State Environmental Protection Key Laboratory of Atmospheric Ozone Pollution Control， State Key Joint Laboratory of Environmental Simulation and Pollution Control， College of Environmental Sciences and Engineering， Peking University， Beijing 100871， China
Hydroxyl （OH） radicals， as key oxidants in the atmosphere， play a critical role in regulating atmospheric chemical composition and influencing both air quality and climate change. Accurately assessing the global OH concentration levels and trends is essential for understanding atmospheric chemical processes and evaluating environmental and climate conditions. This paper systematically reviews the global OH evaluation indicators， and summarizes the current quantitative methods for global OH in research， including inversion of ground-based indicator observation， model simulations， and satellite-based evaluation methods. Existing research on OH concentration trends reveal discrepancies between ground-based indicator inversion methods and forward model simulations regarding long-term trends. Results from indicator inversion methodsvary across studies， while model-based studies suggest an increasing trend in OH concentrations after 1980. Satellite methods still exhibit significant uncertainties in OH assessment and require further development. In the future， it is necessary to further strengthen the relevant observations of indicators and precursors to provide more observational constraints for OH assessment. At the same time， it is essential to further develop new indicators， optimize atmospheric chemical model mechanisms， and explore new assessment methods to improve the accuracy and reliability of global OH assessment.
Contents
1 Introduction
2 Evaluation indicators for global OH
2.1 Concentration evaluation indicators
2.2 Trend evaluation indicators
3 Atmospheric chemical processes and influencing factors of OH
4 Quantitative methods for global OH
4.1 Inversion of ground-based indicator observation
4.2 Model simulations
4.3 Satellite-based evaluation methods
5 Recent research progress on global OH evaluation
6 Current theoretical and technical limitations
6.1 Inherent uncertainty based on climate variability
6.2 Sources of uncertainty based on inversion methods
6.3 Sources of uncertainty based on model simulations
Hong Huang, Zhaofeng Tan, Keding Lu, Yuanhang Zhang.
Quantitative Methods and Application of Global Atmospheric Hydroxy Radicals Concentrations.
Progress in Chemistry, 2026, 38(5): 974-988 DOI:10.7536/PC20250921
Atmospheric oxidizing capacity (AOC) is the main driving force of atmospheric chemical processes, manifested as the ability of oxidants in the atmosphere to remove organic or inorganic reduced substances[1-2]. Among them, hydroxyl (OH) radicals are the most active oxidants in the atmosphere. OH is mainly produced by the reaction of excited singlet oxygen atoms (O(1D)) generated from the photolysis of ozone (O3) with H2O. Although its concentration in the atmosphere is extremely low, its chemical activity is high, and it can undergo chemical reactions with the vast majority of trace components in the atmosphere[3]. Therefore, it plays an important role in regulating atmospheric chemical composition, affecting air quality, and influencing climate change.
On one hand, atmospheric oxidizing species represented by OH determine both the removal of primary pollutants and the formation of secondary pollutants, thereby affecting regional air quality and global atmospheric composition changes. OH is the dominant mechanism for the removal of various atmospheric trace gases, such as methane (CH4), non-methane volatile organic compounds (NMVOCs), halides, etc. OH removes a total of approximately 3.65×1015 g of gas annually; at this rate, the mass of gas removed every 1.4 million years is equivalent to the mass of the entire atmosphere[2]. Although atmospheric oxidizing capacity has the ability to remove primary pollutants, the reactions simultaneously produce highly oxidized products. The secondary pollutants formed by these products (such as PM2.5and O3) may cause more severe hazards. On the other hand, OH is also closely linked to the greenhouse effect and climate change. Atmospheric oxidizing capacity is closely related to short-lived climate forcers (SLCF)[4-5], among which CH4, O3, and halides belong to direct forcing agents, while nitrogen oxides (NOx), carbon monoxide (CO), NMVOCs, etc., belong to indirect forcing agents. These substances exert different effects on the climate; for example: CH4and O3, as greenhouse gases, generate positive radiative forcing, promoting climate warming; aerosols, however, can absorb and reflect solar radiation, overall generating negative radiative forcing and promoting atmospheric cooling[4-5]. Atmospheric oxidizing capacity is closely related to the atmospheric lifetime (e.g., of CH4, halides, etc.) and formation rates (e.g., of aerosol particles, O3, etc.) of these short-lived climate forcers, thereby impacting climate change.
Due to the significant role of OH in atmospheric composition and climate effects on a global scale, accurately assessing and simulating global OH concentrations and trends is crucial for understanding atmospheric chemical processes and evaluating air quality and climate change dynamics. For instance, OH trends are a core parameter for assessing interannual to decadal variations in methane[6], and also serve as the foundation for top-down quantification of global emissions of substances such as CO, NOx, and isoprene[7-9]. However, due to the extremely low concentration and very short atmospheric lifetime of OH radicals in the atmosphere, accurate quantification of OH faces enormous challenges. This paper will systematically review key indicators and mainstream methods for global OH assessment, summarize existing research findings on OH variation trends, analyze uncertainties in the quantification process, and point out critical issues that urgently need breakthroughs in current research, providing direction for precise global OH assessment studies.
2 Global OH Assessment Indicators
2.1 Concentration Assessment Indicators
For the global OH concentration indicator, most studies adopt the global average concentration of OH ([OH]GM), while some use the atmospheric lifetime of speciesXto assess global changes in OH[10].
