# Modeling Exposure to Heat Stress with a Simple Urban Model

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## Abstract

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## 1. Introduction

## 2. Model

#### 2.1. Simplified City Model

#### 2.2. Traffic Model

#### 2.3. ${T}_{mrt}$ Model

#### 2.4. Meteorology

#### 2.5. Exposure Model

## 3. Simulations

#### 3.1. General Set-Up

#### 3.2. Reference Case

#### 3.3. Influence of City Structure

#### 3.4. Influence of Albedo

## 4. Discussion

## 5. Conclusions and Outlook

## Acknowledgments

## Author Contributions

## Conflicts of Interest

## Abbreviations

CBD | Central business district |

CET | Central European time |

HUSCO | Hamburg Urban Soil Climate Observatory |

PT | perceived temperature |

SURM | Simple Urban Radiation Model |

UrbWellth | health-related urban well-being |

UTCI | Universal Thermal Climate Index |

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**Figure 1.**Schematic diagram of the model components (black boxes), inputs, and outputs (gray boxes).

**Figure 3.**Average building heights as a function of distance to the CBD (Coordinates: 53.5488${}^{\circ}$ N, 9.9913${}^{\circ}$ W) for Hamburg. The average is calculated from building height data of a study by Schoetter et al. [4] using 1 km bins (i.e., 0 km–1 km, …, 19 km–20 km). The red line shows the linear fit, which has an explained variance ${R}^{2}$ of 0.78.

**Figure 4.**Probability distribution of the location of workplaces (combined ${f}_{wrk}$, in the CBD ${f}_{wrk1}$, and near home location ${f}_{wrk2}$) for urban dwellers living 10 km away from CBD. ${\chi}_{CBD}$ (dotted black line) is set to 3 km and $\sigma $ (dotted gray lines) to 1 km. A grid spacing $\mathrm{\Delta}x$ = 10 m is used to create a smooth curve.

**Figure 5.**Normalized traffic density in terms of ${\rho}_{max}$ for different time steps. Traffic is directed towards city center. Note that the area decreases with decreasing distance to the CBD.

**Figure 6.**Time series of observed (black) and fitted (red) (

**a**) 2m temperature ${T}_{2m}$, (

**b**) surface temperature ${T}_{surf}$, and (

**c**) 2m relative humidity $R{H}_{2m}$ at the station “Innenhof Stadthausbrücke” for 4 July 2015. The equations for the non-linear fit are given as well as the corresponding explained variance ${R}^{2}$.

**Figure 7.**Distribution of the population and workplaces as a function of distance to the CBD for the simplified city with the reference case configuration.

**Figure 8.**Time series of simulated total commuters (blue), exposed commuters (red) and the maximum ${T}_{mrt}$ (orange) in the city for 4 July 2015. As a threshold for heat stress 58.8 ${}^{\circ}\mathrm{C}$ is used (dashed orange line).

**Figure 9.**Area averaged ${T}_{mrt}$ at: (

**a**) 8:00 CET; (

**b**) 9:00 CET; (

**c**) 14:00 CET; and (

**d**) 17:00 CET for different street widths W and building heights in the CBD ${H}_{CBD}$. Black contour lines indicate the aspect ratio $H/W$ averaged over the whole city while the red dashed line indicates ${T}_{thr}$ (i.e., 58.8 ${}^{\circ}\mathrm{C}$). Albedo of walls, ${A}_{0W}$, and streets, ${A}_{0S}$, are set to 0.15.

**Figure 10.**(

**a**) Total time spend on the road; and (

**b**) percentage of time spend in a traffic jam with respect to the total commuting time as a function of building height in the CBD ${H}_{CBD}$ and distance from home to the CBD.

**Figure 11.**Time exposed to heat stress ($OD{H}_{ave}$) in minutes per commuter as a function of building height in the CBD and street width.

**Figure 12.**Difference in the averaged ${T}_{mrt}$ of simulations with different albedo ${A}_{0}$ minus the simulation with ${A}_{0}=0.1$. Solid lines correspond to results where only ${A}_{0}$ of the walls are changed (${A}_{0}$ of streets is set to 0.15) and dashed lines to results where ${A}_{0}$ of the walls as well as the ${A}_{0}$ of the streets are changed. All other parameters are taken from the reference case (Table 1 and Table 2).

**Figure 13.**Difference in the time exposed to heat stress ($ODH$) as a function of W and ${H}_{CBD}$ (

**a**) for simulations with ${A}_{0W}=0.6$ minus ${A}_{0W}=0.1$ (${A}_{0S}$ is set to 0.15); and (

**b**) ${A}_{0W}={A}_{0S}=0.6$ minus ${A}_{0W}={A}_{0S}=0.1$. Please note the different scaling of both figures.

**Table 1.**List of parameters for city properties, ${T}_{mrt}$ module and traffic model. Parameters that are varied in this study are indicated as flexible.

