Quantitative Assessment of Variability and Uncertainty of Hazardous Trace Element (Cd, Cr, and Pb) Contents in Chinese Coals by Using Bootstrap Simulation

ABSTRACT

The quantitative measurements of uncertainties regarding the contents of hazardous trace elements (HTEs) serve as a basis for better assessment of the geochemistry and mineralogical characteristics of coals and their environmental impacts. In this paper, by using bootstrap simulation methodology, a quantitative procedure was demonstrated to characterize the variability and uncertainty of HTE (Cd, Cr, and Pb) contents in Chinese coals, which were specified by 27 different provinces and mining areas. Original data samples for Cd, Cr, and Pb contents in Chinese coals were compiled and summarized from the results reported in published literature. Sampling distributions for uncertainties in statistics such as the mean, median, and confidence interval were calculated. The national average contents were estimated at approximately 0.61 μg/g for Cd, 30.37 μg/g for Cr, and 23.04 μg/g for Pb. The ranges of uncertainties for bootstrap samples of national HTE contents were nearly symmetrical, and the ranges of the 95% confidence interval for the arithmetic mean were relatively small, with relative uncertainties of −16.39% to +21.31% for Cd, −10.11% to +11.72% for Cr, and −8.55% to +8.64% for Pb. This shows that the arithmetic mean contents of HTEs in Chinese coals are higher in southern provinces than those in northern provinces, obviously differing because of different coal basins. The high values of HTE contents occur in provinces such as Sichuan, Chongqing, Yunnan, Hubei, and Guangxi. Provinces with low contents are located in northwestern China and include Xinjiang, Qinghai, Gansu, and Inner Mongolia; this can be mainly attributed to the medium moisture content, low ash, and low sulfur content in coals. Several provinces with high HTE contents such as Ningxia for Cd, Guangdong for Cr, and Shaanxi for Pb may be associated with the representativeness of the original data samples.

IMPLICATIONS

The negative effects of HTEs on the environment and public health have received increasing concern throughout the world. Errors during content determination may lead to large bias of the HTE emission inventories. It is necessary for decision-makers to be aware of the strengths and limitations of HTE contents in coals and emission inventories so that decisions regarding air quality management can be made that are robust to uncertainty. This study provides a quantitative assessment methodology for HTE contents in Chinese coals that will serve as a basis for assessing the geochemistry and mineralogical characteristics of coals and their potential environmental impacts and be helpful in developing probabilistic emission inventories of HTEs from coal. However, more research is still needed.

INTRODUCTION

With the rapid increasing use of coal, the growing negative impacts on the environment and human health from hazardous trace elements (HTEs) have become a great concern in China. The emission of HTEs from coal combustion is one of the main sources of anthropogenic discharge and pollution.1,2 Negative effects of HTEs on the environment and public health are well documented in the literature and have received much attention throughout the world.3–5

China is one of the few countries with coal comprising more than 75% of its total energy consumption.6,7 With its rapid economical development, coal consumption has increased considerably. By the end of 2009, total coal consumption reached 3.02 billion t.8 Although it is estimated that coal consumption will drop to approximately 54% by 2020,9 the total amounts of raw coal consumed are expected to exceed as much as 2.6 billion t until then.6 The contents of HTEs in coals can provide useful information from an environmental point of view about the pollution control during coal combustion and utilization.10 Even when present in only parts-per-million (ppm) levels in coals, HTEs can result in emissions of tons of these toxic pollutants into the environment. Assessing the geochemistry and mineralogical characteristics of trace elements in coals can provide useful data to estimate the emissions of HTEs from coal combustion and assess their environmental impacts. Previous studies have demonstrated that the contents and distributions of HTEs differ from different provinces, sources, and even among coals of the same seams.11–17

In addition to the modes of occurrence, mineral contents, and distributions of HTEs in coals, there are several other sources that can cause uncertainty of concentration determination, including random sampling error, measurement error, and nonrepresentative samples.18–20 These errors during content determination may lead to a large bias in assessment of trace element geochemistry and mineralogical characteristics as well as in estimation of emission inventories of HTEs into the environment. Moreover, errors in content determination of HTEs may have an adverse impact on decision-making regarding pollution control and environment quality management.

