Compositional data analysis of smoke emissions from debris piles with low-density polyethylene

ABSTRACT

Data describing the composition of smoke are inherently multivariate and always non-negative parts of a whole. The data are relative and the information is contained in the ratios between parts of the composition. A prior analysis of smoke emissions produced from the burning of manzanita wood mixed with low-density polyethylene plastic applied traditional statistical methods to the compositional data and found no effect. The current paper applies compositional data techniques to these smoke emissions to determine if the prior analysis was accurate. Analysis of variance of the isometric log-ratios showed that LDPE significantly affected the CO₂ emission ratio for 8 of the 191 trace gases; this analysis showed none of the gases identified in the previous analysis were affected by LDPE. LDPE did not affect the CO₂ emission ratios for the alkanes, alkenes, alkynes, aldehydes, cycloalkanes, cycloalkenes, diolefins, ketones, MAHs, and PAHs. Compositional data analysis should be used to analyze smoke emissions data. Burning contaminant-free LDPE should produce emissions like wood.

Implications

Reanalysis of impact of burning LDPE plastic in silvicultural debris piles using appropriate statistical techniques confirmed previously published results from inappropriate techniques that LDPE did not change the composition of the smoke emissions. Being able to dispose of these LDPE-covered forest debris by burning can save thousands of dollars in labor costs annually. Disposal of pesticide-free agricultural LDPE plastic by burning should only produce wood-like smoke emissions. This applies to LDPE/total mass ratios of 0.25– 2.5% as studied.

Introduction

Shrubs and small diameter trees exist in the understories of many western forests in the United States. They are important from an ecological perspective; however, this vegetation also presents a potential hazard as “ladder fuels” or as a heat source to damage the overstory during prescribed burns. Cutting and piling of this material to burn under safe conditions is a common silvicultural practice. To improve ignition success and flammability of the piled debris, polyethylene plastic (LDPE) is often used to cover a portion of the pile. While burning of piled forest debris is an acceptable practice in southern California from an air quality perspective, inclusion of LDPE in the piles changes these debris piles to rubbish piles (a legal term) which should not be burned. A review of available literature (Wrobel and Reinhardt 2003) suggested that emissions resulting from burning piles with LDPE would be similar to emissions from debris piles without LDPE. The literature review was based on bench-scale tests of LDPE pyrolysis and combustion. With support from the four National Forests in southern California, we conducted a laboratory experiment to determine if the presence of LDPE in a pile of burning wood changed the smoke emissions. Using conventional statistical analysis techniques, we concluded that the presence of LDPE did not have an effect on the emissions (Hosseini et al. 2014). A field study in Oregon examined emissions from burning debris piles and similarly reported no significant effect due to the presence of LDPE (Aurell et al. 2016). In our original analysis, the chemical compounds comprising the gaseous and particulate components of the smoke were analyzed as isolated variables containing separable information. In actuality, the individual parts are intrinsically interrelated and multicollinear, with their values being relative to each other.

Recently, Weise et al. (2020) have shown that emissions data are compositional data because they describe the parts of some whole. They contain only relative information which is contained in ratios of the individual emissions. Emissions data are typically expressed in some form of ratio (emission factor, emission ratio, concentration, mole ratio, etc.). Furthermore, using a stoichiometric argument, modified combustion efficiency (MCE) was shown to be linearly linked to all other wildfire emissions thus making its use in linear regression as a predictor variable for other emissions problematic (Weise et al. 2020). Using correlation to describe relationships between parts of a composition can lead to spurious conclusions because of the relative nature of the data (Aitchison 1986; Lovell et al. 2015; Pearson 1896). A well-principled methodological body to analyze compositional data has been developed in the past 30 years and this is an active area of statistical research so we have chosen to apply it to fire emissions data. Interestingly, it has been successfully applied in varied fields but appears to have seldom been applied to combustion or emissions data (Bandeen-Roche 1994; Billheimer 2001; Buccianti and Pawlowsky-Glahn 2006; Speranza et al. 2018).

The relative nature of emissions data defines emissions data as compositional data which are coherently analyzed using Compositional Data Analysis (CoDA) (Aitchison 1986; Filzmoser, Hron, and Templ 2018; Pawlowsky-Glahn, Egozcue, and Tolosana-Delgado 2015; van den Boogaart and Tolosana-Delgado 2013). CoDA methodology has three underlying principles. The first is scale invariance – vectors with proportional positive components represent the same composition, and form what is known as an equivalence class. This means changing the units should not change relative relationships between the parts nor affect results and scientific conclusions. The second is that inferences about subcompositions, i.e. smaller compositions formed from subsets of parts, must not contradict the inferences from the full composition. The third principle states that the order of the parts of the composition must not affect the inferences. While the initial work on CoDA explicitly assumed in the definition of a composition that the parts sum (are closed) to a constant total, theory has developed to show that this is only a particular representation of the data in a simplex and equivalent non-closed compositions carry the same relative information (Barceló-Vidal and Martín-Fernández 2016). The field of compositional data analysis is a well-developed body of statistical methodology that provides models and methods equivalent to traditional ones yet accounts for these special constraining features of relative data. The approach has been used for decades to analyze analogous types of data in the geosciences and, more recently, in other disparate areas such as microbiome studies, animal green-house gases emissions or physical activity epidemiology (Chastin et al. 2015; Fernandes et al. 2014; Palarea-Albaladejo et al. 2017).

In CoDA today, in order to use familiar statistical techniques such as exploratory data analysis, linear regression, multivariate analysis of variance and other multivariate techniques, the mainstream approach is to transform the parts from the simplex to the real numbers space using isometric log-ratio (ilr) coordinates (Egozcue and Pawlowsky-Glahn 2005; Mateu-Figueras, Pawlowsky-Glahn, and Egozcue 2011; Pawlowsky-Glahn, Egozcue, and Tolosana-Delgado 2015; van den Boogaart and Tolosana-Delgado 2013). Software to perform compositional data analysis is available, including the stand-alone point-and-click CoDaPack package (Thió-Henestrosa and Comas 2016) (http://www.compositionaldata.com/codapack.php) and comprehensive libraries on the open-source R statistical computing system (R Core Team 2018): compositions (van den Boogaart and Tolosana-Delgado 2013), robCompositions (Templ, Hron, and Filzmoser 2011) and zCompositions (Palarea-Albaladejo, Martín-Fernández, and Buccianti 2014). This paper reports the reanalysis of the data previously reported (Hosseini et al. 2014) using compositional data analysis techniques that are consonant with the nature of the data in order to improve the scientific rigor of the previous conclusions.