On a global scale, research mainly focuses on the removal efficiency (4, CH3CCl3, etc.) of specific gases (such as CO, CHηOE(X)), i.e., the reciprocal of atmospheric lifetime). [OH]GMshould have a specific consistent relationship with the lifetime of a given gas (τ(X)) to be a good indicator of oxidizing capacity. Lawrence et al.[10]summarized several existing methods for calculating [OH]W) to calculate [OH]GM, for example, by air volume (W = Vair), air mass (W = Mair), or by weighting with the reaction rate (X(such as CH4, CH3CCl3, etc.) with long-lived tracers W = kXMX). These different weighting factors can yield different [OH]GMvalues (Eq. (1)).
where: [OH]GMis the global average concentration of OH;Wis the weighting factor;irepresents different grid regions within the selected area for weighted averaging (generally the entire tropospheric atmosphere).
To make [OH]GMvalues have a consistent relationship with removal efficiency, Lawrence et al.[10]recommended adopting air mass weighting and specific gasX(especially CH4) reaction rate weighting as two methods for indicators of atmospheric oxidizing capacity. At this time,[OH]GM(X)and removal efficiencyηOE(X) are proportional (Eq. (2)), while the proportionality α usually depends only on the temperature distribution in the atmosphere, the temperature dependence of the reaction, and the region selected for the weighted average (Eq. (3)). Meanwhile, the atmospheric lifetimes of CH4and CH3CCl3(τ(CH4) and τ(CH3CCl3)) can be provided as additional parameters related to the OH distribution. Many studies[11-13]have adopted their recommendation; most literature chooses or implicitly uses air mass weighting and specific gasX(mainly CH4and CH3CCl3) reaction rate weighted[OH]GMas an indicator of global atmospheric oxidizing capacity.
where:ηOE(X) is the removal efficiency of gasX;kXis the reaction rate constant betweenXand OH radicals;MXis the mass ofXin the atmosphere (whenXis a uniformly mixed gas, it can be replaced byMair).
2.2 Trend Assessment Indicators
In OH trend assessment, in addition to using the time series of absolute OH concentrations [OH]GM(t)[14-17], trend indicators such as Relative anomaly, Growth rate, and Interannual variability (IAV) are commonly employed for quantitative analysis of OH trends[16].
Relative anomaly usually represents the value at a specific time point [OH]GM(t) relative to the average over the reference period or the entire study period ($\overline{{\left[\mathrm{O}\mathrm{H}\right]}_{\mathrm{G}\mathrm{M}}}$), generally presented as a percentage, as shown in Equation (4). Since calculation results of OH concentrations by different methods usually differ significantly in absolute values[18-19], and compared to absolute values, research focuses more on their relative change characteristics, therefore the relative anomaly method is widely used for trend comparison analysis across multiple studies and methods[16,20-24]. The average reference intervals adopted by different studies may vary; the most commonly used reference interval is the entire duration of the study.
The growth rate is used to represent the growth rate of OH concentration on interannual or decadal scales. Similar to relative anomalies, the relative value of the annual growth rate (unit: %/a) is usually calculated; see Equation (5) for the calculation method. Bousquet et al.[16]defined the growth rate as the first derivative of the change in OH concentration after removing seasonal variations, while some studies directly perform inversion optimization on the relative growth rate[14-15,25].
in the formula: GR is the relative value of the annual growth rate (%/a).
Interannual variability is used to represent the fluctuations of OH on an interannual scale. Common indicators for assessing interannual variability include standard deviation (SD), relative standard deviation (RSD), mean absolute deviation (MAD), and average percentage deviation of the mean (APDM).[26-27], with calculation methods shown in Equations (6) to (9). SD and MAD can represent the absolute value of interannual variability, while RSD and APDM represent the interannual variability relative to then-year average concentration. Similar to relative anomalies, the relative value of interannual variability, RSD, is typically used as an assessment indicator; however, most studies[20,22-24]have not provided specific calculation processes for their interannual variability (or have been rather vague). Therefore, although the interannual variability calculated in various studies can all represent the fluctuations of OH on an interannual scale, their specific meanings may differ.
where:V is the interannual variability, and the subscript corresponds to different calculation indicators.
3 Atmospheric chemical processes and influencing factors of OH
Due to the short atmospheric lifetime of OH (approximately 1.5 s)[12], OH will rapidly reach a steady state between its production and removal processes; compared to other terms related to the OH budget (such as transport), the chemical processes of OH are faster, thus the concentration of OH is determined by the balance between chemical production and removal.
The main reactions related to OH in the troposphere are asTable 1shows. The primary generation of tropospheric OH occurs through the photodissociation of tropospheric O by ultraviolet radiation with wavelengths less than 310 nm3producing (R1), a process that generates O(1D), which then reacts with water vapor to generate OH (R2). On a global average (Table 2), primary OH generation dominates the sources (30%~40%)[12,28-29], with contributions to total OH sources ranging from 20% to 80% in different regions [5,30], controlling the total supply of HOx in the troposphere. The primary generation process is closely related to meteorological factors; since it requires water vapor and ultraviolet radiation, its generation rate is highest in the lower tropical troposphere where UV radiation is strong and temperature and humidity are high[5].
OH can also be generated through secondary mechanisms, the core of which is the regeneration of OH from HO2 (R3~R5). In areas with high NOx concentrations, such as severely polluted urban environments, HO2 can regenerate OH by reacting with NO (R3), which is the main regeneration pathway, thereby leading to the accumulation of tropospheric O3. This process is also known as the NOx cycle mechanism, and its global average proportion is comparable to primary generation[12,28](Table 2). In unpolluted regions with low NOx concentrations, other secondary generation processes dominate, collectively known as the Ox cycle mechanism, including the consumption of O3 (R4) and the photolysis of H2O2 (R5).
