Thermodynamic Characterization of Mexico City Aerosol during MILAGRO 2006

measurements ISORROPIA-II equilibrium model are used to study the partitioning of semivolatile inorganic species and phase state of Mexico City aerosol sampled at the T1 site during the MILAGRO 2006 campaign. Overall, predicted semivolatile partitioning agrees well with measurements. PM 2.5 is insensitive to changes in ammonia but is to acidic semivolatile species. For particle sizes up to 1µm diameter, semi-volatile partitioning requires 30-60 min to equilibrate; longer time is typically required during the night and early morning hours. When the aerosol sulfate-to-nitrate molar ratio is less than unity, predictions improve substantially if the aerosol is assumed to follow the deliquescent phase diagram. Treating crustal species as “equivalent sodium” (rather than explicitly) in the thermodynamic equilibrium calculations introduces important biases in predicted aerosol water uptake, nitrate and ammonium; neglecting crustals further increases errors dramatically. This suggests that explicitly considering crustals in the thermodynamic calculations is required to accurately predict the partitioning and phase state of aerosols.


Introduction
Atmospheric particulate matter plays a central role in atmospheric phenomena like visibility reduction, public health, formation of acid rain and climate change. Fine particles, otherwise called PM 2.5 (particles with diameter less than 2.5µm) are prime contributors to the above processes, a quantitative understanding of which requires knowledge of their phase and composition. Much of the dry particle mass is inorganic (25-75 %) (Heitzenberg, 1989) with the main components often being ammonium (NH 4 + ), sulfate (SO 4 2-), and nitrate (NO 3 -). Depending on the location, sodium (Na + ) and chloride (Cl -) may also be found as well as crustal species (Ca 2+ , K + , Mg 2+ ) which are associated with dust (Heitzenberg, 1989;Malm et al., 1994). These species may be dissolved in the aqueous phase, or in the form of precipitated solids, and some may partially volatilize (e.g. NH 3 , HNO 3 , HCl). The partitioning of these species between gas, liquid and solid phase is determined by dynamical processes (e.g. condensation/evaporation), which, if fast enough lead to thermodynamic equilibrium and can be simulated by aerosol equilibrium models, such as AIM2 (Wexler and Clegg, 2002), SCAPE2 (Meng et al., 1995), GFEMN (Ansari and Pandis, 1999a,b), UHAERO (Amundson et al., 2006) and ISORROPIA-II . These models differ in the chemical species that they can treat, the method used to solve for equilibrium composition, the type of input they can accept, and their computational efficiency. Similarities and differences between these models are discussed elsewhere (e.g., Ansari and Pandis, 1999a,b;Zhang et al., 2000;Amundson et al., 2006;Fountoukis and Nenes, 2007).
An important question is whether equilibrium models (all of which embody simplified representations of aerosol composition) can adequately predict the equilibrium partitioning of semivolatile inorganic species. This is often assessed by comparing model predictions against measurements, assuming thermodynamic equilibrium applies between the aerosol and gas phases. Equilibrium partitioning of semi-volatile species is often assumed in online aerosol simulations, therefore another important issue is understanding when it can be used. A key factor is aerosol size Seinfeld 1991, 1992;Meng and Seinfeld, 1996;Dassios and Pandis, 1999;Cruz et al., 2000); for submicron particles, equilibrium is achieved typically within a few minutes, often faster than the timescale of ambient condition change (Meng and Seinfeld, 1996;Dassios and Pandis, 1999;Cruz et al., 2000) so that the assumption of instantaneous equilibrium can be used to model composition. Coarse mode particles however require substantial time, on the order of an hour or more (Meng and Seinfeld, 1996;Dassios and Pandis, 1999;Cruz et al., 2000), so explicit condensation/evaporation dynamics is required for modeling composition (e.g., Pilinis et al., 2000;Capaldo et al., 2000). Capaldo et al. (2000) found that application of bulk equilibrium is adequate for particles up to 1 µm diameter; larger particles require modeling using a dynamical approach.
