# Sky View Factor Calculation in Urban Context: Computational Performance and Accuracy Analysis of Two Open and Free GIS Tools

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## Abstract

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## 1. Introduction

- the analytical solution is only adapted for urban canyons having an infinite length, which is rarely the case in real urban tissues. Moreover, when averaged at block scale, the $SV{F}_{mid-canyon}$ is underestimated since it is only calculated at the center of the street.
- Concerning the empirical method, the relationship proposed by Bernabé et al. [16] is not valid for the SVF as defined in the LCZ properties. Bernabé et al. [16] calculated the SVF averaged to all urban surfaces (roofs, facades and ground), whereas, in the LCZ classification, it should only be averaged to ground surfaces.
- Last but not least, these methods are not adapted to all complexes urban tissues: the estimated SVF for some of them can be far from the real SVF value.

## 2. Material

## 3. Methodology

#### 3.1. Presentation of the SVF Algorithm Used in OrbisGIS

- for each ray (each direction);
- the ray is split into segments of $RSL=$ 5 m length in order to optimize the calculation speed (according to a preliminary study, this parameter has very little effect on the calculation speed when its value is included within a (3–7) m range),
- the obstacles intersecting each of these segments are identified,
- for each intersection, the angle ${\Theta}_{i}$ is calculated by means of Equation (3),
- the highest ${\Theta}_{m}$ value encountered along the ray is conserved and used to calculate the corresponding sky hemisphere hidden in this direction (Equation (4)),

- the SVF is finally calculated subtracting the sum of the hidden surfaces ${S}_{{H}_{d}}$ in the $ND$ directions to the total surface hemisphere (Equation (5)).

#### 3.2. Global Methodology for Algorithm Evaluation

- when they compared values based on a 300 m ray length to the ones obtained with a 500 m ray length, the largest difference reported in their domain was just 0.031,
- no difference was reported in their domain when they used either 180 or 360 numbers of directions.

#### 3.3. Identification of the Reference Algorithm

#### 3.4. Empirical Relationship between Block Mean SVF and Morphological Indicators

## 4. Results

#### 4.1. Identification of the Reference Algorithm

#### 4.2. Effect of the Algorithm Input Parameters

#### 4.3. Ideal Input Parameters for Block Mean SVF Calculation

- C1: (RL = 300 m, ND = 180, GR = 10 m, SAGA algorithm, SAGA grid): it is the fastest of the (almost) no biased SAGA combination,
- C2: (RL = 100 m, ND = 60, GR = 2 m, SAGA algorithm, SAGA grid): the combination C1 has no bias but a high interquartile, whereas this combination has a limited bias and is one of the fastest having one of the lowest interquartiles,
- C3: (RL = 100 m, ND = 60, GR = 5 m, OrbisGIS algorithm, Orbis grid): it is the fastest of the almost no biased OrbisGIS combinations (the median error is less than 0.001),
- C4: (RL = 100 m, ND = 60, GR = 10 m, OrbisGIS algorithm, Orbis grid): the fastest combination having about the same bias and interquartile error as combination C2.

#### 4.4. Sensitivity of the Block Mean SVF Calculation to the LCZ Built Type

#### 4.5. Uncertainty on the SVF Value Predicted by the Algorithms or by the Morphological Indicators

## 5. Discussion

## 6. Conclusions

- some of the values obtained using the SAGA software are negative. A further description and analysis of the SAGA algorithm and performance should be conducted and shared with the urban climate community.
- The nonlinearity of the relation between SVF and the $SV{F}_{CAN}$ indicator may be further investigated, as well as the curious simplicity of the relation between SVF and ${F}_{F}$.
- All results have been produced on a limited dataset. Only the city of Paris was sampled, it would then be interesting to verify that the optimized combinations identified for the city of Paris are identical for other urban configurations and urban tissues (such as American or Asian large cities).
- The influence of the LCZ built type on the SVF calculation error has been investigated. However, the LCZ dataset used seems slightly biased regarding the SVF parameter. Very few LCZ classification algorithms have been elaborated taking into account the SVF values. This issue is addressed to the urban climate community.
- The effect of the $RSL$ parameter (OrbisGIS) on the computation time has been studied on a limited number of points. More investigations could be performed in order to further increase the performance of this algorithm.

