In many cities around the world people are exposed to
elevated levels of air pollution. Often local air quality is not well known
due to the sparseness of official monitoring networks or unrealistic
assumptions being made in urban-air-quality models. Low-cost sensor
technology, which has become available in recent years, has the potential to
provide complementary information. Unfortunately, an integrated
interpretation of urban air pollution based on different sources is not
straightforward because of the localized nature of air pollution and the
large uncertainties associated with measurements of low-cost sensors.
This study presents a practical approach to producing high-spatiotemporal-resolution maps of urban air pollution capable of assimilating air quality
data from heterogeneous data streams. It offers a two-step solution: (1)
building a versatile air quality model, driven by an open-source atmospheric-dispersion model and emission proxies from open-data sources, and (2) a
practical spatial-interpolation scheme, capable of assimilating observations
with different accuracies.
The methodology, called Retina, has been applied and evaluated for nitrogen
dioxide (NO2) in Amsterdam, the Netherlands, during the summer of 2016.
The assimilation of reference measurements results in hourly maps with a
typical accuracy (defined as the ratio between the root mean square error
and the mean of the observations) of 39 % within 2 km of an observation
location and 53 % at larger distances. When low-cost measurements of the
Urban AirQ campaign are included, the maps reveal more detailed
concentration patterns in areas which are undersampled by the official
network. It is shown that during the summer holiday period, NO2
concentrations drop about 10 %. The reduction is less in the historic city
centre, while strongest reductions are found around the access ways to the
tunnel connecting the northern and the southern part of the city, which was
closed for maintenance. The changing concentration patterns indicate how
traffic flow is redirected to other main roads.
Overall, it is shown that Retina can be applied for an enhanced
understanding of reference measurements and as a framework to integrate
low-cost measurements next to reference measurements in order to get better
localized information in urban areas.
Introduction
Due to growing urbanization in the last decades, more than half of the
world's population lives in cities nowadays. Dense traffic and other human
activity, in combination with unfavourable meteorological conditions, often
cause unhealthy air pollution concentrations. Over 80 % of the urban
dwellers are forced to breathe air which does not meet the standards of the
World Health Organization (WHO, 2016). In 2015, an estimated 4.5 million
people died prematurely from diseases attributed to ambient air pollution
(Lelieveld et al., 2018). Good monitoring is important to better understand
the local dynamics of air pollution, to identify hot spots, and to improve
the ability to anticipate events. This is especially relevant for nitrogen
dioxide (NO2) concentrations, which can vary considerably from street
to street. NO2 is, apart from being a toxic gas on its own, an
important precursor of particulate matter, ozone, and other regional air
pollutants. Observations from a single location are not necessarily
representative for a larger area. Unfortunately, urban-air-quality reference
networks are usually sparse or even absent due to their high installation
and maintenance costs. New low-cost sensor technology, available for several
years now, has the potential to extend an official monitoring network
significantly, even though the current generation of sensors has
significant lower accuracy (WMO, 2018).
However, exploiting these measurements (either official or unofficial),
apart from publishing the data as dots on a map, is not straightforward.
Here, the aim is to make better use of the existing measurement networks to
get the best description of hourly urban air quality, and to create value
from low-cost measurements towards a Level 4 product, according to the
classification proposed by Schneider et al. (2019).
To obtain high-resolution information of air pollutants with sharp
concentration gradients, a very sparse observation network needs to be
accompanied by a valid high-resolution air quality model, whereas a very
dense network can do with simple spatial interpolations. The situation in
most large cities is somewhere in between. There is often a reasonably large
reference network present (10+ stations), sometimes complemented with an
experimental network of low-cost air quality sensors. Assumptions about underlying
unresolved structures in the concentration field are still needed, but this
can be done with a simplified air quality model, using the available
measurements to correct simulation biases where needed.
A popular approach in detailed mapping of air quality is land use regression
modelling (LURM; see e.g. Beelen et al., 2013). LURM uses multiple linear
regression to couple a broad variety of predictor variables (geospatial
information such as traffic, population, altitude, and land use classes) to the
observed concentrations. It is typically used in exposure studies, which
target long integration intervals by definition. Problems of overfitting
might arise when too many predictor variables are used. Alternatively, Denby
(2015) advocates the use of less proxy data and a model based on more
physical principles. In his approach, the emission proxies are first (quasi)
dispersed with a parameterized inverse-distance function, before being
coupled to observed concentrations in a regression analysis.
Mapping of air pollution for short timescales is challenging. Only a few
scientific studies are published aiming at the assimilation of near-real-time
observations in hourly urban-concentration maps. Tilloy et al. (2013) use
the 3-hourly output of a well-developed implementation of the AMDS-Urban
dispersion model in Clermont-Ferrand, France, to assimilate in situ NO2
measurements at nine reference sites in an optimal-interpolation scheme. With a
leave-one-out validation they show a strong reduction in the root mean square
error (RMSE) of the time series after assimilation. Schneider et al. (2017) use
universal kriging to combine hourly NO2 observations of 24 low-cost
sensors in Oslo, Norway, with a time-invariant basemap. The basemap is
created from a yearly average concentration field calculated with an
Eulerian–Lagrangian dispersion model on a 1 km grid, downscaled to 100 m resolution. Averaged over reference locations, their study shows that hourly
values compare well with official values, showing the potential of low-cost
sensor data for complementary air quality information at these timescales.
This paper presents a more advanced yet practical approach to map hourly
air pollutant concentrations, named Retina. Its main system design
considerations are
an observation-driven nature
an ability to assimilate observations of different accuracy
a potential near-real-time application
a versatility and portability to other domains
an open-data base
a reasonable usage of computer resources.
The method is applied to Amsterdam, where, like many cities, NO2
emissions are dominated by transport and residential emissions and where
local exceedances of limit values are regularly observed. Amsterdam is the
most populous city in the Netherlands, with an estimated population of
863 000. Located at 52∘22′ N 4∘54′ E, it
has a maritime climate with cool summers and moderate winters.
