Reactive nitrogen-driven atmospheric multiphase buffering induces unintended concomitant pollution

Domain: physics
Published: 2025-12-12
Editorial outcome: major_revision

Abstract
Atmospheric multiphase buffering capacity is a crucial physicochemical property of aerosol that significantly influences the Earth’s radiative budget, climate, air quality, and public health. However, its implications for air pollution remain largely unexplored. Here, we present four years of continuous observation and laboratory experiments as evidence that reactive nitrogen (Nr)-driven atmospheric multiphase buffering can induce unintended Concomitant Pollution. Specifically, gaseous pollutants undergo phase partitioning into aerosol aqueous phases during the process of pH change under buffering constraints, subsequently transforming into concomitant particulate pollution. Furthermore, from a global perspective, we reveal that NH4+/NH3-induced Concomitant Pollution exhibits greater intensity in South Asia during winter, while in summer, it intensifies in North America, Europe, and East Asia. And anthropogenic emissions, particularly buffering agents like NH3, exert a greater impact on Concomitant Pollution across continents than meteorological factors. Thus, the relentless rise in global NH3 emissions has positioned Concomitant Pollution as an urgent challenge.

Introduction
Aerosol acidity (defined as aerosol pH), a critical regulator of ecosystem dynamics, operates at the nexus of the Earth’s radiative budget, atmospheric chemistry, biogeochemical cycling, and climate feedbacks and public health1–6. While anthropogenic emissions of sulfur, nitrogen, and alkaline species (e.g., ammonia (NH3), dust) drive large-scale perturbations in aerosol pH, emerging evidence reveals a counterintuitive planetary feedback: aerosols possess the capacity to autonomously resist external acid-base disturbances through self-regulating proton (H+) exchange at gas-aqueous-particle interfaces7, known as atmospheric multiphase buffering capacity. This multiphase buffering capacity, enabled by dynamic buffering agents (conjugate acid-base pairs, including NH4+/NH3, HNO3/NO3−, and HSO4−/SO42−) that shuttle protons across phases7,8 (Fig. 1a), acts as an atmospheric chemical thermostat, stabilizing aerosol acidity against anthropogenic emission disturbance while recalibrating gas-to-particle partitioning of climate-altering organics. Notably, NH4+, NH3, HNO3, and NO3− are key reactive nitrogen (Nr) species9, with multiphase buffering thereby driving phase-selective reconfiguration of Nr concentrations across gas-particle interfaces and affecting nitrogen deposition10. Deciphering the multiphase buffering deeply is thus pivotal for predicting cascading failures in air quality governance, carbon-climate feedbacks, and the acidification tipping points of vulnerable biomes.

In recent years, the scientific community has started providing important knowledge on the multiphase buffering capacity of aerosols. Studies commonly focus on the mechanistic interactions between multiphase buffering capacity and aerosol pH11,12. For example, there is literature revealing mechanisms behind the mismatch between changed NH3, nitrogen oxides (NOx), and sulfur dioxide (SO2) emissions and stable aerosol acidity in the southeastern United States and Canada based on multiple buffering capacity11, which represents only a part of the extensive impacts. Furthermore, subsequent research has expanded to examine the role of multiple buffering capacity in chemical reaction kinetics, emphasizing its significance in maintaining stable aerosol pH and increasing overall sulfate production across diverse regions, including the southeastern United States, North China Plain, northern India, western Europe, and other regions worldwide13. Notwithstanding the findings from earlier studies, however, a comprehensive understanding of the effects of emerging multiphase buffering capacity in the atmosphere has remained enigmatic. This study seeks to establish the critical significance of multiphase buffering capacity in regulating air pollution dynamics.

Results
Declining buffering capacity precipitates concomitant pollution
To advance our understanding of the complex interactions governing buffering capacity and particulate pollution, we monitored buffering capacity (β) and aerosol pH dynamics across PM2.5 gradients, applying the multiphase buffer theory framework established by Zheng et al.7 (see Methods). Utilizing four years long-term observation data (2018–2021), we quantified the total buffering capacity β values and individual buffering capacity β of three buffer agents NH4+/NH3 or HNO3/NO3−, HSO4−/SO42− (Supplementary Fig. 1). Aerosol pH displayed an initial marginal increase, but then stabilized as the level of pollution worsened (Fig. 1b). Conversely, β manifested a pronounced decreasing trend of aerosol pH and Acid-Base buffering capacity at different PM2.5 concentration levels. c Decadal evolution of dominant buffering pairs. d The buffering capacity β curve for the average during the entire observation period.

Since the industrial revolution, atmospheric pollution has gradually become a prominent issue, but its causative factors have evolved incrementally and vary distinctly across contexts. The study of the Los Angeles smog in 1943 led people to realize that some components of the atmosphere, through chemical reactions involving sunlight14, can be converted into harmful pollutants that further impact the environment. Another classic event is the London Smog in 1952, where they have since found that it’s not the SO2 directly emitted by coal burning, but the secondary sulfates formed by SO2 chemical conversion that caused the air pollution15. A more recent case is the severe photochemical haze pollution16,17, which is affected by the emissions of primary pollutants and the formation of secondary particulate matter (PM2.5) from gaseous and multi-phase heterogeneous reactions and hygroscopic growth of aerosols15,18,19. Notably, the rapid episodic enhancement of secondary inorganic aerosols (SIAs)-dominated by ammonium nitrate bursts-has emerged as a persistent enigma, which may be related to the interconversion between Nr species20. Our previous research has also shown that the chemical reactions of Nr in the atmospheric nitrogen cycle can regulate the formation of PM2.5-O3 co-pollution21. Here, inspired by the theory of multiple buffers, we propose a viewpoint that unintended concomitant pollution (defined as an increase in PM2.5 mass concentration resulting from the gas-to-particle conversion of buffering agents during aerosol acidity stabilization) always emerges during atmospheric multiphase buffering processes driven by key Nr species (Fig. 1a), through combining long-time field observations and global model analyses. Consequently, we have sufficient reason to suspect that unintended concomitant pollution caused by the multiphase buffering process could emerge as a critical driver behind the anomalously rapid SIAs accumulation observed in recent winter haze episodes.

To address this issue, we conduct exploration and discover a trade-off effect between buffering capacity and PM2.5 concentration, as well as a response mechanism between the two issues. Surprisingly, we find that concomitant pollution can be triggered by negative response mechanisms between buffering capacity and air pollution during the pH buffering process, thereby inadvertently exacerbating the pollution. Transmission electron microscopy experiments also provide solid evidence to confirm this phenomenon. Machine learning emphasizes the importance of relative humidity (RH), NH3, and temperature (T) in concomitant pollution. In addition, we further investigate the global spatiotemporal patterns of concomitant pollution. We provide conclusive quantitative evidence demonstrating that concomitant pollution caused by NH4+/NH3 is stronger than that caused by HNO3/NO3−. The concomitant pollution in summer is stronger than in winter, especially prevalent in North America, Europe, South Africa, and East Asia. The theoretical mechanism analysis disentangled the effects of complex and diverse factors on concomitant pollution on a global scale, highlighting that the anthropogenic factor (AF), buffering agent NH3, plays a predominant role in concomitant pollution. Agricultural sources are the main source of NH3, the 2024 Statistical Yearbook released by the Food and Agriculture Organization of the United Nations reports that inorganic fertilizers used in agriculture reached 185 million tonnes of nutrients in 2022, with 58% of this amount being nitrogen, which represents an increase of 37% compared with 200022. The NH4+/NH3 buffering-induced concomitant pollution highlights a self-reinforcing cycle: agricultural NH3 emissions sustain buffering capacity while simultaneously fueling ammonium nitrate-driven PM2.5 growth, creating policy dilemmas for simultaneous air quality and food security goals. Therefore, we propose that prior prevention and control of NH3 represents a crucial strategy for alleviating global secondary pollution and achieving the World Health Organization’s PM2.5 global air quality guidelines by 2050. This study not only advances our fundamental understanding of atmospheric chemistry but also provides a scientific basis for developing more effective air pollution control strategies in urban environments.

Mechanism of pH buffering-induced concomitant pollution
We systematically investigated the mechanistic basis of pH buffering-induced concomitant pollution. Based on nine pollution events during the four years of long-term observation, we found that the trade-off effect between buffering capacity and PM2.5 concentration is universal in the ambient atmosphere (Supplementary Figs. 5–7 and Text 2), which regulates aerosol acidity and air pollution. Therefore, we proposed a novel perspective that the dynamic exchange between gas-phase and particle-phase buffering agents plays a pivotal role in both exacerbating and alleviating air pollution during the acid-base buffering process. To better uncover this response mechanism, we first unveiled the essence of buffering for NH4+/NH3. Wherein, the chemical mechanism of acid buffering is that H+ can be depleted by bonding with NH3 to form NH4+ when acid (such as SO42− from other sources) is added into the liquid phase of the aerosol30,31, thereby maintaining the stability of the aerosol acidity. In this process, since NH3 enters the aerosol phase to form NH4+, it amplifies the load of inorganic PM2.5. This process was termed the “acid-base buffering-air pollution” negative response mechanism, characterized by triggering of concomitant pollution (Fig. 2a). Likewise, for base buffering, the OH- brought by base (such as calcium ions (Ca2+) from other sources) will be neutralized to generate H2O and release NH3 to gas phase, which maintains the stability of the aerosol acidity. In this process, since NH4+ escapes into the gas phase as NH3, it suppresses inorganic PM2.5 formation. This process was termed the “acid-base buffering-air pollution” positive response mechanism, connected with pollution diminishing. As a result, pH values can be stabilized within a specific range without large fluctuations despite the addition of abundant acids or bases, while PM2.5 loading can be either enhanced or reduced (Supplementary Text 3 and Supplementary Figs. 8–10). We have incorporated high-time-resolution online monitoring experiments to conduct an in-depth investigation of the negative response mechanism (Supplementary Text 4 and Supplementary Figs. 11–13). Our experimental results demonstrate the validity of this response mechanism.

Long-term observational data (2018–2021) provide quantitative evidence for substantiating the emergence of concomitant pollution. The ε(NH4+) (fraction of total ammonia (NHT) that partitions to the particle phase) and PM2.5 concentration showed synchronous variation patterns (Supplementary Fig. 14). From the clean stage to the pollution stage, the aerosol pH value regulated by the buffering agent NH4+/NH3 remained relatively stable (Supplementary Fig. 15), fluctuating within a narrow range of approximately 2 units (Supplementary Fig. 16) (see Supplementary Text 5 and “Materials and Methods” for specific calculations), which sustained consistently high nitrate partitioning efficiency (ε(NO3−) ≈ 0.9) (Supplementary Fig. 17). Crucially, ε(NH4+) showed a remarkable increasing trend (approximately from 0.5 to 0.7) with the increment of PM2.5 concentration (Supplementary Fig. 14), reflecting that a large amount of NH3 was converted into NH4+ to neutralize the acidic components formed in the atmosphere, that is, to form the concomitant nitrate particulate pollution. We also utilize single-particle transmission electron microscopy to provide technical verification of these findings: samples from the clean period mostly exhibit a circular shape and have a slightly elemental mass, while samples from the polluted period predominantly show irregular shapes and heavier elemental mass (Fig. 2b, c and Supplementary Fig. 18). Therefore, we have ample reason to believe that long-term observation and laboratory analysis results are strong evidence that buffering capacity can bring unexpected concomitant pollution while maintaining aerosol pH stability. Notably, through theoretical calculations, we found that the concomitant pollution caused by buffering agents varied within the range of approximately 0–200 mol kg−1 (about 0–13 μg m−3 after conversion) when causing 0.5 pH changes, with an average of 23.2 mol kg−1, during clean period (PM2.5 ≤ 75 μg m−3) (Fig. 2d). Therefore, quantitative theoretical analysis mechanistically demonstrated that atmospheric multiphase buffering can induce severe concomitant pollution.

Deciphering concomitant pollution drivers with machine learning
Disentangling the drivers behind this concomitant pollution change requires understanding the role of influencing factors. To this end, we assessed the importance of factors, including meteorological conditions (T, RH), non-volatile ions (SO42−, Ca2+, etc., emitted from pollution sources), volatile compound (HNO3/NO3−), and concentration of the buffering agents (NHT), using a random forest (RF) algorithm with partial dependence plot (PDP) analysis. Factor importance rankings revealed that RH contributed the most to concomitant pollution, followed by NHT and T, while Ca2+, SO42−, and NOT exerted minimal influence (Supplementary Fig. 20), indicating that the variations in T, RH, and NHT significantly influence the concomitant pollution. We further applied the random forest-partial dependence plot (RF-PDP) method to describe the response of concomitant pollution to drivers (Fig. 3). The ten-fold cross-validation was applied to ensure the generalization ability and reliability of the model, with average R2 values for the training set and test set being 0.97 and 0.80 (Supplementary Fig. 21), respectively. These data-driven methods provided basic information for the change of concomitant pollution. RF-PDP simulations demonstrated nonlinear concomitant pollution responses: the increase of RH, NOT, and SO42− dampened concomitant pollution increased, while the effects of T, NHT, and Ca2+ were opposite (Fig. 3). We found that when RH increased from 20% to 40%, concomitant pollution decreased significantly by 72.1 mol kg−1, while the changes in concomitant pollution caused by variations in other factors were basically below 15 mol kg−1. Additionally, to gain a deeper understanding of the response of concomitant pollution to driver change, from a theoretical mechanism perspective, we constructed a thermodynamic model (see “Methods”) and quantified the effects of various factors on concomitant pollution through sensitivity simulation experiments (Supplementary Text 6 and Supplementary Figs. 22–27). The results indicate that changes in these factors primarily influence concomitant pollution by affecting pH and aerosol water content (AWC). For instance, increases in RH, SO42−, and NOT compounds enhance aerosol acidity and AWC, leading to a reduction in the molar concentration of buffering agents and consequently a decrease in concomitant pollution. In contrast, the effects of NHT and Ca2+ are the opposite. The sensitivity experiments for T show some discrepancies with the machine learning results, which may be because the RF-PDP simulations reflect the average concomitant pollution outcomes across multiple data points, whereas the sensitivity experiments demonstrate the actual variations in concomitant pollution under specific scenarios. The results for sensitivity simulation experiments mirrored those obtained for machine learning, corroborating the findings. Altogether, this dual-method convergence establishes RH, NHT, and T as pivotal levers in concomitant pollution modulation, a finding critical for targeted pollution mitigation in anthropogenically perturbed atmospheres.

It should be noted that the above analysis was based on our long-term observations, and this situation mainly applies to regions with abundant ammonia emissions, which are dominated by NH4+/NH3 buffering. However, the dominant buffering agents and their drivers exhibit spatiotemporal heterogeneity globally. Despite this diversity, the underlying mechanisms are fundamentally the same: concomitant pollution is governed by a negative response mechanism, in which gas-phase buffering agents (NH3 or HNO3) are exchanged for particle-phase counterparts (NH4+ or NO3−) to preserve aerosol acidity stability. Building on this framework, we further extend our investigation to global scales, evaluating region-specific buffering regimes, concomitant pollution, and their environmental implications in various regions worldwide.

Global spatiotemporal pattern and driving of concomitant pollution
We further combined response mechanisms with global simulation to explore the spatiotemporal pattern of concomitant pollution and its driving factors from a global perspective. Disparate dominated regimes of buffering capacity prevailed in different regions and seasons, depending on meteorological conditions, aerosol properties, and buffer agent concentrations. This raises critical questions regarding the spatiotemporal patterns of concomitant pollution across global regions. Supplementary Fig. 28 and Text S7 showed the global distribution of the buffering capacity in January, April, July, and October 2019. The analysis revealed that NH4+/NH3 constitutes the primary source of buffering capacity, followed sequentially by HNO3/NO3−, whereas HSO4−/SO42− makes a substantially reduced contribution globally (Supplementary Figs. 29–31). Additionally, buffering capacity levels are relatively low in January and high in July, with April and October showing similar conditions (Supplementary Figs. 28–31). We presented the global distribution of NH4+/NH3 buffering-induced concomitant pollution (Co-P-NH4+/NH3) and HNO3/NO3− buffering-induced concomitant pollution (Co-P-HNO3/NO3−) in winter (January) and summer (July). The result indicated that the Co-P-NH4+/NH3 was stronger than Co-P-HNO3/NO3−, and concomitant pollution in summer was higher than that in winter (Fig. 4). Co-P-NH4+/NH3 Hotspots occurred across the globe in areas characterized by dense populations and intensive agricultural activities32,33, most notably in South Asia but also United States, Mexico, and Brazil in winter, which aligned spatially with buffering capacity distribution. Meanwhile, the Co-P-NH4+/NH3 at 40°–60°N in winter remained weak, but remained at a high level in summer due to the seasonal NH3 emission cycles in these areas (Supplementary Fig. 32). Overall, the Co-P-HNO3/NO3− was weaker than Co-P-NH4+/NH3, which is consistent with their respective contributions to buffering capacity. Furthermore, the Co-P-HNO3/NO3− was weaker in winter than in summer, which was similar to the seasonal variation in Co-P-NH4+/NH3. The weaker Co-P in winter is associated with the typical meteorological conditions of this season. Such an atmospheric environment greatly promotes the conversion process of gaseous components to the particulate phase. This rapid and efficient conversion mechanism effectively consumes the Co-P in the atmosphere, resulting in a relatively low level of Co-P. In winter, the Co-P-HNO3/NO3− was stronger in Central Africa and South Asia. In summer, strong Co-P-HNO3/NO3− appeared in South Africa, Europe, and Central North China, which mirrors HNO3 source regions (Supplementary Fig. 33). Another interesting phenomenon was that during summer, areas with strong concomitant pollution gradually expand towards the north latitude, which may also be related to the increase in temperature. Therefore, on a global scale, concomitant pollution was relatively weak in winter and strong in summer. And Co-P-NH4+/NH3 was stronger than Co-P-HNO3/NO3−. Meanwhile, we found that the Co-P-NH4+/NH3 can reach up to about 200 mol kg−1 when causing 0.5 pH changes in winter, while Co-P-HNO3/NO3− can only reach up to 100 mol kg−1. When subjected to equivalent pH changes, Co-P-NH4+/NH3 and Co-P-HNO3/NO3− concentrations during summer periods remain predominantly below the 50 mol kg−1 threshold (Supplementary Fig. 34). This hierarchy reflects the thermodynamic dominance of NH4+/NH3 buffering in aerosol acidity regulation and air pollution formation, consistent with their relative β contributions.

We further discovered how driving factors affect the global distribution and seasonal variations of concomitant pollution. To address these distinctions, we decomposed the driving factors into meteorological factor (MF, consisting of T and AWC) and anthropogenic factor (AF, consisting of gas-phase buffering agents and ionic composition). A normalized influence metric, MF/AF (details in Methods), was developed to quantify their relative contributions. When MF/AF is greater than 1, MF have a greater influence; otherwise, AF play a more significant role.

Figure 5 delineates the global spatiotemporal patterns of indicator MF/AF, which characterize the importance of factors on NH4+/NH3 buffering-induced concomitant pollution (Co-P-NH4+/NH3) and HNO3/NO3− buffering-induced concomitant pollution (Co-P-HNO3/NO3−) in winter (January) and summer (July). For Co-P-NH4+/NH3, in winter, the breakdown indicated that the areas with weak Co-P-NH4+/NH3 in January were mostly dominated by MFs (Fig. 5). In Russia and Canada, the cold air and increased water content hindered the rise of concomitant pollution. Conversely, the strong Co-P-NH4+/NH3 in South Asia stemmed from intensive agricultural activities emitting high NH3 concentrations34 (Supplementary Fig. 32). The contribution of MF to strong Co-P-NH4+/NH3 in North America was higher than that in South Asia, which exhibited mixed drivers. The combination of high temperature, low AWC, and appropriate aerosol acidity collectively contributes to the high levels of Co-P-NH4+/NH3 (Supplementary Fig. 35–37). The MF contributed more to Co-P-NH4+/NH3 in Brazil and South Africa, which may be due to the high T and low AWC environment (Supplementary Fig. 35–38). In summer, the contribution of MF to high Co-P-NH4+/NH3 was gradually increasing in North America and Europe, possibly because of increased T and diminished AWC (Supplementary Fig. 35–38). These meteorological conditions favor the partitioning of NH4+/NH3 as gaseous NH3 rather than aerosol-phase NH4+, elevating the NH4+/NH3 Concomitant Pollution Index. Additionally, high-temperature and low-humidity conditions enhance aerosol buffering capacity. Consequently, the elevated NH4+/NH3 Concomitant Pollution Index, combined with increased buffering capacity, synergistically intensifies concomitant pollution during summer. This dual mechanism explains the significantly higher concomitant pollution levels in regions like North America and Europe during summer compared to winter. Basically, most regions globally were dominated by AFs, which may be a result of the rising anthropogenic NH3 burdens worldwide (Supplementary Fig. 32). For Co-P-HNO3/NO3−, in winter, the contribution of AF to the strong Co-P-HNO3/NO3− gradually decreases poleward, mirroring Co-P-NH4+/NH3 gradients. The strong Co-P-HNO3/NO3− in Central Africa and South Asia was mainly dominated by AFs owing to the abundant concentration of HNO3 (Supplementary Fig. 33). Moreover, in the Sahara desert, the combination of a strong alkaline aerosol environment and low T results in relatively weak Co-P-HNO3/NO3−, and the contributions of MF and AF were comparable. In summer, the contribution of AF to Co-P-HNO3/NO3− gradually strengthened, possibly due to the increase in HNO3 concentration, such as in East Asia and North America. Increased HNO3 concentration was the result of enhanced photochemical reactions. The global distributions of oxidants OH radical indicated that the OH radical has undergone strong increases in summer compared to winter, especially in regions with latitudes between 0° and 60°N (Supplementary Fig. 39). The OH radical concentrations in East Asia, South Asia, Europe, and North America are significantly higher during summer than in winter (Supplementary Fig. 40). The elevated nitrate production rate for the photochemical reactions pathway further confirmed the above results (Supplementary Figs. 40 and 41).

