We examine the potential benefits of very high resolution for air-quality
forecast simulations using a nested system of the Global Environmental
Multiscale – Modelling Air-quality and Chemistry chemical transport model.
We focus on simulations at 1 and 2.5 km grid-cell spacing for the same time
period and domain (the industrial emissions region of the Athabasca oil sands). Standard grid cell to observation station pair analyses show no
benefit to the higher-resolution simulation (and a degradation of
performance for most metrics using this standard form of evaluation).
However, when the evaluation methodology is modified, to include a search
over equivalent representative regions surrounding the observation locations
for the closest fit to the observations, the model simulation with the
smaller grid-cell size had the better performance. While other sources of
model error thus dominate net performance at these two resolutions,
obscuring the potential benefits of higher-resolution modelling for
forecasting purposes, the higher-resolution simulation shows promise in
terms of better aiding localized chemical analysis of pollutant plumes,
through better representation of plume maxima.
Introduction
Numerical modelling of the atmosphere in an Eulerian framework relies on
discretization of the computational domain into a numerical grid. The
horizontal grid-cell size of atmospheric simulations can range from hundreds
of kilometres to the metre-scale of large eddy simulation models.
Air-quality model grid-cell size typically follows the grid-cell sizes used
in weather forecasting models, which in turn have followed a gradual
progression towards finer discretization where more explicit representation
of cloud formation and local radiative transfer effects may be represented.
The most recent weather forecasting applications (e.g. Leroyer et al.,
2014) have reached grid-cell sizes as small as 250 m over limited domains such
as individual cities, and have shown promising results in terms of being able
to resolve some aspects of local circulation. In addition, as grid resolution
reaches the 3 to 4 km scale, explicit cloud microphysics packages may be
used, allowing potentially better performance, particularly with regards to
feedbacks between meteorology and chemistry (Yu et al., 2014; Gong et
al., 2015). However, while these models promise better physical
representation of local chemistry, their performance may be limited by the
quantity and availability of initialization and boundary condition
meteorological data; these data may be used in a data assimilation context to
improve their initial state. The accuracy of broader-scale meteorological
predictions may thus influence local model accuracy, despite the ongoing
decrease in meteorological model (and consequently air-quality model) grid-cell size. Some recent air-quality model simulation studies with grid-cell
sizes on the order of 1 to 4 km include Thompson and Selin (2012), Li et
al. (2014), Joe et al. (2014), Kheirbek et al. (2014, 2016), and Pan et al. (2017).
For the purposes of this study, very high resolution (VHR) modelling refers
to the current higher-resolution limits of chemical transport models (CTMs),
employing a horizontal grid-cell spacing of 1 km or less. It is in this
regime that the photochemical processes may be forecasted with resolved
microphysics (e.g. Milbrandt and Yau, 2005a, b) and detailed particle and
gas-phase chemistry, using currently available computer technology. VHR
modelling is very computationally expensive, and also introduces its own set
of challenges, such as the availability of surface boundary condition fields
as the model grid-cell size decreases. Moreover, it is not currently clear
whether decreases in model grid-cell size leads to more accurate results when
compared to observations. The motivation behind VHR modelling in CTMs is to
reduce the impact of diluting chemical concentrations – especially from
averaging emission plumes into large grid cells – in order to better capture
inhomogeneities in emission profiles, to better simulate local transport
processes associated with terrain that would otherwise be smoothed by the use
of a coarse grid, and to reduce truncation errors and hence achieve better
numerical accuracy (Jacobson, 1999).
We note here that while the terms “grid-cell size” and “resolution” tend
to be used interchangeably in the literature, this is not true in a precise
mathematical sense; more formally, the ability to resolve features of size
2Δx requires a grid-cell spacing of size Δx, and the highest
spatial frequency which can be reconstructed from a discrete sampling of the
latter grid-cell spacing will be 12Δx, the Nyquist
wavenumber of the grid-cell size discretization. Furthermore, atmospheric
models may make use of energy dissipation techniques that broaden the size of
resolvable wavelengths to 3 to 4 Δx (Grasso, 2000; Pielke,
2001). Model resolution is thus a function of, but not equivalent to, grid-cell size. Here, we define “resolution” as the ability of a model to
clearly distinguish components of a predicted atmospheric variable, as a
function of grid-cell size.
The issue of a model to distinguish these features is also compounded by
uncertainties in model inputs. For example, in a large rural setting, a large
model grid cell will represent an area containing many roads, whose emissions
will be averaged into one value per species per time. As the grid-cell size
decreases, however, this averaging effect will be reduced, giving each road's
emissions more impact on the resulting concentrations in the grid cell
containing it. However, the smaller grid-cell size will also result in
steeper concentration gradients in the model between adjacent grid cells,
which can in turn result in numerical instabilities that contaminate
predictions (Salvador et al., 1999). At the same time, a reduction in
grid-cell size can be shown formally to reduce inaccuracies in the
discretization of the governing equations for atmospheric motion (Coiffier,
2011). Previous efforts to address these issues through variable grid size or
structure in air quality modelling have not received sustained attention, and
therefore most current air quality models use a uniform (albeit nested) grid-cell size in applications (Garcia-Menendez et al., 2010; Kumar et al.,
1997).
As resolution increases further, the presence of local topographical features
(e.g. buildings and street canyons) becomes more important. Both the increased
topographic complexity and potential numerical instabilities can lead to
differences in meteorological forcing as resolution increases (Wolke et
al., 2012; Gego et al., 2005). The contribution of meteorological
uncertainties due to resolution becomes more significant, especially for
secondary pollutants such as ozone (Valari and Menut, 2008) or secondary
particulate matter (PM). For example, Markakis et al. (2015) in their
analysis of 4 km CHIMERE simulations for the relatively flat terrain of
Paris, France, suggested that model meteorological grid-cell size does not
significantly impact forecast accuracy. That may not have been the case, had
their terrain been more complex. In contrast, Queen and Zhang (2008) observed
considerable meteorological sensitivity to the more complex terrain in their
4 km resolution Community Multiscale Air Quality (CMAQ; EPA, 1999) model
simulations over the Appalachian Mountains in the eastern United States, as
did Salvador et al. (1999) for meteorological model simulations.
A number of studies have tried to evaluate the benefits of higher-resolution
simulations and to quantify the impact of sub-grid variability by using
different model grid-cell sizes (Vardoulakis et al., 2003; Ching et al.,
2006; Pepe et al., 2016). These studies have often demonstrated that failure
to account for higher-resolution features may result in mischaracterization
of concentrations or health impacts (Isakov et al., 2007), although the
capability of current models to provide this information with sufficient
accuracy is unclear. One study found that increasing resolution did not
change predicted health outcomes and concluded that “resolution
requirements should be assessed on a case-by-case basis” (Thompson and
Selin, 2012), while others (e.g. Kheirbek et al., 2014,
2016) have employed 1 km resolution without discussing the impacts of
resolution on predicted health outcomes. Population exposure studies using
air pollution models may be affected by resolution in a more complex fashion,
given that both the predicted field (a pollutant with a known health impact)
and the data to which the predicted field is to be linked (the human
population) both have resolution dependencies. The health studies carried out
to date highlight the need for better understanding of the underlying
controlling factors for model accuracy with decreasing grid-cell size.
Terrain and meteorology are not the only factors that contribute to greater
uncertainties as horizontal grid-cell size is reduced – for example, the
ability of the model to locally resolve emission fluxes may also become a
factor. This may result in improved or deteriorated model performance as the
size of the grid cells decreases. Gridded model emissions may have an
intrinsic resolution dependence due to the underlying spatial disaggregation
fields, and this can contribute to uncertainties and errors in emissions as
grid-cell size is decreased. For instance, Valari and Menut (2008) found that
the discrepancy between their modelled and observed concentrations grew
rather than shrank, in response to decreases in grid-cell size from 48 to
6 km, and they associated these results with changes in the resulting local
emission fluxes. They showed that in their model setup, with regard to ozone,
a grid-cell size was reached (12 km × 12 km) where errors in inputs (errors
in the emission inventory, wind direction, etc.) outweighed the importance
of other sources of model error such as grid-cell size. The authors, however,
noted that Paris' ozone photochemistry very often resides on the transition
between a NOx--sensitive and a VOC-sensitive regime (Sillman et al.,
2003). These are chemical conditions which can alternatively produce or
titrate ozone and hence have a degree of sensitivity to precursor emissions,
and therefore, also, to any errors in those emissions. Conversely, in a
3-level nested MM5–CMAQ simulation with grid-cell sizes going from 9 to 3 to 1 km over Osaka, Japan,
Shrestha et al. (2009) found that ozone comparisons to observations
improved as the grid resolution increased. This was also the case for a 3-level nested MM5–CMAQ simulation going from 36 to 12 to 4 km over Houston, USA (Ching et al.,
2006), where the ozone forecast improvement associated with higher resolution
was attributed to the ability of the finer grid-cell size model nests to
adequately resolve high concentrations of freshly emitted
NOx and hence allow for more local ozone titration. The
latter process might not take effect until the grid-cell size is sufficiently
fine to resolve the NOx source patterns (i.e. a level
where traffic and industrial sources can be identified.) This titration was
not seen until they decreased their grid-cell sizes to 2 km and smaller.
Stroud et al. (2011) noted a similar grid-cell-size-dependent chemical impact
on model performance, where secondary organic aerosol formation maxima were
better simulated with a 2.5 km grid-cell size model than a 10 km grid-cell
size model. In general, the impact of resolution on model performance appears
to depend on a number of factors, such as the terrain, spatial distribution
of sources, pollutant of concern, season, etc. (Arunachalam et al., 2006;
Queen and Zhang, 2008; Dore et al., 2012).
Salvador et al. (1999) studied the prediction accuracy impacts of
meteorological model grid-cell size in a region with a complex domain and
found that 2 km or smaller grid-cell sizes were required to resolve local-scale complex terrain flow features, and that daytime vertical advection and
predictions of turbulent kinetic energy and potential temperature were
influenced by grid-cell size. Dore et al. (2012) evaluated air quality
model NO2 simulations employing 1, 5, and 50 km grid-cell sizes
against observations and found the best performance for the 1 km
simulation, with more physically realistic distributions of reactive
nitrogen, attributing this performance gain to more realistically
precipitation simulations and emissions inputs for the smallest grid-cell
size. The availability of high-resolution emissions information may be a
limiting factor in improved simulations as grid-cell size decreases. Valari
and Menut (2008) noted that emissions inaccuracy was the principal cause of
noise in small grid-cell size simulations conducted for the Paris area, and
proposed the use of statistical downscaling in favour of predictive modelling
at scales at or below 1 km grid-cell size. The current state of model
science is typically evaluated through multi-model intercomparisons (e.g. Im
et al., 2015), and the meta-analysis of these studies can be used to
provide useful benchmarks to assess current model performance for specific
model species and observations (Emery et al., 2017). However, such studies
do not identify the causes for good or poor performance relative to the
benchmarks – diagnostic studies “in which chemical and physical processes
within the model are analyzed individually and collectively” (Emery et
al., 2017) are required for this purpose. Examinations of the impact of
model grid-cell size on performance are an example of such a diagnostic
evaluation.
The benefits for model performance with increased spatial resolution are
unclear, based on the above literature. However, most papers converge
towards the following qualitative conclusions:
The impact of terrain topology on meteorological forcing as grid-cell
size decreases can dwarf the impact of a more accurate spatial apportionment
of the corresponding emissions.
Decreases in grid-cell size result in a more realistic spatial distribution
of chemical species, whether or not model performance is improved.
Uncertainties in spatial and temporal emissions allocation have an increasing
influence on overall model uncertainty as model grid-cell size decreases.
The 1980s saw several studies in which the potential impacts of wind
direction errors on dispersion model performance were examined. Fox (1981)
noted that pairing of model output at observation station locations could be
done as a function of both time and space: as a function of time (by
combining the data across all stations), as a function of space (by combining
all times, at each station location), or without any pairing (observations
and data were compared as cumulative frequency distributions). The accuracy
of regulatory dispersion models in the early 1980s was such that Fox (1984)
concluded that model and observation values paired in time and space
exhibited “little to no correlation” and discussed potential errors
associated with transport. Poor correlations were also noted
in the report on the first generation of reactive-transport models by Hanha (1988), who stated “wind
direction errors are the major cause of the poor agreement in hourly
predictions of concentrations at short distances downwind of point sources,” and described metrics for air-quality model evaluation. Hanha (1988)
also noted that model predictions could be offset in space and time relative
to observations, leading to poor performance statistics, despite a greater
degree of similarity of behaviour if the offsets are taken into account.
Errors in wind-field modelling were described as the main source of error in
simulations of plumes by Carhart et al. (1989), who again showed how better
agreement resulted when model and observations were unpaired in time and/or
space and noted that other metrics such as maximum plume width might better
represent model performance. Lee (1987) found that small perturbations in
space and time could result in poor correlations, despite similar histogram
distributions of both model and observations.
More recently, Kang et al. (2007) examined the concept of using the area of
the limiting resolution of the model (2 to 3Δx, where Δx is
the horizontal grid-cell size) to weight or spatially average model
evaluation metrics for a single grid-cell size, noting how the model's rated
ability to capture high-concentration events (“hits”) was increased when
the limiting resolution of the model was incorporated into the performance
metrics. However, the use of averaging may mask the potential for a model
with a small grid-cell size to contain both the desired plume magnitude and much lower concentrations, within the same larger representative
area, in turn masking the potential impact of the reduction in grid-cell
size.
We expand on this concept to evaluate the impact of model grid-cell size in
the context of an equivalent area about a given observation location. We
examine area-weighted metrics in the form of averages over roughly equivalent
areas for different model grid-cell sizes, and also use the a priori
knowledge of the observations to determine whether the closest match to
observations may be found within an equivalent area. We show that the latter
metric demonstrates a positive impact of model grid-cell size on simulation
results, while more simple paired comparisons, and averages over similar
areas, mask these benefits.
We examine the impact of grid-cell size on model performance in a region of
intense petrochemical extraction and upgrading, the Athabasca oil sands
region (AOSR). The AOSR refers to the northernmost of three large bitumen
deposits located the northern part of the province of Alberta in Canada: the
Athabasca, Peace River, and Cold Lake areas. Together these areas cover
142 200 km2 in total and constitute the third largest oil reserves in
the world (Government of Alberta, 2016), as shown in Fig. 1. The oil sands
sector is the second largest source of SO2 and the third largest
source of industrial NOx in the province of Alberta. This
sector is also a significant source of industrial PM, CO, and volatile
organic compound (VOC) emissions (Zhang et al., 2018), from a variety of
source types and industrial processes (e.g. open pit mine tailings ponds,
large diesel fleets, bitumen upgrading facilities). As is described below,
very high resolution emissions data are available for these sources, and
emissions take place in a region with significant topography, hence the
region provides a good test case for the relative impact of grid-cell size on
air-quality model prediction results.
Next we describe our model, the simulation domains and forecasting setup,
the emissions data, our evaluation methodology, and the results of our
analysis.
Map
showing the oil sands regions (based on an image from Government of Alberta, 2016).
MethodologyGEM-MACH
The air-quality model used in this work is Environment and Climate Change
Canada's (ECCC) Global Environmental Multiscale – Modelling Air-quality and
Chemistry (GEM-MACH) model, which has been in use as Canada's operational
air-quality forecast model since 2009 (Moran et al., 2010). GEM-MACH is an
on-line model; that is, both meteorological and chemistry processes are
handled within a single model. The chemical processes reside within the
physics module of the Global Environmental Multiscale meteorological forecast
model (Côté et al., 1998a, b), originate with Environment Canada's
earlier off-line model (A Unified Regional Air-quality Modelling System,
AURAMS; Gong et al., 2006), and include process representation for particle
microphysics (Gong et al., 2003a, b), inorganic heterogeneous chemistry
(Makar et al., 2003), aqueous phase chemistry, in-cloud and below-cloud
scavenging (Gong et al., 2006), and secondary organic aerosol formation
(Stroud et al., 2011). GEM-MACH employs a sectional approach to represent
the size distribution of atmospheric particles, with 12-bin (Makar et al.,
2015a, b; Gong et al., 2015) or 2-bin configurations (Moran et al., 2010).
The latter configuration is designed for maximum computational efficiency,
with re-binning to the 12-bin distribution for key particle microphysics
processes, in order to improve accuracy. Here, the 2-bin version of the model
has been used, the main focus of the work being the impact of horizontal grid-cell size on model results. Eight aerosol chemical components are resolved in
GEM-MACH (sulfate, nitrate, ammonium, elemental carbon, primary organic
aerosol, secondary organic aerosol, sea salt, and crustal material). In the
present study, we make use of GEM-MACH v.1.5.1, described in more detail in
Makar et al. (2015a, b), employing 80 levels in a hybrid vertical
coordinate system extending up to 0.1 hPa (∼30 km). Both model grid-cell size simulations compared here (2.5 and 1 km grid-cell sizes; see
below) make use of the Milbrandt–Yau double-moment explicit microphysics
scheme; that is, cloud processes are resolved explicitly at these scales
(Milbrandt and Yau, 2005a, b).
Model setupGrid nesting
Four levels of nesting have been employed in our simulations, shown in
Fig. 2a. This version of GEM-MACH operates on a rotated latitude–longitude
coordinate system wherein the position of the coordinate system poles is set
by the user, allowing rotations of the grid with decreasing grid-cell size
during nesting. The outermost nested grid corresponds to the westernmost
two-thirds of the operational GEM-MACH forecasting domain, with a 10 km grid-cell size, and employ a combination of the Kain–Fritsch sub-gridscale
convective cloud scheme (Kain and Fritsch, 1990; Kain, 2004) and a
Sunqvist (1988) scheme for cloud parameterizations. Within that outer grid is nested a 10 km
grid-cell size western Canada domain (yellow region, Fig. 2a) which has been
rotated to match the horizontal orientation of the Rocky Mountains, and which
makes use of a double-moment microphysics scheme (Milbrandt and Yau, 2005a,
b) in place of the Sundqvist (1988) parameterization. The intention of this
intermediate local 10 km simulation domain was to provide initial
hydrometeors for the two innermost domains, to reduce the “spin-up” time
required for the inner domains' meteorology to reach an equilibrium with
respect to cloud formation. The latter two domains (2.5 and 1 km grid-cell
sizes) resolve the cloud microphysics explicitly using the double-moment
scheme alone and no convective parameterization (Milbrandt and Yau, 2005a,
b). The third nested grid inset (green region, Fig. 2a) is the 2.5 km grid-cell size domain, which covers most of the Canadian provinces of Alberta and
Saskatchewan. This grid will hereafter be referred to as the OS2.5km
domain. The fourth and final nested grid (blue square, Fig. 2a) is a 1 km
grid-cell size domain, roughly centered over and covering the immediate
environs of the Athabasca oil sands, and is referred to hereafter as the
OS1km model. This last nest also shows the region within which 22
instrumented aircraft flights were conducted during August and September of
2013, providing a unique measurement data set for our evaluation of the OS2.5
and OS1km model output for the same time period. Table 1 provides details
on the horizontal dimensions of each of these nested domains and the
duration of the simulations on each grid. All four model nests make use of
the same vertical coordinate and levels. Figure 2b shows the topography of
the 1 km domain in detail; the region to be modelled is situated in a broad
river valley, with a local vertical relief of 750 m. Significant wind shears
and frequent inversions are observed in the region, and part of our interest
in 1 km grid-cell size simulations is to determine the extent to which these
local features may influence model prediction accuracy.
Simulation cycling strategy
Model simulations mimic an operational forecasting system, starting from the
use of archived, data-assimilated meteorological analyses as meteorological
input and boundary conditions every 36 h. The use of analysis fields is a
standard meteorological forecasting practice to prevent the chaotic drift of
the model results from observed meteorology over time. The outermost 10 km
domain uses initial and boundary conditions from the output of a
meteorological simulation, that is itself driven by an analysis field. The
outermost domain model then carries out a 36 h forecast, of which the first
6 h is discarded as spin-up; the final 30 h is used as initial and
boundary conditions for the rotated 10 km grid-cell size domain (the
OS10 km domain). An OS10 km simulation of 30 h is then carried out, with
the first 6 h being discarded as spin-up, and the latter 24 h forming
the initial and boundary conditions for the 2.5 km grid-cell size OS2.5km
simulation. The OS2.5km simulation is of 24 h duration. The OS1km
simulation covers the same 24 h (and hence both 2.5 and 1 km simulations
start from the same OS10 km initial conditions for every 24 h forecast),
with the 2.5 km simulation providing boundary conditions thereafter to the
OS1km model. Continuity between 24 h forecasts is thus maintained at the
level of the outermost nest. The outermost domain is cycled every 12 h
starting at 00:00 and 12:00 UT; however, we have selected the set of
contiguous OS2.5 and OS1km 24 h simulations starting from the 12:00 UT
continental domain for our comparison.
Meteorological boundary conditions for the lowest-resolution GEM-MACH
simulations are taken from operational GEM forecasts, in turn driven by data
assimilation analyses performed at the Canadian Meteorological Centre.
(a) The four nested domains of the GEM-MACH simulations.
From outermost to innermost domains, these are CONT10 km (outermost, red
dots), OS10 km (yellow), OS2.5km (green), and OS1km (blue). The model
simulations from the two innermost domains are the focus of the present
study. (b) Topography in the OS1km domain centered on Fort
McMurray, Alberta (m a.g.l.). The coloured area corresponds to the central blue
domain in (a).
* Note that both OS2.5 and OS1km output frequency was
hourly.
Model emissions
All emissions data used in this work are described in Zhang et al. (2018).
These emissions data include
direct observations of stack-specific hourly emissions measured by
continuous emission monitoring systems (CEMS);
regional emissions inventory
data from the Cumulative Environmental Management Association (CEMA) – which
had the most detailed stack and process level emission data for the AOSR
facilities, including emissions from mine faces, tailings ponds, and the
off-road mining feet);
the 2010 Canadian Air Pollutant
Emissions Inventory (APEI) – which is the most comprehensive national
emissions inventory, and which has the largest spatial coverage for area
sources outside the AOSR; and
the 2013 National Pollutant Release Inventory
(NPRI) (a subset of the APEI) that is based on emissions reports from large
industrial facilities.
These emissions data sets primarily describe emissions of pollutants known as
criteria air contaminants (NOx, VOCs, SO2,
NH3, CO, PM2.5, and PM10) for major-point sources
(i.e. large emission stacks) and area sources. Area emissions
sources typically consist of multiple small mobile sources spread over a
large area (e.g. off-road vehicles), large flux sources such as mine
tailings settling ponds or mine faces, and/or large numbers of small stacks
for which no stack characteristic data (volume flow rates, temperatures of
emissions, stack diameters), needed to estimate plume-rise heights, are
available.
Major-point sources are represented by a single geographical (latitude,
longitude) pair of coordinates, and are assigned to the grid cell in which
the point is located. These sources are likely to be the most impacted by
model horizontal grid-cell size, as even a large major-point source plume,
which in reality may only occupy an emissions horizontal area on the order of
100 m2, is represented by a flux spread over an entire grid cell. A
plume from a major point source within a 2.5 km grid cell will thus be
immediately diluted to a size of 6.25 km2 upon emission, whereas the
same source with a 1 km grid cell will have a cross-sectional horizontal
extent of 1 km2. At the same time, higher resolution may require a much
more accurate representation of model winds close to the sources to maintain
accuracy in evaluation metrics dependant on plume position such as
correlation – a wider plume being more likely to at least partially
intersect a monitoring station location than a narrower plume.
Area sources that are large compared to both model grid-cell sizes (2.5 and
1 km) can be expected to be approximated by model grid cells of both
resolutions and are thus expected to be less impacted by model resolution
than emissions from point sources. However, smaller area sources (i.e. areas
intermediate between 2.5 and 1 km to the side) may be better resolved, and
hence have less dilution and higher downwind concentrations, when higher
spatial resolution is employed.
