# Land Use Quantile Regression Modeling of Fine Particulate Matter in Australia

^{*}

## Abstract

**:**

## 1. Introduction

## 2. Literature Review

## 3. Study Area and Data

#### 3.1. Study Area and Air Pollution Data

#### 3.2. Explanatory Variables

#### 3.2.1. Land Use

#### 3.2.2. Population

#### 3.2.3. Road Network

#### 3.2.4. Elevation

#### 3.2.5. Vegetation

## 4. Land Use Quantile Regression (LUQR) for Air Pollution Prediction

## 5. Results

#### 5.1. Optimal Spatial Buffers and Variable Selection

#### 5.2. LUQR Model

#### 5.3. Model Validation

#### 5.4. Spatial Prediction

## 6. Discussion

#### 6.1. Methodological Contributions

#### 6.2. Findings from the LUQR-Based Predictions

#### 6.3. Limitations and Future Recommendations

## 7. Conclusions

## Author Contributions

## Funding

## Institutional Review Board Statement

## Informed Consent Statement

## Data Availability Statement

## Acknowledgments

## Conflicts of Interest

## References

- Kitchin, R.; Lauriault, T.P. Small data in the era of big data. GeoJournal
**2015**, 80, 463–475. [Google Scholar] [CrossRef] - Phillips, S.J.; Dudík, M.; Elith, J.; Graham, C.H.; Lehmann, A.; Leathwick, J.; Ferrier, S. Sample selection bias and presence-only distribution models: Implications for background and pseudo-absence data. Ecol. Appl.
**2009**, 19, 181–197. [Google Scholar] [CrossRef] [PubMed][Green Version] - Hernandez, P.A.; Graham, C.H.; Master, L.L.; Albert, D.L. The effect of sample size and species characteristics on performance of different species distribution modeling methods. Ecography
**2006**, 29, 773–785. [Google Scholar] [CrossRef] - Grinand, C.; Arrouays, D.; Laroche, B.; Martin, M.P. Extrapolating regional soil landscapes from an existing soil map: Sampling intensity, validation procedures, and integration of spatial context. Geoderma
**2008**, 143, 180–190. [Google Scholar] [CrossRef] - Oliver, M.A.; Webster, R. The Variogram and Modelling. In Basic Steps in Geostatistics: The Variogram and Kriging; Springer International Publishing: Cham, Switzerland, 2015; pp. 15–42. [Google Scholar]
- Wang, J.; Xu, C.; Hu, M.; Li, Q.; Yan, Z.; Zhao, P.; Jones, P. A new estimate of the China temperature anomaly series and uncertainty assessment in 1900–2006. J. Geophys. Res. Atmos.
**2014**, 119, 1–9. [Google Scholar] [CrossRef] - Deng, Y.; Wang, S.; Bai, X.; Wu, L.; Cao, Y.; Li, H.; Wang, M.; Li, C.; Yang, Y.; Hu, Z.; et al. Comparison of soil moisture products from microwave remote sensing, land model, and reanalysis using global ground observations. Hydrol. Process.
**2020**, 34, 836–851. [Google Scholar] [CrossRef] - Luo, P.; Song, Y.; Huang, X.; Ma, H.; Liu, J.; Yao, Y.; Meng, L. Identifying determinants of spatio-temporal disparities in soil moisture of the Northern Hemisphere using a geographically optimal zones-based heterogeneity model. ISPRS J. Photogramm. Remote Sens.
**2022**, 185, 111–128. [Google Scholar] [CrossRef] - Liu, J.; Chai, L.; Lu, Z.; Liu, S.; Qu, Y.; Geng, D.; Song, Y.; Guan, Y.; Guo, Z.; Wang, J.; et al. Evaluation of SMAP, SMOS-IC, FY3B, JAXA, and LPRM soil moisture products over the Qinghai-Tibet plateau and its surrounding areas. Remote Sens.