Implications of concomitant pollution
Our work reveals that pH buffering-induced concomitant pollution is indeed a critical driver behind the anomalously rapid SIAs accumulation observed in recent winter haze episodes. We find that the concomitant pollution can be triggered by the acid-base buffering-air pollution negative response mechanism, which paradoxically amplifies PM2.5 initiation and evolution. This phenomenon is mainly achieved by maintaining pH stability through the gas-liquid exchange of buffering agents composed of important reactive nitrogen species (NH4+/NH3 or HNO3/NO3−). Theoretical analysis and field emission transmission electron microscopy experiments have both confirmed our finding. Machine learning attribution analysis identifies RH as a key leverage point: curbing ammonia emissions during periods of low RH (<40%) could prove significantly more effective, which particularly emphasizes the timing of ammonia emissions controls in northern China. Sensitivity experiments and theoretical analysis also confirm this result (Supplementary Text S8; Supplementary Figs. 42 and 43). Strategic emission curtailment during meteorologically favorable windows (e.g., RH < 40%) could disrupt the self-reinforcing pollution-buffering cycle while maintaining ecosystem nitrogen thresholds. Therefore, this finding underscores the importance of preemptive action against gaseous buffering agents (e.g., NH3, NOx) before a rise in pollution levels.

Global spatiotemporal analysis reveals pronounced seasonality in concomitant pollution. Overall, the concomitant pollution in summer is higher than that in winter. Thus, NH4+/NH3-induced concomitant pollution in North America, Europe, South Africa, and East Asia requires more attention. In contrast, South Asia exhibits inverse seasonality, where winter NH3 emissions from intensive agriculture and biomass burning elevated concomitant pollution compared to monsoon seasons. Furthermore, the importance of anthropogenic emissions is emphasized globally. Global NH3 emissions have surged from 20.6 Tg N yr−1 in 1860 to 58.2 Tg N yr−1 in 1993, with current trajectories projecting a doubling to 118 Tg N yr−1 by 205035. Therefore, this threefold anthropogenic acceleration of buffering agent NH3 -from preindustrial baselines to Anthropocene extremes—portends a commensurate amplification of PM2.5 pollution burdens. We estimated that the concomitant pollution caused by NH3 could reach up to about 24 μg m−3 by 2050 (based on the maximum concomitant pollution that can be caused by buffering 0.5 pH), which will be 1.8 times higher than in 2019. These findings corroborate the status of reactive nitrogen as a pressing global environmental challenge. As a response measure, the United Nations Environment Assembly has established an unprecedented ambition to halve anthropogenic nitrogen waste by 2030 in its Sustainable Nitrogen Management Resolution (UNEP/EA.4/L16)36 and the 2019 Colombo Declaration37. Therefore, our analyses underscore the significance of persistent NH3 control to achieve the WHO Global Air Quality Guidelines targets for PM2.5 by 2050, and they have been proven to be cost-effective29,38. This strategy balances ecological nitrogen thresholds with air quality imperatives in the Anthropocene.

The main potential for NH3 abatement lies in agricultural activities, as they are the primary source of NH3 emissions39. This study emphasizes that the environmental benefits of emission reduction measures (such as reducing PM2.5) are highly dependent on the region and season in which they are implemented. To maximize cost-effectiveness, emission reduction measures should be prioritized during meteorological windows most sensitive to NH3 emissions (e.g., periods of low RH). This measure mainly includes two aspects: optimizing nitrogen fertilizer and improving manure management40. For optimizing nitrogen fertilizer, deep placement of N fertilizer is a good option, as it mainly reduces NH3 volatilization by applying the fertilizer deeper into the soil rather than surface broadcasting41. The use of efficient nitrogen fertilizers containing urease or nitrification inhibitors can also suppress the release of NH3 into the atmosphere42. It is particularly important that the timing of these measures is crucial. For instance, in regions like Northern China and South Asia, emphasis should be placed on implementing these measures during the pre-monsoon dry season (spring), as the low RH conditions during this period cause a significant portion of gaseous NH3 to remain in the gas phase without converting into particulate matter. For North America and Europe, focus should be placed on summer months-these periods coincide with peak fertilizer application, and are accompanied by low RH and high solar radiation, which facilitate the rapid formation of secondary particulate matter. At this stage, emission reduction proves most effective in lowering PM2.5 concentrations. And optimized management practices such as the “4R Nutrient Stewardship” approach promoted by the International Fertilizer Association43,44 are the best management practices, which help reduce agricultural NH3 emissions without causing crop yield loss. This approach mainly includes the right fertilizer type, the right amount, the right placement, and the right time. Therefore, we propose to refine the “Right Time” principle in the “4R Nutrient Stewardship” framework into concrete practice: minimizing fertilizer application during adverse weather conditions characterized by low RH (<40%) and limited precipitation. This approach leverages targeted best management practices to achieve optimal emission reduction outcomes. For livestock production systems, NH3 abatement measures include manipulation of feed rations and manure management practices, such as improvement of storage facilities and covering the surface to reduce gas diffusion45,46. Given that manure application similarly constitutes a significant source of NH3, the aforementioned recommendation regarding optimized fertilization timing remains equally applicable to the field application of manure. Strategic timing of fertilizer and manure application to coincide with beneficial meteorological windows, alongside the synergistic adoption of high-efficiency fertilizers and improved manure management, can dramatically cut agricultural NH3 emissions without sacrificing crop yields47. Additionally, mitigating combustion-related NH3 emissions is another option for reducing NH3 emissions, which can alleviate pressure on agricultural NH3 mitigation efforts48–50.

Additionally, buffering agents NH3 and NOx, recognized as short-lived climate forcers51, exert complex climate impacts through dual radiative pathways. Their gas-to-particle conversion generates secondary inorganic aerosols, which induce net negative radiative forcing via light scattering and cloud interactions52. This aerosol-driven cooling temporarily offsets anthropogenic CO2 warming, creating a precarious climate penalty. Nevertheless, future improvements in air quality could paradoxically intensify global warming. Therefore, it’s crucial to integrate considerations among “acid-base buffering-concomitant pollution-climate”, to better develop an effective emission reduction strategy that is beneficial to both air quality and climate change, which is a critical frontier in Anthropocene sustainability science.

Methods
Field observations
The 1-h resolution observations were collected at the air quality research supersite located in Nankai University from January 1, 2018, to November 31, 2021. The PM2.5 mass concentrations were measured using an ambient ion monitor (AIM URG-9000D, URG Corporation). The concentrations of SO2, NOx, and O3 were measured using corresponding gas analyzers (Teledyne API T101, T201, and T400). The temperature (T) and RH were recorded using a miniature weather station (WS600-UMB, Lufft). Details of the observation stations were described in our previous work21,53.

Global simulation
To conduct global distribution of concomitant pollution, we used monthly average meteorological data T and RH, gaseous components SO2, HNO3, NH3, HCl, and ionic data NH4+, Mg2+, K+, Ca2+, NO3−, NH4+, Cl− from the three-dimensional chemical transport model GEOS-Chem (version 14.5.3) in January, April, July, and October 2019 (https://doi.org/10.1038/s41467-024-48793-1)54. The relevant datasets for reference and validation can be referred to https://doi.org/10.6084/m9.figshare.28532636. GEOS-Chem is driven by the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2) reanalysis meteorological fields with 2°(latitude)×2.5°(longitude) horizontal resolution within the regional domains. The specific model settings can be found in our previous research54.

For data calibration, the simulation results of PM2.5 in this work are verified by comparing with the reanalysis datasets or observation-constrained datasets. The global reanalysis dataset “Satellite-derived PM2.5” from the Atmospheric Composition Analysis Group at Washington University in St. Louis (https://sites.wustl.edu/acag/datasets/surface-pm2-5/) is utilized (Supplementary Fig. S44). In addition, we thoroughly discuss the spatiotemporal resolution of the NH3 emission inventory and evaluate how emission uncertainties impact the results (Supplementary Text 9 and Figs. 45–48).

pH estimation
Aerosol pH and AWC were estimated using the thermodynamic equilibrium model ISORROPIA-II (http://isorropia.eas.gatech.edu), assuming that the aerosol system is in equilibrium55. This model solves the equilibrium state of K+-Ca2+-Mg2+-NH4+-Na+-SO42−-NO3−-Cl−-H2O aerosol system, and it has been widely used in many other studies56–58. The forward mode and metastable state were selected in this study. The aerosol pH was calculated by the following equation:

pH = −log10(1000γH+cH+ / AWC) (1)

Where cH+ is the concentration of H+ per volume of air (μg m−3), γH+ is the activity coefficient of H+ (assumed to be 1.0)55, and AWC is the concentration of AWC (μg m−3).

Buffering capacity β
The buffering capacity β, also known as differential buffer capacity, is defined as the amount of strong base (db (mol)) that needs to be added to a 1 L solution to increase its pH by dpH units; Or conversely, to reduce the pH of a 1 L solution by dpH units, the amount of strong acid that need to be added to the solution (da (mol))59. The mathematical expression is as follows:

β = db/dpH = −da/dpH (2)

Based on this formula, the specific mathematical expression of buffer value β for conjugate acid-base equivalent buffer systems is derived7,59, which is the sum of the self-buffering capacity of water and the buffering capacity of the buffering agent:

β = 2.303([H+] + [OH−]) + 2.303 Σi ci (Ka,i* [H+] / ([H+] + Ka,i*)2) (3)

Where [H+] and [OH−] are the concentrations of H+ and OH− in the solution, respectively. The c represents the total equivalent molality of the buffer agent. And the Ka,i* is the effective dissociation constant of the buffer agent, which can be expressed by:

Ka,BOH* = [H+(aq)] ([BOH(aq)] + [BOH(g)]) / [B+(aq)] = Ka,BOH (1 + H*i RT ρw / AWC) (4)

Ka,HA* = [H+(aq)] ([HA(aq)] + [HA(g)]) / [A−(aq)] = Ka,HA (1 + H*i RT ρw / AWC) (5)

for volatile base BOH and volatile acid HA that dissociate in the form

B+(aq) + H2O ⇌ H+(aq) + BOH(aq) (6)

HA(aq) ⇌ H+(aq) + A−(aq) (7)

where Ka and Ka are acid dissociation constants, ρw is the density of water (1012 μg m−3), Hi is Henry’s law constant, R is the ideal gas constant (0.0825 atm L mol−1 kg−1), T is the temperature in K and AWC is aerosol water content in μg m−3.

Therefore, for NH4+/NH3 buffering agent:

βNH4+=NH3 = 2.303 [NHT] (Ka,NH3* [H+] / ([H+] + Ka,NH3*)2) (8)

Ka,NH3* = [H+(aq)] ([NH3(aq)] + [NH3(g)]) / [NH4+(aq)] = γNH4+ Ka,NH3 (1 + HNH3 RT ρw / AWC) (9)

Kw = Ka,NH3 = Kb,NH3 (10)

Where [NHT] is total equivalent molality of NH3 and NH4+ in mol kg−1; Ka,NH3 is the acid dissociation constant of NH3 in mol kg−1; γNH4+ is the activity coefficient of NH4+; Ka,NH3* is the effective dissociation constant of NH3 in mol kg−1; Kw is the water dissociation constant in mol2 kg−2.

For HNO3/NO3− buffering agent:

βHNO3=NO3− = 2.303 [NOT] (Ka,HNO3* [H+] / ([H+] + Ka,HNO3*)2) (11)

Ka,HNO3* = [H+(aq)] ([HNO3(aq)] + [HNO3(g)]) / [NO3−(aq)] = γNO3− Ka,HNO3 (1 + HHNO3 RT ρw / AWC) (12)

Where [NOT] is total equivalent molality of HNO3 and NO3− in mol kg−1; Ka,HNO3 is the acid dissociation constant of HNO3 in mol kg−1; γNO3− is the activity coefficient of NO3−.

For HSO4−/SO42− buffering agent:

βHSO4−=SO42− = 2.303 [SOT] (Ka,HSO4−* [H+] / ([H+] + Ka,HSO4−*)2) (13)

Ka,HSO4−* = [H+(aq)] ([HSO4−(aq)] + [SO42−(aq)]) / [HSO4−(aq)] = γHSO4− Ka,HSO4− / γSO42− (14)

Where [SOT] is total equivalent molality of HSO4− and SO42− in mol kg−1; Ka,HSO4− is the acid dissociation constant of HSO4− in mol kg−1; γHSO4− is the activity coefficient of HSO4−.

And total buffering capacity:

βTotal = βwater + βNH4+=NH3 + βHNO3=NO3− + βHSO4−=SO42− = 2.303 [H+] + 2.303 [OH−] + 2.303 [NHT] (Ka,NH3* [H+] / ([H+] + Ka,NH3*)2) + 2.303 [NOT] (Ka,HNO3* [H+] / ([H+] + Ka,HNO3*)2) + 2.303 [SOT] (Ka,HSO4−* [H+] / ([H+] + Ka,HSO4−*)2) (15)

[OH−] = Kw / [H+] (16)

The meaning of all parameters is the same as above. The calculation of the acid dissociation constant and Henry’s coefficient is shown in Supplementary Table 1.

The calculation of pH change by integral buffer capacity α
In the actual world environment, the buffering process is usually a continuous process, and the buffering capacity β described above describes the instantaneous buffering capacity of aerosols. To describe the entire continuous buffering process, we introduce the integral buffering capacity α proposed by Dai et al.60. The corresponding mathematical expression (Eq. (17)) is defined as the amount of strong acid or base required to change the pH of 1 L of solution within the specified pH range.

α = ΔC = ∫pH1pH2 β dpH (17)

Among them, C is the required acidity and alkalinity, pH1 is the initial pH value before the buffering process occurs, and pH2 is the pH value after the buffering process occurs. The specific derivation process of integral buffering capacity α is as follows. Based on the Brønsted–Lowry theory of acids and bases, a buffer solution is usually a balanced system of weak acids and their conjugate acids in water. For a solution consisting of a weak acid HA and a conjugate acid A−, a dissociation equilibrium is defined as follows:

[HA] ⇌ H+ + [A−] (18)

Ka = [H+] [A−] / [HA] (19)

Therefore, the pH of the buffer solution is obtained:

pH = pKa + lg ([A−] / [HA]) = pKa + lg ([A−] / (C − [A−])) (20)

Where C is the total concentration of weak acid HA and conjugate acid A−. Based on the equation of differential buffer capacity with [H+] and total concentration C:

β = 2.303 (Ka [H+] / (Ka + [H+])2) C (21)

Combining Eq. 19, we obtain:

β = 2.303 [A−] (C − [A−]) / C (22)

In the integral of both sides of Eq. 22, the pH value changes, that is pH2 = pH1 + n. [A−]1 is the concentration of A− corresponding to pH1, and [A−]2 is the concentration of A− corresponding to pH2.

∫pH1pH2 β dpH = ∫[A−]1[A−]2 (2.303 [A−] (C − [A−]) / C) d[A−] = ∫pH1pH2 β dpH (23)

Thus, we have:

n = pH2 − pH1 = lg ([A−]2 / (C − [A−]2)) − lg ([A−]1 / (C − [A−]1)) (24)

[A−]2 = C / (1 + 10−n (C − [A−]1) / [A−]1) (25)

We then obtain the expression of the integral buffer capacity when base is added:

αb = [A−]2 − [A−]1 = (10n − 1) [A−]1 (C − [A−]1) / (C + (10n − 1) [A−]1) (26)

Similarly, when adding acid, we set pH2 = pH1 − n to obtain the corresponding integral buffering capacity as follows:

αa = [A−]2 − [A−]1 = (10−n − 1) [A−]1 (C − [A−]1) / (C + (10−n − 1) [A−]1) (27)

Where n is the change of pH, and the remaining variables are the same as in β. Therefore, when adding acidity or alkalinity, the above equation can also be transformed into Eqs. 28–29 to calculate the change in pH value.

n = log10 ([A−]1 αb + [A−]1 (C − [A−]1)) / (C − [A−]1) αb + C [A−]1) (28)

n = log10 (C [A−]1) / ([A−]1 αa + [A−]1 (C − [A−]1)) (29)

Field emission transmission electron microscopy experiment
We collected single particle samples during the clean and polluted periods using the DKL-2 single particle sampler on the second floor of the School of Environmental Science and Engineering at Nankai University on October 30, 2023. Aerosol particles are deposited on a copper TEM grid coated with carbon film using a single-stage cascade impactor with a nozzle diameter of 0.5 mm and an air flow rate of 1.0 l min−1. The sampling time range is 30 to 120 s, depending on visibility. After sampling, seal the TEM grid in dry plastic capsules to prevent contamination. Afterwards, the sample was analyzed using a field emission transmission electron microscope (TEM). TEM images are used to determine particle size, morphology, and mixing state. Use energy dispersive X-ray spectroscopy (EDX) to determine elemental composition.

The calculation of concomitant pollution
The essence of the buffering process is neutralization of acid and base, which is accompanied by the gas-particle partitioning process. The buffering agents in the ambient air are the source of particle-phase pollutants, ultimately leading to the degree of pollution. For this purpose, the ratio of gas-phase buffering agent NH3 concentration to total buffering agent (NH3 + NH4+) concentration is defined as “Concomitant Pollution Index” (Co-P index, Eq. 30). Moreover, the calculation of “concomitant pollution” (Co-P) has been further defined, with the following equations:

Co-P Index = [NH3] / ([NH3] + [NH4+]) (30)

Co-P = βNH4+=NH3 = 2.303 [NHT] (Ka,NH3* [H+] / ([H+] + Ka,NH3*)2) (31)

Ka,NH3* = γNH4+ Ka,NH3 (1 + HNH3 RT ρw / AWC) (32)

where, [NH3] and [NH4+] are the concentration of NH3 and NH4+ in ambient environment, respectively. C is the total concentration of NH3 and NH4+ in μg m−3. Similarly, HNO3/NO3− induced concomitant pollution is as follows:

Co-P Index = [HNO3] / ([HNO3] + [NO3−]) (33)

Co-P = βHNO3=NO3− = 2.303 [NOT] (Ka,HNO3* [H+] / ([H+] + Ka,HNO3*)2) (34)

Ka,HNO3* = γNO3− Ka,HNO3 (1 + HHNO3 RT ρw / AWC) (35)

where, [HNO3] and [NO3−] are the concentration of HNO3 and NO3− in ambient environment, respectively. C is the total concentration of HNO3 and NO3− in μg m−3, M is the relative molecular mass of HNO3.

Machine learning methods, including RF, Xgboost, and Neural Networks, can effectively utilize observation datasets, construct models from the perspective of measured data, and evaluate the effects of pollutant influencing factors. Among them, RF performs well in classification and importance assessment in the environmental field61–63, which was applied to evaluate the importance of multiple factors (SO42−, Ca2+, T, RH, NHT, and NOT) to concomitant pollution. Here, randomly extract 70% of the samples from all datasets, forming a new training dataset for model training. The remaining 30% of the samples will be used as the test dataset to evaluate the performance of the model. As shown in Supplementary Fig. 49, the coefficient of determination (R2) is 0.88, indicating good model performance.

Random forest-partial dependence plot (RF-PDP)
PDP is a visualization tool used to understand how a model’s prediction depends on one or more features. It provides a visual understanding of the internal working mechanism of the model by showing how the average value of the model’s prediction changes as the feature value varies. The calculation principle of RF-PDP is as follows:

f(XS) = 1/n Σi=1n RF(XS, X(i)C) (36)

Where f(XS) represents the predicted value of the RF model when the input is XS; RF stands for the trained RF model; XS is the feature selected for calculating the partial dependence function in the RF model; X(i)C represents the features that are not selected in the RF model, and these features are input into the model as fixed values; n is the number of samples.

The hyperparameter settings and validation methods of the machine learning model was set as follows:

Hyperparameter settings: in the RF regressor, we set the hyperparameter n_estimators=500, indicating that the model will train 500 decision trees. Another hyperparameter random_state=0 to ensure consistent results in each run. The main hyperparameters in pdp.pdp_isolate include (1) percentile_range=(1, 100), this hyperparameter sets the range of features for the PDP graph from the 1st percentile to the 100th percentile, which determines the range of feature data used to generate the PDP; (2) num_grid_points=20, this hyperparameter indicates the number of discrete points of the PDP graph, meaning that the feature values will be divided into 20 discrete points.

Validation methods: In terms of data partitioning, the data is randomly partitioned into a training set and a test set. We set train_test_split(X, Y, test_size=0.3, random_state=8), where 30% of the data is used for testing and 70% of the data is used for training. random_state=8 ensures the reproducibility of the data division. We split the data into a training set and a test set, fitted the model using the training set and tested its performance. In addition, the ten-flod cross-validation was applied to ensure the generalization ability and reliability of the model, with average R2 values for the training set and test set being 0.97 and 0.80 (Supplementary Fig. 21), respectively, indicating that the model used in this study has strong predictive capabilities and can effectively capture the main trends and relationships in the data.

