We present a computationally inexpensive method for individually quantifying the contributions from different sources to local air pollution. It can explicitly distinguish between regional–background and local–urban air pollution, allowing for fully consistent downscaling schemes.

The method can be implemented in existing Eulerian chemical transport models and can be used to distinguish the contribution of a large number of emission sources to air pollution in every receptor grid cell within one single model simulation and thus to provide detailed maps of the origin of the pollutants. Hence, it can be used for time-critical operational services by providing scientific information as input for local policy decisions on air pollution abatement. The main limitation in its current version is that nonlinear chemical processes are not accounted for and only primary pollutants can be addressed.

In this paper we provide a technical description of the method and discuss various applications for scientific and policy purposes.

The origin of atmospheric pollutants within a given region is one of the fundamental questions of air quality research. Degradation of air quality, either temporary or sustained, is often the result of both local and long-range-transported air pollution, originating from anthropogenic but also natural emission sources. Anthropogenic emissions are due to a large number of different categories such as road traffic, industrial point sources and large area sources.

In order to devise optimal strategies for air pollution abatement, for example short-term or long-term emission reduction measures, air quality managers need to have access to reliable scientific knowledge about the origin of air pollution. Typical questions include the following: (a) by what amount can local air pollution be reduced through local measures only, and in which cases will regional or countrywide measures be necessary? (b) What will be the benefit of emission reduction measures imposed on one or several specific emission sectors? (c) Will these measures be efficient on a short time frame or should they be implemented on a longer-term basis?

Many different methods exist to extract information about the origin of air pollution

The simplest method to evaluate the importance of different emission sources in a CTM is the “direct” method

Many chemical processes in the atmosphere are nonlinear. For example, a doubling of the emissions from one specific source will not necessarily double its contribution to air pollution levels. This also implies that the sum of contributions (from individual sources) calculated by the direct method (or by perturbation methods) will in general not be equal to the total air pollution level calculated in a simulation in which emissions from all sources are included in full. Consequently, one has to distinguish between two different questions: (1) what is the effect of a change in emissions from individual sources on air pollution (air pollution sensitivity)? (2) What are the contributions of individual sources to air pollution (source apportionment)? Due to nonlinearities, question 2 cannot be answered by reducing the emissions of individual sources to zero one by one. An alternative approach to estimate contributions from individual sources in model calculations is a technique known as “tagging”, which distinguishes chemically identical molecules according to their sources. In the calculation the molecule is labeled (e.g., by a separate index) according to its source and then keeps this label during transport and chemical transformations. When analyzing air pollution levels within a given receptor area, the fractions of molecules with different labels can be considered separately, thereby giving an estimate of the contributions from the different sources. A series of methods have been proposed to address the contribution from different sources based on the tagging method

Tagging methods are also useful for tracing primary pollutants

In this regard, “adjoint models”

Still, only a relatively small number of sources or receptors at a time can be analyzed by all these methods. Perturbation methods calculate all receptor values for one source group, tagging methods compute all receptors for a limited number of source groups and adjoint models address all sources for one receptor group. Ideally, all contributions to all receptor points should be described.

In this paper we present a method that can efficiently calculate the contribution of a significantly larger number of sources (thousands or more) to a limited (but large) number of receptor regions. This method does not provide results that cannot be obtained by other means, but it does so at a lower computational cost and is thus well suited, especially for time-critical operational applications. It can be built on top of existing Eulerian CTMs relatively easily and thereby has the potential to offer a new range of applications.

An important limitation is that the method is limited to primary pollutants, for which linearity can be assumed. It will thus complement existing methods but not replace them.

In principle the method allows for the definition of any group of sources, but here we will show results only for the case in which each source is defined within a single grid cell. One key limitation, which makes the method manageable, is that the tagged values are stored only up to a preset horizontal and vertical distance from their source. We will call the region within this distance the “local region”. The size of this region must be set as a balance between computational cost and the accuracy requirement of the application.

In the following section we describe the method in technical detail, while in Sect. 3 we show concrete examples of what kind of results the method can provide and how to quantify some of the limitations associated with the method. The results will also be compared against the direct method. In Sect. 4 we will give an overview of what is required to implement the method in an existing CTM and discuss the performance in the EMEP MSC-W implementation. Finally, in the last section we discuss possible applications of the method and plans for further development.

In theory the method corresponds to a tagging method, whereby pollutants from different origins are tagged and their values are traced and stored individually. However, the total amount of pollutant is not computed as a sum of tagged values; instead the tagged values show which fraction of the total pollutants originates from a specific origin.