In the AOSR, approximately 95 % of the SO2 emissions originate
in major-point sources, while NO2 is apportioned ∼40 %
to major-point sources and ∼60 % to area sources (Zhang et al.,
2018). Consequently our a priori expectation is that the impact of the
resolution change will be strongest for species like SO2, and less
strong for species like NO2 that are emitted in part by point
sources, but may also be apparent for other species and secondary products,
such as O3.
Model evaluation methodology and metrics
Comparisons between air-quality models and observations usually take the
approach of comparing observation and model-generated values paired in time
and space, from the observation location and corresponding model grid-cell
respectively. We refer to this approach hereafter as our “standard”
evaluation, for both 2.5 and 1 km simulations. However, we note additional
factors aside from grid-cell size may influence the outcome of air-quality
model evaluations. For example, the relative skill of the meteorological
component of the air-quality model will depend in part on the density of
meteorological observation data, incorporated into the model via data
assimilation, for the construction of the model's initial meteorological
state. This in turn will influence the local skill of the model's predicted
wind directions and hence the skill of its plume transport. The simulations
carried out here focus on the Fort McMurray area, where the nearest available
upper air meteorological sounding site is located at the ECCC Stony Plain
station, located approximately 500 km south-west of the study area. The
advantage of higher-resolution simulations (e.g. reduced numerical error
associated with the discretization of transport operators, and better
treatment of local topographic influences) may thus be offset by errors in
the predicted large-scale flow.
While meteorological model synoptic-scale forecast errors may manifest
themselves locally as errors in the direction of winds driving local plume
transport, other advantages may result from the use of higher-resolution
air-quality models. Since lower resolution models de facto instantaneously
redistribute plumes emitted from large stack sources over a larger area, such
artificial diffusion will reduce the model's ability to accurately simulate
concentration maxima, and the resulting chemistry, within simulated model
plumes. However, the spatial extent of a plume in a model employing a large
horizontal grid-cell size may be such that its existence may be captured at
discrete observing sites. In contrast, forecast plumes in models with smaller
horizontal grid-cell sizes may correctly capture plume magnitude and chemical
behaviour, but may be more subject to errors in the larger-scale wind
direction. To illustrate this point, Fig. 3 shows a conceptual diagram of an
actual plume, a large grid-cell size model plume, and a small grid-cell size
model plume, where the latter two simulated plumes are both subject to the
same synoptic-scale error in wind forecast direction (indicated by large red
arrows; the smaller red arrow in Fig. 3c indicates the impact of local
forcing predicted for the second model). Observation station “+A” is
located downwind, and records the presence of the actual plume (Fig. 3a). The
coarse grid-cell size simulated plume (Fig. 3b), despite the error in the
forecast wind direction, captures part of the observed plume in the resulting
time series at the observation station location. In contrast, the small grid-cell size plume (Fig. 3c), despite resolving the plume shape (and
plume internal chemistry) to a greater degree than the coarse grid-cell size
simulated plume, fails to record the presence of the plume at the observation
location. A simple paired observation–model time series evaluation would thus
suggest that the former model has superior performance to the latter model in
this example, despite the latter model having created a more “realistic”
plume in terms of the maximum concentration reached, albeit in the wrong
location, due to synoptic-scale forecast wind direction error. In this
particular instance, the magnitude of the smaller grid-cell size simulated
plume is more realistic than that of the coarse grid-cell size plume, but
this improvement will not be captured in a standard evaluation analysis.
Shifts in plume location across individual grid cells away from the location
of an in situ observation are more likely grid-cell size decreases.
In this example, a standard analysis would impose a more stringent
expectation on the smaller grid-cell size simulation to correctly identify
plume locations.
Schematic comparison of surface concentration contours and model
grid-cell values of a transported pollutant plume from a large stack (termed
a “point” source). Wind direction shown by red arrows. Monitoring station
location marked by “+A”. (a) Actual plume. (b) Coarse grid-cell size
air-quality model prediction. (c) Fine grid-cell size air-quality model
prediction. Note the change in wind direction between observations (a) and
simulations (b, c) associated with errors in the forecast of the synoptic
wind.
In addition to the standard analysis, we perform additional analyses that
examine the model's ability to resolve plumes in the vicinity of the
observation station, in order to attempt to evaluate the potential for higher-resolution simulations to provide benefits which may be masked by synoptic-scale forcing errors. This strategy is illustrated in Fig. 4.
Figure 4a shows an observation station enclosing the nine nearest-neighbour
model grid cells for a 2.5 km grid-cell size, while Fig. 4b shows the
corresponding 1 km grid-cell size map, with the 9 nearest-neighbour model
grid cells shown in light grey and the 49 nearest grid cells shown in
the region enclosed in dark grey. Figure 4a encloses a region of
56.25 km2 (7.5 km × 7.5 km), while the light grey region in Fig. 4b encloses
9 km2, and the darker grey region encloses 49 km2.
Scale diagram of the same region in (a) a 2.5 km grid-cell size
simulation and (b) a 1 km grid-cell size simulation. Region enclosed by
light grey (dark grey) shading in (b) represents the nearest 9
(49) 1 km grid points surrounding the observation location “A”.
As noted above, in a formal mathematical sense, the smallest region
resolvable by an Eulerian grid model is twice the size of the model grid-cell
size (relating to the Nyquist frequency of the model); hence the smallest
resolvable feature spans two model grid cells in each direction. However, in
a practical sense, a total of nine grid cells centered on the observation
station must be used to allow a boundary of two grid cells in any direction.
Sampling any or all of the nine grid cells in Fig. 4a may thus be said to be
representative of the model's ability to simulate events occurring at
discrete location “+A”. The closest corresponding sampling region
available to the 1 km model (Fig. 4b) is shown in dark grey. The light grey
region of Fig. 4b represents the closest 1 km grid-cell size region that
corresponds to the single 2.5 km grid cell in which the observation station
is located in Fig. 4a. We attempt to ascertain model performance in these
approximately equivalent regions around each observation station, in the
analysis that follows.
Our approach follows two steps:
From the 2.5 km simulation, in addition to the predicted model value at the
grid cell containing the observation location, we determine the model
grid-cell value in the nine grid cells surrounding the observation station
location which has the closest value to that observed at the station. This
represents the model's “best estimate” of the value at the observation
station location itself and represents the model's ability to resolve features at 2.5 km
grid-cell size.
From the 1 km simulation, in addition to the model value at the grid-cell
location, we select the closest value to the observation value from
the nearest nine grid cells to the observation station location, and
the nearest 49 grid cells to the observation station location.
The former represents the model's “best estimate” of the value
at the observation station location itself, while the latter represents the
1 km model's best estimate in the closest equivalent region to the limiting
resolution of the 2.5 km model.
Comparing the resulting statistical measures of each of these selected values
with observations, in addition to the standard analysis, thus evaluates the
model's best attempt to resolve features for the specified grid-cell size
and allows cross-comparison of model performance within nearly equivalent
areas. Cross-comparing the statistical values for the different regions
described above shows the model's ability to resolve features such as plumes
from the standpoint of the region represented at the different grid-cell
sizes. If synoptic-scale transport direction errors create situations
similar to that depicted in Fig. 3a, a standard comparison of error would be
expected to show little benefit to higher resolution. However, the “best
model estimate” comparisons would capture the ability of the higher-resolution model to more accurately simulate the magnitude of the plume, if
not its spatial location. Each of these selection procedures will be employed
in the surface concentration comparisons which follow.
We evaluate our model simulations against observations made at surface
monitoring networks in the vicinity of the Athabasca oil sands, and aboard
an instrumented aircraft, the National Research Council of Canada Convair.
For the surface monitoring data, hourly time series of model output were
matched to station time series using the different strategies described
above. For the aircraft observations, we extract model values through
temporal and spatial interpolation to the aircraft's position during the
flights and only perform the standard analysis, as well as examining the
behaviour of the two simulations along cross sections corresponding to the
flight paths.
Our statistical metrics for evaluation are common to many other air-quality
applications and were computed using the “modstat” function from the OpenAir
R package (Carslaw and Ropkins, 2012). Further discussion of different
metrics for model evaluation may also be found in Yu et al. (2006). The
statistics calculated here include mean bias (MB; perfect score: zero), mean
absolute gross error (MGE; perfect score: zero), normalized mean bias (NMB;
perfect score: zero), normalized mean gross error (NMGE: perfect score:
zero), root mean squared error (RMSE; perfect score: zero), correlation
coefficient (r, perfect score: unity), coefficient of efficiency (COE: a perfect
score is unity, a zero or negative score means the model is equivalent or less
predictive, respectively, than the mean of the observations), and the index of agreement
(IoA; perfect agreement is unity, and -1 indicates no agreement or little
variability).
