Mobile monitoring is becoming increasingly popular for
characterizing air pollution on fine spatial scales. In identifying local
source contributions to measured pollutant concentrations, the detection and
quantification of background are key steps in many mobile monitoring
studies, but the methodology to do so requires further development to
improve replicability. Here we discuss a new method for quantifying and
removing background in mobile monitoring studies, State-Informed Background Removal (SIBaR).
The method employs hidden Markov models (HMMs), a popular modeling
technique that detects regime changes in time series. We discuss the
development of SIBaR and assess its performance on an external dataset. We
find 83 % agreement between the predictions made by SIBaR and the
predetermined allocation of background and non-background data points. We
then assess its application to a dataset collected in Houston by mapping
the fraction of points designated as background and comparing source
contributions to those derived using other published background detection
and removal techniques. The presented results suggest that the SIBaR-modeled source contributions contain source influences left undetected by other techniques,
but that they are prone to unrealistic source contribution estimates when they
extrapolate. Results suggest that SIBaR could serve as a framework for
improved background quantification and removal in future mobile monitoring
studies while ensuring that cases of extrapolation are appropriately
addressed.
Introduction
Understanding air pollution exposure is important, as it has been linked to
various adverse health conditions (Caplin et al., 2019;
Zhang et al., 2018). Mobile monitoring, a technique in
which continuous air pollution measurements are collected using
instrumentation on a mobile platform, is becoming increasingly important for
characterizing exposure because air pollution varies on spatial scales finer
than the typical distance between stationary monitors (Apte
et al., 2017; Chambliss et al., 2020; Messier et al., 2018).
A key component of mobile monitoring analysis is identifying ambient
background levels, defined here as measured air pollution concentrations
independent of local source influences (Brantley
et al., 2014). Background quantification is vital from both policy and
exposure perspectives, as it is important to assess the contribution of
local sources to pollution concentrations accurately. Table 1 summarizes the
wide variety of methods used to estimate background in studies incorporating
mobile monitoring published within the past 5 years. The wide variance in
the approaches used is problematic, as estimates of source contributions to
measurements have been shown to be sensitive to the technique used
(Brantley
et al., 2014). To improve the replicability and power of mobile monitoring
studies, a more consistent technique for background estimation is needed.
Summary of previous methodologies for estimating background levels
of air pollution in mobile monitoring campaigns.
StudyMethod used to determine background concentrationApte et al. (2017)Applied 10 s moving average filter, then selected the smaller of the given data value or the 2 min 5th percentile to derive baseline concentrations.Brantley et al. (2019)Fitted quantile regression with cubic natural spline basis expansion of time with degrees of freedom equal to the number of hours in the time series.Hankey and Marshall (2015)Used pollutant-specific underwrite functions to estimate instantaneous background concentrations and subtracted these concentrations from the original time series, averaged reference monitor measurements, then added averaged measurements to underwrite adjusted time series.Hankey et al. (2019)Used hourly averaged measurements in centrally located site for additive correction factor; used daily median fixed-site measurement for temporal correction factor.Hudda et al. (2014)Applied rolling 30 s 5th percentile of the original time series.Larson et al. (2017)Applied 10 min rolling minimum.Li et al. (2019)Applied 1 min moving median filter, then calculated 1 h rolling 5th percentile of smoothed data; additionally, used wavelet decomposition to isolate concentration changes across 8 h at stationary monitors, then subtracted lowest decoupled concentration from mobile monitoring time series across 15 min time windows.Patton et al. (2014)Used mobile measurements in designated urban background neighborhoods removed from highway.Robinson et al. (2018)Linearly interpolated averaged data collected at designated background locations.Shairsingh et al. (2018)Applied rolling 60 s mean, then applied spline of minimums technique (Brantley et al., 2014) across different time windows dependent on a desired background scale.Tessum et al. (2018)Used daily 5th percentile for all pollutants other than fine-particle number concentration; used rolling 30 min 5th percentile for fine-particle number concentration.Van den Bossche et al. (2015)Used averaged measurements from stationary monitor located in an urban green to apply additive correction factors to measurements greater than background, then averaged site measurement and multiplicative correction factors to measurements lower than background.