We define the local fraction LF

The total pollutant is abbreviated TP; it could be the air concentration of particulate matter, for example. The local pollutant, LP

In a time-splitting framework the different physical processes are included sequentially, and we will show in the next sections how the value of the local pollutant changes during each of them. For simplicity, the initial value for LF

The local pollutant and local fraction are associated with a particular emission source category (

For instance,

Transport of pollutants will mix pollutants from different origins. We will individually trace the local pollutant due to different sources and from every horizontal grid cell within the source region. We need then two sets of position indices, one for the origin (source region) and one for the actual position (receptor grid cell):

We call the region delimited by all

Pollutants can be traced within this region. If they leave the local region, they are no longer identifiable by the method, even if they return to the local region.

Let us consider a flux of pollutant,

If the flux is exiting the grid cell

For diffusion we compute the effect of diffusion directly on every local pollutant:

In a practical implementation it is not necessary to include all the vertical levels, as the contribution from higher levels is negligible (it corresponds to pollutants leaving and returning to the local region during the same time step). In our implementation we include only two layers above the highest local region considered.

For convection the same procedure can be used by replacing the diffusion operator in Eq. (

For deposition (dry or wet), we can assume that the same fractions of local and total pollutants are removed. Therefore, the local fraction will not vary during the deposition process:

To fully follow the pollutants through all the chemical reactions would, in principle, require an explicit reference to all the sources and grids. It is possible to reduce the size of the problem if linearity is assumed. This has been done by other groups

Time evolution of the local fraction of PM

The local fractions will depend on a broad range of factors such as emission distributions, meteorological conditions, grid resolution, chemical regime and the size of the local region. It is beyond the scope of this article to systematically quantify how all the possible situations affect the local fractions. The limitations of the method should be estimated for each concrete application. The examples in this section also provide methods for estimating different errors associated with the method (limitation of the size of the local region, nonlinearities).

The local fraction

Example of the spatial distribution of the local fraction of PM

Example of local fractions as a source map. The values show the fraction of PM

The results shown in this section are based on a grid with a resolution of 0.3

In Fig.

Figure

For a fixed value of

Figure

In order to compare with the direct method, one can “invert” LP

Receptor map for a single grid cell emission obtained through the direct method (left panels) and the local fraction method (right panels) averaged over 1 month (March 2016). Concentrations of PM

Figure

by removing the emissions from a single grid cell and computing the difference with the normal case (direct method) and

by using one single run and Eq. (

Note that for the purposes of this experiment we have chosen a zero-order advection scheme in all model runs. The default fourth-order scheme is slightly nonlocal, and the direct method would give spurious results very close to the sources; tracking and direct methods would give different results. For example, in the fourth-order scheme, if emissions are

For source apportionment applications, the focus is typically on horizontal transport. Nevertheless, the code should trace the pollutants with a combination of vertical and horizontal transport. Over short distances only transport through the lowest layers needs to be considered. If the focus is on regions where most of the pollutants are transported over long distances, the vertical extent of the local area should be chosen large enough.

Sensitivity of the concentration of PM

Concentration of

Figure

For

For local regions that are large enough, the source of all primary particles can be accounted for. This can be verified directly by summing all the local fractions for a given grid cell:

Sum of all local fractions (Eq.

Sum of all local fractions (Eq.

A sum of 1 means that all sources are accounted for. The difference between the sum of the local fractions and 1 gives the fraction of pollutants with sources outside the local region.
In Fig.

Figure

Note that incomplete results are not a measure of an error in the method. Rather, they show the amount of pollutant with sources outside the local region, which is useful information.

From an implementation point of view the method is a “diagnostic” calculation in the sense that it gives additional information extracted from existing data, in opposition to a modification of the method for the computation of the concentrations of air pollutants. Therefore, the method can be implemented on top of an existing CTM without having to rewrite the code for the main processes. What is required is including calls to new routines that can perform the operations described in Sect.

Define the instantaneous local fraction six-dimensional array

Write a routine that performs the operations from Sect.

As input for those routines, the main code must make available the emission rates of the relevant sectors and the advection fluxes.
If the fluxes are not available or in a simplified version, the fluxes could be defined directly by another method. For example, an already good approximation would be to take

In Eq. (

In addition, of course, the calls to those new routines have to be integrated into the main code. Also, switches to choose the pollutants and the sizes of the local region have to be created.

There is no feedback of the LF calculations to the concentrations of air pollutants; those will be unaffected by the new routines. This clear separation greatly simplifies the practical development.

In the EMEP MSC-W implementation (rv4_33), all the extra routines are put in a separate file (uEMEP_mod.f90), except for the LF communication routine. If no LF output is required, those routines are not used at all, and if the LF routines are called, the rest of the code still performs exactly the same operations.

Since one of the key advantages of the local fraction method is its low computational demand, we will give a few concrete examples of the computational cost for providing the local fraction values in our implementation. The transformations carried out for the calculation of local fractions presented in Sect.