## Author Contributions

## Funding

## Acknowledgments

## Conflicts of Interest

## References

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**Figure 1.**Abridged definitions for LCZ built types. Source: Stewart and Oke [14]—©American Meteorological Society, used with permission.

**Figure 2.**Selected 10 Paris urban blocks by LCZ type (defined Figure 1) and the corresponding buildings located within a 300 m radius. Based on the LCZ database produced by the IAUIdF. Note that the LCZ corresponding to each urban block has been colored at the 300 m buffer scale in order to make them identifiable.

**Figure 3.**Calculation of the approximated surface hemisphere (blue) hidden by the buildings’ obstacles (red) in a given direction (green line). In this example, the hemisphere is split into height sectors (number of directions) and the surface of the hemisphere considered as hidden by the buildings in the given direction is shown in grey.

**Figure 5.**The SAGA-GIS and OrbisGIS grids and the corresponding buildings used for the SVF calculation.

**Figure 6.**Building configuration for the analytical solution calculation: (

**a**) configuration 1: circularly extruded building; (

**b**) configuration 2: street canyon.

**Figure 7.**Scheme of the raster-based approach (SAGA software) for the configuration 1–scenario 1. The squares represent the pixels of the raster: the blue ones are considered as building surfaces, the white ones as ground surfaces. The SVF is calculated from the pixel covered by the pink circle.

**Figure 8.**Effect of the input parameters value on the SVF difference recorded at point scale using OrbisGIS or SAGA-GIS algorithm: (

**a**) grid resolution; (

**b**) ray length; and (

**c**) number of directions. The red line is the median point, the upper and lower box limits are, respectively, the first and third quartiles and the lower and upper whisker are the 5 and 95 percentiles.

**Figure 10.**Block mean SVF error versus processing time duration using (

**a**) SAGA-GIS algorithm and SAGA grid; (

**b**) OrbisGIS algorithm and SAGA grid; and (

**c**) OrbisGIS algorithm and Orbis grid. The marker is the median value of the 72 blocks and the whiskers are the lower and upper quartile.

**Figure 11.**Block mean SVF error regarding the LCZ built type for (

**a**) combination C1; (

**b**) combination C2; (

**c**) combination C3; and (

**d**) combination C4. The blue dot represents the median SVF error, the blue segment is the range of the SVF error. Based on the LCZ database produced by the IAUIdF.

**Figure 12.**Relationship between block mean SVF value calculated using the reference algorithm combination $SV{F}_{REF}$ and (

**a**) canyon street SVF; (

**b**) aspect ratio; (

**c**) facade density; and (

**d**) facade density fraction. The red line is the regression line and the dotted-lines represent the 95% prediction interval. Based on the LCZ database produced by the IAUIdF.

**Figure 13.**Urban block SVF values (red dots) splitted by LCZ built type and their corresponding SVF lower and upper threshold (green segments), based on the LCZ database produced by the IAUIdF.

**Figure 14.**SVF of the Paris urban blocks: (

**a**) values obtained using combination C4; (

**b**) difference between the values obtained using combination C2 and the ones using combination C4; and (

**c**) difference between the values obtained using the facade density ratio formulae and the ones using combination C4.

Parameter to Evaluate | Values to Test |
---|---|

Ray length (m) | 100, 200, 300 |

Number of directions | 60, 120, 180 |

Grid resolution (m) | 1, 2, 5, 10 |

Scenario | Configuration 1 | Configuration 2 | |||
---|---|---|---|---|---|

${\mathbf{H}}_{\mathit{ext}-\mathit{bu}}$ | ${\mathbf{D}}_{\mathit{ctyd}}$ | ${\mathbf{H}}_{\mathit{can}-\mathit{bu}}$ | ${\mathbf{W}}_{\mathit{can}-\mathit{str}}$ | ${\mathbf{L}}_{\mathit{can}-\mathit{str}}$ | |

1 | 20 m | 39 m | 20 m | 39 m | 2000 m |

2 | 20 m | 40 m | 20 m | 40 m | 2000 m |

Notation | Name | Description | Formulae | Reference |
---|---|---|---|---|

${D}_{F}$ | Facade density | The building external free facades area (${S}_{F}$) is divided by the block surface (${S}_{REF}$) | $\frac{{S}_{F}}{{S}_{REF}}$ | Bocher et al. [29] |