Several studies have been conducted to concurrently test the applicability of the equilibrium assumption and model prediction skill by comparing thermodynamic model predictions against observational data. Moya et al., (2001) used ISORROPIA, SCAPE2 and GFEMN to study the partitioning of nitrate and ammonium in Mexico City during the 1997 IMADA-AVER field campaign. Using daily and 6-hour average PM 2.5 data, Moya et al., (2001) found the equilibrium approach reproduced most of the data, however a few discrepancies were found and were attributed to the implicit treatment of crustal species (treated as "equivalent" sodium by ISORROPIA and GFEMN) as opposed to the explicit treatment (by SCAPE2) and to the use of IMADA observations averaged over long periods of time (6 h). Zhang et al. (2003) assessed the nitrate -ammonium equilibrium assumption using the ISORROPIA model and high resolution (5-minute average) data obtained during the 1999 Atlanta Supersite Experiment. They found good agreement for nitrate and ammonium when a 15% correction (within measurement uncertainty) in PM 2.5 SO 4 2was applied. Takahama et al., (2004)  Using 1 and 2-hour average measurements of PM 2.5 they found most of the predictions of nitrate to agree with observations to within experimental uncertainty. Other factors can also influence the agreement between predictions and observations. Yu et al., (2005)  aerosol nitrate concentrations. Moya et al., (2002) showed that the assumption of metastable state for sub-micrometer particles may introduce large errors when RH < 60% highlighting the importance of deliquescence predictions at low RH.
Most studies to date either use measurements averaged over long times or use models that do not explicitly treat crustals. If measurements are slow, significant variations in T, RH and aerosol precursor concentrations may occur during sampling which cannot be accounted for in equilibrium calculations. Additionally, the consideration of crustal material in predicting the partitioning of nitrate and ammonium, especially in areas where dust comprises a significant portion of total PM, can affect the aerosol thermodynamics and improve model prediction skill (Ansari and Pandis, 1999;Moya et al., 2002).
In the present work, we use ISORROPIA-II, which treats the thermodynamics of  . The advantage of this instrument is the simultaneous measurements of important inorganic anions and cations at high time-resolution. NH 3(g) concentrations were obtained every minute with quantum-cascade laser (QCL) spectrometer (Fischer et al., 2007), while volatile nitrate (i.e. HNO 3(g) + NH 4 NO 3 ) concentrations were measured every 5 minutes by a thermal dissociation-laser induced fluorescence of nitrogen oxides (TD-LIF, Day et al., 2002;Farmer et al., 2006). Ambient temperature (T), pressure and relative humidity (RH) data are based on the measurements of the Vaisala Y50 Sensor which was operated with a 1-min time resolution. Aerosol particles (PM 2.5 ) were also collected (6-hour samples) with filters at the same site and sampling period.
