Emissions relationships in western forest ﬁre plumes – Part 1: Reducing the effect of mixing errors on emission factors

Abstract. Studies of emission factors from biomass burning using
aircraft data complement the results of lab studies and extend them to
conditions of immense hot conflagrations. A new theoretical development of
plume theory for multiple tracers is developed after examining aircraft
samples. We illustrate and discuss emissions relationships for 422 individual
samples from many forest fire plumes in the Western USA. Samples are from
two NASA investigations: ARCTAS (Arctic Research of the Composition of the
Troposphere from Aircraft and Satellites) and SEAC4RS (Studies of Emissions
and Atmospheric Composition, Clouds and Climate Coupling by Regional
Surveys). This work provides sample-by-sample enhancement ratios (EnRs) for
23 gases and particulate properties. Many EnRs provide candidates for
emission ratios (ERs, corresponding to the EnR at the source) when the
origin and degree of transformation is understood. From these, emission
factors (EFs) can be estimated, provided the fuel dry mass consumed is known
or can be estimated using the carbon mass budget approach. This analysis
requires understanding the interplay of mixing of the plume with surrounding
air. Some initial examples emphasize that measured Ctot=CO2+CO in a fire plume does not necessarily describe the emissions of the
total carbon liberated in the flames, Cburn. Rather, it represents
Ctot=Cburn+Cbkgd, which includes possibly varying
background concentrations for entrained air. Consequently, we present a
simple theoretical description for plume entrainment for multiple tracers
from the flame tops to hundreds of kilometers downwind and illustrate some intrinsic
linear behaviors. The analysis suggests a mixed-effects regression emission
technique (MERET), which can eliminate occasional strong biases associated
with the commonly used normalized excess mixing ratio (NEMR) method. MERET
splits Ctot to reveal Cburn by exploiting the fact that Cburn
and all tracers respond linearly to dilution, while each tracer has
consistent EnR behavior (slope of tracer concentration with respect to
Cburn). The two effects are separable. Two or three or preferably more
emission indicators are required as a minimum; here we used eight. In
summary, MERET allows a fine spatial resolution (EnRs for individual
observations) and comparison of similar plumes that are distant in time and space.
Alkene ratios provide us with an approximate photochemical timescale. This
allows discrimination and definition, by fire situation, of ERs, allowing us
to estimate emission factors.



Note on CO Fill-in (Section 2):
In order to provide a suitably complete dataset for SEAC4RS, we used the can samples to infer likely concentrations at one-minute intervals of key species, i.e., CH4 for all flights and CO for the first few flights, using available can samples at slightly lower frequency. The R package for multiple imputations by chained equations (mice()) was employed, using the whole data period, but filling in observations with missing data. (Our assessment of the effect of imputation was informal and is reviewed again below.) It was highly desirable to include the imputed concentrations of methane, since it is commonly measured and appears to be a prominent signal of different types of "fire chemistry", i.e., enhanced emission of reduced species; methanol and acetone are often correlated with CH4 and give support to this idea.
The use of imputation seemed justified by three observations: (1) Checks made when both LAS and GC data were available suggested agreement. In an early period, missing tunable-laser absorption spectrometry data for both CO and CH4, some periods did not pass this test and all observations from this period were deleted. (2) The use of regression in both mice() and succeeding emission ratio analyses suggested that when observations were filled in, very little information was added, i.e., if the technique allowed missing observations, the results would be extremely similar. CH4 was omitted from tracer variables used since its cumulative probability distribution, differing from 8 others, suggested non-burning effects that could not be removed.
(3) Comparisons of 10-second and 1-minute averages for the more detailed ARCTAS dataset (not reported here) suggested that the essential variability had been captured by 60-second data. We surmised that 30-second averages might have captured more. We are unsure how averaging affects difference-based methods.

Note on Volumes (Section 3):
For example, the sequence of increasingly large boxes in Figure 5 emphasizes that the relative effect of entrained non-fire air is largest near the flames, but the absolute effect of entrained air on the composition of an observed parcel is often largest close to the parcel at its point of sampling. The following section gives a framework illustrating effects of emissions and entrainment on EnRs. The box volumes of parcels at different altitudes are similar to the mole amounts shown; to be consistent with adiabatic rise of parcels, volumes should be about ~11%-14% larger in linear dimension for most plume tops)

