Across multiple environments (Fig. 1), we observe similarities in the range of the OXL:SO₄^2- ratio (i.e., slope) across campaigns except for CAMP²Ex (discussed in Section 3.2). A combined plot of all campaigns suggests a common range of OXL:SO₄^2- across different environments (Fig. S1). Visually, the range in OXL:SO₄^2- (Fig. S1) decreases with increasing concentrations, perhaps from a clearer signal of aqueous processing at higher concentrations.

Bootstrapping across all campaigns reveals a stable median OXL:SO₄^2- of 0.0217 (R = 0.76; N = 2948) (details in Table S1) with 95% confidence interval bounds (0.0154 – 0.0296) indicating a relative uncertainty range of ~±30% about the median. The bootstrapped statistics are supported by averaging the OXL:SO₄^2-slopes between campaigns in Fig. 1 (mean: 0.0184, standard deviation: 0.007, median absolute deviation (MAD): 0.004), which, similar to our bootstrapping method, weights all campaigns equally and removes the statistical bias towards larger datasets. The bootstrapped 95% confidence interval of our observed OXL:SO₄^2- (0.0154 – 0.0296) is in excellent agreement with the ratio of yields between aqueous SOA (0.008 – 0.033; Ervens et al., 2011) and SO₄^2- (approximately unity), corroborating the hypothesis of a general range in OXL:SO₄^2-. Numerous studies spanning a diverse set of environments have reported OXL:SO₄^2- values (Table S2) with several falling within our bootstrapped range.

Cumulative probability functions (CDFs) were plotted to more easily compare OXL:SO₄^2- between campaigns (Fig. S2). As point-by-point ratios are sensitive to background levels of OXL and SO₄^2-, we plotted CDFs of their enhancement ratio (ΔOXL/ΔSO4) where values were subtracted by their 10^th percentile to approximate background levels per campaign. The resulting CDFs showed similar curves between multiple campaigns and revealed that approximately 20% of point-by-point OXL:SO₄^2- values fall within our bootstrapped 95% confidence interval (0.0154 – 0.0296) while ~50% of OXL:SO₄^2-values fall within 0.010 – 0.050. In comparison with the linear regression slope, point-to-point ratios are more susceptible to differences in background, resulting in differences in agreement with our 95% confidence interval (e.g., CHECSM). This is a consequence of the point-by-point calculation: although the dataset as a whole may have a mean slope within our confidence interval, there may still be variability in the OXL:SO₄^2- ratios of individual points. Thus, as the 10^th percentile merely accounts for campaign backgrounds, the linear regression slopes (Fig. 1) may better handle different environments by implicitly accounting for individual background levels via non-zero intercepts.

Surface OXL:SO₄^2- values from CHECSM agree with the bootstrapped 95% confidence interval for non-BB samples for PM₁₈ (0.0264; Fig. 1g) and PM₁(0.0196) modes (R = 0.73 for both). Size-resolved data show that this agreement is greatest between 0.32–1 μm (Fig. S3a), where OXL and SO₄^2- masses mostly reside (Cruz et al., 2019). An increase in supermicrometer OXL:SO₄^2- (Fig. S3a) suggests the enhancement of OXL via gas-particle partitioning of OXL and/or its precursors onto coarse particles as documented for the CHECSM region (Stahl et al., 2020b; Stahl et al., 2021). These results suggest the ratio may be applicable to the mixed layer for submicrometer particles.

AToM provides insight into the OXL:SO₄^2- ratio over remote marine environments in both hemispheres. The Pacific and Atlantic Oceans (< 3 km AGL) have a combined OXL:SO₄^2- ratio of 0.0207 (R = 0.51) (Fig. 1f). Separately, the Pacific and Atlantic have ratios of 0.0180 (R = 0.36) and 0.0251 (R = 0.72), respectively, remarkably similar to other environments (Fig. 1). Across altitudes (Fig. S4), OXL:SO₄^2- values for the Pacific between 0 – 7.5 km AGL are within our 95% confidence interval (Fig. S4a) but only near-surface Atlantic samples fall within our confidence interval (Fig. S4c), possibly due to OXL and/or its precursors undergoing gas-particle partitioning onto Saharan dust.

Variability in OXL:SO₄^2- across campaigns was most evident in MASE-II (Fig. 1d) and CAMP²Ex (Fig. 1h), which had instances of very low OXL:SO₄^2-, attributable to (1) fresher plumes that have not had time to form OXL (Wonaschuetz et al., 2012), (2) the degradation of OXL into CO₂ (Zhou et al., 2020), (3) the formation of OXL-metal complexes (Sorooshian et al., 2013; Tao & Murphy, 2019), and (4) the presence of high SO₄^2- backgrounds. Correlation coefficients below 0.50 (Fig. 1) signify the presence of confounding sources, an expected result given the diversity of environments analyzed. Seasonal factors may also influence the ratio (Tao & Murphy, 2019). Variability between campaigns (Fig. 1) may be suggestive of SO₄^2- from cloud-free photochemistry and gas-phase oxidation (Ervens, 2015), which are important sources of uncertainty when using the OXL:SO₄^2-ratio to assess aqueous processing, as our proposed range implies that SO₄^2- is mainly from aqueous processing.

The main utility of this ratio is to gauge relative rather than absolute extents of aqueous processing between air masses via a comparison of inferred OXL. Considering the differences between OXL and SO₄^2- in terms of their precursors, formation mechanisms, and sinks, the consistency of the OXL:SO₄^2- ratio across multiple environments implies a convergence towards a fairly narrow range, which is assisted in part by the large sample sizes used in this study.