The Clean Air Act Amendment of 1990 includes 11 HTEs: Sb, Be, As, Cd, Cr, Pb, Mn, Hg, Co, Ni, and Se,21 among which Hg, As, Se, Cd, Cr, and Pb require the most attention.22 Cd, Cr, and Pb have been given a particular attention and became priority contaminants within various international conventions and programs aiming at the reduction of environmental and human exposure to air pollution.23 Pb is regulated in the Ambient Air Quality Standard of China. Although the Chinese government has not regulated Cd and Cr, many negative impacts can already be found. In recent years, there are more and more trace element poisoning accidents reported in China. For example, the incident of excess blood Pb levels in Fengxiang County in 2009 has received much attention. However, the comprehensive and detailed studies on Cd, Cr, and Pb emissions in China are quite limited. The authors' previous work has published some data of Hg, As, and Se, including contents in coals and emissions in coal combustion.24 In this study, the contents of Cd, Cr, and Pb in coals by province are presented (see also the supplemental materials, published at http://secure.awma.org/onlinelibrary/samples/10.3155-1047-3289.61.7.755_supplmaterial.xls).

The main objective of this paper is to quantify the variability and uncertainty in the contents of HTEs in different Chinese coals by province using a quantitative approach when possible by summarizing existing data in published literature.

DATA SOURCES AND METHODOLOGY

Data Sources of Content of Cd, Cr, and Pb in Raw Coal as Produced

China is a huge country with 34 provinces and regions. China's coal reserves are unevenly allocated among different provinces and are mainly located in the provinces in the northwest and southwest of China, including Shanxi, Shaanxi, Inner Mongolia, Xinjiang, Sichuan, Yunnan, and Guizhou. Further, the content of HTEs such as Cd, Cr, and Pb in coals mined from different places varies substantially, which is mainly due to the different coal-forming plants and geological environments.25 The reported contents of Cd, Cr, and Pb in raw coal samples as produced from 26 provinces (autonomous regions and municipalities) in the Chinese mainland were collected and compiled based on a thorough review of available literature as the input data in this study. HTE contents in coals of the Shenfu-Dongsheng mining area (ShenDong) are also included separately. ShenDong is located in north Shaanxi and south Inner Mongolia in one of the largest thermal coal production areas. The Hong Kong Special Administrative Region, Macau Special Administrative Region, and the Taiwan province are tentatively not included. Beijing, Shanghai, Tianjin, Hainan, and Xizang are also not considered because the amounts of raw coal produced in these areas are very small or even zero.

The original data samples cited from references are the direct analytical results of contents of HTEs in coals or the arithmetic mean values of different coals in the same area and were grouped by provinces in this study. In view of the comparison of elemental contents obtained from one coal sample by a different analytical method, there is no literature focused on it to the authors' knowledge.

Bootstrap Simulation

In recent decades, quantitative approaches for characterizing uncertainty in emission inventories have been widely recommended by governmental agencies and academic communities in North America and Europe26 and have been applied in real-world emission inventory development because they can provide quantitative information to guide how future emission inventories can be improved.27

Errors in emission factors (e.g., grams of pollutant per unit of product produced) or activity data (e.g., number of units of product produced in 1 yr, HTE contents in coals for estimation of pollutant emissions during coal combustion) can bring about errors in emission inventory development. Single-component distribution models such as normal or lognormal distribution are often used to describe variability in emission factors or activity data in previous studies that cannot describe the variation well or fit to the data sets.20 Because the accuracy of quantifying variability and uncertainty in part depends on the fitness of the distributions with respect to available data, single distributions are poorly fit to data and will bring bias into the quantification of variability and uncertainty. As a finite mixture of distributions, bootstrap simulation is recommended as an alternative method.28

Bootstrap simulation is a numerical technique originally developed for the purpose of estimating confidence intervals for statistics. This method can provide solutions for confidence intervals in situations in which exact analytical solutions may be unavailable and in which approximate analytical solutions are inadequate.28–30 Up until now, bootstrap simulation has been widely used to estimate uncertainty of average emission factors and has been successfully demonstrated to quantify the variability of emission factors of oxides of nitrogen (NO_x) and total hydrocarbons.31,32 Thus, bootstrap simulation was applied to evaluate the variability and uncertainty of contents of HTEs in different coals in this study.

