Chemical mass balance models

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The text on this page is taken from an equivalent page of the IEHIAS-project.

Chemical mass balance (CMB) models combine the chemical and physical characteristics of gases and particles measured at the sources and measurement sites (receptors) both to identify the presence of, and to quantify source contributions to, receptor concentrations. The CMB model is a multiple regression model. Although most commonly used for PM and VOC source apportionment in air, it can equally be applied to other contaminants and environmental media, such as soil and sediments, wet and dry deposition and water pollution. CMB models quantify contributions from chemically distinct source-types and major individual sources (e.g. industries), rather than from individual emitters.



Chemical mass balance models are one of a suite of statistical methods that can be used to apportion measured pollutant concentrations (or exposures or doses) to their sources, and to assess the proportional contribution of each source.

Major assumptions

  • all sources contributing significantly to measured concentrations are identified and their emission source profiles are characterised;
  • the source profiles are constant over the receptor and source sampling period;
  • species included are not reactive (i.e. they add linearly);
  • numbers of species (j) are greater than or equal to number of sources (p);
  • source profiles (fpj) are linearly independent of each other;
  • measurement errors (eij) are random, uncorrelated and normally distributed.

Weaknesses and limitations

  • complete information is necessary on the composition of emissions for each and every significant source (emission profiles) - these data are often limited;
  • source profiles are often site-specific so cannot easily be generalised - e.g. local sources of soil and road dust are usually different from location to location; power plant emissions may vary from one power plant to another;
  • emission profiles vary over time so data based on short runs of measurements may not be representative - e.g. road vehicle emissions change due to short-term changes in driving behaviour and ambient conditions, and longer term changes in fuel composition, vehicle design, emission control technology, and vehicle fleet composition;
  • missing data can greatly impair the analysis;
  • the method does not directly identify the presence of unknown and unspecified sources, so a considerable proportion of the measured pollutant load may be unexplained;
  • chemically similar sources may result in analytical problems (collinearity);
  • the method does not apportion secondary pollitants, but secondary compounds can be used to identify the contribution from sources outside the studied area


For exposure assessment the number of samples taken and analysed must be representative both in time and space.

Method description


CMB models require input data on:

  • measured pollutant concentrations at sample (receptor) locations;
  • pollutant composition of emissions for all major sources (source profiles).

Source profiles comprise data on the mass fraction of chemical species (or other components) in the emissions from each source type. Information about uncertainties in the measured concentrations and source profiles should also be provided, where available.

A requirement is that the number of species considered is equal to, or greater than, the number of sources.


CMB models estimate the amount contributed by each source type to the total concentration (mass) both of each chemical species, and the overall pollutant load, at the receptor locations. The output also includes estimates of uncertainties.


The CMB approach is designed to provide estimates of the source contributions to observed pollutant concentrations on the basis of knowledge about source characteristics - i.e. the emission profile for each source.

One of its advantages is that only a few measurements are needed and single ambient samples can be analysed. The CMB source apportionment identifies specific, known sources and estimates quantitative uncertainties in the source contribution estimates.


The ambient chemical concentrations are expressed as the sum of the products of species abundances and source contributions. The equations are solved for source contributions, using the ambient concentrations and source profiles as inputs

CMB models can be applied when the measured ambient concentration of different species (Cij ) and the number of sources and their profiles (p and fpj) are known. The mass contribution from each source to each sample (gip) is found by a least squares solution of the overdetermined system of equations.

The chemical mass balance can be expressed in the following way:

CMB equation.jpg


p is the number of sources;

j is the number of species, with jp;

Cij is the measured ambient concentration of species j in samplei;

fpj (source profile) is the fractional concentration of species j in the emissions from source p;

gip is the concentration contribution of source p to samplei;

eij is the portion of the measured elemental concentration that cannot be explained by the model.

See also

Tools for CMB:

More information on source attribution:

Other source attribution methods: