Estimation of secondary organic aerosol formation parameters for the volatility basis set combining thermodenuder, isothermal dilution, and yield measurements

. Secondary organic aerosol (SOA) is a major fraction of the total organic aerosol (OA) in the atmosphere. SOA is formed by the partitioning onto pre-existent particles of low-vapor-pressure products of the oxidation of volatile, intermediate-volatility, and semivolatile organic compounds. Oxidation of the precursor molecules results in a myriad of organic products, making the detailed analysis of smog chamber experiments difﬁcult and the incorporation of the corresponding results into chemical transport models (CTMs) challenging. The volatility basis set (VBS) is a framework that has been designed to help bridge the gap between laboratory measurements and CTMs. The parametrization of SOA formation for the VBS has been traditionally based on ﬁtting yield measurements of smog chamber experiments. To reduce the uncertainty in this approach, we developed an algorithm to estimate the SOA product volatility distribution, effective vaporization enthalpy, and effective accommodation coefﬁcient combining SOA yield measurements with thermograms (from thermod-enuders) and areograms (from isothermal dilution chambers) from different experiments and laboratories. The algorithm is evaluated with “pseudo-data” produced from the simulation of the corresponding processes, assuming SOA with known properties and introducing experimental error. One of the novel features of our approach is that the proposed al-gorithm estimates the uncertainty in the predicted yields for different atmospheric conditions (temperature, SOA concentration levels, etc.). The uncertainty in these predicted yields is signiﬁcantly smaller than that of the estimated volatility distributions for all conditions tested.


S1. Constructing Data for Evaluation
Table S1: Values of the true properties (volatility distribution of the products, vaporization enthalpy, accommodation coefficient) for three SOA systems used to generate data for pseudo-experiments A, B and C.     highest count in every X column (Tikkanen et al., 2019).highest count in every X column (Tikkanen et al., 2019).

Figure S1 :
Figure S1: "Measurements" of Test A1 in Experiment A (red dots), true (red line) and estimated (blue line) yields at (a) 5 o C, (b) 15 o C, (c) 25 o C, and (d) 35 o C), (e) TD (thermogram), and (f) dilution (areogram) values.The relative curve density is calculated by discretizing the dependent variable Y and independent X variable into grids, counting how many curves go through a grid box and finally normalized by the

Figure S2 :
Figure S2: "Measurements" of Test B1 in Experiment B (red dots), true (red line) and estimated (blue line) yields at (a) 5 o C, (b) 15 o C, (c) 25 o C, and (d) 35 o C), (e) TD (thermogram), and (f) dilution (areogram) values.The relative curve density is calculated by discretizing the dependent variable Y and independent X variable into grids, counting how many curves go through a grid box and finally normalized by the

Figure S3 :
Figure S3: "Measurements" of Test C1 in Experiment C (red dots), true (red line) and estimated (blue line) yields at (a) 5 o C, (b) 15 o C, (c) 25 o C, and (d) 35 o C), (e) TD (thermogram), and (f) dilution (areogram) values.The relative curve density is calculated by discretizing the dependent variable Y and independent X variable into grids, counting how many curves go through a grid box and finally normalized by the highest count in every X column(Tikkanen et al., 2019).

Figure S5 :
Figure S5: "Measurements" of Test A4 in Experiment A (red dots), true (red line) and estimated (blue line) yields at (a) 5 o C, (b) 15 o C, (c) 25 o C, and (d) 35 o C), (e) TD (thermogram), and (f) dilution (areogram) values.The blue area shows the range of good solutions of Test A4.The black dashed line corresponds to the estimated yields, thermogram and areogram in Test A1.

Figure S6 :
Figure S6: "Measurements" of Test B2 in Experiment B (red dots), true (red line) and estimated (blue line) yields at (a) 5 o C, (b) 15 o C, (c) 25 o C, and (d) 35 o C), (e) TD (thermogram), and (f) dilution (areogram) values.The blue area shows the range of good solutions of Test B2.The black dashed line corresponds to the estimated yields, thermogram and areogram in Test B1.

Figure S7 :
Figure S7: "Measurements" of Test A1 in Experiment A (red dots), true (red line) and estimated (blue line) yields at (a) 5 o C, (b) 15 o C, (c) 25 o C, and (d) 35 o C), (e) TD (thermogram), and (f) dilution (areogram) values when only TD and isothermal dilution measurements are provided as inputs.The blue area shows the range of good solutions of Test A1.

Figure S8 .
Figure S8.Estimated (bars) and true (red lines) parameter values of Experiment A in Test A1 combining only TD and isothermal dilution measurements for: (a) the volatility distribution of the products, (b) ΔHvap, and (c) αm.The error bars represent the uncertainty of the estimated values.

Figure S9 :
Figure S9: "Measurements" of Test A1 in Experiment A (red dots), true (red line) and estimated (blue yields at (a) 5 o C, (b) 15 o C, (c) 25 o C, and (d) 35 o C), (e) TD (thermogram), and (f) dilution (areogram) values when only yield and isothermal dilution measurements are provided as inputs.The blue area shows the range of good solutions of Test A1.

Figure S10 .
Figure S10.Estimated (bars) and true (red lines) parameter values of Experiment A in Test A1 combining only yield and isothermal measurements for: (a) the volatility distribution of the products, (b) ΔHvap, and (c) αm.The error bars represent the uncertainty of the estimated values.

Figure S11 :
Figure S11: "Measurements" of Test A1 in Experiment A (red dots), true (red line) and estimated (blue line) yields at (a) 5 o C, (b) 15 o C, (c) 25 o C, and (d) 35 o C), (e) TD (thermogram), and (f) dilution (areogram) values when only yield and TD measurements are provided as inputs.The blue area shows the range of good solutions of Test A1.

Figure S12 .
Figure S12.Estimated (bars) and true (red lines) parameter values of Experiment A in Test A1 combining only yield and TD measurements for: (a) the volatility distribution of the products, (b) ΔHvap, and (c) αm.The error bars represent the uncertainty of the estimated values.

Table S2 :
"Εxperimental" conditions and properties used to obtain the "measurements" of TD and isothermal dilution for pseudo-experiments A, B and C.

Table S3 :
Number of solutions under the <5% threshold for the 8 different tests and two values of the sum of the yields Σ(αi) .

S3. Effect on the Estimated Parameters in the Abscence of Yield Measurements (TD and isothermal dilution)Table S5 :
The mean normilized error between the "true" and estimated values (MNET) * The errors for TD were calculated up to the denoted temperature in the parenthesis.

Table S6 :
The average relative standard deviation (ARSD) for the different tests when only TD and isothermal dilution measurements are provided as inputs.
* The ARSD for the TD MFR values were calculated in the 20-120 o C temperature range.

Table S7 :
Relative errors (%) between the "true" and estimated parametrization when only TD and isothermal dilution measurements are provided as inputs.

Sensitivity tests to the upper limit of the sum of the yieldsTable S8 :
True and estimated volatility distribution of the products for 8 different tests for Σ(αi) < 2.0.The uncertainty of the estimates (±σ) is also included.

Table S9 :
The mean normilized error between the "true" and estimated values (MNET) for the different tests when Σ(αi) < 2.0.