Global chemistry-climate models are vital for simulating atmospheric composition and its changes by representing the relevant physical and chemical processes in the atmosphere. However, these models face challenges in accurately reproducing observed concentrations of short-lived species, such as ozone (O₃). Global models typically have coarse spatial resolution, and this limitation hampers the representation of small-scale processes, leading to systematic biases in simulations . There are currently no simple methods to address these issues effectively without increasing model resolution. However, higher resolution significantly increases computational demands. Besides, increasing model resolution does not consistently improve accuracy, sometimes even introducing new biases . Moreover, evaluating model performance is challenging due to uncertainties in comparing grid-scale outputs with localized, site-based measurements .

Considering these issues, surface ozone simulations in current global chemistry-climate models exhibit notable biases, particularly at regional scales . Although large-scale ozone distributions are generally well-captured , regional ozone concentrations remain challenging to reproduce, especially at the surface where precursor emissions and surface deposition exert strong influences. The assessment of the Tropospheric Ozone Assessment Report (TOAR) also reported that global models exhibit systematic biases in their surface ozone simulations across all seasons, with a multi-model mean bias of 7.7 ppb (approximately a 20 % overestimation) in the Northern Hemisphere . These biases may stem from inadequate representation of dynamics (e.g., meteorology and deposition), and oversimplified ozone chemistry . However, efforts to improve individual modules, such as chemistry schemes, can even result in greater biases in ozone simulation . Progress in addressing these issues has been limited over recent decades .

Deep learning, a transformative approach in fields like computer vision and natural language processing , is increasingly applied in physical science . Recent studies have demonstrated its growing use in atmospheric science. It has shown promise in weather modeling and data generation. Specific applications include mimicking atmospheric photochemical processes , and directly predicting future weather , often outperforming traditional numerical methods in speed and accuracy. The uncertain parameterizations e.g., moist physics and radiation processes in climate models can also be replaced by deep learning models . Another key advantage of deep learning is its ability to fuse multi-source data, enabling the creation of global datasets, such as surface ozone concentrations . However, its application to air pollution modeling, particularly for ozone, is challenging due to the localized nature of pollution and limited observational data for key variables. To address this, we adopt a hybrid approach, integrating process-based chemistry-climate models with deep learning to improve the accuracy of ozone simulations.

Bias correction, as a way to further improve model accuracy, has been developed for different goals. For instance, aim to distinguish the impacts of different uncertainties (e.g., emissions, scenario, model designs, etc.) on model biases. and focus on preserving temporal properties in bias correction, such as the frequency of heatwaves over long periods. Machine learning has also been applied to surface ozone bias correction (e.g., ), achieving substantial error reduction. However, most studies have not fully explored the performance of different deep learning approaches, and their impacts on prediction remain uncertain. In our work, we therefore explore several deep learning models for ozone bias correction and propose a weighted ensemble to achieve more robust results.

In this study we investigate the potential of deep learning to correct surface ozone biases in a global chemistry-climate model. In Sect. 2, we describe the chemistry-climate model and introduce six statistical models used for bias correction. Section 3 evaluates their performance and proposes a weighting scheme to optimize results. Section 4 demonstrates the advantages of this approach for projecting future surface ozone changes. In Sect. 5, we analyze the sensitivity of ozone in both the original and bias-corrected models. Finally, Sect. 6 presents our conclusions.

The performance of all 6 statistical models is evaluated using testing data to give an independent assessment, see Fig. 2. All models generally simulate the surface ozone biases in UKESM1 effectively, capturing both underestimations and overestimations. However, the deep learning models (Fig. 2c–f) clearly outperform the simpler linear and random forest models (Fig. 2a, b). A primary limitation of the linear and random forest models is their inability to capture extreme bias values, with many predictions clustering around 0 ppb. Overall, the systematic biases are smoothly distributed with a mean near 0, indicating that underestimations and overestimations occur with comparable frequency in UKESM1.

Both the ResNet and Transformer approaches perform best, with their predictions closely aligning with the 1:1 line across the full range of biases. These models yield higher correlation coefficients (up to 0.997) and lower root-mean-square errors (RMSE). From MLP to Transformer, the error is reduced by 64 % from 2.25 to 0.8 ppb, highlighting the importance of architecture in this task. However, the improvement from convolution-based models (CNN and ResNet) to the Transformer is marginal. In the deep learning field, the optimal architecture for processing 2D data, whether convolution-based or attention-based, remains a subject of ongoing debate .