Concentrations of NO2 within the city vary considerably, being partly
produced locally and partly transported from outside the city. Measurements
of 2016 show that, compared with regional background values from the Copernicus Atmosphere Monitoring Service (CAMS)
ensemble (see Sect. 3.2.3), urban background concentrations are on average
around 50 % higher, while at road sides NO2 concentrations are about
100 % higher.
Retina uses a two-stage approach. It runs an urban-air-quality model to
account for hourly variability in meteorological conditions (described in
Sect. 3), which is dynamically calibrated with recent measurements (Sect. 4). In the second stage it assimilates current measurements using
statistical interpolation (Sect. 5). Section 6 presents the validation of
the system, while Sect. 7 shows the added value when assimilating
additional low-cost sensor measurements. The last section is reserved for
discussion, conclusion, and outlook.
Air quality measurements
The Public Health Service of Amsterdam (GGD) is the responsible authority
for air quality measurements in the Amsterdam area. Within the domain used
in this study their NO2 network consists of 15 reference stations: 5
stations classify as road stations, 5 as urban-background stations, 2 as
industry, 2 as rural, and 1 as undecided (see Fig. 1). Alternatingly, GGD operates a
Teledyne API 200E and a Thermo Electron 42i NO/NOx analyser, both
based on chemiluminescence. A catalytic–reactive converter converts NO2
in the sample gas to NO, which, along with the NO present in the sample, is
reported as NOx. NO2 is calculated as the difference between
NOx and NO. The accuracy of both types of reference instruments is
estimated at 3.7 % (GGD, 2014), following the EN 14211 standard which
includes all aspects of the measurements method: uncertainties in
calibration gas and zero gas, interfering gases, repeatability of the
measurement, derivation of NO2 from NOx and NO, and averaging
effects.
Low-cost NO2 measurements are taken from the 2016 Urban AirQ campaign
(Mijling et al., 2018). Sixteen low-cost air quality sensor devices were
built and distributed among volunteers living close to roads with high
traffic volume for a 2-month measurement period, from 13 June to 16 August.
The devices are built around the NO2-B43F electrochemical cell by Alphasense
Ltd (Alphasense, 2018). The sensor generates an electrical current when the
target gas diffuses through a membrane where it is chemically reduced at the
working electrode. Better sensor performance at low-ppb levels is obtained
by using low-noise interface electronics. The sensor devices were carefully
calibrated using side-by-side measurements next to a reference station,
solving issues related to sensor drift and temperature dependence (Mijling
et al., 2018). After calibration, they are found to have a typical accuracy
of 30 %.
Setting up a versatile urban-air-quality model
One of the largest unknowns when modelling urban air quality is a detailed,
up-to-date emission inventory capable of describing the local contribution.
For cities such as Amsterdam the local emissions are dominated by the
transport and residential sector. This is confirmed by the EDGAR (Emission Database for Global Atmospheric Research) HTAP (Hemispheric Transport of Air Pollution) v2
emission inventory (Janssens-Maenhout et al., 2013), which estimates the
contribution of NOx emissions in a 20 km × 33 km (0.3∘) area around the centre being 62 %, 20 %, 12 %, and 6 % for
the transport, residential, energy, and industry sectors respectively.
Especially the contribution of road transport is relevant, as its emissions
are close to the ground in densely populated areas. Traffic information and
population density will be used as proxies for urban emission (see Sects. 3.2.1 and 3.2.2).
In contrast to the regional atmosphere, the urban atmosphere is more
dominated by dispersion processes, while many chemical reactions are less
important due to a relatively short residence time (Harrison, 2018). For the
dispersion of the emission sources, the open-source steady-state plume model
AERMOD (Cimorelli et al., 2004) is used, developed by the American
Meteorological Society (AMS) and United States Environmental Protection
Agency (EPA). Based on the emission inventory and meteorology (see Sect. 3.2.4), AERMOD calculates hourly concentrations of air pollutants. The
concentration distribution of emission sources is assumed to be Gaussian
both horizontally and vertically when boundary layer conditions are stable.
In a convective boundary layer, the vertical distribution is described by a
bi-Gaussian probability density function. Note that any other dispersion
model can be used in the Retina methodology, as long as it is capable of
simulating concentrations from individual emission sectors on an arbitrary
receptor mesh.
AERMOD simulation settings
AERMOD version 16216r is used with simulation settings summarized in Table 1, operating on a rectangular domain of 18 km × 22 km covering
the municipality of Amsterdam for the most part. All coordinates are
reprojected in a custom oblique stereographic projection (EPSG:9809) around
the city centre coordinate such that the coordinate system can be
considered equidistant at the urban scale. Instead of using a regular grid,
a road-following mesh (Lefebvre et al., 2011) is used. This reduces the
number of receptor points, while maintaining an accurate description of strong
gradients found close to roads. Receptor locations are chosen at every 75 m along the parallel curves with 25 m distance to the road and at every 125 m along the parallel curves with 50 m distance to the road. The open spaces
between these points are filled with a regular grid at 125 m resolution.
Roads are modelled as line sources, while residential emissions are
described as area sources. The dispersion is calculated for NOx to
avoid a detailed analysis of the rapid cycling between its constituents NO
and NO2. Afterwards, an NO2/NOx ratio is applied, depending
on the available ozone (O3) (see Sect. 3.1.1).
Memory usage of AERMOD for the Amsterdam domain is proportional to the total
number of emission source elements (here 17 069 road fragments and 12 182
residential squares) and the number of receptor points in the road-following
mesh (here 42 128). The calculation time for a single concentration field is
around 10 min but can be reduced to a fraction of this by parallelizing
the code.
Ozone chemistry and lifetime
Primary emissions of NO2 (e.g. directly from the tailpipe) are only
5 %–10 % of the total emitted NOx (Sokhi et al., 2007). At short timescales, secondary NO2 is formed by oxidation of NO with O3, while
this reaction is counterbalanced by photolysis converting NO2 to NO.
