# 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 |

## References

- Charlesworth, S.M. A review of the adaptation and mitigation of global climate change using sustainable drainage in cities. J. Water Clim. Chang.
**2010**, 1, 165–180. [Google Scholar] [CrossRef] - Ciriminna, D.; Ferreri, G.B.; Noto, L.V.; Celauro, C. Numerical Comparison of the Hydrological Response of Different Permeable Pavements in Urban Area. Sustainability
**2022**, 14, 5704. [Google Scholar] [CrossRef] - Qi, W.; Ma, C.; Xu, H.; Chen, Z.; Zhao, K.; Han, H. A review on applications of urban flood models in flood mitigation strategies. Nat. Hazards
**2021**, 108, 31–62. [Google Scholar] [CrossRef] - Liu, T.; Lawluvy, Y.; Shi, Y.; Yap, P.S. Low Impact Development (LID) Practices: A Review on Recent Developments, Challenges and Prospects. Water Air Soil Pollut.
**2021**, 232, 344. [Google Scholar] [CrossRef] - Huang, C.L.; Hsu, N.S.; Liu, H.J.; Huang, Y.H. Optimization of Low Impact Development Layout Designs for Megacity Flood Mitigation. J. Hydrol.
**2018**, 564, 542–558. [Google Scholar] [CrossRef] - Woods Ballard, B.; Wilson, S.; Udale-Clarke, H.; Illman, S.; Ashley, R.; Kellagher, R. The SUDS Manual; Ciria: London, UK, 2015; p. 937. [Google Scholar]
- Fletcher, T.D.; Shuster, W.; Hunt, W.F.; Ashley, R.; Butler, D.; Arthur, S.; Trowsdale, S.; Barraud, S.; Semadeni-Davies, A.; Bertrand-Krajewski, J.L.; et al. SUDS, LID, BMPs, WSUD and More—The Evolution and Application of Terminology Surrounding Urban Drainage. Urban Water J.
**2015**, 12, 525–542. [Google Scholar] [CrossRef] - Fletcher, T.D.; Andrieu, H.; Hamel, P. Understanding, management and modelling of urban hydrology and its consequences for receiving waters: A state of the art. Adv. Water Resour.
**2013**, 51, 261–279. [Google Scholar] [CrossRef] - Salvadore, E.; Bronders, J.; Batelaan, O. Hydrological modelling of urbanized catchments: A review and future directions. J. Hydrol.
**2015**, 529, 62–81. [Google Scholar] [CrossRef] - Ahiablame, L.M.; Shakya, R. Modeling flood reduction effects of low impact development at a watershed scale. J. Environ. Manag.
**2016**, 171, 81–91. [Google Scholar] [CrossRef] - Luo, P.; Luo, M.; Li, F.; Qi, X.; Huo, A.; Wang, Z.; He, B.; Takara, K.; Nover, D.; Wang, Y. Urban flood numerical simulation: Research, methods and future perspectives. Environ. Model. Softw.
**2022**, 156, 105478. [Google Scholar] [CrossRef] - Kaykhosravi, S.; Khan, U.T.; Jadidi, A. A comprehensive review of low impact development models for research, conceptual, preliminary and detailed design applications. Water
**2018**, 10, 1541. [Google Scholar] [CrossRef][Green Version] - Eckart, K.; McPhee, Z.; Bolisetti, T. Performance and Implementation of Low Impact Development—A Review. Sci. Total Environ.
**2017**, 607, 413–432. [Google Scholar] [CrossRef] - Kuruppu, U.; Rahman, A.; Rahman, M.A. Permeable pavement as a stormwater best management practice: A review and discussion. Environ. Earth Sci.
**2019**, 78, 1–20. [Google Scholar] [CrossRef] - Zhu, Y.; Li, H.; Liang, X.; Yang, B.; Zhang, X.; Mahmud, S.; Zhang, X.; Zhuang, L.; Zhu, Y. Permeable Pavement Design Framework for Urban Stormwater Management Considering Multiple Criteria and Uncertainty. J. Clean. Prod.
