Chemical Mass Balance Model ( CMB8.2)

04/22/2023 Aerosol & Particulate Research Lab 1

Chemical Mass Balance Model (CMB8.2)

• A receptor model for assessing source apportionment using ambient data and source profile data with appropriate uncertainty estimates.

• Version 8.2 available at EPA Support Center for Regulatory Air Models - http://www.epa.gov/ttn/scram/receptor_cmb.htm

Q: What’s the use of CMB?

http://www.epa.gov/ttn/scram/receptor_cmb.htm

http://www.epa.gov/ttn/scram/receptor_cmb.htm


Where CMB can be used• Complement rather than replace other modeling

methods• Explain observations already have been taken; does

not predict the future• Can be use to estimate the effects of emission

reduction if source contributions are proportional to emissions

• Can be coupled with visibility model or aerosol equilibrium model to estimate the effects on secondary pollutants.

• Discrepancies between model results help identify and improve their weakness and apply uncertainty bounds that should be used when designing control strategies.


Principles• A solution to linear equations that express each receptor

chemical concentration as a linear sum of products of source profile abundances and source contributions.

• Mass and chemical compositions of source emissions are conserved from the time of emission to the time the sample is taken.

Q: What are the most common species data for CMB?


81

23,4,5,12

6

7

9

1011

1314

PM10 emissions from permitted sources in Alachua County (tons) (ACQ,2002)

2000 Values1. GRU Deerhaven 144.22. Florida Rock cement plant 34.353. Florida Power UF cogen. plant 3.19

1997 Values4. VA Medical Center incinerator 0.25. UF Vet. School incinerator 0.26. GRU Kelly 1.97. Bear Archery 9.58. VE Whitehurst asphalt plant 4.99. White Construction asphalt plant 0.710. Hipp Construction asphalt plant 0.311. Driltech equipment manufacturing 0.2

Sources and Receptors

Q: Include sources from Tampa, Orlando & Jacksonville?

Receptor Sites12. University of Florida13. Gainesville Regional Airport14. Gainesville Regional Utilities

(MillHopper)


Modeling Procedures

• Identify the types of contributing sources• Select chemical species or other properties to be

included in the calculation• Determine the fraction of each of the chemical

species which is contained in each source type (source profiles)

• Estimate the uncertainty in both ambient concentrations and source profiles

• Solve the chemical mass balance equations


CMB Mathematics• Source contribution (Sj) present at a receptor during

a sampling period of length T due to a source j with constant emission rate Ej is

• Exact knowledge of Dj is not necessary for CMB• The total mass measured at the receptor from J

number of sources, is a linear sum of the contributions from individual sources

jjj EDS

dtxttudDT

jj 0

),(),( Dispersion factor

J

jj

J

jjj SEDC

11


• For elemental component i,

Ci is the concentration of species i measured at the receptor site,Fij is the mass fraction of species i in the emission from source j, and Sj is the total mass contribution from source j in the sample at the receptor site.Q: What factors can affect Fij?

J

jjiji SC

1

F


Example• Total Pb concentration (ng/m3) measured at the site:

a linear sum of contributions from independent source types such as motor vehicles, incinerators, smelters, etc PbT = Pbauto + Pb incin. + Pbsmelter +…

• Next consider further the concentration of airborne lead contributed by a specific source. For example, from automobiles in ng/m3, Pbauto, is the product of two cofactors: the mass fraction (ng/mg) of lead in automotive particulate emissions, FPb, auto, and the total mass concentration (mg/m3) of automotive emission to the atmosphere, Sauto

• Pbauto = Fauto (ng/mg) × Sauto (mg/m3air)

Q: What are the assumptions used in CMB?


Assumptions• Compositions of source emissions are constant over

period of ambient and source sampling,• Chemicals do not react with each other (i.e. they add

linearly),• All sources have been identified and have had their

emission characterized,• The number of source categories (J) is less than or

equal to the number of chemical species (I) for a unique solution to these equations,

• The source profiles are linearly independent of each other, and

• The measurement uncertainties are random, uncorrelated, and normally distributed (EPA, 1990).

Q: Can all these assumptions be totally complied?


Solution to CMB Equations• Single unique species to represent each source

(tracer solution)• Linear programming solution• Ordinary weighted least squares, weighting only

by uncertainty of ambient measurements• Ridge regress weighted least squares• Partial least squares• Neural networks• Effective variance weighted least squares


Effective Variance Weighted Linear Least Square Method

• The most probable values for Sj when I > J are achieved by minimizing 2 (difference between measured value, ci, and calculated value, FijSj, weighed by analytical uncertainty)

where the denominator is called effective variance

I

i

J

jJI 1

2

1

2 /1ijejiji VSFC

222iji FjC S

ijeV iC Standard deviation uncertainty

of the Ci measurement

Standard deviation uncertainty of the Fij measurementijF


• The solution in matrix form is

• Sj is initially set to 0. An iterative procedure is applied until Sj does not change more than 1% from step to step (k k+1)

CVFFVFS 1e

T11e

T

01.0/ 11 kj

kj

kj SSS


Why Effective Variance Weighted Solution?

• Theoretically yields the most likely solution to the CMB equations

• Uses all available chemical measurements, not just so-called “tracer” species

• Analytically estimates the uncertainty of the source contributions based on uncertainty of both the ambient concentrations and source profiles

• Gives greater influence to chemical species with lower uncertainty in both the source and receptor measurements than to species with higher uncertainty


7-Step Applications & Validation Protocol

• Determine model applicability• Select a variety of profiles to represent identified

contributors• Evaluate model outputs and performance measures• Identify and evaluate deviations from model

assumptions• Identify and correct model input deficiencies• Verify consistency and stability of source

contribution estimates• Evaluate CMB results with respect to other data

analysis and source assessment methods


Modified CMB

• Risk Apportionment: instead of chemical abundance, risk is the target goal

• Isotopic abundances, specific organic compounds, single particle morphology may also be used

Q: Can aged profiles be used in CMB?


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Chemical Mass Balance Model ( CMB8.2)