Bootstrap simulation is a kind of Monte Carlo simulation, which is a statistical processing by resampling with replacement. The details of bootstrap simulation can be found in the literature.33,34 Firstly, an estimation population distribution is created through fitting a parametric distribution to the original data sets. A random sample of the same size as the original data set is then simulated under the assumed population distribution with replacement, which is called a “bootstrap sample.” Bootstrap simulations can be repeated several times to evaluate numerical stability by comparing results among the multiple bootstrap simulations. A probability distribution for a statistic is called a “sampling distribution.” Confidence intervals for a statistic are inferred from its sampling distribution. For example, the 2.5th and 97.5th percentiles of sampling distribution enclose a 95% confidence interval. The mathematical description is as follows.30,33

A random sample X = (x ₁, x ₂, …, x _n) of size n is observed from a completely unspecified probability distribution F. The sampling distribution R (X, F) is the function of X and F. Assume θ=θ(F) is a parameter of F, F _n is the empirical distribution function of X, is the estimator of θ, and the estimation error can be expressed as

(1)

The basic steps of computing the distribution R (X, F) by bootstrap simulation are summarized as follows:

1.	The value of observed samples X = (x 1 , x 2, …, xn) are finite overall samples (called original samples), x i ∼ F(x), i = 1, 2, …, n. The empirical distribution function of original samples is shown as (2) where x (1) ≤ x (2) ≤ … ≤x (n) is the statistics of x 1 , x 2, …, x n sorted in ascending order.
2.	Monte Carlo simulation is used to randomly simulate N groups of samples x (j)* = (x 1*, x 2*, …, x n*), j = 1, 2, …, N (a very large number) from F n, and these regeneration samples are called bootstrap samples. The generation method of empirical distribution function by Monte Carlo simulation can be expressed as follows: • Generate a random integer η with independence and uniformity between 0 and M (M >> n) by computer; • Let i =η mod n, i is the remainder of η divided by n. • Find the sample x i as the regeneration, (x*) in observed samples, and x* is the needed random sample.
3.	Calculate the statistics of bootstrap samples: (3) where is the empirical distribution function of bootstrap samples. Because small samples cannot derive θ(F), is used to approximate it.
4.	Use the distribution of R n (under a given situation) to simulate the distribution of T n; that is, , which can receive N numbers of θ(F). Then the distribution and eigenvalue of unknown parameter θ can be obtained.

RESULTS

Verification of Uncertainty in Statistics of Original Data and Bootstrap Samples

An example of statistical analysis in original samples and bootstrap samples of Cd content in coals from Guizhou province is illustrated. The comparing characterization of variability and uncertainty is described in Figures 1–3. The quantile-quantile figure (Figure 1), which is used to detect the pattern of the data samples, shows that the original samples are not normally distributed (Figure 1a). The variability of contents is more than 1 order of magnitude, from approximately 0.02 to 10.00 μg/g, with most of the samples having values less than approximately 1.50 μg/g. However, the part of the range between 0.50 and 1.20 μg/g shows nearly a linear distribution, which indicates it nearly belongs to the normal distribution.

Figure 1. The distribution pattern of (a) original samples and (b) bootstrap samples of Cd content in coals from Guizhou province, China.

Figure 2. The density distribution of (a) original samples and (b) bootstrap samples of Cd content in coals from Guizhou province, China.

Figure 3. The distribution comparison box plot between original and bootstrap samples of Cd content in coals from Guizhou province, China.

The bootstrap samples were generated by simulating N (N = 1000) times with the fitted distribution of original samples (Figure 1b). When N = 500, the mean standard deviation is 0.08, and when N = 5000, the mean standard deviation is 0.01. To produce adequate information, the simulation of N = 1000 is enough. The arithmetic mean standard deviation is 0.03, which is smaller than 0.05 and shows that there are only minor deviations of the results by simulating N different bootstrap samples.34 The spe cific density distribution of samples is shown in Figure 2. For the original samples (Figure 2a), contents of less than 2.00 μg/g share nearly 95% of the total samples, among which approximately 80% are samples with values less than 1.00 μg/g. It shows that the most possible Cd content in the coals of Guizhou province is less than 1.00 μg/g. There are more groups in every content range for bootstrap samples (Figure 2b). Samples with values less than 2.00 μg/g share more than 95% of the totals, and samples with values less than 0.50 μg/g share approximately 82% of the range of 0.00–1.00 μg/g. Therefore, the most possible Cd content in the coals of Guizhou province is less than 0.50 μg/g.