${F}_{F}$ | Facade density fraction | The building external free facades area is divided by the block surface plus the building free facades area | $\frac{{S}_{F}}{{S}_{REF}+{S}_{F}}$ | Bernabé et al. [16] |

$H/W$ | Aspect ratio | The street canyon definition is extended to any urban tissue using the ratio of the building external free facades and the land free surface (urban block area minus building footprint area–${S}_{B}$) | $\frac{{S}_{F}}{{S}_{REF}-{S}_{B}}$ | - |

$SV{F}_{CAN}$ | Canyon street SVF | The SVF is calculated using the aspect ratio considering all the streets of the urban block as street canyons | $cos\left(atan\right(2\phantom{\rule{0.166667em}{0ex}}\xb7\phantom{\rule{0.166667em}{0ex}}H/W\left)\right)$ | Oke [15] |

**Table 4.**SVF values calculated for each combination of method (algorithm or analytical solution), scenario and building configuration.

Scenario | Building Configuration | OrbisGIS | SAGA-GIS | Analytical Solution |
---|---|---|---|---|

1 | 1 (circular courtyard) | 0.50000 (≃0%) | 0.50000 (=0%) | 0.5 |

2 (street canyon) | 0.70713 (+0.004%) | 0.70608 (−0.15%) | 0.70711 | |

2 | 1 (circular courtyard) | 0.52199 (≃0%) | 0.52438 (+0.45%) | 0.52199 |

2 (street canyon) | 0.72252 (+0.003%) | 0.71993 (−0.35%) | 0.72249 |

Method | Morphological Indicators | Algorithm Combinations | ||||||
---|---|---|---|---|---|---|---|---|

${\mathit{F}}_{\mathit{F}}$ | ${\mathit{D}}_{\mathit{F}}$ | $\mathit{H}/\mathit{W}$ | ${\mathit{SVF}}_{\mathit{CAN}}$ | C1 | C2 | C3 | C4 | |

Standard deviation of the estimate | 0.087 | 0.107 | 0.147 | 0.073 | 0.085 | 0.033 | 0.014 | 0.027 |

Name | C1 | C2 | C3 | C4 | ${\mathit{F}}_{\mathit{F}}$ | ${\mathit{D}}_{\mathit{F}}$ | $\mathit{H}/\mathit{W}$ | ${\mathit{SVF}}_{\mathit{CAN}}$ | |
---|---|---|---|---|---|---|---|---|---|

Method | Type | SAGA GIS | SAGA GIS | Orbis GIS | Orbis GIS | Morpho indic | Morpho indic | Morpho indic | Morpho indic |

ND | 180 | 60 | 60 | 60 | - | - | - | - | |

RL (m) | 300 | 100 | 100 | 100 | - | - | - | - | |

GR (m) | 10 | 2 | 5 | 10 | - | - | - | - | |

Results | $SV{F}_{REF}=f\left(SV{F}_{CALC}\right)$ | OK | OK | OK | OK | Non normal residuals | OK | Non normal residuals | Non normal residuals |

Particular LCZ bias | LCZ1, 2 & 3 | LCZ1, 2 & 3 | No | No | - | - | - | - | |

Particular LCZ uncertainty | No | No | No | LCZ3 & 6 | - | - | - | - | |

Stand. dev. estimate | 0.085 | 0.033 | 0.014 | 0.027 | 0.087 | 0.107 | 0.147 | 0.073 | |

Comput. time for Paris (s) | - | 18,970 | - | 2890 | - | 250 | - | - |

© 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**

Bernard, J.; Bocher, E.; Petit, G.; Palominos, S.
Sky View Factor Calculation in Urban Context: Computational Performance and Accuracy Analysis of Two Open and Free GIS Tools. *Climate* **2018**, *6*, 60.
https://doi.org/10.3390/cli6030060

**AMA Style**

Bernard J, Bocher E, Petit G, Palominos S.
Sky View Factor Calculation in Urban Context: Computational Performance and Accuracy Analysis of Two Open and Free GIS Tools. *Climate*. 2018; 6(3):60.
https://doi.org/10.3390/cli6030060

**Chicago/Turabian Style**

Bernard, Jérémy, Erwan Bocher, Gwendall Petit, and Sylvain Palominos.
2018. "Sky View Factor Calculation in Urban Context: Computational Performance and Accuracy Analysis of Two Open and Free GIS Tools" *Climate* 6, no. 3: 60.
https://doi.org/10.3390/cli6030060