**2019**, 11, 792. [Google Scholar] [CrossRef][Green Version] - Liu, J.; Chai, L.; Dong, J.; Zheng, D.; Wigneron, J.P.; Liu, S.; Zhou, J.; Xu, T.; Yang, S.; Song, Y.; et al. Uncertainty analysis of eleven multisource soil moisture products in the third pole environment based on the three-corned hat method. Remote Sens. Environ.
**2021**, 255, 112225. [Google Scholar] [CrossRef] - Ross, Z.; Jerrett, M.; Ito, K.; Tempalski, B.; Thurston, G.D. A land use regression for predicting fine particulate matter concentrations in the New York City region. Atmos. Environ.
**2007**, 41, 2255–2269. [Google Scholar] [CrossRef] - Beelen, R.; Voogt, M.; Duyzer, J.; Zandveld, P.; Hoek, G. Comparison of the performances of land use regression modelling and dispersion modelling in estimating small-scale variations in long-term air pollution concentrations in a Dutch urban area. Atmos. Environ.
**2010**, 44, 4614–4621. [Google Scholar] [CrossRef] - Olvera, H.A.; Garcia, M.; Li, W.W.; Yang, H.; Amaya, M.A.; Myers, O.; Burchiel, S.W.; Berwick, M.; Pingitore, N.E., Jr. Principal component analysis optimization of a PM
_{2.5}land use regression model with small monitoring network. Sci. Total Environ.**2012**, 425, 27–34. [Google Scholar] [CrossRef] [PubMed][Green Version] - Wang, J.; Xu, H. A novel hybrid spatiotemporal land use regression model system at the megacity scale. Atmos. Environ.
**2021**, 244, 117971. [Google Scholar] [CrossRef] - Li, Z.; Tong, X.; Ho, J.M.W.; Kwok, T.C.; Dong, G.; Ho, K.F.; Yim, S.H.L. A practical framework for predicting residential indoor PM
_{2.5}concentration using land-use regression and machine learning methods. Chemosphere**2021**, 265, 129140. [Google Scholar] [CrossRef] - Wong, P.Y.; Lee, H.Y.; Chen, Y.C.; Zeng, Y.T.; Chern, Y.R.; Chen, N.T.; Lung, S.C.C.; Su, H.J.; Wu, C.D. Using a land use regression model with machine learning to estimate ground level PM
_{2.5}. Environ. Pollut.**2021**, 277, 116846. [Google Scholar] [CrossRef] - Song, Y.; Shen, Z.; Wu, P.; Viscarra Rossel, R. Wavelet geographically weighted regression for spectroscopic modelling of soil properties. Sci. Rep.
**2021**, 11, 17503. [Google Scholar] [CrossRef] - Halliru, A.M.; Loganathan, N.; Hassan, A.A.G.; Mardani, A.; Kamyab, H. Re-examining the environmental Kuznets curve hypothesis in the Economic Community of West African States: A panel quantile regression approach. J. Clean. Prod.
**2020**, 276, 124247. [Google Scholar] [CrossRef] - Tang, J.; Gao, F.; Liu, F.; Han, C.; Lee, J. Spatial heterogeneity analysis of macro-level crashes using geographically weighted Poisson quantile regression. Accid. Anal. Prev.
**2020**, 148, 105833. [Google Scholar] [CrossRef] - Xu, B.; Lin, B. Investigating drivers of CO2 emission in China’s heavy industry: A quantile regression analysis. Energy
**2020**, 206, 118159. [Google Scholar] [CrossRef] - Cade, B.S.; Noon, B.R. A gentle introduction to quantile regression for ecologists. Front. Ecol. Environ.
**2003**, 1, 412–420. [Google Scholar] [CrossRef] - Koenker, R. Quantile Regression: Economic Society Monograph Series; Cambridge University Press: Cambridge, UK, 2005. [Google Scholar]
- Song, Y.Z.; Yang, H.L.; Peng, J.H.; Song, Y.R.; Sun, Q.; Li, Y. Estimating PM
_{2.5}concentrations in Xi’an City using a generalized additive model with multi-source monitoring data. PLoS ONE**2015**, 10, e0142149. [Google Scholar] [CrossRef] [PubMed][Green Version] - Zou, B.; Luo, Y.; Wan, N.; Zheng, Z.; Sternberg, T.; Liao, Y. Performance comparison of LUR and OK in PM
