Modeling Indoor Inorganic Aerosol Concentrations During the ATHLETIC Campaign with IMAGES

In 2018, the ATHLETIC campaign was conducted at the University of Colorado Dal Ward Athletic Center and characterized dynamic indoor air composition in a gym environment. Among other parameters, inorganic particle and gas-phase species were alternatingly measured in the gym’s supply duct and weight room. The Indoor Model of Aerosols, Gases, Emissions, and Surfaces (IMAGES) uses the inorganic aerosol thermodynamic equilibrium model, ISORROPIA, to estimate the partitioning of inorganic aerosols and corresponding gases. In this study herein, measurements from the ATHLETIC campaign were used to evaluate IMAGES’ performance. Ammonia emission rates, nitric acid deposition, and particle deposition velocities were related to observed occupancy, which informed these rates in IMAGES runs. Initially, modeled indoor inorganic aerosol concentrations were not in good agreement with measurements. A parametric investigation revealed that lowering the temperature or raising the relative humidity used in the ISORROPIA model drove the semivolatile species more toward the particle phase, substantially improving modeled-measured agreement. One speculated reason for these solutions is that aerosol water was enhanced by increasing the RH or decreasing the temperature. Another is that thermodynamic equilibrium was not established in this indoor setting or that the thermodynamic parametrizations in ISORROPIA are less accurate for typical indoor settings. This result suggests that applying ISORROPIA indoors requires further careful experimental validation.


S1. Note on preprocessing ATHLETIC Campaign data
During the ATHLETIC campaign, instruments switched between sampling the room and supply air every 5-10 minutes via an automated valve system. 1,2However, IMAGES requires continuous inputs over consistent timesteps.Therefore, all measured data (such as room and supply duct concentrations, RH, supply T, and occupancy) were linearly interpolated over 5-min intervals before being used as inputs to IMAGES.NH 3 and HNO 3 were measured less frequently in the duct due to sampling concerns.Thus, three input datasets for the IMAGES framework were created and run separately.These datasets' date/time stamps are as follows: 1) Nov. 7 00:33 -Nov.10 02:53, 2) Nov. 10 15:48 -Nov.12 09:28, and Nov. 15 14:48 -Nov.19 11:33.