Designing a method to determine the background in mobile monitoring studies
presents several challenges. Measurements in remote locations are often
regarded as the most reliable representation of background concentrations;
however, remote locations may be inaccessible for some mobile monitoring
studies and are themselves subject to occasional source influences. These
drawbacks make time series methods for determining background more
desirable. However, many time-series-based methods often rely on setting
static time windows, which are usually determined by the expected duration
of influence from source plumes within the mobile monitoring study
(Bukowiecki et al., 2002).
The underlying physical representation of these time series methods remains
unclear for more extensive mobile monitoring campaigns, as the setting of
static time windows does not often capture the entire variation in timescales that source impacts can have on mobile measurements.
Here we show the results of a newly developed method called State-Informed
Background Removal (SIBaR) used to estimate background for several traffic-related air pollutants, namely nitrogen oxides (NOx) and carbon dioxide
(CO2). The method incorporates hidden Markov models (HMMs), a time
series regime modeling technique used in a wide variety of contexts in
signals processing, finance, and the social sciences and that has been used
to model background in stationary monitors (Gómez-Losada
et al., 2016, 2018, 2019; Visser and Speekenbrink, 2010). HMMs assume that
observations within a time series are drawn from probability distributions
governed by a hidden sequence of states. We propose decoding this hidden
sequence of states as a way to determine whether measurements were taken
during time periods representative of background versus time periods subject
to local influences. We illustrate that a more physically meaningful
representation of background is captured in this modeling context for
mobile monitoring time series and show its application to a wide variety of
traffic-related air pollutant measurements. As a proof of concept, we run
the method on a published external dataset already marked as background and
non-background and assess its performance. As a first application and to
provide further proof of concept, we map points binned as background by
SIBaR to show their spatial distributions. As a proof of importance, we
highlight differences in mapped source contributions derived from SIBaR
background and background derived from other time-series-based techniques.
Results indicate that our consistent method for background identification
and removal has a noticeable impact on mapped mobile source contributions.
MethodsMobile campaign
Measurements were taken during the Houston Mobile Monitoring Google Street
View (GSV) campaign and are described in detail elsewhere
(Miller et al., 2020). Measurements
were conducted over a 9 month period spanning July 2017 to March 2018.
Sampling primarily took place between 07:00 and 16:00 local standard time
(Miller et al., 2020) in a variety of census tracts across metropolitan
Houston. Census tracts are included in the current analysis if they were
sampled a minimum of 15 times during this 9-month period
(Apte
et al., 2017; Li et al., 2019). Details and names used to describe each
census tract are given in Table S1 in the Supplement. The time of day and day of week for each
census tract visit were predetermined to minimize temporal biases in
sampling to the greatest extent possible. Instruments (Table S2) were loaded
into two gasoline-powered GSV cars that sampled every drivable road in 22
different census tracts in the greater Houston area. Details and names used
to describe each of the census tracts considered are given in Table S1.
Individual observations are aggregated to 50 m points in neighborhoods
and 90 m points on highways using a road network created from U.S.
Census TIGER/Line roads (TIGER/Line Shapefile, 2018). More details on the
road network creation and data quality control are provided elsewhere
(Miller et al., 2020). Data quality and control measurements were
implemented to ensure sound statistics were performed. Measurements were
removed if they were taken during calibration periods, during periods of
suspected instrument failure, and if they were outside of an instrument's
reported operating range. Measurements were synchronized to GPS time stamps
and adjusted for inlet residence time differences based on results from
match strike tests. Measured pollutants include black carbon (BC), carbon
dioxide (CO2), nitric oxide (NO), and nitrogen dioxide (NO2)
(NOx= NO + NO2).