Methods

Data set and original analysis

Mean values of the emissions data were presented originally (Hosseini et al. 2014). The original compositional data set consisting of a total of 9 observations composed of 191 compounds resulting from the LDPE study is available (Hosseini et al. 2018). The 9 observations resulted from a randomized block design consisting of three blocks (in time) each with one replication of three masses of LDPE (0, 5, 50 g) incorporated into 2 kg piles of manzanita (Arctostaphylos sp.) wood yielding mass ratios of LDPE to wood of 0%, 0.25% and 2.5%. We estimated the typical LDPE mass ratio in debris piles to be 0.1% (Hosseini et al. 2014). In the western U.S., debris piles are created by cutting woody shrubs and small trees present in the understory of forests to interrupt vertical fuel continuity to reduce the ability of a wildland fire to spread vertically from the ground into the elevated canopies of the trees (Weise, Cobian-Iñiguez, and Princevac 2018). The blocking was used to account for differences caused by changes in the ambient atmosphere in the lab facility which had no control of air temperature and relative humidity. A Horiba PG-250¹ multigas analyzer sampled NO_x, CO and CO₂; carbonyls, volatile organic compounds (VOC), polyaromatic hydrocarbons (PAH), particulate matter (PM) mass and composition were collected using a variety of methods and filters. See Hosseini et al. (2014) for a schematic of the experimental setup and detailed description of the specific measurements and calibrations for the PG-250 and the other methods. The quantity of each part (gas_j) of the composition was expressed as an emission ratio with CO₂ $\left(E{R}_{\mathrm{C}{\mathrm{O}}_2}\left(ga{s}_j\right)=\frac{\mathrm{\Delta }ga{s}_j}{\mathrm{\Delta }\mathrm{C}{\mathrm{O}}_2}\right)$ where Δ is the mass of the gas above background (ambient) values (Delmas, Lacaux, and Brocard 1995); the original data units were g of emission per kg CO₂.

Our original analysis of emission factors treated LDPE as a fixed effect (factor) and we performed both parametric (analysis of variance) and nonparametric (Friedman – based on ranks) tests to determine if LDPE significantly affected the emission ratio for each compound individually as well as the sum of the emission ratios for each class of compound (alkanes, diolefins, monocyclic aromatic hydrocarbons, PAHs, aldehydes, etc.). Recall that parametric tests assume that the data can be described by an underlying statistical distribution such as the normal or log-normal distribution with assumed parameters. Nonparametric tests either assume no underlying statistical distribution or assume a distribution with unspecified parameters (Conover 1999; Mason, Gunst, and Hess 1989; Mendenhall, Schaeaffer, and Wackerly 1981). We assumed agreement between the parametric and nonparametric approaches strengthened our conclusions. Modified combustion efficiency (MCE, Ward and Hao 1991) was included as a covariate to account for differences in the burning characteristics of each test which we have subsequently shown to be an inappropriate approach to analysis of emission factors since MCE is part of the composition of gases (Weise et al. 2020). Due to the large number of tests, the Bonferroni method was used to control type I error when comparing the means; that is, the false-positive error. Using multivariate analysis of variance (MANOVA) was not possible because the number of observations (9) was less than the number of gases (190), i.e. the rank of the matrix was not sufficient in order to estimate the effects (Mardia, Kent, and Bibby 1979). At the time of the original analysis, the authors were not aware of a nonparametric multivariate method (PERMANOVA) similar to MANOVA that does not require that the number of observations be greater than the number of gases (Anderson 2017). Analyzing each gas individually resulted in three statistical comparisons that found a significant difference between the LDPE treatment means for 3 M-octane, pyrene and fluoranthene; the lack of significant difference for the other 180+ compounds supported the hypothesis that burning LDPE with wood would not have an effect on the composition of the smoke (Wrobel and Reinhardt 2003). Means and standard deviations for each emission ratio and for the classes were presented; however, we subsequently discovered that a few of the compounds were assigned to the incorrect chemical class (alkane, alkene, etc.) and these errors were corrected. In the original analysis, values below detection level (BDL) were assigned the value of 0 to calculate totals for each of the classes. The reported results for the individual emissions reflected this approach to handling BDL values.

Statistical methods

In the original data, BDL values occurred for the trace compounds. BDL values are common in emissions research and represent a form of left-censored data in compositional data sets (Palarea-Albaladejo and Martín-Fernández 2013). Several different compositional methods are available to replace BDL values with an estimate; model-based methods are preferred when the covariance structure of the data is rich and the proportion of parts with values BDL exceeds about 10–15% (Palarea-Albaladejo and Martín-Fernández 2013, 2015, 2008). For this data set, the overall percentage of values that were BDL was 9.3%. Multiplicative lognormal replacement, as implemented by the multLN function in the zCompositions package (Palarea-Albaladejo and Martín-Fernández 2015), was applied to replace the BDL values with a fraction of the DL (1 E-07) while adjusting the other parts of the composition multiplicatively to maintain the ratios between parts in accordance with their compositional nature. The interested reader is referred to the documentation of the zCompositions package and the references therein for more details.

Forming log-ratios from the original emission ratios eliminated the numerical influence of CO₂:

(1) $log\left(\frac{E{R}_{C{O}_2}\left(ga{s}_j\right)}{E{R}_{C{O}_2}\left(ga{s}_k\right)}\right)=log\left(\frac{\mathrm{\Delta }ga{s}_j}{\mathrm{\Delta }\mathrm{C}{\mathrm{O}}_2}/\frac{\mathrm{\Delta }ga{s}_k}{\mathrm{\Delta }\mathrm{C}{\mathrm{O}}_2}\right)=log\left(\frac{\mathrm{\Delta }ga{s}_j}{\mathrm{\Delta }ga{s}_k}\right).$(1)

The effect of LDPE on smoke emissions was analyzed using each gas singly as done originally. While the entire composition could be analyzed in a multivariate approach using PERMANOVA which is a distribution-free permutation technique (Anderson 2017), this was not done due to the relatively small sample size in the present study. For the single gas analysis, the data were transformed into log-ratio coordinates using a special ilr transformation (Egozcue et al. 2003) known as pivot coordinates (Filzmoser, Hron, and Templ 2018) using the robCompositions package (Templ, Hron, and Filzmoser 2011). It is important to note that an infinite number of ilr transformations are possible for the data, changing from one another by applying orthogonal rotations of the ilr coordinate system, but it is the nature of the ilr transformation that this preserves the multivariate Euclidean distances within the data set. The pivot coordinate transformation has the characteristic that one part (used as pivot) is isolated in the numerator of the first of the D-1 ilr coordinates associated with a D-part composition, where D is the number of parts (191 in this data set). The first coordinate

(2) $z_1=\sqrt{\frac{D-1}{D}}ln\frac{ga{s}_1}{\sqrt[D-1]{{\prod }_{k=2}^{D}ga{s}_k}}=\sqrt{\frac{1}{D\left(D-1\right)}}\left(ln\frac{ga{s}_1}{ga{s}_2}+ln\frac{ga{s}_1}{ga{s}_3}+\dots +ln\frac{ga{s}_1}{ga{s}_D}\right)$(2)

is the normalized log-ratio of a gas species (gas₁), placed in the first position of the composition, with the geometric mean of all other gases, which can be interpreted as the relative dominance of that gas within the composition. For each gas in the composition, the order of the parts was permuted, which is equivalent to applying an orthogonal rotation of the ilr coordinate representation, so that each gas was placed once in the first position, and hence in the numerator of the first pivot coordinate$z_1$, and an analysis of variance testing the effect of LDPE was individually performed on these first pivot coordinates sequentially. Multiple post hoc pair-wise comparison tests (glht and mcp functions) assessed the differences between the three levels of LDPE using Tukey contrasts; with p-values being adjusted for multiplicity using the default single-step method in the multcomp package (Bretz, Hothorn, and Westfall 2011). It is important to note that the pivot coordinate representations are only useful to make inferences individually about the relative dominances of the gases relative to the others in the composition. That is, the collection of all first pivot coordinates could not be used jointly as representative of the entire original composition nor to investigate associations between pairs of gases (in fact, all first pivot coordinates considered jointly would form a system of linearly dependent coordinates).

