# Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne

^{1}

^{2}

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## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Description of MUNICH

#### 2.1.1. Street Geometry and Main Hypothesis

#### 2.1.2. MUNICH Existing Parametrizations for Vertical Transfers

^{−1}), ${q}_{vert}$ is the vertical transfer coefficient (m${}^{2}$·s${}^{-1}$) and $WL$ is the exchange surface (m${}^{2}$). ${C}_{street}$ and ${C}_{bg}$ are, respectively, the average street and background air pollutant concentrations (μg·m

^{−3}). ${l}_{m}$ is the mixing length within the street (m), and ${\sigma}_{W}$ is a velocity scale corresponding to the standard deviation of the vertical wind velocity at roof level (m·s${}^{-1}$). ${\sigma}_{W}$ is function of the atmosphere stability and the friction velocity above the street ${u}_{*}$ (m·s${}^{-1}$), and is calculated for a neutral atmosphere as [22,40]:

#### 2.1.3. MUNICH Existing Parametrizations for Horizontal Transfers

^{−1}), is computed in MUNICH as the product of the average wind speed in the street direction ${U}_{street}$ (m·s${}^{-1}$), which can be interpreted as a horizontal transfer velocity, the exchange section $HW$ (m${}^{2}$) and the average pollutant concentration in the street ${C}_{street}$ (μg·m

^{−3}). Depending on the wind angle $\phi $ (angle between the wind direction and the street orientation), this flux can be an incoming or outgoing flux:

- -
- Exponential attenuation profile (noted U_exp)

- -
- SIRANE profile (noted U_sir)

#### 2.2. Description of the CFD Simulations

#### 2.2.1. Street Canyon Geometry

#### 2.2.2. Set-Up of the Simulations

- -
- Turbulence closure and fluid properties

- -
- Initial and boundary conditions

^{∘}, where 0

^{∘}corresponds to a wind parallel to the street and 90

^{∘}is perpendicular.

#### 2.2.3. Calculation of Vertical and Horizontal Transfers in Code_Saturne for Comparison to MUNICH

^{−1}for a street canyon with a unit length L. The wind angle is assumed to be normal to the street orientation ($\phi ={90}^{\circ}$), and thus the horizontal transfers are negligible. The initial street and background tracer concentration is zero.

## 3. Adaptation of a Flow Parametrization and Comparison with Existing MUNICH Parametrizations

#### 3.1. Flow in Dense and Sparse Vegetated Canopies

#### 3.2. Vertical Transfers

#### 3.2.1. Vertical Transfer Coefficient Parametrization

#### 3.2.2. Comparison of MUNICH Vertical Transfer Coefficient Parametrizations with Code_Saturne Simulations

#### 3.3. Horizontal Transfers

#### 3.3.1. Horizontal Wind Speed Parametrization

#### 3.3.2. Comparison of MUNICH Horizontal Wind Profiles to Code_Saturne Simulations

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## Appendix A. Lists of Abbreviations, Variables and Parameters

Acronym | Definition |
---|---|

WC | Wide Canyon |

IC | Intermediate Canyon |

NC | Narrow Canyon |

CTM | Chemistry-Transport Model |

CFD | Computational Fluid Dynamics |

Symbol | Definition | Value | Unit |
---|---|---|---|

$\kappa $ | Von Kàrmàn constant | 0.42 | - |

D | Constant in the vertical transfer coefficient expression [24] | 0.45 | - |

PBLH | Boundary layer height | 1000 | m |

${z}_{0}$ | Code_Saturne city roughness length | 1.0 | m |

${z}_{{0}_{s}}$ | Code_Saturne inside street walls roughness length | 0.10 | m |

${u}_{*}$ | Friction velocity | 0.727 | m·s${}^{-1}$ |

${U}_{ref}$ | Wind speed at the reference height | 5.0 | m·s${}^{-1}$ |

e | Passive tracer emission rate | 1000 | μg·s^{−1} |

E | Parameter in modified Wang [38] parametrization | 0.5 | - |

Group of Variables | Symbol | Definition | Unit |
---|---|---|---|

Street characteristics | H | Building height | m |

W | Street width | m | |

B | Building width | m | |

L | Street length | m | |

V | Street volume | m${}^{3}$ | |

${a}_{r}$ | Aspect ratio | - | |

${z}_{ref}$ | Reference height | m | |

Horizontal wind speed | ${U}_{street}$ | Average street horizontal wind speed | m·s${}^{-1}$ |

U | Norm of the horizontal wind speed | m·s${}^{-1}$ | |

${U}_{X}$ | Horizontal wind speed in the X direction | m·s${}^{-1}$ | |

${U}_{Y}$ | Horizontal wind speed in the Y direction | m·s${}^{-1}$ | |

${U}_{H}$ | Average horizontal wind speed at the roof level | m·s${}^{-1}$ | |

$\phi $ | Wind angle | rad or ${}^{\circ}$ | |

A | Constant in the exp. profile attenuation coefficient | - | |

Vertical transfer | ${Q}_{vert}$ | Vertical flux of pollutant | μg·s^{−1} |

${q}_{vert}$ | Vertical transfer coefficient | m${}^{2}$·s${}^{-1}$ | |

${\sigma}_{W}$ | Standard deviation of the vertical wind speed at $z=H$ | m·s${}^{-1}$ | |

${l}_{m}$ | Mixing length in the street | m | |

${C}_{street}$ | Street concentration | μg·m^{−3} | |

${C}_{bg}$ | Background concentration | μg·m^{−3} | |

Modified Wang [37] parametrization | $\alpha $ | Wind attenuation coefficient | - |