Bias, precision, and the minimum detection limit (MDL) for each instrument
are provided in Table S2. Details concerning the calculation of each
parameter for each instrument are given elsewhere (Miller et al., 2020). In
brief, the bias for the T200 NO analyzer and T500U NO2 analyzer were
calculated from gas calibration checks performed every 2 weeks at the start
of the study period and every month towards the end of the study period
because the checks routinely showed bias <±10 %. The bias
for the LI-7000 CO2/H2O Analyzer was determined from a gas phase calibration before the start
of the study to match the manufacturer reported value. Precision values for
the T200 and T500U were calculated as the standard deviation of zeroing
periods taken throughout the entire campaign. Minimum detection limits for
the T200 and T500U were determined as the mean of the time series zero +3σ. The minimum detection limit and precision of the Li-COR were not
considered due to taking measurements at a consistently elevated global
background and the latter manufacturer's reported value having a minuscule
effect on the overall uncertainty of the measurement. For the purposes of
this work, we perform no MDL substitution, as MDL substitution would censor
the underlying modeled background probability distribution.
Hidden Markov model categorization – the background partitioning step
Time series observations are segregated by day and for each GSV car, and
HMMs are fit to each day's worth of data. Before fitting the HMM to each
day's time series realizations, we log transform them. HMMs attempt to
maximize the log-likelihood, LC, determined by the sum of the forward
variables αT(i):
LC=∑iNαT(i)
in which i designates state i (total states N) at the last realization
of the time series T. The forward variables are derived recursively as
2α1(i)=πipy1|θi,z3αt+1(j)=∑iNαt(i)aijpyt|θj,z
in which πi represents the initial probability for state i,
aij represents the state transition probability from state i to state
j, and p(yt|θi,z) represents the conditional
probability of observation yt conditioned on the parameters θi governed by state iand any additional covariates z. For the
purposes of our work, we assume that the probability distributions governing
yt are log normal and parametrize the mean of the response distribution
as
μt=β0^+β1^t,
where μt is the time-dependent mean of the response, β^0 and β^1 are estimated parameters, and t is time.
The log-likelihood of Eq. (1) is maximized using the expectation
maximization algorithm (Dempster et al.,
1977; Visser and Speekenbrink, 2010). Initial starting values of the
transition probabilities are bootstrapped 150 times to produce 150 candidate
models because convergence to a maximum likelihood can be affected by the
starting values. The model with the greatest log-likelihood is then selected
for decoding via the Viterbi algorithm (Forney, 1973).
The Viterbi algorithm seeks to maximize the joint probability of both
observations and state sequence (q1,…,qT) given the
parameters. We define a variable δ recursively as
δt+1(j)=maxδt(i)aijpyt+1|θjz
with the initialization
δ1(i)=πipy1|θiz.
To retrieve the state sequence, we create a matrix ψ such that
7ψ1(i)=0,1≤i≤N8ψt(j)=argmaxδt-1(i)aij,1≤j≤N,2≤t≤T.
We retrieve the state sequence by backtracking:
9qT=argmaxδT(i),1≤i≤N10qt=ψt+1qt+1,t=T-1,T-2,…1.
This state sequence is then used to designate observations as background or
source. State-assigned points with the lower median are designated
background. An example of a decoded sequence is given in Fig. 1 for
NOx (after retransformation).
Example time series of SIBaR background signal (blue) being fit to
background designated points (black) created in the SIBaR partitioning step.
Points are colored red if designated as the source in the partitioning step and
black if designated background. Data presented in this time series were
collected on 30 March 2018 starting at 10:00 Central Daylight Time (CDT).
HMM fits can be highly sensitive to time series outliers
(Svensén and Bishop,
2005; Chatzis and Varvarigou, 2007; Chatzis et al., 2009). Additionally,
while computationally cheap, the linearity assumption embedded in the time
covariate could fail to capture more complex variations in background and
produce flawed state categorizations. To capture misclassification
instances, we recast the step as an unsupervised learning problem, design an
empirical routine to evaluate the quality of created clusters, and
incorporate it into SIBaR. The routine, coined the fitted line classifier,
fits a line between averaged transition measurements and their corresponding
transition times. The method then calculates the percentage of points above
the line that are classified as background and the percentage of points
below the line that are classified as source. If either percentage is
greater than or equal to 50 %, a predetermined percentage threshold, the
method deems the series incorrectly classified. If a series is incorrectly
classified, SIBaR breaks the series into two and performs the background
partitioning step on each half chunk separately. Sixteen example time series,
labeled as classified correctly or incorrectly, are depicted in Figs. S1
and S2. After fitting HMMs to each separate chunk, SIBaR then uses the
fitted line classifier on each chunk, repeating the process if any chunk's
partitioning is labeled misclassified. The process continues recursively
until all created partitions are deemed correctly classified. SIBaR then
combines the state designations from all created chunks into one and returns
those state designations as the corrected designations for the time series.
In running SIBaR on the campaign NOx measurements, we note that the
empirical classifier designates 96 % of the original time series to be
correctly classified for a 50 % threshold. We run a sensitivity analysis
on the percentage threshold and show the results in Fig. S3. The figure
illustrates that changing the percentage threshold causes changes in the
percentage of correctly classified time series to range between 80 %–100 %,
dipping below 50 % only for the most stringent requirement (5 %). These
results give us confidence in the partitioning step.
Natural spline fit
After HMMs have been fit to all time series data, natural splines are fit to
the background points by day. As in the work published by Brantley et al. (2019; “Brantley”), we select a natural spline basis with the degrees of
freedom equal to the number of hours in the time series. However, we fit to
the mean of our partitioned background time series, whereas in Brantley the
focus is on a 10th quantile regression. An example of this spline fit
is given in Fig. 1.
Because SIBaR's partitioning step periodically generates background-assigned
points that differ from one another for the same time series, we perform a
test to evaluate its robustness. We run SIBaR 25 times and evaluate the
pairwise root mean square error (RMSE) between each set of generated
background predictions for NOx as defined by
RMSE=∑tTnta-ntb2T
in which nta is the background realization at time t of signal a,
ntb is the background realization at time t of signal b, and T is
the total number of realizations in the time series.
The pairwise RMSE values for the first 12 runs are given in Table S3. We
calculate an average RMSE of 0.05 ± 0.02 ppb between each background
signal and conclude that the fitting step is robust to small changes in
background-assigned points in the partitioning step.
Evaluating the partitioning step: validation on an external dataset
To test the validity of the partitioning step, we perform external
validation using a mobile monitoring dataset published in Brantley et al. (2014). In that study, a van collecting mobile measurements of carbon
monoxide (CO) systematically looped a route in which it drove through a
predefined background location, on transects to a highway, and on the
highway itself
(Brantley
et al., 2014). The measurements taken in the prescribed background location
were marked as background, and all other measurements were marked as
non-background. We run the partitioning step on these data to determine how
well SIBaR captures the measurements taken in the background location of the
study.
Generating mapped fractional background contribution and source
contribution maps
We explore the spatial extent of our HMM-decoded categorizations from the
partitioning step by creating mapped fractional background contribution
maps. After aggregating time series observations (either CO2 or
NOx, depending on the pollutant analyzed) to road segment points
created within our road segment network, we sum the number of observations
designated as the background state and divide by the total number of
observations assigned to that road segment point. We map the results and
present them in Sect. 3.2.
In Sect. 3.3, we derive source contributions (source signal = original
signal – background signal) using our background method and map them. To
put these source contributions in context with previously published work, we
repeat the same process using background derived from a moving 2 min
5th percentile baseline (Apte et al., 2017; “Apte”) and the Brantley
technique described previously in Sect. 2.2 (Brantley
et al., 2019). To derive our source contributions, we make predictions for
the background for each time series realization collected using the derived
background spline and then subtract those predictions from the original time
series observations. We also derive source contributions using the Apte and
Brantley techniques. We create the maps using the same methodology as Miller
et al. (2020) and described briefly here. Using our created road segment
network, we take the mean of measurements collected as the GSV car drives
past a road segment point in our network, coined the drive pass mean. We
take the median of these drive pass means and map the result. Because we
consider drive pass means taken within 4 h of one another to provide no
new information about the air quality at that road segment, we take the
median of drive pass means occurring within that 4 h time window to
generate a 4 h median of drive pass means. Then, we take the median of
all 4 h medians of drive pass means at that road segment to derive its
map-reduced median. We perform this procedure for the source contributions
derived using our method and the source contributions derived using the
other published methods.