S2. ISORROPIA's performance indoors
As discussed in Section 2.2, a parametric test was performed to determine the specific T and RH combinations that produce the necessary thermodynamic conditions within ISORROPIA to obtain reasonable agreement with measurements.Specifically, the parameters T and RH were varied from 260 to 300 K at intervals of 1 K and 1 to 100% at intervals of 1%, respectively.This parametric test was done to determine if certain T and RH combinations yielded ISORROPIA-partitioned concentrations to be in better agreement with ATHLETIC study measurements (Figure S1).Then, the coefficient of determination ( 2 ), slope (m), and y-intercept (b) of the measured and ISORROPIA partitioning fraction in the weight room,  ,room , were compared for each T and RH combination using an orthogonal regression since there is uncertainty in both modeled and measured data (Figure S1). Figure S1 shows heatmaps of the coefficient of determination ( 2 ) (a, b), slope (m) (c, d), and y-intercept (b) (c, d) from the lines of best fit of ISORROPIA's predicted  ,room vs. the measured  ,room .The areas of best performance are highlighted by the lightest color in the heatmaps shown in Figure S1.Although it remains unclear why agreement improves under these specific environmental conditions, hysteresis and inlet losses of HNO 3 during measurements were hypothesized to be potential pieces to the puzzle and explored.
We first explored the hypothesis that not accounting for hysteresis effects contributes to ISORROPIA not agreeing with measurements.Figure S2 shows a time series of the different temperatures measured at various parts of the HVAC system and the fraction of outdoor air that enters the mixing box during the ATHLETIC campaign.The similar mixed T ( mixed ), discharge T ( discharge ), and supply duct T ( supply ) suggests there was at most slight heating (and no cooling).Instead, the outdoor T closely following the outdoor air fraction implies economizing was done to achieve a fairly constant  mixed , and the target  discharge of ~287-288 K at this main air handling unit (AHU).Prior to the air delivery back to the weight room, the air passes through local variable air volume (VAV) terminal boxes that can provide additional conditioning where likely some heating occurred at times (and/or in transit within ducts).To our knowledge, no humidification processes occurred in the HVAC.Nevertheless, it was thought that particles may have retained their aqueous phase as they were brought indoors.However, since the outdoor RH (RH out ) is not consistently high, this theory was rejected (Figure S2).Still, an unaccounted-for condensation sink may have been present. 3Inputting RH room, meas to ISORROPIA results in the nitrate being simulated as a gas rather than a particle most of the time (Figure S3).Lowering the room T or increasing the RH seems to make up for the unaccounted-for condensation sink, despite us not being unable to identify it.Additionally, using ISORROPIA's stable mode, which allows particles to be aqueous or solids, showed no improvement and resulted in a worse agreement (Figures S4 and S5) than when run with the metastable mode.
The second hypothesis for why ISORROPIA's predicted  ,room disagreed with measurements was because of the complexities associated with measuring sticky gases such as HNO 3 .ISORROPIA was run (and  ,room was calculated) with an increased amount of HNO 3 added to the original measured value (up to ten times as much) to make up for the potential HNO 3 loss.However, Figures S6 and S7 show that no improvements are made when HNO 3 is increased; thus, this hypothesis was rejected.
In Figure S8, the OA ALW was found using OA parameterization from Rickards et al. Figure S8 shows that OA ALW is on the order of about 0.05 -0.1 ug sm -3 .Based on the total inorganic mass and their  (~ 3-6x larger than kappa OA), the increase in IA ALW (caused by adjusting the RH upwards) is on the order of 5-15 ug sm -3 .Therefore, not accounting for OA (in this data set) has no impact on the total ALW needed to explain the observations.Despite generally having poor modeled vs. measured agreement, some instances exist where NO - 3 and NH + 4 are in good agreement.Figures S9 and S10 show one-to-one plots of measured vs. ISORROPIA simulated NO - 3 and NH + 4 with RH room,meas and are colored by pH.When the concentrations are in good agreement, the pH, an output of ISORROPIA, is unrealistically high, with some values reaching ~15.This result shows that the model does not perform well, even when modeled concentrations appear to match measurements when using RH room,meas .However, when RH room,opt is used for the IMAGES simulations, the pH is consistently around a value we would expect indoors (Figure S11 and S12).

S3. Optimizing indoor environmental conditions
The environmental conditions that minimized ISORROPIA's partitioning error were picked based on the minimum distance between a perfect one-to-one correlation and the actual correlation of ISORROPIA vs. measured  room (described in Section 2.3). Figure S13 shows that the distance was smallest when the T was low or RH was high.However, since  room was controlled at ~293 K throughout the ATHLETIC campaign, a single optimized RH value (RH room,opt ) was chosen at 293 K. Figure S14 shows just the 293 K column from Figure S13.The smallest distance in the 293 K column (Figure S14) occurred at RH = 98%, and thus, RH room,opt = 98%.Optimizing the RH at T = 293 K gives a similarly exceptional partitioning agreement as optimizing the T and RH across the full range of values.For instance, the distance at T = 293 K and RH = 98% is 0.25.When considering the full range of environmental conditions, the smallest distance is 0.24, which occurs at T = 274 K and RH = 45%.Since these distances are almost the same, the T = 293 K and RH = 98% condition was chosen to preserve the room temperature measurements.ΔCO 2 can be used as an indicator of building occupancy when the number of occupants is not provided.Therefore, linear trends relating v ,  , v ,  , and    to ∆  (Figure S15) were derived using the same algorithm described in Section 2.5.∆  denotes the difference between indoor and outdoor CO 2 concentrations.Since outdoor CO 2 was not measured, it was taken to be the 5 th percentile of the indoor CO 2 concentration (~424.1 ppm).The analytical solution to Eq. 3 (Eq.S1) allows C i to be approximated after a short period of time (  , h): S1) By using   and an N number of  , measurements with  , (which was computed by ISORROPIA), N-1    ,   , and β   vectors occurring between two adjacent time-series measurements were explicitly back-calculated from Eq. S1 using a built-in Python solver.The source and loss rates (Equations S2 -S7) were specific to the species considered when solving for each parameter.For instance, non-volatile  -  , the species considered when solving for β  , does not have any gas-phase sources or losses indoors.Therefore, the source and loss rates can be defined as: 3 and HNO 3 were the only species considered when solving for β HNO 3 .Thus, the source and loss rates used here were: TNO - 3 = 1 - TNO - 3 ,room ( supply + β HNO 3 ) +  TNO - 3 ,room  TNO - 3 ,room ( supply +  p ) (S5) Similarly, NH + 4 and NH 3 were the only species considered when solving for  NH 3 , and so the source and loss rates for this case were: Table S2.Percentage of room measurements used to evaluate IMAGES simulation that fell below the limit of detection (LOD).

