colors for considered catchment shapes (

**first row**), precipitation depth (

**second row**), pavement slope (

**third row**), and LID layout (

**fourth row**).

**Figure 6.**Nine examples of SCS-CN hydrographs, used as a baseline (red), and fitted LID hydrographs (blue). For each pair, baseline CN, calibrated pavement permeability, storm, width, and NSE are given.

**Figure 7.**Computed NSE values after calibration. Different colours are used for each combination of storm depth and catchment shape.

Property | Units | SCS-CN Value | LID Value |
---|---|---|---|

Area | ha | 0.01 | 0.01 |

Width | m | 1-10-100 | $-{\phantom{\rule{3.33333pt}{0ex}}}^{\left(1\right)}$ |

Slope | % | 1-2-6 | $-{\phantom{\rule{3.33333pt}{0ex}}}^{\left(2\right)}$ |

% Imperv | % | 0 | 0 ${}^{\left(3\right)}$ |

N-Perv | Manning n | ${0}^{3}$ | $-{\phantom{\rule{3.33333pt}{0ex}}}^{\left(4\right)}$ |

Dstore-Perv | mm | 1 | $-{\phantom{\rule{3.33333pt}{0ex}}}^{\left(5\right)}$ |

^{(1)}: defined in the Width for the LID implementation.

^{(2)}: defined in the Slope for the LID properties.

^{(3)}: to activate SCS-CN subroutine and prevent runoff delay [41].

^{(4)}: defined in the Roughness for the LID properties.

^{(5)}: defined in the Berm Height for the LID properties.

LAYER/Factor | Symbol | Units | PC Value | PP Value | PIP Value |
---|---|---|---|---|---|

SURFACE | |||||

Berm Height | ${D}_{1}$ | mm | 1 | 1 | 1 |

Vegetation Volume Fraction | $1-{\varphi}_{1}$ | - | 0 | 0 | 0 |

Roughness | n | Manning n | 0.02 | 0.02 | 0.02 |

Slope | S | % | 1-2-6 | 1-2-6 | 1-2-6 |

PAVEMENT | |||||

Thickness | ${D}_{4}$ | mm | 100 | 100 | 80 |

Void Ratio | ${\varphi}_{4}/(1-{\varphi}_{4})$ | Voids/Solids | 0.25 | 0.25 | 0.25 |

Imperviouss Surf. Frac. | ${F}_{4}$ | - | 0 | 0 | 0.9 |

Permeability | ${K}_{4}$ | mm/h | * | * | * |

SOIL | |||||

Thickness | ${D}_{2}$ | mm | 0 | 50 | 50 |

Porosity | ${\varphi}_{2}$ | vol. frac. | - | 0.45 | 0.45 |

Field Capacity | ${\theta}_{FC}$ | vol. frac. | - | 0.1 | 0.1 |

Wilting Point | ${\theta}_{WP}$ | vol. frac. | - | 0.05 | 0.05 |

Conductivity | ${K}_{2S}$ | mm/h | - | 100 | 100 |

Conductivity Slope | $HCO$ | - | - | 50 | 50 |

Suction Head | ${\psi}_{2}$ | mm | - | 50 | 50 |

STORAGE | |||||

Thickness | ${D}_{3}$ | mm | 400 | 400 | 400 |

Void Ratio | ${\varphi}_{3}/(1-{\varphi}_{3})$ | Voids/Solids | 0.7 | 0.7 | 0.7 |

Seepage Rate | ${K}_{3S}$ | mm/h | 10 | 10 | 10 |

DRAIN | |||||

Flow Coefficient | ${C}_{3D}$ | - | 0 | 0 | 0 |

Property | Units | LID Value |
---|---|---|

Area of each unit | m${}^{2}$ | 100 |

Number of Units | - | 1 |

Surface Width per Unit | m | 1-10-100 |

% Initially Saturated | % | 0 |

% of Subcatchment Occupied | % | 100 |

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## Share and Cite

**MDPI and ACS Style**

Madrazo-Uribeetxebarria, E.; Garmendia Antín, M.; Almandoz Berrondo, J.; Andrés-Doménech, I.
Modelling Runoff from Permeable Pavements: A Link to the Curve Number Method. *Water* **2023**, *15*, 160.
https://doi.org/10.3390/w15010160

**AMA Style**

Madrazo-Uribeetxebarria E, Garmendia Antín M, Almandoz Berrondo J, Andrés-Doménech I.
Modelling Runoff from Permeable Pavements: A Link to the Curve Number Method. *Water*. 2023; 15(1):160.
https://doi.org/10.3390/w15010160

**Chicago/Turabian Style**

Madrazo-Uribeetxebarria, Eneko, Maddi Garmendia Antín, Jabier Almandoz Berrondo, and Ignacio Andrés-Doménech.
2023. "Modelling Runoff from Permeable Pavements: A Link to the Curve Number Method" *Water* 15, no. 1: 160.
https://doi.org/10.3390/w15010160