An interlaboratory comparison of aerosol inorganic ion measurements by ion chromatography: implications for aerosol pH estimate

. Water-soluble inorganic ions such as ammonium, nitrate and sulfate are major components of ﬁne aerosols in the atmosphere and are widely used in the estimation of aerosol acidity. However, different experimental practices and instrumentation may lead to uncertainties in ion concentrations. Here, an intercomparison experiment was conducted in 10 different laboratories (labs) to investigate the consistency of inorganic ion concentrations and resultant aerosol acidity estimates using the same set of aerosol ﬁlter samples. The results mostly exhibited good agreement for major ions Cl − , SO 2 − 4 , NO − 3 , NH + 4 and K + . However, F − , Mg 2 + and Ca 2 + were observed with more variations across the different labs. The Aerosol Chemical Speciation Monitor (ACSM) data of nonrefractory SO 2 − 4 , NO − 3 and NH + 4 generally correlated very well with the ﬁlter-analysis-based data in our study, but the absolute concentrations differ by up to 42 %. Cl − from the two methods are correlated, but the concentration differ by more than a factor of 3. The analyses of certiﬁed reference materials (CRMs) generally showed a good detection accuracy (DA) of all ions in all the labs, the major-ity of which ranged between 90 % and 110 %. The DA was also used to correct the ion concentrations to showcase the importance of using CRMs for calibration check and quality control. Better agreements were found for Cl − , SO 2 − 4 , NO − 3 , NH + 4 and K + across the labs after their concentrations were corrected with DA; the coefﬁcient of variation (CV) of Cl − , SO 2 − 4 , NO − 3 , NH + 4 and K + decreased by 1.7 %, 3.4 %, 3.4 %, 1.2 % and 2.6 %, respectively, after DA correction. We found that the ratio of anion to cation equivalent concentrations / CE) and ion balance (anions–cations) are not good in-dicators for aerosol acidity estimates, as the results in different labs did not agree well with each other. In situ aerosol pH calculated from the ISORROPIA II thermodynamic equilibrium model with measured ion and ammonia concentrations showed a similar trend and good agreement across the 10 labs. Our results indicate that although there are important uncertainties in aerosol ion concentration measurements, the estimated aerosol pH from the ISORROPIA II model is more consistent.

WSIIs in aerosols were reported to be analyzed by multiple techniques such as Cl − by spectrophotometry and Ca 2+ and Mg 2+ by flame atomic absorption in the early 1980s (Harrison and Pio, 1983). However, previous methods were time-consuming as WSIIs were analyzed by different techniques separately. Ion chromatography (IC), which was first introduced in 1975 (Buchberger, 2001), was applied in many studies for routine measurement of atmospheric WSIIs due to its fast, accurate and sensitive determination in a single run (Heckenberg and Haddad, 1984;Baltensperger and Hertz, 1985). IC can be coupled with diverse detection techniques for ion analysis, such as suppressed conductivity, ultravioletvisible spectrophotometry (UV-VIS) absorbance, amperometry, potentiometry and mass spectrometry (Buchberger, 2001). It has been used in various atmospheric studies for many years and is still widely applied at present, such as in the investigation of WSIIs in size-segregated aerosols (Li et al., 2013;Zhao et al., 2011;Ðorðeviae et al., 2012), fine aerosols (Fan et al., 2017;He et al., 2017;Liu et al., 2017a) and coarse aerosols (Li et al., 2014;Guo et al., 2011;Mkoma et al., 2009). IC can also be used for the determination of both water-soluble organic and water-soluble inorganic ions (Yu et al., 2004;Karthikeyan and Balasubramanian, 2006).
Aerosol ion concentrations can also be measured by online methods such as with the Aerosol Chemical Speciation Monitor (ACSM) or an aerosol mass spectrometer (AMS; Ng et al., 2011;Sun et al., 2012). During the recent Atmospheric Pollution and Human Health in a Chinese Megacity (APHH-China) campaigns (Shi et al., 2019), we observed important discrepancies between offline aerosol IC observations from different labs and between online AMS and offline IC methods. This prompted us to carry out this intercomparison exercise.
The IC method had been validated by a common reference standard -NIST SRM 1648 (urban particulate matter) -and the results for Na, K, S and NH + 4 were compared with those from other suitable alternative analytical techniques such as atomic absorption spectroscopy (AAS), UV-VIS and particle-induced X-ray emission (PIXE) in previous studies (Karthikeyan and Balasubramanian, 2006). However, to the best of our knowledge, no investigation has been conducted to compare the results of different laboratories (labs) for such an important and widely used technique.
The aim of this work is to (1) examine the consistency of ion concentrations measured by various labs and by ACSM, (2) explore the impact of the interlaboratory variability in ion concentration measurements on aerosol acidity estimates, and (3) provide recommendations for improving future WSII analysis by IC.

Participating laboratories
Ten laboratories from China, the United Kingdom and Serbia were invited to take part in the interlaboratory comparison of atmospheric inorganic ions and are listed as follows: the University of Birmingham; the University of York; the University of Belgrade; Zhejiang University; Nankai University; Ocean University of China; Beijing Normal University; the Chongqing Institute of Green and Intelligent Technology, Chinese Academy of Sciences; the Institute of Chemistry, Chinese Academy of Sciences; and the Institute of Atmospheric Physics, Chinese Academy of Sciences. The participating laboratories were randomly coded from Lab-1 to Lab-10, not related to the above order.