Note on Initial Point (Section 4.1):
It is natural to ask where this time/molar-expansion integration should start, naming it as = , . A reasonable start location is when the fire plume parcels begin entraining predominantly environmental air, not other fresh emissions. The plume that is characterized by this expansion-period analysis is then that mixture over space and time of all detailed variations in emissions before this transition. We remark that emissions from the very hottest flaming combustion in a fire front are likely mixed with neighboring fumes from less vigorous combustion. The hottest regions seem likely never to be directly sampled. Their relevance to all downwind processing and effects is only as part of a mixture. In our dataset, the very hottest burns, MCE > 0.97, were very rarely sampled. We speculate that values of and -. , which represent the MCE during true flaming combustion, may typically be confined to a region very close to the fire, which is measurable in the laboratory but rarely in the field. Note on Varying Entrainment: As a side note, in simple situations (e.g., observations in a plume with same environment but with decreasing dilution, from upwind to downwind), the equation reduces to for any two observational instances, and , in the same plume. These are supposed chosen so that we know that 1 and all the # 1 remain constant. If there is different dilution in the next stage, say instances and , a similar relation obtains, and the composite retains linearity.
Questions regarding constants of integration and original concentrations at a can be resolved in the regression procedure, Section 5. More generally we need 3 14 − 1 3 ≪ 3 4 − 3 and 3 # 14 − # 1 3 ≪ 3 4# − # 3. Situations in which the entraining concentrations vary are described later in Figure 6d. All these observations invite a more general theoretical statement, one that is necessarily more complex and is appropriate for later work.

Note on an Early Approximate Cburn
After having calculated a normalization as in Equation 21 one can see an approximate description of Cburn, and the the ratioing variable can be given the approximate magnitude of Cburn and in the same units. We found that the mid-range of values of Ctot and 7 gave the best calibration and used order statistics to define the calibration in terms of ppm. Low values of Ctot can be affected by measurement precision, and the highest values suffer from the scattered nature of the statistics of extremes.

Note on Sensitivity to Number of Tracers Used (Section 7)
; 4# − M# < = # ; 4 − M < (13) Figure S1: Estimate of variation in Cburn if x 0 is estimated by only three tracers (green dots: ) and only five tracers (red dots). Green line repeats the pattern of P = Cbkgd shown with appropriate scale in Figure 8, for reference. Figure S2 A heuristic measure of the stability of the situation.
The great variations in estimated S 7 T at a few points in Figure 9 can cause some concern (e.g. around sample numbered 8, 117, 130, 217m 231, 329, and 337) . Figure S2 suggests that sometimes these may be of concern, sometimes not. We constructed a measure of the temporal stability of the sampling situation by ratioing the changes of x0 to the amount of carbon burned, x-x0. The measure of change in ppm was Change Measure = (3 7\, T − 7 T 3 + 3 7 T − 7^, T 3) 2 ⁄ and to obtain a consistent measure of relative magnitude, an estimate of smoothed Cburn over the same span of indices was also used, Magnitude Measure = d( 7^, − 7^, T ) + 2( 7 − 7 T ) + ( 7\, − 7\, T )e 4 ⁄ This ratio of these gives our measure of the possible effect of relative change of actual Cburn during our the airborne measurements on the estimate of Cburn that the algorithm gives. Where the measurement crossed different plume boundaries (light gray lines in Figure 9), one-sided estimates consistent with these two values were calculated. We expect that use of absolute differences ratio may give a pessimistically high measure of potential influence; this was justified by a consideration of many different variations. The ratio Magnitude Measure / Change Measure can reach high values, where changes in 7 T can be 0.2, 0.25, 0.33, and 0.5 the amount of Cburn , as the colors of the points in Figure 8 show. Recall, however, that the neighboring 7 T estimates and Cburn estimates are derived independently, so the ratio does not correspond to traditional measures of high-frequency noise, only the stability and relation to identifiable processes on the ground. Figure S2 suggests that for some periods of high Cburn , variations of 7 T should matter little in calculations of Cburn or of the ER ratios derived from Cburn . In other periods, when Cburn is low, there can be reason for concern, even when sample-to-sample variability of 7 T is not especially high.

Note on Examples of Enhancement Ratios (Section 8.1)
Methods used to prepare these graphs of EnRs for the two periods of observation, Figure S3 and Figure  S4, are described in Sections.7 and 9. Figure S3. Estimates of Cburn , an ethyne/ethene photochemical transformation timescale, (Section 6.2), and enhancement ratios (EnRs) for each of the tracer compounds shown for all observations during the ARCTAS flights used in this analysis. Units for the EnRs are shown in Table 2. These diagrams were made using 10 tracers (including methane and methanol), not 8. Figure S4. Cburn , an ethyne/ethene photochemical transformation timescale, (Section 6.2), and enhancement ratios (EnRs) for the SEAC4R observations. Units are given in Table 2.