The reaction rate of the first reaction is temperature dependent, while the
latter depends on the available sunlight. The NO2/NOx ratio has
therefore an intricate dependence on temperature, radiation, and the
proximity to the source (i.e. the travel time of the air mass since
emission).
A practical approach to estimate this ratio is the Ozone Limiting Method
(OLM), as described in EPA (2015). The method uses ambient O3 to
determine how much NO is converted to NO2. The dispersed (locally
produced) NOx concentration is divided into two components: the primary
emitted NO2 (here assumed to be 10 %) and the remaining NOx,
which is assumed to be all NO available for reaction with ambient O3:
NO+O3→NO2+O2. If the mixing ratio of ozone
(O3) is larger than the 90 % of NOx, then all NO is converted
to NO2. Otherwise, the amount of NO converted is equal to the available
O3, i.e. (NO2)=0.1(NOx)+(O3). The reaction is
assumed to be instantaneous and irreversible. The resulting NO2
concentration is added to the NO2 background concentration.
Removal processes of NOx are modelled with an exponential decay. The
chemical lifetime is in the order of a few hours. Liu et al. (2016) find
NOx lifetimes in a range of 1.8 to 7.5 h using satellite observations
over cities in China and the USA. Given the size of the domain and average
wind speeds, its exact value is not of great importance here. Based on
regression results a practical value of 2 h is chosen.
Simulation input data
The dispersion simulation is driven by input data regarding emissions,
background concentrations, and meteorology, as listed in Table 2. All data,
except for the traffic counts of inner-city traffic, are taken from open-data portals. The emission proxies are mapped in Fig. 2.
EmissionHighway locationsOpenStreetMap (OSM, 2017): street segments labelled motorway and trunkUrban-road locationsOpenStreetMap (OSM, 2017): street segments labelled primary, secondary, and tertiaryHighway traffic flowNational Data Warehouse for Traffic Information (NDW, 2019): weekly cycle of vehicle counts at 29 selected locations (2016), interpolated to street segmentsUrban traffic flowAmsterdam municipality (personal communication): weekly cycle of vehicle counts at 24 locations (2016), interpolated to street segmentsPopulation dataStatistics Netherlands (CBS, 2016): population density (2014) gridded at 100 m resolutionObservationBackground NO2Copernicus Atmosphere Monitoring Service (CAMS, 2019): NO2 analysis from model ensemble; minimum value found in 3×3 grid around domain centreBackground O3Copernicus Atmosphere Monitoring Service (CAMS, 2019): O3 analysis from model ensemble; mean value found in 3×3 grid around domain centreMeteorologyMeteorology (surface)Integrated Surface Database (ISD, 2019): hourly observations from Schiphol airport weather stationMeteorology (upper air)Integrated Global Radiosonde Archive (IGRA, 2019): daily radiosounding at De Bilt (Netherlands)Traffic emissions
A recurrent problem when building urban-air-quality models is finding
sufficiently detailed traffic emission information. Traffic emissions depend
roughly on traffic flow and fleet composition, including engine technology.
For many cities, unfortunately, this information is not available. Here a
distinction is made between highways and primary roads, as both have a
distinct traffic volume and weekly cycle. Differences in driving conditions
and fleet composition are captured by assigning two different emission
factors later on.
Road location data and road type definition data are taken from
OpenStreetMap (OSM, 2017), which is a crowdsourced project to create a free
editable map of the world. A distinction is made between urban roads
(labelled in OSM as “primary”, “secondary”, and “tertiary”) and
highways (labelled as “motorway” and “trunk”), as they have distinct
traffic pulses, fleet compositions, and driving conditions. Road segments
labelled as “tunnel” are not taken into account.
When the traffic flow q (in vehicles per hour) is known, the emission rate
E for a road segment l can be written as
E=αvehql,
with emission factor αveh representing the (unknown) NOx
emission per unit length per vehicle. Hourly traffic flow data are taken from
29 representative highway locations from the National Data Warehouse for
Traffic Information (NDW, 2019), which contains both real-time and historic
traffic data. For the urban traffic flow, data from 24 inductive-loop
counters provided by the traffic research department of Amsterdam
municipality are used. Due to its large numbers, traffic flow is relatively
well predictable, especially when lower volumes during holiday periods and
occasional road closures are neglected. For each counting site a traffic
“climatology” is constructed, parametrized by hour and weekday, based on
hourly data of 2016 (see Fig. 3).
Weekly cycle of highways and urban roads at counting locations
(thin lines), aggregated from hourly data from 2016. The thick lines show
the median of traffic flow for both road types. The morning and evening rush
hours on working days are clearly visible for highways. Urban traffic has,
apart from lower volume, less distinct peaks.
Traffic counts correlate strongly between different highway locations, all
showing a strong commuting and weekend effect. Urban traffic typically
shows, apart from lower volumes, less reduction between morning and evening
rush hours, a less pronounced weekend effect, and higher traffic intensities
on Friday and Saturday night.
For locations x between the counting locations xi, the
traffic flow q(x) is spatially interpolated by inverse-distance
weighting (IDW):
q(x)=∑iwixqi∑iwix,ifd(x,xi)≠0for alliqiifd(x,xi)=0for somei.
in which the weighting factors wi depend on the distance d between
x and the counting location xi:
wi=1d(x,xi)2.
Validation in the Supplement shows that for this counting
network IDW predicts the traffic volume within a 50 % error margin at most
locations. Better results are obtained when more counting locations are
available or when they are selected strategically around crossings and
access roads. Model simulations show that using inferior traffic data is
partly compensated by the calibration (Sect. 4), at the expense of less
pronounced concentration gradients.
Population data
Population density is considered to be a good proxy for residential
emissions, e.g. from cooking and heating. Here, data are taken from the
gridded population database of 2014, compiled by the national Central Bureau
for Statistics (CBS, 2019) at a 100 m resolution. Each grid cell is offered
to the dispersion model as a separate area source. To reflect the
observation that residential emissions per capita are less when people are
living closer to each other (Makido et al., 2012), the emission fluxes are
taken proportional to the square root of the population density p:
E=αpopp.
