Chemical Mass Balance Model (CMB8.2)Where CMB can be usedPrinciplesSources and ReceptorsModeling ProceduresCMB MathematicsSlide 7ExampleAssumptionsSolution to CMB EquationsEffective Variance Weighted Linear Least Square MethodSlide 12Why Effective Variance Weighted Solution?7-Step Applications & Validation ProtocolModified CMBSummaryChemical 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?01/13/20191Aerosol & Particulate Research LabWhere 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. 01/13/20192Aerosol & Particulate Research LabPrinciples•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. 01/13/20193Aerosol & Particulate Research LabQ: What are the most common species data for CMB?8123,4,5,1267910111314PM10 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 0.2Sources and ReceptorsQ: Include sources from Tampa, Orlando & Jacksonville?01/13/2019 4Aerosol & Particulate Research LabReceptor 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 equations01/13/20195Aerosol & Particulate Research LabCMB 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 sources01/13/2019Aerosol & Particulate Research Lab 6jjjEDS  dtxttudDTjj0),(),(Dispersion factorJjjJjjjSEDC11•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.01/13/20197Aerosol & Particulate Research LabQ: What factors can affect Fij? JjjijiSC1FExample•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) 01/13/20198Aerosol & Particulate Research LabQ: 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). 01/13/20199Aerosol & Particulate Research LabQ: 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 squares01/13/2019Aerosol & Particulate Research Lab 10Effective 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 variance01/13/201911Aerosol & Particulate Research Lab  IiJjJI1212/1ijejijiVSFC222ijiFjCSijeViCStandard deviation uncertainty of the Ci measurementStandard 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)01/13/201912Aerosol & Particulate Research Lab CVFFVFS1eT11eT  01.0/11 kjkjkjSSSWhy 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