6-minute averages of NH 3(g) concentrations, T and RH were obtained to correspond to the 5-min averages of HNO 3(g) and 6-min averages of PM 2.5 ion concentrations. In ~26% of the cases, the 5-min averages of HNO 3(g) data were not coincident with the 6-min PILS concentrations, therefore a ~20-min average was considered instead (average of two measurements with a 10-min interval between the two data points). The TD-LIF measurement is the sum of gas-phase and semivolatile nitrate (i.e. HNO 3(g) + NH 4 NO 3 ), from which HNO 3(g) is obtained by subtracting PM 2.5 ammonium nitrate concentrations from the PILS; this can be done because preliminary ISORROPIA-II calculations suggest that the PILS nitrate is entirely semivolatile (i.e. NH 4 NO 3 only). Aerosol K + was not accurately measured by PILS due to a calibration interference; instead, it was estimated based on a nearly constant ratio (~0.4) of K + to the sum of crustal species (Ca 2+ , K + , Mg 2+ ) obtained from the impactor data for the same site and sampling period. Gas-phase hydrochloric acid (HCl (g) ) concentrations were assumed to be zero (hence total Clwas equal to aerosol Cl -). The validity of this assumption is assessed in section 4. The measurement uncertainty was estimated to be approximately ±20% for the PILS instrument , ±10% for the NH 3(g) measurement (Fischer et al., 2007), ±30% for the TD-LIF instrument (Day et al., 2002;Farmer et al., 2006) and ±5% for RH. The HNO 3(g) uncertainty, Temperature did not vary significantly over the measurement period of study (mean value of 289.5 ± 5.1 K) while RH varied significantly (mean value of 58.1 ± 22.6 %), exhibiting a typical diurnal cycle which peaks in the evening and early morning and is minimum at around noon. Fig. 1 shows an example of diurnal profiles of measured ammonium, nitrate and ambient RH for March 27. A detailed overview of the dataset and meteorological conditions is given elsewhere (e.g. Doran et al., 2007;Fast et al., 2007). ISORROPIA-II can predict composition for the "stable" (or deliquescent path) solution where salts precipitate once the aqueous phase becomes saturated with respect to a salt, and, a "metastable" solution, in which the aerosol is composed only of an aqueous phase regardless of its saturation state. For the dataset of this study, the forward mode of ISORROPIA-II is used.
Given that there are no size-resolved data available with a temporal resolution of minutes, applying a size-resolved analysis would require numerous assumptions that would introduce rather important uncertainties. Instead, a bulk equilibrium assumption is used; although this can often lead to large prediction errors (as composition across particle sizes tend to vary), we postulate that it is a reasonable assumption for submicron Mexico City aerosol for the following reasons: • Mexico City is unusually ammonia-rich. Most of NH 3 resides in the gas phase even after equilibration, hence particle acidity is not expected to vary substantially with size.
• Aerosol at the T1 site is often aged, hence tends to be internally mixed.
• Submicron aerosol mass in Mexico City tends to be in the 300-900 nm range (e.g., Salcedo et al., 2006), hence the equilibrium assumption can be used for those particles .

Model vs. observations
In this section we evaluate the ability of ISORROPIA-II to reproduce the observed partitioning of ammonia, nitrate and chloride, which will test the expectation that equilibrium partitioning of semivolatile aerosol species is attained somewhere between 6 and 30 minutes. Fig. 2a-e shows predicted vs. observed concentrations of gasphase ammonia (NH 3(g) ), nitric acid (HNO 3(g) ), aerosol phase ammonium (NH 4(p) ), nitrate (NO 3(p) ) and chloride (Cl (p) ), respectively; Table 1 summarizes the corresponding error metrics. For the simulations of Fig. 2, ISORROPIA-II was run in forward mode and stable state conditions. Most of the total ammonia (88.7% on average) resides in the gas phase. The data have been separated into 4 classes based on a "completeness factor" (CF).
For half of the data analyzed (51%), 6-min average measurements of all (gas + particulate phase) species were available; these data are represented as "CF=0". For ~26% of the data, only 20-min average (two 6-min averages with a 10-min interval) measurement of ion concentrations from the PILS instrument were available and are "CF=1" data.
Subtracting the PILS ammonium nitrate measurement from the TD-LIF (i.e. HNO 3(g) + NH 4 NO 3 ) occasionally resulted in a negative HNO 3(g) . Under such conditions, HNO 3(g) is assumed zero, and the data is indicated as "CF=2" if they correspond to 6-minute averages (13% of the data), and "CF=3" for 20 min averages (10% of the data). The prediction skill of ISORROPIA is quantified in terms of five error metrics, the normalized mean error (NME), , where I i represents predictions of ISORROPIA-II for data point i, O i represents observations and n is the total number of data points. NME and MAGE give an estimation of the overall discrepancy (scatter) between predictions and observations, while NMB and MB are sensitive to systematic errors (biases). MAGE and MB give the error and bias respectively in µg m -3 , while NME and NMB in %; RMSE is the root of the mean square error, which, being the second moment of the error, incorporates both the variance of the prediction and its bias (in µg m -3 ). Both NME and MAGE inherently include the bias which is the reason why the magnitude of NME (and MAGE) is equal or larger than NMB (and MB respectively). For an unbiased prediction, NME and MAGE express the variance. When NME and NMB (or MAGE and MB respectively) are close to each other in magnitude, the discrepancy is explained as a systematic bias rather than scatter. When the magnitude of NME/MAGE is much larger than NMB/MB, part of the discrepancy between predictions and observations is explained as scatter.
