Boundary-Layer Meteorol (2009) 133:1–16
DOI 10.1007/s10546-009-9416-0
ARTICLE
Turbulent Dispersion of Non-uniformly Emitted Passive
Tracers in the Convective Boundary Layer
Jean-François Vinuesa · Stefano Galmarini
Received: 21 January 2009 / Accepted: 4 August 2009 / Published online: 22 August 2009
© Springer Science+Business Media B.V. 2009
Abstract The impact of spatially non-uniform emissions on the turbulence dispersion of
passive tracers in the convective boundary layer is studied bymeans of large-eddy simulation.
We explicitly calculated the different terms of the budget equations for the concentrations,
fluxes and variances, and used sub-domain averaging where each sub-domain is the typ-
ical size of a large-scale model grid cell. We found that the concentration profiles in the
sub-domain where the emission takes place are lightly affected by the size of the emission
release. This effect becomes more relevant in the downwind sub-domain. Although sub-
domain averaged fluxes are not affected by the emission source size, concentration variances
are dramatically increased when the emission shrinks. This increase originates from the mix-
ing of highly concentrated air parcels with those of low concentrations. We also found that
the concentration variance at the surface is driven neither by the position of the emission
source nor the strength of the shear forcing but solely by the emission variance.
Keywords Convective boundary layer · Large-eddy simulation · Non-uniform emission ·
Scalar flux · Scalar variance · Turbulent dispersion
1 Introduction
Air quality models are used to estimate the impact of air pollution on human health and
on vegetation, and to evaluate air pollution abatement strategies. Due to their complexity,
these models do not allow for a realistic representation of the sources. Sources of trace
gases have a wide range of sizes and shapes, and can be point (e.g., power factories), linear
(e.g., roads), or surface (e.g., urban areas) sources. In the case of linear and surface sources,
as with highways or cultivated fields, the shape of the source is rarely square or rectangular.
Nowadays, emission inventories are generated using sources’ shapes as realistic as possible
J.-F. Vinuesa · S. Galmarini (
B
)
Institute for Environment and Sustainability, Joint Research Centre, European Commission,
21020 Ispra, Italy
e-mail: stefano.galmarini@jrc.it
123

2 J.-F. Vinuesa, S. Galmarini
that are defined to a high level of resolution, to the extent that emission rates are allocated to
a specific source using geographic information systems (GIS). However, air quality models
use two-dimensional emission fields with regular grid cells. Therefore, the scalar emissions
from a source, or a number of sources, located in a particular grid cell are attributed to this
cell and are represented by a single value. The amount of emission is located in the centre of
the node as a point emission, and transformed into a mean exhalation rate or mean flux. This
results in neglecting all subgrid information about the emission source.
It is obvious that the projection of a GIS-generated emission inventory onto a mesh results
in dilution of the pollutants and in the neglect of the shape and the size of the emission sources.
One may object to these points arguing that since the pollutant is emitted at the surface, tur-
bulent transport will mix it in any case. In other words, the assumption of a uniformly mixed
first model layer may be supported by the turbulent property of the atmospheric boundary
layer (ABL). However, important questions remain: Is the subgrid-scale spatial variability
of the emission source relevant to the calculation of upper air concentrations? Does this
variability affect higher-order moments such as the regional fluxes or variances? Which are
the driving processes to be taken into account?
In the ABL, pollutant transport is driven by turbulent eddymotions, with the largest eddies
responsible for the turbulent transport of scalars and momentum while the smallest ones are
mainly dissipative. Atmospheric turbulence plays the key role in distributing non-spatial
uniformly emitted pollutants through the ABL. Therefore accurate modelling of the atmo-
spheric boundary layer requires the use of large-eddy simulation (LES) that allows solving
explicitly all relevant turbulent scales.