The calculation of dominated influence factors
For concomitant pollution caused by NH4+/NH3, based on Eq. 30, we take the logarithm ln on both sides of the formula to obtain formula 37:

ln(Co-P) = ln(Co-P Index * C * 103 / (2.303 * AWC * MNH3 * ([H+] + Ka,NH3*)2)) (37)

Moving the constant term to the left of the equation, Eq. 34 is transformed into:

ln(Co-P) − ln(2.303 * 103 / MNH3) = ln(Co-P Index * C * [H+] * Ka,NH3* / ([H+] + Ka,NH3*)2) (38)

Therefore, for Co-P caused by NH4+/NH3, the contributions of anthropogenic and MF to Co-P can be roughly calculated using the following equation:

C anthropogenic factors = ln(Co-P Index * C * [H+] * Ka,NH3* / ([H+] + Ka,NH3*)2) (39)

C meteorological factors = ln(Ka,NH3* / (AWC * ([H+] + Ka,NH3*)2)) (40)

Similarly, for HNO3/NO3− induced Co-P, the contributions of anthropogenic and MF to Co-P can be roughly calculated using the following equation:

C anthropogenic factors = ln(Co-P Index * C * [H+] * Ka,HNO3* / ([H+] + Ka,HNO3*)2) (41)

C meteorological factors = ln(Ka,HNO3* / (AWC * ([H+] + Ka,HNO3*)2)) (42)

MF/AF = C meteorological factors / C anthropogenic factors (43)

It is important to note that the MF/AF ratio employed in this study is a conceptual simplification. In reality, meteorological and AF are highly intertwined. For instance, AWC, a key parameter in heterogeneous chemistry, is co-determined by meteorological conditions (e.g., RH) and anthropogenic aerosol composition. The diagnostic framework for global analysis, while useful, is a simplification and might underestimate their synergistic effects. Nevertheless, the MF/AF indicator serves as a valuable diagnostic tool for identifying the dominant drivers of concomitant pollution across different regions and seasons.

Data availability
The authors declare that the main data supporting the findings of this study are available. Source data are provided with this article, and Supplementary Information is available at Figshare https://doi.org/10.6084/m9.figshare.28532636.

Code availability
The ISORROPIA-II model is available at http://isorropia.epfl.ch.