Results – proof of conceptValidating the partitioning step on an external dataset
A comparison between SIBaR's partitioning and the partitioning originally
published by Brantley et al. (2014) is given in Fig. 2. Initially, the HMM
fitting step is performed and the resulting state sequence decoded. We run
our classifier on the initially decoded time series and find it to be
misclassified, which is apparent from panel (a) of Fig. S4, which shows the
unsmoothed CO data before correction. The algorithm breaks the series into two
chunks and refits the HMM to each part separately, resulting in the state
designations in panel (a) of Fig. 2. We then compute the percentage of
matching background/non-background designations. The SIBaR partitioning step
is able to match 83 % of the originally published
background/non-background designations. The mismatches could be attributed
to the transition between the background/non-background portions of the
route in the original study, which is observed in Fig. 2 in the periods
where background points show larger values than source points near periods
of the transition (for example, the last blue spike at approximately
08:45 Eastern Daylight Time, EDT). Mismatches also could be a result of the effects of traffic on
measurements in the background designated portion of the route. Finally, the
mismatches could be attributed to the inability of the SIBaR linearity
assumption to capture finer scale temporal variations within the background
(see Eqs. 2–4).
Comparison between SIBaR-predicted background and source states
and originally published designations from Brantley et al. (2014) for log-transformed CO. Background designated points are in blue and source designated
points in red. (a) SIBaR-decoded states for the mobile CO measurements. (b) Designations originally published by the authors of the study.
In running this test, we note that the method is sensitive to a smoothing
time window if one is used. Figure S4 illustrates uncorrected SIBaR-decoded
states for three different smoothing time windows on the same CO dataset and
shows that the method produces different state categorizations depending on
the window used, even making correction unnecessary in the 30 s instance. We
hypothesize that smoothing reduces the skewness of the data such that they
better fit two switched lognormal Gaussian distributions.
Mapped fractional background state contributions
For the Houston mobile campaign, maps detailing the fractional contribution
of the background state to the overall mapped points are created for
CO2 and NOx. Individual observations assigned to a road segment
point have their decoded category designations assigned to the same point.
The number of observations assigned the background category are then divided
by the total number of observations assigned to the point to determine the
fractional background state contribution. Figure 3 shows these census tract
maps for NOx. Figure S5 shows the maps for CO2. It is important to
note that these maps represent the fraction of the measurements that are
categorized as background or source for the given pollutant at a given
location.
Fraction of points aggregated to the road segment network designated
as background in SIBaR-decoded states for NOx. Maps were generated
following the methods outlined in Sect. 2.5. Points are mapped on a scale
of 0 to 1; 1 implies all points aggregated to that road segment were
designated as background and 0 implies all points were designated as
non-background. Details of the census tracts are provided in Table S1. Gold
stars indicate locations of elevated NO and/or NO2 medians next to
known industrial facilities published in Miller et al. (2020). Basemap
generated by MATLAB geobasemap “streets” and is hosted by ESRI (Sources:
Esri, DeLorme, HERE, USGS, Intermap, iPC, NRCAN, Esri Japan, METI, Esri
China (Hong Kong), Esri (Thailand), MapmyIndia, Tomtom).
We note the following about the broad spatial patterns in the mapped background
state fraction presented in Fig. 3. First, background state designated
points dominate residential areas for both pollutants. This is encouraging,
as it is expected that few point sources of these two pollutants would be
found in residential neighborhoods except for those near industrial activity
(Miller et al., 2020). Second,
source state designated points dominate highways and busy arterial roads, which
is expected given the large amounts of traffic on these roads. Finally, we
note the appearance of source-dominated hotspots in front of point sources
identified in our previous work (Miller et al., 2020) and denote their
locations in Fig. 3. This is encouraging given that we found these road
segments to be elevated for NO and/or NO2 compared to their surrounding
neighborhood domain.