Simulation comparisons and evaluationModel-to-model comparisons and averages
We begin a comparison of 2.5 and 1 km grid-cell size for specific events,
and for averages across the 1 km domain, in order to provide a qualitative
comparison of the differences in simulations for the two simulations and
then continue with the quantitative comparison. Figure 5 compares OS2.5km
(left column) and OS1km (right column) simulation results for a
cross section located 0.2 km from a major SO2 emissions source at
00:00, 12:00, and 24:00 UT into a given simulation day.
The model results are identical at hour 0 due to both the OS2.5 and OS1km
models being initialized from the OS10 km data at this time (small
differences between Fig. 5a and b are due to slight mismatches in the cross section
locations). Subsequent cross sections show the OS1km model is capable of
resolving both higher absolute mixing ratio values, and sharper gradients,
within 12 h of simulation time (Fig. 5c, d). Multiple plumes are resolved by
12 h of simulation time in the 1 km grid-cell size simulation, along with
markedly different plume heights, plume structure, and an increase of a factor of
2 in the magnitude of plume mixing ratios relative to the lower grid-cell size simulation, and these differences persist into the 24th simulation
hour (Fig. 5e, f). Mixing ratio differences of these magnitudes are to be
expected given the increase in resolution, but Fig. 5 shows that other
important aspects of the predicted plumes have changed. The plume heights are
a function of predicted local stability conditions in the grid square
containing the source, and the variation shown here represents a substantial
change in the predicted local stability for the origin sources of these
plumes, resulting from the change in model horizontal grid-cell size.
Comparison of simulated SO2 plume mixing ratios (ppbv)
located 0.2 km from a major point source, for OS2.5km simulations
(a, c, e) and OS1km simulations (b, d, f), at 0
(a, b), 12 (c, d), and 24 h (e, f) into a 24 h
simulation.
Figure 6 compares the maximum surface SO2 during the entire period
for each simulation, as well as the difference in maximum SO2
between the simulations, along with a scatter plot of OS2.5 vs. OS1km
simulation results. In the latter two panels, OS2.5km values were assigned
to the corresponding OS1km grid-cell locations using the nearest-neighbour
approach.
Comparison of total-simulation maximum surface
SO2 mixing ratios (ppbv) at (a) 2.5 km and (b)
1 km grid-cell size (ppbv). (c) Difference (2.5-1 km).
(d) Scatter plot of 2.5 km (x axis) versus 1 km (y axis) total
simulation average grid-cell surface SO2 mixing ratios.
The maximum surface concentrations tend to show more elongated structures at
the smaller grid-cell size, comparing Fig. 6a and b, particularly for plumes in
the western (left) half of the OS1km domain. The difference plot (Fig. 6c)
shows that local maximum concentration differences of up to -45 ppbv occur,
due to changes in the placement and maximum concentration of high-concentration plumes. The scatter plot of Fig. 6d shows that OS1km model has
a demonstrated ability to achieve higher concentrations than the OS2.5km
model, with a slope of 1.22, and a noticeable clustering of values along the
1:2 line. While these results are not unexpected since approximately
95 % of the SO2 emissions in the domain originate in large
stack, or point, sources, and hence initial concentrations at source would be
expected to 6.25× higher in the OS1km simulation, they also suggest that a
substantial improvement in the OS1km model's ability to capture
SO2 concentrations should be possible. That is, the
results of the two models are substantially different, and given the
reduction in numerical error expected with employing a smaller grid-cell
size, the latter might be expected to outperform a larger grid-cell size
model. However, as we shall demonstrate in the next section, plume placement
errors such as those depicted in Fig. 3 play a substantial role in model
performance as grid-cell size decreases.
The locations of the local network of 10 surface monitoring stations located
near the sources of emissions in the region (oil sands facilities) are shown
in Fig. 7. As noted in Sect. 2.4, we carry out several analyses:
The standard evaluation. The model values are extracted from the model
grid cells containing the observation stations, at both grid-cell sizes.
Equal areas of representativeness, 1 and 2.5 km grid-cell sizes. The nearest
nine OS1km grid cells are compared to the OS2.5km single cell evaluation
in two ways:
averaging of the OS1km results across the nine grid cells prior to
evaluation (to determine whether the mean value is better represented by the
smaller grid-cell size, similar to the approach taken in Kang et al., 2007);
selection of the best of the nine grid cells (closest to the
observation value), to determine the extent to which the OS1km model is
capable of better representing the concentrations somewhere within the
corresponding OS2.5km model grid cell, if not at the OS1km cell closest
to the observation location – higher scores for the 1 km grid-cell size
simulation in this case would indicate that while errors in plume positioning
(for example due to errors in the synoptic-scale flow) negate some of the
advantages of the OS1km simulation, the plume may be better represented by
the OS1km simulation within the 2.5 km grid cell's area.
Equal areas of representativeness and equal regions of variability. The nearest
9 2.5 km cells are compared to the nearest 49 1 km cells. Here
we make the assumption that the 2.5 km grid-cell size model's ability to
resolve features is limited to the surrounding three grid cells in each
horizontal dimension and make use of the closest-in-size block of
corresponding 1 km cells (a 7×7 grid centered on the cell containing
the observation point). In both cases, the model value closest to the
observations is chosen prior to evaluation.
While evaluations (Figs. 2b and 3) deliberately select the “best” value,
they also provide a quantitative estimate of the extent to which each model
is capable of achieving the correct answer within roughly equal
representative areas centered on the observation station locations. These
comparisons are intended to evaluate
the extent to which the 1 km grid-cell size is capable of improving
simulation results despite, for example, the larger-scale flow resulting in errors
in the plume placement, and
whether the 1 km grid-cell size model is capable
of outperforming the 2.5 km grid-cell size model over equivalent regions.
In the last test, we place both models on an equal footing with regards to
the region being represented, as well as with regards to allowing cell-to-cell
variability and the selection of a closest match to observations.
Our evaluation is presented as tables of statistical metrics. The comparisons
employing the nearest-neighbour approach are described with a “Bn”
superscript suffix, denoting that the “best” sample within a square
centered on the observation point containing a total of n grid
cells (e.g. the OS1kmB9 label denotes a comparison between
observed data and the simulation grid cell within a 3×3 grid-cell
square centered about the observation point). Similarly, an An superscript
describes a comparison between the observations and the average of
the n square of grid cells centered on the observation point.
Comparisons to surface concentrations were performed using publicly available
data collected by the Wood Buffalo Environmental Association (WBEA), which
operates the air-quality monitoring network residing within the OS1km
domain. The monitoring station locations are shown in Fig. 7. The statistical
performance of the models, calculated using the procedure outlined above, are
given in Tables 2 through 5, for SO2, NOx,
O3, and PM2.5, respectively.
In the standard model grid cell to observation measurement
comparison for SO2 and NOx (first two columns,
Tables 2 and 3), the OS1km simulation had worse scores for all the
metrics considered here. For O3, the OS1km model had the better
score for the correlation coefficient and root mean square error, and worse
scores for all remaining model evaluation metrics. For PM2.5, the
OS1km model showed a better performance for the correlation coefficient and
biases, while the OS2.5km model outperforms the OS1km model for all other
metrics examined here. Based on a standard analysis, the OS1km model thus
performs poorly compared to the OS2.5km model; the expected advantages
associated with reduced numerical error in transport at smaller grid-cell
sizes are being offset by other factors controlling the net model error.
Illustration of the OS1km domain, with observation station
locations. (a) Entire domain. (b) Close-up view of station
locations. Monitoring stations are shown as purple outline squares in both
images. Light grey regions in the background satellite image (b) are
oil sands open-pit mining operations.