The LES approach has been used for several decades to investigate the dispersion of
passive and reactive scalars in the convective boundary layer. Since the pioneering works
of Lamb (1978); Moeng and Wyngaard (1984); Fiedler and Moeng (1985); Sun and Chang
(1986); Nieuwstadt and de Valk (1987); Chatfield and Brost (1987); Schumann (1989), and
Ebert et al. (1989), several LES studies on inert scalar dispersion have been performed using
idealized conditions, e.g., periodic lateral boundary conditions and simple emission scenarios
such as uniform emission or point source releases. To our knowledge only a few studies used
more realistic conditions for studying turbulent dispersion in the ABL (e.g., Krol et al. 2000;
Auger and Legras 2007 and Galmarini et al. 2008). In particular, Galmarini et al. (2008) used
non-periodic lateral boundary conditions and emission scenarios involving different emission
source sizes, and progressing the use of LES for air quality purposes. By using sub-domain
averaging where each sub-domain represents one large-scale model grid cell, they proposed
a method to account for the subgrid emission heterogeneity in air quality models.
Using the approach proposed by Galmarini et al. (2008), we focus on the role of turbu-
lent mixing in the transport and the variability of inert tracers originating from non-uniform
emissions. To do so, we use LES to explicitly calculate the different terms of the concen-
tration, flux and variance budget equations, and perform a complete analysis of the vertical
distribution and turbulent transport of such pollutants. To our knowledge such an analysis
is the first of its kind. The scope of the paper is also to emphasize the effects of neglecting
subgrid-scale emission variability in air quality models, and identifying the processes that
should be considered to improve the performance of such models.
The structure of the paper is as follows: in Sect. 2, we describe the numerical experiment
and the different emission scenarios. In Sect. 3, we focus on the dispersion of the tracers,
while their vertical transport, i.e. fluxes, and their horizontal variability, i.e. variances, are
analyzed in Sect. 4. In Sect. 5 we look at the effect of the wind shear and the position of the
emission sources, and finally, a summary is presented and conclusions are drawn in the last
section.
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Dispersion of Non-uniform Emitted Scalars 3
2 Numerical Experiment
The LES model used is that developed by Cuijpers and Duynkerke (1993); Siebesma and
Cuijpers (1995); Cuijpers and Holtslag (1998), and Vilà-Guerau de Arellano and Cuijpers
(2000). The atmospheric flow contained in a volume of 8 × 12 × 1.5 km3 is simulated by
means of 80 × 120 × 60 grid points. The LES simulation runs for 5h with a maximum
timestep of 0.5 s using a pre-run of 1h for the dynamics only. The surface sensible heat flux
is set at 0.05K m s−1, and a constant westerly wind of 5m s−1 was imposed but Coriolis
forcing is not considered. The initial potential temperature profile has a constant value of
288K below 662.5m increasing by 6K km−1 above 712.5m. The surface roughness length
z0 is set to 0.01m. Periodic out-flow lateral boundary conditions are assumed.
In order to compare our results to those of a larger-scale model, for instance a Reynolds-
averaged (RA) model, we decompose the simulation domain into six sub-domains of dimen-
sion 4 km × 4 km × 1500m (labelled from A to F in Fig. 1). Each of these sub-domains has
the typical horizontal extension of one cell in a domain used by a RA model. All the results
are averaged on each of the sub-domains and the analysis is performed on the last hour of
the simulation.
The emission of inert scalars takes place in the sub-domain C, with all the released tracers
having a surface flux averaged over the full domain of 0.1 ppbm s−1. Five emission sce-
narios are considered, with each scenario differing from the other in terms of the emission
source coverage of the sub-domain C. For the first scenario, the passive tracer is released
over the entire sub-domain (see Fig. 1), while the other scenarios consider emitting surfaces
corresponding to 56.3, 25.0, 14.1 and 6.3% of the surface of sub-domain C. All tracers have
initially zero concentration and non-periodic boundary conditions are used meaning that
tracer loss at the boundaries is permanent. A snapshot taken at the end of the simulation
of the dispersion of the tracer SC5 is shown in Fig. 2. The outlined grid corresponds to the
sub-domains over which the results have been averaged. Note that we implicitly assume that
the emission data are given at a better resolution than the RA model resolution, but that may
not be always the case.