A box plot can describe the symmetry, dispersion, and outliers of samples with five statistical parameters: minimum, first quartile, median, third quartile, and maximum. The bottom and top sidelines of a box represent the first quartile (Q1) and third quartile (Q3) of samples, respectively. The bold line in the box corresponds to the median. The horizontal lines below and above the box are called the “abnormal cutoff lines” and represent the limits of normal values, corresponding to the distance between the quartile and interquartile range (IQR). The lower limit is the value Q1 - 1.5IQR, and the upper limit is the value of Q3 + 1.5IQR. Values out of this range will be treated as abnormal. Figure 3 is a comparison of box plots between the original samples and bootstrap samples. For the original samples, Q1 and Q3 are approximately 0.05 and 0.70 μg/g, respectively, the median is approximately 0.32 μg/g, the normal range is approximately 0.02–1.50 μg/g, and values not within this scope can be considered as abnormal. Outliers centralize on the side of greater values, which is called “right-skewed distribution.” For bootstrap samples, the box plot averages of each in 1000 groups shows that Q1 and Q3 are approximately 0.70 and 0.85 μg/g, respectively; the median is approximately 0.78 μg/g, higher than that of the originals; and the normal range is approximately 0.40–1.00 μg/g. The box plot is approximately symmetrical, which is called “steady-state distribution.” The comparison analysis shows that samples after bootstrap simulation are more centralized and more likely a normal distribution. This suggests that bootstrap simulation is an adequate fit to original samples and therefore will be a reasonable representation of variability and uncertainty in assessing the average contents of HTEs and their confidential intervals.

Variability and Uncertainty of Cd Content in Coals by Provinces

The provinces reporting relatively more data sets of Cd are Guizhou with 157 samples,12,13,16,35–37 Shanxi with 73 samples,11,17,38–40 and Inner Mongolia with 57 samples.10,41–43 Many surveys have been done in these areas because of their rich-reserves, intensive activities of raw coal mining, and typical landscape characteristics. The provinces that reported very few data samples include Fujian with three samples44,45; Henan with four sam ples41,44–46; Qinghai with four samples45; and other provinces such as Guangdong, Gansu, Jiangsu, and Zhejiang with only one to two samples. For these provinces, statistical analysis was only conducted on the original data because of the available data restriction for bootstrap simulation.

The statistical parameters of the bootstrap simulation for Cd content in coals by provinces are listed in Table 1. The national average Cd content was estimated at approximately 0.61 μg/g, lower than the 1.00 μg/g reported in the literature41 and a little higher than that of U.S. coals (0.47 μg/g)47 and the world coal average (0.30 μg/g),48 which is closely consistent with the existing conclusion that Cd content in Chinese coals is a little higher than the world average.25 The ranges of uncertainty for the arithmetic mean contents of total bootstrap samples nationwide are typically positively skewed, and the uncertainty is relative small—only −16.39% to +21.31%.