Peer review rounds
[{"round": 1, "reviewer_comments": {"reviewer_1": "General comments\nThis study explores the relationship between atmospheric multiphase buffering capacity and associated pollution, revealing\nthe key role of the NH₄⁺/NH₃ system in regulating aerosol acidity and air pollution formation through long-term observations,\nglobal simulations, and machine learning analysis. The paper proposes and validates a new mechanism in which the\ndecline in buffering capacity exacerbates associated pollution, providing quantitative evidence through experimental and\ntheoretical calculations. It presents the first systematic assessment of the global spatiotemporal distribution of associated\npollution, highlighting the dominant role of the NH₄⁺/NH₃ system across different regions and seasons. By incorporating\nmachine learning techniques, the study identifies key driving factors of associated pollution and quantifies the relative\ncontributions of meteorological conditions and human activities. From a policy perspective, it analyzes the impact of NH₃\nemission control on improving air quality, offering some insights for future pollution management and global nitrogen\ngovernance.\nWhile this study presents valuable scientific contributions through its comprehensive dataset and methodological approach,\ncertain aspects of the research design and presentation could benefit from further development. The methodological\ndescriptions occasionally lack sufficient detail to fully evaluate the analytical choices, and the logical progression of the\ndiscussion could be strengthened to better connect findings with broader implications. Additionally, the logical progression\nof mechanistic explanations occasionally lacks clarity, particularly in connecting theoretical frameworks (e.g., proton\nexchange dynamics) to observed pollution events. Addressing these areas would enhance both the clarity and impact of the\nwork. Below are specific suggestions for improvement:\n(1) The study finds that concomitant pollution is more severe in summer; however, it does not delve into the specific\nmeteorological driving mechanisms (such as enhanced photochemical reactions or changes in aerosol liquid water content).\nIt is recommended to include a more detailed discussion on these factors to strengthen the physical explanation of the\nresults.\n(2) Regarding the negative feedback mechanism (acid input → NH3→ NH4⁺ → PM2.5 formation): Although the study\nproposes this mechanism, it lacks experimental validation through real-time tracking of gas-to-particle conversion rates or\nisotope-labeling techniques. Can online mass spectrometry or smoke chamber experiments be supplemented for further\nexploration?\n(3) Regarding the GEOS-Chem global simulation: The study relies on the GEOS-Chem model but does not thoroughly\ndiscuss the spatiotemporal resolution of the NH₃ emission inventory (e.g., seasonal variations in agricultural sources such\nas fertilization periods) or quantify uncertainties in emission data. A sensitivity analysis should be conducted to evaluate\nhow emission uncertainties impact the results.\n(4) The paper suggests strengthening NH₃ emission control to reduce concomitant pollution, but it does not provide a\ndetailed discussion on how to reduce NH₃ emissions while ensuring agricultural production. Additionally, it would be\nvaluable to explore whether there are optimal spatiotemporal windows for NH₃ emission reductions (e.g., being more\neffective under low humidity conditions).\n(5) The hyperparameter settings and validation methods of the machine learning model need to be described in more detail.\nFor example, while the paper mentions the use of the Random Forest (RF) algorithm, it does not clarify whether feature\nselection was performed to avoid multicollinearity issues, or if cross-validation was used to ensure the model's\ngeneralizability.\nSpecific comments\nRegarding terminology consistency: The term 'Concomitant Pollution' is introduced without rigorous definition when first\nappearing in the text, creating potential confusion with similar terms like 'Complex Pollution.' We suggest providing a precise\ndefinition in the introduction section and clearly differentiating it from related pollution concepts.\nLine 28: The units \"13 μg m⁻³\" and \"13 μg /m³\" are used interchangeably in different sections. It is advised to standardize the\nnotation\nLine 248: In Figure 3 (Analysis of main drivers of Concomitant Pollution by machine learning.), the error bars for each\nvariable are not labeled as either standard deviation (SD) or standard error (SE). It is recommended to clarify this in the\nfigure legend or caption.\nLine 351: Figure 5: MF/AF metric readability: The color scale and legend for the\nMF/AF (meteorological factor/anthropogenic factor contribution ratio) metric in Figure 5 lack clear threshold definitions (e.g., MF/AF>1 indicating meteorological\ndominance). We recommend improving the legend annotations and adding explanatory text to clarify these critical\nthresholds.\nLine 533: The spatial resolution of the GEOS-Chem global simulation is not clearly stated. It is recommended to include this\ninformation.\nLine 554: the number for Equation 2 should be right-aligned.", "reviewer_2": "The manuscript discussed the atmospheric multiphase buffering capacity and how that was linked with the aerosol pollution\nconcentration. The authors proposed a concept of concomitant pollution and analyzed the main drivers that control its\nformation and the underlying “Acid-Base buffering-air pollution” feedback mechanism.\nIt is novel and interesting to investigate the interactions between aerosol acidity and concentration; however, I think that the\nmanuscript is very difficult to follow, maybe because of its presentation or a lack of some details explaining the key findings.\nMy main concerns include:\n1) The concept of concomitant pollution. This is not clearly defined in the manuscript. What is concomitant pollution? Is this a\npart of the aerosol concentration? What do you mean by “unintended concomitant pollution”? Although the Methods section\nhas a description of the calculation of concomitant pollution, it is not clear what its physical meaning is and how that is linked\nto the total aerosol concentration, and further why this term is helpful to interpret the pollution formation.\n2) It is also difficult to understand the “Acid-Base buffering-air pollution” feedback mechanism as proposed in Figure 2 and\nthe relevant text (Lines 165-210). How to understand this feedback mechanism? Aerosol pH could remain relatively stable\nwhile the levels of aerosol pollution could vary significantly. What are the interactions between the two? The caption of\nFigure 2 is not clear, i.e., what are the color shadings and y-axis in panel (a), and what is the y-axis in panel (d)? The caption\nof Figure 3 is also not clear. What are the colored shadings, solid and dashed lines represent?\n3) In the analyses of global patterns, the impacts of Arctic stratospheric eddies and El Nino (Lines 321-349) were mentioned\nand also emphasized in the abstract. It does not appear to have sufficient evidence to demonstrate how these climate\nvariations would affect the proposed concomitant pollution. Only four months (for the year 2019) of model results were\nanalyzed. Interpreting the spatial patterns (Figure 4) with specific climate or weather conditions needs to be cautious and\nrequires more direct evidence.\nOverall, the study requires at least substantial revision to better fit the broad audience of Nature Communications."}, "author_response": "Response to reviews\nWe extend our appreciation to the two reviewers for their positive comments and\ninterest in our manuscript. The insightful and constructive suggestions were invaluable\nin the reworking and improvement of this paper. We identified two common concerns\nfrom Reviewers 1 and 2, and we have addressed them in the revised manuscript. A\nsummary is provided below.\nFirst, we are careful in addressing the concerns of both Reviewers 1 and 2. We have\nincorporated a precise definition of “Concomitant Pollution” in the Introduction section\nto delineate it from related pollution concepts and mitigate potential conceptual\nambiguities. New concept maps have been added in the revised manuscript and\nSupporting information section to visualize the feedback mechanism, accompanied by\ndetailed interpretations.\nAnother important piece of advice is the necessity of further discussion of factors on\nConcomitant Pollution from the mechanism perspective. According to Reviewer 2, we\nremoved all assertions related to specific climate models because they were not\nsupported by sufficient evidence. We focused on the impact of the factors and added a\nmore in-depth discussion. For NH +/NH -induced Concomitant Pollution, we have\n4 3\nevaluated the influence of temperature and aerosol water content. The results showed\nthat the high temperature and low humidity environment could favor the formation of\nconcomitant pollution by increasing the NH +/NH concomitant pollution index and\n4 3\nenhancing the buffering capacity of aerosol. For HNO /NO --induced Concomitant\n3 3\nPollution, we have explored the influence of temperature, aerosol water content, NO\n2\nconcentration, and oxidation concentration. The results showed that enhanced\nphotochemical reactions and meteorological conditions promote more severe\nconcomitant pollution.\nMoreover, we appreciate the inquiry regarding the uncertainties in ammonia emission\ninventories. In the revised version, we added a sensitivity experiment to change the\nanthropogenic ammonia emission inventory to investigate the effect of uncertainty in\nammonia emissions on the results of this work. The results indicated that the\nconcentrations of major components are well-correlated between the inventory-\nadjusted (±5%, ±10%, ±20%) and baseline scenarios (±0%), while NH concentrations\n3\nare relatively more significantly affected. However, the comparation of Concomitant\nPollution caused by NH +/NH and HNO /NO - between inventory-adjusted and\n4 3 3 3\nbaseline scenarios indicated that this study’s primary conclusions remain consistent\nwith the baseline scenario despite emission inventory modifications. Therefore, our\nfindings indicate that while emission uncertainties exist, their impact on core\nconclusions is negligible.\nA point-by-point response to the reviewers’ comments has been provided below. The\noriginal comments from reviewers are in normal font, our replies are indented and in\nblue, and revised texts as they appear in the manuscript text are indented and in red.\nPoint-by-point response to reviewers’ comments\nReviewer #1\nGeneral comments\nThis study explores the relationship between atmospheric multiphase buffering\ncapacity and associated pollution, revealing the key role of the NH₄⁺/NH₃ system in\nregulating aerosol acidity and air pollution formation through long-term observations,\nglobal simulations, and machine learning analysis. The paper proposes and validates a\nnew mechanism in which the decline in buffering capacity exacerbates associated\npollution, providing quantitative evidence through experimental and theoretical\ncalculations. It presents the first systematic assessment of the global spatiotemporal\ndistribution of associated pollution, highlighting the dominant role of the NH₄⁺/NH₃\nsystem across different regions and seasons. By incorporating machine learning\ntechniques, the study identifies key driving factors of associated pollution and\nquantifies the relative contributions of meteorological conditions and human\nactivities. From a policy perspective, it analyzes the impact of NH₃ emission control\non improving air quality, offering some insights for future pollution management and\nglobal nitrogen governance.\nWhile this study presents valuable scientific contributions through its comprehensive\ndataset and methodological approach, certain aspects of the research design and\npresentation could benefit from further development. The methodological descriptions\noccasionally lack sufficient detail to fully evaluate the analytical choices, and the\nlogical progression of the discussion could be strengthened to better connect findings\nwith broader implications. Additionally, the logical progression of mechanistic\nexplanations occasionally lacks clarity, particularly in connecting theoretical\nframeworks (e.g., proton exchange dynamics) to observed pollution events.\nAddressing these areas would enhance both the clarity and impact of the work. Below\nare specific suggestions for improvement:\nResponse: Thank you for taking the time to review our manuscript. We sincerely\nappreciate your positive and constructive comments that we have carefully\naddressed in the revised manuscript. We are pleased to hear that you found our\nstudy our study to be valuable, which offers some insights for future pollution\nmanagement and global nitrogen governance. We acknowledge your advice\nregarding the need for a more comprehensive presentation of research methods\nand a clearer and more logical discussion of the mechanistic explanations. We are\ncommitted to addressing your concerns and making necessary revisions to\nimprove the clarity of our manuscript. We have carefully addressed these points\nin our revised manuscript and provided a point-by-point response below.\n(1) The study finds that concomitant pollution is more severe in summer; however, it\ndoes not delve into the specific meteorological driving mechanisms (such as enhanced\nphotochemical reactions or changes in aerosol liquid water content). It is\nrecommended to include a more detailed discussion on these factors to strengthen the\nphysical explanation of the results.\nResponse: We appreciate your valuable comment. According to your suggestion,\nwe have supplemented the more detailed discussion on specific meteorological\ndriving mechanisms to strengthen the physical explanation of the results.\nFor NH +/NH -induced Concomitant Pollution, we primarily investigated the\n4 3\nroles of aerosol water content and temperature, as the formation of NH +/NH\n4 3\ndoes not involve photochemical reactions. Supplementary Fig. 34 and\nSupplementary Fig. 36 demonstrates that globally, summer is characterized by\nhigher temperatures and lower aerosol water content. These meteorological\nconditions favor the partitioning of NH +/NH as gaseous NH rather than\n4 3 3\naerosol-phase NH +, elevating NH +/NH Concomitant Pollution Index.\n4 4 3\nAdditionally, high-temperature and low-humidity conditions enhance aerosol\nbuffering capacity. Consequently, the elevated NH +/NH Concomitant Pollution\n4 3\nIndex combined with increased buffering capacity synergistically intensifies\nConcomitant Pollution during summer. This dual mechanism explains the\nsignificantly higher Concomitant Pollution levels in regions like North America\nand Europe during summer compared to winter.\nFor HNO /NO --induced Concomitant Pollution, we investigated the\n3 3\nmeteorological mechanisms involved in the photochemical formation of HNO\n3\nand the HNO /NO - partitioning process. We first analyzed the global\n3 3\ndistributions of oxidants OH, as they serve as the primary oxidants for the\nphotochemical reaction pathway of HNO . The results indicated that the OH\n3\nradical has undergone strong increases in summer compared to winter, especially\nin regions with latitudes between 0O and 60ON. The OH radical concentrations in\nEast Asia, South Asia, Europe, and North America are significantly higher during\nsummer than in winter. We further calculated roughly the nitrate production rate\nfor the photochemical reactions pathway. The results demonstrated that\nphotochemical reaction was enhanced by photochemical oxidants during summer\nduo to high temperature and intense solar radiation. The enhanced photochemical\nreactions was the one reason behind more severe concomitant pollution in\nsummer. In addition, the higher temperatures and lower aerosol water content\nfavor the persistence of nitric acid in the gaseous form (HNO ), thereby\n3\nincreasing HNO /NO - Concomitant Pollution Index. Therefore, enhanced\n3 3\nphotochemical reactions and meteorological conditions promote more severe\nconcomitant pollution.\nBased on the valuable comments, the meteorological driving mechanisms\nanalysis greatly improved the physical explanation of the results in this work. We\nalso added the meteorological driving mechanisms analysis to the revised\nmanuscript and Supplementary information. Thanks again for the valuable\nadvice.\nPages 18-19, Lines 346-356: In summer, the contribution of MF to high Co-P-\nNH +/NH was gradually increasing in North America and Europe, possibly\n4 3\nbecause of increased T and diminished AWC (Supplementary Fig. 33-36). These\nmeteorological conditions favor the partitioning of NH +/NH as gaseous NH\n4 3 3\nrather than aerosol-phase NH +, elevating NH +/NH Concomitant Pollution\n4 4 3\nIndex. Additionally, high-temperature and low-humidity conditions enhance\naerosol buffering capacity. Consequently, the elevated NH +/NH Concomitant\n4 3\nPollution Index combined with increased buffering capacity synergistically\nintensifies Concomitant Pollution during summer. This dual mechanism explains\nthe significantly higher Concomitant Pollution levels in regions like North\nAmerica and Europe during summer compared to winter.\nPages 19-20, Lines 368-375: Increased HNO concentration was the result of\n3\nenhanced photochemical reactions. The global distributions of oxidants OH\nradical indicated that the OH radical has undergone strong increases in summer\ncompared to winter, especially in regions with latitudes between 0O and 60ON\n(Supplementary Fig. 37). The OH radical concentrations in East Asia, South Asia,\nEurope, and North America are significantly higher during summer than in winter\n(Supplementary Fig. 38). The elevated nitrate production rate for the\nphotochemical reactions pathway further confirmed the above results\n(Supplementary Fig. 38-39).\nSupplementary information Pages 48-53, Fig. S34-Fig. 39:\nFig. S34. Season variation of aerosol water content worldwide\nFig. S35. Season variation of relative humidity (RH) worldwide\nFig. S36 Season variation of temperature worldwide\nFig. S37 Season variation of OH radical worldwide\nFig. S38 The season variation of OH radical, NO concentration, NO - production\n2 3\nrate (P(NO -)), temperature (T), and aerosol water content (AWC) in East Asia,\nFig. S39 Season variation of NO - production rate (P(NO -)) worldwide\n3 3\n(2) Regarding the negative feedback mechanism (acid input → NH → NH ⁺ → PM\n3 4 2.5\nformation): Although the study proposes this mechanism, it lacks experimental\nvalidation through real-time tracking of gas-to-particle conversion rates or isotope-\nlabeling techniques. Can online mass spectrometry or smoke chamber experiments be\nsupplemented for further exploration?\nResponse: We express our gratitude for your valuable advice. In the revised\nmanuscript, we have incorporated high-time-resolution online ion chromatography\nmonitoring experiments and online mass spectrometry observations to conduct an\nin-depth investigation of the negative feedback mechanism (acidity input → NH\n3\n→ NH + → PM formation). Our experimental results demonstrate the validity of\n4 2.5\nthis feedback mechanism. The related content has been incorporated into the\nrevised manuscript.\nThe high-time-resolution (1h-resolution) online ion chromatography monitoring\nexperiment (continuous for 24 hours) was employed to analyze variations in sulfate\n(SO 2-) concentration and ε(NH +), where ε(NH +) represents the ammonium\n4 4 4\npartitioning ratio characterizing the conversion process from NH to NH +.\nThe\n3 4\nresults demonstrate that ε(NH +) exhibited an increasing trend (from 0.14 to 0.56)\n4\nalongside a substantial rise in sulfate (SO 2-) levels (from 4.94 μg m-3 to 21.61 μg\n4\nm-3). This indicates the conversion of NH to NH + to neutralize pH disturbances\n3 4\ncaused by sulfate. Consequently, the increase in PM concentrations is attributed\n2.5\nnot only to direct SO 2- contribution but also to enhanced NH + formation. These\n4 4\nfindings collectively confirm the role of this feedback mechanism in driving\npollution escalation.\nTo further investigate this mechanism, we utilized data from an Aerodyne Time-\nof-Flight Aerosol Chemical Speciation Monitor (ACSM) with 10-minute\nresolution (continuous for 5 hours) to track changes in the NH conversion rate\n3\nduring sulfate (SO 2-) enhancement events. The results also demonstrate\n4\nsynchronous increases in SO 2- and ε(NH +), indicating that during the real-time\n4 4\nformation of SO 2-, NH simultaneously converts to NH + to neutralize SO 2-,\n4 3 4 4\nthereby enhancing PM mass concentration.\n2.5\nBoth high-time-resolution online ion chromatography monitoring experiments\nand online mass spectrometry observations jointly demonstrate the validity of this\nfeedback mechanism. Once again, we sincerely appreciate your valuable advice,\nwhich has significantly enhanced the rigor of our work and improve the quality of\nour manuscript.\nPages 10-11, Lines 185-189: We have incorporated high-time-resolution online\nmonitoring experiments to conduct an in-depth investigation of the negative\nfeedback mechanism (Supplementary Text 4 and Supplementary Figs. 10-11).\nOur experimental results demonstrate the validity of this feedback mechanism.\nSupplementary information Page 6:\nS4. The experimental validation of negative feedback mechanism\nFor experimental validation, we have incorporated high-time-resolution online\nion chromatography monitoring experiments and online mass spectrometry\nobservations to conduct an in-depth investigation of the negative feedback\nmechanism (acidity input → NH → NH + → PM formation).\n3 4 2.5\nWe conducted a 24-hour continuous monitoring experiment using high-time-\nresolution (1-hour resolution) online ion chromatography, analyzing variations in\nacidic sulfate (SO 2-) concentrations and ε(NH +) - the ammonium partitioning\n4 4\nratio characterizing the conversion of NH to NH +.\nThe results revealed a\n3 4\nsignificant increase in sulfate concentrations (from 4.94 μg m-3 to 21.61 μg m-3),\naccompanied by a rising trend in ε(NH +) (from 0.14 to 0.56) (Supplementary\n3 4\nperturbations induced by acidic components. Consequently, the observed PM\n2.5\nincrease is attributed not only to direct sulfate contribution but also to amplified\nNH + formation. This dataset was acquired at Tianjin.\nAerodyne Aerosol Chemical Speciation Monitor (ACSM) with 10-minute\ntemporal resolution (5-hour continuous monitoring). This enabled real-time\ntracking of NH conversion rates during SO 2- enhancement events. The data\n3 4\ndemonstrate synchronous increases in SO 2- and ε(NH +), confirming that NH\n4 4 3\nsimultaneously converts to NH + to neutralize SO 2- during its real-time\n4 4\nformation, thereby augmenting PM mass concentrations (Supplementary Fig.\n2.5\n11). This experiment was conducted at Beijing.\nCollectively, these experimental findings validate the role of this feedback\nmechanism in driving pollution episodes.\nSupplementary information Pages 24-25, Fig. S10-Fig. 11:\nFig. S10. Variations in SO 2- and ε(NH +) during high-time-resolution online ion\n4 4\nchromatography monitoring\nFig. S11. Variations in SO 2- and ε(NH +) during Aerodyne Time-of-Flight\n4 4\nAerosol Chemical Speciation Monitor (ACSM) with 10-minute resolution\n(continuous for 5 hours)\n)3-m\ngm(\n-2\nOS\n)+\nHN(ε\n)3-m\ngm(\n-2\nOS\n)+\nHN(ε\n4\n4\n4\n4\n1\n0\n0\n0\n0\n0\n2\n1\n0\n0\n0\n. 2\n. 8\n. 4\n. 3\n. 2\n. 1\n.\n.\n.\n0\n0\n0\n6\n4\n2\n0\nc\n0\nc\na\nb\na\nb\n6\n1 0\nT\ni m\ni m\n1\ne\n2\ne\n(\n(\nm\nh )\ni n\n2 0\n)\n1\n0\n8 2 4\n3 0 0\n(3) Regarding the GEOS-Chem global simulation: The study relies on the GEOS-\nChem model but does not thoroughly discuss the spatiotemporal resolution of the NH₃\nemission inventory (e.g., seasonal variations in agricultural sources such as\nfertilization periods) or quantify uncertainties in emission data. A sensitivity analysis\nshould be conducted to evaluate how emission uncertainties impact the results.\nResponse: Thanks for your constructive advice. We have added the discussion of\nthe spatiotemporal resolution of the NH emission inventory including the\n3\nseasonal variations in agricultural sources such as fertilization periods. And we\nhave conducted the sensitivity analysis to evaluate how emission uncertainties\nimpact the results.\nGlobal anthropogenic NH emissions from the Community Emissions Data\n0.5o×0.5o spatial resolution. Therefore, agricultural NH emissions incorporate\n3\nmonthly temporal profiles based on fertilizer application timing1. To further\ndiscuss the seasonal variations in agricultural NH emissions, we present the\n3\nglobal distribution of agricultural ammonia emissions across different seasons\n(Supplementary Fig. 43). The results reveal substantial agricultural ammonia\nemissions in East Asia during April and July, which may be attributed to\nfertilization practices for crops such as wheat, maize, and rice. Agricultural NH\n3\nemissions in South America are concentrated in October, likely driven by\nfertilization during soybean cultivation. These findings further confirm the\nseasonal patterns of agricultural emissions linked to fertilization periods, which\nhave been incorporated into the GEOS-Chem simulations.\nAs you noted, quantifying uncertainties in emission data is indeed a crucial aspect\nof our work. Accordingly, we have conducted additional sensitivity analyses to\nassess the impacts of emission uncertainties on our results. We performed\nsensitivity analyses by altering the agricultural ammonia emission inventory from\nthe baseline (±0%) to adjustments of ±5%, ±10% and ±20%, examining the\nrelationship between baseline and adjustments in NH , NH +, and associated\n3 4\npollutants including HNO , NO -, SO 2- (Supplementary Fig. 44). The results\n3 3 4\nindicate that the concentrations of major components are well-correlated between\nthe inventory-adjusted and baseline scenarios, with data points distributed near\nthe 1:1 line. In contrast, NH concentrations are relatively more significantly\n3\naffected. When the inventory is adjusted by ±20%, NH changes most\n3\nsubstantially in April (approximately ±11%), while changes in other seasons are\ncomparatively smaller. Variations in other components generally remain within\n3%. Subsequently, we further investigated changes in Concomitant Pollution\ncaused by NH +/NH and HNO /NO - (Supplementary Fig. 45). The results\n4 3 3 3\ndemonstrate that overall, NH +/NH -induced Concomitant Pollution increases\n4 3\nwith rising NH emissions, whereas HNO /NO --induced Concomitant Pollution\n3 3 3\ndecreases with increasing NH emissions. And relatively larger changes in\ninventory modifications, this study’s primary conclusions remain consistent with\nthe baseline scenario: NH +/NH -induced Concomitant Pollution was higher than\n4 3\nHNO /NO --induced Concomitant Pollution; and summer exhibits higher\n3 3\nConcomitant Pollution levels in most regions except South Asia. Consequently,\nour findings indicate that while emission uncertainties exist, their impact on core\nconclusions is negligible.