3 Dispersion of the Tracers
The size of the emission source has only a small impact on the concentration profile in
the sub-domain where the emission takes place (Fig. 3). However, the smaller the source is,
the larger is the concentration in the lower part of the boundary layer and the smaller it is in the
upper boundary layer. Over the downwind sub-domain (sub-domainD), more differences can
be noticed between the scenarios. The tracers SC3, SC4 and SC5 have the same behaviour
as reported in C. While the size of the emission and the shear forcing influence the profile of
the concentration for the smallest releases, SC1 and SC2 show the typical profiles expected
for tracers that are well mixed by turbulence. When non-uniform emissions are considered,
turbulence may not be efficient enough to mix the tracers through the CBL. Depending on
the travel time, the tracers can be transported downwind before being vertically mixed by
turbulence.
Whatever the size of the emission is in the sub-domain, a large-scale model will not make
any difference between tracers. As one sub-domain corresponds to one large-scale model
grid cell, the non-uniformity of the emission occurs at the subgrid scale and so is neglected.
All the scenarios presented here are simulated as one by the RA model; SC1. As we men-
tioned, by neglecting the subgrid-scale emission variability, no important impact is found
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4 J.-F. Vinuesa, S. Galmarini
A B
DC
E F
Fig. 1 Schematic representation of the emission scenarios
on the concentration levels calculated in C. On the contrary, it has an significant impact on
the concentrations calculated downwind. When the emission source is smaller than the RA’s
cell, the concentrations are systematically underestimated by the RA model. This is both the
result of the advection and the turbulent transport.
While the transport of tracers downwind acts as a sink for the concentration in the sub-
domain C, it is both a sink and a source of concentration in the sub-domain D. The scalar
released upwind (in sub-domain C) is advected into the sub-domain D and then removed by
advection downwind. To clarify the effect of the boundaries, it is useful to calculate explicitly
the different terms of the concentration budget equation
∂ci
∂t
= −
∂w
′c′i
∂z
+ Bci , (1)
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Dispersion of Non-uniform Emitted Scalars 5
Fig. 2 Contour plot of the SC5 instantaneous concentration at the end of the simulation and using a threshold
of 0.1ppb. The sub-domains are outlined using solid black lines
Fig. 3 Vertical profiles of the tracer concentrations averaged over the last hour of simulation
where, in addition to the traditional storage term on the l.h.s and the turbulent transport
contribution on the r.h.s, a new contribution appears due to the non-periodicity at the lateral
boundaries and to the sub-domain averaging procedure. This new contribution Bci includes
advection. Note that the overline denotes a sub-domain average. The profiles of the contri-
bution to the concentration budget equation are shown in Fig. 4, the terms are made dimen-
sionless using c
∗
as proposed by Cuijpers and Holtslag (1998):
w
∗
c
∗
=
1
zi
∫ zi
0
w
′c′1dz (2)
where w′c′1 is the concentration flux of the tracer SC1 in the sub-domain C.
In the sub-domain C, since the tracers are emitted at the surface, the boundary contribu-
tion Bci (Bo) acts as a source only there. Throughout the ABL, Bo removes the scalar from
the emitting cell whereas turbulent transport transfers and mixes material upwards. For all
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6 J.-F. Vinuesa, S. Galmarini
Fig. 4 Concentration budgets for SC1, SC2 and SC5. The terms are made dimensionless using c
∗
the scenarios, the budget profiles are similar. However, as the size of the emission reduces,
turbulence is more active in transporting a scalar from the surface to the lower part of the
boundary layer. In the sub-domain D, the boundaries’ contribution acts as a source in the
lower part of the CBL, and its contribution is balanced by turbulence that transports the scalar
from the lower to the upper boundary layer. In the upper CBL, Bo acts as a sink removing
material downwind. One can notice that all scenarios have almost identical profiles in the
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Dispersion of Non-uniform Emitted Scalars 7
upper CBL. However in the lower CBL, differences are noticeable and even increase close
to the surface. In the sub-domain C, the shrinking of the emission source makes its vertical
mixing less efficient. As a result, a larger part of the tracer is advected downwind before
being transported to the upper CBL. To understand further the reasons for this behaviour, we
extend our analysis to the vertical transport and the distribution of the scalars—see below.
4 The Sub-domain Averaged Second-Order Moments
4.1 Tracer Fluxes
In this section,we focus on the vertical transport of the tracers, and in Fig. 5, the dimensionless
concentration fluxes are shown. Within the boundary layer, the profiles of uniformly emitted
inert scalars have a linear shape (Deardorff 1979;Wyngaard andBrost 1984;Wyngaard 1985),
though in the sub-domain C, the fluxes clearly depart from linearity. The difference from
previous studies is the non-uniformity of the emission and the boundary conditions. Since
almost no differences can be noted between the tracer profiles, the non-linearity of the flux
is attributed to the use of non-periodic boundary conditions and therefore to non-stationarity
in the conditions.
In the sub-domain D, the shape of the flux profile is completely different mainly due to
the lack of emissions in this sub-domain. In addition to the question of identifying which
process is responsible for the flux profile, one may ask if the different contributions remain
the same regardless of the emission scenario. To do so, we calculate explicitly the different
terms of the following flux budget equation:
∂w
′c′i
∂t
= −w
′2 ∂ci
∂z
+
g
0
θ
′c′i +
∂w
′2c′i
∂z
− c′i
∂π
∂z
+ 
w
′c′i
+ B
w
′c′i
, (3)
where the storage or temporal term is the l.h.s. (St), and on the r.h.s., the terms are the
mean gradient (Gr ), the buoyancy (Bu), the turbulent transport (T t), the pressure (Pr ), the
dissipation (Di) and the boundary (Bo) contributions. When appropriate scaling is applied,
e.g., using c
∗
, the vertical profiles of the flux budget contributions for all the non-uniform
Fig. 5 Vertical profiles of the tracer fluxes averaged over the last hour of simulation
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8 J.-F. Vinuesa, S. Galmarini
Fig. 6 SC1 and SC2 dimensionless flux budgets. The terms are made dimensionless using w2
∗
c
∗
z−1i
emission scenarios are identical. Therefore we only show the SC1 and SC2 flux budgets in
Fig. 6.
We found similar general behaviours as reported in earlier studies (Moeng and Wyngaard
1984; Cuijpers and Holtslag 1998). The flux budget reveals a balance between the gradient
and the buoyancy production terms on the one hand, which are the major flux sources up to
themiddle of the boundary layer, and on the other hand the pressure and dissipation at smaller
scales that tend to destroy the fluxes. The transport contribution removes flux from the lower
boundary layer upwards with a maximum dissipating effect close to the surface. In addition
to these contributions, we found that the contribution of the boundaries is solely a sink in the
emitting cell and both a sink and a source downwind. Apart from this behaviour, we found
noticeable differences from previous studies, in particular in the relative importance of some
of the contributions. However, the level of non-uniformity is not relevant and no differences
are found between SC2 and the other scenarios.
Over the sub-domain C, the buoyancy production and the removal of flux due to the bound-
ary are the main processes affecting the flux. They are even two orders of magnitude more
important than the other processes. Also none of the contributions shows a peak at the top of
the boundary layer, and second, buoyancy is a source of flux throughout the ABL even in the
entrainment layer where it is known to act as a sink for uniformly emitted scalars (for instance
see Fig. 7a in Vinuesa and Galmarini (2007) where the same scaling approach is used). Over
the sub-domain D, the contributions are more important when the emission is non-uniform.