CO oxidation is the largest OH loss pathway (R6), accounting for approximately 40% of the global OH sink (Table 2). CH4 (approximately 10%) and NMVOCs (20%~30%) oxidation also lead to OH loss (R7) and generate organic peroxy radicals (RO2). In regions with high NOx concentrations, RO2 can react with NO to form NO2, regenerating OH (R8). The NO2 produced via reactions (R3) and (R8) can photolyze to form O3 (R9 and R10), which then further produces OH through primary generation pathways via (R1 and R2). In severely polluted atmospheres, NO2 leads to net OH loss by forming nitric acid (HNO3) (R11). Under clean, unpolluted conditions, radical reaction chains involving HO2 and RO2 can be terminated by self-reactions via (R12) and (R13)[31].
Due to complex photochemical interactions, tropospheric OH concentrations are relatively sensitive to changes in emissions of short-lived climate forcing agents and meteorological conditions. Although chemical and dynamical systems exhibit nonlinearity, several meteorological and chemical drivers have been identified as having a primary controlling effect on global mean tropospheric OH concentrations. Murray et al.[19,32]derived, through steady-state assumptions, a proportional relationship between global OH concentration and O3photolysis rate (j(O1D)), water vapor (q), reactive nitrogen (SN), and reactive carbon emissions (SC), as shown in Equation (10). He et al.[33]further validated this conclusion; in the three simulations studied, theR2=0.8.
due to the steady-state relationship between OH and j(O1D), q, SNand SC, various associated factors influence OH abundance; for example, increases in CH4, CO, and NMVOCs reduce OH concentrations, whereas increases in water vapor, temperature, incoming solar radiation (related to stratospheric ozone concentrations), NOx, and tropospheric ozone promote OH production[4,19]. Therefore, OH concentrations are regulated both by their sensitivity to temperature and water vapor and by the impact of climate on natural emissions (e.g., wetland methane emissions, lightning nitrogen oxides, BVOCs, fire emissions), thereby generating feedback on climate through these associations[5]. Climate variability patterns, such as the El Niño–Southern Oscillation (ENSO), also lead to changes in OH through multiple pathways.
4 Global OH Quantitative Research Methods
Due to the extremely short lifetime of OH, its abundance in the atmosphere is low, making direct measurement of its concentration highly difficult, and extrapolating these measurements to a global scale is nearly impossible[2]; therefore, direct observations of OH are typically limited to field campaigns with narrow spatial and temporal coverage. Although field observations provide new insights into the driving factors of OH[34-35]and chemical mechanisms[36-37], they are not a viable approach for characterizing global OH variations[38].
Therefore, the assessment of global-scale OH radical concentrations and trends is primarily achieved through atmospheric chemistry transport models. Among these, there are two main mature model methods for studying global-scale OH radicals: ground-based indicator observation inversion methods and forward model simulation methods. Currently, with the development of satellite remote sensing, some studies have also used satellite data to conduct quantitative research on OH through various methods such as three-dimensional inversion, data assimilation, indicator and steady-state methods, empirical reconstruction, and machine learning; however, such studies remain relatively scarce and require further development.
4.1 Ground-based indicator observation inversion
The core logic of the inversion method is to utilize measured data of observable physical quantities (observation variables) to establish a quantitative relationship with unobservable physical quantities (state variables) that need optimization through a forward model. Then, optimization algorithms are employed to iteratively adjust the values of the state variables until the theoretical observation values calculated by the forward model achieve optimal matching with the actual acquired observation data. Current mainstream mathematical optimization frameworks are based on Bayes' theorem, with the core principle being: combining the prior probability distribution of state variables (i.e., the probabilistic understanding of state variables in the absence of observation data) and the conditional probability distribution of observation variables given the state variables (likelihood function), the posterior probability distribution of state variables is derived via Bayes' formula. The ultimate objective is to solve for the state variable values that maximize this posterior probability; these values represent the most statistically reasonable estimates of the state variables under the constraints of the current observation data.
In the observational inversion process of OH concentration and trends, the observed variables are typically atmospheric trace gases that react with OH, serving as indicators of OH changes; state variables can be directly selected as OH concentration or trends, or as variables related to OH, such as partial parameters of the forward model and indicator emissions. By observing the concentrations of these indicators and utilizing a forward model constructed based on the physicochemical processes between OH and the indicators in the atmosphere, combined with Bayesian optimization methods, we can obtain relevant information regarding OH concentration and trend changes.
4.1.1 Bayesian inversion framework
This paper only provides a brief introduction to the Bayesian inversion framework; for detailed content, please refer to Rodgers[39]and Brasseur et al.[40]for introductions and related studies employing inversion methods[15-17,41].
</italic>(called the forward model), as shown in Equation (11).
</italic>is a parameter vector, including all mode parameters not optimized during the inversion process;${\mathit{\epsilon }}_{\mathbf{O}}$</italic>is often a single-box model[20,23], two-box or three-box models[17,21-22], a two-dimensional 12-box model[14-15,42-45]or three-dimensional chemical transport models (CTMs)[16,20,41,46-48]etc.
During inversion, the Bayesian inversion framework is generally adopted. According to Bayes' theorem, Equation (12) can be obtained.
</italic>;$P\left(\mathit{y}|\mathit{x}\right)$ is the likelihood function of the observed data;$P\left(\mathit{x}|\mathit{y}\right)$</italic>, we need to find the state variable$P\left(\mathit{x}|\mathit{y}\right)$</italic>.
)</italic> and $P\left(\mathit{y}|\mathit{x}\right)$</italic>, denoted as ${\mathit{x}}_{\mathbf{A}}$. Through theoretical derivation, an analytical solution $\widehat{\mathit{x}}$ can be obtained; the calculation method is shown in Equations (13) and (14).