In order to test the effect of LDPE on the relative amounts of the chemical classes (alkane, alkene, alkyne, cycloalkane, cycloalkene, aldehyde, ketone, diolefin, MAH, PAH), another type of ilr coordinates called compositional balances ${\tilde{z}}_k$ defined as

(3) ${\tilde{z}}_k=\sqrt{\frac{r_k{s}_k}{r_k+s_k}}ln\frac{{\left(x_{i_1}{x}_{i_2}\dots x_{i_{r_k}}\right)}^{1/r_k}}{{\left(x_{j_1}{x}_{j_2}\dots x_{j_{s_k}}\right)}^{1/s_k}},k=1,\dots ,D-1,$(3)

were used to form scientifically meaningful subsets of parts of the composition (Egozcue and Pawlowsky-Glahn 2005). In a balance, the log-ratio compares in relative terms the geometric mean of r_k parts in one subset (class) with the geometric mean of s_k parts in another subset (class). Five balances were defined as detailed in Table 3. The first balance, alkanes vs alkenes and alkynes, examined if the relative reactivity represented by these classes of compounds changed with LDPE. Alkanes tend to be more stable and less reactive than alkenes and alkynes. The next three balances compare the relative importance of these closely related classes of compounds which have are composed of larger molecules and have a wide variety of characteristics. The last balance compared the relative amounts of non-hydrocarbon gases produced by the burning of manzanita with and without LDPE. The emissions data were transformed into balance coordinates and analysis of variance was used to test if the balance means differed between LDPE levels. Individual t-tests of equality of the balances to 0 were also conducted for each LPDE level, with balance equal to 0 here meaning equilibrium between the two classes depicted in numerator and denominator of the log-ratio, respectively. The gases assigned to each class can be found in Table 1.

Table 1. Geometric mean emission ratios ($E{R}_{C{O}_2}$)^a for combustion products produced by burning manzanita (Arctostaphylos sp.) wood-polyethylene (LDPE) plastic mixtures. Values differ from (Hosseini et al. 2014) because geometric mean $\left({\mu }_g\right)$ used instead of arithmetic mean. Gray shading identifies the chemical species that were significantly related to LDPE. Geometric mean and geometric standard deviation $\left({\sigma }_g\right)$based on three replicates.