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

radius of the city R | 20 km |

radius of the CBD ${R}_{CBD}$ | 2 km |

total population ${P}_{tot}$ | 1.785 $\xb7{10}^{6}$ |

working population ${P}_{w}$ | 1.1934 $\xb7{10}^{6}$ |

commuters ${P}_{c}$ | 0.55·${P}_{w}$ |

e-folding distance workplaces in CBD ${\chi}_{CBD}$ | 3 km |

standard deviation workplaces near home $\sigma $ | 1 km |

street width W | 15 m (flexible) |

building height at city boundaries ${H}_{R}$ | 5 m |

building height in the CBD ${H}_{CBD}$ | 16 m (flexible) |

albedo of the building walls ${A}_{0W}$ | 0.15 (flexible) |

albedo of the streets ${A}_{0S}$ | 0.15 (flexible) |

grid size $\mathrm{\Delta}x$ | 1 km |

street orientation step $\mathrm{\Delta}{\theta}_{s}$ | ${10}^{\circ}$ |

${T}_{mrt}$ threshold ${T}_{thr}$ | 58.8 ${}^{\circ}\mathrm{C}$ |

time step $\mathrm{\Delta}t$ | 1 min |

maximum car density ${\rho}_{max}$ | 800 cars km${}^{-2}$ |

maximum bike density ${\rho}_{max}$ | 1083 bikes km${}^{-2}$ |

maximum car velocity ${v}_{max}$ | 50 km h${}^{-1}$ |

maximum bike velocity ${v}_{max}$ | 15 km h${}^{-1}$ |

Group | 1 | 2 | 3 | 4 |
---|---|---|---|---|

start of work | 8:00 CET | 9:00 CET | 8:00 CET | 9:00 CET |

end of work | 16:30 CET | 17:30 CET | 13:00 CET | 14:00 CET |

car percentage | 70% | 90% | 70% | 90% |

bike percentage | 30% | 10% | 30% | 10% |

**Table 3.**Averaged time exposed to heat stress ($OD{H}_{ave}$) of different groups for different albedo values. All other parameters are taken from the reference case (Table 1).

${\mathit{ODH}}_{\mathit{ave}}$ (Minutes per Commuter) | ||||
---|---|---|---|---|

${\mathit{A}}_{\mathbf{0}\mathit{W}}$ = 0.1 ${\mathit{A}}_{\mathbf{0}\mathit{S}}$ = 0.15 | ${\mathit{A}}_{\mathbf{0}\mathit{W}}$ = 0.6 ${\mathit{A}}_{\mathbf{0}\mathit{S}}$ = 0.15 | ${\mathit{A}}_{\mathbf{0}\mathit{W}}$ = ${\mathit{A}}_{\mathbf{0}\mathit{S}}$ = 0.1 | ${\mathit{A}}_{\mathbf{0}\mathit{W}}$ = ${\mathit{A}}_{\mathbf{0}\mathit{S}}$ = 0.6 | |

Group 1 | 0.5 | 1.0 | 0 | 9.7 |

Group 2 | 0 | 0 | 0 | 15.0 |

Group 3 | 3.3 | 7.4 | 0 | 19.2 |

Group 4 | 5.2 | 9.9 | 1.2 | 24.1 |

car commuters | 0.9 | 1.9 | 0.2 | 13.2 |

bike commuters | 2.9 | 5.9 | 0.2 | 21.5 |

© 2018 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 (http://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Hoffmann, P.; Fischereit, J.; Heitmann, S.; Schlünzen, K.H.; Gasser, I.
Modeling Exposure to Heat Stress with a Simple Urban Model. *Urban Sci.* **2018**, *2*, 9.
https://doi.org/10.3390/urbansci2010009

**AMA Style**

Hoffmann P, Fischereit J, Heitmann S, Schlünzen KH, Gasser I.
Modeling Exposure to Heat Stress with a Simple Urban Model. *Urban Science*. 2018; 2(1):9.
https://doi.org/10.3390/urbansci2010009

**Chicago/Turabian Style**

Hoffmann, Peter, Jana Fischereit, Stefan Heitmann, K. Heinke Schlünzen, and Ingenuin Gasser.
2018. "Modeling Exposure to Heat Stress with a Simple Urban Model" *Urban Science* 2, no. 1: 9.
https://doi.org/10.3390/urbansci2010009