Exploring the modeling of spatiotemporal variations in ambient air pollution within the land use regression framework: Estimation of PM₁₀ concentrations on a daily basis

Figures & data

Table 1. List of the 12 models developed

Model	Description	Number of FSMs	Input Data
Vienna 1	Standard MLR approach for Vienna	13	2012
Vienna 2	Standard MLR approach using a longer period of input data	13	2011–2012
Vienna 3	Addition of seasonal and weekly variation	13	2011–2012
Vienna 4	Alternative statistical technique (NPR) using Vienna 3 input data	13	2011–2012
Vienna 5	Alternative statistical technique (ANN) using Vienna 3 input data	13	2011–2012
Dublin 1	Standard MLR a longer period of input data	7	2007–2009
Dublin 2	Addition of seasonal and weekly variation Dublin 1	7	2007–2009
Dublin 3	Alternative statistical technique (NPR) using Dublin 2 input data	7	2007–2009
Dublin 4	Alternative statistical technique (ANN) using Dublin 3 input data	7	2007–2009
Dublin 5	Standard MLR approach using a longer period of input data, but limited FSMs	5	2007–2009
Dublin 6	Standard MLR approach for Dublin	5	2009
Dublin 7	Standard MLR approach, including new predictor variables for air mass history and peak traffic count	5	2009

Table 2. List of predictor variables applied to each model developed

			Vienna			Dublin
Variable	Variable Code		1–2	3–5	1	2–4	5–6	7
Air mass history rating	D1	—						√
Vehicle km traveled* (20 m)	D2							√
Vehicle km traveled* (30 m)	D3	—			√	√	√
Peak traffic count at nearest intersection*	D4	—						√
Major road^# (35 m)	—	V1	√	√
Stability class	D5	—			√	√	√
Open space area (100 m)	D6	V2	√	√	√	√	√
Population density^‡ (50 m buffer)	—	V3	√	√
Temperature* (°C)	—	V4	√	√
Rainfall/precipitation** (mm)	D7	V5	√	√	√	√
Wind speed*^† (m/sec)	D8				√	√	√	√
Maximum sustained wind speed^† (km/hr)	—	V6	√	√
Dew point* (°C)	D9	—			√	√	√	√
Season	D10	V7		√		√
Day of week	D11	V8		√		√

Notes: D_i represents independent variables utilized for Dublin and V_i represents the equivalent for Vienna; numerical values within parentheses indicate the corresponding buffer size; all length/distance is in km and an area is in km² unit. *Daily average, or average; ^†natural-log-transformed variables; **daily total; ^#length; ^‡persons/km².

Figure 1. Maps showing FSMs in (a) Vienna and (b) Dublin.

Figure 2. Air mass history rating grid based on population density and urbanization.