**2021**, 293, 126114. [Google Scholar] [CrossRef] - Li, H.; Kayhanian, M.; Harvey, J.T. Comparative field permeability measurement of permeable pavements using ASTM C1701 and NCAT permeameter methods. J. Environ. Manag.
**2013**, 118, 144–152. [Google Scholar] [CrossRef] [PubMed] - Chandrappa, A.K.; Biligiri, K.P. Pervious Concrete as a Sustainable Pavement Material—Research Findings and Future Prospects: A State-of-the-Art Review. Constr. Build. Mater.
**2016**, 111, 262–274. [Google Scholar] [CrossRef] - Elliott, A.H.; Trowsdale, S.A. A Review of Models for Low Impact Urban Stormwater Drainage. Environ. Model. Softw.
**2007**, 22, 394–405. [Google Scholar] [CrossRef] - Bach, P.M.; Rauch, W.; Mikkelsen, P.S.; McCarthy, D.T.; Deletic, A. A critical review of integrated urban water modelling—Urban drainage and beyond. Environ. Model. Softw.
**2014**, 54, 88–107. [Google Scholar] [CrossRef] - Palla, A.; Gnecco, I. Hydrologic modeling of Low Impact Development systems at the urban catchment scale. J. Hydrol.
**2015**, 528, 361–368. [Google Scholar] [CrossRef] - Jato-Espino, D.; Charlesworth, S.M.; Bayon, J.R.; Warwick, F. Rainfall-Runoff Simulations to Assess the Potential of Suds for Mitigating Flooding in Highly Urbanized Catchments. Int. J. Environ. Res. Public Health
**2016**, 13, 149. [Google Scholar] [CrossRef] - Lee, S.; Kim, D.; Maeng, S.; Azam, M.; Lee, B. Runoff Reduction Effects at Installation of LID Facilities under Different Climate Change Scenarios. Water
**2022**, 14, 1301. [Google Scholar] [CrossRef] - Wilcox, B.P.; Rawls, W.J.; Brakensiek, D.L.; Wight, J.R. Predicting Runoff from Rangeland Catchments: A Comparison of Two Models. Water Resour. Res.
**1990**, 26, 2401–2410. [Google Scholar] [CrossRef] - Ajmal, M.; Waseem, M.; Ahn, J.H.; Kim, T.W. Improved Runoff Estimation Using Event-Based Rainfall-Runoff Models. Water Resour. Manag.
**2015**, 29, 1995–2010. [Google Scholar] [CrossRef] - Hu, C.; Xia, J.; She, D.; Song, Z.; Zhang, Y.; Hong, S. A New Urban Hydrological Model Considering Various Land Covers for Flood Simulation. J. Hydrol.
**2021**, 603, 126833. [Google Scholar] [CrossRef] - Zhang, S.; Guo, Y. SWMM simulation of the Storm Water volume control performance of permeable pavement systems. J. Hydrol. Eng.
**2015**, 20, 06014010. [Google Scholar] [CrossRef] - Baiamonte, G. SCS Curve Number and Green-Ampt Infiltration Models. J. Hydrol. Eng.
**2019**, 24, 04019034. [Google Scholar] [CrossRef] - Ponce, V.M.; Hawkins, R.H. Runoff curve number: Has it reached maturity? J. Hydrol. Eng.
**1996**, 1, 11–19. [Google Scholar] [CrossRef] - Madrazo-Uribeetxebarria, E.; Garmendia Antín, M.; Almandoz Berrondo, J.; Andrés-Doménech, I. Sensitivity analysis of permeable pavement hydrological modelling in the Storm Water Management Model. J. Hydrol.
**2021**, 600, 126525. [Google Scholar] [CrossRef] - Watt, E.; Marsalek, J. Critical review of the evolution of the design storm event concept. Can. J. Civ. Eng.
**2013**, 40, 105–113. [Google Scholar] [CrossRef] - Te Chow, V.; Maidment, D.R.; Mays, L.W. Applied Hydrology; McGraw-Hill: New York, NY, USA, 1988. [Google Scholar]
- MOPU. Norma 6.1-IC-Secciones de Firme; Technical Report; Ministerio de Obras Públicas y Urbanismo (MOPU): Madrid, Spain, 1986. [Google Scholar]
- CALTRANS. Pervious Pavement Design Guidance; Technical Report; California Department of Transportation (CALTRANS): Sacramento, CA, USA, 2013.