</italic>;${\mathit{S}}_{\mathbf{A}}$is the covariance matrix of the prior estimate;${\mathit{S}}_{\mathbf{O}}$is the covariance matrix of the observation errors. This method is often referred to as recursive weighted least squares filtering[15]</italic>, requiring multiple iterations for solution. Therefore, this method is only applicable when the forward model is relatively simple and the number of state variables is small.
</italic>perform optimization[17]. Turner et al.[21]used the Covariance Matrix Adaptation Evolution Strategy (CMA-ES), which is an evolutionary algorithm that modifies the covariance matrix of the proposal distribution based on the fitness of multiple candidate solutions in a given generation, enabling more efficient sampling compared to traditional MCMC methods. There are also various other theoretical and numerical methods, such as inversion based on adjoint models (e.g., Four-Dimensional Variational Data Assimilation (4D-VAR)[20,41,48]), etc. Different numerical methods have their respective scopes of application and advantages; some methods can avoid solving complex Jacobian matrices and are suitable for scenarios with large state vectors, sparse observations, or where both state vectors and observation vectors are large.
4.1.2 Common indicator constraints for OH inversion
The basic principle of the indicator inversion method is: select trace gases that are closely related to OH reactions and have correlated variation trends, and optimize OH radical concentrations and variation trends based on forward models and Bayes' theorem. To achieve effective constraints on OH, the selection of indicators must in principle satisfy two conditions: the emission inventory uncertainty of the gas is small; and its primary sink pathway must be oxidative removal by OH. The most commonly used indicator for OH is methyl chloroform (MCF, CH3CCl3)[49-50], other effective indicators include14CO[51]and some long-lived species[52], such as hydrofluorocarbons (HFCs) and hydrochlorofluorocarbons (HCFCs), etc. (Table 3). When using indicator inversion, the derived OH concentration usually implies a weighting factor equal to the reaction rate of the substance with OH. Since the reaction rate is a function of temperature, typically increasing with rising temperature, the weighting factor is largest in the lower tropical troposphere where temperatures are higher; thus, the OH weighted concentration is more sensitive to changes in OH concentration in tropical regions[53].
(1) Methyl chloroform (MCF).
The main source of MCF is anthropogenic emissions, with natural emissions being low (approximately 10 Gg)[14]; however, due to the signing of the Montreal Protocol, global anthropogenic emissions have been gradually phased out since the 1990s, and emissions approached zero after 1998[20]. Its primary removal process is oxidation by OH (Equation (15)), while photolysis in the stratosphere and uptake by the ocean also exist as removal pathways. However, the latter two account for a small proportion of the total loss[14,60], accounting for approximately 12% and 6%, respectively[52]. Furthermore, with the rapid decline in atmospheric MCF concentrations after 1995, high-latitude ocean regions have gradually shifted from being an atmospheric sink for MCF to becoming a source[60].
mCF has relatively sufficient estimation data for both emission sources and removal pathways, resulting in lower uncertainty compared to other species[14,20,61], making it an ideal OH indicator. Its total atmospheric lifetime is approximately 5 years[14,16,44], allowing it to mix relatively uniformly in the atmosphere. Therefore, changes in its concentration can reflect global OH variations and can be used to constrain interannual changes in global OH. Due to the temperature sensitivity of its reaction rate, it is most sensitive to OH changes in tropical regions[53].
MCF has a long measurement record, which is why it serves as the most commonly used tracer. The ALE/GAGE/AGAGE projects have conducted long-term observations at five global monitoring stations since 1978[62]; meanwhile, since 1992, NOAA/CMDL (now GML) has conducted observations at ten (now twelve) remote global stations[20,63]. However, as atmospheric MCF concentrations gradually decline, dropping rapidly from over 100 ppt in 1990 (1 ppt = 1×10-12) to approximately 3.5 ppt in 2014, and projected to fall to 0.5 ppt by 2025, measurement errors will gradually increase, making it difficult to continue using it as an OH tracer[52,64]. Therefore, it is necessary to identify new OH-related tracers to constrain OH.
（2）14CO。
14CO is produced in the atmosphere by thermal neutrons generated by cosmic rays; the specific production process involves neutrons being intercepted by nitrogen nuclei, via the14N(n,p)14C nuclear reaction to form14C, which is then rapidly oxidized to14CO, with an oxidation yield of approximately 95%[41]. Due to the interaction between cosmic radiation and Earth's magnetic field, most of the production occurs in the upper troposphere and high-latitude regions, providing a stable source; meanwhile, as it is almost entirely removed by OH, it also serves as a commonly used indicator for OH[41]. Given its short lifetime, with an atmospheric lifespan of about 3 months, it cannot mix uniformly in the atmosphere, making it difficult to use for quantifying interannual variations of OH on a global scale; however, the short lifetime causes14CO to exhibit a distinct seasonal cycle, which is primarily influenced by the OH reaction rates related to temperature and the seasonal transport from the stratosphere to the troposphere. Therefore,14CO can reflect OH variations on regional and seasonal scales[41,55-56]. Furthermore, since the primary source of14CO is cosmic rays, its production rate is modulated by the solar cycle, exhibiting a pronounced 11-year cycle[56].
After advancements in measurement technology in the late 1980s, large-scale long-term observations of 14CO became feasible[55]. The longest and most consistent 14CO observation records come from two remote Southern Hemisphere sites: Baring Head, New Zealand (41.4°S) and Scott Base, Antarctica (77.8°S), with measurements starting in 1989 and 1990, respectively[55-56]. Compared to MCF, 14CO inversions still have relatively limited relevant data available; more observation stations need to be established to make conclusions regarding OH concentrations and trends derived from 14CO more reliable.
(3) Other long-lived gases.