Table 1. Cd content of raw coal as mined by provinces in China

Province	Mean (μg/g)	SD	Median (μg/g)	95% CI (μg/g)	Relative Uncertainty
Anhui	0.11	0.01	0.11	0.08–0.14	−27.27% to +27.27%
Chongqing	1.22	0.37	1.20	0.59–1.90	−51.64% to +55.74%
Fujian	0.31	0.01	0.30	0.06–0.58	−80.65% to +87.10%
Gansu	0.08	0.00	0.00	0.08–0.08	−0.00% to +0.00%
Guangdong	0.25	0.00	0.25	0.25–0.25	−0.00% to +0.00%
Guangxi	0.41	0.09	0.42	0.24–0.62	−41.46% to +51.22%
Guizhou	0.79	0.13	0.78	0.57–1.06	−27.85% to +34.18%
Hebei	0.23	0.03	0.23	0.17–0.29	−26.09% to +26.09%
Heilongjiang	0.13	0.02	0.13	0.10–0.17	−23.08% to +30.77%
Henan	0.54	0.25	0.53	0.06–1.03	−88.89% to +90.74%
Hubei	0.36	0.01	0.36	0.11–0.60	−69.44% to +66.67%
Hunan	0.64	0.15	0.63	0.37–0.94	−42.19% to +46.88%
Inner Mongolia	0.10	0.01	0.10	0.08–0.12	−20.00% to +20.00%
Jiangsu	0.06	0.00	0.06	0.02–0.11	−66.67% to +83.33%
Jiangxi	0.56	0.09	0.56	0.40–0.73	−28.57% to +30.36%
Jilin	0.15	0.04	0.15	0.08–0.25	−46.67% to +66.67%
Liaoning	0.16	0.03	0.16	0.11–0.24	−31.25% to +50.00%
Ningxia	1.10	0.20	1.09	0.72–1.48	−34.55% to +34.55%
Qinghai	0.03	0.00	0.04	0.01–0.04	−66.67% to +33.33%
Shaanxi	0.75	0.36	0.75	0.15–1.59	−80.00% to +112.00%
Shandong	0.39	0.11	0.38	0.21–0.61	−46.15% to +56.41%
Shanxi	0.75	0.08	0.74	0.60–0.90	−20.00% to +20.00%
ShenDong	0.15	0.10	0.15	0.04–0.36	−73.33% to +140.00%
Sichuan	1.95	1.18	1.84	0.48–4.43	−75.38% to +127.18%
Xinjiang	0.12	0.05	0.12	0.05–0.23	−58.33% to +91.67%
Yunnan	0.80	0.14	0.79	0.55–1.09	−31.25% to +36.25%
Zhejiang	0.47	0.01	0.47	0.36–0.58	−23.40% to +23.40%
China	0.61	0.06	0.60	0.51–0.74	−16.39 to +21.31%
Notes: SD = standard deviation, CI = confidence interval.

It is said that the enrichment of Cd in coals appears to be associated with sphalerite, which may be caused by low-temperature hydrothermal fluid, volcanic ash, and magma.47 For regional distribution of Cd content, provinces ranking in the top five high mean values are Sichuan (1.95 μg/g), Chongqing (1.22 μg/g), Ningxia (1.10 μg/g), Yunnan (0.80 μg/g), and Guizhou (0.79 μg/g).

Cd content shows an obvious distribution with differing coal basins, and the arithmetic means of provinces in southern China are higher than those of provinces in northern China. Cd and its compounds are enriched in Late Permian coals, which mainly occur in the southern part of China.14 The high Cd content of Ningxia is mainly due to the very few original data samples of the tested content of anthracite coals in the Rujigou and Baijigou mining area of Ningxia,25 where the levels of HTEs are higher than other areas.42 The Early-Middle Jurassic basin mainly lies in northwestern China, so in theory the Cd content should be similar in Shanxi (0.75 μg/g), Shaanxi (0.75 μg/g), and Ningxia (1.10 μg/g). The provinces with lower Cd content are Qinghai (0.03 μg/g), Jiangsu (0.06 μg/g), and Gansu (0.08 μg/g). Coal-basins of these areas are mainly of the Early-Middle Jurassic and the Early Permian basin, with lower values than those found in other basins.41

The relative uncertainty is the difference rate of the 95% confidence interval from the mean value. Seven provinces have relative uncertainty ranges of smaller than ±30%, which illustrates that the bootstrap samples in these provinces are substantially quantified as uncertain. Sichuan, Shaanxi, and ShenDong demonstrate relative uncertainty ranges of more than +100% because original samples in these areas are more discrete, which may be due to coals of different classes, ages, and seams being analyzed by different researchers.25,39,40,49,50

Variability and Uncertainty of Cr Content in Coals by Provinces

The provinces with relatively more data for Cr are Xinjiang with 129 samples,45,50,51 Guizhou with 124 samples,12,16,36,37,52 and Anhui with 111 samples.50,53–57 The provinces with very few data samples include Guangdong, Gansu, and Zhejiang, with one or two averaged content original samples. For these provinces, statistical analysis was only conducted on the original data because of available data restriction for bootstrap simulation.

The statistical parameters of bootstrap simulation of Cr content in coals by provinces are shown in Table 2. The national average value is approximately 30.37 μg/g, higher than the 21.34 μg/g reported in literature41 and markedly higher than that of U.S. coals (15.00 μg/g)47 and the world coal average (10.00 μg/g).48 The ranges of uncertainty for the arithmetic mean contents of total bootstrap samples nationwide are nearly symmetrical, and the uncertainty is very small—only −10.11% to +11.72%.

