# Impact of Blue Space Geometry on Urban Heat Island Mitigation

^{1}

^{2}

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Materials and Methods

#### 2.1. Governing Equations

^{2}s

^{−1}], ${b}_{i}$ is the buoyancy force [ms${}^{-2}$], and ${g}_{i}$ is the gravitational acceleration [ms${}^{-2}$]. Buoyancy is expressed in terms of variation of temperature $\Delta T$ and vapour concentration $\Delta \omega $ with respect to reference values and their volume expansion coefficients ${\beta}_{T}$ [K${}^{-1}$] and ${\beta}_{\omega}$ [–]. The equations for temperature and water vapour read:

#### 2.2. Evaporation Model

#### 2.3. Algorithm and Numerical Schemes

#### 2.4. Case Study Description

#### 2.4.1. Simulation Outline

#### 2.4.2. Initial and Boundary Conditions

`inletOutlet`condition in OpenFOAM). At the top, a constant shear–stress boundary condition ($\tau =\rho {{u}_{ABL}^{*}}^{2}$) is imposed for U to ensure horizontal homogeneity as proposed by Hargreaves and Wright [37]. For all other quantities, a zero-gradient condition is used. Lastly, a symmetry condition is applied to the lateral boundaries.

#### 2.4.3. Computational Domain

#### 2.5. Sensitivity Analysis

## 3. Results and Discussion

#### 3.1. Varying Blue Space Size

#### 3.1.1. Mean Velocity Field

#### 3.1.2. Temperature and Water Vapour Field

#### 3.1.3. Interface Flux Budget

#### 3.2. Varying Blue Space Shape

#### 3.2.1. Mean Velocity Field

#### 3.2.2. Temperature and Water Vapour Field

#### 3.2.3. Interface Flux Budget

#### 3.3. Limitations and Recommendations for Future Work

## 4. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Conflicts of Interest

## Abbreviations

CFD | Computational Fluid Dynamics |

DC | Downwind Canyon |

GCI | Grid Convergence Index |

LSI | Landscape Shape Index |

NBS | Nature-Based Solutions |

RANS | Reynolds-averaged Navier-Stokes |

RNG | Re-Normalisation Group |

SIMPLE | Semi-Implicit Method for Pressure Linked Equations |

TKE | Turbulent Kinetic Energy |

UHI | Urban Heat Island |

WRF | Weather Research and Forecasting |

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**Figure 1.**Overview of the case study geometry and computational grid: (

**a**) schematic representation of the case geometry; (

**b**) sketch of the computational grid; (

**c**) sampling lines used for the analysis of the results.

**Figure 2.**Normalised profiles along a vertical sampling line in the middle of the open square ($y/H=0$) and up to a height of $z/H=1.5$ above the water body: (

**a**) streamwise velocity ($U/{U}_{0}$); (

**b**) temperature (${T}^{*}$); (

**c**) turbulent kinetic energy ($k/{{U}_{0}}^{2}$).

**Figure 3.**Normalised profiles along a horizontal sampling line in the middle of the open square ($y/H=0$) and at pedestrian level ($z/H=0.23$): (

**a**) streamwise velocity ($U/{U}_{0}$); (

**b**) temperature (${T}^{*}$); (

**c**) turbulent kinetic energy ($k/{{U}_{0}}^{2}$).

**Figure 4.**Velocity streamlines for the cases with a warmer water body ($\Delta T=+2$ K) of different size over a vertical plane at $y/H=0$ in the open square ($-1.5\le x/H\le 1.5$). Normalised velocity magnitude is depicted spatially in the background: (

**a**) baseline scenario; (

**b**) original size (S_1:1); (

**c**) half the original size (S_1:2); (

**d**) a quarter of the original size (S_1:4); (

**e**) one-eighth of the original size (S_1:8); (

**f**) one-sixteenth of the original size (S_1:16).

**Figure 5.**Velocity streamlines for the cases with a warmer water body ($\Delta T=+2$ K) of different sizes over a vertical plane at $y/H=0$ in the downwind canyons ($-0.5\le x/H\le 7.5$). Normalised velocity magnitude is depicted spatially in the background: (

**a**) baseline scenario; (

**b**) original size (S_1:1); (

**c**) half the original size (S_1:2); (

**d**) a quarter of the original size (S_1:4); (

**e**) one-eighth of the original size (S_1:8); (

**f**) one-sixteenth of the original size (S_1:16).

**Figure 6.**Velocity streamlines for the cases with a cooler water body ($\Delta T=-2$ K) with different sizes over a vertical plane at $y/H=0$ in the open square ($-1.5\le x/H\le 1.5$). Normalised velocity magnitude is depicted spatially in the background: (

**a**) baseline scenario; (

**b**) original size (S_1:1); (

**c**) one-eighth of the original size (S_1:8); (

**d**) one-sixteenth of the original size (S_1:16).

**Figure 7.**Profiles of normalised velocity ratios over a horizontal line across the middle of the domain ($y/H=0$) at pedestrian level ($z/H=0.23$) for the warm water body cases ($\Delta T=+2$ K) and for different water body sizes: (

**a**,

**b**) results within the open square ($-1.5\le x/H\le 1.5$) for streamwise ($U/{U}_{0}$) and vertical velocity ($W/{U}_{0}$), respectively; (

**c**,

**d**) results within the downwind canyons (DC1: $2.5\le x/H\le 3.5$, DC2: $4.5\le x/H\le 5.5$) for streamwise and vertical velocity, respectively.