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Dispersion of Non-uniform Emitted Scalars 9
The buoyancy acts as a source up to the entrainment zone and then acts as a sink. In the lower
boundary layer, the gradient production does not contribute to the flux and its absence is not
compensated by the impact of the boundaries, leading to an underproduction of flux.
4.2 Tracer Variances
The profiles of the variances are quite different from the traditional view in which two peaks
are found, one close to the surface and the other at the entrainment zone. Since the maximum
scalar flux occurs with high scalar gradients near the surface, it is the mechanical production
of variance that is responsible for the peak observed there. At the entrainment layer, the con-
centration gradient across the capping inversion is mainly responsible for the second peak.
Obviously reducing the size of the emission source results in an increase in the mechanical
production of variance. This increase is dramatic in the sub-domain where the emission is
located (note the logarithmic x-axis used in Fig. 7). Another difference between the two sub-
domains, is that the profiles of the variances in the sub-domain C show significant vertical
gradients while they show a better mixed behaviour in the sub-domain D.
As we have done previously, we explicitly calculate the budget equation for the variance,
which reads:
∂c′2i
∂t
= −2w′c′i
∂ci
∂z
+
∂w
′c′2i
∂z
+ 2c′2i + Bc′2i
, (4)
where the r.h.s terms are the gradient contribution (Gr ), the turbulent transport term (T t),
the dissipation at smaller scales (Di) and the effect of the boundaries that includes advection
(Bo). The different contributions are shown in Fig. 8.
The different contributions show an overall behaviour similar to those in the budget of a
uniformly emitted scalar. The figure can be compared with Fig. 7 in Moeng and Wyngaard
(1984) where the budget for the potential temperature is shown. Briefly, the variance is pro-
duced by the gradient contribution close to the surface, and the turbulent transport transfers
variance for the surface to the upper boundary layer. The main difference is that there is no
(sub-domain C) or small (sub-domain D) variance production at the entrainment zone, which
explains the absence of the variance peak as reported in Fig. 7.
As the size of the emission is reduced, the variability of the tracer concentration increases
close to the surface. This also means that more variance can be transported by turbulence
Fig. 7 Vertical profiles of the tracer concentration variances averaged over the last hour of simulation
123

10 J.-F. Vinuesa, S. Galmarini
Fig. 8 SC1, SC2 and SC5 dimensionless variance budgets. The terms aremade dimensionless usingw
∗
c2
∗
z−1i
in the upper atmosphere and advected across the boundaries. Therefore, the main processes
responsible for the variance behaviour are these two latter contributions.
In the sub-domain C, the effect of the boundaries is to deplete the variance except close
to the surface where the boundaries act as a source. This generation of variance increases as
the emission source size shrinks and the boundaries balance the effect of turbulent transport.
Close to the surface, the removal of tracers by the advection outside of the sub-domain, and
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Dispersion of Non-uniform Emitted Scalars 11
the dilution by advection of clean air from upwind, affects the tracer concentration variability.
When the source is small, the plume concentration is high. These concentration differences
generate variance by mechanical production. Because of the concentration gradient between
the plume and the surrounding atmosphere, the generation of variance is too important to be
compensated by the advection of variance downwind. As a result, the boundaries act as a
source term. At upper levels, the plume concentration is lower due to vertical mixing by tur-
bulent transport. In this latter case, the advection of variance drives the boundary contribution,
ensuring it is a sink term in the budget equation.
In the sub-domain D, the advection of variance from upwind is the main source of con-
centration variability in the lower CBL. Turbulent transport transfers the variance upwards
where it is advected downwind by the boundary contribution.
In both sub-domains, the gradient term is unaffected by the size of the emission, a result
that could have been anticipated by the analysis of the concentration profiles shown in Fig. 3.
The vertical gradient of the tracer concentrations were almost unaffected by the emission
size in the sub-domain C.