\nWe sincerely appreciate your constructive suggestions. Conducting sensitivity\nexperiments to evaluate emission uncertainties and discussing their impacts on\nour findings have significantly enhanced the robustness of this study. We have\nadded the relevant discussion to the revised manuscript. Thank you again.\nPage 26, Lines 486-488: In addition, we thoroughly discuss the spatiotemporal\nresolution of the NH emission inventory and evaluate how emission\n3\nuncertainties impact the results (Supplementary Text 9 and Figs. 43-46).\nSupplementary information Pages 13-14:\nS9. The spatiotemporal resolution of the NH emission inventory and\n3\nuncertainties evaluation\nGlobal anthropogenic NH emissions from the Community Emissions Data\n0.5o× 0.5o spatial resolution. Therefore, agricultural NH emissions incorporate\n3\nmonthly temporal profiles based on fertilizer application timing1. To further\ndiscuss the seasonal variations in agricultural NH emissions, we present the\n3\nglobal distribution of agricultural ammonia emissions across different seasons\n(Supplementary Fig. 43). The results reveal substantial agricultural ammonia\nemissions in East Asia during April and July, which may be attributed to\nfertilization practices for crops such as wheat, maize, and rice. Agricultural NH\n3\nemissions in South America are concentrated in October, likely driven by\nfertilization during soybean cultivation. Therefore, the seasonal patterns of\nagricultural emissions linked to fertilization periods, which have been\nincorporated into the GEOS-Chem simulations.\nMany studies have shown that emission data is uncertain. Therefore, we further\nconducted additional sensitivity analyses to assess the impacts of emission\nuncertainties on our results. We performed sensitivity analyses by altering the\nagricultural ammonia emission inventory from the baseline (±0%) to adjustments\nof ±5%, ±10% and ±20%, examining the relationship between baseline and\nadjustments in NH , NH +, and associated pollutants including HNO , NO -,\n3 4 3 3\nSO 2- (Supplementary Fig. 44). The results show that the change in NH is\n4 3\nrelatively large. When the inventory is adjusted by ±20%, the Δ\ninventory adjustment-\nin NH for January, April, July, and October are approximately ±10%,\nbaseline 3\n±11%, ±6%, ±9%, respectively. For other components, the Δ\ninventory adjustment-baseline\nare mostly within ±3%. Subsequently, we further investigated changes in\nConcomitant Pollution caused by NH +/NH and HNO /NO - (Supplementary\n4 3 3 3\nFig. 45-46). The results demonstrate that overall, NH +/NH -induced\n4 3\nConcomitant Pollution increases with rising NH emissions, whereas HNO /NO -\n3 3 3\n-induced Concomitant Pollution decreases with increasing NH emissions. And\n3\nrelatively larger changes in Concomitant Pollution occur in South Asia and North\nAmerica. Despite emission inventory modifications, this study’s primary\nconclusions remain consistent with the baseline scenario: NH +/NH -induced\n4 3\nConcomitant Pollution was higher than HNO /NO --induced Concomitant\n3 3\nPollution; and summer exhibits higher Concomitant Pollution levels in most\nregions except South Asia. Consequently, our findings indicate that while\nemission uncertainties exist, their impact on core conclusions is negligible.\nSupplementary information Pages 57-60, Fig. S43-Fig. 46:\nFig. S43 Season variation of agricultural NH emission in CEDS worldwide\n3 4 3 3 4\nadjusted emission inventories (±5%, ±10% and ±20%)\nFig. S45 The comparation of Concomitant Pollution caused by NH +/NH and\n4 3\nHNO /NO - in baseline and adjusted emission inventories (±5%, ±10% and\n3 3\n±20%)\nFig. S46 The Concomitant Pollution caused by NH +/NH and HNO /NO - with\n4 3 3 3\nbaseline and adjusted emission inventories (±5%, ±10% and ±20%) in East Asia,\nSouth Asia, Europe, South Africa, and North America.\n(4) The paper suggests strengthening NH₃ emission control to reduce concomitant\npollution, but it does not provide a detailed discussion on how to reduce NH₃\nemissions while ensuring agricultural production. Additionally, it would be valuable\nto explore whether there are optimal spatiotemporal windows for NH₃ emission\nreductions (e.g., being more effective under low humidity conditions).\nResponse: Thanks for your useful comment. According to your suggestion,\nwe have expanded on NH emissions mitigation strategies in the Implication of\n3\nagricultural activity, mainly nitrogen fertilizer application and livestock manure\nmanagement. In addition, Chen et al.1 reported the significant contributions of\ncombustion-related sources to NH emission, mainly fossil fuel combustion,\n3\nvehicle exhausts, and biomass burning. Consequently, NH mitigation can be\n3\nachieved via these pathways. Specifically, as follows:\nAgricultural activities: (1) Optimizing Nitrogen Fertilization: For croplands\nsystems, NH emission abatement measures including deep placement of N\n3\nfertilizer, use of enhanced efficiency N fertilizer, and optimized management\npractices such as “4R Nutrient Stewardship” approach promoted by the\nInternational Fertilizer Association 2, 3, 4, including right fertilizer type, right\namount, right placement and right time. (2) Improved Manure Management:\nFor livestock production systems, NH abatement measures include manipulation\n3\nof feed rations and manure management practices, such as improvement on\nstorage facility and covering the surface to reduce gas diffusion 3, 5, 6. Through the\nuse of efficient fertilizers and improved manure management measures, it is\ntechnically feasible to reduce agricultural NH emissions without causing yield\n3\nlosses 7.\nNon-agricultural activities: Reducing combustion-related NH emission. NH\n3 3\nabatement can be achieved through measures such as replacing with clean fuels,\nequipping heavy-duty diesel vehicles with ammonia slip catalysts, and promoting\nelectric vehicles 8, 9, 10.\nAdditionally, we fully agree with your suggestion regarding it would be valuable\nto explore whether there are optimal spatiotemporal windows for NH emission\n3\nreductions. Thus, we have supplemented the discussion about the timing of NH\n3\nemissions controls. In the analysis of concomitant pollution drivers, we identified\nRH as a key leverage point: curbing ammonia emissions during periods of low\nRH (<40%) could prove significantly more effective. Our finding indicated that\nunder stable NH T concentrations, concomitant pollution exhibits a negative\n4\ncorrelation with relative humidity (RH). And machine learning results (Figure 3a)\nreveal that greater sensitivity of concomitant pollution to RH changes under low-\nRH conditions (RH≤40%) compared to high-RH environments (RH>40%),\nwhere RH variations induce smaller fluctuations. In addition, we conducted\nsensitivity experiments (as shown in Supplementary Fig. 40) on NH / NH +\n3 4\npartitioning across varying RH levels. The results demonstrate that as RH\nincreases, gaseous NH transitions into the aqueous phase, forming NH +.\n3 4\nThis\nindicates that at high RH, NH T predominantly exists as NH +, which has already\n4 4\ncontributed to pollution. In contrast, at low RH, NH T remains as gaseous NH in\n4 3\nthe atmosphere, making emission reductions more effective for pollution\nmitigation. Finally, we investigated the response of concomitant pollution to NH\n3\nreduction under varying relative humidity levels (RH = 20%, 40%, and 60%).\nThe results indicate that equivalent NH reductions induced the greatest\n3\nconcomitant pollution mitigation at 20% and 40% RH, whereas concomitant\npollution showed diminished sensitivity to NH abatement at 60% RH. Therefore,\n3\nlow-RH conditions at 40% RH may represent a favorable window for NH\n3\nemission control. In addition, based on the global distribution of NH and RH, the\n3\nwhereas North America, East Asia, and southern Africa would achieve optimal\nresults from summer NH emission reductions.\ndiscussions on both NH emission control measures and the optimal\n3\nspatiotemporal windows for reducing NH emissions. Thank you again for your\n3\nsuggestion.\nReference:\n1. Chen, ZL., Song, W., Hu, CC. et al. Significant contributions of combustion-\nrelated sources to ammonia emissions. Nat Commun 13, 7710 (2022).\nhttps://doi.org/10.1038/s41467-022-35381-4\n2. Bruulsema, T. Managing nutrients to mitigate soil pollution. Environmental\nPollution 243, 1602-1605 (2018).\n3. Gu, B., Zhang, X., Lam, S.K. et al. Cost-effective mitigation of nitrogen\npollution from global croplands. Nature 613, 77-84 (2023).\nhttps://doi.org/10.1038/s41586-022-05481-8\n4. Sutton, M. A., Howard, C. M., Mason, K. E., Brownlie, W. J. & Cordovil, C.\nM. D. S. in UNECE Air Convention: Guidance Document on Integrated\nSustainable Nitrogen Management (UK Centre for Ecology & Hydrology,\n2021).\n5. Liu, M.X., Huang, X., Song, Y. et al. Ammonia emission control in China\nwould mitigate haze pollution and nitrogen deposition, but worsen acid rain.\nProc Natl Acad Sci. U.S.A. 116 (16), 7760-7765 (2019)\nhttps://doi.org/10.1073/pnas.1814880116\n6. Xu, P., Li, G., Zheng, Y. et al. Fertilizer management for global ammonia\nemission reduction. Nature 626, 792-798 (2024).\nhttps://doi.org/10.1038/s41586-024-07020-z\n7. Zhang, W., Cao, G., Li, X. et al. Closing yield gaps in China by empowering\nsmallholder farmers. Nature 537, 671-674 (2016).\nhttps://doi.org/10.1038/nature19368\n8. Liang, X.; Zhang, S.; Wu, Y.; Xing, J.; He, X.; Zhang, K. M.; Wang, S.; Hao,\nJ. Air quality and health benefits from fleet electrification in China. Nat.\nSustainability 2019, 2, 962-971.\n9. Suarez-Bertoa, R.; Pechout, M.; Vojtísek, M.; Astorga, C. Regulated and non-\nRegulated emissions from Euro 6 diesel, gasoline and CNG vehicles under\nreal-world driving conditions. Atmosphere 2020, 11, 204.\n10. Yunjie Wang, Yifan Wen, Shaojun Zhang, Guangjie Zheng, Haotian Zheng,\nXing Chang, Cheng Huang, Shuxiao Wang, Ye Wu, and Jiming Hao.\nVehicular Ammonia Emissions Significantly Contribute to Urban PM\n2.5\nPollution in Two Chinese Megacities. Environmental Science & Technology\n2023 57 (7), 2698-2705\nPage 23, Lines 430-447: The main potential for NH abatement lies in\n3\nagricultural activities, as they are the primary source of NH emissions42. This\n3\nmeasure mainly includes two aspects: optimizing nitrogen fertilizer and\nimproving manure management43. For optimizing nitrogen fertilizer, deep\nplacement of N fertilizer is a good option, as it mainly reduces NH volatilization\n3\nby applying the fertilizer deeper into the soil rather than surface broadcasting44.\nThe use of efficient nitrogen fertilizers can also suppress the release of NH into\n3\nthe atmosphere45. And optimized management practices such as the “4R Nutrient\nStewardship” approach promoted by the International Fertilizer Association46, 47\nare the best management practices, which help reduce agricultural NH emissions\n3\nwithout causing crop yield loss. This approach mainly includes the right fertilizer\ntype, the right amount, the right placement, and the right time. For livestock\nproduction systems, NH abatement measures include manipulation of feed\n3\nrations and manure management practices, such as improvement of storage\nfacilities and covering the surface to reduce gas diffusion48, 49. Reductions in\nagricultural NH emissions can be achieved through high-efficiency fertilizers\n3\nand improved manure management practices without compromising crop yields50.\nAdditionally, mitigating combustion-related NH emissions is another option for\n3\nreducing NH emissions, which can alleviate pressure on agricultural NH\n3 3\nmitigation efforts51, 52, 53.\nPage 21, Lines 397-402: Machine learning attribution analysis identifies RH as a\nkey leverage point: curbing ammonia emissions during periods of low RH\n(<40%) could prove significantly more effective, which particularly emphasizes\nthe timing of ammonia emissions controls in northern China. Sensitivity\nexperiments and theoretical analysis also confirm this result (Supplementary Text\nS8 and Supplementary Figs. 40-41).\nSupplementary information Page 12:\nS8. The optimal spatiotemporal windows for NH emission reductions\ninvestigated the changes in the buffer agent NH +/NH and concomitant pollution\n4 3\nnear this critical point. We conducted sensitivity experiments (as shown in\nSupplementary Fig. 40) on NH / NH + partitioning across varying RH levels. The\n3 4\nresults demonstrate that as RH increases, gaseous NH transitions into the\n3\naqueous phase, forming NH +.\n4\npredominantly exists as NH +, which has already contributed to pollution. In\n4\ncontrast, at low RH, NH T remains as gaseous NH in the atmosphere, making\n4 3\nemission reductions more effective for pollution mitigation. In addition, we\ninvestigated the response of concomitant pollution to NH reduction under\n3\nvarying relative humidity levels (RH = 20%, 40%, and 60%). The results indicate\nthat equivalent NH reductions induced the greatest concomitant pollution\n3\nmitigation at 20% and 40% RH, whereas concomitant pollution showed\ndiminished sensitivity to NH abatement at 60% RH. Therefore, low-RH\n3\nconditions at 40% RH may represent a favorable window for NH emission\n3\ncontrol. In addition, based on the global distribution of NH and RH\n3\n(Supplementary Fig. 30 and Fig. 35), the South Asia region would benefit more\nfrom controlling NH emissions in winter, whereas North America, East Asia, and\n3\nsouthern Africa would achieve optimal results from summer NH emission\n3\nreductions.\nPage 14, Lines 261-265:\nFig. 3. Analysis of main drivers of Concomitant Pollution by machine\nlearning. a, RH, b, T, c, NH T, d, Ca2+, e, SO 2-, and f, NO T. The solid line\n4 4 3\nrepresents the mean prediction, and the shaded region indicates ±1 standard\ndeviation of the predictions across all Bootstrap iterations, reflecting model\nuncertainty due to data variability.\nSupplementary information Page 54, Fig. S40:\nFig. S40 a, The response of NH / NH + partitioning across varying RH. b, The\n3 4\nresponse of Concomitant Pollution to NH emission reduction under different\n3\nrelative humidity conditions (RH = 20%, 40%, and 60%).\n)3-m\ngm(\n+\nHN\n&\nHN\n4\n3\n1\na\nc\ne\n4\n8\n6\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n0\n120\n80\n40\n0\n60\n40\n20\n0\n-20\n60\n40\n20\n0\n-20\na\n0\n20\n2 0\n5\n5\n40\n4 0\nR\nH\nH\nN\nS\n15 20\nT -3 H (m g m )\n4\n10\n2- -3 O (m g m )\n4\n+ N H\n3 4\n6 0 8\n( % )\n80\n15\n0\n25\n1 0 0\n100\n30\n20\nb\nd\nf\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n60\n40\n20\n0\n-20\n60\n40\n20\n0\n-20\n0\n60\n40\n20\n0\n-200.0\n2 0 0\n1 5 0\n1 0 0\n5 0\n0\nb\n270\n5\n0.2\n0\n280 290\nT (K )\n10 15 20\nT -3 N O (m g m )\n3\n0.4 0.6 0.8\n2+ -3 C a (m g m )\n-2 0 -4 0 -6\nN H c h a n g e s ( %\n3\n0\n)\n300\n25\n1.0\nR H\nR H\nR H\n-8 0\n1.2\n= 2\n= 4\n= 6\n000 %%%\nSupplementary information Page 44, Fig. S30:\nFig. S30. Season variation of NH concentration worldwide\nFig. S35. Season variation of relative humidity (RH) worldwide\n(5) The hyperparameter settings and validation methods of the machine learning\nmodel need to be described in more detail. For example, while the paper mentions the\nuse of the Random Forest (RF) algorithm, it does not clarify whether feature selection\nwas performed to avoid multicollinearity issues, or if cross-validation was used to\nensure the model's generalizability.\nResponse: We appreciate your thoughtful advice. We have supplemented\ndetailed information about hyperparameter settings and validation methods of the\nmachine learning model in the Methods.\nFor hyperparameter settings: In the Random Forest Regressor, we set the\nhyperparameter n_estimators=500, indicating that the model will train 500\ndecision trees. Another hyperparameter random_state=0 to ensure consistent\nresults in each run. The main hyperparameters in pdp.pdp_isolate include (1)\npercentile_range=(1, 100), this hyperparameter sets the range of features for the\nPDP graph from the 1st percentile to the 100th percentile, which determines the\nrange of feature data used to generate the PDP; (2) num_grid_points=20, this\nhyperparameter indicates the number of discrete points of the PDP graph,\nmeaning that the feature values will be divided into 20 discrete points.\nFor validation methods: In terms of data partitioning, the data is randomly\npartitioned into a training set and a test set. We set train_test_split (X, Y,\ntest_size=0.3, random_state=8), where 30% of the data is used for testing and\n70% of the data is used for training. random_state=8 ensures the reproducibility\nof the data division. In this model, we simply split the data into a training set and\na test set, fitted the model using the training set and tested its performance.\nThe multicollinearity issue you mentioned is indeed an important issue in\nmachine learning models. In this work, we chose random forest, which is a tree-\nbased ensemble learning method with a natural feature selection capability due to\nthe robustness of Random Forest. During the training process, the tree model\nautomatically selects the optimal features for each node, so it is insensitive to\nmulticollinearity. Moreover, PDP is mainly used to analyze the relationship\nbetween a single feature and the target variable, rather than relying on a\ncombination of other features. Therefore, when doing a one-factor response\nanalysis, the PDP is essentially analyzing the independent effects of each feature\nrather than the joint effects of multiple features. Finally, we used the RF-PDP\nmodel to independently analyze the sensitivity response of concomitant pollution\nto each factor. Thus, the models we currently use avoid the multicollinearity\nproblem to some extent.\nIn addition, in our original model setup, only the training set was considered to fit\nthe model and test its performance without using cross-validation. Therefore, we\nfollowed your suggestion of using 10-flod cross-validation to ensure the model’s\ngeneralizability. The results show that the average R2 values for the training set\nand test set are 0.97 and 0.80, respectively, indicating that the model used in this\nstudy has strong predictive capabilities and can effectively capture the main\ntrends and relationships in the data. The revised results are presented in Fig. 3 and\nSupplementary Fig.17, and the corresponding expressions in the manuscript have\nbeen revised.\nPage 13, Lines 241-245: We further applied the Random Forest-Partial\nDependence Plot (RF-PDP) method to describe the response of Concomitant\nPollution to drivers (Fig. 3). The ten-fold cross-validation was applied to ensure\nthe generalization ability and reliability of the model, with average R2 values for\nthe training set and test set were 0.97 and 0.80 (Supplementary Fig.19),\nrespectively.\nPages 34-35, Lines 661-681: The hyperparameter settings and validation\nmethods of the machine learning model was set as follows:\nHyperparameter settings: In the Random Forest Regressor, we set the\nhyperparameter n_estimators=500, indicating that the model will train 500\ndecision trees. Another hyperparameter random_state=0 to ensure consistent\nresults in each run. The main hyperparameters in pdp.pdp_isolate include (1)\npercentile_range=(1, 100), this hyperparameter sets the range of features for the\nPDP graph from the 1st percentile to the 100th percentile, which determines the\nrange of feature data used to generate the PDP; (2) num_grid_points=20, this\nhyperparameter indicates the number of discrete points of the PDP graph,\nmeaning that the feature values will be divided into 20 discrete points.\nValidation methods: In terms of data partitioning, the data is randomly partitioned\ninto a training set and a test set. We set train_test_split (X, Y, test_size=0.3,\nrandom_state=8), where 30% of the data is used for testing and 70% of the data is\nused for training. random_state=8 ensures the reproducibility of the data division.\nWe split the data into a training set and a test set, fitted the model using the\ntraining set and tested its performance. In addition, the 10-flod cross-validation\nwas applied to ensure the model’s generalizability. The results show that the\naverage R2 values for the training set and test set are 0.97 and 0.80\n(Supplementary Fig.19), respectively, indicating that the model used in this study\nhas strong predictive capabilities and can effectively capture the main\ntrends and relationships in the data.\nPage 14, Lines 261-265:\nFig. 3. Analysis of main drivers of Concomitant Pollution by machine\nlearning. a, RH, b, T, c, NH T, d, Ca2+, e, SO 2-, and f, NO T. The solid line\n4 4 3\nrepresents the mean prediction, and the shaded region indicates ±1 standard\ndeviation of the predictions across all Bootstrap iterations, reflecting model\nuncertainty due to data variability.\nSupplementary information Page 33, Fig. S19:\nFig. S19. The average R2 of training set and test set in 10-fold cross-validation.\nSpecific comments\na\nc\ne\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n120\n80\n40\n0\n60\n40\n20\n0\n-20\n60\n40\n20\n0\n-20\n0\n20\n5\n1\n0\n0\n0\n0\n0\n.0\n.8\n.6\n.4\n.2\n.0\n5\n40\nS\nH\nO\n15 20\nT -3 (m g m )\n4\n10\n2- -3 (m g m )\n80\n15\ni n s\n25\ne t\n100\n30\n20\nb\nd\nf\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n60\n40\n20\n0\n-20\n60\n40\n20\n0\n-20\n60\n40\n20\n0\n-20\n0\n0.0\n270\n5\n0.2\n280\n0.4\nC a\nT e s t\nT (K )\n3\n0.6\n2+ (m g m\ns e t\n290\n20\n-3)\n0.8\n-3)\n300\n25\n1.0 1.2\n0 .9 7\n0 .8 0\nRegarding terminology consistency: The term “Concomitant Pollution” is introduced\nwithout rigorous definition when first appearing in the text, creating potential\nconfusion with similar terms like “Complex Pollution”. We suggest providing a\nprecise definition in the introduction section and clearly differentiating it from related\npollution concepts.\nResponse: We appreciate your constructive advice. This is indeed a point that we\nhad previously overlooked in the manuscript, and your suggestion helps to make\nour manuscript clearer and easier to understand. We have incorporated a precise\ndefinition of “concomitant pollution” in the Introduction section to delineate it\nfrom related pollution concepts and mitigate potential conceptual ambiguities.\nNext, I will elaborate on the concept of concomitant pollution in this study and\nhow it differs from other related pollution concepts.\nIn this manuscript, we focus on pollution phenomena intrinsically linked to\natmospheric multiphase buffering. Within aerosols, conjugate acid-base pairs\n(e.g., NH +/NH , HNO /NO -, and HSO -/SO 2-) act as buffering agents. When\n4 3 3 3 4 4\nexternal acids or bases perturb aerosol acidity, these pairs neutralize the intruding\nspecies via proton transfer, thereby stabilizing pH within a constrained range.\nSpecifically, when exogenous acidic or alkaline pollutants are introduced into an\naerosol system, the inherent conjugate acid-base pairs (e.g., NH +/NH ,\n4 3\nHNO /NO -) regulate the acid-base equilibrium through phase-partitioning\n3 3\nreactions, thereby stabilizing the pH of the system. That is, the influx of acidic or\nalkaline pollutants triggers the buffering agents to undergo phase-partitioning\nreactions. For instance:\n(1) Acidic pollutant input: gaseous HA enters the aerosol liquid aqueous phase by\ngaseous diffusion and dissociates into H+ and A- (Reaction 1):\nHA (g) → H+ (aq) +A- (aq) (Reaction 1)\nThis process significantly reduces aerosol pH (acidification). Therefore, the\nNH +/NH buffer stabilizes aerosol acidity by NH entering the liquid phase to\n4 3 3\nform NH + to neutralize H+ (Reaction 2). However, additional NH + enters the\n4 4\nparticulate phase in this process, causing contamination, and this part of the\ncontamination caused by NH + is called Concomitant Pollution.\n3 4\n(2) Alkaline pollutant input: gaseous BOH dissolves in the aerosol liquid aqueous\nphase and reacts with H⁺ to form B+ and H O (Reaction 3), which neutralizes the\n2\nacidity:\nBOH (g) + H+ (aq) → B+ (aq) + H O (Reaction 3)\n3 3\nstabilizes the acidity of the aerosol by releasing H through the formation of NO -\n+ 3\nfrom HNO into the liquid phase (Reaction 4). However, during this process,\n3\nmore NO - enters the particulate phase, causing contamination, and this part of\n3\nthe contamination caused by NO - is called concomitant contamination.\n3 3\nThis process effectively stabilizes aerosol acidity but concurrently introduces\nionic species (e.g., NO -, NH +) into the particulate phase, amplifying pollution\n3 4\nloads. We term this secondary pollution arising from buffering-driven ion\naccumulation “Concomitant Pollution” - a distinct mechanism from conventional\nprimary emissions or photochemical secondary formation.\nIn addition, the HSO -/SO 2- acid-base pair does not generate associated pollution\n4 4\nwhen acting as a buffer because the buffering process does not involve phase\ntransfer of the conjugate acid-base pair, as both HSO - and SO 2- remain in the\n4 4\nliquid phase. Additionally, the buffering capacity of this pair in our study is\nrelatively weaker compared to the NH +/NH and HNO /NO - systems.\n4 3 3 3\nTherefore, we focus primarily on the NH +/NH and HNO /NO - buffering agents\n4 3 3 3\nin this research.\nIn summary, the concomitant pollution in this study refers to pollution arising\nfrom the gas-to-particle conversion of buffering agents during their pH-stabilizing\nfunction in aerosols. This mechanism fundamentally differs from conventional\nsecondary pollution (formed via atmospheric oxidation) and compound pollution\n(involving multi-pollutant interactions), as it is intrinsically tied to acid-base\nequilibria rather than photochemical processes or source mixing.\nPage 5, Lines 81-86: Here, inspired by the theory of multiple buffers, we propose\na viewpoint that unintended Concomitant Pollution (defined as an increase in\nPM mass concentration resulting from the gas-to-particle conversion of\n2.5\nbuffering agents during aerosol acidity stabilization) always emerges during\natmospheric multiphase buffering processes driven by key Nr species (Fig. 1b),\nthrough combining long-time field observations and global model analyses.\nLine 28: The units \"13 μg m⁻³\" and \"13 μg /m³\" are used interchangeably in different\nsections. It is advised to standardize the notation\nResponse: We appreciate you pointing it out. We have carefully checked the\nmanuscript and supporting information and standardized the symbol to μg m-3.\nSupplementary information Pages 44-45, Fig. S30-31:\nFig. S30. Season variation of NH concentration worldwide\nFig. S34. Season variation of aerosol water content worldwide\nLine 248: In Figure 3 (Analysis of main drivers of Concomitant Pollution by machine\nlearning.), the error bars for each variable are not labeled as either standard deviation\n(SD) or standard error (SE). It is recommended to clarify this in the figure legend or\ncaption.