Background concentrations
As AERMOD only describes the local contribution to air pollution, background
concentrations must be added. These are taken from the Copernicus Atmosphere
Monitoring Service (CAMS) European air quality ensemble (Marécal et al.,
2015). The CAMS ensemble consists of seven regional models producing hourly air
quality and atmospheric-composition forecasts on a 0.1∘× 0.1∘
resolution. The analysis of the ensemble is based on the assimilation of
up-to-date (UTD) air quality observations provided by the European
Environment Agency (EEA). Each model has its own data assimilation system.
In the CAMS product the local contributions are already present. To get a
better estimate for regional background concentrations avoiding double
counts, the lowest concentration found in a 0.3∘× 0.3∘ area
around the city for NO2 is taken, together with the mean concentration
found in this area for O3.
Meteorological data
The dispersion of air pollution is strongly governed by local meteorological
parameters, especially the winds driving the horizontal advection and the
characterization of the boundary layer which defines the vertical mixing.
Meteorology also affects the chemical lifetime of pollutants.
AERMET (EPA, 2019) is used as a meteorological preprocessor for organizing
available data into a format suitable for use by the AERMOD model. AERMET
requires both surface and upper-air meteorological data but is designed to
run with a minimum of observed meteorological parameters. Vertical profiles
of wind speed, wind direction, turbulence, temperature, and temperature
gradient are estimated using all available meteorological observations and
extrapolated using similarity (scaling) relationships where needed (EPA,
2018).
Hourly surface data from the nearby Schiphol airport weather station can be
obtained from the Integrated Surface Database (ISD; see Smith et al., 2011). Observations of temperature, winds, cloud cover, relative humidity,
pressure, and precipitation are retrofitted to match the SAMSON (Solar and Meteorological Surface Observation Network) data format
(WebMet, 2019a), which is supported by AERMET. Upper-air observations are
taken from daily radiosonde observations in De Bilt (35 km from
Amsterdam), archived in the Integrated Global Radiosonde Archive (IGRA)
(Durre et al., 2006). Pressure, geopotential height, temperature, relative
humidity, dew point temperature, and wind speed and direction are converted to
the TD6201 data format (WebMet, 2019b) for each reported level up to 300 hPa.
Calibrating the model
Using proxy data instead of real emission introduces the problem of finding the
emission factors which best relate the activity data to their corresponding
emissions. Instead of using theoretical values or values found in
literature, effective values are derived which best fit the hourly averaged
NO2 observations of a network of N stations.
For a certain hour t, the emission of a source element i belonging to source
sector k can be written as
Eik(t)=αkPik(t),
in which Pik represents the corresponding emission proxy. The
contribution of this source to the concentration at a receptor location j is
cijk(t)=fij(t)Eik(t),
with fij describing the dispersion of a unit emission from i to j,
including the conversion from NOx to NO2 from the OLM. Equation (6) is
assumed to describe a linear relation between emission and concentration,
although strictly speaking the variable NO2/NOx ratio introduces a
weak nonlinearity. A regression analysis is applied for a certain period,
assuming that for each t the total NO2 concentration cj at station
j can be described as a background field b and a local contribution consisting
of a linear combination of the dispersed fields of K emission sectors:
cj(t)=b(t)+∑k=1Kak∑iSkfij(t)Pik(t),
where Sk represents the number of source elements for an emission sector k.
The second sum in this equation is calculated for every hour with the
Gaussian dispersion model taking the meteorological conditions during t into
account. Note that both background concentrations b(t) and local
concentrations cj(t) are taken from external data (see Sects. 3.2.3 and
2). Considering a period of T hours, Eq. (7) can be interpreted as a matrix
equation from which the emission factors ak can be solved using ordinary
least squares. Given the physical meaning of ak, only positive
regression results are allowed.
In this setup, the emissions are approximated by the three sectors of highway
traffic, urban traffic, and population density (K=3). The resulting
ak values do not necessarily represent real emission factors. Their values
partly compensate for unaccounted emission sectors and unrealistic modelling
(e.g. based on wrong traffic data or an incorrect chemical lifetime). In
Retina ak is recalculated every 24 h, based on observations of the preceding week
(T=168). Doing so, the periodic calibration adjusts itself to seasonal
cycles and episodes not captured by the climatologies (e.g. cold spells or
holiday periods). To avoid reducing the predictability of the regression
model too much (ak dropping to zero), not all reference stations are
used for calibration but rather only stations classified as roadside or urban
background. For the Amsterdam network, N=11. The residential emissions are
represented by the population density, which is a time-invariant proxy. To
allow for a diurnal cycle, the residential emission factor is evaluated for
2 h bins. This brings the total number of fitted emission factors to
14: 1 for highway traffic, 1 for urban traffic, and 12 describing the
daily residential emission cycle.
Figure 4 shows an example of the air quality simulation after the emission
factors have been determined. The stacked colours in the time series of Fig. 4b show that the contribution from different emission sectors to local air
pollution can strongly vary from site to site.
(a) Dispersion maps of NO2 concentrations for each emission
sector on 8 July 2016 at 09:00. The lower-right panel shows the linear
combination which best fits the time series at the calibration sites. Wind
is blowing from the southwest at 16 km h-1. The grey dots indicate an urban-background location, a street location, and a highway location.
(b) Comparison of observed and simulated NO2 time series (date format of day-month-year) for the
urban-background location, the street location, and the highway location.
The colours indicate the simulated contribution of the three source sectors
and the background.