5 Sensitivity Analysis
In this section, we extend our analysis by modifying the shear and the emission localization.
We look to the effects of changing the position of the emission source to the right, left, upwind
and downwind of the original scenarios, and try to identify whether substantial differences
occur. This is important since large-scale models do not discriminate between the mentioned
scenarios.
The three scalars included in each set have the same source size as SC3, SC4 and SC5
scenarios. All tracers have initially zero concentration and non-periodic boundary conditions
are used. In addition, we repeated the simulation for different constant westerly winds: 3
and 8m s−1 to look at the combined effect of advection and turbulence on our results. In the
following, we focus our analysis on the scenario SC5. In Fig. 9 a snapshot of the contour
plots of the different instantaneous concentration from the emission scenarios based on SC5
is shown. The results of these simulations are discussed in Sect. 5.
5.1 Effect of Emission Source Positioning
On the emitting cell, the shift of the centre of emission to the right and to the left of its original
location have no impact on the vertical profiles (Fig. 10). The profiles are strongly influenced
by the location when the change of the localization of the emission source follows the wind
direction. Obviously, when the source is located upwind, turbulence acts over a longer time
to transport the tracer upwards, and to mix it before the tracer is transported downwind. This
results in higher and better mixed concentration profiles than the profiles obtained for the
other emission scenarios.
In the sub-domain D, the picture is more complex. First the results for the right and left
tracers are not as similar as before. One should remember that each sub-domain has an even
number of cells in the x- and y-directions, meaning that the centre of the scenario SC5 is
not exactly in the centre of the sub-domain. Therefore even if the tracers emitted within the
left and right experiments have emission sources symmetrically positioned with respect to
the centre of emission of SC5, the distances between their emission sources and the side of
the sub-domain are different. In the previous paragraph, we noted that the profiles of tracers
123

12 J.-F. Vinuesa, S. Galmarini
Fig. 9 Contour plot of the different instantaneous concentration based on SC5 at the end of the simulation
and using a threshold of 0.1ppb. The sub-domains are outlined using solid black lines. The sets upwind,
downwind, right and left are represented in red, white, green and purple, respectively
Fig. 10 Same as Fig. 3 but tracers released from a source of same size as SC5
emitted from these sources were similar. But since the tracers are transported by turbulent
dispersion, greater differences will be found in cells located downwind of the actual emitting
cell.
The tracer released downwind shows a noticeable different behaviour than the others;
its concentration is higher in the lower boundary layer. Since the tracer is emitted close to
the downwind wall of the sub-domain, turbulence does simply not have time to transport it
upwards and to mix it. As a result the concentrations are higher in the low CBL and lower in
the upper CBL. The concentration budget (not shown), reveals that the boundary contribution
Bo is more than twice more active than for SC5, as shown in Fig. 4. If one considers the
travel time as the time needed for the tracer to reach the wall of the sub-domain and compare
it with the mixing time or turbulent turn-over time one can derive a criterion for the efficiency
of the mixing based on these two time scales. By analogy with the turbulent time scale, t
∗
,
which is defined as the boundary-layer depth zi divided by the convective velocity w∗, one
123

Dispersion of Non-uniform Emitted Scalars 13
can define a travel time scale Tt as the distance from the centre of emission source to the wall
divided by the mean wind. The mixing time scale Tm can be defined as the time needed for
a tracer to reach the top of the boundary layer i.e. 0.5 t
∗
. If the travel time scale is greater
than the mixing time scale, the tracer will be well-mixed in the sub-domain; turbulence is
efficient enough to transport it upwards and to mix it. If the travel time scale is smaller than
the mixing time scale, the tracer is transported downwind before being vertically mixed.
The travel time scales calculated for the different scenarios and shown in Table 1 indicate
that the tracer released upwind will show a not well-mixed profile in the sub-domain C for all
the westerly winds considered. Also for a constant westerly wind of 8m s−1, turbulence is
not efficient enough to mix the tracers before they are transported downwind. These results
are in agreement with those shown in Figs. 10 and 12.