Sample and data collection
Eight daily PM 2.5 samples were collected on quartz filters (total area 406.5 cm 2 ) from 16 to 23 January 2019 by a highvolume air sampler (1.13 m 3 /min; Tisch Environmental Inc., USA) at an urban site, located at the Institute of Atmospheric Physics (IAP) of the Chinese Academy of Sciences in Beijing, China. The sampling site (39.98 • N, 116.39 • E) is located between the North 3rd Ring Road and North 4th Ring Road and approximately 200 m from the G6 highway. It is 8 m above the ground and surrounded by high-density roads and buildings; detailed information regarding the sampling site can be found elsewhere (Shi et al., 2019). Apart from the aerosol samples, five field blank filters were also collected in the same manner with the pump off. All ion concentrations in this study were corrected by the values obtained from field blanks. Hourly PM 2.5 mass concentrations were obtained from a nearby Olympic Park station available via the national monitoring network operated by the China National Environmental Monitoring Center (CNEMC). Shi et al. (2019) showed that the PM 2.5 data at this station are close to those observed at IAP during the APHH-China campaigns. The close observed PM 2.5 concentrations at different air quality stations in Beijing provide further reassurance of the representability of the observed concentration at the Olympic Park station. The original hourly data were averaged to 24 h for comparison.
An Aerodyne time-of-flight aerosol chemical speciation monitor (ToF-ACSM) with a PM 2.5 aerodynamic lens was also deployed on the same roof of the building at IAP for real-time measurements of nonrefractory (NR) chemical species (organics, Cl − , NO − 3 , SO 2− 4 and NH + 4 ) in PM 2.5 (NR-PM 2.5 ) with a 2 min time resolution (Sun et al., 2020). Another ToF-ACSM was also used to measure the PM 2.5associated nonrefractory chemical species at the Beijing University of Chemical Technology (BUCT), which is located at the West 3rd Ring Road of Beijing and approximately 10 km away from the sampling location of IAP. The collection efficiencies (CEs) applied for the ACSM at IAP and BUCT were different. For IAP, a capture vaporizer was used, and the CE was assumed to be close to 1 (Sun et al., 2020). For BUCT, a standard vaporizer was applied with a compositionand acidity-dependent CE calculated according to Middlebrook et al. (2012). Details regarding quality control of the ACSM at IAP and BUCT can be found elsewhere (Sun et al., 2020;Liu et al., 2020). The concentrations of nonrefractory species were calculated from mass spectra using a fragmentation table (Allan et al., 2004). The ToF-ACSM data were then averaged to 24h for a comparison with those from filter analysis in our study. Note that the ToF-ACSM data at IAP on 19 and 20 January and data at BUCT on 17 and 18 January are excluded from the comparison due to the maintenance of the instrument. An ammonia analyzer (DLT-100, Los Gatos Research, USA) which applies a unique laser absorption technology called off-axis integrated-cavity-output spectroscopy was used for the ambient NH 3 measurements. It has a precision of 0.2 ppb, and the original data with 5 min intervals were averaged to 24 h for the calculation of aerosol pH. More information on NH 3 measurement can be found elsewhere .

Sample analysis
Filter cuts of 5 and 6 cm 2 from the same set of samples were used for extraction in the 10 labs. Filters were extracted ultrasonically for 30 min with 10 mL ultrapure water in all laboratories and then filtered before IC analysis. The instrument details are given in Table 1, and the extraction details including the purity of ultrapure water, model and power of ultrasonicator, and type of syringe filter and vials used for analysis are provided in Table S1 in the Supplement. In total, nine ionic species were reported: F − , Cl − , SO 2− 4 , NO − 3 , Na + , NH + 4 , K + , Mg 2+ and Ca 2+ . Other ions including Br − , NO − 2 , PO 3− 4 and Li + were not included due to their relatively low concentrations in aerosol samples. The calibration detail and quality assurance and quality control (QA-QC) procedures are provided in Table S2.
The CRM for anion (CRM-A, Multi Anion Standard 1 for IC, Sigma-Aldrich) contains 3 mg/L F − , 10 mg/L Cl − , 20 mg/L Br − , 20 mg/L NO − 3 , 20 mg/L SO 2− 4 and 30 mg/L PO 3− 4 . CRM-C and CRM-A were diluted 180 and 6 times, respectively. Of the diluted CRM solutions, 20 mL was marked as unknown solution and sent along with the aerosol samples to each lab for analysis. All CRM solutions were measured by each lab as unknown samples. All filters and solutions were kept frozen during transportation to prevent any loss due to volatilization.