Table 2. Cr content of raw coal as mined by provinces in China

Province	Mean (μg/g)	SD	Median (μg/g)	95% CI (μg/g)	Relative Uncertainty
Anhui	31.25	2.47	30.88	26.75–36.61	−14.40% to +17.15%
Chongqing	28.44	2.91	28.35	22.75–34.10	−20.01% to +19.90%
Fujian	30.48	0.99	40.40	11.70–49.36	−61.61% to +61.94%
Gansu	23.70	0.33	23.70	17.13–30.27	−27.72% to +27.72%
Guangdong	74.00	0.00	74.00	74.00–74.00	−0.00% to +0.00%
Guangxi	116.41	28.91	112.16	68.13–177.90	−41.47% to +52.82%
Guizhou	28.47	3.02	28.28	23.25–34.35	−18.34% to +20.65%
Hebei	32.52	3.81	32.51	25.12–39.82	−22.76% to +22.45%
Heilongjiang	15.48	2.83	15.36	10.18–21.48	−34.24% to +38.76%
Henan	24.94	5.02	24.31	16.13–34.77	−35.32% to +39.41%
Hubei	40.52	8.82	38.83	25.06–60.73	−38.15% to +49.88%
Hunan	37.03	11.19	35.70	19.48–60.10	−47.39% to +62.30%
Inner Mongolia	13.02	1.84	12.74	10.00–17.21	−23.20% to +32.18%
Jiangsu	19.82	5.54	19.80	10.06–30.10	−49.24% to +51.87%
Jiangxi	39.75	6.89	39.22	28.36–53.97	−28.65% to +35.77%
Jilin	23.09	10.08	22.11	8.52–44.47	−63.10% to +92.59%
Liaoning	26.24	3.88	25.76	19.36–35.71	−26.22% to +36.09%
Ningxia	10.63	3.30	10.24	5.25–18.21	−50.61% to +71.31%
Qinghai	30.82	0.52	27.74	23.85–42.09	−22.62% to +36.57%
Shaanxi	32.73	8.39	32.38	17.46–50.04	−46.65% to +52.89%
Shandong	20.62	3.64	20.37	14.33–28.18	−30.50% to +36.66%
Shanxi	21.57	1.92	21.45	17.59–25.50	−18.45% to +18.22%
ShenDong	27.04	8.62	26.33	12.96–45.15	−52.07% to +66.97%
Sichuan	33.00	4.89	32.87	24.59–44.81	−25.48% to +35.79%
Xinjiang	7.83	1.02	7.79	6.06–9.93	−22.61% to +26.82%
Yunnan	73.62	10.83	72.34	52.80–95.21	−28.28% to +29.33%
Zhejiang	24.20	0.47	24.20	14.66–33.74	−39.42% to +39.42%
China	30.37	1.70	30.33	27.30–33.93	−10.11% to +11.72

Cr in coals is associated with organic matter and clay mineral.47 For regional distribution of Cr content in coals, provinces ranking in the top five high mean values are Guangxi (116.41 μg/g), Yunnan (73.62 μg/g), Guangdong (74.00 μg/g), Hubei (40.52 μg/g), and Jiangxi (39.75 μg/g). The high content of Cr in the coals of southern China is mainly related to the unique coal accumulating sedimentary environmental background of a low energetic and shallow confined carbonate platform. Under these environmental conditions, evaporation of seawater has probably resulted in the increase of trace element contents in coal-bearing sediments, and Cr is highly concentrated and enriched in the lower part of most coal seams.51 In addition, the Fe content in these coal seams is relatively high. This might be associated with formation of root soil before the formation of peat moor in the basin. The high Cr content of Guangdong (74.00 μg/g) is mainly due to only one available data sample of meager coal in Shaoguan, Guangdong province,44 in which most HTEs, especially Cr, are higher in concentration than other classes of coal.41

Compared with Cd, Cr content shows an unremarkable distribution in coal basins. The provinces with lower values are Xinjiang (7.38 μg/g), Ningxia (10.63 μg/g), and Inner Mongolia (13.02 μg/g). Most coal basins in these areas are of the Early-Middle Jurassic and the Early Permian basin, with the lowest value of other basins.41 Coal fields of these areas are characterized by medium moisture content, low ash, high volatile matter yields, and low sulfur content. Cr content shows a high positive correlation with sulfur content and ash yield.25,51 This may be attributed to the sedimentological setting, with rapid peat bog aggradation in a very shallow lake environment with a low detrital supply.51