When the standard evaluation is compared to the average of the
nearest nine 1 km simulation grid cells surrounding the observation point
(third column of the tables), an intermediate result appears. For
SO2 (Table 2) the nine-cell OS1km average has the best
performance for correlation coefficient – indicating a better time
distribution of events may be achieved by a nine-cell average at 1 km grid-cell size. The other metrics for the A9 simulation are intermediate between
the two standard evaluations for each simulation, indicating that some of the
performance loss resulting from the use of 1 km grid-cell size is reduced
through averaging results to approximately the same size regions as the
OS2.5km grid-cell size. The latter result holds for all metrics for
NOx (including R, see Table 3). For ozone (Table 4),
averaging the nine nearest OS1km grid cells prior to measurement gives the
best performance for R and RMSE, and worse performance for the other
metrics. For PM2.5 (Table 5), all metrics for the OS1km nine grid-cell
average aside from the bias fall mid-way between the two standard methodology
evaluations. Averaging the smaller grid-cell size model results thus shows a
marginal improvement, depending on the species, but overall does not
compensate for the decrease in performance resulting from going to the
smaller grid-cell size.
We next ask the question, “does a more accurate simulation value
exist within the same region of the 1 km model as is encompassed by
a 2.5 km grid cell?” (fourth column of Tables 2–5), by selecting the
model value in the nearest nine 1 km grid cells with the closest match to
observations and comparing to the corresponding single 2.5 km grid cell. A
dramatic improvement in the relative OS1km performance metric scores can be
seen. For each of Tables 2 through 5, this “best of nine” 1 km comparison
outperforms the previous 3 comparisons (columns 1 through 3), for all
metrics. These improvements are sometimes dramatic (e.g. a doubling of
correlation coefficient along with a reduction in mean bias by a factor of
3, a reduction of NOx mean bias values by a factor of
3, a shift of coefficient of error from negative to positive values for
O3, and a reduction in the coefficient of error for PM2.5 by a
factor of 2.5 compared to the nearest competing value from the previous
evaluations. The coefficients of efficiency for SO2 and O3
make the transition from negative to positive values when the
“best-of-nine” methodology is used, indicating that the model is able to
predict the observations better than the observed mean, somewhere within an
equivalent area. This evaluation suggests that the OS1km model does
contain a better result within the same approximate region
encompassed by a 2.5 km grid cell. However, the location of that better
result may be subject to positioning error, such as those described in Fig. 3.
A valid argument could be made that the methodology employed in this fourth
evaluation is subject to selection bias, in that the selection of a
best value in the case of the nearest nine 1 km simulation places
that model simulation at an advantage relative to the 2.5 km model. To
address this last issue, the final two additional methodologies for
evaluation were employed, still maintaining the same approximate area of
representativeness for a grid cell, namely choosing the best value out of the
nearest 9 2.5 km grid cells (the limiting resolution of this
model simulation), and the best value out of the nearest 49
1 km grid cells (fifth and sixth columns,
respectively, of Tables 2 through 5). That is, we attempt to place the two models on an equal basis
with regards to selection bias within a given region containing an
observation station.
Two important results can be seen from this final evaluation. First, as was
the case for the “best of 9” for the OS1km simulation compared to the
standard OS1km evaluation, the best of 9 for the OS2.5km simulation
has a considerably better performance than the standard OS2.5km evaluation
(compare fifth and first columns, Tables 2 through 5). That is, the OS2.5km
model may also be subject to location errors in transported species
representation which influence model performance. However, when performance
within the 56.25 km2 area surrounding each measurement point in the
OS2.5km best of 9 evaluation is compared to the 49 km2 area
surrounding the measurement points in the OS1km best of 49 simulation
(i.e. compare columns five and six in Tables 2 through 5), it can be seen
that the OS1km model outperforms the OS2.5km model for all metrics for
O3 and PM2.5, and all metrics aside from bias for
SO2 and NOx. That is, despite the OS1km model
having a slight disadvantage in the relative size of the representative area
containing the measurement station location, and both models being allowed a
similar selection strategy, the OS1km model is capable of generating values
closer to the observations than the OS2.5km model within an equivalent
sub-region, across most of the metrics and chemical species considered here.
This final result is strongly suggestive of the presence of issues such as
those illustrated in Fig. 3. These may include errors in the larger-scale synoptic
wind flow, combined with the reduced size of plumes as grid-cell size is
reduced, leading to more “misses” than “hits” for a given recorded event
at a measurement station compared to the coarse grid-cell size model. There
may be multiple additional causes for such errors (examples include poor
observation density in the region for model initialization, underlying lower-resolution boundary condition fields such as topography not improving with
the reduction in grid-cell size, inaccuracies in land use fields used in
meteorological modelling due to rapid development, and errors in other
aspects of the reaction transport modelling system aside from horizontal
resolution). The expected advantages of the small grid-cell size, such as
better representation of the concentrations of species within plumes and
hence better representation of their reactive chemistry (see for example Lonsdale et
al., 2012), may be lost in a standard performance analysis due to these
other issues.
Our analysis suggests that a practical limit in the benefits of increasing
model accuracy may be reached when resolution exceeds some threshold, as a
result of other errors inherent in the modelling system. However, the
analysis also suggests that if these non-resolution-related errors are
corrected, the benefits of adopting a smaller grid-cell size may be
substantial. For example, meteorological data assimilation employing a dense
monitoring network for a specific area of interest would be expected to show
a greater impact for smaller rather than larger grid-cell sizes, due to the greater
ability of the former to take advantage of the observation density in
correcting the initial meteorological state. We note that recent work
applying land use data assimilation (Carrera et al., 2015) to regional
2.5 km grid-cell size weather simulations (Milbrandt et al., 2016) have
suggested that such data assimilation may indeed improve forecast skill at
the very local scale.
Surface SO2 observations to model comparison for entire
simulation period (ppbv, 5466 model–observation pairs).
Evaluation metricOS2.5kmOS1kmOS1kmA9OS1kmB9OS2.5kmB9OS1kmB49Index of agreement0.2370.1540.2070.6010.7010.810Pearson correlation coefficient0.2900.2300.2950.6040.6720.848Normalized mean gross error2.1282.3632.2121.1140.8340.529Mean gross error2.9183.2403.0341.5281.1430.725Coefficient of error-0.525-0.693-0.5850.2020.4030.621Root mean square error7.0639.6657.8764.4363.6712.618Normalized mean bias1.1301.3761.2990.347-0.0100.017Mean bias1.5501.8871.7810.475-0.0130.024
Surface NOx observations to model comparison for
entire simulation period (ppbv, 3257 model–observation pairs).
Evaluation metricOS2.5kmOS1kmOS1kmA9OS1kmB9OS2.5kmB9OS1kmB49Index of agreement0.1770.1380.1520.4160.5890.665Pearson correlation coefficient0.1430.1140.1160.1650.3050.388Normalized mean gross error1.5201.5931.5671.0790.7600.619Mean gross error12.89813.51813.2969.1566.4475.255Coefficient of error-0.646-0.725-0.697-0.1680.1770.329Root mean square error28.05235.19734.64425.78215.31513.704Normalized mean bias0.4930.5700.5420.174-0.027-0.063Mean bias4.1834.8344.5971.477-0.231-0.531
Surface O3 observations to model comparison for entire
simulation period (ppbv, 2189 model–observation pairs).
Evaluation metricOS2.5kmOS1kmOS1kmA9OS1kmB9OS2.5kmB9OS1kmB49Index of agreement0.4140.4050.4040.5270.6370.690Pearson correlation coefficient0.4960.5060.5150.6060.6880.738Normalized mean gross error0.6600.6700.6720.5340.4100.349Mean gross error10.75710.91510.9498.6926.6735.687Coefficient of error-0.172-0.189-0.1930.0530.2730.380Root mean square error16.04015.85915.79413.30511.0849.719Normalized mean bias0.5270.5590.5790.4630.3370.304Mean bias8.5799.1049.4317.5365.4884.945
Surface PM2.5 observations to model comparison for entire
simulation period (µg m-3, 3377 model–observation pairs).
