Statistical Comparison and Assessment of Four Fire Emissions Inventories for 2013 and a Large Wildfire in the Western United States

Abstract

Wildland fires produce smoke plumes that impact air quality and human health. To understand the effects of wildland fire smoke on humans, the amount and composition of the smoke plume must be quantified. Using a fire emissions inventory is one way to determine the emissions rate and composition of smoke plumes from individual fires. There are multiple fire emissions inventories, and each uses a different method to estimate emissions. This paper presents a comparison of four emissions inventories and their products: Fire INventory from NCAR (FINN version 1.5), Global Fire Emissions Database (GFED version 4s), Missoula Fire Labs Emissions Inventory (MFLEI (250 m) and MFLEI (10 km) products), and Wildland Fire Emissions Inventory System (WFEIS (MODIS) and WFEIS (MTBS) products). The outputs from these inventories are compared directly. Because there are no validation datasets for fire emissions, the outlying points from the Bayesian models developed for each inventory were compared with visible images and fire radiative power (FRP) data from satellite remote sensing. This comparison provides a framework to check fire emissions inventory data against additional data by providing a set of days to investigate closely. Results indicate that FINN and GFED likely underestimate emissions, while the MFLEI products likely overestimate emissions. No fire emissions inventory matched the temporal distribution of emissions from an external FRP dataset. A discussion of the differences impacting the emissions estimates from the four fire emissions inventories is provided, including a qualitative comparison of the methods and inputs used by each inventory and the associated strengths and limitations.

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Citation: Faulstich, S.D.; Schissler,
A.G.; Strickland, M.J.; Holmes, H.A.
Statistical Comparison and
Assessment of Four Fire Emissions
Inventories for 2013 and a Large
Wildfire in the Western United States.
Fire 2022,5, 27. https://doi.org/
10.3390/fire5010027
Academic Editor: Alan F. Talhelm
Received: 20 January 2022
Accepted: 15 February 2022
Published: 18 February 2022
Publisher’s Note: MDPI stays neutral
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Copyright: © 2022 by the authors.
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4.0/).
fire
Article
Statistical Comparison and Assessment of Four Fire Emissions
Inventories for 2013 and a Large Wildfire in the Western
United States
Sam D. Faulstich 1,* , A. Grant Schissler 2, Matthew J. Strickland 3and Heather A. Holmes 1
1Department of Chemical Engineering, University of Utah, Salt Lake City, UT 84112, USA;
heather.holmes@chemeng.utah.edu
2
Department of Mathematics and Statistics, University of Nevada, Reno, NV 89557, USA; aschissler@unr.edu
3School of Public Health, University of Nevada, Reno, NV 89557, USA; mstrickland@unr.edu
*Correspondence: sam.faulstich@utah.edu
Abstract:
Wildland fires produce smoke plumes that impact air quality and human health. To
understand the effects of wildland fire smoke on humans, the amount and composition of the smoke
plume must be quantified. Using a fire emissions inventory is one way to determine the emissions rate
and composition of smoke plumes from individual fires. There are multiple fire emissions inventories,
and each uses a different method to estimate emissions. This paper presents a comparison of four
emissions inventories and their products: Fire INventory from NCAR (FINN version 1.5), Global
Fire Emissions Database (GFED version 4s), Missoula Fire Labs Emissions Inventory (MFLEI (250 m)
and MFLEI (10 km) products), and Wildland Fire Emissions Inventory System (WFEIS (MODIS) and
WFEIS (MTBS) products). The outputs from these inventories are compared directly. Because there
are no validation datasets for fire emissions, the outlying points from the Bayesian models developed
for each inventory were compared with visible images and fire radiative power (FRP) data from
satellite remote sensing. This comparison provides a framework to check fire emissions inventory
data against additional data by providing a set of days to investigate closely. Results indicate that
FINN and GFED likely underestimate emissions, while the MFLEI products likely overestimate
emissions. No fire emissions inventory matched the temporal distribution of emissions from an
external FRP dataset. A discussion of the differences impacting the emissions estimates from the four
fire emissions inventories is provided, including a qualitative comparison of the methods and inputs
used by each inventory and the associated strengths and limitations.
Keywords: fire; Bayesian statistics; air quality; wildfire smoke; Rim Fire
1. Introduction
Wildland fires harm humans and the environment. Impacts range from environmental
destruction to serious health complications from smoke inhalation [
1
,
2
]. Wildland fire
smoke inhalation can cause health complications, such as headaches and shortness of
breath, and exacerbate existing conditions such as asthma and COPD [
3
–
5
]. Studies have
also shown a link between wildland fire smoke exposure and non-fatal heart attacks [
2
,
6
].
PM
2.5
emissions from wildland fires may be more harmful than other sources of PM
2.5
due
to the differences in chemical composition [7,8].
Atmospheric processes can transport smoke hundreds of miles, affecting communities
far from the physical fire [
9
]. Wildland fire smoke transported through the atmosphere
varies in concentration and composition after transport, impacting air quality and health
downwind uniquely [
2
]. Understanding the downwind impact of wildland fire smoke re-
quires knowing the concentration of the transported chemical constituents [
10
]. It is difficult
to measure the characteristics of a smoke plume directly. Directly collected measurements
lack generalizability due to the variable nature of fire behavior and emissions [
11
]. On the
Fire 2022,5, 27. https://doi.org/10.3390/fire5010027 https://www.mdpi.com/journal/fire

Fire 2022,5, 27 2 of 24
ground, ambient air quality monitoring networks miss data related to the smoke plumes
above the surface and collect information on all sources of pollution in the air (i.e., vehi-
cle and industrial emissions). It is impossible to measure all the information needed to
estimate emissions in the field, and once the atmosphere transports the smoke plume, the
composition changes significantly [
12
]. Knowing the type and amount of pollution emitted
by a wildland fire is challenging.
A fire emissions inventory is a mathematical representation of emissions that uses vari-
ous inputs about the fire, land, and vegetation (biomass) burned to estimate the amount and
type of pollution from an individual fire. Fire emissions inventories provide information
about the smoke before it is transported and aged in the atmosphere and can be used as in-
puts to atmospheric dispersion models (e.g., HYSPLIT (HYbrid Single-Particle Lagrangian
Integrated Trajectory model)) and chemical transport models (i.e., CMAQ (Community
Multiscale Air Quality model)). These atmospheric models simulate the smoke plume
concentration changes due to atmospheric transport. Both types of atmospheric models use
mathematical representations of the physical processes to simulate atmospheric conditions.
By combining fire emissions inventory estimates and atmospheric models, human exposure
can be estimated in areas impacted by smoke plumes, which is crucial to understanding
health outcomes.
Comparisons of fire emissions inventories have found variability between inventory
results. In one study, fire area was the most significant driver of emissions variability, with
fuel characterization and consumption determination methods also impacting emissions
estimates [
13
]. Many of the differences between emissions inventories are most apparent at
the smaller regional scale, as studies have reported less disagreement between inventories
for larger country-wide and global scale studies compared to the smaller regional scale
studies [
14
–
17
]. The variability and uncertainty of each input into the emission estimates
makes it difficult to attribute the final variability in each emissions inventory to a specific
data source; thus, determining the accuracy of a fire emissions inventory is challenging [
16
].
This paper provides a comparison of four fire emissions inventories and their as-
sociated products: Fire INventory from NCAR (FINN version 1), Global Fire Emissions
Database (GFED version 4 s), Missoula Fire Labs Emissions Inventory (MFLEI (250 m) and
MFLEI (10 km) products), and Wildland Fire Emissions Inventory System (WFEIS (MODIS)
and WFEIS (MTBS) products). Results include a direct comparison of emissions estimates
from each inventory for 2013 and the Yosemite Rim Fire. In addition to quantitatively com-
paring the estimates from each fire emissions inventory, a qualitative comparison using a
Bayesian model is presented. Bayesian models determine influential points in the modeled
distribution, where a point represents daily emissions amounts. These influential points
help investigate how each emissions inventory represents the conditions for a specific day.
We provide a discussion using the Bayesian model to identify the differences observed
across emissions inventories. Results indicate that FINN and GFED likely underestimate
emissions, while the MFLEI products likely overestimate emissions. No fire emissions
inventory matched the temporal distribution of emissions from an external FRP dataset.
2. Fire Emissions Inventories and Satellite Remote Sensing
Fire emissions inventories estimate the amount and type of air pollution emissions
from individual fires. The amount of area burned by the fire, the amount of each fuel type
(biomass) in that burned area, and an emissions factor drive the emissions intensity from a
fire [
15
]. Burned area is crucial to the amount of emissions released by a fire because the
amount of area burned by the fire determines how much fuel was available for the fire. A
fire that burns more area has access to more fuel and thus can create more emissions. Fuel
characteristics also impact fire behavior, affecting fire emissions [
18
]. It is important to know
the amount and type of biomass to determine fire characteristics and emissions. Because
different biomass types release different emissions compounds in different amounts, an