Boxplots of mapped background NOx fractions, presented in
Fig. 3, binned by distance from the highway. The red line represents the
median, the top and bottom edges represent the 75th and 25th
percentiles, respectively, and the whiskers extend to the most extreme data
points not considered outliers.
We take the background state fractions depicted in Fig. 3 and bin them by distance to the highway. The results are presented in Fig. 4. We do the same for CO2 and present the results in Figs. S5–S6. The exponential behavior
exhibited in Fig. 4 mirrors published exponential decays in roadside
source pollutant concentrations (Apte et
al., 2017; Karner et al., 2010), while the sizable interquartile ranges
within each bin highlight the complexity and variability of source roadside
gradients, which depend on emission rates, meteorology, geography, and other
factors (Baldwin
et al., 2015; Patton et al., 2014).
Comparison of source contribution maps using different background
removal techniques
To put SIBaR predicted source contributions in context, we compare the
source contribution maps generated using SIBaR to the ones generated by the
Apte and Brantley techniques. We zoom in on the Ship Channel domain for ease
of comparison in Fig. 5. We refer the reader to Figs. S7–S15 to see maps
for all other areas in the mobile monitoring campaign for both NOx and
CO2. The average NOx background predicted by the Apte, Brantley,
and SIBaR techniques are 15.25, 11.58, and 13.02 ppb, respectively.
Comparison of source contributions derived using different
techniques in the Ship Channel domain. Source contributions were aggregated
according to the methods described in Sect. 2.4. (a) Source contributions derived using the Apte technique. (b) Source contributions derived using the Brantley technique. (c) Source contributions derived using the SIBaR technique. Basemap generated by MATLAB geobasemap “streets” and is hosted by ESRI (Sources: Esri, DeLorme, HERE, USGS, Intermap, iPC, NRCAN, Esri Japan, METI, Esri China (Hong Kong), Esri (Thailand), MapmyIndia, Tomtom).
Figure 5 shows that the source contributions derived using the Apte
technique are lower on highways compared to the source contributions derived
using SIBaR and the Brantley techniques. Additionally, both the Brantley and
SIBaR techniques derive higher source contributions on road segments with
elevated NO and NO2 concentrations compared to the Apte technique, as identified in Miller et al. (2020). We hypothesize that this occurs due to the
smaller time window utilized in the Apte technique. The GSV vehicles would
often sit in traffic on highways for extended periods of time, making a 2 min time window unsuitable for describing source durations during those
time periods. While the 2 min assumption would be better suited for
situations in which the car was exposed to source durations within that time
interval (which occurred in the Apte study), it would not be for source
durations of a larger time interval, highlighting the challenges in assuming
a static time window for extensive mobile monitoring campaigns with varying
source durations.
Scatterplots of road segment median source contributions predicted
by two different techniques against their corresponding SIBaR median source
contributions for NOx. The line of best fit is derived using OLS
regression and is depicted in red. The 1 : 1 line is depicted in black. Points are colored by their distance to the closest highway. (a) SIBaR source contribution medians plotted against Apte source contribution medians. (b) SIBaR source contribution medians plotted against Brantley source contribution medians. The plots in red rectangles designate a blown-up portion near the origin.
We plot road segment median source contributions derived by Apte and
Brantley algorithms against the road segment median concentrations derived
by SIBaR and present the results for NOx in Fig. 6. Additionally, we
plot lines of best fit derived using ordinary least squares (OLS)
regression. Figure 6a illustrates that SIBaR derives higher
source contributions medians than the Apte technique, which is largely driven
by differences in highway road segment medians. The slope determined using
OLS regression suggests that, on average, SIBaR median source contributions
are ∼ 41 % higher than Apte median source contributions.
