The convergence of PM2.5 concentration in Chinese cities: a distribution dynamic approach

Figures & data

Table 1. Air quality grade corresponding to the PM2.5 index.

Air quality index	Average daily concentration of PM2.5 ($\mathrm{\mu }\mathrm{g}/{\mathrm{m}}^3$)	Air quality level
0–50	0–35	Level 1 (Excellent)
51–100	36–75	Level 2 (Good)
101–150	76–115	Level 3 (Light pollution)
151–200	116–150	Level 4 (Moderate pollution)
201–300	151–250	Level 5 (Severe pollution)
301–500	251–500	Level 6 (Extreme pollution)

Source: The Ambient Air Quality Standards (GB 3095—2012) formulated by the Ministry of Environmental Protection of China.

Table 2. PM2.5 urban agglomerations.

Symbol	Annual average concentration of PM2.5 ($\mathrm{\mu }\mathrm{g}/{\mathrm{m}}^3$)	Club
C1	0–35	Superior City Group
C2	36–75	Good urban agglomeration
C3	76–115	Lightly polluted urban agglomeration
C4	> =116	Heavily polluted urban agglomeration

Note: Since almost no cities exhibit an annual average PM2.5 concentration higher than 150, levels four, five, and six are combined as ‘heavy pollution’.

Source: Calculated by the authors.

Figure 1. Left: Annual average PM2.5 kernel density of Chinese cities from 1998 to 2013. Right: Annual average PM2.5 kernel density of Chinese cities from 2015 to 2019. Note: 1998–2013 average PM2.5 concentration data source: Columbia University project (van Donkelaar et al., 2016).

Table 3. The transition probability matrix of PM2.5 in Chinese cities from 2015 to 2019.

	SUA	GUA	LPUA	HPUA	$n_i$
SUA	0.981	0.019	0	0	52
GUA	0.366	0.634	0	0	205
LPUA	0	1	0	0	30
HPUA	0	0	0	0	0

Note: SUA = Superior City agglomeration, GUA = Good urban agglomeration, LPUA = Lightly polluted urban agglomeration, HPUA = Heavily polluted urban agglomeration.

Source: Calculated by the authors.

Figure 2. Left: 2015–2019 PM2.5 transition probability density three-dimensional diagram. Right: 2015–2019 PM2.5 transition probability density two-dimensional contour.

Source: Organized by the authors.

Figure 3. Left: The ergodic distribution in 1998–2013 and 2015–2019. Right: The actual distribution in 2019 and the ergodic distribution in 2015–2019.

Source: Organized by the authors.

Figure 4. The distribution of average PM2.5 in winter in Chinese cities from 2015 to 2018.

Source: Organized by the authors.

Table 4. The transition probability matrix of winter PM2.5 in Chinese cities from 2015 to 2018.

	SUA	GUA	LPUA	HPUA	$n_i$
SUA	0.826	0.174	0	0	46
GUA	0.181	0.75	0.061	0.007	144
LPUA	0	0.476	0.452	0.071	84
HPUA	0	0	0.923	0.077	13

Note: SUA = Superior City agglomeration, GUA = Good urban agglomeration, LPUA = Lightly polluted urban agglomeration, HPUA = Heavily polluted urban agglomeration.

Source: Calculated by the authors.

Figure 5. Three-dimensional diagram of the transition probability and the corresponding two-dimensional contour.

Source: Organized by the authors.

Figure 6. The ergodic distribution of PM2.5 in winter 2015–2018 and the actual distribution of PM2.5 in the winter of 2015.

Source: Organized by the authors.

Figure 7. Three regions of China.

Note: Described in section 2.2.2.

Table 5. The transition probability matrix of annual PM2.5 of cities in eastern, central, and western regions from 2015 to 2019.

Eastern regions	SUA	GUA	LPUA	HPUA	ni
SUA	1	0	0	0	27
GUA	0.429	0.571	0	0	70
LPUA	0	1	0	0	18
HPUA	0	0	0	0	0
Central regions
SUA	0.875	0.125	0	0	8
GUA	0.269	0.730	0	0	89
LPUA	0	1	0	0	12
HPUA	0	0	0	0	0
Western regions
SUA	1	0	0	0	17
GUA	0.457	0.544	0	0	46
LPUA	0	0	0	0	0
HPUA	0	0	0	0	0

Note: SUA = Superior City agglomeration, GUA = Good urban agglomeration, LPUA = Lightly polluted urban agglomeration, HPUA = Heavily polluted urban agglomeration.

Source: Calculated by the authors.

Table 6. The transition probability matrix of winter PM2.5 of cities in eastern, central, and western regions from 2015 to 2018.

Eastern regions	SUA	GUA	LPUA	HPUA	ni
SUA	0.8	0.2	0	0	30
GUA	0.265	0.735	0	0	49
LPUA	0	0.481	0.519	0	27
HPUA	0	0	0.889	0.111	9
Central regions
SUA	1	0	0	0	5
GUA	0.119	0.712	0.153	0.017	59
LPUA	0	0.476	0.405	0.119	42
HPUA	0	0	1	0	3
Western regions
SUA	0.819	0.182	0	0	11
GUA	0.167	0.833	0	0	36
LPUA	0	0.467	0.467	0.067	15
HPUA	0	0	1	0	1

Note: SUA = Superior City agglomeration, GUA = Good urban agglomeration, LPUA = Lightly polluted urban agglomeration, HPUA = Heavily polluted urban agglomeration.

Source: Calculate by the authors.

Figure 8. The annual average PM2.5 ergodic distribution of cities in three regions from 2015 to 2019.

Source: Organized by the authors.

Figure 9. The ergodic distribution of winter PM2.5 of cities in three regions from 2015 to 2018.

Source: Organized by the authors.

van Donkelaar, A., Martin, R. V., Brauer, M., Hsu, N. C., Kahn, R. A., Levy, R. C., Lyapustin, A., Sayer, A. M., & Winker, D. M. (2016). Global estimates of fine particulate matter using a combined geophysical-statistical method with information from satellites, models, and monitors. Environmental Science & Technology, 50(7), 3762–3772. https://doi.org/10.1021/acs.est.5b05833

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