Diurnal and seasonal analysis of calibration results
It is important to realize that the numerous modelling assumptions prevent the calibration from realistically solving the underdetermined inverse
problem of finding the underlying NOx emissions based on the observed
NO2 concentrations. Instead, it evaluates how much NOx must be
injected into the model to explain the observed spatial NO2 patterns
(unbiased with respect to the calibration locations). To study the results
of the regression analysis, a comparison was made between a summer month
(July 2016, mean temperature of 18.4 ∘C) and a winter month
(January 2017, mean temperature of 1.6 ∘C). Figure 5 shows the
diurnal emissions for a 0.2∘× 0.1∘ area, corresponding to the
two grid cells of the EDGAR inventory covering the city centre.
Diurnal emission cycles after calibration of emission factors in
different seasons.
Ideally, the emissions would be around the values found in the EDGAR
inventory (6.23 and 7.18×10-10 kg NOx m-2 s-1 for summer and
winter respectively) and a corresponding ratio between residential and
transport emissions (8 % and 48 % for summer and winter respectively).
Unlike traffic, however, the diurnal cycle for the residential contribution
is not prescribed but is shaped in the regression analysis. The seasonal
analysis shows that its fitted diurnal cycle not only describes changing
residential emissions but also compensates for changing NO2/NOx
ratios over the day (not included in the OLM) due to changing photochemistry
and temperature. In daylight, the destruction of NO2 by photolysis
(NO2+hv→NO+O3) is strong, reducing the
NO2/NOx ratio. At low temperatures, the formation of NO2 from
NO (NO+O3→NO2+O2) is slow, also reducing the
NO2/NOx ratio. Also, due to collinearity, part of the traffic
emissions will be explained by population density. Therefore, the found
emission factors (and the corresponding sectoral emissions) should be
considered as “effective” rather than real, i.e. as factors which best
describe the observations under the given model assumptions.
Assimilation of observations
As the air quality network is spatially undersampling the urban area, the
observations need to be combined with additional model information to
preserve the fine local structures in air pollutant concentrations. The
interpolation technique of choice here is optimal interpolation (OI) (Daley,
1991), having the desired property that the Bayesian approach allows for
assimilation of heterogeneous measurements with different error bars. At an
observation location the model value is corrected towards the observation,
with the innovation depending on the balance between the observation error and
the simulation error. The error covariances determine how the simulation in
the surroundings of this location is adjusted. Note that OI is essentially
the same assimilation scheme as kriging-based approaches. The main advantage
here is that one has detailed manual control over the error covariance
matrix, which allows for a more comprehensive specification of the area of
influence for each contributing observation. Outside the representativity
range (i.e. the correlation length) of the observations, the analysis
relaxes to the model values.
Consider a state vector x representing air pollutant concentrations
on the (road-following) receptor mesh (n≈40000). Define
xb as the background, i.e. the model simulation. Observation
vector z contains m measurements, typically 10–100. Following the
convention by Ide et al. (1997), the OI algorithm can now be written as:
8xa=xb+Kz-Hxb9K=PbHTHPbHT+R-110Pa=I-KHPb.
Matrix R is the m×m observation error covariance matrix. As
all observations are independent (the measurement errors are uncorrelated),
R is a diagonal matrix with the measurement variances on its
diagonal.
Pb is the n×n model error covariance matrix,
describing how model errors are spatially correlated. The calculation of
Pb is not straightforward; in Sect. 5.1 an approximation is
derived.
Operator H is the forward model, which maps the model state to the observed
variables and locations. The matrix calculations can be simplified by
reserving the first m elements of the state vector for the observation
locations and the other n-m elements for the road-following mesh. The
Gaussian dispersion model is evaluated “in situ” at the observation
locations. Avoiding reprojection or interpolation means that there are no
representation errors associated with H. The simulations at the observation
locations zb can then be written as a matrix multiplication
zb=Hxb=Hxb,
in which H is an m×n matrix for which its first m columns
form a unity matrix, while its remaining elements are 0.
Equation (8) describes the analysis xa, i.e. how the observations
z are combined (assimilated) with the model xb. It is
a balance between the model covariance and the observation covariances,
described by the gain matrix K in Eq. (9). K determines
how strong the analysis must incline towards the observations or remain at
the simulated values to obtain the lowest analysis error variance,
Pa in Eq. (10).
Note that Eqs. (8)–(10) are analogous to the first step in Kalman filtering.
The second step of the filter, propagating the analysis to the next time
step, cannot be made here as the plume model solves a stationary state which
is independent of the initial air pollutant concentration field. Also note
that since an approximated model error covariance matrix will be used,
generally these equations do not lead to an optimal analysis; hence this
approach is more correctly referred to as statistical interpolation.
Let vector c represent the observed NO2 mass concentrations,
as described in Sect. 2. The distribution of the air pollutant
concentrations resembles better the lognormal distribution than the Gaussian
distribution, as can be seen from the Q–Q plots in Fig. 6. The analysis is
done in log space (zj=lncj), stabilizing the results by
reducing the impact of less frequent measurements of high concentrations.
Once returning from the log domain, Eq. (8) can be rewritten as
ca=expxa=cbexpKΔz,with innovation vectorΔz=z-zb.
By doing the analysis in the log domain the assimilation updates correspond
to multiplication instead of addition:
exp(KΔz) represents the
local multiplication factor with which the simulated concentration
cb is corrected. This means that the shape of the model field
(e.g. strong gradients found close to busy roads) is locally preserved. Note
that the error in zj corresponds to the relative error in cj:
dz=dlnc/dc=dc/c. The observation
error covariance matrix is therefore R=diag(σ12,σ22,…,σm2), with
σj being the relative error corresponding to observation j.
(a) Distribution of the NO2 observations at reference
station Oude Schans in July 2016 compared to a standard normal distribution.
(b) The logarithm of the observed values correspond better to a Gaussian
distribution, shown by the quantile value pairs being almost on a straight
line.
Modelling the model error covariance matrix
For an optimal result in the data assimilation a realistic representation of
the model covariance matrix Pb is essential. The model
covariances influence the spatial representativity of the observations: when
model errors correlate over larger distances, the assimilated observation
will change the analysis over a longer range.