Given that we employ a variety of models, it is logical to consider combining them to reduce the uncertainties inherent in each. Previous studies have demonstrated that integrating multiple models can effectively decrease both uncertainties and prediction errors . However, assigning weights to each model based on their respective performances can produce a more robust outcome compared to simple averaging . Therefore, we adopt a simple weighted ensemble mean scheme, following the approach outlined by . The calculation of the weights for each model i is presented as follows: 1wi=exp⁡-Di2Niσ2×100∑iexp⁡-Di2Niσ2 Here, Di2 represents the squared error between the predictions of an individual model and the reference data, derived from the testing data. Ni denotes the number of testing data points. The parameter σ is adjustable and can be optimized to determine the most effective weight values. As illustrated in Fig. 3, the error of the weighted-mean model is lower than that of any single model, including the best-performing single model, Transformer, which exhibits an error of 0.80 ppb. The optimal value of σ=0.35 corresponds to the lowest error of the weighted-mean model (0.69 ppb), resulting in a 14 % improvement over the Transformer model. We note that the optimal value of σ may differ across various model ensembles. High-performing models, such as ResNet and Transformer, are assigned large weights, approximately 40 % each, while the CNN model has a weight of 17 %. Models with low performance are excluded due to their limited contribution. This demonstrates that a simple weighting scheme can effectively integrate the outputs of all models, and further improve prediction accuracy. The optimal weighted-mean predictions are used for subsequent analyses.

Considering the expected biases in future simulations of surface O₃ using UKESM1, we employ deep learning models to predict these biases based on input variables generated from UKESM1 future simulations. Subsequently, a bias-corrected surface O₃ concentration is derived by subtracting the O₃ bias from the simulated O₃ values. Figure 4 illustrates seasonal variations in weighted-mean surface O₃ concentrations under SSP3-7.0 and SSP3-7.0-lowNTCF scenarios. Compared with bias-corrected results, UKESM1 simulations demonstate much higher global mean O₃ concentrations in summer and similar levels in winter (Fig. 4a, d, g, j). This indicates that the UKESM1 has a greater sensitivity of seasonal O₃ changes, showing a 12 ppb increase compared to the corrected 5 ppb. Higher emissions of O₃ precursors under SSP3-7.0 lead to higher surface O₃ mixing ratios compared to SSP3-7.0-lowNTCF, with differences of 4 ppb in summer and 1.5 ppb in winter (Fig. 4b, e, h, k). In addition, seasonal O₃ variation (winter to summer) becomes more pronounced under SSP3-7.0 (4.4 ppb increase; Fig. 4b, e) than under SSP3-7.0-lowNTCF (2.0 ppb increase; Fig. 4g, h), which is also observed in UKESM1 simulations. Decreased O₃ titration by NO in winter and lower photochemical O₃ production in summer in the lower-emission scenario will both contribute to a reduced seasonal variation.

Figure 4c, f, i, l shows the changes in surface O₃ from the present day to the future, as simulated by the bias-corrected weighted-mean model. It reveals that distinct emission pathways result in divergent O₃ responses. Under SSP3-7.0, surface O₃ mixing ratios exhibit a consistent increase across both seasons, whereas under SSP3-7.0-lowNTCF, a decrease is simulated. However, the magnitude of O₃ responses is greater under SSP3-7.0-lowNTCF compared to SSP3-7.0. At regional scales, substantial reductions in surface O₃ are shown in North America during summer (Fig. 4c, i), attributable to lower precursor emissions in both scenarios. In contrast, in East Asia, surface O₃ changes vary markedly between scenarios and seasons, driven primarily by differing O₃ chemical environments due to the current high local emissions. These variations pose significant challenges for addressing regional air pollution. Additionally, we compare surface O₃ changes with and without bias correction. While the direction of surface O₃ changes remains generally consistent across most continental regions, opposing signs emerge in certain oceanic areas. This discrepancy may stem from the limited availability of observational constraints in oceanic regions, which hinders both the development of process-based models and the reliable reference data for bias correction. Overall, the influence of different emission pathways on future O₃ concentrations are certain at large scales, particularly over land areas.

In Fig. 5, we further show regional surface O₃ changes from the present day to the future, and compare the predictions of UKESM1 with those derived from the bias-corrected weighted-mean model. Under both future scenarios, surface O₃ changes in most geographical regions fall in quadrants where the signs of the changes are the same, indicating that the effects of emission changes on future O₃ are generally robust. However, in the wintertime, there are differences in sign, especially in high-emission regions such as Asia (Fig. 5a and b) and North America (Fig. 5b). This suggests that the response of O₃ to its precursors, particularly in high-NO_x environments in winter is not well represented in current models. In contrast, there is broad agreement in the sign of O₃ changes in the summertime.