Fire 2022,5, 27 3 of 24
emissions factor is crucial to determining emissions from a wildfire. The relationship
between these variables is defined mathematically in Equation (1) [13].
Amount of SpeciesiEmitted =A∗B∗C∗EFi(1)
A
represents fire size,
B
represents available biomass,
C
represents combustion com-
pleteness, and
EFi
represents the emissions factor for the species of interest (
i
). The emis-
sions factor links the amount of emissions released to dry matter burned. Fire emissions
inventories rely heavily on remotely sensed data, often from satellites, to determine many
of these input variables.
2.1. The Fire INventory from NCAR (FINN)
The Fire INventory from NCAR (FINN) [
17
] provides daily estimates globally at a
1 km spatial resolution. FINN version 1.5 is available for 2002 through 2020. FINN was
primarily developed as a consistent emissions framework for atmospheric chemistry and
air quality models. Therefore, FINN provides extensive information on chemical speciation,
offering emissions estimates for over 40 different species.
The main advantage of FINN lies in its ability to produce data that is ready for input
into chemical transport models in near real-time. FINN also uses rapidly available data
sources, creating emissions estimates within a few hours of a satellite overpass. The MODIS
burned area product is not available this quickly as the data processing for the burned area
product can take months. Significant uncertainties in the assumed burned area product
reduce the advantage of this rapidly available data when it is not being used for a near
real-time simulation. FINN’s use of the MODIS active fire product means that FINN can
miss small fires because of remote sensing limitations. FINN also overestimates the size of
small fires, in addition to misidentifying land cover and having significant uncertainties in
fuel loadings and combustion completeness [
17
]. The generic land cover assignments used
to apply emissions factors and fuel loading are broad, meaning that the average values
of these variables applied to these regions do not always represent actual conditions [
17
].
FINN is in the process of updating its emissions inventory, and that update may address
some of the disadvantages of this product.
2.2. Global Fire Emissions Database
The Global Fire Emissions Database (GFED) [
16
] is a monthly emissions inventory
with a spatial resolution of 0.25
°×
0.25
°
( 27 km
×
27 km). Additional data from satellite
remote sensing instruments redistributes monthly emissions to daily and 3-hourly scales
with diurnal cycles based on a method from Mu et al.
[19]
. GFED reports emissions in
terms of dry matter. Dry matter must be converted to emissions using Equation
(1)
and
the data provided by GFED. This method makes it easy to update the emissions factors
used. GFED provides emissions factors for over 40 species and can also be used in chemical
transport models. GFED version 4.1s provides an updated burned area product with an
algorithm for small fire emissions. GFEDv4.1s is available from 1997–2020. This version
of GFED includes updated fire severity estimates for boreal regions, fuel consumption for
areas that frequently burn, and emissions factors for temperate and boreal areas.
GFED was developed primarily for global studies of climate and fire interactions,
reflected by GFED’s large spatial resolution [
16
]. According to regional studies, GFED is
reliable for estimating emissions from large fires in specific locations, but has difficulties
representing small fires and fires in certain regions [
20
,
21
]. Emissions estimates included in
GFEDv4s are more reliable than estimates created by previous versions of GFED due to
the numerous updates, but the remaining uncertainties are significant and challenging to
quantify. The inclusion of small fires is a crucial step forward, but the limitations of remote
sensing mean that the small fires product has significant uncertainties. An improvement on
the original burned area dataset from MODIS [
22
], based on Randerson et al.
[23]
, is used
to determine a small fire burned area, but the dataset resolution is coarse compared to the
size of the fires, introducing resampling error.

Fire 2022,5, 27 4 of 24
However, the main advantage of GFEDv4s is still the inclusion of small fires. Even
though the small fire estimates have high uncertainty, GFED is the only fire emissions
inventory with a specific algorithm to include small fires. The primary disadvantages of
GFED are in the spatial and temporal resolution. GFED’s large spatial resolution makes
it less useful for regional-scale studies. The temporal profile used to rescale emissions
to daily and 3-hourly scales may not appropriately represent the temporal nature of fire
emissions, particularly in the western United States. For example, there is a significant
nocturnal component to the emissions from fires in California [
24
,
25
]. The temporal profile
used in GFED does not reflect this critical nocturnal component, meaning the rescaled data
may inaccurately represent the temporal distribution of emissions.
2.3. Missoula Fire Lab Emissions Inventory (MFLEI)
The Missoula Fire Lab Emissions Inventory (MFLEI) [
26
] reports daily fire emissions
from 2003–2015 for the contiguous United States. MFLEI gives estimates of the daily
emissions of carbon monoxide, carbon dioxide, methane, and PM
2.5
. MFLEI offers fire
emissions at a 250 m
×
250 m resolution (MFLEI (250 m)) and a spatially aggregated product
at 10 km
×
10 km spatial resolution (MFLEI (10 km)). The 10 km spatially aggregated
product combines the data of the 250 m pixels into the larger spatial resolution using
an uncertainty estimation approach [
15
], making the 10 km product better suited for
atmospheric modeling applications. However, due to the limited number of species in
MFLEI, the emissions estimates cannot directly be used in a chemical transport model.
The MFLEI method contains many updates that the developers promise increase
accuracy in determining fire emissions, but this promised accuracy increase is difficult
to quantify. The primary innovations in MFLEI come from updated emissions factors
and a new wildland fuels map. The wildland fuels map forms the basis of fuel loading,
which provides emissions estimates when combined with emissions factors [
15
]. Using
specific emissions factors for different areas also reduces error compared to using a single
emissions factor for the entire United States. Updating these inputs can significantly impact
the emissions estimates from the fire emissions inventory. MFLEI still reports significant
uncertainties in daily fuel consumption and PM
2.5
emissions. MFLEI also reports much
larger PM
2.5
emissions in the west than other fire emissions inventories, likely related to
the significantly higher emissions factor [15].
2.4. The Wildland Fire Emissions Inventory System (WFEIS)
The Wildland Fire Emissions Inventory System (WFEIS) [
27
] is a fire emissions inven-
tory for the contiguous United States, with a daily temporal resolution and
1 km ×1 km
spatial resolution. WFEIS allows for convenient retrieval and viewing of emissions esti-
mates from their website, which also offers yearly fire emissions data at-a-glance. WFEIS
provides emissions estimates for 2000–2020 and includes emissions for CO
2
, CO, CH
4
,
PM2.5, PM10 , and non-methane hydrocarbons.
WFEIS describes itself as a “system that provides open access to the modeling tools
needed to quantify emissions from past fires” [
27
]. WFEIS developers do not consider
their product an emissions inventory but an aggregation of tools that estimate input
parameters for quantifying emissions. WFEIS has not developed methods of quantifying
input variables and determining emissions. Instead, they use other tools to determine the
input variables used to estimate emissions.
An advantage of the WFEIS method is that fuel consumption estimates are closer
to measured values, especially the temporal variability, because they use a product to
determine these values that is focused solely on fuel consumption [27]. WFEIS has higher
greenhouse gas emissions and fuel consumption estimates than other inventories. There
are several ways WFEIS approaches fuel consumption differently than other inventories
(e.g., assigning
smoldering and flaming consumption separately) that could cause an in-
crease in WFEIS emissions estimates. Other advantages of WFEIS are the ease of data
retrieval and use and the number of different burned area products available. However, the