As shown in Table 2, nine provinces demonstrate relative uncertainty ranges of less than ±30%, which illustrates that the bootstrap samples in these provinces are substantially quantified as uncertain. The province with maximum uncertainty is Jilin (+92.59%) because samples in this area are more discrete and different classes and ages of coals were analyzed.42,58

Variability and Uncertainty of Pb Content in Coals by Provinces

The provinces with relatively more data samples of Pb are Guizhou with 168 samples,12,13,16,35,37,52 Shanxi with 83 samples,17,39,40,59 and Xinjiang with 74 samples.45,51 For provinces with very few data samples such as Fujian, Qinghai, Guangdong, Gansu, and Zhejiang, statistical analysis was only conducted on the original data because of the available data restriction for bootstrap simulation.

The statistical parameters of bootstrap simulation of Pb content in coals by provinces are shown in Table 3. The national average value is approximately 23.04 μg/g, which is higher than the 19.37 μg/g reported in literature,41 markedly higher than that of U.S. coals (11.00 μg/g),47 and a little lower than that of the world coal (25.00 μg/g).48 The ranges of uncertainty for the arithmetic mean contents of total nationwide bootstrap samples are nearly symmetrical, and the uncertainty is very small—only -8.55% to +8.64%.

Table 3. Pb content of raw coal as mined by provinces in China

Province	Mean (μg/g)	SD	Median (μg/g)	95% CI (μg/g)	Relative Uncertainty
Anhui	13.24	0.78	13.24	11.74–14.80	−11.33% to +11.78%
Chongqing	30.44	3.17	30.37	24.60–36.86	−19.19% to +21.09%
Fujian	25.53	0.85	29.40	7.42–40.92	−70.94% to +60.28%
Gansu	8.35	0.24	8.80	3.36–13.03	−59.76% to +56.05%
Guangdong	24.40	0.00	24.40	24.40–24.40	−0.00% to +0.00%
Guangxi	29.94	4.90	29.50	21.12–39.11	−29.46% to +30.63%
Guizhou	23.81	3.37	23.25	18.07–30.36	−24.11% to +27.51%
Hebei	29.30	3.81	29.23	21.68–36.45	−26.01% to +24.40%
Heilongjiang	22.15	3.12	21.94	16.67–28.53	−24.74% to +28.80%
Henan	16.78	1.87	16.68	12.97–20.14	−22.71% to +20.02%
Hubei	47.39	13.64	45.36	25.71–76.86	−45.75% to +62.19%
Hunan	26.29	5.85	25.86	15.28–38.58	−41.88% to +46.75%
Inner Mongolia	26.67	1.95	26.53	23.22–30.31	−12.94% to +13.65%
Jiangsu	20.98	7.21	20.34	7.35–36.80	−64.97% to +75.41%
Jiangxi	19.33	2.36	19.34	14.91–23.68	−22.87% to +22.50%
Jilin	29.00	5.66	28.89	18.63–40.33	−35.76% to +39.07%
Liaoning	19.68	2.00	19.70	16.04–23.89	−18.50% to +21.39%
Ningxia	14.05	3.69	14.16	7.89–21.26	−43.84% to +51.32%
Qinghai	10.72	0.44	7.00	6.26–20.38	−41.60% to +90.11%
Shaanxi	35.17	3.27	34.81	28.45–41.86	−19.11% to +19.02%
Shandong	16.64	2.10	16.52	12.71–20.51	−23.62% to +23.26%
Shanxi	26.23	1.77	26.16	22.94–30.13	−12.54% to +14.87%
ShenDong	14.84	7.21	14.62	5.47–30.00	−63.14% to +102.16%
Sichuan	28.29	4.13	28.18	20.13–36.88	−28.84% to +30.36%
Xinjiang	2.68	0.43	2.65	1.94–3.52	−27.61% to +31.34%
Yunnan	42.54	7.55	42.22	28.11–57.98	−33.92% to +36.30%
Zhejiang	17.25	0.25	17.25	12.17–22.34	−29.45% to +29.51%
China	23.04	1.02	23.01	21.07–25.03	−8.55% to +8.64%