Very good agreement between model predictions and observations was found for NH 3(g) (Fig. 2a) with a NME of 5.3%, a slope of 0.991, an intercept of -0.676 µg m -3 (much smaller than concentrations of NH 3(g) ) and an R 2 of 0.992. When compared to the observed value (16.89 µg m -3 ), the mean error and bias, as well as the RMSE for NH 3(g) are notably low (0.94, -0.83 and 1.27 µg m -3 respectively). This is not surprising, as most of the ammonia resides in the gas phase, so NH 3(g) is relatively insensitive to aerosol ammonium prediction errors. Particulate ammonium ( Fig. 2b) was systematically overpredicted, as shown by the 37.1% NMB and the 0.83 µg m -3 mean bias compared to the measured value of 2.24 µg m -3 (Table 1). This overprediction could arise from the phase state assumption, departure from equilibrium or measurement uncertainty; all of these possibilities are explored in section 4.4.
Predictions of HNO 3(g) were subject to significant scatter ( Fig. 2c), with a NME of 80.8% and MAGE=1.46 µg m -3 but the bias was comparable to the other species (Table   1). The scatter is attributed to that a) particles larger than 2.5 µm in diameter are not included in our calculations (although too large to be in equilibrium with the gas phase, they could still react with nitric acid and introduce some prediction error), b) zero concentrations of HNO 3(g) for a portion of the data (CF=2 and 3), and, c) low, on average, concentrations of gas phase nitrate which results in predictions of HNO 3(g) being very sensitive to errors in particulate nitrate (NO 3(p) ). When partitioning is predominantly in one phase, small errors in its predicted concentration are substantially amplified in the other phase. Additionally, the estimated uncertainty for HNO 3(g) (using Eq. 1) was found to be roughly ~100%; the agreement between predicted and observed HNO 3(g) is in fact within the estimated uncertainty. For particulate nitrate (Fig. 2d), ISORROPIA-II predictions agree well with observations with a NME of 27.2% and a small bias (NMB = 8.0%).
Observed concentrations of Clagree well (NME=15.5%, MAGE=0.04 µg m -3 ) with predicted values (Fig. 2e); ISORROPIA-II predicts very small amounts of chloride in the gas phase because the large excess of NH 3(g) tends to drive Clalmost completely into the aerosol phase. This justifies (to first order) the assumption of effectively zero HCl (g) in the thermodynamic calculations. However, the NME and NMB, as well as MAGE and MB, are almost identical in magnitude; this suggests that the prediction error is likely only from the "missing" (small) amount of HCl ( with measurements (~1 ppb) reported by Moya et al., (2004).
Although NMB strongly depends on the averaging time, NME does not. The same is seen for MB and MAGE respectively. This may be the residual effect of particles with diameter larger than 2.5 µm reacting with nitrates; since coarse particles vary significantly throughout the dataset and are not included in our calculations, their effect likely manifests as "scatter" in the predictions. This suggests that up to 1.46 µg m -3 (MAGE value for nitrate) out of the 5.38 µg m -3 observed, which is roughly 30% of the unresolved particulate nitrate (also expressed as ~30% NME) could be associated with particles larger than 2.5 µm diameter.