_{2.5}concentration mapping: A multidimensional perspective. Sci. Rep.**2015**, 5, 8698. [Google Scholar] [CrossRef] [PubMed][Green Version] - Han, L.; Zhao, J.; Gao, Y.; Gu, Z.; Xin, K.; Zhang, J. Spatial distribution characteristics of PM
_{2.5}and PM_{10}in Xi’an City predicted by land use regression models. Sustain. Cities Soc.**2020**, 61, 102329. [Google Scholar] [CrossRef] [PubMed] - Shi, Y.; Bilal, M.; Ho, H.C.; Omar, A. Urbanization and regional air pollution across South Asian developing countries–A nationwide land use regression for ambient PM
_{2.5}assessment in Pakistan. Environ. Pollut.**2020**, 266, 115145. [Google Scholar] [CrossRef] - Harper, A.; Baker, P.N.; Xia, Y.; Kuang, T.; Zhang, H.; Chen, Y.; Han, T.L.; Gulliver, J. Development of spatiotemporal land use regression models for PM
_{2.5}and NO_{2}in Chongqing, China, and exposure assessment for the CLIMB study. Atmos. Pollut. Res.**2021**, 12, 101096. [Google Scholar] [CrossRef] - Hoek, G.; Beelen, R.; De Hoogh, K.; Vienneau, D.; Gulliver, J.; Fischer, P.; Briggs, D. A review of land-use regression models to assess spatial variation of outdoor air pollution. Atmos. Environ.
**2008**, 42, 7561–7578. [Google Scholar] [CrossRef] - Shi, Y.; Ren, C.; Cai, M.; Lau, K.K.L.; Lee, T.C.; Wong, W.K. Assessing spatial variability of extreme hot weather conditions in Hong Kong: A land use regression approach. Environ. Res.
**2019**, 171, 403–415. [Google Scholar] [CrossRef] - Tsin, P.K.; Knudby, A.; Krayenhoff, E.S.; Brauer, M.; Henderson, S.B. Land use regression modeling of microscale urban air temperatures in greater Vancouver, Canada. Urban Clim.
**2020**, 32, 100636. [Google Scholar] [CrossRef] - Shi, Y.; Katzschner, L.; Ng, E. Modelling the fine-scale spatiotemporal pattern of urban heat island effect using land use regression approach in a megacity. Sci. Total Environ.
**2018**, 618, 891–904. [Google Scholar] [CrossRef] - Guo, Y.; Su, J.G.; Dong, Y.; Wolch, J. Application of land use regression techniques for urban greening: An analysis of Tianjin, China. Urban For. Urban Green.
**2019**, 38, 11–21. [Google Scholar] [CrossRef][Green Version] - Chen, D.; Chen, H.; Zhao, J.; Xu, Z.; Li, W.; Xu, M. Improving spatial prediction of health risk assessment for Hg, As, Cu, and Pb in soil based on land-use regression. Environ. Geochem. Health
**2020**, 42, 1415–1428. [Google Scholar] [CrossRef] - Henderson, S.B.; Beckerman, B.; Jerrett, M.; Brauer, M. Application of land use regression to estimate long-term concentrations of traffic-related nitrogen oxides and fine particulate matter. Environ. Sci. Technol.
**2007**, 41, 2422–2428. [Google Scholar] [CrossRef] - Jones, R.R.; Hoek, G.; Fisher, J.A.; Hasheminassab, S.; Wang, D.; Ward, M.H.; Sioutas, C.; Vermeulen, R.; Silverman, D.T. Land use regression models for ultrafine particles, fine particles, and black carbon in Southern California. Sci. Total Environ.
**2020**, 699, 134234. [Google Scholar] [CrossRef] - Tularam, H.; Ramsay, L.F.; Muttoo, S.; Brunekreef, B.; Meliefste, K.; de Hoogh, K.; Naidoo, R.N. A hybrid air pollution/land use regression model for predicting air pollution concentrations in Durban, South Africa. Environ. Pollut.
**2021**, 274, 116513. [Google Scholar] [CrossRef] - Eeftens, M.; Beelen, R.; De Hoogh, K.; Bellander, T.; Cesaroni, G.; Cirach, M.; Declercq, C.; Dedele, A.; Dons, E.; De Nazelle, A.; et al. Development of land use regression models for PM
_{2.5}, PM_{2.5}absorbance, PM_{10}and PMcoarse in 20 European study areas; results of the ESCAPE project. Environ. Sci. Technol.**2012**, 46, 11195–11205. [Google Scholar] [CrossRef] - Lee, H.J.; Chatfield, R.B.; Strawa, A.W. Enhancing the applicability of satellite remote sensing for PM