	0% LDPE		0.25% LDPE		2.5% LDPE
Chemical Species	${\mu }_g$	${\sigma }_g$	${\mu }_g$	${\sigma }_g$	${\mu }_g$	${\sigma }_g$
Propane	1.22E-02	1.73E+00	2.17E-02	3.59E+00	5.22E-03	3.27E+00
2M-Propane	2.03E-03	1.78E+00	8.94E-04	2.46E+00	1.83E-03	1.72E+00
Butane	2.44E-03	3.93E+00	1.17E-03	4.84E+00	7.42E-05	1.44E+02
2*2-DM-Propane	2.73E-03	2.09E+00	3.35E-03	1.38E+00	9.68E-04	2.24E+00
2M-Butane	2.56E-03	2.15E+00	3.92E-03	2.46E+00	5.41E-03	3.51E+00
Pentane	3.28E-03	3.71E+00	5.19E-03	1.59E+00	1.59E-03	2.75E+00
2*2-DM-Butane	2.14E-03	3.07E+00	5.55E-03	3.05E+00	1.06E-03	2.69E+00
2*3-DM-Butane	2.05E-03	7.45E+00	3.80E-03	4.43E+00	1.08E-03	2.93E+00
2M-Pentane	1.39E-03	2.84E+00	1.21E-03	2.19E+00	2.97E-03	1.17E+00
3M-Pentane	1.58E-03	1.46E+00	2.00E-03	1.11E+00	2.00E-03	2.23E+00
Hexane	9.54E-04	4.96E+00	1.73E-03	3.09E+00	1.64E-03	4.97E+00
2*2-DM-Pentane	1.07E-04	2.15E+00	2.27E-04	1.64E+00	1.50E-04	2.81E+00
2*4-DM-Pentane	3.68E-05	8.23E+01	3.48E-05	7.57E+01	1.63E-05	4.83E+01
2*2*3-TM-Butane	2.73E-04	1.82E+00	2.59E-04	2.81E+00	1.84E-05	5.99E+01
3*3-DM-Pentane	3.99E-04	5.72E+00	3.54E-04	3.45E+00	1.74E-04	2.17E+00
2M-Hexane	2.68E-04	3.69E+00	1.18E-03	2.71E+00	2.07E-04	2.92E+00
2*3-DM-Pentane	1.41E-04	3.11E+00	2.00E-04	1.58E+00	3.70E-04	2.99E+00
3M-Hexane	1.30E-04	3.77E+00	4.28E-04	1.31E+00	1.98E-04	4.26E+00
3E-Pentane	1.81E-04	5.07E+00	1.65E-04	3.14E+00	2.16E-04	2.29E+00
2*2*4-TM-Pentane	1.25E-05	5.15E+01	2.25E-04	3.62E+00	3.24E-04	2.43E+00
Heptane	1.89E-04	2.80E+00	3.30E-04	1.32E+00	2.75E-04	4.04E+00
2*2-DM-Hexane	1.88E-05	4.30E+01	9.47E-05	2.30E+00	1.04E-05	2.93E+01
2*5-DM-Hexane	1.03E-05	3.79E+01	7.51E-05	1.82E+00	8.57E-05	1.82E+00
2*4-DM-Hexane	6.66E-06	2.68E+01	5.78E-06	2.18E+01	1.74E-05	6.18E+01
3*3-DM-Hexane	4.97E-06	1.71E+01	7.84E-06	2.41E+01	6.84E-06	2.09E+01
2*3*4-TM-Pentane	6.08E-06	2.75E+01	7.76E-05	2.47E+02	8.57E-05	2.10E+00
2*3*3-TM-Pentane	1.04E-05	2.81E+01	9.06E-06	2.48E+01	6.80E-05	1.53E+00
2*3-DM-Hexane	1.51E-04	1.16E+01	6.54E-04	1.23E+00	9.35E-04	1.98E+00
2M-Heptane	1.57E-05	6.74E+01	2.61E-04	1.62E+00	1.91E-04	3.06E+00
4M-Heptane	1.14E-05	3.07E+01	1.81E-04	2.89E+00	1.61E-04	2.61E+00
3M-Heptane	6.78E-05	2.28E+00	1.38E-05	3.65E+01	2.40E-04	3.36E+00
2*2*5-TM-Hexane	1.14E-05	4.49E+01	1.47E-04	2.80E+00	4.14E-04	1.55E+00
Octane	1.07E-05	3.07E+01	2.57E-04	2.29E+00	5.74E-04	2.17E+00
2*3*5-TM-Hexane	1.73E-06	6.59E+01	1.24E-05	3.80E+01	1.46E-04	1.24E+00
2*4-DM-Heptane	1.24E-05	3.08E+01	8.21E-06	2.39E+01	7.47E-05	1.15E+00
3*5-DM-Heptane	3.92E-06	1.42E+01	8.39E-07	2.26E+01	8.56E-06	2.57E+01
2*3-DM-Heptane	6.27E-07	1.57E+01	6.51E-07	1.65E+01	1.17E-06	3.78E+01
2M-Octane	2.30E-05	5.81E+01	2.83E-04	6.10E+00	9.21E-04	1.83E+00
3M-Octane	4.92E-06	1.68E+01	8.58E-05	1.71E+00	2.22E-04	1.18E+00
Nonane	9.98E-05	3.04E+00	1.50E-04	1.63E+00	2.75E-04	2.19E+00
2*2-DM-Octane	8.64E-06	3.05E+01	2.07E-04	1.45E+00	1.84E-04	1.72E+00
2*4-DM-Octane	8.84E-06	3.17E+01	8.07E-05	1.80E+00	7.56E-06	2.40E+01
Decane	2.43E-05	5.96E+01	3.50E-04	1.45E+00	1.78E-04	1.64E+00
Undecane	2.67E-05	5.66E+01	2.80E-04	1.47E+00	1.71E-04	1.72E+00
Dodecane	1.07E-05	2.84E+01	1.87E-04	1.98E+00	1.35E-04	1.53E+00
Tridecane	1.68E-05	4.77E+01	2.21E-04	2.20E+00	1.45E-04	2.52E+00
∑ Alkanes	3.57E-02		5.76E-02		3.10E-02
2M-Propene	4.38E-03	2.85E+00	1.16E-02	1.79E+00	6.50E-03	3.18E+00
1-Butene	3.01E-03	3.61E+00	9.29E-03	1.80E+00	7.47E-03	3.14E+00
t-2-Butene	1.94E-03	1.35E+00	3.99E-03	1.35E+00	1.36E-03	2.43E+00
c-2-Butene	1.15E-04	2.43E+00	1.78E-04	1.23E+00	9.98E-05	1.64E+00
3M-1-Butene	2.14E-03	4.38E+00	1.84E-03	1.18E+00	8.99E-04	3.11E+00
1-Pentene	6.20E-03	2.70E+00	6.35E-04	1.62E+00	1.30E-03	2.51E+00
2M-1-Butene	2.04E-03	4.81E+00	2.40E-03	2.23E+00	8.54E-04	1.40E+00
t-2-Pentene	4.58E-03	3.95E+00	5.16E-03	1.67E+00	9.94E-03	3.32E+00
3*3-DM-1-Butene	6.53E-04	5.29E+00	3.07E-03	6.56E+00	6.98E-03	4.55E+00
c-2-Pentene	1.34E-03	1.32E+00	3.12E-03	1.85E+00	1.58E-03	4.12E+00
2M-2-Butene	1.89E-03	1.19E+01	1.32E-03	3.41E+00	6.55E-04	4.17E+00
4M-1-Pentene	7.01E-04	8.97E+00	1.31E-03	3.35E+00	1.62E-03	1.13E+00
3M-1-Pentene	9.65E-04	3.65E+00	3.53E-03	1.35E+00	1.21E-04	2.38E+00
4M-c-2-Pentene	3.89E-04	1.50E+01	3.95E-03	8.39E+00	2.93E-04	2.72E+00
4M-t-2-Pentene	5.26E-03	3.08E+00	3.62E-03	2.40E+00	3.45E-03	2.17E+00
2M-1-Pentene	7.33E-04	3.56E+00	6.66E-05	1.22E+02	6.66E-04	1.41E+00
1-Hexene	1.95E-03	2.63E+00	1.35E-03	6.70E+00	1.57E-03	3.75E+00
t-3-Hexene	8.75E-04	2.30E+00	1.09E-03	6.81E+00	1.87E-04	4.19E+00
c-3-Hexene	5.47E-04	2.36E+00	6.33E-04	5.19E+00	7.35E-05	1.15E+00
t-2-Hexene	2.13E-04	2.25E+00	2.72E-04	3.71E+00	2.73E-04	5.57E+00
3M-t-2-Pentene	5.95E-05	3.21E+00	3.36E-04	4.55E+00	2.85E-04	4.37E+00