\nResponse: We appreciate your valuable comment. In this study, we employed\nRandom Forest-based Partial Dependence Plots (RF-PDPs) to analyze the\nsensitivity of Concomitant Pollution to key drivers. The figures depict the mean\npredicted responses of each factor along with their standard deviations (SDs), and\ncomprehensive descriptions have been integrated into the figure legends for\nclarity.\nPage 14, Lines 261-265:\nFig. 3. Analysis of main drivers of Concomitant Pollution by machine\nlearning. a, RH, b, T, c, NH T, d, Ca2+, e, SO 2-, and f, NO T. The solid line\n4 4 3\nrepresents the mean prediction, and the shaded region indicates ±1 standard\ndeviation of the predictions across all Bootstrap iterations, reflecting model\nuncertainty due to data variability.\nLine 351: Figure 5: MF/AF metric readability: The color scale and legend for the\nMF/AF (meteorological factor/anthropogenic factor contribution ratio) metric in Figure\n5 lack clear threshold definitions (e.g., MF/AF>1 indicating meteorological dominance).\nWe recommend improving the legend annotations and adding explanatory text to clarify\nthese critical thresholds.\nResponse: We appreciate you for this thoughtful advice. We have improved the\nlegend annotations and added explanatory text to clarify these critical thresholds\nand enhance the MF/AF metric readability.\nPages 20-21, Lines 376-387:\na\nc\ne\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n1 2\n8\n4\n6\n4\n2\n-2\n6\n4\n2\n-2\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n2 0\n5\n5\n4 0\n1 0\nN\nS\nH\nO\n6 0\nR H (% )\n1 5\nT (m g m\n4\n1 0\n2- (m g m\n4\n2\n-3)\n-3)\n0\n1\n8\n5\n0\n2 5\n1 0 0\n3 0\n2 0\nb\nd\nf\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n)1-gk\nlom(\nnoitulloP\ntnatimocnoC\n6\n4\n2\n-2\n6\n4\n2\n-2\n6\n4\n2\n-2\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0\n0 .0\n2 7 0\n5\n0 .2\n2 8\n1 0\nN\n0 .4\nC\na\nT (K )\n1 5\nT (m g m\n3\n0 .6\n2+ (m g m\n2 9 0\n-3)\n-3)\n0\n2 0\n.8\n3 0 0\n2 5\n1 .0 1 .2\nFig. 5 Contribution of meteorological factors (MF) and anthropogenic\nfactors (AF) to Concomitant Pollution caused by NH +/NH and HNO /NO -.\n4 3 3 3\na, MF/AF to Concomitant Pollution caused by NH +/NH in January. b, In July. c,\n4 3\nMF/AF to Concomitant Pollution caused by HNO /NO - in January. d, In July. In\n3 3\nFigures a-d, MF/AF serves as an indicator characterizing the relative\ncontributions of meteorological factors (MF) and anthropogenic factors (AF),\ndefined as the ratio of meteorological to anthropogenic factors. When MF/AF\nexceeds 1 (depicted in green in the figures), meteorological factors dominate;\nconversely (depicted in red), anthropogenic factors exert a greater influence. e,\nThe season variation of Concomitant Pollution, HNO concentration, and NH\n3 3\nconcentration in East Asia, South Asia, Europe, South Africa, and North America.\nLine 533: The spatial resolution of the GEOS-Chem global simulation is not clearly\nstated. It is recommended to include this information.\nResponse: Thanks for your comment. We have supplemented the spatial\nresolution of the GEOS-Chem global simulation and provided more details about\nthe GEOS-Chem global simulation.\nPage 25, Lines 471-480: To conduct global distribution of Concomitant\nPollution, we used monthly average meteorological data T and RH, gaseous\ncomponent data HNO , NH , HCl, and ion data Na+, Mg2+, K+, Ca2+, NO -, NH +.\n3 3 3 4\nCl-, SO 2- from the three-dimensional chemical transport model GEOS-Chem\n4\n(version 14.5.3) in January, April, July, and October 2019\n(https://doi.org/10.1038/s41467-024-48793-1)57. GEOS-Chem is driven by the\nModern-Era Retrospective Analysis for Research and Applications, version 2\n(MERRA-2) reanalysis meteorological fields with 2o(latitude)×2.5o (longitude)\nhorizontal resolution within the regional domains, nested within a global\nsimulation at 4o (latitude)×5o (longitude) resolution. The specific model settings\ncan be found in our previous research57.\nLine 554: the number for Equation 2 should be right-aligned.\nResponse: Thanks for the helpful comment. We have right-aligned the number\nfor Equation 2 to ensure consistent formatting of equations in manuscripts.\nPage 27, Lines 506-507: The mathematical expression is as follows:\ndb da\nβ = = − (2)\ndpH dpH\nReviewer #2 (Remarks to the Author):\nThe manuscript discussed the atmospheric multiphase buffering capacity and how that\nwas linked with the aerosol pollution concentration. The authors proposed a concept\nof concomitant pollution and analyzed the main drivers that control its formation and\nthe underlying “Acid-Base buffering-air pollution” feedback mechanism.\nIt is novel and interesting to investigate the interactions between aerosol acidity and\nconcentration; however, I think that the manuscript is very difficult to follow, maybe\nbecause of its presentation or a lack of some details explaining the key findings.\nResponse: Thanks sincerely for sincerely for your insightful and supportive review of our\nmanuscript. We greatly appreciate your time and thoughtful advice. We are\ncommitted to addressing your concerns and making necessary revisions to\nimprove the clarity of our manuscript. We have carefully addressed these points\nin our revised manuscript and provided a point-by-point response below.\nMy main concerns include:\n1) The concept of concomitant pollution. This is not clearly defined in the manuscript.\nWhat is concomitant pollution? Is this a part of the aerosol concentration? What do\nyou mean by “unintended concomitant pollution”? Although the Methods section has\na description of the calculation of concomitant pollution, it is not clear what its\nphysical meaning is and how that is linked to the total aerosol concentration, and\nfurther why this term is helpful to interpret the pollution formation.\nResponse: Thanks for your comment. We apologize for the confusion caused by\nthe lack of a clear definition of “concomitant pollution” in the manuscript.\nConcomitant pollution refers to the increased concentration of buffering agents\n(i.e., conjugate acid-base pairs such as HNO /NO - or NH +/NH ) in the aerosol\n3 3 4 3\nparticulate phase, resulting from their gas-to-particle conversion during pH-\nbuffering actions to stabilize aerosol acidity. In fact, it is part of the aerosol\nconcentration. The characterization of “unintended concomitant pollution”\nemphasizes that this pollution arises as an additional byproduct of buffering\nprocesses (e.g., acid-base equilibria regulating aerosol pH), rather than\noriginating from direct secondary formation pathways such as atmospheric\noxidation or precursor condensation. We have incorporated a comprehensive\ndefinition of concomitant pollution in the Introduction section (Page 5, Lines 81-\n86) to enhance readers’ comprehension of its mechanistic distinction from\nconventional secondary aerosol formation processes.\nThe quantification of concomitant pollution is derived from the calculation of\nbuffering capacity (β), which is defined as the amount of acid or base required to\ninduce a ΔpH change in aerosol acidity (β = Δn/ΔpH, where Δn represents moles\nof H⁺/OH⁻ added per kilogram of aerosol water), as shown in Equation 1:\nβ = dn 𝑏𝑎𝑠𝑒 = − dn 𝑎𝑐𝑖𝑑 = 2.303[H+]+2.303[OH−]+2.303∑ c∗[H+]∗K a,i ∗ (1)\ndpH dpH 𝑖 ([H+]+K ∗)2\na,i\nwhere 2.303[H+]+2.303[OH-] is the self-buffering capacity of the water and\nc∗[H+]∗K ∗\n2.303∑ a,i is the buffering capacity of the buffering agent, including\n𝑖 ([H+]+K ∗)2\na,i\nNH +/NH , HNO /NO -, and HSO -/SO 2-. Thus the buffering capacity of these\n4 3 3 3 4 4\nthree buffers is calculated as follows:\nβ = 2.303\n[NH\n(2)\nNH 4 +/NH3 ([H+]+Ka,NH3 ∗)2\nβ HNO3/NO 3 − = 2.303 [N ( O [H 3 T + ]∗ ] [ + H K + a ] , ∗ H K N a O ,H 3 N ∗) O 2 3 ∗ (3)\nβ = 2.303\n[SO\na,HSO4\n−∗\n(4)\nHSO 4 −/SO 4 2− ([H+]+K a,HSO4 −∗)2\nGiven the stoichiometric equivalence of 1 mol H+ neutralizing 1 mol OH- (H+ +\nOH- → H O), the consumption of buffering agents is quantitatively equal to the\n2\namount of acid or base added that requires neutralization. Furthermore,\nconcomitant pollution arises solely when gaseous species of buffering agents\nundergo phase partitioning into the aqueous phase and dissociate into ionic\ncounterparts (e.g., NH (g) → NH +(aq), HNO (g) → NO -(aq)), thereby\n3 4 3 3\nincreasing aerosol particulate mass concentrations.\nTherefore, for NH +/NH buffering agent: neutralizing 1 mol of exogenous H+\n4 3\nwould consume 1 mol of NH (NH + H+ → NH +), so we define a concomitant\n3 3 4\npollution index and further calculate the concomitant pollution caused by the\nNH +/NH buffering agent:\n4 3\nCo−P Index =\n[NH3]\n(5)\n[NH3 ]+[NH\n4\n+]\nCo−P = 2.303\nCO−P Index∗C\nNH4\nT∗103∗[H+]∗Ka,NH3 ∗\n(6)\nAWC∗MNH3 ∗([H+]+Ka,NH3 ∗)2\nSimilarly, for HNO /NO - buffering agent: neutralizing 1 mol of exogenous OH-\n3 3\nwould consume 1 mol of HNO (HNO + OH- → NO - + H O), so we define a\n3 3 3 2\nconcomitant pollution index and further calculate the concomitant pollution\ncaused by the HNO /NO - buffering agent:\n3 3\nCo−P Index =\n[HNO3]\n(7)\n[HNO3 ]+[NO\n3\n−]\nCo−P = 2.303\nCO−P Index∗C\nNO3\nT∗103∗[H+]∗Ka,𝐻𝑁𝑂3 ∗\n(8)\nAWC∗MHNO3 ∗([H+]+Ka,𝐻𝑁𝑂3 ∗)2\nThe HSO -/SO 2- acid-base pair does not generate associated pollution when\n4 4\nacting as a buffer because the buffering process does not involve phase transfer of\nthe conjugate acid-base pair, as both HSO - and SO 2- remain in the liquid phase.\n4 4\nAdditionally, the buffering capacity of this pair in our study is relatively weaker\ncompared to the NH +/NH and HNO /NO - systems. Therefore, we focus\n4 3 3 3\nprimarily on the NH +/NH and HNO /NO - buffering agents in this research.\n4 3 3 3\nIn summary, concomitant pollution specifically refers to the fraction of buffering\nagents that transition from the gaseous phase into the aqueous phase as ionic\nspecies (e.g., NH (g) → NH +(aq), HNO (g) → NO -(aq)) during pH stabilization\n3 4 3 3\nprocesses, thereby constituting a measurable component of total aerosol mass\nconcentration.\nPage 5, Lines 81-86: Here, inspired by the theory of multiple buffers, we propose\na viewpoint that unintended Concomitant Pollution (defined as an increase in\nPM mass concentration resulting from the gas-to-particle conversion of\n2.5\nbuffering agents during aerosol acidity stabilization) always emerges during\natmospheric multiphase buffering processes driven by key Nr species (Fig. 1b),\nthrough combining long-time field observations and global model analyses.\n2) It is also difficult to understand the “Acid-Base buffering-air pollution” feedback\nmechanism as proposed in Figure 2 and the relevant text (Lines 165-210). How to\nunderstand this feedback mechanism? Aerosol pH could remain relatively stable\nwhile the levels of aerosol pollution could vary significantly. What are the\ninteractions between the two? The caption of Figure 2 is not clear, i.e., what are the\ncolor shadings and y-axis in panel (a), and what is the y-axis in panel (d)? The caption\nof Figure 3 is also not clear. What are the colored shadings, solid and dashed lines\nrepresent?\nResponse: Thanks for the insightful comment. We have added a detailed\nexplanation of the feedback mechanism in the revised manuscript to facilitate\nbetter understanding. This feedback mechanism fundamentally describes how the\nneutralization of exogenous acids or bases by buffering agents stabilizes aerosol\nacidity, which in turn lowers the energy barrier for further acid/base uptake\n(governed by Henry’s law and acid-base equilibria), thereby facilitating the influx\nof additional reactive species into the aerosol phase - a self-perpetuating cycle\nthat amplifies pollution through buffering-driven phase partitioning.\nFor NH +/NH buffering agent: When acidic species are introduced into an\n4 3\naerosol system, gaseous NH partitions into the aqueous phase to neutralize the\n3\nadded acid, thereby mitigating aerosol acidification. This pH stabilization allows\nadditional acid influx, necessitating further NH dissolution to maintain buffering\n3\ncapacity. This self-reinforcing cycle drives continuous conversion of NH (g) to\n4\nnegative feedback mechanism of buffering-driven pollution amplification. When\nalkaline species are introduced into an aerosol system, particulate NH + escapes\n4\ninto the gas phase as NH (g) (via the reverse of NH + (aq) →NH (g) + H+ (aq)),\n3 4 3\ncounteracting reductions in aerosol acidity. This pH stabilization lowers the\nthermodynamic driving force for alkaline uptake (governed by Henry’s law\nconstants and ion activity coefficients), enabling further alkaline influx and\nnecessitating additional NH + volatilization to maintain buffering capacity. This\n4\nself-limiting cycle converts particulate NH + to gaseous NH , thereby partially\n4 3\noffsetting aerosol mass accumulation - a regulatory process we define as the\npositive feedback mechanism of buffering-mediated pollution modulation. As\nshown in Supplementary Fig. 8:\nFig. S8. Schematic of the “Acid-Base buffering-PM concentration”\n2.5\npositive/negative feedback mechanism for NH +/NH dominated buffering.\n4 3\nFor HNO /NO - buffering agent: When alkaline substances are introduced into\n3 3\nthe aerosol system, gaseous HNO partitions into the aqueous phase to neutralize\n3\nthe added base, thereby mitigating aerosol acidification. This pH stabilization\nenables additional alkaline influx, necessitating further dissolution of HNO to\n3\nmaintain buffering capacity. Such a self-reinforcing cycle drives continuous\nconversion of HNO (g) to NO -(aq), progressively amplifying aerosol ionic mass\n3 3\n- a process we term the negative feedback mechanism of buffering-driven\npollution amplification. Conversely, when acidic substances are introduced,\nparticulate NO - volatilizes as HNO (g) (via the reverse reaction: NO -(aq) +\n3 3 3\nH+(aq) → HNO (g)), offsetting reductions in aerosol acidity. The stabilized pH\n3\nlowers the thermodynamic driving force for acid uptake (governed by Henry’s\nlaw constants and ion activity coefficients), allowing further acid influx while\nrequiring additional NO - volatilization to sustain buffering. This self-limiting\n3\ncycle converts particulate NO - to gaseous HNO , partially counteracting aerosol\n3 3\nmass accumulation - a regulatory process defined as the positive feedback\nmechanism of buffering-mediated pollution modulation. As shown in\nSupplementary Fig. 9:\nFig. S9. Schematic of the “Acid-Base buffering-PM concentration”\n2.5\npositive/negative feedback mechanism for HNO /NO - dominated buffering.\n3 3\nTherefore, this very aerosol pH stabilization induced by atmospheric multiphase\nbuffering lowers the thermodynamic resistance to pollutant uptake (as governed\nby Henry’s law and solubility equilibria), enabling continuous influx of reactive\nspecies into the aerosol phase. While buffering agents stabilize aerosol pH\nthrough acid-base equilibria, they may simultaneously amplify particulate matter\nconcentrations via phase-partitioning of ionic species (e.g., NH +/NO -),\n4 3\na\nparadoxical phenomenon termed buffering-driven concomitant pollution. This\ntrade-off between pH homeostasis and aerosol mass accumulation is\nmechanistically rooted in the shifts of gas-particle partitioning under varying\nacidity regimes. In order to better understand the concept of the feedback\nmechanism, we have added relevant content to both the main manuscript and the\nsupporting information to make the manuscript clearer.\nWe apologize for the non-detailed diagram caption. Figure 2a depicts schematic\nof the mechanism of Concomitant pollution in the negative feedback mechanism,\nsynthesized from nine pollution episodes systematically extracted from our four-\nyear observational dataset (2018-2021). This schematic diagram illustrates the\ntrade-off relationship between pollution levels and buffering capacity. As\npollution intensifies (denoted by rising total PM in Fig. 2a), the buffering\n2.5\ncapacity (yellow curve) exhibits a declining trend. The total pollution burden\nconsists of secondary pollution (pink curve) and concomitant pollution (blue\ncurve). We have modified the original figure and added details to the caption of\nFigure 2 to better demonstrate the relationship between buffering capacity,\nconcomitant contamination, and contaminant levels.\nFigure 2d illustrates the distribution of concomitant pollution caused by the pH\nshift of 0.5 units induced by the NH +/NH -dominated buffering mechanism\n4 3\nduring the clean period. The Y-axis of the histogram represents probability\ndensity (bin width = 10). The approximate percentage of data within a given\ninterval can be derived by multiplying the probability density by the bin width\n(e.g., density  10), reflecting the proportion of total data in that range. We have\nmodified the legend to make it clearer.\nThe Figure 3 displays the sensitive response of influence factors to Concomitant\nPollution by applying RF-PDP, thus the solid line represents the mean prediction,\nand the shaded region indicates ±1 standard deviation of the predictions across all\nBootstrap iterations, reflecting model uncertainty due to data variability. We have\nsupplemented a detailed explanation in the legend of Figure 3.\nPages 9-10, Lines 166-185: Therefore, we proposed a novel perspective that the\ndynamic exchange between gas-phase and particle-phase buffering agents plays a\npivotal role in both exacerbating and alleviating air pollution during the Acid-\nBase buffering process. To better uncover this feedback mechanism, we first\nunveiled the essence of buffering for NH +/NH . Wherein, the chemical\n4 3\nmechanism of acid buffering is that H+ can be depleted by bonding with NH to\n3\nform NH + when acid (such as SO 2- from other sources) is added into the liquid\n4 4\nphase of the aerosol30, 31, thereby maintaining the stability of the aerosol acidity.\nIn this process, since NH enters the aerosol phase to form NH +, it amplifies the\n3 4\nload of inorganic PM . This process was termed the “Acid-Base buffering-air\n2.5\npollution” negative feedback mechanism, characterized by triggering of\nConcomitant Pollution (Fig. 2a). Likewise, for base buffering, the OH- brought by\nbase (such as Ca2+ from other sources) will be neutralized by to generate H O and\n2\nrelease NH to gas phase, which maintains the stability of the aerosol acidity.\n4 3\ninorganic PM formation. This process was termed the “Acid-Base buffering-air\n2.5\npollution” positive feedback mechanism, connected with pollution diminishes. As\na result, pH values can be stabilized within a specific range without large\nfluctuations despite the addition of abundant acids or bases, while PM loading\n2.5\ncan be either enhanced or reduced (Supplementary Text 3 and Supplementary\nFigs. 8-9).\nSupplementary information Pages 4-5:\nS3. The “Acid-Base buffering-air pollution” feedback mechanism\nFor NH +/NH buffering agent: When acidic species are introduced into an\n4 3\naerosol system, gaseous NH partitions into the aqueous phase to neutralize the\n3\nadded acid, thereby mitigating aerosol acidification. This pH stabilization allows\nadditional acid influx, necessitating further NH dissolution to maintain buffering\n3\ncapacity. This self-reinforcing cycle drives continuous conversion of NH (g) to\n4\nnegative feedback mechanism of buffering-driven pollution amplification. When\nalkaline species are introduced into an aerosol system, particulate NH + escapes\n4\ninto the gas phase as NH (g) (via the reverse of NH + (aq) →NH (g) + H+ (aq)),\n3 4 3\ncounteracting reductions in aerosol acidity. This pH stabilization lowers the\nthermodynamic driving force for alkaline uptake (governed by Henry’s law\nconstants and ion activity coefficients), enabling further alkaline influx and\nnecessitating additional NH + volatilization to maintain buffering capacity. This\n4\nself-limiting cycle converts particulate NH + to gaseous NH , thereby partially\n4 3\noffsetting aerosol mass accumulation - a regulatory process we define as the\npositive feedback mechanism of buffering-mediated pollution modulation. The\nschematic of the “Acid-Base buffering-PM concentration” positive/negative\n2.5\nfeedback mechanism for NH +/NH dominated buffering was shown in\n4 3\nSupplementary Fig. 8.\nIn addition to the NH +/NH buffering mechanism, HNO /NO - also\n4 3 3 3\nproduces this feedback mechanism when exerting its buffering effect. For\nHNO /NO - buffering agent: When alkaline substances are introduced into the\n3 3\naerosol system, gaseous HNO partitions into the aqueous phase to neutralize the\n3\nadded base, thereby mitigating aerosol acidification. This pH stabilization enables\nadditional alkaline influx, necessitating further dissolution of HNO to maintain\n3\nbuffering capacity. Such a self-reinforcing cycle drives continuous conversion of\nHNO (g) to NO -(aq), progressively amplifying aerosol ionic mass - a process we\n3 3\nterm the negative feedback mechanism of buffering-driven pollution\namplification. Conversely, when acidic substances are introduced, particulate\nNO - volatilizes as HNO (g) (via the reverse reaction: NO -(aq) + H+(aq) →\n3 3 3\nHNO (g)), offsetting reductions in aerosol acidity. The stabilized pH lowers the\n3\nthermodynamic driving force for acid uptake (governed by Henry’s law constants\nand ion activity coefficients), allowing further acid influx while requiring\nadditional NO - volatilization to sustain buffering. This self-limiting cycle\n3\nconverts particulate NO - to gaseous HNO , partially counteracting aerosol mass\n3 3\naccumulation - a regulatory process defined as the positive feedback\nmechanism of buffering-mediated pollution modulation. Schematic of the “Acid-Base\nbuffering-PM concentration” positive/negative feedback mechanism for\n2.5\nHNO /NO - dominated buffering was shown in Supplementary Fig. 9.\n3 3\nPages 12-13, Lines 216-230:\nFig. 2 The Schematic of the Concomitant Pollution in the negative feedback\nmechanism and samples of experimental analysis. a, Schematic of the mechanism\nof Concomitant pollution in the negative feedback mechanism. This schematic\ndiagram illustrates the trade-off relationship between pollution levels and buffering\ncapacity. As pollution intensifies, the buffering capacity (yellow curve) exhibits a\ndeclining trend. The total pollution burden consists of secondary pollution (pink\ncurve) and concomitant pollution (blue curve). b, Field emission transmission electron\nmicroscopy experiment. The samples during the cleaning period were collected at a\nPM of 31 μg m-3 on October 30, 2023, while the samples during the pollution\n2.5\nperiod were collected at a PM of 185 μg m-3 on the same day. All other sampling\n2.5\nconditions were the same. d, Distribution of the Concomitant pollution with\nProbability Density (Bin width = 10). The Concomitant pollution was caused by\nchanging the pH value by 0.5 units during the NH +/NH dominated buffering regime\n4 3\nin the clean period. \nPage 14, Lines 261-265:\na 1-gk ) \nlom 120\nb1-gk ) \nlom\n60\n( no\nt\ni\nn\ntu\na\nl\nt\nl\ni\no\nm\nP\n8\n4\n0\n0\n( no\nt\ni\nn\ntu\na\nl\nt\nl\ni\no\nm\nP\n4\n2\n0\n0\n0\nocnoC 0 ocnoC\n-20\n20 40 60 80 100 270 280 290 300\nRH (%) T (K)\nc 1-gk ) \nlom\n( no\nt\ni\nn\ntu\na\nl\nt\nl\ni\no\nm\nP\n6\n4\n2\n0\n0\n0\n0\nd1-gk ) \nlom\n( no\nt\ni\nn\ntu\na\nl\nt\nl\ni\no\nm\nP\n6\n4\n2\n0\n0\n0\n0\nocnoC\n-20\nocnoC\n-20\n5 10 15 20 25 30 0 5 10 15 20 25\nNHT (mg m-3) NOT (mg m-3)\n4 3\ne\n1-gk ) \nlom\n( no\nt\ni\nn\ntu\na\nl\nt\nl\ni\no\nm\nP\n6\n4\n2\n0\n0\n0\n0\nf 1-gk ) \nlom\n( no\nt\ni\nn\ntu\na\nl\nt\nl\ni\no\nm\nP\n6\n4\n2\n0\n0\n0\n0\nocnoC\n-20\nocnoC\n-20\n0 5 10 15 20 0.0 0.2 0.4 0.6 0.8 1.0 1.2\nSO2- (mg m-3) Ca2+ (mg m-3)\nlearning. a, RH, b, T, c, NH T, d, Ca2+, e, SO 2-, and f, NO T. The solid line\n4 4 3\nrepresents the mean prediction, and the shaded region indicates ±1 standard\ndeviation of the predictions across all Bootstrap iterations, reflecting model\nuncertainty due to data variability.\n3) In the analyses of global patterns, the impacts of Arctic stratospheric eddies and El\nNino (Lines 321-349) were mentioned and also emphasized in the abstract. It does not\nappear to have sufficient evidence to demonstrate how these climate variations would\naffect the proposed concomitant pollution. Only four months (for the year 2019) of\nmodel results were analyzed. Interpreting the spatial patterns (Figure 4) with specific\nclimate or weather conditions needs to be cautious and requires more direct evidence.\nResponse: We sincerely appreciate your insightful comments and thorough\nreview of our manuscript. We have removed all assertions linking specific\nclimate modes (Arctic eddies, El Niño) to concomitant pollution in the Abstract\nand Results following your suggestion. We agree that the spatial patterns in\nFigure 4 require more evidence to tie them to specific climate events. In the\nrevised manuscript, we have shifted focus from climate drivers to direct\nmeteorological influences (e.g., temperature, humidity, boundary layer height).\nWe will further explore climate drivers in future research to better understand\nregional differences in concomitant pollution.\nWe thank you again for your suggestions, which have significantly improved the\nrigor of our manuscript.\nPage 2, Abstract: In addition, extreme weather conditions such as Arctic\nstratospheric eddies and El Niño can also significantly affect Concomitant\nPollution in the high-latitude regions of the Arctic and the areas near the Pacific\nOcean.\nPages 18-19, Lines 336-356: In Russia and Canada, the arctic stratospheric polar\nvortex and Siberian high pressure triggered cold air and increased water content\nhindering the rise of Concomitant Pollution. Conversely, the strong Co-P-\nNH +/NH in South Asia stemmed from intensive agricultural activities emitting\n4 3\nhigh NH concentrations35 (Supplementary Fig. 30). The contribution of\n3\nmeteorological factors to strong Co-P-NH +/NH in North America was higher\n4 3\nthan that in South Asia, which exhibited mixed drivers. The combination of high\ntemperature, low AWC, and appropriate aerosol acidity collectively contributes to\nthe high levels of Co-P-NH +/NH (Supplementary Fig. 33-35). The\n4 3\nmeteorological factors contributed more to Co-P-NH +/NH in Brazil and South\n4 3\nAfrica, which may be due to the high T and low AWC environment\n(Supplementary Fig. 33-36). At the beginning of 2019, the tropical Pacific was in\na weak El Niño state, which has preconditioned the reduced rainfall and higher T\nin eastern Brazil and South Africa36, 37. In summer, the contribution of MF to high\nCo-P-NH +/NH was gradually increasing in North America and Europe, possibly\n4 3\nbecause of increased T and diminished AWC (Supplementary Fig. 33-36). These\nmeteorological conditions favor the partitioning of NH +/NH as gaseous NH\n4 3 3\nrather than aerosol-phase NH +, elevating NH +/NH Concomitant Pollution\n4 4 3\nIndex. Additionally, high-temperature and low-humidity conditions enhance\naerosol buffering capacity. Consequently, the elevated NH +/NH Concomitant\n4 3\nPollution Index combined with increased buffering capacity synergistically\nintensifies Concomitant Pollution during summer. This dual mechanism explains\nthe significantly higher Concomitant Pollution levels in regions like North\nAmerica and Europe during summer compared to winter.