Equilibrium timescale
Agreement between predictions and measurements depends on many factors, such as equilibrium timescale and measurement uncertainty. Fig. 2 (and Table 1) shows that the closure for CF=0 data is slightly worse than for CF=1 to 3, which could be an indication that the averaging timescale might affect the bias. Since the NMB and NME for particulate nitrate are consistent between CF classifications, this suggests that the TD-LIF provides an excellent measure of volatile nitrate. Based on work to date (e.g., Meng and Seinfeld, 1996;Dassios and Pandis, 1999;Cruz et al., 2000) we expect the equilibration timescale to be ~ 20 minutes; indeed the Table 1 results support this, as NMB is consistently minimum for the 20 min data (Table 1). However, since different data correspond to different atmospheric conditions (temperature, relative humidity, time), no definite conclusion on the equilibration timescale can be drawn based on the error metrics. An equilibrium timescale and its sensitivity to changes in RH, T and aerosol precursor concentration can still be derived from the measurements. For this, we start from the mass transport equation from/to particle: where k is the mass transfer coefficient, c is the ambient concentration of a species and c eq is its concentration at equilibrium. k depends on the gas-phase diffusivity, D g , and the size of the particle (Seinfeld and Pandis, 1998), where R p is the effective radius of the particle. k also depends on the mass accommodation coefficient, α, but for values of α > 0.1 the mass transfer rate is not sensitive to the exact value of α (Seinfeld and Pandis, 1998). D g was calculated from the Chapman-Enskog theory for binary diffusivity (Chapman and Cowling, 1970) and was found to be 0.2 cm 2 s -1 for NH 3 and 0.14 cm 2 s -1 for HNO 3 (average for the conditions of T and P observed during the measurement period).
Assuming that c changes with time, with a rate obtained from observations, Equation (2) gives: The characteristic time for equilibrium establishment can be estimated by scaling Eq. (4).
If the characteristic aerosol mass concentration is m p and the characteristic timescale is τ eq one can scale t, m as Assuming that eq eq p dt dc k m a characteristic equilibrium timescale can be defined as, where ∆c, ∆t are the changes in concentration and time, respectively, between two consecutive measurements.
Assuming a particle density of 1.0 g cm -3 (characteristic for deliquesced aerosol exposed to high RH) a mass accommodation coefficient of 0.1 for gas-phase NH 3 , HNO 3 and an aerosol diameter of 1 µm, the timescale for equilibrium for all semivolatile species is computed using Eq. 6. As can be seen in Fig.3, semivolatile partitioning equilibrates (on average) on a timescale between 15 -30 min (Fig 3a,b) during the measurement period of March 21 -30 (27±19 min for HNO 3 , 14±11 min for NH 3 , 18±15 min for NO 3 and 15±13 min for NH 4 , on average). These values are consistent with the detailed calculations of Wexler and Seinfeld (1992), more recent literature (Meng and Seinfeld, 1996;Dassios and Pandis, 1999;Cruz et al., 2000) and the high resolution measurements of nitrate by Hennigan et al., (2008), which shows that measured nitrate lags about 30 minutes with respect to predictions based on bulk equilibrium. Furthermore, the equilibration timescale for NH 3 is close to that of NH 4 , and, the timescale of HNO 3 is close to that of NO 3 , despite that they include independent measurements of aerosol and gas-phase precursors; this strongly suggests consistency in the timescale analysis.
Interestingly, by focusing on specific days, one can notice a systematic diurnal cycle of the equilibration timescale. Figure 3c shows the timescale of NH 4 and NO 3 for two days (March 28 and 29). The timescale reaches a maximum during midnight, when T is lower, RH is high and concentrations of species are high (because of the collapse of the boundary layer). Increasing the particle diameter to 2 µm increases the timescales by a factor of 2, while an increase in aerosol density from 1 to 2 g cm -3 increases the equilibration timescale by ~40% (not shown).
It is also important to evaluate the influence of environmental changes to the equilibration timescale. This is done by evaluating the instantaneous eq τ (computed from Introduction of Equation 7 into 4 gives: The terms on the right hand side of Equation (8)  is the observed change in T between two consecutive measurements.
Finally, one can define the ratio of instantaneous equilibration timescale to the rate of change of precursor as: where ∆c is the change in precursor concentration between two consecutive measurements.