${l}_{c}$ | Characteristic length in the street | m | |

${s}_{H}$ | Characteristic length factor | - | |

${C}_{u}$ | Empiric coefficient in $\alpha $ equation | - | |

${C}_{B}$ | Function of ${a}_{r}$ and $\phi $ | - |

## Appendix B. Comparison of Street-Average Concentrations in Code_Saturne and MUNICH

## Appendix C. Definition of the Statistical Indicators

- Normalized Mean Absolute Error (%):$$NMAE=100\times \frac{{\displaystyle \sum _{i=1}^{n}}|{m}_{i}-c{s}_{i}|}{\left(\right)}$$
- Normalized Mean Bias (%):$$NMB=100\times \frac{{\displaystyle \sum _{i=1}^{n}}\left(\right)open="("\; close=")">{m}_{i}-c{s}_{i}}{}{\displaystyle \sum _{i=1}^{n}}c{s}_{i}$$
- Relative Deviation (%):$$R{D}_{i}=100\times \frac{{m}_{i}-c{s}_{i}}{c{s}_{i}}$$

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**Figure 1.**2D scheme of the canyon geometry with the street and background domain borders, and the boundary conditions.

**Figure 3.**Comparison of the Code_Saturne vertical profile of wind speed in the street direction (${U}_{Y}\left(z\right)$) normalized by the wind speed at the roof level (${U}_{H,\phi}$) for different wind angle ($\phi $) and for (

**a**) WC, (

**b**) IC and (

**c**) NC. (

**d**) Comparison of the Code_Saturne average wind speed in the street (${U}_{street}$) normalized by ${U}_{H,\phi}$ depending on $\phi $ and for the three canyons.

**Figure 5.**Comparison of ${U}_{street}$ normalized by ${U}_{H,\phi}$ between Code_Saturne and the different MUNICH parametrizations for (

**a**) WC, (

**b**) IC and (

**c**) NC and depending on $\phi $.

**Figure 6.**Comparison of ${U}_{Y}\left(z\right)$ normalized by ${U}_{H,\phi}$ between Code_Saturne and the different MUNICH parametrizations for (

**a**,

**d**,

**g**,

**j**) WC, (

**b**,

**e**,

**h**,

**k**) IC, (

**c**,

**f**,

**i**,

**l**) NC and for (

**a**–

**c**) $\phi ={0}^{\circ}$, (

**d**–

**f**) $\phi ={20}^{\circ}$, (

**g**–

**i**) $\phi ={45}^{\circ}$ and (

**j**,

**k**,

**l**) $\phi ={70}^{\circ}$.

Canyon | Building Height H (m) | Street Width W (m) | Street Aspect Ratio ${\mathit{a}}_{\mathit{r}}$ (-) | Reference Height ${\mathit{z}}_{\mathit{ref}}=\mathit{H}+17$ (m) | Maximum Height of the Domain (m) |
---|---|---|---|---|---|

WC | 8.5 | 27.5 | 0.3 | 25.5 | 25.5 |

IC | 14.0 | 27.5 | 0.5 | 31.0 | 42.0 |

NC | 27.5 | 27.5 | 1.0 | 44.5 | 82.5 |

Parameter | Value | Unit |
---|---|---|

Temperature | 293.15 | K |

Pressure | 101,325.0 | Pa |

Density | 1.204 | kg·m^{−3} |

Viscosity | 1.83 × 10^{−5} | Pa·s |

Specific heat | 1017.24 | J·kg${}^{-1}$·K${}^{-1}$ |

Thermal conductivity | 0.02495 | W·m${}^{-1}$·K${}^{-1}$ |

**Table 3.**The ${q}_{vert}$ relative deviation (%) between Code_Saturne and MUNICH parametrizations for the three canyon heights.

**Table 4.**Normalized Mean Absolute Error (NMAE) and Bias (NMB) (%) between Code_Saturne and MUNICH parametrized ${U}_{street}$ for the three canyons studied and for all $\phi $ ($n=8$).

Canyon | U_exp $\mathit{A}=0.5$ | U_exp $\mathit{A}=1$ | U_sir | U_mw | ||||
---|---|---|---|---|---|---|---|---|

NMAE | NMB | NMAE | NMB | NMAE | NMB | NMAE | NMB | |

WC | 16.9 | 16.9 | 8.6 | 8.6 | 2.1 | 2.1 | 1.0 | −1.0 |

IC | 10.8 | 10.8 | 5.1 | −1.6 | 5.1 | −2.3 | 1.9 | −1.9 |

NC | 11.1 | 5.2 | 15.5 | −15.5 | 17.8 | −17.8 | 1.2 | −1.2 |

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**MDPI and ACS Style**

Maison, A.; Flageul, C.; Carissimo, B.; Tuzet, A.; Sartelet, K.
Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne. *Atmosphere* **2022**, *13*, 527.
https://doi.org/10.3390/atmos13040527

**AMA Style**

Maison A, Flageul C, Carissimo B, Tuzet A, Sartelet K.
Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne. *Atmosphere*. 2022; 13(4):527.
https://doi.org/10.3390/atmos13040527

**Chicago/Turabian Style**

Maison, Alice, Cédric Flageul, Bertrand Carissimo, Andrée Tuzet, and Karine Sartelet.
2022. "Parametrization of Horizontal and Vertical Transfers for the Street-Network Model MUNICH Using the CFD Model Code_Saturne" *Atmosphere* 13, no. 4: 527.
https://doi.org/10.3390/atmos13040527