\nPage 22, Lines 425-428: Notably, extreme climate perturbations, such as Arctic\nstratospheric eddies and El Niño, amplify Concomitant Pollution through\nteleconnection shifts in relative humidity (RH) and temperature, mirroring the RH\nand T sensitivity identified in our machine learning attribution analysis.\nTherefore, our analyses underscore the significance of persistent NH control to\n3\nachieve the WHO Global Air Quality Guidelines targets for PM by 2050, and\n2.5\nthey have been proven to be cost-effective29, 41.\nOverall, the study requires at least substantial revision to better fit the broad audience\nof Nature Communications.\nResponse: We sincerely appreciate your constructive feedback regarding\nbroadening the manuscript’s accessibility. To better fit the broad audience of\nNature Communications, we have implemented the following substantial\nrevisions:\n(1) Conceptual clarity: We have clarified the concepts and descriptions of\n“concomitant pollution” and “feedback mechanisms” to enhance reader\ncomprehension. The figure legends in the manuscript have been substantially\nenhanced with more comprehensive and specific descriptions, significantly\nimproving the accessibility of the manuscript.\n(2) Strengthened the robustness and validity of the discussion: We have removed\nthe insufficiently substantiated findings from the original manuscript, and\nsupplemented the in-depth mechanistic analysis of key contributing factors,\nthereby significantly enhancing the critical rigor of the research conclusions.\nThese adjustments enhance accessibility while preserving scientific rigor, making\nour findings impactful for broad audience. Thank you again for your valuable\nadvices."}, {"round": 2, "reviewer_comments": {"reviewer_1": "I would like to commend the authors for their diligent and comprehensive revisions. They have thoughtfully addressed the\nmajority of the concerns raised in the initial review.However, there are a few remaining points that, if addressed, would fully\nsolidify its conclusions and complete the narrative from theory to validation.\nDirect Validation of the “Concomitant Pollution” (Co-P) Metric: The authors have done an excellent job of providing a\ntheoretical basis for their novel Co-P metric. The final step to make this concept fully convincing is to validate the calculated\nmetric against direct measurements. The new high-resolution data presented in Supplementary Figs. I encourage the\nauthors to perform a direct comparison for the pollution events shown in these figures. Can they plot their calculated\n“Concomitant Pollution” values (in µg m-3) against the measured increase in particulate ammonium (NH4+) mass\nconcentration during these specific events? Demonstrating a strong correlation between the calculated Co-P and the\nobserved PM increase would provide the ultimate validation for their new metric, closing the loop between theory and\nobservation.\nDiscussion of the MF/AF indicator's methodological limitations: A point from the initial review that would benefit from further\nattention is the simplification inherent in the Meteorological Factor/Anthropogenic Factor (MF/AF) ratio. While this indicator\nis a useful diagnostic tool, it categorizes variables into discrete bins when they are, in reality, co-dependent (e.g., Aerosol\nWater Content is a function of both meteorological RH and anthropogenic aerosol composition). To enhance scientific\ntransparency and rigor, a discussion in the Methods or Discussion section acknowledging these limitations would\nstrengthen the global analysis.\nClarification of Figure 2a construction: The caption for Figure 2 has been improved, clarifying that the schematic in panel (a)\nwas “synthesized from nine pollution episodes”. For maximum clarity and reproducibility of the concept, it would be helpful to\nadd a sentence further clarifying how the figure was synthesized. For instance, is the schematic a conceptual illustration\ninspired by the general trends observed, or is it quantitatively based on an average of the data from those nine events?\nMain text Page 21, Lines 397–402 & Page 23, Lines 430–447; Supplementary S8: The mitigation measures are too generic\nand lack a direct quantitative linkage to the study results; it is suggested to include a regional and seasonal priority list for\nNH₃ mitigation (e.g., South Asia in winter, North America in summer) to enhance the specificity of the mitigation strategy.\nMain text Pages 9–10, Lines 166–185; Supplementary Figs. S8, S9: the acid–base buffering–pollution feedback mechanism\ncurrently relies heavily on chemical equations and lengthy descriptions, which may be difficult for readers without a\nchemistry background to follow. It is recommended to add a simplified schematic diagram that clearly illustrates the flows,\nphase transitions, and pollution changes involved in both positive and negative feedback processes, accompanied by a\nconcise one-sentence physical interpretation to enhance clarity and accessibility.\nEnsure that all abbreviations and units are clearly defined at their first appearance in the main text (e.g., AWC for aerosol\nwater content), including both the full term and the unit of measurement where applicable, to enhance clarity and\naccessibility for readers from different disciplinary backgrounds.", "reviewer_2": "The revised manuscript has been largely improved for interpreting the concept of concomitant pollution (CP). I think the\nmanuscript now presents a nice study that quantifies the interactions between the buffering capacity and PM2.5\nconcentrations.\nSome further revisions are still needed to better understand the key findings.\n(1) Page 10, Line 175-181\nIt is still not clear to me why the process is called “Acid-Base buffering-air pollution” negative or positive feedback. When we\nconsider the term “feedback”, it typically describes the interactions between two items to be enhanced (positive) or\nsuppressed (negative), such as the case of climate warming - water vapor positive feedback. Thus, here why triggering of\nconcomitant pollution is called negative feedback? And how to understand the feedback?\n(2) Page 11, Discussion of Figure 2\nAs shown in Figure 2a, the concomitant pollution is a proportion of secondary pollution; therefore, how do we know that\nFigure 2c illustrates this pollution? Also in Figure 2d, it is not clear what the blue bars present. Please clarify in the caption.\n(3) Page 13, Line 248-249\nHere, I would suggest adding 1-2 sentences explaining the effects of RH, NO3T, T, etc., on concomitant pollution. e.g., why\ndoes concomitant pollution decrease as RH increases?\n(4) Page 16, Discussion of Figure 4\nThe concomitant pollution levels are generally much higher in July than in January over northern mid-latitudes, while PM2.5\npollution in most of these regions is heavier in winter (January) than in summer. Can you please comment on the\nimplications of CP on wintertime PM pollution?\n(4) Page 16, Discussion of Figure 4\nThe concomitant pollution levels are generally much higher in July than in January over northern mid-latitudes, while PM2.5\npollution in most of these regions is heavier in winter (January) than in summer. Can you please comment on the\nimplications of CP on wintertime PM pollution?\n(5) Page 25, Line 475-479\nThe resolution for the GEOS-Chem model is not clear. 2x2.5 degrees or 4x5 degrees? Both resolutions can be run at a\nglobal scale rather than nested regions in GEOS-Chem. Please check."}, "author_response": "Response to reviews\nWe sincerely thank the two reviewers for their positive recognition of our revised\nmanuscript and their acknowledgment of the thorough and comprehensive revisions\nwe have made in response to the initial review comments. We also appreciate the\nvaluable suggestions provided to help readers better understand the key findings of\nthis study. We have identified the main concerns raised by Reviewer 1 and Reviewer 2\nand have addressed them in the revised manuscript. A summary is provided below.\nFirst, in response to Reviewer 1’s comments, we have enhanced the direct validation\nof the “Concomitant Pollution (Co-P)” metric by using our observational data.\nInspired by the helpful advice, we have compared the correlation between Co-P and\nobserved NH + concentration. The results demonstrated a strong correlation (r=0.92),\n4\nindicating a synchronous increase between the two during pollution events, indicating\nstrong consistency between our theoretical framework and observational evidence.\nAnother important piece of advice is the establish direct quantitative links between\nemission reduction measures and research findings to enhance the specificity of the\nstrategies. We have supplemented the revised manuscript with a regional and seasonal\npriority list for ammonia emission mitigation. For instance, in northern China and\nSouth Asia, control measures should be prioritized for deployment during the dry\nseason prior to the monsoon, when RH is low and NH concentrations are relatively\n3\nhigh. In contrast, for North America and Europe, focus should be placed on summer\nmonths-these periods coincide with peak fertilizer application, and are accompanied\nby low RH and high solar radiation, which facilitate the rapid formation of secondary\nparticulate matter.\nAdditionally, according to Reviewer 2’s advice, we have conducted a detailed analysis\nof the influencing factors of winter concomitant pollution and the formation\nmechanisms of winter PM pollution. The low level of “concomitant pollution” in\nwinter precisely occurs because, due to unfavorable meteorological conditions (low\ntemperature and high humidity), components in the gas phase have already been\nconverted into actual PM components. This process ultimately leads to the observed\n2.5\nmore severe particulate matter pollution.\nFurthermore, a discussion of the methodological limitations regarding the MF/AF\nindicator has been incorporated into the Methods section, thereby enhancing the\nscientific transparency and rigor of our manuscript. Meanwhile, we have refined the\nlabeling and descriptions of figures (e.g., Figure 2) We have also characterized the\ninteraction between acid-base buffering and pollution as a more precise response\nmechanism and supplemented them with a simplified schematic diagram, which has\nfurther improved the readability of the paper.\nA point-by-point response to the reviewers’ comments has been provided below. The\noriginal comments from reviewers are in normal font, our replies are indented and in\nblue, and revised texts as they appear in the manuscript text are indented and in red.\nPoint-by-point response to reviewers’ comments\nReviewer #1:\nI would like to commend the authors for their diligent and comprehensive revisions.\nThey have thoughtfully addressed the majority of the concerns raised in the initial\nreview. However, there are a few remaining points that, if addressed, would fully\nsolidify its conclusions and complete the narrative from theory to validation.\nResponse: Thank you very much for reviewing the manuscript again, and giving\nus an opportunity to revise our manuscript. We sincerely appreciate your positive\nand constructive comments that we have carefully addressed in the revised\nmanuscript. We are committed to addressing your concerns and making necessary\nrevisions to improve the clarity of our manuscript. We have carefully addressed\nthese points in our revised manuscript and provided a point-by-point response\nbelow.\nDirect Validation of the “Concomitant Pollution” (Co-P) Metric: The authors have\ndone an excellent job of providing a theoretical basis for their novel Co-P metric. The\nfinal step to make this concept fully convincing is to validate the calculated\nmetric against direct measurements. The new high-resolution data presented in\nSupplementary Figs. I encourage the authors to perform a direct comparison for the\npollution events shown in these figures. Can they plot their calculated “Concomitant\nPollution” values (in µg m-3) against the measured increase in particulate ammonium\n(NH +) mass concentration during these specific events? Demonstrating a strong\n4\ncorrelation between the calculated Co-P and the observed PM increase would provide\nthe ultimate validation for their new metric, closing the loop between theory and\nobservation.\nResponse: We sincerely appreciate you raising this critical question regarding\nvalidation. This has prompted us to refine our analysis of the “Concomitant\nPollution” (Co-P) Metric and its conceptual framework, thereby making our\nmanuscript more detailed and rigorous.\nAccording to your advice, we have plotted the Co-P values calculated during the\nhigh-resolution events against the measured incremental mass concentrations of\nparticulate NH + (now presented in Supplementary Fig. 12). The results indicate\n4\nthat Co-P exhibits a gradually increasing trend, while NH + increment show a\n4\nslightly increasing trend. And there is a certain correlation between the two\nparameters, which is modulated by the complex interplay of multiple factors such\nas emissions and meteorology. Therefore, inspired by your helpful advice, we\nfurther investigated the relationship between the NH + concentration and Co-P.\nincrease between the two parameters during pollution events. This finding further\nvalidates the theory against observational data, provides the most robust\nvalidation for the new metric, and closes the loop between theory and\nobservation.\nWe have revised the manuscript to present this more sophisticated validation\nframework, which we believe provides a far more compelling and scientifically\nhonest demonstration of the Co-P metric’s utility.\nSupplementary information Page 6:\nS4. The experimental validation of negative response mechanism\nIn addition, to further achieve a closed loop between theory and observation, we\ninvestigated the relationships between Concomitant Pollution, the incremental\nmass of NH +, and the ambient NH + concentration during pollution episodes\n4 4\n(Supplementary Fig. 13). The results reveal a discernible correlation between\nConcomitant Pollution and NH + increment, albeit modulated by the interplay of\n4\nemissions and meteorological conditions. Importantly, a strong correlation\n(r=0.92) with synchronous increases was found between Concomitant Pollution\nand NH + concentration, unambiguously demonstrating that pollution occurrence\n4\nis associated with Concomitant Pollution.\nSupplementary information Page 48, Fig. S34:\nFig. S13. The relationships between Concomitant Pollution, the incremental mass\nof NH +, and the ambient NH + concentration during pollution episodes.\n4 4\nDiscussion of the MF/AF indicator’s methodological limitations: A point from the\ninitial review that would benefit from further attention is the simplification inherent in\nthe Meteorological Factor/Anthropogenic Factor (MF/AF) ratio. While this indicator\nis a useful diagnostic tool, it categorizes variables into discrete bins when they are, in\nreality, co-dependent (e.g., Aerosol Water Content is a function of both meteorological\nRH and anthropogenic aerosol composition). To enhance scientific transparency and\nrigor, a discussion in the Methods or Discussion section acknowledging these\nlimitations would strengthen the global analysis.\nResponse: We sincerely thanks for this insightful and constructive comment. We\nfully agree that meteorological factors (MF) and anthropogenic factors (AF) are\ninterdependent and exist on a continuum in reality, and that the discrete MF/AF\nratio we employed represents a necessary simplification. To enhance the\ntransparency and rigor of our study, we have accordingly added a paragraph in\nthe Methods section to explicitly discuss this limitation.\nPage 38, Lines 742-751: It is important to note that the MF/AF ratio employed in\nthis study is a conceptual simplification. In reality, meteorological and\nanthropogenic factors are highly interdependent and exist on a continuum rather\nthan as discrete categories. For instance, AWC, a key parameter influencing\nheterogeneous chemistry, is co-determined by meteorological conditions (e.g.,\nRH) and anthropogenic aerosol composition. The discrete categorization, while\nenabling a clear and practical diagnostic framework for global analysis, may\nintroduce uncertainties in precisely quantifying the absolute contributions of each\nfactor and might underestimate their synergistic effects. Nevertheless, the MF/AF\nindicator serves as a valuable diagnostic tool for identifying the dominant drivers\nof Concomitant Pollution across different regions and seasons.\nClarification of Figure 2a construction: The caption for Figure 2 has been improved,\nclarifying that the schematic in panel (a) was “synthesized from nine pollution\nepisodes”. For maximum clarity and reproducibility of the concept, it would be\nhelpful to add a sentence further clarifying how the figure was synthesized. For\ninstance, is the schematic a conceptual illustration inspired by the general trends\nobserved, or is it quantitatively based on an average of the data from those nine\nevents?\nResponse: We would like to thank you for pointing out this point, which allows\nus to provide clarification. Figure 2a is indeed a conceptual schematic drawn\nbased on the common trends observed across nine pollution events, which aims to\ncomprehensively illustrate Concomitant Pollution events in a clear and intuitive\nmanner. This presentation method can effectively convey to readers the overall\nconceptual model of the dynamic evolution of Concomitant Pollution events,\navoiding interference from minor differences in data of individual events, which\nis crucial for understanding subsequent analyses based on actual data (e.g., Figure\n2b-d).\nWe have further revised the figure caption of Figure 2a, explicitly stating it as\n“Conceptual schematic of the mechanism of Concomitant pollution in the\nnegative response mechanism, based on the common trends observed across the\nnine studied events. This schematic diagram illustrates the trade-off relationship\nbetween pollution levels and buffering capacity. As pollution intensifies, the\nbuffering capacity (yellow curve) exhibits a declining trend. The total pollution\nburden consists of secondary pollution (pink curve) and concomitant pollution\n(blue curve).”, to ensure no misunderstanding arises in all subsequent versions of\nthe manuscript. This conceptual presentation, combined with the subsequent\nfigures that display specific observational data, enables readers to gain a\ncomprehensive understanding from conceptualization to empirical evidence.\nPages 12-13, Lines 216-222: a, Conceptual schematic of the mechanism of\nConcomitant Pollution in the negative response mechanism, based on the\ncommon trends observed across the nine studied events. This schematic diagram\nillustrates the trade-off relationship between pollution levels and buffering\ncapacity. As pollution intensifies, the buffering capacity (yellow curve) exhibits a\ndeclining trend. The total pollution burden consists of secondary pollution (pink\ncurve) and Concomitant Pollution (blue curve).\nMain text Page 21, Lines 397–402 & Page 23, Lines 430–447; Supplementary S8:\nThe mitigation measures are too generic and lack a direct quantitative linkage to the\nstudy results; it is suggested to include a regional and seasonal priority list for NH\n3\nmitigation (e.g., South Asia in winter, North America in summer) to enhance the\nspecificity of the mitigation strategy.\nResponse: We sincerely appreciate this crucial comment. We fully agree that\ndirectly linking our specific quantitative research findings to targeted emission\nreduction strategies will greatly enhance the practical application value of our\nstudy. To this end, we have supplemented a regional and seasonal priority list for\nNH mitigation to the revised manuscript. This priority list is based on our key\n3\nmechanistic finding: controlling NH emissions during periods of low relative\n3\nhumidity is particularly effective for reducing PM concentrations.\n2.5\nWe have identified regions and seasons characterized by persistently low RH and\nhigh agricultural activity as the primary targets for NH emission reduction. For\n3\ninstance, in northern China and South Asia, control measures should be\nprioritized for deployment during the dry season prior to the monsoon, when RH\nis low and NH concentrations are relatively high. In contrast, for North America\n3\nand Europe, focus should be placed on summer months-these periods coincide\nwith peak fertilizer application, and are accompanied by low RH and high solar\nradiation, which facilitate the rapid formation of secondary particulate matter.\nFurthermore, we have refined the discussion on agricultural measures (such as\ndeep fertilizer placement and 4R nutrient stewardship), emphasizing that the\nenvironmental benefits of these measures can only be maximized when\nimplemented during the identified seasons with low RH and high sensitivity. For\nexample, we recommend the use of high-efficiency nitrogen fertilizers during\nagricultural fertilization periods, and avoiding dry, low-RH time windows as\nmuch as possible where agronomically feasible.\nThese revisions have established a direct connection between our emission\nreduction recommendations and research findings, and provide a regional and\nseasonal priority list for NH mitigation, thereby enhancing the specificity of the\n3\nmitigation strategies. We would like to express our gratitude again for your\nvaluable comments.\nPages 23-25, Lines 445-485: The main potential for NH abatement lies in\n3\nagricultural activities, as they are the primary source of NH emissions42. This\n3\nstudy emphasizes that the environmental benefits of emission reduction measures\n(such as reducing PM ) are highly dependent on the region and season in which\n2.5\nthey are implemented. To maximize cost-effectiveness, emission reduction\nmeasures should be prioritized during meteorological windows most sensitive to\nNH emissions (e.g., periods of low RH). This measure mainly includes two\n3\naspects: optimizing nitrogen fertilizer and improving manure management43. For\noptimizing nitrogen fertilizer, deep placement of N fertilizer is a good option, as\nit mainly reduces NH volatilization by applying the fertilizer deeper into the soil\n3\nrather than surface broadcasting44. The use of efficient nitrogen fertilizers\ncontaining urease or nitrification inhibitors can also suppress the release of NH\n3\ninto the atmosphere45. It is particularly important that the timing of these\nmeasures is crucial. For instance, in regions like Northern China and South Asia,\nemphasis should be placed on implementing these measures during the pre-\nmonsoon dry season (spring), as the low RH conditions during this period cause a\nsignificant portion of gaseous NH to remain in the gas phase without converting\n3\ninto particulate matter. For North America and Europe, focus should be placed on\nsummer months-these periods coincide with peak fertilizer application, and are\naccompanied by low RH and high solar radiation, which facilitate the rapid\nformation of secondary particulate matter. At this stage, emission reduction\nproves most effective in lowering PM concentrations. And optimized\n2.5\nmanagement practices such as the “4R Nutrient Stewardship” approach promoted\nby the International Fertilizer Association46, 47 are the best management practices,\nwhich help reduce agricultural NH emissions without causing crop yield loss.\nplacement, and the right time. Therefore, we propose to refine the “Right Time”\nprinciple in the “4R Nutrient Stewardship” framework into concrete practice:\nminimizing fertilizer application during adverse weather conditions characterized\nby low RH (<40%) and limited precipitation. This approach leverages targeted\nbest management practices to achieve optimal emission reduction outcomes. For\nlivestock production systems, NH abatement measures include manipulation of\n3\nfeed rations and manure management practices, such as improvement of storage\nfacilities and covering the surface to reduce gas diffusion48, 49. Given that manure\napplication similarly constitutes a significant source of NH , the aforementioned\n3\nrecommendation regarding optimized fertilization timing remains equally\napplicable to the field application of manure. Strategic timing of fertilizer and\nmanure application to coincide with beneficial meteorological windows,\nalongside the synergistic adoption of high-efficiency fertilizers and improved\nmanure management, can dramatically cut agricultural NH emissions without\n3\nsacrificing crop yields50. Additionally, mitigating combustion-related NH\n3\nemissions is another option for reducing NH emissions, which can alleviate\n3\npressure on agricultural NH mitigation efforts51, 52, 53.\nbuffering–pollution feedback mechanism currently relies heavily on chemical\nequations and lengthy descriptions, which may be difficult for readers without a\nchemistry background to follow. It is recommended to add a simplified schematic\ndiagram that clearly illustrates the flows, phase transitions, and pollution changes\ninvolved in both positive and negative feedback processes, accompanied by a\nconcise one-sentence physical interpretation to enhance clarity and accessibility.\nResponse: We sincerely thanks for this insightful and constructive comment. We\nfully agree with your view that a visual schematic diagram will greatly help the\nmechanism we proposed to be more widely understood and accepted by readers.\nWe have added a schematic diagram to clearly illustrate the two regulatory\npathways between the buffer system and contaminants.\nFor NH +/NH buffering agent: “Negative Response” Mechanism (Acid Input):\n4 3\nClear arrows in the figure illustrate how acid input drives gaseous NH to enter\n3\nthe particulate phase and form NH +, thereby leading to an increase in PM\n4 2.5\nmass. “Positive Response” Mechanism (Base Input): The figure intuitively shows\nhow alkali input drives NH + in the particulate phase to volatilize into gaseous\n3 2.5\nto the figure explains: “The NH +/NH system buffers acids and bases through\n4 3\nphase partitioning, modulating particulate mass”. Simplified schematic diagram\nof the “Acid-Base buffering-PM concentration” positive/negative response\n2.5\nmechanism for NH +/NH dominated buffering was shown in Supplementary Fig.\n4 3\n10a.