Evaluation metricOS2.5kmOS1kmOS1kmA9OS1kmB9OS2.5kmB9OS1kmB49Index of agreement0.2800.2620.2670.4120.5080.572Pearson correlation coefficient0.2010.2160.2140.3140.3760.466Normalized mean gross error0.7910.8110.8060.6470.5410.471Mean gross error5.3425.4785.4414.3653.6513.181Coefficient of error-0.439-0.476-0.466-0.1760.0160.143Root mean square error8.2868.7868.6637.1176.1695.690Normalized mean bias-0.268-0.257-0.257-0.289-0.299-0.287Mean bias-1.812-1.734-1.736-1.948-2.016-1.937
The surface observation data were also analyzed by the time of day, with both
observations and simulations split into daytime (09:00 to 18:00 LT)
and nighttime (19:00 to 08:00 LT) data pairs (Appendix A, Tables A1
through A8; Carslaw and Ropkins, 2012). Within each of these diurnally
segregated time periods, the broad aspects of the comparison were the same as
for the “all data” Tables 2 to 5 above: the OS1km simulations tended to
have reduced performance in a standard analysis, averaging improved but did not
completely ameliorate the performance of the OS1km simulation, a
methodology employing the best of nine OS1km grid cells had superior
performance to the two standard comparisons, and comparison of the “best
of” methodologies for equal areas showed better performance for the OS1km
compared to the OS2.5km simulation. We also noted substantial differences
in the day and night performance of both models across the methodologies. For
example, daytime SO2 and NOx performance within
a given model and comparison methodology was usually better than nighttime
performance for IOA, R, NMGE, COE, and NMB, while worse for RMSE, while
nighttime O3 performance was better for IOA, r, NMGE, and COE.
Daytime PM2.5 performance was better than nighttime for IOA, r, COE,
and NMB. The study area is located in a broad river valley with frequent
slope-defined anabatic/akatabic and drainage flow events. These often have a
diurnal nature, and may explain part of the day–night differences. Example
sources of these differences may include the relative ability of the driving
meteorological model to capture daytime versus nighttime mixed layer
turbulence and the planetary boundary layer height.
Comparisons to aircraft observations
A total of 22 aircraft observation flights were carried out during the study
simulation period – here we present statistical comparisons using the standard
approach only (model grid cell containing the observation point to
observation data at the aircraft location). Model values were linearly
interpolated in time and space to the aircraft observation locations and
times (aircraft observations were on a 10 s interval.) We begin with a
composite comparison across all observation times, in Table 6.
Aircraft observation comparisons, SO2 and NO2
(ppbv).
SO2 (21 787 samples) NO2 (18 310 samples) OS2.5kmOS1kmOS2.5kmOS1kmIndex of agreement0.630.620.610.58Pearson correlation coefficient0.260.280.390.34Normalized mean gross error1.071.090.900.96Mean gross error3.984.061.561.68Coefficient of error0.270.250.230.17Root mean square error12.8413.973.123.62Normalized mean bias-0.31-0.29-0.26-0.20Mean bias-1.17-1.07-0.45-0.34
The results are in general similar to the surface analysis, in that the
OS1km simulation tended to have worse performance than the OS2.5km
simulation (exceptions being the biases for both SO2 and
NO2, and the slightly better OS1km correlation coefficient for
SO2). One striking difference between the first two columns of Tables 2 and 3,
compared to Table 6, is the magnitude of the differences between the
simulations. Aloft (Table 6), the differences in performance metric
magnitudes between OS2.5 and OS1km simulations are much smaller than at the
surface (Tables 3 and 4). The biases are negative aloft and positive at
the surface, indicating that both models may be lofting plumes to
insufficient distances; one of the possible (non-horizontal grid-cell-size-dependent) causes of model error may be in the extent of vertical transport.
This possibility is examined in more detail in Akingunola et al. (2018) and
Gordon et al. (2018). An example of this behaviour is shown in Fig. 8; both
plumes fumigate to the surface, while the observed plume resides largely
aloft. The OS1km model captures the higher concentrations to a better
degree, but the impact of excessive fumigation more than offsets this
improvement, as is shown by the performance evaluation of Table 7, where both
models have negative biases aloft. In this particular case, the tendency of
the model to overestimate the extent of fumigation has a bigger impact on
performance than grid-cell size. Garcia-Menendez et al. (2014) have noted
similar results for forest fire plume prediction.
Figure 8a and c provide a further example of the kind of
situation referenced in Fig. 3; surface monitoring station locations are
depicted as grey circles, one of which is identified with a pink arrow. This
station lies within the plume at 2.5 km resolution (Fig. 8a), and outside of
the plume at 1 km resolution (Fig. 8c). While the plume direction is the
same at both scales, that is, the large-scale wind field controls the
positioning of the plume axis, the smaller grid-cell size simulation places a
stronger constraint on the accuracy of the wind field. For example, if the
simulated large-scale flow direction was inaccurately predicted by only a few
degrees, the plume would not appear in the 1 km simulation time series at
this location but would register as present in the 2.5 km simulation.
Nevertheless, the plume maximum concentration is better captured by the
smaller grid-cell size simulation (compare maximum values in observed
aircraft SO2; Fig. 8b, d). The higher-resolution simulation may
thus more accurately simulate the plume maximum concentration – but not its
placement in space, as was hypothesized in Fig. 3.
Comparison between OS2.5km (a, b) and OS1km (c, d) simulations for SO2 relative to aircraft observations (ppbv).
(a, c) Simulated surface concentrations of SO2, with the
flight track shown as a red line. Grey circles: surface monitoring station
locations; pink arrow indicates a station located inside a plume at 2.5 km
resolution (a), and outside the plume at 1 km resolution
(c). (b, d) Portion of the simulated concentration profiles
along the flight path as a function of time. Successive intersections of the
flight path with the plume appear as background colour contours; observed
SO2 aboard the aircraft is shown between the two black lines.
Vertical axis is elevation above the ground; the aircraft elevation is
increasing with successive passes around the facility. Dotted lines show the
upper and lower vertical extent of the observed plume; note that for both
model simulations, the plume erroneously fumigates the surface.
Standard performance evaluation of Flight 8 for SO2
(ppbv, 1261 model–observation pairs).
OS2.5kmOS1kmIndex of agreement0.690.68Pearson correlation coefficient0.420.31Normalized mean gross error1.041.09Mean gross error4.024.25Coefficient of error0.390.35Root mean square error16.7220.57Normalized mean bias-0.42-0.34Mean bias-1.63-1.32
Meanwhile other flights show a clear advantage of the OS1km model. One
example is given by the NO2 performance evaluation of Table 8 and
depicted in Fig. 9, for Flight 17 (a similar flight plan carried out around
the same facility as Flight 8). While the correlation coefficient degraded
slightly in the OS1km resolution simulation, all other performance measures
were improved with the decrease in grid-cell size. Two time-versus-height-profile cross sections for Flight 17 are shown in Fig. 9. In Fig. 9a and b, the OS2.5km and OS1km simulations, respectively, are
compared for the portion of the overall flight track circling the given
facility. This comparison clearly shows that the OS1km model does a better
job of capturing the width of the high-concentration region of the plume –
however, the location of the model plume lags the observations. During this
portion of the flight alone, the OS2.5km model statistics, particularly the
correlation coefficient, outperform the OS1km model, due to this issue of
plume location mismatching. Figure 9a and b may be compared to Fig. 3a and b – the
same situation is depicted in both figures. Figure 9c and d show the OS2.5km
simulation (Fig. 10c) and OS1km simulation results in another portion of
the flight – here the OS1km performance for most statistics was better
than the OS2.5km model performance. The OS1km model (Fig. 9d) captures
the existence of a lower-concentration layer aloft in the right-hand side of
the cross section, and the existence of low-concentration intervening layers,
as well as the overall lower concentrations of SO2, while the
OS2.5km model does not resolve these fine-scale and lower-concentration
features. We note here that IoA, COE, and the other error measures capture the
visual impression that the OS1km model outperforms the OS2.5km model for
this flight, while the correlation coefficient is highly dependent on the
placement of the plume maximum in the upper two panels.
These and the snap-shot comparisons described in Sect. 3.1 show that the
higher-resolution model is having a significant impact on predictions –
however, other aspects of the overall model performance are preventing the
potential benefits of higher resolution from influencing the standard
performance evaluation.
Standard performance evaluation of Flight 17 for NO2
(ppbv, 1174 model–observation pairs).