Species
Percentage below LOD SO    No data points were removed from the linear regressions here.S5. IMAGES evaluation IMAGES was run using the ΔCO 2 -based deposition and emission trends described in Section S3.Figures S18 and S19 show similar timeseries and one-to-one comparison results to those presented in Section 3.3; thus, the analysis is similar.However, one distinct difference is that NH 3 has slightly worse modeled-measured agreement when using the ΔCO 2 -based trends than when using the occupant-based trends.This may be because ΔCO 2 is not as accurate at indicating the level of occupancy in a building as physically counting each person.Despite this, IMAGES was still run with ΔCO 2 -based trends since it is a more standard field measurement than counting occupants.(right column).

Figure S7 .
Figure S7.A comparison of standalone ISORROPIA simulated vs. measured ε NO - 3 ,room best fit lines for each increased HNO 3 case.The amount HNO 3 was increased by was ranged from no increase ( HNO 3 Multiplier = 1x) toten times the original amount (HNO 3 Multiplier = 10x10) and is listed on the right-side table.The table also includes the line of best-fit statistics, which are  2 , m, and b.

Figure S8 .
Figure S8.Time series of OA mass on left y-axis and OA ALW on right y-axis (calculated using Rickards et al. 5 ) This data assumes a constant RH of 75%.

Figure S13 .Figure S14 .
Figure S13.Heatmap of the distance between a perfect one-to-one correlation and the actual

Figure S15 .
Figure S15.Linear trends relating ∆  to  ,  (a),  , (b), and    (c).A probability density function (PDF) (d) is also displayed to show the distribution of data points related to ∆  .The best fit line (black line), best-fit equations, and   value are displayed in each plot (a-c).

Figure S16 .
Figure S16.Linear trends relating occupants to  ,  (a),  , (b), and    (c).A probability density function (PDF) (d) is also displayed to show the distribution of data points related to occupants.The best fit line (black line), best-fit equations, and   value are displayed in each plot (a-c).No data

Figure S17 .
Figure S17.Linear trends relating ∆  to  ,  (a),  , (b), and    (c).A probability density function (PDF) (d) is also displayed to show the distribution of data points related to ∆  .The best fit line (black line), best-fit equations, and   value are displayed in each plot (a-c).No data points were

Figure S18 .Figure S19 .
Figure S18.Timeseries of IMAGES simulated (black line) particle and gas concentrations using

Figure S20 .
Figure S20.One-to-one plots comparing modeled NH + 4 concentrations in the room to NH + 4

Figure S21 .Figure S22 .
Figure S21.One-to-one plots comparing modeled NO - 3 concentrations in the room to NO - 3

Table S3 .
Standard errors of slopes from linear regression relating that relate occupants or ∆CO 2 to v d,HNO 3 , v d, p , and  NH 3 .