2M-2-Pentene	6.66E-05	2.28E+00	3.87E-04	3.20E+00	2.56E-04	3.65E+00
c-2-Hexene	4.30E-04	2.33E+00	5.11E-04	1.40E+00	1.47E-04	1.15E+00
3M-c-2-Pentene	1.56E-04	1.50E+00	1.82E-04	3.38E+00	1.06E-05	2.91E+01
3*4-DM-1-Pentene	1.58E-04	3.69E+00	1.20E-05	3.23E+01	7.57E-06	2.40E+01
3M-1-Hexene	5.24E-04	2.02E+00	9.97E-04	1.98E+00	3.99E-04	2.25E+00
1-Heptene	3.92E-04	4.22E+00	2.76E-04	4.11E+00	2.27E-03	1.58E+00
t-3-Heptene	8.39E-05	3.15E+00	2.81E-04	3.97E+00	7.92E-05	1.93E+00
2M-2-Hexene	1.08E-04	2.65E+00	1.61E-05	4.20E+01	7.56E-04	2.46E+00
3M-t-3-Hexene	2.38E-05	4.99E+01	3.11E-04	1.35E+00	2.36E-04	2.63E+00
t-2-Heptene	1.47E-06	4.62E+01	1.63E-05	3.73E+01	3.75E-04	1.63E+00
3E-c-2-Pentene	1.38E-05	3.78E+01	3.09E-04	1.29E+00	2.75E-04	2.65E+00
2*4*4-TM-1-Pentene	1.91E-05	4.48E+01	7.71E-06	2.28E+01	3.22E-04	1.32E+00
2*3-DM-2-Pentene	1.45E-06	4.97E+01	1.00E-04	2.44E+00	1.47E-04	1.74E+00
c-2-Heptene	1.26E-06	4.47E+01	8.60E-06	2.61E+01	1.35E-04	4.08E+00
2*4*4-TM-2-Pentene	1.00E-06	2.97E+01	1.34E-04	1.46E+00	1.96E-04	3.26E+00
1-Octene	1.00E-05	2.92E+01	2.36E-04	1.59E+00	4.41E-04	3.33E+00
t-4-Octene	2.44E-05	5.46E+01	1.48E-04	1.63E+00	2.12E-04	4.02E+00
t-2-Octene	1.14E-05	3.19E+01	9.30E-05	1.79E+00	2.01E-04	4.36E+00
c-2-Octene	1.66E-05	4.78E+01	1.37E-05	3.61E+01	1.09E-04	3.00E+00
1-Nonene	5.12E-04	2.89E+00	7.95E-04	1.76E+00	1.56E-03	2.12E+00
∑ Alkenes	4.25E-02		6.36E-02		5.43E-02
1-Butyne	6.71E-05	2.01E+00	7.75E-04	1.52E+00	2.85E-05	6.28E+01
2-Butyne	2.11E-04	4.03E+00	3.35E-04	4.86E+00	4.31E-04	6.56E+00
∑ Alkynes	2.78E-04		1.11E-03		4.59E-04
CycPentane	5.78E-04	8.85E+00	9.32E-06	3.81E+01	1.65E-04	5.37E+00
M-CycPentane	2.72E-04	2.32E+00	1.44E-04	1.94E+00	2.48E-04	2.34E+00
CycHexane	2.67E-04	1.41E+00	1.69E-04	2.92E+00	3.22E-04	4.79E+00
c-1*3-DM-CycPentane	4.38E-05	1.28E+00	5.86E-05	1.30E+00	5.68E-04	2.25E+00
t-1*2-DM-CycPentane	7.24E-05	1.18E+00	1.34E-04	2.19E+00	1.12E-04	2.15E+00
M-CycHexane	1.17E-05	3.83E+01	2.13E-04	1.58E+00	9.98E-05	2.66E+00
1c*2 t*3-TM-CycPentane	4.96E-06	1.67E+01	4.65E-05	1.39E+00	6.83E-06	2.05E+01
c-1*3-DM-CycHexane	8.28E-06	2.89E+01	3.38E-04	3.41E+00	1.66E-05	5.10E+01
t-1*4-DM-CycHexane	7.04E-07	1.79E+01	8.45E-05	1.71E+00	9.98E-05	2.66E+00
t-1*3-DM-CycHexane	8.19E-06	2.31E+01	5.86E-05	1.91E+00	5.84E-05	1.29E+00
c-1*2-DM-CycHexane	8.48E-06	2.81E+01	6.40E-07	1.66E+01	1.15E-06	3.78E+01
E-CycHexane	3.91E-06	1.39E+01	7.76E-06	2.39E+01	4.63E-05	1.21E+00
∑ Cycloalkanes	1.28E-03		1.26E-03		1.74E-03
CycPentene	2.73E-04	1.41E+00	5.77E-04	1.39E+00	1.54E-04	3.35E+00
3M-CycPentene	1.41E-04	3.02E+00	1.74E-04	1.23E+00	3.74E-04	2.10E+00
1M-CycPentene	2.13E-04	3.55E+00	1.61E-04	2.70E+00	2.19E-04	3.93E+00
CycHexene	2.27E-04	3.11E+00	2.08E-04	2.17E+00	4.00E-04	4.55E+00
∑ Cycloalkenes	8.53E-04		1.12E-03		1.15E-03
1*3-Butadiene	1.21E-03	4.42E+00	1.23E-02	2.18E+00	9.60E-04	6.88E+00
2M-1*3-Butadiene	5.93E-04	1.75E+00	2.62E-03	1.99E+00	1.26E-03	6.20E+00
CycPentadiene	3.28E-04	6.68E+00	5.52E-05	1.91E+00	2.90E-04	5.64E+00
∑ Diolefins	2.13E-03		1.50E-02		2.51E-03
Acetone	4.26E-02	1.85E+00	3.74E-02	1.47E+00	4.22E-02	1.50E+00
MEK	1.73E-02	2.41E+00	2.28E-02	1.83E+00	1.15E-02	2.08E+00
∑ Ketones	5.99E-02		6.02E-02		5.37E-02
Benzene	6.70E-02	2.51E+00	1.00E-01	1.21E+00	7.77E-02	1.45E+00
Toluene	1.05E-02	4.11E+00	2.45E-02	1.42E+00	1.78E-02	1.68E+00
Ethyl Benzene	1.92E-03	4.69E+00	3.42E-03	2.17E+00	3.56E-03	1.76E+00
m&p-xylene	1.68E-03	5.98E+00	3.14E-03	2.12E+00	3.08E-03	2.92E+00
Styrene	2.56E-03	6.06E+00	6.73E-03	2.05E+00	6.28E-03	1.85E+00
o-Xylene	1.00E-03	3.51E+00	1.31E-03	1.81E+00	1.16E-03	1.79E+00
i-PropBenzene	1.85E-06	7.34E+01	1.28E-04	2.19E+00	8.01E-05	1.31E+00
n-PropBenzene	2.43E-06	1.19E+02	2.72E-04	2.40E+00	2.00E-04	3.58E+00
1M-3E-Benzene	2.16E-06	9.20E+01	2.75E-04	2.45E+00	1.27E-04	1.46E+00
1M-4E-Benzene	1.11E-05	3.07E+01	1.12E-04	2.25E+00	2.99E-04	2.78E+00
1*3*5-TM-Benzene	2.38E-04	2.90E+00	2.66E-04	2.84E+00	2.72E-04	1.81E+00
1M-2E-Benzene	1.08E-04	7.97E+00	8.47E-05	2.41E+00	2.69E-04	3.70E+00
1*2*4-TM-Benzene	1.51E-04	3.24E+00	2.66E-03	1.84E+00	1.44E-03	3.02E+00
i-ButylBenzene	4.20E-05	2.10E+00	1.87E-05	4.53E+01	8.24E-07	2.42E+01
s-ButylBenzene	1.22E-05	5.10E+01	7.36E-06	2.47E+01	8.86E-07	3.07E+01
1M-3-i-PropBenzene	5.34E-06	1.94E+01	2.56E-04	1.89E+00	8.08E-06	2.45E+01
1*2*3-TM-Benzene	1.55E-04	4.52E+00	1.68E-04	1.96E+00	2.43E-04	2.80E+00
1M-4-i-PropBenzene	1.43E-05	3.80E+01	4.45E-05	1.39E+00	7.42E-06	2.31E+01
Indan	3.74E-06	1.35E+01	7.89E-06	2.29E+01	7.41E-06	2.25E+01
1M-2-i-PropBenzene	1.39E-05	4.33E+01	8.08E-05	1.94E+00	7.03E-05	1.15E+00