While the sign of O₃ changes is generally consistent between UKESM1 simulations and bias-corrected predictions, the magnitudes of these changes differ substantially. Under the SSP3-7.0 scenario (Fig. 5a), surface O₃ increases in most regions are greater in UKESM1 simulations than in bias-corrected estimates, with notably larger overestimations in regions such as North America and Europe during winter, where UKESM1-simulated increases exceed bias-corrected values by more than a factor of 2. This suggests that UKESM1 may overestimate surface O₃ increases. Similarly, under the SSP3-7.0-lowNTCF scenario (Fig. 5b), surface O₃ decreases in most regions are less pronounced in bias-corrected predictions compared to UKESM1 simulations, indicating an overestimation of O₃ reductions by UKESM1. These findings imply that the impacts of emission and climate policies on surface O₃ concentrations under both scenarios may be smaller than projected by UKESM1 simulations.

It is acknowledged that large uncertainties remain in these comparisons at regional scales, as the CAMS dataset exhibits substantial biases in certain regions when compared to the TOAR dataset, particularly in East Asia and Southeast Asia . In addition, we also find that there are notable discrepancies between CAMS and UKESM1 especially in regions where observations are unavailable, such as the Middle East (shown as light markers in Fig. 5). Therefore, in these regions exhibiting large biases in UKESM1 simulations, large differences in surface O₃ predictions between UKESM1 and bias-corrected UKESM1 also tend to be observed. Bias correction in these regions may lack reliability. Nevertheless, in North America and Europe, where the CAMS data are more consistent with TOAR observations, with biases of less than 10 % , the overestimation of surface O₃ changes by UKESM1 appears more substantiated.

At the global scale, it is evident that UKESM1 simulations consistently overestimate surface O₃ changes during summer (Fig. 6a). In summer, surface O₃ biases peak at approximately 15–30 ppb for NO_x mixing ratios of 10–15 ppb, typically corresponding to polluted urban areas with large populations . The SSP3-7.0 scenario exhibits the largest biases, followed by SSP3-7.0-lowNTCF. Both future scenarios, characterized by high or low emissions, show greater biases (up to 25 ppb) than the present-day scenario, suggesting that emissions are not the primary driver of these larger biases. In contrast, during winter (Fig. 6b), O₃ biases are generally lower. The SSP3-7.0 and SSP3-7.0-lowNTCF biases appear to shift from negative values in the present day to positive or near-zero values. These findings indicate that the underlying biases in surface O₃ simulations are likely to increase under both emission pathways in the future, presenting a challenge to accurately assessing the impacts of future emissions, particularly during summer.

Given that the chemical environment affects both the magnitude and sign of surface O₃ changes, it is important for models to accurately represent the non-linear responses of surface O₃ to its precursors. We integrate monthly mean data from all surface grid cells in both scenarios to derive a relationship between surface O₃ mixing ratios and NO_x / VOC ratios as simulated by UKESM1, see Fig. 7. Additionally, we show the O₃ sensitivity to the NO_x / VOC ratio using bias-corrected O₃ data for comparison. The NO_x / VOC ratio is a simple but effective indicator that distinguishes high- and low-NO_x environments, which reflect different O₃ chemical regimes . We calculate NO_x concentrations by aggregating NO and NO₂ values, and VOC concentrations are calculated by summing the concentrations of all primary emitted non-methane VOC species.

We find that the NO_x / VOC ratios corresponding to the peaks of surface O₃ concentrations are similar between corrected and uncorrected UKESM1 across different seasons (Fig. 7). The NO_x / VOC ratio thresholds, which indicate the transition from NO_x-limited to VOC-limited O₃ production regimes, are higher in summer (1.0–2.0) than in winter (about 0.1). This demonstrates that UKESM1 effectively captures the seasonal variation in critical NO_x / VOC ratios. The chemical mechanism of UKESM1 accurately represents this transition. In addition, we see that as the NO_x / VOC ratio increases, the differences between corrected and uncorrected surface O₃ concentrations become more pronounced in summer, but this is less apparent in winter. This suggests that biases in O₃ simulations are amplified under two specific conditions: (1) in regions with high NO_x levels, such as polluted environments, and (2) in warmer climates, such as during summer. It is noteworthy that NO_x / VOC thresholds may vary across different chemistry-climate models; however, analyzing O₃ sensitivity to these ratios provides valuable insights into model limitations.