Fire 2022,5, 27 5 of 24
ability to adjust the methods used to determine input variables is unavailable, as separate
programs determine the input variables outside WFEIS. Another disadvantage is the high
greenhouse gas emissions, as it is unknown which part of the WFEIS framework causes
this increase.
2.5. Satellite Remote Sensing
The Visible Infrared Imaging Radiometer Suite (VIIRS) is an instrument onboard the
polar-orbiting Suomi National Polar-orbiting Partnership (NPP) satellite. VIIRS products
provide information on fire conditions to provide additional context for evaluating the fire
emissions inventories. Multiple products based on remote sensing algorithms are available
from the VIIRS instrument. VIIRS fire related products include fire radiative power (FRP),
detection confidence level, and fire location. The remote sensing algorithm determines fire
information based on thermal anomalies (i.e., detections of high-temperature pixels) [
28
].
These thermal anomalies are detected by an algorithm applied to the radiometer data,
which includes information on the thermal infrared temperature of the pixels, allowing for
the algorithm to detect differences in temperature between a pixel and those surrounding
it. Fire radiative power is related to the fire size and the amount of emissions released.
Because VIIRS is a satellite-based data set not used to create fire emissions inventories,
it gives additional information on fire characteristics that can be used to understand the
differences between fire emissions inventories.
3. Methods
A combination of techniques, from direct comparison to Bayesian statistical analysis,
were used to compare the outputs of each fire emissions inventory. Because there is
no evaluation dataset to determine the accuracy of each fire emissions inventory, using
multiple types of comparisons helps uncover the variability in each emissions inventory.
Each inventory’s emissions estimates were compared for an annual case (2013) and a multi-
day fire event in California (Yosemite Rim Fire). The geographic domain for 2013 included
Washington, Oregon, California, Nevada, Arizona, Idaho, and part of Utah. A smaller
geographic boundary based on the burned area information from CalFire was used for the
Yosemite Rim Fire [
29
]. The period of the Yosemite Rim Fire was 17 August to 06 September
2013 [
29
]. The same geographic domains and times were used to filter the data from each
emissions inventory. The spatial filter was exclusive, so it was excluded from the data if
only part of a pixel was within the geographic boundary.
3.1. Direct Comparison
Each fire emissions inventory’s estimates of burned area and CO, CO
2
, CH
4
, and PM
2.5
emissions were summed, both daily and annually, and compared for 2013 and the smaller
case study of the Yosemite Rim Fire. While there are four inventories, there are six products
to compare: FINNv1.5, GFEDv4s, MFLEI (250 m), MFLEI (10 km), WFEIS (MODIS), WFEIS
(MTBS), shown in Table 1. The daily emissions were compared to understand how each
inventory estimates the variability of fire activity day to day. Burned pixels were mapped
using the latitude and longitude reported by the emissions inventory to investigate the
spatial variation between each fire emissions inventory. The Yosemite Rim Fire provides
insight into the differences in data reported by each inventory for a single, large wildfire.
Understanding how fire emissions inventory estimates differ over the Yosemite Rim Fire
case study is essential for understanding fire emissions inventory performance during
the large wildfire events typical in the western United States, where existing fire behavior
models may not capture fire behavior well [
24
,
25
]. An additional comparison was made
between the fire emissions inventories and VIIRS FRP data. To have comparable results
between all emissions inventories and VIIRS FRP, the emissions or FRP for each day were
normalized to represent the percentage of annual emissions or FRP emitted on that day.

Fire 2022,5, 27 6 of 24
Table 1.
Summary of fire emissions inventory characteristics: spatial resolution, number of data
points for emissions estimates in 2013, the years of available data, temporal resolution, and the
reference for the fire emissions inventory are included.
FINN GFED MFLEI (250 m) MFLEI (10 km) WFEIS
(MODIS)
WFEIS
(MTBS)
Spatial
Resolution 1 km2770 km20.063 km2100 km21 km20.0009 km2
Data Points 7985 921 119,669 3430 9272 159
Years Available 2002–2020 1997–2021 2003–2015 2003–2015 2000–2021 1984–2019
Temporal
Resolution Daily Monthly, Daily,
3-hourly Daily Daily Daily Fire Start Date
Reference Paper
Wiedinmyer
et al. [17]
van der Werf
et al. [16]
Urbanski
et al. [15]
Urbanski
et al. [15]
French
et al. [27]
French
et al. [27]
3.2. Bayesian Statistical Analysis
The daily PM
2.5
estimates from each fire emissions inventory were used to create
Bayesian models that further investigate the daily emissions distributions provided by each
fire emissions inventory. Multiple Bayesian models were created for each fire emissions
inventory, fit to actual inventory data. Understanding these Bayesian model parameters
allows us to infer information about the distribution of emissions estimates from each fire
emissions inventory. These models can provide an innovative methodology to detect each
point’s influence on the Bayesian model distribution. These influence metrics quantify
how well the Bayesian model distribution predicts specific time points. Points that outlie
and influence the overall distribution can then be investigated using external data sources
(i.e., the VIIRS remote sensing products).
The Bayesian model created for each fire emissions inventory relates the day of the year
and the amount of PM
2.5
emissions reported by each fire emissions inventory. These models
were created for 2013, the 2013 fire season (June–September), and the Yosemite Rim Fire.
When creating a time series, it is essential to check for autocorrelation and correct it. An
autoregressive (AR) model was also created for each fire emissions inventory to check and
correct for autocorrelation. Correcting autocorrelation is crucial because many statistical
analyses require that the data be independent of each other, and if they are correlated in
time, they are not independent. The input data is formulaically corrected if autocorrelation
is present. An AR model is advantageous in this context because the Bayesian model now
represents how the previous days’ fire characteristics relate to the following days once
corrected. It is more likely that the amount of emissions released is related to the amount
of emissions released the day before than to what day of the year it is. An autoregressive
Bayesian model was created for each fire emissions inventory to determine how PM
2.5
emissions reported for each day are related to the next day’s emissions. In all cases,
the autoregressive model was a better fit than the non-autoregressive model. While the
Bayesian models for each fire emissions inventory are not directly comparable to the
Bayesian models of the other fire emissions inventories, each model can provide other
directly comparable information, such as cross-validation statistics.
Now, we mathematically describe our AR model (Equation
(2)
). First, we denote the
daily PM
2.5
emissions in grams as the outcome variable
Y
. The model assumes that
Y
is
normally distributed with its mean conditional on the previous day’s PM
2.5
. Since we only
explicitly include the previous day, a single lag, this specific AR is denoted AR(1). Note,
this structure induces longer-range autocorrelation as a consequence of this correction. To
complete the Bayesian model, prior distributions are specified on each parameter outcome
of the model. We choose to employ weakly informative priors to improve estimation
efficiency and avoid entirely unreasonable parameter values. At the same time, we allow the
posterior distribution to be predominantly influenced by the likelihood of the parameters
conditional on the data. In the AR(1), we set weakly informative priors by specifying
the constant values for
α
and
β
’s prior distributions to be skeptical, centered at 0, with

Fire 2022,5, 27 7 of 24
large variances (Equation
(2)
). The first line in Equation
(2)
below denotes an AR(1) model
related to PM
2.5
emissions in grams for current day n, and the following three lines specify
the prior distribution for the Bayesian model parameters.
Yn∼normal(α+βyn−1,σ)
α∼N(0, 10)
β∼N(0, 2.5)
σ∼ex ponential(rate =1)
(2)
Finally, we select a prior for the exponential scale parameter with a rate of 1, the
maximum entropy distribution for a positively constrained random variable, thereby
improving predictive performance [30].
To estimate the posterior and predictive distributions, the R program RStan was
used [
30
–
32
]. Markov Chain Monte Carlo (MCMC) was used to investigate the Bayesian
model distributions. MCMC creates samples from a continuous random variable, with
the probability density proportional to a known function (i.e., Equation
(2)
). The MCMC
model was set up to obtain four chains of 2000 samples each from every model created.
There must be enough samples for the chains to converge for the model to run well.
When the chains converge, the model has run enough simulations to effectively create a
reasonable posterior predictive distribution. The chain convergence for these models was
investigated using ShinyStan, a part of the RStan package, and showed that all chains for
each model converged.
3.3. Influential Points Investigation
An innovative way to use our statistical models to investigate fire emissions inventories
is to use cross-validation techniques to determine influential points in the Bayesian model.
The “leave one out” (loo) technique is used for cross-validation. This technique removes
a single data point from the Bayesian model distribution and compares the new results
to the results of the Bayesian model distribution when all points are included. The loo
process in R provides an estimation of this refitting. This estimation uses the impact of
each point on the posterior distribution, referred to as importance. Importance can be
estimated without refitting the model. Unlikely observations will have more importance
than expected observations, so investigating the influential points determines which points
do not match the rest of the predicted model distribution and thus have the most influence
on the overall distribution of the Bayesian model [
30
]. It is impossible to check every data
point in a fire emissions inventory against daily fire reports and satellite images. Narrowing
the investigation down to only influential points makes it possible to use other data to help
evaluate if the fire emissions inventory reasonably captures the fire’s characteristics for that
specific point.
The influential points investigation uses Pareto Smoothed Importance Sampling (PSIS)
plots created using leave one out cross-validation on the autoregressive models created
for each fire emissions inventory. PSIS uses importance sampling to determine cross-
validation, reporting information on the relative importance of each point in the Bayesian
model distribution [
33
]. Outlying influential points are defined as points with a Pareto-
k influence score outside of a specified threshold (k > 0.7). Above this threshold, error
estimates from the PSIS sampling become unreliable, and thus, the PSIS model cannot
accurately represent these points, meaning the point is outlying the predicted distribution
of the Bayesian model [
34
,
35
]. Some models do not have influential points that outlie the
Bayesian model distribution. In this case, it can still be helpful to investigate the most
influential point of a Bayesian model distribution, even if it is not an outlier. This influential
points investigation will not provide definitive answers on which fire emissions inventory
best models real-world conditions. However, it provides additional context outside of the
quantitative emissions estimates comparison on how the emissions inventories represent
specific days.