1*3-DE-Benzene	1.41E-06	4.87E+01	2.61E-04	2.59E+00	1.10E-05	3.16E+01
1*4-DE-Benzene	5.51E-06	2.33E+01	7.06E-05	1.08E+00	3.82E-05	1.04E+02
1M-3-n-PropBenzene	1.65E-05	3.91E+01	4.26E-04	2.60E+00	2.32E-04	1.79E+00
1M-4-n-PropBenzene	9.73E-06	3.02E+01	1.38E-05	3.82E+01	1.31E-04	2.55E+00
1*2-DE-Benzene	1.09E-05	2.97E+01	1.70E-05	4.60E+01	8.17E-06	2.41E+01
1M-2-n-PropBenzene	7.88E-06	2.30E+01	8.90E-05	2.21E+00	1.37E-05	3.40E+01
1*4-DM-2-E-Benzene	1.14E-05	3.63E+01	1.80E-05	5.09E+01	1.39E-05	3.70E+01
1*3-DM-4-E-Benzene	1.04E-05	3.47E+01	1.47E-05	5.00E+01	7.85E-07	2.51E+01
1*2-DM-4-E-Benzene	1.31E-05	4.25E+01	1.27E-04	3.58E+00	1.08E-05	3.16E+01
1*3-DM-2-E-Benzene	2.20E-05	5.07E+01	2.27E-04	1.60E+00	2.24E-05	5.06E+01
1*2-DM-3-E-Benzene	8.61E-06	3.24E+01	1.33E-05	3.76E+01	1.20E-04	2.49E+00
1*2*4*5-TetM-Benzene	8.21E-06	2.43E+01	1.22E-05	3.09E+01	1.20E-06	3.56E+01
2-M-ButylBenzene	9.00E-07	3.11E+01	1.45E-05	4.99E+01	6.17E-07	1.83E+01
1*2*3*5-TetM-Benzene	6.76E-06	2.42E+01	1.11E-05	3.08E+01	6.68E-07	1.72E+01
tert-1-But-2-M-Benzene	6.42E-06	2.03E+01	8.98E-06	2.67E+01	4.45E-05	1.21E+00
1*2*3*4-TetM-Benzene	7.63E-05	2.25E+00	1.42E-05	3.54E+01	5.48E-06	1.81E+01
n-Pent-Benzene	1.37E-05	4.27E+01	1.21E-04	2.01E+00	8.90E-05	1.48E+00
tert-1-But-3*5-DM-Benzene	8.72E-06	2.60E+01	7.85E-06	2.37E+01	7.55E-06	2.28E+01
∑ MAH	8.57E-02		1.45E-01		1.13E-01
Naphthalene (gas)	6.33E-02	1.61E+00	3.75E-02	1.25E+00	2.74E-02	3.55E+00
Acenaphthylene (gas)	1.95E-02	3.63E+00	1.07E-02	1.53E+00	6.03E-03	2.25E+00
Acenaphthene (gas)	5.65E-04	2.47E+00	5.09E-04	1.45E+00	1.51E-04	4.59E+00
Fluorene (gas)	2.60E-03	2.16E+00	1.85E-03	1.95E+00	1.09E-03	1.79E+00
Phenanthrene (gas)	6.58E-03	2.61E+00	5.02E-03	1.60E+00	3.21E-03	1.41E+00
Anthracene (gas)	9.58E-04	1.86E+00	8.39E-04	1.61E+00	1.77E-04	4.14E+00
Fluoranthene (gas)	9.78E-04	1.31E+00	9.56E-04	1.84E+00	9.84E-04	1.28E+00
Pyrene (gas)	9.94E-04	1.31E+00	1.55E-03	2.35E+00	1.12E-03	1.07E+00
Benz(a)anthracene (gas)	3.21E-05	1.84E+00	2.53E-05	3.14E+00	1.59E-05	2.04E+00
Chrysene (gas)	2.61E-05	1.59E+00	1.64E-05	2.60E+00	1.27E-05	1.68E+00
Benzo(b)fluoranthene (gas)	4.85E-05	1.85E+00	1.98E-05	4.68E+00	7.59E-06	3.78E+00
Benzo(k)fluoranthene (gas)	6.95E-06	1.45E+00	2.23E-05	1.45E+00	1.49E-05	2.87E+00
Benzo(a)pyrene (gas)	3.01E-05	1.37E+00	3.44E-05	3.86E+00	2.62E-05	2.60E+00
Indeno(1,2,3-cd)pyrene (gas)	1.26E-05	1.07E+00	2.10E-05	5.13E+00	1.38E-05	1.93E+00
Dibenzo(a,h)anthracene (gas)	9.80E-06	2.01E+00	2.84E-05	3.79E+00	4.18E-06	1.11E+01
Benzo(ghi)perylene (gas)	3.34E-05	2.21E+00	7.00E-05	3.64E+00	2.79E-05	1.65E+00
Fluorene (particle)	5.15E-05	1.56E+00	1.21E-04	1.24E+00	1.06E-04	1.16E+00
Phenanthrene (particle)	1.11E-04	1.56E+00	2.46E-04	1.09E+00	2.00E-04	1.15E+00
Anthracene (particle)	9.59E-06	1.37E+00	2.75E-05	1.33E+00	1.52E-05	1.11E+00
Fluoranthene (particle)	8.92E-05	1.43E+00	2.63E-04	1.40E+00	1.33E-04	1.09E+00
Pyrene (particle)	1.07E-04	1.55E+00	2.70E-04	1.16E+00	1.63E-04	1.05E+00
Benz(a)anthracene (particle)	9.13E-05	2.06E+00	3.35E-04	1.42E+00	1.15E-04	1.65E+00
Chrysene (particle)	8.00E-05	1.95E+00	2.70E-04	1.42E+00	1.36E-04	1.35E+00
Benzo(b)fluoranthene (particle)	2.08E-04	1.93E+00	3.28E-04	1.85E+00	1.97E-04	1.34E+00
Benzo(k)fluoranthene (particle)	6.63E-05	1.90E+00	1.02E-04	1.54E+00	7.84E-05	1.43E+00
Benzo(a)pyrene (particle)	1.52E-04	1.83E+00	4.98E-04	1.70E+00	3.03E-04	2.68E+00
Indeno(1,2,3-cd)pyrene (particle)	1.71E-04	1.89E+00	5.94E-04	1.67E+00	3.10E-04	2.37E+00
Dibenzo(a,h)anthracene (particle)	3.01E-05	1.79E+00	1.51E-04	2.40E+00	1.23E-04	4.20E+00
Benzo(ghi)perylene (particle)	2.26E-04	1.89E+00	7.38E-04	1.56E+00	4.24E-04	2.43E+00
Naphthalene	1.08E-05	3.23E+01	4.04E-04	5.94E+00	1.21E-05	3.61E+01
∑ PAH	9.71E-02		6.35E-02		4.26E-02
Formaldehyde	1.67E-01	2.04E+00	2.63E-01	1.93E+00	1.35E-01	1.47E+00
Acetaldehyde	9.63E-02	2.29E+00	1.78E-01	1.71E+00	8.07E-02	1.46E+00
Acrolein	2.34E-02	2.54E+00	4.10E-02	2.40E+00	1.69E-02	1.78E+00
Propionaldehyde	1.50E-02	2.32E+00	2.70E-02	1.64E+00	1.16E-02	1.79E+00
Crotonaldehyde	9.71E-03	2.21E+00	1.67E-02	1.76E+00	8.57E-03	1.68E+00
Methacrolein	3.28E-03	1.95E+00	5.22E-03	1.65E+00	2.05E-03	2.17E+00
Butyraldehyde	4.39E-03	2.01E+00	6.98E-03	1.67E+00	4.00E-03	2.55E+00
Benzaldehyde	7.00E-03	1.92E+00	1.08E-02	1.73E+00	7.73E-03	1.19E+00
Valeraldehyde	3.59E-03	1.64E+00	5.80E-03	1.56E+00	1.96E-03	2.42E+00
Tolualdehyde	2.93E-03	2.55E+00	6.27E-03	1.38E+00	2.43E-03	1.10E+00
Hexanal	9.44E-02	2.15E+00	1.57E-01	1.72E+00	7.90E-02	1.67E+00
∑ Aldehydes	4.27E-01		7.18E-01		3.50E-01
CO	1.31E+01	1.30E+00	1.21E+01	1.32E+00	9.70E+00	1.23E+00
NOx	1.53E+00	1.09E+00	1.83E+00	1.04E+00	1.95E+00	1.05E+00