_{2.5}estimation using MODIS deep blue AOD and land use regression in California, United States. Environ. Sci. Technol.**2016**, 50, 6546–6555. [Google Scholar] [CrossRef] - Derdouri, A.; Murayama, Y. A comparative study of land price estimation and mapping using regression kriging and machine learning algorithms across Fukushima prefecture, Japan. J. Geogr. Sci.
**2020**, 30, 794–822. [Google Scholar] [CrossRef] - Munyati, C.; Sinthumule, N. Comparative suitability of ordinary kriging and Inverse Distance Weighted interpolation for indicating intactness gradients on threatened savannah woodland and forest stands. Environ. Sustain. Indic.
**2021**, 12, 100151. [Google Scholar] [CrossRef] - Wang, J.; Cohan, D.S.; Xu, H. Spatiotemporal ozone pollution LUR models: Suitable statistical algorithms and time scales for a megacity scale. Atmos. Environ.
**2020**, 237, 117671. [Google Scholar] [CrossRef] - Rahman, M.M.; Karunasinghe, J.; Clifford, S.; Knibbs, L.D.; Morawska, L. New insights into the spatial distribution of particle number concentrations by applying non-parametric land use regression modelling. Sci. Total Environ.
**2020**, 702, 134708. [Google Scholar] [CrossRef] - Fritsch, M.; Behm, S. Agglomeration and infrastructure effects in land use regression models for air pollution—Specification, estimation, and interpretations. Atmos. Environ.
**2021**, 253, 118337. [Google Scholar] [CrossRef] - Australian Bureau of Statistics. National, State and Territory Population; Australian Bureau of Statistics: Canberra, Australia, 2020.
- Department of Planning, Industry and Environment, New South Wales. New South Wales Air Quality Data Services; Department of Planning, Industry and Environment: New South Wales, Parramatta, Australia, 2021. [Google Scholar]
- Tucker, W.G. An overview of PM
_{2.5}sources and control strategies. Fuel Process. Technol.**2000**, 65, 379–392. [Google Scholar] [CrossRef] - Chen, R.; Yin, P.; Meng, X.; Wang, L.; Liu, C.; Niu, Y.; Liu, Y.; Liu, J.; Qi, J.; You, J.; et al. Associations between coarse particulate matter air pollution and cause-specific mortality: A nationwide analysis in 272 Chinese cities. Environ. Health Perspect.
**2019**, 127, 017008. [Google Scholar] [CrossRef][Green Version] - Giugliano, M.; Lonati, G.; Butelli, P.; Romele, L.; Tardivo, R.; Grosso, M. Fine particulate (PM
_{2.5}–PM1) at urban sites with different traffic exposure. Atmos. Environ.**2005**, 39, 2421–2431. [Google Scholar] [CrossRef] - Kinney, P.L.; Gichuru, M.G.; Volavka-Close, N.; Ngo, N.; Ndiba, P.K.; Law, A.; Gachanja, A.; Gaita, S.M.; Chillrud, S.N.; Sclar, E. Traffic impacts on PM
_{2.5}air quality in Nairobi, Kenya. Environ. Sci. Policy**2011**, 14, 369–378. [Google Scholar] [CrossRef][Green Version] - Hu, H.; Chen, Q.; Qian, Q.; Lin, C.; Chen, Y.; Tian, W. Impacts of traffic and street characteristics on the exposure of cycling commuters to PM
