Gridded bias correction of modeled PM_2.5 for exposure assessment, and estimation of background concentrations over a coastal valley region of northwestern British Columbia, Canada

Figures & data

Figure 1. (Left) The Terrace–Kitimat valley (TKV) in the Coast Mountains of northwestern British Columbia, Canada. PM_2.5 monitoring stations are indicated with red markers, with an aluminum smelter (factory icon) located just south of the Haul Road Station. The red line is a transect denoting valley centerline used in this study. (Right) land cover types over the TKV: 1. Temperate needleleaf forest, 2. Temperate broadleaf deciduous forest, 3. Mixed forest, 4. Temperate shrubland, 5. Barren land, 6. Urban and built-up, 7. Water

Table 1. PM_2.5 monitoring locations, and hourly observation data completeness for the year 2017, to the nearest percentage (%)

Station	Latitude ° N	Longitude ° W	Spring	Summer	Autumn	Winter	Total
Terrace	54.522	128.608	100	96	98	62	89
Riverlodge	54.054	128.671	100	99	99	100	100
Haul Road	54.029	128.702	97	98	98	99	98

Table 2. Pearson’s correlation coefficients (r) and coefficients of divergence (CoD), for daily average PM_2.5 between station pairs in 2017

Statistic	Station pairs	Spring	Summer	Autumn	Winter	All year
r	RVL/HRD	0.48	0.89	0.38	0.23	0.51
	TER/HRD	0.38	0.79	0.23	0.39	0.39
	TER/RVL	0.45	0.82	0.71	0.67	0.65
COD	RVL/HRD	0.21	0.18	0.29	0.33	0.26
	TER/HRD	0.27	0.23	0.50	0.39	0.36
	TER/RVL	0.21	0.20	0.40	0.22	0.28

RVL, HRD, TER are Riverlodge, Haul Road and Terrace, respectively. The formulas of r and CoD are in Appendix B.

Figure 2. Seasonal distribution of PM_2.5 in the TKV. Top: Pollution roses for summer (I) and winter seasons (II) at monitoring stations. Seasonal averages (in μg m⁻³) are in blue. Bottom: Average of hourly PM_2.5 concentrations and their coefficients of variation (CoV). CoV is the standard deviation of hourly concentrations divided by the diurnal mean

Figure 3. (a.) Regression plots of quantile mean concentrations of the original model output against those of observational data at Terrace, and derivation of bias-correction formulae. Small open circles are the data points for both (b.) Quantile plot for modeled and observed (OBS) data at pollutant monitoring stations. The concentration at each octile is the mean of all hourly concentration values within that octile. SIMPLE, POWER and DEG_2 are post-correction profiles

Table 3. Statistical measures for bias-correction evaluations. In the formulae, M_i is modeled/corrected concentration, with corresponding observation O_i, while $\bar{\mathrm{M}}$($\bar{\mathrm{O}}$) are their respective means. Overbar denotes computation of a mean value

Measure	Formula	Performance
		Ideal	Recommended
FAC2	-	100%	50%
NMB	$\frac{\bar{\mathrm{M}}-\bar{\mathrm{O}}}{\bar{\mathrm{O}}}$	0	±0.3
NMSE	$\frac{\overline{{(\mathrm{M}\mathrm{i}-\mathrm{O}\mathrm{i})}^2}}{\bar{\mathrm{M}}\bar{\mathrm{O}}}$	0

Figure 4. Top: Tiered air management threshold values and actions for ambient PM_2.5 adapted to British Columbia from (CCME 2012). Bottom: Conformity of original and corrected outputs to observed CCME 2012 PM_2.5 management categories

Table 4. Statistical evaluation of bias-corrections in comparison to original model output, per season. Comparisons are based on daily means