Notes. ^a$E{R}_{C{O}_2}\left(ga{s}_j\right)=\frac{\mathrm{\Delta }ga{s}_j}{\mathrm{\Delta }C{O}_2}$ where Δ denotes amount above ambient level. Units are g/10³ g CO₂.

Table 2. Summary of analysis of variance testing the effect of LDPE plastic on pivot coordinates (isometric log-ratios) for individual smoke emissions. When the effect of LDPE was statistically significant (p-value ≤ 0.05), the p-values associated with the t-tests for the multiple pair-wise comparisons of the mean values for the levels of LDPE are provided.

Chemical Species	F-test p-value^a	Pivot coordinate mean estimate^b			Pairwise t-test p-values for LDPE mean differences^c
		LDPE 0	LDPE 5	LDPE 50	5– 0	50– 0	50– 5
M-1-Pentene	0.004	3.865	0.681	1.712	0.003	0.022	0.247
3M-1-Pentene	0.002	2.000	2.401	−0.663	0.722	0.004	0.002
3M-CycPentene	0.041	0.074	−0.619	0.466	0.164	0.493	0.036
c-1*3-DM-CycPentane	0.025	−1.099	−1.709	0.885	0.686	0.071	0.025
1-Heptene	0.037	1.096	−0.153	2.275	0.253	0.286	0.031
2*4*4-TM-2-Pentene	0.026	−4.888	−0.878	−0.181	0.055	0.030	0.866
Nonane	0.029	−0.274	−0.766	0.158	0.205	0.275	0.024
1*2*4-TM-Benzene	0.005	0.142	2.116	1.815	0.006	0.012	0.737

Notes. ^aP-value from F-statistic testing overall effect of LDPE. LDPE 0 = LDPE 0%, LDPE 5 = LDPE 0.25%, LDPE 50 = LDPE 2.5% on an LDPE mass basis.

^bMean value of pivot coordinate for level of LDPE plastic. Pivot coordinate is the normalized log-ratio of the single gas to all other gases (Filzmoser, Hron, and Templ 2018).

^cAdjusted p-value of t-test for Tukey multiple pair-wise tests of differences between pivot coordinate means by LDPE level.

Table 3. Summary of analyses of variance examining effect of LDPE plastic on selected compositional balances between classes of smoke emissions.

Balance	LDPE mean effect^a			t-test of balance equal to 0 p-values^b			F-test p-value^c
	0	5	50	0	5	50
Alkane vs Alkene & Alkyne	−4.67	−3.45	−3.60	0.154	0.707	0.707	0.92
Cycloalkane vs Cycloalkene	−3.90	−2.80	−2.54	0.001	0.223	0.217	0.78
Aldehyde vs Diolefin & Ketone	3.03	3.22	2.61	0.027	0.875	0.875	0.91
MAH vs PAH	−6.44	−3.08	−3.45	0.675	0.675	0.675	0.91
NOx vs CO	−1.52	−1.34	−1.13	0.000	0.380	0.136	0.77

Notes. ^aEstimated mean value of compositional balance by LDPE level. Values 0, 5 and 50 indicate LDPE 0%, LDPE 0.25%, and LDPE 2.5% levels.

^bAdjusted p-value associated with t-test that the balance is equal to 0 (false discovery rate (FDR) adjustment for testing across LDPE levels (Benjamini and Hochberg 1995)).

^cP-value associated with F-statistic testing overall significance of effect of LDPE on compositional balance.

Results

After fixing the assignment errors in the original data, the geometric mean of each part of the composition for each level of LDPE is contained in Table 1. These values supersede the values reported in Tables 3–5 of Hosseini et al. (2014) which had been calculated as arithmetic means. Recall that the original data were relative to the amount of CO₂ produced. If $E{R}_{C{O}_2}$ is multiplied by 1.8 to estimate an emission factor based on fuel mass (Hosseini et al. 2014), the log-ratio of any two gases or groups of gases will not change due to compositional equivalence (van den Boogaart and Tolosana-Delgado 2013).

Determining if LDPE influenced emissions by analyzing the ilr pivot coordinate of each gas, i.e. the normalized log-ratio of each gas with the geometric mean of all other gases, resulted in 191 analyses of variance. The mean pivot coordinates were found to differ statistically significantly between levels of LDPE for 8 of the 191 compounds (Table 2) as indicated by the F-statistic p-values. For 5 of the 8 compounds, the mean pivot coordinates for the 50 g LDPE differed significantly from the 5 g LDPE. With the exception of 3M-1-pentene, whose pivot coordinate decreased in mean from 5 g LDPE to 50 g LDPE indicating that the relative dominance of 3M-1-pentene in the composition decreased as LDPE increased, the relative dominance of the other 4 gases increased as LDPE increased from 5 to 50 g. When the 50 g treatment was compared to the 0 g treatment, 2 of the four significant pivot coordinates increased and 2 decreased. In 1 of the 2 significant comparisons between the 0 and 5 g LDPE there was an increase, the other was a decrease.

Comparisons of the effects of LDPE on the defined balances between relevant classes of compounds did not find any statistically meaningful differences (as indicated by the non-significant F-statistics in Table 3), while the individual t-tests indicated that the balances for the cycloalkanes vs cycloalkenes, aldehydes vs diolefins and ketones, and NOx vs CO were significantly different from 0 in the piles without LDPE. Note that the signs of the balances were unchanged as the amount of LDPE increased. The relative amounts of cycloalkanes compared to cycloalkenes, and NOx compared to CO were significantly smaller in mean as indicated by the negative sign of the respective balances for the no LDPE level. Similarly, the relative amount of aldehydes compared to diolefins and ketones was consistently larger in mean.

A large suite of chemicals was analyzed as part of this study to identify whether the toxicity of the smoke plume from burning silvicultural wood piles would be increased by the use of non-pesticide agricultural LDPE plastic coverings. Hosseini et al. (2014) provide the detailed sampling/analysis protocols. The detailed hydrocarbon analysis protocol SAE 930142HP (Siegl et al. 1993) was used to identify a wide array of C₄-C₁₂ gas-phase species typically present in combustion emissions, inclusive of many monocyclic aromatic species including the subset of benzene-toluene-ethyl benzenes-xylenes (BTEX) and 1,3-butadiene. The SAE 930142HP protocol for DNPH-based carbonyl methods was also used to quantify emissions of light carbonyl species, which include harmful species such as formaldehyde, acetaldehyde, and acrolein. Further detailed quantification of PAHs following the modified EPATO13A protocol (Winberry and Jungclaus 1999) provided insight into changes in PAH emissions.

The detailed and target chemical analysis yielded no statistically significant changes to PAHs, BTEX, 1,3-butadiene, and carbonyls along with the hundreds of other species analyzed demonstrates that an increase in the toxicity of the plume is not expected due to the use of the pesticide-free agricultural LDPE. Further, no statistical differences were observed for alkanes, alkenes, alkynes, aldehydes, cycloalkanes, cycloalkenes, diolefins, ketones, MAHs, and PAHs. Emission rates of non-hydrocarbon toxic species (PM, CO, NO₂) were also not impacted by the LDPE.