, then the equilibrium timescale is dominated by transients in ambient concentration, RH, T and vice versa. Fig. 4 shows the calculated timescale ratios for gas-phase HNO 3 , NH 3 and aerosol NO 3 , NH 4 during the measurement period of March 21-30, 2006. If c, RH and T change slowly enough, the timescale ratios are much larger than 1; this was found to frequently apply in the dataset (88% for NH 3 , 58% for NH 4 , 55% for HNO 3 and 75% for NO 3 ). This suggests that calculation of the equilibrium timescale based on instantaneous values of c, RH, T is representative. For times where the ratio was less than unity, C eq τ τ was almost always larger than T eq τ τ and RH eq τ τ . This suggests that τ c is less than τ RH or τ Τ , meaning that changes in RH and T affect the equilibration timescale more strongly than changes in aerosol precursor concentration.

Deliquescence vs. Metastable state
Due to the hysteresis effect, there is always an issue on what is the appropriate thermodynamic state assumption for RH < 60%, where crystallization may occur (Ansari and Pandis, 2000;Moya et al. 2002). This dataset covers a wide range of RH (19-94%) and makes it possible to assess the preferred phase transition path (i.e. deliquescence or metastable branch) for Mexico City aerosol. In Fig. 5 we plot the stable ("deliquescence") and metastable ("metastable") solution predictions of ISORROPIA-II compared to observations for NH 4(p) and NO 3(p) as a function of RH for the whole dataset (March 21-30). The stable state solution of ISORROPIA-II predicts higher concentrations of aerosol ammonium and aerosol nitrate at RH <50%. This is in agreement with previous studies (Ansari and Pandis, 2000) and is primarily attributed to high . At low RH (<50%), the stable state solution predicts a solid phase consisting mainly of (NH 4 ) 2 SO 4 and NH 4 NO 3 . The metastable state solution assumes the particulates are composed of an aqueous supersaturated solution throughout the whole RH regime; hence no solid NH 4 NO 3 is allowed to form. At RH >50%, solid NH 4 NO 3 dissolves and "stable" and "metastable" aerosol predictions become identical. This can also be seen in Fig. 6, which presents the  Table 2; NME, NMB, MAGE and MB are computed only for data with RH < 50%. For aerosol ammonium, although the NME (and MAGE) for the two solutions of ISORROPIA II is essentially the same, the opposite sign in NMB and MB (Table 2), indicates an overprediction (+11%) of ammonium by the stable state and an underprediction (-9%) by the metastable solution. The systematic overprediction of ammonium by the stable solution (seen in Fig. 2) may partially reflect measurement uncertainty, which is analyzed in detail in section 4.4. For aerosol nitrate, the error and bias between predictions and observations is significantly larger when using the metastable solution (NME=47.4%, NMB=-46.4%, MAGE=2.8µg m -3 , MB=-2.74µg m -3 ) of ISORROPIA II compared to the stable state solution (NME=25.8%, NMB=-18.5%, MAGE=1.5µg m -3 , MB=-1.1µg m -3 ) for RH < 50%, suggesting that aerosols in Mexico City prefer the deliquescence branch of the phase diagram. However, Moya et al. (2007) showed that the metastable branch gives better agreement between predictions and giving the "appearance" of a metastable state (Marcolli et al., 2004). Unfortunately, there were no in-situ measurements of particle phase state or size-resolved compositional data available with the time resolution required to further support our results, although the model suggests the semi-volatile inorganic partitioning is mostly consistent with a metastable state whenever dust is not present in significant amounts.
ISORROPIA-II (and most other thermodynamic aerosol models as well) use of the water activity-molality polynomials for inorganic salts developed by fitting electrodynamic balance measurements at > 30% RH .
Inaccuracies in water content associated with extrapolation of the water activity polynomials could bias the "favored" state in the low-RH samples. Fortunately, most of the datapoints in our study are for an ambient RH above 30%. Repeating the exercise neglecting datapoints for which RH < 30% yielded no discernable difference in the performance metrics (not shown).