Coefficient of divergence analysis
In order to investigate the differences in ionic concentrations measured by different labs, Pearson's correlation coefficient (R) and the coefficient of divergence (COD) were calculated. The COD is a parameter to evaluate the degree of uniformity or divergence of two datasets. The COD and R were computed for Lab j -Lab-Median pairs, in which Lab j indicates the results of each lab and Lab-Median represents the median values of the 10 labs. Median values are chosen here to better represent the theoretical true concentrations of the ions, as there are some outliers in some labs, and the averages may be less representative. The results of COD and R were also computed for Lab j -Lab-Mean, Lab j -Lab-Upper and Lab j -Lab-Lower pairs (Figs. S1-S3 in the Supplement), where Lab-Mean, Lab-Upper and Lab-Lower represent the mean value, upper values (84th percentile) and lower values (16th percentile) of ion concentrations measured by the 10 labs. The COD of ionic concentrations of two datasets is determined as follows: where j represents the ion concentrations measured by an individual lab, k stands for the median ion concentrations of the 10 labs and P is the number of samples. X ij and X ik represent the concentration of ion i measured by Lab j and the median concentration of ion i measured by the 10 labs, respectively. A COD value equal to 0 implies no difference between two datasets, while a COD of 1 means absolute heterogeneity and maximum difference between two datasets (Liu et al., 2017c). A COD value of 0.2 is applied as an indicator for similarity and variability (Krudysz et al., 2008). A higher COD (> 0.2) implies variability between two datasets, while a lower COD (< 0.2) indicates similarity between them. Overall, a lower COD (< 0.2) and higher R (> 0.8) of a lab suggest a similar variation pattern and similar ion concentrations of this lab to the median values of 10 labs.

ISORROPIA II
ISORROPIA II is a thermodynamic equilibrium model for predicting the composition and physical state of atmospheric inorganic aerosols (available at http://isorropia.eas.gatech. edu, last access: 16 September 2020; Fountoukis and Nenes, 2007). It was applied in this study to calculate the aerosol water content (AWC) and pH. Aerosol pH in this study (pH i ) was defined as the molality-based hydrogen ion activity on a logarithmic scale, calculated applying the following equation (Jia et al., 2018;Song et al., 2019): where a H + represent the molality and the molality-based activity coefficient of H + (aq) , respectively. m is the standard molality (1 mol/kg). Model inputs include aerosol-phase Cl − , SO 2− 4 , NO − 3 , Na + , NH + 4 , K + , Mg 2+ and Ca 2+ and gas-phase NH 3 concentrations, along with daily averaged temperature and relative humidity (Table S3). In this study, the model was run only in forward mode (with gas + aerosol inputs) in the thermodynamically metastable phase state, assuming salts do not precipitate under supersaturated conditions. More information regarding applications of ISORROPIA II can be found in other studies Weber et al., 2016;Song et al., 2018).

Results and discussion
3.1 Quality assurance and quality control (QA and QC)

Certified reference materials (CRMs) -detection accuracy and repeatability
Certified reference materials for both cations and anions were investigated for quality control. CRM-C and CRM-A were analyzed three consecutive times in each lab. The detection accuracy (DA) of each ion was determined as the ratio of measured concentration divided by its certified concentration as a percentage. The results of the DAs of all ions are listed in Table 2. As reported in Table 2, most ions were observed with a DA in the range of 90 %-110 % among the 10 laboratories. However, SO 2− 4 in Lab-3 and NH + 4 in Lab-2 were overestimated, the DAs of which were 132.4 % ± 31.4 % and 135.0 % ± 6.0 %, respectively. The standard deviation of SO 2− 4 measured by Lab-3 was the largest (31.4 %), followed by Cl − measured by Lab-7 (21.3 %), which indicated their poor repeatability. Even though NH + 4 in Lab-2 was observed with a high value of DA, its deviation of three repeats was relatively small, which may be attributable to the evaporation of ammonium in calibration standards in Lab-2; hence, the level it represented was higher than its real concentration. K + in Lab-7 was underestimated, and was observed with a DA of only 72.1 % ± 0.8 %. This may be due to contamination in  the water blanks or the IC system, as the average concentration of K + in three water blanks of Lab-7 was 8.0 ng/L, much higher than the median value of 10 labs (3.4 ng/L).

Detection limits
The detection limits (DLs) in this study were calculated as where SD i is the standard deviation of the blank filters. The mean concentrations of the ions in blanks and DLs (3SD) of all ions are provided in Table 3.