Table 3. MLR models for Dublin and Vienna

Model	Variables with ≤0.001 Significance	Adjusted R^2*	P	SE	N	Max.VIF
Vienna 1	Ln(PM) = 5.041 + 2.543 × 10^−2V1 − 8.970 × 10^−2V2 + 8.233 × 10^−6 V3 − 1.935 × 10^−2V4 − 3.475 × 10^−2V5 − 6.869 × 10^−1 V6	0.35	<2.2 × 10^−16	0.47	4624	1.08
Vienna 2	Ln(PM) = 4.906 + 3.242 × 10^−2V1 − 9.933 × 10^−2V2 + 6.304 × 10^−6 V3 − 2.098 × 10^−2V4 − 3.925 × 10^−2V5 − 5.936 × 10^−1V6	0.37	<2.2 × 10^−16	0.47	9264	1.10
Vienna 3	Ln(PM) = 4.707 + 3.242 × 10^−2V1 − 9.934 × 10^−2V2 + 6.321 × 10^−6V3 − 1.599 × 10^−2V4 − 3.667 × 10^−2V5 − 6.061 × 10^−1V6 + 1.682 × 10^−1Winter + 7.794 × 10^−2Tuesday + 1.275 × 10^−1 Wednesday + 1.569 × 10^−1Thursday + 3.743 × 10^−2Friday − 3.339 × 10^−2Saturday − 9.908 × 10^−2Sunday	0.39	<2.2 × 10^−16	0.46	9264	1.28
Dublin 1	Ln(PM) = 2.630 + 4.107 × 10^−6D3 − 1.002 × 10^−1D6 − 9.688 × 10 ^−3D7 − 4.763 × 10^−1D8 − 4.169 × 10^−2 D9 + 2.363 × 10^−1D5	0.39	<2.2 × 10^−16	0.41	5503	1.78
Dublin 2	Ln(PM) = 2.485 + 4.016 × 10^−6D3 − 1.032 × 10^−1D6 − 8.901 × 10^−3D7 − 4.953 × 10^−1D8 − 3.002 × 10^−2D9 + 2.118 × 10^−1D5 + 1.915 × 10^−1Winter + 8.677 × 10^−2 + Tuesday + 9.783 × 10^−2Wednesday + 1.310 × 10^−1Thursday + 1.115 × 10^−1Friday + 4.332 × 10^−2 Saturday − 8.700 × 10^−2Sunday	0.42	<2.2 × 10^−16	0.42	5503	1.33
Dublin 5	Ln(PM) = 2.736 + 4.090 × 10^−6D3 − 8.648 × 10^−2D6 − 4.964 × 10^−1D8 − 4.433 × 10^−2D9 + 2.108 × 10^−1D5	0.39	<2.2 × 10^−16	0.41	4116	1.93
Dublin 6	Ln(PM) = 2.968 + 4.042 × 10^−6D3 − 3.212 × 10^−1D5 − 4.243 × 10^−1D8 − 4.549 × 10^−2D9 + 1.207 × 10^−1D5	0.38	<2.2 × 10^−16	0.40	1624	1.75
Dublin 7	Ln(PM) = 3.071 + 4.936 × 10^−4D1 + 7.297 × 10^−6D2 + 4.904 × 10^−5D4 − 4.554 × 10^−1D8 − 4.288 × 10^−2D9	0.43	<2.2 × 10^−16	0.43	1273	1.61

Table 4. Nonparametric and neural network models for Dublin and Vienna

Model	Model Structure	R^2	No. of Data points
Vienna 4	LOWESS method, polynomial degree: 1; k-nearest neighbors: % = 50; kernel: tricube; bandwidth: standard deviation; smoothing factor: 0.1	0.51	9264
Vienna 5	Two layer Levenberg-Marquardt backpropagation (network structure 15-15-1-1)	0.66	7875
			(85%* of 9264)
Dublin 3	LOWESS method, polynomial degree: 1; k-nearest neighbors: % = 35; kernel: tricube; bandwidth: standard deviation; smoothing factor: 0.6	0.45	5503
Dublin 4	Two layer Levenberg-Marquardt backpropagation (network structure 15-20-1-1)	0.51	4678
			(85%* of 5503)

Notes: *70% for model training and 15% data of model generalization, which also ensured stop training before overfitting.

Figure 3. Graphical representation of the performances of different models. MLR (Vienna 3), (b) NPR (Vienna 4), (c) ANN (Vienna 5), (d) MLR (Dublin 2), (e) NPR (Dublin 3), and (f) ANN (Dublin 4) models.

Table 5. Results from model validation

		SD			RMSE
Model	No. of Sites	PM10 (µg/m^3)	Model R^2	ValidationR^2	PM10(µg/m^3)
Vienna 1	13	15.77	0.35	0.36	12.96
Vienna 2	13	17.83	0.37	0.38	14.46
Vienna 3	13	17.83	0.39	0.39	14.36
Vienna 4	13	17.83	0.51	0.48	13.05
Vienna 5	13	17.83	0.66	0.65	10.69
Dublin 1	7	9.18	0.39	0.28	8.17
Dublin 2	7	9.18	0.42	0.30	8.07
Dublin 3	7	9.18	0.45	0.39	7.33
Dublin 4	7	9.18	0.51	0.54	6.27
Dublin 5	5	8.92	0.39	0.35	7.32
Dublin 6	5	7.80	0.38	0.37	6.28
Dublin 7	5	7.52	0.43	0.34	6.28

Figure 4. Graphical outputs of average daily PM₁₀ concentrations from (a) Dublin 6 and (b) Vienna 5 for winter Mondays.