Tilloy et al. (2013) choose to model the covariances depending on the road
network. Error correlations are assumed to be high on the same road or on
connected roads. For background locations, the correlation decreases fast in
the vicinity of a road, while the error correlation between two background
locations remains significant across a larger distance. The error
covariances are kept constant in time and taken independent of traffic
conditions.
However, Pb changes from hour to hour, mainly because varying
meteorology changes the atmospheric-dispersion properties. Here, the model
error covariance is estimated for each hour based on the spatial coherence
of the simulated concentration field. The covariance between two grid
locations xi and xj can be expressed as their
correlation ρ and their standard deviations σ:
Pijb=σiρ(xixj)σj.
The model error σ can only be evaluated at locations of the
reference network using time series analysis. These model errors are
spatially interpolated to other grid locations using IDW, analogous to Eqs. (2)–(3). The correlation of model errors between different locations is
parametrized with a downwind correlation length Ldw and a crosswind
correlation length Lcw. The extent of the correlation lengths reflects
the turbulent diffusion and transport of the Gaussian-dispersed plumes for a
specific hour.
From spatial analysis of the simulation data a heuristic model is derived
which describes the dependence of the correlation on distance:
ρ(d)=exp-d,
with d being the scaled distance between xi and xj
(expressed as xdw and xcw along the downwind and crosswind axes),
d=xdwLdw2+xcwLdw2,
such that all points on an ellipse with semi-major axis Ldw and
semi-minor axis Lcw have the same correlations.
To fit the parameters Ldw and Lcw for a certain hour, 1000 sample
locations are selected from the road-following mesh. To represent both
polluted and less polluted areas, the locations are selected such that their
concentrations are homogeneously distributed over the value range, excluding
the first and last five percentiles. For this sample, correlation lengths
Ldw and Lcw are fitted using Eqs. (14) and (15).
Figure 7 shows the results of this analysis for two different hours. For
fields with low gradients (e.g. when traffic contribution is low at night),
large values of L can occur. To prevent assimilation instabilities, the
fitted values of L are limited to a maximum of 10 km. During the 2016 summer
months, the longest correlation lengths are found for fields with low gradients.
Average midnight values, when traffic contribution is low, are about 8 km.
Correlation lengths are shortest during the morning rush hour
(∼1 km), increasing to 3 km during the late morning and
afternoon. There is a wind dependency, as stronger winds stretch the
pollution plumes, increasing correlation lengths. From the fit results the
average ratio between Lcw and Ldw is found to be 68 %.
Left panels show simulated NO2 concentration fields at 2 different hours. The middle panels show the spatial correlations along the
downwind and crosswind axes based on a sample of n=1000. The right panels
show the spatial correlations of the sample and the resulting modelled
spatial correlation model.
Once the covariance parameters are known, the covariance matrix elements are
calculated with Eq. (13). Note that for the calculation of the gain matrix
K there is no need to calculate the full Pb matrix.
Instead, PbHT is calculated, which due to the
structure of H this matrix product corresponds to the first m
columns of the n×n matrix Pb.
Validation of simulation and assimilation
To assess the data quality across the domain, a leave-one-out analysis is
performed at all locations of the reference network for the period 1 June–31 August 2016. The results are summarized in Table 3. Figure 8 illustrates
two examples; plots for all validation locations can be found in the
Supplement. For the observation-free simulation (i.e. the model
forecast) an average RMSE is found of 13.6 µg m-3 with a correlation
of 0.57. When assimilating observations, the average RMSE drops to 10.4 µg m-3, while the correlation increases to 0.78. Strong systematic
underestimations of the simulation (characterized by a large negative bias)
are observed at street locations NL49002 and NL49007 and industrial locations
NL49546 and NL49704. These are most likely caused by unrealistic assumptions of
local emissions of either traffic or industry. The strong positive bias
found at NL49014, located in a city park separated from the nearby main road
by a block of four-storey buildings, might be explained by an incorrect
simulation of air pollutants in the direct vicinity of these buildings.
Validation results at reference locations on 1 June–31 August 2016.
IDNameTypenaMean obs.CAMS ensemble Model forecast Assimilated observations RMSEbBiasCorrRMSEbBiasCorrRMSEbBiasCorrDistcNL49002Amsterdam –HaarlemmerwegStreet214542.231.4-25.60.4922.6-14.30.5518.6-14.50.830.99NL49007Amsterdam –EinsteinwegStreet214538.129.2-21.40.4219.6-6.90.5716.5-6.20.721.26NL49012Amsterdam – Van DiemenstraatStreet214529.120.2-12.50.5315.7-2.70.579.7-0.50.870.99NL49017Amsterdam –StadhouderskadeStreet214030.117.9-13.50.4514.31.90.509.0-2.70.781.60NL49020Amsterdam –Jan vanGalenstraatStreet213134.824.0-18.20.5916.6-4.70.5811.1-5.30.861.26NL49003Amsterdam –NieuwendammerdijkUrban backgr.214516.68.60.10.6010.52.00.477.50.80.713.28NL49014Amsterdam – VondelparkUrban backgr.211517.39.0-0.70.5214.97.90.449.96.50.751.73NL49019Amsterdam – Oude SchansUrban backgr.212420.710.3-4.10.5913.85.80.508.74.60.811.60NL49021Amsterdam –KantershofUrban backgr.208214.97.51.60.6510.75.60.568.04.40.737.33NL49022Amsterdam –Sportpark OokmeerUrban backgr.212414.38.42.40.659.23.40.668.03.70.803.89NL49565Oude Meer – AalsmeerderdijkRural212717.39.1-0.60.579.0-2.40.598.0-3.00.735.94NL49703Amsterdam – SpaarnwoudeRural212513.08.73.70.618.12.10.607.52.40.714.47NL49546Zaanstad –HemkadeIndustry214522.914.3-6.20.6315.0-8.10.6613.0-8.30.833.26NL49704Zaanstad – HoogtijIndustry212019.612.7-3.00.6613.4-6.00.7212.1-6.40.843.72NL49561Badhoevedorp –SloterwegUndecided214520.510.6-3.90.6410.8-2.90.618.9-4.20.793.96Average of street locations34.924.5-18.20.5017.8-5.30.5513.0-5.80.81Average of urban-background locations16.88.8-0.10.6011.84.90.538.44.00.76Average of all locations23.414.8-6.80.5713.6-1.30.5710.4-1.90.78
a Number of samples.b In units of µg m-3.c The distance to the nearest observation site (in km).