PM 2.5 and ion concentrations
The results for PM 2.5 and all inorganic ion concentrations measured by the 10 labs are presented in Fig. 1. During 16-23 January 2019, the daily mean PM 2.5 ranged from 8.4 to 53.8 µg/m 3 , with an average of 31.4 µg/m 3 . Among these days, 16, 17 and 18 January were deemed moderately polluted days with PM 2.5 concentrations > 35 µg/m 3 , while the rest were nonhaze days with PM 2.5 concentrations falling in the range of 8.4-27.9 µg/m 3 . The time series of all inorganic ions are shown in Fig. 1 to demonstrate the consistency among different laboratories. In Fig. 1, Cl − , NO − 3 , SO 2− 4 and NH + 4 showed a similar trend to PM 2.5 and good correlations among the 10 labs, suggesting the consistency and reliability of using ion chromatography for analyzing these ions, despite various instruments and analyzing methods. Larger variations in Cl − , NO − 3 , SO 2− 4 and NH + 4 concentrations between different laboratories were observed on moderately polluted days, whereas results for the nonhaze days, especially for 19 and 20 January, were observed with good agreement in the 10 labs. Good agreement was also observed for the mass ratios of NO − 3 / SO 2− 4 in most of the labs during the study period (Fig. S4), which basically followed a similar trend to PM 2.5 . On more polluted days, NO − 3 /SO 2− 4 ratios were obviously higher than on less polluted days, suggesting the dominance of mobile The average SNA concentrations of eight samples varied from 6.3 ± 3.3 to 9.1 ± 5.0 µg/m 3 (Lab-4 and Lab-1, respectively) in the 10 labs, accounting for 20.6 % ± 4.8 % to 29.0 % ± 6.7 % of the PM 2.5 mass concentrations. However, their contributions to total ions measured by each lab, which ranged between 83.6 % ± 2.7 % and 86.3 % ± 2.3 %, were not significantly different. The total ions summed to Note that the detection limits were calculated based on large-volume sampling (total filter size: 406.5 cm 2 ; total sampling volume: 1560 m 3 ); n.a.: not available due to no relevant peaks being identified in the chromatography.
24.3 ± 4.9 % (Lab-4) to 33.8 % ± 7.1 % (Lab-1) of PM 2.5 . These results are comparable with those in another study in Beijing which found that SNA accounted for 88 % of total ions and 9 %-70 % of PM 2.5 concentrations (Xu et al., 2019b). As shown in Table 2, the DAs of most ions measured by Lab-4 were < 100 %, while those of Lab-1 were much higher, especially for major ions (> 100 %). Corresponding to this, the ion concentrations in Lab-4 were mostly lower than in other labs, while those of Lab-1 were mostly higher than in other labs. For Lab-6 which was also observed to have lower DA of ions such as SO 2− 4 (89.2 %) and NH + 4 (88.4 %) in the 10 labs, its SNA concentrations and total ions accounted for 24.5 % ± 5.6 % and 28.7 % ± 6.0 % of PM 2.5 , respectively, the second lowest among all labs. Hence, it is very important to run certified reference materials before any sample analysis to ensure the accuracy and good quality of data. K + concentrations analyzed by the 10 labs followed a similar trend to PM 2.5 mass, except with the sample measured on a moderately polluted day (19 January) by Lab-6, which is 2-3 times higher than those measured by other labs. F − concentrations varied across the 10 labs, but most of them shared a similar trend. Some labs like Lab-8 did not follow the same trend due to reporting undetectable F − concentrations. The Na + concentration on the least polluted day (20 January) was abnormally high in Lab-9, while its concentrations measured by other labs were generally low. This may be due to Na + contamination during the preparation or measurement of this sample, as Na + concentrations in the rest of the samples measured by Lab-9 followed a similar trend to those of other labs. The alkaline ions Mg 2+ and Ca 2+ mostly originate from crustal dust and mainly exist in coarse particles (Zou et al., 2018). Their mass concentrations varied considerably due to their relatively low concentrations in aerosol samples and being sometimes below the detection limits in some labs, such as Lab-6. Nevertheless, some labs like Lab-2, Lab-3 and Lab-10 still followed a similar trend.

Comparison with ToF-ACSM data
As shown in Fig. 1, Cl − , NO − 3 , SO 2 − 4 and NH + 4 generally exhibited similar patterns, but due to some outliers, such as the NO − 3 concentration measured by Lab-8 on 16 January, the median values were selected to better represent the general levels and theoretical actual concentrations of ions measured by different labs. The scatter plots of the median mass concentrations of Cl − , NO − 3 , SO 2− 4 and NH + 4 in the 10 labs (IC-Cl − , IC-NO − 3 , IC-SO 2− 4 and IC-NH + 4 ) versus the nonrefractory (NR) species measured by the ToF-ACSM (ACSM-Cl − , ACSM-NO − 3 , ACSM-SO 2− 4 and ACSM-NH + 4 ) are shown in Fig. 2. The time series of IC and ACSM data at IAP and BUCT are plotted in Fig. S5.
Chloride is reported to arise mainly from biomass burning and coal combustion in China . Its average concentration in the 10 labs correlated very well with ACSM-Cl − (R 2 = 0.82 for IAP). However, IC-Cl − in IAP is 2-3 times higher than ACSM-Cl − ; this may be due to the small contribution of Cl − to the overall mass spectrum which made it difficult to quantify by the ToF-ACSM (Allan et al., 2004). Additionally, the ACSM is incapable of measuring Cl − in the form of KCl, as the ACSM only measures nonrefractory Cl − . Poor correlation of chloride (R 2 = 0.21) was also discovered between two collocated ACSMs with a much larger set of data points, while other NR species were observed with strong correlation (R 2 > 0.8) in another study (Budisulistiorini et al., 2014), suggesting the quantification of chloride by ACSM has large uncertainties.
Sulfate, an important component of atmospheric secondary inorganic aerosols, plays an important role in the formation of haze Yue et al., 2019). The correlation coefficient (R 2 ) between the measured IC-SO 2− 4 and ACSM-SO 2− 4 was only 0.26 for IAP with a slope of 0.54. The correlation of IC-SO 2− 4 and ACSM-SO 2− 4 from BUCT was 0.84 (R 2 ) with a slope of 0.56. Judging from the slopes, ACSM-SO 2− 4 and ACSM-NH + 4 were similarly higher than the median values of measured SO 2− 4 and NH + 4 concentrations in this study. The NR species followed the same trend as NR-PM 2.5 , and chemical species measured through filter analysis also shared the same trend as PM 2.5 measured in our study.
Very good correlation between measured IC and ACSM data was found for NO − 3 and NH + 4 with R 2 > 0.9. The lab median value of NO − 3 was very close to the ACSM-NO − 3 from the same sampling site IAP, with a slope of 0.88 for IC-NO − 3 /ACSM−NO − 3 , while that of BUCT was only 0.57. The slopes of IC-NH + 4 /ACSM−NH + 4 were 0.58 and 0.60 for IAP and BUCT, respectively. Comparing IC-NH + 4 to ACSM-NH + 4 , the absolute concentration of IC-NH + 4 differed the most among all ions (42 %), except Cl − . Generally, ACSM-NO − 3 and ACSM-NH + 4 were higher than the median values of measured NO − 3 and NH + 4 concentrations in the 10 labs. Higher concentrations in the online ACSM observations compared to the daily filter sample measurements may be partially due to differences in the performance of the two PM 2.5 cut-point selectors, which led to different transmission efficiencies of particles. Other reasons could be as follows: (1) the uncertainties in ACSM observations themselves -Crenn et al. (2015) reported the uncertainties in NO − 3 , SO 2− 4 and NH + 4 in ACSM analysis were 15 %, 28 % and 36 %, respectively -and (2) negative filter artifacts, such as volatilization of semivolatile ions (Kim et al., 2015), although the latter would not be expected to affect sulfate. Sun et al. (2020) also compared ACSM and filter-based IC results and showed that the concentrations of NO − 3 , NH + 4 and SO 2− 4 in the ACSM measurement were also higher than those of the filter-based measurements, although the slopes were smaller than in our study. It is also possible that the representative ions of ACSM-NO − 3 and ACSM-NH + 4 could have significant interferences from other species in the mass spectrum, caus- ing large uncertainties even after correction for those interferences.
To summarize, SO 2− 4 , NO − 3 , NH + 4 from lab analysis generally correlated very well with the ACSM data, but the absolute concentrations differ by up to 42 %. Cl − from the two methods is correlated, but the concentrations differ by more than a factor of 3. It appears that Cl − is less accurate in online ACSM observations. NO − 3 was comparable for the online data and filter-based data, while SO 2− 4 and NH + 4 in online data may be generally overestimated by a similar factor. It should be noted that higher SO 2− 4 concentrations in online ACSM data could potentially be due to ACSM not being able to separate organosulfate from sulfate. ACSM-NO − 3 , ACSM-SO 2− 4 and ACSM-NH + 4 were also reported to be higher (approximately 10 %-20 %) than filter-analysisbased NO − 3 , SO 2− 4 and NH + 4 in another study (Sun et al., 2020). Although the comparison between IC and ACSM provided important information about the data from the two methods, we recognize that we only have eight data points here. Future studies should be carried out and include more data points in order to comprehensively study the relationship between the online ACSM data and filter-based data. We emphasize that it is essential that both ACSM and filterbased observations are robustly quality controlled before any ACSM and IC intercomparison.