One should notice that we do not include Coriolis forcing in our simulations, meaning
that the tracers released upwind, in the centre and downwind are aligned with the mean wind
while the scenarios right, centre and left are aligned across the wind. These two alignments
represent extreme cases; if one considers aligned sources of tracers, the angle between the
line of tracers and the mean wind can vary from zero, i.e. the sources are aligned with the
wind, to 90◦, i.e. the alignment is perpendicular to the wind. It is likely that real emission
situations will show alignment of source with the centre of the cell not perfectly parallel or
perpendicular to the direction of the mean wind. Therefore this sensitivity analysis shows
the extrema of the effects of the position of the emission sources on the turbulent disperion
of the tracers.
Figure11 shows differences between the profiles of the tracers.However in the sub-domain
C, and in the first layer of the model, the variances are the same. The emissions are imposed
Table 1 Travel and mixing time-scales in seconds calculated over the last hour of simulation for SC5
3m s−1 5m s−1 8m s−1
Tm Tt Tm Tt Tm Tt
Centre-left-right 331 667 334 400 345 250
Upwind 331 1000 334 600 345 375
Downwind 331 300 334 180 345 112.5
Fig. 11 Same as Fig. 7 but tracers released from a source of same size as SC5
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14 J.-F. Vinuesa, S. Galmarini
as a flux, meaning that the amount of pollutant released in the atmosphere depends on the
turbulent properties of the ABL and the position of the source, as do the concentrations.
One could expect to find the same result for the variances since they are calculated from
the concentrations, i.e. we do not impose a boundary condition at the surface or a “surface
concentration variance flux”. However we found that the variance close to the surface, i.e. in
the first layer of the model, does not depend on the emission source position.
5.2 Effect of Different Westerly Winds
Reducing shear results in reducing the amount of tracer advected downwind (Fig. 12). The
tracers remain longer in the sub-domain C, and as a result, turbulent transport is able to
improve the vertical mixing.
Figure13 shows that the concentration variance at the surface in the sub-domain C
is not affected by the imposed westerly winds. We have seen earlier that the variance
does not depend on the position of the emission source, which is of great importance for
Fig. 12 Same as Fig. 3 with different constant westerly winds and with tracers released solely from a source
of same size as SC5
Fig. 13 Same as Fig. 7 with different constant westerly winds and with tracers released solely from a source
of same size as SC5
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Dispersion of Non-uniform Emitted Scalars 15
large-scale modelling. It means that providing the large-scale model with the appropriate
emission variance flux as a boundary condition is sufficient to account for the subgrid-scale
emission variability. The accuracy of concentration variance calculations will only depend
on the performance of the existing turbulent closure included in the model.
6 Summary and Conclusions
Using large-eddy simulation in realistic conditions, i.e. non-periodic lateral boundary
conditions for the tracer and emission scenarios involving different emission source sizes, we
performed a complete analysis of the vertical distribution and turbulent transport of spatially
non-uniformly emitted tracers. We used sub-domain averaging where each sub-domain has
the typical horizontal extension of a large-scale model grid cell. We explicitly calculated the
different contributions to the concentration, flux and variance budget equations, and identified
the scale of interaction between the emission patterns and the upper-air concentrations.
At the subgrid scale, whatever the size of the emission source, a large-scale model does
not make any differences between tracers released from different sources. We found that this
assumption leads to an important under-estimation of the concentration downwind. From
the concentration budget equation, we found a perfect balance between turbulent transport
and the effect of the boundary. The flux profiles in the emitting cell and downwind are not
influenced by the size of the emission as are the different contributions to the flux budget.
However, the variances are dramatically affected by the size of the emission, mainly by turbu-
lence that transports scalar variability from the surface to the whole CBL. This contribution
becomes more and more important as the emission size shrinks.