Validation of hourly time series for the period 1 June to 31
August 2016, for a well-performing street location (above) and a less
performing urban-background location (below). Statistics of the n data pairs
are given in correlation (ρ), coefficient of determination
(R2), and RMSE. The right-hand panels compare the error distributions:
the observation minus forecast (OmF) against the observation minus analysis
(OmA).
The CAMS regional ensemble analysis compares well with the average of the
urban-background stations; the very low bias (-0.1µg m-3)
corresponds with the fact that data of these stations are used in its
analysis. (Note that the CAMS values used here correspond to the Amsterdam
grid cell, not the 3×3 minimum values used as background for the
modelling.) On the other hand, it shows strong underestimations at street
locations, as expected. It is here where the Retina simulation outperforms
the low-resolution results of CAMS.
From Table 3 it can be seen that the relative error in the model forecast
(defined as the ratio between the RMSE and the mean of the observations) is
around 58 % on average. When assimilating, the error becomes dependent on
the distance to the nearest observation locations. For sites having the
nearest assimilated observation within 2 km distance, the average RMSE drops
from 16.8 to 11.9 µg m-3, corresponding to an average relative
error of 39 %. For sites where the nearest assimilated observation is
further away than 2 km, the average RMSE drops from 10.8 to 9.1 µg m-3, corresponding to an average relative error of 53 %.
Added value of low-cost sensors
The previous analysis is purely based on high-quality reference
measurements. In this section it is explored whether the statistical-interpolation scheme can be used to derive useful information from low-cost
measurements, despite their lower accuracy.
This is done by testing different assimilation configurations during the
Urban AirQ campaign, from 15 June to 15 August 2016 (see Sect. 2). The
campaign targeted a central area with 4 reference stations and 14 low-cost
sensors (see Fig. 10a). Validation is done for five different assimilation
scenarios (ASs):
AS1 – assimilation of all reference measurements (leave-one-out)
AS2 – assimilation of measurements from three central reference sites
(leave-one-out)
AS3 – assimilation of low-cost data only
AS4 – assimilation of measurements from three central reference sites
(leave-one-out) and all low-cost data
AS5 – assimilation of all reference measurements (leave-one-out) and all
low-cost data.
The results are summarized in Fig. 9. As expected, results deteriorate
when the number of reference locations in the assimilation is reduced from
14 (AS1) to 3 (AS2). The correlation decreases at all four validation
locations. At NL49012, the RMSE increases significantly due to a positive
jump in the bias. The lower analysis with respect to the observations is due
to the absence of assimilation of high values at nearby street location
NL49002, which enlarges the influence of lower observations found at urban-background location NL49019. At NL49019, located in the middle of three assimilation locations, the RMSE does not change significantly. Apparently,
the effect of assimilation of observations farther than the surrounding
locations is small.
Validation of the model forecast and five different
assimilation scenarios at four central reference sites, for the period 15 June
to 15 August 2016.
When only observations of 14 low-cost sensors are assimilated (AS3), instead
of observations at 3 reference sites (AS2), there is a notable improvement
visible in bias and RMSE at location NL49019. Here, the low-cost sensors are
relatively nearby, the closest being sensor SD04 at 120 m distance. At the
other validation locations, the low-cost sensor assimilation results in a
similar RMSE (i.e. within 1 µg m-3) and a comparable bias but a
slightly lower correlation.
The results can be further improved if both reference and low-cost sensor
data are included (AS4 and AS5). At NL49019, the RMSE drops to 5.1 µg m-3 (compared to 7.8 µg m-3 when no low-cost data are
included) while the correlation increases to 0.89. Again, there is no
significant difference between including the three surrounding reference
locations and including all reference locations. Also at street location
NL49017 and urban-background location NL49003, the inclusion of low-cost
sensor data improves RMSE and correlation compared to assimilations with
reference data only (AS4 vs. AS2 and AS5 vs. AS1). At location NL49012, the
bias reduces considerably only when all reference data are included in the
assimilation (AS1 and AS5).
The different assimilation scenarios show that low-cost sensor data
assimilation improve the results locally, even in absence of reference
data. Generally, the best results are obtained when both reference data and
low-cost data are included. Assimilation can reduce local model biases.
However, unrealistically modelled covariances can lead locally to the
introduction of an additional bias.
Next, a monthly averaged concentration map of Amsterdam is constructed with
all reference data and all low-cost sensor data from the first half of the
Urban AirQ (see Fig. 10b). The addition of the low-cost data lowers the
assimilation results by several micrograms per cubic metre in the undersampled area
west of Oude Schans (NL49019), while the NO2 increases by several
micrograms per cubic metre around the traffic arteries found south and east of this
location (Fig. 10c). A large fraction of traffic on these roads uses the
IJtunnel to cross the river. On a monthly basis, this tunnel is used by
approximately 1 million vehicles.
The second half of the Urban AirQ campaign coincides with the start of the
summer holiday period and the closure of the IJtunnel for maintenance.
Comparison of the NO2 concentration maps of both periods reveal
interesting features (Fig. 11). Based on averaged NO2 measurements at rural
stations NL49565 and NL49703, the NO2 reduction due to meteorological
variability is estimated to be 7 %. The overall drop in NO2
concentrations in the central area, however, is around 10 % due to reduced
traffic during the summer break. A notable exception is the historic city
centre, where the NO2 reduction is only a few percent, probably related
to the steady economic activity driven by tourism. The strongest NO2
reductions, around 15 %, are found around the access ways of the
IJtunnel. A few main roads (e.g. De Ruijterkade/Piet Heinkade and
Ceintuurbaan) show less NO2 reduction than average, apparently due to
redirected traffic avoiding the tunnel.