Divergence and correlation analysis
As shown above, some ions like Cl − , NO − 3 , SO 2− 4 and NH + 4 generally exhibited similar patterns, but some of the ions varied significantly in different laboratories. Therefore, Pearson's correlation coefficient (R) and the coefficient of divergence (COD) were both calculated to identify the uniformity and divergence of ionic concentrations measured by different labs. The COD and R values of all ions for Lab j -Lab-Median pairs are presented in Fig. 3. Cl − , NO − 3 , SO 2− 4 , NH + 4 and K + clearly showed high R values (> 0.8) and low COD values (< 0.2) in all labs, suggesting the reliability of the measurement of these ions in different labs. However, F − and Ca 2+ in most of the labs were observed with higher COD values, and Ca 2+ was also found to have a lower R value, suggesting heterogeneity of Ca 2+ detection in different labs, which made this ion less reliable. Mg 2+ was observed with good correlation (> 0.7) between each lab and the Lab-Median, but a higher COD was found between Lab-3, Lab-5 and Lab-6 than with the Lab-Median. Similarly, Na + was also observed with good correlation (> 0.7) between each lab and the Lab-Median, except Lab-9, and a higher COD was found between Lab-5 and Lab-8 than with the Lab-Median.

Ion concentrations calculated by detection accuracy of CRMs
The detection accuracy of the certified reference materials was used to correct the ion concentrations in this study to show the importance of using CRMs for calibration checking and quality control. The correction was conducted by dividing the measured ion concentrations by their corresponding DA value. The coefficient of variation (CV), which indicates the variance of data, was applied here to compare the variation in uncorrected or corrected ion concentrations among the 10 labs. It was calculated as the standard deviation of ion concentrations measured by the 10 labs divided by the mean and expressed in a percentage. A lower CV value indicates the closeness of data measured by the 10 labs and reflects more precise results, while a higher CV value reflects the opposite. As F − , Na + , Mg 2+ and Ca 2+ were undetectable in some labs, only Cl − , SO 2− 4 , NO − 3 , NH + 4 and K + were investigated, and the results are shown in Table 4.
In Table 4, Lab-7 was excluded from the calculation of the CV of both uncorrected and corrected chloride, due to its poor repeatability. The CV of uncorrected chloride concentration in eight samples varied between 11.7 % and 19.3 %, with an average of 14.3 %. The CV of corrected chloride concentration in eight samples varied between 10.4 % and 17.0 %, with an average of 12.6 %. The averaged CV decreased 1.7 % for corrected chloride concentration. Small changes in CV were observed during moderately polluted days (16, 17, 18 January), but more obvious changes occurred during nonhaze days.
The average CV of SO 2− 4 surprisingly increased from 9.8 % for uncorrected SO 2− 4 to 10.9 % for corrected SO 2− 4 (Supplement , Table S4). However, when excluding Lab-3 from the calculation, the averaged CV of uncorrected sulfate concentration was 10.3 %, and it significantly decreased to 6.9 % once corrected. Therefore, it is strongly recommended that an excessive DA (> 110 %) with large variation should be avoided for the correction of SO 2− 4 concentrations. Better agreements of NO − 3 and K + concentrations among the 10 labs were also observed after correction, as indicated by lower CV values for corrected samples. Similar to other ions, the mean concentration of NH + 4 of the 10 labs remained almost the same after correction, but the CV of corrected samples increased from 12.5 % to 13.2 % after correction (Table S4). Nevertheless, it decreased 1.2 % after correction when excluding Lab-2 (the DA of NH + 4 was 135.0 ± 6.0 %) from the calculation. The small change in the coefficient of variation here could be due to the high volatility of ammonia which leads to differing results measured by different analytical procedures in the labs.
To sum up, certified reference materials should be applied for quality control. If the values of the DA highly deviate from 100 % (e.g., > 110 % or < 90 %) or there are large inter-CRM variations, then the measurement procedures have to be checked, including repeating the analysis or repreparing the calibration standard solutions.