Panel (b) of Fig. 6 comparing Brantley and SIBaR road segment medians
indicates much closer agreement between the two techniques, with SIBaR
estimating source contribution medians at an average offset of 2 ppb lower
than Brantley source contribution medians. Data for CO2 source
contribution medians are shown in Figs. S16 and S17.
1 : 1 scatterplot of the interquartile range (IQR) of predicted
NOx source contributions at individual road segments for the SIBaR and
Brantley techniques. The line of best fit is derived using OLS regression
and is depicted in red. The 1 : 1 line is depicted in black. The inset,
outlined by the red rectangle, shows the IQR at lower values of the Brantley
source contribution IQR. Deviations from the 1 : 1 line suggest that SIBaR
captures source influences the Brantley method fails to detect, despite
predicting lower source contributions on average and the excellent agreement
in median source contribution.
While the road segment median source contributions between the Brantley and
SIBaR techniques exhibit strong agreement, we note that source contributions
evaluated on a more granular level exhibit some disagreement. Figure 7
displays the inter quartile ranges (IQRs) for source contributions assigned
to each road segment plotted against each other for the SIBaR and Brantley
techniques, again colored by distance to the closest highway. We display
additional 1 : 1 plots of the IQR for different techniques and pollutants
(NOx and CO2) in the Supplement (Figs. S18–S20). There are
noticeable deviations from the 1 : 1 line in IQR between SIBaR and the
Brantley technique for both NOx and CO2, suggesting that the two
techniques disagree with one another on individual source contribution
drive pass means. Figure S21 displays a histogram of differences in drive
pass means between the two techniques. While SIBaR predicts lower source
contributions compared to the Brantley technique on average, there are
noticeable discrepancies captured in the tails of the distribution.
Time series plots depicting the original mobile campaign
measurements, colored by their SIBaR-decoded states (background and source),
along with the background signals generated by the SIBaR, Brantley, and Apte
techniques. (a) NOx time series of mobile measurements taken on
3 October 2017, which displays the Apte and Brantley signals overfitting to data decoded as source by the SIBaR partitioning step. (b) NOx time series of mobile measurements taken on 30 November 2017, which shows wildly extrapolated SIBaR predictions at the beginning of the time series due to the lack of background-decoded states.
To provide further context for these results, we present two examples of daily
time series of each background technique's predictions in Fig. 8. It is
apparent that the Apte technique overfits to the data in both cases. The top
panel shows an example of SIBaR's predictions offering an advantage over
Brantley's; since SIBaR is fit to a subset of the data, it avoids
overfitting in the early morning hours of the time series that the Brantley
time series incorporates. Figure 8a illustrates why the cases in the right
tail of the histogram in S21 exist. In contrast, the bottom panel showcases
the potential faults in using SIBaR predictions; since there are no
background designated points at the beginning of this time series example,
the spline fit wildly extrapolates, resulting in unrealistic predictions
that are captured in the left tail of the histogram in Fig. S21. Both
panels illustrate why the medians of Brantley and SIBaR agree so well with
one another, yet display IQRs that deviate from their 1 : 1 line. Both signals
exhibit strong agreement with one another but can capture different source
influences periodically because of the assumptions inherent in each
technique. It is also evident that the appropriate background fit would need
to be investigated on a case-by-case basis, as one should avoid using the
SIBaR technique in instances where extrapolation could occur.
Concluding remarks
We illustrate that SIBaR provides a defensible mechanism to quantify and
remove background from air pollution monitoring data time series. The
method's partitioning step is able to match 83 % of a study's previously
published background/non-background designations. Mapped distributions of
the partitioning step's decoded states show high levels of background state
assignment in residential areas, with notable exceptions in hotspots
published in a previous study. Finally, we show the impact using SIBaR can
have on deriving source contributions in comparing it to the background
signals predicted by other techniques. Most notably, SIBaR does not rely on
a static time window assumption to determine source impacts, and instead
relies on fitting to a subset of the data generated with a time series
regime change modeling technique. Setting a static time window can have
significant impact on the derived source contributions, as exhibited by the
discrepancies between the Apte and SIBaR methods shown in Sect. 3.3. While
the SIBaR and Brantley techniques produce similar source contribution
medians to one another in the context of this campaign's measurements, both
capture different source influences based on the assumptions inherent in
each respective technique.