As air pollution gradients can be strong in the urban environment, it is
essential to combine (sparse) measurements with an air quality model when
aiming at street-level resolution. Retina is a practical approach to
interpolating hourly urban-air-quality measurements. The first step consists
of a simulation by a dispersion model which is driven by meteorological data
and proxies for traffic and residential emissions. The model is daily
calibrated with historic measurements. In the second step, observations of
different accuracy are assimilated using a statistical-interpolation scheme.
Validation analysis confirms that the European CAMS ensemble is a good
predictor for hourly NO2 concentrations found in the urban background.
However, the CAMS data for NO2 can be misleading when interpreted at
the local scale, as the predicted diurnal cycle often deviates substantially
from that observed at urban-air-quality stations. Local effects can be
better resolved when CAMS data are used for background concentrations in a
dispersion model which is driven by proxies for traffic and residential
emissions.
The Retina simulation setup shows that such a system can be built from open
software and open data. Applied to summer 2016 in Amsterdam, it reduces the
relative error at street locations from 70 % to 51 %, mainly by reducing
the negative bias from 18.2 to 5.3 µg m-3. At urban-background locations
the dispersion model often introduces a positive bias, especially when
traffic sources are nearby.
The mapping results improve considerably with the second Retina step when
available observations are assimilated by the statistical-interpolation
scheme. When assimilating measurements of the reference network, the
relative error in NO2 concentrations drops to 44 % on average. The
local error depends on the distance to the nearest observations:
approximately 39 % within 2 km of an observation site, increasing to
53 % for larger distances. The typical correlation increases from 0.6 to
0.8.
The Bayesian assimilation scheme also allows us to improve the results by
including low-cost sensor data, in order to get improved localized
information. However, biases must be removed beforehand with careful
calibration, as most low-cost air quality sensors suffer from issues like
cross-sensitivity or signal drift (see e.g. Mijling et al., 2018). The
assimilation of low-cost sensor data from the Urban AirQ campaign reveals a
more detailed structure in concentration patterns in an area which is
undersampled by the official network. The additional measurements correct
for wrong assumptions in traffic emissions used in the a priori
interpolation and give better insight into how traffic rerouting (for
instance due to closure of an arterial road) affects local air quality.
Retina has been built on open data to facilitate a flexible application to
other cities. The meteorology needed for AERMOD is taken from global data
sets of ISD and IGRA. Road network information can also be obtained globally
from OpenStreetMap. Traffic data tend to be hard to obtain. When no local
data are available on diurnal and weekly traffic flow its patterns should be
estimated. In the absence of local census data, population density data can
be taken from the Global Human Settlement database (Schiavina et al., 2019),
which has global coverage on a 250 m resolution. For application within
Europe, the necessary background pollutant concentrations can be obtained
from CAMS. For applications outside Europe other data sets have to be found.
In general, degraded input data and imperfections in the dispersion
modelling will deteriorate the system's capability to resolve local
structures; it will lower the effective spatial resolution of the
simulations. In its extreme it will only describe the blurry urban-background pollution contribution added to the rural background. Oppositely,
with improved input data and atmospheric modelling, the effective resolution
will improve, reducing local biases. This is the focus of future research.
Significant inaccuracies due to local emissions which are not described
adequately by the proxies (e.g. from industry, port, and airport activity)
can be reduced by including these sources explicitly in the dispersion
modelling. Small-scale structures provoked by the local built-up area will
be better described by introducing the street canyon effect. The model will
also benefit from a more detailed traffic emission model, based on more
counting locations and aggregated from shorter time intervals. Ideally, such
an emission model takes local differences in fleet composition also into
account. Finally, simulations will gain accuracy with a more realistic
NOx chemistry, concerning the NOx chemical lifetime (influencing
the plume length) and the NO2/NOx ratio.
Overall, the error of the assimilation results depends on the accuracy of
the air quality model, the number of assimilated observations, the quality
of observations, and the distance to the observation location. A reasonable
approximation of the model covariance matrix is found by assuming the model
covariance to be isotropic and by fitting correlation lengths along the
downwind and crosswind axes for every hour. Finding a more realistic
description of the model covariance matrix will better suppress the
introduction of bias by the assimilation and will be subject to future
research.
For near-real-time monitoring and forecasting of air quality the CAMS
ensemble analysis must be changed for the ensemble forecast. Instead of
observation-based meteorology one should use data from local or global
numerical weather prediction models, e.g. from the National Centers for
Environmental Prediction (the Global Forecast System, GFS; open data) or the
European Centre for Medium-Range Weather Forecasts (ECMWF; not open data).
Apart from assessment of historic data such as in this study, Retina has
been applied successfully for near-real-time monitoring and forecasting of
NO2 in the cities of Amsterdam, Barcelona, and Madrid. Future work
includes the implementation of other cities inside and outside of Europe
and the application of Retina to other pollutants such as particulate
matter.
Data availability
The data sets used and produced in this study can be accessed by the digital object
identifier (DOI) 10.21944/retina-amsterdam-2016 (Mijling, 2020).
The supplement related to this article is available online at: https://doi.org/10.5194/amt-13-4601-2020-supplement.
Competing interests
The author declares that there is no conflict of interest.
Acknowledgements
The author wishes to acknowledge the people behind the data sources used in
this study, most notably GGD Amsterdam (reference measurements), volunteers
of the Urban AirQ campaign (low-cost measurements), NDW and Amsterdam
Traffic Research Department (traffic data), contributors to OpenStreetMap
(road location and classification), CAMS (background concentrations), IGRA
and ISD (meteorology), and CBS (population data).
Financial support
This research has been supported by the European Commission through the Horizon 2020 programme (AirQast; grant no. 776361).
Review statement
This paper was edited by Dominik Brunner and reviewed by two anonymous referees.
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