Aerosol acidity
In this study, aerosol acidity was evaluated applying three different parameters: the anion and cation equivalence ratio, ion balance, and in situ acidity. Ion balance was calculated by subtracting equivalent cations from anions (Zhang et al., 2007), while in situ aerosol acidity was represented by pH or the concentration of free H + in the deliquesced particles under ambient conditions. In situ aerosol pH can be estimated from various thermodynamic models, for example, SCAPE, GFEMN, E-AIM and ISORROPIA (He et al., 2012;Pathak et al., 2009;Yao et al., 2006). In situ aerosol acidity is most likely to influence the chemical behavior of aerosols (He et al., 2012). Ion balance is widely used to indicate the neutralization status of aerosols with the equivalent ratios of anions / cations in a relative way (Sun et al., 2010;Takami et al., 2007;Chou et al., 2008). It is noteworthy that ion balance and in situ aerosol acidity estimations are empirical approaches which are strongly dependent on the selection of ion species.

Anion and cation equivalence ratio
The ratio of the anion molar equivalent concentrations to the cation molar equivalent concentrations (AE / CE) can be applied to reflect the potential aerosol acidity (Meng et al., 2016;Zou et al., 2018). In this study, AE and CE were calculated as AE = SO 2 − 4 /96 2 + NO − 3 /62 + Cl − /35.5 CE = NH + 4 /18 + Na + /23 + K + /39 + Mg 2+ /24 2 AE represents the equivalent concentrations of all anions; and CE denotes all cation equivalent concentrations. The AE / CE ratios of all samples were compared among the 10 labs (Table 5). The ratios in Lab-1 and Lab-3 were close to unity. The ratios in Lab-5 and Lab-10 were above 1, indicating the deficiency of cations in neutralizing all anions and contrary to Lab-4, Lab-6 and Lab-9. In Table 2, the detection accuracies of major cations (Na + , NH + 4 , K + ) were < 100 % and much lower than those of the major anions (Cl − , NO − 3 , SO 2− 4 ) in Lab-5 and Lab-10, which may have caused lower cation concentrations than their real concentrations and a constantly higher ratio of AE/CE. For Lab-9, the detection accuracies of all ions were very close to 100 %, except NH + 4 which was found with a detection accuracy of > 110 %. Therefore, the AE/CE < 1 of all samples measured by Lab-9 could be the result of overestimation of ammonium. Similarly, in addition to ammonium detection accuracy of > 110 %, generally lower anion detection accuracies than cations were reported by Lab-4, which may explain the AE/CE < 1 in all samples measured by this lab as well. The other three labs (Lab-2, Lab-7 and Lab-8) were found with various AE/CE ratios with both > 1 and < 1 values; moderately polluted days were generally observed with a higher ratio of AE/CE. These results indicate that AE / CE ratios bear large uncertainties in different labs. Stricter quality control measures should be adopted if applying AE/CE ratios to evaluate aerosol acidity.

Ion balance
The calculation of ion balance is an alternative way to evaluate the aerosol acidity (Han et al., 2016;He et al., 2012). Three methods are listed below for the calculation of ion balance in this study: In Method 1, only SO 2− 4 , NO − 3 and NH + 4 were applied for the calculation (Tian et al., 2017), assuming that these three ions and H + alone control PM 2.5 acidity (Ziemba et al., 2007). SO 2− 4 , NO − 3 and NH + 4 were also used in other studies to assess aerosol acidity. For example, the mole charge ratio of NH + 4 to the sum of SO 2− 4 and NO − 3 was applied to represent aerosol acidity (Chandra Mouli et al., 2003;. SO 2− 4 , NO − 3 and NH + 4 were selected because they contributed approximately 90 % of the total ionic species in fine aerosols and play predominant roles in controlling aerosol acidity (Zhou et al., 2012). Salt ions Na + , K + and Cl − were added for the calculation in Method 2. Based on this calculation, Mg 2+ and Ca 2+ were added in Method 3 to include the effects of crustal dust on aerosol acidity (Huang et al., 2014).
The ion balance of all labs varied when applying different methods, especially for the first 3 heavily polluted days, as shown in Fig. 4. Positive ion-balance values indicated a deficiency of cations in neutralizing anions, while negative values implied an excess of cations to neutralize anions. Lab-10  Lab-2, Lab-3 and Lab-7 were excluded for calculating CVs (%) of ammonium, sulfate and chloride, respectively. showed the highest variation among all labs; when excluding Lab-10, the results of the other nine labs agreed very well, with most of the values below 0, suggesting sufficient ammonium to neutralize sulfate and nitrate. By applying Method 1, comparable results were found. The average ion-balance values in all samples were consistent in Lab-1, Lab-2, Lab-6, trations measured by different labs showed good agreement (Fig. 1). This method could reduce the large discrepancy in ion-balance results calculated by adding other ions from the different labs, as their concentrations varied largely in different labs due to varying detection limits.