Comparison of SIBaR state designations for (a) log-transformed versus (b) non-transformed NOx data on 30 October 2017 (local time, i.e., Central Daylight Time, CDT) in the Houston mobile monitoring campaign. Transformation can
affect state assignments, which in this case results in 38 % of the
observations having a different categorization upon transformation.
Despite SIBaR's rigor and advancements relative to previously published
methods, our approach needs careful consideration and improvement. The
method is sensitive to how data in the time series are distributed, and
transforming the measurements can provide different results. For example,
Fig. 9 exhibits a side-by-side comparison of SIBaR state predictions for
transformed (Fig. 9a) and non-transformed (Fig. 9b) NOx data. The transformation in
this instance results in portions of the measurements in the early morning
period being classified as background, whereas none are designated as
background in the non-transformed case. While we think data are more
appropriately described in the lognormal regime (Seinfeld and
Pandis, 2016), careful consideration of transformation is necessary.
Additionally, as discussed in Sect. 3.1 and exhibited in Fig. S4,
applying a smoothing time window can also affect the state categorizations.
While the linearity assumption in the time covariate is computationally
cheap and easy to implement, it is limited. It is unrealistic to expect
background air pollution to exhibit linear behavior, especially as the time
series duration extends (Luke
et al., 2010). While the linearity assumption seems to be acceptable for
time series of several hours of data, problems with that assumption arose in
this work and will most likely arise on time series of data by day or when
time series are impacted by abrupt meteorological changes. Future work
should incorporate assumptions of non-linear behavior into the analysis. Several
studies have been published showing the applicability of HMMs to covariates
expressed as splines (Langrock et al., 2015,
2018). However, trade-offs between computational time and precision would
need to be considered. In its current version, SIBaR takes ∼ 6.5 h to model background for millions of data points (performing the
portioning step, evaluating and/or correcting the fit, and fitting the
spline for all time series). The Brantley technique, in contrast, takes
several minutes.
Despite these shortcomings, SIBaR holds promise as a framework to quantify
and remove background from air pollution monitoring time series. In its
current state, it is inferior to the Brantley technique with regards to
computation time. However, these problems with SIBaR are computational ones
rather than problems with its underlying theory. The SIBaR partitioning step
captures transient behavior between background and non-background quite
well, as the diagnostic results of Sect. 3.1 and the maps in Sect. 3.2
indicate. In addition to addressing other issues highlighted here, future
work should focus on methods to reduce its computational time to make its
use more straightforward.
Code and data availability
Both the code and data are available on request. Additionally, time series comparisons for all 312 time series taken in the campaign, as well as a demo of the SIBaR partitioning step, are available at 10.5281/zenodo.5022590 (Actkinson et al., 2021). Data are also
free to download from OpenAQ (https://openaq.org/#/project/28974, Environmental Defense Fund, 2021).
The supplement related to this article is available online at: https://doi.org/10.5194/amt-14-5809-2021-supplement.
Author contributions
BA developed, wrote, and tested the method in R (R: The R Project for Statistical Computing, 2021) with critical input and scientific guidance from RJG and KE. RJG supervised the project and provided feedback on the
significance of the method's results. BA wrote the manuscript. All authors
contributed to the editing and review of the manuscript.
Competing interests
The authors declare that they have no conflict of interest.
Disclaimer
Publisher’s note: Copernicus Publications remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.
Acknowledgements
We thank Halley Brantley for the provision of data and
comments concerning results in Sect. 3.1 of the paper. We also
appreciate support from the Environmental Defense Fund for the collection
and provision of mobile data.
Financial support
This research has been supported by the National Institute of Environmental Health Sciences (grant no. R01ES028819-01).
Review statement
This paper was edited by Glenn Wolfe and reviewed by two anonymous referees.
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