Sensitivity of Model Predictions to Aerosol Precursor Concentrations
In this section we explore the sensitivity of predictions to aerosol precursor concentrations to a) assess the importance of measurement uncertainty on predictions, and, b) assess the sensitivity of PM 2.5 to changes in emitted precursors. The sensitivity is assessed by perturbing the input concentrations of total ammonia (TA), total nitrate (TN), total sulfate (TS), crustals and sodium by ±20% (approximately the PILS measurement uncertainty). The results of this analysis are shown in Table 4. A 20% increase in TS does not improve the agreement between predictions and observations; in fact, a slight increase of the NME was found for ammonia and nitrate. Since the impactor data showed ~40% (on average) higher TS than the PILS (not shown), we further perturb TS by 40%, but NME does not decrease (67.9% for NH 4(p) and 27.8% for NO 3(p) ). A +20% perturbation in crustals and sodium concentrations however, slightly improved predictions of NH 3(g) and NH 4(p) and decreased the observed overprediction seen in Fig.   2b; this is because crustals and sodium preferentially neutralize sulfates, so less ammonia binds to form (NH 4 ) 2 SO 4 which decreases the predicted NH 4(p) concentration and increases the amount of NH 3(g) . In fact, the impactor data suggest that Ca 2+ , Mg 2+ and Na 2+ are much higher (approximately 4 times) than obtained with the PILS. Increasing crustals and sodium by a factor of 4 significantly decreases the systematic error between predictions and measurements for particulate ammonium (NMB = 13.6%); predictions for NH 3(g) (mean predicted value = 17.42 µg m -3 ) and NH 4(p) (mean predicted value = 2.55 µg m -3 ) are improved. This implies that the PILS in this dataset may not account for all the crustals present in PM 2.5 .
In Fig. 7 we plot the predicted change (%) in PM 2.5 nitrate as a function of RH when a 20% decrease in input concentrations of TA, TS and TN is applied. The nitrate response to sulfate is negligible, ∆x=0.36%, (Fig. 7, Table 4) because TA concentrations are substantially in excess, and, thus a 20% change in TS is not enough to affect the formation of ammonium nitrate. (In an ammonia-limited environment, a reduction in sulfate would increase aerosol nitrate as ammonia is freed and allowed to react with nitric acid). As seen in Fig. 7, nitrate predictions are sensitive to changes in TA only for RH < 60%. This is expected since below the deliquescence point of NH 4 NO 3 the partitioning of nitrate is strongly dependent on the ammonia vapor pressure and thus reducing TA reduces the amount of NH 4 NO 3 formed. At RH > 60%, nitrate is mostly dissolved and unaffected by the changes in TA. Aerosol nitrate predictions are more directly influenced by reductions in TN as shown in Fig. 7 and Table 4 (∆x=-22.8%), and is in agreement with Takahama et al., (2004). The sensitivity of aerosol nitrate is RH-dependent as the partitioning of nitrate strongly depends on the amount of aerosol water.