To find substitutes for MCF, several studies have attempted inversions using long-lived species such as HFCs and HCFCs. The main removal pathway for HFCs and HCFCs is reaction with tropospheric OH; therefore, their concentration changes can reflect variations in OH. However, the lack of a global bottom-up emission inventory is the primary obstacle to selecting MCF substitutes.[52].
Miller et al.[57]employed HCFC-22 for assessment; its inversion-calculated OH concentrations were similar to those of MCF, but accuracy was lower due to greater emission uncertainties and a smaller measurement range. Huang et al.[58]and O'Doherty et al.[59]suggested that industrial gases HFC-134a, HCFC-141b, and HCFC-142b could serve as useful OH indicators, though the accuracy of their emission estimates needs improvement. Liang et al.[52]proposed that interhemispheric gradients of long-lived species can be used to derive their global emissions. They also found that combinations of HFC-32, HFC-134a, HFC-152a, and HCFC-22 within a two-box model inversion method based on gradient trends can estimate atmospheric OH concentrations and potential interhemispheric OH differences. Multi-species combination inversions reduce uncertainties without requiring detailed knowledge of emissions for all four substances. Among these, the combination of HFC-32 and HFC-134a is the optimal MCF alternative for inferring global OH abundance, while HCFC-22 and HFC-152a can provide information on hemispheric ratios and seasonal variations of tropospheric OH abundance. Thompson et al.[45]used five HFCs (HFC-134a, HFC-152a, HFC-365mfc, HFC-245fa, HFC-32) and simultaneously employed three HFCs in a single simulation process for OH inversion. They found that OH estimates from different combinations were very similar (within ±2%) from 2004 to 2017, demonstrating significant potential for constraining OH concentrations.
4.2 Forward Mode Simulation Method
Current forward simulation methods for OH primarily rely on three-dimensional atmospheric chemistry models (such as Chemical Transport Models (CTM) and Chemistry-Climate Models (CCM)), which, by inputting precursor emissions (such as NOx, VOCs, etc.), meteorological fields, and initial and boundary conditions, simulate atmospheric physical processes and chemical reactions to ultimately obtain the distribution of OH concentrations across different periods, as well as trends and interannual variability in global average OH concentrations.
To evaluate the simulation performance of various models, several international Model Intercomparison Projects (MIPs) involving global tropospheric chemistry models have been established, primarily to provide references for major international assessment activities. Recent MIPs that have conducted detailed evaluations of OH include those shown inTable 4. The experimental design of MIPs is typically based on simulating identical conditions using different models, such as the same anthropogenic precursor emissions and the same meteorological conditions or greenhouse gas concentrations, aerosols, and solar forcing, to ensure direct comparability between different models and obtain more credible evaluation results. Meanwhile, relevant independent studies have also evaluated OH using different model settings, anthropogenic precursor emissions, and meteorological fields, providing additional references for assessing OH trends[28,65-69].
4.3 Satellite-based inversion, assimilation, and machine learning methods
In recent years, the development of satellite observations has provided a new approach for observational constraints on atmospheric OH and its related drivers. These methods use various satellite datasets as proxies for OH drivers (e.g., CH4, water vapor (H2O(v)), NO2, CO, formaldehyde (HCHO), isoprene, tropospheric O3) to derive OH concentrations and trends through the following five methods: 1) inversion method[77-79]; 2) data assimilation method[80-81]; 3) proxy and steady-state method[53,82-83]; 4) sensitivity-based empirical reconstruction method[13,84-85]; 5) machine learning method[86-87]. Among these: the first two methods belong to the inversion category, where the assimilation method combines inversion methods with forward model simulations; the latter three are based on satellite observations capable of obtaining higher-resolution two-dimensional concentration data, directly calculating OH concentrations through linear relationships, box models, and machine learning methods without requiring Bayesian optimization. Benefiting from decades of contemporary data records, these methods have opened new pathways for quantifying long-term OH concentration changes. Recently, Duncan et al.[38]provided a detailed review of new methods and challenges to be addressed for constraining tropospheric OH concentrations based on satellite data.
The principle of inversion methods based on satellite data is similar to indicator inversion based on ground observation stations; both rely on a Bayesian inversion framework to derive global OH distribution and trends. Since satellite data can provide two-dimensional observational data with higher resolution, the inversion process typically employs a three-dimensional model (such as GEOS-Chem) as the forward model. In existing studies, CH4satellite data are often used to invert OH trends and distribution[77-79,88].
Data assimilation methods incorporate satellite observations of OH precursors (such as NO2, CH4, O3, etc.) into CTM models to constrain tropospheric OH. They use inversion or chemical data assimilation methods[89]to reconcile model estimates of OH precursors with observations, and calculate OH concentrations consistent with the assimilated observations of OH precursors through the model's chemical mechanisms[80-81]. A significant advantage of data assimilation is that it can provide more accurate concentration estimates, and the resulting increments can indicate where model parameterizations are flawed or need improvement.
Methods based on indicators and steady state primarily utilize the photochemical linear relationship between satellite-observable species and tropospheric OH to directly calculate the spatial distribution of OH. For example: Pimlott et al.[82]Based on the relevant chemical mechanisms of OH, a simplified steady-state approximation formula was derived theoretically, expressing the relationship between OH concentration and multiple trace gases observed by satellites (namely O3, CO, CH4, and H2O(v)), thereby directly calculating OH concentration and trends; this method best represents OH concentrations at 600~700 hPa; Wolfe et al.[53]Using satellite observations of HCHO and assuming HCHO is in a steady state, theoretical derivation indicates a pseudo-linear relationship between OH column concentration and HCHO column concentration (ΩHCHO); Wells et al.[83]found that the ratio of isoprene to HCHO column concentrationsΩISOP∶ΩHCHOis inversely proportional to OH concentration and can serve as an indicator for OH.