Measure		Spring (3.5 μ gm^−3)			Summer (4.1 μ gm^−3)			Autumn (6.5 μ gm^−3)			Winter (5.2 μ gm^−3)
		Haul road	Riverlodge	Terrace	Haul road	Riverlodge	Terrace	Haul road	Riverlodge	Terrace	Haul road	Riverlodge	Terrace
NMB	ORIGINAL	−0.2	−0.2	−0.1	−0.5	−0.3	−0.2	−0.5	−0.5	−0.7	−0.4	−0.6	−0.6
	SIMPLE	0.3	0.4	1.1	−0.3	0.2	0.8	−0.3	−0.1	−0.3	0.0	−0.4	−0.3
	POWER	0.4	0.4	1.2	−0.2	0.2	0.8	−0.2	−0.1	−0.3	0.1	−0.3	−0.2
	DEG_2	0.3	0.4	1.2	−0.2	0.2	0.8	−0.3	−0.1	−0.3	0.1	−0.1	−0.2
NMSE	original	0.4	0.3	0.4	1.2	0.6	0.6	1.9	1.1	2.1	0.5	1.3	1.9
	SIMPLE	0.8	0.7	1.4	0.6	0.4	0.9	1.4	0.6	0.6	0.7	0.8	1.2
	POWER	0.8	0.8	1.8	0.5	0.5	1.0	1.2	0.6	0.6	0.6	0.6	1.2
	DEG_2	0.8	0.8	2.0	0.5	0.5	1.0	1.3	0.7	0.6	0.6	0.7	1.3
FAC2	original	76	78	70	60	74	80	54	58	24	72	32	39
	SIMPLE	61	67	47	60	71	56	54	57	57	53	54	57
	POWER	71	72	43	77	73	59	68	70	59	70	57	64
	DEG_2	70	73	48	73	73	59	64	68	59	68	57	64

Values in bold italics indicate where bias-corrected outputs are worse than the original output.

Table 5. CoD between stations as proxies of PM_2.5 spatial variability for original and bias-corrected model outputs, per season

	Station pair	Spring	Summer	Autumn	Winter	All year
Original	RVL/HRD	0.12	0.14	0.11	0.11	0.12
	TER/HRD	0.26	0.31	0.27	0.20	0.27
	TER/RVL	0.21	0.22	0.23	0.19	0.21
SIMPLE	RVL/HRD	0.57	0.34	1.46	1.57	1.12
	TER/HRD	0.46	0.57	0.72	2.20	1.2
	TER/RVL	0.33	0.40	0.78	0.75	0.60
DEG_2	RVL/HRD	0.20	0.22	0.21	0.21	0.21
	TER/HRD	0.40	0.46	0.45	0.33	0.41
	TER/RVL	0.31	0.32	0.37	0.32	0.33
POWER	RVL/HRD	0.21	0.21	0.20	0.20	0.20
	TER/HRD	0.40	0.45	0.43	0.32	0.40
	TER/RVL	0.31	0.33	0.36	0.31	0.33

Comparisons are based on daily means. Values in bold italics indicate where the degree of heterogeneity are dissimilar with observational data.

Table 6. Accuracy (NMB × 100%, see Table 3) of original and corrected values for the 24 hr and annual PM_2.5 metrics

	24-hr metric					Annual metric
	Haul road	Riverlodge	Terrace	Mean error		Haul road	Riverlodge	Terrace	Mean error
Original	−62	−55	−67	61		−42	−44	−50	45
SIMPLE	−10	12	12	11		−11	−5	7	8
POWER	−6	19	1	9		−3	0	11	5
DEG_2	−7	18	3	9		−6	−9	9	8
Mean error	8	16	5	10		7	5	9	7

The mean error is the absolute (||) average of the accuracies for the original and corrected outputs, respectively.

Figure 5. Spatial plot of bias-corrected annual mean PM_2.5 concentrations (a), and ratio of bias-corrected concentrations to those of the original model output (b) for (i) SIMPLE (ii) POWER and (iii) DEG_2

Figure 6. Centerline profile of bias-corrected annual mean concentrations

Table 7. Annual and seasonal background PM_2.5 levels in the TKV with the various bias-correction formulas

Bias correction	Spring	Summer	Autumn	Winter	Annual
SIMPLE	2.10	2.22	1.78	1.68	1.95
DEG2	2.32	2.41	2.10	2.03	2.21
POWER	2.35	2.44	2.13	2.07	2.25

Figure 7. Color-coded classification of modeled PM_2.5 ambient exposure risk from POWER scheme using thresholds in Figure 4a. (a) annual metric; (b) daily metric

CCME (Canadian Council of Ministers of the Environment). 2012. Guidance document on air zone management. https://www.ccme.ca/files/Resources/air/aqms/pn_1481_gdazm_e.pdf.

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