_{2.5}and PM_{10}in urban street environments. Build. Environ.**2021**, 188, 107476. [Google Scholar] [CrossRef] - Xue, W.; Zhang, J.; Zhong, C.; Li, X.; Wei, J. Spatiotemporal PM
_{2.5}variations and its response to the industrial structure from 2000 to 2018 in the Beijing-Tianjin-Hebei region. J. Clean. Prod.**2021**, 279, 123742. [Google Scholar] [CrossRef] - Fang, D.; Yu, B. Driving mechanism and decoupling effect of PM
_{2.5}emissions: Empirical evidence from China’s industrial sector. Energy Policy**2021**, 149, 112017. [Google Scholar] [CrossRef] - Aguilera, R.; Corringham, T.; Gershunov, A.; Benmarhnia, T. Wildfire smoke impacts respiratory health more than fine particles from other sources: Observational evidence from Southern California. Nat. Commun.
**2021**, 12, 1493. [Google Scholar] [CrossRef] - Hua, J.; Zhang, Y.; de Foy, B.; Mei, X.; Shang, J.; Feng, C. Competing PM
_{2.5}and NO2 holiday effects in the Beijing area vary locally due to differences in residential coal burning and traffic patterns. Sci. Total Environ.**2021**, 750, 141575. [Google Scholar] [CrossRef] - Zhang, Y.; Shen, Z.; Sun, J.; Zhang, L.; Zhang, B.; Zou, H.; Zhang, T.; Ho, S.S.H.; Chang, X.; Xu, H.; et al. Parent, alkylated, oxygenated and nitrated polycyclic aromatic hydrocarbons in PM
_{2.5}emitted from residential biomass burning and coal combustion: A novel database of 14 heating scenarios. Environ. Pollut.**2021**, 268, 115881. [Google Scholar] [CrossRef] [PubMed] - Ikemori, F.; Uranishi, K.; Asakawa, D.; Nakatsubo, R.; Makino, M.; Kido, M.; Mitamura, N.; Asano, K.; Nonaka, S.; Nishimura, R.; et al. Source apportionment in PM
_{2.5}in central Japan using positive matrix factorization focusing on small-scale local biomass burning. Atmos. Pollut. Res.**2021**, 12, 162–172. [Google Scholar] [CrossRef] - Xu, W.; Jin, X.; Liu, M.; Ma, Z.; Wang, Q.; Zhou, Y. Analysis of spatiotemporal variation of PM
_{2.5}and its relationship to land use in China. Atmos. Pollut. Res.**2021**, 12, 101151. [Google Scholar] [CrossRef] - Song, J.; Zhou, S.; Peng, Y.; Xu, J.; Lin, R. Relationship between neighborhood land use structure and the spatiotemporal pattern of PM
_{2.5}at the microscale: Evidence from the central area of Guangzhou, China. Environ. Plan. B Urban Anal. City Sci.**2021**, 49, 485–500. [Google Scholar] [CrossRef] - Lu, D.; Mao, W.; Xiao, W.; Zhang, L. Non-Linear Response of PM
_{2.5}Pollution to Land Use Change in China. Remote Sens.**2021**, 13, 1612. [Google Scholar] [CrossRef] - Mhawish, A.; Banerjee, T.; Sorek-Hamer, M.; Bilal, M.; Lyapustin, A.I.; Chatfield, R.; Broday, D.M. Estimation of high-resolution PM
_{2.5}over the indo-gangetic plain by fusion of satellite data, meteorology, and land use variables. Environ. Sci. Technol.**2020**, 54, 7891–7900. [Google Scholar] [CrossRef] [PubMed] - Australian Bureau of Agricultural and Resource Economics and Sciences. ABARES 2021, Catchment Scale Land Use of Australia—Update December 2020; Australian Bureau of Agricultural and Resource Economics and Sciences: Canberra, Australia, 2021. [CrossRef]
- Australian Bureau of Statistics. 1270.0.55.001—Australian Statistical Geography Standard (ASGS): Volume 1—Main Structure and Greater Capital City Statistical Areas, July 2016; Australian Bureau of Statistics: Canberra, Australia, 2017.