Sensitivity-based empirical reconstruction method, which uses a prior OH concentration field simulated by a 3D model as the initial field, and then utilizes a model (typically a box model) to calculate the sensitivity of OH to its driving factors (such as O3, H2O, temperature, CH4, NOx, etc.) in different regions and under different conditions. By combining the temporal variation characteristics of driving factors obtained from satellite observations, the change in OH concentration is directly calculated through the product of sensitivity and this variation, thereby adjusting the OH concentration in each region[13,84-85]. Similar to inversion methods, this empirical reconstruction method also requires a prior OH concentration field, observational data, and sensitivity (the Jacobian matrix in inversion methods); however, their principles differ: inversion methods rely on a Bayesian inversion framework to solve for the mathematical optimum via a forward model; whereas the empirical reconstruction method directly calculates OH concentration changes based on the product of driving factor sensitivity and their variations. This approach is not only more intuitive logically and avoids the complex iterative processes required by inversion methods, but also clearly distinguishes the relative contributions of different factors. However, the accuracy of the assessment results from this method depends on whether the selected driving factors can fully cover the mechanisms of OH concentration changes, as well as the reliability of the model's quantitative simulation of sensitivity.
Machine learning methods combine satellite observation data, forward models, and the training of machine learning models[86-87]. The main process is: 1) Use forward models (CTM, CCM) to simulate and output relevant variables that drive changes in OH concentrations and can be constrained by satellite observation data (such as HCHO and CO column concentrations), other model variables affecting OH (such as temperature and humidity), as well as model-simulated OH concentrations to construct a training dataset; 2) Train using machine learning methods (such as Gradient Boost Regression Tree, GBRT) by inputting the training data to learn the relationship between the OH concentrations calculated by the forward model and the selected variables; 3) Input satellite observation data into the trained machine learning model to predict OH concentrations, thereby achieving observational constraints on OH. The effectiveness of machine learning methods in constraining tropospheric OH depends on the accuracy of the training dataset[38], that is, the difference between the relationships simulated by the model and the real environment. Currently, this method only targets the photochemical environments represented in the training dataset; for example, Zhu et al.[90-91] and Anderson et al.[86,92]were designed specifically for polluted urban environments and clean tropical and subtropical environments, respectively.
5 Recent progress in global OH assessment
For the results of MCF observation inversion, by summarizing relevant studies on OH trends and interannual variations over the past nearly 40 years globally (Figure 1), the results indicate that early studies showed large interannual variability in inversions before 2000, with inversion results of 7%~9%, and trends had significant uncertainty[14-16,25,42]. However, Montzka et al.[20]research results indicate that the large interannual variability before 2000 may be caused by uncertainties in MCF emissions and the interhemispheric gradient of MCF. After 1998, emissions approached zero, making residual emissions a secondary source of uncertainty; furthermore, as the atmospheric gradient decreased and uncertainty from limited observation stations in assessing global MCF burden declined, the interannual variability of OH ultimately became small (2.3%±1.3%). Subsequent studies show better consistency in estimates of global mean OH interannual variability, estimated at 2%~3% during the period 1980–2015[13,23,46,48]. This has also been verified by relevant models; Lelieveld et al.[12]found through simulation analysis of OH sources and sinks that the cyclic regeneration process of OH accounts for approximately 67% of total OH production, indicating that global OH is a buffered system insensitive to chemical perturbations caused by natural and anthropogenic emissions. Although the interannual variability derived from different inversion studies is relatively consistent, there remains considerable debate regarding the long-term trend of global OH. Studies using multi-box model inversions with MCF and methane isotope observations[17,21]indicate that since the 1990s, the most likely results for global mean OH have shown large positive and negative trends (Figure 1), but both found that observational constraints are weak, allowing multiple ways to match observational data, making it impossible to determine from the data whether the trend is significant. Naus et al.[22]after analyzing uncertainties and biases in atmospheric MCF and methane isotope inversions, found that for the most likely results, global OH overall showed a positive trend over the past 20 years ((0.18±0.15)%/a); after bias correction, the direction of OH change reversed, but observational constraints remained weak. Meanwhile, numerous inversion studies using different methods have also indicated no significant long-term trend in OH[13,20,23,46,48].
For14CO, Manning et al.[55]used 13 years of data from the Baring Head and Scoot Base observatories14CO measurements to infer short-term variations in OH. The study indicates that there was no significant long-term trend in Southern Hemisphere OH from 1989 to 2003, but provides evidence that monthly OH variations are approximately 10%. Morgenstern et al.[56]used a modified NIWA-UKCA model to simulate the production and removal of14CO and compared it with observational data, finding that data from both sites indicate an increasing trend in Southern Hemisphere OH since 1997.
For HFCs, Thompson et al.[45]selected five HFCs (HFC-134a, HFC-152a, HFC-365mfc, HFC-245fa, HFC-32) and used the AGAGE 12-box model for multi-species inversion. The results indicate that from 2004 to 2021, the interannual variability of the inverted results was small (<2%), consistent with Montzka et al.[20]who used MCF to estimate uncertainty, and no significant trend was observed.