Fire 2022,5, 27 8 of 24
4. Results
4.1. Spatial Distribution
The map of all products over the spatial domain for 2013 (Figure 1) shows that all the
fire emissions inventories have a similar spatial distribution. GFED (Figure 1c) has few
points due to the low spatial resolution. WFEIS (MTBS) has very few points because of how
the burned pixels are assigned with the MTBS burned area product. The location reported
by WFEIS (MTBS) (Figure 1e) is in the center of the fire area. MTBS does not provide the
spatial extent of the burned area unless the burned area perimeter is incorporated, which it
is not in WFEIS (MTBS). Each fire emissions inventory has burned pixels in similar areas,
but some fire emissions inventories (i.e., MFLEI (250 m) and WFEIS (MODIS)) have more
pixels in those fire locations. In the central part of Nevada, there are fires sensed by some
emissions inventories that are not reported by other inventories.
The difference in spatial distribution between WFEIS (MODIS) and WFEIS (MTBS)
is pronounced, though they are products from the same fire emissions inventory. WFEIS
(MTBS) has fewer fire locations points, but there are WFEIS (MTBS) points where WFEIS
(MODIS) does not have any points, such as in northwestern Arizona or the Oregon-Idaho
border. MTBS does not assign temporal progression of burned area, so there are fewer
fire pixels for the WFEIS (MTBS) product. MTBS also has a higher spatial resolution than
MODIS, which explains why burned pixels with WFEIS (MTBS) are not included in the
WFEIS (MODIS) product. The MFLEI products have a similar temporal resolution because
the MFLEI (10 km) burned area is determined by aggregating the MFLEI (250 m) burned
pixels (Figure 1d).
(a) (b)
Figure 1. Cont.

Fire 2022,5, 27 9 of 24
(c) (d)
(e) (f)
Figure 1.
(
a
) All Inventories (
b
) FINN (
c
) GFED (
d
) MFLEI (250 m) + MFLEI (10 km) (
e
) WFEIS
(MODIS) + WFEIS (MTBS) (
f
) Yosemite Rim Fire. Maps showing the burned area pixels reported by
each fire emissions inventory. These maps show the difference in fire location between each inventory
due to inventory resolution and methods.
4.2. Annual Evaluation (2013)
4.2.1. Burned Area
For the spatial domain, WFEIS (MTBS) had the largest burned area for 2013, followed
by the MFLEI products, GFED, WFEIS (MODIS), and FINN, in that order (Figure 2). Each
emissions inventory has a similar burned area for the entire year, with FINN reporting
84.5% of the burned area reported by WFEIS (MODIS). Most fire emissions inventories use
MODIS data in their burned area products, explaining the similarity. WFEIS (MTBS) has the
highest burned area due to the higher spatial resolution of the MTBS burned area product
compared to the MODIS burned area product. FINN’s assumed burned area method
seems to underestimate emissions compared to the other inventories. All fire emissions
inventories have a burned area maximum in August, but the spatial distribution of burned
area in months with less fire activity varies greatly (Figure 3).
4.2.2. Emissions
All inventories show a very different total amount of emissions in 2013. MFLEI (250 m),
WFEIS (MODIS), and WFEIS (MTBS) are similar in all emissions species. GFED and MFLEI

Fire 2022,5, 27 10 of 24
(10 km) are consistently lower than all other emissions inventories, with GFED the lowest
(Figure 2). Each emissions inventory shows a similar temporal variability over the year,
with prominent peaks in August (Figure 3). Though they all show a similar temporal
variability, the daily emission magnitudes reported daily by each emissions inventory are
vastly different. The magnitude of emissions from MFLEI (250 m) is much higher than all
other inventories. FINN and GFED are well correlated in magnitude during the emissions
peak of the year, but the temporal variation of GFED for the rest of the year is enormously
different from what any other emissions inventory shows. GFED captures fires during the
peak of fire season but does not detect fires during other parts of the year when fires are
typically smaller. Each emissions inventory captures emissions maxima throughout the
year similarly but reports different variability for periods with lower emissions.
Figure 2.
Burned area and emissions from each emissions inventory for 2013, with the top, darker
color indicating the Yosemite Rim Fire emissions. For GFED, the Yosemite Rim Fire emissions
are so much lower than the yearly emissions that the darker color cannot be discerned. Because
each inventory reports drastically different emissions estimates, each category needed to be scaled
differently to represent them all on the same graph. Burned area is reported in m
2
, while all chemical
species are reported in grams. Burned area is scaled by 10
−3
, CH
4
is scaled by 10
−4
, CO is scaled by
10
−5
, CO
2
is scaled by 10
−6
, and PM
2.5
is scaled by 10
−5
. The y-axis is represented linearly with a
break at zero.
4.3. Yosemite Rim Fire
4.3.1. Burned Area
The burned area reported for the Yosemite Rim Fire was more variable than the yearly
burned area (Figure 2). WFEIS (MTBS) has the highest burned area for the Yosemite Rim
Fire, followed by WFEIS (MODIS), the MFLEI products, FINN, and GFED, respectively.
The difference between GFED and FINN is approximately a factor of 10. The burned area
reported by GFED for the Yosemite Rim Fire is 11.3% of the burned area reported by WFEIS
(MTBS). Though MFLEI (250 m) has the most points, it does not have the highest burned
area. Because burned area is a fundamental part of the emissions equation (Equation
(1)
),
differences in burned area significantly impact emissions estimates. The large differences

Fire 2022,5, 27 11 of 24
between fire emissions inventories seen for a single fire event compared to the whole
year show how inventory selection can impact work done using single-fire data from fire
emissions inventories.
4.3.2. Emissions
Though the burned area is different, the variability between emissions for the Yosemite
Rim Fire is similar to the 2013 total emissions. The WFEIS products and MFLEI (250 m)
report similar emissions. GFED has the lowest emissions of all constituents, which is
expected with the smallest burned area (Figure 2). Each emissions inventory shows a
different magnitude of PM
2.5
emissions and temporal distribution of those emissions for
the Yosemite Rim Fire (Figure 3). MFLEI (250 m), MFLEI (10 km), and WFEIS (MODIS)
show similar temporal variation, which is likely because they all use the MODIS burned
area product. GFED shows a distinctly different emissions profile that is difficult to discern
due to the low emissions from GFED. FINN also shows a different temporal variation, with
emissions increasing and decreasing from day to day in a sawtooth pattern. This pattern
could be due to the assumed burned area product, with difficulties in satellite remote
sensing (e.g., cloud cover) leading to instability in the number of thermal anomalies sensed
each day. The MFLEI products and WFEIS (MODIS) show maximum emissions on the
same day (22 August). FINN and GFED show maximum emissions on 26 August, but the
other inventories also show an increase in emissions on that day.
Figure 3.
Daily PM
2.5
emissions in grams for each fire emissions inventory over 2013. Note: The
y-axis is scaled linearly, with a break at the origin. All inventories show an increase in PM
2.5
emissions
between July and October, but the magnitude of the increase varies significantly between inventories.
There is also significant disagreement between inventories during lower fire activity months.
4.4. VIIRS Fire Radiative Power Comparison
In addition to providing data for investigating influential points, the VIIRS FRP can be
compared with PM
2.5
estimates from each inventory. Using the time series of VIIRS FRP as
an independent evaluation dataset, the temporal pattern in the emissions inventories can
be investigated. The highest individual FRP values are in August (Figure 4). Interestingly,