- Australia, G. Digital Elevation Model (DEM) of Australia Derived from LiDAR 5 Metre Grid; Commonwealth of Australia and Geoscience Australia: Canberra, Australia, 2015. [Google Scholar]
- Gorelick, N.; Hancher, M.; Dixon, M.; Ilyushchenko, S.; Thau, D.; Moore, R. Google Earth Engine: Planetary-scale geospatial analysis for everyone. Remote Sens. Environ.
**2017**, 202, 18–27. [Google Scholar] [CrossRef] - Sheng, Q.; Zhang, Y.; Zhu, Z.; Li, W.; Xu, J.; Tang, R. An experimental study to quantify road greenbelts and their association with PM
_{2.5}concentration along city main roads in Nanjing, China. Sci. Total Environ.**2019**, 667, 710–717. [Google Scholar] [CrossRef] - Witkowska, A.; Lewandowska, A.U.; Saniewska, D.; Falkowska, L.M. Effect of agriculture and vegetation on carbonaceous aerosol concentrations (PM
_{2.5}and PM_{10}) in Puszcza Borecka National Nature Reserve (Poland). Air Qual. Atmos. Health**2016**, 9, 761–773. [Google Scholar] [CrossRef][Green Version] - Song, Z.; Li, R.; Qiu, R.; Liu, S.; Tan, C.; Li, Q.; Ge, W.; Han, X.; Tang, X.; Shi, W.; et al. Global land surface temperature influenced by vegetation cover and PM
_{2.5}from 2001 to 2016. Remote Sens.**2018**, 10, 2034. [Google Scholar] [CrossRef][Green Version] - Didan, K. MOD13A1 MODIS/Terra Vegetation Indices 16-Day L3 Global 500m SIN Grid V006, NASA EOSDIS Land Processes DAAC. 2015. Available online: https://lpdaac.usgs.gov/products/mod13a1v006/ (accessed on 30 October 2021).
- Hair, J.; Anderson, R.; Babin, B.; Black, W. Multivariate Data Analysis: A Global Perspective (Vol. 7); Pearson Upper Saddle River: Hoboken, NJ, USA, 2010. [Google Scholar]
- Song, Y.; Ge, Y.; Wang, J.; Ren, Z.; Liao, Y.; Peng, J. Spatial distribution estimation of malaria in northern China and its scenarios in 2020, 2030, 2040 and 2050. Malar. J.
**2016**, 15, 345. [Google Scholar] [CrossRef][Green Version] - Ge, Y.; Song, Y.; Wang, J.; Liu, W.; Ren, Z.; Peng, J.; Lu, B. Geographically weighted regression-based determinants of malaria incidences in northern China. Trans. GIS
**2017**, 21, 934–953. [Google Scholar] [CrossRef] - Buchinsky, M. Estimating the asymptotic covariance matrix for quantile regression models a Monte Carlo study. J. Econom.
**1995**, 68, 303–338. [Google Scholar] [CrossRef] - Koenker, R.; Machado, J.A. Goodness of fit and related inference processes for quantile regression. J. Am. Stat. Assoc.
**1999**, 94, 1296–1310. [Google Scholar] [CrossRef] - Bernales, A.; Antolihao, J.; Samonte, C.; Campomanes, F.; Rojas, R.; Silapan, J. Modelling the relationship between land surface temperature and landscape patterns of land use land cover classification using multi linear regression models. Int. Arch. Photogramm. Remote Sens. Spat. Inf. Sci.
**2016**, 41, 851–856. [Google Scholar] [CrossRef][Green Version] - Ross, Z.; English, P.B.; Scalf, R.; Gunier, R.; Smorodinsky, S.; Wall, S.; Jerrett, M. Nitrogen dioxide prediction in Southern California using land use regression modeling: Potential for environmental health analyses. J. Expo. Sci. Environ. Epidemiol.
**2006**, 16, 106–114. [Google Scholar] [CrossRef] - John, O.O. Robustness of quantile regression to outliers. Am. J. Appl. Math. Stat.
**2015**, 3, 86–88. [Google Scholar] - Furno, M.; Vistocco, D. Quantile Regression: Estimation and Simulation; John Wiley & Sons: Hoboken, NJ, USA, 2018; Volume 216. [Google Scholar]