The calculation of the local fractions only needs information from the nearest neighbors (see Eq.

Additional computation time needed for the calculation of local fractions in different settings, expressed in percent in comparison to the total time needed when the calculation of local fractions is not included. The first column shows the dimensions of the local region. The second column shows the total additional time required. Columns three to eight show the breakdown of those fractions into the different subroutines (“comm.” stands for communication time between compute nodes). “Other” shows the difference between total time and its components (it is principally due to uncontrolled differences in the speed of the different compute nodes). The last column shows the additional memory required in total; it has to be multiplied by the number of species or sectors requested. The total time without the calculation of local fractions in our test was 553 s.

In order to illustrate the computational cost, we can consider a typical model run on a

If one is only interested in the nearby sources (within a city, for example), the local fractions can be calculated at almost no additional cost. Remote sources can still be described, but at an additional cost.

A substantial amount of time can be required for writing results to disk if all results are required at finer time resolution, for example every hour (in Table

Local fractions are a new concept that can help us understand and analyze the origin of primary pollutants. It has the potential to be developed further, and a new range of applications is still being developed.

Compared to other approaches, there are always trade-offs. The present method cannot at present describe nonlinearities. That excludes all studies of ozone. Long-range transport will also become unpractical at some point, although this is not inherent to the method and could be implemented in the near future.

Source–receptor relationships can be produced for any source and receptor within a region around the source. The size of this region can be chosen to be relatively large (100 grid cells or more). Since the fluxes are given from and to individual grid cells, small regions (typically cities) can be studied simply by adding up individual grid cell contributions. These small regions do not have to be predefined in the model simulations. Indeed, the relative contributions of sources that contribute to the pollutants within a city covering several grid cells can be determined in a post-processing step using graphical user interfaces at which the user can choose the source region and source categories interactively.

Still, the method provides information about transport within a limited region only (the local region). The choice of the size of this region is a balance between the computational cost and the distance to the sources of interest. For the study of a city, it may be sufficient to include a region covering the agglomeration. The total pollutants from sources outside the local region are still quantified, but without the specification of their location, using the method presented in Sect.

If the goal is to provide source–receptor matrices for large regions (countries), then this method is probably not appropriate in its present form as the computational cost may be too high, and the level of detail provided is not needed. For such an application the method should be modified so that the tracking is not done for individual grid cells but for larger source areas or group of emission sources.

One obstacle to combining fine-scale (urban) and regional modeling is the problem of “double counting”. In the regional-scale model, there is usually only one total concentration value, without distinction between its origins. Distinguishing between urban and background pollution can be difficult in practice

Ideally, the regional model should only compute the background–regional contributions and the fine-scale model can then add the local contribution. In a city, scales down to street level may be required. Those very fine-scale models will not accurately compute the transport between distant streets within the city, and the regional model must account for those. But if the same emission sources are included in both the regional- and fine-scale model, they will be accounted for twice.

The local fractions can give the relative contributions from different sources directly. Thus, it is possible to either redistribute or replace only the appropriate local contributions using the more accurate fine-scale model.

An example for an operational downscaling tool is uEMEP (urban EMEP), which combines the method described in this paper with the EMEP MSC-W air quality model

Concentrations of pollutants near the surface are required to assess health impacts or dry deposition. However, in many CTMs, the lowest layer is several tens of meters thick, and the concentrations of pollutants will have a nonconstant vertical profile within the layer. The shape of the profile will depend on the local conditions: if the pollutants are emitted locally at the surface the concentration will typically decrease with height, while the opposite is true for background pollutants. With knowledge of the local fractions it is possible to improve the description of the vertical profile and thus obtain a more accurate estimation of, for instance, 3 m concentrations (useful for health impact studies) or dry deposition rates.

As shown in Figs.

In this work, sources are always defined in an individual grid cell. The relative position of the source,

In the future we plan to generalize the method to also include chemical processes in some simplified form. The ambition is to still provide information for a very large number of sources but to describe chemical processes in an approximate way. Compared to existing tagging methods, it will trade accuracy for computational efficiency.

The full EMEP MSC-W model code and main input data are publicly available through a GitHub repository under a GNU General Public License v3.0 (name emep-ctm). The routines related to the local fractions are part of the standard model. The exact version of the model used to produce the illustrative examples used in this paper (rv4.33) is archived on Zenodo (

All authors contributed to the discussion and development of the main ideas, the applications, and the preparation of the paper. PW wrote the corresponding Fortran code.

The authors declare that they have no conflict of interest.

The computations were performed on resources provided by UNINETT Sigma2 – the National Infrastructure for High Performance Computing and Data Storage in Norway.

This research has been supported by the AirQuip project funded by Norges Forskningsråd (grant no. 267734).

This paper was edited by Patrick Jöckel and reviewed by two anonymous referees.