Fire 2022,5, 27 12 of 24
there are also some high FRP values in July. This July increase in the FRP is not reflected in
the fire emissions inventories temporal distribution of fire activity. This increase may be due
to a hotter burning fire, which may not be well represented in fire emissions inventories as
emissions inventories calculate emissions based solely on burned area. Because emissions
are related to fire temperature, a hotter burning fire can have more emissions than a lower
temperature fire of the same area.
Figure 4.
Fire radiative power (FRP) in megawatts from VIIRS. Each point represents the FRP of a
single thermal anomaly detected by VIIRS. FRP is related to fire intensity and emissions amount. The
VIIRS FRP is not included in any fire emissions inventories and provides an independent dataset
for evaluation.
The data of the percentage of annual FRP emitted per day (Figure 5) shows that VIIRS
captured the most fire activity on 16 August (6.87% of annual FRP), followed by 22 August
(6.55%) and 10 August (5.31%). Only FINN captures the same maxima in fire activity as
VIIRS, showing that 2.70% of yearly PM
2.5
emissions were emitted on 16 August, which is
the maximum for FINN. The MFLEI products and WFEIS (MODIS) report their maximum
annual percentage of PM
2.5
emissions emitted in a single day on 22 August, which is
the second-highest day for VIIRS. GFED reports the highest percentage of annual PM
2.5
emissions emitted in a single day on 24 August, which is not in the top five highest days of
the VIIRS data.
The annual time series of FRP can be compared with the time series from each in-
ventory. Pearson correlation coefficients between the daily PM
2.5
emissions and the daily
VIIRS FRP are shown in Table 2. MFLEI (250 m) has the highest correlation coefficient,
followed by GFED. Based on the results shown above, these emissions inventories have not
accurately represented physical conditions, so the strong correlation with VIIRS FRP is in-
teresting. GFED captured the peaks in fire activity on 10 August, 16 August, and 22 August
quite similarly to VIIRS FRP, but the GFED data aside from these days is not particularly
close with the VIIRS FRP data. Because GFED captures the same maxima as VIIRS, the
correlation increases, though the other data is not similar. The high correlation coefficient
could also mean that MODIS satellite data used in the GFED disaggregation to the daily

Fire 2022,5, 27 13 of 24
time is similar to the VIIRS data, which is likely. MFLEI (250 m) also closely captures the
fire activity peaks represented by VIIRS on 10 and 22 August and captures the 16 August
peak, but less closely than GFED did. No other fire emissions inventories are close to the
VIIRS data on 10 August or 16 August, thus leading to weaker correlations because they
are not similarly capturing the three fire activity maxima seen by VIIRS in August.
Figure 5.
The percentage of annual FRP from VIIRS emitted per day with the percentage of annual
PM
2.5
emitted per day from all fire emissions inventories for 9–25 August 2013. This period contains
all of the frequently occurring influential points. The MFLEI (10 km) points that exceed the y-axis
correspond to 13.57%, 8.19%, and 17.07%, in chronological order. VIIRS FRP shows peaks in fire
activity on 10 August, 16 August, and 22 August. GFED captures these maxima closest, explaining
the strong correlation between VIIRS and GFED. However, GFED does not closely agree with the
VIIRS data aside from those three days.
4.5. Bayesian Statistical Modeling
4.5.1. Influential Points Investigation
Table 3provides information on the influential points of each model for each fire
emissions inventory and each temporal filter (annual, fire season, and Rim Fire). Fire
season is defined as June through September. Modeling daily PM
2.5
emissions for only
the fire season creates a temporal filter that removes many of the low or no emissions
days that can be difficult for the Bayesian model to represent accurately. The influential
points found in each inventory were compared with visual satellite images to evaluate fire
activity on that date. These images are not included here because this inspection was done
manually using NASA Worldview [
36
]. This investigation is an initial qualitative check to
determine if fires are occurring in the spatial domain on the days of the influential points.
All fire emissions inventories were found to pass the qualitative visual check using NASA
Worldview, meaning that there were thermal anomalies detected in the spatial boundary
on the days of the influential points. VIIRS FRP data (Figure 4) provides context for the
fire activity of the surrounding days to provide quantitative analysis. Analyzing the fire
activity captured by a fire emissions inventory for an influential point and relating it to the

Fire 2022,5, 27 14 of 24
fire activity captured by VIIRS helps explain why that point may have been outlying in the
Bayesian model.
Table 2.
Pearson correlation coefficients between daily, summed VIIRS FRP and daily, summed PM
2.5
for each emissions inventory. The correlation between VIIRS FRP, an external dataset, and daily PM
2.5
for each inventory assesses the trends captured by each emissions inventory compared to VIIRS FRP
data. All correlation coefficients are statistically significant (p≤0.05).
Inventory Correlation
FINN 0.66
GFED 0.84
MFLEI (250 m) 0.86
MFLEI (10 km) 0.77
WFEIS (MODIS) 0.80
WFEIS (MTBS) 0.20
FINN did not have an outlying point for the fire season Bayesian model, but the most
influential point of the model occurred on 07 August. FINN reported significant PM
2.5
emissions for that day. This point was also influential in the 2013 Bayesian model for FINN.
VIIRS reports several fires but a relatively low level of FRP. 07 August has a lower FRP than
the days around it. FINN replicates the pattern seen in the FRP data, with 07 August having
lower emissions than the days around it. The lower emissions for a single day may create a
pattern that strongly influences the distribution of the Bayesian model, primarily since it
occurs at a low point. The model likely predicts a smooth transition between 06 August
and 08 August, causing this increase/decrease/increase pattern to outlie the predicted
distribution of the model. For the Yosemite Rim Fire Bayesian model, FINN had no outlying
influential points. The most influential point of the Yosemite Rim Fire Bayesian model was
28 August. FINN reports a large amount of PM
2.5
and burned area for this day. VIIRS FRP
shows that 28 August has several fires but fewer high FRP points than the surrounding
days. FINN does not represent the same trend as the VIIRS FRP on the surrounding days.
Where VIIRS reports a decline in FRP from 26 August–28 August, FINN reports 27 August
has lower emissions than the days around it. This is the same trend that was flagged in
the previous outlying point. These single-day decreases may be causing these points to be
marked as outlying the predicted Bayesian model distribution. Incorporating the VIIRS
FRP data shows that FINN captures a different fire activity trend than VIIRS.
The most influential point of the fire season Bayesian model for GFED was 24 August.
24 August was also an outlying influential point for the 2013 Bayesian model. GFED
showed a significant spike in emissions on 24 August and estimated the largest percentage
of yearly PM
2.5
emissions on this day. The emissions of the days surrounding 24 August
are also lower. Not only is the percentage of yearly emissions emitted on this day at a
maximum, but the emissions of the days around it are also lower, and this pattern is likely
why this point was selected as influential. A maximum that is different from its neighbors
will impact the distribution. VIIRS FRP data for 24 August does not show the same increase
as reported by GFED.
The influential point for GFED during the Yosemite Rim Fire occurred on 26 August.
The Pareto-k influence value of this point is significant, greater than 1.5. This point is highly
influential and outlying in the predicted distribution of the Bayesian model. Referencing
the daily PM
2.5
graph (Figure 3), GFED shows an increase on 26 August, with the rest of
the Yosemite Rim Fire emissions being low. It makes sense that this would be the most
influential point of the model for GFED, as this is a point with some of the highest emissions
in the entire model. The satellite imagery shows the Yosemite Rim Fire emits a large smoke
plume on this day, so emissions are likely to be high. This reveals a limitation of the
investigation of the influential points. From this single influential point, all that can be
determined is whether GFED is representing this day reasonably or not. It does not provide
any information on how emissions should progress from day to day. The remote sensing

Fire 2022,5, 27 15 of 24
imagery shows that the Yosemite Rim Fire had large smoke plumes for several days, so it is
not reasonable to represent the temporal distribution of the Yosemite Rim Fire by having
only one day of high emissions. While the investigation of the influential point cannot
reveal any information about the temporal variability of the Yosemite Rim Fire, it did bring
attention to this point, encouraging investigation of why this point influences the model so
heavily. The investigation of this influential point revealed that GFED is not representing
the temporal distribution of the Yosemite Rim Fire in a way that is close to reality. This is
confirmed by comparing the percentage of annual PM
2.5
emissions emitted each day by
GFED with the percentage of annual FRP for each day from VIIRS. Figure 5shows that
GFED does capture a few large spikes in fire activity similarly to VIIRS FRP, but GFED
shows jagged, sawtooth points, where VIIRS FRP shows more consistent increases and
decreases in emissions.
Table 3.
Dates corresponding to the influential points for each fire emissions inventory Bayesian
model (2013, fire season, and Rim Fire) and the number of fire pixels, PM
2.5
emissions (grams), and
burned area (m
2
) for each point. The percentage of annual emissions emitted on each day is also
provided. An asterisk denotes the maximum percentage of annual emissions emitted. The Pareto-k
influence value is only presented for points that were not outliers. Note: GFED does not provide
pixel information for each fire.
Date Model
Pareto-k
Influence
Value
Pixels PM2.5
(Grams)
Percent of
Annual PM2.5
Emissions
Burned
Area (m2)
FINN 07 August 2013, Fire
Season 0.29 34 7.50 ×1080.62% 3.04 ×107
28 August Rim Fire 0.31 63 1.44 ×1091.60% 6.14 ×107
GFED 17 August 2013 – – 7.62 ×1082.55% 1.10 ×108
24 August 2013, Fire
Season – – 2.21 ×1097.14% * 1.47 ×108
25 August 2013 – – 8.58 ×1082.87% 9.45 ×107
27 August 2013 – – 2.39 ×1080.80% 4.77 ×107
26 August Rim Fire – – 2.09 ×1085.45% 1.12 ×108
MFLEI (250 m) 10 August 2013 – 8959 1.51 ×1010 4.13% 5.60 ×108
22 August
2013, Fire
Season,
Rim Fire
– 3278 2.15 ×1010 5.88% * 1.19 ×108
23 August 2013 – 1904 1.17 ×1010 3.22% 1.19 ×108
MFLEI (10 km) 10 August 2013, Fire
Season – 48 2.51 ×10913.57% 5.60 ×108
22 August
2013, Fire
Season,
Rim Fire
– 52 7.87 ×10917.07% * 2.33 ×108
23 August
2013, Fire
Season,
Rim Fire
– 50 1.23 ×1092.46% 1.19 ×108
WFEIS
(MODIS) 22 August 2013, Rim
Fire 0.58 195 1.23 ×1010 4.66% * 2.16 ×108
18 August Fire Season 0.39 176 7.46 ×1092.81% 1.24 ×108
MFLEI (250 m) had one outlier influential point for the fire season, 22 August. Again,
this point was also influential in the 2013 model. This day had the highest percentage of the
yearly emissions emitted, and closely matches the VIIRS percentage of yearly FRP emitted,
so it is appropriate to have a spike here. Additionally, the days surrounding 22 August
report lower emissions, pointing again to a pattern that will impact the distribution of a
Bayesian model based on this data.