Aerosol pH using ISORROPIA II
A thermodynamic equilibrium model ISORROPIA II was applied to estimate the in situ aerosol acidity. This was run only in forward mode, as the results from the use of reverse mode (using only particle-phase composition) are reported to be unreliable (Song et al., 2018). The only gas-phase data were for ammonia, but this introduces little error as concentrations of HNO 3 and HCl are likely to be very low in this high-ammonia environment (Song et al., 2018). The inputs include aerosol-phase Cl − , SO 2− 4 , NO − 3 , Na + , NH + 4 , K + , Mg 2+ and Ca 2+ and gas-phase NH 3 concentrations. The daily ammonia concentrations during the study period derived from 5 min data ranged from 13.9 ± 0.6 to 20.1 ± 0.7 ppb (average 17.2 ± 2.2 ppb). The small standard deviations of the daily average (< 1 ppb) suggest that the diurnal variation in NH 3 was not significant. Hence, aerosol pH was only investigated using daily mean NH 3 concentrations. Mean NH 3 concentrations during moderately polluted and nonhaze days were 19.6 ± 0.6 and 15.9 ± 1.5 ppb, respectively. Daily temperature ranged between −4.4 and 4.3 • C with an average of 1.0 • C, and RH ranged from 13.8 % to 40.1 % with a mean value of 22.4 %. The aerosol pH, as well as aerosol water content (AWC), was calculated for all samples by the model (Table S5); details of the calculation of pH and AWC can be found elsewhere (Liu et al., 2017b;Masiol et al., 2020). The calculated aerosol pH results of the 10 labs are presented in Fig. 5. The predicted gas-phase NH 3 by ISORROPIA II was well correlated with the measured NH 3 with slope of 1.02 and R 2 of 0.95 (Fig. S6), which demonstrated the accuracy of thermodynamic calculations by the model (Song et al., 2018).
The computed aerosol pH during the study period generally exhibited good agreement among the 10 labs. Lab-6 was observed with a higher pH and lower ion balance than other labs on 19 January, which could be mainly due to the K + concentration measured by Lab-6 on that day that was 2-3 times higher (Fig. 1), while other ions measured by this lab were more comparable with other labs. The aerosol pH on 3 moderately polluted days was above 7, indicating an alkaline nature of aerosols during these days. This result is consistent with the discussion mentioned above that ion balance estimated by Method 1 was below 0 as more NH + 4 neutralizes NO − 3 and SO 2− 4 . It should be noted that the higher pH (> 7) of those samples could be due to the lower temperature (−4.4 to 4.3 • C) during the sampling period (Table S3), in addition to their relatively alkalic nature. The equilibrium of water (H 2 O) with OH − (aq) + H + (aq) is temperature-dependent. For highly dilute aqueous systems, the values of pK w (= −log 10 [K w ]; K w is the temperaturedependent equilibrium constant on molality basis) at 25 • C (13.99) and 0 • C (14.95) can result in corresponding pH values of 6.995 and 7.475, respectively, both of which are considered neutral (Bandura and Lvova, 2006;Pye et al., 2020). In addition, the low RH in these samples (Table S3) may have also contributed to the high pH values we calculated. Different RH values were tested for aerosol pH among the 10 labs. The results (Fig. S7) showed that at different RH levels (40 %, 50 %, 60 %, 70 %, 80 %), the pH values in the 10 labs were consistent; and the pH values were mostly lower than 6 in all samples. Hence, the higher pH (> 7) of some samples could have resulted from the combination of lower temperature and RH and the nature of the aerosols. Excellent agreement among the 10 labs for the aerosol pH during these moderately polluted days was also found. Nonhaze days, especially the least polluted day on 20 January, showed higher variation among the different labs. The calculated pH values of nine labs mostly fall on the same side of the neutralization line (pH = 7), and only Lab-9 on 20 January falls onto a different side of the pH = 7 line from the other labs. A sensitivity test of Na + , K + , Mg 2+ and Ca 2+ showed that this abnormal pH value was mainly due to the significantly higher Na + concentration of Lab-9 on 20 January.
Our results suggest AE/CE and ion balance are flawed representations of particle acidity, which are not recommended for the evaluation of aerosol acidity. This is also consistent with the conclusions from previous studies (Hennigan et al., 2015;Guo et al., 2015;Pye et al., 2020). ISOR-ROPIA II gives more consistent aerosol pH values among different laboratories. But there are uncertainties within this calculation: (1) RH during some periods in this study was relatively low (around 20 %), and as a result, aerosol water content was very low. Under such conditions, ions mostly exist in the solid phase. Hence, the pH of aerosols with very low RH may not be reliable. (2) The calculation of AWC was only considered for inorganics in this study. Water associated with organics also contributes to AWC. For example, Guo et al. (2015) indicated that it accounts for 29 %-39 % of total PM 2.5 water in the southeastern United States.
NH 3 is the main driving factor affecting aerosol pH and leads to the more alkaline nature of aerosols. To investigate the effect of NH 3 concentration on aerosol pH, we conducted a sensitivity test which showed the aerosol pH of samples measured by the 10 labs at NH 3 levels of 0.5, 1, 2, 5 and 10 ppb (Fig. S8). When the concentration of NH 3 ≥ 2 ppb, the aerosol pH estimates of the 10 labs were generally consistent and less affected by the variation in ion concentrations. But there is more variation of aerosol pH in the 10 labs when NH 3 concentration is under 2 ppb. This suggests when NH 3 concentration < 2 ppb, the aerosol pH could be more affected by the variation in ion concentrations. Wang et al. (2020) also reported that the high concentration of total ammonium (gas + aerosol) was likely an important factor causing lower aerosol acidity of fine particles during a severe haze period in Henan province, China. It is also confirmed in another study that ammonia played an important role in influencing aerosol pH during a winter haze period in northern China (Song et al., 2018).