For the results of forward model simulations, the estimation of interannual variability is around 2%–3%, similar to results derived from atmospheric inversions. However, regarding the long-term trend of OH, global ESMs, CCMs, and CTMs indicate that global OH showed no significant trend from 1850 to 1980, but increased after 1980, differing from trends obtained via atmospheric inversions and empirical methods. ACCMIP indicates substantial uncertainty among multi-models; from 1850 to 2000, positive and negative trends among multi-models are uncertain, with a multi-model average increase of (-0.6 ± 8.8)% (2000 relative to 1850); whereas from 1980 to 2000, all models show positive trends, though magnitudes vary, with a multi-model average increase of (3.5 ± 2.2)% (2000 relative to 1980).[11]. CCMI results indicate that after 1980 (after 1990 for CMAM), all models show OH trending toward stability or an upward trend, with an increase of (4.6 ± 2.4)%, similar to ACCMIP; meanwhile, interannual variations of OH from 2000 to 2010 were smaller compared to previous decades. References to the latest CMIP6/AerChemMIP model evaluations consistently show results from three ESMs (GFDL-ESM4, CESM2-WACCM, UKESM-0-LL) indicating that global OH has increased by approximately 9% since 1980.[24]. Multi-model sensitivity analyses indicate that since 1980, the increase in OH is primarily driven by changes in anthropogenic SLCF emissions, as well as NOx increases and reductions in CO emissions.[24]. Regarding simulations using different models in other independent studies, relevant research employing CTMs (such as GEOS-Chem, OsloCTM3, UCI, etc.) and CCMs (such as GFDL-AM4.1, CAM-Chem, etc.) in both early and recent periods all exhibit growth trends similar to those of the three model intercomparison projects (Figure 1), although the magnitudes of growth vary, reflecting differences in the implementation of physical and chemical processes among models. This indicates that existing models reach a relatively consistent conclusion regarding the increase in OH since 1980.
Existing literature using satellite methods to assess OH trends indicates that, on a global scale, except for studies using CO assimilation methods[80]and Zhao et al.[84]which showed growth trends consistent with model simulations based on sensitivity-driven empirical reconstructions, other methods indicate insignificant OH trends. Satellite retrievals still provide weak constraints on OH trends; similar to inversion methods, they cannot determine whether the OH trend is positive or negative[13,78-79,82,87], with large uncertainties. Meanwhile, some satellite studies on regional-scale OH indicate that OH in urban and forest areas of the United States shows a decreasing trend[90-91,93], whereas in tropical regions, the overall OH growth rate exhibits an increasing trend, but with significant spatial variations[92].
Overall, based on the latest CMIP6 model evaluations, global mean tropospheric OH showed no significant trend from 1850 to 1980. However, for the period 1980–2014, results from global models constrained by precursors conflict with those from inversion methods constrained by observations. Regarding interannual variability, both inversion and modeling approaches indicate small interannual variability in OH, ranging from 2% to 3%. However, for long-term trends, results from observational inversions exhibit substantial uncertainty; some studies suggest stability, while others indicate increasing or decreasing trends. In contrast, most global model results show an upward trend. Three CMIP6 models consistently indicate a 9% increase in OH since 1980, yet other studies reveal large discrepancies among models, with some simulations showing insignificant trends. Therefore, further research is needed to reduce uncertainties in OH simulations and enhance the reliability of results. For satellite-based assessment methods, existing uncertainties remain large, warranting further refinement and development of these methodologies.
6 Current theoretical and technical limitations
6.1 Inherent uncertainty due to climate variability
The interannual variability of OH is driven by ENSO, exhibiting significant feedback with the same cycle as ENSO, which is an inherent uncertainty of OH itself. ENSO is the dominant pattern of naturally occurring climate variability, and numerous studies have shown that it affects OH. ENSO can influence OH through multiple mechanisms[94], for example: 1) by altering the Walker circulation and affecting stratospheric and tropospheric ozone concentrations, thereby influencing the ozone photolysis rate (j(O1D))[95-96]; 2) by affecting temperature changes, influencing water vapor (q)[30,95]; 3) by altering convection and changing lightning NOx emissions (SN)[94]; 4) by altering wetland or biomass burning emissions, thereby affecting BVOC emissions (SC)[25,97]. Turner et al.[94] and Zhu et al.[87] studies indicate that 5%–10% variations in the annual mean tropospheric OH column concentration can be caused solely by climate variability, suggesting that OH is also strongly influenced by internal climate variability.
6.2 Sources of uncertainty in inversion-based studies
The uncertainty in the indicator emission inventory is a critical factor. For example, studies around the year 2000 regarding MCF all reported large uncertainties and trend fluctuations, such as Prinn et al.[14]who suggested an increase of (15±22)% ((1.4±2.1)%/a) from 1979 to 1989, whereas from 1989 to 2000 it decreased by (10±24)% (-2.3%/a) compared to 1979; the primary reason for the large uncertainty was the inaccurate assessment of MCF emissions. Montzka et al.[20]research indicates that from 1980 to 2003, the interannual variability of OH inversion was significantly influenced by its emission uncertainty, while after 1998, emissions approached zero, reducing the uncertainty of OH inversion. Subsequent studies all exhibit huge uncertainties related to emission assessments[17,21-22]; different scenario assumptions (such as fixed OH, fixed CH4emissions, and other extreme scenarios) can all match the bottom-up MCF inventory[21]. Therefore, Turner et al.[21]argue that current surface observation systems cannot strongly constrain OH trends, relying entirely on MCF data and estimates of its emission uncertainty.
Observation errors are also a significant source of error in inversion. Existing observational data come from two global observation networks, NOAA and AGAGE; however, their measurement methods and absolute calibrations differ slightly, leading to minor discrepancies in the MCF, HFCs, and HCFCs results measured by stations of these two networks in the same region.[17,23,45]. Meanwhile, as MCF in the atmosphere continues to be depleted, the measurement error of MCF gradually increases, making it difficult to continue using it as a reference indicator for atmospheric OH abundance. Although existing studies recommend using other indicators (such as HFC-32, HFC-134a, etc.)[52], relevant studies have already used other long-lived gases for inversion[45]; however, due to the still significant uncertainties in the emission inventories of these substances, the accuracy of inverted OH remains inferior to that of MCF.