Fire 2022,5, 27 16 of 24
MFLEI (10 km) had three outlier influential points for the fire season, 10 August,
22 August
, and 24 August, also outlying in the 2013 Bayesian model. 22 August is also
the highest percentage of yearly emissions emitted in a single day for MFLEI (10 km), but
the percentage is much higher than found in MFLEI (250 m) (i.e., 17% vs. 6%).
10 August
reports the second-highest percentage of yearly emissions emitted in a single day for MFLEI
(10 km). VIIRS FRP shows a peak in FRP on 10 August, but it is the third-largest peak for
the VIIRS FRP. In MFLEI (10 km), 24 August shows a slight increase in emissions from
23 August
, but because 23 August is so much lower than 22 August, an increase after this
steep decrease can influence and outlie the distribution of the Bayesian model since it
would likely predict a continued decrease.
MFLEI (250 m) had fewer influential points using the fire season Bayesian model than
the annual model, but MFLEI (10 km) had the same influential points using the fire season
and annual Bayesian models. For the Yosemite Rim Fire model, MFLEI (250 m) had an
outlying influential point on 22 August. MFLEI (10 km) has outlying influential points on
22 and 23 August. These points were also found in the annual and fire season Bayesian
models. This points to the differences that spatial aggregation can create, even when using
the same data and methods.
WFEIS (MODIS) did not have an outlying influential point for the fire season Bayesian
model. The most influential point occurred on 18 August. 18 August was not the maximum
percentage of emissions, nor is it higher or lower than both days surrounding it. For this
to be the most influential point of the model is particularly interesting. It may point to
the influential points being “decision points” of a model or places where the algorithm
must decide if it will increase or decrease at this point. WFEIS (MODIS) had no outlying
influential points in the Yosemite Rim Fire Bayesian model. The most influential point was
on 22 August. WFEIS (MODIS) reports significant PM
2.5
emissions for this day. 22 August
had the highest percentage of yearly PM
2.5
emissions recorded by WFEIS (MODIS). As
with other emissions inventories, this maxima makes sense as an influential point because
it drives the distribution. Compared to the VIIRS data, WFEIS (MODIS) captures the peak
in fire activity on 22 August but does not closely match VIIRS on other features of temporal
fire activity on the days before and after the influential point.
The qualitative investigation of fire emissions inventories using satellite imagery from
NASA Worldview proved that fires occurred in the spatial domain on all days of influential
points. The VIIRS FRP dataset provided a comparison dataset for quantitative investigation
of the influential points via an additional temporal record of fire activity. Many influential
points were days with a high percentage of yearly emissions emitted on a single day.
Comparing the estimations of the fire emissions inventories with the VIIRS FRP data for
August, when all of the influential points took place, the fire emissions inventories capture
some of the same maxima, with all inventories but FINN representing a large amount of
fire activity on 22 August. There are not many similarities beyond this, and none of the
fire emissions inventories closely represent the temporal profile of VIIRS or the other fire
emissions inventories. Because the data has been normalized to represent the percent of
annual emissions or FRP on that day, this investigation cannot provide information about
if a fire emissions inventory is correctly estimating the amount of emissions. It can only
provide information on if the inventories and VIIRS are representing the same temporal
fire activity profile, which they are not.
4.5.2. Frequent Influential Points
Comparing the emissions reported by each fire emissions inventory for the most often
occurring influential points provides insight into how each emissions inventory represents
emissions for days frequently reported as influential. In this investigation, the frequently
reported influential points are 10 August (3 occurrences), 22 August (8 occurrences), and
23 August (4 occurrences). MFLEI (250 m) reports the highest emissions for all frequent
influential points. WFEIS (MODIS) reports the subsequent highest emissions for all frequent
influential points (Table 4). FINN reports the lowest emissions for 10 August, but GFED

Fire 2022,5, 27 17 of 24
reports the lowest emissions for 22 and 23 August. 10 August is a relatively clear day
for the spatial domain, so it is not likely that missing remote sensing data will influence
the results due to cloud cover. 22 August has more cloud cover, meaning that the clouds
obscure some thermal anomalies. However, the Yosemite Rim Fire area is clear, so it is
likely being captured by satellite remote sensing products. More fires are seen from VIIRS
throughout the boundary on 22 August than 10 August (Figure 4). The increase in fires is
reflected in the inventory emissions results, with all inventories reporting higher emissions
and burned area on 22 August than 10 August.
10 August does not correspond to the Yosemite Rim Fire period, while 22 and
23 August
do. Additional fire radiative power data from VIIRS shows 22 and 23 Au-
gust have some of the highest fire activity for the entire year of 2013 (Figures 4and 5). The
differences in fire emissions inventory emissions estimates for 10 August and 22 August
provide insight into how the inventories capture this change in fire activity. On 10 August,
FINN reported 36.7% of the PM
2.5
emissions in grams reported on 22 August. GFED re-
ported 66.5% of 22 August PM
2.5
emissions in grams on 10 August. MFLEI (250 m) reported
70.2% of 22 August PM
2.5
emissions in grams on 10 August, and MFLEI (10km) reported
31.9% of 22 August PM
2.5
emissions in grams on 10 August. WFEIS (MODIS) reported
39.9% of 22 August PM
2.5
emissions on 10 August. VIIRS FRP on 10 August reports 65.8%
of the 22 August FRP. This is in line with the percentage from day to day reported by MFLEI
(250 m) and GFED. MFLEI (250 m) and GFED are well correlated, as found in this analysis
and other literature [
15
]. Both inventories may be better representing the high emissions
days and maximum emissions days than other emissions inventories. This is confirmed by
comparing and correlating with VIIRS data, discussed in the previous section. However,
other analyses in this paper have found that GFED does not accurately represent the overall
temporal distributions of emissions from fires, and no emissions inventory represents the
same temporal distribution of fire activity seen in the VIIRS data.
The first frequently detected influential point is 10 August. The VIIRS FRP data for
August 2013 shows that 10 August has a higher FRP than the nearby days. VIIRS also
showed an increased number of points with FRP on 10 August, corresponding to more
fires. Fires are occurring, and the FRP of those fires is higher than the FRP on surrounding
days. This single-day increase could be difficult for the Bayesian model to estimate, leading
to an increase in importance for this point (i.e., day). 22 August shows significant FRP
from VIIRS (Figures 4and 5). Higher emissions are reported from all emissions inventories
on 22 August compared to 10 August or 23 August. 22 August contains the third-highest
daily-summed VIIRS FRP for August. This increase suggests high fire activity and thus
higher emissions, which is well captured by all fire emissions inventories. 23 August is also
a frequent influential point. VIIRS FRP data for 23 August shows a lower FRP than both
10 August and 22 August. The fire emissions inventories that reflect this VIIRS FRP trend
are GFED, MFLEI (250 m), and MFLEI (10 km). FINN and WFEIS (MODIS) report that
23 August
has lower PM
2.5
emissions than 22 August but higher emissions than 10 August.
Based on data from VIIRS, 10 August is a lower FRP day than 22 and 23 August. FINN
may be capturing the daily variability of fires better than GFED because FINN reports
the lowest emissions on 10 August, while GFED reports the lowest emissions on 22 and
23 August
. GFED reports higher emissions than other inventories for a lower FRP day
and lower emissions on higher FRP days. 22 August is the day with the third-highest FRP
reported by VIIRS. High FRP is also reported for 10 August. This could explain why these
days are frequently influential in the Bayesian model. Larger emisisons estimates will have
more influence on the model.