**Figure 8.**Profiles of (

**a**) normalised streamwise ($U/{U}_{0}$) and (

**b**) normalised spanwise ($V/{U}_{0}$) velocity over a horizontal line in the middle of the street canyon ($y/H=1$) at pedestrian level ($z/H=0.23$) for the warm water body cases ($\Delta T=+2$ K) and different water body sizes. The shaded areas denote the position of the water body (blue) and the downwind canyons DC1 and DC2 (grey). The location of the open square is shown with the vertical dotted lines.

**Figure 9.**Profiles of (

**a**) normalised streamwise ($U/{U}_{0}$) and (

**b**) normalised spanwise ($V/{U}_{0}$) velocity over a horizontal line in the middle of the street canyon ($y/H=1$) at pedestrian level ($z/H=0.23$) for the cool water body cases ($\Delta T=-2$ K) and different water body sizes. The shaded areas denote the position of the water body (blue) and the downwind canyons DC1 and DC2 (grey). The location of the open square is shown with the vertical dotted lines.

**Figure 10.**Contours of normalised temperature (${T}^{*}$) and water vapour concentration (${\omega}^{*}$) over a vertical plane in the middle of the domain ($y/H=0$) for the warm water body cases ($\Delta T=+2$ K) and different water body sizes: (

**a**) original size (S_1:1). (

**b**) half the original size (S_1:2). (

**c**) a quarter of the original size (S_1:4); (

**d**) one-eighth of the original size (S_1:8); (

**e**) one-sixteenth of the original size (S_1:16).

**Figure 11.**Contours of normalised temperature (${T}^{*}$) and water vapour concentration (${\omega}^{*}$) over a horizontal plane at pedestrian level ($z/H=0.23$) for the warm water body cases ($\Delta T=+2$ K) and different water body sizes: (

**a**) original size (S_1:1); (

**b**) half the original size (s_1:2); (

**c**) a quarter of the original size (S_1:4); (

**d**) one-eighth of the original size (s_1:8); (

**e**) one-sixteenth of the original size (S_1:16).

**Figure 12.**Contours of normalised temperature (${T}^{*}$) and water vapour concentration (${\omega}^{*}$) over a horizontal plane at pedestrian level ($z/H=0.23$) for the cool water body cases ($\Delta T=-2$ K) and different water body sizes: (

**a**) original size (s_1:1); (

**b**) half the original size (s_1:2); (

**c**) a quarter of the original size (s_1:4); (

**d**) one-eighth of the original size (s_1:8); (

**e**) one-sixteenth of the original size (S_1:16).

**Figure 13.**Profiles of non-dimensional (

**a**,

**b**) vertical velocity ($W/{U}_{0}$), (

**c**,

**d**) TKE ($k/{{U}_{0}}^{2}$) and (

**e**,

**f**) vertical flux budget ($\langle uw\rangle /{{U}_{0}}^{2}$) over a horizontal line at roof level ($z/H=1$) across the domain’s centre line ($y/H=0$) for the warm water body cases and different sizes. Results for (

**a**,

**c**,

**e**) the open square and (

**b**,

**d**,

**f**) the downwind canyons; In panels (

**e**,

**f**), single lines denote mean values, whilst lines with points denote turbulent values.

**Figure 14.**Velocity streamlines for the cases with a cooler water body ($\Delta T=-2$ K) and different shapes over a vertical plane at $y/H=0$ in the open square ($-1.5\le x/H\le 1.5$). Normalised velocity magnitude is depicted spatially in the background: (

**a**) original square water body (LSI_1.1); (

**b**) LSI_1.2; (

**c**) LSI_1.4; (

**d**) LSI_1.6.

**Figure 15.**Profiles of normalised velocity ratios over a horizontal line across the middle of the domain ($y/H=0$) at pedestrian level ($z/H=0.23$) for the warm water body cases ($\Delta T=+2$ K) and for different water body shapes: (

**a**,

**b**) results within the open square ($-1.5\le x/H\le 1.5$) for streamwise ($U/{U}_{0}$) and vertical velocity ($W/{U}_{0}$), respectively; (

**c**,

**d**) results within the downwind canyons (DC1: $2.5\le x/H\le 3.5$, DC2: $4.5\le x/H\le 5.5$) for streamwise and vertical velocity, respectively.