For regional distribution of Pb content, provinces ranking in the top five high mean values are Hubei (47.39 μg/g), Yunnan (42.54 μg/g), Shaanxi (35.17 μg/g), Chongqing (30.44 μg/g), and Guangxi (29.94 μg/g). Pb in coals is associated with gelenite and pyrite, and the enrichment is mainly associated with low-temperature hydrothermal fluid.42 Veined minerals (including quartz, calcite, ankerite, pyrite, and clay), which originated from well developed low-temperature hydrothermal fluids in the Late Permian coals from southern China, could lead to the enrichment of Pb in coals.47

The distribution of Pb content in different coal basins also shows little variation. The provinces with lower value are Xinjiang (2.68 μg/g), Gansu (8.35 μg/g), and Qinghai (10.72 μg/g). This may be also attributed to the medium moisture content, low ash, high volatile matter yields, and low sulfur content of coals in these areas. Pb content shows obvious affinities with sulfur content and ash yield of coals.25,51

As shown in Table 3, 13 provinces have relative uncertainty ranges of less than ±30%, which demonstrates that the bootstrap samples in these provinces are substantially quantified as uncertain. The relative uncertainty of Pb in coals from the ShenDong area is −63.14% to + 102.16%, which is more discrete than other provinces, maybe because of the diversities in classes, ages, and seams of the coals analyzed.25,49,60,61

CONCLUSIONS AND RECOMMENDATIONS

Conclusions

This paper demonstrated a procedure for quantifying variability and uncertainty in three types of HTE contents in Chinese coals using bootstrap simulation. Data sets for Cd, Cr, and Pb contents in Chinese coals have been collected and compiled based on a thorough review of available literature.

The contents of Cd, Cr, and Pb in Chinese coals show that the arithmetic means of HTEs in coals of provinces in southern China are higher than those in northern China because they differ in the sedimentary environment of their coal basins.

The national average content of Cd is estimated at approximately 0.61 μg/g, which is lower than that reported in previous literature. The national average values of Cr and Pb of 30.37 and 23.04 μg/g, respectively, are higher than those reported in previous literature. The lowest HTE contents in coals occur in the provinces of northwestern China such as Xinjiang, Qinghai, Gansu, and Inner Mongolia. This is mainly attributed to the medium moisture content, low ash, and low sulfur content of coals in these areas. Contents of Cr and Pb show high positive correlation with sulfur content and ash yield in coals. Several provinces with high HTE contents such as Ningxia for Cd, Guangdong for Cr, and Shaanxi for Pb may be associated with the representativeness of original data samples.

The ranges of uncertainty of national HTE contents are nearly symmetrical, and the uncertainty is relatively small. The ranges of relative uncertainty are −16.39% to +21.31% for Cd, −10.11% to +11.72% for Cr, and −8.55% to +8.64% for Pb.

Recommendations

The large ranges of quantified uncertainty in HTE content in coals suggest that it is very important to quantify uncertainty. It is very difficult to quantify all sources of uncertainty (e.g., different coal seams, coal types, sampling and analytical methods, human factors, etc.). Nonetheless, the quantifiable portion of uncertainty should be taken into account when reporting and using contents of HTEs in coals. Decision-makers should be aware of the strengths and limitations of contents of HTEs in coals and in emission inventories so that decisions regarding air quality management can be made that are robust to uncertainty. The probabilistic methodology presented here is part of a helpful approach on policy-making, program management, and research planning.

To better understand the geochemistry and mineral-ogical characteristics of coals, it is of great importance to obtain content data that are representative of the real world. Therefore, HTE content data should be evaluated with respect to their representativeness. To quantify uncertainty related to the representativeness, the number of samples, uniformity of sampling time, quality of samples, and reliability of sampling operation must be considered. This study has not attempted to quantify the uncertainty related to a potential lack of representativeness, which is a recommendation to regulatory agencies and researchers for future work.

ACKNOWLEDGMENTS

This work is funded by the National Natural Science Foundation of China (NSFC; 20677005 and 40975061) and the special program on environmental protection of the Ministry of Environmental Protection (MEP) of China (200909024). However, the opinions expressed herein are those of the authors themselves and should not be construed as representing the official positions of NSFC or MEP. The authors thank the editors and the anonymous reviewers for their valuable comments and suggestions on the paper.