Fire 2022,5, 27 18 of 24
Table 4.
Frequent influential points from each model. These dates correspond to the points found most
frequently in the influential points analysis. Even on the same individual days that influenced the
models, the inventories show vastly different emissions and burned areas each day. The percentage
of annual PM
2.5
emissions emitted on that day is presented for all inventories, and the percentage of
annual FRP emitted that day per VIIRS data is also provided for comparison.
FINN GFED MFLEI (250 m) MFLEI (10 km) WFEIS
(MODIS) VIIRS
10 August 2013 (3 occurrences)
PM2.5 (grams) 7.32 ×1081.25 ×1091.51×1010 2.51 ×1010 4.91 ×109–
Percent of Annual
PM2.5 Emissions 0.62% 4.16% 4.14% 1.36% 1.86% 4.31%
Burned Area (m2) 7.02 ×1074.84 ×1085.60 ×10 85.60 ×1083.44 ×108–
22 August 2013 (8 occurrences)
PM2.5 (grams) 1.99 ×1091.88 ×1092.15 ×1010 7.87 ×1091.23 ×1010 –
Percent of Annual
PM2.5 Emissions 1.66% 6.29% 5.88% 17.07% 4.66% 6.55%
Burned Area (m2) 8.93 ×1071.27 ×1082.33 ×1082.33 ×1082.16 ×108–
23 August 2013 (4 occurrences)
PM2.5 (grams) 1.35 x 1091.05 ×1091.17 ×1010 1.13 ×1081.13 ×1010 –
Percent of Annual
PM2.5 Emissions 1.13% 3.51% 3.22 % 2.46% 4.11% 1.91%
Burned Area (m2) 8.03 ×1071.03 ×1081.19 ×1081.19 ×1081.15 ×108–
5. Discussion
Although it is impossible to determine which fire emissions inventory best represents
real-world conditions, it is possible to investigate the emissions inventories to make an
informed choice. Lacking an evaluation data set, selecting any fire emissions inventory
becomes difficult, as each has benefits and drawbacks. This section discusses the advantages
and disadvantages of each fire emissions inventory based on the results shown above.
5.1. Inventory Resolution
The maps of fire locations for each inventory compare each inventory’s spatial resolu-
tions and reported fires. The number of fires and their spatial distribution differs, despite
many emissions inventories using the same burned area dataset. The table comparing
information from the inventories (Table 1) quantifies the difference between the number of
fire pixels reported by each fire emissions inventory. For example, for 2013, MFLEI (
250 m
)
has nearly 120,000 different fire pixels, but GFED has 921. Much of this discrepancy is
related to the different spatial resolution of each inventory, with MFLEI (250 m) having a
much smaller spatial resolution than GFED. The 921 pixels where fires occurred as reported
by GFED cover an area of 709,170 km
2
, but the 119,669 pixels reported by MFLEI (250 m)
cover 7490 km
2
. This difference in spatial resolution is essential to consider, as it impacts
how each fire emissions inventory reports fires.
Each fire emissions inventory has a pixel grid system for reporting emissions that
differs from the resolution of the burned area dataset. The burned area dataset is reassigned
to the inventories own pixel system, which creates slight spatial discrepancies in the fire
pixels reported for each fire emissions inventory. This grid system transformation may play
a part in why the MFLEI (250 m) emissions are so high, especially since MFLEI (
10 km
)
emissions are lower than the MFLEI (250 m) emissions. The MFLEI (250 m) grid has
a much finer resolution than the MODIS burned area product (250 m
×
250 m versus
500 m ×500 m
for MODIS burned area), which could lead to resampling in the process of
converting to the finer resolution grid. This resampling is then reduced when aggregating
to the larger to 10 km product, which may be why the emissions for MFLEI (10 km) are

Fire 2022,5, 27 19 of 24
lower even though both products use the same input data. This is one way the spatial
resolution of a fire emissions inventory impacts the estimated emissions.
WFEIS (MTBS) has the highest spatial resolution used to estimate fire perimeters, but
it does not provide the daily fire progression data. GFED has a coarse spatial and temporal
resolution. The profile used by GFED to distribute emissions to a finer temporal resolution
may not accurately represent diurnal cycles of emissions in the western United States.
FINN, the MFLEI products, and WFEIS (MODIS) all have a reasonable spatial and temporal
resolution, but the MFLEI (10 km) emissions estimates are closer to the other inventories
than MFLEI (250 m).
5.2. Burned Area
For both the Yosemite Rim Fire and 2013, all inventories report the same magnitude of
burned area (i.e., 10
9
m
2
for 2013 and 10
8
m
2
for the Yosemite Rim Fire). Apart from FINN
and WFEIS (MTBS), all fire emissions inventories use the MODIS burned area product
to determine the burned area input for each emissions inventory. The difference in the
reported burned area from each emissions inventory relates to the method used, whether
it is a different burned area product or spatial aggregation. All fire emissions inventories
have a maximum burned area in August, but there is a significant disparity between the
distribution of burned area for the rest of the year. The pixel grid system that each emissions
inventory uses to report emissions, which can impact emissions estimates and the spatial
distribution of fire location, can also impact burned area estimates.
Notably, there is no burned area difference between the two MFLEI products because
of the method used to aggregate burned area and emissions from the 250 m product to the
10 km product. Emissions are provided for the 10 km product already aggregated from
the 250 m product, but the burned area is provided as the number of pixels in the 250 m
with fuel burned. Since these two burned areas are the same, MFLEI (250 m) assumes
that all 62,500 m
2
of fuel in a pixel has burned in a fire. This pixel area is still relatively
small in remote sensing fires (the MTBS fire detection threshold is nearly 65 times larger),
but the assumption that the entire area in a pixel burns can lead to overestimates in the
burned area.
FINN uses the MODIS thermal anomalies product to determine burned area, assuming
burned area as a function of pixel vegetation cover. The assumed burned area in FINN
is highly uncertain. Based on the burned area results of the other inventories, FINN’s
assumed burned area product based on vegetation cover seemingly underestimates burned
area. Based on the spatial distribution maps, the WFEIS (MTBS) burned area product
provides better estimates than the MODIS burned area product for this comparison due to
the finer spatial resolution. While GFED included a small fire algorithm for determining
the emissions contributions of small fires, it has large uncertainties. In addition to the
uncertainty, GFED had a smaller burned area for the Yosemite Rim Fire. The small fire
product should excel in these situations, which means the coarse spatial resolution of GFED
may be hampering the efficacy of the small fire product.
5.3. Fuels Classification and Emissions Factors
The number of vegetation categories included in an emissions inventory and the
emissions factors used determine how an emissions inventory captures real-world fuel
combustion. A fire emissions inventory with fewer vegetation categories may have more
emissions uncertainties as more vegetation types are combined in one category. While
MFLEI appears to have fewer vegetation categories than the other emissions inventories,
they only provide emissions estimates for the contiguous United States. GFED has eight
overall vegetation categories, but only three apply to the spatial domain in this paper–
boreal forest, savanna, and temperate forest [
16
]. Most fuel loading for North America in
FINN is assigned to tropical forest, boreal forest, and temperate forest, three of the five total
vegetation categories included in FINN [
17
]. The Fuel Characteristic Classification System
FCCS used for the fuel bed classifications [
37
] used in WFEIS [
27
] provides a more robust