\nFor HNO /NO - buffering agent: “Negative Response” Mechanism (Base Input):\n3 3\nClear arrows in the figure illustrate how alkali input drives gaseous HNO to\n3\nenter the particulate phase and form NO -, thereby leading to an increase in PM\n3 2.5\nmass. “Positive Response” Mechanism (Acid Input): The figure intuitively shows\nhow acid input drives NO - in the particulate phase to volatilize into gaseous\n3 2.5\nnext to the figure explains: “The HNO /NO - system buffers acids and bases\n3 3\nthrough phase partitioning, modulating particulate mass”. Simplified schematic\ndiagram of the “Acid-Base buffering-PM concentration” positive/negative\n2.5\nresponse mechanism for HNO /NO - dominated buffering was shown in\n3 3\nSupplementary Fig. 10b.\nFig. S10a. Simplified schematic diagram of the “Acid-Base buffering-PM\n2.5\nconcentration” positive/negative response mechanism for NH +/NH dominated\n4 3\nbuffering.\nFig. S10b. Simplified schematic diagram of the “Acid-Base buffering-PM\n2.5\nconcentration” positive/negative response mechanism for HNO /NO - dominated\n3 3\nbuffering.\nThis visual representation makes abstract atmospheric processes tangible by\nillustrating substance phase transitions driven by acid-base inputs, effectively\nincreasing the intuitiveness and disseminative impact of the scientific\ninterpretation. Thanks again for this insightful and constructive comment.\nSupplementary information Page 5:\nS3. The “Acid-Base buffering-air pollution” response mechanism\nMeanwhile, to facilitate understanding of this mechanism, we also present a\nsimplified schematic diagram of “Acid-Base buffering-PM concentration”\n2.5\npositive/negative response mechanism in Supplementary Fig. 10.\nEnsure that all abbreviations and units are clearly defined at their first appearance in\nthe main text (e.g., AWC for aerosol water content), including both the full term and\nthe unit of measurement where applicable, to enhance clarity and accessibility for\nreaders from different disciplinary backgrounds.\nResponse: We sincerely thank you for this critical reminder, which is essential\nfor improving the clarity and accessibility of our manuscript for a broad,\ninterdisciplinary audience. We have systematically reviewed the entire\nmanuscript, including the main text and supplementary information, to ensure\nthat every acronym and abbreviation is explicitly defined upon its first use,\nfollowing the format “Full Name (Abbreviation)”.\nPage 3, Lines 32-40: Aerosol acidity (defined as aerosol pH), a critical regulator\nof terrestrial ecosystem dynamics, operates at the nexus of the Earth’s radiative\nbudget, atmospheric chemistry, biogeochemical cycling, and climate feedbacks\nand public health1, 2, 3, 4, 5, 6. While anthropogenic emissions of sulfur, nitrogen,\nand alkaline species (e.g., ammonia (NH ), dust) drive large-scale perturbations\n3\nin aerosol pH, emerging evidence reveals a counterintuitive planetary feedback:\naerosols possess the capacity to autonomously resist external acid-base\ndisturbances through self-regulating proton (H+) exchange at gas-aqueous-particle\ninterfaces7, known as atmospheric multiphase buffering capacity.\nPages 4-5, Lines 74-80: A more recent case is the severe photochemical haze\npollution16, 17, which is affected by the emissions of primary pollutants and the\nformation of secondary particulate matter (PM ) from gaseous and multi-phase\n2.5\nheterogeneous reactions and hygroscopic growth of aerosols15, 18, 19. Notably, the\nrapid episodic enhancement of secondary inorganic aerosols (SIAs)-dominated by\nammonium nitrate bursts-has emerged as a persistent enigma, which may be\nrelated to the interconversion between Nr species20.\nPage 10, Lines 176-178: Likewise, for base buffering, the OH- brought by base\n(such as calcium ions (Ca2+) from other sources) will be neutralized by to\ngenerate H O and release NH to gas phase, which maintains the stability of the\n2 3\naerosol acidity.\nPage 11, Lines 189-191: The ε(NH +) (fraction of total ammonia (NH T) that\n4 4\npartitions to the particle phase) and PM concentration showed synchronous\n2.5\nvariation patterns (Supplementary Fig. 14).\nPage 11, Lines 200-205: We also utilize single-particle transmission electron\nmicroscopy to provide technical verification of these findings: samples from the\nclean period mostly exhibit a circular shape and have a slightly elemental mass,\nwhile samples from the polluted period predominantly show irregular shapes and\nheavier elemental mass (Fig. 2b-c and Supplementary Fig. 18).\nPage 14, Lines 257-259: The results indicate that changes in these factors\nprimarily influence Concomitant Pollution by affecting pH and aerosol water\ncontent (AWC).\nReviewer #2:\nThe revised manuscript has been largely improved for interpreting the concept of\nconcomitant pollution (CP). I think the manuscript now presents a nice study that\nquantifies the interactions between the buffering capacity and PM concentrations.\n2.5\nSome further revisions are still needed to better understand the key findings.\nResponse: Thanks sincerely for your insightful and supportive review of our\nmanuscript again. We greatly appreciate your time and thoughtful advice. We are\ndelighted to hear that you found our revised manuscript has been largely\nimproved. We are committed to addressing your concerns and making necessary\nrevisions to improve the clarity of our manuscript. We have carefully addressed\nthese points in our revised manuscript and provided a point-by-point response\nbelow. We hope the revision has addressed your concerns.\n(1) Page 10, Line 175-181\nIt is still not clear to me why the process is called “Acid-Base buffering-air pollution”\nnegative or positive feedback. When we consider the term “feedback”, it typically\ndescribes the interactions between two items to be enhanced (positive) or suppressed\n(negative), such as the case of climate warming - water vapor positive feedback. Thus,\nhere why triggering of concomitant pollution is called negative feedback? And how to\nunderstand the feedback?\nResponse: Thanks for your comment. The issue you pointed out regarding the\nunclear use of the term “feedback” is crucial. After in-depth reflection and careful\nconsideration, the previous expressions of “positive/negative feedback” have\nbeen replaced with “positive/negative response”, and the relevant content has\nbeen rephrased as the “acid-base buffering-PM concentration response”\n2.5\nmechanism.\nWe agree with your judgment. For the process we described-“acid/base input →\nbuffering → PM change”-its core driving force (acid/base emissions) stems\n2.5\nfrom external and independent human activities. The true nature of this process\nlies in “the response of the secondary particulate matter on atmospheric acid-base\nbuffering process”. For NH +/NH buffering agent: when acidic species are\n4 3\nintroduced into an aerosol system, gaseous NH partitions into the aqueous phase\n3\nto neutralize the added acid, thereby mitigating aerosol acidification. This process\ndrives continuous conversion of NH (g) to NH +(aq), progressively increasing\n3 4\naerosol ionic mass. Therefore, this process represents a negative response of\naerosol pollution to the buffering process. When alkaline species are introduced\ninto an aerosol system, particulate NH + escapes into the gas phase as NH (g) (via\n4 3\nthe reverse of NH + (aq) →NH (g) + H+ (aq)), counteracting reductions in\n4 3\naerosol acidity. This process converts particulate NH + to gaseous NH , thereby\n4 3\npartially offsetting aerosol mass accumulation. This process represents a positive\nresponse of aerosol pollution to the buffering process. For HNO /NO - buffering\n3 3\nagent, when alkaline substances are introduced into the aerosol system, gaseous\nHNO partitions into the aqueous phase to neutralize the added base, thereby\n3\nmitigating aerosol acidification. This process drives continuous conversion of\nHNO (g) to NO -(aq), progressively amplifying aerosol ionic mass, which\n3 3\nrepresents a negative response of aerosol pollution to the buffering process.\nConversely, when acidic substances are introduced, particulate NO - volatilizes as\n3 3 3\nreductions in aerosol acidity. This process converts particulate NO - to gaseous\n3\nrepresents a positive response of aerosol pollution to the buffering process.\nWe sincerely thank you again for your rigorous review. Your comments have\nprompted us to refine the research mechanism at a deeper level, allowing us to\nreplace the previously description of feedback with a more accurate scientific\nterm (“response”). This has significantly enhanced the scientific rigor and clarity\nof expression in our paper. We hope the above explanations and the\ncorresponding revisions to the manuscript can address your concerns.\nPage 5, Lines 92-97: To address this issue, we conduct exploration and discover\na trade-off effect between buffering capacity and PM concentration, as well as a\n2.5\nresponse mechanism between the two issues. Surprisingly, we find that\nConcomitant Pollution can be triggered by negative response mechanisms\nbetween buffering capacity and air pollution during the pH buffering process,\nthereby inadvertently exacerbating the pollution.\nPage 10, Lines 168-187: To better uncover this response mechanism, we first\nunveiled the essence of buffering for NH +/NH . Wherein, the chemical\n4 3\nmechanism of acid buffering is that H+ can be depleted by bonding with NH to\n3\nform NH + when acid (such as SO 2- from other sources) is added into the liquid\n4 4\nphase of the aerosol30, 31, thereby maintaining the stability of the aerosol acidity.\nIn this process, since NH enters the aerosol phase to form NH +, it amplifies the\n3 4\nload of inorganic PM . This process was termed the “Acid-Base buffering-air\n2.5\npollution” negative response mechanism, characterized by triggering of\nConcomitant Pollution (Fig. 2a). Likewise, for base buffering, the OH- brought by\nbase (such as calcium ions (Ca2+) from other sources) will be neutralized by to\ngenerate H O and release NH to gas phase, which maintains the stability of the\n2 3\naerosol acidity. In this process, since NH + escapes into the gas phase as NH , it\n4 3\nsuppresses inorganic PM formation. This process was termed the “Acid-Base\n2.5\nbuffering-air pollution” positive response mechanism, connected with pollution\ndiminishing. As a result, pH values can be stabilized within a specific range\nwithout large fluctuations despite the addition of abundant acids or bases, while\nPM loading can be either enhanced or reduced (Supplementary Text 3 and\n2.5\nSupplementary Figs. 8-10). We have incorporated high-time-resolution online\nmonitoring experiments to conduct an in-depth investigation of the negative\nresponse mechanism (Supplementary Text 4 and Supplementary Figs. 11-13). Our\nexperimental results demonstrate the validity of this response mechanism.\nPage 12, Lines 215-218: Fig. 2 The Schematic of the Concomitant Pollution\nin the negative response mechanism and samples of experimental analysis. a,\nConceptual schematic of the mechanism of Concomitant Pollution in the negative\nresponse mechanism, based on the common trends observed across the nine\nstudied events.\nPage 15, Lines 281-284: Despite this diversity, the underlying mechanisms are\nfundamentally the same: Concomitant Pollution is governed by a negative\nresponse mechanism, in which gas-phase buffering agents (NH or HNO ) are\n3 3\nexchanged for particulate-phase counterparts (NH + or NO -) to preserve aerosol\n4 3\nacidity stability.\nPage 16, Lines 289-291: We further combined response mechanisms with global\nsimulation to explore the spatiotemporal pattern of Concomitant Pollution and its\ndriving factors from a global perspective.\nPage 22, Lines 406-408: We find that the Concomitant Pollution can be triggered\nby the Acid-Base buffering-air pollution negative response mechanism, which\nparadoxically amplifies PM initiation and evolution.\n2.5\nSupplementary information Pages 4-5:\nS3. The “Acid-Base buffering-air pollution” response mechanism\nFor NH +/NH buffering agent: When acidic species are introduced into an\n4 3\naerosol system, gaseous NH partitions into the aqueous phase to neutralize the\n3\nadded acid, thereby mitigating aerosol acidification. This pH stabilization allows\nadditional acid influx, necessitating further NH dissolution to maintain buffering\n3\ncapacity. This self-reinforcing cycle drives continuous conversion of NH (g) to\n4\nnegative response mechanism of buffering-driven pollution amplification. When\nalkaline species are introduced into an aerosol system, particulate NH + escapes\n4\ninto the gas phase as NH (g) (via the reverse of NH + (aq) →NH (g) + H+ (aq)),\n3 4 3\ncounteracting reductions in aerosol acidity. This pH stabilization lowers the\nthermodynamic driving force for alkaline uptake (governed by Henry’s law\nconstants and ion activity coefficients), enabling further alkaline influx and\nnecessitating additional NH + volatilization to maintain buffering capacity. This\n4\nself-limiting cycle converts particulate NH + to gaseous NH , thereby partially\n4 3\noffsetting aerosol mass accumulation - a regulatory process we define as the\npositive response mechanism of buffering-mediated pollution modulation. The\nschematic of the “Acid-Base buffering-PM concentration” positive/negative\n2.5\nresponse mechanism for NH +/NH dominated buffering was shown in\n4 3\nSupplementary Fig. 8.\nIn addition to the NH +/NH buffering mechanism, HNO /NO - also produces this\n4 3 3 3\nresponse mechanism when exerting its buffering effect. For HNO /NO - buffering\n3 3\nagent: When alkaline substances are introduced into the aerosol system, gaseous\nHNO partitions into the aqueous phase to neutralize the added base, thereby\n3\nmitigating aerosol acidification. This pH stabilization enables additional alkaline\ninflux, necessitating further dissolution of HNO to maintain buffering capacity.\n3 3\n(aq), progressively amplifying aerosol ionic mass - a process we term the\nnegative response mechanism of buffering-driven pollution amplification.\nConversely, when acidic substances are introduced, particulate NO - volatilizes as\n3 3 3\nreductions in aerosol acidity. The stabilized pH lowers the thermodynamic\ndriving force for acid uptake (governed by Henry’s law constants and ion activity\ncoefficients), allowing further acid influx while requiring additional NO -\n3\nvolatilization to sustain buffering. This self-limiting cycle converts particulate\nNO - to gaseous HNO , partially counteracting aerosol mass accumulation - a\n3 3\nregulatory process defined as the positive response mechanism of buffering-\nmediated pollution modulation. Schematic of the “Acid-Base buffering-PM\n2.5\nconcentration” positive/negative response mechanism for HNO /NO - dominated\n3 3\nbuffering was shown in Supplementary Fig. 9.\nMeanwhile, to facilitate understanding of this mechanism, we also present a\nsimplified schematic diagram of “Acid-Base buffering-PM concentration”\n2.5\npositive/negative response mechanism in Supplementary Fig. 10.\nSupplementary information Page 6:\nS4. The experimental validation of negative response mechanism\nFor experimental validation, we have incorporated high-time-resolution online\nion chromatography monitoring experiments and online mass spectrometry\nobservations to conduct an in-depth investigation of the negative response\nmechanism (acidity input → NH → NH + → PM formation).\n3 4 2.5\nSupplementary information Page 23, Fig. S8:\nFig. S8. Schematic of the “Acid-Base buffering-PM concentration”\n2.5\npositive/negative response mechanism for NH +/NH dominated buffering.\n4 3\nSupplementary information Page 24, Fig. S9:\nFig. S9. Schematic of the “Acid-Base buffering-PM concentration”\n2.5\npositive/negative response mechanism for HNO /NO - dominated buffering.\n3 3\n(2) Page 11, Discussion of Figure 2\nAs shown in Figure 2a, the concomitant pollution is a proportion of secondary\npollution; therefore, how do we know that Figure 2c illustrates this pollution? Also in\nFigure 2d, it is not clear what the blue bars present. Please clarify in the caption.\nResponse: We would like to thank you for pointing out this point. We confirm\nthat Figure 2c displays the particulate matter generated after the occurrence of\nConcomitant Pollution, which is primarily based on the following analysis of the\nmorphology and chemical composition of TEM images-these characteristics are\nconsistent with the formation process of secondary pollution.\nThe left image in Figure 2c shows a sample collected during a clean period\n(PM =31 μg m-3), while the right image depicts a sample collected during a haze\n2.5\nepisode (PM =185 μg m-3). It can be observed that the sample from the polluted\n2.5\nperiod exhibits aggregated particles, which is distinctly different from the\nmorphological characteristics of the sample from the clean period1-4. Additionally,\nenergy-dispersive X-ray spectroscopy (EDS) results indicate that the clean-period\nsample primarily consists of elements such as C and O, whereas the polluted-\nperiod sample shows significantly higher abundances of O, S, N, Al, and Si. In\nsummary, both morphological and elemental composition analyses demonstrate\nthat Figure 2c represents the already-formed Concomitant Pollution. The electron\nmicroscopy results provide complementary observational evidence to the\ntheoretical analysis, aiding in a better understanding of Concomitant Pollution.\nWe have updated the caption of Figure 2d in the revised manuscript to clarify its\nmeaning. The revised caption will read as follows: “Probability density\ndistribution (Bin width = 10) of the Concomitant pollution induced by a slight\nchange in pH (ΔpH=0.5) under the NH +/NH -dominated buffering regime during\n4 3\nthe clean period. The blue bars represent the distribution of this Concomitant\nPollution. The x-axis indicates the magnitude of the Concomitant Pollution\ntriggered by the pH perturbation, while the y-axis represents the Corresponding\nprobability density.” Thanks again for your constructive comment.\nReference:\n1. Zhang, J., Liu, L., Wang, YY. et al. Chemical composition, source, and process\nof urban aerosols during winter haze formation in Northeast China.\nEnvironmental Pollution, 231 (5), 357-366, (2017).\nhttp://dx.doi.org/10.1016/j.envpol.2017.07.102\n2. Li, W., Shao, LY., Shi, ZB. et al. Mixing state and hygroscopicity of dust and\nhaze particles before leaving Asian continent. J. Geophys. Res. Atmos., 119,\n1044-1059, (2014). http://dx.doi:10.1002/2013JD021003.\n3. Li, W., Sun, JX., Xu, L. et al. A conceptual framework for mixing structures in\nindividual aerosol particles, J. Geophys. Res. Atmos., 121, (2016). http://dx.\ndoi:10.1002/2016JD025252.\n4. Shao, LY, Liu, PJ, Jones, T. et al. A review of atmospheric individual particle\nanalyses: Methodologies and applications in environmental research.\nGondwana research: international geoscience journal, 117, 347-369, (2022).\nhttp://dx.doi.org/10.1016/j.gr.2022.01.007.\nPage 12, Lines 226-231: d, Probability density distribution (Bin width = 10) of\nthe Concomitant Pollution induced by a slight change in pH (ΔpH=0.5) under the\nNH +/NH -dominated buffering regime during the clean period. The blue bars\n4 3\nrepresent the distribution of this Concomitant Pollution. The x-axis indicates the\nmagnitude of the Concomitant Pollution triggered by the pH perturbation, while\nthe y-axis represents the Corresponding probability density.\n(3) Page 13, Line 248-249\nHere, I would suggest adding 1-2 sentences explaining the effects of RH, NO T, T,\n3\netc., on concomitant pollution. e.g., why does concomitant pollution decrease as RH\nincreases?\nResponse: Thanks for your comment. We have incorporated the influence\nmechanisms of various factors on concomitant pollution in the section on RF-\nPDP results. This addition has significantly enhanced the readability and\ninterpretability of the machine learning outcomes for readers.\nPages 13-14, Lines 247-266: RF-PDP simulations demonstrated nonlinear\nConcomitant Pollution responses: the increase of RH, NO T, and SO 2- dampened\n3 4\nConcomitant Pollution increased, while the effects of T, NH T, and Ca2+ were\n4\nopposite (Fig. 3). We found that when RH increased from 20% to 40%,\nConcomitant Pollution decreased significantly by 72.1 mol kg-1, while the\nchanges in Concomitant Pollution caused by variations in other factors were\nbasically below 15 mol kg-1. Additionally, to gain a deeper understanding of the\nresponse of Concomitant Pollution to driver change, from a theoretical\nmechanism perspective, we constructed a thermodynamic model (see Methods))\nand quantified the effects of various factors on Concomitant Pollution through\nsensitivity simulation experiments (Supplementary Text 6 and Supplementary\nFigs. 22-27). The results indicate that changes in these factors primarily influence\nConcomitant Pollution by affecting pH and aerosol water content (AWC). For\ninstance, increases in RH, SO 2-, and NO T compounds enhance aerosol acidity\n4 3\nand AWC, leading to a reduction in the molar concentration of buffering agents\nand consequently a decrease in Concomitant Pollution. In contrast, the effects of\nNH T and Ca2+ are the opposite. The sensitivity experiments for T show some\n4\ndiscrepancies with the machine learning results, which may be because the RF-\nPDP simulations reflect the average Concomitant Pollution outcomes across\nmultiple data points, whereas the sensitivity experiments demonstrate the actual\nvariations in Concomitant Pollution under specific scenarios.\n(4) Page 16, Discussion of Figure 4\nThe concomitant pollution levels are generally much higher in July than in January\nover northern mid-latitudes, while PM pollution in most of these regions is heavier\n2.5\nin winter (January) than in summer. Can you please comment on the implications of\nCP on wintertime PM pollution?\nResponse: Thanks for your comment. You have observed that the level of\n“concomitant pollution” in the mid-latitudes of the Northern Hemisphere is\nhigher in summer (July) than in winter (January), while actual PM pollution is\n2.5\nusually more severe in winter. This phenomenon precisely confirms the core\nessence of “concomitant pollution” as defined in our study-it characterizes the\npotential of the atmosphere to generate particulate matter due to the stable acidity\nof aerosols.\nSummer favors the accumulation and maintenance of high concentrations of\ngaseous precursors (e.g., NH , HNO ) in the atmosphere, which constitutes a\n3 3\nstrong potential driving force for concomitant pollution. The relatively high\ntemperatures in summer inhibit the efficiency of heterogeneous conversion of\ngaseous precursors to the particulate phase, allowing substances such as NH and\n3\natmospheric oxidizing capacity, promoting the conversion of precursors into\nsecondary particulate matter. Therefore, there exists a “reservoir” of gaseous\nreactants with high concentrations in the summer atmosphere, which will be\nrapidly converted into a large amount of secondary particulate matter to cause\npollution when it encounters interference from external acid-base components or\nmeteorological disturbances. This manifests as the high level of concomitant\npollution revealed in our study.\nIn winter, concomitant pollution levels are generally low, while PM pollution is\n2.5\nheavier in most of regions. This is primarily because the global results in our\nmanuscript are based on monthly averages, thus depicting concomitant pollution\nwhen PM concentrations are elevated. From a theoretical perspective, the\n2.5\nessence of concomitant pollution is: before pollution episodes occur, concomitant\npollution exhibits a high level, coinciding with low PM concentrations.\n2.5\nWhen\ninfluenced by factors such as meteorological conditions, boundary layer\ncompression and pollutant accumulation, this pollution potential is rapidly\nconverted into actual secondary pollution. In winter, meteorological conditions\n(low temperatures and high relative humidity), combined with the pollutant\naccumulation caused by boundary layer compression, promote the efficient and\nrapid conversion of gaseous components (e.g., NH and HNO ) into particulate-\n3 3\nphase NH + and NO -. As a result, the concomitant pollution present in the\n4 3\natmosphere has already been largely converted into secondary particulate matter.\nConsequently, the residual concentration of concomitant pollution remaining in\nthe atmosphere is relatively low. These findings provide a robust scientific basis\nfor our proposed pollution control strategy: implementing preemptive control of\nNH emissions before this pollution potential transforms into actual pollution will\n3\nyield significantly greater cost-effectiveness.\nTherefore, the high level of “concomitant pollution” in summer represents an\nunfulfilled yet strong potential for secondary pollution formation (characterized\nby a high-concentration reserve of gaseous NH and HNO ). In contrast, the low\n3 3\nlevel of concomitant pollution in winter is precisely because this potential had\nbeen efficiently consumed, being converted into actual PM components (NH +\n2.5 4\nand NO -)-a process that ultimately leads to more severe observed particulate\n3\npollution.\nWe have added a clear elaboration on the aforementioned mechanisms in the\nDiscussion section of the paper accordingly to enhance the readability of the\narticle. We would like to thank you again for helping us improve the clarity of the\nmanuscript’s arguments.\nPage 17, Lines 311-322: Overall, the Co-P-HNO /NO - was weaker than Co-P-\n3 3\nNH +/NH , which is consistent with their respective contributions to buffering\n4 3\ncapacity. Furthermore, the Co-P-HNO /NO - was weaker in winter than in\n3 3\nsummer, which was similar to the seasonal variation in Co-P-NH +/NH .\nThe\n4 3\nweaker Co-P in winter is associated with the typical meteorological conditions of\nthis season. Such an atmospheric environment greatly promotes the conversion\nprocess of gaseous components to the particulate phase. This rapid and efficient\nconversion mechanism effectively consumes the Co-P in the atmosphere,\nresulting in a relatively low level of Co-P. In winter, the Co-P-HNO /NO - was\n3 3\nstronger in Central Africa and South Asia. In summer, strong Co-P-HNO /NO -\n3 3\nappeared in South Africa, Europe, and Central North China, which mirrors HNO\n3\nsource regions (Supplementary Fig. 33).\n(5) Page 25, Line 475-479\nThe resolution for the GEOS-Chem model is not clear. 2x2.5 degrees or 4x5 degrees?\nBoth resolutions can be run at a global scale rather than nested regions in GEOS-\nChem. Please check.\nResponse: Thanks for the helpful comment. Our GEOS-Chem model employs a\nhorizontal resolution of 2o2.5o, and this clarification has been incorporated into\nthe revised manuscript. Thank you again for your valuable advice.\nPage 27, Lines 513-516: GEOS-Chem is driven by the Modern-Era\nRetrospective Analysis for Research and Applications, version 2 (MERRA-2)\nreanalysis meteorological fields with 2o(latitude)×2.5o(longitude) horizontal\nresolution within the regional domains. Thank you again for your valuable advice."}]

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