# Air Quality Monitoring Network Design Optimisation for Robust Land Use Regression Models

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## Abstract

**:**

## 1. Introduction

## 2. Related Work

## 3. Material

- y is an n × 1 vector of air pollution concentration from monitoring sites at any particular time (in our case annual mean $N{O}_{2}$ concentration at monitoring stations);
- X is an n × k matrix with observations of k independent variables for the n available air pollution monitoring stations;
- $\beta $ is a k × 1 vector of unknown parameters that we want to estimate; and
- $\u03f5$ is an n × 1 vector of errors, assumed to be independent and identically distributed.

## 4. Method

#### 4.1. Spatial Simulated Annealing (SSA)

#### 4.2. Optimisation Criterion Estimation

#### 4.3. The Optimisation Procedure

- A LUR model is chosen for the study area by selecting predictors that explain the air pollutant considered.
- An initial (possibly existing) monitoring design ${D}_{0}$ is defined, consisting of n observations to be optimised.
- The area of study A is discretised, the raster is defined with N raster nodes.
- ${D}_{0}$ is modified, returning a monitoring design ${D}_{1}$ and the new mean prediction error is calculated
- A new monitoring design is accepted if it reduced the optimisation criterion value or rejected as the basis for further optimisation based on Equation (8).
- The optimisation continues until the proposal monitoring designs are no longer accepted, based on energy transition and iteration parameters.

## 5. Results

#### 5.1. Optimisation without a Weighted Function for the Study Area

#### 5.2. Optimisation with a Population Weighted Function for the Study Area

#### 5.3. Sensitivity of the Optimisation Methods

#### 5.4. Comparative Analysis

## 6. Discussion

#### Limitations and Future Work

## 7. Conclusions

## Author Contributions

## Acknowledgments

## Conflicts of Interest

## Abbreviations

MND | Monitoring Network Design |

LUR | Land Use Regression |

ESCAPE | European Study of Cohorts for Air Pollution Effects |

OECD | Organisation for Economic Co-operation and Development |

WHO | World Health Organisation |

PM | Particulate Matter |

EC | Elemental Carbon |

${O}_{3}$ | Ozone |

CORINE | coordination of information on the environment |

## Appendix A

**Figure A1.**Populated housing area map with initial monitoring station locations (red plus signs) for study area.

## Appendix B

## Appendix C

Various other configurations realised during the study for different probability of acceptance | |
---|---|

Without weight optimisation | Population weighted optimisation |

Spatial mean prediction Error: 0.1990 | Spatial mean prediction Error: 404.57 |

Spatial mean prediction Error: 0.2039 | Spatial mean prediction Error: 363.34 |

Spatial mean prediction Error: 0.21179 | Spatial mean prediction Error: 332.86 |

Spatial mean prediction Error: 0.2018 | Spatial mean prediction Error: 370.25 |

Spatial mean prediction Error: 0.1918 | Spatial mean prediction Error: 385.52 |

Spatial mean prediction Error: 0.2027 | Spatial mean prediction Error:405.39 |

Spatial mean prediction Error: 0.2579 | Spatial mean prediction Error: 387.15 |

Spatial mean prediction Error: 0.2043 | Spatial mean prediction Error: 387.57 |

Spatial mean prediction Error: 0.19381 | Spatial mean prediction Error: 27798.28 |

Spatial mean prediction Error: 0.2094 | Spatial mean prediction Error: 333.96 |

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**Figure 1.**Study area: City of Münster. (

**a**) Administrative boundary and monitoring station locations in the study area. (

**b**) Study area divided into 599 grid cells.

**Figure 2.**$N{O}_{2}$ concentration ($\mathsf{\mu}$g/m${}^{3}$) map predicted by CHIMERE model as of 20 October 2017 for Münster.

**Figure 3.**Schematic overview of the proposed optimisation method. Since no LUR regression model was available for the study area at the moment of the analysis, the LUR model from the ESCAPE study was used in this paper.

**Figure 4.**Spatial mean prediction error achieved by SSA at different probabilities of acceptance using the optimisation method without weights.

**Figure 5.**Energy transition while running optimisation in SSA using parameters of 0.3 probability of acceptance after removing five higher values.

**Figure 6.**Monitoring network designs realised after using the first optimisation criterion. (

**a**) Initial monitoring network design (D

_{0}). (

**b**) Optimised monitoring network design after using criterion.

**Figure 7.**Spatial mean prediction error achieved by SSA at different probability of acceptance using optimisation method with population weighted criterion.

**Figure 8.**Monitoring network designs obtained using a population weighted optimisation criterion. (

**a**) Initial monitoring network design (D

_{0}). (

**b**) Monitoring network design after population weighted optimisation.

**Figure 9.**Deviation of the spatial mean prediction error values from mean value obtained after 15 repetitions with same parameters.

**Figure 10.**Summary of least spatial mean prediction error values obtained for different numbers of monitoring stations .

Variable | Variable Description |
---|---|

rdcount_1000 | Road count in 1000 m buffer |

minrdcount_100 | Minor road count in 100 m buffer |

minrdcount_500 | Minor road count in 500 m buffer |

rdlength_100 | Road length count in 100 m buffer |

rdlength_5000 | Road length count in 5000 m buffer |

rdlength_50 | Road length count in 50 m buffer |

mjrdlength_300 | Major road length count in 300 m buffer |

dist.mjrd | Distance to major roads |

minrdlength_5000 | Minor road count in 5000 m |

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## Share and Cite

**MDPI and ACS Style**

Gupta, S.; Pebesma, E.; Mateu, J.; Degbelo, A. Air Quality Monitoring Network Design Optimisation for Robust Land Use Regression Models. *Sustainability* **2018**, *10*, 1442.
https://doi.org/10.3390/su10051442

**AMA Style**

Gupta S, Pebesma E, Mateu J, Degbelo A. Air Quality Monitoring Network Design Optimisation for Robust Land Use Regression Models. *Sustainability*. 2018; 10(5):1442.
https://doi.org/10.3390/su10051442

**Chicago/Turabian Style**

Gupta, Shivam, Edzer Pebesma, Jorge Mateu, and Auriol Degbelo. 2018. "Air Quality Monitoring Network Design Optimisation for Robust Land Use Regression Models" *Sustainability* 10, no. 5: 1442.
https://doi.org/10.3390/su10051442