Summary and recommendations
Despite the use of variable methods and instruments for measuring ion concentrations, data from all the participating labs show a reasonably good agreement in the overall trend for major ions like chloride, sulfate, nitrate and ammonium. The coefficients of divergence of these ions across the 10 labs were lower than 0.2, and the correlation coefficients were higher than 0.8, suggesting a reasonably high reliability of measuring major ions by IC in different labs. However, the interlaboratory difference can be as high as 30 % if excluding the two extreme values for each day and reached up to 100 % in extreme cases if including all data. Furthermore, ions like F − , Mg 2+ , K + and Ca 2+ were observed with large variations in different labs, which may be due to their relatively low concentrations in the samples. Good correlations were found for nonrefractory ion species measured by ACSM with those in our study. However, the absolute mass levels were quite different, which may be due to the differences in the performance of the two PM 2.5 cut-point selectors, the uncertainties in ACSM observations themselves and negative filter artifacts. Certified reference materials were applied to show the detection accuracy of IC measurement in the 10 laboratories. By comparing the coefficient of variation in samples among the 10 labs before and after correction by the detection accuracy of CRMs, we emphasize the importance of using certified reference materials for quality control for future ionic species analysis.
Aerosol acidity was studied through the investigation of ion-balance-based acidity and in situ acidity. Firstly, the ratios of anion equivalent concentrations to cation equivalent concentrations (AE / CE) varied significantly in different labs, which could be attributed to measurement errors, as supported by the different detection accuracies of ions in CRMs. Secondly, by calculating the ion balance, Method 1, which only applied SNA for the calculation, was more consistent in most labs. Poor agreement of acidity estimation was observed in all labs when adding other ions like Ca 2+ and Mg 2+ . Finally, ISORROPIA II was applied for estimating in situ aerosol acidity by calculating aerosol pH in forward (gas + aerosol phases as input) mode. The results showed a similar trend between labs and exhibited a good agreement. This indicates that, if including gaseous pollutant equilibrium in the ISORROPIA II model, the estimated aerosol pH is more consistent even if there are relatively large differences in the measured concentrations of ions.
Based on this analysis and our experience, we recommend the following: 1. Literature aerosol ion data based on online and offline methods should be treated with a degree of uncertainty in mind. The uncertainties are particularly large for minor ions like Ca 2+ from the aerosol filter-based ion chromatography analysis.
2. The ion-balance approach is not recommended for estimating aerosol acidity due to its large uncertainty. Instead, in situ aerosol pH may be used to represent acidity and can be calculated from a thermodynamic model considering gas-aerosol equilibrium (e.g., NH + and NH 3 ). This requires the measurements of aerosol composition as well as of NH 3 .
3. The variation in ion concentrations is expected to strongly affect aerosol acidity estimated by ISOR-ROPIA II when the NH 3 concentration is low (e.g., < 2 ppb in this case). Additionally, the impact of the diurnal variation in NH 3 on aerosol acidity is worthy of investigation, particularly when the NH 3 concentration is low.
4. Certified reference materials should be used on a regular basis to assess the accuracy and reliability of the measurement method. Calibration standards should be reprepared and the IC performance should be checked when the detection accuracy highly deviates from 100 % (e.g., > 110 % or < 90 %).
5. The detection accuracy of ammonium varied significantly among the 10 labs (88.4 %-135.0 %) with the median value close to 100 %. Stock NH + 4 solutions that are used for the preparation of calibration standards should be freshly prepared to ensure good detection accuracy.
6. Robust quality control processes should be put in place to avoid contamination, particularly for those ions with low concentrations, such as K + and Na + . For example, water blanks should be run before any standard or sample analyses to ensure no contamination from water blanks or the IC system.
7. Some batches of commercial quartz filters may be contaminated with Na + and PO 3− 4 , and thus testing each batch of blank filters is necessary before any field sampling (data not shown here). Filter washing may be needed in some cases. 8. Ionic concentration from ACSM observations should be calibrated although the observed trend is robust. Future research should be carried out to compare the offline ASCM and IC using the same filters to clearly identify the discrepancies between the two methods.
Data availability. The data in this article are available from the corresponding author upon request.
Author contributions. ZS conceived the study after discovering large interlaboratory variability in water-soluble inorganic ions from offline and online methods. JX prepared the paper with the help of ZS, RMH and all co-authors. JX, LW, QZ, CZ, XY, DC, WeijL, MW, HT, LiL, ST, WeirL, JW, GS, YH, SS, CP, YC, FY,