Importance of Explicitly Treating Crustal Species
Often thermodynamic models treat the presence of crustals as mole-equivalent sodium (i.e. Ca 2+ = 2Na + , Mg 2+ = 2Na + , K + = Na + ) or as insoluble. In this section we examine the impact of these assumptions, versus using full thermodynamics. Table 5 displays a summary of this sensitivity test; shown are average concentrations and error metrics for nitrate, ammonium and water with ISORROPIA-II. For all the simulations we used the concentrations of crustals and sodium from the impactor data. When Ca 2+ , K 2+ and Mg 2+ are treated as insoluble (unreactive), ISORROPIA-II predicts higher, on average, concentrations of ammonium compared to both the equivalent-Na and explicit treatment, since more sulfate is available to bind with ammonium, and thus the error and bias between predicted and observed ammonium increases for the insoluble approach (Table 5). For particulate nitrate, NME, NMB, MAGE and MB are the lowest when crustals are treated explicitly. The changes in NME and NMB among the three crustal treatment approaches are rather small since ammonia is enough to fully neutralize the available nitrate regardless of the treatment of crustals. The difference in nitrate prediction when treating crustals explicitly vs. as equivalent sodium is expected to be large in environments where non-volatile nitrate (Ca(NO 3 ) 2 , Mg(NO 3 ) 2 , KNO 3 ) is present in significant amounts (Moya et al., 2002;Jacobson, 1999). In the current dataset, aerosol nitrate is present in the form of ammonium nitrate (due to ammonia-rich environment) and thus replacing crustals with sodium is expected to have a minor effect on predicted nitrate response, primarily from differences in predicted water uptake ( Table 5). The equivalent Na approach predicts aerosol water content which is higher (by 13.5%) than the one predicted by the explicit treatment of crustals and very close to the insoluble approach (Table 5). This is attributed to the formation of salts with low solubility (e.g., CaSO 4 ) which does not significantly contribute to water uptake. The difference in water content also affects aerosol acidity (i.e. pH) and water-soluble species concentration. It should be noted that the differences described in Table 5 between the equivalent Na and explicit treatment of crustals are the minimum expected considering the large amounts of ammonia in Mexico City which minimizes the effect of replacing crustals with sodium.
In agreement with observations, ISORROPIA-II predicts that ammonia (82.4 ± 10.1 %) primarily resides in the gas phase, while most of total nitrate (79.8 ± 25.5%) and chloride (75.3 ± 29.1%) resides in the aerosol phase. The mean observed value for NH 3(g) was 17.73 µg m -3 and 5.37 µg m -3 for NO 3(p) . An excellent agreement between predicted and observed concentration of NH 3(g) was found with a NME of 5.3%. Very good agreement was also found for NO 3(p) (NME=27.2%), NH 4(p) (NME=37.1%) and Cl (p) (NME=15.5%) concentrations for most of the data. Larger discrepancies were seen in predicted HNO 3(g) since uncertainties in the volatile nitrate measurement (HNO 3(g) + NH 4 NO 3 ) are magnified by the high sensitivity of HNO 3(g) because nitrate partitioned primarily to the aerosol phase. A number of important conclusions arise from this study: 1. Application of ISORROPIA-II is largely successful, suggesting that the assumption of bulk thermodynamic equilibrium is to first order applicable (i.e. to with 20% of measured concentrations) for Mexico City fine aerosol particulate matter. We suggest that this happens because i) Mexico City is unusually ammonia-rich, so most of it resides in the gas phase even after equilibration -hence particle acidity is not expected to vary substantially with size (aerosol nitrate is not systematically underpredicted, which further supports that acidity does not vary substantially between submicron particles), ii) aerosol at T1 is generally aged and its aerosol heterogeneity is expected to be much less, when compared to aerosol collected from downtown (T0).
2. Assuming a particle diameter of 1 µm, the timescale for thermodynamic equilibrium of semi-volatile species was found to be 27±19 min for HNO 3 , 14±11 min for NH 3 , 18±15 min for NO 3 and 15±13 min for NH 4 , on average with a maximum during the night and early morning hours. These timescales are consistent with high-resolution measurements of aerosol nitrate (Hennigan et al., 2008), and with the observation that most of the PM2.5 mass is in the submicron range (Salcedo et al., 2006). Changes in RH and temperature tend to affect the equilibration timescale more than changes in aerosol precursor concentration.
3. The scatter in nitrate prediction error (~30%) can be attributed to reaction of particles between 2.5 and 10 µm diameter with nitrate (the effect of which is not considered in our analysis). If true, this suggests that on average, up to 30% of the total aerosol nitrate can be associated with particles having diameter larger than 2.5 µm.          forward mode) to a -20% change in TA, TS and TN as a function of RH. All data (CF=0 -CF=3) are used in the dataset.