We further investigate the sensitivity of surface O₃ biases to different input variables in the statistical models, usually termed the “feature importance”, see Fig. 8. This is calculated as the response of the O₃ bias to a minor perturbation (10 %) in each variable, then normalized across all variables and expressed as a percentage. Figure 8 shows the feature importance of the eight most influential variables. It reveals that temperature is the primary contributor to O₃ biases, associated with the overestimation of O₃ in summer, as demonstrated in Fig. 7. While other variables also play a role, their impacts are substantially less pronounced than that of temperature. This suggests that temperature-sensitive processes are likely the dominant source of O₃ biases in the model. Other physical variables, including photolysis rates, humidity, boundary layer height and dry deposition, are also associated with surface O₃ biases. Chemical species such as hydroxyl radicals (OH) and peroxyacetyl nitrate (PAN), which are linked to the oxidation of O₃ precursors and regional transport, play a notable role in influencing these biases. While deep learning models highlight the importance of these variables, simpler statistical models, such as MLR and RF, show little sensitivity to them. This suggests that simpler models tend to overemphasize the most dominant variables, whereas complex models may overdistribute feature importance across a broader range of variables. Furthermore, we find that the positive or negative values of feature importance are generally consistent with physical expectations. For example, an increase in the NO₂ photolysis rate, j(NO2), enhances O₃ production and tend to result in higher O₃ biases, which is hence reflected by the positive feature importance of j(NO2). In contrast, an increase in the O(¹D) photolysis rate, j(O1D), promotes O₃ destruction and leads to lower O₃ biases, which is reflected by its negative feature importance. Although MLR and RF models fail to capture these nuanced relationships, they remain useful for identifying the most influential variables. We highlight that the underlying causes of O₃ biases are complex; however, temperature consistently emerges as the dominant factor, potentially exerting a significant influence on the accuracy of O₃ simulations under future warmer climate conditions.

We have successfully applied a range of statistical approaches to correct surface O₃ biases in UKESM1, a state-of-the-art chemistry-climate model. This model typically overestimates surface O₃ concentrations in summer and underestimates them in winter. While these model biases can be corrected using any of the statistical approaches, deep learning models significantly outperform traditional approaches such as multiple linear regression (MLR) and random forest (RF). Among the deep learning architectures, the residual network (ResNet) and Transformer models yield consistent results, with small differences between them. The convolutional neural network (CNN) also produces comparable predictions to ResNet and Transformer. We note that while complex models generally achieve higher prediction accuracy, the full potential of the Transformer architecture may not be fully realized in this task due to the specific nature of the task.

A simple weighted ensemble mean scheme is proposed, demonstrating an additional 14 % improvement in performance compared to the best individual approach, the Transformer model. To assess future changes in surface O₃, we apply bias correction to simulations generated by UKESM1. The signs of surface O₃ changes are generally consistent between corrected and uncorrected UKESM1. However, the magnitudes of these changes differ. Surface O₃ changes simulated by UKESM1 are typically overestimated in both seasons compared to the bias-corrected changes. Under the SSP3-7.0 scenario, the corrected global summer mean O₃ mixing ratios are projected to increase by 1.2 ppb, whereas under the SSP3-7.0-lowNTCF scenario, they are expected to decrease by 2.8 ppb. In winter, the corrected surface O₃ mixing ratios are projected to increase by 0.5 ppb under SSP3-7.0 and to decrease by 1.1 ppb under SSP3-7.0-lowNTCF.

The sensitivities of surface O₃ to its precursors are also investigated for both UKESM1 and the bias-corrected UKESM1. It reveals that UKESM1 effectively captures the seasonal differences in O₃ sensitivities, as represented by NO_x / VOC ratios in different seasons. However, under high NO_x / VOC conditions, UKESM1 notably overestimates O₃ concentrations, particularly during summer. This suggests that under warmer conditions in the future, UKESM1 tends to overestimate O₃ concentrations. This is further confirmed by examining the feature importance for simulated O₃ biases, which identifies temperature as the most important variable influencing these biases. Deep learning models also highlight the importance of other variables; however, their importance is considerably less substantial than that of temperature. This suggests that processes sensitive to temperature variations may have a pronounced influence on O₃ concentrations simulated by UKESM1.

Despite the demonstrated capabilities of deep learning models in capturing surface O₃ biases, we acknowledge that uncertainties remain, particularly regarding the use of CAMS data as a reference for model training. Nevertheless, this exploratory study tests the methodology’s feasibility and provides insights into mitigating uncertainties associated with approach selection. It establishes a robust foundation for the broader application of bias correction techniques, particularly through the integration of deep learning with chemistry-climate models. This integration presents a promising pathway for addressing systematic errors in chemistry-climate models, while also facilitating the diagnosis of the underlying causes of model biases. Bias correction techniques stand to gain from the increasing availability of high-quality observational data, with applications extending beyond O₃ to other atmospheric components. This will strengthen the robustness of assessments in regions where observations are currently lacking, ultimately producing more reliable projections of O₃ changes across different climate scenarios.