Differences in inversion models and internal parameters are also important factors affecting computational uncertainty. Different inversion models may be based on different assumptions, algorithms, and data inputs, which can lead to different results for the same set of observational data. For example, Naus et al.[22]compared the two-box model optimized using the TM5 three-dimensional model with Rigby et al.[17]and Turner et al.[21]used two-box models for comparison and found that temporal variations in parameters such as interhemispheric transport, sampling errors, interhemispheric OH ratios, and MCF loss to the stratosphere can cause biases in the results of the two-box model.
6.3 Sources of uncertainty in pattern-based simulation
Intercomparison of global atmospheric chemistry model results indicates significant inter-model diversity in simulated OH distribution, variability, and trends[11,18-19,71,98]; Murray et al.[19]research indicates a ±30% deviation in the absolute concentration of global annual mean OH across multiple ACCMIP models.
This model diversity is primarily attributed to differences in physical and chemical mechanisms, Naik et al.[11]attributed it to differences in how models simulate NOxand CO burdens; Murray et al.[19]further demonstrated by comparing various ACCMIP models that larger inter-model variability is mainly related to NMVOC oxidation efficiency (ɛC), while intra-model variability is primarily associated with the tropospheric lifetime of NOx(τNOx), indicating that simulated OH is highly sensitive to NMVOC oxidation efficiency and NOxtropospheric lifetime. For a given model, oxidation efficiency is typically fixed, determined by the reaction kinetics and species included in the model; whereas NOxlifetime varies much more significantly between models and even within certain models, being particularly sensitive to the altitude of lightning NOxemissions, heterogeneous chemical processes, and the model's mechanistic treatment of reactive nitrogen reservoir species. Nicely et al.[99]attributed differences in OH simulated by different CTMs, in descending order of importance, to different chemical mechanisms, varying treatments of O3photolysis rates, as well as simulated O3and CO concentrations. Fiore et al.[5]summarized current uncertainties in physical and chemical mechanisms related to OH, including heterogeneous (gas-phase–aerosol) chemistry, photolysis and kinetic reaction rates, weather-sensitive emissions, reaction mechanisms of isoprene oxidation products, NOxreaction mechanisms, halogen chemistry, and water vapor distribution; each of these contributes 10%–15% uncertainty. Assuming independence of errors, the root-sum-square calculation yields a total uncertainty of 25%–40%.
Differences in precursor emission inventories and model mechanisms also lead to discrepancies between the precursors (such as NOx, CO, VOCs) simulated by various models and actual observations, thereby resulting in biases in OH assessment. For example, Gaubert et al.[80]used MOPITT CO assimilation research results to show that the total CO burden after assimilation is higher than before assimilation, and the average temporal decline rate of CO burden after assimilation (-1.4%/a) is greater than that before assimilation (-0.01%/a), thereby affecting OH assessment.
7 Conclusion and Outlook
Hydroxyl (OH) radicals, as key oxidants in the atmosphere, play a crucial role in regulating atmospheric chemical composition, affecting air quality, and influencing climate change. Regarding OH trends, there is a discrepancy between inversion methods and forward model simulations over long-term periods. Inversion results have high uncertainty, making it difficult to determine positive or negative trends; while most studies suggest stability, others indicate rising or falling trends. In contrast, model results mostly show an upward trend since 1980. Results from three CMIP6 models indicate a 9% increase since 1980, showing good consistency. However, significant differences exist among models evaluated by ACCMIP and CCMI, with some models showing insignificant trends. Nevertheless, both approaches are relatively consistent in estimating interannual variability, at 2%~3%. Assessments using satellite methods still have large uncertainties, remain in the validation stage, and require further optimization and development.
Inverse methods rely on observational data and can utilize indicators to constrain OH, but they suffer from numerous drawbacks, such as strong dependence on indicator emission inventories. The gradual decline of MCF makes it increasingly difficult to serve as a reference metric, while other alternative indicator emission inventories carry significant uncertainties. Furthermore, the diversity of inverse models and the selection of parameters introduce additional uncertainties. Model simulations offer advantages such as high resolution, enabling the derivation of information on OH distribution and trends; however, they are plagued by large discrepancies among different models and significant uncertainties in simulation results arising from differences in physical and chemical mechanisms. Recently developed satellite methods provide new, high-resolution observational constraints for OH, yet their uncertainties remain substantial, necessitating further development of corresponding methodologies.
To conduct a more accurate assessment of OH, its future development directions mainly include the following points.
(1) Conduct more extensive atmospheric observations to provide additional observational constraints for inversions, models, and model optimization. Specifically, it is necessary to advance field observations of OH to validate chemical mechanisms, and to conduct atmospheric and satellite observations of indicators and drivers related to CO, CH4, NOx, HCHO, and other OH driving factors associated with model assimilation and satellite data, thereby providing support for methods such as inversion and model assimilation.
(2) Continue to develop satellite-based, machine learning, and other related methods to enrich OH assessment approaches and conduct comparative validation using multiple methods. Current satellite data-based methods have significant uncertainties and require further refinement. Meanwhile, promote the development of machine learning techniques to enhance the credibility of OH assessment conclusions through multiple independent methods, thereby fully leveraging the role of satellite data in global atmospheric oxidation research.
(3) Further optimize inversion and model evaluation methods. For example, while continuing to use 14indicators such as CO, HFCs, and HCFCs, attempt to use more indicators for constraints, improve the measurement accuracy of indicators, optimize the emission inventories of indicators, and refine the representation of inversion models, such as using three-dimensional models or a combination of two-box and three-dimensional models[22]. Further optimize relevant model representations, such as inversion parameters and the physical and chemical mechanisms corresponding to the models, to achieve better model calibration. Apply observational constraints to the models through various methods to reduce uncertainties in model simulations.
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