**Figure 1.**Spatial distributions of air quality monitoring stations and annual mean PM${}_{2.5}$ in Great Sydney Region, New South Wales, Australia.

**Figure 2.**Spatial distributions of explanatory variables: land use (

**a**), population density (

**b**), road network (

**c**), elevation (

**d**), and vegetation (NDVI) (

**e**).

**Figure 3.**Coefficients of explanatory variables in the land use quantile regression (LUQR) model for PM${}_{2.5}$ prediction. The orange lines are coefficients by quantiles in LUQR model, and orange areas show the 95% CIs of LUQR coefficients. The blue horizontal lines are coefficients of the linear regression model, and the blue dashed lines are the 95% confidence intervals (CIs) of the coefficients in the linear regression model.

**Figure 4.**The leave-one-out cross-validation (LOOCV) of land use quantile regression (LUQR) models of PM${}_{2.5}$ with different values of quantile parameter $\tau $. (

**a**) Comparison of R${}^{2}$ of LUR (dashed orange line) and LUQR (orange line); (

**b**) Comparison of RMSE (blue) and MAE (green) of LUR (dash lines) and LUQR (lines).

**Figure 5.**Comparison of LOOCV results between LUR and LUQR models: relationship between observations and predictions of PM${}_{2.5}$ concentrations in LOOCV (

**a**) and relationship between predictions and residuals of PM${}_{2.5}$ concentrations in LOOCV (

**b**).

**Figure 6.**Spatial predictions of PM${}_{2.5}$ concentrations using LUQR ($\tau $ = 0.37), LUQR ($\tau $ = 0.50), LUQR ($\tau $ = 0.53) and LUR models.

**Figure 8.**Spatial distributions of the difference between LUR-based prediction (${Z}_{LUR}$) and LUQR-based prediction (${Z}_{LUQR}$) (

**a**), and transect along red (

**b**) and orange (

**c**) lines. (“Z” is predictions of models).

Variable | Code | Optimal Buffer (km) | Min | Mean | Median | Max | Std ${}^{\mathit{a}}$ | |
---|---|---|---|---|---|---|---|---|

PM${}_{2.5}$ ($\mathsf{\mu}$g/m${}^{3}$) | / | / | 5.60 | 7.83 | 7.80 | 9.10 | 0.86 | |

Land use: ratio (%) | Natural environments | NE | 3 | 0.38 | 12.22 | 6.51 | 63.19 | 15.38 |

Production from natural environments | PNE | 3.5 | 0.00 | 3.87 | 0.56 | 30.04 | 7.51 | |