By analysing different emission source localizations and constant westerly winds, we
found that the concentration variance at the surface in the emitting sub-domain is solely
dependent on the emission flux variance. This is particularly significant for air quality mod-
els that do not solve explicitly turbulence, since they can use the emission variance flux from
the emission inventory as a boundary condition or a source term in their parameterization for
the variability of the pollutant concentration as anticipated by Galmarini et al. (2008).
Acknowledgements Computations were performed on the Linux cluster of the PROCAS action of the Insti-
tute for Environment and Sustainability. The authors wish to thank A. Stips and P. Simons who kindly provided
the access to this facility.
References
Auger L, Legras B (2007) Chemical segregation by heterogeneous emissions. Atmos Environ 41:2303–2318
Chatfield RB, Brost RA (1987) A two-stream model of the vertical transport of trace species in the convective
boundary layer. J Geophys Res 92:13262–13276
Cuijpers JWM, Duynkerke PG (1993) Large eddy simulations of trade wind with cumulus clouds. J Atmos
Sci 50:3894–3908
Cuijpers JWM, Holtslag AAM (1998) Impact of skewness and nonlocal effects on scalar and buoyancy fluxes
in convective boundary layers. J Atmos Sci 55:151–162
Deardorff J (1979) Prediction of convective mixed-layer entrainment for realistic capping inversion structure.
J Atmos Sci 36:424–436
Ebert EE, SchumannU, Stull RB (1989) Nonlocal turbulentmixing in the convective boundary layer evaluated
from large-eddy simulation. J Atmos Sci 46:2178–2207
Fiedler BH, Moeng C-H (1985) A practical integral closure model for the mean vertical transport of a scalar
in a convective boundary layer. J Atmos Sci 42:359–363
123

16 J.-F. Vinuesa, S. Galmarini
Galmarini S, Vinuesa J-F, Martilli A (2008) Modelling the impact of sub-grid scale emission variability on
upper-air concentration. Atmos Chem Phys 8:141–158
Krol MC, Molemaker MJ, Vilà-Guerau de Arellano J (2000) Effects of turbulence and heterogeneous emis-
sions on photochemically active species in the convective boundary layer. J Geophys Res 105:6871–6884
Lamb RG (1978) A numerical simulation of dispersion from an elevated point source in the convective bound-
ary layer. Atmos Environ 12:1297–1304
Moeng C-H, Wyngaard JC (1984) Statistics of conservative scalars in the convective boundary layer. J Atmos
Sci 41:3161–3169
Nieuwstadt JC, de Valk JPJMM (1987) A large eddy simulation of buoyant and non-buoyant plume dispersion
in the atmospheric boundary layer. Atmos Environ 21:2573–2587
Schumann U (1989) Large-eddy simulation of turbulent diffusion with chemical reactions in the convective
boundary layer. Atmos Env 23:1713–1729
Siebesma AP, Cuijpers JWM (1995) Evaluation of parametric assumptions for shallow cumulus convection.
J Atmos Sci 52:650–666
Sun W-Y, Chang C-Z (1986) Diffusion model for a convective layer. Part 2: plume released from a continuous
point source. J Climate Appl Meteorol 25:1454–1463
Vilà-Gueraude Arellano J, Cuijpers JWM (2000) The chemistry of a dry cloud: the effects of radiation and
turbulence. J Atmos Sci 57:1573–1584
Vinuesa J-F, Galmarini S (2007) Characterization of the 222Rn family turbulent transport in the convective
atmospheric boundary layer. Atmos Chem Phys 7:697–712
Wyngaard JC (1985) Structure of the planetary boundary layer and implications for its modeling. J Appl
Meteorol 24:1131–1142
Wyngaard JC, Brost RA (1984) Top-down and bottom-up diffusion of a scalar in the convective boundary
layer. J Atmos Sci 41:102–112
123