It is impractical to measure every potential harmful species in the smoke plume. Given that the combustion of LDPE begins by evaporation of light hydrocarbons, it is unlikely that large molecular weight compounds needed additional study. Analysis was not required for harmful metals (LDPE is hydrocarbon-based) and was not performed. Further analysis for nitro- and oxy-PAHs and dioxins were beyond the scope of this study; however, it is very unlikely that these species are enhanced by combusting LDPE, confirmed in part by the lack of change of PAH emissions. Chlorine, sulfur and nitrogen-containing compounds are not expected in the emissions given that LDPE does not contain these precursors. Similarly, reduced species are not expected during oxidation of the LDPE. Therefore, it can be reasonably concluded that none of the compounds included on the US EPA list of 187 Hazardous Air Pollutants (HAPs) (U.S. Environmental Protection Agency 2020) identified by Section 112 of the Clean Air Act are expected to increase.

While the chemical composition of wood and its relative amounts of cellulose, hemicellulose and lignin can vary somewhat (Pettersen 1984), manzanita wood was assumed to be representative of the several hundred species of woody plants found in western forests. Several studies have documented the composition of smoke over the past several decades resulting from the burning of forest fuels. These fuels often contain foliage, fruits such as cones, decomposing wood and organic soil. Many of these fuels, while hydrocarbon-based, different from wood in terms of trace elements and the relative amounts of cellulose, hemicellulose, and lignin (e.g., Jolly et al. 2012; Li et al. 2011; Matt, Dietenberger, and Weise 2020). Thus, the composition of smoke from a complex mixture of different fuels as typically reported will likely differ slightly compared to the present study. In the original paper, ranges of previously reported emission factors were provided for comparison. Those data points are still valid; however, comparison of those results with the LDPE results should be done in light of the relative nature of the emissions data. The cited data should first be transformed into log-ratios to honor its compositional nature and then appropriate, commonly used, mainstream statistical methods could be applied to compare the present results with the cited data. Such an analysis is worthy but beyond the scope of the present paper.

A method denoted “positive matrix factorization” (Paatero and Tapper 1994) has been applied to emissions data (Sekimoto et al. 2018; Ulbrich et al. 2009). This method recognizes the nonnegative nature of emissions data which is a desirable characteristic. Like principal component analysis on which it is based, the method identifies linear combinations of the parts of a composition. However, the solution is constrained so that the fitted values are all non-negative. This imposed constraint is not a result of the nature of the data, but a means to provide a solution. In contrast, Aitchison (1983) showed that principal component analysis can be used with compositional data with no such constraints on the solution once the data have been transformed appropriately using log-ratios. With this approach, each principal component becomes a log-linear combination of the parts that acknowledges the non-negative nature of the data. The compositional data approach matches analysis techniques to the data type instead of artificially imposing numerical constraints to enable solution.

Summary

Smoke emissions data describe the composition of the smoke produced by the burning of biomass and wildland fuels. As such, the data are inherently multivariate and relative in nature. This has been recognized for many years; however, the statistical techniques commonly used to analyze this type of data have ignored these characteristics. Reanalysis of our previously published study using compositional data techniques confirmed that the composition or toxicity of smoke produced by the burning of low-density polyethylene plastic mixed with manzanita wood was not affected by the presence of the plastic. Measured composition of the wood smoke with plastic did not differ significantly from the composition of the wood smoke alone. The result of the present analysis agrees with the earlier published result; however, the original means as reported were in error due to wrong class assignment as well as inappropriate use of the arithmetic mean instead of geometric mean for ratios. When the individual gases were considered singly, a different set of affected gases was identified compared to the original paper. The original analysis did not account for the relative nature of the data, so the original single gas results are in error and the present results are derived from statistical methods based on the nature of the data. To paraphrase Lovell et al. (2015), various statistical measures and algorithms will produce numbers. It is incumbent upon the analyst to ensure that the methods and measures are appropriate for the data. The present approach, based on CoDA, has matched the methodology and measures to the relative nature of smoke emissions. This reanalysis further strengthens the conclusion that use of LDPE in silvicultural practices does not introduce pollutants in addition to what is produced by burning wood alone. The simulated debris piles represented near-optimum burning conditions. The manzanita wood was dry and there was no dirt and other material which might reduce the combustion efficiency thus altering the composition of the smoke emissions. While the log-ratios between compounds may change as a result (Weise et al. 2020), the LDPE portion of the fuel bed should respond as the wood does. If the woody fuels contain significant moisture, the LDPE component may actually burn better than the wood since it does not easily adsorb water and the emissions produced in that situation should be similar to the results in the present study. Recent measurements of burning debris piles covered by LDPE plastic burned operationally (Aurell et al. 2016) reported limited effect of LDPE on measured emissions; however, these data were not treated as compositional data.

The compositional data analysis techniques used in this study should be applied to other smoke emissions data as well as other compositional data related to wildland fire. While many of the compounds measured are gases at flame temperatures, the data set also contained particulate data (see the MAH in Table 1). The techniques presented here can be applied to any emissions data describing composition. Particle size class distributions are an example of discrete compositional data that can be analyzed using techniques based on CoDA (Huston and Schwarz 2012). Citations in the Introduction illustrate the wide-ranging nature of data that are collected to describe the composition of “things.” Analyzing smoke emissions data after transformation into ilr coordinates enables correct application of methods such as linear regression, analysis of variance, time series models and generalized linear models to examine and predict the complex nature of smoke emissions. The references provided herein to the literature and to easily acquired software should permit the appropriate statistical analysis of wildland fire data to provide an improved scientific basis for fire and smoke management decisions.

Acknowledgments

The data used in this paper resulted from the DOD/DOE/EPA Strategic Environmental Research and Development Program project RC-1648. Support for this study was also provided by the Angeles, Cleveland, Los Padres, and San Bernardino National Forests of the USDA Forest Service. J. P.-A. was supported by the Spanish Ministry of Science, Innovation and Universities under the project CODAMET (RTI2018-095518-B-C21, 2019-2021).

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported by the DOD/DOE/EPA Strategic Environmental Research and Development Program [RC-2640]; Spanish Ministry of Science, Innovation, and Universities [CODAMET (RTI2018-095518-B-C21, 2019-2021)].

Notes on contributors

David R. Weise

David R. Weise is a Research Forester at the USDA Forest Service Pacific Southwest Research Station, Riverside, CA, USA.

Heejung Jung

Heejung Jung is a Professor, Department of Mechanical Engineering, University of California, Riverside, CA, USA.

Javier Palarea-Albaladejo

Javier Palarea-Albaladejo is Principal Statistical Scientist at Biomathematics and Statistics Scotland, Edinburgh, Scotland, UK.

David R. Cocker

David R. Cocker is a Professor and Chair, Department of Chemical and Environmental Engineering, University of California, Riverside, CA, USA.

Notes

¹ The use of trade or firm names in this publication is for reader information and does not imply endorsement by the U.S. Department of Agriculture of any product or service.