Fire 2022,5, 27 20 of 24
framework for applying emissions factors when combined with the Consume emissions
framework. FCCS has numerous specific vegetation categories integrated directly with
Consume to calculate emissions. While some emissions inventories may appear to have
more categories than others, only WFEIS has a complex vegetation assignment for the
domain of interest.
There are a few notable differences in the emissions factors between inventories.
MFLEI has an exceptionally high emissions factor for PM
2.5
in western and northern forests.
The emissions factor in MFLEI is nearly double what is used in the other emissions inven-
tories. Determining which emissions factors approach used by a fire emissions inventory
is most effective is challenging. MFLEI uses a large emissions factor for PM
2.5
in forests
to better reflect information in new literature. However, MFLEI assigns emissions factors
based on three land cover types, a coarse representation of the entire United States. The
Consume model used in WFEIS includes emissions factors for flaming and smoldering
combustion. This is advantageous because smoldering combustion is a significant contribu-
tor to emissions, and many fire emissions inventories do not differentiate between flaming
and smoldering combustion when applying emissions factors. It is also worth noting that
the emissions factors used in WFEIS are significantly different based on the combustion
type (e.g., flaming or smoldering). The differences between emissions factors for the com-
bustion types make it essential for the method WFEIS uses to apportion combustion types
properly. GFED provides additional biomes for assigning emissions factors to forests, but
the emissions factors used may not represent the most up-to-date research on emissions
factors. FINN also assigns emissions factors based on the highly generalized land cover
type that may over-aggregate vegetation type. It is difficult to determine which emissions
factors are most advantageous to use, as they lack generalizability between fires, making it
difficult to determine even a range of accuracy for emissions factors.
5.4. Fuel Loading
The influence of fuel loading on the emissions results can be seen in comparing all
common emissions and burned areas for 2013. The emissions inventories show the same
pattern for emissions (i.e., GFED has the lowest emissions for all species). However, this
is different from the distribution for the burned area (i.e., FINN has the lowest burned
area, but GFED emissions are lower than FINN). Either fuel loading characteristics or the
emissions factors used in the inventories could cause this. Because all emissions inventories
do not report information on fuel loading in their products, it is impossible to understand
the impact of fuel loading on the emissions estimates definitively.
5.5. Influential Points Investigation
Many of these fire emissions inventories have influential points in common, and
these points are often the days with the highest percentage of annual PM
2.5
emissions
emitted in a single day. However, each of these emissions inventories provide different
magnitudes of PM
2.5
emissions for the days of influential points. While this influential
points investigation helps determine if an emissions inventory represents a similar temporal
fire activity compared to VIIRS FRP data, it cannot determine which fire emissions inventory
is modeling conditions most accurately. It is beneficial to see under what conditions the
temporal fire activity profile from a fire emissions inventory does not match VIIRS FRP
data as quality control for specific points. It is also interesting to see which inventories
reflect the trends in VIIRS FRP data for their influential points. GFED and MFLEI (250 m)
have high correlation coefficients between the emissions and FRP because these inventories
best capture some of the fire activity maxima reported by VIIRS.
The variety in the timing of influential points for each inventory during the Yosemite
Rim Fire shows that each fire emissions inventory captures a different temporal distribution
of emissions for the Rim Fire. The variability in the emissions estimates for the Yosemite Rim
Fire is more varied than the variability between emissions inventories for more extended
periods, such as several months or a year. When using fire emission inventory estimates

Fire 2022,5, 27 21 of 24
as data inputs for atmospheric dispersion modeling, inventory selection will significantly
impact atmospheric dispersion modeling on a per-fire basis versus a longer time scale.
5.6. Overall Performance
While GFED has reasonable total emissions of PM
2.5
for 2013, the coarse spatial
resolution is a severe drawback for this emissions inventory. GFED also fails to create a
reasonable temporal apportionment of emissions for the Yosemite Rim Fire, showing its
limitations on a regional scale. The direct comparison reveals that MFLEI (250 m) is likely
overestimating fire emissions, even when compared to MFLEI (10 km). While this could
be a product of both the high emissions factor for PM
2.5
in western forests and the small
number of vegetation classifications, since the MFLEI (10 km) product emissions are not
as high, this points to the possibility that there may be some resampling error with the
smaller spatial resolution product. However, the MFLEI (10 km) product also suffers from
unreasonable estimates, showing a very high percentage of annual PM
2.5
emissions emitted
on single days, nearly tripling the highest annual percentage emitted in a day values of the
other inventories. WFEIS is advantageous in its complex fuel characteristics and includes
both flaming and smoldering combustion emissions calculations. The downsides of the
WFEIS products are the higher greenhouse gas emissions than other inventories because
the cause of this difference is unknown. The lack of a daily burned area progression for the
MTBS product is also a downside. The temporal progression of WFEIS does not closely
match the temporal fire activity data from VIIRS, but none of the emissions inventories
studied here do. WFEIS (MODIS) does not capture the maxima as well as MFLEI (250 m)
or GFED, but the day-to-day fire progression is more reasonable.
5.7. Study Implications and Limitations
The nature of modeling biomass burning emissions for fire emissions inventories is
highly uncertain. Each emissions inventory takes a different approach to modeling the
input variables needed to estimate emissions, creating differences in the final emissions
reported by each inventory. Some emissions inventories prioritize the timeliness of data but
are forced to assume burned area, which creates significant uncertainties. Other emissions
inventories prioritize detecting small fires, but that algorithm also introduces significant
uncertainties. Some emissions inventories incorporate data from field or laboratory mea-
surements, but these measurements are also uncertain. Each of these uncertainties is
propagated through the fire emissions inventory and into the work that incorporates the
estimated emissions (i.e., chemical transport modeling or dispersion modeling).
When selecting a fire emissions inventory for atmospheric modeling, these uncer-
tainties and limitations require a “fit for purpose” approach. Because each inventory
has strengths and limitations, the inventory selection should be determined based on the
fire or smoke modeling purpose. Our future work will use the fire emissions as inputs
to an atmospheric dispersion model to simulate smoke transport and estimate smoke
exposures. The smoke exposures will be used in a time-series epidemiologic study to
estimate associations between smoke and acute cardiorespiratory health outcomes. In this
case, capturing the daily variability in the ambient smoke concentrations is of primary
importance. Additionally, we aim to identify smoke contributions from each fire in the
domain, requiring a fine spatial resolution inventory. Based on the results in this paper, the
inventory selected for our future dispersion modeling is WFEIS, specifically, to combine
WFEIS(MTBS) and WFEIS(MODIS). This will provide the best inventory available for our
health study, where the MTBS products provide high-quality spatial information about fire
location, and MODIS provides the variability of the day-to-day emissions.
While the Bayesian model created for each fire emissions inventory was used for
a limited influential points investigation in this paper, there are many ways a Bayesian
model can provide additional information. Bayesian measurement error is helpful for this
application because the actual value does not need to be known since the true value can be
modeled as an unknown variable with a probability distribution [
30
]. Future studies could

Fire 2022,5, 27 22 of 24
implement a Bayesian measurement error model, where the uncertainties of each variable
used in determining fire emissions must be quantified for input into the measurement error
model. Further investigation of the inputs into each emissions inventory, such as emissions
factors, is required to decrease uncertainties in emissions estimates. Incorporating data from
the new generation of geostationary satellites could also improve the inputs to emissions
modeling and provide an additional comparison dataset.
6. Conclusions
Understanding the type and constituents of wildland fire emissions is crucial to
understanding their impacts on human health and climate. A fire emissions model must
balance simplifying the real world to be usable and maintaining complexity to represent
actual conditions accurately. Each fire emissions inventory uses a different method to model
fire behavior, burned area, and emissions. The methodology each fire emissions inventory
uses significantly impacts the emissions estimates. Comparing the results from four fire
emissions inventories for 2013 revealed how each method of determining emissions impacts
the estimates provided by these inventories. The differences between each inventory were
exacerbated when investigating a single large fire, showing how inventory selection can
vastly impact models that use a fire emissions inventory as an input. Using a direct
comparison and Bayesian modeling to understand the differences between fire emissions
inventories allows for an informed decision about which fire emissions inventory to use for
a particular application.
Author Contributions:
Conceptualization, S.D.F. and H.A.H.; methodology, S.D.F., H.A.H. and
A.G.S.; formal analysis, S.D.F.; investigation, S.D.F., H.A.H., A.G.S. and M.J.S.; resources, H.A.H.;
writing—original draft preparation, S.D.F.; writing—review and editing, S.D.F., H.A.H., A.G.S. and
M.J.S.; visualization, S.D.F.; supervision, H.A.H. and A.G.S.; project administration, H.A.H.; funding
acquisition, M.J.S. All authors have read and agreed to the published version of the manuscript.
Funding:
This work is supported in part by the National Institutes of Health under award number
R01ES029528.
Institutional Review Board Statement: Not applicable.
Informed Consent Statement: Not applicable.
Data Availability Statement: Not applicable.
Acknowledgments:
This work is supported in part by the National Institutes of Health under award
number R01ES029528. We acknowledge the use of imagery and data from the NASA Worldview
application (https://worldview.earthdata.nasa.gov/ (last accessed: 19 January 2022)), part of the
NASA Earth Observing System Data and Information System (EOSDIS). We acknowledge the use of
fire emissions data from FINN ((https://www.acom.ucar.edu/Data/fire/ (last accessed: 19 January
2022)), GFED ((https://globalfiredata.org/pages/data/ (last accessed: 19 January 2022)), MFLEI
((https://www.fs.usda.gov/rds/archive/Catalog/RDS-2017-0039 (last accessed: 19 January 2022)),
and WFEIS (https://wfeis.mtri.org/home (last accessed: 19 January 2022)).
Conflicts of Interest:
The authors declare no conflict of interest. The funders had no role in the design
of the study; in the collection, analyses, or interpretation of data; in the writing of the manuscript, or
in the decision to publish the results.
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