OS2.5kmOS1kmIndex of agreement0.260.58Pearson correlation coefficient0.260.25Normalized mean gross error2.031.15Mean gross error0.520.29Coefficient of error-0.480.16Root mean square error1.370.70Normalized mean bias0.83-0.54Mean bias0.21-0.14
Flight 17 comparison for NO2 (ppbv) for portions of the
net flight track circling the CNRL facility for OS2.5km (a) and
OS1km (b) simulations, and for a later section of the same flight
path for the OS2.5km (c) and OS1km (d) simulations.
Discussion
A key result of our current work is that 1 km grid-cell size simulations
resulted in improved prediction of plume concentration maxima relative to
2.5 km grid-cell size simulations, despite having no improvement using
standard scoring methodologies. We also have described a scoring approach
wherein these potential advantages of higher resolution may be quantified. We
believe that flow field effects such as those described in Fig. 3 are a general
result of increasing grid resolution, but note important caveats, which
include the following:
The availability of meteorological observation and high-resolution emissions data to provide model driving information, and the resolution and proximity of this information to the simulation location. Both will influence
the relative importance of grid-cell size on model results. If this
information is available in a higher resolution than the lower of two grid-cell size simulations being compared, and/or is used via data assimilation to
improve model initial meteorological conditions, our expectation is that the
smaller grid-cell size model may outscore the larger grid-cell size model,
even for more standard metrics.
The extent to which local, versus synoptic, weather conditions drive flow in a given region. For example, in the urban heat island meteorological
simulations of Leroyer et al. (2014), the accuracy of local flow predictions
was shown to be extremely dependent on the representation of the urban heat
island, and the accuracy of the latter was critically dependent on the grid-cell size (which in this example went down to 250 m). In this respect, for
meteorological conditions wherein local factors can dominate the flow, and
where those conditions may be adequately modelled only at very high
resolution, we would again expect the smaller grid-cell size simulation to
provide better performance, for standard metrics.
The results apply as grid-cell size decreases, but are not necessarily true for grid-cell size increases. Conversely, model performance using standard metrics should not be expected
to increase with successively larger and larger grid sizes; the
accuracy of even the synoptic flow field will not be captured as model
resolution decreases.
Given these considerations, we
recommend that modellers should attempt successively smaller grid-cell sizes
to determine the following: first, the point at which, for their particular
system and simulation location, subsequent grid-cell size reductions fail to
improve performance, and second, to make use of still higher resolutions for
studies wherein the point-to-point comparison is less important, and other
factors such as accurately capturing the plume chemistry are more crucial.
Summary and conclusions
Our work suggests the following: decreasing air-quality model horizontal grid-cell size will not necessarily result in improvements to model performance in
standard performance evaluations, in which the model values at the grid cells
encompassing measurement location stations are used in a pairwise comparison
to observations. Other considerations, such as the accuracy of the larger-scale wind direction and speed forecast, and the accuracy of the plume rise
parameterization used within the model may play a greater role in the overall
performance of the model, and reduce the benefits of the smaller grid-cell
size. In the context of a standard model performance evaluation, there may be
fixed limits to the benefits of decreasing model grid-cell size.
Despite this difficulty, our results also show that the use of smaller grid-cell sizes have some potential benefits, in that these models do a better job
of resolving specific air pollution features, like high-concentration maxima
within plumes. Both coarse and fine grid-cell size plumes may be misplaced in
both time and space, with the net result that the latter model has a worse
performance in a standard comparison, but is nevertheless more likely to
capture the correct in-plume concentrations, and hence the chemistry, of the
actual plume, in the neighbourhood of the observation location. When
the evaluation is broadened to find the closest fit to observations in the
vicinity of the observation station, with models confined to a similar
representative area around the observation station, these potential benefits
of the smaller grid-cell size become apparent.
Our results should not be taken as an indication that the standard metrics
for model comparison are in some way flawed – they provide the most rigorous
method for evaluating the performance of a model at specific monitoring
locations and specific times. However, the ancillary performance assessment
methodology presented here shows that models with very small grid sizes,
which may have standard performance metric scores that have not improved or
have even degraded relative to larger grid-cell size models, nevertheless
have scientific value, in terms of being better able to capture plume
concentrations and hence plume chemistry, if not plume position. The work
also suggests that the prediction accuracy of very local transport conditions
may be a large factor in preventing the smaller grid-cell size models from
achieving improved performance in standard performance analyses.
These findings suggest that at the current state of development, VHR
air-quality models are of benefit for the specific purpose of chemical
process studies, in which the main aim of the work is to accurately simulate
plume chemistry – and in which accurate forecasting of the position
of the plume in time and space is a secondary concern. Our work also suggests
that efforts to improve other aspects of the overall modelling framework
which improve the large-scale flow (for example, the use of data assimilation
of local meteorology to improve wind direction predictions) may result in
greater benefits as smaller grid-cell sizes are employed.
Data availability
Surface station air monitoring data used in this study were
obtained and are publicly available from the Wood Buffalo Environmental
Association (https://wbea.org/network-and-data/monitoring-stations/, last access: 1 April 2019). The
2013 aircraft data used in this study are available from the Oil Sands
Monitoring site
(http://donnees.ec.gc.ca/data/air/monitor/ambient-air-quality-oil-sands-region/pollutant-transformation-summer-2013-aircraft-intensive-multi-parameters-oil-sands-region/?lang=en,
last access: 1 April 2019). GEM-MACH model output data generated for this study are available on email
request to Paul A. Makar (paul.makar@canada.ca).
The model output generated from the study requires a large amount of memory
space (several gigabytes per day of simulation) in a binary format specific to
Environment and Climate Change Canada's modelling systems. The size of the
files precludes maintenance on a public site, but conversion to other formats
and arrangements for uploading may be made on request to Environment and
Climate Change Canada at paul.makar@canada.ca.
Model evaluation statistics
Model comparison statistics.
Metric and formulaRangeIdeal scoreIndex of agreement (IOA) =1-∑Mi-Oi2Oi-O‾,when∑Mi-Oi≤2Oi-O‾2Oi-O‾∑Mi-Oi-1,when∑Mi-Oi>2Oi-O‾[-1,1]1Coefficientoferror(COE)=1-∑Mi-OiOi-O‾.[-∞,1]1Meanbias(MB)=1N∑Mi-Oi=M‾-O‾.0Meangrosserror(MGE)=1N∑Mi-Oi.0Normalizedmeanbias(NMB)=∑Mi-Oi∑Oi=M‾O‾-1.0Normalizedmeangrosserror(NMGE)=∑Mi-Oi∑Oi.0Rootmeansquareerror(RMSE)=1N∑Mi-Oi2.0Pearsoncorrelationcoefficient(r)=∑Mi-M‾Oi-O‾∑Mi-M‾2∑Oi-O‾2.[-1.1]1
The limits on the summations were removed for brevity; all are from i=1
to N where N is the number of observation–model pairs, Mi is the
ith model value, O is the ith observation value, and MO‾
are the model and observed mean values, respectively.
Day versus night model performance for the different testing
methodologies
Surface SO2 observations to model
comparison, daytime (09:00–18:00 LT) (ppbv, 2119 model–observation pairs).
MR conducted computer simulations and analysis and created graphical outputs and the initial manuscript draft. AH supervised MR, provided research advice and infrastructure, contributed to manuscript writing, and provided comments on manuscript drafts. PAM co-supervised MR, provided research advice and infrastructure, contributed to manuscript writing, and was the lead for revisions and responses to referees. AA provided model code assistance and setup, and the scoring package for model–observation comparisons. JZ provided 2.5 and 1 km resolution emissions files. MDM provided 2.5 and 1 km resolution emissions files and commented on manuscript drafts. QZ contributed to the provision of 2.5 and 1 km resolution emissions files.
Competing interests
The authors declare that they have no conflict of
interest.
Acknowledgements
The authors wish to thank the support of Environment and Climate Change
Canada (ECCC), under the CCAP program, for supporting this research. The
authors also gratefully acknowledge the assistance of Michel Valin and Sylvie
Gravel for advice and assistance with the installation of GEM-MACH on the
Carleton University workstations during the early stages of this project.
Review statement
This paper was edited by Jason West and reviewed by two
anonymous referees.
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