Dryland agriculture | DA | 0.5 | 0.00 | 7.86 | 0.00 | 45.00 | 13.18 | |

Built-up region | BUR | 3 | 16.08 | 61.81 | 62.75 | 78.44 | 15.62 | |

Industrial region | IR | 3 | 0.85 | 14.93 | 13.37 | 27.04 | 8.07 | |

Population density (persons/km${}^{2}$) | PPDS | 5 | 110 | 3077 | 2328 | 9292 | 2767 | |

Highway density (km/km${}^{2}$) | HWDS | 2.5 | 0.000 | 0.821 | 0.688 | 2.600 | 0.790 | |

Major road density (km/km${}^{2}$) | MRDS | 4.5 | 0.169 | 1.710 | 1.828 | 3.925 | 1.093 | |

Elevation (m) | ELV | 5 | 14.04 | 81.54 | 45.28 | 416.71 | 108.23 | |

NDVI | NDVI | 0.5 | 0.368 | 0.534 | 0.533 | 0.732 | 0.107 |

^{a}Std: Standard deviation.

**Table 2.**Goodness-of-fit and errors of land use regression (LUR) models for selected individual explanatory variables. The unit of RMSE and MAE is $\mathsf{\mu}$g/m${}^{3}$.

Variable | Code | Optimal Buffer (km) | R${}^{2}$ | RMSE | MAE | |
---|---|---|---|---|---|---|

Land use: ratio (%) | Natural environments | NE | 3 | 0.187 | 0.835 | 0.706 |

Production from natural environments | PNE | 3.5 | 0.001 | 1.129 | 0.813 | |

Dryland agriculture | DA | 0.5 | 0.057 | 0.894 | 0.684 | |

Built-up regions | BUR | 3 | 0.234 | 0.754 | 0.638 | |

Industrial regions | IR | 3 | 0.033 | 0.902 | 0.741 | |

Population density (persons/km${}^{2}$) | PPDS | 5 | 0.002 | 0.898 | 0.735 | |

Highway density (km/km${}^{2}$) | HWDS | 2.5 | 0.053 | 0.847 | 0.693 | |

Major road density (km/km${}^{2}$) | MRDS | 4.5 | 0.037 | 0.910 | 0.746 | |

Elevation (m) | ELV | 5 | 0.189 | 0.765 | 0.620 | |

NDVI | NDVI | 0.5 | 0.034 | 0.905 | 0.708 |

**Table 3.**Model evaluation using a leave-one-out cross validation. The unit of RMSE and MAE is $\mathsf{\mu}$g/m${}^{3}$.

Model | R${}^{2}$ | RMSE | MAE |
---|---|---|---|

LUQR ($\tau $ = 0.37) | 0.568 | 0.569 | 0.412 |

LUQR ($\tau $ = 0.50) | 0.540 | 0.587 | 0.395 |

LUQR ($\tau $ = 0.53) | 0.564 | 0.574 | 0.385 |

LUR | 0.430 | 0.657 | 0.511 |

Publisher’s Note: MDPI stays neutral with regard to jurisdictional claims in published maps and institutional affiliations. |

© 2022 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 (https://creativecommons.org/licenses/by/4.0/).

## Share and Cite

**MDPI and ACS Style**

Wu, P.; Song, Y.
Land Use Quantile Regression Modeling of Fine Particulate Matter in Australia. *Remote Sens.* **2022**, *14*, 1370.
https://doi.org/10.3390/rs14061370

**AMA Style**

Wu P, Song Y.
Land Use Quantile Regression Modeling of Fine Particulate Matter in Australia. *Remote Sensing*. 2022; 14(6):1370.
https://doi.org/10.3390/rs14061370

**Chicago/Turabian Style**

Wu, Peng, and Yongze Song.
2022. "Land Use Quantile Regression Modeling of Fine Particulate Matter in Australia" *Remote Sensing* 14, no. 6: 1370.
https://doi.org/10.3390/rs14061370