- CASQA. Stormwater Best Management Practice Handbook; Technical Report; California Stormwater Quality Association (CASQA): Sacramento, CA, USA, 2003. [Google Scholar]
- R Core Team. R: A Language and Environment for Statistical Computing; R Foundation for Statistical Computing: Vienna, Austria, 2020. [Google Scholar]
- Leutnant, D.; Döring, A.; Uhl, M. swmmr—An R package to interface SWMM. Urban Water J.
**2019**, 16, 68–76. [Google Scholar] [CrossRef] - Ardia, D.; Mullen, K.M.; Peterson, B.G.; Ulrich, J. DEoptim: Differential Evolution in R. Version 2.2-5. 2020. Available online: https://cran.r-project.org/web/packages/DEoptim/DEoptim.pdf (accessed on 1 March 2021).
- SCS. Hydrology, National Engineering Handbook; USDA: Washington DC, USA, 1956.
- Balbastre-Soldevila, R.; García-Bartual, R.; Andrés-Doménech, I. A Comparison of Design Storms for Urban Drainage System Applications. Water
**2019**, 11, 757. [Google Scholar] [CrossRef][Green Version] - Hawkins, R.H.; Ward, T.J.; Woodward, D.E.; Van Mullem, J.A. Curve Number Hydrology: State of the Practice; Technical Report; Environmental and Water Resources Institute (EWRI) of the American Society of Civil Engineers: Reston, VA, USA, 2009. [Google Scholar] [CrossRef]
- Rossman, L.A.; Huber, W.C. Volume I—Hydrology. In Storm Water Management Model Reference Manual; US EPA Office of Research and Development: Washington, DC, USA, 2016. [Google Scholar]
- Rossman, L.A. Modeling low impact development alternatives with SWMM. J. Water Manag. Model.
**2010**, 11, 167–182. [Google Scholar] [CrossRef][Green Version] - Rossman, L. Storm Water Management Model User’s Manual Version 5.1; US EPA Office of Research and Development: Washington, DC, USA, 2015.
- Rammal, M.; Berthier, E. Runoff Losses on Urban Surfaces during Frequent Rainfall Events: A Review of Observations and Modeling Attempts. Water
**2020**, 12, 2777. [Google Scholar] [CrossRef] - Mullaney, J.; Lucke, T. Practical Review of Pervious Pavement Designs. Clean Soil Air Water
**2014**, 42, 111–124. [Google Scholar] [CrossRef] - Rossman, L.A.; Huber, W.C. Volume III—Water Quality. In Storm Water Management Model Reference Manual; US EPA Office of Research and Development: Washington, DC, USA, 2016. [Google Scholar]
- Hargreaves, G.H.; Samani, Z.A. Reference crop evapotranspiration from temperature. Appl. Eng. Agric.
**1985**, 1, 96–99. [Google Scholar] [CrossRef] - Nash, J.E.; Sutcliffe, J.V. River flow forecasting through conceptual models part I—A discussion of principles. J. Hydrol.
**1970**, 10, 282–290. [Google Scholar] [CrossRef] - Dietz, M.E. Low impact development practices: A review of current research and recommendations for future directions. Water Air Soil Pollut.
**2007**, 186, 351–363. [Google Scholar] [CrossRef] - Pant, M.; Zaheer, H.; Garcia-Hernandez, L.; Abraham, A. Differential Evolution: A review of more than two decades of research. Eng. Appl. Artif. Intell.
**2020**, 90, 103479. [Google Scholar] [CrossRef] - Mullen, K.; Ardia, D.; Gil, D.; Windover, D.; Cline, J. DEoptim: An R Package for Global Optimization by Differential Evolution. J. Stat. Softw.
**2011**, 40, 1–26. [Google Scholar] [CrossRef]

**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 |

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content. |

© 2022 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/).

## 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