**Figure 16.**Profiles of (

**a**) normalised streamwise ($U/{U}_{0}$) and (

**b**) normalised spanwise ($V/{U}_{0}$) velocity over a horizontal line in the middle of the street canyon ($y/H=1$) at pedestrian level ($z/H=0.23$) for the warm water body cases ($\Delta T=+2$ K) and different water body shapes. The shaded areas denote the position of the downwind canyons DC1 and DC2. The location of the open square is shown with the vertical dotted lines.

**Figure 17.**Profiles of (

**a**) normalised streamwise ($U/{U}_{0}$) and (

**b**) normalised spanwise ($V/{U}_{0}$) velocity over a horizontal line in the middle of the street canyon ($y/H=1$) at pedestrian level ($z/H=0.23$) for the cool water body cases ($\Delta T=-2$K) and different water body shapes. The shaded areas denote the position of the downwind canyons DC1 and DC2. The location of the open square is shown with the vertical dotted lines.

**Figure 18.**Contours of normalised temperature (${T}^{*}$) and water vapour concentration (${\omega}^{*}$) over a vertical plane in the middle of the domain ($y/H=0$) for the warm water body cases ($\Delta T=+2$ K) and different shapes: (

**a**) LSI_1.2; (

**b**) LSI_1.4; (

**c**) LSI_1.6; (

**d**) LSI_1.7; (

**e**) LSI_1.9; results of the original $LSI=1.1$ case can be found in Figure 11a.

**Figure 19.**Contours of normalised temperature (${T}^{*}$) and water vapour concentration (${\omega}^{*}$) over a horizontal plane at pedestrian level ($z/H=0.23$) for the cool water body cases ($\Delta T=-2$ K) and different shapes: (

**a**) $LSI=1.2$; (

**b**) $LSI=1.4$; (

**c**) $LSI=1.6$; (

**d**) $LSI=1.7$; (

**e**) $LSI=1.9$; results of the original $LSI=1.1$ case can be found in Figure 12a.

**Figure 20.**Profiles of non-dimensional (

**a**,

**b**) vertical velocity ($W/{U}_{0}$); (

**c**,

**d**) TKE ($k/{{U}_{0}}^{2}$); and (

**e**,

**f**) vertical flux budget ($\langle uw\rangle /{{U}_{0}}^{2}$) over a horizontal line at roof level ($z/H=1$) across the domain’s centre line ($y/H=0$) for the warm water body cases ($\Delta T=+2$ K) and different shapes. Results for (

**a**,

**c**,

**e**) the open square and (

**b**,

**d**,

**f**) the downwind canyons. In panels (

**e**,

**f**), single lines denote mean values, whilst lines with points denote turbulent values.

**Table 1.**Configuration settings and simulation outline for the simulations under consideration: characteristic airflow velocity (${U}_{0}$), air–water temperature difference ($\Delta {T}_{0}$), dimensionless parameters and simulations conducted for different sizes and shapes including simulation labels. For the definitions of the Richardson ($Ri$) and Grashof ($Gr$) numbers, the reader is referred to Ampatzidis et al. [22].

Airflow | Mixed Convection | ||
---|---|---|---|

Water | Baseline | Warmer | Cooler |

${U}_{0}$ [m/s] | 0.3 | 0.3 | 0.3 |

$\Delta {T}_{0}$ [K] | 0 | +2 | −2 |

$Ri$ | 0 | +1.9 | −1.7 |

$Re$ | $2.9\times {10}^{4}$ | $2.9\times {10}^{4}$ | $2.9\times {10}^{4}$ |

$Gr$ | – | 1.6$\times {10}^{9}$ | 1.4$\times {10}^{9}$ |

Size ($5\times 2$) | – | 1:1 (S_1:1) *, 1:2 (S_1:2), 1:4 (S_1:4), 1:8 (S_1:8), 1:16 (S_1:16) | |

$LSI$ ($6\times 2$) | – | 1.13 (LSI_1.1) *, 1.18 (LSI_1.2), 1.41 (LSI_1.4) | |

1.59 (LSI_1.6), 1.72 (LSI_1.7), 1.88 (LSI_1.9) |

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**MDPI and ACS Style**

Ampatzidis, P.; Cintolesi, C.; Kershaw, T. Impact of Blue Space Geometry on Urban Heat Island Mitigation. *Climate* **2023**, *11*, 28.
https://doi.org/10.3390/cli11020028

**AMA Style**

Ampatzidis P, Cintolesi C, Kershaw T. Impact of Blue Space Geometry on Urban Heat Island Mitigation. *Climate*. 2023; 11(2):28.
https://doi.org/10.3390/cli11020028

**Chicago/Turabian Style**

Ampatzidis, Petros, Carlo Cintolesi, and Tristan Kershaw. 2023. "Impact of Blue Space Geometry on Urban Heat Island Mitigation" *Climate* 11, no. 2: 28.
https://doi.org/10.3390/cli11020028